of sessions 1 session, full day


Table 6. Core description of Platform Overnight Parking Game

By 'gaming' these processes it should become clear whether and to what extent the (platform) rail capacity can be used for the preparation of passenger rolling stock. If a carousel process is theoretically feasible, then follow-up actions are defined to carry out a practical test. Table 6 describes the core features of the game.

The game delivered the results requested in time, by which it became the first game in the row of six that not only drew conclusions based upon the mechanisms of the game play, but also on the numbers generated in the game. Halfway the first scenario in the session there was an intervention required because the service area supervisor felt that the game play was 'not realistic'. After a thorough joint review it appear there were two trains left in the wrong location. The game leader corrected this, and from this point all agreed the outcomes were valid and representative for a normal evening with no major disturbances.

Gaming Simulations for Railways:

comment and criticize the validity very well.

**7. Conclusions** 

**6.2 Validation** 

Lessons Learned from Modeling Six Games for the Dutch Infrastructure Management 291

analog games to expect that continuous time will improve on stress and pressure level when computer models are more easily deployable and integrated in the games. Analog simulators are surprisingly good but require extensive and thus expensive expert support.

The sessions usually run only once. Drawing conclusions on just one session puts emphasis on the validity of the behavior observed and decisions made in the simulation. The number of people to validate a full game with is limited in terms of availability (they work in de 24/7 operation) and costs, validation approaches need to be done differently. By modularizing the toolkit of gaming into sub-models and software components, validation of the components can be done outside of the final game sessions in analogy with the recent insights in multi-agent simulation of social systems (Gilbert, 2011). Work on the validation requires deeper understanding of train traffic control and train driver behavior. This encompasses the knowledge base in the organization. Work on this gives methodological

challenges that go beyond the literature on gaming methodology (Peters et al, 1998).

In the railway gaming simulation described above (but for the RCG) processes of selfvalidation were used to overcome the validation issue for now. During every session signs of discomfort of the players and comments on 'how real' something was were constantly monitored and discussed openly even if this led to time-outs or moments of difficult discussion during the game play. The game leader always stated that everything to make the session better would be welcome at any time. In the debriefing the explicit questions were asked: which part is realistic and which part would be different in the real world, and why? This gave often very valuable information, even when in case of the NAU game when the network and service controller were not very involved in the game play, but could

By ensuring immersive game play and having the self-validation during the games the Raser categories of psychological reality and process validity are addressed to an extent that is satisfying for the organization. The structural validity is a design issue and is difficult to improve when using analog simulators. You simply cannot model the exact train flow and safety and interlocking systems in an analog way. Computer simulators have a lot to offer here in interaction with the players during a game session. This is future work for integration. The predictive validity is currently under review as the project follows all game projects longitudinally to determine the extent to which the conclusions based upon game

The series of six projects shows the purpose and usefulness of building gaming simulations to help the Dutch railway infrastructure manager ProRail innovate on its core processes. Over the projects methodological lessons on involving operators as game participants have been drawn, as well as for the abstraction and reduction of information and the modeling of time. These modeling challenges appear to be highly interrelated. The lessons learned show the need, contrary to the traditional modeling approaches in gaming simulation, for very little abstraction and reduction in modeling the game where it concerns items that the operators have to play with. The model for less operational aspects can be more abstract, in

sessions hold true in the real operation. Future work will report on outcomes.

In this game the modeling of infrastructure and information followed the infrastructure schematic layout and timetabling information that was previously successful in the ETMET and NAU games. The time was for the first time not continuous but step-based. The reason for this was the long time to simulate (6 hours) during which many moments are trivial, as trains stand still and some cleaning is done. As no more game time than 2 hours per scenario was available, a speed-up was required, but just faster time would not contribute to the game as some time periods need more attention than others. The solution was found in 5-minute time steps in the game time that could take anywhere between 30 seconds to 20 minutes to execute in clock-time. In this way the players (most of them operational practitioners, two of them near illiterate) could keep up with the more abstract representation of their real work. The two foremen of the cleaning teams had most issues getting involved. Their whole task consisted out of taking 1 toothpick out of a wagon once it was cleaned, and they could each take out one stick per 5-minute step. Once they got used to this task they could make choices for priority over the service area easily and got their behavior realistic according to both their own and others judgments.

### **6. Methodological challenges**

In this section the lessons learned on methodological challenges are discussed on two levels. The first subsection answers the three modeling issues raised in Section 4. The second subsection discusses how to guarantee validity in gaming simulations for railways.

### **6.1 Modeling issues**

In the six projects, the modeling issues appeared to have a large interaction. The question how to immerse train traffic controllers in a gaming simulation appears to be largely dependent on the display of information. For train traffic controllers we learned that a detailed representation of the infrastructure is key for their involvement. However, the geographical representation did not work, where the common abstracted versions as used in practice performed flawlessly, both in digital (RBG) and in analog game board format (ETMET, NAU, POP). More abstraction and reduction of complexity of the infrastructure does not work for operators (RCM). For the timetabling and similar information like personnel and rolling stock planning similar mechanisms worked: give the players the information on a detailed level but keep the format they are used to in practice, even tough the medium (computer or paper) is different. The same held true for delays and other process information. Once the delays are presented directly after a train number in the format of +3, +5, + 10 minutes everybody understood it immediately. Once the players could understand the information well they could concentrate on their task, which they automatically did fully immersed.

Regarding the question how to model time we learned that the logical model of continuous time for rail operations works well and puts pressure on the process. In the ETMET game the frustrations over problems under time pressure became so high that the game leader had to intervene, and other games showed real pressure on the players who are so aware of the real-time nature of their real-world process that this can be triggered immediately in the game. Care should be taken to give players sufficient situational awareness without all their real tools available. Based on the experiences with the Railway Bridge Game versus the analog games to expect that continuous time will improve on stress and pressure level when computer models are more easily deployable and integrated in the games. Analog simulators are surprisingly good but require extensive and thus expensive expert support.

### **6.2 Validation**

290 Infrastructure Design, Signalling and Security in Railway

In this game the modeling of infrastructure and information followed the infrastructure schematic layout and timetabling information that was previously successful in the ETMET and NAU games. The time was for the first time not continuous but step-based. The reason for this was the long time to simulate (6 hours) during which many moments are trivial, as trains stand still and some cleaning is done. As no more game time than 2 hours per scenario was available, a speed-up was required, but just faster time would not contribute to the game as some time periods need more attention than others. The solution was found in 5-minute time steps in the game time that could take anywhere between 30 seconds to 20 minutes to execute in clock-time. In this way the players (most of them operational practitioners, two of them near illiterate) could keep up with the more abstract representation of their real work. The two foremen of the cleaning teams had most issues getting involved. Their whole task consisted out of taking 1 toothpick out of a wagon once it was cleaned, and they could each take out one stick per 5-minute step. Once they got used to this task they could make choices for priority over the service area easily and got their

In this section the lessons learned on methodological challenges are discussed on two levels. The first subsection answers the three modeling issues raised in Section 4. The second

In the six projects, the modeling issues appeared to have a large interaction. The question how to immerse train traffic controllers in a gaming simulation appears to be largely dependent on the display of information. For train traffic controllers we learned that a detailed representation of the infrastructure is key for their involvement. However, the geographical representation did not work, where the common abstracted versions as used in practice performed flawlessly, both in digital (RBG) and in analog game board format (ETMET, NAU, POP). More abstraction and reduction of complexity of the infrastructure does not work for operators (RCM). For the timetabling and similar information like personnel and rolling stock planning similar mechanisms worked: give the players the information on a detailed level but keep the format they are used to in practice, even tough the medium (computer or paper) is different. The same held true for delays and other process information. Once the delays are presented directly after a train number in the format of +3, +5, + 10 minutes everybody understood it immediately. Once the players could understand the information well they could concentrate on their task, which they

Regarding the question how to model time we learned that the logical model of continuous time for rail operations works well and puts pressure on the process. In the ETMET game the frustrations over problems under time pressure became so high that the game leader had to intervene, and other games showed real pressure on the players who are so aware of the real-time nature of their real-world process that this can be triggered immediately in the game. Care should be taken to give players sufficient situational awareness without all their real tools available. Based on the experiences with the Railway Bridge Game versus the

subsection discusses how to guarantee validity in gaming simulations for railways.

behavior realistic according to both their own and others judgments.

**6. Methodological challenges** 

automatically did fully immersed.

**6.1 Modeling issues** 

The sessions usually run only once. Drawing conclusions on just one session puts emphasis on the validity of the behavior observed and decisions made in the simulation. The number of people to validate a full game with is limited in terms of availability (they work in de 24/7 operation) and costs, validation approaches need to be done differently. By modularizing the toolkit of gaming into sub-models and software components, validation of the components can be done outside of the final game sessions in analogy with the recent insights in multi-agent simulation of social systems (Gilbert, 2011). Work on the validation requires deeper understanding of train traffic control and train driver behavior. This encompasses the knowledge base in the organization. Work on this gives methodological challenges that go beyond the literature on gaming methodology (Peters et al, 1998).

In the railway gaming simulation described above (but for the RCG) processes of selfvalidation were used to overcome the validation issue for now. During every session signs of discomfort of the players and comments on 'how real' something was were constantly monitored and discussed openly even if this led to time-outs or moments of difficult discussion during the game play. The game leader always stated that everything to make the session better would be welcome at any time. In the debriefing the explicit questions were asked: which part is realistic and which part would be different in the real world, and why? This gave often very valuable information, even when in case of the NAU game when the network and service controller were not very involved in the game play, but could comment and criticize the validity very well.

By ensuring immersive game play and having the self-validation during the games the Raser categories of psychological reality and process validity are addressed to an extent that is satisfying for the organization. The structural validity is a design issue and is difficult to improve when using analog simulators. You simply cannot model the exact train flow and safety and interlocking systems in an analog way. Computer simulators have a lot to offer here in interaction with the players during a game session. This is future work for integration. The predictive validity is currently under review as the project follows all game projects longitudinally to determine the extent to which the conclusions based upon game sessions hold true in the real operation. Future work will report on outcomes.

### **7. Conclusions**

The series of six projects shows the purpose and usefulness of building gaming simulations to help the Dutch railway infrastructure manager ProRail innovate on its core processes. Over the projects methodological lessons on involving operators as game participants have been drawn, as well as for the abstraction and reduction of information and the modeling of time. These modeling challenges appear to be highly interrelated. The lessons learned show the need, contrary to the traditional modeling approaches in gaming simulation, for very little abstraction and reduction in modeling the game where it concerns items that the operators have to play with. The model for less operational aspects can be more abstract, in

Gaming Simulations for Railways:

Education 46 (3) 249-264

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Lessons Learned from Modeling Six Games for the Dutch Infrastructure Management 293

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As the game projects reported in this chapter are not for learning but for testing of designs and hypotheses, the findings on how to make real operators show valid behavior in a game session contributes to the small but growing field of gaming simulation for testing. For the categories psychological reality and process validity the current approach has found ways to address given the limited time and capacity available for traditional validation. For structural validity and predictive validity future work is defined.

The sequence of gaming simulations led to a successful introduction in the ProRail organization of the gaming method. Full support has led to a four-year partnership between academics and the operation to make gaming suited for ProRail and ProRail suited for gaming. Once this project has been carried out, ProRail will have at its disposal a gaming suite that connects with existing rail traffic simulators. The gaming suite will make it possible to configure a game simulation session without the need to call in outside expertise by selecting timetables, locations, actors, duration and measurement variables. The key feature is the possibility to create 'what-if' scenarios. The outcomes of these scenarios support the decision-making process by providing an understanding of the problems and the pros and cons of the possible solutions.

### **8. Acknowledgements**

This research has been funded by ProRail and the Next Generation Infrastructure Foundation (NGI). Special thanks go out to the team members both on the side of ProRail (Jelle van Luipen, Emdzad Sehic, the steering committee, amongst many others) and the side of TU Delft (Rens Kortmann, Igor Mayer, Alexander Verbraeck, Bas van Nuland, Gert Jan Stolk and the Game Lab a.o.). Research like this is teamwork.

### **9. References**


line with literature on the need for fidelity for learning in games. While this finding may be not surprising to experienced game developers, the value of using abstractions that are used

As the game projects reported in this chapter are not for learning but for testing of designs and hypotheses, the findings on how to make real operators show valid behavior in a game session contributes to the small but growing field of gaming simulation for testing. For the categories psychological reality and process validity the current approach has found ways to address given the limited time and capacity available for traditional validation. For

The sequence of gaming simulations led to a successful introduction in the ProRail organization of the gaming method. Full support has led to a four-year partnership between academics and the operation to make gaming suited for ProRail and ProRail suited for gaming. Once this project has been carried out, ProRail will have at its disposal a gaming suite that connects with existing rail traffic simulators. The gaming suite will make it possible to configure a game simulation session without the need to call in outside expertise by selecting timetables, locations, actors, duration and measurement variables. The key feature is the possibility to create 'what-if' scenarios. The outcomes of these scenarios support the decision-making process by providing an understanding of the problems and the pros and cons of the possible solutions.

This research has been funded by ProRail and the Next Generation Infrastructure Foundation (NGI). Special thanks go out to the team members both on the side of ProRail (Jelle van Luipen, Emdzad Sehic, the steering committee, amongst many others) and the side of TU Delft (Rens Kortmann, Igor Mayer, Alexander Verbraeck, Bas van Nuland, Gert Jan

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**8. Acknowledgements** 

**9. References** 

sector.


**12** 

*Poland* 

**Application of 3D Simulation Methods to the** 

Elżbieta Szychta, Leszek Szychta, Mirosław Luft and Kamil Kiraga

**Process of Induction Heating of Rail Turnouts** 

*Technical University of Radom, Institute of Transport Systems and Electrical Engineering* 

Keeping turnouts fully functional is necessary for safety of both train passengers and personnel operating railroads, particularly in winter. This is of particular importance since turnouts, key railroad elements, are exposed to adverse weather conditions. Proper function of turnouts is obstructed by snow falling between the point and the rail and between components of the setting lock which, combined with low ambient temperatures, causes the point to freeze to the sliding chairs and the components of the setting lock to freeze. This leads to blocking of a turnout1. Effective protection of turnouts against such weather

The presented methods of heating railway turnouts all over the World are designed to prove operation efficiency turnouts during the winter. The authors set the goal of work to develop a new method of heating railway turnouts, using an inductive heating phenomenon. To do that it is necessary to know the properties of magnetic and electric rails. These properties are not explicitly specified by the manufacturers of rails, so the determination of their value by the laboratory tests is required. The chapter discusses the measurement methods used to determine the basic properties of electric and magnetic rails. Based on laboratory results a simulation model of inductive heating rails in 3D space is developed. In the final part of the

Methods of clearing snow and ice have evolved in line with the state of engineering art, weather conditions in a region as well as availability and costs of energy sources. The most

water heating, used in smaller rail facilities, mainly in Germany. The first systems of

1Kiraga K., Szychta E., Andrulonis J. (2010). Wybrane metody ogrzewania rozjazdów kolejowych –

2Brodowski D., Andrulonis J. (2002). Ogrzewanie rozjazdów kolejowych, Problemy kolejnictwa

conditions greatly reduces accident rates and improves efficiency of rail traffic.

chapter results of a simulation model tests are presented and discussed.

**2. Contemporary methods of turnout heating** 

common methods of heating turnouts in Europe include2:

this type in Poland were installed at Boguszów station,

**1. Introduction** 

gas heating,

geothermal heating,

artykuł przeglądowy


## **Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts**

Elżbieta Szychta, Leszek Szychta, Mirosław Luft and Kamil Kiraga *Technical University of Radom, Institute of Transport Systems and Electrical Engineering Poland* 

### **1. Introduction**

294 Infrastructure Design, Signalling and Security in Railway

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Keeping turnouts fully functional is necessary for safety of both train passengers and personnel operating railroads, particularly in winter. This is of particular importance since turnouts, key railroad elements, are exposed to adverse weather conditions. Proper function of turnouts is obstructed by snow falling between the point and the rail and between components of the setting lock which, combined with low ambient temperatures, causes the point to freeze to the sliding chairs and the components of the setting lock to freeze. This leads to blocking of a turnout1. Effective protection of turnouts against such weather conditions greatly reduces accident rates and improves efficiency of rail traffic.

The presented methods of heating railway turnouts all over the World are designed to prove operation efficiency turnouts during the winter. The authors set the goal of work to develop a new method of heating railway turnouts, using an inductive heating phenomenon. To do that it is necessary to know the properties of magnetic and electric rails. These properties are not explicitly specified by the manufacturers of rails, so the determination of their value by the laboratory tests is required. The chapter discusses the measurement methods used to determine the basic properties of electric and magnetic rails. Based on laboratory results a simulation model of inductive heating rails in 3D space is developed. In the final part of the chapter results of a simulation model tests are presented and discussed.

### **2. Contemporary methods of turnout heating**

Methods of clearing snow and ice have evolved in line with the state of engineering art, weather conditions in a region as well as availability and costs of energy sources. The most common methods of heating turnouts in Europe include2:

gas heating,


<sup>1</sup>Kiraga K., Szychta E., Andrulonis J. (2010). Wybrane metody ogrzewania rozjazdów kolejowych – artykuł przeglądowy

<sup>2</sup>Brodowski D., Andrulonis J. (2002). Ogrzewanie rozjazdów kolejowych, Problemy kolejnictwa

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 297

Water heating is another way of heating rail turnouts. An oil unit heats the working fluid, a mixture of water and anti-freeze agents. The heated fluid is supplied to pipe heat exchanges (heaters) which are fitted along a rail and turnout saddles. The fluid yields its heat and returns to the unit, cooled, to be re-heated. In a water heating system, the energy contained in the fuel (heating oil) is converted into heating power in the heating unit placed in the immediate vicinity of turnouts (normally in a building nearest to a signal cabin, which can

 a heating station – including a heating unit, fuel tank, and a control system, 220V~/12V= (or 24V =) power supply to the heating unit, 12V (24V) battery as a reserve power source for the unit, and plumbing (surge tanks, pumps, pipes, cut-off valves),

Fig. 2. Single-flow MAS water heating of a short turnout: 1 – return to unit, 2 – Ø 12mm steel

Geothermal systems are the third method of turnout heating discussed here. Geothermal heating, which uses the natural underground heat, is a new alternative to the systems presented above. A heat pump is its core element. Depending on the season and depth, soil temperatures may range from 4 to 8°C. At more than 15m below the ground level, season-related thermal motions cease and the temperature is constantly around 8-10°C. Still deeper, the soil is

regenerated by flowing underground waters, heat from the earth's core and from above.

3Materiały seminaryjne CNTK. Wodne ogrzewanie rozjazdów kolejowych typu MAS 4Badania eksploatacyjne wodnego system ogrzewania rozjazdów typu MAS-Guben

pipe (heater), 3 – a heater located near a rail edge and sliding chair,

4 – heating of a setting lock, 5 – support heater, 6 - input

Design of a MAS water heating system comprises the following elements4:

installation feeding the operating fluid from the heating station to turnouts.

heating elements, i.e. heat exchangers inside a turnout,

Layout of a MAS system is shown in Figure 2.

itself be heated by the unit as well)3.

 electric heating by means of resistance heaters (most often supplied with 3Χ400 [V] systems, 230 [V] power supply, or with 15 [kV] 16 2 <sup>3</sup> [Hz] traction networks via voltage-reducing transformers).

Gas heating is used in extremely hard weather conditions (heavy snowfall and low temperatures of down to – 30°C) on Austrian, Norwegian and Swiss railroads (the Alpine region) or in the Netherlands, where the weather is mild but very damp. Gas systems of turnout heating are characterised by high thermal efficiency. Gas burners reach power of up to 1000 [W/running metre of a rail]. Liquid mixtures of propane and butane or butane alone are most often employed as fuel. The gases display varied pressure depending on temperatures of condensed gas. The pressure reduces as the temperatures diminish. Mixtures of propane and butane are utilised where ambient temperatures are above – 17°C, replaced with butane itself below that temperature. Gas turnout heating is diagrammatically presented in Figure 1.

Fig. 1. Gas system of turnout heating

Water heating is another way of heating rail turnouts. An oil unit heats the working fluid, a mixture of water and anti-freeze agents. The heated fluid is supplied to pipe heat exchanges (heaters) which are fitted along a rail and turnout saddles. The fluid yields its heat and returns to the unit, cooled, to be re-heated. In a water heating system, the energy contained in the fuel (heating oil) is converted into heating power in the heating unit placed in the immediate vicinity of turnouts (normally in a building nearest to a signal cabin, which can itself be heated by the unit as well)3.

Design of a MAS water heating system comprises the following elements4:


Layout of a MAS system is shown in Figure 2.

296 Infrastructure Design, Signalling and Security in Railway

electric heating by means of resistance heaters (most often supplied with 3Χ400 [V]

Gas heating is used in extremely hard weather conditions (heavy snowfall and low temperatures of down to – 30°C) on Austrian, Norwegian and Swiss railroads (the Alpine region) or in the Netherlands, where the weather is mild but very damp. Gas systems of turnout heating are characterised by high thermal efficiency. Gas burners reach power of up to 1000 [W/running metre of a rail]. Liquid mixtures of propane and butane or butane alone are most often employed as fuel. The gases display varied pressure depending on temperatures of condensed gas. The pressure reduces as the temperatures diminish. Mixtures of propane and butane are utilised where ambient temperatures are above – 17°C, replaced with butane itself below that temperature. Gas turnout heating is diagrammatically

<sup>3</sup> [Hz] traction networks via

systems, 230 [V] power supply, or with 15 [kV] 16 2

voltage-reducing transformers).

presented in Figure 1.

Fig. 1. Gas system of turnout heating

Fig. 2. Single-flow MAS water heating of a short turnout: 1 – return to unit, 2 – Ø 12mm steel pipe (heater), 3 – a heater located near a rail edge and sliding chair, 4 – heating of a setting lock, 5 – support heater, 6 - input

Geothermal systems are the third method of turnout heating discussed here. Geothermal heating, which uses the natural underground heat, is a new alternative to the systems presented above. A heat pump is its core element. Depending on the season and depth, soil temperatures may range from 4 to 8°C. At more than 15m below the ground level, season-related thermal motions cease and the temperature is constantly around 8-10°C. Still deeper, the soil is regenerated by flowing underground waters, heat from the earth's core and from above.

 3Materiały seminaryjne CNTK. Wodne ogrzewanie rozjazdów kolejowych typu MAS

<sup>4</sup>Badania eksploatacyjne wodnego system ogrzewania rozjazdów typu MAS-Guben

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 299

Electric heating is the final method of turnout heating to be discussed here. The electric heating currently prevails in Poland among the equipment used to melt snow and ice on rail turnouts. It functions on more than 18 000 turnouts. Its combined installed power reaches approximately 110 [MW]5. The electric systems heat for an average of 300 hrs in a season. Providing 330W per running metre of rail assures effective warming of railroad turnouts during the heating season. The electric heating employing 330W/m heaters provides for good functioning of railroad turnouts under normal weather conditions (i.e. temperatures above -20°C) and with average (other than catastrophic) snowfall. A diagram of electric

Recent years of cold winters and violent snowfalls have unfortunately shown that electric systems fail to provide effective heating of turnouts. The method of electric heating has

Performance trials are under way using heat insulation on Dutch, German, and Polish railroads. The rail foot is additionally insulated as part of these solutions. Arrangement of

turnout heating is shown in Figure 4.

Fig. 4. Electric turnout heating

therefore been modified to enhance its efficiency.

heat insulations on a rail is presented in Figure 5 below6.

6Prospekt informacyjny o otulinach firmy Haet Point, 2009.

5Brodowski D., Andrulonis J.(2000). Efektywność ogrzewania rozjazdów kolejowych

Heat pumps operate like fridges which take advantage of the hot, not the cold section of the heat cycle. An appropriate working agent is compressed and decompressed producing a desired heating or cooling effect. To generate useful heat, for instance, soil or underground water heat (at low temperatures of approx. 10°C) is employed to evaporate the operating agent (harmless gas R497C) that boils at a low temperature. Thus, the originally liquid working agent leaves an evaporator (heat exchanger on the side of ground collector) as gas. The gas is then compressed and condensated in a liquefier (heat exchanger on the side of heating installation) at high temperatures (50-60°C), yielding the condensation and compression heat to the water contained in the heating installation. The still pressurised working agent is subsequently decompressed in a valve and enters the low-pressure section, thereby initiating the cycle once again.

A complete system of geothermal turnout heating is illustrated in Figure 3.

Fig. 3. Design of a geothermal turnout heating system including: 1 – a local control and monitoring system, 2 – an automatic control system containing an automatic weather unit, 3 – heat pump and heat cycle, 4 – snowfall and ambient temperature sensor, 5 – humidity and rail temperature sensors, 6 – junction box, 7 – heat exchangers (heaters) with heatconducting insulation

Electric heating is the final method of turnout heating to be discussed here. The electric heating currently prevails in Poland among the equipment used to melt snow and ice on rail turnouts. It functions on more than 18 000 turnouts. Its combined installed power reaches approximately 110 [MW]5. The electric systems heat for an average of 300 hrs in a season. Providing 330W per running metre of rail assures effective warming of railroad turnouts during the heating season. The electric heating employing 330W/m heaters provides for good functioning of railroad turnouts under normal weather conditions (i.e. temperatures above -20°C) and with average (other than catastrophic) snowfall. A diagram of electric turnout heating is shown in Figure 4.

Fig. 4. Electric turnout heating

298 Infrastructure Design, Signalling and Security in Railway

Heat pumps operate like fridges which take advantage of the hot, not the cold section of the heat cycle. An appropriate working agent is compressed and decompressed producing a desired heating or cooling effect. To generate useful heat, for instance, soil or underground water heat (at low temperatures of approx. 10°C) is employed to evaporate the operating agent (harmless gas R497C) that boils at a low temperature. Thus, the originally liquid working agent leaves an evaporator (heat exchanger on the side of ground collector) as gas. The gas is then compressed and condensated in a liquefier (heat exchanger on the side of heating installation) at high temperatures (50-60°C), yielding the condensation and compression heat to the water contained in the heating installation. The still pressurised working agent is subsequently decompressed in a valve and enters the low-pressure section,

A complete system of geothermal turnout heating is illustrated in Figure 3.

Fig. 3. Design of a geothermal turnout heating system including: 1 – a local control and monitoring system, 2 – an automatic control system containing an automatic weather unit, 3 – heat pump and heat cycle, 4 – snowfall and ambient temperature sensor, 5 – humidity and

rail temperature sensors, 6 – junction box, 7 – heat exchangers (heaters) with heat-

thereby initiating the cycle once again.

conducting insulation

Recent years of cold winters and violent snowfalls have unfortunately shown that electric systems fail to provide effective heating of turnouts. The method of electric heating has therefore been modified to enhance its efficiency.

Performance trials are under way using heat insulation on Dutch, German, and Polish railroads. The rail foot is additionally insulated as part of these solutions. Arrangement of heat insulations on a rail is presented in Figure 5 below6.

 5Brodowski D., Andrulonis J.(2000). Efektywność ogrzewania rozjazdów kolejowych

<sup>6</sup>Prospekt informacyjny o otulinach firmy Haet Point, 2009.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 301

Elementary theory concerning induction heating is not introduced as it is commonly known and easily available in engineering literature8 9. Knowledge of fundamental electric and magnetic properties of rails forming parts of turnouts is necessary to construct a fully functional induction heating system. Since not all of those properties are easily accessible or clearly defined, their values had to be determined experimentally by one of the methods

Attention focused then on the mathematical apparatus based on Maxwell's equations and used to describe the electromagnetic field in space. Final element method (FEM) was subsequently discussed. Maxwell's equations and FEM provide the foundations for an

Rails (stock) are fundamental design elements of a turnout, beside switch points, sliding chairs or switching closure assemblies. Rails are principally designed to set the proper travel direction of rolling stock wheel sets. Shape of a rail comprises three characteristic sections: head (the part along which rolling stock wheels move), web, and foot (the part supporting

Two main rail types are used on routes administered by Polish State Railways PKP PLK: 60E1 and 49E1. They differ in the weight of a running metre and cross-section dimensions. 49E1 (49.39 kg/ running metre and cross-section surface area of 62.92 cm3) is used on routes with light rolling stock load. 60E1 (60.21 kg/ running metre and cross-section surface area of 76.70 cm3) is operated on heavily loaded routes where trains travel at speeds over 100 km/h. Table 1 presents steel grades to be used in rail manufacture10 11. The grade references follow from applicable European and Polish standards (PN-EN 10027-1 and PN-EN10027-2). The

8Sajdak Cz., Samek E. (1985). Nagrzewanie indukcyjne. Podstawy teoretyczne i zastosowanie 9Gozdecki T., Hering M., Łobodziński W. (1979). Urządzenia elektroniczne. Elektroniczne urządzenia

analytical model of induction turnout heating as executed in Flux 3D software.

**4. Electric and magnetic properties of e160 rail** 

10Wielgosz R. (2009). Łączenie bezstykowych szyn kolejowych

the whole and carrying the load on to sleepers).

grzejne

Fig. 6. System of induction turnout heating

described in the following section.

Fig. 5. Situation of insulations on the internal and external sides of a rail and on rail foot for every rail type

Such a solution is offered to PKP (Polish State Railroads) by Heat Point of the Netherlands, Research and testing will demonstrate potential advantages and drawbacks of this solution.

### **3. Induction heating of turnouts now and in the past**

Induction turnout heating (an original Polish concept) was tested by PKP in 1978/1979 on selected turnouts and stations7. Insulated heating wires were used. They were not in galvanic contact with rails. Rails were heated with eddy currents induced inside the rails. The wires were heated to temperatures in the range +15°C to +20°C.

The heating wires were made of copper, wrapped with Tarflon tape, and placed inside a steel envelope. 3-3.3 [V] and 50 [Hz] were supplied to the wire, where the current was 350 [A].

The following types of heating wires were used:


A 2800 [VA] transformer was employed to supply power to each type of heaters. Given the mains frequency of 50 [Hz], the heating wires vibrated and produced human-audible acoustic waves whose frequency was twice greater than the frequency of the supplied voltage.

The inductive nature of power distribution system loading by ior equipment of the time required an additional capacitor to set off the reactive power and to improve the power factor cosφ from approx. 0.5 to 0.85 – 0.9. Capacitors capable of adjusting reactive power of 4 [kVA] or more were employed in a single given turnout. Work on the system and its application was abandoned due to insufficient technological resources at the time (1978/1979). The material on testing of inductive turnout heating discussed here is the only, scarce material still extant in the archives of the then COBiRTK (Centre for Rail Engineering Research and Development), currently named IK (Rail Engineering Institute).

These authors have decided to revive the idea of induction turnout heating and to use it, as part of a greater operating frequency system, to heat rail turnouts. A flow diagram of induction turnout heating as proposed by the authors is shown in Figure 6.

 7Praca zbiorowe: Studium na temat wyboru optymalnego systemu ogrzewania rozjazdów

Fig. 6. System of induction turnout heating

300 Infrastructure Design, Signalling and Security in Railway

Fig. 5. Situation of insulations on the internal and external sides of a rail and on rail foot for

Such a solution is offered to PKP (Polish State Railroads) by Heat Point of the Netherlands, Research and testing will demonstrate potential advantages and drawbacks of this solution.

Induction turnout heating (an original Polish concept) was tested by PKP in 1978/1979 on selected turnouts and stations7. Insulated heating wires were used. They were not in galvanic contact with rails. Rails were heated with eddy currents induced inside the rails.

The heating wires were made of copper, wrapped with Tarflon tape, and placed inside a steel envelope. 3-3.3 [V] and 50 [Hz] were supplied to the wire, where the current was 350

A 2800 [VA] transformer was employed to supply power to each type of heaters. Given the mains frequency of 50 [Hz], the heating wires vibrated and produced human-audible acoustic waves whose frequency was twice greater than the frequency of the supplied

The inductive nature of power distribution system loading by ior equipment of the time required an additional capacitor to set off the reactive power and to improve the power factor cosφ from approx. 0.5 to 0.85 – 0.9. Capacitors capable of adjusting reactive power of 4 [kVA] or more were employed in a single given turnout. Work on the system and its application was abandoned due to insufficient technological resources at the time (1978/1979). The material on testing of inductive turnout heating discussed here is the only, scarce material still extant in the archives of the then COBiRTK (Centre for Rail Engineering

These authors have decided to revive the idea of induction turnout heating and to use it, as part of a greater operating frequency system, to heat rail turnouts. A flow diagram of

Research and Development), currently named IK (Rail Engineering Institute).

induction turnout heating as proposed by the authors is shown in Figure 6.

7Praca zbiorowe: Studium na temat wyboru optymalnego systemu ogrzewania rozjazdów

**3. Induction heating of turnouts now and in the past** 

The following types of heating wires were used: 2.55 [m], power 750 [W] for the rail UIC-49 3.00 [m], power 900 [W] for the rail UIC-60

The wires were heated to temperatures in the range +15°C to +20°C.

every rail type

[A].

voltage.

Elementary theory concerning induction heating is not introduced as it is commonly known and easily available in engineering literature8 9. Knowledge of fundamental electric and magnetic properties of rails forming parts of turnouts is necessary to construct a fully functional induction heating system. Since not all of those properties are easily accessible or clearly defined, their values had to be determined experimentally by one of the methods described in the following section.

Attention focused then on the mathematical apparatus based on Maxwell's equations and used to describe the electromagnetic field in space. Final element method (FEM) was subsequently discussed. Maxwell's equations and FEM provide the foundations for an analytical model of induction turnout heating as executed in Flux 3D software.

### **4. Electric and magnetic properties of e160 rail**

Rails (stock) are fundamental design elements of a turnout, beside switch points, sliding chairs or switching closure assemblies. Rails are principally designed to set the proper travel direction of rolling stock wheel sets. Shape of a rail comprises three characteristic sections: head (the part along which rolling stock wheels move), web, and foot (the part supporting the whole and carrying the load on to sleepers).

Two main rail types are used on routes administered by Polish State Railways PKP PLK: 60E1 and 49E1. They differ in the weight of a running metre and cross-section dimensions. 49E1 (49.39 kg/ running metre and cross-section surface area of 62.92 cm3) is used on routes with light rolling stock load. 60E1 (60.21 kg/ running metre and cross-section surface area of 76.70 cm3) is operated on heavily loaded routes where trains travel at speeds over 100 km/h.

Table 1 presents steel grades to be used in rail manufacture10 11. The grade references follow from applicable European and Polish standards (PN-EN 10027-1 and PN-EN10027-2). The

<sup>8</sup>Sajdak Cz., Samek E. (1985). Nagrzewanie indukcyjne. Podstawy teoretyczne i zastosowanie 9Gozdecki T., Hering M., Łobodziński W. (1979). Urządzenia elektroniczne. Elektroniczne urządzenia grzejne

<sup>10</sup>Wielgosz R. (2009). Łączenie bezstykowych szyn kolejowych

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 303

Fig. 7. Geometrical dimensions of the normal-gauge E160

Fig. 8. 60E1 sample removal locations and their geometric dimensions

symbols of rail materials are based on rolling surface hardness, in Brinell degrees, with the added symbol of an element used to refine the rail steel or in reinforcement heat treatment. Table 1 also includes references to previously used steel grades, of chemical compositions similar to the new steels recommended by the EU in accordance with EN 13674-1:2003 (E).

Two steel grades most commonly used in Poland are R260 (hardness range 260÷300 HB) and R350HT (hardness range 350÷390 HB, heat treated head).


Table 1. Rail steel markings

The steels formerly used in rails contain 0.40 to 0.82% carbon, 0.60 to 1.70% manganese, 0.05 to 0.90% silica, and some additionally contain up to 1.30% chromium. The new steels recommended by the EU contain: 0.38 - 0.82% carbon, 0.65 - 1.70% manganese, 0.13 - 1.12% silica, and some additionally contain up to 1.25% chromium.

As steel is heated and cooled and temperatures change in rail manufacturing processes, structural transformations occur. In the final production process, a rail is hot rolled at temperatures of 700 – 900°C. The (heterogeneous) structure and material properties of the rail result from such processes.

60E1 is selected for purposes of testing electric and magnetic properties because it serves trans which travel at up to 100 km/h. Standardised dimensions of normal-gauge 60E112 <sup>13</sup> are illustrated in Figure 7.

The following elements of a heating circuit are analysed as part of testing aimed at developing a method of induction turnout heating: structure of rail material, resistivity and magnetic permeaability, skin effect and depth of magnetic field penetration into the rail structure, discharge of active power in the form of impact of the magnetic field on the rail. These parameters depend, inter alia, on magnetising current frequency and are not defined by rail manufacturers. It appears rails may come from different charges, may be produced by means of diverse rolling, straightening, and possibly hardening technologies. It was therefore important to determine locations from which rail samples would be removed. To generate a maximum quantity of data for further research, samples were withdrawn (cut) from key points of a rail. Sample removal locations and their geometric dimensions are shown in Figure 8.

<sup>11</sup>strona internetowa odnośnie szyn kolejowych: www. inzynieria-kolejowa.dl.pl 12Grobelny M. (2009) Budowa, modernizacja, naprawa i remonty nawierzchni kolejowej – urządzenia i elementy

<sup>13</sup>Instrukcja eksploatacji i utrzymania urządzeń elektrycznego ogrzewania rozjazdów

symbols of rail materials are based on rolling surface hardness, in Brinell degrees, with the added symbol of an element used to refine the rail steel or in reinforcement heat treatment. Table 1 also includes references to previously used steel grades, of chemical compositions similar to the new steels recommended by the EU in accordance with EN 13674-1:2003 (E). Two steel grades most commonly used in Poland are R260 (hardness range 260÷300 HB) and

**Steel marking Description Material number Previous marking**  R200 Carbon-manganese 1.0521 R0700 R220 Carbon-manganese 1.0524 R0800 R260 Carbon-manganese 1.0623 R0900; St90PA R260Mn Carbon-manganese 1.0624 R0900Mn; St90PB R320Cr Low alloy 1.0915 R1100Cr R350HT Heat treated carbon-manganese 1.0631 R1200

The steels formerly used in rails contain 0.40 to 0.82% carbon, 0.60 to 1.70% manganese, 0.05 to 0.90% silica, and some additionally contain up to 1.30% chromium. The new steels recommended by the EU contain: 0.38 - 0.82% carbon, 0.65 - 1.70% manganese, 0.13 - 1.12%

As steel is heated and cooled and temperatures change in rail manufacturing processes, structural transformations occur. In the final production process, a rail is hot rolled at temperatures of 700 – 900°C. The (heterogeneous) structure and material properties of the

60E1 is selected for purposes of testing electric and magnetic properties because it serves trans which travel at up to 100 km/h. Standardised dimensions of normal-gauge 60E112 <sup>13</sup>

The following elements of a heating circuit are analysed as part of testing aimed at developing a method of induction turnout heating: structure of rail material, resistivity and magnetic permeaability, skin effect and depth of magnetic field penetration into the rail structure, discharge of active power in the form of impact of the magnetic field on the rail. These parameters depend, inter alia, on magnetising current frequency and are not defined by rail manufacturers. It appears rails may come from different charges, may be produced by means of diverse rolling, straightening, and possibly hardening technologies. It was therefore important to determine locations from which rail samples would be removed. To generate a maximum quantity of data for further research, samples were withdrawn (cut) from key points of a rail. Sample removal locations and their geometric dimensions are

11strona internetowa odnośnie szyn kolejowych: www. inzynieria-kolejowa.dl.pl 12Grobelny M. (2009) Budowa, modernizacja, naprawa i remonty nawierzchni kolejowej – urządzenia i

13Instrukcja eksploatacji i utrzymania urządzeń elektrycznego ogrzewania rozjazdów

R350HT (hardness range 350÷390 HB, heat treated head).

R350LHT Heat treated low alloy 1.0632

silica, and some additionally contain up to 1.25% chromium.

Table 1. Rail steel markings

rail result from such processes.

are illustrated in Figure 7.

shown in Figure 8.

elementy

Fig. 7. Geometrical dimensions of the normal-gauge E160

Fig. 8. 60E1 sample removal locations and their geometric dimensions

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 305

Table 2 summarises results of electric resistivity measurements for samples from

 *HP bridge:* active and passive magnetic hardness as well as the loss tangent are determined. Initial magnetic hardness can also be defined since the intensity of the

Hewlett Packard 4284A 20Hz – 1MHz Precision LCR Meter helps to conduct measurements

A connection link is replaced with a measurement coil of known length *l* and number of coils *z*. A sample is placed inside the coil. The bridge circuit is supplied with AC. A millivoltimetre of very high internal resistance is connected in parallel to the coils with the sample inside. It can measure the voltage drop across this element and, consequently, select the magnetising field as appropriate. The device also provides for de-magnetising of samples using a 50Hz field whose amplitude reduces towards zero, for regulation and

of selected rail sections.

of the tested rail sections

.

**Source of the sample Mean electric resistivity ρ [m]** 

Edge of rail web 2.62·10-7

Centre of rail web 2.85·10-7

Rail foot 2.75·10-7

Taper of rail foot 2.57·10-7

Taper of rail web 2.7·10-7

Rail head 2.58·10-7

Table 2. Values of electric resistivity for the tested samples

in order to determine relative magnetic permeability

The system used to determine relative magnetic permeability

(hp) Hewlett Packard 4284A 20Hz – 1MHz Precision LCR Meter,

Figure 10 contains a diagram of the measurement stand serving to determine

where:

*U*x – voltage drop across the sample,

*l –* distance between the measurement probes.

Ix – measurement current, S – cross-section of the sample,

characteristic rail locations.

magnetic field is low.

stabilisation of temperature.

a PC and its software,

and a measurement coil.

Aligent 34401A 6 ½ Digital Multimeter,

consisted of:

Determining key electric and magnetic parameters of construction materials for railroad turnouts was essential in designing a system of induction heating and employed a variety of testing methods. Electric and magnetic parameters were determined by means of the following methods:

 *four-point linear probe method* to determine electric resistivity (taken into consideration as rotary currents arise when the magnetic field penetrates the internal structure of a rail).

A flow diagram of electric resistivity measurements is illustrated in Figure 9.

Fig. 9. Flow diagram of electric resistivity measurement system

Electric resistivity can be measured by means of a four-point linear probe and a measurement system which employs a PC to record the voltage drop across a tested sample and across a reference resistor *R*w. Voltage is checked by running the current (10 times) in two directions. Once averaged, both the results are added and contact effects are eliminated in this way. The result is averaged and saved to the memory. The current's value can be calculated according to:

$$I\_x = \frac{\mathcal{U}\_{Rw}}{R\_w} \tag{1}$$

With known geometric dimensions of the sample, that is, its height *a* and width *b*, electric resistivity can be determined on the basis of:

$$
\rho = \frac{\mathcal{U}\_x}{I\_x} \cdot \frac{S}{l} = R\_{mixz} \cdot \frac{S}{l} \tag{2}
$$

where:

304 Infrastructure Design, Signalling and Security in Railway

Determining key electric and magnetic parameters of construction materials for railroad turnouts was essential in designing a system of induction heating and employed a variety of testing methods. Electric and magnetic parameters were determined by means of the

 *four-point linear probe method* to determine electric resistivity (taken into consideration as rotary currents arise when the magnetic field penetrates the internal structure of a rail).

A flow diagram of electric resistivity measurements is illustrated in Figure 9.

Fig. 9. Flow diagram of electric resistivity measurement system

*Rw*

resistivity can be determined on the basis of:

Electric resistivity can be measured by means of a four-point linear probe and a measurement system which employs a PC to record the voltage drop across a tested sample and across a reference resistor *R*w. Voltage is checked by running the current (10 times) in two directions. Once averaged, both the results are added and contact effects are eliminated in this way. The result is averaged and saved to the memory. The current's value can be

> *<sup>x</sup> <sup>w</sup> U*

With known geometric dimensions of the sample, that is, its height *a* and width *b*, electric

*<sup>x</sup> mierz*

*<sup>U</sup> S S <sup>R</sup> Il l*

*x*

*<sup>R</sup> I* (1)

(2)

following methods:

calculated according to:

*U*x – voltage drop across the sample,

Ix – measurement current,

S – cross-section of the sample,

*l –* distance between the measurement probes.

Table 2 summarises results of electric resistivity measurements for samples from characteristic rail locations.


Table 2. Values of electric resistivity for the tested samples

 *HP bridge:* active and passive magnetic hardness as well as the loss tangent are determined. Initial magnetic hardness can also be defined since the intensity of the magnetic field is low.

Hewlett Packard 4284A 20Hz – 1MHz Precision LCR Meter helps to conduct measurements in order to determine relative magnetic permeability of selected rail sections.

A connection link is replaced with a measurement coil of known length *l* and number of coils *z*. A sample is placed inside the coil. The bridge circuit is supplied with AC. A millivoltimetre of very high internal resistance is connected in parallel to the coils with the sample inside. It can measure the voltage drop across this element and, consequently, select the magnetising field as appropriate. The device also provides for de-magnetising of samples using a 50Hz field whose amplitude reduces towards zero, for regulation and stabilisation of temperature.

The system used to determine relative magnetic permeability of the tested rail sections consisted of:


Figure 10 contains a diagram of the measurement stand serving to determine .

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 307

Substituting (6) to (5) produces the following equation of passive magnetic permeability:

2 2 0 0

Measuring voltage drop across the resistance R helps to determine intensity of the electric current across the winding and then the intensity of the magnetic field at which magnetic

> *Z U <sup>H</sup> l R*

2 2 *rdz <sup>o</sup> <sup>b</sup> R l RR l Z fS Z fS*

 

( )

initial = f (*f*) of a sample from the rail's head (black) as well from the

inital=f(*f*) for a sample from the edge of rail web and

*R RR rdz* <sup>0</sup> (6)

(7)

(8)

initial=f(*f*) of a sample from the rail

inital = f

*R*rdz, or the core's resistance, is calculated:

*R* – resistance of the coil containing the sample.

permeability is measured using the dependence:

Figure 11 illustrates the initial magnetic permeability

U – voltage drop across the resistor R, l – length of the measurement coil.

*R*0 – resistance of an empty coil,

where:

where:

z – number of coils,

web edge (red) and

rail's core (the green curve).

Fig. 11. Magnetic permeability

(*f*) for the remaining samples.

Fig. 10. Measurement apparatus serving to determine relative magnetic permeability 

An AC bridge is the chief component of the system which provides for accurate measurement of combined magnetic permeability:

$$
\underline{\mu} = \mu\_{cz} + \mathrm{i}\,\mu\_b \tag{3}
$$

The combined permeability comprises:


The active magnetic permeability can be formulated:

$$
\mu\_{cz} = \frac{\left(L\_x - L\_0\right) \cdot l}{\mu\_0 z^2 S\_p} + 1 \tag{4}
$$

here:

*L*x – inductivity of the coil containing the sample,

*L*0 – inductivity of an empty coil,

0 – magnetic permeability of the vacuum 0 = 410-7H/m,

*S*p – cross-sectional surface area of the tested sample,

*z* – number of coils,

*l* – length of the coil.

As cz >> 1, 1 is ignored in the calculations.

The passive magnetic permeability is computed:

$$\mu\_b = \frac{R\_{rdz} \cdot l}{\mu\_0 \cdot Z^2 \cdot 2\pi \cdot f \cdot S\_p} \tag{5}$$

*R*rdz, or the core's resistance, is calculated:

$$R\_{rdz} = R - R\_0 \tag{6}$$

where:

306 Infrastructure Design, Signalling and Security in Railway

Fig. 10. Measurement apparatus serving to determine relative magnetic permeability

 

*cz*

*b*

measurement of combined magnetic permeability:

the component active magnetic permeability

*L*x – inductivity of the coil containing the sample,

cz >> 1, 1 is ignored in the calculations. The passive magnetic permeability is computed:

*S*p – cross-sectional surface area of the tested sample,

0 – magnetic permeability of the vacuum

*L*0 – inductivity of an empty coil,

*z* – number of coils, *l* – length of the coil.

the component passive magnetic permeability

The active magnetic permeability can be formulated:

The combined permeability comprises:

here:

As 

An AC bridge is the chief component of the system which provides for accurate

 <sup>0</sup> 2 0

2 <sup>0</sup> 2 *rdz*

*R l Z f S*

 

*LLl z S*

*cz b*

 

1 *<sup>x</sup>*

*p*

0 = 410-7H/m,

*p*

*R*0 – resistance of an empty coil,

*R* – resistance of the coil containing the sample.

Substituting (6) to (5) produces the following equation of passive magnetic permeability:

$$
\mu\_b = \frac{R\_{rdz} \cdot l}{\mu\_0 Z^2 \,\text{2}\,\text{\pi}\,\text{fS}} = \frac{(R - R\_o) \cdot l}{\mu\_0 Z^2 \,\text{2}\,\text{\pi}\,\text{fS}}\tag{7}
$$

Measuring voltage drop across the resistance R helps to determine intensity of the electric current across the winding and then the intensity of the magnetic field at which magnetic permeability is measured using the dependence:

$$H = \frac{Z \cdot U}{l \cdot R} \tag{8}$$

where:

*i* (3)

cz responsible for magnetising processes,

(5)

b responsible for magnetic losses.

(4)

z – number of coils,

U – voltage drop across the resistor R,

l – length of the measurement coil.

Figure 11 illustrates the initial magnetic permeability initial=f(*f*) of a sample from the rail web edge (red) and initial = f (*f*) of a sample from the rail's head (black) as well from the rail's core (the green curve).

Fig. 11. Magnetic permeability inital=f(*f*) for a sample from the edge of rail web and inital = f (*f*) for the remaining samples.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 309

= f(*H*) for a sample of the rail web

Intensity of the coercion field of magnetically soft and hard materials can be measured by means of a coercion metre. The relevant measurement diagram is presented in Figure 14.

Fig. 13. Curves *B* = f(*H*) and

*coercion metre* measures intensity of the coercion field,

Fig. 14. Measurement diagram using a coercion metre and its components

16Kuryłowicz J. (1962). Badania materiałów magnetycznych

Magnetic coercion16 (also referred to as coercive force) is the value of an external magnetic field that must be applied to a material (e.g. a ferromagnetic material) to bring the magnetic residue down to zero. The magnetic residue (also remanence or residual magnetisation) is the magnetic induction remaining after an external magnetic field magnetising a given material is removed.

 A *fluxmetre* serves to plot the curves *B* = f(*H*) and = f(*H*)14 15,

Prime magnetising curves were determined by means of the measurement system shown in Figure 12.

Fig. 12. Measurement system employing the fluxmetre and its components

The tested sample is placed inside the coil in magnetising and measurement winding. A fluxmetre to measure magnetic flow variations in the tested material sample is the element of the measurement system. Variations in the tested material sample result from commutations of the current across the magnetising winding *z*m. The electric current pulse induced in the measurement winding over time *dt* is measured by the fluxmetre. The magnetic flow variations *dΦ* generate an electromotor force *ε* which can be expressed:

$$
\varepsilon = -\frac{d\phi\_c}{dt} = -z\_p \cdot \frac{d\phi}{dt} \tag{9}
$$

Fluxmetre readings are proportional to magnetic flow variations.

When a uniform external magnetic field is applied, magnetic induction *B* can be computed according to:

$$B = \frac{d\phi}{2z\_pS} \tag{10}$$

where *S* is the cross-sectional surface area of the tested sample. The sample is demagnetised prior to each measurement by means of the system.

A prime magnetising curve for a sample from the rail web and maximum magnetic permeability in respect of the same sample determined using the fluxmetre are shown in Figure 13.

<sup>14</sup>Gignoux D., Schlenker M.(2005). *Magnetism Fundamentals*

<sup>15</sup>Jiles D. (1991). Introduction to Magnetism and Magnetic Materials

Prime magnetising curves were determined by means of the measurement system shown in

Fig. 12. Measurement system employing the fluxmetre and its components

Fluxmetre readings are proportional to magnetic flow variations.

prior to each measurement by means of the system.

14Gignoux D., Schlenker M.(2005). *Magnetism Fundamentals*

15Jiles D. (1991). Introduction to Magnetism and Magnetic Materials

The tested sample is placed inside the coil in magnetising and measurement winding. A fluxmetre to measure magnetic flow variations in the tested material sample is the element of the measurement system. Variations in the tested material sample result from commutations of the current across the magnetising winding *z*m. The electric current pulse induced in the measurement winding over time *dt* is measured by the fluxmetre. The magnetic flow variations *dΦ* generate an electromotor force *ε* which can be expressed:

> *<sup>c</sup> <sup>p</sup> d d z dt dt*

When a uniform external magnetic field is applied, magnetic induction *B* can be computed

2 *<sup>p</sup> <sup>d</sup> <sup>B</sup> z S* 

where *S* is the cross-sectional surface area of the tested sample. The sample is demagnetised

A prime magnetising curve for a sample from the rail web and maximum magnetic permeability in respect of the same sample determined using the fluxmetre are shown in

(9)

(10)

 = f(*H*)14 15,

A *fluxmetre* serves to plot the curves *B* = f(*H*) and

Figure 12.

according to:

Figure 13.

Fig. 13. Curves *B* = f(*H*) and = f(*H*) for a sample of the rail web

*coercion metre* measures intensity of the coercion field,

Intensity of the coercion field of magnetically soft and hard materials can be measured by means of a coercion metre. The relevant measurement diagram is presented in Figure 14.

Fig. 14. Measurement diagram using a coercion metre and its components

Magnetic coercion16 (also referred to as coercive force) is the value of an external magnetic field that must be applied to a material (e.g. a ferromagnetic material) to bring the magnetic residue down to zero. The magnetic residue (also remanence or residual magnetisation) is the magnetic induction remaining after an external magnetic field magnetising a given material is removed.

<sup>16</sup>Kuryłowicz J. (1962). Badania materiałów magnetycznych

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 311

and an easyLab Pcell 30kbar pressure chamber to measure resistance at high pressure of

Fig. 15. Physical Property Measurement System to test magnetic properties of rail samples

magnetising curves and to determine saturation of the tested rail samples.

amplitude and vibration frequency. It can be described as follows:

A magnetometer suction cup with the vibrating sample was employed to plot prime

A sample is positioned on a non-magnetic, mobile bar and vibrates vertically at a set frequency. The sample's oscillations generate (induce) a variable voltage signal in the measurement coil system under impact of the magnetic field. The signal is proportional to the magnetic moment of the sample and to parameters characterising its motion, i.e. to the

*cewki* sin *d d dz <sup>V</sup> CmA t*

(11)

*dt dz dt*

 

 measurement capability of electric resistance in the range of 350mK, vertical rotator to regulate sample position in relation to the magnetic field,

The overall flow diagram of PPMS platform is shown in Figure 15.

up to 30kbar.

where:

– frequency.

*C* –proportionality constant,

*m* – a known moment of the sample, *A* – vibration (oscillation*)*amplitude,


Table 3 summarises measurement results of magnetic coercion intensity for samples removed from key rail locations.

Table 3. Coercion field intensity in respect of all samples

*PPMS VSM* was utilised to plot the curve *J* = f(*H*),

A Physical Property Measurement System (PPMS) by Quantum Design (San Diego, USA) is a unique, state-of-the-art concept of a laboratory facility.

The PPMS platform comprises the following elements:


The overall flow diagram of PPMS platform is shown in Figure 15.

Fig. 15. Physical Property Measurement System to test magnetic properties of rail samples

A magnetometer suction cup with the vibrating sample was employed to plot prime magnetising curves and to determine saturation of the tested rail samples.

A sample is positioned on a non-magnetic, mobile bar and vibrates vertically at a set frequency. The sample's oscillations generate (induce) a variable voltage signal in the measurement coil system under impact of the magnetic field. The signal is proportional to the magnetic moment of the sample and to parameters characterising its motion, i.e. to the amplitude and vibration frequency. It can be described as follows:

$$V\_{cewki} = -\frac{d\phi}{dt} = -\left(\frac{d\phi}{dz}\right)\left(\frac{dz}{dt}\right) = \mathbf{C} \text{ } m \text{ A } oo \text{ } \sin\left(\text{ } o \text{ } t\right) \tag{11}$$

where:

310 Infrastructure Design, Signalling and Security in Railway

Table 3 summarises measurement results of magnetic coercion intensity for samples

**Source of the sample Sample number Hc [A/m] Mean Hc [A/m]** 

1 820

3 828

1 772

3 772

1 772

3 788

1 876

2 884 3 1003 4 884

1 860

2 860 3 804 4 796

1 812

2 860 3 820 4 908

A Physical Property Measurement System (PPMS) by Quantum Design (San Diego, USA) is

specific heat measurement system (Heat Capacity 4He) in the temperature range

specific heat measurement system (Helium-3) in the temperature range

 vibration magnetometer VSM for precise magnetising measurements In a broad temperature range of 2K to 1000K. It is additionally fitted with an oven (P527 Sample

superconducting magnet of up to 7 Tesla (and, more recently, even 16 Tesla),

AC/DC magnetisation measurement system for magnetic fields of up to 7 Tesla,

2 820 823

2 776 774

2 772 778

912

830

850

removed from key rail locations.

Edge of rail web

Centre of rail web

Taper of rail foot

Taper of rail web

Table 3. Coercion field intensity in respect of all samples

*PPMS VSM* was utilised to plot the curve *J* = f(*H*),

a unique, state-of-the-art concept of a laboratory facility. The PPMS platform comprises the following elements:

2K – 400K and magnetic fields of up to 7 Tesla,

350mK – 350K and magnetic fields of up to 7 Tesla,

Magnetometer Oven) for measurements of up to 1000K. heat conductivity and thermal force measurement system,

Rail head

Rail foot

*C* –proportionality constant,


– frequency.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 313

 *ACMS* determines combined magnetic susceptibility, including its real and imaginary components, the loss tangent for varied intensities of the magnetic field and for

ACMS (AC Measurement System) provides for a single sequence of measurements of AC and DC susceptibility in a broad temperature range from 1.9K – 350K. AC measurements are thrice as sensitive (2×10-8emu (2×10-11 Am2) at 10kHz) as DC measurements. Better results may be occasionally obtained by means of the DC method. Application of a powerful external field can increase the sample's magnetic moment and generate signals above the noise (the range of DC magnetising DC: 2.5×10-8Am2 - 5× 10-3Am2 (2.5×10-5emu – 5emu). DC measurement uses a constant field in the measurement area where the sample moves by means of detection coils and induces voltage there according to Faraday's law. Amplitude of this signal depends on the sample's magnetic moment and the rate of its removal. As part of this system, the sample is extracted at an approximate speed of 100cm/s. The signal's force grows considerably as a result compared to other systems. The measurements can be

executed as a function of both temperature and of the magnetic field. Flow diagram of ACMS and its key elements are shown in Figure 18.

different temperatures.

Fig. 18. Flow diagram of ACMS

A flow diagram of vibrating sample magnetometer (VSM) is illustrated in Figure 16.

Fig. 16. Flow diagram of VSM measurement platform

Figure 17 presents a magnetising curve *J* = f(*H*) and magnetic saturation *J*s for rail head samples.

Fig. 17. Magnetising curve *J* = f(*H*) and magnetic saturation *J*s for rail head samples

Figure 17 presents a magnetising curve *J* = f(*H*) and magnetic saturation *J*s for rail head

Fig. 17. Magnetising curve *J* = f(*H*) and magnetic saturation *J*s for rail head samples

A flow diagram of vibrating sample magnetometer (VSM) is illustrated in Figure 16.

Fig. 16. Flow diagram of VSM measurement platform

samples.

 *ACMS* determines combined magnetic susceptibility, including its real and imaginary components, the loss tangent for varied intensities of the magnetic field and for different temperatures.

ACMS (AC Measurement System) provides for a single sequence of measurements of AC and DC susceptibility in a broad temperature range from 1.9K – 350K. AC measurements are thrice as sensitive (2×10-8emu (2×10-11 Am2) at 10kHz) as DC measurements. Better results may be occasionally obtained by means of the DC method. Application of a powerful external field can increase the sample's magnetic moment and generate signals above the noise (the range of DC magnetising DC: 2.5×10-8Am2 - 5× 10-3Am2 (2.5×10-5emu – 5emu). DC measurement uses a constant field in the measurement area where the sample moves by means of detection coils and induces voltage there according to Faraday's law. Amplitude of this signal depends on the sample's magnetic moment and the rate of its removal. As part of this system, the sample is extracted at an approximate speed of 100cm/s. The signal's force grows considerably as a result compared to other systems. The measurements can be executed as a function of both temperature and of the magnetic field.

Fig. 18. Flow diagram of ACMS

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 315

*<sup>D</sup> H J <sup>t</sup>* 

> *<sup>B</sup> <sup>E</sup> t*

0

*lS S H dl J dS D dS <sup>t</sup>* 

> *l S E dl B dS t*

*S V D dS dV* 

The vector quantities present in Maxwell's equations meet the following dependencies at

1 2 ( ) *nD D*

In the case of numerical electromagnetic field calculations for low frequencies, Maxwell's equations are solved indirectly with the aid of a couple of potentials and boundary conditions. Where the potentials are given, the field vectors *E*, *D*, *H*, *B*, *J* can be

*S*

Maxwell's equations are complimented with the material dependences:

*D*

Maxwell's equations are integrated into:

environment boundaries:

determined.

(12)

(13)

(15)

*B* 0 (14)

(16)

(17)

*B dS* (18)

(19)

*B BH* ( ) (20)

*D DE* ( ) (21)

1 2 *nJ J* ( )0 (22)

1 2 *nB B* ( )0 (23)

1 2 ( ) *<sup>S</sup> nH H J* (24)

*<sup>S</sup>* (25)

1 2 *nE E* ( )0 (26)


Table 4 summarises loss factors on eddy currents and magnetic hysteresis for samples collected in key rail locations determined at varied temperatures by means of ACMS platform.

Table 4. Loss factors on eddy currents and magnetic hysteresis

A 3D simulation model of induction turnout heating was constructed in FLUX 3D software on the basis of 60E1 rail's electric and magnetic parameters discussed above.

### **5. Issues relating to spatial descriptions of magnetic field**

Beside the foregoing electric and magnetic parameters, a magnetic field description in threedimensional space by means of scalar magnetic potential, finite elements method (FEM), and normalised geometric dimensions of 60E1 (Fig. 7) served to construct a 3D simulation model of induction turnout heating. The magnetic field description by means of scalar magnetic potential and finite element method will be explained in detail below

In a non-linear environment, the electromagnetic field at any type of input function is described with Maxwell's equations which relate intensities of the magnetic field, electric field, and charge as parts of the following differential dependencies (12 – 15):

$$
\nabla \times \underline{\mathbf{H}} = \underline{\mathbf{J}} + \frac{\partial \underline{\mathbf{D}}}{\partial t} \tag{12}
$$

$$
\nabla \times \underline{\mathbf{E}} = -\begin{array}{c}
\underline{\partial} \underline{B} \\
\underline{\partial} t
\end{array}
\tag{13}
$$

$$\nabla \cdot \underline{\underline{B}} = 0 \tag{14}$$

$$\nabla \cdot \underline{D} = \rho \tag{15}$$

Maxwell's equations are integrated into:

314 Infrastructure Design, Signalling and Security in Railway

Table 4 summarises loss factors on eddy currents and magnetic hysteresis for samples collected in key rail locations determined at varied temperatures by means of ACMS platform.

> **Loss factor on eddy currents w [10-4 s]**

0 [ºC] 2.49 2.31 25 [ºC] 2.33 2.62 -25 [ºC] 2.7 2.44

0 [ºC] 2.53 2.42 25 [ºC] 2.33 2.8 -25 [ºC] 2.72 2.78

0 [ºC] 2.31 1.42 25 [ºC] 2.13 1.45 -25 [ºC] 2.49 1.63

0 [ºC] 2.39 1.94 25 [ºC] 2.2 1.97 -25 [ºC] 2.6 1.77

0 [ºC] 1.83 1.55 25 [ºC] 1.69 1.76 -25 [ºC] 2.56 1.83

0 [ºC] 2.62 2.49 25 [ºC] 2.42 2.4 -25 [ºC] 2.83 2.68

A 3D simulation model of induction turnout heating was constructed in FLUX 3D software

Beside the foregoing electric and magnetic parameters, a magnetic field description in threedimensional space by means of scalar magnetic potential, finite elements method (FEM), and normalised geometric dimensions of 60E1 (Fig. 7) served to construct a 3D simulation model of induction turnout heating. The magnetic field description by means of scalar

In a non-linear environment, the electromagnetic field at any type of input function is described with Maxwell's equations which relate intensities of the magnetic field, electric

**Loss factor on magnetic hysteresis loop [10-5 m/A]** 

**Source of the sample** 

**Edge of rail** 

**Centre of rail** 

**web**

**web**

**foot**

**web**

**Rail foot**

**Taper of rail** 

**Taper of rail** 

**Rail head**

**Temperature [°C]** 

Table 4. Loss factors on eddy currents and magnetic hysteresis

on the basis of 60E1 rail's electric and magnetic parameters discussed above.

magnetic potential and finite element method will be explained in detail below

field, and charge as parts of the following differential dependencies (12 – 15):

**5. Issues relating to spatial descriptions of magnetic field** 

$$\oint\_{l} \underline{\Phi} \, \underline{\mathbf{H}} \cdot d\underline{l} = \oint\_{\mathcal{S}} \underline{\mathbf{J}} \cdot d\underline{\mathbf{S}} + \frac{\partial}{\partial t} \Big[\_{\mathcal{S}} \underline{\mathbf{D}} \cdot d\underline{\mathbf{S}}\tag{16}$$

$$\oint\_{l} \underline{E} \cdot d\underline{l} = -\frac{\partial}{\partial t} \int\_{S} \underline{B} \cdot d\underline{S} \tag{17}$$

$$\int\_{S} \underline{B} \cdot d\underline{S} = 0 \tag{18}$$

$$\int\_{S} \underline{D} \cdot d\underline{S} = \int\_{V} \rho dV \tag{19}$$

Maxwell's equations are complimented with the material dependences:

$$
\underline{B} \equiv \underline{B}(\underline{H})\tag{20}
$$

$$
\underline{D} \equiv D(\underline{E}) \tag{21}
$$

The vector quantities present in Maxwell's equations meet the following dependencies at environment boundaries:

$$m \cdot (\underline{J}\_1 - \underline{J}\_2) = 0 \tag{22}$$

$$m \cdot (\underline{B}\_1 - \underline{B}\_2) = 0 \tag{23}$$

$$m \times (\underline{H}\_1 - \underline{H}\_2) = \underline{I}\_S \tag{24}$$

$$m \cdot (\underline{D}\_1 - \underline{D}\_2) = \rho\_S \tag{25}$$

$$m \times (\underline{E}\_1 - \underline{E}\_2) = 0 \tag{26}$$

In the case of numerical electromagnetic field calculations for low frequencies, Maxwell's equations are solved indirectly with the aid of a couple of potentials and boundary conditions. Where the potentials are given, the field vectors *E*, *D*, *H*, *B*, *J* can be determined.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 317

Expressing *H*m as a function of magnetically reduced scalar potential Φ results in:

 <sup>2</sup> 1 1 4

*r*

> 

 

*<sup>r</sup> <sup>J</sup> H B dV*

 

Consequently, (35) describing the magnetically reduced scalar potential becomes:

opposite orientations. In effect, the resultant vector of intensity *H* reduces.

intensity vector on the boundary of *V*Ψ and *V*Φ, which can be expressed:

 

The following material dependency is applied to models comprising a permanent magnet:

*B HHH* 

In current-free areas, the resultant vector of magnetic field intensity *H* can only be described

Low accuracy of determining the magnetic field in the area of magnetic materials is the fundamental drawback of the reduced scalar potential method. This results from the fact that components of the magnetic field intensity vector *H*s and *H*m have similar values but

diminishing resultant vector of magnetic field intensity in numerical calculations, the area is

which includes the remaining area under consideration. Field distribution across *V*Ψ is described by global scalar magnetic potential whereas *V*Φ is described by reduced scalar magnetic potential. To obtain a unique solution to (37) and (38), conditions present on boundaries of the different sub-areas described with the different types of scalar magnetic potential must be defined. This relates to the need to provide continuity of the normal component of magnetic induction vector and the tangential component of the magnetic field

> *Hst t t s s*

Based on (30) and (31), the magnetic intensity can be expressed:

*B* 0 *Hm* (32)

*Hm* (33)

*Hs* (35)

*<sup>c</sup>* (36)

*H H s c* (37)

is high, great errors arise. To avoid the error in effect of the

(39)

*Hc* (38)

0 including current sources and a sub-area *V*<sup>Ψ</sup>

(34)

The following obtains for *H*m:

Considering (14), (34) becomes:

by means of the total magnetic potential.

divided into a sub-area *V*Φ of permeability

Where magnetic permeability

Fig. 19. Boundary of environments of diverse material properties

Maxwell's equations are most often solved by two types of potentials:


In the literature describe the vector of magnetic field intensity using a scalar potential function *Ψ*, expressed as:

$$
\underline{\underline{H}} = -\nabla \underline{\nu} \tag{27}
$$

When the material formula *B HH* and the condition of source-free magnetic field are taken into account, a differential equation of total magnetic scalar potential results:

$$\nabla \cdot \left( \mu \nabla \psi \right) = 0 \tag{28}$$

Where conduction currents appear, the vector of magnetic field intensity *H* includes two components:

$$
\underline{\mathbf{H}} = \underline{\mathbf{H}}\_s + \underline{\mathbf{H}}\_m \tag{29}
$$

where: *H*s – magnetic field intensity component enforced by flow of currents in a uniform environment, *H*m – magnetic field intensity component arising from magnetisation of the environment material.

*H*s is computed according to Biot-Savart law as:

$$\underline{H}\_s = \begin{cases} \frac{J \times \mathbf{1}\_r}{4\pi \, r^2} dV \\\\ \end{cases} \tag{30}$$

where: *r* is the distance from the observation point *O=(x, y, z)* where *H*s is calculated to the source point *Z=(x′, y′, z′ )*. *1*r is a unit vector oriented from *Z* to *O*.

In addition, *H*s in the area *V* fulfils the condition:

$$
\nabla \times \underline{\mathbf{H}}\_s = \underline{\mathbf{J}} \tag{31}
$$

The following obtains for *H*m:

316 Infrastructure Design, Signalling and Security in Railway

In the literature describe the vector of magnetic field intensity using a scalar potential

*H* 

 

Where conduction currents appear, the vector of magnetic field intensity *H* includes two

where: *H*s – magnetic field intensity component enforced by flow of currents in a uniform environment, *H*m – magnetic field intensity component arising from magnetisation of the

> 2 1

*r*

4

where: *r* is the distance from the observation point *O=(x, y, z)* where *H*s is calculated to the

*)*. *1*r is a unit vector oriented from *Z* to *O*.

*<sup>J</sup> H dV r*

*s*

taken into account, a differential equation of total magnetic scalar potential results:

(27)

0 (28)

*HH H s m* (29)

(30)

*H J <sup>s</sup>* (31)

and the condition of source-free magnetic field are

Fig. 19. Boundary of environments of diverse material properties

 Magnetic vector potential *A* ( *B AA* , 0 ), Total magnetic scalar potential *Ψ* ( *H* ).

function *Ψ*, expressed as:

components:

environment material.

source point *Z=(x′, y′, z′*

When the material formula *B HH*

*H*s is computed according to Biot-Savart law as:

In addition, *H*s in the area *V* fulfils the condition:

Maxwell's equations are most often solved by two types of potentials:

$$\nabla \times \underline{H}\_m = 0\tag{32}$$

Expressing *H*m as a function of magnetically reduced scalar potential Φ results in:

$$
\underline{H}\_m = -\nabla \Phi \tag{33}
$$

Based on (30) and (31), the magnetic intensity can be expressed:

$$\underline{H} = \frac{1}{\mu\left(\underline{B}\right)} \underline{B} = \int \frac{I \times \mathbf{1}\_r}{4\pi \left|\,^2 r\right|} dV - \nabla \Phi \tag{34}$$

Considering (14), (34) becomes:

$$\nabla \cdot \left( \mu \nabla \Phi \right) = \nabla \cdot \left( \mu \underline{\mathbf{H}}\_{\ast} \right) \tag{35}$$

The following material dependency is applied to models comprising a permanent magnet:

$$
\underline{B} = \mu \left( \underline{H} \right) \left( \underline{H} - \underline{H}\_c \right) \tag{36}
$$

Consequently, (35) describing the magnetically reduced scalar potential becomes:

$$\nabla \cdot \left( \mu \nabla \Phi \right) = \nabla \cdot \left( \mu \underline{H}\_{\ast} \right) - \nabla \cdot \left( \mu \underline{H}\_{\ast} \right) \tag{37}$$

In current-free areas, the resultant vector of magnetic field intensity *H* can only be described by means of the total magnetic potential.

$$\nabla \cdot \left( \mu \nabla \Psi \right) = \nabla \cdot \left( \mu \underline{H}\_c \right) \tag{38}$$

Low accuracy of determining the magnetic field in the area of magnetic materials is the fundamental drawback of the reduced scalar potential method. This results from the fact that components of the magnetic field intensity vector *H*s and *H*m have similar values but opposite orientations. In effect, the resultant vector of intensity *H* reduces.

Where magnetic permeability is high, great errors arise. To avoid the error in effect of the diminishing resultant vector of magnetic field intensity in numerical calculations, the area is divided into a sub-area *V*Φ of permeability 0 including current sources and a sub-area *V*<sup>Ψ</sup> which includes the remaining area under consideration. Field distribution across *V*Ψ is described by global scalar magnetic potential whereas *V*Φ is described by reduced scalar magnetic potential. To obtain a unique solution to (37) and (38), conditions present on boundaries of the different sub-areas described with the different types of scalar magnetic potential must be defined. This relates to the need to provide continuity of the normal component of magnetic induction vector and the tangential component of the magnetic field intensity vector on the boundary of *V*Ψ and *V*Φ, which can be expressed:

$$\left(-\frac{\partial \Psi}{\partial t}\right)\_{S\_{\Phi-\Psi}} = \left(-\frac{\partial \Phi}{\partial t} + H\_{st}\right)\_{S\_{\Phi-\Psi}}\tag{39}$$

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 319

Triangular three-node elements are most often used to discretise 2D areas. A sample

into triangular elements is illustrated in Figure 22.

(*x*,*y*) inside the triangular element (e) is approximated

*x y* (41)

(42)

 

division of

Values of

where:

of boundary

Dependence of the sought quantity

by means of a first-degree polynomial:

Fig. 22. Division of a two-dimensional area into triangular elements

( )

( )

*e*

( )

*e*

( )

*e*

*e* 

 

 

 

 

The system will solve for factors 1, 2, 3. Substituting them in (41) produces:

12 3

12 3

*i ii*

*j jj*

*k kk*

12 3

12 3

(*x*,*y*) at nodes of eth element are described by a system of equations:

( ) 11 1 ( )( )( ) 2 *<sup>e</sup> <sup>i</sup> jj jj kk kk a bx cy a bx cy a bx cy*

*i i j j k k*

*x y x y x y*

 

*x y x y x y*

 

> 

(43)

*<sup>i</sup> <sup>j</sup> k k <sup>j</sup> a x y x y* , *<sup>i</sup> <sup>j</sup> <sup>k</sup> b y y* , *i k <sup>j</sup> cxx* (44)

(45)

 

where:

*S*Φ-Ψ – boundary area between *V*Ψ and *V*Φ; *H*st – active component of *H*s on the area *S*Φ-Ψ.

One of the most commonly used numerical methods of solving field (boundary) problems is the Finite Element Method. Its idea is to divide an area under consideration into some discrete sub-areas of any shape (finite elements). The smaller the elements into which an analysed area is split, the more precise results of the calculations.

Triangular, quadrangular, six- or four-sided elements are those used most frequently. A four-sided element can serve to interpolate a given area (Figure 20) to produce the equations below (38):

Fig. 20. Nodes of a sample four-sided element

$$
\begin{bmatrix}
\mu\_1^\epsilon \\
\mu\_2^\epsilon \\
\mu\_3^\epsilon \\
\mu\_4^\epsilon
\end{bmatrix} = \begin{bmatrix}
\mathbf{1} & \mathbf{x}\_{11} & \mathbf{x}\_{21} & \mathbf{x}\_{31} \\
\mathbf{1} & \mathbf{x}\_{12} & \mathbf{x}\_{22} & \mathbf{x}\_{32} \\
\mathbf{1} & \mathbf{x}\_{13} & \mathbf{x}\_{23} & \mathbf{x}\_{33} \\
\mathbf{1} & \mathbf{x}\_{14} & \mathbf{x}\_{24} & \mathbf{x}\_{34}
\end{bmatrix} \begin{bmatrix}
\mathcal{J}\_1 \\
\mathcal{J}\_2 \\
\mathcal{J}\_3 \\
\mathcal{J}\_4
\end{bmatrix} \tag{40}
$$

where: e –element number, *x*1, *x*2, *x*3 – coordinates of a point inside the element, 1234 ,,, - constants of an approximating function.

Solving this equation produces field values in the individual nodes. Figure 21 shows the most common discretisation shapes applied to 3D problems as part of FEM.

Fig. 21. Examples of three-dimensional elements utilised in FEM: a) five-sided element, b) six-sided element

Triangular three-node elements are most often used to discretise 2D areas. A sample division of of boundary into triangular elements is illustrated in Figure 22.

Fig. 22. Division of a two-dimensional area into triangular elements

Dependence of the sought quantity (*x*,*y*) inside the triangular element (e) is approximated by means of a first-degree polynomial:

$$
\boldsymbol{\phi}^{(\epsilon)} = \boldsymbol{\alpha}\_1 + \boldsymbol{\alpha}\_2 \cdot \boldsymbol{\chi} + \boldsymbol{\alpha}\_3 \cdot \boldsymbol{y} \tag{41}
$$

Values of (*x*,*y*) at nodes of eth element are described by a system of equations:

$$\begin{cases} \rho\_i^{(\epsilon)} = \alpha\_1 + \alpha\_2 \cdot \boldsymbol{\chi}\_i + \alpha\_3 \cdot \boldsymbol{y}\_i \\ \rho\_j^{(\epsilon)} = \alpha\_1 + \alpha\_2 \cdot \boldsymbol{\chi}\_j + \alpha\_3 \cdot \boldsymbol{y}\_j \\ \rho\_k^{(\epsilon)} = \alpha\_1 + \alpha\_2 \cdot \boldsymbol{\chi}\_k + \alpha\_3 \cdot \boldsymbol{y}\_k \end{cases} \tag{42}$$

The system will solve for factors 1, 2, 3. Substituting them in (41) produces:

$$\boldsymbol{\phi}^{(c)} = \frac{(\boldsymbol{a}\_1 + \boldsymbol{b}\_1 \boldsymbol{\chi} + \boldsymbol{c}\_1 \boldsymbol{y})\boldsymbol{\phi}\_i + (\boldsymbol{a}\_j + \boldsymbol{b}\_j \boldsymbol{\chi} + \boldsymbol{c}\_j \boldsymbol{y})\boldsymbol{\phi}\_j + (\boldsymbol{a}\_k + \boldsymbol{b}\_k \boldsymbol{\chi} + \boldsymbol{c}\_k \boldsymbol{y})\boldsymbol{\phi}\_k}{2\boldsymbol{\Delta}} \tag{43}$$

where:

318 Infrastructure Design, Signalling and Security in Railway

One of the most commonly used numerical methods of solving field (boundary) problems is the Finite Element Method. Its idea is to divide an area under consideration into some discrete sub-areas of any shape (finite elements). The smaller the elements into which an

Triangular, quadrangular, six- or four-sided elements are those used most frequently. A four-sided element can serve to interpolate a given area (Figure 20) to produce the

> 1 11 21 31 1 2 12 22 32 2 13 23 33 3 3 14 24 34 4 <sup>4</sup>

where: e –element number, *x*1, *x*2, *x*3 – coordinates of a point inside the element,

Solving this equation produces field values in the individual nodes. Figure 21 shows the

(a) (b) Fig. 21. Examples of three-dimensional elements utilised in FEM: a) five-sided element, b)

(40)

*u xxx u xxx u xxx xxx <sup>u</sup>*

*e e e e*


most common discretisation shapes applied to 3D problems as part of FEM.

where:

equations below (38):

1234

six-sided element

 ,,, 

*S*Φ-Ψ – boundary area between *V*Ψ and *V*Φ; *H*st – active component of *H*s on the area *S*Φ-Ψ.

Fig. 20. Nodes of a sample four-sided element

analysed area is split, the more precise results of the calculations.

$$a\_i = \mathbf{x}\_j y\_k - \mathbf{x}\_k y\_j \quad \text{ } b\_i = y\_j - y\_k \text{ } \quad \mathbf{c}\_i = \mathbf{x}\_k - \mathbf{x}\_j \tag{44}$$

$$\mathbf{2}\Delta = \begin{vmatrix} \mathbf{1} & \mathbf{x}\_i & \mathbf{y}\_i \\ \mathbf{1} & \mathbf{x}\_j & \mathbf{y}\_j \\ \mathbf{1} & \mathbf{x}\_k & \mathbf{y}\_k \end{vmatrix} \tag{45}$$

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 321

where *s* is the number of all elements in the calculation area. Differentiating (50) with

*<sup>J</sup> <sup>k</sup> <sup>k</sup> dxdy x xy y*

for values *i*, *j* and *k* of *m.* Taking (43) and (47) into consideration, the differential expressions

*j i k*

*N N N x xxx*

*j i k*

*N N N y yyy*

*m*

*N x x N y y*

*m*

() () ()

() () () () () ()()

*e e <sup>i</sup> J J eee e e hhh h ji jj jk <sup>j</sup> <sup>j</sup> eee hhh <sup>k</sup> <sup>e</sup> ki kj kk <sup>J</sup>*

[ ]

*N N N N j j i i h k <sup>k</sup> dxdy pq x <sup>y</sup> xx yy <sup>e</sup>* 

for values *i*, *j*, *k* of *p* and *q.* The matrix *h(e)* in (53) is called *element rigidity matrix* (the upper index '(e)' is a reference to an element) and specifies material properties. On appropriate transformations of (44), (45), and (48), the following can be said in respect of a triangular

 

() () () ( )

*eee <sup>i</sup> hhh ii ij ik*

*x y mm m*

 

( )

*m*

*m*

( )

*k*

( )

*e J*

 

( )

[ () ( )]

 

 

. (52)

*i*

 

*j k i*

*j k* (53)

(54)

(55)

respect to the sought

.

in (52) can be found:

Substituting (52) in (51) results in:

where:

element:

( )

*e*

(*x*,*y*) results in:

( )

*e*

The remaining factors are obtained by cyclical shifting of the indices *i*, *j*, *k*. (43) can be expressed as a matrix:

$$\boldsymbol{\phi}^{(e)} = \begin{bmatrix} \mathbf{N}\_i & \mathbf{N}\_j & \mathbf{N}\_k \end{bmatrix} \begin{bmatrix} \boldsymbol{\phi}\_i \\ \boldsymbol{\phi}\_j \\ \boldsymbol{\phi}\_k \end{bmatrix} = \mathbf{N} \boldsymbol{\phi} \tag{46}$$

where:

$$\mathbf{N}\_{i,j,k} = \frac{a\_{i,j,k} + b\_{i,j,k}\mathbf{x} + c\_{i,j,k}y}{2\Delta} \tag{47}$$

*N*i, *N*j, *N*k are functions of variables x and y, referred to as *shape* or *base functions* while **N** is a *shape function matrix*. (46) describes the value of (e) above the surface of a single element (e) (three values of (e) for nodes *i*, *j* and *k*). Solving with the aid of the finite element method consists in finding values of in respect of all the nodes of .

$$\boldsymbol{\rho} = \begin{bmatrix} \rho\_1 \\ \rho\_2 \\ \vdots \\ \rho\_r \end{bmatrix} \tag{48}$$

where *r* is the number of discretisation network nodes. To this end, the functional *J*() is minimised in relation to :

$$\begin{aligned} \frac{\partial f}{\partial \rho} &= \begin{bmatrix} \frac{\partial f}{\partial \rho\_1} \\ \frac{\partial f}{\partial \rho\_2} \\ \frac{\partial f}{\partial \rho\_3} \\ \vdots \\ \frac{\partial f}{\partial \rho\_r} \end{bmatrix} = 0 \\ \end{aligned} \tag{49}$$

The energetic functional with regard to the fields described by Laplace equation including Dirichlet's or Neuman's boundary conditions becomes:

$$f(\boldsymbol{\varphi}) = \frac{1}{2} \iiint\_{\Omega} [k\_x (\frac{\partial \boldsymbol{\varphi}}{\partial \mathbf{x}})^2 + k\_y (\frac{\partial \boldsymbol{\varphi}}{\partial y})^2] d\mathbf{x} dy + \int\_{\Gamma} \boldsymbol{\varphi} d\mathbf{l} \tag{50}$$

where *k*x and *k*y are the material constants in the direction of *x* and *y* (e.g. magnetic or electric permeability) while *l* is the length of the arc along the boundary . The principle of summing all elements of applied to the functional, therefore (49) can be formulated:

$$\frac{\partial \hat{J}}{\partial \mathcal{O}} = \sum\_{i=1}^{s} \frac{\partial \hat{J}\_i^{(e)}}{\partial \mathcal{O}} = 0 \tag{51}$$

where *s* is the number of all elements in the calculation area. Differentiating (50) with respect to the sought (*x*,*y*) results in:

$$\frac{\partial f^{(\varepsilon)}}{\partial \rho\_m} = \iint\_{\Omega^{(\varepsilon)}} [k\_x \frac{\partial \rho}{\partial x} \frac{\partial}{\partial \rho\_m} (\frac{\partial \rho}{\partial x}) + k\_y \frac{\partial \rho}{\partial y} \frac{\partial}{\partial \rho\_m} (\frac{\partial \rho}{\partial y})] dx dy \,\,\,\tag{52}$$

for values *i*, *j* and *k* of *m.* Taking (43) and (47) into consideration, the differential expressions in (52) can be found:

$$\begin{aligned} \left[\frac{\partial \rho}{\partial x} = \begin{bmatrix} \frac{\partial N\_i}{\partial x} & \frac{\partial N\_j}{\partial x} & \frac{\partial N\_k}{\partial x} \\\\ \frac{\partial \rho}{\partial y} = \begin{bmatrix} \frac{\partial N\_i}{\partial y} & \frac{\partial N\_j}{\partial y} & \frac{\partial N\_k}{\partial y} \\\\ \frac{\partial \rho}{\partial y} = \begin{bmatrix} \frac{\partial N\_i}{\partial y} & \frac{\partial N\_j}{\partial y} & \frac{\partial N\_k}{\partial y} \end{bmatrix} \cdot \begin{bmatrix} \rho\_i \\\\ \rho\_j \\\\ \rho\_k \end{bmatrix} \end{aligned} \right] \tag{53}$$
 
$$\begin{aligned} \frac{\partial}{\partial \rho\_m} (\frac{\partial \rho}{\partial x}) &= \frac{\partial N\_m}{\partial x} \\\ \frac{\partial}{\partial \rho\_m} (\frac{\partial \rho}{\partial y}) &= \frac{\partial N\_m}{\partial y} \end{aligned} \tag{54}$$

Substituting (52) in (51) results in:

$$
\begin{bmatrix}
\frac{\partial f}{\partial \phi}(\epsilon) \\
\frac{\partial f}{\partial \phi}(\epsilon) \\
\frac{\partial f}{\partial \phi}(\epsilon) \\
\frac{\partial f}{\partial \phi}(\epsilon) \\
\frac{\partial f}{\partial \phi}(\epsilon) \\
\end{bmatrix} = \begin{bmatrix}
h\_{li}^{(\epsilon)} & h\_{li}^{(\epsilon)} & h\_{li}^{(\epsilon)} \\
h\_{li}^{(\epsilon)} & h\_{lj}^{(\epsilon)} & h\_{jk}^{(\epsilon)} \\
h\_{jl}^{(\epsilon)} & h\_{lj}^{(\epsilon)} & h\_{lk}^{(\epsilon)} \\
\end{bmatrix} \cdot \begin{bmatrix}
\boldsymbol{\sigma}\_{\dot{i}} \\
\boldsymbol{\sigma}\_{\dot{j}} \\
\boldsymbol{\sigma}\_{k} \\
\end{bmatrix} = h^{(\epsilon)} \cdot \boldsymbol{\rho}^{(\epsilon)} \tag{54}
$$

where:

320 Infrastructure Design, Signalling and Security in Railway

The remaining factors are obtained by cyclical shifting of the indices *i*, *j*, *k*. (43) can be

*i j kj*

*a b xc <sup>y</sup> <sup>N</sup>*

*N*i, *N*j, *N*k are functions of variables x and y, referred to as *shape* or *base functions* while **N** is a

in respect of all the nodes of

where *r* is the number of discretisation network nodes. To this end, the functional *J*(

*<sup>J</sup> <sup>J</sup>*

*i*

 

(47)

(e) above the surface of a single element (e)

(48)

(49)

. The principle of

) is

**N** (46)

,, ,, ,,

1 2 : *r*

1

*J*

 

:

*J*

 

*r*

The energetic functional with regard to the fields described by Laplace equation including

<sup>1</sup> 2 2 ( ) [ ( ) ( )] <sup>2</sup> *x y J k k dxdy dl x y*

where *k*x and *k*y are the material constants in the direction of *x* and *y* (e.g. magnetic or

1

*i J J*

 

( )

 

*s e i*

electric permeability) while *l* is the length of the arc along the boundary

<sup>2</sup> 0

applied to the functional, therefore (49) can be formulated:

0

(51)

(50)

*i j k i j k i j k*

 

*k*

(e) for nodes *i*, *j* and *k*). Solving with the aid of the finite element method

.

( ) [ ]

, , 2

*NNN*

*e*

*ijk*

*shape function matrix*. (46) describes the value of

:

Dirichlet's or Neuman's boundary conditions becomes:

consists in finding values of

minimised in relation to

summing all elements of

expressed as a matrix:

where:

(three values of

$$\delta h\_{pq} = \underset{\Omega^{\text{(e)}}}{\text{[{]}}} [k\_{\text{x}} \frac{\partial N\_{\text{i}}}{\partial \text{x}} \frac{\partial N\_{\text{j}}}{\partial \text{x}} + k\_{\text{y}} \frac{\partial N\_{\text{i}}}{\partial y} \frac{\partial N\_{\text{j}}}{\partial y}] \text{dx} dy \tag{55}$$

for values *i*, *j*, *k* of *p* and *q.* The matrix *h(e)* in (53) is called *element rigidity matrix* (the upper index '(e)' is a reference to an element) and specifies material properties. On appropriate transformations of (44), (45), and (48), the following can be said in respect of a triangular element:

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 323

Vectoral magnetic potential *A* is the sought quantity in 2D problems involving magnetic field. Scalar potential Ψ-Φ is the sought quantity in 3D problems (*A* can also be determined in FLUX 3D). These solutions overcome the need to apply analytical methods to solving of complicated differential equations, which is occasionally time-consuming and complex. At the present stage of computer technology, introducing several or a dozen thousand unknowns instead of a mere few makes little difference. FEM is additionally popular when

any boundaries of discretised shapes can be very precisely approximated with straight-

any desirable accuracy of calculations (restrictions on analysis time) can be attained by

the method is universal and can help to solve electromagnetic, electrostatic, magnetic

The need to analyse complex physical models requires application of numerical methods that provide approximate results. Such results are subject to errors, however, due to a range

errors due to simplifying assumptions (e.g. ignoring certain properties of some

In the literature17 18 have discussed errors at the stage of problem solving (a central element of numerical calculations). These errors depend on the calculation method and are sources of distortions that may lead to misrepresentations of phenomena. Sources of errors as part of

approximation errors generated when solutions are sought within a limited area;

 errors arising at magnetic field boundaries described by means of different potentials; errors arising in ferromagnet areas described by means of reduced scalar potential.

A local error in a point of a model generated by FEM is inherently connected to the size of its elements surrounding a given point whereas it is only loosely related to average size of

17Leśniewska E. (1997). Zastosowanie symulacji pól elektromagnetycznych w projektowaniu

przekładników 18Wincenciak S. (1998). Metody i algorytmy optymalizacji kształtu obiektów w polu

errors relating to discontinuity of an environment's physical parameters;

 errors in representations of structure (geometry); errors relating to rounding of node values.

Additionally, 3D problems are exposed to:

may represent both scalar and vectoral magnetic potential.

choice of shapes (and dimensions) which will serve to discretise is unlimited,

compared to other numerical methods since:

diverse boundary conditions can be defined,

or curving-line elements,

varying element sizes,

and heat-flow problems.

differential equation errors,

of factors, such as:

phenomena).

interpolation errors;

elektromagnetycznym

FEM include:

where 

$$\mathbf{h}^{(e)} = \begin{vmatrix} k\_{\mathbf{x}}b\_{\mathbf{i}}b\_{\mathbf{i}} + k\_{\mathbf{y}}c\_{\mathbf{i}}c\_{\mathbf{i}} & k\_{\mathbf{x}}b\_{\mathbf{i}}b\_{\mathbf{j}} + k\_{\mathbf{y}}c\_{\mathbf{i}}c\_{\mathbf{j}} & k\_{\mathbf{x}}b\_{\mathbf{i}}b\_{\mathbf{k}} + k\_{\mathbf{y}}c\_{\mathbf{i}}c\_{\mathbf{k}} \\ k\_{\mathbf{x}}b\_{\mathbf{j}}b\_{\mathbf{i}} + k\_{\mathbf{y}}c\_{\mathbf{j}}c\_{\mathbf{i}} & k\_{\mathbf{x}}b\_{\mathbf{j}}b\_{\mathbf{j}} + k\_{\mathbf{y}}c\_{\mathbf{j}}c\_{\mathbf{j}} & k\_{\mathbf{x}}b\_{\mathbf{j}}b\_{\mathbf{k}} + k\_{\mathbf{y}}c\_{\mathbf{j}}c\_{\mathbf{k}} \\ k\_{\mathbf{x}}b\_{\mathbf{k}}b\_{\mathbf{i}} + k\_{\mathbf{y}}c\_{\mathbf{k}}c\_{\mathbf{i}} & k\_{\mathbf{x}}b\_{\mathbf{k}}b\_{\mathbf{j}} + k\_{\mathbf{y}}c\_{\mathbf{k}}c\_{\mathbf{j}} & k\_{\mathbf{x}}b\_{\mathbf{k}}b\_{\mathbf{k}} + k\_{\mathbf{y}}c\_{\mathbf{k}}c\_{\mathbf{k}} \end{vmatrix} \cdot \frac{1}{4\Delta} \,. \tag{56}$$

(51) describes a differential of functional *J* with respect to the variable (*x*,*y*) sought for (e). When components of (54) in *s* elements are summed according to:

1 *s H h ij ij <sup>k</sup>* (57)

a differential of the functional can be expressed for the entire area:

$$\frac{\left.\partial\right|\_{\dot{1}}}{\left.\partial\right|\_{\dot{0}}} = H\varphi = 0\tag{58}$$

*H* in (58) is known as a *condition* or *rigidity matrix.* This is a band square matrix of the dimension r and a band width lower than the matrix's dimension.

To introduce the node variables defined by means of Dirichlet's boundary conditions to (58), the equations describing nodes of known can be eliminated. This procedure can be troublesome, however, when computer calculation algorithms are created as it requires appropriate lines and columns to be removed from the rigidity matrix. Another method of introducing Dirichlet's conditions has been proposed by Payne and Irons. Elements of *H* diagonals relating to a specific boundary node must be multiplied by a great number (e.g. 1015) and the resultant product must be entered in an appropriate position of the zero vector which forms the right-handed side of (58). This procedure is widely used as it is easy to programme and does not require many operations, thereby minimising the time and cost of the calculations.

To find an approximate solution to a problem using FEM, the objective function needs to be defined, most often as a minimum error of the solution, Galerkin's method is of use in solving non-linear problems. The best solution for an area *V* delimited with certain boundary conditions is zeroing of the weighted average residuum *R* , where is the precise solution and an approximate solution. A general solution according to Galerkin's method can be presented as:

$$\int\_{V} w\_{i} R dV = 0 \quad i = 1, \ 2, \ 3, \dots, \ m \tag{59}$$

where: *w*i – tapering functions

According to the weighted residuum method, the tapering functions are those which interpolate an approximate distribution of the solution across the area under analysis *V*. *Poisson's* equation is the most commonly applied differential equation:

$$\frac{\partial}{\partial \mathbf{x}} \left( \upsilon\_x \frac{\partial \mathcal{L}}{\partial \mathbf{x}} \right) + \frac{\partial}{\partial y} \left( \upsilon\_y \frac{\partial \mathcal{L}}{\partial y} \right) + \frac{\partial}{\partial z} \left( \upsilon\_z \frac{\partial \mathcal{L}}{\partial z} \right) = -f \begin{pmatrix} \mathbf{x} & \mathbf{y} \ \mathbf{z} \end{pmatrix} \in V \tag{60}$$

where may represent both scalar and vectoral magnetic potential.

Vectoral magnetic potential *A* is the sought quantity in 2D problems involving magnetic field. Scalar potential Ψ-Φ is the sought quantity in 3D problems (*A* can also be determined in FLUX 3D). These solutions overcome the need to apply analytical methods to solving of complicated differential equations, which is occasionally time-consuming and complex. At the present stage of computer technology, introducing several or a dozen thousand unknowns instead of a mere few makes little difference. FEM is additionally popular when compared to other numerical methods since:


The need to analyse complex physical models requires application of numerical methods that provide approximate results. Such results are subject to errors, however, due to a range of factors, such as:

differential equation errors,

322 Infrastructure Design, Signalling and Security in Railway

( ) 1

*kbb kcc kbb kcc kbb kcc xki yki xk j yk j xkk ykk*

1

*s H h ij ij <sup>k</sup>* 

> <sup>0</sup> *<sup>J</sup> i H*

*H* in (58) is known as a *condition* or *rigidity matrix.* This is a band square matrix of the

To introduce the node variables defined by means of Dirichlet's boundary conditions to (58), the

however, when computer calculation algorithms are created as it requires appropriate lines and columns to be removed from the rigidity matrix. Another method of introducing Dirichlet's conditions has been proposed by Payne and Irons. Elements of *H* diagonals relating to a specific boundary node must be multiplied by a great number (e.g. 1015) and the resultant product must be entered in an appropriate position of the zero vector which forms the right-handed side of (58). This procedure is widely used as it is easy to programme and does not require many

To find an approximate solution to a problem using FEM, the objective function needs to be defined, most often as a minimum error of the solution, Galerkin's method is of use in solving non-linear problems. The best solution for an area *V* delimited with certain

0 1, 2, 3,..., *<sup>i</sup>*

According to the weighted residuum method, the tapering functions are those which interpolate an approximate distribution of the solution across the area under analysis *V*.

, , *xyz v v v fx y z V*

*<sup>e</sup> h k bb k cc k bb k cc k bb k cc x ji y ji x j j y j j x jk y jk*

(51) describes a differential of functional *J* with respect to the variable

When components of (54) in *s* elements are summed according to:

a differential of the functional can be expressed for the entire area:

dimension r and a band width lower than the matrix's dimension.

operations, thereby minimising the time and cost of the calculations.

boundary conditions is zeroing of the weighted average residuum *R*

*Poisson's* equation is the most commonly applied differential equation:

*x xy yz z* 

*V*

equations describing nodes of known

precise solution and

method can be presented as:

where: *w*i – tapering functions

*k bb k cc k bb k cc k bb k cc xii yii xi j yi j xik yik*

 

4

(57)

(58)

can be eliminated. This procedure can be troublesome,

 , where

an approximate solution. A general solution according to Galerkin's

*w RdV i <sup>m</sup>* (59)

is the

(60)

. (56)

(*x*,*y*) sought for (e).

 errors due to simplifying assumptions (e.g. ignoring certain properties of some phenomena).

In the literature17 18 have discussed errors at the stage of problem solving (a central element of numerical calculations). These errors depend on the calculation method and are sources of distortions that may lead to misrepresentations of phenomena. Sources of errors as part of FEM include:

interpolation errors;


Additionally, 3D problems are exposed to:


A local error in a point of a model generated by FEM is inherently connected to the size of its elements surrounding a given point whereas it is only loosely related to average size of

<sup>17</sup>Leśniewska E. (1997). Zastosowanie symulacji pól elektromagnetycznych w projektowaniu

przekładników 18Wincenciak S. (1998). Metody i algorytmy optymalizacji kształtu obiektów w polu elektromagnetycznym

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 325

Fig. 23. Division of a rail into areas of varying magnetic properties, associated with

Fig. 24. Process of defining new materials and their magnetic properties

appropriate characteristics (prime magnetising curves)

elements in a space under consideration19 20. The latter type of errors are more significant and more difficult to eliminate in non-linear problems.

In the literature21 <sup>22</sup> <sup>23</sup> <sup>24</sup> 25 have presented various examples of applying FEM to magnetic field calculations, explained problems of discretising models, and discussed detailed requirements of shape functions.

### **6. Simulation model of induction heating in flux 3D software**

Based on laboratory research which determined electric and magnetic properties of a 60E1 rail, the internal rail structure was divided into areas of different properties. A fundamental magnetic model of a rail was created in this manner. Rail web and its edges are characterised by diverse material and magnetic properties. Magnetic properties of the remaining rail portions (e.g. centre) are identical. A 3D model on the basis of geometric dimensions given in Figure 7 is extended with areas in respect of which separate prime magnetising curves were obtained, evidence of structural differences generated by the rolling process. Figure 23 shows a rail divided into areas of varying magnetic properties, associated with appropriate characteristics (prime magnetising curves in the respective colours).

Figure 24 illustrates the way material properties of the individual rail areas are defined. 'Magnetic property' tab is selected, a curve type is chosen by means of 'Isotropic spline saturation', then specific values frem the characteristic **B**=f (**H**) are input. The more points are defined, the more accurate description of a given area.

Figure 25 presents a 3D rail model including divisions into areas of varying magnetic properties. The Figure distinguishes head, web edges, and central part of a rail.

Construction of a grid for further field calculations was the next step. Flux 3D automatically creates and generates a calculation grid from among three sizes available in the programme. The grid may also be more or less dense. The denser a calculation grid, the more precise the field calculations. Too dense a grid considerably prolongs the calculation process, unfortunately. A selected grid type is then generated and imposed upon the model. Figures 26 and 27 show a calculation grid for a constructed rail model.

A numerical model of the rail, serving to simulate induction heating, is shown in Figure 18 including a complete calculation grid imposed and a heating wire near a web edge.

<sup>19</sup>Mendrela E., Łukaniszyn M., Macek-Kamińska K. (2002). *Tarczowe silniki prądu stałego z komutacją elektroniczną*

<sup>20</sup>Wróbel R. (2000). *Analiza wpływu parametrów obwodu magnetycznego i elektrycznego na pracę silnika tarczowego prądu stałego z magnesami trwałymi i elektronicznym komutatorem*

<sup>21</sup>Binns K.J., Lawrenson P.J., Trowbridge C.W. **(**1995). *The Analytical and Numercial Solution of Electric and Magnetic Fields*

<sup>22</sup>Bolkowski S., Stabrowski M., Skoczylas J., Sroka J., Sikora J., Wincenciak S. (1993). *Komputerowe metody analizy pola elektromagnetycznego*

<sup>23</sup>Gawrylczyk K.M. (2007). *Analiza wrażliwościowa pola elektromagnetycznego z użyciem metody elementów skończonych*

<sup>24</sup>Jianming J. (1993). *The finite element method in electromagnetic*

<sup>25</sup>Sikora R. (1997). *Teoria pola elektromagnetycznego*

elements in a space under consideration19 20. The latter type of errors are more significant

In the literature21 <sup>22</sup> <sup>23</sup> <sup>24</sup> 25 have presented various examples of applying FEM to magnetic field calculations, explained problems of discretising models, and discussed detailed

Based on laboratory research which determined electric and magnetic properties of a 60E1 rail, the internal rail structure was divided into areas of different properties. A fundamental magnetic model of a rail was created in this manner. Rail web and its edges are characterised by diverse material and magnetic properties. Magnetic properties of the remaining rail portions (e.g. centre) are identical. A 3D model on the basis of geometric dimensions given in Figure 7 is extended with areas in respect of which separate prime magnetising curves were obtained, evidence of structural differences generated by the rolling process. Figure 23 shows a rail divided into areas of varying magnetic properties, associated with appropriate characteristics (prime magnetising curves in the respective

Figure 24 illustrates the way material properties of the individual rail areas are defined. 'Magnetic property' tab is selected, a curve type is chosen by means of 'Isotropic spline saturation', then specific values frem the characteristic **B**=f (**H**) are input. The more points

Figure 25 presents a 3D rail model including divisions into areas of varying magnetic

Construction of a grid for further field calculations was the next step. Flux 3D automatically creates and generates a calculation grid from among three sizes available in the programme. The grid may also be more or less dense. The denser a calculation grid, the more precise the field calculations. Too dense a grid considerably prolongs the calculation process, unfortunately. A selected grid type is then generated and imposed upon the model. Figures

A numerical model of the rail, serving to simulate induction heating, is shown in Figure 18

including a complete calculation grid imposed and a heating wire near a web edge.

19Mendrela E., Łukaniszyn M., Macek-Kamińska K. (2002). *Tarczowe silniki prądu stałego z komutacją*

20Wróbel R. (2000). *Analiza wpływu parametrów obwodu magnetycznego i elektrycznego na pracę silnika* 

21Binns K.J., Lawrenson P.J., Trowbridge C.W. **(**1995). *The Analytical and Numercial Solution of Electric and* 

22Bolkowski S., Stabrowski M., Skoczylas J., Sroka J., Sikora J., Wincenciak S. (1993). *Komputerowe metody* 

23Gawrylczyk K.M. (2007). *Analiza wrażliwościowa pola elektromagnetycznego z użyciem metody elementów* 

properties. The Figure distinguishes head, web edges, and central part of a rail.

and more difficult to eliminate in non-linear problems.

are defined, the more accurate description of a given area.

26 and 27 show a calculation grid for a constructed rail model.

*tarczowego prądu stałego z magnesami trwałymi i elektronicznym komutatorem*

24Jianming J. (1993). *The finite element method in electromagnetic*

25Sikora R. (1997). *Teoria pola elektromagnetycznego*

**6. Simulation model of induction heating in flux 3D software** 

requirements of shape functions.

colours).

*elektroniczną*

*Magnetic Fields*

*skończonych*

*analizy pola elektromagnetycznego*

Fig. 23. Division of a rail into areas of varying magnetic properties, associated with appropriate characteristics (prime magnetising curves)


Fig. 24. Process of defining new materials and their magnetic properties

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 327

Fig. 27. A view of calculation grid executed in Flux 3D for rail web edges (pink) and rail

Fig. 28. Numerical model of the rail including a heating wire

rail when heated with eddy currents as part of induction heating.

This model is then subjected to the simulation process in order to determine behaviour of a

centre (blue).

Fig. 25. Magnetic model of 60E1 rail in FLUX 3D software.

Fig. 26. Calculation grid for the rail head – red

Fig. 25. Magnetic model of 60E1 rail in FLUX 3D software.

Fig. 26. Calculation grid for the rail head – red

Fig. 27. A view of calculation grid executed in Flux 3D for rail web edges (pink) and rail centre (blue).

Fig. 28. Numerical model of the rail including a heating wire

This model is then subjected to the simulation process in order to determine behaviour of a rail when heated with eddy currents as part of induction heating.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 329

Fig. 30. Direction of magnetic field lines generated by the heating wire

would increase.

31.

This is the first model of induction heating of a rail forming part of a turnout to be developed by these authors. It was designed to demonstrate what phenomena occur when the rail is under the impact of a magnetic field. The rail and the wire do not form a full, closed magnetic loop. The magnetic field around the wire partly escapes into the air. As a result, penetration of the magnetic field into the rail structure is weaker and the magnetic induction on the rail surface is low. This weakened magnetic field may be insufficient to produce high eddy current densities in the rail and, in effect, it will be impossible to use induction heating for turnouts. Greater intensity of the magnetic field may improve the value of induction yet power losses associated with dispersion effects

Intensity of the magnetic field generated by the current across the coil is shown in Figure

The following assumptions underlie simulatiton testing of a rail at the time of induction heating in FLUX 3D software26 27:


The sample results were obtained in the simulation process at 650H frequency and 11.14 MA/mm2 density of the current across the wire. Set ranges of frequency and rms values of the current across the wire can be varied as part of this model.

Figure 29 presents a sample distribution of the absolute values of magnetic induction as obtained in the simulation process.

Fig. 29. Distribution of magnetic induction in the rail and its environment

Magnetic induction on the lateral web surface and on its foot reached a maximum of 0.037 T. This low value is due to the fact that an air gap appeared between the rail and the heating wire, impeding and dispersing the magnetic field. The wire itself was circular and its entire surface did not adhere to the rail, therefore magnetic field penetration into the rail was not effective.

Figure 30 shows the direction of magnetic field lines with regard to a rail placed inside the magnetic field of the heating wire.

<sup>26</sup>Femm, User′s Manual, 2009

<sup>27</sup>Flux3d, *User′s guide,* vol. 1-4, 2009

The following assumptions underlie simulatiton testing of a rail at the time of induction

 electric and magnetic parameters of a rail: electrical resistivity **ρ**, prime magnetising curve **B** = f (**H**) or **J**=f (**H**), intensity of the coercion field **Hc**, loss factors of eddy currents

The sample results were obtained in the simulation process at 650H frequency and 11.14 MA/mm2 density of the current across the wire. Set ranges of frequency and rms values of

Figure 29 presents a sample distribution of the absolute values of magnetic induction as

magnetic field description in 3D space with the aid of scalar magnetic potential,

heating in FLUX 3D software26 27:

obtained in the simulation process.

effective.

magnetic field of the heating wire.

26Femm, User′s Manual, 2009 27Flux3d, *User′s guide,* vol. 1-4, 2009

constant density of current across the heating wire,

the current across the wire can be varied as part of this model.

Fig. 29. Distribution of magnetic induction in the rail and its environment

Magnetic induction on the lateral web surface and on its foot reached a maximum of 0.037 T. This low value is due to the fact that an air gap appeared between the rail and the heating wire, impeding and dispersing the magnetic field. The wire itself was circular and its entire surface did not adhere to the rail, therefore magnetic field penetration into the rail was not

Figure 30 shows the direction of magnetic field lines with regard to a rail placed inside the

**w** and of magnetic hysteresis loop **h**, zero boundary conditions: **n**·**H** = 0.

Fig. 30. Direction of magnetic field lines generated by the heating wire

This is the first model of induction heating of a rail forming part of a turnout to be developed by these authors. It was designed to demonstrate what phenomena occur when the rail is under the impact of a magnetic field. The rail and the wire do not form a full, closed magnetic loop. The magnetic field around the wire partly escapes into the air. As a result, penetration of the magnetic field into the rail structure is weaker and the magnetic induction on the rail surface is low. This weakened magnetic field may be insufficient to produce high eddy current densities in the rail and, in effect, it will be impossible to use induction heating for turnouts. Greater intensity of the magnetic field may improve the value of induction yet power losses associated with dispersion effects would increase.

Intensity of the magnetic field generated by the current across the coil is shown in Figure 31.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 331

*Badania eksploatacyjne wodnego system ogrzewania rozjazdów typu MAS-Guben*, CNTK

Binns K.J., Lawrenson P.J., Trowbridge C.W. (1995). *The Analytical and Numercial Solution of* 

Bolkowski S., Stabrowski M., Skoczylas J., Sroka J., Sikora J., Wincenciak S. (1993).

Brodowski D., Andrulonis J.(2000). *Efektywność ogrzewania rozjazdów kolejowych*, CNTK,

Brodowski D., Andrulonis J. (2002). *Ogrzewanie rozjazdów kolejowych*, *Problemy kolejnictwa*,

Gawrylczyk K.M. (2007). *Analiza wrażliwościowa pola elektromagnetycznego z użyciem metody elementów skończonych*, Instytut Naukowo-Badawczy ZTUREK, Warszawa

Gozdecki T., Hering M., Łobodziński W. (1979). *Urządzenia elektroniczne. Elektroniczne urządzenia grzejne*, Wydawnictwa Szkolne i Pedagogiczne, Warszawa Grobelny M. (2009) *Budowa, modernizacja, naprawa i remonty nawierzchni kolejowej – urządzenia* 

*Instrukcja eksploatacji i utrzymania urządzeń elektrycznego ogrzewania rozjazdów*, PKP Polskie

Jianming J. (1993). *The finite element method in electromagnetic*, A Wiley-Interscience

Jiles D. (1991). *Introduction to Magnetism and Magnetic Materials*, Chapman & Hall, ISBN 0-

Kiraga K., Szychta E., Andrulonis J. (2010). *Wybrane metody ogrzewania rozjazdów kolejowych –* 

Kuryłowicz J. (1962). *Badania materiałów magnetycznych*, Wydawnictwo Naukowo-

Leśniewska E. (1997). *Zastosowanie symulacji pól elektromagnetycznych w projektowaniu przekładników*, Zeszyty Naukowe Politechniki Łódzkiej, Nr 766, Łódź Materiały seminaryjne CNTK. (2004). *Wodne ogrzewanie rozjazdów kolejowych typu MAS*,

Mendrela E., Łukaniszyn M., Macek-Kamińska K. (2002). *Tarczowe silniki prądu stałego z* 

Praca zbiorowe: *Studium na temat wyboru optymalnego systemu ogrzewania rozjazdów*,

Sajdak Cz., Samek E. (1985). *Nagrzewanie indukcyjne. Podstawy teoretyczne i zastosowanie*,

Sikora R. (1997). *Teoria pola elektromagnetycznego*, Wydawnictwo Naukowo-Techniczne,

*komutacją elektroniczną*, Wydawnictwo Gnome, Katowice

*artykuł przeglądowy,* PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 86

Gignoux D., Schlenker M.(2005). *Magnetism Fundamentals*, Springer, Grenoble

*i elementy,* RYNEK KOLEJOWY, 2009-03-09

Publication, John Wiley & Sons, INC., New York

Linie Kolejowe S.A., Warszawa, 2007

412-386-30-5,New York

Techniczne, Warszawa

Warszawa, 21-22 Kwiecień

*Prospekt informacyjny o otulinach firmy Haet Point*, 2009.

Wydawnictwo "Śląsk", Katowice

COBiRTK, 1971

Warszawa

NR 2/2010

*Electric and Magnetic Fields*, A Wiley-Interscience Publication, John Wiley & Sons,

*Komputerowe metody analizy pola elektromagnetycznego*, Wydawnictwo Naukowo –

**8. References** 

Warszawa, Styczeń 2004

Techniczne, Warszawa

zeszyt 135, CNTK

INC., New York

Warszawa

Femm, *User′s Manual, 2009*  Flux3d, *User′s guide,* vol. 1-4, 2009

Fig. 31. Intensity of the magnetic field generated by the current across the heating wire

It is easy to read the value of magnetic field intensity arising from the heating wire: it approaches 11000A/m in the centre of the wire and reduces to 3000A/m at the contact of the rail and the wire after covering a distance of circa 1 centimetre (drag).

The air gap must be fully eliminated in continuing research and, should it prove impossible, the gap needs to be minimised in order to reduce magnetic field dispersion as much as practicable.

### **7. Conclusion**

This chapter has presented elementary knowledge concerning 3D model illustrations of induction heating as applied to rail turnouts. It should be borne in mind, however, that a simulation model can differ widely from reality due, for instance, to simplifications discussed by the authors. The magnetic model itself must be modified in order to solve the issue of the air gap, for example.

It is also necessary to verify simulation results against those obtained in an actual model of turnout induction heating. Work on developing an actual model is in progress.

At the present stage, the magnetic model developed by the authors in Flux3D provides for observation of electric and magnetic effects in the rail's internal structure triggered by flow of eddy currents. The model will be utilised to determine the depth of magnetic field penetration into the rail structure as dependent on variations of magnetising current frequency and will serve to determine a temperature distribution along the rail in the process of heating. Knowledge of this temperature distribution or, to be more exact, of maximum temperature values attained by the individual rail sections is the key to success of this research.

### **8. References**

330 Infrastructure Design, Signalling and Security in Railway

Fig. 31. Intensity of the magnetic field generated by the current across the heating wire

the rail and the wire after covering a distance of circa 1 centimetre (drag).

practicable.

**7. Conclusion** 

this research.

issue of the air gap, for example.

It is easy to read the value of magnetic field intensity arising from the heating wire: it approaches 11000A/m in the centre of the wire and reduces to 3000A/m at the contact of

The air gap must be fully eliminated in continuing research and, should it prove impossible, the gap needs to be minimised in order to reduce magnetic field dispersion as much as

This chapter has presented elementary knowledge concerning 3D model illustrations of induction heating as applied to rail turnouts. It should be borne in mind, however, that a simulation model can differ widely from reality due, for instance, to simplifications discussed by the authors. The magnetic model itself must be modified in order to solve the

It is also necessary to verify simulation results against those obtained in an actual model of

At the present stage, the magnetic model developed by the authors in Flux3D provides for observation of electric and magnetic effects in the rail's internal structure triggered by flow of eddy currents. The model will be utilised to determine the depth of magnetic field penetration into the rail structure as dependent on variations of magnetising current frequency and will serve to determine a temperature distribution along the rail in the process of heating. Knowledge of this temperature distribution or, to be more exact, of maximum temperature values attained by the individual rail sections is the key to success of

turnout induction heating. Work on developing an actual model is in progress.


**13** 

*France* 

**EMC Analysis of Railway Power Substation** 

*1Université Lille 1 Sciences et Technologies, USTL, IEMN/TELICE Laboratory* 

The first part of the chapter will present the global aspect of the railway power infrastructures and specially the power supply substation. The goals of this study consist in proposing a high frequency model of the railway systems and verifying by simulation the conformity with the EMC standards. Thus, each component of the railway power infrastructure (transformer, power rectifier) is modeled and the simulation results of the conducted emissions are

A railway system might pollute, in an electromagnetic sense, the surrounding environment, disturbing radio and communication systems which can be not related to the railway itself. In this case the whole railway can be considered as a source of Electromagnetic Interference (EMI). In order to avoid the disruption of the electronic equipments near to the railway, the overall field generated by railway system must be kept below certain safety values given by standards [1]. Obviously, there are many sources of the electromagnetic field and their



compared to measurements on a reduced scale of the power supply substation.

because of power circuits that might become a source of emissions.

**1. Introduction** 

**2. EMI sources in railway system** 

contributions can come from:

kilohertz up to one gigahertz.

**Modeling and Measurements Aspects** 

*2Université Lille 1 Sciences et Technologies, USTL, L2EP Laboratory,* 

S. Baranowski1, H. Ouaddi1, L. Kone1 and N. Idir2

*F-59650 Villeneuve d'Ascq,* 

strona internetowa szyn: www. inzynieria-kolejowa.dl.pl.


## **EMC Analysis of Railway Power Substation Modeling and Measurements Aspects**

S. Baranowski1, H. Ouaddi1, L. Kone1 and N. Idir2 *1Université Lille 1 Sciences et Technologies, USTL, IEMN/TELICE Laboratory 2Université Lille 1 Sciences et Technologies, USTL, L2EP Laboratory, F-59650 Villeneuve d'Ascq, France* 

### **1. Introduction**

332 Infrastructure Design, Signalling and Security in Railway

Wielgosz R. (2009). *Łączenie bezstykowych szyn kolejowych,* MECHANIKA CZASOPISMO

Wincenciak S. (1998). *Metody i algorytmy optymalizacji kształtu obiektów w polu elektromagnetycznym*, Oficyna wydawnicza Politechniki Warszawskiej, Warszawa Wróbel R. (2000). *Analiza wpływu parametrów obwodu magnetycznego i elektrycznego na pracę*

TECHNICZNE, Wydawnictwo Politechniki Krakowskiej, 2-M/2009, Zeszyt 6, Rok

*silnika tarczowego prądu stałego z magnesami trwałymi i elektronicznym komutatorem,* 

strona internetowa szyn: www. inzynieria-kolejowa.dl.pl.

Rozprawa doktorska, Łódź

106.

The first part of the chapter will present the global aspect of the railway power infrastructures and specially the power supply substation. The goals of this study consist in proposing a high frequency model of the railway systems and verifying by simulation the conformity with the EMC standards. Thus, each component of the railway power infrastructure (transformer, power rectifier) is modeled and the simulation results of the conducted emissions are compared to measurements on a reduced scale of the power supply substation.

### **2. EMI sources in railway system**

A railway system might pollute, in an electromagnetic sense, the surrounding environment, disturbing radio and communication systems which can be not related to the railway itself. In this case the whole railway can be considered as a source of Electromagnetic Interference (EMI). In order to avoid the disruption of the electronic equipments near to the railway, the overall field generated by railway system must be kept below certain safety values given by standards [1]. Obviously, there are many sources of the electromagnetic field and their contributions can come from:


However, a train might be or be not compliant to field standards depending on the line characteristics and on its position on the railway. Nowadays, trains are designed to meet EMC rules, but the non-compliances can be remedied thanks to identification of the different resonances frequency, which can occur mainly in a frequency range from some kilohertz up to one gigahertz.

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 335

EN 50121-3-1 limit

Resonance due to Infrastructure or train

0.01 0.1 1 **Frequency (MHz)**

As presented previously, the aim of the standards is to limit the disturbance of the external environment produced by the railway infrastructure but also on the railways system itself. Indeed, the new generation of rolling stock is equipped with safety communication systems with on board antennas which must not be disturbed neither. These elements of safety system operate in frequency range from 10 kHz to 30MHz, which constitute the frequency range considered in this study but also above, for example, the GSMR signal frequency is around 900MHz. Thus, it becomes important to know which source can introduce the

Besides, sensitivity of these communication systems must also be evaluated for the resonant

A schematic representation of the railway infrastructure is shown in Fig. 3. In this figure, we can see that the power supply system constituted by the substation, the rails, the catenaries and the train which constitutes the load of the power line. This figure also shows a location system based on telecommunication between on board antenna and



power transformer, sometimes static converters, and cables, bus bars...etc.

The railway power supply system is generally composed by two main systems:

lines, multi-conductors structures, conductivity of the ballast, ...)


0

**2.2 Effect of the resonances** 

**3. Railway power infrastructures** 

antenna along the track.

Fig. 2. Example of the measured magnetic field

20

**H (dBµA/m)**

disturbances.

frequencies.

40

60

### **2.1 Description of standards EMI measurement methods**

The EMC standard EN 50121 [1] is used to characterize the EM environment, in the railway systems; it notably aim to limit the EMI levels from the railway infrastructures to the external environment. This standard EN 50121 describes the methodologies and the limits to apply, relating to the EM radiations and immunity of railway equipments, vehicles and infrastructures. The emissions of the whole railway system, including vehicles and infrastructure, are dealt with the section 2 of the EN 50121. The objective of the tests specified in this standard is to verify that the EM emissions produced by the whole railway systems do not disturb the neighboring equipments and systems.

The methodology then consists in measuring the radiated EM emissions at a distance of 10 m from the middle of the tracks and at about 1.5 m from the floor (Fig.1) and in comparing them with the maximum levels (limit curve in red in Fig.2). The measurements protocol and the limits are specified for the frequencies varying from 9 kHz to 1 GHz.

For each frequency band (9kHz-150kHz; 150kHz-30MHz; 30MHz-1GHz), the standards define among others:


During measurements of the electromagnetic field radiated at 10 m from the railway track, we can observe that, sometimes, for some frequency, the standards limit can be exceeded. An example of measurement from 10 kHz to 1 MHz is given in fig. 2. The exceeding is characterized by resonance phenomena which appeared for some frequencies of the power supply current.

Fig. 1. On site measurement of the electromagnetic radiation of the train (stationary and moving)

Fig. 2. Example of the measured magnetic field

### **2.2 Effect of the resonances**

334 Infrastructure Design, Signalling and Security in Railway

The EMC standard EN 50121 [1] is used to characterize the EM environment, in the railway systems; it notably aim to limit the EMI levels from the railway infrastructures to the external environment. This standard EN 50121 describes the methodologies and the limits to apply, relating to the EM radiations and immunity of railway equipments, vehicles and infrastructures. The emissions of the whole railway system, including vehicles and infrastructure, are dealt with the section 2 of the EN 50121. The objective of the tests specified in this standard is to verify that the EM emissions produced by the whole railway

The methodology then consists in measuring the radiated EM emissions at a distance of 10 m from the middle of the tracks and at about 1.5 m from the floor (Fig.1) and in comparing them with the maximum levels (limit curve in red in Fig.2). The measurements protocol and

For each frequency band (9kHz-150kHz; 150kHz-30MHz; 30MHz-1GHz), the standards



During measurements of the electromagnetic field radiated at 10 m from the railway track, we can observe that, sometimes, for some frequency, the standards limit can be exceeded. An example of measurement from 10 kHz to 1 MHz is given in fig. 2. The exceeding is characterized by resonance phenomena which appeared for some frequencies of the power

Fig. 1. On site measurement of the electromagnetic radiation of the train (stationary and

1.5 m

**2.1 Description of standards EMI measurement methods** 

systems do not disturb the neighboring equipments and systems.

define among others:

be measured,

supply current.

moving)

as shown until 1MHz in fig.2

10 m

the limits are specified for the frequencies varying from 9 kHz to 1 GHz.

As presented previously, the aim of the standards is to limit the disturbance of the external environment produced by the railway infrastructure but also on the railways system itself. Indeed, the new generation of rolling stock is equipped with safety communication systems with on board antennas which must not be disturbed neither. These elements of safety system operate in frequency range from 10 kHz to 30MHz, which constitute the frequency range considered in this study but also above, for example, the GSMR signal frequency is around 900MHz. Thus, it becomes important to know which source can introduce the disturbances.

Besides, sensitivity of these communication systems must also be evaluated for the resonant frequencies.

### **3. Railway power infrastructures**

A schematic representation of the railway infrastructure is shown in Fig. 3. In this figure, we can see that the power supply system constituted by the substation, the rails, the catenaries and the train which constitutes the load of the power line. This figure also shows a location system based on telecommunication between on board antenna and antenna along the track.

The railway power supply system is generally composed by two main systems:


EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 337

**Sim ulations Measurem ents**

**<sup>0</sup> 0.5 <sup>1</sup> 1.5 <sup>2</sup> -110**

Fig. 5. Example of obtained results (corrsponding to the Fig. 4 configuration). The generator

In the world, many kind of railway power supply exist: alternative (AC) or direct current (DC), with various amplitudes: 1500kV, 3kV, 25kV… Then, we have worked on a general power substation constituted by a transformer and a power converter as

In case of AC power supply substation, there is no AC/DC converter. The power

In order to propose a high frequency model of the whole system, it's necessary to determine a model for each element, especially of power transformer, which accuracy will be highly dependent of the accuracy of each primary model. The low frequency model of the transformer, defined at 50Hz, is not valuable when the frequency increases. Indeed, some phenomena can be predominant in high frequencies as the Eddy current, which depends on the variation of the magnetizing impedance and the winding resistance, but also the

**Freque ncy (MHz)**

**-105 -100 -95 -90 -85 -80 -75 -70 -65**

**5. Power supply substation** 

presented in fig. 6.

give a sinusoidal signal of 1V amplitude.

Fig. 6. Schematic circuit of a railway substation

transformer constitutes the main device of the substation.

**Normalized magnetic field H/V**

**in (db S/m)**

Fig. 3. Simplified diagram of railway infrastructure

### **4. Problem of EMC in railway**

In order to avoid EMI with high levels of electromagnetic disturbances, measurements are usually performed. Test results can lead to different comments and from an industrial point of view, it is important to distinguish the disturbances due to the railway power supply infrastructure (substation – line catenaries/rail) and others due to the train itself. Indeed, it is important to know which kind mitigations solutions have to be done to reduce the disturbances and who should do that: the train manufacturer or the power supplier.

In a previous research project [2], the lines system has been modeled. The proposed model enables to estimate the field radiated by the power line taken into account various parameters like the geometry of the line; the conductivity of the soil … The model is based on line theory, the train is the load (Ztrain) and a generator feeds the lines.

An example of the simulation conditions and the obtained results is given in figures 4 and 5

This model gives good results and many details on how each parameter has been taken into account can be found in [2]. But it is only a model of the lines and the generator used in this simulation is a sinusoidal one with constant amplitude.

Then, it was necessary to model the power substation to obtain a more realistic generator and this has constituted the goal of the CEMRAIL project of which some results are presented here.

Fig. 4. Simplified model of the power supplier line

Fig. 5. Example of obtained results (corrsponding to the Fig. 4 configuration). The generator give a sinusoidal signal of 1V amplitude.

### **5. Power supply substation**

336 Infrastructure Design, Signalling and Security in Railway

In order to avoid EMI with high levels of electromagnetic disturbances, measurements are usually performed. Test results can lead to different comments and from an industrial point of view, it is important to distinguish the disturbances due to the railway power supply infrastructure (substation – line catenaries/rail) and others due to the train itself. Indeed, it is important to know which kind mitigations solutions have to be done to reduce the

In a previous research project [2], the lines system has been modeled. The proposed model enables to estimate the field radiated by the power line taken into account various parameters like the geometry of the line; the conductivity of the soil … The model is based

An example of the simulation conditions and the obtained results is given in figures 4 and 5 This model gives good results and many details on how each parameter has been taken into account can be found in [2]. But it is only a model of the lines and the generator used in this

Then, it was necessary to model the power substation to obtain a more realistic generator and this has constituted the goal of the CEMRAIL project of which some results are

disturbances and who should do that: the train manufacturer or the power supplier.

on line theory, the train is the load (Ztrain) and a generator feeds the lines.

simulation is a sinusoidal one with constant amplitude.

Fig. 4. Simplified model of the power supplier line

Fig. 3. Simplified diagram of railway infrastructure

**4. Problem of EMC in railway** 

presented here.

In the world, many kind of railway power supply exist: alternative (AC) or direct current (DC), with various amplitudes: 1500kV, 3kV, 25kV… Then, we have worked on a general power substation constituted by a transformer and a power converter as presented in fig. 6.

Fig. 6. Schematic circuit of a railway substation

In case of AC power supply substation, there is no AC/DC converter. The power transformer constitutes the main device of the substation.

In order to propose a high frequency model of the whole system, it's necessary to determine a model for each element, especially of power transformer, which accuracy will be highly dependent of the accuracy of each primary model. The low frequency model of the transformer, defined at 50Hz, is not valuable when the frequency increases. Indeed, some phenomena can be predominant in high frequencies as the Eddy current, which depends on the variation of the magnetizing impedance and the winding resistance, but also the

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 339

In order to analyze the behavior or the railway substation we have built a test bench which

The experimental setup is composed with a three phase power transformer, a diodes rectifier and loads. The transformer is a 15 kVA - 220 V/110 V with Δ connected high voltage (HV) winding and Δ connected low voltage (LV) winding. The power rectifier is designed with twelve power diodes and is connected to 47 Ω resistor. All these elements are placed over a common ground plane (Fig. 8). The different devices are connected using 1m

A high frequency model of the power transformer, which takes into account the various physical phenomena has been studied [4][8]. Figure 9 presents this model applied to the

Starting from an ideal transformer model with transformation ratio η, the proposed model takes into account, for each phase, the leakage inductances, the skin effects, the magnetizing impedance and stray capacitances of which become significant at high frequency. Moreover the iron core has been considered linear at frequency above 10 kHz [12] [13] consequently its

The subject of the work is to identify the important physical parameters which contribute to induce resonance phenomena. We have chosen to propose a model as physical as possible

Loads

Ground Plane

Rectifier Power

transformer

15kVA three phase power transformer used in the laboratory test bench (fig.8).

This model is valid in the frequency band varying from 40 Hz to 30 MHz.

and after, if necessary, to add black box to model more intricate phenomena.

**6.2 Laboratory test bench** 

**6.3 Transformer model** 

long cable.

reproduces the substation in small scale.

effect can be neglected at high frequencies.

Fig. 8. Circuit diagram and photo of the test bench

parasitic capacitances which appear between windings due to the insulated parts of the transformer. The analysis of the transformer behavior shows that it's possible to use an equivalent electrical circuit model which is valid in the considered frequency band.

During the past decades, many models of power transformer have been studied for several applications. Most of those models, often in a reduced frequency band, are based on the representation of the transformer by an arrangement of resistive, inductive and capacitive elements which can take into account the physical behavior of power transformer [3]; some others are wide band models established using the black box principle [7]. Obviously, it's also possible to apply the FEM (Finite Element Method) method to have a precise model, but in this case, the exact constitution of the transformer must be known. Some additional difficulties are found in the studied problem: how to found the appropriate data sheet when the transformer is operated in the railway system since many years? In the following sections, we will present the proposed equivalent model and two techniques used to identify the transformer parameters.

### **6. High frequency model of transformer**

### **6.1 Preliminary study**

Making measurements in railways power substation is not easy, then preliminary investigations have been done on various power transformers. Primary and secondary winding impedances measurements in various configurations have been done on two different transformers:


Figure 7-a (15kVA transformer) and Fig. 7-b (2.38MVA transformer) show the secondary winding impedance measured when the primary is short circuited for these two transformers.

These two impedances have been measured in the same frequency band: 100 kHz to 40MHz. We can note that these two responses are globally identical. Thus, we will model, in the first time, a low power transformer before to apply this model to a real substation transformer.

Fig. 7. Secondary winding impedance measurements when the primary is short circuited for two tested transformers (a- 15kVA and b- 2.38MVA)

### **6.2 Laboratory test bench**

338 Infrastructure Design, Signalling and Security in Railway

parasitic capacitances which appear between windings due to the insulated parts of the transformer. The analysis of the transformer behavior shows that it's possible to use an

During the past decades, many models of power transformer have been studied for several applications. Most of those models, often in a reduced frequency band, are based on the representation of the transformer by an arrangement of resistive, inductive and capacitive elements which can take into account the physical behavior of power transformer [3]; some others are wide band models established using the black box principle [7]. Obviously, it's also possible to apply the FEM (Finite Element Method) method to have a precise model, but in this case, the exact constitution of the transformer must be known. Some additional difficulties are found in the studied problem: how to found the appropriate data sheet when the transformer is operated in the railway system since many years? In the following sections, we will present the proposed equivalent model and two techniques used to

Making measurements in railways power substation is not easy, then preliminary investigations have been done on various power transformers. Primary and secondary winding impedances measurements in various configurations have been done on two

Figure 7-a (15kVA transformer) and Fig. 7-b (2.38MVA transformer) show the secondary winding impedance measured when the primary is short circuited for these two

These two impedances have been measured in the same frequency band: 100 kHz to 40MHz. We can note that these two responses are globally identical. Thus, we will model, in the first time, a low power transformer before to apply this model to a real substation transformer.

Fig. 7. Secondary winding impedance measurements when the primary is short circuited

equivalent electrical circuit model which is valid in the considered frequency band.

identify the transformer parameters.

**6.1 Preliminary study** 

different transformers:

transformers.

**6. High frequency model of transformer** 


for two tested transformers (a- 15kVA and b- 2.38MVA)


In order to analyze the behavior or the railway substation we have built a test bench which reproduces the substation in small scale.

The experimental setup is composed with a three phase power transformer, a diodes rectifier and loads. The transformer is a 15 kVA - 220 V/110 V with Δ connected high voltage (HV) winding and Δ connected low voltage (LV) winding. The power rectifier is designed with twelve power diodes and is connected to 47 Ω resistor. All these elements are placed over a common ground plane (Fig. 8). The different devices are connected using 1m long cable.

### **6.3 Transformer model**

A high frequency model of the power transformer, which takes into account the various physical phenomena has been studied [4][8]. Figure 9 presents this model applied to the 15kVA three phase power transformer used in the laboratory test bench (fig.8).

Starting from an ideal transformer model with transformation ratio η, the proposed model takes into account, for each phase, the leakage inductances, the skin effects, the magnetizing impedance and stray capacitances of which become significant at high frequency. Moreover the iron core has been considered linear at frequency above 10 kHz [12] [13] consequently its effect can be neglected at high frequencies.

This model is valid in the frequency band varying from 40 Hz to 30 MHz.

The subject of the work is to identify the important physical parameters which contribute to induce resonance phenomena. We have chosen to propose a model as physical as possible and after, if necessary, to add black box to model more intricate phenomena.

### Fig. 8. Circuit diagram and photo of the test bench

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 341


**Note:** The proposed model can be used to model a single phase transformer by using only

The experimental results, in time or in frequency domain presented in the next sections, allow determining the various parameters of the proposed model. Figure 10 shows an

Fig. 10. Comparison within measurements and simulation results (impedance of the

The determination of each parameter of the equivalent circuit (Fig.9) of the transformer model is realized from impedance measurements versus frequency, in different test

The magnetizing impedance of each phase is modeled by a resistance in parallel with an inductance; their values are deduced from the impedance measured on the primary

**7. Determination of the various elements of the transformer model** 


fitting method; details are given in [4-5-6].

primary winding, the secondary being open)

configurations [7] [8].

**7.1 The magnetizing impedance** 

example of modeling results compared to experimental data.

one circuit by phase.

**6.4 Validation results** 


Fig. 9. High frequency model of three-phase power transformer

Each element of the equivalent circuit will be detailed and the method used to determine these parameters will be presented in the next section.

	- Turn-to-turn capacitance of the primary and secondary windings: Ca1, Ca2, Cb1, Cb2, Cc1, Cc2,
	- Capacitances between windings (divided in two capacitances): Ca31, Ca32, Cb31, Cb32, Cc31, Cc32,
	- Capacitance between the input of the primary winding and the output of the secondary: Car, Cbr, Ccr,

**Note:** The proposed model can be used to model a single phase transformer by using only one circuit by phase.

### **6.4 Validation results**

340 Infrastructure Design, Signalling and Security in Railway

Fig. 9. High frequency model of three-phase power transformer

these parameters will be presented in the next section.

resp.) [14].

[16], [17] :

Cc1, Cc2,

Cc31, Cc32,

secondary: Car, Cbr, Ccr,

Each element of the equivalent circuit will be detailed and the method used to determine







course, the magnetizing impedance changes with the frequency [7] [15].

The experimental results, in time or in frequency domain presented in the next sections, allow determining the various parameters of the proposed model. Figure 10 shows an example of modeling results compared to experimental data.

Fig. 10. Comparison within measurements and simulation results (impedance of the primary winding, the secondary being open)

### **7. Determination of the various elements of the transformer model**

The determination of each parameter of the equivalent circuit (Fig.9) of the transformer model is realized from impedance measurements versus frequency, in different test configurations [7] [8].

### **7.1 The magnetizing impedance**

The magnetizing impedance of each phase is modeled by a resistance in parallel with an inductance; their values are deduced from the impedance measured on the primary

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 343

Leakage

inductance with

skin effects

Fig. 12. Primary impedance with secondary short circuited (phase A)

Fig. 13. Equivalent circuit of the leakage impedance

of measurements.

for the studied transformer.

is supposed equivalent to phase A)

Li in

The leakage impedance can be modeled using a R-L ladder network as shown in Fig. 13

In order to have an efficient approximation, the parameters of the equivalent circuit are computed with a less square algorithm; the identification being performed with the results

Table1 presents the parameters of the equivalent circuit of the leakage impedance obtained

Ri in R1 R2 R3 R4 R5 R6 R7 R8 Phase A 0.6 58 49 132 45 472 746 679 Phase B 0.6 58 0.001 33 37 1082 15 39

mH L1 L2 L3 L4 L5 L6 L7 L8 Phase A 1.1 1.08 3.6 100 13 11 54 14 Phase B 1.1 2.3 2.4 2.5 8.3 11 36 69 Table 1. Parameters of the leakage impedance model of the laboratory transformer (phase C

winding, at low frequency, when the secondary winding is open as shown in Fig 11. The values of these parameters for the phase A and B are given as following:

Ram= 13.44 kΩ, and Lam=31.19 mH, Rbm= 15.87 kΩ and Lbm=32.14 mH

However, if we take into account the geometry of the transformer, phases A and C are considered, to have the same behavior, then the corresponding parameters are supposed to have the same value.

### **7.2 The leakage impedance**

The leakage inductance and the wire resistance (the skin effect) of the winding can be determined by measuring the primary impedance when the secondary winding is shortcircuited. Winding losses can be estimated from the impedance measured in the low frequency band as shown in Fig. 12.

Fig. 11. Primary winding impedance when the secondary is opened (measuremens on the Phase A of the test bench transformer)

winding, at low frequency, when the secondary winding is open as shown in Fig 11. The

However, if we take into account the geometry of the transformer, phases A and C are considered, to have the same behavior, then the corresponding parameters are supposed to

The leakage inductance and the wire resistance (the skin effect) of the winding can be determined by measuring the primary impedance when the secondary winding is shortcircuited. Winding losses can be estimated from the impedance measured in the low

Fig. 11. Primary winding impedance when the secondary is opened (measuremens on the

values of these parameters for the phase A and B are given as following:

Ram= 13.44 kΩ, and Lam=31.19 mH, Rbm= 15.87 kΩ and Lbm=32.14 mH

have the same value.

**7.2 The leakage impedance** 

frequency band as shown in Fig. 12.

Magnetizing impedance

Phase A of the test bench transformer)

Fig. 12. Primary impedance with secondary short circuited (phase A)

The leakage impedance can be modeled using a R-L ladder network as shown in Fig. 13

In order to have an efficient approximation, the parameters of the equivalent circuit are computed with a less square algorithm; the identification being performed with the results of measurements.

Fig. 13. Equivalent circuit of the leakage impedance

Table1 presents the parameters of the equivalent circuit of the leakage impedance obtained for the studied transformer.


Table 1. Parameters of the leakage impedance model of the laboratory transformer (phase C is supposed equivalent to phase A)

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 345

The impedance characteristics presented in Figures 11 and 12 show the same evolution at high frequency (above 3 MHz) with fast variations and consequently it costs time to model. Thanks to "augmented method" [5], it is possible to consider this part by using an inductance in parallel with a "black box". The "black box" is elaborated by using the principle of the "vector fitting" [13]. This algorithm consists in approximating a frequency response with a rational function, expressed by a sum of partial fractions. This principle is implemented in the IdEM® software [6] [18] used for our study. This code generates a macro-model which could be integrated in software like Pspice. Figure 9 presents the main equivalent circuit of the transformer with the added impedance issued from "augmented model" (Fig.15) which takes into account the high frequency effects. Figure 16 shows the effect of this 'augmented model impedance' on the HF accuracy of the model, by

MACRO HF

R=300 Ω

Fig. 16. Primary impedance with secondary short circuited (Phase A). Comparison between measurement and simulation result with and without the augmented model (named black

Fig. 15. Equivalent circuit for high frequency behavior of the transformer.

This circuit is repesented by a component named "augmented model" in figure 9.

L=4.8 uH

**7.4 The augmented model impedance** 

box in the figure).

comparison of the measurements results with the model ones.

### **7.3 Stray Capacitances**

The stray capacitances of each phase of the transformer are estimated separately. As an example, here, the phase A (A0A1-a0a1) is studied. The transformer is modeled as a "black box", and it's necessary to determine the capacitance Ca1, Ca2, Ca31, Ca32, Car, Ca1g and Ca2g. Their effects are located in high frequencies so they will be evaluated in this frequency range.

For each phase, seven measurement configurations are necessary to determine these capacitances. Thus, they provide seven equations which unknowns are the capacitances of the equivalent circuit. Following, the equation system is solved using mathematical tools. Figure 14 presents the seven measurements configurations with the associated equations, in the case of the phase A. The arrows show the measurements points, the short circuits are presented by the lines and Cme represents the measured capacitance. As well as the magnitude, the phase of the impedance is measured in order the make an efficient characterization.

Moreover some precautions are taken for example it is proper to short-circuit the two other phases when the third is characterized in order to inhibit their influences.

Fig. 14. Measurement configuration used for determining capacitances (example for phase A)

#### **7.4 The augmented model impedance**

344 Infrastructure Design, Signalling and Security in Railway

The stray capacitances of each phase of the transformer are estimated separately. As an example, here, the phase A (A0A1-a0a1) is studied. The transformer is modeled as a "black box", and it's necessary to determine the capacitance Ca1, Ca2, Ca31, Ca32, Car, Ca1g and Ca2g. Their effects are located in high frequencies so they will be evaluated in this frequency

For each phase, seven measurement configurations are necessary to determine these capacitances. Thus, they provide seven equations which unknowns are the capacitances of the equivalent circuit. Following, the equation system is solved using mathematical tools. Figure 14 presents the seven measurements configurations with the associated equations, in the case of the phase A. The arrows show the measurements points, the short circuits are presented by the lines and Cme represents the measured capacitance. As well as the magnitude, the phase of the impedance is measured in order the make an efficient

Moreover some precautions are taken for example it is proper to short-circuit the two other

Fig. 14. Measurement configuration used for determining capacitances (example for phase A)

phases when the third is characterized in order to inhibit their influences.

**7.3 Stray Capacitances** 

range.

characterization.

The impedance characteristics presented in Figures 11 and 12 show the same evolution at high frequency (above 3 MHz) with fast variations and consequently it costs time to model. Thanks to "augmented method" [5], it is possible to consider this part by using an inductance in parallel with a "black box". The "black box" is elaborated by using the principle of the "vector fitting" [13]. This algorithm consists in approximating a frequency response with a rational function, expressed by a sum of partial fractions. This principle is implemented in the IdEM® software [6] [18] used for our study. This code generates a macro-model which could be integrated in software like Pspice. Figure 9 presents the main equivalent circuit of the transformer with the added impedance issued from "augmented model" (Fig.15) which takes into account the high frequency effects. Figure 16 shows the effect of this 'augmented model impedance' on the HF accuracy of the model, by comparison of the measurements results with the model ones.

Fig. 15. Equivalent circuit for high frequency behavior of the transformer.

This circuit is repesented by a component named "augmented model" in figure 9.

Fig. 16. Primary impedance with secondary short circuited (Phase A). Comparison between measurement and simulation result with and without the augmented model (named black box in the figure).

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 347

and the Fourier calculation of the current which can be calculated through a FFT algorithm for all measurements. The various impedances of the equivalent circuit shown in Fig. 9 can

then be determined through various configurations of the transformer.

Fig. 18. Voltage waveform in primary winding when the secondary is open

Fig. 17. Measurement bench in time domain

### **8. Characterization of the transformer in frequency domain**

As detailed in the previous section, the determination of the proposed model parameters is based on impedance measurements which can easily be done in frequency domain with impedance or network analyzer.

This method gives good results for low power transformer but there are some problems to make this kind of measurement with very high power transformer as the ones used in railways substation, which are the followings:


We propose a measurement method, carried out in time domain and based on the injection of higher level signals in the transformer. The principle of the proposed method and the obtained results are presented in the next section. [9]

### **9. Characterisation in time domain**

### **9.1 Measurements principle**

A square voltage waveform is applied at terminals of the transformer in the various configuration tests. The input current and input voltage are measured in time domain and determined in frequency domain via Fourier transforms and then the corresponding impedance can be deduced.

This experimental method has been applied in reduced scale on the laboratory test bench, to characterize the 15kVA three phases transformer. For this characterization, a square signal of magnitude 30 V with a period equal to 30µs, duty cycle equal to 0.5 and the rise time and fall time equal to 10ns. A differential voltage probe (bandwidth: 100MHz) is used to measure the voltage at the generator terminals. The current is measured with a current probe (bandwidth: 100MHz). The connection wires between the generator and the transformer are chosen as short as possible. Figure 17 shows a diagram of the measurement bench; we can see the generator, one phase of the transformer and the position of measurements probes.

Figure 18 and 19 show respectively the waveforms of the primary voltage and current of one phase of the transformer, in the configuration described in figure 17 when the voltage signal is applied at the primary winding with the secondary being open. These measurements allow determining the magnetizing impedance. The sample frequency used for these measurements is 125 Msample/s. All impedances can then be measured with this technique, but now the data have to be processed.

### **9.2 Impedance calculation**

The measurements results obtained in time domain will be converted in frequency domain. The impedance can be expressed as the ratio between the Fourier calculation of the voltage and the Fourier calculation of the current which can be calculated through a FFT algorithm for all measurements. The various impedances of the equivalent circuit shown in Fig. 9 can then be determined through various configurations of the transformer.

Fig. 17. Measurement bench in time domain

346 Infrastructure Design, Signalling and Security in Railway

As detailed in the previous section, the determination of the proposed model parameters is based on impedance measurements which can easily be done in frequency domain with

This method gives good results for low power transformer but there are some problems to make this kind of measurement with very high power transformer as the ones used in



A square voltage waveform is applied at terminals of the transformer in the various configuration tests. The input current and input voltage are measured in time domain and determined in frequency domain via Fourier transforms and then the corresponding

This experimental method has been applied in reduced scale on the laboratory test bench, to characterize the 15kVA three phases transformer. For this characterization, a square signal of magnitude 30 V with a period equal to 30µs, duty cycle equal to 0.5 and the rise time and fall time equal to 10ns. A differential voltage probe (bandwidth: 100MHz) is used to measure the voltage at the generator terminals. The current is measured with a current probe (bandwidth: 100MHz). The connection wires between the generator and the transformer are chosen as short as possible. Figure 17 shows a diagram of the measurement bench; we can see the generator,

Figure 18 and 19 show respectively the waveforms of the primary voltage and current of one phase of the transformer, in the configuration described in figure 17 when the voltage signal is applied at the primary winding with the secondary being open. These measurements allow determining the magnetizing impedance. The sample frequency used for these measurements is 125 Msample/s. All impedances can then be measured with this technique,

The measurements results obtained in time domain will be converted in frequency domain. The impedance can be expressed as the ratio between the Fourier calculation of the voltage

one phase of the transformer and the position of measurements probes.

**8. Characterization of the transformer in frequency domain** 

impedance or network analyzer.

railways substation, which are the followings:

seen, especially at high frequency.

**9. Characterisation in time domain** 

but now the data have to be processed.

**9.2 Impedance calculation** 

**9.1 Measurements principle** 

impedance can be deduced.

obtained results are presented in the next section. [9]

Fig. 18. Voltage waveform in primary winding when the secondary is open

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 349

The obtained results show a good agreement between these methods. However, we note a small difference, in the impedance variation between these methods in low frequency, which may be due to two reasons: the low accuracy of measurement equipments in the time domain (oscilloscope, probes ...) and the behavior of the magnetic material at low frequency. We can say that these results validate the proposed temporal method. This method is based on measurement of the voltage and current waveforms in the study system by reference to the method of Frequency Response Analysis FRA [10] which is based on the determination of the transfer function and voltage measurements. In the proposed method, the injection of

higher current values allows us to obtain the nominal operating of the transformer.

The test bench (Fig. 8) is composed by the 15 kVA power transformer, a rectifier (twelve diodes) and a load constituted by four power resistances. The high frequency model of the

The output current of the power transformer is measured for each phase using an

Figure 22 shows an example of current measured for phase A and obtained by the simulation. The test bench is simulated by using the high frequency equivalent circuit of the power transformer, presented previously, loaded with twelve diodes which model is available in the components library of the software simulator (SPICE) and four resistors.

Fig. 22. Measured (left) and simulated (right) output current of the power transformer (Phase A)

**10. Application to the test bench** 

**10.1 The laboratory setup without the line** 

power transformer is used in this simulation.

Fig. 21. Circuit diagram of the test bench

oscilloscope and current probe.

Fig. 19. Current waveform in primary winding when the secondary is open

Figure 20 shows the comparison between the impedance measured at the primary winding when the secondary is short circuited measured directly in frequency domain with impedance analyzer and the impedance issued from the data processing applied to measurements in time domain.

Fig. 20. Comparison between measurement of impedance in frequency domain and with temporal method applied to impedance of the primary winding, the secondary being short circuited.

The obtained results show a good agreement between these methods. However, we note a small difference, in the impedance variation between these methods in low frequency, which may be due to two reasons: the low accuracy of measurement equipments in the time domain (oscilloscope, probes ...) and the behavior of the magnetic material at low frequency.

We can say that these results validate the proposed temporal method. This method is based on measurement of the voltage and current waveforms in the study system by reference to the method of Frequency Response Analysis FRA [10] which is based on the determination of the transfer function and voltage measurements. In the proposed method, the injection of higher current values allows us to obtain the nominal operating of the transformer.

### **10. Application to the test bench**

348 Infrastructure Design, Signalling and Security in Railway

Fig. 19. Current waveform in primary winding when the secondary is open

measurements in time domain.

circuited.

Figure 20 shows the comparison between the impedance measured at the primary winding when the secondary is short circuited measured directly in frequency domain with impedance analyzer and the impedance issued from the data processing applied to

Fig. 20. Comparison between measurement of impedance in frequency domain and with temporal method applied to impedance of the primary winding, the secondary being short

### **10.1 The laboratory setup without the line**

The test bench (Fig. 8) is composed by the 15 kVA power transformer, a rectifier (twelve diodes) and a load constituted by four power resistances. The high frequency model of the power transformer is used in this simulation.

Fig. 21. Circuit diagram of the test bench

The output current of the power transformer is measured for each phase using an oscilloscope and current probe.

Figure 22 shows an example of current measured for phase A and obtained by the simulation. The test bench is simulated by using the high frequency equivalent circuit of the power transformer, presented previously, loaded with twelve diodes which model is available in the components library of the software simulator (SPICE) and four resistors.

Fig. 22. Measured (left) and simulated (right) output current of the power transformer (Phase A)

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 351

These curves show that the model seems very good until 10MHz. These results on a reduced scale power system are very encouraging and this study has to be continued on a real

The results obtained with a laboratory power transformer show a good agreement between

Depending on the application, the measurements approach, in frequency domain, is often used and gives good results. However, for the high power system it is not possible to use to impedance analyzer (specific apparatus) thus other methods can be used as the Frequency Response Analysis (FRA). Nevertheless, the power necessary for these experimental determinations is low and can be a problem when the goal of the measurements is to define a model functioning at high power level for a large frequency band. The proposed experimental method, in time domain, allows making measurements with high injected power. The preliminary results, obtained on a laboratory transformer are very interesting.

This work has been done with the help of V. Deniau and J. Rioult from IFSTTAR LEOST laboratory and G Nottet from Alstom Transport within CEMRAIL project, with

[1] European Standards EN 50121: 2006 Railway applications – Electromagnetic

[2] A Cozza, "Railways EMC : assessment of infrastructure impact" PhD thesis Lille and

[3] C. Andrieu, E. Daupahant and D. Boss, "A frequency- Dependant Model for a MV/LV

[4] H. Ouaddi, S. Baranowski, N. Idir "High frequency modelling of power transformer :

[5] J. Kolstad, C. Blevins, J. Dunn, A. Weisshaar, " NewCircuit Augmentation Method for

[7] S. Chimklai, J.R Marti, "Simplified Three-Phase Transformer Model for Electromagnetic

[8] H. Ouaddi, S. Baranowski, N. Idir " High frequency modelling of power transformer:

(Electrical Review), ISSN 0033-2097, R.86 May 2010. pp 165-169.

Transformer", IPST'99 – International Conference on Power Systems Transient,

application to railway substation in scale model", XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering,

Modeling ofInterconnects and Passive Components", IEEE Trans, Advanced

Transient Studies", IEEE Trans, Power Delivery, vol. 10, no. 3, July 1995, pp. 1316-

Application to railway substation in scale model" Przegląd Elektrotechniczny

simulations and experimental results in time and in frequency domain.

railway power substation

**12. Acknowledgment** 

**13. References** 

competitiveness cluster I-TRANS

Compatibility.

Torino , 2005

June 20-24,1999, Budapest

[6] www.emc.polito.it section IDEM®.

1325.

Arras, France, September 2009.

packaging, Vol. 29, no.1, February 2006

**11. Conclusion** 

As shown in Figure 22, we note a good agreement between the measured and simulated currents. Nevertheless, the waveform of the measured current is disturbed by digital noise of the oscilloscope. Moreover in our simulation we used sources without noise which does not exist in real case.

### **10.2 The laboratory setup with the line**

As a conclusion of the laboratory study, we have realized a complete simulation of a railway power system by adding a power line and a power load to the transformer. Fig. 23 shows the experimental setup.

Fig. 23. Laboratory test bench simulating a railway power infrastucture

The test bench is constituted by the previous laboratory transformer (15kVA) used in one phase transformer configuration (the two others phases are short circuited), connected to a 5.6m power line and load by power resistances.

This system is fed by a network analyzer (connected to port 1) which allows measuring the current in the power line via the S21 parameter as presented in figure 23, thru a current sensor (connected to the port 2 of the analyzer) .

Figure 24 shows a comparison between measurements and modeling for two extreme positions of the current sensor: near the transformer (z = 0) and near the load (z = 5.6m).

Fig. 24. Comparison between measurement and modeling : frequency variation of the current in the power line for two positions of the sensors

These curves show that the model seems very good until 10MHz. These results on a reduced scale power system are very encouraging and this study has to be continued on a real railway power substation

### **11. Conclusion**

350 Infrastructure Design, Signalling and Security in Railway

As shown in Figure 22, we note a good agreement between the measured and simulated currents. Nevertheless, the waveform of the measured current is disturbed by digital noise of the oscilloscope. Moreover in our simulation we used sources without noise which does

As a conclusion of the laboratory study, we have realized a complete simulation of a railway power system by adding a power line and a power load to the transformer. Fig. 23 shows

The test bench is constituted by the previous laboratory transformer (15kVA) used in one phase transformer configuration (the two others phases are short circuited), connected to a

This system is fed by a network analyzer (connected to port 1) which allows measuring the current in the power line via the S21 parameter as presented in figure 23, thru a current

Figure 24 shows a comparison between measurements and modeling for two extreme positions of the current sensor: near the transformer (z = 0) and near the load (z = 5.6m).

**z=0 m z=5,6 m**

Fig. 24. Comparison between measurement and modeling : frequency variation of the

Fig. 23. Laboratory test bench simulating a railway power infrastucture

5.6m power line and load by power resistances.

sensor (connected to the port 2 of the analyzer) .

current in the power line for two positions of the sensors

not exist in real case.

the experimental setup.

**10.2 The laboratory setup with the line** 

The results obtained with a laboratory power transformer show a good agreement between simulations and experimental results in time and in frequency domain.

Depending on the application, the measurements approach, in frequency domain, is often used and gives good results. However, for the high power system it is not possible to use to impedance analyzer (specific apparatus) thus other methods can be used as the Frequency Response Analysis (FRA). Nevertheless, the power necessary for these experimental determinations is low and can be a problem when the goal of the measurements is to define a model functioning at high power level for a large frequency band. The proposed experimental method, in time domain, allows making measurements with high injected power. The preliminary results, obtained on a laboratory transformer are very interesting.

### **12. Acknowledgment**

This work has been done with the help of V. Deniau and J. Rioult from IFSTTAR LEOST laboratory and G Nottet from Alstom Transport within CEMRAIL project, with competitiveness cluster I-TRANS

### **13. References**


**Part 3** 

**Signalling, Security and Infrastructure** 

**Construction in Railway** 


## **Part 3**

## **Signalling, Security and Infrastructure Construction in Railway**

352 Infrastructure Design, Signalling and Security in Railway

[9] H. Ouaddi, S. Baranowski, G. Nottet, B. Demoulin, L. Koné, "Study of HF Behaviour of

[10] WG A2.26 report. "Mechanical condition assessment of transformer windings using

[11] H. Ouaddi, G. Nottet S. Baranowski, L. Koné, N. Idir, 'Determination of the high

[13] B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain response

[14] B.Cogitore, J. P. Kéradec, "The two-winding transformer: an experimental method to

[15] T. Noda, H. Nakamoto, S. Yokoyama, "Accurate modeling of core-type distribution

[16] F. Blache, J. P. Kéradec, B. Cogitore, "Stray capacitance of two winding transformers:

[17] H.Y. Lu, J.G. Zhu,V.S. Ramsden, S.Y.R. Hui, "Measurement and modeling of stray

[18] I. A. Maio, P. Savin, I. S. Stievano, F. Canavero, " Augmented models of high frequency

instrumentation and measurement, Vol. 43, No. 2, April 1994.

transactions on Powers Electronics Specialists Conference,, 1994.

Electronics Specialists Conference, Vol. 2, Page(s): 763 – 768, 1999.

frequency response analysis (FRA)" Electra n°228 October 2006.

IEEE VPPC 2010, Lille, 1-3 September 2010. proceeding sur clef USB [12] A. Oguz Soysal, "A method for wide frequency range modelling of power transformers

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capacitance in high frequency transformers", IEEE transactions on Powers

transformees for SMPS", Proceeding, 20th Int. Zurich Symposium on EMC, Zurich

**14** 

*Spain* 

*University of Castilla-La Mancha* 

, (1)

**Criteria for Improving the Embankment-**

Inmculada Gallego, Santos Sánchez-Cambronero and Ana Rivas

**Structure Transition Design in Railway Lines** 

In the design of a railroad track there are some situations in which the introduction of a structure in the track is needed, for example a bridge, a viaduct or a pontoon. This circumstance is even more frequent in the High Speed lines, since the design criteria, fundamentally slopes and radius, are stricter than those for conventional lines. The introduction of a structure determines the appearance of a point with an abrupt change in

The experience has shown that these transition zones between embankment and structure are the source of many problems (related to safety, passengers' comfort, maintenance expenses, etc.), causing differential settlements among adjacent track cross sections and

In order to diminish this unfavorable effect, the well known "technical blocks" are designed in a length determined between the structure and the embankment of access to this one. However, in spite of this structural disposition, it has not been found yet any design solution that notably reduces the track geometrical quality defects that have been observed in the mentioned zones. This is an important issue, because they produce a relevant increase in the maintenance expenses of the High Speed lines and they affect the availability of the

originating which is known as "dip" (European Rail Research Institute, ERRI., 1999)

**2. Theoretical foundation of embankment-structure transition behavior** 

The wheel load transmitted by a train to the track does not correspond to the static load; instead, random dynamic overloads appear due to the sprung and un-sprung masses. Among the great amount of existing formulations relative to these overloads, there is an outstanding contribution made by Prud 'Homme (Prud`Homme, 1970) according to the expression (1)

> 0.45 <sup>100</sup> *NS V*

where: σ(ΔQNS) is the standard deviation of the dynamic overloads due to the un-sprung masses of the material; *V* is the running speed of the vehicle; *b* is a variable related to the track defects and to the vehicle defects; *m* is the un-sprung mass of the vehicle; *k* is the

 

*Q b mK*

the vertical stiffness from a track cross section to another.

track (Gallego, López, Ubalde, & Texeira, 2005).

vertical track stiffness; φ(ε) is Damping of the track.

**1. Introduction** 

## **Criteria for Improving the Embankment-Structure Transition Design in Railway Lines**

Inmculada Gallego, Santos Sánchez-Cambronero and Ana Rivas *University of Castilla-La Mancha Spain* 

### **1. Introduction**

In the design of a railroad track there are some situations in which the introduction of a structure in the track is needed, for example a bridge, a viaduct or a pontoon. This circumstance is even more frequent in the High Speed lines, since the design criteria, fundamentally slopes and radius, are stricter than those for conventional lines. The introduction of a structure determines the appearance of a point with an abrupt change in the vertical stiffness from a track cross section to another.

The experience has shown that these transition zones between embankment and structure are the source of many problems (related to safety, passengers' comfort, maintenance expenses, etc.), causing differential settlements among adjacent track cross sections and originating which is known as "dip" (European Rail Research Institute, ERRI., 1999)

In order to diminish this unfavorable effect, the well known "technical blocks" are designed in a length determined between the structure and the embankment of access to this one. However, in spite of this structural disposition, it has not been found yet any design solution that notably reduces the track geometrical quality defects that have been observed in the mentioned zones. This is an important issue, because they produce a relevant increase in the maintenance expenses of the High Speed lines and they affect the availability of the track (Gallego, López, Ubalde, & Texeira, 2005).

### **2. Theoretical foundation of embankment-structure transition behavior**

The wheel load transmitted by a train to the track does not correspond to the static load; instead, random dynamic overloads appear due to the sprung and un-sprung masses. Among the great amount of existing formulations relative to these overloads, there is an outstanding contribution made by Prud 'Homme (Prud`Homme, 1970) according to the expression (1)

$$
\sigma(\Delta Q\_{\rm NS}) = 0.45 \frac{V}{100} b \sqrt{m K \rho(\varepsilon)} \,\,\,\,\,\tag{1}
$$

where: σ(ΔQNS) is the standard deviation of the dynamic overloads due to the un-sprung masses of the material; *V* is the running speed of the vehicle; *b* is a variable related to the track defects and to the vehicle defects; *m* is the un-sprung mass of the vehicle; *k* is the vertical track stiffness; φ(ε) is Damping of the track.

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 357

This revision of the solutions employed, shows a lack of homogeneity of the design criteria: each Railway Administration uses different designs for the longitudinal sections of the

The previous analysis shows a lack of homogeneity in the design criteria. Besides, it must be added what the experience has pointed out, a remarkable deterioration of the quality in the transitions. These two facts, lead to think about two reflections: a) it does not exist a precise knowledge of the behavior of transitions, and b), the current designs have certain limitations since they are unable to reduce in a remarkable way the deterioration experimented in these areas. The first reflection invites us to deepen in the knowledge of the deterioration process and the second one induces us to consider two more aims: 1) introducing new design criteria and 2) giving an analytical basis to the already existent, to overcome some of those limitations. In order to achieve those aims a numerical modelization of the embankment-

Therefore, within the scope of this work it is sought to carry out a model of finite elements which simulates the behavior of embankment-structures transitions. This model will enable to quantify the vertical stiffness of the track according to the type of disposition of the materials which the transition is carried out with (PA and PB, Fig 1) as well as the

Rail steel 2.1x1011 0.3 - - 7.5 104 Elastic bearing 2.952x108 - - - -

element 1 8.01x1010 0.25 - - -

element 2 5.02x1010 0.25 - - -

element 3 3.68x1010 0.25 - - - Ballast 1.3x108 0.2 0 45 1.9x104 Sub-ballast 1.2x108 0.3 0 45 1.9x104 Track bed 8.107 0.3 0 35 2x104 Material QS1 1.25x107 0.4 15000 10 2x104 Material QS2 2.50x107 0.3 10000 20 2x104 Material QS3 8x107 0.3 0 35 2x104

Rock 3x109 0.2 2.7x104

Table 1. Values of geotechnical parameters considered in the models

1.6x108 0.25 2.3x104

**(0)**  **(N/m3)** 

structure transition is shown in this chapter (Gallego & López, , 2009)

geotechnical characteristics of these materials (See Tab 1 and Tab 2).

**Material E (N/m2) υ** *c* **(N/m2)** 

embankment-structure transitions.

**3. Motivation of the chapter** 

Sleeper

Sleeper

Sleeper

Cement-treated granular material

Expression (1) introduces a new criterion to reduce the mutual aggressiveness between track and vehicle. From that it is deduced the importance of having a low value of the vertical stiffness of the track *(K)* and of the un-sprung mass of the vehicle *(m)* to avoid increasing the dynamic overloads due to the un-sprung masses. This influence is a more relevant fact in high speed trains.

In addition, it is not only the stiffness value which determines the dynamic overloads. They are also influenced by the variation of the stiffness value that might exist from one sleeper to another.

The first studies carried out to deal with this problem were carried out by Amielin, 1974, later on in the eighties they stand out those by Lopez, 1983, Hettle, 1986, Hunt, 1997, Esveld, 2001, López A. , 2001 or Teixeira, 2003 shown that as the difference between the stiffness values of two consecutive sleepers increases, the reaction on the sleepers increases, thereby increasing the load on the sleeper. On the other hand, next to these increments of stress, the experience has proved that some differential settlements are originated. As a result of these two factors hanging sleepers can be developed that in turn increase the stress on the ballast. In order to avoid this deterioration experimented in the transitions, these sections are built the well known "technical blocks", whose aim is achieving a gradual increase in the stiffness from one sleeper to the following one, as we reach the structure.

Now, it is interesting to know: How are these designs? What criteria are used to define them? To answer these questions a revision of the designs used by the different European Railway Administrations has been made. Five types of the most used measures have been identified. They are enumerated next, being the first one the most frequently employed:


Along with these measures, they have been also identified a variety of track formation materials behind the abutment. There are three types that stand out, just as it is schematized in Fig 1. The first two types are the more frequently used, and with regard to that work they will be called slope type PA and slope type PB.

Fig. 1. Types of dispositions of the backfill behind the abutment in embankment-structure transitions.

This revision of the solutions employed, shows a lack of homogeneity of the design criteria: each Railway Administration uses different designs for the longitudinal sections of the embankment-structure transitions.

### **3. Motivation of the chapter**

356 Infrastructure Design, Signalling and Security in Railway

Expression (1) introduces a new criterion to reduce the mutual aggressiveness between track and vehicle. From that it is deduced the importance of having a low value of the vertical stiffness of the track *(K)* and of the un-sprung mass of the vehicle *(m)* to avoid increasing the dynamic overloads due to the un-sprung masses. This influence is a more relevant fact in

In addition, it is not only the stiffness value which determines the dynamic overloads. They are also influenced by the variation of the stiffness value that might exist from one sleeper to

The first studies carried out to deal with this problem were carried out by Amielin, 1974, later on in the eighties they stand out those by Lopez, 1983, Hettle, 1986, Hunt, 1997, Esveld, 2001, López A. , 2001 or Teixeira, 2003 shown that as the difference between the stiffness values of two consecutive sleepers increases, the reaction on the sleepers increases, thereby increasing the load on the sleeper. On the other hand, next to these increments of stress, the experience has proved that some differential settlements are originated. As a result of these two factors hanging sleepers can be developed that in turn increase the stress on the ballast. In order to avoid this deterioration experimented in the transitions, these sections are built the well known "technical blocks", whose aim is achieving a gradual increase in the stiffness

Now, it is interesting to know: How are these designs? What criteria are used to define them? To answer these questions a revision of the designs used by the different European Railway Administrations has been made. Five types of the most used measures have been identified. They are enumerated next, being the first one the most

Backfill behind the abutment either with materials of a high compression level or

Along with these measures, they have been also identified a variety of track formation materials behind the abutment. There are three types that stand out, just as it is schematized in Fig 1. The first two types are the more frequently used, and with regard to that work they

Fig. 1. Types of dispositions of the backfill behind the abutment in embankment-structure

 Use of a transition slab built with reinforced concrete or another material. Introduction of horizontal layers on a track formation of different materials.

Use of geosynthetics to achieve an abutment reinforced backfill.

Treatment of the track bed and sub-ballast with cement.

from one sleeper to the following one, as we reach the structure.

granular material treated with cement.

will be called slope type PA and slope type PB.

high speed trains.

frequently employed:

transitions.

another.

The previous analysis shows a lack of homogeneity in the design criteria. Besides, it must be added what the experience has pointed out, a remarkable deterioration of the quality in the transitions. These two facts, lead to think about two reflections: a) it does not exist a precise knowledge of the behavior of transitions, and b), the current designs have certain limitations since they are unable to reduce in a remarkable way the deterioration experimented in these areas. The first reflection invites us to deepen in the knowledge of the deterioration process and the second one induces us to consider two more aims: 1) introducing new design criteria and 2) giving an analytical basis to the already existent, to overcome some of those limitations. In order to achieve those aims a numerical modelization of the embankmentstructure transition is shown in this chapter (Gallego & López, , 2009)

Therefore, within the scope of this work it is sought to carry out a model of finite elements which simulates the behavior of embankment-structures transitions. This model will enable to quantify the vertical stiffness of the track according to the type of disposition of the materials which the transition is carried out with (PA and PB, Fig 1) as well as the geotechnical characteristics of these materials (See Tab 1 and Tab 2).



Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 359

Fig. 2. General schematic of an embankment–structure. The transition is the zone adjacent to

Suitable accuracy can be achieved by modeling only a transition section. However, the track section chosen to be modeled should be such that possesses the fundamental characteristics of a transition. However, the track section chosen for modeling should have the fundamental characteristics of a transition. For both slope types considered (PA and PB), these characteristics occur when the material changes from one material to another, either at the beginning or end of the slope (see Fig 2). Thus, the sections to be modeled are those

Fig. 3. Schematic of the beginning and end of the technical block in the slope of type PB and PA

The directions considered for the model are the following ones: the axis *x* indicates the

sleeper direction, the axis *y* the vertical and the axis z the rail direction (see Fig 2).

the structure (see Gallego I.,2006)

shown within the rectangles in Fig 3.

**4.2 Geometry of the analyzed domain** 


\*MGT = Cement-treated granular material

Table 2. Geometric and geotechnical parameter considered in the model

### **4. Description of the numerical model and the work assumptions**

In order to quantify the vertical track stiffness value and the incidence that the disposition and type of material of the track formation have on it, it is considered more accurate to analyze the track as a whole system. So as to carry out this analysis, the most appropriate approach is to apply the finite elements method. This method enables the numerical simulation of different materials and diverse boundary conditions, facilitating the study of the interaction among the different elements that compose the railway superstructure and infrastructure.

The employment of the finite elements method is accurate to evaluate the global behavior of the track structure, but it is very limited to quantify the efforts in the ballast: the intergranular stress is very different from stress and strain assumed in a continuous medium. However, the use of a discrete elements model, or a mixed one, finite and discrete elements, implies a tremendous computational cost and an enormous complexity.

In the Railway field, the finite elements method has been used by authors as López A. , 1977, Sauvage & Larible, 1982, Profillidis, 1983, Sahu, Rao, & Yudhbir., 1999 Mira, Férnández, Pastor, Nasarre, & Carrillo, 2000, among others. Some studies developed in the eighties stand out, such as Profillidis, 1983, since the results of those works were integrated by the Committee D-117 of the ORE in the Record (Comité D-117 (ORE), 1983). The sizing graphics of the track bearing structure are collected in this work. Together with the previous works, it is also worth mentioning those carried out by the "Ministerio de Fomento Español", which have been the basis for making some recommendations for the Railways track construction.

In order to generate the model proposed in this chapter, the contributions collected in the different models of Railways track formations carried out so far and enunciated previously have been taken into consideration.

### **4.1 Description of the analyzed domain**

The length of an embankment-structure transition depends on the type of structure and the height of the access embankment. In the case of embankment heights around 15 meters, the technical block can reach lengths of up to 85 meters (Fig 2). A 3D Model for such that length require an extremely powerful software and hardware, implying a huge computational cost due to the long time calculation that would be needed.

**GEOTECHNICAL PARAMETERS** 

PA 1:1 QS2/QS3 QS1 H7PA11QS2QS3QS1

In order to quantify the vertical track stiffness value and the incidence that the disposition and type of material of the track formation have on it, it is considered more accurate to analyze the track as a whole system. So as to carry out this analysis, the most appropriate approach is to apply the finite elements method. This method enables the numerical simulation of different materials and diverse boundary conditions, facilitating the study of the interaction among the different elements that compose the railway superstructure and

The employment of the finite elements method is accurate to evaluate the global behavior of the track structure, but it is very limited to quantify the efforts in the ballast: the intergranular stress is very different from stress and strain assumed in a continuous medium. However, the use of a discrete elements model, or a mixed one, finite and discrete elements,

In the Railway field, the finite elements method has been used by authors as López A. , 1977, Sauvage & Larible, 1982, Profillidis, 1983, Sahu, Rao, & Yudhbir., 1999 Mira, Férnández, Pastor, Nasarre, & Carrillo, 2000, among others. Some studies developed in the eighties stand out, such as Profillidis, 1983, since the results of those works were integrated by the Committee D-117 of the ORE in the Record (Comité D-117 (ORE), 1983). The sizing graphics of the track bearing structure are collected in this work. Together with the previous works, it is also worth mentioning those carried out by the "Ministerio de Fomento Español", which have been the basis for making some recommendations for the Railways track construction. In order to generate the model proposed in this chapter, the contributions collected in the different models of Railways track formations carried out so far and enunciated previously

The length of an embankment-structure transition depends on the type of structure and the height of the access embankment. In the case of embankment heights around 15 meters, the technical block can reach lengths of up to 85 meters (Fig 2). A 3D Model for such that length require an extremely powerful software and hardware, implying a huge computational cost

**Original ground**

QS2 QS3 ROCA

**Type material of transition (type1/type2)** 

QS3/MGT\*

**4. Description of the numerical model and the work assumptions** 

Table 2. Geometric and geotechnical parameter considered in the model

implies a tremendous computational cost and an enormous complexity.

**Name of case studies H embankment (H7)- Disposition – value of the slope- material 1 material2-original ground** 

**GEOMETRIC PARAMETERS** 

> **Slope value (H:V)**

PB 3:1 QS2/MGT\*

\*MGT = Cement-treated granular material

have been taken into consideration.

**4.1 Description of the analyzed domain** 

due to the long time calculation that would be needed.

**Type of design (Fig 1)** 

infrastructure.

Fig. 2. General schematic of an embankment–structure. The transition is the zone adjacent to the structure (see Gallego I.,2006)

Suitable accuracy can be achieved by modeling only a transition section. However, the track section chosen to be modeled should be such that possesses the fundamental characteristics of a transition. However, the track section chosen for modeling should have the fundamental characteristics of a transition. For both slope types considered (PA and PB), these characteristics occur when the material changes from one material to another, either at the beginning or end of the slope (see Fig 2). Thus, the sections to be modeled are those shown within the rectangles in Fig 3.

### **4.2 Geometry of the analyzed domain**

The directions considered for the model are the following ones: the axis *x* indicates the sleeper direction, the axis *y* the vertical and the axis z the rail direction (see Fig 2).

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 361

The model also sought to make the vertical stiffness equal for all of the elastic bearings (see Fig 4). The vertical dimension and the modulus of elasticity were fixed so that the vertical stiffness of the element coincided with the stiffness of the elastic bearing provided by the manufacturer. For the high-speed Madrid–Seville line, the elastic bearings have a stiffness of

Because the sleeper section is not constant along its entire length, the dimensions of its most representative section were used for the sleeper model elements. For each element (See Fig 5),

To obtain homogeneity in the calculations, the elements of the model had to have a constant width, which is not the case in the real sleeper. Thus, the model width must be considered to be an average width. This average width must be such that the load bearing surface in the

The sleeper–ballast contact zones contain a high concentration of strains. This local phenomenon requires refining of the mesh used to model these zones. However, applying this procedure is sometimes impossible because of the computational resources and model complexity needed. The most common alternative to modeling the contact zones is to use bounded degrees of freedom. In fact, this solution was adopted by ORE Committee D-117

*E I EI model model real real* (2)

the modeled flexural stiffness must be equal to the real flexural stiffness, as follows

Fig. 4. Model of the rail and elastic bearings carried out in this study

Fig. 5. Schematic of a real sleeper and a modeled sleeper

model is equal to that in reality.

**4.4 Sleeper–ballast contact** 

nearly 500kN/mm (López A. , 2001)

### **4.2.1 Transverse section**

The measures adopted for the transversal section are the ones used in the High Speed line Madrid-Sevilla, but considering the track as simple and applying symmetry with respect to the plane *x* = 0.

The slope of the embankment varies with the type of material from which it is made; between H/V=3/2 and 1/2. The value 3/2 has been adopted in the model, because it was employed in the Madrid–Seville line.

### **4.2.2 Vertical direction**

In the vertical direction (axis y) not only all the elements that compose the super structure are considered but also the, sub-ballast , the formation layer, 7m for the embankment and 3m for the original ground.

Values of 30, 25, and 60 cm, respectively were adopted for the thicknesses of the ballast under a sleeper, the sub-ballast the formation layer. These values are the same values as those applied in the transversal section of the High Speed line between Madrid and Seville.

### **4.2.3 Longitudinal direction**

For domain analysis, the load applied on a sleeper is transmitted to the adjacent sleepers through some transmission coefficients. These coefficients clearly decrease as the distance from the point of load application increases; the coefficient is only 7 per cent in the third sleeper, when the first sleeper is defined as the one on which the load is applied (Comité D-117 (ORE), 1983)

To determine the real value of the settlement of the head of the rail when the load acts on it, one must not only solve for that load but also consider the history of the previous loads that have affected that sleeper. The load applied on a sleeper transmits it to the two adjacent sleepers. In order to observe the behavior of two consecutives sleepers with different stiffness under a load, while taking into account their load history also, four successively loaded sleepers (T5, T6, T7, and T8) were considered in order to analyze the behavior of sleepers T7 and T8.

In 1983, a test in Derby showed that important phenomena are apparent up to the fourth sleeper from the one loaded (Comité D-117 (ORE), 1983). Therefore, four unloaded sleepers were introduced at both ends of the model. This set-up avoided artefacts and yet included a substantial number of sleepers onto which the load could be applied. This approach required consideration of a transition sector comprising 12 sleepers, leading to a model system with a total length of 7.20 m.

### **4.3 Modelling rail track, elastic bearing, and sleeper section**

In order to model the rail track, its resistance to bending was simulated in the most accurate way possible (Fig 4), which is why the inertia of the modelled rail must be equal to that of the real rail.

The measures adopted for the transversal section are the ones used in the High Speed line Madrid-Sevilla, but considering the track as simple and applying symmetry with respect to

The slope of the embankment varies with the type of material from which it is made; between H/V=3/2 and 1/2. The value 3/2 has been adopted in the model, because it was

In the vertical direction (axis y) not only all the elements that compose the super structure are considered but also the, sub-ballast , the formation layer, 7m for the embankment and

Values of 30, 25, and 60 cm, respectively were adopted for the thicknesses of the ballast under a sleeper, the sub-ballast the formation layer. These values are the same values as those applied in the transversal section of the High Speed line between Madrid and

For domain analysis, the load applied on a sleeper is transmitted to the adjacent sleepers through some transmission coefficients. These coefficients clearly decrease as the distance from the point of load application increases; the coefficient is only 7 per cent in the third sleeper, when the first sleeper is defined as the one on which the load is applied (Comité D-

To determine the real value of the settlement of the head of the rail when the load acts on it, one must not only solve for that load but also consider the history of the previous loads that have affected that sleeper. The load applied on a sleeper transmits it to the two adjacent sleepers. In order to observe the behavior of two consecutives sleepers with different stiffness under a load, while taking into account their load history also, four successively loaded sleepers (T5, T6, T7, and T8) were considered in order to analyze the behavior of

In 1983, a test in Derby showed that important phenomena are apparent up to the fourth sleeper from the one loaded (Comité D-117 (ORE), 1983). Therefore, four unloaded sleepers were introduced at both ends of the model. This set-up avoided artefacts and yet included a substantial number of sleepers onto which the load could be applied. This approach required consideration of a transition sector comprising 12 sleepers, leading to a model

In order to model the rail track, its resistance to bending was simulated in the most accurate way possible (Fig 4), which is why the inertia of the modelled rail must be equal to that of

**4.2.1 Transverse section** 

**4.2.2 Vertical direction** 

3m for the original ground.

**4.2.3 Longitudinal direction** 

employed in the Madrid–Seville line.

the plane *x* = 0.

Seville.

117 (ORE), 1983)

sleepers T7 and T8.

the real rail.

system with a total length of 7.20 m.

**4.3 Modelling rail track, elastic bearing, and sleeper section** 

Fig. 4. Model of the rail and elastic bearings carried out in this study

The model also sought to make the vertical stiffness equal for all of the elastic bearings (see Fig 4). The vertical dimension and the modulus of elasticity were fixed so that the vertical stiffness of the element coincided with the stiffness of the elastic bearing provided by the manufacturer. For the high-speed Madrid–Seville line, the elastic bearings have a stiffness of nearly 500kN/mm (López A. , 2001)

Because the sleeper section is not constant along its entire length, the dimensions of its most representative section were used for the sleeper model elements. For each element (See Fig 5), the modeled flexural stiffness must be equal to the real flexural stiffness, as follows

$$E\_{model} I\_{model} = E\_{real} I\_{real} \tag{2}$$

Fig. 5. Schematic of a real sleeper and a modeled sleeper

To obtain homogeneity in the calculations, the elements of the model had to have a constant width, which is not the case in the real sleeper. Thus, the model width must be considered to be an average width. This average width must be such that the load bearing surface in the model is equal to that in reality.

#### **4.4 Sleeper–ballast contact**

The sleeper–ballast contact zones contain a high concentration of strains. This local phenomenon requires refining of the mesh used to model these zones. However, applying this procedure is sometimes impossible because of the computational resources and model complexity needed. The most common alternative to modeling the contact zones is to use bounded degrees of freedom. In fact, this solution was adopted by ORE Committee D-117

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 363

 In the vertical plans limits of the model, z=0 and z=7.20m, the boundary condition adopted is to impose the nullity of movement in the perpendicular direction to these

 In the vertical plans limits of the model, x=0 and x=18.45m, the boundary condition is, like the previous one, to impose the nullity of movement in the perpendicular direction

In the horizontal inferior plan of the model y=-3m, the condition to be imposed is the

An elastic, isotropic, and linear model was used to develop a mechanic model of the rail tracks, elastic bearings, sleepers, and the granular material processed with cement. In contrast, a perfect plastic model, i.e. the Drucker–Prager model (Oliver & Arlet, 2000), was used to model the rest of the materials, including the ballast, sub-ballast, track bed, embankment fill, and original ground. Finite strain was used to simulate the kinematics of

Granular material treated with cement is considered to behave elastically, at least until it reaches a substantial percentage of its stress limit; one can assume its modulus of elasticity

To model the embankment material on which the track is laid, a perfect elasto-plastic behavior was assumed. This assumption implies that reloading occurs in the same way as downloading, and that the material experiences no hardening (hardening parameter *H=0*). For modeling of the yield surfaces, the most accurate approach is to use a model dependent on hydrostatic pressure. These models are the Drucker–Prager and Mohr–Coulomb models, which limit the material behavior for states of hydrostatic stress (in traction). For the present study, the Drucker–Prager model was selected because it has been used in several elasto-plastic models

The principle formulated by Drucker and Prager in 1952 includes the influence of pressure through the first invariant of the stress tensor *I*1 and the internal friction angle . It also depends on the second invariant *J*2 of the deviatoric stress tensor, as well as on two parameters: the friction angle among particles and the cohesion *c*. This criterion is expressed by means of the principal stress invariant and *J2* (the second invariant of

F , , ; ( ) K( , ) 0 1 2 1 2 *IJc I J*

K( , ) 6 ( ) cos /(3 3 3 sen )

( ) 2sen /(3 3 3 sen )

 

 *c* (4)

 (5)

, (3)

 

> 

 

used to design railway projects, and it has been validated by ORE Committee D-171.

plans (uz=0).

to these plans (ux=0).

**4.6 Material constitutive model** 

the continuous medium.

deviatoric stress), as follows:

where

and

null vertical displacement (uy=0).

to remain essentially constant under normal stress.

and was used by the Railway Track Formations Project in its recommendations on railway track construction (Ministerio de fomento, 1999).

The use of bounded degrees of freedom requires the introduction of different nodes for each material at the contact surface. These nodes must move equivalently in the direction perpendicular to the contact plane (see Fig. 6). However, these nodes can move at different values in the directions parallel to the contact plane.

This solution is effective because it solves the tensional discontinuities that appear at the interface between two materials that differ significantly in their stiffness. In this model, bounded degrees of freedom were used at the sleeper–ballast contacts.

Fig. 6. Schematic of the ballast-sleeper contact

#### **4.5 Boundary conditions**

The model in this study differs from many existing models of railway track construction (Gallego, López, Ubalde, & Texeira, 2005), in which all vertical planes are constrained in all directions. In the Supertrack project (European comunity, 2005) and in this work, the planes that shape the slopes of embankments are left completely free, with no restrictions. In particular, the boundary conditions used here are as follows (see Fig. 7):

Fig. 7. Boundary conditions


### **4.6 Material constitutive model**

362 Infrastructure Design, Signalling and Security in Railway

and was used by the Railway Track Formations Project in its recommendations on railway

The use of bounded degrees of freedom requires the introduction of different nodes for each material at the contact surface. These nodes must move equivalently in the direction perpendicular to the contact plane (see Fig. 6). However, these nodes can move at different

This solution is effective because it solves the tensional discontinuities that appear at the interface between two materials that differ significantly in their stiffness. In this model,

The model in this study differs from many existing models of railway track construction (Gallego, López, Ubalde, & Texeira, 2005), in which all vertical planes are constrained in all directions. In the Supertrack project (European comunity, 2005) and in this work, the planes that shape the slopes of embankments are left completely free, with no restrictions. In

track construction (Ministerio de fomento, 1999).

values in the directions parallel to the contact plane.

Fig. 6. Schematic of the ballast-sleeper contact

**4.5 Boundary conditions** 

Fig. 7. Boundary conditions

bounded degrees of freedom were used at the sleeper–ballast contacts.

particular, the boundary conditions used here are as follows (see Fig. 7):

An elastic, isotropic, and linear model was used to develop a mechanic model of the rail tracks, elastic bearings, sleepers, and the granular material processed with cement. In contrast, a perfect plastic model, i.e. the Drucker–Prager model (Oliver & Arlet, 2000), was used to model the rest of the materials, including the ballast, sub-ballast, track bed, embankment fill, and original ground. Finite strain was used to simulate the kinematics of the continuous medium.

Granular material treated with cement is considered to behave elastically, at least until it reaches a substantial percentage of its stress limit; one can assume its modulus of elasticity to remain essentially constant under normal stress.

To model the embankment material on which the track is laid, a perfect elasto-plastic behavior was assumed. This assumption implies that reloading occurs in the same way as downloading, and that the material experiences no hardening (hardening parameter *H=0*).

For modeling of the yield surfaces, the most accurate approach is to use a model dependent on hydrostatic pressure. These models are the Drucker–Prager and Mohr–Coulomb models, which limit the material behavior for states of hydrostatic stress (in traction). For the present study, the Drucker–Prager model was selected because it has been used in several elasto-plastic models used to design railway projects, and it has been validated by ORE Committee D-171.

The principle formulated by Drucker and Prager in 1952 includes the influence of pressure through the first invariant of the stress tensor *I*1 and the internal friction angle . It also depends on the second invariant *J*2 of the deviatoric stress tensor, as well as on two parameters: the friction angle among particles and the cohesion *c*. This criterion is expressed by means of the principal stress invariant and *J2* (the second invariant of deviatoric stress), as follows:

$$\mathcal{F}(I\_1, I\_2, c; \phi) = \overline{\alpha}(\phi)I\_1 + \sqrt{I\_2} - \overline{\mathcal{K}}(\kappa; \phi) = 0 \tag{3}$$

where

$$\overline{\mathbf{K}}(\kappa, \phi) = \mathbf{6} \ c(\kappa) \cos \phi \,/\, \left(\mathbf{3} \sqrt{\mathbf{3}} + \sqrt{\mathbf{3}} \sin \phi\right) \tag{4}$$

and

$$
\sqrt{\alpha}(\phi) = 2 \operatorname{sen} \phi \mid \left( 3 \sqrt{3} + \sqrt{3} \operatorname{sen} \phi \right) \tag{5}
$$

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 365

To simulate the constructive process of an embankment and to ensure convergence of the solution, the first load state (only the material weight) was divided into 250 substeps of the gravitational load application and 50 balance iterations for each one. For railway loads, 15 sub-steps proved to be sufficient to achieve convergence. The program used is ANSYS

To carry out the calculations, the load of only one axle was considered while assuming the

The increased value of the dynamic overloads was calculated using Prud'Homme's formulation, with 1mm used as the value for *b* and the speed set to be 300 km/h. With this approach, the value of a dynamic overload was obtained according to the dynamic stiffness, which is unknown because its calculation requires knowing the value of the point dynamic load on the track. It is customary to carry out railway calculations assuming that the dynamic stiffness has a value similar to that of the static stiffness; this assumption has been validated by experience and confirmed by calculations (Ministerio de fomento, 1999). Thus, this assumption was also made in the present study, and numerical tests were used to justify

Fig. 10. Schematic of the different load states

Structural, which enables nonlinear analysis.

effects of the remaining axles to be negligible.

this choice.

When the function that defines the yield surface (3) is represented in the main stress space, a cone is obtained, the axis of which is the hydrostatic axis (see Fig 8).

Fig. 8. Schematic of yield surfaces Drucker–Prager

Of the elements used, a quadratic 'brick' element of 20 nodes was selected; this is the most common type of element in three-dimensional models used to design railway tracks. The final meshes are shown in Fig 9.

Fig. 9. Finite-element model for transitions with slopes of type PA31 and PB11

### **4.7 Hypothesis adopted**

The load application must be carried out in several stages. In the first stage, only the material's own weight is considered until reaching the stress balance, while at later stages the loads due to the train are also taken into account. The stresses and displacements of interest are the ones that correspond to the application of the train loads; therefore, they can be calculated from the difference between the totals obtained after applying the train loads to the first stage.

Here, it was convenient to apply four load states due to the train passage, matching each state to the application of the static load per wheel in the four central sleepers of the model: T5, T6, T7, and T8 (See Fig 10).

When the function that defines the yield surface (3) is represented in the main stress space, a

Of the elements used, a quadratic 'brick' element of 20 nodes was selected; this is the most common type of element in three-dimensional models used to design railway tracks. The

Fig. 9. Finite-element model for transitions with slopes of type PA31 and PB11

The load application must be carried out in several stages. In the first stage, only the material's own weight is considered until reaching the stress balance, while at later stages the loads due to the train are also taken into account. The stresses and displacements of interest are the ones that correspond to the application of the train loads; therefore, they can be calculated from the difference between the totals obtained after applying the train loads

Here, it was convenient to apply four load states due to the train passage, matching each state to the application of the static load per wheel in the four central sleepers of the model:

cone is obtained, the axis of which is the hydrostatic axis (see Fig 8).

Fig. 8. Schematic of yield surfaces Drucker–Prager

final meshes are shown in Fig 9.

**4.7 Hypothesis adopted** 

T5, T6, T7, and T8 (See Fig 10).

to the first stage.

Fig. 10. Schematic of the different load states

To simulate the constructive process of an embankment and to ensure convergence of the solution, the first load state (only the material weight) was divided into 250 substeps of the gravitational load application and 50 balance iterations for each one. For railway loads, 15 sub-steps proved to be sufficient to achieve convergence. The program used is ANSYS Structural, which enables nonlinear analysis.

To carry out the calculations, the load of only one axle was considered while assuming the effects of the remaining axles to be negligible.

The increased value of the dynamic overloads was calculated using Prud'Homme's formulation, with 1mm used as the value for *b* and the speed set to be 300 km/h. With this approach, the value of a dynamic overload was obtained according to the dynamic stiffness, which is unknown because its calculation requires knowing the value of the point dynamic load on the track. It is customary to carry out railway calculations assuming that the dynamic stiffness has a value similar to that of the static stiffness; this assumption has been validated by experience and confirmed by calculations (Ministerio de fomento, 1999). Thus, this assumption was also made in the present study, and numerical tests were used to justify this choice.

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 367

H7PA11QS2QS3 11.242 17.227 37.206 42.752

H7PB11QS2QS3 18.847 19.957 36.054 39.325

H7PA31QS2QS3 10.800 16.380 34.139 39.744

H7PB31QS2QS3 14.015 19.296 34.519 38.512

H7PA11QS2MGT 15.380 25.499 43.859 47.795

H7PB11QS2MGT 28.721 32.644 37.657 40.000

H7PA31QS2MGT 13.182 18.275 36.549 42.077

H7PB31QS2MGT 21.524 25.961 35.777 38.592

H7PA11QS3MGT 32.193 53.563 71.692 75.374

H7PB11QS3MGT 54.186 59.936 69.294 70.473

H7PA31QS3MGT 29.354 51.068 70.875 74.650

H7PB31QS3MGT 48.668 58.069 70.340 73.444

Table 3. Values of vertical static track stiffness at the beginning of transition *KI* (kN/mm)

**ORIGINAL GROUND QS2**

( *K QS* ( 2) ) 10.186 15.717 33.226 38.433

( *K QS* ( 3) ) 28.899 50.929 70.606 74.027

( *K MGT* ( ) ) 67.782 73.676 83.214 87.800

Table 4. Values of vertical static track stiffness *K* for conventional embankments (kN/mm)

**ORIGINAL GROUND QS3**  **ORIGINAL GROUND ROCK** 

**ORIGINAL GROUND QS1** 

ORIGINAL GROUND QS2

ORIGINAL GROUND QS3 ORIGINAL GROUND ROCK

TRANSITION TYPE

for all cases studied

**EMBANKMENT MATERIAL** 

**FULL QS2** 

**FULL QS3** 

**FULL MGT** 

ORIGINAL GROUND QS1

### **5. Results from the model: Presentation and critical analysis**

This modeling study was carried out in two phases with different aims. In the first phase, different case studies were analyzed numerically, and the results were studied. These results then determined whether to carry out more case studies or proceed with the second phase. The main objective of the first phase was to observe how changing from a less rigid material to a more rigid one would affect the vertical stiffness of the track.

In the second phase, variations caused by the different stiffness values were analyzed for all the case studies from the first phase.

### **5.1 First phase**

In the first phase, the main differences among the designs of the embankment–structure transitions are the types of materials used and the construction design. This justifies defining two types of case studies based on different geotechnical and geometrical parameters.

The geometrical parameters include the type and grade of slope; the latter is defined, e.g., as 1 : 1 and 3 : 2 (*H* : *V* , horizontal and vertical). The geotechnical parameters are the modulus of elasticity of the materials that compose the embankment fill and the original ground. For the modulus of elasticity, a range of values was used, matching those adopted in the numerical model presented by ORE Committee D-117. The values coincide with the lower limit values corresponding to the material types QS1, QS2, QS3, and rock (see Tab 1).

To fill the embankment, granular material processed with cement (MGT) was added to the model, since this material is so frequently used. Combining all these values with the technical block and the four load states already described, yielded a total of 48 case studies (see Tab 2). The modeling results for the case studies are shown in Tab 3.

To make additional comparisons, the stiffness was calculated for cases in which the fill corresponded to conventional embankments made with the same type of material (see Tab 4).

1. It is useful to apply stiffness values not only at the beginning but also at the end of the technical block; therefore, the cases corresponding to the ends of the technical blocks were calculated. Since the calculated stiffness values in the first 48 cases were similar for original ground QS1 and QS2, and for QS3 and rock, it was sufficient to calculate the cases corresponding to QS2 and QS3, thereby reducing the number of cases from 48 to 24 (see Tab 5).

### **5.2 Second phase**

The second phase involved analyzing the results of the first phase. The criteria were to limit the following:


This modeling study was carried out in two phases with different aims. In the first phase, different case studies were analyzed numerically, and the results were studied. These results then determined whether to carry out more case studies or proceed with the second phase. The main objective of the first phase was to observe how changing from a less rigid material

In the second phase, variations caused by the different stiffness values were analyzed for all

In the first phase, the main differences among the designs of the embankment–structure transitions are the types of materials used and the construction design. This justifies defining two types of case studies based on different geotechnical and geometrical

The geometrical parameters include the type and grade of slope; the latter is defined, e.g., as 1 : 1 and 3 : 2 (*H* : *V* , horizontal and vertical). The geotechnical parameters are the modulus of elasticity of the materials that compose the embankment fill and the original ground. For the modulus of elasticity, a range of values was used, matching those adopted in the numerical model presented by ORE Committee D-117. The values coincide with the lower limit values corresponding to the material types QS1, QS2, QS3,

To fill the embankment, granular material processed with cement (MGT) was added to the model, since this material is so frequently used. Combining all these values with the technical block and the four load states already described, yielded a total of 48 case studies

To make additional comparisons, the stiffness was calculated for cases in which the fill corresponded to conventional embankments made with the same type of material (see

1. It is useful to apply stiffness values not only at the beginning but also at the end of the technical block; therefore, the cases corresponding to the ends of the technical blocks were calculated. Since the calculated stiffness values in the first 48 cases were similar for original ground QS1 and QS2, and for QS3 and rock, it was sufficient to calculate the cases corresponding to QS2 and QS3, thereby reducing the number of cases from 48 to 24 (see

The second phase involved analyzing the results of the first phase. The criteria were to limit

(see Tab 2). The modeling results for the case studies are shown in Tab 3.

**5. Results from the model: Presentation and critical analysis** 

to a more rigid one would affect the vertical stiffness of the track.

the case studies from the first phase.

**5.1 First phase** 

parameters.

Tab 4).

Tab 5).

**5.2 Second phase** 

 The upper value of the vertical stiffness The lower value of the vertical stiffness The value of the longitudinal variation

the following:

and rock (see Tab 1).


Table 3. Values of vertical static track stiffness at the beginning of transition *KI* (kN/mm) for all cases studied


Table 4. Values of vertical static track stiffness *K* for conventional embankments (kN/mm)

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 369

The analysis identified some problems related to the type of material. Based on these, the

 Excessive deformations were observed in the rail when material of type QS1 exists in the original ground (see Fig 11). These deformations reached 14mm under the rail when transitions QS2 and QS3 were used (Tab 7). In these cases, the deformations were large, as were the deformation values between adjacent sleepers. For this reason, it is appropriate to substitute the original ground material of type QS1 with another material or to treat the existing QS1 material in such a way as to obtain a modulus of

In transitions from material of type QS2 to treated granular material, which occurs commonly in buried structures, the stiffness increased significantly at the beginning of the technical block when there was a relatively compressible material in the original ground. The solution with the smallest increase in the stiffness value was PA31. Fig 12 shows this value to be 16.4% which is too large. For this reason, transition-type QS2/MGT is not

elasticity corresponding to that of a material of at least type QS2.

**6. Proposed design recommendations** 

most relevant recommendations include:

appropriate for use in the surface structure.

Fig. 11. Deflection of the head of loaded rails


Table 5. Values of vertical static track stiffness at the beginning *KI* and end of transition *KF (kN/mm)* for all cases studied

These criteria were applied in two steps. Initially, the first two criteria were applied, and solutions were discarded if they resulted in either very high stiffness values, which generate elevated dynamic overloads, or very low stiffness values, which generate excessive rail deformations of the rail. To determine whether the stiffness values were high or low, they were compared to the values for designs using the same original ground material and the same materials as the simulated transition. Tab 6 shows the solutions remaining after this elimination process.


Table 6. Transition types obtained after eliminating the transition types that with extreme stiffness values

The second step consisted of applying the third criterion, limiting the longitudinal variation value. From among the case studies, the cases selected were those with the smallest increase in the K value at the beginning and end of the technical blocks. In this way, the most appropriate solutions were obtained for each type of original ground material (QS2 and QS3). This approach yields certain design recommendations, which are described in the following section.

### **6. Proposed design recommendations**

368 Infrastructure Design, Signalling and Security in Railway

**H7PA11QS2QS3** 17.227 37.581 37.206 61.927 **H7PB11QS2QS3** 19.957 47.071 36.054 64.276 **H7PA31QS2QS3** 16.380 41.982 34.139 65.175 **H7PB31QS2QS3** 19.296 49.312 34.519 67.536

**H7PA11QS2MGT** 25.499 62.550 43.859 72.812 **H7PB11QS2MGT** 32.644 66.571 37.657 80.345 **H7PA31QS2MGT** 18.275 68.029 36.549 76.708 **H7PB31QS2MGT** 25.961 69.294 35.777 79.658

**H7PA11QS3MGT** 53.563 68.278 71.692 79.658 **H7PB11QS3MGT** 59.936 71.145 69.294 78.319 **H7PA31QS3MGT** 51.068 71.418 70.875 82.844 **H7PB31QS3MGT** 58.069 71.009 70.340 82.115

Table 5. Values of vertical static track stiffness at the beginning *KI* and end of transition *KF*

These criteria were applied in two steps. Initially, the first two criteria were applied, and solutions were discarded if they resulted in either very high stiffness values, which generate elevated dynamic overloads, or very low stiffness values, which generate excessive rail deformations of the rail. To determine whether the stiffness values were high or low, they were compared to the values for designs using the same original ground material and the same materials as the simulated transition. Tab 6 shows the solutions remaining after this

> ORIGINAL GROUND QS2

> > PB31 PA11

> > PB31 PA11

> > PB31 PA11

Table 6. Transition types obtained after eliminating the transition types that with extreme

yields certain design recommendations, which are described in the following section.

The second step consisted of applying the third criterion, limiting the longitudinal variation value. From among the case studies, the cases selected were those with the smallest increase in the K value at the beginning and end of the technical blocks. In this way, the most appropriate solutions were obtained for each type of original ground material (QS2 and QS3). This approach

ORIGINAL GROUND QS3

> PB11 PA31

> PB11 PA31

> PB31 PA31

ORIGINAL GROUND ROCK

> PB11 PA31

> PB11 PA31

> PB31 PA31

ORIGINAL GROUND QS1

PA11

PA11

PA11

**ORIGINAL GROUND QS2 ORIGINAL GROUND QS3 BEGINNING (** *KI* **) END (** *KF* **) BEGINNING (** *KI* **) END (** *KF* **)** 

**TRANSITION TYPE** 

*(kN/mm)* for all cases studied

elimination process.

QS2/QS3 PB31

QS2/MGT PB31

QS3/MGT PB31

Materials of transition: Type1/Type 2

stiffness values

The analysis identified some problems related to the type of material. Based on these, the most relevant recommendations include:

 Excessive deformations were observed in the rail when material of type QS1 exists in the original ground (see Fig 11). These deformations reached 14mm under the rail when transitions QS2 and QS3 were used (Tab 7). In these cases, the deformations were large, as were the deformation values between adjacent sleepers. For this reason, it is appropriate to substitute the original ground material of type QS1 with another material or to treat the existing QS1 material in such a way as to obtain a modulus of elasticity corresponding to that of a material of at least type QS2.

In transitions from material of type QS2 to treated granular material, which occurs commonly in buried structures, the stiffness increased significantly at the beginning of the technical block when there was a relatively compressible material in the original ground. The solution with the smallest increase in the stiffness value was PA31. Fig 12 shows this value to be 16.4% which is too large. For this reason, transition-type QS2/MGT is not appropriate for use in the surface structure.

Fig. 11. Deflection of the head of loaded rails

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 371

Fig. 12. Analysis of the stiffness variations assuming material transition from type QS2 to

 Near the abutment, the stiffness increased abruptly when using a granular material treated with cement as fill (MGT, 3% by weight). In fact, the stiffness value of the abutment could oscillate between 200KN/mm and 300KN/mm. The maximum of 87.8 KN/mm obtained for the case of treated granular material (Tab 4) is outside of that range. In this case, it is necessary to put a material with greater stiffness than MGT next

 A direct transition from QS2 or QS3 material to the structure is not recommended. At best, the stiffness is 38.43 KN/mm when the embankment material is QS2 and 74.027 KN/mm if it is QS3 (see Tab 4), as compared to200-300 KN/mm of vertical stiffness on

 It is sometimes necessary to build the embankment adjacent to the abutment before building the structure. For example, this occurs when the original ground adjacent to the abutment is preloaded, and the load is removed immediately before building the transition. In that case, a slope of type PA (right column) is used instead of a slope of type PB (left column) in the transition from embankment material QS2 to QS3. In this research, a suitable value is obtained for the slope of the transition for each type (PA, PB). For that reason, it is necessary to distinguish between both slope types when considering whether a better approach would be to build the embankment before or

In this way, based on these analyses, this study can make some recommendations about construction designs. Moreover, this study has proposed some ideas relating to the geometric designs of the different materials and has classified the designs according to the original ground and according to when the adjacent embankment is built, either before or

granulartreated material

to the abutment.

the abutment.

after fabricating the structure.

after the construction of the structure (Fig 13).


Table 7. Settlements of rail for the different load steps. Case study: original ground QS1

LOADED SLEEPER 5 **-0.0083** -0.0077 -0.0069 -0.0063 LOADED SLEEPER 6 -0.0104 **-0.0106** -0.0100 -0.0091 LOADED SLEEPER 7 -0.0113 -0.0117 **-0.0118** -0.0112 LOADED SLEEPER 8 -0.0117 -0.0120 -0.0123 **-0.0125** 

LOADED SLEEPER 5 **-0.0050** -0.0045 -0.0038 -0.0032 LOADED SLEEPER 6 -0.0054 **-0.0057** -0.0052 -0.0044 LOADED SLEEPER 7 -0.0051 -0.0057 **-0.0060** -0.0055 LOADED SLEEPER 8 -0.0049 -0.0054 -0.0059 **-0.0062** 

LOADED SLEEPER 5 **-0.0086** -0.0081 -0.0074 -0.0069 LOADED SLEEPER 6 -0.0111 **-0.0114** -0.0109 -0.0101 LOADED SLEEPER 7 -0.0121 -0.0126 **-0.0129** -0.0124 LOADED SLEEPER 8 -0.0127 -0.0131 -0.0136 **-0.0139** 

LOADED SLEEPER 5 **-0.0067** -0.0062 -0.0055 -0.0049 LOADED SLEEPER 6 -0.0079 **-0.0083** -0.0078 -0.0071 LOADED SLEEPER 7 -0.0083 -0.0089 **-0.0092** -0.0087 LOADED SLEEPER 8 -0.0085 -0.0090 -0.0096 **-0.0099** 

LOADED SLEEPER 5 **-0.0061** -0.0056 -0.0048 -0.0043 LOADED SLEEPER 6 -0.0072 **-0.0074** -0.0069 -0.0062 LOADED SLEEPER 7 -0.0074 -0.0079 **-0.0082** -0.0077 LOADED SLEEPER 8 -0.0076 -0.0080 -0.0084 **-0.0087** 

LOADED SLEEPER 5 **-0.0032** -0.0027 -0.0020 -0.0015 LOADED SLEEPER 6 -0.0030 **-0.0032** -0.0027 -0.0020 LOADED SLEEPER 7 -0.0026 -0.0029 **-0.0031** -0.0026 LOADED SLEEPER 8 -0.0022 -0.0025 -0.0028 **-0.0030** 

LOADED SLEEPER 5 **-0.0071** -0.0066 -0.0059 -0.0053 LOADED SLEEPER 6 -0.0086 **-0.0089** -0.0084 -0.0077 LOADED SLEEPER 7 -0.0091 -0.0096 **-0.0099** -0.0094 LOADED SLEEPER 8 -0.0094 -0.0098 -0.0103 **-0.0106** 

LOADED SLEEPER 5 **-0.0043** -0.0038 -0.0031 -0.0025 LOADED SLEEPER 6 -0.0044 **-0.0047** -0.0042 -0.0034 LOADED SLEEPER 7 -0.0040 -0.0045 **-0.0048** -0.0043 LOADED SLEEPER 8 -0.0036 -0.0040 -0.0045 **-0.0048** 

LOADED SLEEPER 5 **-0.0029** -0.0025 -0.0020 -0.0016 LOADED SLEEPER 6 -0.0028 **-0.0031** -0.0027 -0.0022 LOADED SLEEPER 7 -0.0024 -0.0029 **-0.0032** -0.0028 LOADED SLEEPER 8 -0.0021 -0.0025 -0.0029 **-0.0032** 

LOADED SLEEPER 5 **-0.0017** -0.0014 -0.0010 -0.0007 LOADED SLEEPER 6 -0.0015 **-0.0017** -0.0014 -0.0010 LOADED SLEEPER 7 -0.0011 -0.0015 **-0.0017** -0.0014 LOADED SLEEPER 8 -0.0008 -0.0011 -0.0015 **-0.0017** 

LOADED SLEEPER 5 **-0.0032** -0.0028 -0.0022 -0.0018 LOADED SLEEPER 6 -0.0031 **-0.0035** -0.0031 -0.0025 LOADED SLEEPER 7 -0.0028 -0.0033 **-0.0036** -0.0033 LOADED SLEEPER 8 -0.0025 -0.0029 -0.0034 **-0.0037** 

LOADED SLEEPER 5 **-0.0019** -0.0016 -0.0012 -0.0009 LOADED SLEEPER 6 -0.0017 **-0.0019** -0.0016 -0.0012 LOADED SLEEPER 7 -0.0013 -0.0017 **-0.0019** -0.0016 LOADED SLEEPER 8 -0.0010 -0.0013 -0.0016 **-0.0019**  Table 7. Settlements of rail for the different load steps. Case study: original ground QS1

**H7PA11QS2QS3** 

**H7PB11QS2QS3** 

**H7PA31QS2QS3** 

**H7PB31QS2QS3** 

**H7PA11QS2MGT** 

**H7PB11QS2MGT** 

**H7PA31QS2MGT** 

**H7PB31QS2MGT** 

**H7PA11QS3MGT** 

**H7PB11QS3MGT** 

**H7PA31QS3MGT** 

**H7PB31QS3MGT** 

**SLEEPER 5 SLEEPER 6 SLEEPER 7 SLEEPER 8** 

Fig. 12. Analysis of the stiffness variations assuming material transition from type QS2 to granulartreated material


In this way, based on these analyses, this study can make some recommendations about construction designs. Moreover, this study has proposed some ideas relating to the geometric designs of the different materials and has classified the designs according to the original ground and according to when the adjacent embankment is built, either before or after the construction of the structure (Fig 13).

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 373

 An abrupt increase in the stiffness takes place when a granular material treated with cement (MGT at 3% by weight) is used near the abutment. This problem remains unresolved, but future solutions should focus on improving the modulus of elasticity of the material without producing excessive stiffness increases at the extremes of the

The application of all of those conclusions leads to a succession of recommendations for the most suitable building designs. When developing such designs, those factors which have an influence on the transition behavior (original ground, transition materials, and slope type)

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in a reduced scale model on the track sinking/downfall/collapse in a section of a bridge/embankment transition ). *ETR (Spanish translation from the original in* 

la nivelación longitudinal: una aproximación al problema. *Revista de Obras Públicas,* 

de elementos finitos a la ingeniería ferroviaria. *Revista de Ingeniería Civi* (118), 71-82.

Recherches et d'Essais del'Union Internationale des Chemins de Fer.

*no. 27. Comportement des structures d'assise de la voiesous charges répétées.* Office de

transition from the material of type QS3 to the treated material.

Russian, by Fundación de los Ferrocarriles Españoles).

Esveld, C. (2001). *Modern railway track.* The Netherlands: MRTProductions.

design. *Journal of Rail and Rapid Transit , 223*, 331-342.

structure transitions. *Congress on Railway Engineering.* London.

*Numerical simulation of train-track dynamics.*

*Structure transitions.*

*German)* .

, 719-735.

*Transp*, (págs. 68-73).

método de elementos finitos. *AIT* (15).

*Revista de Obras Públicas* , 222-232.

must be considered.

**8. References** 

Fig. 13. Proposed design schemes

### **7. Conclusions**

The designs currently used in embankment–structure transitions lead to zones that suffer significant deterioration. In addition, the various European railway systems have adopted many different design specifications when constructing these zones.

Increased railway speeds enhance the deterioration problems in the embankment–structure transitions, which has important implications for operating and maintenance costs, as well as for passenger safety and comfort.

From the numerical analysis carried out in this study, the following conclusions are drawn:


 An abrupt increase in the stiffness takes place when a granular material treated with cement (MGT at 3% by weight) is used near the abutment. This problem remains unresolved, but future solutions should focus on improving the modulus of elasticity of the material without producing excessive stiffness increases at the extremes of the transition from the material of type QS3 to the treated material.

The application of all of those conclusions leads to a succession of recommendations for the most suitable building designs. When developing such designs, those factors which have an influence on the transition behavior (original ground, transition materials, and slope type) must be considered.

### **8. References**

372 Infrastructure Design, Signalling and Security in Railway

The designs currently used in embankment–structure transitions lead to zones that suffer significant deterioration. In addition, the various European railway systems have adopted

Increased railway speeds enhance the deterioration problems in the embankment–structure transitions, which has important implications for operating and maintenance costs, as well

From the numerical analysis carried out in this study, the following conclusions are drawn: The embankment must not be built on excessively compressible material, as shown for material of type QS1 on original ground. Such material must be replaced with another material or treated to obtain a modulus of elasticity corresponding to that of a material

 Transitions from material of type QS2 to material of type MGT should be carried out when there the original ground is of type QS3, or when the buried structure is treated. For each disposition type (PA, PB), there exists an optimal value for the slope. This value is not always the lowest one (3:1), as expected. The most suitable slope value (3:1 or 1:1) depends on the of original ground material, on the disposition type, and on the

many different design specifications when constructing these zones.

Fig. 13. Proposed design schemes

as for passenger safety and comfort.

materials used in the transition.

of at least type QS2.

**7. Conclusions** 


**15** 

*1Botswana 2Nigeria* 

**of Earth Embankments** 

*1University of Botswana, Gaborone 2University of Ibadan, Ibadan* 

**Influence of the Phreatic Level on the Stability** 

Slopes in soils and rocks are common place in nature and man-made structures partly due to the fact that they are generally less expensive than constructing walls. However slope stability problems may arise due to the construction of artificial slopes in cuttings and embankments for roads and railways, or the construction of earth dams and water retaining embankments. Other reasons may include the study of the process of large scale natural slips or the application of remedial measures when such slips have taken place (Capper & Cassie, 1971). Existing slopes that have been stable may experience significant movement due to natural or man-made conditions. Such changes can result from the occurrence of earthquake, subsidence, erosion, the progression of tension or shrinkage cracks coupled with water ingress, changes in groundwater elevation or changes in the slope's subsurface flow which induces new seepage forces (McCarthy, 1998). Further causes may include the removal of earth below the toe of a slope or increased loading close to the crest of the slope. Slips may occur suddenly or gradually, commencing with a crack at the top of an earth embankment and slight upheaval near to the bottom and subsequently developing to a complete slip. All the foregoing actions make slip surface stability analysis of earth

Several notable methods of analyzing slip surface stability have been developed over the years. Among the earliest was one that had its slip circle passing through soil materials whose shear strength is based upon internal friction and effective stresses (Fellenius, 1927). In this method an area of unit thickness of the volume tending to slide is divided into vertical strips and it is assumed that for each slice the resultant of the interslice forces is zero. A more significant and certainly more widely used approach utilizing the method of slices assumed a circular failure surface and fulfilled moment equilibrium but did not fully satisfy force equilibrium (Bishop, 1955). Yet another method considered a cylindrical slip surface and assumed that the forces on the sides of the slices are parallel (Spencer, 1967). A generalized approach (Morgenstern & Price, 1965) was developed in which all boundary and equilibrium equations are satisfied and the failure surface could assume any shape. The method involved solving systems of singular simultaneous equations and was unduly long in obtaining approximate answers despite the several assumptions made. An alternative generalized procedure (Bell, 1968) has been advanced

**1. Introduction** 

embankments complex and very difficult.

Shodolapo Oluyemi Franklin1 and Gbenga Matthew Ayininuola2


## **Influence of the Phreatic Level on the Stability of Earth Embankments**

Shodolapo Oluyemi Franklin1 and Gbenga Matthew Ayininuola2 *1University of Botswana, Gaborone* 

*2University of Ibadan, Ibadan 1Botswana 2Nigeria* 

### **1. Introduction**

374 Infrastructure Design, Signalling and Security in Railway

Oliver, X., & Arlet, C. (2000). *Mecánica de medios continuos para ingenieros.* Barcelona:

Profillidis, V. (1983). *La voie et sa fondation modelisation mathematique.* París: Doctoral Thesis,

Sahu, J., Rao, & Yudhbir. (1999). Parametric study of resilient response of tracks with a sub-

Sauvage, G., & Larible, G. (1982). La modélisation par éléments finis des couches d`assise de

Teixeira, P. F. (2003). *Contribución a la reducción de los costes de mantenimiento de vías de alta* 

*velocidad mediante la optimización de su rigidez vertical.* Doctoral Thesis, Polytechnic

Ediciones UPC.

University of Cataluña.

École Nationale des Ponts et Chaussées.

Prud`Homme, M. A. (1970). La voie. *Revue Générales des Chemins de Fer* .

ballast layer. *Canadian Geotechnical Journal , 36*, 1137-1150.

la voie ferrée. *Revue Générale des Chemins de Fer* , 475-484.

Slopes in soils and rocks are common place in nature and man-made structures partly due to the fact that they are generally less expensive than constructing walls. However slope stability problems may arise due to the construction of artificial slopes in cuttings and embankments for roads and railways, or the construction of earth dams and water retaining embankments. Other reasons may include the study of the process of large scale natural slips or the application of remedial measures when such slips have taken place (Capper & Cassie, 1971). Existing slopes that have been stable may experience significant movement due to natural or man-made conditions. Such changes can result from the occurrence of earthquake, subsidence, erosion, the progression of tension or shrinkage cracks coupled with water ingress, changes in groundwater elevation or changes in the slope's subsurface flow which induces new seepage forces (McCarthy, 1998). Further causes may include the removal of earth below the toe of a slope or increased loading close to the crest of the slope. Slips may occur suddenly or gradually, commencing with a crack at the top of an earth embankment and slight upheaval near to the bottom and subsequently developing to a complete slip. All the foregoing actions make slip surface stability analysis of earth embankments complex and very difficult.

Several notable methods of analyzing slip surface stability have been developed over the years. Among the earliest was one that had its slip circle passing through soil materials whose shear strength is based upon internal friction and effective stresses (Fellenius, 1927). In this method an area of unit thickness of the volume tending to slide is divided into vertical strips and it is assumed that for each slice the resultant of the interslice forces is zero. A more significant and certainly more widely used approach utilizing the method of slices assumed a circular failure surface and fulfilled moment equilibrium but did not fully satisfy force equilibrium (Bishop, 1955). Yet another method considered a cylindrical slip surface and assumed that the forces on the sides of the slices are parallel (Spencer, 1967). A generalized approach (Morgenstern & Price, 1965) was developed in which all boundary and equilibrium equations are satisfied and the failure surface could assume any shape. The method involved solving systems of singular simultaneous equations and was unduly long in obtaining approximate answers despite the several assumptions made. An alternative generalized procedure (Bell, 1968) has been advanced

Influence of the Phreatic Level on the Stability of Earth Embankments 377

slice, then the equilibrium of the body (soil skeleton) and water (hydrostatic) as well as

In order to properly assess the effect of water pressure forces on the stability of earth embankments, two algorithms which utilize both the limit equilibrium approach and method of slices are presented. The algorithms satisfy all the conditions stated above and in addition, the stability problem is treated as a 2-dimensional one in order to arrive at the final solution more quickly. A comprehensive description of the two algorithms and their application to a number of embankments reported in the literature is given elsewhere (Ayininuola & Franklin, 2008). Only the more important features will be considered here. The basic assumptions adopted for the present purpose are as follows: (a) The line of thrust on a slice and the pore water pressure forces are within the slice, preferably at one-third distance from the base or mid-point of the slice vertical sides (b) Factor of safety is defined in terms of the average shear stress developed along the potential failure surface and the average shear strength within the soil (c) Failure

occurs simultaneously throughout the soil mass within the assumed rupture boundary.

Consider an elemental slice in Fig. 1. Due to the many unknown forces acting on the nth slice, the free body diagram in Fig. 2(a) is further divided into two separate bodies (Figs. 2(b) and 2(c)) under the basic requirements for the analysis of earth embankment stability. Since Fig. 2(a) is in equilibrium with all the forces acting on it, consequently Figs. 2(b) and

On examining Fig. 2(a) critically, it is observed that of the twelve forces acting on the slice, only four have known magnitudes. This makes the analysis statically indeterminate of order eight. For the remaining eight forces to be determined there is need to establish logical relationships between the forces. With reference to Fig. 2(c) and letting ∆Pw(n) be the

The hydrostatic force Un is obtained by measuring the free standing height of water in an installed piezometric tube at the slice base. If the piezometric height at the base is Hw(n) then

> . . *U H n w w n*

where g is the acceleration due to gravity. Alternatively, since the forces acting in Fig. 2(a) are in equilibrium, it implies that the forces in Figs. 2(b) and 2(c) are also in equilibrium. Hence the hydrostatic force Un at the base of the slice can be determined from the weight of water in the slice. From force equilibrium in the x and y directions the following expressions are obtained:

sec *U W n n w n*

*n n* sin *w n P U*

where Ww(n) is the weight of water in the nth slice and αn is angle at the base of the slice.

Substituting the value of Un in equation (3) into equation (4) yields

*wn wn wn* <sup>1</sup> *P PP* (1)

*g* (2)

(4)

(3)

elemental increment of water pressure forces Pw(n+1) and Pw(n) across the slice, then

normal and shear forces is maintained.

**2.1 Formulation A** 

2(c) are in equilibrium as well.

which satisfies all conditions of equilibrium and assumed any failure surface. Here a solution is obtained by assuming a distribution of normal stress along the rupture surface. An approach involving the determination of the critical earthquake acceleration required to produce a condition of limiting equilibrium has been developed (Sarma, 1979). Also stability charts have been proposed which were partly based on the work of previous investigators and are applicable to a wide range of practical conditions (Cousins, 1978).

In practically all the afore-mentioned methods, the mass of soil assumed to be associated with the slope slide is divided into vertical slices. A slice is selected, the free body diagram of the forces acting on the slice is drawn and subsequently, based on limit equilibrium methods, an expression is derived for determining the factor of safety of the slope. The stability problem is dealt with by assuming that the tangential interslice forces are equal and opposite (Bishop, 1955). An iterative method for analyzing the stability problem in non-circular slip failures (Janbu, 1973) utilized a full rigorous algorithm and assumed a known line of thrust for the interslice horizontal forces. The method is best suited for computer solution. Similarly analytical solutions have been presented (Morgenstern & Price, 1965) which incorporate all interslice forces but are dependent on several assumptions and are quite lengthy.

### **1.1 Role of water pressure forces**

The action of water is highly significant in slope movement. In clay and shale, softening by rain may lead to slip of a whole layer of material as a mud run. In addition water percolating into fissured clay may result in progressive deterioration and weakening that eventually results in reduction of shear strength so that a rotational or translational slip occurs. Consequently, for the various methods of slices highlighted above, it is important to stress the need to consider the water pressure forces acting not only at the interslice but also at the slice base, for such neglect may produce erroneous results.

More accurate but lower factors of safety are claimed for methods which account for the variation in seepage forces acting on and in the slice (King, 1989). Nevertheless such refinements depend on good estimates of water pressure. The factors of safety obtained for a given slope using different methods of slices are sensitive to the assumptions made in deriving them (Morrison & Greenwood, 1989). Furthermore the interslice forces play an important role in the resulting factors of safety. Hence the present study focuses on the effects of omitting the interslice pore water pressure forces on the overall stability of earth embankments and also endeavours to reduce the complexity features common to the more recent methods of slices outlined earlier.

### **2. Methodology**

In general, any proposed method to evaluate the factor of safety must satisfy several requirements such as fulfilling limit equilibrium laws, account for all forces acting on the slice, adopt few assumptions, which should be easily comprehensible, be applicable to nonhomogeneous soils, account for the water pressure distribution at the base of the slice as well as at the interslice, and treat stability problems in terms of both effective and total stresses. Furthermore, it is immaterial whether the horizontal interslice forces are considered as total or effective together with the force due to water pressure. When the force due to water pressure is correctly accounted for at the base as well as on the vertical sides of the slice, then the equilibrium of the body (soil skeleton) and water (hydrostatic) as well as normal and shear forces is maintained.

In order to properly assess the effect of water pressure forces on the stability of earth embankments, two algorithms which utilize both the limit equilibrium approach and method of slices are presented. The algorithms satisfy all the conditions stated above and in addition, the stability problem is treated as a 2-dimensional one in order to arrive at the final solution more quickly. A comprehensive description of the two algorithms and their application to a number of embankments reported in the literature is given elsewhere (Ayininuola & Franklin, 2008). Only the more important features will be considered here. The basic assumptions adopted for the present purpose are as follows: (a) The line of thrust on a slice and the pore water pressure forces are within the slice, preferably at one-third distance from the base or mid-point of the slice vertical sides (b) Factor of safety is defined in terms of the average shear stress developed along the potential failure surface and the average shear strength within the soil (c) Failure occurs simultaneously throughout the soil mass within the assumed rupture boundary.

#### **2.1 Formulation A**

376 Infrastructure Design, Signalling and Security in Railway

which satisfies all conditions of equilibrium and assumed any failure surface. Here a solution is obtained by assuming a distribution of normal stress along the rupture surface. An approach involving the determination of the critical earthquake acceleration required to produce a condition of limiting equilibrium has been developed (Sarma, 1979). Also stability charts have been proposed which were partly based on the work of previous investigators and are

In practically all the afore-mentioned methods, the mass of soil assumed to be associated with the slope slide is divided into vertical slices. A slice is selected, the free body diagram of the forces acting on the slice is drawn and subsequently, based on limit equilibrium methods, an expression is derived for determining the factor of safety of the slope. The stability problem is dealt with by assuming that the tangential interslice forces are equal and opposite (Bishop, 1955). An iterative method for analyzing the stability problem in non-circular slip failures (Janbu, 1973) utilized a full rigorous algorithm and assumed a known line of thrust for the interslice horizontal forces. The method is best suited for computer solution. Similarly analytical solutions have been presented (Morgenstern & Price, 1965) which incorporate all

The action of water is highly significant in slope movement. In clay and shale, softening by rain may lead to slip of a whole layer of material as a mud run. In addition water percolating into fissured clay may result in progressive deterioration and weakening that eventually results in reduction of shear strength so that a rotational or translational slip occurs. Consequently, for the various methods of slices highlighted above, it is important to stress the need to consider the water pressure forces acting not only at the interslice but also

More accurate but lower factors of safety are claimed for methods which account for the variation in seepage forces acting on and in the slice (King, 1989). Nevertheless such refinements depend on good estimates of water pressure. The factors of safety obtained for a given slope using different methods of slices are sensitive to the assumptions made in deriving them (Morrison & Greenwood, 1989). Furthermore the interslice forces play an important role in the resulting factors of safety. Hence the present study focuses on the effects of omitting the interslice pore water pressure forces on the overall stability of earth embankments and also endeavours to reduce the complexity features common to the more

In general, any proposed method to evaluate the factor of safety must satisfy several requirements such as fulfilling limit equilibrium laws, account for all forces acting on the slice, adopt few assumptions, which should be easily comprehensible, be applicable to nonhomogeneous soils, account for the water pressure distribution at the base of the slice as well as at the interslice, and treat stability problems in terms of both effective and total stresses. Furthermore, it is immaterial whether the horizontal interslice forces are considered as total or effective together with the force due to water pressure. When the force due to water pressure is correctly accounted for at the base as well as on the vertical sides of the

interslice forces but are dependent on several assumptions and are quite lengthy.

applicable to a wide range of practical conditions (Cousins, 1978).

at the slice base, for such neglect may produce erroneous results.

**1.1 Role of water pressure forces** 

recent methods of slices outlined earlier.

**2. Methodology** 

Consider an elemental slice in Fig. 1. Due to the many unknown forces acting on the nth slice, the free body diagram in Fig. 2(a) is further divided into two separate bodies (Figs. 2(b) and 2(c)) under the basic requirements for the analysis of earth embankment stability. Since Fig. 2(a) is in equilibrium with all the forces acting on it, consequently Figs. 2(b) and 2(c) are in equilibrium as well.

On examining Fig. 2(a) critically, it is observed that of the twelve forces acting on the slice, only four have known magnitudes. This makes the analysis statically indeterminate of order eight. For the remaining eight forces to be determined there is need to establish logical relationships between the forces. With reference to Fig. 2(c) and letting ∆Pw(n) be the elemental increment of water pressure forces Pw(n+1) and Pw(n) across the slice, then

$$P\_{w(n+1)} - P\_{w(n)} = \Delta P\_{w(n)} \tag{1}$$

The hydrostatic force Un is obtained by measuring the free standing height of water in an installed piezometric tube at the slice base. If the piezometric height at the base is Hw(n) then

$$\mathcal{U}\_n = \mathcal{Y}\_w.\mathcal{H}\_{w(n)}.\mathcal{g}\tag{2}$$

where g is the acceleration due to gravity. Alternatively, since the forces acting in Fig. 2(a) are in equilibrium, it implies that the forces in Figs. 2(b) and 2(c) are also in equilibrium. Hence the hydrostatic force Un at the base of the slice can be determined from the weight of water in the slice. From force equilibrium in the x and y directions the following expressions are obtained:

$$\mathcal{U}\_n = \mathcal{V}\_{w(n)} \sec \alpha\_n \tag{3}$$

$$
\Delta P\_{w(n)} = -\mathcal{U}\_n \sin \alpha\_n \tag{4}
$$

where Ww(n) is the weight of water in the nth slice and αn is angle at the base of the slice. Substituting the value of Un in equation (3) into equation (4) yields

Influence of the Phreatic Level on the Stability of Earth Embankments 379

Fig. 2. Forces acting on an nth slice

Fig. 1. Cross-section of an earth embankment made of non-homogeneous strata or soil layers

Fig. 1. Cross-section of an earth embankment made of non-homogeneous strata or soil layers

Fig. 2. Forces acting on an nth slice

Influence of the Phreatic Level on the Stability of Earth Embankments 381

*EZ b n n n nn* 3 2 tan . 2 tan 3

Equations (10), (12) and (14) can now be assembled together as a set of simultaneous

cos sin cos cos tan sin cos sin sin cos sin

( ) ( )

*n nn*

and cos tan sin cos sin tan 3 *w n n n n n nn n w n <sup>n</sup> w n F W*

tan ( 3)

. *KD F* (17)

*K D R E X*

 

In the above expressions the matrices D and F represent the nodal unknown forces and the

Equation (17) above is for the nth slice, and when such sets of equations are assembled for

where Kg is the global stiffness matrix, Dg is the global forces matrix and Fg is the global applied forces matrix. The simultaneous equation (18) can be solved for various values of Rn, ∆En and ∆Xn using the Gaussian elimination, Jacobi or Gauss-Siedel iterative techniques. The Gaussian elimination method is, relatively speaking, the simplest and easiest of the three procedures to implement. Once the values of Rn are obtained, the values of Nn and Tn

*WW W H*

(cos tan sin ) cos sin

 

*wn n n n n n n n wn n wn*

*R E XW W R X EW EZ b Xb W H*

 

cos sin cos sin cos sin 0 { 3 ( 2)tan } 2

 

*W W W W H*

 

0 - 3 2 tan 2

*nn n*

*Zb b*

cos sin - cos

where sin - cos -sin ,

 

*n nnn n n w n n nn n n n n n n n nn n n n n nn w n n w n*

*nn n n n nn n*

*Zb b X*

3 2 tan . 2 tan 3

 *Xb W H w n <sup>n</sup> w n* (14)

 

> 

 

> 

> > *R E*

 

(16)

<sup>1</sup>

  1

(15)

 

*n nn n*

*n n n nn n*

 

> 

. *KD F gg g* (18)

equations in the following form

In compact form this can be written as

can also be found using equations (7) and (8).

nodal applied forces respectively.

the whole rupture mass this yields

In matrix format the simultaneous equation (15) becomes

( )

$$
\Delta P\_{w(n)} = -W\_{w(n)} \tan \alpha\_n \tag{5}
$$

From Fig. 2(b) let ∆En and ∆Xn be the elemental increments of horizontal interslice lateral thrusts En, En+1 and vertical interslice shear forces Xn, Xn+1 respectively across the slice, that is

$$
\Delta E\_n = E\_n - E\_{n+1} \quad \Delta X\_n = X\_n - X\_{n+1} \tag{6}
$$

In Fig. 2(a) since the total normal force Nn and shear force Tn acting at the base of the slice are orthogonal, they have the same resultant Rn. In order to reduce the number of unknowns at the base of the slice the forces Tn and Nn are expressed in terms of Rn as follows:

$$T\_n = R\_n \sin \alpha\_{n'} \; N\_n = R\_n \cos \alpha\_n \tag{7}$$

It should be noted at this stage that the total and effective normal forces, Nn and Nn' respectively, are related to Un as follows:

$$N\_n{}^{\prime} = N\_n - \mathcal{U}\_n \tag{8}$$

Limit equilibrium laws can be applied to the slice in Fig. 2(a). Firstly resolving the forces acting on the slice in the Nn-direction yields

$$N\_n - W\_n \cos a\_n - \Delta X\_n \cos a\_n + \Delta E\_n \sin a\_n + \Delta P\_{w(n)} \sin a\_n - W\_{w(n)} \cos a\_n = 0 \tag{9}$$

Substituting the values of ∆Pw(n) and Nn from equations (5) and (7) respectively into equation (9) and re-arranging yields

$$\left(R\_n \cos a\_n + \Delta E\_n \sin a\_n - \Delta X\_n \cos a\_n = W\_{w(n)} \left(\cos a\_n + \tan a\_n \sin a\_n\right) + W\_n \cos a\_n \tag{10}$$

Also, resolving the forces acting on the slice in the Tn-direction yields

$$\left(T\_n - \mathcal{W}\_n \sin \alpha\_n - \Delta X\_n \sin \alpha\_n - \Delta E\_n \cos \alpha\_n - \mathcal{W}\_{w(n)} \sin \alpha\_n - \Delta P\_{w(n)} \cos \alpha\_n = 0\tag{11}$$

Substituting the values of ∆Pw(n) and Tn from equations (5) and (7) into equation (11) and simplifying and re-arranging results in

$$R\_n \sin \alpha\_n - \Delta X\_n \sin \alpha\_n - \Delta E\_n \cos \alpha\_n = \mathcal{W}\_n \sin \alpha\_n \tag{12}$$

Examination of equations (10) and (12) reveals that there are three unknowns in the two equations which render them indeterminate; in order to solve for these unknowns it is necessary at this stage to introduce an equilibrium equation based on moments. From Fig. 2(b), taking moments of the resultants of the interslice forces and other forces about the midpoint of the slice base width gives

$$
\Delta X\_n.b\_n\left\{2 - \Delta E\_n\left(Z\left\{3 + \left(b\_n/2\right)\tan\alpha\_n\right\} - \Delta P\_{w(n)}\left(H\_{w(n)}\right)\right\}\right\} = 0\tag{13}
$$

where Z is the elevation of one side of the slice, or more correctly, the greater of Zn and Zn+1, and Hw(n) is the height of water in the nth slice. Substituting for the value of ∆Pw(n) from equation (5) into equation (13) and re-arranging results in

From Fig. 2(b) let ∆En and ∆Xn be the elemental increments of horizontal interslice lateral thrusts En, En+1 and vertical interslice shear forces Xn, Xn+1 respectively across the slice, that is

In Fig. 2(a) since the total normal force Nn and shear force Tn acting at the base of the slice are orthogonal, they have the same resultant Rn. In order to reduce the number of unknowns

It should be noted at this stage that the total and effective normal forces, Nn and Nn'

Limit equilibrium laws can be applied to the slice in Fig. 2(a). Firstly resolving the forces

cos cos sin sin cos 0 *NW X E P W nn n n n n n*

Substituting the values of ∆Pw(n) and Nn from equations (5) and (7) respectively into

sin sin cos sin cos 0 *TW X E W P nn n n n n n*

Substituting the values of ∆Pw(n) and Tn from equations (5) and (7) into equation (11) and

*R X EW n n n n n nn n* sin sin cos sin

Examination of equations (10) and (12) reveals that there are three unknowns in the two equations which render them indeterminate; in order to solve for these unknowns it is necessary at this stage to introduce an equilibrium equation based on moments. From Fig. 2(b), taking moments of the resultants of the interslice forces and other forces about the mid-

where Z is the elevation of one side of the slice, or more correctly, the greater of Zn and Zn+1, and Hw(n) is the height of water in the nth slice. Substituting for the value of ∆Pw(n) from

 

 

, cos *N R nn n*

at the base of the slice the forces Tn and Nn are expressed in terms of Rn as follows:

*T R nn n* sin

Also, resolving the forces acting on the slice in the Tn-direction yields

respectively, are related to Un as follows:

acting on the slice in the Nn-direction yields

equation (9) and re-arranging yields

simplifying and re-arranging results in

point of the slice base width gives

*R E XW n nnn n n* cos sin cos

 

*Xb E Z b nn n n n* . 2 3 2 tan

equation (5) into equation (13) and re-arranging results in

*EEE nnn* <sup>1</sup> , *XXX nnn* 1 (6)

*N NU n nn* (8)

 

> 

 

*w n* cos tan sin cos *n nn n n W* (10)

 

*<sup>n</sup>* (5)

(7)

 *w n <sup>n</sup> w n <sup>n</sup>* (9)

 *w n <sup>n</sup> w n <sup>n</sup>* (11)

*P H wn wn* 3 0 (13)

 

(12)

*P W wn wn* tan

$$-\Delta E\_n \left\{ Z/\mathfrak{Z} + \left( b\_n/2 \right) \tan \alpha\_n \right\} + \Delta X\_n, b\_n/2 = -\mathcal{W}\_{w(n)} \tan \alpha\_n \left( H\_{w(n)} / \mathfrak{Z} \right) \tag{14}$$

Equations (10), (12) and (14) can now be assembled together as a set of simultaneous equations in the following form

$$R\_n \cos \alpha\_n + \Delta E\_n \sin \alpha\_n - \Delta X\_n \cos \alpha\_n = \mathcal{W}\_{w(n)} \left(\cos \alpha\_n + \tan \alpha\_n \sin \alpha\_n \right) + \mathcal{W}\_n \cos \alpha\_n \bigg| \tag{15}$$

$$R\_n \sin \alpha\_n - \Delta X\_n \sin \alpha\_n - \Delta E\_n \cos \alpha\_n = \mathcal{W}\_n \sin \alpha\_n$$

$$-\Delta E\_n \left( Z/3 + \left( b\_n/2 \right) \tan \alpha\_n \right) + \Delta X\_n, b\_n/2 = -\mathcal{W}\_{w(n)} \tan \alpha\_n \left( H\_{w(n)} / 3 \right)$$

In matrix format the simultaneous equation (15) becomes

$$\begin{bmatrix} \cos \alpha\_n & \sin \alpha\_n & -\cos \alpha\_n \\ \sin \alpha\_n & -\cos \alpha\_n & -\sin \alpha\_n \\ 0 & -\{\mathbf{Z}/3 + (b\_n/2)\tan \alpha\_n\} & b\_n/2 \end{bmatrix} \begin{bmatrix} R\_n \\ \Delta E\_n \\ \Delta X\_n \\ \Delta X\_n \end{bmatrix}$$

$$= \begin{bmatrix} \mathcal{W}\_{w(n)}(\cos \alpha\_n + \tan \alpha\_n \sin \alpha\_n) + \mathcal{W}\_n \cos \alpha\_n \\ \mathcal{W}\_n \sin \alpha\_n \\ -\mathcal{W}\_{w(n)} \tan \alpha\_n (H\_{w(n)}/3) \end{bmatrix} \tag{16}$$

In compact form this can be written as

$$K.D = F \tag{17}$$

$$\begin{array}{c|cccc} & \cos a\_n & \sin a\_n & \cdot \cos a\_n \\ \text{where} & \text{\$K=\left|} \sin a\_n & \cdot \cos a\_n & \cdot \sin a\_n \\ & \text{\$0\$} & \cdot \left\{ \text{\$Z/3+\left(b\_n/2\right)\tan a\_n} \right\} & b\_n/2 \\ \end{array} \\ & \begin{array}{c|cccc} & \text{\$\sim\$B\_n\$} & \text{\$\sim\$B\_n\$} & \text{\$\sim\$X\_n\$} \\ \end{array} \\ \end{array}$$

$$\text{and} \quad F = \left[ \mathcal{W}\_{w(n)} \left( \cos a\_n + \tan a\_n \sin a\_n \right) + \mathcal{W}\_n \cos a\_n \quad \mathcal{W}\_n \sin a\_n \quad - \mathcal{W}\_{w(n)} \tan a\_n \left( H\_{w(n)} / 3 \right) \right]^{-1}$$

In the above expressions the matrices D and F represent the nodal unknown forces and the nodal applied forces respectively.

Equation (17) above is for the nth slice, and when such sets of equations are assembled for the whole rupture mass this yields

$$K\_{\mathcal{K}}.D\_{\mathcal{K}} = F\_{\mathcal{K}} \tag{18}$$

where Kg is the global stiffness matrix, Dg is the global forces matrix and Fg is the global applied forces matrix. The simultaneous equation (18) can be solved for various values of Rn, ∆En and ∆Xn using the Gaussian elimination, Jacobi or Gauss-Siedel iterative techniques. The Gaussian elimination method is, relatively speaking, the simplest and easiest of the three procedures to implement. Once the values of Rn are obtained, the values of Nn and Tn can also be found using equations (7) and (8).

Influence of the Phreatic Level on the Stability of Earth Embankments 383

cos sin cos ( )cos sin cos sin ( )sin 0 { 3 ( 2)tan } 2 0

 

Again proceeding along the same lines as the previous formulation, an expression very

*R* 

Although equations (25) and (22) are very similar, the procedures for evaluating the values of Rn in both equations are certainly not the same. Consequently different values of factors of safety will be obtained using both approaches. The methods developed can be used for slip surface stability analysis either manually or with a programmable calculator. However while this may be true for fairly homogeneous slopes, for real or nonhomogeneous soils the computation work is quite daunting for practical design. This is on account of the number of rupture surfaces that may need to be analyzed in order to obtain the most critical rupture surface for design purposes as well as the fact that the global stiffness matrix Kg mentioned earlier may be of the order 60 x 60 or more, depending on the number of slices within the rupture mass. Hence comprehensive computer software was developed involving two minimization computer programmes which can handle problems of up to three soil strata; some details of the programmes are given elsewhere

In order to assess the effect of the pore water pressure forces, the procedures developed in the present study have been applied to a number of earth embankments some of which are reported in the literature. Firstly, the Lodalen Landslide (Sevaldson, 1956) is examined and then, the case of a non-homogeneous earth dam (Sherard et al, 1978) is investigated. Finally the effect of altering the phreatic level on the Okuku dam in South-Western Nigeria

Fig. 3 shows a sectional view of the Lodalen Landslide. A stability analysis of the earth embankment prior to the occurrence of the slide will be carried out. Towards this end the initial rupture surface has been divided into 13 slices. The necessary data have been taken from the initial rupture surface and fed into the computer programme mentioned earlier. A total of 100 rupture surfaces have been considered in the analysis. Details of the computer output are not presented here, but a summary of the main findings are shown in Table 1 and

 

sin *nn n n w n n n*

*n n*

cos sec tan

*n nn n*

*Zb b X*

*cL R W*

*n n n n wn n n n n n n wn n n*

 

  ( ) ( )

> 

(25)

(24)

*R W W E WW*

For the typical nth slice the above equation in matrix format becomes

similar to equation (22) can be obtained as follows:

*s*

*F*

(Ayininuola, 1999).

(Ayininuola & Franklin, 2008) is studied.

these results are discussed at a later stage.

**3.1 Stability analysis of the Lodalen Landslide (Sevaldson, 1956)** 

**3. Results** 

The factor of safety can be defined in terms of the shear strength of the soil and the shear stress developed along the potential failure surface based on the Coulomb-Mohr failure criteria in terms of effective stress as follows:

$$T\_n = \left(c\_n \, ^\prime \Delta L\_n + N\_n \, ^\prime \tan \phi\_n \, ^\prime \right) \Big/ F\_s \tag{19}$$

where Fs is the factor of safety and n' is the angle of shearing resistance with respect to effective stress. Substituting for the values of Tn and Nn' from equations (7) and (8) into equation (19) yields

$$R\_n \sin \alpha\_n = \left[ c\_n' \Delta L\_n + \left( R\_n \cos \alpha\_n - \mathcal{U}\_n \right) \tan \phi\_n' \right] \Big| \mathcal{F}\_s \tag{20}$$

Also substituting the value of Un from equation (3) into equation (20) and then considering the whole of the rupture mass consisting of the set of slices will give

$$\sum R\_n \sin \alpha\_n = \sum \left[ c\_n' \Delta L\_n + \left( R\_n \cos \alpha\_n - \mathcal{W}\_{w(n)} \sec \alpha\_n \right) \tan \phi\_n' \right] \Big| F\_s \tag{21}$$

Making Fs the subject of the expression in equation (21) will yield

$$F\_s = \frac{\sum \left[ c\_n \, ^\prime \Delta L\_n + \left( R\_n \cos \alpha\_n - W\_{w(n)} \sec \alpha\_n \right) \tan \phi\_n^{\prime} \right]}{\sum \left( R\_n \sin \alpha\_n \right)} \tag{22}$$

Equation (22) can be use to analyze stability problems involving both homogeneous and non-homogeneous soils types.

Irrespective of whether the earth embankment is partially or wholly drained, the equation can be applied because during its formulation both states of stress were taken into account.

#### **2.2 Formulation B**

The present study seeks to investigate the effect of hydrostatic pore water pressure forces on the overall stability of earth embankments and as such, in order to establish a basis of comparison with the earlier algorithm presented, an alternative approach is developed. This treats stability problems in terms of effective stresses and assumes that the influence of water pressure forces acting at the interslice can be neglected. The lines of action of Pw(n+1) and Pw(n) are taken to be coincident and also ∆Pw(n) = 0. Proceeding along the same lines as the previous formulation, the following set of simultaneous equations can be arrived at:

$$\begin{aligned} \left(R\_n \cos \alpha\_n + \Delta E\_n \sin \alpha\_n - \Delta X\_n \cos \alpha\_n = \left(\mathcal{W}\_{w(n)} + \mathcal{W}\_n \right) \cos \alpha\_n \right) \\ \left(R\_n \sin \alpha\_n - \Delta X\_n \sin \alpha\_n - \Delta E\_n \cos \alpha\_n = \left(\mathcal{W}\_{w(n)} + \mathcal{W}\_n \right) \sin \alpha\_n \right) \\ -\Delta E\_n \left(Z/3 + \left(b\_n/2\right) \tan \alpha\_n \right) + \Delta X\_n, b\_n/2 = 0 \end{aligned} \tag{23}$$

For the typical nth slice the above equation in matrix format becomes

$$
\begin{bmatrix}
\cos a\_n & \sin a\_n & -\cos a\_n \\
\sin a\_n & -\cos a\_n & -\sin a\_n \\
0 & -\langle \mathbf{Z}/3 + (b\_n/2)\tan a\_n \rangle & b\_n/2
\end{bmatrix}
\begin{bmatrix}
R\_n \\
\Delta E\_n \\
\Delta X\_n
\end{bmatrix} = 
\begin{bmatrix}
(\mathcal{W}\_{w(n)} + \mathcal{W}\_n)\cos a\_n \\
(\mathcal{W}\_{w(n)} + \mathcal{W}\_n)\sin a\_n \\
0
\end{bmatrix}
\tag{24}
$$

Again proceeding along the same lines as the previous formulation, an expression very similar to equation (22) can be obtained as follows:

$$F\_s = \frac{\sum \left[ c\_n \, ^\prime \Delta L\_n + \left( R\_n \cos \alpha\_n - \mathcal{W}\_{w(n)} \sec \alpha\_n \right) \tan \phi\_n^{\prime} \right]}{\sum \left( R\_n \sin \alpha\_n \right)} \tag{25}$$

Although equations (25) and (22) are very similar, the procedures for evaluating the values of Rn in both equations are certainly not the same. Consequently different values of factors of safety will be obtained using both approaches. The methods developed can be used for slip surface stability analysis either manually or with a programmable calculator. However while this may be true for fairly homogeneous slopes, for real or nonhomogeneous soils the computation work is quite daunting for practical design. This is on account of the number of rupture surfaces that may need to be analyzed in order to obtain the most critical rupture surface for design purposes as well as the fact that the global stiffness matrix Kg mentioned earlier may be of the order 60 x 60 or more, depending on the number of slices within the rupture mass. Hence comprehensive computer software was developed involving two minimization computer programmes which can handle problems of up to three soil strata; some details of the programmes are given elsewhere (Ayininuola, 1999).

### **3. Results**

382 Infrastructure Design, Signalling and Security in Railway

The factor of safety can be defined in terms of the shear strength of the soil and the shear stress developed along the potential failure surface based on the Coulomb-Mohr failure

*T cL N F n nn n n s* tan

where Fs is the factor of safety and n' is the angle of shearing resistance with respect to effective stress. Substituting for the values of Tn and Nn' from equations (7) and (8) into

*R cL R U F n n nn n n n n s* sin

Also substituting the value of Un from equation (3) into equation (20) and then considering

 

sin *nn n n w n n n*

*R* 

Equation (22) can be use to analyze stability problems involving both homogeneous and

Irrespective of whether the earth embankment is partially or wholly drained, the equation can be applied because during its formulation both states of stress were taken into

The present study seeks to investigate the effect of hydrostatic pore water pressure forces on the overall stability of earth embankments and as such, in order to establish a basis of comparison with the earlier algorithm presented, an alternative approach is developed. This treats stability problems in terms of effective stresses and assumes that the influence of water pressure forces acting at the interslice can be neglected. The lines of action of Pw(n+1) and Pw(n) are taken to be coincident and also ∆Pw(n) = 0. Proceeding along the same lines as the previous formulation, the following set of simultaneous equations can be

cos sin cos cos

*n nnn n n w n n n*

sin sin cos sin

*n n n nn*

*EZ b X b*

*nn nnn n w n n n*

3 2 tan . 2 0

 

*R E X WW*

*R X E WW*

*n n*

cos sec tan *w n n ns*

*<sup>F</sup>* (21)

cos sec tan

 

 

(23)

(19)

cos tan (20)

 

(22)

criteria in terms of effective stress as follows:

*s*

*F*

non-homogeneous soils types.

account.

arrived at:

**2.2 Formulation B** 

the whole of the rupture mass consisting of the set of slices will give

Making Fs the subject of the expression in equation (21) will yield

*R cL R W n n nn n n* sin

*cL R W*

equation (19) yields

In order to assess the effect of the pore water pressure forces, the procedures developed in the present study have been applied to a number of earth embankments some of which are reported in the literature. Firstly, the Lodalen Landslide (Sevaldson, 1956) is examined and then, the case of a non-homogeneous earth dam (Sherard et al, 1978) is investigated. Finally the effect of altering the phreatic level on the Okuku dam in South-Western Nigeria (Ayininuola & Franklin, 2008) is studied.

#### **3.1 Stability analysis of the Lodalen Landslide (Sevaldson, 1956)**

Fig. 3 shows a sectional view of the Lodalen Landslide. A stability analysis of the earth embankment prior to the occurrence of the slide will be carried out. Towards this end the initial rupture surface has been divided into 13 slices. The necessary data have been taken from the initial rupture surface and fed into the computer programme mentioned earlier. A total of 100 rupture surfaces have been considered in the analysis. Details of the computer output are not presented here, but a summary of the main findings are shown in Table 1 and these results are discussed at a later stage.

Influence of the Phreatic Level on the Stability of Earth Embankments 385

A non-homogeneous earth dam is shown in section in Figs. 4 and 5 and it is required to carry out a stability analysis of both the upstream and downstream sides of the dam. The assumed initial rupture surface on both sides of the dam has been divided into 12 slices each and the necessary data taken from the rupture surfaces have been fed into the computer programme referred to earlier. A total of 200 rupture surfaces have been considered at both the upstream and downstream sections. Again details of the computer output are not given in the present study, however a summary of the main findings are

Earth Embankment Method Factor of Safety

0.80 0.90 0.90

1.49 1.83 1.83

0.66 0.78 0.78

Authors' Formulation A Authors' Formulation B Bishop's Simplified

Authors' Formulation A Authors' Formulation B Bishop's Simplified

Authors' Formulation A Authors' Formulation B Bishop's Simplified

Table 1. Results of stability analysis of Lodalen slide and a non-homogeneous earth dam

On account of the accessibility to data, the Okuku dam has been utilized as a case study in order to investigate and understand the response of the proposed formulations to changes in the phreatic levels in the earth embankment due to variation in water levels in the storage reservoir. The dam was constructed in 1995 at Okuku town located on the 8o 02′N and 4o 40′E coordinates and approximately 40 km North-East of Osogbo in Osun State, South-Western Nigeria. The dam axis located across River Anle, a seasonal stream, is about 1.5 km South-East of Okuku town. The dam is a homogeneous earth dam built with poorly graded sand clay mixtures which possess the following soil characteristics, namely, cohesion c′ = 45 KN/m2, angle of shearing resistance ′ = 12o and additionally, average dry density of dam construction materials, γ = 19.63 KN/m3. The height of the crest above the base of the dam is 10 metres and the upstream and downstream sections are sloped at ratios 1:3 and 1:2.5 respectively. In Figs. 6 and 7, diagrams of the dam embankment for both the upstream and downstream sections at different levels of water in the storage reservoir are shown. Additional details in respect of the dam design may be found elsewhere (Ayininuola, 1999). The factors of safety at different phreatic levels for both the upstream and downstream sections of the dam have been estimated using the two formulations developed earlier. A total of 500 rupture surfaces have been examined for each section. A summary of the results

**3.2 Stability analysis of a non-homogeneous earth dam (Sherard et al, 1978)** 

shown in Table1.

1956)

Lodalen slide (Sevaldson,

Downstream section of nonhomogeneous earth dam (Sherard et al, 1978)

Upstream section of nonhomogeneous earth dam (Sherard et al, 1978)

**3.3 Stability analysis of Okuku earth dam, Nigeria** 

is presented in Table 2 and Figs. 8 and 9.

Fig. 3. Re-examination of the Lodalen slide (Modified from Sevaldson, 1956)

Fig. 3. Re-examination of the Lodalen slide (Modified from Sevaldson, 1956)

### **3.2 Stability analysis of a non-homogeneous earth dam (Sherard et al, 1978)**

A non-homogeneous earth dam is shown in section in Figs. 4 and 5 and it is required to carry out a stability analysis of both the upstream and downstream sides of the dam. The assumed initial rupture surface on both sides of the dam has been divided into 12 slices each and the necessary data taken from the rupture surfaces have been fed into the computer programme referred to earlier. A total of 200 rupture surfaces have been considered at both the upstream and downstream sections. Again details of the computer output are not given in the present study, however a summary of the main findings are shown in Table1.


Table 1. Results of stability analysis of Lodalen slide and a non-homogeneous earth dam

### **3.3 Stability analysis of Okuku earth dam, Nigeria**

On account of the accessibility to data, the Okuku dam has been utilized as a case study in order to investigate and understand the response of the proposed formulations to changes in the phreatic levels in the earth embankment due to variation in water levels in the storage reservoir. The dam was constructed in 1995 at Okuku town located on the 8o 02′N and 4o 40′E coordinates and approximately 40 km North-East of Osogbo in Osun State, South-Western Nigeria. The dam axis located across River Anle, a seasonal stream, is about 1.5 km South-East of Okuku town. The dam is a homogeneous earth dam built with poorly graded sand clay mixtures which possess the following soil characteristics, namely, cohesion c′ = 45 KN/m2, angle of shearing resistance ′ = 12o and additionally, average dry density of dam construction materials, γ = 19.63 KN/m3. The height of the crest above the base of the dam is 10 metres and the upstream and downstream sections are sloped at ratios 1:3 and 1:2.5 respectively. In Figs. 6 and 7, diagrams of the dam embankment for both the upstream and downstream sections at different levels of water in the storage reservoir are shown. Additional details in respect of the dam design may be found elsewhere (Ayininuola, 1999). The factors of safety at different phreatic levels for both the upstream and downstream sections of the dam have been estimated using the two formulations developed earlier. A total of 500 rupture surfaces have been examined for each section. A summary of the results is presented in Table 2 and Figs. 8 and 9.

Influence of the Phreatic Level on the Stability of Earth Embankments 387

Fig. 5. Downstream section of an earth dam embankment (Modified from Sherard et al, 1978)

Fig. 4. Upstream section of an earth dam embankment (Modified from Sherard et al, 1978)

Fig. 4. Upstream section of an earth dam embankment (Modified from Sherard et al, 1978)

Fig. 5. Downstream section of an earth dam embankment (Modified from Sherard et al, 1978)

Influence of the Phreatic Level on the Stability of Earth Embankments 389

Fig. 7. Downstream section of Okuku earth dam (Courtesy Konsadem Associates Ltd., Nigeria)

Fig. 6. Upstream section of Okuku earth dam (Courtesy Konsadem Associates Ltd., Nigeria)

Fig. 6. Upstream section of Okuku earth dam (Courtesy Konsadem Associates Ltd., Nigeria)

Fig. 7. Downstream section of Okuku earth dam (Courtesy Konsadem Associates Ltd., Nigeria)

Influence of the Phreatic Level on the Stability of Earth Embankments 391

Fig. 9. Variation of factor of safety of dam embankment with reservoir water depth

elsewhere (Ayininuola & Franklin, 2008; Ayininuola, 1999).

The comments outlined here are based primarily on the results presented in Tables 1 and 2, as well as in Figs. 8 and 9. As noted in the preceding section, details of the computer output in respect of the stability analysis carried out are not presented here, but may be obtained

The procedures developed in the present study as well as Bishop's have been applied to the Lodalen landslide as well as the non-homogeneous earth dam described in the preceding section. Using Table 1 and the results of the computer generated output for the Lodalen landslide as guide, several points may be noted. Firstly the water pressure forces acting at the interslice have great influence on the elemental horizontal thrusts generated at the interslice. They also have a direct influence on the elemental shear forces at the interslice. In this region when the elemental water pressure forces are assumed to be zero, the values of the elemental horizontal thrusts and shear forces that develop are much smaller than those obtained when water pressure forces are taken into

In addition to the above, water pressure forces, elemental horizontal thrusts and elemental shear forces are directly affected by the slice inclination angles. When for example the inclination angle is zero, the effect of all the forces mentioned is practically negligible. At the

interslice when the piezometric height Hw(n) is zero, the values of elemental

**4.1 Comparison between formulations A and B and Bishop's simplified method** 

(downstream section)

**4. Discussion** 

account.


Table 2. Results of stability analysis of Okuku Dam using Formulation A and B

Fig. 8. Variation of factor of safety of dam embankment with reservoir water depth (upstream section)

### **4. Discussion**

390 Infrastructure Design, Signalling and Security in Railway

Stability values for Formulation A

> 2.43 2.60 2.81 3.01

> 2.25 2.53 2.74 2.89

Table 2. Results of stability analysis of Okuku Dam using Formulation A and B

Fig. 8. Variation of factor of safety of dam embankment with reservoir water depth

Stability values using formulation B

> 2.78 2.85 2.93 3.03

> 2.67 2.76 2.83 2.90

Difference (%)

14.40 9.62 4.27 0.66

18.67 9.09 3.28 0.35

Section of dam under consideration

Upstream

Downstream

(upstream section)

Water level (metres)

> 9.00\* 6.55\* 5.25\* 3.70\*

9.00\*\* 6.55\*\* 5.25\*\* 3.70\*\*

> The comments outlined here are based primarily on the results presented in Tables 1 and 2, as well as in Figs. 8 and 9. As noted in the preceding section, details of the computer output in respect of the stability analysis carried out are not presented here, but may be obtained elsewhere (Ayininuola & Franklin, 2008; Ayininuola, 1999).

### **4.1 Comparison between formulations A and B and Bishop's simplified method**

The procedures developed in the present study as well as Bishop's have been applied to the Lodalen landslide as well as the non-homogeneous earth dam described in the preceding section. Using Table 1 and the results of the computer generated output for the Lodalen landslide as guide, several points may be noted. Firstly the water pressure forces acting at the interslice have great influence on the elemental horizontal thrusts generated at the interslice. They also have a direct influence on the elemental shear forces at the interslice. In this region when the elemental water pressure forces are assumed to be zero, the values of the elemental horizontal thrusts and shear forces that develop are much smaller than those obtained when water pressure forces are taken into account.

In addition to the above, water pressure forces, elemental horizontal thrusts and elemental shear forces are directly affected by the slice inclination angles. When for example the inclination angle is zero, the effect of all the forces mentioned is practically negligible. At the interslice when the piezometric height Hw(n) is zero, the values of elemental

Influence of the Phreatic Level on the Stability of Earth Embankments 393

the design of the Okuku earth dam embankment. In addition the assistance received from staff of Ete-Aro and Partners Limited, Ibadan, is gratefully acknowledged. The authors would also wish to place on record the encouragement of staff of the Department of Civil Engineering, University of Ibadan, Nigeria as well as staff of the Department of Civil

Capper, P. & Cassie, W. (1971). *The Mechanics of Engineering Soils,* 5th Edition, E. & F.N. Spon,

McCarthy, D. (1998). *Essentials of Soil Mechanics and Foundations - Basic Geotechnics*, 5th

Fellenius, W. (1927). *Erdstatische Berechnungen mit Reibung und Kohasion Adhasion und unter* 

Bishop, A. (1955). The Use of the Slip Circle in the Stability Analysis of Slopes, *Geotechnique*,

Spencer, E. (1967). A Method of Analysis of the Stability of Embankments Assuming Parallel

Morgenstern, N. & Price, V. (1965). The Analysis of the Stability of General Slip Surfaces,

Bell, J. (1968). General Slope Stability Analysis, *J. Soil Mech. & Found. Div., ASCE,* Vol.94,

Sarma, S. (1973). Stability Analysis of Embankments and Slopes, *Geotechnique*, Vol.23, No.2,

Cousins, B. (1978). Stability Charts for Simple Earth Slopes, *J. Geotechnical. Eng. Div., ASCE*,

Janbu, N. (1973). Slope Stability Computations, In: *Embankment Dam Engineering- Casagrande* 

King, G. (1989). Revision of Effective Stress Method of Slices, *Geotechnique*, Vol.39, No.3,

Morrison, I. & Greenwood, J. (1989). Assumptions in Simplified Slope Analysis by the

Ayininuola, G. & Franklin, S. (2008). Water Pressure Forces Effect on Earth Embankments

Ayininuola, G. {1999). *The Effect of Hydrostatic Pore Water Pressure Forces on the Stability of* 

Sevaldson, R. (1956). The Slide in Lodalen, Oct. 6th 1954, *Geotechnique*, Vol.6, No.4,

*Memorial Volume*, R.C. Hirschfield & S.J. Poulos (Ed.), 47–86, John Wiley & Sons,

Method of Slices, *Geotechnique*, Vol.39, No.3, (September 1989), pp. 503–509, ISSN

Stability, *Global Journal of Engineering and Technology*, Global Research Publication,

*Earth Embankments,* Unpublished M.Sc. Dissertation, University of Ibadan,

*Geotechnique*, Vol.15, No.1, (March 1965), pp 79–93, ISSN 0016-8505

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Edition, Prentice-Hall, ISBN 0-13-506932-7, New Jersey, USA

*Annahme Kreiszylindrischer Gleitflachen*, W. Ernst, Berlin

Vol.5, No.1, (March 1955), pp 7–17, ISSN 0016-8505

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Engineering, University of Botswana, Gaborone, Botswana.

ISBN 419-10700-2, London, United Kingdom

**7. References** 

8505

0016-8505

Nigeria.

horizontal thrust and elemental shear force are zero. Furthermore the factors of safety obtained when the net effect of water pressure forces at the interslice is taken to be zero are higher than the corresponding values when the afore-mentioned forces are considered by the order of 8% – 24% depending on the phreatic level. Also the results given by Formulation B, which ignores the water pressure forces effect at the interslices, are practically identical to those obtained using Bishop's method.

### **4.2 Influence of the phreatic level on earth dam stability**

With reference to Table 2 and Figs. 8 and 9, the results of stability analysis of Okuku earth dam reveal that the higher the phreatic level in the storage reservoir of the earth dam, the greater the variation between the stability values obtained using Formulations A and B. When the water pressure forces are ignored, higher factors of safety of the order of 0.35% – 18.67% are obtained. With regards to the curves in Figs. 8 and 9, and also from a study of the computer generated output, it is observed that at low phreatic levels in the storage reservoir of between 20% and 30% of the dam height, both approaches yield similar stability values.

### **5. Conclusions**

An in-depth study of the effect of the pore water pressure forces acting at the interslice on the stability of earth dams has been carried out. This has been achieved by developing two procedures and applying the formulations to a number of practical cases. Based on the results of the investigation, a number of conclusions can be drawn: Firstly the magnitudes of effective horizontal thrusts and shear forces generated at the interslice when pore water pressure forces induced are taken into consideration are higher than those obtained when these forces are ignored. This demonstrates that the pore water pressures developed have an influence on the values of other interslice forces. Secondly the inclusion of net water pressure forces in the stability analysis of the earth embankments studied clearly show that the action of the water pressure forces serves to promote instability, as would be expected. Thirdly the popular practice amongst geotechnical engineers of resolving the water pressure within a given slice in a direction of normal at the slice base in order to estimate its value, whilst the horizontal effect of the slice base water pressure is taken as zero, constitutes a grave error. This action is not in line with limit equilibrium procedures and yields erroneous results. Fourthly at low phreatic levels the proposed approaches give practically similar factors of safety. This implies that the effect of water pressure forces acting on the interslice can only be neglected when the phreatic line in an embankment is at its lowest stage, a considerable period after drawdown, or preferably between 20% and 30% of the overall height of the embankment. Finally the factors of safety found using Bishop's simplified method and that based on Formulation B, which ignores the pore water pressure forces effect, are in very close agreement. This simply implies that the inclusion of only the effective horizontal thrusts and shear forces acting at the interslice has little influence on the resulting factors of safety.

### **6. Acknowledgments**

The present investigators would wish to thank the management of Konsadem Associates Limited, Ibadan, Nigeria for making readily available the data and other aspects relating to the design of the Okuku earth dam embankment. In addition the assistance received from staff of Ete-Aro and Partners Limited, Ibadan, is gratefully acknowledged. The authors would also wish to place on record the encouragement of staff of the Department of Civil Engineering, University of Ibadan, Nigeria as well as staff of the Department of Civil Engineering, University of Botswana, Gaborone, Botswana.

### **7. References**

392 Infrastructure Design, Signalling and Security in Railway

horizontal thrust and elemental shear force are zero. Furthermore the factors of safety obtained when the net effect of water pressure forces at the interslice is taken to be zero are higher than the corresponding values when the afore-mentioned forces are considered by the order of 8% – 24% depending on the phreatic level. Also the results given by Formulation B, which ignores the water pressure forces effect at the interslices, are

With reference to Table 2 and Figs. 8 and 9, the results of stability analysis of Okuku earth dam reveal that the higher the phreatic level in the storage reservoir of the earth dam, the greater the variation between the stability values obtained using Formulations A and B. When the water pressure forces are ignored, higher factors of safety of the order of 0.35% – 18.67% are obtained. With regards to the curves in Figs. 8 and 9, and also from a study of the computer generated output, it is observed that at low phreatic levels in the storage reservoir of between 20% and 30% of the dam height, both approaches yield similar stability values.

An in-depth study of the effect of the pore water pressure forces acting at the interslice on the stability of earth dams has been carried out. This has been achieved by developing two procedures and applying the formulations to a number of practical cases. Based on the results of the investigation, a number of conclusions can be drawn: Firstly the magnitudes of effective horizontal thrusts and shear forces generated at the interslice when pore water pressure forces induced are taken into consideration are higher than those obtained when these forces are ignored. This demonstrates that the pore water pressures developed have an influence on the values of other interslice forces. Secondly the inclusion of net water pressure forces in the stability analysis of the earth embankments studied clearly show that the action of the water pressure forces serves to promote instability, as would be expected. Thirdly the popular practice amongst geotechnical engineers of resolving the water pressure within a given slice in a direction of normal at the slice base in order to estimate its value, whilst the horizontal effect of the slice base water pressure is taken as zero, constitutes a grave error. This action is not in line with limit equilibrium procedures and yields erroneous results. Fourthly at low phreatic levels the proposed approaches give practically similar factors of safety. This implies that the effect of water pressure forces acting on the interslice can only be neglected when the phreatic line in an embankment is at its lowest stage, a considerable period after drawdown, or preferably between 20% and 30% of the overall height of the embankment. Finally the factors of safety found using Bishop's simplified method and that based on Formulation B, which ignores the pore water pressure forces effect, are in very close agreement. This simply implies that the inclusion of only the effective horizontal thrusts and shear forces acting at the interslice has little influence on the

The present investigators would wish to thank the management of Konsadem Associates Limited, Ibadan, Nigeria for making readily available the data and other aspects relating to

practically identical to those obtained using Bishop's method.

**4.2 Influence of the phreatic level on earth dam stability** 

**5. Conclusions** 

resulting factors of safety.

**6. Acknowledgments** 


**16** 

*Latvia* 

**Evolutionary Algorithms in** 

**Using Satellite Navigation** 

**for Railway Transport** 

*Riga Technical University* 

**Embedded Intelligent Devices** 

Anatoly Levchenkov, Mikhail Gorobetz and Andrew Mor-Yaroslavtsev

Nowadays, the most widely spread type of a computer is an embedded system. The embedded systems consist of the following hardware (i.e. nano-electronic components) – programmable microcontrollers or microprocessors; transmitters, including the receivers of global positioning information systems, which demonstrate the state and measuring parameters of a controlled object, and which relay that to the programmable microcontroller; actuators, which receive a signal from the programmed microcontroller and relay it to an antenna, a display or an electro-drive device; and communication devices, including wireless communication with other devices and the software with algorithms of

Railway traffic flow is limited by safety criteria. Therefore, routing and scheduling task is actual for a railway transport. As well an optimal braking control and safety of braking process are very important (Luo, Zeng, 2009). The analysis of human behavior and simulation of train's braking are investigated (Hasegawa et al., 2009). An intelligent transport control system gives a possibility to make traffic control safer and more costeffective (Gorobetz, 2008). It may find an optimal solution to a conflict faster than a human as a decision support system (Levchenkov et al., 2009). In addition in case of emergency it

Authors propose the intelligent braking control device, which warns the driver about the necessity of starting the working braking, taking into account the signal of the traffic light. If working braking has not been started the controller activates emergency brakes with a purpose to stop before the beginning of the next block-section if it is possible, or to choose a free way with enough free distance to stop without a crash. The primary task of the diagnostics device is to separate dangerous situations in braking system by critical values of sensor measurements from the regular states of the system, to detect and to warn about changes in the system and to prevent emergencies immediately. The system allows stopping

**1. Introduction** 

artificial intelligence (Russel, Norvig, 2006).

may prevent crashes and accidents without human intervention.

the train timely before the problem has occurred.

Sherard, J., Woodward, R., Gizienski, S. & Clevenger, W. (1978). *Earth-Rock Dams: Engineering Problems of Design and Construction*, J. Wiley and Sons, ISBN 0-471- 78547-4, New York, USA

## **Evolutionary Algorithms in Embedded Intelligent Devices Using Satellite Navigation for Railway Transport**

Anatoly Levchenkov, Mikhail Gorobetz and Andrew Mor-Yaroslavtsev *Riga Technical University Latvia* 

### **1. Introduction**

394 Infrastructure Design, Signalling and Security in Railway

Sherard, J., Woodward, R., Gizienski, S. & Clevenger, W. (1978). *Earth-Rock Dams:* 

78547-4, New York, USA

*Engineering Problems of Design and Construction*, J. Wiley and Sons, ISBN 0-471-

Nowadays, the most widely spread type of a computer is an embedded system. The embedded systems consist of the following hardware (i.e. nano-electronic components) – programmable microcontrollers or microprocessors; transmitters, including the receivers of global positioning information systems, which demonstrate the state and measuring parameters of a controlled object, and which relay that to the programmable microcontroller; actuators, which receive a signal from the programmed microcontroller and relay it to an antenna, a display or an electro-drive device; and communication devices, including wireless communication with other devices and the software with algorithms of artificial intelligence (Russel, Norvig, 2006).

Railway traffic flow is limited by safety criteria. Therefore, routing and scheduling task is actual for a railway transport. As well an optimal braking control and safety of braking process are very important (Luo, Zeng, 2009). The analysis of human behavior and simulation of train's braking are investigated (Hasegawa et al., 2009). An intelligent transport control system gives a possibility to make traffic control safer and more costeffective (Gorobetz, 2008). It may find an optimal solution to a conflict faster than a human as a decision support system (Levchenkov et al., 2009). In addition in case of emergency it may prevent crashes and accidents without human intervention.

Authors propose the intelligent braking control device, which warns the driver about the necessity of starting the working braking, taking into account the signal of the traffic light. If working braking has not been started the controller activates emergency brakes with a purpose to stop before the beginning of the next block-section if it is possible, or to choose a free way with enough free distance to stop without a crash. The primary task of the diagnostics device is to separate dangerous situations in braking system by critical values of sensor measurements from the regular states of the system, to detect and to warn about changes in the system and to prevent emergencies immediately. The system allows stopping the train timely before the problem has occurred.

Evolutionary Algorithms in Embedded


the collision (Fig. 3.).





Fig. 2. Selection of the necessary signal on the way.




Intelligent Devices Using Satellite Navigation for Railway Transport 397



The following functions of the track-side embedded device are required:

Fig. 3. Detection of the safest state of the station points to avoid the collision.

provide safety for a vehicle, its passengers or cargo, and other traffic participants.

There are many embedded transport control systems on the market which are designed to

a) Initial state, b) Collision is possible, c) Collision is avoided.

### **2. Problem formulation**

Railway safety is an actual and important task. Nowadays a human factor is the main reason for 74% of railway accidents and crashes. This problem is actual as in Latvia as all over the world. Various crashes like in Riga (Latvia) in February 2005, in Ventspils (Latvia) in December 2008, in Aegvidu (Estonia) in December 2010, in Brussels (Belgium) in February 2010, in Magdeburg (Germany) in January 2011 prove the necessity of finding the problem solution.

The main reason of railway accidents is a human factor, when


Therefore, auxiliary embedded electronic devices are needed


Fig. 1. Graphical representation of the task.

The primary task is to stop the train before the restrictive signal. For this task a warning point G should be detected, where regular braking still may be applied (Fig. 1.). The point G\* is a marginal point and also must be defined, where only emergency braking may be applied to stop the train before the signal. Using of regular braking in G\* follows the passing of the restrictive signal.

The purpose of the research is to develop a prototype of a new control command and a signalling track-side and on-board locomotive's devices to improve train movement safety.

The following functions of the on-board locomotive's embedded device are required:


Railway safety is an actual and important task. Nowadays a human factor is the main reason for 74% of railway accidents and crashes. This problem is actual as in Latvia as all over the world. Various crashes like in Riga (Latvia) in February 2005, in Ventspils (Latvia) in December 2008, in Aegvidu (Estonia) in December 2010, in Brussels (Belgium) in February 2010, in Magdeburg


The primary task is to stop the train before the restrictive signal. For this task a warning point G should be detected, where regular braking still may be applied (Fig. 1.). The point G\* is a marginal point and also must be defined, where only emergency braking may be applied to stop the train before the signal. Using of regular braking in G\* follows the passing

The purpose of the research is to develop a prototype of a new control command and a signalling track-side and on-board locomotive's devices to improve train movement safety.


The following functions of the on-board locomotive's embedded device are required:


control points (signals, section points) in the location of the train;


(Germany) in January 2011 prove the necessity of finding the problem solution.


The main reason of railway accidents is a human factor, when - train driver does not stop a train on the restrictive signal

Therefore, auxiliary embedded electronic devices are needed


Fig. 1. Graphical representation of the task.


of the restrictive signal.

**2. Problem formulation** 


The following functions of the track-side embedded device are required:


Fig. 2. Selection of the necessary signal on the way.

Fig. 3. Detection of the safest state of the station points to avoid the collision. a) Initial state, b) Collision is possible, c) Collision is avoided.

There are many embedded transport control systems on the market which are designed to provide safety for a vehicle, its passengers or cargo, and other traffic participants.

Evolutionary Algorithms in Embedded

Intelligent Devices Using Satellite Navigation for Railway Transport 399

or degree of binding between the antigen and the antibody is similar to complementarity level in biological IS and it defines the fate of each individual antibody as well as the termination of the whole algorithm. Individual antibodies are replaced, cloned and hypermutated until a satisfactory level of affinity is reached. Partial replacement of the solutions' population with fresh randomly generated candidates maintains diversity which allows solving a wider set of problems. The probability of cloning or hypermutating a candidate depends on its affinity.

Fig. 4. Wireless network structure's scheme of embedded devices for a rail transport

In the rolling stock safety system (Fig. 5) (Mor-Yaroslavtsev, Levchenkov, 2011), the invading object *I* is picked up by sensors *S* and the data is transmitted to the nearest cell

In the commercial railway transport segment an example of such a safety system is KLUB-U, currently used on Russian Railways. It is installed in the locomotives and by interacting with existing signaling systems and its own modules provides information about the train's and its closest neighbors' coordinates, diagnostics of the brakes, current railway segment profile and maximum allowed speed, and controls the vigilance of the locomotive driver. Still, despite the wide array of features, it lacks automation and many decisions require manual operation.

A significant component of the whole safety system is the circuits, engines and brakes diagnostics complex. While the most complete diagnostics can be performed only in the technical service environment, most failures can be detected during its operation using circuit integrity indicators and different sensors designed to uncover electrical mechanical damage.

All kinds of damages which could lead to failures can be combined into distinctive value sets, thus recognizing them in the stream of incoming data allows early identification of problems in the engine.

Artificial immune systems (AIS) were mentioned in some papers in mid 1980s but became a subject in its own right in 1994 in the papers on negative selection (Forrest et al., 1994, Kephart, 1994). Currently the systems are actively explored for possible use cases. For example, there are studies on a real-valued negative selection algorithm for an aircraft fault detection (Dasgupta et al., 2004).

### **3. Structure of proposed system for railway safety tasks**

The chapter will demonstrate some issues of design and modelling of a part of a modern embedded system for a rail transport (Fig. 4.). This embedded system is intended for managing the rail transport's electrical drive and the traffic lights, and it consists of the microcontrollers, the developed software and the information system, the wireless communication possibilities and the global positioning system.

Fig. 4 illustrates a complete scheme of a structure of the rail transport's embedded system. In the figure, the brown colour shows the train's embedded devices; the green colour stands for the devices of the traffic lights' embedded system; the purple colour – the devices of the crossing's embedded system; the yellow colour – coordination embedded system devices; the light blue colour – software which provides operation of the network of the wireless embedded system, operation of the communication network of the wireless devices and which is responsible for making operational decisions.

The device receives the signal from the defined traffic light and defines its position using a wireless communication network and has data storage with route control points as well.

Artificial immune systems use evolutionary data processing paradigm based on biological immune systems. It differs from computational immunology which models biological immune systems. Immune algorithms are mainly used to solve anomaly recognition, data collection and analysis tasks. From the computational point of view the most interesting features of the immune systems are self-learning, diversity maintenance and memory.

The problem is represented as an antigen and a solution candidates as antibodies which are randomly generated from the library of available solutions or genes. The evaluation of affinity

In the commercial railway transport segment an example of such a safety system is KLUB-U, currently used on Russian Railways. It is installed in the locomotives and by interacting with existing signaling systems and its own modules provides information about the train's and its closest neighbors' coordinates, diagnostics of the brakes, current railway segment profile and maximum allowed speed, and controls the vigilance of the locomotive driver. Still, despite the wide array of features, it lacks automation and many decisions require

A significant component of the whole safety system is the circuits, engines and brakes diagnostics complex. While the most complete diagnostics can be performed only in the technical service environment, most failures can be detected during its operation using circuit integrity indicators and different sensors designed to uncover electrical mechanical damage. All kinds of damages which could lead to failures can be combined into distinctive value sets, thus recognizing them in the stream of incoming data allows early identification of

Artificial immune systems (AIS) were mentioned in some papers in mid 1980s but became a subject in its own right in 1994 in the papers on negative selection (Forrest et al., 1994, Kephart, 1994). Currently the systems are actively explored for possible use cases. For example, there are studies on a real-valued negative selection algorithm for an aircraft fault

The chapter will demonstrate some issues of design and modelling of a part of a modern embedded system for a rail transport (Fig. 4.). This embedded system is intended for managing the rail transport's electrical drive and the traffic lights, and it consists of the microcontrollers, the developed software and the information system, the wireless

Fig. 4 illustrates a complete scheme of a structure of the rail transport's embedded system. In the figure, the brown colour shows the train's embedded devices; the green colour stands for the devices of the traffic lights' embedded system; the purple colour – the devices of the crossing's embedded system; the yellow colour – coordination embedded system devices; the light blue colour – software which provides operation of the network of the wireless embedded system, operation of the communication network of the wireless devices and

The device receives the signal from the defined traffic light and defines its position using a wireless communication network and has data storage with route control points as well.

Artificial immune systems use evolutionary data processing paradigm based on biological immune systems. It differs from computational immunology which models biological immune systems. Immune algorithms are mainly used to solve anomaly recognition, data collection and analysis tasks. From the computational point of view the most interesting features of the immune systems are self-learning, diversity maintenance and memory.

The problem is represented as an antigen and a solution candidates as antibodies which are randomly generated from the library of available solutions or genes. The evaluation of affinity

**3. Structure of proposed system for railway safety tasks** 

communication possibilities and the global positioning system.

which is responsible for making operational decisions.

manual operation.

problems in the engine.

detection (Dasgupta et al., 2004).

or degree of binding between the antigen and the antibody is similar to complementarity level in biological IS and it defines the fate of each individual antibody as well as the termination of the whole algorithm. Individual antibodies are replaced, cloned and hypermutated until a satisfactory level of affinity is reached. Partial replacement of the solutions' population with fresh randomly generated candidates maintains diversity which allows solving a wider set of problems. The probability of cloning or hypermutating a candidate depends on its affinity.

Fig. 4. Wireless network structure's scheme of embedded devices for a rail transport

In the rolling stock safety system (Fig. 5) (Mor-Yaroslavtsev, Levchenkov, 2011), the invading object *I* is picked up by sensors *S* and the data is transmitted to the nearest cell

Evolutionary Algorithms in Embedded


where a and b are half-axes of the ellipsoid orbit;

Fig. 6. Differential satellite navigation system elements

<sup>3</sup> *n a* 


where μ – Earth gravimetric constant. - x, y, z – coordinates of the satellite



Base station M parameters:

and real distance:


 *mi* , 

Intelligent Devices Using Satellite Navigation for Railway Transport 401

<sup>2</sup> *e ba* 1 (/) , (1)

/ , (2)

2 22 *D xx yy zz mi i m i m i m* ( )( )( ) (3)

*mi* - distance measurement result and necessary correction between measured

tower *CT*, which relays it to the control center *CC* and the nearest locomotives wireless modems *M*. Through the same modem the locomotive *L* receives data about the closest neighbors' rolling stock position and status, railway segment profile and maximum allowed speed.

Fig. 5. The intelligent rolling stock safety system functional design

*L* also hosts: a positioning receiver *G* which receives data from a positioning satellite *ST*; data analysis module *AIS* which communicates to the immune detector database *DBD* and control cell database *DBC*. Depending on the results of control cell maturation the module makes a decision and executes it by sending a control signal or displaying an alert to the driver.

Analogous to the hybrid IDS (Powers, He, 2009) the most feasible way to implement such a system would be through the two phases of anomaly detection and determination of their type to draw a conclusion. In this case the incoming data from the sensors is the set of antigens. The data includes but is not limited to speed, acceleration, voltage, rotation, temperature, and presence of smoke.

### **4. Mathematical models for problem solution**

### **4.1 Model of differential positioning system**

Differential satellite navigation systems are used to increase precision of the positioning systems that is very significant for safety-critical systems, such as transport.

Differential satellite navigation systems (Fig. 6.) contain the following object types:


Each satellite S is described by the following parameters:



400 Infrastructure Design, Signalling and Security in Railway

tower *CT*, which relays it to the control center *CC* and the nearest locomotives wireless modems *M*. Through the same modem the locomotive *L* receives data about the closest neighbors' rolling stock position and status, railway segment profile and maximum allowed

*L* also hosts: a positioning receiver *G* which receives data from a positioning satellite *ST*; data analysis module *AIS* which communicates to the immune detector database *DBD* and control cell database *DBC*. Depending on the results of control cell maturation the module makes a decision and executes it by sending a control signal or displaying an alert to the

Analogous to the hybrid IDS (Powers, He, 2009) the most feasible way to implement such a system would be through the two phases of anomaly detection and determination of their type to draw a conclusion. In this case the incoming data from the sensors is the set of antigens. The data includes but is not limited to speed, acceleration, voltage, rotation,

Differential satellite navigation systems are used to increase precision of the positioning

systems that is very significant for safety-critical systems, such as transport.

Differential satellite navigation systems (Fig. 6.) contain the following object types:



Fig. 5. The intelligent rolling stock safety system functional design

speed.

driver.


temperature, and presence of smoke.

**4. Mathematical models for problem solution** 

Each satellite S is described by the following parameters: - α – slope of the satellite's orbit to the equator plane;


**4.1 Model of differential positioning system** 

$$e = \sqrt{1 - \left(b \,/\, a\right)^2} \,, \tag{1}$$

where a and b are half-axes of the ellipsoid orbit;

Fig. 6. Differential satellite navigation system elements


$$m = \sqrt{\mu \,/\, a^3} \,, \tag{2}$$

where μ – Earth gravimetric constant.


Base station M parameters:


$$D\_{mi} = \sqrt{(x\_i - x\_m)^2 + (y\_i - y\_m)^2 + (z\_i - z\_m)^2} \tag{3}$$


Evolutionary Algorithms in Embedded

system, SD – real braking distance

chock material.

the following expression :

The total braking factor:

For the standard cast iron braking chocks:

The cast iron- phosphorus braking chocks:

For the braking chocks of composite materials:

The main force resistive to the motion in idle running

where N - quantity of the carriages.

factor

Intelligent Devices Using Satellite Navigation for Railway Transport 403

where ST is the braking distance, Sp – distance of moving during the preparation of braking

The braking power of the train should be defined taking into account a real force of the braking chock influencing the train wheels. A real friction factor depends on the braking

> 16 100 100 0,6 80 100 5v 100 *<sup>K</sup> K+ v+ <sup>=</sup> K+ +*

The cast iron braking chocks containing phosphorus of 1,0-1,4% are characterised with the

The mentioned above factor for braking chocks of composite materials can be defined with

20 100 0,44 4K 100 2v 100 *<sup>K</sup> K+ v+ <sup>=</sup> + +*

16 100 2,22 80 100 *<sup>P</sup> K + K= K*

16 100 1,85 52 100 *<sup>P</sup> K + K= K*

<sup>20</sup> 1,22 4K 20 *<sup>P</sup> K + K= K*

*PO*

 *P*

*u K Q P*

The calculations of braking force of the chocks also depend on a type of chocks.

; (7)

; (8)

*K +* ; (9)

*K +* ; (10)

*<sup>+</sup>* ; (11)

; (12)

*W =W +N W Ox O1 Oc* ; (13)

The following factor characterises the braking chock made of cast iron:

$$
\Delta \rho\_{\rm mi} = \rho\_{\rm mi} - D\_{\rm mi} = \varepsilon\_{m, \rm sat} + \varepsilon\_{m, \rm con} + \varepsilon\_{m, \rm rec} + \mathbf{c} \cdot \delta t\_{m \, \prime} \tag{4}
$$

where *m sat* , - satellite apparatus error, satellite clock error, *m con* , - control error, incorrect ephemerid forecast, *m rec* , - receiver's error, ionosphere, troposphere and other noises, *tm* base station clock deviation from satellite clock, c - light speed.


$$\begin{aligned} \rho \rho\_{ri} &= D\_{ri} + \varepsilon\_{r, \text{sat}} + \varepsilon\_{r, \text{cou}} + \varepsilon\_{r, \text{rcv}} + \mathbf{c} \cdot \delta \mathbf{t}\_m - \Delta \rho\_{mi} = D\_{ri} + \varepsilon\_r + \mathbf{c} \cdot \delta \mathbf{t}\_{mr} = \\ \sqrt{(\mathbf{x}\_i - \mathbf{x}\_r)^2 + (y\_i - y\_r)^2 + (z\_i - z\_r)^2} &+ \varepsilon\_r + \mathbf{c} \cdot \delta \mathbf{t}\_{mr} \end{aligned} \tag{5}$$

where *<sup>r</sup>* – receiver's result segment error, *mr t* – combined clock deviation,

xr, yr, zr – coordinates of the receiver.

#### **4.2 Model of railway station**

The model of the station may be described with the following sets of objects:


Fig. 7. Graphical interpretation of station model

#### **4.3 Model of braking of rolling stock**

The braking way consists of preparation and real segments:

$$\mathbf{S}\_T = \mathbf{S}\_P + \mathbf{S}\_D \; ; \tag{6}$$

*mi mi mi m sat m con m rec m D* ,, ,

*ri ri r sat r con r rec m mi ri r mr*

*D ct D ct*

 

 


 

> 

 

 

*S =S +S T PD* ; (6)

*t* – combined clock deviation,

*c t* , (4)


*tm* -

, (5)

 


*ri* - corrected distance measurement between recipient and satellite:

*i r i r i r r mr*

The model of the station may be described with the following sets of objects:

 

*x x y y z z ct*

 

where *m sat* , 

where *<sup>r</sup>* 


ephemerid forecast, *m rec* ,

**4.2 Model of railway station** 

xr, yr, zr – coordinates of the receiver.


Fig. 7. Graphical interpretation of station model

The braking way consists of preparation and real segments:

**4.3 Model of braking of rolling stock** 

base station clock deviation from satellite clock, c - light speed.

,, , 2 22 ( )( )( )

 

– receiver's result segment error, *mr*

where ST is the braking distance, Sp – distance of moving during the preparation of braking system, SD – real braking distance

The braking power of the train should be defined taking into account a real force of the braking chock influencing the train wheels. A real friction factor depends on the braking chock material.

The following factor characterises the braking chock made of cast iron:

$$
\rho\_K = 0.6 \frac{16K + 100}{80K + 100} \cdot \frac{v + 100}{5v + 100},
\tag{7}
$$

The cast iron braking chocks containing phosphorus of 1,0-1,4% are characterised with the factor

The mentioned above factor for braking chocks of composite materials can be defined with the following expression :

$$
\rho\_K = 0.44 \frac{\text{K} + 20}{4\text{K} + 100} \cdot \frac{v + 100}{2\text{v} + 100} \,, \tag{8}
$$

The calculations of braking force of the chocks also depend on a type of chocks.

For the standard cast iron braking chocks:

$$K\_P = 2,22K \frac{16K + 100}{80K + 100};\tag{9}$$

The cast iron- phosphorus braking chocks:

$$K\_p = 1,85K \frac{16K + 100}{52K + 100};\tag{10}$$

For the braking chocks of composite materials:

$$K\_p = 1,22K \frac{\text{K} + 20}{\text{4K} + 20};\tag{11}$$

The total braking factor:

$$\mathcal{G}\_{\rm PO} = \frac{\sum K\_{\rm P}}{Q + P\_u} \quad ; \tag{12}$$

The main force resistive to the motion in idle running

$$\mathcal{W}\_{\rm Ox} = \mathcal{W}\_{\rm O1} + \mathcal{N} \cdot \mathcal{W}\_{\rm Ox} \; ; \tag{13}$$

where N - quantity of the carriages.

Evolutionary Algorithms in Embedded

to *is* is following for different point types:

dual point: { , , , , , } *D ss ss ss p ij ik im* ;

cross point: { , , , , , , , } *D ss ss s s s s p ij ik mj mk* .

single point: {, ,, } *D ss ss p ij ik* ;

"V" – violet, "W" – moonlight white.

Multi-criteria target function for braking:


criteria (EL)

**4.5 Assessment functions** 

of point *Dp* , where , *<sup>n</sup>*

time: *<sup>p</sup> dt* .

the track.

Intelligent Devices Using Satellite Navigation for Railway Transport 405

Each point *p C* has a connecting set W of three or more sections and a set of possible states

Each state of point *p p d D* has a speed limit \* *<sup>p</sup> <sup>d</sup> v* ; maximal each point's *p p d D* switching

Railway signal G is an object with fixed coordinates x0, y0 connected to the fixed position on

Each signal *g G* has the following states of signals { , , , , , } *L R Y YG G V W <sup>g</sup>* , where "R" – red, and rolling stock must stop before the signal; "Y" – yellow, can move and be ready to stop, the next signal is red; "YG" – yellow and green, next two sections are free; "G" – green,

Each signal sets up speed limits for the next block-section: *vdef* - maximal predefined speed on the section, *v0* - 0 kmh, stop; *v1* - < 50 kmh, movement on turnouts 1/9 and 1/11 types; *v2* - < 80 kmh for movement on turnout 1/18 type; *v3* - < 120kmh for movement on turnout 1/22 type.

1 2

 

() { , , , , , , }

*t S t IQ*

 



 

() { , , , , , , }

*t S t IQ*

*p B i m dcp v f ff f ff f B i m v dcp*

(21)

{0, , ,...} | ( ) ( )|

*C C t t*

( , , , ) min 0 () \*

*br*

 

 

*F DL CL EL DL S CL t*

*<sup>d</sup> EL const dt*


 

*<sup>p</sup> <sup>i</sup> <sup>j</sup> d ss* means opened in both directions from *is* to *<sup>j</sup> s* and from *<sup>j</sup> s*

Locomotive without the train:

$$\mathcal{W}\_{01} = \mathbf{24} + \mathbf{0}\mathbf{11}\upsilon + \mathbf{0}\mathbf{0}\mathbf{0}\mathbf{3}5\upsilon^2;\tag{14}$$

Cargo carriages:

$$w\_{0c} = 7 + \frac{a + v + 0.025v^2}{q\_0};\tag{15}$$

Passenger trains:

$$w\_{0\epsilon} = 12 + 0.12v + 0.002v^2 \cdot \tag{16}$$

As within the time interval *Δ<sup>t</sup>* the braking force and the opposite self-resistive force*ωOx* to the motion of the train are assumed as constant values then the increasing of the speed can be calculated according to :

$$
\Delta v = \frac{\xi \left( h\_T + \alpha\_{Ox} + i\_c \right) \Delta t}{3600}.\tag{17}
$$

The speed of the braking force distribution is a braking wave: *<sup>t</sup> t L v = <sup>t</sup>* ; where: L is the length of the train; *tt* – time from the moment when the driver turns the handle of the hoist till the pressure appears (?) in the braking cylinders; air wave : 20 *<sup>v</sup> v T* ; where: 273 *° T= +t C* absolute temperature of gas.

The preparation braking distance:

$$S\_P = 0.278v\_0 t\_p = \frac{v\_0 t\_n}{3\rho \epsilon}.\tag{18}$$

Real braking distance:

$$S\_D = \sum \frac{500\left(v\_N^2 - v\_K^2\right)}{\zeta\left(w\_{\alpha x} + b\_m + i\_C\right)}\;\!\!\prime\tag{19}$$

Thus the total braking way:

$$S\_T = \frac{v\_0 t\_n}{3\epsilon \hbar} + \sum \frac{500\left(v\_N^2 - v\_K^2\right)}{\zeta \left(w\_{\alpha x} + b\_m + i\_C\right)}\tag{20}$$

#### **4.4 Model of railway infrastructure and command and control system**

Rail ways can be represented as a graph *R CS* {,} , where rails are divided into sections S, and each section *s S* is connected with each other by two connectors ,*<sup>i</sup> <sup>j</sup> s cc* .

Each section *s S* has a constant length *sl* , a curve *<sup>s</sup> a* , and a speed limit \**<sup>s</sup> v* .

Each point *p C* has a connecting set W of three or more sections and a set of possible states of point *Dp* , where , *<sup>n</sup> <sup>p</sup> <sup>i</sup> <sup>j</sup> d ss* means opened in both directions from *is* to *<sup>j</sup> s* and from *<sup>j</sup> s* to *is* is following for different point types:

single point: {, ,, } *D ss ss p ij ik* ;

404 Infrastructure Design, Signalling and Security in Railway

0c

The speed of the braking force distribution is a braking wave: *<sup>t</sup>*

0

*D*

*S =*

0

3,6

**4.4 Model of railway infrastructure and command and control system** 

and each section *s S* is connected with each other by two connectors ,*<sup>i</sup> <sup>j</sup> s cc* .

Each section *s S* has a constant length *sl* , a curve *<sup>s</sup> a* , and a speed limit \**<sup>s</sup> v* .

*w=+*

2 0l *W = + v+ v ;* 24 0,11 0,0035 (14)

2

2

0c *w = + v+ v* 12 0,12 0,002 . (16)

*Δv =* . (17)

*v t S = vt =* . (18)

; (19)

(20)

*t L v =*

*<sup>t</sup>* ; where: L is the length

; (15)

0 0,025 <sup>7</sup> *a+v+ v*

*q*

As within the time interval *Δ<sup>t</sup>* the braking force and the opposite self-resistive force*ωOx* to the motion of the train are assumed as constant values then the increasing of the speed can

> 3600 *T Ox c ξ b + ω + i Δt*

of the train; *tt* – time from the moment when the driver turns the handle of the hoist till the pressure appears (?) in the braking cylinders; air wave : 20 *<sup>v</sup> v T* ; where: 273 *° T= +t C* -

> <sup>0</sup> 0,278 3,6 *<sup>n</sup> P p*

> > 2 2 500 *N K*

*v v*

*ox m C*

 

*ox m C*

*ζ w +b +i*

2 2

*ζ w +b +i*

500

*N K <sup>n</sup> <sup>T</sup>*

Rail ways can be represented as a graph *R CS* {,} , where rails are divided into sections S,

*v v v t S= +*

Locomotive without the train:

Cargo carriages:

Passenger trains:

be calculated according to :

absolute temperature of gas.

Real braking distance:

Thus the total braking way:

The preparation braking distance:

dual point: { , , , , , } *D ss ss ss p ij ik im* ;

cross point: { , , , , , , , } *D ss ss s s s s p ij ik mj mk* .

Each state of point *p p d D* has a speed limit \* *<sup>p</sup> <sup>d</sup> v* ; maximal each point's *p p d D* switching time: *<sup>p</sup> dt* .

Railway signal G is an object with fixed coordinates x0, y0 connected to the fixed position on the track.

Each signal *g G* has the following states of signals { , , , , , } *L R Y YG G V W <sup>g</sup>* , where "R" –

red, and rolling stock must stop before the signal; "Y" – yellow, can move and be ready to stop, the next signal is red; "YG" – yellow and green, next two sections are free; "G" – green, "V" – violet, "W" – moonlight white.

Each signal sets up speed limits for the next block-section: *vdef* - maximal predefined speed on the section, *v0* - 0 kmh, stop; *v1* - < 50 kmh, movement on turnouts 1/9 and 1/11 types; *v2* - < 80 kmh for movement on turnout 1/18 type; *v3* - < 120kmh for movement on turnout 1/22 type.

### **4.5 Assessment functions**

Multi-criteria target function for braking:

$$\begin{cases} \begin{aligned} &F^{br}(\text{DL}\_{\mathcal{L}}\text{CL}\_{\mathcal{L}}\text{EL}\_{\tau}\text{A}) \rightarrow \min\\ &DL = \Delta S \rightarrow 0\\ &\Pi = \varepsilon(t) \rightarrow \varepsilon^\*\\ &EL = \frac{d\varepsilon}{dt} = const\\ &\Delta \rightarrow \{\overline{0}, \mathcal{C}\_{1}, \mathcal{C}\_{2}, \dots\}\\ &\Delta = \Phi(t) - \mathcal{E}(t) \mid\\ &\Delta(t) = \{\mathcal{g}\_{p}, \mathcal{S}\_{\mathcal{B}}, \mathcal{E}\_{i}, t\_{m}, \tau, I\_{\text{dcp}}, \mathcal{Q}\_{v}\} \\ &\Phi(t) = \{\mathcal{G}^{f}, \mathcal{S}\_{\mathcal{B}}^{f}, \mathcal{E}\_{i}^{f}, t\_{m}^{f}, \tau^{f}, I\_{\text{dcp}}^{f}, \mathcal{Q}\_{v}^{f}\} \end{aligned} \tag{21}$$


Evolutionary Algorithms in Embedded

Step 3.2. Function STOPS

**5.2 Genetic algorithm** 

the defined crossover algorithm:

*S S <sup>C</sup>* ;

2

recalculate time with acceleration conditions Step 2.4. j = j + 1, select next section of the route

Step 3. Check if the train reached the goal, then Gi = 1

Step 4. Update summary time of i-th train *i ii TTt SUM SUM <sup>j</sup>*

Step 5.1. If *<sup>i</sup> T t SUM <sup>p</sup>* then 1 2 min( , ,..., ) *k n T TT T SUM SUM SUM SUM*

Step 6. Check occupancy of tracks in switching moment

Step 6.1. Recalculate position of the train ( ) *i ii S vT t t beg i SUM j p*

If switching points are busy, then TΣ = ∞, algorithm ENDS; else Goto 1

1 step: Initialize random set of possible solutions: { , ,..., } (0) (0)

3 step: Arrange solutions by evaluation: { , ,..., }, ( ) ( ) <sup>1</sup> <sup>2</sup> <sup>1</sup>

4 step: Duplicate the best solutions in the elite set: *S S <sup>E</sup>* ;

A genetic algorithm for the task solution may be described with the following steps.

2 step: Evaluate each solution with a target function: { ( ), ( ),..., ( )} <sup>1</sup> <sup>2</sup> *<sup>p</sup>*

5 step: **Selection.** Select from the set of solution pairs according to the defined selection:

6 step: **Crossover:** Generate a new population from the set of the solution pair according to

(0)

2 (0) 1

*<sup>S</sup> V F s F s F s* ;

max *<sup>s</sup> S s s s* ;

*<sup>S</sup> S s s s <sup>p</sup> F s opt V* ;

Step 5.2 If *k = i* then Goto 6, else *i = k*, Goto 1

Step 6.2. Find "tail" of the train *<sup>i</sup> S SL end be <sup>g</sup> <sup>i</sup>*

Step 6.3. Check the occupancy of all tracks.

Intelligent Devices Using Satellite Navigation for Railway Transport 407

*b r j b r b jrb i i v S <sup>v</sup> S SSS t t ttt v*

else if the j-th section is not a signal then j = j + 1, select the next section of the route

Step 5. Check if the summary time is less than the next point switching time ? *<sup>i</sup> T t SUM p*

Step 3.1. Check if all trains reached the goal then 1 2 max( , ,..., ) *<sup>n</sup> T TT T SUM SUM SUM*

Step 2.3. If train is already stopped then check If all sections in Step 2.1 are free, then

*i i i r*

; ; ; ; ;0 <sup>2</sup>

 *v* 

 


The routing task for accident prevention consists of a generation of a new route and schedule for rolling stocks V moving on points P.

The target function for scheduling and routing is to arrange points for each train to reach a destination and assigning of time moments t to each train and each point.


The target function for an optimal point state on the station is the following:

$$T\_{\Sigma} = f(\mathbf{t}\_1, \mathbf{t}\_2, \dots, \mathbf{t}\_n; \quad \mathbf{x}\_{11}, \mathbf{x}\_{12}, \dots, \mathbf{x}\_{1q}; \quad \dots \quad \mathbf{x}\_{n1}, \mathbf{x}\_{n2}, \dots, \mathbf{x}\_{nq}) \to \min \tag{22}$$

ti – the i-th time moment of switching points

xij – state of the j-th point in the i-th time moment

### **5. Evolutionary algorithms for problem solution**

#### **5.1 Fitness function for genetic algorithm**

Step 0. Initialization

Ti sum = 0 – for each i-th train summary time

Gi = 0, for each i-th train goal achievement

i = 1 – selected train number

Step 1. Moving the time calculation of the i-th train on the j-th railway section, / *<sup>i</sup> j j <sup>i</sup> tSv* where

Sj – length of the j-th section,

vi – current i-th train speed

Step 2. Check if the j-th section ends with signal.

Step 2.1. Check the occupancy of all tracks to the next signal.

Step 2.2. If any of sections in Step 2.1 is busy and the train is moving, then recalculate time with braking conditions and Goto 4.

$$S\_b^i = \frac{-\upsilon\_i^2}{2\mathcal{E}}; \quad S\_r = S\_j - S\_b; \quad t\_r = \frac{S\_r}{\upsilon\_i}; \quad t\_b = \frac{\upsilon}{\mathcal{E}}; \quad t\_j^i = t\_r + t\_b; \quad \upsilon\_i = 0$$

Step 2.3. If train is already stopped then check If all sections in Step 2.1 are free, then recalculate time with acceleration conditions

Step 2.4. j = j + 1, select next section of the route

else if the j-th section is not a signal then j = j + 1, select the next section of the route

Step 3. Check if the train reached the goal, then Gi = 1

Step 3.1. Check if all trains reached the goal then 1 2 max( , ,..., ) *<sup>n</sup> T TT T SUM SUM SUM*

Step 3.2. Function STOPS

406 Infrastructure Design, Signalling and Security in Railway




The routing task for accident prevention consists of a generation of a new route and

The target function for scheduling and routing is to arrange points for each train to reach a

Step 1. Moving the time calculation of the i-th train on the j-th railway section, / *<sup>i</sup>*

Step 2.2. If any of sections in Step 2.1 is busy and the train is moving, then recalculate time

1 2 11 12 1 1 2 *T ft t t x x x x x x* ( , ,..., ; , ,..., ; ... , ,..., ) min *<sup>n</sup> q n n nq* (22)

*j j <sup>i</sup> tSv*

destination and assigning of time moments t to each train and each point.

*V tt t p p pm*

The target function for an optimal point state on the station is the following:

*<sup>v</sup> P tt t v v vs*



schedule for rolling stocks V moving on points P.

 Train's schedule: 1 2 : { , ,..., } 

 Point's schedule: <sup>1</sup> 1 2 : { , ,..., } 

ti – the i-th time moment of switching points xij – state of the j-th point in the i-th time moment

**5.1 Fitness function for genetic algorithm** 

Ti sum = 0 – for each i-th train summary time Gi = 0, for each i-th train goal achievement

Step 2. Check if the j-th section ends with signal.

Step 2.1. Check the occupancy of all tracks to the next signal.

Step 0. Initialization

where

i = 1 – selected train number

Sj – length of the j-th section, vi – current i-th train speed

with braking conditions and Goto 4.

**5. Evolutionary algorithms for problem solution** 

*p*

estimates and the actual value of the difference is zero;

and the actual values.


actual values;

Step 4. Update summary time of i-th train *i ii TTt SUM SUM <sup>j</sup>*

Step 5. Check if the summary time is less than the next point switching time ? *<sup>i</sup> T t SUM p*

Step 5.1. If *<sup>i</sup> T t SUM <sup>p</sup>* then 1 2 min( , ,..., ) *k n T TT T SUM SUM SUM SUM*

Step 5.2 If *k = i* then Goto 6, else *i = k*, Goto 1

Step 6. Check occupancy of tracks in switching moment

Step 6.1. Recalculate position of the train ( ) *i ii S vT t t beg i SUM j p*

Step 6.2. Find "tail" of the train *<sup>i</sup> S SL end be <sup>g</sup> <sup>i</sup>*

Step 6.3. Check the occupancy of all tracks.

If switching points are busy, then TΣ = ∞, algorithm ENDS; else Goto 1

#### **5.2 Genetic algorithm**

A genetic algorithm for the task solution may be described with the following steps.

1 step: Initialize random set of possible solutions: { , ,..., } (0) (0) 2 (0) 1 (0) max *<sup>s</sup> S s s s* ;

2 step: Evaluate each solution with a target function: { ( ), ( ),..., ( )} <sup>1</sup> <sup>2</sup> *<sup>p</sup> <sup>S</sup> V F s F s F s* ;

3 step: Arrange solutions by evaluation: { , ,..., }, ( ) ( ) <sup>1</sup> <sup>2</sup> <sup>1</sup> *<sup>S</sup> S s s s <sup>p</sup> F s opt V* ;

4 step: Duplicate the best solutions in the elite set: *S S <sup>E</sup>* ;

5 step: **Selection.** Select from the set of solution pairs according to the defined selection: *S S <sup>C</sup>* ;

6 step: **Crossover:** Generate a new population from the set of the solution pair according to the defined crossover algorithm:

Evolutionary Algorithms in Embedded

**5.3.2 The negative selection algorithm** 

not to match any normal system state.

signal depending on the detected fault.

**6.1 Computer experiment of genetic algorithm** 

**6. Computer experiments** 

the risk of their collision.

positive rate. The algorithm:

detection including those in engines and other devices.

Step 2. Generate a set of candidate detectors *C* = {c*1, c2, …, cn* }.

possible future actions instead of simply reporting the incidents.

Step 3. Compare each candidate ci to the set of known good elements *P*.

move the matched candidate away from the closest element *pj*, then store it in *D*.

Intelligent Devices Using Satellite Navigation for Railway Transport 409

1 (,) | | *L <sup>p</sup> <sup>p</sup> <sup>M</sup> i i i D Ag Ab Ag Ab* 

By varying the value of the parameter *p* a suitable measure of distance can be obtained.

Negative selection is the paradigm describing the evolution of the T-lymphocytes where they are randomly generated and learn to recognize all except the self structures, specic to the host. Negative selection algorithms need training samples only from one class (self, normal), thus, they are especially suited for the tasks such as novelty, anomaly or change

The key advantage of anomaly detection systems is their ability to detect novel attack patterns for which no signature exists, while their most notable disadvantage is a larger false

Step 1. Define a set *S* which needs to be monitored and the set *P* of the know self 1 2 , ,..., *<sup>L</sup> m mm m S <sup>L</sup>* elements in a feature space *U*. The set *U* corresponds to all the possible system states, *P* – normal states and *S* – the current state which changes in time.

Step 4. If a match occurs, discard the individual *ci*, otherwise store it in the mature detector set *D*. Or, to maximize the nonself space coverage with a minimum number of detectors,

Step 5. Monitor *S* for changes by continually matching it against the detectors in *D*. If any detector matches, the change which has occurred most likely is dangerous, as *D* is designed

This algorithm produces a set of the detectors capable to recognize non-self patterns. The action following the recognition varies according to the problem under consideration. In the case of transport safety control system it could be an alarm or issue of an immediate stop

The detectors and the caught fault conditions are stored in an immune memory for further processing and to provide further information about the consequences of the attack and

The task of the experiment is to minimize idle time of trains on the station and to minimize

$$\overline{s}\_i \Pi \overline{s}\_j \to \mathbf{s}\_i' = \mathbf{s}\_{ij} \mathbf{;} \mathbf{s}\_j' = \mathbf{s}\_{ji}, \quad i, j = \overline{1, p} \text{ :} \tag{23}$$

7 step: **Mutation:** Random change of one of solution parameter that helps to find a global optimum of the function:

$$\mathbf{x}\_{j}^{x\_{i}^{\circ}} = \mathbf{x}\_{j}^{x\_{i}^{\circ}} + 1, \quad \mathbf{s}\_{i}^{\circ} \in S^{\prime}, \quad j = rand(\overline{1,k}), \quad i = rand(\overline{1,p}); \tag{24}$$

8 step: Evaluate the new population using the target function:

$$W^{S^{\prime}} = \{ F(\mathbf{s}^{\prime}\_{\perp}), F(\mathbf{s}^{\prime}\_{\perp}), \dots, F(\mathbf{s}^{\prime}\_{\perp}) \}\; \; \; \tag{25}$$

9 step: Arrange the new population by the evaluation values:

$$\overline{S}' = \{\overline{s}'\_{\perp}, \overline{s}'\_{\perp}, \dots, \overline{s}'\_{\perp}\}, \quad F(\overline{s}'\_{\perp}) = opt(V^{\,^S});\tag{26}$$

10 step: Add the new population of solution to the elite set: *S* (*S S* '); *<sup>E</sup>*

11 step: Delete the last solutions from the population *S* if its size exceeds predefined population size *p*: /{ , ,...} *<sup>p</sup>*<sup>1</sup> *<sup>p</sup>*2| *S S s s* ;

12 step: Algorithm stops by time, generation, convergence or by another predefined criteria. If stop criteria is false then repeat the algorithm from step 4. If true then the result of the algorithm is solution s1.

#### **5.3 Algorithm for an artificial immune system**

#### **5.3.1 Shape-space concept**

AIS are modeled after biological IS and carry the terms of antigens and antibodies. They can be modeled using the shape-space concept (see Fig. 8.) (Musilek et al., 2009). The shapespace S allows defining antigens, receptors and their interactions in a quantitative way.

Fig. 8. A shape-space model of an antigen and an antibody.

Like chromosomes in the in the evolutionary algorithms, depending on a problem being solved it also could be a set of integers or binary numbers – *m ZL* or {0,1}*<sup>L</sup> m* .

The affinity of an antigen–antibody pair is related to their distance in the shape-space S and can be estimated using any distance measure between the two attribute strings. The distance between an antigen, *Ag*, and an antibody, *Ab*, can be dened, for example, using a general class of Minkowski distance measures:

$$D\_M(Ag\_\prime Ab) = \sqrt[p]{\sum\_{i=1}^L |Ag\_i - Ab\_i|^{p^\*}}$$

By varying the value of the parameter *p* a suitable measure of distance can be obtained.

### **5.3.2 The negative selection algorithm**

Negative selection is the paradigm describing the evolution of the T-lymphocytes where they are randomly generated and learn to recognize all except the self structures, specic to the host. Negative selection algorithms need training samples only from one class (self, normal), thus, they are especially suited for the tasks such as novelty, anomaly or change detection including those in engines and other devices.

The key advantage of anomaly detection systems is their ability to detect novel attack patterns for which no signature exists, while their most notable disadvantage is a larger false positive rate.

The algorithm:

408 Infrastructure Design, Signalling and Security in Railway

7 step: **Mutation:** Random change of one of solution parameter that helps to find a global

1, ' ', (1, ), (1, ) ' ' *x x s S j rand k i rand p <sup>i</sup>*

{ ( ' ), ( ' ),..., ( ' )} <sup>1</sup> <sup>2</sup>

{ ' , ' ,..., ' }, ( ' ) ( )

11 step: Delete the last solutions from the population *S* if its size exceeds predefined

12 step: Algorithm stops by time, generation, convergence or by another predefined criteria. If stop criteria is false then repeat the algorithm from step 4. If true then the result of the

AIS are modeled after biological IS and carry the terms of antigens and antibodies. They can be modeled using the shape-space concept (see Fig. 8.) (Musilek et al., 2009). The shapespace S allows defining antigens, receptors and their interactions in a quantitative way.

Like chromosomes in the in the evolutionary algorithms, depending on a problem being

The affinity of an antigen–antibody pair is related to their distance in the shape-space S and can be estimated using any distance measure between the two attribute strings. The distance between an antigen, *Ag*, and an antibody, *Ab*, can be dened, for example, using a

solved it also could be a set of integers or binary numbers – *m ZL* or {0,1}*<sup>L</sup> m* .

1 2 1

10 step: Add the new population of solution to the elite set: *S* (*S S* '); *<sup>E</sup>*

optimum of the function:

*s j*

8 step: Evaluate the new population using the target function:

9 step: Arrange the new population by the evaluation values:

'

'

*s j*

population size *p*: /{ , ,...} *<sup>p</sup>*<sup>1</sup> *<sup>p</sup>*2| *S S s s* ;

**5.3 Algorithm for an artificial immune system** 

Fig. 8. A shape-space model of an antigen and an antibody.

general class of Minkowski distance measures:

algorithm is solution s1.

**5.3.1 Shape-space concept** 

*s s s s s s i j p ji <sup>j</sup> <sup>i</sup> <sup>j</sup> <sup>i</sup> ij* ' ; , , 1, ' ; (23)

*<sup>i</sup> <sup>i</sup>* ; (24)

*p <sup>S</sup> V F s F s F s* ; (25)

*<sup>S</sup> S s s s <sup>p</sup> F s opt V* ; (26)

'

Step 1. Define a set *S* which needs to be monitored and the set *P* of the know self 1 2 , ,..., *<sup>L</sup> m mm m S <sup>L</sup>* elements in a feature space *U*. The set *U* corresponds to all the possible system states, *P* – normal states and *S* – the current state which changes in time.

Step 2. Generate a set of candidate detectors *C* = {c*1, c2, …, cn* }.

Step 3. Compare each candidate ci to the set of known good elements *P*.

Step 4. If a match occurs, discard the individual *ci*, otherwise store it in the mature detector set *D*. Or, to maximize the nonself space coverage with a minimum number of detectors, move the matched candidate away from the closest element *pj*, then store it in *D*.

Step 5. Monitor *S* for changes by continually matching it against the detectors in *D*. If any detector matches, the change which has occurred most likely is dangerous, as *D* is designed not to match any normal system state.

This algorithm produces a set of the detectors capable to recognize non-self patterns. The action following the recognition varies according to the problem under consideration. In the case of transport safety control system it could be an alarm or issue of an immediate stop signal depending on the detected fault.

The detectors and the caught fault conditions are stored in an immune memory for further processing and to provide further information about the consequences of the attack and possible future actions instead of simply reporting the incidents.

### **6. Computer experiments**

### **6.1 Computer experiment of genetic algorithm**

The task of the experiment is to minimize idle time of trains on the station and to minimize the risk of their collision.

Evolutionary Algorithms in Embedded

**6.2.1 Collecting the location data** 

Fig. 11. The location data collection scheme.

Intelligent Devices Using Satellite Navigation for Railway Transport 411

1 88087.15753678 610.47947316824 2 82128.38630517 413.47947316824 3 70197.754252487 270 4 50320.950968194 270 5 32391.38814628 270 6 26405.504351969 270 7 14391.055583579 270 8 2366.4284573351 270 9 2332.525484097 270 10 329.57671570692 270 11 307.08794731682 270 12 270 270

One data set for the experiment was taken from the two PLCs in the field attached to a

The communication between the PLCs is facilitated by GPRS modules and a server running on a PC. Through the chain of software tools the data is piped from the PLCs to DB tables. The data was collected into two tables for records related to a vehicle and a level crossing. The report (Fig. 4) contains this data cross-matched using the date and time — as all the data

was simultaneously recorded with discrete steps of 1 s, the matches are 1:1.

This provides a set of data for test runs of the algorithms.

**Generation Average Best** 

Table 1. Average and best values of fitness function on each generation

vehicle and a level crossing. The data collection scheme is presented in Fig. 11.

**6.2 Computer experiment for an artificial immune system** 

The station (Fig. 9.) with 4 points p1, p2, p3, p4 is given and two trains V1 and V2 are approaching. Railway tracks of the station are split into the sections, where start and end of each section is a point or a signal. The length of the trains Lv1 = 500 m and Lv2 = 300 m is given.

Fig. 9. Structure of the station for the computer experiment


Fig. 10. Results of Genetic Algorithm - a) first iteration, b) last iteration

The fitness function and the algorithm are realised in the program and the following parameters for genetic algorithm are used:


Table 1. shows the dynamics of genetic algorithm. The algorithm is performed in 2 seconds and the algorithm converges completely in the 12th generation, where an average value of the population is equal with the best value.


Table 1. Average and best values of fitness function on each generation

### **6.2 Computer experiment for an artificial immune system**

### **6.2.1 Collecting the location data**

410 Infrastructure Design, Signalling and Security in Railway

The station (Fig. 9.) with 4 points p1, p2, p3, p4 is given and two trains V1 and V2 are approaching. Railway tracks of the station are split into the sections, where start and end of each section is a point or a signal. The length of the trains Lv1 = 500 m and Lv2 = 300 m

a) b)

The fitness function and the algorithm are realised in the program and the following

Table 1. shows the dynamics of genetic algorithm. The algorithm is performed in 2 seconds and the algorithm converges completely in the 12th generation, where an average value of

Fig. 10. Results of Genetic Algorithm - a) first iteration, b) last iteration

parameters for genetic algorithm are used:

the population is equal with the best value.


Fig. 9. Structure of the station for the computer experiment

is given.

One data set for the experiment was taken from the two PLCs in the field attached to a vehicle and a level crossing. The data collection scheme is presented in Fig. 11.

Fig. 11. The location data collection scheme.

The communication between the PLCs is facilitated by GPRS modules and a server running on a PC. Through the chain of software tools the data is piped from the PLCs to DB tables.

The data was collected into two tables for records related to a vehicle and a level crossing. The report (Fig. 4) contains this data cross-matched using the date and time — as all the data was simultaneously recorded with discrete steps of 1 s, the matches are 1:1.

This provides a set of data for test runs of the algorithms.

Evolutionary Algorithms in Embedded

Fig. 13. The first generation of detectors with unscaled values.

Fig. 14. The fourth generation of detectors after running several suppressions.

Fig. 15. Test runs with a sample of antigens on each detector generation with detection results.

Intelligent Devices Using Satellite Navigation for Railway Transport 413

### **6.2.2 The real-value negative selection algorithm**

The RNS detector generation starts with a population of candidate detectors, which are then matured through an iterative process. In particular, the center of each detector is chosen at random and the radius is a variable parameter which determines the size of the detector in m-dimensional space. The basic algorithmic steps of the generation algorithm are given in 5.3.2.

The whole detector generation process terminates when a set of mature (minimum overlapping) detectors are evolved which can provide significant coverage of the non-self space.

A detector is defined as *d = (c, rd)*, where *c = (c1, c2, …, cm)* is an *m*-dimensional point that corresponds to the center of a hypersphere with *rd* as its radius. The following parameters are used (Fig. 12):





Fig. 12. A screenshot from the computer program running a real-valued negative selection algorithm showing the initial settings for training the detector set.

During the straightforward detection process the matured detectors are continually compared to new test data samples. The distance *D* between a sample pattern *p = (cp, rs)* and a detector *d = (cd, rd)* is computed in the same way as in the detector generation phase*.* If *D < (rs + rd)* then the detector *d* gets activated indicating possible fault.

#### Evolutionary Algorithms in Embedded Intelligent Devices Using Satellite Navigation for Railway Transport 413

412 Infrastructure Design, Signalling and Security in Railway

The RNS detector generation starts with a population of candidate detectors, which are then matured through an iterative process. In particular, the center of each detector is chosen at random and the radius is a variable parameter which determines the size of the detector in m-dimensional space. The basic algorithmic steps of the generation algorithm are given in

The whole detector generation process terminates when a set of mature (minimum overlapping) detectors are evolved which can provide significant coverage of the non-self

A detector is defined as *d = (c, rd)*, where *c = (c1, c2, …, cm)* is an *m*-dimensional point that corresponds to the center of a hypersphere with *rd* as its radius. The following parameters

 *α*: variable movement of a detector away from a self sample or existing detectors; *ξ*: maximum allowable overlap among the detectors, allowing some overlap can reduce

Fig. 12. A screenshot from the computer program running a real-valued negative selection

During the straightforward detection process the matured detectors are continually compared to new test data samples. The distance *D* between a sample pattern *p = (cp, rs)* and a detector *d = (cd, rd)* is computed in the same way as in the detector generation phase*.* If

algorithm showing the initial settings for training the detector set.

*D < (rs + rd)* then the detector *d* gets activated indicating possible fault.

**6.2.2 The real-value negative selection algorithm** 

5.3.2.

space.

are used (Fig. 12):

*rs*: threshold variation of a self point;

holes in the non-self coverage.


#### Fig. 13. The first generation of detectors with unscaled values.


Fig. 14. The fourth generation of detectors after running several suppressions.


Fig. 15. Test runs with a sample of antigens on each detector generation with detection results.

Evolutionary Algorithms in Embedded

Fig. 17. Input data from PLC to computer model

Fig. 18. Model of the railway system

Intelligent Devices Using Satellite Navigation for Railway Transport 415

The testing of the algorithms on a 2-dimentional space proves that the detectors show good coverage of the non-self space and a stable detection of non-self antigens. Fig. 13. shows the coordinates, radii, overlap and detection score of the first detector generation. The population should stay the same but after 3 generations the detector population decreased (Fig. 14.) but still detected the pathogens (Fig. 15). The chosen actions did not differ much probably because of the implementation which needs further research and improvement.

### **6.3 Computer simulation of the railway station**

For the experiments the program for programmable controller was implemented. The controller performs all the calculations and controls the electric drive and traffic lights on the functional prototype.

The computer model is created to show the results of controller's operations to perform an emergency stop before the red signal of the traffic lights.

The specific environment is developed by the authors for the modelling of railway system for safety improving algorithms (Fig. 16).

The data from the specific memory addresses of the controller is read by the server (Fig. 17.) and transferred to the model.

Fig. 16. Simulation environment

The testing of the algorithms on a 2-dimentional space proves that the detectors show good coverage of the non-self space and a stable detection of non-self antigens. Fig. 13. shows the coordinates, radii, overlap and detection score of the first detector generation. The population should stay the same but after 3 generations the detector population decreased (Fig. 14.) but still detected the pathogens (Fig. 15). The chosen actions did not differ much probably because of the implementation which needs further research and

For the experiments the program for programmable controller was implemented. The controller performs all the calculations and controls the electric drive and traffic lights on the functional

The computer model is created to show the results of controller's operations to perform an

The specific environment is developed by the authors for the modelling of railway system

The data from the specific memory addresses of the controller is read by the server (Fig. 17.)

improvement.

prototype.

**6.3 Computer simulation of the railway station** 

emergency stop before the red signal of the traffic lights.

for safety improving algorithms (Fig. 16).

and transferred to the model.

Fig. 16. Simulation environment


Fig. 17. Input data from PLC to computer model

Fig. 18. Model of the railway system

Evolutionary Algorithms in Embedded

any sector of a railway.

PCT/EP2011/067474.

installed on the demonstrator.

Intelligent Devices Using Satellite Navigation for Railway Transport 417

regular braking evaluates whether the regular braking is started. The device warns the driver about the necessity of starting process of the emergency braking taking into account the signal of the traffic light and speed limitation and allows to perform an automatic operation of the emergency braking in time and stops the train preventing trains collision at

Fig. 20. presents the demonstration of this device that can be installed on the train. Two traffic lights; the electric motor; sensors and wireless communication equipment are

According to the traffic light signal the controller selects the appropriate engine speed. When the red light is on, the control system automatically stops the engine. In response to the light sensor, the control unit in addition to the fan is turned on and switches to another mode of operation. Remote monitoring and control of the processes is possible using wireless communication. In a real system, it could be dispatching control centres, from which it is possible to switch both signals and also take over control of the train speed.

Taking into account the pieces of advice and the recommendations from the State joint stock company "Latvian Railways" (Latvijas Dzelzceļš/LDz) specialists, the prototypes of the locomotive and the signal devices have been created. Both inventions were issued Latvian and International Patents No. LV13978 B, LV14156 B, LV14187 B, WO 2011/115466 A2,

Fig. 20. Functional prototype and information screen with satellite navigation data

The authors and the LDz staff had tested the prototypes of the devices in real service conditions. A non-busy section of the railway was chosen to play the role of a proving ground. During the experiment all the devices were working steadily and without troubles, thus the experiment proved that the ideas adopted in the devices can be implemented into practice.

The task of the locomotive's embedded SAFE-R 3 device and the traffic lights' embedded SAFE-R 4 device, which was designed by the RTU and LDz, is to stop the train automatically at the restrictive signal of the traffic lights, in those cases when a driver does not react to this restrictive signal. It is provided that these devices will also work in unencoded railway sections, where the automatic locomotive signalling did not work.

Fig. 19. Fragment of the electrical part of the computer model of the rolling stock

The current experiment is proposed for modelling of crash prevention of two trains moving towards each other. The model consists of 3 series block-sections; 2 rolling stocks; 4 railway signals (Fig. 18.).

Each rolling stock and signal is equipped with receiving and transmitting devices that give a possibility in a multi-agent system.

Electrical part of the model (Fig. 19.) consists of a DC drive with characteristics of 8 DC motors, 1 switch to connect or disconnect the electric drive from the electric contact network, and 2 pairs of switches for acceleration and for braking that changes direction of field current If flow. A braking branch contains braking resistance. An output of a DC drive is an electrical torque which handles the mechanical part of a rolling stock.

### **7. Experiments of prototype in real conditions**

The result of this work is a train emergency braking device. The invented device is proposed to increase safety on railway transport. It gives possibility to stop rolling stock automatically before a closed signal timely.

In contrast to the known devices that actuate brake only after the passing of a closed signal, the invented device provides a train emergency braking and stopping before a closed section, even if it is not equipped with automatic locomotive signalling. The device also provides a distance control and an emergency braking way calculation.

The detector of the regular braking distance determines an emergency braking distance, but the detector of the starting point of regular braking defines the point on the route when braking should be started. The module for checking the reaching the starting point of regular braking evaluates location of the train, defines starting point of regular braking and operates braking signalling device in the cabin, the module for controlling starting of

Fig. 19. Fragment of the electrical part of the computer model of the rolling stock

electrical torque which handles the mechanical part of a rolling stock.

provides a distance control and an emergency braking way calculation.

**7. Experiments of prototype in real conditions** 

signals (Fig. 18.).

possibility in a multi-agent system.

before a closed signal timely.

The current experiment is proposed for modelling of crash prevention of two trains moving towards each other. The model consists of 3 series block-sections; 2 rolling stocks; 4 railway

Each rolling stock and signal is equipped with receiving and transmitting devices that give a

Electrical part of the model (Fig. 19.) consists of a DC drive with characteristics of 8 DC motors, 1 switch to connect or disconnect the electric drive from the electric contact network, and 2 pairs of switches for acceleration and for braking that changes direction of field current If flow. A braking branch contains braking resistance. An output of a DC drive is an

The result of this work is a train emergency braking device. The invented device is proposed to increase safety on railway transport. It gives possibility to stop rolling stock automatically

In contrast to the known devices that actuate brake only after the passing of a closed signal, the invented device provides a train emergency braking and stopping before a closed section, even if it is not equipped with automatic locomotive signalling. The device also

The detector of the regular braking distance determines an emergency braking distance, but the detector of the starting point of regular braking defines the point on the route when braking should be started. The module for checking the reaching the starting point of regular braking evaluates location of the train, defines starting point of regular braking and operates braking signalling device in the cabin, the module for controlling starting of regular braking evaluates whether the regular braking is started. The device warns the driver about the necessity of starting process of the emergency braking taking into account the signal of the traffic light and speed limitation and allows to perform an automatic operation of the emergency braking in time and stops the train preventing trains collision at any sector of a railway.

Fig. 20. presents the demonstration of this device that can be installed on the train. Two traffic lights; the electric motor; sensors and wireless communication equipment are installed on the demonstrator.

According to the traffic light signal the controller selects the appropriate engine speed. When the red light is on, the control system automatically stops the engine. In response to the light sensor, the control unit in addition to the fan is turned on and switches to another mode of operation. Remote monitoring and control of the processes is possible using wireless communication. In a real system, it could be dispatching control centres, from which it is possible to switch both signals and also take over control of the train speed.

Taking into account the pieces of advice and the recommendations from the State joint stock company "Latvian Railways" (Latvijas Dzelzceļš/LDz) specialists, the prototypes of the locomotive and the signal devices have been created. Both inventions were issued Latvian and International Patents No. LV13978 B, LV14156 B, LV14187 B, WO 2011/115466 A2, PCT/EP2011/067474.

Fig. 20. Functional prototype and information screen with satellite navigation data

The authors and the LDz staff had tested the prototypes of the devices in real service conditions. A non-busy section of the railway was chosen to play the role of a proving ground. During the experiment all the devices were working steadily and without troubles, thus the experiment proved that the ideas adopted in the devices can be implemented into practice.

The task of the locomotive's embedded SAFE-R 3 device and the traffic lights' embedded SAFE-R 4 device, which was designed by the RTU and LDz, is to stop the train automatically at the restrictive signal of the traffic lights, in those cases when a driver does not react to this restrictive signal. It is provided that these devices will also work in unencoded railway sections, where the automatic locomotive signalling did not work.

Evolutionary Algorithms in Embedded

Alamitos, CA.

2009.

Kaunas.

2009.

(26.07.2011.)

26.07.2011.

23.05.2011.

17.03.2010.

A.Bobeško. 22.09.2011. (17.03.2010.)

Ļevčenkovs A., Balckars P., Ribickis L. 14.05.2009.

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Forrest S., Perelson A.S., Allen L., Cherukuri R. Self-nonself discrimination in a computer. In

Kephart J.O.. A biologically inspired immune system for computers. In proceedings of

Dasgupta D., Krishna Kumar K., Wong D., Berry M.. Negative Selection Algorithm for

Mor-Yaroslavtsev A., Levchenkov A. Rolling Stock Location Data Analysis Using an

Powers S. T., He J.. A hybrid articial immune system and Self Organising Map for network

Musilek P., Lau A., Reformat M., Wyard-Scott L.. Immune Programming. Elsevier IS 179,

Gorobetz M., Alps I., Levchenkov A.. Mathematical Formulation of Public Electric Transport

Masutti, T. A. S. Castro L. N. de. A self-organizing neural network using ideas from the immune system to solve the traveling salesman problem. Elsevier IS 179, 2009. Tavakkoli-Moghaddam R., Rahimi-Vahed A., Mirzaei A. H.. A hybrid multi-objective

PCT/EP2011/067474. Device for Safe Passing of Motor Vehicle over Level Crossings

WO 2011/115466 A2, (PCT/LV2011/000004) Controlling Device of Railway Track Sections.

Patent application Nr. P-11-102. Device for Safe Passing of Motor Vehicle over Level

Patent application Nr. P-11-76. Train anticollision device with satellite navigation.

Patent Nr. LV13978 B. Train Emergency Braking Device. Gorobecs M., Greivulis J.,

Patent Nr. LV 14156 B. Controlling Device of Railway Track Sections. A.Ļevčenkovs,

Simulation of Living Systems, 1994. MIT Press.

Telecommunications Forum TELFOR 2011.

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Using Satellite Navigation Systems. A.Ļevčenkovs, M.Gorobecs, I.Raņķis, L.Ribickis, P.Balckars, A.Potapovs, I.Alps, I.Korago, V.Vinokurovs, 6.10.2011.

A.Ļevčenkovs, M.Gorobecs, J.Greivulis, P.Balckars, L.Ribickis, I.Korago,

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A.Ļevčenkovs, M.Gorobecs, I.Raņķis, L.Ribickis, P.Balckars, A.Potapovs,

M.Gorobecs, J.Greivulis, P.Balckars, L.Ribickis, I.Korago, A.Bobeško.

### **8. Conclusions**

Advantages of the proposed device are the following: The device is not using rail circuits and works independently of automatic locomotive signalization system. The proposed device is an alternative or auxiliary to existing safety systems. As opposed to existing systems the new device uses wireless communication network and may work in railway sections without an automatic interlocking system. The possibility to prevent a dangerous situation and a crash corresponding to the condition of the braking system of rolling stock allows stopping the train before dangerous failure time point; possibility of using of already existing measurement devices and sensors together with the new sensors.

The results of the experiment show the possibility to use the proposed system as an auxiliary safety device to prevent breaches of red signal and crashes on the railway.

The most relevant features of immune algorithms are self-learning, diversity maintenance, memory about the past decisions, and detection of previously unknown but related elements, noise rejection and classifying ability.

An intelligent rolling stock safety control system could benefit from using a combination of both an immune negative selection algorithm and a clonal selection algorithm. A fault detection system for railway electric transport could benefit from using an immune negative selection algorithm.

The most feasible way to implement a railway electric transport safety control system would be through the two phases of anomaly detection and determination of their type to draw a conclusion about further action.

Single string data encoding is better suited for use on PLC. The PLC program needs a data buffer to eliminate the risk of data loss due to unstable radio signal.

The authors need to assess the possibility to run the data analysis using these algorithms in real time. The detector maturation and control cell selection processes need improvement.

### **9. References**


Advantages of the proposed device are the following: The device is not using rail circuits and works independently of automatic locomotive signalization system. The proposed device is an alternative or auxiliary to existing safety systems. As opposed to existing systems the new device uses wireless communication network and may work in railway sections without an automatic interlocking system. The possibility to prevent a dangerous situation and a crash corresponding to the condition of the braking system of rolling stock allows stopping the train before dangerous failure time point; possibility of using of already

The results of the experiment show the possibility to use the proposed system as an

The most relevant features of immune algorithms are self-learning, diversity maintenance, memory about the past decisions, and detection of previously unknown but related

An intelligent rolling stock safety control system could benefit from using a combination of both an immune negative selection algorithm and a clonal selection algorithm. A fault detection system for railway electric transport could benefit from using an immune negative

The most feasible way to implement a railway electric transport safety control system would be through the two phases of anomaly detection and determination of their type to draw a

Single string data encoding is better suited for use on PLC. The PLC program needs a data

The authors need to assess the possibility to run the data analysis using these algorithms in real time. The detector maturation and control cell selection processes need improvement.

Russel S. J., Norvig P.. Artificial Intelligence. A Modern Approach, 2 edition. Prentice Hall,

Luo R., Zeng J. Computer simulation of railway train braking and anti-sliding control. //In

Hasegawa Y., Tsunashima H., Marumo Y., Kojima T. Detection of unusual braking behavior

Gorobetz M. Research of Genetic Algorithms for Optimal Control of Electric Transport.

Levchenkov А., Gorobetz М., Ribickis L., Balckars P. "Generating of Multi-Criteria

Vehicles on Roads and Tracks (IAVSD'09), 2009 – 166 p.

Proceedings of 21st International Symposium on Dynamics of Vehicles on Roads

of train driver //In Proceedings of 21st International Symposium on Dynamics of

Alternatives for Decision-Making in Electric Light Rail Control" //In China-USA

auxiliary safety device to prevent breaches of red signal and crashes on the railway.

existing measurement devices and sensors together with the new sensors.

buffer to eliminate the risk of data loss due to unstable radio signal.

and Tracks (IAVSD'09), 2009 – 189 p.

Promotional thesis. Riga, 2008 - 189 p.

Business review, December 2009, pp. 49-55.

elements, noise rejection and classifying ability.

**8. Conclusions** 

selection algorithm.

**9. References** 

conclusion about further action.

2006, 1408p.


**17** 

*France* 

**Study and Design of an Electro Technical** 

Clavel Edith, Meunier Gérard, Bellon Marc and Frugier Didier

The security on the railway network is a real important challenge since today, the number of

In this chapter, an electrical system is presented in order to improve the electrical detection of trains on the network and correctly manage the lights. That is how security is

In the next section, the context of the study is presented. The management of lights on

The third part deals with the electrical system which is experimented by the French National Railway Company to overcome this problem. The way it works and its main characteristics

In order to base the further developments of this solution not only on experiments, a modeling process is presented in the following part. For other industrial fields, it has proved

In order to validate the modeling approach, an experimental set is developed since it is very difficult to make measurements in situ. It will be presented in the fifth part of this chapter.

Finally in a last section, the results of the modeling process are successfully compared to the

The outlook of improving the studied system is important since the impact of some dimensional parameters on its performances is analyzed whether being geometrical or

The distance between trains on a railway is controlled by signals similar to road lights. The railroad line is divided into several sections from 1500m to 20km. Every section is protected by a signal. When a train enters a section , an electrical device detects it and makes the

trains is growing and the saturation of the network is close to be reached.

network is explained to emphasize the possible trouble which may occur.

to be efficient and its use in the case of a railway system seems possible.

**1. Introduction** 

ensured.

will be detailed.

measures.

physical parameters.

**2. Context of the study** 

**Device for Safety on Railway Network** 

*G2Elab Grenoble Electrical Engineering Laboratory, Saint Martin d'Hères, BP46, Saint Martin d'Hères, Cedex,* 

Patent Nr. LV 14187 B. Train's Braking Way Control Device. A.Ļevčenkovs, M.Gorobecs, J.Greivulis, I.Uteševs, P.Balckars, L.Ribickis, V.Stupins, S.Holodovs, I.Korago

## **Study and Design of an Electro Technical Device for Safety on Railway Network**

Clavel Edith, Meunier Gérard, Bellon Marc and Frugier Didier *G2Elab Grenoble Electrical Engineering Laboratory, Saint Martin d'Hères, BP46, Saint Martin d'Hères, Cedex, France* 

### **1. Introduction**

420 Infrastructure Design, Signalling and Security in Railway

Patent Nr. LV 14187 B. Train's Braking Way Control Device. A.Ļevčenkovs,

S.Holodovs, I.Korago

M.Gorobecs, J.Greivulis, I.Uteševs, P.Balckars, L.Ribickis, V.Stupins,

The security on the railway network is a real important challenge since today, the number of trains is growing and the saturation of the network is close to be reached.

In this chapter, an electrical system is presented in order to improve the electrical detection of trains on the network and correctly manage the lights. That is how security is ensured.

In the next section, the context of the study is presented. The management of lights on network is explained to emphasize the possible trouble which may occur.

The third part deals with the electrical system which is experimented by the French National Railway Company to overcome this problem. The way it works and its main characteristics will be detailed.

In order to base the further developments of this solution not only on experiments, a modeling process is presented in the following part. For other industrial fields, it has proved to be efficient and its use in the case of a railway system seems possible.

In order to validate the modeling approach, an experimental set is developed since it is very difficult to make measurements in situ. It will be presented in the fifth part of this chapter.

Finally in a last section, the results of the modeling process are successfully compared to the measures.

The outlook of improving the studied system is important since the impact of some dimensional parameters on its performances is analyzed whether being geometrical or physical parameters.

### **2. Context of the study**

The distance between trains on a railway is controlled by signals similar to road lights. The railroad line is divided into several sections from 1500m to 20km. Every section is protected by a signal. When a train enters a section , an electrical device detects it and makes the

Study and Design of an Electro Technical Device for Safety on Railway Network 423

In the case of the electrified lines, which represent 90 % of the French network, rails are very often used to ensure the return of drive current towards the substations. Drive currents are about 1000A. And they have to coexist with currents of 1A from the detecting electrical

In order to be able to easily separate these two currents, the kind of current inside the detecting system depends on the electrified lines. In the case of DC lines, alternative currents are used for the detecting electrical system and in the case of alternative power supply different frequencies are used for the detecting circuit. In that case, the insulation between two detecting systems is carried out using inductive connections which allow the return of

Current of the detecting circuits can be modulated with various frequencies, which can be detected by equipments on board the trains to give to the drivers all the indications in the cabin. This principle of the transmission between the way and the machine is used in the

Sometimes, the short circuit between wheels and rails is not of good quality. This is the case of weak machines, parts of the railway network rarely used, bad wheel/rail contact due to insulating body. So errors of detection by the system can lead to dangerous situations. The light is green even if there is a train in the section. If a more rapid train arrives, an accident

As a consequence, in order to be sure that the signal is well interrupted by the train on a section, the French National Railway Company (SNCF) has added an electrical device which

To avoid this problem of detection, several solutions have been explored:

R

famous French High Speed Train (TGV).

will be described in the following part.



**3. The proposed device** 

Fig. 2. The principle of the detecting electrical system

Busy way

R

Free way

Receiver

system.

the drive current.

could occur.

G

Generator

G

**i**

**i**

light becomes red . When the train penetrates into the following section, its signal turns to a red light, while the signal of the first section becomes yellow. When the train penetrates into the third section, its signal indicates a red light. The signal of the second section gives the indication yellow, and the signal of the first section gives the indication that the way is clear by a green light. So if a train is stopped in a section, the following train will meet a yellow light announcing to the driver that the following light is red. He will have to reduce the speed of the train to be able to stop if necessary. This is illustrated of Fig. 1.

As said before, an electrical system is used to guarantee this security working. It is constituted by:


The generator sends a coded signal through the electric circuit constituted by the rails and the receptor. When the zone included between the generator and the receptor is free, the receptor is able to detect the coded signal: the way is then considered free. When a train enters this section, a great part of current is derived by wheels and axles (what we call "shuntage"); the receptor does not receive this coded signal coming from the generator anymore: the way is then considered busy. Such a device is thus able to detect the presence of trains on a section by the change of the impedance value of the circuit between the rails. When a train is on a section, the rails are short-circuited by the train and the group wheels, axles, rails 1 and 2 have lower impedance. So the measure of the voltage drop at the receptor implies a busy section. This change of electrical circuit is illustrated on Fig. 2.

Fig. 1. The principle of railway lights

light becomes red . When the train penetrates into the following section, its signal turns to a red light, while the signal of the first section becomes yellow. When the train penetrates into the third section, its signal indicates a red light. The signal of the second section gives the indication yellow, and the signal of the first section gives the indication that the way is clear by a green light. So if a train is stopped in a section, the following train will meet a yellow light announcing to the driver that the following light is red. He will have to reduce

As said before, an electrical system is used to guarantee this security working. It is




The generator sends a coded signal through the electric circuit constituted by the rails and the receptor. When the zone included between the generator and the receptor is free, the receptor is able to detect the coded signal: the way is then considered free. When a train enters this section, a great part of current is derived by wheels and axles (what we call "shuntage"); the receptor does not receive this coded signal coming from the generator anymore: the way is then considered busy. Such a device is thus able to detect the presence of trains on a section by the change of the impedance value of the circuit between the rails. When a train is on a section, the rails are short-circuited by the train and the group wheels, axles, rails 1 and 2 have lower impedance. So the measure of the voltage drop at the receptor

the speed of the train to be able to stop if necessary. This is illustrated of Fig. 1.

implies a busy section. This change of electrical circuit is illustrated on Fig. 2.

imposes a difference of potential between the two rails,

difference of potential between the two rails,

constituted by:

section.

Fig. 1. The principle of railway lights

Fig. 2. The principle of the detecting electrical system

In the case of the electrified lines, which represent 90 % of the French network, rails are very often used to ensure the return of drive current towards the substations. Drive currents are about 1000A. And they have to coexist with currents of 1A from the detecting electrical system.

In order to be able to easily separate these two currents, the kind of current inside the detecting system depends on the electrified lines. In the case of DC lines, alternative currents are used for the detecting electrical system and in the case of alternative power supply different frequencies are used for the detecting circuit. In that case, the insulation between two detecting systems is carried out using inductive connections which allow the return of the drive current.

Current of the detecting circuits can be modulated with various frequencies, which can be detected by equipments on board the trains to give to the drivers all the indications in the cabin. This principle of the transmission between the way and the machine is used in the famous French High Speed Train (TGV).

Sometimes, the short circuit between wheels and rails is not of good quality. This is the case of weak machines, parts of the railway network rarely used, bad wheel/rail contact due to insulating body. So errors of detection by the system can lead to dangerous situations. The light is green even if there is a train in the section. If a more rapid train arrives, an accident could occur.

As a consequence, in order to be sure that the signal is well interrupted by the train on a section, the French National Railway Company (SNCF) has added an electrical device which will be described in the following part.

### **3. The proposed device**

To avoid this problem of detection, several solutions have been explored:


Study and Design of an Electro Technical Device for Safety on Railway Network 425

To be efficient, this system has to create a minimum voltage drop between a wheel and the rail. The working frequency of this system is imposed by the French National Railway





But the degrees of freedom are limited because a lot of mechanical constraints exist:


In practice, the environment of the loop changes (shunt, ballast, metallic parts …) and the value of the inductance of the loop changes too. So the resonance frequency is modified. In order to avoid this, it is necessary to continuously adjust the frequency so that the current is

Thanks to three electronic cards, every change of frequency is detected and automatically


A modeling process has to be run in order to take into account all the requirements and

As said before, the aim of the modeling process is to be able to evaluate the voltage and current in the studied structure. This implies to solve the Maxwell's equations and to establish an electrical equivalent circuit on which the circuit equations could be

In order to reach an optimal design of the loop, experiments are not sufficient.

This is the aim of the following part: to present a modeling approach.

The performances of the loop are directly linked to its geometrical size.



In order to perform this, a Phase-locked loop (PLL) is used.



**3.2 Electrical and mechanical requirements** 

Company. The design data for the loop are:



by the driver,

**3.3 Design of the loop** 

sufficient inside the loop.

system (24V),

desired performances.

**4. Modeling method** 

compensated:

This last solution has been generally adopted. This can be made by cleaning the rails. A special accessory has been designed to scrape the rails.

But another way to improve the contact is to help the short circuit created by the wheels and the rails to be efficient by adding an electrical device.

This last option is the topic of this paper.

### **3.1 Working principle of the inductive loop**

The principle of the proposed device is to create a voltage drop of sufficient level in order to make possible a current to flow. This is done by an inductive loop able to induce in the wheels/axles/rails circuit a current of sufficient value.

The proposed device is presented on Fig. 3. It is constituted by:


This loop is in fact the primary circuit of a transformer. The secondary part is constituted by the axles and the rails. The current induced by the loop flows through the axles and the rails and must be high enough to guarantee the electrical contact between the wheels and the rails. During a bad contact rail / wheel, the secondary circuit of the transformer is open and an induced voltage appears between the wheel and the rail and establishes again the electrical contact insuring the "shuntage".

The chariot near the inductive loop constitutes a third circuit of the transformer which can reduce the value of the current inside the axles – rails circuit.

### **3.2 Electrical and mechanical requirements**

To be efficient, this system has to create a minimum voltage drop between a wheel and the rail. The working frequency of this system is imposed by the French National Railway Company. The design data for the loop are:


424 Infrastructure Design, Signalling and Security in Railway

This last solution has been generally adopted. This can be made by cleaning the rails. A

But another way to improve the contact is to help the short circuit created by the wheels and

The principle of the proposed device is to create a voltage drop of sufficient level in order to make possible a current to flow. This is done by an inductive loop able to induce in the

a parallel LC circuit made of capacitors located on the bogies and the inductance of the

This loop is in fact the primary circuit of a transformer. The secondary part is constituted by the axles and the rails. The current induced by the loop flows through the axles and the rails and must be high enough to guarantee the electrical contact between the wheels and the rails. During a bad contact rail / wheel, the secondary circuit of the transformer is open and an induced voltage appears between the wheel and the rail and establishes again the

The chariot near the inductive loop constitutes a third circuit of the transformer which can

Inductive Loop

Chariot

Axles + Rails

special accessory has been designed to scrape the rails.

the rails to be efficient by adding an electrical device.

wheels/axles/rails circuit a current of sufficient value.

a high frequency current controlled generator,

electrical contact insuring the "shuntage".

inductive loop.

The proposed device is presented on Fig. 3. It is constituted by:

reduce the value of the current inside the axles – rails circuit.

Capacitor

Fig. 3. The principle of the detecting electrical system

This last option is the topic of this paper.

**3.1 Working principle of the inductive loop** 


### **3.3 Design of the loop**

The performances of the loop are directly linked to its geometrical size.

But the degrees of freedom are limited because a lot of mechanical constraints exist:


In practice, the environment of the loop changes (shunt, ballast, metallic parts …) and the value of the inductance of the loop changes too. So the resonance frequency is modified. In order to avoid this, it is necessary to continuously adjust the frequency so that the current is sufficient inside the loop.

In order to perform this, a Phase-locked loop (PLL) is used.

Thanks to three electronic cards, every change of frequency is detected and automatically compensated:


In order to reach an optimal design of the loop, experiments are not sufficient.

A modeling process has to be run in order to take into account all the requirements and desired performances.

This is the aim of the following part: to present a modeling approach.

### **4. Modeling method**

As said before, the aim of the modeling process is to be able to evaluate the voltage and current in the studied structure. This implies to solve the Maxwell's equations and to establish an electrical equivalent circuit on which the circuit equations could be

Study and Design of an Electro Technical Device for Safety on Railway Network 427

The mains equations will be detailed in the following paragraph to obtain the equation (13)

In order to easily solve the equation (13) for each considered part, the most important assumption is that current density is uniform. But according the frequency and geometry of the studied structure, skin and proximity effects have to be taken into account during the modeling. So in a first step, all the conductors of the studied structure have to be meshed so

Moreover, as presented in (13), relative permeability µr is assumed to be equal 1. Otherwise further developments of PEEC method are presented and detailed in (Aimé et al., 2009b) and (Kéradec et al., 2005) in order to take into account magnetic material influence on

Finally no propagation aspect is considered for this first presentation. Otherwise, another modeling method has to be applied such as rPEEC or transmission lines approach (Antonini

The problem can be better formalized by considering the integral form of the Maxwell's

**rotE B** *j*

> <sup>0</sup> **B H**

> > **J E**

**E A grad** *j V* 

> **A J**

0 *div***B** (3)

**rotH J** (1)

. (4)

**B rotA** (6)

(5)

(7)

0 (8)

(2)


which is the base to establish the electrical equivalent circuit.

that the current density is uniform inside each mesh.

current distribution.

et al., 2007) and (Clavel et al., 2007).

equations and by assuming: - quasi-static conditions;

From (3), it comes:

**4.2.2 Equations and associated model** 





In such conditions, the following equations can be written:

solved. In the field of electromagnetic approach, two families of modeling methods are facing:


### **4.1 Choice of the modeling method**

Each family of modeling method has advantages and drawbacks.

Concerning the FEM, it is well known and gives good results on the evaluation of the electromagnetic fields everywhere in the space. But it requires the meshing of all the space, i.e. the studied structure but also the air around. Moreover good results imply a good use of the formulations and assumptions at the limits of the studied domain. The results are principally the electromagnetic fields. Then to obtain the electrical equivalent circuit, postprocessing evaluations have to be done.

Concerning the integral methods, the only meshing of the conductive parts makes them very attractive. The number of unknowns is limited. Moreover, an electrical equivalent circuit can directly be deduced from the solving.

The most famous integral methods are the method of moment (MoM) and the PEEC method (Partial Element Equivalent Circuit).

Since the studied structure could be very large and the amount of air around significant, the use of FEM could lead to solve problems with too high a number of unknowns.

So an integral method is chosen to model the studied structure and more particularly the PEEC method which is detailed in the following paragraph.

### **4.2 Principle of the PEEC method**

The PEEC method was firstly introduced by A. Ruehli (Ruehli, 1974). Based on low frequency exact analytical formulae, it consists in extracting the electric parameters from the geometries of conductors. This allows taking into account the electrical parasitic effects of interconnections while evaluating the electromagnetic behavior of an electronic or electrical system.

Full PEEC method takes into account resistive, inductive and capacitive parts.

### **4.2.1 Assumptions**

According the frequency range of the study, the electrical equivalent model could be more or less complicated. Indeed for not so high frequencies, only resistive and inductive effects of cabling are involved in the electromagnetic behavior of the studied system. That is why it is possible to partly use the PEEC method which allows reducing the size of the equivalent model. For the present studied application, frequency is low enough (around some kHz) to limit the evaluation to the resistive and inductive parts.

Nevertheless the capacitive aspect is detailed in (Ardon et al., 2009) to complete the study.

The mains equations will be detailed in the following paragraph to obtain the equation (13) which is the base to establish the electrical equivalent circuit.

In order to easily solve the equation (13) for each considered part, the most important assumption is that current density is uniform. But according the frequency and geometry of the studied structure, skin and proximity effects have to be taken into account during the modeling. So in a first step, all the conductors of the studied structure have to be meshed so that the current density is uniform inside each mesh.

Moreover, as presented in (13), relative permeability µr is assumed to be equal 1. Otherwise further developments of PEEC method are presented and detailed in (Aimé et al., 2009b) and (Kéradec et al., 2005) in order to take into account magnetic material influence on current distribution.

Finally no propagation aspect is considered for this first presentation. Otherwise, another modeling method has to be applied such as rPEEC or transmission lines approach (Antonini et al., 2007) and (Clavel et al., 2007).

### **4.2.2 Equations and associated model**

The problem can be better formalized by considering the integral form of the Maxwell's equations and by assuming:


426 Infrastructure Design, Signalling and Security in Railway

solved. In the field of electromagnetic approach, two families of modeling methods are

Concerning the FEM, it is well known and gives good results on the evaluation of the electromagnetic fields everywhere in the space. But it requires the meshing of all the space, i.e. the studied structure but also the air around. Moreover good results imply a good use of the formulations and assumptions at the limits of the studied domain. The results are principally the electromagnetic fields. Then to obtain the electrical equivalent circuit, post-

Concerning the integral methods, the only meshing of the conductive parts makes them very attractive. The number of unknowns is limited. Moreover, an electrical equivalent

The most famous integral methods are the method of moment (MoM) and the PEEC method

Since the studied structure could be very large and the amount of air around significant, the

So an integral method is chosen to model the studied structure and more particularly the

The PEEC method was firstly introduced by A. Ruehli (Ruehli, 1974). Based on low frequency exact analytical formulae, it consists in extracting the electric parameters from the geometries of conductors. This allows taking into account the electrical parasitic effects of interconnections while evaluating the electromagnetic behavior of an electronic or electrical

According the frequency range of the study, the electrical equivalent model could be more or less complicated. Indeed for not so high frequencies, only resistive and inductive effects of cabling are involved in the electromagnetic behavior of the studied system. That is why it is possible to partly use the PEEC method which allows reducing the size of the equivalent model. For the present studied application, frequency is low enough (around some kHz) to

Nevertheless the capacitive aspect is detailed in (Ardon et al., 2009) to complete the

use of FEM could lead to solve problems with too high a number of unknowns.

Full PEEC method takes into account resistive, inductive and capacitive parts.

facing:


**4.1 Choice of the modeling method** 

processing evaluations have to be done.

(Partial Element Equivalent Circuit).

**4.2 Principle of the PEEC method** 

system.

study.

**4.2.1 Assumptions** 

circuit can directly be deduced from the solving.

PEEC method which is detailed in the following paragraph.

limit the evaluation to the resistive and inductive parts.

Each family of modeling method has advantages and drawbacks.



In such conditions, the following equations can be written:

$$\text{rootH} = \text{I} \tag{1}$$

$$\mathbf{rotE} = -j\alpha \mathbf{B} \tag{2}$$

$$\operatorname{div} \mathbf{B} = \mathbf{0} \tag{3}$$

$$\mathbf{B} = \mu\_0 \mathbf{H} \tag{4}$$

$$
\mathbf{J} = \sigma \mathbf{E} \tag{5}
$$

From (3), it comes:

$$\mathbf{B} = \mathbf{rot}\mathbf{A}\tag{6}$$

$$\mathbf{E} = -j\alpha \mathbf{A} - \mathbf{grad}\,V\tag{7}$$

$$
\Delta \mathbf{A} = -\mu\_0 \mathbf{J} \tag{8}
$$

Study and Design of an Electro Technical Device for Safety on Railway Network 429

*B*

*Lk*

Introducing the mutual inductance between two elementary conductors k and i (17), the

*k i ki i k c c L d cd c r*

1 1 . . <sup>4</sup> *k i m m l i k i k kl l*

*c c i l <sup>I</sup> <sup>j</sup> dc dc <sup>j</sup> L I r*

Concerning the term on the right of (13) the following equations can be established

<sup>0</sup> 0 0 . ( . ) . ..

*V d V d V d VV U ext k k k a k a k b k b k a b k*

with *<sup>k</sup>* is the edge of volume ck; **n***<sup>k</sup>* is the normal vector oriented towards the exterior of

<sup>0</sup> .

*k ext k k*

 *LI U* 

1 . . *m k k ki i k i*

*V dc U*

*k ext k ext k k ext k k k*

*V d div V d V d*

**J grad <sup>J</sup> J n** (20)

**Jn Jn Jn** (22)

*k kk*

<sup>000</sup> . .. .. ..

*k*

*R I j*

*c*

*k ab*

 

0 00 .

<sup>4</sup> *k i*

0 0 0

 

assuming the electrokinetic solution gives 0 *div***J** 0 :

*c c*

the surface, *a* and *b* are the current outputs surfaces.

Hence, the electrical equation is deduced (23) and (24):

*A*

*Rk*

**J J** (17)

 

**<sup>J</sup> <sup>J</sup>** (18)

0 0 <sup>0</sup> (. ) . . *k k div V* **J J grad J** *V V div* (19)

<sup>0</sup> . 0 **J n***k k* (21)

**J grad** (23)

(24)

*B*

*k* 

*A* 

Fig. 4. kth element of the conductor

second term of (13) leads to (18).

*j*

*0k*

(7) is the Faraday's law and (8) the Poisson's equation.

Considering a conducting volume c in an external electrical field (Vext), the total electrical field Etotal at any point P in the conductor is given by (9):

$$\mathbf{E}\_{\text{total}}(P) = -j a \mathbf{a}(P) - \mathbf{grad} \, V\_{\text{charge},c}(P) - \mathbf{grad} \, V\_{\text{ext}}(P) \tag{9}$$

Vcharge is the potential due to the electrical charges in the conductor.

If, in a first approximation, the capacitive effects can be neglected, this term is null.

From (8), without propagation effects and magnetic material, it comes (10):

$$\mathbf{A}(P) = \frac{\mu\_0}{4\pi} \int\_{\Omega} \frac{\mathbf{J}}{r} d\Omega \tag{10}$$

where **J** is current density and r the distance between the integration point and P.

Taking (5) and (10) in (9) gives (11):

$$\frac{\mathbf{J}(P)}{\sigma} + j\alpha \frac{\mu\_0}{4\pi} \int\_{\Omega^c} \mathbf{\overline{J}} \, d\Omega = -\mathbf{grad}\, V\_{ext} \tag{11}$$

In order to reach the desired model, it is necessary to suppose a uniform current density. For that, the volume c is divided into m elementary conductors. On each elementary conductor, (12) is written:

$$\mathbf{J}\_k = \mathbf{J}\_{0k}.I\_k\tag{12}$$

J0k is the electrokinetic solution for a 1A current.

Multiplying (11) by J0k, it comes (13):

$$\int\_{\Omega c\_{k}} \mathbf{J}\_{0k} \cdot \frac{\mathbf{J}\_{k}}{\sigma} d\Omega \mathbf{c}\_{k} + j\alpha \frac{\mu\_{0}}{4\pi} \int\_{\Omega c\_{k}} \mathbf{J}\_{0k} \left( \sum\_{i=1}^{m} \int \frac{\mathbf{J}\_{0i} \cdot \mathbf{I}\_{i}}{r} d\Omega \mathbf{c}\_{i} \right) d\Omega \mathbf{c}\_{k} = - \int\_{\Omega c\_{k}} \mathbf{J}\_{0k} \mathbf{grad} \, V\_{ext} \, d\Omega \mathbf{c}\_{k} \tag{13}$$

From (13), the electrical equivalent circuit of a conductor can be deduced (Fig. 4) (Ruehli & Cangellaris, 2001).

(12) inside the first term of (13) gives (14):

$$\int\_{\Omega c\_k} \mathbf{J}\_{0k} \cdot \frac{\mathbf{J}\_k}{\sigma} d\Omega \mathbf{c}\_k = \frac{1}{\sigma} I\_k \int\_{\Omega c\_k} \mathbf{J}\_{0k}^2 d\Omega \mathbf{c}\_k \tag{14}$$

Knowing (15), (16) can be deduced.

$$\frac{1}{\sigma} \int\_{\Omega\_k^c} \mathbf{J}\_{0k}^2 \, d\Omega \mathbf{c}\_k = \mathbf{R}\_k \tag{15}$$

$$\int\_{\Omega\_{k}} \mathbf{J}\_{0k} \cdot \frac{\mathbf{J}\_{k}}{\sigma} d\Omega \mathbf{c}\_{k} = \mathbf{R}\_{k} I\_{k} \tag{16}$$

Fig. 4. kth element of the conductor

Considering a conducting volume c in an external electrical field (Vext), the total electrical

arg () () () () *total P ch e ext* **E A** *j*

If, in a first approximation, the capacitive effects can be neglected, this term is null.

where **J** is current density and r the distance between the integration point and P.

 

> 

<sup>0</sup> ( ) <sup>4</sup> *<sup>c</sup> P d r*

*c <sup>P</sup> jd V r*

In order to reach the desired model, it is necessary to suppose a uniform current density. For that, the volume c is divided into m elementary conductors. On each elementary

*k k k i k k ext k*

From (13), the electrical equivalent circuit of a conductor can be deduced (Fig. 4) (Ruehli &

0 0

*k k k kk*

 

*k k*

2 0 <sup>1</sup> . *k*

*k*

*c c*

*c*

 

*<sup>I</sup> dc j dc dc V dc r*

**J J <sup>J</sup> <sup>J</sup> J grad** (13)

2

**<sup>J</sup> J J** (14)

**<sup>J</sup>** (15)

**<sup>J</sup> <sup>J</sup>** (16)

<sup>1</sup> .

*dc I dc*

*k kk*

<sup>0</sup> .

*k k kk*

*dc RI*

*dc R*

4 *ext*

From (8), without propagation effects and magnetic material, it comes (10):

<sup>0</sup> ( )

0 0 0 0 0 1 . . <sup>4</sup> *<sup>k</sup> k i <sup>k</sup>*

*c c c i c*

*k*

*k*

*c*

*<sup>m</sup> <sup>k</sup> i i*

 

> 

*P V P VP* **grad grad** (9)

**<sup>J</sup> <sup>A</sup>** (10)

**<sup>J</sup> <sup>J</sup> grad** (11)

<sup>0</sup> . *k kk* **J J** *I* (12)

(7) is the Faraday's law and (8) the Poisson's equation.

field Etotal at any point P in the conductor is given by (9):

Taking (5) and (10) in (9) gives (11):

J0k is the electrokinetic solution for a 1A current.

Multiplying (11) by J0k, it comes (13):

Knowing (15), (16) can be deduced.

(12) inside the first term of (13) gives (14):

conductor, (12) is written:

Cangellaris, 2001).

Vcharge is the potential due to the electrical charges in the conductor.

Introducing the mutual inductance between two elementary conductors k and i (17), the second term of (13) leads to (18).

$$L\_{ki} = \frac{\mu\_0}{4\pi} \int\_{\Omega c\_k} \int\_{\Omega c\_i} \frac{\mathbf{J}\_{0k} \mathbf{J}\_{0i}}{r} d\Omega \, c\_i d\Omega \, c\_k \tag{17}$$

$$jao\frac{\mu\_0}{4\pi} \int\_{\Omega c\_k} \mathbf{J}\_{0k} \left(\sum\_{i=1}^m \int\_{\Omega c\_i} \frac{\mathbf{J}\_{0l} \cdot I\_i}{r} d\Omega dc\_i \right) d\Omega dc\_k = jao\sum\_{l=1}^m L\_{kl} \cdot I\_l \tag{18}$$

Concerning the term on the right of (13) the following equations can be established assuming the electrokinetic solution gives 0 *div***J** 0 :

$$\operatorname{div}(V.\mathbf{J}\_{0k}) = \mathbf{J}\_{0k}\mathbf{\cdot}\mathbf{grad}\,V + V.\operatorname{div}\mathbf{J}\_{0} \tag{19}$$

$$\int\_{\Omega c\_k} \mathbf{J}\_{0k} \mathbf{grad} \, V\_{ext} \, d\Omega\_k = \int\_{\Omega c\_k} \operatorname{div} (V\_{ext} \mathbf{J}\_{0k}) d\Omega\_k = \oint\_{\Gamma\_k} V\_{ext} \mathbf{J}\_{0k} \cdot \mathbf{n}\_k \, d\Gamma\_k \tag{20}$$

$$\mathbf{J}\_{0k} \cdot \mathbf{n}\_k = \mathbf{0} \tag{21}$$

$$\oint\_{\Gamma\_{k}} V\_{ext} \mathbf{J}\_{0k} \mathbf{n}\_{k} \, d\Gamma\_{k} = V\_{a} \int \mathbf{J}\_{0k} \mathbf{n}\_{a} \, d\Gamma\_{k} + V\_{b} \int \mathbf{J}\_{0k} \mathbf{n}\_{b} \, d\Gamma\_{k} = -V\_{a} + V\_{b} = -\mathcal{U}\_{k} \tag{22}$$

with *<sup>k</sup>* is the edge of volume ck; **n***<sup>k</sup>* is the normal vector oriented towards the exterior of the surface, *a* and *b* are the current outputs surfaces.

Hence, the electrical equation is deduced (23) and (24):

$$-\int\_{\Omega c\_k} \mathbf{J}\_{0k} \mathbf{grad} \, V\_{ext} \, d\Omega \boldsymbol{c}\_k = \mathcal{U}\_k \tag{23}$$

$$R\_k.I\_k + jo\sum\_{i=1}^{m} L\_{ki}.I\_i = \mathsf{U}\_k\tag{24}$$

Study and Design of an Electro Technical Device for Safety on Railway Network 431

ln

ln

ln

22 4 4

*yz y z*

4 24 24

22 4 4

*xz x z*

22 4 4

*yx y x*

<sup>1</sup> 4 24 24 , , 4. . . . <sup>1</sup> <sup>333</sup>

Arctan

*x yz zy*

60

3

6

combined to a user friendly and efficient graphical interface.

assumption of 1D or 2D current flowing inside them.

4 24 24

2 22

2 22

*xx y z*

The evaluation of the electrical equivalent circuit of the meshed structure has been implemented into the dedicated software InCa3D® which offers a robust and fast solver

For simple shapes of elements, analytical formulations (25) and (26) are used. But if the geometrical configuration is more complex, a numerical technique is used to find the values

In order to properly describe the current distribution inside conductors, an adapted meshing technique has to be applied. Indeed the shape of conductors often allows the

For massive bars, or cables the 1D current leads to only mesh the cross section of conductor. Since no propagation effect is described, the length of conductors has not to be subdivided (Fig. 6). For this kind of conductor, the skin effect can be taken into account concentrating the meshes on the edges of the conductors so that the number of subdivisions is not too big.

Arctan Arc

3 3

6 6

*xyz xy xy z zx y z*

*xx xyz*

*yy xyz*

*zz xyz*

2 22

2 22

2 22

2 22

tan

*xz yx y z*

4 4 4 22 22 22 2 2 2

*x y z yx yz xz x y z*

of the equivalent circuit.

**4.2.3 Meshing techniques** 

Fig. 6. The 1D meshing of conductors

0

*f xyz abcd*

So each term of (13) leads to an electrical characteristic of conductor which is only function of its geometry.

To compute the parasitic resistance Ri in each volume element Vi of length ℓi, section Si, and resistivity , the following analytical formula is used:

$$R\_i = \rho \frac{l\_i}{S\_i} \tag{25}$$

Because of the parallelepiped shape of the elements the double integral in (17) can be expressed in an analytical form and easily computed. For the case of parallel elements, the mutual inductances Mij are computed thanks to an analytical expression. And for the general case presented on Fig. 5, the expressions (26) can be used either to evaluate Mij but also partial inductance Li if a=d, b=c, l1=L2 and E=p=l3=0 (Hoer & Love, 1965). If elements are not parallel an analytical/numerical integration technique is used (an analytical expression for the first integral is used, the second one being computed thanks to an adaptive gauss point integration ensuring a good accuracy). All values of Li and Mij can then be organized in a dense and square matrix [L-M] whose size is equal to the number of mesh elements (Aimé et al., 2007).

Fig. 5. General case of parallel elements for the evaluations of Mij

$$M\_{ij} = \begin{bmatrix} \begin{bmatrix} \begin{bmatrix} \end{bmatrix} f\left(\mathbf{x}, y, \mathbf{z} \right) \end{bmatrix} \begin{bmatrix} \mathbf{x} \\ \mathbf{x} \end{bmatrix} \begin{bmatrix} \mathbf{y} \\ \mathbf{y} \end{bmatrix} \begin{bmatrix} y \\ \mathbf{y} \end{bmatrix} \begin{bmatrix} \mathbf{z} \\ \mathbf{z} \end{bmatrix} \tag{26}$$
 
$$\begin{bmatrix} \begin{bmatrix} \begin{bmatrix} f\left(\mathbf{x}, y, \mathbf{z} \right) \end{bmatrix} \begin{pmatrix} \mathbf{x}\_{1}, \mathbf{x}\_{3} \\ \mathbf{x}\_{2}, \mathbf{x}\_{4} \end{bmatrix} \begin{bmatrix} y\_{1}, y\_{3} \\ \mathbf{y} \end{bmatrix} \begin{bmatrix} \mathbf{z} \\ \mathbf{z} \end{bmatrix} = \sum\_{i=1}^{4} \sum\_{j=1}^{4} \begin{pmatrix} -1 \\ \end{pmatrix}^{i+j+k+1} f\left(\mathbf{x}\_{i}, y\_{j}, \mathbf{z} \right)$$

$$f(x,y,z) = \frac{\mu\_0}{4\pi} \frac{1}{a.b.c.d} \begin{pmatrix} \left(\frac{y^2z^2}{4} - \frac{y^4}{24} - \frac{z^4}{24}\right) x \ln\left(x + \sqrt{x^2 + y^2 + z^2}\right) + \\ \left(\frac{x^2z^2}{4} - \frac{x^4}{24} - \frac{z^4}{24}\right) y \ln\left(y + \sqrt{x^2 + y^2 + z^2}\right) + \\ \left(\frac{y^2x^2}{4} - \frac{y^4}{24} - \frac{x^4}{24}\right) z \ln\left(z + \sqrt{x^2 + y^2 + z^2}\right) + \\ \frac{1}{60} \left(x^4 + y^4 + z^4 - 3y^2x^2 - 3y^2z^2 - 3x^2z^2\right) \sqrt{x^2 + y^2 + z^2} - \\ \frac{xyz}{6} \text{Area}\frac{xy}{z\sqrt{x^2 + y^2 + z^2}} - \frac{xy^3z}{6} \text{Area}\frac{xz}{y\sqrt{x^2 + y^2 + z^2}} - \\ \frac{x^3yz}{6} \text{Area}\frac{zy}{x\sqrt{x^2 + y^2 + z^2}} \end{pmatrix}$$

The evaluation of the electrical equivalent circuit of the meshed structure has been implemented into the dedicated software InCa3D® which offers a robust and fast solver combined to a user friendly and efficient graphical interface.

For simple shapes of elements, analytical formulations (25) and (26) are used. But if the geometrical configuration is more complex, a numerical technique is used to find the values of the equivalent circuit.

#### **4.2.3 Meshing techniques**

430 Infrastructure Design, Signalling and Security in Railway

So each term of (13) leads to an electrical characteristic of conductor which is only function

To compute the parasitic resistance Ri in each volume element Vi of length ℓi, section Si, and

*i*

y

l2

, , 3 2, 3 1

1 3 1 3 1 3

, , 1 ,, *xx zz y y ijk*

, , , <sup>444</sup> <sup>1</sup>

*f xyz x y z fxy z* 

, , 3 2 1, 3

*E dE a l l l l pcpb*

*E d aE l l l l pcbp*

E

c

*<sup>l</sup> <sup>R</sup> <sup>S</sup>* 

Because of the parallelepiped shape of the elements the double integral in (17) can be expressed in an analytical form and easily computed. For the case of parallel elements, the mutual inductances Mij are computed thanks to an analytical expression. And for the general case presented on Fig. 5, the expressions (26) can be used either to evaluate Mij but also partial inductance Li if a=d, b=c, l1=L2 and E=p=l3=0 (Hoer & Love, 1965). If elements are not parallel an analytical/numerical integration technique is used (an analytical expression for the first integral is used, the second one being computed thanks to an adaptive gauss point integration ensuring a good accuracy). All values of Li and Mij can then be organized in a dense and square matrix [L-M] whose size is equal to the number of mesh

*i*

(25)

l3

*i j k*

x

(26)

p

*i*

of its geometry.

elements (Aimé et al., 2007).

a

l1

I1

d

*ij*

I2

Fig. 5. General case of parallel elements for the evaluations of Mij

, ,

2 4 2 4 2 4

*M f xyz x y z*

, , , 111

*xx zz y y ijk*

b

z

resistivity , the following analytical formula is used:

In order to properly describe the current distribution inside conductors, an adapted meshing technique has to be applied. Indeed the shape of conductors often allows the assumption of 1D or 2D current flowing inside them.

For massive bars, or cables the 1D current leads to only mesh the cross section of conductor. Since no propagation effect is described, the length of conductors has not to be subdivided (Fig. 6). For this kind of conductor, the skin effect can be taken into account concentrating the meshes on the edges of the conductors so that the number of subdivisions is not too big.

Fig. 6. The 1D meshing of conductors

Study and Design of an Electro Technical Device for Safety on Railway Network 433

On Fig. 10, the modeling process of every kind of electrical structure is detailed.



For the studied case, the unknowns are the currents inside the equivalent circuit. For that purpose it is necessary to describe the electrical environment of the problem in order to solve the right circuit equations. This last step can be achieved in a circuit solver like SPICE® or Portunus® exporting automatically the equivalent circuit inside these tools. But the size of the equivalent circuit is linked to the number of meshes and can be too big for these tools. Moreover it is not necessary to keep the information of local current inside each mesh. What is interesting is the global current inside the conductors. So a reduced equivalent circuit is better appropriated for this goal. To that aim, the user has to clearly identify the outputs of each conductor and then using parallel and series associations, the equivalent impedance between these points can be evaluated for each frequency. This reduced circuit is afterwards more practical in order to evaluate all necessary currents and voltages. Even if it is frequency dependent, a time simulation can be efficiently done. Indeed, according the frequency range, this dependence can be negligible and if not, numerical techniques to find a non dependent circuit with more components exist (Tan &

**4.3 Modeling process** 

It consists of four steps:


He, 2007).

Fig. 10. Modeling process

In the case of very thin and large conductors such as sheet of copper, ground plane, the 1D current assumption is no more valid. Indeed current is generally flowing in a plane so that a 2D approximation can be sufficient in order to properly describe the physical phenomenon. Two quadrate directions for current inside the conductor are defined. So the developed 2D meshing technique consists in dividing the plane as presented on Fig. 7.

Fig. 7. The 2D meshing of conductors

For both cases, according to the shape of the cross section or conductor, a refinement meshing technique is applied so that the description is close to the real structure (Fig. 8).

Fig. 8. Examples of meshing for complex cross section for 1D assumption

The associated electrical equivalent models for the 1D and 2D elements are summarized on Fig. 9.

Fig. 9. R-L-M electrical equivalent circuit for 1D and 2D elements (mutual inductances are not represented on the figure)

### **4.3 Modeling process**

432 Infrastructure Design, Signalling and Security in Railway

In the case of very thin and large conductors such as sheet of copper, ground plane, the 1D current assumption is no more valid. Indeed current is generally flowing in a plane so that a 2D approximation can be sufficient in order to properly describe the physical phenomenon. Two quadrate directions for current inside the conductor are defined. So the developed 2D

For both cases, according to the shape of the cross section or conductor, a refinement meshing technique is applied so that the description is close to the real structure (Fig. 8).

The associated electrical equivalent models for the 1D and 2D elements are summarized on

Fig. 9. R-L-M electrical equivalent circuit for 1D and 2D elements (mutual inductances are

1D element 2D element

meshing technique consists in dividing the plane as presented on Fig. 7.

Fig. 8. Examples of meshing for complex cross section for 1D assumption

Fig. 7. The 2D meshing of conductors

Fig. 9.

not represented on the figure)

On Fig. 10, the modeling process of every kind of electrical structure is detailed.

It consists of four steps:


For the studied case, the unknowns are the currents inside the equivalent circuit. For that purpose it is necessary to describe the electrical environment of the problem in order to solve the right circuit equations. This last step can be achieved in a circuit solver like SPICE® or Portunus® exporting automatically the equivalent circuit inside these tools. But the size of the equivalent circuit is linked to the number of meshes and can be too big for these tools. Moreover it is not necessary to keep the information of local current inside each mesh. What is interesting is the global current inside the conductors. So a reduced equivalent circuit is better appropriated for this goal. To that aim, the user has to clearly identify the outputs of each conductor and then using parallel and series associations, the equivalent impedance between these points can be evaluated for each frequency. This reduced circuit is afterwards more practical in order to evaluate all necessary currents and voltages. Even if it is frequency dependent, a time simulation can be efficiently done. Indeed, according the frequency range, this dependence can be negligible and if not, numerical techniques to find a non dependent circuit with more components exist (Tan & He, 2007).

Fig. 10. Modeling process

Study and Design of an Electro Technical Device for Safety on Railway Network 435

Different configurations have been tested and for each of them maximum data have been


A

Voltage

Wheel

A

Chariot

source Inductive loop

i\_chariot

i-loop

represent the non perfect electrical contact between the wheel and the rail.

Rail

Current measure Voltage drop measure

Knowing the current I in the loop, the voltage source V, their phase and the frequency (f, =2f) an equivalent circuit for the measured system can be calculated using (27) (Fig. 15).

For each of them open circuit and short circuit measurements have been made.


measured:

V

Wheel

Urw



A

i-rail

Axles

Fig. 13. Measurements procedure

Fig. 14. Used probes (Fluke 867B, current probe PR30)


This proposed modeling process has proved to be very efficient not only for high current electrical systems (Gonnet et al., 2004) but also power electronics devices and structures (Aimé et al., 2009a), electronic card (Clavel et al., 2007a), PCB application (Vialardi et al., 2010) and aircraft structures (Jazzar et al., 2011).

### **5. The experimental structure**

In order to validate the modeling process, experiments have been undertaken.

Unfortunately, measures on real structures are very tricky. A simplified system has thus to be defined. It is presented on Fig. 11. The chariot has been replaced by copper tubes (diameter 42mm); the rails and axles have been replaced by cables (35 mm²). Sizes have been chosen so that the experimental set is close to a real system (Fig. 12).

The characteristics of the voltage source are the same as described in the requirements paragraph.

Rails + axles

Inductive loop

Fig. 11. The experimental system

Fig. 12. Sizes of the experimental system

The measurement procedure consists in measuring (Fig. 13-14):


Different configurations have been tested and for each of them maximum data have been measured:


434 Infrastructure Design, Signalling and Security in Railway

This proposed modeling process has proved to be very efficient not only for high current electrical systems (Gonnet et al., 2004) but also power electronics devices and structures (Aimé et al., 2009a), electronic card (Clavel et al., 2007a), PCB application (Vialardi et al.,

Unfortunately, measures on real structures are very tricky. A simplified system has thus to be defined. It is presented on Fig. 11. The chariot has been replaced by copper tubes (diameter 42mm); the rails and axles have been replaced by cables (35 mm²). Sizes have been

The characteristics of the voltage source are the same as described in the requirements

255 mm

30 mm 1675 mm

185 mm


1535 mm

Inductive loop

Chariot

Chariot

In order to validate the modeling process, experiments have been undertaken.

chosen so that the experimental set is close to a real system (Fig. 12).

2010) and aircraft structures (Jazzar et al., 2011).

**5. The experimental structure** 

Rails + axles

Fig. 12. Sizes of the experimental system


a current probe);

2060 mm

The measurement procedure consists in measuring (Fig. 13-14):


Inductive Loop

Fig. 11. The experimental system

1535 mm

paragraph.


For each of them open circuit and short circuit measurements have been made.

Fig. 13. Measurements procedure

Current measure Voltage drop measure

Fig. 14. Used probes (Fluke 867B, current probe PR30)

Knowing the current I in the loop, the voltage source V, their phase and the frequency (f, =2f) an equivalent circuit for the measured system can be calculated using (27) (Fig. 15).

Study and Design of an Electro Technical Device for Safety on Railway Network 437

In this part the electrical equivalent circuit given by the modeling process is presented as

The CAD complete studied structure is presented on Fig. 17 on which the wheels, chariot,

Indeed in order to correctly solve the problem, some geometrical simplifications have been done. The wheels, the rails and the axles have been replaced by straight massive conductors; four shunts have been added to connect the chariot to the axles in order to represent a

The geometry has been meshed in order to take into account the proximity and frequency

Rail

Wheel

Shunt

Axles

Chariot

Inductive loop

well as comparisons between the circuit simulation and measurements.

**6. Results** 

**6.1 Modeling of the real system** 

Using InCa3D, the result is presented on Fig. 18.

inductive loop clearly appear.

Fig. 17. The complete structure

Fig. 18. InCa3D description of the studied structure

realistic situation.

effects.

Fig. 15. Fresnel's diagram for the evaluation of equivalent circuit

$$\begin{cases} R = \frac{V \cos(\varphi)}{I} \\ L = \frac{V \sin(\varphi)}{2\pi f \cdot I} \end{cases} \tag{27}$$

The second configuration is very close to the classical case of two coupled inductances like a simple transformer. The first one is supplied with an alternative source and an induced current (short-circuit situation) or voltage (open circuit situation) is created on the second one (Fig. 16).

The theoretical study is briefly reminded in the following equations (28) with only one turn for our case (n1=n2=1).

Fig. 16. The simple transformer

$$\begin{aligned} V\_1 &= R\_1.I\_1 + L\_1 \frac{dI\_1}{dt} + M \frac{dI\_2}{dt} \\ V\_2 &= R\_2.I\_2 + L\_2 \frac{dI\_2}{dt} + M \frac{dI\_1}{dt} \end{aligned} \tag{28}$$

The open circuit configuration gives (29). The voltage drop is directly the Urw voltage characterizing the working of the loop.

$$\begin{aligned} V\_{10} &= R\_1 I\_{10} + L\_1 \frac{dI\_{10}}{dt} = R\_1 I\_{10} + L\_1 I\_{10}.ao\\ V\_{20} &= M \frac{dI\_{10}}{dt} = M.I\_{10}.ao \end{aligned} \tag{29}$$

### **6. Results**

436 Infrastructure Design, Signalling and Security in Railway

cos( )

V2

1 2

*dt dt*

2 1

*dt dt*

1 11 1

.

*dI dI V RI L M*

*dI dI V RI L M*

The open circuit configuration gives (29). The voltage drop is directly the Urw voltage

10 10 1 10 1 1 10 1 10

*dI V RI L RI LI dt*

. .

. . ..

2 22 2

10 20 10

*dI V M MI dt*

.

.sin( ) 2 .

*f I*

*I*

The second configuration is very close to the classical case of two coupled inductances like a simple transformer. The first one is supplied with an alternative source and an induced current (short-circuit situation) or voltage (open circuit situation) is created on the second

The theoretical study is briefly reminded in the following equations (28) with only one turn

*L.I.*

(27)

(28)

(29)

*R.I*

*<sup>V</sup> <sup>R</sup>*

 

*<sup>V</sup> <sup>L</sup>*

Fig. 15. Fresnel's diagram for the evaluation of equivalent circuit

V1

one (Fig. 16).

for our case (n1=n2=1).

Fig. 16. The simple transformer

characterizing the working of the loop.

V

In this part the electrical equivalent circuit given by the modeling process is presented as well as comparisons between the circuit simulation and measurements.

### **6.1 Modeling of the real system**

The CAD complete studied structure is presented on Fig. 17 on which the wheels, chariot, inductive loop clearly appear.

Indeed in order to correctly solve the problem, some geometrical simplifications have been done. The wheels, the rails and the axles have been replaced by straight massive conductors; four shunts have been added to connect the chariot to the axles in order to represent a realistic situation.

Using InCa3D, the result is presented on Fig. 18.

The geometry has been meshed in order to take into account the proximity and frequency effects.

Fig. 17. The complete structure

Fig. 18. InCa3D description of the studied structure

Study and Design of an Electro Technical Device for Safety on Railway Network 439

Conditions I\_loop (A) (°) L (µH) R () Only the loop Measure 10.07 -98 5.15 0.25

Loop + Rails + Axles Measure 11.13 -96 4.5 0.44

Table 1. Current in the loop and electrical characteristics for a closed circuit - simulation and

Loop + Rails + Axles Measure 10.8 -95.9 5.21 0.46 24.1 4.66 % Simulation 11.68 -89.8 4.84 0.01 25.22

Table 2. Rail-Wheel voltage and electrical characteristics for an open circuit - simulation and

Once the modeling process is established with satisfactory results, it is possible to make some changes to analyze the influence of some parameters on the performances of the system.

Indeed, using InCa3D, it is possible to define geometrical and physical parameters and

For the studied structure, the following characteristics can be defined as parameters:

make them varying to improve the design of the inductive loop.

Loop + Rails + Axles +

Loop + Rails + Axles + Chariot + 4 shunts

Loop + Rails + Axles

Loop + Rails + Axles + Chariot + 4 shunts

**6.3 Parametric analysis** 






The main performance is the rail/wheel voltage Urw.

+ Chariot

measurements

Conditions I\_loop

Chariot

measurements

Closed circuit

Simulation 10.72 -89.9 4.84 0.01

Simulation 12.84 -89.8 3.98 0.01

Measure 12.6 -95.8 4.05 0.38 Simulation 14.65 -89.8 3.5 0.01

Measure 12.5 -95 4.16 0.34 Simulation 14.95 -89.8 3.49 0.01

Measure 12.04 -95.5 4.59 0.38 21.67 5.45 % Simulation 13.8 -89.8 4.02 0.01 22.85

Measure 12.3 -95.3 4.35 0.37 8.4 1.9% Simulation 14.7 -89.8 3.65 0.01 8.56

Open circuit

(A) (°) L (µH) R () Urw (V) urw

After the PEEC solving, the equivalent circuit has been reduced in order to obtain the simple SPICE-like circuit drawn on Fig. 19 where each part of the system is well identified by an L-R series equivalent circuit. On this circuit all the inductances are coupled with mutual coefficients but they have been cut off to make it clearer.

### **6.2 Comparison between measures and simulation on the experimental set**

The experimental case has been modeled (Fig. 11) using the same process and for each configuration simulation results with the same operating conditions (value of the supply voltage source, frequency) have been compared to the measurements.

The results are presented in Table 1 for the closed circuit and Table 2 for an open one.

A good agreement between simulations and measurements can be observed.

Fig. 19. Reduced electrical equivalent circuit for the studied structure (mutual inductances have been removed)


Table 1. Current in the loop and electrical characteristics for a closed circuit - simulation and measurements


Table 2. Rail-Wheel voltage and electrical characteristics for an open circuit - simulation and measurements

### **6.3 Parametric analysis**

438 Infrastructure Design, Signalling and Security in Railway

After the PEEC solving, the equivalent circuit has been reduced in order to obtain the simple SPICE-like circuit drawn on Fig. 19 where each part of the system is well identified by an L-R series equivalent circuit. On this circuit all the inductances are coupled with mutual

The experimental case has been modeled (Fig. 11) using the same process and for each configuration simulation results with the same operating conditions (value of the supply

**6.2 Comparison between measures and simulation on the experimental set** 

The results are presented in Table 1 for the closed circuit and Table 2 for an open one.

voltage source, frequency) have been compared to the measurements.

A good agreement between simulations and measurements can be observed.

chariot1a chariot1b

wheel1 wheel2

contact1 contact2

rail1

axle1

shunt1

have been removed)

shunt2

chariot2a chariot2b

Fig. 19. Reduced electrical equivalent circuit for the studied structure (mutual inductances

wheel3 wheel4

contact3 contact4

rail2

loop

axle2

Chariot\_middle

shunt4

shunt3

coefficients but they have been cut off to make it clearer.

Once the modeling process is established with satisfactory results, it is possible to make some changes to analyze the influence of some parameters on the performances of the system.

Indeed, using InCa3D, it is possible to define geometrical and physical parameters and make them varying to improve the design of the inductive loop.

For the studied structure, the following characteristics can be defined as parameters:


The main performance is the rail/wheel voltage Urw.

Study and Design of an Electro Technical Device for Safety on Railway Network 441

For example, by reducing by half the length of the loop, the Urw decreases by 32.8%. And by reducing by half the width of the loop, the Urw decreases between 26% and 52% (depending on the place where it is measured -close to the loop or not). If, on the contrary,

The results obtained during these simulations confirm that the coupling between the primary constituted by the loop, and the secondary constituted by the circuit rails-axles, depends on the geometry of the loop. The purpose is obviously that the secondary circuit shares as many lines of magnetic field as possible with the primary one. Since there is no magnetic material which can guide the magnetic flux, contrary to a classic transformer, it is necessary to move as close as possible from the inductive loop of the secondary conductors

Keeping the same loop and moving it under the train so that it is no more under the chariot, the distance between the primary part and the secondary one will increase and the performances will decrease. A secondary part constituted by both rails and axles of two different chariots can also be imagined. Yet the distance between the axles of two consecutive chariots is approximately 15 meters. The length of the loop is then considerably increased, and thus its inductance (ratio 3.7). The voltage source of the loop would then be oversized to obtain an Urw voltage equivalent to that of the current loop. Moreover the cost of the loop would be drastically increased and additional mechanical constraints to fix the

Keeping the same external sizes for the loop, the diameter of the copper tube has been increased in this part of the study. As presented on Fig. 22, this implies a reduction of the

Fig. 21. Three configurations for the sizes and the position of the loop

the length of the loop is increased of 25%, Urw decreases by 11.6%.

to increase the coupling.

loop would appear.

internal surface of the loop.

**6.3.3 Variation of the diameter of the loop** 

Fig. 22. Increase of the diameter f the loop

### **6.3.1 Variation of the height**

The distance between the inductive loop and the rails is varying in this study.

On Fig. 20, results show that the lower this distance is, the higher the Urw is.

This result is quite logical since according to (30) the induced voltage is linked to the magnetic flux. And when the distance between the two loops is low this flux is maximal.

$$e = -\frac{d\varphi}{dt}\tag{30}$$

Nevertheless, the range of variation of this parameter is quite limited because mechanical constraints on the train and required standards for some sizes. There is a minimum value to respect.

By way of contrast, if the distance between the loop and the chariot decreases, the value of Urw decreases too. This is due to the fact that, as said before, the chariot creates a supplementary winding (Fig. 3) in which an induced current can be created. The inductive coupling in this case is higher than between the loop and the rails.

Fig. 20. Urw voltage vs. distance between the loop and the rails

### **6.3.2 Variation of the sizes and the position of the loop**

On Fig. 21, three configurations have been modeled in order to evaluate the impact of the sizes and the position of the loop.

Along the simulations, it has been observed that it is essential that the loop is parallel to the rails and axles unless it performance drastically decreases.

This result is quite logical since according to (30) the induced voltage is linked to the magnetic flux. And when the distance between the two loops is low this flux is maximal.

*d*

*dt* 

Nevertheless, the range of variation of this parameter is quite limited because mechanical constraints on the train and required standards for some sizes. There is a minimum value to

By way of contrast, if the distance between the loop and the chariot decreases, the value of Urw decreases too. This is due to the fact that, as said before, the chariot creates a supplementary winding (Fig. 3) in which an induced current can be created. The inductive

> 10 30 50 70 90 110 **Distance between loop and rails (mm)**

> > I\_loop (A) I\_Rail (A) Urw (V)

On Fig. 21, three configurations have been modeled in order to evaluate the impact of the

Along the simulations, it has been observed that it is essential that the loop is parallel to the

(30)

*e*

The distance between the inductive loop and the rails is varying in this study. On Fig. 20, results show that the lower this distance is, the higher the Urw is.

coupling in this case is higher than between the loop and the rails.

Fig. 20. Urw voltage vs. distance between the loop and the rails

**6.3.2 Variation of the sizes and the position of the loop** 

rails and axles unless it performance drastically decreases.

**6.3.1 Variation of the height** 

respect.

sizes and the position of the loop.

Fig. 21. Three configurations for the sizes and the position of the loop

For example, by reducing by half the length of the loop, the Urw decreases by 32.8%. And by reducing by half the width of the loop, the Urw decreases between 26% and 52% (depending on the place where it is measured -close to the loop or not). If, on the contrary, the length of the loop is increased of 25%, Urw decreases by 11.6%.

The results obtained during these simulations confirm that the coupling between the primary constituted by the loop, and the secondary constituted by the circuit rails-axles, depends on the geometry of the loop. The purpose is obviously that the secondary circuit shares as many lines of magnetic field as possible with the primary one. Since there is no magnetic material which can guide the magnetic flux, contrary to a classic transformer, it is necessary to move as close as possible from the inductive loop of the secondary conductors to increase the coupling.

Keeping the same loop and moving it under the train so that it is no more under the chariot, the distance between the primary part and the secondary one will increase and the performances will decrease. A secondary part constituted by both rails and axles of two different chariots can also be imagined. Yet the distance between the axles of two consecutive chariots is approximately 15 meters. The length of the loop is then considerably increased, and thus its inductance (ratio 3.7). The voltage source of the loop would then be oversized to obtain an Urw voltage equivalent to that of the current loop. Moreover the cost of the loop would be drastically increased and additional mechanical constraints to fix the loop would appear.

### **6.3.3 Variation of the diameter of the loop**

Keeping the same external sizes for the loop, the diameter of the copper tube has been increased in this part of the study. As presented on Fig. 22, this implies a reduction of the internal surface of the loop.

Fig. 22. Increase of the diameter f the loop

Study and Design of an Electro Technical Device for Safety on Railway Network 443

So by changing the resistivity of material, aluminum instead of copper (ratio 1.6), no impact

This aspect is very interesting in an economic point of view because the loop could be made

To model the electrical contact between the wheel and the rail a resistor has been added

And for a 42V voltage source, the Urw is about 3.7V. This characteristic has been drawn on

This study shows that even if the four wheels of the chariot are not in electric contact with the rails, as with a resistance of contact of 1M, the inductive loop always allows to obtain a sufficient Urw voltage which corresponds in this case to the open circuit voltage of a

The bad quality of contacts which is one of the causes of non detection of trains inside a

R I loop I Rail Urw

0 Ω 12.9 A 2.55 A 4.2 V

1 Ω 12.57 V 1.50 A 3.96 V

5 Ω 12.42 V 0.367 A 3.73 V

10 Ω 12.42 A 0.185 A 3.68 V

100 Ω 12.41 V 1.85 10-2 A 3.68 V

1 kΩ 12.41 V 1.85 10-3 A 3.68 V

10 kΩ 12.41 V 1.85 10-4 A 3.68 V

50 kΩ 12.41 V 3.71 10-5 A 3.68 V

100 kΩ 12.41 V 1.85 10-5 A 3.68 V

500 kΩ 12.41 V 3.71 10-6 A 3.68 V

1 MΩ 12.41 V 1.85 10-6 A 3.68 V

Table 3. Comparison between simulation and measurements for an open circuit

By making the value of this resistor vary, it is possible to deteriorate the contact.

Fig. 23 and is close to that of the voltage at the secondary winding of a transformer.

Results are presented on Table 3 for a resistance varying from 1 to 1M.

For values higher than 5, the Urw voltage remains constant.

on the Urw voltage can be underlined.

**6.3.7 Variation of the electrical contact** 

because this is not a perfect short-circuit (Fig. 19).

of a material cheaper than copper.

transformer.

section is then swept away.

The simulations show that for a constant supply voltage the magnetic flux remains constant too. Since =BS, when the diameter of the tube increases the internal surface of the loop decreases. So the induction B increases. As the current is directly proportional to the induction and as =LI, the increase of the induction leads to an increase of the current and thus a decrease of the inductance of the system.

By dividing the diameter of the tube by 2 (21mm), the surface increases by 7.5% and the current in the loop decreases by 13.6%. The inductance increases by 16.7%. The result of this variation of diameter is the decrease of Urw voltage by 8%.

On the contrary, if the diameter of the tube is doubled (84mm), the surface decreases by 13.8%, the current in the loop increases by 20%. The Urw voltage increases by 8%.

But it is not possible to increase this parameter too much because the increase of the current would imply more Joule losses and a higher temperature.

At this step, a question could be to determine the maximum value for the current in the loop regarding the losses but also the EMC performances of the whole system.

### **6.3.4 Variation of the number of turns for the loop**

Keeping the same external shape as the current loop, a second turn has been added using a copper tube of 20mm of diameter.

This additional turn considerably increases the inductance (ratio 3.7). Theoretically, the inductance is proportional to the square of the number of turn (4 in this case).

So with a constant voltage source, the current inside the loop thus decreases with the same ratio and the created magnetic field is also weaker. The Urw voltage is then decreasing by 46%. So it is necessary to increase the voltage source to keep the same performances.

### **6.3.5 Variation of the number of the shunts**

On Fig. 19, it is clear that the four shunts, which connect the chariot to the axles to ensure a return path for the current and protect the persons of an electric risk, introduce new loops in which current can flow.

Using simulations it is possible to connect -or not- these shunts in order to evaluate their impact on the Urw voltage.

Indeed, considering only two shunts Urw voltage increases by 110%. And with only one shunt, no induced current can flow since the circuit is open and the Urw voltage increases then by 210%.But since these shunts ensure the electric safety of the persons, it is not possible to eliminate them.

### **6.3.6 Variation of the resistivity of the material**

Considering the results presented in Table 1, the impedance of the loop is mainly inductive , all the more because the resistive part becomes negligible since the frequency is high.

So by changing the resistivity of material, aluminum instead of copper (ratio 1.6), no impact on the Urw voltage can be underlined.

This aspect is very interesting in an economic point of view because the loop could be made of a material cheaper than copper.

### **6.3.7 Variation of the electrical contact**

442 Infrastructure Design, Signalling and Security in Railway

The simulations show that for a constant supply voltage the magnetic flux remains constant too. Since =BS, when the diameter of the tube increases the internal surface of the loop decreases. So the induction B increases. As the current is directly proportional to the induction and as =LI, the increase of the induction leads to an increase of the current and

By dividing the diameter of the tube by 2 (21mm), the surface increases by 7.5% and the current in the loop decreases by 13.6%. The inductance increases by 16.7%. The result of this

On the contrary, if the diameter of the tube is doubled (84mm), the surface decreases by

But it is not possible to increase this parameter too much because the increase of the current

At this step, a question could be to determine the maximum value for the current in the loop

Keeping the same external shape as the current loop, a second turn has been added using a

This additional turn considerably increases the inductance (ratio 3.7). Theoretically, the

So with a constant voltage source, the current inside the loop thus decreases with the same ratio and the created magnetic field is also weaker. The Urw voltage is then decreasing by 46%. So it is necessary to increase the voltage source to keep the same

On Fig. 19, it is clear that the four shunts, which connect the chariot to the axles to ensure a return path for the current and protect the persons of an electric risk, introduce new loops in

Using simulations it is possible to connect -or not- these shunts in order to evaluate their

Indeed, considering only two shunts Urw voltage increases by 110%. And with only one shunt, no induced current can flow since the circuit is open and the Urw voltage increases then by 210%.But since these shunts ensure the electric safety of the persons, it is not

Considering the results presented in Table 1, the impedance of the loop is mainly inductive ,

all the more because the resistive part becomes negligible since the frequency is high.

13.8%, the current in the loop increases by 20%. The Urw voltage increases by 8%.

regarding the losses but also the EMC performances of the whole system.

inductance is proportional to the square of the number of turn (4 in this case).

thus a decrease of the inductance of the system.

variation of diameter is the decrease of Urw voltage by 8%.

would imply more Joule losses and a higher temperature.

**6.3.4 Variation of the number of turns for the loop** 

**6.3.5 Variation of the number of the shunts** 

**6.3.6 Variation of the resistivity of the material** 

copper tube of 20mm of diameter.

performances.

which current can flow.

impact on the Urw voltage.

possible to eliminate them.

To model the electrical contact between the wheel and the rail a resistor has been added because this is not a perfect short-circuit (Fig. 19).

By making the value of this resistor vary, it is possible to deteriorate the contact.

Results are presented on Table 3 for a resistance varying from 1 to 1M.

For values higher than 5, the Urw voltage remains constant.

And for a 42V voltage source, the Urw is about 3.7V. This characteristic has been drawn on Fig. 23 and is close to that of the voltage at the secondary winding of a transformer.

This study shows that even if the four wheels of the chariot are not in electric contact with the rails, as with a resistance of contact of 1M, the inductive loop always allows to obtain a sufficient Urw voltage which corresponds in this case to the open circuit voltage of a transformer.

The bad quality of contacts which is one of the causes of non detection of trains inside a section is then swept away.


Table 3. Comparison between simulation and measurements for an open circuit

Study and Design of an Electro Technical Device for Safety on Railway Network 445

3,4

1 10 100 1000 10000 100000 1000000 **Frequency (Hz)**

The number of trains on the national network is increasing. In order to ensure a maximum

For that purpose, the French National Railway Company (SNCF) uses an electronic

In case of a bad shuntage, an additional device is used; its working, as well as its main

A modeling process is applied with the support of the PEEC method to generate a complete electrical equivalent circuit of the device. Thanks to measurements, the accuracy of the modeling approach has been validated. The influence of geometrical and physical parameters on the performances of the studied device has been analyzed in order to find the

Future works concerning the evaluation of the supplementary losses, the modeling of magnetic material as well as the modeling of the contact wheel/rail which is not fixed but

Authors want to thank the French National Railway Company for its financial support for

Hoer, C. & Love, C. (1965). Exact Inductance Equations for Rectangular Conductors with

*and Instrumentation*, Vol. 69C, No.2, (April-June 1965), pp. 127-137

Applications to More Complicated Geometries. *Journal of Research C. Engineering* 

detection based on the fact that the set wheel/axles/chariot short circuits the rails.

3,6

3,73,6 3,8

3,18

Urw (V)

0 0,5 1 1,5 2 2,5 3 3,5 4

parameters, is studied in this article.

flowing have to be achieved.

**8. Acknowledgment** 

**9. References** 

main parameters and to optimize the structure.

this study and its help for the experimental sets.

**7. Conclusions** 

Fig. 24. Urw (V) vs. frequency (Hz) of the voltage source

security, it is necessary to localize all the trains all the time.

Fig. 23. Urw vs. resistance of the rail/wheel contact

### **6.3.8 Variation of the frequency of the source**

The supply source of the inductive loop is a 147kHz sinusoidal voltage which is obtained from the 72V battery embedded on the train and electronic cards. This is a specific source and no particular constraints are linked to the other electric systems embedded on the train. So it is possible to imagine a variation of the level of voltage as well as the frequency.

It is clear that, the Urw voltage is directly linked to the voltage value (proportionality). This is logical since no magnetic material has been taken into account in this study.

If there is a magnetic material, with the increase of the voltage, saturation will appear and this proportionality relation will be wrong.

Concerning the frequency, using simulations, it has been changed from 50Hz to 1MHz.

On Fig. 24 the frequency evolution of the Urw voltage is represented.

With the obtained results, since the resistive part of the loop is very low, the famous relation U = LI even for low frequencies is valid. So the current into the loop could be very high for low frequency and but could decrease with increasing frequency.

And to ensure a sufficient value for the Urw voltage it must be higher than some 10A.

So compromise has to be reached to improve the inductive loop, between the values of the voltage source, its frequency, losses, possible saturation if magnetic materials are used.

Fig. 24. Urw (V) vs. frequency (Hz) of the voltage source

### **7. Conclusions**

444 Infrastructure Design, Signalling and Security in Railway

1 10 100 1000 10000 100000 1000000

The supply source of the inductive loop is a 147kHz sinusoidal voltage which is obtained from the 72V battery embedded on the train and electronic cards. This is a specific source and no particular constraints are linked to the other electric systems embedded on the train. So it is possible to imagine a variation of the level of voltage as well as the

It is clear that, the Urw voltage is directly linked to the voltage value (proportionality). This

If there is a magnetic material, with the increase of the voltage, saturation will appear and

With the obtained results, since the resistive part of the loop is very low, the famous relation U = LI even for low frequencies is valid. So the current into the loop could be very high for

So compromise has to be reached to improve the inductive loop, between the values of the voltage source, its frequency, losses, possible saturation if magnetic materials are

Concerning the frequency, using simulations, it has been changed from 50Hz to 1MHz.

And to ensure a sufficient value for the Urw voltage it must be higher than some 10A.

is logical since no magnetic material has been taken into account in this study.

On Fig. 24 the frequency evolution of the Urw voltage is represented.

low frequency and but could decrease with increasing frequency.

Resistance of the rail/wheel contact ()

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5

Fig. 23. Urw vs. resistance of the rail/wheel contact

**6.3.8 Variation of the frequency of the source** 

this proportionality relation will be wrong.

Urw (V)

frequency.

used.

The number of trains on the national network is increasing. In order to ensure a maximum security, it is necessary to localize all the trains all the time.

For that purpose, the French National Railway Company (SNCF) uses an electronic detection based on the fact that the set wheel/axles/chariot short circuits the rails.

In case of a bad shuntage, an additional device is used; its working, as well as its main parameters, is studied in this article.

A modeling process is applied with the support of the PEEC method to generate a complete electrical equivalent circuit of the device. Thanks to measurements, the accuracy of the modeling approach has been validated. The influence of geometrical and physical parameters on the performances of the studied device has been analyzed in order to find the main parameters and to optimize the structure.

Future works concerning the evaluation of the supplementary losses, the modeling of magnetic material as well as the modeling of the contact wheel/rail which is not fixed but flowing have to be achieved.

### **8. Acknowledgment**

Authors want to thank the French National Railway Company for its financial support for this study and its help for the experimental sets.

### **9. References**

Hoer, C. & Love, C. (1965). Exact Inductance Equations for Rectangular Conductors with Applications to More Complicated Geometries. *Journal of Research C. Engineering and Instrumentation*, Vol. 69C, No.2, (April-June 1965), pp. 127-137

**18** 

*Romania* 

**General Principles Regarding the Rehabilitation** 

Rehabilitation and maintenance of existing steel constructions, especially steel bridges is one of the most important actual problems [1],[2],[3],[8],[14]. The infrastructure in Romania and in other East – European countries has an average age of about seventy to ninety years. Many of these structures are still in operation after damages, several phases of repair and strengthening. Replacement with new structures raises financial, technical and political problems. The budget of the administration gets smaller. The present tendency to raise the speed on the main lines to a level of v 160 km / h must be

Fig. 1. The European corridors crossing Romania's territory: IV, VII and IX

During service, bridges are subject to wear. In the last decades the initial volume of traffic has increased. Therefore many bridges require a detailed investigation and control. The examination should consider the age of the bridge and all repairs, the extent and location of

**1. Introduction** 

emphasized (Figure 1).

any defects etc (Figure 2).

**of Existing Railway Bridges** 

*"Politehnica" University of Timişoara & SSF-RO Ltd* 

Petzek Edward and Radu Băncilă


## **General Principles Regarding the Rehabilitation of Existing Railway Bridges**

Petzek Edward and Radu Băncilă *"Politehnica" University of Timişoara & SSF-RO Ltd* 

*Romania* 

### **1. Introduction**

446 Infrastructure Design, Signalling and Security in Railway

Gonnet, J-P.; Clavel, E.; Mazauric; V. & Roudet, J. (2004). PEEC Method dedicated to the

Aimé, J.; Ardon, V.; Clavel; E., Roudet, J. & Loizelet, Ph. (2009a). EMC behavior of static

Ruehli, A.E. (1974). Equivalent circuit models for three dimensional multiconductor

Ardon, V.; Aimé, J.; Chadebec, O.; Clavel, E. & Vialardi, E. (2009). MoM and PEEC Method

Clavel, E. & Prémont, Ch. (2007a). Function transfer sensitivity of an electronic filter versus

Jazzar, A.; Clavel, E.; Meunier, G.; Vincent, B.; Goleanu, A. & Vialardi, E. (2011). Modeling

Ruehli, A. E. & Cangellaris, A. C. (2001). Progress in the methodologies for the electrical

Kéradec, J-P.; Clavel, E.; Gonnet, J-P. & Mazauric, V. (2005). Introducing Linear Magnetic

Aimé, J.; Roudet, J.; Clavel, E.; Aouine, O.; Labarre, C.; Costa, F. & Ecrabey, J. (2007).

Antonini, G.; Deschrijver, D. & Dhaene, T. (2007). Broadband Macromodels for Retarded

Clavel, E.; Roudet, J.; Chevalier, Th. & Postariu, D. (2007b). Modelling connections taking

Vialardi, E.; Clavel, E.; Chadebec, O.; Guichon, J-M. & Lionet, M. (2010). Electromagnetic

Tan, S. X.-D.; He L. (2007) Advanced Model Order Reduction Techniques in VLSI Design,

*Electromagnetic Compatibility*, Vol 49 , Issue: 1, 2007, pp. 35-48

*IEEE – IAS Industrial Applications Society*, Hong Kong, October 2-6 2005 Aimé, J.; Tran, S-T.; Clavel, E. & Meunier, G. (2009b). Far field extrapolation from near field

*Research Symposium*, Pise, Italie, March 28-31 2004

*Society*, Porto, Portugal, November 2-5 2009

Zurich, Switzerland, January 12-16 2009

*Industrial Electronics*, Gdansk, Poland, June 27-30 2011

(March 1974), pp. 216-221

USA, September 20-24 2009

Macedonia, September 6-8 2010.

*Cambridge University Press*, New York, USA

pp. 2550-2555.

2526-2531.

19 2007

design of electrical systems. *Proceedings of PIERS 2004 Progress In Electromagnetic* 

converters thanks to radiated field modeling using an equivalent electrical circuit. *IEEE-IECON 35th International Annual Conference of the IEEE Industrial Electronics* 

systems, *IEEE transaction on microwave theory and techniques*, Vol. MTT 22, No.3,

to Reach a Complete Equivalent Circuit of a Static Converter. IEEE – EMC'09,

capacitors location on a printed circuit board. *2EMC07* Rouen, France, October 18-

and simulating the lightning phenomenon: aeronautic materials comparison in conducted and radiated modes. *IEEE – ISIE11 20th International Symposium on* 

modeling of interconnects and electronic packages. *Proc. IEEE*, Vol. 89, no. 5, May 2001.

Materials in PEEC Simulations. Principles, Academic and Industrial Applications.

interactions and shielding influence investigations based on a FE-PEEC coupling method. *IEEE Energy Conversion Congress and Exposition ECCE,* San José, Californie,

Prediction and measurement of the magnetic near field of a static converter. *IEEE-ISIE 16th International Symposium on Industrial Electronics*, Vigo, Spain, June 4-7 2007,

Partial Element Equivalent Circuit (rPEEC) Method. *IEEE Transactions on* 

into account return plane: application to EMI modelling for railway. . *IEEE-ISIE 16th International Symposium on Industrial Electronics*, Vigo, Spain, June 4-7 2007, pp.

Simulation of Power Modules via Adapted Modelling Tools. *EPE-PEMC 14th International Power Electronics and Motion Control Conference*, Ohrid, Republic of Rehabilitation and maintenance of existing steel constructions, especially steel bridges is one of the most important actual problems [1],[2],[3],[8],[14]. The infrastructure in Romania and in other East – European countries has an average age of about seventy to ninety years. Many of these structures are still in operation after damages, several phases of repair and strengthening. Replacement with new structures raises financial, technical and political problems. The budget of the administration gets smaller. The present tendency to raise the speed on the main lines to a level of v 160 km / h must be emphasized (Figure 1).

Fig. 1. The European corridors crossing Romania's territory: IV, VII and IX

During service, bridges are subject to wear. In the last decades the initial volume of traffic has increased. Therefore many bridges require a detailed investigation and control. The examination should consider the age of the bridge and all repairs, the extent and location of any defects etc (Figure 2).

General Principles Regarding the Rehabilitation of Existing Railway Bridges 449

Rehabilitation and maintenance of existing steel bridges is one of the most important actual

A continuous maintenance, which generally must increase in time, is important in order to

The evaluation of the current technical condition of an existing steel bridge structure with the help of in situ evaluation depends, in a high percentage, on the engineer's qualification. In the case of in situ inspection it is recommended to insist on the appeared fatigue defects, of riveted or welded connections (the expert must to insist on the connections between the stringers with cross girders and cross girders with main girders), critical details (which are included in standards or catalogues), corrosion level, the structure deformations due to traffic, bridge bearings. The expert can use non-destructive techniques to determine the integrity of base material or structural components. The non destructive testing of the

 *visual inspection* – the most common method which includes microscopes, mirrors, portable video cameras, robotic crawlers; this method is very useful in case of surface cracks; *magnetic particle inspection* – this method is also very simple and does not need high qualification personnel, but can be applied just in case of ferromagnetic materials (not for austenitic steels). The method consists in the magnetization of the high stress elements or critical details and indicates directly the surface discontinuity through forming a distorted

 *liquid penetration inspection* – is a simple method including the qualification of the personnel; it uses penetrate liquids with fluorescent pigment and UV – light in order to

 *radiographic inspection* – the method is applied for hidden defects and it uses Gamma or Roentgen radiation. The inspected element is placed between the radiation and the film. The interpretation of the radiographic images should be done by experts, otherwise

 *ultrasonic inspection* – this testing is used for flaws and cracks in the material thickness, on the surface or hidden defects; highly qualified personnel is needed. High frequency sound waves are introduced into a material and they are reflected back from surfaces or flaws. This process is recorded by an oscilloscope. This method cannot be used for

*Eddy Current testing* – this method can detect surface defects but can also be used for

The usual simplified analysis methods do not always give the lowest resistance values for the structure, but usually the more refined assessment methods which give greater resistance are expensive. According to the experience of the expert a progressive analysis can be applied. In a first step simple classical methods can be applied [2]. If they fail, more sophisticated methods can be used, until either it is shown that the bridge is adequate, or it is concluded that strengthening is needed. An engineer with experience can jump over some time consuming steps which do not give any benefit (an interesting proposal is that the engineer will be paid on a percentage on the saving basis [4]). Actual loads are lower than

**2. Technical condition of existing bridges** 

assure the safety in operation of the existing structures.

indicate the surface defections;

elements made of multiple plates (riveted sections).

defects could be ignored;

thickness inspection.

inspection of in service damage in bridge elements are the following:

magnetic field, which can be detected under proper lighting conditions;

problems.

Fig. 2. Assessment and control of existing steel bridges

Carefully inspection of the structure is the most important aspect in evaluating the safety of the bridge. On the accuracy of the in situ inspection depends the level of evaluation.

The check of existing structures should be based on the complete bridge documentation (drawings with accuracy details, dimensions and cross sections of all structural elements, information about structural steel, stress history. However, in many cases these documentations are incomplete or missing. But these informations can be recovered due to the carefully investigations and inspections of the structures, experimental determination of the material characteristics and stresses in structural elements, full scale in situ tests (static and dynamic), calibration of structure and spatial static analysis.

Today, the budget of the administration and the owners (i.e. the railways and highway companies) get smaller. In consequence it is necessary to invest the available money where there will be the greatest benefit. Therefore, those responsible for the decisions need information about the safety of the structure, the remaining life, the costs for maintenance etc. Nobody will take the responsibility for failure of a structure as a result of budget restrictions.

Bridge life is generally given by fatigue; difficult is the estimation of the loading history. For bridges where the stress history is known the fatigue life may be calculated using the Miners's rule and an appropriate S-N curve; also the assumption of the same spectrum for bridge life (or for certain periods) must be made. During the process of assessment the fatigue life of old riveted bridges, is important to establish the proportion of the whole fatigue life that has been already got through. For stringers and cross girders of existing railway bridges the number of 107 cycles is exceeded. It might be affirmed that for such bridges if no fatigue cracks can be detected, no fatigue damage has occurred! Subsequently, if the loading spectrum remains the same in the future as in the past, fatigue cracking might not take place! In almost all the cases the loadings increased; in this situation survival for 100 years (or more) without cracking would not justify the assumption that no damage has yet occurred! Minor cracking is difficult to detect during usual inspections.

### **2. Technical condition of existing bridges**

448 Infrastructure Design, Signalling and Security in Railway

Carefully inspection of the structure is the most important aspect in evaluating the safety of

The check of existing structures should be based on the complete bridge documentation (drawings with accuracy details, dimensions and cross sections of all structural elements, information about structural steel, stress history. However, in many cases these documentations are incomplete or missing. But these informations can be recovered due to the carefully investigations and inspections of the structures, experimental determination of the material characteristics and stresses in structural elements, full scale in situ tests (static

Today, the budget of the administration and the owners (i.e. the railways and highway companies) get smaller. In consequence it is necessary to invest the available money where there will be the greatest benefit. Therefore, those responsible for the decisions need information about the safety of the structure, the remaining life, the costs for maintenance etc. Nobody will take the responsibility for failure of a structure as a result of budget

Bridge life is generally given by fatigue; difficult is the estimation of the loading history. For bridges where the stress history is known the fatigue life may be calculated using the Miners's rule and an appropriate S-N curve; also the assumption of the same spectrum for bridge life (or for certain periods) must be made. During the process of assessment the fatigue life of old riveted bridges, is important to establish the proportion of the whole fatigue life that has been already got through. For stringers and cross girders of existing railway bridges the number of 107 cycles is exceeded. It might be affirmed that for such bridges if no fatigue cracks can be detected, no fatigue damage has occurred! Subsequently, if the loading spectrum remains the same in the future as in the past, fatigue cracking might not take place! In almost all the cases the loadings increased; in this situation survival for 100 years (or more) without cracking would not justify the assumption that no damage has yet occurred! Minor cracking is difficult to detect during

the bridge. On the accuracy of the in situ inspection depends the level of evaluation.

Fig. 2. Assessment and control of existing steel bridges

and dynamic), calibration of structure and spatial static analysis.

restrictions.

usual inspections.

Rehabilitation and maintenance of existing steel bridges is one of the most important actual problems.

A continuous maintenance, which generally must increase in time, is important in order to assure the safety in operation of the existing structures.

The evaluation of the current technical condition of an existing steel bridge structure with the help of in situ evaluation depends, in a high percentage, on the engineer's qualification. In the case of in situ inspection it is recommended to insist on the appeared fatigue defects, of riveted or welded connections (the expert must to insist on the connections between the stringers with cross girders and cross girders with main girders), critical details (which are included in standards or catalogues), corrosion level, the structure deformations due to traffic, bridge bearings. The expert can use non-destructive techniques to determine the integrity of base material or structural components. The non destructive testing of the inspection of in service damage in bridge elements are the following:


The usual simplified analysis methods do not always give the lowest resistance values for the structure, but usually the more refined assessment methods which give greater resistance are expensive. According to the experience of the expert a progressive analysis can be applied. In a first step simple classical methods can be applied [2]. If they fail, more sophisticated methods can be used, until either it is shown that the bridge is adequate, or it is concluded that strengthening is needed. An engineer with experience can jump over some time consuming steps which do not give any benefit (an interesting proposal is that the engineer will be paid on a percentage on the saving basis [4]). Actual loads are lower than

General Principles Regarding the Rehabilitation of Existing Railway Bridges 451

Grinding

Observation

New additional plate

Element **CRACK REPAIR** 0 1 2

Main girder

Main girder

Main girder

Stringer

Stringer

Table 1. Typical defects in welded and riveted steel bridges

those used for design purposes. Fatigue tests on elements taken from demolished structures gives – generally - greater fatigue life than the values according the codes [5].

The applied stress range, the geometry of the detail and the number of stress cycles has a decisive effect on the remaining fatigue life of the structures.

By differences of more than 5 % of the cross section – due to corrosion, the actual values must be introduced.

However, from the overall examination of a large number of bridges many defects can be pointed out. The defects are widespread, having a heterogeneous character from the point of view of location, development and development tendency; their amplification was also due to the climate and polluting factors that caused the reduction of the cross section due to corrosion. Statistically, in 283 from among 1088 welded bridges, and in 356 from among 3201 steel riveted bridges cracks were detected and repaired. It is not allowed to weld cracks! Old bridges can have welds executed in the early years; a special attention must be paid to these parts. Generally the riveted connections have a good behavior in time due to the initial pre-stressing force which can reach 70 – 80 N/mm². In Table 1 some typical defects in stringers, cross girders, main girders wind bracings and orthotropic deck and their repair are presented [6],[7].

In figure 3 there is presented a crack of a joint plate from a wind bracing and in figure 4 also cracks in the lower flange joint of a double T girder, near to the bearing.

Fig. 3. Crack in the joint plate

Fig. 4. Crack in the lower flange near to the bearing

those used for design purposes. Fatigue tests on elements taken from demolished structures

The applied stress range, the geometry of the detail and the number of stress cycles has a

By differences of more than 5 % of the cross section – due to corrosion, the actual values

However, from the overall examination of a large number of bridges many defects can be pointed out. The defects are widespread, having a heterogeneous character from the point of view of location, development and development tendency; their amplification was also due to the climate and polluting factors that caused the reduction of the cross section due to corrosion. Statistically, in 283 from among 1088 welded bridges, and in 356 from among 3201 steel riveted bridges cracks were detected and repaired. It is not allowed to weld cracks! Old bridges can have welds executed in the early years; a special attention must be paid to these parts. Generally the riveted connections have a good behavior in time due to the initial pre-stressing force which can reach 70 – 80 N/mm². In Table 1 some typical defects in stringers, cross girders, main

In figure 3 there is presented a crack of a joint plate from a wind bracing and in figure 4 also

gives – generally - greater fatigue life than the values according the codes [5].

girders wind bracings and orthotropic deck and their repair are presented [6],[7].

cracks in the lower flange joint of a double T girder, near to the bearing.

decisive effect on the remaining fatigue life of the structures.

must be introduced.

Fig. 3. Crack in the joint plate

Fig. 4. Crack in the lower flange near to the bearing

Table 1. Typical defects in welded and riveted steel bridges

General Principles Regarding the Rehabilitation of Existing Railway Bridges 453

Hole at the end of the crack

Replacement

bracing Replacement of the gusset

Table 1. Typical defects in welded and riveted steel bridges - continuation

Element **CRACK REPAIR**

Stringer

Stringer

Stringer

Stringer

Twin girders

Twin girders

Wind

Table 1. Typical defects in welded and riveted steel bridges - continuation

Element **CRACK REPAIR**

Stringer

Stringer

Cross girder

Cross girder

Orthotropic deck

Orthotropic deck

Stringer

Table 1. Typical defects in welded and riveted steel bridges - continuation

Table 1. Typical defects in welded and riveted steel bridges - continuation

General Principles Regarding the Rehabilitation of Existing Railway Bridges 455

 Old bridges are in many cases erected using material with very poor welding qualities and basing on railway administration data and specialized literature it is known that

 The specialized literature doesn't offer enough information about this structural steel; The structural material comes from several producers (for South Eastern Europe mostly

The presented study's results can be extended to Middle and South Eastern Europe when the history of communication ways and the state of old railway and highway steel bridges in this region is regarded. In this context the following event can be mentioned: on the 1st of January 1855 the "Kaiserliche und Königliche Privilegierte Österreichische Staatseisenbahngesellschaft" (St.E.G.) took over all steel producers in Banat. The investments in Reschitz (in present Resita) turn the steel mill into an important bridges' factory. The production of steel bridges reached 3960 tonnes in 1910. Bridges made by St.E.G. Reschitz are still in use in Romania, Austria and Hungary. Between 1911 – 1913, 1620 tonnes of bridge structures made of cast iron were replaced in the western part of Romania (Banat), namely on the railway segment Timişoara – Orşova. In this sense the material study took into account bridges from this region, built around 1911. Following material analysis were performed in order to determine the characteristics of the material: chemical analysis, metallographic analysis, tensile tests, Brinell tests, Charpy "V Notch" tests. The samples were taken from secondary elements, but also in some cases (Bridges in Arad and Şag which were replaced) from main elements: stringers, cross girders, main girders [7]). The results of

The following facts show that a material analysis for old riveted bridges is very useful:

**3. Characteristics of materials** 

cast iron was used to build bridges;

from Reschitz – Romania and Györ – Hungary).

Table 2. The bridges on which the present material study basis

the chemical analysis are presented in the following table.

Signs of cracks and defects are rust traces, which occur by friction between jointed plates of the elements. These are of relevance for hidden constructive elements.

Defects of the bearings are frequent as well. In figure 5 there are presented two examples.

Fig. 5. Defects on bearings

Due to deficient maintenance the riveted structures are strongly corroded, especially in the lower zones (figure 6). These corroded surfaces represent also a critical detail for fatigue. Fatigue under corrosion factor is an aspect treated only qualitatively and not quantitatively. The interaction between the two aspects is obvious. There can also found inefficient joints, like weakened rivets (figure 7).

Fig. 6. Strong corrosion at the lower flange – railway bridge on a main line

Fig. 7. Inefficient joints – railway bridge on a main line

### **3. Characteristics of materials**

454 Infrastructure Design, Signalling and Security in Railway

Signs of cracks and defects are rust traces, which occur by friction between jointed plates of

Due to deficient maintenance the riveted structures are strongly corroded, especially in the lower zones (figure 6). These corroded surfaces represent also a critical detail for fatigue. Fatigue under corrosion factor is an aspect treated only qualitatively and not quantitatively. The interaction between the two aspects is obvious. There can also found inefficient joints,

Fig. 6. Strong corrosion at the lower flange – railway bridge on a main line

Fig. 7. Inefficient joints – railway bridge on a main line

Defects of the bearings are frequent as well. In figure 5 there are presented two examples.

the elements. These are of relevance for hidden constructive elements.

Fig. 5. Defects on bearings

like weakened rivets (figure 7).

The following facts show that a material analysis for old riveted bridges is very useful:



Table 2. The bridges on which the present material study basis

The presented study's results can be extended to Middle and South Eastern Europe when the history of communication ways and the state of old railway and highway steel bridges in this region is regarded. In this context the following event can be mentioned: on the 1st of January 1855 the "Kaiserliche und Königliche Privilegierte Österreichische Staatseisenbahngesellschaft" (St.E.G.) took over all steel producers in Banat. The investments in Reschitz (in present Resita) turn the steel mill into an important bridges' factory. The production of steel bridges reached 3960 tonnes in 1910. Bridges made by St.E.G. Reschitz are still in use in Romania, Austria and Hungary. Between 1911 – 1913, 1620 tonnes of bridge structures made of cast iron were replaced in the western part of Romania (Banat), namely on the railway segment Timişoara – Orşova. In this sense the material study took into account bridges from this region, built around 1911. Following material analysis were performed in order to determine the characteristics of the material: chemical analysis, metallographic analysis, tensile tests, Brinell tests, Charpy "V Notch" tests. The samples were taken from secondary elements, but also in some cases (Bridges in Arad and Şag which were replaced) from main elements: stringers, cross girders, main girders [7]). The results of the chemical analysis are presented in the following table.

General Principles Regarding the Rehabilitation of Existing Railway Bridges 457

KV-Arad-SpanIII-Stringers KV-Arad-SpanIII-Main Girder KV-Arad-SpanIII-Cross Girders KV-Sag-SpanI-III KV-Sag-SpanIV-V KV-V.Cernei1 KV-V.Cernei2 KV-Branisca1 KV-Branisca2 KV-Mehadia KV-B.Sarata Ref\_value Expon. (KV-B.Sarata)

**27**

**Transition curves**


**T = -20°C; mild steel 1910**

0 50 100 150 200

In the present state of knowledge it is generally accepted that the fatigue failure of materials is a process containing three distinct steps: (1) initiation of defect (crack), (2) crack propagation in material, (3) separation through complete failure of the material in two or more pieces. Practically, the safety service life of an element under fatigue conditions can be

Fig. 10. Charpy V Notch Energy vs. material toughness Jc (Arad Bridge 1912)

**J [N/mm]**

*N NN <sup>f</sup> <sup>i</sup> <sup>p</sup>* (1)

Fig. 8. Transition curves for the analyzed bridge structures

Fig. 9. Experimental tests for determining of J values

0

expressed as follows (figure 11):

5

10

15

**KV [J]**

**Charpy Energy KV(10) [J]**


Table 3. Chemical analysis results

The statistical interpretation of the tensile tests results shows a minimal value for the yield stress of 230 N/mm2.

The impact tests on Charpy V Notch specimens lead to conclusion that the transition temperature is situated in many cases in the range from -10°C to 0°C (figure 8).

By analyzing the laboratory results it can be concluded that the steel is a mild one, that could be associated to the present steel types St 34 or St 37.1 (S 235 according to the Eurocodes). Also, on the two dismantled bridges – Arad and Şag – fracture mechanics tests were made [7] in order to establish the integral value Jc according to ASTM E813-89 (figure 9), the CTOD and to determine the fatigue crack growth rate and the material constants C and m according to ASTM E647-93. For these tests compact specimens CT (thickness 8 mm) as well as bending specimens for CTOD, have been used.

They have been obtained from the stringers, cross girders and main girder – lower chord. The minimal value of material toughness in term of J-Integral for these old riveted steel bridges is Jcrit = 10 … 20 N/mm for a temperature of -20°C.

The method of fatigue assessment for structural elements with defects, was developed basing on the possibility of crack propagation modeling under fatigue loads and with the help of known laws.

The method is founded on the recommendations of the BS 7910:1999.

The statistical interpretation of the tensile tests results shows a minimal value for the yield

The impact tests on Charpy V Notch specimens lead to conclusion that the transition

By analyzing the laboratory results it can be concluded that the steel is a mild one, that could be associated to the present steel types St 34 or St 37.1 (S 235 according to the Eurocodes). Also, on the two dismantled bridges – Arad and Şag – fracture mechanics tests were made [7] in order to establish the integral value Jc according to ASTM E813-89 (figure 9), the CTOD and to determine the fatigue crack growth rate and the material constants C and m according to ASTM E647-93. For these tests compact specimens CT (thickness 8 mm)

They have been obtained from the stringers, cross girders and main girder – lower chord. The minimal value of material toughness in term of J-Integral for these old riveted steel

The method of fatigue assessment for structural elements with defects, was developed basing on the possibility of crack propagation modeling under fatigue loads and with the

temperature is situated in many cases in the range from -10°C to 0°C (figure 8).

as well as bending specimens for CTOD, have been used.

bridges is Jcrit = 10 … 20 N/mm for a temperature of -20°C.

The method is founded on the recommendations of the BS 7910:1999.

Table 3. Chemical analysis results

stress of 230 N/mm2.

help of known laws.

Fig. 8. Transition curves for the analyzed bridge structures

Fig. 9. Experimental tests for determining of J values

Fig. 10. Charpy V Notch Energy vs. material toughness Jc (Arad Bridge 1912)

In the present state of knowledge it is generally accepted that the fatigue failure of materials is a process containing three distinct steps: (1) initiation of defect (crack), (2) crack propagation in material, (3) separation through complete failure of the material in two or more pieces. Practically, the safety service life of an element under fatigue conditions can be expressed as follows (figure 11):

$$N\_f = N\_i + N\_p \tag{1}$$

General Principles Regarding the Rehabilitation of Existing Railway Bridges 459

The calculation of the structural elements remaining service life can be done basing on the

*a m*

*C K* (3)

(4)

da

*dN* (5)

**RSL**

<sup>0</sup> 0 *N acrit*

*da N dN*

N - number of stress cycles necessary in order that the crack extends from its initial

This integral can be numerically calculated by taking into account a critical detail knowing

<sup>0</sup> /2 ( )

2 Ic crit 2 2

K

<sup>Y</sup>

max

 

*a mm m*

*C Ya* 

The number of cycles Ni obtained with the help of relation (4) represents the remaining service life of the detail, by regarding the initial length a0 up to the critical length acrit, by

No. of cycle (N) No. of cycle (N) or time

The critical crack value can be calculated basing on the K criterion respectively on the J or

The C and m material constants from the Paris law are experimentally determined by fracture mechanical tests. In this sense in most cases compact specimens C(T), three point bended specimens SEN(B) and middle central panels M(T) are used. Such a standard which describes the test methods for the determination of the crack growth rate, is the American Standard ASTM E 647 (Standard Test Method for Measurement of Fatigue Crack Rates).

Basing on the determined values da/dN and K the program presented below, also

ln( ) ln ln *da Cm K*

automatically determines the C and m material constants by the Paris relation:

Initial dN crack **a0**

Paris law, more precisely by integration of this law:

a – crack length;

K – stress intensity factor range.

dimension a0 to the critical value acrit, where failure occurs;

C, m – material constants from the crack propagation law;

admitting stable crack propagation (Figure 13).

Crack length, a

0

CTOD criterions or with the help of the failure assessment diagram.

Fig. 13. Principles for determining the remaining service life

the crack values (initial and critical), basing on the following relation:

*crit a*

Final crack **acr**

a

*da <sup>N</sup>*

Ni = number of cycles necessary for the initiation of the defect (crack)

Np = number of cycles necessary for the propagation of the defect until the occurrence of failure.

Number of Cycles to failure, N = N N i p

Fig. 11. Fatigue life of structural elements

The evaluation of crack propagation conditions can be accomplished with the help of characteristically values, which are founded on fracture mechanics concepts: material toughness express by the stress intensity factor K or J integral value and the crack growth rate da/dN (crack growth for each load cycle). A relation of the following type can express the crack growth rate (Figure 12):

$$\frac{da}{dN} = f\left(\Lambda K, R, H\right) \tag{2}$$

da/dN - crack extension for one load cycle; K- stress intensity range, established basing on the stress range ; R- stress ratio; H- indicates the stress history dependence.

The crack growth rate da/dN, defined as a crack extension - da obtained through a load cycle dN (it can also be defined as da/dt, in which case the crack extension is related to a time interval), represents a value characteristic of the initiation phases respectively the stable crack propagation. It has been experimentally observed that the connection between the crack growth rate and stress intensity factor variation represents a suitable solution for the description of the behavior of a metallic material containing a crack, as in the case of steel. In a logarithmic graphical representation of the crack growth rate da/dN versus the stress intensity range K a curve as the one in the following figure (Fig. 12), is obtained.

Fig. 12. Logarithmic representation of the fatigue crack growth in steel

The calculation of the structural elements remaining service life can be done basing on the Paris law, more precisely by integration of this law:

$$N = \int\_0^N dN = \int\_{a\_0}^{a\_{crit}} \frac{da}{C \cdot \Delta K^m} \tag{3}$$

N - number of stress cycles necessary in order that the crack extends from its initial dimension a0 to the critical value acrit, where failure occurs;

a – crack length;

458 Infrastructure Design, Signalling and Security in Railway

Np = number of cycles necessary for the propagation of the defect until the occurrence of

The evaluation of crack propagation conditions can be accomplished with the help of characteristically values, which are founded on fracture mechanics concepts: material toughness express by the stress intensity factor K or J integral value and the crack growth rate da/dN (crack growth for each load cycle). A relation of the following type can express

, , *da <sup>f</sup> KRH*

da/dN - crack extension for one load cycle; K- stress intensity range, established basing

The crack growth rate da/dN, defined as a crack extension - da obtained through a load cycle dN (it can also be defined as da/dt, in which case the crack extension is related to a time interval), represents a value characteristic of the initiation phases respectively the stable crack propagation. It has been experimentally observed that the connection between the crack growth rate and stress intensity factor variation represents a suitable solution for the description of the behavior of a metallic material containing a crack, as in the case of steel. In a logarithmic graphical representation of the crack growth rate da/dN versus the stress

> log K

Region III

\* Fracture

*dN*

on the stress range ; R- stress ratio; H- indicates the stress history dependence.

intensity range K a curve as the one in the following figure (Fig. 12), is obtained.

dN Paris Law

Region I

\*

Fig. 12. Logarithmic representation of the fatigue crack growth in steel

Threshold K**th**

Region II

 da <sup>m</sup> = C K

m

 log da dN Number of Cycles to failure, N = N N i p

(2)

Ni = number of cycles necessary for the initiation of the defect (crack)

**Dtot** Crack initiation

Crack propagation

Stress

Fig. 11. Fatigue life of structural elements

the crack growth rate (Figure 12):

failure.

C, m – material constants from the crack propagation law;

K – stress intensity factor range.

This integral can be numerically calculated by taking into account a critical detail knowing the crack values (initial and critical), basing on the following relation:

$$N = \int\_{a\_0}^{a\_{crit}} \frac{da}{\mathbf{C} \cdot \Delta \sigma^m \cdot Y^m \cdot (\pi a)^{-m/2}} \tag{4}$$

The number of cycles Ni obtained with the help of relation (4) represents the remaining service life of the detail, by regarding the initial length a0 up to the critical length acrit, by admitting stable crack propagation (Figure 13).

Fig. 13. Principles for determining the remaining service life

The critical crack value can be calculated basing on the K criterion respectively on the J or CTOD criterions or with the help of the failure assessment diagram.

The C and m material constants from the Paris law are experimentally determined by fracture mechanical tests. In this sense in most cases compact specimens C(T), three point bended specimens SEN(B) and middle central panels M(T) are used. Such a standard which describes the test methods for the determination of the crack growth rate, is the American Standard ASTM E 647 (Standard Test Method for Measurement of Fatigue Crack Rates).

Basing on the determined values da/dN and K the program presented below, also automatically determines the C and m material constants by the Paris relation:

$$\ln(\frac{da}{dN}) = \ln C + m \cdot \ln \Delta K \tag{5}$$

General Principles Regarding the Rehabilitation of Existing Railway Bridges 461

The classical fatigue concept is based on the assumption that a constructive element has no defects or cracks. However, discontinuities and cracks in the components of structures are unavoidable, basically because of the material fabrication and the erection of structures. It is very clear that the kind of fatigue cracks, which are initiated by structural non-homogeneity (possible non-metallic inclusions or other impurities), surface defects (including corrosion)

The presence of cracks in structural elements modifies essentially their fracture behavior. Fracture, assimilated in this case as crack dimensions growth process under external loadings, will be strongly influenced by the deformation capacity of material. The FM approach has acceleration in damage increase; with increasing damage a smaller stress range contribute to the damage increase. The authors proposed [9], a complementary

 D < 0,8 the probability to detect cracks is very low. The inspection intervals (generally between 3 – 6 years) can be established on criteria independent of fatigue. Nevertheless,

 D 0,8 cracks are probable and possible. An in situ inspection and the analysis of critical details are strongly necessary. Also a fracture mechanics approach is

*I Ic J J* (7)

Fig. 15. Methodology of the Romanian standard SR 1911-98 [3]

and the stress factor, are present in the old riveted structures.

method based on the fracture mechanics basic concept

a special attention must be paid to critical details.

in order to calculate the remaining fatigue life. In practice two situations can be distinguished:

recommended.

The experimental tests on 26 CT specimens from two old bridges have shown that for the oldest mild steels the values of the material constants from the Paris relation are in the following intervals: m = 2,05 … 5,65 and C = 2,2 x 10-11 … 10-18.

Relatively large value of m corresponding to very small values of C, for example for m > 4 C 10-15 … 10-18.

Fig. 14. Experimental tests in order to establish the material constants C and m

### **4. Present verification concept**

During service bridges are subjected to repeated loadings causing fatigue. Therefore many bridges require an inspection. The examination should consider the age of the bridge and all repairs, the extent and location of any defects etc. [8]. A continuous maintenance, which generally must increase in time, is important in order to assure the safety in operation of the existing structures. The present methodology includes the following stages [9]:


This methodology adopted by the Romanian standard is illustrated in Figure 15.

The calculation of remaining fatigue life is normally carried out by a damage accumulation calculation. The cumulative damage caused by stress cycles will be calculated; failure criteria will be reached.

$$D = \sum \frac{n\_i}{N\_i} \le 1\tag{6}$$

The experimental tests on 26 CT specimens from two old bridges have shown that for the oldest mild steels the values of the material constants from the Paris relation are in the

Relatively large value of m corresponding to very small values of C, for example for m > 4

Fig. 14. Experimental tests in order to establish the material constants C and m

existing structures. The present methodology includes the following stages [9]:

This methodology adopted by the Romanian standard is illustrated in Figure 15.

During service bridges are subjected to repeated loadings causing fatigue. Therefore many bridges require an inspection. The examination should consider the age of the bridge and all repairs, the extent and location of any defects etc. [8]. A continuous maintenance, which generally must increase in time, is important in order to assure the safety in operation of the

**Step 1.** estimation of the loading capacity of the structure based on a detailed inspection;

**Step 2.** the accurate determination of the stresses in the structure and of the remaining

The calculation of remaining fatigue life is normally carried out by a damage accumulation calculation. The cumulative damage caused by stress cycles will be calculated; failure

*<sup>n</sup> <sup>D</sup>*

analysis of drawings, inspection reports, repairs, reinforcements, analysis of the general behavior of the bridge (displacements, vibrations, corrosion and cracks). In this phase the stresses in the structure can be calculated with the usual simplified

safety of the elements. This phase includes: tests on materials, computer aided analysis of the space structure, remaining safety calculated on the base of the real

> 1 *<sup>i</sup> i*

*<sup>N</sup>* (6)

following intervals: m = 2,05 … 5,65 and C = 2,2 x 10-11 … 10-18.

C 10-15 … 10-18.

**4. Present verification concept** 

hypothesis;

criteria will be reached.

time - stress history; **Step 3.** in situ static and dynamic tests.

Fig. 15. Methodology of the Romanian standard SR 1911-98 [3]

The classical fatigue concept is based on the assumption that a constructive element has no defects or cracks. However, discontinuities and cracks in the components of structures are unavoidable, basically because of the material fabrication and the erection of structures. It is very clear that the kind of fatigue cracks, which are initiated by structural non-homogeneity (possible non-metallic inclusions or other impurities), surface defects (including corrosion) and the stress factor, are present in the old riveted structures.

The presence of cracks in structural elements modifies essentially their fracture behavior. Fracture, assimilated in this case as crack dimensions growth process under external loadings, will be strongly influenced by the deformation capacity of material. The FM approach has acceleration in damage increase; with increasing damage a smaller stress range contribute to the damage increase. The authors proposed [9], a complementary method based on the fracture mechanics basic concept

$$\mathbf{J}\_{\mathrm{I}} \le \mathbf{J}\_{\mathrm{Ic}} \tag{7}$$

in order to calculate the remaining fatigue life.

In practice two situations can be distinguished:


General Principles Regarding the Rehabilitation of Existing Railway Bridges 463

The methodology is conceived as an advanced, complete analysis of structural elements containing fatigue defects, being founded on fracture mechanics principles and containing two steps: namely one of determination of defects' acceptability with the help of Failure Assessment Diagrams (level 2) [10] and of determination of final acceptable values of defect dimensions; this is followed by a second step which in fact represents a fatigue evaluation of the analyzed structural elements basing on the present stress history recorded on the structure, on the initial and final defect dimensions and the FM parameters, namely the material characteristics C and m from the Paris relation (crack growth under real traffic stress) and further on the exact determination of the number of cycles N needed in order that a fracture take place, respectively the determination of the remaining service life of the structural elements (years, months, days). In order to determine the remaining service life it is important to know how long it will take the crack to grow from the minimum detectable size to the critical value. In this situation the

Na = the number of cycles computed for a crack extension rate of 5 mm during two

The life prediction computing was performed with the help of a soft developed by one of

Three European corridors cross Romania's territory: IV, VII and IX. Of a special interest for many European countries is the Pan-European Corridor IV "Berlin - Nürnberg - Prague - Budapest - Constanta /Istanbul/ Thessaloniki". On Romania's territory the railway component of Pan - European Corridor IV has the following route: Curtici - Arad -

Tinsp = NRFL / NΔa, (8)

safe inspection intervals can be calculated with the following relation:

NRFL = the remaining fatigue life calculated for the structural element

Sighisoara - Brasov – Predeal – Campina - Bucharest - Constanta.

Fig. 17. Soft for life prediction analysis

where

successive inspections.

the authors [7].

**5. Case studies** 

Generally, the establishing of the maintenance program, the determination of inspection intervals, the inspection priorities of structural elements and finally the calculation with high accuracy of the remaining service life of old riveted bridges takes into account the following main data:


Fig. 16. Assessment of the remaining fatigue life and the crack growth procedure

Fig. 17. Soft for life prediction analysis

The methodology is conceived as an advanced, complete analysis of structural elements containing fatigue defects, being founded on fracture mechanics principles and containing two steps: namely one of determination of defects' acceptability with the help of Failure Assessment Diagrams (level 2) [10] and of determination of final acceptable values of defect dimensions; this is followed by a second step which in fact represents a fatigue evaluation of the analyzed structural elements basing on the present stress history recorded on the structure, on the initial and final defect dimensions and the FM parameters, namely the material characteristics C and m from the Paris relation (crack growth under real traffic stress) and further on the exact determination of the number of cycles N needed in order that a fracture take place, respectively the determination of the remaining service life of the structural elements (years, months, days).

In order to determine the remaining service life it is important to know how long it will take the crack to grow from the minimum detectable size to the critical value. In this situation the safe inspection intervals can be calculated with the following relation:

$$
\Delta \mathbf{T}\_{\rm insp} = \mathbf{N}\_{\rm RF} \Big/ \mathbf{N}\_{\Delta \mathbf{a} \prime} \tag{8}
$$

where

462 Infrastructure Design, Signalling and Security in Railway

Generally, the establishing of the maintenance program, the determination of inspection intervals, the inspection priorities of structural elements and finally the calculation with high accuracy of the remaining service life of old riveted bridges takes into account the

 information about structural steel (mechanical properties – yield strength, tensile strength, hardness, transition curve ductile – brittle and transition temperatures,

crack detection and inspection techniques for evaluation of the initial crack size – a0 and

recording of the stress spectrum for the critical members under the actual traffic loads;

(automatical) procedure for the detremination of the af value according to **FAD-2**

Classification of the damaged element in one of the predefined cathegories Definition of the initial crack size Definition of the final (critical) crack growth lenght

Determination of the real time stress history Experimental determination of material parameters C and m from the crack propagation law Applying of the crack propagation law (Paris law) on the computing of the growth dai corresponding to the cycle Ni

Determination of resulting crack: ai = a(i-1) + dai

**ai = af**

**Remaining fatigue life of the analysed Remaining fatigue life of the analysed element element** given by the number of cycles **N**

YES

NO

Establishing of number of number of days, months, years of use

Establishing of inspection interval & interval maintenance maintenance program

evaluation of the critical crack size – acrit based on failure assessment diagrams;

fracture mechanics parameter – Kcrit, crit, Jcrit (fracture toughness);

type of structure and exploitation conditions (traffic events);

chemical composition, metallographic analysis); determination of critical members and details;

following main data:

crack configuration;

 simulation of the fatigue crack growth; temperature, environment conditions.

> **Assessment of remaining fatigue life**

> **Applied stress and stress range Number of stress cycles N**

> > **Geometry of detail**

**Accumulated damage Dp**

> **Preventive strengthening**

**Dd 0,8**

**Inspection Identification and monitoring of critical details**

> **Fracture mechanics approach**

Fig. 16. Assessment of the remaining fatigue life and the crack growth procedure

**Dd < 0,8 Regular inspections Usual maintenance measures**

NRFL = the remaining fatigue life calculated for the structural element Na = the number of cycles computed for a crack extension rate of 5 mm during two successive inspections.

The life prediction computing was performed with the help of a soft developed by one of the authors [7].

### **5. Case studies**

Three European corridors cross Romania's territory: IV, VII and IX. Of a special interest for many European countries is the Pan-European Corridor IV "Berlin - Nürnberg - Prague - Budapest - Constanta /Istanbul/ Thessaloniki". On Romania's territory the railway component of Pan - European Corridor IV has the following route: Curtici - Arad - Sighisoara - Brasov – Predeal – Campina - Bucharest - Constanta.

General Principles Regarding the Rehabilitation of Existing Railway Bridges 465

After the stress analysis (Figure 20) and the fatigue verifications based on the Wöhler concept which were made in relation with the prescriptions of the Romanian standard SR 1911-1998, Swiss code 161 & SBB Richtlinie 2002 and the German code DS 805-2002, a life prediction analysis based on fracture mechanics principles was performed in order to evaluate the remaining fatigue life for these structures for the new traffic UIC conditions.

For example, a plate girder bridge (no. 28, at km 125+323.25) is presented, which is a riveted structures crossing the Prahova River. The structure has four spans, one of 13.90 m and three of 14.10 m each and is skew (skew to the right - 48°37') and its superstructure is made

Fig. 20. The static model of the structure no. 6, km 108+690,34

out of independent plate girder decks.

Fig. 21. The general disposition of the bridge no. 28

Due to the fact that the Campina - Predeal railway route crosses the sub-Carpathians area and the southern part of the Southern Carpathians it was necessary to adapt it to the difficult geographical conditions; actually this section is the most complicated part from the whole Romanian route. The railway line was built step by step beginning with 1879. The doubling of the 43 km long railway line Campina - Predeal was accomplished between 1939 - 1942. The line electrification was completed during 1961 - 1965.

Generally, the line is oriented from the south to the north. It follows the valley of the Prahova River crossing this river in 17 points.

This section includes 41 bridges. From this total number 22 are plate girder bridges, 6 are truss structures, 12 concrete bridges and 1 are conceived in the filler beams deck solution.

Fig. 18. Emplacement plan

All these structures were verified. In the following some aspects regarding the verification of the steel bridges are presented. The methodology which was adopted is showed in the figure 19.

Fig. 19. The methodology and the constructive details for the evaluation of the RFL

Due to the fact that the Campina - Predeal railway route crosses the sub-Carpathians area and the southern part of the Southern Carpathians it was necessary to adapt it to the difficult geographical conditions; actually this section is the most complicated part from the whole Romanian route. The railway line was built step by step beginning with 1879. The doubling of the 43 km long railway line Campina - Predeal was accomplished between 1939

Generally, the line is oriented from the south to the north. It follows the valley of the

This section includes 41 bridges. From this total number 22 are plate girder bridges, 6 are truss structures, 12 concrete bridges and 1 are conceived in the filler beams deck solution.

All these structures were verified. In the following some aspects regarding the verification of the steel bridges are presented. The methodology which was adopted is showed in the

Fig. 19. The methodology and the constructive details for the evaluation of the RFL


Prahova River crossing this river in 17 points.

Fig. 18. Emplacement plan

figure 19.

After the stress analysis (Figure 20) and the fatigue verifications based on the Wöhler concept which were made in relation with the prescriptions of the Romanian standard SR 1911-1998, Swiss code 161 & SBB Richtlinie 2002 and the German code DS 805-2002, a life prediction analysis based on fracture mechanics principles was performed in order to evaluate the remaining fatigue life for these structures for the new traffic UIC conditions.

Fig. 20. The static model of the structure no. 6, km 108+690,34

For example, a plate girder bridge (no. 28, at km 125+323.25) is presented, which is a riveted structures crossing the Prahova River. The structure has four spans, one of 13.90 m and three of 14.10 m each and is skew (skew to the right - 48°37') and its superstructure is made out of independent plate girder decks.

Fig. 21. The general disposition of the bridge no. 28

General Principles Regarding the Rehabilitation of Existing Railway Bridges 467

For the material toughness in terms of Jcrit a minimal value of 20 N/mm at a temperature of - 20°C was chosen. For the life prediction procedure in the case of the material constants

A stress history was established using the following mixed traffic from EC 1. This is actually the future traffic which will be characteristic for the new rehabilitated railway corridor. All these trains were moved on the structure in order to establish the multi-block

> Train weight [t]

**67** 24,95

All these trains were moved on the structure in order to establish the multi-block stress

Traffic volume [Mil. t/year]

> 2,90 2,30 1,72 0,93 5,52 6,27 3,02 2,27

following values have been chosen: m = 3 and C = 3 x 10-12 (see also [11]).

No. of trains / day

stress history.

Train type

Table 4. Mixed traffic from EC 1

Fig. 23. The stress range diagram Δσ for train type 1

history.

Calculation elements:


Fig. 22. Dimensions of the steel elements – Main girders


The traffic on one main railway line was considered:


The traffic expressed in pairs of trains per day in the peak month that took place on the line Câmpina – Predeal in the year 2004, was:


Total – 48 assimilated pairs of trains / day

For the main girders of the steel decks, all the fatigue checks were performed in the section from the middle of the span.

According to the stress analysis, the maximal stress range for UIC 71 convoy is:

$$\text{ } \text{max} \, \Delta \sigma\_{\text{LIC}} = \text{ } \text{ } \text{97.13 N } / \text{ mm}^2$$

The resulted damage accumulated value (Miner rule) is D = 0.98.

Also, the complementary method of fracture mechanics was applied. For the material characteristics followings values were considered: the material is mild steel similar to the former steel St 34 - 37. n (Romanian standard - STAS 500/2 – 80); yield stress is σy = 230 N/mm2; tensile stress σult = 360 N/mm2.

For the material toughness in terms of Jcrit a minimal value of 20 N/mm at a temperature of - 20°C was chosen. For the life prediction procedure in the case of the material constants following values have been chosen: m = 3 and C = 3 x 10-12 (see also [11]).

A stress history was established using the following mixed traffic from EC 1. This is actually the future traffic which will be characteristic for the new rehabilitated railway corridor. All these trains were moved on the structure in order to establish the multi-block stress history.


Table 4. Mixed traffic from EC 1

466 Infrastructure Design, Signalling and Security in Railway


Calculation elements:


measured in the emplacement (Figure 22).

Fig. 22. Dimensions of the steel elements – Main girders


the reference traffic 20-24x106 t/ line/ year

Câmpina – Predeal in the year 2004, was: 28 pairs of passenger trains / day; 17 pairs of freight trains / day;

Total – 48 assimilated pairs of trains / day

N/mm2; tensile stress σult = 360 N/mm2.

from the middle of the span.

/ line/ year.


the Calculation Centre of SNCF CFR S.A. for the year 2004: 13,7 t/ line / year =>12-16 t

The traffic expressed in pairs of trains per day in the peak month that took place on the line

For the main girders of the steel decks, all the fatigue checks were performed in the section

<sup>2</sup> max 97.13 /

Also, the complementary method of fracture mechanics was applied. For the material characteristics followings values were considered: the material is mild steel similar to the former steel St 34 - 37. n (Romanian standard - STAS 500/2 – 80); yield stress is σy = 230

*UIC N mm*

According to the stress analysis, the maximal stress range for UIC 71 convoy is:

The resulted damage accumulated value (Miner rule) is D = 0.98.

All these trains were moved on the structure in order to establish the multi-block stress history.

Fig. 23. The stress range diagram Δσ for train type 1

General Principles Regarding the Rehabilitation of Existing Railway Bridges 469

Fig. 27. The stress range diagram Δσ for train type 5

Fig. 28. The stress range diagram Δσ for train type 6

Fig. 29. The stress range diagram Δσ for train type 7

Fig. 24. The stress range diagram Δσ for train type 2

Fig. 25. The stress range diagram Δσ for train type 3

Fig. 26. The stress range diagram Δσ for train type 4

Fig. 24. The stress range diagram Δσ for train type 2

Fig. 25. The stress range diagram Δσ for train type 3

Fig. 26. The stress range diagram Δσ for train type 4

Fig. 27. The stress range diagram Δσ for train type 5

Fig. 28. The stress range diagram Δσ for train type 6

Fig. 29. The stress range diagram Δσ for train type 7

General Principles Regarding the Rehabilitation of Existing Railway Bridges 471

**Stress history**

20

1 2 3 4 5 6 7 8 9 10 11 12 13 **No. of classified intervals**

The crack case assumed for these structures (riveted bridges) is illustrated in figures 32; it is

In order to determine the remaining service life it is important to know how long it will take

through thickness flaw with initial size a0 = 2.0 mm which is undetectable because it is

through thickness flaw with initial size a0 = 2.0 mm which is also undetectable during a

the crack to grow from the minimum detectable size to the critical value.

situated under rivet head in the web steel plate, and

visual inspection appearing in the corner (lower flange).

149

291

94

36

80 100

12

94

0

50

100

150

200

**No. of cycles n**

250

300

350

19

0

Fig. 31. Stress history

a trough thickness defect.

Fig. 32. Theoretical crack models

Two cases were studied:

100

200

300

**Stress range**

Ds

**[daN/cm2**

**]**

400

500

600

249

34

108

Fig. 30. The stress range diagram Δσ for train type 8


Table 5. Classification of the stress range intervals

Fig. 31. Stress history

T1 T2 T3 T4 T5 T6 T7 T8 **Total** 0 0 0 0 105 36 0 108 **249** 0 0 0 0 7 12 0 0 **19** 12 12 10 0 0 0 0 0 **34** 0 108 0 0 0 0 0 0 **108** 132 0 0 10 105 36 8 0 **291** 12 0 65 60 0 0 0 12 **149** 0 0 10 10 0 0 0 0 **20** 12 12 10 0 0 60 0 6 **100** 0 12 0 0 0 60 8 0 **80** 0 0 0 0 0 36 0 0 **36** 0 0 0 0 0 0 88 6 **94** 12 0 0 0 0 0 0 0 **12** 0 0 0 0 14 72 8 0 **94**

**MAIN GIRDER (L/2) mix**

**381.36** Total/day **1037**

Fig. 30. The stress range diagram Δσ for train type 8

Table 5. Classification of the stress range intervals

Ds**<sup>e</sup>** [daN/cm<sup>2</sup>

Ds [daN/cm<sup>2</sup> ]

] =

The crack case assumed for these structures (riveted bridges) is illustrated in figures 32; it is a trough thickness defect.

Fig. 32. Theoretical crack models

In order to determine the remaining service life it is important to know how long it will take the crack to grow from the minimum detectable size to the critical value.

Two cases were studied:


General Principles Regarding the Rehabilitation of Existing Railway Bridges 473

**type / main elements Photo** 

**Bridge nr.** 

**Constr.** 

4 1940 6,60 m

5 1942 2 x 11,8 m

8 1942 2 x 11,8 m

9 1942 8,60 m

13 1942 9,80 m +

15 1942 19,00 m +

26,90 m

18,80 m

Table 6. Analyzed plate girder bridges

**year Span Cross section** 

Fig. 33. The two studied defect cases

In the first case the remaining fatigue life is estimated at a value of 8.31 years (corresponding to a number of cycles of 1 566 000). In the second case the administrator must be acquainted with the fact, that propagation of the crack to the critical value will occur in 8.89 years (N=1 676 000 cycles).

In this case the safe inspection intervals, calculated with formula 8, are situated between 1.2 and 2.0 years.

Finally due to the high corrosion level (Figure 34) and also based on the fatigue assessment, the superstructure was proposed for the replacement.

Fig. 34. Corrosion attack details

Also all the other plate girder bridges were verified. They are presented in the next table.

In the first case the remaining fatigue life is estimated at a value of 8.31 years (corresponding to a number of cycles of 1 566 000). In the second case the administrator must be acquainted with the fact, that propagation of the crack to the critical value will occur in 8.89 years (N=1

In this case the safe inspection intervals, calculated with formula 8, are situated between 1.2

Finally due to the high corrosion level (Figure 34) and also based on the fatigue assessment,

Also all the other plate girder bridges were verified. They are presented in the next table.

Fig. 33. The two studied defect cases

Fig. 34. Corrosion attack details

the superstructure was proposed for the replacement.

676 000 cycles).

and 2.0 years.


Table 6. Analyzed plate girder bridges

General Principles Regarding the Rehabilitation of Existing Railway Bridges 475

28 1940 56,20 m

29 1940 9,00 m

30 1979 16,30 m

31 1942 8,30 m

32 1940 53,40 m

33 1942 10,60 m

Table 6. Analyzed plate girder bridges - continuation


Table 6. Analyzed plate girder bridges - continuation

16 1942 26,90 m

<sup>17</sup>1880/

<sup>1942</sup>8,40 m

20 1942 37,20 m

22 1942 14,00 m

24 1944 53,60 m

<sup>25</sup>1940-

<sup>1944</sup>58,25 m

Table 6. Analyzed plate girder bridges - continuation


Table 6. Analyzed plate girder bridges - continuation

General Principles Regarding the Rehabilitation of Existing Railway Bridges 477

Fig. 35. Cross section of the new structure and calculation model

economical solutions with the high level sustainability.

konstruktive Hinweise, August 2002.

Român de Standardizare, Bucuresti, 1998.

The Structural Engineer, Volume 79 / No 9, May 2001.

[6] \* \* \*, "Maintenance of steel bridges", Romanian Pre-standard, Bucharest – 2000.

The progress recorded in the last decades allows on one part an accurate evaluation of the remaining safety of the structures and on the others part the proposal of new efficient,

[1] \* \* \* Code UIC 778-2R; Recommandations pour la détermination de la capacité portante

[2] \*\*, DS 805 "Bestehende Eisenbahnbrücken. Bewertung der Tragsicherheit und

[3] \*\*, SR 1911-98, "Poduri metalice de cale ferată. Prescripţii de proiectare", Institutul

[4] Jackson, P. "Is bridge assessment losing its credibility?" The Structural Engineer, Volume

[5] Xie, M., Bessant G.T., Chapman, J.C., Hobbs, R.E., "Fatigue of riveted bridge girders"

[7] Petzek, E., "Safety in Operation and Rehabilitation of Steel Bridges", Doctoral Thesis, UP

des structures métalliques existantes; Union Internationale des Chemins de fer,

**6. Conclusion** 

**7. References** 

Paris, 1986.

79 / No 9, May 2001.

Timişoara, 2004.


#### Table 6. Analyzed plate girder bridges - continuation

For the replacement different solutions can be proposed. A modern economical and robust structure is the Schmitt Stumpf Frühauf solution (VFT-WIB®), [12] – which has a high degree of prefabrication and goes along with a significant improvement of working conditions, as weather-independent working; also improved environment conditions for the workers while erecting formwork, placing re-bars and casting concrete is guaranteed. Furthermore a smaller amount of man-hours outdoors at the construction site is needed.

The constructive depth was optimized by a computer specialized program (Figure 35).

Fig. 35. Cross section of the new structure and calculation model

### **6. Conclusion**

476 Infrastructure Design, Signalling and Security in Railway

34 1966 14,20 m

37 1960 23,00 m

<sup>1944</sup>31,20 m

<sup>1942</sup>16,00 m

Table 6. Analyzed plate girder bridges - continuation

For the replacement different solutions can be proposed. A modern economical and robust structure is the Schmitt Stumpf Frühauf solution (VFT-WIB®), [12] – which has a high degree of prefabrication and goes along with a significant improvement of working conditions, as weather-independent working; also improved environment conditions for the workers while erecting formwork, placing re-bars and casting concrete is guaranteed. Furthermore a

The constructive depth was optimized by a computer specialized program (Figure 35).

smaller amount of man-hours outdoors at the construction site is needed.

<sup>40</sup>1942-

<sup>41</sup>1880/

The progress recorded in the last decades allows on one part an accurate evaluation of the remaining safety of the structures and on the others part the proposal of new efficient, economical solutions with the high level sustainability.

### **7. References**


**19** 

*India* 

**Railway Projects** 

More Ramulu

**Special Tunnel Blasting Techniques for** 

Excavations of tunnels are common features in mining and civil engineering projects. In absence of initial free face, solid blasting method is employed for excavation of tunnels, drifts and mine roadways, which have many similarities in configurations and in different cycles of operation followed during excavation. A greater proportion of world's annual tunnel advance is still achieved by drilling and blasting. In spite of inherent disadvantages of damaging the rock mass, drilling and blasting has an unmatched degree of flexibility and can overcome the limitations of machine excavations by Tunnel Boring Machine (TBM) or road headers. In spite of no major technical breakthrough, the advantages like low investment, availability of cheap chemical energy in the form of explosives, easy acceptability to the practicing engineers, the least depreciation and wide versatility have collectively made the drilling and blasting technique prevail so far over the mechanical

Since tunnels of different sizes and shapes are excavated in various rock mass conditions, appropriate blast design including drilling pattern, quantity and type of explosive, initiation sequence is essential to achieve a good advance rate causing minimal damage to the surrounding rock mass. The cost and time benefit of the excavation are mostly decided by

Excavation of tunnels, except in geologically disturbed rock mass conditions, is preferred with full face blasting. It is common to excavate large tunnels of 80-90 m2 cross-section in sound rock masses by full face in a single round. However, tunnels larger than 50m2 crosssectional area driven through incompetent ground condition are generally excavated in

Introduction of electro-hydraulic jumbo drills with multiple booms, non-electric initiation system, small diameter explosives for contour blasting and fracture control blasting are some of the recent developments in tunnel blasting. Prediction and monitoring the blast damage, application of computers in drilling, numerical modelling for advanced blast design, use of rock engineering systems for optimization and scheduling of activities have been the areas of intense research in today's competitive

**1. Introduction** 

excavation methods.

smaller parts.

the rate of advance and undesired damage.

and high-tech tunnelling world

*Central Institute of Mining & Fuel Research, Nagpur,* 


## **Special Tunnel Blasting Techniques for Railway Projects**

### More Ramulu

*Central Institute of Mining & Fuel Research, Nagpur, India* 

### **1. Introduction**

478 Infrastructure Design, Signalling and Security in Railway

[8] \*\* I-AM 08/2002. Richtlinie für die Beurteilung von genieteten Eisenbahnbrücken, SBB

[9] Petzek E., Kosteas D., Bancila R., 2005. Sicherheitsbestimmung bestehender Stahlbrücken

[10] \*\*\*, BS 7910:1999, "Guide on the Methods for Assessing the Acceptability of Flaws in

[11] Eriksson, K., Toughness requirements for old structural steel, IABSE Report Congress,

[12] SCHMITT, V., et alt.: VFT-Bauweise, Entwicklung von Verbundfertigteilträgern im

[13] SEIDL, G. et al. (2006), "Prefabricated Enduring Composite Beams based on Innovative

in Rumänien", Stahlbau Nr. 8, 9, ISSN 0038-9145, Ernst & Sohn.

Metallic Structures", British Standards Institution, London, 1999.

Brückenbau, Beton- und Stahlbetonbau 96, 2001, Heft 4.

Shear Transmission – Proposal RFSR-CT-2006-00030 ".

CFF FFS.

2000.

Excavations of tunnels are common features in mining and civil engineering projects. In absence of initial free face, solid blasting method is employed for excavation of tunnels, drifts and mine roadways, which have many similarities in configurations and in different cycles of operation followed during excavation. A greater proportion of world's annual tunnel advance is still achieved by drilling and blasting. In spite of inherent disadvantages of damaging the rock mass, drilling and blasting has an unmatched degree of flexibility and can overcome the limitations of machine excavations by Tunnel Boring Machine (TBM) or road headers. In spite of no major technical breakthrough, the advantages like low investment, availability of cheap chemical energy in the form of explosives, easy acceptability to the practicing engineers, the least depreciation and wide versatility have collectively made the drilling and blasting technique prevail so far over the mechanical excavation methods.

Since tunnels of different sizes and shapes are excavated in various rock mass conditions, appropriate blast design including drilling pattern, quantity and type of explosive, initiation sequence is essential to achieve a good advance rate causing minimal damage to the surrounding rock mass. The cost and time benefit of the excavation are mostly decided by the rate of advance and undesired damage.

Excavation of tunnels, except in geologically disturbed rock mass conditions, is preferred with full face blasting. It is common to excavate large tunnels of 80-90 m2 cross-section in sound rock masses by full face in a single round. However, tunnels larger than 50m2 crosssectional area driven through incompetent ground condition are generally excavated in smaller parts.

Introduction of electro-hydraulic jumbo drills with multiple booms, non-electric initiation system, small diameter explosives for contour blasting and fracture control blasting are some of the recent developments in tunnel blasting. Prediction and monitoring the blast damage, application of computers in drilling, numerical modelling for advanced blast design, use of rock engineering systems for optimization and scheduling of activities have been the areas of intense research in today's competitive and high-tech tunnelling world

Special Tunnel Blasting Techniques for Railway Projects 481

According to Langefors and Kihlstrom (1973), the specific charge (q) is related to the cross-

The specific charge in the cut holes remain maximum and it can be upto 7 kg/m3 in a

The aspects of blast induced rock mass damage around a tunnel opening and its assessment have been the subjects of in-depth research for quite a long time. The type of damage can be grouped into three categories: (i) fabric damage due to fracturing, (ii) structural damage exploiting discontinuities and shears, and (iii) lithological damage causing parting between two different rock units or lithological boundaries between

Chakraborty et al. (1996a) observed in the tunnels of Koyna Hydro-electric Project, Stage–IV poor pull and small overbreak in volcanic breccia having low Q value, P-wave velocity and modulus of elasticity. On the other hand, large overbreak on the sides due to vertical and subvertical joints and satisfactory pull were found in the compact basalts having comparatively much higher Q value, P-wave velocity and modulus of elasticity. The fact is attributed to the

The effects of joint orientations on overbreak/underbreak and pull in heading and benching operations during tunnel excavations are explained by Johansen (1998). The work of Johansen (1998) describes that joints normal to tunnel direction are favorable for good pull and parallel to the tunnel advance direction yield poor pull. advance direction. The obtuse angle between joints and tunnel direction results in more damage and breakage towards the

The dip direction of the blasted strata on pull could be well experienced while blasting in the development faces of Saoner coal mine where the pull was increased by 11 per cent in the rise galleries compared to that in the dip galleries (Chakraborty, 2002). Longer rounds in tunnels can be pulled when the dominant joint sets are normal to the tunnel axis. Whereas, better pull can be obtained in shaft sinking if the discontinuities are parallel to the line

presence of well defined joints in compact basalts which is absent in volcanic breccia.

q1=specific charge for breaking of rock against a free face in kg/m3,

swr = relative weight strength of explosive (ANFO = 1), and

st = factor for structure and texture of rock,

def = factor for diameter of explosive cartridge,

sectional area of the tunnel (A, m2) as given below:

joining the apex of the Vs in a V-Cut Hagan (1984).

where,

A= area of tunnel (m2),

**5. Rock mass damage** 

similar rock types.

wall of that angle.

parallel cut.

q = q1. st. f. swr. def, kg/m3 (1)

f = rock confinement = 6.5 / A, (1a)

q = (14/A) + 0.8 kg/m3 (2)

In tunnel blasting, explosives are required to perform in a difficult condition, as single free face (in the form of tunnel face) is available in contrast to bench blasting where at least two free faces exist. Hence, more drilling and explosives are required per unit volume of rock to be fragmented in the case of tunnel blasting. A second free face, called 'cut', is created initially during the blasting process and the efficiency of tunnel blast performance largely depends on the proper development of the cut. The factors influencing the development of the cut and the overall blast results are dependent on a host of factors involving rock mass type, blast pattern and the tunnel configurations.

### **2. Blasting mechanics**

The tunnel blasting mechanics can be conceptualised in two stages. Initially, a few holes called cut holes are blasted to develop a free face or void or cut along the tunnel axis. This represents a solid blasting condition where no initial free face is available. Once the cut is created, the remaining holes are blasted towards the cut. This stage of blasting is similar to bench blasting but with larger confinement. The results of tunnel blasting depend primarily on the efficiency of the cut hole blasting. The first charge fired in cut resembles crater blasting. Livingston's spherical charge crater theory (Livingston, 1956) suggests that the blast induced fracturing is dominated by explosion gas pressure which is supported by Liu and Katsabanis (1998). Duvall and Atchison (1957), Wilson (1987) and others believe that the stress wave induced radial fracturing is the dominating cause of blast fragmentation and gas pressure is responsible only for extension of the fractures developed by the stress wave.

The natures of influence of the two pressures i.e. of stress and gas are different in the jointed rock mass where the stress waves is useful in fragmentation as the joints restrict the stress wave propagation. The gases, on the other hand, penetrate the joint planes and try to separate the rock blocks. The fragments' size and shape in jointed formations are dominated by the gas pressure and the joint characteristics. The roles of the stress wave and the gas pressures are no different in the second stage of tunnel blasting. But with the availability of free face, the utilisation of stress wave is increased. The rock breakages by rupturing and by reflected tensile stress are more active in the second stage because of cut formation in the first stage.

### **3. Parameters influencing tunnel blast results**

The parameters influencing the tunnel blast results may be classified in three groups:


### **4. Models for prediction of tunnel blast results**

Specific Charge is one of the important paprameter of prediction of tunnel blast results. Pokrovsky (1980) suggested the following empirical relation to determine the specific charge (q) in tunnels (Eq. 1):

$$\mathbf{q} = \mathbf{q}1. \text{ s}, \text{ f. s.} \text{ s}, \text{ d.e.} \text{ kg/m}^3 \tag{1}$$

where,

480 Infrastructure Design, Signalling and Security in Railway

In tunnel blasting, explosives are required to perform in a difficult condition, as single free face (in the form of tunnel face) is available in contrast to bench blasting where at least two free faces exist. Hence, more drilling and explosives are required per unit volume of rock to be fragmented in the case of tunnel blasting. A second free face, called 'cut', is created initially during the blasting process and the efficiency of tunnel blast performance largely depends on the proper development of the cut. The factors influencing the development of the cut and the overall blast results are dependent on a host of factors involving rock mass

The tunnel blasting mechanics can be conceptualised in two stages. Initially, a few holes called cut holes are blasted to develop a free face or void or cut along the tunnel axis. This represents a solid blasting condition where no initial free face is available. Once the cut is created, the remaining holes are blasted towards the cut. This stage of blasting is similar to bench blasting but with larger confinement. The results of tunnel blasting depend primarily on the efficiency of the cut hole blasting. The first charge fired in cut resembles crater blasting. Livingston's spherical charge crater theory (Livingston, 1956) suggests that the blast induced fracturing is dominated by explosion gas pressure which is supported by Liu and Katsabanis (1998). Duvall and Atchison (1957), Wilson (1987) and others believe that the stress wave induced radial fracturing is the dominating cause of blast fragmentation and gas pressure is responsible only for extension of the fractures

The natures of influence of the two pressures i.e. of stress and gas are different in the jointed rock mass where the stress waves is useful in fragmentation as the joints restrict the stress wave propagation. The gases, on the other hand, penetrate the joint planes and try to separate the rock blocks. The fragments' size and shape in jointed formations are dominated by the gas pressure and the joint characteristics. The roles of the stress wave and the gas pressures are no different in the second stage of tunnel blasting. But with the availability of free face, the utilisation of stress wave is increased. The rock breakages by rupturing and by reflected tensile stress are more active in the second stage because of cut formation in the

The parameters influencing the tunnel blast results may be classified in three groups:

ii. Semi-controllable (a) Tunnel geometry & (b) Operating factors, and iii. Controllable Blast design parameters including the explosive properties.

Specific Charge is one of the important paprameter of prediction of tunnel blast results. Pokrovsky (1980) suggested the following empirical relation to determine the specific charge

type, blast pattern and the tunnel configurations.

**3. Parameters influencing tunnel blast results** 

i. Non controllable Rock mass properties,

**4. Models for prediction of tunnel blast results** 

**2. Blasting mechanics** 

developed by the stress wave.

first stage.

(q) in tunnels (Eq. 1):

q1=specific charge for breaking of rock against a free face in kg/m3, st = factor for structure and texture of rock,

$$\mathbf{f} \triangleq \text{rock confinement} = 6.5 \, / \, \text{\AA} \, \text{\AA} \tag{1a}$$

A= area of tunnel (m2),

swr = relative weight strength of explosive (ANFO = 1), and def = factor for diameter of explosive cartridge,

According to Langefors and Kihlstrom (1973), the specific charge (q) is related to the crosssectional area of the tunnel (A, m2) as given below:

$$\mathbf{q} = (14/\text{A}) + 0.8 \text{ kg/m}^3 \tag{2}$$

The specific charge in the cut holes remain maximum and it can be upto 7 kg/m3 in a parallel cut.

### **5. Rock mass damage**

The aspects of blast induced rock mass damage around a tunnel opening and its assessment have been the subjects of in-depth research for quite a long time. The type of damage can be grouped into three categories: (i) fabric damage due to fracturing, (ii) structural damage exploiting discontinuities and shears, and (iii) lithological damage causing parting between two different rock units or lithological boundaries between similar rock types.

Chakraborty et al. (1996a) observed in the tunnels of Koyna Hydro-electric Project, Stage–IV poor pull and small overbreak in volcanic breccia having low Q value, P-wave velocity and modulus of elasticity. On the other hand, large overbreak on the sides due to vertical and subvertical joints and satisfactory pull were found in the compact basalts having comparatively much higher Q value, P-wave velocity and modulus of elasticity. The fact is attributed to the presence of well defined joints in compact basalts which is absent in volcanic breccia.

The effects of joint orientations on overbreak/underbreak and pull in heading and benching operations during tunnel excavations are explained by Johansen (1998). The work of Johansen (1998) describes that joints normal to tunnel direction are favorable for good pull and parallel to the tunnel advance direction yield poor pull. advance direction. The obtuse angle between joints and tunnel direction results in more damage and breakage towards the wall of that angle.

The dip direction of the blasted strata on pull could be well experienced while blasting in the development faces of Saoner coal mine where the pull was increased by 11 per cent in the rise galleries compared to that in the dip galleries (Chakraborty, 2002). Longer rounds in tunnels can be pulled when the dominant joint sets are normal to the tunnel axis. Whereas, better pull can be obtained in shaft sinking if the discontinuities are parallel to the line joining the apex of the Vs in a V-Cut Hagan (1984).

Special Tunnel Blasting Techniques for Railway Projects 483

Pusch and Stanfors (1992) and others observed that the minimum disturbance by blasting is

Yu and Vongpaisal (1996) concluded that the damage is a function of blast induced stress and rock mass resistance to damage. They proposed Blast Damage Index (Dib) to estimate the type of damage due to blasting. It is the ratio of the blast induced stress to the resistance


Dmax=322.5(Vs)-0.61 m (4)

Contour blasting in tunnelling is adopted to obtain a smooth tunnel profile and minimise damage to the surrounding rock mass. Despite a large amount of drilling required, it is

iv. Overbreak is reduced to minimise unwanted excavations and filling to bring down the

The performance of contour blasting is frequently measured in terms of `Half cast factor' (HCF) which is dominated by the design parameters of the contour holes, the joint

Generally, two types of contour blasting are used in tunnelling, i) pre-splitting and ii) smooth blasting. When two closely spaced charged holes are fired simultaneously the stress waves generated from the two holes collide at a plane in between the holes and create a secondary tensile stress front perpendicular to the hole axis and facilitates extension of radial cracks along the line joining the holes. The wedging action from the explosion gas acts in favour of extending the crack along the same line. It is, therefore, essential to contain the gas pressure till the cracks from both ends meet by adequate stemming. Further, the delay timing of the adjacent holes need to be very accurate so that the stress waves should collide at the mid-point and the arbitrariness of the breakage between the holes can be reduced.

following equation with reasonably good correlation coefficient (R2=0.76).

Dmax – Maximum extent of rock mass damage due to repeated vibrations, m

preferred over conventional blasting because of the following advantages:

ii. Stability of the opening and the stand-up-time of the tunnel are improved.

i. The shape of the opening is maintained with smooth profile.

reported when the tunnel orientation was within 15o with the strike of the joint sets.

Ramulu et al (2009) categorised blast induced damage as,


offered against damage.

Vs – S-wave velocity, m/s

**6. Contour blasting** 

iii. Support requirement is reduced.

v. Ventilation improves due to smooth profile.

orientation and the explosive energy distribution.

cost and cycle time.

where,


Chakraborty (2002) observed the following influences of joint directions on pull and overbreak (Table 1).

Table 1. Influence of joint direction on overbreak (Chakraborty, 2002)

The gentle, moderate and steeply dipping joint planes signify the dip angles as 0o-30o, 30o-60o and 60o-90o respectively. Similarly, strikes with respect to tunnel axis are mentioned as parallel, oblique and across to indicate that the joint strike intersection angle with the tunnel axis as 0o-30o, 30o-60o and 60o-90o respectively.

If the geo-mechanical properties of the constituting formations of a tunnel are quite different, the stress energy utilisation and resulting fragmentation are adversely affected. Chakraborty et al. (1996b) suggested an increase of specific charge by a per cent equal to ten times the number of contact surfaces.

Engineers International Inc. modified Basic RMR (MBR) considering blast-induced-damage adjustments, as shown in Table 2, were suggested for planning of caving mine drift supports (Bieniawski,1984). Chapter 4 in the present publication defines basic RMR.


Table 2. Blast damage adjustments in MBR (after Bieniawski, 1984)

Ouchterlony et al. (1991) observed that the damage zone could be to the extent of 0.5 m with cautious tunnel blasting. McKenzie (1994) related the threshold peak particle velocity PPV (vmax) for incipient fracture with uniaxial tensile strength (qt), Young's modulus and P-wave velocity (Vp, m/s) as shown below:

$$\mathbf{v}\_{\text{max}} = \frac{\mathbf{q}\_{\text{t}} \times \mathbf{V}\_{\text{p}} \times 10^{-3}}{\mathbf{E}} \text{, m/s} \tag{3}$$

where

qt = uniaxial tensile strength, MPa, Vp = P-wave velocity, m/s, and E = Young's modulus, GPa.

Pusch and Stanfors (1992) and others observed that the minimum disturbance by blasting is reported when the tunnel orientation was within 15o with the strike of the joint sets.

Yu and Vongpaisal (1996) concluded that the damage is a function of blast induced stress and rock mass resistance to damage. They proposed Blast Damage Index (Dib) to estimate the type of damage due to blasting. It is the ratio of the blast induced stress to the resistance offered against damage.

Ramulu et al (2009) categorised blast induced damage as,


$$\mathbf{D}\_{\text{max}} \equiv 322.5 \text{(V}\_{\text{s}}\text{)} \, ^{0.61}\text{m} \tag{4}$$

where,

482 Infrastructure Design, Signalling and Security in Railway

Chakraborty (2002) observed the following influences of joint directions on pull and

Face Advance Roof Overbreak Dip Strike with respect to

Steep Parallel Very poor Very small Steep Across Very good Very large Gentle Across Fair Large Moderate Across/oblique Good Small

The gentle, moderate and steeply dipping joint planes signify the dip angles as 0o-30o, 30o-60o and 60o-90o respectively. Similarly, strikes with respect to tunnel axis are mentioned as parallel, oblique and across to indicate that the joint strike intersection angle with the tunnel

If the geo-mechanical properties of the constituting formations of a tunnel are quite different, the stress energy utilisation and resulting fragmentation are adversely affected. Chakraborty et al. (1996b) suggested an increase of specific charge by a per cent equal to ten

Engineers International Inc. modified Basic RMR (MBR) considering blast-induced-damage adjustments, as shown in Table 2, were suggested for planning of caving mine drift supports

Factor

, m/s (3)

Per cent Reduction

overbreak (Table 1).

Joint Orientation

axis as 0o-30o, 30o-60o and 60o-90o respectively.

times the number of contact surfaces.

velocity (Vp, m/s) as shown below:

qt = uniaxial tensile strength, MPa, Vp = P-wave velocity, m/s, and E = Young's modulus, GPa.

where

tunnel axis

Table 1. Influence of joint direction on overbreak (Chakraborty, 2002)

(Bieniawski,1984). Chapter 4 in the present publication defines basic RMR.

Table 2. Blast damage adjustments in MBR (after Bieniawski, 1984)

Method of Excavation Damage Level Blast Damage Adjustment

1. Machine boring No damage 1.0 0 2. Controlled blasting Slight 0.94-0.97 3-6 3. Good conventional blasting Moderate 0.9-0.94 6-10 4. Poor conventional blasting Severe damage 0.9-0.8 10-20

Ouchterlony et al. (1991) observed that the damage zone could be to the extent of 0.5 m with cautious tunnel blasting. McKenzie (1994) related the threshold peak particle velocity PPV (vmax) for incipient fracture with uniaxial tensile strength (qt), Young's modulus and P-wave

t p

q V 10

E

max

v =


Dmax – Maximum extent of rock mass damage due to repeated vibrations, m Vs – S-wave velocity, m/s

### **6. Contour blasting**

Contour blasting in tunnelling is adopted to obtain a smooth tunnel profile and minimise damage to the surrounding rock mass. Despite a large amount of drilling required, it is preferred over conventional blasting because of the following advantages:


The performance of contour blasting is frequently measured in terms of `Half cast factor' (HCF) which is dominated by the design parameters of the contour holes, the joint orientation and the explosive energy distribution.

Generally, two types of contour blasting are used in tunnelling, i) pre-splitting and ii) smooth blasting. When two closely spaced charged holes are fired simultaneously the stress waves generated from the two holes collide at a plane in between the holes and create a secondary tensile stress front perpendicular to the hole axis and facilitates extension of radial cracks along the line joining the holes. The wedging action from the explosion gas acts in favour of extending the crack along the same line. It is, therefore, essential to contain the gas pressure till the cracks from both ends meet by adequate stemming. Further, the delay timing of the adjacent holes need to be very accurate so that the stress waves should collide at the mid-point and the arbitrariness of the breakage between the holes can be reduced.

Special Tunnel Blasting Techniques for Railway Projects 485

Line drilling is adopted as an alternative technique where a number of uncharged holes are drilled along the contour with a spacing of 2-4 times the hole diameter (Du Pont, 1977). The distance of the row of empty holes from the final row of charged holes is kept as 0.5-0.75 times the normal burden. The empty holes are joined during the main blasting round and a

According to Holmberg and Persson (1978), the spacing of pre-split holes should be 8-12 times the blast hole diameter. The following design parameters for contour hole spacing, burden to spacing ratio of contour holes and linear charge concentration in smooth blasting

Sdc = 16 x db, m (5)

mdc = 1.25 (6)

qlcc = 90 x (db)2 , kg/m (7)

Controlled blast design details recommended by Olofsson (1988) are presented in Table 3.

Spacing of Blast Holes (m)

> 0.25-0.35 0.5-0.7 0.8-0.9

Pre-splitting 38-44 0.3-0.45 - 0.12-0.37

Some special blasting techniques were practised in tunnels and underground coal mine to attain greater advance and better safety in some critical working sites under the recommendations and supervision of Central Mining Research Institute, Regional Centre,

A 123 m deep pilot shaft was excavated in 95 days time using Long Hole Raise Blasting (LHRB) method for faster and safer shaft sinking in the surge shaft, passing through various kinds of basaltic formations, in Ghatghar Hydro-electric Project of Maharashtra. The blast hole charging pattern is shown in Figure 3. Application of this techniques resulted in saving of 75% time 60% cost of excavation in comparison to the conventional

Table 3. Recommended blast design for contour blasting (Olofsson, 1988)

Nagpur. Those cases are discussed in brief in the following paragraphs.

Burden (m)

0.3-0.5 0.7-0.9 1.0-1.2

Linear Charge Concentration (kg/m)

> 0.11 0.23 0.42-0.45

separation is created along the contour.

are suggested by Holmberg (1982) :

db = diameter of blast holes, m.

Type of Blasting Blast Hole

Smooth blasting

Sdc = spacing of contour holes while drilling, m,

Diameter (mm)

25-32 25-48 51-64

**7. Special tunnel blasting techniques** 

**7.1 Long hole raise driving by blasting** 

shaft sinking method.

mdc = burden to spacing ratio of contour holes while drilling, qlcc = linear charge concentration in the contour holes, kg/m, and

where

The contour blasting performance largely depends on the nature and the orientation of joint planes. Gupta et al. (1988) found that the joint orientation adversely influences the presplitting results to a maximum when these are at an angle of 1-30o to the pre-split axis.

In smooth blasting, the delay intervals between the contour holes and the nearest production holes are kept high to facilitate complete movement of material in production holes before the contour holes detonate so that the gas expansion in contour holes occurs towards the opening. Sometimes, holes are drilled in between two charged blast holes and are kept uncharged. These are called dummy holes (Figure 1). The stress concentration at the farthest and the nearest points of the dummy holes become high to initiate cracks from the dummy holes extending towards the charged holes. The fracture is, thus, controlled along the desired contour.

In some cases, slashing or trimming techniques are used where the central core of excavation area is removed first to reduce the stress and then post-splitting is adopted to remove the remaining rock mass along the desired contour. The technique is generally referred to as 'slashing' or 'trimming' [Calder and Bauer (1983), Figure 2].

Fig. 1. Smooth blasting pattern with dummy holes

Fig. 2. Cushion blast holes for trimming of a tunnel after pilot excavation

Line drilling is adopted as an alternative technique where a number of uncharged holes are drilled along the contour with a spacing of 2-4 times the hole diameter (Du Pont, 1977). The distance of the row of empty holes from the final row of charged holes is kept as 0.5-0.75 times the normal burden. The empty holes are joined during the main blasting round and a separation is created along the contour.

According to Holmberg and Persson (1978), the spacing of pre-split holes should be 8-12 times the blast hole diameter. The following design parameters for contour hole spacing, burden to spacing ratio of contour holes and linear charge concentration in smooth blasting are suggested by Holmberg (1982) :

$$\mathbf{S}\_{\rm dc} = 16 \times \mathbf{d}\_{\rm b} \text{ m} \tag{5}$$

$$\mathbf{m}\_{\rm dc} = \mathbf{1.25} \tag{6}$$

$$\mathbf{q}\_{\rm lxc} = 90 \times (\mathbf{d}\_b)^2 \text{, kg/m} \tag{7}$$

where

484 Infrastructure Design, Signalling and Security in Railway

The contour blasting performance largely depends on the nature and the orientation of joint planes. Gupta et al. (1988) found that the joint orientation adversely influences the presplitting results to a maximum when these are at an angle of 1-30o to the pre-split axis.

In smooth blasting, the delay intervals between the contour holes and the nearest production holes are kept high to facilitate complete movement of material in production holes before the contour holes detonate so that the gas expansion in contour holes occurs towards the opening. Sometimes, holes are drilled in between two charged blast holes and are kept uncharged. These are called dummy holes (Figure 1). The stress concentration at the farthest and the nearest points of the dummy holes become high to initiate cracks from the dummy holes extending towards the charged holes. The fracture is, thus, controlled

In some cases, slashing or trimming techniques are used where the central core of excavation area is removed first to reduce the stress and then post-splitting is adopted to remove the remaining rock mass along the desired contour. The technique is generally

referred to as 'slashing' or 'trimming' [Calder and Bauer (1983), Figure 2].

Fig. 2. Cushion blast holes for trimming of a tunnel after pilot excavation

Fig. 1. Smooth blasting pattern with dummy holes

along the desired contour.

Sdc = spacing of contour holes while drilling, m, mdc = burden to spacing ratio of contour holes while drilling, qlcc = linear charge concentration in the contour holes, kg/m, and db = diameter of blast holes, m.

Controlled blast design details recommended by Olofsson (1988) are presented in Table 3.


Table 3. Recommended blast design for contour blasting (Olofsson, 1988)

### **7. Special tunnel blasting techniques**

Some special blasting techniques were practised in tunnels and underground coal mine to attain greater advance and better safety in some critical working sites under the recommendations and supervision of Central Mining Research Institute, Regional Centre, Nagpur. Those cases are discussed in brief in the following paragraphs.

### **7.1 Long hole raise driving by blasting**

A 123 m deep pilot shaft was excavated in 95 days time using Long Hole Raise Blasting (LHRB) method for faster and safer shaft sinking in the surge shaft, passing through various kinds of basaltic formations, in Ghatghar Hydro-electric Project of Maharashtra. The blast hole charging pattern is shown in Figure 3. Application of this techniques resulted in saving of 75% time 60% cost of excavation in comparison to the conventional shaft sinking method.

Special Tunnel Blasting Techniques for Railway Projects 487

Fig. 4. Profile of pilot surge shaft excavated by long hole raise driving at Koilsagar

A borehole from the top was used to convey initiation to the blast holes.

the following salient features:

fragmentation.

rock mass damage.

holes.

Based on the blast performance of the trail rock plug final plug blast design was made with

Specific charge was increased from 1.25 kg/m3 to 1.33 kg/m3 to improve throw and

Only gelatine explosive was recommended considering the water inflow from the blast

Dummy holes were made above the crown holes, at a distance of 0.3 m, to minimise

A ventilation shaft of 40m depth was also excavated by using the same technique at diversion tunnel of Latur-Osmanabad Railway tunneling project of Central Railways in 20 days. This techniques yielded in saving of time by 80% and cost of excavation by 60% in comparison to the conventional shaft sinking method, which mainly suffer from weather effects, confined working space and low cycle time.

Similarly, a pilot surge shaft of 3.0m diameter130m depth was excavated by long hole raise driving technique at a lift irrigation scheme of Koilsagar project. This swift and cost effective shaft excavation technique was completed in just 60 days with cost savings of 70% and time saving by 95% in contrast to conventional shaft sinking method. The profile of excavated pilot surge shaft at Koilsagar project is shown in Figure 4.

### **7.2 Lake tap blasting**

The lake taping of fist of its kind with indigenous technology was carried out in India by CMRI (now CIMFR) at granitic rock mass in South India. The Andhra Pradesh Power Generation Corporation (APGENCO), India, executed a lift irrigation scheme (SLBC) for the Government of Andhra Pradesh to install 4 Nos. of 4 x 25000 hp pumps to lift 2400 cusecs of water from the Nagarjuna Sagar reservoir for irrigation purpose. A 4 m thick rock plug, designed by CMRI, was left for lake tapping at the end of project. The area of cross section of the tunnel was 40 m2. Considering proximity of the nearby structures a controlled blast strategy in phased manner was evolved prior to final plug blasting. Vibration and damage characteristics were ascertained to finalise the blast design of the final plug.

Fig. 3. Charging pattern in raise blasting

A ventilation shaft of 40m depth was also excavated by using the same technique at diversion tunnel of Latur-Osmanabad Railway tunneling project of Central Railways in 20 days. This techniques yielded in saving of time by 80% and cost of excavation by 60% in comparison to the conventional shaft sinking method, which mainly suffer from weather

Similarly, a pilot surge shaft of 3.0m diameter130m depth was excavated by long hole raise driving technique at a lift irrigation scheme of Koilsagar project. This swift and cost effective shaft excavation technique was completed in just 60 days with cost savings of 70% and time saving by 95% in contrast to conventional shaft sinking method. The profile of excavated

The lake taping of fist of its kind with indigenous technology was carried out in India by CMRI (now CIMFR) at granitic rock mass in South India. The Andhra Pradesh Power Generation Corporation (APGENCO), India, executed a lift irrigation scheme (SLBC) for the Government of Andhra Pradesh to install 4 Nos. of 4 x 25000 hp pumps to lift 2400 cusecs of water from the Nagarjuna Sagar reservoir for irrigation purpose. A 4 m thick rock plug, designed by CMRI, was left for lake tapping at the end of project. The area of cross section of the tunnel was 40 m2. Considering proximity of the nearby structures a controlled blast strategy in phased manner was evolved prior to final plug blasting. Vibration and damage characteristics were ascertained to finalise the blast design of the

effects, confined working space and low cycle time.

pilot surge shaft at Koilsagar project is shown in Figure 4.

**7.2 Lake tap blasting** 

final plug.

Fig. 3. Charging pattern in raise blasting

Fig. 4. Profile of pilot surge shaft excavated by long hole raise driving at Koilsagar

Based on the blast performance of the trail rock plug final plug blast design was made with the following salient features:


Special Tunnel Blasting Techniques for Railway Projects 489

Hole Diameter = 32 mm; Total no.of blast holes = 113,

Length of blast holes = 3.5 to 4.0 m, Specific Charge = 1.33 kg/m3

Fig. 5. Lake tap blast design

The final plug-blasting pattern is shown in Figure 5. This novel technology being an indigenous one could save Crores of national exchequers.

### **7.3 Cautious blasting**

By adopting an extremely cautious approach, all 10 reinforced concrete plugs, each of 125 m3 volume, in 5 units were removed by controlled blasting without causing any damage to the surrounding periphery and pier nose in Srisailam left bank project of the APPGENCO while the power house was in running condition. The controlled blasting pattern is described below:


Pre and post blast ultrasonic measurements were taken at the exposed areas of the pier nose walls to know the change in physical property the reinforced mass due to blasting. The compressional wave velocities (P-wave) were measured by Roop telesonic ultrasonix instrument 'Ultrasonix 4600' which is shown in Figure 6. The average P-wave velocity was 2075 m/s and 2100m/s before and after blasting respectively. The values indicate that there has been no blast-induced damage to the structure under consideration.

The cautious blasting was also applied at Koldam Hydroelectric Power Project (KHEPP) to reduce overbreak and to get a smoother tunnel wall profile. The rock mass encountered in all the tunnels of KHEPP was Dolomite, which was very heterogeneous, highly weathered, metamorphosed, compact, foliated, sheared and crushed due to the effect of Chamiatar Khad fault striking N1700 E and 450 W. Joints are open, closely spaced, intersecting, which are having clay fillings due to mechanical and chemical weathering of the rocks. One main joint with angle of N 750 E/800W is running parallel to the axis of the tunnels which is very unfavourable. At some places huge wedges were formed due to the intersection of the joints, which caused excessive overbreaks in the tunnels. The Q values of most of the rock mass of tunnels range from 0.12 to 0.21, which indicates that the rock was very poor. Core samples were collected from both the monitoring locations by underground coring machine. Engineering properties like Rock Quality Designation (RQD) compressive strength, tensile strength, density and compressional wave velocity (Vp) were determined from the core samples.

The final plug-blasting pattern is shown in Figure 5. This novel technology being an

By adopting an extremely cautious approach, all 10 reinforced concrete plugs, each of 125 m3 volume, in 5 units were removed by controlled blasting without causing any damage to the surrounding periphery and pier nose in Srisailam left bank project of the APPGENCO while the power house was in running condition. The controlled blasting pattern is

i. Line drilling holes of 1.5m depth were drilled with spacing of 0.15 m between the holes

ii. The periphery holes were pre-split with air-decking. The half cast factor of the periphery blasting was around 95%, which indicates low damage level. The pre-split blasting connections and the post-blast wall with half cast holes are shown in Figures.

iii. A cut was created at the heading and it was widened and deepened to make a pilot hole

iv. The balance concrete mass of the heading was slashed with less charge against the void.

vii. Continuous blast vibration monitoring was carried out during the blasts at near,

viii. Analysis of vibration data was done for subsequent blasting and to develop general

Pre and post blast ultrasonic measurements were taken at the exposed areas of the pier nose walls to know the change in physical property the reinforced mass due to blasting. The compressional wave velocities (P-wave) were measured by Roop telesonic ultrasonix instrument 'Ultrasonix 4600' which is shown in Figure 6. The average P-wave velocity was 2075 m/s and 2100m/s before and after blasting respectively. The values indicate that there

The cautious blasting was also applied at Koldam Hydroelectric Power Project (KHEPP) to reduce overbreak and to get a smoother tunnel wall profile. The rock mass encountered in all the tunnels of KHEPP was Dolomite, which was very heterogeneous, highly weathered, metamorphosed, compact, foliated, sheared and crushed due to the effect of Chamiatar Khad fault striking N1700 E and 450 W. Joints are open, closely spaced, intersecting, which are having clay fillings due to mechanical and chemical weathering of the rocks. One main joint with angle of N 750 E/800W is running parallel to the axis of the tunnels which is very unfavourable. At some places huge wedges were formed due to the intersection of the joints, which caused excessive overbreaks in the tunnels. The Q values of most of the rock mass of tunnels range from 0.12 to 0.21, which indicates that the rock was very poor. Core samples were collected from both the monitoring locations by underground coring machine. Engineering properties like Rock Quality Designation (RQD) compressive strength, tensile strength, density and compressional wave velocity (Vp) were determined from the core

has been no blast-induced damage to the structure under consideration.

indigenous one could save Crores of national exchequers.

on the pier nose side and at 0.20 m inside the periphery.

**7.3 Cautious blasting** 

described below:

5(a) and 5(b).

in the plug along its axis.

intermediate and far field.

predictor equation.

samples.

v. The bottom was blasted with benching method. vi. Mucking was done by mechanical and manual means.

Hole Diameter = 32 mm; Total no.of blast holes = 113, Length of blast holes = 3.5 to 4.0 m, Specific Charge = 1.33 kg/m3

Fig. 5. Lake tap blast design

Special Tunnel Blasting Techniques for Railway Projects 491

In-situ compressive strengths were also determined by using Schmidt hammer rebound testing. The average RQD values of Dolamite rock mass ranging from of 40-60%. Water absorption properties measured at the test site was 1.2% at both the sides. The improved blast performance of smooth blasting in the form of smooth profile is shown in Figure 7. The results were consistent for 12 trial blasts at the Dolomite tunnel. The controlled blasting restricted the overbreak to only 3%, which was 27% with the conventional tunnel blasting.

Fig. 7. Improved blast performance of smooth blasting in the form of smooth profile at

Following the trend of opencast blasting, in hole delay blasting technique using delay electric detonators were used in some mines and tunnels to improve the pull per blast and reduce the ground vibration. As the confinement in the cut holes are maximum and the blast performance in tunnels depend mainly on the development of the cut portion, the in-hole delay were used in the cut holes only. The salient features of the in-hole delay pattern are: 1. The collar portion of the hole was blasted prior to the bottom. Thus, the confinement at

2. Mid-column decking between the two charges in a hole was kept at least 0.6 m to avoid sympathetic detonation. This decking provided confinement for the bottom charge.

The average half cast factor was calculated as 85%.

KHEPP

**7.4 In-hole delay blasting** 

the hole bottom was less during firing.

The charging pattern is explained in Figure 8.

Fig. 5(a). Connections for pre-split blasting

Fig. 5(b). Pier nose wall after pre-split blasting

Fig. 6. Compressional wave velocity (P-wave) measuring device 'Ultrasonix 4600'

Fig. 5(a). Connections for pre-split blasting

Fig. 5(b). Pier nose wall after pre-split blasting

Fig. 6. Compressional wave velocity (P-wave) measuring device 'Ultrasonix 4600'

In-situ compressive strengths were also determined by using Schmidt hammer rebound testing. The average RQD values of Dolamite rock mass ranging from of 40-60%. Water absorption properties measured at the test site was 1.2% at both the sides. The improved blast performance of smooth blasting in the form of smooth profile is shown in Figure 7. The results were consistent for 12 trial blasts at the Dolomite tunnel. The controlled blasting restricted the overbreak to only 3%, which was 27% with the conventional tunnel blasting. The average half cast factor was calculated as 85%.

Fig. 7. Improved blast performance of smooth blasting in the form of smooth profile at KHEPP

### **7.4 In-hole delay blasting**

Following the trend of opencast blasting, in hole delay blasting technique using delay electric detonators were used in some mines and tunnels to improve the pull per blast and reduce the ground vibration. As the confinement in the cut holes are maximum and the blast performance in tunnels depend mainly on the development of the cut portion, the in-hole delay were used in the cut holes only. The salient features of the in-hole delay pattern are:


The charging pattern is explained in Figure 8.

Special Tunnel Blasting Techniques for Railway Projects 493

bottom. The diameter of the spacer should be preferably one third of the blasthole diameter for easy lowering and not allowing the charge to go to bottom side while loading. The reported values of air-deck length was taken as basis for optimum bottom deck length which was about 10% of the hole depth (Mead et al, 1993). The hole contains explosive and stemming column as in conventional loading but with a spacer at the bottom. The principle of bottom hole air decking in achieving optimum explosive energy interaction on rock mass

Reduced shock energy around the blast hole due to cushioning effect of air decking,

Explosive energy-rock interaction is more at the bottom due to relative relief zone

Effective toe breakage is due to striking and reflection of shock waves at the bottom face

The procedure and sequence of blast hole loading and initiation for the bottom hole decking

Loading the primer explosive cartridge attached by delay detonator charging the

The advantages of the bottom air decking technique in comparison to the conventional

i. The highly confined toe is free of explosive charge but exposed to high concentration

Stemming of the hole by proper stemming material, preferably by sand mixed clay

shock energy, resulting in good toe breakage and low vibration intensity.

Blast hole charge design for production blasts with bottom air-decking is Figure 9.

Fig. 9. Blast hole charge design for production blasts with bottom air-decking

improving the opencast blasting productivity as well as safety.

The bottom air decking also resulted in the overall progress/pull per round of 36% with 1.5 deep rounds and 22% with 1.8 m deep rounds even with the powder factor improvement (ton/kg) upto 70%. The increase of detonator factor was very predominant in case of tests with bottom decking in comparison to tests with bottom decking technique. The technique was also resulted in reduction of ground vibrations by 20-26%. The laboratory and field experimental results prove that the bottom-hole air decking is an effective technique for

ii. The reduced overall peak shock reduces the back break and damage.

is given below:

of hole

are given below:

existing at that zone.

column charge conventionally

middle air decking are given below:

which otherwise would result in crushing

Inserting the spacer in to the hole bottom by stemming rod.

Fig. 8. Charging pattern of cut holes with in-hole delay

This technique was successfully applied at basaltic rock mass of Central railway tunnels and gneiss rock mass of Lohari Nag Pala Hydel power project.

The advantages of the in-hole delay cut blasting includes:


### **7.5 Bottom hole decking technique**

The mining industry is striving to enhance the productivity by improving fragmentation to reduce the system cost. In order to achieve this objective, development of new techniques and their application is essential. The authors at CIMFR, experimented a blasting technique called 'bottom hole decking technique' to achieve the objective of blasting productivity improvement of the mining industry. The technique consists of air decking at the bottom of the blasthole in dry holes by means of a wooden spacer or a closed PVC pipe. Although, practice of air decking is not new thing in blastholes, the concept of inserting bottom hole decking below the explosive column is relatively new. Explosives provide a very concentrated source of energy, which is often well in excess of that required to adequately fragment the surrounding rock material. Blast design, environmental requirements and production requirement limits the degree to which the explosive energy distribution within the blasthole can be significantly altered using variable loading techniques. Use of air-decks provide an increased flexibility in alteration and distribution of explosive charge in blast holes.

The bottom hole air-decking was developed to avoid the general disadvantages of middle air decking and to simplify the complex charging procedure, associated with it. The design aspects of the technique are explained in the following sections. The bottom hole decking consists of air decking at the bottom of the hole in dry holes by means of a spacer or a closed PVC pipe, covered at the upper end. The fume characteristics of the spacer are to be tested before applying in underground coal mine. If blast holes are wet, water decking will be created at the bottom by means of a spacer with a weight attached to it for sinking to the

This technique was successfully applied at basaltic rock mass of Central railway tunnels and

1. The average face pull improve by nearly 30-50%. The specific charge also reduces

2. The blast vibration intensity reduces by 20 to 25% as the cut hole charge is distributed

The mining industry is striving to enhance the productivity by improving fragmentation to reduce the system cost. In order to achieve this objective, development of new techniques and their application is essential. The authors at CIMFR, experimented a blasting technique called 'bottom hole decking technique' to achieve the objective of blasting productivity improvement of the mining industry. The technique consists of air decking at the bottom of the blasthole in dry holes by means of a wooden spacer or a closed PVC pipe. Although, practice of air decking is not new thing in blastholes, the concept of inserting bottom hole decking below the explosive column is relatively new. Explosives provide a very concentrated source of energy, which is often well in excess of that required to adequately fragment the surrounding rock material. Blast design, environmental requirements and production requirement limits the degree to which the explosive energy distribution within the blasthole can be significantly altered using variable loading techniques. Use of air-decks provide an increased flexibility in alteration and distribution of explosive charge in blast

The bottom hole air-decking was developed to avoid the general disadvantages of middle air decking and to simplify the complex charging procedure, associated with it. The design aspects of the technique are explained in the following sections. The bottom hole decking consists of air decking at the bottom of the hole in dry holes by means of a spacer or a closed PVC pipe, covered at the upper end. The fume characteristics of the spacer are to be tested before applying in underground coal mine. If blast holes are wet, water decking will be created at the bottom by means of a spacer with a weight attached to it for sinking to the

in two delays. This is going to reduce the overbreak proportionately.

Fig. 8. Charging pattern of cut holes with in-hole delay

proportionately.

holes.

**7.5 Bottom hole decking technique** 

gneiss rock mass of Lohari Nag Pala Hydel power project. The advantages of the in-hole delay cut blasting includes:

bottom. The diameter of the spacer should be preferably one third of the blasthole diameter for easy lowering and not allowing the charge to go to bottom side while loading. The reported values of air-deck length was taken as basis for optimum bottom deck length which was about 10% of the hole depth (Mead et al, 1993). The hole contains explosive and stemming column as in conventional loading but with a spacer at the bottom. The principle of bottom hole air decking in achieving optimum explosive energy interaction on rock mass is given below:


The procedure and sequence of blast hole loading and initiation for the bottom hole decking are given below:


The advantages of the bottom air decking technique in comparison to the conventional middle air decking are given below:


Blast hole charge design for production blasts with bottom air-decking is Figure 9.

The bottom air decking also resulted in the overall progress/pull per round of 36% with 1.5 deep rounds and 22% with 1.8 m deep rounds even with the powder factor improvement (ton/kg) upto 70%. The increase of detonator factor was very predominant in case of tests with bottom decking in comparison to tests with bottom decking technique. The technique was also resulted in reduction of ground vibrations by 20-26%. The laboratory and field experimental results prove that the bottom-hole air decking is an effective technique for improving the opencast blasting productivity as well as safety.

Special Tunnel Blasting Techniques for Railway Projects 495

Fig. 11. Loading and unloading of sand into the stemming column of a blasthole at KHEPP

Some of the software developed for blast design and optimisation are reported in Table 4. Few blasting software on tunnel blasting are commercially available and the details can be

Software Purpose Reference

TUNNEL BLAST Blast design in tunnels Chakraborty et al. (1998)

ALEGRA Air-decking blasting Jensen and Preece (1999)

PFC-2D/3D Crack and heaving simulation Itasca Consulting Group

networking Model free computing Leu S. S. et al. (1998)

CAD Optimum design of ring hole blasting Myers et al. (1990)

efficiency and cost analyses in tunnels Rusilo et al. (1994)

mass Pusch et al. (1993)

effects of air decking and decoupling Liu and Katsabanis (1996)

Inc. (2002)

OPTES Blast optimisation in tunnels Vierra (1984)

**9. Computer aided blast design** 

VOLADOR Estimation of blast results, blast

FLAC and UDEC Blasting effects on the near field rock

ABAQUS V 5.4 Mechanics of crater blasting and the

Table 4. Various routines for computer aided tunnel blast design

obtained through web search.

Name of

Neural

### **8. Sand stemming device for horizontal blast holes**

The device of sand stemming for horizontal blast holes constitutes an assembly of a plastic pipe with proper cut and slits, a wooden block with pulley arrangement for resisting sand and an anti-static (non metallic) rope to pull out the plastic pipe from blast hole. The device essentially consists of a plastic pipe tied with an anti-static rope which is passed through a wooden resisting block to which a pulley is attached. The main objective of the device is for efficient use of sand as stemming material in horizontal blast holes. Another objective of the present device is to provide an effective and economic and fast stemming method which can find a mass application in underground blasting. The device essentially consists of a plastic pipe tied with a non metallic rope which is passed through a wooden resisting block to which a pulley is attached, an assembly of a plastic pipe cut and slit properly and a rope passed through a wooden block which can insert the sand in to blast hole and resist the sand to come out while pipe is pulled out of the blast hole. The position of stemming device while inserting the sand with plastic pipe and the position of removal of the plastic pipes are shown in the Figure 10. Actual application of the device in the field is shown in the Figure 11.

Fig. 10. Position of stemming device for loading and unloading in the blasthole.

Application of this tool in place of conventional stemming resulted in pull improvement of 5-10% in dolomite tunnels and 8-12% in gneiss tunnel. The improved blast performance was recorded consistently for 20 trial blasts at the gneiss tunnels and 25 trial blasts at the dolomite tunnels.

The device of sand stemming for horizontal blast holes constitutes an assembly of a plastic pipe with proper cut and slits, a wooden block with pulley arrangement for resisting sand and an anti-static (non metallic) rope to pull out the plastic pipe from blast hole. The device essentially consists of a plastic pipe tied with an anti-static rope which is passed through a wooden resisting block to which a pulley is attached. The main objective of the device is for efficient use of sand as stemming material in horizontal blast holes. Another objective of the present device is to provide an effective and economic and fast stemming method which can find a mass application in underground blasting. The device essentially consists of a plastic pipe tied with a non metallic rope which is passed through a wooden resisting block to which a pulley is attached, an assembly of a plastic pipe cut and slit properly and a rope passed through a wooden block which can insert the sand in to blast hole and resist the sand to come out while pipe is pulled out of the blast hole. The position of stemming device while inserting the sand with plastic pipe and the position of removal of the plastic pipes are shown in the

Figure 10. Actual application of the device in the field is shown in the Figure 11.

Fig. 10. Position of stemming device for loading and unloading in the blasthole.

dolomite tunnels.

Application of this tool in place of conventional stemming resulted in pull improvement of 5-10% in dolomite tunnels and 8-12% in gneiss tunnel. The improved blast performance was recorded consistently for 20 trial blasts at the gneiss tunnels and 25 trial blasts at the

**8. Sand stemming device for horizontal blast holes** 

Fig. 11. Loading and unloading of sand into the stemming column of a blasthole at KHEPP

### **9. Computer aided blast design**

Some of the software developed for blast design and optimisation are reported in Table 4. Few blasting software on tunnel blasting are commercially available and the details can be obtained through web search.


Table 4. Various routines for computer aided tunnel blast design

Special Tunnel Blasting Techniques for Railway Projects 497

After feeding the input information the software process the entire data and gives the blast hole geometry and charge pattern for cut holes and other holes separately. The utput information given by TUNNELBLAST software is given in Figure 12, Figure 13 and Table 5 and Table 6.

The blast design generated by TUNNEL BLAST software was applied at intermediate adit and the blast results were satisfactory in terms of pull per round and overbreak control. The trial blast results with felid application of TUNNEL BLAST software are given in Table 7. The blast results indicate the efficacy of the TUNNEL BLAST software, as a preliminary tool for tunnel blast design for various geological conditions. The fine tuning of this design can

Explosives strength: 80% (60% may also be required in the periphery holes

be done for further improvements in the progress and yield of tunnel blasting.

Fig. 12. Blast design output from TUNNELBLAST for cut holes of intermediate adit

Boundary conditions:

 Av. rock density: 2.6 t/m3 Type of explosives: Emulsion Blast hole diameter: 45 mm

 Length of blast hole: 2 m Delay: Long delay (NONEL)

Explosives diameter: 40 mm & 32 mm

and hence provisions may be made)

Rock Type: Metabasic (Amphibolite) & quartz vein

### **9.1 TUNNEL BLAST2.0 software**

Based on the past experience and extensive field investigations over a variety of underground structures of varying lithologies, CMRI Nagpur Centre devised a software "TUNNELBLAST" for generating blast design for Tunnels and underground workings. This software is a handy intelligent tool for the site engineers to optimise the blasting process and improve productivity without spending their valuable time on scrutinising variety of documents, books and literature available. The software is simple to operate and user friendly. The input and output parameters of the software are as under:

Input parameters:


Output parameters:


### **9.2 Field application of TUNNEL BLAST software at gneiss rock mass**

The TUNNEL BLAST software was applied to design the parallel cut blast pattern at Lohari-Nag Pala Hydroelectric Power Project (LNPHPP). The LNPHPP falls in the Uttrakhand Himalayas and is located on the River Bhagirathii upstream of Uttarkashi district. The main rock type of powerhouse complex is schistose gneiss and augen gneiss with abundance of mica and geotechnically the rock mass is negotiating in "Fair Category" and it's having three prominent joint sets. The Rock Mass Quality (Q) was varying from 1-10. The main two joint sets intersecting at right angle which makes wedge continuously. Some weak zone/clay filling, altered rock, sheared rock mass and excessive flow of water at places makes the rock poor. In maximum area it is found that the regional trend of foliation is perpendicular to the tunnel alignment, another joint which is intersecting the foliation at right angle and creates wedge on roof. The strike of the foliation is going through along the tunnel alignment which is geologically not favourable because of probabilities of plane failure and wedge failure in presence of heavy joint planes.

The input geological parameters required for the blast design software are as follows:


Boundary conditions:

496 Infrastructure Design, Signalling and Security in Railway

Based on the past experience and extensive field investigations over a variety of underground structures of varying lithologies, CMRI Nagpur Centre devised a software "TUNNELBLAST" for generating blast design for Tunnels and underground workings. This software is a handy intelligent tool for the site engineers to optimise the blasting process and improve productivity without spending their valuable time on scrutinising variety of documents, books and literature available. The software is simple to operate and user

5. Burden, spacing and charge of holes in cut area, floor periphery and in the middle of

The TUNNEL BLAST software was applied to design the parallel cut blast pattern at Lohari-Nag Pala Hydroelectric Power Project (LNPHPP). The LNPHPP falls in the Uttrakhand Himalayas and is located on the River Bhagirathii upstream of Uttarkashi district. The main rock type of powerhouse complex is schistose gneiss and augen gneiss with abundance of mica and geotechnically the rock mass is negotiating in "Fair Category" and it's having three prominent joint sets. The Rock Mass Quality (Q) was varying from 1-10. The main two joint sets intersecting at right angle which makes wedge continuously. Some weak zone/clay filling, altered rock, sheared rock mass and excessive flow of water at places makes the rock poor. In maximum area it is found that the regional trend of foliation is perpendicular to the tunnel alignment, another joint which is intersecting the foliation at right angle and creates wedge on roof. The strike of the foliation is going through along the tunnel alignment which is geologically not favourable because of probabilities of plane

The input geological parameters required for the blast design software are as follows:

friendly. The input and output parameters of the software are as under:

1. Rock properties (density, compressive strength and joint spacing),

4. Explosive properties (weight strength, weight and length of cartridge).

**9.2 Field application of TUNNEL BLAST software at gneiss rock mass** 

**9.1 TUNNEL BLAST2.0 software** 

2. Tunnel (shape, width and height),

2. Probable deviation of blast holes, 3. Optimum depth of round,

4. Look out angle of peripheral holes,

6. Front and sectional views of the blast pattern

failure and wedge failure in presence of heavy joint planes.

Weathering Highly Weathered/Fractured Filling Clay seam, width 10-20cm

Critical joint 0450/350, 2100/450

Water Condition Dry

Rock type Metabasic (Amphibolite) & quartz vein Joint sets Three + Random (0450/350, 2100/450, 1300/800)

the tunnel section,

3. drilling (diameter and length of blast hole), and

Input parameters:

Output parameters: 1. Size of the tunnel,


After feeding the input information the software process the entire data and gives the blast hole geometry and charge pattern for cut holes and other holes separately. The utput information given by TUNNELBLAST software is given in Figure 12, Figure 13 and Table 5 and Table 6.

The blast design generated by TUNNEL BLAST software was applied at intermediate adit and the blast results were satisfactory in terms of pull per round and overbreak control. The trial blast results with felid application of TUNNEL BLAST software are given in Table 7. The blast results indicate the efficacy of the TUNNEL BLAST software, as a preliminary tool for tunnel blast design for various geological conditions. The fine tuning of this design can be done for further improvements in the progress and yield of tunnel blasting.

Fig. 12. Blast design output from TUNNELBLAST for cut holes of intermediate adit

Special Tunnel Blasting Techniques for Railway Projects 499

Easer holes 8 6 0.6 0.75 0.95 5.7 Support holes 9 6 0.6 0.75 0.95 5.7 Support holes-II 10 6 0.6 0.75 0.95 5.7 Bottom Holes 11 10 0.4 0.70 1.8 18 Crown Holes-I 12 5 0.8 1.2 1.6 8 Crown Holes-II 13 5 0.8 1.2 1.6 8 Crown Holes-III 14 4 0.8 1.2 1.6 6.4

holes 15 3 0.6 0.3 0.6 1.8 Side Periphery holes 16 8 0.6 0.3 0.6 4.8

> No. Of holes

TRT 40 3.5 91 217 2.1 1.98

TRT 40 3.5 89 225 1.85 3.1

TRT 40 3.5 89 250 1.98 3..0

TRT 40 3.5 91 220 2.0 1.95

The reviews on the developments in rock mass damage and contour blasting brings an important information on field application of controlled blasting and damage assessment and control The contributions of CIMFR on special tunnel blasting techniques resulted in improvement of both productivity and safety. The following conclusions can be drawn

i. Application of this techniques resulted in saving the time of 75-80% and cost of 60%- 95% in comparison to the conventional shaft sinking method at three different projects ii. Lake Tap Blasting of a 4 m thick 40 m2 cross sectional area was carried out as of fist of its kind with indigenous technology in India by CMRI (now CIMFR) at granitic rock mass in Andhra Pradesh Power Generation Corporation (APGENCO), which could

iii. Ultra cautious blasting techniques were adopted as an extremely cautious approach, for removal of 10 reinforced concrete plugs, each of 125 m3 volume, without causing any

Charge per round, kg

holes Burden Spacing Charge per

hole (kg)

Specific charge, kg/m3

Total Charge/ delay (kg)

Pull/round, m

No. of

Table 6. Design and charging details of blast holes, other than cut holes

Depth of holes, m

Table 7. Trial blast results with felid application of TUNNEL BLAST software

Description of holes Delay

Crown Periphery

S No. Location

<sup>1</sup>Downside,

<sup>2</sup>Upsideside,

<sup>3</sup>Upsideside,

<sup>3</sup>Downside,

**10. Conclusions** 

No.

Hole diameter, mm

based on the various topics discussed in the paper:

save Crores of national exchequer.

Nos. in the boxes denote the delay numbers; Total Charge per round = 97.7 kg Total no. of holes= 3-Relief holes + 69-Charged holes+ 12-Dummy holes; Powder factor = 1.52 kg/m3

Fig. 13. Controlled blast design output from TUNNEL BLAST for rest of the holes at intermediate adit of LNPHPP


Table 5. Blast pattern and charge configuration of the cut holes

Nos. in the boxes denote the delay numbers; Total Charge per round = 97.7 kg

Burden, m

Table 5. Blast pattern and charge configuration of the cut holes

intermediate adit of LNPHPP

Name of square

Short Delay No. (25 ms delay)

Total no. of holes= 3-Relief holes + 69-Charged holes+ 12-Dummy holes; Powder factor = 1.52 kg/m3

Spacing, m

1 First 0.15 0.2 4 1.2 4.8

2/3 Second 0.20 0.4 4 2.4 9.6

4/5 Third 0.35 0.75 4 2.4 9.6

6/7 Fourth 0.45 1.2 4 2.4 9.6

No. of holes

Charge/hole, kg

Total charge, kg

Fig. 13. Controlled blast design output from TUNNEL BLAST for rest of the holes at


Table 6. Design and charging details of blast holes, other than cut holes


Table 7. Trial blast results with felid application of TUNNEL BLAST software

### **10. Conclusions**

The reviews on the developments in rock mass damage and contour blasting brings an important information on field application of controlled blasting and damage assessment and control The contributions of CIMFR on special tunnel blasting techniques resulted in improvement of both productivity and safety. The following conclusions can be drawn based on the various topics discussed in the paper:


Special Tunnel Blasting Techniques for Railway Projects 501

Itasca Consulting Group Inc. (2202). Partcile Flow Code in 2 Diemnsions – Theory &

Jensen, R. P. and Preece, D. S. (1999). Modelling explosive/rock interaction during pre-

Johansen, J. (1998). Modern trends in tunnelling and blast design, IDL Industries Ltd.,

Langefors, U. and Kihlstrom, B. (1973). *The Modern Technique of Rock Blasting*, John Willey &

Leu S. S., Lin S. -F., Chen C. –K. And Wang S. -W. (1998). Analysis of powder factors for

Livingston, C. W. (1956). Fundamentals of rock failure, *Quarterly of the Colorado School of* 

Lopez Jimeno, C., Lopez Jimeno, E., Carcedo, F. J. A. and De Ramiro, Y. V. (1995). *Drilling and Blasting of Rocks*, Balkema A. A., Rotterdam, pp. 200-204 and 259-260. McKenzie, C. J. (1994). *Blasting for Engineers*, Blastronics Pty. Ltd., Brisbane, Australia. Olofsson, S., O. (1988). Applied Explosives Technology for Construction and Mining,

Ouchterlony, F., Nyberg , Sjoberg, C., Johansson, S-E. (1991). Damage zone assessment by

Pokrovsky, N. M. (1980). *Driving Horizontal Workings and Tunnels*, Mir Publishers, Moscow,

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Pusch, R., Hokmark, H. and Borgesson, L. (1993). Characterisation of structure and stress

Ramulu, M., (2009), Rock mass damage due to repeated blast vibrations in underground excavations, IISc Dept.of CE PhD Thesis- G23635, 624.15132 P09, IISc Press. Ramulu, M., Chakraborty A. K. and Sitharam T.G., (2009), Damage assessment of basaltic

Tunnelling and Underground Space Technology, Vol.24, pp. 208–221. Ramulu, M., Sitharam, T.G., (2011), Blast induced rock mass damage In underground

vibration measurements, *Aspo hard rock laboratory*, Progress Report, , No. 3, pp. 25-

*International Journal Rock Mech. Mining Sci. & Geomech. Abstr*., Vol. 29, No. 5, pp.

state of nearfield rock with respect to the influence of blasting, *Proc. 4th International Symp. on Rock Fragmentation by Blasting, FRAGBLAST-4,* Vienna, Austria, pp.175-

rock mass due to repeated blasting in a railway tunnelling project – a case study,

excavations -Applications to civil engineering projects, LAMBERT Academic Publishing GmbH& Co. KG, 66123 Saarbrücken, Germany, ISBN (978-3-8433-9318-

fragmentation, Balkema A. A. , Netherlands, Vol. 2., No. 4, pp. 433-448. Liu, L. and Katsabanis, P. D. (1996). Numerical modelling of the effects of air-decking/

splitting using ALE computational method, *Proc. 6th. International Symposium for Rock Fragmentation by Blasting*, The South African Inst. of Mining and Metall.,

tunnel blasting using neural networks, The Int. Journal for Blasting and

decoupling in production and controlled blasting, *Proc. 5th International Symposium on Rock Fragmentation by Blasting, FRAGBLAST-5*, Montreal, Quebec, 25-29.,pp. 319-

Background, Mnneapolis, USA. p. 1.1-1.28.

Johannesburg, Aug. 8-12, pp. 199-202.

Hyderabad, India, pp. 34-41.

Sons, pp. 188-257, 299-301.

*Mines*, Vol. 51, No. 3, Jul..

Applex, Arla, Sweden, 303 pp.

330.

91.

pp. 38-41.

447-456.

181.

8)

damage to the surrounding periphery and pier nose in Srisailam left bank project of the APPGENCO while the power house was in running condition.


### **11. References**


iv. Successful application of in-hole delay cut blasting method at basaltic rock mass and gneiss rock mass improved average face pull improve by nearly 30-50%. Blast vibration intensity reduces by 20 to 25% which resulted in reduction of the overbreak

v. Bottom hole decking technique resulted in the overall progress/pull per round of 36% with 1.5 deep rounds and 22% with 1.8 m deep rounds even with the powder factor

vi. Application of sand stemming device for horizontal blast holes in place of conventional stemming resulted in pull improvement of 5-10% in dolomite tunnels and 8-12% in

Bieniawski, Z. T., (1993). Classification of rock masses for engineering: the RMR system and

Calder, P. N. and Bauer, A. (1983). Presplit blast design for open pit and underground mines, *5th International Cong. on Rock Mechanics*, Melbourne, Vol. 2, pp. E185- E190. Chakraborty, A. K. (2002). Development of predictive models for optimum blast design in

Chakraborty, A. K., Jethwa, J. L. and Dhar, B. B. (1996b). Predicting powder factor in mixed-

Chakraborty, A. K., Murthy, VMSR and Jethwa, J.L. (1996a). Blasting problems in

Chakraborty, A. K., Murthy, VMSR, Jhanwar, J. C., Raina, A. K., Ramulu, M. and Jethwa J. L.

du Pont, E.I., (1977). Blasters hand book, 175th Anniversary edition, E.I. du Pont de

Duvall, W. I. and Atchion, T. C. (1957). Rock breakage by explosives, USBM, RI 5356,

Gupta, R. N., Singh, R. B., Adhikari, G. R. and Singh, B. (1988). Controlled Blasting for

Holmberg, R., and Persson, P. A. (1978). The Swedish approach to contour blasting, Proc. of

Elsevier Science Ltd., Great Britain, Vol. 11, No. 3, pp. 311-324.

Nemours, Inc., Wilmington, Delaware. Pp.526-541.

practice, and projects, Oxford: Pergamon Press. V.4, pp. 553-573

*Indian School of Mines*, Dhanbad, India, 298 p.

*Resources*, Govt. of India, 136 pp.

*Engineers*, Ohio, USA, 1997.

17 Apr., New Delhi, India, pp. 449-460.

future trends. In J.A. Hudson (Ed.), Comprehensive rock engineering: principles,

mine roadways and tunnels under various rock mass conditions, *Ph.D. Thesis,* 

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APPGENCO while the power house was in running condition.

proportionately.

gneiss tunnel.

47, pp. 31-41.

**11. References** 

improvement (ton/kg) upto 70%.

damage to the surrounding periphery and pier nose in Srisailam left bank project of the


**20** 

*2Assystem,* 

*1,2France 3Brazil* 

**Susceptibility of the GSM-R Transmissions to** 

The Electromagnetic radiations are non-ionising radiations; they cannot involve the ionisation of atoms or molecules. Nevertheless, they can cause various adverse effects. From a biological point of view, they provoke heating due to the occurring of induced current in the body. But, this issue will not be considered in this chapter. From a technological point of view, they can cause malfunctions, permanent damages for electronic devices or telecommunication systems. In this chapter we will focus on their impact on a telecommunication system dedicated to the European railway and potential consequences

Today, the European railway network is undergoing significant changes, which aim at deploying a unique management system in Europe which will replace local systems. This unique management system called ERTMS (European Railway Traffic Management System), involves the deployment of a telecommunication network dedicated to railway management, the GSM-Railway network, in order to harmonize in Europe the system of communication between the trains and the infrastructures. This harmonization is intended to clear the technological boundaries between railway networks of European countries and thus to remove border for trains. GSM-R is a key element in the management system as it provides the vocal exchanges, but also the transmission of signalling data. However, as all the telecommunication systems, the GSM-R can be vulnerable to the Electromagnetic (EM) interferences and the railway environment is particularly rich in EM interferences. This

After a general background about the electromagnetic interferences and the management of the European railway network, we present the standards and approaches applied in the railway domain to control the Electromagnetic compatibility (EMC). The GSM-R and the EM disturbances which can affect it are then detailed. Finally, a methodology for testing the vulnerability of the GSM-R transmissions and the test results are presented and

**1. Introduction** 

on the management of the railway network.

chapter will then focus on this issue.

analysed.

**the Railway Electromagnetic Environment** 

Stephen Dudoyer1, Virginie Deniau1,

*1Univ Lille Nord de France, IFSTTAR,* 

*3Federal University of Minas Gerais,* 

Nedim Ben Slimen2 and Ricardo Adriano3


## **Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment**

Stephen Dudoyer1, Virginie Deniau1,

Nedim Ben Slimen2 and Ricardo Adriano3 *1Univ Lille Nord de France, IFSTTAR, 2Assystem, 3Federal University of Minas Gerais, 1,2France 3Brazil* 

### **1. Introduction**

502 Infrastructure Design, Signalling and Security in Railway

Rusilo, L. C., Sansone, E. C., Hennies, W. T. and Ayres Da Silva, L. A.(1994). Design and

*Planning and Equipment Selection*, Istanbul, Turkey, 18-20 Oct., pp. 651-655. Singh, S. P. (1995). Mechanism of cut blasting, Trans. Inst. Mining and Metall., Section A,

Wilson, W. H. (1987). An experimental and theoretical analysis of stress wave and gas pressure effects in bench blasting, *Ph.D. Thesis*, University of Maryland. Yu, T. R. and Vongpaisal. S. (1996). New blast damage criteria for underground blasting,

*CIM Bulletin*, No. 998, Vol. 89, pp. 139-145.

A138

optimization of tunnel blasting operations, *Proc. 3rd International Symposium on Mine* 

Mining Industry, Vol. 104, Sept-Dec.,*The Inst. of Mining and Metall*., U.K., pp. A134-

The Electromagnetic radiations are non-ionising radiations; they cannot involve the ionisation of atoms or molecules. Nevertheless, they can cause various adverse effects. From a biological point of view, they provoke heating due to the occurring of induced current in the body. But, this issue will not be considered in this chapter. From a technological point of view, they can cause malfunctions, permanent damages for electronic devices or telecommunication systems. In this chapter we will focus on their impact on a telecommunication system dedicated to the European railway and potential consequences on the management of the railway network.

Today, the European railway network is undergoing significant changes, which aim at deploying a unique management system in Europe which will replace local systems. This unique management system called ERTMS (European Railway Traffic Management System), involves the deployment of a telecommunication network dedicated to railway management, the GSM-Railway network, in order to harmonize in Europe the system of communication between the trains and the infrastructures. This harmonization is intended to clear the technological boundaries between railway networks of European countries and thus to remove border for trains. GSM-R is a key element in the management system as it provides the vocal exchanges, but also the transmission of signalling data. However, as all the telecommunication systems, the GSM-R can be vulnerable to the Electromagnetic (EM) interferences and the railway environment is particularly rich in EM interferences. This chapter will then focus on this issue.

After a general background about the electromagnetic interferences and the management of the European railway network, we present the standards and approaches applied in the railway domain to control the Electromagnetic compatibility (EMC). The GSM-R and the EM disturbances which can affect it are then detailed. Finally, a methodology for testing the vulnerability of the GSM-R transmissions and the test results are presented and analysed.

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 505

Conductive coupling can be viewed as a common impedance coupling. Conductive coupling occurs when the source and the receptor circuits are physically connected with a conductor and share a common-impedance path. Magnetic coupling occurs when two objects exchange energy through their varying or oscillating magnetic fields. It can be represented by a mutual inductance between the source and the receptor. Electric field coupling (or capacitive coupling) is caused by a voltage difference between conductors. It dominates in high-impedance circuits and can be represented by mutual capacitance. Finally, Electromagnetic coupling is a combination of both electric and magnetic fields. It is the most common coupling mechanism observed. It occurs when source and receptor are separated by a large distance, (typically more than a wavelength). In this case, source and receptor act as radio antennas. The electromagnetic field radiated by the source propagates across coupling path and is picked up by the receptor.

Any device which drives an electric current is likely to radiate an electromagnetic field. This electromagnetic field may act in two ways on electronic and telecommunication equipment. It can either be picked up by cables of other systems (or lines of electronic circuits) on which unwanted electrical signals appear and can cause malfunctions or it can also interfere with the telecommunication signals when they reach the receivers causing losses of information. In the first situation, the interference occurs because the dimensions of the conductors in the electronic equipment are comparable with the wavelength of the electromagnetic

There are numerous sources of unintentional electromagnetic radiation such as lighting, relays, electric motors and digital systems. The number of emitters is increasing rapidly. Some of these emitters employ very high power levels; others such as digital systems are using faster digital electronics and are becoming more efficient radiators of unintentional electromagnetic energy. Consequently, EMC has become a particularly important topic. In order to ensure that EMC will be not a problem, many EMC standards are used. These are often supported by EMC legislation to ensure that existing equipment conforms to the required standards. EMC standards specify a limited number of essential emission and immunity tests, as well as minimum test levels. The aim is to ensure adequate compatibility. Section 4 summarizes the major standards concerning the electromagnetic emissions in

The management of a railway network is generally performed thanks to several key components, notably a ground-train radio which allows the vocal exchanges, a lateral signalling system including lights and traffic signs and a localization system of the trains which can also control the speed of the trains. However, these different components are not necessary ensured by similar technologies in all the European countries. This situation inhibits the carrying out of a real European railway network which would allow the different railway operators to offer their services anywhere in Europe. Today, trains crossing borders are necessarily equipped with various national systems and at the borders the trains have to change their system to be in accordance with the cross border country. This increases the costs of equipment and maintenance of the trains, the operating costs and extends the travel time.

disturbance. In this case conducting elements can act as receiving antennas.

railway environment while section 5 addresses the immunity problems.

**3. Management and signalling of european railway network** 

**2.3 Electromagnetic radiation, emission and immunity** 

### **2. General notions**

Understanding the electromagnetic emission from the railway environment is important to prevent and control electromagnetic interference. Currently, trains are more and more often equipped with potentially sensitive systems from an electromagnetic compatibility point of view. Consequently, railway systems have to be sufficiently robust to guarantee the safety of the railway transportation. In this section the fundamental concepts related to EMC are briefly introduced. For this purpose, the following definitions given in (IEC 60050, 1990), International Electrotechnical Vocabulary (IEV), chapter 161, apply:

**Electromagnetic environment:** The totality of electromagnetic phenomena existing at a given location.

**Immunity (to a disturbance):** The ability of a device, equipment or system to perform without degradation in the presence of electromagnetic disturbance.

**(Electromagnetic) Susceptibility:** The inability of a device, equipment or system to perform without degradation in the presence of an electromagnetic disturbance.

**Immunity level:** The maximum level of a given electromagnetic disturbance incident on a particular device, equipment or system for which it remains capable of operating at a required degree of performance.

### **2.1 Electromagnetic disturbances and electromagnetic compatibility**

A system is electromagnetically compatible with its environment if it is able to operate satisfactorily in its electromagnetic environment without introducing intolerable electromagnetic disturbances to anything in that environment. Typically, an EMC problem can be decomposed into three main parts. A source that intentionally or unintentionally produce the emission, a coupling path that transfers the emission energy to a receptor and the receptor that can be susceptible if the received energy exceeds its immunity level.

During their operation, electrical or electronic systems generally produce radiated or conducted signals, which can lead to equipment malfunctions neighbours. The "electromagnetic disturbance" term then assigns these signals that can be voltages, currents or electromagnetic fields. In general, the higher the frequency of the electromagnetic disturbance is, the more efficient the coupling path. It is important to keep in mind that the source and receiver can be classified as intend or unintended. For instance, the GSM-R system intentionally transmits and receives electromagnetic fields in some frequencies between 876 MHz and 925 MHz. Consequently, the equipment near the GSM-R antennas must be designed to operate properly under the influence of the GSM-R signals. On the other hand, the GSM-R antenna will collect all the signals generated by the railway environment at these frequencies. Depending on the coverage of the GSM-R system and the levels of the electromagnetic disturbances, the communication between rolling stocks can be affected or even interrupted.

### **2.2 Electromagnetic coupling**

Electromagnetic disturbances produced by the emitter can be coupled to the receptor by either radiated or conductive paths. The coupling mechanism can be classified into Conductive coupling, Magnetic coupling, Electric field coupling and Electromagnetic field coupling.

Conductive coupling can be viewed as a common impedance coupling. Conductive coupling occurs when the source and the receptor circuits are physically connected with a conductor and share a common-impedance path. Magnetic coupling occurs when two objects exchange energy through their varying or oscillating magnetic fields. It can be represented by a mutual inductance between the source and the receptor. Electric field coupling (or capacitive coupling) is caused by a voltage difference between conductors. It dominates in high-impedance circuits and can be represented by mutual capacitance. Finally, Electromagnetic coupling is a combination of both electric and magnetic fields. It is the most common coupling mechanism observed. It occurs when source and receptor are separated by a large distance, (typically more than a wavelength). In this case, source and receptor act as radio antennas. The electromagnetic field radiated by the source propagates across coupling path and is picked up by the receptor.

### **2.3 Electromagnetic radiation, emission and immunity**

504 Infrastructure Design, Signalling and Security in Railway

Understanding the electromagnetic emission from the railway environment is important to prevent and control electromagnetic interference. Currently, trains are more and more often equipped with potentially sensitive systems from an electromagnetic compatibility point of view. Consequently, railway systems have to be sufficiently robust to guarantee the safety of the railway transportation. In this section the fundamental concepts related to EMC are briefly introduced. For this purpose, the following definitions given in (IEC 60050, 1990),

**Electromagnetic environment:** The totality of electromagnetic phenomena existing at a

**Immunity (to a disturbance):** The ability of a device, equipment or system to perform

**(Electromagnetic) Susceptibility:** The inability of a device, equipment or system to perform

**Immunity level:** The maximum level of a given electromagnetic disturbance incident on a particular device, equipment or system for which it remains capable of operating at a

A system is electromagnetically compatible with its environment if it is able to operate satisfactorily in its electromagnetic environment without introducing intolerable electromagnetic disturbances to anything in that environment. Typically, an EMC problem can be decomposed into three main parts. A source that intentionally or unintentionally produce the emission, a coupling path that transfers the emission energy to a receptor and

During their operation, electrical or electronic systems generally produce radiated or conducted signals, which can lead to equipment malfunctions neighbours. The "electromagnetic disturbance" term then assigns these signals that can be voltages, currents or electromagnetic fields. In general, the higher the frequency of the electromagnetic disturbance is, the more efficient the coupling path. It is important to keep in mind that the source and receiver can be classified as intend or unintended. For instance, the GSM-R system intentionally transmits and receives electromagnetic fields in some frequencies between 876 MHz and 925 MHz. Consequently, the equipment near the GSM-R antennas must be designed to operate properly under the influence of the GSM-R signals. On the other hand, the GSM-R antenna will collect all the signals generated by the railway environment at these frequencies. Depending on the coverage of the GSM-R system and the levels of the electromagnetic disturbances, the communication between rolling stocks can be affected or even interrupted.

Electromagnetic disturbances produced by the emitter can be coupled to the receptor by either radiated or conductive paths. The coupling mechanism can be classified into Conductive coupling, Magnetic coupling, Electric field coupling and Electromagnetic field coupling.

the receptor that can be susceptible if the received energy exceeds its immunity level.

International Electrotechnical Vocabulary (IEV), chapter 161, apply:

without degradation in the presence of electromagnetic disturbance.

without degradation in the presence of an electromagnetic disturbance.

**2.1 Electromagnetic disturbances and electromagnetic compatibility** 

**2. General notions** 

given location.

required degree of performance.

**2.2 Electromagnetic coupling** 

Any device which drives an electric current is likely to radiate an electromagnetic field. This electromagnetic field may act in two ways on electronic and telecommunication equipment. It can either be picked up by cables of other systems (or lines of electronic circuits) on which unwanted electrical signals appear and can cause malfunctions or it can also interfere with the telecommunication signals when they reach the receivers causing losses of information. In the first situation, the interference occurs because the dimensions of the conductors in the electronic equipment are comparable with the wavelength of the electromagnetic disturbance. In this case conducting elements can act as receiving antennas.

There are numerous sources of unintentional electromagnetic radiation such as lighting, relays, electric motors and digital systems. The number of emitters is increasing rapidly. Some of these emitters employ very high power levels; others such as digital systems are using faster digital electronics and are becoming more efficient radiators of unintentional electromagnetic energy. Consequently, EMC has become a particularly important topic. In order to ensure that EMC will be not a problem, many EMC standards are used. These are often supported by EMC legislation to ensure that existing equipment conforms to the required standards. EMC standards specify a limited number of essential emission and immunity tests, as well as minimum test levels. The aim is to ensure adequate compatibility. Section 4 summarizes the major standards concerning the electromagnetic emissions in railway environment while section 5 addresses the immunity problems.

### **3. Management and signalling of european railway network**

The management of a railway network is generally performed thanks to several key components, notably a ground-train radio which allows the vocal exchanges, a lateral signalling system including lights and traffic signs and a localization system of the trains which can also control the speed of the trains. However, these different components are not necessary ensured by similar technologies in all the European countries. This situation inhibits the carrying out of a real European railway network which would allow the different railway operators to offer their services anywhere in Europe. Today, trains crossing borders are necessarily equipped with various national systems and at the borders the trains have to change their system to be in accordance with the cross border country. This increases the costs of equipment and maintenance of the trains, the operating costs and extends the travel time.

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 507

(CENELEC), describing EMC for railway applications, or railway industry standards such as Railtrack Group Standard GM/RC 1031 (GMRC1500, 1994), which provide guidance on

A complete list of standards related to railway applications is presented and discussed in (Konefal et al., 2002), some of these standards are presented in the table 1 for convenience.

CISPR/C/116/CDV Interference from overhead power lines, high voltage

GM/RC 1500 Code of Practice for EMC between the Railway and its Neighbourhood

Emission Test Vehicle

measurement

Emissions of

The standards applied in Europe in order to characterize the EM environment in the railway context are the EN 50121 while in USA, the electromagnetic emission limits are imposed by the Urban Mass Transportation Administration of the U.S. Department of Transport (UMTA standards). The EN 50121 standards notably aim to control the emission levels from the railway infrastructures to the outside world while UMTA standards aim to avoid interferences with the wayside equipment (transit signalling systems). In both cases, no method is proposed to characterize the EM environment on board trains, i.e. above, inside, and under the trains, especially where new and future sensitive systems can be located.

The standards EN 50121 indicate the methodologies and the limits to apply, relating to the EM emissions and immunity of railway equipment, vehicles and infrastructures. The emissions of the whole railway system, including vehicles and infrastructure are dealt with the section 2 of the EN 50121. The objective of the tests specified in this standard is to verify that the EM emissions produced by the railway systems do not disturb the neighbouring equipment and systems. The methodology then consists in measuring the radiated EM emissions at a distance of 10 m from the middle of the tracks and at about 1.5 m from the ground and to compare them with the maximum allowed levels. The limits are specified for the frequencies included between 9 kHz and 1 GHz. The measurement protocol is specified for four frequency bands

which are 9 kHz-150 kHz, 150 kHz - 30 MHz, 30 MHz - 300 MHz and 300 MHz-1 GHz.

Table 1. List of EMC standards applied to railway domain

EN 50121 parts 1-5 Railway Applications Electromagnetic Compatibility

equipment and electric traction systems.

ISM radio-frequency equipment – Radio disturbance characteristics – (CISPR 11) Limits and methods of

Conductive Interference in Rapid Transit Signalling Systems, Suggested Test Procedures for Conducted

Inductive Interference in Rapid Transit Signalling Systems Suggested Test Procedures for Inductive Emissions of Vehicular Electrical Power Subsystem,

Radiated Interference in Rapid Transit Signalling Systems Suggested Test Procedures for Broadband

Rail-to-Rail Voltage from 20 Hz to 20 kHz

Rapid Transit Vehicles -140 kHz to 400 MHz

EMC between railway infrastructure and trains.

EN 55011 (CISPR 11)

UMTA-MA-06-0153-85-6

UMTA-MA-06-0153-85-8

UMTA-MA-06-0153-85-11

The ERTMS (European Railway Traffic Management System) standard was then thought out in order to remove these obstacles and to optimize the use of the European railway network and to improve the reactivity, adaptability and affordability of the European railway. ERTMS would allow the interoperability of trains on the European territory (Jarašūnienė, 2005). This standard is generally presented as composed of two main components, which are the European Train Control System called ETCS, a standard for in-cab train control, and the GSM-R (Global System for Mobile communications-Railway) system, an international wireless communications standard dedicated to railway applications.

ETCS can allow automatically controlling the speed of the train if necessary. ETCS is composed of trackside and on-board modules. The trackside module transmits information to the train which enables the on-board computer, called Eurocab, to calculate the maximum permitted speed.

Nevertheless, the implementation of ETCS requires major adjustments on the European network, such as the installing of standard beacons called "Eurobalise" and GSM-R deployment. Indeed, the most complete version of ETCS relies heavily on the use of GSM-R. Three levels of deployment are then scheduled in order to progressively equip the railway network.

In the first level "ETCS level 1", the trackside equipment transmits information to the train in order that it calculates its maximum authorized speed. The information given by the trackside signalling (lights and traffic signs allowing the driver to know the permitted speed), can be forwarded to the train by the Eurobalise beacons located along the track.

The second level "ETCS level 2" includes a partial deployment of the GSM-R and information can then be forwarded to the train by the GSM-R. The position of trains is still detected by trackside systems but the trackside signalling is no longer necessary since all information is transmitted directly to the train.

Finally, the third level aims to optimise railway lines capacity and further reduce the trackside equipment. ETCS Level 3 is a major revision of the classic management system which is based on fixed intervals between the trains. In ETCS level 3, the route is thus no longer managed in fixed track sections but the intervals depend on the braking distances. The trains find their position themselves by means of positioning beacons or sensors and transmit the positioning signal to the radio block centre.

Then, this highlight the GSM-R is an essential and safety component in the management of the railway European network and it is necessary to warrant its immunity facing the railway electromagnetic environment (Midya, 2008).

### **4. Control of the radiated EM emissions in railway**

The railway environment is a severe electromagnetic environment where railway equipment performs safety critical functions. Additionally, the railway runs very close to commercial and residential areas. For these reasons, it is important to provide guidance on EMC issues by applying specific EMC standards to railway applications. These standards fall generally into two categories: governmental standards, such as the EN50121:2006 part 1- 5 (EN50121, 2006) published by European Committee for Electrotechnical Standardization

The ERTMS (European Railway Traffic Management System) standard was then thought out in order to remove these obstacles and to optimize the use of the European railway network and to improve the reactivity, adaptability and affordability of the European railway. ERTMS would allow the interoperability of trains on the European territory (Jarašūnienė, 2005). This standard is generally presented as composed of two main components, which are the European Train Control System called ETCS, a standard for in-cab train control, and the GSM-R (Global System for Mobile communications-Railway) system, an international wireless

ETCS can allow automatically controlling the speed of the train if necessary. ETCS is composed of trackside and on-board modules. The trackside module transmits information to the train which enables the on-board computer, called Eurocab, to calculate the maximum

Nevertheless, the implementation of ETCS requires major adjustments on the European network, such as the installing of standard beacons called "Eurobalise" and GSM-R deployment. Indeed, the most complete version of ETCS relies heavily on the use of GSM-R. Three levels of deployment are then scheduled in order to progressively equip the railway

In the first level "ETCS level 1", the trackside equipment transmits information to the train in order that it calculates its maximum authorized speed. The information given by the trackside signalling (lights and traffic signs allowing the driver to know the permitted speed), can be forwarded to the train by the Eurobalise beacons located along the track.

The second level "ETCS level 2" includes a partial deployment of the GSM-R and information can then be forwarded to the train by the GSM-R. The position of trains is still detected by trackside systems but the trackside signalling is no longer necessary since all

Finally, the third level aims to optimise railway lines capacity and further reduce the trackside equipment. ETCS Level 3 is a major revision of the classic management system which is based on fixed intervals between the trains. In ETCS level 3, the route is thus no longer managed in fixed track sections but the intervals depend on the braking distances. The trains find their position themselves by means of positioning beacons or sensors and

Then, this highlight the GSM-R is an essential and safety component in the management of the railway European network and it is necessary to warrant its immunity facing the railway

The railway environment is a severe electromagnetic environment where railway equipment performs safety critical functions. Additionally, the railway runs very close to commercial and residential areas. For these reasons, it is important to provide guidance on EMC issues by applying specific EMC standards to railway applications. These standards fall generally into two categories: governmental standards, such as the EN50121:2006 part 1- 5 (EN50121, 2006) published by European Committee for Electrotechnical Standardization

communications standard dedicated to railway applications.

information is transmitted directly to the train.

electromagnetic environment (Midya, 2008).

transmit the positioning signal to the radio block centre.

**4. Control of the radiated EM emissions in railway** 

permitted speed.

network.

(CENELEC), describing EMC for railway applications, or railway industry standards such as Railtrack Group Standard GM/RC 1031 (GMRC1500, 1994), which provide guidance on EMC between railway infrastructure and trains.

A complete list of standards related to railway applications is presented and discussed in (Konefal et al., 2002), some of these standards are presented in the table 1 for convenience.


Table 1. List of EMC standards applied to railway domain

The standards applied in Europe in order to characterize the EM environment in the railway context are the EN 50121 while in USA, the electromagnetic emission limits are imposed by the Urban Mass Transportation Administration of the U.S. Department of Transport (UMTA standards). The EN 50121 standards notably aim to control the emission levels from the railway infrastructures to the outside world while UMTA standards aim to avoid interferences with the wayside equipment (transit signalling systems). In both cases, no method is proposed to characterize the EM environment on board trains, i.e. above, inside, and under the trains, especially where new and future sensitive systems can be located.

The standards EN 50121 indicate the methodologies and the limits to apply, relating to the EM emissions and immunity of railway equipment, vehicles and infrastructures. The emissions of the whole railway system, including vehicles and infrastructure are dealt with the section 2 of the EN 50121. The objective of the tests specified in this standard is to verify that the EM emissions produced by the railway systems do not disturb the neighbouring equipment and systems. The methodology then consists in measuring the radiated EM emissions at a distance of 10 m from the middle of the tracks and at about 1.5 m from the ground and to compare them with the maximum allowed levels. The limits are specified for the frequencies included between 9 kHz and 1 GHz. The measurement protocol is specified for four frequency bands which are 9 kHz-150 kHz, 150 kHz - 30 MHz, 30 MHz - 300 MHz and 300 MHz-1 GHz.

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 509

the trains, they cannot be tested in nominal operating condition inside an anechoic chamber. In this context, component and sub-system testing becomes very important to prevent EMC

Although the immunity levels presented in EN 50121 provide an overall view of the railway electromagnetic environment, they are not suitable to perform immunity tests on the on board components, especially in the case of modern communication systems such as GSM-R. Additionally, high speed trains as other rolling stock apparatus are supplied by a catenary. In this particular context the train can be considered as a fixed equipment supplied by an electrical network. Consequently, EMC standard EN 61000-4-4 should apply. This standard aims at defining a common and reproducible basis for the evaluation of the performances of electrical and electronic equipment facing electrical fast transients on its different inputs. It is clearly adapted to test the immunity of the electronics and we would have referred to it if our objective had been to test the electronics of a GSM-R

However, as it will be shown in section 7, the test signals defined in this standard EN 61000- 4-4 differ significantly from the typical transient disturbances received by GSM-R antennas. Additionally, as presented in (Knobloch, 2002), modern communication systems use digitally coded radio signals that operate with a much smaller signal-to-noise ratio (SNR) in comparison to analogical ones. The explanation lies in the fact that digital data streams are discontinuous and include redundancy to correct errors. (Knobloch, 2002) also points out that peak detector or QP detectors are not suitable to convert electromagnetic disturbance in some measure of deterioration in communication. Consequently, it is important to envisage component immunity testing solution which permits us to evaluate the telecommunication system against electromagnetic conditions representative of the railway electromagnetic

The GSM-R (Global System for Mobile communication-Railways) is a wireless digital communication system, based on the public European GSM Phase 2+. This system is used to ensure the vocal exchanges and to transmit railway signalling information between trains and railway control centres. The GMS-R is currently deployed in numerous European countries in order to ensure the interoperability of trains throughout the whole European


The base stations are generally spaced from about 3 or 4 km and the GSM-R signal level has to be superior to -92 dBm, 95 % of the time and the space (UIC, 2003). In practise, the power of the received signal on board train varies between -20 dBm at proximity of the base station and -90 dBm at middle distance between two successive base stations

shielded cables to GSM-R mobile on board the train, as shown in Fig. 2.

problems.

mobile.

environment.

(Hammi, 2009).

**6. The GSM-R communication system** 

railroad network. The GSM-R system includes two parts:

Fig. 1. Emission limits according EN 50121-2. A=25 kV ac; B = 15 kV ac, 3 kV dc or 1.5 kV dc; C = 750 V dc and bw1 = 200 Hz; bw2 = 9 kHz; bw3 = 120 kHz

The basis for the level derived in EN50121 has been the actual levels measured at a number of railways sites around Europe. While the scope of this standard covers the frequency range DC to 400 GHz, in practice limits are not set above 1 GHz. In general words, this standard does not consider the wider impact on the radio spectrum, it mostly sets the actual stage of the current levels around the railway structure.

Additionally, when comparing the EN 50121 standards to common EMC measurement standards, it is noted that there are several crucial differences in the methods of measurement. In many EMC tests, emission limits are specified in terms of a measurement with a quasi-peak detector (QP). However, the use of a quasi-peak detector in EN 50121 standards is not possible due to the highly dynamic environment. For EN 50121, a peak detector is prescribed.

### **5. EM immunity of the railway equipment and systems**

The railway immunity levels for radiated interference are comparable with those specified by the industrial generic standard; 10V/m for trackside equipment. For rail borne equipment mounted externally to the rolling stock or within the driver's cab or passenger compartment 20V/m is specified. This level is comparable to the 24V/m specified by the Automotive Directive 95/54/EC. However, tests are different from automotive industry where full vehicle tests are performed in anechoic chamber to guarantee that all the systems can work together in the presence of electromagnetic disturbances. In the railway environment full vehicle tests are often not feasible. Due to the dimension and the speed of

Fig. 1. Emission limits according EN 50121-2. A=25 kV ac; B = 15 kV ac, 3 kV dc or 1.5 kV dc;

The basis for the level derived in EN50121 has been the actual levels measured at a number of railways sites around Europe. While the scope of this standard covers the frequency range DC to 400 GHz, in practice limits are not set above 1 GHz. In general words, this standard does not consider the wider impact on the radio spectrum, it mostly sets the actual

Additionally, when comparing the EN 50121 standards to common EMC measurement standards, it is noted that there are several crucial differences in the methods of measurement. In many EMC tests, emission limits are specified in terms of a measurement with a quasi-peak detector (QP). However, the use of a quasi-peak detector in EN 50121 standards is not possible due to the highly dynamic environment. For EN 50121, a peak

The railway immunity levels for radiated interference are comparable with those specified by the industrial generic standard; 10V/m for trackside equipment. For rail borne equipment mounted externally to the rolling stock or within the driver's cab or passenger compartment 20V/m is specified. This level is comparable to the 24V/m specified by the Automotive Directive 95/54/EC. However, tests are different from automotive industry where full vehicle tests are performed in anechoic chamber to guarantee that all the systems can work together in the presence of electromagnetic disturbances. In the railway environment full vehicle tests are often not feasible. Due to the dimension and the speed of

C = 750 V dc and bw1 = 200 Hz; bw2 = 9 kHz; bw3 = 120 kHz

stage of the current levels around the railway structure.

**5. EM immunity of the railway equipment and systems** 

detector is prescribed.

the trains, they cannot be tested in nominal operating condition inside an anechoic chamber. In this context, component and sub-system testing becomes very important to prevent EMC problems.

Although the immunity levels presented in EN 50121 provide an overall view of the railway electromagnetic environment, they are not suitable to perform immunity tests on the on board components, especially in the case of modern communication systems such as GSM-R. Additionally, high speed trains as other rolling stock apparatus are supplied by a catenary. In this particular context the train can be considered as a fixed equipment supplied by an electrical network. Consequently, EMC standard EN 61000-4-4 should apply. This standard aims at defining a common and reproducible basis for the evaluation of the performances of electrical and electronic equipment facing electrical fast transients on its different inputs. It is clearly adapted to test the immunity of the electronics and we would have referred to it if our objective had been to test the electronics of a GSM-R mobile.

However, as it will be shown in section 7, the test signals defined in this standard EN 61000- 4-4 differ significantly from the typical transient disturbances received by GSM-R antennas. Additionally, as presented in (Knobloch, 2002), modern communication systems use digitally coded radio signals that operate with a much smaller signal-to-noise ratio (SNR) in comparison to analogical ones. The explanation lies in the fact that digital data streams are discontinuous and include redundancy to correct errors. (Knobloch, 2002) also points out that peak detector or QP detectors are not suitable to convert electromagnetic disturbance in some measure of deterioration in communication. Consequently, it is important to envisage component immunity testing solution which permits us to evaluate the telecommunication system against electromagnetic conditions representative of the railway electromagnetic environment.

### **6. The GSM-R communication system**

The GSM-R (Global System for Mobile communication-Railways) is a wireless digital communication system, based on the public European GSM Phase 2+. This system is used to ensure the vocal exchanges and to transmit railway signalling information between trains and railway control centres. The GMS-R is currently deployed in numerous European countries in order to ensure the interoperability of trains throughout the whole European railroad network. The GSM-R system includes two parts:


The base stations are generally spaced from about 3 or 4 km and the GSM-R signal level has to be superior to -92 dBm, 95 % of the time and the space (UIC, 2003). In practise, the power of the received signal on board train varies between -20 dBm at proximity of the base station and -90 dBm at middle distance between two successive base stations (Hammi, 2009).

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 511

On board a moving train and in normal operating conditions, the GSM-R system can meet different transient or permanent EMIs, with various amplitudes, time durations, repetition rates, frequency bands… Moreover, the GSM-R antennas are generally multi-band antennas and are not really selective around the frequency bands dedicated to the railway. They can

(Mansson, 2008) showed that out-band EMIs observed in railway environment could be a serious threat to the low noise amplifier (LNA) installed at the GSM-R receiver input. The susceptibility of this component can be reached with such EMIs and permanent damages on

In this effort, we will mainly focus on the in-band EMIs acting basically on the GSM-R useful signal. A description of the sources and different characteristics of these disturbances will be presented in the next part. Their impact on the GSM-R communication will also be

From an EMC point of view, the railway infrastructure is a harsh complex EM environment where cohabitation between high power and digital communication systems with numerous eventual coupling mechanisms could be hazardous for the useful signal of the GSM-R. In this part, we will show that, on board moving trains, the GSM-R system is mainly affected by transient EM disturbances occurring between the catenary and the pantograph, in addition to the permanent disturbances coming from the public GSM base

Fig. 3 synthesizes the different EMIs that could impact the GSM-R useful signals and describes the mechanism responsible of the generation of the transient disturbances on a GSM-R antenna fixed on the roof of a train. In fact, when a bad sliding contact occurs between the catenary and pantograph, a transient event could appear between these elements. This phenomenon can be observed with naked eye as a spark appearing between the catenary and the pantograph. Thus, a transient current circulates through these elements, which behave as transmission antennas, emitting EMI that the GSM-R antenna

Fig. 3. EMIs received by GSM-R antenna and acting on the GSM-R useful signals

**7. The EM noise sources affecting the GSM-R signals** 

thus receive GSM-R in-band and out-band EMIs (Mansson, 2008).

the system can happen.

**7.1 Description of the EM noise sources** 

described.

stations.

can receive.

Fig. 2. Illustration of the on-board GSM-R system

The GSM-R is used in order to maintain a continuous voice and data link between the train and the control centres, and different trains located in the same neighbourhood. In the final version of ERTMS, the train sends its position through the uplink (from the train to the base stations) and receives signalling traffic information (speed limit, pass-through authorization…) through the downlink (from base stations to the train).

In Europe, the GSM-R uplink occupies the frequencies between 876 MHz and 880 MHz and the downlink between 921 MHz and 925 MHz. These frequency bands are separated by a frequency bandwidth dedicated to public and extended GSM.

Each frequency band used by the GSM-R is divided into 19 frequency channels of 200 kHz bandwidth. Only 19 channels are used by the system, in order to reduce the risk of interference with the public and extended GSM, using adjacent frequency bands.

The GSM-R is a TDMA (Time Division Multiple Access) system. The information is transmitted through each channel, according to 4.516 ms periodical TDMA frames, divided into 8 time intervals called "Time Slots" of 577 µs. During this time slot, the transmitted information is called burst, including 156 bytes, transmitted during 3.7 µs.

The data transmitted through the GSM-R system are very sensitive and the good operation of the GSM-R system is crucial to the capability and security of the European railway network. Thus, this system has been developed in order to be robust, with the capability of standing to some electromagnetic interference (EMI).

In fact, the GSM-R is included in the Euroradio protocol, which is specific to the railway and manages with altered received information, notably by resending some altered bursts until good reception. The use of such robust communication system is essentially motivated by the severity of the railway electromagnetic environment and the safety requirements.

In the next section we will focus on the different EMI that the GSM-R transmission signals can meet in the railway electromagnetic environment.

### **7. The EM noise sources affecting the GSM-R signals**

On board a moving train and in normal operating conditions, the GSM-R system can meet different transient or permanent EMIs, with various amplitudes, time durations, repetition rates, frequency bands… Moreover, the GSM-R antennas are generally multi-band antennas and are not really selective around the frequency bands dedicated to the railway. They can thus receive GSM-R in-band and out-band EMIs (Mansson, 2008).

(Mansson, 2008) showed that out-band EMIs observed in railway environment could be a serious threat to the low noise amplifier (LNA) installed at the GSM-R receiver input. The susceptibility of this component can be reached with such EMIs and permanent damages on the system can happen.

In this effort, we will mainly focus on the in-band EMIs acting basically on the GSM-R useful signal. A description of the sources and different characteristics of these disturbances will be presented in the next part. Their impact on the GSM-R communication will also be described.

### **7.1 Description of the EM noise sources**

510 Infrastructure Design, Signalling and Security in Railway

The GSM-R is used in order to maintain a continuous voice and data link between the train and the control centres, and different trains located in the same neighbourhood. In the final version of ERTMS, the train sends its position through the uplink (from the train to the base stations) and receives signalling traffic information (speed limit, pass-through

In Europe, the GSM-R uplink occupies the frequencies between 876 MHz and 880 MHz and the downlink between 921 MHz and 925 MHz. These frequency bands are separated by a

Each frequency band used by the GSM-R is divided into 19 frequency channels of 200 kHz bandwidth. Only 19 channels are used by the system, in order to reduce the risk of

The GSM-R is a TDMA (Time Division Multiple Access) system. The information is transmitted through each channel, according to 4.516 ms periodical TDMA frames, divided into 8 time intervals called "Time Slots" of 577 µs. During this time slot, the transmitted

The data transmitted through the GSM-R system are very sensitive and the good operation of the GSM-R system is crucial to the capability and security of the European railway network. Thus, this system has been developed in order to be robust, with the capability of

In fact, the GSM-R is included in the Euroradio protocol, which is specific to the railway and manages with altered received information, notably by resending some altered bursts until good reception. The use of such robust communication system is essentially motivated by the severity of the railway electromagnetic environment and the safety requirements.

In the next section we will focus on the different EMI that the GSM-R transmission signals

interference with the public and extended GSM, using adjacent frequency bands.

information is called burst, including 156 bytes, transmitted during 3.7 µs.

**Pantographe GSM-R**

**Mobile GSM-R**

**Câble blindé**

**Shielded cable**

**Antenne**

**GSM-R antenna**

**Afficheur**

Fig. 2. Illustration of the on-board GSM-R system

**Screen**

**Caténaire**

**Catenary**

**Câble blindé**

authorization…) through the downlink (from base stations to the train).

frequency bandwidth dedicated to public and extended GSM.

standing to some electromagnetic interference (EMI).

can meet in the railway electromagnetic environment.

**Shielded cable**

**Pantograph**

From an EMC point of view, the railway infrastructure is a harsh complex EM environment where cohabitation between high power and digital communication systems with numerous eventual coupling mechanisms could be hazardous for the useful signal of the GSM-R. In this part, we will show that, on board moving trains, the GSM-R system is mainly affected by transient EM disturbances occurring between the catenary and the pantograph, in addition to the permanent disturbances coming from the public GSM base stations.

Fig. 3 synthesizes the different EMIs that could impact the GSM-R useful signals and describes the mechanism responsible of the generation of the transient disturbances on a GSM-R antenna fixed on the roof of a train. In fact, when a bad sliding contact occurs between the catenary and pantograph, a transient event could appear between these elements. This phenomenon can be observed with naked eye as a spark appearing between the catenary and the pantograph. Thus, a transient current circulates through these elements, which behave as transmission antennas, emitting EMI that the GSM-R antenna can receive.

Fig. 3. EMIs received by GSM-R antenna and acting on the GSM-R useful signals

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 513

Measurement campaigns have been carried out on board moving train, on railway lines equipped with the GSM-R system, in order to show the relation between the public GSM signal and the permanent interferences that can be observed in the closest downlink GSM-R

In Fig. 5 the top curve gives the variation of the EM power signal obtained through the last GSM-R channel along 20 km. The second one is the result obtained into an intermediary channel, supposed to be free. The last curve is obtained through the first public GSM

**zz**

Measurements over 20 km *time*

**7.1.2 Permanent EMI acting on GSM-R antenna** 

frequency channel.

**Last GSM-R channel**

**Unused channel**

**7.2 Impacts of the EM noises** 

924.8 MHz 925 MHz 925.2 MHz

frequency channel to the public GSM band (Hammi, 2009).

**First public GSM channel**

GSM along 20 km railway line equipped with GSM-R system

Frequency

Fig. 5. EM measurement in different frequency channels used by the GSM-R and public

Fig. 5 shows clearly that the variation of the measured amplitudes into the unused frequency channel and the last GSM-R frequency channel are partially similar to the EM noise variation observed through the first public GSM channel. This result proves that the public GSM signal sent through the first channel can disturb the GSM-R bandwidth, and confirms that the public GSM signal can be considered as a serious threat to the GSM-R useful signal. Indeed, as can be seen on Fig. 5, a signal of -44 dBm on the first public GSM channel induces an EMI of -75 dBm on the last GSM-R frequency channel. Knowing that the GSM-R signal level can decrease to a minimum value of -92 dBm (UIC, 2003), this interference level can be sufficient to severely disturb a GSM-R transmission on this channel.

According to the type of the disturbance affecting the GSM-R system, the effect of the received EMI can vary. In fact, the transient events taking place between the catenary and the pantograph are wideband disturbances that can affect all the frequency channels used by the GSM-R system. It is obvious that the useful signal sent through the GSM-R system at the occurrence of the transient disturbance will be somehow disturbed. In fact, compared to the 3.7 µs time duration of one GSM-R bit, the transient duration of some ns is quietly small. So we need to investigate the real impact of such short time duration events on the

The generated wideband signal can easily cover the frequency bandwidth of the GSM-R system. However, from the train side, the GSM-R transmissions are mainly vulnerable to the EMIs covering the down-link frequency band. Indeed, on board trains, the signals emitted by the GSM-R antenna (up-link) have power levels highly superior to the power levels of the useful signals received by the antennas (down-link).

In addition, the GSM-R system uses frequency bands quietly close to the public GSM bandwidths, and when public GSM base stations use the adjacent frequency bands of the GSM-R, the risk for the GSM-R communications increases. This phenomenon is mainly observed when the train is operating in the vicinity of a city, where public GSM base stations and user numbers highly increase.

### **7.1.1 Transient EMI acting on the GSM-R useful signal**

Measurement campaigns carried out on board moving trains (Hammi, 2009) showed that the transient events, triggered when a bad sliding contact occurs between the catenary and the pantograph, are the most penalizing events for the GSM-R useful signals. Fig. 4 (a) shows an example of a transient signal recorded by an oscilloscope connected to a GSM-R antenna. The analysis of a large number of transients collected on board trains showed that their time duration is generally inferior to 20 ns (Ben Slimen, 2009), with a typical value of 5 ns and a typical value of the rise time is 0.4 ns. Fig. 4 (b) shows the maximal EM amplitude generated by 284 successive transient events on the downlink frequency band of the GSM-R in normal operation conditions. Each point in this graph links the rank of the recorded transient and its maximal amplitude within the 921 – 925 MHz frequency band, corresponding to the down-link frequency band.

These results show that these transients generate high level EMIs that can reach - 40 dBm. Moreover, statistical analysis (Ben Slimen, 2009) of these transient disturbances highlighted that they can be very frequent, especially on high speed lines.

Fig. 4. (a) Example of transient disturbance in time domain and (b) maximal EM power generated by 284 successive transients in downlink GSM-R band

### **7.1.2 Permanent EMI acting on GSM-R antenna**

512 Infrastructure Design, Signalling and Security in Railway

The generated wideband signal can easily cover the frequency bandwidth of the GSM-R system. However, from the train side, the GSM-R transmissions are mainly vulnerable to the EMIs covering the down-link frequency band. Indeed, on board trains, the signals emitted by the GSM-R antenna (up-link) have power levels highly superior to the power levels of

In addition, the GSM-R system uses frequency bands quietly close to the public GSM bandwidths, and when public GSM base stations use the adjacent frequency bands of the GSM-R, the risk for the GSM-R communications increases. This phenomenon is mainly observed when the train is operating in the vicinity of a city, where public GSM base

Measurement campaigns carried out on board moving trains (Hammi, 2009) showed that the transient events, triggered when a bad sliding contact occurs between the catenary and the pantograph, are the most penalizing events for the GSM-R useful signals. Fig. 4 (a) shows an example of a transient signal recorded by an oscilloscope connected to a GSM-R antenna. The analysis of a large number of transients collected on board trains showed that their time duration is generally inferior to 20 ns (Ben Slimen, 2009), with a typical value of 5 ns and a typical value of the rise time is 0.4 ns. Fig. 4 (b) shows the maximal EM amplitude generated by 284 successive transient events on the downlink frequency band of the GSM-R in normal operation conditions. Each point in this graph links the rank of the recorded transient and its maximal amplitude within the 921 – 925 MHz frequency band,

These results show that these transients generate high level EMIs that can reach - 40 dBm. Moreover, statistical analysis (Ben Slimen, 2009) of these transient disturbances highlighted

Fig. 4. (a) Example of transient disturbance in time domain and (b) maximal EM power

generated by 284 successive transients in downlink GSM-R band

the useful signals received by the antennas (down-link).

**7.1.1 Transient EMI acting on the GSM-R useful signal** 

stations and user numbers highly increase.

corresponding to the down-link frequency band.

that they can be very frequent, especially on high speed lines.

Measurement campaigns have been carried out on board moving train, on railway lines equipped with the GSM-R system, in order to show the relation between the public GSM signal and the permanent interferences that can be observed in the closest downlink GSM-R frequency channel to the public GSM band (Hammi, 2009).

In Fig. 5 the top curve gives the variation of the EM power signal obtained through the last GSM-R channel along 20 km. The second one is the result obtained into an intermediary channel, supposed to be free. The last curve is obtained through the first public GSM frequency channel.

Fig. 5. EM measurement in different frequency channels used by the GSM-R and public GSM along 20 km railway line equipped with GSM-R system

Fig. 5 shows clearly that the variation of the measured amplitudes into the unused frequency channel and the last GSM-R frequency channel are partially similar to the EM noise variation observed through the first public GSM channel. This result proves that the public GSM signal sent through the first channel can disturb the GSM-R bandwidth, and confirms that the public GSM signal can be considered as a serious threat to the GSM-R useful signal. Indeed, as can be seen on Fig. 5, a signal of -44 dBm on the first public GSM channel induces an EMI of -75 dBm on the last GSM-R frequency channel. Knowing that the GSM-R signal level can decrease to a minimum value of -92 dBm (UIC, 2003), this interference level can be sufficient to severely disturb a GSM-R transmission on this channel.

### **7.2 Impacts of the EM noises**

According to the type of the disturbance affecting the GSM-R system, the effect of the received EMI can vary. In fact, the transient events taking place between the catenary and the pantograph are wideband disturbances that can affect all the frequency channels used by the GSM-R system. It is obvious that the useful signal sent through the GSM-R system at the occurrence of the transient disturbance will be somehow disturbed. In fact, compared to the 3.7 µs time duration of one GSM-R bit, the transient duration of some ns is quietly small. So we need to investigate the real impact of such short time duration events on the

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 515

Two immunity criteria can be employed: Rxqual and Bit Error Rate (BER). The BER corresponds to the percentage of erroneous bits in a given transmission length (Breed, 2003):

Number of erroneous bits BER= ×100%

The Rxqual is a quality parameter measured by the GSM-R mobile and it defines the quality of the received signal on a level from 0 to 7 (the lower the Rxqual is, the higher is the quality). The Rxqual is linked to the BER calculated on the learning sequences included in the GSM-R frames. The specifications defined in standards such as (ITU-T, 2003) require that the Rxqual is inferior or equal to 3 in order to ensure a good quality of communication. A relationship exists between BER and Rxqual: each value of Rxqual is associated with a range of values of BER (Lagrange et al., 1996) as can be seen in the

The test bench which was employed to perform immunity tests in laboratory is presented in Fig. 7. This test bench aims at reproducing the EM conditions that the GSM-R system is




Total number of bits (1)

**8.2 Definition of the immunity criteria** 

Table 2. Correspondence table between BER and Rxqual

simulator called CMU 200 from Rohde & Schwarz.

signals at the input of the GSM- R mobile.

susceptible to meet on board trains. It is composed of three main parts:

**8.3 Employed test bench** 

separately.

following table.

interpretation of a disturbed GSM-R bit. This work will be presented in the next part of this effort.

When it comes to permanent EM disturbances coming from the public GSM base stations, the impact of these disturbances can be mainly observed when the GSM-R system is using the last frequency channel and the public GSM system is using the first frequency channel. So, even if the last frequency band of the GSM-R system is affected by the public GSM signal, the useful GSM-R signal is not necessary affected. In fact, when such scenario occurs, the GSM-R system could use different advanced protocols, mainly Euroradio protocol that can allow the system to stand to such disturbances. However, when the whole GSM-R channels are used, the system could be really affected by these disturbances.

However, among the current EMC standards, none methodology of immunity testing is adapted to the GSM-R system and to the characteristics of the EMIs that it can meet in the railway environment. The next section is then focused on a specific immunity approach to this system in order to assess the real risks for the GSM-R transmissions.

### **8. Immunity testing of the GSM-R signals in laboratory**

### **8.1 Methodology**

To evaluate the impact of the interferences on the quality of the GSM-R transmissions, a GSM-R mobile was employed. This mobile can be connected to one network either simulated by a specific piece of equipment or coming from a base station installed at proximity. In our case, we use a network simulator allowing controlling the network parameters such as GSM-R channel used for the communication, power of signals… and performing BER measurements. The principle of this methodology of test is to first connect the mobile to the simulated network and to establish a communication with the simulator. Then, the EM disturbance signals (permanent noise + transient signals) were generated and their impact on the quality of the GSM-R communication was evaluated thanks to criteria introduced in the following paragraph. Fig. 6 gives an illustration of this test methodology.

Fig. 6. Principle of the employed methodology of test

### **8.2 Definition of the immunity criteria**

514 Infrastructure Design, Signalling and Security in Railway

interpretation of a disturbed GSM-R bit. This work will be presented in the next part of this

When it comes to permanent EM disturbances coming from the public GSM base stations, the impact of these disturbances can be mainly observed when the GSM-R system is using the last frequency channel and the public GSM system is using the first frequency channel. So, even if the last frequency band of the GSM-R system is affected by the public GSM signal, the useful GSM-R signal is not necessary affected. In fact, when such scenario occurs, the GSM-R system could use different advanced protocols, mainly Euroradio protocol that can allow the system to stand to such disturbances. However, when the whole GSM-R

However, among the current EMC standards, none methodology of immunity testing is adapted to the GSM-R system and to the characteristics of the EMIs that it can meet in the railway environment. The next section is then focused on a specific immunity approach to

To evaluate the impact of the interferences on the quality of the GSM-R transmissions, a GSM-R mobile was employed. This mobile can be connected to one network either simulated by a specific piece of equipment or coming from a base station installed at proximity. In our case, we use a network simulator allowing controlling the network parameters such as GSM-R channel used for the communication, power of signals… and performing BER measurements. The principle of this methodology of test is to first connect the mobile to the simulated network and to establish a communication with the simulator. Then, the EM disturbance signals (permanent noise + transient signals) were generated and their impact on the quality of the GSM-R communication was evaluated thanks to criteria introduced in the following paragraph. Fig. 6 gives an illustration of this

> Network simulator

Base station

channels are used, the system could be really affected by these disturbances.

this system in order to assess the real risks for the GSM-R transmissions.

**8. Immunity testing of the GSM-R signals in laboratory** 

Establishment of a communication

Fig. 6. Principle of the employed methodology of test

Communication channel or

effort.

**8.1 Methodology** 

test methodology.

GSM-R mobile

> EM disturbance signals

Two immunity criteria can be employed: Rxqual and Bit Error Rate (BER). The BER corresponds to the percentage of erroneous bits in a given transmission length (Breed, 2003):

$$\text{BER} = \frac{\text{Number of erroneous bits}}{\text{Total number of bits}} \times 100\% \tag{1}$$

The Rxqual is a quality parameter measured by the GSM-R mobile and it defines the quality of the received signal on a level from 0 to 7 (the lower the Rxqual is, the higher is the quality). The Rxqual is linked to the BER calculated on the learning sequences included in the GSM-R frames. The specifications defined in standards such as (ITU-T, 2003) require that the Rxqual is inferior or equal to 3 in order to ensure a good quality of communication. A relationship exists between BER and Rxqual: each value of Rxqual is associated with a range of values of BER (Lagrange et al., 1996) as can be seen in the following table.


Table 2. Correspondence table between BER and Rxqual

### **8.3 Employed test bench**

The test bench which was employed to perform immunity tests in laboratory is presented in Fig. 7. This test bench aims at reproducing the EM conditions that the GSM-R system is susceptible to meet on board trains. It is composed of three main parts:


Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 517

0 10 20 Temps (ns)

Contrary to duration and rise time, it is not possible to determine a typical value for the recurrence of transients since it is very variable and depends on several operating conditions (speed of the train, one or two pantographs, state and age of the catenary and pantograph…). During the measurement campaign performed on board trains, we generally noticed that very few transients appeared at low speed whereas they could occur with a time interval of about 5 µs at about 200 km/h. As a consequence, the recurrence of transients is considered as a variable parameter for the immunity tests: for each measurement, the transient disturbances are generated with a constant time interval (TI) between two successive transients as illustrated in Fig. 9 and the immunity results are given in relation to

Time interval

Fig. 9. Illustration of the time interval (TI) between the successive transient disturbances

Three different configurations, as shown on Fig. 10, are considered when studying the effect

The aim is, in a first step, to observe and quantify the impact of each type of interference separately and in different conditions of test (different power levels for permanent interferences, different time intervals for transient interferences…). In a second step, the

produced by the interference signals on the quality of the GSM-R transmissions:

**9. Results of EM immunity tests on GSM-R transmissions** 


combined effect of the two types of disturbances is assessed.

Time

Time (ns)

Amplitude (V)

Fig. 8. Used transient test signal

the value of the time interval.

**9.1 Configurations of test** 


1.0 -

0.5 -

0 -



Fig. 7. Employed immunity test bench

### **8.4 Employed test signals**

The GSM-R communication is established using the last useful GSM-R channel (924.8 MHz) from the down-link frequency band. The power level of the signals generated by the network simulator is adjusted so as to obtain a level of -70 dBm at the input of the GSM-R mobile. That corresponds to realistic operational conditions on board trains.

As for the public GSM signals, the communication channel employed is the first one (925.2 MHz) which is adjacent to the last useful GSM-R channel (924.8 MHz) used for the tests. The level of these signals is variable in order to study the effect produced on the quality of the GSM-R communication depending on the power level of the interference signals.

The signal used to simulate the presence of transient signals is a double exponential (duration=5ns, rise time=0.4 ns) modulated by a sinus at the frequency 923 MHz which corresponds to the center frequency of the GSM-R down-link frequency band. The corresponding mathematical expression is the following one:

$$\mathbf{S(t) = A \times (e^{\frac{1}{\mathbf{D}} \mathbf{t}} - e^{\frac{1}{\mathbf{R} \mathbf{T}} \mathbf{t}}) \times \boldsymbol{\mu}(t) \times \sin(2\pi F t)}\tag{2}$$

where D=5 ns, RT=0.4 ns, F=923 MHz and u is the unit step function.

The values employed for rise time (RT) and duration (D) result from a statistical analysis we performed on transients collected on board trains during one measurement campaign (Ben Slimen, 2009). Fig. 8 gives the time representation of this test signal.

Fig. 8. Used transient test signal

CMU 200 924.8 MHz

SMIQ Public GSM 925.2 MHz

The GSM-R communication is established using the last useful GSM-R channel (924.8 MHz) from the down-link frequency band. The power level of the signals generated by the network simulator is adjusted so as to obtain a level of -70 dBm at the input of the GSM-R

As for the public GSM signals, the communication channel employed is the first one (925.2 MHz) which is adjacent to the last useful GSM-R channel (924.8 MHz) used for the tests. The level of these signals is variable in order to study the effect produced on the quality of the GSM-R communication depending on the power level of the interference

The signal used to simulate the presence of transient signals is a double exponential (duration=5ns, rise time=0.4 ns) modulated by a sinus at the frequency 923 MHz which corresponds to the center frequency of the GSM-R down-link frequency band. The

The values employed for rise time (RT) and duration (D) result from a statistical analysis we performed on transients collected on board trains during one measurement campaign (Ben

1 1 -t - t D RT S(t) A (e - e ) sin *u t Ft*

mobile. That corresponds to realistic operational conditions on board trains.

corresponding mathematical expression is the following one:

where D=5 ns, RT=0.4 ns, F=923 MHz and u is the unit step function.

Slimen, 2009). Fig. 8 gives the time representation of this test signal.

GSM-R Mobile

Fig. 7. Employed immunity test bench

**8.4 Employed test signals** 

signals.

**Establishment of a communication between the mobile and a network simulator**

> Spectrum analyzer *Calibration of the power levels*

**Analysis in frequency domain**


*Loop back*

combiner

Combiner

Signal generator

**Noise generation**

(2)

50 load

Directional combiner

Amplifier

Contrary to duration and rise time, it is not possible to determine a typical value for the recurrence of transients since it is very variable and depends on several operating conditions (speed of the train, one or two pantographs, state and age of the catenary and pantograph…). During the measurement campaign performed on board trains, we generally noticed that very few transients appeared at low speed whereas they could occur with a time interval of about 5 µs at about 200 km/h. As a consequence, the recurrence of transients is considered as a variable parameter for the immunity tests: for each measurement, the transient disturbances are generated with a constant time interval (TI) between two successive transients as illustrated in Fig. 9 and the immunity results are given in relation to the value of the time interval.

Fig. 9. Illustration of the time interval (TI) between the successive transient disturbances

### **9. Results of EM immunity tests on GSM-R transmissions**

### **9.1 Configurations of test**

Three different configurations, as shown on Fig. 10, are considered when studying the effect produced by the interference signals on the quality of the GSM-R transmissions:


The aim is, in a first step, to observe and quantify the impact of each type of interference separately and in different conditions of test (different power levels for permanent interferences, different time intervals for transient interferences…). In a second step, the combined effect of the two types of disturbances is assessed.

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 519

In Fig. 11, the public GSM signal has to exceed -20 dBm to start affecting the quality of the GSM-R communication (the BER starts to increase). That means that the interference signals on the 400 kHz adjacent channel have to be 50 dB higher than the wanted signal on the GSM-R communication channel to deteriorate the quality of the transmission, which well complies with the specifications (ETSI, 2000). Indeed, the standard EN 300 910 stipulates

Then, we also notice that a level of -13 dBm is necessary to induce a Rxqual equal to 1. It will be highlighted later that this level is different when transient interferences are

**9.3 Impact of transient EM interferences produced by catenary-pantograph sliding** 

These tests and measurements are related to "configuration 2" in Fig. 10. The GSM-R signal can be set to the desired value and the interference level produced by transient signals on the GSM-R frequency band can be controlled by using a variable attenuator in order to obtain the desired signal-to-noise ratio (SNR) at the mobile input. As for the measurements, during a test sequence we vary the time interval between two consecutive transients and one measure of BER is made for each chosen time interval. Then, the same test sequence is applied with one other signal-to-noise ratio. Three different SNR at the mobile input are tested: +5, 0 and -5 dB. The results are presented in Fig. 12 where the vertical axis of the graph corresponds to the value of the BER in % and the horizontal axis gives the time

0 200 400 600 800 1000 1200 1400 1600

Fig. 12. Results of the BER measurement in the presence of transients for different values of

The first thing to notice is that the BER evolves with the time interval between transients: it increases with the recurrence of transients. Indeed, the BER is higher for small values of time interval whatever the value of the SNR. In (Adriano, 2008), a relation was proposed to estimate the BER from the TI between the transient interferences, under the assumption that

Time interval between two successive transients (µs)

SNR = - 5 dB SNR = 0 dB SNR = + 5 dB

that a mobile has to tolerate a 400 kHz adjacent interference level of -50 dB.

simultaneously present.

interval between two successive transients in µs.

0.0

0.4

0.8

BER (%)

the signal-to-noise ratio (SNR)

the SNR is equal to 0 dB.

1.2

1.6

2.0

**contact** 

Fig. 10. The different configurations used for immunity testing

### **9.2 Impact of public GSM signals**

The configuration of test corresponds to "configuration 1" from Fig. 10. As previously explained in paragraph 8.4, the GSM-R transmissions takes place on the channel 924.8 MHz with a power level of -70 dBm and the public GSM ones on the channel 925.2 MHz with a variable level from -72 to -12 dBm. Fig. 11 presents the results of the BER measurements as a function of the power level of public GSM signals. The vertical axis gives the value of the BER in % and the horizontal axis represents the power level of the public GSM band signal (on the channel 925.2 MHz) which induces the permanent noise on the GSM-R channel.

Fig. 11. Results of the BER measurement in the presence of public GSM signals

The configuration of test corresponds to "configuration 1" from Fig. 10. As previously explained in paragraph 8.4, the GSM-R transmissions takes place on the channel 924.8 MHz with a power level of -70 dBm and the public GSM ones on the channel 925.2 MHz with a variable level from -72 to -12 dBm. Fig. 11 presents the results of the BER measurements as a function of the power level of public GSM signals. The vertical axis gives the value of the BER in % and the horizontal axis represents the power level of the public GSM band signal (on the channel 925.2 MHz) which induces the permanent noise on the GSM-R channel.

Fig. 11. Results of the BER measurement in the presence of public GSM signals

Fig. 10. The different configurations used for immunity testing

**9.2 Impact of public GSM signals** 

In Fig. 11, the public GSM signal has to exceed -20 dBm to start affecting the quality of the GSM-R communication (the BER starts to increase). That means that the interference signals on the 400 kHz adjacent channel have to be 50 dB higher than the wanted signal on the GSM-R communication channel to deteriorate the quality of the transmission, which well complies with the specifications (ETSI, 2000). Indeed, the standard EN 300 910 stipulates that a mobile has to tolerate a 400 kHz adjacent interference level of -50 dB.

Then, we also notice that a level of -13 dBm is necessary to induce a Rxqual equal to 1. It will be highlighted later that this level is different when transient interferences are simultaneously present.

#### **9.3 Impact of transient EM interferences produced by catenary-pantograph sliding contact**

These tests and measurements are related to "configuration 2" in Fig. 10. The GSM-R signal can be set to the desired value and the interference level produced by transient signals on the GSM-R frequency band can be controlled by using a variable attenuator in order to obtain the desired signal-to-noise ratio (SNR) at the mobile input. As for the measurements, during a test sequence we vary the time interval between two consecutive transients and one measure of BER is made for each chosen time interval. Then, the same test sequence is applied with one other signal-to-noise ratio. Three different SNR at the mobile input are tested: +5, 0 and -5 dB. The results are presented in Fig. 12 where the vertical axis of the graph corresponds to the value of the BER in % and the horizontal axis gives the time interval between two successive transients in µs.

Fig. 12. Results of the BER measurement in the presence of transients for different values of the signal-to-noise ratio (SNR)

The first thing to notice is that the BER evolves with the time interval between transients: it increases with the recurrence of transients. Indeed, the BER is higher for small values of time interval whatever the value of the SNR. In (Adriano, 2008), a relation was proposed to estimate the BER from the TI between the transient interferences, under the assumption that the SNR is equal to 0 dB.

Susceptibility of the GSM-R Transmissions to the Railway Electromagnetic Environment 521

Obviously, these results are linked to the GSM-R signal power used for the test (-70 dBm) and we would obtain a better level of immunity if setting up the GSM-R signal to a higher level of power. However, we are not going to develop this point in this chapter, since further studies on the immunity of the GSM-R system can be found in (Dudoyer et al., to be

This chapter outlined the major developments underway on the European rail network and highlighted the electromagnetic vulnerability of the GSM-R which is a key component of the management system. Indeed, immunity testing carried out in laboratory to confront the GSM-R transmissions to EM disturbances representative to those measured on trains, have shown that the quality of the transmissions can be significantly affected. The results of the section 9 highlighted that the impact of the transient disturbances on the quality of the GSM-R transmissions is linked to two main factors: the levels of noise produced on the GSM-R down-link frequency band and the repetition rate of the transient disturbances. Moreover, their impact can also be related to the presence of permanent interferences with the GSM public. Consequently, the assess of the risks of disturbances of the GSM-R transmissions requires to monitor the spectral distribution of the EM noise over the time, and with a high temporal resolution which permits us to perform direct comparison with the transmission of

The current European standard methodologies of measurement of the EM emissions in the railway domain (EN 50121, 2006) which only consist in spectral analysis of the radiated emissions without taking into account the time dimension are then not adapted to the control of the EM emissions in order to protect the GSM-R transmissions. This chapter which proposed a methodology to perform immunity testing of GSM-R transmissions in laboratory, has also highlighted the main features of the EM noise it is necessary to characterize on board trains to ensure that the radiated emissions will not affect the ability

The authors of this chapter would like to thanks SNCB and SNCF to have given them access to their trains to perform measurements in real conditions and also ALSTOM which provided them specific railway equipment. This work was performed in the framework of the RAILCOM project supported by the PCRD 6 and CISIT projects supported by the North

Adriano, R., Ben Slimen, N., Deniau, V., Berbineau, M. & Massy, P. (2008). Prediction of the

Ben Slimen, N., Deniau, V., Rioult, J., Dudoyer S. & Baranowski S. (2009). Statistical

BER on the GSM-R communications provided by the EM transient disturbances in the railway environment, *Proceeding of EMC Europe*, pp. 771-775, Hamburg,

characterisation of the EM interferences acting on GSM-R antennas fixed above

published).

**10. Conclusion** 

the digital data.

of the GSM-R system.

**11. Acknowledgment** 

Region and the FEDER.

Germany, September 2008.

**12. References** 

The second thing to observe is that the SNR has an impact on the BER. Indeed, if taking the curve obtained for SNR = 0 dB (at the mobile input) as a reference, we see that, when the transient level is 5 dB higher than the GSM-R signal (SNR=-5 dB), the measured BER increases. Consequently, the transmission could be more severely disturbed when the SNR decreases to - 5 dB whereas, in the reverse case (SNR=+5 dB), the BER is lower (less than 0.4 %) which guarantees a good quality of communication whatever the recurrence of the transient interferences.

#### **9.4 Tests and measurements in the presence of both types of interference signals simultaneously**

In this section, we now consider "configuration 3" in Fig. 10: presence of permanent noise and transients simultaneously with two arbitrarily chosen values for the transient time interval which are TI=150 µs and TI=550 µs. The following graph, on the right of Fig. 13, shows the results of the BER measurements in this configuration of test. The first curve (black one with points) corresponds to the evolution of the BER without transient and the two others (orange with squares and blue with triangles ones) with transients for the two considered values of time interval. These values were chosen so that 3 transients can occur during the time duration of one GSM-R burst in the first case (TI=150 µs) and only one in the second case (TI=550 µs), as can be seen in the illustration on the left of Fig. 13.

Fig. 13. Results of the BER measurements in the presence of public GSM signals and transient signals with GSM-R signal power = -70 dBm at the mobile input

In the absence of transient signals (black curve with points), the public GSM signals have to reach a power level of -9 dBm to induce a Rxqual equal to 3 whereas in the presence of transient disturbances with a time interval of 150 µs, a level of -15 dBm is sufficient. In other words, the impact on the GSM-R communication of the transient disturbances "adds" to the one of signals in the public GSM band. We thus conclude that the susceptibility of the GSM-R to permanent noise is higher in the presence of transient disturbances.

Obviously, these results are linked to the GSM-R signal power used for the test (-70 dBm) and we would obtain a better level of immunity if setting up the GSM-R signal to a higher level of power. However, we are not going to develop this point in this chapter, since further studies on the immunity of the GSM-R system can be found in (Dudoyer et al., to be published).

### **10. Conclusion**

520 Infrastructure Design, Signalling and Security in Railway

The second thing to observe is that the SNR has an impact on the BER. Indeed, if taking the curve obtained for SNR = 0 dB (at the mobile input) as a reference, we see that, when the transient level is 5 dB higher than the GSM-R signal (SNR=-5 dB), the measured BER increases. Consequently, the transmission could be more severely disturbed when the SNR decreases to - 5 dB whereas, in the reverse case (SNR=+5 dB), the BER is lower (less than 0.4 %) which guarantees a good quality of communication whatever the recurrence of the transient

**9.4 Tests and measurements in the presence of both types of interference signals** 

second case (TI=550 µs), as can be seen in the illustration on the left of Fig. 13.

RXQUAL = 3

RXQUAL = 1

transient signals with GSM-R signal power = -70 dBm at the mobile input

R to permanent noise is higher in the presence of transient disturbances.

Fig. 13. Results of the BER measurements in the presence of public GSM signals and

In the absence of transient signals (black curve with points), the public GSM signals have to reach a power level of -9 dBm to induce a Rxqual equal to 3 whereas in the presence of transient disturbances with a time interval of 150 µs, a level of -15 dBm is sufficient. In other words, the impact on the GSM-R communication of the transient disturbances "adds" to the one of signals in the public GSM band. We thus conclude that the susceptibility of the GSM-

t t

150 µs

550 µs

In this section, we now consider "configuration 3" in Fig. 10: presence of permanent noise and transients simultaneously with two arbitrarily chosen values for the transient time interval which are TI=150 µs and TI=550 µs. The following graph, on the right of Fig. 13, shows the results of the BER measurements in this configuration of test. The first curve (black one with points) corresponds to the evolution of the BER without transient and the two others (orange with squares and blue with triangles ones) with transients for the two considered values of time interval. These values were chosen so that 3 transients can occur during the time duration of one GSM-R burst in the first case (TI=150 µs) and only one in the

> Transient with time interval = 550 µs Transient with time interval = 150 µs BER without transient


interferences.

**simultaneously** 

This chapter outlined the major developments underway on the European rail network and highlighted the electromagnetic vulnerability of the GSM-R which is a key component of the management system. Indeed, immunity testing carried out in laboratory to confront the GSM-R transmissions to EM disturbances representative to those measured on trains, have shown that the quality of the transmissions can be significantly affected. The results of the section 9 highlighted that the impact of the transient disturbances on the quality of the GSM-R transmissions is linked to two main factors: the levels of noise produced on the GSM-R down-link frequency band and the repetition rate of the transient disturbances. Moreover, their impact can also be related to the presence of permanent interferences with the GSM public. Consequently, the assess of the risks of disturbances of the GSM-R transmissions requires to monitor the spectral distribution of the EM noise over the time, and with a high temporal resolution which permits us to perform direct comparison with the transmission of the digital data.

The current European standard methodologies of measurement of the EM emissions in the railway domain (EN 50121, 2006) which only consist in spectral analysis of the radiated emissions without taking into account the time dimension are then not adapted to the control of the EM emissions in order to protect the GSM-R transmissions. This chapter which proposed a methodology to perform immunity testing of GSM-R transmissions in laboratory, has also highlighted the main features of the EM noise it is necessary to characterize on board trains to ensure that the radiated emissions will not affect the ability of the GSM-R system.

### **11. Acknowledgment**

The authors of this chapter would like to thanks SNCB and SNCF to have given them access to their trains to perform measurements in real conditions and also ALSTOM which provided them specific railway equipment. This work was performed in the framework of the RAILCOM project supported by the PCRD 6 and CISIT projects supported by the North Region and the FEDER.

### **12. References**

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0


**BER (%)**


moving train*. The European Physical Journal Applied Physics,* Vol. 48*,* No.2, *(*2009), ISSN 1286-0042


Breed, G. (2003). Bit Error Rate: Fundamental Concepts and Measurement Issues. *High* 

Dudoyer, S., Deniau, V., Adriano, R., Ben Slimen, M. N., Rioult, J., Meyniel, B. &

*accepted for publication in IEEE Transactions on electromagnetic compatibility*. EN 50121. (2006). European standards for Railway applications: Electromagnetic

ETSI EN 300 910 V8.5.1 (2000). European Standard on Digital cellular telecommunication system (Phase 2+); Radio transmission and reception, November 2000. GM/RC 1500, (1994). Code of Practice for EMC between the Railway and its

Hammi, T., Ben Slimen, N., Deniau, V., Rioult, J. & Dudoyer, S. (2009). Comparison between

IEC 60050-161. (1990). International Electrotechnical Vocabulary. Chapter 161:

ITU-T Recommendation K.48 (2003). EMC requirements for each telecommunication

Jarašūnienė, A. (2005). General Description of European Railway Traffic Management

Knobloch, A. & Garbe, H. (2002). Critical Review of Converting Spectral Data into

Konefal, T., Pearce, D.A.J., Marshman, C.A. & McCormack, L.M., (2002). Potential

Mansson, D., Thottappillil*,* R., Bäckström*,* M & Lundén, O. (2008). Vulnerability of European

UIC Project EIRENE (2003). System Requirements Specification, v14.0, 21 October 2003.

GSM-R coverage level and EM noise level in railway environment, *Proceedings of the 9th International Conference on Intelligent Transport System-Telecommunications, ITST* 

Electromagnetic compatibility, Edition: 1.0, International Electrotechnical

System (ERTMS) and Strategy of ERTMS implementation in Various Railway Managements, *Transport and Telecommunication,* Vol.6, No.5, (2005), pp. 21-27, ISSN

Prospective Bit Error Rates, *Proceeding of IEEE International Symposium on Electromagnetic Compatibility, Volume 1,* pp. 173-178, ISBN 0-7803-7264-6,

electromagnetic interference to radio services from railways, *Final Report, University of York*, 2002, Retrieved from <http://www.yorkemc.co.uk/research/railways/>. Lagrange, X., Godlewski, P. & Tabbane, S. (1996). GSM-DCS Networks, Hermès, Paris, 1996,

Rail Traffic Management System to Radiated Intentional EMI. *IEEE Transactions on Electromagnetic Compatibility,* Vol.50, No.1, (2008), pp. 101-109, ISSN 0018-9375 Midya, S. & Thottappillil, R. (2008). An Overview of Electromagnetic Compatibility

Challenges in European Rail Traffic Management System, *Journal of Transportation Research Part C: Emerging Technologies,* Elsevier, (Ed.), Vol.16C, Issue.5, (2008), pp.

*Frequency Electronics*, Vol.2, No.1, (January 2003), pp. 46-48

ISSN 1286-0042

Compatibility-Part 1-5

Commission, 1990

1407-6160

Neighbourhood, December 1994

*2009*, pp. 123-128, Lille, France, October 2009

Minneapolis, MN, USA, August 2002

pp. 207-208, ISBN 2-86601-558-4

515-534, ISSN 0968090X

Source : EIRENE Project Team

equipment - Product family Recommendation, July 2003.

moving train*. The European Physical Journal Applied Physics,* Vol. 48*,* No.2, *(*2009),

Berbineau, M. (to be published). Study of the Susceptibility of the GSM-R Communications to the Electromagnetic Interferences of the Rail Environment,

## *Edited by Xavier Perpiñà*

Railway transportation has become one of the main technological advances of our society. Since the first railway used to carry coal from a mine in Shropshire (England, 1600), a lot of efforts have been made to improve this transportation concept. One of its milestones was the invention and development of the steam locomotive, but commercial rail travels became practical two hundred years later. From these first attempts, railway infrastructures, signalling and security have evolved and become more complex than those performed in its earlier stages. This book will provide readers a comprehensive technical guide, covering these topics and presenting a brief overview of selected railway systems in the world. The objective of the book is to serve as a valuable reference for students, educators, scientists, faculty members, researchers, and engineers.

Infrastructure Design, Signalling and Security in Railway

Infrastructure Design,

Signalling and Security in

Railway

*Edited by Xavier Perpiñà*

Photo by southtownboy / iStock