Operation and Maintenance of Hydraulic Structures

*Musa Abubakar Tadda, Amimul Ahsan, Monzur Imteaz, Abubakar Shitu, Umar Abdulbaki Danhassan and Aliyu Idris Muhammad*

#### **Abstract**

Water is among the most valuable resources that nature has endowed to human beings. Water has cut across all spans of life from cradle to grave. Since time immemorial, man continuously developed methods and techniques to harness the benefits of water and as well to protect himself from the destruction that may be caused by the same water. Therefore, for a hydraulic structure to answer its name, it must be capable of being used smoothly for the purposes it was designed for and also be able to be controlled effectively without the risk of causing any havoc to the environment. Using water, especially for agricultural purposes, cannot be overemphasized. Hence, this chapter discusses the hydraulic structures based on the work they performed, challenges facing hydraulic structures, and management procedures of the hydraulic structures in order to adequately and efficiently serve their purpose.

**Keywords:** hydraulic structures, operation, maintenance, water, design

#### **1. Introduction**

Hydraulic structures play an important role in drainage, irrigation, and hydraulic projects. If hydraulic structures fail, it may cause serious damages of wealth, properties, and environment as well as losses of life and injury to economy. The water related infrastructures are constructed at the aims to facilitate human needs/desires and enhance the quality of life such as drainage channel, river/channel, irrigation canal, bank/foot protection work, embankment, dam, spur dike/groyne, bridge/ culvert, regulator, barrage/large regulator, aqueduct, pump station, siphon, and sluice. The details of some of the hydraulic structures are presented below.

#### **1.1 Types of hydraulic structures**

Hydraulic structures are structures that are fully or partially submerged in water. The essence of building hydraulic structures is to either divert, disrupt, store, or completely stop the natural flow of water bodies. Based on the work they are designed to perform on streamflow, hydraulic structures are categorized as waterretaining structures (dams and barrages), water-conveying structures (artificial channels), and special-purpose structures (structures for hydropower generation or inland waterways) [1].

**4**

*Hydraulic Structures - Theory and Applications*

[1] Chane B, Behailu S. Hydraulic Structures I. Lecture Note. Addis Ababa, Ethiopia: Department of Civil Engineering, Faculty of Technology, Addis Ababa University; 2006

**References**

[2] Novak P, Moffat AIB, Nalluri C, Narayanan R. Hydraulic Structures. 4th ed. Oxon, UK: Taylor & Francis; 2007

[3] HiNative. What is the Difference Between Dam and Embankment and Causeway? Available from: https:// hinative.com/en-US/questions/237962

[4] Gąsiorowski D, Artichowicz W. Distribution of flows in a channel network under steady flow conditions. Acta Scientiarum Polonorum-Formatio Circumiectus. 2019;**18**(1):27-37. DOI:

[5] Ghomri A, Riguet F, Debabeche M. Effect for a single roughness e=5,63mm of experimental to study hydraulic jump profile in a channel in u a rough bottom. Journal of Fundamental and Applied Sciences. 2015;**5**(1):25-39. DOI: 10.4314/ jfas.v5i1.3. Available from: https:// www.ajol.info/index.php/jfas/article/

10.15576/ASP.FC/2019.18.1.27

view/120940/110380

[6] Kałuża T, Radecki-Pawlik A, Szoszkiewicz K, Plesiński K,

Radecki-Pawlik B, Laks I. Plant basket hydraulic structures (PBHS) as a new river restoration measure. Science of the Total Environment. 2018;**627**:245-255

[Accessed: 30 July 2019]

#### *1.1.1 Water-retaining structures*

The dam is an essential hydraulic structure that all other structures directly or indirectly relied upon. Dams and barrages are typical *water-retaining structures* that are built purposely to impound water. The retained water behind dams and barrages could be used for other purposes such as irrigation, recreational activities, navigation, and a lot more. As of September 2019, there are 57,985 registered dams in the world [2]. Regardless of their size and type, dams demonstrate high complexity in their load response and interactive relationship with site hydrology and geology. Dams are of different sizes and shapes and made of various materials such as soil or rockfill embankment, mass concrete, reinforced concrete, masonry, and wood. However, based on the construction materials used, dams are broadly classified into concrete dams and embankment dams.


#### *1.1.2 Water-conveying structures*

Any artificial facility cut in the ground with the sole purpose of transporting water diverted from main sources (river and dams) is termed as the *water-conveying structure*. These types of structures are comprised of canals (**Figure 2a**) and tunnels (**Figure 2b**) (usually made from soil and rocks) or siphons, aqueducts (**Figure 2c**), flumes (**Figure 2d**), and pipelines (usually made from concrete and metals) [1]. Before the construction of any water-conveying structure, a detailed geotechnical soil test and analysis is recommended to avail the surface and subsurface properties of the soil on which the structure is upon rest. The same soil test and analysis also applies to other types and classes of hydraulic structures to ensure safety and to save resources.

#### *1.1.3 Special-purpose hydraulic structures*

As the name implies, *special-purpose hydraulic structures* are built as an integral part of hydraulic project to meet a special purpose such as hydropower generation (e.g., surge towers and shafts, forebays, and head ponds), navigation (e.g., landings, berths, substations for ship repair, etc.), fishing (e.g., fish nursery ponds, fish lifts and locks, fishways, etc.), water supply for domestic and industrial uses (e.g., water intakes to treatment plant, pumping stations, etc.), waste disposal/sewerage (e.g., sewage headers, pumping stations, channels after treatment plant to water bodies, etc.), and land reclamation (e.g., irrigation canals, drainage systems, silt tanks, etc.) [1, 7].

**7**

**Figure 2.**

**Figure 1.**

*Source: [3].*

*(a) Canals, (b) tunnels, (c) aqueducts, and (d) flumes. Source: [4–6].*

*(a) Gravity dam, (b) arch dam, (c) buttress dam, (d) multiple-arch dam, (e) earthfill and rockfill dam.* 

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

#### **Figure 1.**

*Hydraulic Structures - Theory and Applications*

concrete dams and embankment dams.

*1.1.2 Water-conveying structures*

*1.1.3 Special-purpose hydraulic structures*

The dam is an essential hydraulic structure that all other structures directly or indirectly relied upon. Dams and barrages are typical *water-retaining structures* that are built purposely to impound water. The retained water behind dams and barrages could be used for other purposes such as irrigation, recreational activities, navigation, and a lot more. As of September 2019, there are 57,985 registered dams in the world [2]. Regardless of their size and type, dams demonstrate high complexity in their load response and interactive relationship with site hydrology and geology. Dams are of different sizes and shapes and made of various materials such as soil or rockfill embankment, mass concrete, reinforced concrete, masonry, and wood. However, based on the construction materials used, dams are broadly classified into

• Concrete dams comprised of gravity (PG), arch (VA), buttress (CB), barrage (BM), and multiple-arch dams (MV) as shown in **Figure 1a**–**e**. All these dams are constructed of mass concrete and sometimes of masonry with appropriate structural quality [1, 2]. Recent statistics show that concrete dams occupied

• Embankment dams are of two types, earthfill (TE) and rockfill (ER), both of which are constructed by mass filling of naturally existing ground materials (soil and rocks). The construction materials are graded and well compacted to resist seepage and sliding. Embankment dams are characterized by having similar moderate face slopes at both upstream and downstream. This feature gives rise to a broad trapezoidal cross section and a high construction volume,

Any artificial facility cut in the ground with the sole purpose of transporting water diverted from main sources (river and dams) is termed as the *water-conveying structure*. These types of structures are comprised of canals (**Figure 2a**) and tunnels (**Figure 2b**) (usually made from soil and rocks) or siphons, aqueducts (**Figure 2c**), flumes (**Figure 2d**), and pipelines (usually made from concrete and metals) [1]. Before the construction of any water-conveying structure, a detailed geotechnical soil test and analysis is recommended to avail the surface and subsurface properties of the soil on which the structure is upon rest. The same soil test and analysis also applies to other types and classes of hydraulic structures to ensure safety and to save

As the name implies, *special-purpose hydraulic structures* are built as an integral part of hydraulic project to meet a special purpose such as hydropower generation (e.g., surge towers and shafts, forebays, and head ponds), navigation (e.g., landings, berths, substations for ship repair, etc.), fishing (e.g., fish nursery ponds, fish lifts and locks, fishways, etc.), water supply for domestic and industrial uses (e.g., water intakes to treatment plant, pumping stations, etc.), waste disposal/sewerage (e.g., sewage headers, pumping stations, channels after treatment plant to water bodies, etc.), and land reclamation (e.g., irrigation canals, drainage systems, silt

only 20–22%, while embankment dams accounted for 78–80%.

which is relative to the dams' height that can cover >300 m [2].

*1.1.1 Water-retaining structures*

**6**

tanks, etc.) [1, 7].

resources.

*(a) Gravity dam, (b) arch dam, (c) buttress dam, (d) multiple-arch dam, (e) earthfill and rockfill dam. Source: [3].*

#### **2. Purposes of hydraulic structures**

Hydraulic structures are purposely for managing and controlling the flow of water in natural and built environment systems. Moreover, the primary purposes may include the following flood control, water conveyance, irrigation, navigation, power generation, domestic and industrial purposes, environment protection, and recreation, among others.

#### **2.1 Flood control**

Flooding is a geophysical hazard that nonuniformly dispersed in both space and time. Over a decade, several watershed areas are frequently suffering from flood disaster, which causes massive destruction and loss of lives, farmlands, crops, access roads, and houses [8]. The effective way of flood control and reducing its negative impacts is by the construction of dams, water conveyance structures, culverts, canals, and reservoirs [9]. Many control structures are not solely constructed mainly for dealing with flood control only. However, sometimes, hydraulic structures are purposely built for flood control only. In the designing and building of flood control structures, some vital point of views must be taken into consideration in such that the cost of construction of such a project structure should be of benefit, concerning the damage reduction and the public interest when comparing to similar benefits to be derived by the alternative means. Also, the flood control structures should be reliable and effective as predicted. Even in some instance, the methods of controlling floods should rather be automatic, not manual.

#### **2.2 Power generation**

Hydropower generation is the production of electrical energy from running water through turbines without reducing its quantity. The flexibility; long-lasting, storing capability; less environmental pollution; and the cost-effectiveness of hydropower plants make it attract more investment as a renewable energy source and role as a way of drought mitigation [10]. It has been demonstrated that hydropower generated about 16.4% of the global total electricity supply equivalent to the installed capacity of about 1064 GW [9]. The hydropower system is the leading global source of an estimated 71% of total renewable energy. Furthermore, hydropower plant reservoirs can also be used as a tool in minimizing the adverse impacts of climate change and in achieving sustainable development goals [11].

#### **2.3 Navigation**

Inland water transportation plays a significant role in the national and global markets. Building dams and draining of river streams will considerably raise the capacity of inland water transportation, thereby allowing the smooth movement of a shipping vessel. An important point to note is that a chain of storage reservoirs would advance navigation depth, straightening out navigation channels, and support the passage of both small, medium, and even large ships. However, it is recommended to provide pathways or locks for vessels when dam structures are built on a large river stream for easy navigation from upstream to the downstream. Also, the topography of the surrounding environment should be taken into consideration. Hence, the pathways might be an integral part of the dam or a completely different structure.

**9**

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

Recently, it was reported that about 20% of the global total arable land is under different forms of irrigation schemes. More than 70% of freshwater withdrawn from rivers is utilized for irrigating crops, and 75% of the total water hardly returns to the rivers [1]. In many regions of the world, with water scarcity, farming without irrigation would not be possible. The quantity of water kept in the storage reservoirs and the power required for water pumping are provided by hydropower plants, which are integral parts of the multipurpose hydraulic structure. In the present world, irrigation projects depend on the supply from multipurpose hydraulic dams, reservoirs, and rivers. For irrigation schemes to be successful, the water supply from sources must be adequately available whenever needed and at a reasonable cost of investment. Also, the operation and maintenance of such a structure should be

A large quantity of freshwater is being consumed daily by food processing; mineral mining and processing; textile, paper, and pulps; nuclear and thermal power plants; and drugs and pharmaceutical, petrochemical, and metallurgical industries, among others. However, some of the major industries that use a large volume of water are nuclear and thermal power plants. To meet both domestic and industrial needs, due to the higher demand for water by many industries, especially in industrially developed nations, large capacity storage structures are always built to store local rainfall runoff and water diverted from other river basins. Multipurpose hydraulic structures are the primary storage and sources of most water supply for domestic and industrial purposes. Although public water consumption constitutes nearly only 10% of the water consumed by the industries, still the immediate needs of public water supply must be taken seriously [12]. The water supply from hydraulic projects should always meet the standards of quality required for domestic and industrial uses in terms of its color, test, hardness, odor, and bacterial purity. Also, the treatment methods for the water should be cost-effective and daily available all year round. Necessary control and protection measures should be provided in the river basin areas where the hydraulic project is sited which are mainly for the municipal water supply. The need for hydraulic projects is also in a region with the

Another vital reason for hydraulic projects is for environmental protection and water management, which may include farmland improvement by controlling soil erosion; environmentally friendly hydropower supply; improved quality water supply for human, animal, and industrial consumption; aquatic food supply; and recreational development [8]. Nevertheless, the negative impacts posed by the massive hydraulic structures on the environment and public safety should always be considered in the course of design and construction processes [1]. The essential environmental issues are for the well-being of people living around the hydraulic projects and to the other plants and animals for the social needs of humankind.

Many hydraulic projects also serve as a place for tourism, recreational, and sports activities. In fact, in some countries, sometimes hydraulic projects are

**2.4 Irrigation schemes**

smooth and cost-effective.

**2.5 Municipal and industrial water supply**

seasonal variation of rainfall distribution of the year.

**2.6 Environment protection**

**2.7 Recreation and other purposes**

#### **2.4 Irrigation schemes**

*Hydraulic Structures - Theory and Applications*

**2. Purposes of hydraulic structures**

recreation, among others.

**2.1 Flood control**

manual.

**2.2 Power generation**

ment goals [11].

**2.3 Navigation**

Hydraulic structures are purposely for managing and controlling the flow of water in natural and built environment systems. Moreover, the primary purposes may include the following flood control, water conveyance, irrigation, navigation, power generation, domestic and industrial purposes, environment protection, and

Flooding is a geophysical hazard that nonuniformly dispersed in both space and time. Over a decade, several watershed areas are frequently suffering from flood disaster, which causes massive destruction and loss of lives, farmlands, crops, access roads, and houses [8]. The effective way of flood control and reducing its negative impacts is by the construction of dams, water conveyance structures, culverts, canals, and reservoirs [9]. Many control structures are not solely constructed mainly for dealing with flood control only. However, sometimes, hydraulic structures are purposely built for flood control only. In the designing and building of flood control structures, some vital point of views must be taken into consideration in such that the cost of construction of such a project structure should be of benefit, concerning the damage reduction and the public interest when comparing to similar benefits to be derived by the alternative means. Also, the flood control structures should be reliable and effective as predicted. Even in some instance, the methods of controlling floods should rather be automatic, not

Hydropower generation is the production of electrical energy from running water through turbines without reducing its quantity. The flexibility; long-lasting, storing capability; less environmental pollution; and the cost-effectiveness of hydropower plants make it attract more investment as a renewable energy source and role as a way of drought mitigation [10]. It has been demonstrated that hydropower generated about 16.4% of the global total electricity supply equivalent to the installed capacity of about 1064 GW [9]. The hydropower system is the leading global source of an estimated 71% of total renewable energy. Furthermore, hydropower plant reservoirs can also be used as a tool in minimizing the adverse impacts of climate change and in achieving sustainable develop-

Inland water transportation plays a significant role in the national and global markets. Building dams and draining of river streams will considerably raise the capacity of inland water transportation, thereby allowing the smooth movement of a shipping vessel. An important point to note is that a chain of storage reservoirs would advance navigation depth, straightening out navigation channels, and support the passage of both small, medium, and even large ships. However, it is recommended to provide pathways or locks for vessels when dam structures are built on a large river stream for easy navigation from upstream to the downstream. Also, the topography of the surrounding environment should be taken into consideration. Hence, the pathways might be an integral part of the dam or a completely different

**8**

structure.

Recently, it was reported that about 20% of the global total arable land is under different forms of irrigation schemes. More than 70% of freshwater withdrawn from rivers is utilized for irrigating crops, and 75% of the total water hardly returns to the rivers [1]. In many regions of the world, with water scarcity, farming without irrigation would not be possible. The quantity of water kept in the storage reservoirs and the power required for water pumping are provided by hydropower plants, which are integral parts of the multipurpose hydraulic structure. In the present world, irrigation projects depend on the supply from multipurpose hydraulic dams, reservoirs, and rivers. For irrigation schemes to be successful, the water supply from sources must be adequately available whenever needed and at a reasonable cost of investment. Also, the operation and maintenance of such a structure should be smooth and cost-effective.

#### **2.5 Municipal and industrial water supply**

A large quantity of freshwater is being consumed daily by food processing; mineral mining and processing; textile, paper, and pulps; nuclear and thermal power plants; and drugs and pharmaceutical, petrochemical, and metallurgical industries, among others. However, some of the major industries that use a large volume of water are nuclear and thermal power plants. To meet both domestic and industrial needs, due to the higher demand for water by many industries, especially in industrially developed nations, large capacity storage structures are always built to store local rainfall runoff and water diverted from other river basins. Multipurpose hydraulic structures are the primary storage and sources of most water supply for domestic and industrial purposes. Although public water consumption constitutes nearly only 10% of the water consumed by the industries, still the immediate needs of public water supply must be taken seriously [12]. The water supply from hydraulic projects should always meet the standards of quality required for domestic and industrial uses in terms of its color, test, hardness, odor, and bacterial purity. Also, the treatment methods for the water should be cost-effective and daily available all year round. Necessary control and protection measures should be provided in the river basin areas where the hydraulic project is sited which are mainly for the municipal water supply. The need for hydraulic projects is also in a region with the seasonal variation of rainfall distribution of the year.

#### **2.6 Environment protection**

Another vital reason for hydraulic projects is for environmental protection and water management, which may include farmland improvement by controlling soil erosion; environmentally friendly hydropower supply; improved quality water supply for human, animal, and industrial consumption; aquatic food supply; and recreational development [8]. Nevertheless, the negative impacts posed by the massive hydraulic structures on the environment and public safety should always be considered in the course of design and construction processes [1]. The essential environmental issues are for the well-being of people living around the hydraulic projects and to the other plants and animals for the social needs of humankind.

#### **2.7 Recreation and other purposes**

Many hydraulic projects also serve as a place for tourism, recreational, and sports activities. In fact, in some countries, sometimes hydraulic projects are

specially constructed for recreation purposes. Some recreational activities carried out at the hydraulic project sites might include swimming, fishing, boating, canoeing, scuba diving, and lakeside walking. Recreational activities provide job opportunities to the teeming population and generate incomes to the government and, at the same time, conserve the natural environment.

#### **3. Operation and maintenance of hydraulic structures**

Strategies for sustainable operation and maintenance of hydraulic structures are initiated before design and are optimized during its service life for the safety of lives and properties, which stabilizes the environment and the national economy. Consequently, improper hydraulic structures' operation and maintenance may lead to loss of life, properties, economy, and the environment. The responsibilities for the operation and maintenance of hydraulic systems vary in different countries, depending on the ownership and purposes. In Nigeria, the responsibilities rest on the central government, coordinated by the department of water resources. This section has highlighted the necessary strategies for safe operation, maintenance, and consequences due to failure. The strategies can be long term, seasonal, frequent, and daily. The primary tasks to exemplary operation and maintenance of hydraulic structures according to Chen [1] are as follows: hydrologic monitoring and forecasting, detection and mitigation of aging of structures, safety surveillance and instrumentations, and remedial actions.

#### **3.1 Hydrologic monitoring and forecasting**

Safe operation and management of hydraulic structure primarily depend on the efficiency of metrological stations to provide independent data of water regime and observation. The data obtained can be used during the analysis and prediction of future hydrologic events. Nowadays, automated facilities are installed at various locations in the catchment area to provide hydrologic data. After the analysis of the data, the forecasted value and period must be provided with some reliable accuracy. The short-term forecasting, developed on runoff and other fundamental theories, provides the basis of flood controls in the catchment. Mid- and long-term forecasting give essential information to the hydropower sector [1].

#### **3.2 Safety surveillance and instrumentations**

The continuous, systematic assessments of the physical condition of hydraulic structures without compromise are encouraged. The large capacity hydraulic structures constitute a more significant threat to downstream life and properties. Mostly, failure arises from extreme flood events and inter- or obvious structural distress, which necessitates safety surveillance and instrumentation programs to detect the possible symptom and specific problem at an early stage in hydraulic structures and create strategies for the solution to the possible abnormalities [1, 13]. The selection and installation of equipment or instrumentation at appropriate locations in the surveillance area, adequate interpretation of the surveillance data, and immediate actions are more important than the number of instruments installed.

#### *3.2.1 Safety inspection*

The safety inspection is a regular inspection of some deteriorations to determine the current state of hydraulic structures based on purposes related to the operation.

**11**

operations.

**3.3 Remedial actions**

remedial measures included:

and abdication

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

put into the remedial action plan.

*3.2.2 Surveillance and instrumentation*

Safety inspections are categorized into routine, specialized, and periodic inspections. Specifically, the embankments of large capacity structures should be closely and routinely examined against any physical defect [13]. This inspection is categorized into routine, specialized, and periodic inspections [1], and thus, their cumulative records determine whether a defect is new, gradual, and/or rapidly changing in the structures [13]. The routine inspection aims to identify the physical deficiencies of the hydraulic structures during day-to-day operations. Periodic inspections are carried out by experienced technical crews at an interval of 2–3 years and are meant to detect physical defects on the structures by visual examination so that strategic remedial actions can be taken. Specialized inspections include earthquake and check-flood inspections. Earthquake and check-flood are identified as a potential threat to hydraulic structures. Their inspection is carried out by experienced and well-trained dam engineers. Thus, the documented reports for mitigations are then

Surveillance is the continuous monitoring of physical conditions through medium to large instruments. It is being done to check the deterioration concerning the actual performance of the hydraulic structure and its trends for compliance with the design expectations. In this operation, the collection, presentation, and evaluation of data from the equipment installed in the system are paramount. The equipment must cover critical components and should be installed at positions where normal behavior is anticipated. It is a good practice to draft an ideal instrumentational plan at an early stage to eliminate the less essential provisions until an adequate, balanced, and affordable plan is determined. In large-scale structures such as a dam, surveillance through high-level technology should be enhanced. Monitoring of change in temperature and cracks occurring in the embankments are used to reveal seepage and sediments during

Remedial actions are meant to prevent failures of hydraulic structures, especially the large capacity structures that pose a significant threat to lives and properties. The deficiencies are classified as minor, moderate, and major accidents [1]. Their remedial actions are necessary before the failure of the entire structure. The defects may earlier be detected through surveillance, and the defects may probably be design-related, such as improper design capacity, or construction-related such as inappropriate choice of materials. The common and challenging operation- and maintenance-related incidents are the rapid rises in seepage, overtopping of earth embankment, excessive beaching, erosion of spillway and embankments, cracking in the concrete dam and spillway, and fractured gates. The remedial actions to be considered depend on the condition of structures and hydrologic events. The

1.Preventive control to reduce the condition from escalation

2.Short-term actions to modify the nearby catchment conditions, such as increasing surveillance, emergency evacuations, and lowering the overtopping

3.Long-term remedies in the structures, such as reinforcements, gates, dredging,

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

*Hydraulic Structures - Theory and Applications*

the same time, conserve the natural environment.

and instrumentations, and remedial actions.

**3.1 Hydrologic monitoring and forecasting**

ing give essential information to the hydropower sector [1].

actions are more important than the number of instruments installed.

**3.2 Safety surveillance and instrumentations**

**3. Operation and maintenance of hydraulic structures**

specially constructed for recreation purposes. Some recreational activities carried out at the hydraulic project sites might include swimming, fishing, boating, canoeing, scuba diving, and lakeside walking. Recreational activities provide job opportunities to the teeming population and generate incomes to the government and, at

Strategies for sustainable operation and maintenance of hydraulic structures are initiated before design and are optimized during its service life for the safety of lives and properties, which stabilizes the environment and the national economy. Consequently, improper hydraulic structures' operation and maintenance may lead to loss of life, properties, economy, and the environment. The responsibilities for the operation and maintenance of hydraulic systems vary in different countries, depending on the ownership and purposes. In Nigeria, the responsibilities rest on the central government, coordinated by the department of water resources. This section has highlighted the necessary strategies for safe operation, maintenance, and consequences due to failure. The strategies can be long term, seasonal, frequent, and daily. The primary tasks to exemplary operation and maintenance of hydraulic structures according to Chen [1] are as follows: hydrologic monitoring and forecasting, detection and mitigation of aging of structures, safety surveillance

Safe operation and management of hydraulic structure primarily depend on the efficiency of metrological stations to provide independent data of water regime and observation. The data obtained can be used during the analysis and prediction of future hydrologic events. Nowadays, automated facilities are installed at various locations in the catchment area to provide hydrologic data. After the analysis of the data, the forecasted value and period must be provided with some reliable accuracy. The short-term forecasting, developed on runoff and other fundamental theories, provides the basis of flood controls in the catchment. Mid- and long-term forecast-

The continuous, systematic assessments of the physical condition of hydraulic structures without compromise are encouraged. The large capacity hydraulic structures constitute a more significant threat to downstream life and properties. Mostly, failure arises from extreme flood events and inter- or obvious structural distress, which necessitates safety surveillance and instrumentation programs to detect the possible symptom and specific problem at an early stage in hydraulic structures and create strategies for the solution to the possible abnormalities [1, 13]. The selection and installation of equipment or instrumentation at appropriate locations in the surveillance area, adequate interpretation of the surveillance data, and immediate

The safety inspection is a regular inspection of some deteriorations to determine the current state of hydraulic structures based on purposes related to the operation.

**10**

*3.2.1 Safety inspection*

Safety inspections are categorized into routine, specialized, and periodic inspections. Specifically, the embankments of large capacity structures should be closely and routinely examined against any physical defect [13]. This inspection is categorized into routine, specialized, and periodic inspections [1], and thus, their cumulative records determine whether a defect is new, gradual, and/or rapidly changing in the structures [13]. The routine inspection aims to identify the physical deficiencies of the hydraulic structures during day-to-day operations. Periodic inspections are carried out by experienced technical crews at an interval of 2–3 years and are meant to detect physical defects on the structures by visual examination so that strategic remedial actions can be taken. Specialized inspections include earthquake and check-flood inspections. Earthquake and check-flood are identified as a potential threat to hydraulic structures. Their inspection is carried out by experienced and well-trained dam engineers. Thus, the documented reports for mitigations are then put into the remedial action plan.

#### *3.2.2 Surveillance and instrumentation*

Surveillance is the continuous monitoring of physical conditions through medium to large instruments. It is being done to check the deterioration concerning the actual performance of the hydraulic structure and its trends for compliance with the design expectations. In this operation, the collection, presentation, and evaluation of data from the equipment installed in the system are paramount. The equipment must cover critical components and should be installed at positions where normal behavior is anticipated. It is a good practice to draft an ideal instrumentational plan at an early stage to eliminate the less essential provisions until an adequate, balanced, and affordable plan is determined. In large-scale structures such as a dam, surveillance through high-level technology should be enhanced. Monitoring of change in temperature and cracks occurring in the embankments are used to reveal seepage and sediments during operations.

#### **3.3 Remedial actions**

Remedial actions are meant to prevent failures of hydraulic structures, especially the large capacity structures that pose a significant threat to lives and properties. The deficiencies are classified as minor, moderate, and major accidents [1]. Their remedial actions are necessary before the failure of the entire structure. The defects may earlier be detected through surveillance, and the defects may probably be design-related, such as improper design capacity, or construction-related such as inappropriate choice of materials. The common and challenging operation- and maintenance-related incidents are the rapid rises in seepage, overtopping of earth embankment, excessive beaching, erosion of spillway and embankments, cracking in the concrete dam and spillway, and fractured gates. The remedial actions to be considered depend on the condition of structures and hydrologic events. The remedial measures included:


#### *3.3.1 Emergency remedial actions*


#### **3.4 Detection and mitigation of aging**

#### *3.4.1 Aging of hydraulic structures*

Aging of a hydraulic structure is referring to the time-related deformations in the properties of the material and its foundation used during construction of the hydraulic structures, which developed within at least 5 years of working period. Also, it is the entire lifespan of hydraulic structure before abdication or decommissions. The deterioration of the structures may be due to the defects developed through unusual events such as an earthquake or a result of environmental factors during service life.

#### *3.4.2 Detection of aging*

Detection of aging should start during the operation and maintenance of hydraulic structures. Factors that influence the degradation of the structural properties of hydraulic systems should be identified and must immediately be managed. Alternatively, nondestructive examinations could be essential to detect the aging of hydraulic structures. The nondestructive examinations are the direct and indirect evaluation of information regarding the state of the hydraulic structure. This is to allow for immediate interventions in the situation and avoid severe consequences. Indirect assessment of aging should be accomplished by monitoring the effects and consequences of aging.

On the other hand, the direct assessment is performed by inspecting and testing the data of the structural properties of the hydraulic structures. The laboratory experiments and the in situ assessments, where the physical and mechanical properties of the sediment, including concrete, are extracted and analyzed, are examples of destructive examination. According to Chen [1], the destructive examination with in situ tests may or may not be destructive. The destructive examinations may include (i) hydraulic pumping tests for porosity and (ii) permeability and leak detection through a physical and chemical test of catchment and leakage, among others.

Similarly, a nondestructive examination is designed to ascertain the flows of materials while it protects the object's usability, successfully nondestructive tests, and requires an understanding of its limitations and data manipulation. Various methods, such as electromagnetic, resistivity, acoustic, induce polarization, and visual assessment, are employed.

#### *3.4.3 Mitigations for aging*

Adequate mitigations of aging of hydraulic structures start during the designs, effected during construction, which continues through monitoring and surveillance

**13**

**4.1 Erosion**

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

istered for overlay operations.

**4. Challenges facing hydraulic structures**

commendable:

in operation and maintenance stages. The prior understanding of the factors that influence the degradation of the structural properties of the materials used in the constructions of the hydraulic structures must be scrutinized. Also, the provision of extra quality to meet the designed lifespan of the system must be put into consideration during the constructions. Alternatively, the following mitigations steps are

a.*Analysis:* The analysis of the aging process is carried out to ascertain its severity

b.*Prevention:* It is well known that all structural materials have a finite lifespan and can be affected by the environment. The prevention stage to mitigate aging of a hydraulic structure is proceeded by detailed analysis to know the structure's safety and its economic condition. If the effect is infinite, immediate remedial action such as an emergency action plan is necessary. However, if the effect is finite, and the structure has an economic lifespan, then, provision of

to the safety of life, properties, national economy, and environment.

concrete structures from uniquely selected materials is encouraged.

The importance of hydraulic structures cannot be overemphasized, and therefore their maintenance and safe utilization are critical. The structures should neither leak nor erode; channels and structures should be clean and free from siltation with noncorrosive or rotten moving parts. The breakdown or failure of these hydraulic structures can lead to a disastrous situation within the surrounding areas.

For instance, a catastrophic dam collapse could lead to flooding and erosion. The challenges of maintaining hydraulic structures at the initial stage can be achieved by managing the characteristic of the flow to meet the desired goal of the project needs. According to Chen [1], this can be realized by considering the public safety and ecological, environmental, and the design objectives of each structure. Some of the challenges facing hydraulic structures and the way they can

Soil is a nonrenewable resource that supports human and animal life. Soil provides living beings with food, fiber, and protection from harsh environmental conditions such as high temperatures and heavy rainfall. Soil is lost due to erosion as a result of continuous cultivation of land, drastic reduction in vegetation, and collapsing of hydraulic structures such as dams. Erosion is the washing away of the topmost soil layer by the agents of erosion, including water, wind, and human activities [14]. Erosion by water is caused by overland flow and transport of sediments due to the interactive action of water flow and heavy rain droplets. In hydraulic structures, erosion can occur in canals, for example, in an unlined canal at downstream or lined canal section that receives water jet flow from a gate or pipe or water that spills over a weir. This type of erosion can be remediated by dissipating the energy of the incoming water through the construction of a stilling

be addressed are further discussed in the subsequent section.

c.*Rehabilitations:* Many physical and chemical methods like geomembrane are employed to enhance waterproof. Additionally, the repair and replacement of corroded steels and the use of excellent impermeable materials are also admin-

#### *Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

*Hydraulic Structures - Theory and Applications*

a.*Erosion control:* During floods, the use of polyethylene sheeting and sandbag

b.*Overtopping control:* Overtopping must be avoided, and the provision of tempo-

c.*Seepage control:* The seepage must not be allowed to saturate the downstream slope, and if saturated, the provision of permeable material to reduce pressure

Aging of a hydraulic structure is referring to the time-related deformations in the properties of the material and its foundation used during construction of the hydraulic structures, which developed within at least 5 years of working period. Also, it is the entire lifespan of hydraulic structure before abdication or decommissions. The deterioration of the structures may be due to the defects developed through unusual events such as an earthquake or a result of environmental factors

Detection of aging should start during the operation and maintenance of hydraulic structures. Factors that influence the degradation of the structural properties of hydraulic systems should be identified and must immediately be managed. Alternatively, nondestructive examinations could be essential to detect the aging of hydraulic structures. The nondestructive examinations are the direct and indirect evaluation of information regarding the state of the hydraulic structure. This is to allow for immediate interventions in the situation and avoid severe consequences. Indirect assessment of aging should be accomplished by monitoring the effects and

On the other hand, the direct assessment is performed by inspecting and testing the data of the structural properties of the hydraulic structures. The laboratory experiments and the in situ assessments, where the physical and mechanical properties of the sediment, including concrete, are extracted and analyzed, are examples of destructive examination. According to Chen [1], the destructive examination with in situ tests may or may not be destructive. The destructive examinations may include (i) hydraulic pumping tests for porosity and (ii) permeability and leak detection through a physical and chemical test of catchment and leakage, among others. Similarly, a nondestructive examination is designed to ascertain the flows of materials while it protects the object's usability, successfully nondestructive tests, and requires an understanding of its limitations and data manipulation. Various methods, such as electromagnetic, resistivity, acoustic, induce polarization, and

Adequate mitigations of aging of hydraulic structures start during the designs, effected during construction, which continues through monitoring and surveillance

controls the erosion of the slope embankment [1].

rary barrier above the predicted altitude is applied.

buildup on the embankment is needed.

**3.4 Detection and mitigation of aging**

*3.4.1 Aging of hydraulic structures*

during service life.

*3.4.2 Detection of aging*

consequences of aging.

visual assessment, are employed.

*3.4.3 Mitigations for aging*

*3.3.1 Emergency remedial actions*

**12**

in operation and maintenance stages. The prior understanding of the factors that influence the degradation of the structural properties of the materials used in the constructions of the hydraulic structures must be scrutinized. Also, the provision of extra quality to meet the designed lifespan of the system must be put into consideration during the constructions. Alternatively, the following mitigations steps are commendable:


#### **4. Challenges facing hydraulic structures**

The importance of hydraulic structures cannot be overemphasized, and therefore their maintenance and safe utilization are critical. The structures should neither leak nor erode; channels and structures should be clean and free from siltation with noncorrosive or rotten moving parts. The breakdown or failure of these hydraulic structures can lead to a disastrous situation within the surrounding areas. For instance, a catastrophic dam collapse could lead to flooding and erosion.

The challenges of maintaining hydraulic structures at the initial stage can be achieved by managing the characteristic of the flow to meet the desired goal of the project needs. According to Chen [1], this can be realized by considering the public safety and ecological, environmental, and the design objectives of each structure. Some of the challenges facing hydraulic structures and the way they can be addressed are further discussed in the subsequent section.

#### **4.1 Erosion**

Soil is a nonrenewable resource that supports human and animal life. Soil provides living beings with food, fiber, and protection from harsh environmental conditions such as high temperatures and heavy rainfall. Soil is lost due to erosion as a result of continuous cultivation of land, drastic reduction in vegetation, and collapsing of hydraulic structures such as dams. Erosion is the washing away of the topmost soil layer by the agents of erosion, including water, wind, and human activities [14]. Erosion by water is caused by overland flow and transport of sediments due to the interactive action of water flow and heavy rain droplets. In hydraulic structures, erosion can occur in canals, for example, in an unlined canal at downstream or lined canal section that receives water jet flow from a gate or pipe or water that spills over a weir. This type of erosion can be remediated by dissipating the energy of the incoming water through the construction of a stilling basin as part of the hydraulic structure immediately downstream of the pipe or weir [15]. Another critical point of canals that is prone to erosion is the intersection of a lined and unlined canal, that is, the transition point from a lined canal to the unlined canal, as shown in **Figure 3**. This type of problem is called undermining and, if not taken care of, can cause a collapse of the lining and destruction of the structure [16]. So, periodic maintenance should be observed to solve this problem. Undermining can be avoided or controlled by the provision of cutoff that will protect the foundation of the structure.

#### **4.2 Leakage**

Leakage in hydraulic structures refers to the ability of confined or upstream water bodies to exploit the least available exit, space, or crack underneath or along the structure to escape to the downstream or unconfined surrounding area. The moment the water found these small spaces, then there is a leakage problem, which is the beginning of erosion in the area. These small openings and cracks are widened with time and intensity of leakage. Thus, the soil is washed away as time goes on and the structure will collapse. At this point, preventing the collapse of such a structure will be very difficult. Take a dam, for instance, the water level is very high at the upstream. Water can flow along the dam embankment; if no measure is taken to save the structure, it can be undermined and collapse due to erosion [17].

It has been recommended by van den Bosch and Snellen [16] to observe and identify leakages at their initial stage and correct them. Leakages in the crack can be repaired by cleaning the wall or the floor where the crack is located. Then remove any sand, clay, plant growth, or debris. Open up the crack to become broader and more in-depth. Prepare cement-sand mortar to fill the hole and smoothen it with a trowel. Provide adequate curing to the repaired crack.

On the other hand, vertical cutoffs can be constructed on the structures to obstruct the flow of water underneath and along with the structure. An example of a cutoff wall in a dam is showcased in **Figure 4a**. Similarly, drop structures can also be equipped with cutoffs to block the water flow along and underneath the structure (**Figure 4b**). The cutoffs are part of the structure, driven into the embankments of a canal by digging deep into the banks of the canal and canal bed. During the installation, the earth around the canal banks and the cutoffs must be well compacted.

**15**

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

Siltation is the process of deposition of debris and sand particles and their buildup in hydraulic structures that obstruct the full functioning of the structures. The problems caused by siltation are usually the changes in water flow, changes in velocities and water levels, decreased energy dissipation, and so on. Examples of these problems include deposition of large volumes of sand in the intake chamber of pumps, which usually causes damage to the pumps and subsequent silting of the canals by sand particles. Another instance is siltation at the stilling basin. This type of sand deposits reduces the energy dissipation of the structure. Similarly, the changes in flow and velocities of water inflow division box are affected by sand particles deposited in the structure [16]. Because of these problems, large sand traps are usually constructed at the end of the upper main

*(a) The function of the cutoff here was to prevent piping failure and reduce leakage or seepage. The cutoff was constructed parallel to the centerline of the dam (b) intake structure provided with a concrete cutoff wall.*

canal to collect the sand deposits and remove them by periodic cleaning.

Hydraulic structures are made from different materials, including concrete, wood, or steel. These structures are liable to deterioration with time and with alternating wet and dry conditions subjected. The wooden parts in the structure, for instance, rot and decompose, whereas the steel parts corrode, as a rule, causing their expansion, and get jammed in the sliding slots. Such a condition affects the smooth operation of the structures. Routine maintenance is necessary to curtail the problems and reduce their effects. Painting of the affected parts can preserve them against corrosion. Lubrication of moving parts (steel) such as sluice gates and

**4.3 Siltation**

**Figure 4.**

**4.4 Corrosion/rot**

valves can prevent jamming.

**Figure 3.** *Points of transition between a lined and unlined canal.*

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

#### **Figure 4.**

*Hydraulic Structures - Theory and Applications*

protect the foundation of the structure.

**4.2 Leakage**

erosion [17].

well compacted.

basin as part of the hydraulic structure immediately downstream of the pipe or weir [15]. Another critical point of canals that is prone to erosion is the intersection of a lined and unlined canal, that is, the transition point from a lined canal to the unlined canal, as shown in **Figure 3**. This type of problem is called undermining and, if not taken care of, can cause a collapse of the lining and destruction of the structure [16]. So, periodic maintenance should be observed to solve this problem. Undermining can be avoided or controlled by the provision of cutoff that will

Leakage in hydraulic structures refers to the ability of confined or upstream water bodies to exploit the least available exit, space, or crack underneath or along the structure to escape to the downstream or unconfined surrounding area. The moment the water found these small spaces, then there is a leakage problem, which is the beginning of erosion in the area. These small openings and cracks are widened with time and intensity of leakage. Thus, the soil is washed away as time goes on and the structure will collapse. At this point, preventing the collapse of such a structure will be very difficult. Take a dam, for instance, the water level is very high at the upstream. Water can flow along the dam embankment; if no measure is taken to save the structure, it can be undermined and collapse due to

It has been recommended by van den Bosch and Snellen [16] to observe and identify leakages at their initial stage and correct them. Leakages in the crack can be repaired by cleaning the wall or the floor where the crack is located. Then remove any sand, clay, plant growth, or debris. Open up the crack to become broader and more in-depth. Prepare cement-sand mortar to fill the hole and smoothen it with a

On the other hand, vertical cutoffs can be constructed on the structures to obstruct the flow of water underneath and along with the structure. An example of a cutoff wall in a dam is showcased in **Figure 4a**. Similarly, drop structures can also be equipped with cutoffs to block the water flow along and underneath the structure (**Figure 4b**). The cutoffs are part of the structure, driven into the embankments of a canal by digging deep into the banks of the canal and canal bed. During the installation, the earth around the canal banks and the cutoffs must be

trowel. Provide adequate curing to the repaired crack.

**14**

**Figure 3.**

*Points of transition between a lined and unlined canal.*

*(a) The function of the cutoff here was to prevent piping failure and reduce leakage or seepage. The cutoff was constructed parallel to the centerline of the dam (b) intake structure provided with a concrete cutoff wall.*

#### **4.3 Siltation**

Siltation is the process of deposition of debris and sand particles and their buildup in hydraulic structures that obstruct the full functioning of the structures. The problems caused by siltation are usually the changes in water flow, changes in velocities and water levels, decreased energy dissipation, and so on. Examples of these problems include deposition of large volumes of sand in the intake chamber of pumps, which usually causes damage to the pumps and subsequent silting of the canals by sand particles. Another instance is siltation at the stilling basin. This type of sand deposits reduces the energy dissipation of the structure. Similarly, the changes in flow and velocities of water inflow division box are affected by sand particles deposited in the structure [16]. Because of these problems, large sand traps are usually constructed at the end of the upper main canal to collect the sand deposits and remove them by periodic cleaning.

#### **4.4 Corrosion/rot**

Hydraulic structures are made from different materials, including concrete, wood, or steel. These structures are liable to deterioration with time and with alternating wet and dry conditions subjected. The wooden parts in the structure, for instance, rot and decompose, whereas the steel parts corrode, as a rule, causing their expansion, and get jammed in the sliding slots. Such a condition affects the smooth operation of the structures. Routine maintenance is necessary to curtail the problems and reduce their effects. Painting of the affected parts can preserve them against corrosion. Lubrication of moving parts (steel) such as sluice gates and valves can prevent jamming.

#### **Author details**

Musa Abubakar Tadda1,2, Amimul Ahsan3,4\*, Monzur Imteaz4 , Abubakar Shitu1,2, Umar Abdulbaki Danhassan1,5 and Aliyu Idris Muhammad1,2

1 College of Biosystems Engineering and Food Science, Zhejiang University, Hangzhou, China

2 Department of Agricultural and Environmental Engineering, Faculty of Engineering, Bayero University, Kano, Nigeria

3 Department of Civil Engineering, Uttara University, Dhaka, Bangladesh

4 Department of Civil and Construction Engineering, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Australia

5 Department of Agricultural and Bio-environmental Engineering, SCA/DAC, Ahmadu Bello University, Zaria, Nigeria

\*Address all correspondence to: ashikcivil@yahoo.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**17**

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

[10] Chilkoti V, Bolisetti T,

Balachandar R. Climate change impact assessment on hydropower generation using multi-model climate ensemble. Renewable Energy. 2017;**109**:510-517

[11] Hasan MM, Wyseure G. Impact of climate change on hydropower generation in Rio Jubones Basin, Ecuador. Water Science and Engineering. 2018;**11**(2):157-166

[12] Kucukali S. Municipal water supply dams as a source of small hydropower

[13] Zhu P, Leng YB, Zhou Y, Jiang GL.

in Turkey. Renewable Energy.

Safety inspection strategy for earth embankment dams using fully distributed sensing. Procedia Engineering. 2011;**8**:520-526

[14] van Lier HN, Pereira LS, Steiner FR. CIGR Handbook of Agricultural Engineering, First., Vol. I, No. 2. United States of America: American Society of Agricultural

[15] Hager WH, Boes RM. Hydraulic structures: A positive outlook into the future. Journal of Hydraulic Research.

[16] van den Bosch BE, Snellen WB. Structures for Water Control and Distribution. Rome: Food & Agriculture

Organisations - Technology &

[17] Paxson GS, McCann MWJ,

Landis ME. A risk based framework for evaluating gated spillway operations. In: Hydraulic Structures and Water System Management. 6th IAHR International Symposium on Hydraulic Structures; Portland, OR; 27-30 June, 2016.

Engineers; 1999

2014;**52**(3):299-310

Engineering; 1993

pp. 630-640

2010;**35**(9):2001-2007

[1] Chen S. Hydraulic Structures, First

[2] ICOLD. 2019 Data. International Commission on Large Dams [Online]. 2019. Available from: https://www. icold-cigb.org/GB/world\_register/

[3] How it Works: Dam Engineering [Online]. 2013. Available from: https:// www.howitworksdaily.com/damengineering/ [Accessed: 07 October

[4] Panoramio [Online]. 2019. Available from: http://www.panoramio.com/ photo/14830796 [Accessed: 07 October

Aqueducts Could Spill Climate Secrets. Earth and Space Science [Online]. 2015. Available from: https://eos.org/articles/ ancient-roman-aqueducts-could-spillclimate-secrets [Accessed: 07 October

[6] OCF. Fiberglass Parshall Flumes at Wastewater Plants. Open Channel Flow [Online]. 2019. Available from: https://www.openchannelflow.com/ blog/fiberglass-parshall-flumes-atwastewater-plants [Accessed: 07

[7] UDFCD. Urban Storm Drainage Criteria Manual: Hydraulic Structures.

[8] Yazdi J, Salehi Neyshabouri SAA. Optimal design of flood-control multireservoir system on a watershed scale. Natural Hazards. 2012;**63**(2):629-646

[9] Nguyen-Tien V, Elliott RJR, Strobl EA. Hydropower generation, flood control and dam cascades: A national assessment for Vietnam. Journal of Hydrology.

[5] JoAnna W. Ancient Roman

edit. London: Springer; 2015

general\_synthesis.asp

**References**

2019]

2019]

2019]

October 2019]

USA: Colorado; 2017

2018;**560**:109-126

*Operation and Maintenance of Hydraulic Structures DOI: http://dx.doi.org/10.5772/intechopen.91949*

### **References**

*Hydraulic Structures - Theory and Applications*

**16**

**Author details**

Hangzhou, China

Australia

Musa Abubakar Tadda1,2, Amimul Ahsan3,4\*, Monzur Imteaz4

Umar Abdulbaki Danhassan1,5 and Aliyu Idris Muhammad1,2

Engineering, Bayero University, Kano, Nigeria

Ahmadu Bello University, Zaria, Nigeria

provided the original work is properly cited.

\*Address all correspondence to: ashikcivil@yahoo.com

1 College of Biosystems Engineering and Food Science, Zhejiang University,

2 Department of Agricultural and Environmental Engineering, Faculty of

3 Department of Civil Engineering, Uttara University, Dhaka, Bangladesh

4 Department of Civil and Construction Engineering, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne,

5 Department of Agricultural and Bio-environmental Engineering, SCA/DAC,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, Abubakar Shitu1,2,

[1] Chen S. Hydraulic Structures, First edit. London: Springer; 2015

[2] ICOLD. 2019 Data. International Commission on Large Dams [Online]. 2019. Available from: https://www. icold-cigb.org/GB/world\_register/ general\_synthesis.asp

[3] How it Works: Dam Engineering [Online]. 2013. Available from: https:// www.howitworksdaily.com/damengineering/ [Accessed: 07 October 2019]

[4] Panoramio [Online]. 2019. Available from: http://www.panoramio.com/ photo/14830796 [Accessed: 07 October 2019]

[5] JoAnna W. Ancient Roman Aqueducts Could Spill Climate Secrets. Earth and Space Science [Online]. 2015. Available from: https://eos.org/articles/ ancient-roman-aqueducts-could-spillclimate-secrets [Accessed: 07 October 2019]

[6] OCF. Fiberglass Parshall Flumes at Wastewater Plants. Open Channel Flow [Online]. 2019. Available from: https://www.openchannelflow.com/ blog/fiberglass-parshall-flumes-atwastewater-plants [Accessed: 07 October 2019]

[7] UDFCD. Urban Storm Drainage Criteria Manual: Hydraulic Structures. USA: Colorado; 2017

[8] Yazdi J, Salehi Neyshabouri SAA. Optimal design of flood-control multireservoir system on a watershed scale. Natural Hazards. 2012;**63**(2):629-646

[9] Nguyen-Tien V, Elliott RJR, Strobl EA. Hydropower generation, flood control and dam cascades: A national assessment for Vietnam. Journal of Hydrology. 2018;**560**:109-126

[10] Chilkoti V, Bolisetti T, Balachandar R. Climate change impact assessment on hydropower generation using multi-model climate ensemble. Renewable Energy. 2017;**109**:510-517

[11] Hasan MM, Wyseure G. Impact of climate change on hydropower generation in Rio Jubones Basin, Ecuador. Water Science and Engineering. 2018;**11**(2):157-166

[12] Kucukali S. Municipal water supply dams as a source of small hydropower in Turkey. Renewable Energy. 2010;**35**(9):2001-2007

[13] Zhu P, Leng YB, Zhou Y, Jiang GL. Safety inspection strategy for earth embankment dams using fully distributed sensing. Procedia Engineering. 2011;**8**:520-526

[14] van Lier HN, Pereira LS, Steiner FR. CIGR Handbook of Agricultural Engineering, First., Vol. I, No. 2. United States of America: American Society of Agricultural Engineers; 1999

[15] Hager WH, Boes RM. Hydraulic structures: A positive outlook into the future. Journal of Hydraulic Research. 2014;**52**(3):299-310

[16] van den Bosch BE, Snellen WB. Structures for Water Control and Distribution. Rome: Food & Agriculture Organisations - Technology & Engineering; 1993

[17] Paxson GS, McCann MWJ, Landis ME. A risk based framework for evaluating gated spillway operations. In: Hydraulic Structures and Water System Management. 6th IAHR International Symposium on Hydraulic Structures; Portland, OR; 27-30 June, 2016. pp. 630-640

**Chapter 3**

*Costel Boariu*

**1. Introduction**

infiltration path.

**19**

solve the following aspects [1]:

**Abstract**

Bottom Discharge Conduit for

The structural calculation methods of the conduits that cross the embankment dams can be divided into two approaches. On the one hand, the estimation of the earth's characteristics is done by the multiparameter subgrade model, and on the other hand, the usual finite element software describes the parameters of the earth based on the modulus of elasticity. The conduits have a moment of inertia value for the cross section that is combined with the modulus of elasticity of the material (concrete, steel) resulting in a great rigidity to the assembly. This stiffness, quantified in the stiffness matrix, is much higher than the rigidity of the soil. This work goes in two directions: on the one hand, it argues that the complex methods of calculating the soil characteristics are not relevant for conduits that cross the embankment dams. Second in the longitudinal direction, the conduit has joints that diminish the rigidity of the assembly and whose effect cannot be included in the FEM calculation, as it is usually done in a plane strain model. A calculation method is proposed that contains an inertial moment adjustment that takes into account joints. Finally, a computational method is used in which FEM is used with the

**Keywords:** bottom discharge conduit, embankment dam, soil-structure interaction, finite element method, multiple-parameter subgrade model, matrix condensation

Bottom discharge conduits are pipes that cross the body of the dam from the upstream to the downstream. Conduits can be made of reinforced concrete or metal. Less rigid materials can be used for small dams (PEHD, GRP-glass reinforced plastic). Passing a conduit through the body of an embankment dam or beneath its foundation requires a lot of caution and adequate construction measures [1]. The contact surface between the pipe and the embankment is a possible way for infiltration. These are prevented by special shoulders that increase the water

The modeling of the interaction between the structure and the earth filler must

a. Calculating the pressures of the embankment on the conduit

b.Assessment of the soil (subgrade) reaction

Embankment Dams

empirically estimated momentum variation.

#### **Chapter 3**

## Bottom Discharge Conduit for Embankment Dams

*Costel Boariu*

#### **Abstract**

The structural calculation methods of the conduits that cross the embankment dams can be divided into two approaches. On the one hand, the estimation of the earth's characteristics is done by the multiparameter subgrade model, and on the other hand, the usual finite element software describes the parameters of the earth based on the modulus of elasticity. The conduits have a moment of inertia value for the cross section that is combined with the modulus of elasticity of the material (concrete, steel) resulting in a great rigidity to the assembly. This stiffness, quantified in the stiffness matrix, is much higher than the rigidity of the soil. This work goes in two directions: on the one hand, it argues that the complex methods of calculating the soil characteristics are not relevant for conduits that cross the embankment dams. Second in the longitudinal direction, the conduit has joints that diminish the rigidity of the assembly and whose effect cannot be included in the FEM calculation, as it is usually done in a plane strain model. A calculation method is proposed that contains an inertial moment adjustment that takes into account joints. Finally, a computational method is used in which FEM is used with the empirically estimated momentum variation.

**Keywords:** bottom discharge conduit, embankment dam, soil-structure interaction, finite element method, multiple-parameter subgrade model, matrix condensation

#### **1. Introduction**

Bottom discharge conduits are pipes that cross the body of the dam from the upstream to the downstream. Conduits can be made of reinforced concrete or metal. Less rigid materials can be used for small dams (PEHD, GRP-glass reinforced plastic). Passing a conduit through the body of an embankment dam or beneath its foundation requires a lot of caution and adequate construction measures [1].

The contact surface between the pipe and the embankment is a possible way for infiltration. These are prevented by special shoulders that increase the water infiltration path.

The modeling of the interaction between the structure and the earth filler must solve the following aspects [1]:

a. Calculating the pressures of the embankment on the conduit

b.Assessment of the soil (subgrade) reaction

c. Calculating the displacements and deformations of the structure

d.Evaluating the state of stress of the cross section and longitudinal section

ground, another deficiency results from the fact that the loads are obtained by a

Everyone agrees that MEF is the best (exact) calculation method. How do we

Most software models the ground through the Winkler springs. Is it accurate enough, or do we need more sophisticated methods of assessing the ground characteristics of the foundation? There are soil-modeling methods [5–7] that quantify the

There are finite element programs (GeoStudio [12]) that model the behavior of the earth using for soil stiffness—Young's modulus (E). This modulus, which represents the stiffness of the soil, is dependent on the effective confining stress. In FEM (finite element method), finally, an equation is obtained that has unknown

Both the use of the multiparameter model subgrade and the use of the modulus

In order to evaluate these calculation methods, the structure and earth influence on the rigidity matrix are calculated next. Considering the pipe geometry (large

In the traditional method for simulation, the mathematical load-deformation response of a beam in uniaxial bending is a differential equation [6]. The basic form

where [*S*] is the stiffness matrix; {*d*} is the displacement vector; {*q*} is the load

The relevance of (Eq. (1)) is that all of the variations in beam behavior can be

p xð Þ¼ kww xð Þ

kw is the Winkler coefficient of subgrade reaction; E is the modulus of elasticity

explained as variations solely in the formulation of the stiffness matrix, [*S*]. In the Winkler model (**Figure 1**), the flexural behavior of this beam is given

w xð Þ

EI <sup>d</sup><sup>4</sup>

where subgrade reaction in one (*x*-axis) direction only is

(Young's modulus); I is the moment of inertia of beam section.

½ � S f gd ¼ f gq (1)

dx4 <sup>þ</sup> p xð Þ¼ q xð Þ (2)

of elasticity as a function of stress represent approximations of the effective

structural horse considering the fixed supports [5].

Winkler spring stiffness and a shear effect in the ground.

displacements and whose terms are stiffness matrices and loads.

length element), it is possible to approximate the pipe with a beam.

**2.1 Stiffness matrix calculation for continuous support**

of the matrix formulation for beam flexure is (Eq. (1)):

define the soil in the calculation model?

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

situation.

(force) vector.

by Eq. (2):

**Figure 1.** *The Winkler model.*

**21**

e. Cross-sectional and longitudinal cross-sectional composition (joints)

Due to the complexity of the interaction among the structure, the foundation, and the filling, the only current method able to accurately model this phenomenon is the finite element method (FEM).

For the first aspect, (a) the Marston theory of embankment pressures has typically been adopted for calculating loads on a conduit that is partially or fully projecting above the original ground surface [2–4]. Using the Marston theory, vertical load on the conduit is considered to be a combination of the weight of the fill directly above the conduit and the frictional forces, acting either upward or downward, from the adjacent fill.

For aspect (b) assessment of the ground reaction, there are calculation methods in which the behavior of the earth is modeled by springs with behavior not necessarily linearly elastic with or without interaction between them (between springs) [5]. These models introduce more parameters between the linear stiffness of the soil layers and the shear layers. Later [6, 7] the interaction between the structure and the terrain was described by the beam-column analogy as it incorporates the lowest level multiple-parameter subgrade model possible.

For aspects (c) and (d), guidance on the design and construction of conduits are provided in [2, 3, 8, 9]. The references contain accepted methods to design conduits. Reinforced concrete conduits are used for medium and large dams, and precast pipes are used for small dams, urban levees, and other levees where public safety is at risk or substantial property damage could occur [2]. Corrugated metal pipes are acceptable through agricultural levees where the conduit diameter is 900 mm (36 in.) and when levee embankments are no higher than 4 m (12 ft) above the conduit invert. Inlet structures, intake towers, gate wells, and outlet structures should be constructed of cast-in-place reinforced concrete. However, precast concrete or corrugated metal structures may be used in agricultural and rural levees.

Conduit composition in cross-sectional and longitudinal is detailed in [1, 10]. The conduits are made from 10 to 12-m-long sections in order to be able to adapt without cracking with the eventual differentiation of the foundation ground settlement. The outer shape of the cross sections should consider the interaction of the structure with the filler. Curved vault sections are the most recommended. Rectangular outer sections contour lead to stress concentrations and may lead to cracking of the sealing core along the structure.

Next we aim to find the importance of the assessment of the soil (subgrade) reaction. There are many methods of calculating the soil characteristics [5–8]. Which one is suitable for this type of structure? We propose to answer this question.

#### **2. Interaction between soil and conduit**

Most structural computing software currently used (e.g., SAP 2000 [11]) included only the spring stiffness connection for the ground displacements similar to the Winkler environment. Computational programs with geotechnical specialization allow the adoption of more complex models of behavior for the earth. However, besides the inability to capture the interaction between the structure and the

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

c. Calculating the displacements and deformations of the structure

d.Evaluating the state of stress of the cross section and longitudinal section

Due to the complexity of the interaction among the structure, the foundation, and the filling, the only current method able to accurately model this phenomenon

For the first aspect, (a) the Marston theory of embankment pressures has typi-

For aspect (b) assessment of the ground reaction, there are calculation methods in which the behavior of the earth is modeled by springs with behavior not necessarily linearly elastic with or without interaction between them (between springs) [5]. These models introduce more parameters between the linear stiffness of the soil layers and the shear layers. Later [6, 7] the interaction between the structure and the terrain was described by the beam-column analogy as it incorporates the lowest

For aspects (c) and (d), guidance on the design and construction of conduits are provided in [2, 3, 8, 9]. The references contain accepted methods to design conduits. Reinforced concrete conduits are used for medium and large dams, and precast pipes are used for small dams, urban levees, and other levees where public safety is at risk or substantial property damage could occur [2]. Corrugated metal pipes are acceptable through agricultural levees where the conduit diameter is 900 mm (36 in.) and when levee embankments are no higher than 4 m (12 ft) above the conduit invert. Inlet structures, intake towers, gate wells, and outlet structures should be constructed of cast-in-place reinforced concrete. However, precast concrete or corrugated metal structures may be used in agricultural and

Conduit composition in cross-sectional and longitudinal is detailed in [1, 10]. The conduits are made from 10 to 12-m-long sections in order to be able to adapt without cracking with the eventual differentiation of the foundation ground settlement. The outer shape of the cross sections should consider the interaction of the structure with the filler. Curved vault sections are the most recommended. Rectangular outer sections contour lead to stress concentrations and may lead to cracking

Next we aim to find the importance of the assessment of the soil (subgrade) reaction. There are many methods of calculating the soil characteristics [5–8]. Which one is suitable for this type of structure? We propose to answer this

Most structural computing software currently used (e.g., SAP 2000 [11]) included only the spring stiffness connection for the ground displacements similar to the Winkler environment. Computational programs with geotechnical specialization allow the adoption of more complex models of behavior for the earth. However, besides the inability to capture the interaction between the structure and the

e. Cross-sectional and longitudinal cross-sectional composition (joints)

cally been adopted for calculating loads on a conduit that is partially or fully projecting above the original ground surface [2–4]. Using the Marston theory, vertical load on the conduit is considered to be a combination of the weight of the fill directly above the conduit and the frictional forces, acting either upward or

is the finite element method (FEM).

*Hydraulic Structures - Theory and Applications*

downward, from the adjacent fill.

rural levees.

question.

**20**

level multiple-parameter subgrade model possible.

of the sealing core along the structure.

**2. Interaction between soil and conduit**

ground, another deficiency results from the fact that the loads are obtained by a structural horse considering the fixed supports [5].

Everyone agrees that MEF is the best (exact) calculation method. How do we define the soil in the calculation model?

Most software models the ground through the Winkler springs. Is it accurate enough, or do we need more sophisticated methods of assessing the ground characteristics of the foundation? There are soil-modeling methods [5–7] that quantify the Winkler spring stiffness and a shear effect in the ground.

There are finite element programs (GeoStudio [12]) that model the behavior of the earth using for soil stiffness—Young's modulus (E). This modulus, which represents the stiffness of the soil, is dependent on the effective confining stress. In FEM (finite element method), finally, an equation is obtained that has unknown displacements and whose terms are stiffness matrices and loads.

Both the use of the multiparameter model subgrade and the use of the modulus of elasticity as a function of stress represent approximations of the effective situation.

In order to evaluate these calculation methods, the structure and earth influence on the rigidity matrix are calculated next. Considering the pipe geometry (large length element), it is possible to approximate the pipe with a beam.

#### **2.1 Stiffness matrix calculation for continuous support**

In the traditional method for simulation, the mathematical load-deformation response of a beam in uniaxial bending is a differential equation [6]. The basic form of the matrix formulation for beam flexure is (Eq. (1)):

$$\mathbf{[S]}\{\mathbf{d}\} = \{\mathbf{q}\} \tag{1}$$

where [*S*] is the stiffness matrix; {*d*} is the displacement vector; {*q*} is the load (force) vector.

The relevance of (Eq. (1)) is that all of the variations in beam behavior can be explained as variations solely in the formulation of the stiffness matrix, [*S*].

In the Winkler model (**Figure 1**), the flexural behavior of this beam is given by Eq. (2):

$$\text{EI}\frac{\text{d}^4\text{w}(\text{x})}{\text{dx}^4} + \text{p}(\text{x}) = \text{q}(\text{x}) \tag{2}$$

where subgrade reaction in one (*x*-axis) direction only is

$$\mathbf{p}(\mathbf{x}) = \mathbf{k}\_{\mathbf{w}} \mathbf{w}(\mathbf{x})$$

kw is the Winkler coefficient of subgrade reaction; E is the modulus of elasticity (Young's modulus); I is the moment of inertia of beam section.

**Figure 1.** *The Winkler model.*

Solving Eq. (2) by FEM is expressed by Eq. (3):

$$\mathbf{a} \left( \left[ \mathbf{S}\_{\mathbf{e}} \right] + \left[ \mathbf{S}\_{\mathbf{w}} \right] \right) \{ \mathbf{d} \} = \{ \mathbf{q} \} \tag{3}$$

The meaning of the notations can be inferred from the following equation, which generally defines a stiffness matrix for a finite element with four degrees of

> S11 S12 S13 S14 S21 S22 S23 S24 S31 S32 S33 S34 S41 S42 S43 S44

In the calculation of the beams on elastic support by the finite element method, the determination of the stiffness matrix of the elastic foundation was determined

Eq. (10) is directly suggested by the calculation scheme of **Figure 4** where it can be seen that only the S11 and S33 elements of the stiffness matrix have values other than zero (a Sij element of the stiffness matrix is the generalized force that develops in the direction i when a unit displacement or rotation is imposed in the direction j). Eq. (10) can also be obtained by solving Eq. (6) in which the shape functions have

; N2ð Þ¼ x 0*,* x∈½ � 0*;* l (11)

(9)

(10)

S ¼

**2.2 Stiffness matrix calculation for support only at the nodes**

½ �¼ Sw

1*,* x , l 2

0*,* l 2

, x , l

kwl 2

by other authors [15] in the form (10):

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

N1ð Þ¼ x

*Stiffness matrix calculation by continuous bearing.*

the expressions (11):

**Figure 3.**

**23**

freedom (9):

in which the expressions of the elastic stiffness matrix of the beam [Se] and subgrade reaction matrix [Sw] are [5].

$$\begin{aligned} \text{[S}\_{\text{e}}\text{]} &= \frac{\text{EI}}{\text{l}^3} \begin{bmatrix} \text{12} & \text{6l} & -\text{12} & \text{6l} \\ \text{6l} & \text{4l}^2 - \text{6l} & \text{2l}^2 \\ -\text{12} - \text{6l} & \text{12} - \text{6l} \\ \text{6l} & \text{2l}^2 - \text{6l} & \text{4l}^2 \end{bmatrix} \end{aligned} \tag{4}$$

$$\mathbf{[S\_w]} = \frac{\mathbf{k\_w}l}{420} \begin{bmatrix} 156 & 22\mathbf{l} & 54 & -13\mathbf{l} \\ 22\mathbf{l} & 4\mathbf{l}^2 & 13\mathbf{l} & -3\mathbf{l}^2 \\ 54 & 13\mathbf{l} & 156 & -22\mathbf{l} \\ -13\mathbf{l} & -3\mathbf{l}^2 - 22\mathbf{l} & 4\mathbf{l}^2 \end{bmatrix} \tag{5}$$

In the Pasternak model (**Figure 2**), the flexural behavior of this beam is given by Eq. (6) [5, 6]:

$$\mathrm{EI}\frac{\mathrm{d}^4\mathrm{w}(\mathbf{x})}{\mathrm{d}\mathbf{x}^4} + \mathrm{p}(\mathbf{x}) - \mathrm{g}\frac{\mathrm{d}^2\mathrm{w}(\mathbf{x})}{\mathrm{x}^2} = \mathrm{q}(\mathbf{x})\tag{6}$$

Solving Eq. (6) by FEM is expressed by Eq. (7):

$$\left( \left[ \mathbf{S}\_{\mathbf{e}} \right] + \left[ \mathbf{S}\_{\mathbf{w}} \right] + \left[ \mathbf{S}\_{\mathbf{g}} \right] \right) \{ \mathbf{d} \} = \{ \mathbf{q} \} \tag{7}$$

in which the expressions of the elastic stiffness matrix of the beam [Se] and subgrade reaction matrix [Sw] are the same like those from Eqs. (4) and (5), and shear matrix [Sg] is given by Eq. (8):

$$\mathbf{f}\left[\mathbf{S}\_{\mathbf{g}}\right] = \frac{\mathbf{g}}{\mathbf{30l}} \begin{bmatrix} \mathbf{36} & \mathbf{3l} & -\mathbf{36} & \mathbf{3l} \\ \mathbf{3l} & \mathbf{4l}^2 & -\mathbf{3l} & -\mathbf{l}^2 \\ -\mathbf{36} & -\mathbf{3l} & \mathbf{36} & -\mathbf{3l} \\ \mathbf{3l} & -\mathbf{l}^2 & -\mathbf{3l} & \mathbf{4l}^2 \end{bmatrix} \tag{8}$$

Inserting the second parameter for the soil (shear stiffness) has the effect of increasing the stiffness of the beam (increasing the stiffness matrix terms). The stiffness matrices were obtained by considering a continuous bearing of the beam according to **Figure 3** and using a cubic displacement function [13, 14].

**Figure 2.** *The Pasternak model.*

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

Solving Eq. (2) by FEM is expressed by Eq. (3):

½ �¼ Se

½ �¼ Sw

EI <sup>d</sup><sup>4</sup>

Solving Eq. (6) by FEM is expressed by Eq. (7):

Sg � � <sup>¼</sup> <sup>g</sup> 30l

shear matrix [Sg] is given by Eq. (8):

w xð Þ

dx4 <sup>þ</sup> p xð Þ� <sup>g</sup>

½ �þ Se ½ �þ Sw Sg

according to **Figure 3** and using a cubic displacement function [13, 14].

in which the expressions of the elastic stiffness matrix of the beam [Se] and subgrade reaction matrix [Sw] are the same like those from Eqs. (4) and (5), and

3l �l

Inserting the second parameter for the soil (shear stiffness) has the effect of increasing the stiffness of the beam (increasing the stiffness matrix terms). The stiffness matrices were obtained by considering a continuous bearing of the beam

EI l 3

kwl 420

subgrade reaction matrix [Sw] are [5].

*Hydraulic Structures - Theory and Applications*

Eq. (6) [5, 6]:

**Figure 2.**

**22**

*The Pasternak model.*

ð Þ ½ �þ Se ½ � Sw f gd ¼ f gq (3)

x2 <sup>¼</sup> q xð Þ (6)

(4)

(5)

(8)

in which the expressions of the elastic stiffness matrix of the beam [Se] and

12 6l � 12 6l 6l 4l2 � 6l 2l<sup>2</sup> �12 � 6l 12 � 6l 6l 2l<sup>2</sup> � 6l 4l2

156 22l 54 � 13l 22l 4l<sup>2</sup> 13l � 3l2 54 13l 156 � 22l �13l � 3l2 � 22l 4l<sup>2</sup>

In the Pasternak model (**Figure 2**), the flexural behavior of this beam is given by

d2 w xð Þ

36 3l �36 3l 3l 4l2 �3l �<sup>l</sup>

�36 �3l 36 �3l

<sup>2</sup> �3l 4l<sup>2</sup>

� � � � f g<sup>d</sup> <sup>¼</sup> f g<sup>q</sup> (7)

2

The meaning of the notations can be inferred from the following equation, which generally defines a stiffness matrix for a finite element with four degrees of freedom (9):

$$\mathbf{S} = \begin{bmatrix} \mathbf{S}\_{11} & \mathbf{S}\_{12} & \mathbf{S}\_{13} & \mathbf{S}\_{14} \\\\ \mathbf{S}\_{21} & \mathbf{S}\_{22} & \mathbf{S}\_{23} & \mathbf{S}\_{24} \\\\ \mathbf{S}\_{31} & \mathbf{S}\_{32} & \mathbf{S}\_{33} & \mathbf{S}\_{34} \\\\ \mathbf{S}\_{41} & \mathbf{S}\_{42} & \mathbf{S}\_{43} & \mathbf{S}\_{44} \end{bmatrix} \tag{9}$$

#### **2.2 Stiffness matrix calculation for support only at the nodes**

In the calculation of the beams on elastic support by the finite element method, the determination of the stiffness matrix of the elastic foundation was determined by other authors [15] in the form (10):

$$\begin{aligned} [\mathbf{S}\_{\mathbf{w}}] = \frac{\mathbf{k}\_{\mathbf{w}} \mathbf{l}}{2} \begin{bmatrix} \mathbf{1} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} \end{bmatrix} \end{aligned} \tag{10}$$

Eq. (10) is directly suggested by the calculation scheme of **Figure 4** where it can be seen that only the S11 and S33 elements of the stiffness matrix have values other than zero (a Sij element of the stiffness matrix is the generalized force that develops in the direction i when a unit displacement or rotation is imposed in the direction j). Eq. (10) can also be obtained by solving Eq. (6) in which the shape functions have the expressions (11):

$$\mathbf{N}\_1(\mathbf{x}) = \begin{array}{c} \mathbf{1}, \mathbf{x} < \frac{1}{2} \\ \vdots \\ \mathbf{0}, \frac{1}{2} < \mathbf{x} < \mathbf{l} \end{array} ; \qquad \mathbf{N}\_2(\mathbf{x}) = \mathbf{0}, \mathbf{x} \in [\mathbf{0}, \mathbf{l}] \tag{11}$$

**Figure 3.** *Stiffness matrix calculation by continuous bearing.*

**Figure 4.** *Stiffness matrix calculation by nodes bearing.*

$$\mathbf{N}\_{\mathbf{3}}(\mathbf{x}) = \begin{array}{c} \mathbf{0}, \mathbf{x} < \frac{1}{2} \\ \mathbf{1}, \frac{1}{2} < \mathbf{x} < \mathbf{l} \end{array}; \qquad \mathbf{N}\_{\mathbf{4}}(\mathbf{x}) = \mathbf{0}, \mathbf{x} \in [\mathbf{0}, \mathbf{l}]$$

With the same expressions (Eq. (10)) for shape functions shear matrix, [Sg] = 0. This result it can be understood that the absence of friction between springs considering that the springs are positioned only in the nodes (at a sufficient distance between them).

b.For the ground under conduit:

*Finite element scheme and degrees of freedom.*

*Cross and longitudinal section by bottom discharge (reinforced concrete).*

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

*B* = 3.2 m is the width of the conduit

other ones according to [15].

given by:

**Figure 5.**

**Figure 6.**

following relations:

**25**

Each node will be thought of as a spring with its elasticity determined by:

The marginal nodes will have the same coefficient of subgrade reaction as the

The coefficient of subgrade reaction according to Vesić apud Bowles [15] is

ffiffiffiffiffiffiffiffiffiffi EpB<sup>4</sup> EbIb

Ep B 1 � μ<sup>2</sup> p

12s

Ground parameters are (silty clay): Ep = 35 MPa; μ<sup>p</sup> = 0.35; γ<sup>p</sup> = 19 kN/m<sup>3</sup>

Foundation parameters *k* and *g* may be calculated according [6, 7] with the

k ¼ 0*,* 65

With these values, it results in *ks* = 3.2 � 5875 = 28.200 kN/m.

<sup>g</sup> <sup>¼</sup> Ep 2 1 þ μ<sup>p</sup>

Shear modulus for shear layer in foundation is.

*ks* ¼ *B* � *k* in which (12)

� � <sup>¼</sup> 13 MPa (14)

*gs* ¼ *B* � *g* (15)

� � (13)

.

#### **3. Conduit calculation as a beam**

#### **3.1 Calculation scheme**

We have noticed that the influence of the earth parameters is quantified in the rigidity matrix of the FEM specific equations (1), (5), and (7). Depending on the multiparameter subgrade model, this influence is variable. Is it also significant for the behavior of the structure, if the values of the matrix elements, which quantify the rigidity of the earth, are comparable to those of the rigidity of the pipe? Further, for comparing the value of the matrix elements and their influence on the final result, we will compute these matrices for a real case [16]. Bottom discharge conduit from an embankment dam is considered as a structural element (Ibaneasa dam from Botosani county—Romania). The pipe is from reinforced concrete with polygonal section (inner rectangle, exterior trapeze) (see **Figure 5**).

The conduit was built in 9 m sections. We will make a calculation of a 9-m-long section in the central area of the dam. It is considered a single finite element between two longitudinal joints of length *l* (see **Figure 6**). The beam loading and support scheme are shown in **Figure 7**.

Numerical parameters are:

a. For the conduit parameters:

A = 5.36 m2 , area of concrete section

Ib = 6.67 m<sup>4</sup> , moment of inertia

Eb = 26 GPa (for C12/15), modulus of elasticity

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

#### **Figure 5.**

N3ð Þ¼ x

*Hydraulic Structures - Theory and Applications*

*Stiffness matrix calculation by nodes bearing.*

**3. Conduit calculation as a beam**

support scheme are shown in **Figure 7**. Numerical parameters are:

a. For the conduit parameters:

A = 5.36 m<sup>2</sup>

Ib = 6.67 m<sup>4</sup>

**24**

between them).

**Figure 4.**

**3.1 Calculation scheme**

0*,* x , l 2

, x , l

polygonal section (inner rectangle, exterior trapeze) (see **Figure 5**).

, area of concrete section

Eb = 26 GPa (for C12/15), modulus of elasticity

, moment of inertia

section in the central area of the dam. It is considered a single finite element between two longitudinal joints of length *l* (see **Figure 6**). The beam loading and

With the same expressions (Eq. (10)) for shape functions shear matrix, [Sg] = 0. This result it can be understood that the absence of friction between springs considering that the springs are positioned only in the nodes (at a sufficient distance

We have noticed that the influence of the earth parameters is quantified in the rigidity matrix of the FEM specific equations (1), (5), and (7). Depending on the multiparameter subgrade model, this influence is variable. Is it also significant for the behavior of the structure, if the values of the matrix elements, which quantify the rigidity of the earth, are comparable to those of the rigidity of the pipe? Further, for comparing the value of the matrix elements and their influence on the final result, we will compute these matrices for a real case [16]. Bottom discharge conduit from an embankment dam is considered as a structural element (Ibaneasa dam from Botosani county—Romania). The pipe is from reinforced concrete with

The conduit was built in 9 m sections. We will make a calculation of a 9-m-long

; N4ð Þ¼ x 0*,* x∈½ � 0*;* l

1*,* l 2 *Cross and longitudinal section by bottom discharge (reinforced concrete).*

#### **Figure 6.**

*Finite element scheme and degrees of freedom.*

b.For the ground under conduit:

Each node will be thought of as a spring with its elasticity determined by:

$$k\_s = B \cdot k \text{ in which }\tag{12}$$

*B* = 3.2 m is the width of the conduit

The marginal nodes will have the same coefficient of subgrade reaction as the other ones according to [15].

The coefficient of subgrade reaction according to Vesić apud Bowles [15] is given by:

$$\mathbf{k} = \mathbf{0}, \mathbf{65} \sqrt[\text{n}]{\frac{\mathbf{E\_p} \mathbf{B}^4}{\mathbf{E\_b} \mathbf{I\_b}}} \frac{\mathbf{E\_p}}{\mathbf{B} \left(1 - \mu\_\mathbf{p}^2\right)} \tag{13}$$

Ground parameters are (silty clay): Ep = 35 MPa; μ<sup>p</sup> = 0.35; γ<sup>p</sup> = 19 kN/m<sup>3</sup> . With these values, it results in *ks* = 3.2 � 5875 = 28.200 kN/m. Shear modulus for shear layer in foundation is.

$$\mathbf{g} = \frac{\mathbf{E\_p}}{2\left(1 + \mu\_\mathbf{p}\right)} = \mathbf{13 MPa} \tag{14}$$

$$\mathbf{g}\_s = \mathbf{B} \cdot \mathbf{g} \tag{15}$$

Foundation parameters *k* and *g* may be calculated according [6, 7] with the following relations:

**Figure 7.** *Beam loading and support scheme.*

$$\mathbf{k} = \frac{\mathbf{E\_p}}{\mathbf{H}} \tag{16}$$

Solving the equation system (1), (7) is done by partitioning the S-matrices, D and Q separating the displacements according to the free degrees of freedom (2 and 4) by the degrees of freedom with elastic resistances (1 and 3) (see **Figure 6**):

> <sup>¼</sup> Qn Qr � �

Eq. (20) results in two matrix equations representing the equations of the struc-

SnnDn þ SnrDr ¼ Qn þ Rn SrnDn þ SrrDr ¼ Qr þ Rr

þ

Rn Rr

� � are displacement subvectors (22)

� � (20)

are load subvectors (23)

¼ ksDr are reactions*:* (24)

¼ ks ½ �Dr (25)

(26)

(21)

Dr � �

w2

Qr ¼ q

� l 2 � l 2 9 >>=

>>;

8 >><

>>:

In solving Eqs. (21), there may be four situations depending on the connections

a. Fixed connections when *Dr* ¼ 0 and from the first relationship in (21) result displacements and from the second relation (21) result the reactions.

b. In the case of known displacements of support, Dr has a known value from

¼ ks

d1 d3 � �

> d3 � �

c. In the case of elastic connections at the nodes (see **Figures 6** and **7b**).

R3 � �

> <sup>¼</sup> ks <sup>0</sup> 0 ks � � d1

> > 1 ks

1 ks � I � �Rr <sup>¼</sup> Qr

Rr ¼ Qn

Snn Snr Srn Srr � � Dn

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

� �; Dr <sup>¼</sup> w1

9 >>=

>>;

Eq. (21) that results displacements and reactions.

� �; Rr <sup>¼</sup> R1

Rr <sup>¼</sup> R1 R3 � �

SnnDn þ Snr

SrnDn þ Srr

� l 2 12 l 2 12

8 >><

>>:

ture (21):

where

Rn <sup>¼</sup> R2 R4 � �

Eq. (24) can be written as

By replacing (24) in (21), we get

From the last Eq. (26) results

**27**

Dn <sup>¼</sup> <sup>θ</sup><sup>1</sup> θ2

Qn ¼ q

of the structure with the soil [14]:

<sup>¼</sup> <sup>0</sup> 0

$$\mathbf{g} = \frac{\mathbf{E\_p}}{2\left(1 + \mu\_p\right)} \frac{\mathbf{H}}{2} \tag{17}$$

where H is depth to effective rigid base.

The effective rigid base is defined as the depth at which settlements caused by the structure can be taken to be zero. For decades it has been assumed that the "depth of influence" for settlement equivalent conceptually to the effective depth to rigid base is twice the width of a square loaded area and four times the width of an infinite strip [7].

With this assumptions H = 6.4 m; k = 5468 kN/m<sup>2</sup> ; g = 41.5 MPa.

The load on the conduit from the ground weight can be considered uniformly distributed. The load from the ground with its own pipe weight is 826 kN/m. With these parameters, it is necessary to determine the stresses in conduit schematized by the finite element from **Figures 6** and **7**.

#### **3.2 Solving the FEM equilibrium equation**

The matrix equilibrium equation is (7)

$$\left( \left[ \mathbf{S}\_{\mathbf{e}} \right] + \left[ \mathbf{S}\_{\mathbf{w}} \right] + \left[ \mathbf{S}\_{\mathbf{g}} \right] \right) \{ \mathbf{d} \} = \{ \mathbf{q} \} \tag{18}$$

which is written in form (1)

$$\mathbb{E}[\mathbf{S}]\{\mathbf{D}\} = \{\mathbf{Q}\} \tag{19}$$

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

Solving the equation system (1), (7) is done by partitioning the S-matrices, D and Q separating the displacements according to the free degrees of freedom (2 and 4) by the degrees of freedom with elastic resistances (1 and 3) (see **Figure 6**):

$$
\begin{Bmatrix} \mathbf{S\_{nn}} & \mathbf{S\_{nr}} \\ \mathbf{S\_{rn}} & \mathbf{S\_{rr}} \end{Bmatrix} \begin{Bmatrix} \mathbf{D\_{n}} \\ \mathbf{D\_{r}} \end{Bmatrix} = \begin{Bmatrix} \mathbf{Q\_{n}} \\ \mathbf{Q\_{r}} \end{Bmatrix} + \begin{Bmatrix} \mathbf{R\_{n}} \\ \mathbf{R\_{r}} \end{Bmatrix} \tag{20}
$$

Eq. (20) results in two matrix equations representing the equations of the structure (21):

$$\begin{aligned} \mathbf{S\_{nn}D\_n + S\_{nr}D\_r = Q\_n + R\_n} \\ \mathbf{S\_{rn}D\_n + S\_{rr}D\_r = Q\_r + R\_r} \end{aligned} \tag{21}$$

where

<sup>k</sup> <sup>¼</sup> Ep

The effective rigid base is defined as the depth at which settlements caused by the structure can be taken to be zero. For decades it has been assumed that the "depth of influence" for settlement equivalent conceptually to the effective depth to rigid base is twice the width of a square loaded area and four times the width of an

The load on the conduit from the ground weight can be considered uniformly distributed. The load from the ground with its own pipe weight is 826 kN/m. With these parameters, it is necessary to determine the stresses in conduit schematized by

½ �þ Se ½ �þ Sw Sg

H

<sup>g</sup> <sup>¼</sup> Ep 2 1 þ μ<sup>p</sup> 

where H is depth to effective rigid base.

*Hydraulic Structures - Theory and Applications*

the finite element from **Figures 6** and **7**.

which is written in form (1)

**3.2 Solving the FEM equilibrium equation**

The matrix equilibrium equation is (7)

With this assumptions H = 6.4 m; k = 5468 kN/m<sup>2</sup>

infinite strip [7].

**26**

**Figure 7.**

*Beam loading and support scheme.*

<sup>H</sup> (16)

; g = 41.5 MPa.

f g¼ <sup>d</sup> f g<sup>q</sup> (18)

½ � *S* f g *D* ¼ f g *Q* (19)

<sup>2</sup> (17)

$$\mathbf{D\_n} = \begin{Bmatrix} \theta\_1 \\ \theta\_2 \end{Bmatrix}; \quad \mathbf{D\_r} = \begin{Bmatrix} \mathbf{w\_1} \\ \mathbf{w\_2} \end{Bmatrix} \text{ are displacement subvectors} \tag{22}$$

$$\begin{Bmatrix} \mathbf{1}^2 \end{Bmatrix} \qquad \text{( $\mathbf{1}$ ) }$$

$$\mathbf{Q\_n} = \mathbf{q} \begin{Bmatrix} -\frac{\mathbf{l^2}}{12} \\ \frac{\mathbf{l^2}}{12} \end{Bmatrix} \qquad \mathbf{Q\_r} = \mathbf{q} \begin{Bmatrix} -\frac{\mathbf{l}}{2} \\ -\frac{\mathbf{l}}{2} \end{Bmatrix} \text{ are load subvectors} \tag{23}$$

In solving Eqs. (21), there may be four situations depending on the connections of the structure with the soil [14]:


$$\mathbf{R\_{n}} = \begin{Bmatrix} \mathbf{R\_{2}} \\ \mathbf{R\_{4}} \end{Bmatrix} = \begin{Bmatrix} \mathbf{0} \\ \mathbf{0} \end{Bmatrix}; \qquad \mathbf{R\_{r}} = \begin{Bmatrix} \mathbf{R\_{1}} \\ \mathbf{R\_{3}} \end{Bmatrix} = \mathbf{k\_{s}} \begin{Bmatrix} \mathbf{d\_{1}} \\ \mathbf{d\_{3}} \end{Bmatrix} = \mathbf{k\_{s}} \mathbf{D\_{r}} \text{ are reactions.} \tag{24}$$

Eq. (24) can be written as

$$\mathbf{R\_{f}} = \begin{Bmatrix} \mathbf{R\_{f}} \\ \mathbf{R\_{3}} \end{Bmatrix} = \begin{bmatrix} \mathbf{k\_{s}} & \mathbf{0} \\ \mathbf{0} & \mathbf{k\_{s}} \end{bmatrix} \begin{Bmatrix} \mathbf{d\_{1}} \\ \mathbf{d\_{3}} \end{Bmatrix} = [\mathbf{k\_{s}}] \mathbf{D\_{r}} \tag{25}$$

By replacing (24) in (21), we get

$$\begin{aligned} \mathbf{S\_{nn}} \mathbf{D\_n} + \mathbf{S\_{nr}} \frac{\mathbf{1}}{\mathbf{k\_s}} \mathbf{R\_r} &= \mathbf{Q\_n} \\ \mathbf{S\_{rn}} \mathbf{D\_n} + \left( \mathbf{S\_{rr}} \frac{\mathbf{1}}{\mathbf{k\_s}} - \mathbf{I} \right) \mathbf{R\_r} &= \mathbf{Q\_r} \end{aligned} \tag{26}$$

From the last Eq. (26) results

*Hydraulic Structures - Theory and Applications*

$$\mathbf{R\_{r}} = \left(\frac{\mathbf{1}}{\mathbf{k\_{s}}}\mathbf{S\_{rr}} - \mathbf{I}\right)^{-1} \left(\mathbf{Q\_{r}} - \mathbf{S\_{rn}}\mathbf{D\_{n}}\right) \tag{27}$$

Krr <sup>¼</sup> K11 K13

**3.3 Obtained results**

Stiffness matrix is

tion on the rotation of the beam ends.

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

K31 K33 Krn <sup>¼</sup> K12 K14

*3.3.1 Results for the Winkler (single-parameter) scheme*

The displacements of the conduit ends are:

The rigidity matrix (Eq. (30)) has the value

**29**

Displacements w1 and w2 are measured in [m] and rotation in [rad]

K32 K34 Koo <sup>¼</sup> K22 K24

The condensed rigidity matrix includes the effect of the rigidity of the founda-

½ �¼ S ½ �þ Se ½ � Sw

K42 K44 (34)

which introduced in the first Eq. (26) leading to the calculation of the displacements, which is depicted below

$$\begin{aligned} \mathbf{S\_{nn}D\_{n} + S\_{\mathrm{nr}}} \frac{1}{\mathbf{k}\_{\mathrm{s}}} \left( \frac{1}{\mathbf{k}\_{\mathrm{s}}} \mathbf{S\_{\mathrm{rr}} - I} \right)^{-1} (\mathbf{Q\_{r}} - \mathbf{S\_{\mathrm{rn}}} \mathbf{D\_{n}}) &= \mathbf{Q\_{n}} \\ \mathbf{S\_{nn}D\_{n} + S\_{\mathrm{nr}}} \frac{1}{\mathbf{k}\_{\mathrm{s}}} \left( \frac{1}{\mathbf{k}\_{\mathrm{s}}} \mathbf{S\_{\mathrm{rr}} - I} \right)^{-1} \mathbf{Q\_{r}} - \mathbf{S\_{\mathrm{nr}}} \frac{1}{\mathbf{k}\_{\mathrm{s}}} \left( \frac{1}{\mathbf{k}\_{\mathrm{s}}} \mathbf{S\_{\mathrm{rr}} - I} \right)^{-1} \mathbf{S\_{\mathrm{rn}}} \mathbf{D\_{n}} &= \mathbf{Q\_{n}} \\ \left[ \mathbf{S\_{nn}} - \mathbf{S\_{n}} \frac{1}{\mathbf{k}\_{\mathrm{s}}} \left( \frac{1}{\mathbf{k}\_{\mathrm{s}}} \mathbf{S\_{\mathrm{rr}} - I} \right)^{-1} \mathbf{S\_{\mathrm{rn}}} \right] \mathbf{D\_{n}} &= \mathbf{Q\_{n}} + \mathbf{S\_{n}} \frac{1}{\mathbf{k}\_{\mathrm{s}}} \left( \frac{1}{\mathbf{k}\_{\mathrm{s}}} \mathbf{S\_{\mathrm{rr}} - I} \right)^{-1} \mathbf{Q\_{n}} \end{aligned}$$

Displacements in the directions of unrestrained degrees of freedom are

$$\mathbf{D\_n} = \left(\mathbf{S\_{nn}^\*}\right)^{-1} \mathbf{Q\_n^\*} \tag{28}$$

where

$$\mathbf{S}\_{\rm nn}^{\*} = \mathbf{S}\_{\rm nn} - \mathbf{S}\_{\rm nr} \frac{1}{\mathbf{k}\_{\rm s}} \left(\frac{1}{\mathbf{k}\_{\rm s}} \mathbf{S}\_{\rm rr} - \mathbf{I}\right)^{-1} \mathbf{S}\_{\rm rn}; \qquad \mathbf{Q}\_{\rm n}^{\*} = \mathbf{Q}\_{\rm n} + \mathbf{S}\_{\rm nr} \frac{1}{\mathbf{k}\_{\rm s}} \left(\frac{1}{\mathbf{k}\_{\rm s}} \mathbf{S}\_{\rm rr} - \mathbf{I}\right)^{-1} \mathbf{Q}\_{\rm r} \tag{29}$$

d.In case of elastic connection and continuous support

In this case, (**Figure 7a**, continuum bearing) the rotations are not independent movements; they depend on the rotational stiffness of the ground. In the situation of (c), the rigidity of the displacement matrix had the form

$$\begin{bmatrix} \mathbf{k}\_{\mathbf{s}} \end{bmatrix} = \begin{bmatrix} \mathbf{k}\_{\mathbf{s}} & \mathbf{0} \\ \mathbf{0} & \mathbf{k}\_{\mathbf{s}} \end{bmatrix} \tag{30}$$

In case (d), we will obtain the matrix [ks] by static condensation of the sum of matrices:

$$\mathbf{[K]} = \mathbf{[S\_w]} + \mathbf{[S\_{\mathfrak{g}}]} \tag{31}$$

For condensation we will use the Guyan method [13]. The condensed matrix *Kr* is obtained from the matrix *K* whose terms have the meaning below. DOFs (degrees of freedom) retained are 1 and 3, and DOFs omitted are 2 and 4 (rotation):

$$\mathbf{K} = \begin{bmatrix} \mathbf{K}\_{11} & \mathbf{K}\_{12} & \mathbf{K}\_{13} & \mathbf{K}\_{14} \\ \mathbf{K}\_{21} & \mathbf{K}\_{22} & \mathbf{K}\_{23} & \mathbf{K}\_{24} \\ \mathbf{K}\_{31} & \mathbf{K}\_{32} & \mathbf{K}\_{33} & \mathbf{K}\_{34} \\ \mathbf{K}\_{41} & \mathbf{K}\_{42} & \mathbf{K}\_{43} & \mathbf{K}\_{44} \end{bmatrix} \tag{32}$$

Calculation relation for condensed rigidity matrix of earth parameters is (33) [13].

$$\mathbf{K\_{r}} = \mathbf{K\_{rr}} - \mathbf{K\_{ro}} \mathbf{K\_{oo}^{-1}} \mathbf{K\_{ro}^{T}} \tag{33}$$

where

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

$$\mathbf{K\_{rr}} = \begin{bmatrix} \mathbf{K\_{11}} & \mathbf{K\_{13}} \\ \mathbf{K\_{31}} & \mathbf{K\_{33}} \end{bmatrix} \quad \mathbf{K\_{rn}} = \begin{bmatrix} \mathbf{K\_{12}} & \mathbf{K\_{14}} \\ \mathbf{K\_{32}} & \mathbf{K\_{34}} \end{bmatrix} \quad \mathbf{K\_{60}} = \begin{bmatrix} \mathbf{K\_{22}} & \mathbf{K\_{24}} \\ \mathbf{K\_{42}} & \mathbf{K\_{44}} \end{bmatrix} \tag{34}$$

The condensed rigidity matrix includes the effect of the rigidity of the foundation on the rotation of the beam ends.

#### **3.3 Obtained results**

Rr <sup>¼</sup> <sup>1</sup> ks

> 1 ks

Srr � I � ��<sup>1</sup>

Srr � I � ��<sup>1</sup>

displacements, which is depicted below

*Hydraulic Structures - Theory and Applications*

SnnDn þ Snr

Snn � Snr

where

S∗

matrices:

where

**28**

nn ¼ Snn � Snr

SnnDn þ Snr

1 ks

1 ks

" #

1 ks

1 ks

1 ks

1 ks

Srr � I � ��<sup>1</sup>

d.In case of elastic connection and continuous support

of (c), the rigidity of the displacement matrix had the form

K ¼

Srr � I � ��<sup>1</sup>

which introduced in the first Eq. (26) leading to the calculation of the

1 ks

Srr � I � ��<sup>1</sup>

Srn

Dn <sup>¼</sup> <sup>S</sup><sup>∗</sup> nn � ��<sup>1</sup>

Srn; Q<sup>∗</sup>

In this case, (**Figure 7a**, continuum bearing) the rotations are not independent movements; they depend on the rotational stiffness of the ground. In the situation

ks ½ �¼ ks <sup>0</sup>

½ �¼ K ½ �þ Sw Sg

of freedom) retained are 1 and 3, and DOFs omitted are 2 and 4 (rotation):

For condensation we will use the Guyan method [13]. The condensed matrix *Kr* is obtained from the matrix *K* whose terms have the meaning below. DOFs (degrees

> K11 K12 K13 K14 K21 K22 K23 K24 K31 K32 K33 K34 K41 K42 K43 K44

Calculation relation for condensed rigidity matrix of earth parameters is (33) [13].

oo K<sup>T</sup>

Kr <sup>¼</sup> Krr � KroK�<sup>1</sup>

In case (d), we will obtain the matrix [ks] by static condensation of the sum of

0 ks � �

Displacements in the directions of unrestrained degrees of freedom are

Qr � Snr

1 ks

Dn ¼ Qn þ Snr

Q<sup>∗</sup>

<sup>n</sup> ¼ Qn þ Snr

1 ks

ð Þ Qr � SrnDn (27)

SrnDn ¼ Qn

Qr

Qr (29)

(30)

(32)

ð Þ¼ Qr � SrnDn Qn

Srr � I � ��<sup>1</sup>

> 1 ks

> > 1 ks

1 ks

1 ks

Srr � I � ��<sup>1</sup>

<sup>n</sup> (28)

Srr � I � ��<sup>1</sup>

� � (31)

ro (33)

#### *3.3.1 Results for the Winkler (single-parameter) scheme*

Stiffness matrix is

½ �¼ S ½ �þ Se ½ � Sw

The displacements of the conduit ends are:

$$\mathbf{D} \coloneqq \begin{pmatrix} -0.068 \\ -3.78 \times 10^{-4} \\ -0.068 \\ -0.068 \\ 3.78 \times 10^{-4} \end{pmatrix}^{-1} = \begin{cases} w\_1 \\ \theta\_1 \\ w\_2 \\ \theta\_2 \end{cases}$$

Displacements w1 and w2 are measured in [m] and rotation in [rad] The rigidity matrix (Eq. (30)) has the value

$$\mathbf{k\_s} = \begin{pmatrix} 3.008 \times 10^4 & 0\\ & \\ & 0 & 3.008 \times 10^4 \end{pmatrix}$$

The displacement of the center of the beam (conduit) is

$$\mathbf{w} = -0.0689 \,\mathrm{[m]}$$

Displacement in the center of the beam is calculated using shape functions according to relation:

$$\mathbf{w}(\mathbf{l}/2) = \begin{bmatrix} \mathbf{N\_1} & \mathbf{N\_2} & \mathbf{N\_3} & \mathbf{N\_4} \end{bmatrix} \begin{Bmatrix} \mathbf{w\_1} & \theta\_1 & \mathbf{w\_2} & \theta\_2 \end{Bmatrix}^T \tag{35}$$

*3.3.2 Results for multiple-parameter subgrade model scheme (Pasternak)*

The stiffness matrix is

$$\mathbf{[S]} = \mathbf{[S\_{e}]} + \mathbf{[S\_{w}]} + \mathbf{[S\_{g}]} \tag{36}$$

The condensed rigidity matrix of earth parameters, according relation (33) is:

Displacements w1 and w2 are measured in [m] and rotation in [rad]. The dis-

The calculation of rigidity for the conduit and for the terrain is common. Solving equilibrium Eq. (7) for situations (a), (b), and (c) is usual. For continuous support (d) we used condensation of stiffness matrices, the method that I consider new, through which includes the rigidity of rotation of the bar and the rigidity of the terrain in the stiffness of the bar ends. In this way we have reduced the number of unknowns—reactions, and solving the equation in the case (d) becomes similar to

The purpose of calculating rigidity matrices and conduit (beam) displacements,

for the two methods of determining the ground parameters (the Winkler and multiple-parameter subgrade model, the Pasternak), is to highlight the small difference between the calculated values. This small difference between displacements

A first conclusion is that for structures with a high transversal moment of inertia, the method of determining the parameters of the earth is not very important. The difference between the elements of rigidity matrices for the structure and for the Winkler earth is about 100 times and between the Winkler earth and the

(4%) is due to the high rigidity (high moment of inertia) of the conduit.

The displacements of the conduit ends are:

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

placement of the center of the beam (conduit) is

**3.4 Comments about conduit calculation as a beam**

the solution in the case (c).

Pasternak rigidity is about 10 times.

**31**

The stiffness matrix values are:

$$\begin{aligned} \text{S}\_{\text{G}} &= \begin{pmatrix} 2.855 \times 10^{6} & 1.285 \times 10^{7} & -2.855 \times 10^{6} & 1.285 \times 10^{7} \\ 1.285 \times 10^{7} & 7.708 \times 10^{7} & -1.285 \times 10^{7} & 3.854 \times 10^{7} \\ -2.855 \times 10^{6} & -1.285 \times 10^{7} & 2.855 \times 10^{6} & -1.285 \times 10^{7} \\ 1.285 \times 10^{7} & 3.854 \times 10^{7} & -1.285 \times 10^{7} & 7.708 \times 10^{7} \end{pmatrix} \\\\ \text{S}\_{\text{W}} &= \begin{pmatrix} 6.285 \times 10^{4} & 7.977 \times 10^{4} & 2.175 \times 10^{4} & -4.713 \times 10^{4} \\ 7.977 \times 10^{4} & 1.305 \times 10^{5} & 4.713 \times 10^{4} & -9.789 \times 10^{4} \\ 2.175 \times 10^{4} & 4.713 \times 10^{4} & 6.285 \times 10^{4} & -7.977 \times 10^{4} \\ -4.713 \times 10^{4} & -9.789 \times 10^{4} & -7.977 \times 10^{4} & 1.305 \times 10^{5} \end{pmatrix} \end{aligned}$$

$$\mathbf{S\_g} = \begin{pmatrix} 5.531 \times 10^3 & 4.148 \times 10^3 & -5.531 \times 10^3 & 4.148 \times 10^3 \\\\ 4.148 \times 10^3 & 4.978 \times 10^4 & -4.148 \times 10^3 & -1.244 \times 10^4 \\\\ -5.531 \times 10^3 & -4.148 \times 10^3 & 5.531 \times 10^3 & -4.148 \times 10^3 \\\\ 4.148 \times 10^3 & -1.244 \times 10^4 & -4.148 \times 10^3 & 4.978 \times 10^4 \end{pmatrix}$$

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

The displacement of the center of the beam (conduit) is

*Hydraulic Structures - Theory and Applications*

according to relation:

The stiffness matrix is

**30**

The stiffness matrix values are:

Displacement in the center of the beam is calculated using shape functions

w lð Þ¼ *=*2 ½ � N1 N2 N3 N4 f g w1 θ<sup>1</sup> w2 θ<sup>2</sup>

½ �¼ *S Se* ½ �þ ½ �þ *Sw Sg*

*3.3.2 Results for multiple-parameter subgrade model scheme (Pasternak)*

<sup>T</sup> (35)

(36)

$$\mathbf{S} = \begin{pmatrix} 2.923 \times 10^{6} & 1.293 \times 10^{7} & -2.838 \times 10^{6} & 1.28 \times 10^{7} \\\\ 1.293 \times 10^{7} & 7.726 \times 10^{7} & -1.28 \times 10^{7} & 3.843 \times 10^{7} \\\\ -2.838 \times 10^{6} & -1.28 \times 10^{7} & 2.923 \times 10^{6} & -1.293 \times 10^{7} \\\\ 1.28 \times 10^{7} & 3.843 \times 10^{7} & -1.293 \times 10^{7} & 7.726 \times 10^{7} \end{pmatrix}^{7}$$

The condensed rigidity matrix of earth parameters, according relation (33) is:

$$\mathbf{k\_{S}} = \begin{pmatrix} 2.871 \times 10^{4} & 472.813 \\\\ 472.813 & 2.871 \times 10^{4} \end{pmatrix}$$

The displacements of the conduit ends are:

$$\mathbf{D} := \begin{pmatrix} -0.0657 \\ -3.694 \times 10^{-4} \\ -0.0657 \\ -0.0657 \\ 3.694 \times 10^{-4} \end{pmatrix} = \begin{Bmatrix} \boldsymbol{w}\_1 \\ \boldsymbol{\theta}\_1 \\ \boldsymbol{w}\_2 \\ \boldsymbol{\theta}\_2 \\ \boldsymbol{\theta}\_2 \end{Bmatrix}$$

Displacements w1 and w2 are measured in [m] and rotation in [rad]. The displacement of the center of the beam (conduit) is

$$\text{w = -0.0665 \quad [m]}$$

#### **3.4 Comments about conduit calculation as a beam**

The calculation of rigidity for the conduit and for the terrain is common. Solving equilibrium Eq. (7) for situations (a), (b), and (c) is usual. For continuous support (d) we used condensation of stiffness matrices, the method that I consider new, through which includes the rigidity of rotation of the bar and the rigidity of the terrain in the stiffness of the bar ends. In this way we have reduced the number of unknowns—reactions, and solving the equation in the case (d) becomes similar to the solution in the case (c).

The purpose of calculating rigidity matrices and conduit (beam) displacements, for the two methods of determining the ground parameters (the Winkler and multiple-parameter subgrade model, the Pasternak), is to highlight the small difference between the calculated values. This small difference between displacements (4%) is due to the high rigidity (high moment of inertia) of the conduit.

A first conclusion is that for structures with a high transversal moment of inertia, the method of determining the parameters of the earth is not very important. The difference between the elements of rigidity matrices for the structure and for the Winkler earth is about 100 times and between the Winkler earth and the Pasternak rigidity is about 10 times.

A second conclusion is that the use of the SAP 2000 finite element software which includes the Winkler spring model is acceptable for bottom discharge conduit due to their high rigidity (of the conduit).

From these considerations, we can identify two calculation methods for this type of conduits. In a first method, the pipeline is calculated as a beam supported by the Winkler-type springs. You can use any finite element software that allows you to use springs. The joints between the conduit segments are introduced into the calculation scheme with their specific conditioning (restraints). In a second method the calculation can be done with a geotechnical software (e.g., GeoStudio) in which the modulus of elasticity is introduced as input parameters and the calculation is performed in a plane strain condition [17]. In this calculation method, somehow the influence of the joints between the pipe sections must be simulated. The following relationship is proposed for calculating the equivalent inertia moment of the pipe in which joints are taken into account:

$$\mathbf{I}\_{\mathbf{e}} = \mathbf{I}\frac{\mathbf{1}}{2\mathbf{n}}\tag{37}$$

The vertical load on the pipe is after Marston [4]:

Ce <sup>¼</sup> <sup>e</sup>2Kμð Þ He*=*De � <sup>1</sup> 2Kμ

this plane, the interior and exterior prisms of soil settle equally.

(considering the plane of equal compaction to the surface H = He).

, area of the concrete conduit

, moment of inertia for section

Eb = 26 GPa (for concrete C12/15), modulus of elasticity for concrete Foundation parameters *k* may be calculated according Horvath [6] with the

De is the outer diameter (width) of the pipe.

The pipeline calculation parameters are

A = 11.67 m2

**Figure 9.**

*Longitudinal section through conduit.*

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

Ib = 16.05 m<sup>4</sup>

following relations:

**33**

Pv <sup>¼</sup> Ce*γD*<sup>2</sup>

Ce <sup>¼</sup> <sup>e</sup>2Kμð Þ <sup>H</sup>*=*De � <sup>1</sup> 2Kμ

þ

H De

where K <sup>¼</sup> tg <sup>2</sup> 45o ð Þ � <sup>j</sup>*=*<sup>2</sup> is Rankine's lateral pressure coefficient; <sup>μ</sup> = tg <sup>φ</sup> is the coefficient of friction of the earth; He is the position of the plan of equal settlement. Marston determined the existence of a horizontal plane above the conduit where the shearing forces are zero. This plane is called the *plane of equal settlement*. Above

The relation (39)is valid for He > H (the plane of equal compressionis imaginary) and the relation (40) is valid for He <H (the additional load relative to the weight of the earth column) depend on the top-down friction forces appearing in the earth column above the. conduit in the vertical planes tangent to the pipe. In the case of the Tungujei dam, the thickness of the filling of 15 m over a 7.45 m width of the earth column is per linear meter of the pipe. According to the Marston relationship, it follows

Ce ¼ 2*:*64; Pv ¼ 2784 kN*=*m

<sup>k</sup> <sup>¼</sup> Ep

� He De

<sup>e</sup>*,* where : (38)

<sup>e</sup>2Kμð Þ He*=*De (40)

<sup>H</sup> (41)

or (39)

where *Ie* is the equivalent inertial momentum; *I* is the current section inertial momentum; *n* is the number of joints.

#### **4. Conduit calculation example**

The calculation will be made for the bottom discharge conduit of the Tungujei earth dam in Iasi County, Romania, designed as a cross-sectional structure of three rectangular reinforced concrete cassettes (**Figure 8**) [18]. In the longitudinal profile, the structure has joints between 5 and 10 m. The joints are sealed with PVC tape, and the reinforcement has no continuity in the joint.

The calculation scheme is the Winkler elastic beam and the EngiLab Beam 2D software [19]. The conduit consists of 2 reinforced concrete sections of 5 m and another 11 sections of 10 m length each (**Figure 9**). Between the sections there were joints of 2.5 cm, and the continuity is achieved with the sealing tape.

**Figure 8.** *Transverse section through conduit.*

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

A second conclusion is that the use of the SAP 2000 finite element software which includes the Winkler spring model is acceptable for bottom discharge con-

type of conduits. In a first method, the pipeline is calculated as a beam

From these considerations, we can identify two calculation methods for this

supported by the Winkler-type springs. You can use any finite element software that allows you to use springs. The joints between the conduit segments are introduced into the calculation scheme with their specific conditioning

(restraints). In a second method the calculation can be done with a geotechnical software (e.g., GeoStudio) in which the modulus of elasticity is introduced as input parameters and the calculation is performed in a plane strain condition [17]. In this calculation method, somehow the influence of the joints between the pipe sections must be simulated. The following relationship is proposed for calculating the equivalent inertia moment of the pipe in which joints are taken

Ie <sup>¼</sup> <sup>I</sup> <sup>1</sup>

where *Ie* is the equivalent inertial momentum; *I* is the current section inertial

The calculation will be made for the bottom discharge conduit of the Tungujei earth dam in Iasi County, Romania, designed as a cross-sectional structure of three rectangular reinforced concrete cassettes (**Figure 8**) [18]. In the longitudinal profile, the structure has joints between 5 and 10 m. The joints are sealed with

The calculation scheme is the Winkler elastic beam and the EngiLab Beam 2D software [19]. The conduit consists of 2 reinforced concrete sections of 5 m and another 11 sections of 10 m length each (**Figure 9**). Between the sections there were

PVC tape, and the reinforcement has no continuity in the joint.

joints of 2.5 cm, and the continuity is achieved with the sealing tape.

2n (37)

duit due to their high rigidity (of the conduit).

*Hydraulic Structures - Theory and Applications*

momentum; *n* is the number of joints.

**4. Conduit calculation example**

into account:

**Figure 8.**

**32**

*Transverse section through conduit.*

**Figure 9.** *Longitudinal section through conduit.*

The vertical load on the pipe is after Marston [4]:

$$\mathbf{P\_v = C\_e \dot{\gamma} D\_{e^\*}^2} \text{ where:} \tag{38}$$

$$\mathbf{C\_e = \frac{\mathbf{e^{2K\mu(H/D\_o)} - 1}{2K\mu}} \quad \text{or} \tag{39}$$

$$\mathbf{C\_e = \frac{e^{2\mathbf{K}\mu(\mathbf{H\_e/D\_e})} - 1}{2\mathbf{K}\mu} + \left(\frac{\mathbf{H}}{\mathbf{D\_e}} - \frac{\mathbf{H\_e}}{\mathbf{D\_e}}\right) \mathbf{e^{2\mathbf{K}\mu(\mathbf{H\_e/D\_e})}}\tag{40}$$

where K <sup>¼</sup> tg <sup>2</sup> 45o ð Þ � <sup>j</sup>*=*<sup>2</sup> is Rankine's lateral pressure coefficient; <sup>μ</sup> = tg <sup>φ</sup> is the coefficient of friction of the earth; He is the position of the plan of equal settlement.

Marston determined the existence of a horizontal plane above the conduit where the shearing forces are zero. This plane is called the *plane of equal settlement*. Above this plane, the interior and exterior prisms of soil settle equally.

De is the outer diameter (width) of the pipe.

The relation (39)is valid for He > H (the plane of equal compressionis imaginary) and the relation (40) is valid for He <H (the additional load relative to the weight of the earth column) depend on the top-down friction forces appearing in the earth column above the.

conduit in the vertical planes tangent to the pipe. In the case of the Tungujei dam, the thickness of the filling of 15 m over a 7.45 m width of the earth column is per linear meter of the pipe. According to the Marston relationship, it follows (considering the plane of equal compaction to the surface H = He).

$$\mathbf{C}\mathbf{e} = \mathbf{2}.64; \mathbf{P}\mathbf{v} = \mathbf{2784}\,\mathbf{kN}/\mathbf{m}.$$

The pipeline calculation parameters are

A = 11.67 m2 , area of the concrete conduit

Ib = 16.05 m<sup>4</sup> , moment of inertia for section

Eb = 26 GPa (for concrete C12/15), modulus of elasticity for concrete

Foundation parameters *k* may be calculated according Horvath [6] with the following relations:

$$\mathbf{k} = \frac{\mathbf{E\_p}}{\mathbf{H}} \tag{41}$$

where Ep = 18,000 kN/m<sup>2</sup> earth (foundation) modulus; H = 2 7.5 m = 15 m, depth of influence; k = 1200 kN/m3 .

When loading with the weight of the ground, the weight of the conduit cassette was added.

In the second calculation scheme, the nine continuous pipe sections were considered without interruptions in joints. A maximum of 32.6 cm settlement

2n <sup>¼</sup> <sup>16</sup>*:*<sup>04</sup>

We calculated conduits through FEM using analytical calculation for a finite element and calculation with a software (EngiLab Beam). In the calculation for a finite element, we have highlighted the stiffness matrices to understand the large value difference between the terms of the matrices and the physical significance of

The low rigidity of the ground slightly influences the state of stresses and deformations in the conduit. It follows that it is sufficient that the parameters of the

A first conclusion is that computational programs that allow the use of the Winkler-type springs give results with good accuracy (e.g., below 5%) for this type of structure. The overall view at this point is that the Winkler model is outdated. The difference in conduit displacements calculated with the two methods of estimating the ground characteristics (the Winkler and multiple-parameter subgrade model) is small. It means that the shear stiffness introduced by multipleparameter subgrade models does not significantly change the result. It is therefore reasonable to use the Winkler parameters for the terrain characteristics. These considerations apply to conduits where the stiffness of the conduit (measured in the stiffness matrix) is 100 times higher than the rigidity of the earth (also expressed by

The calculation of bottom discharge conduit as well as other long hydrotechnical structures is done with reasonable accuracy in the plane strain state. Finite element programs calculate stress state and deformations with this scheme. In the case of conduits, the influence of the joints between the sections must be modeled. If this is not done, the results are not credible. In the calculated example, we used two schemes: one with the pipe provided with joints and with the respective struts and the second with the pipe without joints (continuous) and with the inertia moment adjusted with the relation (37). The difference between the results obtained with these two schemes is small (1%). Models of finite element type are credible if the

Using the rigidity matrix condensation, to solve the equilibrium equation for beams with deformable supports, facilitates solving the equation system (21).

We appreciate that the use of the Winkler-type springs is suitable for long rigid

Calculation of conduit sections in plane strain state leads to credible results only

if the moment of inertia is adjusted in accordance with pipe joints. For this we propose a relation of calculating the moment of equivalent inertia (37). If the inertia

moment is not adjusted, the result obtained is not credible.

The author declares that there is no conflict of interest.

1 <sup>2</sup> � <sup>8</sup> <sup>¼</sup> 1m4

The equivalent moment of inertia is calculated with Eq. (37):

Ie <sup>¼</sup> <sup>I</sup> <sup>1</sup>

earth are defined by the Winkler-type springs.

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

conduit is made jointless, which is unlikely. Resuming the findings of this work are:

resulted.

**5. Conclusions**

this difference.

the stiffness matrix).

structures.

**35**

**Conflict of interest**

Two pipeline calculation schemes were used between the R3 and R12 joints (see **Figure 9**). The 5 m sections were removed from the calculation scheme and the terminal sections embedded in the portal.

In the first diagram, the nine sections of the pipe were considered to be articulated at the ends. A maximum of 32.9 cm settlement resulted (**Figures 10–12**).

**Figure 10.** *Vertical loads that the earth filling exerts on the conduit.*

**Figure 11.** *Conduit displacement with articulations in joints.*

**Figure 12.**

*Conduit displacements without articulations and equivalent moment of inertia.*

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

In the second calculation scheme, the nine continuous pipe sections were considered without interruptions in joints. A maximum of 32.6 cm settlement resulted.

The equivalent moment of inertia is calculated with Eq. (37):

$$\mathbf{I\_e = I} \frac{1}{2\mathbf{n}} = \mathbf{16.04} \frac{1}{2 \times 8} = \mathbf{1m^4}$$

#### **5. Conclusions**

where Ep = 18,000 kN/m<sup>2</sup> earth (foundation) modulus; H = 2 7.5 m = 15 m,

When loading with the weight of the ground, the weight of the conduit cassette

Two pipeline calculation schemes were used between the R3 and R12 joints (see **Figure 9**). The 5 m sections were removed from the calculation scheme and the

In the first diagram, the nine sections of the pipe were considered to be articulated at the ends. A maximum of 32.9 cm settlement resulted (**Figures 10–12**).

.

depth of influence; k = 1200 kN/m3

*Hydraulic Structures - Theory and Applications*

terminal sections embedded in the portal.

*Vertical loads that the earth filling exerts on the conduit.*

*Conduit displacement with articulations in joints.*

*Conduit displacements without articulations and equivalent moment of inertia.*

was added.

**Figure 10.**

**Figure 12.**

**34**

**Figure 11.**

We calculated conduits through FEM using analytical calculation for a finite element and calculation with a software (EngiLab Beam). In the calculation for a finite element, we have highlighted the stiffness matrices to understand the large value difference between the terms of the matrices and the physical significance of this difference.

The low rigidity of the ground slightly influences the state of stresses and deformations in the conduit. It follows that it is sufficient that the parameters of the earth are defined by the Winkler-type springs.

A first conclusion is that computational programs that allow the use of the Winkler-type springs give results with good accuracy (e.g., below 5%) for this type of structure. The overall view at this point is that the Winkler model is outdated.

The difference in conduit displacements calculated with the two methods of estimating the ground characteristics (the Winkler and multiple-parameter subgrade model) is small. It means that the shear stiffness introduced by multipleparameter subgrade models does not significantly change the result. It is therefore reasonable to use the Winkler parameters for the terrain characteristics. These considerations apply to conduits where the stiffness of the conduit (measured in the stiffness matrix) is 100 times higher than the rigidity of the earth (also expressed by the stiffness matrix).

The calculation of bottom discharge conduit as well as other long hydrotechnical structures is done with reasonable accuracy in the plane strain state. Finite element programs calculate stress state and deformations with this scheme. In the case of conduits, the influence of the joints between the sections must be modeled. If this is not done, the results are not credible. In the calculated example, we used two schemes: one with the pipe provided with joints and with the respective struts and the second with the pipe without joints (continuous) and with the inertia moment adjusted with the relation (37). The difference between the results obtained with these two schemes is small (1%). Models of finite element type are credible if the conduit is made jointless, which is unlikely.

Resuming the findings of this work are:

Using the rigidity matrix condensation, to solve the equilibrium equation for beams with deformable supports, facilitates solving the equation system (21).

We appreciate that the use of the Winkler-type springs is suitable for long rigid structures.

Calculation of conduit sections in plane strain state leads to credible results only if the moment of inertia is adjusted in accordance with pipe joints. For this we propose a relation of calculating the moment of equivalent inertia (37). If the inertia moment is not adjusted, the result obtained is not credible.

#### **Conflict of interest**

The author declares that there is no conflict of interest.

*Hydraulic Structures - Theory and Applications*

**References**

Editura Tehnica; 2002

[1] Popovici A. Dams for Water Storage. (in Romanian). Vol. 2. Bucuresti:

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

> [11] CSI. SAP2000 Analysis Reference Manual. Berkeley, CA: Computers and

[12] Geo-Studio. Stress-Deformation Modeling with SIGMA/W. Canada:

[13] Chandrupatla TR, Belegundu AD. Finite Elements in Engineering. 3rd ed.

[14] Jerca SH, Ungureanu N, Diaconu D. Numerical Methods in Construction Design (in Romanian). Romania: UT

[15] Bowles JE. Foundation Analysis and Design. 5th ed. Singapore: McGraw-Hill

[16] Boariu C. Soil structure interaction calculus, for rigid hydraulic structures, using FEM. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE).

[17] Kasey J. Stress Analysis of Soils Adjacent to Selected Outlet Conduit Configurations for Small Embankment Dams [Internet]. 2015. Available from: http://dnrc.mt.gov/divisions/water/ operations/dam-safety/OutletResearch FinalReport2015.08.18.pdf [Accessed:

[18] Boariu C, Bofu C. Safety Assurance on Existing Dams. Case Study— Tungujei Dam. In: 16th National Technical-Scientific Conference on Modern Technologies for the 3rd Millennium. ISBN: 978-88-87729-41-2; Oradea, Romania; Date: MAR 23–24,

[19] EngiLab. EngiLab Beam.2D 2015 (v2.2) software. 2015. http://www.

Structures, Inc.; 2016

Calgary, Alberta; 2012

Prentice Hall; 2002

Gh. Asachi Iasi; 1997

Book Co; 1996

2015;**12**:60-68

07 July 2018]

2017. pp. 7-12

engilab.com*/*

Construction, Problem Identification and Evaluation, Inspection, Maintenance, Renovation, and Repair, Technical Manual. Denver Colorado; 2005

[2] Federal Emergency Management Agency. Conduits through Embankment

Dams, Best Practices for Design,

[3] U.S. Army Corps of Engineers, Culverts, Conduits, and Pipes, EM

[4] Moser AP, Folkman SL. Buried Pipe Design. 3rd ed. New York: Mc Graw Hill; 2008. DOI: 10.1036/007147689X

[5] Teodoru IB, Musat V. Numerical Modeling of Structure Soil Interaction. Foundation Beams (in Romanian). Romania: Editura Politehnium Iasi;

[6] Horvath JS. Soil-Structure Interaction Research Project [Internet]. 2002. Available from: www.engineering. manhattan.edu/civil/CGT.html [Accessed: 12 September 2015]

[7] Horvath JS, Colasanti RJ. Practical Subgrade Model for Improved Soil-Structure Interaction Analysis: Model Development. International Journal of Geomechanics. 2011;**11**(1):59-64

Embankment Dams—Embankment Design, Design Standards No. 13,

[9] Bureau of Reclamation. Appurtenant Structures for Dams (Spillways and Outlet Works) Design Standards,

[10] Bureau of Reclamation. Design of Small Dams, 3rd ed. Washington DC;

[8] Bureau of Reclamation,

Chapter 2, 2012

October 2011

1987

**37**

1110–2-2902, 1997, 1998

2009

### **Author details**

Costel Boariu

Faculty of Hydrotechnical Engineering, Geodesy and Environmental Engineering, Gheorghe Asachi Technical University of Iasi, Romania

\*Address all correspondence to: costelboariu@gmail.com

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Bottom Discharge Conduit for Embankment Dams DOI: http://dx.doi.org/10.5772/intechopen.82357*

#### **References**

[1] Popovici A. Dams for Water Storage. (in Romanian). Vol. 2. Bucuresti: Editura Tehnica; 2002

[2] Federal Emergency Management Agency. Conduits through Embankment Dams, Best Practices for Design, Construction, Problem Identification and Evaluation, Inspection, Maintenance, Renovation, and Repair, Technical Manual. Denver Colorado; 2005

[3] U.S. Army Corps of Engineers, Culverts, Conduits, and Pipes, EM 1110–2-2902, 1997, 1998

[4] Moser AP, Folkman SL. Buried Pipe Design. 3rd ed. New York: Mc Graw Hill; 2008. DOI: 10.1036/007147689X

[5] Teodoru IB, Musat V. Numerical Modeling of Structure Soil Interaction. Foundation Beams (in Romanian). Romania: Editura Politehnium Iasi; 2009

[6] Horvath JS. Soil-Structure Interaction Research Project [Internet]. 2002. Available from: www.engineering. manhattan.edu/civil/CGT.html [Accessed: 12 September 2015]

[7] Horvath JS, Colasanti RJ. Practical Subgrade Model for Improved Soil-Structure Interaction Analysis: Model Development. International Journal of Geomechanics. 2011;**11**(1):59-64

[8] Bureau of Reclamation, Embankment Dams—Embankment Design, Design Standards No. 13, Chapter 2, 2012

[9] Bureau of Reclamation. Appurtenant Structures for Dams (Spillways and Outlet Works) Design Standards, October 2011

[10] Bureau of Reclamation. Design of Small Dams, 3rd ed. Washington DC; 1987

[11] CSI. SAP2000 Analysis Reference Manual. Berkeley, CA: Computers and Structures, Inc.; 2016

[12] Geo-Studio. Stress-Deformation Modeling with SIGMA/W. Canada: Calgary, Alberta; 2012

[13] Chandrupatla TR, Belegundu AD. Finite Elements in Engineering. 3rd ed. Prentice Hall; 2002

[14] Jerca SH, Ungureanu N, Diaconu D. Numerical Methods in Construction Design (in Romanian). Romania: UT Gh. Asachi Iasi; 1997

[15] Bowles JE. Foundation Analysis and Design. 5th ed. Singapore: McGraw-Hill Book Co; 1996

[16] Boariu C. Soil structure interaction calculus, for rigid hydraulic structures, using FEM. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE). 2015;**12**:60-68

[17] Kasey J. Stress Analysis of Soils Adjacent to Selected Outlet Conduit Configurations for Small Embankment Dams [Internet]. 2015. Available from: http://dnrc.mt.gov/divisions/water/ operations/dam-safety/OutletResearch FinalReport2015.08.18.pdf [Accessed: 07 July 2018]

[18] Boariu C, Bofu C. Safety Assurance on Existing Dams. Case Study— Tungujei Dam. In: 16th National Technical-Scientific Conference on Modern Technologies for the 3rd Millennium. ISBN: 978-88-87729-41-2; Oradea, Romania; Date: MAR 23–24, 2017. pp. 7-12

[19] EngiLab. EngiLab Beam.2D 2015 (v2.2) software. 2015. http://www. engilab.com*/*

**Author details**

Faculty of Hydrotechnical Engineering, Geodesy and Environmental Engineering,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Gheorghe Asachi Technical University of Iasi, Romania

\*Address all correspondence to: costelboariu@gmail.com

provided the original work is properly cited.

*Hydraulic Structures - Theory and Applications*

Costel Boariu

**36**

**Chapter 4**

**Abstract**

**1. Introduction**

cally measured.

experiment [4].

**39**

Structures

*Adeniyi Ganiyu Adeogun and*

*Apalando Abdulrasaq Mohammed*

determine discharge where weirs are not useful.

**Keywords:** flumes, notch, orifices, streamflow, weirs

Review of Methods of Measuring

The measurement of streamflow is very critical to hydraulic engineers and hydrologists as it provides vital information for environmental monitoring issues connected to water resources. The objective of this study is to examine various means of measuring streamflow specifically application of hydraulic structures installed across the direction of flow. Weirs are restricted to small rivers where the provision for sufficient head and constriction in the river is acceptable. Sharpcrested weir is easy to construct, and it is commonly used as a flow measuring device in an open channel. Flumes are self-cleaning due to the fact that the flow velocity through a flume is usually high. Traditionally, flume is used in measuring flow in agricultural systems, and it requires low maintenance cost. It has capacity to measure more flow rates than weir. Accurate streamflow measurement using flume is within 2–5% while that of weir is 2%. Generally, flumes are employed to

Streamflow is very important in estimating hydrology cycle [1]. In practice, hydraulic structures are installed in open channels or rivers with a free water level to estimate discharge based on the measured upstream water level [2]. The main critical factors in constructing hydraulic structures across an open channel

throughout the world are need for the reliable source of water supply, flood control, irrigation schemes, recreation activities and hydropower generation [3]. Technological interventions are needed for harnessing, conserving and proper management of water resources. Application of hydraulics structures in measuring streamflows in open channels is very important. Flumes and weirs are used in measuring streamflow in natural and artificial channels. Streamflow is manually or automati-

Flumes and weirs are designed and constructed to change flow regime from one

state to another. The parameters of flow measured in laboratory experiment of flume and models of weirs or spillways can be applied to an open channel prototype in real-life situation by manipulating the various scale models in the laboratory

Streamflow Using Hydraulic

#### **Chapter 4**
