Inspection Techniques

and Engineering. 2014;15(1):243-265. DOI: 10.1007/s11081-012-9199-x

Bridge Optimization - Inspection and Condition Monitoring

[21] Ryberg AB, Domeij Bäckryd R, Nilsson L. Metamodel-Based

for Automotive Applications. Linköping: Linköping University

W. Extended objective oriented sequential sampling method for robust design of complex systems against design uncertainty. In: Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE.

Electronic Press; 2012

2012. pp. 12-15

Springer; 2015

Multidisciplinary Design Optimization

[22] Zhang SL, Zhu P, Arendt PD, Chen

[23] Martinez J, Marti P. Metamodelbased multi-objective robust design optimization of structures. In: 12th International Conference on Optimum Design of Structures and Materials in Engineering; New Forest, UK. 2012

[24] Dellino G, Meloni C. Uncertainty

Optimization of Complex Systems: Algorithms and Applications. New York:

Management in Simulation

multioperator search strategy based on cheap surrogate models for evolutionary optimization. IEEE Transactions on Evolutionary Computation. 2015;19(5): 746-758. DOI: 10.1109/TEVC.2015.

[16] Zhou Q, Shao X, Jiang P, Gao Z, Zhou H, Shu L. An active learning variable-fidelity metamodelling approach based on ensemble of metamodels and objective-oriented sequential sampling. Journal of Engineering Design. 2016;27(4–6): 205-231. DOI: 10.1080/09544828.

[17] Belyaev M, Burnaev E, Kapushev E, Panov M, Prikhodko P, Vetrov D, et al. GTApprox: Surrogate modeling for industrial design. Advances in

Engineering Software. 2016;102:29-39. DOI: 10.1016/j.advengsoft.2016.09.001

[18] Sun C, Jin Y, Cheng R, Ding J, Zeng J. Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems. IEEE Transactions on Evolutionary Computation. 2017;21: 644-660. DOI: 10.1109/TEVC.2017.

[19] Sayyafzadeh M. Reducing the computation time of well placement optimisation problems using selfadaptive metamodelling. Journal of Petroleum Science and Engineering. 2017;151:143-158. DOI: 10.1016/j.

[20] Chatterjee T, Chakraborty S, Chowdhury R. A critical review of surrogate assisted robust design optimization. Archives of

Computational Methods in Engineering. 2017:1-30. DOI: 10.1007/s11831-017-

[15] Gong W, Zhou A, Cai Z. A

2449293

2015.1135236

2675628

9240-5

34

petrol.2016.12.015

**37**

**Chapter 3**

**Abstract**

*and Masahiro Ishida*

technical maintenance guidelines

**1. Introduction**

On-Site Bridge Inspection by

950 keV/3.95 MeV Portable

X-Band Linac X-Ray Sources

*Mitsuru Uesaka, Yuki Mitsuya, Katsuhiro Dobashi,* 

Many bridges around the world face aging problems and degradation of structural strength. Visual and hammering sound inspections are under way, but the status of inner reinforced iron rods and prestressed concrete (PC) wires has not yet been confirmed. Establishing a diagnosis method for bridges based on X-ray visualization is required to evaluate the health of bridges accurately and to help with the rationalization of bridge maintenance. We developed 950 keV/3.95 MeV X-band electron linac-based X-ray sources for on-site bridge inspection and visualized the inner structure of a lower floor slab. The information regarding wire conditions by X-ray results was used for the structural analysis of a bridge to evaluate its residual strength and sustainability. For more precise inspection of wire conditions, we applied three-dimensional image reconstruction methods for bridge mock-up samples. Partial-angle computed tomography (CT) and tomosynthesis provided cross-sectional images of the samples at 1 mm resolutions. Image processing techniques such as the curvelet transform were applied to evaluate diameter of PC wires by suppressing noise. Technical guidelines of bridge maintenance using the 950 keV/3.95 MeV X-ray sources are proposed. We plan to offer our technique and guidelines for safer and more reliable maintenance of bridges around the world.

**Keywords:** bridge inspection, X-ray, nondestructive test, linear accelerator, structural analysis, computed tomography, tomosynthesis, curvelet transform,

Maintaining the health of civil infrastructures such as bridges, roads, and tunnels is important to achieve a safe and reliable society [1–3]. Because a large number of concrete structures were built in the age of rapid economic growth in Japan, many of them are approaching their designed life spans. Thus, the development of a reliable health diagnosis technology is currently an urgent task. For example, many of the prestressed concrete (PC) bridges have life spans of 50 years, and they show apparent damage as they approach their designed life spans (**Figure 1**). Approximately 42 and 63% of all bridges will be over 50 years of age by 2021 and 2031, respectively.

*Joichi Kusano, Eiji Yoshida, Yoshinobu Oshima*

#### **Chapter 3**

## On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources

*Mitsuru Uesaka, Yuki Mitsuya, Katsuhiro Dobashi, Joichi Kusano, Eiji Yoshida, Yoshinobu Oshima and Masahiro Ishida*

### **Abstract**

Many bridges around the world face aging problems and degradation of structural strength. Visual and hammering sound inspections are under way, but the status of inner reinforced iron rods and prestressed concrete (PC) wires has not yet been confirmed. Establishing a diagnosis method for bridges based on X-ray visualization is required to evaluate the health of bridges accurately and to help with the rationalization of bridge maintenance. We developed 950 keV/3.95 MeV X-band electron linac-based X-ray sources for on-site bridge inspection and visualized the inner structure of a lower floor slab. The information regarding wire conditions by X-ray results was used for the structural analysis of a bridge to evaluate its residual strength and sustainability. For more precise inspection of wire conditions, we applied three-dimensional image reconstruction methods for bridge mock-up samples. Partial-angle computed tomography (CT) and tomosynthesis provided cross-sectional images of the samples at 1 mm resolutions. Image processing techniques such as the curvelet transform were applied to evaluate diameter of PC wires by suppressing noise. Technical guidelines of bridge maintenance using the 950 keV/3.95 MeV X-ray sources are proposed. We plan to offer our technique and guidelines for safer and more reliable maintenance of bridges around the world.

**Keywords:** bridge inspection, X-ray, nondestructive test, linear accelerator, structural analysis, computed tomography, tomosynthesis, curvelet transform, technical maintenance guidelines

#### **1. Introduction**

Maintaining the health of civil infrastructures such as bridges, roads, and tunnels is important to achieve a safe and reliable society [1–3]. Because a large number of concrete structures were built in the age of rapid economic growth in Japan, many of them are approaching their designed life spans. Thus, the development of a reliable health diagnosis technology is currently an urgent task. For example, many of the prestressed concrete (PC) bridges have life spans of 50 years, and they show apparent damage as they approach their designed life spans (**Figure 1**). Approximately 42 and 63% of all bridges will be over 50 years of age by 2021 and 2031, respectively.

#### **Figure 1.**

*Images of degraded bridge and parts. (i) Whole view of the bridge, (ii) degraded surface, and (iii) crack and leak of Ca components.*

Normally, concrete bridges are regularly inspected by visual check and hammering tests. If damages or abnormalities are detected, more detailed nondestructive tests (NDTs) must be conducted.

**39**

respectively.

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

NDT by X-ray radiography is one of the promising technologies for the detailed local inspection of a bridge. X-ray radiography provides high-resolution images of steel wires and rods inside thick concrete bridges. Its penetration capability depends on the thickness of the object and the energy of the X-ray; higher energy X-rays penetrate thicker concrete structures. However, the energy produced by X-ray sources for industrial NDTs is not sufficiently high for the inspection of bridges, because of their thick concrete structure. A low energy source does not provide clear contrast inside the concrete, and in addition, the exposure time required is very long. Some radioisotopes provide high-energy X(γ)-rays. However, they continuously emit X(γ)-rays and operator health becomes another concern. Thus, a new, safer bridge inspection technology using high-energy powerful X-ray sources is needed.

We have developed X-band electron linear accelerator (linac)-based portable X-ray sources with high maximum energies of 950 keV and 3.95 MeV and have been demonstrating X-ray inspection of infrastructures using these sources [4–7]. We have successfully conducted ten on-site inspections using these X-ray sources to date, and we are also working on technology development in laboratories using

The main focus of X-ray visualization of a bridge is damage of prestressed concrete (PC) wires and unfilled sheath pipes. Not only the rupture of wires but also the wastage of wires by corrosion reduces the residual strength of a bridge. Therefore, the quantitative evaluation of wire diameters within a resolution of 1 mm is required for X-ray imaging. The grout fill in the sheath pipes of a PC bridge is important to prevent wire corrosion from rainwater and to make the wires and the concrete operate as a composite material. Detecting unfilled sheath pipe areas by X-ray is therefore important for detecting wire damage or for calculating stress imbalances in the bridge. The results of X-ray visualization are used to evaluate the

residual strength of a bridge using a reliable numerical calculation method. The goal of our research is to establish a structural health diagnosis method based on X-ray imaging of the inner structure of a bridge. In this chapter, we present the results of X-ray imaging of an actual bridge still in use and the calculated results of its residual strength through a numerical simulation. Investigation of the validity of X-ray partial-angle computed tomography (CT) or tomosynthesis image

We used X-band (9.3 GHz) linac-based 950 keV/3.95 MeV X-ray sources for the inspection of the actual bridge. The systems are shown in **Figures 2** and **3**,

In the former, the electrons are accelerated up to 950 keV by radio-frequency (RF) fields. We also adopted the side-coupled standing wave-type accelerating structure. Electrons are injected into a Tungsten target that generates bremsstrahlung X-rays. The generated X-rays are collimated by a Tungsten collimator into the shape of a cone which has an opening angle of 17°. The most important is the X-ray intensity, which is 50 mSv/min at 1 m for a full magnetron RF power of 250 kW. The system consists of a 50-kg X-ray head, 50-kg magnetron box, and stationary electric power source and water chiller unit. The X-ray head and magnetron box are portable, and because they are connected to each other by a flexible waveguide, only the position and angle of the X-ray head are finely tuned. We have optimized the design with respect to X-ray intensity, compactness, and weight. The

reconstruction for precise bridge inspection was also performed.

**2. X-ray inspection and structural analysis of a bridge**

**2.1 950 keV/3.95 MeV X-ray sources**

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

samples from dismantled bridges.

#### *On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

NDT by X-ray radiography is one of the promising technologies for the detailed local inspection of a bridge. X-ray radiography provides high-resolution images of steel wires and rods inside thick concrete bridges. Its penetration capability depends on the thickness of the object and the energy of the X-ray; higher energy X-rays penetrate thicker concrete structures. However, the energy produced by X-ray sources for industrial NDTs is not sufficiently high for the inspection of bridges, because of their thick concrete structure. A low energy source does not provide clear contrast inside the concrete, and in addition, the exposure time required is very long. Some radioisotopes provide high-energy X(γ)-rays. However, they continuously emit X(γ)-rays and operator health becomes another concern. Thus, a new, safer bridge inspection technology using high-energy powerful X-ray sources is needed.

We have developed X-band electron linear accelerator (linac)-based portable X-ray sources with high maximum energies of 950 keV and 3.95 MeV and have been demonstrating X-ray inspection of infrastructures using these sources [4–7]. We have successfully conducted ten on-site inspections using these X-ray sources to date, and we are also working on technology development in laboratories using samples from dismantled bridges.

The main focus of X-ray visualization of a bridge is damage of prestressed concrete (PC) wires and unfilled sheath pipes. Not only the rupture of wires but also the wastage of wires by corrosion reduces the residual strength of a bridge. Therefore, the quantitative evaluation of wire diameters within a resolution of 1 mm is required for X-ray imaging. The grout fill in the sheath pipes of a PC bridge is important to prevent wire corrosion from rainwater and to make the wires and the concrete operate as a composite material. Detecting unfilled sheath pipe areas by X-ray is therefore important for detecting wire damage or for calculating stress imbalances in the bridge. The results of X-ray visualization are used to evaluate the residual strength of a bridge using a reliable numerical calculation method.

The goal of our research is to establish a structural health diagnosis method based on X-ray imaging of the inner structure of a bridge. In this chapter, we present the results of X-ray imaging of an actual bridge still in use and the calculated results of its residual strength through a numerical simulation. Investigation of the validity of X-ray partial-angle computed tomography (CT) or tomosynthesis image reconstruction for precise bridge inspection was also performed.

#### **2. X-ray inspection and structural analysis of a bridge**

#### **2.1 950 keV/3.95 MeV X-ray sources**

We used X-band (9.3 GHz) linac-based 950 keV/3.95 MeV X-ray sources for the inspection of the actual bridge. The systems are shown in **Figures 2** and **3**, respectively.

In the former, the electrons are accelerated up to 950 keV by radio-frequency (RF) fields. We also adopted the side-coupled standing wave-type accelerating structure. Electrons are injected into a Tungsten target that generates bremsstrahlung X-rays. The generated X-rays are collimated by a Tungsten collimator into the shape of a cone which has an opening angle of 17°. The most important is the X-ray intensity, which is 50 mSv/min at 1 m for a full magnetron RF power of 250 kW. The system consists of a 50-kg X-ray head, 50-kg magnetron box, and stationary electric power source and water chiller unit. The X-ray head and magnetron box are portable, and because they are connected to each other by a flexible waveguide, only the position and angle of the X-ray head are finely tuned. We have optimized the design with respect to X-ray intensity, compactness, and weight. The

*Bridge Optimization - Inspection and Condition Monitoring*

**38**

**Figure 1.**

*leak of Ca components.*

tests (NDTs) must be conducted.

Normally, concrete bridges are regularly inspected by visual check and hammering tests. If damages or abnormalities are detected, more detailed nondestructive

*Images of degraded bridge and parts. (i) Whole view of the bridge, (ii) degraded surface, and (iii) crack and* 


#### **Figure 2.**

*950 keV portable X-band linac-based X-ray source and its specifications. The maximum X-ray energy is 950 keV. The system consists of three units: X-ray head, magnetron, and power units.*

#### **Figure 3.**

*3.95 MeV portable X-band linac-based X-ray source and its major parameters. The system consists of four units: X-ray head, magnetron, power, and chiller units.*

parameters of the 950 keV X-ray source are summarized in the table of **Figure 2**. We place an X-ray detector on the opposite site of the X-ray source between the object and source to detect the transmitted X-rays through the object. We use a flat panel detector (FPD) from PerkinElmer Corporation for the detector.

The 3.95 MeV system is shown in **Figure 3**. This system consists of a 62-kg X-ray head with target collimator of 80 kg, magnetron box of 62 kg, electric power sources of 116 kg, and water cooling system of 30 kg. The X-ray head and magnetron box are portable, and the position and angle of the former are also finely tuned. The X-ray intensity of this system is 2 Gy/min at 1 m.

Calculated attenuations in concrete for the X-rays from the 950 keV/3.95 MeV sources are shown in **Figure 4**. The results indicate that concrete with thicknesses of up to 400 mm and 800 mm can be penetrated by the 950 keV/3.95 MeV sources, respectively.

#### **2.2 Compliance**

We comply with Japan's Law Concerning Prevention of Radiation Hazards Due to Radioisotopes and Regulations on Prevention of Ionizing Radiation Hazards when we use the 950 keV/3.95 MeV X-ray sources in the field for on-site bridge inspection. According to the law, an electron beam source below 1 MeV is not

**41**

similar to the 950 keV case.

**Figure 4.**

**2.3 X-ray transmission imaging**

are applicable for those types of inspections.

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

an accelerator. Thus, we comply with this regulation. The 950 keV X-ray source is registered with the local agency of labor supervision. We usually operate the source in a radiation-controlled area, which has a radiation safety system complying with the Regulations on Prevention of Ionizing Radiation Hazards. The use of the source outside the controlled area is also allowed. In this case, we temporally set up a controlled area at the measurement site and place sufficient shielding around the source and object to suppress the air dose rate below 1.3 mSv/3 months.

*Calculated results of attenuation for the X-rays in concrete from the 950 keV/3.95 MeV X-ray sources.*

Moreover, we have to set a temporal facility boundary of 250 μSv/3 months. Amendment of the law that allows the use of accelerators below 4 MeV only for on-site bridge inspection was implemented in Japan in 2005. After we completed governmental registration as a radiation source, we submitted for permission of use outside the radiation-controlled area. Finally, we performed the on-site inspection under the Regulations on Prevention of Ionizing Radiation Hazards

Three types of PC bridges (T-shaped bar type, box-shaped type, and hollow floor bar type) are investigated by the X-ray sources. Possible patterns of X-ray transmission and scanning (partial-angle CT and tomosynthesis) are depicted in **Figure 5**. An X-ray flat panel detector (FPD) and imaging plate (IP) are used for X-ray imaging acquisition. By using the FPD, online measurement in seconds is available so that sparse and fine-tuning of the position of the X-ray sources and detector can be accomplished. Stacking measurement in minutes is more appropriate for the IP. Imaging processing of IPs can be carried out on-site immediately. An aerial work platform and stage are used for measurement of the web and flange parts of a T-shaped bar bridge. The X-ray source can be installed inside a box for bottom floor slab inspection or on a pedestal for upper slabs of box-shaped bar types with the help of a crane. As for hollow floor bar types, the X-ray source is placed on the road or inside a hollow box. Even partial-angle CT and tomosynthesis

**Figure 6** shows typical transmission images of the inner structure of the slab of a

certain T-shaped bar-type bridge obtained by the 950 keV X-ray source. We successfully observed the inner structure in detail with the linac-based X-ray system.

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

#### **Figure 4.**

*Bridge Optimization - Inspection and Condition Monitoring*

parameters of the 950 keV X-ray source are summarized in the table of **Figure 2**. We place an X-ray detector on the opposite site of the X-ray source between the object and source to detect the transmitted X-rays through the object. We use a flat

*3.95 MeV portable X-band linac-based X-ray source and its major parameters. The system consists of four units:* 

*950 keV portable X-band linac-based X-ray source and its specifications. The maximum X-ray energy is* 

*950 keV. The system consists of three units: X-ray head, magnetron, and power units.*

The 3.95 MeV system is shown in **Figure 3**. This system consists of a 62-kg X-ray head with target collimator of 80 kg, magnetron box of 62 kg, electric power sources of 116 kg, and water cooling system of 30 kg. The X-ray head and magnetron box are portable, and the position and angle of the former are also finely tuned.

Calculated attenuations in concrete for the X-rays from the 950 keV/3.95 MeV sources are shown in **Figure 4**. The results indicate that concrete with thicknesses of up to 400 mm and 800 mm can be penetrated by the 950 keV/3.95 MeV sources,

We comply with Japan's Law Concerning Prevention of Radiation Hazards Due to Radioisotopes and Regulations on Prevention of Ionizing Radiation Hazards when we use the 950 keV/3.95 MeV X-ray sources in the field for on-site bridge inspection. According to the law, an electron beam source below 1 MeV is not

panel detector (FPD) from PerkinElmer Corporation for the detector.

The X-ray intensity of this system is 2 Gy/min at 1 m.

*X-ray head, magnetron, power, and chiller units.*

**40**

respectively.

**Figure 2.**

**Figure 3.**

**2.2 Compliance**

*Calculated results of attenuation for the X-rays in concrete from the 950 keV/3.95 MeV X-ray sources.*

an accelerator. Thus, we comply with this regulation. The 950 keV X-ray source is registered with the local agency of labor supervision. We usually operate the source in a radiation-controlled area, which has a radiation safety system complying with the Regulations on Prevention of Ionizing Radiation Hazards. The use of the source outside the controlled area is also allowed. In this case, we temporally set up a controlled area at the measurement site and place sufficient shielding around the source and object to suppress the air dose rate below 1.3 mSv/3 months. Moreover, we have to set a temporal facility boundary of 250 μSv/3 months. Amendment of the law that allows the use of accelerators below 4 MeV only for on-site bridge inspection was implemented in Japan in 2005. After we completed governmental registration as a radiation source, we submitted for permission of use outside the radiation-controlled area. Finally, we performed the on-site inspection under the Regulations on Prevention of Ionizing Radiation Hazards similar to the 950 keV case.

#### **2.3 X-ray transmission imaging**

Three types of PC bridges (T-shaped bar type, box-shaped type, and hollow floor bar type) are investigated by the X-ray sources. Possible patterns of X-ray transmission and scanning (partial-angle CT and tomosynthesis) are depicted in **Figure 5**. An X-ray flat panel detector (FPD) and imaging plate (IP) are used for X-ray imaging acquisition. By using the FPD, online measurement in seconds is available so that sparse and fine-tuning of the position of the X-ray sources and detector can be accomplished. Stacking measurement in minutes is more appropriate for the IP. Imaging processing of IPs can be carried out on-site immediately. An aerial work platform and stage are used for measurement of the web and flange parts of a T-shaped bar bridge. The X-ray source can be installed inside a box for bottom floor slab inspection or on a pedestal for upper slabs of box-shaped bar types with the help of a crane. As for hollow floor bar types, the X-ray source is placed on the road or inside a hollow box. Even partial-angle CT and tomosynthesis are applicable for those types of inspections.

**Figure 6** shows typical transmission images of the inner structure of the slab of a certain T-shaped bar-type bridge obtained by the 950 keV X-ray source. We successfully observed the inner structure in detail with the linac-based X-ray system.

#### **Figure 5.**

*Typical techniques of X-ray transmission/scanning inspections for bridges of T-shaped bar type, box-shaped bar type, and hollow floor bar type.*

**Figure 6.**

*Series of X-ray images of PC wires in a bottom slab of a box-shaped bar-type bridge acquired by the 950 keV X-ray source. Cutting and thinning of PC wires are observed.*

The PC wires were clearly visualized. Cutting and thinning of PC wires are clearly apparent. Reduction of the PC wire cross sections is estimated visually, and images are used for the structural analysis to evaluate any reduction of structural strength quantitatively.

PC wires, sheath, and grout in a web part of other T-shaped bar types obtained by the 950 keV X-ray source are given in **Figure 7**. Even grout filling and missing grout are clearly visible.

**43**

**Figure 7.**

**Figure 8.**

*in concrete are visualized.*

deep in the concrete are visualized.

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

**Figure 8** shows an X-ray transmission imaged by the 3.95 MeV X-ray source from a cut sample of a hollow flow bar-type PC bridge. Several PC wires located

*Cut sample from a hollow flow bar-type bridge and X-ray transmission image acquired by the 3.95 MeV X-ray source. The total thickness of the concrete where the X-rays penetrate is ~400 mm. Several PC wires located deep* 

*Surface view and X-ray transmission images of near PC wires, sheath, and grout in a web part of a T-shaped bar-type bridge acquired by the 950 keV X-ray source. Cracks and leak of Ca components are visible. Moreover,* 

*grout filling and missing grout are clearly observed in the near PC sheath.*

However, the contrast between the wires and concrete was not sufficiently high. We consider that one reason is noise produced by X-rays scattered by the concrete structure. The probability of Compton scattering of an X-ray becomes higher as the energy of the X-ray becomes higher. If Compton scattering occurs between an X-ray photon and an atom of the material, the photon loses a portion of its energy and changes its direction. Because the original energies of X-rays are high, the energies of scattered X-rays are also high. Thus, many photons may have been scattered within the concrete structure and were detected at the FPD. It is an important task to reduce the image noise caused by scattering X-rays. A possible means to resolve this issue is by introducing a fine pitch metal mesh in front of the FPD to absorb only the X-rays impinging on the FPD and block scattered X-rays coming from other directions. Of course, image processing can be used to reduce noise. This aspect is discussed later.

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

#### **Figure 7.**

*Bridge Optimization - Inspection and Condition Monitoring*

The PC wires were clearly visualized. Cutting and thinning of PC wires are clearly apparent. Reduction of the PC wire cross sections is estimated visually, and images are used for the structural analysis to evaluate any reduction of structural strength

*Series of X-ray images of PC wires in a bottom slab of a box-shaped bar-type bridge acquired by the 950 keV* 

*Typical techniques of X-ray transmission/scanning inspections for bridges of T-shaped bar type, box-shaped bar* 

PC wires, sheath, and grout in a web part of other T-shaped bar types obtained by the 950 keV X-ray source are given in **Figure 7**. Even grout filling and missing

**42**

quantitatively.

**Figure 6.**

**Figure 5.**

*type, and hollow floor bar type.*

grout are clearly visible.

*X-ray source. Cutting and thinning of PC wires are observed.*

*Surface view and X-ray transmission images of near PC wires, sheath, and grout in a web part of a T-shaped bar-type bridge acquired by the 950 keV X-ray source. Cracks and leak of Ca components are visible. Moreover, grout filling and missing grout are clearly observed in the near PC sheath.*

#### **Figure 8.**

*Cut sample from a hollow flow bar-type bridge and X-ray transmission image acquired by the 3.95 MeV X-ray source. The total thickness of the concrete where the X-rays penetrate is ~400 mm. Several PC wires located deep in concrete are visualized.*

**Figure 8** shows an X-ray transmission imaged by the 3.95 MeV X-ray source from a cut sample of a hollow flow bar-type PC bridge. Several PC wires located deep in the concrete are visualized.

However, the contrast between the wires and concrete was not sufficiently high. We consider that one reason is noise produced by X-rays scattered by the concrete structure. The probability of Compton scattering of an X-ray becomes higher as the energy of the X-ray becomes higher. If Compton scattering occurs between an X-ray photon and an atom of the material, the photon loses a portion of its energy and changes its direction. Because the original energies of X-rays are high, the energies of scattered X-rays are also high. Thus, many photons may have been scattered within the concrete structure and were detected at the FPD. It is an important task to reduce the image noise caused by scattering X-rays. A possible means to resolve this issue is by introducing a fine pitch metal mesh in front of the FPD to absorb only the X-rays impinging on the FPD and block scattered X-rays coming from other directions. Of course, image processing can be used to reduce noise. This aspect is discussed later.

#### **Figure 9.**

*Typical results of 3D nonlinear structural analysis of iron-reinforced concrete based on DuCOM-COM3 simulation using the cross-sectional reduction based on the measured X-ray transmission images such as those in*  **Figure 6***. Mesh model of the finite element method (FEM) and typical load pattern for structural degradation evaluation and stress contour results are shown in (i) and (ii), respectively. Curves of applied moment versus stress for the initial and degraded (measured) states are shown in (iii).*

#### **2.4 Three-dimensional structural analysis**

We calculated the residual strength of a block of the bridge using X-ray inspection results and the 3D nonlinear three-dimensional finite element method (FEM) software for reinforced concrete, named DuCOM-COM3 developed by Prof. Hirokazu Maekawa (Department of Civil Engineering, University of Tokyo). The model for FEM analysis is shown in **Figure 9**. We modeled a block of the bridge with an X-ray inspected part at its center, as shown in **Figure 9(i)**. The X-ray inspected part is 1600 mm in the longitudinal direction. The boundary conditions were the moments when the designed load is applied, which were calculated by Newmark's method.

As a result of the FEM analysis, we found that the stress increased about 0.3 MPa at the lower edge of the box girder. This is because the stress resistance was decreased owing to damage of some PC wires. On the other hand, the compressive stress at the upper edge was not affected. The 3D distributions of stress after wire damage are depicted in **Figure 9(ii)**. From the calculations, the load that generates concrete cracks is estimated as 8417 kN for the healthy condition and 8016 kN for the damaged condition. Curves of given moment versus stress for the initial and degraded states are shown in **Figure 9(iii)**. Although the residual strength decreased by approximately 5%, the stress after damage remained within the range of the allowable stress, and the bridge was judged as operable at its current condition.

#### **3. Three-dimensional image reconstruction methods for bridge inspection**

#### **3.1 Computed tomography and tomosynthesis for partial angle**

Three-dimensional information of the inner structure of the concrete bridge is more helpful than a simple X-ray transmission image if the structure is complicated by densely concentrated wires. In a simple radiography image, the wires are superimposed, and thus a precise evaluation of wire condition is not possible. However,

**45**

**Figure 10.**

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

at the detector, *Ii*, along the arrow in the figure is approximately given as

∞ ∫

*Coordinate system for the partial-angle CT. (i) Spatial domain, and (ii) Frequency domain.*

−∞

<sup>∞</sup> *f*(*x*, *y*) *exp*{−*j*2*π*(*x* + *vy*)}*dxdy*

The Fourier transform of *f(x, y)*, *F(μ, v)*, is given by the measured Radon trans-

∫*<sup>s</sup> f*(*x*, *y*)*ds* = *ln*\_\_

Therefore, the Radon integral is measured by

<sup>∞</sup> *f*(*x*, *y*)*ds* = ∫−∞

−∞

∫

= ∫−∞

−∞ ∞ ∫

−∞

*p*(*r*, *θ*) = ∫

form data as

where

*F*(*μ*, *v*) =

in a three-dimensional image, each wire can be separated, and evaluating the

X-ray CT has been a powerful tool used for this type of purpose in a wide variety of fields, such as medical and industrial applications. In a CT system, the X-ray source and the detector are rotated 360° around the object, and X-ray images are obtained at different angles. Slice images of the object will be reconstructed from the X-ray absorption factors calculated from the images. CT is widely used for the precise inspection of industrial products in the field of NDT; thus, we can expect it is also applicable for bridge inspections using higher energy

However, it is usually impossible to widely rotate the source and detector around a target part of a bridge because of limited spaces around the target. We therefore consider applying partial-angle CT for bridge inspections. In partial-angle CT, the source and the detector are rotated less than 360°, and cross-sectional images are reconstructed from those partial-angle projection images. Partial-angle CT formulation is explained as follows, and its coordinate system for the spatial domain is illustrated in **Figure 10(i)**. When the 2D X-ray attenuation constant distribution is *f(x, y)*, the relation between the initial X-ray intensity from the X-ray source, *I0*, and input intensity

*I*<sup>0</sup> = *Ii exp*{−∫<sup>s</sup> *f*(*x*, *y*)*ds*}, (1)

*Ii I*0

<sup>∞</sup> *p*(*r*, *θ*) *exp*(−*j*2*r*)*dr*, (4)

. (2)

<sup>∞</sup> *f*(*x*, *y*)*δ*(*xcosθ* + *ysinθ* − *r*)*dxdy*. (3)

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

X-rays.

diameters of the wires is easier and more precise.

#### *On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

in a three-dimensional image, each wire can be separated, and evaluating the diameters of the wires is easier and more precise.

X-ray CT has been a powerful tool used for this type of purpose in a wide variety of fields, such as medical and industrial applications. In a CT system, the X-ray source and the detector are rotated 360° around the object, and X-ray images are obtained at different angles. Slice images of the object will be reconstructed from the X-ray absorption factors calculated from the images. CT is widely used for the precise inspection of industrial products in the field of NDT; thus, we can expect it is also applicable for bridge inspections using higher energy X-rays.

However, it is usually impossible to widely rotate the source and detector around a target part of a bridge because of limited spaces around the target. We therefore consider applying partial-angle CT for bridge inspections. In partial-angle CT, the source and the detector are rotated less than 360°, and cross-sectional images are reconstructed from those partial-angle projection images. Partial-angle CT formulation is explained as follows, and its coordinate system for the spatial domain is illustrated in **Figure 10(i)**. When the 2D X-ray attenuation constant distribution is *f(x, y)*, the relation between the initial X-ray intensity from the X-ray source, *I0*, and input intensity at the detector, *Ii*, along the arrow in the figure is approximately given as

$$I\_0 = I\_i \exp\left\{-\int\_{\mathbb{S}} f(\mathbf{x}, \mathbf{y}) d\mathbf{s}\right\},\tag{1}$$

$$f\_i \, f(\infty, \mathcal{y}) \, d\mathfrak{s} = \, \ln \frac{I\_i}{I\_0}.\tag{2}$$

Therefore, the Radon integral is measured by

$$p(r, \theta) \quad = \prescript{\sim}{}{\ulcorner}\_{\rightsquigarrow}^{\rightsquigarrow} f(\mathbf{x}, \mathbf{y}) d\mathbf{s} \quad = \prescript{\sim}{}{\ulcorner}\_{\rightsquigarrow}^{\rightsquigarrow} f(\mathbf{x}, \mathbf{y}) \delta(\mathbf{x} \cos \theta + \mathbf{y} \sin \theta - r) d\mathbf{x} d\mathbf{y} . \tag{3}$$

The Fourier transform of *f(x, y)*, *F(μ, v)*, is given by the measured Radon transform data as

$$F(\mu, \upsilon) = \begin{bmatrix} \int\_{-\circ \circ}^{\circ \circ} \int\_{-\circ}^{\circ \circ} f(\varkappa, \upsilon) \exp\{-j2\pi(\mu \varkappa + \upsilon \eta)\} dxd\eta \\ = \int\_{-\circ}^{\circ \circ} p(r, \theta) \exp\{-j2\pi\rho r\} dr, \end{bmatrix} \tag{4}$$

where

*Bridge Optimization - Inspection and Condition Monitoring*

**2.4 Three-dimensional structural analysis**

*stress for the initial and degraded (measured) states are shown in (iii).*

Newmark's method.

**Figure 9.**

**for bridge inspection**

We calculated the residual strength of a block of the bridge using X-ray inspection results and the 3D nonlinear three-dimensional finite element method (FEM) software for reinforced concrete, named DuCOM-COM3 developed by Prof. Hirokazu Maekawa (Department of Civil Engineering, University of Tokyo). The model for FEM analysis is shown in **Figure 9**. We modeled a block of the bridge with an X-ray inspected part at its center, as shown in **Figure 9(i)**. The X-ray inspected part is 1600 mm in the longitudinal direction. The boundary conditions were the moments when the designed load is applied, which were calculated by

*Typical results of 3D nonlinear structural analysis of iron-reinforced concrete based on DuCOM-COM3 simulation using the cross-sectional reduction based on the measured X-ray transmission images such as those in*  **Figure 6***. Mesh model of the finite element method (FEM) and typical load pattern for structural degradation evaluation and stress contour results are shown in (i) and (ii), respectively. Curves of applied moment versus* 

As a result of the FEM analysis, we found that the stress increased about 0.3 MPa at the lower edge of the box girder. This is because the stress resistance was decreased owing to damage of some PC wires. On the other hand, the compressive stress at the upper edge was not affected. The 3D distributions of stress after wire damage are depicted in **Figure 9(ii)**. From the calculations, the load that generates concrete cracks is estimated as 8417 kN for the healthy condition and 8016 kN for the damaged condition. Curves of given moment versus stress for the initial and degraded states are shown in **Figure 9(iii)**. Although the residual strength decreased by approximately 5%, the stress after damage remained within the range of the allow-

Three-dimensional information of the inner structure of the concrete bridge is more helpful than a simple X-ray transmission image if the structure is complicated by densely concentrated wires. In a simple radiography image, the wires are superimposed, and thus a precise evaluation of wire condition is not possible. However,

able stress, and the bridge was judged as operable at its current condition.

**3. Three-dimensional image reconstruction methods** 

**3.1 Computed tomography and tomosynthesis for partial angle**

**44**

**Figure 10.** *Coordinate system for the partial-angle CT. (i) Spatial domain, and (ii) Frequency domain.*

$$\begin{array}{rcl} \mu & = & \rho \cos \theta, \nu & = & \rho \sin \theta, \\\\ \rho & = & \sqrt{u^2 + \nu^2}, \end{array}$$

and the coordinate system in the frequency domain is shown in **Figure 10(ii)**. In case of the partial-angle CT, the angle range is rather limited so that the Fourier transform data cannot be obtained in the whole frequency domain. Finally, the original X-ray attenuation distribution is calculated numerical by the filtered back projection method in the following:

$$f(\mathbf{x}, \mathbf{y}) = \int\_{-\infty}^{\infty} \int\_{-\infty}^{\infty} \mathbf{F}(\mu, \nu) \exp\left\{j2\pi(\mu\mathbf{x} + \nu\mathbf{y})\right\} d\mu d\nu. \tag{5}$$

Typical results for limited angles are introduced in Section 3.2.

Another promising technology for obtaining three-dimensional information inside a bridge is tomosynthesis. Tomosynthesis has been used for applications such as breast imaging or dental imaging [8]. In normal tomosynthesis, the source is rotated against the detector with limited angle, and "parallax" X-ray images are obtained. The cross-sectional images of a target object are reconstructed from the parallax images. Tomosynthesis has been used in applications where full-angle CT cannot be applied. Thus, it is also a promising technology for bridge inspections.

As a first step, we experimentally investigated the feasibility of partial-angle CT and tomosynthesis using mock-up samples of bridges.

#### **3.2 Image reconstruction**

We have applied the partial-angle CT and tomosynthesis to cut samples from the real PC bridge and acrylic phantoms.

The CT reconstructed results for PC wires in a cut sample of the flange part of a T-shaped bar bridge by scanning at 360, 180, and 90° using the 3.95 MeV X-ray

#### **Figure 11.**

*CT reconstructed results of PC wires in the flange part of a T-shaped bar bridge by scanning at 360, 180 and 90° using the 3.95 MeV X-ray source. All PC wires in a sheath are perfectly reconstructed by 360° scanning.*

**47**

**Figure 13.**

**Figure 12.**

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

the ellipse is almost the same as the real diameter of the PC wires.

source are shown in **Figure 11**. All PC wires in a sheath are perfectly reconstructed by 360° scanning. The circular shape is intrinsically deformed to an elliptic shape by partial-angle scanning using the CT algorithm. However, the minor axis diameter of

**Figure 12** is a reconstructed image of the cross section of an acrylic phantom

*Cross-sectional X-ray images of the acrylic phantom reconstructed by (i) full-angle CT and (ii) tomosynthesis.* 

*The tomosynthesis image was obtained with 25 projections taken in 3° steps.*

*Gray value plot of a profile in the tomosynthesis image of the acrylic phantom.*

by tomosynthesis. Although we also observed the deformation of the crosssectional shapes from circles to ellipses in tomosynthesis, we can estimate the original diameters from the minor axes of the ellipses. We extracted a profile from

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

#### *On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

source are shown in **Figure 11**. All PC wires in a sheath are perfectly reconstructed by 360° scanning. The circular shape is intrinsically deformed to an elliptic shape by partial-angle scanning using the CT algorithm. However, the minor axis diameter of the ellipse is almost the same as the real diameter of the PC wires.

**Figure 12** is a reconstructed image of the cross section of an acrylic phantom by tomosynthesis. Although we also observed the deformation of the crosssectional shapes from circles to ellipses in tomosynthesis, we can estimate the original diameters from the minor axes of the ellipses. We extracted a profile from

**Figure 12.**

*Bridge Optimization - Inspection and Condition Monitoring*

ρ = √

projection method in the following:

*f(x, y)* =

**3.2 Image reconstruction**

real PC bridge and acrylic phantoms.

*μ* = *cosθ*, *v* = *sinθ*,

∫

and tomosynthesis using mock-up samples of bridges.

−∞ ∞ ∫

−∞

Typical results for limited angles are introduced in Section 3.2.

\_\_\_\_\_\_ *u*<sup>2</sup> + *v*<sup>2</sup> ,

<sup>∞</sup> F*(μ, v) exp*{*j2π(μx + vy)*}*dμdv.* (5)

and the coordinate system in the frequency domain is shown in **Figure 10(ii)**. In case of the partial-angle CT, the angle range is rather limited so that the Fourier transform data cannot be obtained in the whole frequency domain. Finally, the original X-ray attenuation distribution is calculated numerical by the filtered back

Another promising technology for obtaining three-dimensional information inside a bridge is tomosynthesis. Tomosynthesis has been used for applications such as breast imaging or dental imaging [8]. In normal tomosynthesis, the source is rotated against the detector with limited angle, and "parallax" X-ray images are obtained. The cross-sectional images of a target object are reconstructed from the parallax images. Tomosynthesis has been used in applications where full-angle CT cannot be applied. Thus, it is also a promising technology for bridge inspections. As a first step, we experimentally investigated the feasibility of partial-angle CT

We have applied the partial-angle CT and tomosynthesis to cut samples from the

The CT reconstructed results for PC wires in a cut sample of the flange part of a T-shaped bar bridge by scanning at 360, 180, and 90° using the 3.95 MeV X-ray

*CT reconstructed results of PC wires in the flange part of a T-shaped bar bridge by scanning at 360, 180 and 90° using the 3.95 MeV X-ray source. All PC wires in a sheath are perfectly reconstructed by 360° scanning.*

**46**

**Figure 11.**

*Cross-sectional X-ray images of the acrylic phantom reconstructed by (i) full-angle CT and (ii) tomosynthesis. The tomosynthesis image was obtained with 25 projections taken in 3° steps.*

**Figure 13.** *Gray value plot of a profile in the tomosynthesis image of the acrylic phantom.*

**Figure 14.** *Image processing using the curvelet transform and evaluation of the diameter of PC wires.*

the tomosynthesis image and plotted its gray values (see **Figure 13**). The profile included three rods with different diameters (6, 8, and 10 mm). We were able to estimate the diameter of the center rod (8 mm) within 1 mm accuracy. From the profile plotting, the estimated diameter of the rods was between 7.2 and 8.0 mm.

#### **3.3 Image processing**

Software image processing is inevitable for this work. Fourier transform (FT) with low-pass filter, high-pass filter, and band-pass filter is a standard technique. If we apply FT with a low-pass filter, the image becomes blurred, and the boundary between an iron rod and a PC wire is difficult to recognize. As for FT with a high-pass filter, the boundary is emphasized, but the overall view is spotty. When we construct a gray value profile to evaluate the diameter of a rod or PC wire, the profile is noisy. Regarding a band-pass filter, trial and error is necessary to choose an appropriate band. Instead, the wavelet transform is effective for emphasizing local signals. Recently, the curvelet transform has become popular. It is an upgraded wavelet transform fit to emphasize curved and declined boundaries. We applied the curvelet transform to the X-ray transmission images of PC wires of the upper slab of the hollow box bar-type bridge (**Figure 6**). We attempted to evaluate the diameter of one of the PC wires in the somewhat blurred image of the 400 mm slab, which is close to the transmission limit of the X-rays from the 950 keV source. We can observe that spatially high-frequency noises are suppressed and the full width at half maximum (FWHM) can be used to estimate the diameter, which is 6.18 mm for the designed 7 mm wire as shown in **Figure 14**.

#### **4. Highlights from recent inspections of real bridges**

#### **4.1 Relationships between states of concrete surface and near PC wires**

We check the relationship between the states of a concrete surface and near inner PC wires. We evaluate cut samples from a decommissioned T-shaped bartype bridge. One example is shown in **Figure 15**. The surface concrete is somewhat degraded and cracked (see **Figure 15(i)**). The cut cross-sectional view and X-ray transmission image of the near PC wires are shown in **Figure 15(ii)** and **(iii)**, respectively. The PC wires look healthy in this case. Because this bridge was located near the sea, the degradation of the concrete was due to salt damage. Furthermore, a load

**49**

**Figure 16.**

*bar bridge measured by the 950 keV X-ray source.*

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

test was performed on this bridge. It was confirmed that its mechanical strength was not degraded, and this mechanically healthy bridge was wastefully decommissioned. In the above case, inner PC wires were healthy even though the surface concrete was degraded and cracked. Opposite cases involving corroded PC wires in bridges

*Typical case of heavily corrupted concrete surface (i) and healthy PC wires in a cut sample from a T-shaped bar bridge. The direction of the X-ray transmission is shown in (ii). X-ray transmission images of PC wires in* 

These facts indicate that visible and hammer-sound inspections are not necessarily sufficient for checking the degradation of a bridge's mechanical strength. X-ray inspection is needed to check the state of inner PC wires and to evaluate the

X-ray transmission images using the 950 keV source in the web part of the T-shaped bar-type bridge in the case of **Figure 7** overlap at the designated location of the two PC sheaths and wires, as shown in **Figure 16**. Grout fills the upper sheath but is missing in the lower. This is the first observation of grout missing after the initial construction. This vacancy may become a puddle of rainwater which would

*X-ray transmission images of grout filling and missing grout in the PC sheaths in the web part of a T-shaped* 

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

with healthy surface concrete have also been found.

mechanical strength of a bridge.

**Figure 15.**

*two sheaths are shown in (iii).*

**4.2 Filling and missing grout in PC sheath**

induce corrosion of PC wires in the near future.

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

*Bridge Optimization - Inspection and Condition Monitoring*

the tomosynthesis image and plotted its gray values (see **Figure 13**). The profile included three rods with different diameters (6, 8, and 10 mm). We were able to estimate the diameter of the center rod (8 mm) within 1 mm accuracy. From the profile plotting, the estimated diameter of the rods was between 7.2 and 8.0 mm.

*Image processing using the curvelet transform and evaluation of the diameter of PC wires.*

Software image processing is inevitable for this work. Fourier transform (FT) with low-pass filter, high-pass filter, and band-pass filter is a standard technique. If we apply FT with a low-pass filter, the image becomes blurred, and the boundary between an iron rod and a PC wire is difficult to recognize. As for FT with a high-pass filter, the boundary is emphasized, but the overall view is spotty. When we construct a gray value profile to evaluate the diameter of a rod or PC wire, the profile is noisy. Regarding a band-pass filter, trial and error is necessary to choose an appropriate band. Instead, the wavelet transform is effective for emphasizing local signals. Recently, the curvelet transform has become popular. It is an upgraded wavelet transform fit to emphasize curved and declined boundaries. We applied the curvelet transform to the X-ray transmission images of PC wires of the upper slab of the hollow box bar-type bridge (**Figure 6**). We attempted to evaluate the diameter of one of the PC wires in the somewhat blurred image of the 400 mm slab, which is close to the transmission limit of the X-rays from the 950 keV source. We can observe that spatially high-frequency noises are suppressed and the full width at half maximum (FWHM) can be used to estimate the diameter, which is 6.18 mm for the designed 7 mm wire as shown in

**4. Highlights from recent inspections of real bridges**

**4.1 Relationships between states of concrete surface and near PC wires**

We check the relationship between the states of a concrete surface and near inner PC wires. We evaluate cut samples from a decommissioned T-shaped bartype bridge. One example is shown in **Figure 15**. The surface concrete is somewhat degraded and cracked (see **Figure 15(i)**). The cut cross-sectional view and X-ray transmission image of the near PC wires are shown in **Figure 15(ii)** and **(iii)**, respectively. The PC wires look healthy in this case. Because this bridge was located near the sea, the degradation of the concrete was due to salt damage. Furthermore, a load

**48**

**Figure 14**.

**3.3 Image processing**

**Figure 14.**

**Figure 15.** *Typical case of heavily corrupted concrete surface (i) and healthy PC wires in a cut sample from a T-shaped bar bridge. The direction of the X-ray transmission is shown in (ii). X-ray transmission images of PC wires in two sheaths are shown in (iii).*

test was performed on this bridge. It was confirmed that its mechanical strength was not degraded, and this mechanically healthy bridge was wastefully decommissioned.

In the above case, inner PC wires were healthy even though the surface concrete was degraded and cracked. Opposite cases involving corroded PC wires in bridges with healthy surface concrete have also been found.

These facts indicate that visible and hammer-sound inspections are not necessarily sufficient for checking the degradation of a bridge's mechanical strength. X-ray inspection is needed to check the state of inner PC wires and to evaluate the mechanical strength of a bridge.

#### **4.2 Filling and missing grout in PC sheath**

X-ray transmission images using the 950 keV source in the web part of the T-shaped bar-type bridge in the case of **Figure 7** overlap at the designated location of the two PC sheaths and wires, as shown in **Figure 16**. Grout fills the upper sheath but is missing in the lower. This is the first observation of grout missing after the initial construction. This vacancy may become a puddle of rainwater which would induce corrosion of PC wires in the near future.

#### **Figure 16.**

*X-ray transmission images of grout filling and missing grout in the PC sheaths in the web part of a T-shaped bar bridge measured by the 950 keV X-ray source.*

**Figure 17.**

*Special inspection car for the 950 keV/3.95 MeV X-ray sources. (i) Front view, (ii) Back view, (iii) Control units, and (iv) On site set-up.*

#### **4.3 Special inspection car**

Our collaborator, Kanto Giken Co. (Tokai, Ibaraki, Japan), developed a new special inspection car for the X-ray sources as shown in **Figure 17**. It can carry the X-ray sources, detectors, computers, and inspectors and contains a diesel engine 100 V power source. Some diesel engine power sources have poor quality unstable output voltage and frequency (50 and 60 Hz in east and west Japan, respectively). The electric power source of the magnetron may be sensitive to such instability. To avoid this, we decided to acquire our own reliable diesel engine power source, which we can carry to perform on-site X-ray inspections anywhere in Japan.

#### **4.4 Tuning of position and angle of X-ray sources**

The most important procedure of this task are the sparse and fine-tuning of the position and angle of the X-ray sources with respect to the bridge part and the X-ray detectors (FPD and IP) as shown in **Figure 18(i)**, **(ii)**, and **(iii)**. The procedure typically requires approximately 1 h. We use an aerial work platform, stage, and special inspection car for initial settings ((i)), and then by using a rotating function of the X-ray head, we adjust its angle. Finally, fine-tuning among the X-ray source, targeted area, and detector is performed. The whole tuning procedure takes approximately 1 h. This procedure consists of using and setting many devices, including the X-ray sources, detectors, mechanical positioners, and so on.

Usually, we start setting up all devices at 9 am. We then perform sparse and finetuning of the position and angle of the X-ray sources and detectors and begin taking real measurement at 11 am. We scan several parts until 3 pm. Finally, dismantling and storing the equipment occurs between 3 pm and 5 pm. Targeted bridge parts are

**51**

complicated situations.

**Figure 18.**

*platform.*

**X-ray sources**

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

completely different depending on the three types of bridges (T-shaped bar, boxshaped bar, or hollow floor bar). Thus, we are always improving and upgrading not only the X-ray sources but also our devices and software to better deal with many

*Initial setup (i), control of angle (ii), and fine positioning (iii) of the 950 keV X-ray source with an aerial work* 

Damage to bridges in northern and highland areas in Japan is serious because water in the concrete of a bridge freezes and expands, causing cracks in the concrete. It may snow in those areas in winter. Therefore, inspections should not be carried out during winter. It often rains from June through October in the semitropical climate areas of Japan. We have to be prepared for rain and high humidity, so we use waterproof housing for electric sources and perform very careful equipment

treatments and inspections to avoid electric breakdown.

**5. Guidelines for special inspections using 950 keV/3.95 MeV** 

The Public Works Research Institute and the University of Tokyo are developing new technical guidelines for special inspections of bridges using 950 keV/3.95 MeV X-ray sources. An overview is provided in **Figure 19**. First, visual and hammer-sound inspection screening should be performed based on regular inspection guidelines. Advanced hardware and software techniques such as drawn and acoustic analysis are adopted in this step. If degraded parts are found, the special X-ray transmission inspection is performed using the 950 keV or 3.95 MeV X-ray sources, depending on the thickness of the concrete containing the degraded parts. Here, the states of PC wires and rods as affected by corrosion, cuts, and reduction of cross sections are quantitatively evaluated with spatial resolution of 1 mm. Then, 3D nonlinear structural analysis is performed to evaluate

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

**Figure 18.**

*Bridge Optimization - Inspection and Condition Monitoring*

**4.3 Special inspection car**

*units, and (iv) On site set-up.*

**Figure 17.**

anywhere in Japan.

**4.4 Tuning of position and angle of X-ray sources**

the X-ray sources, detectors, mechanical positioners, and so on.

Our collaborator, Kanto Giken Co. (Tokai, Ibaraki, Japan), developed a new special inspection car for the X-ray sources as shown in **Figure 17**. It can carry the X-ray sources, detectors, computers, and inspectors and contains a diesel engine 100 V power source. Some diesel engine power sources have poor quality unstable output voltage and frequency (50 and 60 Hz in east and west Japan, respectively). The electric power source of the magnetron may be sensitive to such instability. To avoid this, we decided to acquire our own reliable diesel engine power source, which we can carry to perform on-site X-ray inspections

*Special inspection car for the 950 keV/3.95 MeV X-ray sources. (i) Front view, (ii) Back view, (iii) Control* 

The most important procedure of this task are the sparse and fine-tuning of the position and angle of the X-ray sources with respect to the bridge part and the X-ray detectors (FPD and IP) as shown in **Figure 18(i)**, **(ii)**, and **(iii)**. The procedure typically requires approximately 1 h. We use an aerial work platform, stage, and special inspection car for initial settings ((i)), and then by using a rotating function of the X-ray head, we adjust its angle. Finally, fine-tuning among the X-ray source, targeted area, and detector is performed. The whole tuning procedure takes approximately 1 h. This procedure consists of using and setting many devices, including

Usually, we start setting up all devices at 9 am. We then perform sparse and finetuning of the position and angle of the X-ray sources and detectors and begin taking real measurement at 11 am. We scan several parts until 3 pm. Finally, dismantling and storing the equipment occurs between 3 pm and 5 pm. Targeted bridge parts are

**50**

*Initial setup (i), control of angle (ii), and fine positioning (iii) of the 950 keV X-ray source with an aerial work platform.*

completely different depending on the three types of bridges (T-shaped bar, boxshaped bar, or hollow floor bar). Thus, we are always improving and upgrading not only the X-ray sources but also our devices and software to better deal with many complicated situations.

Damage to bridges in northern and highland areas in Japan is serious because water in the concrete of a bridge freezes and expands, causing cracks in the concrete. It may snow in those areas in winter. Therefore, inspections should not be carried out during winter. It often rains from June through October in the semitropical climate areas of Japan. We have to be prepared for rain and high humidity, so we use waterproof housing for electric sources and perform very careful equipment treatments and inspections to avoid electric breakdown.

#### **5. Guidelines for special inspections using 950 keV/3.95 MeV X-ray sources**

The Public Works Research Institute and the University of Tokyo are developing new technical guidelines for special inspections of bridges using 950 keV/3.95 MeV X-ray sources. An overview is provided in **Figure 19**. First, visual and hammer-sound inspection screening should be performed based on regular inspection guidelines. Advanced hardware and software techniques such as drawn and acoustic analysis are adopted in this step. If degraded parts are found, the special X-ray transmission inspection is performed using the 950 keV or 3.95 MeV X-ray sources, depending on the thickness of the concrete containing the degraded parts. Here, the states of PC wires and rods as affected by corrosion, cuts, and reduction of cross sections are quantitatively evaluated with spatial resolution of 1 mm. Then, 3D nonlinear structural analysis is performed to evaluate

**Figure 19.**

*Guidelines for special X-ray transmission inspection using 950 keV/3.95 MeV X-ray sources accompanied with visual and hammer-sound inspections, structural analysis, final repair, and/or reinforcement.*

the degradation of the structural strength quantitatively. Based on this evaluation, repair, reinforcement, or other decisions should be reviewed. Several inspection industries are joining our project and technical transfer is being promoted. We hope to soon apply these guidelines to all aged bridges in Japan and finally across the world.

#### **6. Summary**

We have been developing a new X-ray diagnostic method for social and industrial infrastructures using linear accelerator-based X-ray sources. Our 950 keV/3.95 MeV X-ray sources have been applied to many different cases involving on-site X-ray inspection of bridges in Japan. We are currently undertaking on-site inspections of actual bridges. We have demonstrated X-ray inspection of an actual bridge still in use. Clear X-ray transmission images inside the concrete were successfully obtained in the demonstration. The information regarding PC wire conditions from X-ray images was applied to the structural analysis using the finite element method to evaluate the residual strength of a bridge. We found that the residual strength of the bridge in question had decreased by approximately 5% from its original state based on application of the designed load.

We also studied three-dimensional image reconstruction methods that can be applied to bridge inspections. Because of the limitations in spaces and rotation angles involved in actual on-site inspections, full-angle CT is normally not possible to apply for bridge inspections. Thus, we investigated the effectiveness of partialangle CT and tomosynthesis for bridge inspections. Although the cross-sectional shape of a wire or rod was deformed from its original circular shape to an ellipselike shape, we could estimate the diameter of the rod or wire from the length of the minor axis of the ellipse. The estimated diameter of a steel rod in a tomosynthesis image was in good agreement with its real value.

Further studies are required to realize the practical use of this X-ray bridge inspection method. We should continue the demonstrations involving on-site bridge inspection for different types of bridges and evaluate the effectiveness of the special X-ray transmission inspection using the 950 keV/3.95 MeV X-ray sources based on the new technical guidelines.

**53**

**Author details**

Mitsuru Uesaka1

Ibaraki, Japan

Yoshinobu Oshima3

provided the original work is properly cited.

\*, Yuki Mitsuya1

2 Accuthera Inc., Kawasaki, Kanagawa, Japan

Public Works Research Institute, Ibaraki, Japan

and Masahiro Ishida<sup>3</sup>

\*Address all correspondence to: uesaka@tokai.t.u-tokyo.ac.jp

© 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,

, Katsuhiro Dobashi1

1 Nuclear Professional School, School of Engineering, The University of Tokyo,

3 Center for Advanced Engineering Structural Assessment and Research,

, Joichi Kusano2

, Eiji Yoshida<sup>3</sup>

,

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources*

Mr. Kentaro Murata of XIT Co. for the partial CT analysis.

This work was supported by the "Infrastructure Maintenance, Renovation, and Management program" of Cross-ministerial Strategic Innovation Promotion Program (SIP), Cabinet Office, Government of Japan. The authors thank for

*DOI: http://dx.doi.org/10.5772/intechopen.82275*

**Acknowledgements**

*On-Site Bridge Inspection by 950 keV/3.95 MeV Portable X-Band Linac X-Ray Sources DOI: http://dx.doi.org/10.5772/intechopen.82275*

#### **Acknowledgements**

*Bridge Optimization - Inspection and Condition Monitoring*

the degradation of the structural strength quantitatively. Based on this evaluation, repair, reinforcement, or other decisions should be reviewed. Several inspection industries are joining our project and technical transfer is being promoted. We hope to soon apply these guidelines to all aged bridges in Japan and finally across

*Guidelines for special X-ray transmission inspection using 950 keV/3.95 MeV X-ray sources accompanied with* 

*visual and hammer-sound inspections, structural analysis, final repair, and/or reinforcement.*

We have been developing a new X-ray diagnostic method for social and industrial infrastructures using linear accelerator-based X-ray sources. Our 950 keV/3.95 MeV X-ray sources have been applied to many different cases involving on-site X-ray inspection of bridges in Japan. We are currently undertaking on-site inspections of actual bridges. We have demonstrated X-ray inspection of an actual bridge still in use. Clear X-ray transmission images inside the concrete were successfully obtained in the demonstration. The information regarding PC wire conditions from X-ray images was applied to the structural analysis using the finite element method to evaluate the residual strength of a bridge. We found that the residual strength of the bridge in question had decreased by approximately 5% from

We also studied three-dimensional image reconstruction methods that can be applied to bridge inspections. Because of the limitations in spaces and rotation angles involved in actual on-site inspections, full-angle CT is normally not possible to apply for bridge inspections. Thus, we investigated the effectiveness of partialangle CT and tomosynthesis for bridge inspections. Although the cross-sectional shape of a wire or rod was deformed from its original circular shape to an ellipselike shape, we could estimate the diameter of the rod or wire from the length of the minor axis of the ellipse. The estimated diameter of a steel rod in a tomosynthesis

Further studies are required to realize the practical use of this X-ray bridge inspection method. We should continue the demonstrations involving on-site bridge inspection for different types of bridges and evaluate the effectiveness of the special X-ray transmission inspection using the 950 keV/3.95 MeV X-ray sources

its original state based on application of the designed load.

image was in good agreement with its real value.

based on the new technical guidelines.

**52**

the world.

**Figure 19.**

**6. Summary**

This work was supported by the "Infrastructure Maintenance, Renovation, and Management program" of Cross-ministerial Strategic Innovation Promotion Program (SIP), Cabinet Office, Government of Japan. The authors thank for Mr. Kentaro Murata of XIT Co. for the partial CT analysis.

#### **Author details**

Mitsuru Uesaka1 \*, Yuki Mitsuya1 , Katsuhiro Dobashi1 , Joichi Kusano2 , Eiji Yoshida<sup>3</sup> , Yoshinobu Oshima3 and Masahiro Ishida<sup>3</sup>

1 Nuclear Professional School, School of Engineering, The University of Tokyo, Ibaraki, Japan

2 Accuthera Inc., Kawasaki, Kanagawa, Japan

3 Center for Advanced Engineering Structural Assessment and Research, Public Works Research Institute, Ibaraki, Japan

\*Address all correspondence to: uesaka@tokai.t.u-tokyo.ac.jp

© 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.

#### **References**

[1] Chang P et al. Review paper: Health monitoring of civil infrastructure. Structural Health Monitoring. 2003;**2**(3):257-267

[2] Cao H et al. Form-finding analysis of suspension bridges using an explicit iterative approach. Structural Engineering and Mechanics. 2017;**62**(1):85-95

[3] Qin S et al. Dynamic model updating for bridge structures using the kriging model and PSO algorithm ensemble with higher vibration modes. Sensors. 2018;**18**(6):1879

[4] Uesaka M et al. 950 keV, 3.95 MeV and 6 MeV X-band linacs for nondestructive evaluation and medicine. Nuclear Instruments and Methods in Physics Research A. 2011;**657**(1):82-87

[5] Natsui T et al. Development of a portable 950 KeV X-band Linac for NDT. American Institute of Physics Conference Proceedings Series. 2009;**1099**:75-78

[6] Uesaka M et al. Commissioning of portable 950 keV/3.95 MeV X-band linac X-ray source for on-site transmission testing. E-Journal of Advanced Maintenance. 2013;**5**(2):93-100

[7] Uesaka M et al. On-site nondestructive inspection of the actual bridge using the 950 keV X-band electron linac X-ray source. Journal of Disaster Research. 2017;**12**(3):578-584

[8] Niklason LT et al. Digital tomosynthesis in breast imaging. Radiology. 1997;**205**:399-406

**55**

Section 4

Fatigue Assessment

Section 4

## Fatigue Assessment

**54**

*Bridge Optimization - Inspection and Condition Monitoring*

[1] Chang P et al. Review paper: Health monitoring of civil infrastructure. Structural Health Monitoring.

[2] Cao H et al. Form-finding analysis of suspension bridges using an explicit iterative approach. Structural

[3] Qin S et al. Dynamic model updating for bridge structures using the kriging model and PSO algorithm ensemble with higher vibration modes. Sensors.

Engineering and Mechanics.

[4] Uesaka M et al. 950 keV,

3.95 MeV and 6 MeV X-band linacs for nondestructive evaluation and medicine. Nuclear Instruments and Methods in Physics Research A.

[5] Natsui T et al. Development of a portable 950 KeV X-band Linac for NDT. American Institute of Physics Conference Proceedings Series.

[6] Uesaka M et al. Commissioning of portable 950 keV/3.95 MeV X-band linac X-ray source for on-site transmission testing. E-Journal of Advanced Maintenance. 2013;**5**(2):93-100

[7] Uesaka M et al. On-site nondestructive inspection of the actual bridge using the 950 keV X-band electron linac X-ray source. Journal of Disaster Research. 2017;**12**(3):578-584

[8] Niklason LT et al. Digital tomosynthesis in breast imaging. Radiology. 1997;**205**:399-406

**References**

2003;**2**(3):257-267

2017;**62**(1):85-95

2018;**18**(6):1879

2011;**657**(1):82-87

2009;**1099**:75-78

**57**

bridge.

**1. Introduction**

**Chapter 4**

*and Chaoran Xu*

**Abstract**

Development of a Fatigue Life

Assessment Model for Pairing

Bridge Management Systems

*Timothy Saad, Chung C. Fu, Gengwen Zhao* 

Fatigue Damage Prognoses with

Fatigue damage is one of the primary safety concerns for steel bridges reaching the end of their design life. Currently, US federal requirements mandate regular inspection of steel bridges for fatigue cracks; however, these inspections rely on visual inspection, which is subjective to the inspector's physically inherent limitations. Structural health monitoring (SHM) can be implemented on bridges to collect data between inspection intervals and gather supplementary information on the bridges' response to loads. Combining SHM with finite element analyses, this paper integrates two analysis methods to assess fatigue damage in the crack initiation and crack propagation periods of fatigue life. The crack initiation period is evaluated using S-N curves, a process that is currently used by the FHWA and AASHTO to assess fatigue damage. The crack propagation period is evaluated with linear elastic fracture mechanic-based finite element models, which have been widely used to predict steady-state crack growth behavior. Ultimately, the presented approach will determine the fatigue damage prognoses of steel bridge elements and damage prognoses are integrated with current condition state classifications used in bridge management systems. A case study is presented to demonstrate how this approach can be used to assess fatigue damage on an existing steel

**Keywords:** fatigue, fatigue damage, structural health monitoring, damage prognoses,

In 2013, the American Society for Civil Engineers (ASCE) released an updated Infrastructure Report Card that found nearly 25% of the nation's bridges to be either structurally deficient or functionally obsolete. A bridge is considered structurally deficient (SD) when it is in need of significant maintenance, rehabilitation, or replacement due to deteriorated physical conditions and is considered functionally obsolete (FO) when it does not meet current standards, such as vertical clearances or lane widths. To make these condition assessments, the Federal Highway

fatigue assessment, bridge management systems, condition ratings

#### **Chapter 4**

## Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses with Bridge Management Systems

*Timothy Saad, Chung C. Fu, Gengwen Zhao and Chaoran Xu*

### **Abstract**

Fatigue damage is one of the primary safety concerns for steel bridges reaching the end of their design life. Currently, US federal requirements mandate regular inspection of steel bridges for fatigue cracks; however, these inspections rely on visual inspection, which is subjective to the inspector's physically inherent limitations. Structural health monitoring (SHM) can be implemented on bridges to collect data between inspection intervals and gather supplementary information on the bridges' response to loads. Combining SHM with finite element analyses, this paper integrates two analysis methods to assess fatigue damage in the crack initiation and crack propagation periods of fatigue life. The crack initiation period is evaluated using S-N curves, a process that is currently used by the FHWA and AASHTO to assess fatigue damage. The crack propagation period is evaluated with linear elastic fracture mechanic-based finite element models, which have been widely used to predict steady-state crack growth behavior. Ultimately, the presented approach will determine the fatigue damage prognoses of steel bridge elements and damage prognoses are integrated with current condition state classifications used in bridge management systems. A case study is presented to demonstrate how this approach can be used to assess fatigue damage on an existing steel bridge.

**Keywords:** fatigue, fatigue damage, structural health monitoring, damage prognoses, fatigue assessment, bridge management systems, condition ratings

#### **1. Introduction**

In 2013, the American Society for Civil Engineers (ASCE) released an updated Infrastructure Report Card that found nearly 25% of the nation's bridges to be either structurally deficient or functionally obsolete. A bridge is considered structurally deficient (SD) when it is in need of significant maintenance, rehabilitation, or replacement due to deteriorated physical conditions and is considered functionally obsolete (FO) when it does not meet current standards, such as vertical clearances or lane widths. To make these condition assessments, the Federal Highway

Administration uses information from inspection reports that are hosted by state and federal bridge management systems (BMS). BMS are heavily dependent on field inspectors, who collect information on bridge elements and bridge components, evaluate their condition, and enter this data into the BMS database. Among the various tasks of BMS, field inspection is the most essential in evaluating the current condition of steel bridges, which are vulnerable to fatigue-induced damage: the process of material degradation and/or cracking by repeated loads. Fatigue damage occurs over a long period of time and is the primary failure mechanism in steel bridges reaching their original design life [1]. Fatigue damage is largely dependent on the size of the traffic loadings, the frequency of the loads, and the type of detail under examination [2]. The damage usually initiates at the fatigue-prone areas of the bridge: the bridge connections, attachments, and details, such as welds connecting connection plates to steel girders. The defects begin to grow under repetitive loads until a bridge inspector finds the crack in a visual inspection. If the crack is not attended to, it will continue to grow until the structural component is capable of fracture and is also considered to be at the end of its total fatigue life.

Currently, the Federal Highway Administration (FHWA) uses fatigue life estimations to predict the performance of steel bridge members [3]. These fatigue estimates describe the onset of a crack by correlating the magnitude of the stress ranges with the number of load cycles the member has experienced. However, once cracking has occurred, there are no federal or state specifications for crack analysis or crack growth predictions. The fatigue life assessment can be more accurately characterized when crack growth analysis is also included in the assessment. This paper presents a fatigue life assessment method that combines the stress-cycle approach, currently used in AASHTO LRFD Bridge Design Specifications 2014, with a fracture mechanics approach. The damage accumulation results are integrated with current condition state classifications used in BMS.

#### **2. Fatigue life assessment modeling**

The fatigue life of a member is the number of load cycles a member can endure before confronting the structure's serviceability limit state. Within a structure's fatigue life, a structure is considered to experience deterioration in two different periods in time: crack initiation and crack propagation. The crack initiation period describes the time when cracks are just beginning to initiate from points of stress concentrations in structural details. Starting with an inclusion in the material, an initial microscopic crack grows a microscopically small amount in size each time a load is applied. The crack initiation period ends when a microscopic crack reaches a predefined critical crack size, typically a crack that is visible in size. The initiation period covers a significant part of the fatigue life. Once a fatigue crack has initiated, applied repeated stresses cause propagation, or growth, of a crack across the section of the member until the member is capable of fracture. The crack propagation period ends when a crack has reached a critical size or final crack size, determined from the material fracture toughness. When a structure has experienced a crack size at the end of the propagation life, the structure is capable of fracture and is also considered to be at the end of its total fatigue life. It is technically significant to consider the crack initiation and crack propagation stages separately because the practical conditions that have a large influence on the crack initiation period are different from the conditions that will influence the crack propagation period [4].

**59**

below 1 ksi [12].

*2.1.2 Bridge global model*

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

The crack initiation period corresponds to the onset of a fatigue crack in a component under traffic loads due to an applied stress. To properly account for the dynamic effects in traffic loads, it is necessary to gather a realistic set of data on the stress history that depends upon bridge traffic [5]. This can be accomplished

A SHM system gathers real-time measurements of a structure behavior under the effects of varying vehicle weights and their random combinations in multiple lanes. Therefore, the measured strain data reflects the loading conditions in the particular location of the strain gage. SHM methodologies can be divided into two main categories: a statistical/data model-based approach and a physical model-based approach. In the statistical model-based approach, only the measured response of the structure is considered for an assessment, while a physical model-based approach concentrates on the understanding of the structure from its physical model, and a finite element analysis is frequently employed and validated through SHM [6]. In the physical model-based approach, the field measurements verify and validate the finite element models, and a simulation of traffic loads can be used to

To accurately characterize load histories, the content of a measured signal should be summarized and quantified in a meaningful way. The rainflow cycle counting method is recognized as the most accurate way of representing variable amplitude loading [7] and is preferred for statistical analysis of load-time histories, as described in the standard of the American Society for Testing and Materials [8]. Rainflow counting method is advantageous to other range counting methods because it offers realistic counting results while preserving the amplitudes of the acquired stress ranges. As part of the cycle counting process, it is customary to remove small oscillations that are negligible contributors to fatigue damage. Further, the stress ranges caused from smaller vehicles are often considered negligible compared to trucks. This is not only established in *AASHTO Standard Specifications for Highway Bridges* [9], but the NCHRP Report, *Fatigue Evaluation of Steel Bridges* [10], also pays distinct attention to truckloads when estimating fatigue life, stating "the effective stress range shall be estimated as either the measured stress range or a calculated stress range value determined by using a fatigue truck as specified in the AASHTO LRFD Bridge Design Specification 2014 [11]." Because of the significance of truckloads compared with smaller vehicular passages, it is rational to neglect stress cycles

Alongside structural health monitoring, a three-dimensional finite element global model can be developed for linear elastic structural analyses. For a typical steel highway bridge, the global model includes the deck, girders, connection plates, and the cross frames to the girders. The global model contains only the main components of the bridge and is primarily used for modal analysis, finding the displacement output of the whole bridge, and critical fatigue location determination known as hotspots, i.e., the locations of known high tensile strength. Field measurements were taken to calibrate the finite element model,

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

through structural health monitoring (SHM).

conduct a structural damage assessment.

*2.1.1 Structural evaluation using structural health monitoring*

**2.1 Fatigue crack initiation period**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

#### **2.1 Fatigue crack initiation period**

*Bridge Optimization - Inspection and Condition Monitoring*

at the end of its total fatigue life.

**2. Fatigue life assessment modeling**

used in BMS.

Administration uses information from inspection reports that are hosted by state and federal bridge management systems (BMS). BMS are heavily dependent on field inspectors, who collect information on bridge elements and bridge components, evaluate their condition, and enter this data into the BMS database. Among the various tasks of BMS, field inspection is the most essential in evaluating the current condition of steel bridges, which are vulnerable to fatigue-induced damage: the process of material degradation and/or cracking by repeated loads. Fatigue damage occurs over a long period of time and is the primary failure mechanism in steel bridges reaching their original design life [1]. Fatigue damage is largely dependent on the size of the traffic loadings, the frequency of the loads, and the type of detail under examination [2]. The damage usually initiates at the fatigue-prone areas of the bridge: the bridge connections, attachments, and details, such as welds connecting connection plates to steel girders. The defects begin to grow under repetitive loads until a bridge inspector finds the crack in a visual inspection. If the crack is not attended to, it will continue to grow until the structural component is capable of fracture and is also considered to be

Currently, the Federal Highway Administration (FHWA) uses fatigue life estimations to predict the performance of steel bridge members [3]. These fatigue estimates describe the onset of a crack by correlating the magnitude of the stress ranges with the number of load cycles the member has experienced. However, once cracking has occurred, there are no federal or state specifications for crack analysis or crack growth predictions. The fatigue life assessment can be more accurately characterized when crack growth analysis is also included in the assessment. This paper presents a fatigue life assessment method that combines the stress-cycle approach, currently used in AASHTO LRFD Bridge Design Specifications 2014, with a fracture mechanics approach. The damage accumulation results are integrated with current condition state classifications

The fatigue life of a member is the number of load cycles a member can endure before confronting the structure's serviceability limit state. Within a structure's fatigue life, a structure is considered to experience deterioration in two different periods in time: crack initiation and crack propagation. The crack initiation period describes the time when cracks are just beginning to initiate from points of stress concentrations in structural details. Starting with an inclusion in the material, an initial microscopic crack grows a microscopically small amount in size each time a load is applied. The crack initiation period ends when a microscopic crack reaches a predefined critical crack size, typically a crack that is visible in size. The initiation period covers a significant part of the fatigue life. Once a fatigue crack has initiated, applied repeated stresses cause propagation, or growth, of a crack across the section of the member until the member is capable of fracture. The crack propagation period ends when a crack has reached a critical size or final crack size, determined from the material fracture toughness. When a structure has experienced a crack size at the end of the propagation life, the structure is capable of fracture and is also considered to be at the end of its total fatigue life. It is technically significant to consider the crack initiation and crack propagation stages separately because the practical conditions that have a large influence on the crack initiation period are different from the conditions that will influence the crack

**58**

propagation period [4].

The crack initiation period corresponds to the onset of a fatigue crack in a component under traffic loads due to an applied stress. To properly account for the dynamic effects in traffic loads, it is necessary to gather a realistic set of data on the stress history that depends upon bridge traffic [5]. This can be accomplished through structural health monitoring (SHM).

#### *2.1.1 Structural evaluation using structural health monitoring*

A SHM system gathers real-time measurements of a structure behavior under the effects of varying vehicle weights and their random combinations in multiple lanes. Therefore, the measured strain data reflects the loading conditions in the particular location of the strain gage. SHM methodologies can be divided into two main categories: a statistical/data model-based approach and a physical model-based approach. In the statistical model-based approach, only the measured response of the structure is considered for an assessment, while a physical model-based approach concentrates on the understanding of the structure from its physical model, and a finite element analysis is frequently employed and validated through SHM [6]. In the physical model-based approach, the field measurements verify and validate the finite element models, and a simulation of traffic loads can be used to conduct a structural damage assessment.

To accurately characterize load histories, the content of a measured signal should be summarized and quantified in a meaningful way. The rainflow cycle counting method is recognized as the most accurate way of representing variable amplitude loading [7] and is preferred for statistical analysis of load-time histories, as described in the standard of the American Society for Testing and Materials [8]. Rainflow counting method is advantageous to other range counting methods because it offers realistic counting results while preserving the amplitudes of the acquired stress ranges. As part of the cycle counting process, it is customary to remove small oscillations that are negligible contributors to fatigue damage. Further, the stress ranges caused from smaller vehicles are often considered negligible compared to trucks. This is not only established in *AASHTO Standard Specifications for Highway Bridges* [9], but the NCHRP Report, *Fatigue Evaluation of Steel Bridges* [10], also pays distinct attention to truckloads when estimating fatigue life, stating "the effective stress range shall be estimated as either the measured stress range or a calculated stress range value determined by using a fatigue truck as specified in the AASHTO LRFD Bridge Design Specification 2014 [11]." Because of the significance of truckloads compared with smaller vehicular passages, it is rational to neglect stress cycles below 1 ksi [12].

#### *2.1.2 Bridge global model*

Alongside structural health monitoring, a three-dimensional finite element global model can be developed for linear elastic structural analyses. For a typical steel highway bridge, the global model includes the deck, girders, connection plates, and the cross frames to the girders. The global model contains only the main components of the bridge and is primarily used for modal analysis, finding the displacement output of the whole bridge, and critical fatigue location determination known as hotspots, i.e., the locations of known high tensile strength. Field measurements were taken to calibrate the finite element model, accelerometers were used to capture the bridge frequency, laser sensors and potentiometers were used to measure the dynamic deflection of the bridge, and strain gages were used on connection plates to capture the stresses of bridge components. The simulation of truckloads on the global model will output the stresses of all the components on the bridge.

#### *2.1.3 Global simulation modeling*

Global simulation modeling uses a three-dimensional model of a bridge with a traffic simulation to estimate fatigue damage. The fidelity of the fatigue assessment is dependent on the accuracy of the traffic load model and the accuracy of the structural model. Since larger loads (i.e., truckloads) are major contributors to fatigue damage and the global simulation model requires computational complexity, the traffic simulation only considers truck loading data for the fatigue assessment. There are two main components of truckloads to consider: the loading configuration (i.e., axle weights and axle spacing) and the traffic patterns. Weigh stations and traffic monitoring systems are often used by State Transportation Departments to acquire loading configuration and traffic pattern data. This data can be used to develop a traffic load simulation, also referred to as the truckload spectra.

To generate load configuration data, the *Guide Specifications for Fatigue Evaluation of Existing Steel Bridges* [13] recommends collecting data through weigh station measurements. A weigh station is a checkpoint equipped with truck scales. Trucks and commercial vehicles are subject to passing the scales at a very low speed and return to the highway after inspection. Data collected from weigh station measurements includes the number of axles and the axle spacing. The collection of truck traffic data at weigh stations can be used to calculate the effective gross weight of the truck spectra:

$$\mathbf{W} = \left(\sum f\_i^r \mathbf{W}\_i^3\right)^{1/3} \tag{1}$$

**61**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

or the specimen can be classified to have (100 – x)% remaining useful life. This damage may not be visible upon inspection but is still present in the material. Since the data in S-N curves were developed under constant amplitude cyclic loading, an effective stress range should be calculated to equivalently represent the variable amplitude cyclic loading on bridge structures. The effective stress range for a variable amplitude spectrum is defined as the constant amplitude stress range that would result in the same fatigue life as the variable amplitude spectrum. For steel structures, the root mean cube stress range (Eq. 2) is calculated from a variable amplitude stress range histogram and is used with the constant amplitude S-N

> 3 ) 1/3

where Sri is the midwidth of the *i*th bar, or interval, in the frequency-of-occurrence

The damage accumulation of crack initiation period, *di*, is calculated by comparing the effective stress range to the predefined laboratory values of specimens which are used to construct the S-N curve. Thus, the cumulative damage from the crack initiation life is written as a percentage of the fatigue life by dividing the number of current cycles at the effective stress range, N*e*, by the number of stress cycles to fatigue failure, N*f*:

In the crack propagation period, the crack is considered to be a macro-crack and is now growing through the material. The rate of this crack growth is highly dependent on the material type. While the nature of the material cracking is a nonelastic deformation, the region beyond the crack (at the crack tip) experiences a linear

Because the stresses at the crack tip are so small in fatigue problems, the plastic zone is limited, and linear elastic fracture mechanics (LEFM) can be used to assess fatigue crack propagation. Paris model is most widely used model in linear elastic fracture mechanics for the prediction of crack growth. In this model, the range of the stress intensity factor is the main factor driving the crack growth with two

where *a* is the initial crack size, *N* is the number of fatigue loading cycles, C and m are material properties, and ∆*<sup>K</sup>* is the stress intensification factor. For a given initial crack size, once the crack growth rate is determined, then the existing crack size can be easily calculated through a summation over crack size increments start-

(100)% (3)

dN <sup>=</sup> C(∆K)m (4)

histogram, 3 is the reciprocal of the slope in the constant S-N curve, and <sup>γ</sup>*<sup>i</sup>*

⁄N*f*

(2)

is the

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

curves for fatigue life analyses [14]:

*Sre* = (∑γ*iSri*

fraction of stress ranges in that same interval [15].

*2.1.5 Damage accumulation: crack initiation period*

*di* = <sup>N</sup>*<sup>e</sup>*

**2.2 Fatigue crack propagation period**

elastic stress field under load.

*2.2.1 Linear elastic fracture mechanics*

\_\_\_ <sup>d</sup>*<sup>a</sup>*

ing from the known size.

parameters C and m that reflect the material properties:

where *fi* is the fraction of gross weights within an interval and *Wi* is the midwidth of the interval.

The traffic patterns are another influence to fatigue damage. The actual traffic flow through a bridge is affected by the traffic on the connecting roadways. Automatic traffic recorders can be used to realistically capture the actual traffic patterns, such as vehicle speed, lane distribution, and vehicle position. Timevarying vehicular count data combined with weigh station measurements are used to develop a probabilistic-based truck simulation model. After obtaining the timehistory spectra, the fatigue life and the remaining fatigue life for this detail can be calculated as a function of stress range and number of cycles. Detailed traffic load simulation is reported in a separate companion paper, *Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic Simulation*.

#### *2.1.4 Crack initiation life prediction*

The crack initiation period is characterized by the S-N curve. S-N curves are used to relate the stress range (S) vs. number of loading cycles (ni) and ultimately define the fatigue life of the material. S-N curves comprise the influence of material, the geometry of the local structure, and the surface condition. Failure for the crack initiation period is defined by a crack that is of a critical size. Until the onset of this fatigue crack, the specimen can be characterized by the amount of current fatigue damage in terms of its fatigue life. So, the specimen may be at x% of its fatigue life,

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

or the specimen can be classified to have (100 – x)% remaining useful life. This damage may not be visible upon inspection but is still present in the material.

Since the data in S-N curves were developed under constant amplitude cyclic loading, an effective stress range should be calculated to equivalently represent the variable amplitude cyclic loading on bridge structures. The effective stress range for a variable amplitude spectrum is defined as the constant amplitude stress range that would result in the same fatigue life as the variable amplitude spectrum. For steel structures, the root mean cube stress range (Eq. 2) is calculated from a variable amplitude stress range histogram and is used with the constant amplitude S-N curves for fatigue life analyses [14]:

$$\mathbf{S}\_{rc} = \left(\boldsymbol{\Sigma}\boldsymbol{\gamma}\_i \mathbf{S}\_{ri}^3\right)^{1/3} \tag{2}$$

where Sri is the midwidth of the *i*th bar, or interval, in the frequency-of-occurrence histogram, 3 is the reciprocal of the slope in the constant S-N curve, and <sup>γ</sup>*<sup>i</sup>* is the fraction of stress ranges in that same interval [15].

#### *2.1.5 Damage accumulation: crack initiation period*

The damage accumulation of crack initiation period, *di*, is calculated by comparing the effective stress range to the predefined laboratory values of specimens which are used to construct the S-N curve. Thus, the cumulative damage from the crack initiation life is written as a percentage of the fatigue life by dividing the number of current cycles at the effective stress range, N*e*, by the number of stress cycles to fatigue failure, N*f*:

$$d\_i = \text{"}\!\!\!\!\!/\text \!\!\/(\mathbf{100})\,\text{@}\!\!\!\mathbf{0}\,\text{d}\mathbf{amage}\,\text{}\tag{3}$$

#### **2.2 Fatigue crack propagation period**

In the crack propagation period, the crack is considered to be a macro-crack and is now growing through the material. The rate of this crack growth is highly dependent on the material type. While the nature of the material cracking is a nonelastic deformation, the region beyond the crack (at the crack tip) experiences a linear elastic stress field under load.

#### *2.2.1 Linear elastic fracture mechanics*

Because the stresses at the crack tip are so small in fatigue problems, the plastic zone is limited, and linear elastic fracture mechanics (LEFM) can be used to assess fatigue crack propagation. Paris model is most widely used model in linear elastic fracture mechanics for the prediction of crack growth. In this model, the range of the stress intensity factor is the main factor driving the crack growth with two parameters C and m that reflect the material properties:

$$\frac{d\mathbf{a}}{d\mathbf{N}} = \mathbf{C} \left(\Delta \mathbf{K}\right)^{\mathbf{m}} \tag{4}$$

where *a* is the initial crack size, *N* is the number of fatigue loading cycles, C and m are material properties, and ∆*<sup>K</sup>* is the stress intensification factor. For a given initial crack size, once the crack growth rate is determined, then the existing crack size can be easily calculated through a summation over crack size increments starting from the known size.

*Bridge Optimization - Inspection and Condition Monitoring*

of all the components on the bridge.

*2.1.3 Global simulation modeling*

of the truck spectra:

of the interval.

*W* = (∑*fiWi*

*2.1.4 Crack initiation life prediction*

accelerometers were used to capture the bridge frequency, laser sensors and potentiometers were used to measure the dynamic deflection of the bridge, and strain gages were used on connection plates to capture the stresses of bridge components. The simulation of truckloads on the global model will output the stresses

Global simulation modeling uses a three-dimensional model of a bridge with a traffic simulation to estimate fatigue damage. The fidelity of the fatigue assessment is dependent on the accuracy of the traffic load model and the accuracy of the structural model. Since larger loads (i.e., truckloads) are major contributors to fatigue damage and the global simulation model requires computational complexity, the traffic simulation only considers truck loading data for the fatigue assessment. There are two main components of truckloads to consider: the loading configuration (i.e., axle weights and axle spacing) and the traffic patterns. Weigh stations and traffic monitoring systems are often used by State Transportation Departments to acquire loading configuration and traffic pattern data. This data can be used to

> 3 ) 1/3

(1)

is the midwidth

develop a traffic load simulation, also referred to as the truckload spectra. To generate load configuration data, the *Guide Specifications for Fatigue Evaluation of Existing Steel Bridges* [13] recommends collecting data through weigh station measurements. A weigh station is a checkpoint equipped with truck scales. Trucks and commercial vehicles are subject to passing the scales at a very low speed and return to the highway after inspection. Data collected from weigh station measurements includes the number of axles and the axle spacing. The collection of truck traffic data at weigh stations can be used to calculate the effective gross weight

where *fi* is the fraction of gross weights within an interval and *Wi*

*Bridges under Traffic Loading Using Microscopic Traffic Simulation*.

The traffic patterns are another influence to fatigue damage. The actual traffic flow through a bridge is affected by the traffic on the connecting roadways. Automatic traffic recorders can be used to realistically capture the actual traffic patterns, such as vehicle speed, lane distribution, and vehicle position. Timevarying vehicular count data combined with weigh station measurements are used to develop a probabilistic-based truck simulation model. After obtaining the timehistory spectra, the fatigue life and the remaining fatigue life for this detail can be calculated as a function of stress range and number of cycles. Detailed traffic load simulation is reported in a separate companion paper, *Fatigue Assessment of Highway* 

The crack initiation period is characterized by the S-N curve. S-N curves are used to relate the stress range (S) vs. number of loading cycles (ni) and ultimately define the fatigue life of the material. S-N curves comprise the influence of material, the geometry of the local structure, and the surface condition. Failure for the crack initiation period is defined by a crack that is of a critical size. Until the onset of this fatigue crack, the specimen can be characterized by the amount of current fatigue damage in terms of its fatigue life. So, the specimen may be at x% of its fatigue life,

**60**

#### *2.2.2 Stress intensity factor*

The stress in the local crack tip is described as a function of the applied stress in the form of a stress intensity factor (SIF). SIFs are used to describe the severity of a stress distribution around a crack tip, the rate of crack growth, and the onset of fracture [16]. Even at relatively low loads, there will be a high concentration of stress at the crack tip, and plastic deformation can occur [17]. The simplest form to describe the "intensity" of a stress distribution around a crack tip can be written as

$$K = \rho \mathbf{S} \mathbf{S} \sqrt{\overline{\mathbf{n} \mathbf{a}}} \tag{5}$$

where *S* is the remote loading stress, *a* is the crack length, and β is a dimensionless factor depending on the geometry of the specimen or structural component. One important feature this equation illustrates is that the stress distribution around the crack tip can be described as a linear function.

For many ordinary cases of cracking, the calculations of stress intensification factors for various crack geometries and loading cases have already been computed and can be obtained from previously published literature, e.g., elliptical cracks embedded in very large bodies [4]. However, for cases with more complex geometries, more accurate *K* values should be independently calculated. Finite element modeling (FEM) offers a variety of techniques and efficient computation and has proven to offer satisfactory results for the stress intensification factors [4]. In finite element models, the crack is treated as an integral part of the structure and can be modeled in as much detail as necessary to accurately reflect the structural load paths, both near and far from the crack tip.

#### *2.2.3 Fracture toughness*

When the crack grows to a particular size, the stresses at the crack tip are too high for the material to endure, and fracture takes place. This critical stress intensity value is more often referred to as the fracture toughness, *K*Ic, where *I* denotes opening mode and *c* represents critical. Fracture toughness is a measured material property, just like Poisson's ratio or Young's modulus, and is usually measured through standard compact specimens. The fracture toughness is used to describe the ability of an already cracked material to resist fracture or to indicate the sensitivity of the material and the material's susceptibility to experiencing cracks under loading [4]. Thus, SIFs can be compared with the fracture toughness variables to determine if the crack will propagate and to determine the size of crack a material can endure until fracture [18]. When the applied stress intensity equals or exceeds the material fracture resistance, *KIC*, fracture is predicted.

#### *2.2.4 Crack propagation period cumulative damage*

Models that predict fatigue crack growth propagation emphasize that crack growth is largely dependent on the cycle-by-cycle process. Prediction models are referred to as interaction models and non-interaction models. Interaction effects imply that the crack growth rate in a particular cycle is also dependent on the load history of the preceding cycles rather than an independent effect from one cycle. A non-interaction prediction model is used if the interaction effects in the variable amplitude history are assumed to be absent. In a non-interaction model, crack growth in each cycle is assumed to be dependent on the severity of the current cycle only and not on the load history in the preceding cycles. While it is expected that a non-interaction model will lead to a more conservative life prediction than models

**63**

**Figure 1.**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

that account for interaction effects, considering interaction effects account for retardation in crack growth, a non-interaction model can provide quick and useful information about fatigue crack growth behavior, particularly crack growth rates [4]. The non-interaction prediction model leads to a simple numerical summation

> *i*=1 *i*=*n*

The accumulation of damage for fatigue crack growth models is consequent of the change in crack size, *a*, where *a*0 is the initial crack size, ∆*ai* is the change in crack size per cycle, and *an* is the updated crack size [4]. Thus, the cumulative damage from the fatigue crack propagation period, *dp*, is written as a percentage of the fatigue life by

The assessment for the crack initiation period and the assessment for the crack propagation period can be combined to determine a damage prognosis, *DTotal*, for the

where *Ne* is the number of cycles the element has currently experienced, *Nf*

α*Idi*,*Ne* ≤ *Nf* <sup>α</sup>*Idi* <sup>+</sup> <sup>α</sup>*<sup>P</sup> dp*,*Ne* <sup>&</sup>gt; *Nf*

dividing the current crack size, a*n*, by the critical crack size at failure, a*crit*:

∆*ai* (6)

(8)

is

⁄a*crit*(100) % damage (7)

is obtained from Eq. (3) and *dp* is obtained from

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

*an* = *a*<sup>0</sup> + ∑

*dp* = <sup>a</sup>*<sup>n</sup>*

**3. Damage prognoses fatigue life**

*DTotal* <sup>=</sup> {

*Fatigue damage prognoses with structural health monitoring.*

the number of cycles to failure, *di*

entire fatigue life:

in Eq. (6), where ∆*a* = *da*/*dN*:

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

that account for interaction effects, considering interaction effects account for retardation in crack growth, a non-interaction model can provide quick and useful information about fatigue crack growth behavior, particularly crack growth rates [4]. The non-interaction prediction model leads to a simple numerical summation in Eq. (6), where ∆*a* = *da*/*dN*:

$$\mathfrak{a}\_n = \mathfrak{a}\_0 + \sum\_{i=1}^{i=n} \Delta \mathfrak{a}\_i \tag{6}$$

The accumulation of damage for fatigue crack growth models is consequent of the change in crack size, *a*, where *a*0 is the initial crack size, ∆*ai* is the change in crack size per cycle, and *an* is the updated crack size [4]. Thus, the cumulative damage from the fatigue crack propagation period, *dp*, is written as a percentage of the fatigue life by dividing the current crack size, a*n*, by the critical crack size at failure, a*crit*:

$$d\_p = "\succcurlyeq\_{\text{area}} \text{(100) }\text{\% d-damage} \tag{7}$$

#### **3. Damage prognoses fatigue life**

*Bridge Optimization - Inspection and Condition Monitoring*

*K* = *S* √

the crack tip can be described as a linear function.

paths, both near and far from the crack tip.

the material fracture resistance, *KIC*, fracture is predicted.

*2.2.4 Crack propagation period cumulative damage*

*2.2.3 Fracture toughness*

The stress in the local crack tip is described as a function of the applied stress in the form of a stress intensity factor (SIF). SIFs are used to describe the severity of a stress distribution around a crack tip, the rate of crack growth, and the onset of fracture [16]. Even at relatively low loads, there will be a high concentration of stress at the crack tip, and plastic deformation can occur [17]. The simplest form to describe the "intensity" of a stress distribution around a crack tip can be written as

\_\_\_

where *S* is the remote loading stress, *a* is the crack length, and β is a dimensionless factor depending on the geometry of the specimen or structural component. One important feature this equation illustrates is that the stress distribution around

For many ordinary cases of cracking, the calculations of stress intensification factors for various crack geometries and loading cases have already been computed and can be obtained from previously published literature, e.g., elliptical cracks embedded in very large bodies [4]. However, for cases with more complex geometries, more accurate *K* values should be independently calculated. Finite element modeling (FEM) offers a variety of techniques and efficient computation and has proven to offer satisfactory results for the stress intensification factors [4]. In finite element models, the crack is treated as an integral part of the structure and can be modeled in as much detail as necessary to accurately reflect the structural load

When the crack grows to a particular size, the stresses at the crack tip are too high for the material to endure, and fracture takes place. This critical stress intensity value is more often referred to as the fracture toughness, *K*Ic, where *I* denotes opening mode and *c* represents critical. Fracture toughness is a measured material property, just like Poisson's ratio or Young's modulus, and is usually measured through standard compact specimens. The fracture toughness is used to describe the ability of an already cracked material to resist fracture or to indicate the sensitivity of the material and the material's susceptibility to experiencing cracks under loading [4]. Thus, SIFs can be compared with the fracture toughness variables to determine if the crack will propagate and to determine the size of crack a material can endure until fracture [18]. When the applied stress intensity equals or exceeds

Models that predict fatigue crack growth propagation emphasize that crack growth is largely dependent on the cycle-by-cycle process. Prediction models are referred to as interaction models and non-interaction models. Interaction effects imply that the crack growth rate in a particular cycle is also dependent on the load history of the preceding cycles rather than an independent effect from one cycle. A non-interaction prediction model is used if the interaction effects in the variable amplitude history are assumed to be absent. In a non-interaction model, crack growth in each cycle is assumed to be dependent on the severity of the current cycle only and not on the load history in the preceding cycles. While it is expected that a non-interaction model will lead to a more conservative life prediction than models

*a* (5)

*2.2.2 Stress intensity factor*

**62**

The assessment for the crack initiation period and the assessment for the crack propagation period can be combined to determine a damage prognosis, *DTotal*, for the entire fatigue life:

me rangue me:

$$D\_{Total} = \begin{cases} & \mathfrak{a}\_{I}d\_{i\cdot}N\_{\epsilon} \le N\_{f} \\ & \mathfrak{a}\_{I}d\_{i\cdot} \star \mathfrak{a}\_{P}d\_{p}, N\_{\epsilon} > N\_{f} \end{cases} \tag{8}$$

where *Ne* is the number of cycles the element has currently experienced, *Nf* is the number of cycles to failure, *di* is obtained from Eq. (3) and *dp* is obtained from

**Figure 1.** *Fatigue damage prognoses with structural health monitoring.*

Eq. (7), and <sup>α</sup>*I* and <sup>α</sup>*P* are rate adjustment factors since the crack initiation period and crack propagation period are not equal in time. These factors can be altered to reflect the rate of damage. **Figure 1** displays the various aspects of fatigue analyses that are considered in the derivation of a fatigue damage prognosis. The diagram summarizes the analyses that are detailed in the preceding sections of this paper. As seen in the diagram, the damage accumulation model that defines crack initiation is informed by a structural evaluation, which can be conducted by means of a global simulation model that is validated with structural health monitoring. SHM gathers information about the actual load distributions and operating conditions of the bridge components. This information is processed and evaluated with damage tolerance information, which describes the material characteristics and material properties, such as the number of stress cycles a structural element can endure before cracking. The damage accumulation model that defines the crack propagation period is informed by finite element models of fatigue hotspots with existing cracks. The finite element modeling provides insight of the stress rate at the crack tip. Fracture toughness is then used to determine the critical crack size, at which the structure is described to be at the end of its fatigue life. Ultimately, the damage accumulation models in the crack initiation period and crack propagation period are used to determine the structure's damage prognosis (remaining useful life).

#### **3.1 Integration of damage prognosis with bridge management systems**

Currently, most US state Departments of Transportation (DOTs) report their bridge inspection findings using AASHTO Pontis software, which poses the guidelines for capturing damage of bridge elements. The conditions of bridge elements are categorized into element condition states to reflect these damages. The AASHTO Pontis software is most useful for state DOTs, since it provides an internal tool for mapping the element condition states back into the national condition ratings. **Table 1** summarizes the four condition states related to fatigue damage. These condition states are found in the *Maryland Pontis Element Data Collection Manual* [19].

The condition states in **Table 1** can be used with the fatigue life curve (**Figure 2**) to gather quantitative information of the fatigue life. An element in condition state one is considered a new element or in "like new" condition; it has no fatigue damage present. This element falls within the early stages of the crack life-initiation period. Condition state two recognizes fatigue damage. This damage could be found from a stress-cycle analysis that showed the structure was nearing the end of the crack initiation life or could be the result of a visual inspection from of a small crack that is not considered to be in immediate need of repair. An element in condition state two will be approaching the critical crack size of the crack initiation period and is merging into the crack propagation period. Thus, an element is in the propagation period in condition state three, which explicitly calls for additional analyses. In many state DOTs, it is suggested that deterioration modeling be used to assess the fatigue damage and evaluate the probability of transitioning from condition states [19]. A stress-cycle history can be used to obtain information about the daily or yearly cycle count and stress ranges on the structure. In the event there is enough information about the crack, crack growth models can be used to obtain information about the crack growth rate. This is particularly important information to obtain if the fatigue damage is on a primary component of the structure. Finally, an element in condition state four is in need of immediate rehabilitation or replacement. Analysis can still be used to understand the problem with this section of the bridge to make appropriate changes and to increase the bridge life.

A description of the national bridge element condition states is described in **Table 1** and is used in parallel with the FHWA Bridge Preservation Guide, which

**65**

**4. Case study**

**Figure 2.**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

**Condition state 2 (fair)**

damage

Fatigue damage exists but has been repaired or arrested. The element may still be fatigue prone

**Condition state 3** 

Fatigue damage (Analysis warranted)

Fatigue damage exists which is not arrested. Condition state used for first time element is identified with crack

**Condition state 4 (severe)**

Severe fatigue damage

Fatigue damage exists which warrants analysis of the element to ascertain the serviceability of the element or bridge

**(poor)**

hosts the commonly employed feasible actions that inspectors and state DOTs should take, given the condition state of their bridge. The purpose of the FHWA Bridge Preservation Guide is to provide a framework for a preventive maintenance

The fatigue assessment in this paper was conducted as part of the University of Maryland project to design and implement an integrated structural health monitoring system that is particularly suited for fatigue detection on highway bridges. Data for the analyses was acquired from a highway bridge carrying traffic from interstate 270 (I-270) over Middlebrook Road in Germantown, MD, seen in **Figure 3**. This

The Middlebrook Bridge was built in 1980 and reconstructed in 1991. With help from Maryland bridge inspectors, this bridge was selected as a good candidate for fatigue monitoring due to the average daily truck traffic, the bridge's maintenance

program for bridge owners or agencies [20].

*BME condition states integrated into fatigue life curve.*

bridge is referred to as the Middlebrook Bridge.

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

Cracking/fatigue None Fatigue

*Pontis system condition states related to fatigue [19].*

**Condition state 1 (good)**

**National bridge element condition states**

**Defect**

**Table 1.**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*


#### **Table 1.**

*Bridge Optimization - Inspection and Condition Monitoring*

Eq. (7), and <sup>α</sup>*I* and <sup>α</sup>*P* are rate adjustment factors since the crack initiation period and crack propagation period are not equal in time. These factors can be altered to reflect the rate of damage. **Figure 1** displays the various aspects of fatigue analyses that are considered in the derivation of a fatigue damage prognosis. The diagram summarizes the analyses that are detailed in the preceding sections of this paper. As seen in the diagram, the damage accumulation model that defines crack initiation is informed by a structural evaluation, which can be conducted by means of a global simulation model that is validated with structural health monitoring. SHM gathers information about the actual load distributions and operating conditions of the bridge components. This information is processed and evaluated with damage tolerance information, which describes the material characteristics and material properties, such as the number of stress cycles a structural element can endure before cracking. The damage accumulation model that defines the crack propagation period is informed by finite element models of fatigue hotspots with existing cracks. The finite element modeling provides insight of the stress rate at the crack tip. Fracture toughness is then used to determine the critical crack size, at which the structure is described to be at the end of its fatigue life. Ultimately, the damage accumulation models in the crack initiation period and crack propagation period are used to determine the structure's damage prognosis (remaining useful life).

**3.1 Integration of damage prognosis with bridge management systems**

bridge to make appropriate changes and to increase the bridge life.

A description of the national bridge element condition states is described in **Table 1** and is used in parallel with the FHWA Bridge Preservation Guide, which

Currently, most US state Departments of Transportation (DOTs) report their bridge inspection findings using AASHTO Pontis software, which poses the guidelines for capturing damage of bridge elements. The conditions of bridge elements are categorized into element condition states to reflect these damages. The AASHTO Pontis software is most useful for state DOTs, since it provides an internal tool for mapping the element condition states back into the national condition ratings. **Table 1** summarizes the four condition states related to fatigue damage. These condition states are found in the *Maryland Pontis Element Data Collection Manual* [19]. The condition states in **Table 1** can be used with the fatigue life curve (**Figure 2**) to gather quantitative information of the fatigue life. An element in condition state one is considered a new element or in "like new" condition; it has no fatigue damage present. This element falls within the early stages of the crack life-initiation period. Condition state two recognizes fatigue damage. This damage could be found from a stress-cycle analysis that showed the structure was nearing the end of the crack initiation life or could be the result of a visual inspection from of a small crack that is not considered to be in immediate need of repair. An element in condition state two will be approaching the critical crack size of the crack initiation period and is merging into the crack propagation period. Thus, an element is in the propagation period in condition state three, which explicitly calls for additional analyses. In many state DOTs, it is suggested that deterioration modeling be used to assess the fatigue damage and evaluate the probability of transitioning from condition states [19]. A stress-cycle history can be used to obtain information about the daily or yearly cycle count and stress ranges on the structure. In the event there is enough information about the crack, crack growth models can be used to obtain information about the crack growth rate. This is particularly important information to obtain if the fatigue damage is on a primary component of the structure. Finally, an element in condition state four is in need of immediate rehabilitation or replacement. Analysis can still be used to understand the problem with this section of the

**64**

*Pontis system condition states related to fatigue [19].*

**Figure 2.**

*BME condition states integrated into fatigue life curve.*

hosts the commonly employed feasible actions that inspectors and state DOTs should take, given the condition state of their bridge. The purpose of the FHWA Bridge Preservation Guide is to provide a framework for a preventive maintenance program for bridge owners or agencies [20].

#### **4. Case study**

The fatigue assessment in this paper was conducted as part of the University of Maryland project to design and implement an integrated structural health monitoring system that is particularly suited for fatigue detection on highway bridges. Data for the analyses was acquired from a highway bridge carrying traffic from interstate 270 (I-270) over Middlebrook Road in Germantown, MD, seen in **Figure 3**. This bridge is referred to as the Middlebrook Bridge.

The Middlebrook Bridge was built in 1980 and reconstructed in 1991. With help from Maryland bridge inspectors, this bridge was selected as a good candidate for fatigue monitoring due to the average daily truck traffic, the bridge's maintenance

**Figure 3.** *Maryland bridge carrying I-270 over Middlebrook Road.*

history, the geometric configuration, and the identification of existing fatigue cracks on the connection plates.

The Middlebrook Bridge is a composite steel I-girder bridge consisting of 17 welded steel plate girders with a span length of 140 ft. The bridge has three traffic lanes in the southbound roadway and five traffic lanes in the northbound, i.e., a high occupancy vehicle lane, an exit lane, and three travel lanes. Four fatigue cracks were reported in the Maryland State Highway June 2011 Bridge Inspection Report. These four cracks were all found in the welded connections between the lower end of the cross brace connection plate and the girder bottom flange.

The Middlebrook Bridge is built with skewed supports to accommodate the roadway below the bridge. Due to the skewed supports, the corresponding cross frames are also built with skewed angles. The Middlebrook Bridge was built with K-brace cross frame, seen in **Figure 4**.

The skew angle of the cross frames are built to code and are in accordance with AASHTO LRFD Bridge Design Specifications [11], so long as the skew angle is less than 20 degrees. A bridge with skewed cross braces is more prone to fatigue damages because its geometric configuration enhances the live load effects. The connections of the skewed cross braces are bent at an angle to connect with the transverse stiffeners of the bridge girders. When the bridge girders deflect, this angle introduces a bending effect into the transverse stiffeners.

**67**

**Figure 5.**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

material next to the stiffener and begins at the toe of the weld" [21].

*Connection plate with known crack (left) and schematic of strain gage location (right).*

A connection plate of a steel girder highway bridge is selected for long-term

Only one strain transducer was used to continue monitoring the bridge in a long-term monitoring evaluation. The strain transducer was placed on one of the stiffeners that showed to high tension stress. The bridge itself is loaded in bending by the dynamic effects caused from the vehicle passage. Specifically, **Figure 6** displays a sample of the acquired stress data as a function of time that was taken from a connection plate. The variation in loading of the load spectrum on the connection plate is dependent on the number of vehicles passing the bridge and the weight of the vehicle. Given that the traffic volumes and patterns are sporadic, the captured bridge loads are also sporadic. Strain data was collected from the bridge over the course of 1 year.

The acquired variable amplitude strain data is converted to stress for linear damage accumulation models, where stress ranges are the main contributor to fatigue damage. In addition, methods of extrapolation were used to fill in missing points of data. The method of extrapolation that has been applied to the fatigue data is done in the rainflow domain. The results of the extrapolated rainflow matrix were modeled from a measured rainflow history, where the density of rainflow cycles was calculated. The calculation of this density provided the number of stress cycles and stress ranges that were to be estimated for each specific hour of the day. The data was then processed with the rainflow cycle counting method to count the number of stress ranges. **Figure 7** displays a histogram of measured stress ranges. This particular histogram displays the traffic data that was accumulated on the bridge over 8 days. With variable amplitude stress history, the variable stress cycles are associated with a particular stress range value that will map the measured data with the S-N

This connection plate was identified by Maryland State Bridge inspectors in 2011 to have an existing active crack, i.e., a crack that is growing in size. The crack was described in inspection reports as "… very fine crack in the weld that connects the web stiffener to the top of the lower flange. The crack runs along the top of the weld

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

monitoring, shown in **Figure 5**.

**4.2 Fatigue analysis**

**4.1 Structural health monitoring and data processing**

**Figure 4.** *K-type cross brace on Middlebrook Bridge.*

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

#### **4.1 Structural health monitoring and data processing**

A connection plate of a steel girder highway bridge is selected for long-term monitoring, shown in **Figure 5**.

This connection plate was identified by Maryland State Bridge inspectors in 2011 to have an existing active crack, i.e., a crack that is growing in size. The crack was described in inspection reports as "… very fine crack in the weld that connects the web stiffener to the top of the lower flange. The crack runs along the top of the weld material next to the stiffener and begins at the toe of the weld" [21].

Only one strain transducer was used to continue monitoring the bridge in a long-term monitoring evaluation. The strain transducer was placed on one of the stiffeners that showed to high tension stress. The bridge itself is loaded in bending by the dynamic effects caused from the vehicle passage. Specifically, **Figure 6** displays a sample of the acquired stress data as a function of time that was taken from a connection plate. The variation in loading of the load spectrum on the connection plate is dependent on the number of vehicles passing the bridge and the weight of the vehicle. Given that the traffic volumes and patterns are sporadic, the captured bridge loads are also sporadic. Strain data was collected from the bridge over the course of 1 year.

#### **4.2 Fatigue analysis**

*Bridge Optimization - Inspection and Condition Monitoring*

*Maryland bridge carrying I-270 over Middlebrook Road.*

cracks on the connection plates.

K-brace cross frame, seen in **Figure 4**.

duces a bending effect into the transverse stiffeners.

history, the geometric configuration, and the identification of existing fatigue

of the cross brace connection plate and the girder bottom flange.

The Middlebrook Bridge is a composite steel I-girder bridge consisting of 17 welded steel plate girders with a span length of 140 ft. The bridge has three traffic lanes in the southbound roadway and five traffic lanes in the northbound, i.e., a high occupancy vehicle lane, an exit lane, and three travel lanes. Four fatigue cracks were reported in the Maryland State Highway June 2011 Bridge Inspection Report. These four cracks were all found in the welded connections between the lower end

The Middlebrook Bridge is built with skewed supports to accommodate the roadway below the bridge. Due to the skewed supports, the corresponding cross frames are also built with skewed angles. The Middlebrook Bridge was built with

The skew angle of the cross frames are built to code and are in accordance with AASHTO LRFD Bridge Design Specifications [11], so long as the skew angle is less than 20 degrees. A bridge with skewed cross braces is more prone to fatigue damages because its geometric configuration enhances the live load effects. The connections of the skewed cross braces are bent at an angle to connect with the transverse stiffeners of the bridge girders. When the bridge girders deflect, this angle intro-

**66**

**Figure 4.**

*K-type cross brace on Middlebrook Bridge.*

**Figure 3.**

The acquired variable amplitude strain data is converted to stress for linear damage accumulation models, where stress ranges are the main contributor to fatigue damage. In addition, methods of extrapolation were used to fill in missing points of data. The method of extrapolation that has been applied to the fatigue data is done in the rainflow domain. The results of the extrapolated rainflow matrix were modeled from a measured rainflow history, where the density of rainflow cycles was calculated. The calculation of this density provided the number of stress cycles and stress ranges that were to be estimated for each specific hour of the day. The data was then processed with the rainflow cycle counting method to count the number of stress ranges. **Figure 7** displays a histogram of measured stress ranges. This particular histogram displays the traffic data that was accumulated on the bridge over 8 days.

With variable amplitude stress history, the variable stress cycles are associated with a particular stress range value that will map the measured data with the S-N

#### **Figure 5.** *Connection plate with known crack (left) and schematic of strain gage location (right).*

**Figure 6.** *Illustration of variable amplitude loading.*

curves. The measured histograms showed an un-proportionally large amount of cycles occur at smaller stress ranges. Therefore the stress ranges are truncated, and an effective stress range is solved for; with S-N curves the number of cycles to

**69**

**Figure 8.**

*AASHTO S-N curve with cumulative points plotted until failure.*

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

failure is based on the effective stress range. For this case study, the effective stress range (*Sre*) was found to be = 7.2 *ksi*, and the number of cycles over the course of 1

In accordance with the histograms for this case study, as the effective stress range increases, the number of stress cycles decreases dramatically. Without including an increase in traffic volumes, the effective stress range and number of cycles are assumed consistent for each year. Under this assumption, the estimated fatigue life for the crack initiation period was 18.0 years. **Figure 8** displays the yearly

A three-dimensional global model of the southbound direction, seen in **Figure 9**, was created to evaluate a bridge's response to loading. The model of the southbound superstructure consisted of eight I-girders. The concrete deck, the eight I-girders, and connection plates which connected cross frames to the girders were modeled by shell elements, while all the cross frames were modeled by spatial frames along their center of gravity. Special link members were defined to connect girder elements and concrete deck elements at the actual spatial points where these members intersect. The translations in the x-, y-, and z-directions were fixed at the abutments to

To study the dynamic effects of the Middlebrook Bridge, simulated truckloads were applied to the global finite element model through traffic simulation software, Traffic Software Integrated System (TSIS) 6.0. The data that was used to simulate the truckloads were taken from Maryland State Highway Administration's Internet Traffic Monitoring System (ITMS) and a local weigh station that is approximately 10 miles north of the Middlebrook Bridge but on the same interstate [23]. The ITSM features permanent Automatic Traffic Recorders that count traffic continuously throughout the year and breaks down the traffic count data by class, volume, and lane distribution [24]. The average hourly volume varied from 505 to 4215, and the

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

year were approximately 5.8 million cycles.

**4.3 Global model and simulation**

accumulation until failure is reached on the S-N curve.

represent the actual characteristics of support and continuity.

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

failure is based on the effective stress range. For this case study, the effective stress range (*Sre*) was found to be = 7.2 *ksi*, and the number of cycles over the course of 1 year were approximately 5.8 million cycles.

In accordance with the histograms for this case study, as the effective stress range increases, the number of stress cycles decreases dramatically. Without including an increase in traffic volumes, the effective stress range and number of cycles are assumed consistent for each year. Under this assumption, the estimated fatigue life for the crack initiation period was 18.0 years. **Figure 8** displays the yearly accumulation until failure is reached on the S-N curve.

#### **4.3 Global model and simulation**

*Bridge Optimization - Inspection and Condition Monitoring*

**68**

**Figure 7.**

*Histogram of measured stress ranges.*

**Figure 6.**

*Illustration of variable amplitude loading.*

curves. The measured histograms showed an un-proportionally large amount of cycles occur at smaller stress ranges. Therefore the stress ranges are truncated, and an effective stress range is solved for; with S-N curves the number of cycles to

A three-dimensional global model of the southbound direction, seen in **Figure 9**, was created to evaluate a bridge's response to loading. The model of the southbound superstructure consisted of eight I-girders. The concrete deck, the eight I-girders, and connection plates which connected cross frames to the girders were modeled by shell elements, while all the cross frames were modeled by spatial frames along their center of gravity. Special link members were defined to connect girder elements and concrete deck elements at the actual spatial points where these members intersect. The translations in the x-, y-, and z-directions were fixed at the abutments to represent the actual characteristics of support and continuity.

To study the dynamic effects of the Middlebrook Bridge, simulated truckloads were applied to the global finite element model through traffic simulation software, Traffic Software Integrated System (TSIS) 6.0. The data that was used to simulate the truckloads were taken from Maryland State Highway Administration's Internet Traffic Monitoring System (ITMS) and a local weigh station that is approximately 10 miles north of the Middlebrook Bridge but on the same interstate [23]. The ITSM features permanent Automatic Traffic Recorders that count traffic continuously throughout the year and breaks down the traffic count data by class, volume, and lane distribution [24]. The average hourly volume varied from 505 to 4215, and the

**Figure 8.** *AASHTO S-N curve with cumulative points plotted until failure.*

**Figure 9.** *Global model of Middlebrook Bridge and location of local model [22].*

truck percentages also varied from about 10.5 to 20%. The weigh station-collected weight data of the truck traffic and the trucks were categorized into seven classes based on the number of axles. The majority of trucks were 2-axle which made up 25% of trucks and 5-axle, which made up 68% of trucks. The simulated truck network contained the mainline section of the highway with the Middlebrook Bridge in the center and adjacent ramps. Three classes of trucks were used for the simulation, shown in **Figure 10**. From the collected data, the simulation included the axle weight, axle spacing, vehicle position, and speed at each time step in the simulation.

The loading data from the simulation matched the loading data from field monitoring, and the simulated truckloads on the global modeL of the Middlebrook Bridge confirmed high tensile stresses between cross-frame connection plates and girder bottom flanges. These stresses are highest at the outer edge of the connection plate where the existing fatigue crack on the I-270 Bridge over Middlebrook Road was located. More detailed traffic load simulation is reported in a separate companion paper, *Fatigue Assessment of Highway Bridges Under Traffic Loading Using Microscopic Traffic Simulation*.

**71**

**Figure 11.**

*FEM local model with applied displacements and forces.*

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

Since the interest is to obtain a SIF, the global model cannot be any more refined, and a local model of this critical region was created for the purpose of understanding the stress field around the crack. A local model was created by applying the resulting deflections from the global model as resulting displacements in the local model. Since the deflections are a result of simulated traffic loads, applying the deflections simulates the loads transferred across a free-body section of the global

Additionally, the stress loads at the location of the strain gage were applied to the local model at the corresponding perimeter location. **Figure 9** displays the location of the local model within the global structure. This location is described with white lines that outline the local model geometry. **Figure 11** displays the local model with applied displacements and forces. A dashed rectangle outlines the location of the existing crack. A fine mesh is created around the previously identified existing crack, and a radial mesh is created around the crack tip. The crack was modeled with an assumed depth of 0.05 inch, which is slightly greater than a largest depth of micro-crack (0.05 mm <a <1 mm) and approximately the length of the penetration of the fusion in a fillet weld [25]. **Figure 12** displays the stress contour of the y-component of the cross section and a magnified view at the location of the crack.

The specifications of the American Society for Testing and Materials for A572 Grade 50 steel require a minimum yield strength value of 50 ksi. The fracture

length that corresponds to the fracture toughness comes from the fracture mechanics equation for critical SIF. Under the parameters that fit the Middlebrook Bridge,

\_\_

*in*. The critical crack

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

model where the local model resides.

*4.4.1 Damage tolerance and fracture toughness*

the critical crack size is *acrit* <sup>=</sup> \_\_\_\_\_ *KIC*

toughness for the steel on the Middlebrook Bridge is *KIC* <sup>=</sup> <sup>56</sup> *ksi* <sup>√</sup>

*<sup>π</sup>*β<sup>2</sup>σ<sup>2</sup> <sup>=</sup> .15 *in*.

**4.4 Fracture analysis**

**Figure 10.**

*Fatigue truck configurations (a), small truck, (b) medium truck, and (c) large truck.*

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

#### **4.4 Fracture analysis**

*Bridge Optimization - Inspection and Condition Monitoring*

*Global model of Middlebrook Bridge and location of local model [22].*

truck percentages also varied from about 10.5 to 20%. The weigh station-collected weight data of the truck traffic and the trucks were categorized into seven classes based on the number of axles. The majority of trucks were 2-axle which made up 25% of trucks and 5-axle, which made up 68% of trucks. The simulated truck network contained the mainline section of the highway with the Middlebrook Bridge in the center and adjacent ramps. Three classes of trucks were used for the simulation, shown in **Figure 10**. From the collected data, the simulation included the axle weight, axle spacing, vehicle position, and speed at each time step in the

The loading data from the simulation matched the loading data from field monitoring, and the simulated truckloads on the global modeL of the Middlebrook Bridge confirmed high tensile stresses between cross-frame connection plates and girder bottom flanges. These stresses are highest at the outer edge of the connection plate where the existing fatigue crack on the I-270 Bridge over Middlebrook Road was located. More detailed traffic load simulation is reported in a separate companion paper, *Fatigue Assessment of Highway Bridges Under Traffic Loading Using* 

*Fatigue truck configurations (a), small truck, (b) medium truck, and (c) large truck.*

**70**

**Figure 10.**

simulation.

**Figure 9.**

*Microscopic Traffic Simulation*.

Since the interest is to obtain a SIF, the global model cannot be any more refined, and a local model of this critical region was created for the purpose of understanding the stress field around the crack. A local model was created by applying the resulting deflections from the global model as resulting displacements in the local model. Since the deflections are a result of simulated traffic loads, applying the deflections simulates the loads transferred across a free-body section of the global model where the local model resides.

Additionally, the stress loads at the location of the strain gage were applied to the local model at the corresponding perimeter location. **Figure 9** displays the location of the local model within the global structure. This location is described with white lines that outline the local model geometry. **Figure 11** displays the local model with applied displacements and forces. A dashed rectangle outlines the location of the existing crack. A fine mesh is created around the previously identified existing crack, and a radial mesh is created around the crack tip. The crack was modeled with an assumed depth of 0.05 inch, which is slightly greater than a largest depth of micro-crack (0.05 mm <a <1 mm) and approximately the length of the penetration of the fusion in a fillet weld [25]. **Figure 12** displays the stress contour of the y-component of the cross section and a magnified view at the location of the crack.

#### *4.4.1 Damage tolerance and fracture toughness*

The specifications of the American Society for Testing and Materials for A572 Grade 50 steel require a minimum yield strength value of 50 ksi. The fracture toughness for the steel on the Middlebrook Bridge is *KIC* <sup>=</sup> <sup>56</sup> *ksi* <sup>√</sup> \_\_ *in*. The critical crack length that corresponds to the fracture toughness comes from the fracture mechanics equation for critical SIF. Under the parameters that fit the Middlebrook Bridge, the critical crack size is *acrit* <sup>=</sup> \_\_\_\_\_ *KIC <sup>π</sup>*β<sup>2</sup>σ<sup>2</sup> <sup>=</sup> .15 *in*.

**Figure 11.** *FEM local model with applied displacements and forces.*

**Figure 12.** *Stress contour of crack to illustrate plastic zone at crack tip.*

#### *4.4.2 Crack growth and total cumulative damage*

The computed SIF from the local model was used alongside Paris law to solve for the yearly crack growth rate. Rearranging Eq. (5), the crack size, *a*, at any given time, is a function of the SIF and the effective stress range. The accumulation of damage for fatigue crack growth models (shown in Eq. 6) is consequent of the change in crack size, ∆*ai* ; then the crack would reach the critical size after 9.6 years. Since the bridge inspectors first noticed the bridge cracking in 2011, at the time of testing (2012–2013), the crack had been present for about 1–2 years. The crack was repaired in 2014, at which time the remaining useful life for this bridge element was calculated to be 6.6 years to failure.

#### **4.5 Integration of damage with Maryland condition states**

The case study was estimated from measured and extrapolated load distributions to assess the life of the bridge. The fatigue life of the crack initiation period was found to be 18 years, and the fatigue life of the crack propagation period was found to be about 9 years. Accordingly, rate adjustment factors were selected to be <sup>α</sup>*I* = 0.7 and <sup>α</sup>*P* = 0.3. The second row in **Table 2** illustrates the amount of damage for each condition state. The third row is a simplified explanation of the condition states which are found in the *Maryland Pontis Element Data Collection Manual*, and the last row is the feasible actions for these condition states from the FHWA Bridge Preservation Guide.


**73**

**Author details**

**Acknowledgements**

Timothy Saad1

USA

provided the original work is properly cited.

, Chung C. Fu1

\*Address all correspondence to: ccfu@umd.edu

© 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,

\*, Gengwen Zhao2

rates and ultimately derive a damage prognosis of the bridge element.

2 Virginia Department of Transportation, Richmond, VA, USA

1 The Bridge Engineering Software and Technology (BEST) Center, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD,

This research was partially sponsored by the US Department of Transportation's Office of the Assistant Secretary for Research and Technology (USDOT/OST-R), under The Commercial Remote Sensing and Spatial Information (CRS&SI) Technologies Program. This support is acknowledged and greatly appreciated.

and Chaoran Xu1

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

element to ascertain the serviceability of the element or bridge."

In 2014, when the crack was repaired, the calculated percent damage was 87.2%, correlating to condition state 4, "Fatigue damage exists which warrants analysis of the

This paper proposes a damage accumulation model to more accurately characterize fatigue damage prognoses of bridge elements. The fatigue life has been described and divided into two periods: the initiation period and the propagation period. An empirical correlation approach, characterized by the S-N curve, is used to analyze the initiation period, and the data acquired from SHM and traffic simulation models are used to inform the crack initiation analyses. SHM is shown to have a significant contribution in damage prognosis, where the sensing information instrumentation is used to validate FEM models and acquire information about a bridge's response to loads. It is shown how this data can be particularly useful when processed through cycle counting algorithms, and methods of extrapolation are applied to gather information on stress range distributions to estimate future traffic loads of the bridge. Fatigue damage assessments in the crack initiation period can be supplemented with a fracture mechanics analysis, which defines the crack propagation period and estimates crack growth. It is also shown how finite element modeling can be used to solve for the SIF, which is then used to estimate the growth rate. A case study is presented to illustrate the application of the fatigue damage prognoses on a steel highway bridge element. The damage accumulation models are used to estimate the onset of a fatigue crack and fatigue crack growth

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

**5. Summary and conclusions**

**Table 2.**

*Damage accumulation mapped to bridge condition states.*

In 2014, when the crack was repaired, the calculated percent damage was 87.2%, correlating to condition state 4, "Fatigue damage exists which warrants analysis of the element to ascertain the serviceability of the element or bridge."

### **5. Summary and conclusions**

*Bridge Optimization - Inspection and Condition Monitoring*

*4.4.2 Crack growth and total cumulative damage*

*Stress contour of crack to illustrate plastic zone at crack tip.*

**4.5 Integration of damage with Maryland condition states**

<sup>2</sup> <sup>α</sup>*<sup>i</sup>* \_1

Feasible action Do nothing Preventive

*Damage accumulation mapped to bridge condition states.*

change in crack size, ∆*ai*

*DTotal* 0→ \_1

**Figure 12.**

calculated to be 6.6 years to failure.

The computed SIF from the local model was used alongside Paris law to solve for the yearly crack growth rate. Rearranging Eq. (5), the crack size, *a*, at any given time, is a function of the SIF and the effective stress range. The accumulation of damage for fatigue crack growth models (shown in Eq. 6) is consequent of the

Since the bridge inspectors first noticed the bridge cracking in 2011, at the time of testing (2012–2013), the crack had been present for about 1–2 years. The crack was repaired in 2014, at which time the remaining useful life for this bridge element was

The case study was estimated from measured and extrapolated load distributions to assess the life of the bridge. The fatigue life of the crack initiation period was found to be 18 years, and the fatigue life of the crack propagation period was found to be about 9 years. Accordingly, rate adjustment factors were selected to be <sup>α</sup>*I* = 0.7 and <sup>α</sup>*P* = 0.3. The second row in **Table 2** illustrates the amount of damage for each condition state. The third row is a simplified explanation of the condition states which are found in the *Maryland Pontis Element Data Collection Manual*, and the last row is the feasible actions for these condition states from the FHWA Bridge Preservation Guide.

*DTotal*, % 0–35% 35–70% 70–85% 85–100% Cracking/fatigue None Fatigue damage Analysis warranted Severe fatigue damage

maintenance

; then the crack would reach the critical size after 9.6 years.

**Condition state 1 Condition state 2 Condition state 3 Condition state 4**

<sup>2</sup> <sup>α</sup>*p*) (α*<sup>i</sup>* <sup>+</sup> \_1

Rehabilitation Rehabilitation or

<sup>2</sup> <sup>α</sup>*p*) <sup>→</sup> (α*<sup>i</sup>* <sup>+</sup> <sup>α</sup>*p*)

replacement

<sup>2</sup> <sup>α</sup>*<sup>i</sup>* <sup>→</sup> <sup>α</sup>*<sup>i</sup>* <sup>α</sup>*<sup>i</sup>* <sup>→</sup> (α*<sup>i</sup>* <sup>+</sup> \_1

**72**

**Table 2.**

This paper proposes a damage accumulation model to more accurately characterize fatigue damage prognoses of bridge elements. The fatigue life has been described and divided into two periods: the initiation period and the propagation period. An empirical correlation approach, characterized by the S-N curve, is used to analyze the initiation period, and the data acquired from SHM and traffic simulation models are used to inform the crack initiation analyses. SHM is shown to have a significant contribution in damage prognosis, where the sensing information instrumentation is used to validate FEM models and acquire information about a bridge's response to loads. It is shown how this data can be particularly useful when processed through cycle counting algorithms, and methods of extrapolation are applied to gather information on stress range distributions to estimate future traffic loads of the bridge. Fatigue damage assessments in the crack initiation period can be supplemented with a fracture mechanics analysis, which defines the crack propagation period and estimates crack growth. It is also shown how finite element modeling can be used to solve for the SIF, which is then used to estimate the growth rate. A case study is presented to illustrate the application of the fatigue damage prognoses on a steel highway bridge element. The damage accumulation models are used to estimate the onset of a fatigue crack and fatigue crack growth rates and ultimately derive a damage prognosis of the bridge element.

#### **Acknowledgements**

This research was partially sponsored by the US Department of Transportation's Office of the Assistant Secretary for Research and Technology (USDOT/OST-R), under The Commercial Remote Sensing and Spatial Information (CRS&SI) Technologies Program. This support is acknowledged and greatly appreciated.

### **Author details**

Timothy Saad1 , Chung C. Fu1 \*, Gengwen Zhao2 and Chaoran Xu1

1 The Bridge Engineering Software and Technology (BEST) Center, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA

2 Virginia Department of Transportation, Richmond, VA, USA

\*Address all correspondence to: ccfu@umd.edu

© 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.

### **References**

[1] FHWA. Focus Accelerating Infrastructure Innovations. Federal Highway Administration Launches Steel Bridge Testing Program. 2011

[2] Haldipur P, Jalinoos F. Detection and Characterization of Fatigue Cracks in Steel Bridges. 2010. Available from: www.structuralfaultsandrepair.com

[3] FHWA. Bridge Inspector's Reference Manual. Vol. 2. Washington DC: FHWA NHI Publication No. 12-050; 2012

[4] Schijve J. Fatigue of Structures and Materials. 2nd ed. Netherlands: Springer Science+Business Media B.V.; 2009

[5] Mohammadi J, Guralnick SA, Polepeddi R. Bridge fatigue life estimation from field data. Practice Periodical on Structural Design and Construction. 1998;**3**(3):128-133

[6] Zhou YL, Maia NM, Sampaio RP, Wahab MA. Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure. Structural Health Monitoring. Sage Publication. 2017;**16**(6):711-731. Available from: https://www.nafems.org/downloads/ FENet\_Meetings/Trieste\_Italy\_ Sep\_2002/FENET\_Trieste\_Sept2002\_ DLE\_Zafosnik.pdf/

[7] Shantz CR. Uncertainty Quantification in Crack Growth Modeling Under Multi-Axial Variable Amplitude Loading. Nashville, Tennessee: Graduate School of Vanderbilt University; 2010

[8] ASTM E-1049. Standard Practices for Cycle Counting in Fatigue Analysis. West Conshohocken: ASTM International; 2011

[9] AASHTO. Standard Specifications for Highway Bridges. Washington, D.C.: American Association of State Highway and Transportation Officials. 2002

[10] NCHRP. Fatigue Evaluation of Steel Bridges. Washington, D.C.: National Academy of Sciences, Transportation Research Board. 2012

[11] AASHTO. LRFD Bridge Design Specifications. 7th ed. Washington DC: American Association of State Highway and Transportation Officials. 2014

[12] Massarelli PJ, Baber TT. Fatigue Reliability of Steel Highway Bridge Details. US DOT FHWA, Charlottesville, Virginia: Virginia Transportation Research Council; Virginia DOT. 2001

[13] AASHTO. Guide Specifications for Fatigue Evaluation of Existing Steel Bridges. Washington DC: American Association of State Highway and Transportation Officials; 1990

[14] Zhou YE. Assessment of bridge remaining fatigue life through field strain measurement. Journal of Bridge Engineering. 2006;**11**(6):737-744

[15] Keating PB, Fisher JW. Fatigue Tests and Design Criteria. Bethlehem, PA: National Cooperative Highway Research Program and Fritz Engineering Laboratory; 1986

[16] Zafosnik B, Ren Z, Ulbin M, Flasker J. Evaluation of stress intensity factors using finite elements. FENet: A NAFEMS Project; 2002

[17] Mertz D. Steel Bridge Design Handbook: Design for Fatigue. Washington, D.C.: FHWA-IF-12-052- Vol.12; 2012

[18] CAE Associates. Fracture Mechanics in Workbench v14.5 ANSYS e-Learning Session. Middlebury. 2013

**75**

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses…*

*DOI: http://dx.doi.org/10.5772/intechopen.82050*

[20] FHWA. Bridge Preservation Guide. U.S. Department of Transportation Federal Highway Administration. New Jersey Avenue, SE Washington, DC.

[21] MDSHA. Maryland State Highway Administration Bridge Inspection Report. MDSHA, Maryland State Highway Administration. North Calvert Street, Baltimore, Maryland. 2013

[22] Fu CC, Wang S. Computational Analysis and Design of Bridge

Structures. Boca Raton, FL: CRC Press Taylor and Francis Group; 2014

[23] SHA. Internet Traffic Monitoring System. Maryland State Highway Administration. 29 July 2015. [Online]. Available from: http://shagbhisdadt. mdot.state.md.us/ITMS\_Public/default.

[24] Zhao G. Truck Loading Simulation for the Fatigue Assessment of Steel Highway Bridges. College Park: University of Maryland; 2015

[25] Janosch J. Investigation into the Fatigue Strength of Fillet Welded Assemblies of E-36-4 Steel as a Function of the Penetration of the Weld Subjected to Tensile and Bending Loads. 1993

[19] MDSHA. Pontis Element Data Collection Manual. Baltimore, MD: Bridge Inspection and Remedial Engineering Division, Office of Bridge

Development; 2003

2011

aspx

*Development of a Fatigue Life Assessment Model for Pairing Fatigue Damage Prognoses… DOI: http://dx.doi.org/10.5772/intechopen.82050*

[19] MDSHA. Pontis Element Data Collection Manual. Baltimore, MD: Bridge Inspection and Remedial Engineering Division, Office of Bridge Development; 2003

[20] FHWA. Bridge Preservation Guide. U.S. Department of Transportation Federal Highway Administration. New Jersey Avenue, SE Washington, DC. 2011

[21] MDSHA. Maryland State Highway Administration Bridge Inspection Report. MDSHA, Maryland State Highway Administration. North Calvert Street, Baltimore, Maryland. 2013

[22] Fu CC, Wang S. Computational Analysis and Design of Bridge Structures. Boca Raton, FL: CRC Press Taylor and Francis Group; 2014

[23] SHA. Internet Traffic Monitoring System. Maryland State Highway Administration. 29 July 2015. [Online]. Available from: http://shagbhisdadt. mdot.state.md.us/ITMS\_Public/default. aspx

[24] Zhao G. Truck Loading Simulation for the Fatigue Assessment of Steel Highway Bridges. College Park: University of Maryland; 2015

[25] Janosch J. Investigation into the Fatigue Strength of Fillet Welded Assemblies of E-36-4 Steel as a Function of the Penetration of the Weld Subjected to Tensile and Bending Loads. 1993

**74**

*Bridge Optimization - Inspection and Condition Monitoring*

American Association of State Highway and Transportation Officials. 2002

[10] NCHRP. Fatigue Evaluation of Steel Bridges. Washington, D.C.: National Academy of Sciences, Transportation

[11] AASHTO. LRFD Bridge Design Specifications. 7th ed. Washington DC:

Highway and Transportation Officials.

[12] Massarelli PJ, Baber TT. Fatigue

[13] AASHTO. Guide Specifications for Fatigue Evaluation of Existing Steel Bridges. Washington DC: American Association of State Highway and Transportation Officials; 1990

[14] Zhou YE. Assessment of bridge remaining fatigue life through field strain measurement. Journal of Bridge Engineering. 2006;**11**(6):737-744

[15] Keating PB, Fisher JW. Fatigue Tests and Design Criteria. Bethlehem, PA: National Cooperative Highway Research

Program and Fritz Engineering

[16] Zafosnik B, Ren Z, Ulbin M, Flasker J. Evaluation of stress intensity factors using finite elements. FENet: A

[17] Mertz D. Steel Bridge Design Handbook: Design for Fatigue. Washington, D.C.: FHWA-IF-12-052-

[18] CAE Associates. Fracture Mechanics in Workbench v14.5 ANSYS e-Learning

Laboratory; 1986

Vol.12; 2012

NAFEMS Project; 2002

Session. Middlebury. 2013

American Association of State

Reliability of Steel Highway Bridge Details. US DOT FHWA, Charlottesville, Virginia: Virginia Transportation Research Council;

Virginia DOT. 2001

Research Board. 2012

2014

**References**

[1] FHWA. Focus Accelerating Infrastructure Innovations. Federal Highway Administration Launches Steel

Bridge Testing Program. 2011

[2] Haldipur P, Jalinoos F. Detection and Characterization of Fatigue Cracks in Steel Bridges. 2010. Available from: www.structuralfaultsandrepair.com

[3] FHWA. Bridge Inspector's Reference Manual. Vol. 2. Washington DC: FHWA NHI Publication No. 12-050; 2012

[4] Schijve J. Fatigue of Structures and Materials. 2nd ed. Netherlands: Springer Science+Business Media B.V.; 2009

[5] Mohammadi J, Guralnick SA, Polepeddi R. Bridge fatigue life estimation from field data. Practice Periodical on Structural Design and Construction. 1998;**3**(3):128-133

[6] Zhou YL, Maia NM, Sampaio RP, Wahab MA. Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure. Structural Health Monitoring. Sage Publication. 2017;**16**(6):711-731. Available from: https://www.nafems.org/downloads/ FENet\_Meetings/Trieste\_Italy\_ Sep\_2002/FENET\_Trieste\_Sept2002\_

DLE\_Zafosnik.pdf/

[7] Shantz CR. Uncertainty Quantification in Crack Growth Modeling Under Multi-Axial Variable Amplitude Loading. Nashville, Tennessee: Graduate School of Vanderbilt University; 2010

[8] ASTM E-1049. Standard Practices

Analysis. West Conshohocken: ASTM

[9] AASHTO. Standard Specifications for Highway Bridges. Washington, D.C.:

for Cycle Counting in Fatigue

International; 2011

**77**

**Chapter 5**

**Abstract**

assessment.

**1. Introduction**

Simulation

Fatigue Assessment of Highway

Bridges under Traffic Loading

*Gengwen Zhao, Chung C. Fu, Yang Lu and Timothy Saad*

Fatigue is a common failure mode of steel bridges induced by truck traffic. Despite the deterioration caused by environmental factors, the increasing truck traffic volume and weight pose a premier threat to steel highway bridges. Given the uncertainties of the complicated traffic loading and the complexity of the bridge structure, fatigue evaluation based on field measurements under actual traffic flow is recommended. As the quality and the quantity of the available long-term traffic monitoring data and information have been improved, methodologies have been developed to obtain more realistic vehicular live load traffic. A case study of a steel interstate highway bridge using microscopic traffic simulation is presented herein. The knowledge of actual traffic loading may reduce the uncertainty involved in the evaluation of the load-carrying capacity, estimation of the rate of deterioration, and prediction of remaining fatigue life. This chapter demonstrates a systematic approach using traffic simulation and bridge health monitoring-based fatigue

Using Microscopic Traffic

**Keywords:** fatigue, finite element modeling, truck traffic loading,

Fatigue is a common failure mode of steel bridges. About 80–90% of failures in steel structures are related to fatigue and fracture [1]. Despite the deterioration caused by environmental factors, the increasing traffic volume and weight pose a premier threat to steel highway bridges. The total number of truck passages in the 75 year life of a highway bridge could exceed 100 million [2]. With the aging of existing steel highway bridges and the accumulated damage under truck loading, the fatigue assessment for continuing service has become important for decision makings on the

Given the uncertainties of the complicated traffic loading and the complexity of the bridge structure, fatigue evaluation based on field measurements under actual traffic flow is recommended by many researchers. As the quality and quantity of the available long-term traffic monitoring data and information have been improved, a set of methodologies has been developed to obtain a more realistic vehicular live

structure maintenance, component replacement, and other major retrofits.

microscopic traffic simulation, cross-frame

#### **Chapter 5**

## Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic Simulation

*Gengwen Zhao, Chung C. Fu, Yang Lu and Timothy Saad*

#### **Abstract**

Fatigue is a common failure mode of steel bridges induced by truck traffic. Despite the deterioration caused by environmental factors, the increasing truck traffic volume and weight pose a premier threat to steel highway bridges. Given the uncertainties of the complicated traffic loading and the complexity of the bridge structure, fatigue evaluation based on field measurements under actual traffic flow is recommended. As the quality and the quantity of the available long-term traffic monitoring data and information have been improved, methodologies have been developed to obtain more realistic vehicular live load traffic. A case study of a steel interstate highway bridge using microscopic traffic simulation is presented herein. The knowledge of actual traffic loading may reduce the uncertainty involved in the evaluation of the load-carrying capacity, estimation of the rate of deterioration, and prediction of remaining fatigue life. This chapter demonstrates a systematic approach using traffic simulation and bridge health monitoring-based fatigue assessment.

**Keywords:** fatigue, finite element modeling, truck traffic loading, microscopic traffic simulation, cross-frame

#### **1. Introduction**

Fatigue is a common failure mode of steel bridges. About 80–90% of failures in steel structures are related to fatigue and fracture [1]. Despite the deterioration caused by environmental factors, the increasing traffic volume and weight pose a premier threat to steel highway bridges. The total number of truck passages in the 75 year life of a highway bridge could exceed 100 million [2]. With the aging of existing steel highway bridges and the accumulated damage under truck loading, the fatigue assessment for continuing service has become important for decision makings on the structure maintenance, component replacement, and other major retrofits.

Given the uncertainties of the complicated traffic loading and the complexity of the bridge structure, fatigue evaluation based on field measurements under actual traffic flow is recommended by many researchers. As the quality and quantity of the available long-term traffic monitoring data and information have been improved, a set of methodologies has been developed to obtain a more realistic vehicular live

load. The knowledge of actual traffic loading may reduce the uncertainty involved in the evaluation of the load-carrying capacity, estimation of the rate of deterioration, and prediction of remaining fatigue life. However, there are still some difficulties in field measurements. For example, some highway bridges are not accessible for field tests; the maintenance of monitoring system is difficult and costly, especially for long-term monitoring; some highway bridges will not even be considered for field tests with economic concerns.

The results of several NCHRP reports, written by Dr. John Fisher in 1970s, have confirmed that for welded details, fatigue life is primarily a function of stress range, detail category, and the number of applied cycles. The live load of a bridge includes static and dynamic parts while the early research and studies focused on the static portion. Schilling [3] and Raju et al. [4] suggested to improve the accuracy of the fatigue truck model by adjusting the fatigue truck axle weights in proportion to an equivalent total weight calculated from the specific site load distribution. The collected weigh station measurements, or data measured in stationary weight scales, were used by Nowak et al. [5] to determine the truck-load spectra for highway bridges on highways I-75 and I-94. Later, Laman and Nowak [6] developed a fatigue-load model from weigh station measurements and calculated the statistical parameters of stress for girder bridges. The results indicated that magnitude and frequency of truck load spectra are strongly site-specific and the live load stress spectra are strongly component-specific. With the advantage of weigh-in-motion (WIM) technology, Miao and Chan developed a methodology by using 10 year WIM data for deriving highway bridge live load models for short span bridges in Hong Kong [7]. NCHRP developed a set of protocols and methodologies for using available nation-wide, state-specific, or site-specific truck traffic data collected at different U.S. sites to obtain live load models for LRFD superstructure design, fatigue design, deck design, and design for overload permits [8].

In the early studies, it was commonly assumed that a certain percentage of the total weight was loaded on the front axle or rear axle for the magnitude and configuration. Further, there was no real traffic simulation considering the truck flow pattern. Bridge behavior simulations under truck loading were usually performed using the Monte Carlo method, which is a statistical projection approach with generic nature and does not consider any vehicle and driver behavior models when simulating truck traffic flow. In recent years, traffic flow simulation method has been applied to provide instantaneous information of individual vehicle by many researchers. Chen and Wu developed a general framework of modeling the live load from traffic for a long-span bridge by using the cellular automation (CA) traffic flow simulation technique. A typical four-lane long-span bridge was studied using the proposed method. Each lane was divided into cells with an equal length of 7.5 m. Three conditions, the free flow, the moderate flow, and the congested flow, were considered in the simulation. A simple comparison between the simulated static traffic load and the AASHTO LRFD HL-93 design load was conducted. The results showed that the HL-93 may be insufficient for the congested flow condition [9].

This research has developed a framework for the fatigue assessment of steel highway bridges based on simulated truck loading. The proposed methodology is implemented on a steel highway girder bridge on interstate 270 (I-270) over Middlebrook Road in Germantown, Maryland. With the help of the available longterm monitoring traffic data, truck loading was also obtained through the probability-based model. Then, the three-dimensional finite element (FE) global bridge models were studied subjected to the simulated truck loading. Meanwhile, the preliminary field test and the long-term monitoring test were also conducted. The FE models were calibrated with the collected field measurements through monitoring systems, and the simulated numerical structural responses were validated.

**79**

**Figure 1.**

*Cross section with lane positions.*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

Lastly, this model has been used for identifying the cause of fatigue cracks reported in the biennial bridge inspection. Thus, the proposed methodology could be used to realistically simulate the fatigue behavior of steel highway bridges under current or future truck loading, to direct the experimental designs and instrumentation plans before performing experiments on laboratory or on site, and to better understand the fatigue mechanism and prevent the fatigue damage of steel highway bridges.

The I-270 Bridge over Middlebrook road (MD Bridge No.15042) is a simple-span composite steel I-girder bridge with a span length of 140 ft. This bridge is comprised of two structures for the northbound (NB) and southbound (SB) roadways respectively, separated at the centerline. It carries three traffic lanes in the southbound and

The southbound superstructure provides a curb-to-curb roadway width of 61′-2″ and consists of eight identical welded steel plate girders with a composite reinforced concrete deck constructed with shear connectors. The eight girders are equally spaced at 7′-11″ and each girder has a constant web depth of 60″ throughout the entire bridge. The northbound superstructure provides a curb-to-curb roadway width of 73′-1″ and consists of nine identical welded steel plate girders with a composite reinforced concrete deck constructed with shear connector. The nine girders are equally spaced at 8′-5″ and each girder has a constant web depth of 60″ throughout the entire bridge. This bridge has a 76 degree parallel skew of its bearing lines (or 14 degree measured from normal). The cross-frames are inverted K-type braces with bottom chords only. All of them are parallel to the bearing lines. Girders of the southbound superstructure are numbered as G1 through G8 from the exterior

four traffic lanes in the northbound with equal lane widths of 12′-0″.

to the centerline of the bridge. The cross section is depicted in **Figure 1**.

Designed in 1988, the I-270 Bridge over Middlebrook Road has been in-service for over 20 years. In addition to the deterioration caused by environmental factors, the bridge structure has also been subjected to increasing traffic volume and weight. Four fatigue cracks as marked on **Figure 2** were reported in the June 2011 Bridge Inspection Report, and all in the welded connection between the lower end of the cross frame (**Figure 3**) connection plate and the girder bottom flange of the southbound superstructure. **Figure 4(a)** shows one of the four crack locations at G3B2D3 (Girder 3 Bay 2 Diaphragm 3). Therefore, only the southbound superstructure will be discussed in the following sections. Most bridge components with fatigue cracks are repaired or replaced shortly after the crack is found in an inspection. However, since the crack on the I-270 Bridge was identified on a secondary bridge member,

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

**2. Fatigue cracks and bridge testing**

**2.1 Bridge introduction**

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

Lastly, this model has been used for identifying the cause of fatigue cracks reported in the biennial bridge inspection. Thus, the proposed methodology could be used to realistically simulate the fatigue behavior of steel highway bridges under current or future truck loading, to direct the experimental designs and instrumentation plans before performing experiments on laboratory or on site, and to better understand the fatigue mechanism and prevent the fatigue damage of steel highway bridges.

#### **2. Fatigue cracks and bridge testing**

#### **2.1 Bridge introduction**

*Bridge Optimization - Inspection and Condition Monitoring*

for field tests with economic concerns.

load. The knowledge of actual traffic loading may reduce the uncertainty involved in the evaluation of the load-carrying capacity, estimation of the rate of deterioration, and prediction of remaining fatigue life. However, there are still some difficulties in field measurements. For example, some highway bridges are not accessible for field tests; the maintenance of monitoring system is difficult and costly, especially for long-term monitoring; some highway bridges will not even be considered

The results of several NCHRP reports, written by Dr. John Fisher in 1970s, have confirmed that for welded details, fatigue life is primarily a function of stress range, detail category, and the number of applied cycles. The live load of a bridge includes static and dynamic parts while the early research and studies focused on the static portion. Schilling [3] and Raju et al. [4] suggested to improve the accuracy of the fatigue truck model by adjusting the fatigue truck axle weights in proportion to an equivalent total weight calculated from the specific site load distribution. The collected weigh station measurements, or data measured in stationary weight scales, were used by Nowak et al. [5] to determine the truck-load spectra for highway bridges on highways I-75 and I-94. Later, Laman and Nowak [6] developed a fatigue-load model from weigh station measurements and calculated the statistical parameters of stress for girder bridges. The results indicated that magnitude and frequency of truck load spectra are strongly site-specific and the live load stress spectra are strongly component-specific. With the advantage of weigh-in-motion (WIM) technology, Miao and Chan developed a methodology by using 10 year WIM data for deriving highway bridge live load models for short span bridges in Hong Kong [7]. NCHRP developed a set of protocols and methodologies for using available nation-wide, state-specific, or site-specific truck traffic data collected at different U.S. sites to obtain live load models for LRFD superstructure design,

fatigue design, deck design, and design for overload permits [8].

In the early studies, it was commonly assumed that a certain percentage of the total weight was loaded on the front axle or rear axle for the magnitude and configuration. Further, there was no real traffic simulation considering the truck flow pattern. Bridge behavior simulations under truck loading were usually performed using the Monte Carlo method, which is a statistical projection approach with generic nature and does not consider any vehicle and driver behavior models when simulating truck traffic flow. In recent years, traffic flow simulation method has been applied to provide instantaneous information of individual vehicle by many researchers. Chen and Wu developed a general framework of modeling the live load from traffic for a long-span bridge by using the cellular automation (CA) traffic flow simulation technique. A typical four-lane long-span bridge was studied using the proposed method. Each lane was divided into cells with an equal length of 7.5 m. Three conditions, the free flow, the moderate flow, and the congested flow, were considered in the simulation. A simple comparison between the simulated static traffic load and the AASHTO LRFD HL-93 design load was conducted. The results showed that the HL-93 may be insufficient for the congested flow condition [9]. This research has developed a framework for the fatigue assessment of steel highway bridges based on simulated truck loading. The proposed methodology is implemented on a steel highway girder bridge on interstate 270 (I-270) over Middlebrook Road in Germantown, Maryland. With the help of the available longterm monitoring traffic data, truck loading was also obtained through the probability-based model. Then, the three-dimensional finite element (FE) global bridge models were studied subjected to the simulated truck loading. Meanwhile, the preliminary field test and the long-term monitoring test were also conducted. The FE models were calibrated with the collected field measurements through monitoring systems, and the simulated numerical structural responses were validated.

**78**

The I-270 Bridge over Middlebrook road (MD Bridge No.15042) is a simple-span composite steel I-girder bridge with a span length of 140 ft. This bridge is comprised of two structures for the northbound (NB) and southbound (SB) roadways respectively, separated at the centerline. It carries three traffic lanes in the southbound and four traffic lanes in the northbound with equal lane widths of 12′-0″.

The southbound superstructure provides a curb-to-curb roadway width of 61′-2″ and consists of eight identical welded steel plate girders with a composite reinforced concrete deck constructed with shear connectors. The eight girders are equally spaced at 7′-11″ and each girder has a constant web depth of 60″ throughout the entire bridge. The northbound superstructure provides a curb-to-curb roadway width of 73′-1″ and consists of nine identical welded steel plate girders with a composite reinforced concrete deck constructed with shear connector. The nine girders are equally spaced at 8′-5″ and each girder has a constant web depth of 60″ throughout the entire bridge. This bridge has a 76 degree parallel skew of its bearing lines (or 14 degree measured from normal). The cross-frames are inverted K-type braces with bottom chords only. All of them are parallel to the bearing lines. Girders of the southbound superstructure are numbered as G1 through G8 from the exterior to the centerline of the bridge. The cross section is depicted in **Figure 1**.

Designed in 1988, the I-270 Bridge over Middlebrook Road has been in-service for over 20 years. In addition to the deterioration caused by environmental factors, the bridge structure has also been subjected to increasing traffic volume and weight. Four fatigue cracks as marked on **Figure 2** were reported in the June 2011 Bridge Inspection Report, and all in the welded connection between the lower end of the cross frame (**Figure 3**) connection plate and the girder bottom flange of the southbound superstructure. **Figure 4(a)** shows one of the four crack locations at G3B2D3 (Girder 3 Bay 2 Diaphragm 3). Therefore, only the southbound superstructure will be discussed in the following sections. Most bridge components with fatigue cracks are repaired or replaced shortly after the crack is found in an inspection. However, since the crack on the I-270 Bridge was identified on a secondary bridge member,

**Figure 1.** *Cross section with lane positions.*

**Figure 2.** *Crack locations and sensor placements on the framing plan.*

**Figure 3.** *Cross frame detail.*

**81**

sections.

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

and delaying repair would not jeopardize the safety of drivers, this crack was

Structural Health Monitoring System sponsored by the U.S. Department of Transportation, Office of the Assistant Secretary for Research and Technology (USDOT/OST-R). This smart bridge condition monitoring system, termed the ISHM system, features a number of technology innovations, including remote sensing capability, piezo paint acoustic emission sensors, wind and solar based energy harvesting devices to power the sensor network, high-speed wireless sensing ability and advanced data analysis methods for remaining life estimation of aging bridges. Through successful advancement and commercialization in the state-of-the-art technology of remote infrastructure sensing, the ISHM system is promising to reduce life cycle costs while significantly maintaining the sustainability of the highway

The field test of the I-270 Bridge was conducted through a Wireless Integrated

The main data acquisition systems used in this test consisted of a PXI-based data acquisition system by National Instruments, which was used for data collection by the BDI strain transducers, string pots and Acoustic Emission (AE) sensors, and a multi-channel data acquisition equipment CR5000 manufactured by Campbell Scientific, Inc., which was used for the extra BDI strain transducer. Types of sensors used in this project were: (1) piezoelectric paint AE sensors; (2) wireless accelerometers; (3) laser sensor; (4) ultrasonic distance sensors; (5) BDI strain transducers; and (6) string pots. Sensors were strategically placed where the cracks on the SB bridge were identified and their related strain, AE or supplemental data can be collected by the data acquisition system and later used for validating the FE models. The instrumentation plan is shown in **Figure 2**. Girder displacement and stress range records due to truck traffic were part of the field measurements in this study.

A total of four wireless accelerometers were used to monitor the vibration responses of the bridge. Wireless sensors were installed on four girders (Girders 2–5) and acceleration data were acquired at 100 Hz sampling rate synchronically. The acceleration data were used to provide modal frequency information that was used to calibrate the finite element model of the bridge. The fundamental frequency measured is 3.22 Hz, which was very close to the value of the first vertical mode from the finite element analysis of 3.24 Hz discussed in the following

Both laser sensor and ultrasonic distance sensors were used to measure the dynamic deflection of the bridge. Only one laser sensor and one ultrasonic distance sensor were used each time. The measured deflection value from the laser sensor agreed well with the string pot, and its accuracy was also validated by the fundamental frequency indicated by fast Fourier transform (FFT) of the laser sensor measured deflection data. The measured maximum deflection of the I-270 bridge

over Middlebrook Road under traffic loading is summarized in **Table 1**.

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

**2.2 Field test and results**

infrastructure in the US.

*2.2.1 Instrumentation plan*

*2.2.2 Vibration response*

*2.2.3 Bridge deflection*

selected for research purposes and long-term monitoring.

**Figure 4.**

*Crack locations and sensor placements: (a) details at G3B2D3 and (b) details at G3B3D3.*

and delaying repair would not jeopardize the safety of drivers, this crack was selected for research purposes and long-term monitoring.

#### **2.2 Field test and results**

*Bridge Optimization - Inspection and Condition Monitoring*

*Crack locations and sensor placements on the framing plan.*

**80**

**Figure 4.**

*Crack locations and sensor placements: (a) details at G3B2D3 and (b) details at G3B3D3.*

**Figure 3.** *Cross frame detail.*

**Figure 2.**

The field test of the I-270 Bridge was conducted through a Wireless Integrated Structural Health Monitoring System sponsored by the U.S. Department of Transportation, Office of the Assistant Secretary for Research and Technology (USDOT/OST-R). This smart bridge condition monitoring system, termed the ISHM system, features a number of technology innovations, including remote sensing capability, piezo paint acoustic emission sensors, wind and solar based energy harvesting devices to power the sensor network, high-speed wireless sensing ability and advanced data analysis methods for remaining life estimation of aging bridges. Through successful advancement and commercialization in the state-of-the-art technology of remote infrastructure sensing, the ISHM system is promising to reduce life cycle costs while significantly maintaining the sustainability of the highway infrastructure in the US.

#### *2.2.1 Instrumentation plan*

The main data acquisition systems used in this test consisted of a PXI-based data acquisition system by National Instruments, which was used for data collection by the BDI strain transducers, string pots and Acoustic Emission (AE) sensors, and a multi-channel data acquisition equipment CR5000 manufactured by Campbell Scientific, Inc., which was used for the extra BDI strain transducer. Types of sensors used in this project were: (1) piezoelectric paint AE sensors; (2) wireless accelerometers; (3) laser sensor; (4) ultrasonic distance sensors; (5) BDI strain transducers; and (6) string pots. Sensors were strategically placed where the cracks on the SB bridge were identified and their related strain, AE or supplemental data can be collected by the data acquisition system and later used for validating the FE models. The instrumentation plan is shown in **Figure 2**. Girder displacement and stress range records due to truck traffic were part of the field measurements in this study.

#### *2.2.2 Vibration response*

A total of four wireless accelerometers were used to monitor the vibration responses of the bridge. Wireless sensors were installed on four girders (Girders 2–5) and acceleration data were acquired at 100 Hz sampling rate synchronically. The acceleration data were used to provide modal frequency information that was used to calibrate the finite element model of the bridge. The fundamental frequency measured is 3.22 Hz, which was very close to the value of the first vertical mode from the finite element analysis of 3.24 Hz discussed in the following sections.

#### *2.2.3 Bridge deflection*

Both laser sensor and ultrasonic distance sensors were used to measure the dynamic deflection of the bridge. Only one laser sensor and one ultrasonic distance sensor were used each time. The measured deflection value from the laser sensor agreed well with the string pot, and its accuracy was also validated by the fundamental frequency indicated by fast Fourier transform (FFT) of the laser sensor measured deflection data. The measured maximum deflection of the I-270 bridge over Middlebrook Road under traffic loading is summarized in **Table 1**.


**Table 1.**

*Maximum deflections measured by laser sensor.*

#### *2.2.4 Stress*

Cracks occur in the direction perpendicular to the direction of principal tensile stress. To assess the driving force of the fatigue cracks in the connection welds, strain gages were placed vertically on the connection plate just beyond the tip of the existing crack. Strain gages were also placed longitudinally on the girder flanges to correlate with the occurrence of vehicular loads. For comparison with the results from analytical methods, field testing is applied as it is the most accurate approach since no assumptions need to be made for uncertainties in load distribution such as unintended composite action between structural components, contribution of nonstructural members, stiffness of various connections, and behavior of the concrete deck in tension. The actual strain histories experienced by bridge components are directly measured by strain gages at the areas of concern. The effects of varying vehicle weights and their random combinations in multiple lanes are also reflected in the measured strains.

BDI 1-4 strain transducers were placed on both sides of the connection plates while BDI 5-8 strain transducers were placed at the top and bottom flanges on Girders 3 and 4 (**Figure 2**). **Figure 5** shows the measured stresses on the flanges and connection plates, respectively. The maximum stress measured at the bottom flange was 1.604 ksi in tension for BDI 3215 on the bottom flange of Girder 3 due to regular traffic loading, which was very low comparatively. As for the connection plates, the maximum stresses were 16.18 ksi in tension for BDI 1641 on Girder 3 and 16.1 ksi in tension for BDI 1644 on Girder 4 (**Figure 5**).

**Figure 5.**

*BDI strain transducer measurements of connection plates and flanges (positive indicates compression; 1641 G3 cracked side; 1642 G3 uncracked side, 1643 G4 uncracked side and 1644 G4 cracked side).*

**83**

**Figure 6.**

*Observation points on I-270 in Montgomery County.*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

vehicle count data obtained from the Traffic Monitoring System Program

Wednesday and Thursday to reflect typical weekday travel patterns.

These monitoring systems are installed across Maryland and monitor most of the arterials, freeways, and interstates. **Figure 6** displays the location of several

The TMSP has also created an Internet Traffic Monitoring System (I-TMS) that provides access to detailed traffic count data. On the I-TMS, the user can select an individual location to view reports (class, volume, lane distribution, etc.). Based on the hourly traffic volume, one typical day was divided into four different time periods: midnight, early morning and night, morning peak hour, and noon to evening, as shown in **Table 2**. The durations for these four time periods are 5, 5, 5, 9 hours, respectively. The average hourly volume varied from 505 to 4215, and the truck percentage also varied from 10.39 to 20.10%. Lane distribution of I-270 Bridge over Middlebrook Road is shown in **Table 3**. The main purpose of this time division is to realistically simulate the major characteristics of the traffic flow for

Following the specifications in the Guide Specifications for Fatigue Evaluation of Existing Steel Bridges (1989), weigh station measurements were collected at Hyattstown Weigh Station. From these measurements, a gross-weights histogram was obtained for the truck traffic, which was used to calculate the effective gross weight of the fatigue truck. The Hyattstown Weigh and Inspection Station is located approximately 10 miles north of I-270 Bridge over Middlebrook Road,

The traffic data that is used to simulate the traffic flow were the time-varying

(TMSP); operated and maintained by the Highway Information Services Division under Maryland Department of Transportation, State Highway Administration (MDSHA) [10]. The TMSP has been responsible for the collection, processing, analysis, and management of Maryland highway traffic data since 1997. Under this program, MDSHA has implemented 79 permanent continuous automatic traffic recorders (ATRs) counting traffic continuously throughout the year, and over 3800 short-term (48 hour) program count locations throughout the state, with data taken during the week on either Tuesday and Wednesday or

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

**3. Finite element modeling**

**3.1 Traffic loading**

ATRs on I-270.

each time period.

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

#### **3. Finite element modeling**

#### **3.1 Traffic loading**

*Bridge Optimization - Inspection and Condition Monitoring*

*Maximum deflections measured by laser sensor.*

Cracks occur in the direction perpendicular to the direction of principal tensile stress. To assess the driving force of the fatigue cracks in the connection welds, strain gages were placed vertically on the connection plate just beyond the tip of the existing crack. Strain gages were also placed longitudinally on the girder flanges to correlate with the occurrence of vehicular loads. For comparison with the results from analytical methods, field testing is applied as it is the most accurate approach since no assumptions need to be made for uncertainties in load distribution such as unintended composite action between structural components, contribution of nonstructural members, stiffness of various connections, and behavior of the concrete deck in tension. The actual strain histories experienced by bridge components are directly measured by strain gages at the areas of concern. The effects of varying vehicle weights and their random combinations in multiple lanes are also reflected

**Girder number 3 4 5** Max D (in) 0.2598 0.2717 0.2480

BDI 1-4 strain transducers were placed on both sides of the connection plates while BDI 5-8 strain transducers were placed at the top and bottom flanges on Girders 3 and 4 (**Figure 2**). **Figure 5** shows the measured stresses on the flanges and connection plates, respectively. The maximum stress measured at the bottom flange was 1.604 ksi in tension for BDI 3215 on the bottom flange of Girder 3 due to regular traffic loading, which was very low comparatively. As for the connection plates, the maximum stresses were 16.18 ksi in tension for BDI 1641 on Girder 3 and 16.1 ksi in

*BDI strain transducer measurements of connection plates and flanges (positive indicates compression; 1641 G3* 

*cracked side; 1642 G3 uncracked side, 1643 G4 uncracked side and 1644 G4 cracked side).*

*2.2.4 Stress*

**Table 1.**

in the measured strains.

tension for BDI 1644 on Girder 4 (**Figure 5**).

**82**

**Figure 5.**

The traffic data that is used to simulate the traffic flow were the time-varying vehicle count data obtained from the Traffic Monitoring System Program (TMSP); operated and maintained by the Highway Information Services Division under Maryland Department of Transportation, State Highway Administration (MDSHA) [10]. The TMSP has been responsible for the collection, processing, analysis, and management of Maryland highway traffic data since 1997. Under this program, MDSHA has implemented 79 permanent continuous automatic traffic recorders (ATRs) counting traffic continuously throughout the year, and over 3800 short-term (48 hour) program count locations throughout the state, with data taken during the week on either Tuesday and Wednesday or Wednesday and Thursday to reflect typical weekday travel patterns. These monitoring systems are installed across Maryland and monitor most of the arterials, freeways, and interstates. **Figure 6** displays the location of several ATRs on I-270.

The TMSP has also created an Internet Traffic Monitoring System (I-TMS) that provides access to detailed traffic count data. On the I-TMS, the user can select an individual location to view reports (class, volume, lane distribution, etc.). Based on the hourly traffic volume, one typical day was divided into four different time periods: midnight, early morning and night, morning peak hour, and noon to evening, as shown in **Table 2**. The durations for these four time periods are 5, 5, 5, 9 hours, respectively. The average hourly volume varied from 505 to 4215, and the truck percentage also varied from 10.39 to 20.10%. Lane distribution of I-270 Bridge over Middlebrook Road is shown in **Table 3**. The main purpose of this time division is to realistically simulate the major characteristics of the traffic flow for each time period.

Following the specifications in the Guide Specifications for Fatigue Evaluation of Existing Steel Bridges (1989), weigh station measurements were collected at Hyattstown Weigh Station. From these measurements, a gross-weights histogram was obtained for the truck traffic, which was used to calculate the effective gross weight of the fatigue truck. The Hyattstown Weigh and Inspection Station is located approximately 10 miles north of I-270 Bridge over Middlebrook Road,

**Figure 6.** *Observation points on I-270 in Montgomery County.*


#### **Table 2.**

*Traffic condition under different time period.*


#### **Table 3.**

*Lane distribution of one typical day.*

along Interstate 270 (I-270). Around 2200 samples during 1 year were chosen as the database to generate the truck weight and configuration. The measured data were filtered before the statistical analyses were made, where five samples were deleted. All the trucks were cataloged into seven classes based the number of axles (**Figure 7**). It is clear that 2-axle trucks and 5-axle trucks were the majority, which occupies about 24.87 and 67.99%, respectively. The 3-axle trucks, 4-axle trucks and the heaviest 6-axle trucks and over accounted for 1.61, 2.98 and 2.55%, respectively, which adds up to 7.14% in total.

**85**

**Figure 8.**

*Fatigue truck configurations: (a) small truck; (b) medium truck; and (c) large truck.*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

Because of the limitation of the traffic simulation software CORSIM, only three different types of trucks can be defined during traffic simulation: the small truck, the medium truck, and the large truck. Since 2-axle trucks and 5-axle trucks were the majority, the small truck was defined to consist 2-axle trucks and 3-axle trucks, and the medium truck to include 4-axle trucks and 5-axle trucks. For safety consideration, the heaviest 6-axle trucks and over were also considered as the third type,

The effective gross weight of the fatigue truck was computed from Eq. (1)

where *fi* is the fraction of gross weights within an interval and *Wi* is the midwidth of the interval. The gross weight was distributed to axles in accordance with the site data. The final fatigue truck configurations were shown in **Figure 8**.

3 ) 1/3

(1)

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

although it only takes a very small percentage.

*W* = (∑*fiWi*

**Figure 7.** *Truck class distribution.*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

Because of the limitation of the traffic simulation software CORSIM, only three different types of trucks can be defined during traffic simulation: the small truck, the medium truck, and the large truck. Since 2-axle trucks and 5-axle trucks were the majority, the small truck was defined to consist 2-axle trucks and 3-axle trucks, and the medium truck to include 4-axle trucks and 5-axle trucks. For safety consideration, the heaviest 6-axle trucks and over were also considered as the third type, although it only takes a very small percentage.

The effective gross weight of the fatigue truck was computed from Eq. (1)

$$\mathbf{W} = \begin{pmatrix} \sum f\_i \mathbf{W}\_i^3 \end{pmatrix}^{1/3} \tag{1}$$

where *fi* is the fraction of gross weights within an interval and *Wi* is the midwidth of the interval. The gross weight was distributed to axles in accordance with the site data. The final fatigue truck configurations were shown in **Figure 8**.

**Figure 8.** *Fatigue truck configurations: (a) small truck; (b) medium truck; and (c) large truck.*

*Bridge Optimization - Inspection and Condition Monitoring*

**Time Average** 

**total volume (no. of vehicles per hour)**

**Passenger car (no. of vehicles per hour)**

**Truck by axle number (no. of vehicles per hour)**

**2 3 4 5 6**

505 403 25 2 3 69 3 20.10%

1934 1712 55 4 7 150 6 11.40%

4215 3759 113 7 14 310 12 10.82%

3021 2707 78 5 9 213 8 10.39%

**Truck percentage**

**Time period**

Early morning and night

Moring peak

Noon to evening

**Table 2.**

**Table 3.**

Midnight 23:00–24:00

0:00–3:00 (5 hours)

4:00–5:00 19:00–23:00 (5 hours)

5:00–10:00 (5 hours)

10:00–19:00 (9 hours)

*Traffic condition under different time period.*

along Interstate 270 (I-270). Around 2200 samples during 1 year were chosen as the database to generate the truck weight and configuration. The measured data were filtered before the statistical analyses were made, where five samples were deleted. All the trucks were cataloged into seven classes based the number of axles (**Figure 7**). It is clear that 2-axle trucks and 5-axle trucks were the majority, which occupies about 24.87 and 67.99%, respectively. The 3-axle trucks, 4-axle trucks and the heaviest 6-axle trucks and over accounted for 1.61, 2.98 and 2.55%, respectively,

**Vehicle type Left lane (%) Middle lane (%) Right lane (%)** Total (passage car and truck) 31.87 30.62 37.51 Truck 1.45 44.84 53.71

**84**

**Figure 7.**

*Truck class distribution.*

which adds up to 7.14% in total.

*Lane distribution of one typical day.*

#### *Bridge Optimization - Inspection and Condition Monitoring*

As an intercorrelated component of a whole transportation network, the actual traffic flow through a bridge is affected by the traffic on the connecting roadway segments. Therefore, to realistically capture the major characteristics of the traffic flow, a road network system consisting of the bridge, highway, and two neighboring ramps was studied in the present work. The detailed procedure is summarized in four steps:


**87**

**Figure 10.**

**Table 4.**

*CORSIM simulation results.*

*(b) zoom-in view (refined meshing around the welds).*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

4.After the simulation network is created, the traffic demand is input and calibrated, and the detectors are installed, the CORSIM simulation can begin. The simulation provides the following meaningful results for the analysis. First, it records the animation of the simulation, which is used to observe the passage time of the trucks. Second, it provides text output including the volume and speed statistics by each interval (set to be 1 s here). Combining the above two outputs, the passage time and the lane occurred and speed of the truck could

The results (**Table 4**) could provide vehicle position and speed at each time step of the simulation. It was found from the results that the 20 min simulation period currently used can lead to stable pattern and matched field monitoring results. Details of the field monitoring are reported in a separate companion paper,

To investigate the fatigue performance of the bridge, a three-dimensional finite element model was developed for linear-elastic structural analysis using the CSiBridge [12], as depicted in **Figure 10**. The model of the southbound superstructure consisted eight I-girders. The concrete deck, the eight I-girders, and connection plates which connected cross-frames to the girders were modeled by shell elements, while all the cross-frames were modeled by spatial frames along their center-of-gravity. Special link members were defined to connect girder elements and concrete deck elements at the actual spatial points where these members intersect. The translations in the x-, y-, z-directions were fixed at the abutments to represent the actual characteristics of support and continuity. It is complicated to establish a comprehensive finite element model of a large practical structure for fatigue damage analysis, since the finite element model should

**Average speed (mph) Number Average headway (s)**

*Finite element model of I-270 Bridge in CSiBridge: (a) isometric view of FEM for I-270 Bridge and* 

*"Integrating Bridge Management Systems with Fatigue Damage Assessments."*

**Time periods CORSIM**

Midnight 53.69 32 37.5 Early morning and night 52.94 78 15.38 Morning peak 35.45 165 7.27 Noon to evening 42.07 98 12.24

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

be successfully matched.

**3.2 Bridge global model**

**Figure 9.** *Traffic simulation network.*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

4.After the simulation network is created, the traffic demand is input and calibrated, and the detectors are installed, the CORSIM simulation can begin. The simulation provides the following meaningful results for the analysis. First, it records the animation of the simulation, which is used to observe the passage time of the trucks. Second, it provides text output including the volume and speed statistics by each interval (set to be 1 s here). Combining the above two outputs, the passage time and the lane occurred and speed of the truck could be successfully matched.

The results (**Table 4**) could provide vehicle position and speed at each time step of the simulation. It was found from the results that the 20 min simulation period currently used can lead to stable pattern and matched field monitoring results. Details of the field monitoring are reported in a separate companion paper, *"Integrating Bridge Management Systems with Fatigue Damage Assessments."*

#### **3.2 Bridge global model**

*Bridge Optimization - Inspection and Condition Monitoring*

is set to be 1 hour.

input for CORSIM simulation.

the detected vehicles.

As an intercorrelated component of a whole transportation network, the actual traffic flow through a bridge is affected by the traffic on the connecting roadway segments. Therefore, to realistically capture the major characteristics of the traffic flow, a road network system consisting of the bridge, highway, and two neighboring ramps was studied in the present work. The detailed procedure is summarized in four steps:

1.Build the simulation network (**Figure 9**) in TSIS 5.1 [11] around the I-270 over Middlebrook Road based on the background map obtained from Google Maps. The background map is adjusted to the correct scale, and the simulation network is drawn along the real roadway segment. The network contained the mainline of I-270 and adjacent on-ramps of the bridge in the study. Since the focus is on the southbound of the bridge, the network only contains one-way southbound link. The simulation time

2.Use the time varying vehicle count data collected from nearby detectors, which were placed on the I-TMS website, and combine with the weigh station measurements collected from the Hyattstown southbound station as the input data for the simulation model. The truck count data from the vehicle count report are converted to truck percentage (truck count/total vehicle count) as the

3.Set three different types of trucks corresponding to fatigue trucks generated in the last section. Install three loop detectors at the bridge in the created simulation network, one for each lane to record the speed, type, and passage time of

**86**

**Figure 9.**

*Traffic simulation network.*

To investigate the fatigue performance of the bridge, a three-dimensional finite element model was developed for linear-elastic structural analysis using the CSiBridge [12], as depicted in **Figure 10**. The model of the southbound superstructure consisted eight I-girders. The concrete deck, the eight I-girders, and connection plates which connected cross-frames to the girders were modeled by shell elements, while all the cross-frames were modeled by spatial frames along their center-of-gravity. Special link members were defined to connect girder elements and concrete deck elements at the actual spatial points where these members intersect. The translations in the x-, y-, z-directions were fixed at the abutments to represent the actual characteristics of support and continuity. It is complicated to establish a comprehensive finite element model of a large practical structure for fatigue damage analysis, since the finite element model should


#### **Figure 10.**

*Finite element model of I-270 Bridge in CSiBridge: (a) isometric view of FEM for I-270 Bridge and (b) zoom-in view (refined meshing around the welds).*

embody the sectional properties of structural members (e.g., the weld between two members). In addition, fatigue damage is a local failure mode and often occurs around welded regions. Therefore, a global model with refined meshing around the welded connection between the connection plates and the bottom flanges was constructed for analysis.

#### **3.3 Convergence test**

The accuracy of a finite element analysis depends on the mesh size of the elements; the smaller the size of the elements, the greater the accuracy of the analysis. However, the desire for increased calculation accuracy can significantly increase the computational time. Therefore, in finite element analysis, a convergence test is used to determine appropriate mesh size for a model without increasing the computation time. The measurement of a finite element model's mesh size depends on the purpose of the model. Since this bridge model is to investigate the vertical stress or shear stress in the cracked connection weld, it needs to have a very fine mesh in the connection area but needs to also transit gradually to coarser meshes because otherwise the model would become unnecessarily too large. A more uniform mesh may then be used along the rest of the bridge length for all the girders. However, there are multiple parameters related to the accuracy of a twodimensional or three-dimensional finite element model, including the dimensions and aspect ratios of the elements for the girder top flange, bottom flange, and web, as well as the bridge deck.

To simplify the convergence test for these finite element models of the I-270 Bridge over Middlebrook Road, a consistent refined mesh around the weld region was employed in all the models, and the maximum element size was used to control the uniform mesh along the bridge longitudinal length for all the girders and the deck. The determination of the first natural frequency was used as the measurement during the convergence test. As the maximum mesh size changed from 1000 in to 0.5 in, the results of the first natural frequency gradually increased from 2 to 3.20 Hz. The results of the first natural frequency were all beyond 3 Hz when the maximum mesh size of the finite element models was smaller than 200 in, which means that the error rate of the first natural frequency was under 6.25%. When the maximum mesh size was equal to or less than 50 in, the results of the first natural frequency were accurate enough with an error rate less than 2%, and were therefore used as the basis for the selection of an accurate finite element mesh in CSiBridge.

#### **3.4 Modal analysis**

Modal analysis is used to determine the vibration modes of a structure. These modes are useful to understand the behavior of the structure. They can also be used as the basis for modal superposition in response-spectrum and modal time-history load cases. An eigenvector analysis was used to determine the undamped freevibration mode shapes and frequencies of the system.

The first six mode shapes of torsion, vertical and lateral modes are shown in **Figure 11**. To validate the finite element models, experimental data from the field test and numerical results from CSiBridge were studied. In the numerical study, the bridge was only subjected to dead load. The results obtained from the finite element model and field measurements were compared, and the differences of most of the compared frequencies were less than 6%, which was considered acceptable for the finite element analysis. All the mode shapes matched well with each other. Therefore, the CSiBridge model was considered reasonably accurate for the purposes of this study.

**89**

**3.5 Stresses by simulation**

*(second vertical), and (f) mode shape 6 (third torsion).*

**Figure 11.**

for the previous deflection studies.

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

Possible driving forces for the fatigue cracks shown in **Figure 4** are vertical tensile stress, horizontal shear stress, or the principal tensile stress due to their combined actions along the connection welds. Live load induced stresses from the welded connections between the cross-frame connection plates and the girder bottom flanges were extracted in the refined portion of the finite element models. A total of four different traffic loading cases obtained from the traffic simulation were studied as described below and the key results were summarized in **Table 5**. For all the four cases analyzed, the longitudinal positions of trucks remained the same as

*Mode shapes of I-270 Bridge over Middlebrook Road in CSiBridge: (a) mode shape 1 (first torsion), (b) mode shape 2 (first vertical), (c) mode shape 3 (second torsion), (d) mode shape 4 (first lateral), (e) mode shape 5* 

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

**Figure 11.**

*Bridge Optimization - Inspection and Condition Monitoring*

flanges was constructed for analysis.

**3.3 Convergence test**

as well as the bridge deck.

**3.4 Modal analysis**

embody the sectional properties of structural members (e.g., the weld between two members). In addition, fatigue damage is a local failure mode and often occurs around welded regions. Therefore, a global model with refined meshing around the welded connection between the connection plates and the bottom

The accuracy of a finite element analysis depends on the mesh size of the elements; the smaller the size of the elements, the greater the accuracy of the analysis. However, the desire for increased calculation accuracy can significantly increase the computational time. Therefore, in finite element analysis, a convergence test is used to determine appropriate mesh size for a model without increasing the computation time. The measurement of a finite element model's mesh size depends on the purpose of the model. Since this bridge model is to investigate the vertical stress or shear stress in the cracked connection weld, it needs to have a very fine mesh in the connection area but needs to also transit gradually to coarser meshes because otherwise the model would become unnecessarily too large. A more uniform mesh may then be used along the rest of the bridge length for all the girders. However, there are multiple parameters related to the accuracy of a twodimensional or three-dimensional finite element model, including the dimensions and aspect ratios of the elements for the girder top flange, bottom flange, and web,

To simplify the convergence test for these finite element models of the I-270 Bridge over Middlebrook Road, a consistent refined mesh around the weld region was employed in all the models, and the maximum element size was used to control the uniform mesh along the bridge longitudinal length for all the girders and the deck. The determination of the first natural frequency was used as the measurement during the convergence test. As the maximum mesh size changed from 1000 in to 0.5 in, the results of the first natural frequency gradually increased from 2 to 3.20 Hz. The results of the first natural frequency were all beyond 3 Hz when the maximum mesh size of the finite element models was smaller than 200 in, which means that the error rate of the first natural frequency was under 6.25%. When the maximum mesh size was equal to or less than 50 in, the results of the first natural frequency were accurate enough with an error rate less than 2%, and were therefore used as the basis for the selection of an accurate finite element mesh in CSiBridge.

Modal analysis is used to determine the vibration modes of a structure. These modes are useful to understand the behavior of the structure. They can also be used as the basis for modal superposition in response-spectrum and modal time-history load cases. An eigenvector analysis was used to determine the undamped free-

The first six mode shapes of torsion, vertical and lateral modes are shown in **Figure 11**. To validate the finite element models, experimental data from the field test and numerical results from CSiBridge were studied. In the numerical study, the bridge was only subjected to dead load. The results obtained from the finite element model and field measurements were compared, and the differences of most of the compared frequencies were less than 6%, which was considered acceptable for the finite element analysis. All the mode shapes matched well with each other. Therefore, the CSiBridge

model was considered reasonably accurate for the purposes of this study.

vibration mode shapes and frequencies of the system.

**88**

*Mode shapes of I-270 Bridge over Middlebrook Road in CSiBridge: (a) mode shape 1 (first torsion), (b) mode shape 2 (first vertical), (c) mode shape 3 (second torsion), (d) mode shape 4 (first lateral), (e) mode shape 5 (second vertical), and (f) mode shape 6 (third torsion).*

#### **3.5 Stresses by simulation**

Possible driving forces for the fatigue cracks shown in **Figure 4** are vertical tensile stress, horizontal shear stress, or the principal tensile stress due to their combined actions along the connection welds. Live load induced stresses from the welded connections between the cross-frame connection plates and the girder bottom flanges were extracted in the refined portion of the finite element models. A total of four different traffic loading cases obtained from the traffic simulation were studied as described below and the key results were summarized in **Table 5**. For all the four cases analyzed, the longitudinal positions of trucks remained the same as for the previous deflection studies.

#### *Bridge Optimization - Inspection and Condition Monitoring*


**Table 5.**

*Stresses in cross frame connection plate-to-girder bottom flange connections at G3 without dynamic impact (FE results) (ksi).*

There were many live load cases that could have produced significant tensile stresses in the connections of concern. The simulated truck loading contained most of the possible truck loading patterns. Magnitudes of tensile stresses in the connection plates depend on the magnitudes and positions of the wheel loads of crossing vehicles. The stresses listed in **Table 5** are for illustration and are taken from the connection plates at Girder 3 for the four different time periods. A comparison of live load cases for the four different time periods suggest that live loads during morning peak may have caused the highest tensile stress of 12.94 ksi in the connection of concern. All the shear stresses in the connection welds were much lower than the vertical stresses at the same spot during each time period. Considering a factor of dynamic load allowance, the dynamic maximum vertical stress was 16.822 ksi, which perfectly matched with the field measurements.

#### **4. Cause of fatigue cracks**

#### **4.1 Connection plate configuration**

The results of the finite element analysis were verified and validated with the field test data; all the cracks were located on the western sides of the connection plates. The vertical stress near the welded edges of the connection plates followed the same pattern; the western sides of the connection plates were under tension; and the eastern sides of the connection plates were under compression. To further discuss the cause of this phenomenon, a series of controlled FEM tests were established for the comparison study.

According to the design drawings and the existing bridge construction, crossframe connection plates and bearing stiffeners are normal to the girders and connection plates connecting the cross-frames are bent. Therefore, for the original FE model, all the connection plates were normal (90°) to the girders and the crossframes are parallel to the two abutments with a skew angel of 76°. For the controlled model, all the connection plates were parallel to the cross frames with the same skew angel of 76 degree (**Figure 12**).

#### **4.2 Bracing system configuration**

The K-type bracing system was modeled for studying the influence of the bracing system configuration on the stress distribution in the connection plates. The K-type cross-frame without top chord was modeled in the original FE model, while the K-type cross-frame with top chord was modeled in the controlled

**91**

**Figure 13.**

*K-frame without top chord (left) and K-frame with top chord (right).*

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

model. The cross section of the diagonal and bottom chords was employed for the additional top chords (**Figure 13**). All the models were subjected to the same live load case. The live load case was defined as an HS20 truck in the right traffic lane passing across the bridge from north to south at the speed limit of 55 mph. The vertical stress at the crack location (Girder 3 Diaphragm 3) and the axial forces in the top chord located at Diaphragm 3 Bay 2, directly connecting with the crack side, were analyzed and are shown in **Table 6**. Maximum vertical stresses in the model with the non-skewed connection plates were much higher than the stresses in the model with the skewed connection plates. The maximum axial forces in the models during the load time history analysis were quite small; the values were only 3.47 and 1.12 kip. The values of maximum vertical stresses did not change much due to the addition of a top chord. It demonstrates that the connection plate configuration has a significant influence on the stress distribution in the connection plates, while

> **Bracing system configuration**

K-frame without top chord

K-frame with top chord

K-frame without top chord

K-frame with top chord

*Maximum vertical stress and axial force through simulated numerical analyses.*

**Maximum axial force (kip)**

**Maximum vertical stress of crack location (ksi)**

— 13.50

3.47 12.66

— 0.33

1.12 0.30

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

*Skewed (right) and non-skewed (left) connection plates.*

**Figure 12.**

**Connection plates configuration**

Skewed connection

Non-skewed connection plats

plats

**Table 6.**

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

**Figure 12.** *Skewed (right) and non-skewed (left) connection plates.*

model. The cross section of the diagonal and bottom chords was employed for the additional top chords (**Figure 13**). All the models were subjected to the same live load case. The live load case was defined as an HS20 truck in the right traffic lane passing across the bridge from north to south at the speed limit of 55 mph. The vertical stress at the crack location (Girder 3 Diaphragm 3) and the axial forces in the top chord located at Diaphragm 3 Bay 2, directly connecting with the crack side, were analyzed and are shown in **Table 6**. Maximum vertical stresses in the model with the non-skewed connection plates were much higher than the stresses in the model with the skewed connection plates. The maximum axial forces in the models during the load time history analysis were quite small; the values were only 3.47 and 1.12 kip. The values of maximum vertical stresses did not change much due to the addition of a top chord. It demonstrates that the connection plate configuration has a significant influence on the stress distribution in the connection plates, while


#### **Table 6.**

*Bridge Optimization - Inspection and Condition Monitoring*

**Time period Max vertical stress Max shear** 

There were many live load cases that could have produced significant tensile stresses in the connections of concern. The simulated truck loading contained most of the possible truck loading patterns. Magnitudes of tensile stresses in the connection plates depend on the magnitudes and positions of the wheel loads of crossing vehicles. The stresses listed in **Table 5** are for illustration and are taken from the connection plates at Girder 3 for the four different time periods. A comparison of live load cases for the four different time periods suggest that live loads during morning peak may have caused the highest tensile stress of 12.94 ksi in the connection of concern. All the shear stresses in the connection welds were much lower than the vertical stresses at the same spot during each time period. Considering a factor of dynamic load allowance, the dynamic maximum vertical stress was 16.822 ksi, which perfectly matched with the field

*Stresses in cross frame connection plate-to-girder bottom flange connections at G3 without dynamic impact* 

Midnight 6.665 2.165 7.629 Early morning and night 7.586 2.563 8.70 Morning peak 12.94 4.327 14.84 Noon to evening 7.905 2.664 9.061

**stress**

**Max principal stress**

The results of the finite element analysis were verified and validated with the field test data; all the cracks were located on the western sides of the connection plates. The vertical stress near the welded edges of the connection plates followed the same pattern; the western sides of the connection plates were under tension; and the eastern sides of the connection plates were under compression. To further discuss the cause of this phenomenon, a series of controlled FEM tests were estab-

According to the design drawings and the existing bridge construction, cross-

frame connection plates and bearing stiffeners are normal to the girders and connection plates connecting the cross-frames are bent. Therefore, for the original FE model, all the connection plates were normal (90°) to the girders and the crossframes are parallel to the two abutments with a skew angel of 76°. For the controlled model, all the connection plates were parallel to the cross frames with the same

The K-type bracing system was modeled for studying the influence of the bracing system configuration on the stress distribution in the connection plates. The K-type cross-frame without top chord was modeled in the original FE model, while the K-type cross-frame with top chord was modeled in the controlled

**90**

measurements.

**Table 5.**

*(FE results) (ksi).*

**4. Cause of fatigue cracks**

**4.1 Connection plate configuration**

lished for the comparison study.

skew angel of 76 degree (**Figure 12**).

**4.2 Bracing system configuration**

*Maximum vertical stress and axial force through simulated numerical analyses.*

**Figure 13.** *K-frame without top chord (left) and K-frame with top chord (right).*

the top chord of K-type bracing plays a negligible role in this situation. Further, the results showed that X-type or K-type bracing made no difference on the vertical stress at the crack location.

The measured high vertical tensile stress around the connection plate welds was proven caused by the configuration of the connection plates instead of the configuration of the cross-frames. The connection plates, which were bent to be parallel to the skewed abutment, induced torsion in the connection plate welds. Differential displacements between the girders caused one diagonal cross frame to be in tension and the other diagonal to be in compression. Measured vertical tensile stresses from field tests up to 16.1 ksi in the connection plate explains why fatigue cracks have occurred at their connections to the girder bottom flange. Girders 3 and 4 are located under the slow-moving lane which most heavy trucks are using while Girders 1 and 2 support a shoulder and thus larger differential deflections typically occur between Girders 2 and 3 (with up to 0.5″ to 0.75″ vertical deflections due to observed live load). The connection plate configuration is a key factor in the stress distribution that results in the connection plates.

#### **5. Conclusions**

The passage of trucks on the bridge deck can cause vertical tensile stresses in the welded connections between cross-frame connection plates and girder bottom flanges. These stresses were highest at the outer edge of the connection plate where all the existing four fatigue cracks on the I-270 Bridge over Middlebrook Road were located. Girder 4 located at the center left of the middle traffic lane, and Girder 3 located at the center right of the right traffic lane, are the most critical locations for the bridge deflections and the resulting stresses.

The live load-induced stresses in the connection plates were localized around the welded connections and would not be anticipated to spread from the bottom to the top of connection plates. At the same face of the connection plate, both tensile and compressive stresses were observed at the symmetric positions around the girder web. The cracked side of the connection plates was always under tensile stress, while the uncracked side was always under compressive stress during each time period. At the same location of the cracked side, the north face and the south face sustained the same stresses, (although opposite directions). It was proved that the high vertical tensile stress around the connection plate welds was caused by the configuration of the connection plates instead of by the configuration of the cross-frames. The connection plates, which were bent to be parallel to the skewed abutment, induced torsion in the connection plate welds. The connection plate configuration is a key factor in the stress distribution that results in the connection plates.

Different from the explicit equation-based method, the proposed approach combines a comprehensive traffic loading model, which includes information on vehicle types, axle weights, axle spacing, and the lane occupation, and a detailed 3D FE model, which enables fatigue analysis on unreachable or complicated details where complex stress conditions may exist. The proposed approach may be used as a tool accompanying a monitoring program to find the stresses in unmonitored details or to reduce the frequency of structural health monitoring resulting in lower costs in fatigue assessment. In such case, the proposed approach also provides a tool to predict the fatigue reliabilities of these hard-to-reach details. When combined with the fracture damage mechanics, the proposed approach can help understand the accumulation of fatigue damage and crack propagation.

**93**

USA

**Author details**

Gengwen Zhao1

provided the original work is properly cited.

, Chung C. Fu2

\*Address all correspondence to: ccfu@umd.edu

\*, Yang Lu3

3 Asian Development Bank, Mandaluyong, Metro Manila, Philippines

1 Virginia Department of Transportation, Richmond, VA, USA

and Timothy Saad<sup>2</sup>

© 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,

2 The Bridge Engineering Software and Technology (BEST) Center, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD,

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic…*

This work was partially sponsored by the US Department of Transportation's Office of the Assistant Secretary for Research and Technology (USDOT/OST-R) under The Commercial Remote Sensing and Spatial Information (CRS&SI) Technologies Program. This support is acknowledged and greatly appreciated.

*DOI: http://dx.doi.org/10.5772/intechopen.81520*

**Acknowledgements**

*Fatigue Assessment of Highway Bridges under Traffic Loading Using Microscopic Traffic… DOI: http://dx.doi.org/10.5772/intechopen.81520*

#### **Acknowledgements**

*Bridge Optimization - Inspection and Condition Monitoring*

distribution that results in the connection plates.

the bridge deflections and the resulting stresses.

stress at the crack location.

**5. Conclusions**

connection plates.

crack propagation.

the top chord of K-type bracing plays a negligible role in this situation. Further, the results showed that X-type or K-type bracing made no difference on the vertical

The measured high vertical tensile stress around the connection plate welds was proven caused by the configuration of the connection plates instead of the configuration of the cross-frames. The connection plates, which were bent to be parallel to the skewed abutment, induced torsion in the connection plate welds. Differential displacements between the girders caused one diagonal cross frame to be in tension and the other diagonal to be in compression. Measured vertical tensile stresses from field tests up to 16.1 ksi in the connection plate explains why fatigue cracks have occurred at their connections to the girder bottom flange. Girders 3 and 4 are located under the slow-moving lane which most heavy trucks are using while Girders 1 and 2 support a shoulder and thus larger differential deflections typically occur between Girders 2 and 3 (with up to 0.5″ to 0.75″ vertical deflections due to observed live load). The connection plate configuration is a key factor in the stress

The passage of trucks on the bridge deck can cause vertical tensile stresses in the welded connections between cross-frame connection plates and girder bottom flanges. These stresses were highest at the outer edge of the connection plate where all the existing four fatigue cracks on the I-270 Bridge over Middlebrook Road were located. Girder 4 located at the center left of the middle traffic lane, and Girder 3 located at the center right of the right traffic lane, are the most critical locations for

The live load-induced stresses in the connection plates were localized around the welded connections and would not be anticipated to spread from the bottom to the top of connection plates. At the same face of the connection plate, both tensile and compressive stresses were observed at the symmetric positions around the girder web. The cracked side of the connection plates was always under tensile stress, while the uncracked side was always under compressive stress during each time period. At the same location of the cracked side, the north face and the south face sustained the same stresses, (although opposite directions). It was proved that the high vertical tensile stress around the connection plate welds was caused by the configuration of the connection plates instead of by the configuration of the cross-frames. The connection plates, which were bent to be parallel to the skewed abutment, induced torsion in the connection plate welds. The connection plate configuration is a key factor in the stress distribution that results in the

Different from the explicit equation-based method, the proposed approach combines a comprehensive traffic loading model, which includes information on vehicle types, axle weights, axle spacing, and the lane occupation, and a detailed 3D FE model, which enables fatigue analysis on unreachable or complicated details where complex stress conditions may exist. The proposed approach may be used as a tool accompanying a monitoring program to find the stresses in unmonitored details or to reduce the frequency of structural health monitoring resulting in lower costs in fatigue assessment. In such case, the proposed approach also provides a tool to predict the fatigue reliabilities of these hard-to-reach details. When combined with the fracture damage mechanics, the proposed approach can help understand the accumulation of fatigue damage and

**92**

This work was partially sponsored by the US Department of Transportation's Office of the Assistant Secretary for Research and Technology (USDOT/OST-R) under The Commercial Remote Sensing and Spatial Information (CRS&SI) Technologies Program. This support is acknowledged and greatly appreciated.

#### **Author details**

Gengwen Zhao1 , Chung C. Fu2 \*, Yang Lu3 and Timothy Saad<sup>2</sup>

1 Virginia Department of Transportation, Richmond, VA, USA

2 The Bridge Engineering Software and Technology (BEST) Center, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA

3 Asian Development Bank, Mandaluyong, Metro Manila, Philippines

\*Address all correspondence to: ccfu@umd.edu

© 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.

### **References**

[1] Banjara NK, Sasma S. Evaluation of fatigue remaining life of typical steel plate girder bridge under railway loading. Structural Longevity. 2013;**10**:151-166

[2] AASHTO. Guide Specifications for Fatigue Evaluation of Existing Steel Bridges. Washington, D.C: American Association of State Highway and Transportation Officials; 1990

[3] Schilling CG. Stress cycles for fatigue design of steel bridges. Journal of Structural Engineering. 1984;**110**(6):1222-1234

[4] Raju S, Moses F, Schilling C. Reliability calibration of fatigue evaluation and design procedures. Journal of Structural Engineering. 1990;**116**(5):1356-1369

[5] Nowak AS, Nassif H, DeFrain L. Effect of truck loads on bridges. Journal of Transportation Engineering. 1993;**119**:853-867

[6] Laman JA, Nowak AS. Fatigueload models for girder bridges. Journal of Structural Engineering. 1996;**122**:726-733

[7] Miao TJ, Chan THT. Bridge live load models from WIM data. Engineering Structures. 2002;**24**:1071-1084

[8] NCHRP. Protocols for Collecting and using Traffic Data in Bridge Design. Washington, D.C: Transportation Research Board; 2011

[9] Chen S, Jun W. Dynamic performance simulation of long-span bridge under combined loads of stochastic traffic and wind. Journal of Bridge Engineering. 2010;**15**:219-230

[10] Internet Traffic Monitoring System. Maryland Department of Transportation State Highway Administration. Available from: http:// maps.roads.maryland.gov/itms\_public. Accessed Jul. 29, 2015

[11] ITT Industries, Inc., Systems Division: ATMS R&D and Systems Engineering Program Team; Colorado Springs, CO 80935-5012

[12] CSiBridge. Integrated 3D Bridge Design Software. Berkeley, CA: Computer and Structures, Inc; 2010

**94**

*Bridge Optimization - Inspection and Condition Monitoring*

Administration. Available from: http:// maps.roads.maryland.gov/itms\_public.

[11] ITT Industries, Inc., Systems Division: ATMS R&D and Systems Engineering Program Team; Colorado

[12] CSiBridge. Integrated 3D Bridge Design Software. Berkeley, CA: Computer and Structures, Inc; 2010

Accessed Jul. 29, 2015

Springs, CO 80935-5012

[1] Banjara NK, Sasma S. Evaluation of fatigue remaining life of typical steel plate girder bridge under

railway loading. Structural Longevity.

[2] AASHTO. Guide Specifications for Fatigue Evaluation of Existing Steel Bridges. Washington, D.C: American Association of State Highway and Transportation Officials; 1990

[3] Schilling CG. Stress cycles for fatigue design of steel bridges. Journal of Structural Engineering.

[4] Raju S, Moses F, Schilling C. Reliability calibration of fatigue evaluation and design procedures. Journal of Structural Engineering.

[5] Nowak AS, Nassif H, DeFrain L. Effect of truck loads on bridges. Journal of Transportation Engineering.

[6] Laman JA, Nowak AS. Fatigueload models for girder bridges. Journal of Structural Engineering.

[7] Miao TJ, Chan THT. Bridge live load models from WIM data. Engineering Structures. 2002;**24**:1071-1084

[8] NCHRP. Protocols for Collecting and using Traffic Data in Bridge Design. Washington, D.C: Transportation

performance simulation of long-span bridge under combined loads of stochastic traffic and wind. Journal of Bridge Engineering. 2010;**15**:219-230

1984;**110**(6):1222-1234

1990;**116**(5):1356-1369

1993;**119**:853-867

1996;**122**:726-733

Research Board; 2011

[9] Chen S, Jun W. Dynamic

[10] Internet Traffic Monitoring System. Maryland Department of Transportation State Highway

**References**

2013;**10**:151-166

### *Edited by Yun Lai Zhou and Magd Abdel Wahab*

This is a collection of several applications for condition monitoring and damage identification in bridge structures. Bridge structural condition monitoring is essential since it can provide early warning of potential defects in bridges, which may induce catastrophic accidents and result in huge economic loss. Such bridge condition monitoring relies on sensing techniques, especially advanced sensing techniques that can provide detailed information on bridge structures. Additionally, postprocessing systems can interpret the captured data and warn of any potential faults. This book will give students a thorough understanding of bridge condition monitoring.

Published in London, UK © 2020 IntechOpen © FotoMak / iStock

Bridge Optimization - Inspection and Condition Monitoring

Bridge Optimization

Inspection and Condition Monitoring

*Edited by Yun Lai Zhou and Magd Abdel Wahab*