Effects of shear keys and track system on the behavior of simply-supported bridges for high-speed trains subjected to transverse earthquake excitations

Abstract

China railway track system II (CRTS-II) slab ballastless track is usually constructed on high-speed railway (HSR) bridges to ensure the rail smoothness and the running safety of high-speed trains, but the use of the longitudinal continuous track system would significantly alter the dynamic characteristics of the bridges and therefore influence the bridge seismic responses. The pounding at shear keys has also been identified as one of the critical factors affecting the seismic behavior of bridges. To investigate the effects of shear keys and CRTS-II track system on the seismic behavior of HSR simply-supported bridges subjected to transverse earthquake excitations, detailed 3D finite element models are developed by using ABAQUS. The seismic responses calculated from the bridges with and without considering shear keys are firstly compared. The result shows that the shear keys can effectively limit the development of pier-girder relative displacement and thus decrease the potential of girder dislocation. However, large pounding forces would be generated between the shear keys and bearing pads and transferred to bridge piers, which will amplify the seismic responses of the bridge piers. The result of seismic analyses of multiple-span simply-supported bridges with and without considering the track system shows that the track system will significantly influence the distribution of seismic forces among the bridge spans. For a bridge with equal pier heights, considering the track system will reduce the seismic responses of side spans (close to subgrade) but will increase those of the middle spans. Whereas an opposite trend is found for bridges with high middle piers and short side piers.

Keywords

CRTS-II track system earthquake high-speed railway seismic responses shear keys simply-supported bridge transverse pounding

Introduction

Rapid construction of high-speed railway (HSR) bridges usually requires a typical structural design. The simply-supported bridge with 32 m standard-span prestressed concrete girder is the most commonly used bridge structure in China (Yan et al., 2015). Unlike highway bridges and low-speed railway bridges, the China railway track system II (CRTS-II) is usually constructed on the HSR bridges to ensure the running safety of high-speed trains. The CRTS-II slab ballastless track system consisting of the base plate, track plate, and rails is longitudinal continuous, which would alter the dynamic characteristics of bridges and therefore inevitably influence the bridge seismic behavior. Therefore, the influence of the track system must be considered when performing seismic analyses of railway bridge structures (Guo et al., 2020; Wei et al., 2018a; Yan and Dai, 2013).

The analyses of train-track-bridge systems during earthquakes have been extensively performed (Chen et al., 2018; Zeng et al., 2015; Zhai et al., 2019), but these studies were mainly focused on the moving safety of trains. Considering that the possibility of a train traveling on a bridge during an earthquake is very small, some researchers have paid more attention to the seismic behavior of track-bridge systems without considering the running train. Dicleli and Bruneau (1995) found that bearing is the key component in a track-bridge system and is prone to be damaged. Yan et al. (2017) established a 3D nonlinear dynamic model for simply-supported bridges considering the influence of the CRTS-II track system and numerical analyses were performed. Their result shows that the track system and piers are easily damaged during earthquakes. Wei et al. (2018b, 2018c) investigated the effects of ground motion characteristics on seismic vulnerabilities of a continuous HSR track-bridge system and concluded that the vertical part of ground motions should be carefully considered in seismic design of HSR track-bridge systems. Cui et al. (2019) did a numerical study on the risk assessment of HSR continuous girder bridge considering the effect of track constraint and found that a bridge without considering the track system is prone to be damaged compared to that with considering the track system. Kang et al. (2017) and Jiang et al. (2019) conducted a series of shaking table tests on a 1/12-scaled HSR bridge with CRTS-II track system to evaluate the seismic responses of bridge components subjected to different intensities of earthquake excitations. The experimental result revealed that the piers, bearings, and the track system are more likely to suffer damage.

The above studies highlighted the necessity of considering the track system in seismic analyses of HSR bridges. However, most of the aforementioned studies were focused on the seismic behavior of the track-bridge systems subjected to earthquake excitations along the longitudinal direction. The effect of CRTS-II track structure on the seismic responses of bridges under transverse earthquake excitations was rarely investigated. Moreover, I-shaped steel shear keys are normally installed at the bottom of bridge girders and are expected to restrain the excessive transverse displacements of bridge superstructures by pounding with bearing pads. Previous investigations have highlighted the importance of considering pounding in seismic analyses of bridge structures (Bi et al., 2013; Chouw et al., 2006; He et al., 2017a; Shrestha et al., 2015). However, shear keys were usually ignored in analyzing bridge seismic responses due to the relatively small dimension compared to the main components of bridges (girder, pier, etc.). In reality, the pounding at shear keys is also one of the critical factors affecting the seismic responses of bridges (Goel and Chopra, 2008; Han et al., 2009; Li et al., 2008; Meng et al., 2019b).

Previous studies on the effect of pounding at shear keys on the seismic responses of bridges were mainly focused on highway bridges. Wu et al. (2018) and Bi and Hao (2015) performed numerical investigations on the influence of shear keys on seismic behavior of small-to-medium-span highway bridges and concluded that neglecting shear keys in seismic analyses of bridges may result in inaccurate predictions of seismic responses in bridge substructures. Están et al. (2017) evaluated the influence of external shear keys on the bridge seismic behavior and concluded that the most vulnerable bridge is that without considering shear keys. Wu (2019) developed a simplified method to calculate the maximum pounding force at abutment shear keys of skew bridges and recommended that increasing gap size between the pounding components can significantly reduce the pounding forces generated in the shear keys. Physical experiments were also conducted by some researchers to investigate the role of shear keys in bridges. Xiang and Li (2016) and Li et al. (2017) conducted a large number of shake table experiments to evaluate the influence of transverse unseating-prevention devices including concrete shear keys on simply-supported highway bridges. The experimental results revealed the capacity of the shear keys in limiting transverse displacements of the bridge girders relative to their piers. The results also indicated that the proper design of shear keys can effectively reduce the pounding forces transferred to the piers.

Shear keys used for HSR bridges, however, are significantly different from those used for highway bridges. As shown in Figure 1(a), concrete shear keys placed at the cap beam are commonly used in highway bridges, and they are expected to collide with bridge girders to prevent the girders from falling down in the transverse direction. Whereas, I-shaped steel shear keys are normally installed at the bottom of girders in HSR bridges, and poundings occur between the shear keys and bearing pads, as shown in Figure 1(b). Very limited research has been done to investigate the effect of steel shear keys on the seismic behavior of HSR bridges. Recently, Yang et al. (2019) and Meng et al. (2019b) performed experimental investigations on this topic. The results showed that the presence of shear keys can pronouncedly decrease the potential of girder dislocation, but the generated pounding forces would be transferred to the bridge substructures and therefore influence the bending moment developed in the pier.

Figure 1.

The shear keys in (a) highway and (b) HSR bridges.

To the authors’ best knowledge, there is no investigation on the effect of the CRTS-II track system on HSR bridges with considering the influence of shear keys simultaneously. This study aims to narrow the knowledge gap through numerical simulations. Detailed 3D finite element models considering the track system and pounding at shear keys are developed by using ABAQUS. The effect of pounding at shear keys on the seismic behavior of HSR bridges is firstly evaluated by comparing the seismic responses of bridges with and without shear keys. Then, to investigate the effect of the track system on bridges with different pier configurations, seismic analyses of the bridges with and without considering the track system are performed.

Methodology

Description of the track-bridge system

Figure 2(a) shows the layout of a five-span simply supported track-bridge structure used for HSR. The whole structure can be divided into two parts, i.e. the CRTS-II track system and bridge system. As shown in Figure 2(b), the CRTS-II slab ballastless track system mainly consists of the sliding layer, base plate, mortar layer, track plate, fasteners, and rails. The base plate is continuous along the longitudinal axis of the bridge and continues to the transition sections, and it is connected to the girders by the sliding layer. Moreover, stoppers are set at the sides of the base plate to restrict its movement in the transverse and vertical directions. Similarly, the continuous track plate is connected on the base plate by using the mortar layer. The rails are connected on the track plate by using fasteners. More details of the CRTS-II track system can be found in Yan et al. (2015), People’s Republic of China National Railway Administration (CNRA-PRC, 2014a), and He et al. (2017b). To consider the influence of the track system at the subgrade on the bridge seismic behavior, the 50 m transition section consisting of the friction plate and anchor is taken into account in the present study.

Figure 2.

(a) The longitudinal layout of the track-bridge structure and (b) the CRTS-II track system on the bridge girder.

The box girders with a standard span of 32.6 m are simply supported by four round-ended solid piers and two abutments. The clearance between the adjacent girders is 100 mm. The heights of the 1^#–4^# piers are 5, 10, 15, and 10 m, respectively. The longitudinal and transverse lengths of the 1^#, 2^#, and 4^# piers are 2.3 and 6 m, respectively. And the corresponding values are 2.5 and 6 m for the 3^# pier. At the top of each pier, four bearings including a fixed bearing, a transverse movable bearing, a longitudinal movable bearing, and a bidirectional movable bearing are placed on the bearing pads to support the girders, as shown in Figure 3(c). Corresponding to the bearings, I-shaped shear keys are installed at the bottom of the girders to restrain the excessive transverse pier-girder relative displacement by pounding with bearing pads (refer to Figures 3(a) and (c)). The shear key is made of grade 235 mild steel, and the detailed dimension is shown in Figure 3(b). The gap size between the shear keys and bearing pads is 30 mm.

Figure 3.

(a) Transverse dimension of the track-bridge structure, (b) dimension of the I-shaped steel shear key, and (c) the arrangement of shear keys and bearings.

Numerical model

To study the effects of shear keys and CRTS-II track system on the seismic behavior of HSR simply-supported bridges, solid element models are established by ABAQUS/Standard. Part of the finite element (FE) model is shown in Figure 4. Since this study focuses on the behavior of bridges subjected to earthquake excitations in the transverse direction, the following descriptions of the numerical modeling of the track-bridge system are also focused on mechanical simulations in the transverse direction.

Figure 4.

Part of the finite element model established by ABAQUS.

Modeling of the track system

In the FE model, elastic beam elements are used to simulate the rails. The friction plates, base plates, and track plates are assumed to work in the elastic state during earthquakes (Wei et al., 2018c), and they are modeled by solid elements with elastic modules of 3.0 × 10⁴, 3.25 × 10⁴, and 3.6 × 10⁴ MPa, respectively. Inelastic connection elements are employed to simulate the fasteners in the transverse direction, and the corresponding force-displacement relationship is given in Figure 5(a). Due to a lack of experimental data, the transverse force-displacement relationship of the mortar layer is simplified to be the same as that along the longitudinal direction and is modeled by inelastic connection elements. Figure 5(b) shows the force-displacement relationship of the mortar layer in the longitudinal direction (Yan et al., 2017; Yang et al., 2018). Many stoppers are placed at the sides of the base plate (see Figure 2(b)), and they can well restrict the movement of the base plate relative to the bridge girders in the transverse and vertical directions (Wei et al., 2018b). Therefore, the base plate is assumed to be fixed on the girders in the FE model.

Figure 5.

The force-displacement relationships of the (a) fastener and (b) mortar layer.

Modeling of the bridge system

The bridge girders are usually not damaged during earthquakes (Goel and Chopra, 2008). They are modeled by solid elements with elastic modules of 4.4 × 10⁴ MPa. Bearings play an important role in bridge structures. The bearings adopted in the bridge are pot bearings with a vertical design force of 5500 kN (CNRA-PRC, 2014b). Figures 6(a) and (b) show the sketches of pot bearings in the moveable and fixed directions, respectively. The sliding plate of the bearing can slide on the sliding surface in the moveable direction, whereas a restrainer is set to limit the movement of the sliding plate in the fixed direction. The force-displacement curve of the bearing along the moveable direction is shown in Figure 6(c). An inelastic connection element with shear stiffness of 23 kN/mm and yielding strength of 165 kN is employed to model the bearing in the moveable direction. Figure 6(d) shows the force-displacement relationship of the bearings along the fixed direction. The failure load of the bearing in the fixed direction (i.e. the restrainer is cut off) is 1650 kN. Note that the mechanical properties of the pot bearing in the fixed direction are the same as those in the moveable direction following the damage to the restrainer. In the FE model, an elastic connection element with high stiffness and an inelastic connection element are used in parallel to simulate a fixed bearing, as shown in Figure 6(d). The elastic connection element with high stiffness is expected to simulate the behavior of the bearing before the restrainer is cut off. During seismic analyses, once the shearing force acting on the fixed bearing reaches the failure load, the elastic connection element will fail and quit working.

Figure 6.

Sketches of pot bearings in the (a) moveable and (b) fixed directions, and the force-displacement relationships in the (c) moveable, and (d) fixed directions.

The shear keys are modeled by solid elements with elastic modules of 2.0 × 10⁵ MPa and yield stress of 235 MPa. They are fixed to the bottom of the bridge girders, i.e. the damage to the connection between the shear keys and girders is not considered since the strength of the connection is higher than that of the shear key itself. The bearing pads made of reinforced concrete are used to support the bearings. The damage to the bearing pads would make the bearings lose the ability to support the bridge superstructure, which should be avoided in bridge structures. To ensure the integrity of bearing pads when subjected to seismic force transferred from the bearings and pounding forces generated between the shear keys and bearing pads, the bearing pads are usually constructed of concrete with a high reinforcement ratio. Therefore, considering the convergence and calculation efficiency of the numerical analyses, the damage to the bearing pads is not considered. They are modeled by solid elements with elastic modules of 3.0 × 10⁴ MPa. The pounding between the shear keys and bearing pads is modeled by contact elements in ABAQUS, and the penalty method is selected to calculate the interaction between the pounding members. The contact surface at the bearing pad is set as the master surface, whereas the corresponding surface at the shear key is set as the slave surface. This is because the stiffness of the bearing pads is much larger than that of the shear keys (Meng et al., 2019a).

The bridge piers are also simulated by solid elements. The Mander stress-strain curve (see Figure 7(a)) is applied to the confined concrete C35 with the Q235 stirrup ratio of 0.45%. Simultaneously, the Giuffré–Menegotto–Pinto stress-strain curve is used to simulate the longitudinal steel bar HRB335 with a ratio of 0.75%, as shown in Figure 7(b). Many previous investigations (e.g. Chouw and Hao, 2008; Shrestha et al., 2015) had revealed that soil-structure interaction (SSI) can further alter the seismic responses of bridges. Not to further complicate the problem, the piers and friction plates are fixed on the foundation, i.e. the soil-structure interaction (SSI) is not considered in the present study. This can help us better focus on the primary aim of this study since less influence factor is involved. It is believed that although SSI is not considered, the general findings regarding the effects of shear keys and track system on the bridges will not be changed. In fact, many researchers (e.g. Bi and Hao, 2015; Están et al., 2017; Jiang et al., 2019; Kang et al., 2017; Kun et al., 2017; Xiang and Li, 2016; Yang et al., 2019) did not consider the influence of SSI when investigating seismic behavior of bridges with considering pounding or track system.

Figure 7.

Stress-strain curves of (a) concrete and (b) steel materials used for the bridge piers.

The Rayleigh damp is used for the track-bridge system and the damping ratio ξ is 0.05. The damping coefficients α and β are calculated as (Yan et al., 2017; Yan and Dai, 2013):

α = 2 ξ \frac{w_{1} w_{2}}{w_{1} + w_{2}}, β = 2 ξ \frac{1}{w_{1} + w_{2}}

(1)

where ω₁ and ω₂ are the former two-class nature frequencies of the structure.

Ground motion

The bridge is designed with a seismic fortification intensity of 8 degrees, and the site type is soil profile III. According to China’s code (CNRA-PRC, 2014a), the peak ground acceleration (PGA) of the design earthquake (with a return period of 475 years) is 0.3 g and the characteristic period of the response spectrum is 0.55 s. The design response spectrum is indicated by the red dashed line in Figure 8(b). To facilitate comparison with other relevant studies, the 1940 Imperial Valley earthquake recorded at El-Centro Array #9, 180 station is selected as the earthquake excitation. The duration of the input ground motion is the first 20 s containing the ground motion peak. Figure 8(a) shows the time histories of the acceleration and displacement of the ground motion with a PGA of 0.3 g, and the corresponding spectral acceleration is present in Figure 8(b). Note that in the numerical analyses, the track-bridge system is only subjected to excitations in the transverse direction.

Figure 8.

(a) The time histories of acceleration and displacement of the input ground motion and (b) spectral acceleration of the ground motion and the design spectrum.

Effect of shear keys on the seismic behavior of the bridge

Time histories and maximum values of seismic responses

To investigate the effect of pounding at shear keys on the bridge seismic behavior, indicatively, the comparisons between the time histories of seismic responses obtained at the 3^# pier of the bridges with and without considering shear keys are made, as present in Figure 9. The location of the 3^# pier is indicated in Figure 2(a). Note that the track system is also taken into account when investigating the effect of shear keys on the bridge.

Figure 9.

Effect of shear keys on the time histories of seismic responses: (a) relative displacement between the 3^# girder and 3^# pier, (b) pounding forces at the west and east shear keys for the bridge with pounding, (c) displacement at the top of 3^# pier, and (d) shear force at the base of 3^# pier.

Figure 9(a) compares the time histories of transverse relative displacements between the 3^# pier and 3^# girder obtained from the bridges with and without shear keys. It can be seen that the presence of shear keys can effectively limit the development of pier-girder relative displacement. The maximum relative displacement significantly decreases from 71.7 to 45.3 mm, i.e., a reduction of 36.8%. For the bridge with shear keys, the pier-girder relative displacement in the range of −30 to 30 mm can be considered as a free gap since the shear keys do not interact with the corresponding bearing pads. It is found that the pier-girder relative displacement will not significantly develop after the free gap is consumed. This further verifies the capacity of the used steel shear keys in limiting excessive pier-girder relative displacement in the transverse direction.

A pounding occurs once the pier-girder relative displacement reaches the gap size between the pounding members. The time histories of pounding forces at the shear keys between the 3^# pier and 3^# girder are shown in Figure 9(b). Note that in the figure, a positive pounding force indicates that it occurs at the west shear key, but a negative one represents that it happens at the east shear key. The location of the shear keys is indicated in Figures 3(a) and (c). The maximum pounding forces generated between the west and east shear keys and the corresponding bearing pads are 1319 and 1320 kN, respectively. The interaction between the pounding components is very complex, which will induce plastic deformation and friction during a short period (Masroor and Mosqueda, 2012). Indicatively, a close-up view of the first pounding at the west shear key is present in Figure 10(a). Although the duration of the pounding is transient (about 0.16 s), multiple loads and unloads are found, during which energy is mainly dissipated as heat (Goldsmith, 2001). Wang et al. (2013) conducted an experimental investigation on structural behavior when subjected to poundings. They found that the process of a pounding could be generally divided into three phases: (i) peak value phase; (ii) platform phase (in which the pounding force almost retains a steady value); and (iii) unloading phase. The numerical result in the present study (Figure 10(a)) is similar to their findings, indicating that the adopted simulation method is appropriate. The distribution of Mises stress of the west shear key at the first pounding is given in Figure 10(b). Larger stress is found at the web of the shear key compared to the wing plates, and the maximum Mises stress reaches the yield stress of the steel, that is, the shear key would work in the plastic range during the pounding.

Figure 10.

The first pounding occurred at the west shear key between the 3^# girder and 3^# pier: (a) time history and (b) distribution of Mises stress in the shear key.

The effect of shear keys on the seismic behavior of bridge substructure is evaluated by comparing the displacements at the top of piers relative to those at the pier supports as well as the shear forces at the bottom of the piers, as shown in Figures 9(c) and (d). For the bridge without shear keys, the maximum pier-top displacement (3.43 mm) and shear force at the pier support (2862 kN) occur at the time of damage to the fixed bearings (0.8 s). This is because at this moment the seismic force of the superstructure transmitted through the bearings to the piers is the largest. For the bridge with shear keys, however, many spikes corresponding to the pounding forces are found in the time histories of pier-top displacement and shear force at the pier support. For example, a pounding happens at 1.94 s (see Figure 9(b)) and sudden increases are found in Figures 9(c) and (d). Due to the poundings, the maximum responses increase to 5.17 mm and 3880 kN respectively for the pier-top displacement and shear force at the pier support. It is worth noting that previous investigations on the effect of girder-abutment pounding along the longitudinal direction of bridges on the seismic responses found that the pounding can significantly reduce the seismic responses in bridge piers (Chouw and Hao, 2008; Kun and Chouw, 2019). A possible reason is that the pounding between the girder and abutments limits the movement of the girder and therefore limits the bending of the piers. Whereas, in the present study, the pounding forces generated between the shear keys and bearing pads would be transferred to piers directly and the piers can bend freely in the transverse direction, which would inevitably increase the seismic responses of the piers.

Table 1 summarises the maximum seismic responses of the bridges with and without considering pounding. The average ratios of the pounding to no pounding cases are 0.71, 1.58, and 1.32 respectively for the maximum pier-girder relative displacement, pier-top displacement, and shear force at pier support. The results clearly show that the use of shear keys can effectively reduce the dislocation potential of the bridge superstructure, but it will also lead to a significant increase in the seismic responses of the bridge substructure. Ignoring the pounding at shear keys may underestimate the seismic demand of the bridge piers.

Table 1.

Effect of shear keys on the maximum seismic responses.

Pier	Girder	Pier-girder relative displ. (mm)			Pounding force (kN)	Pier-top displ. (mm)			Shear force at pier support (kN)
Pier	Girder	NP	P	P/NP	P	NP	P	P/NP	NP	P	P/NP
1^#	1^#	74.9	59.3	0.79	1450	0.46	0.80	1.74	2702	3800	1.41
1^#	2^#	74.2	56.8	0.77	1426	0.46	0.80	1.74	2702	3800	1.41
2^#	2^#	72.3	48.8	0.67	1337	1.49	2.14	1.44	2904	3630	1.25
2^#	3^#	72.4	48.3	0.67	1337	1.49	2.14	1.44	2904	3630	1.25
3^#	3^#	71.7	45.3	0.63	1320	3.43	5.17	1.51	2862	3880	1.36
3^#	4^#	71.6	45.4	0.63	1321	3.43	5.17	1.51	2862	3880	1.36
4^#	4^#	74.1	56.2	0.76	1422	1.33	2.14	1.61	3014	3820	1.27
4^#	5^#	74.6	58.5	0.78	1442	1.33	2.14	1.61	3014	3820	1.27
Average				0.71				1.58			1.32

NP: without pounding; P: with pounding.

The pounding force in the table denotes the maximum pounding force at the two shear keys between the corresponding pier and girder obtained from the pounding case.

Contribution of pounding to the seismic response in bridge piers

The analysis in Section 3.1 shows that the pounding between the shear keys and bearing pads will increase the seismic demand of bridge piers. To further evaluate the contribution of pounding to the seismic response in the bridge piers, indicatively, short-time Fourier transforms (STFT) of the shear forces at the support of 3^# pier of the bridges are performed. The results are present in Figures 11(b) and (c) respectively for the no pounding and pounding cases. For comparison, the STFT result of the input ground motion and the time history of pounding force between the shear keys and bearing pads are also present in Figures 11(a) and (d), respectively.

Figure 11.

STFT of (a) the ground motion and shear forces at the base of the 3^# pier from the (b) no pounding and (c) pounding cases, and (d) the time history of pounding force of the pounding case.

Figure 11(b) shows that the predominant response of the shear force without considering pounding happens at around 0.8 s. This is because the fixed bearings are damaged at this time, which leads to the occurrence of the maximum response, as presented in Figure 9(d). A relatively large Fourier amplitude is also found at around 2.0 s since the energy of the earthquake excitation concentrates at the time instant (as indicated in Figure 11(a)). For the bridge with considering pounding (Figure 11(c)), however, much larger Fourier amplitudes of the shear force at the support of 3^# pier are found compared to those without considering pounding. This is mainly attributed to the poundings between the shear keys and bearing pads. It is found in Figure 11(d) that the poundings mainly occur in two time ranges, i.e., around 1.0 to 6.0 s and 9.0 to 17.0 s (as marked by the two dashed boxes in the figure). The poundings consequently lead to larger Fourier amplitudes in these two time ranges than those in other time ranges. The above analysis highlights the contribution of pounding at the shear keys to the seismic response in the bridge piers.

Effect of track system on the seismic behavior of bridges

The presence of the track system would restrain the free out-of-phase vibration between the adjacent bridge girders. Moreover, it will also limit the relative displacement between the bridge girders and transition sections on the subgrade (see Figure 1). Due to the constraining effect of the track system, the dynamic properties of the bridge would be significantly altered (the transverse fundamental frequency increases from 3.3 to 3.6 Hz) and therefore influence the bridge seismic responses. This section aims to evaluate the effect of the CRTS-II track system on the seismic responses of HSR simply-supported bridges. It should be noted that in the present study, “a bridge without considering the track system” only means that the track system is disconnected between the adjacent bridge girders and between the girder and abutment, that is, the track system is simply considered as an additional mass on the bridge girders.

Time histories and maximum values of seismic responses

Indicatively, the comparisons between the time histories of seismic responses at the 3^# pier are made. Figure 12(a) compares the transverse relative displacement between the 3^# pier and 3^# girder obtained from the bridges with and without considering the constraint of the track system. The time history is pronouncedly altered when considering the track system. For the bridge without considering the track system, the damage to the transverse fixed bearing occurs at 1.81 s. Whereas it is advanced to 0.8 s when considering the track system. Although the consideration of the track system decreases the maximum transverse relative displacement from 64.9 to 45.3 mm, it also leads to more poundings between the shear keys and bearing pads, as shown in Figure 12(b). The maximum pounding force generated at the shear keys between the 3^# pier and 3^# girder is also influenced by the track system. The maximum pounding forces obtained from the models without and with the track system are 1540 and 1320 kN, respectively. The influence of the track system on the time histories of the pier-top displacement and the shear force at the bottom of the pier is present in Figures 12(c) and (d), respectively. It can be seen that the seismic responses in the bridge pier will be significantly influenced when considering the track system. The maximum pier-top displacements are 5.27 and 5.17 mm, respectively for the cases without and with considering the track system. And the corresponding values are respectively 4410 and 3880 kN for the shear forces at the pier support.

Figure 12.

Effect of track system on the time histories of the seismic responses: (a) transverse relative displacement between the 3^# girder and the 3^# pier, (b) pounding forces at the shear keys, (c) displacement at the top of 3^# pier, and (d) shear force at the support of 3^# pier.

Table 2 summarises the maximum seismic responses of the whole bridges with and without considering the track system. The results show that for the bridge without the track system, the maximum seismic responses are found at the 3^# pier, and the seismic responses at the side piers are relatively small. When considering the track system, the seismic responses at the middle piers (2^# and 3^# piers) would be decreased, but an opposite trend is found for the responses at the side piers (1^# and 4^# piers). For example, the ratios of the pier-top displacements of the bridge with the track system to those without considering the track system are 1.54, 0.94, 0.98, and 1.18 respectively for the 1–4^# piers. This indicates that the consideration of the track system would significantly alter the distribution of seismic forces in different bridge spans. More detailed discussions on this topic will be carried out in the following section. The above result also highlights the importance of considering the constraining effect of the CRTS-II track system in seismic analyses of HSR bridges.

Table 2.

Effect of track system on the maximum seismic responses.

Pier	Girder	Pier-girder relative displ. (mm)			Pounding force (kN)			Pier-top displ. (mm)			Shear force at pier support (kN)
Pier	Girder	NT	T	T/NT	NT	T	T/NT	NT	T	T/NT	NT	T	T/NT
1^#	1^#	55.3	59.3	1.07	1413	1450	1.03	0.52	0.80	1.54	3490	3800	1.09
1^#	2^#	52.0	56.8	1.09	1403	1426	1.02	0.52	0.80	1.54	3490	3800	1.09
2^#	2^#	56.5	48.8	0.86	1425	1337	0.94	2.27	2.14	0.94	4040	3630	0.90
2^#	3^#	63.3	48.3	0.76	1490	1337	0.90	2.27	2.14	0.94	4040	3630	0.90
3^#	3^#	64.9	45.3	0.70	1504	1320	0.88	5.27	5.17	0.98	4410	3880	0.88
3^#	4^#	46.4	45.4	0.98	1341	1321	0.99	5.27	5.17	0.98	4410	3880	0.88
4^#	4^#	52.3	56.2	1.07	1389	1422	1.02	1.81	2.14	1.18	3600	3820	1.06
4^#	5^#	51.8	58.5	1.13	1384	1442	1.04	1.81	2.14	1.18	3600	3820	1.06

NT: without the track system; T: with the track system.

The pounding force in the table denotes the maximum pounding force at the two shear keys between the corresponding pier and girder.

Effect of track system on the seismic behavior of bridges with different pier-height arrangements

The analysis in Section 4.1 reveals that the CRTS-II track system could significantly alter the distribution of seismic forces among the bridge spans. To further investigate the effect of the track system on the seismic responses of bridges with different pier-height arrangements subjected to transverse earthquake excitations, four bridges are considered:

Bridge 1: a five-span bridge with pier heights of 5, 10, 15, and 10 m (i.e. the aforementioned bridge);

Bridge 2: a five-span bridge with equal pier heights (10 m);

Bridge 3: a seven-span bridge with pier heights of 5, 10, 15, 15, 10, and 5 m;

Bridge 4: a seven-span bridge with equal pier heights (10 m).

It should be noted that the pounding between the shear keys and bearing pads are considered in the numerically seismic analyses in this section.

The effect of the track system on the seismic behavior of bridges with different pier-height arrangements is evaluated by comparing the ratios of the maximum seismic responses with considering the track system (T) to those without considering the track system (NT). Figures 13(a)–(d) compare the effect of the track system on the seismic behavior of bridges 1 and 2 in the transverse relative displacements, pounding forces, pier-top displacements, and shear forces at pier supports, respectively. As analyzed in Section 4.1, the presence of the track system enlarges the maximum seismic responses at the side piers (1^# and 4^# piers) but decreases the responses at the middle piers (2^# and 3^# piers) for bridge 1. A possible reason is that for the bridge without considering the track system, the seismic responses at the middle piers are larger than those at the side piers, as shown in Table 2. For the bridge with considering the track system, however, the constraint between the bridge girders will limit the development of pier-girder relative displacements at the middle spans but increase that at the side spans (see Figure 14(a)). Consequently, pounding forces, pier-top displacements, and shear forces at the pier supports are also decreased at the middle spans but increased at the side spans, as shown in Figures 13(b)–(d). In other words, the track system will transfer the seismic forces from the middle spans to the side spans for bridge 1.

Figure 13.

Comparison between bridges 1 and 2 in the ratios of the maximum seismic responses with track system (T) to those without track system (NT): (a) pier-girder relative displacements, (b) pounding forces, (c) pier-top displacements, and (d) shear forces at pier supports.

Figure 14.

Comparison between bridges 3 and 4 in the ratios of the maximum seismic responses with track system (T) to those without track system (NT): (a) pier-girder relative displacements, (b) pounding forces, (c) pier-top displacements, and (d) shear forces at pier supports.

An opposite trend is found for bridge 2, that is, the consideration of the track system decreases the maximum seismic responses at the side spans but amplifies the responses at the middle spans, as shown in Figure 13. The authors believe that it is because, for a bridge with equal pier heights, the seismic responses are almost the same between different bridge spans when the track system is not involved. When the track system is considered, however, the constraint between the girders of side spans and transition section at the subgrade will limit the development of pier-girder relative displacements at the side spans. Moreover, the constraint between the bridge girders makes the middle spans the unfavorable position of the bridge, thus amplifying the corresponding seismic responses (Yang et al., 2020).

The calculated results of the bridges with seven spans (bridges 3 and 4) are similar to those of the bridges with five spans (bridges 1 and 2), as shown in Figure 14. Therefore, it can be concluded that the track system will reduce the seismic responses at side bridge spans but will increase the responses of the middle bridge spans for a bridge with equal pier heights. Whereas it will amplify the seismic responses at side bridge spans but will reduce the responses of the middle spans for a bridge with high middle piers and short side piers.

Conclusions

This study investigates the effects of shear keys and CRTS-II track system on the behavior of simply-supported bridges for high-speed trains subjected to transverse earthquake excitations. Detailed 3D finite element models are developed by using ABAQUS and non-linear seismic analyses are performed. The seismic responses of bridges with and without considering pounding between the shear keys and bearing pads are compared to evaluate the influence of shear keys on the bridge seismic behavior. The effect of the track system on the seismic responses is analyzed by comparing the numerical results of bridges with and without considering the track system. Moreover, the effect of the track system on the seismic responses of bridges with different pier-height arrangements is also investigated. The results of this study reveal that:

The interaction between the shear keys and bearing pads is complex and would significantly influence the seismic behavior of bridges. The installation of shear keys significantly limits the development of transverse relative displacements between the bridge girders and piers after the initial gap between the pounding components is consumed and thus decrease the dislocation potential of bridge girders.

The pounding forces generated between the shear keys and bearing pads will be transferred to bridge piers directly and therefore increase the seismic responses of the piers. Ignoring the pounding at shear keys in seismic analyses of HSR bridges may induce a significant underestimate in seismic demand of bridge piers.

The CRTS-II track system significantly influences the distribution of seismic forces among the bridge spans. For a bridge with equal pier heights, the track system will reduce the seismic responses of the bridge spans close to the subgrade but will increase the responses of the bridge spans far from the subgrade compared to bridges without considering the track system. Whereas an opposite trend is found for the bridges with high middle piers and short side piers.

It should be noted that in the present study the soil-structure interaction (SSI) is not considered and only a simple ground motion is selected. Further studies on the effects of SSI and ground motion characteristics on the behavior of the track-bridge system are needed. It should also be noted that most of the structural components are simulated by solid elements in the finite element models of this study, which makes the numerical calculation very time-consuming. Therefore, the authors would suggest that when a lot of numerical simulations are required, for example, seismic vulnerability analysis, it would be better to choose a verified simplified finite element model.

Footnotes

Acknowledgements

The authors would like to thank China Scholarship Council (CSC) and Central South University for providing the scholarship for the first author to study at the University of Auckland for 2 years.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the National Natural Science Foundation of China (No. 51978667) and the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts191). The support is greatly appreciated.

ORCID iD

Dongliang Meng

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