Analysis of seismic damage mechanism of simply supported girder bridges at near‐fault liquefaction sites

This work uses the Yematan Bridge as an example to explore the seismic damage mechanism of simply supported girder bridges at near‐fault liquefaction site. It analyzes the bridge from the local portion to the complete bridge, considering the effects of the near‐fault and liquefied soil layers. First, a three‐dimensional model of the pile‐soil seismic action of Pier No.17 was created using simulated near‐field ground motion, and analysis was performed to simulate the action of the liquefied soil layers on the pile foundation, getting pile‐soil dynamic p‐y curves. After that, the accuracy of the pile spring parameters was verification by doing an equivalent static analysis. Finally, to identify the seismic damage mechanism of high‐damping rubber (HDR) bearings and the dynamic unseating process of the Yematan Bridge, a finite element model of the complete bridge was developed. During this procedure, the near‐field ground motion amplitude and soil spring parameters were iterated and optimized continually, such that the simulated earthquake damage was identical to the real one. The findings suggest that the bridge was destroyed by significant structural vibration. The near‐fault impulse effect and lack of equivalent limiting measures induced the entire collapsing girders to move consistently and destroyed the HDR bearings. Liquefied soil can cause some damage to pile foundations, and lateral spreading can cause the piers of the same span to perform differently.


INTRODUCTION
The response of near-fault bridges has shown the exact characteristics of bridge collapse or large unseating in several major earthquakes in history.In the 1999 Mw 7.4 Kocaeli, Turkey earthquake, the Arifiye Overpass collapsed.
In the same year, Mw 7.2 Duzce, Turkey earthquake, Bolu Viaduct #1 was crossed by a slip fault, and the bridge did not fall, but all the unseating devices were destroyed.Pamuk et al. 1 studied the Arifiye Overpass and the Bolu Viaduct #1 and concluded that near-fault effects are the leading cause of the damage.Near-fault effects created significant impulsive fault-normal ground motion, vertical accelerations, and surface fault ruptures.In the 1999 Mw 7.6 Chi-Chi, Taiwan earthquake, several bridges, such as Wu-Shi Bridge and Ming-Tus Bridge, were crossed by the fault surface rupture zone, and several main girders of bridges fell.Lin et al. 2 concluded that the structural response and collapse mechanism of a simply supported girder bridge is mainly controlled by low-frequency ground motion.The large differential static offset across the fault is the main reason for the collapse of the simply-supported bridges.In the 2008 Mw 7.9 Wenchuan, China earthquake, several bridges collapsed due to surface rupture zones passing through them, and Liu 3 concluded that many of the severe damages to near-fault bridges were the result of a combination of permanent displacement of fault ruptures, earthquake-induced geological hazards, and strong ground motions based on field investigations.All the damage mentioned above is difficult to repair after the earthquake, and studying the seismic damage mechanism is meaningful for the design and construction of existing structures.Moreover, saturated sandy soils are highly susceptible to liquefaction under strong earthquakes, and bridge structures are often damaged by lateral spreading due to site liquefaction.O'Rourke and Hamada 4 attributed the collapse of the Showa Bridge in the 1964 Niigata earthquake to the lateral spreading of liquefaction that caused the pile foundation damage of the Showa Bridge.Zhou et al. 5 believed that the failure of the Baihua Bridge during the 2008 Wenchuan earthquake in China was due to the lateral spreading of soil liquefaction near the bridge site, resulting in pile foundation failure.Verdugo and González 6 found that during the 2010 Chilean earthquake, the longitudinal cracks along the riverbank were closely related to the lateral spreading of liquefaction.Cubrinovski and Robinson 7 found that different soil layers and their thicknesses on the Avon riverbank affected the displacement of liquefied lateral spreading in the 2011 Christchurch earthquake, and soils such as chalk, fine sand, and powder-fine sand are easily liquefied to produce maximum lateral displacement.Therefore, liquefied soil can significantly impact bridges under strong earthquakes, and it is necessary to consider the role of liquefied soil when analyzing the seismic damage mechanism of bridges.In these studies, the seismic damage mechanism of collapsed bridges is either analyzed from the characteristics of near-fault ground motion or only for liquefied soil, and there are few comprehensive analyzes for near-fault liquefaction sites.
On May 22, 2021, a 7.4 magnitude earthquake occurred in Maduo County, Guoluo Prefecture, Qinghai Province, with a source depth of 17 km.The epicenter of the Maduo earthquake was located near Huanghe Township (34.59 • N, 98.34 • E), nearly 7 km from the Yematan Bridge in a straight line.Approximately 70% of the girders of the Yematan Bridge fell.Zu et al. 8 discussed the seismic damage mechanism of the up line of the Yematan Bridge under strong near fault ground motion.Ding et al. 9 established a finite element model of a three-span simply supported girder bridge based on the analysis of the seismic damage characteristics of the Yematan Bridge without considering the liquefied soil.However, there are significant differences in the seismic damage between the downline and up line bridges of the Yematan Bridge at the 4th consecutive segment, especially at the Pier No.17.The seismic damage was distinct on the east and west sides of the downline's Pier No.17.There were water gushing and sand liquefaction near the bridge.The Yematan Bridge is a near-fault bridge with severe soil liquefaction after the earthquake.
In this paper, first, the actual ground motion records of Dawu station were used to synthesize the near-fault ground motion, and the pile-soil 3D model 10 of Pier No.17 in the downline was used as a starting point to perform nonlinear dynamic time analysis and obtain the spring parameters of the pile foundation-liquefied soil layers.The equivalent static analysis (ESA) of Pier No.17 11 was performed to confirm the validity of the pile spring curves in conjunction with the site investigation findings.Then the nonlinear dynamic time analysis of the entire bridge was completed.The ground motion amplitude at the Yematan Bridge was iteratively improved and inverted to produce the best consistent findings with the factual earthquake damage inquiry.Finally, the dynamic girders' falling process and the seismic damage mechanism of the Yematan Bridge's HDR bearings were examined and studied.Figure 1 depicts the technical flowchart.

BASIC STRUCTURES AND SEISMIC DAMAGE OF THE YEMATAN BRIDGE
The Yematan Bridge is near Yematan in Maduo County, Guoluo Tibetan Autonomous Prefecture, and southeastern Qinghai Province.In this Maduo earthquake, the surface rupture zone had a total length of about 160 km, with an overall orientation of NW, starting from the south of Euling Lake (34.8 • N, 97.6 • E) in the west and ending at the east of The Yematan Bridge has two bridges for up and down lines, totaling 507 m in length.The bridge plane is situated on a flat curve and the bridge is a simply supported girder bridge with the continuous deck.The bridge width is 10 m, the superstructure is a 5× (5 × 20 m) prestressed concrete hollow slab structure made of C50 concrete, and the substructure is made of a column pier, column platform, drilled, and grouted pile made of C30 concrete.The bridge deck's continuous end is supported by HDR (III)-D225-G10/8 bearings, and the rest are HDR-D200-H/8 bearings.In Figure 3B, the elevation of the bridge structure is depicted in meters, while the other dimensions are given in centimeters.
After the Maduo earthquake, there were 18 girders that fell in the downline, and 17 girders fell in the up line.All of the girders fell on the structure's south side and were supported by the piers on the north side.HDR bearings that were inverted and damaged slipped.There was damage to the expansion joints.The concrete cracked, exposing reinforcement on the piers, and the pavement was arched. 12Figure 4 shows part of the seismic damage of the Yematan Bridge in the downline.
Many bead-like sandblasting bubbles and sand liquefaction phenomena were also apparent. 13In addition, the rupture zone in the section from the Yematan Bridge to Huanghe Township was primarily spread along the valley of the Heihe River. Figure 5 depicts the Yematan Bridge's whole bridge site, which displayed extensive liquefaction.The drainage ditch on the side of the bridge abutment had been filled in, and the area of visible sand emergence at the northern end measured around 300 m × 300 m.The south end of the bridge also showed severe liquefaction, and the sand outflow area was about 100 m × 100 m, with the most extensive sand outflow hole reaching 3 m.The soil structure below the middle of the bridge was the same as the two sides, and severe liquefaction also occurred. 14

GROUND MOTION SIMULATIONS
Near-fault ground motion simulation is primarily based on the artificial synthesis of velocity pulses and ground motion modeling based on the source model.Method of artificial synthesis based on velocity pulse is that after modeling low-frequency pulse and high-frequency non-pulse components, they are filtered at a cross-frequency point and overlaid to produce broadband pulse-type ground motion.Ground motion simulation using a source model is that the ground motion at the ground observation site is computed based on the characteristics of the source utilizing the propagation path impact of seismic waves, which is classified into three types: deterministic, stochastic, and hybrid techniques. 15fter the Maduo earthquake, the Qinghai Seismological Bureau received 16 sets of severe ground motion recordings, with Dawu station having the smallest epicenter distance with a maximum acceleration peak of 46.0 cm/s 2 and a maximum velocity peak of 7.5 cm/s, as shown in Figures 6 and 7.An apparent near-fault pulse characteristic can be seen from the velocity time history of Dawu station.The time history has a significant pulse peak and a specific pulse period.
However, the distance between Dawu station and the epicenter is 175.6 km, which is significantly more than the distance between the Yematan Bridge and the epicenter, making it impossible to represent the features of ground motion at the Yematan Bridge.As a result, ground motion modeling at the bridge site is required to obtain an accurate seismic response of the Yematan Bridge.
The low-frequency component of the near-fault earthquake is first synthesized with the equivalent velocity pulse function, then with the Dawu station ground motion, and finally, a genetic algorithm is used to select the optimal ground motion to amplitude modulate the synthesized ground motion as the input to the structure in order to match the simulated ground motion with the actual earthquake.As shown in Figure 8, the peak accelerations of ground motion in the vertical fault direction, parallel to the fault direction, and vertical direction were computed to be 0.68, 0.41, and 0.37 g, respectively. 8This result is the optimal solution most consistent with the seismic results.In the optimal solution, the near-fault velocity pulse effect is well modeled.A unidirectional velocity pulse appears in the parallel fault direction, and a bidirectional velocity pulse appears in the vertical fault direction, as shown in Figure 9.

4
ANALYSIS THE FOUNDATION OF PIER NO.17

3D numerical simulation model of seismic response
Pier No.17 of the downline of the Yematan Bridge showed severe damage to the pier column on the east side with suspected shear failure, while the pier column on the west side showed no apparent tilt or damage, as shown in Figure 10.We  speculate that the reason for this phenomenon is that the pile foundation was damaged due to the liquefaction of a large area of sand in the region under the effect of a strong earthquake, thus causing the pier column to be damaged.
A finite element model of the pile-soil combination was established using MIDAS/GTS, and horizontal bi-directional and vertical ground motions were input to perform a nonlinear dynamic time history analysis to verify that our conjecture is correct.The nonlinear analysis can consider the nonlinear dynamic characteristics of geotechnical soil and the process of pore water pressure generation and dissipation.
According to the Yematan Bridge ground study report, Pier No.17 lies in the center of fine sand, silt, and gravelly sand, and the water table line is 1 m, as indicated in Figure 11.The pile-soil action relationship is represented by MIDAS/GTS as beam unit-pile unit-solid unit, with the pile foundation using beam unit (elastic principal), the soil using solid unit (Mohr-Coulomb principal), and the pile unit acting as the contact unit, which represents the connection of the one-dimensional beam unit and the three-dimensional soil unit.Furthermore, using the groundwater table line, the model correctly replicates the dynamic liquefaction properties of sandy soil.As seen in Figure 11, the model is 40 m × 30 m × 34 m.Table 1 shows the particular soil properties.

Liquefaction performance in results
Figure 12 depicts the time history of pile top and surface displacement after computation.It can be observed that the pile top displacement reaction and the lateral surface displacement response were essentially the same at the start.However, after the top pile displacement reached the maximum displacement of 12.72 cm, it diminished while the surface displacement expanded gradually.This means that when the sandy soil was liquefied, the fine sand became liquid and began to flow around the pile, the pile's displacement was essentially stable, and lateral flow of the sandy soil occurred.When the soil reached its maximum displacement of 23.37 cm, and there was no more lateral flow, the displacement at the top of the pile continued to decrease and remained stable at the 60s, and the permanent displacement of 7.49 cm after stabilization was much smaller than the permanent displacement of the soil at the surface of 18.74 cm.According to the analytical results, the site liquefied during the earthquake, causing a certain displacement of the pile foundation and weakening the surrounding soil's action on the pile foundation.

Pile springs parameters in results
The seismic response estimates for the entire bridge must adequately consider the liquefied soil's impact around the structure's pile side.The p-y curve replicates the horizontal resistance of the soil body on the pile side and displays the relationship between the horizontal reaction force of the soil body at a certain depth and the deflection of the pile at that location under horizontal pressure.At the moment, the study of p-y curves for sandy soils under static action is more mature, mainly the p-y curve for sandy soils recommended in the American Petroleum Institute (API) code, but the study of p-y curves for liquefied sandy soils under dynamic action is not mature enough. 16n this paper, referring to the simplified Boulanger model in Winkler foundation beam, 17 the pile is considered as a beam placed in the soil and the action of the soil around the pile on the pile is considered as a mutually independent spring simulation based on which the model simulates the pile-soil interaction with a p-y curve, as shown in Figure 13.
To accurately simulate the nonlinear behavior of the liquefied soil on the pile at the Yematan Bridge in the absence of tests, this paper uses numerical simulation to create a 3D model of the pile foundation's seismic response, as shown in Figure 10, and the pile-soil dynamic p-y curve is calculated.Figure 14 depicts computation results.

F I G U R E 14 Dynamic p-y curves
The numerically calculated pile spring parameters outperform the technique of discount factor of bearing capacity of liquefied soil layer provided in China's existing seismic design code for bridge pile foundations, overcoming its blindness and arbitrariness.However, its correctness must be demonstrated, which is done below by doing an equivalent static analysis on Pier No.17 to check if the findings are commensurate with the actual seismic damage.

EQUIVALENT STATIC ANALYZES OF PIER NO.17
Since the soil-pile-structure interaction is strongly nonlinear in liquefied soils, pile foundations require nonlinear analysis, either equivalent static or equivalent dynamic, and equivalent static nonlinear analysis may be accomplished using equivalent linear techniques.The Winkler foundation beam technique is classified into two types: force-based approaches and displacement-based methods, as shown in Figure 15. 18The lateral pressures on piles at liquefied sites in earthquakes primarily comprise motion loads and superstructure inertia forces for pile-based bridges.The displacement-based technique is utilized in this research, in which the lateral displacement of the soil is transferred to the free end of the p-y spring, and the resulting soil pressure is determined by the relative displacement of the pile and soil.

Lateral spreading
Under seismic action, lateral spreading occurs due to the liquefaction of saturated sandy soil, which causes shear, tensile rupture, and lateral flow of the surface soil, resulting in limited and permanent lateral displacements in the slightly inclined and near-shore horizontal sites.Based on a vast database of historical lateral spreading cases, Bartlett and Youd 19 utilized multiple regressions to derive an estimation Equation ( 1) for lateral spreading ground displacement for ground slopes with gently sloping sites and uniform slopes: where DH is estimated lateral ground displacement (m); MW is moment magnitude; R is horizontal distance to the earthquake source (km); S is slope rate of the ground (%); T15 is cumulative thickness of saturated granular layer of (N1)60 < 15(m); F15 is average content of fine particles constituting the T15 granular layer (%); and (D50)15 is average of the mean size of the particles composing the T15 granular layer (mm).It was calculated that the ground lateral spreading displacement of the Yematan Bridge was 0.67 m.

Superstructure inertia load
According to Liyanapathirana and Poulos, 20 structural inertial loads in liquefied lateral spread flow sites should be calculated using peak ground acceleration and added to pile foundations simultaneously with maximum foundation displacement to calculate pile foundation forces and deformations, as shown in Equation (2) .
where I ss is superstructure inertia load; m ss is Mass; and a ss is acceleration.
The corresponding static analysis of Pier No.17 and pile foundation was performed in Midas using Pushover analysis, and Figure 16 illustrates its finite element model.

Verification results
Figure 17 depicts the yield diagram of Pier No.17's pushover hinge.Moreover, the final cracking moment of the west pier is less than that of the east pier, as seen by the moment-curvature in Figure 18.This conclusion reveals that when liquefied soil flowed laterally during seismic activity, the east pier was more easily damaged than the west pier.
The pile displacement results are shown in Figure 19, where it can be seen that the displacement in the Z direction is greater than the remaining two directions, the X-directional displacement of the east and west sides is the same, the Y-directional displacement of the west side piles is greater than the east side piles, both moving in the direction of the river center, and the Z-directional displacement of the east side piles is greater than the west side piles, leading to a more obvious tilt of the east side piers than the west side piers after the earthquake.
The calculated results are broadly congruent with the empirical observation that the right pier of the bridge pier is slightly damaged while the left pier is undamaged primarily, demonstrating that the numerical simulation's pile spring parameters are mostly correct.

THE FULL BRIDGE FINITE ELEMENT MODEL
The finite element analysis software Midas/Civil was used to establish the finite element model for the seismic response analysis of the Yematan Bridge (downline), as shown in Figure 20.
Throughout this study, we employ constant ground motion input and ignore traveling wave effects.Additionally, we assume that the soil begins to liquefy as the earthquake occurs.

Collision simulation
Spatial beam units were used for the model's main girders, cap beams, and piers.A simplified hysteresis model based on the Megally test was used for the reinforced concrete transverse shear key of the Yematan Bridge, as shown in Figure 21.

F I G U R E 22 Gap unit model
The gap units simulate the collision between the main beams, as shown in Figure 22.
The Yematan Bridge has a continuous deck construction allows for force transfer during a collision.This model approximates link slabs as an incomplete hinge action with significant bending and shear stiffness in the cross-bridge direction to connect the main girders, but its vertical shear stiffness and bending stiffness around the cross-bridge direction are very weak. 22

Bridge supports simulation
The mechanical behavior of the HDR bearing is modeled in this article utilizing bilinear model.However, due to the HDR bearing showing severe damage in this earthquake, the elastic bilinear model suggested by the code under regular use cannot effectively mimic the earthquake damage of this bridge.We suggest a bearing model accounting damage in this regard. 8

Modal analysis of the bridge
The natural period of the Yematan Bridge is shown in Table 3.

Damage to HDR bearings
As a complete seismic isolation bearing, HDR bearings have a particular seismic isolation effect, can extend the structure's natural period, reduce the structure's natural frequency, and effectively avoid resonance to reduce the impact of seismic action on the structure.HDR bearings damage on the Yematan Bridge is one of the few cases.Anchor bolts ripping out and shearing off, moveable bearing pulling off, bearing body damage, bearing pad stone cracking, and other types of bearing damage may be found in the Yematan Bridge.
The displacement time history of bearings at abutment No.0 and 25, the fixed bearing, and the sliding bearing show that the displacement in the Y direction is the greatest, while the displacement in the Z direction is less than 30 cm, as shown in Figure 23.The displacement of the bearing on abutment 0 is much larger than that of abutment 25.In rare earthquakes, the shear displacement of a fixed bearing is 60 cm, which surpasses the design shear displacement of 315 mm.The displacement in the sliding bearing is 120 cm, indicating that this bearing has sustained significant damage and has broken.The HDR bearing's damage time history corresponds to the arrival of the peak seismic acceleration, indicating that the bearing damage is primarily affected by the directional effect of the bearing along F I G U R E 23 Bearing displacement time histories the bridge near the fault, while the slip effect primarily affects the displacement of the main girder after the bearing damaged.

7.2
Analysis of falling girders mechanism

Displacements
The relative and residual displacements of the cap beam and main girders were calculated as shown in the Figure 24A.The displacement is negative in the north direction and the west direction.When the displacement of the main girders in the downline direction exceeded the width of the cover beam, which is 170 cm, the continuous structure of the bridge deck could not bear the weight of the main beam and fractured at this time, resulting in 50% of the girders falling off.
The results show that due to the existence of expansion joints, the displacements among the girders of each consecutive segment are not the same, the residual displacements of the main girders of consecutive segment 1, 2, and 5 are mainly in the north direction, but the main girders of consecutive segment 3 and 4 have large displacements, and the residual displacements are mainly in the south direction.However, the displacement changes of the main girders within each consecutive segment are the same, showing a significant large pulse effect in the near field of ground motion.
As seen in the Figure 24B, the transverse displacements of the girders fluctuated along the longitudinal direction, indicating that the bridge experienced strong structural vibration in an east-west direction parallel to the earthquake fault zone.When the girders have a large displacement along the bridge, the bearings cannot withstand the tremendous shear force that exceeds their shear deformation, and the bearings fall off.Furthermore, the link slabs will break since they cannot support the weight of the main girders.Take girders No.11 and 12 as an example.The girders and link slabs stress diagram are shown in the figure.It can be seen from the Figure 25 that the stress at the link slabs is concentrated and less than the stress of the main girders on both sides, resulting in the link slabs fracture and the main girders falling under the large displacement of girders on both sides.

Collision
The collision time history of the transverse shear key at the abutment, as shown in Figures 26 and 27, demonstrates that the transverse collision at the south end of Abutment No.25 is less than that at the north end.Furthermore, the transverse shear key at the south end of the abutment has essentially slight displacement and damage, but the transverse shear key at the north end is subjected to east-west reciprocal contact, which creates a more significant collision force.This is because the north end is closer to the fault, whereas the south is distant.

CONCLUSIONS
This research studies the seismic damage mechanism of a bridge at a near-fault liquefaction site using the Yematan Bridge as an example.And this work uses the local analysis of the bridge as a starting point, obtains the soil spring parameters of the liquefied soil layer at the bridge site under synthetic near-site ground motion, and performs the seismic damage analysis of the entire bridge.The numerical simulation results are generally consistent with the actual seismic damage.We can get the following conclusions.The near-fault ground motion impulse effect is the cause of the neat fall of the girders on the Yematan Bridge's up line and downline.The lateral spreading generated by the liquefied soil layer is an important reason for the different seismic damage on the east and west sides of the bridge.From the whole bridge, although the HDR bearings have excellent seismic isolation effect, under the action of near-fault ground vibration, due to the lack of corresponding limiting measures, with the occurrence of falling girders, the HDR bearings also appear severe damage.It is necessary to choose the appropriate anti-falling girders measures.

F I G U R E 1
Technical flowchart F I G U R E 2 Location map of the Yematan Bridge Changmahe Township (34.4 • N, 99.3 • E) via the Yematan Bridge and Huanghe River Valley in the east, which was a rupture activity dominated by left-slip movement.The Yematan Bridge is in the X degree area of the Maduo earthquake, only 7 km from the epicenter of the Huanghe Township in a straight line.The bridge axis and the fault line are close to vertical.The angle of the vertical fault line is about 60 • and the fault line and the relative position of the bridge, as shown in Figure 2. From the location of surface cracking, the Yematan Bridge is in the seismic slip fault fragmentation zone and belongs to the near-fault bridge.

4
Part of the seismic damage of the Yematan Bridge (downline).(A) Fallen beam from north to south, (B) bearings overturning and failure, (C) expansion joint failure, (D) arching of pavement, and (E) pier destruction

F
I G U R E Liquefaction at the Yematan Bridge site.(A) Near bridge site and (B) middle site at the south end F I G U R E Acceleration records at Dawu station.(A) EW, (B) NS, and (C) UD.EW, east-west; NS, north-south; UD, up-down F I G U R E Velocity records at Dawu station. (A) EW, (B) NS, and (C) UD.EW, east-west; NS, north-south; UD, up-down F I G U R E Simulation of acceleration time history.(A) FP, (B) FN, and (C) UD.FN, fault normal direction; FP, fault parallel direction; UD, up-down F I G U R E Simulation of velocity time history.(A) FP, (B) FN, and (C) UD.FN, fault normal direction; FP, fault parallel direction; UD, up-down F I G U R E Seismic damage of pier No.17

F
I G U R E 11 Pile-soil coupled model.(A) Soil layer information (cm) and (B) 3D finite element numerical model TA B L E 1 Specific soil parameters

F I G U R E 12
Time history of pile top and surface displacement F I G U R E 13 Soil spring simulation model

15
Seismic response model for pile foundations at liquefaction side spread flow sites.(A) Force-based seismic design method and (B) displacement-based seismic design method

F I G U R E 16
Equivalent static force analysis model of Pier 17 F I G U R E 17 Pushover hinge yielding diagram F I G U R E 18 Moment-curvature diagram.(A) West pier and (B) east pier F I G U R E 19 Pile displacement results

F I G U R E 20
The full bridge model.(A) Elevation view, (B) planar graphs F I G U R E 21 Simplified hysteresis model for reinforced concrete transverse shear key

F
I G U R E Main girders residual displacement and relative displacement diagram.(A) Longitudinal and (B) lateral F I G U R E Continuous stress diagram for main girders and link slabs (kN/cm 2 ) F I G U R E North and south abutment transverse shear key collision displacement time history.(A) Abutment No.0 and (B) Abutment No.25 F I G U R E 27 Time history of transverse shear key collision force for north and south abutments.(A) Abutment No.25 and (B) Abutment No.0 Table 2 displays the mechanical properties of the bearing.