The dynamic response of near-fault bridge pile foundation under strong earthquake can be used to evaluate the stability of pile foundation, which is an important means to predict the stability of pile foundation. In this paper, acceleration, displacement, bending moment, and fundamental frequency were selected to describe the dynamic response of the model pile. If there is no special description, the solid lines in the data graph of this paper indicates the 38 − 1# pile (on the hanging wall of the fault), and the dotted lines indicates the 37 − 1# pile (in the footwall of the fault).

## Acceleration response

*Peak acceleration of pile.* The peak acceleration (PAC) distribution of pile foundations on both sides of the fault are shown in Fig. 2. The acceleration distribution law of pile foundation on both sides of fault is similar. The PAC decreases along the pile length, which has a turning point in the muddy soil layer. The reason is that loose soil can absorb part of seismic wave energy. The porosity of the muddy soil layer is relatively large, and the particle size is small, which can absorb more energy. Under different intensity ground motion, the PAC of pile on the hanging wall of the fault is larger than that in the footwall. It reflects “the hanging wall effect” of the fault. The reason for this is that the fault filling materials are granular particles, and their physical and mechanical states are unevenly distributed. The contact between the rock and soil on both sides of the fault and the fault filling materials is uneven, leading to the significant nonlinear difference of rock and soil around the pile on both sides of the fault.

The difference of the PAC between pile top and pile bottom is shown in Fig. 3. The PAC difference of 38 − 1# (on the hanging wall) is larger than 37 − 1# (in the footwall). Under different intensity ground motion, the difference is significantly different. In the 0.15g ~ 0.25g, the difference increases slowly. In the 0.30g ~ 0.35g, the difference is small. In the 0.40g ~ 0.60g, the difference is significantly larger. The greater the intensity of ground motion, the more obvious the difference.

*Acceleration magnification fact.* The PAC and acceleration amplification factor (AAF) of each measuring point of piles on both sides of the fault are shown in Fig. 4. The AAF α (shown in Eq. (1)) is the ratio of the PAC of pile top (amax) to the input seismic wave (ainput). It can reflect the properties of rock and soil layers and the magnifying effect of elevation on pile acceleration.

The PAC and AAF of the pile on the hanging wall of the fault are larger than those in the footwall. There are obvious differences in the “the hanging wall effect” of fault in different soil layers. In different soil layers, the various rule of MAC on both sides of fault is approximately the same, and there is a slight difference in the law of AAF. As the increase of ground motion intensity, the PAC increase, and the AAF decrease. Under different intensity ground motion, the PAC and AAF of the pile on both sides of the fault are quite different at the pile top and in the pebble soil (Fig. 4**(a) and Fig. (d)**); the PAC increases approximately linearly and the AAF stabilizes around 1 in the bedrock (Fig. 4**(e)**); the difference of the PAC and AAF are small in the mucky clay and gravel sand (Fig. 4**(b) and Fig. (c)**).

## Horizontal displacement response of pile top

The relative displacement of the pile top on both sides of the fault is shown in Fig. 5. Under different input seismic intensities, the maximum relative horizontal displacement of the pile top on the hanging wall is larger than that in the footwall. With the increase of ground motion intensity, the maximum relative displacement of pile top increases gradually, and the difference of those also increases gradually. When the ground motion intensity is 0.15g ~ 0.25g, the difference of those are small, which are 0.05mm, 0.05mm, and 0.04mm. When 0.30g ~ 0.40g, the difference increases gradually, which are 0.30mm, 0.48mm, and 0.50mm. When 0.45g ~ 0.60g, the difference is large, which are 0.50mm, 0.77mm, 0.61mm, and 0.77mm. Under the pile-soil-fault interaction, the pile foundation on the hanging wall is greatly affected by ground motion.

## Bending moment response of the pile

The bending moment of the pile on both sides of the fault is shown in Fig. 6. With the increase of earthquake intensity, the variation law of pile bending moment is similar. The bending moment is the largest at the interface between the muddy clay layer and g the ravel layer. And there also have a sudden change in the bending moment value on the bedrock surface. Under different intensity ground motion, the bending moment of the pile on the hanging wall is larger than that in the footwall, which also shows the “the hanging wall effect” of the fault.

According to the Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts (JTGD62-2018) [32], the bending bearing capacity of pile foundation was 168.54 kN•m. The maximum bending moment of the pile on both sides of the fault is shown in Fig. 7 **(a)**. The safety degree of the flexural bearing capacity of the pile is shown in Fig. 7 **(b)**. The safety degree of flexural bearing capacity of pile β is defined as:

*β* = (*M*max - *M*0)/*M*0×100% (2)

where β is the safety degree of flexural bearing capacity of pile(%), *M**max* is the maximum bending moment of pile (kN•m), *M**0* is the flexural capacity of the pile (kN•m). The negative value of *β* indicates the surplus of bending bearing capacity, and the positive value of *β* indicates that it exceeds the bending bearing capacity.

In the intensity ground motion from 0.15g to 0.25g, the maximum bending moment difference is small and there is a surplus of flexural bearing capacity. In 0.30g ~ 0.40g, the difference is increases by degrees. In 0.45g ~ 0.60g, the difference increases rapidly. It is worth noting that the maximum bending moment of the pile on the hanging wall exceed the flexural capacity of the pile in 0.45g, while the maximum bending moment of the pile in the footwall not.

## Fundamental frequency of the pile

The above analysis shows that “the hanging wall effect” of fault is significant under the strong earthquake-fault coupling action. Therefore, the pile foundation on the hanging wall is selected as the analysis object. The change of the fundamental frequency of the pile foundation is not obvious when the input seismic intensity is less than 0.35g. Therefore, the damage of pile foundation is analyzed when the ground motion intensity is greater than 0.35g. The Fourier spectrum of the pile on the fault wall is shown in Fig. 8.

The fundamental frequency of pile foundation before loading is 3.54Hz. In the input seismic intensity 0.35g ~ 0.60g, the fundamental frequencies are 3.57Hz, 3.48Hz, 3.26Hz, 1.78Hz, 0.93Hz and 0.84Hz, respectively. When the input seismic intensity is 0.35g ~ 0.45g, the foundation frequency of pile foundation does not change obviously. It shows that the overall stiffness of the pile foundation is not reduced, and there is no obvious damage. When the input seismic intensity reaches 0.50g, the fundamental frequency of the pile foundation decreases obviously and decreases by 49.7% (Fig. 9). In 0.50g, the foundation frequency of pile foundation decreases slowly and tends to be stable. At this time, there is a big difference between the maximum acceleration of the pile top and the pile bottom, the horizontal displacement of the pile top is larger, and the safety degree of flexural bearing capacity of pile is positive, that is, it exceeds the bending bearing capacity. At this time, under the pile-soil-fault interaction, the pile foundation is damaged by the earthquake, which is consistent with the macroscopic phenomenon of the Section *Damage analysis of the pile*.

## Damage analysis of the pile

There is no obvious damage on the surface of the model pile under 0.15g ~ 0.45g seismic intensities. A slight crack was generated at the connection between the top of the pile and the cap under input seismic intensity of 0.50g. From 0.50g to 0.60g, the pile produced a slight tilt, and cracks propagation further. The dynamic failure process of the model pile is shown in Fig. 10. Results show that the dynamic failure is mainly reflected in the cracks appeared near the joint of pile top and platform, soil interface and bedrock surface. With the increase of the seismic intensities, the cracks further expand, leading to loss of bearing capacity of the model pile.