## 3 Dynamic Response Analysis of the Test Model
### Distribution Characteristics of Pile Shaft Bending Moment  
The concrete was tested using strain gauges in a Wheatstone quarter bridge circuit. The bending moment of the pile shaft was calculated according to the tensile and compressive strain values, using the following formula, where \(E\) is the elastic modulus of the micro-concrete, \(I\) is the moment of inertia of the section, \(EI\) is the flexural stiffness of the pile shaft, \(\varepsilon_{+}\) and \(\varepsilon_{-}\) are the micro-strains on the tension side and the compression side, respectively, and \(h\) is the linear distance between the measurement points on the tension side and the compression side, respectively, of the same section.  
\[M=\frac{EI\cdot(\varepsilon_{+}+\varepsilon_{-})}{h} \tag{1}\]  
When the test model was loaded with El Centro waves with different peak accelerations, the bending moment of the back-row anti-slide piles was as shown in Figure 15a. As the peak acceleration of the seismic wave increased from 0.1 g to 0.3 g, the bending moment of the back-row anti-slide piles gradually increased, with the maximum bending moment of the pile shaft occurring near the sliding  
Figure 14: Distribution of peak earth pressure in different sections. (**a**) Behind back-row anti-slide piles; (**b**) front side of back-row anti-slide piles; (**c**) behind bridge foundation; (**d**) front side of bridge foundation; (**e**) behind front-row anti-slide piles.  
surface. Because the anti-slide piles were anchored by the bedrock, there was a certain bending moment below the sliding surface of the pile shaft. When the peak acceleration of the seismic wave reached 0.4 g, the anti-slide piles cracked, and the bending moment of the pile shaft decreased substantially, but the piles still had a certain bearing capacity. As the vibration intensity continued to increase, the damage to the slope increased, the cracks in the anti-slide piles propagated rapidly, and the bending moment of the pile shaft continued to decrease until the tensile steel bars yielded and the concrete was crushed. Figure 15b shows that the dynamic load of the superstructure caused the peak negative bending moment to occur at the top of the pile foundation behind the pier. Under the soil resistance around the pile, the negative bending moment along the pile depth gradually changed to a positive bending moment, which reached its peak value at the bottom of the sliding mass, which restrained the flexural deformation of the pile shaft. Figure 15c shows that the variation pattern of the bending moment of the pile foundation in front of the pier was similar to that behind the pier; because of the steep slope in front of the pier, the soil around the pile had limited resistance during vibration, causing the attenuation rate of the negative bending moment along the pile depth to be smaller. The front-row anti-slide piles were located in the anti-sliding section of the slope. As shown in Figure 15d, the bending moment of the pile shaft above the sliding surface was very small. Therefore, the seismic reinforcement design of the front-row anti-slide piles needs to be further optimized.