## 3 Results and Discussion
### The Influence of Soil Response on Cumulative Deformation of the Pile Group  
To explore the impact of the soil dynamic response on the accumulated deformation of the pile group, the horizontal cyclic loading-induced soil cracks and the pore water pressure in the vicinity of the pile-soil interface will be investigated in this section. In this test, the presence of cracks in the soil surrounding the pile is regarded as localized damage within the pile-soil system induced by horizontal loading. Figure 10 displays the development of soil cracks around the pile under different pile spacings. As shown in Figure 10, the development of cracks within the soil around the pile under horizontal cyclic loading followed the following process: (1) At the beginning of loading, a micro-crack was generated in the soil behind the pile, and with the increase of cycles, the micro-crack started to link up, and formed a circular crack around the pile side; then, the crack width widened, and the depth continuously extended under the continuous action of horizontal loading. (2) The water in the upper layer of soil around the pile continuously drained along the crack and interacted with the soil around the pile, causing the mud to flow into the crack, which then softened the soil surrounding the pile. (3) The pile foundation underwent repeated movements under cyclic loading, which resulted in the compression of the soil in front of the pile. As a result, the displaced soil was forced upwards, forming an elevated and convex slope. (4) The soil around the pile was driven by the pile foundation and performed a reciprocal movement under the horizontal cyclic loading, which then generated a cyclic tension crack, and eventually manifested as a radial crack perpendicular to the pile foundation at the end of the test. (5) The mud flowed into the crack, and the crack at the pile-soil interface kept extending outward and downward under the coupling effect between the horizontal cyclic loading and the cohesive force of the silty clay, which made the pile-soil interface become completely detached. It can also be observed from Figure 10 that the above phenomenon became weaker and weaker under the same loading amplitude with the increase of the pile spacing, and there was also no pile-soil separation when the pile spacing was set at 5 times the pile diameter, but the overall development law was still similar. The findings of this study suggest that the observed phenomenon can be attributed to the influence of the pile group effect. Specifically, it was observed that there was a larger superimposed area of soil stress and plastic deformation around the pile with the smaller pile spacing, resulting in more significant soil movement in the vicinity of the pile. Under the cyclic horizontal loading, the pore water pressure in the vicinity of the pile group foundation in saturated clay soil exhibited a cumulative effect. This can result in a reduction in the effective stress within the saturated clay soil, ultimately leading to a degradation in the bearing capacity of the pile group foundation. Figure 11 shows the variations of pore water pressure at different depths near pile 1 in the pile group foundation, where \(p^{\prime}_{c}\) is the measured pore water pressure, and \(\sigma^{\prime}_{z}\) is the vertical effective stress at the same depth. Figure 10: Development process of soil cracks around the pile under different pile spacings. **(a)** File spacing is set at 3 times the pile diameter. **(b)** Pile spacing is set at 4 times the pile diameter. **(c)** Pile spacing is set at 5 times the pile diameter. As depicted in Figure 11, the pore water pressure adjacent to the pile increased with the increase of cycles. The rate of growth for the pore water pressure at the location of the P2 and P3 sensors rapidly speed up during the initial cycles, but gradually decelerated thereafter (the schematic diagram of sensor arrangement is shown in Figure 6).