## 5 Comparative Analysis of the Pile Foundation Dynamic p-y Curve
### Comparison of p-y Curves between the Straight Pile Group and the Inclined Pile Group  
This section mainly explores the p-y hysteretic curve rule of straight pile groups and inclined pile groups in three working conditions. The grating point 0.205 m away from the fixed end is selected for analysis. Figure 17 shows the pore pressure time-history diagram corresponding to the upper and lower sets of the straight pile group. The lower layer pressure gauge is 120 mm away from the bottom of the model box, and the upper layer pressure gauge is 260 mm away from the bottom of the model box. Figure 18 shows that the p-y hysteresis curves have common features under the six operating conditions. Three typical periods are taken for the rise in the pore pressure in liquefied soil conditions. First, at the initial stage of vibration (5.00-5.34 s) the lateral force and displacement increase rapidly from small to large, and no hysteresis loop is formed. Second, when the vibration tends to be stable (6.00-6.34 s and 6.60-6.94 s) the p-y curve of  
Figure 17: Pore pressure time–history diagram. the pile body has a similar stress and displacement hysteresis loop. At different moments when the vibration is stably input, the force and displacement of the pile are slightly reduced due to the compaction of the sand during the vibration process, but the p-y curves are substantially coincident. From the analysis of different thicknesses of saturated sand soil, regardless of whether it is the straight pile group or inclined pile group, an increase in the saturated sand thickness results in the lateral force decreasing in the stable stage, but the pile-soil relative displacement increases obviously. Additionally, the reduction of the lateral force is obviously smaller than the increase in the pile-soil relative displacement. From the analysis of the type of the pile foundation, the lateral force of the straight pile group is obviously larger than that of the inclined pile group under the same acceleration input, and the peak values of the pile-soil relative displacement of the straight pile group is also larger than that of the inclined pile group. The hysteretic loop formed by them is an eccentric ellipse, and the area enclosed by the straight pile group is larger than that of the inclined pile group. In order to further compare and study the law of the p-y hysteretic curve of the straight inclined pile group, Figure 19 shows the p-y hysteretic curve at 6.60-6.94 s in the same coordinate system. The envelop area formed by the p-y hysteresis curve of the straight and inclined pile groups in saturated sand is larger than that of non-liquefied soil. It indicates that the energy consumption of the pile group in liquefied soil is higher than that of non-liquefied soil. This is because the saturated sand becomes liquefied under the input of the sine wave. The soil is suspended in water and then loses its bearing capacity. The lateral bearing capacity is mainly borne by the pile group. However, the lateral bearing capacity in non-liquefied soil is borne by the pile groups and sand, which results in a significant increase in the energy consumption of pile groups in liquefied soil compared with the non-liquefied soil. The envelop area formed by the p-y hysteresis curve of the pile group in 380 mm saturated sand is larger than that in 300 mm saturated sand. It shows that with the increase in saturated sand thickness, the lateral dynamic response of the pile group becomes more significant, and the energy consumption of the pile also increases. At the same time, the pile-soil relative displacement in 380 mm saturated sand is larger than that between pile and soil in 300 mm saturated sand. It shows that the interaction between the pile group and soil becomes more significant with the increase in saturated sand thickness. The connection between the two vertices of the long axis in the p-y curve is defined as the principal slope of the dynamic p-y curve, which can reflect the soil stiffness around pile.