## 4 Simulation of the Response of the Used Pile under New Pile Penetration
### Comparison of Analytical Solution and Simulation  
Figure 8 shows the lateral displacement of the existing pile at 5 m, 10 m, 15 m and 20 m of new pile penetration. It can be seen from Figure 8 that the existing pile causes  
Figure 6: FEM model of new pile penetration with existing pile in stratum. Figure 7: File tip optimization. lateral displacement away from the new pile as the new pile penetrates, and the deeper the penetration, the greater the lateral displacement. This is attributable to the significant squeezing impact induced by the new pile's penetration. Figures 9 and 10 present a comparison of the analytical results of the Winkler foundation model and the simulation. Figure 9 shows the result of the pile top and pile end being free. Figure 10 displays the result of the pile top being free and the pile end being fixed. Both the theoretical results and the numerical results demonstrate that when the new pile's penetration depth grows, the existing pile's deformation increases as well. There is a good agreement between the two in terms of the deformation trend. Within 10 m depth of new pile penetration, the theoretical results and simulation results are basically consistent. When the static-pressure pile penetrates to a depth greater than 10 m, the theoretical results are slightly greater than the simulation results. This is mainly due to the usage of a pre-set auxiliary pipe in the simulation. Meanwhile, the Winkler model mainly reflects the squeezing effect, but the shear stress effect on the surrounding soil cannot be well reflected. This may also result in the lateral displacement of the theoretical calculation being larger than that of the simulation results. From Figures 9 and 10, it can be found that different forms of pile end restraint have little effect on the lateral deformation at 5 m, 10 m and 15 m of new pile penetration. However, when the new pile penetration is close to 20 m, the lateral displacement of the existing pile in the theoretical results for the fixed case of the pile end is significantly smaller than for the free case of the pile end. This is because when the penetration length is short, the influence of the boundary conditions is limited to the upper pile body. Moreover, when the penetration depth is close to the length of the existing pile, the fixed boundary conditions limit the displacement of the bottom pile body, which has a significant impact on the deformation of the bottom of the pile body. Figures 11 and 12 display a comparison of analytical results of the Pasternak foundation model and the simulation results; Figures 11 and 12 show the results of the pile end being free and the pile end being fixed, respectively. The analytical results are in general agreement with those of the simulation, as shown in Figures 11 and 12. That means both the Winkler model and Pasternak model used in this article can better reflect the deformation pattern of the adjacent existing pile under the penetration of a static-pressure pile. Figure 8: Nephogram of existing pile lateral displacement caused by new pile penetrating to different depths. Figure 10: Comparison of calculation results between numerical simulation and [PERSON] foundation model with pile tip fixed. Figure 9: Comparison of calculation results between numerical simulation and Winkler foundation model with pile tip free. From Figures 9-12, it can be found that the difference between the results of the two analytical models is mainly in the deformation near the top of the existing pile. Figure 13 displays the comparison of lateral deformation of the existing pile body between the Winkler foundation model and the [PERSON] foundation model. It is worth noting that the lateral deformation of the existing pile body computed by the Pasternak foundation model is larger than the results of the [PERSON] foundation model, which is compatible with the findings of [PERSON] et al. (2018). Figure 11: Comparison of calculation results between numerical simulation and [PERSON] foundation model with pile tip free.