## 4 Finite Difference Method Simulation
### Loading and Analysis of the Effect of Pile Diameter  
Loading was carried out in accordance with the requirements of the Technical Specification for Inspection of Building Pile Foundations (JGJ106-2014), with the first load level corresponding to a surface force of 1400 kPa at the top of the pile, and each load increased by 700 kPa until it was loaded to 9800 kPa for a total of 13 applied loads. Q-s curves for different diameters of pipe piles obtained by testing the displacement at each node of the pile-soil model are shown in Figure 15.  
Comparing the load-settlement curves of the test pile (PHC\(-2\)) with the simulated load-settlement curves of different pile diameters, it can be seen that the curves obtained from the numerical simulation and the test curves are in good agreement at the early stage of loading, with almost the same slope, and the slope of the corresponding load-settlement curves of the test pile increases faster with an increase in load and there is no obvious inflection point. The simulated load-settlement curve has a slow increase in slope in the middle of loading, and a rapid increase in slope in the later period with obvious inflection points. Figure 14: Horizontal displacement of piles and soil of numerical test (unit: m): (**a**) Horizontal displacement of the soil for the numerical test (PHC\(-1\)); (**b**) horizontal displacement of the soil for the numerical test (PHC\(-2\)). It can be seen that the load-settlement curves of the top and end of the large diameter pipe pile with a wall thickness of 25 cm are distributed in a straight line in the early and middle periods of loading. When the load is applied to 6120 kN, the load-settlement curve shows a significant steep drop segment. We can obtain the following results from the load-settlement curves and comparison graphs of the three pile types:  
1. The inflection points of the load-settlement curves of the three pile types are obvious, and the linear section curves of the three pile types in the middle period before loading are very close. This is because all three pile types are large diameter deep and long piles, and according to the model soil parameters, it is known that all three pile types are friction piles, and the load applied at the top is mainly borne by the frictional resistance of the soil on the side of the pile. Since the outer diameter of the three pile types is the same, the surface area on the pile side of the three types is also the same, and the contact area with the soil on the pile side is also the same. This causes the vertical bearing performance of the three pile types to not change greatly when the frictional resistance on the pile side is not fully exerted. This is consistent with the results obtained by [PERSON], [PERSON] et al. [38]. However, the straight line section of the precompression interim curve of the 10 cm wall pile is steeper than the first two, indicating that this pile type is weaker than the others in terms of settlement at the top of the pile when subjected to the same load and the ability to withstand vertical loads than the other two pile types. This is due to the smaller volume of the wall 0.1 m pipe pile, its pile can withstand less elastic compression, and the pile displacement is mainly the rigid displacement of the pile body. 2. From the comparative graph of load-settlement of the three pile types, it can be seen that as the inner diameter of the pile increases, the position of the inflection point of the three curves gradually moves to the left side of the curve and does not completely coincide. This is because although the lateral frictional resistance of the pile takes up most of the top load before the load-settlement curve enters the steeply descending section, a small portion of the load is still provided by the soil layer at the pile end. As the internal diameter of the pile gradually increases, the contact area between the pile end position and the pile end soil layer becomes smaller, resulting in a smaller load-carrying capacity provided by the pile end soil layer. 3.