## 4 Finite Difference Method Simulation
### Loading and Analysis of the Effect of Pile Diameter
From the comparison graph of load-settlement of the three pile types it can be seen that after the load-settlement curve enters the steep fall section, the steep fall section curve of the three curves gradually becomes steeper with an increase in the inner diameter of the pile body. This is because at the late stage of loading, the lateral  
Figure 15: Numerical simulation of load-settlement curves at the top and end of piles with different wall thicknesses of PHC piles. frictional resistance of the pile has exerted its ultimate value, and the increased load at the top of the pile is all borne by the soil layer at the end of the pile thereafter. As the internal diameter of the pile becomes larger, the contact area between the pile end position and the pile end soil layer becomes smaller, resulting in a reduction in the bearing capacity that the pile end soil layer can provide. The value of the load borne by the soil layer at the pile end increases at this stage, resulting in relatively large differences in the curves of the steeply descending section of the three curves. The calculation of the pile lateral frictional resistance was carried out by monitoring and recording the pile axial force distribution. The calculation method is the same as Equation (1). The pile lateral friction resistance diagrams for the three pile types under all levels of loading are shown in Figure 16.  
From the pile lateral friction resistance curves for different pile types under all levels of loading, we can see that with increasing pile depth into the soil, the pile lateral friction resistance shows a more obvious turning phenomenon at the position of the partition interface of each soil layer, which is caused by the inconsistent pile-soil contact surface stiffness  
Figure 16: The pile lateral friction resistance curve obtained from numerical simulation: (**a**) The lateral pile friction resistance curve of ZL-25; (**b**) the lateral pile friction resistance curve of ZL-20; (**c**) the lateral pile friction resistance curve of ZL-10. at the position of the partition interface of the soil layer. For example, the pile-soil contact surface stiffness was 2.693 \(\times\) 10\({}^{9}\) kPa for the upper fine sandy soil and 1.223 \(\times\) 10\({}^{9}\) kPa for the lower pulverized soil at 20 m. The contact surface stiffness is reduced, resulting in a significant decrease in the pile lateral friction resistance and a large turn in the curve. With an increase in load, the pile lateral friction resistance of the shallow part of the pile gradually exerts its ultimate lateral resistance, and the lateral friction resistance curves of the powdered clay and powdered soil layers gradually tend to overlap. Finally, the pile lateral resistance curves under two load levels almost completely overlap, and the pile lateral resistance has reached its ultimate value. To compare the pile lateral resistance curves of the three pile types, the pile lateral resistance curves of the three pile types under 1600 kN, 4400 kN, and 7200 kN were compared. As shown in Figure 17.  
Comparing the pile lateral friction curves for three pile types subjected to 1600 kN, 4400 kN, and 7200 kN, we can see that the trend of the pile lateral friction curves of different pile types remains the same under different pile top load conditions. When the top pile load is small, the curves are more undulating, and the smaller the internal diameter, the stronger  
Figure 17: Pile lateral resistance curves of the three pile types under different loads: (**a**) Pile lateral resistance curves of the three pile types under 1600 kN; (**b**) pile lateral resistance curves of the three pile types under 4400 kN; (**c**) pile lateral resistance curves of the three pile types under 7200 kN. the undulation. With an increase in pile top load, the curves gradually converge, and the undulation gradually decreases. This is because when the top pile load is small, the pile side frictional resistance is less, and the top load is mainly borne by the pile body.