## 5 Analysis of the Combined Load-Bearing Characteristics of Piles and Soil in Composite Foundations  
The Variation in Additional Internal Forces on the Central Pile and Inter-Pile Soil along the Depth Direction  
In order to study the influence of the pile length, soil modulus \(Es\), pile modulus \(Ep\), and pile type on the additional vertical force on the central pile and inter-pile soil, the variation in the additional axial force along the depth direction of the central pile was plotted for a pile length of 30 m and a soil modulus of 50 MPa (Figure 11). To compare the performance of the central pile and inter-pile soil under different conditions, the variation in the additional axial force along the depth direction was plotted for a pile length of 20 m and soil moduli of 50 MPa and 100 MPa (Figures 12 and 13), as well as the percentage of the additional vertical force on the central pile and inter-pile soil for soil moduli of 50 MPa and 100 MPa (Figure 14). From Figures 11-14, it can be observed that, under two different soil modulus conditions, the variation curves of the additional vertical force on the pile and inter-pile soil, as well as the percentage of additional axial force on the pile, were basically consistent along the depth direction. This indicates that the influence of the soil modulus on the load-bearing characteristics of the pile and soil was minimal. By comparing the variation curves of the additional axial force along the depth direction for different pile lengths of the central pile, it was found that the length of the pile hardly affected the variation trend of the additional axial force along the depth direction. Under the action of the upper load, the variation  
Figure 10: Influence of soil elastic modulus on displacement distribution of two pile types: (**a**) displacement of friction pile; (**b**) displacement of end-bearing pile. trend in the additional axial force on the central pile and the additional vertical force on the inter-pile soil in the depth direction mainly showed the following characteristics:  
1. With an increase in the soil depth, the additional axial force on the central pile generally increased rapidly and then gradually decreased. In the depth range of 0 to 1/10 \(L\), the cushion layer directly transmitted the pressure to the top of the pile, while the deformation of the inter-pile soil was greater than that of the pile, resulting in a rapid increase in the additional axial force on the pile. In the depth range of 1/10 \(L\) to 1 \(L\), the vertical deformation of the pile was greater than that of the inter-pile soil, and the pile was subjected to the upward frictional force from the inter-pile soil, leading to a gradual decrease in the additional axial force on the pile. Compared with end-bearing friction piles, the additional axial force of the friction piles was smaller, and it increased with the pile modulus and decreased with the soil modulus. It is important to note that, within a depth range of 1 m from the top and bottom of the pile, there were significant variations in the additional internal forces acting on both the pile and the soil. 2. With an increasing depth into the soil, the additional vertical force acting on the soil between the piles underwent five distinct stages: a rapid decrease, a gradual decrease, constant maintenance, a gradual increase, and then a rapid increase. The cushion layer directly transferred pressure to the soil between the piles. Within a depth range of 1 m from the pile's top, the additional vertical force acting on the soil between the piles decreased sharply due to the pile support. Within the depth range from 1 m to 0.1 L from the pile top, the additional vertical force decreased gradually. In the depth range of 0.1 \(L\) to 0.9 \(L\), it remained relatively constant. Within the depth range from 0.9 L to 1 m from the pile bottom, the additional vertical force on the soil between the piles gradually increased.