## 4 Results
### Analysis of Lateral Friction Resistance of the Pile Body  
When a planted pile is under tension, the stress conditions at the core axial load, the core-concrete interface, and the concrete-surrounding soil interface are complex. The applied top-of-pile load is first transferred to the concrete through surface friction at the core-concrete interface and then to the surrounding soil through the cement-soil interface [31,32]. Defining the frictional resistance due to relative displacement at the interface between the core column and the outer concrete ring as the internal frictional resistance, while the friction at the interface between the exterior concrete and the surrounding soil is defined as external friction. Figure 9 illustrates the force analysis of the core pile and the outer concrete micro-elements. \(f_{i}\) represents internal friction; \(f_{i}^{\prime}\) represents external friction; and \(N_{i}\) and \(N_{i}^{\prime}\) represent the axial forces in the core pile and outer concrete at the section \(i\), respectively. Based on the force balance of the pile body, balance equations for the core pile and outer concrete can be derived:  
\[\pi d_{1}L_{i}f_{i}=N_{i} \tag{3}\]  
\[\pi d_{2}L_{i}f_{i}^{\prime}=N_{i}^{\prime}+\pi d_{1}L_{i}f_{i} \tag{4}\]  
Here, \(d_{1}\) is the diameter of the core pile; \(d_{2}\) is the diameter of the planted pile; and \(L_{i}\) is the length between section \(i\) and section \(i+1\). Although the length of each section interval is the same, the frictional resistance of each section is different because the normal force acting on the pile surface varies with increasing pile depth. The axial forces in the core pile and outer concrete obtained through numerical simulations allow for the calculation of internal and external friction forces at section \(i\) using Equations (3) and (4). The distribution of internal and external lateral friction forces along the pile stem for planted piles without an isolated stone and those with an  
Figure 8: Distribution diagram of axial forces in the outer concrete; they should be listed as: (**a**) axial forces in the outer concrete for planted pile without an isolated stone and (**b**) axial forces in the outer concrete for planted pile with an isolated stone. isolated stone at the pile bottom is illustrated in Figures 10 and 11 (due to the influence of the isolated stone, the lateral friction force for piles with an isolated stone is only calculated up to 17 cm into the pile body). As shown in Figures 10 and 11, the distribution patterns of internal and external friction forces along the pile stem are similar. The mobilization of lateral friction resistance is related to the magnitude of the upward load applied at the pile top, which increases with the ascending load. The friction in the upper soil layer is mobilized first; when the upward load is relatively small, the lateral friction in the upper soil layer is not fully mobilized, and the lower soil layer friction has no effect. As the load level increases, the lateral friction in the upper soil layer reaches its limit before the lower soil layer friction starts to mobilize. Using an external load of 12.8 N shown in Figure 10 as an example, the internal and external friction forces along the stem of the planted pile without an isolated stone gradually decrease. At a load of 12.8 N, the lateral friction force decreases rapidly with increasing depth, indicating that the lateral soil friction is fully mobilized, suggesting that the load of 12.8 N is the ultimate bearing capacity of the planted pile. Additionally, it can be observed from the figures that the internal friction force is greater than the external friction  
Figure 10: Distribution diagram of internal and external friction forces along the stem for planted piles without an isolated stone.