# Study on Vertical Uplift Resistance Characteristics of Pre-Drilled Planted Piles in Boulder Strata
## 5 Calculation Results and Analysis
### Analysis of Shear Damage Slip Fracture Surfaces and Surface Deformation  
The shear failure sliding surface of the soil refers to the slipping surface formed during shear failure around the pile, which typically develops along a path of relatively lower shear strength within the soil. The ultimate load in this study is defined as the applied load just before the abrupt increase in pile head displacement (at the inflection point). Considering that the surrounding soil may not have fully deformed at this time, the paper presents the sliding failure surface morphology during the 3D displacement of the uplift of the pile, as obtained from numerical simulations (Figure 10).  
Figure 10a shows the sliding failure surface for Condition 1, where the angle between the sliding surface and the horizontal plane is \(75^{\circ}\), indicating that the influence of the pile  
Figure 10: Sliding failure surface during 3D displacement of planted pile under uplift: (a) Condition 1; (b) Condition 2.  
on the soil is primarily concentrated in a narrow region along the pile shaft. Figure 9 presents the sliding failure surface for Condition 2, where the boulder is in the pile; thus, the sliding surface can be divided into two parts, above and below the boulder. Below the boulder, the movement of the soil is influenced by the boulder, resulting in a decrease in the sliding surface angle from 75\({}^{\circ}\) to 72\({}^{\circ}\). Simultaneously, the angle of the sliding surface of the soil above the boulder diminishes from 75\({}^{\circ}\) to 49\({}^{\circ}\). The presence of the boulder significantly affects the morphology of the sliding failure surface during the uplift of the pile, leading to changes in the angle of the sliding surface.  
Figure 11 illustrates the surface deformation characteristics under different conditions. When the uplift displacement of the pile is 3D, the sliding failure surface has extended to the ground surface. In this case, the influence range of surface uplift for Condition 1 extends up to 7.5D, as shown in Figure 10a, while for Condition 2, it expands to 13D. The presence of the boulder provides the pile with more pathways for load transfer and resistance, significantly increasing both the uplift load and displacement, thus enhancing the pile's influence on the soil, as illustrated in Figure 11b. Thus, for the same upward displacement, the range of surface uplift is influenced by the presence of a boulder. The influence range of piles containing a boulder on the ground surface is larger. This may be attributed to the boulder enabling the pile to withstand greater uplift forces, thereby subjecting the surrounding soil to higher stress and affecting a wider area. It is also worth noting that the presence of the boulder increases the bearing capacity of the pile and correspondingly expands its influence on the surrounding soil. Therefore, when the cross-sectional area of the boulder is approximately four times that of the pile and it is located in the middle of the pile, attention should be paid to the impact of the pile on other piles in engineering practice, with a recommended spacing greater than 8D.