# Study on Vertical Uplift Resistance Characteristics of Pre-Drilled Planted Piles in Boulder Strata
## 6 Analysis of the Influence of Boulder Position  
To further examine the effect of boulder position on the angle between the sliding failure surface and the horizontal plane, as well as its influence range, numerical simulations were conducted for boulders located at distances of 0, 50, 100, and 150 mm from the pile tip, compared with piles without boulders. The position of the boulder along the pile is illustrated in Figure 12, circles in the picture represent boulders, different colors are used to distinguish isolated stones in different locations.  
Figure 11: Surface uplift influence range during 3D displacement of planted pile under uplift: (a) Condition 1; (b) Condition 2.  
Figure 13 shows the relationship between the uplifting load and displacement of the pile under different boulder burial depth conditions, circles in the picture represent boulders, different colors are used to distinguish isolated stones in different locations. It can be observed from Figure 13 that, compared to piles without boulders, the presence of a boulder at each position enhances the uplift capacity of the pile. With the same load at the pile head, the boulder caused the pile head displacements to decrease to varying degrees, and the deeper the boulder is buried, the lesser the pile head displacement. Additionally, as boulder position increases along the depth of the pile, the Q-S curve gradually becomes gentler, yet all exhibit a steep drop-off type of curve.  
The Q-S curve indicates that the boulder increases the contact area with the surrounding soil, thereby utilizing the pressure from the overlying soil to resist the uplift load. As the burial depth of the boulder increases, the thickness of the overlying soil also increases, enabling greater side friction and resistance, which in turn raises the ultimate uplift capacity of the pile, indicating that the contribution of the boulder to the pile's bearing capacity increases with burial depth. Notably, when the boulder is located at the pile tip, its contribution to the pile's bearing capacity is greater compared to other positions of the boulder. As the boulder moves from the pile bottom to the pile top, the ultimate uplift resistance values are 38.4 N, 32 N, 25.6 N, and 19.2 N, representing increases of 3 times, 2.5 times, 2 times, and 1.5 times compared to piles without a boulder, respectively.  
Figure 14 illustrates the morphology of the sliding failure surface of the pile during uplift under different burial depth conditions of the boulder. As observed in Figure 14,  
Figure 12: Schematic diagram of boulder locations.  
Figure 13: The load–displacement curves of planted piles under different boulder burial depths.  
as the position of boulder moves from the pile bottom to the top, the angle between the sliding surface and the horizontal plane decreases from 56\({}^{\circ}\) when boulder is at the pile tip to 41\({}^{\circ}\) when boulder is located 150 mm above the pile bottom. At the same time, the horizontal influence range of the sliding surface extending to the ground surface gradually reduces as the burial depth of boulder decreases. In the vertical direction, the closer the boulder is to the ground surface, the greater the height of the ground uplift caused by the pile during uplift, while the extent of the uplift decreases correspondingly.  
In this study, the bearing characteristics of grouted piles in a boulder stratum were analyzed using a combination of transparent soil scaled-down laboratory tests and coupled PFC-FLAC numerical simulations. The results provided valuable insights into the micro-scale deformation, stress distribution, and dynamic response. However, due to the errors associated with the scale effect in the scaled-down tests, the findings are still subject to certain limitations. Future work will focus on conducting large-scale tests and optimizing the experimental equipment to enhance the accuracy and universality of the research results.