# Study on Vertical Uplift Resistance Characteristics of Pre-Drilled Planted Piles in Boulder Strata
## 5 Calculation Results and Analysis
### Axial Force Transmission Analysis of the Core Pile  
By calculating the strain at various sections of the core pile under different pile head loads, the axial force distribution along the core pile is obtained, as shown in Figure 6. The results show that under the applied load, the upper section of the core pile plays a dominant role. As the load increases, the upper load is transmitted downward along the pile shaft and transferred to the surrounding soil through the outer concrete. When a boulder is present in the pile, the load can also be transmitted to the boulder through the outer concrete and ultimately to the surrounding soil.  
To counteract the uplift tendency of the core pile, the outer concrete layer exerts downward frictional resistance on the core pile. The axial force curves at different pile sections exhibit varying rates of decrease, with their slopes directly reflecting the magnitude of the frictional resistance. Figure 7a displays the change in axial force along the core pile under Condition 1. It can be observed that the axial force decreases gradually with depth, reaching a minimal value near zero at the pile tip, indicating that the end resistance is negligible, and the load is primarily borne by side friction. Within 3 cm from the pile top, the rate of decrease of the axial force curve of the core pile is the greatest, because under loading, the core pile undergoes deformation due to tensile forces at the pile head, resulting in the displacement difference between the core pile and the outer concrete at the head being maximized, leading to significant internal friction resistance at the head. As the depth increases, the displacement difference between the core pile and the outer concrete gradually decreases, and the internal friction resistance correspondingly diminishes and stabilizes, indicating a strong cohesion between the concrete and pipe pile and good compatibility of deformation between the core pile and outer concrete. In Condition 2 (Figure 7b), the axial force of the pile also decreases with depth. However, due to the presence of boulder, the cross-sectional diameter of the pile increases, providing greater vertical support force from the overlying soil and increasing the contact area with the surrounding soil, thereby expanding the pathways for load transfer to the surrounding soil. Consequently, in the region where boulders are present, the axial force along the core pile decreases sharply. When the uplift load reaches the ultimate uplift resistance of 25.6 N, the pile tip contributes approximately 32% of the total uplift resistance.  
Figure 7: Axial force diagram of core pile: (**a**) Variation of axial force in core pile under Condition 1; (**b**) Variation of axial force in core pile under Condition 2.  
Under both conditions, the load is transferred from the pile head to the pile tip, and the axial force of the core pile decreases in depth, with the axial force at the pile bottom being small and the axial force of the pile approaching zero, indicating that the end resistance is negligible, and the load is primarily borne by side friction. However, the presence of a boulder provides additional vertical support and pathways for load transfer, thus offering some end resistance to the pile, enhancing its uplift capacity.