## 3 Numerical Simulation of Uplift Capacity in Composite-Anchor Piles
### Parameter Study Results Based on Finite Element Method  
Figure 3 displays the load-displacement curves of the C-shaped pile obtained through both numerical simulation and field static load testing. The simulated and experimental results show a difference of approximately 0.57 mm in the pile head displacement at the maximum ultimate load, indicating an error of about 3.1%. A comparative analysis of the results indicates that, on the one hand, the model is reliable and suitable for future studies. On the other hand, considering the actual soil conditions, the analysis suggests that the discrepancy may be attributed to the incomplete uniformity and complexity of the soil layers. Figure 4 shows the simulation results of Type-B piles at load levels 1, 5, 9, and 11. Generally speaking, the vertical displacement of the lifting pile and the surrounding soil will be higher as the load is increased. At a depth of 1.5-2 times that of the pile base, there is no influence on the displacement of the surrounding earth. With the increase in the load, the displacement of the soil around the pile increases gradually, but tends to be the same gradually, which shows that in the early stage of uplift, the side resistance of the pile is smaller, the soil layer moves up with the pile, and the slope of the curve is lower. During the process of uplift, the side friction of the pile increases, exceeding the frictional resistance at the pile-soil interface. This results in a significant relative displacement between the pile and the soil, reducing the influence of the pile on the surrounding soil displacement. At this stage, the slope of the curve is larger. Therefore, the load displacement curve in Figure 3 is nonlinear. Additionally, it is crucial to note that the pile shaft and the surrounding foundation undergo coordinated deformation. The displacement at the interface between the two remains consistent, indicating that the pile-soil interface has not been damaged. Figure 3: Comparison of load–displacement curves from numerical simulations and field load tests. The composite-anchor uplift pile falls into the category of friction piles, and pile-side frictional resistance plays a predominant role in providing support. The extent of this frictional resistance is determined by the dimensions of the interface between the pile and the surrounding soil. Figure 5 illustrates the load-displacement curves of Type-C for various pile diameters. Upon scrutinizing the figure, it is evident that augmenting the pile diameter from 800 mm to 1200 mm yields a 26% increase in the bearing capacity of the composite-anchor pile. However, when evaluating each 100 mm increment in the pile diameter individually, the uplift pile's bearing capacity merely elevates by 11% when the diameter reaches 900 mm. Additionally, as the pile diameter continues to increase, the rate of improvement in the uplift pile's bearing capacity diminishes. This implies that while expanding the pile diameter enhances the bearing capacity to a certain extent, there are limitations to its growth rate. Figure 4: Vertical displacement distribution of soil layers under different load levels: (**a**) level 1: 880 kN; (**b**) level 5: 2640 kN; (**c**) level 9: 4400 kN; (**d**) level 11: 5280 kN. The rationale behind this observation may be attributed to the fact that an 800 mm-diameter pile already falls within the realm of large diameter uplift piles. Consequently, increasing the pile diameter without adjusting the pile length hampers the ability to transfer the load at the pile tip to deeper soil, thereby restricting any substantial enhancement in the pile's bearing capacity. Furthermore, increasing the pile diameter can lead to higher manufacturing and installation costs. Moreover, employing multiple smaller diameter piles may be more cost-effective than employing a single larger diameter pile. The combined bearing capacity of multiple smaller diameter piles can be equivalent to or even greater than that of a single larger diameter pile, while the overall cost may be lower.