## 5 Study on the Behavior Parameters of Existing Piles
### Pile Arrangement  
Common supplementary pile arrangements around existing piles include central positioning, dispersed around the existing pile, and gap-filling methods. Based on the original positions of the existing piles in this study, two pile arrangement forms are proposed:  
Figure 11: Relationship between settlement of existing piles and \(d_{\text{N}}\)(s): (**a**) existing pile (pile-f); (**b**) existing pile (pile-b).  
symmetric (new piles arranged on both sides of the existing piles) and lateral (new piles arranged on one side of the existing piles). The distance from the applied load to the center point of the pile cap (n = 1, 0.75, 0.5) is defined as e (0, 0.125L, 0.25L), as shown in Figure 12. For certain \(h_{\rm N}\)(s) and \(d_{\rm N}\)(s), the settlement differences under different arrangements of new and existing piles vary.  
The form of pile arrangement determines the load-sharing mechanism between new and existing piles. Figure 13 shows the settlement results of existing piles under different load forms and pile arrangements. When the load is evenly distributed over the pile cap, the settlement of new and existing piles in the lateral arrangement is slightly higher than that in the symmetric arrangement. When the load is partially applied, the settlement difference between new and existing piles varies depending on the overlying load. As shown in the stress contour plot in Figure 14, under uniform load distribution, the stress difference between new and existing piles in the lateral arrangement is not significant, though the new piles experience relatively larger settlements. With the load shifting, the piles not subjected to the load experience uneven stress distribution due to lateral forces. The results under the symmetric arrangement are similar but numerically different from the lateral arrangement. Combining displacement and stress, the results indicate that eccentric loading is not advantageous for a symmetric pile arrangement. Under the same load variation, the symmetric pile arrangement slightly increases the difference between new and existing piles. At \(n\) = 0.75, the normalized settlement of the pile in the symmetric arrangement ranges from approximately 0.29 to 0.41, while the settlement difference in the lateral arrangement ranges from 0.30 to 0.40. At \(n\) = 0.5, the normalized settlement in the symmetric arrangement ranges from approximately 0.16 to 0.32, while the settlement difference in the lateral arrangement ranges from 0.18 to 0.30. Although the symmetric arrangement shows some advantages under uniform load (\(n\) = 1), considering the uncertainties of dynamic loads on the bridge in the later stages, the lateral arrangement would be simpler to reinforce.  
Figure 12: Load distribution conditions of pile cap.  
Figure 13: Settlement of pile and arrangement of new and existing piles: (**a**) symmetric arrangement; (**b**) lateral arrangement.  
In addition, Figure 14 shows that, in both arrangements, eccentric loads cause tensile stress in the unloaded piles, resulting in upward displacement and bending moment of the pile body, especially in the unloaded new pile. Therefore, in the context of new and existing piles, it is crucial to consider the impact of uneven settlement on bridge stability. Additionally, eccentric loading may induce tensile stress in the bridge pile, compromising the stability of the foundation. This consideration is a key factor in selecting the arrangement of new and existing piles.