## 4 Interaction Between Parameters of New and Existing Piles
### Behavior of New Piles  
Figures 8 and 9 show the vertical settlement deformation of new piles under different \(h_{\rm N}\)(s) and \(d_{\rm N}\)(s), respectively, subjected to a certain vertical load.  
Figure 8 indicates a negative correlation between \(h_{\rm N}\) and pile foundation settlement. Within the range of 0.9-1.3\(h\), the settlement of the new pile consistently decreases with the increase in \(h_{\rm N}\). At the pile head, the settlement variation ranges from 0.481 to 0.417, while at the pile bottom, it ranges from 0.364 to 0.228. The influence of larger \(h\)N on the pile bottom gradually decreases. In the displacement contour, longer piles transfer the load to deeper soil layers, where the high confining pressure constrains pile foundation deformation, effectively reducing settlement. The deeper \(h_{\rm N}\), the more pronounced the effect.  
In the relationship between \(d_{\rm N}\) and the settlement of new piles, there is a notable attenuation at the pile head, then the settlement increased with \(d_{\rm N}\). For both large-diameter piles and small-diameter piles, negative friction was distributed in the upper part of the pile and positive friction was distributed in the lower part of the pile, and the shaft friction of the large-diameter pile was greater than that of the small-diameter pile at the same depth [38]. This phenomenon can be attributed to the gradual dissipation of vertical soil  
Figure 8: Relationship between new pile settlement and \(h_{\rm N}\)(s).  
Figure 9: Relationship between new pile settlement and \(d_{\rm N}\)(s).  
stress between surface piles with increasing depth, while the negative friction in the upper section of the pile effectively offsets a portion of the vertical stress. In contrast, in the lower section, vertical soil stress increases due to the cumulative effects of soil self-weight and positive friction. Furthermore, the normal stress acting on the pile shaft is proportional to the vertical soil stress, leading to higher normal stresses on large-diameter piles. This effect becomes more pronounced as the diameter difference increases. Meanwhile, large-diameter piles carry greater loads; their pile-soil relative displacement is also more significant than that of small-diameter piles. These results indicate that pile diameter's effect on settlement follows a nonlinear trend. At the initial stage, increasing the pile diameter significantly reduces settlement. However, as the pile diameter continues to increase, normal stress growth between piles and the pile-soil relative displacement may contribute to an increase in settlement.  
[PERSON]'s study shows that the total bearing capacity \(Q(t)\) of an axially loaded pile consists of the end-bearing capacity \(Q_{\text{s}}(t)\) and the side resistance \(Q_{\text{b}}(t)\), expressed as [39]:  
\[Q(t)=Q_{\text{s}}(t)+Q_{\text{b}}(t)=\int_{0}^{l}2\pi r_{p}f_{s}(t)dz+\pi r_{p} ^{2}q_{\text{b}}(t) \tag{4}\]  
where \(l\) is the pile length, \(r_{p}\) is the pile radius, and \(q_{\text{b}}\) is the unit end bearing resistance of a pile, defined as \(q_{\text{b}}(t)=N_{\text{c}}(t)s_{\text{u}0}\), \(t\) represents the consideration of time-dependent effects caused by clay creep, \(S_{\text{u}0}\) is the initial undrained shear strength of the soil, and Nc is the pile end coefficient. From the expression, both the increase in \(h_{\text{N}}\) and \(d_{\text{N}}\) enhance the overall bearing capacity. Theoretical explanations provide insights into the influence of \(h_{\text{N}}\) and \(d_{\text{N}}\) on pile-bearing capacity and settlement behavior. However, numerical simulations demonstrate that the settlement induced under identical vertical stress is relatively limited, particularly for variations in \(d_{\text{N}}\) at a fixed pile length. When a new pile and existing piles are integrated into the same pile cap, the connection through the pile cap directly impacts the settlement of the existing piles, in addition to the soil-pile interaction.