# Deformation and Stress Analysis of Pile-Supported Immersed Tunnels under Seismic Loads
## 4 Parametric Analysis
### Effects of the Slenderness Ratio  
#### 4.3.1 \(p\)-\(y\) Curve of the Piles  
Figure 12a-c show the resistances-deflection (\(p\)-\(y\)) curves along the depth direction for piles with \(\Upsilon\) = 15 (plum piles), \(\Upsilon\) = 9.37 (diagonal piles), and \(\Upsilon\) = 6.25 (rectangular piles), respectively. The characteristic lines at two points, the tip of the pile and the end of the pile are used to reflect the change in the \(p\)-\(y\) relationship of the pile. As the seawater depth \(H\) increases, the characteristic lines of SCP under all three \(\Upsilon\) are rotated clockwise, which coincides with the results of [PERSON] et al. (2017), who found that the \(p\)-\(y\) curves of piles under compression conditions are steeper. At this time, the deflections at the tip of the pile varied more by 0.23 m, 0.23, and 0.2 m, respectively, while the difference in deflection variation at the end of the pile was not significant. The stiffness represented by the slope of the curve increases with depth, and similar results were obtained by [PERSON] (2017) and [PERSON] et al. (2017) from centrifuge modeling tests of monopiles and jacketed piles. At \(\Upsilon\) = 15, the characteristic line is rotated clockwise by 45\({}^{\circ}\), and the resistances at the tip of the pile are increased by 95 KPa, and that at the end of the pile is increased by 43 KPa. At \(\Upsilon\) = 9.37, the angle of rotation of the characteristic line is 11\({}^{\circ}\), the resistances at the tip of the pile increase by 70 KPa, and the resistances at the end of the pile increase by 70 KPa. At \(\Upsilon\) = 6.25, the angle of rotation of the characteristic line is 10\({}^{\circ}\), the resistances at the tip of the pile increase by 105 KPa, and the resistances at the end of the pile increase by 140 KPa. The above data indicate that the seawater pressure has an effect on the lateral behavior of the piled foundations. The effect of seawater pressure on the lateral behavior of the pile foundation is through increasing the degree of soil densification and increasing the axial force to generate additional bending moment, as in [PERSON] and [PERSON] (2017). It can be seen that the change in seawater depth affects the \(p\)-\(y\) value at the tip of the pile more than the end of the pile, while the change of \(\Upsilon\) affects the \(p\)-\(y\) value at the end of the pile more than the tip  
Figure 11: Vertical strain at the bottom of the gravel cushion.  
of the pile. The combined consideration of seawater pressure and the slenderness ratio of the pile can prevent localized injury to the pile.  
Figure 12: Cont.  
The injury to the SIS system by seawater depth is significantly less than the direct effect of seismic transverse waves, indicating that the damping of seismic waves by the structure and the suppression frequency of seawater are favorable for seismic design. It is clearly observed that the equilibrium that occurs in the pile roof and pile end resistances when \(\gamma\) from 15 to 9.35. It confirms the existence of an optimum slenderness ratio for the SCP-reinforced marine foundation in Section 3.