# Full Life Cycle Evaluation of Stability Pile in High Slope with Multi-Layer Weak Interlayers
## 5 Result
### The Effect of the Ratio of On-Center Spacing to Diameter of Pile (\(S_{\mathrm{p}}/D\))  
Under the initial state (Figure 11a), the \(F\) decreased from 1.42 to 1.37 and from 1.40 to 1.34 in Model 1 and Model 2, respectively, as the \(S_{\mathrm{p}}/D\) increased from 1.875 to 8. In this case, \(F<1.35\) as \(S_{\mathrm{p}}/D\) increased from 6 to 8 in Model 2, which failed to satisfy the requirement of GB 50330-2013 [32]. At the same time, the \(F\) in Model 2 was lower than that in Model 1, regardless of the \(S_{\mathrm{p}}/D\). In addition, the decreasing rate of \(F\) continuously decreased with the increase of \(S_{\mathrm{p}}/D\), illustrating that the pile group effect was weakening, which is consistent with the conclusions presented in the literature [45; 46; 47].  
Figure 10: (**a**) The correlation between the safety factor and the pile diameter. (**b**) The correlation between the maximum compressive stress of piles and the pile diameter under the 1.35 state. (**c**) The correlation between the maximum shear stress of piles and the pile diameter under the 1.35 state. (**d**) The correlation between the maximum displacement of the pile head and the pile diameter under the 1.35 state.  
In the results for the 1.35 state, the maximum compressive stress increased from 15.47 MPa to 59.09 MPa, and the maximum shear stress increased from 7.72 MPa to 29.91 MPa, the maximum displacement of pile head increased from 393.40 mm to 2128.00 mm as \(S_{\rm p}/D\) increased from 1.875 to 8 in Model 1 (Figure 11b-d). Furthermore, as \(S_{\rm p}/D\) increased from 1.875 to 5 in Model 2, the maximum compressive stress, the maximum shear stress, and the maximum displacement of pile head increased from 17.28 MPa to 53.90 MPa, from 9.84 MPa to 29.67 MPa, and from 1198.00 mm to 4432.00 mm (Figure 11b-d), respectively, presenting higher values than those in Model 1.  
Figure 12 exhibits the displacement arch in the Y direction 10 m below the pile top in Model 1. The arching effect was clearly shown when \(S_{\rm p}/D\) = 1.875. Then, the effect showed a weakened trend with the increase of \(S_{\rm p}/D\) until it was no longer obvious that \(S_{\rm p}/D\) was greater than or equal to 6.  
Figure 13 shows the plastic zone distribution in the middle of two piles in Model 1 for a variety of \(S_{\rm p}/D\)s in the limit equilibrium state. The plastic zones were separated if \(S_{\rm p}/D\leq 3\), indicating that \(S_{\rm p}/D\) = 2 was an optimal parameter for the evaluation of \(D\) in Section 5.4. However, the originally separated plastic zones gradually connected together as \(S_{\rm p}/D\) increased, as shown in Figure 13c,d.  
Figure 11: **(a)** The correlation between the \(F\) and the \(S_{\rm p}/D\). **(b)** The correlation between the maximum compressive stress of piles and the \(S_{\rm p}/D\) under the 1.35 state. **(c)** The correlation between the maximum shear stress of piles and the \(S_{\rm p}/D\) under the 1.35 state. **(d)** The correlation between the maximum displacement of the pile head and the \(S_{\rm p}/D\) under the 1.35 state.