## 4 Discussion
### Influence of Initial Inclination Angle of Pile Shaft  
In this subsection, the influence of the initial inclination angle \(\varphi_{IN}\) for the pile shaft is analyzed by setting up its value as 0, 5 mrad, 10 mrad and 15 mrad, respectively. Assuming that the downhill direction is positive in direction, the relative results are illustrated in Figure 13. It is clear that when the \(\varphi_{IN}\) is varying from 0 to 15 mrad, the maximum horizontal deformation for the pile shaft is increasing by 4.91%, 9.74% and14.66%, respectively; the maximum bending moment for the pile shaft is increasing by 6.24%, 12.48%, and 18.71%, respectively. Therefore, this indicates that there is an obvious enlargement effect caused by the increase in \(\varphi_{IN}\) on the lateral response of the pile shaft when the length of the free segment is adequate.  
Similarly, in order to further delineate the influences evoked by the initial inclination angle over the lateral responses of the pile shaft, it will be of interest to examine several parameters, including fixed base of the maximum lateral displacement \(\eta_{\text{ymax},\varphi_{IN}}\), that of the maximum bending moment \(\eta_{\text{Mmax},\varphi_{IN}}\), the sequential variation ratio of maximum horizontal deformation \(\Delta y_{\text{max},\varphi_{IN}}\) and that of the maximum bending moment \(\Delta M_{\text{max},\varphi_{IN}}\), in which the corresponding parameters are, respectively, defined as:  
\[\begin{array}{l}\eta_{\text{ymax},\varphi_{IN}}=\frac{y_{\text{max}}}{y_{ \text{max},\varphi_{IN}^{2}}=0}\\ \eta_{\text{Mmax},\varphi_{IN}}=\frac{M_{\text{max},\varphi_{IN}^{2}}}{M_{ \text{max},\varphi_{IN}^{2}}=0}\end{array} \tag{44}\]  
Figure 13: Influence of initial angle of pile on pile lateral behavior. (**a**) Lateral displacement/mm; (**b**) bending moment/kN \(\times\) m.  
\[\Delta y_{\max,\varphi_{IN}}=\frac{y_{\max,\varphi_{IN}-y_{\max, \varphi_{IN}-1}}}{y_{\max,\varphi_{IN}-\varphi_{IN}-1}} \tag{45}\] \[\Delta M_{\max,\varphi_{IN}}=\frac{M_{\max,\varphi_{IN}-M_{\max, \varphi_{IN},j-1}}}{M_{\max,\varphi_{IN},j-1}}\]  
The analysis results involved in the above definitions and the \(\varphi_{IN}\) are listed in Figure 14. It is shown that there is a linear increase relationship between the \(\varphi_{IN}\) and both the \(\eta_{y\max,\varphi_{IN}}\) and \(\eta_{M\max,\varphi_{IN}}\), which indicates that the increase in \(\varphi_{IN}\) has an amplification effect on those parameters. Moreover, the gaps of the increments between \(\eta_{y\max,\varphi_{IN}}\) and \(\eta_{M\max,\varphi_{IN}}\) generated by changing \(\varphi_{IN}\) are gradually distinguished; in addition, compared with those of the \(\eta_{y\max,\varphi_{IN}}\) and \(\eta_{M\max,\varphi_{IN}}\), the relationships between the \(\varphi_{IN}\) and \(\Delta y_{\max,\varphi_{IN}}\) or \(\Delta M_{\max,\varphi_{IN}}\) initially experienced a non-linearly decreasing trend and then flattened, which revealed that, as the \(\varphi_{IN}\) is increasing, there is an attenuation effect for the influence of the \(\Delta y_{\max,\varphi_{IN}}\) and \(\Delta M_{\max,\varphi_{IN}}\) over the lateral response of the pile shaft, and such effect is unceasingly diminishing.