# Method to Control the Deformation of Anti-Slide Piles in Zhenzilin Landslide
## 4 Influencing Factors and Control Methods of Anti-Slide Pile Deformation
### Effect of Thickness of First Weak Bedrock on the Displacement and Internal Force of the Piles  
The thicknesses of the first weak rock (\(\Delta\)y\({}_{1}\)) were 0.5, 1, 1.5, 2, and 2.5 m, and the corresponding thicknesses of the second hard bedrock (\(\Delta\)y\({}_{2}\)) were 8, 7.5, 7, 6.5, and 6 m, while maintaining the slide layer depth at 15 m and pile embedded length of 8.5 m in the calculation. Other parameters are shown in Table 2. Using the above approach, shear force, bending moment, and the displacement of a pile were determined and plotted in Figure 7. \begin{table}
\begin{tabular}{c c c} \hline
**Influential Factors** & **Factors with Fixed Values** & **Values of Factors that Were Varied** \\ \hline h = 8.5 m & \(\Delta\)y\({}_{1}\) = 0.5 m \\ k\({}_{1}\) = \(0.5\times 10^{5}\) kPa/m & \(\Delta\)y\({}_{1}\) = 1 m \\ k\({}_{2}\) = \(1.7\times 10^{5}\) kPa/m & \(\Delta\)y\({}_{1}\) = 1.5 m \\ The thickness of the first weak rock (\(\Delta\)y\({}_{1}\)) & P = 1,550 kN/m & \(\Delta\)y\({}_{1}\) = 2 m \\  & & \(\Delta\)y\({}_{1}\) = 2.5 m \\  & \(\Delta\)y\({}_{1}\) = 1 m & k\({}_{1}\) = \(0.7\times 10^{5}\) kPa/m \\ The modulus of subgrade reaction of the first weak bedrock (k\({}_{1}\)) & k\({}_{2}\) = \(1.7\times 10^{5}\) kPa/m & k\({}_{1}\) = \(1.0\times 10^{5}\) kPa/m \\  & P = 1,550 kN/m & k\({}_{1}\) = \(1.3\times 10^{5}\) kPa/m \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the calculation model under the change of the main influencing factors. With the embedded length of the anti-slide pile maintained at 8.5 m, the horizontal displacement of the pile head increases with the increase of the thickness of the first layer of weak rock below the sliding surface. The pile exhibits a combined flexural and rotational deflection shape with the pile toe kicking out. Two local maximum shear forces were noted at the slip surface and in the embedded bedrock. Similar behavior was obtained in experimental study of piles subjected to soil movement [22, 23]. They are called the maximum positive shear force and maximum negative shear force in the following discussion. As expected, the maximum positive shear force of the pile remains unchanged at the slip surface, however, the maximum negative shear forces increase with increasing thickness of the first weak bedrock. The bending moment of the pile increases first and then decreases. The depth at which the maximum bending moment takes place is approximately 2 m below the slip surface. The behavior of the pile will be discussed further later. Figure 7: Calculated values of internal forces for piles of various thicknesses of first soft bedrock (\(\Delta\)y\({}_{1}\)) with h = 8.5 m: (**a**) shear force; (**b**) bending moment; (**c**) horizontal displacement. Effect of the Modulus of Subgrade Reaction for the First Weak Bedrock on the Reasonable Embedded Length  
The modulus of subgrade reaction of the first weak bedrock was set to change from 70,000 kPa/m to 130,000 kPa/m (i.e., k\({}_{1}\) = 70,000 kPa/m, k\({}_{1}\) = 100,000 kPa/m and k\({}_{1}\) = 130,000 kPa/m) in this study. Other parameter values are listed in Table 2. The results of the internal force and horizontal displacement of the pile with various values of the modulus of subgrade reaction of the first weak bedrock are shown in Figures 8-10. Figure 8: Calculated values of internal forces for piles of various embedded lengths with k\({}_{1}\) = 70,000 kPa/m: (**a**) shear force; (**b**) bending moment; (**c**) horizontal displacement. Figure 9: Calculated values of internal forces for piles of various embedded lengths with k\({}_{1}\) = 100,000 kPa/m: (**a**) shear force; (**b**) bending moment; (**c**) horizontal displacement. Figures 8-10 show that when the value of k\({}_{1}\) is unchanged, the absolute value of the maximum shear force below the sliding surface decreases markedly as the embedded length increases. The horizontal displacement shows the same trend, whereas the maximum bending moment of the pile shows the opposite trend.