# 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
When the k\({}_{1}\) value increases, the maximum absolute value of pile internal forces and the displacement of the pile decrease steadily. Figure 8c, Figure 9c, and Figure 10c indicate that pile displacement decreases with an increasing embedded length; however, following a nonlinear manner. To better quantify this relationship, the embedded ratio (\(\varepsilon\)) of the anti-slide pile can be defined as the ratio of the depth of the pile-embedded section (h) to the length of the pile (h + h\({}_{1}\)). The buried length of the anti-slide pile is 8.5 m (h = 8.5 m) under the sliding surface, and the pile length above the sliding surface is 15 m (h\({}_{1}\) = 15); therefore, the current embedded ratio of the anti-slide pile is 0.362. The corresponding displacement of the pile head is 123 mm (see Figure 8c). According to the principle of equivalence ( E*I=E*0.01625*\(\pi\)*\({}^{\rm{th}}\)De\({}_{\rm{eq}}\)4) [39], the rectangular cross-section is equivalent to a circular solid pile with an equivalent diameter (De\({}_{\rm{eq}}\)) of 3.095 m; therefore, the current normalized displacement of the pile head (\(\Gamma\)/De\({}_{\rm{eq}}\)) is 0.0397. In this way,  
Figure 10: Calculated values of internal forces for piles of various embedded lengths with k\({}_{1}\) = 130,000 kPa/m: (**a**) shear force; (**b**) bending moment; (**c**) horizontal displacement. differently embedded ratios of piles can be calculated, and the corresponding normalized displacement of the pile head can be determined. The variation of the normalized displacement of the pile heads with the embedded ratio of the piles at various values of modulus of subgrade reactions of the first weak bedrock (k\({}_{1}\)) was plotted in Figure 11.  
When the displacement of the pile head was limited to the same allowable value, the embedment ratio was observed to differ in accordance when using different values of the modulus of subgrade reaction of the first weak bedrock (refer to Figure 11). According to industrial standards [40], the allowable value of pile-head deformation (\(\Gamma_{\text{max}}\)) must not exceed 10 cm. When \(\Gamma_{\text{max}}\) = 10 cm, \(\Gamma_{\text{max}}\)/D\({}_{\text{eq}}\) = 0.0323, the corresponding embedded ratio (\(\varepsilon\)) of the pile was determined as 0.411 with k\({}_{1}\) = 50,000 kPa/m from Figure 11, and the reasonable embedded length (h) equaled 10.5 m, then the current normalized reasonable embedded length (h/h\({}_{1}\)) was 0.7. In this way, other reasonable embedded lengths (h) of piles can be calculated using different values of subgrade reaction moduli of the first weak bedrock (k\({}_{1}\)). Subsequently, an normalized equation between the reasonable embedded length (h) and subgrade reaction modulus of the first weak bedrock (k\({}_{1}\)) was fitted in, which the k\({}_{1}\) was normalized by the standard atmospheric pressure (pa) of 101 kPa, as follows:  
\[\frac{\text{h}}{h_{1}}\ =\ 1.48\times\left(\frac{k_{1}\times D_{\alpha\text{t}}}{pa }\right)^{-0.103} \tag{11}\]  
The relationship between the reasonable embedded length (h) and modulus of the subgrade reaction of the first weak bedrock (k\({}_{1}\)) is nonlinear. If there are some factors that may lead to a decrease in the (k\({}_{1}\)) value, it may be necessary to increase the reasonable embedded length of the pile in practical applications.