# Method to Control the Deformation of Anti-Slide Piles in Zhenzilin Landslide
## 5 Discussion
### Effect of The Embedded Length on the Deformation and Internal Forces of the Pile  
When the modulus of the subgrade reaction of the first weak bedrock (k\({}_{1}\)) is maintained at 70,000 kPa/m, the value of the maximum shear force of the pile is maintained at 9300 kN at the slip surface as the embedded length (h) increases from 8.5 m to 11.5 mm. The maximum negative shear force value of the pile decreases by 29.5% from 11,937 to 8414 kN with its depth shifting down below the slip surface (refer to Figure 8a). The maximum bending moment of the pile increases by 6.3% from 54,291 to 57,747 kN.m as the embedded length increases from 8.5 m to 11.5 m, and the position of the maximum bending moment of the pile is approximately 2 m below the slip surface (refer to Figure 8b). The displacement of pile head decreases by 29% from 123 to 87 mm as the embedded length increases from 8.5 m to 11.5 mm (refer to Figure 8c).  
When the modulus of subgrade reaction of the first weak bedrock (k\({}_{1}\)) is kept at 100,000 kPa/m, the response of the pile is shown in Figure 9. The value of maximum positive shear force of the pile is 9300 kN at the slip surface, irrespective of the increasing of the embedded length from 8.5 m to 11.5 mm. The value of the maximum negative shear force of the pile decreases by 29% from 11,438 to 8124 kN. The maximum bending moment of the pile increases by 5% from 53,742 to 56,443 kN.m with the embedded length increasing from 8.5 m to 11.5 m, and the position of the maximum bending moment of the pile is approximately 2 m below the slip surface. The displacement of the pile head decreases by 28.4% from 116 to 83 mm as the embedded length increases from 8.5 m to 11.5 mm. When the modulus of subgrade reaction of the first weak bedrock (k\({}_{1}\)) is increased to 130,000 kPa/m, similar response of the piles are observed as shown in Figure 10.  
The above comparisons demonstrate that when the embedded length of an anti-slide pile increases, the horizontal displacement on the pile and its maximum absolute shear force reduce. However, the bending moment of the pile demonstrates the opposite trend because an increase in pile length and change in the force arm increase the bending moment of the pile.  
Figure 11 shows the increase in the embedded ratio (\(\varepsilon\)) of a pile as the modulus of the subgrade reaction of the first weak bedrock (k\({}_{1}\)) decreases when the normalized displacement of the pile head remains unchanged. The relationship between the reasonable embedded length (h) of a pile and the subgrade reaction modulus of the first weak bedrock (k\({}_{1}\)) is power function. In engineering practice, increasing the embedded length (h) of the anti-slide pile may result in increasing cost. However, decreasing the embedded length (h) of the anti-slide pile may have the risk of not ensuring safety and the required landslide slope stability. Hence, Equation (11) is useful to determine the optimally reasonable embedded length of the pile.  
The modulus of the subgrade reaction of the first weak bedrock (k\({}_{1}\)) was 50,000 kPa/m in the Zhenzilin landslide; hence, the reasonable embedded length of the pile was 10.04 m based on Equation (11). However, the original designed embedded length (h) was only 8.5 m, which may be the main reason for the excessive displacement of the pile head in the Zhenzilin landslide. The deformation of the pile is highly dependent on the subgrade reaction modulus. Many scholars have proposed different calculation formulas [41; 42], but they all have a certain scope of application, and no universally applicable formula has been formed. In our engineering practice, a range of values is suggested [36], and we adopt a linear interpolation. Further studies are needed to study the rock-structure interaction to determine the accurate value of the subgrade reaction modulus.