# Method to Control the Deformation of Anti-Slide Piles in Zhenzilin Landslide
## 3 Methodology and Validation
### Validation of the Calculation Method for the Zhenzilin landslide  
The anti-slide pile (A-type) with a cross-section from A to A\({}^{\prime}\) of the Zhenzilin landslide was selected in the calculation. The spacing between the piles is 6m. The moment of inertia of the anti-slidepile (I) is equal to b \(\times\) a\({}^{3}\)/12 = 4.5 m\({}^{4}\). The Young's modulus (E) of the anti-slide pile is 30 GPa. The driving force of the landslide (p) was 1500 kN/m. Each pile bears driving force of the landslide in the range of 6m [2]. The additional load that acted on the anti-slide pile because of highway toll stations is 50 kN/m. At present, the total load is 1550 kN/m. The upper layer of mudstone is 1 m (\(\Delta\)y\({}_{1}\) = 1m). The lower limestone layer is approximately 7.5 m (\(\Delta\)y\({}_{2}\) = 7.5m). Therefore, the buried length of the anti-slide pile is 8.5 m (h = 8.5m), and the pile length above the slip surface is 15 m (h\({}_{1}\) = 15m). The upper mudstone and limestone near the sliding surface are affected by landslide sliding, for which the weathering conditions should be allowed. A reduction factor, g, of 0.5 was taken for the modulus of the subgrade reaction [31]. Hence, the modulus of subgrade reaction of the first rock was k\({}_{\text{lg}}\) = g \(\times\) k\({}_{1}\) = 0.5 \(\times\) 10\({}^{5}\) kPa/m, and the modulus of the subgrade reaction for the second rock was k\({}_{\text{2g}}\) = g \(\times\) k\({}_{2}\) = 1.7 \(\times\) 10\({}^{5}\) kPa/m.  
To compare the calculation method proposed herein and the single-layer calculation method presented in reference [29], the modulus of the subgrade reaction of the single-layer below the sliding surface (k) is set as 1.7 \(\times\) 10\({}^{5}\) kPa/m, while the driving force of the landslide (p) is considered in two cases: new additional load (p = 1550 kN/m) and only landslide thrust (p = 1500 kN/m). Other parameters of the anti-slide pile were the same as above. The above parameters are substituted into Equation (10), and then the displacement of the pile along depth is as shown in Figure 6.  
The finite element method is often used to study the stress-strain relationship of pile-soil using an elastoplastic rock mass model [37; 38]. To compare the difference between the calculation method presented above and the finite element method, ABAQUS 6.14.3 program was used to study the pile deformation of the Zhenzilin landslide. The pile and bedrock geometry was built using a plane-strain geometry model. The length of the model in the x-direction equaled 20 m, the width along the y-direction equaled 5 m, and the height along the z-direction equaled 30 m. The bedrock was divided into two layers simulated using an elastic-plastic model satisfying [PERSON]'s yield criterion and modeled using C3D8 hex elements. The properties of the bedrock are listed in Table 1. The pile was considered to be made of a linear elastic material and modeled using C3D8 hex elements. The properties of the pile were as described above. The model comprised 4966 elements, 6586 nodes, and 18,708 variables. The driving force of the landslide (p) was considered in the form of an additional  
Figure 6: Calculation results of pile displacement under different methods.  
load (p = 1550 kN/m) and landslide thrust (p = 1500 kN/m); the resulting displacement of the pile along the depth is shown in Figure 6.  
The displacement of the pile head calculated from the finite element method with the driving force of the landslide (p = 1500 kN/m) was 126 mm; this result exceeds that calculated using the proposed calculation method (approximately 124 mm). When considering only the landslide thrust (p = 1550 kN/m), the measured displacement of the pile head was 132 mm. This result exceeds that calculated using the proposed calculation method (approximately 128 mm). However, the difference in the results is small, thereby implying that the proposed calculation method can be employed in engineering applications.