# Study on the Optimization of Pile Length of Micropiles in Soil Landslides
## 2 Methods
### Optimization of Micropiles Length Based on Numerical Simulation
#### 2.4.3. Programmatic Implementation of Optimization Algorithms
Based on the continuity conditions of displacement, rotation, bending moment, and shear force at the sliding surface position of the micropile, combined with the recursive calculation equation derived from Equation (6), the following linear equation group can be obtained by taking the five points near the sliding surface as shown in Figure 3: X \(-\) 2, X \(-\) 1, X, X + 1, X + 2:  
Displacement continuity: \(y_{X}=y_{X\prime}\)  
Continuous cornering: \(y_{X+1}-y_{X-1}=-(y_{X\prime+1}-y_{X\prime-1})\)  
Shear continuity: \(-y_{X-2}+2y_{X-1}-2y_{X+1}+y_{X+1}=y_{X\prime-2}-2y_{X\prime-1}+2y_{X\prime+1 }-y_{X\prime+2}\)  
Continuous bending moment: \(y_{X-1}+y_{X+1}-2y_{X}=y_{X\prime-1}+2y_{X\prime+1}-2y_{X\prime}\)  
Recurrence formula for the loaded section: \(y_{X}=a_{X}y_{X+1}-b_{X}y_{X+2}+c_{X}\)  
\(y_{X-1}=a_{X-1}y_{X}-b_{X-1}y_{X+1}+c_{X-1}\)  
\(y_{X-2}=a_{X-2}y_{X-1}-b_{X-2}y_{X}+c_{X-2}\)  
Recursive formula for embedded segments: \(y_{X\prime}=A_{X\prime}y_{X\prime+1}-B_{X\prime}y_{X\prime+2}\)  
\(y_{X\prime-1}=A_{X\prime-1}y_{X\prime}-B_{X\prime-1}y_{X\prime+1}\)  
\(y_{X\prime-2}=A_{X\prime-2}y_{X\prime-1}-B_{X\prime-2}y_{X\prime}\)  
A set of ten equations is provided, which can be solved to determine ten unknown displacement variables. Then, according to the corresponding recursive formula, the displacement values of all nodes of the micropile can be iteratively obtained, and the internal force of the micropile and the soil pressure can be further calculated. The \"m-k\" method The main difference between the \"m-k\" method and the \"m-m\" method is that the former uses a constant foundation coefficient in the embedded section of the pile. Based on the \"m-m\" method derivation results mentioned above, the recursive outcomes of embedded section parameters reflect the primary discrepancy between the two calculations. For the \"m-k\" method:  
Parameter recursive formula for the loaded section:  
Initial value: same as the \"m-m\" method; Recursive: same as the \"m-m\" method;  
Parameter recursive formula for the embedded section:  
Initial value: \(C_{3}=2+kb_{0}h^{4}/EI\), the rest are the same as the \"m-m\" method;  
Recursion: \(C_{j}=A_{j-2}A_{j-1}-B_{j-2}-4A_{j}-1+6+b_{0}kh^{4}/EI\); the rest are the same as the \"m-m\" method;  
In the formula \(j\in[4,h_{2}/h+5]\), refer to the previous section for the meaning of other parameters. The continuity condition and recursive equation at the sliding surface for the \"m-k\" method are identical to those of the \"m-m\" method, while the solution approach remains essentially unchanged. This will not be reiterated herein. The m-method and k-method are based on the code to determine the deformation characteristics presented under the action of landslide thrust, i.e., whether it is a rigid or elastic anti-slip pile. This directly affects the form of distribution of soil pressure at the embedded end. The distribution form of earth pressure is determined by the type of judgment through the actual parameter calculation, and the distribution form of the finite element model is determined by the actual force form. Then, the m-m method and m-k method are used to screen out the optimal pile length, which is applied in the finite element model. Numerical simulation rapid modeling technology is the key to the finite difference solution used in the optimization method in this study. In order to achieve the engineering operability of the optimization process, modeling work must be fast, convenient, and easy to master. Therefore, this study designs an automated rapid modeling algorithm for numerical simulation from section to model and briefly introduces this module.