# 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
According to the calculation profile and stratigraphic parameters provided by the survey, the landslide thrust is calculated using the transfer coefficient method recommended by the code, and the landslide thrust at the proposed pile location is about 548.64 kN/m (the safety factor is taken as 1.2). The load-sharing ratios obtained under static and dynamic working conditions can be calculated separately to obtain the load-sharing table, as shown in Table 5.  
Based on the landslide form and thrust level of the treatment project, the engineering design proposes utilizing a minipile group for landslide remediation. As shown in Figure 6, three rows of minipiles with 0.15 m pile diameter, 1.5 m pile spacing, and 1.4 m row spacing are used in a plum-shaped arrangement. In order to simplify the engineering calculation and reduce the construction difficulty, the same design section is used for the three rows of piles, and the maximum thrust force is \(p=225.5\) kN/m. It is assumed that the thrust is triangularly distributed for the design calculation of the minipile and the calculation method is based on the calculation theory in Section 1, and the \"m-m\" method is used. The values of foundation coefficients are taken as shown in Table 6 below. The calculation assumes a fixed pile bottom, and the determined length of the pile is based on empirical evidence to ensure that the minipile can penetrate the clay rock layer by at least 3 m, which is temporarily set as 18 m in this study. The calculated displacement, internal force, and earth pressure curves are shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline
**Stratigraphic** & **Q\({}_{4}\)del Stacking Layer** & **Red Clay** & **Pebble and Gravel Layer N\({}_{2}\)2** & **Claystone N\({}_{2}\)1** \\ \hline Foundation factor m(kPa/m2) & 3500 & 5000 & 9000 & 12000 \\ \hline \end{tabular}
\end{table} 
Table 6: Table of values of foundation coefficients. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Serial Number** & **Stratigraphic** &
\begin{tabular}{c} **Modulus of** \\ **Elasticity/MPa** \\ \end{tabular} & **C\({}_{\textbf{k}}\) (kPa)** & **\(\Phi_{\textbf{k}}\) (°)** & **\(\Gamma\) (kN/m°)** & **Poisson’s Ratio** \\ \hline
1 & Sliding Body & 20.0 & 23.84 & 19.18 & 19.2 & 0.32 \\
2 & \(\text{Q}_{4}\)del Stacking & 20.0 & 24.10 & 20.12 & 19.2 & 0.32 \\  & layer & 25.0 & 27.83 & 20.95 & 19.6 & 0.30 \\
3 & Red clay & 30.0 & 34.25 & 22.15 & 19.8 & 0.27 \\
4 &
\begin{tabular}{c} Layer N\({}_{2}\)2 \\ \end{tabular} & 40.0 & 42.04 & 23.65 & 19.8 & 0.25 \\
5 &
\begin{tabular}{c} Sliding surface \\ \end{tabular} & — & 15.3 & 14.6 & — & — \\ \hline \end{tabular}
\end{table} 
Table 4: Table of surveyed stratigraphic parameters. \begin{table}
\begin{tabular}{c c c c} \hline
**Pile Position** & **Rear Pile** & **Middle Row Pile** & **Front Row Piles** \\ \hline Share ratio & 0.411 & 0.348 & 0.241 \\ Load sharing (kN/m) & 225.5 & 190.9 & 132.2 \\ \hline \end{tabular}
\end{table} 
Table 5: Load sharing table. From the figure, it can be seen that the maximum bending moment is about 15.44 kN-m, and the maximum shear force is about 35.25 kN, from which the reinforcement calculation is carried out. In order to facilitate the construction, a steel pipe concrete minipile is used for this minipile, so according to the Technical Specification for Steel Pipe Concrete Structure (GB50936-2014) [30], Q235 steel pipe with 152 mm outer diameter is used and C30 fine stone concrete is injected inside, according to the wall thickness was calculated to be about 2.7 mm according to the requirements of bending shear resistance, so the steel pipe specification was selected as \(\upmu\)152 mm \(\times\) 3 mm. According to the calculation results in the previous section, the optimal design is carried out with PL\({}_{\text{max}}\) = 18 m, PL\({}_{\text{min}}\) = 10 m, and setting the allowable safety factor [Fs] = 1.40.