## 2 Laboratory Investigation of the Effect of a Landslide on Stabilizing Piles
### Analysis of the Test Model Results  
The bending moment of the stabilizing pile in the physical model test is obtained through the pile body strain conversion. The bending moment at the corresponding measured point along the length of the pile can be calculated as:  
\[M=\begin{matrix}W\times E_{s}\times\left(\varepsilon_{h}-\varepsilon_{q}\right) /2\\ W=bh^{2}/6\end{matrix} \tag{1}\]  
where \(W\) is the section modulus in bending, and \(b\), \(h\) are the section width and height of the pile, respectively. \(E_{s}\) is the elastic modulus of the pile, which is considered 1.68 GPa in this study, and \(\varepsilon_{h}\)\(\varepsilon_{q}\) are the strains measured at the front and back of the pile, respectively.  
The experiment was divided into five loading stages, starting at times 0, 10, 20, 30, and 50 min. The load remains constant for 10 min in the first, second and third stages, and given it is gradually difficult to apply load with the load increasing and the applied load is instable, the interval time is approximately set to 20 min in the fourth stage [41, 44]. By monitoring the strain along the length of the pile, the bending moment can be determined using Equation (1), see Figure 7.  
Figure 5: The strength testing of the samples.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Rock Type**} & **Density \(\rho\)** & \begin{tabular}{c} **Elastic** \\ **Modulus E** \\ **(GPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio \(\mu\)** \\ \end{tabular} & \
\begin{tabular}{c} **Cohesion \(c\)** \\ **(kPa)** \\ \end{tabular} &
\begin{tabular}{c} **Friction Angle** \\ \(\varphi\) **(°)** \\ \end{tabular} \\ \hline Stabilizing pile & 2150 & 1.68 & 1.16 & 1300 & 22 \\ Sliding body & 1870 & 0.009 & 0.02 & 24 & 15 \\ Hard rock & 2160 & 2.42 & 1.81 & 5160 & 30 \\ Soft rock & 1960 & 2.31 & 0.77 & 400 & 29 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mechanical parameters of the similar materials.  
Figure 6: The raw materials of the mode.  
The pressure sensor monitored the values applied to the sliding body, as shown in Figure 8. By using the indicator monitoring of the top displacement of the middle stabilizing pile, the displacement of the mid-pile head was recorded when the load at each stage reached the stable condition, as shown in Figure 9.  
Figure 8: Loading curve with time.  
Figure 7: Bending moment diagram for the stabilizing pile.  
Figure 9: Top displacement of the stabilizing pile.  
The distribution of the moment is obtained by using MATLAB (cubic spline interpolation). Through the first and second derivation of the bending moment, the distribution of the pile shear force and the distribution of the geotechnical resistance were obtained, respectively, and the displacement distribution of the pile body was obtained from the second integral of the bending moment.  
The displacement of the top pile is in accordance with the measured values (Figure 13), while the increase of the load classification, the point of the shear force that is zero, gradually moves down (Figure 11). It is also illustrated that the point of the maximum moment value gradually moves downward. The results illustrate that the loading ways and time should be considered in the design of stabilizing piles.