## 3 Results
### Analysis of Landslide Deformation and Damage in the Study Area  
Numerous researchers domestically and internationally have investigated the combination of the strength reduction method and numerical analysis to calculate the stability coefficient of the slope, in order to overcome the drawback that the numerical analysis method cannot give the stability coefficient of slope intuitively, such as the limit equilibrium method [18; 19; 20; 21; 22]. The principle behind the strength reduction method is to continually reduce the rock slope's shear strength parameter, and repeat the iterative calculation until the slope reaches the critical failure state. The reduction coefficient at this time represents the stability coefficient of the slope. That is the following:  
\[C^{\prime}=\frac{C}{FS} \tag{5}\]  
\[\phi^{\prime}=arctan\left(\frac{tan\phi}{FS}\right) \tag{6}\]  
The slope stability coefficient calculated by the working condition II is 1.097, while that calculated by the working condition IV is 0.992. Rainwater infiltration by rainfall stagnation is the primary cause of slope instability. In order to analyze the critical state when the slope is unstable, the calculation and analysis scheme as shown in Table 3 is established.  
The plastic strain diagrams and \(X\)-axis displacement diagrams of the four cases are analyzed (see Figures 7 and 8).  
Figure 6: Statistics of stability coefficients for different working conditions in the study area.  
Figure 8: X-direction displacement diagrams at the top of the slope, where the unit is m. (**a**) Working condition V; (**b**) Working condition VI; (**c**) Working condition VII; (**d**) Working condition VIII.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Condition** & **Rainfall Intensity** & **Rainfall Duration** & **Rainfall** \\  & **(mm/d)** & **(d)** & **Stagnation (d)** \\ \hline Working condition V & 80 & 0.4 & - \\ Working condition VI & 80 & 1 & - \\ Working condition VII & 40 & 1 & 0.2 \\ Working condition VIII & 80 & 1 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Rainfall design table under different working conditions of rainfall stagnation.  
Figure 7: Plastic strain diagrams. (**a**) Working condition V; (**b**) Working condition VI; (**c**) Working condition VII; (**d**) Working condition VIII.  
As indicated in Figure 7, the foot of the slope experiences the maximal strain, and the maximum strain at the critical state of slope instability is 0.078. The primary cause of the strain at the foot is that rainfall causes the mudstone to soften and the strength to deteriorate. So, the stresses accumulate here. Secondly, the location of the foot of the slope was influenced by the construction excavation, creating a local void at the foot and increasing the slope angle of the slide surface here. This increases the local sliding force and reduces the safety stability coefficient. Similarly, it can be seen from Figure 7 that the critical state of slope failure is that the rainfall intensity of 80 mm lasts for 1 day and stagnates for 5 h. At this time, the plastic strain runs through the entire landslide zone, causing the cutting slope to fail.  
Figure 8 displays the maximum displacement of the \(X\)-axis of the slope top. Compared with the four plots, it can be seen that the maximum displacement decreases from 466.025 mm to 151.834 mm with the increase in rainfall, indicating that the slope is prone to local instability.