## 4 Slope Dynamic Stability Analysis
### Slope Stability Calculation  
#### 4.1.1 Calculation of Initial Slope Stability  
According to the original survey results, the slope strata can be divided into quaternary deposits, weathered layer, moderately weathered sandstone with mudstone and moderately weathered basalt. The calculation parameters for the initial stability of the slope were set according to laboratory test results, as presented in Table 4.  
After achieving initial equilibrium, the minimum safety factor of the slope in its natural state was determined to be 1.212, indicating that the slope is in a stable condition. To provide a more visual representation of the safety factor of the three-dimensional slope, the safety factor was extracted using the Fish function and displayed as a cloud map, as shown in Figure 13. The figure shows that the slope exhibits a minimum safety factor of 1.212 and a maximum safety factor of 1.737. Following a heavy rainfall event in September 2020, the slope showed signs of sliding. Therefore, calculations were conducted to assess the stability of the slope after the rainfall event. The simulated rainfall scenario involved two components of fluid-soil coupling. The first component pertains to the region below the groundwater level, which is already \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multirow{2}{*}{**Density (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Young’s**} & \multirow{2}{*}{**Poisson’s Ratio**} & \multirow{2}{*}{**Cohesion (kPa)**} & \multicolumn{2}{c}{**Internal Friction**} \\  & & & **Modulus (kPa)** & & & **Angle (\({}^{\circ}\))** \\ \hline Quaternary deposits & 1850.00 & 2.00 \(\times\) 10\({}^{4}\) & 0.30 & 23.00 & 24.00 \\ Weathered layer & 2200.00 & 1.00 \(\times\) 10\({}^{6}\) & 0.28 & 40.00 & 15.00 \\ Moderately weathered sandstone & 2300.00 & 3.00 \(\times\) 10\({}^{7}\) & 0.25 & 70.00 & 35.00 \\ with mudstone & Moderately & & & & & \\ weathered basalt & 2900.00 & 4.00 \(\times\) 10\({}^{7}\) & 0.20 & 75.00 & 55.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model calculation parameter table. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multirow{2}{*}{**Quaternary Deposits**} & \multicolumn{4}{c}{**Weathered Layer**} & \multicolumn{4}{c}{**Interbedded Sandstone and**} & \multicolumn{4}{c}{**Moderately Weather**} \\  & & & & & & & **Shale Layer** & & & **Basalt Layer** \\ \hline Parameter & Y\({}_{1}\) & C\({}_{1}\) & \(\varphi_{1}\) & Y\({}_{2}\) & C\({}_{2}\) & \(\varphi_{2}\) & Y\({}_{3}\) & C\({}_{3}\) & \(\varphi_{3}\) & Y\({}_{4}\) & C\({}_{4}\) & \(\varphi_{4}\) \\ Unit & MPa & kPa & \({}^{\circ}\) & MPa & kPa & \({}^{\circ}\) & GPa & kPa & \({}^{\circ}\) & GPa & kPa & kPa & \({}^{\circ}\) \\ \hline Original value & 32.8 & 19.7 & 30.3 & 19.3 & 23.1 & 23.4 & 30.6 & 53.9 & 29.9 & 64.2 & 76.2 & 42.6 \\ Improved value & 31.9 & 16.9 & 29.5 & 18.4 & 33.4 & 17.4 & 42.3 & 55.2 & 35.3 & 70.7 & 75.4 & 32.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Inversion results of mechanical parameters of each model. in a saturated state. The second component relates to the region above the groundwater level, where fluid-soil coupling occurs due to rainfall infiltration. For the region below the groundwater level, the fluid-soil coupling was achieved by altering the pore water pressure based on the given groundwater table position. For the region above the groundwater level, which predominantly consists of fourth-grade coarse-grained soil, the infiltration process occurs rapidly. Therefore, a strength reduction method was employed to couple this region. The calculated safety factor cloud map is shown below (Figure 14). From Figure 14, it is evident that the minimum safety factor of the slope after the rainfall is only 0.954, indicating an unstable condition. The high-risk zone is concentrated in the lower-left area of the landslide region, where all safety factors are less than 1.