# From Climate Conditions to the Numerical Slope Stability Analysis of Surface Coal Mines
## 5 Numerical Analysis of Slope Stability of Lignite Mines under Extreme Rainfall Events
### Effect of Rainfall on Slope Stability
Higher g\({}_{\text{a}}\) values correspond to lower suction (lower effective saturation degree) and lower soil permeability values within the unsaturated zone. Thus, as the parameter g\({}_{\text{a}}\) increases, the unsaturated soil permeability, k\({}_{\text{w}}\), decreases, and rainwater's infiltration into the unsaturated zone becomes more difficult than before. Indicatively, for the extremes g\({}_{\text{a}}\) = 0.001 m\({}^{-1}\) and g\({}_{\text{a}}\) = 0.1 m\({}^{-1}\), the values of soil's unsaturated permeability, in the area of the slope's crest, are equal to 10\({}^{-5}\) cm/s and 10\({}^{-7}\) cm/s, respectively, i.e., they differ by two orders of magnitude. \begin{table}
\begin{tabular}{c c c c c c} \hline SWCC material parameter g\({}_{\text{a}}\) (m\({}^{-1}\)) & 0.001 & 0.005 & 0.01 & 0.05 & 0.1 \\ \hline Saturated permeability k\({}_{\text{s}}\) (cm/s) & \(10^{-5}\) & \(5\times 10^{-5}\) & \(10^{-4}\) & \(5\times 10^{-4}\) & \(10^{-3}\) \\ \hline Initial groundwater head H\({}_{\text{w}}\) (m) & 10 & 15 & 20 & 30 & 40 \\ \hline Rainfall intensity q (mm/h) & 1.2 & 2.4 & 3.6 & 4.8 & 6 \\ \hline \end{tabular}
\end{table} 
Table 3: Selected values of the investigated parameters. Figure 10b presents the variation of the pit slope SF for different initial groundwater heads; H\({}_{\rm w}\) ranges from a medium shallow (10 m) to a deep (40 m) groundwater table. Before the rainfall, the initial SF increases with the groundwater's head rise--an expected result, since a high groundwater table corresponds to lower SF, whereas a deep groundwater table corresponds to higher SF. During the rainfall event, the safety factor reduction rate decreases with the increase of the groundwater head. The SF's reduction rate for the groundwater head of H\({}_{\rm w}\) = 10 m is 9.5%, for H\({}_{\rm w}\) = 15 m is 7.0%, and for H\({}_{\rm w}\) = 20 m is 4.7%. For the cases of deep groundwater tables corresponding to the high groundwater heads of H\({}_{\rm w}\) = 30 m and H\({}_{\rm w}\) = 40 m, the slope safety factor is practically constant. Again, high suction stresses and low effective saturation degrees develop in the extended unsaturated zones, leading to lower unsaturated permeability, impeding the infiltration procedure. It is noted that the groundwater head of H\({}_{\rm w}\) = 0 m, corresponding to a groundwater table that starts from the ground surface, was also examined. Since this value corresponds to a high groundwater table, the unsaturated zone's extent is quite limited for large suction stresses to develop. Figure 8: Failure surface characterized by large shear strains for the reference slope. Figure 9: Distribution of matrix suction for the reference slope (**a**) at the initial stage and (**b**) at the final stage. Figure 11a presents the SF with time during rainfall for various values of saturated permeability; the permeability range covers fine-grained but not impermeable soil materials. The reduction rate of the SF during rainfall increases slightly with the increase of the saturated soil permeability. For higher saturated permeability values k\({}_{\text{s}}\) = 10\({}^{-3}\) cm/s, 5 \(\times\) 10\({}^{-4}\) cm/s, and 10\({}^{-4}\) cm/s, the SF reduction rates are equal to 5.3%, 5.1%, and 4.7%, respectively. The slope's SF is practically constant for lower saturated permeability values, k\({}_{\text{s}}\) = 5 \(\times\) 10\({}^{-5}\) cm/s and 10\({}^{-5}\) cm/s. Obviously, as the saturated permeability decreases, soil permeability in the unsaturated zone decreases, and hence water infiltration during rainfall becomes more difficult. The observed minor effect is because of the low values of k\({}_{\text{s}}\). Figure 11b presents SF with time for different rain intensities lasting 24 h. As the rainfall intensity increases, the SF reduction rate also increases. The SF is practically constant for the lower rainfall intensity, 0.8 mm/h and 2.2 mm/h (19.2 mm/day and 52.8 mm/day, respectively).