# 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
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Young’s modulus & E\({}^{\prime}\) (MPa) & 50 \\ \hline Poisson’s ratio & \(\
u^{\prime}\) (-) & 0.25 \\ \hline Effective cohesion & \(c^{\prime}\) (kPa) & 50 \\ \hline Effective friction angle & \(\varphi^{\prime}\) (\({}^{\circ}\)) & 25 \\ \hline Dilation angle & \(\psi\) (\({}^{\circ}\)) & 0 \\ \hline SWCC parameter & g\({}_{\text{a}}\) (m\({}^{-1}\)) & 0.01 \\ \hline SWCC parameter & g\({}_{\text{n}}\) (-) & 1.3 \\ \hline SWCC parameter & g\({}_{\text{l}}\) (-) & 0.5 \\ \hline Bulk water unit weight & \(\gamma_{\text{w}}\) (kN/m\({}^{3}\)) & 9.81 \\ \hline Unsaturated soil unit weight & \(\gamma^{\prime}\) (kN/m\({}^{3}\)) & 16 \\ \hline Saturated soil unit weight & \(\gamma_{\text{s}}\) (kN/m\({}^{3}\)) & 18 \\ \hline Void ratio & e\({}_{\text{o}}\) (-) & 0.8181 \\ \hline Residual saturation degree & S\({}_{\text{r}}\) (-) & 0.2 \\ \hline Saturated saturation degree & S\({}_{\text{s}}\) (-) & 1.0 \\ \hline Saturated permeability & k\({}_{\text{s}}\) (cm/s) & \(10^{-4}\) \\ \hline Geostatic stress coefficient & K\({}_{\text{o}}\) (-) & 0.3333 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical and hydro-mechanical parameters of the simulated soil material. For the reference case and the 3.6 mm/h rain, the average infiltration amount was 28.4 mm (33% of the rain) and the runoff 58.0 mm (67% of the rain). Notice that fine-grained soil was simulated, thus a low percentage of rain infiltration was expected. For the very low rainfall of 0.8 mm/h, this amount rises to 77%, while for the extreme rainfall of 17 mm/h, this amount becomes 19%. An essential aspect of these amounts is that they are averages and do not entirely reflect the suction conditions and the stability. Although 33% of the rain infiltrates the slope for the baseline model, near the toe of the slope, all the rain infiltrates, raising the groundwater and crucially altering stability (i.e., the failure surface shape, failure surface place, and the soil's effective stresses and deformations). The reference case has a very high initial SF, equal to 2.08; the failure surface (Figure 8) is a typical circular surface on homogeneous slopes. This high SF is expected, as the reference model presents a mild slope of medium height for mining excavations. Soil strength is enhanced by the artificial cohesion resulting from matric suction (Figure 9a). At the initial stage, the matric suction--and the related artificial cohesion--increase linearly over the groundwater table, reaching 280 kN/m\({}^{2}\) at the slope's crest. As the rainfall infiltrates the slopes, the suction decreases at the slope's edges, where the rainfall infiltrates. Figure 9b illustrates the final matric suction distribution in the slope at the end of the one-day rainfall. As time passes, rainfall infiltrates deeper into the soil, and thus a new distribution emerges with zero suction at the slopes' edges and the groundwater table. For fine-grained materials, such as those investigated herein, the suction reduction is the primary mechanism of rainfall affecting slope stability. Figure 10a displays the effect of the SWCC material parameter, g\({}_{\text{a}}\), on the pit slope's safety factor for a 3.6 mm/h intensity rainfall event that lasts 24 h (total rainfall height equal to 86.4 mm). The selected values of the SWCC material parameter, g\({}_{\text{a}}\), cover the range of a fine-grained over-consolidated clayey soil. The safety factor reduction rate increases significantly with the decrease of parameter g\({}_{\text{a}}\). In particular, for g\({}_{\text{a}}\) values equal to 0.001 m\({}^{-1}\), 0.005 m\({}^{-1}\), and 0.01 m\({}^{-1}\), SF reduces with a rate of 16.5%, 10.0%, and 4.7%, respectively. As g\({}_{\text{a}}\) increases further (0.05 m\({}^{-1}\) and 0.1 m\({}^{-1}\)), the slope safety factor is practically constant during rainfall. This difference between the five examined cases is attributed to the shape of the SWCC and the permeability function.