## 5 Stability Analysis  
The stability of a slope depends on its geometry, its material properties, and the position of the phreatic surface [37]. The geometry and the material properties of the Xigou tailings dam were obtained according to the results of the geotechnical investigations and laboratory experiments, as listed in Table 3. The previously calculated effect of the three-dimensional FEM was used to locate the phreatic surface [38]. For simplicity, the stability of the tailings dam can be viewed as a two-dimensional plane-strain problem, and the stability analysis can be performed using the Slope/w software packages in the basis of saturated soil mechanism [39]. According to the Chinese national codes, ordinary rigid LEMs, including the Swedish method of slices and a simplified Bishop method, are recommended to obtain a factor of safety (FOS) and analyze the stability of tailings dams under different conditions. (a) For the Swedish method of slices, the FOS is written as  
\[F_{s}=\frac{\Sigma[c^{\prime}j_{b}j\sec\alpha_{j}+(W_{j}\cos\alpha_{j}-u_{j}b_ {j}\sec\alpha_{j})\tan\phi^{\prime}_{j}]}{\Sigma W_{j}\sin\alpha_{j}} \tag{7}\]  
(b) For the simplified Bishop's method of slices, the FOS is written as  
\[F_{s}=\frac{\Sigma[c^{\prime}j_{b}j+(W_{j}-u_{j}b_{j})\tan\phi^{\prime}]\frac {1}{m_{j}}}{\Sigma W_{j}\sin\alpha_{j}+\Sigma Q_{j}e_{j}/R} \tag{8}\]  
\[m_{j}=\cos\alpha_{j}+\frac{\tan\phi^{\prime}_{j}\sin\alpha_{j}}{F_{s}} \tag{9}\]  
where \(b_{j}\) is the width of the \(j\)th slice; \(\alpha_{j}\) is the angle of the \(j\)th slice bottom with the horizontal slice; \(W_{j}\) is the weight of the slice; \(c^{\prime}\) and \(\phi^{\prime}\) are the effective cohesion and the effective angle of friction that develop along the potential failure surface, respectively; and \(u_{j}\) is the average pore water pressure at the bottom of the \(j\)th slice; \(Q_{j}\) is the horizontal inertial force; \(R\) is radius of circular failure surface; and \(e_{j}\) is vertical height between \(Q_{j}\) and the center of the failure circle. To estimate the stability of the tailings dam, the FOSs of the heightened tailings dam were calculated under various conditions, such as a normal water level, an extremely high water, and special operations. The seepage-proof system played a significant role in the stability. For comparison, the cases of no drainage and horizontal drainage were estimated. At the same time, considering the randomness of the tailings drainage process and the uncertainty of sedimentation, the FOSs under the condition of a change in the permeability coefficient were calculated. Under the seismic working condition, the FOSs were obtained using a quasi-static method according to the National Code of China [31]. An earthquake ground acceleration of 0.15 g was used based on the location of the mine, which was classified as being in earthquake zone VII. The calculation results, presented in Figure 17 and Table 4, show that when the new drainage system is implemented properly, the tailings dam is safe under a variety of working conditions, and the safety factors, including the Swedish method of slices and the simplified Bishop's method, meet the requirements. When there was no drainage system, the slope was unstable under different working conditions. If only the horizontal drainage system was used, the FOSs met the national standard under the normal water level, while the FOSs were marginally lower than the value required by the national code under the extremely high level; for the seismic working condition, the FOSs of the Swedish method of slices and the simplified Bishop's method were 1.106 and 1.165, respectively, and marginally satisfied the national code. Therefore, the design of the new drainage system effectively reduced the phreatic surface and enabled the higher tailings dam to meet the relevant national requirements for sliding stability.