# Slope Stability Analysis of Open-Pit Mine Considering Weathering Effects
## 4 Slope Stability Evaluation and Discussion  
Utilizing the FLAC finite software (version 5.00), initial findings revealed that when the black-shale slope underwent 28 days of weathering at the slope angle of 47\({}^{\circ}\), the slope's stability was significantly compromised. To further evaluate the potential for slope failure under different scenarios, a slope stability analysis was performed using the limit equilibrium method [40]. This method involves applying static equilibrium conditions to determine the safety factors, which represent the ratio of resisting forces to the driving forces acting on the potential sliding mass. The static equilibrium conditions are applied in both horizontal and vertical directions to the sliding mass. The resisting forces on the sliding surface are calculated based on the shear strength parameters, including cohesion and internal friction angle. When applying the limit equilibrium method to analyze slope stability in open-pit mines, the slope within the mining area is systematically divided into a sequence of vertical slices with uniform width. For each slice, static equilibrium equations are established in both horizontal and vertical directions. By considering any individual slice, the balance of forces in the X- and Y-directions, as well as the moment balance, are calculated. The Swedish arc method is then utilized to derive the expression for calculating the engineering stability coefficient, as outlined in Equation (1). Additionally, when the pore pressure ratio is known, a specific formula is employed to compute the stability coefficient, as detailed in Equation (2). This approach enables a precise assessment of slope stability in open-pit mines, taking into account various factors that influence stability. \[F=\frac{\sum\limits_{i=1}^{n}\left[\overline{\varepsilon}b_{i}\sec\theta_{i}+ (\gamma h_{i}-\gamma_{w}h_{inv})b_{i}\cos\theta_{i}\tan\overline{\varphi} \right]}{\sum\limits_{i=1}^{n}\left(W_{i}\sin\theta_{i}+Q_{i}\ /R\right)} \tag{1}\]\[F=\frac{\sum\limits_{i=1}^{n}\left[\overline{\omega}b_{i}\sec\theta_{i}+(1-r_{u})W_ {i}\cos\theta_{i}\tan\overline{\varphi}\right]}{\sum\limits_{i=1}^{n}\left(W_{i }\sin\theta_{i}+Q_{i}\ /R\right)} \tag{2}\]  
where \(C\) represent effective stress shear strength index of soil cohesion, KPa; \(\varphi\) is the effective stress shear strength index of internal friction angle; \(\alpha\) represents the moment arm from the center of gravity of the strip to the center of the sliding arc; \(R\) is the radius of the sliding arc, m; \(\theta\) represents the seismic inertial force (horizontal direction), KN; \(W\) is the weight of the strip of soil, KN; \(\theta\) represents the inclination angle of the sliding surface of the strip; and \(r_{u}\) is the ratio of pore pressure, which is the ratio of the weight of the soil column to the weight of the water column. The resisting forces on the slope surface are calculated, taking into account the shear strength parameters specific to the black shale as well as the normal stress exerted on each individual slice. The safety factor, a crucial metric, is defined as the ratio between the resisting forces and the driving forces acting on the potential sliding mass. To accurately assess the slope safety factor during various weathering periods, the physical and mechanical parameters are carefully assigned, drawing upon the results of rigorous laboratory tests. Stability calculations are conducted for the slope at different weathering stages, considering two slope angles of 45 and 47, with the aim of exploring the optimal final slope angle under diverse conditions. Tables 8 and 9 present the calculated safety factors for slopes, considering various combinations of slope angles, heights, and weathering times. For slopes with an angle of 45, it is observed that under identical slope height conditions, the strength of the slope surface rock diminishes gradually as weathering time increases. Consequently, the safety factor of the slope decreases progressively.