# Geomechanical Basis for Assessing Open-Pit Slope Stability in High-Altitude Gold Mining
## 2 Materials and Methods
### Analysis of Fracture Orientations and Weakness Planes
According to research conducted by VNIMI [1; 2], these values are related through a structural weakening coefficient \(\lambda_{0}\), which can be determined using the following formula:  
\[\lambda_{0}=\frac{1}{1+\alpha\textit{In}\frac{\textit{H}}{\textit{T}}}, \tag{1}\]  
where \(\alpha\) is a coefficient that depends on the strength of the intact rock specimen and the degree of fracturing. \(\frac{H}{\textit{T}}\)--the ratio of burial (embedment) depth. The results of the structural weakening coefficient \(\lambda_{0}\) calculations are summarized in Table 1.  
The cohesion of rocks in the in situ mass was determined as follows. Based on the provided geological cross-sections along the pit walls, the main rock types were identified, and their strength characteristics, obtained through laboratory testing, were assigned to each. Then, using the structural weakening coefficient, the in situ cohesion of the rocks was calculated according to the following formula:  
\[\textit{k}_{m}=\textit{k}_{lab}\lambda_{0}, \tag{2}\]  
The calculated values of in situ rock cohesion are presented in Table 2.  
To obtain the design strength characteristics of the rocks, a safety factor **n\({}_{\text{s}}\)**-1,2 was applied to the in situ values, in accordance with VNIMI research recommendations. \[\textit{K}_{design}=\frac{\textit{k}_{m}}{\textit{n}_{s}};\varphi_{design}= \textit{arctg}\bigg{(}\frac{\textit{tg}\varphi_{m}}{\textit{n}_{s}}\bigg{)}, \tag{3}\]  
The calculated values of design cohesion \(\textit{K}_{design}\) and the internal friction angle \(\varphi_{design}\) are presented in Table 1.  
These strength parameters for granodiorites and limestones were used in the slope stability assessment of benches and pit walls at the Bozymchak open-pit mine based on the defined geological cross-sections. The presence of a tectonic fault in the granodiorites of the southern pit wall required the application of adjusted strength parameters that considered the fractured structure and reduced stability of the rock mass in the fault zone. For the southern wall, the following values were accepted: cohesion of 1.5 t/m\({}^{2}\) and an internal friction angle of 25.5\({}^{\circ}\), which were obtained through back-calculations based on observed conditions at the pit site [19]. The slope stability assessment for the pit benches and walls was carried out using custom-developed software, taking into account the structural features and measured strength properties of the rocks. The analysis was based on the geomechanical models of the near-slope rock masses (Figure 5). Figure 6 shows the results of slope stability analysis for the northern and southern walls. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Rock Type** & **Depth H, m** & **Estimated Cohesion** & **Estimated Cohesion** & **Density** & **Density** & **Estimated Angle of** \\  & & **k\_pac, t/m2** & **k\_pac, kN/m2** & **\(\gamma\), t/m3** & **\(\gamma\), kN/m3** & **Internal Friction, Degrees** \\ \hline Weathered crust in & & & & & & \\ grandoitories & 50 & 49.2 & 482.9 & 2.89 & 28.35 & 33 \\ \hline Grandiorites in & & & & & & \\ middle part & 50–100 & 106.9 & 1041.0 & 2.89 & 28.35 & 33 \\ \hline Granoidorites in & & & & & & \\ bedrocks at depth & 100–250 & 114.3 & 1121.28 & 2.89 & 28.35 & 33 \\ \hline Weathered crust in the & & & & & & \\ marbelized limestone & 30 & 30.0 & 294.0 & 2.73 & 26.78 & 30 \\ \hline Marbleized limestone & & & & & & \\ the middle part & 50–100 & 58.3 & 571.7 & 2.73 & 26.78 & 32 \\ \hline Marbleized limestone & & & & & & \\ at depth & 100–250 & 66 & 647.4 & 2.73 & 26.78 & 31 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated strength values of rocks. Figure 5: Classification of geomechanical models. The slope stability calculations for the pit walls (Table 3) show that, overall, the near-slope rock masses of both the southern and northern walls are in a stable condition, with safety factors ranging from 1.31 to 2.90.