# Stability and Distribution of Rock Slope under Asymmetric Excavation
## 3 Study on the Stability of a Rock Slope and Its Influence Area Distribution
### Range Analysis  
In reference [28], the safety factors, the starting points of the stable areas on the north and south sides of the surfaces, and the widths of the unstable areas in the 27 models were analyzed according to formula 8 and formula 9, and the results are shown in Table 5. Using the results of the range analysis, the influence trends of different factors on the safety factor, the starting points of the stable areas on the north and south sides of the surface, and the range of the unstable area were drawn, as shown in Figure 8.  
A range analysis identifies the difference between the maximum value and the minimum value for each factor level, which indicates the influence of each factor on the performance at different levels. The calculation formula is as follows:  
\[B_{\mathrm{ij}}=\frac{\sum\limits_{m=1}^{n}K_{ij,m}}{n} \tag{8}\]  
where \(K_{ij,m}\) is the \(m\)th calculation result of factor \(i\) at level \(j\) and \(n\) is the horizontal number. \(R_{i}\) represents the difference between the maximum and minimum values at each level (\(B_{ij}\)):  
\[R_{i}=\max\bigl{(}B_{ij}\bigr{)}-\min\bigl{(}B_{ij}\bigr{)} \tag{9}\]  
According to the range analysis results in Table 5, it can be seen that among the nine factors, the open-pit mining method had the greatest influence on the safety factor. The order of influence was as follows: excavation inclination of the north slope > excavation inclination of the south slope > excavation depth of the north slope > excavation depth of the south slope. The main influence range of the starting point of the south slope was \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{2}{c}{**Starting Point of the South**} & \multicolumn{2}{c}{**The Width of the Unstable**} & \multicolumn{2}{c}{**Starting Point of the North**} & \multirow{2}{*}{**Safety Factor**} \\  & **Stable Zone (m)** & & **Zone (m)** & & **Stable Zone (m)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & **South Slope** & **North Slope** & **South-Side** & **North-Side** & **F1 Fault** & **F1 Distance** & **F1a Fault** & **F1a Distance** & **F1a Distance** & **Thickness of** \\  & **of excavation** & **of excavation** & **Decwidth** & **Decwidth** & **Decwidth** & **Decwidth** & **Decwidth** & **Decwidth** & **Decwidth** \\ \hline Safety factor & 0.283 & 0.770 & 0.137 & 0.165 & 0.036 & 0.043 & 0.025 & 0.033 & 0.044 \\ South side, & 213.56 & 243.67 & 236.00 & 157.33 & 151.89 & 93.33 & 139.11 & 180.89 & 57.22 \\ North side, & 448.00 & 374.33 & 130.11 & 96.11 & 190.89 & 261.67 & 37.56 & 129.00 & 184.11 \\ Range of instability & 21.56 & 38.67 & 41.78 & 29.44 & 76.78 & 118.67 & 28.00 & 50.11 & 19.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Extreme analysis results. as follows: north slope > south slope > north slope > north slope. The main influence range of the stability point of the north slope was as follows: excavation inclination of the south slope > excavation inclination of the north slope > distance between the F1 fault and the top of the slope > F1 fault inclination > coal seam thickness. The main influencing sequence of the instability range was as follows: distance between the F1 fault and the top of the slope > F1 fault dip angle > distance between the F1a fault and the top of the slope > southern excavation depth. Figure 10 shows the influence trends of nine factors on the safety factor, the starting points of the stable areas on the north and south surfaces, and the extent of the unstable area. With an increase in the north-slope excavation inclination, the decreasing trend of the safety factor increased clearly. When the north-slope excavation inclination increased by 10 degrees, the safety factor decreased by 25.9% or 16.6%. When the excavation inclination of the south slope increased by 10 degrees, the safety factor decreased by 13.7% or 1.9%.