# Factors Influencing the Stability of a Slope Containing a Coal Seam in a Goal
## 4 Analysis of the Influencing Factors
### Orthogonal Multifactor Simulation Test
#### 4.2.2 Variance Analysis of the Slope Stability Coefficient  
The range analysis method could only be used to determine the relative influence of each factor on the slope stability coefficient, but could not be used to determine whether the influence of each factor on the slope stability coefficient was significant and the magnitude of the significance. The variance analysis, as a method of analyzing experimental data, can be used to study whether the influence of factors on the experimental results is significant. Therefore, through the analysis of variance on the slope stability coefficient, we investigated the significance of the influence of the eight factors \(H\), \(W\), \(i\), \(T\), \(R\), \(c\), \(\varphi\), and \(\alpha\) on the slope stability coefficient. According to the theory of the variance analysis of the orthogonal test and the data of the slope stability coefficient in Table 10, we calculated the mean square, degree of freedom, the sum of squares, and \(p\) value of each factor, where \(p<0.05\) indicated that the factor significantly influenced the slope stability coefficient. The results are shown in Table 12.  
Table 12 shows that among the eight factors analyzed, the corresponding \(p\) values of factors H, W, i, T, \(c\), \(\varphi\), and \(\alpha\) were all less than 0.05, indicating that these seven factors significantly influenced the slope stability coefficient. The \(p\) value of factor R was 0.675 \(>\) 0.05, indicating that this factor had no significant influ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Factor**} \\ \cline{2-9}  & \(H\) & \(W\) & \(i\) & \(T\) & \(R\) & \(c\) & \(\varphi\) & \(\alpha\) \\ \hline \(T_{11}\) & 12.03 & 13.17 & 11.60 & 11.34 & 10.09 & 9.13 & 9.19 & 9.30 \\ \(T_{22}\) & 10.16 & 10.00 & 10.04 & 10.21 & 10.36 & 10.29 & 10.24 & 10.28 \\ \(T_{3}\) & 8.50 & 7.52 & 9.05 & 9.14 & 10.24 & 11.27 & 11.26 & 11.11 \\ Average 1 & 4.01 & 4.39 & 3.87 & 3.78 & 3.36 & 3.04 & 3.06 & 3.10 \\ Average 2 & 3.39 & 3.33 & 3.35 & 3.40 & 3.45 & 3.43 & 3.41 & 3.43 \\ Average 3 & 2.83 & 2.51 & 3.02 & 3.05 & 3.41 & 3.76 & 3.75 & 3.70 \\ Range & \(-\)1.18 & \(-\)1.88 & \(-\)0.85 & \(-\)0.73 & 0.05 & 0.71 & 0.69 & 0.60 \\ Range order & 2 & 1 & 3 & 4 & 8 & 5 & 6 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Range analysis of the factors affecting slope stability. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variance** & **Mean** & **Degrees of** & **Sum of** & **F Value** & \(p\)**Value** \\
**Source** & **Square** & **Freedom** & **Squares** & \\ \hline H & 0.368 & 2 & 0.737 & 104.751 & \textless{}0.0001 \\ W & 0.863 & 2 & 1.726 & 245.375 & \textless{}0.0001 \\ i & 0.177 & 2 & 0.354 & 50.375 & \textless{}0.0001 \\ T & 0.128 & 2 & 0.257 & 36.522 & \textless{}0.0001 \\ R & 0.001 & 2 & 0.003 & 0.409 & 0.675 \\ \(c\) & 0.121 & 2 & 0.241 & 34.298 & \textless{}0.0001 \\ \(\varphi\) & 0.126 & 2 & 0.252 & 35.865 & \textless{}0.0001 \\ \(\alpha\) & 0.082 & 2 & 0.164 & 23.259 & \textless{}0.0001 \\ Residual & 0.004 & 10 & 0.035 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Variance analysis of the factors affecting slope stability. differences in the F values, we further compared the significant differences among the seven factors that had a significant influence. Among them, the F value of the roadway width was 245.375, which was the most significant influence. This showed that reducing the roadway width can considerably improve the stability of a slope containing a coal seam in a goat, during the implementation of practical projects. The F value of the coal seam position was 104.751, and its influence degree was second only to the roadway width. If the roadway width cannot be changed, the coal seam position plays a decisive role in the stability of the coal seam containing a slope in the goat. The F value of the slope gradient was 50.375, ranking it third in terms of influence.