## 4 Results  
### Range Analysis  
The range of a parameter can be used to evaluate the significance of factors, and the amplitude of change therein represents the degree of influence of the changes in the levels of a factor on the dependent variables. A larger range indicates greater influences of changes in the levels of the factor on the dependent variables. Range analysis is qualitative [29; 30]; in this study, the horizontal displacement of the coal wall and the volume of the plastic zone in the coal wall in the unit length of the dip direction were taken as dependent variables. The range analysis results are listed in Table 3.  
Based on the data in Table 3, by taking the levels of each influencing factor as the horizontal coordinate and the averages of range between the horizontal displacement and the volume of the plastic zone as the vertical coordinate, curves were plotted (Figure 8). As demonstrated in Table 3 and Figure 8:  
1. The rank-order of the factors in terms of their influences on the horizontal displacement of the coal wall and the volume of the plastic zone differs; however, the ranges of the cutting height and the breaking position of the main roof are greater than those of the other factors, indicating that they have a greater (and more sensitive) influence on the horizontal displacement of the coal wall and the volume of the plastic zone. The support strength and sidewall-protecting force of the support are less influential. The factors were ranked in the order of the breaking position of the main roof, cutting height, sidewall-protecting force, and support strength in terms of influences on the horizontal displacement of the coal wall. The breaking position of the main roof plays a dominant role in affecting the horizontal displacement, followed by the cutting \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Index** & **Factor** & \(\overline{K}_{\text{ij}}\) & \(\overline{K}_{\text{j}}\) & \(\overline{K}_{\text{ij}}\) & \(\overline{K}_{\text{ij}}\) & \(\overline{R}_{\text{N}}\) & **Rank of Influence Level** \\ \hline \multirow{6}{*}{\begin{tabular}{c} Horizontal \\ displacement \\ \end{tabular} } & Cutting height & 269.12 & 339.96 & 404.86 & 461.28 & 192.17 & • & Breaking position of main roof \\  & Breaking position & 521.79 & 353.23 & 317.17 & 283.03 & 238.77 & • & Cutting height \\  & \begin{tabular}{c} of main roof \\ Support strength \\ Sidewall protecting force \\ \end{tabular} & 368.82 & 379.82 & 370.53 & 356.05 & 23.77 & • & Sidewall-protecting force \\  & \begin{tabular}{c} Sidewall protecting force \\ \end{tabular} & 393.61 & 367.71 & 360.41 & 353.48 & 40.13 & • & Support strength \\ \hline \multirow{6}{*}{\
\begin{tabular}{c} Volume of \\ plastic zone \\ \end{tabular} } & Cutting height & 7.36 & 11.27 & 14.92 & 18.27 & 10.91 & • & Cutting height \\  & Breaking position & 17.06 & 13.03 & 11.34 & 10.40 & 6.66 & • & Breaking position of main roof \\  &
\begin{tabular}{c} of main roof \\ Support strength \\ Sidewall protecting force \\ \end{tabular} & 13.76 & 13.45 & 12.67 & 11.96 & 1.8 & • & Support strength \\ \cline{1-1}  & Sidewall protecting force & 13.13 & 13.03 & 13.11 & 12.56 & 0.57 & • & Sidewall-protecting force \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Range analysis results. height. The factors were ranked in descending order as the cutting height, breaking position of the main roof, support strength, and sidewall-protecting force regarding their influences on the volume of the plastic zone. The cutting height plays a dominant role in affecting the volume of the plastic zone, followed by the breaking position of the main roof. 2. By affecting the thickness of the top coal and the ranges of influence of the abutment pressure, the cutting height changes the horizontal displacement of the coal wall and the volume of the plastic zone.