## 4 Numerical Simulation of Repeated Supportability of Roadway Roof
### The Influence of Varying Buried Depths of Different Roadways on the Repeatability of Roof Support
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**X1**} & \multicolumn{3}{c}{**Direct Roof Thickness**} \\  & **X2** & **0.8** & **1.6** & **2.4** \\  & **X3** & & \\ \hline \multirow{6}{*}{Direct roof lithology} & \multirow{2}{*}{sandstone} & 0.23 m & 0.25 m & 0.26 m \\  & & 15 mm & 18 mm & 20 mm \\  & & 0.9 mm & 1.0 mm & 1.0 mm \\ \cline{2-4}  & \multirow{2}{*}{Sandy mudstone} & 0.59 m & 0.6 m & 0.62 m \\  & & 28 mm & 32 mm & 35 mm \\  & & 4.1 mm & 1.5 mm & 1.6 mm \\ \cline{2-4}  & \multirow{2}{*}{mudstone} & 0.8 m & 0.96 m & 1.02 m \\  & & 25 mm & 33 mm & 34 mm \\  & & 7.5 mm & 1.6 mm & 1.8 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical simulation results for a roadway buried at a depth of 200 m. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**X1**} & \multicolumn{3}{c}{**Direct Roof Thickness**} \\  & **X2** & **0.8** & **1.6** & **2.4** \\  & **X3** & & \\ \hline \multirow{6}{*}{Direct roof lithology} & \multirow{2}{*}{sandstone} & 0.32 m & 0.3 m & 0.31 m \\  & & 21 mm & 23 mm & 25 mm \\  & & 1.1 mm & 1.1 mm & 1.2 mm \\ \cline{2-4}  & \multirow{2}{*}{Sandy mudstone} & 0.8 m & 0.9 m & 0.95 m \\  & & 28 mm & 32 mm & 35 mm \\  & & 6 mm & 1.5 mm & 1.6 mm \\ \cline{2-4}  & \multirow{2}{*}{mudstone} & 0.8 m & 1.2 m & 1.28 m \\  & & 29 mm & 36 mm & 38 mm \\  & & 9.2 mm & 1.6 mm & 1.8 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Numerical simulation results for a roadway buried at a depth of 500 m.  
increases to 0.8-1 m. Thus, it is determined that the roadway roof maintains repeatability when the direct roof thickness exceeds 1 m.  
Based on the numerical simulation results presented in Section 4.2 and Table 5 for a roadway buried at a depth of 500 m, it is observed that different thicknesses of the direct roof can satisfy the requirements for repeated support of the roadway roof when the direct roof is made of sandstone. In the case of sandy mudstone, the range of direct roof fracturing extends from 0.8 m to 1 m, indicating that the roadway roof is considered to have repeated support when the direct roof thickness exceeds 1 m. Similarly, when the direct roof is composed of mudstone, the range of direct roof fracturing extends from 0.8 m to 1.3 m. Therefore, the roadway roof is considered to have repeated support when the direct roof thickness exceeds 1.3 m.  
Furthermore, based on the numerical simulation results provided in Table 6 for a roadway buried at a depth of 800 m, it is determined that different thicknesses of the direct roof can meet the requirements for repeated support of the roadway roof when the direct roof is made of sandstone. For sandy mudstone, the range of direct roof fracturing extends from 0.8 m to 1.2 m, indicating that the roadway roof is considered to have repeated support when the direct roof thickness exceeds 1.2 m. Similarly, when the direct roof is composed of mudstone, the range of direct roof fracturing extends from 0.8 m to 1.5 m. Therefore, the roadway roof is considered to have repeated support when the direct roof thickness exceeds 1.5 m.