## 3 Mechanical Analysis and Numerical Simulation of Roadway Wall Rock
### Numerical Simulation of Roadway Wall Rock Based on FLAC 3D
The length of the model was 20 m, the width was 9 m, and the height was 16 m. The shape of the roadway section was rectangular, and the section size was 4.5 \(\times\) 3.5 m, with a section area of 15.75 m\({}^{2}\); it was composed of four layers of siltstone, coal seam, silty sandstone, and medium fine sandstone from bottom to top. The definition of its geological data is shown in Table 2.  
The wall rock model grid was divided unevenly, and the wall rock model grid parameters are shown in Table 3.  
We defined the boundary conditions of the roadway model as shown in Formula (17):  
\[\left\{ \begin{array}{c}\Delta_{x1}=0\\ \Delta_{x2}=0\\ \Delta_{y}=0\\ q_{f}=1.5\text{ MPa}\end{array} \right. \tag{17}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rock Type** & **Thickness (m)** & **Cohesion (MPa)** & **Internal Friction Angle (\({}^{\circ}\))** & **Density (kg/m\({}^{3}\))** \\ \hline Silstone & 3.0 & 7.2 & 35.0 & 2730 \\ Coal seam & 3.5 & 1.1 & 32.3 & 1330 \\ Silty sandstone & 2.5 & 5.6 & 38.4 & 2815 \\ Medium fine sandstone & 7 & 7.0 & 40.5 & 2615 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Rock mass parameters of wall rock model. Figure 4: Roadway wall rock- support system model. (**a**) Initial model of wall rock, (**b**) excavation roadway model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rock Type** & **Length (m)** & **Width (m)** & **Height (m)** \\ \hline Silstone & 0.5 & 0.2 & 0.6 \\ Coal seam & 0.5 & 0.2 & 0.5 \\ Silty sandstone & 0.5 & 1.0 & 0.5 \\ Medium fine sandstone & 0.5 & 1.0 & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Grid parameters of wall rock model. where \(\Delta_{x1}\) is the lateral horizontal displacement of the model side, \(\Delta_{x2}\) is the horizontal displacement of the model bottom, and \(\Delta_{y}\) is the vertical displacement of the model bottom. \(q_{f}\) is the overburden load on the model top, as defined in Formula (18). \[q_{f}=\sum_{i=1}^{n}\gamma_{i}L_{i} \tag{18}\]  
where \(\gamma_{i}\) represents the unit weight of each rock layer, \(L_{i}\) represents the thickness of each rock layer, \(i\) represents different rock layers above the roadway, and \(n\) represents the total number of rock layers. Here, the value of \(\gamma_{i}\) is 25 \(\text{KN}/\text{m}^{3}\), which is the average value. We ran FLAC 3D to conduct a numerical simulation on the roadway wall rock model established above, and we analyzed the displacement, stress, and plastic failure characteristics of the roadway roof before and after the temporary support equipment support according to the operation results. The support force required for the roadway roof was calculated in Section 3.1. Here, we added this support force to the lower surface of the roadway roof to replace the actual support. In this process, the influence of support stiffness on the roof was ignored. 1. Distribution characteristics of vertical displacement of roadway roof  
The vertical displacement distribution of the roadway roof before and after temporary support is shown in Figure 5. The comparative analysis of (a) and (b) shows that the maximum vertical displacement of the roof before the support was 2.14 mm, the maximum vertical displacement of the roof after the support was 1.76 mm, and the maximum vertical displacement of the roof after the support was 17.8% lower than before, indicating that the temporary support could protect the roof and reduce the roof subsidence. The vertical displacement curve of the roadway roof before and after temporary support is shown in Figure 6. The comparative analysis of (a) and (b) shows that the vertical displacement of the wall rock on both sides of the roadway was small, indicating that the wall rock on both sides of the roadway had a strong bearing capacity. The closer to the roadway center, the greater the roof displacement. At x = 7.75 m and x = 12.25 m, that is, at the side wall of the roadway, the vertical displacement of the roof increased rapidly.