## 3 Case Study
### Construction of Numerical Model  
A numerical simulation model, as depicted in Figure 11, was established to reflect the specific geological conditions and grouting filling scenarios of the 8006 working face at the Wuyang Coal Mine. The model's dimensions are set at 800 m \(\times\) 4 m \(\times\) 620 m, incorporating a working face width of 280 m, a mining height of 5.5 m, and a grouting hole depth of 352.85 m. To realistically simulate the natural environment, slip boundaries are implemented along the model's perimeter, and lateral stress is applied to accommodate the varying burial depths of the mine. Additionally, a fixed boundary condition is \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Lithology**} & \multirow{2}{*}{**Density** (kg/m3)**} & \multirow{2}{*}{\begin{tabular}{c} **Elastic** \\ **Modulus** \\ **(GPa)** \\ \end{tabular} } & \multirow{2}{*}{**Poisson’s**} & \multirow{2}{*}{**Cohesion**} & \multirow{2}{*}{\
\begin{tabular}{c} **Internal** \\ **Friction** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Tensile** \\ **Strength** \\ **(MPa)** \\ \end{tabular} } \\ \hline
31 & Loose strata & 2500 & 0.2 & 0.44 & 0.2 & 22\({}^{\circ}\) & 0.03 \\
30 & Medium-grained & 2560 & 40 & 0.19 & 13.9 & 42\({}^{\circ}\) & 6.1 \\
29 & Mudstone & 2630 & 25 & 0.23 & 3.9 & 40\({}^{\circ}\) & 3.7 \\
28 & Sand–mud interbedding & 2440 & 23 & 0.18 & 8.2 & 42\({}^{\circ}\) & 3.9 \\
27 & Mudstone & 2630 & 24 & 0.24 & 7.9 & 42\({}^{\circ}\) & 3.6 \\
26 & Medium-grained & 2560 & 41 & 0.22 & 14.4 & 44\({}^{\circ}\) & 11.6 \\
25 & Mudstone & 2630 & 23 & 0.15 & 5.2 & 42\({}^{\circ}\) & 3.8 \\
24 & Silstone & 2560 & 43 & 0.16 & 17.2 & 39\({}^{\circ}\) & 4.32 \\
23 & Mudstone & 2630 & 19 & 0.22 & 7.5 & 42\({}^{\circ}\) & 3.8 \\
22 & Coarse sandstone & 2450 & 39 & 0.21 & 16.9 & 42\({}^{\circ}\) & 5.8 \\
21 & Sandy mudstone & 2530 & 22 & 0.25 & 4.8 & 40\({}^{\circ}\) & 4.0 \\
20 & Medium-grained & 2560 & 44 & 0.22 & 8.5 & 42\({}^{\circ}\) & 7.1 \\
19 & Coarse sandstone & 2450 & 38 & 0.19 & 8.8 & 40\({}^{\circ}\) & 2.2 \\
18 & Sandy mudstone & 2530 & 22 & 0.22 & 3.1 & 39\({}^{\circ}\) & 4.0 \\
17 & Silstone & 2560 & 38 & 0.22 & 13.9 & 42\({}^{\circ}\) & 6.8 \\
16 & Sandy mudstone & 2530 & 24 & 0.18 & 6.5 & 44\({}^{\circ}\) & 4.0 \\
15 & Silstone & 2560 & 37 & 0.22 & 8.8 & 42\({}^{\circ}\) & 4.7 \\
14 & Fine sandstone & 2540 & 26 & 0.21 & 8.5 & 39\({}^{\circ}\) & 5.8 \\
13 & Sandy mudstone & 2530 & 26 & 0.25 & 4.5 & 39\({}^{\circ}\) & 4.0 \\
12 & Medium-grained & 2560 & 33 & 0.22 & 6.1 & 42\({}^{\circ}\) & 5.0 \\
11 & Sandy mudstone & 2530 & 27 & 0.23 & 10.0 & 39\({}^{\circ}\) & 4.3 \\
10 & Medium-grained & 2560 & 31 & 0.24 & 5.3 & 42\({}^{\circ}\) & 4.8 \\
19 & Sand–mud interbedding & 2440 & 26 & 0.15 & 5.4 & 39\({}^{\circ}\) & 3.8 \\
8 & Medium-grained & 2560 & 29 & 0.16 & 8.3 & 44\({}^{\circ}\) & 7.4 \\
7 & Sandy mudstone & 2530 & 25 & 0.22 & 7.9 & 42\({}^{\circ}\) & 3.8 \\
6 & Medium-grained stone & 2560 & 26 & 0.24 & 15.8 & 42\({}^{\circ}\) & 3.8 \\
5 & Sandy mudstone & 2530 & 23 & 0.22 & 8.5 & 44\({}^{\circ}\) & 3.8 \\
4 & Silstone & 2560 & 38 & 0.25 & 8.8 & 39\({}^{\circ}\) & 1.7 \\
3 & Sandy mudstone & 2530 & 22 & 0.18 & 12.9 & 42\({}^{\circ}\) & 3.8 \\
2 & Coal seam & 1400 & 12 & 0.31 & 2.2 & 14\({}^{\circ}\) & 0.7 \\
1 & Sandy mudstone & 2630 & 24 & 0.23 & 2.3 & 40\({}^{\circ}\) & 3.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical–mechanical parameters of strata.