## 2 Research Methods
### Verification Methods  
1. Verification of the numerical simulation method  
We used the UDEC numerical model to verify the feasibility of the above calculation method and the result. The advantage of numerical simulation verification is the use of discrete element methods to truly reflect the shape of a goaf under the same geological conditions. The design model was 300 m \(\times\) 87 m (length \(\times\) height). The advancing distance of the working face was 200 m, the horizontal displacement was constrained by the horizontal boundary around the model, the vertical displacement was constrained by the bottom, and the upper boundary was free. The Coulomb-Moore model was used. Table 1 shows the parameters of each layer, and Table 2 shows the joint parameters. The above parameters were selected based on the actual test results of the adjacent working faces of the mine. The immediate roof strata were constructed by the Voronoi unit, as it could simulate the irregular fracture of the immediate roof. After the initial balancing of the model, an excavation was carried out every 10 m. The overlying strata's top and bottom displacement were monitored during the excavation. The numerical model is shown in Figure 3. After the program was run, we used the plot model command in UDEC to display the void space and used ImageJ software to analyze the void ratio in the diagram. The analysis method is shown in Figure 4. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & **Strata** & **Height** & **Bulk (pa)** & **Shear (pa)** & **Tensile (pa)** & **Cohesion (pa)** & **Friction** & **Density (kg \(\cdot\) m\({}^{-3}\))** \\ \hline
1 & Mudstone & 20 & \(4.0\times 10^{9}\) & \(2.0\times 10^{9}\) & \(1.25\times 10^{6}\) & \(2.5\times 10^{6}\) & \(22^{\circ}\) & 1600 \\
2 & Coal & 4 & \(2.5\times 10^{9}\) & \(1.8\times 10^{9}\) & \(1.17\times 10^{6}\) & \(2.0\times 10^{6}\) & \(23^{\circ}\) & 1400 \\
3 & Sandy mudstone & 2 & \(6.0\times 10^{9}\) & \(3.0\times 10^{9}\) & \(1.5\times 10^{6}\) & \(3.0\times 10^{6}\) & \(24^{\circ}\) & 2000 \\
4 & Fine sandstone & 3 & \(8.0\times 10^{9}\) & \(4.0\times 10^{9}\) & \(2.0\times 10^{6}\) & \(3.5\times 10^{6}\) & \(26^{\circ}\) & 2500 \\
5 & Sandy mudstone & 3 & \(6.0\times 10^{9}\) & \(3.0\times 10^{9}\) & \(1.5\times 10^{6}\) & \(3.0\times 10^{6}\) & \(24^{\circ}\) & 2000 \\
6 & Fine sandstone & 3 & \(8.0\times 10^{9}\) & \(4.0\times 10^{9}\) & \(2.0\times 10^{6}\) & \(3.5\times 10^{6}\) & \(26^{\circ}\) & 2500 \\
7 & Sandy mudstone 1 & 4 & \(6.0\times 10^{9}\) & \(3.0\times 10^{9}\) & \(1.5\times 10^{6}\) & \(3.0\times 10^{6}\) & \(24^{\circ}\) & 2000 \\
8 & Sandy mudstone 2 & 6 & \(6.0\times 10^{9}\) & \(3.0\times 10^{9}\) & \(1.5\times 10^{6}\) & \(3.0\times 10^{6}\) & \(24^{\circ}\) & 2000 \\
9 & Fine sandstone & 10 & \(8.0\times 10^{9}\) & \(4.0\times 10^{9}\) & \(2.0\times 10^{6}\) & \(3.5\times 10^{6}\) & \(26^{\circ}\) & 2500 \\
10 & Medium sandstone & 12 & \(12.0\times 10^{9}\) & \(5.0\times 10^{9}\) & \(3.0\times 10^{6}\) & \(3.8\times 10^{6}\) & \(28^{\circ}\) & 2800 \\
11 & Coarse sandstone & 20 & \(14.0\times 10^{9}\) & \(6.0\times 10^{9}\) & \(3.2\times 10^{6}\) & \(4.0\times 10^{6}\) & \(27^{\circ}\) & 2600 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the strata.