## 3 Numerical Model and Calculation Scheme
### Establishment of Numerical Calculation Model
#### 3.2.2 Establishment of the Model  
A working face in Wanggialing coal mine is located in the northeast of 123 panel. The elevation of the floor of the working face is +518\(\rightarrow\)+607 m, the burial depth of the coal seam is 415-570 m, the strike of the working face is east-west, the strike length is 784.9 m, the tendency direction is north-south, and the length is 100 m. The working face mining coal seam is 2# coal seam, the thickness of the coal seam is 3.09-8.50 m, the average coal thickness is 6.20 m, and the dip angle of the coal seam is \(-\)3\(\rightarrow\)+2\({}^{\circ}\). The roof of the working face is mostly mudstone and sandstone, and its basic roof is a layer of medium-fine grain sandstone, the condition of the top plate is shown in Table 1.  
According to the geological information of a working face in the Wanggialing coal mine, the numerical simulation model is established by combining the physical parameters of rock mechanics. Since the actual hydrogeological conditions are complex, considering the purpose of the simulation study, the model is simplified to the following conditions: Model length \(X\) = 150 m, high \(Y\) = 100 m, particle size in the range of 0.6-1.0 m, according to the different lithology given the corresponding mechanical parameters, the lithology similar rock into a group, the model consists of 13 groups. In the original geological conditions, the average dip angle of 2# coal seam is 2.5\({}^{\circ}\), which can be approximated as a horizontal coal seam, so the coal seam is arranged horizontally in the model. The basic boundary conditions of the model are set as follows: the upper boundary is a free boundary, and the equivalent load of 10 MPa is applied to the top wall of the model by servo function control. When the load on the wall corresponds to the gravity of the overlying rock mass, the wall stops moving. The lower boundary is fixed to restrict the vertical motion. Fixed left and right boundaries limit horizontal movement and allow vertical movement. In order to prevent boundary effects, the excavation roadway is 30 m away from the left and right boundaries of the model as a protective coal pillar. The model plan is divided into nine excavations, and the excavation distance is 10 m, 20 m, 30 m, 40 m, 50 m, 60 m, 70 m, 80 m, and 90 m. Through the actual situation and access to information, coal and rock macro mechanical parameters and particle micromechanical parameters are shown in Tables 2 and 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Roof Name** & **Rock Name** & **Thickness (m)** & **Lithological Characteristics** \\ \hline Main roof & Fine sandstone & 13.8 & Clay cementation, thin layer, rich in mica fragments \\ \hline Immediate roof & sandy mudstone & 8.85 & Clay-based, brittle containing a small amount of plant fossils \\ \hline \hline \end{tabular}
\end{table}
Table 1: Coal seam roof condition table.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithologic Characters** & **Elastic Modulus** & **Poisson** & **Angle of** & **Cohesion** & **Density** & **Tensile Strength** \\  & **/GPa** & **Ratio** & _I\({}^{\circ}\)_ & _/MPa_ & _/kg/m\({}^{3}\)_ & _/MPa_ \\ \hline Medium sandstone & 30.05 & 0.29 & 33.90 & 13.35 & 2350 & 3.1 \\ Mudstone & 15.9 & 0.33 & 20.90 & 10.98 & 1860 & 2.5 \\ Fine sandstone & 33.40 & 0.25 & 34.5 & 14.62 & 2500 & 3.2 \\ Mudstone & 15.90 & 0.33 & 20.90 & 10.98 & 1860 & 2.4 \\ Silstone & 31.20 & 0.31 & 33.40 & 11.61 & 2480 & 4.6 \\ Mudstone & 15.90 & 0.33 & 20.90 & 10.68 & 1860 & 2.1 \\ Fine sandstone & 33.40 & 0.25 & 34.5 & 14.62 & 2500 & 3.1 \\ Sandy mudstone & 3.33 & 0.33 & 22.01 & 4.00 & 1950 & 2.6 \\
2\#Coal & 5.0 & 0.35 & 38.02 & 3.00 & 1360 & 1.6 \\ Mudstone & 15.90 & 0.33 & 20.90 & 10.98 & 1860 & 1.9 \\ Silstone & 31.20 & 0.31 & 33.40 & 11.61 & 2480 & 3.8 \\ Medium sandstone & 30.05 & 0.29 & 33.90 & 13.35 & 2350 & 2.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rock macro physical and mechanical parameters.