## 4 Numerical Simulation Calculation
### Analysis of Numerical Simulation Results  
1. Stress distribution of roadways with coal pillars of different widths  
After the excavation model reaches equilibrium, the stress cloud diagram of the coal column of different widths (as shown in Figure 7) is analyzed. The stress concentration of the coal column near the goal area is clear, and the maximum stress of the coal column with widths of 3 m, 5 m, 8 m, and 10 m is 27.7 MPa, 22.3 MPa, 23.6 MPa, and 24.9 MPa, respectively. When the width of the coal column is greater than 5 m, the maximum principal stress gradually increases with the width. The maximum principal stress is much greater when the width of the coal column is 3 m than when it is 5 m, and the stress on the solid coal side is relatively small, while the stress on the goat side is relatively large. When, in area 130,205, the width of the coal column in the ventilation return lane is 5 m, the stress peak area is not connected with the stress peak area of the goat area in the upper section and the coal column is in a position with low stress, which does not cause instability. 2. Displacement analysis for coal column roadways of different widths  
The vertical and horizontal displacements of the surrounding rocks of coal columns of different widths (3 m, 5 m, 8 m, and 10 m) were simulated, and the deformation cloud map of the surrounding rock of the roadway was obtained, as shown in Figure 8. According to the measurement point monitoring data, for coal column widths of 3 m, 5 m, 8 m, and 10 m, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Numbering**} & \multirow{2}{*}{**Rock Name**} & \multirow{2}{*}{**Thickness**} & \multirow{2}{*}{**Depth [m]**} & **Compressive** & **Tensile** & **Elastic** & \multirow{2}{*}{**Poisson’s**} & **Cohesion** & **Unit Weight** \\  & & & & **[MPa]** & **[MPa]** & **[GPa]** & **Ratio** & **[MPa]** & **[Mg]** & **[kg/m\({}^{3}\)]** \\ \hline M3 & Silstone & 5.24 & 589.54 & 45.2 & 4.52 & 14.6 & 0.23 & 4.66 & 2.35 \\ M2 & Medium & 12.00 & 601.54 & 38.6 & 4.6 & 14.4 & 0.23 & 4.83 & 2.35 \\ M1 & Silstone & 8.56 & 610.10 & 35.7 & 3.57 & 12.5 & 0.22 & 4.27 & 2.2 \\ M0 & 2 coal & 8.70 & 618.80 & 13.0 & 1.3 & 1.86 & 0.25 & 0.87 & 1.45 \\ F1 & Silstone & 1.45 & 620.45 & 45.2 & 4.52 & 14.6 & 0.23 & 4.66 & 2.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 7: Displacement analysis of coal column roadways of different widths: (**a**) 3 m coal pillars; (**b**) 5 m coal pillars; (**c**) 8 m coal pillars; (**d**) 10 m coal pillars. the displacement of the top and bottom plates of the roadway is 117 mm, 87 mm, 93 mm and 97 mm, respectively, and the displacement of the two vertical supports is 259 mm, 174 mm, 183 mm, and 192 mm, respectively. For any given column width, the displacement of the top and bottom plate of the roadway is less than that of the two vertical supports moving closer; as the width increases  
Figure 8: Cloud diagram of different-width coal column displacement distributions: (**a**) vertical displacement distribution of the 3 m coal column; (**b**) horizontal displacement distribution of the 3 m coal column; (**c**) vertical displacement distribution of the 5 m coal column; (**d**) horizontal displacement distribution of the 5 m coal column; (**e**) vertical displacement distribution of the 8 m coal column; (**f**) horizontal displacement distribution of the 8 m coal column; (**g**) vertical displacement distribution of the 10 m coal column; (**h**) horizontal displacement distribution of the 10 m coal column. (\(>\)5 m), there is a decreasing trend in the amount of horizontal approach of the surrounding rock of the roadway and the displacement of the top and bottom plate. Among the four sets of wide coal pillars, the surrounding rock of the 3 m coal column condition moved closer, and the maximum vertical displacement occurred at the junction of the top plate of the small coal column side of the roadway and the vertical support, while the maximum horizontal displacement occurred in the middle of the alley.