## 4 Study on Mining Layout Pattern Based on Numerical Simulation
### Effect of Coal Pillar Width on Stability of Panel-Isolated Coal Pillar  
Under the condition of different widths of the panel-isolated coal pillar, the vertical stress tendency slice contour and elastic strain energy plane distribution contour of the panel-isolated coal pillar area after excavation in the second and third panels are shown in Figures 9 and 10. When the width of the panel-isolated coal pillar is less than 200 m, there is a higher degree of stress concentration and energy accumulation in the panel-isolated coal pillar area. When the coal pillar width exceeds 210 m, the stress and energy accumulation in the panel isolated coal pillar area are higher only near the areas adjacent to the two sides  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lithology** & **Density (kg/m\({}^{3}\))** & **Bulk Modulus (GPa)** & **Shear Modulus (GPa)** & **Friction Angle (\({}^{\circ}\))** & **Cohesion (MPa)** \\ \hline Loess & 1640 & 2.21 & 0.37 & 25 & 0.01 \\ Sandy mudstone & 2480 & 1.13 & 0.67 & 39 & 2.92 \\ Medium grain sandstone & 2400 & 7.32 & 4.57 & 41 & 1.91 \\ Coarse grain sandstone & 2510 & 9.68 & 6.37 & 41 & 2.32 \\ Coal seam & 1400 & 3.49 & 2.01 & 36 & 1.18 \\ Mudstone & 2550 & 0.98 & 0.70 & 37 & 2.61 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of model.  
Figure 8: Numerical model of panel excavation.  
of the goat, while the stress concentration and energy accumulation in the elastic core zone of the isolation coal pillar are relatively low.  
The variation curve of stress along the inclination of the panel-isolated coal pillar is shown in Figure 11. With the increase in the width of the panel-isolated coal pillar, the degree of stress concentration in the panel-isolated coal pillar weakens. The stress peak decreases from 57.34 MPa to 49.20 MPa, and the stress concentration factor decreases from 2.07 to 2.41. When the width of the panel-isolated coal pillars is 150 m and 180 m, the stress peaks are 57.34 MPa and 55.80 MPa, respectively, both exceeding the uniaxial compressive strength of three times the coal, which is 54 MPa. At this point, the panel-isolated coal pillar is in a critical and unstable state.  
Figure 11: Vertical stress variation curve of the panel-isolated coal pillar area under different widths of the panel-isolated coal pillar.  
Figure 10: Plane distribution contour of elastic strain energy in the panel-isolated coal pillar with different widths.  
Figure 9: Vertical stress tendency slice contour of panel-isolated coal pillar with different widths.  
The analysis of the above simulation results shows that under the condition that the goal area on both sides of the panel-isolated coal pillar is unchanged, the stress transferred from the goat on both sides of the panel-isolated coal pillar remains unchanged, but the width of the panel-isolated coal pillar increases, leading to a gradual reduction in stress concentration and energy accumulation in the panel-isolated coal pillar area. Considering the stability of the panel-isolated coal pillar and resource recovery rate, combined with the simulation results mentioned above, under the current small panel mining scale of 550 m, the reasonable range for the width of the panel-isolated coal pillar is 210 m to 270 m, and the mining district recovery ratio is between 75% and 77%.