## 4 Numerical Simulation of Coal Pillar Width of Gob-Side Entry Driving in Inclined Coal Seams
### Analysis of the Model Results  
The analysis of the influence range of the residual coal pillar can provide a certain basis for the selection of the width of the coal pillar during the mining of the lower coal seam. From the numerical simulation results (Figure 7), it can be seen that the peak value of the advance abutment pressure during the mining of the #2 coal seam is 16.9 MPa. The residual coal pillar has a certain impact on the mining of the #2 coal seam, and the influence range of the stress concentration is 10.5 m (Figure 7b), which is almost identical to the theoretical calculated value of 11 m for the concentrated influence range of the remaining coal pillar of the coal seam; thus, the accuracy of theoretical calculation is further verified. Therefore, when roadways are driven along the goat in coal seam #2, the roadways should be arranged to avoid the influence of the #1 residual coal pillar as much as possible. When the coal and rock masses boast a strong bearing capacity, stress concentration is likely to occur in a certain range. Stress is re-distributed after roadway excavation. The simulation and analysis of the stress distribution in the coal pillars is of certain guiding significance for determining the reasonable coal pillar width. The stress nephograms and distribution curves of different coal pillar widths were obtained by numerical calculation results (Figure 8). According to Figure 8, overall, the stress distributions of different coal pillar widths show the following rules:  
1. At coal pillar widths of 8\(\sim\)14 m, the internal stress of coal pillars presents an asymmetric bimodal distribution with high stress on the gob sides and low stress on the roadway sides. When the width is below 6 m, the internal stress presents a single peak distribution. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Lithology** & \(\rho\) **(kg/m3)** & \(E_{i}\) **(GPa)** & \(c_{i}\) **(MPa)** & \(\varphi_{i}\) **(deg.)** & \(\sigma_{Hi}\) **(MPa)** & \(\
u_{i}\) \\ \hline Coarse sandstone & 2556 & 10.25 & 7.64 & 29.31 & 1.86 & 0.20 \\ No.1 coal seam & 1335 & 2.46 & 2.91 & 23.59 & 1.35 & 0.25 \\ Silstone & 2548 & 7.25 & 4.59 & 28.42 & 1.62 & 0.18 \\ Fine sandstone & 2552 & 10.63 & 6.90 & 31.74 & 1.72 & 0.19 \\ Mudstone & 1220 & 3.58 & 1.50 & 15.53 & 0.80 & 0.27 \\ No.2 coal seam & 1329 & 2.97 & 2.35 & 21.86 & 1.10 & 0.23 \\ \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of the coal rock mass. Figure 7: Influence range of residual coal pillar stress. (**a**) Stress distribution. (**b**) Stress monitoring curve. 2. After the roadway excavation, the vertical stress is re-distributed. At a small coal pillar width, stress is concentrated on the right side of the roadway. As the width increases, the position of the stress concentration gradually shifts to the gob side. 3. At widths of 4 m and 6 m, fractures develop in the coal pillars, leading to serious damage and poor bearing capacity, which fails to form stress concentration. However, as the width continuously increases to 8 m, the mechanical properties of the coal and rock mass improve, and the peak value of the stress nucleus rises. When the width reaches 10 m, the maximum stress peak value is 11.30 MPa. When the width exceeds a certain value and reaches 12 m, the abutment pressure increases and surpasses the ultimate strength of the coal body. In this case, the stress in the coal pillar is relieved, and the peak value of the stress nucleus decreases. The peak stress value rises first and then decreases in turn in the following order: 1.67 MPa, 7.22 MPa, 10.67 MPa, 11.30 MPa, 10.27 MPa, and 10.25 MPa. 4. When the width of the coal pillar reaches 8 m, the coal pillar boasts an overall good bearing capacity. An increase in the width improves the integrity of the coal pillar, but this will cause a significant waste of coal resources.