# Stability Assessment of Gob Side Entry at the Steeply Inclined Mining Face
## 3 Results
### Coal Pillar Width Analysis  
The 3308 track entry is adjacent to the 3306 goaf. The width of the coal pillar directly affects the stress distribution and deformation characteristics of the surrounding rock. Analyzing the appropriate coal pillar width can not only improve the recovery rate, but also reduce the risk of rock burst. By analyzing the destruction mode of surrounding rock, the support countermeasure of roadway could be proposed. (1) Vertical Stress  
Figure 5 illustrates the vertical stress distribution of the surrounding rock with varying coal pillar widths. The stress concentration zone occurs when the contour surpasses 22 MPa. Three regions of stress concentration are indicated, with the stress maxima in each region illustrated in Figure 6. Regions #1 and #2 are situated in the upper and lower sections of the coal pillar, influencing its stability. When the pillar's width is 3 m, the range and peak stress in the two concentrated places are minimal; there exists a pressure relief zone within the pillar, where the stress value is below 22 MPa. As the width of the coal increases, the range and stress values of regions #1 and #2 also rise. When the breadth attains 4 m, the stress value in the center of the coal pillar hits 22 MPa. When the breadth attains 5 m, the two stress concentration zones in the coal pillar become interconnected, which compromises safety. The stress of the coal pillar suggest optimal widths of 3 m and 4 m. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Point** & **Principle** & **Value/MPa** & **Direction/\({}^{\circ}\)** & **Dip/\({}^{\circ}\)** & **s\({}_{\rm v}\)/MPa** & **s\({}_{\rm s}\)/\(\sigma\)v** & **s\({}_{\rm 1}\)–\(s_{\rm 3}\)** & **s\({}_{\rm 1}\)/\(s_{\rm 3}\)** \\ \hline \multirow{3}{*}{\#1} & \(s_{1}\) & 21.3 & 119.5 & 5.2 & & 1.45 & & \\  & \(s_{2}\) & 12.4 & 9.7 & 75.1 & 14.7 & 0.84 & 13.4 & 2.7 \\  & \(s_{3}\) & 7.9 & 210.8 & 13.9 & & 0.54 & & \\ \hline \multirow{3}{*}{\#2} & \(s_{1}\) & 20.2 & 121.2 & 9.3 & & 1.37 & & \\  & \(s_{2}\) & 14.7 & \(-\)3.9 & 74.1 & 14.7 & 1 & 10.2 & 2.0 \\  & \(s_{3}\) & 10.0 & 213.3 & 12.8 & & 0.68 & & \\ \hline \multirow{3}{*}{\#3} & \(s_{1}\) & 35.0 & 161.4 & \(-\)6.6 & & 1.49 & & \\  & \(s_{2}\) & 23.4 & 28.8 & \(-\)80.3 & 23.2 & 1.01 & 15.3 & 1.8 \\ \cline{1-1}  & \(s_{3}\) & 19.7 & 252.3 & \(-\)7.1 & & 0.85 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Components of in situ trees. (2) Plasticity State  
The distribution characteristics of the plastic regions are shown in Figure 7. According to the destruction criteria, after the yield, the force state is located outside the M-C envelope. The plastic zone shows a combination of yield form and yield state. Where \"shear\" and \"tension\" are t yield forms, \"n\" is the critical yield state and \"p\" means already yielded. The types of plastic zones are distinguished by different colors. Marked in green, the plasticity state of the coal pillar is the combination of \"shear-n\" and \"shear-p\". With the increase in width, the color in the coal pillar gradually changes from green to cyan (only \"shear-p\"). This phenomenon shows that the pressure of the coal pillar is positively correlated with the width. In other words, the larger pillar width can easily cause destruction and even the  
Figure 5: Surrounding rock stress: (a) 3 m; (b) 4 m; (c) 5 m; (d) 6 m.  
Figure 6: Stress peak vs. coal pillar width. collapse of the pillar. The characteristics of the plastic zone indicate that a smaller width should be selected. Marked in red, the plasticity state of roadway roof is the combination of \"tension-p\" and \"shear-p\". This phenomenon indicates that the stability of the roadway roof is worse than that of the coal pillar. Figure 8 shows the statistical results of the plastic area of the roadway roof. The area marked red is 10.88 m\({}^{2}\) when the pillar is 3 m. Shear and tensile yield occur at the roadway roof and floor.