# Research on the Roof Failure Law of Downward Mining of Gently Inclined Coal Seams at Close Range
## 2 Overview of the Mining Area
### Calculation of the Development Height of the \"Two Zones\" for Close-Range Coal Seam Group Mining
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coal Seam** & **Mining Thickness** & **Average Distance From the** & **Average Inclination Angle of** \\
**Working Face** & **/m** & **Upper Coal Seam/m** & **Coal Seam/\({}^{\circ}\)** \\ \hline
1 Coal 110104 & 2.9 & \(\backslash\) & 15 \\
2 Coal 110204 & 3.8 & 8 & 15 \\
4 Coal 110404 & 2.7 & 23 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: A list of the spatial relationships of coal seams in the Yindonggou Coal Mine research area. mining thickness \(M_{L}\) of Coal Seam 2 is 3.8 m. Therefore, after mining of the 110204 working face of Coal Seam 2, the subsidence coefficient of the interlayer rock layer is:  
\[q_{i}=1-\frac{\sum h(K_{s}-1)}{M_{L}}\cos\alpha=1-\frac{8\times(1.04-1)}{3.8} \times\cos 15=0.92 \tag{6}\]  
The subsidence value of the interlayer rock strata is:  
\[m=q_{i}M_{L}=0.92\times 3.8=3.5\text{m} \tag{7}\]  
The comprehensive mining thickness of double-layer coal is:  
\[M_{eq}=M_{L}+m=2.9+3.5=6.4\text{m} \tag{8}\]  
Height of the collapse zone:  
\[H_{k}=\frac{100M_{eq}}{0.49M_{eq}+19.12}\pm 4.71=\frac{100\times 6.4}{0.49\times 6.4+19.12}\pm 4.71=24.05\sim 33.47\text{m} \tag{9}\]  
Height of the water-conducting fissure zone:  
\[H_{li}=\frac{100M_{eq}}{0.23M_{eq}+6.1}\pm 10.42=\frac{100\times 6.4}{0.23\times 6.4+6.1}\pm 10.42=74.10\sim 94.94\text{m} \tag{10}\]  
After mining the 110204 working face in Coal Seam 2, the top of the interlayer rock subsided by 3.5 m, resulting in a comprehensive mining thickness of 6.4 m for the coal seam group. The development height range of the caving zone is 24.05 to 33.47 m above the top of Coal Seam 1, and the development height range of the water-conducting fracture zone is 74.10 to 94.94 m above the top of Coal Seam 1. After mining the 110404 working face of Coal 4, the rockfall and fragmentation coefficient \(K_{s}\) of Coal Seam 4 is taken as 1.04, the coal seam dip angle \(\alpha\) is 15\({}^{\circ}\), the distance \(h\) between Coal Seam 2 and Coal Seam 4 is 23 m, and the mining thickness \(M_{L}\) of Coal Seam 4 is 2.7 m. Therefore, after the mining of Coal Seam 4, the subsidence coefficient of the rock layer between Coal Seam 2 and Coal Seam 4 is:  
\[q_{i}=1-\frac{\sum h(K_{s}-1)}{M_{L}}\cos\alpha=1-\frac{23\times(1.04-1)}{2.7} \times\cos 15=0.67 \tag{11}\]  
The subsidence value of the rock layer between Coal Seam 2 and Coal Seam 4 is:  
\[m=q_{i}M_{L}=0.67\times 2.7=1.8\text{m} \tag{12}\]  
At this time, the subsidence coefficient of the rock layer between Coal Seam 1 and Coal Seam 2 has changed. The changed subsidence coefficient is:  
\[q_{i}=1-\frac{\sum h(K_{s}-1)}{M_{L}}\cos\alpha=1-\frac{8\times(1.04-1)}{5.6} \times\cos 15=0.94 \tag{13}\]  
The subsidence value of the rock layer between Coal Seam 1 and Coal Seam 2 changes to:  
\[m=q_{i}M_{L}=0.94\times 5.6=5.3\text{m} \tag{14}\]  
In Equations (13) and (14), \(M_{L}\) is the sum of the mining thickness of Coal Seam 2 (3.8 m) and the subsidence value of the top position of the rock layer between Coal Seams 2 and 4, caused by the mining of Coal Seam 4 (1.8 m). The comprehensive mining thickness of the three-layer coal is:  
\[q_{i}=1-\frac{\sum h(K_{s}-1)}{M_{L}}\cos\alpha=1-\frac{8\times(1.04-1)}{3.8} \times\cos 15=0.92 \tag{6}\]0  
Height of the collapse zone:  
\[q_{i}=1-\frac{\sum h(K_{s}-1)}{M_{L}}\cos\alpha=1-\frac{8\times(1.04-1)}{3.8} \times\cos 15=0.92 \tag{6}\]1  
Height of the water-conducting fissure zone:  
\[q_{i}=1-\frac{\sum h(K_{s}-1)}{M_{L}}\cos\alpha=1-\frac{8\times(1.04-1)}{3.8} \times\cos 15=0.92 \tag{6}\]2  
After mining of the 110404 working face of Coal Seam 4 was completed, the top rock strata of the spacer layer between Coal Seam 1 and Coal Seam 2 sank by 5.3 m. At this time, the comprehensive mining thickness of the coal seam group after mining was 8.2 m. The height development range of the sag zone is 30.73-40.15 m above the top of Coal Seam 1, and the height development range of the water-conducting fracture zone is 92.26-113.10 m above the top of Coal Seam 1.