# Research on the Roof Failure Law of Downward Mining of Gently Inclined Coal Seams at Close Range
## 2 Overview of the Mining Area
### Numerical Simulation Analysis of the Evolution Law of Overlying Rock Fractures  
As shown in Figure 6, when the working face of Coal Seam 1 advances 20 m, no collapse occurs in the overlying roof strata. When the working face advances to 40 m, the immediate roof space undergoes its initial break and collapse, with a collapse height of approximately 2 m. The thick, hard rock strata above the roof do not show significant fracturing, and only slight disturbances appear in front of the coal wall. When the working face advances to 60 m, the main roof experiences its initial break, with a fracture height of 8 m. The entire main roof collapses, and the fallen strata cover the entire goat area. Separation fractures are formed, with a relatively small separation height. After the working face stabilizes, the fracture development height reaches 8 m, and the fractures continue to propagate upward. When the working face advances to 100 m, the overlying strata in the middle of the goat break at a location 15 m behind the working face. At this point, a hinged structure forms in the thick, hard rock strata, which still serve a load-bearing function. The collapse height reaches 6 m, and the fracture zone extends up to 28 m. After this, the height of the water-conducting fracture zone increases slowly. When the working face advances to 240 m, as the goat area expands, the collapse zone height reaches approximately 8 m, and the water-conducting fracture zone height increases to 36 m. The fractures in the overlying strata are mainly concentrated on both sides of the working face. Beyond this point, the water-conducting fracture zone does not develop further, and the strata in the goat gradually become compacted. When the working face advances to 320 m, with the continued retreat of the working face, the collapse zone height remains at 8.4 m, and the height of the water-conducting fracture zone remains at 36 m. Therefore, after the extraction of Coal Seam 1, the final development height of the collapse zone is 8.4 m, and the development height of the water-conducting fracture zone is 36 m.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Rock Strata** & **Stratum** & **Thickness** & **Density** & **Volume Modulus** & **Shear** & **Internal Friction Angle** & **Cohesion** & **Tensile Strength** \\
**Name** & **Age** & **m** & **kg/m\({}^{3}\)** & **GPa** & **GPa** & **GPa** & \(\circ\) & **MPa** & **MPa** \\ \hline \multirow{3}{*}{Silstone} & Yanan & \multirow{3}{*}{20} & \multirow{3}{*}{2500} & \multirow{3}{*}{0.6  
face continues to advance, reaching 100 m, the collapse zone penetrates the interburden and connects with the goaf of the upper coal seam. The degree of disturbance to the upper coal seam increases, and the height of the water-conducting fracture zone above the mined-out Coal Seam 1 begins to develop further upward, extending to 44 m above the top of Coal Seam 1. The collapse zone height develops to 24 m above Coal Seam 1, after which its growth slows. When the working face advances to 160 m, the water-conducting fractures continue to expand, with increasing fracture aperture. Reactivation of the overlying strata occurs behind the working face. At this stage, the maximum height of fracture development reaches 60 m above the top of Coal Seam 1. When the working face advances to 260 m, differences in lithology and physical-mechanical properties among the overlying strata result in varying deformation and subsidence rates between adjacent layers, leading to interlayer separation. The separation space develops at 105 m above the top of Coal Seam 1. At this point, the height of the water-conducting fracture zone reaches 89 m above the top of Coal Seam 1 but does not extend through to the upper separation layer. Beyond this stage, the height of the water-conducting fracture zone no longer increases, reaching its maximum extent. When the working face advances to 320 m, mining has reached the stopping line.