## 5 Numerical Simulation Analysis of the Damage Rule of the Loose Layer
### Study on the Damage Law of the Loose Layer  
#### 5.2.1 Evolution Process of Loose Layer Damage  
As the working face advanced to 80 m (Figure 10a), cracks began to form in the loose layer due to the influence of mining activities. At this stage, minor non-penetrating cracks emerged in the lower gravel portion of the loose layer. As the working face progressed 100 m (Figure 10b), cracks in the loose layer predominantly emerged in the center of the goat, while vertical cracks formed in front of the working face. Cracks began to form transverse clusters in the gravel layer, with some transverse cracks also appearing in the loose layer. The black-brown loose layer also developed a few vertical cracks. However, these cracks in different layers did not fully penetrate, and instead, they exhibited a staggered development pattern.  
As the working face progressed to 140 m (Figure 10c), more extensive transverse crack groups began to develop across the layers of the loose overburden. These groups were mainly concentrated in the gravel and loose layers, while the black-brown loess layer showed a vertical jumping development of the cracks. At 180 m (Figure 10d), vertical penetrating cracks appeared in the loose layer above the goat, with significant crack formation in both the gravel and loess layers. The trend toward full penetration of these cracks became more pronounced.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **Lithology** & **Density/ (kg/m\({}^{-3}\))** & **Friction** & \(\overline{E_{n}}\) **(Bond** & \(\overline{k\!n}\) **(Normal** & \(\overline{k\!s}\) **(Parallel** & \(\overline{k\!n}\)**/\(ks\) \\ **Stiffness of** & **Band Shear** & **Stiffness of** & **Parallel Bond)** & **Stiffness** & **Ratio)** \\ \hline J1 & Sandy mudstone & 2560 & 0.2 & 3.10 & 5.36 & 7.83 & 1.46 \\ \hline J2 & 2 II coal & 1340 & 0.4 & 5.10 & 4.60 & 9.84 & 2.14 \\ \hline J3 & Sandy mudstone & 2600 & 0.5 & 5.77 & 7.16 & 9.45 & 1.32 \\ \hline J4 & 2 II coal & 1429 & 0.4 & 5.10 & 6.3 & 13.42 & 2.13 \\ \hline J5 & Sandy mudstone & 2478 & 0.5 & 5.77 & 7.16 & 9.45 & 1.32 \\ \hline J6 & Kern stone & 2357 & 0.7 & 7.58 & 8.82 & 11.64 & 1.32 \\ \hline J7 & Post stone & 2230 & 0.8 & 16.90 & 10.58 & 16.93 & 1.60 \\ \hline J8 & Sandy mudstone & 2560 & 0.4 & 4.94 & 3.77 & 4.52 & 1.20 \\ \hline J9 & Post stone & 2230 & 0.8 & 10.89 & 9.06 & 10.42 & 1.15 \\ \hline J10 & Sandy mudstone & 2560 & 0.3 & 4.68 & 5.50 & 6.6 & 1.20 \\ \hline J11 & Post stone & 2340 & 0.6 & 16.90 & 13.2 & 21.12 & 1.60 \\ \hline J12 & Sandy mudstone & 2428 & 0.3 & 4.6 & 5.7 & 6.84 & 1.20 \\ \hline J13 & Post stone & 2412 & 0.6 & 16.90 & 13.2 & 21.12 & 1.60 \\ \hline J14 & Kern stone & 2357 & 0.8 & 11.13 & 10.83 & 19.06 & 1.76 \\ \hline J15 & Gravel & 2800 & 0.85 & 17.20 & 11.52 & 21.77 & 1.89 \\ \hline J16 & Red-bodied & & & & & & \\  & weathered sand & 2200 & 0.3 & 4.50 & 21.1 & 25.32 & 1.20 \\ \hline J17 & Loess & 2070 & 0.2 & 3.50 & 7.6 & 13.68 & 1.80 \\ \hline J18 & Black brown & & & & & \\  & loess & 2183 & 0.4 & 4.83 & 12.50 & 18.75 & 1.50 \\ \hline J19 & Drift-sand & 2155 & 0.2 & 0.24 & 4.3 & 4.82 & 1.12 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fine mechanical parameters of each rock layer.  
By the time the working face advanced to 200 m (Figure 10e), the loose layer above the middle of the goaf exhibited fully developed cracks that extended directly to the surface, resulting in surface ground cracks (D1). When the working face reaches 300 m (Figure 10f), coal seam mining has been halted. At this point, the loose layer showed extensive transverse cracking, primarily in the gravel and loose layers. The surface was fully penetrated by 20 ground fissures, predominantly located in the center of the goaf, with fewer boundary and working face cracks.