## 3 Numerical Simulation
### Numerical Simulation Results  
Figure 10 displays the failure depth of the floor with varying excavation distance. The depth of the floor failure is positively correlated with the excavation of the coal seam during the initial and middle stages, following which the relationship stabilized. The simulation results shown in Figure 10 demonstrate that the maximum damage depth of the horizontal stratum above a confined aquifer is roughly 14.57 m when the mining excavation reaches a critical value of 180 m, slightly less than that of the inclined stratum (i.e., 16.71 m). Subsequent to all calculations, the failure zones in the horizontal and inclined floor rocks were further analyzed, with Figures 11 and 12 showing the profiles in the middle of the numerical models along the inclination. The numerically obtained result of Figure 11 demonstrates that the overall failure mode of the horizontal floor strata is clearly an \"inverted saddle\", and the mining-disturbed boundary on both sides (approximately 14.57 m) is deeper than that in the middle (approximately 9 m). By comparison, the distribution of the mining failure zone shows a characteristic pattern of decreasing from the bottom to the top (i.e., upper small and lower large), as evident in Figure 12, and the maximum depth of failure appears in the strata beneath the area around the lower part of the inclined floor. Therefore, the comparison of the theoretical calculations in Figure 5 and the simulated results exhibits good agreement, which can also be confirmed by the previous work of [PERSON] et al. [48]. According to the results of micro-seismic monitoring \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & \(\gamma\)**/(g-cm\({}^{-3}\))** & \(G\)**/(MPa)** & \(K\)**/(MPa)** & \(c\)**/(MPa)** & \(\varphi\)**/(\({}^{\circ}\))** & \(\sigma_{\
u}\)**/(MPa)** & \(n\) & \(k\)**/(m\({}^{2}\cdot\)(Pa\(\cdot\)s)\({}^{-1}\))** \\ \hline Roof 5 & 2.5 & \(3.6\times 10^{3}\) & \(4.2\times 10^{3}\) & 4.5 & 33 & 3.7 & 0.3 & \(3\times 10^{-15}\) \\ Roof 4 & 2.7 & \(2.8\times 10^{3}\) & \(4.5\times 10^{3}\) & 5.2 & 32 & 3.6 & 0.4 & \(5\times 10^{-14}\) \\ Roof 3 & 2.6 & \(4.3\times 10^{3}\) & \(4.1\times 10^{3}\) & 5.8 & 32 & 4.2 & 0.3 & \(3\times 10^{-14}\) \\ Roof 2 & 2.6 & \(2.0\times 10^{3}\) & \(3.0\times 10^{3}\) & 3.2 & 31 & 2.8 & 0.2 & \(4\times 10^{-16}\) \\ Roof 1 & 2.5 & \(3.6\times 10^{3}\) & \(4.2\times 10^{3}\) & 4.5 & 33 & 3.7 & 0.3 & \(3\times 10^{-15}\) \\ Coal seam & 1.4 & \(0.6\times 10^{3}\) & \(1.3\times 10^{3}\) & 2.3 & 20 & 1.6 & 0.5 & \(3\times 10^{-13}\) \\ Floor 1 & 2.7 & \(2.8\times 10^{3}\) & \(4.5\times 10^{3}\) & 5.2 & 32 & 3.6 & 0.4 & \(5\times 10^{-14}\) \\ Floor 2 & 2.5 & \(3.6\times 10^{3}\) & \(4.2\times 10^{3}\) & 4.5 & 33 & 3.7 & 0.3 & \(3\times 10^{-15}\) \\ Floor 3 & 2.7 & \(2.8\times 10^{3}\) & \(4.5\times 10^{3}\) & 5.2 & 32 & 3.6 & 0.4 & \(5\times 10^{-14}\) \\ Floor 4 & 2.6 & \(2.0\times 10^{3}\) & \(3.0\times 10^{3}\) & 3.2 & 31 & 2.8 & 0.2 & \(4\times 10^{-16}\) \\ Aquifer & 2.5 & \(1.6\times 10^{3}\) & \(2.3\times 10^{3}\) & 2.0 & 30 & 2.2 & 0.7 & \(8\times 10^{-7}\) \\ \hline \hline \end{tabular} Note: \(\gamma\)—unit weight; \(G\)—shear modulus; \(K\)—bulk modulus; \(c\)—cohesive strength; \(\varphi\)—frictional angle; \(\sigma_{\
u}\)—tensile strength; \(n\)—porosity; \(k\)—permeability.  
\end{table} 
Table 1: Physico-mechanical parameters of rocks and the coal seam. Figure 10: Failure depth of the floor with varying excavation distance. shown in Figure 13, the damage in the inclined coal mine floor propagates asymmetrically downward in the shape of \"down-large-up-small\". Assuming that the area with the deepest depth of floor failure is at most risk to forming a water-inrush channel, a large volume of uncontrolled groundwater in the underlying aquifer may preferentially penetrate into the excavation space through the lower roadway of the inclined floor rock mass, thus resulting in immeasurable casualties and economic losses to underground geological engineering.