## 5 Analysis of Numerical Simulation Results  
### Coal Seam Mining and Surface Deformation  
We took the mining depth as an example to study its impact on surface subsidence. Data extraction and processing were performed on the monitoring lines laid out in the FLAC3D numerical model. The surface subsidence and horizontal movement curves at different mining depths were obtained, as shown in Figure 4a,b, respectively. When the mining depth changed from 884 m to 1284 m, the maximum surface subsidence value decreased from 0.734 m to 0.697 m, and the maximum horizontal movement value of ground surface decreased from 0.276 m to 0.256 m. As the mining depth increases, the thickness of the overlying mass gradually increases. When the damage caused by the mining of the coal seam spreads upward, the overlying rock mass first moves and deforms. When the overlying rock mass is thick, the damage is difficult to reach the surface, and the surface subsidence and deformation will become smaller. Figure 3: The FLAC3D numerical model. (**a**) Numerical model diagram; (**b**) mining face. According to the maximum subsidence value and the maximum horizontal movement value of the ground surface at different mining depths, the regression curves of the maximum subsidence value and the maximum horizontal movement value of the ground surface and the mining depth were drawn (curves 1 and 2, respectively), as shown in Figure 5a,b. Figure 4: Surface deformation curves of different mining depths. (**a**) Surface subsidence curves of different mining depths. (**b**) Horizontal movement curves of different mining depths. Figure 5: _Cont_. In the following formulas, \(W_{\text{max}}\) and \(U_{\text{max}}\) are the maximum subsidence value and the maximum value of the horizontal movement of the surface, respectively, when they are fully mined. The calculation formulas are as follows:  
\[W_{\text{max}}=q\cdot m \tag{3}\]  
\[U_{\text{max}}=b\cdot W_{\text{max}} \tag{4}\]  
where \(q\) represents the subsidence coefficient; \(m\) represents the thickness (mm); \(b\) represents the horizontal movement coefficient. Based on the maximum surface subsidence value, the surface subsidence coefficient could be further calculated, and then a regression curve (curve 3) between the surface subsidence coefficient and the mining depth was drawn, as shown in Figure 5c. The fitting errors of the three regression curves are shown in Table 7.  
From the function fitting errors table, it can be seen that the sum of squares due to the error (SSE) and root mean squared error (RMSE) of the three regression curves were close to 0, and the coefficient of determination (R-Square) and degree-of-freedom adjusted coefficient of determination (Adjusted R-Square) of the three regressions were close to 1. This shows that the fitting degree of the three regression curves was better. It can be seen from the regression curve that as the mining depth increased, the maximum \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Curve Types** & **SSE** & **RMSE** & **R-Square** & **Adjusted R-Square** \\ \hline Mining depth and maximum surface subsidence & 3.194 \(\times\) 10\({}^{-5}\) & 2.826 \(\times\) 10\({}^{-3}\) & 0.978 & 0.972 \\ Mining depth and maximum horizontal movement of surface & 6.657 \(\times\) 10\({}^{-7}\) & 1.490 \(\times\) 10\({}^{-3}\) & 0.974 & 0.956 \\ Mining depth and surface subsidence coefficient & 4.613 \(\times\) 10\({}^{-7}\) & 3.396 \(\times\) 10\({}^{-4}\) & 0.979 & 0.974 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Function fitting errors of the mining depth and surface deformation. Figure 5: Fitting curves of the mining depth and surface deformation. (**a**) Fitting curve of the mining depth and maximum surface subsidence. (**b**) Fitting curve of the mining depth and maximum horizontal movement value of the ground surface. (**c**) Fitting curve of the mining depth and surface subsidence coefficient.