## 5 Analysis of Numerical Simulation Results
### Internal Deformation Law of Rock Formation in Coal Seam 3 Mining  
(1) Fitting function of the maximum subsidence value of rock formation  
The maximum subsidence value of each rock formation along the strike center line was extracted, based on the computation results of the numerical simulation following coal seam mining, as shown in Table 8. Sections of each rock formation were made parallel to the x, y plane. The fitting function of the maximum subsidence value of each rock formation was analyzed. After regression analysis of the various function models, the four function equations with the best regression degree were selected to draw the fitting curve successively, as shown in Figure 6.  
According to the analysis of the function fitting error as shown in Table 9, the best fit function model is the exponential function, which is consistent with the results of [PERSON] and [PERSON] et al. [45,46]. The equation obtained in this paper is as follows. \[y=-664\exp(0.2488x)+2.128e^{5}\exp(-7.869x) \tag{8}\]  
Figure 7 shows the analysis of the exponential function equation. The data points were all within the 95% confidence interval. The first derivative of the function equation was less than 0, so the function curve monotonically decreased and was continuous. The second derivative was greater than 0, and the concavity and convexity of the function was concave. The integral curve decreased monotonically, and the function equation curve was on one side of the X axis. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Rock Formations** & **Loose Layer** & **Fine Sandstone** & **Sandy** & **Fine Sandstone** & **Sandy** & **Fine Sandstone** & **Sandy** & **Fine Sandstone** \\ \hline Buried depth (m) & 0 & –180 & –460 & –516 & –806 & –884 & –1092 & –1202 \\ Maximum & 0.716 & 0.735 & 0.808 & 0.840 & 1.103 & 1.240 & 1.793 & 2.459 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Maximum subsidence of the rock formations. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Fitting Types** & **SSE** & **RMSE** & **R-Square** & **Adjusted R-Square** \\ \hline Quadratic polynomial & \(9.796\times 10^{4}\) & 140 & 0.9232 & 0.8925 \\ Cubic polynomial & \(4.312\times 10^{4}\) & 103.8 & 0.9662 & 0.9409 \\ Power function & \(2.124\times 10^{4}\) & 65.18 & 0.9834 & 0.9767 \\ Exponential function & 7590 & 43.56 & 0.9941 & 0.9896 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Function fitting errors of the maximum subsidence value of the rock formation. Figure 6: Fitting curve of the maximum subsidence value of the rock formation. (**a**) Quadratic polynomial fitting curve. (**b**) Cubic polynomial fitting curve. (**c**) Power function fitting curve. (**d**) Exponential function fitting curve. Figure 7: Analysis of the exponential function equation. (**a**) The 95% confidence interval of the fitting curve. (**b**) First derivative of the exponential function equation. (**c**) Second derivative of the exponential function equation. (**d**) Integral curve of the exponential function equation. Fitting function of the subsidence basin boundary within the rock formation  
Based on the calculation results of the numerical simulation of coal seam mining, the sections of each rock formation parallel to the x, y plane were made, and the location of the 10 mm subsidence was used as the boundary of the mining influence range. The influence ranges of rock formation mining are shown in Table 10. After analyzing the fitting function of the subsidence basin boundary of each rock formation, through regression analysis of the various function models, four function equations with the best fitting degree were selected to draw the fitting curve in turn, as shown in Figure 8.  
The fitting errors of each function equation are shown in Table 11.