## 3 Materials and Methods
### Simulation Results
A zone of reduced stress occurred above the 817 longwall, while, above the 815 longwall, after the compression of rocks in the goat, stress gradually recovered. This stress distribution aligns with the modern understanding of the geomechanical processes that occur above the longwall goat. The adequacy of numerical models was evaluated by the deviation value of the simulation results from actual field-measured parameters. Since in situ subsidence monitoring was not conducted within this study, the model validation and calibration were performed using predicted subsidence values, as calculated according to the regulation MFEU 101.00159226.001-2003 [31]. Table 3 presents the calculated results of the subsidence trough according to the regulation MFEU [31]. The surface subsidence graphs, used in this study as a criterion for validation of numerical model, are presented in Figure 9.  
The accuracy of the numerical model was assessed based on the percentage error calculation. The percentage error for subsidence was calculated as follows:  
\[\mu_{\text{s}}=\frac{S^{mon}-S^{sim}}{S^{mon}}100\% \tag{2}\]  
where \(S^{mon}\)--Subsidence according to MFEU, mm; \(S^{sim}\)--Subsidence based on numerical simulation results, mm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Length of the Semi-Trough, m** & **Subsidence, m** \\ \hline
0.00 & \(-\)1.80524 \\ \hline
62.00 & \(-\)1.78719 \\ \hline
124.00 & \(-\)1.71498 \\ \hline
186.00 & \(-\)1.55251 \\ \hline
248.00 & \(-\)1.28172 \\ \hline
310.00 & \(-\)0.90262 \\ \hline
372.00 & \(-\)0.52352 \\ \hline
434.00 & \(-\)0.25273 \\ \hline
496.00 & \(-\)0.09026 \\ \hline
558.00 & \(-\)0.01805 \\ \hline
620.00 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the calculation of semi-trough parameters [31]. To assess the error across the entire subsidence curve, the cumulative error was used. For the calculation of this error, the subsidence data were read from graphs along the length of the subsidence trough with a 50 m step. The scheme explaining this process is presented in Figure 10.  
The uniform step of data reading from graphs aided to eliminate an error accumulation. The results of the analysis are presented in Table 4. This table also includes the step-by-step calculation of percentage error. The percentage error calculated according to (2):  
\[\mu_{\text{s}}=\frac{18948-20046.1}{18948}100\%=-5.79\% \tag{3}\]  
The cumulative error is 5.79%, a result that indicates sufficient model accuracy. Based on this, it can be concluded that the numerical model is adequate and can be used in this study. Figure 10: The scheme of reading data from graphs. Figure 9: Surface subsidence calculated according to MFEU 101.00159226.001-2003 [31] and the finite element method. Three horizontal monitoring lines were used for the stress-strain analysis of the rock mass above the goaf, the edge of the 817 longwall, and the coal seam (Figure 11). Monitoring line 1 was located along the lower boundary of the aquifer (elevation mark \(-\)487.0 m). \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Length of the Semi-Trough, m**} & \multicolumn{2}{c}{**Subsidence According to**} & \multirow{2}{*}{**Absolute**} & \multirow{2}{*}{**Percentage**} \\ \cline{2-2} \cline{5-5}  & & & **MFEU, mm** & & **Method, mm** \\ \hline  
Total & 18,948.3 & 20,046.1 & \(-\)1097.8 & \\ \hline \end{tabular}
\end{table} 
Table 4: Results of percentage error calculation. Figure 11: Position of monitoring lines in model. Monitoring line 2 was located along the lower boundary of the fractured zone (upper boundary of the caved zone), which is also at the most hazardous intersection (where the seam depth is minimal, at the crest of the anticline) (elevation mark \(-\)587.0 m). Monitoring line 3 was located between two previous lines along the upper boundary of the fractured zone at the most hazardous intersection (elevation mark \(-\)557.0 m).