## 3 The Study on the Evolution of Overlying Strata Fractures
### Result and Discussion  
#### 3.2.1 Overlying Strata Failure Law  
To investigate the fracture and collapse behavior of the overlying strata during the mining process, the simulation results of goat overburden cavity at different mining distances are shown in Figure 4. Based on the simulation results, the relationship between the heights of bed separation fractures and breakage fractures and the mining distance was analyzed, as shown in Figure 5. The results indicate that before the working face advances 40 m, Mudstone 4 collapses synchronously with mining. When the mining reaches 40 m (Figure 4a), the initial collapse occurs in Kern Stone 3, Mudstone 3, and Sandy Mudstone. These three strata subsequently undergo periodic collapse at intervals of approximately 15 m. When mining distance reaches 75 m, the first fractures appear in Kern Stone 2 and the two overlying layers, followed by collapse at 90 m. Thereafter, the strata below Kern Stone 1 undergo deformation and failure in response to the collapse of Kern Stone 3. Once the working face advances to 105 m, the overlying strata begin to exhibit a stable pattern of periodic failure. Based on the analysis and key stratum theory [39; 40; 41], Kern Stone 3  
Figure 3: Comparison of loaded stress–strain curves and damage patterns. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Rock Stratum Name**} & \multirow{2}{*}{**Ball Radius (m)**} & \multirow{2}{*}{**Density Modu- (GPa)**} & \multirow{2}{*}{\begin{tabular}{c} **Effective Modu- \\ **loss (GPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Normal-to-** \\ **Shear Softness** \\ **Ratio** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Parallel Bond** \\ **Bond** \\ **Effective** \\ **Modulus (GPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Parallel-to** \\ **Normal-to-** \\ **Shear Stiffness** \\ **Ratio** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Parallel-to** \\ **Normal-to-** \\ **Shear Stiffness** \\ **Ratio** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Transile** \\ **Strength** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Cohesion** \\ **Angle (°)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Friction** \\ **Angle (°)** \\ \end{tabular} } \\ \hline Mudstone 1 & 0.2–0.3 & 2500 & 1.8 & 1.2 & 2.0 & 1.2 & 3.8 & 4.9 & 30.9 \\ Kern stone 1 & 0.2–0.3 & 2500 & 7.0 & 1.8 & 7.0 & 1.8 & 10.2 & 18.5 & 37.5 \\ Limestone & 0.2–0.3 & 2500 & 6.2 & 1.3 & 6.5 & 1.3 & 9.6 & 16.1 & 36.8 \\ Mudstone 2 & 0.2–0.3 & 2500 & 2.0 & 1.4 & 2.0 & 1.4 & 3.5 & 4.1 & 34.9 \\ Kern stone 2 & 0.2–0.3 & 2500 & 3.3 & 1.3 & 3.3 & 1.3 & 9.0 & 16.5 & 30.9 \\ Sandy mudstone & 0.2–0.3 & 2500 & 1.1 & 2.5 & 3.0 & 2.5 & 8.0 & 14.0 & 30.6 \\ Mudstone 3 & 0.2–0.3 & 2500 & 0.6 & 2.3 & 2.8 & 2.3 & 3.8 & 4.5 & 35.3 \\ Kern stone 3 & 0.2–0.3 & 2500 & 4.2 & 1.5 & 4.6 & 1.5 & 9.1 & 15.7 & 33.4 \\ Mudstone 4 & 0.2–0.3 & 2500 & 0.32 & 2.9 & 2.4 & 2.9 & 5.0 & 8.5 & 30.1 \\ Coal 3 & 0.1 & 1800 & 0.8 & 1.0 & 0.8 & 1.0 & 1.0 & 2.0 & 30.0 \\ Filling structure & 0.1–0.15 & 2500 & 5.5 & 2.3 & 6.0 & 2.3 & 9.7 & 17.9 & 35.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mesoscopic mechanical parameters. and Kern Stone 2 are identified as the first and second subordinate key strata, respectively, while Kern Stone 1 is recognized as the primary key stratum within 140 m above the coal seam. The first weighting interval of the working face is 40 m, and the periodic weighting interval is approximately 14 m. After the working face has advanced 105 m, the overlying strata begin to exhibit a stable pattern of periodic failure. Mine pressure monitoring at the working face indicates a first weighting interval of 36 m and a periodic weighting interval of 14 m. The numerical simulation results are in close agreement with these observations, demonstrating the accuracy of the meso-macro parameter mapping in the model and confirming its effectiveness in reproducing the real-world behavior of the overlying strata.