## 4 Mechanism of Shock Failure of the Main Roadway Roof in the Coal Seam with Asymmetric Goal  
### Stress Distribution Characteristics of Main Roadway  
To investigate the stress distribution characteristics in the area of the coal seam main roadway in the fourth-district region influenced by an asymmetric goat, a FLAC3D numerical model was established. The model dimensions (length \(\times\) width \(\times\) height) were 5000 m \(\times\) 4950 m \(\times\) 435 m. The model adopts the Mohr-Coulomb elastoplastic material model, where the goat is replaced by an empty model. Horizontal constraints were applied to all sides of the model, and the bottom was subjected to both horizontal and vertical constraints, while the top was considered a free surface. Based on the measured depth of coal seam mining and in situ stress values, a vertical stress of 7.25 MPa was applied to the model's top, and horizontal stresses of 20.55 MPa and 13.10 MPa were applied along the x and y axes, respectively. The mechanical parameters of different strata in the model were determined through on-site investigations and rock mechanics property tests, as detailed in Table 1. The simplified cross-section of the numerical model is illustrated in Figure 6.  
Considering the actual conditions at the engineering site, the model first simulates the excavation of LW21204 and, subsequently, the excavation of the main headgate and auxiliary main headgate. Finally, based on the designed mining sequence for the fourth-district working faces, the model simulates the sequential excavation of working faces such as 21405 and 21406. The vertical stress profile cloud map in Figure 7 illustrates the effects of sequential mining on both sides of the main roadway. As can be seen from the picture, after the mining of LW21205, the stress in the roadway area is generally within the 20-25 MPa stress contour; following the mining of LW21405, a small area of stress increase is evident in the main tailgate and main headgate regions. Post mining of LW21406, the stress-increase region expands to cover the entire main roadway area, resulting in the roadway area being mostly within the 25-35 MPa stress contour; subsequent mining activities in the 21407, 21408, and other working faces lead to a slight increase in stress in the roadway area, but the stress distribution characteristics remain unchanged. After the mining of LW21404, where the mining direction does not intersect with the goat of LW21205, the stress in the roadway area decreases. The subsequent mining activities in 21403, 21402, and other working faces exhibit similar stress levels in the roadway area, aligning with the stress levels in the original rock stress. Therefore, the subsequent analysis will primarily focus on the mining characteristics of the 21406, 21407, and other working faces on the south side of the 21405 initial mining face. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lithology** & **Density (kg/m\({}^{3}\))** & **Bulk (GPa)** & **Shear (GPa)** & **Cohesion (MPa)** & **Friction (\({}^{\circ}\))** \\ \hline Coal & 1540 & 4.12 & 1.47 & 8.60 & 36 \\ Packsand & 2250 & 1.44 & 3.35 & 13.0 & 35 \\ Sandy mudstone & 2450 & 1.55 & 3.82 & 8.0 & 36 \\ Medium sandstone & 2700 & 2.50 & 1.80 & 1.70 & 38 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of coal and rock. Figure 6: Simplified diagram of numerical model section. To further refine this study and examine the stress evolution characteristics of the roadway roof after the formation of goafs on both sides, Figure 8 illustrates the vertical stress variation curves of the main roadway roof in different mining stages. From Figure 8, it can be observed that after the mining of LW21205 on the east side of the roadway, a stress-elevated zone resembling a \"double-peak\" is formed on the roof of the main roadway area, the maximum peak stress is 28.06 MPa, and the maximum peak position is close to the belt transport roadway.