## 4 The Dynamic Changes of Stress and Energy Distributions Induced by Mining Activities
### Vertical Stress Variation of Coal Pillars and the GSWF Roof  
(1) Influence of secondary mining on the vertical stress distribution within the coal pillar  
We analyzed the vertical stress within the coal pillar at various advance distances, considering four typical coal pillar widths of 5, 10, 20, and 40 m. The stress distribution within the coal pillar during the mining process of the GSWF for various coal pillar widths is shown in Figure 13. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithology** & **Density/ (kg/m\({}^{3}\))** & **Shear** & **Bulk** & **Cohesion/MPa** & **Friction/(\({}^{\circ}\))** & **Tensile Strength/MPa** \\ \hline Sandy & 2510 & 4.2 & 5.6 & 4.7 & 34 & 4.3 \\ mudstone & 2750 & 5.0 & 6.9 & 3.0 & 32 & 3.6 \\ Sindy & 2510 & 3.5 & 5.2 & 5.0 & 33 & 4.5 \\ mudstone & 2650 & 2.9 & 3.9 & 2.8 & 36 & 3.5 \\ Medium- & 2850 & 2.4 & 4.2 & 3.0 & 38 & 3.7 \\ sandstone & 2600 & 2.5 & 4.2 & 3.2 & 32 & 3.0 \\ Fine-grained & 2640 & 3.3 & 4.4 & 3.1 & 35 & 2.9 \\ Silstone & 2750 & 4.5 & 6.7 & 2.9 & 34 & 3.3 \\ No. 3-1 seam & 1380 & 1.2 & 2.3 & 2.6 & 25 & 1.3 \\ Sandy & 2470 & 3.8 & 4.8 & 5.0 & 34 & 4.6 \\ Backfill material & 1700 & 0.2 & 1.0 & 0.4 & 15 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of the geological strata employed for the numerical model. Figure 12: Illustrative representation of stress monitoring lines at GSWF. Figure 13 illustrates that the excavation of the GSWF has a profound influence on the vertical stress patterns within coal pillars. This impact varies depending on the coal pillar width. Notably, the stress experienced by the coal pillar during the secondary mining stage exceeds that of the first mining stage. After the excavation of the first working face, vertical stress concentrates in the coal pillar area, potentially causing plastic deformation. Subsequent excavation of the adjacent working face results in superposition of secondary mining-induced stress in the coal pillar area. Consequently, the vertical stress within the coal pillars increases. Furthermore, the adjacent DWFs form a symmetrical T-shaped structure in the gob area, leading to the complete fracturing of the overlaying strata. Consequently, these fractured layers impose a substantial load on the coal pillar. This leads to a marked increase in the vertical stress within the coal pillar. Meanwhile, the vertical stress in the coal pillar also rises within about 150 m in front of the working face. Consequently, high stress concentrates on the coal pillar side of the GSR. This stress concentration often leads to dynamic pressure behavior in the GSR and, in extreme cases, may trigger coal bursts. With a coal pillar width of 5 m, vertical stresses ranged from 7.42 to 9.45 MPa, exhibiting a maximum growth rate of 30.89% compared to the first mining stage. The coal pillar width being increased to 10 m led to higher vertical stresses, reaching 18.97 to 23.23 MPa, though the maximum growth rate decreased to 22.54%. Further widening to 20 m coal pillars caused a significant increase in vertical stress, ranging from 36.96 to 52.15 MPa, with the maximum growth rate rising to 27.92%. Notably, the 40 m coal pillar width showed lower vertical stresses of 31.40 to 42.28 MPa, with the lowest maximum growth rate of 22.33% compared to the first mining stage. Within the simulated range, vertical stress in the coal pillar side on the GSR under secondary mining initially increases with coal pillar width, then decreases. This pattern generates stress relief areas with lower vertical stress. Consequently, placing roadways in stress relief areas can create a low static load condition. Under the same conditions of dynamic load disturbance, the potential risk of coal bursts in the roadway can be reduced.