# Mechanism of Stratum Instability and Dynamic Deformation under Discontinuous Boundary Conditions
## 6 Numerical Simulation Analysis of Discontinuous-Boundary Fault Activation
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Rock Name** & **Thickness (m)** & **Bulk (GPa)** & **Shear (GPa)** & \(\sigma_{\text{tension }}\) (MPa)** & **Fric. (\({}^{\circ}\))** & **Coh. (MPa)** \\ \hline Silstone & 26 & 9.94 & 6.5 & 3.2 & 35 & 2.4 \\ Fine sandstone & 5 & 9.82 & 6.7 & 1.6 & 32 & 2.5 \\ Sandy mudstone & 4 & 8.16 & 5.8 & 0.7 & 26 & 1.7 \\ Silstone & 22 & 3.68 & 3.1 & 0.56 & 20 & 2.4 \\ Sandy mudstone & 6 & 8.16 & 5.8 & 0.7 & 26 & 1.7 \\ Fine sandstone & 8 & 10.6 & 9.1 & 2.2 & 32 & 2.0 \\ Silstone & 3 & 9.94 & 6.5 & 3.2 & 30 & 2.4 \\ Silty mudstone & 4 & 8.16 & 5.8 & 0.7 & 26 & 1.7 \\ \#1 coal seam & 5 & 3.22 & 1.0 & 0.6 & 25 & 0.2 \\ Silty mudstone & 5 & 8.16 & 5.8 & 0.7 & 26 & 1.7 \\ Fine sandstone & 7 & 9.82 & 6.7 & 1.6 & 32 & 2.0 \\ \#2 coal seam & 3.2 & 3.22 & 1.0 & 0.6 & 25 & 0.23 \\ Sandy mudstone & 4 & 8.16 & 5.8 & 0.7 & 26 & 1.7 \\ Silstone & 26 & 9.94 & 6.5 & 3.2 & 35 & 2.4 \\ Fault zone & 1.2 & 0.0083 & 0.0038 & 0.002 & 15 & 0.30 \\ \hline \end{tabular}
\end{table} 
Table 2: Rock mechanics parameters of each rock stratum. Figure 11: Numerical model of fault zone. As shown in Figures 14 and 15, as the advancing distance increases, the suspended area of the goat gradually increases, and the supporting area of the lower part of the rock layer on the inner side of the fault zone decreases, leading to the occurrence of pressure-relief zones and stress-concentration zones in the surrounding rock of the fault zone. According to Figure 15a,b, it can be seen that the vertical stress at measurement  
Figure 12: Vertical stress distribution of rock strata in goat with discontinuous boundary. **(a)** Working face advancing 0 m. **(b)** Working face advancing 30 m. **(c)** Working face advancing 60 m. **(d)** Working face advancing 90 m. **(e)** Working face advancing 120 m. **(f)** Working face advancing 150 m.  
Figure 13: Distribution of plastic zone of rock strata in discontinuous-boundary goat. point A of the surrounding rock in the upper part of the fault zone has decreased from 8.76 to 4.88 MPa, and the vertical stress at measurement point B has decreased from 8.41 to 3.14 MPa. The monitoring results indicate that as the working face advances, the vertical stress in the hanging-wall area of the fault zone decreases, and a pressure-relief zone appears in the upper part of the fault zone. From Figure 15c, it can be seen that the vertical stress value of measuring point C in the middle of the fault zone changes from 8.76 to 5.53 to 6.19 to 5.53 MPa. The vertical stress value of this measuring point undergoes a process of decreasing, then rising, then decreasing. The stress decrease is caused by the activation of the upper fault surrounding rock, and the intermediate stress-increase stage is caused by the increase in the advanced support pressure of the working face. The overall vertical stress shows a downward trend. According to Figure 15d, it can be seen that the vertical stress value of measuring point D in the middle of the fault zone changes from 7.09 to 5.63 to 9.52 MPa. The vertical stress value of this measuring point undergoes a process of decreasing and increasing. The stress decrease is caused by the activation of the upper fault's surrounding rock, and the later stage of stress increase is caused by the increase in advanced support pressure of the working face. According to Figure 15e,f, it can be seen that the vertical stress at measuring point M in the upper surrounding rock of the fault zone increases from 7.65 to 13.12 MPa, and the vertical stress at measuring point N increases from 14 to 19.67 MPa. The monitoring results indicate that as the working face advances, the vertical stress in the footwall area of the fault zone shows a decreasing trend, and a stress-concentration area appears in the lower part of the fault zone.