## 4 Model Establishment and Instability Evaluation Method  
### Development of a Numerical Model  
Select (4-5) 06w belt groove head-on end to the rear 80 m to establish the model. The model adopts the Mohr-Coulomb constitutive model, based on the geomechanical parameters obtained from a mine in Xinjiang, along with the accompanying report. The mechanical properties of each rock layer within the model are presented in Table 1.  
The dimensions of the research model are specified as length \(\times\) width \(\times\) height = 120 m \(\times\) 80 m \(\times\) 70 m. The roadway is designed in a rectangular configuration, with a net width and net height of the section measuring 4.95 m \(\times\) 3.7 m, as depicted in Figure 10. In FLAC(30), the propagation of stress waves within the medium can be effectively simulated through appropriate element division and node placement. Through the application of Hypermesh modeling software (2021), we determine the minimum modeling dimensions and the criteria for discretization quality relevant to vibration waves. Additionally, we incorporate the quality assessment and optimization tools provided by Hypermesh to ensure that the constructed model is consistent with the propagation characteristics of the vibration wave. This methodology significantly improves the accuracy and reliability of the numerical simulation. The anchor bolt and anchor cable are represented by cable elements, while the prestressed anchor bolt and anchor cable are modeled by assigning distinct attributes to the free segment and the anchorage segment, as illustrated in Figure 11. The anchor bolt and anchor cable are represented by cable elements, while the prestressed anchor bolt and anchor cable are modeled by assigning distinct attributes to the free segment and the anchorage segment, as illustrated in Figure 11. As a result, once the shock wave is introduced, the sphere is removed from the model. Following the removal of the sphere, a plastic zone will develop around it, leading to excessive absorption of the vibrational wave, which will cause the level of attenuation to exceed the true attenuation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lithology** & \begin{tabular}{c} **Elastic Modulus** \\ **(GPa)** \\ \end{tabular} & **Poisson Ratio** & \begin{tabular}{c} **Internal Friction** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Cohesion** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Tensile Strength** \\ **(MPa)** \\ \end{tabular} \\ \hline Sandstone & 14.0 & 0.36 & 38.06 & 12.60 & 3.28 \\ Mudstone & 12.36 & 0.24 & 38.36 & 19.69 & 5.24 \\ Fine sandstone & 15.55 & 0.29 & 46.82 & 11.83 & 7.95 \\ Coarse sandstone & 20.55 & 0.21 & 35.94 & 12.6 & 6.3 \\ NO. 4-5 coal seam & 2.56 & 0.24 & 24.00 & 2.4 & 1.34 \\ Mudstone & 11.70 & 0.24 & 36.61 & 8.76 & 3.56 \\ NO. 7 coal seam & 2.56 & 0.24 & 24.00 & 2.4 & 1.34 \\ Sandstone & 30.73 & 0.28 & 41.21 & 12.6 & 6.84 \\ Coarse sandstone & 16.21 & 0.41 & 46.82 & 11.83 & 7.95 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geomechanical material properties.  
Figure 9: Velocity diagram for different source radii.  
Therefore, the corresponding FISH function is developed to calculate the range of the plastic zone generated by the removal of the spherical source. This region is defined using an elastic constitutive model to mitigate the impact of the plastic zone created by the excavation on the propagation of vibration waves, as illustrated in Figure 12.