## 4 Example Analysis Validation
### Numerical Simulation Analysis of WFZDH  
#### 4.3.1 Modeling  
For extending the UDEC two-dimensional discrete medium description to three dimensions, the 3 DEC (v.7.0) procedure is used. It can describe the basic constituent objects of a rock body, i.e., rock masses and structural surfaces. Also, it has a rich library of structural material models for geotechnical bodies, which is especially suitable for studying the motion, deformation, and damage characteristics of discrete media. To study the destruction of overburdened rock and the development of fractures as the working face advances, we used 3 DEC to carry out simulation and analysis. The numerical simulation method is more complex and comprehensive, providing richer information and better visualization of results, as well as allowing for comparison between theoretical analysis and field measurement parts of this study.  
In order to facilitate numerical model calculations based on the geological conditions of the Yeping Coal Mine, thinner rock layers were merged and simplified. Using 3 DEC simulation software, a calculation model of 400 \(\times\) 280 \(\times\) 120 m (strike \(\times\) tendency \(\times\) height) was established, in which the working face size was 300 \(\times\) 180 \(\times\) 4 m (strike \(\times\) tendency \(\times\) height), as shown in Figure 7. The numerical model selected was a Mohr-Coulomb model for the block and the contact Coulomb slip model for the joint. Based on field drilling data and indoor test results, physical and mechanical parameters were determined, as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Lithology** & **Thickness/m** & **D/(kg\(\cdot\)m\({}^{-3}\))** & **K/GPa** & **G/GPa** & \(\varphi_{\text{m}}\)/(\({}^{\circ}\)) & **C\({}_{\text{m}}\)/MPa** & \(\sigma_{\text{tm}}\)/MPa \\ \hline Medium sandstone & 5 & 2.4 & 26.7 & 7 & 35 & 3 & 4 \\ Mudstone & 9 & 2.5 & 18.9 & 5 & 25 & 1.5 & 3 \\ Medium sandstone & 5 & 2.4 & 26.7 & 7 & 35 & 3 & 4 \\ Mudstone & 8 & 2.5 & 18.9 & 5 & 25 & 1.5 & 3 \\ inferior key stratum 3 & 14 & 2.5 & 26.7 & 7 & 35 & 3 & 4 \\ Mudstone & 12 & 2.5 & 18 & 5 & 25 & 1.5 & 3 \\ inferior key stratum 2 & 12 & 2.4 & 26.7 & 7 & 35 & 3 & 4 \\ Mudstone & 12 & 2.5 & 18 & 5 & 25 & 1.5 & 3 \\ inferior key stratum 1 & 10 & 2.6 & 26.7 & 7 & 15 & 4 & 4 \\ Mudstone & 9 & 2.5 & 20 & 5 & 25 & 1.5 & 3 \\
3\#coal seam & 4 & 1.5 & 13.2 & 10 & 20 & 1.2 & 2.6 \\ Medium sandstone & 20 & 2.5 & 18.9 & 7 & 35 & 3 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coal rock mechanics parameter table. D is the density; K is the bulk modulus; G is the shear modulus; C\({}_{\text{m}}\) is the cohesion; \(\sigma_{\text{tm}}\) is the tensile strength; \(\varphi_{\text{tm}}\) is the friction angle.  
Figure 7: Numerical model diagram.  
To minimize boundary effects, 50 m coal pillars were left around each side of the 1301 working face. Each step of excavation was 5 m, with a mining height of 4 m, for a total of 60 steps of excavation. When the rock formation in the model breaks and gradually moves to a steady state, the model can be considered to have converged at this point.  
Horizontal displacement constraints were applied around the perimeter boundary of the numerical model while constraining vertical displacements at the bottom boundary. The upper boundary was an unconstrained boundary. The numerical model height is only 120 m, while the depth of cover is 600 m, so it is necessary to apply vertical stress. The stress calculation expression is given in Equation (20):  
\[P=\gamma H, \tag{20}\]  
where \(\gamma\) is the average bulk density of the overlying rock layers, and \(H\) is the overlying rock thickness (m).  
The result calculated according to Equation (20) is 12.96 MPa.