## 2 Project Overview
### Building a Numerical Model with Different Angles Between Tectonic Stress and the Roadway  
We use FLAC\({}^{\text{3D}}\) software (FLAC\({}^{\text{3D}}\) v5.0) to create a three-dimensional numerical simulation model and simulate the five groups of operating conditions presented in Table 2. The initial stress shown in Table 2 is applied in the \(x\) and \(y\) directions of the model. The ratio of \(\sigma^{{}^{\prime}}_{xx}\) to \(\sigma^{{}^{\prime}}_{zz}\) gives you the lateral pressure coefficient. Different stress gradients are simulated by changing the lateral pressure coefficients. Figure 6 shows the numerical calculation model. Table 3 shows the mechanical properties of rock layers. The mechanical parameters listed in Table 3 were obtained through laboratory testing of standard specimens sampled from the roof, floor, and coal seam. Testing followed procedures outlined in the Chinese national standard GB/T 50266-99 [37]. Bulk modulus values were derived from measured elastic modulus and Poisson's ratio. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working Condition** & **\(\theta\)/(\({}^{\circ}\))** & \(\sigma^{{}^{\prime}}_{xx}\)/MPa & \(\sigma^{{}^{\prime}}_{yy}\)/MPa & \(\sigma^{{}^{\prime}}_{zz}\)/MPa \\ \hline
1 & 0 & 33 & 9 & 20 \\
2 & 30 & 27 & 15 & 20 \\
3 & 45 & 21 & 21 & 20 \\
4 & 60 & 15 & 27 & 20 \\
5 & 90 & 9 & 33 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculation of main ground stress. Figure 5: Calculation model of roadway in any direction. Distribution Characteristics of Horizontal Stress Under Different Angles Between Tectonic Stress and Roadway  
Cloud diagrams showing horizontal stress distributions in the surrounding rock at various angles to the axial direction of the roadway plan and the direction of tectonic stress are displayed in Figure 7. The horizontal stress reduction zone manifests in the floor and roof's shallow layers, as well as those on either side of the roadway, when the angle is 0 degrees. The horizontal stress concentration zone appears in the deep layers on the roof and floor. The highest horizontal stress in the deep rock layer of the top plate is 39.6 MPa. The deeper rock layers of the top plate have more horizontal stress than the bottom plate. When the angle is 30\({}^{\circ}\), the peak horizontal stress of the deep rock in the roof rises to 46.2 MPa, after which it progressively diminishes in the deeper rock layer of the roof. When the angle is 45\({}^{\circ}\), the pressure relief range on both sides of the roadway and the shallow layers of the roof and floor gets bigger. The deep rock layer of the roof has a wider range of horizontal stress concentrations. The highest horizontal stress is 49.8 MPa. The highest level of horizontal stress concentration in the deep rock layer of the roof rises to 55.0 MPa when the angle is 60\({}^{\circ}\). The area of the roadway that can relieve pressure has grown, but the amount of pressure relief is getting less. When the angle is 90\({}^{\circ}\), the horizontal stress concentration in the deep rock strata of the roof attains its maximum level, with a peak value of 59.4 MPa. As mentioned earlier, the surrounding rock mainly consists of mudstone, sandy mudstone, and fine sandstone, with a tensile strength of less than 2 MPa, based on laboratory test results. Given that the roadway is located in a deep soft rock environment, the surrounding rock mass exhibits low load-bearing capacity and is highly susceptible to failure induced by high horizontal stress. Under these conditions, the concentrated stress far exceeds the tensile strength, increasing the likelihood of tensile cracking, interlayer separation, and roof deformation. Therefore, the  
Figure 6: Numerical simulation model.