## 2 Project Overview
### Building a Numerical Model with Different Angles Between Tectonic Stress and the Roadway
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \begin{tabular}{c} **Name of** \\ **Rock** \\ **Formation** \\ \end{tabular} & \begin{tabular}{c} **Density** \\ **/(kg/m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Bulk** \\ **Modulus/GPa** \\ \end{tabular} & \begin{tabular}{c} **Shear** \\ **Modulus/GPa** \\ \end{tabular} & \begin{tabular}{c} **Tensile** \\ **Strength/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Cohesion** \\ **/MPa** \\ \end{tabular} &
\begin{tabular}{c} **Internal** \\ **Friction** \\ **Angle/\({}^{\circ}\)** \\ \end{tabular} \\ \hline Coal seam 13-1 & 1470 & 0.95 & 0.57 & 0.7 & 0.8 & 30 \\ Mudstone & 2600 & 1.38 & 0.83 & 1.4 & 2 & 35 \\ Sandy & 2580 & 10.35 & 6.21 & 1.5 & 4.2 & 41 \\ mudstone & 2790 & 12.82 & 7.69 & 2.58 & 6.4 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rock mechanics parameters. \(90^{\circ}\) orientation represents the most unfavorable stress configuration and a critical condition for roof instability. The horizontal tectonic stress directly controls the amount of horizontal stress around the roadway and how it is released by directional extrusion. As the angle gets bigger, the shallow rock layer of the roadway's pressure relief range gets bigger, and the deep rock layer of the roadway's horizontal stress gets bigger. The roof causes horizontal stress to build up in certain areas because of horizontal tectonic stress extrusion. The roadway roof is the most likely to change shape. Vertical Stress Distribution Characteristics Under Different Angles Between Tectonic Stress and Roadway  
Figure 8 illustrates the vertical stress distribution of the roadway surrounding rock at various angles. At an angle of \(0^{\circ}\), a vertical stress reduction zone manifests in the ceiling and floor of the roadway, whereas a vertical stress concentration zone emerges on the two sides of the roadway. Additionally, vertical stress concentration areas are present on both sides of the roadway. The pressure relief range of the roadway roof and floor remains relatively stable when the angle is \(30^{\circ}\). The vertical stress concentration peak is \(24.7\) MPa, and the vertical stress concentration degree on both sides of the roadway is going down. At an angle of \(45^{\circ}\), the vertical stress concentration peak drops to \(23.8\) MPa, and the vertical stress concentration degree on both sides of the roadway is even lower. A stress disturbance zone is present at a \(60^{\circ}\) angle around the roadway, along with a localized vertical stress concentration zone in the deep rock strata of the roof and floor. The deep rock layers in the roof and floor experience their highest vertical stress concentration range at an angle of \(90\) degrees. In conclusion, the horizontal tectonic stress leads to a redistribution of stress following roadway excavation by altering the original rock stress field's distribution state, thereby influencing the spatial distribution characteristics of vertical stress. As the angle incrementally rises from \(0^{\circ}\) to \(90^{\circ}\), there is a noticeable increase in the vertical stress concentration within the rock strata at the base of the roadway, while the vertical stress concentration on the sides of the roadway exhibits a declining trend. The horizontal tectonic stress extrusion alleviates the vertical stress in the center of the roof and floor, resulting in the formation of a compressive stress zone at the upper section of the roadway, which leads to roof separation. Distribution Characteristics of the Flexible Zone in Surrounding Rock at Varying Angles Between Tectonic Stress and the Roadway  
Figure 9 illustrates that, at an angle of 0\({}^{\circ}\), the majority of the damage to the roof and floor of the roadway, as well as the two sides, exhibits a yield state following shear failure. Notably, the extent of damage on the two sides of the roadway is the most significant, demonstrating a ladder-like progression into the deeper strata on both sides.