## 3 Stability Analysis of Roadways Under High Horizontal Stress Conditions
### Stability Analysis of Surrounding Rock Under Different Stress Angles  
To discuss the condition of the horizontal stress when the included angle between the direction of the \(\sigma_{\rm H}\) and the roadway strike varies, numerical simulations are carried out for seven included angles of \(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\), respectively. The simulation results are shown in Figure 6. Based on the simulation results, the curves of the horizontal stress varying with the distance from the roof and floor under different angles are plotted, as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Lithology**} & **Density** & **Tensile** & **Cohesion** & **Internal** & **Bulk** & **Shear** & **Thickness** \\  & **kg/m\({}^{3}\)** & **Strength** & **MPa** & **Argle\({}^{\circ}\)** & **Modulus** & **GPa** & **GPa** & **m** \\ \hline Silstone & 2448 & 2.56 & 3.94 & 36.02 & 9.12 & 4.41 & 19 \\ Mudstone & 2183 & 1.47 & 3.17 & 35.84 & 3.67 & 1.92 & 18 \\ Coal Seam & 1443 & 0.85 & 1.89 & 26.65 & 1.98 & 1.02 & 3 \\ Sandy Mudstone & 2297 & 1.63 & 3.25 & 30.71 & 4.72 & 2.27 & 18 \\ Medium-grained Sandstone & 2613 & 2.79 & 4.13 & 33.56 & 8.73 & 4.65 & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of each rock layer. Figure 5: Model diagram. the roadway center, the stress concentration phenomenon becomes more and more significant, and the roadway stability weakens. 2. With increasing angle, the peak value of the horizontal stress also increases. When the angle is 0\({}^{\circ}\), the horizontal stress is at its minimum, 6.5 MPa, and the roadway is the most stable at this time. When the included angle is 90\({}^{\circ}\), the peak value reaches 18.8 MPa, approximately twice the initial rock stress, and at this point, the stability of the roadway is the worst. 3. As the distance from the roof and floor increases, the horizontal stress increases accordingly. Within 4 m of the roof and floor, the horizontal stress increases rapidly and slows down when it exceeds 4 m. The horizontal stress tends to stabilize when the distance from the roof and floor is beyond 6-8 m. When the angle is between 0\({}^{\circ}\) and 60\({}^{\circ}\), the horizontal stress stabilizes and does not exceed the vertical stress at the roadway's position. At this point, the roadway's stability is relatively good. When the angle exceeds 60\({}^{\circ}\), the horizontal stress exceeds the vertical stress, and the roadway is greatly affected by the horizontal structural stress field. The roadway's stability significantly decreases, and instability and failure are prone to occur. To discuss the deformation of the surrounding rock when the angle varies, numerical simulations were carried out respectively for seven angles of 0\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\), and 90\({}^{\circ}\). The simulation results are shown in Figure 8. Based on the simulation outcomes presented in Figure 8, the curves of deformation under different angles are plotted, as depicted in Figure 9.  
From the analysis of Figures 8 and 9, the following can be observed:  
1. When the angle varies, the roadway deformation is significantly different, the roof subsidence is the largest, followed by the floor heave, and the overall trend is increasing. Therefore, during roadway excavation, the direction with the smallest angle to the principal stress direction should be selected, whenever possible, to enhance the stability of the roadway. 2. When the angle ranges from 0\({}^{\circ}\) to 15\({}^{\circ}\), the deformation is relatively small, and the roadway remains generally stable. As the angle increases to 30-75\({}^{\circ}\), the deformation increases rapidly, leading to phenomena such as roof separation and side spalling. When the angle reaches 90\({}^{\circ}\), the deformation is maximized, the roadway is severely damaged, and its support becomes more difficult.