## 3 Numerical Simulation Analysis
### Numerical Simulation Results and Analysis
#### 3.3.2 Evolution Characteristics of the Plastic Zone under a \(\sigma_{Z}\)-Dominant Stress Field
When \(\alpha\) is 0\({}^{\circ}\), the plastic zone morphology of roadway surrounding rock is quasi-circular and the plastic zone is evenly distributed around the roadway. With an increase in the axial angle of the roadway (10-50\({}^{\circ}\)), the plastic zone area of the two sides gradually decreases. When \(\alpha\) is 50\({}^{\circ}\), the plastic zone area of the two sides is significantly smaller than that of the roof and the floor and the plastic zone is overall thin and highly elliptical. When \(\alpha\) is 60\({}^{\circ}\), distortion begins at the four corners of the plastic zone, and the butterfly plastic zone is gradually generated. The uneven malignant expansion occurs with the increase in the angle \(\alpha\). Figure 12 shows the variation curve of the plastic zone size of the roadway with the axial angle \(\alpha\) of the roadway. The following can be seen from the curve:  
1. When \(\alpha\) is 0-60\({}^{\circ}\), the maximum radius of the plastic zone in the rock surrounding the circular roadway occurs in the middle of the roadway roof. When \(\alpha\) is 60-90\({}^{\circ}\), the maximum size of the plastic zone of the surrounding rock occurs in the two roadway wings. 2. When \(\alpha\) is in the 0-40\({}^{\circ}\) range, the size of the plastic zone of the two roadway wings does not change much and is in a relatively stable stage. When \(\alpha\) = 40\({}^{\circ}\), the size of the plastic zone of the wing angle begins to increase sharply and the failure radii are 1.50, 1.68, 2.44, 3.32, 4.04, and 4.42 m, respectively. When the axial angle is 90\({}^{\circ}\), the radius of the roadway plastic zone expands by 1.95 times. 3. When the axial angle of roadway increases from 0\({}^{\circ}\) to 40\({}^{\circ}\), the size of the plastic zone in the middle of roof decreases gradually. When \(\alpha\) is 30\({}^{\circ}\), the size of the plastic zone in the middle of the roof is the smallest, 1.50 m. From 40\({}^{\circ}\), the depth of the plastic zone in the middle of the roof gradually increases, with the maximum value of 2.76 m, increasing by 0.84 times. 4. Overall, the plastic zone size in the middle of the roadway decreases with the increase in the axial angle of the roadway. The size of the plastic zone is the largest at 0\({}^{\circ}\), which is 1.74 m, and it is stable at 0.26 m at 40-80\({}^{\circ}\). When \(\alpha\) is 90\({}^{\circ}\), the radius of the plastic zone in the sidewall increases slightly. 5. In the \(\sigma_{\rm H}\)-dominated stress field, with the increase in the axial angle \(\alpha\) of the roadway, the size slope of the wing angle plastic zone shows high sensitivity. The curve slope changes greatly, followed by the sidewall curve slope, and the roof is the smallest. Therefore, in the \(\sigma_{\rm H}\)-dominant stress field, the sensitivity of different positions of the roadway to angle \(\alpha\) is wing angle > side > roof. Figure 11: Distribution pattern of the roadway plastic zone under different values of angle \(\alpha\) under the dominant stress field of \(\sigma_{\rm H}\).