## 3 Numerical Simulation Analysis
### Numerical Simulation Results and Analysis  
The formation, development, and evolution of the surrounding rock plastic zone are the basis of the roadway surrounding rock deformation and failure. The morphological characteristics and distribution law of the plastic zone of surrounding rock are closely related to the stability of surrounding rock and the failure mode of a roadway. Only by fully understanding the evolution law and distribution characteristics of plastic zones in different roadway axial directions can a reasonable optimization scheme be made for the roadway layout so as to avoid the formation of a butterfly plastic zone morphology, which causes greater dynamic disasters. In this section, the evolution law of the plastic zone in different orientations of the roadway under three dominant stress fields is studied from the point of view of two core elements, plastic zone morphology and size, in different axial directions of the roadway. 3.1 Evolution Characteristics of the Plastic Zone under the \(\sigma_{\rm HZ}\)-Dominant Stress Field  
Figure 7 shows the distribution pattern of the plastic zone when angle \(\alpha\) between the axial direction of the roadway and the direction of the maximum horizontal principal stress varies from \(0^{\circ}\) to \(90^{\circ}\) under the dominant stress field of \(\sigma_{\rm HZ}\). When the axial direction of the roadway is parallel to the maximum horizontal principal stress, the plastic zone of the surrounding rock of the roadway is quasi-circular. With the increase in the axial angle \(\alpha\) of the roadway, the area of the two sides of the roadway decreases significantly and the area of the roof and the floor increases gradually. The plastic zone gradually transits from quasi-circular to vertical elliptical, and the area of the roof and the floor is much larger than that of the two sides. When \(\alpha\) starts from \(60^{\circ}\), the plastic zone size of roadway surrounding rock begins to develop obliquely and the butterfly shape is slowly revealed. The plastic zone of the roadway roof and floor continues to expand. When \(\alpha\) is \(90^{\circ}\), the plastic zone shape of the roadway is transverse butterfly. Figure 6: Boundary loading conditions under three stress fields. Figure 7: Distribution pattern of the roadway plastic zone under different values of angle \(\alpha\) under the dominant stress field of \(\sigma_{\rm HZ}\). Figure 8 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 plastic zone size of the roadway occurs in the middle of the roof, and when \(\alpha\) is 60-90\({}^{\circ}\), the maximum plastic zone size of the roadway surrounding rock occurs at the wing angle. 2. When \(\alpha\) = 0\({}^{\circ}\), the plastic zone at the roadway wing angle is 2.21 m. When \(\alpha\) is 0-40\({}^{\circ}\), the depth of the wing angle decreases by 0.83 m. When \(\alpha\) is 40-90\({}^{\circ}\), the size of the wing angle begins to increase rapidly and the sizes of the plastic zone are 1.38, 1.74, 2.06, 3.12, 4.04, and 4.40 m, respectively, increasing by 2.19 times. 3. The depth of the plastic zone in the middle of the roof gradually decreases from 2.50 to 1.49 m when \(\alpha\) increases from 0\({}^{\circ}\) to 40\({}^{\circ}\), a decrease of 1.01 m. In the 50-90\({}^{\circ}\) range, the size of the plastic zone in the middle of the roof gradually increases, by 0.77 m.
4. When the axial angle \(\alpha\) of the roadway is in the 0-70\({}^{\circ}\) range, the size of the plastic zone in the middle of the roadway sidewall gradually decreases from 2.00 to 0.25 m, a decrease of 1.75 m or by 0.88 times. When \(\alpha\) is 80-90\({}^{\circ}\), the size of the plastic zone in the middle of roadway the sidewall slowly increases by 0.25 m.
5.