## 3 Results
### The Influence of Turning Radius on the Failure of Surrounding Rocks of a Turning Roadway  
Theoretically, the asymmetric failure of a turning roadway should be attributed to its geometrical shape; therefore, the turning radius might also influence the failure of the surrounding rocks of the roadway. In this part of the study, the roadway advance processes with two turning radii (50.93 and 101.85 m) were simulated to investigate the influence of turning radius on the failure of the turning roadway.  
The maximum principal stress distribution of the turning roadway is shown in Figures 8 and 9 (for 101.85 and 50.93 m turning radii, respectively). Five cross-sections of the turning roadway were selected as the analysis objects. The results show that the roadways with two different turning radii have similar stress distributions; the part of the roadway located at the junction of the straight and turning roadways exhibits a large maximum principal stress at the boundary, while the maximum principal stress in the other parts of the turning roadway is relatively small. The change in turning radius has little effect on the distribution of stress in the roadway's surrounding rocks.  
Figure 8: Maximum principal stress distribution of the roadway with a 50.93 m turning radius.  
Figure 7: The ratio of principal stresses and plastic zone distribution of the roadways at two different depths.  
To further explore the difference between the roadways with two types of turning radius, the deformation of the surrounding rocks and the distribution of the plastic zone were examined. Figures 10 and 11 display the plastic zone distribution and the deformation of the surrounding rocks. Figure 10 indicates that the shape of the plastic zone is primarily elliptical, with the minor axis parallel to the X-axis. In addition, the tension failure zone located at the junction of straight and turning roadways is relatively small, which may indicate that the surrounding rock deformation is relatively small there. When fully entering the turning part, there is little difference in the distribution of the plastic zone between the roadways with a 50.93 m and 101.85 m turning radius. Therefore, for a turning roadway, the plastic zone of surrounding rocks has different distribution modes at the junction and after entering the turning part. However, the change in turning radius has little effect on the plastic zone distribution of surrounding rocks.  
Figure 11 presents the deformations of the cross-sections with different turning radii. It is evident that the deformation of the part at the junction of the straight and turning roadways has the smallest deformation of the surrounding rocks. The \(5^{\circ}\) cross-section of the roadway with a 50.93 m radius exhibits a larger deformation of the surrounding rocks, but this phenomenon was not observed in the other cross-sections, which may have resulted from the combined effects of high maximum principal stress and a large turning angle. In addition, in the other sections, there is no significant difference in deformation between the two roadways with different radii. However, on the whole, the deformation of the left rib is larger than that of the right rib, revealing that, regardless of the turning radius, there is still asymmetric deformation of the roadway.  
Figure 10: Plastic zone distribution of the turning roadway.  
Figure 9: Maximum principal stress distribution of the roadway with a 101.85 m turning radius.  
In general, this section found that at the junction of the straight and turning roadways, there are abnormal changes in the stress, plastic zone, and surrounding rock deformation. However, after fully entering the turning roadway, the change in turning radius does not affect the asymmetric deformation of the roadway; that is, the asymmetric failure of the roadway is only related to the behavior of turning, not to the turning radius.