## 3 Results  
### The Influence of Stress (Depth) on the Failure of Surrounding Rocks of a Turning Roadway  
Due to the increase in ground stress with advancing depth, the failure of deep roadways often differs from that of shallow roadways. This study investigated TBM roadways at two depths (700 and 1200 m) to explore the effect of stress on roadway failure. The deformation of the straight and turning roadways at 700 m is shown in Figure 5. The deformations of the roof, floor, left rib, and right rib of the straight roadway are 83.1, 69.6, 86.3, and 73.1 mm, respectively, while those of the turning roadway are 85.1, 66.0, 58.9, and 61.0 mm, respectively. The deformations of the roof and floor of the straight and turning roadways are almost equal, and the rib deformation of the straight roadway is slightly larger than that of the turning roadway. Accordingly, at a depth of 700 m, the surrounding rock stress is relatively small, and there is no significant difference in failure characteristics between the straight and turning roadways. When the excavation reaches a depth of 1200 m underground, the distribution of roadway deformation changes, as shown in Figure 6. The deformations of the roof, floor, left  
Figure 4: Support scheme applied in the numerical model. Figure 5: Deformation of the roadways at 700 m depth. rib, and right rib of the straight roadway are 207.3, 185.4, 191.8, and 191.9 mm, respectively, while those of the turning roadway are 175.0, 172.0, 161.6, and 108.2 mm, respectively. The overall deformation of the straight roadway is greater than that of the turning roadway, and the rib deformations of the turning roadway show significant asymmetry, with the deformation on the outside of the turn being 49.4% larger than on the inside. The results indicate that ground stress significantly affects the deformation and failure of the surrounding rocks in the roadways. As the excavation depth increases from 700 to 1200 m, the ground stress increases by 70%, resulting in asymmetric deformation of the two ribs of the turning roadway and a reduction in overall deformation. To further explore the causes of the change in deformation patterns of the turning roadway, the principal stresses and the plastic zone distribution were analyzed. The rock mass model was arranged according to the Mohr-Coulomb yield criterion with a tension cutoff, and the yield functions are expressed as follows:  
\[f^{s}=\sigma_{1}-\sigma_{3}N_{\varnothing}+2c\sqrt{N_{\varnothing}} \tag{1}\]  
\[f^{t}=\sigma^{t}-\sigma_{3} \tag{2}\]  
where \(N_{\varnothing}\) is the function of internal friction angle \(\varnothing\); \(c\) is the cohesion; and \(\sigma^{t}\) is the tension strength. The rock mass is considered to have undergone shear yield if \(f^{s}<0\) and tension yield if \(f^{t}<0\). In the calculation, the last term \(2c\sqrt{N_{\varnothing}}\) in Equation (1) is relatively small compared to the first two terms and cannot influence the result of Equation (1); therefore, the shear failure of the rock mass can be described by the maximum and minimum principal stresses. The ratio of the maximum principal stress to the minimum principal stress and the plastic zone distribution are shown in Figure 7. The ratios of the principal stresses in the turning roadway at 700 and 1200 m are 2.38 and 2.40, respectively, and those in the straight roadway are 2.27 and 2.10. The excavation depth does not affect the maximum principal stress ratio in the surrounding rocks of the turning roadway, but it has an effect in the case of the straight roadway. Based on Equation (1), a higher ratio of principal stresses indicates greater instability of the surrounding rocks, leading to the conclusion that the stability of the surrounding rocks of the straight roadway is greater than that of the turning roadway, and this stability difference increases with depth. From the perspective of plastic zone distribution, the turning of the roadway results in a small increase in the tension failure zone and a small decrease in the shear failure zone.