# Stress Analysis and Spalling Failure Simulation on Surrounding Rock of Deep Arch Tunnel
## 4 Discussion  
### Stress Distribution Analysis of Surrounding Rock under Different Working Conditions  
The literature [69] adopted the method of opening the hole first and loading it afterward to simulate rockburst, mainly focusing on the rockburst caused by static stress adjustment. In this section, the stress distribution of the surrounding rock of tunnels with different arch heights at each stage under static stress adjustment is based on this loading path. The correlation between the boundary points and the polar angle of the tunnel is schematically drawn for subsequent convenience in describing the variation characteristics of the stress curve around the tunnel, as shown in Figure 13. Taking the origin of the coordinate system \(O_{1}\) and the \(x\)-positive half-axis as the starting edge, the polar angle \(\theta\) is obtained. The arch section was divided into four regions and five points, and named regions 1-4 (which are polar angles 0\({}^{\circ}\)-60\({}^{\circ}\), 60\({}^{\circ}\)-96\({}^{\circ}\), 96\({}^{\circ}\)-130\({}^{\circ}\), and 130\({}^{\circ}\)-180\({}^{\circ}\)) and points 1-5 (which are polar angles 0\({}^{\circ}\), 54\({}^{\circ}\)-66\({}^{\circ}\), 96\({}^{\circ}\), 126\({}^{\circ}\)-132\({}^{\circ}\), and 180\({}^{\circ}\)). Figures 14-16 show the tangential stress distributions around the hole during the simulated stress adjustment. The stress distribution of the surrounding rock of the tunnel  
Figure 12: The diversion tunnel of Jinping II Hydropower Station peels off rock chips [68]: (**a**) thin section failure in branch tunnels; (**b**) thin spalling failure in branch tunnels; (**c**) wedge-shaped spalling failure in branch tunnels. Figure 13: The relationship between tunnel boundary point and polar angle. with three arch heights is consistent. When \(\sigma_{Z}>40\) MPa, in the vast majority of cases, the lowest tangential stress occurs at points 1 and 5. The tangential stress at point 4 is the largest, followed by that at point 2. With the adjustment of vertical stress, the tangential stress at points 1 and 5 gradually decreases, which transfers from compressive stress to tensile stress. For a semi-circular arch with a rise-span ratio of \(f/B=1/2\), the \(\sigma_{Z}\) should be loaded to more than 40 MPa at point 5, and a three-centered arch with a rise-span ratio of \(f/B=1/3\) and \(f/B=1/4\)\(\sigma_{Z}\) should be loaded to more than 30 MPa at point 5. However, tensile stress appears at point 1 after \(\sigma_{Z}\) rises about 20 MPa. As \(\sigma_{Y}\) doubles, the \(\sigma_{Z}\) value of tensile stress at the arch top and the floor middle increases by 20 MPa correspondingly. The tangential stress in region 2, region 3, and region 4 gradually increases with stress adjustment and is manifested as the compressive stress. With the increase in \(\sigma_{Z}\) or \(\sigma_{Y}\), the same maximum tangential stress is first reached at point 3, where precedence order is the rise-span ratio of \(f/B=1/4\) arch tunnel, \(f/B=1/3\) arch tunnel, \(f/B=1/2\) arch tunnel. Under the initial burial depth stresses, the magnitudes of the tangential stresses at points 4 and point 2 are as follows: \(f/B=1/3\) three-centered arch \(>\)\(f/B=1/4\) three-centered arch \(>\)\(f/B=1/2\) semi-circular arch. With an increase in vertical stress (\(\sigma_{Z}=40\) MPa), the magnitude of the tangential stress at point 2 follow \(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch. The magnitude of tangential stress at point 4 is as follows: \(f/B=1/4\) three-centered arch \(\approx\)\(f/B=1/3\) three-centered arch. The tangential stress of the semi-circular arch with \(f/B=1/2\) is the lowest in this part. When the vertical stress increased to 70 MPa, the magnitude of the tangential stresses at point 2 and point 4 satisfied a sequence of \(f/B=1/4\) three-centered arch \(>\)\(f/B=1/3\) three-centered arch \(>\)\(f/B=1/2\) semi-circular arch. The tangential stress of the tunnels with three \(f/B\) ratios increased with burial depth.