# Structural Stress Characteristics and Joint Deformation of Shield Tunnels Crossing Active Faults
## 3 Analysis of Segmental Tunnel Influenced by Fault Movement  
### Mechanical Response of Segmental Tunnel  
Figures 6 and 7 illustrate the damage contours of the segmental tunnel subjected to normal faulting. When the normal fault dislocation of 5 cm is imposed, the tensile damage and compressive damage of the tunnel structure are slight, indicating that the structure is in a safe state. When the normal faulting of 10 cm is imposed, the tensile damage value is 0.298, and the compressive damage value is 0.417. In the moment, the fault dislocation caused non-negligible threats to the tunnel structure. When the fault displacement was 15 cm, the structural tensile and compressive damage exceeded 0.9, indicating that the tunnel structure was severely damaged. Figure 4: Numerical model of the segmental tunnel. Figure 5: Boundary conditions of the numerical model and the fault simulation method. Meanwhile, it was found that when the 15 cm fault movement occurred, the structural damage of the segmental tunnel was mainly located at the circumferential joints, where the concrete is prone to apparent tensile and compressive damage. Therefore, it can be seen that the concrete at the circumferential joints is more likely to be damaged under normal faulting, and the most severely damaged area is located in the foot wall. [PERSON] et al. (2016) [25] conducted a centrifuge test for a cross-fault shield tunnel with a 1:50 similarity ratio, and then studied the effect of normal fault dislocation on the existing segmental tunnel. Figure 8 indicates the test results of the existing shield tunnel subjected to normal faulting. According to the model test results, the longitudinal bolts and the tunnel structure near the annular joints are damaged remarkably under the normal fault displacement. Figure 6: Tensile damage distribution of the segmental tunnel under normal fault dislocation: (**a**) under 5 cm fault displacement, (**b**) under 10 cm fault displacement, (**c**) under 15 cm fault displacement. Some like +3.484e-02 means 3.484 \(\times\) 10\({}^{-2}\). Figure 7: Compressive damage distribution of segmental lining under normal faulting: (**a**) under 5 cm fault displacement, (**b**) under 10 cm fault displacement, and (**c**) under 15 cm fault displacement. Some like +9.770e-02 means 9.770 \(\times\) 10\({}^{-2}\). Figure 9 shows the contour of the longitudinal deformation of the shield tunnel subjected to normal faulting. Under normal fault displacement, significant tension deformation occurs in the annular joints, and the tension deformation area includes the tunnel arch bottom of the hanging wall zone, the tunnel vault of the foot wall zone, and the tunnel arch haunch near the fault projection surface. On the basis of the characteristics mentioned above, the annular joint deformation of the segmental tunnel can be divided into three fields, namely the opening area of the arch bottom at the annular joints, the opening area of arch haunch at the annular joints, and the opening area of the vault at the annular joints. The stress contours of the longitudinal and annular bolts subjected to normal fault movement are presented in Figure 10. When a fault movement of 15 cm was imposed, the maximum stress of the annular bolts was 394.7 MPa, which was less than the bolt yield stress of 480 MPa, and the maximum stress of the longitudinal bolts was 497.5 MPa, which means the bolt yielded at that moment. Therefore, under normal faulting, the annular joints of the segmental tunnel are more prone to cause large tensile deformation compared to longitudinal joints. Figures 11 and 12 show the damage contours of the segmental tunnel subjected to reverse fault movement. When reverse faulting of 10 cm was imposed, the compressive  
Figure 8: Model test results of the cross-fault segmental tunnel [25]. Figure 10: Stress of the joint bolts subjected to normal fault dislocation: (**a**) stress of circumferential bolts and (**b**) stress of circumferential bolts. Some like +3.947e+08 means \(3.947\times 10^{8}\).