# Structural Stress Characteristics and Joint Deformation of Shield Tunnels Crossing Active Faults
## 4 Parametric Study and -Discussions
### Fault Dip Influence on Tunnel Behavior  
Figure 23 indicates the relationship between the tunnel structural damage and fault dip angles subjected to 10 cm normal faulting. The structural damage of the segmental tunnel decreased with the increase of the fault dip angle. When the fault dip angle increased from 55\({}^{\circ}\) to 85\({}^{\circ}\), the maximum tensile damage value of the segmental lining decreased from 0.907 to 0.114. Moreover, the tensile and compressive damage of the segments were located at the circumferential joints. The result indicates that changing the fault dip angle does not significantly affect the structural stress state of the segmental tunnel under the normal fault dislocation condition.  
The relation between the tunnel structural damage and fault dip angles subjected to 15 cm reverse fault displacement is presented in Figure 24. When the fault dip angle was 55\({}^{\circ}\), the tensile and compressive damages of the segmental lining were located at the arch haunch, and the segments were mainly subjected to lateral force. When the fault dip angle was 85\({}^{\circ}\), the tensile and compressive damages of the segmental lining were located at the circumferential joints, and the segments were mainly subjected to longitudinal stress. The main reason was that when the fault dip angle was larger, the longitudinal shear effect of the tunnel structure increased, and the annular joints could withstand much more shearing force. Therefore, concrete located at the circumferential joints is more likely to produce tensile and compressive damage. Therefore, under reverse fault displacement, the structural stress state of the segmental tunnel near the projection of the fault is significantly affected by the fault dip angle.  
Figure 23: Development of structural damage changing with fault dip angle under normal faulting: (**a**) compression damage of segments and (**b**) tensile damage of segments. Some like +8.434e-01 means 8.434 \(\times\) 10\({}^{-1}\).  
Figure 25 illustrates the relationship between the maximum shear force of the longitudinal bolts, the displacement of circumferential joints, and the dip angle of the fault under different fault dip angles when reverse faulting of 15 cm was imposed. It can be observed from the figure that with the increase of the fault dip angle, the maximum shear force of the longitudinal bolts and the displacement of the circumferential joints increased significantly, for which it is extremely easy to produce shear failure.  
Figure 26 shows the relation between the maximum stress of the longitudinal bolts and the fault dip angle. Under 10 cm normal fault displacement, the maximum stress of the longitudinal bolts decreased with the increase of the fault dip angle, and the annular bolts were less affected by the fault dip angle. Under 15 cm reverse faulting, the maximum stress of the annular bolts and longitudinal bolts increased with the increase of the fault dip angle. Since the longitudinal bolts were significantly affected by the fault dip angle subjected to normal and reverse fault displacement, reasonable longitudinal bolts should be selected in practical projects.  
Figure 24: Development of structural damage changing with fault dip angle under reverse faulting: (**a**) compression damage of segments and (**b**) tensile damage of segments. Some like +3.623e-01 means \(3.623\times 10^{-1}\).  
Figure 25: Effect of the fault dip angle on the shear force of longitudinal bolts and annular joints dislocation.