# Structural Stress Characteristics and Joint Deformation of Shield Tunnels Crossing Active Faults
## 4 Parametric Study and -Discussions
### Elastic Modulus of Stratum Influence on Tunnel Behavior  
Figure 17 shows the relation between the maximum damage value of the tunnel segments and the elastic modulus of soil subjected to 10 cm normal fault dislocation and 15 cm reverse fault dislocation. In the normal faulting cases, the tensile and compressive damage values of the segmental tunnel increased significantly with the increase of the elastic modulus of the stratum. In other words, under the same fault displacement distance, the larger the elastic modulus of the soil, the more severe the damage to the segmental linings.  
When the elastic modulus of soil was 20 MPa, the tensile damage value of the segments was 0.074, for which the tensile damage value of the segments was slight. When the elastic modulus of the stratum was 50 MPa, the tensile damage of the segments was 0.298, and the tensile damage value of the segmental lining increased sharply, which seriously threatened the safety of the tunnel structure. When the elastic modulus of the stratum was 70 MPa, the tensile damage value already exceeded 0.913, indicating that the concrete at the circumferential joints was damaged locally.  
It can be seen from Figure 17b that under the reverse fault displacement condition, the compressive damage value of the shield tunnel was raised significantly with the increase of the elastic modulus of the soil, demonstrating that the compressive damage of the segments was significantly affected by the soil elastic modulus. The elastic modulus of the soil slightly affected the tensile damage value, and the tensile damage value of the segments remained in a small range.  
Subjected to 10 cm normal fault displacement and 15 cm reverse fault displacement, the relation between the maximum stress of the longitudinal bolts and the elastic modulus of the stratum is illustrated in Figure 18. Under fault displacement conditions, the maximum stress of longitudinal bolts increased with the increase in the elastic modulus of soil, and the maximum stress of the annular bolts decreased with the increase of the elastic modulus of the stratum.  
The maximum stress of the annular bolts was more significantly affected by the elastic modulus of the stratum. For example, under 15 cm reverse fault dislocation, when the soil elastic modulus increased from 20 MPa to 90 MPa, the maximum stress of the annular bolts decreased from 390.6 MPa to 230 MPa--the reduction accounted for 41%. By contrast, the maximum stress of longitudinal bolts increases from 361.6 MPa to 418.3 MPa, and the stress increase purely accounted for 15.7%.  
Figure 17: Effect of the elastic modulus of stratum on the structural damage of the segments: (**a**) normal faulting condition and (**b**) reverse faulting condition.  
The relation between the maximum deformation of segmental joints and the elastic modulus of soil is shown in Figure 19. In the normal faulting cases, the maximum opening of the annular joints increased nonlinearly with the increase of the elastic modulus of the stratum. Under the reverse fault displacement condition, the maximum opening of the longitudinal joint showed a nonlinear decrease with the increase of the elastic modulus of soil. In other words, under the same fault displacement, the larger the elastic modulus of soil, the smaller the opening of the longitudinal joints.  
The above research findings can be explained as follows. With the large elastic modulus of the stratum around the tunnel, due to the strong restraint ability of the stratum on the shield tunnel, the segmental tunnel was subjected to a large forced displacement and consequently caused severe structural damage and large joint deformation of the shield tunnel. On the contrary, with the small elastic modulus of the stratum around the tunnel, the soil around the shield tunnel would be compressed to a certain extent under fault dislocation, thereby reducing the forced displacement of the segmental tunnel to some degree.