# Seismic Response of Shield Tunnel with Double-Layer Lining
## 5 Influence of Calculation Parameters on Dynamic Response of Double-Layer Lining Shield Tunnel
### Segmental Lining Stiffness Degradation
#### 5.1.1 Structural Bending Moment  
Under the condition of segmental lining stiffness degradation, the bending moments of the shield tunnel under the seismic motion (depicted in Figure 3) are illustrated in Figures 9 and 10.  
From these figures, it can be observed that the distribution characteristics of bending moments in both the segmental lining and the secondary lining remain unchanged regardless of the stiffness degradation. The maximum bending moments in the segmental lining and the secondary lining of all cases consistently occur in the conjugate 45\({}^{\circ}\) region. Specifically, the maximum positive bending moment occurs in the springing, while the maximum negative bending moment occurs in the spandrel.  
The maximum bending moments for the tunnel structure are shown in Figure 11.  
Figure 11 shows that as the segmental lining stiffness degrades from 100% to 60%, the maximum positive bending moment of the segmental lining gradually decreases from 165.31 kN\(\cdot\)m to 103.38 kN\(\cdot\)m, while the maximum negative bending moment decreases from 144.27 kN\(\cdot\)m to 89.61 kN\(\cdot\)m, approximately in a linear manner. The maximum positive bending moment remains greater than the maximum negative bending moment. The changes in the maximum positive and negative bending moments of the segmental lining are relatively consistent, with the decreasing rate of the maximum positive bending moment being approximately 1.13 times higher than that of the maximum negative bending moment.  
Figure 10: Maximum bending moments of secondary lining (Different segment stiffness. Unit: kN\(\cdot\)m).  
Figure 9: Maximum bending moments of segment (Different segment stiffness. Unit: kN\(\cdot\)m).  
For the secondary lining, when the segmental lining stiffness decreases from 100% to 60%, the maximum positive bending moment remains around 35 kN\(\cdot\)m, while the maximum negative bending moment remains around 31 kN\(\cdot\)m.  
As the stiffness of the segmental lining degrades, the bending moment of the segmental lining gradually decreases, while the bending moment of the secondary lining remains almost unchanged. Numerically, although the stiffness of the segmental lining decreases, it remains greater than that of the secondary lining. This indicates that when the segmental lining stiffness degrades, the segmental lining remains to be the primary load-bearing structure, while the bending moment of the secondary lining is hardly affected.  
As the stiffness of the segmental lining degrades, the ratio of the maximum bending moment between the segmental lining and the secondary lining gradually decreases. When the segmental lining stiffness decreases from 100% to 60%, the ratios of the maximum positive bending moment decrease from 4.77 to 2.86, a decrease of 40.04%. Similarly, the ratios of the maximum negative bending moment decrease from 4.75 to 2.84, a decrease of 40.02%. This indicates a significant change in the load distribution of the tunnel structure under seismic loads.