# Study on the Seismic Response of Shield Tunnel Structures with the Preload Loss of Bolts
## 4 Result Analysis
### Tensile Damage Analysis  
To analyse the mechanical behaviour and damage condition of the shield tunnel structure, a damage reduction stiffness variable SDEG is used to characterize the damage degree of the segmental structure [44; 45]. This parameter reflects the remaining load-bearing capacity of the structure. When SDEG = 0, it indicates an intact structure; when 0 < SDEG < 1, it signifies a gradual reduction in stiffness and the occurrence of damage;  
Figure 15: Maximum longitudinal relative displacement. (**a**) Vertical displacement time history. (**b**) Maximum relative settlement.  
when SDEG = 1, it means that the stiffness has completely degraded to zero, and the structure has failed.  
When the PGA was 0.1 g or 0.3 g, the shield tunnel did not exhibit significant damage. The tensile damage factor for the segment was only 0.42. Therefore, taking the condition with a PGA of 0.5 g as an example, the structural damage state is analysed. As shown in Figure 16 for a PGA of 0.5 g, the overall tensile damage and stiffness degradation of the structure are illustrated. It can be observed that with the decrease in preload, both the tensile damage factor and stiffness degradation rate increase. Analysing the slope of the stiffness degradation curve, it can be seen that with an increase in the degree of preload loss, the stiffness degradation slope gradually decreases. This suggests that the impact of early changes in bolt preload loss on stiffness degradation is more significant than in the later stages. Additionally, as the preload loss rate increases, the local tensile damage rate of concrete segments significantly increases.  
The damage cloud diagram of the shield tunnel structure after an earthquake with PGA of 0.5 g under the condition of complete preload loss is shown in Figure 17. It can be observed that structural damage mainly occurs at the crown, shoulder, inside of the arch bottom, and outside of the arch waist, as well as at the key segments, as shown in Figure 17. Figures 17a and 17b, respectively, show the damage cloud diagrams at the crown and the arch bottom. By comparing the stiffness degradation cloud diagram at the most prominent damage location, the crown (Figure 17a), with the tensile and compressive damage cloud diagrams (Figure 17c,d), it is found that the distribution of stiffness degradation is closely aligned with the tensile damage cloud diagram. Therefore, it can be inferred that the primary reason for the overall structural stiffness degradation is the tensile damage of the concrete segments. Additionally, based on Figure 17, it can be seen that the overall tensile damage of the structure increases as preload loss gradually occurs. This suggests that applying preload to the bolts can optimize the overall structural performance to some extent and reduce local tensile damage to the concrete segments.  
For the study of the impact of preload on the segment joints, the BP block and the A1 block were selected for analysis. Figure 18a-c show the structural damage maps of the overlap block under different preload loss conditions after the seismic wave load with PGA of 0.5 g. It was observed that the damage was concentrated at the inner side of the arch shoulder, and with an increase in the degree of preload loss, the damage showed a clear upward trend. Figure 18d,e illustrate the structural damage maps of the standard block at the arch waist under different preload loss conditions after the seismic wave load with a peak acceleration of 0.5 g. While it may not be the primary location of structural damage based on numerical values, an increase in damage values is observed with an increase in preload loss. By comparing the damage maps, it can be concluded that preload loss leads to an overall increase in damage in this area.  
Figure 16: Structural damage rate under seismic load of 0.5 g.