## 5 Seismic Response of Anchor Joint
### Strain Response of Anchor Joint  
Based on the stress and deformation results of the anchor joint, the sleeve has the largest deformation among the different components, which play a key role in the bearing capacity of the whole system. Although plastic deformation occurs locally in other components, the value is very small and has little influence on the joint's performance. Therefore, only the main deformation component, namely the sleeve, is analyzed in this section. The plastic strain distribution of the sleeve is shown in Figure 14.  
It can be seen from Figure 14a that after the anchor joint is assembled, plastic strain occurs in most areas of the side walls of the sleeve, which is consistent with the stress distribution results. By comparing the plastic strain results at the completion time of assembly and after the application of the most unfavorable seismic displacement responses, it can be found that the plastic strain distribution of the sleeve changes little under the action of different seismic waves, and the maximum plastic strain remains unchanged. It can be inferred that the maximum plastic strain of the side walls of the sleeve occurs at the end of the assembly process. This should happen at the same time with the appearance of the maximum deformation of the sleeve side walls.  
Figure 13: Stress distribution of anchor joint. (**a**) After assembly. (**b**) Case1. (**c**) Case2. (**d**) Case3. (**e**) Case4. (**f**) Case5. (**g**) Case6.  
Besides, the mutual position change between the joint members within a certain range will not cause the increase of the maximum plastic strain. However, it is worthy of noting that the distribution range of the maximum plastic strain has expanded in Figure 14b-g, and it changes from the edge of the sleeve side walls to the sleeve center. The above results indicate that although the maximum plastic strain value remains the same, the plastic deformation of the sleeve side walls actually increases after the earthquake. The cumulative effect of plastic strain under seismic action has a negative impact on the mechanical performance of the anchor joint. With the continuous expansion of the distribution range of plastic strain, the recovery level of the bearing capacity of each component in the anchor joint after separation and reassembly is bound to decline. Accordingly, it is of critical importance to conduct a detailed seismic response study on the anchor joint based on  
Figure 14: Plastic strain of lantern ring. (**a**) After assembly. (**b**) Case1. (**c**) Case2. (**d**) Case3. (**e**) Case4. (**f**) Case5. (**g**) Case6.  
the proposed method in this paper. In this way, the deformation characteristics, bearing capacity, and safety state of the anchor joint can be reasonably evaluated in the light of the cumulative plastic deformation of sleeve walls during the earthquake motion.  
In fact, most of the existing seismic response studies on shield tunnels have neglected the detailed structural features of the segmental joints. The most important reason is to simplify the model to gain less computational cost. Another critical reason is that it is really difficult to reach convergence during the complicated three-dimensional numerical simulations with too detailed characteristics of the structures. However, in this section, an apparent cumulative effect of plastic strain has been found for the anchor joint under seismic action. This phenomenon demonstrates that it is quite necessary to propose advanced methods, which can reproduce and reflect the real structural features of the segmental joints. Additionally, it can be inferred that for the segmental joints with complex structural components, more detailed investigations are still in need to gain a comprehensive knowledge of their seismic performance.