## 6 Conclusions  
This paper aimed to study the seismic response of the anchor joint in shield tunnel considering the SSI effect. For this purpose, an improved method was first developed and introduced in detail. Then, joint deformation characteristics were discussed based on the results obtained from the soil-tunnel system. Finally, the detailed stress and strain distribution features were interpreted to reveal the seismic performance and evaluate the safety state of the anchor joint. The specific conclusions are as follows:  
1. Combing the dynamic time history method and the response displacement method, an improved approach is proposed for the overall and detailed seismic response study of the anchor joint. Using this method can effectively reduce the modeling difficulty and computing resource consumption caused by the complex structure of the anchor joint.
2. The maximum opening and offset of the anchor joint under the axial seismic input are greater than those under the transverse seismic input. The distribution features of joint opening and offset are obviously different under different seismic excitations. The seismic action leads to a more negative impact on the joint opening than the joint offset.
3. Compared with the unidirectional seismic input conditions, the maximum opening and offset of the anchor joint under the bidirectional seismic action are increased. However, the deformation of joints at different locations is rather distinct, which cannot be directly obtained from the sum of results from unidirectional seismic input conditions.
4. The opening and offset caused by earthquake can cause the separation of the components in the anchor joint, resulting in the decrease of the contact pressure among the components, and further reduce the bearing capacity of the anchor joint. The stress distribution of the sleeve shows obvious changes, while the distribution range of the maximum plastic strain of the sleeve walls is expanded.
5. For the evaluation on the deformation resistance and post-earthquake performance of the anchor joint, the final deformation of the anchor joint and the cumulative plastic strain of the sleeve can be used as the quantitative indicators.  
The seismic response of anchor joint has been preliminarily studied with the proposed improved numerical method. In this paper, only the results of joint opening, offset, stress, and strain were considered, while more detailed investigations are still necessary to gain a comprehensive understanding of the seismic performance of anchor joints. The influence of geology conditions and seismic waves should also be taken into account, which will be the further work.  
**Author Contributions:** Methodology, formal analysis, software, writing--original draft, G.Z.; conceptualization, funding acquisition, writing--review & editing, W.Z.; software, validation, J.Q.; visualization, R.N.; validation, C.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by the National Natural Science Foundation of China (Grant No. 51978460), which is gratefully acknowledged.  
**Conflicts of Interest:** The authors declare no conflict of interest.