## 4 Conclusions  
Taking a tunnel crossing an active fault as the research background, the damage response of the tunnel under the combined actions of fault dislocation and earthquake is analyzed by numerical simulation. The key conclusions are summarized as follows:  
1. The peak acceleration observed at monitoring points throughout the tunnel demonstrates an amplification effect due to the combined impacts of fault dislocation and an earthquake. This effect is particularly pronounced at the tunnel vault located at the fault plane, with an acceleration amplification coefficient of 4.7.
2. The energy dissipation of the tunnel lining in Case 3 is about 3000 kJ; in Case 2, the energy dissipation of the tunnel lining in the seismic phase is about 5500 kJ, which is an increase of 85% compared with that in Case 3. This shows that the damage to the tunnel caused by the combined effects of fault dislocation and seismicity is not a simple superposition, and the initial damage caused by fault dislocation will aggravate the damage of the tunnel during the seismic action stage.
3. The lining damage is mainly concentrated in the fault fracture zone area under fault dislocation, and after superimposed seismic action, the scope and degree of lining damage increase, and the increase in tensile damage is more significant compared with compression damage, indicating that seismic action is the main cause of tensile damage in the tunnel.
4. Both the initial fault dislocation and an increase in seismic intensity elevate the damage level of the tunnel. The OLDC index is symmetrically distributed along the fault plane in an inverted V-shape, with damage primarily concentrated within 14 m on either side of the fault plane. Notably, the compressive damage to the lining intensifies under stronger seismic effects. The OLDT index follows a similar distribution pattern, with complete damage (DS4) concentrated within \(-\)20 m to 30 m on both sides of the fault plane.
5. Due to the limitations of the research methodology, this study only analyzes the tunnel damage characteristics under different fault initial displacements and various peak seismic accelerations. In future work, we will conduct a sensitivity analysis of key parameters under more conditions. Additionally, due to the lack of seismic damage records under fault dislocation-coupled seismic loading, model tests are needed to validate the theoretical results.  
**Author Contributions:** J.D., methodology, software, validation, writing--original draft; S.Y., methodology, supervision, review and editing, formal analysis; W.S., conceptualization, methodology, supervision, validation, review and editing; Y.L., conceptualization, review and editing, formal analysis; M.C., methodology, review and editing, supervision. 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 (Nos. 52068044 and 52208392) and the Natural Science Foundation of Gansu Province (No. 21)R7 RA309).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Some or all of the data that support the findings of this study are available from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.