The foundation of a seismic safety assessment of cross-fault hydraulic tunnels is an acceptable and accurate seismic response. A dynamic contact force algorithm that may take into consideration the interaction between the fault–surrounding rock–lining structure was devised in light of the contact characteristics of various media in cross-fault hydraulic tunnels under seismic activity. A quantitative instability criterion using a relative displacement ratio as the criterion was devised based on the cusp catastrophe model. By using the cross-fault hydraulic tunnel of the Lawa Hydropower Station as an example, it was possible to evaluate and assess the impacts of four working circumstances on the seismic response of the tunnel lining structure. The findings demonstrated that the lining haunch exhibited stronger stress and displacement responses when subjected to seismic activity. The consideration of fault–surrounding rock–lining interaction exacerbated the displacement and stress seismic responses of the lining structure. The haunch, bottom arch, and top arch of the lining’s characteristic parts—which ranged in size from large to small—responded more seismically as peak ground acceleration rose. Applying the aforementioned instability criterion, the haunch, bottom arch, and top arch of the liner structure could withstand maximum peak ground accelerations of 0.10 g, 0.20 g, and 0.35 g, respectively. The aforementioned technique offers a fresh perspective on how to evaluate the seismic response and seismic safety of the tunnel’s lining structure, and the study’s findings can serve as a guide for seismic design.
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