Abstract: Pasternak′s double-parameter foundation and elastic beam theory are used to establish a differential equation for measuring the longitudinal response of tunnels that traverse multiple fault surfaces when they are subjected to forced fault displacement. By solving this equation mathematically, the longitudinal deformation and internal force responses of the tunnel structure under fault displacement can be derived. Subsequently, the effectiveness of the proposed theoretical model is validated using both physical model experiments and numerical simulations. Based on these experiments and simulations, a sensitivity analysis of the factors that influence the longitudinal dynamic response of tunnel structures is conducted using the theoretical model. The main conclusions are as follows. (1) The value trends observed with the theoretical analysis model are entirely consistent with those of the model experiments and numerical simulations, although the numerical values are somewhat conservative. (2) The displacement pattern of the fault slip and the stiffness match between the surrounding rock and the lining significantly impact the tunnel′s longitudinal response. An appropriate fault slip displacement function based on the specific form of the fault fracture zone must be selected for accurate analysis results. (3) As the stiffness ratio between the surrounding rock and the lining increases, the effect of the constraint of the surrounding rock on the tunnel structure intensifies, which leads to a greater concentration of the internal forces in the tunnel′s longitudinal response. However, the range that is affected by the fault slip decreases. Therefore, in practical engineering design, the surrounding rock and the lining stiffness should be appropriately matched by considering factors such as the construction costs and times of rapid access.

Key words: tunnel engineering, fault rupture, model test, elastic foundation beam, analytical solution