Analytical solution for longitudinal seismic response of tunnels with segmental flexible joints crossing faults

The seismic damage induced by fault dislocation is a long-standing problem in the disaster prevention and control of tunnels crossing faults. Setting segmental flexible joints is an effective aseismic measure in the engineering practices. At present, no analytical solutions are available for the design of segmental flexible joints. An analytical solution for longitudinal seismic response of tunnels with segmental flexible joints crossing faults is presented. For the derivation, the segmental tunnel is assumed as a finite Euler-Bernoulli beam on the Pasternak two-parameter foundation, and the tunnel joints are simplified as the shear and bending spring elements. The discontinuous displacement fields in the fault zone are simplified as the external loads exerted on the beam, which considers the discontinuity of the fault site. The analytical solution for the longitudinal seismic response of tunnels with segmental flexible joints under fault dislocation is derived based on the established governing equations and boundary conditions. The proposed solution is verified by comparing its results with those from the tests and FEM model. Finally, the sensitivity analysis is carried out to investigate the influences of the setting plans for segmental flexible joints and the tunnel-joint stiffness ratio on the response of internal force of tunnel structures. The results indicate that flexible joints can effectively reduce the response of longitudinal internal force of tunnel structures in the affected area by the fault dislocation, and the response of internal force of tunnel structures is effectively reduced with the increase of flexible joints. It is concluded that the response of internal force can be significantly reduced when the flexible joints are respectively arranged on the fault dislocation surface and the interface between the faults and the hanging wall/footwall. Besides, the response of internal force of tunnels can be further reduced by increasing the tunnel-joint stiffness ratio. The research may provide a theoretical basis for the seismic analysis and the design of tunnels with flexible joints crossing faults.