Simplified analytical solution for responses of fault-crossing tunnels with flexible joints under fault movement

An approach is developed for estimating the responses of a tunnel with multiple flexible joints under fault movements. Initially, a new simplified mechanical model of flexible joints is built, and a closed-form solution for a tunnel with multiple flexible joints is derived using Green’s function method. Then, the explicit solution of a tunnel with flexible joints subjected to fault movement is subsequently obtained and verified by comparing its results with those from the numerical modeling. Finally, the responses caused by different factors, i.e., fault displacement, lining stiffness, surrounding rock property in the fault zone and joint stiffness, are investigated in detail to provide a better understanding of the mechanical mechanism of flexible joints. The results show the differences in displacement and rotation induced by flexible joints can be quantitatively calculated by the proposed solution in different cases. The flexible joint is capable of reducing the internal forces of the lining and the influence ranges of fault dislocation on tunnel responses. A lower joint stiffness increases the displacement difference monotonically and efficiently reduces the internal forces of the lining. The proposed analytical solution can be used to predict the seismic responses of fault-crossing tunnels with multiple flexible joints under fault movement in engineering design.