Analytical solution for longitudinal mechanical response of tunnels with flexible joints under fault movement

In this study, a method of calculating the longitudinal mechanical responses of tunnels with flexible joints through active fault zones is proposed. The tunnel is assumed to be a variable-stiffness Timoshenko foundation beam model based on the deformation characteristics of a tunnel with flexible joints. The Timoshenko beam model takes into account the shear effect of the deformation joints as well as the deep beam characteristics of lining segments, and it is capable of reflecting the shear dislocation behavior of the tunnel through active faults with flexible joints. The transfer matrix method is introduced to consider the influence of flexible joints on the overall structural mechanical response of the tunnel, thereby enabling the direct utilization of the real material stiffness of the tunnel lining segments and flexible deformation joints in the calculation, eliminating the need for the concept of an equivalent stiffness. This method facilitates the determination of the deformations and internal forces of the tunnel lining segments and flexible joints, respectively. The model test results verified the correctness of the theoretical model established in this paper. This model is clear in concept and easy to implement, and it provides more scientific and reasonable theoretical support and methodological guidance for the design of tunnels with flexible joints across active faults.