Numerical simulation and simplified analytical model for the longitudinal joint bending stiffness of a tunnel considering axial force

As a discontinuous ring structure, segmental longitudinal joints are a weakness of shield tunnels and play an important role in the determination of tunnel deformation caused by ground pressure. A longitudinal joint bending test is first carried out by employing a detailed 3D numerical model for the Shanghai Metro tunnel. This reveals that the joint stiffness varies nonlinearly with the axial force and bending moment. Based on numerical results, an analytical model for determining the joint rotational stiffness is provided, which takes the influence of the mechanical behavior of the concrete and steel bolts, the geometrical dimensions of the joint cross section and the subjected loads into account. Then, a simplified fitting equation is proposed, which has been verified by the experimental test results. This reveals that the results obtained from the proposed fitting equation are in good agreement with the experimental results before the joint reaches the limit state. Therefore, this proposed equation can be preliminarily adopted for the simulation of joint bending behavior and the determination of tunnel deformation in the tunnel design stage.