Analytical solution for the longitudinal response of cross-fault shield tunnel considering plastic deformation of circumferential joints

This paper proposes an analytical model for the longitudinal deformation response of cross-fault shield tunnels, in which the tunnel is assumed to be a Timoshenko beam placed on Winkler's foundation. The plastic deformation behavior of circumferential joints and the influence of horizontal foundation friction are considered in the proposed model. A case study of normal faulting based on convincing numerical simulations is carried out to verify the rationality of the proposed model. Subsequently, the plastic deformation characteristics and distribution of circumferential joints are analyzed, and the factors affecting the longitudinal response of the tunnel are discussed through parametric analysis. The analysis results demonstrate that the proposed analytical model is reliable and applicable to calculating the longitudinal response of cross-fault shield tunnel, especially in evaluating the deformation of the circumferential joints under normal faulting. Severe plastic deformation is observed on the annular joints when the shield tunnel is subjected to 10 cm faulting. Under crossing active fault, the ground has a more significant restriction on the longitudinal deformation of the shield tunnel, resulting in a larger deformation of circumferential joints. A larger elastic modulus of the ground leads to a more notable longitudinal deformation of the tunnel lining. When the width of the fault fracture zone is not considered, the results of longitudinal internal force and deformation of shield tunnels are conservative. In the plastic deformation stage of the circumferential joints, the larger the plastic equivalent bending stiffness ratio of the shield tunnel, the slighter the plastic deformation of circumferential joints. The proposed analytical solution can be used to predict the joint deformation of cross-fault shield tunnels and provide guidance for the waterproof design of shield tunnels.