Study on seismic performance of shield tunnels under combined effect of axial force and bending moment in the longitudinal direction

Shield tunnels are usually subject to combined axial force and bending moment in the longitudinal direction during earthquake. In traditional analytical models, the combined effects of axial force and bending moment are considered separately. In this paper, the modified longitudinal nonlinear stiffness model considering the combined effects of axial load and bending moment together is proposed. The structural deformation of the shield tunnel is divided into five patterns based on the elastic-plastic state of joint bolts and the contact state of circumferential joints. For each pattern, the longitudinal equivalent bending stiffness and tensile stiffness are obtained individually. In order to verify the accuracy of the proposed model, a case study based on a real tunnel structure in Tianjin in China is carried out. The longitudinal seismic response of the tunnel is investigated. The study shows that the elastic-plastic state of longitudinal bolts has significant influence on the structural deformation when the seismic intensity is large. The deformation of the modified longitudinal nonlinear stiffness model is 20.79% smaller than that of the longitudinal continuous model. The research results also show that the opening of the circumferential joint and the internal force of the longitudinal bolt both reach the maximum value when the incident angle of the seismic wave reaches about 45 degrees.