Analysis of longitudinal deformation of shield tunnel subjected to shield tail asymmetric thrust

When the shield machine is driving along a curve alignment or during deviation correction, the asymmetrical thrust will generate an additional bending moment on the head of the tunnel ring, which will cause longitudinal deformation of the shield tunnel. Current analytical methods commonly simplify the existing tunnel as an equivalent continuous beam, which will overlook the weakening of the circumferential joint. In this study, a simplified longitudinal beam-spring shield tunnel model (SLBSM) is established, which can simultaneously consider the opening and dislocation between segmental rings. Then, the shield tunnel under construction is simplified as a SLBSM resting on the Winkler foundation. The shield tunnel longitudinal deformation subjected to the shield tail asymmetric thrust is solved using the state space method; the reliability and applicability of the proposed method are verified by comparing with the results from finite element analysis and two existing continuous beam model. The parametric analysis is further performed to investigate the influences of some parameters on the deformation of shield tunnel. The results show that the longitudinal displacement of shield tunnel based on the continuous beam model exhibits continuous characteristics. While the longitudinal displacement predicted by the proposed method exhibits discontinuous characteristics, "gaps" appear at the joints between adjacent rings. Through the parametric analyses, it is found that increasing the rotation stiffness of the circumferential joint will effectively reduce the tunnel heave and opening of joint; increasing the shearing stiffness of the circumferential joint will effectively lead to the decrease of dislocation between adjacent rings, but it will increase the tunnel heave and shear force; improving the foundation stiffness will effectively reduce the tunnel heave and opening of joint, but it will result in the increase of the dislocation between adjacent rings. The effect of the axial force at the beginning of the segment on the longitudinal deformation of the tunnel cannot be ignored. Increasing the axial force will effectively reduce the tunnel heave, opening ofjoint, and dislocation between adjacent rings.