Analytical solution for longitudinal deformation of shield tunnel induced by overcrossing tunnelling considering circumferential joints

This paper presents a new analytical solution for assessing the longitudinal deformation of shield tunnel associated with overcrossing tunnelling in consideration of circumferential joints. A simplified longitudinal beam-spring model (SLBSM) is established to model the longitudinal behaviours of shield tunnel, which can consider the opening and dislocation between segmental rings simultaneously. Then, the existing tunnel is treated as the SLBSM resting on the elastic foundation. The state equations including tunnel displacements and internal forces are constructed to solve the discontinuous deformation of circumferential joint-segmental ring. The feasibility of the proposed solution is verified through three well-documented cases. The predictions from the proposed method are also compared with other analytical methods. It is found that the proposed method can well capture the deformation of tunnel segmental rings and joints, where the rigid displacement mainly occurs in the segmental rings while the rotation and dislocation occur in the circumferential joints. Some dominant parameters are also analysed to explore the effects on existing tunnel deformation, including the rotation stiffness and shearing stiffness of joints, the skew angle and the clearance between new and old tunnels.