Longitudinal structural modelling of shield tunnels considering shearing dislocation between segmental rings

Abstract

Shield tunnels in soft deposits are often subjected to differential settlement and longitudinal structural deformation during long-term operation. Since the shear stiffness in circumferential joints between rings is relatively low, shearing induced dislocation between segmental rings becomes a significant aspect of longitudinal deformation of tunnels. The longitudinal deformation mode comprises both rigid rotation of segmental rings (bending mode) and dislocation between rings (dislocation mode). The existing modelling method is usually based on Euler–Bernoulli beam theory, which only considers the bending effect and ignores the shearing deformation. This paper proposes a new longitudinal structural model to consider the shearing dislocation between rings. In the proposed model, the tunnel is simplified as a homogenous Timoshenko beam, and an equivalent shear stiffness is proposed to consider the influence of joints. Since Timoshenko beam theory considers both flexural deformation and shear deformation of the beam, it can describe the actual deformation mode of a tunnel reasonably. The proposed model is compared with the traditional Euler–Bernoulli beam model based on a field measured longitudinal deformation of a Shanghai metro tunnel. The results indicate that the traditional Euler–Bernoulli model overestimates the longitudinal internal forces of a tunnel. The proposed model based on Timoshenko beam theory predicts a smaller joint opening and a greater dislocation between rings than the Euler–Bernoulli beam model.