Calculation method and application of discontinuous longitudinal deformation of shield tunnels considering variable stiffness of the ring joints

Abstract

Shield tunnels are typical underground structures assembled from segmental rings and bolts. The relatively small stiffness of the ring joints compared to segmental rings can easily lead to the discontinuous deformation, and even damage or spalling of the segments, which poses a serious threat to safe tunnel operation. How to consider the discontinuous stiffness and deformation of longitudinal structure has become the core problem in tunnel calculation. In this paper, regarding the ring joint stiffness as special singularities in longitudinal structural stiffness, a physical and mechanical model which can consider the discontinuities of longitudinal structural stiffness and deformation is proposed. Variable stiffness and discontinuous deformation of longitudinal structure is considered by Delta and Heaviside function. The analytical solutions of discontinuous deformation of the segmental rings and the ring joints are obtained by using normalized functions. The case analysis shows that proposed method is in good agreement with measured field data and the error of maximum settlement is 5%. The deformation peak is smaller than that of Timoshenko beam model, but the internal force peak is larger than that of Timoshenko beam model. The jump phenomenon of longitudinal deformation can be better described. Deformation and bending stiffness of the ring joints are highly coupled. With the increase of longitudinal differential settlement, the attenuation of ring joint bending stiffness will go through four stages: constant stiffness stage, sharp attenuation stage, stable attenuation stage and decelerated attenuation stage. Proposed analytical solution can solve the difficulties of calculating discontinuous longitudinal structure of shield tunnels, and provide theoretical reference for the evaluation of running subway tunnel.