Analytical Method for Segmental Tunnel Linings Reinforced by Secondary Lining Considering Interfacial Slippage and Detachment

Abstract

The reinforcement of shield tunnels with secondary linings is a widely used method to enhance the overall rigidity of tunnels; therefore, ensuring tunnel safety during construction and operational periods. According to a new composite curved Euler beam theory, an analytical method will be proposed to analyze a shield tunnel that is reinforced by a secondary lining, in which the radial joints and the interaction between the segmental lining and the surrounding soil will be simulated by a series of concentrated and distributed springs, respectively. In contrast to the radial rigid connection that was assumed in previous studies, radial detachment and tangential slippage between the segmental and secondary linings will be allowed. The solutions for the internal forces and deformations will be derived using the state-space method with arbitrary loads and joint distributions. In addition, the proposed method will be extended to cases with partial reinforcement that have a segment of secondary lining and a reinforcement connected by bolts. The proposed method will be validated using finite element numerical simulations. In addition, the variations in the internal forces and deformation for the soil reaction stiffness under different joint and interfacial stiffnesses will be examined. The results indicate that the internal forces and deformations of the linings decreased with the increase of soil reaction spring stiffness, and the interfacial radial spring stiffness had a more significant influence on the axial force transfer between the linings.