A boundary integral equation-based method for analyzing the bending behavior of longitudinal joints in shield tunnels

Traditional mechanical analyses of segmental lining longitudinal joints commonly adopt the plane section assumption, assuming a linear normal strain distribution along the contact interface. However, full-scale tests and contact mechanics indicate that such models deviate significantly from actual responses. This study employs the discrete form of boundary integral equations (BIE) to characterize the nonlinear normal stress distribution and compatible deformation, thereby replacing empirical assumptions in conventional models. A coupled formulation between the BIE and the mechanical equilibrium equations of the joint is established, providing a solution method for the mechanical behavior of the longitudinal joint independent of empirical assumptions. To capture the evolution process of the compressed contact region, a contact detection algorithm is developed to classify all possible interface evolutions. Additionally, built upon elastoplastic BIE and stress integral equations, the proposed model accounts for how domain plastic strains attenuate normal contact stress. The effectiveness and computational accuracy of the proposed method are validated through comparisons with both the finite element models and the analytical approach. Furthermore, the developed method is employed to investigate the deformation characteristics of longitudinal joints under complex loading conditions, as well as the influence of load amplitude on the recoverability of joint deformation.