Abstract: Tunnel lining uplift frequently arises during shield tunneling excavation. To accurately characterize the dislocation between adjacent rings and joint openings induced by uplift pressure during shield tunneling, we propose a theoretical calculation method for uplift deformation of shield tunnels based on the short beam-spring model. Initially, we establish Euler-Bernoulli short beams and joint springs to simulate the longitudinal structure of shield tunnels, considering the arbitrary restraining effect of the shield tail through boundary springs. Subsequently, we apply the finite difference theory to derive the uplift deformation of shield tunnels under uplift forces during tunneling. Ultimately, we validate the correctness and effectiveness of the method through comparisons with engineering cases, numerical modeling results, and traditional equivalent beam calculations. We discuss the sensitivities of key parameters, analyzing the influence of the unconsolidated zone length, circumferential joint stiffness, and modulus of elasticity on the deformation pattern of tunnel uplift. The results indicate that, compared to conventional continuous beam models, our calculation method accurately reflects discontinuous deformation characteristics and reasonably captures the dislocation between adjacent rings and joint openings. Analysis of related parameters reveals that increasing the length of the unconsolidated zone significantly enhances both the maximum uplift deformation and its range of influence. Appropriately increasing the shear and rotational stiffness of circumferential joints can mitigate uplift displacement and reduce dislocation between adjacent rings and joint openings. The uplift deformation of shield tunnels in weak strata with low modulus of elasticity is more difficult to control.

Key words: shield tunnel, lining uplift, circumferential joint, theoretical calculation, finite difference method