General solutions for the longitudinal deformation of shield tunnels with multiple discontinuities in strata

This paper proposes an approach for evaluating the longitudinal deformation of shield tunnels caused by potential disturbance after construction, advocating consideration of the stratum with multiple discontinuities. A Timoshenko beam resting on the Winkler foundation is employed to represent the soil-tunnel interaction. New developments include the analytical solutions for the longitudinal equivalent flexural and shear stiffness of circumferential joints with the consideration of the elastic-plastic behavior of the bolt and concrete. A theoretical model is suggested for the shear load transfer of two structural layouts of circumferential joints. Continuity at the discontinuity in the underlying stratum of the tunnel is imposed to solve the governing equations of equilibrium. Consequently, the advantage of this approach is can well predict the deformation characteristics of shield tunnel, i.e., settlement, dislocation, opening of circumferential joints. The proposed approach is tested against the data from the model test available in the literature and can provide a satisfactory estimate of the tunnel deformation. Additionally, parametric studies are further presented to analyze the influence of loading patterns and ground conditions on the longitudinal behavior of the tunnels.