Timoshenko-beam-based response of existing tunnel to single tunneling underneath and numerical verification of opening and dislocation

Abstract

Longitudinal deformation of shield tunnels consists of a combination of both bending and shearing, which is characterized by the opening of the joints and the dislocation between rings. The response of existing tunnels induced by undercrossed tunnels is thus studied with elastic continuum and Winkler solutions, considering the tunnel as a Timoshenko beam with equivalent bending and shear stiffness. A displacement-based single variable governing differential equation is then proposed to resolve the shear locking problem of the Timoshenko beam. The applicability of the proposed Winkler modulus is verified against the elastic continuum solution. Next, the applicability of the equivalent stiffnesses in the prediction of the opening and dislocation is examined using a field case and an elaborate finite element shield tunnel model that considers the soil as the PSI (pipe/beam-soil interaction) element with the proposed Winkler spring stiffness. Finally, the Winkler model is used to establish four design charts for quick assessments of the maximum opening of the joints and the maximum dislocation between rings, and the maximum tunnel displacement. Their effectiveness is verified by compared with the finite element results.