Study on the influence of above-crossing tunneling on the existing shield tunnels based on timoshenko beam

Based on the modified Loganathan theory, the longitudinal displacement of an existing tunnel caused by the ground loss in the process of shield crossing was studied. Timoshenko beam theory considering shear deformation was used to analyze the change of tunnel internal force and the amount of the dislocation between the adjacent rings. Based on the shear effect in elastic mechanics theory, the differential equation of tunnel longitudinal deformation was established and solved. After the bending deformation of Timoshenko beam, the difference between the beam cross-section of euler-Bernoulli beam which was not perpendicular to the neutral axis was analyzed. Furthermore, the variation of tunnel bending moment, shear force, and displacement between tunnel segments on tunnel shear stiffness and the ground loss ratio was studied. The results showed that the theoretical solution considering the shear deformation of the tunnel could predict the longitudinal deformation of the tunnel accurately. The proposed theory can correct the excessive internal forces such as bending moment and shear force without considering shear deformation and make up for the defect of unable to calculate the dislocation between the adjacent ring misalignment without considering shear deformation. The research results provide an effective method for predicting the influence of shield on existing tunnels.