Longitudinal deformations of existing discontinuous tunnels induced by shield tunneling based on Kerr foundation model

At present, the theoretical researches on the structural deformation of the existing tunnels induced by shield excavation generally regard the existing tunnels as the Euler Bernoulli beam resting on the Winkler foundation without taking into account the effects of non-linear shear deformation of the foundations and shear deformation of the segments, especially the mechanical effects of the existence of circumferential joints of the tunnels. Firstly, the Loganathan and Poulos formula is used to calculate the vertical displacements of soils at the axis of the existing tunnel caused by shield under-crossing excavation. Then, the existing tunnel is regarded as a Timoshenko beam connected by circumferential joints and resting on the Kerr foundation model. The finite difference method is used to calculate the longitudinal deformations of the existing tunnel. Finally, the engineering monitoring data are used to compare and verify the theoretical solutions by the proposed method, and a good agreement is obtained. In addition, the parameter analysis is carried out for the stiffness influence parameters of elastic modulus of soil layer, equivalent bending stiffness and equivalent shear stiffness of the existing tunnel. The results of the analysis show that with the increase in the modulus of elasticity of the soil and the decrease in the equivalent flexural stiffness of the existing tunnel, the displacements of the existing tunnel, the relative turning angles of the circumferential joint and the bending moments at the segment and circumferential joint increase. As the equivalent shear stiffness of the existing tunnel increases, the displacements of the existing tunnel decrease, while the relative turning angles of the circumferential joint and the bending moments at the segment and circumferential joint increase. The relative turning angles of the circumferential joint and the bending moments at the segment and circumferential joint tend to decrease and then increase with the increasing distance from the axis of the new tunnel. When the stiffness discount factor of the circumferential joint of the existing tunnel increases, the bending moments at both the segment and circumferential joint increase, while the tunnel displacements and relative turning angles of the circumferential joint decrease.