Mathematical modelling for shield tunneling induced displacement effects on in-service tunnel: theoretical solution including shearing deformation of segment and stiffness reduction of circumferential joints

Abstract

Tunneling beneath adjacent in-service tunnel can generate displacement of soil, causing adverse impact on the in-service tunnel. Many previous researches simplify the in-service tunnel as a continuous Euler-Bernoulli beam on Winkler foundation, disregarding the shearing deformation of tunnel and existence of joints. A two-stage analysis based on the Timoshenko beam model and Kerr foundation model is presented for estimating the response of in-service tunnel including the effects of segment shearing and circumferential joints stiffness reduction. Firstly, the Loganathan and Poulos solution is adopted to acquire the greenfield displacement induced by shield tunneling. Secondly, the mathematical modeling considering the interaction between shield and in-service tunnel with joint virtual forces reflects the shearing deformation of segments and discontinuity of joints. To take into full consideration for non-linearity and continuity of soil, the Kerr foundation model is employed in tunnel displacement analysis by applying the finite difference method. The accuracy of the two-stage method is then verified with three engineering cases, receiving good alignments. Finally, parametric analyses reveal that soil elastic modulus and in-service tunnel embedment depth have positive effects on tunnel displacement and internal force responses, while in-service tunnel diameter and equivalent bending stiffness have negative relationship. Equivalent shearing stiffness exhibits a complex relationship, increasing one response but decreasing another. The reduction factor has a minimal effect on tunnel displacement and segment moment, but does impact local rotation around joints.