Analytical solution for the response of an existing tunnel to a new tunnel excavation underneath

This paper proposed an analytical solution to investigate the response of an existing tunnel induced by new tunnel excavation underneath. A Timoshenko beam lying on a Kerr foundation was adopted to model the existing tunnel subjected to ground disturbance induced by new tunnel excavation. The proposed analytical solution was tested against a centrifuge test and a field case study available in literature. Results indicate that the predictions given by the proposed analytical method show agreement with the experimental test data and the field measurements at a construction site. Further parametric study examined some influences on the structural response of the existing tunnel to new tunnel construction, including longitudinal shear stiffness, volume loss, clearance between the two tunnels, and tunnel-soil relative rigidity factor. The parametric study highlights the significant influence of the longitudinal tunnel shear stiffness on the response of existing tunnel. The proposed analytical solution can be used as a reference to predict the potential risk of new tunnel excavation to the existing tunnel in relevant engineering practice.