Timoshenko beam solution for the response of existing tunnels because of tunneling underneath

Abstract

SummaryAn analytical solution for the deflection and internal forces of an existing tunnel because of tunneling underneath is presented. The existing tunnel is modeled as a Timoshenko beam resting on a Winkler foundation, which takes into account the contribution of shear deformation to the total deflection of the existing tunnel. The validity of the analytical solution is verified by a centrifuge test, and the merit of this analytical method is confirmed by comparison with the conventional Euler–Bernoulli beam model. Influential factors on the behavior of the existing tunnel are investigated by consideration of the variations of subgrade modulus, ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Results show that the proposed analytical method is a valid and effective method to evaluate shearing‐induced deformation in existing tunnels with large diameters. Results also show that the pattern and the amplitude of the response of the existing tunnel are affected largely by ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Copyright © 2015 John Wiley & Sons, Ltd.