Analytical solutions for circular tunnels under longitudinally propagating shear waves based on improved foundation beam models considering tangential interaction

Abstract

The tangential interaction at the ground-tunnel interface has significant effect on the longitudinal seismic response of tunnels, which has not been well considered in previous analytical solutions based on elastic foundation beam models. Firstly, improved elastic foundation beam models of Timoshenko beam resting on Pasternak or Winkler foundation are developed for circular tunnels under longitudinally propagating shear waves. Wherein, the tangential interaction effect is taken into account by setting independent rotational springs on the Timoshenko beam. The seismic shear waves are converted into free filed responses, whose displacement and two-times shear strain are applied at the non-structural side of the Winkler and rotational springs, respectively. Then, based on the improved foundation beam models, quasi-static analytical solutions of the longitudinal response of the circular tunnel are developed, which is subjected to longitudinally propagating harmonic shear waves. The new analytical solutions are verified by comparing with the three-dimensional dynamic numerical results, which perform far better than those based on traditional foundation beam models. Finally, with the aid of proposed analytical solutions, parametric studies are conducted to investigate the effects of the seismic frequency, the ground condition and the lining thickness on the seismic-induced bending moment and shearing force of the tunnel lining. The improved foundation beam models and the proposed analytical solutions are applicable for approximately evaluating the longitudinal response of circular tunnels in seismic area.