Analytical solution for the longitude bending response of tunnels and its application to evaluate the influence of peak ground parameters

This study aims to predict the longitude bending response of infinite tunnels subjected to arbitrary longitudinally propagating shear waves. New analytical solutions are derived based on an improved Timoshenko beam on Pasternak foundation model, considering tangential interactions at the ground-tunnel interface. By accounting for the traveling wave effect, the governing equations are processed using Fourier transform and related mathematical techniques. Expressions for tunnel displacement, bending moment and shearing force are obtained. The proposed analytical solutions demonstrate excellent agreement with three-dimensional numerical simulation results, significantly outperforming traditional beam foundation models in terms of accuracy. Finally, with the aid of the proposed analytical solutions, a parametric analysis is conducted to assess the influence of various factors on the longitudinal dynamic response of tunnels, with particular emphasis on the effect of peak ground parameters. These analytical solutions offer valuable insights for engineering design, providing a reliable framework for predicting the longitudinal bending response of infinite circular tunnels under arbitrary shear waves.