Analytical solutions considering tangential contact conditions for circular lined tunnels under longitudinally propagating shear waves

Analytical solutions based on the elastic foundation beam model for the bending response of circular tunnels under longitudinally propagating shear waves are studied considering the tangential contact conditions at the ground-tunnel interface. First, two kinds of new analytical solutions based on Timoshenko beams resting on Winkler or Pasternak foundations are developed considering different contact conditions at the ground-tunnel interface. The contact conditions are considered by introducing a spring-type flexibility coefficient in the force–displacement relationship. Then, the new analytical solutions, as well as the traditional solutions using Euler or Timoshenko beams on Winkler or Pasternak foundations, are compared with the dynamic numerical results. The new analytical solutions exhibit good agreement with the dynamic numerical results for different contact conditions. However, due to the neglect of the tangential interaction between the tunnel and surrounding ground, traditional solutions are only suitable for predicting the seismic response of tunnels in the full-slip condition. Finally, a parametric study is conducted to investigate the effects of the earthquake frequency, ground condition, lining thickness and contact condition. The proposed analytical solutions can be used to predict the seismic response of circular tunnels under longitudinally propagating shear waves in engineering design.