Three-dimensional analytical model for vibrations from a tunnel embedded in an unsaturated half-space

An analytical model for predicting the vibrations from an underground railway tunnel embedded in an unsaturated half-space is proposed. The tunnel lining is modeled as an infinite Flugge cylindrical shell, and the unsaturated soil is modeled as a three-phase medium comprising solid grains and pores containing water and air. By using the transformation properties between the plane wave functions and the cylindrical wave functions, the model is coupled based on the boundary conditions. The developed model is validated by comparison with existing tunnel models, and the effect of saturation on the dynamic response of the tunnel–soil system is demonstrated through a case study.