An exact solution for three-dimensional (3D) dynamic response of a cylindrical lined tunnel in saturated soil to an internal blast load

The dynamic response of tunnel under internal explosion in reality is a three dimensional geotechnical problem, however, it is often simplified as a plane strain problem in 2D model which can only deal with the dynamic responses of tunnel at the source of explosion. This note proposes a set of exact solutions for three-dimensional (3D) dynamic responses of a cylindrical lined tunnel in saturated soil due to internal blast loading are derived by using Fourier transform and Laplace transform. The surrounding soil is modeled as a saturated medium on the basis of Biot's theory and the lining structure modeled as an elastic medium. By utilizing a reliable and efficient numerical method of inverse Laplace transform and Fourier transform, the numerical solutions for the dynamic response of the lining and surrounding soil are obtained. The 3D dynamic responses of the lined tunnel and the surrounding saturated soil medium due to internal blast loading are then presented and discussed. The results demonstrate that the proposed solutions can help to evaluate the damage of the explosion to surrounding areas of the tunnel in 3D condition at any given elapsed time apart from the section at the source of explosion.