Exact solutions for dynamic responses of a cylindrical lined tunnel in saturated soil to internal blast loads

The dynamic response of tunnels 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 tunnels at the source of explosion. To evaluate the damage of the explosion to the surrounding areas of the tunnel apart from the section at the source of explosion, a set of exact solutions for the three-dimensional dynamic responses of a cylindrical lined tunnel in saturated soil due to internal blast loads are derived by using the Fourier transform and Laplace transform. The surrounding soil is modelled as the saturated medium based on the Biot theory and the lining structure modeled as the elastic medium. By utilizing a reliable and efficient numerical method for the inverse Laplace transform and Fourier transform, the numerical solutions for the dynamic responses 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 loads are then presented and discussed. The results show that (a) compared to the simplified 2D plane strain model, the 3D model yields smaller predictions in the hoop stresses, radial displacements, and pore water pressures; (b) the dynamic responses of tunnels decrease sharply in an oscillating manner as the time elapses, while such responses attenuate exponentially with the increasing distance away from the explosion source center at both radial and axial directions of the tunnel.