Simulation of buried cylindrical/spherical explosions in a soil medium using the semi-analytical solution of a cavity expansion problem

The existing literature on the dynamic spherical/cylindrical cavity expansion (CCE) due to pressure loading at the cavity boundary, shows that all the analytical solutions deal with constant pressure only. A general solution is developed for the non-stationary dynamic problem of a cavity expansion, due to prescribed pressure time-history applied at the cavity boundary. This solution can be applied for different problems such as the response of a medium in the event of a buried explosion. This is a rather complex non-linear non-stationary problem, and the attempt to develop an analytical or a semi-analytical solution of the problem suggests adopting simplified constitutive relationships. In the present study, a simplified material model is implemented, representing the medium by a locked equation of state (EOS) and a linear shear failure relationship. This solution is intended for a soil medium and may be applied as well to rock and concrete media and other materials that may be described by these constitutive models. The paper derives a semi-analytical solution for the cavity boundary motion due to a variable pressure acting on the cavity boundary and provides the analytical expressions for the radial stress variation in the medium. The developed solution is applied to problems of spherical and cylindrical buried explosions in different soil media. The results obtained by the developed model are compared to presently available solutions and experimental data reported in the literature, and good agreement is obtained.