UNDERGROUND EXPLOSION ACTION: RAPID EXPANSION OF A SPHERICAL CAVITY IN AN ELASTIC MEDIUM

Abstract—: An exact analytical solution to the problem of dynamic expansion of a spherical cavity in an elastic medium (soil) with an arbitrary constant speed is obtained. It is assumed that this speed can be large, up to the velocity of propagation of bulk waves in the medium, and therefore the boundary conditions must be set on the moving boundary. The found solution makes it possible to judge the impact (or control the impact) of underground explosions on objects in the “far” zone, at distances significantly exceeding the size of the cavity. Fixed incorrectness in the approximate solution of this problem, given by J. Achenbach and S. Sun. It is found that the approximate solution obtained by the Horn method, which requires a large parameter in the problem, is not valid in some regions of variation of the Poisson’s ratio of the medium and the rate of expansion of the cavity. It is shown that for those values of the indicated parameters at which an approximate solution can be taken, it agrees with the exact solution.