SOLUTION OF THE PROBLEM ON THE EXPANSION OF A SPHERICAL CAVITY IN TERMS OF ESTIMATION OF THE RESISTANCE TO THE PENETRATION OF A SOLID INTO THE SOIL

Solutions of the problem on constant-velocity expansion of a spherical cavity into a soil medium are analyzed. The cavity expands from a point in the half-space occupied by an elastoplastic soil medium. The previously obtained linearized analytical solution of this problem that was obtained under the assumption that the medium behind the shock wave front was incompressible is presented. Having performed the comparison with the results of the numerical solution of the problem in the full formulation, it is shown that the approximate solution is reasonable for the dependence of the pressure at the boundary of the cavity on the velocity of its expansion. The linearized solution is applied to calculate the force of resistance to the penetration of a rigid sphere into soft soil. The dynamic compressibility and shear resistance are characterized by the Rankine-Hugoniot relations and the Mohr-Coulomb-Tresca yield criterion. The results of analytical and numerical calculations are compared with the known experimental data, presented in the form of dependences on the impact velocity of the force of resistance to the penetration of spheres (impactors) into water-saturated sand. A good agreement between theoretical and experimental data has been demonstrated.