Moving step load on the surface of a half-space of granular material

Abstract

The two-dimensional steady-state problem of the effect of a step pressure traveling with superseismic velocity on the surface of a half-space is treated for an elastic-plastic material. The plasticity condition selected is a function of the first and second invariants of the stress tensor, and is suitable for a granular medium where inelastic deformations are due to internal slip subject to Coulomb friction.The problem is inherently nonlinear and leads to a system of coupled nonlinear differential equations which are solved by digital computer. The character of the solutions is radically dependent on the significant nondimensional parameters, i.e. the Mach number, Poisson's ratio and a value α defining the angle of internal friction. A table giving the solutions for various combinations of the parameters is given.