ОЦЕНКА КОНТАКТНЫХ НАПРЯЖЕНИЙ ПРИ ВНЕДРЕНИИ УДАРНИКА В ПРОЧНЫЙ ГРУНТ

Abstract

Finite formulas have been derived for evaluating contact stresses in a rigid impactor penetrating a soil, taking into account the friction in the framework of the local interaction model. In analyzing dynamic deformation of the soil, its volumetric compressibility, shear resistance and initial strength are accounted for. The obtained evaluations of resistance to penetration of an impactor into the soil are based on a quadratic relation between the stress normal to the impactor surface and impact velocity. The authors have pioneered in deriving finite expressions for coefficients of a trinomial approximation as a function of experimentally determined physical-mechanical parameters of the soil - a dynamic compressibility diagram (a shock adiabat) and a yield strength - pressure diagram. Impact compressibility of soils is described based on Hugoniot's adiabat - a linear relation between shock wave velocity and mass velocity of the medium particles behind the shockwave front. Plastic deformation obeys the Mohr - Coulomb yield criterion with a constraint on the limiting value of maximal tangential stresses according to Tresca's criterion - the Mohr - Coulomb - Tresca plasticity condition. An earlier obtained analytical solution of a one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a half-space occupied by a plastic soil medium is used. A formula for determining critical pressure (a minimal pressure required for the formation of a cavity, accounting for internal pressure in the framework of Mohr - Coulomb's yield criterion) is also used, which generalizes a known solution for an elastic ideally plastic medium with Tresca's criterion. The derived formulas have been verified by comparing their results with the available data from experiments on the penetration of a steel conical impactor into a frozen sandy soil. It is shown that the disagreement between the numerical and experimental results is within 10%.