Analysis of models for calculating the motion of solids of revolution of minimum resistance in soil media*

Abstract

The solution of problems of searching for the optimal shape of a body when it penetrates into dense media is considered using local interaction models (LIMs) and Grigoryan's model of a soil medium in an axisymmetric formulation. A new LIM is obtained that is improved by taking account of the non-linear compressibility and shear strength in the analytical solution of a problem on the expansion of a spherical cavity. The applicability of an LIM that is quadratic with respect to the velocity in determining the forces resisting penetration of sharp bodies into soft soil is justified theoretically and experimentally and the violation of the conditions for the model to be applicable in the case of blunt bodies is established. It is shown that a solution taking account of non-linear flow effects in a two-dimensional formulation enables both the shape as well as power and kinematic characteristics of the optimal blunt bodies as they pass through soil media to be improved considerably. The ratio of the finite depths of penetration of solids of revolution into soft ground taking account of internal friction is estimated by the ratio of the coefficients in the Rankine–Resal formulae.