Numerical-analytical method for investigating the stability of motion of bodies of revolution in soft soil media

A method is presented of investigating the stability of rectilinear motion of a body of revolution in a compressible soil medium with nonlinear physical-mechanical properties of the soil and two-dimensional effects of flow taken into account. The parameters of the axisymmetric process are calculated numerically, whereas the perturbed motion – the radial displacement and rotation relative to the centre of mass – is determined analytically. In the particular case of a conical projectile and linear pressure distribution along the generatrix, an estimate is obtained of the critical position of the centre of mass as a function of the taper angle, the mass and velocity of the body, the coefficient of friction, and the hydrodynamic parameters of the soil medium. Unlike the usually implemented situation of constant pressure postulated by the local interaction models, a displacement of the critical position of the centre of mass by up to 20% of the length of the cone has been found, which leads to a substantial decrease in the margin of stability in a restricted sense. Here, the force parameters and the kinematic parameters of motion of the cone on the boundary of the stability region differ both qualitatively and quantitatively. The stability of motion of bodies in soil media with a nonlinear pressure distribution over the contact surface has not previously been investigated.