A contribution to soil dynamics

Abstract

OPERATIONS associated with high soil-deformation rates, such as roto-tilling, highspeed bulldozing, aircraft landing on unprepared terrain, and soil measurements by an impacting probe, have stimulated interest in the inertia effects of soil. Since little experimental data are available as yet, I would like to report some tests on soil dynamics performed a few years ago [1]. The problem was this: Can soft soil be deformed at a rate high enough to generate inertia forces that will contribute effectively to supporting a vehicle? Since this question is especially important when locomotion is planned over very weak soils, where static forces due to cohesion and internal friction will not support or propel a vehicle, we focused our attention on the rapid deformation of muddy soils. We approached the solution of this problem by first listing all possible forces that could contribute to the flotation of a vehicle, and then applying dimensional reasoning. From numerous publications on theological properties of clay, we knew that at low deformation rates the relationship between the deforming force and the deformation speed is governed by Bingham's law F = F o + c o n s t × v. (1) To verify this law for the muddy soil in our experiment, we placed a soil specimen of 30 in ~ in a stirring apparatus set at low speeds. Figure 1 shows that the stirring force increases linearly with the speed as predicted by formula (1). Clearly, at low speed inertia forces are negligible. The increase of deforming force is caused by an alteration of the friction mechanism between the soil particles; therefore, the second term in formula (1) can be identified as viscous force. Since the viscous force of the muddy soil increased very little with speed, we neglected it. The first term in formula (1) represents the static force at a very low deformation rate. We thought it appropriate to identify this force by Coulomb's law, where the total shear force just before failure is the sum of cohesion force and friction force. Expressing these two forces in terms of a characteristic length l gives cohesion force a l~c (2) friction force----N tan ~p (3) where c is cohesion, cp is the angle of internal friction, and N is a force perpendicular to the friction force. Since the force N depends in some way upon all the forces causing soil deformation, we cannot specify N until finishing our review of all the contributing forces. Our first interest was the inertia force, expressed by Newton's law in terms of a characteristic length I and a characteristic speed v, as inertia force ct p lSv ~ (4) where p is the density of soil.