No abstract

The impact of a sphere with velocity u0 on a fine, loose granular system under the acceleration due to gravity has been studied by fast video photography. The behavior of the granular bed is found to be similar to a fluid during initial impact, followed by a cavity drag during projectile penetration. From the trajectory of the projectile it is found that the drag on the projectile can be well described by adding a bulk frictional force f to the hydrostatic force kappa(z) where kappa is a constant and z denotes the penetration depth. Both kappa and f are u0 dependent. This form of the drag force suggests that fluidlike viscous dissipations in the bed can be neglected in these three-dimensional (3D) experiments. However, due to the imposed boundary this hydrodynamic term of the drag force is found to be not negligible in quasi-2D granular beds.

Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some draw-backs. Therefore, a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from 26 • to the more realistic value of 30 • . (2) Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them.(3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan and Matsuoka-Nakai -realizing each, and interpolating between them, by shifting a single scalar parameter.

Depth dependence of vertical plunging force in granular medium is studied experimentally by measuring the slow-pushing force of different size and shape objects intruding vertically into a granular bed. It is found that all of the force curves of fully immersed intruders have concave-to-convex transition. The depth dependence of the force turns from supralinear to sublinear. By studying the properties of the inflection point of the concave-convex transition, we find that the plunging force at inflection point is proportional to intruder's volume, and the inflection point occurs when the intruder is fully buried to a level around twice its diameter. Testing by plunging a long cylinder, which is always partially immersed, we find no inflection point in this case, which verifies that the inflection of the plunging force is related to the filled-in loose granules on top of the intruder. The slowdown of the increasing rate of the force is, therefore, not a result of sidewall support proposed by previous researchers.