No abstract

Two problems representative of the gravity flow of granular materials are considered in the context of a theory presented by Goodman (1970). The problems consist of steady fully-developed flow of a granular material down an inclined plane and between vertical parallel plates. It is shown that the dynamical behaviour of these materials is quite different from that of a viscous fluid. For the inclined flow problem, the normal stresses are not only unequal but vary non-linearly with depth. Also the maximum value of the mass flux distribution does not necessarily occur at the upper surface. For the vertical channel-flow problem, the material behaves somewhat like a Bingham fluid in that a plug region exists in the central part of the channel. The interesting feature of this problem is that the concentration of material volume in the shearing region outside the plug may either increase or decrease from the plug to the channel wall, depending on the boundary conditions. Experimental evidence for these phenomena in real granular materials is cited.The results of this investigation suggest that the gravity flow of granular materials is essentially governed by two factors-a material characteristic length, which is possibly related to the grain size, and the externally imposed constraints such as the gravity field or the pressure exerted upon the granular material from the confining plates.

A variational principle for the continuum theory of granular materials is presented. This principle is used to obtain the basic equations of the equilibrium theory and the boundary conditions for both the incompressible granule case, and the compressible granule case.