Analytical stress and velocity fields for gravity flows of highly frictional granular materials

Summary.

For granular materials the Coulomb-Mohr yield condition characterizes the two physical processes of inter-particle cohesion and inter-particle friction. The latter effect is quantified by the so-called angle of internal friction, denoted here by φ. The special case arising from zero angle of internal friction corresponds to the standard Tresca yield condition of metal plasticity. For certain materials such as coal, alumina filter cake, waste rock and silica, angles of internal friction φ occur in the vicinity 70^∘−80^∘, and therefore the study of an idealized granular theory with an angle of internal friction equal to ninety degrees has real practical significance. Here for the special case of φ=90^∘, the governing second-order nonlinear partial differential equations for the non-dilatant double-shearing model of granular flow are presented for both plane and axially symmetric flows, and a number of simple analytical solutions of these novel equations are determined. Some of these solutions are illustrated graphically by showing the orthogonal grids which give the maximum and minimum principal stress directions and by showing the streamlines which give the particle paths.