Inclined glass-sand flow and the angle of repose

Abstract

Systematic experimental study on inclined orifice flow and the measurement of the angle of repose are carried out in this work. The inclined orifice flow is formed by glass beads in an inclined channel. The flow is discharged near the bottom of the channel under gravity. The flow rates are measured at various inclination angles of the channel and opening sizes of the orifice. We then record the inclination angle when the rate becomes zero. We compare this zero-rate inclination angle with the repose angle of glass-beads, and the internal friction angle is determined by the yield stress obtained from a direct shear experiment. It is interesting to find that the experimental values at these three measured critical angles are equal within the experimental errors: 1) the supplementary angle of the extrapolating inclined angle at which the flow rate becomes zero and the inclined hole of diameter approaches infinitely large value (i. e. D), s= 180-c, where c is the critical angle for the inclined hole of diameter D and cc(D); 2) the repose angle r of a cone-shaped pile, which is formed when particles fall from the top point of the heap onto a smooth bottom plate; and 3) the internal friction angle that is measured by direct shear experiment. This result intends to support that the solid-liquid transitions occurring in the inclined orifice flow and free surface of granular heap, and the Coulomb yield occurring in the bulk of the granular solid all originate from the same critical property. Owing to the fact that the internal stresses and strains of samples in the three cases all have complicated and nonuniform distributions so that they cannot be analyzed quantitatively at present, Only some qualitative discussion on this issue is given in this paper.