Motion of a granular avalanche in a convex and concave curved chute: experiments and theoretical predictions

Abstract

This paper deals with the theoretical-numerical and experimental treatment of two dimensional avalanches of cohesionless granular materials moving down a confined curved chute. Depth-averaged field equations of balance of mass and linear momentum as prescribed by Savage & Hutter (1991) are used. They describe the temporal evolution of the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of friction, ϕ,and the bed friction angle, δ, both as constitutive properties of Coulomb-type behaviour. The equations incorporate weak to moderate curvature effects of the bed. Experiments were carried out with different granular materials in a chute with partly convex and partly concave curved geometry. In these experiments the motion of the granular avalanche is followed from the moment of release to its standstill by using high speed photography, whence recording the geometry of the avalanche as a function of position and time. Two different bed linings, drawing paper and no. 120 SIA sandpaper, were used to vary the bed friction angle, δ. Both, the internal angle of friction, ϕ, and the bed friction angle, δ, were measured, and their values used in the theoretical model. Because of the bump and depending upon the granulate-bed combination an initial single pile of granular avalanche could evolve as a single pile throughout its motion and be deposited above or below the bump in the bed; or it could separate in the course of the motion into two piles which are separately deposited above and below the bump. Comparison of the experimental findings with the computational results proved to lead to good to excellent correspondence between experiment and theory. Even the development of the detailed geometry of the granular avalanche is excellently reproduced by the model equations, if δ < ϕ. Occasional deviations may occur; however, they can in all cases be explained by onsetting instabilities of the numerical scheme or by experimental artefacts that only arise when single particles have shapes prone to rolling.