ALBERT

Notes: Summary This paper describes a model to predict the flow of an initially stationary mass of cohesionsless granular material down a rough curved bed and checks it against laboratory experiments that were conducted with two different kinds of granular materials that are released from rest and travel in a chute consisting of a straight inclined section, a curved segment that is followed by a straight horizontal segment. This work is of interest in connection with the motion of landslides, rockfalls and ice and dense flow snow avalanches. Experiments were performed with two different granular materials, nearly spherical glass beads of 3 mm nominal diameter, Vestolen particles (a light plastic material) of lense type shape and 4 mm nominal diameter and 2,5 mm height. Piles of finite masses of these granular materials with various initial shapes and weight were released from rest in a 100 mm wide chute with the mentioned bent profile. The basal surface consisted of smooth PVC, but was in other experiments also coated with drawing paper and with sandpaper. The granular masses under motion were photographed and partly video filmed and thus the geometry of the avalanche was recorded as a function of position and time. For the two granular materials and for the three bed linings the angle of repose and the bed friction angle were determined. The experimental technique with which the laboratory avalanches were run are described in detail as is the reliability of the generated data. We present and use the depth-averaged field equations of balance of mass and linear momentum as presented by Savage and Hutter [28]. These are partial differential equations for the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of friction, ø, and a bed friction angle, δ, both as constitutive properties of Coulomb-type behaviour. We present the model but do not derive its equations. The numerical integration scheme for these equations is a Lagrangian finite difference scheme used earlier by Savage and Hutter [27],[28]. We present this scheme for completeness but do not discuss its peculiarities. Comparison of the theoretical results with experiments is commenced by discussing the implementation of the initial conditions. Observations indicate that with the onset of the motion a dilatation is involved that should be accomodated for in the definition of the initial conditions. Early studies of the temporal evolution of the trailing and leading edges of the granular avalanche indicate that their computed counterparts react sensitively to variations in the bed friction angle but not to those of the internal angle of friction. Furthermore, a weak velocity dependence of the bed friction angle, δ, is also scen to have a small, but negligible influence on these variables. We finally compare the experimental results with computational findings for many combinations of the masses of the granular materials and bed linings. It is found that the experimental results and the theoretical predictions agree satisfactorily. They thus validate the simple model equations that were proposed in Savage and Hutter [28].