THE DYNAMICS OF AVALANCHES OF GRANULAR-MATERIALS FROM INITIATION TO RUNOUT .2. EXPERIMENTS

This paper describes a model to predict the now of an initially statio nary mass of cohesionsless granular material down a rough curved bed a nd checks it against laboratory experiments that were conducted with t wo different kinds of granular materials that are released from rest a nd travel in a chute consisting of a straight inclined section, a curv ed segment that is followed by a straight horizontal segment. This wor k is of interest in connection with the motion of landslides, rockfall s and ice and dense flow snow avalanches. Experiments were performed w ith two different granular materials, nearly spherical glass beads of 3 mm nominal diameter, Vestolen particles (a light plastic material) o f lense type shape and 4 mm nominal diameter and 2,5 mm height. Piles of finite masses of these granular materials with various initial shap es 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 sand paper. The granular masses under motion were photographed and partly v ideo filmed and thus the geometry of the avalanche was recorded as a f unction of position and time. For the two granular materials and for t he three bed linings the angle of repose and the bed friction angle we re determined. The experimental technique with which the laboratory av alanches 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 Hut ter [28]. These are partial differential equations for the depth avera ged streamwise velocity and the distribution of the avalanche depth an d involve two phenomenological parameters, the internal angle of frict ion, phi, and a bed friction angle, delta, both as constitutive proper ties of Coulomb-type behaviour. We present the model but do not derive its equations. The numerical integration scheme for these equations i s a Lagrangian finite difference scheme used earlier by Savage and Hut ter [27], [28]. We present this scheme for completeness but do not dis cuss its peculiarities. Comparison of the theoretical results with exp eriments 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 definitio n of the initial conditions. Early studies of the temporal evolution o f the trailing and leading edges of the granular avalanche indicate th at 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, de lta, is also seen to have a small, but negligible influence on these v ariables. We finally compare the experimental results with computation al findings for many combinations of the masses of the granular materi als 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].