Granular avalanches across irregular three-dimensional terrain: 2. Experimental tests
Scaling considerations indicate that miniature experiments can be used to test models of granular avalanches in which the effects of intergranular fluid and cohesion are negligible. To test predictions of a granular avalanche model described in a companion paper, we performed bench top experiments involving avalanches of dry sand across irregular basal topography that mimicked the complexity of natural terrain. The experiments employed a novel method of laser-assisted cartography to map the three-dimensional morphology of rapidly moving avalanches, thereby providing high-resolution data for comparison with model output. Model input consisted of two material properties (angles of internal and basal Coulomb friction of the sand), which were measured in independent tests, and of initial and boundary conditions that characterized the geometry of the experimental apparatus. Experimental results demonstrate that the model accurately predicts not only the gross behavior but also many details of avalanche motion, from initiation to deposition. We attribute this accuracy to a mathematical and computational formulation that conserves mass and momentum in three-dimensional physical space and satisfies the Coulomb equation in three-dimensional stress space. Our results support the hypothesis that a Coulomb proportionality between shear and normal stresses applies in moderately rapid granular flows and that complicated constitutive postulates are unnecessary if momentum conservation is strictly enforced in continuum avalanche models. Furthermore, predictions of our Coulomb continuum model contrast with those of a Coulomb point mass model, illustrating the importance of multidimensional modeling and model testing.