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THE ROLE OF INTERNAL STRESSES IN THE FLOW OF GRANULAR AVALANCHES -- 30/10/03
Roger P. Denlinger, (US Geological Survey) roger@usgs.gov
Understanding the flow of granular debris is prerequisite to assessment and mitigation of debris flow and avalanche hazards. As part of a research team working toward more realistic hazard assessments, I formulated a finite-volume model to solve equations describing depth-averaged granular flow in an earth-centered coordinate system. The equations assume Coulomb resistance to flow, both internally and from basal sliding, and include the effects of variable vertical acceleration. Horizontal mass and momentum flux between cells is determined using high-resolution methods borrowed from shock wave research, and this flux is combined with the vertical momentum equation to determine corresponding velocities in three dimensions (3D). Subsequently, these velocities are used to determine (3D) stresses in the flowing material using finite-element methods. Detailed comparisons of the model output with laboratory experiments of the flow of sand demonstrate the efficacy of the model and illustrate the role that internal stresses play in the flow of granular debris. The role of internal deviatoric stresses, derived from the friction between grains or fragments in continuous contact, is significant in all of our comparisons with experminents. Replacement of deviatoric stresses with isotropic stresses (by neglecting intergranular friction) will yield different results for collapse of a sand cylinder to form a cone, for release of sand from a hopper, for flow of sand in a channel, or for deposition of sand at the base of a slope. In collapse of a cylinder, the forces driving outward flow are reduced by intergranular friction and consequently are less than obtained assuming isotropic stress states. Neglect of intergranular friction results in higher lateral accelerations and a flatter cone. Similarly, release of material on a slope is affected by the same mechanisms: for a uniform slope and any variation in basal friction or support, more material is mobilized and accelerates faster (as a result of higher lateral stresses) in the case of an isotropic formulation that ignores inter-granular friction. As sand flows down a channel, its behavior continues to depend upon internal stresses within the flow. For example, in comparisons with an experiment using an irregular channel that has a shallow mid-channel ridge, model flows will not be completely divided by the ridge (as observed), but tend to flow over the ridge when inter-granular friction and the stress it generates is ignored. As the sand comes to rest at the base of a slope, an isotropic formulation for internal stresses produces a more rounded deposit with shallower slopes as a result of higher velocities during transport. These comparisons show that internal stresses play a crucial role in many aspects of the flow and deposition of granular debris, one that should not be eliminated in the interests of model efficiency or simplification.