Numerical, Analytical, and Laboratory Experimental Studies of Granular Avalanche Flows

Abstract

Flow avalanches may be regarded as being composed of a granular fluid. When dislodged, the snow masses accelerate down a slope until the inclination of its bed tends towards the horizontal, at which stage bed friction eventually brings the snow to rest. We present a completely new analysis of the motion of a finite mass of granular material along an inclined base.We regard a granular snow mass as an incompressible continuum to which a Coulomb-like basal friction law can be applied. Depth-averaged equations of motion are formulated in terms of a curvilinear coordinate system along a curved bed, and incorporate an averaged longitudinal velocity and a height distribution. A numerical finite-difference technique is employed to integrate these equations. We present numerical results obtained for motion along a curved bed and compare this with the solutions of the equations with results from laboratory observations. The experiments have been performed in order to monitor the motion of a finite mass of granules, either plastic particles or glass beads, along a chute consisting of both an inclined and a horizontal zone, the two zones being connected by a curved element. The particle spread along the chute and the mass distribution of the granules in the run-out zone, as obtained from these experiments, are compared with those derived from theoretical computations. The results show that the model used predicts the motion of a granular avalanche reasonably well.Finally, it is indicated how the basal friction law may be extended or altered in order to reproduce the dynamic processes involved in causing the abrupt cessation of the snow mass-motion characteristic in the run-out zone.