Modeling granular material flows: The angle of repose, fluidization and the cliff collapse problem

Abstract

I discuss theories of granular material flows, with application to granular flows on the earth and planets. There are two goals. First, there is a lingering belief of some that the standard continuum plasticity Mohr–Coulomb and/or Drucker–Prager models are not adequate for many large-scale granular flow problems. The stated reason for those beliefs is the fact that the final slopes of the run-outs in collapse, landslide problems, and large-scale cratering are well below the angle of repose of the material. That observation, combined with the supposition that in those models flow cannot occur with slopes less than the angle of repose, has led to a number of researchers suggesting a need for lubrication or fluidization mechanisms and modeling.That issue is investigated in detail and shown to be false. A complete analysis of slope failures according to the Mohr–Coulomb model is presented, with special attention to the relations between the angle of repose and slope failures. It is shown that slope failure can occur for slope angles both larger than and smaller than the angle of repose.Second, to study the details of landslide run-outs, finite-difference continuum code simulations of the prototypical cliff collapse problem, using the classical plasticity models, are presented, analyzed and compared to experiments. Although devoid of any additional fluidization models, those simulations match experiments in the literature extremely well. The dynamics of this problem introduces additional important features relating to the run-out and final slope angles. The vertical free surface begins to fall at the initial 90° and flow continues to a final slope less than 10°. The detail in the calculation is examined to show why flow persists at slope angles that appear to be less than the angle of repose. The motions include regions of solid-like, fluid-like, and gas-like flows without invoking any additional models.