Charles Campbell

Elastic Granular Flows

Abstract: Large scale landslide simulations provided the surprising result that the effective friction coefficient (the ratio of shear to normal forces at the base of the slide) increased with the shear rate. This might possibly explain the effect of slide volume on the runout of large landslides, but it also indicates that landslides operated in an entirely new and unexplored flow regime.

Previously, granular flows had been divided into (1) the slow, quasistatic regime, in which the effective friction coefficient is taken to be a material property and thus constant, and (2) the fast, rapid-flow regime, where the particles interact collisionally, but which scales in such a way that the effective friction coefficient is independent of the shear rate. Consequently the landslides operated in a separate intermediate regime.

This talk will discuss detailed computer simulation studies into this intermediate regime and into the transitions between regimes. In this way, it is possible to draw the entire flowmap connecting the quasistatic and rapid-flow regimes. The key was to include the elastic properties of the solid material in the set of rheological parameters; in effect this put solid properties into the rheology of granular solids, properties that were unnecessary in previous theories as a result of the plasticity and kinetic theory formalisms on which quasistatic and rapid-flow theories are respectively based. Granular flows are then divided into two broad categories, the Elastic Regimes, in which the particles are locked in force chains and interact elastically over long duration contact with their neighbors and the Inertial regimes, where the particles have broken free of the force chains. The Elastic regimes can be further subdivided into the Elastic-Quasistatic regime (the old quasistatic regime) and the Elastic-Inertial regime. The Elastic-Inertial regime is the “new” regime observed in the landslide simulations, in which the inertially induced stresses are significant compared to the elastically induced stresses. The Inertial regime can also be sub-divided into an Inertial-Non-Collisional where the stresses scale inertially, but the particles interact through long duration contacts, and the Inertial-Collisional or rapid-flow regime.

Finally, it will be shown that Stress-Controlled flows are rheologically different from Controlled-Volume flows. Physically, there is a range of dense concentrations (0.5<v<0.6) in which it is possible to form force chains and thus to demonstrate elastically. But there are conditions under which force chains do not form at the same average concentrations. (In other words it is possible for the material to exhibit two different states at the same concentration.) By forcing the material to support an applied loads across force chains, Stress-Controlled flows generally behave elastically through this range of concentrations under the same conditions where Controlled-Volume flows behave inertially.