**[Elastic Granular Flows]{.underline}**

Charles S. Campbell, University of Southern California, Los Angeles, CA
90089-1453 USA

There is no fundamental understanding of the mechanics of granular
solids. Partially this is because granular flows have historically been
divided into two very distinct flow regimes, (1) the slow, quasistatic
regime, in which the bulk friction coefficient is taken to be a material
constant, and (2) the fast, rapid-flow regime, where the particles
interact collisionally. But slow hopper flow simulations indicate that
the bulk friction coefficient is not a constant. Rapidly moving large
scale landslide simulations never entered the collisional regime and
operate in a separate intermediate flow regime. In other words, most
realistic granular flows are not described by either the quasistatic or
rapid flow models and it is high time that the field look beyond those
early models.

This talk will discuss computer simulation studies that draw out the
entire flowmap of shearing granular materials, spanning the quasistatic,
rapid and the intermediate regimes. The key was to include the elastic
properties of the solid material in the set of rheological parameters;
in effect, this puts solid properties back into the rheology of granular
solids. The solid properties were previously unnecessary in the
plasticity and kinetic theory formalisms that respectively form the
foundations of the quasistatic and rapid-flow theories. Granular flows
can now be 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 in clusters through long
duration contacts, and the Inertial-Collisional (or the old rapid-flow)
regime.

Finally, the simulations show that Stress-Controlled flows are
rheologically different from Controlled-Volume flows. Physically, there
is a range of dense concentrations (0.5\<ν\<0.6) in which it is
possible, but not necessary to form force chains and demonstrate elastic
behavior. (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
may behave elastically through this range of concentrations while, at
the same shear rates rate Controlled-Volume flows, fixed at the average
concentration of the Stress-Controlled flow, behave inertially.

The Controlled-Stress studies, backed by shear cell experiments indicate
that the minimum shear rate, γ~min~, at which a ten particle-layer deep
layer of a sand-like material of diameter *d*, enters the rapid flow
regime to be roughly *d*γ~min~ = 0.1m/s, which requires shear rates of
the order of 100s^-1^ for 1mm particles. Hence, it is unlikely that
rapid granular flow theory is applicable to any flows to be obtained
outside the laboratory.