  A continuum description of granular flows would be of considerable help in
predicting natural geophysical hazards or in designing industrial processes.
However, the constitutive equations for dry granular flows, which govern how
the material moves under shear, are still a matter of debate. One difficulty is
that grains can behave like a solid (in a sand pile), a liquid (when poured
from a silo) or a gas (when strongly agitated). For the two extreme regimes,
constitutive equations have been proposed based on kinetic theory for
collisional rapid flows, and soil mechanics for slow plastic flows. However,
the intermediate dense regime, where the granular material flows like a liquid,
still lacks a unified view and has motivated many studies over the past decade.
The main characteristics of granular liquids are: a yield criterion (a critical
shear stress below which flow is not possible) and a complex dependence on
shear rate when flowing. In this sense, granular matter shares similarities
with classical visco-plastic fluids such as Bingham fluids. Here we propose a
new constitutive relation for dense granular flows, inspired by this analogy
and recent numerical and experimental work. We then test our three-dimensional
(3D) model through experiments on granular flows on a pile between rough
sidewalls, in which a complex 3D flow pattern develops. We show that, without
any fitting parameter, the model gives quantitative predictions for the flow
shape and velocity profiles. Our results support the idea that a simple
visco-plastic approach can quantitatively capture granular flow properties, and
could serve as a basic tool for modelling more complex flows in geophysical or
industrial applications.
