(445a) Development of a Visco-Plastic Constitutive Law for Dense Flow of Granular Matter

The rheological behavior of dense granular materials was studied using a modified annular Couette cell, which allows for porosity changes inside the bed. In these experiments, a small increase in porosity partially breaks the force chains and provides enough space for random collision to occur inside the bed resulting in a significant decrease of shear stresses on the rotating cylinder. This also increases the domain (width) of shear bands and eliminates the existence of points with zero velocity.

We were able to measure normal stresses inside the shearing zone (on the rotating cylinder) and on the stationary (outside) walls of the Couette cell. We found that the coefficient of apparent friction, which is the ratio of shear to normal stress, remains constant (material property) at low shear rates when the regime of flow is quasi-static and plasticity rules applies but it increases exponentially (n < 1) by increasing the shear rate to moderately high values when the granular matter behaves somewhat like a liquid, i.e. both collisions and enduring contacts play a role.

The experimental results suggest a visco-plastic constitutive law for dense granular materials. In this model, shear stresses were found to be independent of shear rate so that the quasi-static regime dominates while increasing the shear rate makes the bed acquire a fluid-like behavior and changes the regime of flow to intermediate. We also found that the dependency of the shear stress to shear rate increases by further increases in shear rate because collisions between particles become more important. In order to generalize the idea, we did experiments with different materials like glass beads (different size), acrylic powders, elastomer granules and catalytic powders. We found that material properties like bulk density, size and stiffness have an important effect on the rheology of flow.