Shear-weakening of the transitional regime for granular flow

This paper experimentally investigates the rheology of dense granular flow through its solid-like to fluid-like transition. Between the well-established flow regimes - quasi-static and grain-inertial - the physical description of the transition remains elusive. Our experiment uses a top-rotating torsional shear cell capable of +/- 1 mu m accuracy in height and 5 decades (10(-3) - 100 rad s(-1)) in rotation rate. The data on beach sand shows that shear and normal stresses exhibit an inverse rate-dependence under a controlled volume environment in the transitional regime, while in the limiting regimes the results are in agreement with previous work. The shear-weakening stresses illustrate a previously unknown 'dip' with increasing shear rate. Under a controlled-pressure environment, however, the shear-compacting volume-fraction 'peaks' with increasing shear-rate. We combine these results from both configurations to infer a constitutive law based on a rate-invariant granular fluid compressibility. The formulation provides an equation-of-state for dynamic granular systems, with state variables of pressure, strain rate and free-volume-fraction. Fitting parameters from independent constant-volume and constant-pressure data shows good agreement in validating our model. Moreover, the degree of grain jaggedness is essential to the rate-dependence within the transitional regime. The results on the solid-fluid transition may elucidate the evolution of granular flow anisotropies.