Shear-weakening of the transitional regime for granular flow

Abstract

This paper experimentally investigates the rheology of dense granular flow through itssolid-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 μm 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 controlledvolume environment in the transitional regime, while in the limiting regimes the results are in agreement with previous work. Theshear-weakening stresses illustrate a previouslyunknown ‘dip’ with increasingshear 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 transitionmay elucidate the evolution of granular flow anisotropies.

A thermodynamic unification of jamming

“…For dry sand, the constants κ 1 ≈ 7 × 10 −4 Pa −1 and κ 2 ≈ 2 × 10 −5 s. These constants also match values found independently from experimental data using the cyclic rule 2 . The free volume ε ≡ (V − V RCP ) is the flowing shear-band volume V referenced to its dynamic random-close-packing volume, V RCP .…”

“…The theoretical fit uses equation (1) with an extra grain-inertial term 17 , MρD 2γ 2 , in terms of grain density, ρ, averaged grain diameter, D, and fitting constant, M. The sweet spot signifies the optimum efficiency in achieving steady-state flow. Shear rateγ is calculated on the basis of a two-grain-diameter thickness 2 . The values for the isochoric fit are C = 0.990 ± 0.004, progressively hindering the process of particle rearrangement.…”

Geometric and rheological asperities in an exposed fault zone

“…At present, Layer II is stiffer than the surroundings and the boudinaging in Figure 7 suggests that this was the case, at least during the last episodes of the deformation. However, the appropriate rheology of the granular flow at the fault conditions is extremely uncertain [Brodsky and Kanamori, 2001;Lu et al, 2007]. For an ordinary coefficient of friction in optimally oriented Andersonian faults, fault parallel compression is larger than fault normal, which would suggest that the mullion-type instability was a better explanation.…”

Friction memory in the stick-slip of a sheared granular bed

“…Although fundamentally different in nature, granular matter has been shown to share many similarities with solid surfaces as far as shear stress is concerned [3], with the addition of possible hardening when the top plate velocity becomes large enough [13][14][15][16]. It has been found in particular that the ageing of static friction with time and the weakening of dynamic friction with velocity in granular gouges can be described by the same phenomenological laws as solids [3,8,9], generally known as rate-and-state friction laws (RS).…”

“…[4]) in the stochastic motion equation for the plate. To this end classic rate-andstate equations are suitably modified to allow for the Bagnold [13] and weakening-hardening [14][15][16][17] regimes characteristic of granular systems. However some discrepancies do remain and we shall discuss their possible origin.…”