Origin of the critical state in sheared granular materials

Dense granular flow is common in nature and industrial applications. A hallmark behaviour of granular flow is the emergence of a critical state when sufficient strain is applied, which has traditionally been understood with empirical constitutive theories. However, these theories are macroscopic ones without microscopic basis and, therefore, the physical origin of the critical state remains unknown. Here we demonstrate that the critical state corresponds to the random loose packing state where all the microstates are sampled with equal probability. X-ray tomography and shear force measurements allow us to monitor the microscopic processes of sheared granular materials and show that interparticle frictional contacts alter the density of states. This, consequently, leads to different critical state volume fractions. Despite this qualitative difference, we find universal equations of rescaled state variables (effective temperature, entropy and contact number as functions of volume fraction) for systems with different friction coefficients (mu = 0.52, 0.66 and 0.86), which suggests that frictional granular packings can be mapped directly to the frictionless hard-sphere system. In addition, we show that shear force barely affects the Edwards ensemble statistics, while its behaviour can be empirically explained by simply adding the contributions from particle structural rearrangements and frictional dissipation on contacts. When applying sufficient strain, the flow of dense granular matter becomes critical. It is now shown that this state corresponds to random loose packing for spheres with different friction coefficients and that these packings can be mapped onto the frictionless hard-sphere system.