Scaling of Granular Temperature and Local Inertia Number of Dense Dry Granular Flow

The behaviours of dry granular flows involved in geophysical flows are typically described by rheological laws. While these models enable effective discrimination of distinct flow regimes, in-depth elaboration on the differentiating characteristics pertaining to various regimes remains lacking. In this study, an independently developed rate-controlled parallel-plate rheometer was employed to conduct rheological tests on glass bead samples with a diameter of 3 mm and varied initial solid concentrations (C_V0​), under constant pressure across 9 shear rates. Two novel indicators were introduced to distinguish different flow regimes, namely the scaling parameter (β) that reflects the exponential relationship between granular temperature (T) and inertial number (I), and apparent viscosity (η_app​). η_app ​ decreases with the reduction of C_V0​ and the increase of shear speed (N), exhibiting a typical shear thinning behaviour. Correspondingly, β decreases with decreasing C_V0​ and increasing N, which corresponds to the flow regime transition from the dense and slow quasi-static regime to the dilute and fast intermediate regime.