This work examines the algebraic $$\mu -I$$ μ - I relation proposed for steady uniform dry granular flows via unsteady granular avalanche experiments of finite nearly identical dry glass spheres down an inclined narrow reservoir of smooth bed. Lateral high-speed digital imaging permits particle tracking velocimetry with which we can evaluate bulk local instantaneous volume fraction and velocity components to conduct a quasi-two-dimensional control volume analysis of streamwise momentum assuming an internal shear stress based on the $$\mu -I$$ μ - I rheology, a hydrostatic normal stress and a Coulomb yielding condition at lateral walls. Hence, the desired $$\mu $$ μ is a function of flow dynamics and a wall friction coefficient $$\mu _w$$ μ w . Complementary sliding table experiments were conducted to estimate an upper bound of $$\mu _w=0.17$$ μ w = 0.17 which was used with a chosen nonzero lower bound $$\mu _w=0.05$$ μ w = 0.05 to extract possible range of $$\mu $$ μ at a local instantaneous inertial number I. The so-obtained local instantaneous $$\mu -I$$ μ - I data conform to the non-linear monotonically increasing trend proposed for steady inertial flows above a crossover value $$I_c\approx 0.03$$ I c ≈ 0.03 . Below $$I_c$$ I c , a peculiar segment of decaying $$\mu $$ μ with I was revealed agreeing to the rheology tests in quasi-static regime.
Granular Matter – Springer Journals
Published: Jun 28, 2017
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