Granular flow down an inclined plane: Bagnold scaling and rheology.

By L. Silbert, Deniz Ertas, Gary S. Grest, T. Halsey, D. Levine, S. Plimpton. Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

913 citations recorded by the source corpus.

We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.

Subfields: Civil and Structural Engineering, Computational Mechanics, Management, Monitoring, Policy and Law

View Paper: https://www.semanticscholar.org/paper/e8212594cc496b56174512e499c244518521b440

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Citations in the corpus

Flows of Dense Granular Media (2008, background): “The coefficient K represents the ratio of the normal horizontal stress (x direction) to the normal vertical stress (z direction) and is close to 1 for steady uniform flows (Silbert et al. 2001).”
Rheology of sheared suspensions of rough frictional particles (2014, neutral): “2001; Sh¨afer et al. 1996).”
A theory for particle size segregation in shallow granular free-surface flows (2005, methodology): “…grain inertia regime in which Article submitted to Royal Society the shear stress is proportional to the square of the strain-rate, σxz = A 2(∂u/∂z)2, Silbert et al (2001) derived an expression for the downslope velocity profile u = 2 3A h3/2 √ ρg sin ζ [ 1 − ( h− z h )3/2 ] , (4.27) which…”
A constitutive model with microstructure evolution for flow of rate-independent granular materials (2011, methodology): “The force is calculated using a spring–dashpot model, which has been tested and used in many other studies (Cundall & Strack 1979; Silbert et al. 2001, 2007; Campbell 2002; Rycroft, Kamrin & Bazant 2009).”
Continuum modelling and simulation of granular flows through their many phases (2014, background): “Reasonable codirectionality (with rotations of the principal axes only a handful of degrees apart) between D0 and σ0 in dense granular flow has been observed in DEM simulations by da Cruz et al. (2005); Silbert et al. (2001); Koval et al. (2009).”
Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts (2009, background): “The introduction of particles of different sizes and roughnesses introduces a rich variety of behaviour, which is rather different from what happens in steady monodisperse twodimensional granular flows down slopes or in very wide three-dimensional channels, where particle dynamics simulations ( Silb”
Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory (2010, background): “The profiles of volume fraction at the lowest angle of inclination exhibit the features seen in numerical simulations [29,30]: there are solutions over a range of volume hold-ups and the individual profiles of volume fraction exhibit a core in which the volume fraction is constant.”