On the role of the ambient fluid on gravitational granular flow dynamics

Meruane, Carolina; Tamburrino, Aldo; Roche, Olivier

doi:10.1017/s0022112009993181

Cited by 71 publications

(72 citation statements)

References 41 publications

(72 reference statements)

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“…These effects can be diverse, but in mixtures of fluid and macroscopic grains (subject to negligible Brownian forces), the effects are commonly dominated by buoyancy and viscous drag [33,60]. Other interaction forces include hydrodynamic-lift, added-mass and Basset forces, but these forces are probably muted in debris flows owing to restriction of fluid flow caused by high concentrations of grains with differing shapes and sizes [5,6].…”

Section: (B) Definitions Of Volume Fractions Densities and Velocitiesmentioning

confidence: 99%

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

2014

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To simulate debris-flow behaviour from initiation to deposition, we derive a depth-averaged, twophase model that combines concepts of critical-state soil mechanics, grain-flow mechanics and fluid mechanics. The model's balance equations describe coupled evolution of the solid volume fraction, m, basal pore-fluid pressure, flow thickness and two components of flow velocity. Basal friction is evaluated using a generalized Coulomb rule, and fluid motion is evaluated in a frame of reference that translates with the velocity of the granular phase, v s . Source terms in each of the depth-averaged balance equations account for the influence of the granular dilation rate, defined as the depth integral of ∇ · v s . Calculation of the dilation rate involves the effects of an elastic compressibility and an inelastic dilatancy angle proportional to m − m eq , where m eq is the value of m in equilibrium with the ambient stress state and flow rate. Normalization of the model equations shows that predicted debris-flow behaviour depends principally on the initial value of m − m eq and on the ratio of two fundamental timescales. One of these timescales governs downslope debris-flow motion, and the other governs pore-pressure relaxation that modifies Coulomb friction and regulates evolution of m. A companion paper presents a suite of model predictions and tests.

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Section: (B) Definitions Of Volume Fractions Densities and Velocitiesmentioning

confidence: 99%

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

2014

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“…As a matter of fact, many numerical studies addressed the granular column released problem using typically three different approaches: shallow-type models (Mangeney-Castelnau et al, 35 Kerswell, 27 Larrieu et al, 32 and Doyle et al 12 ), Discrete Element Methods (DEM) (Staron and Hinch, 51 Zenit, 54 Lacaze et al, 29 and Girolami et al 16 ), and complete viscousplastic or elasto-plastic models (Crosta et al, 8 Lacaze and Kerswell, 28 Meruane et al, 40 Lagrée et al, 30 and Ionescu et al 24 ).…”

Section: Introductionmentioning

confidence: 99%

Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects

et al. 2017

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We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22°) and compare precisely the results with laboratory experiments. Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called μ(I) rheology that induces a Drucker-Prager yield stress and a variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel, is added to the model. We demonstrate that this term is crucial to accurately reproduce granular collapses on slopes ≳10°, whereas it remains of little effect on the horizontal slope. Quantitative comparison between the experimental and numerical changes with time of the thickness profiles and front velocity makes it possible to strongly constrain the rheology. In particular, we show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order. However, only a fine tuning of the constant viscosity (η=1 Pa s) makes it possible to predict the slow propagation phase observed experimentally at large slopes. Finally, we observed that small-scale instabilities develop when refining the mesh (also called ill-posed behavior, characterized in the work of Barker et al. [“Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow,” J. Fluid Mech. 779, 794–818 (2015)] and in the present work) associated with the mechanical model. The velocity field becomes stratified and the bands of high velocity gradient appear. These model instabilities are not avoided by using variable viscosity models such as the μ(I) rheology. However we show that the velocity range, the static-flowing transition, and the thickness profiles are almost not affected by them.

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“…The compression/dilation of the granular phase changes the interstitial fluid pressure that in turn couples with the solid momentum equations. This coupling appears in the non-hydrostatic pressure terms (see [30]), not included in the approximations made in this work. The consistency of the whole model can be evaluated by the local energy balance equation.…”

Section: Mass and Momentum Equationsmentioning

confidence: 99%

A two-phase shallow debris flow model with energy balance

et al. 2015

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Abstract. This paper proposes a thin layer depth-averaged two-phase model provided by a dissipative energy balance to describe avalanches of solid-fluid mixtures. This model is derived from a 3D two-phase model based on the equations proposed by Jackson [R. Jackson, The Dynamics of Fluidized Particles, 2000] which takes into account the force of buoyancy and the forces of interaction between the solid and fluid phases. Jackson's model is based on mass and momentum conservation within the two phases, i.e. two vector and two scalar equations. This system has five unknowns: the solid volume fraction, the solid and fluid pressures and the solid and fluid velocities, i.e. three scalars and two vectors. As a result, an additional equation is necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been developed on the basis of Jackson's work. In particular, Pitman and Le [E.B. Pitman, L. Le, Phil. Trans. R. Soc. A, 2005] replaced this closure simply by imposing an extra boundary condition. If the pressure is assumed to be hydrostatic, this condition can be considered as a closure condition. However, the corresponding model cannot account for a dissipative energy balance. We propose here a closure equation to complete Jackson's model, imposing incompressibility of the solid phase. We prove that the resulting whole 3D model is compatible with a dissipative energy balance. From this model, we deduce a 2D depth-averaged model and we also prove that the energy balance associated with this model is dissipative. Finally, we propose a numerical scheme to approximate the depth-averaged model. We present several numerical tests for the 1D case that are compared to the results of the model proposed by Pitman and Le.1991 Mathematics Subject Classification. 65C20,81T80,91B74,97M10.The dates will be set by the publisher.

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On the role of the ambient fluid on gravitational granular flow dynamics

Cited by 71 publications

References 41 publications

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects

A two-phase shallow debris flow model with energy balance

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