Shallow granular flows down flat frictional channels: Steady flows and longitudinal vortices

Brodu, Nicolas; Richard, Patrick; Delannay, Renaud

doi:10.1103/physreve.87.022202

Cited by 54 publications

(81 citation statements)

References 42 publications

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“…An intuitive explanation of this velocity-weakening is that, whatever the scale, higher velocities increase the fluctuations in granular flows and may locally decrease the volume fraction, possibly decreasing frictional dissipation and enabling more complex flows (vortices and so on). Indeed, recent discrete element modelling of dry granular flows highlights the appearance of possible regimes dominated by large-scale vortices, significantly reducing the effective friction 56 , although this remains to be observed in laboratory experiments. Different mechanisms may also be responsible for this friction weakening, owing to the great complexity of natural landslides that involve very different material properties (for example, composition and strength), environment variables (for example, air pressure and gravity) and physical processes at play (for example, fluid/grain interactions and erosion/deposition processes).…”

Section: Resultsmentioning

confidence: 99%

Frictional velocity-weakening in landslides on Earth and on other planetary bodies

2014

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One of the ultimate goals in landslide hazard assessment is to predict maximum landslide extension and velocity. Despite much work, the physical processes governing energy dissipation during these natural granular flows remain uncertain. Field observations show that large landslides travel over unexpectedly long distances, suggesting low dissipation. Numerical simulations of landslides require a small friction coefficient to reproduce the extension of their deposits. Here, based on analytical and numerical solutions for granular flows constrained by remote-sensing observations, we develop a consistent method to estimate the effective friction coefficient of landslides. This method uses a constant basal friction coefficient that reproduces the first-order landslide properties. We show that friction decreases with increasing volume or, more fundamentally, with increasing sliding velocity. Inspired by frictional weakening mechanisms thought to operate during earthquakes, we propose an empirical velocity-weakening friction law under a unifying phenomenological framework applicable to small and large landslides observed on Earth and beyond.

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Section: Resultsmentioning

confidence: 99%

Frictional velocity-weakening in landslides on Earth and on other planetary bodies

2014

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“…Jop et al 2005) show a maximum in the thickness profile down the centre of the channel, but the variations are small in magnitude (Brodu et al 2013). Similarly, the measured transverse velocities are negligible (<1 % of the downslope magnitudes according to Jop et al 2005) and so the statements (4.2) and (4.4) are plausible as leading-order approximations.…”

Section: Steady Fully-developed Flows Between Parallel Platesmentioning

confidence: 92%

A two-dimensional depth-averaged -rheology for dense granular avalanches

2015

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Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the momentum-balance equations by extending the recent depth-averaged µ(I)-rheology for dense granular flows to two spatial dimensions, using the principle of material frame indifference or objectivity. Scaling the cross-slope coordinate on the width of the channel and the velocity on the one-dimensional steady uniform solution, we show that the steady two-dimensional downslope velocity profile is independent of scale. The only controlling parameters are the channel aspect ratio, the slope inclination angle and the frictional properties of the chute and the sidewalls. Solutions are constructed for both no-slip conditions and for a constant Coulomb friction at the walls. For narrow chutes, a pronounced parabolic-like depth-averaged downstream velocity profile develops. However, for very wide channels, the flow is almost uniform with narrow boundary layers close to the sidewalls. Both of these cases are in direct contrast to conventional inviscid avalanche models, which do not develop a cross-slope profile. Steady-state numerical solutions to the full three-dimensional µ(I)-rheology are computed using the finite element method. It is shown that these solutions are also independent of scale. For sufficiently shallow channels, the depth-averaged velocity profile computed from the full solution is in excellent agreement with the results of the depth-averaged theory. The full downstream velocity can be reconstructed from the depth-averaged theory by assuming a Bagnold-like velocity profile with depth. For wide chutes, this is very close to the results of the full three-dimensional calculation. For experimental validation, a laser profilometer and balance are used to determine the relationship between the total mass flux in the chute and the flow thickness for a range of slope angles and channel widths, and particle image velocimetry (PIV) is used to record the corresponding surface velocity profiles. The measured values are in good quantitative agreement with reconstructed solutions to the new depth-averaged theory.

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“…A large body of work in the last decade has been devoted to the so-called µ(I) rheology [4,10]. While this rheology seems to work well (and should be probably better referred to) as an empirical, macroscopic scaling law, its colinear extension to 3D [11] was shown to have some drawbacks for complex flows, particularly when approaching the quasistatic regime of flow [12,13,6]. These problems seem to be related to the local nature of the µ(I) rheology and motivated research on nonlocal models of granular flows such as fluidity-based models [14][15][16][17] and models inspired by kinetic theories [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Torsional shear flow of granular materials: shear localization and minimum energy principle

Artoni¹,

Richard²

2016

Comp. Part. Mech.

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The rheological properties of granular matter submitted to torsional shear are investigated numerically by means of Discrete Element Method. The shear cell is made of a cylinder filled by grains which are sheared by a bumpy bottom and submitted to a vertical pressure which is applied at the top. Regimes differing by their strain localization features are observed. They originate from the competition between dissipation at the sidewalls and dissipation in the bulk of the system. The effects of the (i) the applied pressure (ii) sidewall friction and (iii) angular velocity are investigated. A model, based on the purely local µ(I)-rheology and a minimum energy principle is able to capture the effect of the two former quantities but unable to account the effect of the latter. Although, an ad-hoc modification of the model allows to reproduce all the numerical results, our results point out the need for an alternative rheology.

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Shallow granular flows down flat frictional channels: Steady flows and longitudinal vortices

Cited by 54 publications

References 42 publications

Frictional velocity-weakening in landslides on Earth and on other planetary bodies

Frictional velocity-weakening in landslides on Earth and on other planetary bodies

A two-dimensional depth-averaged -rheology for dense granular avalanches

Torsional shear flow of granular materials: shear localization and minimum energy principle

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