Revisiting the 1954 suspension experiments 
of R. A. Bagnold

Hunt, M. L.; Zenit, Roberto; Campbell, Charles S.; Brennen, Christopher E.

doi:10.1017/s0022112001006577

Cited by 122 publications

(85 citation statements)

References 37 publications

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“…This equilibration of σ e to an imposedγ and m is tantamount to development of steady dispersive normal stress in the enclosed shear cell experiments of Bagnold [80] (cf. [81,82]). On the other hand, if a steadily shearing grainfluid mixture freely dilates or contracts when a step change in σ e is externally imposed, then (3.17) implies thatγ subsequently equilibrates to a new steady state as dm/dt → 0 and ψ → 0.…”

Section: (D) Definition Of Dilation Ratementioning

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: (D) Definition Of Dilation Ratementioning

confidence: 99%

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

2014

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“…13,14 At low Reynolds number, the viscosity can suppress this radial motion, but, as the Reynolds number increases, secondary flows, often referred to as Taylor vortices, may change the character of the flow field from a simple shear flow; this change in flow character can affect the measurement of the stresses. A detailed analysis by Hunt et al 15 demonstrated that Bagnold's experimental results were marred by the presence of secondary flows that developed at the boundaries of the rheometric device. By accounting for the contribution of the vortices to the shear stress, Hunt et al demonstrated that Bagnold's linear to quadratic transition could be explained by assuming a laminar Newtonian flow with an effective viscosity that depended on the solid concentration.…”

Section: -mentioning

confidence: 99%

Rheological measurements of large particles in high shear rate flows

et al. 2012

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How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semiflexible fiber rheology J. Chem. Phys. 136, 064901 (2012) This paper presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Stokes and Reynolds numbers. The experiments were performed in a coaxial rheometer that was designed to minimize the effects of secondary flows. By changing the shear rate, particle size, and liquid viscosity, the Reynolds numbers based on shear rate and particle diameter ranged from 20 to 800 (Stokes numbers from 3 to 90), which is higher than examined in earlier rheometric studies. Prior studies have suggested that as the shear rate is increased, particleparticle collisions also increase resulting in a shear stress that depends non-linearly on the shear rate. However, over the range of conditions that were examined in this study, the shear stress showed a linear dependence on the shear rate. Hence, the effective relative viscosity is independent of the Reynolds and Stokes numbers and a nonlinear function of the solid fraction. The present work also includes a series of roughwall experiments that show the relative effective viscosity is also independent of the shear rate and larger than in the smooth wall experiments. In addition, measurements were made of the near-wall particle velocities, which demonstrate the presence of slip at the wall for the smooth-walled experiments. The depletion layer thickness, a region next to the walls where the solid fraction decreases, was calculated based on these measurements. The relative effective viscosities in the current work are larger than found in low-Reynolds number suspension studies but are comparable with a few granular suspension studies from which the relative effective viscosities can be inferred.

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“…Bagnold's original 1954 work [Hunt et al, 2002]. An alternative to the inertial regime is the elastic regime, which is characterized as ''granular materials under dense conditions where particles are in persistent contact with their neighbors and the elasticity of the material becomes an important rheological parameter'' [Campbell, 2002, p. 261].…”

Section: Discussionmentioning

confidence: 99%

Correction to “Experimental study of bedrock erosion by granular flows”

Hsu¹,

Dietrich²,

Sklar³

2008

J. Geophys. Res.

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[1] Field studies suggest that bedrock incision by granular flows may be the primary process cutting valleys in steep, unglaciated landscapes. An expression has been proposed for debris flow incision into bedrock which posits that erosion rate depends on stresses due to granular interactions at the snout of debris flows. Here, we explore this idea by conducting laboratory experiments to test the hypothesis that bedrock erosion is related to grain collisional stresses which scale with shear rate and particle size. We placed granular material in a 56-cm-diameter rotating drum to explore the relationship between erosion of a synthetic bedrock sample and variables such as grain size, shear rate, water content, and bed strength. Grain collisional stresses are estimated as the inertial stress using the product of the squares of particle size and vertical shear rate. Our uniform granular material consisted of 1-mm sand and quartzite river gravel with means of 4, 6, or 10 mm. In 67 experimental runs, the eroded depth of the bed sample varied with inertial stresses in the granular flow to a power less than 1.0 and inversely with the bed strength. The flows tended to slip on smooth boundaries, resulting in higher erosion rates than no-slip cases. We found that lateral wall resistance generated shear across the channel, producing two cells whose widths depended on wall roughness. While the hypothesized inertial stress dependency is supported with these data, wear mechanics needs to account for grain dynamics specifically at the snout and possibly to include lateral shear effects.

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Revisiting the 1954 suspension experiments of R. A. Bagnold

Cited by 122 publications

References 37 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

Rheological measurements of large particles in high shear rate flows

Correction to “Experimental study of bedrock erosion by granular flows”

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