Predictability and granular materials

Behringer, R. P.; Howell, Daniel W.; Kondic, Lou; Tennakoon, Sarath G. K.; Veje, Christian

doi:10.1016/s0167-2789(99)00094-9

Cited by 71 publications

(55 citation statements)

References 27 publications

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“…In doing so, one reduces the granular force chains to simple fibres, characterized by a single variable s, their ability to bear stress. It is known that a GM under either static or dynamic loading displays an exponential distribution of internal forces [6,9,11,7,12,10,13,14,15,8], a property generally encountered in disordered systems [40,41,14]. We have computed therefore the internal load distribution p(τ ) as a function of the reduced bundle load f = σ/σ c .…”

Section: The Internal Distribution Of Loadsmentioning

confidence: 99%

A random neighbour model for yielding

2010

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Abstract.We introduce a model for yielding, inspired by fracture models and the failure of a sheared granular medium in which the applied shear is resisted by self-organized force chains. The force chains in the granular medium (GM) are considered as a bundle of fibres of finite strength amongst which stress is randomly redistributed after any other fibre breaks under excessive load. The model provides an exponential distribution of the internal stress and a log-normal shaped distribution of failure stress, in agreement with experimental observations. The model displays critical behaviour which approaches mean field as the number of random neighbours k becomes large and also displays a failure strength which remains finite in the limit of infinite size. From comparison with different models it is argued that this is an effect of uncorrelation. All these macroscopic properties appear statistically stable with respect to the choice of the chains' initial strength distribution. The investigated model is relevant for all systems in which some generic external load or pressure is borne by a number of units, independent of one another except when failure of a unit causes load transfer to some random choice of neighbouring units.

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Section: The Internal Distribution Of Loadsmentioning

confidence: 99%

A random neighbour model for yielding

2010

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“…Mg, 83.50.Ax Shear bands in dense granular materials are localized regions of large velocity gradients; they are the antithesis of the broad uniform flows seen in slowly-sheared Newtonian fluids [1,2,3,4,5,6]. Until recently it was generally assumed that all granular shear bands were narrow.…”

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confidence: 99%

Three-Dimensional Shear in Granular Flow

et al. 2006

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The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations we find a transition in the nature of the shear as a characteristic height H * is exceeded. Below H * there is a central stationary core; above H * we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height while the axial width remains narrow and fixed.PACS numbers: 45.70. Mg, 83.50.Ax Shear bands in dense granular materials are localized regions of large velocity gradients; they are the antithesis of the broad uniform flows seen in slowly-sheared Newtonian fluids [1,2,3,4,5,6]. Until recently it was generally assumed that all granular shear bands were narrow. However, in 2003 Fenistein et al. [7] discovered that in modified Couette cells granular shear bands can be made arbitrarily broad. In this geometry, the bottom of a cylindrical container is split at radius r = R s and shear is produced by rotating both the outer ring and the cylindrical boundary of the container while keeping the central disk (r < R s ) stationary. For very shallow packs, the shear band measured at the top surface is narrow and located at r = R s so that the inner region directly above the central disk is stationary while the remaining part rotates as a solid. As the filling height of the material, H, increases, the shear band increases in radial width and moves toward the cylinder axis. For sufficiently large H, the shear band overlaps the axis at r = 0 and one might expect qualitatively new behavior. Indeed, Unger et al. [8] predicted that the shape of the boundary between moving and stationary material would undergo a first-order transition as H is increased past a threshold value H * : the shearing region which for H < H * is open at the top and intersects the free surface abruptly collapses to a closed cupola completely buried inside the bulk.Previous experiments focused primarily on the surface flows in shallow containers and left unexplored many questions about the shape and evolution of the shear profiles for large H. Here, we combine magnetic resonance imaging (MRI) and high-speed video observations with large-scale simulations to explore shear flow both for shallow and tall packs. In addition to monitoring the evolution of the flow profiles in the radial direction, we also examine shear in the vertical direction. Instead of a first order collapse of the shear zone as proposed by Unger et al.[8], we find that above H * ≃ 0.6R s , the inner core of immobile material disappears gradually as shear along the central axis of the cylinder sets in. Our setup is similar to that of Fenistein et al. [7] except that we rotate the inner disk instead of the outer ring and cylinder (Fig.1b inset). In the absence of inertial effects, this makes no difference to the results. For surface observations with high-speed video ...

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“…Although the conventional approach is constrained by suitable container size and vane immersion criteria, they serve only to minimize wall and end effects (Dzuy and Boger 1985). Unlike gelled polymer solutions and fine grained flocculated particle networks, coarse granular matter can form a continuous contact networks that transmit interparticle stress both laterally and vertically (Behringer et al 1999). This, along with interparticle friction and lubrication, makes shear strength a process property, like hydrostatic pressure, rather than a gel-related intensive material property.…”

Section: 3mentioning

confidence: 99%

“…For deep beds or beds in thin containers (such as pipes or grain silos), the stress profile tends to show stress saturation. The latter phenomenon results from the contact force networks and nonuniform force networks called stress chains (Behringer et al 1999). If stress chains propagate forces to the wall, then friction between the wall and particles allows the wall to carry part of the lithostatic load.…”

Section: Shear Strength Modelmentioning

confidence: 99%

“…Interpreting vane rheograms is difficult because of the dependence of stress-strain behavior on granular density and pressure as well as potential discontinuities in the velocity and solid-fraction profiles (Cheng and Farley 1965). Continuous contact networks formed between the particles transmit interparticle stress both laterally and vertically (Behringer et al 1999). The intergranular pressure and the resulting frictional force between particles can vary significantly over the vertical depth of the bed.…”

Section: 1mentioning

confidence: 99%

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Characterization and Correlation of Particle-Level Interactions to the Macroscopic Rheology of Powders, Granular Slurries, and Colloidal Suspensions

Poloski¹,

Daniel²,

Rector³

et al. 2006

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Executive SummaryHanford TRU tank sludges are complex mixtures of undissolved minerals and salt solids in an aqueous phase of high ionic strength. They show complex rheological behavior resulting from interactions at the macroscopic level, such as interparticle friction between grains in the coarse fraction, as well as from interactions at the nano-scale level, such as the agglomeration of colloidal particles. An understanding of phenomena such as interparticle friction and aggregate stability under shear will allow better control of Hanford TRU tank sludges being processed for disposal.The project described in this report had two objectives. The first was to understand the physical properties and behavior of the Hanford transuranic (TRU) tank sludges under conditions that might exist during retrieval, treatment, packaging, and transportation for disposal at the Waste Isolation Pilot Plant (WIPP). The second objective was to develop a fundamental understanding of sludge physical properties by correlating the macroscopic behavior with interactions occurring at the particle/colloidal scale. These objectives were accomplished by: 1) measuring the physical and rheology properties of actual Hanford tank samples, 2) developing continuum models for coarse granular slurries, and 3) studying the behavior of colloidal agglomerates under shear and under ion irradiation.The shear strength of coarse granular powders and slurries was studied to determine ways of characterizing (quantifying) the effect of interparticle friction and cohesion on incipient motion. Additional studies were performed to develop and validate a continuum model for cohesionless granular powders and slurries undergoing three-dimensional shear. With regard to incipient motion in dense slurries, the immersion depth and containing vessel diameter significantly impact shear strength . A model accounting for the effects of interparticle friction, slurry cohesion, vane size and immersion depth, and container geometry was derived using a saturating vertical stress profile. This model was able to adequately explain experimental observations with regards to variations in container size and vane immersion depth. The functional form of the Janssen formula provides a potential scaling relationship to apply small-scale shear vane results to engineering-scale applications dealing with coarse-grained slurry systems.For granular systems undergoing three-dimensional flow, a constitutive model was developed to describe flows of cohesionless granular solids. The model is based on the postulate that the friction coefficient and the solids fraction in a moving granular material are exclusive functions of an inertial number, which represents the ratio of inertial to normal stress forces. The constitutive equation obtained has the same form as a multidimensional Bingham fluid model, albeit with an apparent viscosity and yield stress that depend on the vertical normal stress distribution. The model was applied to previously published experimental results dealing with three-dim...

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Predictability and granular materials

Cited by 71 publications

References 27 publications

A random neighbour model for yielding

A random neighbour model for yielding

Three-Dimensional Shear in Granular Flow

Characterization and Correlation of Particle-Level Interactions to the Macroscopic Rheology of Powders, Granular Slurries, and Colloidal Suspensions

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