K. M. Hill

Theory for shear-induced segregation of dense granular mixtures

It is well known that a mixture of different sized particles will segregate in a gravitational field. However, it has only recently been shown that a gradient of shear rate alone can drive segregation in dense sheared systems. In contrast with sparse energetic granular materials, in dense sheared systems, large particles segregate to regions with higher shear rates. In this paper, we develop a model for shear-induced segregation in dense mixtures of different sized particles. The model is comprised of two primary parts. The first involves the tendency of a gradient in kinetic stress—stress associated with velocity fluctuation correlations—to drive all particles toward regions of low shear rate. The second is essentially a kinetic sieving effect in which small particles are more likely than large particles to find voids into which they can travel. The two features together segregate small particles to regions of low shear rate and squeeze large particles in the opposite direction. We validate this model via three- dimensional discrete element method simulations in a vertical chute.

Mixing of granular materials: A test-bed dynamical system for pattern formation

Mixing of granular materials provides fascinating examples of pattern formation and self-organization. More mixing action — for example, increasing the forcing with more vigorous shaking or faster tumbling — does not guarantee a better-mixed final system. This is because granular mixtures of just barely different materials segregate according to density and size; in fact, the very same forcing used to mix may unmix. Self-organization results from two competing effects: chaotic advection or chaotic mixing, as in the case of fluids, and flow-induced segregation, a phenomenon without parallel in fluids. The rich array of behaviors is ideally suited for nonlinear-dynamics-based inspection. Moreover, the interplay with experiments is immediate. In fact, these systems may constitute the simplest example of coexistence between chaos and self-organization that can be studied in the laboratory. We present a concise summary of the necessary theoretical background and central physical ideas accompanied by illustrative experimental results to aid the reader in exploring this fascinating new area.

Effects of coarse grain size distribution and fine particle content on pore fluid pressure and shear behavior in experimental debris flows

Debris flows are typically a saturated mixture of poorly sorted particles and interstitial fluid, whose density and flow properties depend strongly on the presence of suspended fine sediment. Recent research suggests that grain size distribution (GSD) influences excess pore pressures (i.e., pressure in excess of predicted hydrostatic pressure), which in turn plays a governing role in debris flow behaviors. We report a series of controlled laboratory experiments in a 4 m diameter vertically rotating drum where the coarse particle size distribution and the content of fine particles were varied independently. We measured basal pore fluid pressures, pore fluid pressure profiles (using novel sensor probes), velocity profiles, and longitudinal profiles of the flow height. Excess pore fluid pressure was significant for mixtures with high fines fraction. Such flows exhibited lower values for their bulk flow resistance (as measured by surface slope of the flow), had damped fluctuations of normalized fluid pressure and normal stress, and had velocity profiles where the shear was concentrated at the base of the flow. These effects were most pronounced in flows with a wide coarse GSD distribution. Sustained excess fluid pressure occurred during flow and after cessation of motion. Various mechanisms may cause dilation and contraction of the flows, and we propose that the sustained excess fluid pressures during flow and once the flow has stopped may arise from hindered particle settling and yield strength of the fluid, resulting in transfer of particle weight to the fluid. Thus, debris flow behavior may be strongly influenced by sustained excess fluid pressures controlled by particle settling rates.

Moon patterns, sun patterns, and wave breaking in rotating granular mixtures

Granular materials, such as powders and sand, tend to segregate due to differences in particle properties. When a cylindrical drum is partially filled with particles of different sizes and rotated about its axis, this leads to radial segregation patterns in which the smaller particles concentrate in a radial core near the axis, and the larger particles near the outside walls of the drum. Under certain conditions, undulations in the radial core of smaller particles grow into radial stripes that extend toward the outer walls of the drum in a manner somewhat reminiscent of viscous fingering. The patterns are strongly dependent on the fill level and rotation speed of the drum. These observations can be explained by two spatially disjoint mechanisms: (1) a wave-breaking mechanism that promotes the growth of the stripes and (2) a filtering mechanism that limits the growth of stripes.

Infiltration experiments demonstrate an explicit connection between heterogeneity and anomalous diffusion behavior

Transport in systems containing heterogeneity distributed over multiple length scales can exhibit anomalous diffusion behaviors, where the time exponent, determining the spreading length scale of the transported scalar, differs from the expected value of n=12. Here we present experimental measurements of the infiltration of glycerin, under a fixed pressure head, into a Hele-Shaw cell containing a 3-D printed distribution of flow obstacles; a system that is an analog for infiltration into a porous medium. In support of previously presented direct simulation results, we experimentally demonstrate that, when the obstacles are distributed as a fractal carpet with fractal dimension H < 2, the averaged progress of infiltration exhibits a subdiffusive behavior n<12. We further show that observed values of the subdiffusion time exponent appear to be quadratically related to the fractal dimension of the carpet.

Mechanistic modelling of tests of unbound granular materials

Various tests are used to characterise the strength and resilience of granular materials used in the subbase of a pavement system, but there is a limited understanding of how particle properties relate to the bulk material response under various test conditions. Here, we use discrete element method (DEM) simulations with a mechanistically based contact model to explore influences of the material properties of the particle on the results of two such tests: the dynamic cone penetrometer (DCP) and the resilient modulus tests. We find that the measured resilient modulus increases linearly with the particle elastic modulus, whereas the DCP test results are relatively insensitive to particle elastic modulus. The DCP test results are also relatively insensitive to inter-particle friction coefficient but strongly dependent on the particle shape. We discuss strengths and weaknesses of our modelling approach and include suggestions for future improvements.

Unified mechanistic approach for modeling tests of unbound pavement materials

AbstractSeveral tests are used for the characterization of unbound materials for pavement applications. The resilient modulus has been one of the most common tests for design specification of unbound materials. The California bearing ratio (CBR) is another laboratory test that is frequently used. The dynamic cone penetrometer (DCP) test is a more common test for in situ quality assessment/quality control of unbound materials. For better connection between design and quality assurance (QA)/quality control (QC), it would be helpful to have a reliable, mechanistic method for correlating test results. This is particularly true for the use of new materials, for which there is not an extensive body of data to empirically draw such connections. This paper presents a framework for a unified approach for modeling these tests. A discrete-element method (DEM) is used to simulate the CBR test, the DCP test, and the resilient modulus test. An initial evaluation demonstrated that the simulations can account for the eff...

Preliminary investigations on the rheology and boundary stresses associated with granular mixtures

Recent advances in rheological models for monodisperse dense granular materials are exciting. However, they do not account for the effect of local particle size distributions on the rheology mixtures of particles. It is well‐known that particulate mixtures tend to unmix, and their rheological properties are dependent on species concentration. Typically, expressions for the rheology of dense granular flows are explicitly dependent on particle size. However, there is no indication of what may be used for a representative size in a mixture of particles of different sizes. We find, in the absence of gravity, plane Couette cells present an effective geometry for investigating the rheology of binary mixtures of different sized particles. Unlike the behavior of more sparse systems, we find that the dense systems do not segregate much, indicating the usefulness of the geometry for studying the dependence of the mixture rheology on particle sized distribution systematically. In our preliminary studies we find that...

Discrete element modeling and large scale experimental studies of bouldery debris flows

INTRODUCTION Bouldery debris flows –consisting of particles ranging from boulders to fine particles with a variety of potential interstitial fluids – are dramatic features in steep upland regions (e.g., iveRson, 1997) and references within). They play an important role in sculpting the landscape in steep upland regions and have the potential for causing tremendous loss of damage and property (e.g., stoCk & dietRiCH, 2006 and references within). Of additional interest is the wide variety of complex behaviors exhibited by debris flows. They exhibit a rich variety of dynamics including complex solid-like and fluid-like behaviour and dynamic spontaneous examples of pattern formation. Debris flows often start to flow under conditions such as a large rainfall event, but the initiation point is difficult to predict. Once they start to move, they exhibit a variety of behaviours from those similar to a shallow fluid flow, to that of an energetic granular material. Segregation of particles by size mediates the behaviour while the debris flow travels and also in the manner in which it comes to rest. Like a granular material, debris flows stop flowing over a bed of nonzero slope; in other words, they resist macroscopic shear. However, the angle of the slope at which they stop is significantly lower than the measured angle of repose of the debris flow giving rise to a so-called long-runout avalanches (PHilliPs et alii, 2006; linaRes-GueRReRo, 2007). This is likely due in part to a dynamic pore pressure effect giving rise to complex fluid-particle interactions ABSTRACT Bouldery debris flows exhibit a rich variety of dynamics including complex fluid-like behaviour and spontaneous pattern formation. A predictive model for these flows is elusive. Among the complicating factors for these systems, mixtures of particles tend to segregate into dramatic patterns whose details are sensitive to particle property and interstitial fluids, not fully captured by continuum models. Further, the constitutive behaviour of particulate flows are sensitive to the particle size distributions. In this paper, we investigate the use of Discrete Element Model (DEM) techniques for their effectiveness in reproducing these details in debris flow. Because DEM simulations individual particle trajectories throughout the granular flow, this technique is able to capture segregation effects, associated changes in local particle size distribution, and resultant non-uniformity of constitutive relations. We show that a simple computational model study using DEM simulations of a thin granular flow of spheres reproduces flow behaviour and segregation in an experimental model debris flows. Then, we show how this model can be expanded to include variable particle shape and different interstitial fluids. Ultimately, this technique presents a manner in which sophisticated theoretical models may be built which consider the evolving effects of local particle size distribution on debris flow behaviour.

Discrete Element Modeling of Effect of Moisture and Fine Particles in Lightweight Deflectometer Test

The physical properties of the aggregate base of a pavement system have a significant influence on the bulk mechanical properties of that system. Simulations based on the discrete element method provide a powerful method to investigate the mechanics of granular materials, but they are limited, particularly when it comes to representing moisture and finer particles. Established discrete element method simulations were adapted with additional terms to account for moisture and finer particles to model established tests of the aggregate base of a pavement system. The presence of moisture in unsaturated granular material was modeled by using published experimental work with consideration of the form of the standard liquid bridge model, and the finer particle content was modeled through an effective friction coefficient. This combined model was used to simulate the lightweight deflectometer test, an established in situ test for a measure of the modulus of an aggregate base, and the results were compared with estimated target values of aggregate bases for Minnesota roads. When either the model moisture content or model fines content was increased systematically, there was a decrease in the elastic modulus computed from the simulations, similar to trends seen in existing experimental data.