Granular Packing Research Articles

Experimental and numerical study on the force transmission in granular packings under the hypergravity

Granular materials are ubiquitous in our environment, and their mechanical behavior is determined by particle-scale properties. The contact forces under hypergravity, which are crucial to planetary geology, remain underexplored, while extensive research has focused on behavior under surface pressure. We measured the contact forces between granular particles using a novel matrix film sensor under both hypergravity and surface pressure conditions, which were achieved in centrifugal and servo-hydraulic tests. Additionally, computations using the discrete element method were conducted to investigate the different patterns of force transmission from a microscopic perspective. We found an intriguing invariance in the contact force distribution under increased surface pressure. However, hypergravity enhances the contact forces between unjammed fine particles, causing contact forces converge to the distribution observed under surface pressure. Finally, a power-law fitted correlation was proposed to estimate the difference in contact force distributions between conditions of hypergravity and equivalent surface pressure.

Acoustical dissipation in biobased granular packings

Biobased building materials have many advantages, including local availability and functional performance in terms of mechanical, acoustic and hygrothermal properties. Besides, the biobased solutions coming from plants that uptake CO2 during their growth, are good opportunities to reach carbon-neutral building construction. However, mastering their acoustical performance still raises a number of questions directly linked to their microstructure, which is characterised by a high degree of porosity spread over several scales. The work presented here aims to highlight the effect of the porosity distribution in biobased granular packings on their acoustical performances. Several plant aggregates are considered, such as hemp shiv, sunflower pith or reed as a function of their density and water content. Characterizations are performed in normal incidence and compared to fluid equivalent modellings based on various assumptions, to analyze the effective contribution of the various types of pores at the aggregate level, and between the aggregates.

Stress field on intermediate length scales during triaxial compression

Defining a continuum stress field in a granular medium involves an approximation, as the underlying contact force network between particles is inhomogeneous and random. The continuum approximation introduces some baseline noise or variability in stress, which becomes more significant as the length scale of interest approaches the typical size of the grains. In this study, the authors evaluate how the stress variability resulting from the homogenisation of intergranular forces changes as the homogenisation scale is increased. This is done by obtaining the probability distribution function of stresses from a large number of repeated discrete-element method-based simulations of the triaxial compression of granular samples. The numerical experiments share sample dimensions, generation protocols and imposed stresses, but involve randomly generated sets of granular packings made of different numbers of particles. The results from this study are used to propose and develop a consistent general framework to rigorously describe mesoscale stress fields and hence fill the gap between existing micro- and macromechanical approaches. A backbone curve is obtained expressing the change in stress variability as the mesoscale is traversed. The results deduced from the backbone curve are in good agreement with those of independent numerical and physical experiments on granular soils.

Evident structural anisotropies arising from near-zero particle asphericity in granular spherocylinder packings.

With magnetic resonance imaging experiments, we study packings of granular spherocylinders with merely 2% asphericity. Evident structural anisotropies across all length scales are identified. Most interestingly, the global nematic order decreases with increasing packing fraction, while the local contact anisotropy shows an opposing trend. We attribute this counterintuitive phenomenon to a competition between gravity-driven ordering aided by frictional contacts and a geometric frustration effect at the marginally jammed state. It is also surprising to notice that such slight particle asphericity can trigger non-negligible correlations between contact-level and mesoscale structures, manifested in drastically different nonaffine structural rearrangements upon compaction from that of granular spheres. These observations can help improve statistical mechanical models for the orientational order transformation of nonspherical granular particle packings, which involves complex interplays between particle shape, frictional contacts, and external force field.

Experimental study of particle impact on cohesive granular packing.

We investigate experimentally the impact process of sand particles onto a cohesive granular packing made of similar particles. We use a sand-oil mixture with varying liquid content to tune the cohesive strength of the packing. The outcome of the impact is analyzed in terms of the production of ejected particles from the packing. We quantify this production as a function of the impact velocity of the particles for increasing cohesion strength. We identified three different regimes depending on the cohesion number Co, defined as the ratio of the interparticle cohesive force to the particle weight. For small cohesion (i.e., Co⪅1), the ejection process is not modified by the cohesion. For intermediate cohesion (i.e., 1⪅Co⪅20), the ejection process becomes less efficient: the number of ejected particles per impact for a given impact velocity is decreased but the critical impact velocity to trigger the ejection process remains unchanged. Finally, for strong cohesion (i.e., Co⪆20), we observed a progressive increase of the critical impact velocity. These experimental results confirm spectacularly the outcomes of recent numerical simulations on the collision process of a particle onto a cohesive packing and open avenues to model the aeolian transport of moist sand.

THE EFECT OF DIMENSIONALITY AND CURRENT STRENGHT ON CONDUCTIVITY OF GRANULAR METALS

<p>Metallic materials in granular packings show different electrical properties from their bulk counterparts.<br />In this paper, we investigate the temporal evolution of the electrical conductivity of granular metals. We<br />use metallic beads arranged in different one-, two- and three-dimensional ensembles through which<br />different constant currents are injected. The conductivity behavior in all three types of systems is<br />qualitatively similar. The results show the rise of conductivity which is more pronounced in the earlier<br />stages of the time evolution. We investigate the influence of the dimensionality, number of the beads,<br />and the values of the injected currents on the conductivity behavior.</p>

Impacts of packed bed polydispersity and deformation on fine particle transport

AbstractStatic granular packings play a central role in numerous industrial applications and natural settings. In these situations, fluid or fine particle flow through a bed of static particles is heavily influenced by the narrowest passage connecting the pores of the packing, commonly referred to as pore throats, or constrictions. Existing studies predominantly assume monodisperse rigid particles, but this is an oversimplification of the problem. In this work, we illustrate the connection between pore throat size, polydispersity, and particle deformation in a packed bed of spherical particles. Simple analytical expressions are provided to link these properties of the packing, followed by examples from Discrete Element Method (DEM) simulations of fine particle percolation demonstrating the impact of polydispersity and particle deformation. Our intent is to emphasize the substantial impact of polydispersity and particle deformation on constriction size, underscoring the importance of accounting for these effects in particle transport in granular packings.

Exploring the combined effect of particle shape and friction on cell structures in granular packings via LS-DEM modeling

To comprehensively understand and predict the macroscopic behavior of a granular system, one must consider not only the properties of individual particles but also the local structures. In this study, we prepare mechanically stable granular packings of super disks using the two-dimensional level set discrete element method (LS-DEM). We identify the cells, the irreducible loops enclosed by contacting particles, in the prepared granular packings and then analyze the statistics of these structures. We find the following. (1) The packing fraction or mean coordination number of studied systems exhibits a non-trivial dependency on particle shapes and inter-particle frictions, making it challenging to establish a direct correlation between them. (2) Using the cell-based description as a bridge, we can measure the packing behavior without considering the influence of particle shape and inter-particle friction. Specifically, the mean coordination number can be explicitly represented as a function of the mean cell order according to Euler’s topological relation. Upon the assumption that all cells are regular polygons, we can also approximately estimate the rattlers-free packing fraction via the mean cell order. (3) We have observed a nearly linear relationship between the mean cell order and rattler fraction. This enables us to determine the packing fraction as well.

An explicit granular-mechanics approach to marine sediment acoustics.

Here, we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms, which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

Statistical physics of frictional grains: Some simple applications of the Edwards statistics

Granular matter like sand is composed of a large number of interacting grains and is, thus, expected to be amenable to a statistical physics treatment. Yet, the frictional properties of grains make the statistical physics of granular matter significantly different from the equilibrium statistical physics of atomic or molecular systems. We use three simple models to illustrate some of the key concepts of the statistical physics introduced by Edwards and co-workers more than 30 years ago to describe shaken granular piles: non-interacting frictional grains attached to a wall by a spring, a chain of frictional grains connected by springs, and a simplified mean-field model of a granular packing. We observe that a chain of frictional grains connected by springs exhibits a critical point at an infinite effective temperature (i.e., infinitely strong shaking) at odds with the zero-temperature critical point generically found in one-dimensional systems at thermal equilibrium in the presence of local interactions.

Structural properties of different sphere packings with arbitrary porosities for planetary-science applications

Granular solids in planetary science are found in the regolith that covers planetary surfaces as well as in the bulk of rubble-pile asteroids, comets and planetesimals. To help understand the physics of these planetary bodies, we aim at deriving the structural properties of granular packings over a large range of porosities. Relevant to fluid flow and gas diffusion are the void spaces inside the granular packings so that we analyze the mean free path of point-like particles, their diffusion constant and their total traveled path lengths. For mechanical and heat-transport properties, the coordination number and the absolute chain length of the inter-connected particles are important. Generally, we also derive the homogeneity and isotropy of the granular solids. We compare granular packings generated by four algorithms for porosities in the range between 85 and 42%, which are the upper and lower limits for natural packings of equal-sized spheres. All produced sphere packings arrive at very similar quantities for the mean free path, the free path probability distribution function, the diffusion constant and the total traveled path length for the entire range of porosities. Hence, transport processes governed by the void-space properties are independent of the specific generation algorithm for the granular packing. In contrast, heat conduction or mechanical stresses almost exclusively depend on the existence and properties of particle contacts and particle chains in the network of spheres. In this case, the four algorithms deliver very different results.Graphic abstract

Estimating angoricity and granular equationsof state for monodisperse packings of frictional hard spheres in a wide range of densities.

In this paper, we study the granular equationof state (EOS) for computer-generated three-dimensional mechanically stable packings of frictional monodisperse particles over a wide range of densities (packing fractions), φ=0.56-0.72. As a statistical physics framework, we utilize the statistical ensemble for granular matter, specifically the "angoricity" ensemble, where the compressional component Σ_{p} of the force-moment tensor serves as granular energy and angoricity A_{p} is the corresponding granular "temperature." We demonstrate that the systems under study conform well to this statistical description, and the simple equationof state Σ_{p}=2.8NA_{p} holds very well, where N is the number of particles. We show that granular temperature exhibits a rapid drop around the random-close packing (RCP) limit φ≈0.64-0.65, and, hence, one can say that granular packings "freeze" at the RCP limit. We repeat these calculation for shear angoricity A_{sh} and shear component Σ_{sh} of the force-moment tensor and obtain a similar EOS, Σ_{sh}=0.85NA_{sh}. Additionally, we measure the so-called keramicity, an inverse temperature variable corresponding to the determinant of the force-moment tensor, while pressure angoricity corresponds to its trace. We show that inverse keramicity κ^{-1} and angoricity A_{p} conform to an EOS 1/A_{p}Σ_{p}/N+0.11κ(Σ_{p}/N)^{3}=1.2, whose form is predicted by mean-field theory. Finally, we demonstrate that the alternative statistical ensemble where Voronoi volumes serve as granular energy (and so-called compactivity serves as temperature) does not describe the systems under study well.

Dynamic imaging of force chains in 3D granular media

Granular media constitute the most abundant form of solid matter on Earth and beyond. When external forces are applied to a granular medium, the forces are transmitted through it via chains of contacts among grains-force chains. Understanding the spatial structure and temporal evolution of force chains constitutes a fundamental goal of granular mechanics. Here, we introduce an experimental technique, interference optical projection tomography, to study force chains in three-dimensional (3D) granular packs under triaxial shear loads and illustrate the technique with random assemblies of spheres and icosahedra. We find that, in response to an increasing vertical load, the pack of spheres forms intensifying vertical force chains, while the pack of icosahedra forms more interconnected force-chain networks. This provides microscopic insights into why particles with more angularity are more resistant to shear failure-the interconnected force-chain network is stronger (that is, more resilient to topological collapse) than the isolated force chains in round particles. The longer force chains with less branching in the pack of round particles are more likely to buckle, which leads to the macroscopic failure of the pack. This work paves the way for understanding the grain-scale underpinning of localized failure of 3D granular media, such as shear localization in landslides and stick-slip frictional motion in tectonic and induced earthquakes.

Revealing void anisotropies in vertically-vibrated granular sphere packings with various structural characterizations

We utilize magnetic resonance imaging (MRI) techniques to study granular sphere packings prepared with vertical vibration, and reveal the extremely slight global anisotropies of the void phase with systematic analyses on Delaunay pores and chords. Unexpectedly, the global orientational orders of the eigenvectors of tensors quantifying (i) pore throats, (ii) chords going through individual pores, (iii) shape of Voronoi cells and (iv) contact fabrics have consistent evolution laws when packing fraction changes, but the orientational order of the eigenvectors of a pore volume tensor exhibits a peculiarly different trend. With an orientation-dependent spatial correlation function, we attribute their different behaviors to the fact that different anisotropy variables probe the void phase at different length scales, so that their dependences on packing fraction are different. The segmentation of the void region into pores sensitively captures a unique and intricate structural anisotropy at an intermediate length scale.

Simulation of proppant conductivity test: effect of particle size dispersion

A conductivity test of proppant material consists in confining a sample of the granulate at high pressure and then set a flow through the pack. The proppant particle size is the main variable controlling conductivity, but also particle size dispersion is considered important. Even though several studies consider mixtures of proppants of different meshes, there are not clear evidences as to whether the changes in conductivity with respect to a monosized proppant are caused by the mix itself or by the overall change in mean particle size. Hence, we use numerical simulations to answer the question: Does particle size dispersion significantly affects the proppant conductivity if mean particle size is kept the same? We measure conductivity and permeability by simulating (via a coupled Computational Fluid Dynamics–Discrete Element Method) the flow of water through binary granular packs. We find that size dispersion does not affect conductivity (in the dispersion range explored) if the mean particle size is conserved. However, we observe that in a binary mixture the large particles are subjected to larger stresses than in a monosized system, which makes them prone to crushing.

Vibrational spectrum of Granular packings with random matrices

The vibrational spectrum of granular packings can be used as a signature of the jamming transition, with the density of states at zero frequency becoming nonzero at the transition. It has been proposed previously that the vibrational spectrum of granular packings can be approximately obtained from random matrix theory. Here, we show that the autocorrelation function of the density of states shows good agreement between dynamical numerical simulations of frictionless bead packs near the jamming point and the analytic predictions of the Laguerre orthogonal ensemble of random matrices; there is clear disagreement with the Gaussian orthogonal ensemble, establishing that the Laguerre ensemble correctly reproduces the universal statistical properties of jammed granular matter and excluding the Gaussian orthogonal ensemble. We also present a random lattice model which is a physically motivated variant of the random matrix ensemble. Numerical calculations reveal that this model reproduces the known features of the vibrational density of states of frictionless granular matter, while also retaining the correlation structure seen in the Laguerre random matrix theory.Graphic abstract

The crucial role of granular packing structure in marine sediment acoustics

Motivated by the acoustic properties of marine sediments, we study via discrete-element method simulations the frequency dependence of dispersion and attenuation in model marine sediments. By numerically solving for the motion of each grain in a packing, rather than solving a continuum wave equation, we find that the granular packing structure, which is not explicitly considered in existing sediment-acoustics models, plays a crucial role in determining how attenuation and wave speed vary with frequency. Prior work has typically postulated a wave equation that is motivated by grain- scale forces, including viscous effects from the interstitial fluid, without explicitly considering the disordered packing structure of the grains. However, the packing structure is known to produce complex, nonlinear behavior (e.g., during shear or quasistatic compression), and how it affects dispersion and attenuation is not known. We consider linearized forces between particles (i.e., springs and dashpots), and demonstrate that the disordered packing structure leads to emergent scaling laws that do not agree with PDE-based approaches. Our results demonstrate that the granular packing structure must be explicitly considered when constructing theories for the acoustic properties of marine sediments.

Exploring the role of particle-form polydispersity in the fabric of granular packing: Insights from DEM simulations with ellipsoidal particle assemblies

Granular materials, such as sand, exhibit a wide range of particle sizes and shapes, known as polydispersity. This study aims to investigate the effects of particle-form (first-level approximation of particle shape) polydispersity on a fabric of granular packing using DEM simulations of ellipsoidal particle assemblies. A framework for DEM simulations is proposed to investigate the particle-form polydispersity, and an overall polydispersity index (OPI) is introduced to quantify its magnitude. Various parameters are employed to quantify the fabric, including packing density, coordination number, contact force, and fabric anisotropy. The results highlight that the particle-form polydispersity notably affects the packing density and mean coordination number of the granular packings. Furthermore, a prediction model for the packing density and mean coordination number of polydisperse packings is proposed based on the correlations fitted from the monodisperse packing data.

Understanding slow compression of frictional granular particles by network analysis.

We consider frictional granular packings exposed to quasi-static compression rates, with a focus on systems above the jamming transition. For frictionless packings, earlier work (S. Luding et al., Soft Matter, 2022, 18(9), 1868-1884) has uncovered that the system evolution/response involves smooth evolution phases, interrupted by fast transitions (events). The general finding is that the force networks' static quantities correlate closely with the pressure, while their evolution resembles the kinetic energy for both frictionless and frictional packings. The former represents reversible (elastic) particle deformations with affine and non-affine components, whereas the latter also involves much stronger, irreversible (plastic) rearrangements of the packings. Events are associated with jumps in the overall kinetic energy as well as dramatic changes in the force networks describing the particle micro-structure. The frictional nature of particle interactions affects both their frequency and the relevant time scale magnitude. For intermediate friction, events are often followed by an unexpected slow-down during which the kinetic energy drops below its average value. We find that these slow-downs are associated with a significant decrease in the non-affine dynamics of the particles, and are strongly influenced by friction. Friction modifies the structure of the networks, both through the typical number of contacts of a particle, and by influencing topological features of the resulting networks. Furthermore, friction modifies the dynamics of the networks, with larger values of friction leading to smaller changes of the more stable networks.

A soft departure from jamming: the compaction of deformable granular matter under high pressures.

The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follow the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.