Granular Packing Research Articles

Impact of the timestep in some molecular dynamics simulations on compression of granular systems

We conduct two-dimensional molecular dynamics simulations to study the statistical distribution of the force-moment (defined as stress multiplied by volume) of static granular packings under external isotropic compression. To that end, we generate packings by compressing initially ordered lattices using irregular, randomly generated, walls. Velocity-Verlet algorithm and linear spring-dashpot interactions are employed. With this specific method, the obtained statistical distributions of the force-moment are similar for different initial packings. However they depend on the timestep selection within a range of values. This shows that inadequate molecular dynamic simulations may provide different classes of solutions for the same physical process, and this could cause problems to validate theoretical approaches based on statistical mechanics.

Acoustic probing of elastic behavior and damage in weakly cemented granular media.

We investigate the elastic behavior and damage of weakly cemented granular media under external load with ultrasound. The cementation controlled experiments are performed by freezing the capillary liquid at the bead contact in a dense glass or polymeric [poly(methyl methacrylate)] bead pack wet by tetradecane of volume fraction ϕ = 0.1%-4%. When the pendular rings are solidified, an abrupt increase by a factor of 2 in the compressional wave velocity is observed. We interpret the data in terms of effective medium models in which the contact stiffnesses are derived by either a bonded contact model [P. J. Digby, J. Appl. Mech. 48, 803 (1981)] or a cemented contact model [J. Dvorkin, A. Nur, and H. Yin, Mech. Mater. 18, 351 (1994)]. The former fails to quantitatively account for the results with a soft cement relative to the grain, whereas the latter considering the mechanical properties of the cement does apply. Moreover, we monitor the irreversible behavior of the cemented granular packs under moderate uniaxial loading (1.3 MPa) with the correlation method of ultrasound scattering. The damage of the cemented materials is accompanied by a compressional wave velocity decrease up to 60%, likely due to the fractures induced at the grain-cement interfaces.

Monitoring three-dimensional packings in microgravity

We present results from experiments with granular packings in three dimensions in microgravity as realized on parabolic flights. Two different techniques are employed to monitor the inside of the packings during compaction: (1) X-ray radiography is used to measure in transmission the integrated fluctuations of particle positions. (2) Stress-birefringence in three dimensions is applied to visualize the stresses inside the packing. The particle motions below the transition into an arrested packing are found to produce a well agitated state. At the transition, the particles lose their energy quite rapidly and form a stress network. With both methods, non-arrested particles (rattlers) can be identified. In particular, it is found that rattlers inside the arrested packing can be excited to appreciable dynamics by the rest-accelerations (g-jitter) during a parabolic flight without destroying the packings. At low rates of compaction, a regime of slow granular cooling is identified. The slow cooling extends over several seconds, is described well by a linear law, and terminates in a rapid final collapse of dynamics before complete arrest of the packing.

Effects of Contact Force Model and Size Distribution on Microsized Granular Packing

Granular packing of microsized particles with different size distributions and contact force models is studied using discrete element method (DEM). Three kinds of size distributions, monosized, uniform, and Gaussian, with mean diameter of 50, 60, and 70 μm are studied. Two aspects of microscale particle packing issues are addressed: one is the importance of van der Waals force when the particle size approaching to microscale, the other one is the structure variation caused by different contact force models. The results indicate that compared with contact force, the van der Waals force contributes very insignificantly to the final packing structure. The packing structures obtained using two different force models are similar to each other. The effects of particle size and its distribution on the packing structure are more significant than the force model.

Research a Model of the Dynamic Stiffness in Granular Packs

Based on the experimental study of the gravel layer under the horizontal vibration load, and the variation of particles response behavior according to experimental phenomenon, we study the distribution of the shear along the depth direction, propose the main factors which affect particle moves and dynamic stiffness and their distribution in the granular packs. Then deduce the probability distribution model under horizontal vibration by the stochastic theory, and discuss the prediction method.

Denser fluids of charge-stabilized colloids form denser sediments.

Granular matter, where solid-like elasticity emerges in the absence of crystalline order, has been actively studied over the last few decades, targeting fundamental physical understanding of granular packings and glasses, abundant in everyday life and technology. We employ charge-stabilized sub-micron particles in a solvent, known as colloids, to form granular packings through a well-controlled process, where initially homogeneous and thermodynamically equilibrated colloidal fluids form solid sediments, when subjected to an effective gravity in a centrifuge. We demonstrate that particles' volume fraction φj in these sediments increases linearly with that in the initial fluid φ0, setting an upper limit φRCP≈ 0.64 on both φj and φ0, where φRCP coincides with the well-known, yet highly controversial, 'random close packing' density of spheres, providing new insight into the physics of granular packings. The observed φj(φ0) dependence is similar to the one recently reported for colloidal hard spheres, sterically stabilized by surface-linked polymer combs (S. R. Liber, et al., Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 5769-5773). However, the lower limit on sediment densities drops to φj≈ 0.49 in the present work, suggesting that sedimented charge-stabilized silica are able to overcome mutual electrostatic repulsions, forming gel-like structures stabilized by occasional van der Waals contacts. Finally, by introducing particle size polydispersity, which significantly modifies fluid structure and sedimentation dynamics, we almost completely diminish the φj(φ0) dependence, bringing φj(0) close to its value in frictionless systems.

Effects of grain shape on packing and dilatancy of sheared granular materials.

A granular material exposed to shear shows a variety of unique phenomena: Reynolds dilatancy, positional order and orientational order effects may compete in the shear zone. We study granular packing consisting of macroscopic prolate, oblate and spherical grains and compare their behaviour. X-ray tomography is used to determine the particle positions and orientations in a cylindrical split bottom shear cell. Packing densities and the arrangements of individual particles in the shear zone are evaluated. For anisometric particles, we observe the competition of two opposite effects. On the one hand, the sheared granules are dilated, on the other hand the particles reorient and align with respect to the streamlines. Even though aligned cylinders in principle may achieve higher packing densities, this alignment compensates for the effect of dilatancy only partially. The complex rearrangements lead to a depression of the surface above the well oriented region while neighbouring parts still show the effect of dilation in the form of heaps. For grains with isotropic shapes, the surface remains rather flat. Perfect monodisperse spheres crystallize in the shear zone, whereby positional order partially overcompensates dilatancy effects. However, even slight deviations from the ideal monodisperse sphere shape inhibit crystallization.

Particle shape effects on the stress response of granular packings

We present measurements of the stress response of packings formed from a wide range of particle shapes. Besides spheres these include convex shapes such as the Platonic solids, truncated tetrahedra, and triangular bipyramids, as well as more complex, non-convex geometries such as hexapods with various arm lengths, dolos, and tetrahedral frames. All particles were 3D-printed in hard resin. Well-defined initial packing states were established through preconditioning by cyclic loading under given confinement pressure. Starting from such initial states, stress-strain relationships for axial compression were obtained at four different confining pressures for each particle type. While confining pressure has the largest overall effect on the mechanical response, we find that particle shape controls the details of the stress-strain curves and can be used to tune packing stiffness and yielding. By correlating the experimentally measured values for the effective Young's modulus under compression, yield stress and energy loss during cyclic loading, we identify trends among the various shapes that allow for designing a packing's aggregate behavior.

Evolving design rules for the inverse granular packing problem.

If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a solution to this inverse-packing problem by framing it in the context of artificial evolution. By representing shapes as bonded spheres, we show how shapes may be mutated, simulated, and selected to produce particularly dense or loose packing aggregates, both with and without friction. Moreover, we show how motifs emerge linking these shapes together. The result is a set of design rules that function as an effective solution to the inverse packing problem for given packing procedures and boundary conditions. Finally, we show that these results are verified by experiments on 3D-printed prototypes used to make packings in the real world.

The other entropy

Granular materials are not in thermodynamic equilibrium. Nevertheless, concepts borrowed from equilibrium statistical mechanics are extensively used to characterise granular systems. One often-invoked concept is the so-called granular entropy. In this paper, we consider what it would take to compute granular entropy numerically. Our focus is the analogy (or, more accurately, lack thereof) between statistical mechanical ensembles, as used in Monte Carlo simulations of thermal systems, and preparation protocols used in the generation of granular packings. Attempts to phrase the description of granular media in ‘thermal’ Monte Carlo language reveal some awkward problems. Whilst some of these problems had been reported in the existing literature, the present perspective yields new insights.

Coupled solid and fluid mechanics modeling of formation damage near wellbore

The infiltration of drilling mud below the bit and into the wellbore wall causes pressure gradients that significantly degrade drilling performance, wellbore stability and production. Due to heterogeneity, standard constitutive relationships and models yield poor predictions for flow (e.g. permeability) and rock properties (e.g. elastic moduli) of the invaded (damaged) formations. This severely reduces our ability to, for instance, estimate pressure build-up, optimize the mud cake properties or predict rock mechanical behavior. We propose a numerical model for permeability estimation in damaged formations near wellbore (e.g. sediments invaded by fines or sand crushing remnants). Grains of two length scales are present, but only larger ones are load-bearing. Detailed cemented granular packs were modeled using a discrete element method software, and ensuring mechanical stability. The particle positions and arrangement were available for subsequent pore throat network analysis. The standard network modeling approach for analysis of packing of nearly equal grains (Delaunay tessellation) cannot be used since grains of two different length scales create a high fraction of distorted pores. The main novelty of this work is adapting the network flow model to work with two length scales, and we present both the network creation and flow model in the multi-scale case. The effects of particle size and initial formation porosity on formation damage are studied in detail. Our study confirms that large particles tend to occupy the formation face, while small particles invade deep into the formation. Moreover, particles which are smaller than pore throats (entrances) impair permeability more than those larger than pore throats. Our study also indicates that a higher initial formation porosity leads to more particle invasion and permeability impairment. Thus in order to reduce formation damage, mud particle size distributions should be carefully selected according to given formation properties.

Vibrations of jammed disk packings with Hertzian interactions

Contact breaking and Hertzian interactions between grains can both give rise to nonlinear vibrational response of static granular packings. We perform molecular dynamics simulations at constant energy in 2D of frictionless bidisperse disks that interact via Hertzian spring potentials as a function of energy and measure directly the vibrational response from the Fourier transform of the velocity autocorrelation function. We compare the measured vibrational response of static packings near jamming onset to that obtained from the eigenvalues of the dynamical matrix to determine the temperature above which the harmonic approximation breaks down. We compare packings that interact via single-sided (purely repulsive) and double-sided Hertzian spring interactions to disentangle the effects of the shape of the potential from contact breaking. Our studies show that while Hertzian interactions lead to weak nonlinearities in the vibrational behavior (e.g. the generation of harmonics of the eigenfrequencies of the dynamical matrix), the vibrational response of static packings with Hertzian contact interactions is dominated near jamming by contact breaking as found for systems with repulsive linear spring interactions.

Current challenges for pre-earthquake electromagnetic emissions: shedding light from micro-scale plastic flow, granular packings, phase transitions and self-affinity notion of fracture process

Abstract. Are there credible electromagnetic (EM) potential earthquake (EQ) precursors? This a question debated in the scientific community and there may be legitimate reasons for the critical views. The negative view concerning the existence of EM potential precursors is enhanced by features that accompany their observation which are considered as paradox ones, namely, these signals: (i) are not observed at the time of EQs occurrence and during the aftershock period, (ii) are not accompanied by large precursory strain changes, (iii) are not accompanied by simultaneous geodetic or seismological precursors and (iv) their traceability is considered problematic. In this work, the detected candidate EM potential precursors are studied through a shift in thinking towards the basic science findings relative to granular packings, micron-scale plastic flow, interface depinning, fracture size effects, concepts drawn from phase transitions, self-affine notion of fracture and faulting process, universal features of fracture surfaces, recent high quality laboratory studies, theoretical models and numerical simulations. We try to contribute to the establishment of strict criteria for the definition of an emerged EM anomaly as a possibly EQ-related one, and to the explanation of potential precursory EM features which have been considered as paradoxes. A three-stage model for EQ generation by means of pre-EQ fracture-induced EM emissions is proposed. The claim that the observed EM potential precursors may permit a real-time and step-by-step monitoring of the EQ generation is tested.

Influence of spontaneous percolation on apparent mass at the bottom of a Janssen granular column

The effect of spontaneous percolation on apparent mass at the bottom of granular assemblies has been investigated experimentally. Bi-layered arrangements of two types of granules which differ in size are poured in a vertical silo. In this configuration, the smaller grains are layered at the top of larger grains in order to realize percolation. Contrary to the description that apparent mass decreases for denser granular packing [L. Vanel, E. Clement, Pressure screening and fluctuations at the bottom of a granular column, Eur. Phys. J. B 11 (1999) 525–533], we find that apparent mass increases due to the increase in packing density by spontaneous percolation. This behavior may be the consequence of the development of a stronger force network in bigger particles after percolation is achieved. Furthermore, due to inhomogeneous force chains in grains, we find that the value of the product of the friction coefficient by the Janssen coefficient decreases with the increasing of saturation mass.

Microslips as precursors of large slip events in the stick‐slip dynamics of sheared granular layers: A discrete element model analysis

We investigate the stick‐slip behavior of a granular system confined and sheared by deformable solid blocks using three‐dimensional discrete element method simulations. Our modeling results show that large slip events are preceded by a sequence of small slip events—microslips—whose occurrence accelerates exponentially before the large slip event onset. Microslips exhibit energy release several orders of magnitude smaller than the large slip events. The microslip event rate is proposed as a measure of slip activity in the granular gouge layer. A statistical analysis shows that microslip event rate correlates well with large slip event onset and that variations in it can be used to predict large slip events. The emergence of microslips and their duration are found to be controlled by the value of the slipping contact ratio and are therefore related to the jamming/unjamming transition of frictional granular packings.

Influence of granular packing on porosity and tortuosity

In a granular porous medium the packing configuration and the shape of the grains influence how fluid flows through it. This is directly related to the porosity and tortuosity of the pore space. In this paper we present an analytical function relating the porosity φ and the tortuosity τ of a granular pore medium by means of a packing parameter B. A general expression to estimate B for different representative elementary volumes and grain shapes is presented; in particular, for polyhedral packings. Exploring the packing parameter properties, we discuss the nonuniqueness of the packing-shape combination in relation to B and the porosity behavior for the special cases 0<B<1, B=1, and B>1.

Two-state model to describe the rheological behavior of vibrated granular matter

In this paper, we present a model aimed at predicting the rheological response of a 3D dry granular system to nonstationary mechanical solicitations, subjected or not to vibrations. This model is based on a phenomenological two-state approach related to the inherent bimodal behavior of chain forces in granular packing. It is set up from a kinetic equation describing the dynamics of the contact network. To allow experimental assessment, the kinetic equation is transformed into a differential constitutive equation, relating stress to strain, from which rheological properties can be derived. Its integration allows predicting and describing several rheological behaviors, in stationary and nonstationary conditions, including viscous (Newtonian) and frictional (Coulombian) regimes, as well as elastic linear (Hookean and Maxwellian) and nonlinear behaviors. Despite its simplicity, since it involves only three independent parameters, the model is in very close agreement with experiments. Moreover, within experimental errors, the values of these parameters are independent of the type of test used to determine them, evidence of the self-consistency of the model.

Lift and drag in intruders moving through hydrostatic granular media at high speeds

Recently, experiments showed that forces on intruders dragged horizontally through dense, hydrostatic granular packings mainly depend on the local surface orientation and can be seen as the sum of the forces exerted on small surface elements. In order to understand such forces more deeply, we perform a two-dimensional soft-sphere molecular dynamics simulation, on a similar setup, of an intruder dragged through a 50-50 bi-disperse granular packing, with diameters 0.30 and 0.34 cm. We measure, for both circular and half-circle shapes, the forces parallel (drag) and perpendicular (lift) to the drag direction as functions of the drag speed, with V=10.3-309 cm/s, and intruder depths, with D=3.75-37.5 cm. The drag forces on an intruder monotonically increase with V and D, and are larger for the circle. However, the lift force does not depend monotonically on V and D, and this relationship is affected by the shape of the intruder. The vertical force was negative for the half-circle, but for a small range of V and D, we measure positive lift. We find no sign change for the lift on the circle, which is always positive. The explanation for the nonmonotonic dependence is related to the decrease in contacts on the intruder as V increases. This is qualitatively similar to supersonic flow detachment from an obstacle. The detachment picture is supported by simulation measurements of the velocity field around the intruder and force profiles measured on its surface.

Packings of irregular polyhedral particles: Strength, structure, and effects of angularity

We present a systematic numerical investigation of the shear strength and structure of granular packings composed of irregular polyhedral particles. The angularity of the particles is varied by increasing the number of faces from 8 (octahedronlike shape) to 596. We find that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below 46 faces). At the same time, the packing fraction increases to a peak value but declines for more angular particles. We analyze the connectivity and anisotropy of the microstructure by considering both the contacts and branch vectors joining particle centers. The increase of the shear strength with angularity is shown to be due to a net increase of the fabric and force anisotropies but at higher particle angularity a rapid falloff of the fabric anisotropy is compensated by an increase of force anisotropy, leading thus to the saturation of shear strength.

3D Modelling of Doped and Multi-Materials during Sintering of a Granular Packing

This paper presents a level set framework for the modelling of doping effect during surfacediffusion phenomena in a granular packing. The molecular flux of the doped compound is related tothe chemical potentials of all the diffusion species. The evolution of the grain compact is simulatedin three dimensions, based on the resulting kinetic law relating the surface diffusion velocity to thethermodynamic driving force. An anisotropic adaptive mesh, based on the level set function propertiesis used to refine the mesh in the surroundings of the grain surface. The simulations have been perfomedby using parallel computing strategy.