Granular Packing Research Articles

Numerical insight into the micromechanics of jet erosion of a cohesive granular material

Here we investigate the physical mechanisms behind the surface erosion of a cohesive granular soil induced by an impinging jet by means of numerical simulations coupling fluid and grains at the microscale. The 2D numerical model combines the Discrete Element and Lattice Boltzmann methods (DEM-LBM) and accounts for the granular cohesion with a contact model featuring a paraboloidal yield surface. Here we review first the hydrodynamical conditions imposed by the fluid jet on a solid granular packing, turning then the attention to the impact of cohesion on the erosion kinetics. Finally, the use of an additional subcritical debonding damage model based on the work of Silvani and co-workers provides a novel insight into the internal solicitation of the cohesive granular sample by the impinging jet.

Effective friction of granular flows made of non-spherical particles

Understanding the rheology of dense granular matter is a long standing problem and is important both from the fundamental and the applied point of view. As the basic building blocks of granular materials are macroscopic particles, the nature of both the response to deformations and the dissipation is very different from that of molecular materials. In the absence of large gradients, the best approach formulates the constitutive equation as an effective friction: for sheared granular matter the ratio of the off-diagonal and the diagonal elements of the stress tensor depends only on dynamical parameters, in particular the inertial number. In this work we employ numerical simulations to extend this formalism to granular packings made of frictionless elongated particles. We measured how the shape of the particles affects the effective friction, volume fraction and first normal stress difference, and compared it to the spherical particle case. We had to introduce polydispersity in particle size in order to keep the systems of the more elongated particles disordered.

Janssen ratio in granular solid measured by photoelastic method

In this work Janssen ratio is measured in a dense granular pack. The pressure on the side walls as a function of the depth of the pack with top load under gravity is measured by photoelastic method. The samples are prepared by point source method with and without tapping. A non-monotonic distribution of the side pressure along the depth is found. Numerical simulation is performed and shows qualitative consistency with the experimental finding. The apparent weight of the sample is measured for different filling heights and for different top loads. Comparing with the normal stresses on the silo wall for different heights, we obtain the Janssen ratio J =xx/zz as a function of height. We find that although uJ = 0.11 is a constant as is expected, the Janssen Ratio is height dependent. It becomes height independent only when the top load is large enough.

Influence of polydispersity on the microstructure of frictionless disc packings under simple shear

By means of 2D Contact Dynamics simulations, we explored the effects of the shape and size span of the grain size distribution (GSD) on the microstructure of a sheared granular packing, in terms of its packing fraction and the connectivity of its contact network. We focused on GSDs that can be represented by a power law, which are widely used in several engineering and industrial contexts. The interest in power law GSDs originates in the works of Fuller and Thompson in 1907 and 1919, in which it was found that a maximum density is obtained for a power law GSD with an exponent of 0.5. This disagrees with recent DEM results where the densest packing is obtained for linear cumulative volume distributions. In order to explore this discrepancy, we performed systematic simulations in which we varied both the size span (the ratio between the largest and the smallest diameter) and the exponent (shape) of the distribution. We find that the exponent equal to 0.5 produces the highest density for all size spans. Furthermore, the proportion of rattlers and coordination were also analyzed, showing that the system’s connectivity is strongly affected by both the size span and the shape of the distribution.

Slow creep in soft granular packings.

Transient creep mechanisms in soft granular packings are studied numerically using a constant pressure and constant stress simulation method. Rapid compression followed by slow dilation is predicted on the basis of a logarithmic creep phenomenon. Characteristic scales of creep strain and time exhibit a power-law dependence on jamming pressure, and they diverge at the jamming point. Microscopic analysis indicates the existence of a correlation between rheology and nonaffine fluctuations. Localized regions of large strain appear during creep and grow in magnitude and size at short times. At long times, the spatial structure of highly correlated local deformation becomes time-invariant. Finally, a microscale connection between local rheology and local fluctuations is demonstrated in the form of a linear scaling between granular fluidity and nonaffine velocity.

A local view on the role of friction and shape

Leibniz said "Naturam cognosci per analogiam": nature is understood by making analogies. This statement describes a seminal epistemological principle. But one has to be aware of its limitations: quantum mechanics for example at some point had to push Bohr's model of the atom aside to make progress. This article claims that the physics of granular packings has to move beyond the analogy of frictionless spheres, towards local models of contact formation.

Analysis of dense packing of highly deformed grains

This paper concerns modeling of soft granular materials in which the grains are highly deformable. In order to simulate these materials, an approach based on an implicit formulation of the Material Point Method in the context of the finite strain theory, allowing for large deformations of grains, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains, is proposed. In this context, the Mooney-Rivlin constitutive relationship is applied with two different set of elastic parameters. Considering these two material behaviors, a uniaxial compression of 2D soft granular packings is analyzed. The stress-strain relation and the evolution of the packing fraction as well as of the connectivity of the grains are discussed.

Jamming by compressing a system of granular crosses

A disordered stress-free granular packing can be jammed, transformed into a mechanically rigid structure, by increasing the density of particles or by applying shear deformation. The jamming behavior of systems made of 2D circular discs has been investigated in detail, but very little is known about jamming for non-spherical particles, and particularly, non-convex particles. Here, we perform an experimental study on jamming by compression of a system of quasi-2D granular crosses made of photo-elastic crosses. We measure the pressure evolution during cyclic compression and decompression. The Jamming packing fraction of these quasi-2D granular crosses is ϕJ ≃ 0.475, which is much smaller than the value ϕJ ≃ 0.84 for-2D granular disks. The packing fraction shifts systematically to higher values under compressive cycling, corresponding to systematic shifts in the stress-strain response curves. Associated with these shifts are rotations of the crosses, with minimal changes in their centers of mass.

Granular packing as model glass formers**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175121, 11675110, and U1432111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110073120073).

Static granular packings are model hard-sphere glass formers. The nature of glass transition has remained a hotly debated issue. We review recent experimental progresses in using granular materials to study glass transitions. We focus on the growth of glass order with five-fold symmetry in granular packings and relate the findings to both geometric frustration and random first-order phase transition theories.

Inverting Dynamic Elastic Moduli of a Granular Pack to Get Shear Modulus of the Grain

Elastic moduli of rocks derived from its powder is a new concept and can be applied in practical geophysics studies. To develop this concept, we make ultrasonic velocity measurement on granular packs of quartz sand. We calculate dynamic elastic moduli from that measurement and invert afterwards to find the shear modulus of quartz. The inversion technique follows Extended Walton Model that relies on the grain’s contact surface condition between infinitely rough and perfectly smooth. We use different coordination numbers from previous studies (for different samples) in the process of forward modelling and inversion. Forward models have good match with the laboratory measurements both in bulk and shear moduli of the granular pack. Our overall inverted results for the shear modulus are stable and close to actual shear modulus of quartz. However, the coordination numbers that has better match in forward modelling a little bit overestimates shear modulus. On the contrary, the coordination numbers that predicts the higher effective moduli of the pack is giving closest result. As the experiment set up and procedure are simple and robust, this technique can be extended and run in very rigorous situation such as at hard rock drilling rig site to get the elastic properties of the penetrated rocks in real time, where the effective elastic moduli of a grain can be represented as a statistical averaging of elastic moduli of hard rock minerals. This information can be helpful for planning and monitoring the ongoing drilling procedure. It can also be a replacement of solid cores that are missing or damaged for elasticity study.

Modeling soft granular materials

Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.

Effective elastic properties and pressure distribution in bidisperse granular packings: DEM simulations and experiment

The effective elastic properties and pressure distribution in granular mixtures depend on both, material and geometric properties of particles. Using the discrete element method, the effect of geometric and statistical factors on the mechanical response of binary packings of steel beads under uniaxial confined compression was studied. The ratio of the diameter of small and large spheres in bidisperse mixtures was chosen to prevent small particles from percolating through bedding. The study addressed lateral-to-vertical pressure ratio and effective elastic modulus of particulate beds. The bimodality of mixtures was found to have a strong effect on the packing density of samples with the ratio between large and small particles larger than 1.3; however, no effect of particle size ratio and contribution of particle size fractions on the distribution of pressure and elasticity of bidisperse packings was observed. Regardless on the composition of mixtures, the lateral-to-vertical pressure ratio followed the same paths with increasing contribution of small particles in mixtures. The effective elastic modulus of granular packings increased with increasing compressive load and was slightly affected by geometric and statistical factors. The experimental data followed the same trend of the DEM predictions; however, only qualitative agreement between numerical and experimental results was obtained. The discrete element method generated packings with smaller density and overpredicted pressure ratios and elastic parameters of mixtures.

The transient dynamics of dilation waves in granular phase transitions during silo discharge

Granular material has the unique ability to transition between solid and liquid-like phases, but quantitative observations of the dynamics involved in this process remain rare. We hypothesize that granular packing of the solid phase has a leading control on this transition. To test this, we visualize the flow transitions that occur during discharge from a grain-filled silo. X-ray fluoroscopy and high-speed video analysis are used to detect and characterize the kinematics of dilation waves that trigger the phase transitions. Wave velocities are shown to vary by an order of magnitude with strong dependence on the packing density of the initially static bed. The speed of dilation waves exceeds any granular flow velocity in the system, and a simple model based upon conservation of mass is presented to describe this phenomenon. Our results have major implications for the quantitative description and prediction of granular system behaviour in natural and industrial applications, particularly with regards to the onset of avalanche motion and the handling of powders and grains.

Liquid Fluidized Beds of Granular Particles

We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate N = O(106) particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after fast and slow changes in flow rate and determine the timescales to reach a stationary state.

Water retention against drying with soft-particle suspensions in porous media.

Polymers suspended in granular packings have a significant impact on water retention, which is important for soil irrigation and the curing of building materials. Whereas the drying rate remains constant during a long period for pure water due to capillary flow providing liquid water to the evaporating surface, we show that it is not the case for a suspension made of soft polymeric particles called microgels: The drying rate decreases immediately and significantly. By measuring the spatial water saturation and concentration of suspended particles with magnetic resonance imaging, we can explain these original trends and model the process. In low-viscosity fluids, the accumulation of particles at the free surface induces a recession of the air-liquid interface. A simple model, assuming particle transport and accumulation below the sample free surface, is able to reproduce our observations without any fitting parameters. The high viscosity of the microgel suspension inhibits flow towards the free surface and a drying front appears. We show that water vapor diffusion over a defined and increasing length sets the drying rate. These results and model allow for better controlling the drying and water retention in granular porous materials.

Simulation of granular packing of frictional cohesive particles with Gaussian size distribution

The granular packing of frictional cohesive particles with Gaussian distribution is investigated based on distinct element method. Different sliding frictional coefficients are considered in the simulation. Due to the inelastic collision between the particles, the agglomeration of the particles occurs and the packing structure is formed finally. The range of the diameter of the particle is between 50 and 100 μm, and the distribution of the particle diameter is Gaussian. The inelastic interaction is caused by the viscoelastic force and the frictional force. The internal structure of the granular matter is quantified by the coordination number, packing density, and the force distribution. It is found that the increase in the sliding frictional coefficient looses the packing structure, and the distribution range of the contact force is larger than that of the van der Waals force.

Gradation and Packing Characteristics Affecting Stability of Granular Materials: Aggregate Imaging-Based Discrete Element Modeling Approach

AbstractUnbound aggregate base and subbase in layered pavement structures provide an essential function of wheel load distribution through proper angular or crushed particle interlocking of coarse aggregate particles in the granular matrix. This paper used a validated model utilizing a particle image-aided discrete element method (DEM) to evaluate aggregate gradation and shape/morphological properties on pavement granular layer packing characteristics and load-carrying performance. The DEM packing simulations for different granular material gradations and particle shape categories were first performed to investigate the influence of the No. 4 (4.75-mm) sieve, separator of sand-sized and gravel-sized particles according to the Unified Soil Classification System (USCS), for typical dense-graded aggregates specified by the Minnesota Department of Transportation (MnDOT). Aggregate particles were modeled in the DEM as three-dimensional (3D) polyhedral discrete elements with both low and high angularity categor...

Microstructure evolution of granular soils in cyclic mobility and post-liquefaction process

Understanding the evolution of microstructure in granular soils can provide significant insights into constitutive modeling of soil liquefaction. In this study, micromechanical perspectives of the liquefaction process are investigated using the Discrete Element simulation. It is observed that during various stages of undrained cyclic loading, the soil exhibits definitive change in the load-bearing structure, indicated by evolution of the coordination number and non-affine displacements. A new particle-void fabric, termed as “centroid distance”, is also proposed to quantify the evolution of particles and voids distribution in the granular packing. The fabric index is found to have strong correlation with cyclic mobility and post-liquefaction deformation of granular soils. Evolution of the fabric index indicates that particles and voids redistribute irreversibly before and after liquefaction. A highly anisotropic particle-void structure and loading-bearing capacity can be formed in the post liquefaction stage.

Failure in granular media from an energy viewpoint

The present paper examines failure in discrete granular media with respect to its mode and nature based on energetic considerations through a comprehensive discrete element modelling computational analysis. The mode of failure refers to whether deformations will localize into an intense shear band or be diffuse. More subtly, a given failure mode can be effective with a burst of kinetic energy, or non-effective with a more controlled release of kinetic energy, depending on the control parameter. Physical quantities based on energy considerations with elementary decompositions of externally applied energy into elastic, plastic and kinetic contributions at the particle level are computed for a number of granular assemblies under a variety of failure scenarios. With the picture of a particle system experiencing macroscopic deformations according to underlying micro- and meso-mechanisms, it is concluded that computed grain-energy components depend on the microstructural detail that emerges as a function of loading program and control parameter. The relationship between elastic unloading outside a shear band and plastic dissipation inside it under both strain and stress control modes determines the genesis of shear banding in terms of plastic work dissipation minimization. Most interestingly, it is found that the energy signature inside the shear band in a dense granular packing is germane to energy characteristics of diffuse failure in a loose assembly, suggesting some similarities in microscopic failure processes between shear banding and diffuse failure.

Reorganization of a granular medium around a localized transformation.

Physical and chemical transformation processes in reactive granular media involve the reorganization of the structure. In this paper, we study experimentally the rearrangements of a two-dimensional (2D) granular packing undergoing a localized transformation. We track the position and evolution of all the disks that constitute the granular packing when either a large intruder shrinks in size or is pulled out of the granular structure. In the two situations the displacements at long time are similar to 2D quasistatic silo flows whereas the short-time dynamic is heterogeneous in both space and time. We observe an avalanchelike behavior with power-law distributed events uncorrelated in time. In addition, the instantaneous evolutions of the local solid fraction exhibit self-similar distributions. The averages and the standard deviations of the solid fraction variations can be rescaled, suggesting a single mechanism of rearrangement.