Granular Packing Research Articles

Numerical analysis of compression mechanics of highly polydisperse granular mixtures with different PSD-s

The deformation of three-dimensional highly polydisperse packings of frictional spheres with continuous unimodal and discrete uniform particle size distributions (PSDs) under uniaxial compression was investigated, using the discrete element method. The stress transmission and elasticity parameters, i.e., the effective elastic modulus and the Poisson’s ratio of the granular assemblies were examined; these parameters are important in many engineering disciplines. The influence of the shape of the PSD on the porosity and the transmission of pressures in samples was observed; however, the shape of the PSD did not affect the stiffness and the Poisson’s ratio of polydisperse granular packings. The results revealed that, in some cases, knowledge of the grain size distribution is not a critical issue for modeling granular packings composed of non-uniformly sized spheres.

Wet granular matter mechanical spectroscopy under low-frequency shear

Dry granular materials consist of a collection of macroscopic discrete particles interacting solely via contact forces. By changing the external conditions, the granular packing displays rich phenomena ranging from fluid-like properties to jamming glassy behavior and to aging observed when these grains are trapped in a frozen state. Once the grains contact liquid, the force between the liquid and grains has an influence on the mechanical properties of the wet granular materials, and some mechanical behaviors are quite different from those of the dry granular materials. However, the underlying mechanism of the complex dynamics of granular assemblies is still not completely understood. In this paper, mechanical spectroscopy (the shear modular G and the related energy dissipation tan) of NaCl wet granular system is investigated with different liquid content (weight fraction) under the constant temperature 25℃ and air humidity by a modified low-frequency inverted torsion pendulum. The NaCl wet granular system also displays jamming behavior when subjected to an external vibration with increasing intensity, which is quiet similar to dry granular matter. With the increase of water content, all the spectra of tan and modular G show a peak at the water content about 11% (critical water content). At the same time, the applied shear force has little influence on the positions of these peaks. All of these behaviors illustrate that the main interaction forces among granular matters in the system are changed at the moment.

A computational geometry approach to pore network construction for granular packings

Pore network construction provides the ability to characterize and study the pore space of inhomogeneous and geometrically complex granular media in a range of scientific and engineering applications. Various approaches to the construction have been proposed, however subtle implementational details are frequently omitted, open access to source code is limited, and few studies compare multiple algorithms in the context of a specific application. This study presents, in detail, a new pore network construction algorithm, and provides a comprehensive comparison with two other, well-established Delaunay triangulation-based pore network construction methods. Source code is provided to encourage further development. The proposed algorithm avoids the expensive non-linear optimization procedure in existing Delaunay approaches, and is robust in the presence of polydispersity. Algorithms are compared in terms of structural, geometrical and advanced connectivity parameters, focusing on the application of fluid flow characteristics. Sensitivity of the various networks to permeability is assessed through network (Stokes) simulations and finite-element (Navier-Stokes) simulations. Results highlight strong dependencies of pore volume, pore connectivity, throat geometry and fluid conductance on the degree of tetrahedra merging and the specific characteristics of the throats targeted by the merging algorithm. The paper concludes with practical recommendations on the applicability of the three investigated algorithms.

Propagation and dissipation of elasto-plastic stress waves in two dimensional ordered granular media

We investigate elasto-plastic wave propagation in ordered two-dimensional granular media consisting of contacting metallic granules. A Hopkinson bar generates a high-amplitude wave pulse – sufficient to yield the contact points between granules – and is used to load two configurations of brass beads: a square packing and a hexagonal packing. Selected beads that have embedded piezoelectric sensors are used to measure the arrival time and magnitude of the elasto-plastic wave in situ. Postmortem optical microscopy of the bead contact points elucidates the propagation of plasticity by allowing measurement of the residual plastic contact area. Results show that the elasto-plastic wave propagates in similar directions to a purely elastic wave, but with decaying amplitude due to the plastic deformation. It is found, however, that even small amounts of disorder in a nominally perfect 2D packing significantly affects both wave transit time and peak force. To explore the effects of such disorder further, the dynamic behavior of the 2D granular packing is numerically modeled using a molecular dynamics simulation that incorporates an elasto-plastic contact model and allows for a variability of particle size that incorporates bead diameter tolerance. The results qualitatively confirm the experimental findings of the significance of even limited amounts of disorder on wave arrival time and peak amplitude. This result has significant implications on the feasibility of designing 2D ordered granular media for practical applications.

Treatment of hypersaline hazardous landfill leachate using a baffled constructed wetland system: effect of granular packing media and vegetation

ABSTRACT Constructed wetland is an engineered system that attains more attention as a feasible technology for the treatment of municipal landfill leachate. However, its feasibility for treatment of toxic, hazardous, and hypersaline leachate remains unexplored. This study aimed to investigate the feasibility of using a baffled constructed wetland (BCW) system for the treatment of hypersaline hazardous landfill leachate. Furthermore, the effects of granular packing media, toxicity, and hyper salinity conditions on the removal efficiency of COD fractions (CODt, CODs, and CODp), nitrogen, heavy metals, and coarse solids were extensively investigated. Our findings indicated that BCWs were highly effective in removing heavy metals particularly Cu2+, Mn2+, Fe2+, and Zn2+ and exhibited moderate efficiency for other contaminants (e.g. COD fractions, solids, and nitrogen species). Furthermore, use of a sand and gravel mixture for bed materials demonstrated higher performance over sand alone. However, we found that Phragmites australis is not tolerant enough to extreme toxicity and salinity conditions, and this reed could not survive for more than 27 and 33 days in sand BCW and sand/gravel BCW, respectively. Consequently, survivorship of reed and efficiency of treatment using vegetation were limited in the long-term operation with high salinity and toxicity conditions.

3D particle shape modelling and optimization through proper orthogonal decomposition

Based on proper orthogonal decomposition (POD), a new method is presented in order to statistically characterize arbitrary particle shapes using an optimal choice of shape functions identified on a set of 1000 digitized railway ballast particles obtained through 3D Scan. The coefficients of the POD expansion enable a description of ballast grains with varying levels of accuracy. On exploiting the knowledge of their statistical distribution we are able, implementing an appropriate multivariate kernel density estimation method, to generate irregular particles with similar morphological features. The description and generation methods are validated by comparing statistical distributions of basic characteristics: surface area, volume, average radius, elongation, flatness, and aspect ratio. Using suitable geometric descriptors defining local curvatures, we identify which surface points might be regarded as forming faces. This shows that the proposed particle generation method is well suited for irregularly shaped granular materials, as a first geometric definition step, before numerical simulations of their collective mechanical properties are carried out by a Discrete Element code dealing with polyhedral shapes. We illustrate this process with the simple case of the assembling of a granular pack from a loose configuration, by one-dimensional compression, using different levels of accuracy in the representation of grain shape.

Investigation of heat exchange in a blown dense layer of granular materials

Experimental studies of heat exchange between a dense layer of granular material and a stream of heated air have been carried out. As a granular material, claydite and gravel were used in a moving and a stationary layer. Temperature curves were obtained for the air flow and the solid component at the inlet and outlet of the installation. The shape of the curves indicates presence of two distinct zones with different heating rates. It was stated that it is expedient to set the heating period in the heat accumulators with a stationary bed within the first period which is characterized by a high heating rate. When calculating duration of the heating period, it is rational to take the value of the final material temperature 10 ‒ 15 % lower than the temperature of the heating air at the inlet. It was established that the coefficient of intercomponent heat exchange depends on the gas velocity, the velocity of the bed motion, the gas temperature at the input to the installation and the process duration. It was found that the curves of the dependence of the coefficients of intercomponent heat exchange on the process duration are described by a sigma function. Intensity of heat transfer for a moving layer in the investigated region was commensurable or somewhat higher than that for a stationary layer. It was shown that claydite is the preferred material for a granular packing. The time to onset of a stationary mode for a moving claydite layer was reduced by 2.4 times in comparison with gravel layer and by 2.2 times for a stationary layer.

Anisotropic surface-wave characterization of granular media

In unconsolidated granular media, the state of stress has a major effect on the elastic properties and wave velocities. Effective media modeling of granular packs shows that a vertically oriented uniaxial state of stress induces vertical transverse isotropy (VTI), characterized by five independent elastic parameters. The Rayleigh wave velocity is sensitive to four of these five VTI parameters. We have developed an anisotropic Rayleigh wave inversion that solves for four of the five independent VTI elastic parameters using anisotropic Thomson-Haskell matrix equations that can be used to determine the degree of anisotropy and the state of stress in granular media. The proposed method incorporates an initial model search guided by rock-physics models and dispersion curve inversion that uses a gradient-based solver. We carried out the inversion on a synthetic example and a real data set in which we inverted for in situ elastic moduli of unconsolidated sands at very low effective stress. The synthetic data example results showed that we are able to correctly estimate the granular media’s effective elastic moduli. When the inversion was carried out with real data, the results indicate that the sand at very low effective stress is elastically anisotropic and that it is stiffer along the vertical axis than the horizontal axis. Furthermore, our results are in agreement with past studies related to granular media.

DEM modeling on stress profile and behavior in granular matter

This paper presents a systematic numerical investigation of static stress profile within a confined granular packing using discrete element method. The vertical and horizontal stress profiles are carefully identified within the packing structure, and the effects of container diameter and friction coefficient on the stress distributions are systematically investigated and analyzed. The results show a quantitative agreement between the vertical stress profile gauged at the bottom and the stress profile calculated within the packing structure. I.e. beyond a hydrostatic region, the static vertical stresses saturate exponentially with the packing depth. A positive correlation between the saturation stress and the container size and a negative correlation with the friction coefficient can be observed. Besides, it is also found that the well-known Janssen coefficient (or Janssen constant) is not a constant value; it decreases asymptotically to a constant with the packing depth, which implies a non-constant friction effects existed between the granular assemblies and the boundaries. And the analysis of contact forces within the packing structure also indicates a stabilized condition beyond the hydrostatic region. It is believed that these findings could develop a comprehensive insight on the stress distribution of granular matter.

Stress Response of Granular Systems

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

The Quantified Characterization Method of the Micro-Macro Contacts of Three-Dimensional Granular Materials on the Basis of Graph Theory.

We have attempted a multiscale and quantified characterization method of the contact in three-dimensional granular material made of spherical particles, particularly in cemented granular material. Particle contact is defined as a type of surface contact with voids in its surroundings, rather than a point contact. Macro contact is a particle contact set satisfying the restrictive condition of a two-dimensional manifold with a boundary. On the basis of graph theory, two dual geometrical systems are abstracted from the granular pack. The face and the face set, which satisfies the two-dimensional manifold with a boundary in the solid cell system, are extracted to characterize the particle contact and the macro contact, respectively. This characterization method is utilized to improve the post-processing in DEM (Discrete Element Method) from a micro perspective to describe the macro effect of the cemented granular material made of spherical particles. Since the crack has the same shape as its corresponding contact, this method is adopted to characterize the crack and realize its visualization. The integral failure route of the sample can be determined by a graph theory algorithm. The contact force is assigned to the weight value of the face characterizing the particle contact. Since the force vectors can be added, the macro contact force can be solved by adding the weight of its corresponding faces.

Yielding of complex liquid foams

Foamy complex matter is increasingly encountered in various application fields. Whereas final functional properties of hardened foams have been widely investigated, rheology of complex foamy materials has received less attention. Here, we consider two different types of complex matter to be mixed with aqueous foam and we investigate the resulting yield stress, which is known to control both static and flow properties of foams: (1) A concentrated emulsion possessing intrinsic yield stress properties and (2) granular suspensions which are known to exhibit particle size effects when incorporated into foam. Yield stress of emulsion foams is found to be governed by both the Bingham-capillary number (i.e., the emulsion yield stress scaled by the bubble capillary pressure) and the volume fraction of interstitial emulsion. Foams made with small solid particles reveal granular packings confined between foam bubbles and the resulting yield stress is shown also to be governed by the Bingham-capillary number, here based on Mohr-Coulomb criterion applied to the interstitial granular material. Yield stress of foams made with large particles is well described by the theory developed from micromechanics of particle-loaded yield stress materials, suggesting that for such size ratios, foam can be considered as a continuous matrix. Within the range of intermediate size ratio values, the normalized foam yield stress undergoes an exponential decay that seems to be related to the number of bubbles separating neighboring particles. Finally, reported results are used to estimate the thicknesses of a foamed material, such as isolating foamed mortars, that can be deposited on vertical substrates.

Geometrical properties of rigid frictionless granular packings as a function of particle size and shape.

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedra) achieve higher solid fraction values than amorphous packings of spherical or rounded particles, thus fulfilling the analog of Ulam's conjecture stated by Jiao and co-workers for random packings [Y. Jiao and S. Torquato, Phys. Rev. E 84, 041309 (2011)PLEEE81539-375510.1103/PhysRevE.84.041309]. This seeming discrepancy between experimental and numerical results is believed to result from difficulties in overcoming inter particle friction through experimental densification processes. Moreover, solid fraction is shown to increase further with bidispersity and peak when the volume proportion of small particles reaches 30%. Contrarily, substituting up to 50% of flat pinacoids for isometric ones yields solid fraction decrease, especially when flat particles are also elongated. Nevertheless, particle shape seems to play a minor role in packing solid fraction compared to polydispersity. Additional investigations focused on the packing microstructure confirm that pinacoid packings fulfill the isostatic conjecture and that they are free of order except beyond 30% to 50% of flat or flat-elongated polyhedra in the packing. This order increase progressively takes the form of a nematic phase caused by the reorientation of flat or flat-elongated particles to minimize the packing potential energy. Simultaneously, this reorientation seems to increase the solid fraction value slightly above the maximum achieved by monodisperse isometric pinacoids, as well as the coordination number. Finally, partial substitution of elongated pinacoids for isometric ones has limited effect on packing solid fraction or order.

Contact angle entropy and macroscopic friction in noncohesive two-dimensional granular packings.

We study the relationship between the granular contact angle distribution and local particle friction on the macroscopic friction and bulk modulus in noncohesive disk packings. Molecular dynamics in two dimensions are used to simulate uniaxial loading-unloading cycles imposed on the granular packings. While macroscopic Mohr friction depends on the granular pack geometric details, it reaches a stationary limit after a finite number of loading-unloading cycles that render well-defined values for bulk modulus, grain coordination, porosity, and friction. For random packings and for all polydispersities analyzed, we found that as interparticle friction increases, the bulk modulus for the limit cycle decreases linearly, while the mean coordination number is reduced and the porosity increased, also as approximately linear functions. On the other hand, the macroscopic Mohr friction increases in a monotonous trend with interparticle friction. The latter result is compared to a theoretical model that assumes the existence of sliding planes corresponding to definite Mohr-friction values. The simulation results for macroscopic friction are well described by the theoretical model that incorporates the local neighbor angle distribution that can be quantified through the contact angle entropy. As local friction is increased, the limit entropy of the neighbor angle distribution is reduced, thus introducing the geometric component to granular friction. Surprisingly, once the limit cycle is reached, the Mohr friction seems to be insensitive to polydispersity as has been recently reported.

Ultrasound wave propagation in glass-bead packing under isotropic compression and uniaxial shear**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274354 and11474326) and the Strategic Priority Research Program-SJ-10 of the Chinese Academy of Sciences (Grant No. XDA04020200).

The axial-stress dependence of sound wave velocity in granular packing is experimentally investigated with tri-axial and uni-axial devices. Preparing samples by repetitive loadings and unloadings in a range of 20 kPa–1000 kPa, we find that the axial-stress dependence of sound wave velocity approaches the Hertz scaling with an exponent of 1/6 for large axial stresses (). Weak deviation from the Hertz scaling is seen at low stresses. Repetitive axial loadings slightly reduce this deviation, and sound velocities increase nonlinearly approaching some saturated values. Velocities for uni-axial case are found slightly to be bigger than those for tri-axial isotropic compression case. These effects are discussed in the frameworks of granular solid hydrodynamics (GSH) and effective medium theory (EMT), which indicate that they cannot be explained with density nor Janssen ratio only. Dissipation occurring during wave propagation may be a non-negligible factor.

X-ray tomography study on the structure of the granular random loose packing**Project supported by the Thirteenth Shanghai Jiao Tong University Students Innovation Practice Plan, China (Grant No. IPP13086), 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).

Random loose packing is the minimum-density granular packing which can maintain mechanical stability. In this study, x-ray tomography is used to investigate the internal structure of an isotropically prepared random loose packing through a special apparatus to minimize the effect of gravity. It is found that the minimum packing density is around 0.587. The microscopic structural analysis of the packing is also carried out.

Origin of Noncubic Scaling Law in Disordered Granular Packing.

Recent diffraction experiments on metallic glasses have unveiled an unexpected noncubic scaling law between density and average interatomic distance, which led to the speculation of the presence of fractal glass order. Using x-ray tomography we identify here a similar noncubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within the first nearest neighbor shell, and, therefore, is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with a contact number around 6, and we argue that the exponent should not be universal.

The sands of time run faster near the end

Grains exiting an underwater silo exhibit an unexpected surge in discharge rate as they empty. This contrasts with the constant flow rate of dry granular hoppers and the decreasing flow rate of pure liquids. Here we find that this surge depends on hopper diameter and happens also in air. The surge can be turned off by fixing the rate of fluid flow through the granular packing. With no flow control, dye injected on top of the packing gets drawn into the grains. We conclude that the surge is caused by a self-generated pumping of fluid through the packing. The effect is modelled via a driving pressure set by the exit speed of the grains. This highlights a surprising and unrecognized role that interstitial fluid plays in setting the discharge rate, and perhaps in controlling clog formation, for granular hoppers whether in air or under water.

The electrical conductance growth of a metallic granular packing

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ ∞ − Δσ E α [ − (t/τ) α ], where E α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.

Discrete element method to simulate the elastic behavior of 3D heterogeneous continuous media

The paper aims to investigate the suitability of a discrete element method to simulate the elastic behavior of 3D heterogeneous continuous media. In the present work, the cohesion is modeled using beam elements introduced between each pair of particles in contact within the granular packing describing the investigated domain. Such an approach is an interesting alternative to classical continuous methods which enables to take into account more naturally discontinuities and damaging effects under various solicitations. Besides, the development of coupling strategies and efficient codes open new prospects due to ongoing reduction of calculation cost which was again recently the major drawback of discrete approaches. In the present work, we focus our studies on four points. We first take benefit of the new MULTICOR3D code developed in our laboratory to better define the representative volume element in terms of number of particles in the context of a homogeneous domain. Then, we investigate the definition of the stress tensor in the framework of simple heterogeneous configurations, namely a single cylindrical problem and a spherical inclusion one. The third objective is to highlight the suitability of the discrete element method to predict effective elastic coefficients for the same study cases and a large range of contrast of properties. Finally, we apply the cohesive discrete element approach to the case of an interpenetrating phase composite. In this last case, the influence of interfacial debonding effects are also considered and comparisons are done with experimental measures. Whatever the configuration of the heterogeneous medium, results in terms of stress fields and elastic coefficients are always in quite good agreement with the predictions given by other numerical approaches such as the finite element method and the fast Fourier based technique.