Granular Packing Research Articles

Influence of particle size on the buffering efficiency of soil cushion layer against rockfall impact

Soil cushion layers are commonly paved in front of protection structures to avoid the direct impact of rockfall and debris flow. This study is devoted to investigating the influence of particles size on the buffering efficiency of a soil cushion layer by experimental and numerical tests. A series of experimental tests are performed by releasing a spherical granite rock block from different heights to impact onto a soil cushion layer consisting of uniformly graded particles. The influence of particle grading on the buffering efficiency is then analyzed in a set of parametric studies. The impact force of rock block and the interacting force at the interface between the soil layer and the protection structure are monitored and evaluated. The discrete element method is utilized to explore the cratering process of rock block, together with the force chains and energy evolutions in the soil cushion layer. The results indicate that soil particles size can influence significantly on the impact force, especially for high-velocity impacts. This effect can be explained by the number and the stability of force chains formed in the granular packing. These findings can provide some insights to designing effective soil cushion layers for protection structures.

Interacting jammed granular systems.

More than 30 years ago Edwards and co-authors proposed a model to describe the statistics of granular packings by an ensemble of equiprobable jammed states. Experimental tests of this model remained scarce so far. We introduce a simple system to analyze statistical properties of jammed granular ensembles to test Edwards theory. Identical spheres packed in a nearly two-dimensional geometrical confinement were studied in experiments and numerical simulations. When tapped, the system evolves toward a ground state, but due to incompatible domain structures it gets trapped. Analytical calculations reproduce relatively well our simulation results, which allows us to test Edwards theory on a coupled system of two subsystems with different properties. We find that the joint system can only be described by the Edwards theory if considered as a single system due to the constraints in the stresses. The results show counterintuitive effects as in the coupled system the change in the order parameter is opposite to what is expected from the change in the compactivity.

Electrocatalytic oxygen reduction performances of surface Ag granular packs electrodeposited from dual-phase Ag35.5Zn64.5 precursor alloys by triangle wave potential cycling

Surface Ag granular packs (SAgPs) have been fabricated from dual-phase Ag35.5Zn64.5 precursor alloy consisting of both e and γ phases by using a facile one-step triangle wave potential cycling in 0.5 mol·L−1 KOH. During the continuous potential cyclic sweeping, the γ phases preferentially dissolve during the anodic scan and dominant reduction reactions of Ag cations lead to redeposition and accumulation of Ag atoms together to form SAgPs during cathodic scan. The e phases stay inactive to form a continuous skeleton in the inner regions. SAgPs with an average particle size of 94–129 nm can be obtained at scan rates of 25, 50 and 100 mV·s−1 for 100 triangle wave potential cycles. SAgPs formed at a scan rate of 50 mV·s−1 exhibit superior oxygen reduction reaction performances with the onset potential of 0.93 V, half-wave potential of 0.72 V and an electron transfer number of 4.0. The above-mentioned SAgPs have superior stabilities as ORR catalysts.

Level statistics and Anderson delocalization in two-dimensional granular materials

Contrary to the theoretical predictions that all waves in two-dimensional disordered materials are localized, Anderson localization is observed only for sufficiently high frequencies in an isotropically jammed two-dimensional disordered granular packing of photoelastic disks. More specifically, we have performed an experiment in analyzing the level statistics of normal mode vibrations. We observe delocalized modes in the low-frequency boson-peak regime and localized modes in the high frequency regime with the crossover frequency just below the Debye frequency. We find that the level-distance distribution obeys Gaussian-Orthogonal-Ensemble (GOE) statistics, i.e. Wigner-Dyson distribution, in the boson-peak regime, whereas those in the high-frequency regime Poisson statistics is observed. The scenario is found to coincide with that of harmonic vibrational excitations in three-dimensional disordered solids.

Shear response of granular packings compressed above jamming onset.

We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power law in the interparticle overlap with exponent α, have found that the ensemble-averaged shear modulus 〈G(P)〉 increases with pressure P as ∼P^{(α-3/2)/(α-1)} at large pressures. 〈G〉 has two key contributions: (1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and (2) discontinuous jumps during compression that arise from changes in the contact network. Using numerical simulations, we show that the form of the shear modulus G^{f} for jammed packings within near-isostatic geometrical families is largely determined by the affine response G^{f}∼G_{a}^{f}, where G_{a}^{f}/G_{a0}=(P/P_{0})^{(α-2)/(α-1)}-P/P_{0},P_{0}∼N^{-2(α-1)} is the characteristic pressure at which G_{a}^{f}=0,G_{a0} is a constant that sets the scale of the shear modulus, and N is the number of particles. For near-isostatic geometrical families that persist to large pressures, deviations from this form are caused by significant nonaffine particle motion. We further show that the ensemble-averaged shear modulus 〈G(P)〉 is not simply a sum of two power laws, but 〈G(P)〉∼(P/P_{c})^{a}, where a≈(α-2)/(α-1) in the P→0 limit and 〈G(P)〉∼(P/P_{c})^{b}, where b≳(α-3/2)/(α-1), above a characteristic pressure that scales as P_{c}∼N^{-2(α-1)}.

Stress correlations in frictional granular media

This paper investigates whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. The pressure and torque fluctuations being respectively normal and hyperuniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyper-uniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen. Whether this is true for frictional matter in general or is it the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.

Morphological characterization and elastic response of a granular material

The granular structures of energetic materials made of hexogene particles embedded in a matrix are characterized using a combination of flotation, light-scattering measurements and micro-computed tomography images. The complementary nature of the three characterization techniques, when employed with this type of material, allows one to derive accurate estimates for the grain size distribution and the particle bulk density distribution. Three types of granular formulations, with the same weight fraction of particles but markedly different grains morphology and shock-sensitivity properties, are addressed. The particles granulometry and intra-granular porosities differ from one material to another. The grains spatial dispersion in the three formulations, characterized by the scale-dependent local density, also varies from one formulation to another. Specifically, we show that samples containing elongated grains display “abnormal” variance scalings for the grains local density, as a result of long-range correlations in the granular packing structure. The use of virtual microstructures to predict the materials mechanical properties is addressed and discussed.

Finite element analyses of rate-dependent thermo-hydro-mechanical behaviors of clayey soils based on thermodynamics

Clayey soils in the vicinity of energy geostructures may be exposed to long-term periodic thermal cycles. The creep and consolidation behaviors of the clayey soils can be both rate-dependent and temperature-dependent, and the underlying physical mechanisms are merely investigated theoretically. In this study, based on the theory of thermodynamics, a fully coupled thermo-hydro-mechanical (THM) finite element (FE) program for saturated soils is developed for this purpose. The FE formulation accounts for the combined effect of rate and temperature through the novel concept of granular temperature. Simulations of THM coupled validation cases and a series of experimental observations on the soft Bangkok clay are carried out. The obtained numerical results exhibit good agreement with analytical solutions and laboratory measurements. It is found that three fundamental physical mechanisms contribute to the irreversible thermal contraction observed for normally consolidated and lightly overconsolidated clays under drained thermal cycles: (1) the thermal creep excited by mass exchange from adsorbed water to free water; (2) the mechanical creep induced by confining stresses; and (3) the increase in granular packing caused by the thermal expansion of soil particles. The thermal contraction generally stabilizes within a few thermal cycles, as a result of the noticeable reduction in the thermal creep rate. It is further demonstrated that the transient heat transfer and the heating rate can greatly influence the deformation of clays subjected to thermal cycles.

Poroelastic shape relaxation of hydrogel particles.

Hydrogels are commonly used in research and energy, manufacturing, agriculture, and biomedical applications. These uses typically require hydrogel mechanics and internal water transport, described by the poroelastic diffusion coefficient, to be characterized. Sophisticated indentation-based approaches are typically used for this purpose, but they require expensive instrumentation and are often limited to planar samples. Here, we present Shape Relaxation (SHARE), an alternative way to assess the poroelastic diffusion coefficient of hydrogel particles that is cost-effective, straightforward, and versatile. This approach relies on first indenting a hydrogel particle via swelling within a granular packing, and then monitoring how the indented shape of the hydrogel relaxes after it is removed from the packing. We validate this approach using experiments in packings with varying grain sizes and confining stresses; these yield measurements of the poroelastic diffusion coefficient of polyacrylamide hydrogels that are in good agreement with those previously obtained using indentation approaches. We therefore anticipate that the SHARE approach will find broad use in a range of applications of hydrogels and other swellable soft materials.

Direct numerical simulation of wave propagation in saturated random granular packings using coupled LBM-DEM

Poroelasticity theory predicts wave velocities in a saturated porous medium through a coupling between the bulk deformation of the solid skeleton and porous fluid flow. The challenge emerges below the characteristic wavelengths at which hydrodynamic interactions between grains and pore fluid become important. We investigate the pressure and volume fraction dependence of compressional- and shear-wave velocities in fluid-saturated, random, isotropic, frictional granular packings. The lattice Boltzmann method (LBM) and discrete element method (DEM) are two-way coupled to capture the particle-pore fluid interactions; an acoustic source is implemented to insert a traveling wave from the fluid reservoir to the saturated medium. We extract wave velocities from the acoustic branches in the wavenumber-frequency space, for a range of confining pressures and volume fractions. For random isotropic granular media the pressure-wave velocity data collapse on a single curve when scaled properly by the volume fraction.

How universal is the vibration-velocity controlled granular convection?

Recently, a number of articles have reported that granular convection induced by continuous vibration is controlled by vibration velocity, in contrast with some previous studies. We have reported such an example for the Brazil nut effect when the vibration is given discontinuously, using a one-layer granular bed in a cell with down-facing side walls. Here, we report the effect of vibration phase and wall friction using the same experimental system, to confirm rising motion of an intruder induced by granular convection is again governed by vibration velocity. We compare two different cases of vibration phase for giving intermittent vibration cycles, and found one, in which granular packing is well established before grains start to lose contacts due to vibration, provides distinctly high reproducibility. We further control the side wall friction using a microfabrication technique, and found that significantly high reproducibility is attained in a cell with vertical side walls when a millimeter texture is introduced on the side walls. Our results indicate that the granular convection is universally controlled by vibration velocity. The present study opens a way to conduct highly reproducible experiments on granular dynamics, which is indispensable for deep physical understanding of granular flow and segregation.

Evolution of shear zones in granular packings under pressure.

Stress transmission in realistic granular media often occurs under external load and in the presence of boundary slip. We investigate shear localization in a split-bottom Couette cell with smooth walls subject to a confining pressure experimentally and by means of numerical simulations. We demonstrate how the characteristics of the shear zone, such as its center position and width, evolve as the confining pressure and wall slip modify the local effective friction coefficient of the material. For increasing applied pressure, the shear zone evolves toward the center of the cylinder and grows wider and the angular velocity reduces compared to the driving rate of the bottom disk. Moreover, the presence of slip promotes the transition from open shear zones at the top surface to closed shear zones inside the bulk. We also systematically vary the ratio of the effective friction near the bottom plate and in the bulk in simulations and observe the resulting impact on the surface flow profile. Besides the boundary conditions and external load, material properties such as grain size are also known to influence the effective friction coefficient. However, our numerical results reveal that the center position and width of the shear zone are insignificantly affected by the choice of the grain size as far as it remains small compared to the radius of the rotating bottom disk.

X-ray tomographies of a water-sensitive granular material (couscous) exposed to high relative humidity: an experimental study

Several granular materials are hydro-sensitive, i.e., contact with water severely affects their morphology and mechanical behaviour. To this broad class belong a series of materials of great relevance for the pharmaceutical and food industry. Former studies have been conducted on the effect that moisture or humidity have on granular flow or on the individual grain mechanical response, but the processes occurring at the microlevel and their influence on the overall granular packing behaviour is yet to be fully understood. This study presents an experimental investigation of the response of a water-sensitive material (couscous) exposed to high relative humidity (97%). 4D (3D plus time) x-ray tomographies were acquired in operando. A data treatment approach based on Dicrete Digital Image Correlation (dDIC) is developed and detailed here. This allows for following each individual grain throughout the 4+ days of the humidification test. This, in turn, allows the study of the interand intra-granular strain, which is particularly pronounced in water sensitive materials. The expansion of the individual grains also severely affects the contact network, whose evolving properties are here analysed and correlated to the macroscopic (sample-scale) deformation.

Particle dynamics in two-dimensional point-loaded granular media composed of circular or pentagonal grains

Granular packings exhibit significant changes in rheological and structural properties when the rotational symmetry of spherical or circular particles is broken. Here, we report on experiments exploring the differences in dynamics of a grain-scale intruder driven through a packing of either disks or pentagons, where the presence of edges and vertices on grains introduces the possibility of rotational constraints at edge-edge contacts. We observe that the intruder’s stick-slip dynamics are comparable between the disk packing near the frictional jamming fraction and the pentagonal packing at significantly lower packing fractions. We connect this stark contrast in packing fraction with the average speed and rotation fields of grains during slip events, finding that rotation of pentagons is limited and the flow of pentagonal grains is largely confined in front of the intruder, whereas disks rotate more on average and circulate around the intruder to fill the open channel behind it. Our results indicate that grain-scale rotation constraints significantly modify collective motion of grains on mesoscopic scales and correspondingly enhance resistance to penetration of a local intruder.

Rheology of soft granular materials: uniaxial compression

Soft granular materials are assemblies of highly deformable grains interacting via surface forces. The large grain deformations of these materials differ them from hard granular systems, in which, their behaviors are essentially governed by grain rearrangements. In this paper, we study the uniaxial compression of soft granular materials using a numerical approach based on the Material Point Method allowing for large grain deformations, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains. Considering the neo-Hookean and elasto-plastic grains, the compaction of 2D soft granular packings is analyzed. We focus essentially on the evolution of the packing vertical stress as a function of the packing fraction and the predictive models are proposed.

Optimal packing in 2D and 3D granular systems: Density, connectivity, and force distributions

In this work, we explore the influence of the grain size distribution (GSD) on density, connectivity and internal forces distributions, for both 2D and 3D granular packings built mechanically. For power law GSDs, we show that there is an exponent for which density and connectivity are optimized, and this exponent is close to those that characterize other well known GSDs such as the Fuller and Thompson distribution and the Appollonian packing. In addition, we studied the distributions of normal forces, finding that these can be well described by a power-law tail, specially for the GSDs with large size span. These results highlight the role of the GSD on internal structure and suggest important consequences on macroscopic properties.

Structural characteristics of ordered clusters in packs of ellipses

Structural characteristics of two-dimensional elliptic granular packs with various aspect ratios and intergranular friction coefficients were studied using the Discrete Element Method (DEM). Isotropic compaction from random unjammed state leads to a jammed state with polycrystals of orientationally ordered clusters (OOC). The OOCs were identified using a cluster labelling algorithm, based on the relative angle Δθ between the major axes of two contacting particles. The threshold value of Δθ was optimised to give the strongest correlation between OOCs and the force chain network. We found that the resulting OOC size distribution decays algebraically with an exponent of −2, independently of grain aspect ratio and material properties.

Micromechanics of slow granular flows

It has been contemplated for a long time that dense granular materials flow in a stick-slip manner, and large fluctuations in the stresses are associated with it. However, the particle scale mechanics for this type of macroscopic motion has not been understood so far. We have analyzed the time evolution of contact networks from particle dynamics simulations and found that the rate of change of elastic energy of the packing can distinguish the stick regimes and the slip events. The isostatic criterion (number of contacts for a minimally stable particle) has been used to construct a cascade failure mechanism which reveals that the effect of the random breaking of contacts due to applied shear can be system-spanning for some cases. The size of the cascade failures follows a power law that explains experimentally observed large fluctuations is stresses. We expect that this power law distribution can connect the microstructure of a granular packing to its mechanical response.

Effects of mechanical constraint on thermally induced reverse martensitic transformation in granular shape memory ceramic packings

Zirconia-based ceramics exhibit shape memory and superelastic effects based on the reversible martensitic transformation between tetragonal and monoclinic crystal structures. In the form of granular packings, these shape memory ceramics can be scaled up for bulk applications despite their intrinsic brittleness, while displaying drastically different transformation characteristics than the monolithic counterparts. Here, we present a comparative study to understand the thermally induced reverse martensitic transformation in granular packings and the influence of mechanical constraints. This study employs ZrO2–CeO2 shape memory ceramics of the same composition but with different degrees of mechanical constraints. The explored material forms include loose and jammed granular packings, themselves consisting of polycrystalline or single crystal particles, as well as sintered bulk polycrystals. Except for the latter, no endothermic peak is observed in the heat flow measurement of the reverse transformation process. This unusual behavior is shown to stem from the weak inter-particle mechanical constraint and the transformation heterogeneity among individual particles, rather than stress relaxation or particle rearrangement. To compare, conspicuous endothermic peaks only appear in bursting-type transformations under a strong mechanical constraint. For granular packings, the intra-particle mechanical constraint does not affect the presence of any endothermic peaks in thermal reversion but can influence the austenite start temperature.

Agro Waste Sugarcane Bagasse as a Cementitious Material for Reactive Powder Concrete

In the field of advanced concrete science, the construction industry has risen to great heights. Due to its own characterisation, the manufacturing cost of reactive powder concrete (RPC) is very high. This can be minimised by substituting the components of the RPC with the aid of agro waste. Because of the production of sugar from the sugar cane industry, bagasse ash is abundantly available in India. It is not ideal for the direct replacement of ingredients in concrete because of the presence of carbon dioxide in bagasse ash. The study of bagasse ash’s actions under different temperatures and different exposure times is discussed in this paper. It is inferred from the findings obtained from the energy dispersive study of X-ray (EDAX) that the presence of reactive silica in bagasse ash could be substituted by RPC ingredients due to heat treatment. RPC is composed of exceptionally fine powders (cement, sand, quartz powder and silica smolder) and superplasticiser. The superplasticiser, utilised at its ideal dose, decreases the water to cement proportion (w/c) while enhancing the workability of the concrete. A thick matrix is accomplished by optimising the granular packing of the dry fine powders. This compactness gives RPC ultra-high quality and durability. Reactive powder concretes have compressive qualities extending from 200 to 800 MPa.