Granular packing: influence of different parameters on its stability

A packing of equal glass beads is placed on a box with a rough bottom. The box is slowly inclined till an avalanche begins at a critical angle. The avalanche dynamics decreases the surface slope until a second critical angle is reached. In previous works [1–3], the stability of the packing was found to be affected by the number of layers, the packing length and the surrounding humidity. In this work we verify the influence of the packing compacity on the angle at which the avalanche starts. Also, the rough bed affects the avalanche mass and the critical angles. Experiments are done to determine the role of these factors on the avalanche dynamics. Received: 30 March 2000     

Simulation of the packing of granular mixtures of non-convex particles and voids characterization

The simulation of granular materials has considerably developed in the last decades essentially with simple geometry particles. The purpose of this paper is to study granular systems of non-convex particles which are present in many industrial processes. Two shapes of large and two shapes of small non-convex particles resulting from the cutting of a hollow cylinder are modelled, and binary mixtures containing varying proportions of small and large particles are generated with a Monte Carlo simulation. Two different states of the granular systems are studied: suspensions and packings obtained after sedimentation. No contact force model is used and only steric repulsion is taken into account. The density, the pore size distribution and the tortuosity of the granular systems are studied. The results are compared to those obtained with granular systems of convex particles.     

Anisotropy in granular materials at different scales

This paper is dedicated to the analysis of the local phenomena which give rise to anisotropy in granular materials. This anisotropy can be observed for small strains (“elastic strains”) as well as large irreversible strains (“plastic strains”). Elastic anisotropy appears to be due to the distribution of contacts, the shape of particles and the non-linear local contact law. Anisotropic non-reversible behaviour seems to be related to two kinds of anisotropy, the usual geometric anisotropy and a static anisotropy governing the distribution of contact forces.     

FE-investigations of a deterministic and statistical size effect in granular bodies within a micro-polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during shearing of an infinite layer under plane strain conditions and free dilatancy. For a simulation of the mechanical behavior of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. To describe a deterministic size effect, the calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2,000 mm. To investigate a statistical size effect, the distribution of the initial void ratio in infinite granular layers was assumed to be spatially correlated. As only primary stochastic calculations were performed, single examples of different random fields of the initial void ratio were generated. For this purpose a conditional rejection method was used.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

Simulation of Granular Compacts in two dimensions

Simulations of granular packings in 2-D by throwing disks in a rectangular die are performed. Different size distributions as bimodal, uniform and gaussian are used. Once the array of particles is done, a relaxation process is carried on using a large-amplitude, low-frequency vertical shaking. This relaxation is performed a number N of times. Then, we measure the density of the package, contact distribution, coordination number distribution, entropy and also the disks size distribution vs. height. The dependence of all these magnitudes on the number N of “shakings” used to relax the packing and on the size distribution parameters are explored and discussed. Received: 30 March 2000     

Effect of external factors on segregation of different granular mixtures

Segregation is a common problem faced by different pharmaceutical, chemical, and food processing industries due to non-uniformity in the end-products. Our aim is to minimize the segregation of binary granular mixture by changing the external chute-related factors rather than internal factors like material properties which is often not possible in industries. We investigate the effect of inclination angle, friction, fill volume and channel geometry in a steady, gravity driven flow of granular mixture in an inclined plane. We perform the numerical simulation using an open-source Discrete Element Method code - LIGGGHTS. We observe that the segregation of dry granular particles in stream-wise direction of the chute is minimum at low stream-wise velocity i.e. by keeping the chute at a low inclination and adding the wall roughness. The segregation in cross-stream and vertical direction is at a minimum when the chute is filled to at least 40% of its height. We also investigated the optimal conditions for minimum segregation in different granular mixtures and found that a mixture with size or density ratio up to 4 can have minimum segregation, if we fill the chute to 75% height. For a greater size or density ratio, it is difficult to minimize the segregation. The optimal segregation conditions for mixtures with different elastic modulus ratio were generally constant.     

Living quicksand

The image of quicksand merciless swallowing a victim has inspired the fantasy of kids and helped writers and moviemakers to get rid of evil figures. Is this really possible? This is still disputed since till today it is not even clear what quicksand exactly is. In soil mechanics, the “quick-condition” is usually described as a liquefaction due to high water pressure essentially possible with any soil. However, previous studies have detected anomalous rheological properties from natural quicksand. Pushed by these contradicting points of view we set off to Lençois Maranhenses in North-East Brazil, where quicksands are common, to investigate rheology and strength in situ. We found that along very quiet drying lakes cyanobacteria cement an impermeable crust above a suspension of grains. Beyond a critical pressure, the crust fails releasing water from the collapsing colloidal structure and radically changing the depth dependence of the shear strength from a constant to a linear function. The sedimenting solid fraction and the rapid increase of shear strength can indeed trap an intruder endangering his life if the basin is sufficiently deep. As opposed to some previous studies, we find that this quicksand condition cannot be restored once it has collapsed. Finally, we also show some preliminary results from a contact dynamics model specially designed to mimic the living quicksand behavior.     

DEM simulation of the packing structure and wall load in a 2-dimensional silo

The filling and discharge of a two-dimensional wedged-bottom silo holding circular objects was modelled using DEM technique to examine the influence of method of silo filling on distribution of orientations of unit vectors normal to contact points (contact normals) and normal contact forces. It was found that packing structure determined through method of generation of grain bedding significantly influenced distribution of contact normals. Nearly hexagonal network of contact normals was obtained for central filling of silo while sprinkle filling provided higher anisotropy of contact normals. The significance of frictional conditions and number of particles in system on distribution of contact normals was analysed. Increase in number of grains reduced disturbance from boundaries on behaviour of assembly. Distribution of loads on silo bottom obtained in simulation for different wall roughness was found in qualitative agreement with experimental data.     

Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment

This paper investigates the interaction between rapid granular flow and an obstacle. The distinct element method (DEM) is used to simulate the flow regimes observed in laboratory experiments. The relationship between the particle properties and the overall flow behaviour is obtained by using the DEM with a simple linear contact model. The flow regime is primarily controlled by the particle friction, viscous normal damping and particle rotation rather than the contact stiffness. Rolling constriction is introduced to account for dispersive flow. The velocity depth-profiles around the obstacles are not uniform but varying over the depth. The numerical results are compared with laboratory experiments of chute flow with dry granular material. Some important model parameters are obtained, which can be used to optimize defense structures in alpine regions.     

Effects of particle shapes to achieve angle of repose and force displacement behaviour on granular assembly

Circular or spherical particles in Discrete Element Method (DEM) possess limitations on achieving desired angle of repose for some granular assemblies. However, by using various shapes/clumps of particles, the limitation posed by the circular or spherical particles on achieving angle of repose can be minimized. In this paper, 2D DEM simulation has been used to investigate the effect of particle shapes on (a) angle of repose, where the aim is to achieve the angle of repose of 35° observed in a laboratory scale sand pile experiment, and (b) force displacement behaviour of granular assembly. The simulated results show that the particle shapes have strong influence on the angle of repose but have a less effect on force displacement behaviour on the granular assembly.     

An entropy-like parameter of particle size distributions as packing density index in complex granular media

Information entropy dimension (ED) has been used earlier in the characterization of the particle size distribution (PSD) in complex multi-particle granular media. In this work the ED is first proposed as an indicator of the packing density on the basis of the theoretical based interpretation of the ED in the granular media PSD context. A one-parametric exact self-similar PSD model, where the information ED is known, together with a 2-D computational random packing algorithm, are used to test the ability of the ED as an indicator of packing density. It is found that the packing density increases when the ED does. Moreover, results show a strong linear dependence between packing density and the ED. Empirical results from a large soil data base also reinforce the computational results. As ED may be estimated from field or laboratory data, the above mentioned results suggest its use as an indicator of packing density in complex granular media and material science in order to predict their properties.     

连续粒径水泥2矿粉双组分体系在浆体中的堆积密度计算公式

首先推导出双组分连续粒径粉体在浆体中的堆积密度公式;通过测定多组粒径分布不同的复合水泥在流动度相同的情况下的需水量,得到不同粒径分布对应着的不同堆积密度。所采用的15 种试样的需水量相差4%～10%。用该公式计算上述不同粒径分布的复合水泥浆体的堆积密度及需水量与试验值基本吻合。对公式的适用性进行了验证,说明该公式可以用来模拟诸如水泥和磨细矿粉体系、水泥和粉煤灰体系等胶凝材料细颗粒的堆积密度。     

Simulations for dynamics of granular mixtures in a rotating drum

We present a simple model and carry out simulations to investigate the dynamics of mixtures of granular material within a rotating drum. On the basis of the commonly held belief (supported by considerable experimental evidence) that segregation is due to motion of particles on the active layer, the bulk playing little or no role, we introduce a 2d lattice gas model which takes into account the rotational frequency, frictional forces, and the gravitational field, and represents segregation tendencies via activated effective grain-grain interactions. Our results include the onset of segregation perpendicular to the drum axis, the appearance and subsequent coarsening of bands and peculiarities of the effects of periodic modulation of the drum. Observed effects such as the segregation of rougher (smoother) particles into the bellies (necks) of the modulation are reproduced by our simulation. Received: 30 March 2000     

Determination of size distributions in nanosized powders by TEM,XRD, and SAXS

Crystallite size distributions and particle size distributions were determined by transmissions electron microscopy (TEM), X-ray powder diffraction (XRD), and small-angle X-ray scattering (SAXS) for three commercially available TiO₂ powders (P25, UV100, and TiO2_5?nm) and one SSEC produced powder (SSEC78). The theoretical Guinier model was fitted to the experimental obtained XRD data and compared to analytical expressions. Modeling of the XRD spectra showed a difference between the analytical size dependent expressions and the theoretical Guinier model. Primary particle size distributions were extracted from SAXS measurements by the hard sphere model including an interparticle interference factor. The sizes obtained from SAXS were smaller than the sizes obtained from the XRD experiments; however, a good agreement was obtained between the two techniques. Electron microscopy confirmed the primary particle sizes and the shapes obtained by XRD and SAXS. The SSEC78 powder and the commercially available powders showed different morphologies, but SSEC78, UV100, and TiO2_5?nm all consisted of both primary particles as well as a secondary structure comprised of nanosized primary particles agglomeration into larger clusters. P25 showed the largest primary particle size, but did not show a secondary structure.     

A particle packing algorithm for packed beds with size distribution

A particle packing algorithm for simulating realistic packed beds of spheres with size distribution is described. The algorithm used the Monte Carlo method combined with the simulated annealing minimisation algorithm to solve the packed bed simulations. The objective function which was minimised was a combination of two functions, one describing the deviation from the target mean coordination number of the spheres in each size interval and the other the average fraction of overlapping volume of the spheres per contact. In this way a realistic bed structure was maintained while at the same time controlling the coordination number of the spheres. The algorithm used an experimentally validated model to predict the mean coordination number of the spheres in each size interval.     

Future continuum models for granular materials in penetration analyses

This paper presents an investigation on future continuum models for granular materials in penetration analyses. A two-dimensional discrete element method has been used to numerically simulate penetration tests on a granular ground. The stress paths of soil elements in the ground have been studied, and then used to highlight the main features of granular materials based on most-advanced knowledge in soil mechanics. The study shows that the penetration makes the soil near the penetrometer undergo a significant changes of stresses in both magnitude and direction. The soil of large deformation rate may arrive at a stress state slightly over the strength envelope obtained from conventional tests. As a result, shear dilatancy, rate-dependency, non-coaxiality and particle crushing are the four main features that future continuum models should capture for granular materials in penetration analyses.     

Impact response of elasto-plastic granular and continuum media: A comparative study

A comparative study of the impact response of three-dimensional ordered granular sphere packings and continuum half-spaces made of elastic-perfectly plastic materials is conducted. Energy dissipation and plastic zone volume are characterized, and scaling laws with respect to material properties, size and loading variables are derived for both continuum and discrete (granular) systems. Due to stress concentration at contacts, energy dissipation in granular systems occurs at much smaller impact loads than in continuum systems. At higher impact loads, the fraction of energy dissipated and the extent of plastic zone are much larger in the discrete system than in the continuum case. Though the size of plastic zone is much larger in discrete systems, the volume of material involved in dissipating a fraction of impact energy is comparable for continuum and granular systems.     

Hydrodynamics of rapid granular flow of inelastic particles into vacuum

The problem of expansion of a dilute granular gas consisting of smooth, inelastic hard spheres into vacuum was investigated by three different methods: both (1) analytical and (2) computational (CFD) treatments of a hydrodynamic model, and (3) by Discrete Element Method (DEM) simulation. Furthermore, the systems were followed for long times, over which the granular kinetic energy decreases by several hundredfold. The hydrodynamic model assumes that the particles are uniformly distributed in space, yet, in the DEM simulations, the particles are free to cluster. Thus the comparison allows us to evaluate the effects of cluster formation on the system. All three methods give quantitatively similar results for the escape momentum, energy evolution, and for the hydrodynamic velocity distribution, even for restitution coefficients as small as e=0.8. The maximum deviation between the escape momentum computed from the hydrodynamic model and from DEM is shown to be no more than 4%. This means that cluster formation exerts only a relatively minor effect on the hydrodynamic quantities, suggesting to us that the hydrodynamic model in combination with the CFD algorithm may provide an efficient tool in other related problems. In addition, it is one of few cases where hydrodynamic theory and DEM agree quantitatively. Received: 17 June 2002     

Regimes of segregation and mixing in combined size and density granular systems: an experimental study

Granular segregation in a rotating tumbler occurs due to differences in either particle size or density, which are often varied individually while the other is held constant. Both cases present theoretical challenges; even more challenging, however, is the case where density and size segregation may compete or reinforce each other. The number of studies addressing this situation is small. Here we present an experimental study of how the combination of size and density of the granular material affects mixing and segregation. Digital images are obtained of experiments performed in a half-filled quasi-2D circular tumbler using a bi-disperse mixture of equal volumes of different sizes of steel and glass beads. For particle size and density combinations where percolation and buoyancy both contribute to segregation, either radial streaks or a “classical” core can occur, depending on the particle size ratio. For particle combinations where percolation and buoyancy oppose one another, there is a transition between a core composed of denser beads to a core composed of smaller beads. Mixing can be achieved instead of segregation if the denser beads are also bigger and if the ratio of particle size is greater than the ratio of particle density. Temporal evolution of these segregated patterns is quantified in terms of a “segregation index” (based on the area of the segregated pattern) and a “shape index” (based on the area and perimeter of the segregated pattern).