Showing papers in "Granular Matter in 2012"

An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code

Abstract: We present our implementation of the soft-sphere discrete element method (SSDEM) in the parallel gravitational N-body code pkdgrav, a well-tested simulation package that has been used to provide many successful results in the field of planetary science. The implementation of SSDEM allows for the modeling of the different contact forces between particles in granular material, such as various kinds of friction, including rolling and twisting friction, and the normal and tangential deformation of colliding particles. Such modeling is particularly important in regimes for which collisions cannot be treated as instantaneous or as occurring at a single point of contact on the particles’ surfaces, as is done in the hard-sphere discrete element method already implemented in the code. We check the validity of our soft-sphere model by reproducing successfully the dynamics of flows in a cylindrical hopper. Other tests will be performed in the future for different dynamical contexts, including the presence of external and self-gravity, as our code also includes interparticle gravitational force computations. This will then allow us to apply our tool with confidence to planetary science studies, such as those aimed at understanding the dynamics of regolith on solid celestial body surfaces, or at designing efficient sampling tools for sample-return space missions.

Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials

Abstract: This paper presents a novel method to generate realistic packings for discrete modelling of granular materials. To generate a packing of 2D dense sample in a container of arbitrary shape, a number of key particle properties are identified as the targeted ones to reproduce, including the grain size distribution, density, particles orientations as well as specific shape characteristics of the particles. Four descriptors, including elongation, circularity, roundness, regularity, are chosen to characterize the particle shape. The considered container is discretized by a Voronoi tessellation with prescribed cell size and orientation distributions. Each Voronoi cell is then filled with a particle with prescribed shape characteristics. Several algorithms are proposed and are compared in terms of their computational efficiency and accuracy to define the particle contours, to constrain the Voronoi tessellation and to fill the Voronoi cells with particles. Two examples are further employed to demonstrate the accuracy and the potential usefulness of the proposed method for a wide range of applications where discrete modelling of granular media is important.

The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions

Abstract: Previous research studies have used either physical experiments or discrete element method (DEM) simulations to explore, independently, the influence of the coefficient of inter-particle friction (μ) and the intermediate stress ratio (b) on the behaviour of granular materials. DEM simulations and experiments using photoelasticity have shown that when an anisotropic stress condition is applied to a granular material, strong force chains or columns of contacting particles transmitting relatively large forces, form parallel to the major principal stress orientation. The combined effects of friction and the intermediate stress ratio upon the resistance of these strong force chains to collapse (buckling failure) are considered here using data from an extensive set of DEM simulations including triaxial and true triaxial compression tests. For all tests both μ and b affected the macro- and micro-scale response, however the mechanisms whereby the force chain stability was improved differ. While friction clearly enhances the inherent stability of the strong force chains, the intermediate stress ratio affects the contact density and distribution of orthogonal contacts that provide lateral support to the force chains.

From discrete particles to continuum fields near a boundary

Abstract: An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch (Granul Mat 12(3):239–252, 2010), which is consistent with the continuum equations everywhere but does not account for boundaries. Our extension accounts for the boundary interaction forces in a self-consistent way and thus allows the construction of continuous stress fields that obey the macroscopic conservation laws even within one coarse-graining width of the boundary. The resolution and shape of the coarse-graining function used in the formulation can be chosen freely, such that both microscopic and macroscopic effects can be studied. The method does not require temporal averaging and thus can be used to investigate time-dependent flows as well as static or steady situations. Finally, the fore-mentioned continuous field can be used to define ‘fuzzy’ (very rough) boundaries. Discrete particle simulations are presented in which the novel boundary treatment is exemplified, including chute flow over a base with roughness greater than one particle diameter.

Closure relations for shallow granular flows from particle simulations

Abstract: The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed where the flow is either highly energetic and strongly layered in depth for small inclinations, or non-uniform and oscillating for larger inclinations. For steady uniform flows, depth profiles of density, velocity and stress have been obtained using an improved coarse-graining-method, which allows accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations obtained from micro-scale DPM simulations of steady flows. We thus obtain relations for the effective basal friction, shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal roughness. For collisional flows, the functional dependencies are well determined and have been obtained.

Fabric evolution and accessible geometrical states in granular materials

Abstract: We analyze the geometrical states of granular materials by means of a fabric tensor involving the coordination number and fabric anisotropy as the lowest-order descriptors of the contact network. In particular, we show that the fabric states in this representation are constrained by steric exclusions and the condition of mechanical equilibrium required in the quasi-static limit. A simple model, supported by numerical data, allows us to characterize the range of accessible fabric states and the joint evolution of fabric parameters. The critical state in this framework appears as a jammed state in the sense of a saturation of contact gain and loss along the principal strain-rate directions.

On the quasi-static granular convective flow and sand densification around pile foundations under cyclic lateral loading

Abstract: The saturated sand surrounding an offshore pile foundation under quasi-static cyclic lateral load can show the physical phenomena of macromechanical densification and convective granular flow. Based on the results from physical model tests at different geometrical scales, this paper provides a certain quantification of such phenomena and discusses their causes and consequences. The progressive sand densification leads to subsidence of the soil surface and a significant stiffening of the pile behaviour. Conversely, the ratcheting convective motion of two closed cells of soil beneath the pile-head is responsible for an endless grain migration at the soil surface, the inverse grading of the convected material and a direct shear of the sand at the distinct boundary of the revolving soil domain. In this respect, and from a macromechanical perspective considering the soil as a continuum, it appears that the convecting material tends to follow gradient lines of shear stress during its ratcheting motion. Concluding the paper, the practical relevance of these phenomena and their extrapolation to other conditions are briefly discussed.

On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis

Abstract: Mechanical behavior of granular soils is a classic research realm but still yet not completely understood as it can be influenced by a large number of factors, including confining pressure, soil density, loading conditions, and anisotropy of soil etc. Traditionally granular materials are macroscopically regarded as continua and their particulate and discrete nature has not been thoroughly considered although many researches indicate the macro mechanical behavior closely depends on the micro-scale characteristics of particles. This paper presents a DEM (discrete element method)-based micromechanical investigation of inter-particle friction effects on the behavior of granular materials. In this study, biaxial DEM simulations are carried out under both ‘drained’ and ‘undrained’ (constant volume) conditions. The numerical experiments employ samples having similar initial isotropic fabric and density, and the same confining pressure, but with different inter-particle friction coefficient. Test results show that the inter-particle friction has a substantial effect on the stress-strain curve, peak strength and dilatancy characteristics of the granular assembly. Clearly, it is noted that apart from the inter-particle friction, the shear resistance is also contributed to the dilation and the particle packing and arrangements. The corresponding microstructure evolutions and variations in contact properties in the particulate level are also elaborated, to interpret the origin of the different macro-scale response due to variations in the inter-particle friction.

A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments

Abstract: In this paper, we used a 3-D discrete-element model, Grains3D, which allows the simulation of unsteady granular flows of monodisperse soft spherical particles in a common situation (i.e., down a rectangular channel). A series of numerical dam-break experiments was performed to predict the behavior of granular columns that propagate down a rough horizontal surface from different initial conditions (varying the initial aspect ratio). Numerical results were compared to those obtained experimentally by Lajeunesse et al. (Phys Fluids 17:103302, 2005) from a similar configuration. Runout distance, temporal flow evolution, deposit morphology and internal flow structures of similar laboratory experiments were quantitatively reproduced as well as prediction of empirical and theoretical scaling laws. This paper highlights that such fully 3-D simulations of soft-spheres can remarkably capture dam-break collapses performed in a rectangular channel. Moreover, Grains3D can provide a complete physical description of such complex unsteady systems which will be the topic of future on-going studies.

Effect of grain roughness on strength, volume changes, elastic and dissipated energies during quasi-static homogeneous triaxial compression using DEM

Abstract: A quasi-static homogeneous drained triaxial compression test on cohesionless sand under constant lateral pressure was simulated using a three-dimensional DEM model. Grain roughness was modelled by means of symmetric clusters composed of rigid spheres imitating irregular particle shapes. The effect of grain roughness on shear strength, dilatancy, kinetic, elastic and dissipated energies was numerically analyzed. Some numerical results were compared with available experimental results.

Highly nonlinear solitary waves in chains of cylindrical particles

Abstract: We study the dynamic response of uniform gran- ularchainscomposedofshortcylindricalparticlesexcitedby animpulse.Theparticlesinthechainsarearrangedwiththeir axesorthogonaltothechain'saxis,andtheparticlesmaintain a constant relative orientation angle. We study the formation and propagation of solitary waves in the chains varying the orientation angle (α) between particles, and show tunabil- ity of the stress transfer as a function of α. We use the gen- eralHertziancontacttheorytomodeltheinteractionbetween

A discrete model for simulating shear strength and deformation behaviour of rockfill material, considering the particle breakage phenomenon

Abstract: This study focuses on numerical modelling of rockfill material with the discrete element method (DEM). This method was used due to the special features of rockfill material, such as intense particle breakage and high contracting behaviour, which are inherently due to large particle size. Because the DEM models the interaction of separate elements, it is capable of modelling discrete structures of granular materials and particle breakage. The model used in this study uses PFC2D and considers breakable clumps. To validate the presented model for rockfill material, numerical single crushing tests and triaxial tests on the Purulia dam’s material were simulated. Due to the size-dependant crushing strength being involved in the breakage criterion, and also considering particle confinement, size-dependant and stress level-dependant behaviour was successfully simulated on modelled rockfill material. The variation of the sample’s particle grading from before the biaxial tests and after shear failure occurred was reported. The obtained results demonstrate the accuracy of the adopted model and the model’s capability for considering a rockfill material’s strength, deformation and crushing behaviour.

Dynamical arching in a two dimensional granular flow

Abstract: A study of grains flow in a two dimensional hopper using particle tracking and photoelastic methods is presented in this article. An intermittent network of contact forces consisting of force chains and arches is observed. This network is responsible for fluctuations in the average vertical velocity. The magnitude of these fluctuations depends on the hopper’s geometry, and it quickly reduces for large aperture size and small inclination angles. The average velocity field is described using a combination of harmonic angular functions and a power law of radial position. The mass flow rate is determined through the average velocity field and a Beverloo type scaling is obtained. We found that the effect of the inclination angle on the mass flow rate is given by $${\alpha/ \,(\sin\alpha)^{3/2}}$$ . It is also found that the critical aperture size, approaching jamming, depends linearly on $${\sin\alpha}$$ . At small D/d, the time average of the network of contact forces shows a boundary with characteristics resembling the free fall arch. We show that an arch can be built following the principal compression orientation of the stress tensor which captures the characteristics of the arches observed experimentally.

Asymptotic behaviour of granular materials

Abstract: The concept of the asymptotic behaviour of particulate materials is described, including its enhancement by considering asymptotic states in extension. A 3D discrete element model with elastic spherical particles and the granulometry of a real sand is set up. The numerical sample is stretched from different initial states, and the influence of the strain rate direction on the final state is studied within the stress ratio, void ratio and mean stress space. Asymptotic behaviour is clearly observed, although the grains remain intact (no grain crushing is considered). The extension asymptotic states were observed, and the notion of a normal extension line is introduced. The extension asymptotic states coincide with the peak states observed in the shear tests with constant stress path direction in dense samples.

Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method

Abstract: This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.

Three dimensional fabric evolution of sheared sand

Abstract: Granular particles undergo translation and rolling when they are sheared. This paper presents a three-dimensional (3D) experimental assessment of fabric evolution of sheared sand at the particle level. F-75 Ottawa sand specimen was tested under an axisymmetric triaxial loading condition. It measured 9.5 mm in diameter and 20 mm in height. The quantitative evaluation was conducted by analyzing 3D high-resolution x-ray synchrotron micro-tomography images of the specimen at eight axial strain levels. The analyses included visualization of particle translation and rotation, and quantification of fabric orientation as shearing continued. Representative individual particles were successfully tracked and visualized to assess the mode of interaction between them. This paper discusses fabric evolution and compares the evolution of particles within and outside the shear band as shearing continues. Changes in particle orientation distributions are presented using fabric histograms and fabric tensor.

Distinct element method analyses of idealized bonded-granulate cut slope

Abstract: This paper presents a numerical study of idealized bonded-granulate cut slope subject to sudden strength reduction. A 2-D Distinct Element Method (DEM) has been used to carry out a simulation of full-process slope failure with focus on very-rapid and extremely-rapid landslide process. The numerical results show that during the landslide process: (1) the soil moves either in a rather random/chaotic way (diffuse failure) or in different curved shear bands (localized failure). The soil close to slope surface moves along downward slope while the soil close to the slope toe moves significantly in the horizontal direction. The landslide experiences very rapid flow most of the time, with its maximum velocity increaseing obviously with time at first to its peak value, then decreasing gradually to zero. (2) The soil close to slope undergo a repeated loading and unloading process, and an evident rotation of principal stresses. Their stress state may arrive slightly over the peak strength envelope as a result of extremely rapid flow. (3) There is little grain-size effect for the grains at low velocity, but an evident grain-size effect for the grains at high velocity, with large-size grains tending to move fast. (4) The post-failure inclination is much smaller than the peak/residual internal friction angle of the material. The post-failure slope surface passes through the centre of the initial slope surface instead of the initial slope toe.

Granular contact dynamics with particle elasticity

Abstract: A granular contact dynamics formulation for elastically deformable particles is detailed. The resulting scheme bears some similarity to traditional molecular dynamics schemes in that the consideration of a finite elastic contact stiffness implies the possibility for inter-particle penetration. However, in contrast to traditional molecular dynamics schemes, there are no algorithmic repercussions from operating with a large or, in the extreme case infinite, contact stiffness. Indeed, the algorithm used—a standard second-order cone programming solver—is independent of the particle scale model and is applicable to rigid as well as elastically deformable particles.

Granular element method (GEM): linking inter-particle forces with macroscopic loading

Abstract: We present a new method capable of inferring, for the first time, inter-particle contact forces in irregularly-shaped natural granular materials (e.g., sands), using basic Newtonian mechanics and balance of linear momentum at the particle level. The method furnishes a relationship between inter-particle forces and corresponding average particle stresses, which can be inferred, for instance, from measurements of average particle strains emanating from advanced experimental techniques (e.g., 3D X-ray diffraction). Inter-particle forces are the missing link in understanding how forces are transmitted in complex granular structures and the key to developing physics-based constitutive models. We present two numerical examples to verify the method and showcase its promise.

Two-dimensional discrete element modelling of bender element tests on an idealised granular material

Abstract: The small-strain (elastic) shear stiffness of soil is an important parameter in geotechnics. It is required as an input parameter to predict deformations and to carry out site response analysis to predict levels of shaking during earthquakes. Bender element testing is often used in experimental soil mechanics to determine the shear (S-) wave velocity in a given soil and hence the shear stiffness. In a bender element test a small perturbation is input at a point source and the propagation of the perturbation through the system is measured at a single measurement point. The mechanics and dynamics of the system response are non-trivial, complicating interpretation of the measured signal. This paper presents the results of a series of discrete element method (DEM) simulations of bender element tests on a simple, idealised granular material. DEM simulations provide the opportunity to study the mechanics of this testing approach in detail. The DEM model is shown to be capable of capturing features of the system response that had previously been identified in continuum-type analyses of the system. The propagation of the wave through the sample can be monitored at the particle-scale in the DEM simulation. In particular, the particle velocity data indicated the migration of a central S-wave accompanied by P-waves moving along the sides of the sample. The elastic stiffness of the system was compared with the stiffness calculated using different approaches to interpreting bender element test data. An approach based upon direct decomposition of the signal using a fast-Fourier transform yielded the most accurate results.

Kinetic theory applied to inclined flows

Abstract: We apply the continuum equations of a kinetic theory to predict the features of uniform, steady, inclined flows of identical, frictional, inelastic spheres over a rigid, bumpy base between vertical, frictional side walls. Numerical solutions of these equations over a range of mass flow rates exhibit features seen in physical experiments and numerical solutions in the absence of side walls. For the densest flows, we employ a phenomenological extension of kinetic theory that involves a length scale associated with particle correlations. When a dense flow is thick enough, an algebraic balance between the production and dissipation of fluctuation energy reproduces the relation between mass flow rate and mass hold-up obtained when solving the boundary-value problem of the extended theory.

Dynamics of drop formation in granular suspensions: the role of volume fraction

Abstract: The presence of grains strongly modifies the detachment of drops of a viscous liquid. We have shown previously that the detachment of drops of granular suspensions takes place via different regimes (Bonnoit et al. submitted, 2011). Here we study the influence of the volume fraction of particles on the formation and shape of the droplets by means of visual observations. We measure the minimal neck diameter as well as the height of the detachment as a function of time to quantify the evolution of the drop shape. We also address the question of the thinning dynamics of the neck in the different regimes. Linking the dynamics to the properties of the effective fluid or to rearrangements of individual grains in the thread gives insights in the origin of the different regimes.

Vortex formation and dissolution in sheared sands

Abstract: Using digital image correlation, we track the displacement fluctuations within a persistent shear band in a dense sand specimen bounded by glass walls undergoing plane strain compression. The data evidences a clear, systematic, temporally recurring pattern of vortex formation, dissolution, and reformation throughout macroscopic softening and critical state regimes. During softening, locally affine deformation zones are observed at various locations along the shear band, which we argue to be kinematic signatures of semi-stable force chains. Force chain collapse then occurs, inducing vortex formation. Local jamming at the conflux of opposing displacements between adjacent vortices arrests the vortices, providing an avenue for potential new force chains to form amidst these jammed regions. The process repeats itself temporally throughout the critical state. The pattern further correlates with fluctuations in macroscopic shear stress. We characterize the nature of the observed vortices, as they are different in our sands comprised of irregular shaped particles, as compared to previous observations from experiments and numerical simulations which involved circular or rounded particles. The results provide an interesting benchmark for behavior of non-circular/non-spherical particles undergoing shear.

Shock dynamics in granular chains: numerical simulations and comparison with experimental tests

Abstract: The aim of this paper is to simulate the nonlinear wave propagation in granular chains of beads using a recently introduced multiple impact model and to compare numerical results to experimental ones. Different kinds of granular chains are investigated: monodisperse chains, tapered chains and stepped chains. Particular attention is paid to the dispersion effect, and the wave propagation in tapered chains, the interaction of two solitary waves in monodisperse chains, and the formation of solitary wave trains in stepped chains. We show that the main features of the wave propagation observed experimentally in these granular chains are very well reproduced. This proves that the considered multiple impact model and numerical scheme are able to encapsulate the main physical effects that occur in such multibody systems.

Periodic propagation of localized compaction in a brittle granular material

Abstract: Experiments that involve the monotonic compre- ssion of granular packs composed of brittle porous grains in a piston-die press reveal evidence of a localized compaction band that propagates periodically within the specimen oppo- site to the direction of loading and faster than the imposed specimen shortening rate.

Homogeneous cooling of hard ellipsoids

Abstract: We study the homogeneous cooling of hard, smooth ellipsoids in three dimensions using event driven numerical simulation. The elongation of the particle has a strong effect on the cooling behavior. Weakly elongated ellipsoids display two distinct cooling regimes. For small times, the translational and rotational energy decay at a different rates. Once their ratio reaches a time-independent value (different from equipartition), the overall temperature of the system decays like t−2, as predicted by Haff’s law. For more elongated ellipsoids the translational and rotational temperatures rapidly reach a constant ratio near unity. The cooling behavior in the homogeneous state can be predicted from Haff’s law and the equilibrium collision rate.

Experimental and numerical investigation of the bulk behavior of wood pellets on a model type grate

Abstract: Transport and storage equipment for wood pellets can in theory be readily improved through simulation approaches like the discrete element method. However, scientific investigations verifying the applicability of the discrete element method in case of non-spherical particles are still limited. The sensitivity of simulations on the size and shape approximation of particles and mixing and segregation behavior are not well studied. These issues are addressed in the current paper. For a model type grate system experimental and numerical investigations of the mixing behavior of wood pellets under different motion patterns are performed. Results indicate that the discrete element method is well capable of representing experimentally obtained results. Altering the representation of the size distribution has impact on the segregation behavior, but does not strongly impact the overall mixing tendencies.

Discrete modelling of electrical transfer in multi-contact systems

Abstract: In this work we propose to study the electrical transfer in metallic granular materials under mechanical loading. A new model of electrical conductance and the associated numerical treatment in the Discrete Element Method (DEM) framework are presented. The approach differs from the Holm’s model by considering several electrical potentials inside a particle. The electrical properties of the different paths in granular medium depend on the contact reaction through the Hertz’s theory. A DEM modelling allows to study the electromechanical behaviour of granular materials. Numerical simulations are carried out in 1D and 2D and are compared to experimental results in the case of a metal–metal contact. The results show a good agreement with experimental ones.

Optimal description of two-dimensional complex-shaped objects using spheropolygons

Abstract: Recent advances in the morphological description of particles in granular material systems allow two-dimensional complex-shaped particles to be realistically simulated using spheropolygons, i.e., the Minkowski sum of a disk and a polygon. For identical numbers of vertices, spheropolygons achieve a better description of shapes than polygons, but require that the optimal spheroradius be determined. Here we propose a method for generating spheropolygons that optimizes the description of particle morphologies, i.e., minimizes the error images and the numbers of vertices. Because the error images of individual particles are a proxy for the accuracy of granular matter flow calculations, while the numbers of vertices are a proxy for the computational time, the method is optimally applicable to discrete element methods. We demonstrate the proposed method using pebbles, gravel, and crushed shells.

Oblique Impact of Frictionless Spheres On the Limitations of Hard Sphere Models for Granular Dynamics

Abstract: When granular systems are modeled by hard spheres, particle–particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the particles are the same before and after such an event. We show that depending on the material and system parameters, this assumption may fail. For the case of viscoelastic particles we present a universal condition which allows to assess whether hard-sphere modeling and, thus, event-driven Molecular Dynamics simulations are justified.