Cohesive Granular Materials Research Articles

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

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

Piping flow of cohesive granular materials in silo modelled by finite element method

Granular materials can exhibit complex solid- and liquid-like behaviours which are not fully understood. In this work, the piping flow of cohesive granular materials in a flat-bottomed silo is investigated using finite element method (FEM). The aim is to provide a dynamic picture of the piping formation, so as to explore the variation of field variables (velocity and stress) in time and space and obtain new insights into the piping mechanism. To be illustrative and consistent with the previous studies, it is conducted under ideal, simplified conditions including constant shear cohesion and negligible dilation. And a simple cohesive-frictional model is employed for describing the granular material. The results confirm that the low flowable granular materials, represented by high shear cohesion or internal friction, are prone to piping. But some more complicated mechanisms are recognised. First, the tensile stress is important for preventing velocity discontinuities and piping in the bulk of particles. Even for the same shear cohesion, different tensile strengths can result in distinct flow behaviours. Secondly, the final stress state is history-dependent. Only small stresses are observed in the vicinity of the channel because of the high velocity therein at the flowing stage. The radial, vertical and hoop stresses also depend on the development of plasticity. Finally, a governing rule of piping is yielded based on FEM results and is shown to agree qualitatively with the Jenike theory. The need for future studies is also discussed.

A cohesive granular material with tunable elasticity.

By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an additional control over the elasticity of the bonds holding the particles together. We show that its mechanical response can be varied over several orders of magnitude by adjusting the size and stiffness of the bridges, and the size of the particles. We also investigate its mechanism of failure under unconfined uniaxial compression in combination with in situ x-ray microtomography. We show that a broad linear-elastic regime ends at a limiting strain of about 8%, whatever the stiffness of the agglomerate, which corresponds to the beginning of shear failure. The possibility to finely tune the stiffness, size and shape of this simple material makes it an ideal model system for investigations on, for example, fracturing of porous rocks, seismology, or root growth in cohesive porous media.

Fracture reveals clustering in cohesive granular matter

We report an experimental study of the morphology of fractures in cohesive granular materials. Cohesion is introduced by equilibrating the grains with a humid atmosphere. The setup allows to produce a controlled crack in a thin layer of a glass beads assembly, and observe with an extremely high resolution the edge of the fracture at the free surface of the layer. The detailed multi-scale analysis of the fracture profile reveals the presence, in the bulk of the material, of clusters of grains whose size increases monotonically with the relative humidity. These results are important because the formation of clusters, resulting in a heterogeneity of the cohesion force, governs the mechanical properties of cohesive granular matter in contact with a humid atmosphere.

Fracture of granular materials composed of arbitrary grain shapes: A new cohesive interaction model

Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesive phase lying between the grains. Contact situations are solved according to unilateral contact and Coulomb friction laws. In order to test the developed model, 2D uniaxial compression simulations are performed. Numerical results show the ability of the model to mimic the macroscopic behavior of an aggregate grain subject to axial compression, as well as fracture initiation and propagation. A study of the influence of model and sample parameters provides important information on the ability of the model to reproduce various behaviors.

Reprint of "Experiments and discrete element simulation of the dosing of cohesive powders in a simplified geometry"

We perform experiments and discrete element simulations on the dosing of cohesive granular materials in a simplified geometry. The setup is a canister box where the powder is dosed out through the action of a constant-pitch coil feeder connected to a motor. A dosing step consists of a rotation followed by a period of rest before the next step. From the experiments, we report on the operational performance of the dosing process through a variation of dosage time, coil pitch and initial powder filling mass. We find that the mass per dose shows an increasing linear dependence on the dosage time and rotation speed. In contrast, the mass output from the canister is inversely proportional (as expected) to an increase in the number of coils.After calibrating the interparticle friction and cohesion, we show that DEM simulations with upscaled particles can quantitatively reproduce the experimental findings for smaller masses but also overestimate arching and blockage. For some parameters, with appropriate homogenization tools, further insights into macroscopic fields can be obtained.This work shows that the calibration of (upscaled) meso-particle properties is a viable approach to overcome the untreatable number of particles inherent in experiments with fine, cohesive powders and thus opens the gateway to simulating their flow in more complex geometries.

Experiments and discrete element simulation of the dosing of cohesive powders in a simplified geometry

We perform experiments and discrete element simulations on the dosing of cohesive granular materials in a simplified geometry. The setup is a canister box where the powder is dosed out through the action of a constant-pitch coil feeder connected to a motor. A dosing step consists of a rotation followed by a period of rest before the next step. From the experiments, we report on the operational performance of the dosing process through a variation of dosage time, coil pitch and initial powder filling mass. We find that the mass per dose shows an increasing linear dependence on the dosage time and rotation speed. In contrast, the mass output from the canister is inversely proportional (as expected) to an increase in the number of coils.After calibrating the interparticle friction and cohesion, we show that DEM simulations with upscaled particles can quantitatively reproduce the experimental findings for smaller masses but also overestimate arching and blockage. For some parameters, with appropriate homogenization tools, further insights into macroscopic fields can be obtained.This work shows that the calibration of (upscaled) meso-particle properties is a viable approach to overcome the untreatable number of particles inherent in experiments with fine, cohesive powders and thus opens the gateway to simulating their flow in more complex geometries.

A micro-mechanical model for the plasticity of porous granular media and link with the Cam clay model

A micro-mechanical constitutive model for the plastic behavior of cohesive granular materials with hardening due to porosity changes is proposed. The plasticity model is based on a re-interpretation of a micro-mechanical strength model for cohesive frictional granular media. The hardening law by porosity changes explicitly stems from the homogenization process. The micro-macro plasticity model, analytical and fully explicit, depends only on two constant material parameters with a clear physical signification at the microscopic scale: the friction angle and the tensile strength of the grain to grain interfaces. The seminal ideas of critical state soil mechanics are retrieved: critical state line, state boundary surface in the stress/porosity space, hardening or softening due to change in porosity and ability to describe both dilatancy and contractancy. The established micro-mechanical model is very similar to the phenomenological modified Cam clay model, providing to the latter a microstructural based interpretation.

Experimental investigation of particle contact laws for discrete element model of granular materials

This paper aims to present a failure criterion for cohesive granular materials subjected to combined loads, which can be applied to computational modelling with a general framework of discrete element method. The failure of a cohesive granular material with the stress–strain behaviour is investigated using the experimental method, and tests on couple of aluminium rods glued with epoxy resin were carried out under various loading conditions. Five series of tests (namely tension, compression, shearing, rotation and simply combined loading) were conducted to characterise the behaviours of cohesive bonds (load–displacement relationship, failure conditions). A failure criterion for the granular materials subjected to combined loads was presented by analysing the test results both separately and together. This criterion will provide positive support for the failure criterion equation and can be used in the further study of micro-mechanism of cemented soils using the discrete element method.

Modelling cohesion in snow avalanche flow

AbstractFlowing snow is a cohesive granular material. Snow temperature and moisture content control the strength of the cohesive bonding between granules and therefore the outcome of granular interactions. Strong, cohesive interactions reduce the free mechanical energy in the avalanche core and therefore play a significant role in defining the avalanche flow regime. We introduce cohesion into avalanche dynamics model calculations by (1) treating cohesion as an additional internal binding energy that must be overcome to expand the avalanche flow volume, (2) modifying the Coulomb stress function to account for the increase in shear because of cohesive interactions and (3) increasing the activation energy to control the onset of avalanche fluidization. The modified shear stress function is based on force measurements in chute experiments with flowing snow. Example calculations are performed on ideal and real terrain to demonstrate how snow cohesion modifies avalanche flow and runout behaviour.

Rheology of cohesive granular materials across multiple dense-flow regimes.

We investigate the dense-flow rheology of cohesive granular materials through discrete element simulations of homogeneous, simple shear flows of frictional, cohesive, spherical particles. Dense shear flows of noncohesive granular materials exhibit three regimes: quasistatic, inertial, and intermediate, which persist for cohesive materials as well. It is found that cohesion results in bifurcation of the inertial regime into two regimes: (a) a new rate-independent regime and (b) an inertial regime. Transition from rate-independent cohesive regime to inertial regime occurs when the kinetic energy supplied by shearing is sufficient to overcome the cohesive energy. Simulations reveal that inhomogeneous shear band forms in the vicinity of this transition, which is more pronounced at lower particle volume fractions. We propose a rheological model for cohesive systems that captures the simulation results across all four regimes.

FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At microscopic level, Discrete Element Method (DEM) is used to model dense grains packing. At the macroscopic level, the numerical solution is obtained by a Finite Element Method (FEM). In order to bridge the micro- and macro-scales, the concept of Representative Elementary Volume (REV) is applied, in which the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM’s simulation. In this way, the numerical constitutive law is determined through the detailed modelling of the microstructure, taking into account the nature of granular materials. We first elaborate the principle of the computation homogenisation (FEM × DEM), then demonstrate the features of our multiscale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.

Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials.

Derivation of dimensionless relationships for the agitation of powders of different flow behaviours in a planetary mixer

This study investigates the bulk agitation of free flowing or nearly cohesive granular materials in a pilot-scale planetary mixer equipped with a torque measurement system. Our major aim is to investigate the effect of the flow properties of several powders, as well as that of the set of experimental conditions (engine speeds NR and NG), on the power consumption of such a mixer. Thanks to a previous dimensional analysis of the system, this influence is studied through the variations of the power P with a characteristic speed uch, defined from engine speeds and geometrical considerations. Two relationships involving dimensionless numbers are derived to describe the agitation process: NpG=fFrG,NRNG and NpM=f(FrM). For free flowing powders, a linear relationship is observed when plotting P against uch, and the resulting process relationship linking dimensionless numbers is NpM=15FrM−1. In the more cohesive case, power values vary around an average value (P=54W) and the resulting process relationship is NpM=1.8072FrM−1.467. It is argued that the exponent in the representation of NpM against FrM may be a useful parameter for powder classification, and should be linked to powder rheometrical considerations.

Analogy between electrochemical behaviour of thick silicon granular electrodes for lithium batteries and fine soils micromechanics

In this paper we study the influence of the distribution and the shape of the carbon conductive additives on the cyclability of thick silicon based composite electrodes. Results pinpoint the influence of carbon additives is not only to play on the electronic conductivity but also to play on the micromechanics (stress distribution) of the composite films. The lack of correlation between electrochemical performance and the macroscopic electronic conductivity of the pristine electrodes and the observation of repeated drops and jumps in capacity during cycling brought us to make an analogy between the silicon composite electrodes and cohesive granular materials such as fine soils media. Considering the collective mechanical behavior of a stack of silicon particles upon repeated volume variations shed a novel understanding to the electrochemical behavior of composite electrodes based on silicon and alloying materials and tells us how critically important is the design at the different scales (the particle, a few particles, the composite electrode, the cell) to engineer the mechanical stress and strain and improve cycle life.

Micro-mechanics and dynamics of cohesive particle systems

Cohesiveparticlesystemsareubiquitousinnatureandindus-trial applications. Besides the ordinary repulsive interactionbetweenparticles,themacroscopicbehaviorofcohesivesys-tems is determined by attractive interactions between parti-cles, such as van der Waals forces, liquid bridges and elec-trostatics.Much insight in the dynamics of cohesive granular mate-rials was obtained by means of discrete element modeling(DEM). First introduced by Cundall and Strack [1], thismethod offers a robust numerical approach to explore themacroscopic behaviour of granular materials with detailedanalysis of particle interactions. As one of the pioneers inDEM, Colin Thornton and his co-workers have advanced

Time to Failure Prediction Scheme for Rocks

The lifetime of solids under loads has been studied by many researchers (e.g., Mishnaevsky 1996; Ignatovich 1996; Sun and Hu 1997; Aubertin et al. 2000; Miura et al. 2003; Kemeny 2003, 2005; Guedes 2006; Le et al. 2009; Damjanac and Fairhurst 2010). In this study, the lifetime of rocks under load is governed by microstructural defects such as microcracks. The natural rock contains microcracks which propagate and coalesce under loads. The macroscopic fractures formed by these microcracks could finally lead to the failure of the rock. This process has been simulated by Konietzky et al. (2009), based on cellular automata. As a further development of this research work, this study improved the crack propagation scheme by considering initial crack orientations and wing cracks. The developed scheme is especially valid for cohesive granular material, like rocks, which consists of mineral grains of different shape, size, and mechanical properties, like strength and stiffness. Like seismoacoustic monitoring documents (e.g., Yang et al. 2012; Fortin et al. 2011; Mayr et al. 2011; Yoon et al. 2012), the damage and final failure of rocks are not characterized by the growth of one single crack, but, instead, by the growth and coalescence of many microcracks, which grow at different speeds at the same time. The proposed simulation scheme is an attempt to reproduce this process up to the formation of a final macroscopic failure (macroscopic tensile crack or shear band). As a limitation of the current numerical model, the evaluated lifetime value is influenced by the mesh size.

Depth and minimal slope for surface flows of cohesive granular materials on inclined channels

AbstractWe present analytical predictions of the depth and onset slope of the steady surface flow of a cohesive granular material in an inclined channel. The rheology of Jop, Forterre & Pouliquen (Nature, vol. 441, 2006, pp. 727–730) is used, assuming co-axiality between the stress and strain-rate tensors, and a coefficient of friction dependent on the strain rate through the dimensionless inertial number $I$. This rheological law is augmented by a constant stress representing cohesion. Our analysis does not rely on a precise $\mu (I)$ functional, but only on its asymptotic power law in the limit of vanishing strain rates. Assuming a unidirectional flow, the Navier–Stokes equations can be solved explicitly to yield parametric equations of the iso-velocity lines in the plane perpendicular to the flow. Two types of channel walls are considered: rough and smooth, depicting walls whose friction coefficient is respectively larger or smaller than that of the flowing material. The steady flow starts above a critical onset angle and consists of a sheared zone confined between a surface plug flow and a deep dead zone. The details of the flow are discussed, depending on dimensionless parameters relating the static friction coefficient, cohesion strength of the material, incline angle, wall friction, and channel width. The depths of the flow at the centre of the channel and at the walls are calculated by a force balance on the flowing material. The critical angle for the onset of the flow is also calculated, and is found to be strongly dependent on the channel width, in agreement with experimental results on heap stability and in rotating drums. Our results predict the important conclusion that a cohesive material always starts to flow for an incline angle lower than 90° between smooth walls, whereas in a narrow enough channel with rough walls, it may not flow, even if the channel is inclined vertically.

Cohesive granular materials composed of nonconvex particles

The macroscopic cohesion of granular materials made up of sticky particles depends on the particle shapes. We address this issue by performing contact dynamics simulations of 2D packings of nonconvex aggregates. We find that the macroscopic cohesion is strongly dependent on the strain and stress inhomogeneities developing inside the material. The largest cohesion is obtained for nearly homogeneous deformation at the beginning of unconfined axial compression and it evolves linearly with nonconvexity. Interestingly, the aggregates in a sheared packing tend to form more contacts with fewer neighboring aggregates as the degree of nonconvexity increases. We also find that shearing leads either to an isotropic distribution of tensile contacts or to the same privileged direction as that of compressive contacts.

The dynamics of wet granular matter under a vertical vibration bed

This study investigates the dynamic properties of convection rolls in a 2D wet vibrated granular bed. A particle tracking method with the help of image-processing technology was used to measure the velocity fields, convection flow rate, and the granular temperatures in the wet vibrated granular bed. This study examines the dynamic behaviors of wet granular materials subjected to external vertical vibration. Different liquid contents, viscosities, and surface tensions were added to glass beads forming cohesive granular materials in the vibrated granular bed. This study presents a systematic investigation of the effects of the addition of liquid content, viscosity, and surface tension on dynamic properties of wet particulates. Results show that the convection flow rate and granular temperature decrease monotonically as the added liquid content and liquid viscosity increase. However, the effects of surface tension on the convection flow rate are more significant at the smaller liquid content than that at a higher liquid content. The convection flow rate also decreases in a power decay as the modified Bond number increases.