Energy and averages in the mechanics of granular materials

We derive a general thermo-mechanical theory for particulate materials consisting of granules of arbitrary whose material points possess three translational and three independent rotational degrees of freedom. Additional field variables are the translational and rotational granular temperatures, the kinetic energies shape and size. The kinematics of granulate is described within the framework of a polar continuum theory of the velocity and spin fluctuations respectively and the usual thermodynamic temperature. We distinguish between averages over particle categories (averages in mass/velocity and moment of inertia/spin space, respectively) and particle phases where the average extends over distinct subsets of particle categories (multi phase flows). The relationship between the thermal energy in the granular system and phonon energy in a molecular system is briefly discussed in the main body of the paper and discussed in detail in the Appendix A. (C) 2001 Elsevier Science B.V. All rights reserved.

Effects of grain shape on packing and dilatancy of sheared granular materials

Aus: Soft matter, Vol. 10.2014, H. 28, S. 5157 - 5167

Theoretical Analysis and Simulations of Vertically Vibrated Granular Materials

The dynamical properties ofshaken granular materials are important in many industrial applications where the shaking is used to mix, segregate and transport them. In this work asystematic, large scale simulation study has been performed to investigate the rheology of dense granular media, in the presence of gas, in a three dimensional vertical cylinder filled with glass balls. The base wall of the cylinder is subjected to sinusoidal oscillation in the vertical direction. The viscoelastic behavior of glass balls during a collision, have been studied experimentally using a modified Newton's Cradle device. By analyzing the results of the measurements, using numerical model based on finite element method, the viscous damping coefficient was determinedfor the glass balls. To obtain detailed information about the interparticle interactions in a shaker, a simplified model for collision between particles of a granular material was proposed. In order to simulate the flow of surrounding gas, a formulation of the equations for fluid flow in a porous medium including particle forces was proposed. These equations are solved with Large Eddy Simulation (LES) technique using a subgrid-model originally proposed for compressible turbulent flows. For a pentagonal prism-shaped container under vertical vibrations, the results show that oscillon type structures were formed. Oscillons are highly localized particle-like excitations of the granular layer. This self-sustaining state was named by analogy with its closest large-scale analogy, the soliton, which was first documented by J.S. Russell in 1834. The results which has been reportedbyBordbar and Zamankhan(2005b)also show that slightly revised fluctuation-dissipation theorem might apply to shaken sand, which appears to be asystem far from equilibrium and could exhibit strong spatial and temporal variations in quantities such as density and local particle velocity. In this light, hydrodynamic type continuum equations were presented for describing the deformation and flow of dense gas-particle mixtures. The constitutive equation used for the stress tensor provides an effective viscosity with a liquid-like character at low shear rates and a gaseous-like behavior at high shear rates. The numerical solutions were obtained for the aforementioned hydrodynamic equations for predicting the flow dynamics ofdense mixture of gas and particles in vertical cylindrical containers. For a heptagonal prism shaped container under vertical vibrations, the model results were found to predict bubbling behavior analogous to those observed experimentally. This bubbling behavior may be explained by the unusual gas pressure distribution found in the bed. In addition, oscillon type structures were found to be formed using a vertically vibrated, pentagonal prism shaped container in agreement with computer simulation results. These observations suggest that the pressure distribution plays a key rolein deformation and flow of dense mixtures of gas and particles under vertical vibrations. The present models provide greater insight toward the explanation of poorly understood hydrodynamic phenomena in the field of granular flows and dense gas-particle mixtures. The models can be generalized to investigate the granular material-container wall interactions which would be an issue of high interests in the industrial applications. By following this approach ideal processing conditions and powder transport can be created in industrial systems.

Pneumatic Conveying of Granular Materials in a Pilot Scale Downer-Riser System

Studies regarding the field of this work aim to substitute industrial mechanical conveyors with pneumatic conveyors to overcome the disadvantages in solids flow regulation and risks posed to production and health. The experimental part of this work examines how the granular material properties, fluidizing airflow rate, equipment geometry, and pressures along the pipes affect the mass flow rate through the system. The results are compared with those obtained from previous experiments conducted with alumina. Experiments were carried out with a pilot scale downer-riser system at Outotec Research Center Frankfurt. Granular materi-als used in this work are named as sand, ilmenite, iron ore 1 and iron ore 2.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

Aggregation and caking processes of granular materials:continuum model and simulation with application to sugar

Aggregation and caking of particles are common severe problems in many operations and processing of granular materials, where granulated sugar is an important example. Prevention of aggregation and caking of granular materials requires a good understanding of moisture migration and caking mechanisms. In this paper, the modeling of solid bridge formation between particles is introduced, based on moisture migration of atmospheric moisture into containers packed with granular materials through vapor evaporation and condensation. A model for the caking process is then developed, based on the growth of liquid bridges (during condensation), and their hardening and subsequent creation of solid bridges (during evaporation). The predicted caking strengths agree well with some available experimental data on granulated sugar under storage conditions.

Shear Strength of Granular Materials, 1967

A theory was developed to allow the separate determination of the effects of the interparticle friction and interlocking of particles on the shearing resistance and deformational behavior of granular materials. The derived parameter, angle of solid friction, is independent of the type of shear test, stress history, porosity and the level of confining pressure, and depends solely upon the nature of the particle surface. The theory was tested against published data concerning the performance of plane strain, triaxial compression and extension tests on cohesionless soils. The theory also was applied to isotropically consolidated undrained triaxial tests on three crushed limestones prepared by the authors using vibratory compaction. The authors concluded that, (1) the theory allowed the determination of solid friction between particles which was found to depend solely on the nature of the particle surface, (2) the separation of frictional and volume change components of shear strength of granular materials qualitatively corroborated the postulated mechanism of deformation (sliding and rolling of groups of particles over other similar groups with resulting dilatancy of specimen), (3) the influence of void ratio, gradation confining pressure, stress history and type of shear test on shear strength is reflected in values of the omega parameter, and (4) calculation of the coefficient of solid friction allows the establishment of the lower limit of the shear strength of a granular material.

Behavior of Granular Materials Under Triaxial Compression with Pulsating Deviator Stress, HR-131, Special Report

Behavior of granular material subjected to repeated load triaxial compression tests is characterized by a model based on rate process theory. Starting with the Arrhenius equation from chemical kinetics, the relationship of temperature, shear stress, normal stress and volume change to deformation rate is developed. The proposed model equation includes these factors as a product of exponential terms. An empirical relationship between deformation and the cube root of the number of stress applications at constant temperature and normal stress is combined with the rate equation to yield an integrated relationship of temperature, deviator stress, confining pressure and number of deviator stress applications to axial strain. The experimental program consists of 64 repeated load triaxial compression tests, 52 on untreated crushed stone and 12 on the same crushed stone material treated with 4% asphalt cement. Results were analyzed with multiple linear regression techniques and show substantial agreement with the model equations. Experimental results fit the rate equation somewhat better than the integrated equation when all variable quantities are considered. The coefficient of shear temperature gives the activation enthalpy, which is about 4.7 kilocalories/mole for untreated material and 39.4 kilocalories/mole for asphalt-treated material. This indicates the activation enthalpy is about that of the pore fluid. The proportionality coefficient of deviator stress may be used to measure flow unit volume. The volumes thus determined for untreated and asphalt-treated material are not substantially different. This may be coincidental since comparison with flow unit volumes reported by others indicates flow unit volume is related to gradation of untreated material. The flow unit volume of asphalt-treated material may relate to asphalt cement content. The proposed model equations provide a more rational basis for further studies of factors affecting deformation of granular materials under stress similar to that in pavement subjected to transient traffic loads.

Micromechanical insight into the undrained instability of granular materials: deformation characteristics of geomaterials.

There is no agreement between experimental researchers whether the point where a granular material responds with a large change of stresses, strains or excess pore water pressure given a prescribed small input of some of the same variables defines a straight line or a curve in the stress space. This line, known as the instability line, may also vary in shape and position if the onset of instability is measured from drained or undrained triaxial tests. Failure of granular materials, which might be preceded by the onset of instability, is a subject that the geotechnical engineers have to deal with in the daily practice, and generally speaking it is associated to different phenomena observed not only in laboratory tests but also in the field. Examples of this are the liquefaction of loose sands subjected to undrained loading conditions and the diffuse instability under drained loading conditions. This research presents results of DEM simulations of undrained triaxial tests with the aim of studying the influence of stress history and relative density on the onset of instability in granular materials. Micro-mechanical analysis including the evolution of coordination numbers and fabric tensors is performed aiming to gain further insight on the particle-scale interactions that underlie the occurrence of this instability. In addition to provide a greater understanding, the results presented here may be useful as input for macro-scale constitutive models that enable the prediction of the onset of instability in boundary value problems.

Exploring the effects of stress history on the drained and undrained cyclic behaviour of granular materials.

This paper presents the results of 3D DEM simulations of granular materials subject to cyclic loading. While both the drained and undrained conditions are considered, the effects of depositional history and consolidation stress history on the stress-strain response are specifically evaluated. It is demonstrated that the different stress histories have a significant effect on soil response and that such effects can be attributed to differences in the initial particle arrangement (fabric).