Interface roughness effect on slow cyclic annular shear of granular materials

We experimentally investigate the mechanical behaviour in cyclic shear of a granular material near a solid wall in a pressure controlled annular shear cell. The use of a model system (glass beads and saw-tooth shaped solid surface) enables the study of the influence of the wall roughness. After an initial shakedown procedure ensuring reproducible results in subsequent tests, wall shear stress S, volumetric variation ΔV, and the displacement field of the sample bottom surface, are recorded as functions of wall displacement. A dimensionless roughness parameter R _n is shown to control the interface response. The local grain-level or mesoscale behaviour is directly correlated to the global one on the scale of the whole sample.     

DEM modeling of shear bands in crushable and irregularly shaped granular materials

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.     

Study of the shear behavior of binary granular materials by DEM simulations and experimental triaxial tests

This paper aims at studying the shear behavior of mixtures of fine and coarse particles by classical triaxial tests. The work is performed both on experimental tests and computer simulations by discrete element method. The comparisons between experimental and simulation results on monosized and binary samples show that the DEM model can reproduce deviatoric curves satisfactorily in experimental conditions. The shear behavior of monosized and binary systems with the same initial void ratio differs significantly, suggesting that the state of compaction of the system is more influential than the initial void ratio. Comparison between compacted and uncompacted samples confirms that compaction increases the shear strength of granular matter. At the particle scale, the coordination number decreases with the augmentation of the volume fraction of coarse particles. The average rotation velocity of fine particles is higher than coarse particles, but their particle stress tensor is smaller than coarse ones.     

An entropy model for shear deformation of granular materials

A statistical mechanical analogy for characterization of granular materials is discussed by using such notions as the state of the material, the density of states, entropy, canonical distribution and the partition function. The transition law of states during shear deformations of the material is microscopically investigated in the case of two-dimensional model granular materials. The assumption of entropy growth is shown to characterize the dilatancy of the material. A rough proof is given by assuming the measure preserving property of the transition and showing its ergodicity.     

Study of shear behavior of granular materials by 3D DEM simulation of the triaxial test in the membrane boundary condition

This paper studies the shear behavior of granular materials by using a three-dimensional (3D) discrete element method (DEM) simulation of the triaxial test. The experimental triaxial tests were conducted on glass beads samples for verification. DEM simulations of the triaxial test were carried out in the membrane boundary condition consisting of 37,989 membrane particles. A new method that divides the irregular sample shape into two parts of cones and parts of three-dimensional simplexes is used to follow the volume change of irregular deformation of samples. The free rotatable upper platen is considered during the shearing process, which influences the shear behavior of samples especially in the residual stage and formations of a single shear band or X-shape shear band. The confining pressures have been demonstrated to influence the rotation angle and angular velocity of the upper platen. Moreover, the timing of replacing a rigid wall boundary condition with the membrane boundary condition is investigated, which affects the porosity of samples before shearing and the mechanical strength. The DEM model in the membrane boundary condition reflects well the evolution of irregular sample deformation and shear band in the shearing process. From the perspective of micro structures, the normal force decreases and the tangential stress increases during the shearing stage. This study greatly improves the accuracy of DEM simulations of the triaxial test in the membrane boundary condition.     

DEM analysis of the size effects on the behavior of crushable granular materials

Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.     

DEM simulation on the one-dimensional compression behavior of various shaped crushable granular materials

In order to investigate the effects of particle shape on the compression behavior of granular materials, a series of simulations was conducted using a two-dimensional discrete element method employing moment springs. Fracturable granular assemblies were constructed from particles of the same shape and size. The range of possible particle shapes includes disk, ellipse and hexagon, with different aspect ratios. Simulations of single particle crushing tests on elliptical particles showed that crushing could be classified into three types: cleavage destruction, bending fracture and edge abrasion, depending on the manner of compression. A series of simulations of one-dimensional compression tests was then conducted on six types of crushable particle assemblies; the three types of crushing mentioned above were also observed, but their rates of occurrence depended on the particle shape. Cleavage destruction was mainly observed with circular and elliptical particles; bending fracture was observed only with elongated particles; edge abrasion was frequently observed with angular particles. Despite the difference in crushing type, all samples, when subjected to intense compression, converged to a critical grading with unique void ratio, grain size distribution and aspect ratio, with a similar distribution of number of contact points.     

Influence of relative density on granular materials behavior: DEM simulations of triaxial tests

The rheological behavior of non-cohesive soils results from the arrangement and complex geometry of the grains. Numerical models based on discrete element modeling provides an opportunity to understand these phenomena while considering the discrete elements with a similar shape to that of the grains the soil is composed of. However, dealing with realistic shapes would lead to a prohibitive calculation cost. In a macroscopic modeling approach, simplification of the discrete elements’ shape can be done as long as the model can predict experimental results. Since the intrinsic non-convex geometry property of real grains seems to play a major role on the response of the granular medium, it is thus possible to keep this geometrical feature by using cluster of spherical discrete elements, which has the advantage to reduce dramatically the computation cost. Since the porosities found experimentally could not always be obtained with the numerical model—owing to the huge difference in shape, the notion of relative density, which requires a search for minimum and maximum porosities for the model, was chosen to compare the experimental and numerical results. Comparing the numerical simulations with the experimental triaxial tests conducted with relative densities and different confining pressures shows that the model is able to predict the experimental results.     

DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials

The importance of particle rotation to the mechanical behavior of granular materials subject to quasi-static shearing has been well recognized in the literature. Although the physical source of the resistance to particle rotation is known to lie in the particle surface topography, it has been conveniently studied using the rolling resistance model installed typically on spherical particles within the DEM community. However, there has been little effort on assessing the capability of the rolling resistance model to produce more realistic particle rotation behavior as exhibited by irregular-shaped particles. This paper aims to eliminate this deficiency by making a comprehensive comparison study on the micromechanical behavior of assemblies of irregular-shaped particles and spherical particles installed with the rolling resistance model. A variety of DEM analysis techniques have been applied to elucidate the full picture of micromechanical processes occurring in the two types of granular materials with different particle-level anti-rotation mechanisms. Simulation results show that the conventional rheology-type rolling resistance models cannot reproduce the particle rotation and strain localization behavior as displayed by irregular-shaped materials, although they demonstrate clear effects on the macroscopic strength and dilatancy behavior, as have been adequately documented in the literature. More insights into the effects of particle-level anti-rotation mechanism are gained from an in-depth inter-particle energy dissipation analysis.     

Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations

This paper presents the results of numerical simulations using the three-dimensional discrete element method (DEM) on the critical state behaviour of isotropically compressed and rebounded assemblies of granular materials. Drained and undrained (constant volume) numerical simulations were carried out. From these numerical simulations of drained and undrained tests, it has been shown that the steady state is same as the critical state. Critical state for both isotropically compressed and rebounded assemblies form unique curved line that can be approximated by a bilinear line as proposed by Been et al. [Géotechnique 41(3): 365–381, 1991]. Further more, evolution of the internal variables such as average coordination number and induced anisotropy coefficients during shear deformation has been studied.     

Effect of particle size and boundary conditions on the shear stress in an annular shear cell

The effect of particle size and boundary geometry in granular shear flows is investigated. The measured shear stress of glass spheres in an annular shear cell experiment is reported. In order to explore the particle size effect, the experiments are run using four different particle diameters, d = 2, 3, 4, and 5 mm. It is found that the shear stress follows the Bagnold scaling with respect to the apparent shear rate, but deviates from it with respect to particle size. For high solids concentration the results deviate qualitatively from the kinetic theory for bounded granular shear flows, where the non-dimensional shear stress measured with large particles exceeds that measured for small particles by as much as one order of magnitude. The effect of the boundary geometry is explored by using three different boundary types; type 1 employs aluminum radial half-cylinders, type 2 employs aluminum hemispheres arranged in a polar hexagonal closed packed configuration, and type 3 employs sandpaper. It is shown that the geometry of the boundary has an insignificant effect on dilute flows of small particles. For denser flows and/or larger particles the difference is evident. The sandpaper boundary, which is different from the aluminum ones both in geometry and in its material properties, yields the lowest stress. These results imply that in granular materials-structure interaction, the structure’s properties are just as important as the properties of the granular material. Their interaction may also depend on the relative size between the structure and the grain size.     

Velocity fields of granular flows down a rough incline: a DEM investigation

This paper describes a statistical method to explore the velocity profiles of granular flows down rough inclines. Using 3D Discrete Element Method (DEM), granular material is released from a box onto a slope and allowed to flow indefinitely. Fluctuating velocity fields are observed, as particle motions become more dynamic and agitated. Linear regression is used to decompose the fluctuating velocity field into a best-fit velocity profile and a fluctuating component. Analysis shows that the slope inclination has a considerable influence on the rheology, in terms of both the fluctuating velocity and the shear rate of the flow.     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

Selection of material for X-ray tomography analysis and DEM simulations: comparison between granular materials of biological and non-biological origins

Granular Matter - Field observations were carried out in Qingtu Lake observation array on the vertical electric field $$(E_{z})$$ , where the average spatial resolution can reach 1 m. Our...     

Forces in piles of granular material: an analytic and 3D DEM study

We investigate the stress distribution at the base of a conical sandpile using both analytic calculations and a three dimensional discrete element code. In particular, we study how a minimum in the normal stress can occur under the highest part of the sandpile. It is found that piles composed of particles with the same size do not show a minimum in the normal stress. A stress minimum is only observed when the piles are composed of particles with different sizes, where the particles are size segregated in an ordered, symmetric, circular fashion, around the central axis of the sandpile. If a pile is composed of particles with different sizes, where the particles are randomly distributed throughout the pile, then no stress dip is observed. These results suggest that the stress dip is due to ordered, force contacts between equiheight particles which direct stress to the outer parts of the pile. Received: 14 June 2000     

A fast first order model of a rough annular shear cell using cellular automata

The motivation of the current work is to simulate granular phenomena in a rough annular shear cell without load using a physics-based cellular automata (CA) modeling approach. A simple yet powerful two-dimensional (2D) cellular automata model was developed to model granular flows inside a 2D annular shear cell from a tribological perspective. Physics-based equations developed from first-principles to model collisions have been adopted to form the cellular automata local rules of interaction. This combines the computational efficiency of CA modeling with the accuracy and generalization of first-principle physics modeling. The local flow properties—solid fraction, velocity and granular temperature profiles- were predicted from the CA simulation and compared to the granular shear cell experiments. The resulting steady-state CA model profiles show good agreement with the experimental results. The ability of the CA model to probe the effect of each granular flow property is demonstrated by performing parametric studies of the particle–particle coefficient of restitution and roughness factor.