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).     

A stochastic multiscale algorithm for modeling complex granular materials

Modeling of granular materials in which the grains have irregular shapes and surface is a long-standing problem that has been studied for decades. Almost all the current models either represent the grains as particles with geometrically-regular shapes or attempt to infer some low-order statistical properties of the materials in order to describe granular media. We use an approach to modeling of granular materials that utilizes a two- or three-dimensional image of the material’s morphology. It reconstructs realizations of the image based on a Markov process, and uses a multiscale approach and graph-theoretical concepts to refine the realizations and make them free of artefacts. The method is applied to several complex 2D and 3D examples of granular materials. Various morphological properties of the models are computed and are compared with those of the original images; very good agreement is found for all the cases. Furthermore, the computational cost of the method is very low and, therefore, the method can generate large-size models for complex granular materials.     

A nonlocal multiscale discrete‐continuum model for predicting mechanical behavior of granular materials

A three‐dimensional nonlocal multiscale discrete‐continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information‐passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete‐continuum coupling method retains the simplicity and efficiency of a continuum‐based finite element model, while circumventing mesh pathology in the post‐bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure‐sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single‐scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

A heterarchical multiscale model for granular materials with evolving grainsize distribution

Naturally occurring granular flows, such as landslides, debris flows and avalanches typically have size ratios of up to \(10^{6}\) between the smallest and largest constituent particles. For the purposes of modelling, however, it is generally assumed that a single representative size can adequately describe the grains. Polydisperse flows are not described more completely primarily because of two reasons: The first is a lack of understanding of the physical mechanisms which affect polydisperse flows. The second is a lack of models with which to describe such systems. Here, we present a heterarchical multiscale model which accounts for both the microstructural evolution within representative elementary volumes, and also the associated changes in bulk flow properties. Three key mechanisms are addressed; segregation, comminution and mixing. Granular segregation is an important mechanism for industrial processes aiming at mixing grains. Additionally, it plays a pivotal role in determining the kinematics of geophysical flows. Because of segregation, the grainsize distribution in a granular medium varies in space and time during flow. Additional complications arise from the presence of comminution, where new particles are created, potentially enhancing segregation. This has a feedback on the comminution process, as particles change their local neighbourhood. Simultaneously, particles are generally undergoing remixing, further complicating the segregation and comminution processes. The interaction between these mechanisms is explored using a stochastic lattice model with three rules: one for each of segregation, comminution and mixing. The interplay between these rules creates complex patterns, as seen in segregating systems, and depth dependent log-normal grading curves, which have been observed in avalanche runout.     

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.     

Instability of steady shear flow of granular materials

Summary We consider simple shearing flow of a granular material in which the stress is governed by the Coulomb-Mohr yield condition, and which deforms according to the double-shearing model of granular material behaviour for incompressible material. We also investigate deformations of a dilatant material in which this shearing deformation is accompanied by an expansion in the direction normal to the shear plane, in this case using the dilatant double-shearing model proposed by Mehrabadi and Cowin. In both cases it is found that in addition to the expected steady stress solution, the equations admit time-dependent stress solutions. For suitable initial conditions these solutions satisfy the positive energy dissipation requirements up to some finite shear. In the unsteady solutions the rotation of the principal stress axes is always away from the steady solution, and in no case is the steady solution approached as a limit of the unsteady solution; this indicates that the steady flow solutions are unstable.With 2 Figures     

The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials

The behavior of granular materials is very complex in nature and depends on particle shape, stress path, fabric, density, particle size distribution, amongst others. This paper presents a study of the effect of particle geometry (aspect ratio) on the mechanical behaviour of granular materials using the discrete element method (DEM). This study discusses 3D DEM simulations of conventional triaxial and true triaxial tests. The numerical experiments employ samples with different particle aspect ratios and a unique particle size distribution (PSD). Test results show that both particle aspect ratio (AR) and intermediate stress ratio \((b=({\upsigma }_{2}'-{\upsigma }_{3}')/({\upsigma }_{1}'-{\upsigma }_{3}'))\) affect the macro- and micro-scale responses. At the macro-scale, the shear strength decreases with an increase in both aspect ratio and intermediate stress ratio b values. At the micro-scale level, the fabric evolution is also affected by both AR and b. The results from DEM analyses qualitatively agree with available experimental data. The critical state behaviour and failure states are also discussed. It is observed that the position of the critical state loci in the compression \((e-p')\) space is only slightly affected by aspect ratio (AR) while the critical stress ratio is dependent on both AR and b. It is also demonstrated that the influence of the aspect ratio and the intermediate stress can be captured by micro-scale fabric evolutions that can be well understood within the framework of existing critical state theories. It is also found that for a given stress path, a unique critical state fabric norm is dependent on the particle shape but is independent of critical state void ratio.     

A method for investigating the strength characteristics of sheet materials under impulse loading

We propose a method for the determination of the strength characteristics of metallic and nonmetallic materials under conditions of repeated impulse loading. By using this method, one can apply impulse loading to the tested objects both directly from an inductor and by hydroimpact, i.e., transferring impact pulses via a contact liquid. The method of electric pulses used as a basis of the suggested method of loading enables us to realize gradual control over the power of pulses and the frequency of their repetition.     

A method for investigating the strength characteristics of sheet materials under impulse loading

We propose a method for the determination of the strength characteristics of metallic and nonmetallic materials under conditions of repeated impulse loading. By using this method, one can apply impulse loading to the tested objects both directly from an inductor and by hydroimpact, i.e., transferring impact pulses via a contact liquid. The method of electric pulses used as a basis of the suggested method of loading enables us to realize gradual control over the power of pulses and the frequency of their repetition. Translated from Problemy Prochnosti, No. 5, pp. 122–125, September–October, 1997.     

A novel approach to examining double-shearing type models for granular materials

A novel method, designated as the Rotation of Principal Axes Method (RPAM), capable of examining the double-shearing type kinematic models for granular materials is presented herein. A planar velocity field, which is proposed to represent a continuous rotation of principal strain rate axes, is applied to each model to analyse the rotation of principal stress axes. The proposed approach was proven to show main features of the double-shearing model, the double-sliding free-rotating model, and the revised double-shearing model, in a simple way interesting to geo-researchers. Furthermore, the RPAM was efficient in investigating the choice of a Cosserat rotation rate in kinematic theories and determining a key model parameter in the revised double-shearing model.     

FE-investigation of shear localization in granular bodies under high shear rate

Shear localization in granular materials under high shear rate is analysed with the finite element method and a micro-polar hypoplastic constitutive model enhanced by viscous terms. We consider plane strain shearing of an infinitely long and narrow granular strip of initially dense sand between two very rough walls under conditions of free dilatancy. The constitutive model can reproduce the essential features of granular materials during shear localization. The calculations are performed under quasi-static and dynamic conditions with different shear rates. In dynamic regime, the viscosity terms are formulated based on a modified Newtonian fluid and according to the formula by Stadler and Buggisch (Proceedings of the conference on Reliable flow of particulate solids, EFCE Pub. Series, vol 49. Chr. Michelsen Institute, Bergen, 1985). Emphasis is given to the influence of inertial and viscous forces on the shear zone thickness and mobilized wall friction angle.     

Discrete element analysis for shear band modes of granular materials in triaxial tests

The discrete element method (DEM) is adopted to simulate the triaxial tests of granular materials in this study. In the DEM simulations, two different membrane-forming methods are used to generate triaxial samples. One method is to pack the internal particles first, then to generate the enclosed membrane; the other is to generate the internal particles and the enclosed membrane together. A definition of the effective strain, which combines microscopic numerical results with macroscopic expression in three-dimensional space, is presented to describe the macroscopic deformation process of granular materials. With these two membrane generation methods, the effective strain distributions in longitudinal section and transverse section of the triaxial sample are described to investigate the progressive failure and the evolution of the shear bands in granular materials. Two typical shear band failure modes in triaxial tests are observed in the DEM simulations with different membrane-forming methods. One is a single shear band like a scraper bowl, and the other is an axial symmetric shear band like two hoppers stacking as the shape of rotational “X” in triaxial sample. The characteristics of the shear bands during the failure processes are discussed in detail based on the DEM simulations.     

Heterogeneity and patterning in the quasi-static behavior of granular materials

Heterogeneity is classified in five categories– topologic, geometric, kinematic, static, and constitutive–and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments show that the topology and geometric fabric become more variable during loading. The measured fluctuations in inter-particle movements are large, they increase with loading, and they extend to distances of at least eight particle diameters. Deformation and rotation heterogeneity are large and are expressed in spatial patterning. Stress heterogeneity is moderate throughout loading.     

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 simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.     

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.     

Micromechanical behavior of granular materials with inherent anisotropy under cyclic loading using 2D DEM

This paper presents the micromechanical behavior of granular materials due to different initial inherent anisotropic conditions during cyclic loading using the discrete element method (DEM). Oval particles were used to model the samples. Three samples, with three different inherent anisotropic conditions based on the particle’s bedding direction, were prepared and subjected to biaxial cyclic loading. The differences in the inherent anisotropic conditions of the samples affect the stress–strain-dilative behavior of granular materials. The width of the stress–strain cyclic loops decreases as the preferred bedding angle changes from vertical to horizontal. Contact fabric evolution is found to be dependent on the inherent anisotropic fabric of the sample during loading and unloading. The fabric anisotropy is dominant for horizontal particle bedding at the end of loading and for vertical particle bedding at the end of unloading. A change in fabric anisotropy is observed only for the first few loading–unloading cycles for the given conditions depicted in the present study.