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 hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.     

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.     

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 study of the shear behavior and formation of shear band in biaxial test

This paper aims to study the shear behavior of granular matter by DEM simulations. Granular samples are prepared by automatic clump generation algorithm to create particles of irregular shapes. Simulations of the biaxial test with membrane boundary condition are used to test the shear behavior of samples. A new method for computing sample volume in membrane boundary condition is proposed. Deviatoric stress and volumetric strain curves are plotted to describe contracting-dilatancy of granular materials during the shearing stage. Formation of the shear band is studied from particle rotation and particle displacement fields. The influence of confining pressure, initial porosity, and friction coefficient on the development of shear band are studied. Lower confining pressure, higher initial porosity can be resulted in later formation of shear bands.     

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.     

Strength of non-spherical particles with anisotropic geometries under triaxial and shearing loading configurations

This paper presents a study on the macroscopic shear strength characteristics of granular assemblies with three- dimensional complex-shaped particles. Different assemblies are considered, with both isotropic and anisotropic particle geometries. The study is conducted using the discrete element method (DEM), with so-called sphero-polyhedral particles, and simulations of mechanical true triaxial tests for a range of Lode angles and confining pressures. The observed mathematical failure envelopes are investigated in the Haigh–Westergaard stress space, as well as on the deviatoric-mean pressure plane. It is verified that the DEM with non-spherical particles produces results that are qualitatively similar to experimental data and previous numerical results obtained with spherical elements. The simulations reproduce quite well the shear strength of assemblies of granular media, such as higher strength during compression than during extension. In contrast, by introducing anisotropy at the particle level, the shear strength parameters are greatly affected, and an isotropic failure criterion is no longer valid. It is observed that the strength of the anisotropic assembly depends on the direction of loading, as observed for real soils. Finally simulations on a virtual shearing test show how the velocity profile within the shear band is also affected by the grain’s shape.     

Micromechanical modelling of oval particulates subjected to bi-axial compression

One of the questions that still remain unanswered among researchers dealing with granular materials is how far the particle shape affects the micro-macroscopic features of granular assemblies under mechanical loading. The latest advances made with particle instrumentation allow us to capture realistic particle shapes and size distribution of powders to a fair degree of accuracy at different length scales. Industrial applications often require information on the micromechanical behaviour of granular assemblies having different particle shapes and varying surface characteristics, which still remains largely unanswered. Traditionally, simulations based on discrete element method (DEM) idealise the shape of individual particles as either circular or spherical. In the present investigation, we analyse the influence of particle shape on the shear deformation characteristics of two dimensional granular assemblies using DEM. We prepared the assemblies having nearly an identical initial packing fraction (dense), but with different basic shapes of the individual particles: (a) oval and (b) circular for comparison purposes. The granular assemblies were subjected to bi-axial compression test. We present the evolution of macroscopic strength parameters and microscopic structural/topological parameters during mechanical loading. We show that the micromechanical properties of granular systems are significantly influenced by the shape of the individual particles constituting the granular assemblies.     

The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data

Testing the mechanical response of coarse granular materials requires very large and expensive laboratory equipments. During the 1960s, pioneering experimental programs were carried out on several rockfill dam materials, and those results are still a reference for engineers and researchers. However, only few experimental works have been reported to this day, and due to the scarcity of empirical data, the role of the size effect caused by grain crushing is not well known. To improve understanding of this rarely studied issue and the influence of individual particle strength, this paper analyzes the size effect on rock aggregate crushing strength and its connection with the shear envelope of rockfills. The suitability of the 4-parameter Weibull equation to describe size effects on the crushing strength reported in the literature is discussed. Furthermore, a Weibull statistical analysis was carried out for a wide number of experimental results on rock aggregates, where it has been observed that strength decreases with particle size. In parallel, the results of large triaxial tests on homothetic scaled rockfill samples of 250 and 1,000 mm in diameter reveal that the coarser the material, the higher the amount of grain breakage and the lower the shear strength. The impact of size effects obtained from the experiments is analyzed and discussed in terms of the factor of safety of rockfill slope stability. Furthermore, the results are compared with the only existing theoretical method that links the rock aggregate with the strength of the granular assembly. Good agreement between the empirical results and this theoretical method has been confirmed.     

The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies

This paper presents an investigation into the effects of particle-size distribution on the critical state behavior of granular materials using discrete element method (DEM) simulations on both spherical and non-spherical particle assemblies. A series of triaxial test DEM simulations examine the influence of particle-size distribution (PSD) and particle shape, which were independently assessed in the analyses presented. Samples were composed of particles with varying shapes characterized by overall regularity (OR) and different PSDs. The samples were subjected to the axial compression through different loading schemes: constant volume, constant mean effective stress, and constant lateral stress. All samples were sheared to large strains to ensure that a critical state was reached. Both the macroscopic and microscopic behaviors in these tests are discussed here within the framework of the anisotropic critical state theory. It is shown that both OR and PSD may affect the response of the granular assemblies in terms of the stress–strain relations, dilatancy, and critical state behaviors. For a given PSD, both the shear strength and fabric norm decrease with an increase in OR. The critical state angle of shearing resistance is highly dependent on particle shape. In terms of PSD, uniformly distributed assemblies mobilize higher shear strength and experience more dilative responses than specimens with a greater variation of particle sizes. The position of the critical state line in the e–p′ space is also affected by PSD. However, the effects of PSD on critical strength and evolution of fabric are negligible. These findings highlight the importance of particle shape and PSD that should be included in the development of constitutive models for granular materials.     

Breakage of an artificial crushable material under loading

The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.     

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.     

Influence of pile shape and pile interaction on the crushable behavior of granular materials around driven piles: DEM analyses

This study presents an analysis and a visualization of the effect that the pile shape has on the penetration resistance of driven piles in crushable granular materials. Discrete Element Method (DEM) simulations of single piles with different shapes (flat tip, open pile, triangular tip) being driven into a previously compacted uniform crushable soil are presented. The results from the DEM simulations showed that the shape of the driven piles has a significant influence on the development of penetration resistance and particle crushing. This study also presents the penetration resistance and particle crushing results when a second flat tip pile was driven in a region near a pre-existing single flat tip pile. It was found that considerable high crushing was induced by the second pile. The second pile induced crushing not only on the particles surrounding itself but also on the particles surrounding the pre-existing pile, showing that particle crushing around a driven pile not only takes place when the pre-existing pile is being driven, but it also occurs during the installation of a second pile, in a region closely located to the first one.     

DEM simulation of shear vibrational fluidization of granular material

Fluidization of dry granular material is the transition from a solid state to a liquid state when sufficient energy is applied during vibration. This behavior is important because it is closely related to deformations of geotechnical structures during an earthquake. The scientific challenge lies in the understanding on how strain localization is related to the fluidization zone during the entire shearing process. Despite the importance of the mechanical behavior of granular material during fluidization, it cannot be easily characterized using traditional direct shear test. In this paper, 2D DEM model is firstly conduct, shear vibrational fluidization is defined for dry granular material, and the discrete element method has been used to simulate the direct shear test on granular material under vibrational loading during shearing. The peak, residual and vibro-residual shear strength envelopes have been obtained from the numerical simulations. Three distinct zones have been identified in the upper shear box based on the observed changes in volumetric strain before vibration. During vibration, fluidization occurs in the three zones with the characteristics that the shear stress, porosity, volumetric strain, and the coordination number drop to relatively lower values. During vibration, material becomes denser than the critical state, and strain localization has been relieved. Densification of the material at the shear zone leads to a strengthening of the material which increases the shearing resistance after vibration. Furthermore, a comparison of the 2D and 3D simulations is performed. Results reveal that the motion of particles in the out-of-plane direction in the 3D simulations lead to smoother shear stress and more consistent with the experimental result.     

Influence of particle elasticity in shear testers

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.     

Stress-chain based micromechanics of sand with grain shape effect

The mechanical behaviors of granular media are controlled by grain properties and microstructure. The primary property of granular media is denoted by its grain shape, grain size distribution, stiffness, and interparticle friction. The grain shape itself is of particular importance. Microstructures are formed in the connection paths of contact points between grains. In this paper, the deformation of granular materials with different grain shapes was simulated using two-dimensional DEM under different stress-levels and densities. After analyzing the results, the authors investigated fabric changes. The evolution rule of stress-induced anisotropy and its limitation as well as the existence of a critical state of fabric are revealed.     

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

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.     

Existence of a threshold for brittle grains crushing strength: two-versus three-parameter Weibull distribution fitting

Grain crushing plays an important role in the mechanical behavior of granular media, in chemo-hydro-thermo-mechanical couplings, in instabilities related to strain localization such as shear bands and compaction bands, in geophysical and geotechnical processes, in reservoir and petroleum engineering and in many other domains. The strength of brittle particles seems to be quite well described by a two-parameter Weibull distribution. Nevertheless, such a distribution predicts that failure is possible under any level of applied stress. On the contrary a three-parameter Weibull distribution contains a stress threshold under which grain failure is unlikely. Based on existing experiments on crushing of individual grains from various geomaterials and surrogate materials, and on new experiments performed on rock sugar particles, the present paper explores and compares the applicability of a two- versus a three parameter Weibull distribution. It is shown that in most of the cases the three-parameter Weibull distribution better describes the experimental results.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.