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at the particle level, the shear strength parameters are greatly affected, and an isotropic failure criterion is no longer valid.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.     

DEM investigations of failure mode of sands under oedometric loading

It will be practically useful to explore the evolutions of the failure modes of sand grains within a sand specimen subject to compression for the particle breakage research. This paper attempts to deal with this challenge by conducting a discrete element method (DEM) simulation study on oedometric compression of two kinds of sands (spherical and non-spherical particles). In this study, particle morphologies reconstructed by the spherical harmonic (SH) analysis were created using the agglomerate method, and the micro-parameters used to define the contact model and the properties of walls and balls were adopted based on the single particle crushing tests. The effects of particle shape on the crushing behavior of granular materials and on the evolutions of failure modes of sand grains were captured, and the experimental data was used to evaluate the feasibility and reliability of the proposed DEM modelling strategy. The simulation results show that particle shape affects not only the number, type and orientation of cracks but also the evolution of the particle failure modes. The failure mode of chipping is the most common way to crush for both spherical and non-spherical particles. The particles that have less aspect ratio, sphericity and convexity are more likely to experience the failure mode of comminution. These findings shed light on the key role of particle shape in the investigation of the failure mode of sand grains and facilitate a better understanding of grain-scale behavior of granular materials.     

Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method

This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.     

Freestanding loadbearing structures with Z-shaped particles

Architectural structures such as masonry walls or columns exhibit a slender verticality, in contrast to the squat, sloped forms obtained with typical unconfined granular materials. Here we demonstrate the ability to create freestanding, weight-bearing, similarly slender and vertical structures by the simple pouring of suitably shaped dry particles into a mold that is subsequently removed. Combining experiments and simulations we explore a family of particle types that can entangle through their non-convex, hooked shape. We show that Z-shaped particles produce granular aggregates which can either be fluid and pourable, or solid and rigid enough to maintain vertical interfaces and build freestanding columns of large aspect ratio (\(>\)10) that support compressive loads without external confinement. We investigate the stability of such columns with uniaxial compression, bending, and vibration tests and compare with other particle types including U-shaped particles and rods. We find a pronounced anisotropy in the internal stress propagation together with strong strain-stiffening, which stabilizes rather than destabilizes the structures under load.     

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.     

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.     

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.     

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.     

Numerical investigation of particle shape on mechanical behaviour of unsaturated granular soils using elliptical particles

The unsaturated soils mechanic is of significant importance for understanding and predicting the actual behavior of unsaturated soils in plenty of geo-environmental condition including tailing dams and earth dams during construction and operation, soil slopes, and shallow foundations. In this research, a micromechanical model for unsaturated assemblies composed of elliptical particles is presented so that the effect of capillary force, confining stress, and particle shape on unsaturated granular media behavior is analyzed in the pendular regime. As one of the early attempts, the toroidal liquid bridge for elliptical particles is studied in granular assemblies using modified ELLIPSE program, Discrete Element Method based program. The results show that although the strength of spherical particles grows when the saturated degree increases, the strength of elliptical particles rises and then decreases; however, the friction angle remains almost constant. Furthermore, the highest percentage of apparent-cohesion rise takes place at saturation degree of 10% at the highest eccentricity. As long as the eccentricity increases, the effect of capillary force on shear strength grows continuously. Not only do unsaturated assemblies contract more at low strains, but also they expand more after the phase transfer point at high stains. The assembly composed of particles with eccentricity of 0.15 has the highest coordination number. The coordination number constantly increases with the saturation degree for circular particles. In contrast, for elliptical particles assemblies, when degree of saturation increases, the coordination number increases at the beginning then drops.     

Analysis of internal state and strains in granular material at meso-scale: influence of particle shape

Using Non Smooth Contact Dynamic formalism to conduct contact dynamics simulations, we investigate the internal state and deformation of two granular numerical materials composed of poly-sized circular and polygonal rigid particles. The 2D granular specimens are subjected to classical biaxial loading. The main goal of this study is to generalize the results previously obtained for assemblies of disks (Nguyen et al. in Int J Solids Struct 46:3257–3271, 2009). Since the spherical geometry of this type of grain leads to overestimating the role of rotations and facilitates deformation, we want to evaluate incremental response by using circular and angular particles Furthermore, as rigid contacts are modeled, the simulations considered allow accurate information on irreversible strains to be obtained. These samples are analyzed at a meso scale composed of closed loops of particles in contact. The texture at the meso level is characterized by parameters such as local density and the shape and orientation of the meso domains. Six types of meso domain, called six phases, are defined to perform a thorough analysis at this level. It is shown that throughout compression tests the phases composed of meso domains oriented in the compression direction increase, leading to greater anisotropy in the direction of compression. All these evolutions were more marked for the material containing polygonal particles. Based on an analysis proposed in a previous paper (Cambou et al. in Euro J Mech A Solids 19:999–1014, 2000), the incremental strain at meso scale is defined, whatever the particle shapes. The local strain tensor in the six phases is analyzed throughout the loading. The phases of meso domains oriented in the compression direction present more rigid behavior and greater dilatancy.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

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).     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

Effect of particle shape on domino wave propagation: a perspective from 3D,anisotropic discrete element simulations

A fundamental understanding of the underlying physics of granular systems is not only of academic interest, but is also relevant for industrial applications. One specific aspect that is currently only poorly understood is the effect of particle shape on the dynamics of such systems. In this work the effect of particle shape on domino wave propagation was studied using 3D, anisotropic discrete element simulations. The dominoes were modelled using the three-dimensional super-quadric equation and very good agreement between the intrinsic collision speeds predicted by the simulations and the corresponding experimental data was observed. Furthermore, the influence of particle blockiness on the collision dynamics of dominoes was investigated numerically using particle shapes ranging from ellipsoids to almost cuboid particles. It was found that the intrinsic collision speed increased with increasing particle blockiness. It was also shown that a higher initial contact point favours the transmission of kinetic energy in the direction of the wave propagation, leading to a higher intrinsic collision speed for dominoes of higher blockiness.     

An efficient algorithm for granular dynamics simulations with complex-shaped objects

One of the most difficult aspect of the realistic modeling of granular materials is how to capture the real shape of the particles. Here we present a method to simulate two-dimensional granular materials with complex-shaped particles. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well defined interaction force between these bodies is derived. The algorithm for identification of neighbor particles reduces force calculations to O(N), where N is the number of particles. The method is much more efficient, accurate and easier to implement than other models. We prove that the algorithm is consistent with energy conservation, which is numerically verified using non-dissipative granular dynamics simulations. Biaxial test simulations on dissipative granular systems demonstrate the relevance of shape in the strength and stress fluctuations at the critical state.     

Investigation on tectonically deformed coal particle crushing by DEM under triaxial loading: Implication for coal and gas outburst

Tectonically deformed coal is composed of loosely bonded and brittle particles. The effect of particle crushing on tectonically deformed coal was studied through triaxial loading tests using the discrete element method. Coal particles are highly sensitive to crushing under confining pressure. When confined pressure at 2.5 MPa, the sample behaves similarly to an uncrushed sample. The majority of boundary work is consumed by particle friction and crushing during loading. The porosity increases obviously, the granular system is transferred into fluid-like state. With an increase in confining pressure, particle crushing intensifies, resulting in a growth in weak force chains and crushing energy, and a decrease in porosity. The pattern of particle crushing is closely linked to specific force chains. Particle rotation is a significant factor affecting particle crushing, and it hinders the connection of shear zones. Crushed particles decrease porosity by filling the gaps between larger particles. After compaction, crushed particles form a crushing and compaction belt, which creates local gas sealing conditions and makes gas extraction difficult in tectonically deformed coal areas. These characteristics play a crucial role in understanding how in-situ stress impacts gas outbursts and the difficulty of gas extraction.     

DEM of triaxial tests on crushable sand

This paper presents simulations of high-pressure triaxial shear tests on a crushable sand. The discrete element method is used, featuring a large number of particles and avoiding the use of agglomerates. The triaxial model features a flexible membrane, therefore allowing realistic deformation, and a simple breakage mechanism is implemented using the octahedral shear stress induced in the particles. The simulations show that particle crushing is essential to replicate the realistic behaviour of sand (in particular the volumetric contraction) in high-pressure shear tests. The general effects of crushing during shear are explored, including its effects on critical states, and the influence of particle strength and confining pressure on the degree of crushing are discussed.