Macro deformation and micro structure of 3D granular assemblies subjected to rotation of principal stress axes

This paper presents a numerical investigation on the behavior of three dimensional granular materials during continuous rotation of principal stress axes using the discrete element method. A dense specimen has been prepared as a representative element using the deposition method and subjected to stress rotation at different deviatoric stress levels. Significant plastic deformation has been observed despite that the principal stresses are kept constant. This contradicts the classical plasticity theory, but is in agreement with previous laboratory observations on sand and glass beads. Typical deformation characteristics, including volume contraction, deformation non-coaxiality, have been successfully reproduced. After a larger number of rotational cycles, the sample approaches the ultimate state with constant void ratio and follows a periodic strain path. The internal structure anisotropy has been quantified in terms of the contact-based fabric tensor. Rotation of principal stress axes densifies the packing, and leads to the increase in coordination numbers. A cyclic rotation in material anisotropy has been observed. The larger the stress ratio, the structure becomes more anisotropic. A larger fabric trajectory suggests more significant structure re-organization when rotating and explains the occurrence of more significant strain rate. The trajectory of the contact-normal based fabric is not centered in the origin, due to the anisotropy in particle orientation generated during sample generation which is persistent throughout the shearing process. The sample sheared at a lower intermediate principal stress ratio \((b=0.0)\) has been observed to approach a smaller strain trajectory as compared to the case \(b=0.5\), consistent with a smaller fabric trajectory and less significant structural re-organisation. It also experiences less volume contraction with the out-of plane strain component being dilative.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

Manifestation of particle morphology on the mechanical behaviour of granular ensembles

This paper presents the effect of particle morphology (grain shape) on the mechanical response of granular materials. Two model systems with extreme differences in morphology were selected (spherical glass ballotini and angular sand) for this experimental programme. A series of hollow cylinder torsion tests were conducted in this programme under monotonic drained conditions on specimens reconstituted to the same relative density. Tests were conducted under different intermediate principal stress ratio (b) on both the model materials. The glass ballotini shows increased dilation at the outset of the test, however, at large strains, the particle rearrangement in the sand and the increased interlocking leads to higher strength at the critical state. The effect of individual particle morphology is manifested in both the increased friction angle and a larger sized failure locus in stress space with increase in angularity. The stresses developed in these two model materials are also accompanied by intriguing volume change behaviour. The glass ballotini despite a lower strength presents a predominantly dilative response immaterial of the ‘b’ value, while the angular sand shows increased strength at large strains, while showing a contractive response. These results allow incorporation of particle morphology effects at the ensemble level in plasticity based constitutive models.     

Study of powder flow patterns in a Couette cell with axial flow using tracers and solid fraction measurements

We present different aspects of dense granular flows in a Couette geometry using a variety of particulate materials with shape and size distributions. Tracer studies point to an apparent coupling of particle size with flow and stress field gradients. While there is a clear industrial motivation to use “real” materials as a means to expand basic physical and engineering research in granular dynamics, the current study suggests additional academic motivations. Indeed, particles with distributed characteristics uncover rich interactions between flow and stress fields that might otherwise go un-noticed with model materials such as spherical glass beads. Distribution of size and shape play a strong role in how stress is transmitted in granular media (Kheiripour Langroudi et al. in Powder Technol 203:23–32, 2010) and how particle pattern arrangements evolve. Direct solid fraction measurements, using a capacitance probe, show that dense particle flows exhibit significant variations in solid fraction in both sheared and stagnant layers. Furthermore, these measurements also show different dependence of the solid fraction on shearing rate: solid fraction decreases in sheared layers and increases in stagnant layers as the shear rate is increased. From these results the thickness of the shear band could be estimated and was found to vary as a function of particle shape and the roughness of the container walls. The main result is that shear stress (or torque) (see also Kheiripour Langroudi et al. in Powder Technol 197:91–101, 2010) and solid fraction profiles depend on particle shape and whether or not an extra degree of freedom in their movement is provided so that the system can dilate under various shear states in the Couette cell. This extra degree of freedom is assured in the present experimental work by allowing a slight axial outflow from the Couette device while the driven shear fields are in the radial and tangential directions.     

Development of micromechanical models for granular media

Micromechanical analysis has the potential to resolve many of the deficiencies of constitutive equations of granular continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to granular media is the projection scheme to relate continuum variables to particle-scale variables. Within the confines of a projection scheme that assumes affine motion, contact laws based on binary interactions do not fully capture important instabilities. Specifically, these contact laws do not consider mesoscale mechanics related to particle group behaviour such as force chains commonly seen in granular media. The implications of this are discussed in this paper by comparison of two micromechanical constitutive models to particle data observed in computer simulations using the discrete element method (DEM). The first model, in which relative deformations between isolated particle pairs are projected from continuum strain, fails to deliver the observed behaviour. The second model accounts for the contact mechanics at the mesoscale (i.e. particle group behaviour) and, accordingly, involves a nonaffine projection scheme. In contrast with the first, the second model is shown to display strain softening behaviour related to dilatancy and produce realistic shear bands in finite element simulations of a biaxial test. Importantly, the evolution of microscale variables is correctly replicated. This paper is dedicated to Professor Ching S. Chang on the occasion of his 60th birthday.     

Modeling of a cyclic plane strain compression-extension test in granular bodies within a polar hypoplasticity

In a recent paper, the effect of cyclic shearing on forced shear localization in an infinite granular strip between rough boundaries was numerically investigated. The present paper focuses on the evolution of spontaneous developed shear localization within an granular body under plane strain conditions, constant lateral pressure and cyclic vertical compression-extension. For a simulation of the mechanical behavior of a cohesionless granular material, a micro-polar hypoplastic constitutive is used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. For the calibration of the constitutive constants, the data of a medium quartz sand are used. The attention of numerical simulations is laid on the influence of the number of cycles, the magnitude of the vertical deformation amplitude and the initial density on the evolution of shear zones in an initially prismatic granular specimen.     

Origin of subcritical shear-banding instability in a dense two-dimensional sheared granular fluid

The granular plane Couette flow is known to be linearly unstable to shear-banding instability beyond a critical density, and our nonlinear analysis suggests that the nature of bifurcation (supercritical/subcritical) in dense flows depends strongly on the choice of the constitutive model. While the standard Enskog model for nearly elastic hard-disks predicts supercritical bifurcations for moderate to dense systems, a more realistic model with global equation of states for hard-disks (that are likely to hold for the whole range of densities) predicts a subcritical bifurcation in the dense limit. The latter prediction agrees with recent particle simulations of a sheared inelastic hard-disk system.     

Coupled effects of capillary suction and fabric on the strength of moist granular materials

This paper discusses the coupled effects of capillary suction and fabric on the behavior of partially saturated granular materials at pendular state when discrete liquid bridges form around particle contacts. Experimental results show that the soil–water characteristic curves of granular materials are affected by the internal structure formed during reconstitution of the specimen. The effect of capillary suction on the shear strength of moist sand varies with the direction of shearing relative to the bedding plane which is generally perpendicular to the major principal direction of the fabric tensor. When treating capillary attraction as interparticle forces at particle contacts, a micromechanics analysis shows that the coupling between capillary-attracting forces and fabric results in an additional stress tensor, which describes the anisotropic effect of capillary suction on the behavior of moist sand.     

FE Analysis of Contractant Shear Zones in Loose Granular Materials

The paper focuses on the formation of contractant shear zones in initially loose cohesionless granular materials subject usually to continuous densification. For a simulation of the mechanical behaviour of a granular material during monotonous deformation paths, a micro-polar hypoplastic constitutive model was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The FE investigations of shear localization were carried out with initially very loose quartz sand during four different rate boundary value problems: shearing of an infinite layer between two very rough walls, plane strain compression under constant lateral pressure, biaxial compression with rigid and deformable boundaries and passive earth pressure on a horizontally translating retaining wall. The calculations were carried out with a simple random distribution of the initial void ratio under conditions of large deformations and curvatures.     

Plane wave propagation in 2D and 3D monodisperse periodic granular media

Plane wave propagation in periodic ordered granular media comprising of elastic spherical particles is investigated. The spheres are under zero precompression and are assumed to interact via the Hertzian contact potential. Various two- and three-dimensional granular structures such as hexagonal packing (2D and 3D), face-centered cubic and body-centered cubic packings are considered in the present study, with the plane impact either normal or oblique to the granular system. For the normal impact case, 1D chains equivalent to the 2D and 3D structures are obtained. A universal relation between the wavefront speed and the force amplitude is derived, valid for all the granular structures studied. In the angular impact case, the shear component of the amplitude of the particle velocity is found to initially decay exponentially and further in a series of linear regimes. By employing simpler models, semi-analytical predictions are obtained for the decay of shearing effect.     

Avalanches in anisotropic sheared granular media

We study the influence of particle shape anisotropy on the occurrence of avalanches in sheared granular media. We use molecular dynamic simulations to calculate the relative movement of two tectonic plates. Our model considers irregular polygonal particles constituting the material within the shear zone. We find that the magnitude of the avalanches is approximately independent of particle shape and in good agreement with the Gutenberg–Richter law, but the aftershock sequences are strongly influenced by the particle anisotropy yielding variations on the exponent characterizing the empirical Omori’s law. Our findings enable one to identify the presence of anisotropic particles at the macro-mechanical level only by observing the avalanche sequences of real faults. In addition, we calculate the probability of occurrence of an avalanche for given values of stiffness or frictional strength and observe also a significant influence of the particle anisotropy.     

Macroscopic model with anisotropy based on micro–macro information

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.     

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.     

Stress-path dependency of resilient behaviour of granular materials

This paper describes an experimental study that was completed to investigate the resilient constitutive characteristics of a granular limestone, as well as to assess the applicability of conventional modelling within the framework of elasticity theory for the material that was studied. Test results corresponding to various stress paths are reported for a well-graded, sub-angular coarse sand. Noticeable differences are found with regard to the measured deformation responses when compared with those from linear elastic model predictions. On the basis of studying the stress–strain responses in terms of invariants, the authors conclude that the difference in the resilient responses of the material for various stress paths is largely due to the inherent nonlinear anisotropic nature of the material, and that stress-induced fabric associated with, for example, rearrangement of particles and particle connectivity should be taken into account for better interpretation of resilient behaviour of granular soil.     

等压固结条件下湘江饱和砂土动力特性研究

在大量的动三轴试验基础上,研究了等压固结条件下湘江饱和砂土振动孔隙水压力、应力应变滞回圈以及应力路径的发展变化规律。研究结果表明:孔压发展变化过程与土体的剪胀、剪缩密切相关;孔压与轴向动应变之间的变化关系显示饱和砂土具有明显的各向异性;从孔压与滞回圈面积累积之和的关系看,孔压的增长伴随着能量的损失;对于围压较大的情形,用ExpAssoc函数进行拟合效果较好。隧振次增加应力应变滞回圈也在发生变化,第一阶段滞回圈呈倒置的帽子形,第二阶段呈菱角形状。在振动初始阶段,应力路径基本上呈倾斜的直线变化;随孔压的增加,加载和卸载两条应力路径逐渐分开,呈纺锤形。     

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).     

FE-studies on Shear Localization in an Anistropic Micro-polar Hypoplastic Granular Material

The effect of transverse isotropy on shear localization in cohesionless granular materials is numerically investigated upon monotonous plane strain deformation paths using a hypoplastic constitutive model enhanced by micro-polar terms. In this model, a so-called density function is reformulated and made anisotropic. Dense sand specimens under constant lateral pressure are numerically tested for uniform and stochastic distributions of the initial void ratio and for two different mean grain diameters.     

Experimental Study on Shear Localisation in Granular Materials Within Combined Strain and Stress Field

Abstract: The characteristic features of the shear zones formation in deforming granular materials were investigated using particle image velocimetry (PIV), which was combined with a photo‐elastic study of the stress field. Laboratory tests were performed for an active translation of rigid retaining wall. PIV is an optical technique for measuring displacement fields from successive digital images and was employed to analyse experiments on two different granular materials, composed of (1) sand grains and (2) glass granules. The tests on glass granules were supplemented by taking photo‐elastic images in circularly polarised light to gather information on changes in the average stress field, accompanying the specimen deformation. Attention was focused on the effect of the initial density, grain coarseness and magnitude of wall displacement on shear localisation within a strain field and its geometrical relation to some structures found in the stress field.     

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.     

Measurement of Bulk Mechanical Properties and Modeling the Load Response of Rootzone Sands. Part 3: Effect of Organics and Moisture Content on Continuous Sand Mixtures

The interactions between organics and sand particles at different moisture contents are important in understanding the general mechanical behavior of rootzone sand mixtures. Towards this end, eight rootzone sand mixtures (4 shapes 2 2 moisture contents) used in golf green construction were tested using the cubical triaxial tester (CTT). These eight mixtures consist of sphagnum peat as the organic source and four sands of varying particle shape (round, subround, subangular, and angular). The sand-peat mixtures were tested at two moisture contents (air-dried and 30 cm tension). Of all the test samples, air-dried round sand with peat had the highest initial bulk density (IBD) value (1.49 g/cc), while moist angular sand with peat had the lowest IBD value (1.23 g/cc). These values influenced the compression behavior of samples, for example, the air-dried round sand with peat was least compressible while moist angular sand with peat was most compressible. Generally, moisture enhanced the compressibility of test specimens. At an isotropic pressure of 100 kPa, the volumetric strain value of moist round sand with peat was 47% higher than the volumetric strain value of the air-dried round sand with peat. Consequently, moisture and peat in bulk sand samples act as lubricants and assist in the compression process. In addition, bulk modulus values decreased with moisture. Due to the dominant effect of peat, there were no large differences between bulk modulus values of different particle shapes. The shear and failure responses of the above-mentioned eight compositions were also analyzed, compared, and modeled. Of all sand mixtures tested, air-dried angular sands with peat had the highest brittle-type failure stress value, 181 kPa at 34.5 kPa confining pressure, and moist subangular sand with peat had the lowest ductile-type failure stress value, 141 kPa at the same confining pressure. Shear modulus values increased with the increase of mean pressure, but in the case of sands containing both moisture and peat, shear modulus values increased gradually. Overall, peat and moisture content have a dominant effect on the compression and failure behavior of the rootzone sands. rootzone sand mixtures moisture effect particle shape effect organics effect mechanical behavior compression response shear/failure response prediction models