Response Of Granular Materials Research Articles

Micro-mechanical study of stress path and initial conditions in granular materials using DEM

The macroscale response of granular materials under different loading conditions stems from the alteration of micromechanical properties during loading. Previous studies have used either physical experiments or discrete element method simulations to explore the effect of initial conditions and stress path on granular materials. However, microscale studies are not sufficient, especially for various loading paths. We study micromechanics of granular materials using the stress-force-fabric (SFF) relationship for a better understanding of the behavior of granular materials. Triaxial compression and extension tests are conducted on samples containing 1000 spherical particles, with periodic boundaries, and the effect of initial porosity is studied. In the next step, using the SFF relationship, we study the effect of anisotropic consolidation ratio. In addition to providing an appropriate explanation for shear strength out of evolution of anisotropy coefficients, our results show that anisotropic consolidation does not affect the micromechanical properties of granular materials in a way to change mobilized friction angle of sample at failure point.

Interplay between the inclusions of different sizes and their proximity to the wall boundaries on the nature of their stress distribution within the inclusions inside particulate packing

Micromechanical responses of granular materials are complex to understand when their behaviour is viewed in a single grain-scale. Experimental sensing of stresses within a grain-scale inside three dimensional particulate packing is still difficult to perform. In this work, photo stress analysis tomography (PSAT) is used to sense the fundamental nature of the stress experienced by different sizes of optically-sensitive inclusions inside granular packing (quasi-three dimensional) under an external axial-compression loading. The distribution of the maximum shear stress and the direction of the major principal stress experienced by the inclusions are analysed to understand the interplay between the size of the inclusions and their proximity to the wall boundary. The outcomes of this study provide a new understanding on the dual nature of stress transmission experienced by the inclusions, as a result of the combined size and wall effects. Relatively large inclusions experience dominantly shear stress close to the wall boundaries while this nature tends towards hydrostatic away from the wall boundaries. Smaller size inclusions could experience shear at both close to and away from wall boundaries of the granular assembly. Computer simulations using three-dimensional discrete element method (DEM) are also performed to compare the qualitative nature of stress experienced by inclusions inside particulate media. Qualitatively, the simulation results also agree with the experimental outcomes, that an increase in the relative size of the inclusion decreases its ability to experience shear. Using DEM simulations, the fabric structure of the inclusions is examined in depth under mechanical loading. An increase in the size of the inclusions tends to decrease the fabric anisotropy of the contacts and in particular the strong contacts, surrounding them. Hence the microscale origin of the weak mobilisation of shear in the large inclusions could be attributed to their relatively weak fabric anisotropy of the strong contacts surrounding them. These findings help to advance our understanding of the micromechanics of particulate systems, due to their size and proximity to wall boundaries: different sizes of the particles could sustain different nature of stresses within single-particle scale depending on their proximity to the wall boundaries.

Stress–Strain Response of Unbound Granular Materials Under Static and Cyclic Loading

Resilient modulus is an important parameter in flexible pavement engineering design. The stress–strain behavior of unbound granular base materials under static and cyclic loading and the effects of the state of stress, moisture content and loading conditions have been analyzed in the present study. In this paper, the resilient behavior of unbound granular materials and the applicability of different constitutive models are examined in order to understand the behavior of granular material under static and cyclic loading. Since the aggregate material exhibits a complex stress–strain behavior, more than one model will be required to predict the stress–strain response of granular materials. Hence, different constitutive models have been considered in the present study which can adequately predict the stress–strain response of aggregate materials. Considering the constitutive models used in the present study, it could be said that the Lentz and Baladi model and the normalized degradation model suitably bring out a relation between static and cyclic tests. This is a useful input in pavement design and explains the variation of modulus with load repetitions.

Stress fluctuations in granular material response during cyclic direct shear test

This paper presents the results of an intensive series of experiments on various types of sands using cyclic direct shear testing apparatus. Two different grain shapes (rounded and angular) of sands having distinct sizes (0.25–0.5 and 1.0–2.0 mm) were tested in an automated constant normal load cyclic direct shear testing apparatus at an 100 kPa vertical effective stress, and two rates of shearing (2.0 and 0.025 mm/min). Experiments on the specimens resulted in sharp decreases followed by gradual increases in shear stress values. The results suggest that these successive drops and formations give a stick–slip nature to the fluctuations, which might be attributed mainly to the rate of loading, shape of grains, size of grains, and fines contents.

Cyclic Behaviors of Granular Materials under Generalized Stress Condition Using DEM

AbstractMost behaviors of granular materials have been studied under the limit conditions of stress paths such as cyclic triaxial compression and extension tests. Furthermore, the macrobehavior and micromechanical response of granular materials under more comprehensive cyclic loading tests in the generalized stress condition are not well understood. The objectives of this paper are to ensure the ability of the Discrete Element Method (DEM), to simulate the macrobehavior of granular materials under various cyclic stress paths of the generalized stress condition, and to explore the micromechanical response. To this end, four different cyclic stress paths under generalized stress simulations, following the stress-controlled method on a sample of spheres, were conducted. To check the validity of DEM results, the experimental results of the real sand under cyclic stress programs were used. The macrobehaviors, indicated by the stress–strain–dilation relationship and the directions of principal strain increment ...

Simulations of Defense Strategies for Bennu: Material Characterization and Impulse Delivery

Assessments of asteroid deflection strategies depend on material characterization to reduce the uncertainty in predictions of the deflection velocity resulting from impulsive loading. In addition to strength, equation of state, the initial state of the material including its competency (i.e. fractured or monolithic) and the amount of micro- or macroscopic porosity are important considerations to predict the thermomechanical response. There is recent interest in observing near-Earth asteroid (101955) Bennu due to its classification of being potentially hazardous with close approaches occurring every 6 years. Bennu is relatively large with a nominal diameter of 492 m, density estimates ranging from 0.9-1.26 g/cm3 and is composed mainly of carbonaceous chondrite. There is a lack of data for highly porous carbonaceous chondrite at very large pressures and temperatures. In the absence of the specific material composition and state (e.g. layering, porosity as a function of depth) on Bennu we introduce a continuum constitutive model based on the response of granular materials and provide impact and standoff explosion simulations to investigate the response of highly porous materials to these types of impulsive loading scenarios. Simulations with impact speeds of 5 km/s show that the shock wave emanating from the impact site is highly dispersive and that a 10% porous material has a larger compacted volume compared with a 40% porous material with the same bulk density due to differences in compaction response. A three-dimensional simulation of a 190 kT standoff explosion 160 m off the surface of a shape model of Bennu estimated a deflection velocity of 10 cm/s.

Simulation of triaxial response of granular materials by modified DEM

A modified discrete element method (DEM) with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study. Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior, mesoscale contact parameters at particle level and external loading rate. It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk. The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials. The parametric study indicates that Poisson’s ratio only varies with stiffness ratio, while Young’s modulus is proportional to contact modulus and grows with stiffness ratio, both of which agree with the micromechanical model. The peak friction angle is dependent on both inter-particle friction angle and rolling resistance. The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large. Finally, we have recommended a calibration procedure for cohesionless soil, which was at once applied to the simulation of Chende sand using a series of triaxial compression tests. The responses of DEM model are shown in quantitative agreement with experiments. In addition, stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.

X-ray tomography system to investigate granular materials during mechanical loading.

We integrate a small and portable medical x-ray device with mechanical testing equipment to enable in situ, non-invasive measurements of a granular material's response to mechanical loading. We employ an orthopedic C-arm as the x-ray source and detector to image samples mounted in the materials tester. We discuss the design of a custom rotation stage, which allows for sample rotation and tomographic reconstruction under applied compressive stress. We then discuss the calibration of the system for 3D computed tomography, as well as the subsequent image reconstruction process. Using this system to reconstruct packings of 3D-printed particles, we resolve packing features with 0.52 mm resolution in a (60 mm)(3) field of view. By analyzing the performance bounds of the system, we demonstrate that the reconstructions exhibit only moderate noise.

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.

Behaviour of sand during release from a shocked state

The dynamic response of granular materials to an applied shockwave is of wide ranging importance. While the shock Hugoniot has been studied, the shock-release of granular systems has never been experimentally characterised. Here, we present a simple approach to such measurements and present a series of plate impact experiments providing release data for a well characterised dry sand. We discuss the origin of the release behaviour, which we support with further measurements on a weakly bound sandstone.

Quantifying the evolution of soil fabric during shearing using directional parameters

Over the past 50 years, experimental studies have repeatedly demonstrated that the mechanical behaviour of sand is sensitive to the material fabric, that is, the arrangement of the grains. Up until now there have been relatively few attempts to describe this fabric quantitatively. Much of our understanding of the link between the particle movements and interactions and the macro-scale response of granular materials, including sand, comes from discrete-element modelling and experiments on ‘analogue' sands with simple, idealised shapes. This paper investigates methods of quantifying the directional fabric of a real sand and its evolution under loading. Statistical analyses of the distribution of fabric directional data in terms of particle, contact normal, branch vector and void orientations were carried out at different stages of shearing deformation. The data show that the initial particle orientation fabric that develops during the deposition of the material tends to persist during shearing, while in the post-peak regime the contact normals seem to be reoriented along the direction of the major principal stress. Different patterns were observed within the shear band, as both the particles and the contact normal vectors appeared to rotate along the shear plane.

Gradation effects on the mechanical response of crushed stone aggregate

A study was conducted to evaluate the effects of varying the gradation of aggregate base course (ABC) on material performance. Five different gradations consistent with a range of common ABC were selected. Experimental trials were performed to classify the materials and assess the performance differences between the five gradations. The gradation was found to affect the behaviour of the aggregate in that coarser gradations gave better strength and resilience values under conditions most similar to those found in the field. From research and experience during the laboratory testing, it was concluded that the coarsest blends became too difficult to realistically work with and they also lacked the stability of the well-graded combinations. It was also observed that as the amount of fines in the specimens exceeded 8–12% by mass, the fines governed the behaviour of the material. Results are interpreted using previously published work on specific surface, ‘ideal’ gradations and micromechanical models for the response of granular materials.

Effects of grain size and gradation on the dynamic responses of quartz sands

The dynamic compression responses of quartz sands of different grain sizes and gradations are tested with a modified spilt Hopkinson pressure bar in which a single-pulse loading system is implemented. The yield stresses, the compressibility and the energy-absorption densities of the granular materials are calculated from the compression curves. The effects of the grain size and the gradation on those dynamic macro responses are investigated and presented. The grain size distributions of the samples after loading are obtained with a laser diffractometry instrument, and are analyzed quantitatively with the Hardin relative breakage index. The effects of the grain-scale properties on the dynamic macro responses of granular materials can be interpreted well with the particle breakage mechanism. The Theoretical analyses show that the energy-absorption density and the particle breakage extent are linearly related to the logarithm of axial stress respectively, and the slopes are both proportional to the compressibility. Moreover, a simple model for predicting the dynamic energy-breakage efficiency of the granular materials is derived. Based on the discrete element method (DEM), simulation of the granular material under one-dimensional dynamic compression is conducted to further interpret the experimental results. The size dependence of the coordination number of grains and its influence on particle breakage is discussed.

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

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

DEM Simulation of Micro-Macro Mechanical Behaviour of Granular Materials

The mechanical responses of granular materials are affected significantly by the properties of the individual particle. In order to establish the link between the micro and macro parameters, series of numerical biaxial simulations are carried out using two-dimensional discrete element method. The microscale mechanisms of mechanical behavior of granular materials are investigated through sensitivity analyses. The key influence of microscale parameters on the strength and deformation are discussed respectively. The peak strength depends on void ratio, friction coefficient and confining stress significantly. The elastic modulus is affected by friction coefficient, confining pressure and stiffness ratio, especially when the friction coefficient ranges from 0.1 to 0.3. The samples with different initial void ratio under the same loading condition can finally achieve the same critical state; the critical states at micro and macro scale are both independent of the initial void ratio.

Non-invasive characterization of particle morphology of natural sands

Particle morphologies, i.e. particle sizes and shapes, have a marked influence on the mechanical response of granular materials including soils. Until now most investigations of particle shape have been two-dimensional and size has been most often assessed using sieving. This paper makes use of recent developments in three-dimensional imaging technologies to characterize the internal features of a soil in 3D including quantification of particle morphology. The soil investigated was Reigate sand (from Southeast England), a geologically old sand, which in its intact state exhibits significant interlocking amongst the constituent grains. Intact and reconstituted specimens having similar densities were tested under triaxial compression. The specimens were impregnated with an epoxy resin at three different stages of shear deformation and small cores from each specimen were scanned using X-ray micro-tomography. Different systems and scanning parameters were explored in order to obtain 3D, high-resolution, images with a voxel size of 5μm (0.018×d50). The morphology measurements were compared with sieve data and measurements obtained using a 2D, image based, laser system. The sieve size is shown to correlate well with the intermediate principal axis length. Clear differences are noted between the 2D and 3D shape measurements. Breakage of fractured grains, along existing fissures, occurs both during reconstitution and shearing of the intact soil, a phenomenon that cannot be observed using invasive techniques such as sieve analysis.

Macro-Micro Responses of Granular Materials under Different b Values Using DEM

AbstractGranular materials, such as sand, experience different stress paths in nature; and the behavior of granular materials depends on stress conditions. This paper presents a study of the relationship between the macro- and microscale responses of granular materials using the discrete element method (DEM) under general three-dimensional stress conditions specified by the parameter b, which describes the relative magnitude of the intermediate principal stress with respect to the major and minor principal stresses. With this view, a cubical numerical sample consisting of 8,000 spheres was prepared. Six true triaxial tests were conducted with the same numerical sample with no bias in the initial fabric. Different macroscopic results, including the relationship between principal strains, principal deviatoric strains, the evolution of stress and strain increment vectors, and the behavior of strain increment vectors on the π-plane, are discussed. Good consistency between the numerical and experimental result...

Strain accumulation in dense sands due to shear stress cycles

This paper investigates the response of granular materials to large numbers of shear stress cycles applied after monotonic loading to various levels of mobilized shear strength. Such stress conditions occur underneath the foundations of structures loaded by non-seismic oscillating forces, e.g. those due to wind and sea waves in tall buildings and offshore structures or induced by vibrating machines. Large numbers of load cycles can induce severe irreversible settlements of foundations and occasionally collapse, even when large safety factors are adopted with respect to bearing capacity in static conditions. Dense Toyoura sand has been used throughout the experimental investigation. Monotonic and cyclic tests have been carried out on specimens loaded in triaxial compression and extension, both in drained and undrained conditions. Specimens have undergone a large number of shear stress cycles and the conditions which cause accumulation of large deformations and even collapse have been analysed. An empirical approach for evaluating the accumulated irreversible strains is also presented.

Unilateral interactions in granular packings: a model for the anisotropy modulus

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.

Discrete element simulations of two wetting effects on granular materials

To explore the microscopic responses of granular materials to wetting, the inter-particle lubrication effect and particle breakage in an odometer were simulated using a two-dimensional discrete element method. The lubrication effect was modeled by reduction of the inter-particle friction coefficient and particle breakage was initiated by decreasing the particle strength. Once the strength of the particles decreased to a threshold value, the particles began to break so that new contacts could be established to transfer the external loads. Numerical simulations successfully reproduced the additional compaction of the material and the intensification of the horizontal stress in addition to the microscopic responses of the granular assemblies. The microscopic interpretation of the earth pressure coefficient at rest and the evolution of the grain number distribution during particle breaking were also investigated.