Response Of Granular Materials Research Articles

A non-local plasticity theory for slow granular flows

Motivated by experimental observations of apparent non-locality in the mechanical response of granular materials, a few recent studies have proposed non-local rheological models. Though their predictions agree with some aspects of experimental observations, the tenets of the models are not experimentally verified, nor do they have an experimentally verifiable or plausible mechanical basis. Here we present a non-local model that is based on the simple idea of volume averaging, and show that it overcomes many of the shortcomings of the previously proposed models, and is superior in its predictive capabilities.

Fast shear behavior of granular materials in ring-shear tests and implications for rapid landslides

The high mobility of rapid landslides is one of the most important subjects of both theoretical and practical interest to engineers and scientists. The idea that ultralow resistance could explain the high mobility inspires researchers to examine the shear behavior of granular materials under a wide range of conditions, but the response of granular materials to fast loading rates is largely unknown. The motivation for this study was to examine several fundamental issues of particle properties and mechanical conditions on the fast shear behavior of granular materials. Two granular materials were studied in the oven-dried state and were sheared by employing a ring-shear apparatus. Results indicated that angular particles (silica sand) had higher shear strength parameters than spherical particles (glass beads). In addition, the dilative process was observed during shearing, which depended on normal stress and particle shape. A slightly negative shear-rate effect on shear strength was observed for both granular materials under a certain range of shear rates. Furthermore, cumulative shear displacement had a significant effect on the degree of particle crushing. Fast ring-shear tests also revealed that shear rate had a slightly negative effect on particle crushing. Based on these experimental results, the possible applications of dynamic grain fragmentation theory to assess the high mobility of rapid landsliding phenomena were discussed. It was indicated that the magnitude and release rate of elastic strain energy generated by grain fragmentation played important roles on the dynamic process of landslide mobility.

A numerical investigation of the incremental behavior of crushable granular soils

SummaryThe mechanical behavior of granular materials is characterized by strong nonlinearity and irreversibility. These properties have been differently described by a variety of constitutive models. To test any constitutive model, experimental data relative to the nature of the incremental stress–strain response of the material is desirable. However, this type of laboratory data is scarce because of being expensive and difficult to obtain. The discrete element method has been used several times as an alternative to obtain incremental responses of granular materials. Crushable grains add one extra source of irreversibility to granular materials. Crushability has been variously incorporated into different constitutive models. Again, it will be helpful to obtain incremental responses of crushable granular materials to test these models, but the experimental difficulties are increased. Making use of a recently introduced crushing model for discrete element simulation, this paper presents a new procedure to obtain incremental responses in discrete analogs of granular crushable materials. The parallel probe approach, previously used for uncrushable discrete analogs, is here extended to account for the presence of crushable grains. The contribution of grain crushing to the incremental irreversible strain is identified and separately measured. Robustness of the proposed method is examined in detail, paying particular attention to aspects such as dynamic instability or crushing localization. The proposed procedure is later applied to map incremental responses of a discrete analog of Fontainebleau sand on the triaxial plane. The effect of stress ratio and granular state on plastic flow characteristics is highlighted. Copyright © 2016 John Wiley & Sons, Ltd.

Estimation of resilient modulus of unbound granular materials used as pavement base: combined effect of grain-size distribution and aggregate source frictional properties

The resilient modulus of granular materials used in base layers is influenced by numerous factors, such as grain-size distribution and aggregate source properties. Resilient modulus tests were performed on three aggregate sources for five identical gradations in order to study their respective effects on the mechanical response of granular materials. To consider these effects, two new parameters associated with frictional properties and gradation are introduced. For the proposed model, standard grain-size distribution and flow tests are needed to estimate of the resilient modulus of granular materials.

Acoustic detection and nonlinear response of granular materials under vertical vibrations

Owing to their efficient penetration into elastic media, the measurement of sound waves can provide a sensitive probe of both the structural and mechanical properties of the materials through which they propagate. In this work, we first investigate the transversal and longitudinal wave velocities in granular assemblies composed of glass beads under uniaxial load by the time-of-flight method. Then the ratio G/B, (G is the shear modulus and B is the bulk modulus) as a function of pressure is analyzed, based on the theory of classical elasticity. Experimental results show that, with the pressure increasing from 10 to 100 kPa, i) the velocity of longitudinal wave (cL ) is obviously faster than that of transversal one (cT ) in the granular system(the ratio cL/cT is about 1.6), and the cL and cT of the system show power law scaling, i.e. cL p0.3817, cT p0.2809; ii) the ratio G/B decreases in the low pressure range for glass beads packing, i.e. G/B p-0.4539. It is found that the power-law exponent of G/B with pressure is very close to -1/2 (the prediction in 2015 Phys. Rev. Lett. 114 035502), suggesting that the granular system lies in glass L state within the pressure range in our experiment. Furthermore, the fast Fourier transform method is used to study the variation of acoustic attenuation and nonlinear characteristics in granular materials. Our results reveal that the acoustic attenuation coefficient () and the ratio of the second harmonic amplitude ( 2 ) to the square of fundamental amplitude ( 1 ) at the receiving end in the granular system, 2/12, both decrease in power law with the increase of pressure, i.e. p-0.1879, 2/12 p-0.866, respectively.

Granular Flow Impact Forces on Protection Structures: MPM Numerical Simulations with Different Constitutive Models

Flows of granular materials are among the most destructive of all landslide phenomena. The assessment of the potential damage caused by the granular flow and the design of protection structures require the knowledge of the landslide-structure interaction. Numerical simulations of these phenomena are very complex because large displacements, soil-structure interaction and complex non-linear soil behavior have to be considered. A key issue in the simulation of these phenomena is the definition of a constitutive model able to describe the granular material response under a wide range of strain rates. This study examines and compares the results obtained by different constitutive models, namely the elastic perfectly plastic model with Mohr-Coulomb failure criterion, and the viscoplastic model with Drucker-Prager yielding condition. To this aim, we consider a finite volume of granular material instantaneously released from the top of an inclined channel; the material flows downslope and bumps a rigid wall on which the forces are measured.

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.