Behavior Of Granular Materials Research Articles

Correlation of fabric parameters and characteristic features of granular material behaviour in DEM in constitutive modelling

AbstractThe anisotropic microstructure of granular materials has a profound effect on their macroscopic behaviour and can be characterised using a fabric tensor. To include of fabric in the critical state theory (CST), anisotropic critical state theory (ACST) was proposed by modifying the state parameter $$(\psi )$$ ( ψ ) of CST to a fabric-dependent dilatancy state parameter $$(\upzeta )$$ ( ζ ) . Noteworthy that $$\uppsi$$ ψ showed a very strong correlation with characteristic features (e.g. instability, phase transformation and characteristic state) of macroscopic behaviour and, as a result, it has been adopted in many constitutive models. While $$\upzeta$$ ζ aided the inclusion of fabric in ACST models, the correlation between $$\upzeta$$ ζ and characteristic features has not been evaluated in detail yet, although a large number of works are found on micromechanics and fabric only. In this study, a large number of discrete element method simulations for drained and undrained triaxial were conducted to evaluate the correlation between $$\upzeta$$ ζ and characteristic features. To this purpose, the correlation between stress ratio and both classic and dilatancy state parameter ($$\psi$$ ψ and $$\upzeta$$ ζ ) were studied in important characteristic features (e.g. instability, phase transformation and characteristic state). It was found that this correlation was improved using $$\upzeta$$ ζ which might be due to the inclusion of fabric in our model. This observation is new and significant for inclusion of fabric evolution in constitutive modelling.

Shear rate dependency on flowing granular biomass material

The commercialization of bioenergy has been significantly limited by various material handling issues due to the poor flowability of granular biomass materials. Addressing these issues demands a fundamental understanding of flow physics and robust models to predict the multi-regime flow behavior of biomass particles. In this study, we investigated the multi-regime flow behavior of loblolly pine chips, a widely used bioenergy feedstock, through combined experiments and simulations. A quasi-static hypoplastic model and a cross-regime Drucker–Prager (DP)-μ(I) model were utilized and validated against inclined plane flow experiments to understand the quasi-static and dense flow behavior of milled pine chips. The results show that along the inclined plane, loblolly pine chips mainly present in heap flow (varying thickness along the plane), and in plane flow (iso-thickness along the plane) only when the inclination closes to the material’s critical state internal friction angle. The results also show that the multi-regime DP-μ(I) model predicts a completely different velocity profile from the hypoplastic model. DP-μ(I) model can capture the flow behavior of pine chips in both flow regimes well but at the cost of extra parameter determination, and the shear-rate dependent rheology model can successfully capture the flow of elongated high-frictional particles. These findings advance the scientific understanding of the multi-regime flow behavior of granular biomass materials and shed light on formulating novel constitutive models to assist granular biomass handling in the bioenergy industry.

Micromechanics of multiphase geomaterials based on micro-CT image analysis: unsaturated soil, vegetated soil, and bio-cementation

Under the influence of climate change, extreme weather events such as rainstorms may induce fluctuations in soil water content above the groundwater level, thereby causing geological disasters (e.g., landslides). To mitigate these hazards, green and low-carbon engineering measures such as vegetation reinforcement and bio-cementation are proposed. This study investigates the micromechanical properties of multiphase geomaterials—unsaturated soil, vegetation-reinforced sand, and bio-cemented sand—utilizing high-resolution computed tomography (CT) scanning technology and associated image analysis techniques. The findings are presented as follows: (1) a 4D examination of the macroscopic and microscopic behaviors of unsaturated granular materials under triaxial loading conditions was conducted using self-designed in situ CT scanning equipment. (2) Triaxial loading alters the distribution of phase interfacial surfaces in unsaturated soil, affecting its overall strength. This loading also increases the anisotropy of the solid skeleton and suction stress. (3) The global saturation of the root–soil complex diminishes with root growth, with pore distribution significantly influencing local saturation. (4) In the unsaturated MICP process, low-saturation conditions are preferable for effective cementation, although the saturation levels should be restricted to 20%. After calcification, the particle contact coordination number increases, maintaining the isotropy in the contact between the soil particles.

Macro and microscopic analysis of granular flow in curved hoppers

The geometry of vessels has a significant influence on granular flow. In this study, discrete element method is used to simulate the flow behavior of granular materials in curved hoppers. The results confirm that curved hoppers can achieve a higher discharge rate than conical hoppers, accompanying with a large converging flow region. The macro and microscopic characteristics such as flow and force structures are analysed in detail, revealing that the hopper curves causes the preferred flow direction of granular materials to the central region and the converging flow near the orifice is more developed, leading a higher particle velocity. The observation of flow patterns developed in hoppers shows that the affected region by the curves only occurs at the bottom, and the transition height from the mass flow to the converging flow increases with the curves deviating from the conical.

Mechanical effects of nanomaterials on the residual shear strength of dry sandy mixtures: Implication for the high mobility of rock avalanches

Nanoparticles found in rock avalanches and natural faults were inferred to be the reason for the ultra-low shear resistance of the materials along the shear surface. Nevertheless, this inference has not been physically verified yet. To investigate the role of nanoparticles in the shear behavior of granular materials, we conducted a series of ring shear tests on silicon dioxide nanoparticles (SN), silica sand (S8), and mixtures of the S8 with different contents of SN, under varying normal stresses (σ) and shear velocities (V). Our results showed that the shear strength (μ) of SN is high when σ is small (≤ 215 kPa at our test range), even though the maximum shear velocity is about 210 cm/s, but shows a great decrease under higher σ (≥ 619 kPa). The shear strength of mixtures varied with SN content. For S8 (M0) and the mixture of 10% SN (M10), when sheared under small σ, μ first decreased slightly with increasing V when V is smaller than 1 cm/s, after that it increased slightly with further increase of V. Nevertheless, this kind of shear-rate dependent behavior was not observed in the tests under higher σ. When the content of SN in the mixture was <20%, μ increased with the increase of SN content. However, with further increase of SN content, μ decreased. Under high normal stress conditions, distinctive powder rolls were observed on the shear surface formed on the tests. When the mixtures with lower SN content (≤50%), the powder rolls were not observed. We inferred that powder rolls can be produced under high SN content and high normal stress conditions, and this structure altered the particle movement mode from sliding friction to rolling resistance, resulting in a significant decrease in the shear strength. These findings provide valuable insights into the shear behavior of granular materials with nanoparticles and then provide evidence for a better understanding of the high mobility of rock avalanches.

Effect of gravity on granular material flows

Most geohazards and industrial processes are essentially gravity-driven dense granular flows. Deep understanding of the effect of gravity on granular flow is of crucial importance in analyzing the evolution of planetary surfaces. By using a discrete element numerical simulation method, we obtain the evolutionary characteristics of velocity, volume fraction, shear rate and granular temperature during granular flow, and analyze the effect of gravity on the rheological behavior of granular materials. The results indicate that gravity significantly affects the flow characteristics of granular materials, especially in the case of large inclination angle. With the increase of gravity, the flow velocity, shear rate and granular temperature of the granular material tend to increase. When the inclination angle exceeds the critical value, the volume fraction of the granular system in the high gravity environment decreases significantly, while the inertia number increases.

Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement

AbstractIn the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated that FEM×DEM approach naturally captures the discrete and anisotropic nature of granular materials. Despite its advantages, FEM×DEM with classical FEM, suffers from mesh dependency, especially when material enters softening phase and exhibits strain localization. To overcome this limitation, FEM×DEM model has been enriched by incorporating a local second gradient model. Nevertheless, the existence of multiple possible solutions is observed. In this paper, we study the variability and loss of uniqueness of numerical solutions to a boundary value problem. Different VEs with equivalent mechanical properties are generated and used to model the pressuremeter tests by means of FEM×DEM. The modeling results show a great variability of the numerical results, both in shape of borehole and in different modes of shear bands. For the same VE, the loss of uniqueness of numerical solutions is evidenced by a slight modification of loading history at the level of the internal pressure applied to the borehole. Finally, we show that when a certain heterogeneity is introduced by using different VEs within the same BVP, even if the uniqueness of the solution is not guaranteed, the set of possible solutions seems more restrained.

3D DEM-based particle-scale analysis of drained and undrained triaxial behaviors of granular materials

3D DEM-based particle-scale analysis of drained and undrained triaxial behaviors of granular materials

High-cycle shakedown, ratcheting and liquefaction behavior of anisotropic granular material with fabric evolution: Experiments and constitutive modelling

Although the mechanical response of granular materials strongly depends on the interplay between their anisotropic internal structure (fabric) and loading direction, such coupling is not explicitly considered in existing high-cycle experimental datasets and models. High-cycle experiments on granular specimens specifically prepared with various fabric orientations are presented. It is found that the high-cycle strain accumulation behavior can change remarkably, from shakedown to ratcheting, when the fabric orientation deviates more from the loading direction. Inspired by the experimental observations, a fabric-dependent anisotropic high-cycle model is proposed, by proper recasting of an existing model formulated within Critical State Theory, into the framework of Anisotropic Critical State Theory. The model explicitly accounts for the fabric evolution, which is linked to plastic modulus, dilatancy and kinematic hardening rules. The model can quantitatively reproduce the high-cycle strain accumulation (i.e., shakedown and ratcheting) under drained conditions, as well as pre-liquefaction and post-liquefaction responses granular materials having widely ranged fabric anisotropy, densities and cyclic loading types using a unified set of constants. It exhibits a unique feature of simulating the distinct high-cycle strain accumulation and liquefaction of granular material with various fabric anisotropy, while the existing high-cycle models treat them equally. The successful reproduction of the anisotropic sand element response under high-cycle drained and undrained conditions makes it possible to perform whole life analysis of various foundations on granular soil subjected to high-cycle loading events.

Systematic investigation into the role of particle multi-level morphology in determining the shear behavior of granular materials via DEM simulation

This study aims to numerically investigate the dependence of shear behaviors of granular materials on particle multi-level morphology, encompassing form (mean of elongation and flatness), angularity, and roughness. To this end, four series of particles—ellipsoidal particles with varying elongation indices (EI) and flatness indices (FI), and equiaxed concave particles with varying angularity indices (AI) and roughness (RG)—are adopted to isolate the effects of particle morphology at each level. Through discrete element method (DEM) simulations, granular assemblies with varying values of EI, FI, AI, and RG are consolidated to achieve the maximum packing density under the same confining pressure. Subsequently, they are subjected to triaxial drained compression tests until reaching a critical state. Based on numerical results, the independent effects of EI, FI, AI, and RG on the macro- and micro-mechanical response of granular materials are examined and compared in detail. Furthermore, using the ‘Stress-force-fabric’ (SFF) relationship, the anisotropic origins of the peak- and critical-state shear strengths induced by EI, FI, AI, and RG are also analyzed.

Investigating the Mechanical Behaviour of Unbound Granular Material (UGM) for Road Pavement Construction Applications: A Western Victoria Case Study

The behaviour of unbound granular materials (UGMs) used in road construction is crucial in determining the longevity and performance of road pavement. Geotechnical analysis can assist engineers in selecting suitable materials and designing road pavements that meet industry standards. This paper presents the results of laboratory geotechnical tests conducted on unbound granular materials (UGMs) collected from three sites (Roses Gap, Rules East, and Polkemmet Road) in Horsham, Victoria, Australia. UGMs were investigated for their mechanical behaviour and suitability as subgrade materials for road pavements. The study utilised laboratory geotechnical tests, including particle size distribution (PSD), Atterberg limits, compaction (Proctor) test, unconfined compressive strength (UCS), California Bearing Ratio (CBR), and repeated load triaxial (RLT) tests, to evaluate the physical and mechanical properties of the UGM samples. The study indicates that UGM samples collected from different locations displayed variations in their geotechnical properties, such as particle size distribution, water absorption, and CBR strength. Roses Gap samples showed weak cohesion properties, and significant vertical displacements after repeated triaxial tests. However, among the samples in this site, samples with higher clay content (RG21) demonstrated the most promise in triaxial tests. Similarly, the Rules East samples were found to be suitable for low-traffic subgrades due to their satisfactory CBR and RLT testing results, albeit with little cohesion from clay content. Out of three locations, Polkemmet samples were identified as potential subgrade applications, with PR12 being the top recommendation overall. It satisfied PSD, CBR, and RLT test conditions due to acceptable particle size in the largest range, highest CBR strength value, and lowest permanent displacement. The study's findings provide useful information for the design of road pavements using these materials and the characterisation of rural materials around the Horsham region for future use in various other contexts.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method (DEM) modelling. The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions. A side wall node loading method is used to exert bi-directional shear of various angles. The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials. However, the relationship between bi-directional shear and mechanical responses relies on loading conditions, i.e. constant vertical stress or constant volume conditions. The stress states induced by static shear consolidation are affected by loading angles, which are enlarged by subsequent shear, consistent with the relationship between bi-directional shear and principal stresses. It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials. The presence of bi-directional principal stress rotation (PSR) is demonstrated, which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction. Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts, but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts. It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions. Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined, providing further insights into understanding granular behaviour under bi-directional shear.

Elasticity and rheology of auxetic granular metamaterials

The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials.

Viscoelastic material properties determine the contact mechanics of hydrogel spheres

Granular materials are ubiquitous in nature and industry; their mechanical behavior has been a subject of academic and engineering interest for centuries. One of the reasons for their rather complex mechanical behavior is that stresses exerted on a granular material propagate only through contacts between the grains. These contacts can change as the packing evolves. This makes any deformation and mechanical response from a granular packing a function of the nature of contacts between the grains and the material response of the material the grains are made of. We present a study in which we isolate the role of the grain material in the contact forces acting between two particles sliding past each other. By using hydrogel particles, we find that a viscoelastic material model, in which the shear modulus decays with time, coupled with a simple Coulomb friction model, captures the experimental results. The results suggest that particle material evolution itself may play a role in the collective behavior of granular materials.

Effects of intermediate principal stress on the granular material behavior under partial drainage conditions

Effects of intermediate principal stress on the granular material behavior under partial drainage conditions

Cementor: A toolbox to generate bio-cemented soils with specific microstructures

Bio-cemented soils can exhibit various types of microstructure depending on the relative position of the carbonate crystals with respect to the host granular skeleton. Different microstructures can have different effects on the mechanical and hydraulic responses of the material, hence it is important to develop the capacity to model these microstructures. The discrete element method (DEM) is a powerful numerical method for studying the mechanical behaviour of granular materials considering grain-scale features. This paper presents a toolbox that can be used to generate 3D DEM samples of bio-cemented soils with specific microstructures. It provides the flexibility of modelling bio-cemented soils with precipitates in the form of contact cementing, grain bridging and coating, and combinations of these distribution patterns. The algorithm is described in detail in this paper, and the impact of the precipitated carbonates on the soil microstructure is evaluated. The results indicate that carbonates precipitated in different distribution patterns affect the soil microstructure differently, suggesting the importance of modelling the microstructure of bio-cemented soils.

Experimental study on dynamic angle of repose formation: Effect of granular type and water content

The experiment of granular in rotating cylinder is a common experiment to study granular material behaviour. In this study, we investigate the effect of granular type and water content on the dynamic angle of repose in a rotating cylinder. Rice seed, mung bean, and sand are used as samples. Experimental results show each sample has a different dynamic angle of repose that is related to the shape of the sample. We also study the effect of the water content on the sand sample. The addition of water content has no significant effect on the dynamic angle of repose. This occurs because the water content used has passed the critical point.

A micromechanical model for estimating the shear modulus and damping ratio of loose sands under low stresses. Application to a Mars regolith simulant

The dynamic properties of loose sands under low stresses have been poorly investigated because of the higher order of magnitude of stress levels in terrestrial geotechnical structures. However, low densities and low stresses prevail in the sandy surface deposits of some other rocky planets, making low stress conditions relevant for extra-terrestrial soil mechanics. This is the case of Mars, on the surface of which a seismometer has been placed during the InSight mission. In this context, a dynamic shear rheometer was used to measure the shear modulus and damping ratio of a Martian regolith simulant under very low stresses to improve the interpretation of the InSight dataset on surface materials. This paper also revisits the grain contact stiffness and the overall modulus of a random packing of identical spheres, based on the Hertz-Mindlin contact theory. A micromechanical model accounting for the effects of both grain roughness and slipping in the soil degradation curve is proposed. The results of the model show a good agreement with experimental data, capturing the non-linear transition from low to high-shear strains. The model hence provides a new framework for a better understanding of the behaviour of granular materials in low gravity (extra-terrestrial) conditions.

Micro computed tomography images of capillary actions in rough and irregular granular materials

The present work investigates the effect of both surface roughness and particle morphology on the retention behaviour of granular materials via X-ray micro-computed tomography (µCT) observations. X-ray µCT images were taken on two types of spherical glass beads (i.e. smooth and rough) and two different sands (i.e. natural and roughened). Each sample was subjected to drainage and soaking paths consisting in a multiphase ‘static’ flow of potassium iodine (KI) brine (wetting phase) and dry air (non-wetting phase). Tomograms were obtained at different saturation states ranging from fully brine saturated to air dry conditions with 6.2 μm voxel size resolution. The data acquisition and pre-processing are here described while all data, a total of 48 tomograms, are made publicly available. The combined dataset offers new opportunities to study the influence of surface roughness and particle morphology on capillary actions as well as supporting validation of pore-scale models of multiphase flow in granular materials.

Understanding the interplay between particle shape, grading and sample density on the behaviour of granular assemblies: A DEM approach

This study investigates the interplay between particle shape, grading and initial sample density, three of the most important factors influencing the mechanical behaviour of sheared granular assemblies. Using the discrete element method (DEM), two-dimensional assemblies of varying initial sample density, particle aspect ratio, AR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AR$$\\end{document}, and coefficients of uniformity, Cu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${C}_{u}$$\\end{document}, were prepared and subjected to drained biaxial shearing until the critical state was reached. We assessed the interplay between each of these parameters by evaluating whether the effect of any given parameter on a mechanical quantity is influenced by any other parameter. Our analyses show that the effect of some of these key parameters on mechanical response, can indeed be influenced by other key parameters. The effect of the particle AR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AR$$\\end{document} on the peak shear strength for the initially dense assemblies differs when compared with the medium-dense assemblies. The mechanical coordination number of the assemblies at the initial state correlates with the peak strength thereby explaining the interplay between particle AR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AR$$\\end{document} and initial sample density on the peak shear strength. The linear relationship established between strength and dilatancy for a combination of all assemblies studied suggests that the strength-dilatancy relationship is a unique characteristic of granular assemblies. The dilatancy of the assemblies correlates strongly with the amount of contacts lost during shearing. The interplays found between particle shape, grading and initial sample density in this study show that to develop robust constitutive models for the prediction of granular material behaviour, the effects of multiple factors must be considered.Graphic abstract