Behavior Of Granular Materials Research Articles

DEM investigation of strength and critical state behaviours of granular materials under true triaxial loadings

This paper investigates the strength and critical state (CS) behaviours of granular materials via DEM simulations of true triaxial drained tests under three different loading modes including constant b (intermediate stress ratio) tests with constant σ1′ (major principal stress), constant p′ (mean pressure) and constant σ3′ (minor principal stress) respectively. To this end, a series of samples are generated with the same particle size distribution, and with the confining stresses ranging from 100 kPa to 900 kPa. The CS is achieved for all samples. Both the macroscopic behaviours and the microscopic behaviours are examined and compared considering different loading modes, confining stresses and intermediate stress ratios (b). The critical state lines (CSLs) are found to be unique and independent of the loading modes, but dependent on the b values. The CSLs with b=0 and b=1 form the two boundaries of CSLs respectively beyond which CSLs under all other b tests cannot go beyond. Six different strength criteria are examined and compared in terms of both peak and CS failures. The Mohr–Coulomb strength criterion is found to be only suitable for axisymmetric loading conditions. The Lade-Duncan criterion is only suitable for describing peak strengths, which is dependent on the loading modes and confining stresses. The Satake criterion and Matsuoka-Nakai criterion are the more appropriate strength criteria for describing CS failures, indicating that the CS values of both the Satake parameter and the Matsuoka-Nakai parameter describe an inherent property that characterizes the CS failure for a given type of soil. The CS mechanical coordination number is fitted by a curved line for a given b value, which is unique regardless of the loading modes. The peak and CS values of both major and minor principal fabric tensors decrease with increasing b values, while they increase with increasing b values for the intermediate principal fabric tensor.

Analysis of dilatancy relation and shear‐band formation in granular materials based on Eshelby‐Mandel tensor

AbstractThe theory of configurational or material forces based on the Eshelby stress tensor (also called energy‐momentum tensor) has provided a general and efficient way to describe the motion of material defects and other inhomogeneities within the framework of continuum mechanics. In this paper, we explore how to use the configurational forces to describe the behavior of homogeneous granular materials by considering the material characteristics on both continuum and discrete particle levels. In particular, dissipative driving forces based on the Eshelby‐Mandel stress tensor are utilized as the driving force of the configuration variations in the form of shear‐induced volume change. The energy dissipation induced by the relative sliding at particle contacts is considered in the configurational forces. To characterize the dilation of a homogeneous granular material with uniform deformation, a virtual plane is introduced to facilitate the analysis and to derive the dilatancy formulation. With the consideration of the shear‐band geometry and the requirement of configurational force equilibrium across the boundary of a shear‐band, the condition for the onset of a shear band is derived. For granular specimens subjected to biaxial compression, the analyses recover the well‐known Rowe's dilatancy formulation and yield the shear‐band orientation identical to that obtained from the classical bifurcation analysis within the framework of elasto‐plasticity.

Macro-micro mechanical study of principal stress rotation in granular materials using DEM simulations of hollow cylinder test

The dependency of sand behavior anisotropy on microstructure reveals the importance of macro-micro mechanical analysis of the principal stresses rotation effect on the strength-deformation response of granular material. In this study multi-scale analysis of the granular material's behavior using three-dimensional discrete element method simulations of the hollow cylinder test was presented. The effect of principal stresses rotation (α) on the macro-mechanical behavior of the soil was investigated from the micro-mechanical anisotropy aspect. It was observed that principal stress rotation affects the anisotropy coefficient and directional distribution of all micro-parameters which can change the soil's behavior according to loading conditions. The stress-force-fabric relationship was used to analyze the microstructure's stress state based on micro-parameters anisotropy coefficients. In addition to the good agreement between stress-force-fabric and general stress tensors, the decreasing trend of the maximum deviator stress and internal friction coefficient angle with increasing α can be observed for both stress tensors.

Recognition of the granular airborne portion in a flighted rotary drum

This article deals with numerical simulation via Discrete Element Method (DEM) in a flighted rotary drum with a varying number of flights from 1 to 25 at a constant load of particles. The granular behavior kinematics is studied in the three regimes: under-, design- and over-loading. It was shown that the behavior of granular material during the unloading process from the flights governs the regime transitions. The cross-sectional distribution analysis of the granular material in the different parts of the drum established the existence of two dense media (bed and flights) and one dilute medium (in the airborne portion). Since one of the criteria that affect the efficiency of heat transport between the gas and the particle media is the number of particles in the airborne phase, three recognition methods are proposed to detect the airborne portion. Based on geometry, velocity magnitude, and minimal separation distance, the comparison between them provides a basis for discussion about the relevance of each method in detecting these airborne particles.

Research on representation of particle size distribution for standard sands

The determination of favorite engineering indexes which are sufficient and necessary to reflect particle size distribution (PSD) is a key issue to bridge micro to macro behaviors of granular materials. Focusing on the continuous gradings, standard sand is selected as a representative, and the data of six typical sands is firstly collected to establish a database of PSD. Secondly, the cumulative central beta distribution is adopted to describe grading curves of particles due to its greater flexibility and fewer parameters, and the physical validation of its parameters is analyzed further. Six combinations of five engineering indexes are respectively applied to calculate the parameters of cumulative central beta distribution. The deviation between the analysis results and the observed data is evaluated. The study reveals that mean particle size D50 and coefficient of uniformity Cu are the most proper combination to describe PSD and can be used to link the PSDs to micro-macro mechanical responses.

Hierarchical MPM-ANN Multiscale Terrain Model for High-Fidelity Off-Road Mobility Simulations: A Coupled MBD-FE-MPM-ANN Approach

AbstractA new hierarchical multiscale terrain model is developed using the material point method (MPM) to enable effective modeling of large terrain deformation for high-fidelity off-road mobility simulations. Unlike the Lagrangian finite element (FE) model, MPM allows for modeling large deformation of a continuum without mesh distortion using material points as moving quadrature points for the background grid. This unique feature is extended to account for complex granular soil material behavior with the hierarchical multiscale modeling approach in the context of off-road mobility simulations. The grain-scale discrete-element (DE) representative volume element (RVE) and its neural network surrogate model (artificial neural network (ANN) RVE) are developed and introduced to the upper-scale MPM model through the scale-bridging algorithm. The DE RVE is used to generate training data for the ANN RVE, allowing for predicting the history-dependent grain-scale soil material behavior efficiently at every material point that moves through the upper-scale MPM background grid. A numerical procedure for modeling the interaction of the nonlinear FE tire model with the MPM-ANN multiscale terrain model is developed considering moving soil patches generalized for the upper-scale MPM terrain model. It is fully integrated into the general off-road mobility simulation framework by leveraging scalable high-performance computing techniques. The predictive ability of the proposed MPM-ANN multiscale off-road mobility model is examined and validated against the full-scale vehicle test data, involving large deformation of soft terrain. The computational benefit from the neural network surrogate model is also demonstrated.

Constitutive modelling of idealised granular materials using machine learning method

Predicting the constitutive response of granular soils is a fundamental goal in geomechanics. This paper presents a machine learning (ML) framework for the prediction of the stress-strain behaviour and shear-induced contact fabric evolution of an idealised granular material subject to triaxial shearing. The ML-based framework is comprised of a set of mini-triaxial tests which provide a benchmark for the setup and validation of the discrete element method (DEM) model of the granular materials, a parametric DEM simulation programme of virtual triaxial tests which provides datasets of micro- and macro-mechanical information, as well as a multi-layer perceptron (MLP) neural network which is trained and tested using the DEM-based datasets. The ML model only requires the initial void ratio of the granular sample as the input for predicting its constitutive response. The excellent agreement between the ML model prediction and experimental test and DEM simulation results indicates that the ML–based modelling approach is capable of capturing accurately the effects of initial void ratio on the constitutive behaviour of idealised granular materials, bypassing the need to incorporate the complex micromechanics underlying the macroscopic mechanical behaviour of granular materials. Lastly, a detailed comparison between the used MLP model and long short-term memory (LSTM) model was made from the perspective of technical algorithm, prediction accuracy, and computational efficiency.

Energy equation and stress–dilatancy relationship for crushable granular materials incorporating particle breakage

The ROWE’s stress–dilatancy relationship is widely employed to characterise the shear dilatancy behaviour of granular materials. However, particle breakage energy dissipation is excluded from the ROWE’s energy balance equation. In this study, three crushable granular soils with significantly different strengths were subjected to triaxial testing, and the dissipation of energy during the tests was explored. For all three materials, the incremental particle breakage energy dissipation increases and then decreases. It was assumed that at the critical state, particle breakage ended and only frictional energy dissipation occurred. To more accurately characterise the energy dissipation process, an exponential expression of particle breakage energy dissipation is added to the ROWE’s stress–dilatancy relationship. The proposed stress–dilatancy relationship is consistent with the shear dilatancy behaviour of crushable granular materials, and the modified energy equation can more precisely describe the energy dissipation process. The hypothesised stress–dilatancy relationship is applicable to three distinct types of crushable granular materials with varying strengths, including sand-gravel material, landslide dam material and calcareous sand.

Role of particle rotation in sheared granular media

When granular assemblies are subject to external loads or displacements, particles interact with each other through contact and may exhibit translations and rotations. From a micromechanical perspective, particle rotations are an essential mechanism influencing the macroscopic behavior of granular materials. In this study, biaxial shearing tests were conducted on assemblies of dual-sized circular particles at different confining pressures. A high-precision image analysis method was developed to extract the particle-level motion of all the particles, including the rotational behavior. Experimental results showed that most of the particles exhibited rotations. Particles within the shear band exhibited more significant rotations and were characterized by low connectivity (number of contacts per particle). In contrast, the particles outside the shear band rotated lesser, only in the beginning stage of shearing. Every rotation in either direction is accompanied by an opposite rotation of almost the same magnitude in the neighboring region, and rotation clusters have been observed. Rotations in both directions are normally distributed within the assembly, and the average particle rotation is zero. The average rotations in both directions evolve symmetrically with major principal strain. Generally, the rotation rate (degrees per incremental strain) is observed to be maximum at the start of the shearing, and gradually it becomes constant toward the end of the shearing. The average value of the absolute cumulative rotation observed for whole particles is 18.6° at the end of shearing, i.e., 20% deviatoric strain. Smaller size particles tend to exhibit 67% higher rotations than bigger particles. Confining pressures have no significant effect on the rotational behavior of circular particles.

Combined effects of initial static shear and continuous principal stress rotation on the liquefaction behavior of granular materials

Extensive efforts have been made separately to investigate the effects of the initial static shear and the continuous principal stress rotation on the liquefaction behavior of sandy soils. However, the interplay and the combined effects of these two important factors have not been adequently studied, which may simply be attributed to the difficulty of implementing such complex loading path in the labrotory tests without introducing severe stress consentration. In this study, a newly-developed discrete element approach that avoids stress concentration and can apply arbitrary undrained loading path was implemented. Based on this approach, the cyclic resistance of both inherently anisotropic and isotropic granular materials under continuous principal stress rotation were studied considering different initial static shear levels. The internal structure evolution of the specimens were quantified through a contact-normal-based fabric tensor that describes the load-bearing structure of the granular specimens. The simulation results show that under otherwise identical condition, the specimen with higher initial static shear stress level is more prone to plastic shear strain accumulation and has weaker cyclic resistance under continuous principal stress rotation, which can be well explained by the fabric evolution.

Accurate determination of the shapes of granular charge distributions.

Experiments have shown that charge distributions of granular materials are non-Gaussian, with broad tails that indicate many particles with high charge. This observation has consequences for the behavior of granular materials in many settings, and may bear relevance to the underlying charge transfer mechanism. However, there is the unaddressed possibility that broad tails arise due to experimental uncertainties, as determining the shapes of tails is nontrivial. Here we show that measurement uncertainties can indeed account for most of the tail broadening previously observed. The clue that reveals this is that distributions are sensitive to the electric field at which they are measured; ones measured at low (high) fields have larger (smaller) tails. Accounting for sources of uncertainty, we reproduce this broadening in silico. Finally, we use our results to back out the true charge distribution without broadening, which we find is still non-Guassian, though with substantially different behavior at the tails and indicating significantly fewer highly charged particles. These results have implications in many natural settings where electrostatic interactions, especially among highly charged particles, strongly affect granular behavior.

Linking the macro-scale response of granular materials during drained cyclic loading to the evolution of micro-structure, contact network and energy components

This study has considered the behaviour of granular materials subjected to drained cyclic loading under constant mean effective stress. Using the discrete element method, cubical, isotropically compressed samples were subjected to 50 loading cycles at different values of mean stress (p' = 100, 200, 300 kPa) and different loading amplitudes (zeta = 5%, 10% and 20% of p'). At low cycle numbers, the deformation mechanism is controlled by contractive volumetric strains, before transitioning to the ratcheting regime, characterised by the persistent accumulation of plastic strains. An energy/work analysis showed that the volumetric work per cycle decreased as hysteresis loops tighten. During ratcheting, most boundary work was dissipated by contact sliding. The mechanical response was controlled by zeta, with little to no influence of p'. For zeta = 5%, deformations were confined to the elastic range, with no increase in secant stiffness G_{sec} or shear strength after cyclic loading. For zeta = 10%, G_{sec} and the shear strength increased after cyclic loading, although no significant expansion of the yield surfaces was observed. The largest loading amplitude (zeta = 20%) induced yielding at low cycles, leading to significant changes in the fabric, volume and yield surfaces of the samples, and a significant increase of shear strength and G_{sec}. At the micro-scale, graph theory was used to quantify the evolution of the contact network. After sim 20 loading cycles, the network reached a steady-state of constant but persistent topology changes in the material, with most of the topology retained between loading cycles.

Shape characteristics of granular materials through realistic particle avatars

The micro- and macroscale mechanical behaviors of granular materials strongly depend on the morphological features of the grains. Imaging techniques, such as X-ray computed tomography, have been used to scan realistic particle geometries and obtain shape characteristics. However, these methods are expensive, laborious, and only applicable to limited grain sizes. A simpler alternative would be to estimate 3D shape features from 2D digital photographs in the field, but they might be affected by image resolution and particle orientation. This study aims to assess the effect of image quality for shape characterization and obtain relationships between widely used 2D and 3D shape descriptors through randomly generated computational particle geometries termed ‘avatars.’ Additionally, X-ray μ-CT scans are performed on beach sand grains with irregular shapes. Particle avatar-based 2D-3D form relationships are compared with μ-CT data of 38 beach sand grains and at least 2300 particles of other material types from literature. Changes in the resolution of the images affected both geometrical and morphological features of the particles. Volume and surface area measurements are affected by the 3D image quality, and low-quality 2D digital images influenced shape characterization. From the observed relationships between 2D and 3D shape descriptors, some 3D shape characteristics such as true sphericity and convexity can be reliably approximated from 2D digital images of randomly oriented particles.

Prediction of acoustical behavior of granular material stacks as measured in a standing wave tube by using a Biot theory-based model

The acoustical behavior of granular materials, such as activated carbon and silica gel, has drawn attention in recent studies, due to their favorable properties such as good low frequency sound absorption. Like other more traditional porous materials, granular materials can also be tested in a standing wave tube for a convenient assessment of their acoustical properties. However, the behavior of granular materials stacked in a standing tube is more complex than that of traditional materials. For example, the response of lightweight glass bubbles reveals a clear dependence on the sound pressure level of the input signal. Also, when tested in standing wave tubes of different diameters, the same type of granular materials displays differences in their behavior. The apparent stiffness of granule pack is also related to the depth of the stack. In the present work, a model based on Biot theory is proposed, together with a consideration of the effect of the change of boundary conditions and the granule stack stiffness in different test configurations. The model is realized by using a finite difference method, and the simulation results are compared with measurements of different types of granular materials.

Study of the impact of boundary conditions on acoustical behavior of granular materials and their implementation in the finite difference method

Granular materials display significant differences in their acoustical response when tested in a standing wave tube, compared with the behavior of more traditional sound absorbing materials such as fibrous webs and foams. The latter materials can often be modeled as an equivalent fluid with the further assumption that the material properties do not depend on the input signal level. In contrast, the level dependence of the acoustical behavior of granular materials has been observed in measurements of glass bubbles, as reported in previous studies, for example. When the input level is low, the absorption coefficient of the glass bubble stack shows solid-like behavior with multiple peaks associated with modal response of the stack. On the other hand, when the input level is high, glass bubble stacks show fluid-like behavior, with the quarter wavelength resonance in the direction of the tube axis dominating the response. In the current work, the boundary conditions at the air/granule interface and the granule/tube wall boundary are studied, as is the mechanism causing the variation of the apparent stiffness of the granule stack. The proposed model is implemented with a finite difference approach, and the model predictions are compared with acoustic measurements of granule stacks.

Experimental application and accuracy assessment of 2D-DIC in meso-direct-shear test of sandy soil

The examination of the meso-mechanical properties of soils is fundamental to understand its macro-behaviour. This paper aims to evaluate the potential application of Digital Image Correlation (DIC), an optical image processing approach, in direct shear test (DST) for soils. Hence, a new shear box was designed to investigate the close behaviour of granular materials. The noise-floor and shear displacement accuracy were discussed to assess the reliability of DIC, besides the effectiveness of the new box was also examined. The distribution of the displacements, strains, and shear angle were measured under four different normal stresses. From the results, the immediate settlement, and the dilative behaviour of the sand during shearing were observed. Furthermore, the investigation revealed a strain concentration at the interface between the boxes, where a shear band was formed. The use of DIC opens up new ways in soil mechanics, overcoming some limitations of the conventional DST.

A micro-investigation on water bridge effects for unsaturated granular materials with constant water content by discrete element method

The most common state of surface soil is unsaturated. Changes in water content will substantially impact its strength, leading to geological and engineering catastrophes. This paper used LIGGGHTS software to simulate the water bridge effect of unsaturated granular materials with constant water content and verify the rationality of the simplification of the stress-force-fabric (SFF) relationship. The results showed that the capillary force was not isotropic, which was different from the previous study, thus it cannot be overlooked in the simplification of the SFF relationship. Moreover, the influence of water content on the macroscopic mechanical behavior of unsaturated granular materials was interpreted through the evolutions of coordination number, interparticle force, fabric and force anisotropy, and other microscopic parameters. Compared to the literature, we found that different water bridge models would not change the characteristics of the solid skeleton.

Evolution of the force chain structure of partially saturated granular material under triaxial compression conditions

Saturation conditions play a significant role in the mechanical behavior of granular material and the evolution of an interparticle contact system during the loading process. Using data derived from discrete element simulations of granular assemblies subject to triaxial compression loading with different suctions, we examine the properties of an interparticle contact network and force chain structure to provide a comprehensive picture of the evolution of a particle-scale contact system. The study focuses on the evolution of the topological statistic features (including degree and triangles) and the force chain structure characteristics influenced by suction conditions. To comprehensively evaluate the characteristics of the force chain system, combined statistical parameters are proposed for describing the linearization and intensity of the force chain structure, which account for multiple features of force chains. Accordingly, a novel expression combined with multiscale properties is proposed for strength prediction that convincingly explains data results in the studied suction range. This study illustrates the consistency of the evolving force chain structure features with mechanical behavior that provides new insights for understanding the particle-scale force chain structure evolution from which these properties dominate the macroscopic response.

Time-dependent behaviour of industrial granular materials under vibration: Modelling and phenomenology.

Several industrial and fundamental studies focus on the consolidation of granular materials as this covers many technological fields. When a granular material is shaken, it densifies. The energy needed to compact or decompact a powder column is of great interest in handling, filling and transport operations. This work studies the dynamic behaviour of four industrial granular materials–wheat flour, sericite, microcrystalline cellulose and glass beads–when submitted to vertical vibration using a particle damper. The effect of the vibration wave was studied by varying two dimensionless parameters: the relative acceleration, Γ and relative frequency, Ω including the relaxation time between periods. Our results show that despite the cohesiveness of the samples, their compaction dynamics occurs in at least two-compaction steps that a succession of stretched exponentials can model, denoted herein as a generalised KWW model. Also the absence of a relaxation time between periods leads to fluidisation during the first periods of vibration.The Fluidisation phenomena–the convective movement, granular jets, bubbling and slugging–appear to enhance particle reorganisation giving rise to higher packing fractions depending on the nature of the grains and operational conditions. A classification of the observed behaviours is proposed and related to the compaction kinetics.

Monte Carlo simulations of deformation behaviour of unbound granular materials based on a real aggregate library

ABSTRACT The Monte Carlo simulation (MCS) has been developed to estimate the strength distributions of heterogeneous materials influenced by different factors. The method presents a statistical correlation between the macroscopic properties and the non-uniform characteristics at meso scale. This study proposes an extensive MCS to investigate the influence of the aggregate morphology on deformation behaviour of unbound granular materials (UGMs) based on a real aggregate library and the discrete element method. Two indexes, elongation index (EI) and flatness index (FI), were used to evaluate the morphological characteristics of 3D aggregates rebuilt by the X-ray CT technique. Furthermore, repeated load triaxial tests of UGMs were simulated by 50 MCS samples. The effects of shapes and sizes of aggregates on deformation behaviours were statistically analysed. The results show that the deformation behaviour is dependent on the size and the EI distribution, but insensitive to the loading frequencies and FI distribution.