Granular Assemblies Research Articles

Particle scale study on the crystallization of mono-sized cylindrical particles subject to vibration

In this paper, the transition from random to ordered packings of mono-sized cylindrical particles under 3D mechanical vibration was simulated by discrete element method (DEM). The effects of particle aspect ratio, size of the particulate system and container wall on the granular crystallization were investigated. And the mechanisms were analyzed through the characterization of the order transition process in terms of packing density, coordination number (CN), orientational ordering parameter (O), nucleation and growth of cluster and granular temperature (θ). The results show that nearly perfect crystallization of mono-sized cylindrical particles can be achieved with specific aspect ratio and proper vibration conditions in a cylindrical container. The orientational ordering parameter demonstrates that the crystallization firstly starts from the container wall and then propagates inward gradually. The lower granular temperature in a cuboid container indicates less vibration energy transferred to the granular assembly compared with that in a cylindrical container, illustrating the critical role of container shape in crystallization. The vibrated crystallization of mono-sized cylindrical particles is analogous to entropy-driven process, which can be gradually achieved by the self-assembly of particles with parallel alignments along the already formed ordered clusters (nuclei) or the container wall. These results can help design complex and ordered granular structures.

Natural Thermoresponsive Rice Granules as Biocompatible Drug Carriers.

Through thermal gravimetric, X-ray diffraction, infrared spectroscopy, and scanning electron microscopic analyses, here we reveal that the 4–5 μm diameter pentagonal shaped rice granules are surprisingly stable against α-amylase, trypsin, lipase, diluted acids, and diluted bases. Some papain-sensitive proteins play an important role in the granular shape stabilization. We employ the reversible thermoresponsive expansion/shrinking character in aqueous medium of this biopolymeric pentagonal granular assembly to encapsulate the antibiotic vancomycin into the granule at the drug loading content of 80% drug mass with only 20% rice granule mass. The obtained drug-loaded granules display no-burst but steady sustained release of the water-soluble vancomycin in an aqueous environment for more than 24 h.

Effect of cement matrix on mechanical properties of cemented granular materials

A well-defined cemented granular materials (CGMs) is created by filling cement matrix into a densely packed granular assembly without disturbing granular backbone, in which particles are held together by solidified and hence elastic matrix. In this study, a formula between strength and matrix volume fraction is theoretically deduced for CGMs, and it is verified through experimental tests. The CGMs samples, which are fabricated by filling high performance self-compacting cement paste into alumina ceramics beads assembly, are used to investigate the mechanical behavior and properties of CGMs under uniaxial compression. It can be found in the stress-strain curves that a nonlinear regime is remarkable and the extent of nonlinear section increases as the matrix content increases. In the post-peak region, a dominant strain-softening phase is followed by a transient strain-hardening phase. The strength, strain at failure and Young's modulus of CGMs get greater with the increase of matrix volume fraction. Interestingly, the peak strength of CGMs is relied on the particle-matrix adhesion and the matrix volume fraction. In additions, the uniaxial strain at failure and elastic modulus of CGMs are found to be a linear function of matrix volume fraction.

Effect of fabric on shear wave velocity in granular soils

The small-strain elastic shear wave velocity ($$V_S$$) is a basic mechanical property of soils and is an important parameter in geotechnical engineering. Recently, $$V_S$$ has been adopted as one of the indices for development of liquefaction charts. This implies that if a parameter affects $$V_S$$, it may also affect liquefaction resistance. Some of the parameters whose effects have been accounted for include relative density, stress state and geologic age. An important parameter that affects both liquefaction resistance and $$V_S$$ is fabric. Quantification of in situ fabric is still an open problem and hence, considerable judgement is needed in order to map laboratory test results to field conditions. In this paper, we conduct numerical simulations at the grain-scale to investigate the effect of fabric on $$V_S$$. We start by showing that two granular assemblies, with the same stress state and void ratio but different fabrics, can exhibit different trends in liquefaction behavior. Furthermore, via a numerical implementation of the bender element test, we obtain two distinct trends of $$V_S$$ anisotropy for the two granular assemblies. Finally, we consider three different fabric measures based on contact properties and explore correlations between $$V_S$$ anisotropy and fabric anisotropy. We also look at fabric tensors of the ‘strong’ and ‘weak’ network, respectively, of the granular assemblies. Our results suggest that for liquefiable soils, i.e., recent Holocene-age deposits with negligible cementation and with a stress history of seismic loading, a knowledge of $$V_S$$ anisotropy can give information about fabric anisotropy. A knowledge of in situ fabric could help in more accurately mapping laboratory test results to field conditions.

Particle size effects on the contact force distribution in compacted polydisperse granular assemblies

Contact force distribution in a polydisperse granular assembly under uniaxial compaction is investigated using DEM simulations. In general, the contact force network generated in a compacted granular assembly is inhomogeneous. The effect of the relative particle size distribution on the nature of the contact force network in a compacted polydisperse granular assembly is investigated. The probability distribution and cumulative distribution of the normal contact forces for particles of different radii in a polydisperse granular assembly are analyzed. Distribution of the coordination number and the maximum force on each particle in a group of particles of the same size are also investigated. The study reveals that the larger particles have a higher probability of experiencing stronger contact forces than the smaller particles. The smaller particles in the assembly experience a lower maximum force and coordination number when compared to the larger particles. The small particles are observed to escape from the force chains by occupying the voids formed amongst the larger particles in the assemblies with considerable particle size variation. The particle size effect on the contact force distribution reduces as the size difference between the particles reduces. The knowledge of the distribution of the contact forces in a polydisperse assembly helps in estimating the probability of crushing amongst particles of different sizes.

An iterative Bayesian filtering framework for fast and automated calibration of DEM models

The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy.The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density.As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young’s modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.

From discrete to continuum modelling of boundary value problems in geomechanics: An integrated FEM‐DEM approach

SummaryDouble‐scale numerical methods constitute an effective tool for simultaneously representing the complex nature of geomaterials and treating real‐scale engineering problems such as a tunnel excavation or a pressuremetre at a reasonable numerical cost. This paper presents an approach coupling discrete elements (DEM) at the microscale with finite elements (FEM) at the macroscale. In this approach, a DEM‐based numerical constitutive law is embedded into a standard FEM formulation. In this regard, an exhaustive discussion is presented on how a 2D/3D granular assembly can be used to generate, step by step along the overall computation process, a consistent Numerically Homogenised Law. The paper also focuses on some recent developments including a comprehensive discussion of the efficiency of Newton‐like operators, the introduction of a regularisation technique at the macroscale by means of a second gradient framework, and the development of parallelisation techniques to alleviate the computational cost of the proposed approach. Some real‐scale problems taking into account the material spatial variability are illustrated, proving the numerical efficiency of the proposed approach and the benefit of a particle‐based strategy.

Impact energy distribution and wavefront shape in granular material assemblies

In this study, we investigated the dynamic response of granular materials subjected to point impact loading based on the discrete element method. The average velocity of the stress pulse was defined. The effect of elastic modulus on wave velocity was analyzed. The energy diffusion process in granular materials is affected by the contact between the particles, which is mainly reflected in two aspects: contact distribution and force transmission ratio. We first compared the wavefront shape in the specimens with different particle arrangements, and then assigned different material properties to the matrix particles. The wavefront shape is consistent with the previous results which proved the influence of the force transmission ratio. Finally, the variations of particle acceleration, kinetic energy and wave velocity at different impact angles are discussed. Our research reveals the energy propagation process through the contact between particles within granular materials. Our research results can be a reference for material design using granular materials for energy collection, energy absorbing etc.

DEM modelling of sequential fragmentation of zeolite granules under oedometric compression based on XCT observations

The objective of our research is to define a new Discrete Element Method (DEM) that can describe the processes involved in particle breakage and the resulting macroscopic behaviour of the particulate assembly, by directly observing and characterizing breakage mechanisms. To this aim, an oedometer compression test is performed on a dry granular assembly of zeolite, while acquiring 3D images of the specimen at several strain levels with an x-ray computed tomography device. We construct a DEM model that reproduces experimental observations, mainly: axial splitting is the main breakage mode; fragments are subjected to further breakage; very few fragments pass through the breakage plane. A fragment size limit is defined to reduce the computational cost associated with large numbers of breakage generations. We simulate the oedometer test for the same initial microstructure as in the lab test and with realistic particle mechanical properties, and compare the results to the 3D images. The numerical results show that our proposed model can capture the size evolution, shape change and mechanical response of the tested specimens.

Simulations of large-scale triaxial shear tests on ballast aggregates using sensing mechanism and real-time (SMART) computing

Since Discrete Element Method (DEM) was first introduced for modeling micromechanical interactions of granular materials back in late 1970s, significant progress has been made to improve the performance of DEM algorithms. For example, a variety of approaches have been developed to simulate triaxial tests using DEM to better understand the fundamental mechanical behavior of granular materials. Nevertheless, potential error accumulation over the necessary large number of timesteps as a part of the explicit time integration may undermine the simulation accuracy. This paper presents the development, implementation and validation of a computing scheme that is based on real-time data fusion between a sensing mechanism and real time (SMART) computing. This computing framework consists of: (1) real-time data acquisition of particle kinematics through a wireless instrumentation called “SmartRocks” that are embedded at discrete locations in a granular assembly, and (2) a built-in data-fusion-based algorithm using the Kalman filter to integrate the prediction generated by DEM and the measurements reported by “SmartRocks.” To evaluate the performance of the SMART computing algorithm, laboratory large-scale triaxial tests on ballast specimens were conducted and the results were compared to traditional DEM-only and SMART computing simulations. It is concluded the SMART computing improved the simulation accuracy over the DEM-only simulations in terms of the deviatoric stress vs. axial strain, volumetric strain vs. axial strain, and final deformed specimen shape, and hence can be used to model large-scale triaxial tests with high fidelity.

Artificial neural network-based prediction of effective thermal conductivity of a granular bed in a gaseous environment

Artificial neural network (ANN), a machine learning technique, is employed to predict the effective thermal conductivity of granular assemblies in the presence of a stagnant gas. ANN is trained with the help of estimated thermal conductivities calculated through resistor network (RN) model. RN model considers the effect of the presence of stagnant gas and the gas pressure (Smoluchowski effect) for the calculation of effective thermal conductivity. Granular assemblies are generated and compacted through discrete element method (DEM). The ANN is trained to predict the effective thermal conductivity of a granular assembly for a set of measurable experimental parameters (stress and packing fraction) without requiring the knowledge of microstructural details (coordination numbers and overlaps) of the assembly. The predicted effective thermal conductivity values through ANN are in good agreement with the experimental results. Estimation of effective thermal conductivity through the trained ANN is much faster (few seconds compared to few hours required for DEM together with RN approach) with very good accuracy.

A constitutive model for granular materials with evolving contact structure and contact forces\u2014Part I: framework

This and the companion paper present a constitutive model for granular materials with evolving contact structure and contact forces, where the contact structure and contact forces are characterised by some statistics of grain-scale entities such as contact normals and contact forces. And these statistics are actually the “fabric” or “force” terms in the “stress–force–fabric” (SFF) equation. The stress–strain response is obtained by inserting the predicted “fabric” or “force” terms from evolution equations into the SFF equation. Discrete element modelling is used to verify the slightly modified SFF equation and also to obtain the data of how the contact structure and contact forces evolve in various loading paths. It is demonstrated that a normalised contact force is a better measure of the contact forces in polydisperse granular assemblies and strong contacts should be contacts with larger normalised contact forces. The modified SFF equation is shown to predict the stress accurately. The constitutive equations regarding the response of the contact structure and contact forces are presented and they along with the SFF equation form a constitutive model, which is found capable of capturing the observed phenomena correctly and predicting the mechanical response in various loading conditions. The model is shown to be an extension to the hypoplastic models with more state variables.

Discrete element modeling of first shear strain gradient effects on mechanical behaviors in granular materials

The effects of strain gradient on the mechanical behavior of granular materials have attracted attention from many researchers. In this paper, the effects of the first shear strain gradient in granular materials are focused on. Granular assemblies with various particle radii and porosities are built through a two-dimensional discrete element method (2D-DEM) simulations. The results indicate that the macro shear stress is insensitive to the first shear strain gradient at low strains, but is indeed affected at high strains; the third order stress conjugated with the first shear strain gradient is sensitive to the first shear strain gradient in all deformation cases; the third order work done by the third order stress and the ratio of it versus the total work are affected by the first shear strain gradient; the evolutions of the invariants of the third order stresses present severe change of the local relative vertical displacement of particles, which lead to localization occurrence. Based on DEM simulations, it is found that only the effect consideration of the first shear strain gradient on the macro shear stress is not sufficient, whereas the effect on work should also be taken into account and the third order work as a part of strain energy cannot be ignored, which is falsely classified as a portion of the accumulated energy dissipated by frictional sliding.

Evolution of fragment size distributions from the crushing of granular materials.

We study fragment size distributions after crushing single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of the particle we obtain the size distributions of fragments for both cases after large displacements. For the single-particle crushing, this fragmentation mechanism produces a log-normal size distribution, which deviates from the power-law distribution of fragment sizes for the packed bed. We show that as the breaking process evolves, a power-law dependency on the displacement is present for the single grain, while for the many-grains system, the distribution converges to a steady state. We further investigate the force networks and the average coordination number as a function of the particle size, which gives information about the origin of the power-law distributions for the granular assembly under uniaxial compression.

An assessment of discrete element approaches to infer intergranular forces from experiments on 2D granular media

We propose a new way to estimating interparticle contact forces in granular materials, based on the combination of experimental measurements and numerical techniques that take the contact laws respectively from Molecular Dynamics and Non-Smooth Contact Dynamics discrete element methods. Tests are performed in quasi-static conditions on a two-dimensional granular assembly; 80 MPixel pictures of the assembly are shot throughout each test. Image processing and Digital Image Correlation are used in order to get information on the geometry of the assembly (particles and contact points position) and the rigid-body motion of particles (displacements and rotation); based on this information, numerical methods can be applied to assess contact forces. 2D DEM simulations are also performed and the same information is extracted and used for contact force estimation, so that the numerical methods can be validated. The reproducibility of the original set of contact forces is shown to be dependent on the displacement history for the first method, based on contact elasticity, and on the degree of force indeterminacy for the Contact Dynamics-based one. The validation phase also includes a perturbation analysis to predict the influence of measurement error (bad contact detection) when applying the Contact Dynamics-based method, which shows the robustness of this method. After this validation phase, the methods are applied to experimental data. Measurement error on kinematic measurements turns out to be quite significant for the first approach, while it does not affect the second, for which the accuracy of the force estimation can be assumed to be mainly dependent on the degree of force indeterminacy of the system.

Numerical simulations of granular material behavior under rotation of principal stresses: micromechanical observation and energy consideration

A numerical investigation on the behavior of granular materials subjected to the rotation of principal stresses using the discrete element method is presented. A numerical procedure is developed to implement the two-dimensional arbitrary stress or strain paths imposed on polygonal specimens. Significant volumetric strain can be obtained and granular assembly appears to develop an anisotropic internal structure characterized by the contact-normal-based fabric tensor in due course, with its direction being rotated with the rotation of the principal stress. The observations indicate a significant degree of non-coaxiality between the principal-stress direction and the principal-strain increment direction. An ultimate state can be reached after sufficiently large numbers of cycling, resulting in a constant fabric norm and a circular strain trajectory in the deviatoric space. The boundary work, dissipation, and strain energy, are also registered during the entire loading process and its correlation between non-coaxial deformations is analyzed from micro-scale perspective. Before the ultimate state is reached, the applied work is partially dissipated by frictional sliding, and the remainder is stored as the strain energy within the specimen. When the ultimate state is reached, however, no change in the strain energy is obtained, and the plastic work is entirely dissipated, as the elastic portion of the free energy increment only depends on the elastic strain.

Geogrid pull-out modelling using DEM

With the advancement of the use of synthetic reinforcements in geotechnics, a greater understanding of the mechanisms involved in soil-reinforcement interaction is the focus of major research centres on the subject. The topic of this study is the shearing behaviour at interfaces between granular materials and geogrids. The main objective is to provide a more fundamental understanding of some micromechanisms present in this type of interface, which in turn are important to optimize the design of such reinforcement. The numerical modelling of these reinforced structures must deal with the complexity of the material-reinforcement interaction problem; therefore, it requires specific numerical models whose formulations admit localized behaviours in the contacts as well as the granular nature of the material (e.g., soil, gravel, ballast). A robust and flexible way of modelling this problem is through the Discrete Element Method (DEM). The DEM proposes to model this granular nature by representing the soil as interacting constituent particles, whose behaviour is ruled by physical laws defined at the contact points. The numerical approach is desirable since it allows, in an articulated and relatively fast way, studying closely different regions of the interface, in order to identify factors and variables that are important for the problem. The purpose involves the DEM for a 3D modelling of a geogrid pull-out test to calculate the magnitude of forces in different elements of the geogrid (i.e., nodes, longitudinal and transverse members). Preparation of numerical samples has a particular importance in the final results of simulations. Thus, the numerical techniques used to obtain better geometry for the geogrid and a granular assembly with a representative grain rolling effect are also presented in this paper.

DEM analysis of passive failure state behind a rigid retaining wall: effect of boundary conditions

Discrete Element Modelling (DEM) is a virtual testing method that enables multiscale studies on granular materials. DEM provides a well-controlled testing environment, which enables precise systematic evaluation of the factors influencing the bulk response. The current study focuses on the behaviour of cohesionless backfills while a passive state of stress is simulated (i.e. rigid retaining wall translates toward backfill). Though particle-scale properties (e.g. size, shape and cohesion) play an important role on the macro response, the main objective in this study is to highlight the extent by which boundary conditions are important. Thus, identical dense packings are subject to the following boundary conditions: smooth/rough retaining wall and smooth/rough/periodic sidewalls (necessary for maintaining plain-strain conditions). Based on the DEM results, the failure surface geometries, wall pressure distribution and dilative response of the specimens are evaluated. It is seen that a curvilinear slip surface, similar to that observed in experiments, is only obtained once a rough retaining wall and periodic sidewalls are available. The overall observations suggest that the mobilisation of the passive state of stress, for a cohesionless granular assembly, is highly sensitive to the considered various boundary conditions.

Role of the location and size of soluble particles in the mechanical behavior of collapsible granular soil: a DEM simulation

Collapsing soil structure caused by mineral dissolution is a challenge to geoenvironmental projects. Although the parameters affecting the macro-response of collapsible soil have been addressed experimentally, the micromechanical behavior of soluble soil is unclear. The aim of this study was to simulate the dissolution behavior of a granular assembly at the particle level. A DEM code was developed that considers both localized and random dissolution as well as the particle size distribution and stress level. The effect of particle dissolution was simulated by considering the role of particle size in the load-bearing skeleton. The results show that mechanical behavior of a granular assembly is strongly influenced by the location and percentage of dissolution of particles. The loss of the soluble particles decreases physical contact and transfers to neighboring particles due to the arching forces around the voids, as in a honeycomb structure. However, if the soluble areas cut across the load-bearing force chains, a honeycomb fabric cannot form because of the lack of an arching effect, leading to the collapse of the structure and large volume change. Particle loss of up to 3% will not have a serious impact on the mechanical behavior of the granular assembly. After fine particle dissolution of a binary mixture, the arching effect around them decreases the volumetric strain in comparison with the dissolution of coarse particles. Also, during dissolution, the high stress level will decrease the peak friction angle, but the opposite is true for the post-dissolution behavior above 12% strain.

Influence of quasi-static loading rates on crushable granular materials: A DEM analysis

Does granular material show strain rate dependent response, especially with quasi-static loading condition? The answer is both yes and no since it depends on various factors like particle shape, size and crushability. In the present study, a micromechanical analysis is carried out using discrete element modelling (DEM) to explore the effects of variation in the loading rates, within/near the quasi-static regime, on the stress-strain response of crushable and non-crushable granular assemblies. The study considers monotonic loading at two different strain rates and a sudden strain rate shift condition. The numerical simulation of one-dimensional (1D) compression shows quasi-static loading, which usually produces rate-independent response, can demonstrate rate-dependent features during particle crushing. The variation in the contact force distribution within the granular assembly at different loading rates, dictates the stress response and the crushing events. Relatively low strain rate compression favors homogeneous crushing involving a large number of particles that consequently reduces the strength via fragments rearrangement. Conversely, high strain rate promotes localized crushing within fewer particles, and thus strain hardening is observed. Sudden strain rate shift within the granular assembly creates a discontinuous velocity profile that hampers the crushing events.