Granular Assemblies Research Articles

SHape Analyser for Particle Engineering (SHAPE): Seamless characterisation and simplification of particle morphology from imaging data

The mechanical and rheological behaviour of particulate and granular assemblies is significantly influenced by the shape of their individual particles. We present a code that implements shape characterisation of three-dimensional particles in an automated and rigorous manner, allowing for the processing of samples composed of thousands of irregular particles within affordable time runs. The input particle geometries can be provided in one of the following forms: segmented labelled images, three-dimensional surface meshes, tetrahedral meshes or point-clouds. These can be complemented with surface texture profiles. Shape characterisation is implemented for three key aspects of shape, namely surface roughness, roundness and form. Also, simplified particle shapes are generated by the code which can be used in numerical simulations to characterise the mechanical behaviour of particulate assemblies, using numerical approaches such as the Discrete Element method and Molecular Dynamics. Combining these two features in one automated framework, the code allows not only to characterise the original granular material but also to monitor how its morphological characteristics change as the shape of the particles is simplified according to the chosen fidelity level for the application of interest. Program summaryProgram Title: SHAPE: SHape Analyser for Particle EngineeringCPC Library link to program files:https://doi.org/10.17632/7h3n5rxtf4.1Developer's respository link:https://github.com/vsangelidakis/SHAPELicensing provisions: GPLv3Programming language: MatlabNature of problem: Automatic morphological description of three-dimensional particles for material characterisation and generation of simplified particle geometries to be used in numerical simulations of their mechanical behaviour.Solution method: SHAPE [1] analyses the morphology of particles using a range of different morphological descriptors, characterising the form, roundness and roughness of each particle. An object-oriented structure is put in place to ensure a robust handling of the morphological characteristics. The simplified particle geometries are exported in a variety of different formats, supporting some of the most popular Finite Element and Discrete Element codes.

Semi-analytical framework for stress–conductivity correlations in periodic granular assemblies under compaction

The contact network, defined by a fabric tensor, influences phenomena such as force or heat transfer in a granular assembly. The correlation between fabric, stress, and conductivity has, however, been least explored. Furthermore, a link between these quantities may help to build a benchmark method to assist experiments substantially. The present work bridges the gap between the macroscopic quantities, such as stress and conductivity tensor, using its microscopic connection and the fabric tensor. The study presents a few interesting functional forms and non-dimensional macroscopic quantities that couple conductivity, stress, and fabric. The main feature of these functional forms is that they are independent of friction. These functional forms will provide a good estimate of fabric and conductivity which can be used real-time during the experimental investigations as well.

A contact dynamics code implementation for the simulation of asteroid evolution and regolith in the asteroid environment

Over the last decades, simulations by discrete elements methods (DEM) have proven to be a reliable analysis tool in various domains of science and engineering. By providing access to the local physical mechanisms, DEM allows the exploration of microscopic based phenomena related to particles properties and interactions in various conditions and to revisit constitutive equations consequently. The growing computer power and memory now allow us to handle large collections of grains of various shapes and sizes by DEM simulations and in particular, it offers new perspectives in the exploration of the behavior of asteroids seen as self-gravitating and cohesive granular aggregates. In this paper we describe the Contact Dynamics (CD) method, a class of DEM based on non-smooth mechanics, and its implementation in the open-source software LMGC90. In contrast to more classical approach, Hard- and Soft-Sphere DEM, the CD method is based on an implicit time integration of the equations of motion and on a non-regularized formulation of mutual exclusion between particles. This numerical strategy is particularly relevant to the study of dense granular assemblies (even of large size) because it does not introduce numerical artifacts due to contact stiffness. So that it can be used for Small Body research, we implement a parallelized kd-tree and monitor the performance of the code as it simulates a number of granular systems. We provide examples of the simulation of the accretion of self-gravitating aggregates as well as their rotational disruption. We use the routines at our disposal in the code to monitor their behavior through the entire evolution and find agreement with previous research.

Particle shape effects on the shear behaviors of granular assemblies: irregularity and elongation

This study examines the influence of particle shape irregularity and elongation on the shear behaviors of granular materials using the 3D discrete element method (DEM). The particles are generated by combining a Fourier shape descriptor-based method with the random field theory and reconstructed in DEM using the overlapping sphere algorithm. A series of drained and undrained triaxial and true triaxial tests are performed to shear the samples with different particle irregularity and elongation to the critical state. The stress and the strain responses, the evolution of the fabric anisotropy and the coordination number are examined and analyzed within the framework of the anisotropic critical state theory. It is found that the consideration of complex shaped particles in DEM produces more realistic sand behaviors, and the shear strength and the dilation of the granular material increase with increasing irregularity and elongation. While elongation in the range of the study has insignificant influence on the location of the critical state line (CSL) on the void ratio-mean effective stress plane, irregularity is found to positively affect both the absolute slope and the intercept of the CSL. The unique fabric anisotropy norm at the critical state is also sensitive to the particle shape and is greater with larger irregularity and elongation.

Influence of various DEM shape representation methods on packing and shearing of granular assemblies

Realistic yet efficient representation of particle shape is a major challenge for the Discrete Element Method. This paper uses angle-of-repose and direct-shear test simulations to describe the influence of several shape representation methods, and their parameters, on the bulk response of granular assemblies. Three rolling resistance models, with varying coefficient of rolling friction, are considered for spherical particles. For non-spherical particles, superquadrics with varying blockiness and multi-spheres with varying bumpiness are used to model cuboids and cylinders of several aspect ratios. We present extensive quantitative results showing how the various ways used to represent shape affect the bulk response, allowing comparisons between different approaches. Simulations of angle-of-repose tests show that all three rolling friction models can model the avalanching characteristics of cube/cuboid and cylindrical particles. Simulations of direct-shear tests suggest that both the shear strength and the dilative response of the considered non-spherical particles (but not their porosity) can only be predicted by the elasto-plastic rolling resistance model. The quantitative nature of the results allows identifying values of the shape-description parameters that can be used to obtain similar results when using alternative shape representation methods.Graphical abstract

Non-coaxial plastic flow of granular materials through stress probing analysis

The current study investigates the non-coaxial plastic flow in granular media where the principal directions of incremental plastic strain differ from those of the current stress (and of the current fabric tensor). The stress probing technique is used with Discrete Element Method simulations to capture the plastic response of a 2D granular assembly to loading increments along different directions in stress space, including non-coaxial ones. A general form for the plastic flow is suggested, based on multi-mechanism plasticity theory which is demonstrated to be capable of capturing the essential characteristics of the non-coaxial plastic flow. Deviations between DEM results and model predictions are associated with the incrementally nonlinear nature of the response. The analysis of the results indicate that, at a given stress state, the plastic yielding direction is not coaxial with the current stress. The significance of the non-coaxial plastic flow is shown to be around 20% for lower deviatoric stresses, but this value diminishes as the peak stress is achieved, hinting to the dominance of a single mechanism at failure. The study concludes by comparing the developed model with two well-known non-coaxial models in the literature, where the performance of the developed model is found to be close to the double-shearing theory.

Morphological characterisation of 2D packing with bi-disperse particles

The morphological structure of granular materials can dominate their mechanical, hydraulic, electrical, and thermal properties; thus, the formation of order and disorder arrangement of particles is the key characteristic to describe such micro-structures. During the packing procedure, external energy input and perturbations, such as dynamic cyclic load, and the particle size distribution were mentioned by many previous works to be significant in controlling the structure. This study explores order to disorder transition within 2D binary granular assemblies under vibration. A numerical packing method combining particle size growth and dynamic vibration is implemented and verified against experiments to achieve desired packing structure. The Bond orientation order number and pair distribution function are used as indices for characterising the morphological structure. Our packing simulation results show a combination of appropriate vibration and a proper particle size growth rate can facilitate the formation of granular crystallisation. Additionally, for binary packing, the size ratio, and the number fraction of small particles can play a critical role in determining the morphological transformation.

Micromechanical investigation of particle breakage behavior in confined compression tests

This paper aims to give a micromechanical investigation into the progressive size reduction mechanism and its effects on macro responses of granular assemblies during confined compression tests. A series of numerical studies based on the cohesive zone model are presented, incorporating internal deformation and fragmentation behaviors, and the variations of feed profiles are considered. Simulation results reasonably reproduce experimental observations in terms of macro compression responses and typical particle breakage modes. A scaling method is proposed for considering the contributions of fine products. With this method, the fragment size distribution is refined and compare favorably with physical results. The breakage degree is found to be dependent on input energy, regardless of variations of feed profiles including material heterogeneity, gradations, or friction conditions. Furthermore, a quantitative micro-analysis of normalized and cumulative normal contact force distribution, as well as contact orientation distribution is presented in this study, demonstrating the different roles of fragmentation in micro-mechanical response of particle assemblies owing to different materials or boundary friction effects.

A new Delaunay triangulation-based approach to characterize the pore network in granular materials

The ability of granular materials to retain fine particles transported within their void space by seepage flow depends strongly on the geometric characteristics of their pore network (pore sizes and constriction sizes). Hence, characterizing the pore network of a granular assembly obtained by means of a micro-tomography scanning or a numerical discrete simulation is of great importance in assessment of its filtration efficiency. Here, we determine characteristics of the pore network of virtual samples composed of spherical particles simulated by using the DEM. A new criterion is proposed to merge neighboring tetrahedra issued from the weighted Delaunay triangulation. To do so, we extend the concept of inscribed void sphere, initially defined for each tetrahedron, to each polyhedral sub-domain constituted of merged tetrahedra. This inscribed void sphere fits the best the void space within the sub-domain. Flat tetrahedra are first eliminated by a primary merging procedure taking into account two basic geometric conditions required for each pore. Adjacent sub-domains are then merged depending on the level of overlap between their inscribed void spheres. The pore size distributions and constriction size distributions (CSD) of granular samples with different grain size distributions obtained with the new merging criterion are compared to those given by two other criteria often used in the literature. The new criterion allows us to reduce greatly the inherent subjectivity in characterizing the granular pore network and to remediate the drawbacks of the two considered criteria in the literature. Moreover, CSDs given by these different criteria tend to converge for gap-graded and widely graded materials. The CSDs obtained with the new merging criterion are used to estimate the controlling constriction sizes $$D_c^*$$ of the considered samples, and the estimated values of $$D_c^*$$ are compared to Kenney and Lau’s empirical rule.

Particulate Modeling of Sand Production Using Coupled DEM-LBM

Sand production is a complex phenomenon caused by the erosion of borehole walls during the extraction of hydrocarbons. In this paper, the sanding process in a typical Thick-Walled Hollow Cylinder (TWHC) test is numerically simulated. The main objective of the study is to model the particulate mechanism of sand production in granular assemblies with different bonding conditions and examine the effects of parameters such as stress level and cavity size on the sanding model. Due to the discrete nature of sand particles, the Discrete Element Method (DEM) is chosen to model solid particles, and the Lattice-Boltzmann Method (LBM) is implemented to simulate fluid flow through the solid particulate medium. A computer program is developed using the Immersed Moving Boundary (IMB) approach to couple the two methods and model fluid–solid interactions. After the program is validated, the simulations were conducted on 2D models representing cross-sections of TWHC samples under radial fluid flow. The results show that the developed program is able to capture complicated stages of sand production already observed in experiments. The program also proves to be a promising tool in the parametric study of sand production. It successfully simulates different aspects of the sanding phenomenon, including the scale effect, the extension of failure zones in samples under incremental stress, and the stress relaxation during rapid particle erosion.

3D DEM insights into the effect of particle overall regularity on macro and micro mechanical behaviours of dense sands

Particle shape affects the mechanical properties of sands, but the underlying micro-mechanisms are not yet explored, at least partially, due to difficulties in accessing the particle scale information in the laboratory. This study aims to fill this gap through DEM by proposing a general framework for DEM simulation considering realistic particle shape and grading characteristics. Within the proposed framework, the irregular sand particle is approximated by 3D clump, and numerical triaxial drained compression tests are conducted for five granular assemblies of different overall regularity. The simulated critical state friction angles of these five assemblies are consistent with those predicted by an empirical formula proposed in the literature. The simulation results demonstrate that decreasing of overall regularity enhances the interlock effect between particles, making the assembly a higher stiffness and shear strength. Moreover, among different fabric anisotropies, the anisotropies of contact normal and normal contact force fabrics contribute to about 80% of the critical shear strength regardless of the overall regularity. With the decreasing of the overall regularity, the contribution of the anisotropy of contact normal fabric increases while that of normal contact force fabric decreases. The overall regularity mainly affects the anisotropies of contact normal and shear contact force fabrics.

The impact of high-velocity sand columns against rigid and deformable structures based on the smoothed particle hydrodynamics method

The response of a structure subjected to the impact of a dry sand slug has been studied using a fully coupled approach, in which a novel algorithm based on the smoothed particle hydrodynamics (SPH) method is proposed for soil-solid interaction (SSI). The proposed algorithm is a hybrid continuum/discrete approach that can determine two regimes of contact behavior. When the granular assembly has a high relative velocity in dealing with the structure, initially, the short-term particle-to-particle contacts take place, resembling molecular collisions in a fluid and referred to as regime I. Then, the increase of the relative density of aggregate particles leads to semi-permanent contacts, referred to as regime II. The present aim is development of a coupling model that includes both regimes. The simulation of impact of granular slug into a rigid or deformable target leads to large numerical errors and even divergences. To overcome the limitation of traditional SPH approach that the density estimate is a major challenge in high-rate deformation problems, the number-density scheme is extended to the fully compressible approach. Finally, the proposed SSI Algorithm is validated with Liu et al.’s results [1] to simulate the interaction of a structure with sand slugs traveling at high velocities.

Effects of particle gradation and geometry on the pore characteristics and water retention curves of granular soils: a combined DEM and PNM investigation

Pore characteristics play central roles in the transport of water and gas through granular soils, which is relevant to a wide range of geotechnical and geoenvironmental applications. In this study, a numerical procedure combining the discrete element method and pore network model is presented to relate the physically representative pore structure to the particle geometric features, and rapidly predict the macroscopic flow properties of granular assemblies. This numerical procedure is applied to investigate the effects of particle gradation and geometry on the pore characteristics and water retention curves of granular soils under isotropic compression. The results indicate that a larger uniformity coefficient (Cu) of particle diameters results in a lower porosity. The porosity first decreases and then increases as the aspect ratio (AR) of the particles increases from 1.00 to 2.50 and reaches the minimum at AR = 1.75. As Cu ranges from 1.00 to 2.16, the standard deviations and mean values of pore geometry and connectivity parameters, including pore and throat diameters, pore spacings, and coordination numbers, present linear correlations. The logarithm of air entry pressure decreases linearly with the increasing logarithm of mean pore diameter in response to the variations in both Cu and AR. A higher pore diameter variance induced by a smaller Cu produces a lower fitting parameter m in the van Genuchten equation for water retention curves.

Threshold silt content dependency on particle morphology (shape and size) of granular materials: review with new evidence

The threshold silt content is well known as a key parameter affecting the mechanical response of binary granular assemblies considering particle characteristics (size and shape). In this context, the threshold silt content (TSC) is determined from different laboratory tests based on packing density response (emax and emin versus silt content «Sc») and theoretical approaches proposed by several researchers in the specialized published literature using the characteristics of host sand and silt [emax(sand), emin(sand) , emax(silt) , emin(silt) , Gs , Gf and x]. The analysis of the recorded data indicates that the TSC derived from the (emax) curve appears more reliable than that obtained from the (emin) one. Moreover, it is found that the proposed analytical methods are suitable to quantify the threshold silt content (TSC) than that determined experimentally using the packing density (emax and emin). In addition, the test results show that the new introduced ratios [(D50s×As)/(D50f×Af)] and [(Cus×As)/(Cuf×Af)] determined based on particle characteristics (shape and size) appear as appropriate parameters for predicting the threshold silt content (TSC) of sand-silt mixture of the compiled data from the published literature as well as that of the present research related to Chlef sand, Fontainebleau sand and Hostun sand mixed with Chlef silt.

Independence of shear strength with particle size dispersity still valid in polyhedral particle assemblies

A very staggering result that has been constantly highlighted in granular media is that the shear strength of granular assemblies is independent of the particle size dispersity. In other words, a packing composed of monodisperse particles has similar strength properties to those of polydisperse systems. This has been shown numerically for the simplified case of disc and polygon assemblies in 2D and spheres in 3D. In this paper, we use three-dimensional contact dynamics simulations to revisit these results for the more complex case of assemblies composed of highly polydisperse rigid polyhedra. Although non-spherical shapes induce more intricated spatial correlations than spherical shapes because of the multiple contact types (i.e., vertex-face, edge-edge, edge-face, face-face), our numerical data provide evidence that the shear strength independence as the particle size dispersity increases still holds up for assemblies of polyhedra. We explain this finding from compensation mechanisms at the micro-scale between geometrical and mechanical anisotropies developed within the assemblies.

Mesoscale inertial transition in granular materials

Granular assemblies can experience complex failure patterns along a given loading path, with a distribution of ephemeral inertial events marked by local outbursts in kinetic energy. However, investigating such mechanisms appears to be necessary to understand how a certain failure mode develops in a granular material. Using a discrete element method, this study highlights several microstructure reorganizations before the specimen reaches a proper failure state. Meso structures have proven to be efficient to understand the elementary mechanisms responsible for these outbursts in kinetic energy. Strain–like and stress-like quantities are thus defined at a mesoscale and they are used to characterize the nucleation and propagation of these local microstructural events.

LMGC90: a Contact Dynamics open source code for the simulation of granular asteroid with realistic regolith shapes. Application to the accretion process

Granular asteroids are naturally occurring gravitational aggregates (rubble piles) bound together by gravitational forces. For this reason, it is reasonable to use the theoretical concepts and numerical tools developed for granular media to study them. In this paper, we extend the field of applicability of the Contact Dynamic (CD) method, a class of non smooth discrete element approach, for the simulation of three dimensional granular asteroids. The CD method is particularly relevant to address the study of dense granular assemblies of a large number of particles of complex shape and broad particles size distribution, since it does not introduces numerical artefacts due to contact stiffness. We describe how the open source software LMGC90, interfaced with an external library for the calculation of self-gravity, is used to model the accretion process of spherical and irregular polyhedral particles.

Taming the Janssen effect

We investigate both experimentally and theoretically the apparent mass of a ferromagnetic granular assembly filling a cylindrical container and submitted to a magnetic fieldB, aligned vertically along the silo. We show that the mass of the ferromagnetic granular column depends strongly on the applied magnetic field. Notably, our measurements deviate strongly from the exponential saturation of the measured mass as a function of the true mass of the grain packing, as predicted by Janssen [H.A. Janssen, Vereins Eutscher Ingenieure Zeitschrift, 1045 (1895)]. In particular, the measured mass of tall columns decreases systematically as the amplitude of the magnetic field increases. We rationalize our experimental findings by considering the induced magnetic dipole-dipole interactions within the whole packing. We show the emergence of a global magnetic radial force along the walls of the silos, fully determined by the external magnetic field. The resulting tunable frictional interactions allows a full control of the effective mass of the ferromagnetic granular column.

Statistical properties of cell stresses in 2D granular solids

We investigate numerically the statistics of the stresses, defined for cells - the irreducible loops surrounded by particles in contact - in two-dimensional granular solids and the relation between these cell stresses and cell structures. We prepared a number of mechanically stable granular assemblies at various packing fractions and mean coordination numbers, and measured the stress statistics on each cell. We find the following. (1) The mean cell stress agrees with the bulk external pressure; (2) the probability density function of the normalised cell stress ratio collapses into a master curve; (3) the mean stress ratio increases with increasing intergranular friction; (4) the mean stress ratio per cell order decreases with increasing cell order because of their reduced stability; (5) the maximum cell stress direction correlates well with the cell’s long axis. These results are strong evidence that the cell structure and the stress field self-organise together and reveal the co-evolving correlations between the two.

The effect of particle shape on the angle of repose test based calibration of discrete element models

Discrete element method (DEM) is a Lagrangian description based numerical technique used for modelling the mechanical behavior of granular materials. For using the DEM model, the micromechanical parameter values used in the governing equations must be determined beforehand. This is the so-called calibration problem. In most of the cases these micromechanical parameters cannot be directly measured, their values must be systematically changed until the modeled macro behavior of the granular assembly will be the same, as the real-life behavior. In this article we propose the simplest possible calibration method, the so-called angle of repose test for application in case of agricultural crop product related problems. We examine the effect of particle shape on the value of angle of repose, ad give statistically acceptable empirical function to describe this dependence mathematically.