Mechanical Properties Of Granular Materials Research Articles

Smoothed particle hydrodynamics approach for modelling submerged granular flows and the induced water wave generation

In this study, we develop a Smoothed Particle Hydrodynamics (SPH) 2D-model for simulating fully submerged granular flows and their arising water waves. The granular particles are characterised by a non-Newtonian flow pattern, following a Casson constitutive law, generalised by applying the infinitesimal strain theory to avoid numerical singularities inherited from the original law. The implementation of this rheological model on the weakly compressible viscous Navier-Stokes equations enables the simultaneous modelling of the motion of granular flows and their resulting water waves, establishing a monolithic representation of fluid-structure coupling. The novelty of this model lies in the numerical continuity of the generalised rheological model based mainly on the yield stress criterion, which is computed purely from the mechanical properties of granular materials, including internal friction, cohesion, and viscosity coefficients. The proposed SPH model is validated through two benchmarks available in the literature, representing a submarine landslide along an inclined plane and an immersed granular column collapse. The outcomes of our study illustrate the effectiveness of the proposed model in accurately predicting the motions of submerged granular masses and their resulting water waves, which is crucial for accurately predicting the behaviour of underwater landslides and other natural hazards.

Non-convex shape effects on the biaxial compression of granular materials composed of monophasic packing and binary mixture

Driven by external compressions or shears, the granular material composed of non-convex shapes often undergoes self-assembly and becomes entangled, resulting in denser packings. In this work, the biaxial compression of monophasic and binary mixture composed of 2D intersecting crosses have been simulated via the discrete element method. As the aspect ratio increases, both the yield strength and elastic modulus initially increase before reaching a peak at w = 0.5. In binary mixtures, an antagonistic effect has been observed in mechanical properties of granular material. The decrease in strength and stiffness in binary mixtures can be attributed to the constraints imposed by multi-point contacts, along with the local order degree, which is particularly unique for non-convex particle packings. Building upon this understanding, we have extended the empirical formula into predicting the mechanical behavior of non-convex binary mixtures. This extension incorporates an additional non-linear term determined by both the shape factor and component fraction.

Discrete Element Simple Shear Test Considering Particle Shape

The particle shape has significant effects on the slip and rotation of particles in the shear of geomaterials, which is an important factor in the deformation and strength of geomaterials. This paper employed particle flow code (PFC3D) to simulate the simple shear test, and ellipsoidal particles with different aspect ratios were prepared to study the effects of particle shape on the mechanical behavior and fabric evolution of granular materials under complex stress paths. The numerical results show that the particle shape has a significant effect on the peak strength, dilatancy, non-coaxiality, and other mechanical properties of granular materials. The contact fabric evolves from orthotropy to transverse isotropy under the principal stress axes rotation. This paper will provide a reference for natural granular materials with different shapes in the study of mechanical behavior and the micro-constitutive model.

Influence of the interparticle friction coefficient on the mechanical behaviour of breakable granular materials with realistic shape

Interparticle friction coefficient μ is an important factor affecting the mechanical properties of granular materials. In this study, the influence of μ on the mechanical behavior of granular materials is investigated by DEM. Through 3D scanning and Voronoi tessellations, the breakable particle model with realistic shape is constructed. A series of drained triaxial tests were performed at different μ values. Then, the particle breakage characteristics, including the degree of particle breakage and the breakage mode, were evaluated. In addition, microscopic characteristics, including coordination numbers and contact forces, were examined. Finally, the underlying mechanisms of φc evolution are explained from two perspectives of particle movement and fabric anisotropy. First, the rolling behavior of the particles increases with μ values, leading to a larger average displacement of particles. The influence of particle movement and friction coefficient balance each other, resulting in φc remaining constant when μ⩾0.4. Second, the initial increase of φc is due to the increase of the contact normal anisotropy ac, the normal contact force anisotropy an and the tangential contact force anisotropy at. Subsequently, the constant φc is the result of the decrease of ac and an being compensated by the increase of at.

Multi-GPUs DEM algorithm and its application in the simulation of granular materials

The Discrete Element Method (DEM) is one of the most common numerical approach for modeling the physical and mechanical properties of granular materials. However, its computational efficiency can be a major bottleneck, which significantly hinders its application in engineering fields. To overcome this challenge, a multi-GPU framework with OpenMP has been developed. In this framework, the DEM particles in 3D space and their corresponding contact information are sorted in a given direction in the simulation, and each GPU device handles a subdomain of particles and relative contacts. Additionally, the contact information is densely arranged to minimize memory usage. To further enhance efficiency, sorting and packing algorithms for the contact information have been introduced. During calculating loop, the number of contacts on each device is monitored, and the spatial division of devices is adjusted to balance memory distribution. The efficacy of the multi-GPU algorithm is verified through a chute flow test. Using numerical results, the segregation process and mechanics of granular materials during sliding have been studied in detail. Furthermore, the simulations demonstrate that the developed multi-GPU algorithm greatly enhances computational efficiency and reduces memory usage per device.

Thermodynamic constitutive model for granular soils considering particle shape distribution

Particle shape has a significant effect on the shear strength and shear dilatancy properties of granular materials. This study presents a granular thermodynamic theory investigate the effects of particle shape and distribution on the mechanical properties and behavior of granular materials. The theory model outcomes closely resemble experimental results, effectively capturing the impact of particle shape on the mechanical properties and shear dilation of granular materials. The paper analyzes the relationship between a granular system's plastic behavior and granular temperature and explores the influence of irregularly shaped granular on the system's strength and kinetic energy activity. The granular temperature behavior during external loading is studied, showing that granular temperatures increase to a maximum value before gradually decreasing to a more stable state. Simulation results based on the proposed model also indicate obvious effects of nonuniform particle-shape distribution on the mechanical properties of granular materials, providing a comprehensive insight into the underlying mechanisms of the particle-shape effects from the perspective of thermodynamics.

Unified creeping model identifying the critical state of granular materials

The mechanical properties of granular materials at a low shear rate are frequently viewed as rate-independent, and a rate-independent constitutive relation is used to describe the mechanical behaviors of the granular material. However, time-dependent behaviors (or creeping behaviors) become significant in the long run. In this paper, we conduct triaxial experiments to observe the creep of granular materials under both dynamic and static loading conditions. Three typical creeping behaviors, aging, transitional, and fluidic, have been observed. To describe the time-dependent behaviors, an internal state variable characterizing the fluidity of the granular system is introduced to propose a rate-dependent constitutive relation which we call in this paper, a state evolution model. A characteristic strain is also introduced into the model to account for the influences of historic strain on the current state. The experiments are analyzed using the proposed model and it has been found that our model can well discern the observed three creeping behaviors. A criterion to identify the stability of a granular system is also given out based on the proposed model. Two key factors dominating the stability of the granular system are recognized – shear wave velocity and critical velocity. Our laboratory experiments in combination with the proposed criterion offer a physical explanation of the intrinsic triggering mechanism of system evolution from a stable to fluidic state: decrease in wave velocity or/and critical velocity.

How fines content affects granular plasticity of under-filled binary mixtures

In recent years, binary mixtures have been the subject of numerous experimental and numerical studies. However, few attempts have been made on investigating the effect of fines content (fc) on the non-associated plasticity of binary mixtures, which is significant for constitutive modelling of such material. Thanks to 2D DEM simulations, this study aims to provide an understanding of how fc affects the non-associated character of the flow rule and the resulting material instability in binary mixtures. For under-filled materials (where coarse grains constitute most of the load-bearing skeleton), fine grains help to stabilize the granular assembly (1) by limiting macroscopic plastic deformations, which results in strain hardening, and (2) by reducing contractive microstructure reorganizations, which reduces the gap between the associated and non-associated flow rule directions. Fines content influences the plastic flow direction but has no influence on normal direction of yield surface. Eventually, perspectives on mesoscale mechanisms are given to highlight the role of fine grains in the geometrical and mechanical properties of granular materials.

A novel deep learning-based modelling strategy from image of particles to mechanical properties for granular materials with CNN and BiLSTM

It will be practically useful to know the mechanical properties of granular materials by only taking a photo of particles. This study attempts to deal with this challenge by developing a novel deep learning-based modelling strategy. In this strategy, the convolutional neural network (CNN) as image identification algorithm is first used to extract the particle information (particle size distribution PSD and morphology) based on the image of a granular sample, and the bidirectional long short-term memory (BiLSTM) neural network is employed to train the model of reproducing mechanical behaviours and induced fabric evolutions of the sample with corresponding particle information. The datasets of images of samples are generated using discrete element method, and the datasets of mechanical properties together with fabric evolutions are obtained through numerical tests on corresponding samples. As a preliminary attempt, two-dimensional biaxial samples and tests with initially isotropic fabric are considered for the sake of simplicity. The feasibility and reliability of the proposed modelling strategy are evaluated through training and testing. All results indicate that the first part of the model based on CNN is capable of accurately identifying PSD of a granular sample, as well as circularity and roundness of particles, using which as connecting parameters the mechanical behaviours together with induced fabric evolutions of granular materials are subsequently well captured by the second part of the model based on BiLSTM. This study provides a basis and a possible way to obtain immediately particle and packing information, mechanical properties and fabric evolutions by leveraging images of granular materials.

DEM study on effect of particle roundness on biaxial shearing of sand

In this study, discrete element method (DEM) simulations of a biaxial test were used to examine the effect of particle roundness on the mechanical behavior of sands at both the macro and micro scales. First, a stack of microcomputed tomography images were binarized, segmented, and labeled using advanced image processing and analysis techniques. Second, a spherical harmonic (SH) analysis, which involves a complete set of orthogonal functions, was implemented to rebuild the natural particle shape. Then, five templates of virtual particles were built in a DEM simulation, four of which were obtained from SH degrees of 3, 8, 12, and 15, and one template was an elementary sphere. A flexible membrane was numerically generated to allow the material to deform freely under a prescribed confining stress. Finally, the effect of particle roundness on the mechanical properties of granular materials was investigated and discussed. Two shear bands were found to intersect, forming an X shape in both the rotation and displacement fields. Moreover, a lower particle roundness results in higher deviatoric stress and stronger dilation in the volumetric change. A decrease in particle roundness leads to less rotation of particles despite a higher displacement value. In addition, a larger SH degree leads to smaller normalized contact forces of the particles. This implies that decreasing the roundness results in higher anisotropy of the contact forces.

Observation of different regimes of the grain size effect on plasma emission induced by laser ablating granular materials

Plasma emission intensity as a function of laser fluence exhibited a role transition of grain size effect on plasma emission with laser fluence and indicated that there exists a size effect stemming from mechanical properties of granular materials.

Analysis of One-Dimensional Compression under a Wide Range of Stress with Densely Arrayed BPM

In this paper, the densely arrayed bonded particle model is proposed for simulation of granular materials with discrete element method (DEM) considering particle crushing. This model can solve the problem of pore calculation after the grains are crushed, and reduce the producing time of specimen. In this work, several one-dimensional compressing simulations are carried out to investigate the effect of particle crushing on mechanical properties of granular materials under a wide range of stress. The results show that the crushing process of granular materials can be divided into four different stages according to er-logσy curves. At the end of the second stage, there exists a yield point, after which the physical and mechanical properties of specimens will change significantly. Under extremely high stress, particle crushing will wipe some initial information of specimens, and specimens with different initial gradings and void ratios present some similar characteristics. Particle crushing has great influence on grading, lateral pressure coefficient and compressibility of granular materials, and introduce extra irreversible volume deformation, which is necessary to be considered in modelling of granular materials in wide stress range.

Investigate the Effect of Paper Sludge Ash Addition on the Mechanical Properties of Granular Materials

Ignition of waste paper sludge at elevated temperatures to produce electricity in power generation plants utilizing fluidized bed combustion generates paper sludge ash. Due to the high concentration of lime and gelignite in paper sludge ash, it is expected that it will play a vital role as a cementitious material. This paper investigates the use of paper sludge ash to improve the mechanical properties of the granular materials, which are suitable to subbase course for road and building constructions. Also, a comparison study with the use of Portland cement as an additive to granular materials has been covered. The mechanical properties were evaluated by conducting the California bearing ratio test for the two adopted methods. Moreover, the compressive strength of the samples using paper sludge ash and cement are investigated. In accordance to the California bearing ratio test, 4% paper sludge ash was indicated as the optimum ash content at which the California bearing ratio value increased by 173% and 111% in comparison with untreated material and 6% cement, respectively. On the other hand, and by means of the compressive strength, the granular materials with 4% paper sludge ash has compressive strength higher than those with 6% cement.

Effects of particle compressibility on structural and mechanical properties of compressed soft granular materials

Changes in the mechanical properties of granular materials, induced by variations in the intrinsic compressibility of the particles, are investigated by means of numerical simulations based on the combination of the Finite Element and Contact Dynamics methods. Assemblies of athermal 2D particles are subjected to quasi-static uni-axial compactions up to packing fractions close to 1. We show that the effect of the compressibility of the particles both on the global and the local stresses, can be described by considering only the packing fraction of the system. This result, demonstrated in the whole range of accessible packing fractions in case of frictionless particles, remains relevant for moderate inter-particles coefficients of friction. The small discrepancies observed with frictional particles originate from irreversible local reorganizations in the system, the later being facilitated by the compressibility of the particles.

Pressure-dependent bulk compressibility of a porous granular material modeled by improved contact mechanics and micromechanical approaches: Effects of surface roughness of grains

The change of the mechanical properties of granular materials with pressure is an important topic associated with many industrial applications. In this paper we investigate the influence of hydrostatic pressure (Pe) on the effective bulk compressibility (Ceff) of a granular material by applying two modified theoretical approaches that are based on contact mechanics and micromechanics, respectively. For a granular material composed of rough grains, an extended contact model is developed to elucidate the effect of roughness of grain surfaces on bulk compressibility. At relatively low pressures, the model predicts that the decrease of bulk compressibility with pressure may be described by a power law with an exponent of -1/2 (i.e., Ceff ∝Pe−1/2), but deviates at intermediate pressures. At elevated pressures beyond full contact, bulk compressibility remains almost unchanged, which may be roughly evaluated by continuum contact mechanics. As an alternative explanation of pressure-dependent bulk compressibility, we suggest a micromechanical model that accounts for effects of different types of pore space present in granular materials. Narrow and compliant inter-granular cracks are approximated by three-dimensional oblate spheroidal cracks with rough surfaces, whereas the equant and stiff pores surrounded by three and four neighboring grains are modeled as tubular pores with cross sections of three and four cusp-like corners, respectively. In this model, bulk compressibility is strongly reduced with increasing pressure by progressive closure of rough-walled cracks. At pressures exceeding crack closure pressure, deformation of the remaining equant pores is largely insensitive to pressure, with almost no further change in bulk compressibility. To validate these models, we performed hydrostatic compression tests on Bentheim sandstone (a granular rock consisting of quartz with high porosity) under a wide range of pressure. The relation between observed microstructures and measured pressure-dependent bulk compressibility is well explained by both suggested models.

A novel scheme for imposing periodic boundary conditions on RVE in second-order computational homogenization for granular material

Purpose This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials. Design/methodology/approach The proposed scheme is based on the generalized Hill’s lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill’s lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense. Findings Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively. Research limitations/implications Each grain in the particulate system under consideration is assumed to be rigid and circular. Practical implications The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method. Originality/value This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense.

Prediction of 3D size and shape descriptors of irregular granular particles from projected 2D images

Macroscopic mechanical properties of granular materials are closely related to particle morphology. For practical reasons, the morphological features are commonly examined from projected two-dimensional (2D) images of the three-dimensional (3D) particles. This brings forward the need for quantifying the correlations between the 2D and 3D particle descriptors. This paper addresses these correlations for irregular granular particles. Three-dimensional images of sand particles were acquired through microfocus X-ray computed tomography, based on which 3D surfaces of the particles were reconstructed using spherical harmonic analyses. The 3D particle size and shape descriptors were subsequently evaluated. All-around projection and random projection of the particles onto 2D planes were undertaken numerically to obtain the projected 2D images and thus the corresponding 2D size and shape descriptors. The results indicate that there are close correlations between 3D and 2D size descriptors averaged from the all-around projections. 2D and 3D shape descriptors can be approximately fitted with a linear relationship. The mean value of 2D descriptors of the tested sands obtained from a series of independent random-projection tests is essentially identical to that from the all-around projections; except that the data from the random-projection tests show a larger scatter. In light of the relationships among the descriptors, a novel and promising approach to predict the cumulative distribution of 3D descriptors from that of 2D descriptors evaluated from a random-projection test is proposed.

Structural similarity between dry and wet sphere packings

The mechanical properties of granular materials change significantly in the presence of a wetting liquid which creates capillary bridges between the particles. This results e.g. in a reduced value of the volume fraction when a packing is prepared with added liquid. Here we use x-ray tomography to demonstrate that this change in mechanical properties is not accompanied by structural differences between dry and wet sphere packings when compared at the same volume fraction. We characterize the structure of the packings by the average numbers of contacts of each sphere and the shape isotropy of the Voronoi cells of the particles. Additionally, we show that the number of liquid bridges per sphere is approximately equal to , independent of the volume fraction of the packing. These findings will be helpful in guiding the development of both particle-based models and continuum mechanical descriptions of wet granular matter.

Effects of central symmetry and elongation on the dense disordered packings of entangled particles

Geometric shape is an important factor that affects the packing and mechanical properties of granular material. In this paper, we use four families of assembled rods to model an entangled material in simulations. The particles are all non-convex and have the ability to interpenetrate. Together with elongation, central symmetry, which is attributed to the intersection location of the elementary rods, is also a main factor that produces varieties of particle shapes. With a certain total elongation, the dense disordered packing density is verified to be independent of the elongation distribution of the elementary rods. The specific shape hardly affects the packing densities. Therefore, the empirical formula to predict the packing density is extended to apply to all assembled rods with any elongation distribution. Different from the packing density, the shape disparity caused by central symmetry is found to significantly influence the contacts between neighboring particles. Due to more multipoint contacts contributing more constraints around the central particle, the centrally symmetric 3DX-shaped particles can more easily interpenetrate in the granular system. Moreover, the higher number of constraints contributed by neighboring contacts reflects the hyperstaticity of packings, which suggests mechanical stability for disordered packings of non-convex assembled rods.

Relating fragmentation, plastic work and critical state in crushable rock clasts

Grain breakage during compression and shearing is one important mechanism responsible for irrecoverable changes of the mechanical properties of granular materials. Here we present results of triaxial tests on limestone fragments under some monotonic and cyclic stress paths and we investigate the relationships between the progression of grain breakage, the plastic work and the evolution of the critical state line. Using the plastic work concept, we propose a method for determining grain shape and grain breakage indices, and we show how grain breakage influences the critical stress state, and hence the mechanical behaviour. The validity of the relationships is then verified on different granular assemblies (granite fragments and quartz sands), although further tests remain necessary to validate them under more generic stress paths.