Granular Assemblies Research Articles

Discrete element model (DEM) simulations of cone penetration test (CPT) measurements and soil classification

This paper presents a study on the simulation of cone penetration tests (CPTs) using the discrete element model (DEM) method. This study’s main objective is to investigate the effect of different modeling parameters and simulation configurations on the ability of three-dimensional DEM simulations to replicate realistic CPT tip resistance (qc) and friction sleeve shear stress (fs) measurements. The CPT tests were simulated in virtual calibration chambers (VCCs) containing particles calibrated to model the behavior of sand. The parameters investigated included the granular assembly properties, interparticle contact parameters, particle–probe interface characteristics, and simulation configuration. Results indicate that the interparticle contact parameters, boundary conditions, and void ratio have an important role in the tip resistance and friction sleeve measurements obtained from the simulations. Particle-level interactions such as particle displacements and rotations and interparticle contact forces were analyzed throughout to provide insight into the differences in measured CPT response. Interpretation of the qcand fsmeasurements using soil behavior type (SBT) charts for soil classification indicates that the simulated CPT response is representative of the response of coarse-grained soils measured during field soundings. Analysis of results within the SBT framework can provide insight into the influence of soil particle properties on CPT-based soil classification.

Effect of Initial Granular Structure on the Evolution of Contact Force Chains

The effect of initial granular structural conditions on load transmission patterns was experimentally investigated. Two types of granular structures were prepared by laminating cylindrical model particles of different diameters, to which photoelastic sheets were attached. Two-dimensional, reflective photoelasticity tests were performed under two granular conditions: (1) a uniform structure without initial defects and (2) with initial local imperfections at the bottom of the granular assembly. Two granular assemblies were tested for uniaxial compressive loading and shallow foundation loading conditions. For macroscopic analyses of the load–displacement relationship, the photoelastic response of individual particles was measured to microscopically observe the distribution of the main contact force chains within each granular assembly. Furthermore, the effect of initial local defects on the bearing capacity of granular assemblies was examined by confirming particle movement and the expansion of initial local defects in the granular assembly via particle image velocimetry (PIV). As a result, a completely different form of internal contact force chain was developed from the beginning of loading to the final failure stage, depending upon whether or not initial local instability existed in the granular assembly. In particular, a significant effect on the bearing capacity was found under shallow foundation loading conditions.

CFD-DEM model to assess stress-induced anisotropy in undrained granular material

This paper presents CFD-DEM simulations of undrained true triaxial tests on a granular soil. A CFDEM solver that considers compressible fluid and moving meshes has been developed and calibrated against the results of laboratory testing on Nevada sand. The effect of the intermediate stress ratio (b) on the macro- and micro-mechanical features of undrained granular assemblies was studied. The tests were repeated at different confining pressures, and the trends were similar to each other. The lowest effective frictional resistance was observed for specimens for which b = 0 and the highest value was obtained for specimens with b = 0.5. An increase in b caused samples to exhibit the greatest dilative behavior and increased the absolute maximum negative excess pore pressure. The stress-force-fabric equation that represents the stress state of the assembly in terms of the fabric anisotropy and contact force anisotropy tensors was used to study the micromechanics of the undrained granular samples. The tests were varied from compression to extension in order to qualitatively and quantitatively analyze the evolution of anisotropy under anisotropic loading conditions. Observations on the microstructural evolution of undrained samples were in agreement with those already reported for drained samples.

Effect of particle flow dynamics on the fabric evolution in spherical granular assemblies filled under gravity

The evolution of contact anisotropy (or fabric) for a spherical granular assembly filled under gravity is investigated. The effect of filling positions and the particle inlet velocity on the contact anisotropy is presented. Discrete Element Method is used to generate the granular assemblies by filling the particles into a container under gravity. The contact anisotropy and the coordination number shows a strong dependence on the filling locations. However, when these assemblies with distinct initial anisotropy are subjected to uniaxial compression, their contact anisotropy approaches the same value. The initial velocity of the particles shows a significant effect on the contact anisotropy of the granular assembly. It was found that the contact anisotropy first decreases and then increases showing a zone of minimum anisotropy with increase in inlet particle velocity. Initiation of particle whirling motion was found as the reason for this zone of minima. The inlet particle velocity at which the minimum contact anisotropy is observed depends on the direction of the particle motion. The findings in this work will be useful in identifying the critical spots (with high heat or force) and in designing better granular beds with uniform distribution of fabric via filling.

Effects of dynamic fragmentation on the impact force exerted on rigid barrier: centrifuge modelling

Bi-dispersity is a prerequisite for grain-size segregation, which transports the largest particles to the flow front. These large and inertial particles can fragment upon impacting a barrier. The amount of fragmentation during impact strongly influences the force exerted on a rigid barrier. Centrifuge modelling was adopted to replicate the stresses for studying the effects of bi-dispersity in a granular assembly and dynamic fragmentation on the impact force exerted on a model rigid barrier. To study the effects of bi-dispersity, the ratio between the diameters of small and large particles (δs/δl), characterizing the particle-size distribution (PSD), was varied as 0.08, 0.26, and 0.56. The volume fraction of the large particles was kept constant. A δs/δl tending towards unity characterizes inertial flow that exerts sharp impulses, and a diminishing δs/δl characterizes the progressive attenuation of these sharp impulses by the small particles. Flows dominated by grain-contact stresses (δs/δl < 0.26), as characterized by the Savage number, are effective at attenuating dispersive stresses of the large particles, which are responsible for reducing dynamic fragmentation. By contrast, flows dominated by grain-inertial stresses (δs/δl > 0.26) exhibit up to 66% more impulses and 4.3 times more fragmentation. Dynamic fragmentation of bi-disperse flows impacting a rigid barrier can dissipate about 30% of the total flow energy.

Analytical estimation of the effective thermal conductivity of a granular bed in a stagnant gas including the Smoluchowski effect

An analytical model including the Smoluchowski effect to estimate the effective thermal conductivity of a monosized granular assembly with interstitial stagnant gas from the microstructural parameters of the assembly, as well as the bulk properties of the granules and the gas is proposed in this paper. The discrete element method (DEM) is used for the generation and compaction of the granular assemblies. In the granular systems with interstitial gas, heat transfer occurs through the conduction between particles by solid overlap contacts and through the surrounding stagnant gas. Thermal radiation is included in the analytical model to study the influence of radiation on the thermal behavior of the assembly. The effective thermal conductivity is strongly influenced by the pressure of the gas as the conductivity of the gas decreases with decreasing pressure when confined in small gaps. This influence of the gas pressure is implemented in the analytical model. The effect of cyclic loading on the microstructural parameters is investigated through DEM simulations. Parametric correlations are developed to predict the values of microstructural parameters from experimentally measurable parameters so as to bypass any simulations for the estimation of effective thermal conductivity. A good agreement is observed between the analytical model and the experimental results for different assembly parameters and materials. The proposed analytical model can be used to get a first hand estimate of the effective thermal conductivity of a granular assembly to aid in the design process of such systems.

Energy transfer and influence of excitation frequency in granular materials from the perspective of Fourier transform

In this study, we investigated the dynamic responses of granular materials from the perspective of Fourier transform. The frequency components of the stress wave were analyzed. The exponential relationship between particle acceleration (contact force) and the excitation frequency was derived to illustrate the mechanism of the effect of excitation energy on particle contact force. Then according to the average wave velocity in the granular assemblies, the influence of the excitation frequency has been analyzed. Finally, by specifying a number of frequency values, the variation of the wave number with the particle microstructure (i.e., the radius ratio) is analyzed. Our research reveals the energy propagation process through the contact between particles within granular materials. The results can be a reference for material design using granular materials for energy collection, energy absorbing etc.

Force transmission and anisotropic characteristics of sheared granular materials with rolling resistance

We adopt a two-dimensional granular assembly in a direct shear box to systematically investigate the role of rolling resistance during the shearing process. A discrete element method with parallel computation and a rolling friction model is utilized in this paper. The macro- and microscale responses are sensitively subjected to a change in the rolling friction. The critical-state indices are found to be linearly related to each other, and the linear relationship between the critical-state indices and the rolling friction coefficient is evidently observed. The macro- and microscopic relationships are discussed from the connections between the stress and fabric properties. For microscale behaviors, different rolling frictions can generate various magnitudes of arching effects caused by antirotation and pose different characteristics to the force chains. The algorithm related to the extraction of force chains is adopted to explain the local sustaining structures. The localization, length, number and magnitude distribution of the force chains depend on the rolling friction. The influence of the rolling resistance on the friction mobilization is evident. A transition of the force distribution from the exponential to the Gaussian distribution is observed when the rolling resistance conditions change. The strong–weak contact systems and various anisotropic parameters are utilized to characterize the mechanical and geometrical roles of rolling resistance.

DEM-based modelling framework for spray-dried powders in ceramic tiles industry. Part I: Calibration procedure

This work describes a combined experimental-numerical study to characterize fine spray-dried powder used in the ceramic tile pressing process. A DEM-based granular assembly is endowed with a new set of scaling laws that allows for simulating reliably industrial processes using a much lower number of granules. To do it, a calibration strategy relying on three experimental setups is proposed; (i) compression test of bulk for granule stiffness, (ii) dynamic angle of repose and (iii) image analysis of the powder motion in a rotating drum for the intergranular and granular-boundary sliding and rolling friction coefficients. In order to evaluate the powder motion in a rotating drum, a robust method relying on a direct image analysis is proposed. This methodology makes it possible to quantitatively assess the frictional properties of the powder in contact with different surface materials.

How to measure the volume fraction of granular assemblies using x-ray radiography

When investigating dynamical processes in granular systems, it is frequently necessary to measure the time-resolved local material density. Recently, x-ray radiography facilities became available in many laboratories and can be used to measure the volume fraction via the attenuation of x-ray radiation along the beam direction. Naïve application of the Beer-Lambert law yields, however, unacceptably large systematic errors due to beam hardening. We present a calibration protocol which allows to reliably measure the local volume fraction based exclusively on reference measurement of known packing fraction.

Quantifying the impact of rigid interparticle structures on heat transfer in granular materials using networks

Coordination number can be used to quantify the particle connectivity and deformability of a granular material. However, it is a local feature of particles at the microscale, and the use of an average coordination number does not allow for full characterization of the microstructural variation in the granular material. Mesoscale structures can be used to overcome this limitation: triangular-like structures at the mesoscale tend to be rigid, whereas square-like structures tend to be deformable. However, the effect of these structures on heat transfer has not been studied in deforming granular materials. A better understating of how microstructure variation affects effective thermal conductivity is necessary. This work constructs contact networks representing the granular materials with particles as nodes and linking neighbouring nodes with edges that represent particle contacts. Then, ‘3-cycles’ (i.e., a triangular structure) and ‘clustering coefficients’ are extracted from the contact network. As contact thermal conductance is vital to heat transfer and affected by particle shape, microscale three-dimensional particle shape descriptors are also calculated. To compute the effective thermal conductivity of the granular assembly, a thermal network model is established by adding ‘near-contact’ edges to the contact network and assigning a thermal conductance to each edge. The results show that mesoscale local clustering coefficients can indicate the rigidity of granular materials and, together with particle shape descriptors, can be used to predict well the effective thermal conductivity of granular materials under deformation.

Experimental testing of pre-stressed granular assemblies as a surrogate material for the dynamic analysis of launcher cryogenic tanks

This paper focuses on the experimental validation of a new methodology for substitution of Liquid Hydrogen (LH2) on a simplified model of launcher cryogenic tank in vibration analysis by using pre-stressed grains as surrogate materials. The objective of the experiments presented here is to analyze the modal behavior of the (Tank and Granular materials) system during pre-stress procedure. In these experimental tests, a cylindrical tank is fully filled with granular materials and vibrated under swept sine and random excitations. Then, the natural frequency of each vibration mode is measured at different levels of pre-stress. The results obtained from the tests show the evolution of each flexural mode as a function of applied pre- stress. Nonlinear behavior of the analyzed system during vibration was also observed. These experimental values carried out with Tank-Granular material system (TGM) are compared with numerical and analytical results to prove the potential of the new methodology. Finally, based on obtained experimental results, some solutions are proposed in order to improve the new methodology for vibration analysis of cryogenic tank which is an important thematic in aerospace engineering.

A numerical study of particle friction and initial state effects on the liquefaction of granular assemblies

Liquefaction of sandy soil due to cyclic loading can result in catastrophic damage to the built environment. Liquefaction has been previously studied through field testing, laboratory experiments, and numerical simulations. However, the particle-scale behavior of granular materials during the initiation of liquefaction has not been comprehensively quantified. In the current work, the discrete element method is employed to study the effect of global void ratio, initial confining stress, overconsolidation ratio, and particle friction on liquefaction resistance. Mechanical coordination number, local void ratio distribution (LVRD) entropy, fabric anisotropy and average rotational velocity are quantified in each assembly to provide insight into the particle-scale physics governing liquefaction resistance. Results show that lower global void ratio, increased confining stress, higher OCR values, and higher particle friction all increase liquefaction resistance. Immediately prior to the onset of liquefaction, the mechanical coordination number in each assembly sharply decreased to approximately 2.5, with the remaining contacts attributed primarily to particle collision after liquefaction initiation and fabric collapse. Anisotropy induced in the cyclic loading process was due to normal contact force anisotropy, which was more prominent in the specimens with higher initial confining pressures. Liquefaction resistance for overconsolidated specimens was found to be lower than that of normally consolidated specimens at the same void ratio. We observe liquefaction resistance to be sensitive to the coefficient of interparticle sliding friction, especially for lower friction coefficients. Average particle rotational velocities are shown to increase with increasing interparticle friction. The quantity of energy dissipated through frictional sliding was controlled by both the rate of dissipation and the number of loading cycles to liquefaction. In sum, the simulations elucidate significant connections between micromechanical properties and liquefaction response at different initial states and with different particle frictions.

DEM modelling of screw pile penetration in loose granular assemblies considering the effect of drilling velocity ratio

Screw piles have been widely used as foundations for various types of structures. Drilling velocity ratio, the ratio of rotational velocity to driven velocity, is a critical parameter that affects the driven behaviors of screw piles. Three dimensional discrete element method, with a particle refinement method to enhance computation efficiency, is used to study the driven behaviors of screw piles to compare with the laboratory mini screw pile test results achieved by Shi et al. (Rock Soil Mech 39(6):1981–1990, 2018). The driven behaviors of a mini screw pile (900 mm long and 40 mm shaft diameter) with a variable diameter auger into loose granular assemblies under 0.5, 1 and 1.5 critical drilling velocity ratios are studied. The variation of stress distribution in the assemblies, particle movement around the piles, and evolution of void ratio in the assemblies are investigated. The results indicate that particles around the piles behave differently under different drilling velocity ratios. The reduction of driven force with the increase of drilling velocity ratio can be explained using the direction of particle movement around the piles and the vertical force acting on the screw blades. It was found that under high drilling velocity ratio, higher downward vertical force can be provided by the blades.

Thermal analysis of large granular assemblies using a hierarchical approach coupling the macro-scale finite element method and micro-scale discrete element method through artificial neural networks

A hierarchical approach for modelling the thermal response of large-scale granular assemblies by coupling the micro-scale particle-level thermal interactions with the macro-scale continuum system is proposed. The coupling is done by using a machine learning tool that is trained to replicate the effect of discrete particle nature on the macro-scale system using finite elements. A trained Artificial Neural Network (ANN) tool that can estimate the effective local thermal conductivity for each finite element considering the influence of the presence of stagnant gas in the interstitial voids, gas pressure and the granular microstructure is used. This way of hierarchical coupling using ANN eliminates the need to perform thermal discrete element simulations for each finite element at every increment by directly predicting the effective local conductivity. The proposed hierarchical approach is applied to a breeder blanket of fusion reactor that consists of more than 15 million particles to demonstrate the efficacy of the method. The influence of the drop in gas pressure across the breeder unit and the heat generation on the temperature distribution of the full-scale breeder unit is analysed numerically.

Finite element analyses of single particle crushing tests incorporating computed tomography imaging and damage mechanics

Fracture of individual grains within a granular assembly affect the strength and deformation behavior of granular materials under large stress states. Interparticle forces, leading to contact stresses and ultimately fracture initiation, are influenced by particle morphology. A numerical method that incorporates both particle fracture and morphology can provide a more accurate model of a granular material’s macro-scale response. This research investigates an approach to modeling fracture initiation and propagation within individual grains, utilizing high resolution X-ray computed tomography (CT) imaging to consider grain morphology and an explicit finite element code optimized for high performance computing which incorporates damage mechanics. Using precisely measured force-displacement curves from single particle crushing tests of manufactured quartz spheres, the method is validated, and the effects of fracture properties on grain fragmentation are determined. This approach is then used to simulate single particle crushing of Ottawa sand, with grain morphology incorporated through discretized CT images. The effect of grain orientation on the force and applied displacement at catastrophic splitting is also explored. The proposed discrete particle based finite element framework can be applied to modeling granular assemblies, considering the effect of individual particle shape and fracture on the assembly’s deformation response through well calibrated numerical simulations.

Visualization and measurement of load transmission in granular assemblies using mechanoluminescent-coated particles

Glass beads were coated with a mixture of mechanoluminescent (ML) paint and epoxy resin in order to visualize particle-level force distribution through an analog granular material. SEM observation and X-ray CT scanning was used to verify that the application of the ML coating on the glass beads was uniform. Load tests were conducted on single columns of coated glass particles to equate luminance to diametrical forces transmitted through the particles and particle contacts. The relationship between loading (force) rate during elastic loading of the coated particles and luminance was determined using a column of beads placed in an axial loading device. Coated glass particles were placed in a transparent plane strain container and subjected to biaxial loading to visualize the load transmission through the analog granular material placed in a regular packing. The anisotropy of chains of load transmission during loading was detectable using this test arrangement. The sum of contact forces at the top container boundary deduced from particle luminance is shown to be in agreement with applied boundary loads. This novel technique holds promise as an alternative approach to visualize and measure load transmission through idealized 2D assemblies of granular material.

Effect of particle morphology and contacts on particle breakage in a granular assembly studied using X-ray tomography

The macroscopic response of a geomaterial is entirely determined by changes at the particle scale. It has been established that particle crushing is affected by particle size, shape and mineral composition and initial density; and the initiation of breakage has often been related to the onset of yielding. Encouraged by the success of X-ray tomography in revealing particle-scale mechanisms of deformation, we present our findings regarding the onset of particle breakage, deriving from our study of 3D images of a dry granular assembly undergoing crushing. We propose two bespoke image analysis algorithms, which allow us to track breakage and identify contacts prior to breakage. The combination of the two algorithms, along with the high resolution of the 3D images enables us for the first time to track breakage of individual particles, identify different breakage modes for each particle and simultaneously study the effect of particle morphology and coordination number on breakage. Three different breakage types are identified: chipping, splitting and fragmentation. We have found that particle heterogeneity and sphericity mainly contribute to fragmentation, whereas the coordination number also affects chipping. The confining stress state within the particles with high coordination number made them more resistive to fragmentation, whereas particles with low coordination number mainly undergo fragmentation. The shearing of the particles at their contact points, leads to local stress concentrations resulting into surface chipping. Finally, we discuss the relation between the initiation of breakage and yielding, showing that some breakage occurs before the point where yielding is traditionally defined.

Scaling theory of shear-induced inhomogeneous dilation in granular matter.

Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity, various material parameters, and the preparation protocol. In spite of numerous studies of granular flows a predictive theory of the amount of dilation is still lacking. Here, we offer a scaling theory that is focused on such a prediction as a function of shear rate and the dissipative parameters of the granular assembly. The resulting scaling laws are universal with respect to changing the interparticle force laws.

Discrete element method simulations of offshore plate anchor keying behavior in granular soils

The keying mechanism of plate anchors (PLA) embedded into granular sandy soils is investigated in this work using the discrete element method (DEM) modeling to simulate microscale response and to observe the emergent macroscale behavior. Parameters (e.g., padeye eccentricity, loading direction) that influence anchor keying are analyzed in the simulations. The load-displacement response and embedment losses during keying are evaluated and compared to published experimental results from the literature. The keying mechanism of the PLA for different padeye eccentricities and loading directions are investigated. The DEM results are found to have the same trends as published experimental results. The embedment loss has a bilinear response with the padeye eccentricity which is in accordance with the experimental results reported in the literature. Embedment losses increase linearly with increasing loading directions. Microscale observations of mobilized particle friction, particle rotation, contact force network, and steering coefficient during keying are used to provide insights into the keying mechanisms. The potential for particle mobilization is reached more quickly for the larger padeye eccentricities. The particle rotation is the major keying mechanism for all the cases in the simulations. Finally, the granular assembly adjacent to the PLA is steering from horizontal to vertical for all padeye eccentricities.