Granular Assemblies Research Articles

Quasistatic response of loose cohesive granular materials

DEM-simulated model cohesive assemblies of spherical grains of diameterd, with contact tensile strengthF0, once prepared in loose states, are quasistatically subjected to growing isotropic pressureP, and then to triaxial compression, maintaining lateral stresses σ2= σ3=Pwhile increasing axial stress σ1=P+qand strain є1. Reduced pressureP*=d2P/F0varies from 0.1 (cohesion dominated case, for which systems typically equilibrate with solid fraction Ф ≃ 0.35), to large values for which the cohesionless behavior is retrieved. In triaxial compression, while the moderate strain response (є1~ 0.1) is influenced by initial coordination numbers and mesoscale heterogeneities, the approach to the critical state, as bothq(deviator) and Ф steadily increase, gets slower for smallerP*. Critical ratioq/P strongly increases for decreasingP*, as roughly predicted in an “effective stress” scheme. Anomalously small elastic moduli are observed in the gel-like structures. While extensive geometric rearrangements take place, no shear banding is observed. Loose cohesive granular assemblies are thus capable of large quasistatic stable plastic strains and ductile rupture.

A novel CFD-DEM upscaling method for prediction of scour under live-bed conditions

Despite intensive research efforts, the accurate modelling and prediction of bridge pier scour is an outstanding challenge due to the complexities arising from the detailed interactions between granular and fluid mechanics in the riverbed. Pier scour predictions based on empirical formulas are used in conventional bridge design codes which fail to realistically account for these interactions, and thus fail to facilitate pier design optimization. A critical step towards optimal pier design is an improved physical understanding of detailed mechanisms of the scour process and the development of appropriate modelling techniques to resolve these mechanisms in engineering applications. In this study, a combination of computational fluid dynamics (CFD) and discrete element modelling (DEM) is used to improve physical understanding of the scour process, including detailed interactions between river hydrodynamics, transport of suspended particles, and granular mechanics of the riverbed. As CFD-DEM models of turbulent hydrodynamics coupled with densely packed granular assemblies are computationally expensive, it is currently not feasible to accurately model scour in macroscopic engineering applications. To address this problem, we propose a novel upscaling methodology based on highly-resolved microscale simulations that significantly reduces the computational overhead, facilitating macroscopic prediction of scour under live-bed conditions. Predictions of scour initiation, rate and extent from these microscale simulations have been validated against previously published experimental data. Results indicate that the microscale model is reasonably capable of predicting the scour initiation as well as the equilibrium scour depth. This upscaling model provides a viable methodology for the macroscopic prediction of scour in engineering applications with modest computational resources.

Towards rational use of baffle arrays on sloped and horizontal terrain for filtering boulders

Baffle arrays are used to filter boulders from granular flows, such that the impact load exerted on barriers is reduced. However, current guidelines provide limited recommendations on baffle design. In this study, a calibrated discrete element method model was used to model boulders entrained in a bulk granular assembly interacting with baffles and a terminal rigid barrier. Different baffle spacings relative to the boulder diameter (1 < s/δ < 4) were considered. A ratio of s/δ = 1 is recommended for reducing the impact load by up to 80%, whilst s/δ = 4 renders an array of baffles inadequate for filtration. The optimum configuration is a staggered array with three rows of baffles on a horizontal plane in front of a barrier. This layout reduces the peak discharge by up to four times more than a similar array on sloping terrain, compared to channels without baffles. Furthermore, the transition from sloping terrain to a horizontal plane works together with the array of baffles to dissipate flow kinetic energy. On the horizontal plane, baffles attenuate the flow velocity more as the Froude number Fr increases, implying that baffles should be used if high Fr values are anticipated. Finally, guidance is provided on estimating load attenuation from boulder filtration.

Monitoring and Modeling Railway Structures on High-Speed Lines with Asphalt Concrete Underlay: A Study on the Bretagne–Pays de la Loire Line

The design and durability of high-speed railway lines is a major challenge in the field of railway transportation. In France, 40 years of feedback on the field behavior of ballasted tracks led to improvements in the design rules. However, the settlement and wear of ballast, caused by dynamic stresses at high frequencies, remains a major problem on high-speed tracks leading to high maintenance costs. Studies have shown that this settlement is linked to the high acceleration produced in the ballast layer by high-speed trains traveling on the track, disrupting the granular assembly. The “Bretagne–Pays de la Loire” high-speed line (BPL HSL), with its varied subgrade conditions, represents the first large-scale application of asphalt concrete (GB) as the ballast sublayer. This line includes 77 km of conventional track with a granular sublayer of unbound granular material (UGM) and 105 km of track with an asphalt concrete sublayer under the ballast. During construction, instruments such as accelerometers, anchored deflection sensors, and strain gages, among others, were installed on four sections of the track. This paper examines the instrumentation as well as the acquisition system installed on the track. The data processing is explained first, followed by a presentation of the ViscoRail software, developed for modeling railway tracks. The bituminous section’s behavior and response is modeled using a multilayer dynamic response model, implemented in the ViscoRail software. A good match between experimental and calculated results is highlighted.

Influence of mineral dissolution on the mechanical behaviour of a granular assembly under complex stress states

Rock and soil are natural assemblies of mineral grains. Dissolution of mineral compositions in a granular assembly can dramatically disturb and change the microstructure. Once the soil fabric and inter-particle contacts change, large deformations can develop and the shear strength can decrease. Currently there is a lack of understanding and experimental evidence of geomaterial behaviour subjected to mineral dissolution under realistic complex stress conditions. In this experimental study, extensive laboratory tests were conducted to investigate changes in the stress-strain relation, shear strength and critical state of a granular assembly after experiencing a substantial loss of particles by salt dissolution. During the salt dissolution process, a larger shear stress or confining pressure leads to a smaller increase of void ratio, a smaller positive state parameter, and a weaker strain-hardening behaviour. After the salt dissolution, the material grading becomes narrower, the grading state index decreases and the specific void ratio increases, leading to an upward shift of the critical state line. However, the increase of void ratio is more than the upward shift of the critical state line, thus the stress state changes from the dense side to the loose side, accompanied by a change of shearing behaviour from strain-softening to strain-hardening. Nevertheless, as the critical friction angle is dominated by the inter-particle contacts among coarse particles, with almost no change in the coarse content of the post-dissolution materials, only a slight decrease of 2.3° in the critical friction angle is found.

A unified fractional breakage model for granular materials inspired by the crushing tests of dyed gypsum particles

Particle breakage of granular materials is a phenomenon of great importance in engineering practices. This paper presents a unified particle breakage model for granular materials, which is able to capture the evolution of the particle size distribution (PSD) of each size fraction of particles. A novel experimental technique using dyed gypsum particles (DGPs) to track the fractional particle breakage was first adopted in the one-dimensional compression tests. A unique path of the fractional particle breakage, regardless of whether the particles were in a polydisperse medium or in other different granular assemblies, was then experimentally identified. This result has inspired the introduction of the definition of a fractional breakage index, based on which the breakage-plastic work relationship for overall granular assemblies was extended to describe the fractional particle breakage. The established fractional particle breakage model differs from most existing particle breakage models in that it is able to capture both the evolution of the fractional and the overall PSDs of granular materials, even when the initial PSD of the granular material surpassed partially the theoretical fractal PSD. These results set a vision to predict and understand the particle breakage of granular materials in industrial activities.

Micromechanical investigation of liquefaction of granular media by cyclic 3D DEM tests

In order to evaluate numerically the seismic-induced liquefaction potential of gravelly soils, three-dimensional discrete-element method cyclic undrained triaxial tests were performed in a periodic cell. The undrained tests were conducted by deforming the samples under constant volume conditions. The paper presents a detailed investigation into the mechanical phenomena occurring at the grain scale leading to the liquefaction of gravel when subjected to cyclic straining. The influence of variables characterising the granular assembly, such as inertial number, geometrical coordination number, mechanical coordination number, redundancy index and Reynolds stresses, on liquefaction is investigated. Results of the simulations show that the onset of liquefaction occurs when the granular medium becomes on average isostatic – that is the redundancy index is equal to 1, the geometrical coordination number is equal to 2 and the mechanical coordination number is equal to 3. To elucidate further the transition from solid-like to liquid-like behaviour, an analysis of how particles cluster together is presented. It is shown that, as the mean effective stress decreases, contacts are lost, with the maximum cluster size gradually reducing at an increasing rate. The loss of contacts is uniformly distributed throughout the sample and there is no break-up of the largest cluster into smaller clusters.

Interaction between granular flows and flexible obstacles: A grain-scale investigation

Flexible obstacles are used to reduce the impact load exerted by granular flows. However, grain-scale interactions between granular assemblies and flexible obstacles remain poorly understood, making it difficult to estimate the required resisting force. In this fundamental study, a flexible obstacle was simplified as a grain intruder and dragged through a static granular assembly. A new physical intruder apparatus was used to calibrate a discrete element model. The calibrated model was then used to evaluate the effects of the stiffness and loading rate on the force experienced by the intruder and the energy dissipated by the granular assembly. The response of the intruder and the granular assembly depended significantly on both the drag rate and the obstacle stiffness. Softer obstacles caused longer sticks between slips. At least 60% of the work was transferred from the intruder into the granular assembly regardless of the drag rate and obstacle stiffness. Stick-slip behaviour was not observed for stiff obstacles and high drag rates (>1 m/s), where the bulk granular assembly fluidised. The results of this study suggest that rigid obstacles are better for causing energy dissipation in the granular assembly, while flexible obstacles are better for reducing the resisting forces required.

Comparison of undrained behaviors of granular media using fluid-coupled discrete element method and constant volume method

The fluid-coupled discrete element method (DEM) and the constant volume method as two types of discrete modeling methods for fundamental study of undrained responses of granular materials, have been discussed by many researchers. The fluid-coupled DEM, which couples the motions of discrete particles with pore fluid movements, is theoretically robust although it requires a large amount of computation time. As a substitution for the complex fluid-coupled DEM, the constant volume method simulates an undrained condition for a saturated granular material by simply preserving the total volume of a granular assembly without considering interactions between fluids and particles; hence, the validity of its results is questionable. In this paper, the undrained behaviors of granular assemblies simulated using the aforementioned two methods are compared. Based on a comparison of both macroscopic and microscopic responses given by the two methods, it is demonstrated that the constant volume method may reasonably simulate the responses of a loose saturated granular material with very coarse grains, which has a high permeability, and thus a rapid pore pressure equalization. However, it is ineffective in simulating the responses of a loose material with fine components due to its failure to capture the process of a slow dissipation of the excess pore pressure among the individual pores. With regard to the dense material adopted, similar behaviors at the early and intermediate shearing stages given by the two methods are displayed.

Experimental characterizations of fabric correlation in 2D rod assemblies subjected to biaxial shearing

This study provides experimental evidence of the correlation between different fabric tensors in 2D granular assemblies subjected to shearing. Two testing assemblies with different elliptical rods were used and the shearing tests were conducted in a tailor-made biaxial cell. Both the rods and cell were produced using the 3D printing technique. Throughout the shearing, three fabric tensors, i.e., the particle orientation-based, the contact normal-based and the void-based fabric tensors, were studied. In particular, to obtain the void-based fabric tensor, the best-fit ellipse method was used, which can better describe the irregular void geometric information compared with the conventional methods described in the literature. In both samples, a strong linear relationship between the anisotropy intensity factors of the three fabric tensors was found. However, such a correlation was not identified when the void-based fabric tensor was quantified using the conventional methods. The discrepancy demonstrates the importance of properly quantifying the fabric tensor, and by using the best-fit ellipse method, the correlation between the fabric tensors can be better observed, which is crucial to understand the constitutive relationship in granules.

Exploration of the Survival Probability and Shape Evolution of Crushable Particles during One-Dimensional Compression Using Dyed Gypsum Particles

AbstractObserving the fragmentation of individual particles within granular assemblies is a subject of evident theoretical and practical importance. A new technique using dyed gypsum particles (DGP...

Dynamic disintegration processes accompanying transport of an earthquake-induced landslide

Aiming to understand the dynamic disintegration and transport behavior of an earthquake-induced landslide, a dynamic discrete element method has been employed to analyze the Wangjiayan landslide triggered by the 2008 Ms 8.0 Wenchuan earthquake. Absorbing boundary condition is used for the seismic wave transmission and reflection at the slope base. The numerical results show that under seismic loading, internal rock damage initiates, propagates, and coalesces progressively along the weak solid structure and subsequently leads to fragmentation and pulverization of the slope mass. This can be quantitatively interpreted with the continuously rapid increase of the damage ratio and sudden decline of growth ratio of the number of fragments after the peak seismic shaking. During emplacement evolution, fragmented deformation patterns within the translating joint-defined granular assemblies are affected by the locally high dilatancy with a simultaneous occurrence of highly energetic collisions related to the action of shearing, and this can be quantified by the enhancement of particle kinematic activities (high vibrational and rotational granular temperatures) and intense fluctuations of location-dependent global dispersive stress. In this process, slope destabilized and transports downward in a rapid pulsing motion as friction bonds are locally and continually overcome by the seismic- and gravity-induced shear forces. The joint-determined fragment network before movement initiation and the final fragmented depositions after the rapidly sheared transport have been systematically investigated by fragment statistics (fragment size distribution, fragment mass distribution, and fractal dimension) and morphometric characters (fragment shape isotropy) to offer new insights into the disintegration characteristics of the earthquake-induced catastrophic mass movements.

Calibration and validation of DEM-FEM model parameters using upscaled particles based on physical experiments and simulations

The real sand is usually idealized by using upscaled particles, due to the large number of particles of tire-sand interaction. This study aims to determine a unique and complete set of DEM-FEM model parameters to improve numerical accuracy of tire-sand interaction after particles idealization. To achieve this aim, a novel method based on experimental design is proposed to calibrate the DEM-FEM model parameters by a series of single-factor numerical calibration tests. Initially, the interaction properties such as equivalent friction coefficients of particle-particle, particle-soil bin and particle-tire are determined successively by comparing experimental test with numerical simulation using the angle of repose as a bulk response. The material parameters of particles are then obtained by modified iteratively to match the stress-strain behavior of the granular assembly in triaxial test. After that, the calibrated parameter set is used to investigate the interaction mechanisms between the off-road tire and the granular terrain. Finally, the simulation results are qualitatively in agreement with the soil bin experiments, which verifies the effectiveness of the calibrated parameter set for the tractive performance analysis of tire-sand interaction.

Simulation of undrained quasi-saturated soil with pore pressure measurements using a discrete element (DEM) algorithm

A method is presented for using DEM to find the pore pressure, total stress, and effective stress within a granular assembly during either undrained or drained conditions, by using poroelastic principles to directly determine the pore fluid pressure. The paper considers both the saturated and quasi-saturated conditions, the latter meaning a slightly unsaturated granular material, in which isolated gas bubbles reduce the compressibility of the pore fluid but do not form liquid bridges between the particles. The presence of air increases the pore fluid compressibility and is known to improve undrained strength and liquefaction resistance and has been considered for remediation of loose, susceptible soils. Past DEM studies have approximated undrained loading as a constant-volume condition, but this approximation does not allow the simulation of complex loading sequences, even with fully saturated materials. The paper’s method allows the direct control and measurement of total stress, water pressure, and water influx. The method includes the effects of water compressibility, grain compressibility, pore air compressibility, surface tension, air solubility within the pore liquid, and vapor pressure of the water gas phase. These factors all affect the evolving sizes of the bubbles and the consequent compressibility of the air–water mixture. The resulting algorithm is applied in three examples: the laboratory saturation of a soil specimen by increasing chamber pressure and back pressure, the undrained triaxial compression of quasi-saturated specimens, and the cyclic undrained triaxial liquefaction of quasi-saturated specimens. Example simulations agree favorably with laboratory tests.

Hybrid multi-scale model for partially saturated media based on a pore network approach and lattice Boltzmann method

A model combining the efficiency of the pore-network (PN) models and the accuracy of the lattice Boltzmann Method (LBM) is proposed. We introduce a multi-scale approach based on a decomposition of the granular assembly into small subsets. A tetrahedrization is considered to describe the pore space and extract the subsets. Hydrostatic properties such as entry capillary pressure, liquid morphology and capillary pressure - degree of saturation relationship are evaluated for each pore throat (subset) of the granular system. This information is incorporated into the pore-network model to reproduce the macro-scale effects during a primary drainage. The hybrid method is able to reproduce accurately the capillary pressure - volume relationship and the motion of the interface during the drainage process. The results obtained with the hybrid method evidence the capability of the method to investigate complex phenomena. Additionally, the combination of PN and LBM leads to a significant gain in terms of computation resources. Finally, the results obtained with a fully resolved LBM and the hybrid model help us validate the accuracy of pore-scale methods based on approximations (MS-P and Incircle methods).

Characterization of mechanical behavior of binary granular assemblies through the equivalent void ratio and equivalent state parameter

The proposed research of this experimental investigation aims to study the effects of fines content, fabrics type and confining pressure on the undrained shear strength response of Chlef sand-silt mixtures under static loading conditions using the equivalent void ratio (e*) and equivalent state parameter (ψ*) concepts. For this purpose, a series of undrained monotonic triaxial tests was carried out on reconstituted saturated sand-silt mixture samples with fines content ranging from 0 to 40% (Ip=5%) at an initial relative density (Dr=52%) and subjected to different confining pressures (σ’3 = 100 kPa, 200 kPa and 300 kPa). The different samples were prepared in such a way that two fabrics types were produced: dry funnel pluviated fabrics and wet deposited fabrics. The obtained results show that the wet deposited fabrics exhibits a higher state parameter (ψ) than the dry funnel pluviated fabrics. The state parameter confirms that the wet deposited fabrics were more vulnerable to liquefaction phenomenon than the dry funnel pluviated ones. Moreover, the obtained data confirm the existence of a linear relationship between the dry funnel pluviation and wet deposition in terms of equivalent void ratio (e*) and exponential relationship in terms of equivalent state parameter (ψ*).

CFD-DEM modeling of suffusion effect on undrained behavior of internally unstable soils

Abstract This paper investigates the effect of suffusion on the undrained behavior of an internally unstable soil using the coupled computational fluid dynamics and discrete element method (CFD-DEM). A series of eroded specimens are prepared by exerting an upward flow through the granular assembly under a range of hydraulic gradients and suffusion durations. Both the eroded and non-eroded specimens are then subjected to undrained triaxial compression (or equivalently constant volume tests). The results indicate that the erosion rate and volumetric response of the soil skeleton are closely related to the hydraulic conditions. The eroded specimens exhibit a non-uniform distribution of fine particles, higher coordination numbers, higher global void ratio, and lower equivalent intergranular void ratio. The undrained behavior of the specimen changes from a strain hardening behavior before suffusion to a softening behavior with limited flow deformation after suffusion. The undrained shear strength of eroded specimen is enhanced at small axial strain due to the enhanced connectivity of particles, but can increase or decrease at larger strain levels depending on the degree of erosion. It is also observed that both suffusion and shearing can induce some degree of fabric anisotropy by inspecting the directional distribution of contact unit normals and contact normal forces.

ILS-MPM: An implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles

Finite element simulations of frictional multi-body contact problems via conformal meshes can be challenging and computationally demanding. To render geometrical features, unstructured meshes are often generated via a trial-and-error procedure. This treatment also unavoidably increases the degrees of freedom and makes the construction of slave/master pairs cumbersome. In this work, we introduce an implicit material point method designed to bypass meshing of bodies by employing level set functions to represent boundaries at structured grids. This implicit function representation provides an elegant mean to link an unbiased intermediate reference surface with the true boundaries by closest point projection as shown in Leichner et al. (2019). We then enforce the contact constraints by a penalty method where the Coulomb friction law is implemented such that a return mapping algorithm can be used to provide constitutive updates for both the stick and slip states. To evolve the geometry of the contacts properly, the Hamilton–Jacobi equation is solved incrementally such that the level set and material points are both updated according to the deformation field. To improve the accuracy and regularity of the numerical integration of the material point method, a moving least square method is used to project numerical values of the material points back to the standard locations for Gaussian-Legendre quadrature. Several benchmarks are used to verify the proposed model. Comparisons with discrete element simulations are made to analyze the importance of stress fields on predicting the macroscopic responses of granular assemblies.

Analysis of consistent soil–structure interface response in multi–directional shear tests by discrete element modeling

Abstract Structure surface normally owns highly directional properties caused by the properties of the material and the manufacturing process. Proper understanding of soil–structure interface behavior must recognize the structure surface’s highly directional properties and take into consideration its interactions with particulate material. To investigate the mechanical behavior of granular soil–structure interface under multi–directional shear tests, a shear orientation is defined to be an angle θ between the shear direction and the principal rough direction of the directional surface. Using the discrete element method, a series of 3D numerical interface shear tests was conducted, under seven shear orientations ( θ = 0°, 10°, 30°, 45°, 60°, 75°, and 90°). The consistent response of macroscale shear behavior at the interface, loaded by various shear orientations, are presented from the perspectives of the resultant average shear stresses in x – and y – directions and soil volumetric strain. A determination of the thickness of the localized shear band in each specimen is followed by the discussion of particle displacement vector distribution. Furthermore, the evolutions of microscale properties inside and outside the localized shear band, such as the coordination number and material fabric provide a physical meaning or an explanation for the consistent macroscale shear behavior of granular soil–structure interface at a microscale level. The findings emphasize the importance of measuring the horizontal load in x – and y – directions when conducting experimental interface shear tests on rough surface with highly directional properties, because the resultant resistance corresponds to the true resistance of the granular assembly.

Performance traits of a newly proposed modularity function for spatial networks: Better assessment of clustering for unsupervised learning

The “best” partition of a given network helps in revealing its naturally identifiable structures. The most modular structure is often considered as the best partition. Modularity function, is an objective measure of the quality of partitioning in a given network with that of a random graph (“Null model”), where edge between any two nodes is equally probable, are inappropriate to use for spatially embedded networks. Earlier we have proposed a new modularity function, which does not compare the network with a null model. We have analyzed a 2D and 3D granular networks which can be considered as a spatially embedded network. In all considered systems new method identifies the better partition. New function properly detects the better modular partition in 2D as well as in 3D granular assemblies as compared to the most commonly used modularity function, known as Newman modularity function, and thus is more suitable for unsupervised machine learning.