DEM investigation on the evolution of microstructure in granular soils under shearing

The mechanical behaviors of granular soils at different initial densities and confining pressures in the drained and undrained triaxial tests are investigated micromechanically by three-dimensional discrete element method (DEM). The evolutions of the microstructure in the numerical specimen, including coordination number, contact force and anisotropies of contact normal and contact force, are monitored during the shearing. The typical shear behaviors of granular soils (e.g. strain softening, phase transformation, static liquefaction and critical state behavior) are successfully captured in the DEM simulation. It is found that the anisotropies of contact normal, normal and tangential contact forces comprise the shear resistance and show different evolution features during shearing. After large strain shearing, the microstructure of the soil will finally reach a critical state, although the evolution path depends on the soil density and loading mode. Similar to the macroscopic void ratio $e$ and deviatoric stress $q$ , the coordination number and anisotropies of contact normal and contact force at the critical state also depend on the mean normal effective stress $P^{\prime }$ at the critical state.     

Real-scale DEM simulations on the fault evolution process observed in sandbox experiments

The study of fault structures and stress states in accretionary prisms is important to elucidate the building and releasing of seismic energy as they control the generation of great earthquakes and tsunami. In this paper, we present the evolution process of three-dimensional fault structures performed in sandbox simulations using a discrete element method (DEM). To realize a real-scale sandbox simulation, we developed state-of-the-art techniques in high performance parallel computing for the DEM and performed the world’s largest DEM simulation using up to 1.9 billion particles with a similar grain size as real sand to identify the three-dimensional fault structure. The DEM simulations reproduced the undulation of fault structures, similar to those commonly found in nature. In addition, the characteristic grain motion was observed near the frontal fault before the commencement of the uplift event of the sand bed, which could be a precursor of tectonic events behind accretionary prism formation.     

Influence of relative density on granular materials behavior: DEM simulations of triaxial tests

The rheological behavior of non-cohesive soils results from the arrangement and complex geometry of the grains. Numerical models based on discrete element modeling provides an opportunity to understand these phenomena while considering the discrete elements with a similar shape to that of the grains the soil is composed of. However, dealing with realistic shapes would lead to a prohibitive calculation cost. In a macroscopic modeling approach, simplification of the discrete elements’ shape can be done as long as the model can predict experimental results. Since the intrinsic non-convex geometry property of real grains seems to play a major role on the response of the granular medium, it is thus possible to keep this geometrical feature by using cluster of spherical discrete elements, which has the advantage to reduce dramatically the computation cost. Since the porosities found experimentally could not always be obtained with the numerical model—owing to the huge difference in shape, the notion of relative density, which requires a search for minimum and maximum porosities for the model, was chosen to compare the experimental and numerical results. Comparing the numerical simulations with the experimental triaxial tests conducted with relative densities and different confining pressures shows that the model is able to predict the experimental results.     

加压下颗粒移动床空隙率实验研究

在移动床排料装置上,研究加压条件下移动床表观颗粒速度、表观气速及入口压力对并流移动床空隙率的影响。结果表明,在表观颗粒速度或表观气速不变的情况下,移动床空隙率随入口压力的升高而减小;在入口压力不变的情况下,移动床空隙率基本不随表观颗粒速度和表观气速变化。对实验结果进行非线性拟合,得到气固并流移动床空隙率的压力拟合公式,利用该拟合公式和Ergun方程可计算移动床压降,在实验数据范围内,计算压降与实验压降的最大偏差小于±10%。     

DEM simulations: mixing of dry and wet granular material with different contact angles

In solid mixing the raw materials typically differ at least in one material property, such as particle size, solid density and wetting properties, which in turn influence particle mobility. For example, smaller particles can percolate through the voids of larger ones under the influence of strain and gravity. This may produce fine particle accumulation at the bottom of the mixing vessel which results in undesired, inhomogeneous final products. When wet particles with different wetting properties need to be mixed, heteroagglomeration may occur as another segregation mechanism. We present a new capillary bridge force model to study segregation in moist cohesive mixing processes using DEM. New analytical equations of best fit are derived by solving the Young–Laplace equation and performing a regression analysis, in order to investigate discontinuous mixing processes of dry and moist materials with different particle sizes and different contact angles. Compared to a dry mixing process, mixing efficiency is improved by the addition of a small amount of liquid. While percolating segregation is reduced, heteroagglomerates occur in the wet mixing process.     

Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations

This paper presents the results of numerical simulations using the three-dimensional discrete element method (DEM) on the critical state behaviour of isotropically compressed and rebounded assemblies of granular materials. Drained and undrained (constant volume) numerical simulations were carried out. From these numerical simulations of drained and undrained tests, it has been shown that the steady state is same as the critical state. Critical state for both isotropically compressed and rebounded assemblies form unique curved line that can be approximated by a bilinear line as proposed by Been et al. [Géotechnique 41(3): 365–381, 1991]. Further more, evolution of the internal variables such as average coordination number and induced anisotropy coefficients during shear deformation has been studied.     

Study of the shear behavior of binary granular materials by DEM simulations and experimental triaxial tests

This paper aims at studying the shear behavior of mixtures of fine and coarse particles by classical triaxial tests. The work is performed both on experimental tests and computer simulations by discrete element method. The comparisons between experimental and simulation results on monosized and binary samples show that the DEM model can reproduce deviatoric curves satisfactorily in experimental conditions. The shear behavior of monosized and binary systems with the same initial void ratio differs significantly, suggesting that the state of compaction of the system is more influential than the initial void ratio. Comparison between compacted and uncompacted samples confirms that compaction increases the shear strength of granular matter. At the particle scale, the coordination number decreases with the augmentation of the volume fraction of coarse particles. The average rotation velocity of fine particles is higher than coarse particles, but their particle stress tensor is smaller than coarse ones.     

DEM simulations of the small strain stiffness of granular soils: effect of stress ratio

DEM (discrete element method) simulations are carried out to evaluate the small strain stiffness (i.e. Young’s modulus and shear modulus) of a granular random packing with focus on the effect of stress ratio (SR). The results show that the Young’s modulus in a given direction generally depends on the stress component in that direction. The Young’s modulus normalized by the related stress component remains nearly constant when SR is less than a threshold value $SR_\mathrm{th}$ . When SR is larger than $SR_\mathrm{th}$ , the normalized Young’s modulus decreases, particularly in the minor principle stress direction. Moreover, the Young’s modulus during unloading is always smaller than the one during loading at the same stress state, which indicates that the microstructure of the specimen has been modified by the historical shearing process. The shear modulus mainly depends on the mean effective stress and shows similar evolution trend as the Young’s modulus. This study finds that the macroscopic stiffness of the specimen is closely related to the evolutions of particle contact number and contact force during shearing. When SR is less than $SR_\mathrm{th}$ , the specimen only adjusts the distribution of contact forces to resist the external load, without any apparent change of contact number. When SR is larger than $SR_\mathrm{th}$ , however, the specimen has to adjust both contact number and contact forces to resist the external load. The study also illustrates that there is a good relationship between the macroscopic stiffness anisotropy and fabric anisotropy, and therefore the stiffness anisotropy may be used as an indicator of fabric anisotropy.     

An image based clump library for DEM simulations

To create realistic virtual soil specimens for Discrete Element Method simulations, a library containing nearly 100,000 “clumps” was developed. A clump essentially models a soil particle. It consists of numerous overlapping spheres in 3D, or circles in 2D, that are tangent to the particle perimeter. By using a unique corner-preserving algorithm based on the classic 2D definition of particle roundness, the clump generation requires many fewer circles than by previous algorithms. In this paper, the clumps are based on 2D images of real soil particles and they are indexed in the library by their roundness R and sphericity S values. A real soil can be simulated by choosing particles from the library to match the soil’s actual distributions of R and S. The clumps are also enlarged or reduced to match a desired particle size distribution. The utility of the clump library in parametric studies was demonstrated by direct shear tests on five very different virtual materials created from clumps in the library.     

Choice of aggregates for permeable pavements based on laboratory tests and DEM simulations

Permeable pavement plays an important role in the sustainable urban drainage system as they have the potential to reduce splash and spray. While the pavements need to be permeable for the water to drain into the ground, it must also be able to carry the traffic load without altering the permeability characteristics. This paper aims to investigate the permeability performance and serviceability of pavements constructed with aggregates having a range of crushing strength (crushability) and grading (particle size distribution). Laboratory tests consist of modelling a pavement and carrying out permeability and sieving tests before and after the application of the loading. Experimental investigations showed that particles having higher crushing strength will lead a lower reduction in permeability of the pavement without compromising the performance. Furthermore, it was observed that reduction of permeability depends on the particle breakage pattern. Numerical study was conducted using discrete element modelling to understand the underlying mechanism of this phenomenon, and it was found that a wide particle size range could distribute the load uniformly and reduce the particle breakages. It is suggested that all these factors may be considered while choosing the aggregate for permeable pavement.     

Selection of material for X-ray tomography analysis and DEM simulations: comparison between granular materials of biological and non-biological origins

Granular Matter - Field observations were carried out in Qingtu Lake observation array on the vertical electric field $$(E_{z})$$ , where the average spatial resolution can reach 1 m. Our...     

Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations

Fundamental research on the flow and mixing of non-spherical particles is critical for industrial production and design. In this paper, the Discrete Element Method (DEM) is used to study the flow and mixing of granular materials in the horizontal rotating drum, and the periodic boundary condition is employed to eliminate end wall effect. Super-quadric elements are adopted to describe spherical and non-spherical particles. The influences of rotating speed, blockiness, and aspect ratio on the mixing rate are investigated by the Lacey mixing index. The results show that the rotating speed has a primary effect on the mixing rate, whereas the effect of the particle shape on the mixing rate is a secondary factor for non-spherical granular systems. Moreover, the mixing rate of spherical and non-spherical particle systems is significantly different. The mixing rate of spheres is the lowest, and the cubes have a higher mixing rate than the cylinders. As the blockiness decreases or aspect ratio deviates from 1.0, the mixing rate decreases. Ordered face-to-face contacts and dense packing structures result in a higher mixing rate. The analysis of kinetic energy shows that particle shape affects the transfer efficiency of external energy to the granular systems. The translational kinetic energy of non-spherical particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. Meanwhile, the blockiness enhances the transfer efficiency of external energy to the non-spherical systems; in contrast, the aspect ratio reduces the energy conversion efficiency.     

Constitutive modeling for the dynamic recrystallization evolution of AZ80 magnesium alloy based on stress-strain data

In order to improve the understanding of the dynamic recrystallization (DRX) behaviors of as-cast AZ80 magnesium alloy, a series of isothermal upsetting experiments with height reduction 60% were performed at the temperatures of 523 K, 573 K, 623 K and 673 K, and the strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1 s⁻¹ and 10 s⁻¹ on a Gleeble 1500 thermo-mechanical simulator. Dependence of the flow stress on temperature and strain rate is described by means of the conventional hyperbolic sine equation. By regression analysis, the activation energy of DRX in the whole range of deformation temperature was determined to be Q = 215.82 kJ mol⁻¹. Based on dσ/d? versus σ curves and their processing results, the ?ow stress curves for AZ80 magnesium alloy were evaluated that they have some characteristic points including the critical strain for DRX initiation (?_c), the strain for peak stress (?_p), and the strain for maximum softening rate (?*), which means that the evolution of DRX can be expressed by the process variables. In order to characterize the evolution of DRX volume fraction, the modified Avrami type equation including ?_c and ?* as a function of the dimensionless parameter controlling the stored energy, Z/A, was evaluated and the effect of deformation conditions was described in detail. Finally, the theoretical prediction on the relationships between the DRX volume fractions and the deformation conditions were validated by the microstructure graphs.     

DEM analysis of the size effects on the behavior of crushable granular materials

Four sets of individual-particle crushing tests were carried out on sandstone grains of different size with geometric similarity. The tensile strength was analyzed using Weibull statistics, and the size-hardening law was obtained. The experimental data also validated that the Weibull modulus is independent of the grain size. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with a tension cut-off was employed as the fracture criterion of a single particle. When the particle stresses satisfied the fracture criterion, three new fragments modeled by the ‘clump’ were generated to replace the broken particle. Nine spheres with four different sizes were released from the clump and allowed to continue crushing if the fragment stresses fulfilled the criterion again. Two polydisperse assemblies with different particle sizes but same initial fabrics were prepared. DEM simulations of triaxial shear tests with different grain sizes were carried out on the crushable granular material with varied confining pressures. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses of the two samples, including the stress–strain–dilation behavior, the particle crushing, and the normal contact force distribution, were discussed in detail. The cause of the size effect on the shear strength and deformation was thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis.     

Examining the mechanisms of sand creep using DEM simulations

In this study, DEM simulations of triaxial creep tests on dense and loose sand samples were carried out to examine the micromechanics involved during creep. The simulated creep responses reproduce qualitatively the published experimental results. During the primary creep, the creep stress is gradually borne by the contact normal forces instead of contact tangential forces so that the columnar particle structures can be formed. This process also leads to a continuous decrease in the creep rate. The columnar structures eventually are completely formed and the creep rate reaches a minimum. However, the structures become meta-stable and susceptible to buckling. This explains why a sand packing does not show an extended period of secondary creep in the experiment. Buckling of the columnar structures also gives rise to maximum dilatancy and a sharp transition of the major fabric orientation of weak forces from horizontal to vertical. The continuous buckling process of columnar structures increases the creep rate and sliding ratios of contacts during the tertiary creep. In addition, the trend of contact tangential forces decreasing and contact normal forces increasing is reversed. Finally creep rupture occurs as the creep stress–strain line intersects the complete stress–strain curve. All the creep samples follow their original volume-change tendency to continue their dilation or contraction response during creep.     

DEM analysis of swelling behaviour in granular media

Many granular materials change their volume as they absorb fluids. This phenomenon is called swelling and can be observed in a variety of solids, such as soils, wood, absorbent hygiene products (AHPs) and pharmaceutical excipients. Therefore, an in-depth understanding of grain swelling is of great importance. Since experimental investigations can often provide only limited information, while great insight could be gained from numerical modelling, rigorous numerical models for predicting particle swelling are required. Hence, the objective of this research is to develop and validate a Discrete Element Method (DEM) for swelling of particles. A first order kinetic model was employed to predict the volume expansion of a single grain and subsequently implemented in DEM. The validation of the model was accomplished by comparing the expansion with time of a packed bed made of super absorbent polymer (SAP) particles obtained numerically and experimentally. It was shown that the DEM model can accurately predict the bed expansion. The model was then employed to simulate the swelling of three different materials: superabsorbent polymer (SAP), rice and microcrystalline cellulose (MCC Avicel PH102). As expected, it is demonstrated that the material properties play a significant role on the swelling; the fastest to reach its maximum expansion is the granular bed made of MCC PH102, followed by SAP and rice. However, the highest swelling capacity is achieved with SAP. Moreover, a preliminary DEM analysis of the segregation in a swelling binary mixture is presented in this work. Results suggest that systems which contain a small number of particles, and thus are looser, are more prone to segregation. Future study could advance the developed model to analyse consequences of swelling phenomena in granular materials, such as segregation and heat generation.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

An investigation on loose cemented granular materials via DEM analyses

This paper presents the results of a numerical study carried out by 2D discrete element method analyses on the mechanical behavior and strain localization of loose cemented granular materials. Bonds between particles were modeled in order to replicate the mechanical behavior observed in a series of laboratory tests performed on pairs of glued aluminum rods which can fail either in tension or shear (Jiang et al. in Mech Mater 55:1–15, 2012). This bond model was implemented in a DEM code and a series of biaxial compression tests employing lateral flexible boundaries were performed. The influence of bond strength and confinement levels on the mechanical behavior and on the onset of shear bands and their propagation within the specimens were investigated. Comparisons were also drawn with other bond models from the literature. A new dimensionless parameter incorporating the effects of both bond strength and confining pressure, called BS, was defined. The simulations show that shear strength and also dilation increase with the level of bond strength. It was found out that for increasing bond strength, shear bands become thinner and oriented along directions with a higher angle over the horizontal. It also emerged that the onset of localization coincided with the occurrence of bond breakages concentrated in some zones of the specimens. The occurrence of strain localization was associated with a concentration of bonds failing in tension.     

Analysis and DEM simulation of granular material flow patterns in hopper models of different shapes

By using the discrete element method (DEM) a comparison and observations on material flow patterns in plane-wedged, space-wedged, and flat-bottomed hopper were accounted for. Numerical results obtained by combining data of individual particles, statistical processing of particle assemblies and evaluation of the field variables provided the essential characteristics for different regimes of the discharge flow (within steady or unsteady state of flow) and the differences in differently shaped hoppers due to different microscopic inter-particle friction. For validation of the performed simulations, velocity patterns developed in three-dimensional flat-bottomed hopper containing 20,400 pea grains were also analysed. To represent the continuum by avoiding the local effects produced by the individual grains, the simulation results were focused on the mean velocity distributions with data smoothening. The effect of rolling resistance on granular material flow was also considered.