Improved Metaball Discrete Element Method with Robust Contact Algorithm for General-Shaped Particles with Rounded Features

Discrete element method (DEM) has achieved considerable success on simulating complex granular material behaviours. One of the key challenges of DEM simulations is how to describe particles with realistic geometries. Many shape description methods have been developed including sphere-clustering, polyhedrons, sphero-polyhedrons, superquadric particles to name a few. However, to model general shaped particles with round features , these techniques are either introducing artificial surface roughness or are limited to a few regular shapes. Here we proposed a metaball based DEM where the metaball equation is used to describe particle shapes. Because of its flexibility on choosing control points in the metaball equation, many complex shaped particles can be modelled within this framework. The particle collision is handled by solving an optimization problem. A Newton–Raphson method based algorithm of finding the closest points for metaball DEM is developed accordingly. Using 3D printed particles, the proposed scheme is validated by comparing the simulated ran-out distance with granular column collapses experimental results. The model is further applied to study shape effects on vibration induced segregations. It is shown that the proposed metaball DEM can capture shape influence which may crucial in many engineering and science applications.

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.

A modified discrete element method (DEM) with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study. Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior, mesoscale contact parameters at particle level and external loading rate. It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk. The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials. The parametric study indicates that Poisson’s ratio only varies with stiffness ratio, while Young’s modulus is proportional to contact modulus and grows with stiffness ratio, both of which agree with the micromechanical model. The peak friction angle is dependent on both inter-particle friction angle and rolling resistance. The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large. Finally, we have recommended a calibration procedure for cohesionless soil, which was at once applied to the simulation of Chende sand using a series of triaxial compression tests. The responses of DEM model are shown in quantitative agreement with experiments. In addition, stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.

Rockfill materials are widely used in constructions, such as rockfill dams, railroads and embankments. However, the mechanical behavior of rockfill materials is difficult to investigate in laboratory due to the limited size of apparatus. In addition, the microstructural characteristics of rockfill materials under loading is difficult to observe in laboratory experiments. In this study, the scale effect on the macroscopic and microscopic mechanical behavior of rockfill materials was investigated by the discrete element method (DEM). The parallel gradation technique and the mixed technique, were used to reduce the maximum grain size of the prototype gradation (60 mm) to that of the scaled gradation (20 mm). The mechanical behavior of scaled DEM samples was obtained from a series of conventional triaxial compression tests. The results show that the strength of rockfill materials with the same maximum grain size was affected by different modeling techniques in DEM.

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

Discrete Element Method (DEM) is a numerical technique that uses particulate mechanics in simulating the discontinuous behavior of particulate materials. DEM presents the advantage of modelling thosematerials in a particulate level allowing specifications of particle geometry including how their contacts interact. However, identifying microparameters that can accurately simulate the behavior of particulate materials is challenging. This paper presents the calibration of the microparameters of materials used in an earthfill damthat experienced slope movements. The main components of the earthfill dam under study were clay, for the core and blanket, and rockfill materials, for the protective shell. Linear parallel-bond model (LPBM) was used to describe the interactions between clay particles. Microparameters involved with the LPBM were particle stiffness, friction coefficient, bond strength, and bond stiffness. A triaxial test DEM model was developed to calibrate the clay microparameters, and it was successful in simulating the measured macroscopic peak and critical state behavior of clay materials. Rolling resistance linear model was used to describe the interactions between rockfill particles. Microparameters associated with the rolling resistance linear model were particle stiffness, friction coefficient, and rolling resistance coefficient. Large-scale direct shear test was simulated to calibrate rockfill microparameters, and it was able to capture the measured macroscopic shear behavior of rockfill materials. Calibration methodologies performed were successful in identifying appropriate microparameters for both rockfill and clay materials. The calibrated microparameters are beneficial in the development of a DEM model that can analyze movements and landslides in the vicinity of the earthfill dam or other earthfill dams built with similar materials.

Scaled-up rice grain modelling for DEM calibration and the validation of hopper flow

Particle crushing can result in changes in the mechanical properties of granular materials. By using Discrete Element Method (DEM), a model is established to simulate the breakage of two-dimensional particles for three different shapes (triangle, square and hexagon). In the simulations, each particle consists of two sub-particles bonded with each other. Particle crushing will occur during the numerical analysis if the bond between these sub-particles breaks. With this model, the effect of particle breakage on macro mechanical behavior of granular materials can be studied for three particle shapes which have the same equivalent radius. For each of these shapes, two series of biaxial tests, with and without breakable particles, are simulated and the results are compared in terms of shear strength and volume change, then the effect of fragmentation on the global behavior is evaluated for discrepant particle shapes. It is observed that particle breakage has a significant influence on mechanical behavior of granular materials such as a decrease in shear strength as well as volume change; moreover, the particle shape does not have so much effect on the final breakage percentage for this kind of failure.

Study on the relationships between particle shapes and motion responses in the geotechnical coarse-grained system subjected to vibration loads

The deformable discrete-element method (DEM) was employed to study the effect of particle shape on the macroscopic mechanical behavior of rockfill materials. Relationships among the micromechanical parameters and macroscopic response of rockfill materials were identified by simulating triaxial compression tests on numerical samples. The numerical experiment results showed that the particle shape has a significant impact on the macroscopic response of rockfill. For instance, the peak strength and residual strength of the numerical sample and the axial strain corresponding to the peak strength increased with an increase in the aspect ratio of the particle.

Two-scale FE–FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior

The majority of particle scale studies using the Discrete Element Method (DEM) have assumed the particles to be perfect spheres. Despite prevalent acceptability of this assumption, it has been observed that the particle shape and the resulting geometric interlocking between particles is a primary contributor to the overall shearing resistance and is therefore critical for predicting the behaviour of a granular assembly [1]. Micro-scale irregularity, non-sphericity in shape and surface characteristics all affect the relative motion of particles, which leads to change in rheology at macroscale. Additionally, asymmetric shape in grains, such as sands and cereals, induces a resisting moment at each contact that influences stress state over the bulk. Using idealized spherical particles in DEM simulations, studies have suggested an alternative approach to enable the shape effect to be captured by applying a resistance torque between contacts between spherical particles [2-6]. However it is not fully understood whether introducing a rolling resistance in spherical contact can adequately capture the granular friction in non-spherical particles. The present study focuses on this question by evaluating the capability of such rolling resistance as a shape effect parameter in capturing the macro-scale characteristics of dense granular system during silo discharge. In this regard, a series of DEM simulations are performed on a flat bottom silo as the main geometry with two types of particles; perfect sphere, having various values for the rolling friction parameter, and non-spherical particle which has the same mass as the perfect sphere. Consequently, the equivalency of computed macroscopic features through both systems are quantitatively investigated. A novel spatio-temporal averaging tool is used to quantify the mean and standard deviation over the temporal scale of the computation [7] and visualize the velocity profiles along the boundaries and also to monitor the discharge rate through the orifice of the silo. The force chains generation and distribution are monitored during the solids flow in the silo discharge to provide the insight into the particle scale phenomena. The comparison of the results highlights the impact of particle shape effect and also allows the recognition of deficiencies in the proposed rolling friction as a shape factor in predicting realistic flow behaviour of granular assemblies in silos.

The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy.The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density.As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young’s modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.

Unbound permeable aggregate base (UPAB) materials with strong load-transmitting skeleton yet adequate inter-connected pores are desired for use in the sponge-city initiative. However, the micro-scale fabric evolution and instability mechanism of macroscopic strength behavior of such UPAB materials still remain unclear. In this study, virtual monotonic triaxial compression tests were conducted by using the discrete element method (DEM) modeling approach on specimens with different gradations quantified by the parameter of gravel-to-sand ratio (G/S). The realistic aggregate particle shape and inter-particle contact behavior were properly considered in the DEM model. The micromechanical mechanisms of the shearing failure of such UPAB materials and their evolution characteristics with G/S values were disclosed from contact force chains, microstructures, and particle motion. It was found that the proportion of rotating particles in the specimens decreased and the proportion of relative sliding between particles increased as the content of fine particles decreased. The plastic yielding of the specimens originated from the failure of contact force chains and the occurrence of the relative motion between particles, while the final instability was manifested by the large-scale relative motion among particles along the failure plane (i.e., changes in the internal particle topology). By comparing the macroscopic strength, microstructure evolution, and particle motion characteristics of the specimens with different G/S values, it was found that the specimens with G/S value of 1.8 performed the best, and that the G/S value of 1.8 could be regarded as the threshold for separating floating dense and skeletal gap type packing structures. The variation of Euler angles of rotating particles was significantly reduced in the particle size range of 4.75 mm to 9.50 mm, indicating that this size range separates most of the particles from rolling and sliding. Since particle rolling and sliding behavior are directly related to shear strength, this validates the rationality of the parameter G/S for controlling and optimizing gradations from the perspective of particle movement. The findings could provide theoretical basis and technical guidance for the effective design and efficient utilization of UPAB materials.