Discrete Element Method Study Research Articles

The axially-loaded behaviours of Schwarz Primitive (SP)-based structures: An experimental and DEM study

This study delves into the axial responses of Schwarz Primitive (SP) structures. Emphasising on bearing capacity, force distribution, cracking phenomena, load-displacement curve and energy absorption. Discrete element method (DEM) is adopted to analyse the axial load-bearing behaviour and fracture mechanics of Main SP and Secondary SP structures under various unit cell configurations after validated by experimental tests. The results indicates that despite sharing the same 1/8th cell structure, the axially-loaded behaviours of the Main SP and Secondary SP structures are not identical, particularly in scenarios involving a large unit cell size and a small number of unit cells. The Main SP structures display an axial load-bearing behaviour that is largely unaffected by variations in the number of unit cells along the x and y axes, while Secondary SP structures show a more pronounced improvement in average strength and energy absorption capacity when the number of unit cells increases. Main SP structures offer superior axial load-bearing capabilities and energy absorption efficiency, which is a significant consideration for their application in scenarios demanding high structural integrity. This distinction underlines the importance of tailored design and selection of SP configurations based on specific engineering requirements.

Novel designs of blade mixer impellers from the discrete element method and topology optimization

Granular mixers are essential for manufacturing products that require bulk materials as precursors. The modeling of mixers is aided by the discrete element method (DEM), which can simulate the flow of bulk material. DEM is applied in mixer design studies by varying a few design parameters and analyzing the predicted performance, but systematic design via optimization methods has yet to be performed. In this work, we utilized a combined DEM and topology optimization approach to design blade mixer impellers for improved mixing and reduced energy consumption. A DEM model was formulated from a blade mixer setup and validated with experimental particle flow data. The computational cost of the model was then reduced by employing larger particle sizes in the simulations. A binary genetic optimization algorithm was used afterwards to find the tilt angle, number, and shape of impeller blades that would improve mixing or reduce the required driving power. The high mixing impellers have four blades that each have cavities at the center and the tip. The increased blade count promotes convective mixing, while the cavities enhance shear mixing. Meanwhile, the low energy impellers have two blades that both have cavities at the center and less material at the blade tips. These minimize particle-impeller collisions, which in turn reduce the power required to drive the impeller. This work demonstrates the use of optimization methods to design the shape of impeller blades – a variable often overlooked in conventional DEM studies. Our approach may be used to systematically design other mixer types as well.

Analyzing cyclic shear behavior at the sand–rough concrete interface: An experimental and DEM study across varying displacement amplitudes

AbstractPile foundations frequently endure dynamic loads, necessitating an in‐depth examination of the cyclic shear properties at the pile–soil interface. This study involved a series of cyclic direct shear (CDS) tests conducted on sand and concrete with irregular surface, utilizing varying displacement amplitudes (1, 3, 6, and 10 mm) and joint roughness coefficients (0.4, 5.8, 9.5, 12.8, and 16.7). Discrete Element Method (DEM) models, informed by experimental data, facilitated mesoscopic mechanical response analyses. Findings indicate that the sand–concrete interface undergoes softening, with hysteresis loops' morphology dependent largely on displacement amplitude. A maximum ultimate shear stress corresponds to a specific critical surface roughness, while the initial tangent modulus escalates with increased concrete roughness. Volume variations of the specimen inversely correlate with displacement amplitude and directly with surface roughness. As displacement amplitude expands, there is a reduction in the maximum shear stiffness and an elevation in the maximum damping ratio. Empirical formulas for the surface roughness and normalized shear stiffness were proposed. Larger displacement amplitudes result in more substantial shear bands and heightened energy dissipation, yet the incremental energy ratio remains largely unaffected. Predominant energy dissipation mechanisms include both slip and rolling slip, with the former surpassing the latter in energy dissipation capacity. The anisotropy directions of contact normal, normal contact forces, and tangential contact forces consistently fluctuate with shear direction alterations.

Effects of transverse and axial die pressing on the alignment of Nd-Fe-B compacts: A discrete element method study

The effects of transverse die pressing (TDP) and axial die pressing (ADP) processes on the alignment and orientation distribution of the Nd-Fe-B compacts were analyzed by discrete element method (DEM). It was found that ADP-compact had lower alignment than TDP-compact, mainly due to the different degrees of the orientation disruption by particle rotation during pressing. That is, when pressed along the Z-axis, particles rotated mainly along the X-axis and Y-axis. For TDP, only the Y-axis was perpendicular to the particle orientation (X-axis), so the rotation along the Y-axis disrupted the orientation, while the rotation along the X-axis had no effect. However, for ADP, the rotation axes (X-axis and Y-axis) of particles were both perpendicular to their orientation (Z-axis), so rotation along any of these axes decreased the alignment. Therefore, ADP-compact was more impaired by particle rotation than TDP-compact during pressing, in the surface and central regions of the compact.

Computer vision-aided DEM study on the compaction characteristics of graded subgrade filler considering realistic coarse particle shapes

The compaction quality of subgrade filler strongly affects subgrade settlement. The main objective of this research is to analyze the macro- and micro-mechanical compaction characteristics of subgrade filler based on the real shape of coarse particles. First, an improved Viola–Jones algorithm is employed to establish a digitalized 2D particle database for coarse particle shape evaluation and discrete modeling purposes of subgrade filler. Shape indexes of 2D subgrade filler are then computed and statistically analyzed. Finally, numerical simulations are performed to quantitatively investigate the effects of the aspect ratio (AR) and interparticle friction coefficient (μ) on the macro- and micro-mechanical compaction characteristics of subgrade filler based on the discrete element method (DEM). The results show that with the increasing AR, the coarse particles are narrower, leading to the increasing movement of fine particles during compaction, which indicates that it is difficult for slender coarse particles to inhibit the migration of fine particles. Moreover, the average displacement of particles is strongly influenced by the AR, indicating that their occlusion under power relies on particle shapes. The displacement and velocity of fine particles are much greater than those of the coarse particles, which shows that compaction is primarily a migration of fine particles. Under the cyclic load, the interparticle friction coefficient μ has little effect on the internal structure of the sample; under the quasi-static loads, however, the increase in μ will lead to a significant increase in the porosity of the sample. This study could not only provide a novel approach to investigate the compaction mechanism but also establish a new theoretical basis for the evaluation of intelligent subgrade compaction.

Face failure of EPB shield tunnels in dry dense sand: a model test and DEM study

This study aims at addressing the face failure of earth pressure balance (EPB) shield tunnels in dry dense sand by model tests and discrete element method (DEM) models. The model tests incorporated a miniature EPB shield which could fully reproduce the real tunnel construction of excavation and support. DEM models simulating the model tests were developed to capture the underlying face failure mechanism. Results show that both the limit support pressure obtained at chamber board and tunnel face increase with increasing C/ D ( C is tunnel cover depth, and D is tunnel diameter). The ratio of the former to the latter approximates 0.60 due to the soil retaining of cutter head panel, and it is independent of C/ D. The local face failure initializes around tunnel face and develops directly to the global failure outcropping the ground surface in one phase with C/ D ≤ 1.0, while the local failure develops to the global failure in three phases with C/ D = 2.0 due to the soil arching evolution. The soil arching gets weaker when it propagates upward, and the horizontal stress concentration in the longitudinal direction is stronger than the transverse direction due to the difference of arch foot.

Effects of particle shape, physical properties and particle size distribution on the small-strain stiffness of granular materials: A DEM study

The effects of particle shape (angularity α and sphericity S), physical properties (shear modulus Gp and Poisson’s ratio νp) and particle size distribution (uniformity coefficient Cu) on the small-strain stiffness Gmax were investigated via the discrete element method (DEM) in this study. The Gmax values were obtained by DEM simulations of drained triaxial tests. Microscopic analysis indicates that Gmax uniquely depends on two microscale variants, i.e., the mechanical coordination number CNm and contact stiffness between particles. The particle shape effect was only related to CNm. The contact stiffness can be represented by the values of Gp and Cu. Accordingly, an empirical expression composed of CNm, Gp and Cu that can predict the Gmax of granular materials with different particle properties (e.g., particle size distribution, particle shape, and fabric effect) was proposed. The accuracy of the expression has been verified by comparing the data with previous studies.

Discrete element modelling of the effects of particle angularity on the deformation and degradation behaviour of railway ballast

Railroad ballast exhibits distinct morphological characteristics represented by shape irregularity, corner angularity, and surface texture. Upon repeated train loading, the morphology of ballast undergoes inevitable degradation, particularly in terms of its corner sharpness, which can affect track performance and even pose a substantial threat to operational safety. These aspects have rarely been captured insightfully in most DEM studies on ballast. In contrast, this study examines the influence of particle angularity on the deformation and degradation behaviour of railway ballast upon repeated loading using the discrete element method (DEM). The angularity of ballast particles is captured and quantified using the CT scanning technology in conjunction with an image-based processing strategy, after which the irregularly shaped particles are reconstructed in the DEM. In this numerical procedure, aggregates with varying angularities are created by incorporating a particle degradation subroutine to capture corner abrasion and surface attrition of ballast to mimick real-life field processes. The macro-response of a typical ballasted track subjected to cyclic rail loading is investigated, and the results show that as the angularity increases, the permanent deformation of the track corresponds to a lower permanent strain rate and a higher resilient modulus. However, the opposite behaviour is observed if excessive breakage of the aggregates occurs that reduces the angularity of the individual particles. In this study, detailed microscopic analysis based on DEM in terms of interparticle interaction and associated vibration velocity has also been performed. The results offer distinct clarity to the essential micro-mechanisms embracing particle angularity, and the accompanying influence on the deformation and degradation characteristics of ballast is elucidated with greater insight.

Advances in Coupling Computational Fluid Dynamics and Discrete Element Method in Geotechnical Problems

In some cases, the water content in granular soil increases to the extent that it becomes saturated, which noticeably alters its responses. For example, the pore water pressure within saturated granular soil would increase rapidly under sudden external loading, which is equivalent to undrained or constant volume conditions. This reduces the effective stress in soil dramatically and may result in catastrophic failure. There have been different numerical approaches to analyse such a failure mechanism of soil to provide a deeper understanding of soil behaviour at the microscopic level. One of the most common numerical tools for such analysis is the discrete element method (DEM) due to its advantage in obtaining microscopic properties (e.g., statistics on particle contacts and fabric), reproducibility and simple feedback control. However, most DEM studies ignore the fluid phase and merely consider the solid particles while the fluid pressure is indirectly calculated by mimicking undrained condition to a constant volume condition. Note that fluid’s influence does not limit to the change of pore water pressure. For example, the external loading would induce the movement of fluid, and the fluid-solid interaction could subsequently drag the solid particles to shift within the system. In addition, the state of soil could change from solid to suspension under an excess hydraulic gradient. Therefore, the study of the fluid-solid mixture is essential as it is a typical scenario in geotechnical practice, and the simulations of saturated sand should be conducted in numerical forms in which both the solid and fluid phases can be modelled.

Test and DEM study on cyclic hysteresis characteristics of stereoscopic geogrid–soil interface

The bearing resistance provided by the geogrid's transverse ribs is a non-negligible aspect of the strength mechanism in mobilizing the geogrid–soil interface. Therefore, studying its influence on the response mechanism of geosynthetic-reinforced soil structures under cyclic loading is crucial. The stereoscopic geogrids were manufactured using 3D printing technology by quantitatively thickening the transverse ribs of planar geogrids. To investigate the cyclic hysteresis relationship and stress–dilatancy phase-transformation characteristics of the stereoscopic geogrid–coarse particle interface, cyclic direct shear tests were conducted. Additionally, a discrete element method (DEM) was employed to study the evolution of shear bands and fabric anisotropy at the interface under cyclic loading. The results of the study indicate that the stress–displacement phase angle of the stereoscopic geogrid in the horizontal direction of cyclic shear is smaller compared to the planar geogrid. Furthermore, thickening the transverse ribs decreases the stress–dilatancy phase-transformation angle of the interface. The thickness of the interface shear band in the stereoscopic geogrid is greater than that of the planar geogrid. Moreover, as the transverse-rib thickness increases, the principal direction of the average normal contact force and average tangential contact force under cyclic loading also increases.

Discrete element method study of parameter optimization and particle mixing behaviour in a soil mixer

Soil mixing is an emerging research in the field of construction resource recovery. In this study, the mixing behaviour of soil particles in a mixer is numerically simulated by the discrete element method (DEM). A four-factor, three-level orthogonal experiment is designed to optimize the mixer design by selecting the fly-cutter speed, spindle speed, number of blades and fly-cutter diameter, using Lacey mixing index and power consumption as evaluation indicators. Then, the impact of soil cohesion and type on the mixing behaviour is investigated. The results show that the optimal parameter combination of this experiment is 280 rpm fly-cutter speed, 40 rpm spindle speed, 4 blades and 250 mm fly-cutter diameter. This optimal combination reaches a comparatively uniform state mix in 5.9 s with an average power consumption of 704.11 W. In addition, the wear and tear of the mixer increases as soil cohesion increases, while the mixing quality of materials declines, resulting in a “shaft hugging” phenomenon. The mixing efficiency varies greatly among different soil types, but the radial and tangential velocities have a similar law. This work can provide some guidance for the optimization design of a mixer and study of soil mixing.

DEM study on mixing behaviors of concave-shaped particles in rotating drum based on level-set method

Granular mixing is a complex phenomenon that is commonly encountered in various engineering disciplines. A large number of past studies have mainly focused on the mixing properties of convex-shaped granular materials, while the mixing behaviors of concave-shaped granular materials have not been well studied. In this study, spherical harmonic functions are used to describe the spherical and concave shapes of individual particles. The level set function is an implicit function consisting of a set of points that can be used to determine the contact points between particles. Then, the influences of the particle shape and rotational speed on the mixing behaviors of the granular material within a horizontal drum are analyzed by the discrete element method (DEM). Results indicate that concave particles have higher coordination numbers and closer contact patterns than spherical particles, which results in greater normal collision forces, larger dynamic angle of repose and lower mixability.

Discrete element simulations of flexible ribbon-like particles

A flexible ribbon-like particle model is developed based on the Discrete Element Method (DEM) for numerical modelling of biomass materials and many other flexible materials encountered in industries. In the model, a thin, irregular-shaped particle is discretized into triangular facet elements that can deform subject to internal and external forces. A library of particle templates of various shapes is established for numerical generation of a collection of particles with a statistical distribution of particle shapes in the simulations. The developed particle model is adopted to simulate uniaxial compression of biomass materials. With the calibrated model parameters, simulation results of various biomass materials and their mixtures are in good agreement with experimental data. For a better understanding of packing behavior of the biomass materials, DEM studies are performed to reveal the effects of initial particle configuration, particle shape distribution, and particle size distribution on macroscopic and micro-structural properties.

Determination of Material and Interaction Properties of Granular Fertilizer Particles Using DEM Simulation and Bench Testing

The discrete element method (DEM) is an effective tool for obtaining qualitative and quantitative information on particle motion, which aids in the design and optimization of agricultural equipment structures. The accuracy of the DEM simulation parameters significantly impacts the simulation results. This study employed a combination of high-speed camera measurement, DEM simulation, and validation tests to determine the material and interaction property parameters for fertilizer particles. The basic parameters (triaxial size, bulk density, density, and coefficient of static friction) and coefficients of restitution between fertilizer and material were measured for three fertilizer varieties. There was a significant difference in the angle of repose between various material plates and fertilizer particles. The calibration values of coefficients of restitution and coefficients of rolling friction between fertilizer particles were optimized using the Box–Behnken method. The angle of repose was significantly affected by the coefficient of static friction and the coefficient of rolling friction between the fertilizer particles. The determined values for the coefficient of restitution, coefficient of static friction, and coefficient of rolling friction between the fertilizer particles were 0.323, 0.381, and 0.173, respectively. The error in the angle of the repose test was less than 3.0%, and the variation coefficient for each row consistency was less than 1.68 percentage points under the optimal simulation parameters. DEM simulations of the angle of repose and each row consistency variation coefficient test using the measured parameters can accurately predict the experimental results. The findings of this paper provide a theoretical basis for the DEM study of fertilizer particles.

The importance of initial particle position on filter performance in granular soils

This paper conducted an extensive set of gravity-driven filtration simulations using the discrete element method (DEM). The simulations were used to statistically analyse the inherent variability in filter performance due to variations in initial particle position using one-way ANOVA for repeated measures tests. The simulations accounted for group effects associated with the interaction of base particles within the voids of the filter particles, and considered a size ratio that captured the complete range of filtration behaviour. The simulations were performed in a highly controlled manner, such that the sole difference between the base-filter realisations was initial particle position. Four filtration characteristics, based on filter efficiency and filling degree, were considered to define filter performance. One-way ANOVA for repeated measures tests conclusively showed that initial filter particle position had a statistically significant effect on filter performance for all four characteristics. Significant variability was observed with normalised ranges up to 16.0%. Increasing the domain width did not eradicate the observed statistically significant differences in filter performance. These observations highlighted the importance of considering multiple stochastically generated base-filter realisations in DEM studies before drawing conclusions about the performance of filters due to the inherent variability of the particle-scale mechanisms underlying the filtration process.

DEM study of the stress fields around the closed-ended displacement pile driven in sand

Three-dimensional discrete element method (DEM) is employed to model the published calibration chamber test of a closed-ended displacement pile driven in sand. To achieve large chamber-to-pile and pile-to-particle size ratios for unbiased predictions, a high-performance graphics processing unit-powered DEM code is utilised in conjunction with the axisymmetric assumption and particle refinement method. The DEM parameters are first calibrated against the drained triaxial compression test data on Fontainebleau sand. Then, the DEM modelling of pile driving demonstrates quantitative agreement with the experimental counterpart in terms of cone resistance, stress contours, and distributions.

Particle shape effects on dynamic properties of granular soils: A DEM study

Particle shape is an essential aspect of granular soils that affects their mechanical properties. It is challenging to isolate the effect of particle shape from other mechanical properties such as inter-particle friction coefficient and particle shear modulus in laboratory tests. The discrete element method (DEM) makes it feasible to investigate the effect of macroscopic and mesoscopic particle morphologies including sphericity and roundness. This study provides a systematical DEM investigation of the particle shape effect on the dynamic properties of granular soils by simulating cyclic undrained triaxial tests at various initial confining pressures and void ratios. The results indicate that specimen consisting of angular particles generally exhibit a higher secant shear modulus G than that of rounded particles. Additionally, particle shape has no significant effect on modulus ratio G/G0 but a noticeable impact on damping ratio D at relatively large strains due to dilatancy. A weighted coordination number CN' was proposed to reveal the microscopic effect of particle shape on G0. Contact sliding was found to be the main cause of modulus degradation and damping increase with increasing shear strain. The tangential shear modulus ratio Gtan/G0 is inversely correlated to the weighted contact sliding ratio fs'.

Mechanical performance of Bio-Inspired Gyroid and Primitive concrete structures under combined compression and torsion Loads: A discrete element method study

Bioinspired lightweight Primitive and Gyroid structures are two well-known TPMS (triply periodic minimal surface) cellular structures. These structures have been shown to possess high specific strength and energy absorption capacity, and thus hold great promise for a range of prefabricated civil engineering applications. As a result, concrete cellular TPMS structures have garnered the attention of researchers. However, prior to this study, no investigation has been carried out on the mechanical properties and failure patterns of concrete Primitive and Gyroid structures under coupled compressive and torsional loads. This lack of knowledge on the behaviour of these structures can lead to safety concerns in construction projects. To better understand the mechanical behaviour of Primitive and Gyroid structures under combined compression and torsion, the discrete element method (DEM) is adopted to simulate the TPMS structures. Both linear contact and nonlinear softbond contact models are utilized to simulate the brittle mechanical behaviour of concrete material. After validating the DEM parameters using published experimental data, the DEM models are subjected to coupled compressive and torsional loads to study their compressive and torsional bearing capacity and cracking patterns. The results indicate that the Primitive based structures outperform the Gyroid based structures in terms of both compressive and torsional resistance. The study is the world's first to reveal that a compressive load enhances the ultimate torsional bearing capacity of TPMS structures, but a torsional load reduces their compressive bearing capacity. Additionally, the loading conditions have little impact on the cracking patterns of the four TPMS structures.

DEM study of particle scale effect on plain and rotary jacked pile behaviour in granular materials

The capacity of open-ended piles strongly depends on the potential plugging occurring during installation. The Discrete Element Method (DEM) is particularly suitable to the study of pile plugging, as it can model large soil deformation. However, DEM simulation of the 3D boundary value problems is computationally expensive, and particle upscaling is usually used to reduce the number of particles modelled. In this paper, two granular beds were created with the same average porosity, initial stress field and contact parameters, but different particle scales. Two pile geometries were installed by plain and rotary jacking. Normalised results show that the pile penetration mechanism is strongly affected by the particle scale. Larger particles lead to earlier pile plugging, higher shaft resistance and require a greater force to penetrate the ground. This effect can be linked to a modified penetration mechanism, with larger shear zones and less well defined “nose cone” under the pile tip for larger particles. Changing particle scaling has a neutral effect on the total penetration resistance of a rotary jacked pile, but reduces the base penetration and increases the plug resistance. Maximising the ratio of particle scale to wall thickness is key to adequately capturing the pile coring mechanism.

Liquefaction behavior of inherently anisotropic sand under cyclic simple shear: Insights from three-dimensional DEM simulations

Inherent fabric anisotropy has been widely recognized to have significant effects on the liquefaction behavior of sand. A discrete element method (DEM) study was conducted to investigate the liquefaction behavior of inherently anisotropic sand under cyclic simple shear conditions. In the DEM model, the under-compaction method was modified to generate uniform and inherently anisotropic specimens. A series of DEM simulations of undrained cyclic simple shear tests were performed to investigate the effects of bedding plane angles with a full spectrum ranging from −90° to +90°. The relative magnitudes of the three effective normal stress components were compared and analyzed. The internal structure evolution was quantified through a contact-normal-based fabric tensor that could describe the load-bearing structure of granular specimens. The simulation results show that the effect of bedding plane angle on the liquefaction resistance of anisotropic sand is not monotonic. For example, as the bedding plane angle of specimen increases from 0° to 90°, the liquefaction resistance first decreases and then increases, with the most detrimental scenario occurs at 45°. This could be explained by correlating the magnitudes of shear modulus with the discrepancy between the loading direction and the direction of fabric during each cycle.