3D Discrete Element Method Simulations Research Articles

3D DEM simulations of cyclic loading-induced densification and critical state convergence in granular soils

Granular soils exhibit very complex responses when subjected to cyclic loading. Understanding the cyclic behavior of such materials is not only crucial for engineering applications but also the bottleneck of most of constitutive models. This study employs 3D Discrete Element Method (DEM) simulations to explore the accumulative plastic deformation and the internal fabric evolution within granular soils during cyclic loading. Two novel observations are identified: (1) A distinct and unique linear relationship between post-cyclic loading void ratio e and log (p*/p0) is found independent of the amplitude of cyclic load and the initial stress state prior to cyclic loading, where p* is the mean pressure incorporating cyclic loading stress and p0 is the mean pressure prior to cyclic loading; (2) When resuming drained triaxial loadings after cyclic loadings, we observe that both microstructural and macroscopic variables converge to the same values they would have reached for pure monotonic drained triaxial loadings. This intriguing behavior underscores and extends to more general loading paths the influential and attractive power of the critical state.

Assessing cutter-rock interaction during TBM tunnelling in granite: Large-scale standing rotary cutting tests and 3D DEM simulations

The widespread utilisation of tunnel boring machines (TBMs) in underground construction engineering requires a detailed investigation of the cutter-rock interaction. In this paper, we conduct a series of large-scale standing rotary cutting tests on granite in conjunction with high-fidelity numerical simulations based on a particle-type discrete element method (DEM) to explore the effects of key cutting parameters on the TBM cutter performance and the distribution of cutter-rock contact stresses. The assessment results of cutter performance obtained from the cutting tests and numerical simulations reveal similar dependencies on the key cutting parameters. More specifically, the normal and rolling forces exhibit a positive correlation with penetration but are slightly influenced by the cutting radius. In contrast, the side force decreases as the cutting radius increases. Additionally, the side force shows a positive relationship with the penetration for smaller cutting radii but tends to become negative as the cutting radius increases. The cutter's relative effectiveness in rock breaking is significantly impacted by the penetration but shows little dependency on the cutting radius. Consequently, an optimal penetration is identified, leading to a low boreability index and specific energy. A combined Hertz-Weibull function is developed to fit the cutter-rock contact stress distribution obtained in DEM simulations, whereby an improved CSM (Colorado School of Mines) model is proposed by replacing the original monotonic cutting force distribution with this combined Hertz-Weibull model. The proposed model outperforms the original CSM model as demonstrated by a comparison of the estimated cutting forces with those from the tests/simulations. The findings from this work that advance our understanding of TBM cutter performance have important implications for improving the efficiency and reliability of TBM tunnelling in granite.

Impact of particle arrangement and model dimensions on DEM modeling of high-speed railway ballasted tracks in 2D and 3D

Modelling railway projects has a main challenge in the discrete element method (DEM). The granular material of the embankment consists of millions of fine angular particles which are difficult to model due to the long computational time. The long computational time also prevents the modeling of the higher number of loading cycles. As a result, researchers prefer to simulate the project in 2D to accelerate the simulation. While 2D simulations present a seemingly simple option for modeling railways, they tend to oversimplify the intricacies of particle interactions and the distribution of stress. Nonetheless, the extent to which these simplifications affect the authenticity of the simulations has remained ambiguous. In this study, the periodic cell replication method is used to build extensive long railway tracks significantly faster than conventional methods. Then, this DEM model is calibrated against the measurement results of a physical full-scale ballasted track. The model is then used to simulate several railway projects with different initial particle arrangements and model dimensions in both 2D and 3D. The results show that the 2D models are more dependant on the initial particle arrangement which shows different behavior for the same model. In addition, 2D simulations are incapable of reproducing the principal stress rotation in granular layers due to the moving load of the train wheel. As a result, 3D DEM simulations using the periodic cell replication method is suggested for studying the railway tracks.

Lunar highlands simulant — Geotechnical characterization, 3D discrete element modeling, and cone penetration simulations

Lunar regolith on the surface of the Moon has gained great attention as a resource for many proposed lunar exploration projects. Not only is it serving as the ground support for construction projects on the Moon, but it is also the most accessible construction material for building the human habitat and a key component in in-situ resource utilization efforts. Therefore, gaining a fundamental understanding of the characteristics of lunar regolith is a critical step in the success of lunar exploration projects. However, it is challenging and expensive to obtain samples of lunar regolith directly, or conduct physical experiments on lunar regolith samples in situ. Hence, investigative alternatives, such as laboratory experiments and numerical simulation tools are very important means of investigating the properties of lunar regolith. This paper presents a comprehensive study on lunar highlands simulant (LHS-1), using both laboratory experimentation and discrete element method (DEM) simulations. In the laboratory experiment, triaxial tests were conducted on samples of LHS-1 to explore the stress–strain behaviors of the lunar regolith simulant. Correspondingly, 3D DEM simulations of the triaxial tests were conducted to generate the initial model parameters and the Taguchi method was performed to obtain the optimal calibrated input parameters of the DEM model. With the calibrated parameters, 3D DEM model of the cone penetration into LHS-1 was then built to study the responses of the regolith simulant during the penetration process. The effects of porosity and vertical stress on the tip resistance and sleeve friction profiles were investigated for both terrestrial and lunar environments to study the correlation between the in-situ state of the regolith simulants with the force reactions during the penetration.

Shear Resistance Evolution of Geogrid-Aggregate Interfaces under Direct Shear: Insights from 3D DEM Simulations

This paper presents a mesoscopic evaluation of the shear resistance evolution of geogrid-aggregate interfaces subjected to direct shear loading. A three-dimensional discrete element method (DEM) model was developed based on experimental data. The tensile response of geogrid were simulated through a series of calibration tests. Aggregate with complex particle shapes were simulated to accurately capture the interlocking effect among aggregates based on the real particle surface. The individual shear resistance components were quantified based on particle displacement field and contact distribution characteristics. The influences of aperture-aggregate size ratio and geogrid stiffness on the shear resistance components are discussed. The results indicate that the peak value of shear resistance component follows a descending order from frictional resistance of aggregate, to passive resistance of transverse rib, and to geogrid-aggregate interface frictional resistance. During the shear process, the frictional resistance of aggregate becomes active first, followed by the geogrid-aggregate interface frictional resistance, and then the development of passive resistance of transverse ribs starts with a certain lag. Optimizing the geogrid-aggregate size ratio and utilizing geogrids with higher rib stiffness could enhance the passive resistance of transverse ribs but would not significantly affect the geogrid-aggregate interface frictional resistance and frictional resistance of aggregate.

Quantitatively Comparing 3D Discrete Element Method Simulations With Drained Compression Experiments of the Semi-solid Deformation of Al-Cu Alloys

Quantitatively Comparing 3D Discrete Element Method Simulations With Drained Compression Experiments of the Semi-solid Deformation of Al-Cu Alloys

3D DEM Simulations and Experiments on Spherical Impactor Penetrating into the Elongated Particles.

In this study, a brass or glass spherical impactor vertically penetrating into a granular bed composed of mono-sized spherical or elongated particles was simulated with three-dimensional (3D) discrete element method (DEM). Good agreement of the particle masses in the cup before and after penetration can be found in the simulations and experiments. The effects of particle length (Lp), friction coefficient, and particle configuration on the penetration depth of the impactor, ejecta mass, and solid volume fraction describing the response of the granular bed are discussed. The penetration depth is negatively correlated with Lp as the corresponding solid volume fraction of the granular bed decreases. A smaller friction coefficient leads to a larger penetration depth of the impactor and more ejection of particles. When the impactor is penetrating the Lp = 10 mm elongated particles, the penetration depth is negatively correlated to the order parameter and solid volume fraction.

3D DEM Simulation on the Reliquefaction Behavior of Sand Considering the Effect of Reconsolidation Degree

ABSTRACT More and more earthquake cases demonstrate that sandy deposits may be more prone to becoming liquefied again in aftershock events. This phenomenon has also been authenticated by some laboratory element tests and shaking table tests. However, most of the existing studies on reliquefaction only put particular emphasis on the completely reconsolidated soil. Due to the possible short time interval between the main shock and its aftershock events, the generated pore pressure in soil deposits may not have completely dissipated when the aftershock occurred; the reliquefaction is more likely to occur under incomplete consolidation conditions. To investigate the reliquefaction behaviors and the related microscopic mechanisms for the incompletely and completely reconsolidated soil, a series of numerical cyclic triaxial tests are performed in this study via the 3D Discrete Element Method (DEM). Results demonstrated that the reliquefaction resistance of soil is significantly affected by the residual strain and the reconsolidation degree. From the microscopic point of view, the fabric anisotropy and the tightness of inter-particle contacts are the main factors affecting the reliquefaction resistance.

Laboratory experiments and discrete element modeling on the surface failure induced by EPB tunneling: The effects of cutterhead open ratio and relative tunneling depth

This paper presents laboratory tests and high-fidelity numerical simulations to examine the ground failure induced by Earth Pressure Balance (EPB) Shield Tunneling in granular soils. Specifically, we designed and conducted laboratory tests using a reduced-scale EPB Shield Tunnel machine, and built corresponding three-dimensional (3D) discrete-element method (DEM) models to simulate the dynamic excavation process and to gain further understandings of the mechanisms of the ground movement. The study is particularly focused on the combined influences of the cutterhead open ratio and the relative tunnel depth on the ground motions and stress perturbations during the EPB tunneling, which remain understudied in existing studies. The results show that the open ratio of the cutterhead has significant effects on the ground failure in granular soils, especially in cases of relatively shallow tunnels. The larger the open ratio of the cutterhead, the wider the surface and subsurface settlement trough and the greater the soil pressure in the chamber. The pressure distribution in the soil chamber with a larger cutterhead open ratio is significantly more non-linear than that of the case with a smaller cutterhead open ratio. For a given cover-to-diameter ratio (C/D) of the tunnel, the width parameter (k) is generally constant regardless of the depth for the case with a large cutterhead open ratio, especially in the relatively shallow tunnels, while it increases non-linearly with the depth for the case with a small cutterhead open ratio, especially in relatively deep tunnels. Furthermore, soil arching mechanisms are analyzed qualitatively with respect to different cutterhead open ratios and C/Ds. The study demonstrates quantitatively the response of ground surface to the cutterhead open ratios and C/Ds as well as the associated ground failure mechanisms through a combination of laboratory experiments and 3D DEM simulations, providing further insights into the ground behaviors during the dynamic EPB tunneling process.

Modelling the tribocharging process in 2D and 3D

Many discrete element method (DEM) tribocharging models presented in the literature rely on ill-defined or poorly quantified charging parameters. This work presents a straightforward experimental method to quantify key parameters, namely the charge transfer limit, Γ, and the charging efficiency, κc. These parameters are then used in both 2D and 3D DEM simulations to evaluate the applicability of faster 2D models to tribocharge modelling. Both the 2D and 3D models are found to perform well against the experimental data for single-contact and single-particle, multi-contact systems. However, the 2D model fails to produce good agreement with experimental data for multi-contact, multi-particle systems. This approach for determining experimentally the parameters for the DEM tribocharging model is found to be effective and produces good agreement between simulated and experimental data. This method will improve and simplify the DEM modelling of triboelectric charging in dry material handling processes.

Effect of Particle Shape on Soil Arching in the Pile-Supported Embankment by 3D Discrete-Element Method Simulation

Effect of Particle Shape on Soil Arching in the Pile-Supported Embankment by 3D Discrete-Element Method Simulation

Comparative 3D DEM simulations of sand\u2013structure interfaces with similarly shaped clumps versus spheres with contact moments

Three-dimensional simulations of a monotonic quasi-static interface behaviour between initially dense cohesionless sand and a rigid wall of different roughness during tests in a parallelly guided direct shear test under constant normal stress are presented. Numerical modelling was carried out by the discrete element method (DEM) using clumps in the form of convex non-symmetric irregularly shaped grains. The clumps had an aspect ratio of 1.5. A regular grid of triangular grooves (asperities) along the wall with a different height at the same distance was assumed. The numerical results with clumps were directly compared under the same conditions with our earlier DEM simulations using pure spheres with contact moments with respect to the peak and residual interface friction angle, width of the interface shear zone, ratio between grain slips and grain rotations, distribution of contact forces and stresses. The difference between the behaviour of clumps and pure spheres with contact moments proved to be noticeable in the post-peak regime due to a different particle shape. The rolling resistance model with pure spheres was proved to be limited for capturing particle shape effects. Three different boundary conditions along the interface were proposed for micropolar continua, considering grain rotations and grain slips, wall grain moments and wall grain forces, and normalized interface roughness. The numerical results in this paper offer a better understanding of the interface behaviour of granular bodies in DEM and FEM simulations.

Study of shear behavior of granular materials by 3D DEM simulation of the triaxial test in the membrane boundary condition

This paper studies the shear behavior of granular materials by using a three-dimensional (3D) discrete element method (DEM) simulation of the triaxial test. The experimental triaxial tests were conducted on glass beads samples for verification. DEM simulations of the triaxial test were carried out in the membrane boundary condition consisting of 37,989 membrane particles. A new method that divides the irregular sample shape into two parts of cones and parts of three-dimensional simplexes is used to follow the volume change of irregular deformation of samples. The free rotatable upper platen is considered during the shearing process, which influences the shear behavior of samples especially in the residual stage and formations of a single shear band or X-shape shear band. The confining pressures have been demonstrated to influence the rotation angle and angular velocity of the upper platen. Moreover, the timing of replacing a rigid wall boundary condition with the membrane boundary condition is investigated, which affects the porosity of samples before shearing and the mechanical strength. The DEM model in the membrane boundary condition reflects well the evolution of irregular sample deformation and shear band in the shearing process. From the perspective of micro structures, the normal force decreases and the tangential stress increases during the shearing stage. This study greatly improves the accuracy of DEM simulations of the triaxial test in the membrane boundary condition.

3D modeling of the ground deformation along the fault rupture and its impact on engineering structures: Insights from the 1999 Chi-Chi earthquake, Shigang District, Taiwan

The reactivation of the Chelungpu Fault triggered the 1999 Chi-Chi Mw 7.6 earthquake, resulting in substantial ground surface ruptures and severe damage. After the earthquake, the surveys organized by the Central Geology Survey (CGS) of Taiwan and the National Center for Research on Earthquake Engineering (NCREE) immediately investigated a variety of cases related to engineering structures damaged by substantial ground deformation. The investigations gathered valuable in-situ data before human activities disturbed the local setting and altered co-seismic features of interest, providing opportunities for studying the interaction between surface rupture and engineering structures. This study outlines the reconnaissance of damaged engineering structures in Shigang District that cover three typical types of foundations and analyzes the fault geometry and fault slip at the local scale to construct a geomechanical model for numerical simulation. In addition, 3-dimensional (3D) modeling was performed for each case study to investigate the damage mechanisms of the structures subjected to the substantial ground deformations by using PFC3D (Particle Flow Code 3D), which is based on the discrete element method (DEM). The results of the DEM analyses, which have been calibrated with the in-situ data, showed the ability to evaluate the overall ground deformation, the detection of structural movement, and the critical elements of progressive collapse during faulting. This study demonstrates that the 3D DEM simulation is a reliable analysis tool for studying earthquake fault rupture-overburden layer-engineering structure interactions and can produce useful information for hazard assessment with an acceptable computation time. The 3D DEM analysis is therefore suggested to be applied to assess the potential damage scenarios for the engineering structures located in active fault zones.

3D DEM simulations of basic geotechnical tests with early detection of shear localization

Abstract This paper deals with elementary geotechnical tests: triaxial and direct shear of cohesionless sand using the discrete element method (DEM). The capabilities of the numerical DEM code are shown, with a special focus on the early phenomena appearance in localization zones. The numerical tests were performed in 3D conditions with spherical grains. Contact moments law was introduced due to simulate not perfectly round sand grains. The influence of different physical parameters was studied, e.g. initial density or confining pressure. The sieve curve corresponded to the Karlsruhe sand [1]; however, in some tests, it was linearly scaled. Special attention was laid on the behaviour of the sand grains inside localization, e.g. rotation, porosity, fluctuations, etc. and forces redistribution. Emphasis was given on the pre-failure regime and early localization predictors.

3D DEM simulations of monotonic interface behaviour between cohesionless sand and rigid wall of different roughness

The paper deals with three-dimensional simulations of a monotonic quasi-static interface behaviour between cohesionless sand and a rigid wall of different roughness during wall friction tests in a parallelly guided direct shear test under constant normal stress. Numerical modelling was carried out by the discrete element method (DEM) using spheres with contact moments to approximately capture a non-uniform particle shape. The varying wall surface topography was simulated by a regular mesh of triangular grooves (asperities) along the wall with a different height, distance and inclination. The calculations were carried out with different initial void ratios of sand and vertical normal stress. The focus was to quantify the effect of wall roughness on the evolution of mobilized wall friction and shear localization, also to specify the ratios between slip and rotation and between shear stress/force and couple stress/moment in the sand at the wall. DEM simulations were generally in good agreement with reported experimental results for similar interface roughness. The findings presented in this paper offer a new perspective on the understanding of the wall friction phenomenon in granular bodies.

Efficient flexible boundary algorithms for DEM simulations of biaxial and triaxial tests

The accurate modeling of boundary conditions is important in simulations of the discrete element method (DEM) and can affect the numerical results significantly. In conventional triaxial compression (CTC) tests, the specimens are wrapped by flexible membranes allowing to deform freely. To accurately model the boundary conditions of CTC, new flexible boundary algorithms for 2D and 3D DEM simulations are proposed. The new algorithms are computationally efficient and easy to implement. Moreover, both horizontal and vertical component of confining pressure are considered in the 2D and 3D algorithms, which can ensure that the directions of confining pressure are always perpendicular to the specimen surfaces. Furthermore, the boundaries are continuous and closed in the new algorithms, which can prevent the escape of particles from the specimens. The effectiveness of the proposed algorithms is validated by biaxial and triaxial simulations of granular materials. The results show that the algorithms allow the boundaries to deform non-uniformly on the premise of maintaining high control accuracy of confining pressure. Meanwhile, the influences of different lateral boundary conditions on the numerical results are discussed. It is indicated that the flexible boundary is more appropriate for the models with large strain or significant localization than rigid boundary.

Halo approach to evaluate the stress distribution in 3D discrete element method simulation: validation and application to flax/bio based epoxy composite

Discrete element method (DEM) is an interesting alternative to classical approaches as the finite element method (FEM) to simulate homogeneous and heterogeneous materials. Indeed, although DEM was initially developed to simulate granular systems in motion, it also enables to model a continuous medium with the help of a dense granular packing in which the cohesion is introduced between each pair of particles in contact using beam or spring elements. However, among other issues, the local stress field obtained using DEM is heterogeneous, even in the case where it is theoretically homogeneous. In the present contribution, we investigate the stress field distribution in 3D DEM mechanical simulation, and propose an approach we named Halo, to evaluate the level of stress distribution. The idea of the method is to evaluate the stress at the scale of every discrete element (DE) taking into account the contribution of its neighbors, inside the Halo of the DE. The effect of the number of DEs per Halo on the stress distribution is discussed in homogeneous and heterogeneous media. The approach results for homogeneous media are compared to FEM calculations and to the theoretical Hertz solution via a Brazilian test. For the homogeneous media, we use the unidirectional flax/bio based epoxy composite, for which macroscopic longitudinal Young’s modulus is experimentally quantified. Furthermore, comparisons with FEM are performed in this context. Results highlight a good agreement between both approaches in terms of stress fields including extremal values.

Three‐dimensional discrete element method parallel computation of Cauchy stress distribution over granular materials

SummaryThe paper presents Cauchy stress tensor computation over parallel grids of message passing interface (MPI) parallel three‐dimensional (3D) discrete element method (DEM) simulations of granular materials, considering spherical and nonspherical particles. The stress tensor computation is studied for quasi‐static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi's and Nicot's formulations and is verified within MPI parallel 3D DEM simulations involving dynamically adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally deposited particle assemblies exhibits nonuniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc).

Effects of particle sphericity and initial fabric on the shearing behavior of soil–rough structural interface

In this study, the effects of particle sphericity and initial fabric on the shearing behavior of soil-structural interface were analyzed by discrete element method (DEM). Three types of clustered particles were designed to represent irregular particles featuring various sphericities. The extreme porosities of granular materials composed of various clustered particles were affected by particle sphericity. Moreover, five specimens consisting of differently oriented particles were prepared to study the effect of initial fabric. A series of interface shear tests featuring varying interface roughnesses were carried out using three-dimensional (3D) DEM simulations. The macro-response showed that the shear strength of the interface increased as particle sphericity decreased, while stress softening and dilatancy were easily observed during the shearing. From the particle-scale analysis, it was found that the thickness of the localized band was affected by the interface roughness, the normal stress and the initial fabric while independent of the particle sphericity. The thickness generally ranged between 4 and 6 times that of the median particle equivalent diameter. A thicker localized band was formed in the case of rougher interface and in soil composed of inclined placed and randomly placed particles. The coordination number measured in the interface zone and upper zone suggested that the dilation mostly occurs inside the interface zone. Anisotropy was induced by the interface shearing of the initial isotropic specimens. The direction of shear-induced anisotropy correlates with the shearing direction. The evolutions of anisotropies for the anisotropic specimens depend on the initial fabric.