3D Discrete Element Method Research Articles

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.

The Coupling Orbit–Attitude–Structure Evolution of Rubble-Pile Asteroid with Earth Flyby in the Restricted Three-Body Problem

Some asteroids flying close to Earth may pose a threat of impact. Among them, the structural and dynamical characteristics of rubble-pile asteroids can be changed because of the tidal force of the Earth in this process. This can provide key information for predicting the dynamical evolution of potentially hazardous asteroids. In this study, the long-term evolution of the coupling orbit–attitude–structure of these small bodies is presented numerically based on the integration of two models. One is the 3D discrete element method, which models the structure and irregular shape of the rubble-pile asteroid. The other is the dynamical model of the circular restricted three-body problem (CRTBP). This provides a more precise dynamical environment of the asteroid orbital deflection, morphological modification, and attitude angles analysis compared to the frequently adopted two-body problem. Parametric studies on the asteroid evolution were performed focusing on its flyby distance and the bulk porosity. Numerical results indicate that the Earth flyby can form different patterns of modification of asteroids, where the rubble-pile structure can be destructed by considering the bulk porosity. The asteroid orbital deflection and attitude variational trends are also summarized based on the simulations of multi-orbital revolutions.

D.E.M. modeling of biocemented sand: Influence of the cohesive contact surface area distribution and the percentage of cohesive contacts

Microbially induced calcite precipitation (MICP) is a recent technique used to reinforce the soil. In the present work, a 3D Discrete Element Method (DEM) model for biocemented sand is set up. It takes into account real contact properties, such as the cohesive contact surface area distribution and the percentage of cemented bonds, which have been computed from 3D synchrotron X-ray images at high resolution of biocemented sand with different amounts of calcite, ranging from 0 to 14.9% in volume (i.e. 19.6% in mass). Triaxial tests under different confining pressures are simulated. The macroscopic response of numerical and physical specimens are compared. Overall, these simulations show that the above contact properties play an important role on the macroscopic response and the proposed numerical model allows to describe with a good accuracy the macroscopic responses of lightly cemented samples (below 4% in volume), whereas it requires future developments to well represent the behavior of medium and highly cemented samples.

Single Particle Growth, Fragmentation and Morphology Modelling: A DEM Approach

AbstractIn this work, the development of a 3D discrete element method (DEM) modeling concept and application that can describe and explain the catalyst particle growth and fragmentation mechanism and follow the morphology developments is presented. The proposed unified modeling methodology is able to predict the expected particle morphology in terms of exact shape, size, and porosity, taking into account the major contributing effects, including reaction kinetics, thermodynamics as well as mechanical considerations. The developed DEM model is validated based on indicative particle morphology patterns as captured experimentally via the SEM technique, managing to qualitatively predict the observed particle morphology. These results indicate the potential of DEM approach in polymer reaction engineering (PRE), expanding the simulation capabilities and range of application.

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.

Coupled effects of particle overall regularity and sliding friction on the shear behavior of uniformly graded dense sands

Particle morphology has been regarded as an important factor affecting shear behaviors of sands, and covers three important aspects, i.e. global form (overall shape), local roundness (large-scale smoothness), and surface texture (roughness) in terms of different observation scales. Shape features of different aspects can be independent of each other but might have coupled effects on the bulk behavior of sands, which has been not explored thoroughly yet. This paper presents a systematic investigation of the coupled effects of the particle overall regularity (OR) and sliding friction on the shear behavior of dense sands using three-dimensional (3D) discrete element method (DEM). The representative volume elements consisting of ideal spheres and irregular clumps of different mass proportions are prepared to conduct drained triaxial compression simulations. A well-defined shape descriptor named OR is adopted to quantify particle shape differences of numerical samples at both form and roundness aspects, and the particle sliding friction coefficient varies from 0.001 to 1 to consider the surface roughness effect equivalently in DEM. The stress-strain relationships as well as peak and critical friction angles of these assemblies are examined systematically. Moreover, contact network and anisotropic fabric characteristics within different granular assemblies are analyzed to explore the microscopic origins of the multi-scale shape-dependent shear strength. This study helps to improve the current understanding with respect to the influence of the particle shape on the shear behavior of sands from different shape aspects.

A fully coupled hydrodynamic-DEM model for simulating debris dynamics and impact forces

Many post-event field investigations suggest that dramatic flood hydrodynamics and impact of large floating objects contribute significantly to building damage during a tsunami event. However, the interactions between the transient flood waves, floating debris, and structures have neither been well explored nor understood, and few modelling tools have been developed to simulate these complex interactive processes, especially when multiple debris are involved. This paper introduces a novel fully coupled modelling system, based on a high-performance 2D hydrodynamic model and a 3D discrete element method (DEM) model, for simulating the movement of multiple debris carried along by highly convective flows and directly quantifying the induced impact forces on structures. The proposed model is applied to reproduce a series of physical experiments, and the results agree well with the experimental measurements. It is demonstrated that the newly coupled modelling system can capture the interaction between the fluid, debris of different shapes and sizes and structures, making it suitable for real-world applications. The model provides a new robust tool for simulating the extreme hazards caused by tsunamis or flash flooding and assessing their risk, and therefore has the potential to be useful for planning and designing disaster risk reduction schemes in those at-risk areas.

Safety Risk Analysis of a New Design of Basalt Fiber Gabion Slope Based on Improved 3D Discrete Element Method and Monitoring Data.

Gabion has been extensively used in retaining walls and slope protection. This study carries out a safety risk analysis of a new structure combining basalt fiber reinforcement (BFR) and the traditional gabion structure. The micro-parameters of BFR and soil were calibrated by using the 3D discrete element method after the tensile test of BFR was completed. The mechanical property of the gabion unit was investigated by using a refined model and a numerical test of uniaxial compression. This work developed a simplified method to simulate the seepage effect. The stress condition and sliding displacement between gabions were also investigated. Deformation, stress, and porosity were all used to evaluate the stability of the new type of gabion slope. According to this study, BFR has a tensile strength of 68.22 MPa, and the safety factor increased by 25.68% after using these BFR gabions. The damage is mainly manifested by bending the BFRs and the dislocation of the gabion units, as the slope does not slip. It is indicated this novel gabion structure has a lower safety risk compared to traditional ones, and thus can be popularized and used in retaining walls and slope protection.

Dynamic Analysis of the Seismo-Dynamic Response of Anti-Dip Bedding Rock Slopes Using a Three-Dimensional Discrete-Element Method

Earthquakes are a major external factor that induce landslides. In order to systematically study the dynamic effects and failure mechanism of anti-dip bedding rock slopes (the slope trend is the same as the joint trend, while the slope dip direction is opposite to the joint dip direction) under seismic action (as well as the spatial effects of the structural planes in the anti-dip bedding rock slopes), three-dimensional (3D) discrete-element numerical calculations were performed to analyze anti-dip bedding rock slopes with different slope angles, joint angles, and joint trends subjected to the action of natural seismic and sinusoidal waves. The results were analyzed to investigate the amplification effect, change in Fourier spectrum, failure mechanism, and permanent displacement of the slope under the applied seismic action. The permanent displacement of the slope was calculated using Newmark’s method and the results obtained were discussed and compared with those obtained from a dynamic analysis performed using the 3D discrete-element method. The results showed that the regularity of the spatial distribution of the amplification effect was less clear than that encountered in the planar problem (unidirectional or bidirectional dynamical loading), and this leads to the effect of having an overall rhythmical nature. The seismic wave decays in the high-frequency part from the bottom up of the slope, while the dominant frequency of the seismic wave decreases. The value of the permanent displacement obtained using Newmark’s method is much smaller than that obtained using the dynamic 3D discrete-element analysis approach. The angle between the joint and slope trends has a significant effect on the amplification effect, failure mode, permanent displacement, and stability of slopes subjected to seismic action.

Discrete element modelling of mechanical response of crumb rubber-modified asphalt pavements under traffic loads

ABSTRACT This study aims to predict the mechanical response of crumb rubber-modified (CRM) asphalt pavements under traffic loads using three-dimensional (3D) discrete element method (DEM). First, irregular-shaped aggregates were generated in Python language, and discrete element models of six different asphalt layers, which considered the temperature gradient and fatigue damage, were established using 3D DEM. Then, model parameters were obtained through the uniaxial creep test for asphalt mastics at different temperatures. The fatigue damage was implemented by introducing a damage factor into the Burgers model. Finally, three mechanical response parameters (namely, permanent deformation, shear stress and transverse strain) of the six asphalt layers under traffic loads were analysed and compared. Results show that the mechanical response of CRM asphalt layers under traffic loads is significantly influenced by number of repeated loads, temperature, and asphalt layer materials. The shear stress and transverse strain at the wheel centre vary along the depth of asphalt layers, and the middle layer is the principal area of shear stresses in asphalt pavements.

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 Study on Particle Size Effect of Crushable Granular Soils through DEM Simulations

Abstract The particle size plays an important role in the mechanical behavior of granular geomaterials. With respect to the crushable granular soils, the particle breakage under different pressures leads to the variation of the particle size distribution of soils. Therefore, it is essential to accurately model the particle fracture process to reproduce the key response of granular soils in the simulation. In this study, two simulated approaches, cluster method and replacement method, were performed to investigate the particle size effect for the crushable granular soils by three-dimensional (3D) discrete element method (DEM). DEM simulations were validated through the available results of diametric and oedometric compression tests with the help of the Weibull statistics. Based on the evaluation at particle and assemble-scale, it is found that both the cluster method and replacement method could simulate the particle strength and size dependence of sample failure with a good agreement with experimental results. The particle breakage phenomenon is also successfully modeled in DEM simulation and analyzed by the breakage index. Meanwhile, the computational efficiency was analyzed compared with two simulated methods. The findings in this study can provide a viable approach to investigate the particle breakage effect of the crushable geomaterials.

Influence of Block form on the Shear Behaviour of Soft Soil–Rock Mixtures by 3D Block Modelling Approaches

The influence of block forms on the shear behaviour of soil–rock mixtures with soft blocks (soft S–RMs) can be efficiently investigated by the discrete element method (DEM) on the basis of accurate 3D models accounting for the block breakage. This paper proposes a novel modelling approach, based on the spherical harmonics series, for the generation of 3D block geometries with different forms but same convexity and angularity. An already existing non-overlapping modelling approach was improved, characterized by a reduced computational cost, for the set-up of 3D block DEM models accounting for the block breakage. A number of soft S–RM DEM samples, subjected to numerical direct shear tests, were generated to analyze the influence of block forms and volumetric block proportion VBP on the mesoscopic and macroscopic behaviours. The results showed that the breakage degree is maximum for the spheroidal blocks, followed by the oblate, prolate and blade ones, due to the combined influence of the block frictional sliding and rotation. The shear strength of soft S–RMs is mainly controlled by the block interlocking and breakage, being maximum in the case of spheroidal block samples when the applied normal stress is low and in the case of prolate and blade ones for a high normal stress. It was found that a nonlinear Mohr–Coulomb criterion can provide a good description of the shear strength envelope of soft S–RMs. Soft S–RMs are characterized by a higher friction angle if composed by spheroidal and prolate blocks when the VBP is 40%, due to their elevated block interlocking, and in the case of prolate and blade blocks when the VBP is 60% at the higher normal stress, due to their lower block breakage degree.

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.

An integrated UAV photogrammetry-discrete element investigation of jointed Triassic sandstone near Sydney, Australia

Over the last decade, UAV Structure-from-Motion photogrammetry and digital rock mass mapping tools have been rapidly adopted into geotechnical engineering practice. As computing power has increased, numerical models and remote sensing methods have become more sophisticated, and much research has been applied to the development of digital rock mass classification and data collection methods. This investigation presents a case study of UAV photogrammetry mapping, discrete fracture network analysis and discrete element method modelling of jointed sandstone exposed in coastal cliffs and wave-cut platforms near Sydney, Australia. The aim of the study is to investigate a selection of digital mapping and numerical modelling approaches for rock mass geomechanical characterisation. A cohesive workflow is presented for UAV photogrammetry survey, discontinuity mapping, simulation of rock mass scale laboratory tests, and 3D DFN simulations of roof reinforcement in a large-span road tunnel.Digital discontinuity mapping is undertaken using two different software tools, and results are compared with historical conventional mapping. A novel GIS-based workflow is demonstrated to interrogate the mapping data, using a cellular grid approach to measure fracture intensity and fracture network connectivity. The discontinuity statistics are used as inputs to a series of 3D discrete element method numerical UCS, triaxial, and biaxial load tests that investigate the rock mass anisotropy and the impact of confining stress on rock mass shear strength, stiffness, and failure mechanisms. Next, the mapping data are applied to DFN simulations of a 31 m span tunnel, based on upcoming proposed road tunnels in Sydney. The tunnel simulations show how predicted displacements in the tunnel roof are proportional to fracture intensity.

DEM simulation of rock creep in tunnels using Rate Process Theory

The time-dependent (creep) behaviour of rocks affects the safety and stability of tunnels excavated in weak rocks and at great depths. Several theories have been proposed to simulate the creep deformation in rock; i.e., the progressive time-dependent damage that rocks (or other materials) exhibit under constant stress. However, most of these theories do not capture the accelerating strains associated to tertiary creep and leading to rock failure. In this research, the Rate Process Theory (RPT), combined with the Discrete Element Method (DEM), are used to simulate rock creep deformation in deep tunnels. To do that, two-dimensional (2D) DEM tunnel models are built using particles, with their interactions being simulated by a hybrid mixture of the linear and flat joint contact models. The RPT is incorporated into such models by a user-defined Visual C++ script that modifies their friction coefficients during the DEM simulation, depending on the relative velocity between particles. Numerical results show, for the first time, that the joint RPT-DEM approach is able to reproduce all stages of tunnel convergences associated to rock creep, including tertiary creep; and that it can reproduce the rock damage associated to such creep strains.

Effect of relative density of 2D granular materials on the arching effect through numerical trapdoor tests

The relative density and the fill height of granular materials influence the arching effect significantly, from either the overall behavior of granular materials or the formation of the arching effect. In this study, a comprehensive comparison of the arching effect at four fill heights with three relative densities is conducted by numerical trapdoor tests using the two-dimensional (2D) discrete element method. The results indicate that the stick–slip behavior of the arching ratio (the ratio of the average vertical stress on the trapdoor to the overburden stress; the ratio decreases to a minimum value, followed by recovering to the ultimate value) is more obvious for the case with lower fill height at a given relative density or that with higher density at a given fill height. The partial and the full arching can be distinguished by whether the loosen zone propagates to the surface. Two different critical states are identified for the partial and the full arching, respectively. These critical states are insensitive to the relative density. A characteristic height is identified around twice the width of the trapdoor, at which the critical state of the partial arching transfers to that of the full arching with the increase of the relative density.

Flow behavior of granular material during funnel and mixed flow discharges: A comparative analysis

The drainage of granular assembly from a flat-bottomed silo can be in either funnel flow mode or mixed flow mode. The primary motivation of this work is to investigate whether there exist fundamental differences between the rheological behavior of particles under these two discharge modes. The developments and evolutions of flowing zone and also the characteristics of particle velocity fluctuation during funnel and mixed flow discharges were analyzed and compared by performing 3D Discrete Element Method (DEM) simulations. For funnel flow discharge, the characteristic width of flowing zone at the early discharge state presented a clear history-dependent feature. For mixed flow discharge, the flowing zone sharply shrunk when the upper free surface of the material approached a critical height and the discharge mode then shifted to funnel flow mode. Discrete Fourier transform results demonstrate that resonant motion of particles appeared during both funnel and mixed flow discharges. The correlation analyses indicate that for these two flow modes, there both existed an intermediate region in the converging part of the flowing zone. Its upper boundary located at the position where the flowing zone started to converge along the vertical direction and was featured as the maximum particle compressive force. And its bottom boundary corresponded to the location of free-fall arch and acted as the source of the resonant motion of particles. Our simulation results thus suggest that from the perspective of particle velocity fluctuation, there is no essential difference between granular flows under funnel and mixed discharge modes.

Assessment of assembly shape and geometric effects on amplification of shear waves using discrete element method

The discrete element method (DEM) is a capable tool used to simulate shear wave propagation in granular assemblies for many years. Researchers have studied assembly shapes such as rectangles (in 2D simulations) or cylinders and cubes (in 3D simulations). This paper aimed to qualify the effect of assembly shape on the shear wave propagation and maximum amplification in the vertical plane (horizontal and vertical directions) caused by this propagation. To this end, shear wave propagations in different assembly shapes such as rectangle, trapezium, and triangle with rigid boundary conditions were simulated. A sine wave pulse was applied with a point source by moving a particle as the transmitter particle. To evaluate the shear wave velocity of the assemblies, the transmitter and receiver particles were simulated. All the simulations were performed with 2D DEM which is a useful tool to determine the amount and location of the maximum amplification factor of the assembly in both horizontal and vertical directions. An advantage of this study was assessing the effect of parameters such as input wave frequency, assembly height, shape, and aspect ratios on the amplification of the input waves.

Seismic vulnerability assessment of free-standing massive masonry columns by the 3D Discrete Element Method

Free-standing masonry column is a recurrent typology of built cultural heritage. Usually raised without seismic design, columns are subject to intense rocking and overturning under strong ground motions. In this paper, a strategy to assess their seismic vulnerability using the 3-D Discrete Element Method is proposed. It includes calibrating the elastic parameters (joint stiffness parameters) using ambient vibration test data and developing fragility curves from a large set of time history analysis results. This procedure was verified for four selected water towers, a representative archaeological monument in Pompeii, Italy. Based on preliminary structural analyses, the water towers were modeled as rigid monolithic blocks. The outcomes of modal analysis were used to calibrate the input elastic parameters, starting from a range of values given by analytical calculations derived by literature. Artificial earthquakes with peak ground acceleration levels ranging from 0.167 g to 0.803 g were implemented as ground motions. Collapses and non-collapses configurations were subdivided through a threshold concerning the maximum allowable rotation of the blocks. Fragility curves were statistically developed; these revealed the overturning probabilities of the investigated structures and also enabled to conduct a parametric study of the Rayleigh damping constants.