Discrete Element Method

Scaling Effects in Direct Shear Tests. [AIP Conference Proceedings 1145, 413 (2009)]. Andrés D. Orlando, Daniel M. Hanes, Hayley H. Shen. Abstract. Laboratory experiments of the direct shear test were performed on spherical particles of different materials and diameters. ...

The evolution of the microstructure of an assembly of cohesionless granular materials with associated pores, which carry the overall applied stresses through frictional contacts is a complex phenomenon. The macroscopic flow of such materials take place by the virtue of the relative rolling and sliding of the grains on the micro-scale. A new discrete element method for biaxial compression simulations of random assemblies of oval particles with mixed sizes is introduced. During the course of deformation, the new positions of the grains are determined by employing the static equilibrium equations. A key aspect of the method is that, it is formulated for ellipse cross-sectional particles, hence desirable inherent anisotropies are possible. A robust algorithm for the determination of the contact points between neighbouring grains is given. Employing the present methodology, many aspects of the behaviour of two-dimensional assemblies of oval cross-sectional rods have been successfully addressed. The effects of initial void ratio, interparticle friction angle, aspect ratio, and bedding angle on the rolling and sliding contacts are examined. The distribution of normals to the rolling and sliding contacts have different patterns and are concentrated along directions, which are approximately perpendicular to one another. On the other hand, the distribution of all contact normals (combined rolling and sliding) are close to that of rolling contacts, which confirm that rolling is the dominant mechanism. This phenomenon becomes more pronounced for higher intergranular friction angle. Characteristics of the rolling and sliding contacts are also discussed in the context of the force angle, which is the inclination of contact force with respect to the contact normal.

This paper outlines the theoretical framework and experimental validation of a fully Thermo-Hydro-Mechanical model, ThermalEngine, as part of the open source DEM software Yade. ThermalEngine is constructed on top of Yade's existing thoroughly validated and well optimized Pore Finite Volume (PFV) scheme, which enables a highly efficient upwind forward finite difference advection scheme that reuses existing pore scale mass-fluxes to conserve pore energy. Conductive heat transfer within phases and between phases is solved explicitly in time by conserving energy and modeling heat fluxes with classic heat transfer models. In addition to advection and conduction, the thermo-mechanical component of ThermalEngine incorporates the thermal expansion or contraction of particles and pore fluids by estimating pore volume changes and adding them to the existing PFV mass balance. In addition to the theoretical framework, the experimental and numerical validation of the coupled THM ThermalEngine model is presented by heating a cylindrical rock specimen and observing interior cavity fluid pressure changes. Cavity fluid pressure changes follow experimental data closely; as rock temperature increases the cavity fluid expands resulting in an increased cavity pressure until pressure gradients direct fluid out of cavity allowing fluid pressure to stabilize back to initial conditions. It is clear that the foundational, easily modifiable, and open sourced THM-DEM framework presented within is applicable to a wide range of disciplines including geomechanics and powder technologies.

Blasting with explosives and crushing with mills are two major processes for extracting ore minerals. Longstanding problems with these processes are " fines " production in blasting and the related energy consumption of mills. Here, we demonstrate, using numerical simulations and comparison with experiments, that both problems emerge from two universal mechanisms: unstable tensile-crack propagation and com-pressive impact crushing. These lead to a universal mass-passing-fraction function in sieving. Crushing is limited to, and produces almost all the fines, and thereby inherently consumes a lot of fracture energy. Tensile cracks also produce fines, but the majority of the mass is confined in larger fragments. The key to resolving the fines and energy problem thus lies in minimizing crushing while inducing enough tensile load to reach the breakage threshold.

The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material’s strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional discrete element simulations of biaxial plane strain compression with constant mean stress. Assemblies with four different particle shapes were simulated. The measures of contact orientation are the most responsive to loading, and they change greatly at small strains, whereas the other measures lag the loading process and continue to change beyond the state of peak stress and even after the deviatoric stress has nearly reached a steady state. The paper implements a methodology for characterizing the incremental stiffness of a granular assembly during biaxial loading, with orthotropic loading increments that preserve the principal axes of the fabric and stiffness tensors. The linear part of the hypoplastic tangential stiffness is monitored with oedometric loading increments. This stiffness increases in the direction of the initial compressive loading but decreases in the direction of extension. Anisotropy of this stiffness is closely correlated with a particular measure of the contact fabric. Permeabilities are measured in three directions with lattice Boltzmann methods at various stages of loading and for assemblies with four particle shapes. Effective permeability is negatively correlated with the directional mean free path and is positively correlated with pore width, indicating that the anisotropy of effective permeability induced by loading is produced by changes in the directional hydraulic radius.

The powder bed fusion (PBF) process is widely
adopted in many manufacturing industries because of its
capability to 3D print complex parts with micro-scale precision.
In PBF process, a thermal energy source is used to selectively
fuse powder particles layer by layer to build a part. The build
quality in the PBF process primarily depends on the thermal
energy deposition and properties of the powder bed. Powder
flowability, powder spreading, and packing fraction are key
factors that determine the properties of a powder bed.
Therefore, the study of these process parameters is essential to
better understand the PBF process. In our study, we developed
a two-dimensional powder bed model using the granular
package of the LAMMPS molecular dynamics simulator.
Cloud-based deposition was adopted for pouring powder
particles on the powder bed. The spreading of particles over the
substrate was mimicked like a powder bed system. The powder
flowability in the proposed study was analyzed by varying the
particle size distribution. The simulation results showed that a
greater number of larger particles in a power sample results in
an increase in the Angle of Repose (AOR) which ultimately
affects the flowability. Two different kinds of recoater
geometry were considered in this study: circular and
rectangular blades. Simulation results showed that depending
on the recoater shape there is a change in the packing fraction
in the powder bed. Cross-sectional analysis of the power bed showed a significant presence of voids when a greater number
of larger particles existed in the powder batch. The packing
fraction of the powder bed was found to be a strong function of
particle size distribution. These analyses help understand the
influence of particle size and recoater shape on the powder bed
properties. Findings from this study help to provide a guideline
for choosing particle size distribution if the spherical particles
are considered. While the present study focuses on the spherical
powder particles, the proposed system can also be adapted to
the study of powder bed with aspherical particles.

The paper describes the development of a technique to simulate triaxial tests on specimens of railway ballast numerically at the particle scale; and its validation with reference to physical test data. The ballast particles were modelled using potential particles and the well-known discrete element method. The shapes of these elemental particles, the particle size distribution and the number of particles in each numerical triaxial specimen all matched closely the real ballast material being modelled. Confining pressures were applied to the specimen via a dynamic triangulation of the outer particle centroids. A parametric study was carried out to investigate the effects on the simulation of timestep, strain rate, damping, contact stiffness and inter-particle friction. Finally, a set of parameters was selected which provided the best fit to experimental triaxial data, with very close agreement of mobilized friction and volumetric strain behaviour.

The objective of this study is to develop a simulation technique that enables
to describe the interactions between snow and a moving surface. The develop-
ments of this study are focused on the application of the interactions between
a tire tread and a snow-covered road.
Contrary to a continuum mechanics approach snow is considered to exist of
discrete grains which are allowed to bond and collide with each other. There-
fore, a discrete approach based on the extended Discrete Element Method is
applied to the snow. Micro-mechanical models are developed to describe the
deformational behaviour of snow. The micro-mechanical models describe the
deformation and growth of the bonds between grains as well as the contact
behaviour of snow grains on the grain-scale. Further, the age of a snow sample,
the temperature and deformation rate applied are taken into account by the de-
veloped models. The deformational behaviour of snow under brittle and ductile
loading rates is validated with experimental data of common measurements in
the field of snow mechanics. The simulation results successfully recapture the
macro- and micro-scale deformation behaviour of snow and enable to identify
the primary deformation mechanism in charge at the different loading rates,
densities and temperatures.
However, this approach allows treating individual snow grains during loading
due to a rolling tire and predicting both position and orientation of grains. The
micro-mechanical response of each snow grain in contact with the structure of
the tire surface generates a global impact that defines the interaction forces be-
tween the snow and the tire surface, which simultaneously indicate the strength
of traction. In order to predict the elastic deformation of the tire surface the
Finite Element Method is employed.
A coupling method is developed between the discrete approach to characterise
snow and the finite element description of the tire tread. The coupling method
compensates quite naturally the shortages of both numerical methods. Further,
a fast contact detection algorithm has been developed to spare valuable com-
putation time. The coupling approach was successfully tested and validated
with a small scale application but also with the large scale application of tire
- soil interaction. The large-scale simulation results of tire - soil interactions
showed to be accurate in comparison to similar traction measurements.
Finally, the interaction of snow with rigid and deformable tread parts has been
studied in accordance to friction measurements of the field of tire mechanics.
The results show the ability of the simulation technique to describe the targeted
interactions and give valuable insight into the underlying mechanisms.

The abundance of granular materials and powders that are being used in several fields, along with their broad applications, requires a comprehensive understanding of both their macro-and micro-mechanical behavior. The fabric and structural properties, or the inter-particle properties, such as the angle of repose, do affect the behavior of granular materials. This comprehensive review indicates that the angle of repose of granular material is an essential parameter to understand the micro-behavior of the granular material and, then, to relate it with the macro-behavior. Therefore, this extensive review was prepared about the repose angle theory, its definitions, method of measurements, appropriate applications and the influencing factors.

Dramatic shortcomings of mill liner designs, especially of large SAG mills, such as rapid failure and even mill shell damage arising from impacting of the charge directly on the liner, and unsuitable spacing of lifter bars yielding unfavourable compromises between lifter bar height and liner life have highlighted the significance of correct mill liner selection. Liners protect the mill shell from wear and transfer energy to the grinding charge, and a careful balance is required to optimise these conflicting requirements. This review serves to highlight these problems and how they can be tackled in a logical and often inexpensive manner by considering charge trajectories and liner spacing criteria, in conjunction with liner wear monitoring. An overview is given of the principal types and materials of construction of mill liners. Examples of good and bad liner design are given, followed by a rigorous approach to liner design based on the best technology available, combined with experi...

Unsteady flow phenomena are prevalent in a wide range of problems in nature and engineering. These include, but are not limited to, aerodynamics of insect flight, dynamic stall in rotorcraft and wind turbines, leading-edge vortices in delta wings, micro-air vehicle (MAV) design, gust handling and flow control. The most significant characteristics of unsteady flows are rapid changes in the circulation of the airfoil, apparent-mass effects, flow separation and the leading-edge vortex (LEV) phenomenon. Although experimental techniques and computational fluid dynamics (CFD) methods have enabled the detailed study of unsteady flows and their underlying features, a reliable and inexpensive low-order method for fast prediction and for use in control and design is still required. In this research, a low-order methodology based on physical principles rather than empirical fitting is proposed. The objective of such an approach is to enable insights into unsteady phenomena while developing approaches to model them. The basis of the low-order model developed here is unsteady thin-airfoil theory. A time-stepping approach is used to solve for the vorticity on an airfoil camberline, allowing for large amplitudes and nonplanar wakes. On comparing lift coefficients from this method against data from CFD and experiments for some unsteady test cases, it is seen that the method predicts well so long as LEV formation does not occur and flow over the airfoil is attached. The formation of leading-edge vortices (LEVs) in unsteady flows is initiated by flow separation and the formation of a shear layer at the airfoil's leading edge. This phenomenon has been observed to have both detrimental (dynamic stall in helicopters) and

Numerical modelling of rock slopes can involve a number and variety of techniques, the selection and requirement of which depends on the factors deemed to control the potential for instability. This thesis presents a number of case studies involving slopes in fractured rock, encompassing a range of scales. The case study slopes have provided a means to question the way in which particular slope instabilities should be analysed. Currently there are few methods available for analysing the complex behaviour within slopes of fractured rock. A review of available techniques is given within this thesis, with the use of limit equilibrium, finite element and hybrid methods, to highlight their specific advantages and limitations for the chosen case study slopes.

By modelling slope instability within fractured rock, the understanding of both discrete and mass behaviour increases considerably. Numerical modelling can therefore be used as a tool to help improve both the safety and efficiency of open pit mining and the management of natural rock slopes.

The emphasis of the numerical modelling used in this thesis, was to assess the ability of a particular comprehensive dynamic-based code, ELFEN, for modelling fractured rock slopes. In addition, a principal objective of the research was to test the newly developed groundwater version of the code. Investigations revealed ELFEN to be effective for simulation of fracture extension due to the decreased normal stress on discontinuities, relative to pore pressure. In general, the code has the ability to simulate the full failure process in small to medium-scale slopes, providing a means to analyse rock mass and discontinuity strength, along with a representation of the failure mechanism from initiation through to deposition.

At a large scale the sheer complexity of a fractured rock mass makes it impossible to model the whole slope as a representative discrete object with an embedded detailed fracture network. Subsequently an approach is presented in this thesis, whereby one can use numerical modelling to arrive at a mass strength estimate that can be used in a simpler equivalent continuum model of a large slope.

Groundwater pressure was initially applied in a simple planar failure model, to provide confidence in the capability of the newly developed effective stress module within ELFEN. Following this, groundwater was implemented into two step-path failures. This highlighted the sensitivity of the specific models to the level of the phreatic surface, rock-bridge strength and discontinuity related strength. In addition, a fully drained toe-breakout failure was addressed, using various limit equilibrium and finite element methods to assess the potential strength of a rock-bridge within the toe of a 50m slope.

In all numerical models it is necessary to be certain of input parameters, or to understand the implications and effects of any uncertainty. During this thesis an accumulative scheme or modelling methodology has been followed; starting with simple models so that comparisons can be made with other limit equilibrium and finite element methods, allowing calibration of the more advanced properties required within ELFEN. This calibration is made easier with the use of a staged modelling procedure. In particular it was found that, when using a dynamic-based code with fracture capabilities, an inappropriate model procedure can lead to an unrealistic simulation. In summary, particular contributions and novel aspects of the research were:
i. The application of ELFEN to a variety of scale-related failures in fractured rock slopes, covering a range of failure mechanisms. In addition, direct comparisons have been made between the results of ELFEN, limit equilibrium and finite element methods, for the chosen case study slopes. This has provided an analysis and initial review of the capabilities and limitations of each of the individual approaches.
ii. The newly developed groundwater version of ELFEN was tested for the first time in three of the six case study slopes, demonstrating its effectiveness in simulating mode I fracture extension and subsequent slope instability, due to a rise in the phreatic surface.
iii. The development of a suitable staged approach methodology by which a fractured rock slope can be simulated efficiently and accurately, when using a dynamic fracture-based code.
iv. The simulation of a large-scale case study slope using a FracMan-ELFEN approach, whereby a statistically generated fracture network is explicitly incorporated into a numerical model and mass strength is assessed on a large scale, deriving strength properties that represent an equivalent continuum of the fractured mass. Subsequently, a number of approaches were used to assess the strength of the equivalent continuum that formed a 1000m slope. This led to the comparison of the numerical and empirically derived mass strength approach for modelling of slopes.

a civil Engineering, faculty of Engineering and information sciences, centre for geomechanics and railway Engineering, Arc centre of Excellence for geotechnical science and Engineering, university of Wollongong, Wollongong, Australia; b faculty of Engineering and information sciences, centre for geomechanics and railway Engineering, Arc centre of Excellence for geotechnical science and Engineering, ABSTRACT Ballasted rail tracks are the most important mode of transportation in terms of traffic tonnage serving the needs of bulk freight and passenger movement, but under train loads, the particles degrade due to breakage and the progressive accumulation of external fines or mud-pumping under the subgrade, all of which reduce its shear strength and increase track instability. These actions adversely affect the safety, passenger comfort and efficiency of tracks, as well as enforcing speed restrictions and more frequent track maintenance. In spite of advances in rail track geotechnology, the optimum choice of ballast for track design is still considered critical because ballast degradation is influenced by the amplitude and number of load cycles, particle gradation, track confining pressure and the angularity and fracture strength of individual grains. One of the most effective methods of enhancing track stability and reducing the stresses transmitted to a soft subgrade layer is to increase the stiffness of the overlying granular media. This paper presents our current knowledge of rail track geomechanics, including important concepts/topics related to laboratory testing and computational modelling approaches used to study the load–deformation behaviour of ballast improved with waste tyres, synthetic geogrids and geocells.

The Trikokkia Railway tunnel is a 5000 m long single tube tunnel, foreseen to be constructed along the future Kalambaka–Kozani railway line in central Greece. The tunnel alignment is crossing the Molasse formations of the meso-Hellenic trench and a design approach for the tunneling works that account for the specific properties of this formation has been adopted. Mixed modes of failure governed by rock overstressing and discontinuity controlled slides were tackled by considering both rock bulk strength and deformability properties and rock mass architecture. The ground characterization process, was performed using well established empirical rock mass characterization indices. Rock mass characterization was assisted by hand sketching of rock mass structure as well as by generating discrete fracture networks, compatible with the joint statistics of each rock mass class. The identification of different rock mass behavior types is based on metrics that compare rock mass bulk strength with in situ stress state, and in parallel on the visualization of the rock mass structure to describe and quantify structurally controlled failure modes. Both the intuitive procedure to draw rock mass structure sketches, as well as the random joint generation procedure, are found to be effective tools to identify and assess gravity driven modes of failure. The adopted process to assess rock mass behavior contributes significantly to design with confidence the tunneling and support process for tendering purposes.

The global trend towards larger open pits and block cave mining is reliant on effective design at larger scales requiring improved estimates for rock mass strength. In recent years, efforts have focussed on developing synthetic Discrete Fracture Network (DFN)-based rock mass approaches. This paper provides an example of such an approach, modelling explicitly the rock fracture network within large-scale biaxial models. A conceptual large rock slope is analysed and comparisons are made with more conventional empirical strength assessments. Finally the DFN-based mass strength was modelled within a finite element solution, providing stress paths that illustrated the onset of instability during the excavation of a large slope. This example provides an insight into some of the parameters that influence the strength for a DFN-based method. In this case, fracture network geometry, strain and confinement were particularly important. The DFN-based method also demonstrated that fracture intensity has a greater influence on mass strength in low strain environments. These factors all have relevance for the determination of mass strength by any method. The Middleton Limestone was used as the basis for a conceptual case study; in this case a reduction in intact strength was necessary to allow the development of a circular slope failure mechanism. Suggestions for further research are made which are considered important if DFN-based methods are to be used for analysing the stability of large slopes.

Geophysical hazards usually involve multiphase flow of dense granular solids and water. Understanding the mechanics of granular flow is of particular importance in predicting the run-out behaviour of debris flows. The dynamics of a homogeneous granular flow involve three distinct scales: the microscopic scale, the meso-scale, and the macroscopic scale.

Conventionally, granular flows are modelled as a continuum because they exhibit many collective phenomena. ecent studies, however, suggest that a continuum law may be unable to capture
the effect of inhomogeneities at the grain scale level, such as orientation of force chains, which are micro-structural effects. Discrete element methods (DEM) are capable of simulating these micro-structural effects, however they are computationally expensive. In the present study, a multi-scale approach is adopted, using both DEM and continuum techniques, to better understand the rheology of granular flows and the limitations of continuum models.

The collapse of a granular column on a horizontal surface is a simple case of granular flow; however, a proper model that describes the flow dynamics is still lacking. In the present study, the generalised interpolation material point method
(GIMPM), a hybrid Eulerian -- Lagrangian approach, is implemented with the Mohr-Coloumb failure criterion to describe the continuum behaviour of granular flows. The granular column collapse is also simulated using DEM to understand the micro-mechanics of the flow.

The limitations of MPM in modelling the flow dynamics are
studied by inspecting the energy dissipation mechanisms. The lack of collisional dissipation in the Mohr-Coloumb model results in longer run-out distances for granular flows in dilute regimes (where the mean pressure is low). However, the model is able to capture the rheology of dense granular flows, such as the run-out evolution of slopes subjected to lateral excitation, where the inertial number I < 0.1.

The initiation and propagation of submarine flows depend mainly on the slope, density, and quantity of the material destabilised. Certain macroscopic models are able to capture simple mechanical behaviours, however the complex physical mechanisms that occur at the grain scale, such as hydrodynamic
instabilities and formation of clusters, have largely been ignored. In order to describe the mechanism of submarine granular flows, it is important to consider both the dynamics of the solid phase and the role of the ambient fluid. In the present study, a two-dimensional coupled Lattice Boltzmann LBM -- DEM technique is developed to understand the micro-scale
rheology of granular flows in fluid. Parametric analyses are performed to assess the influence of initial configuration, permeability, and slope of the inclined plane on the flow. The effect of hydrodynamic forces on the run-out evolution is analysed by comparing the energy dissipation and flow
evolution between dry and immersed conditions.

This paper presents a multi-layer railway ballast track and substructure model, where a coupled discrete and continuous method is used for macro-meso dynamic behaviour analysis under moving wheel loads. In this coupled model, the discrete element method (DEM) is utilised to build the superstructure of the ballast track (i.e. rail, fastener, sleeper and ballast layer), which considers the complex ballast shape and particle size distribution from mesoscopic level. The finite difference method (FDM) is used to simulate the substructure (i.e. subgrade and foundation) with a consideration of computing cost. And then, the coupled model is achieved by satisfying displacement, velocity and contact force compatibility between the FLAC and the PFC. Finally, the dynamic analysis is carried out by applying the wheel-rail forces obtained from a vehicle-track dynamics model into the coupled model. The DEM parameters of ballast particles are calibrated based on the results of the ballast direct shear tests, and the dynamic behaviour of railway ballast track and subgrade system is validated with the field measurement. Through the numerical analysis, it is confirmed that the coupled DEM/FDM model can reliably reflect macro-meso dynamic behaviour and accurately reveal the contact characteristics between the ballast layer and subgrade. ARTICLE HISTORY

A finite strain multiscale hydro-mechanical model is established via an extended Hill–Mandel condition for two-phase porous media. By assuming that the effective stress principle holds at unit cell scale, we established a micro-to-macro transition that links the micromechanical responses at grain scale to the macroscopic effective stress responses, while modeling the fluid phase only at the macroscopic continuum level. We propose a dual-scale semi-implicit scheme, which treats macroscopic responses implicitly and microscopic responses explicitly. The dual-scale model is shown to have good convergence rate, and is stable and robust. By inferring effective stress measure and poro-plasticity parameters, such as porosity, Biot's coefficient and Biot's modulus from micro-scale simulations, the multiscale model is able to predict effective poro-elasto-plastic responses without introducing additional phenomenological laws. The performance of the proposed framework is demonstrated via a collection of representative numerical examples. Fabric tensors of the representative elementary volumes are computed and analyzed via the anisotropic critical state theory when strain localization occurs.