Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: The main goal of the thesis is to validate the ability of discrete element methods (DEM) to predict forced granular flow. Granular flow occurs in a broad spectrum of industrial applications. The thesis focuses on earthmoving processes typical of the mining and agricultural industries. Existing soil mechanics soil-tool models are also investigated and general flow behaviour in and around blades and buckets are established. Soil mechanics theories are used to predict the draft forces on a flat blade moving through granular material. Com and wheat grains are used as material. The rupture (slip) lines in front of the blade are predicted by soil mechanics and compared to experimental results. A two-dimensional test bench is used to visualise the flow of the granular material. Forces and moments that act on the tools are measured. DEM can be used to model industrial granular flow with large displacements. Two types of earthmoving equipment are simulated. The first is a flat blade and the second is a bucket. The forces on these tools are determined using DEM and compared to experimental results. The ability of DEM to predict material compressibility, the flow of material in and around the tools, the rupture lines and the bucket fill rate are investigated. A particle relative displacement method is used to determine the rupture lines. / AFRIKAANSE OPSOMMING: Die hoofdoel van die tesis is om die vermoë van diskrete-element-metodes (DEM) om geforseerde partikelvloei te voorspel, te ondersoek. Partikelvloei word aangetref in 'n breë spektrum van industriële toepassings. Die tesis fokus op grondverskuiwing soos aangetref in myn- en landbouprosesse. Bestaande grondmeganika-modelle word ook ondersoek, asook die algemene gedrag van partikelvloei in en rondom lemme en bakke. Die grondmeganika-modelle word hoofsaaklik gebruik om die kragte op lemme te voorspel. Glip (skuif)-vlakke word ondersoek en vergelyk met eksperimentele resultate. 'n Twee-dimensionele toetsbank word gebruik om die vloei waar te neem. Die kragte en momente op die toerusting word ook gemeet. Mielie- en koringpitte word as materiaal gebruik. DEM kan gebruik word om industriële partikelvloei met groot verplasings te modelleer. Twee tipes toerusting word gesimuleer. Die eerste is 'n plat lem en die tweede 'n bak. Die kragte en momente op dié toerusting word bepaal m.b.V. DEM en dan vergelyk met die eksperimentele resultate. Die vermoë van DEM om materiaalsamedrukking, vloeipatrone, glipvlakke en bakvul-tempo's te voorspel word ondersoek. 'n Partikelrelatiewe- verplasings-metode word gebruik om die glipvlakke te voorspel.

Wheel loaders are fundamental construction equipment to assist handling of bulk material e.g. gravel and stones. During digging operations, it withstands forces that are both large and very complicated to predict. Moreover, it is very expensive to develop prototypes of wheel loader for verification. Consequently, the Discrete Element Method (DEM) was introduced for gravel modeling a couple of years ago to enable prediction of these forces. The gravel model is connected with a Multibody System (MBS) model of the wheel loader, in this thesis a Volvo L180G. The co-simulation of these two systems is a very computer intensive operation and hence, it is important to investigate which parameters that have the largest influence on the simulation results. The aim of this thesis is to investigate the simulation sensitivity with respect to co-simulation communication interval, collision detection interval and gravel normal stiffness.The simulation results are verified by comparison with measurement data from previous tests performed by Volvo CE. The simulations are compared to investigate the relevant parameters. The conclusion of this thesis is that DEM is a method that in a very good way can predict the draft forces during digging operations.

An imperative task for successful underground mining is to ensure the stability of underground structures, since it influences the safety, and in turn, the production capacity and economic performance of the mine. This is more so for deep excavations in soft rock which may be under significantly high stresses. In this thesis, stability studies on two tunnels, a horseshoe-shaped and an inverted arch-shaped tunnel, have been presented. The tunnels, running at a depth of 1325 m, are part of the Xiezhuang Coal Mine, in the Xinwen mining area, in China. Using the available information on stratigraphy, geological structures, in-situ stress measurements and geo-mechanical properties of intact rock and discontinuity interfaces, a three-dimensional numerical model has been built using the 3DEC 3-Dimensional Distinct Element Code to simulate the stress conditions around the tunnels. Based on available discontinuity geometry constraints, the rock mass has been modelled as a mixture of a discontinuum medium close to the tunnels and as an equivalent-continuum in the far field. Due to the unavailability of field measurements for rock mass mechanical parameters, the parameters have been estimated by incorporating the available intact rock mechanical properties and field deformation monitoring data into a strength reduction model calibration procedure. This back-analysis (calibration) has been carried out through a pseudo-time dependent support installation routine which incorporates the effect of time through a stress-relaxation mechanism. The results from the back-analysis indicate that the rock mass cohesion, tensile strength, uniaxial compressive strength, and elastic modulus values are about 35-45 % of the corresponding intact rock property values. Additionally, the importance of incorporating stress relaxation before support installation in numerical modeling has been illustrated, for the first time in literature, through the increased support factors of safety and reduced grout failures. The calibrated models have been analyzed for different supported and unsupported cases in an attempt to quantify the effect of supports in stabilizing the tunnels and to estimate the adequacy of the existing supports being used in the mine. A direct outcome is that the findings indicate that longer supports may be better suited for the existing geo-mining conditions around the tunnels since they have fractured zones that are larger than the supports currently in use at the mine. The effects of supports have been demonstrated using changes in deformations and yield zones around the tunnels, and changes in the average factors of safety and grout failures of the supports. The use of longer supports and floor bolting has provided greater stability for the rock masses around the tunnels. A comparison between the closure strains in the two differently shaped tunnels indicates that the inverted arch tunnel may be more efficient in reducing roof sag and floor heave for the existing geo-mining conditions. Additional analyses focusing on parametric sensitivity studies on the rock and joint mechanical properties show that the tunnel stability is highly sensitive to changes in cohesion and internal friction angle of the intact rock, and changes in joint basic friction angle. Tunnel stability is seen to not be very sensitive to changes in intact rock tensile strength and joint shear stiffness for the tunnels being studied. Finally, support optimization studies conducted by studying the effect of changing cable diameters and grout uniaxial compressive strengths on support factors of safety and grout failures show the trade-off that is necessary in selecting cable strength vis-à-vis grout strength. The results indicate that simply increasing either one of cable or grout strength parameters without considering their interactions and compatibilities could be detrimental to the stability of the support system.

Simulations are powerful and important tools for gaining insight into powder processes. Ultimately, simulations have the potential to replace experiments. Thus, accurate models and insight into the essential factors for descriptions of powder behaviour are required. In this thesis, discrete element method (DEM) simulations of granule flow and compression were evaluated to deduce parameters and potential models essential for the experimental and numerical correspondence. In addition, the evolution in tablet microstructure during compression was studied using mercury porosimetry. Granule flow was measured using angle of repose, discharge rate, and shear. The granular flow depended primarily on particle shape and surface texture due to the mutual influence of these two parameters on the inter-particle forces. Rolling friction stabilised both the heap formation and promoted shear in the elastic quasi-static flow regime. Thus, rolling friction was established to be an essential simulation parameter for the correspondence to experiments. Current compression models often neglect the elastic compact deformation during particle loading. In this thesis, two fundamentally different models were evaluated with focus of including the elastic deformation. The first model comprised a maximal particle overlap, where elastic deformation commences. The second model accounted for the contact dependence and impingement at high relative densities. This model was based on a truncated-sphere followed by a Voronoi extension. The validity of the models was demonstrated by the elastic qualitative correspondence to experimental compressions for ductile materials. In tablets, the void (inter-granular pore) diameter was dependent on the degree of compression. Thus, the degree of compression provides an indication of the tablet microstructure. The microstructure was subsequently observed to be related to the tablet tensile strength as inferred from a percolation threshold required for formation of coherent tablets. In summary, this thesis has shed light onto the potential of simulating flow and compression of granulated pharmaceutical powders using DEM. Continuous work in the area are required to further improve the models to increase the experimental and numerical correspondence.

Cette étude de la compaction d’un empilement granulaire par vibrations horizontales a été réalisée dans le cadre d’un partenariat avec le groupe MERSEN pour une application au sable contenu dans ses fusibles. L’objectif scientifique est de développer la compréhension des mécanismes mis en jeu dans un milieu granulaire vibré horizontalement. Deux approches ont été utilisées en parallèle, l’une expérimentale, l’autre par simulation numérique. L’approche expérimentale a été réalisée sur des grains de silice de diamètre moyen 500 m. Un récipient de quelques centimètres est soumis à un mouvement sinusoïdal de fréquence comprise entre 20 et 200 Hz avec des accélérations allant jusqu’à 10 g. Le dispositif instrumenté permet la mesure instantanée de la force et de l’accélération, la vitesse des grains aux parois (PIV) ainsi que la densité globale du milieu. L’approche numérique est basée sur la méthode des éléments discrets (DEM). Des méthodes spécifiques d’analyse des résultats ont été développées pour assurer la comparaison avec l’expérience. Elles permettent d’obtenir des informations qui ne sont pas accessibles expérimentalement comme les densités, vitesses et contraintes locales dans l’ensemble de l’empilement. Dans le cas d’un récipient ouvert, la simulation permet de retrouver les résultats expérimentaux : rouleaux de convections, seuils de comportement, influence de l’accélération… Des résultats originaux ont été établis dans les expériences et les simulations comme une croissance de la vitesse des grains avec la longueur du récipient. La simulation a aussi permis d’obtenir des résultats spécifiques comme l’influence du coefficient de friction sur le sens des rouleaux et la caractérisation des contraintes au sein de l’empilement. L’écoulement des grains à travers des orifices circulaires de différentes dimensions a été également étudié. Le comportement du sable dans un récipient fermé (milieu confiné) a été étudié au cours d’un remplissage progressif. Des différences significatives ont été constatées lorsque le taux de remplissage devient élevé. Des mesures d’accélération et de force sur l’ensemble du dispositif ont permis de définir et de mesurer une masse apparente et l’énergie dissipée par le dispositif. Des modèles descriptifs ont permis de comprendre les comportements observés. Ces résultats sont à l’origine d’un brevet déposé par le groupe MERSEN sur le contrôle du remplissage. / This work on the densification of a granular medium under horizontal vibrations was realised in the context of an industrial study on sand in fuses, undertaken by the firm MERSEN. The scientific purpose is the understanding of the mechanisms involved in horizontally vibrated granular media. Both experiments and computer simulations were used. Experiments were conducted with 500 µm silica grains. Sinusoidal accelerations up to 10 g were applied to a container of a few centimetres using frequencies between 20 and 200 Hz. The experimental device enables instantaneous force, acceleration, grain velocity on the walls (PIV) and mean bulk density to be measured. Discrete element method (DEM) was used for the computer simulations. Specific techniques were developed to analyse the results and compare them with experiments. Computer simulations provided data which are not experimentally available such as local values of density, velocities and stress inside the particle packing. In the case of an open container, simulation results are in good agreement with experimental ones (convection rolls, thresholds, effect of acceleration...). Original results are obtained in both experiments and simulations, such as a grain velocity increase with the container length. Simulation provided specific results such as the effect of friction coefficients on the direction of rotation of convection rolls and the characterization of stress inside the particle packing. The flowability of grains across circular holes of various sizes was also studied. The behaviour of sand in a closed container (confined medium) was studied during a progressive filling. Significant differences were observed when the filling rate becomes high. The dissipated energy and the apparent mass of the vibrated device were defined and measured using acceleration and force measurements. Specific models were built to analyse and understand the observed behaviour. Some results on the filling control were patented by MERSEN.

L'objectif de ce travail de recherche est d'étudier numériquement le transport et le dépôt de particules dans des milieux poreux à l'échelle des pores.Premièrement, un couplage entre la méthode de Boltzmann sur réseau (LBM) et la méthode des éléments discrets (DEM) est réalisé et utilisé pour simuler l'écoulement d'un fluide chargé en particules. La LBM est utilisée pour décrire l'écoulement du fluide autour des fibres tandis que la DEM est utilisée pour traiter la dynamique des particules. Ce couplage est bidirectionnel dans le sens où le mouvement des particules affecte le flux de fluide et réciproquement. Ce modèle nous a permis de prédire l'efficacité de capture et la chute de pression à l'étape initiale du processus de filtration. Le facteur de qualité est également calculé pour déterminer la qualité de filtration.Ensuite, on se focalise sur l'étude de l'efficacité de la capture de fibres de formes de section transversale différentes (circulaire, losange et carrée). Les résultats issus de nos simulations du processus de filtration de la fibre circulaire concordent bien avec les corrélations empiriques. L'impaction des particules sur la face avant de la fibre de forme carrée est plus importante que dans les cas de fibre de formes circulaire et losange. Cependant, en raison d'une chute de pression plus faible, la fibre de section losange présente une meilleure qualité de filtration. Ensuite, les variations du facteur de qualité dues à l'angle d'orientation et au rapport d'aspect des fibres ont été étudiées numériquement pour la forme rectangulaire. Pour chaque cas, on a déterminé la valeur optimale de la zone au vent pour laquelle le facteur de qualité est maximal. La comparaison des valeurs du facteur de qualité obtenues pour les différentes formes de fibre monte une meilleure performance pour la fibre de section carrée orientée avec un angle de π/4.Enfin, l'influence de l'arrangement des fibres sur la qualité de la filtration est analysée en considérant la configuration en quinconce pour les différentes formes. Les simulations conduites pour différentes tailles de particules et différentes valeurs de la densité (particule/air) montent que la fibre de section losange est plus performante en termes de facteur de qualité pour les particules de grande taille et pour les valeurs de densité élevée. La présente étude fournit des pistes pour optimiser le processus de filtration et prédire la qualité de filtration. / The objective of the present research was to numerically investigate the transport and deposition of particles in porous media at the pore scale. Firstly, a developed coupled lattice Boltzmann method (LBM) and discrete element method (DEM) is used to simulate the fluid-particle flow. LBM is employed to describe the fluid flow around fibers whereas DEM is used to deal with the particle dynamics. The corresponding method is two-way coupling in the sense that particle motion affects the fluid flow and reciprocally. It allowed us to predict the capture efficiency and pressure drop at the initial stage of filtration process. The quality factor is also calculated for determining the filtration performance. Secondly, we focus on the study the capture efficiency of single fiber with circular, diamond and square cross-section, respectively. The results of LBM-DEM for filtration process of single circular fiber agree well with the empirical correlation. The impaction of particles on the front side of square-shaped fiber is more favorable than those on circular and diamond cases. However, diamond fiber exhibits a good filtration performance. Then the variations of quality factor due to the different orientation angle and aspect ratio of rectangular fiber were studied using LBM-DEM. For each case, we have found the optimal value of the windward area to which corresponds a maximum value of the quality factor. The comparison of the performance of the different forms of fibers shows that the largest quality factor is obtained for square fiber oriented with angle π/4.Finally, the influence of the arrangement of fiber on filtration performance is analyzed by considering the staggered configuration. Simulations conducted for several particle size and density show that the diamond with staggered array performs better for large particles and high particle-to-fluid density ratio in terms of quality factor. The present study provide an insight to optimize the filtration process and predict filtration performance.

Este trabalho apresenta uma formulação do Método dos Elementos Discretos (MED) utilizando uma abordagem vetorial para o tratamento das rotações. As rotações são calculadas com a parametrização de Rodrigues. As principais contribuições do trabalho são: o cálculo dos deslocamentos tangentes utilizando o vetor das rotações incrementais da parametrização de Rodrigues; e, a integração do movimento de rotação utilizando o método leapfrog com as expressões da parametrização das rotações de Rodrigues. A formulação é apresentada para partículas esféricas e superelipsóides. O cálculo do deslocamento tangente, que é utilizado para o cálculo das forças de atrito, é feito a partir da velocidade angular da partícula. Em geral, o deslocamento tangente é calculado a partir da velocidade linear instantânea do ponto de contato. Aqui, o deslocamento do ponto de contato é dado pelo movimento da partícula, tanto de translação quanto de rotação. Apesar da abordagem por meio de rotações, é mostrado este cálculo pode ser feito sem o uso de tensores de segunda ordem. O movimento da partícula é descrito por uma abordagem incremental. É apresentada uma formulação do método de integração leapfrog com a utilização da expressão das rotações sucessivas da parametrização de Rodrigues. A detecção do contato entre superelipsóides é feita por um método do tipo \"vetor normal comum\", resolvido como um problema de minimização. Os resultados mostram que a parametrização de Rodrigues pode ser utilizada com método dos elementos discretos tanto para a execução da rotação quanto para o cálculo de grandezas que envolvem este tipo de movimento como o deslocamento tangente. / This work presents a formulation for Discrete Element Method (DEM) adopting a vector ap-proach to solve rotations. Herein, rotations are solved using Rodrigues parameterization. The main contributions of this work are: tangential displacements using the incremental rotation vector from Rodrigues parameterization, and integration of the rotation movement using leap-frog method and Rodrigues rotation tensor. The formulations are presented to spheres and superelliptical particles. Tangential displacements, which are used to get friction forces, are calculated through angular velocity. In most of DEM implementations, tangential displacements are calculated through the instantaneous linear velocity of the contact point. Instead, here the displacement of the contact point is given through the rotation of the particle. It is showed that the vector of in-cremental rotations can be calculated through the angular velocity. Particle movement is described using an updated Lagrangian approach. Leapfrog method is formulated in such a way to use the Rodrigues expression for successive rotations. Contact detection between superellipsoids is solved using a technic called \"common normal approach\", and it is solved as a minimization problem. The results show that the Rodrigues parameterization can be applied to discrete element method to both execute rotations and to evaluate physical quantities that are related to this kind of movement as tangential displacement.

Cette thèse porte sur le problème fondamental du mottage des poudres suite aux mécanismes de transition de phase. Le projet vise à étudier l'impact des facteurs intrinsèques (structure moléculaire des matériaux, propriétés physiques et/ou physicochimiques, etc.) ou des facteurs environnementaux (conditions de stockage ou paramètres de procédé) sur la stabilité de la structure des poudres. Plus précisément, notre étude a mis en évidence le rôle prépondérant du phénomène de cristallisation et des transitions entre les différents polymorphes du lactose. L'accent a été mis sur le rôle des phénomènes de cristallisation et de la transition de phase dans l'apparition du mottage des poudres de lactose. Deux cas ont particulièrement retenu notre attention: (1) des poudres de lactose monohydrate contenant une fraction de particules amorphes et (2) des échantillons de poudre anhydre composés des anomères α et β du lactose. Dans les deux cas, le mottage a été induite par l'exposition des échantillons à l'air humide, soit dans un dispositif de sorption dynamique de vapeur (SPS), soit par des tests accélérés utilisant deux appareils conçus et réalisés dans notre laboratoire (CLAIR & OLAF). Nos résultats ont montré que, dans les deux cas, la principale cause de prise en masse était la formation de lactose monohydrate, qui est la forme la plus stable parmi tous les polymorphes de lactose. Cependant, les mécanismes élémentaires, les étapes limites et la cinétique du processus de transformation étaient différents dans chaque cas. Les paramètres les plus déterminants étaient l’humidité relative et la température alors que la pression n’a pas eu d’effet significatif. La résistance mécanique des échantillons mottés était étroitement liée au taux et à la cinétique de cristallisation. Enfin, des simulations numériques basées sur la méthode des éléments discrets (DEM) de la résistance mécanique des échantillons mottés ont été réalisées. Le modèle permet de décrire le comportement des échantillons mottés soumis à des contraintes mécaniques de compression ou de traction. / This PhD study focuses on the fundamental problem of powder caking due to phase transition mechanisms. The project aims to study the impact of intrinsic factors (molecular structure of materials, physical and/or physicochemical properties, etc.) or environmental factors (storage conditions or process parameters) on the stability of the structure of powders. More precisely, our study has highlighted the preponderant role of the crystallization phenomenon and the transitions taking place between the different polymorphs of lactose. Emphasis was placed on the role of crystallization phenomena and phase transition on the advent of lactose powder caking. Two cases attracted particular attention: (1) lactose monohydrate powders containing a fraction of amorphous particles and (2) anhydrous powder samples composed of ð and anomers of lactose. In both cases, the caking was induced by exposure of the samples to moist air, either in a Dynamic Vapor Sorption device (SPS) or in accelerated caking tests using two home-made equipment (CLAIR & OLAF). Our results showed that in both cases, the main cause of caking was the formation of lactose monohydrate, which is the most stable form among all lactose polymorphs. However, the elementary mechanisms, the limiting steps and the kinetics of the transformation process were different in each case. The more influencing parameters were the relative humidity and the temperature whereas the pressure has no significant effect. The yield stress of caked samples was closely linked with crystallization extent and kinetics. Finally, numerical simulations based on Discrete Element Method (DEM) of mechanical resistance of caked samples were performed using the "beam model". The model allows describing the behavior of the caked samples subjected to compressive or tractive mechanical stresses.

Ce travail de thèse s'inscrit dans le cadre de recherches sur le retraitement futur du combustible nucléaire usé et notamment sur la gestion poussée des radionucléides à vie longue tels que les actinides mineurs. Il concerne la fabrication de pastilles céramiques de Couvertures Chargées en Actinides Mineurs (CCAM) dédiées à la transmutation pour les réacteurs à neutrons rapides. Les pastilles céramiques utilisées dans le milieu nucléaire sont classiquement fabriquées en utilisant les procédés issus de la métallurgie des poudres. En raison de la pulvérulence des précurseurs poudres utilisés et de la forte radioactivité des actinides mineurs et notamment de l’américium, un procédé « sans poudre » innovant a été proposé. Ce procédé prévoit la fabrication de pastilles céramiques en utilisant des précurseurs oxydes non plus sous forme de poudre mais sous forme de microsphères (Calcined Resin Microspheres Pelletization, CRMP). Le principe de ce procédé consiste à compacter sous forme de pastilles des microsphères d’oxyde puis à fritter le comprimé obtenu.La première partie de cette étude concerne la synthèse et la caractérisation de précurseurs oxyde sous la forme de microsphères sub-millimétriques d’oxyde de lanthanides (simulants les actinides) par le procédé aux résines. Différents lots de microsphères ont pu être synthétisés afin de mieux appréhender l’influence de certains paramètres de synthèse, tel que la température de calcination, le tri en taille de la résine ou encore la teneur en lanthanides dans le cas des oxydes mixtes ont été investigués dans le but de déterminer leur impact sur les propriétés microstructurales et mécaniques de microsphères d’oxyde.L'étude aborde dans un deuxième temps la mise en forme des microsphères d’oxyde à travers une approche à la fois expérimentale et numérique. L’approche numérique utilise la méthode éléments discrets (Discrete Element Method, DEM), bien adaptée pour ces milieux granulaires. Les microsphères d’oxyde, prises individuellement, sont caractérisées mécaniquement notamment à travers la mesure de leur résistance à l'écrasement. Une mise en relation des conditions de synthèse et des tenues mécaniques des microsphères a été entreprise afin de comprendre l'impact de ces paramètres de synthèse sur le comportement mécanique du matériau. La compaction en matrice de lots de ces microsphères sous forme de pastille a été étudiée. En particulier, la compressibilité d'un certain nombre de microsphères a été analysée expérimentalement puis simulée par la DEM en mesurant la densification de la pastille en cru en fonction de la contrainte axiale appliquée et en décrivant l’évolution de sa microstructure. / One option envisioned for the future management of high level nuclear waste is the transmutation of minor actinides into short-lived fission products in sodium fast reactor. This route requires the development of pellet fabrication processes to prepare Minor Actinide Bearing Blanket (MABB) for the transmutation of americium.Currently, those ceramic pellets are produced by powder metallurgy processes involving numerous grinding and milling steps that generate very fine and highly contaminating and irradiating particles. A viable option for reducing the amount of those fine particles would be to develop a dustless process by working on much coarser particles. In this context, this study is concerned with the pelletization of porous and spherical lanthanides oxide precursors (surrogates of actinides). The present work uses both experimental data and numerical simulations to optimize the pelletization step. The final aim is to obtain, after sintering, homogeneous, dense and undistorted ceramic pellets.Firstly, this study concerns the synthesis and characterisation of these oxide microspheres precursors by the Weak Acid Resin process, which consists in loading beads of ion exchange resin with lanthanides cations and mineralizing the metal loaded resin leads into sub-millimetric-sized oxide microspheres. Comprehensive characterisations of the microstructure and mechanical properties of oxide microspheres have been carried out to better understand their behaviour into the matrix when producing pellets.Secondly, the mechanical properties of a single microsphere were investigated in order to better understand its behaviour during compaction steps. They were also analysed using multi-scale simulations based on the Discrete Element Method (DEM), which is well suited for such particulate materials. In a second approach, compaction studies were carried out in a three parts die to characterize the mechanical behaviour under pressure of a large number of oxide precursors. The behaviour of several microspheres in the matrix was finally simulated using DEM in order to describe interactions between microspheres and to have a better understanding of their evolution during pressing.

With the developments in computer technology, the numerical methods are used widely in geotechnical engineering. Finite element and finite difference are the most common methods used to simulate the behavior of soil and rock. Although the reliability of these methods are proven in several fields of application over the years, they are not equally satisfactory in every case and require sophisticated constitutive relations to model the discontinuous behavior of geomaterials since they assume the material is continuum or the location of discontinuum is predictable. The Discrete Element Method (DEM) has an intensive advantage to simulate discontinuity. This method is relatively new and still under development, yet it is estimated that it will replace of the continuum methods largely in geomechanics in the near feature. In this thesis, the theory and background of discrete element method are introduced, and its applicability in bearing capacity calculation of shallow foundations is investigated. The results obtained from discrete element simulation of bearing capacity are compared with finite element analysis and analytical methods. It is concluded that the DEM is a promising numerical analysis method but still have some shortcomings in geomechanical applications.