The Distinct Element Method (DEM) and Discontinuous Deformation Analysis (DDA) are the two most commonly used discrete element methods in rock mechanics. Discrete element approaches are computationally expensive as they involve the interaction of multiple discrete bodies with continuously changing contacts. Therefore, it is very important to ensure that the method selected for the analysis is computationally efficient. In this research, a general assessment of DDA and DEM is performed from a computational efficiency perspective, and relevant enhancements to DDA are developed. The computational speed of DDA is observed to be considerably slower than DEM. In order to identify reasons affecting the computational efficiency of DDA, fundamental aspects of DDA and DEM are compared which suggests that they mainly differ in the contact mechanics, and the time integration scheme used. An in-depth evaluation of these aspects revealed that the openclose iterative procedure used in DDA which exhibits highly nonlinear behavior is one of the main reasons causing DDA to slow down. In order to improve the computational efficiency of DDA, an alternative approach based on a more realistic rock joint behavior is developed in this research. In this approach, contacts are assumed to be deformable, i.e., interpenetrations of the blocks in contact are permitted. This eliminated the computationally expensive open-close iterative procedure adopted in DDA-Shi and enhanced its speed up to four times. In order to consider deformability of the blocks in DDA, several approaches are reported. The hybrid DDA-FEM approach is one of them, although this approach captures the block deformability quite effectively, it becomes computationally expensive for large-scale problems. An alternative simplified uncoupled DDA-FEM approach is developed in this research. The main idea of this approach is to model rigid body movement and the block internal deformation separately. Efficiency and simplicity of this approach lie in keeping the DDA and the FEM algorithms separate and solving FEM equations individually for each block. Based on a number of numerical examples presented in this dissertation, it is concluded that from a computational efficiency standpoint, the implicit solution scheme may not be appropriate for discrete element modelling. Although for quasi-static problems where inertia effects are insignificant, implicit schemes have been successfully used for linear analyses, they do not prove to be advantageous for contact-type problems even in quasi-static mode due to the highly nonlinear behavior of contacts.

Computer simulation using the Discrete Element Method (DEM) has emerged as a powerful tool in studying the behaviour of particulate systems during powder flow and compaction. Contact law between particles is the most important input to the Discrete Element simulation. However, most of the present simulations employ over-simplistic contact laws which cannot capture the real behaviour of particulate systems. For example, plastic yielding, material brittleness, sophisticated particle geometry, surface roughness, and particle adhesion are all vitally important factors affecting the behaviour of particle interactions, but have been largely ignored in most of the DEM simulations. This is because it is very difficult to consider these factors in an analytical contact law which has been the characteristic approach in DEM simulations. This thesis presents a strategy for obtaining the contact laws numerically and a comprehensive study of all these factors using the numerical approach. A numerical method, named as the Material Point Method (MPM) in the literature, is selected and shown to be ideal to study the particle interactions. The method is further developed in this work in order to take into account all the factors listed above. For example, to study the brittle failure during particle impact, Weibull’s theory is incorporated into the material point method; to study the effect of particle adhesion, inter-atomic forces are borrowed from the Molecular Dynamic model and incorporated into the method. These developments themselves represent a major progress in the numerical technique, enabling the method to be applied to a much wider range of problems. The focus of the thesis is however on the contact laws between extremely fine particles. Using the numerical technique as a tool, the entire existing theoretical framework for particle contact is re-examined. It is shown that, whilst the analytical framework is difficult to capture the real particle behaviour, numerical contact laws should be used in its place.

Lunar soil, defined as the finest part of the lunar regolith which covers the entire surface of the Moon, has shown to have remarkable shear strength properties, highlighted by the clearly visible effects of soil cohesion. The main objective of this thesis is to unveil the physical explanations causing this unusual soil behaviour in a waterless, airless, lunar environment. Ultra-High Vacuum (UHV), in particular, is considered responsible for increasing the strength of surface energy forces due to lunar soil outgassing. In turn, the presence of surface energy forces, arising from van der Waals intermolecular forces, is thought to alter the mechanical properties of lunar soil. A particle-based microscopic approach by means of the Discrete Element Method (DEM) was utilised to investigate the effects of surface energy forces on the macroscopic soil be- haviour. A micro-mechanical contact model, based on the JKR theory, was selected to describe the inter-granular behaviour between lunar soil particles. Physical and geometrical parameters typical of lunar soil were employed. Several triaxial tests were run to identify a link, if any, between the microscopic surface energy parameter and the macroscopic soil cohesion, which was interpreted as a true soil cohesion. In addition, very low stress levels and high soil densities were simulated in order to take into account the low gravitational field and the high state of soil compaction caused by continuous meteorite impacts on the Moon. Results from triaxial tests were analysed at both the peak and critical state. It was found that in the ideal case of perfectly spherical grains, the presence of adhesion is a source of noticeable macroscopic soil cohesion. However, no influence was observed in terms of macroscopic friction angle. Furthermore, a brittle macroscopic soil behaviour was revealed, owing to the simulated inter-granular chemical bonds and the very low stress conditions applied. Finally, similar to the behaviour of cemented sands, very little cohesion was recorded at the critical state. Subsequently, particle shape effects were investigated by complementing the numerical model with a simple form of inter-particle rolling resistance. Simulations were also run with non-convex grains of increasing geometrical complexity in order to simulate more realistically the irregular shapes of lunar soil grains. In both cases, the interplay of surface energy forces with particle shape effects resulted in even higher shear strength, with predictions similar to the estimates of shear strength for real lunar soil. Once again, the peak strength was dominated by macroscopic cohesion which, on the other hand, was hardly observable at the critical state, confirming the tendency observed from spherical grains. Finally, the practical implications of the above findings were discussed in terms of bearing capacity, trafficability and slope stability on the lunar surface. In particular an analytical approach, based on the bearing capacity problem, was devised to study the performance of a rigid wheel rotating on a lunar terrain and operating under different dynamic conditions.

Les structures de sphères creuses appartiennent à la famille des matériaux cellulaires qui ont récemment été étudiés pour leurs multiples propriétés. Dans le cas de cette thèse, le but des sphères creuses est de dissiper l’énergie d’impact d’un oiseau sur un cockpit d’avion. Elles sont développées dans le cadre du projet SAMBA (Shock Absorber Material for Birdshield Application) afin d’optimiser leur énergie spécifique absorbée (J/kg).Dans un premier temps, des essais quasi-statiques (v = 5 mm/min) et dynamiques (v = 2 m/s) de compression uni-axiale sont conduits à température ambiante sur une seule sphère creuse de diamètre 30 mm. Une propagation rapide de fissures macroscopiques est observée. Le formalisme de la Mécanique Élastique Linéaire de la Rupture (MELR) est utilisé pour estimer le taux de restitution d’énergie critique dynamique GIdc du matériau constitutif. La position du sommet de fissure est mesurée pendant la propagation de fissure à l’aide d’une caméra rapide. La Méthode des Éléments Discrets (DEM) permet de simuler la rupture dynamique en implémentant une technique de relâchement des nœuds. Le taux de restitution d’énergie GIdc peut être estimé à partir de l’histoire (position et temps) du sommet de fissure. Le modèle numérique montre que les structures sphériques dissipent une proportion importante de l’énergie par des effets dynamiques. A une même vitesse de propagation, plus l’épaisseur de coque est fine, plus les effets inertiels générés par la rupture sont importants et ce pour une même vitesse de propagation.Le modèle numérique DEM est ensuite employé pour reproduire la rupture dynamique sur une sphère creuse à l’aide d’un critère en contrainte seule ou un critère mixte en contrainte – énergie. Les bons résultats obtenus démontrent la capacité de la DEM à représenter la propagation de fissures en régime dynamique.Finalement, des essais numériques et expérimentaux multi-sphères sont réalisés afin évaluer le comportement des sphères creuses au sein d’un assemblage. / Hollow sphere structure (HSS) belongs to cellular solids that have been studied recently for its multiples properties. In our case, HSS aims to absorb soft impacts energy on an airliner cockpit. HSS is investigated through the SAMBA (Shock Absorber Material for Bird-shield Application) project because of its promises in term of specific energy dissipated (J/kg) during impact.First of all, quasi-static and dynamic (v = 5 mm/min to v = 2 m/s) uniaxial compression tests are conducted at room temperature on a single sphere (D = 30 mm). Rapid crack propagation (RCP) is observed to be predominant at macroscopic scale. The formalism of Linear Elastic Fracture Mechanics (L.E.F.M.) is therefore used to estimate the dynamic energy release rate GIdc . The crack tip location is measured during the crack propagation using a high speed camera. The Discrete Element Method (DEM) is used to simulate the dynamic fracture by implementing the node release technique. The dynamic energy release rate can be determined using an experimentally measured crack history. In spherical structures the numerical results reveal a high proportion of energy dissipated through inertial effects as well as a dependence of the thickness of the hollow sphere over the range of 0.04 mm to 1.2 mm.The DEM model Is then employed to reproduce the RCP according to two failure criterions: a stress criterion and a coupled stress-energy criterion. It reveals to be an interesting way to model the mechanical behavior of brittle materials.Eventually, experimental and numerical multi-spheres tests are performed to evaluate the behavior of brittle hollow spheres within an assembly.

Dans les études expérimentales de la micromécanique des matériaux granulaires, la mesure des forces de contact entre particules est de nos jours toujours un challenge en comparaison avec les outils et techniques bien mieux établis pour la caractérisation cinématique à l'échelle des particules. Cette thèse de doctorat s'attaque à cet ambitieux problème. L'approche proposée implique deux aspects : (i) la caractérisation expérimentale du réseau de contact et de la cinématique à l'échelle des particules, qui peut être réalisée avec des techniques d'imagerie standards ; (ii) une approche numérique capable d'exploiter ces mesures afin de déduire les forces de contact.L'une des contraintes qu'on s'était imposée était de ne s'appuyer que sur la connaissance de la géométrie des particules ainsi que du réseau de contacts pour réaliser la déduction des forces de contact. Trois techniques numériques différentes ont été proposées à cet effet : une méthode basée sur l'élasticité des contacts (CEM), une méthode basée sur la dynamique de contact (CDM) et une méthode basée sur l'équilibre élasto-plastique de l'assemblage granulaire (QSM). Chacune de ces techniques repose sur une approche de la famille des méthodes en éléments discrets ; il s'agit respectivement de le DEM de type Cundall, la dynamique des contacts non régulière, et une approche de calcul statique élastoplastique. La non-unicité de la solution est le principal problème avec les techniques choisies, et elles sont étroitement liées à l’indétermination des forces dans le système.Les trois méthodes sont d'abord présentées et validées en les appliquant à l'estimation des forces dans les systèmes granulaires 2D générés au moyen de simulations DEM explicites. Nous prenons ces simulations comme des expériences "idéales" dans le sens où elles fournissent des données similaires à celles extraites des expériences, mais dépourvues d'erreurs de mesure. Un avantage évident de cette stratégie est d’obtenir des ensembles de forces faisant office de référence faisant foi. Sur cette base, les principaux aspects affectant la détermination des forces peuvent être étudiés. En particulier, le rôle crucial de l'histoire du chargement est mis en évidence et certaines solutions pour les prendre en compte dans la détermination des forces ont été prospectées. Une évaluation de l'influence de l'erreur de mesure a également été réalisée pour prédire l'applicabilité de chaque méthode à des expériences réelles. Une brève analyse de la variabilité des solutions est également fournie.Finalement, des tentatives ont été faites pour déduire des forces issues d’expériences effectuées dans le dispositif 1gamma2epsilon. La cinématique des particules et la connectivité ont été évaluées au moyen de la technique de corrélation d'image numérique. Les avantages et inconvénients des trois méthodes ont été éclaircis. Ils nous conduisent à envisager une utilisation combinée des trois méthodes pour tirer parti de leurs atouts respectifs. À l'avenir, il conviendra de réfléchir à la prise en compte de la stabilité de la solution -- dans l'algorithme de convergence vers une solution -- avec l'espoir de limiter la variabilité des solutions. / In the experimental study of the micro-mechanics of granular materials, measuring inter-particle contact forces is still a challenging task, if compared to the well-established tools and techniques for the kinematic characterisation at particle scale. This doctoral thesis addresses this problem. The proposed approach consists of two parts: an experimental characterisation of the granular network geometry and of particle-scale kinematics, which can be carried out with common imaging techniques such as Digital Image Correlation; a numerical approach aiming to exploit these measurements for the estimation of forces.One imposed constraint was to only make use of the rigid motions of particles, together with the knowledge of the contact network, to infer contact forces. Three different numerical techniques have been proposed to this purpose, referred to as Contact Elasticity Method (CEM), Contact Dynamics-based Method (CDM) and Quasi-Static Method (QSM). Each of these techniques is based on the formulation of common approaches in the family of Discrete Element Methods, respectively the classical Cundall-like DEM, the Non Smooth Contact Dynamics and a quasi-static approach accounting for both contact elasticity and plasticity. It is shown that memory of the history of the packing is the main concern with all the chosen techniques.The three methods are first presented and validated by applying them to the estimation of forces in 2D granular systems generated by means of explicit-time DEM simulations. We refer to these simulations as "ideal" experiments since they are meant to provide the same information that can be extracted from experiments, but without any measurement error. An obvious benefit of this strategy is to get reference force sets that are taken as ground truth. Based on this, the main aspects that affect the determination of forces can be investigated. In particular, the crucial role of history is emphasised here, and some solutions to take it into account in the force inference have been investigated.An assessment of the influence of measurement error has also been carried out, to predict the applicability of each method to real experiments. A short analysis of the variability of the solutions is also provided.Finally, some attempts have been made to infer forces from experiments carried out in the 1gamma2epsilon device. Particle kinematics and connectivity have been assessed by means of the Digital Image Correlation technique.The benefits and drawbacks of the three methods have been demonstrated. They conduct us to envision a combined usage of the three methods. In the future, studying the stability of equilibrium might help reducing the variability of the solutions.

A demanda por estruturas mais leves implica num ganho em economia, porém o aumento de esbeltez da estrutura pode tornar ela susceptível a instabilidade frente a tensões compressivas estáticas ou dinâmicas. A instabilidade acontece em várias escalas da estrutura analisada e pode interagir com outras formas de colapso como a propagação instável de fissuras, problema governado pela mecânica da fratura, pela plastificacão do material, ou por uma combinação dos efeitos citados. Neste contexto, no presente trabalho, se explora a capacidade do método dos elementos discretizados por barras (LDEM) na simulação de problemas de instabilidade estática e dinâmica devido as tensões de compressão. Este método permite simular o sólido como um arranjo de barras com rigidez equivalente ao contínuo que se quer representar. Leis constitutivas não lineares permitem modelar ruptura de forma simples. A equação de movimento resultante da discretização permite formular uma equação de movimento desacoplada que pode ser integrada no domínio do tempo com um método explícito (Método das Diferencias Finitas Centrais). O fato das barras serem rotuladas nos seus extremos e a solução do problema ser obtida de forma incremental permite capturar problemas com não linearidade geométrica, entre eles a instabilidade estrutural frente a tensões compressivas. Como último exemplo se realiza a análise de um painel sanduiche por flexão em três pontos, que é composto por um núcleo de poliuretano, com duas lâminas externas de material compósito, neste caso a instabilidade estrutural está associada a flambagem da camada da lâmina comprimida. Finalmente a potencialidade da metodologia de análise utilizada é discutida. / The demand for lighter structures implies a gain in economy, but the increase in slenderness of the structure may make it susceptible to instability against static or dynamic compressive stresses. Instability occurs at various scales of the analyzed structure and may interact with other forms of collapse such as unstable crack propagation, problem governed by fracture mechanics, plastification of the material, or a combination of the cited effects. In this context, in the present work, we explore the ability of the discrete elements methods by bars (LDEM) in the simulation of problems of static and dynamic instability due to the compression stresses. This method allows to simulate the solid as an arrangement of bars with rigidity equivalent to the continuum that one wants to represent. Constitutive non-linear laws allow simple modeling of rupture. The equation of motion resulting from the discretization allows us to formulate a decoupled motion equation that can be integrated in the time domain with an explicit method (Central Finite Differences Method). The fact that the bars are labeled at their ends and the solution of the problem is obtained in an incremental way allows to capture problems with geometric non-linearity, among them the structural instability against compressive tensions. The last example, the analysis of a sandwich panel by three-point bending, which is composed of a polyurethane core, with two external blades of composite material, in this case the structural instability is associated with buckling of the layer of the compressed blade . Finally, the potential of the analysis methodology is discussed.

The Discrete Element Method was first introduced by Cundall and Strack (1979) to model granular soils within the context of geotechnical engineering. The material is modeled as a random assembly of discrete elements. Each particle interacts with neighboring particles through contact forces that can be built up and broken at any time. The particles were modeled as discs in 2-D or as spheres in 3-D. Research studies have been conducted to improve the simulation of actual grain shapes. Ashmawy et al. (2003) developed the overlapping rigid clusters (ORC) method to accurately model irregular particle shapes. The idea relies on clumping a number of overlapping discs such that their coincides with that of the actual particle. In this dissertation, experimental verification program is presented. An experimental setup was built and model-grains were manufactured in the laboratory. A numerical simulation for the experimental test was carried out. The numerical and experimental results were compared qualitatively and quantitatively. A good agreement was observed within small displacements ranges. However, results were considerably different at large displacements. Numerical results utilizing the ORC method were closer to the experimental results than those of discs. A sequential and operator-independent procedure, which relies on the ORC concept, was developed. Identical inertial properties between the actual particle and the model were ensured. The new procedure was implemented for rounded and angular particles. The effect of particle shape and angularity on the strength and dilatancy characteristics of granular soils was investigated. A modified shape factor, which relies on the work introduced by Sukumaran and Ashmawy (2001), was developed. A series of pure shear testing simulations was performed on different shape and angularity particle groups. Angularity had a remarkable effect on strength and dilatancy properties compared to shape. The effect of interparticle friction on dilatancy was studied. An attempt was made to use an equivalent interparticle friction to model different particle shapes. It was concluded that there is no one-to-one equivalency between interparticle friction and shape or angularity. Instead, the interparticle friction must be continuously altered as a function of confining pressure and void ratio to achieve the required effect.

The general objective of the research effort reported in this thesis was to develop the knowledge required to optimize the design and operation of solid and semi-solid manure handling and land application equipment. Selected physical and rheological properties of manure products deemed to have an influence on the performances of manure handling and land application equipment were measured and general trends were identified among the measured properties. Relationships were also established between the measured properties and the type of manure as well as its total solids concentration. Field experiments were carried out to evaluate the effects of selected mechanical configurations, operating parameters and product properties on the discharge of manure spreaders. The influence of the type of conveying system (scraper conveyor and system of four augers) and the velocity at which it is operated, the geometry of the holding system and the position of a flow-control gate were all included in the analysis. The discharge rates of the machines as well as the specific energy required by the unloading operations were measured. A numerical modeling method called discrete element method (DEM) was used to create virtual manure, a numerical model of the real product. The measured physical and flow properties were used to develop and validate the virtual manure models. It was found that manure products could successfully be represented in a DE framework and that several parameters defining the contact constitutive model in the DEM had an influence on the behaviour of the virtual products. The DEM was then used to study machine-product interactions taking place in handling and land application equipment. Results from field experiments carried out using various land application equipment were used in the development and validation of the interaction models. The predicted flow rates and power requirements were in good agreement with measured data. The results obtained allowed for a better understanding of the flow of manure products in manure handling and land application equipment. It was found that the constitutive model used for the product influenced the results of the machine-product interactions models. A precision banded applicator under development at the University of Saskatchewan was also modeled. The discharge rate of this equipment is influenced by a number of parameters. The predicted mass distribution across the width of the banded applicator was well correlated to the experimental results. The models developed in this thesis have the potential to become powerful engineering tools for the design of improved machines for the handling and land application of solid and semi-solid manure.

The objective of the present study was to develop a fluid flow-coupled distinct element model capable of capturing the undrained behaviour of granular soils by considering fundamental physical mechanisms that involve fluid flow and particle interaction. The method considers granular media as assemblies of ellipsoidal particles arranged on a plane and interacting by means of contact forces. Saturation effects are incorporated by assuming that particles are immersed in fluid, the flow of which is simulated as occurring through a network of conduits. The flow through conduits is according to a Hagen-Poiseuille relation; a transient solution is obtained by solving a system of differential equations. The developed fluid-flow coupled distinct element was used to conduct various numerical simulations and the mechanisms of undrained deformations were examined from a micromechanical point of view. The dissertation begins with a literature review on the undrained behaviour of granular materials as observed in laboratory experiments. A review of previous attempts to simulate undrained tests micromechanically is also presented, and the advantages and disadvantages of various methods are examined. The capability of the developed model to simulate two-dimensional fluid-flow and pressure dissipation problems is demonstrated by means of comparisons with analytical solutions. Fluid pressure dissipation problems are qualitatively compared with Terzaghi's one-dimension theory of consolidation. It is shown that transient flow problems are accurately modelled by the fluid flow network approach. Simulated compression tests were carried out to examine the effects of different confining pressures and initial densities on the macroscopic response. The results compare favorably with those commonly observed in undrained laboratory experiments. Simulated tests are analyzed from a micromechanical point of view. It is shown that macroscopic behaviour can be traced to changes in micromechanical fabric descriptors. The effects of the interparticle friction angle on the undrained behaviour of the assemblies are investigated. The undrained strength is considerably increased by increasing interparticle friction. The main mechanism found to be responsible for the development of higher strength is the tendency of the specimens to dilate during shear distortion. The effects of the principal stress direction on the macroscopic response are examined. The behaviour of initially anisotropic samples is significantly altered by the direction of the principal stresses relative to the anisotropy direction. It is demonstrated that macroscopic permeability of the media has a considerable effect on the strength. This behaviour is attributed to the inhomogeneity of pore pressure distributions which increases with decreased permeability. The results presented are generally in agreement with observations previously reported from laboratory experiments. The possible applications of the model for future research are also discussed.

The objective of the present study was to develop a fluid flow-coupled distinct element model capable of capturing the undrained behaviour of granular soils by considering fundamental physical mechanisms that involve fluid flow and particle interaction. The method considers granular media as assemblies of ellipsoidal particles arranged on a plane and interacting by means of contact forces. Saturation effects are incorporated by assuming that particles are immersed in fluid, the flow of which is simulated as occurring through a network of conduits. The flow through conduits is according to a Hagen-Poiseuille relation; a transient solution is obtained by solving a system of differential equations. The developed fluid-flow coupled distinct element was used to conduct various numerical simulations and the mechanisms of undrained deformations were examined from a micromechanical point of view. The dissertation begins with a literature review on the undrained behaviour of granular materials as observed in laboratory experiments. A review of previous attempts to simulate undrained tests micromechanically is also presented, and the advantages and disadvantages of various methods are examined. The capability of the developed model to simulate two-dimensional fluid-flow and pressure dissipation problems is demonstrated by means of comparisons with analytical solutions. Fluid pressure dissipation problems are qualitatively compared with Terzaghi's one-dimension theory of consolidation. It is shown that transient flow problems are accurately modelled by the fluid flow network approach. Simulated compression tests were carried out to examine the effects of different confining pressures and initial densities on the macroscopic response. The results compare favorably with those commonly observed in undrained laboratory experiments. Simulated tests are analyzed from a micromechanical point of view. It is shown that macroscopic behaviour can be traced to changes in micromechanical fabric descriptors. The effects of the interparticle friction angle on the undrained behaviour of the assemblies are investigated. The undrained strength is considerably increased by increasing interparticle friction. The main mechanism found to be responsible for the development of higher strength is the tendency of the specimens to dilate during shear distortion. The effects of the principal stress direction on the macroscopic response are examined. The behaviour of initially anisotropic samples is significantly altered by the direction of the principal stresses relative to the anisotropy direction. It is demonstrated that macroscopic permeability of the media has a considerable effect on the strength. This behaviour is attributed to the inhomogeneity of pore pressure distributions which increases with decreased permeability. The results presented are generally in agreement with observations previously reported from laboratory experiments. The possible applications of the model for future research are also discussed.