Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 203-213).

An investigation into the intruder dynamics of dry dimensionless, frictionless discs in bidispersed, disordered systems is carried out using computer simulations. The velocity of an intruder particle driven under constant force is used as a tool to determine scaling of velocity as a function of packing pressure. Using these velocity for a range of pressures, $4 \times 10^{-7}\leq P \leq 4 \times 10^{-2}$. A universal scaling relation is proposed and plotted. The force required to cause the packing to yield to the driven intruder is determined and plotted as function of pressure. Power law exponents were extracted for the yielding force vs. the pressure. The extracted values were used to study the micro-rheology of the intruder particle. Grain scale characteristics are used to infer global elastic modulus properties.

Les modèles de comportement phénoménologiques développés pour les sols peinent à traduire la complexité du comportement des matériaux granulaires, essentiellement du fait de leur nature discrète. Il est usuel d’avoir recours aux analyses multi-échelle, afin de proposer des comportements macroscopiques prenant finement en compte les propriétés locales du milieu. La question de l’échelle locale a été largement étudiée et il ressort qu’une méso-échelle, définie au niveau d’arrangements locaux de particules, semble plus appropriée que l’échelle du contact entre particules pour comprendre la texture et le comportement de ce type de milieux. Dans ce cadre, ce travail de thèse se propose d’étudier la faisabilité de la définition d’une loi de comportement pour les matériaux granulaires par changement d’échelle mésoscopique-macroscopique. Un échantillon granulaire est analysé par simulation DEM (Méthode aux Eléments Discrets) d’un essai biaxial de charge et de décharge. A l’échelle mésoscopique, le milieu granulaire est subdivisé en méso-domaines dont la texture est caractérisée par deux variables : degré d’allongement et orientation par rapport à la direction de compression. Les méso-domaines ayant des caractéristiques de texture communes sont regroupés en six phases, afin de mieux discriminer leur comportement. Les variables locales sont définies : méso-texture, méso-contrainte et méso-déformation, et leurs évolutions sont analysées. Les simulations montrent que le matériau s’appuie sur les phases orientées dans la direction de compression, d’autant plus qu’elles sont allongées, pour supporter la sollicitation. Ces dernières sont capables de développer une forte dilatance et une forte anisotropie, leur permettant de récupérer une forte valeur de rapport de contraintes. A contrario les phases allongées et perpendiculaires à la direction de compression constituent des maillons faibles pour le système. Sur la base des résultats DEM, un processus de changement d’échelles -dont l’ingrédient est l’évolution des pourcentages volumiques des phases au cours de l’essai- a permis de retrouver le comportement macroscopique. Un modèle élasto-plastique à élasticité linéaire, mécanisme plastique déviatoire et écrouissage cinématique a été proposé pour modéliser le comportement de chaque phase à l’échelle mésoscopique. L’essai de charge a permis d’identifier les 8 paramètres du modèle. L’essai de décharge a permis la validation du modèle proposé. Similairement, un modèle à un paramètre est proposé, et validé, pour l’évolution du pourcentage volumique de chaque phase. Sur la base de ces modélisations, le comportement macroscopique de l’échantillon a pu être retrouvé par changement d’échelle mésoscopique-macroscopique. Cette étude ouvre la voie à la définition d’un nouveau type de modèle de comportement des matériaux granulaires basé sur l’existence de phases à l’échelle mésoscopique. / Most of the developed constitutive models for granular materials cannot capture the complexity of their behavior, due to the discrete nature of the material. The use of a multi-scale approach may help to address this issue by taking account local properties in a more precise way. It seems that the so-called meso-scale defined at the level of a cluster of particles is the relevant scale to have a better insight into the influence of the texture on the behavior of the material. In this framework, the work involved herein studies the feasibility of the definition of a constitutive law for granular materials by means of a meso-macro change of scale. A sample made of particles has been analysed using the Discrete Element Method (DEM). At the mesoscopic scale, the material is divided into meso-domains characterized by two variables: their elongation ratio and their orientation with respect to the compression direction. The meso-domains who share the same characteristics of texture define a phase. Then, six phases were defined. Some local variables such as the meso-texture, the meso-stress and the meso-strain were defined and their evolution analyzed. The simulations show that the material relies all the more on the phases oriented in the direction of compression to bear the loading as the phase holds very elongated domains. Indeed, these latter are able to develop a strong dilatancy and a strong anisotropy to withstand high stress ratios. Conversely, the phases oriented perpendicular to the direction of compression play a minor role in the global behavior of the material. On the basis of the DEM results, a change of scale process (whose key element is the volumetric percentage of a phase in the material) allowed to retrieve the global behavior of the material. An elastic-plastic model with a linear elasticity, a plastic deviatoric mechanism with a kinematic hardening was proposed to model the behavior of each phase at the mesoscopic scale. The eight parameters of the model are identified based on numerical results obtained for a loading path. The unloading path of the numerical test allowed to validate the proposed constitutive model. Similarly, a model is proposed and validated for the evolution of the volumetric percentage of each phase at the mesoscopic scale. Based on these models, the macroscopic behavior of the sample could have been derived with a mesoscopic-macroscopic change of scale technique. This study paves the way to the definition of a new class of constitutive models for granular materials, based on the existence of phases at the mesoscopic scale.

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. Recent 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.

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This thesis presents results from an experimental study of the impact of dense solid spheres onto granular beds. The overall aim is to further our understanding of the dynamical response of granular materials to impact. In order to do this, we will study both the initial penetration stages and peak acceleration exerted on the sphere by using high-speed imaging. Another critical part is to measure the penetration depth of the sphere and calculate the corresponding depth-averaged stopping force. Both of these main focal points will be assessed for not only dry, but wet and “contaminated” grains, whereby the granular bed will be comprised of two distinct size ranges of base grains. In doing so, we aim to broadly determine whether contaminated grains or wet grains are more effective at increasing the tensile strength of granular materials.

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<p>The subject of this thesis is the mechanical response of inherently anisotropic granular materials. The study comprises both the experimental and numerical aspects and provides a rigorous methodology for the solution of geotechnical problems involving anisotropic frictional materials.</p> <p>The experimental investigation has been carried out at both the material and structural levels. The material tests involved a series of direct shear, triaxial and hollow cylinder experiments on crushed limestone sand, whose mechanical characteristics are strongly affected by the orientation of the sample. In addition, a scaled foundation setup was designed and a series of experimental tests was carried out to examine the effects of anisotropy on bearing capacity.</p> <p>The numerical part of this work was associated with development and implementation of a constitutive framework that describes the mechanical response of transversely isotropic frictional materials. The framework is based on elasto-plasticity and accounts for the effects of strain localization and inherent anisotropy of both the deformation and strength characteristics. An implicit scheme was proposed for identification of material parameters/functions, which incorporates predictions based on critical plane analysis. As a part of constitutive modeling, a suitable numerical algorithm was also developed to integrate the constitutive equations.</p> <p>The constitutive framework has been implemented in a commercial FE package (ABAQUS). A series of numerical simulations were carried out focused on the assessment of the bearing capacity of a shallow foundation in transversely isotropic granular medium. The results of numerical simulations have been compared with the experimental data. A parametric study was also carried out aimed at examining the influence of various simplifications in the mathematical framework on its predictive abilities.</p> / Thesis / Doctor of Philosophy (PhD)