Dissertations / Theses on the topic 'Modelling granular materials'

A granular material is usually an irregular packing of particles and its constitutive relationship is very complex. Previous researches have shown that the discrete element method is an effective tool for fundamental research of the behaviour of granular materials. In this research, discrete element modelling was used to obtain the macroscopic stress-strain behaviour of granular material in cavity expansion. The micro mechanical features and the mechanical behaviour of granular material at particle level have been investigated. A simple procedure was used to generate the samples with spherical particles and two-ball clumps. The influence of particle properties on the stress strain behaviour within an aggregate was investigated in biaxial test simulations. It was found that more angular clumps lead to sample more homogeneous and that the interlocking provided by the angular clumps induces a higher strength and dilation in the sample response. Interparticle friction was also found to have significant effect on the strength and dilation of the sample. The sample macromechanical properties can be obtained from these biaxial simulations. For investigating the effect of particle shape, the spherical or non-spherical(two-ball clump) particle shapes were used in the cavity expansion simulations. Monotonic loading was performed on a fan-shaped sample with various particle properties under a range of initial cavity pressures. The results were compared with calculated analytical solutions and existing experimental data in order to optimise the micro mechanical parameters governing the behaviour. The pressuremeter test data were adapted for this comparison since the theory of cavity expansion has been used to describe the pressuremeter tests in soil and rocks by many geotechnical researchers and engineers. This research showed that particle properties play an important role in soil behaviour of cavity expansion under monotonic loading. The contribution of this research is to present that it is possible to model a granular material of boundary value problem (cavity expansion) under static conditions, providing micro mechanical insight into the behaviour.

The permanent deformation of a pavement due to vehicle load is one of the important factors affecting the design life as well as the maintenance cost of a pavement. For the purpose of obtaining a cost-effective design, it is advisable to predict the traffic-loadinduced permanent pavement deformation. The permanent deformation in pavements (i.e. rutting) can be classified into three categories, including the wearing of the asphalt layers, compaction, and shear deformations. In the present study, discrete element analyses have been performed to predict the permanent deformation of a pavement when subjected to moving wheel loads. Note that the wearing of the asphalt layers has been disregarded. DEM biaxial test simulations have been carried out in terms of both unbonded and bonded granular materials. The typical stress-strain response, as well as the volumetric strain development, have been reproduced, in qualitative agreement with the experimental results. The factors affecting the mechanical behaviour of granular materials have been investigated, e.g. particle stiffness, sample compaction and parallel bond strength. In addition, the elastic properties, initial yield stress, strength parameters and so on have been analysed. These compression tests provided guidance for the selection of the particle parameters for the subsequent pavement simulation. The permanent deformation in unbonded pavements was represented under moving wheel loads, and proved to be qualitatively consistent with the laboratory tests. The initial self-weight stress had a significant effect on rutting. When the initial gravity stress was relatively high, both shakedown and surface ratchetting phenomena were observed for different loading levels. However, the accumulation of permanent deformation was continual for pavements with low gravity stress, even if the wheel pressure was small. Other factors affecting the rutting have been taken into consideration, e.g. specimen preparation, interparticle friction, etc. In the case of the single-layered pavement, permanent deformation ceased after the first wheel pass. Plastic deformation increased with the decrease in the self-weight stress. For the double layered pavement, the permanent deformation continually increased with wheel passes, probably owing to compaction of the bottom unbound layer. The pavement shakedown phenomenon was not observed prior to wheel pass 300. The permanent deformation increased augmentation of wheel pressure as well as decrease in the sample density and upper layer thickness. The residual stresses in both vertical and horizontal directions can be obtained using the measurement circle. For all the pavements in the current simulations, the vertical residual stress is nearly always zero, consistent with the equilibrium condition. In the case of the unbonded pavement, the large horizontal residual stress depends on the high initial gravity stress, instead of high wheel pressure or wheel pass number. For the single-layered pavement, the peak of the horizontal residual stress was observed near the pavement surface. The residual stress rises with the augmentation of the wheel pass number and the wheel pressure. In the double-layered pavement, the residual stresses are discontinuous at the interface between different pavement layers. The peak appears near the pavement surface and increases with the reduction in the upper layer thickness as well as the rise in wheel passes and wheel pressure. Nevertheless, residual stress is not apparent in the granular base. The probability density distribution was investigated in terms of the contact and bond forces. For the normal contact force, a peak generally appeared at small contact forces, followed by a drastic decrease and, after that, the probability density progressively approached zero. For the tangential contact force as well as the bond forces, in general, a peak of the probability distribution was observed at small contact forces, and then a sharp drop followed from the two flanks of the peak point. Finally, there was a gradual decrease until the probability density decayed to zero. The factors, e.g. pavement layer, wheel pass number and wheel pressure, mainly affect the probability distribution of the small contact or bond forces. For both single- and double-layered pavements, the absolute extrema of the bond forces in the top layer increased with the augmentation of the wheel pass number and the wheel pressure. For the unbonded pavement, the sliding contact ratio was studied and it was significantly affected by the pavement layer, initial gravity stress and sample compaction. The distribution of the pavement particle displacements were demonstrated. In the unbonded pavement, factors, such as wheel pressure and initial gravity, not only affect the distribution of the relatively large particle displacements but also increase the magnitude of the particle displacements. The directions of the large displacement vectors are diverse as the large gravity acceleration is assigned to the particles but are almost downward when the self-weight stress is small. In the single- or double layered pavement, factors, such as wheel pass number and wheel pressure, merely increase the values of the particle displacements. The distribution of the displacements is hardly affected. For the single-layered pavement, the large displacements were observed near the pavement surface and their directions are almost contrary to the movement direction of the wheel. In the double-layered pavement, relatively large particle displacements are widely distributed in the pavement. Their directions are in an almost vertical direction.

The main objective of this work is to model granular materials comprising particles of aspherical shape and investigate the effect of the grain shape on the hydraulic properties of the material. For this purpose, a Discrete Element Method code for clustered spheres was developed during the course of this work to simulate aspherical particles. The shape of the particles modelled mimics the morphology of real grains obtained from a shape library of real scanned particles for which development this thesis also contributed. The simulation tools are then used to construct models of real sands by simulating the settling under gravity and compaction of the grains. The hydraulic properties of the sand moels are then investigated via numerical simulations using two different approaches. First, we simulate low Reynolds numbers flow in granular packs using a Finite Element method within the Stokes flow approximation. Then we explore the applicability of the two-fluids approach to simulate fluid flow in the presence of solid obstacles and complex microstructures. By integrating the technologies developed during this work, it was possible to simulate the single phase flow in a wide range of Reynolds number in models of sand. The results obtained closely agree with available experimental data and empirical correlations for relatively clean and homogeneous sands. These results show that the hydraulic permeability can vary within a factor of two as a consequence of the particle shape. This indicates that for unconsolidated media the most important parameter with regards to fluid flow conductivity is the porosity.

Cone penetration testing (CPT) is one of the most versatile devices for in situ soil testing. With minimal disturbance to the ground, it provides information about soil classification and geotechnical parameters. Several researchers have used different numerical techniques such as strain path methods and finite element methods to study CPT problems. The Discrete Element Method (DEM) is a useful alternative tool for studying cone penetration problems because of its ability to provide micro mechanical insight into the behaviour of granular materials and cone penetration resistance. This study uses three-dimensional DEM to simulate the cone penetration testing of granular materials in a calibration chamber. Due to the geometric symmetry of this study a 90 degree segment of the calibration chamber and the cone penetrometer was initially considered followed by a 30 degree segment to allow for the simulation of smaller particle sizes and to reduce computational time. This research proposes a new particle refinement method, similar to the mesh refinement of finite-element modelling, in the sense that a large number of small particles were brought into contact with the cone tip, while the large particles were distanced further away from the cone, to reduce computational time effectively. Using a radius expansion method for sample preparation and assigning a constant mass to each particle in the sample was found to reduce computational time significantly with little influence on tip resistance. The effects of initial sample conditions and particle friction coefficient were found to have an important influence on the tip resistance. In addition, prohibiting particle rotation was found to increase tip resistance significantly compared to when the particles were permitted to rotate freely. Particle shape in this study was simulated by replacing the spheres with simple two-ball clumps and was found to have an important effect on the tip resistance. DEM simulations of biaxial tests were conducted to investigate the effect of initial sample conditions, particle shape and particle friction coefficient on the stress-strain behaviour of granular materials. All the above mentioned parameters were found to have a significant effect on the stress-strain behaviour of granular materials. Biaxial test simulations were also conducted to obtain basic granular material properties to derive analytical CPT solutions from continuum mechanics principles. Some of the DEM simulation results were found to be in good agreement with the analytical solutions that used a combined cylindrical-spherical cavity expansion method. Particle crushing was simulated during the cone penetration tests by replacing a broken particle with two new equi-sized smaller particles with mass conserved. The results showed considerable reduction in the tip resistance for the crushing model compared to the non-crushing model and this reduction increased as the confining stress increased.

Dense flows of grains are commonplace throughout natural and industrial environments, from snow-avalanches down the sides of mountains to flows of cereal down chutes as it is transported from one part of a factory to another. A ubiquitous feature in all of these flows is their ability to separate the different grain types when shaken, stirred, sheared or vibrated. Many flows are sheared through gravity and these flows are particularly efficient at segregating particles based on their size, with small particles percolating to the bottom of the flow and large particles collecting at the top. Within this mechanism, an asymmetry between the large and small particles has been observed, with small particles percolating downwards through many large particles at a faster rate than large particles rise upwards through many small particles. This alternative format thesis presents a revised continuum model for segregation of a bidisperse mixture that can account for this asymmetry. A general class of asymmetric segregation flux functions is introduced that gives rise to asymmetric velocities between the large and small grains. Exact solutions for segregation down an inclined chute, with homogenous and normally graded inflow conditions, show that the asymmetry can significantly enhance the distance for complete segregation. Experiments performed using a classical shear-box with refractive index matched scanning are able to quantify the asymmetry between large and small particles on both bulk and particle scales. The dynamics of a single small particle indicate that it not only falls down faster than a single large particle rises, but that it also exhibits a step-like motion compared to the smooth ascent of the large grain. This points towards an underlying asymmetry between the different sized constituents. The relationship between the segregation-time and the volume fraction of small grains is analysed, and solutions presented for the steady-state balance between segregation and diffusive remixing. These help to show the good agreement between the asymmetric model and experimental data. Segregation at the front of natural avalanches produces a recirculation zone, known as a `breaking size-segregation wave', in which large particles are initially segregated upwards, sheared towards the front of the flow, and overrun before being resegregated again. Solutions for the structure of this recirculation zone are derived using the asymmetric flux model, revealing a novel `lens-tail' structure. Critically, it is seen that a few large particles starting close to the bottom of the flow are swept a long way upstream and take a very long time to recirculate. The breaking size-segregation waves highlight the important interplay between segregation and the bulk velocity field. The properties of flowing monodisperse grains are explored through experiments on a cone that produce a beautiful radial fingering pattern. Equations developed in a conical coordinate system reproduce the measured linear relationship between fingering radius and initial flux, whilst also predicting the slowing and thinning dynamics of the flow. Overall, these results illustrate the complex nature of the granular rheology and provide perspectives for future modelling of segregation in dense granular flows.

Granular materials are used in several industrial processes involving natural and man-made materials at a vast range of length scales, such as mining, extraction, and handling of rocks and sand, as well as in agricultural and pharmaceutical industry. They are also widely adopted in civil and military applications (e.g. earthquakes, penetration of projectiles, stress waves attenuation) because of their ability to dissipate energy and attenuate shock loading. However, despite the wide-spread use, the comprehension of their mechanical behaviour at high strain rates is still limited. The main aim of this research is to provide a better understanding of the mechanics of granular materials and to develop a combined experimental/numerical capability to characterise and simulate the effects of high velocity excitations on the boundaries of granular domains and the consequent motion and deformation at high rates of strain. The achievement of this goal requires the knowledge of both meso-structural properties (i.e. initial density, wetness and confinement conditions) and the effects of micro-scale parameters (i.e. grain sizes and shapes, grains microstructure) upon the behaviour of granular assemblies. For this reason, attention is initially focused on the development of novel algorithms capable of correctly representing real mesostructures of granular materials, and on the estimation of their Representative Volume Elements. Subsequently, high strain rate experiments are conducted for a comprehensive mechanical characterisation of different types of sand and to evaluate the effect of micro-scale phenomena and rate dependency on the mechanical response of granular materials subjected to impact loading. In particular, after having assessed the geometric characteristics of given granular media, modelling tools for the generation of numerical samples that are statistically representative of real granular materials are developed. Two new efficient algorithms for the geometrical packing of spheres, able to concurrently assign total number of particles and radii distributions, are proposed. Then, a novel Voronoi-based method is presented to model a wide range of particles shapes. The obtained polyhedral grains are proved to successfully reproduce the relevant microscopic features of many naturally occurring granular media. The statistically representative packings thus generated are then used in Discrete Element simulations, which are executed to help designing experiments for the characterisation of granular materials at the meso-scale and to establish the dimensions of the Representative Volume Element of the investigated sands to be used in large-scale laboratory tests and multiscale simulations. A comprehensive experimental campaign on both single grains and granular assemblies at meso-scale is executed to gain insight into the complex behaviour of granular materials subjected to high strain rates and to produce valuable data for future calibration and validation of rate dependent constitutive models. The adoption of ad-hoc sample sizes allowed for the achievement of an improved dynamic equilibrium condition and enhanced reproducibility of the results with respect to what existing in literature. Additionally, a deeper understanding of the role of particles fracture on the behaviour of granular materials is gained by exploiting a number of conventional (microscopy) and novel (sound measurements) experimental techniques for in-situ and post-mortem analysis of samples subjected to a wide spectrum of rates of deformation. Finally, once identified - through experiments - the central role of micro-scale phenomena (grains failure) on the mechanical response of sand, a new mass-conserving modelling methodology capable of capturing the grains comminution happening during dynamic loading of granular materials is introduced, thus extending the range of applicability of DEM to dynamic phenomena.

The Discrete Element Method (DEM) has been applied to numerical modelling of the bulk compression of low modulus particulates. An existing DE code for modelling the contact mechanics of high modulus particles using a linear elastic contact law was modified to incorporate non-linear viscoelastic contact, real containing walls and particle deformation. The new model was validated against experimental data from the literature and physical experiments using synthetic spherical particles, apple and rapeseed. It was then used to predict particle deformation, optimum padding thickness in a handling line and bulk compression parameters during oilseed expression. The application of DEM has previously been limited to systems of hard particles of high compressive and shear modulii with relatively low failure strain. Material interactions have therefore commonly been modelled using linear contact law. For high modulus particles, particle shape change resulting from deformation is a not a significant factor. Most agricultural particulates however deform substantially before failure and their interaction is better represented with non-linear hysteretic viscoelastic contact relationship. Deformation of geometrically shaped particles in DEM is usually treated as "virtual" deformation, which means that particles are allowed to overlap rather than deform due to contact force. Change to particle shape has not previously been possible other than in the case of particles modelled as 2-D polygons or where each particle is also modelled concurrently with an FE mesh. In this work a new approach has been developed which incorporates a non-linear deformation dependent contact damping relationship and a shape change while maintaining sufficient geometrical symmetry to allow the problem to be handled by the same DE algorithms as used for true spheres. The method was validated with available experimental results on impact behaviour of rubber and the variations with different damping coefficients were simulated for a selected fruit. A fruit handling process dependent on the impact process was then simulated to obtain data required in the design of a fruit processing line. Changes in shape of spherical synthetic rubber particles and rapeseeds under compression were predicted and validated with physical experiments. Images were taken and analysed using image processing techniques with 1: 1 scaling. The method on shape change entails a number of simplifying assumptions such as uniform stress distribution and homogeneous material properties and uniform material distribution when deformed, which are not observed in real agricultural materials and will tend to overestimate the true contact area between particles. In reality for fruits and vegetables, material redistribution is a complex process involving a combination of compaction and movement. However with the new method a better approximation of bed voidage (which standard DEM approaches underestimate) and stress were obtained in the compression of a synthetic material. This is a significant improvement on existing methods particularly with respect to stress distribution within a bulk particulate system comprising deforming elements where the size and orientation of contact surface between particles has a strong influence on the bulk modulus. The new model was used for prediction of mechanical oil expression in four oilseed beds. Similar patterns in the variation of the characteristic parameters were obtained as observed in existing experimental data. The data could not be matched exactly as the quantity and arrangement of seeds in the initial seedbeds were not the same as those used in the experimental work. However the DE model gave approximate oil point data for seedbeds with the same physical properties and initial conditions as in the experiment. This suggests that the new model may be a useful tool in the study of mechanical seed-oil expression and other agricultural particulate compression processes.

Thesis (PhD (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2004.
Granular flow occurs in a broad spectrum of industrial applications that range from separation and mixing in the pharmaceutical industry, to grinding and crushing, blasting, stockpile construction, flow in and from hoppers, silos, bins, and conveyer belts, agriculture, mining and earthmoving. Two totally different approaches of modelling granular flow are the Discrete Element Method (DEM) and continuum methods such as Finite Element Methods (FEM). Continuum methods can be divided into nonpolar or classic continuum methods and polar continuum methods. Large displacements are usually present during granular flow which, without remeshing, cannot be solved with standard finite element methods due to severe mesh distortion. The Particle-in-Cell (PIC) method, which is a so-called meshless method, eliminates this problem since all the state variables are traced by material points moving through a fixed mesh. The main goal of this research was to model the flow of noncohesive granular material in front of flat bulldozer blades and into excavator buckets using a continuum method. A PIC code was developed to model these processes under plane strain conditions. A contact model was used to model Coulomb friction between the material and the bucket/blade. Analytical solutions, published numerical and experimental results were used to validate the contact model and to demonstrate the code’s ability to model large displacements and deformations. The ability of both DEM and PIC to predict the forces acting on the blade and bucket and the material flow patterns were demonstrated. Shear bands that develop during the flow of material were investigated. As part of the PIC analyses, a comparison between classic continuum and polar continuum (Cosserat) results were made. This includes mesh size and orientation dependency, flow patterns and the forces acting on the blade and the bucket. It is concluded that the interaction of buckets and blades with granular materials can successfully be modelled with PIC. In the cases conducted here, the nonpolar continuum was more accurate than the polar continuum, but the polar continuum results were less dependent on the mesh size. The next step would be to apply this technology to solve industrial problems.

Afin de modéliser le comportement des géométariaux sous des charges complexes, plusieurs études et travaux expérimentaux ont été réalisées afin d’établir des modèles constitutifs relatifs. Une caractéristique importante des matériaux granulaires est que la relation entre la contrainte et la déformation et ce même dans le domaine élastique n’est pas linéaire, contrairement aux réponses du métal. Il a également été constaté que la réponse contrainte-déformation des matériaux granulaires montre les caractéristiques de l’anisotropie induite, ainsi que les non-linéarités. En outre, l’anisotropie induite par la contrainte se produit pendant le processus de chargement sur les sols, par exemple, les charges ou les déplacements. Dans ce travail, un nouveau modèle qui est une combinaison de modèle hyperélastique Houlsby et modèle élastoplastique Plasol a été proposé. Ce nouveau modèle a pris en compte la réponse non linéaire de la contrainte dans le domaine élastique et plastique, et l’élasticité anisotrope a également été bien considérée. En outre, les problèmes de l’écoulement de la déformation plastique a été calibré par un algorithme d’intégration approprié. Plus tard, le nouveau modèle a été vérifié en utilisant la méthode numérique et comparé aux expériences de laboratoire dans des conditions triaxiales axisymmétriques. Les résultats de comparaison ont montré un bon effet de simulation du nouveau modèle qui a juste utilisé un seul ensemble de paramètres pour un sol spécifique dans différentes situations de contraintes. Ensuite, l’analyse de la nouvelle variable interne du modèle, c’est-à-dire l’exposant de pression, a montré que la valeur de l’exposant de pression qui correspond au degré d’anisotropie a eu un effet évident sur la réponse contrainte-déformation. De plus, ce type d’effet est également affecté par la densité et l’état de drainage des échantillons. En s’appuyant sur un nouveau modèle, un facteur de sécurité qui fait référence au critère de travail de deuxième ordre a été adopté et testé dans un modèle axisymétrique et un modèle de pente réel. Il a montré que la valeur négative ou la diminution spectaculaire du travail global normalisé de second ordre se produit lors d’une défaillance locale ou globale avec apparition d’énergie cinétique. Cette caractéristique du travail du second ordre peut également être affectée par l’exposant à pression variable. Enfin, un nouveau modèle a également été comparé à un modèle élastoplastique qui considère à la fois l’anisotropie élastique et la dilatation anisotrope, c’est-à-dire le modèle SANISAND modifié. Les avantages et les inconvénients ont été illustrés dans les résultats de comparaison
In order to model the behavior of geometarials under complex loadings, several researches have done numerous experimental works and established relative constitutive models for decades. An important feature of granular materials is that the relationship between stress and strain especially in elastic domain is not linear, unlike the responses of typical metal or rubber. It has been also found that the stress-strain response of granular materials shows the characteristics of cross-anisotropy, as well as the non-linearities. Besides, the stress-induced anisotropy occurs expectedly during the process of disturbance on soils, for example, the loads or displacements. In this work, a new model which is a combination of Houlsby hyperelastic model and elastoplastic Plasol model was proposed. This new model took into account the non-linear response of stress and strain in both elastic and plastic domain, and the anisotropic elasticity was also well considered. Moreover, the overflow problem of plastic strain in plastic part was calibrated by a proper integration algorithm. Later, new model was verified by using numerical method and compared with laboratory experiments in axisymmetric triaxial conditions. The comparison results showed a good simulation effect of new model which just used one single set of parameters for a specific soil in different confining pressure situations. Then the analysis of new model internal variable, i.e., pressure exponent, illustrated that the value of pressure exponent which corresponds to the degree of anisotropy had an obvious effect on the stress-strain response. Moreover, this kind of effect is also affected by the density and drainage condition of samples. Basing on new model, a safety factor which refers to the second-order work criterion was adopted and tested in axisymmetric model and actual slope model. It showed that the negative value or dramatic decreasing of global normalized second-order work occurs accompanying with a local or global failure with a burst of kinetic energy. This feature of second-order work can also be affected by the variable pressure exponent. At last, new model was also compared with an elastoplastic model which considers both anisotropic elastic and anisotropic dilatancy, i.e., modified SANISAND model. Both advantages and disadvantages were illustrated in the comparison results

L'approche multi-échelle FEMxDEM est une méthode numérique innovante pour les problèmes géotechniques impliquant des matériaux granulaires. La méthode des éléments finis (FEM) et la méthode des éléments discrets (DEM) sont simultanément appliquées à résoudre, respectivement, le problème structurel à la macro-échelle et la microstructure du matériau à la micro-échelle. L'avantage d'utiliser une telle configuration à double échelle est de permettre d'étudier un problème d'ingénierie sans la nécessité de lois de comportement standard, capturant ainsi l'essence des propriétés des matériaux. Le lien entre les échelles est obtenu par homogénéisation numérique, de sorte que la loi de comportement continu numérique et la matrice tangente correspondante sont obtenues directement à partir de la réponse discrète de la microstructure.En règle générale, l'approche FEMxDEM présente quelques inconvénients; la vitesse de convergence et la robustesse de la méthode ne sont pas aussi efficaces que dans les modèles FEM classiques. De plus, le coût de calcul de l'intégration de la micro-échelle et la dépendance du maillage typique de la macro-échelle, rendent l'approche multi-échelle FEMxDEM discutable pour des utilisations pratiques. Le but de ce travail est de se concentrer sur ces questions théoriques et numériques avec l'objectif de rendre l'approche multi-échelle FEMxDEM robuste et applicable à des configurations à l'échelle réelle. Une variété d'opérateurs est proposée afin d'améliorer la convergence et la solidité de la méthode dans un cadre quasi-Newton. L'indépendance de l’intégration des différents points de Gauss et les caractéristiques d’intensivité sur les d'éléments sont exploités par l'utilisation d’une parallélisation en utilisant un paradigme OpenMP. Au niveau macro, une relation constitutive second gradient est mise en œuvre afin d'enrichir la relation de Cauchy de premier gradient apportant indépendance du maillage au modèle.Les améliorations susmentionnées rendent l'approche FEMxDEM compétitive avec les modèles FEM classiques en termes de coût de calcul permettant ainsi d'effectuer des simulations multi-échelle FEMxDEM robustes et indépendantes du maillage, depuis l'échelle du laboratoire (par exemple essaie biaxiale test) jusqu’à celle du problème à l'échelle de l'ingénierie (par exemple, excavation d’une galerie).Mots clés:Double échelle, homogénéisation numérique, loi constitutive numérique, élasto-plasticité, second gradient, matériaux microstructurés, grande déformation, éléments finis, éléments discrets, méthode de Newton, parallélisation, unicité
The multi-scale FEMxDEM approach is an innovative numerical method for geotechnical problems involving granular materials. The Finite Element Method (FEM) and the Discrete Element Method (DEM) are simultaneously applied to solve, respectively, the structural problem at the macro-scale and the material microstructure at the micro-scale. The advantage of using such a double scale configuration is that it allows to study an engineering problem without the need of standard constitutive laws, thus capturing the essence of the material properties. The link between scales is obtained via numerical homogenization, so that, the continuum numerical constitutive law and the corresponding tangent matrix are obtained directly from the discrete response of the microstructure.Typically, the FEMxDEM approach presents some drawbacks; the convergence velocity and robustness of the method are not as efficient as in classical FEM models. Furthermore, the computational cost of the microscale integration and the typical mesh-dependency at the macro-scale, make the multi-scale FEMxDEM approach questionable for practical uses. The aim of this work is to focus on these theoretical and numerical issues with the objective of making the multiscale FEMxDEM approach robust and applicable to real-scale configurations. A variety of operators is proposed in order to improve the convergence and robustness of the method in a quasi-Newton framework. The independence of the Gauss point integrations and the element intensive characteristics of the code are exploited by the use of parallelization using an OpenMP paradigm. At the macro level, a second gradient constitutive relation is implemented in order to enrich the first gradient Cauchy relation bringing mesh-independency to the model.The aforementioned improvements makes the FEMxDEM approach competitive with classical FEM models in terms of computational cost thus allowing to perform robust and mesh-independent multi-scale FEMxDEM simulations, from the laboratory scale (e.g. biaxial test) to the engineering-scale problem, (e.g. gallery excavation).Keywords:Double scale, numerical homogenization, numerical constitutive law, elasto-plasticity, second gradient, microstructured materials, large strain, finite elements, discrete elements, Newton method, parallelization, uniqueness

Offshore on-bottom pipelines are subjected to cycles of thermal and pressure-induced axial expansion, which can cause them to buckle laterally. For an elegant and cost-effective solution, lateral buckling is allowed in a controlled manner. Of the various design parameters, the soil resistance has the greatest associated uncertainty. Previous studies of lateral pipe-soil interaction have used laboratory model tests and continuum-based numerical methods. However, they are economically and computationally expensive, and have mostly been restricted to pipes on undrained clay. To overcome this limitation, this thesis introduces the distinct element method (DEM) as a novel numerical tool for the study of lateral pipe-soil interaction for partially embedded offshore pipelines on sandy seabeds. The DEM directly models the particulate nature of sandy soils, allowing large displacements of discrete bodies and providing insights into the mechanics of the soil at a particle level. Pipe{soil interaction is studied by DEM analyses through four separate research stages: (i) mechanical characterisation of the soil, (ii) specimen preparation and pipeline implementation, (iii) small displacement pipe loading tests and (iv) large displacement pipe loading tests. The soil is modelled as an assembly of spherical particles exchanging contact forces, energy and momentum when they interact. At the microscopic scale, a novel moment-relative rotation contact law is introduced to account for the irregular shape of real sand grains. At a macroscopic scale, the mechanical behaviour of the sand is calibrated using experimental triaxial test data. Additional work includes the numerical preparation of a soil assembly and the implementation of a pipeline object in the open-source DEM code Yade. A novel specimen preparation technique is developed to assemble a homogeneous sample at a desired relative density. The pipeline is implemented as a cylindrical body with a continuously curved surface and a specific mass. Small displacement loading tests are performed, with a segment of the pipeline interacting with a 3D prismatic soil domain, replicating plane strain conditions. The influence of particle size, domain thickness, loading velocity and damping are investigated. The findings provide valuable recommendations for performing DEM simulations of this problem, balancing numerical accuracy and computational effort. Large displacement loading tests are performed to validate the DEM approach and to obtain detailed insights into the nature of the pipe-soil interaction. Monotonic vertical and lateral loading simulations are quantitatively compared with laboratory results. To replicate realistic loading conditions of the pipeline on the seabed, cyclic large displacement tests are also performed. Both the monotonic and the cyclic tests show a good level of agreement with experimental results obtained in previous research. Moreover, the numerical analyses provide insights into the evolution of particle motion and the failure mechanism within the soil.

The research presented in this thesis covers the development, calibration and verification of two thin surfaced unbound granular pavement models: one model to predict the response of a pavement to loading by the monotonic application of a single load event (Response model) and the other model to predict the accumulation of permanent deformation of the pavement when it is subjected to a large number of load applications (Performance model). The response model was developed using the finite element method and used an anisotropic stress dependent stiffness model to represent the granular and subgrade materials. The models were verified with an extensive set of stress, strain and surface deflection measurements collected at the CAPTIF facility. The calibrated models were able to predict the subsurface response of the pavement to a range of dual tyre and FWD load levels (23-72 kN). It was found that the measured stress and strain response of the pavement was different under the two loading mechanisms. It was also found that a particular response at a point in the pavement was linear with respect to load. The performance model was based on similarities observed in the performance of granular materials in both laboratory and full-scale experiments. When the specimen or pavement was showing a steady state response, it was found that the rate of accumulation of permanent deformation was related to the resilient strain. This relationship was then used to predict the deformation of CAPTIF pavements based on the outputs from the response model. The application of laboratory derived models required the use of shift functions to be able to be successfully used in replicating field measurements, this was expected given the differences in boundary conditions and loading mechanisms for the laboratory and field systems.

A research program was undertaken to study the effect of particle size on the mechanical response of granular materials, with particular emphasis on supporting the study of the effect of backfill particle size on the soil-pipe interaction of buried pipelines. In this regard, laboratory one-dimensional compression tests of different-sized glass beads and crushed granite were conducted. One-dimensional compression tests on glass beads were simulated in a numerically equivalent discrete element model (DEM), in order to identify suitable DEM particle stiffness microparameters able to reproduce the corresponding laboratory results. Effects of particle size on bulk material behavior were first studied through the analysis of experimental one-dimensional compression test results of both glass beads and crushed granite. Axial stress-strain response of both materials revealed that an increase in particle size of a granular material matrix increased the stiffness of the overall granular matrix. Results also revealed that smaller particles resulted in higher side wall friction values than larger particles of the same material type. The dependence of constrained modulus and shear modulus on effective confining stress determined experimentally from all laboratory tests were in general agreement with relationships previously proposed by other researchers. Numerical simulations of the laboratory specimens were conducted using DEM; i.e. the numerical models were calibrated against experimental results obtained from one-dimensional compression tests of different-sized glass beads to determine suitable particle stiffness microparameters for granular materials of differing particle sizes. The findings indicated that the numerical value of particle stiffness microparameters increased with increasing particle size. In agreement with the experimental results, DEM results also showed that an increase in particle size resulted in increased stiffness of the overall granular matrix under one-dimensional compression. Through evaluation of numerical results, it was proposed that a preliminary relationship between “average” constrained modulus and particle stiffness could be established. Results indicate that DEM simulations of one-dimensional compression tests can be successfully used to calibrate DEM particle stiffness microparameters. The findings suggest that particle stiffness microparameters should be carefully selected for DEM simulations of granular materials of different-sized particles and, in turn, be utilized in quantitative analysis of geotechnical engineering problems.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

Le travail réalisé durant cette thèse a été motivé par l'étude des mécanismes microscopiques à l'origine du fluage dans les matériaux granulaires.%En particulier, on cherche à explorer des techniques expérimentales et numériques pour l'étude d'un tel phénomène.Dans une première partie, on cherche à mesurer les déplacements des grains dans un matériau granulaire par observations en micro-tomographie X. Une telle identification ne peut être efficacement réalisée pour des phénomènes rapides avec les méthodes classiques de corrélation d'images numériques. Une nouvelle méthode nommée emph{corrélation discrète des projections numériques} qui contourne cette difficulté est développée dans cette thèse. Cette méthode, basée sur la corrélation des projections de tomographie, permet de mesurer les déplacements avec un nombre réduit de projections (100 fois moins que les méthodes classiques), ce qui diminue énormément le temps d'acquisition nécessaire pour la mesure. La méthode, appliquée à des données expérimentales, donne une précision comparable à celles des méthodes classiques tandis que le temps d'acquisition nécessaire est réduit à quelques minutes. Une étude portant sur l'analyse des sources d'erreurs affectant la précision des résultats est également présentée.Le but de la deuxième partie est de réaliser des simulations numériques pour fournir une caractérisation de l'essai oedométrique. Différents assemblages de billes de verre légèrement poly-disperses interagissant à travers des contacts élastiques de Hertz-Mindlin et frottement de Coulomb ont été utilisés. Ces simulations ont permis d'étudier l'évolution de certains paramètres structuraux du matériau modèle, préparant ainsi le terrain pour de futures études sur le fluage. Il a été particulièrement souligné que les contacts élastiques utilisés dans ces simulations ne reproduisent pas l'irréversibilité des déformations observée dans les expériences sur des sables. Cependant, l'irréversibilité est bien visible sur le nombre de coordination et l'anisotropie. Alors que les paramètres élastiques peuvent exprimer la réponse pour des petits incréments de déformations, la compression oedometrique est belle et bien anélastique, principalement à cause de la mobilisation du frottement. Le rapport entre les contraintes horizontales et verticales (coefficient du sol au repos) n'est particulièrement constant que lorsque l'anisotropie de structure est instaurée dans l'état initial de l'assemblage. Il est par ailleurs relié à l'anisotropie interne de la structure par une formule simple. Finalement, les coefficients du tenseur élastique dépendent principalement du nombre de coordination et son anisotropie est plus liée à l'anisotropie des contacts qu'à celle des forces
The present work is motivated by the study of creep in granular materials at the microscopic scale.The first part of this thesis deals with displacement measurements by microtomography. Classical digital image correlation fails to catch time-dependent (possibly fast) phenomena such as short-term creep. A new method named emph{Discrete Digital Projection Correlation} is developed to overcome this limitation. This method requires very few projections (about 100 times less than classical methods) of the deformed state to perform the correlation and retrieve grain displacements. Therefore, the acquisition time is remarkably reduced, which allows to study time-dependent phenomena.The method is tested on experimental data. While its accuracy compares favorably to that of conventional methods, it only requires acquisition times of a few minutes. The origins of measurement errors are tracked by numerical means, on simulated grain displacements and rotations.The second part is a numerical simulation study, by the Discrete Element Method (DEM), of oedometric compression in model granular materials, carried out with a simple model material: assemblies of slightly polydisperse spherical beads interacting by Hertz-Mindlin contact elasticity and Coulomb friction. A wide variety of initial states are subject to compression, differing in density, coordination number and fabric anisotropy. Despite apparently almost reversible strains, oedometric compression proves an essentially anelastic and irreversible process,due to friction, with important internal state changes affecting coordination number and anisotropy. Elastic moduli only describe the response to very small stress increments about well equilibrated configurations. The ratio of horizontal stress to vertical stress (or coefficient of earth pressure at rest, commonly investigated in soil mechanics) only remains constant for initially anisotropic assemblies. A simple formula relates it to force and fabric anisotropy parameters, while elastic moduli are mainly sensitive to the latter. Further studies of contact network instabilities and rearrangements should pave the way to numerical investigations of creep behavior

The shape of particles is known to play an important role in soil behaviour, with significant effects of engineering responses. Investigating how the shape of particles can be measured and quantified is therefore considered increasingly important in modern soil mechanics. This is propelled by the advent of computer based image-analyses and discrete modelling algorithms, which have opened new ways to tackle this problem. This work demonstrates how these two techniques can be made to work together. Image analyses are performed on x-rays micro-tomographs (µ-CT) of triaxial sand specimens, focusing on the characterisation and quantification of particle shapes. Two with very different particle shape sands are studied in details: Caicos ooids (rounded) and Hostun sand (angular). A discrete Digital Volume Correlation (DVC) algorithm is then used to track the kinematics of individual grains (around 50000 for each sand specimen) during the triaxial test and measure, with good precision, their cumulated displacements and rotations. Joint analysis of the shape and kinematic databases acquired is performed to find how particle shape descriptors are related to observed kinematics at the microscale level. It appears that true sphericity is a good predictor of upper bound rotational restraint. Modelling is based on the Discrete Element Method (DEM). Models that introduce rolling resistance at the contact are widely employed in DEM simulations, these approaches offer substantial computational benefits at the prize of increased calibration complexity. In this work, the values of true sphericity obtained by image analysis of the grains, either directly by 3D acquisition or by correlation with simpler to obtain 2D shape measures, are used to establish mechanically equivalent rotational restrictions. An empirical relation between a contact parameter (rolling friction) and a 3D grain shape descriptor (true sphericity is first calibrated - using both specimen-scale and grain scale results from two triaxial tests in Hostun sand and Caicos ooids. It is then validated by simulating other triaxial tests (1) with the same sands, but in different conditions (2) with Ottawa sand, for which 3D grain images were also available for examination, and (3) with Ticino sand, for which only 2D grain images were available. Finally, results of large-scale DEM simulations on the Cone Penetration Test (CPT) - exploiting the new proposed contact model - are presented. Experimental data on the CPT performed in a Calibration Chamber (CC) comprised of Ticino sand are successfully fitted by the numerical penetration curves at different confining pressures and conditions. A parametric study about the influence of particle shape and particle shape variability put in evidence the strong-coupled effects of rolling and frictional resistances at the particles contacts. The work described in this thesis will ease the use of DEM for large-scale simulations of geotechnical engineering problems.
Se sabe que la forma de las partículas juega un papel importante en el comportamiento del suelo, con efectos significativos de las respuestas mecánicas relevantes en ingeniería geotécnica. Por lo tanto, investigar cómo se puede medir y cuantificar la forma de las partículas se considera cada vez más importante en la mecánica del suelo moderna. Esto se acrecienta debido a las técnicas de análisis computacionales de imágenes y algoritmos de modelado discreto (DEM), que han abierto nuevas formas de abordar este problema. Este trabajo demuestra cómo se pueden hacer que estas dos técnicas funcionen juntas. Los análisis de imagen se realizan sobre micro-tomografías de rayos X (µ-CT) de muestras de arena en celdas triaxiales, centrándose en la caracterización y cuantificación de la forma de las partículas. Se estudian en detalle dos arenas con la forma de sus partículas muy diferentes: Caicos ooids (redondeados) y Hostun sand (angular). Luego se utiliza un algoritmo discreto de correlación de volumen digital (DVC) para rastrear la cinemática de granos individuales (alrededor de 50000 por cada muestra de arena) durante la prueba triaxial y medir, con buena precisión, sus desplazamientos y rotaciones acumulados. El análisis conjunto de la forma y las bases de datos cinemáticas adquiridas se realiza para encontrar cómo los descriptores de forma de partículas se relacionan con la cinemática observada a nivel de micro-escala. Resulta que la esfericidad verdadera predice bien el límite superior de rotación de una partícula. La modelización numérica se basa en el Método de Elementos Discretos (DEM). Los modelos que introducen resistencia a la rotación en el contacto se emplean ampliamente en simulaciones DEM, estos enfoques ofrecen beneficios computacionales sustanciales a costa de una mayor complejidad de calibración. En este trabajo, los valores de esfericidad verdadera (i.e., true sphericity) obtenidos mediante análisis de imagen de los granos, ya sea directamente por adquisición 3D o por correlación con medidas de forma 2D más simples, se utilizan para establecer restricciones de rotación mecánicamente equivalentes. Una relación empírica entre un parámetro de contacto (rolling friction) y un descriptor de forma de grano 3D (la esfericidad verdadera) se calibra primero, utilizando los resultados de la escala de muestras y de la escala de granos de dos pruebas triaxiales en las arenas de Hostun y de Caicos. Luego se valida simulando otras pruebas triaxiales (1) con las mismas arenas, pero en diferentes condiciones (2) con arena de Ottawa, para la que también estaban disponibles imágenes 3D de granos para su examen, y (3) con arena de Ticino, para la cual solo estaban disponibles imágenes 2D de los granos. Finalmente, se presentan resultados de simulaciones DEM a gran escala de la prueba de penetración de cono (CPT), aprovechando el nuevo modelo de contacto propuesto. Los datos experimentales del CPT realizado en una cámara de calibración (CC) sobre arena de Ticino se ajustan con éxito por las curvas de penetración numérica a diferentes presiones y condiciones de confinamiento. Un estudio paramétrico sobre la influencia de la forma de las partículas y la variabilidad de las formas de las partículas puso de manifiesto los efectos fuertemente acoplados de las resistencias rotacional y friccional en los contactos entre partículas. El trabajo descrito en esta tesis facilitará el uso de DEM para simulaciones a gran escala en problemas de ingeniería geotécnica.

Granular materials are very common both in nature and in industry, and their extensive use means that there are financial incentives for increased efficiency. There are huge costs related to their use and handling, which is a major motivation for increased knowledge of the behaviour of granular materials at different loading conditions. The development of tools for numerical simulation of granular materials at diverse flow conditions gives the opportunity to study and optimise various industrial processes. In order for such tools to be trustworthy, calibration and validation against experimental results is essential. Thus, experimental methods for accurate measurement and characterisation of granular material flow are required. The objective of this thesis is to contribute to the knowledge of experimental characterisation and numerical modelling of non-cohesive, dry granular materials, at dissimilar flow conditions. In order to fulfil this objective, an experimental method, able to capture the flow behaviour of granular materials is developed. The method is based on the digital image correlation technique, and it is used for field measurements of displacement and velocity. The devised method is used to obtain field measurements for the flow of sand, tungsten carbide powder and potassium chloride. For modelling and simulation, the smoothed particle hydrodynamics (SPH) method, and a pressure-dependent, elastic-plastic constitutive model are used. In this thesis, experimental characterisation and numerical modelling of granular material flow is performed in a number of applications. An experimental powder filling rig is used to study the flow during filling of sand into a die. A high-speed digital camera is used to record the flow, and the digital image correlation technique is used to obtain field measurements during the filling. This method is also applied in another experimental setup, where flow during filling of spherical tungsten carbide powder into a die is studied. The filling of tungsten carbide powder is simulated using the SPH method, and the results are compared to the field measurements with good agreement. Furthermore, the flow of potassium chloride is studied experimentally in the collapse of a granular column and in the discharge from a flat bottomed silo. The material flow process in both the column collapse and silo discharge are simulated using the SPH method. The results from simulations are found to be in agreement with observations reported in literature, and with experimental measurements obtained in this work. In conclusion, an experimental method for characterising granular material flow through field measurements is presented. The method is used to support the exploration of numerical tools for modelling and simulation of granular material flow. Furthermore, the high accuracy field measurements are used for improved calibration and validation of numerical methods. Reliable numerical simulations allows for study of the mechanisms that are present during granular material flow, mechanisms that might be hard or even impossible to investigate experimentally. The work within the present thesis contributes to the knowledge of both experimental characterisation and numerical modelling of granular material flow.

The aim of this work is to present a new procedure for modelling industrial processes that involve granular material flows, using a numerical model based on the Particle Finite Element Method (PFEM). The numerical results herein presented show the potential of this methodology when applied to different branches of industry. Due to the phenomenological richness exhibited by granular materials, the present work will exclusively focus on the modelling of cohesionless dense granular flows. The numerical model is based on a continuum approach in the framework of large-deformation plasticity theory. For the constitutive model, the yield function is defined in the stress space by a Drucker-Prager yield surface characterized by two constitutive parameters, the cohesion and the internal friction coefficient, and equipped with a non-associative deviatoric flow rule. This plastic flow condition is considered nearly incompressible, so the proposal is integrated in a mixed formulation with a stabilization of the pressure term via the Polynomial Pressure Projection (PPP). In order to characterize the non-linear dependency on the shear rate when flowing a visco-plastic regularization is proposed. The numerical integration is developed within the Impl-Ex technique, which increases the robustness and reduces the iteration number, compared with a typical implicit integration scheme. The spatial discretization is addressed within the framework of the PFEM which allows treating the large deformations and motions associated to granular flows with minimal distortion of the involved finite element meshes. Since the Delaunay triangulation and the reconnection process minimize such distortion but does not ensure its elimination, a dynamic particle discretization of the domain is proposed, regularizing, in this manner, the smoothness and particle density of the mesh. Likewise, it is proposed a method that ensures conservation of material or Lagrangian surfaces by means of a boundary constraint, avoiding in this way, the geometric definition of the boundary through the classic a-shape method. For modelling the interaction between the confinement boundaries and granular material, it is advocated for a method, based on the Contact Domain Method (CDM) that allows coupling of both domains in terms of an intermediate region connecting the potential contact surfaces by a domain of the same dimension than the contacting bodies. The constitutive model for the contact domain is posed similarly to that for the granular material, defining a correct representation of the wall friction angle. In order to validate the numerical model, a comparison between experimental results of the spreading of a granular mass on a horizontal plane tests, and finite element predictions, is carried out. These sets of examples allow us validating the model according to the prediction of the different kinematics conditions of granular materials while spreading ¿ from a stagnant condition, while the material is at rest, to a transition to a granular flow, and back to a deposit profile. The potential of the numerical method for the solution and optimization of industrial granular flows problems is achieved by focusing on two specific industrial applications in mining industry and pellet manufacturing: the silo discharge and the calculation of the power draw in tumbling mills. Both examples are representative when dealing with granular flows due to the presence of variations on the granular material mechanical response.
El objetivo principal de este trabajo es presentar una nueva metodología para la simulación de procesos industriales que involucren flujos de materiales granulares, mediante un modelo numérico basado en el Método de Elementos Finitos de Partículas (PFEM, por sus siglas en inglés). Los resultados numéricos que se presentan en este documento, muestran el potencial de aplicar esta metodología a diferentes ramas de la industria. Debido a la riqueza fenomenológica exhibida por los materiales granulares, el presente trabajo se centrará exclusivamente en la simulación de flujos granulares densos sin cohesión. El modelo numérico se basa en un enfoque del medio continuo, en el marco teórico de plasticidad en grandes deformaciones. Para el modelo constitutivo, la función de fluencia se define en el espacio de tensiones mediante una superficie de fluencia del tipo Drucker-Prager caracterizada por dos parámetros constitutivos, la cohesión y el coeficiente de fricción interna, y equipado con una regla de flujo desviadora no asociada. Esta condición de flujo plástico se considera incompresible, por lo que se propone su integración mediante una formulación mixta del tipo u- p y estabilizando la expresión de la presión a través de una proyección polinomial (Polynomial Pressure Projection, PPP). A su vez, se propone una regularización visco-plástica con el fin de caracterizar la no linealidad de la velocidad de cizallamiento del material cuando fluye. La integración numérica se desarrolla en el marco de la técnica Impl-Ex, aumentando la robustez y reduciendo el número de iteraciones, en comparación con un esquema típico de integración implícito. La discretización espacial se aborda en el marco del PFEM, permitiendo el manejo de grandes deformaciones y del movimiento asociado a los flujos granulares con una distorsión mínima de las mallas de elementos finitos. La triangulación de Delaunay y el proceso de reconexión minimizan tales distorsiones pero no aseguran su eliminación; por esto, se propone una discretización en partículas del dominio dinámica y constante, regularizando de esta manera, la suavidad y la densidad de las partículas en la malla. Asimismo, se propone un método para asegura la conservación de las superficies materiales o Lagrangeanas por medio de una restricción de la frontera, evitando de esta manera, su definición geométrica a través del método clásico alpha-shape. Para el modelado de la interacción entre el material granular y las superficies de su confinamiento, se apuesta por un método basado en el Contact Domain Method (CDM) que permite el acoplamiento de ambos dominios en términos de una región intermedia que conecta las superficies potenciales de contacto – siendo este dominio de la misma dimensión que los cuerpos en contacto. El modelo constitutivo a emplear para el dominio de contacto se plantea de manera similar al del material granular, definiendo una correcta representación del ángulo de pared. Con el fin de validar el modelo numérico, se llevó a cabo una comparación entre los resultados experimentales de la difusión o desmoronamiento de una masa granular en un plano horizontal y las predicciones obtenidas mediante la simulación por medio de elementos finitos. Este conjunto de ejemplos nos permite validar el modelo de acuerdo a la predicción de las diferentes condiciones de la cinemática de los materiales granulares: desde una condición de confinamiento, con el material en reposo, a una transición hacia el flujo granular y de nuevo, a un estancamiento del material hasta definir su depósito final. El potencial del método numérico, para la solución y optimización de los problemas industriales que involucran flujos granulares, se logra enfocándose en dos aplicaciones industriales específicas en la industria minera y la fabricación de pellets: la descarga de un silo y el cálculo del consumo de energía en molinos rotacionales (tumbling mills). Ambos ejemplos son representativos en cuanto a los flujos granulares en la industria debido a la presencia de variaciones en la respuesta mecánica del material granular.

In dieser Dissertation wird erstmalig ein theoretisches Fundament zur Beschneiung virtueller Szenen entwickelt. Das theoretische Fundament wird als analytisches Modell in Form einer Diffusionsgleichung formuliert. Aus dem analytischen Modell lässt sich eine Gruppe von Algorithmen zur Beschneiung virtueller Szenen ableiten. Eingehende Voruntersuchungen zur allgemeinen Modellierung natürlicher Phänomene in der Computergraphik sowie eine Klassifikation der bestehenden Literatur über mathematische Schneemodellierung bilden den Anfang der Arbeit. Aus der umfassenden Darstellung der Eigenschaften von Schnee, wie er in der Natur vorkommt, ergeben sich die Grundlagen für die Modellbildung. Die Modellbildung fußt auf den grundlegenden Ansätzen der klassischen Mechanik und der statistischen Physik. Für die Beschneiung auf visueller Skala erweist sich der Diffusionsprozess als geeignete Beschreibung. Mit der Beschreibung lassen sich diffusiv Schneeoberflächen erzeugen. Der konkrete computergraphische Wert des theoretischen Fundaments wird anhand zweier Implementierungen exemplarisch dargestellt, und zwar in der Distanzfeldmethode und der Diffusionskernmethode. Die Ergebnisse werden mithilfe dreidimensionaler Rauschtexturen und Alpha-Masken an den Rändern fotorealistisch visualisiert
In this dissertation for the first time a theoretical foundation is developed for snow accumulation in virtual scenes. The theoretical foundation is formulated in an analytical model as diffusion equation. The analytical model leads to a group of algorithms for virtual snow accumulation. Comprehensive investigations for the modelling of natural phenomena in computer graphics in general are used to develop a method classification scheme. Another classification is given for an overview over the aspects of snow in the real world. This allows an efficient presentation of related literature on snow modelling. A new approach of snow modelling is then drawn from first principles of classical mechanics and statistical physics. Diffusion processes provide an efficient theoretical framework for snow accumulation. The mathematical structure of diffusion equations is discussed and demonstrated to be adequate to snow modelling in visual scales. The value of the theoretical foundation for computer graphics is demonstrated with two exemplary implementations, a distance field method and the diffusion kernel method. Results are visualized with 3D noise textures and alpha masks near borders delivering photorealistic snow pictures

Ces derniers années ont vu le développement de nombreux travaux de recherche portant sur la modélisation du comportement des matériaux granulaires à partir d'approches de type micromécanique. Ces approches doivent permettre de relier deux échelles à priori bien distinctes : celle du grain et des contacts, et celle du milieu granulaire dans son ensemble. Elles cherchent ainsi à décrire, contrairement aux modèles phénoménologiques, le comportement des matériaux granulaires à partir de considérations simples sur la physique du contact interparticulaire. L'objectif principal de cette étude est l'amélioration de ces modélisations en réalisant une analyse de certains phénomènes locaux, généralement négligés dans les modélisations actuelles. Pour mener à bien ces travaux, deux types d'approches ont été utilisés : - une approche théorique, par homogénéisation statistique fondée principalement sur la variable orientation du contact ; - une approche numérique, par utilisation d'un code de calcul basé sur la méthode des éléments discrets (PFC2D). Ces deux approches, totalement complémentaires, ont été la clé de voûte de ce travail de recherche, par une comparaison continuelle de celles-ci. Ce travail vise à analyser et améliorer trois axes de l'approche micromécanique : - la cinématique des matériaux granulaires, avec pour objectif l'étude des liens entre les cinématiques locales (roulement, glissement et déplacement des particules qui ne sont pas en contact) et le tenseur de déformation ; - l'influence des couples de contact sur le comportement microscopique et macroscopique, ainsi que l'intérêt de leur prise en compte dans les modélisations micromécaniques ; - l'étude de la rupture des milieux granulaires cimentés, avec pour objectif la détermination des propriétés macroscopiques de rupture, à partir des paramètres du comportement microscopique
Many works concerning the behaviour of granular materials based on micromechanical approaches have been proposed during the last years. These approaches connect two very different scales : the first one concerns grain and contacts, and the second one concerns the representative volume of a granular material. In opposition to phenomenological models, micromechanical approaches try to describe the behaviour of granular materials based on simple concepts relevant of the local phenomena. The main objective of this study is the improvement of a model based on the micromechanical approach, focusing on some local phenomena, generally neglected in a classical approach. In order to do this, two kinds of approaches have been used : - a theoretical one using a statistical homogenization approach mainly based on orientation of a contact variable ; - a numerical one using a software (PFC2D) based on the Discrete Element Method. A constant comparison of the above two approaches is a key ingredient of this work. This work aims to analyse and improve three topics of micromechanical approach : - the granular materials kinematics : the goal is the study of relations between local kinematics (rolling, sliding and displacements of particles which are not in contact) and strain tensor ; - the influence of contact couples on the microscopic and macroscopic behaviour, as well as the interest of taking them into account in micromechanical approaches ; 0 the study of cemented granular materials rupture : the aim is the definition of macroscopic parameters for rupture from local microscopic characteristics

A new dynamic service model based on granular material rheology is presented. The service model is coupled to both a mixed-layer ocean model and a 1-layer thermodynamic atmospheric model which allows for an ice-albedo feedback. Land is represented by a 6-meter thick layer with a constant base temperature. A 10-year integration including both thermodynamic and dynamic effects and incorporating prescribed climatological wind stress and ocean current data was performed in order for the model to reach a stable periodic seasonal cycle. The commonly observed lead complexes, along which sliding and opening of adjacent ice floes occur in the Arctic sea-ice cover, are well reproduced in this simulation. In particular, shear lines extending from the western Canadian Archipelago toward the central Arctic, often observed in winter satellite images, are present. The ice edge is well positioned both in winter and summer using this thermodynamically coupled ocean-ice-atmosphere model. The results also yield a sea-ice circulation and thickness distribution over the Arctic which are in good agreement with observations. The model also produces an increase in ice formation associated with the dilatation of the ice medium along sliding lines. In this model, incident energy absorbed by the ocean melts ice laterally and warms the mixed layer, causing a smaller ice retreat in the summer. This cures a problem common to many existing thermodynamic-dynamic sea-ice models.
The origin and space-time evolution of Beaufort Sea ice anomalies are studied using data and the sea-ice model described above. In particular, the influence of river runoff, atmospheric temperature and wind anomalies in creating anomalous sea ice condition in the Beaufort Sea is studied. The sea-ice model is then used to track the position of an ice anomaly as it is transported by the Beaufort Gyre and the Transpolar Drift Stream out of the Arctic Basin.
It can be inferred from driftwood data collected in the Canadian Arctic Archipelago that very different sea-ice drift patterns were present in the Arctic Ocean during the Holocene. In this study, the sea-ice model described above is used to examine the different modes of Arctic sea-ice circulation during this period, and also to infer characteristics of century-to-millennial scale changes in Arctic atmospheric circulation. (Abstract shortened by UMI.)

This thesis, at the interface between the scientific disciplines of planetary science and granular physics, has two key components, both of which intend to increase our understanding of granular dynamics in varying gravitational conditions. The dynamics of granular materials are involved in the evolution of solid planets and small bodies in our Solar System, whose surfaces are generally covered with regolith. Understanding granular dynamics is also critical for the design and/or operations of landers, sampling devices and rovers to be included in space missions. The first component of this thesis is the validation of the hard-sphere discrete element method implementation in the N-body code pkdgrav to model the dynamics of granular material. By direct comparison with results from laboratory experiments, it is demonstrated that the hard-sphere discrete element method implementation in pkdgrav is valid for modelling granular material in dilute regimes and is capable of reproducing the complex dynamical behaviour of a specific dense system as well. The second component is focussed on the AstEx parabolic flight experiment. This experiment, with the aim of characterising the response of granular material to rotational shear forces in a microgravity environment, was designed, constructed, flown and the data were analysed as part of this thesis. It was found that the effect of constant shearing on a granular material in a direction perpendicular to the gravity field is not strongly influenced by gravity. The AstEx experiment has demonstrated, for the first time, that the efficiency of granular convection may decrease in the presence of a weak gravitational field, similar to that on the surface of small bodies. The first measurements of transient weakening of granular material after shear reversal in microgravity are also reported. Results suggest that the force contact network may be weaker in microgravity, although the influence of any change in the contact network is felt by the granular material over much larger distances. This may have important implications for our interpretation of asteroid surfaces. Continued advancement of our understanding of granular materials in varying gravitational conditions requires futher experiments and the development of the soft-sphere discrete element method implementation in pkdgrav in order to model the granular regimes that are inaccessbile to the hard-sphere implementation.

La prédiction de trajectoire de bloc et la conception de structures de protection sont deux des questions principales de l'ingénierie des chutes de pierres. La prédiction de la trajectoire d'un bloc dépend en grande partie des rebonds de ce bloc tandis que la conception de structures de protection, comme des remblais, est étroitement liée à la force d'impact sur le bloc.En se basant sur ce contexte, la thèse traite aussi bien de l'interaction entre un bloc et un milieu granulaire que des rebonds d'un bloc sur un milieu granulaire, en utilisant une modélisation numérique par la méthode des éléments discrets. L'objectif de la thèse est d'identifier et de mesurer les mécanismes qui contrôlent le rebond du bloc et le transfert de charge à l'intérieur du milieu impacté. Le contenu principal comprend trois parties: la modélisation DEM du processus d'impact, le rebond du bloc et le comportement micromécanique du milieu impacté.La loi de contact classique est utilisée pour modéliser le processus d'impact. Elle est mise en œuvre avec une résistance aux roulements pour considérer les effets de forme des particules et est calibrée par des tests triaxiaux quasi-statiques. Le bloc est modélisé par une sphère avec une vitesse d'incident tandis que le milieu est modélisé par un assemblage de particules sphériques poly-dispersées. La modélisation numérique de l'impact est validé en termes de force d'impact, de durée d'impact et de profondeur de pénétration par des expériences de la littérature.Le rebond du bloc et le processus de propagation d'énergie à l'intérieur du milieu impacté sont examinés ensemble. La résistance du milieu pendant l'impact est représentée par l'énergie de tension élastique. La résistance du milieu n'est pas constante car l'augmentation d'énergie de tension élastique est suivie par l'augmentation d'énergie cinétique, la dissipation d'énergie et par la diminution du nombre de coordination. L'occurrence du rebond du bloc obtenue avec des simulations 3D montre que trois régimes d'impact existent, ce qui est en accord avec les résultats de citet{Bourrier_2008}. De plus, la comparaison entre les diagrammes d'occurrence de rebond 2D et 3D montre que les positions et les formes des diagrammes d'occurrence de rebond changent en raison de résistances et de dissipations d'énergie différentes. En se basant sur les deux aspects de l'étude, la relation entre le rebond du bloc et la propagation d'énergie à l'intérieur du milieu est discutée.Le comportement micromécanique du système impacté est examiné en se focalisant sur les mécanismes des chaînes de force. Le réseau de chaînes de force dans le milieu impacté est caractérisé à partir des tensions entre les particules. L'objectif est d'identifier le rôle des chaînes de force dans la force d'impact sur le bloc et dans la microstructure du milieu. En étudiant la force d'impact sur le bloc avec des impacts sur des échantillons de grains de tailles différentes montre que l'échantillon composé de grands grains a une plus grande force d'impact, des chaînes de force plus longues comparées à l'épaisseur du milieu ainsi qu'un grand pourcentage de chaînes de force avec une longue durée de vie. De plus, l'étude de la distribution spatiale et temporelle des chaînes de force montre que la résistance du milieu pendant l'impact est portée par les particules des chaînes situées entre le bloc et la base du milieu impacté et que la propagation des chaînes de force dans la direction latérale joue un rôle secondaire. Enfin, l'étude des mécanismes du flambage des chaînes de force indique que, provoqués par les mouvements entre les particules de la chaîne, l'augmentation de nombre de flambages est liée à la diminution de la force d'impact sur le bloc ainsi qu'à l'augmentation de l'énergie cinétique et de la dissipation d'énergie à l'intérieur du milieu
The prediction of boulder trajectory and the design of protection structures are particularly two main interests of rockfall engineering. The prediction of boulder trajectory largely depends on the bouncing of the boulder, and the design of protection structures, such as embankments, are closely related to the impact force on the boulder.Based on this background, the thesis deals with the interaction between a boulder and a granular medium as well as the bouncing of a boulder on a granular medium, through numerical modelling based on discrete element method. The objective of the thesis is to identify and quantify the mechanisms that governs the bouncing of boulder and the load transfer inside the impacted medium. The main contents include three parts: DEM modelling of the impact process, global bouncing of the boulder and micromechanical behaviour of the impacted medium.The classical contact law implemented with rolling resistance to consider particle shape effects calibrated based on quasi-static triaxial tests is used to model the dynamic impact process. The boulder is modelled as a single sphere with an incident velocity, the medium is modelled as an assembly composed of poly-disperse spherical particles. The numerical impact modelling is validated in terms of impact force, impact duration, penetration depth by experiments from literature.Bouncing of the boulder is investigated together with the energy propagation process inside the impacted medium. The strength of the medium during impact is represented by elastic strain energy, while the strength of the medium is not persistent since the increase of elastic strain energy is followed by the increase of kinetic energy and energy dissipation, as well as the decrease of the coordination number. Boulder's bouncing occurrence obtained based on 3D simulations shows that three impact regimes exist, which is consistent with the results of citet{Bourrier_2008}. In addition, comparison between 2D and 3D bouncing occurrence diagrams shows that the positions and shapes of bouncing occurrence diagrams shift due to the different strength and energy dissipation properties. Based on the two aspects of investigations, the relation between the bouncing of the boulder and the energy propagation inside the medium is discussed.The micromechanical behaviour of the impacted system is investigated by focusing on force chain mechanisms. The force chain network in the impacted medium is characterized based on particle stress information. The aim is to find the role of force chains in the strength and the microstructure of the medium. Investigations of the impact force on the boulder by impacting samples composed of different grain sizes shows that sample composed of big grains resulting in a larger impact force, longer force chains compared with the medium thickness, and large percentage of long age force chains. In addition, the spatial and temporal distribution of force chains are investigated and the results show that the strength of the medium under impact is built by chain particles located between the boulder and the bottom boundary, and the force chain propagation in the lateral direction of the medium plays a secondary role. Moreover, the investigation of force chain buckling mechanisms indicates that, triggered by the relative movements between the chain particles, the increase of buckling number is related to the decrease of impact force on the boulder as well as the increase of kinetic energy and energy dissipation inside the medium

L’érosion constitue le principal risque auquel sont soumis les ouvrages hydrauliques en terre. Il est donc crucial de quantifier l’érodabilité des sols et plusieurs essais d’érosion ont été mis au point dans ce but. Cependant, leurs modèles d’interprétation sont assez simplistes et des incohérences peuvent être constatées. Malgré plusieurs études expérimentales sur le sujet, les mécanismes d’érosion à l’échelle des grains restent encore mal compris. Dans cette thèse, la méthode numérique LBM-DEM a été mise en œuvre afin d’analyser l’érosion à l’échelle du grain. La cohésion du sol est prise en compte par une loi de contact adaptée incluant éventuellement un modèle d’endommagement dépendant du temps. Une parallélisation GPU a permis en outre d’améliorer la vitesse de calcul et l’efficacité du code. Après une analyse préalable d’un jet impactant laminaire 2D, la pertinence du critère classique de Shields pour les échantillons sans cohésion a d’abord été confirmée avant qu’une généralisation de ce critère ne soit proposée pour les sols faiblement cohésifs avec un accord très satisfaisant. Enfin, le modèle d’interprétation classique de l’essai JET a été adapté à notre problématique afin d’analyser et discuter de façon critique les paramètres d’érodabilité. Enfin, une configuration mieux contrôlée d’écoulement tangentiel à contrainte de cisaillement constante a été étudié, permettant de suggérer une loi de puissance, et non linéaire, pour décrire l’érosion à l’échelle de l’échantillon. Une étude paramétrique sur la cohésion inter-particulaire et la taille des grains a finalement été menée, afin d’examiner le lien entre les paramètres micro et macro
Hydraulic earthworks are frequently subjected to erosion-induced failure as reported in the literature. Accordingly, several erosion tests have emerged to quantify soil’s erodibility. However, they are based on simplified interpretation models and may lead to some inconsistencies. Despite several experimental investigations on the subject, there is still a lack of understanding of the erosion mechanisms taking place at the grain level. To this end, the LBM-DEM method is used in the present study to analyze numerically the erosion phenomena at the grain scale, with the addition of a cohesion model, including a time-dependent damage law. The computational speed and the efficiency of the code was significantly improved here using GPUs parallelization techniques. Next, after a preliminary analysis of 2D laminar impinging jet flow, the relevance of the classical Shields criterion for cohesion-less samples was first recovered, followed by a proposed generalization of this criterion for weakly cohesive soils with satisfactory agreement. Lastly, an adaptation of the classical JET interpretation model was proposed to our 2D laminar problematic and the erodibility parameters were subsequently quantified and critically discussed. Finally, a constant shear-driven fluid flow configuration at the upper surface of a sample was alternatively studied. A power law function was found to be best suited than the usual linear relation to account for the erosion law at sample scale. A parametric study on inter-particle cohesion and grain size was next performed to investigate the link between micro and macro parameters

Soft soil reinforcement by inclusion is a growing technique caracterized by a pile grid and a granular embankment introduced between the reinforced soil and the structure. Unlike traditionnal methods, the load is partially transferred to the pile heads by arching in the embankment. The application area of this research focuses on the shallow foundations case, in which the thickness of the embankment is small. The litterature review shows that only a few studies were dedicated to that case, and that fundamental questions remains concerning the load transfer in the embankment. Chosen method for this research consists in two-dimensionnal physical modelling, analysis of the conducted simulations, and development of an analytical model in order to predict the load transfer to the piles by arching in the embankment. The results of this PhD thesis provide original elements of evidence of the load transfer in the studied system, proposes an analytical model based on block division of the granular embankment by shear bands - which is in good agreement with experimental data - and lead to a better understanding of arching in soils.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Crack damages due to load application are commonly observed in cementitious granular materials such as concrete, cemented sand, and ceramic materials. Previous analytical models for these types of materials have been developed based on continuum mechanics using a phenomenological approach. However, the theories of continuum mechanics have limitations when used for analyzing fracture mechanism and localized damages at a micro-scale level. Therefore, a microstructural approach is desirable for the analysis of these types of materials. In this dissertation, a contact law was derived for the inter-particle behavior of two particles connected by a cement binder. Microcracking process within binder was fully taken into account by regarding crack length as a basic damage factor. The binder initially contains small-size cracks which propagate and grow under external loading. As a result the binder is weakened with lower strength in shear and tension. Theory of fracture mechanics was employed to model the propagation and growth of these microcracks for both the shear fracture mode and normal fracture mode. The contact law was then incorporated in the analysis for the overall damage behaviors of cementitious granular material using the statistical micromechanics approach and the distinct element method. These overall damage behaviors include the stress-strain relationship, fracture strength, development of damage zone, and fatigue deformation. The micro-parameters affecting these behaviors are mainly the microcrack length and density, binder toughness, and binder elastic constants. In the numerical simulations, the cementitious granular materials were represented by 2-D random assemblies of rods bonded by cement binders with preexisting microcracks. Stress-strain relationships were modeled and validated for the uniaxial tension and compression tests, biaxial tension and compression tests, and double cantilever beam test. Force-deflection relationship and fatigue deformation were predicted and validated for the three-point beam tests. The validations tests showed good agreement between the results of numerical simulations and that obtained from available experimental tests. It has been indicated that the proposed models are capable of modeling the mechanical behaviors of cementitious granular materials.

Laboratory characterization of subgrade soils and unbound granular materials is an essential component of the Mechanistic-Empirical Pavement Design Guide (Pavement ME). The design thickness and performance of a pavement structure are highly dependent on the deformation behaviour of subgrade and granular material. Specifications for granular materials vary among transportation agencies based on the availability of materials, climatic conditions, and function. Specifications aim to provide durable materials that meet design requirements and achieve the target design life with cost effective materials. The objectives of the research are to: • evaluate resilient modulus of typical fine-grained soils under traffic loading. • evaluate resilient modulus, permanent deformation, and permeability of typical unbound granular materials. • evaluate the effect of moisture and fines fraction on the performance of unbound granular materials and subgrade soil. • develop prediction models for resilient modulus to improve reliability of Level 2 inputs in the Pavement ME. • provide test data in support of updating Manitoba Infrastructure and Transportation specifications for unbound granular materials to improve the performance of pavement structures. Resilient modulus tests were conducted on three types of subgrade soil (high plastic clay, sandy clay, and silty sand/sandy silt) at four levels of moisture content. Resilient modulus, permanent deformation and permeability tests were conducted on six gradations representing two types of granular material (100% crushed limestone and gravel) at two levels of moisture content. Prediction models were developed for resilient modulus and compared to the models developed under the Long Term Pavement Performance program. The proposed models provided more reliable predictions with lower root mean square error. The deformation behaviour of the granular materials was classified according to the shakedown and dissipated energy approaches. Among the tested fines contents, limestone and gravel materials with optimum fines contents of 4.5% and 9%, respectively, had better resistance to plastic deformation and higher resilient modulus. The dissipated energy approach can be used to determine the stress ratio for the boundary between post compaction and stable zones from multistage triaxial testing. Result of permeability tests showed that the hydraulic conductivity of unbound granular material increased as the fines content decreased.
February 2016