The emphasis of this dissertation is on using numerical and plasticity based methods to study two main areas of offshore geotechnics. The first part of this dissertation focuses on the undrained behavior of deeply embedded anchor plates under combined shear and torsion. Plate anchors are increasingly being used instead of typical foundation systems to anchor offshore floating platforms to sustain uplift operating forces. However extreme loading cases would create general loading conditions involving six degrees of freedom. The focus of my research was to evaluate the bearing capacity of plate anchors under two-way horizontal and torsional loading and to study the decreasing effect of torsional moment on the horizontal bearing capacity of these foundations. The study takes advantage of several approaches: Numerical simulation (two and three dimensional finite element analysis) Evaluating and modification of the available plasticity solutions Developing equations for three degree-of-freedom yield locus surfaces The same methodology is applied to evaluate the response of shallow foundations for subsea infrastructure subjected to significant eccentric horizontal loads. The second part of this study focuses on offshore geohazards. Coastal communities and the offshore industry can be impacted directly by geohazards, such as submarine slope failures, or by tsunamis generated by the failed mass movements. This study aims at evaluating the triggering mechanisms of submarine landslide under cyclic wave and earthquake loading. A simple effective stress elasto-plastic model with a minimal number of parameters accounting for monotonic and cyclic response of fine-grained material is developed. The new constitutive soil model could be used to simulate case histories and conduct parametric study to evaluate the effect of slope inclination angle, the earthquake loading with different PGA, frequency content, and duration, as well as various deposition rates to simulate different over pressure levels. This study will generate more insight on the static and cyclic behavior of submarine slopes and influencing factors on their triggering mechanisms using more comprehensive and realistic modeling tools. Several objectives are defined: Developing an appropriate constitutive formulation, Evaluating the constitutive model and material parameters for available databases.

Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants et des plus importants de l'analyse mathématique ; à savoir qu'une fonction à variation bornée est dérivable presque partout. Le but de ce travail est de fournir, à part la démonstration souvent proposée dans les cours de la théorie de la mesure, d'autres démonstrations élaborées avec des outils mathématiques plus simples. Ma contribution a consisté essentiellement à détailler et à compléter ces démonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité. Nous allons maintenant, pour ce théorème qui se présente sous d'autres variantes, en proposer l'historique et trois démonstrations différentes. / In this dissertation, we will be handling a theorem of Lebesgue, one of the most stricking and ultimate of mathematical analysis ; namely a function with bounded variation has a derivative almost everywhere. The aim of our research is to provide, apart from the proof usually offered in measure theory courses, other demontrations achieved with more simple mathematical tools. My contribution was primarily to simplify and to complete these demonstrations, to include the most of the drawings in order to visualize what is being said. For this theorem, which has other presentations, we will give now the history and three different demonstrations.

The thesis consist of three independent parts. In the first part, we investigate the height sequence of an element of a partially ordered set. Let $x$ be an element of the partially ordered set $P$. Then $h_i(x)$ is the number of linear extensions of $P$ in which $x$ is in the $i$th lowest position. The sequence ${h_i(x)}$ is called the height sequence of $x$ in $P$. Stanley proved in 1981 that the height sequence is log-concave, but no combinatorial proof has been found, and Stanley's proof does not reveal anything about the deeper structure of the height sequence. In this part of the thesis, we provide a combinatorial proof of a special case of Stanley's theorem. The proof of the inequality uses the Ahlswede--Daykin Four Functions Theorem. In the second part, we study two classes of segment orders introduced by Shahrokhi. Both classes are natural generalizations of interval containment orders and interval orders. We prove several properties of the classes, and inspired by the observation, that the classes seem to be very similar, we attempt to find out if they actually contain the same partially ordered sets. We prove that the question is equivalent to a stretchability question involving certain sets of pseudoline arrangements. We also prove several facts about continuous universal functions that would transfer segment orders of the first kind into segments orders of the second kind. In the third part, we consider the lattice whose elements are the subsets of ${1,2,ldots,n}$. Trotter and Felsner asked whether this subset lattice always contains a monotone Hamiltonian path. We make progress toward answering this question by constructing a path for all $n$ that satisfies the monotone properties and covers every set of size at most $3$. This portion of thesis represents joint work with David M.~Howard.

Au cours des 50 dernières années, l’étude du phénomène de liquéfaction de sols sableux saturés ont fait l'objet de nombreuses recherches en laboratoire. La plupart de ces recherches antérieures se sont concentrées sur la liquéfaction de sables propres, en supposant que la présence de fines limite le développement de la surpression interstitielle et donc le risque de liquéfaction. Cependant, les sables sableux naturels se trouvent généralement dans la nature sous la forme d'un mélange de sable et de fines et, l’influence de ces fines sur le risque de liquéfaction de ce type de matériau n'est toujours pas claire. En effet, on trouve des résultats contradictoires, dans la littérature, sur l'effet des particules fines sur le phénomène de liquéfaction des sables. Dans ce contexte, l’objectif principal de ce travail expérimental est de clarifier et de quantifier l’influence des particules fines présentes au sein d’une matrice sableuse sur l’initiation et le développement du phénomène de liquéfaction. On s’est intéressé, en particulier, à la nature des particules fines (plastique/non-plastique), à leur proportion au sein de la matrice, à l’état de compacité de la matrice et à l’état de contrainte initial (état de consolidation). A cet effet, à l'aide d'un nouveau dispositif triaxial servo-hydraulique, une série d'essais monotones et cycliques ont été effectués afin de clarifier cet effet. Les résultats expérimentaux montrent que l'augmentation de la proportion de fines non plastiques augmente la résistance à la liquéfaction du mélange sous chargements monotone et cyclique. Par contre, cette tendance est inversée pour les mélanges qui contiennent des fines plastiques. Enfin, une comparaison a été établie entre le comportement de ces sols sous cisaillement monotone et cyclique non drainé en termes d'évaluation du déclenchement du phénomène d'instabilité et d'autres paramètres mécaniques / Since the last 50 years, the study of the phenomenon of liquefaction of saturated sandy soils has been a topic of extensive laboratory research. Most of the earlier research has focused on the liquefaction of clean sands assuming that the presence of fines resists the development of pore water pressure as well as the risk of liquefaction. However, natural sand is found in nature under the form of a mixture of sand and fines and, the influence of these fines on the liquefaction risk of this type of material is still unclear. In fact, we could find contradictory results in the literature review of the effect of fine particles on the sand liquefaction phenomenon. In this context, the main objective of this study is to clarify and quantify the influence of fine particles (plastic and non-plastic) present in a sandy matrix on the initiation and development of the liquefaction phenomenon .We’ve focused, in particular, on the nature of fine particles (plastic/non-plastic), their proportion in the matrix, the matrix compactness condition and initial stress state (state consolidation). For this purpose, with the aid of a new triaxial servo-hydraulic device, a series of monotonic and cyclic tests were done in order to clarify this effect. Experimental results show that the increase in non-plastic fines increases the resistance to liquefaction of the mixture under both monotonic and cyclic loading. However, this trend is reversed for the mixtures containing plastic fines. Finally a comparison has been established between the behavior of these soils under undrained monotonic and cyclic shearing in terms of evaluation of the initiation of instability phenomenon and other mechanical parameters

We show how the non-monotonic nature of common-sense reasoning can be formalised by circumscription. Various forms of circumscription are discussed. A new form of circumscription, namely naive circumscription, is introduced in order to facilitate the comparison of the various forms. Finally, some issues connected with the automation of circumscriptive reasoning are examined. / Computing / M. Sc. (Computer Science)

Este trabalho procura utilizar algumas das idéias de J. Piaget, em especial a "Lógica Operatória Intraproposicional", para uma análise das relações de herança entre classes empregadas em sistemas de representação de conhecimento. Procura-se sistematizar a noção de taxonomias do conhecimento "científico", ou "classificações sistemáticas". Estas estruturas foram utilizadas por Piaget como ponto de partida para a descoberta de estruturas cognitivas do conhecimento científico. Em especial, define-se a relação CS, que determina quais quais relações de herança seguem de uma taxonomia do conhecimento científico. A noção de classificação do conhecimento científico é comparada com a de "classificação do senso comum". São mostradas as diferenças entre estes conceitos. Determina-se a semântica das classificag6es do senso comum nas estruturas de agrupamentos de Piaget, via uma extensão epistêmica da lógica de classes. É estudada a relação de herança do senso comum que admite exceções. É também apresentada a formulação usual em lógica de predicados, e é proposta uma formulação em lógica de classes estendida. Conclui-se que a definição intuitiva da relação de herança empregada em uma formulação em lógica de classes pode ser diferente daquela que é empregada em uma formulação em lógica do proposições. Observa-se, em especial na formulação em lógica de classes, que as relações de herança não-estrita não se adaptam A estrutura de grafo direcionado acíclico. Na verdade, a relação de herança não-estrita não estabelece uma ordenação entre as classes (no sentido de conjunto parcialmente ordenado, ou CPO), mas uma possível simetria entre estas classes. Esta observação não aparece tão claramente na formulação proposicional, já que a relação de herança é mascarada pelo uso da implicação lógica (->), o que dá uma aparência de ordenação parcial. Verifica-se o que ocorre quando são combinadas relações de herança com ou sem exceções em uma única teoria de herança. É feita ainda alguma sistematização da lógica operatória intraproposicional de Piaget. Esta sistematização não prima pelo rigor, mas em fornecer algum entendimento básico para os não iniciados em Piaget. O trabalho abrange a sistematização dos quatro agrupamento de classes da lógica intraproposicional, e relega o estudo dos quatro agrupamentos de relações para um trabalho posterior. / This work use some ideas of Jean Piaget, mainly the Operating Logic, for an analysis of inheritance relationships used in knowledge representation systems. The notion of "scientific" knowledge classifications as defined by Piaget is shown. These structures were used by Piaget as a starting point to find the cognitive structures of scientific knowledge. It is also defined a relation CS. This relation tells whether an inheritance relationship follows from a scientific knowledge taxonomy or not. The notion of scientific knowledge classification is compared with that of "commonsense classification". The differences between these concepts are shown. The semantics of common sense classifications is determined in terms of Piaget's "groupments", through an epistemic extension of the logic of classes. The common sense inheritance relationship with exceptions is studied. The usual formulation of inheritance in propositional logic is presented, and a formulation in the extended logic of classes is proposed. The conclusion is that the intuitive definition of inheritance relationship in one formulation may be different of that in the other. It is observed in the formulation in logic of classes that non-strict inheritance relationships don't adapt to the structure of an acyclic directed graph. In fact, the non-strict inheritance relation doesn't stablish an ordering between classes (in the sense of a partially ordered set, or POSET), but it stablishes a possible simmetry between these classes. This is not so clear in the propositional formulation, because the inheritance relation is masked by using logic implication (->), what gives an appearance of partial ordering. It is verified what occurs when inheritance relations with or without exceptions are mixed in one single theory. It is made some sistematization of the Piaget's intrapropositional operating logic. This sistematization doesn't try to be rigorous, but gives some basic understanding on this theme. The work involves the sistematization of the four groupmonts of classes of the intrapropositional logic, and leaves the study of the four groupments of relations for a future work.

Este trabalho procura utilizar algumas das idéias de J. Piaget, em especial a "Lógica Operatória Intraproposicional", para uma análise das relações de herança entre classes empregadas em sistemas de representação de conhecimento. Procura-se sistematizar a noção de taxonomias do conhecimento "científico", ou "classificações sistemáticas". Estas estruturas foram utilizadas por Piaget como ponto de partida para a descoberta de estruturas cognitivas do conhecimento científico. Em especial, define-se a relação CS, que determina quais quais relações de herança seguem de uma taxonomia do conhecimento científico. A noção de classificação do conhecimento científico é comparada com a de "classificação do senso comum". São mostradas as diferenças entre estes conceitos. Determina-se a semântica das classificag6es do senso comum nas estruturas de agrupamentos de Piaget, via uma extensão epistêmica da lógica de classes. É estudada a relação de herança do senso comum que admite exceções. É também apresentada a formulação usual em lógica de predicados, e é proposta uma formulação em lógica de classes estendida. Conclui-se que a definição intuitiva da relação de herança empregada em uma formulação em lógica de classes pode ser diferente daquela que é empregada em uma formulação em lógica do proposições. Observa-se, em especial na formulação em lógica de classes, que as relações de herança não-estrita não se adaptam A estrutura de grafo direcionado acíclico. Na verdade, a relação de herança não-estrita não estabelece uma ordenação entre as classes (no sentido de conjunto parcialmente ordenado, ou CPO), mas uma possível simetria entre estas classes. Esta observação não aparece tão claramente na formulação proposicional, já que a relação de herança é mascarada pelo uso da implicação lógica (->), o que dá uma aparência de ordenação parcial. Verifica-se o que ocorre quando são combinadas relações de herança com ou sem exceções em uma única teoria de herança. É feita ainda alguma sistematização da lógica operatória intraproposicional de Piaget. Esta sistematização não prima pelo rigor, mas em fornecer algum entendimento básico para os não iniciados em Piaget. O trabalho abrange a sistematização dos quatro agrupamento de classes da lógica intraproposicional, e relega o estudo dos quatro agrupamentos de relações para um trabalho posterior. / This work use some ideas of Jean Piaget, mainly the Operating Logic, for an analysis of inheritance relationships used in knowledge representation systems. The notion of "scientific" knowledge classifications as defined by Piaget is shown. These structures were used by Piaget as a starting point to find the cognitive structures of scientific knowledge. It is also defined a relation CS. This relation tells whether an inheritance relationship follows from a scientific knowledge taxonomy or not. The notion of scientific knowledge classification is compared with that of "commonsense classification". The differences between these concepts are shown. The semantics of common sense classifications is determined in terms of Piaget's "groupments", through an epistemic extension of the logic of classes. The common sense inheritance relationship with exceptions is studied. The usual formulation of inheritance in propositional logic is presented, and a formulation in the extended logic of classes is proposed. The conclusion is that the intuitive definition of inheritance relationship in one formulation may be different of that in the other. It is observed in the formulation in logic of classes that non-strict inheritance relationships don't adapt to the structure of an acyclic directed graph. In fact, the non-strict inheritance relation doesn't stablish an ordering between classes (in the sense of a partially ordered set, or POSET), but it stablishes a possible simmetry between these classes. This is not so clear in the propositional formulation, because the inheritance relation is masked by using logic implication (->), what gives an appearance of partial ordering. It is verified what occurs when inheritance relations with or without exceptions are mixed in one single theory. It is made some sistematization of the Piaget's intrapropositional operating logic. This sistematization doesn't try to be rigorous, but gives some basic understanding on this theme. The work involves the sistematization of the four groupmonts of classes of the intrapropositional logic, and leaves the study of the four groupments of relations for a future work.

L’effet de l’espacement interlamellaire sur le comportement sous chargements monotone et cyclique de l’acier perlitique C70 a été étudié. Une démarche expérimentale conjuguant les essais de traction « in-situ » sous DRX et traction « in-situ » sous MEB couplées à une modélisation auto-cohérente a été adoptée. Les essais ont été effectués sur deux microstructures, à deux espacements interlamellaires différents. Il a été montré que l'écoulement plastique de la perlite est contrôlé par celui de la ferrite lequel est gouverné par l’espacement interlamellaire, il en est de même pour les distributions des contraintes résiduelles. La modélisation auto-cohérente met en évidence l'anisotropie élastique à l'échelle des phases et l'effet de l'espacement interlamellaire sur les rigidités et les limites d'écoulement directionnelles. L'analyse microstructurale des mécanismes de déformation montre que la déformation plastique de la perlite est caractérisée par le développement de bandes de cisaillement. Ces bandes sont le siège de l'amorçage des fissures par cisaillement des lamelles de cémentite pour les taux de déformation élevés. L’effet de l’espacement interlamellaire sur le comportement en fatigue giga-cyclique a été étudié par des essais de fatigue sous une fréquence de 20 KHz. Des différences de 30 MPa, pour la perlite à SP= 230 nm et de 50 MPa pour la perlite à SP= 170 nm entre les limites de fatigue conventionnelle (106cycles) et giga-cyclique (109cycles) ont été obtenues. L’effet de l’espacement interlamellaire sur le comportement en fatigue apparait peu significatif comparativement aux caractéristiques mécaniques de traction. Les limites de fatigue giga-cycliques obtenues intègrent l’effet bénéfique des contraintes résiduelles stabilisées ainsi que les effets d’écrouissage induit par l’usinage et par écrouissage cyclique. L’examen des sites d’amorçage, révèle essentiellement un amorçage en surface dans le domaine méga-cyclique et mixte en surface et/ou en sous-couches dans le domaine giga-cyclique. Ces résultats peuvent être interprétés sur la base des effets des propriétés de surface stabilisées et de la microstructure. Le recours à un critère de fatigue de type Goodman permet d’identifier d’une manière qualitative la contribution des différents facteurs d’influence, ci-dessus cités, dans l’amorçage des fissures de fatigue. / The effect of interlamellar spacing on the monotonic and cyclic behavior of C70 pearltic steel was investigated. Tensile tests under scanning electron microscope and under X-ray diffraction coupled with self-consistent model have been used. Tests have been carried out on two microstructures with different interlamellar spacing. It has been demonstrated that pearlite yielding is controlled by ferrite critical shear stress), which depend on the interlamellar spacing. The pearlite deforms inhomogeneously under tensile loading by localized shearing in intense shear bands. In the large shear bands, parallel cementite plate offsets before fracture and contributes to the occurrence of localized damage. The residual stress in ferrite is higher for the coarse pearlite. Giga-cycle fatigue tests were performed to identify the effect of interlamellar spacing on the fatigue behavior; tests were performed at a frequency of 20 KHz. The difference of the fatigue strength between 106 and 109 cycles is about 30 MPa for coarse pearlite and 50 MPa for fine pearlite. The effect of interlamellar spacing on the mega-cycle and giga-cycle fatigue limit appears not significant compared to the mechanical characteristics. Giga-cycle fatigue limit obtained includes the beneficial effect of stabilized residual stress. It also includes the effect of hardening induced by machining and cyclic hardening. However, any significant effect of interlamellar spacing on the C70 fatigue limits has been shown. SEM examinations shows that failures initiated on surface for the mega-cycle regime and on different sites for the giga-cycle regime. The experimental results can be interpreted based on the effects of stabilized surface properties and microstructure. The use of a fatigue Goodman criterion would identify qualitatively the contribution of different factors, cited above, in the fatigue life.

Finite volume methods employing second-order gradient reconstruction schemes are often utilized to computationally solve the governing equations of fluid mechanics and transport. These schemes, while not as dissipative as first-order schemes, frequently produce oscillatory solutions in regions of discontinuities and/or unsatisfactory levels of dissipation in smooth regions of the variable field. Limiters are often employed to reduce the inherent variable over- and under-shoot; however, they can significantly increase the numerical dissipation of a solution, eroding a scheme’s performance in smooth regions. A novel gradient reconstruction scheme, which shows significant improvement over traditional second-order schemes, is presented in this work. Two implementations of this Optimization-based Gradient REconstruction (OGRE) scheme are examined: minimizing an objective function based on the mismatch between local reconstructions at midpoints or selected quadrature points between cell stencil neighbors. Regardless of the implementation employed, the resulting gradient calculation is a compact, implicit method that can be used with unstructured meshes by employing an arbitrary computational stencil. An adjustable weighting parameter is included in the objective function that allows the scheme to be tuned towards either greater accuracy or greater stability. To address over- and undershoot of the variable field near discontinuities, non-local, non-monotonic (NLNM) and local, non-monotonic (LNM) limiters have also been developed, which operate by enforcing cell minima and maxima on dependent variable values projected to cell faces. The former determines minimum and maximum values for a cell through recursive reference to the minimum and maximum values of its upwind neighbors. The latter determines these bounding values through examination of the extrema of values of the dependent variable projected from the face-neighbor cell into the original cell. Steady state test cases on structured and unstructured grids are presented, exhibiting the low-dissipative nature of the scheme. Results are primarily compared to those produced by existing limited and unlimited second-order upwind (SOU) and first-order upwind (FOU). Solution accuracy, convergence rate and computational costs are examined.

No