Les cœurs de réacteur à neutrons rapides refroidi au sodium (RNR-Na ) sont constitués d’assemblages combustibles disposés selon un réseau hexagonal régulier, compact en régime de fonctionnement nominal.Sous l’effet de l’irradiation et de la température, les assemblages sont amenés à se déformer axialement et radialement.Les objectifs de cette thèse sont la compréhension des phénomènes neutroniques intervenant lors d’une telle déformation du cœur, l’impact sur la conception ainsi que la mise au point de schémas de calcul neutroniques déterministes innovants aptes à en évaluer l’amplitude.La première partie de ces travaux est dédiée au développement d’une modélisation analytique des causes de variations de réactivité lors de la déformation du cœur. Cette analyse a permis d’identifier à la fois les causes de ces variations de réactivité et l’impact du déplacement des assemblages en fonction de leurs directions et de leurs positions dans le cœur.Un premier schéma neutronique basé sur la méthode de projection de maillage a été conçu et développé à l’aide des codes ERANOS (BISTRO, H3D et VARIANT) et du solveur SNATCH Le deuxième schéma conçu se base sur la transformation géométrique du maillage de calcul : le maillage est modifié en fonction du champ des déformations des assemblages. Cette fonctionnalité a été implémentée pour le solveur SNATCH, initialement prévu pour la résolution de l’équation de Boltzmann pour de mailles régulières.Enfin un modèle itératif basé sur la méthode de projection de maillage a été mis en place afin de déterminer les champs de déformations les plus réactifs en fonction de l’énergie mécanique fournie au cœur dans sa configuration nominale. / The fuel assemblies of SFR cores (sodium fast reactors) are normally arranged in hexagonal regular lattices, whose compactness is ensured in nominal operating conditions by thermal expansion of assemblies pads disposed on the six assembly wrapper faces.During the reactor operations, thermal expansion phenomena and irradiation creep phenomena occur and they cause the fuel assemblies to bow and to deform both radially and axially.The main goal of this PhD is the understanding of the neutronic aspects and phenomena occurring in case of core and lattice deformations, as much as the design and implementation of deterministic neutronic calculation schemes and methods in order to evaluate the consequences for the core design activities and the safety analysis.The first part of this work is focused on the development of an analytical model with the purpose to identify the neutronic phenomena that are the main contributors to the reactivity changes induced by lattice and core deformations.A first scheme based on the spatial mesh projection method has been conceived and implemented for the ERANOS codes (BISTRO, H3D and VARIANT) and to the SNATCH solver.The second calculation scheme propose is based on mesh deformation: the computing mesh is deformed as a function of the assembly displacement field. This methodology has been implemented for the solver SNATCH, which normally allows the Boltzmann equation to be solved for a regular mesh. Finally, an iterative method has been developed in order to fulfill an a-priori estimation of the maximal reactivity insertion as a function of the postulated mechanical energy provided to the core, as much as the deformation causing it.

[pt] Comumente as análises de estabilidade de taludes são realizadas mediante métodos determinísticos, os quais visam o cálculo de um fator de segurança único assumindo os valores dos parâmetros de resistência como representativos e fixos. Estes métodos não conseguem avaliar as incertezas existentes nas propriedades do solo e tampouco indicam a proporção de influência que tem cada parâmetro de resistência no valor do fator de segurança. Os métodos probabilísticos, com base nas teorias de probabilidade, confiabilidade e estatística, permitem estimar a influência dessas incertezas nos cálculos determinísticos, com a possibilidade de prever mais amplamente o risco de insucesso associado a um projeto geotécnico de estabilidade de taludes. O presente trabalho estuda a aplicação de três métodos probabilísticos (Monte Carlo, Hipercubo Latino e Estimativas Pontuais Alternativas) na avaliação de estabilidade de taludes, com auxílio de métodos de equilíbrio limite no cálculo do fator de segurança. Com objetivo de inferir o impacto das variáveis aleatórias nas estimativas de probabilidade e confiabilidade, bem como da importância de uma quantificação adequada dos valores de desvio padrão, são realizadas comparações dos resultados obtidos com métodos probabilísticos e determinísticos (método das fatias, método dos elementos finitos) discutindo as principais vantagens, dificuldades e limitações nas aplicações dos mesmos em problemas de estabilidade de taludes de solo. / [en] Slope stability analyses are usually carried out using deterministic methods, which aim the calculation of a single safety factor assuming the values of the shear strength parameters as representative and fixed. These methods fail to assess the uncertainties in soil properties and do not indicate the proportion of influence that each resistance parameter has on the final value of the safety factor. The probabilistic methods, based on probability, reliability and statistical theories, allow the estimation of the influence of these uncertainties on the deterministic calculations, with the possibility to broadly predict the risk of failure associated with a geotechnical slope stability project. This dissertation studies the application of three probabilistic methods (Monte Carlo, Latin Hypercube, and Alternative Point Estimates) in the evaluation of slope stability, with aid of limit equilibrium methods for the calculation of safety factors. In order to infer the impact of random variables on the estimates of probability and reliability, as well as the importance of an adequate quantification of the standard deviation values, comparisons are made among the results obtained with probabilistic and deterministic methods (limit equilibrium method, finite element method), discussing the main advantages, difficulties and limitations in their application to soil slope stability problems.

Reliability prediction of components operating in complex systems has historically been conducted in a statistically isolated manner. Current physics-based, i.e. mechanistic, component reliability approaches focus more on component-specific attributes and mathematical algorithms and not enough on the influence of the system. The result is that significant error can be introduced into the component reliability assessment process. The objective of this study is the development of a framework that infuses the influence of the system into the process of conducting mechanistic-based component reliability assessments. The formulated framework consists of six primary steps. The first three steps, identification, decomposition, and synthesis, are qualitative in nature and employ system reliability and safety engineering principles for an appropriate starting point for the component reliability assessment. The most unique steps of the framework are the steps used to quantify the system-driven local parameter space and a subsequent step using this information to guide the reduction of the component parameter space. The local statistical space quantification step is accomplished using two newly developed multivariate probability tools: Multi-Response First Order Second Moment and Taylor-Based Inverse Transformation. Where existing joint probability models require preliminary statistical information of the responses, these models combine statistical information of the input parameters with an efficient sampling of the response analyses to produce the multi-response joint probability distribution. Parameter space reduction is accomplished using Approximate Canonical Correlation Analysis (ACCA) employed as a multi-response screening technique. The novelty of this approach is that each individual local parameter and even subsets of parameters representing entire contributing analyses can now be rank ordered with respect to their contribution to not just one response, but the entire vector of component responses simultaneously. The final step of the framework is the actual probabilistic assessment of the component. Variations of this final step are given to allow for the utilization of existing probabilistic methods such as response surface Monte Carlo and Fast Probability Integration. The framework developed in this study is implemented to conduct the finite-element based reliability prediction of a gas turbine airfoil involving several failure responses. The framework, as implemented resulted in a considerable improvement to the accuracy of the part reliability assessment and an increased statistical understanding of the component failure behavior.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Como eventos de fissão induzida por nêutrons não ocorrem nas regiões nãomultiplicativas de reatores nucleares, e.g., moderador, refletor, e meios estruturais, essas regiões não geram potência e a eficiência computacional dos cálculos globais de reatores nucleares pode portanto ser aumentada eliminando os cálculos numéricos explícitos no interior das regiões não-multiplicativas em torno do núcleo ativo. É discutida nesta dissertação a eficiência computacional de condições de contorno aproximadas tipo albedo na formulação de ordenadas discretas (SN) para problemas de autovalor a dois grupos de energia em geometria bidimensional cartesiana. Albedo, palavra de origem latina para alvura, foi originalmente definido como a fração da luz incidente que é refletida difusamente por uma superfície. Esta palavra latina permaneceu como o termo científico usual em astronomia e nesta dissertação este conceito é estendido para reflexão de nêutrons. Este albedo SN nãoconvencional substitui aproximadamente a região refletora em torno do núcleo ativo do reator, pois os termos de fuga transversal são desprezados no interior do refletor. Se o problema, em particular, não possui termos de fuga transversal, i.e., trata-se de um problema unidimensional, então as condições de contorno albedo, como propostas nesta dissertação, são exatas. Por eficiência computacional entende-se analisar a precisão dos resultados numéricos em comparação com o tempo de execução computacional de cada simulação de um dado problema-modelo. Resultados numéricos para dois problemas-modelo com de simetria são considerados para ilustrar esta análise de eficiência. / As neutron fission events do not take place in the non-multiplying regions of nuclear reactors, e.g., moderator, reflector, and structural core, these regions do not generate power and the computational efficiency of nuclear reactor global calculations can hence be improved by eliminating the explicit numerical calculations within the non-multiplying regions around the active domain. Discussed here is the computational efficiency of approximate discrete ordinates (SN) albedo boundary conditions for two-energy group eigenvalue problems in X,Y geometry. Albedo, the Latin word for whiteness, was originally defined as the fraction of incident light reflected diffusely by a surface. This Latin word has remained the usual scientific term in astronomy and in this dissertation this concept is extended for the reflection of neutrons. The non-standard SN albedo substitutes approximately the reflector region around the active domain, as we neglect the transverse leakage terms within the nonmultiplying reflector. Should the problem have no transverse leakage terms, i.e., onedimensional slab geometry, then the offered albedo boundary conditions are exact. By computational efficiency we mean analyzing the accuracy of the numerical results versus the CPU execution time of each run for a given model problem. Numerical results to two symmetric test problems are shown to illustrate this efficiency analysis.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Como eventos de fissão induzida por nêutrons não ocorrem nas regiões nãomultiplicativas de reatores nucleares, e.g., moderador, refletor, e meios estruturais, essas regiões não geram potência e a eficiência computacional dos cálculos globais de reatores nucleares pode portanto ser aumentada eliminando os cálculos numéricos explícitos no interior das regiões não-multiplicativas em torno do núcleo ativo. É discutida nesta dissertação a eficiência computacional de condições de contorno aproximadas tipo albedo na formulação de ordenadas discretas (SN) para problemas de autovalor a dois grupos de energia em geometria bidimensional cartesiana. Albedo, palavra de origem latina para alvura, foi originalmente definido como a fração da luz incidente que é refletida difusamente por uma superfície. Esta palavra latina permaneceu como o termo científico usual em astronomia e nesta dissertação este conceito é estendido para reflexão de nêutrons. Este albedo SN nãoconvencional substitui aproximadamente a região refletora em torno do núcleo ativo do reator, pois os termos de fuga transversal são desprezados no interior do refletor. Se o problema, em particular, não possui termos de fuga transversal, i.e., trata-se de um problema unidimensional, então as condições de contorno albedo, como propostas nesta dissertação, são exatas. Por eficiência computacional entende-se analisar a precisão dos resultados numéricos em comparação com o tempo de execução computacional de cada simulação de um dado problema-modelo. Resultados numéricos para dois problemas-modelo com de simetria são considerados para ilustrar esta análise de eficiência. / As neutron fission events do not take place in the non-multiplying regions of nuclear reactors, e.g., moderator, reflector, and structural core, these regions do not generate power and the computational efficiency of nuclear reactor global calculations can hence be improved by eliminating the explicit numerical calculations within the non-multiplying regions around the active domain. Discussed here is the computational efficiency of approximate discrete ordinates (SN) albedo boundary conditions for two-energy group eigenvalue problems in X,Y geometry. Albedo, the Latin word for whiteness, was originally defined as the fraction of incident light reflected diffusely by a surface. This Latin word has remained the usual scientific term in astronomy and in this dissertation this concept is extended for the reflection of neutrons. The non-standard SN albedo substitutes approximately the reflector region around the active domain, as we neglect the transverse leakage terms within the nonmultiplying reflector. Should the problem have no transverse leakage terms, i.e., onedimensional slab geometry, then the offered albedo boundary conditions are exact. By computational efficiency we mean analyzing the accuracy of the numerical results versus the CPU execution time of each run for a given model problem. Numerical results to two symmetric test problems are shown to illustrate this efficiency analysis.