In the present study, an analysis of plain and reinforced concrete beams under monotonic loading was made based on the Fixed Smeared Crack approach. The objectives of this research were to analyze the nonlinear behavior of the selected cases of analysis and to propose an alternative and simple model for the analysis of beams under service loadings, by means of Committee 435 of the American Concrete Institute. A brittle model for concrete and a linear-elastic behavior for steel reinforcement bars were considered. Results are presented through force-displacement curves and the sequence of cracking propagation. Also, a comparison of calculated instantaneous deflections of simply supported beams was made between the proposed model and other researches. It was verified that the proposed algorithm can predict adequately the cracking process and the deflections of beams subjected to service loadings, taking into account experimental results from other authors.

Com o avanço tecnológico dos computadores e o desenvolvimento de soluções para problemas não lineares através do método dos elementos finitos, hoje é possível fazer uma análise mais complexa e mais próxima da realidade. É de extrema importância à verificação dos resultados obtidos pelos programas com a realidade e saber em quais casos esses modelos podem ser aplicados. Assim, o objetivo deste trabalho é discutir as vantagens e desvantagens da modelagem de estruturas de concreto armado em duas e três dimensões, através dos modelos de fissuras distribuídas. Foram escolhidos três experimentos para a modelagem numérica: o primeiro trata-se de um experimento com uma viga de concreto armado (LEONHARDT; WALTHER, 1962), o segundo experimento também é realizado com uma viga de concreto armado (BRESLER; SCORDELIS, 1963) e o terceiro experimento utiliza vigas de concreto armado em escala reduzida, fabricadas com microconcreto e arame, simulando uma barra de aço lisa (ALMEIDA et al, 2006). Para a modelagem numérica, utilizando-se o modelo de fissuras distribuídas com fissura rotacional e a análise das estruturas de concreto foi escolhido o programa comercial ATENA - \"Advanced Tool Engineering Non-linear Analysis\". / The technological advancement of computers and the development of solutions for nonlinear problems by finite element method are now possible to make more complex the analysis and closer to reality. It is extremely important to verify the results obtained by programs with reality and know which cases these models can be applied. So the objective is to discuss the advantages and disadvantages of modeling reinforced concrete structures in two and three dimensions, through the smeared cracking models. Three experiments were chosen to make the numerical modeling: the first is an experiment with a reinforced concrete beam (LEONHARDT; WALTHER, 1962), the second experiment is also a reinforced concrete beam (BRESLER; SCORDELIS, 1963) and the third experiment is reinforced concrete beams with small-scale and made of wire microconcrete simulating flat steel bar (ALMEIDA et al, 2006). For numerical modeling, using the smeared crack model with rotational crack, and analysis of concrete structures was chosen the commercial program ATENA - Advanced Tool Engineering Non-linear Analysis.

Com o avanço tecnológico dos computadores e o desenvolvimento de soluções para problemas não lineares através do método dos elementos finitos, hoje é possível fazer uma análise mais complexa e mais próxima da realidade. É de extrema importância à verificação dos resultados obtidos pelos programas com a realidade e saber em quais casos esses modelos podem ser aplicados. Assim, o objetivo deste trabalho é discutir as vantagens e desvantagens da modelagem de estruturas de concreto armado em duas e três dimensões, através dos modelos de fissuras distribuídas. Foram escolhidos três experimentos para a modelagem numérica: o primeiro trata-se de um experimento com uma viga de concreto armado (LEONHARDT; WALTHER, 1962), o segundo experimento também é realizado com uma viga de concreto armado (BRESLER; SCORDELIS, 1963) e o terceiro experimento utiliza vigas de concreto armado em escala reduzida, fabricadas com microconcreto e arame, simulando uma barra de aço lisa (ALMEIDA et al, 2006). Para a modelagem numérica, utilizando-se o modelo de fissuras distribuídas com fissura rotacional e a análise das estruturas de concreto foi escolhido o programa comercial ATENA - \"Advanced Tool Engineering Non-linear Analysis\". / The technological advancement of computers and the development of solutions for nonlinear problems by finite element method are now possible to make more complex the analysis and closer to reality. It is extremely important to verify the results obtained by programs with reality and know which cases these models can be applied. So the objective is to discuss the advantages and disadvantages of modeling reinforced concrete structures in two and three dimensions, through the smeared cracking models. Three experiments were chosen to make the numerical modeling: the first is an experiment with a reinforced concrete beam (LEONHARDT; WALTHER, 1962), the second experiment is also a reinforced concrete beam (BRESLER; SCORDELIS, 1963) and the third experiment is reinforced concrete beams with small-scale and made of wire microconcrete simulating flat steel bar (ALMEIDA et al, 2006). For numerical modeling, using the smeared crack model with rotational crack, and analysis of concrete structures was chosen the commercial program ATENA - Advanced Tool Engineering Non-linear Analysis.

Cette thèse s’inscrit dans le contexte d’une optimisation industrielle et économique des éléments de structure en BFUP permettant d’en garantir la ductilité au niveau structural, tout en ajustant la quantité de fibres et en optimisant le mode de fabrication. Le modèle développé décrit explicitement la participation du renfort fibré en traction au niveau local, en enchaînant une phase de comportement écrouissante suivie d'une phase adoucissante. La loi de comportement est fonction de la densité, de l'orientation des fibres vis-à-vis des directions principales de traction, de leur élancement et d'autres paramètres matériaux usuels liés aux fibres, à la matrice cimentaire et à leur interaction. L'orientation des fibres est prise en compte à partir d'une loi de probabilité normale à une ou deux variables permettant de reproduire n'importe quelle orientation obtenue à partir d’un calcul représentatif de la mise en œuvre du BFUP frais ou renseignée par analyse expérimentale sur prototype. Enfin, le modèle reproduit la fissuration des BFUP sur le principe des modèles de fissures diffuses et tournantes. La loi de comportement est intégrée au sein d'un logiciel de calcul de structure par éléments finis, permettant de l'utiliser comme un outil prédictif de la fiabilité et de la ductilité globale d’éléments en BFUP. Deux campagnes expérimentales ont été effectuées, une à l'Université Laval de Québec et l'autre à l'Ifsttar, Marne-la-Vallée. La première permet de valider la capacité du modèle à reproduire le comportement global sous des sollicitations typiques de traction et de flexion dans des éléments structurels simples pour lesquels l’orientation préférentielle des fibres a été renseignée par tomographie. La seconde campagne expérimentale démontre les capacités du modèle dans une démarche d’optimisation, pour la fabrication de plaques nervurées relativement complexes et présentant un intérêt industriel potentiel pour lesquels différentes modalités de fabrication et des BFUP plus ou moins fibrés ont été envisagés. Le contrôle de la répartition et de l’orientation des fibres a été réalisé à partir d'essais mécaniques sur prélèvements. Les prévisions du modèle ont été confrontées au comportement structurel global et à la ductilité mis en évidence expérimentalement. Le modèle a ainsi pu être qualifié vis-à-vis des méthodes analytiques usuelles de l'ingénierie, en prenant en compte la variabilité statistique. Des pistes d'amélioration et de complément de développement ont été identifiées / This Ph.D. project has been prepared within the context of an industrial and economic optimisation of UHPFRC structural elements to ensure ductility at the structural level, while adjusting the amount of fibre and optimising the manufacturing process. The model developed explicitly describes the participation of local fibre reinforcement in tension, thanks to a hardening behaviour followed by a softening one. The constitutive law is a function of the local fibre content, of the fibre orientation with respect to tensile principal directions, of the fibre slenderness and other usual material parameters related to the fibres, the cementitious matrix and their interaction. The fibre orientation is taken into account using a normal probability distribution with one or two variables to reproduce any orientation either obtained from a representative simulation of casting fresh UHPFRC or informed by experimental analysis on prototypes. Lastly, the model reproduces the cracking of UHPFRC based on the principle of smeared rotating crack models. The constitutive law is implemented in a structural finite element software as a predictive tool of reliability and overall ductility of UHPFRC elements. Two experimental campaigns were carried out, one at Laval University in Quebec and one at Ifsttar, Marne-la-Vallée. The first one is used to confirm the model ability to reproduce the overall behaviour under typical tensile and bending loads in simple structural elements for which the preferential fibre orientation was measured by microtomography. The second experimental campaign demonstrates the capabilities of the model, in an optimisation process, to help manufacture relatively complex ribbed triangular plates of industrial interest in which different manufacturing process and fibre volume have been considered. The identification of fibre distribution and orientation has been performed using mechanical tests on sawn samples. The model predictions have been compared to the global structural behaviour, and to the ductility demonstrated experimentally. The model could be qualified through comparison with conventional analytical engineering methods, taking into account the statistical variability. Improvement and additional developments have been identified

El presente estudio trata sobre el análisis del agrietamiento en vigas de concreto sujetas a cargas monotónicas a través de un cálculo pseudo-estático. El fundamento teórico se basa en el Método de Grietas Dispersas (Smeared Crack Approach) de la Mecánica de Fractura, el cual será evaluado dentro de un algoritmo de análisis considerando el Método de Elementos Finitos. El objetivo principal es proponer un modelo computacional para el cálculo de deflexiones instantaneas y la modelación del agrietamiento en vigas de concreto armado sometidas a cargas de servicio. Con este propósito, se evaluaron las vigas analizadas por diversos autores. Los resultados del estudio se presentan mediante curvas fuerza-desplazaminto, la secuencia de propagación del agrietamiento y la evaluación de la resistencia última. Se consideró un modelo frágil de esfuerzo y deformación en la grieta. De esta manera, para los elementos analizados, se demostró que el modelo utilizado es capaz de predecir adecuadamente el proceso de agrietamiento y de calcular las deflexiones instantáneas en vigas de concreto, teniendo en cuenta resultados experimentales existentes. / The present study deals with cracking analysis of concrete beams under monotonic loadings by means of a quasi-static evaluation. The theoretical basis herein used is lies on the Fixed Smeared Crack Approach taking into account Fracture Mechanics within a Finite Element algorithm for the numerical solution of the problem. The main objective is to propose a computational model for the calculus of instantaneous deflection and the simulation of cracking in concrete beams under service loadings. On this purpose, diverse beams evaluated by may authors where analyzed. The results of this study cases are presented through and force-displacement curves, cracking propagation and the evaluation of the ultimate resistance of the beam. Within the computational algorithm, a fragile crack stress-strain relation was implemented. On this way, for the analyzed elements it was demonstrated that the model herein used can predict adequately cracking processes and instantaneous deflections of concrete beams considering existing experimental results. / Tesis

[pt] Em reservatórios complexos com descontinuidades geológicas como falhas, os riscos na produção de petróleo e gás pelos métodos de injeção frequentemente utilizados são maiores. Um dos fenômenos que pode acarretar graves problemas de perda de produção e acidentes ambientais é a reativação de falhas geológicas. Isto ocorre devido às variações de tensões induzidas na formação, as quais podem ser suficientemente altas para reativar as falhas e modificar significativamente o comportamento do reservatório, gerando uma das situações mais críticas na indústria de petróleo. Nessa dissertação investiga-se através do método dos elementos finitos o fenômeno de reativação de falhas com base em modelos de representação explícita da falha através de elementos de interface. Adota-se ainda para efeitos de comparação uma modelagem da falha por meio de uma zona de falha através do conceito de contínuo equivalente. Uma metodologia com base em uma análise poro-elastoplástica desacoplada que permite estimar as pressões limite para a reativação durante a produção em reservatórios de petróleo de uma maneira versátil e eficiente foi empregada nas situações investigadas através do simulador Abaqus. Para tal, foram implementadas uma série de rotinas para incorporar ao programa Abaqus novos elementos de interface, governados pelo modelo constitutivo de Mohr-Coulomb. A metodologia apresentada foi avaliada e verificada através da simulação de um modelo sintético com falha normal comparando os resultados com uma solução analítica simplificada e com os resultados obtidos com o simulador de elementos finitos AEEPECD (Costa, 1984). São apresentados alguns exemplos de aplicação representando a falha com elementos de interface e como um contínuo equivalente. Os resultados obtidos nas análises demonstram a aplicabilidade da metodologia a problemas de campos reais. / [en] In complex reservoirs with geological discontinuities, such as faults, the risk in the production of oil and gas are increase by the injection methods frequently used. The injection and depletion processes induce stress variations in the formation. These can be high enough to reactivate faults and significantly modify the behavior of the reservoir, bringing on one of the most critical situations in the oil industry. In this context, this dissertation investigates the phenomenon of fault reactivation by employing the finite element method based on an explicit representation of the fault with interface elements. In addition, a fault zone model based on an equivalent continuum approach is adopted for comparison. The pressure limits during production of oil reservoirs considering fault reactivation are determined from pore-elastoplastic uncoupled analyses with the software Abaqus. With this purpouse, interfaces elements with Mohr-Coulomb constitutive model were implemented through user subroutine in Abaqus to represent, in an approximate way, the fault behavior. In addition, other tools were developed to facilitate the generation of the models to be analyzed. The presented methodology was evaluated and verified through the simulation of a synthetic model with a normal fault. The results were compared with a simplified analytical approach and the results obtained by finite element simulator AEEPECD (Costa, 1984). Some examples of applications are presented, in which faults are represented using interface elements and alternatively, through an equivalent continuum approach. The analysis results demonstrate the applicability of the methodology to real fields.

Evaluating the safety of unreinforced concrete structures, such as concrete dams, requires an accurate prediction of cracking. Developing a suitable constitutive material model and a reliable computational procedure for analysing cracking processes in concrete has been a challenging and demanding task. Although many analytical methods based on fracture mechanics have been proposed for concrete dams in the last few decades, they have not yet become part of standard design procedures. Few of the current research findings are being implemented by practising engineers when evaluating dam safety. This research is focused on the development of a suitable crack modelling and analysis method for the prediction and study of fracturing in concrete gravity dams, and consequently, for the evaluation of dam safety against cracking. The research aims to contribute to the continuing research efforts into mastering the mechanics of cracking in concrete dams. An analytical method for the purpose of establishing a crack constitutive model and implementing the model for the fracture analysis of concrete structures, in particular massive concrete gravity dams under static loading conditions, has been developed, verified and applied in the safety evaluation of a concrete gravity dam. The constitutive material model is based on non-linear fracture mechanics and assumes a bilinear softening response. The crack model has various improved features: (1) an enhanced mode I bilinear strain-softening approach has been put forward; (2) a new formula for bilinear softening parameters has been developed and their relation with linear softening has been outlined; (3) the influence of bilinear softening parameters on the cracking response has been studied; and (4) an enhanced modification to the shear retention factor which depends on the crack normal strain is included. The material model has been incorporated into a finite element analysis using a smeared crack approach. A sub-program was specially coded for this research. The validity of the proposed cracking model and the computational procedure developed for the purpose of analyzing the tensile fracture behaviour of concrete structures has been confirmed by verification on various concrete structures, including beams, a dam model and actual gravity dams. The crack modelling technique developed was successfully used in evaluating the safety of an existing concrete gravity dam in South Africa and adequately predicted the cracking response of the dam structure under static loadings. The main conclusions drawn are as follows: <ul><li>Both mode I and mode II fracture have been modelled successfully.</li> <li>The proposed bilinear softening model remains relatively simple to implement but significantly improves on predicting the softening response of “small-scale” concrete structures.</li> <li>Both plane stress and plane strain crack analyses have been considered and can be confidently adopted in two-dimensional applications.</li> <li>The proposed method is mesh objective.</li> <li>The crack modelling method developed can correctly predict the crack propagation trajectory and the structural behaviour with regard to fracturing in concrete structures.</li> <li>If not considering shear stress concentration near the tip of a crack, constitutive crack analysis normally indicates a higher safety factor and a higher Imminent Failure Flood (IFF) than the classical methods in the analysis of concrete gravity dams for safety evaluation.</li></ul> / Thesis (PhD(Civil Engineering))--University of Pretoria, 2007. / Civil Engineering / PhD / unrestricted