This study develops a 3D meso-scale fracture characterisation and modelling framework for better understanding of the failure mechanisms in concrete, by combining in-situ micro-scale X-ray computed tomography (XCT) experiments and XCT image-based finite element (FE) simulations. Firstly, sophisticated in-situ XCT experiments are conducted on concrete cubes under Brazilian-like, uniaxial and cyclic compression. Proper procedures for XCT image reconstruction and multi-phasic segmentation are identified. The fracture evolution at different loading stages is characterised and visualised as well as the detailed distributions of aggregates and voids. The Young's moduli of aggregate and cement are obtained by micro-indentation tests and used in XCT-image based asymptotic homogenisation simulations to calculate effective elastic constants of concrete cubes. The XCT technique proves very powerful in characterising and visualising the complicated 3D fracture evolution in concrete. The material properties and the segmented 3D images from the experiments are then used for FE fracture simulations with realistic aggregates, cement and voids. Image-based mesh generation algorithms are developed for 2D in a MATLAB code and identified for 3D in Simpleware. Cohesive interface elements are embedded within cement and aggregate-cement interfaces to simulate the complex nonlinear fracture. Extensive simulations of 40mm and 20mm cubes under compression and tension are carried out. Good agreements are achieved between the load-displacement curves and final crack patterns from the simulations and those from the compressive in-situ XCT tests. The XCT image-based modelling proves very promising in elucidating fundamental mechanisms of complicated crack initiation and propagation in concrete.

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

Thesis (MScEng)--Stellenbosch University, 2013. / Durability and impermeability in a water-retaining structure are of prime importance if the structure is to fulfill its function over its design life. In addition, serviceability cracking tends to govern the design of water retaining structures. This research concentrates on load-induced cracking specifically that due to pure bending and to direct tension in South African reinforced concrete water retaining structures (WRS). As a South African design code for WRS does not exist at present, South African designers tend to use the British codes in the design of reinforced concrete water-retaining structures. However, with the release of the Eurocodes, the British codes have been withdrawn, creating the need for a South African code of practice for water-retaining structures. In updating the South African structural design codes, there is a move towards adopting the Eurocodes so that the South African design codes are compatible with their Eurocode counterparts. The Eurocode crack model to EN1992 (2004) was examined and compared to the corresponding British standard, BS8007 (1989). A reliability study was undertaken as the performance of the EN1992 crack model applied to South African conditions is not known. The issues of the influence of the crack width limit and model uncertainty were identified as being of importance in the reliability crack model.

No contexto do método dos elementos de contorno, este trabalho apresenta comparativamente três formulações em distintos aspectos. Visando a análise de sólidos bidimensionais no campo da mecânica da fratura, primeiramente é estudada a equação singular ou em deslocamentos. Em seguida, a formulação hiper-singular ou em forças de superfície é avaliada. Por último, a formulação dual, que emprega ambas equações é analisada. Para esta análise, elementos contínuos e descontínuos são empregados, equações numéricas e analíticas com ponto fonte dentro e fora do contorno são testadas, usando aproximação linear. A formulação é inicialmente empregada a problemas da mecânica da fratura elástica linear e em seguida extendida a problemas não-lineares, especialmente o modelo coesivo. Exemplos numéricos diversos averiguam as formulações, comparando com resultados analíticos ou disponíveis na literatura. / In this work three boundary elment formulations applied to fracture mechanics are studied. Aiming the analysis of two-dimensional solids with emphasis on the crack problem, the first considered method is the one based on using displacement equations only (singular formulation). The second scheme discussed in this work is a formulation based on the use of traction equations (hyper-singular formulation). Finally the dual boundary element method that uses singular and hyper-singular equations is considered. The numerical schemes have been implemented using continuous and discontinuous linear boundary and crack elements. The boundary and crack integral were all carried out by using analytical expressions, therefore increasing the accuracy of the algebraic system obtained for each one of the studied schemes. The developed numerical programs were applied initially to elastic fracture mechanics and then extended to analyze cohesive cracks. Several numerical examples were solved to verify the accuracy of each one of the studied models, comparing the results with the analytical solutions avaliable in the literature.

No contexto do método dos elementos de contorno, este trabalho apresenta comparativamente três formulações em distintos aspectos. Visando a análise de sólidos bidimensionais no campo da mecânica da fratura, primeiramente é estudada a equação singular ou em deslocamentos. Em seguida, a formulação hiper-singular ou em forças de superfície é avaliada. Por último, a formulação dual, que emprega ambas equações é analisada. Para esta análise, elementos contínuos e descontínuos são empregados, equações numéricas e analíticas com ponto fonte dentro e fora do contorno são testadas, usando aproximação linear. A formulação é inicialmente empregada a problemas da mecânica da fratura elástica linear e em seguida extendida a problemas não-lineares, especialmente o modelo coesivo. Exemplos numéricos diversos averiguam as formulações, comparando com resultados analíticos ou disponíveis na literatura. / In this work three boundary elment formulations applied to fracture mechanics are studied. Aiming the analysis of two-dimensional solids with emphasis on the crack problem, the first considered method is the one based on using displacement equations only (singular formulation). The second scheme discussed in this work is a formulation based on the use of traction equations (hyper-singular formulation). Finally the dual boundary element method that uses singular and hyper-singular equations is considered. The numerical schemes have been implemented using continuous and discontinuous linear boundary and crack elements. The boundary and crack integral were all carried out by using analytical expressions, therefore increasing the accuracy of the algebraic system obtained for each one of the studied schemes. The developed numerical programs were applied initially to elastic fracture mechanics and then extended to analyze cohesive cracks. Several numerical examples were solved to verify the accuracy of each one of the studied models, comparing the results with the analytical solutions avaliable in the literature.

The quantitative description of rough fracture surfaces of concrete has been an important challenge for many years. Looking at the fracture surface of a concrete specimen, one realizes that the self-affine geometry of crack faces results from the stochastic nature of the crack growth. This is due to the heterogeneous nature of concrete that makes the crack tortuous leading its way through weak bonds, voids, mortar and getting arrested on encountering a hard aggregate forming crack face bridges. These mechanisms contribute to the tendency of the crack to follow a tortuous path. The self-similarity contained in the tortuous fracture surface of concrete makes it an ideal candidate to be considered as a fractal. Further, the softening response itself has been treated as a singular fractal function by earlier investigators. The very process of cracking and microcracking, could be considered very close to the stick and slip process and therefore as a fractal. Therefore modeling a crack as a fractal and characterizing it by a fractal dimension have become the focus of research in recent years. Due to randomly distributed discontinuous flaws and high heterogeneity of the internal structure of concrete, mechanical properties also randomly vary. Under the effect of the same external force, the stress intensity factors to which different points in the concrete are subjected are different. Hence the microcracks induced by the external force are distributed discontinuously and randomly. Therefore in the present study the effect of the random nature of the microcracks in the fracture process zone of concrete is investigated using both fractal and probabilistic approach. The most probable fractal dimension of a network of micro cracks is obtained as a function of the branching angle ‘α’ of the microcracks, considered as a random variable. Further, an ensemble of cracks is synthetically generated using Monte Carlo technique imposing a constraint that the random deviations do not exceed the maximum size of the aggregate. Such tortuous cracks are analyzed by extending Fictitious Crack Model (FCM) proposed by Hillerborg et al [37]. A numerical study is carried out to examine the influence of certain important fracture parameters on the beam response of plain concrete beams. The contents of this thesis are organized in seven chapters with references at the end. Chapter-1 summarizes the historical development of fracture mechanics. A brief review of the basic concepts of fracture mechanics theory is presented. In chapter-2 a brief review of literature on fracture mechanics of concrete is presented. An overview of the analytical models, numerical models and fractal models till date has been presented in a systematic way. In chapter-3 the fracture processs zone has been modeled as a fractal following the work of Ji et al [118]. The contribution here has been to improve the work of Ji et al [118] (which considers the region of microcracks as a fractal tree) by considering the branching angle as a random variable. Mean fractal dimension thus obtained is found to match well with the experimental results available in the literature. In chapter-4 FCM, as proposed by Hillerborg et al [37] has been modified to be applicable to cracks with varying inclined faces by considering both horizontal and vertical components of the closing forces. The theoretical aspects of the modified FCM have been described in detail. The procedure for the determination of influence co- efficient matrices for a random tortuous crack in mode-I and mixed-mode along with a fractal crack has been explained. In the subsequent chapters the study has been taken up in two parts. In the first part only one generator of the fractal tree considered by Ji et al [118] has been analyzed by FCM to obtain load-deformation responses and fracture energy. In part two, a random tortuous crack, as already defined earlier has been analyzed both in mode-I and mixed mode using FCM. In chapter-5 plain concrete beams with one generator of fractal tree has been analyzed. The influence of the branching angle on the post-peak response of (P-δ) curves and fracture energy has been obtained. In chapter-6 a random tortuous crack has been analyzed in mode-I by FCM. The analysis reveals the influence of maximum aggregate size upon the pre and post-peak behaviour in support of the experimental findings. The nominal stress at peak is found to depend on the characteristic dimension of the structure thereby confirming the size effect. Further fracture energy values have been obtained by the work of fracture method and the results show good agreement with the results obtained in the literature. In chapter-7 a random tortuous crack has been analyzed in mixed mode by FCM. While modeling, symmetry has been assumed only to facilitate computational work though it is known that loss of symmetry affects the peak load. However analysis of the whole beam can be handled by the code developed in the thesis In chapter-8 a summary of the research work is presented along with a list of major observations and references at the end.

The diploma thesis deals with effective crack model for a cylinder specimen with an chevron-shaped notch, loaded by a three-point bending. The first part of the thesis is theoretical and the it describes the use of fracture mechanics for quasi-brittle materials – concrete and rocks. Furthermore there is described the linear elastic fracture mechanics and founding the geometry function for a different geometries of fracture tests. The second part describes the FEM program, which was used to calculate the fracture parameters, that were used to determine the length of the effective crack and how the program was tested before it was used. The last part describe calculations of fracture toughness by using the effective crack model on selected rock and concrete specimens.

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

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第21374号 / 農博第2298号 / 新制||農||1066(附属図書館) / 学位論文||H30||N5147(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 村上 章, 教授 藤原 正幸, 教授 渦岡 良介 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM