Cette thèse est consacrée à la simulation du comportement à la rupture de bois sous des chargements à long terme et sous des conditions d'Humidité Relatives (HR) de l'air variables. Il est connu que le bois est un matériau fortement hygroscopique, ses propriétés mécaniques et de rupture sont en effet très dépendantes de sa teneur en eau. En outre, la stabilité d'une fissure existante dans un élément structural peut être fortement influencée parles variations, en particulier brusques, d'humidité relative qui peut conduire à la rupture inattendue de l'élément.L'approche thermodynamique proposée intègre l'effet de mécanosorption dans l'expression analytique de la déformation, en découplant les déformations mécaniques et celles dues au comportement mécanosorptif du matériau. En outre, la rupture quasi-fragile du matériau boisest traduite par un modèle de zone cohésive dont les paramètres de cohésion sont fonctions de la teneur en eau afin de simuler l’effet de l'humidité sur les propriétés de rupture. Sur cette base, une formulation incrémentale permet l'intégration de l'effet des variations soudaines d’humidité relative (autrement dit, le choc hydrique) sur la zone d’élaboration(zone cohésive) en introduisant un champ de contraintes supplémentaires le long de cette zone. Fonction de la variation de HR, ce champ de contraintes supplémentaires dépend de l'état de contrainte et de l'ouverture de la fissure le long de la zone cohésive, mais également de l'humidité en pointe de fissure (matériau non endommagé). Dans l'analyse par éléments finis, un opérateur tangent algorithmique est utilisé pour résoudre le problème non linéaire en combinant le modèle de mécanosorption et le modèle de zone cohésive et en intégrant l'effet du choc hydrique.La simulation du comportement d'une éprouvette entaillée soumise à un chargement constant et à des variations cycliques de HR montre un fort couplage entre le comportement mécanosorptif et l'effet du choc hydrique HR sur la zone d’élaboration. Ce couplage entraîne une augmentation de la propagation des fissures et conduit à une fissuration plus précoce par rapport à celle obtenue à partir du modèle de mécanosorption seul ou à partir du modèle de zone cohésive en intégrant l'effet des variations soudaines de HR. En outre, le couplage entre le modèle mécanosorptif et le modèle de zone cohésive en intégrant l'effet du chochydrique montre l'intérêt d'une telle approche numérique pour décrire le comportement complexe des éléments de charpente en bois soumis à des conditions climatiques variables,comportement qui ne peut être prédit par une simple superposition des deux modélisations. / This thesis is dedicated to the simulation of the fracture behavior of wood under long-termloading and variable relative humidity conditions. Indeed, wood is well-known to be a highlyhygroscopic material in so far as its mechanical and fracture properties are very dependenton moisture. Moreover, the stability of an existent crack in a structural element can bestrongly affected by the sudden variations of relative humidity (RH) and can lead tounexpected failure of the element.The thermodynamic approach proposed in this thesis includes the mechano-sorptive effect inthe analytical expression of the deformation, by operating a decoupling of the strain in amechanical part and a mechano-sorptive part in material. Moreover, the quasi-brittle fractureof wood is here simulated from a cohesive zone model whose cohesive parameters arefunctions of the moisture in order to mimic the moisture-dependent character of the fractureproperties. On this basis, an increment formulation allows the integration of the effect ofsudden RH variations on the fracture process zone (cohesive zone) by introducing anadditional stress field along this zone. As a function of the RH variation, this additional stressfield depends on not only the stress state and the crack opening along the cohesive zone butalso the material moisture ahead of the zone (undamaged material). In the finite elementanalysis, an algorithmic tangent operator is used to solve the non-linear problem combiningmechano-sorptive model and cohesive zone model including the effect of sudden RHvariations.The simulation of a notched structural element submitted to a constant load and cyclic RHvariations exhibits a strong coupling between the mechano-sorptive behavior and the effectof the RH variations on the fracture process zone (FPZ). This coupling results in an increaseof the crack propagation kinetic and leads to a precocious failure compared to those obtainedfrom the mechano-sorptive model or from the effect of sudden RH variations on the FPZ.Moreover, the coupling between the mechano-sorptive model and the effect of sudden RHvariations on the FPZ which cannot be predicted by a simple superposition of both effects,showing the interest of such a numerical approach in order to describe the complex behaviorof wood structural elements submitted to variable climatic conditions.

This thesis has discussed both properties and geometry of concrete slabs used in bridges. It gave understanding on behavior of concrete in both tension and compression zones and how crack propagates in specimens by presenting both theory of fracture and performing concrete tests like tension splitting, uniaxial compression and uniaxial tension tests. Furthermore, it supported experimental tests with finite elements modelling for each test, and illustrated both boundary conditions and loads. The thesis has used ARAMIS cameras to observe crack propagations in all experimental tests, and its first study at LNU that emphasized on Brazilian test, because of importance of this test to describe both crushing and cracking behavior of concrete under loading. It’s an excellent opportunity to understand how concrete and steel behave individually and in combination with each other, and to understand fracture process zone, and this has been discussed in theory chapter. The geometry change that could affect stresses distributions has also described in literature and modelled to give good idea on how to model slabs in different angles in the methodology chapter. Thus, thesis will use finite elements program (Abaqus) to model both experimental specimens and concrete slabs without reinforcement to emphasize on concrete behavior and skewness effect. This means studying both properties of concrete and geometry of concrete slabs. This thesis has expanded experimental tests and chose bridges as an application.

Made available in DSpace on 2014-12-17T14:57:54Z (GMT). No. of bitstreams: 1 RenataCTSF_TESE_1-81.pdf: 4666386 bytes, checksum: 75d1cdda6a2cab121f77f0774f7de4e7 (MD5) Previous issue date: 2012-09-14 / There are a number of damaging mechanisms that various materials can suffer in service. However, when working with polymer composite materials, this is something that requires analysis, especially when exposed to adverse environmental conditions. Thus, the objective of the present thesis is the study of the direct influence of environmental aging and the form of hybridization of the reinforcement woven on the structural stability, surfacedegradation and fracture process of polymer composites laminates. For this, the development of two polymer composite laminates was necessary, where one of them was reinforced with a bi-directional woven with hybrid strandsofkevlar-49/glass-Efibers, and the other also with a bi-directionalwoven, however with weft and warpformed of alternating strandsof Kevlar-49 fibers and glass-E fiber The reinforcementwoven are industrially manufactured. Both laminates use a polyester resin as a matrixand are made up of four layers each. All laminates were industrially prepared by the hand lay-up method of manufacturing. To do this, test specimens were manufactured of the respective laminates and submitted to environmental aging accelerated through the aging chamber. They were exposed to alternating cycles of UV radiation and moisture (heated steam) for a standard defined period. At the end of the exposure period the specimens were subjected to mechanical tests of uniaxial tensile and bending in three points and to the characterizationsof the fracture and surface deterioration. In addition, they were submitted to a structural degradation assessment by the measurement of mass variation technique (MMVT) and the measurement of thickness variation technique (MTVT), this last technique being developed in this thesis. At the end of the analysis it was observed that the form of hybridization of the reinforcement woven and the aging process directly influence with losses or gain in mechanical properties, with losses in the structural degradation and in the formation and propagation of damage mechanism of the developedcomposite laminates / S?o v?rios os mecanismos de danos que os diversos materiais podem sofrer em servi?o. No entanto, ao se trabalhar com os materiais comp?sitos polim?ricos isso ? algo que necessita de an?lises principalmente quando expostos a condi??es ambientais adversas. Logo, a respectiva tese objetiva o estudo da influ?ncia direta do envelhecimento ambiental e da forma de hibridiza??o dos tecidos de refor?o no comportamento mec?nico, degrada??o estrutural (dimensional e de massa) de laminados comp?sitos polim?ricos. Para tanto se fez necess?rio o desenvolvimento de dois laminados comp?sitos polim?ricos, onde um deles ? refor?ado com um tecido bidirecional com mecha h?brida de fibras de kevlar-49/vidro-E e o outro com um tecido tamb?m bidirecional, por?m com trama e urdume formadas com mechas alternadas de fibras kevlar-49 e fibras de vidro-E. Os tecidos de refor?o s?o de fabrica??o industrial. Ambos os laminados utilizam como matriz a resina de poli?ster, sendo constitu?dos de quatro camadas cada. Todos os laminados foram confeccionados industrialmente pelo m?todo de fabrica??o handlay-up. Desta forma, foram fabricados corpos de provas (CP s) dos respectivos laminados e submetidos ao envelhecimento ambiental acelerado atrav?s da c?mara de envelhecimento. Os mesmos foram expostos aos ciclos alternados de radia??o UV e umidade (vapor aquecido) por um per?odo definido em norma. Ao t?rmino do per?odo de exposi??o os CP s foram submetidos aos ensaios mec?nicos de tra??o uniaxial e flex?o em tr?s pontos e ?s caracteriza??es da fratura e da deteriora??o superficial. Al?m disso, foram submetidos ? avalia??o da degrada??o estrutural mediante a t?cnica de media??o de varia??o de massa (TMVM) e a t?cnica de medi??o de varia??o de espessura (TMVE), sendo essa ?ltima desenvolvida nesta tese. Ao t?rmino das an?lises foi observado que a forma de hibridiza??o dos tecidos de refor?o e o processo de envelhecimento influenciam diretamente, seja com perdas ou ganho naspropriedades mec?nicas, com perdas na degrada??o estrutural e na forma??o e propaga??o do mecanismo de dano dos laminados comp?sitos desenvolvidos

Orientador: Jose Luiz Antunes de Oliveira e Sousa / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-08T23:02:14Z (GMT). No. of bitstreams: 1 Rosa_AlaorLeandro_M.pdf: 2119051 bytes, checksum: 8f5c501220a7f5599ce9888da3461e86 (MD5) Previous issue date: 2005 / Resumo: Este trabalho enfoca o estudo de processos de fratura em vigas de concreto, concreto reforçado com fibras de aço, concreto armado e concreto armado reforçado com fibras de aço, através da simulação numérica com o código de elementos finitos DIANA. O estudo envolve a área de pesquisa em materiais compósitos à base de cimento, resultantes da adição de fibras de aço descontínuas orientadas aleatoriamente, e a análise numérica de sólidos contendo fissuras. Foram realizadas simulações numéricas de processos de fratura em vigas, sob carregamento monotônico, de acordo com os modelos de fissura discreta (¿discrete crack model¿) e de fissura distribuída (¿smeread crack model¿). As curvas tensão-abertura de fissura (s ¿ ?w), que caracterizam o comportamento do concreto e do concreto reforçado com fibras de aço, após a tensão de tração ser atingida, foram obtidas por retroanálise de vigas entalhadas submetidas ao ensaio de flexão em três pontos. As simulações foram realizadas para comparar resultados numéricos e experimentais de vigas entalhadas carregadas em três pontos e vigas armadas projetadas para ruptura à flexão e ao esforço cortante. Em todos os casos, foram considerados espécimes sem e com adição de fibras de aço / Abstract: This work addresses the study of fracture processes in concrete beams with conventional and steel fiber reinforcements, through numerical simulation with DIANA Finite Element Analysis code. The study include the research area of cementitious material composites, obtained from the addition of discrete and randomly oriented steel fibers to the concrete, and the area of numerical analysis of solids containing cracks. Numerical simulations of fracture processes in beams, subject to flexure and shear under monotonic load, were performed according to the smeared crack model and to the discrete crack model. The stress-crack opening curves (s ¿ ?w), used to characterize the material constitutive behavior of the concrete after tensile stress is reached, were obtained by inverse analysis of notched prismatic specimens subject to three-point-bending tests. The simulations were performed to compare numerical and experimental results from notched three-point-bending specimens and from reinforced beams designed for diagonal shear or flexural failure. Specimens with and without steel fibers were analyzed in all the cases / Mestrado / Estruturas / Mestre em Engenharia Civil

La défaillance des matériaux et structures d'ingénierie peut être considéré comme le résultat d'une interaction complexe entre différents phénomènes physiques tels que la nucléation des cavités, les microfissures, les microvides et d'autres processus irréversibles. Ces micro-défauts se fondent éventuellement en une ou plusieurs macro-fissures conduisant à une diminution de la capacité portante et finalement à une défaillance de la structure considérée. La prévention des défaillances des structures et des composants structurels a toujours été un sujet important et une préoccupation majeure en ingénierie. Cette thèse vise à représenter une défaillance localisée dans des matériaux non linéaires sans dépendance de maillage. Un intérêt particulier sera le cas de l’adoucissement dynamique des déformations. Les phénomènes localisés sont pris en compte en utilisant l'approche des discontinuités embarquées fortes dans laquelle le champ de déplacement est amélioré pour capturer la discontinuité. Sur la base de cette approche, on a d'abord développé un modèle unidimensionnel de barres élasto-plastique capable de représenter une défaillance pour des matériaux ductiles avec un durcissement combiné dans une zone de processus de fracture FPZ et un adoucissement avec des discontinuités fortes encastrées. Les résultats comparant le modèle unidimensionnel proposé aux travaux (semi-) analytiques sont présentés. Il a été démontré que la stratégie proposée offre des solutions indépendantes de maillage. La déformation augmente dans le domaine de l’adoucissement avec une diminution simultanée de la contrainte. Le problème se décharge élastiquement à l'extérieur de la zone d’adoucissement de déformation. L'énergie dissipée se trouve à disparaître. Le modèle a également été comparé à un modèle de dommage unidimensionnel capable de représenter la fracture dynamique de la barre d'endommagementélasto-endommagée dans la zone de traitement de fracture - FPZ et de adoucissement avec de discontinuités fortes encastrées pour trouver un bon accord entre deux modèles. Un modèle d'éléments finis bidimensionnel a été développé, capable de décrire à la fois le mécanisme de dommage diffus accompagné d'un durcissement initial et d'une réponse d’adoucissement ultérieure de la structure. On a analysé les résultats de plusieurs simulations numériques effectuées sur des essais mécaniques classiques sous des charges progressivement croissantes telles que le test Brésilien ou le test de flexion en trois points. Le cadre de dynamique proposé est montré pour augmenter la robustesse de calcul. On a constaté que la direction finale des macro-fissures est assez bien prédite et que l'influence des effets d'inertie sur les solutions obtenues est assez modeste notamment en comparaison entre différentes mailles. Ce modèle bidimensionnel a été étendu plus loin dans le modèle bidimensionnel de discontinuité intégrée en viscodamage pour aider à explorer brièvement la mise en œuvre du schéma de point intermédiaire de second ordre qui peut fournir des résultats améliorés sous limitation de la régularisation visqueuse du modèle de dégâts localisés. / Failure of engineering materials and structures can be considered as a result of a complex interplay between different physical phenomena such as nucleation of cavities, microcracks,microvoids and other irreversible processes. These micro-defects eventually coalesce into one or more macro-cracks leading to a decrease in the load-bearing capability and finally, to failure of the structure under consideration. Prevention of failure of structures and structural parts has always been a critical subject and a major concern in engineering. This thesis aims to represent localized failure in non linear materials without mesh dependency. Of special interest will be the case of dynamic strain-softening. Localized phenomena are taken into account by using the embedded strong discontinuities approach in which the displacement field is enhanced to capture the discontinuity. Based upon this approach, a one-dimensional model for elasto-plastic bar capable of representing failure for ductile materials with combined hardening in FPZ-fracture process zone and softening with embedded strong discontinuities was first developed. Results comparing the proposed one-dimensional model to (semi-) analytical works are presented. It was shown that the proposed strategy provides mesh independent solutions. Strain increases in the softening domain with a simultaneous decrease of stress. The problem unloads elastically outside the strain softening region. The strain energy is found to vanish. The model was also compared with a one dimensional damage model capable of representing the dynamic fracture for elasto-damage bar with combined hardening in fracture process zone - FPZ and softening with strong embedded discontinuities to find a good agreement between two models. A two-dimensional finite element model was developed, capable of describing both the diffuse damage mechanism accompanied by initial strain hardening and subsequent softening response of the structure. The results of several numerical simulations, performed on classical mechanical tests under slowly increasing loads such as Brazilian test or three-point bending test were analyzed. The proposed dynamics framework is shown to increase computational robustness. It was found that the final direction of macro-cracks is predicted quite well and that influence of inertia effects on the obtained solutions is fairly modest especially in comparison among different meshes. This two-dimensional model was expanded further into the two dimensional continuum viscodamage-embedded discontinuity model to help briefly explore the implementation of the second order mid-point scheme that can provide improved results under limitation of viscous regularization of localized failure damage model.

Ce travail concerne des expériences mécaniques, des analyses numériques et des modélisations analytiques de la rupture cohésives (Mode I), vis-à-vis de l’étude du comportement mis en évidence par la courbe de Résistance (Courbe-R) et l’effet d’échelle de structures entaillées en bois massif. Des expériences de fissuration sont combinées à des analyses numériques pour déterminer les propriétés de rupture au moyen d’une procédure appelée Théorie de la Mécanique de la Rupture Linéaire Élastique équivalente (TMRLE), basée sur la complaisance de la structure. La courbe-R, obtenue à partir des expériences, selon une méthode de correction du poids propre, montre l’existence d’un domaine endommagé (Zone de Processus de Rupture) de taille non négligeable se développant en fond de fissure. Dans des conditions de fissuration stationnaire, ce domaine atteint une taille critique, et l’énergie nécessaire pour faire propager la fissure avec ce domaine endommagé (par unité de surface de rupture), reste constante. Le taux de libération de l’énergie de fissuration ainsi attendu, joue un rôle important en Mécanique de la Rupture, car il est possible simuler le comportement quasi-fragile du matériau en combinaison avec les autres propriétés de cohésion. La loi d’effet d’échelle de Bažant, utilisée pour prévoir l’influence de la taille sur la contrainte nominale, est estimée à partir de la réunion de deux comportements asymptotiques réalisés sur de petites tailles (Analyse limite ou RdM) et des grandes tailles. Une procédure analytique est présentée pour évaluer le comportement asymptotique additionnel exhibé par la contrainte nominale dans le régime intermédiaire, de façon plus exacte. Une validation numérique est présentée, et l’information expérimentale vient confirmer ce comportement asymptotique. / This work concerns the mechanical testing, numerical analysis and modelling of cohesive fracture (Mode I) on the purpose to study the Resistance-curve behaviour and the size effect in wooden notched structures. The mechanical testing is combined with the numerical analysis to evaluate fracture properties by means of an equivalent LEFM approach based on the structure compliance. The Resistance-curve being revealed from the experiments, by means of a self-weight compensation method, correction puts into evidence that a non-negligible damaged domain (Fracture Process Zone) is under development in the crack front during the loading process. This being the case, among other fracture parameters issued from the Resistance-curve, the critical (asymptotic) energy release rate is determined, turning possible to use it in combination with other cohesive crack properties in the crack modelling (in Mode I). Thus, for a given geometry it is possible to monitor the critical dimension being revealed by the Fracture Process Zone (FPZ) during the crack propagation. The well known Bažant’s size effect law provides the scaling of the nominal strength through the asymptotic matching performed both on the small (Strength Theory) and on the large (LEFM) structure sizes. An analytical procedure is proposed to determine an additional asymptotic regime in the intermediate size range through a more accurate manner. Numerical validations of the proposed procedure are made and experimental data is presented revealing the scaling of the nominal strength through an envelop of values.

Le béton présente une rupture quasi-fragile du fait de la présence d’une zone d’élaboration de la rupture principalement microfissurée et de taille conséquence, se développant en avant du front de fissure. L’objectif de ces travaux consiste à mettre en évidence le processus d’évolution de la zone d’élaboration et l’étendue de cette dernière, et ce, sur la base d’une campagne d’essai Wedge Splitting suivie de simulations numériques aux éléments-finis utilisant le modèle d’endommagement isotrope de Fichant – La Borderie à l’échelle mésoscopique. Expérimentalement, les courbes de résistance obtenues dans le cadre de la Mécanique Linéaire Élastique de la Rupture équivalente attestent d’un phénomène de confinement précoce de la zone d’élaboration manifestement lié à la géométrie testée et aux propriétés du béton étudié.Les simulations numériques obtenues sur la base du modèle d’endommagement sont en accord avec les résultats expérimentaux et conduisent également à soupçonner ce phénomène de confinement. Par la suite, la simulation numérique est à nouveau utilisée sur cette même géométrie de spécimen mais en réduisant les propriétés de rupture de la matrice cimentaire afin de diminuer la taille de la zone d’élaboration. Les résultats de cette nouvelle simulation montrent un développement libre de la zone d’élaboration suivie d’une propagation auto-similaire de la fissure principale attestée par la présence d’un régime plateau de la courbe de résistance correspondante.Une analyse détaillée du champ d’endommagement puis du champ d’énergie restituée est réalisée et permet de mettre en évidence un critère de développement de la zone d’élaboration fondée sur une valeur maximale du taux local de restitution d’énergie d’endommagement. / Concrete exhibits a quasibrittle fracture due to the existence of a large fracture process zone (FPZ), mainly microcracked, which develops ahead of the crack front. The aim of the current work consists in highlighting the FPZ development and its extent. For that purpose,an experimental campaign using Wedge Splitting Test was carried out and followed by finite element simulation using Fichant – La Borderie isotropic damage model acting at the mesoscale of concrete. Experimental analysis exhibits that by the use from Resistance curves estimated in the framework of equivalent Linear Elastic Fracture Mechanics, the used geometry combined to the studied concrete properties are subjected to a confinement of FPZ. Numerical simulations achieved by the damage model are in agreement with experimental results and also seem to show FPZ confinement. There after, numerical simulations are used again on the same specimen geometry but by decreasing fracture properties of cementitious matrix, in order to minimize the FPZ size. Numerical results exhibit that the FPZ was now freely developed and followed by a self-similar propagation of the main crack as shown by the existence of a “plateau” value on the corresponding Resistance curve. A numerical analysis is performed and leads to the propositionof a FPZ development criteria based on a maximal value of the local damage energy release rate.

The microstructure of concrete contains random features over a wide range of length scales in which each length scale possess a new random composite. The influence of individual material constituents at different scales and their mutual interactions are responsible for the formation of fracture process zone (FPZ). The presence of the FPZ and the various toughening mechanism occurring in it, influences the fatigue and fracture behavior of concrete which also gets influenced by the geometry, spacial distribution and material properties of individual material constituents and their mutual interactions. Hence, in order to study the influence of interfacial transition zone, microcrack and aggregate bridging on the fracture and fatigue behavior of concrete, a multiscale analysis becomes necessary. This study aims at developing a linearized model which helps in understanding the fracture and fatigue behavior of cementitious materials by considering the predominant fracture process zone (FPZ) mechanisms such as microcracking and aggregate bridging. This is achieved by quantifying the critical microcrack length and the bridging resistance offered by the aggregates. Further, the moment carrying capacity of a cracked concrete beam is determined by considering the effect of aggregate bridging. A modified stress intensity factor (SIF) is derived based on linear elastic fracture mechanics (LEFM) approach by considering the material behavior at different scales through a multiscale approach. The model predicts the entire crack growth curve for plain concrete by considering these process zone mechanisms. Furthermore, the fracture and fatigue response of concrete is studied through the development of analytical models which include the properties of the mix constituents using the multiscale based SIF. The effect of the interfacial transition zone, microcracks and resistance offered through aggregate bridging on the resistance to crack initiation and propagation are studied. A fatigue crack growth law is proposed using the concepts of dimensional analysis and self-similarity. Through sensitivity analyses, the influence of different parameters on the overall fracture and fatigue behavior are studied. In addition, studies related to concrete-concrete bi-material interfaces are conducted in order to understand the influence of repair materials on the service life of damaged concrete structures when subjected to fatigue loading. An analytical model is proposed in this study to predict the crack growth curve using the concepts of dimensional analysis and self-similarity in conjunction with the human population growth model. It is seen that a repair done with a patch having similar elastic properties as those of the parent concrete will have a larger fatigue life.

Concrete, which was hitherto considered as a brittle material, has shown much better softening behavior after the post peak load than anticipated. This behavior of concrete did put the researchers in a quandary, whether to categorize concrete under brittle materials or not. Consequently concrete has been called a quasi-brittle material. Fracture mechanics concepts like Linear elastic fracture mechanics (LEFM) and Plastic limit analysis applicable to both brittle and ductile materials have been applied to concrete to characterize the fracture behavior. Because of quasi-brittle nature of concrete, which lies between ductile and brittle response and due to the presence of process zone ahead of crack/notch tip instead of a plastic zone, it is found that non-linear fracture mechanics (NLFM) principles are more suitable than linear elastic fracture mechanics (LEFM) principles to characterize fracture behavior. Fracture energy, fracture process zone (FPZ) size and the behavior of concrete during fracture process are the fracture characteristics, which are at the forefront of research on concrete fracture. Another important output from the research on concrete fracture has been the size effect. Numerous investigations, through mathematical modeling and experiments, have been carried out and reported in literature on the effect of size on the strength of concrete and fracture energy. Identification of the sources of size effect is of prime importance to arrive at a clear analytical model, which gives a comprehensive insight into the size effect. With the support of an unambiguous theory, it is possible to incorporate the size effects into codes of practices of concrete design. However, the theories put forth to describe the size effect do not seem to follow acceptable regression. After introduction in Chapter-1 and literature survey in Chapter-2, Chapter-3 details the study on size effect through three point bend (TPB) tests on 3D geometrically similar specimens. Fracture behavior of beams with smaller process zone size in relation to ligament dimension approaches LEFM. The fracture energy obtained from such beams is said to be size independent. In the current work Size effect law (Bazant et al. 1987) is used on beams geometrically similar in three dimensions with the depth of the largest beam being equal to 750mm, and size independent fracture energy G Bf is obtained. In literature very few results are available on the results obtained from testing geometrically similar beams in three dimensions and with such large depth. In the current thesis the results from size effect tests yielded average fracture energy of 232 N/m. Generally the fracture energies obtained from 2D-geometrically similar specimens are in the range of 60-70 N/m as could be seen in literature. From 3D-geometrically similar specimens, the fracture energies are higher. The reason is increased peak load, could be due to increased width. The RILEM fracture energy Gf , determined from TPB tests, is said to be size dependent. The assumption made in the work of fracture is that the total strain energy is utilized for the fracture of the specimen. The fracture energy is proportional to the size of the FPZ, it also implies that FPZ size increases with increase in (W−a) of beam. This also means that FPZ is proportional to the depth W for a given notch to depth ratio, because for a given notch/depth, (W−a) which is also W(1 − a ) is proportional to W`because (1 − a ) is a constant. WWThis corroborates the fact that fracture energy increases with size. Interestingly, the same conclusion has been drawn by Abdalla & Karihaloo (2006). They have plotted a curve relating fracture process zone length and overall depth the beam. In the present study a new method namely Fracture energy release rate method is suggested. In the new method the plot of Gf / (W−a) versus (W−a) is obtained from a set of experimental results. The plot is found to follow power law and showed almost constant value of Gf / (W−a) at larger ligament lengths. This means that fracture energy reaches a constant value at large ligament lengths reaffirming that the fracture energy from very large specimen is size independent. The new method is verified for the data from literature and is found to give consistent results. In a quasi-brittle material such as concrete, a fracture process zone forms ahead of a pre-existing crack (notch) tip before the crack propagates from the tip. The process zone contains a scatter of micro-cracks, which coalesce into one or more macro-cracks, which eventually lead to fracture. These micro-cracks and macro-cracks release stresses in the form of acoustic waves having different amplitudes. Each micro or macro crack formation is called an acoustic emission (AE) event. Through AE technique it is possible to locate the positions of AE events. The zone containing these AE events is termed the fracture process zone (FPZ). In Chapter-4, a study on the evolution of fracture process zone is made using AE technique. In the AE study, the fracture process zone is seen as a region with a lot of acoustic emission event locations. Instead of the amplitudes of the events, the absolute AE energy is used to quantify the size of the process zone at various loading stages. It has been shown that the continuous activities during the evolution of fracture process zone correspond to the formation of FPZ, the size of which is quantified based on the density of AE events and AE energy. The total AE energy released in the zone is found to be about 78% of the total AE energy released and this is viewed as possible FPZ. The result reasonably supports the conclusion, from Otsuka and Date (2000) who tested compact tension specimens, that zone over which AE energy is released is about 95% can be regarded as the fracture process zone. As pointed out earlier, among the fracture characteristics, the determination of fracture energy, which is size independent, is the main concern of research fraternity. Kai Duan et al. (2003) have assumed a bi-linear variation of local fracture energy in the boundary effect model (BEM) to showcase the size effect due to proximity of FPZ to the specimen back boundary. In fact the local fracture energy is shown to be constant away from boundary and reducing while approaching the specimen back boundary. The constant local fracture energy is quantified as size independent fracture energy. A relationship between Gf , size independent fracture energy GF , un-cracked ligament length and transition ligament length was developed in the form of equations. In the proposed method the transition ligament length al is taken from the plot of histograms of energy of AE events plotted over the un-cracked ligament. The value of GF is calculated by solving these over-determined equations using the RILEM fracture energies obtained from TPB tests. In chapter-5 a new method involving BEM and AE techniques is presented. The histogram of energy of AE events along the un-cracked ligament, which incidentally matches in pattern with the local fracture energy distribution, assumed by Kai Duan et al. (2003), along the un-cracked ligament, is used to obtain the value of GF , of course using the same equations from BEM developed by Kai Duan et al. (2003). A critical observation of the histogram of energy of AE events, described in the previous chapter, showed a declining trend of AE event pattern towards the notch tip also in addition to the one towards the specimen back boundary. The pattern of AE energy distribution suggests a tri-linear rather than bi-linear local fracture energy distribution over un-cracked ligament as given in BEM. Accordingly in Chapter-6, GF is obtained from a tri-linear model, which is an improved bi-linear hybrid model, after developing expressions relating Gf , GF , (W−a) with two transition ligament lengths al and blon both sides. The values of Gf , and GF from both bi-linear hybrid method and tri-linear method are tabulated and compared. In addition to GF , the length of FPZ is estimated from the tri-linear model and compared with the values obtained from softening beam model (SBM) by Ananthan et al. (1990). There seems to be a good agreement between the results. A comparative study of size independent fracture energies obtained from the methods described in the previous chapters is made. The fracture process in concrete is another interesting topic for research. Due to heterogeneity, the fracture process is a blend of complex activities. AE technique serves as an effective tool to qualitatively describe the fracture process through a damage parameter called b-value. In the Gutenberg-Richter empirical relationship log 10N=a−bM, the constant ‘b’ is called the b-value and is the log linear slope of frequency-magnitude distribution. Fault rupture inside earth’s crust and failure process in concrete are analogous. The b-value, is calculated conventionally till now, based on amplitude of AE data from concrete specimens, and is used to describe the damage process. Further, sampling size of event group is found to influence the calculated b-value from the conventional method, as pointed out by Colombo et al. (2003). Hence standardization of event group size, used in the statistical analysis while calculating b-value, should be based on some logical assumption, to bring consistency into analytical study on b-value. In Chapter-7, a methodology has been suggested to determine the b-value from AE energy and its utilization to quantify fracture process zone length. The event group is chosen based on clusters of energy or quanta as named in the thesis. Quanta conform to the damage stages and justify well their use in the determination of the b-value, apparently a damage parameter and also FPZ length. The results obtained on the basis of quanta agree well with the earlier results.

This work is focused on the application of advanced elasto-plastic material model intended for shotcrete. Spatial mathematical models of two laboratory tests are created, where this model is used. The first test is a three-point bending concrete specimen. Next, the behavior of the material is analyzed, in which input parameters are entered. Consequently, two reverse analyzes of the available data are analyzed where a match between prediction and measurement can be obtained. The second test is a modified tensile test, where is describe the material behavior in changing of input parameters. Subsequently, reverse data analysis is created, where an acceptable match between prediction and measurement is possible. In every study, the stress waveform in the fracture process zone is analyzed to more detail.