Dissertations / Theses on the topic 'Plain Concrete Beams'

Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2018.
Cataloged from PDF version of thesis. Page 45 blank.
Includes bibliographical references (pages 43-44).
Topology optimization is a structural design tool that can autonomously generate efficient forms within a design domain by ascribing fabrication material to key locations of a structure while removing it from underutilized areas. It has been known to lead to new design solutions that outperform conventional low-weight designs. This has made topology optimization a popular design tool for a wide range of applications, but examples related to civil structures such as buildings, bridges, or infrastructure remain limited. This is partly because topology optimization is a free-form design technique, and often produces complex, nonlinear designs that would be difficult to fabricate on a buildings-scale. However, this tendency suggests that concrete could be an excellent building material for topology-optimized civil structures, since its initial liquid phase makes it highly formable, and it's low cost and high strength make it a ubiquitous construction material. Materially-specific topology optimization algorithms have been suggested to account for the anisotropic behavior of reinforced concrete, however they have focused on developing strut-and-tie models and improving the damage strength of the design. At current, the validity of these algorithms remains uncertain as no designs have yet been fabricated and tested. This thesis therefore presents tests of plain concrete members designed using two different topology optimization algorithms that make different assumptions about the fabrication material's behavior, and compares their performance. Although plain concrete is rarely used on a structural scale, these initial experiments were designed without reinforcement to more clearly observe how these design algorithms reckon with the complex behavior of concrete. It was found that an algorithm specifically programmed to optimize plain concrete designed specimens that failed at lower maximum forces than beams designed with an algorithm that was not materially specific. It is likely that this result is due to optimization output rounding that was necessary to produce manufacturable designs. The information obtained from these tests is intended to inform topology optimization algorithms of reinforced concrete in future research.
by Jackson Jewett.
M. Eng.

This thesis deals with the exploration and evaluation of the existing bridge carried him on the highway D2. The work is divided into theoretical and practical parts. The theoretical part focuses on the technical surveys, diagnosis of building structures and some methods of investigation and testing of building structures. In the practical part the visual inspection and diagnosis of disorders of the highway bridge substructures ev. No. D2-058, to determine material characteristics substructure and evaluate the state of the bridge. In conclusion, the practical part of the recommendations for the design and method of repairing the bridge.

Diploma work Multifunction Centre Hlinsko - preparation and realization of the covers technological studies throughout the building. Diploma work proposes a temporal, financial and material resources. The work included construction budget, schedule of work, technical regulations for demolition, implementation and installation of reinforced concrete ceiling glulam beams. For each technological regulation is developed inspection and test plan. The work includes the project site equipment. Diploma work is based on the technical documents supplied by the designer. The work also includes specialty.

Les résultats des essais d'identification des paramètres de la loi de comportement en traction disponibles pour les bétons renforcés de fibres métalliques, ne peuvent généralement rendre compte de manière satisfaisante des capacités réelles du matériau. On cherche à apprécier la sensibilité des grandeurs caractéristiques de la loi de comportement (la résistance en traction f#t et l'énergie de post-fissuration g#f) aux facteurs relatifs a la constitution du corps d'épreuve et aux conditions expérimentales. En suivant la méthodologie des plans d'expériences qui permet d'adopter une démarche formelle dans la définition des essais et d'apprécier la confiance a accorder aux résultats expérimentaux, on définit un modèle rhéologique pour les réponses ainsi retenues. Huit facteurs ont été pris en compte. Certains aspects macroscopique du comportement, ne peuvent être expliques que par une analyse portée a l'échelle micro. Une attention particulière est consacrée à l'étude de l'hétérogénéité et l'anisotropie du matériau. Les modèles de comportement élaborés, sont introduits dans un code de calcul aux éléments finis qui a permis en mettant a profit la théorie de la fissure distribuée, d'apprécier l'apport des fibres sur le comportement global des poutres en flexion

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 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.

碩士
國立臺灣科技大學
營建工程技術學系
83
The ultimate torsional strengths of plain concrete beams are currently calculated by the elastic theory, the plastic theory and the skew-bending theory. However, these theories are entirely based on tests of low-strength concrete beams. Therefore, it is necessary to examine the applicability of these theories when applied to plain high-strength concrete beams subject to pure torsion. In this study, twenty specimens were tested under pure torsion to investigate the effects on torsional strength of concrete strength ,specimen shape and specimen size. Tests results indicate that for high-strength concrete beams, the ultimate torsional strengths calculated using the elastic theory are quite reasonable for T- and L- beams , but overly conservative for rectangular beams. The plastic theory can reasonably predict the torsional strengths of smaller concrete beams. For larger beams , however , the plastic theory overestimates their torsional strengths. The torsional strengths predicted using the skew-bending theory in terms of concrete strength are quite reasonable for beams of T- and L- sections , but slightly conservative for smaller rectangular beams.

Self-consolidating concrete (SCC) has wide use for placement in congested reinforced concrete structures in recent years. SCC represents one of the most outstanding advances in concrete technology during the last two decades. In the current work a great deal of cognizance pertaining to mechanical properties of SCC and comparison of fracture characteristics of notched and unnotched beams of plain concrete as well as using acoustic emission to understand the localization of crack patterns at different stages has been done. An artificial neural network (ANN) is proposed to predict the 28day compressive strength of a normal and high strength of SCC and HPC with high volume fly ash. The ANN is trained by the data available in literature on normal volume fly ash because data on SCC with high volume fly ash is not available in sufficient quantity. Fracture characteristics of notched and unnotched beams of plain self consolidating concrete using acoustic emission to understand the localization of crack patterns at different stages has been done. Considering this as a platform, further analysis has been done using moment tensor analysis as a new notion to evaluate fracture characteristics in terms of crack orientation, direction of crack propagation at nano and micro levels. Analysis of B-value (b-value based on energy) is also carried out, and this has introduced to a new idea of carrying out the analysis on the basis of energy which gives a clear picture of results when compared with the analysis carried out using amplitudes. Further a new concept is introduced to analyze crack smaller than micro (could be hepto cracks) in solid materials. Each crack formation corresponds to an AE event and is processed and analyzed for crack orientation, crack volume at hepto and micro levels using moment tensor analysis based on energy. Cracks which are tinier than microcracks (could be hepto), are formed in large numbers at very early stages of loading prior to peak load. The volume of hepto and micro cracks is difficult to measure physically, but could be characterized using AE data in moment tensor analysis based on energy. It is conjectured that the ratio of the volume of hepto to that of micro could reach a critical value which could be an indicator of onset of microcracks after the formation of hepto cracks.

Self-consolidating concrete (SCC) has wide use for placement in congested reinforced concrete structures in recent years. SCC represents one of the most outstanding advances in concrete technology during the last two decades. In the current work a great deal of cognizance pertaining to mechanical properties of SCC and comparison of fracture characteristics of notched and unnotched beams of plain concrete as well as using acoustic emission to understand the localization of crack patterns at different stages has been done. An artificial neural network (ANN) is proposed to predict the 28day compressive strength of a normal and high strength of SCC and HPC with high volume fly ash. The ANN is trained by the data available in literature on normal volume fly ash because data on SCC with high volume fly ash is not available in sufficient quantity. Fracture characteristics of notched and unnotched beams of plain self consolidating concrete using acoustic emission to understand the localization of crack patterns at different stages has been done. Considering this as a platform, further analysis has been done using moment tensor analysis as a new notion to evaluate fracture characteristics in terms of crack orientation, direction of crack propagation at nano and micro levels. Analysis of B-value (b-value based on energy) is also carried out, and this has introduced to a new idea of carrying out the analysis on the basis of energy which gives a clear picture of results when compared with the analysis carried out using amplitudes. Further a new concept is introduced to analyze crack smaller than micro (could be hepto cracks) in solid materials. Each crack formation corresponds to an AE event and is processed and analyzed for crack orientation, crack volume at hepto and micro levels using moment tensor analysis based on energy. Cracks which are tinier than microcracks (could be hepto), are formed in large numbers at very early stages of loading prior to peak load. The volume of hepto and micro cracks is difficult to measure physically, but could be characterized using AE data in moment tensor analysis based on energy. It is conjectured that the ratio of the volume of hepto to that of micro could reach a critical value which could be an indicator of onset of microcracks after the formation of hepto cracks.

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.

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.

Concrete is the most widely used material in the world for construction of infrastructures and there are quite a few gaps in understanding its behaviour under different loads. Fracture in concrete occurs at pre-existing crack tip upon the formation of a fracture process zone (FPZ) with several toughening mechanisms such as micro-cracking, aggregate bridging, crack branching etc., taking place resulting in energy dissipation, which resists further crack propagation. This FPZ is responsible for the post-peak softening response under tension and size effect. The behaviour of reinforced concrete depends on the combined action of concrete and its embedded longitudinal reinforcement. The study of fracture in reinforced concrete is much more complex due to micro-structural changes in concrete, interaction between the concrete and steel and bond between them. There may be other failure mechanisms involved, such as yielding and slippage of steel, and de-lamination between steel and concrete. Under inadequate provision of stirrups or in the case of deep beams, a beam subjected to transverse loads tends to fail by shear. There is a need to develop analytical models which can address failure under shear using the fracture mechanics theory in order to reflect the size effect and the failure mechanisms. In addition, combined flexural and shear mode of failure in reinforced concrete structures also needs to be studied by considering the internal microcracking mechanisms and the effect of size. Bridge decks, highway pavements, airport pavements and offshore structures made of reinforced concrete are subjected to variable amplitude fatigue loading. The mechanism of fatigue in concrete is not yet clearly understood when compared to metallic materials. Hence, it is important to characterize the behaviour of concrete structures subjected to fatigue loading and understand the fracture mechanisms. In this research work, the problems listed above are addressed through experimental investigations into fracture and fatigue behavior of plain and reinforced concrete using the acoustic emission technique. Important elastic and fracture properties of plain concrete including the size independent fracture energy, fracture toughness, critical crack tip opening displacements, critical crack length and size of process zone are determined. These serve as input parameters in the finite element based fracture mechanics models for analysis of concrete structures. Furthermore, the mechanisms of micro-crack formation, their coalescence, macrocrack formation and eventual failure under monotonically increasing and fatigue loading are determined. The evolution of damage under different loading are studied. The effect of varying beam size (depth) and reinforcement ratios are studied in order to understand the fracture mechanisms for failure under flexure, shear, combined flexure-shear and fatigue. It is seen that the acoustic emission technique could provide vital information on the micro-cracking characteristics in concrete.