Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [160]-173).

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Structural concrete is the most widely used material in the construction of bridges, pave-ments, runways, dams and other infrastructures which are subjected to uctuating loads during its service period. Concrete contains internal aws in the form of micro-cracks as an inherent property. When subjected to fatigue loading, distributed micro-cracks are formed at the sites of pre-existing aws, which subsequently, localize to form a major crack and propagates. The crack growth curve of a structural component when subjected to fatigue loading depicts a sigmoidal pattern. This curve is divided into three distinct regions namely sub-threshold crack propagation (short crack), stable crack propagation (long crack) and unstable crack propagation depending on the crack propagation rate. Most of the fatigue life is spent in the sub-critical stage (small crack) before the for-mation of long cracks. Hence, from the view of estimating the fatigue life, the crack initiation and early crack propagation (short crack stage) phase are the most important and correct concepts need to be developed. Hence, in this work, the behavior of propa-gation and non-propagationof short cracks in concrete when subjected to fatigue loading is addressed. Small non-propagating cracks are usually found at notch roots when the nominal stress range is below certain limits that depend on the notch sensitivity. Analysis is performed on geometrically similar three-point bend beams of three di erent sizes and subjected to fatigue loading in order to determine the important factors that a ect the notch sensitivity and to determine the minimum stress range required for the initiation and propagation of short cracks. A criterion for crack initiation and propagation is proposed based on linear elastic fracture mechanics. Using this criterion, the maximum length of non-propagating crack that can be formed from fatigue loading alone and the minimum stress range required to propagate a crack without arrest are computed. It is observed that the notch sensitivity increases with increase in beam size, decrease in notch-tip aspect ratio and increase in the fatigue limit of the material. Since the probability of formation of a non-propagating crack at a notch tip decreases with increase in notch sensitivity, and since it is desirable not to have a non-propagating crack in experimental investigations, it is essential to design a specimen with higher notch sensitivity. A crack spends a considerable amount of time in the short crack regime. The short cracks are found to propagate at higher rates than the long cracks at the same nominal stress intensity factor which is known as the short crack anomaly. It is important to consider this anomaly in the prediction of the residual life of damaged concrete structures. Hence, in the present work, an analytical model is developed using the principles of dimensional analysis and self-similarity in order to estimate the rate of short crack growth in concrete. The important parameters such as load range, threshold value of stress intensity factor range, modulus of elasticity, tensile strength, fracture energy, stress ratio, crack size and the maximum aggregate size are considered in the development of the short crack growth model. The model is calibrated and validated using the experimental results that are available in the literature. A probabilistic analysis is carried out to determine the sensitivity of each of the di erent parameters that has been considered on the crack growth rate using the coe cient of variation method. It is found that the crack length is the most sensitive parameter to short crack growth rate followed by the load range. A term called `characteristic fatigue life of short crack' is de ned as the number of fatigue cycles that can be applied such that not more than ve percent of the short cracks is expected to proceed to the long crack regime. Furthermore, the fatigue life of a crack spent in the short crack regime is determined through a reliability based study using the Monte Carlo technique. It is found that the smaller sized specimens have larger fatigue life in the short crack regime than the larger specimens.

Concrete has established itself as the most widely used structural material. There is hardly any place where human life and concrete structure do not exist together. It's use is seen in wide variety of structures like buildings, bridges, dams, nuclear structures, floating and submerged structures and so on. Hence, in view of safety, serviceability and economy, proper understanding of the behaviour of concrete is imperative in designing these complex structures. Current reinforced concrete codes are based on strength and serviceability concepts. The tensile strength of concrete is totally neglected in the limit state method of analysis. The concrete in tension is assumed to be fully cracked and conservative method of design is adopted. The crack causes a considerable degradation of stiffness of overall structure and gives rise to regions of stress concentration, which are not accounted for, in the present design methods. Besides, it is found that the size of the structural component significantly influences the stress at failure. It has been fairly well established that large specimens fail by catastrophic crack propagation while small specimens tend to fail in a ductile manner with considerable amount of slow crack growth preceding fracture. Initial attempts to understand the cracking of concrete through the principles of fracture mechanics was made in 1960's. It was concluded that the LEFM and small scale yielding fracture mechanics which are developed for metals are inapplicable to concrete structures except for certain limiting situations such as the behaviour at extremely large sizes. The reasons for the inapplicability of LEFM principles to concrete structures are attributed to slow crack growth, formation of nonlinear fracture process zone, and softening behaviour of concrete in tension. Several analytical and numerical models have been proposed to characterize the fracture behaviour of concrete. In the present work a simple numerical method is proposed to analyse the Mode-I fracture behaviour of concrete structures, using finite element method. The stiffness matrices calculated at the beginning of the analysis are used till the end without any modification. For this reason, the method is named as Initial Stiffness Method (ISM). An attempt has also been made to modify the lattice model existing in literature. The contents of the thesis are organised in six chapters. In chapter 1, a brief introduction to basic principles of fracture mechanics theory is presented. This is included mainly for the completeness of the thesis. In chapter 2, a brief review of literature regarding the application of principles of fracture mechanics to concrete structures is presented. The need for the introduction of fracture mechanics to concrete is presented. Early work, applying LEFM principles to concrete structures is discussed. The reasons for the inapplicability of linear elastic fracture mechanics principles to concrete structures are discussed. Necessities for nonlinear fracture mechanics principles are pointed out. Attention is focused on the influence of the factors like slow crack growth, formation of nonlinear fracture process zone and softening behaviour of concrete in tension on the fracture behaviour. Besides a possible use of fracture energy as an alternative fracture criterion for concrete is contemplated. Several analytical and numerical models (assuming concrete as homogeneous continuum), proposed so far to characterize the fracture behaviour of concrete, are presented and discussed in detail. Different heterogeneous models presented so far are also discussed. In chapter 3, a simple numerical method to analyse the fracture of concrete (strain softening material) in Mode-I, using FEM is proposed. The stiffness matrices are generated only once and are used till the end of the analysis. This feature makes the model simple and computationally efficient. A new parameter namely, strain softening parameter α has been introduced. It is found that this strain softening parameter ‘α’ is a structural property. The results obtained from the present method are found to converge with increasing number of elements thus making the method mesh independent, and thus objective. The method was validated by analysing the beams tested and reported by various researchers. The predicted values of maximum load by the present method are found to agree well with the experimental values. Initially, all the beams are analysed using uniform meshes and load-deflection diagrams are plotted. All the beams are again analysed using graded meshes. The load-deflection, load-CMOD diagrams are plotted from the results obtained from the analysis using graded meshes. In chapter 4, the results obtained in chapter 3 are analysed for size effect. Literature regarding size effect of concrete structures has been reviewed. In addition to the size effect on nominal stress at failure which exists in literature, two new parameters namely, post peak slope and softening slope parameter α have been used to confirm the size effect. This does not exist in the literature. In chapter 5, an attempt is made to modify the lattice model existing in literature. This is done with a view to model concrete as a heterogeneous medium, which would be nearer to reality. The softening property of concrete has been incorporated. The model was validated against some of the experimental results existing in literature. The results are found to be encouraging. The results from this model show the post peak softening similar to the experimentally observed ones. The effects of different probabilistic distributions to the properties of mortar on the maximum load of the beam are studied. It is found that normal distribution of properties to mortar gives the best results. A study is made regarding the sensitivity of various properties of mortar on the maximum load of the beam. It is concluded that load carrying capacity of the beam can be increased by using a mortar of higher tensile strength. Finally in chapter 6, general conclusions and suggestions for further investigations are discussed.

It is quite well known that fracture behavior of concrete is complex and is influenced by several factors. Apart from material properties, geometric parameters influence fracture behavior and one notable phenomenon is size effect. The existence of the size effect in concrete is well known and various attempts to model the behavior is well documented in literature. However the approach by Bazant to describe the size effect behavior in concrete has received considerable attention. The major advantage of developing the size effect law for concrete is the ability to describe the fracture behavior (namely failure strength) of large size structures inaccessible to laboratory testing. The prediction of size effect is done on the basis of laboratory testing of small size geometrically similar structures. In all the models developed earlier heterogeneity of concrete has not been quantitatively simulated. Hence, the complete description considering heterogeneity in concrete is attempted using the lattice model to understand size effect behavior in concrete. In the present study, a detailed description of the heterogeneity in concrete is at- tempted by 3D lattice structure. Analytical treatment to gain insights to fracture behavior is difficult and hence a numerical approach capable of handling the het- erogeneous nature of the material is adopted. A parametric study is performed to understand the influence of various model parameters like mesh size, failure criterion, softening model. The conventional size effect studies for 2D geometrically similar structures are performed and a comparison is done with experimentally observed behavior. The variation of fracture process zone with respect to structure size is observed as the reason for size effect. The influence of variation in properties of ag- gregate, matrix and interface are studied to explain the deviation in pre-peak and post-peak response. A statistical study is performed to establish the size dependence of linear regression parameters (Bf ‘t and D0) which are used in Bazant size effect law. An analytical framework is also proposed to substantiate the above results. Size effect in concrete is generally attributed to the effect of depth viz. the dimension in the plane of loads. However although the effect of thickness viz. a dimension in a plane perpendicular to that of the loads is not considered in concrete. The same is quite well known in fracture of metals. Therefore the variation in grading of aggregates along with the influence of thickness on fracture behavior is analysed. To understand the thickness effect a comparison of 2D and 3D geometrically similar structures is performed to understand the effect of thickness on fracture parameters. Heterogeneity is a matter of scale. A material may be homogeneous at a coarser scale while at a finer scale it is heterogeneous. Hence only way to capture the effect of the behavior at micro level on the behavior at meso level particularly in a heterogeneous material like concrete is by a multi-scale modelling. The best numerical tool for multiscale model of a heterogeneous material is lattice model. The heterogeneous nature of concrete is not just due to the presence of aggregates but is evident right from the granular characteristics of cement. The hydration of cement grain leads to the development of products with varying mechanical and chemical properties. As the micro-crack initiation and development of thermal cracking is observed at the micron level, understanding of hydration behavior in concrete can be thought of as a pre-requisite for complete understanding of fracture behavior. The properties of matrix and interface observed during hydration modelling can also be used as an input for fracture predictions at upper scale models (eg. mesoscale). This can also be used to study the coupling of scales to understand the multi-scale fracture behavior in concrete. A numerical model is hence developed to study the hydration of concrete. Due to the existence of complex mechanisms governing the hydration behavior in con- crete and the large number of parameters affecting its rate, the hydration of a grain is assumed to proceed in isolation. A single particle hydration model is developed to study the hydration of isolated grain. A shrinking core model usually used to describe the burning of coal is adopted as a base model for analytically describing the hydra- tion behavior. The shrinkage core model in literature is modified to be applicable to hydration of cement matrix. The effect of particle diameter as well as changing water concentration is incorporated into the model whereas the influence of reduction in pore sizes as well as the effect due to embedding of particles and the constraint due to hydration of neighbouring particles is accounted using correction factor. The effect of temperature on rate of hydration is considered to be independent of the physical and chemical aspects of grain. Hence a temperature function developed using Arrhe- nius equation and activation energy is incorporated separately. The porous nature of reaction products affects the diffusivity leading to the development of tortuous path for flow of water through the hydrated portion. Knowing the tortuosity it is possible to obtain the diffusivity which in turn can be used as an input to the lattice model. An algorithm is developed to determine the tortuosity in diffusion of water through the reaction products. The tortuosity depends on the distribution of pores in the hydrated system. This requires the use of simulation technique to generate the initial position of voids. A simulation technique is also required to generate the initial con- figuration of hydrating cement system. In order to generate the initial configurations of such systems a numerical technique to generate a large scale assembly of particles is proposed. In the present work, parameters of Bazant's size effect law Bf’t and D0 are shown to depend on structure size and heterogeneity. The span to thickness ratio of the structure increases fracture energy and also substantially influences the response of structure. The variation in failure load occurring due to the heterogeneous nature of the material is shown to follow a normal distribution. The fracture behavior of a material is seen to be influenced strongly by the variation in the strength of matrix and interface. The model proposed to describe the hydration process of cement can be used to determine the properties of matrix and interface. The degree of hydration as well as the embedded centre plane area can be adopted as a measure of strength of matrix and interface. The understanding of the hydration process and the wall effect around the aggregate surface can possibly improve our ability to predict the strength of interface. The material strength of the interface is certainly a necessary input to the lattice model. Infact experimental determination of interface strength is a lot more complicated than the present numerical approach. The only weakness of the present numerical approach is the assumption regarding certain empirical constants which of course may be improved further. Understanding of material behavior can be further improved if a molecular dynamics approach is adopted to describe the hydration behavior of cement. The approach via molecular dynamics is suggested as a problem for future research.

Evolution of concrete is continuously taking place to meet the ever-growing demands of the construction industry. Self compacting concrete (SCC) has emerged as a result of this demand to overcome the scarcity of labour. SCC is widely replacing normal vibrated concrete (NVC) these days owing to its advantages such as homogeneity of the mix, filling ability even in heavily congested reinforcement, smooth finish, reduction in construction time etc. The ingredients used for SCC is the same as that of the NVC. But the proportioning of ingredients to achieve self compactability alters the microstructure of SCC which in turn affects the mechanical and fracture properties. Moreover, the mineral admixtures such as fly ash and silica fume when used for improving the workability of SCC help in the development of the microstructural skeleton. In this study, three SCC mixes SCC1- made with only cement, SCC2 - with fly ash in addition to cement and SCC3 - with fly ash and silica fume in addition to cement for achieving normal, medium and high strength SCC respectively are cast. The microstructural changes in SCC with and without mineral admixtures over a period of time are studied using different techniques such as scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and X-ray diffraction (XRD). The modification of mechanical properties at microstructural level brings difference in the behavior at macro level. Hence in this study, the mechanical properties at microstructural are obtained by using microindentation test and are scaled up to the macro level to predict the influence of micromechanical properties on macro response. The fracture properties of SCC is considered to be the interest of this study and is carried out with the help of advanced techniques such as acoustic emission (AE) and digital image correlation (DIC). From the various studies carried out, it is inferred that the mixes with mineral admixtures behave in a more brittle manner when compared to mix having no mineral admixture. It is also observed that class ‘F’ fly ash hydrates at a slow pace and the strength gain is observed after 28 days and even beyond 90 days. Hence, it is concluded that it is appropriate to consider the strength at 90 days instead of 28 days for a SCC mix with class ‘F’ fly ash. Silica fume on the other hand is observed to result in a more rapid gain in strength and this can partially offset the delay in strength gain due to fly ash.

A major distress mode in asphalt pavements is low temperature cracking, which results from the contraction and expansion of the asphalt pavement under extreme temperature changes. The potential for low temperature cracking is an interplay between the environment, the road structure and importantly the properties of the asphalt mixture. The thermal cracking performance of asphalt concrete mixtures can be evaluated by conducting thermal stress restrained specimen tests (TSRST) which is known to be correlated well with the fracture temperatures observed in the field. Although TSRST provides a good estimation of the field performance, it may be unrealistic to implement the obtained results in a design framework. On the other hand, recent studies showed Superpave indirect tension tests can be used to evaluate fracture performance (fatigue, moisture damage, low temperature cracking, etc.) of the asphalt concrete  mixtures. In addition, the obtained elastic and viscoelastic parameters from the Superpave IDT tests can be used as an input parameter to establish a design framework. The study presented in this thesis has a main objective to develop a framework using Superpave IDT test results as input parameters in order to evaluate the low temperature cracking performance of asphalt concrete mixtures. Moreover, the study aims to investigate micro-mechanically the low temperature cracking behavior of bitumen using atomic force microscopy (AFM) as a tool. The numerical model has been developed by integrating fracture energy threshold into an asphalt concrete thermal fracture model, considering non-linear thermal contraction coefficients. Based on the asphalt concrete mixture viscoelastic properties, this integrated model can predict thermally induced stresses and fracture temperatures. The elastic, viscoelastic and fracture energy input parameters of the model were measured by conducting indirect tension tests and the thermal contraction coefficients were measured experimentally. The proposed model has been validated by comparing the predicted fracture temperatures with the results obtained from TSRST tests. It was found that, while there is a quantitative discrepancy, the predicted ranking was correct. In the measurement of the thermal contraction coefficients it was observed that the thermal contraction coefficient in asphalt concrete is non-linear in the temperature range of interest for low temperature cracking. The implications of having non-linear thermal contraction coefficient were investigated numerically. In an effort to understand the effect of bitumen properties on low temperature fatigue cracking, AFM was used to characterize the morphology of bitumen. The AFM topographic and phase contrast image confirmed the existence of bee-shaped microstructure and different phases. The bitumen samples were subjected to both environmental and mechanical loading and after loading, micro-cracks appeared in the interfaces of the bitumen surface, confirming bitumen itself may also crack. It was also found that the presence of wax and wax crystallization plays a vital role in low temperature cracking performance of bitumen. / <p>QC 20120828</p>

Crack propagation in structures when subjected to fatigue loading, follows three different phases namely - short crack growth, stable crack growth and unstable crack growth. Accurate fatigue life prediction demands the consideration of every crack propagation phase rather than only the stable crack growth stage. Further, the use of existing crack growth laws in structures with small cracks under-predicts the growth rate compared to experimentally observed ones, thereby leading to an unsafe design and keeping the structure in a potentially dangerous state. In the present work, an attempt is made to establish fatigue crack propagation laws for plain concrete, reinforced concrete and concrete-concrete jointed interfaces from first principles using the concepts of dimensional analysis and self-similarity. Different crack growth laws are proposed to understand the behavior in each of the three regimes of the fatigue crack growth curve. Important crack growth characterizing material and geometrical parameters for each zone are included in the proposed analytical models. In real life applications to structures, the amplitude of cyclic loading rarely remains constant and is subjected to a wide spectrum of load amplitudes. Furthermore, the crack growth behavior changes in the presence of high amplitude load spikes within a constant amplitude history and this is incorporated in the model formulation. Using scaling laws, an improved understanding of the scaling behavior on different parameters is achieved. The models describing different regimes of crack propagation are finally unified to obtain the entire crack growth curve and compute the total fatigue life. In addition, crack growth analysis is performed for a reinforced concrete member by modifying the model derived for plain concrete in the Paris regime. Energy dissipation occurring due to shake-down phenomenon in steel reinforcement is addressed. The bond-slip mechanism which is of serious concern in reinforced concrete members is included in the study and a method is proposed for the prediction of residual moment carrying capacity as a function of relative crack depth. The application of the proposed analytical model in the computation of fatigue crack growth is demonstrated on three practical problems – beam in flexure, concrete arch bridge and a patch repaired beam. Through a sensitivity study, the influence of different parameters on the crack growth behavior is highlighted.

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.