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

Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a novel plasticity model for plain concrete is proposed in this research. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations, the strain equivalence hypothesis is adopted. The proposed constitutive model has been shown to satisfy the thermodynamics requirements, and detailed numerical algorithms are developed for the Finite Element implementation of the proposed model. Moreover, the numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus, and the overall performance of the proposed model is verified by comparing the model predictions to various experimental data on macroscopic level. Using the proposed coupled plasticity-damage constitutive model, the effect of the micromechanical properties of concrete, such as aggregate shape, distribution, and volume fraction, the ITZ thickness, and the strength of the ITZ and mortar matrix on the tensile behavior of concrete is investigated on 2-D and 3-D meso-scale. As a result of simulation, the tensile strength and thickness of the ITZ is the most important factor that control the global strength and behavior of concrete, and the aggregate shape and volume fraction has somewhat effect on the tensile behavior of concrete while the effect of the aggregate distribution is negligible. Furthermore, using the proposed constitutive model, the pull-out analysis of the single straight and curved CNT embedded in cement matrix is carried out. In consequence of the analysis, the interfacial fracture energy is the key parameter governing the CNT pull-out strength and ductility at bonding stage, and the Young's modulus of the CNT has also great effect on the pull-out behavior of the straight CNT. In case of the single curved CNT, while the ultimate pull-out force of the curved CNT at sliding stage is governed by the initial sliding force when preexisting normal force is relatively high, the ultimate pull-out force, when the preexisting normal force is not significant, is increased linearly proportional to the curvature and the Young's modulus of the CNT due to the additionally induced normal force by the bending stiffness of the curved CNT.

This project focuses on discrete element modelling of fracturing of concrete material at meso-scale, and particularly on calibration of the particle assembly parameters to reproduce phenomenological properties of concrete, and on applying the discrete element method to analyze the failure mechanisms in a three-point bending test and debonding between the FRP sheet and the concrete. The particle flow code PFC2D and PFC3D are employed to carry out the parametric study but only PFC2D is used in the case studies. The calibration of properties of the numerical samples is conducted to determine the effects of the particle level input parameters on the elastic constants, the uniaxial compressive strengths and failure mode of particle assembly. The input parameters are divided into two groups, model constitutive parameters (e.g., particle and bond stiffness, bond shear and normal strengths and friction coefficient) and geometric and physical parameters (e.g., particle and specimen size, particle distribution and loading velocity.). The analysis is constructed using dimensional analysis and numerical uniaxial tests. A random aggregate generation algorithm is incorporated in the DEM code to reproduce the aggregate structure in real concrete material. The aggregate generation algorithm utilizes polygon and polyhedron as the basic shapes of aggregate and is capable of producing multi-graded concrete specimens with aggregate content up to 80% and 60% for two-dimensional and three-dimensional samples respectively. The mode I fracture behavior of three-phased concrete is then simulated by performing a virtual three-point bending test. The mortar matrix phase is simulated with the linear elastic-pure-brittle and softening bond model to ensure a fair comparison. The dynamic debonding process between the FRP sheet and the concrete is simulated with a particle assembly by a regular hexagonal packing arrangement where the heterogeneity of concrete is taken into account by incorporating the Weibull distribution. Based on the analysis of the modelling results, it is conclude that the fracture behavior of concrete can be satisfactorily captured by meso-scale DEM model and comprehensive parameter study allows more confidently implementation of particle flow code.

Orientador: José Luiz Antunes de Oliveira e Sousa / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-16T11:51:43Z (GMT). No. of bitstreams: 1 Rosa_AlaorLeandro_D.pdf: 7941559 bytes, checksum: 806e89b1e919e7a21f82b349d6b6b047 (MD5) Previous issue date: 2010 / Resumo: A pesquisa objeto desta tese refere-se a uma investigação dos processos de fratura no concreto de alta resistência (High Strength Concrete - HSC), com ênfase no estudo da influência da taxa de carregamento (medida como a taxa de deslocamento do ponto de aplicação de carga) nos ensaios de fraturamento e assim caracterizar sua ductilidade em tração. Neste trabalho um modelo de fratura dependente do tempo (modelo coesivo-viscoso) é apresentado e a influência da taxa de carregamento na resposta em fratura quase-frágil é estudada através de simulação numérica. O modelo de fratura dependente do tempo acopla um parâmetro viscoso, dado em função da velocidade de abertura da fratura, ao modelo clássico de fissura fictícia proposto por Hillerborg, tal que uma relação tensão-abertura de fissura dependente do tempo, (?, ?), represente uma zona coesiva-viscosa inserida em um meio elástico não-viscoso. O modelo coesivo-viscoso é implementado no arcabouço teórico do método dos elementos finitos com um método de cálculo iterativo que modela a fratura quase-frágil (comportamento não-linear) como uma superposição de problemas em mecânica da fratura elástica linear (Linear Elastic Fracture Mechanics - LEFM). O modelo numérico implementado é validado com os resultados experimentais obtidos de vigas prismáticas ranhuradas em flexão em três pontos (Three-Point Bend Test - TPBT), com taxas de carregamento variando da ordem de = 10-5 mm/s a 6 = 10+1 mm/s. Os resultados numéricos obtidos mostram que o modelo coesivo-viscoso implementado, apesar de sua simplicidade, reflete o fato experimentalmente documentado de que a nucleação e a propagação de uma fratura coesiva, bem como os fenômenos que governam os processos de fratura, são dependentes da taxa de carregamento. Assim, a diferença obtida por muitos pesquisadores na medida da energia de fratura não se deve unicamente à escala do protótipo ensaiado mas também à taxa de carregamento aplicada nos ensaios. / Abstract: This thesis addresses a numerical investigation to account for loading rate influence (measured as the load-point displacement rate) on the fracture processes of quasi-brittle materials such as high strength concrete (HSC). In this context, fracture tests are simulated by a proposed time-dependent cohesive model. The proposed model couples a viscous parameter, as a function of crack-opening rate, to the classical Hillerborg's fictitious crack approach such that a time-dependent stress crack opening law, (?, ?), represents a viscous-cohesive zone in an elastic, time-independent, body. The viscous cohesive representation is implemented in a finite element framework using a iterative method in such a way that the equations governing the quasebrittle crack propagation (non-linear behaviour) is sought from a triangular system of equations, obtained by superposing linear elastic fracture mechanics (LEFM) cases. To show the accuracy of the model, numerical simulations of notched beams in three-point bend test (TPBT) were performed. In the tests five different loading rates were employed (ranging from = 10-5 mm/s = 10+1 mm/s). The results numerically obtained match very well the experimental ones, particularly the maximum load for the several loading rates used in the tests. A parametric study has also been performed to point out which are the model, geometry and fracture parameters influencing the fracture process due to loading rate. The numerical results show that the model, although its simplicity, provides a general approach to reflect the experimentally documented fact that crack propagation and so the parameters governing the fracture processes in cementious materials depend on the loading rate. So, the differences obtained by several researches worldwide on the fracture energy measurement are not only due to the scale of the tested specimens, but also due to the loading rate influence. / Doutorado / Estruturas

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Most materials including concrete have pre-existing flaws or defects. The fracture energy of concrete is a basic material property needed to understand fracture initiation and propagation in concrete. Whether fracture energy is size dependent or not is being discussed world over. Strictly the fracture energy if taken as a material property should be constant, and should be independent of the method of measurement, test methods, specimen shapes and sizes. A computational study on simulation of fracture in concrete using two dimensional lattice models is presented. A comparison is made with acoustic emission (AE) events with the number of fractured elements. A three-point bend specimen (TPB) is modeled using regular triangular lattice network. It was observed that the number of fractured elements increases near the peak load and beyond the peak load. AE events also increase rapidly beyond the peak load. Singular Fractal Functions (S.F.F) has been employed to interpret the size effect of quasi-brittle materials like concrete. The usual size dependent fracture energy of High Strength Concrete (HSC) beam is reported. The results are presented which are obtained directly from the experiments related to size effect in concrete carried out in the Structural engineering laboratory, Department of Civil engineering, IISc. Various fracture parameters studied in this experimental program are (a) Nominal strength N (b) Fracture energy, Gf (c)Fracture toughness, KIc, (c) Crack mouth opening displacement, CMOD (d) Size effect on the strength of concrete. Three-point-bend (TPB) specimen was chosen for the experimental study. Six different concrete mixes viz. A-mix, B-Mix, C-mix, D-Mix, E-mix, F-Mix were used. Acoustic Emission (AE) experiments are conducted to relate acoustic emission energy to fracture energy. It is interesting to note that both acoustic emission energy and fracture energy have similar characteristics. The advantage of the above relationship is that now it is possible to evaluate fracture energy by non-destructive testing methods. The b-value analysis of AE was carried out to study the damage in concrete structures. The Guttengberg-Richter relation for frequency versus magnitude can be applied to the AE method to study the scaling of the amplitude distribution of the acoustic emission waves generated during the cracking process in the test specimen at laboratory or in engineering structures. In the next part of this chapter b-value at various stages of damage of a reinforced concrete beam are obtained experimentally under typical cyclic loadings. The b-values at different levels of damage are tabulated. As fracture is size dependent, it may not be very useful unless its size dependency is eliminated. An effort is made to obtain size independent fracture energy by a hybrid technique.

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.

The focus of this thesis is to research and develop a uniaxial tensile testing technique and methodology to attain the post-peak softening response for ultra-high performance concrete under confining pressure. This particular multi-axial behavior is valuable in improving current material models in finite element simulations for US Army applications into hardened target structures.

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