Prestressed concrete is a popular construction material for highway bridges. A variety of girder span values, cross-sectional shapes, and prestressing strand layouts has been used in bridges across the United States. A major concern for such bridges is the possibility of corrosion damage in the prestressing strands or reinforcing bars, which is commonly caused by the use of deicing salts on the deck or saltwater spray in coastal regions. The present study aims at establishing analytical tools for the accurate simulation of chloride ingress, corrosion and mechanical damage (cracking) in the concrete, and for the evaluation of the impact of corrosion on the flexural and shear strength of bridge girders. First, an efficient and accurate analytical scheme is formulated to enable the calculation of the load-carrying capacity of corrosion-damaged girders. The analyses rely on two types of models, namely, beam models and nonlinear truss models. The latter are deemed necessary to obtain reliable estimates of the shear capacity, as beam models are not well-tailored for capturing shear failures. A procedure to account for the reduction in area and deformability of corroded strands, based on visually observed corrosion damage, is proposed and implemented. The models are calibrated and validated with the results of experimental tests on prestressed girders which exhibited varying levels of corrosion damage. Further analyses allow the comparison of the capacity of corrosion-damaged girders to that of their undamaged counterparts. The accuracy of a simplified procedure, using equations in the AASHTO code to determine the flexural and shear capacity of the damaged girders, is also determined. Subsequently, a computation scheme was proposed to describe the intrusion of chloride ions in prestressed bridge girder sections. The approach accounts for multiple, coupled processes, i.e., heat transfer, moisture transport, and chloride advective and diffusive transport. The constitutive models for moisture and chloride transport rely on previous pertinent work, with several necessary enhancements. The modeling scheme is calibrated with data from previous experimental tests on concrete cylindrical and prismatic specimens. The calibrated models are then validated using data from chloride titration tests conducted on girders removed from two bridges in Virginia after 34 and 49 years of service. The results indicate that the proposed framework can accurately reproduce the experimentally measured chloride content. The modeling approach also allows the evaluation of the accuracy of simplified, design-oriented tools for estimating the evolution of chloride content with time. The multi-physics simulation scheme is further refined to account for the corrosion-induced mechanical damage (cracking), by incorporating a phenomenological description of the electrochemical reaction kinetics, generation of expansive corrosion products, and subsequent development of tensile stresses and cracking in the surrounding concrete. The impact of cracking on the chloride and moisture transport mechanisms is also taken into account. The last part of this dissertation pursues the quantification of the uncertainty governing the chloride ingress in bridge girders, through the use of a stochastic collocation approach. The focus is on understanding how the inherent uncertainty in the value of input parameters (e.g., material transport parameters, ambient conditions etc.) is propagated, leading to uncertainty in the evolution of chloride content and the expected corrosion initiation time for a given bridge. / Doctor of Philosophy / Prestressed concrete is widely utilized in the construction of highway bridges in the United States. A significant concern arises regarding potential corrosion damage in the prestressing strands or reinforcing bars, which is commonly attributed to the application of deicing salts on the deck or exposure to saltwater spray in coastal regions. This study aims to develop analytical tools that can accurately simulate the intrusion of corrosive agents (namely chloride ions), and subsequent damage (cracking) in concrete. Furthermore, the research seeks to assess the impact of corrosion on the bearing capacity of bridge girders. Two different classes of analytical approaches are pursued. The first class employs purely mechanical (stress/deformation) models for capturing the strength, deformability and failure modes of girders with visual corrosion damage. These models rely on two approaches to capture the flexural and shear capacity of specimens, namely, beam-based models and truss-based models. The impact of corrosion is established through appropriate modification of the model parameters, based on the extent of visually observed corrosion damage. The analytical approaches are validated through a series of experimental tests previously conducted on corrosion-damaged girders. The second class of analytical approaches employs multi-physics models, to describe the mechanisms leading to corrosion-induced damage. The models account for heat transfer, moisture transport, and chloride transport in prestressed beam sections. Model parameters are calibrated with experimental tests in literature. The computational scheme is used to quantitatively describe the chloride ingress on bridge girders decommissioned from two different bridges in Virginia, after 34 and 49 years of service. The analysis results are found capable of capturing the actual chloride content at various depths from the exposure surface, as determined by chloride titration tests. The temporal evolution of chloride on the surface of prestressing strands indicates that corrosion has been taking place over a period of time for the two bridges. The multi-physics simulation approach is further enhanced to account for the corrosion-induced mechanical damage (cracking), by explicitly incorporating a description of the reaction kinetics, generation of expansive corrosion products and subsequent development of cracking in the surrounding concrete. The last part of this dissertation pursues the quantification of the uncertainty in the expected service life of prestressed concrete bridge structures. Given the inherent uncertainty to key values of model parameters, a parametric study is employed to investigate the propagation of uncertainty to the time history of chloride content at particular locations of the section and the probability of corrosion initiation at specific age values.

Vários modelos computacionais que implementam o transporte de soluto em meio poroso saturado surgem constantemente em publicações científicas devido à suma importância dada à compreensão e previsão do transporte de constituintes dissolvidos em água subterrânea. As soluções numéricas obtidas por esquemas computacionais não estão imunes aos erros de discretização. No entanto, a confiabilidade nos resultados obtidos das complexas operações provenientes da dinâmica de fluidos computacional pode ser aumentada através de estimadores de erro a posteriori que indicam a precisão da solução numérica de um modelo matemático que simula o fenômeno físico de interesse. Neste trabalho é apresentado um estimador residual para a equação parabólica que descreve os fenômenos de advecção-dispersão-reação (ADR) em meio poroso saturado, considerando o transporte em regime de pequena advecção. A solução numérica da equação ADR é obtida pelo método dos elementos finitos que emprega termos upwind para minimizar as inconvenientes oscilações espúrias. A implementação do código computacional para obter essa solução numérica e o seu correspondente erro a posteriori, é feita em linguagem JAVA na plataforma Eclipse seguindo o paradigma da Programação Orientada a Objetos (POO). A solução numérica da equação elíptica do fluxo subterrâneo e o seu estimador de erro com características de recuperação do gradiente, o estimador ZZ, também são implementados no código JAVA. Assim, a solução da equação do transporte é obtida em função da reusabilidade POO prevista na implementação da equação do fluxo. A comparação da solução numérica do modelo ADR 2D com a correspondente solução analítica disponível na literatura, demonstra que o estimador residual apresenta excelentes índices de eficiência. Os resultados numéricos obtidos mostraram que o estimador residual encontra-se limitado inferior e superiormente pelo erro real da solução em malha grosseira. O estimador ZZ mostrou-se inadequado para a análise do erro de aproximação das equações ADR. Os exemplos selecionados para verificação e aplicação do estimador residual abrangem, em diferentes escalas, modelos que descrevem reação de primeira ordem e modelos com fenômenos de sorção e retardamento na migração do contaminante em meio poroso saturado. Em conseqüência, o estimador residual proposto provou ser computável, eficiente e robusto no sentido de abranger uma grande variedade das aplicações dos fenômenos de transporte de contaminantes em meio poroso saturado e regime de pequena advecção. / Several computational models that implement the solute migration in saturated porous media constantly appear in scientific publications due to the great importance given to the understanding and forecast of the solute transport in groundwater. The numerical solutions obtained by computational schemes are not immune to errors related to the discretization process. However, the reliability of the results obtained by the complex operations of the computational fluids dynamics can be enhanced by a posteriori error estimates that indicate the accuracy of the numerical solution. In this work a residual error estimator is presented for the parabolic equation that describes the advection-dispersion-reaction phenomena (ADR) in saturated porous media, considering the transport in small advection regime. The numerical solution of the ADR equation is obtained by the finite element method using upwind terms to minimize the spurious oscillations. The computational code and the correspondent a posteriori error estimates are implemented in Java language following the Object Oriented Programming (OOP) paradigm in Eclipse platform. The numerical solution of the elliptic groundwater flow equation and the respective error estimates with gradient recovery characteristic, the ZZ-estimator, are also implemented in the JAVA code. The solution of the transport equation is obtained as a consequence of the OOP reusability intended in the implementation of the flow equation. The numerical solution of the ADR 2D simulation compared to the analytical solution available in the literature, demonstrate the excellent effectivity index presented by the residual error estimator. The obtained results indicate that the residual error estimator is lower and upper bounded by a solution in coarse mesh. The ZZ-estimator showed to be inadequate for the error analysis of the ADR equations. The examples selected for validation and application of the residual estimator include, in distinct scales, models that describe reaction of first order and models with sorption and retardation phenomena in the pollutant migration in saturated porous media. Therefore, the proposed residual error estimator proved to be computable, efficient and robust in the sense of solving a great variety of applications of transport phenomena in saturated porous media at small advection regime.

Vários modelos computacionais que implementam o transporte de soluto em meio poroso saturado surgem constantemente em publicações científicas devido à suma importância dada à compreensão e previsão do transporte de constituintes dissolvidos em água subterrânea. As soluções numéricas obtidas por esquemas computacionais não estão imunes aos erros de discretização. No entanto, a confiabilidade nos resultados obtidos das complexas operações provenientes da dinâmica de fluidos computacional pode ser aumentada através de estimadores de erro a posteriori que indicam a precisão da solução numérica de um modelo matemático que simula o fenômeno físico de interesse. Neste trabalho é apresentado um estimador residual para a equação parabólica que descreve os fenômenos de advecção-dispersão-reação (ADR) em meio poroso saturado, considerando o transporte em regime de pequena advecção. A solução numérica da equação ADR é obtida pelo método dos elementos finitos que emprega termos upwind para minimizar as inconvenientes oscilações espúrias. A implementação do código computacional para obter essa solução numérica e o seu correspondente erro a posteriori, é feita em linguagem JAVA na plataforma Eclipse seguindo o paradigma da Programação Orientada a Objetos (POO). A solução numérica da equação elíptica do fluxo subterrâneo e o seu estimador de erro com características de recuperação do gradiente, o estimador ZZ, também são implementados no código JAVA. Assim, a solução da equação do transporte é obtida em função da reusabilidade POO prevista na implementação da equação do fluxo. A comparação da solução numérica do modelo ADR 2D com a correspondente solução analítica disponível na literatura, demonstra que o estimador residual apresenta excelentes índices de eficiência. Os resultados numéricos obtidos mostraram que o estimador residual encontra-se limitado inferior e superiormente pelo erro real da solução em malha grosseira. O estimador ZZ mostrou-se inadequado para a análise do erro de aproximação das equações ADR. Os exemplos selecionados para verificação e aplicação do estimador residual abrangem, em diferentes escalas, modelos que descrevem reação de primeira ordem e modelos com fenômenos de sorção e retardamento na migração do contaminante em meio poroso saturado. Em conseqüência, o estimador residual proposto provou ser computável, eficiente e robusto no sentido de abranger uma grande variedade das aplicações dos fenômenos de transporte de contaminantes em meio poroso saturado e regime de pequena advecção. / Several computational models that implement the solute migration in saturated porous media constantly appear in scientific publications due to the great importance given to the understanding and forecast of the solute transport in groundwater. The numerical solutions obtained by computational schemes are not immune to errors related to the discretization process. However, the reliability of the results obtained by the complex operations of the computational fluids dynamics can be enhanced by a posteriori error estimates that indicate the accuracy of the numerical solution. In this work a residual error estimator is presented for the parabolic equation that describes the advection-dispersion-reaction phenomena (ADR) in saturated porous media, considering the transport in small advection regime. The numerical solution of the ADR equation is obtained by the finite element method using upwind terms to minimize the spurious oscillations. The computational code and the correspondent a posteriori error estimates are implemented in Java language following the Object Oriented Programming (OOP) paradigm in Eclipse platform. The numerical solution of the elliptic groundwater flow equation and the respective error estimates with gradient recovery characteristic, the ZZ-estimator, are also implemented in the JAVA code. The solution of the transport equation is obtained as a consequence of the OOP reusability intended in the implementation of the flow equation. The numerical solution of the ADR 2D simulation compared to the analytical solution available in the literature, demonstrate the excellent effectivity index presented by the residual error estimator. The obtained results indicate that the residual error estimator is lower and upper bounded by a solution in coarse mesh. The ZZ-estimator showed to be inadequate for the error analysis of the ADR equations. The examples selected for validation and application of the residual estimator include, in distinct scales, models that describe reaction of first order and models with sorption and retardation phenomena in the pollutant migration in saturated porous media. Therefore, the proposed residual error estimator proved to be computable, efficient and robust in the sense of solving a great variety of applications of transport phenomena in saturated porous media at small advection regime.