Processos aleatórios de corrosão e fadiga reduzem lentamente a resistência de estruturas e componentes estruturais, provocando um aumento gradual nas probabilidades de falha. A gestão do risco de falha de componentes sujeitos a corrosão e/ou fadiga é feita através de políticas de inspeção, manutenção e substituição, atividades que implicam em custos, mas visam manter a confiabilidade em níveis aceitáveis, enquanto o componente permanecer em operação. Aparentemente, os objetivos economia e segurança competem entre si, no entanto, a redução de recursos para inspeção e manutenção pode levar a maiores e crescentes probabilidades de falha, implicando em maiores custos esperados de falha, ou seja, maior risco. A otimização de risco estrutural é uma formulação que permite equacionar este problema, através do chamado custo esperado total. Nesta Tese, a otimização de risco é utilizada no intuito de encontrar políticas ótimas de inspeção e manutenção, isto é, quantidades de recursos a serem alocadas nestas atividades que levem ao menor custo esperado total possível. Os processos de corrosão e fadiga são representados através de modelos em polinômios de caos, construídos de maneira inédita, com base em dados experimentais ou observados da literatura. Com base nestes modelos, os problemas de otimização de risco envolvendo processos de fadiga e corrosão são resolvidos para diferentes configurações de custos de falha e de inspeções. Verifica-se que as políticas ótimas de inspeção, manutenção e substituição podem ser bastante diferentes para configurações de custo distintas, e que a determinação destas políticas é bastante desafiadora, devido, dentre outros fatores, à grande quantidade de mínimos locais do problema de otimização em questão, causadas por descontinuidades e oscilações da função custo esperado total. / Random corrosion and fatigue processes reduce slowly but gradually the resistance of structures and mechanical components, leading to gradual increase in failure probabilities. Risk management for mechanical components subject to corrosion and fatigue is made by means of policies of inspection, maintenance and substitution. These activities imply costs, but are made to maintain the reliability at acceptable levels, while the component remains in operation. Apparently, economy and safety are competing objectives; however, reduction in inspection and maintenance spending may lead to larger failure probabilities, increasing expected costs of failure (risk). Risk optimization allows one to solve this problem, by means of the so-called total expected cost. In this Thesis, risk optimization is used in order to find the best inspection and maintenance policy, i.e., the proper amount of resources to allocate to such activities in order to obtain minimum total expected cost. Corrosion and fatigue are modeled by means of polynomial chaos expansions, using a novel approach developed herein and experimental or observed data obtained from the literature. These models are employed within two risk optimization problems, solved for different failure and inspection cost configurations. Results show that the optimal policies of inspection, maintenance and replacements can be very different, for different cost configurations, and that the solution of the associated risk optimization problems is a very challenging task, due to the large number of local minima, caused by discontinuities and fluctuations in the total expected costs.

Uma grande variedade de modelos é utilizada para estimar a pressão de ruptura de dutos contendo defeitos de corrosão. O presente trabalho tem como objetivo estudar a precisão dos modelos mais comuns e avaliar a pressão de ruptura de dutos submetidos à corrosão. Os modelos avaliados são: ASME B31G, ASME B31G modificado, DNV RP F101 e PCORRC. O estudo é baseado em mais de 400 resultados de ensaios de ruptura em dutos corroídos, todos coletados da literatura. A base de dados contem defeitos de corrosão reais e artificiais. Uma análise estatística foi realizada para a variável erro de modelo. Uma análise de regressão não-linear foi realizada para investigar os efeitos da variável erro de modelo, das variáveis mais relevantes, como profundidade e comprimento do defeito, e tensão de ruptura do aço. Uma análise de confiabilidade foi realizada a partir das estatísticas obtidas da variável erro de modelo, sendo estimado o índice de confiabilidade e a probabilidade de falha do duto com defeitos de corrosão, através do método iterativo de primeira ordem, denominado FORM (First Order Reliability Method). Nesta análise avaliou-se a evolução da probabilidade de falha com o aumento da profundidade do defeito, bem como foram identificadas as variáveis aleatórias mais importantes na falha do duto. O estudo pode ajudar aos operadores a eleger qual modelo utilizar em análises de risco, proporcionando mais segurança às operações dutoviárias. / A variety of models exist to estimate burst pressures of pipelines containing corrosion defects. The objective of this work is to study the accuracy of some of the most popular empirical burst pressure models. The study addresses the models: ASME B31G, ASME B31G Modified, DNV RP-F101 and PCORRC. The investigation is based on over 400 burst test results, all collected from the literature, containing both real and artificial corrosion defects. A statistical analysis is performed for assessing the accuracy of semi-empirical models by using a model error variable. A non-linear regression analysis is performed to identify the influence, on model errors, of the most relevant variables, such as defect depth and length and steels rupture tension. A reliability analysis was carried out, using model error statistics developed herein, in order to evaluate reliability index and probability of failure of pipelines containing corrosion defects, through the iterative first order reliability method, or FORM - First Order Reliability Method. The evolution of failure probabilities, with increasing defect depth, was investigated. The most relevant random variables were identified. The study can help operators choose a proper empirical model to use in their risk analysis, leading to greater safety in pipeline operations.

In the thesis, the reliability analysis of structural components and structural details subject to random loading and random resistance degradation is addressed. The study concerns evaluation of the probability of failure due to an overload of a component or structural detail, in consideration of random (environmental) loads and their combination, uncertain resistance parameters, statistical and phenomenological uncertainty and random resistance degradation mechanisms. Special attention is devoted to resistance degradation, as it introduces an additional level of difficulty in the solution of time variant reliability problems. The importance of this study arrives from the ageing of existing infrastructure in a world wide scale and from the lack of standards and codes for the ongoing safety management of general structures past their original design lives. In this context, probabilistic-based risk assessment and reliability analysis provide a framework for the safety management of ageing structures in consideration of inherent load and resistance uncertainty, current state of the structure, further resistance degradation, periodic inspections, in the absence of past experience and on an individual basis. In particular, the critical problem of resistance degradation due to fatigue is addressed. The formal solution of time variant reliability problems involves integration of local crossing rates over a conditional failure domain boundary, over time and over random resistance variables. This solution becomes very difficult in the presence of resistance degradation, as crossing rates become time dependent, and the innermost integration over the failure domain boundary has to be repeated over time. Significant simplification is achieved when the order of integrations is changed, and crossing rates are first integrated over the random failure domain boundary and then over time. In the so-called ensemble crossing rate or Ensemble Up-crossing Rate (EUR) approximation, the arrival rate of the first crossing over a random barrier is approximated by the ensemble average of crossings. This approximation conflicts with the Poisson assumption of independence implied in the first passage failure model, making results unreliable and highly conservative. Despite significant simplification of the solution, little was known to date about the quality of the EUR approximation. In this thesis, a simulation procedure to obtain Poissonian estimates of the arrival rate of the first up-crossing over a random barrier is introduced. The procedure is used to predict the error of the EUR approximation. An error parameter is identified and error functions are constructed. Error estimates are used to correct original EUR failure probability results and to compare the EUR with other common simplifications of time variant reliability problems. It is found that EUR errors can be quite large even when failure probabilities are small, a result that goes against previous ideas. A barrier failure dominance concept is introduced, to characterize those problems where an up-crossing or overload failure is more likely to be caused by a small outcome of the resistance than by a large outcome of the load process. It is shown that large EUR errors are associated with barrier failure dominance, and that solutions which simplify the load part of the problem are more likely to be appropriate in this case. It is suggested that the notion of barrier failure dominance be used to identify the proper (simplified) solution method for a given problem. In this context, the EUR approximation is compared with Turkstra’s load combination rule and with the point-crossing formula. It is noted that in many practical structural engineering applications involving environmental loads like wind, waves or earthquakes, load process uncertainty is larger than resistance uncertainty. In these applications, barrier failure dominance in unlikely and EUR errors can be expected to be small. The reliability problem of fatigue and fracture under random loading is addressed in the thesis. A solution to the problem, based on the EUR approximation, is constructed. The problem is formulated by combining stochastic models of crack propagation with the first passage failure model. The solution involves evaluation of the evolution in time of crack size and resistance distributions, and provides a fresh random process-based approach to the problem. It also simplifies the optimization and planning of non-destructive periodic inspection strategies, which play a major role in the ongoing safety management of fatigue affected structures. It is shown how sensitivity coefficients of a simplified preliminary First Order Reliability solution can be used to characterize barrier failure dominance. In the fatigue and fracture reliability problem, barrier failure dominance can be caused by large variances of resistance or crack growth parameters. Barrier failure dominance caused by resistance parameters leads to problems where overload failure is an issue and where the simplified preliminary solution is likely to be accurate enough. Barrier failure dominance caused by crack growth parameters leads to highly non-linear problems, where critical crack growth dominates failure probabilities. Finally, in the absence of barrier failure dominance, overload failure is again the issue and the EUR approximation becomes not just appropriate but also accurate. The random process-based EUR solution of time-variant reliability problems developed and the concept of barrier failure dominance introduced in the thesis have broad applications in problems involving general forms of resistance degradation as well as in problems of random vibration of uncertain structures. / PhD Doctorate

Corrosion of reinforcing bars is the major cause of deterioration of reinforced concrete (RC) structures in North America, Europe, the Middle East, and many coastal regions around the world. This deterioration leads to a loss of serviceability and functionality and ultimately affects the structural safety. The objective of this research is to formulate and implement a general stochastic finite element analysis (SFEA) framework for the time-dependent reliability analysis of RC beams with corroding flexural reinforcement. The framework is based on the integration of nonlinear finite element and reliability analyses through an iterative response surface methodology (RSM). Corrosion-induced damage is modelled through the combined effects of gradual loss of the cross-sectional area of the steel reinforcement and the reduction bond between steel and concrete for increasing levels of corrosion. Uncertainties in corrosion rate, material properties, and imposed actions are modelled as random variables. Effective implementation of the framework is achieved by the coupling of commercial finite element and reliability software. Application of the software is demonstrated through a case study of a simply-supported RC girder with tension reinforcement subjected to the effects of uniform (general) corrosion, in which two limit states are considered: (i) a deflection serviceability limit state and (ii) flexural strength ultimate limit state. The results of the case study show that general corrosion leads to a very significant decrease in the reliability of the RC beam both in terms of flexural strength and maximum deflections. The loss of strength and serviceability was shown to be predominantly caused by the loss of bond strength, whereas the gradual reduction of the cross-sectional area of tension reinforcement was found to be insignificant. The load-deflection response is also significantly affected by the deterioration of bond strength (flexural strength and stiffness). The probability of failure at the end of service life, due to the effects of uniform corrosion-induced degradation, is observed to be approximately an order of magnitude higher than in the absence of corrosion. Furthermore, the results suggest that flexural resistance of corroded RC beams is controlled by the anchorage (bond) of the bars and not by the yielding of fully bonded tensile reinforcement at failure. This is significant since the end regions can be severely corroded due to chloride, moisture, and oxygen access at connections and expansion joints. The research strongly suggests that bond damage must be considered in the assessment of the time-dependent reliability of RC beams subjected to general corrosion.

Hurricanes have caused severe damage to the electric power system throughout the Gulf coast region of the U.S., and electric power is critical to post-hurricane disaster response as well as to long-term recovery for impacted areas. Managing hurricane risks and properly preparing for post-storm recovery efforts requires rigorous methods for estimating the number and location of power outages, customers without power, and damage to power distribution systems. This dissertation presents a statistical power outage prediction model, a statistical model for predicting the number of customers without power, statistical damage estimation models, and a physical damage estimation model for the gulf coast region of the U.S. The statistical models use negative binomial generalized additive regression models as well as negative binomial generalized linear regression models for estimating the number of power outages, customers without power, damaged poles and damaged transformers in each area of a utility company’s service area. The statistical models developed based on transformed data replace hurricane indicator variables, dummy variables, with physically measurable variables, enabling future predictions to be based on only well-understood characteristics of hurricanes. The physical damage estimation model provides reliable predictions of the number of damaged poles for future hurricanes by integrating fragility curves based on structural reliability analysis with observed data through a Bayesian approach. The models were developed using data about power outages during nine hurricanes in three states served by a large, investor-owned utility company in the Gulf Coast region.

To assess the losses associated with future earthquakes, seismic vulnerability functions are commonly used to correlate the damage or loss of a structure to the level of seismic intensity. A common procedure in seismic vulnerability assessment is to estimate the seismic fragility, which is defined as the conditional probability that a structure fails to meet the specific performance level for given level of seismic intensity. This dissertation proposes a methodology to estimate the fragility of corroded reinforced concrete (RC) bridges with two-column bents subject to seismic excitation. Seismic fragility functions are first developed for the RC bridges with two-column bents. All available information from science/engineering laws, numerical analysis, laboratory experiments, and field measurements has been used to construct the proper form of the fragility functions. The fragility functions are formulated, at the individual column, bent, and bridge levels, in terms of the spectral acceleration and the ratio between the peak ground velocity and the peak ground acceleration. The developed fragility functions properly account for the prevailing uncertainties in fragility estimation. The probabilistic capacity and demand models are then combined with the probabilistic models for chloride-induced corrosion and the time-dependent corrosion rate. The fragility estimates for corroded RC bridges incorporates the uncertainties in the parameters of capacity and demand models, and the inexactness (or model error) in modeling the material deterioration, structural capacity, and seismic demands. The proposed methodology is illustrated by developing the fragility functions for an example RC bridge with 11 two-column bents representing current construction in California. The developed fragility functions provide valuable information to allocate and spend available funds for the design, maintenance, and retrofitting of structures and networks. This study regarding the vulnerability of corroding RC bridges will be of direct value to those making decisions about the condition assessment, residual life, and the ability of lifeline structures to withstand future seismic demands.

Civil infrastructure facilities play a central role in the economic, social and political health of modern society and their safety, integrity and functionality must be maintained at manageable cost over their service lives through design and periodic maintenance. Hurricanes and tropical cyclones, tornadoes, earthquakes and floods are paramount among the potentially devastating and costly natural disasters impacting civil infrastructure. Even larger losses may occur in the future, given the population growth and economic development accompanying urbanization in potentially hazardous areas of the world. Moreover, in recent years, the effects that global climate change might have on both the frequency and severity of extreme events from natural hazards and their effect on civil infrastructure facilities have become a major concern for decision makers. Potential influences of climate change on civil infrastructure are even greater for certain facilities with service periods of 100 years or more, which are substantially longer than those previously considered in life-cycle engineering and may extend across multiple generations. Customary risk-informed decision frameworks may not be applicable to such long-term event horizons, because they tend to devalue the importance of current decisions for future generations, causing an ethical and moral dilemma for current decision-makers. Thus, intergenerational risk-informed decision frameworks that consider facility performance over service periods well in excess of 100 years and extend across multiple generations must be developed. This dissertation addresses risk-informed decision-making for civil infrastructure exposed to natural hazards, with a particular focus on the equitable transfer of risk across multiple generations. Risk-informed decision tools applied to extended service periods require careful modifications to current life-cycle engineering analysis methods to account for values and decision preferences of both current and future generations and to achieve decisions that will be sustainable in the long term. The methodology for supporting equitable and socio-economical sustainable decisions regarding long-term public safety incorporates two essential ingredients of such decisions: global climate change effect on stochastic models of extreme events from natural hazards and intergenerational discounting methods for equitable risk-sharing. Several specific civil infrastructure applications are investigated: a levee situated in a flood-prone city; an existing dam built in a strong earthquake-prone area; and a special moment resisting steel frame building designed to withstand hurricanes in Miami, FL. These investigations have led to the conclusion that risks can and should be shared across multiple generations; that the proposed intergenerational decision methods can achieve goals of intergenerational equity and sustainability in engineering decision-making that are reflective of the welfare and aspirations of both current and future generations; and that intergenerational equity can be achieved at reasonable cost.

A probabilistic framework is developed to assess the structural reliability of offshore wind turbines. Probabilistic models are developed to predict the deformation, shear force and bending moment demands on the support structure of wind turbines. The proposed probabilistic models are developed starting from a commonly accepted deterministic model and by adding correction terms and model errors to capture respectively, the inherent bias and the uncertainty in developed models. A Bayesian approach is then used to assess the model parameters incorporating the information from virtual experiment data. The database of virtual experiments is generated using detailed three-dimensional finite element analyses of a suite of typical offshore wind turbines. The finite element analyses properly account for the nonlinear soil-structure interaction. Separate probabilistic demand models are developed for three operational/load conditions including: (1) operating under day-to-day wind and wave loading; (2) operating throughout earthquake in presence of day-to-day loads; and (3) parked under extreme wind speeds and earthquake ground motions. The proposed approach gives special attention to the treatment of both aleatory and epistemic uncertainties in predicting the demands on the support structure of wind turbines. The developed demand models are then used to assess the reliability of the support structure of wind turbines based on the proposed damage states for typical wind turbines and their corresponding performance levels. A multi-hazard fragility surface of a given wind turbine support structure as well as the seismic and wind hazards at a specific site location are incorporated into a probabilistic framework to estimate the annual probability of failure of the support structure. Finally, a framework is proposed to investigate the performance of offshore wind turbines operating under day-to-day loads based on their availability for power production. To this end, probabilistic models are proposed to predict the mean and standard deviation of drift response of the tower. The results are used in a random vibration based framework to assess the fragility as the probability of exceeding certain drift thresholds given specific levels of wind speed.

Uncertainty analysis of a system response is an important part of engineering probabilistic analysis. Uncertainty analysis includes: (a) to evaluate moments of the response; (b) to evaluate reliability analysis of the system; (c) to assess the complete probability distribution of the response; (d) to conduct the parametric sensitivity analysis of the output. The actual model of system response is usually a high-dimensional function of input variables. Although Monte Carlo simulation is a quite general approach for this purpose, it may require an inordinate amount of resources to achieve an acceptable level of accuracy. Development of a computationally efficient method, hence, is of great importance. First of all, the study proposed a moment method for uncertainty quantification of structural systems. However, a key departure is the use of fractional moment of response function, as opposed to integer moment used so far in literature. The advantage of using fractional moment over integer moment was illustrated from the relation of one fractional moment with a couple of integer moments. With a small number of samples to compute the fractional moments, a system output distribution was estimated with the principle of maximum entropy (MaxEnt) in conjunction with the constraints specified in terms of fractional moments. Compared to the classical MaxEnt, a novel feature of the proposed method is that fractional exponent of the MaxEnt distribution is determined through the entropy maximization process, instead of assigned by an analyst in prior. To further minimize the computational cost of the simulation-based entropy method, a multiplicative dimensional reduction method (M-DRM) was proposed to compute the fractional (integer) moments of a generic function with multiple input variables. The M-DRM can accurately approximate a high-dimensional function as the product of a series low-dimensional functions. Together with the principle of maximum entropy, a novel computational approach was proposed to assess the complete probability distribution of a system output. Accuracy and efficiency of the proposed method for structural reliability analysis were verified by crude Monte Carlo simulation of several examples. Application of M-DRM was further extended to the variance-based global sensitivity analysis of a system. Compared to the local sensitivity analysis, the variance-based sensitivity index can provide significance information about an input random variable. Since each component variance is defined as a conditional expectation with respect to the system model function, the separable nature of the M-DRM approximation can simplify the high-dimension integrations in sensitivity analysis. Several examples were presented to illustrate the numerical accuracy and efficiency of the proposed method in comparison to the Monte Carlo simulation method. The last contribution of the proposed study is the development of a computationally efficient method for polynomial chaos expansion (PCE) of a system's response. This PCE model can be later used uncertainty analysis. However, evaluation of coefficients of a PCE meta-model is computational demanding task due to the involved high-dimensional integrations. With the proposed M-DRM, the involved computational cost can be remarkably reduced compared to the classical methods in literature (simulation method or tensor Gauss quadrature method). Accuracy and efficiency of the proposed method for polynomial chaos expansion were verified by considering several practical examples.

In the present work, an investigation of the fatigue life benefits emerging from fillet weld geometries optimization has been carried out. At first, an introduction to ageing mechanisms, corrosion and especially fatigue, acting on operating marine structures has been made. Residual stresses at weld toes, stress modes, and types, geometrical factors (weld angle, toe radius, leg length), welding techniques selected, post-welding treatment and plate‟s material are some of the principal factors affecting the fatigue life of a fillet weld joint. Especially, the accuracy of various approaches in fatigue life estimation of specific geometries under pre-set types and levels of stress is studied. It is evident so far that even the notch stress concept is the most accurate method based on S-N curves, the Fracture Mechanics approach can offer more accurate solutions of a crack development through the material. Towards this, a literature review on crack evolution aspects in welded and non-welded plates under bending and tension was performed; substantial parameters were determined and finally implemented in the LEFM model which was used for the simulation purposes of Chapter 6. As far as the crack aspect ratio evolution is concerned, an extensive reference is available in literature since many researchers have investigated its contribution to the determination of geometrical paths, commonly known as “Preferred Propagation Paths”. Their significance is related with our ability to determine accurate SIF solutions leading to precise fatigue life estimations. A typical fillet weld joint 2-D model has been developed in CAE Abaqus software and a Finite Element Analysis of subject T-profile has been carried out. Through this analysis, the fillet weld angle, the weld leg length, the weld toe curvature radio ρ and the carrying load plate thickness are examined for their impacts on the maximum surface stress. Finally, a number of stress mitigating measures are proposed and their effects are analyzed. Undoubtedly, the notch stress concept today is gradually gaining more and more acceptance among other fatigue analysis practices, hence the need for an estimation of the actual surface stresses along fillet weld toes, has become imperative. Towards this, different 2-D geometries are tested against stress concentration factors developed at weld toes, which are calculated on the basis of maximum in-plane principal stresses over nominal stresses in mode I pure bending and pure tension respectively. Moreover, validation with corresponding results from literature is provided. Finally, three different concepts for reducing the maximum surface stresses are presented. The first one proposes grinding of the weld toe area and formulation of an artificial U-notch or a part- circular profile. The second one applies to non-penetrating welds and assumes the existence of a root gap of a specific geometry which is related to the fatigue life and stress concentration factor of the fillet weld joint. Last but not least, the relatively recent concept of the variable radius notch is discussed, even though it is applicable mostly to notched bodies, not weld joints. Afterwards, a Linear Elastic Fracture Mechanics analysis of reference 2D fillet weld model is demonstrated. A number of geometrical parameters considered at previous stage for their impact on surface Stress Concentration levels at the weld toe region, have been correlated to fatigue life benefits in terms of increased number of stress cycles till failure. An extensive analysis of 9 different T-butt weld joint geometries has been provided in order to investigate how positively a possible SCF reduction can affect the fatigue life of a weld joint. Essential geometric variations (weld angle, length, toe radius, root slot) were considered in the 2D model. All calculated benefits both in pure bending and pure tension cases have been reported accordingly. Based on a linear interpolation of the points scatter (SCF, N-cycles) both in banding and tension, it was observed that a surface stress mitigation of 1% could lead to 1,33 up to 2,5% fatigue life benefit in the range of SCF=2 – 2,5. It is evident so far that the geometrical optimization of a weld joint in respect of notch stress mitigation can be a powerful tool both in shipbuilding and maintenance practice in the future. However, technically wise their application may incur high initial costs of improved tools of welding and post welding treatment and robots even though it would consist a cost effective solution in a medium/long term basis. Finally, the above process is followed by a reliability analysis of the most critical geometrical parameters affecting the fatigue life of a fillet weld joint. Reliability assessment results concerning medium, high and low cycle fatigue are provided and a comparative analysis of each factor‟s impact on fatigue life has been carried out.