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A reliability-based optimization (RBO) methodology was developed and applied to fiber-reinforced polymer (FRP) bridge decks. Commercially available software was used to optimize a FRP bridge deck panel by weight with structural reliability, stress, and deflection constraints. A methodology using optimization software, finite element analysis, and probabilistic analysis software was developed to examine the effects of load and resistance uncertainties in FRP bridge deck optimization. Eight modular deck designs were considered for use in the RBO methodology. Investigations into random variable sensitivities, design variable sensitivities, wheel positions, and buckling were conducted to minimize computational effort. Five models were eventually optimized with deterministic methods and the RBO methodology. Ply thicknesses were treated as design variables. Material parameters, design variables, and load were taken as random variables in the reliability calculations. A comparison of RBO designs was made with the best candidate chosen based on deck panel weight.

Les structures en voûte sont présentes dans la plupart des anciens ouvrages maçonnés : tunnels, ponts, palais, cathédrales ou autres. Arches et voutes sont avec les murs les structures porteuses utilisées en maçonnerie. Leur bon état est alors la clef du bon fonctionnement d’un ouvrage. Les ouvrages maçonnés constituent à présent une proportion importante du patrimoine culturel. Toutefois, la plupart de ces ouvrages sont centenaires et le processus de dégradation s’est déjà enclenché depuis des décennies. Aujourd’hui, leur maintenance et réparation présentent des problèmes importants à leurs gestionnaires. Parfois des réparations ont été entreprises sans pour autant assurer la durabilité souhaitée. La fréquence des interventions se trouve augmentée et les coûts induits deviennent rapidement insupportables. Une situation qui a poussé certains gestionnaires à abandonner complètement leurs ouvrages, malgré leur valeur et leur importance patrimoniales. En effet, l’une des causes majeures d’abandon d’ouvrage est le coût excessif des inspections et des réparations. La question qui se pose dans de telles circonstances est de savoir comment mettre au point une stratégie à la fois efficace et surtout économique de maintenance de ces ouvrages, capable de prolonger leurs durées de vie ? Deux problèmes particuliers d’inspection sous incertitude sont traités : La présence localisée de perte de matière et la perte de matière généralisée. Pour traiter ces deux cas un programme a été développé. Le modèle, sur lequel il s’appuie, permet l’analyse globale de la voûte tout en minimisant au maximum le temps de calcul. Ce modèle constitue un compromis intéressant entre précision et temps de calcul. Les simulations de Monte Carlo ont été couplées à la méthode des éléments finis et implémentées dans un nouvel outil numérique, baptisé ArcProg_Z, afin de proposer une méthodologie cohérente pour l’évaluation probabiliste de la capacité portante des voûtes et de prévision de son mécanisme de ruine.Enfin, une étude de fiabilité de la voûte étudiée précédemment a été menée. La performance de la voûte a été évaluée à travers le calcul de sa probabilité de défaillance « instantanée et dépendante du temps » en fonction du coefficient de variation du module d’Young des différents segments. Les résultats obtenus pour chaque cas sont présentés et discutés. / The vault structures are present in most of the old masonry structures: tunnels, bridges, palaces, cathedrals or other civil infrastructures. Arches and vaults as well as walls are the supporting structures used in masonry. Their condition is then the key of the proper functioning of a structure. Masonry construction works are now a significant proportion of the cultural heritage. Most of them are century old and the degradation process is already running since several decades. Actually, the maintenance and repair continue to represent serious issues for their managers. Sometimes repairs have been undertaken without ensuring the aimed durability. The frequency of interventions is increased and the resulting costs are rapidly becoming unbearable. A situation has led some managers to completely abandon their buildings, despite their heritage value and national significance. Indeed, one of the major reasons for building abandonment is the excessive cost of inspections and repairs. The question that arises in such circumstances is how to develop a maintenance strategy that is both effective and most economical of these structures, capable to prolong their lifespan?Two particular inspection issues under uncertainty are discussed: The localized presence of material loss and generalized loss of material. To deal both cases, a program was developed. The model on which it is based, provides the overall analysis of the vault while minimizing the computation time. This model presents an interesting compromise between accuracy and computation time. Monte Carlo simulations are coupled with the finite element method and implemented in a software package named ArcProg_Z, in order to propose a consistent methodology for probabilistic assessment of the load bearing capacity of the vaults and predicting its failure mechanism.Finally, reliability study of the vault is carried out. The performance of the vault is assessed by calculating the probability of failure “instantaneous and time-dependent” according to the coefficient of variation of the Young's modulus of several segments.The obtained results for each case are presented and discussed.

The research presented in this dissertation furthers the state of the art for reliability-based design of composite structures subjected to high cycle variable amplitude (spectrum) fatigue loads. The focus is on fatigue analyses for axially loaded fiber reinforced polymer (FRP) composites that contain a significant proportion of fibers in the loading direction and thus have fiber-direction dominated failure. The four papers presented in this dissertation describe the logical progression used to develop an improved reliability-based methodology for fatigue-critical design. Throughout the analysis extensive experimental fatigue data on several material systems was used to verify the assumptions and suggest the path forward. A comparison of 12 fatigue model approaches from the literature showed that a simple linear residual strength approach (Broutman and Sahu) provides an improvement in fatigue life prediction compared to the Palmgren-Miner rule, while more complex residual strength models did not consistently improve on Broutman and Sahu. Evaluation of the effect of load history randomness on fatigue life was made using experimental results for spectra in terms of the first order autocorrelation of the stress events. For approximately reversed Rayleigh distributed fatigue loading, load sequence was not critical in the material behavior. Based on observations of empirical data and evaluation of the micro-mechanics deterioration and failure phenomena of FRP composites under fatigue loading, a new residual strength model for the tension and compression under any load history was proposed. Then this model was implemented in a stochastic framework and a method was proposed to enable calculation of the load and resistance factor design (LRFD) parameters for realistic reliabilities with relatively few computations. The proposed approach has significant advantages over traditional lifetime-damage-sum-based reliability analysis and provides a significant step toward enabling more accurate reliability-based design with composite materials. / Ph. D.

Nowadays, as oil industry gradually moves towards deep sea fields with water depth more than 1000 meters, they are subjected to several threats which can cause failure of the pipeline, of which the accidentally-dropped objects have become the leading external risk factor for subsea developments. In this thesis, a sample field layout introduced in Det Norske Veritas (DNV) guide rules is selected as the study case with 100 m water depth. Six different groups of dropped objects are used in this paper. The conditional hit probability for long/flat shaped objects will be calculated with the methods from both DNV rules and an in-house tool Dropped Objects Simulator (DROBS). The difference between the results will be discussed. Meanwhile, the sensitivity analysis on mass, collision area , the volume, added mass coefficient and drag coefficient of the objects are calculated.

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La presente tesis aplica métodos estadísticos asociados a la probabilidad de falla y factor de seguridad para determinar el riesgo y por consiguiente, desarrollar una propuesta de ingeniería más precisa con respecto al diseño geotécnico de cimentaciones ya que, esta investigación tomaría en cuenta el riesgo de falla a los que se exponen las estructuras; así mismo, se evaluará el impacto económico, del costo de la construcción más la ruina entre el costo de la edificación y el riesgo disminuido; obteniendo así, la respuesta de modificar la normativa y mejorarla consiguiendo así una calidad de vida alta ya que se mejoraría la sostenibilidad y la seguridad. Para el desarrollo de esta tesis se estudió 8 puentes de la carretera Huánuco – Conococha los cuales cuentan cada uno con su análisis geotécnico. / This thesis applies statistical methods associated with the probability of failure and safety factor to determine the risk; and consequently, develop a more precise engineering proposal regarding geotechnical design of foundations. The present investigation considers the risk of failure to which the structures are exposed; likewise, the economic impact of the construction cost plus the ruin, between the construction cost and the diminished risk is evaluated; obtaining the response to modify the regulations and improve it, thus achieving a high quality of life with better sustainability and security. For the development of this thesis, 8 bridges of the Huánuco - Conococha highway were studied, each one having its own geotechnical analysis. / Tesis

A simulation-based reliability analysis method is presented and evaluated. This method is intended for problems for which most probable point of failure (MPP) search-based methods fail or provide inaccurate results, and for which Monte Carlo simulation and its variants are too costly to apply. This may occur in the evaluation of complex engineering problems of low failure probability. The method used to address this problem is a variant of conditional expectation and works by sampling on the failure boundary without relying on the MPP. The effectiveness of the method is compared to a selection of other commonly available reliability methods considering a variety of analytical as well as more complex engineering problems. The results indicate that the method has the potential to deliver solutions of high efficiency and accuracy for a wide range of difficult reliability problems.

Earthen levees are crucial components of a nation's flood protection system. However, in some regions, these levees face the unique challenge of being subjected to both floods and earthquakes throughout their lifespan, an aspect that is relatively unexplored in the existing literature. The primary aim of this research is to examine earthquakes' and floods' effects on earthen levee failures. Using numerical simulations, the seepage, slope stability, and liquefaction potential of an earthen levee were modeled by considering compound of different floods and earthquakes scenarios. Elkhorn Levee in Sacramento, CA, was used as a representative case study for the simulations. The probability of levee failure and the extent of the breach caused by compound flood-earthquake scenarios are further determined by Fault Tree Method. The findings provide a practical approach to analyzing levee systems under multi-hazard conditions and enhancing levee resilience.

This thesis deals with the problem of estimating the probability of failure of a system from computer simulations. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited, which is incompatible with the use of classical Monte Carlo methods. In fact, estimating a small probability of failure with very few simulations, as required in some complex industrial problems, is a particularly difficult topic. A classical approach consists in replacing the expensive-to-simulate model with a surrogate model that will use little computer resources. Using such a surrogate model, two operations can be achieved. The first operation consists in choosing a number, as small as possible, of simulations to learn the regions in the parameter space of the system that will lead to a failure of the system. The second operation is about constructing good estimators of the probability of failure. The contributions in this thesis consist of two parts. First, we derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. Second, we propose a new algorithm, called Bayesian Subset Simulation, that takes the best from the Subset Simulation algorithm and from sequential Bayesian methods based on Gaussian process modeling. The new strategies are supported by numerical results from several benchmark examples in reliability analysis. The methods proposed show good performances compared to methods of the literature.