Design of retaining structures depends upon the load which is transferred from backfill soil as well as external loads and also the resisting capacity of the structure. The traditional safety factor approach of the design of retaining structures does not address the variability of soils and loads. The properties of backfill soil are inherently variable and influence the design decisions considerably. A rational procedure for the design of retaining structures needs to explicitly consider variability, as they may cause significant changes in the performance and stability assessment. Reliability based design enables identification and separation of different variabilities in loading and resistance and recommends reliability indices to ensure the margin of safety based on probability theory. Detailed studies in this area are limited and the work presented in the dissertation on the Optimum design of retaining structures under static and seismic conditions: A reliability based approach is an attempt in this direction. This thesis contains ten chapters including Chapter 1 which provides a general introduction regarding the contents of the thesis and Chapter 2 presents a detailed review of literature regarding static and seismic design of retaining structures and highlights the importance of consideration of variability in the optimum design and leads to scope of the investigation. Targeted stability is formulated as optimization problem in the framework of target reliability based design optimization (TRBDO) and presented in Chapter 3. In Chapter 4, TRBDO approach for cantilever sheet pile walls and anchored cantilever sheet pile walls penetrating sandy and clayey soils is developed. Design penetration depth and section modulus for the various anchor pulls are obtained considering the failure criteria (rotational, sliding, and flexural failure modes) as well as variability in the back fill soil properties, soil-steel pile interface friction angle, depth of the water table, total depth of embedment, yield strength of steel, section modulus of sheet pile and anchor pull. The stability of reinforced concrete gravity, cantilever and L-shaped retaining walls in static conditions is examined in the context of reliability based design optimization and results are presented in Chapter 5 considering failure modes viz. overturning, sliding, eccentricity, bearing, shear and moment failures in the base slab and stem of wall. Optimum wall proportions are proposed for different coefficients of variation of friction angle of the backfill soil and cohesion of the foundation soil corresponding to different values of component as well as lower bounds of system reliability indices. Chapter 6 presents an approach to obtain seismic passive resistance behind gravity walls using composite curved rupture surface considering limit equilibrium method of analysis with the pseudo-dynamic approach. The study is extended to obtain the rotational and sliding displacements of gravity retaining walls under passive condition when subjected to sinusoidal nature of earthquake loading. Chapter 7 focuses on the reliability based design of gravity retaining wall when subjected to passive condition during earthquakes. Reliability analysis is performed for two modes of failure namely rotation of the wall about its heel and sliding of the wall on its base are considering variabilities associated with characteristics of earthquake ground motions, geometric proportions of wall, backfill soil and foundation soil properties. The studies reported in Chapter 8 and Chapter 9 present a method to evaluate reliability for external as well as internal stability of reinforced soil structures (RSS) using reliability based design optimization in the framework of pseudo static and pseudo dynamic methods respectively. The optimum length of reinforcement needed to maintain the stability against four modes of failure (sliding, overturning, eccentricity and bearing) by taking into account the variabilities associated with the properties of reinforced backfill, retained backfill, foundation soil, tensile strength and length of the geosynthetic reinforcement by targeting various component and system reliability indices is computed. Finally, Chapter 10 contains the important conclusions, along with scope for further work in the area. It is hoped that the methodology and conclusions presented in this study will be beneficial to the geotechnical engineering community in particular and society as a whole.

Les structures de génie civil, en particulier les ponts en béton armé, doivent être conçues et gérées pour assurer les besoins de transport et de communication dans la société. Il est indispensable de garantir un fonctionnement convenable et sécuritaire de ces structures, puisque les défaillances peuvent conduire à des perturbations du transport, des pertes catastrophiques de concessions et des pertes de vies humaines, avec des impacts économiques, sociétaux et environnementaux graves, à court et à long termes. Les gestionnaires entreprennent diverses activités pour maintenir la performance et le fonctionnement adéquat à long terme, tout en satisfaisant les contraintes financières et sécuritaires. Idéalement, ils peuvent recourir à des techniques d'optimisation pour établir les compromis entre la réduction du coût du cycle de vie (LCC) et la maximisation de la durée de vie. Cela nécessite le développement de l’analyse du cycle de vie, de l’analyse de fiabilité et de l'optimisation structurale.Les approches actuelles pour la conception et la gestion des structures s’appuyant sur l’analyse du coût de cycle de vie, montrent les besoins suivants : (1) une approche intégrée et systématique pour modéliser de façon cohérente les processus de dégradation, les charges de trafic, le vieillissement et les conséquences directes et indirectes de la défaillance, (2) une considération complète des dépendances économiques, structurales et stochastiques entre les différents éléments de l’ouvrage, (3) une approche permettant de modéliser efficacement un système structural formé de plusieurs éléments interdépendants, (4) une évaluation des conséquences de la dégradation et de la redistribution des charges entre les éléments en tenant compte de la redondance du système et de la configuration de l’ouvrage, (5) une méthode d'optimisation de la conception et de la maintenance qui préserve l’exigence de fiabilité tout en considérant la robustesse de la décision. L'objectif global de cette thèse est de fournir des procédures améliorées qui peuvent être appliquées à la conception et à la gestion fiabilistes et robustes des ouvrages en béton armé, en réduisant les coûts supportés par les gestionnaires et les utilisateurs, tout en tenant compte des dépendances entre les éléments. Dans la première partie de cette thèse, une synthèse bibliographique concernant les procédures de la conception et de la maintenance basée sur des calculs fiabilistes est présentée, et les différents composants du LCC sont développés. Ensuite, une approche est proposée pour la conception des ouvrages en tenant compte du coût aux usagers et en intégrant dans la fonction du coût de cycle de vie. Le modèle couplé corrosion-fatigue est aussi considéré dans l’optimisation de la conception. La planification de la maintenance des ouvrages est ensuite développée, en considérant les différents types d'interaction entre les éléments, en particulier les dépendances économiques, structurales et stochastiques. Ce modèle utilise l'analyse de l'arbre de défaillance et les probabilités conditionnelles pour tenir compte des dépendances dans la planification de la maintenance. Les conséquences de la dégradation et de la redistribution des charges sont prises en compte dans l'approche proposée. Par ailleurs, une méthode pratique de calcul de la fiabilité d'un système formé de plusieurs composantes interdépendantes est proposée, à travers un facteur de redondance calculé par la modélisation mécanique. Enfin, une nouvelle procédure d'optimisation est proposée, permettant de tenir compte des incertitudes dans le système et la capacité structurale de s'adapter aux variabilités intrinsèques. La procédure proposée tient compte des incertitudes et de la variabilité dans une formulation cohérente, validée au moyen des applications numériques. (...) / Civil engineering structures, particularly reinforced concrete bridges, should be designed and managed to ensure the society needs. It is crucial to assure that these structures function properly and safely as damage during the service life can lead to transport disturbance, catastrophic loss of property, causalities, as well as severe economic, social, and environmental impacts, in addition to long term consequences. Decision-makers adopt various activities to maintain adequate long-term performance and functionality while satisfying financial constraints. Ideally, they may employ optimization techniques to identify the trade-offs between minimizing the life-cycle cost (LCC) and maximizing the expected service life. This requires the development of three challenging chores: life cycle analysis, reliability analysis and structural optimization. The current approaches for the design and management of structures through a Life-cycle cost analysis (LCCA) highlight the following needs: (1) an integrated and systematic approach to model coherently the deterioration processes, the increasing traffic loads, the aging and the direct and indirect consequences of failure, (2) a mutual consideration of economic, structural and stochastic dependencies between the elements of a structural system, (3) an adequate approach for the deterioration dependencies and load redistribution between the elements, (4) an improvement of system reliability computation as a function of the structural redundancy and configuration that can take into account the dependencies between the elements, (5) a consideration of design and maintenance optimization procedures that focus coherently on the robustness of the management decision and on the satisfaction of reliability requirements.The overall objective of this study is to provide improved LCCA and procedures that can be applied to select optimal and robust design and maintenance decisions regarding new and existing reinforced concrete structures, by minimizing both manager and user costs, while providing the required safety along the structure lifetime, taking into account the most severe degradation processes and the dependencies between structural elements. In the first part of this thesis, a literature review concerning the current probabilistic design and maintenance procedures is presented, and the LCC components are discussed. Then, a new approach is developed to evaluate the user delay costs on a reinforced concrete bridge structure, based on direct and indirect costs related to degradation and failure, and to integrate it to the life cycle cost function, in order to allow for probabilistic design. In addition,the coupled corrosion-fatigue model is considered in the design optimization. Afterward, a structural maintenance planning approach is developed to consider the three types of interactions, namely economic, structural and stochastic dependencies. The proposed model uses fault tree analysis and conditional probabilities to reflect the dependencies in the maintenance planning. The consequences of degradation are evaluated and a method is proposed to account for the load redistribution. Moreover, a practical formulation for quantifying the reliability of a system formed of interrelated components is proposed, by the mean of a redundancy factor that can be computed by finite element analysis. Finally, a new optimization procedure is proposed, by taking into account the uncertainties in the analysis, and the structural ability to adapt to variability, unforeseen actions or deterioration mechanisms. The proposed procedure takes account of uncertainties andvariability in one consistent formulation, which is shown through numerical applications. (...)

Cette thèse est une contribution à la résolution du problème d’optimisation sous contrainte de fiabilité. Cette méthode de dimensionnement probabiliste vise à prendre en compte les incertitudes inhérentes au système à concevoir, en vue de proposer des solutions optimales et sûres. Le niveau de sûreté est quantifié par une probabilité de défaillance. Le problème d’optimisation consiste alors à s’assurer que cette probabilité reste inférieure à un seuil fixé par les donneurs d’ordres. La résolution de ce problème nécessite un grand nombre d’appels à la fonction d’état-limite caractérisant le problème de fiabilité sous-jacent. Ainsi,cette méthodologie devient complexe à appliquer dès lors que le dimensionnement s’appuie sur un modèle numérique coûteux à évaluer (e.g. un modèle aux éléments finis). Dans ce contexte, ce manuscrit propose une stratégie basée sur la substitution adaptative de la fonction d’état-limite par un méta-modèle par Krigeage. On s’est particulièrement employé à quantifier, réduire et finalement éliminer l’erreur commise par l’utilisation de ce méta-modèle en lieu et place du modèle original. La méthodologie proposée est appliquée au dimensionnement des coques géométriquement imparfaites soumises au flambement. / This thesis is a contribution to the resolution of the reliability-based design optimization problem. This probabilistic design approach is aimed at considering the uncertainty attached to the system of interest in order to provide optimal and safe solutions. The safety level is quantified in the form of a probability of failure. Then, the optimization problem consists in ensuring that this failure probability remains less than a threshold specified by the stakeholders. The resolution of this problem requires a high number of calls to the limit-state design function underlying the reliability analysis. Hence it becomes cumbersome when the limit-state function involves an expensive-to-evaluate numerical model (e.g. a finite element model). In this context, this manuscript proposes a surrogate-based strategy where the limit-state function is progressively replaced by a Kriging meta-model. A special interest has been given to quantifying, reducing and eventually eliminating the error introduced by the use of this meta-model instead of the original model. The proposed methodology is applied to the design of geometrically imperfect shells prone to buckling.

This thesis presents the reader the importance of optimization and probabilistic assessment of structures for civil engineering problems. Chapter 2 further investigates the combination between previously proposed optimization techniques and probabilistic assessment in the form of optimization constraints. Academic software has been developed for the purposes of demonstrating the effectiveness of the suggested methods and their statistical testing. 3th chapter summarizes the results of testing previously described optimization method (called Aimed Multilevel Sampling), including a comparison with other optimization techniques. In the final part of the thesis, described procedures have been demonstrated on the selected optimization and reliability problems. The methods described in text represents engineering approach to optimization problems and aims to introduce a simple and transparent optimization algorithm, which could serve to the practical engineering purposes.

Increasing the operational speed of trains has attracted a lot of interest in the last decades and has brought new challenges, especially in terms of infrastructure design methodology, as it may induce excessive vibrations. Such demands can damage bridges, which in turn increases maintenance costs, endangers the safety of passing trains and disrupts passenger comfort. Conventional design provisions should therefore be evaluated in the light of modern concerns; nevertheless, several previous studies have highlighted some of their shortcomings. It should be emphasized that most of these studies have neglected the uncertainties involved, which preventsthe reported results from representing a complete picture of the problem. In this respect, the present thesis is dedicated to evaluating the performance of conventional design methods, especially those related to running safety and passenger comfort, using probabilistic approaches. To achieve this objective, a preliminary study was carried out using the first-order reliability method for short/medium span bridges passed by trains at a wide range of operating speeds. Comparison of these results with the corresponding deterministic responses showed that applying a constant safety factor to the running safety threshold does not guarantee that the safety index will be identical for all bridges. It also shows that the conventional design approaches result in failure probabilities that are higher than the target values. This conclusion highlights the need to update the design methodology for running safety. However, it would be essential to determine whether running safety is the predominant design criterion before conducting further analysis. Therefore, a stochastic comparison between this criterion and passenger comfort was performed. Due to the significant computational cost of such investigations, subset simulation and crude Monte-Carlo (MC) simulation using meta-models based on polynomial chaos expansion were employed. Both methods were found to perform well, with running safety almost always dominating the passenger comfort limit state. Subsequently, classification-based meta-models, e.g. support vector machines, k-nearest neighbours and decision trees, were combined using ensemble techniques to investigate the influence of soil-structure interaction on the evaluated reliability of running safety. The obtained results showed a significant influence, highlighting the need for detailed investigations in further studies. Finally, a reliability-based design optimization was conducted to update the conventional design method of running safety by proposing minimum requirements for the mass per length and moment of inertia of bridges. It is worth mentioning that the inner loop of the method was solved by a crude MC simulation using adaptively trained Kriging meta-models. / Att öka tågens hastighet har väckt stort intresse under de senaste decennierna och har medfört nya utmaningar, särskilt när det gäller broanalyser, eftersom tågen inducerar stora vibrationer. Sådana vibrationer kan öka underhållskostnaderna, äventyra säkerheten för förbipasserande tåg och påverka passagerarkomforten. Konstruktionsbestämmelser bör därför utvärderas mot bakgrund av dessa problem; dock har flera tidigare studier belyst några av bristerna i dagens bestämmelser. Det bör understrykas att de flesta av dessa studier har försummat de osäkerheter som är involverade, vilket hindrar de rapporterade resultaten från att representera en fullständig bild av problemet. I detta avseende syftar denna avhandling till att utvärdera prestandan hos konventionella analysmetoder, särskilt de som rör körsäkerhet och passagerarkomfort, med hjälp av sannolikhetsmetoder. För att uppnå detta mål genomfördes en preliminär studie med första ordningens tillförlitlighetsnmetod för broar med kort/medellång spännvidd som passeras av tåg med ett brett hastighetsspektrum. Jämförelse av dessa resultat med motsvarande deterministiska respons visade att tillämpa en konstant säkerhetsfaktor för verifieringen av trafiksäkerhet inte garanterar att säkerhetsindexet kommer att vara identiskt för alla broar. Det visar också att de konventionella analysmetoderna resulterar i brottsannolikheter som är högre än målvärdena. Denna slutsats belyser behovet av att uppdatera analysmetoden för trafiksäkerhet. Det skulle emellertid vara viktigt att avgöra om trafiksäkerhet är det dominerande designkriteriet innan ytterligare analyser genomförs. Därför utfördes en stokastisk jämförelse mellan detta kriterium och kriteriet för passagerarkomfort. På grund av den betydande. analystiden för sådana beräkningar användes delmängdssimulering och Monte-Carlo (MC) simulering med metamodeller baserade på polynomisk kaosutvidgning. Båda metoderna visade sig fungera bra, med trafiksäkerhet som nästan alltid dominerade över gränsningstillståndet för passagerarkomfort. Därefter kombinerades klassificeringsbaserade metamodeller som stödvektormaskin och beslutsträd genom ensembletekniker, för att undersöka påverkan av jord-brointeraktion på den utvärderade tillförlitligheten gällande trafiksäkerhet. De erhållna resultaten visade en signifikant påverkan och betonade behovet av detaljerade undersökningar genom ytterligare studier. Slutligen genomfördes en tillförlitlighetsbaserad konstruktionsoptimering för att föreslå ett minimikrav på erforderlig bromassa per längdmeter och tröghetsmoment. Det är värt att nämna att metodens inre loop löstes med en MC-simulering med adaptivt tränade Kriging-metamodeller. / <p>QC 20210910</p>