[pt] Este trabalho apresenta os resultados da aplicação de análises probabilísticas na avaliação da estabilidade de taludes, com base no caso da ruptura de uma barragem de rejeito que rompeu em janeiro de 2019. Realizou-se uma análise estatística dos parâmetros geotécnicos dos materiais presentes na obra, enfatizando a variabilidade inerente dos dados. Nas análises probabilísticas, foi adotado os métodos FOSM. São apresentados os conceitos básicos de confiabilidade e probabilidade de ruptura e as hipóteses e etapas de cálculo consideradas em cada método. Discutem-se brevemente os diferentes métodos de equilíbrio limite utilizados para superfícies circulares de ruptura. Dois cenários foram estudados em relação aos procedimentos adotados: análises em tensões totais, com a resistência da argila mole obtida por ensaios de campo e laboratório; análises em tensões efetivas, com o ângulo de atrito da argila oriundo de ensaios triaxiais e obtidos por ensaios de campo e laboratório. Observou-se que para os dois cenários os valores de probabilidades de ruptura foram, respectivamente da ordem de: 1/3,5 e 1/312,5. / [en] This work aims the results of the application of probabilistic analyzes in the evaluation of slope stability, based on the case of the rupture of a tailings dam that colapse in January 2019. A statistical analysis of the geotechnical characteristics of the materials present in the work was carried out, emphasizing the inherent variability of the data. In the probabilistic analyzes, the FOSM method was adopted. The basic concepts of reliability and probability of rupture and the hypotheses and calculation steps considered in each method are presented. The different limit equilibrium methods used for circular rupture surfaces are briefly discussed. Two scenarios were studied in relation to the adopted procedures: total stress analysis, with the resistance of soft clay obtained by field and laboratory tests; effective stress analysis with the angle of friction of the clay from field and laboratory tests. It was observed that for the two scenarios the values of probability of rupture were, respectively, in the order of 1/3,5 e 1/312,5.

Research in the field of reliability based design is mainly focused on two sub-areas: The computation of the probability of failure and its integration in the reliability based design optimization (RBDO) loop. Four papers are presented in this work, representing a contribution to both sub-areas. In the first paper, a new Second Order Reliability Method (SORM) is presented. As opposed to the most commonly used SORMs, the presented approach is not limited to hyper-parabolic approximation of the performance function at the Most Probable Point (MPP) of failure. Instead, a full quadratic fit is used leading to a better approximation of the real performance function and therefore more accurate values of the probability of failure. The second paper focuses on the integration of the expression for the probability of failure for general quadratic function, presented in the first paper, in RBDO. One important feature of the proposed approach is that it does not involve locating the MPP. In the third paper, the expressions for the probability of failure based on general quadratic limit-state functions presented in the first paper are applied for the special case of a hyper-parabola. The expression is reformulated and simplified so that the probability of failure is only a function of three statistical measures: the Cornell reliability index, the skewness and the kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the MPP. In the last paper, an approximate and efficient reliability method is proposed. Focus is on computational efficiency as well as intuitiveness for practicing engineers, especially regarding probabilistic fatigue problems where volume methods are used. The number of function evaluations to compute the probability of failure of the design under different types of uncertainties is a priori known to be 3n+2 in the proposed method, where n is the number of stochastic design variables. / <p>QC 20160317</p>

[pt] Freqüentemente as análises de estabilidade de taludes são feitas por métodos determinísticos, nos quais é obtido um Fator de Segurança (FS). Estes métodos não quantificam as incertezas existentes nas variáveis de entrada (parâmetros de resistência) na análise. Tampouco mostram detalhes sobre qual variável afeta mais o resultado. Os métodos probabilísticos permitem superar estes problemas. A presente pesquisa tem como objetivo comparar dois métodos probabilísticos geralmente utilizados (Estimativas Pontuais e Segundo Momento). Três projetos utilizados comumente na geotecnia são analisados: barragem de rejeitos, talude de solo e aterro sobre argila mole.Um aspecto importante na análise probabilística é a quantificação adequada do desvio padrão. É sabido que as propriedades dos solos mostram uma correlação no espaço, pelo que o desvio padrão calculado por métodos clássicos da estatística é superestimado em comparação ao valor real no campo. El-Ramly (2001) desenvolveu uma metodologia para o cálculo da probabilidade de ruptura considerando a correlação espacial das propriedades do solo. Esta metodologia é de difícil aplicação prática. Serão, portanto, avaliadas na presente pesquisa as técnicas geralmente usadas de probabilidade e estabilidade de taludes, juntamente com um fator de correção proposto por Vanmarcke (1977a). Estas técnicas de probabilidade de estabilidade de taludes são factíveis de serem utilizadas junto com este fator de correção. Verificou-se que o Método de Segundo Momento é de mais fácil utilização, e portanto adequado para emprego em projetos geotécnicos. / [en] The analysis of slope stability is often determined by deterministic methods, in which a Factor of Security (FS) is obtained. These methods do not quantify the uncertainty in the input variables (strength parameters). Neither these methods show details which variable affects mostly the outcome results. The probabilistic methods allow overcoming these restrictions. This study aims at comparing two probabilistic methods of general use (Point Estimates and First Order Second Moment). Three projects commonly used in geotechnical engineering are analyzed: tailings dam, slope soil and embankment on soft clay. An important aspect of the probabilistic analysis is the proper quantification of the standard deviation. It is known that the soil properties show a correlation in space, so the standard deviation, calculated by traditional methods of statistics, is overestimated when compared to the real field value. El-Ramly (2001) developed a methodology for calculating the probability of failure considering the spatial correlation of the soil properties. This methodology is difficult to apply in practice. The present study will therefore evaluate the techniques generally used in probability of failure of slopes. These probability techniques applied to slope stability can be used together with a correction factor proposed by Vanmarcke (1977b). The Second Moment Method was found to be easier to use, and therefore more suitable for geotechnical projects.

A norma Brasileira NBR 6122/1996 - Projeto e Execução de Fundações utiliza o conceito de coeficiente de segurança global e parcial na verificação da segurança de fundações. Esta dissertação ressalta que essa verificação, utilizada na prática, é necessária, para que se atenda às exigências da norma, porém, não é suficiente para garantir a segurança de uma fundação. Pois, qualquer medida de segurança deve estar associada a uma determinada probabilidade de ruína. Neste contexto, apresenta-se nessa dissertação uma metodologia de verificação da segurança na qual, a escolha da carga admissível de um estaqueamento é baseada na probabilidade de ruína de um elemento isolado de fundação e, a aplicação dessa metodologia em diversas fundações executadas em diferentes regiões do país. / The Brazilian code NBR 6122/1996 for Foundation Design and Execution is based on the concept of Limit States Design (LSD) and on the traditional Working Stress Design (WSD). This paper shows that this approach, as usually carry out in the foundation engineering practice, although being necessary, is not enough to assure a safe foundation, once any safety measurement should be associated to a given probability of failure. Therefore, in the proposed methodology, the safety verification of the piling allowable load is based on the probability of failure of an isolated foundation element.

Cette thèse aborde le problème de l'estimation de la probabilité de défaillance d'un système à partir de simulations informatiques. Lorsqu'on dispose seulement d'un modèle du système coûteux à simuler, le budget de simulations est généralement très limité, ce qui est incompatible avec l’utilisation de méthodes Monte Carlo classiques. En fait, l’estimation d’une petite probabilité de défaillance à partir de simulations très coûteuses, comme on peut rencontrer dans certains problèmes industriels complexes, est un sujet particulièrement difficile. Une approche classique consiste à remplacer le modèle coûteux à simuler par un modèle de substitution nécessitant de faibles ressources informatiques. A partir d’un tel modèle de substitution, deux opérations peuvent être réalisées. La première opération consiste à choisir des simulations, en nombre aussi petit que possible, pour apprendre les régions de l’espace des paramètres du système qui construire de bons estimateurs de la probabilité de défaillance. Cette thèse propose deux contributions. Premièrement, nous proposons des stratégies de type SUR (Stepwise Uncertainty Reduction) à partir d’une formulation bayésienne du problème d’estimation d’une probabilité de défaillance. Deuxièmement, nous proposons un nouvel algorithme, appelé Bayesian Subset Simulation, qui prend le meilleur de l’algorithme Subset Simulation et des approches séquentielles bayésiennes utilisant la modélisation du système par processus gaussiens. Ces nouveaux algorithmes sont illustrés par des résultats numériques concernant plusieurs exemples de référence dans la littérature de la fiabilité. Les méthodes proposées montrent de bonnes performances par rapport aux méthodes concurrentes. / 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.

This thesis presents a new modeling framework and application methodology for the study of aircraft structures. The framework provides a ‘cradle-to-grave’ approach to structural analysis of a component, where structural integrity encompasses all phases of its lifespan. The methodology examines the holistic structural design of aircraft components by integrating fatigue and damage tolerance methodologies. It accomplishes this by marrying the load inputs from a fatigue analysis for new design, into a risk analysis for an existing design. The risk analysis incorporates the variability found from literature, including recorded defects, loadings, and material strength properties. The methodology is verified via formal conceptualization of the structures, which are demonstrated on an actual hydraulic accumulator and an engine nacelle inlet. The hydraulic accumulator is examined for structural integrity utilizing different base materials undergoing variable amplitude loading. Integrity is accomplished through a risk analysis by means of fault tree analysis. The engine nacelle inlet uses the damage tolerance philosophy for a sonic fatigue condition undergoing both constant amplitude loading and a theoretical flight design case. Residual strength changes are examined throughout crack growth, where structural integrity is accomplished through a risk analysis of component strength versus probability of failure. Both methodologies can be applied to nearly any structural application, not necessarily limited to aerospace.

Traditionally design engineers have used the Factor of Safety method for ensuring that designs do not fail in the field. Access to advanced computational tools and resources have made this process obsolete and new methods to introduce higher levels of reliability in an engineering systems are currently being investigated. However, even though high computational resources are available the computational resources required by reliability analysis procedures leave much to be desired. Furthermore, the regression based surrogate modeling techniques fail when there is discontinuity in the design space, caused by failure mechanisms, when the design is required to perform under severe externalities. Hence, in this research we propose efficient Semi-Supervised Learning based surrogate modeling techniques that will enable accurate estimation of a system's response, even under discontinuity. These methods combine the available set of labeled dataset and unlabeled dataset and provide better models than using labeled data alone. Labeled data is expensive to obtain since the responses have to be evaluated whereas unlabeled data is available in plenty, during reliability estimation, since the PDF information of uncertain variables is assumed to be known. This superior performance is gained by combining the efficiency of Probabilistic Neural Networks (PNN) for classification and Expectation-Maximization (EM) algorithm for treating the unlabeled data as labeled data with hidden labels.

The performance and safety assessment of geo-structures is strongly affected by uncertainty; that is, both due a subjective lack of knowledge as well as objectively present and irreducible unknowns. Due to uncertainty in the non-linear variation of the matric suction induced effective stress as a function of the transient soil-atmosphere boundary conditions, the unsaturated state of the subsoil is generally not accounted for in a deterministic slope stability assessment. Probability theory, accounting for uncertainties quantitatively rather than using "cautious estimates" on loads and resistances, may aid to partly bridge the gap between unsaturated soil mechanics and engineering practice. This research investigates the effect of uncertainty in soil property values on the stability of unsaturated soil slopes. Two 2D Finite Element (FE) programs have been developed and implemented into a parallelised Reliability-Based Design (RBD) framework, which allows for the assessment of the failure probability, failure consequence and parameter sensitivity, rather than a deterministic factor of safety. Utilising the Random Finite Element Method (RFEM), within a Monte Carlo framework, multivariate cross-correlated random property fields have been mapped onto the FE mesh to assess the effect of isotropic and anisotropic moderate heterogeneity on the transient slope response, and thus performance. The framework has been applied to a generic slope subjected to different rainfall scenarios. The performance was found to be sensitive to the uncertainty in the effective shear strength parameters, as well as the parameters governing the unsaturated soil behaviour. The failure probability was found to increase most during prolonged rainfall events with a low precipitation rate. Nevertheless, accounting for the unsaturated state resulted in a higher slope reliability than when not considering suction effects. In a heterogeneous deposit failure is attracted to local zones of low shear strength, which, for an unsaturated soil, are a function of both the spatial variability of soil property values, as well as of the soil-water dynamics, leading to a significant increase in the failure probability near the end of the main rainfall event.

Orientador: Carlos Alberto Canesin / Banca: Júlio Borges de Souza / Banca: Denizar Cruz Martins / Resumo: O estudo da confiabilidade operacional de equipamentos se tornou fundamental para as empresas possuírem o devido controle dos seus ativos, tanto pelo lado financeiro quanto em questões de segurança. O estudo da taxa de falha de equipamentos prevê quando as falhas irão ocorrer possibilitando estabelecer atitudes preventivas, porém, seu estudo deve ser realizado em condições de operação estabelecidas e fixas. Os medidores de energia elétrica, parte do ativo financeiro das concessionárias de energia, são equipamentos utilizados em diversas condições de operação, tanto nas condições do fluxo de energia, tais como presenças de harmônicos, subtensões, sobre-tensões e padrões de consumo distintos, quanto pelo local físico de instalação, tais como maresia, temperatura, umidade, etc. As falhas nos medidores eletromecânicos de energia elétrica são de difícil constatação uma vez que a maioria dos erros de medição, ocasionados principalmente por envelhecimento de componentes, não alteram a qualidade da energia fornecida e nem interrompem o seu fornecimento. Neste sentido, este trabalho propõe uma nova metodologia de determinação de falhas em medidores eletromecânicos de energia elétrica ativa. Faz-se uso de banco de dados de uma concessionária de energia elétrica e do processo de descoberta de conhecimento em bases de dados para selecionar as variáveis mais significativas na determinação de falhas em medidores eletromecânicos de energia elétrica ativa, incluindo no conjunto de falhas a operação com erros de medição acima do permitido pela legislação nacional (2010). Duas técnicas de mineração de dados foram utilizadas: regressão stepwise e árvores de decisão. As variáveis obtidas foram utilizadas na construção de um modelo de agrupamento de equipamentos associando a cada grupo uma probabilidade... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The operational reliability study of equipments has become primal in order to enterprises have the righteous control over their assets, both by financial side as by security reasons. The study for the hazard rate of equipments allows to foresee the failures for the equipments and to act preventively, but this study must be accomplished under established and fixed operation conditions. The energy meters, for their part, are equipments utilized in several operating conditions so on the utilization manner, like presence of harmonics, undervoltages and over-voltages and distinct consumption patterns, as on the installation location, like swel, temperature, humidity, etc. Failures in electromechanical Wh-meters are difficult to detect once that the majority of metering errors occurred mainly by aging of components do not change the quality of offered energy neither disrupt its supply. In this context, this work proposes a novel methodology to obtain failure determination for electromechanical Whmeters. It utilizes Wh-databases from an electrical company and of the process of knowledge discovery in databases to specify the most significant variables in determining failures in electromechanical Wh-meters, including in the failure set the operation with metering errors above those permitted by national regulations (2010). Two techniques of data mining were used in this work: stepwise regression and decision trees. The obtained variables were utilized on the construction of a model of clustering similar equipments and the probability of failure of those clusters were determined. As final results, an application in a friendly platform were developed in order to apply the methodology, and a case study was accomplished in order to demonstrate its feasibility. / Mestre

A norma Brasileira NBR 6122/1996 - Projeto e Execução de Fundações utiliza o conceito de coeficiente de segurança global e parcial na verificação da segurança de fundações. Esta dissertação ressalta que essa verificação, utilizada na prática, é necessária, para que se atenda às exigências da norma, porém, não é suficiente para garantir a segurança de uma fundação. Pois, qualquer medida de segurança deve estar associada a uma determinada probabilidade de ruína. Neste contexto, apresenta-se nessa dissertação uma metodologia de verificação da segurança na qual, a escolha da carga admissível de um estaqueamento é baseada na probabilidade de ruína de um elemento isolado de fundação e, a aplicação dessa metodologia em diversas fundações executadas em diferentes regiões do país. / The Brazilian code NBR 6122/1996 for Foundation Design and Execution is based on the concept of Limit States Design (LSD) and on the traditional Working Stress Design (WSD). This paper shows that this approach, as usually carry out in the foundation engineering practice, although being necessary, is not enough to assure a safe foundation, once any safety measurement should be associated to a given probability of failure. Therefore, in the proposed methodology, the safety verification of the piling allowable load is based on the probability of failure of an isolated foundation element.