A systematic review of structural reliability methods for deformation and fatigue analysis of offshore jacket structures

This paper presents the state of the art in Structural Reliability Analysis (SRA) methods with a view of identifying key applications of each method and its proposed variations, qualifying characteristics, advantages, and limitations. Due to the increasing complexity and scale of modern offshore jacket structures, it becomes increasingly necessary to propose an accurate and efficient approach for the assessment of uncertainties in their material properties, geometric dimensions, and operating environments. SRA, as a form of uncertainty analysis, has been demonstrated to be a useful tool in the design of structures because it can directly quantify how uncertainty about input parameters can affect structural performance. Herein, attention was focused specifically on the probabilistic fracture mechanics approach because this accounts accurately for fatigue reliability mostly encountered as being dominant in the design of such structures. The well-established analytical/approximate methods such as the First- and Second-Order Reliability Methods (FORM/SORM) are widely used as they offer a good balance between accuracy and efficiency for realistic problems. They are, however, inaccurate in cases of highly non-linear systems. As a result, they have been modified using methods such as conjugate search direction approach, saddle point approximation, subset simulation, evidence theory, etc. in order to improve accuracy. Initially, direct simulations methods such as the Monte Carlo Simulation Method (MCS) with its various variance reduction techniques such as the Importance Sampling (IS), Latin Hypercube Sampling (LHS), etc. are ideal for structures having non-linear limit states but perform poorly for problems that calculate very low probabilities of failure. Overall, each method has its own merits and limitation, with FORM/SORM being the most commonly used, but recently, simulation methods have increasingly been used due to continuous advances in computation powers. Other relevant methods include the Response Surface Methods (RSM) and the Surrogate Models/Meta-models (SM/MM), which are advanced approximation methods and are ideal for structures with implicit limit state functions and high-reliability indices. Combinations of advanced approximation methods and reliability analysis methods are also found in literature as they can be suitable for complex, highly non-linear problems

Análisis por confiabilidad de la estabilidad de muros de pilas excavadas considerando las incertidumbres de los parámetros

In geotechnical engineering, bored-pile wall stability is evaluated using deterministic design methods based on safety factors to establish a margin against failure. In recent years, reliability-based design methods have been adopted to include uncertainty in the assessment of bored-pile wall stability as well as in the calculation of the feasible embedment depth of the walls. In this study, an expanded reliability-based design approach, along with finite element analysis, was applied to conduct parametric analyses of bored-pile wall stability. In serviceability limit state design framework, the results indicate that cohesion and groundwater level are factors that significantly affect bored-pile wall stability. Moreover, high variability in the cohesion range causes great uncertainty to determine the embedment depth of bored-pile wall. The feasible embedment depth can reach 4 times the free height considering the maximum coefficient of variation (50 %) of the cohesion. In turn, when the groundwater level is located at the retained ground surface, the horizontal displacement of the upper end of the wall reaches 15.2 mm, i.e., 0.0038 times the free height of the wall, for which the soil mobilizes active earth pressures. It was also found that the resolution of probabilistic results is highly influenced by the number of iterations in Monte Carlo simulations.En ingeniería geotécnica, la estabilidad de muros de pilas excavadas es evaluada mediante métodos de diseño determinísticos que se basan en el uso de factores de seguridad para establecer un margen para la falla. En los últimos años, se han adoptado métodos de diseño basados en la confiabilidad para involucrar la incertidumbre en la evaluación de la estabilidad de los muros, así como para el cálculo de la profundidad de empotramiento factible para los muros. En este estudio, se aplica un enfoque de diseño basado en la confiabilidad ampliada para desarrollar análisis paramétricos de la estabilidad de un muro de pilas excavadas, junto con un análisis de elementos finitos. En el marco del diseño por estado límite de servicio, los resultados indican que la cohesión del suelo y el nivel freático son factores que afectan significativamente la estabilidad del muro. Una alta variabilidad en el rango de cohesión causa una gran variabilidad en la incertidumbre para determinar la profundidad de empotramiento del muro. La profundidad de empotramiento factible puede alcanzar 4 veces la altura libre considerando el coeficiente de variación máximo (50 %) de la cohesión del suelo. Por otro lado, cuando el nivel freático se ubica en la superficie del terreno retenido, el desplazamiento horizontal del extremo superior del muro alcanza 15.2 mm, equivalente a 0.0038 veces la altura libre del muro, para el cual el suelo alcanza a movilizar los empujes activos. También se encontró que la resolución de los resultados probabilísticos está altamente influenciada por el número de iteraciones en las simulaciones de Monte Carlo

Efficient System Reliability Analysis for Layered Soil Slopes with Multiple Failure Modes Using Sequential Compounding Method

Evaluating the system reliability of layered soil slopes is a challenging issue because multiple failure modes may be included along the slip surfaces, which makes the overall failure probability greater than any individual slip surface. In this paper, an efficient system reliability analysis concerning the layered soil slopes is conducted based on the sequential compounding method (SCM) that has the ability to compound multiple failure events into an equivalent event sequentially. First, the first order reliability method (FORM) is employed to quantify initial reliability indices and correlation coefficients among these failure modes. Subsequently, the SCM is used to calculate the equivalent reliability indices and correlation coefficients until the multiple failure events are reduced to a compound event, and then the system reliability of the slope is obtained accordingly. The application of the approach to probabilistic evaluation of layered slopes is illustrated by two typical examples, and the correctness is verified by a Monte Carlo simulation (MCS). The results show that the SCM can deliver accurate system failure probability and greatly improve the computational efficiency compared with the MCS, which is an advantageous and promising strategy in evaluating the system reliability of layered soil slopes

Statistischer Maßstabseffekt im Stahlbau und korrespondierender Einfluss auf die Zuverlässigkeit

This thesis aims to investigate the statistical size effect in the elasto-plastic material and the corresponding reliability of steel structures. The core idea is that the stochastic material properties are directly embedded in mechanical calculations to develop a more accurate and economical design method for steel structure. Moreover, the results of the experimental investigation with different specimen sizes, whose diameter is limit up to 32 mm, show that the statistical size effect exists in steel structures. This thesis demonstrates finally that the structural reliability is affected by the statistical size effect and the structural safety can be optimized by considering this effect. Because of the uncertainty and non-uniformity of the microscopic imperfection distribution, the material strength in macroscale presents complex randomness. This study described the randomness of material properties through two different ways: developing a stochastic material model for elasto-plastic material and establishing a discrete random field with a general mathematical program. The proposed stochastic material model is extended to analyze the steel structure with multiaxial stress and is integrated into the commercial FEM software for analysis of the complex structures with stress gradient. The stochastic finite element method is implemented to analyze the response of the 3D structures by a general-purpose FEM program when the random field file is imported into the finite element model. The uniaxial tensile tests with different specimen sizes and different material are carried out to demonstrate the statistical size effect in steel structures. The results show that the variations of the yield and tensile strength increase with the decreasing specimen volume. Moreover, according to the bending tests, it is obvious that the structural component strength is not only related to the specimen volume, but also the stress distribution. These two proposed simulation methods, which are an extension and supplement to traditional simulation methods, can effectively simulate the statistical size effect for the tensile and flexural components in steel structures. Finally, it is found by studying the influence of statistical size effect on structural reliability that the strength, which is obtained by small specimens through statistical analysis in the laboratory, is no more accurately applicable to large construction. The reliability theory for the structural safety which exists over the decades can be compared and validated or improved through the embedding the stochastic material properties in the numerical simulation.Das Ziel dieser Arbeit besteht darin, den Einfluss des statistischen Maßstabseffekts auf die elasto-plastischen Werkstoffeigenschaften und die entsprechende Zuverlässigkeit im Stahlbau zu quantifizieren. Die stochastischen Materialeigenschaften werden direkt in die numerischen Berechnungen implementiert, um eine präzisere und wirtschaftlichere Methodik für die Bemessung von Stahlkonstruktionen zu entwickeln. Darüber hinaus zeigen die Ergebnisse experimenteller Untersuchungen mit verschiedenen Probengrößen (max. Durchmesser bis zu 32 mm), dass der statistische Maßstabseffekt in Stählen existiert. Mittels numerischer Simulationen wird gezeigt, dass die Zuverlässigkeit der Bauteile durch den statistischen Maßstabseffekt beeinflusst wird und dass die strukturelle Sicherheit unter Berücksichtigung dieses Effekts optimiert werden kann. Aufgrund der vorhandenen mikroskopischen Imperfektionen und der Unsicherheiten über deren Verteilung zeigen die mechanischen Eigenschaften des Werkstoffs Zufälligkeiten. Diese Arbeit beschreibt die Zufälligkeit des Werkstoffs auf zwei verschiedene Wege: die Erste ist die Entwicklung eines stochastischen Materialmodells mit elasto-plastischen Materialeigenschaften. Die zweite Möglichkeit ist der Aufbau eines diskreten Zufallsfeldes mit einem allgemeinen mathematischen Programm. Das vorgeschlagene stochastische Materialmodell wird erweitert, um die Stahlkonstruktion unter multiaxialer Beanspruchung zu analysieren. Es wird in die kommerzielle FEM-Software integriert, um komplexe Bauwerke mit Spannungsgradienten zu analysieren. Die stochastische Finite-Elemente-Methode wird implementiert, um die Antworten der 3D-Konstruktion durch ein allgemeines FEM-Programm zu analysieren, nachdem die Zufallsfelddatei in das Finite-Elemente-Modell importiert wurde. Um den statistischen Maßstabseffekt im Stahlbau zu demonstrieren, werden die uniaxialen Zugversuche mit unterschiedlichen Probengrößen und verschiedenen Werkstoffen durchgeführt. Die Ergebnisse zeigen, dass die Streuungen der Streckgrenze und die Zugfestigkeit mit zunehmendem Probenvolumen abnehmen. Darüber hinaus hängt die Festigkeit des Bauteils nicht nur vom Probenvolumen gemäß den Biegetests, sondern auch von der Spannungsverteilung ab. Sowohl die analytische Methode als auch die vorgeschlagene Simulationsmethode, die eine Erweiterung und Ergänzung zu traditionellen Simulationsverfahren sind, können den statistischen Maßstabseffekt für die Zug- und Biegekomponenten in Stahlkonstruktionen erfassen. Die Untersuchungen des Einflusses des statistischen Maßstabseffektes auf die strukturelle Zuverlässigkeit ergaben, dass die Festigkeiten, die an kleinen Proben durch statistische Analysen im Labor ermittelt werden, für größere Bauteile nicht mehr exakt zutreffen. Daher kann die Zuverlässigkeitstheorie für die strukturelle Sicherheit mit der Simulation verglichen und validiert oder verbessert werden, indem die stochastischen Materialeigenschaften in das Simulationsmodell eingebettet werden

Probabilistic-based structural safety analysis of concrete gravity dams

The construction and operation of dams, associated with the use of water resources, aims generically at water supplying, the energy producing and, in many cases, flow regulating and flood controlling. Considering the dam dimensions and the potential risks associated with its structural failure, due to the occupation of the downstream valley, and to the costs of the construction, maintenance and rehabilitation, the use of probabilistic principles in its design, as it is already performed for other type of structures, is justified considering adequate levels of safety. The objections shared throughout the dam engineering community, regarding the difficulty in estimating the probability of failure for concrete dams, are expectedly overcome by the failure mode and uncertainty modeling, allowing the application of probabilistic principles for their safety analysis, based on conservative simplifications regarding the structural behavior, namely: (i) the definition of the failure surface (dam-foundation interface); (ii) the consideration of rigid body failure mechanisms; and (iii) the consideration of the residual shear strength, given only by the frictional component, corresponding to a limit analysis valid for ultimate limit states. For that purpose, the failure modes are derived from the current construction and design practice by comparing analytical and numerical models of a generic, though representative, case study. The uncertainties involved in the safety of concrete dams are statistically quantified, through the definition of probabilistic distributions for loads and material properties, using, in addition to the elements found in the literature, the information available at LNEC about those features, resulting from the monitoring of the concrete dam behavior during the construction, first filling and operation periods. This work explores the required tasks for the adoption of the partial safety factor method for the safety analysis of concrete gravity dams, at the design phase. Two representative studies regarding the reliability-based design of concrete gravity dams and partial safety factor calibration are presented, intending to stimulate the discussion on the applicability of probabilistic principles for the design of concrete dams, as well as, to influence the safety criteria to be considered in a future revision of the dam safety regulation. The obtained results confirm that the seismic load combination and the sliding failure modes are the most conditioning situations. It is also observed that cross-sections profiles flatter than currently used may be needed for high intensity seismic zones. Partial safety factors that approximate reasonably the reliability-based results could be derived

Utilisation de la méthode des éléments finis non-linéaires pour la conception des structures en béton armé: application aux structures massives

RÉSUMÉ L’analyse non-linéaire par éléments finis constitue un outil numérique de pointe pour l’analyse des éléments en béton armé. Elle permet de reproduire le comportement fragile du béton après fissuration et constitue dans certains cas la seule alternative aux essais expérimentaux pour la prédiction précise du comportement des structures en béton. Jusqu’à date, cet outil a surtout été utilisé pour la reproduction de résultats d’essais expérimentaux simples – tirants, poutres et dalles en béton armé – et a rarement été utilisé pour l’analyse ou encore la conception de structures complexes en béton armé. Plusieurs raisons ont contribué à cela. La difficulté de la mise en oeuvre de telles analyses pour les structures complexes constitue le premier obstacle : temps de calcul important par rapport aux analyses linéaires, taille énorme des modèles de calcul et problèmes de convergence liés à la fissuration du béton. La deuxième raison est liée à la complexité du matériau béton et l'existence de plusieurs modèles de bétons issus de différentes théories de la littérature. Finalement, l’absence d’efforts pertinents au niveau de la littérature pour le passage des résultats de ces analyses jusqu’au dimensionnement et au calcul final des armatures a largement contribué à l’intérêt mitigé pour de telles analyses coûteuses. Le présent travail présente des solutions pour ces problèmes avec comme application le domaine des structures massives en béton armé. L'approche de résolution explicite en mode quasi-statique est présentée dans ce travail comme une solution au premier problème et est utilisée comme alternative à l'approche conventionnelle implicite. À travers des exemples d'application réels issus du milieu industriel, on montre que l'analyse de modèles complexes est rendue possible avec cette méthode et que le temps de calcul peut être déterminé à l'avance.----------ABSTRACT Nonlinear finite elements for concrete structures have seen a remarkable advancement in the last half century with more emphasis on constitutive modelling of reinforced and non-reinforced concrete. Applications were restricted to the analysis of simple structures (beams, columns, slabs …etc.), comparisons to experimental tests, and rarely extended to the design of complex structures. Many reasons lie behind this fact. The first is the difficulty to implement such analyses for complex structures: large computation time with respect to conventional linear analyses, and convergence problems generally related to concrete softening. The second important reason is the complexity of the concrete material and the existence of a multitude of models and theories in the literature. Finally, there is a lack in the literature and international codes concerning the reliability framework and the limit state design using nonlinear analyses. The current work presents solutions to these issues and applications in the field of large reinforced concrete structures. To address the first problem, the quasi-static explicit solver algorithm is presented in this work, as an alternative to the conventional static implicit solver. Effectiveness of the explicit solver algorithm compared to the standard implicit one is demonstrated. It is shown through validations that, analysis of complex models with highly non-linear behaviour is being possible without the need for iterations. To address the second and third problems, a methodology that uses nonlinear finite elements analysis for determining a global resistance factor for the design of reinforced concrete structures is suggested

6th International Probabilistic Workshop - 32. Darmstädter Massivbauseminar: 26-27 November 2008 ; Darmstadt, Germany 2008 ; Technische Universität Darmstadt

These are the proceedings of the 6th International Probabilistic Workshop, formerly known as Dresden Probabilistic Symposium or International Probabilistic Symposium. The workshop was held twice in Dresden, then it moved to Vienna, Berlin, Ghent and finally to Darmstadt in 2008. All of the conference cities feature some specialities. However, Darmstadt features a very special property: The element number 110 was named Darmstadtium after Darmstadt: There are only very few cities worldwide after which a chemical element is named. The high element number 110 of Darmstadtium indicates, that much research is still required and carried out. This is also true for the issue of probabilistic safety concepts in engineering. Although the history of probabilistic safety concepts can be traced back nearly 90 years, for the practical applications a long way to go still remains. This is not a disadvantage. Just as research chemists strive to discover new element properties, with the application of new probabilistic techniques we may advance the properties of structures substantially. (Auszug aus Vorwort

The impact of human errors on the performance to failure of concrete bridges

Programa doutoral em Engenharia CivilO colapso de pontes que tiveram lugar em todo o mundo nos últimos 50 anos destacou o erro humano como a principal causa do colapso de pontes. Dadas as implicações financeiras, sociais e psicológicas de tais eventos indesejados, a contribuição do erro humano no colapso de pontes deve ser investigada com o objetivo de compreender como é que a robustez e a segurança estrutural das pontes são afetadas pelos mesmos. A deterioração das pontes, leva à redução das margens de segurança, expondo muitas vezes deficiências causadas por erros de projeto e construção, realçando a importância do desenvolvimento de procedimentos de avaliação estrutural mais abrangentes, tendo em conta numerosas fontes de incertezas. Apesar destes factos conhecidos existem poucos trabalhos disponíveis investigando questões tão relevantes. Neste sentido este trabalho aborda a identificação dos erros humanos em suas inúmeras formas, ou seja, erros de projeto e erros de construção, de acordo com opiniões de especialistas e eventos de colapso de pontes registados. Diferentes erros representam diferentes ameaças à segurança estrutural; como tal o risco relativo dos erros também é investigado. O real impacto dos erros humanos na segurança estrutural é investigado através de três pontes de betão armado, considerando a probabilidade de falha perante um conjunto de incertezas como principal indicador de desempenho. Tal investigação é realizada em duas etapas, uma onde os erros de projeto e construção são introduzidos em cenários onde se entende que eles estão presentes e outra onde a possibilidade de ocorrência de erros de construção é investigada considerando a probabilidade do erro humano e a magnitude do erro. Ocorrências únicas e múltiplas de erros também são discutidas. Modelos de elementos finitos, considerada para fins de análise estrutural não linear, e modelos substitutos são introduzidos como a base das múltiplas análises de fiabilidade estrutural realizadas. Finalmente, a previsão da vida útil de pontes considerando a corrosão induzida por carbonatação e a redução da vida útil das pontes causada por erros de construção são questões também abordadas.The collapse of bridges that have taken place worldwide in the last 50 years has highlighted human error as the main cause of the collapse of bridges. Given the financial, social and phycological implications of such hazardous events, human errors' contribution to the collapse of bridges must be investigated, aiming to understand how their robustness and structural safety are affected. The ageing of bridges leads to safety margin reductions that often expose deficiencies caused by design and construction errors, underling the importance of developing more comprehensive frameworks that consider numerous sources of uncertainty for structural safety assessment purposes. Despite these facts and known needs, few works facing such relevant concerns are available. Accordingly, human errors are identified in their numerous forms, i.e., design errors and construction errors, according to expert opinions and real-world bridge collapse events. Different errors represent different threats to structural safety; thus, their relative risk is also investigated. The actual impact of human errors on structural safety is investigated through one reinforced and two prestressed concrete bridges, using their probability of failure, given a group of uncertainties, as the main performance indicator. Such investigation is performed on two fronts, one where design and construction errors are introduced under scenarios where they are understood to be present, and another where the possibility of occurrence of construction errors is investigated considering probabilistic models to describe human error probabilities and error magnitudes. Single and multiple occurrences of errors are also discussed. Finite element modelling, considered for non-linear structural analysis purposes, and surrogate models are introduced as the backbone of the multiple structural reliability analysis performed. Finally, the service life prediction of bridges considering carbonation-induced corrosion and the service life reduction of bridges due to construction errors are carefully addressed.This work was partially financed by (i) national funds through FCT - Foundation for Science and Technology, under grant agreement “PD/ BD/143003/2018” attributed to the PhD Candidate through the iRail Doctoral program; and (ii) FCT/MCTES through national funds (PIDDAC) under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB/04029/2020

Advancing the analysis of architectural fabric structures, neural networks and uncertainty

PhD ThesisIn current practice a plane stress framework comprising elastic moduli and Poisson’s ratios is most commonly used to represent the mechanical properties of architectural fabrics. This is often done to enable structural analysis utilising commercially available, non-specialist, finite element packages. Plane stress material models endeavour to fit a flat plane to the highly non-linear stress strain response surface of architectural fabric. Neural networks have been identified as a possible alternative to plane stress material models. Through a process of training they are capable of capturing the relationship between experimental input and output data. With the addition of historical inputs and internal variables it has been demonstrated that neural network models are capable of representing complex history dependant behaviour. The resulting neural network architectural fabric material models have been implemented within custom large strain finite element code. The finite element code, capable of using either a neural network or plane stress material model, utilises a dynamic relaxation solution algorithm and includes geodesic string control for soap film form-finding. Analytical FORM reliability analysis using implied stiffness matrices' derived from the equations of the neural network model has also been investigated