Reliability of buildings in service limit state for maximum horizontal displacements

Brazilian design code ABNT NBR6118:2003 - Design of Concrete Structures - Procedures - [1] proposes the use of simplified models for the consideration of non-linear material behavior in the evaluation of horizontal displacements in buildings. These models penalize stiffness of columns and beams, representing the effects of concrete cracking and avoiding costly physical non-linear analyses. The objectives of the present paper are to investigate the accuracy and uncertainty of these simplified models, as well as to evaluate the reliabilities of structures designed following ABNT NBR6118:2003[1&] in the service limit state for horizontal displacements. Model error statistics are obtained from 42 representative plane frames. The reliabilities of three typical (4, 8 and 12 floor) buildings are evaluated, using the simplified models and a rigorous, physical and geometrical non-linear analysis. Results show that the 70/70 (column/beam stiffness reduction) model is more accurate and less conservative than the 80/40 model. Results also show that ABNT NBR6118:2003 [1] design criteria for horizontal displacement limit states (masonry damage according to ACI 435.3R-68(1984) [10]) are conservative, and result in reliability indexes which are larger than those recommended in EUROCODE [2] for irreversible service limit states.

Critical comparative evaluation of design methodologies for the ultimate limit state of fatigue in concrete structures

La aparición de la fatiga ha sido ampliamente investigada en el acero y en otros materiales metálicos, sin embargo no se conoce en tanta profundidad en el hormigón estructural. Esto crea falta de uniformidad y enfoque en el proceso de verificación de estructuras de hormigón para el estado límite último de la fatiga. A medida que se llevan a cabo más investigaciones, la información sobre los parámetros que afectan a la fatiga en el hormigón comienzan a ser difundidos e incluso los que les afectan de forma indirecta. Esto conlleva a que se estén incorporando en las guías de diseño de todo el mundo, a pesar de que la comprobación del estado límite último no se trata por igual entre los distintos órganos de diseño. Este trabajo presentará un conocimiento básico del fenómeno de la fatiga, qué lo causa y qué condiciones de carga o propiedades materiales amplían o reducen la probabilidad de fallo por fatiga. Cuatro distintos códigos de diseño serán expuestos y su proceso de verificación ha sido examinado, comparados y valorados cualitativa y cuantitativamente. Una torre eólica, como ejemplo, fue analizada usando los procedimientos de verificación como se indica en sus respectivos códigos de referencia. The occurrence of fatigue has been extensively researched in steel and other metallic materials it is however, not as broadly understood in concrete. This produces a lack of uniformity in the approach and process in the verification of concrete structures for the ultimate limit state of fatigue. As more research is conducted and more information is known about the parameters which cause, propagate, and indirectly affect fatigue in concrete, they are incorporated in design guides around the world. Nevertheless, this ultimate limit state verification is not addressed equally by various design governing bodies. This report presents a baseline understanding of what the phenomenon of fatigue is, what causes it, and what loading or material conditions amplify or reduce the likelihood of fatigue failure. Four different design codes are exposed and their verification process has been examined, compared and evaluated both qualitatively and quantitatively. Using a wind turbine tower structure as case study, this report presents calculated results following the verification processes as instructed in the respective reference codes.

Structural reliability prediction of a steel bridge element using Dynamic Object Oriented Bayesian Network (DOOBN)

Different from conventional methods for structural reliability evaluation, such as, first/second-order reliability methods (FORM/SORM) or Monte Carlo simulation based on corresponding limit state functions, a novel approach based on dynamic objective oriented Bayesian network (DOOBN) for prediction of structural reliability of a steel bridge element has been proposed in this paper. The DOOBN approach can effectively model the deterioration processes of a steel bridge element and predict their structural reliability over time. This approach is also able to achieve Bayesian updating with observed information from measurements, monitoring and visual inspection. Moreover, the computational capacity embedded in the approach can be used to facilitate integrated management and maintenance optimization in a bridge system. A steel bridge girder is used to validate the proposed approach. The predicted results are compared with those evaluated by FORM method.

Integrated health prediction of bridge systems using dynamic object oriented Bayesian networks (DOOBNS)

The serviceability and safety of bridges are crucial to people’s daily lives and to the national economy. Every effort should be taken to make sure that bridges function safely and properly as any damage or fault during the service life can lead to transport paralysis, catastrophic loss of property or even casualties. Nonetheless, aggressive environmental conditions, ever-increasing and changing traffic loads and aging can all contribute to bridge deterioration. With often constrained budget, it is of significance to identify bridges and bridge elements that should be given higher priority for maintenance, rehabilitation or replacement, and to select optimal strategy. Bridge health prediction is an essential underpinning science to bridge maintenance optimization, since the effectiveness of optimal maintenance decision is largely dependent on the forecasting accuracy of bridge health performance. The current approaches for bridge health prediction can be categorised into two groups: condition ratings based and structural reliability based. A comprehensive literature review has revealed the following limitations of the current modelling approaches: (1) it is not evident in literature to date that any integrated approaches exist for modelling both serviceability and safety aspects so that both performance criteria can be evaluated coherently; (2) complex system modelling approaches have not been successfully applied to bridge deterioration modelling though a bridge is a complex system composed of many inter-related bridge elements; (3) multiple bridge deterioration factors, such as deterioration dependencies among different bridge elements, observed information, maintenance actions and environmental effects have not been considered jointly; (4) the existing approaches are lacking in Bayesian updating ability to incorporate a variety of event information; (5) the assumption of series and/or parallel relationship for bridge level reliability is always held in all structural reliability estimation of bridge systems. To address the deficiencies listed above, this research proposes three novel models based on the Dynamic Object Oriented Bayesian Networks (DOOBNs) approach. Model I aims to address bridge deterioration in serviceability using condition ratings as the health index. The bridge deterioration is represented in a hierarchical relationship, in accordance with the physical structure, so that the contribution of each bridge element to bridge deterioration can be tracked. A discrete-time Markov process is employed to model deterioration of bridge elements over time. In Model II, bridge deterioration in terms of safety is addressed. The structural reliability of bridge systems is estimated from bridge elements to the entire bridge. By means of conditional probability tables (CPTs), not only series-parallel relationship but also complex probabilistic relationship in bridge systems can be effectively modelled. The structural reliability of each bridge element is evaluated from its limit state functions, considering the probability distributions of resistance and applied load. Both Models I and II are designed in three steps: modelling consideration, DOOBN development and parameters estimation. Model III integrates Models I and II to address bridge health performance in both serviceability and safety aspects jointly. The modelling of bridge ratings is modified so that every basic modelling unit denotes one physical bridge element. According to the specific materials used, the integration of condition ratings and structural reliability is implemented through critical failure modes. Three case studies have been conducted to validate the proposed models, respectively. Carefully selected data and knowledge from bridge experts, the National Bridge Inventory (NBI) and existing literature were utilised for model validation. In addition, event information was generated using simulation to demonstrate the Bayesian updating ability of the proposed models. The prediction results of condition ratings and structural reliability were presented and interpreted for basic bridge elements and the whole bridge system. The results obtained from Model II were compared with the ones obtained from traditional structural reliability methods. Overall, the prediction results demonstrate the feasibility of the proposed modelling approach for bridge health prediction and underpin the assertion that the three models can be used separately or integrated and are more effective than the current bridge deterioration modelling approaches. The primary contribution of this work is to enhance the knowledge in the field of bridge health prediction, where more comprehensive health performance in both serviceability and safety aspects are addressed jointly. The proposed models, characterised by probabilistic representation of bridge deterioration in hierarchical ways, demonstrated the effectiveness and pledge of DOOBNs approach to bridge health management. Additionally, the proposed models have significant potential for bridge maintenance optimization. Working together with advanced monitoring and inspection techniques, and a comprehensive bridge inventory, the proposed models can be used by bridge practitioners to achieve increased serviceability and safety as well as maintenance cost effectiveness.

Técnicas de avaliação da confiabilidade em estruturas de concreto armado

Neste trabalho é dado ênfase à inclusão das incertezas na avaliação do comportamento estrutural, objetivando uma melhor representação das características do sistema e uma quantificação do significado destas incertezas no projeto. São feitas comparações entre as técnicas clássicas existentes de análise de confiabilidade, tais como FORM, Simulação Direta Monte Carlo (MC) e Simulação Monte Carlo com Amostragem por Importância Adaptativa (MCIS), e os métodos aproximados da Superfície de Resposta( RS) e de Redes Neurais Artificiais(ANN). Quando possível, as comparações são feitas salientando- se as vantagens e inconvenientes do uso de uma ou de outra técnica em problemas com complexidades crescentes. São analisadas desde formulações com funções de estado limite explícitas até formulações implícitas com variabilidade espacial de carregamento e propriedades dos materiais, incluindo campos estocásticos. É tratado, em especial, o problema da análise da confiabilidade de estruturas de concreto armado incluindo o efeito da variabilidade espacial de suas propriedades. Para tanto é proposto um modelo de elementos finitos para a representação do concreto armado que incorpora as principais características observadas neste material. Também foi desenvolvido um modelo para a geração de campos estocásticos multidimensionais não Gaussianos para as propriedades do material e que é independente da malha de elementos finitos, assim como implementadas técnicas para aceleração das avaliações estruturais presentes em qualquer das técnicas empregadas. Para o tratamento da confiabilidade através da técnica da Superfície de Resposta, o algoritmo desenvolvido por Rajashekhar et al(1993) foi implementado. Já para o tratamento através de Redes Neurais Artificias, foram desenvolvidos alguns códigos para a simulação de redes percéptron multicamada e redes com função de base radial e então implementados no algoritmo de avaliação de confiabilidade desenvolvido por Shao et al(1997). Em geral, observou-se que as técnicas de simulação tem desempenho bastante baixo em problemas mais complexos, sobressaindo-se a técnica de primeira ordem FORM e as técnicas aproximadas da Superfície de Resposta e de Redes Neurais Artificiais, embora com precisão prejudicada devido às aproximações presentes.

A linearization-based system reliability method with application to geotechnical analysis

Los análisis de fiabilidad representan una herramienta adecuada para contemplar las incertidumbres inherentes que existen en los parámetros geotécnicos. En esta Tesis Doctoral se desarrolla una metodología basada en una linealización sencilla, que emplea aproximaciones de primer o segundo orden, para evaluar eficientemente la fiabilidad del sistema en los problemas geotécnicos. En primer lugar, se emplean diferentes métodos para analizar la fiabilidad de dos aspectos propios del diseño de los túneles: la estabilidad del frente y el comportamiento del sostenimiento. Se aplican varias metodologías de fiabilidad — el Método de Fiabilidad de Primer Orden (FORM), el Método de Fiabilidad de Segundo Orden (SORM) y el Muestreo por Importancia (IS). Los resultados muestran que los tipos de distribución y las estructuras de correlación consideradas para todas las variables aleatorias tienen una influencia significativa en los resultados de fiabilidad, lo cual remarca la importancia de una adecuada caracterización de las incertidumbres geotécnicas en las aplicaciones prácticas. Los resultados también muestran que tanto el FORM como el SORM pueden emplearse para estimar la fiabilidad del sostenimiento de un túnel y que el SORM puede mejorar el FORM con un esfuerzo computacional adicional aceptable. Posteriormente, se desarrolla una metodología de linealización para evaluar la fiabilidad del sistema en los problemas geotécnicos. Esta metodología solamente necesita la información proporcionada por el FORM: el vector de índices de fiabilidad de las funciones de estado límite (LSFs) que componen el sistema y su matriz de correlación. Se analizan dos problemas geotécnicos comunes —la estabilidad de un talud en un suelo estratificado y un túnel circular excavado en roca— para demostrar la sencillez, precisión y eficiencia del procedimiento propuesto. Asimismo, se reflejan las ventajas de la metodología de linealización con respecto a las herramientas computacionales alternativas. Igualmente se muestra que, en el caso de que resulte necesario, se puede emplear el SORM —que aproxima la verdadera LSF mejor que el FORM— para calcular estimaciones más precisas de la fiabilidad del sistema. Finalmente, se presenta una nueva metodología que emplea Algoritmos Genéticos para identificar, de manera precisa, las superficies de deslizamiento representativas (RSSs) de taludes en suelos estratificados, las cuales se emplean posteriormente para estimar la fiabilidad del sistema, empleando la metodología de linealización propuesta. Se adoptan tres taludes en suelos estratificados característicos para demostrar la eficiencia, precisión y robustez del procedimiento propuesto y se discuten las ventajas del mismo con respecto a otros métodos alternativos. Los resultados muestran que la metodología propuesta da estimaciones de fiabilidad que mejoran los resultados previamente publicados, enfatizando la importancia de hallar buenas RSSs —y, especialmente, adecuadas (desde un punto de vista probabilístico) superficies de deslizamiento críticas que podrían ser no-circulares— para obtener estimaciones acertadas de la fiabilidad de taludes en suelos. Reliability analyses provide an adequate tool to consider the inherent uncertainties that exist in geotechnical parameters. This dissertation develops a simple linearization-based approach, that uses first or second order approximations, to efficiently evaluate the system reliability of geotechnical problems. First, reliability methods are employed to analyze the reliability of two tunnel design aspects: face stability and performance of support systems. Several reliability approaches —the first order reliability method (FORM), the second order reliability method (SORM), the response surface method (RSM) and importance sampling (IS)— are employed, with results showing that the assumed distribution types and correlation structures for all random variables have a significant effect on the reliability results. This emphasizes the importance of an adequate characterization of geotechnical uncertainties for practical applications. Results also show that both FORM and SORM can be used to estimate the reliability of tunnel-support systems; and that SORM can outperform FORM with an acceptable additional computational effort. A linearization approach is then developed to evaluate the system reliability of series geotechnical problems. The approach only needs information provided by FORM: the vector of reliability indices of the limit state functions (LSFs) composing the system, and their correlation matrix. Two common geotechnical problems —the stability of a slope in layered soil and a circular tunnel in rock— are employed to demonstrate the simplicity, accuracy and efficiency of the suggested procedure. Advantages of the linearization approach with respect to alternative computational tools are discussed. It is also found that, if necessary, SORM —that approximates the true LSF better than FORM— can be employed to compute better estimations of the system’s reliability. Finally, a new approach using Genetic Algorithms (GAs) is presented to identify the fully specified representative slip surfaces (RSSs) of layered soil slopes, and such RSSs are then employed to estimate the system reliability of slopes, using our proposed linearization approach. Three typical benchmark-slopes with layered soils are adopted to demonstrate the efficiency, accuracy and robustness of the suggested procedure, and advantages of the proposed method with respect to alternative methods are discussed. Results show that the proposed approach provides reliability estimates that improve previously published results, emphasizing the importance of finding good RSSs —and, especially, good (probabilistic) critical slip surfaces that might be non-circular— to obtain good estimations of the reliability of soil slope systems.

Ultimate flexural limit states analysis of prestressed concrete sleeper

Railway is one of the most important, reliable and widely used means of transportation, carrying freight, passengers, minerals, grains, etc. Thus, research on railway tracks is extremely important for the development of railway engineering and technologies. The safe operation of a railway track is based on the railway track structure that includes rails, fasteners, pads, sleepers, ballast, subballast and formation. Sleepers are very important components of the entire structure and may be made of timber, concrete, steel or synthetic materials. Concrete sleepers were first installed around the middle of last century and currently are installed in great numbers around the world. Consequently, the design of concrete sleepers has a direct impact on the safe operation of railways. The "permissible stress" method is currently most commonly used to design sleepers. However, the permissible stress principle does not consider the ultimate strength of materials, probabilities of actual loads, and the risks associated with failure, all of which could lead to the conclusion of cost-ineffectiveness and over design of current prestressed concrete sleepers. Recently the limit states design method, which appeared in the last century and has been already applied in the design of buildings, bridges, etc, is proposed as a better method for the design of prestressed concrete sleepers. The limit states design has significant advantages compared to the permissible stress design, such as the utilisation of the full strength of the member, and a rational analysis of the probabilities related to sleeper strength and applied loads. This research aims to apply the ultimate limit states design to the prestressed concrete sleeper, namely to obtain the load factors of both static and dynamic loads for the ultimate limit states design equations. However, the sleepers in rail tracks require different safety levels for different types of tracks, which mean the different types of tracks have different load factors of limit states design equations. Therefore, the core tasks of this research are to find the load factors of the static component and dynamic component of loads on track and the strength reduction factor of the sleeper bending strength for the ultimate limit states design equations for four main types of tracks, i.e., heavy haul, freight, medium speed passenger and high speed passenger tracks. To find those factors, the multiple samples of static loads, dynamic loads and their distributions are needed. In the four types of tracks, the heavy haul track has the measured data from Braeside Line (A heavy haul line in Central Queensland), and the distributions of both static and dynamic loads can be found from these data. The other three types of tracks have no measured data from sites and the experimental data are hardly available. In order to generate the data samples and obtain their distributions, the computer based simulations were employed and assumed the wheel-track impacts as induced by different sizes of wheel flats. A valid simulation package named DTrack was firstly employed to generate the dynamic loads for the freight and medium speed passenger tracks. However, DTrack is only valid for the tracks which carry low or medium speed vehicles. Therefore, a 3-D finite element (FE) model was then established for the wheel-track impact analysis of the high speed track. This FE model has been validated by comparing its simulation results with the DTrack simulation results, and with the results from traditional theoretical calculations based on the case of heavy haul track. Furthermore, the dynamic load data of the high speed track were obtained from the FE model and the distributions of both static and dynamic loads were extracted accordingly. All derived distributions of loads were fitted by appropriate functions. Through extrapolating those distributions, the important parameters of distributions for the static load induced sleeper bending moment and the extreme wheel-rail impact force induced sleeper dynamic bending moments and finally, the load factors, were obtained. Eventually, the load factors were obtained by the limit states design calibration based on reliability analyses with the derived distributions. After that, a sensitivity analysis was performed and the reliability of the achieved limit states design equations was confirmed. It has been found that the limit states design can be effectively applied to railway concrete sleepers. This research significantly contributes to railway engineering and the track safety area. It helps to decrease the failure and risks of track structure and accidents; better determines the load range for existing sleepers in track; better rates the strength of concrete sleepers to support bigger impact and loads on railway track; increases the reliability of the concrete sleepers and hugely saves investments on railway industries. Based on this research, many other bodies of research can be promoted in the future. Firstly, it has been found that the 3-D FE model is suitable for the study of track loadings and track structure vibrations. Secondly, the equations for serviceability and damageability limit states can be developed based on the concepts of limit states design equations of concrete sleepers obtained in this research, which are for the ultimate limit states.