Performance Based Earthquake Engineering With The First Order Reliability Method

Performance-based earthquake engineering is an emerging field of study that complements the prescriptive methods that the design codes provide to ensure adequate seismic performance of structures. Accounting for uncertainties in the performance assessments forms an important component in this area. In this context, the present study focuses on two broad themes; first, treatment of uncertainties and the application of the first-order reliability method (FORM) in finite-element reliability analysis, and second, the seismic risk assessment of reinforced concrete structures for performance states such as, collapse and monetary loss. In the first area, the uncertainties arising from inherent randomness ("aleatory uncertainty") and due to the lack of knowledge ("epistemic uncertainty") are identified. A framework for the separation of these uncertainties is proposed. Following this, the applicability of FORM to the linear and nonlinear finite-element structural models under static and dynamic loading is investigated. The case studies indicate that FORM is applicable for linear and nonlinear static problems. Strategies are proposed to circumvent and remedy potential challenges to FORM. In the case of dynamic problems, the application of FORM is studied with an emphasis on cumulative response measures. The limit-state surface is shown to have a closed and nonlinear geometric shape. Solution methods are proposed to obtain probability bounds based on the FORM results. In the application-oriented second area of research, at first, the probability of collapse of a reinforced concrete frame is assessed with nonlinear static analysis. By modelling the post-failure behaviour of individual structural members, the global response of the structure is estimated beyond the component failures. The final application is the probabilistic assessment of monetary loss for a high-rise shear wall building due to the seismic hazard in the Cascadia subduction zone. A 3-dimensional finite-element.

In the last ten to fifteen years a vast amount of research has been undertaken to improve on earlier methods for analysing the seismic reliability of structures. These efforts focused on identifying aspects of prominent relevance and disregarding the inessential ones, with the goal of producing methods that are both more efficient and easier to use in practice. Today this goal can be said to be substantially achieved. During these years scientific activity covered all of the many aspects involved in such a multi-disciplinary problem, ranging from seismology, to geotechnics, to structural analysis and economy, all of them to be consistently organised into a probabilistic framework. As the output of this research was dispersed into a multitude of technical papers, fib Commission 7 thought it worthwhile to select the essential aspects of this large body of knowledge and to present them into a coherent and accessible document for structural engineers. To this end a task group of specialists was formed, whose qualifications come from their personal involvement in the above-mentioned developments throughout this period of time. From its inception the group decided that the bulletin should have had a distinct educational character and provide a clear overview of the methods available. The outcome is a compact volume that starts by introducing the concepts and definitions of performance-based engineering, continues with two chapters on assessment and design, respectively, presenting the methods in detail accompanied by illustrative examples, and concludes with an appendix with sample programming excerpts for their implementation. It is believed that at present fib Bulletin 68 represents a unique compendium on probabilistic performance-based seismic design.

This multi-contributor book provides comprehensive coverage of earthquake engineering problems, an overview of traditional methods, and the scientific background on recent developments. It discusses computer methods on structural analysis and provides access to the recent design methodologies and serves as a reference for both professionals and res

Performance-based earthquake engineering (PBEE) has emerged as a powerful method of analysis and design philosophy in earthquake engineering and is leading the way to a new generation of seismic design guidelines. PBEE requires a comprehensive understanding of the earthquake response of Soil-Foundation-Structure-Interaction (SFSI) systems when damage occurs in the structural system during the earthquake. In the context of PBEE, this research combines finite element (FE) modeling and seismic response analysis of SFSI systems with state-of-the-art methods in response sensitivity and reliability analysis. New analytical and numerical methods are developed and existing algorithms adopted for studying the propagation of uncertainties in nonlinear static and dynamic analyses of SFSI systems and for probabilistic performance assessment of these systems. This research makes several contributions to reliability analysis of structural and SFSI systems. For the purpose of accurately and efficiently computing the response gradients, an 'exact' FE response sensitivity computation algorithm based on the Direct Differentiation Method (DDM) and available in the widely used FE analysis software framework OpenSees is further extended to various types of material models, finite elements and multi-point constraint equations used in modeling large-scale realistic SFSI systems. As a main contribution to this research, this sensitivity algorithm is extended to a multi-yield surface J2 plasticity model used extensively to model clay soil materials in seismic response analysis. Related to response sensitivity analysis of SFSI systems, several issues are studied, such as discontinuities in response sensitivities, the relative importance of various soil and structural material parameters in regards to a specified aspect of the system response (i.e., response parameters). As contributions to the reliability analysis of structural and SFSI systems, several existing solution tools such as first-order reliability method (FORM), second-order reliability method (SORM), and various sampling techniques, such as importance sampling (IS) and orthogonal plane sampling (OPS), are implemented in OpenSees and/or further improved to solving reliability analysis problems of structural and SFSI systems. A powerful general-purpose optimization toolbox SNOPT, developed by Professor Philip Gill at UCSD, is integrated into the reliability analysis framework in OpenSees and customized for efficiently finding the design point(s) of structural and SFSI systems. For time variant reliability analysis, an existing mean upcrossing rate analysis algorithm is implemented in OpenSees and improved. It is found that the FORM approximation for mean upcrossing rate is significantly inaccurate, especially in cases of highly nonlinear response behavior of the system analyzed. In such case, the OPS method based on the design point(s) of the reliability problem significantly improves the FORM approximation of the mean upcrossing rate and therefore of the upper bound of the failure probability. In order to study the topology of limit-state surfaces (LSS) for reliability problems, a new visualization method called Multi-dimensional Visualization in Principal Plane (MVPP) is developed and implemented in OpenSees. The geometrical insight gained from the MVPP has led to the development of a new hybrid computational reliability method, called the DP-RS-Sim method, which combines the design point (DP) search, the response surface methodology (RS), and simulation techniques (Sim). This method is applied for the time invariant reliability analysis of a realistic nonlinear structural system. Several other closely related topics are studied. A simplified probabilistic response analysis method is developed taking advantage of DDM-based response sensitivity analysis. This method is then applied to a nonlinear structural and SFSI system. It is much more efficient than the crude Monte Carlo Simulation method and provides, at low computational cost, good estimates of the mean and standard deviation of the response for low to moderate level of material nonlinearity in the response. A general-purpose OpenSees-SNOPT based optimization framework was developed and applied to soil model updating problems using numerically simulated data. It is found that the optimization process is significantly more efficient when using the DDM-based over the FDM-based sensitivities. Additionally, nonlinear FE model updating is performed for an actual site, the Lotung downhole array in Taiwan, and based on data recorded during a 1986 earthquake.

The work in this report is motivated by the performance-based engineering approach advocated by PEER. A comprehensive, object-oriented software framework for finite element sensitivity and reliability analysis is developed. The work builds on the existing software OpenSees. The software framework is used to investigate and address challenges particular to nonlinear finite element reliability analysis. As a result, smoothed material models, modifications in existing search algorithms, and a search algorithm hitherto not used in reliability analysis are developed.

This book addresses probabilistic methods for the evaluation of structural reliability, including the theoretical basis of these methods. Partial safety factor codes under current practice are briefly introduced and discussed. A probabilistic code format for obtaining a formal reliability evaluation system that catches the most essential features of the nature of the uncertainties and their interplay is then gradually developed. The concepts presented are illustrated by numerous examples throughout the text. The modular approach of the book allows the reader to navigate through the different stages of the methods.

Large-scale earthquake hazards pose major threats to modern society, generating casualties, disrupting socioeconomic activities, and causing enormous economic loss across the world. Events, such as the 2004 Indian Ocean tsunami and the 2011 Tohoku earthquake, highlighted the vulnerability of urban cities to catastrophic earthquakes. Accurate assessment of earthquake-related hazards (both primary and secondary) is essential to mitigate and control disaster risk exposure effectively. To date, various approaches and tools have been developed in different disciplines. However, they are fragmented over a number of research disciplines and underlying assumptions are often inconsistent. Our society and infrastructure are subjected to multiple types of cascading earthquake hazards; therefore, integrated hazard assessment and risk management strategy is needed for mitigating potential consequences due to multi-hazards. Moreover, uncertainty modeling and its impact on hazard prediction and anticipated consequences are essential parts of probabilistic earthquake hazard and risk assessment. The Research Topic is focused upon modeling and impact assessment of cascading earthquake hazards, including mainshock ground shaking, aftershock, tsunami, liquefaction, and landslide.

Throughout the past few years, there has been extensive research done on structural design in terms of optimization methods or problem formulation. But, much of this attention has been on the linear elastic structural behavior, under static loading condition. Such a focus has left researchers scratching their heads as it has led to vulnerable structural configurations. What researchers have left out of the equation is the element of seismic loading. It is essential for researchers to take this into account in order to develop earthquake resistant real-world structures. Structural Seismic Design Optimization and Earthquake Engineering: Formulations and Applications focuses on the research around earthquake engineering, in particular, the field of implementation of optimization algorithms in earthquake engineering problems. Topics discussed within this book include, but are not limited to, simulation issues for the accurate prediction of the seismic response of structures, design optimization procedures, soft computing applications, and other important advancements in seismic analysis and design where optimization algorithms can be implemented. Readers will discover that this book provides relevant theoretical frameworks in order to enhance their learning on earthquake engineering as it deals with the latest research findings and their practical implementations, as well as new formulations and solutions.

This volume is an outcome of the 11th IFIP WG7.5 working conference on Reliability and Optimization of Structural Systems in Canada. The conference focuses on structural reliability methods and applications and engineering risk analysis and decision-making.

This book provides a new framework for analysis of slope nonlinear stochastic seismic dynamic response based on the new theoretical tool of stochastic dynamics. The coupling effects of uncertainty of geological parameters, strong dynamic nonlinearity, and randomness of ground motion are considered in the process of the seismic dynamic stability assessment of slope. In this book, an intensity frequency non-stationary stochastic ground motion model based on time-domain stochastic process description is preliminarily established to characterize the randomness of earthquakes. The spatial distribution random field model of geotechnical parameters is established to describe the time-space variability of geotechnical parameters. Based on the basic theory of stochastic dynamics, the seismic stability performance evaluation method of slope is established. The slope seismic dynamic model test based on large complex shaking table is performed to verify and modify the proposed framework and method. This book sheds new light on the development of nonlinear seismic stochastic dynamics and seismic design of slope engineering.