Seismic Reliability Analysis of Structures

In the vast field of structural engineering, earthquake-resistant design is the area where applying reliability concepts is not merely a refinement but a necessity. A knowledge of probability theory is a prerequisite for understanding terms such as mean return period, uniform risk spectrum, and many others that are common in design practice. Looking ahead, a clear trend in the new generation of standards is to set design objectives in terms of meeting a certain number of performance limit states, the fulfilment of which is quantified in probabilistic terms. A sound grounding in the theory of probability, stochastic processes and random vibrations, and in the methods used to assess the probability of exceeding specific response levels, is becoming a fundamental requirement for the correct application of the regulations. This book aims to provide the fundamental theoretical foundations and present the state of the art in methods for the probabilistic assessment of seismic performance.

The book comprises four main chapters and two appendices, the latter devoted respectively to a brief exposition of probability theory and stochastic processes. The appendices were selected primarily to fully support the material in the main body of the book, while maintaining the required rigour and completeness.

The first chapter provides a balanced overview of methods for solving time-invariant reliability problems, including the well-known first- and second-order methods (FORM, SORM), response surfaces, and simulations. This chapter also covers the fundamental concepts needed to address time-dependent (seismic) problems.

The second chapter describes models for representing seismic action in the context of a probabilistic assessment of seismic performance. These models include random processes, recorded accelerograms and synthetic accelerograms of a seismological nature. For each model, its relative merits and the most appropriate field of application are discussed.

The third chapter, entitled ‘Time-variant reliability problems’, is more theoretical, as it lays the foundations for time-dependence in more general terms and provides classical solutions from the theory of random vibrations and ‘out-crossing’ theories. These, in turn, serve as a springboard for the development of the latest advanced simulation methods, which represent the state of the art in research and are extremely powerful, even though their scope of applicability is not currently the most suitable for seismic problems. The chapter provides, for the first time, a systematic presentation of material not yet systematically compiled in the specialist literature.

The fourth and final chapter contains what might be regarded as the book’s core, since, building on the material presented in the preceding chapters, it enables the reader to reach the stage where the methods that are actually applicable can be presented and their approximations understood. The methods include proposals that have already been adopted and are widely used in both cutting-edge practice and regulatory documents, as well as more recently developed tools that are equally simple and efficient. Each method is presented and discussed in detail through numerous applications.

In earthquake engineering, no other texts match this level of subject matter and comprehensiveness. The book is recommended for students in postgraduate courses in seismic reliability, researchers in earthquake engineering, and professionals seeking to deepen their knowledge and enhance their professional standards.