Implementations of Statistics, Probability, and Reliability in the Performance-Based Seismic Design of Structures

Abstract

It is well-known that the main objective of building codes is to guarantee life safety by preventing the collapse of structures in major earthquakes. However, there is a knowledge gap about controlling structural damage of buildings subjected to those dynamic demands. Without passing over what happened in other decades, by the end of the eighties and beginning of the nineties, several major earthquakes occurred around the world. Consequently, innumerable structural damages were suffered by buildings. In the aftermath of such events, a revolution in the critical thinking of structural engineers was materialized, providing the foundation of a possible shift in the basic objective of building codes. The change was oriented to control structural damage of buildings by evaluating several performance levels and achieving multiple performance objectives. As a result, the formal introduction of Performance-Based Seismic Design (PBSD) was documented in the literature. In this context, the main change proposed in the PBSD philosophy is to move from the deterministic design, based on a set of rules, to a design based on the performance of the structure subjected to seismic loading. To achieve this, the PBSD philosophy implements several methodologies based on statistics, probability, and reliability concepts. Thus, in this paper, the Author presents a technical review about several implementations of statistics and probability in the PBSD philosophy. The paper is organized as follows. First, the application of the most relevant approaches in statistics, probability, and reliability are covered in terms of meta- or surrogate-models, Bayesian approaches, improved Monte Carlo Simulation, efficient response surface method, direct differentiation methods, out-crossing approaches using importance sampling schemes, adaptive importance sampling techniques to extract multidimensional integrals, and other well-known methodologies. Then, the current challenges and future trends about the integration of the PBSD philosophy with those methods is presented. Finally, based on the current technical information reported in this paper, it is demonstrated that the use of statistics, probability, and reliability concepts in the PBSD philosophy is a step in the right direction towards the design of seismic resilient structures. Unfortunately, practical consensus between structural engineers must be achieved before the PBSD philosophy can be completely incorporated in building codes. In view of this, if PBSD is included in future buildings codes, it will be based most likely on statistics, probability, and reliability theories.