Earthquake response spectra models incorporating fuzzy logic with statistics

It is well accepted that the ground motion at a site depends on the rupture mechanism, source-to-site distance, local geologic conditions, and energy released by the earthquake. However, design spectra represent expected responses that do not explicitly include the influence of the uncertainties associated with these fundamental features. The objective of this article is to present a viable methodology that can be used to develop a response spectra using fuzzy logic and statistical analysis and to demonstrate how fuzzy-statistical response spectra can be used to evaluate potential structural response. Site-specific response spectra from the Northridge earthquake are used to develop response spectra models that quantify uncertainties inherent to the ground motion. The uncertainty in these computational models is quantified using fuzzy-set logic, statistics, and random vibrations. The local geologic conditions are characterized as rock or alluvium, and fuzzy sets are used to represent near, intermediate, and far epicentral distances. Proposed ground-motion models are used to define uncertain input motion for use in dynamic analyses of an example building. The resulting structural responses are compared with those obtained from time-dependent accelerations. Comparisons are made with the current design codes, and suggested implementation strategies for the proposed models are discussed.