An Inverse-Reliability Approach to Generating Composite Seismic Response Spectra

Abstract

This study presents an Inverse-First Order Reliability Method (FORM) approach to generating site-specific composite seismic response spectra. The proposed technique searches the surfaces of Inverse-FORM generated contours for the earthquake statistically most likely to produce the target spectral acceleration at the desired structural period, as modelled by the appropriate attenuation relation. Identification of this spectral acceleration level over a range of periods produces a composite design response spectrum consisting of spectral acceleration levels most likely to occur and all lying on the surface of the n-year contour, hence possessing the desired n-year return period. This composite seismic response spectrum can be used in design and analysis of structural systems having variable levels of complexity. The result is an n-year composite, seismic design response spectrum, found using Inverse-FORM generated contours that are generated in a discrete four-dimensional space. The random variables associated with this four-dimensional space are earthquake magnitude, site-to-source distance, attenuation relation uncertainty, and fault of origin. This study outlines the technique and presents a hypothetical example for a region threatened by three behaviour ally different earthquake source mechanisms. An illustrative example is presented for target spectral accelerations of O.lg and 0.4g, having two different return periods. The number of different earthquakes contributing to each spectrum varied between three and nine, depending on the specifics.