Environmental contours for determination of seismic design response spectra

Abstract

This paper presents a procedure for using environmental contours and structural reliability design points for the purpose of deriving seismic design response spectra for use in structural engineering design checks. The proposed approach utilizes a vector-valued probabilistic seismic hazard analysis to characterize the multivariate distribution of spectral accelerations at multiple periods that may be seen at a given location, and a limit state function to predict failure of the considered system under a given level of shaking. A reliability assessment is then performed to identify the design point the response spectrum with the highest probability of causing structural failure. This is proposed as the spectrum for which engineering design checks can be performed to evaluate performance of a given structure. While the full structural reliability analysis would not be performed in any practical application, this analysis does provide three major insights into appropriate response spectra to use in engineering evaluations. First, when the structure’s limit state function is dependent on a spectral acceleration at a single period, this approach produces risk-targeted spectral accelerations consistent with those recently adopted in several building codes. Second, the design point spectrum can be approximated by a Conditional Mean Spectrum (conditioned at the spectral period most closely related to the structure’s failure). This motivates recent proposals to use the Conditional Mean Spectrum for engineering design checks. Third, the design point spectrum will vary depending upon the structural limit state of interest, meaning that multiple Conditional Mean Spectra will be needed in practical analysis cases where multiple engineering checks are performed (though this can be avoided, at the expense of conservatism, by using a uniform risk spectrum). With the above three observations, this work thus adds theoretical support for several recent advances in seismic hazard characterization. This paper develops a procedure for using environmental contours and structural reliability design points to formulate improved design spectra for use in assessing the performance of buildings under earthquakes. Most seismic building codes and design guidelines are based on implicit performance goals that structures should achieve. Despite the significant uncertainty in future ground motion occurrence, building codes commonly check a structure’s behavior under a single level of earthquake loading, quantified with a design spectrum. However, this explicit design check is often not defined with respect to the performance goals. The objective of this paper is to provide the link between the explicit design check and the implicit performance goals. Using structural reliability approaches, with environmental contours of spectral accelerations at multiple periods, a justification of the use of multiple conditional mean spectra (CMS) (Baker, 2011) for design checks is detailed. More specifically, it is shown that exceedance levels of particular engineering demand parameters (EDP) can be estimated with a small number of structural analyses based on the calibrated CMS. 1. DESCRIPTION OF THE PROBLEM For a structure located a given site, we intend to estimate the value ed p f , the level of EDP exceeded