Conditional Spectrum Computation Incorporating Multiple Causal Earthquakes and Ground-Motion Prediction Models

Abstract

The Conditional Spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions as well as the epistemic uncertainties in ground motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western U.S. (WUS). The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the U.S. using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

Seismic hazard disaggregation in performance‐based earthquake engineering: occurrence or exceedance?

“…This disaggregation usually breaks the total hazard level down into contributions in terms of magnitude, distance and epsilon, with epsilon being the number of standard deviations between a given spectral acceleration (or other intensity measure) and the mean value predicted by a ground-motion prediction equation (GMPE). However, disaggregation can also be carried out for other parameters, such as faulting style or even in terms of GMPEs in the case that more than one is used in the PSHA [3]. The annual rate of occurrence of ground motions in the range x L <Sa<x U , given that these motions arise from events in a particular magnitude, distance and epsilon bin can be determined from Equation (1):…”

“…The issue of exceedance or occurrence disaggregation has been briefly discussed by a number of researchers [3,12,13,14]; however, there does not appear to have been any detailed examination of the effects of disaggregation choices on spectral demands. Furthermore, it is noted that a large number of articles do not provide details of the disaggregation nor do they explicitly state whether exceedance or occurrence disaggregation is used.…”

“…Calculations are carried out using the MATLAB [17] code provided by Jayaram et al [2]; however, this has been modified to account for all causal earthquakes (magnitude and distance pairs) rather than just a single mean or modal event. The consideration of all causal earthquakes is carried out as per Lin et al [3]. All parameters are set to be consistent with the PSHA, including the use of the Campbell and Bozorgnia-2008 GMPE [16].…”

“…magnitude and distance combinations) have contributed most significantly to the design ground motion level so that these scenarios can inform record selection. In a more sophisticated and PBEE focused case, disaggregation is used as tool required for the calculation of conditional spectra [1,2,3], which in turn are used as a target for ground-motion selection. Due to an increasing interest in conditional spectra they are used in this work as a proxy for evaluating the impact that different approaches to disaggregation might have on ground-motion selection and seismic performance assessment.…”

Record-to-Record Variability in the Seismic Response of Rc Walls Buildings Subjected to Ground Motions Matched to the Conditional Spectrum

“…A set of 40 ground motions (Set 1), selected to match the conditional spectrum [11,12,13] is used in the analyses. For the final case, a second set of 40 ground motions (Set 2), selected assuming different site characteristics, is used.…”