On the use of duration in random vibration theory (RVT) based ground motion prediction: a comparative study

The major challenge that remains with random vibration theory (RVT) based predictions of ground motion intensity measures (GMIMs) is the definition of the input ground motion duration. In literature it is reported that random vibration theory optimized duration (Drvto) (Bora et al. in Bull Seismol Soc Am 105(4):2192–2218, 2015, Earthquake Spectra 35(1):61–932019) can be a better measure of duration in situations when empirical models of FAS (Fourier Amplitude Spectrum) and duration are used in predicting response spectra but, such a measure of duration is often questioned for its physical significance. Moreover, no quantitative assessments are performed to analyze the performance of commonly used significant duration measures (D75, D95 and 2D80) in comparison to Drvto in the RVT framework. In this study, we perform a comparative study to evaluate the performance of D75,D95\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}_{75}, {D}_{95}$$\end{document} and 2D80\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2{D}_{80}$$\end{document} in generating PGA (Peak Ground Acceleration) and response spectra using the observed FAS of ground motion. This study also investigates the physical significance of Drvto\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}_{rvto}$$\end{document}. Our main analysis is performed on the recorded acceleration traces compiled from the NGA (Next Generation of Attenuation)-West2 database. The efficacy of different measures of ground motion durations is performed using residuals analysis. The duration measure D75 was found to be resulting in the least variation of residual spread in comparison to the other two duration measures. D95 and 2D80 were found to be longer measures of duration, resulting in smaller values of root mean square motion and, hence underprediction of ground motion. While D75 was found to be performing better in the case of real data, we observed that in the case of stochastic simulations, 2D80 performs better.Scaling of Drvto was found to be identical with that of D75 and 2D80 for real and simulated data, respectively.