Wavelet-based characterization of design ground motions

Sushovan Mukherjee, Vinay K. Gupta ^*

Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, India

Keywords

stochastic analysis; seismic hazard characterization; spectrum-compatible wavelet functionals; non-stationarity simulation; elasto-plastic oscillator; strength reduction factor

Abstract

With the recent emergence of wavelet-based procedures for stochastic analyses of linear and non-linear structural systems subjected to earthquake ground motions, it has become necessary that seismic ground motion processes are characterized through statistical functionals of wavelet coefficients. While direct characterization in terms of earthquake and site parameters may have to wait for a few more years due to the complexity of the problem, this study attempts such characterization through commonly available Fourier and response spectra for design earthquake motions. Two approaches have been proposed for obtaining the spectrum-compatible wavelet functionals, one for input Fourier spectrum and another for input response spectrum, such that the total number of input data points are 30-35% of those required for a time-history analysis. The proposed methods provide for simulating desired non-stationary characteristics consistent with those in a recorded accelerogram. Numerical studies have been performed to illustrate the proposed approaches. Further, the wavelet functionals compatible with a USNRC spectrum in the case of 35 recorded motions of similar strong motion durations have been used to obtain the strength reduction factor spectra for elasto-plastic oscillators and to show that about ±20% variation may be assumed from mean to 5 and 95% confidence levels due to uncertainty in the non-stationary characteristics of the ground motion process.