A seismologically consistent husid envelope function for the stochastic simulation of earthquake ground-motions

Earthquake-induced ground-motion may be realistically described as random processes that are intrinsically non-stationary in both amplitude and frequency content. In order to take into account the finite duration and the amplitude non-stationarity of earthquake-induced ground-motions, it is common practice to modulate a stationary stochastic process with a shaping window, or envelope function, in order to obtain a transient signal. Different shapes have been proposed in literature for such windows but the main problem until now has been how to correlate the parameters of the shaping window to the characteristics of some seismic design scenario (such as magnitude, distance, and site conditions). In this work, an envelope function is proposed that makes use of parameters that are commonly available in seismic design situations involving a scenario-type analysis. Such a scenario may be deterministically prescribed, or may be the result of a probabilistic seismic hazard analysis. The envelope function is also directly related to the Arias intensity of the ground motion and has a functional form closely related to that of a lognormal probability density function. The envelope function may be used, in conjunction with suitable peak factors, to predict the distribution of peak ground acceleration values corresponding to a given earthquake scenario.