Empirical Relationships for Frequency Content Parameters of Earthquake Ground Motions

Abstract

The frequency content of an earthquake ground motion is important because it affects the dynamic response of earth and structural systems. Four scalar parameters that characterize the frequency content of strong ground motions are (1) the mean period (Tm), (2) the average spectral period (Tavg), (3) the smoothed spectral predominant period (To), and (4) the predominant spectral period (Tp). Tm and Tavg distinguish the low frequency content of ground motions, while To is affected most by the high frequency content. Tp does not adequately describe the frequency content of a strong ground motion and is not recommended. Empirical relationships are developed that predict three parameters (Tm, Tavg, and To) as a function of earthquake magnitude, site-to-source distance, site conditions, and rupture directivity. The relationships are developed from a large strong-motion database that includes recorded motions from the recent earthquakes in Turkey and Taiwan. The new relationships update those previously developed by the authors and others. The results indicate that three site classes, which distinguish between rock, shallow soil, and deep soil, provide a better prediction of the frequency content parameters and smaller standard error terms than conventional “rock” and “soil” site classes. Forward directivity significantly increases the frequency content parameters, particularly Tm and To, at distances less than 20 km. Each of the frequency content parameters can be predicted with reasonable accuracy, but Tm is the preferred because it best distinguishes the frequency content of strong ground motions.

Dimensional Response Analysis of Bilinear Systems Subjected to Non-pulselike Earthquake Ground Motions

“…It has been found that a stable value of T m can be obtained for a frequency interval, Δf, lower than 0.05 Hz in the fast Fourier transform calculation (Rathje et al 2004). The frequency interval of the fast Fourier transform is related to the time step, Δt, and the number of points, N, in a time series by Δf=1/(N·Δt).…”

“…Regarding the selection of a representative time scale, Rathje et al (2004) examined various frequency parameters of a large strong motion data set containing both pulse-like and non-pulse-like ground motions and concluded that a reasonable measure of the frequency content of earthquake ground motions is the mean period T m which is defined as…”

“…Such time and length scales are used to normalize the strength, yield displacement and the peak inelastic displacement of the bilinear system. The paper adopts the mean period of the discrete Fourier transform of the ground motion (Rathje et al 2004;Dimitrakopoulos et al 2008) as an appropriate time scale and examines two different length scales which result from the peak ground acceleration and the peak ground velocity. When the normalized peak inelastic displacement is presented as a function of the normalized strength and normalized yield displacement, the response becomes self similar and remarkable order emerges.…”

Sensitivity of site response analysis on the number of ground motion records and implications for PSHA

“…It is therefore expected that consideration of a parameter that describes the frequency content of the records should assist in the selection of records with significantly different characteristics. Although the predominant spectral period mentioned herein is not considered to be the most useful parameter, the existence of various other scalar parameters describing the frequency content of ground motions, such as the mean period T m and the average spectral period T avg (Rathje et al 2004), could prove particularly useful in selecting records covering a wide rock acceleration and frequency content range. Fig.…”

“…It should be noted that the rock response spectra of these three records have a predominant spectral period equal to 0.2s (not shown herein for brevity). Although the predominant period is not the most appropriate parameter for the characterisation of the frequency content of a ground motion (Rathje et al 2004), it does give an indication of a common characteristic among the three outlying records which result in the lowest amplification factors. This suggests that the predominant period could be used to improve the selection of records.…”