Evaluation of Earthquake Response Spectra Directionality Using Stochastic Simulations

Abstract

For earthquake-resistant design purposes, ground-motion intensity is usually characterized using response spectra. The amplitude of response spectral ordinates of horizontal components varies significantly with changes in orientation. This change in intensity with orientation is commonly known as ground-motion directionality. Although this directionality has been attributed to several factors, such as topographic irregularities, near-fault effects, and local geologic heterogeneities, the mechanism behind this phenomenon is still not well understood. This work studies the directionality characteristics of earthquake ground-motion intensity using synthetic ground motions and compares their directionality to that of recorded ground motions. The two principal components of horizontal acceleration are sampled independently using a stochastic model based on finite-duration time-modulated filtered Gaussian white-noise processes. By using the same stochastic process to sample both horizontal components of motion, the variance of horizontal ground acceleration has negligible orientation dependence. However, these simulations’ response spectral ordinates present directionality levels comparable to those found in real ground motions. It is shown that the directionality of the simulated ground motions changes for each realization of the stochastic process and is a consequence of the duration being finite. Simulated ground motions also present similar directionality trends to recorded earthquake ground motions, such as the increase of average directionality with increasing period of vibration and decrease with increasing significant duration. These results suggest that most of the orientation dependence of horizontal response spectra is primarily explained by the finite significant duration of earthquake ground motion causing inherent randomness in response spectra, rather than by some physical mechanism causing polarization of shaking.

Probabilistic characterization of the directionality of horizontal earthquake response spectra

“…A relevant special case of the correlations of Equation ( 6) is when angles 𝜙 and 𝜓 are separated by 90 • (i.e., the orientations are orthogonal to each other), which is usually the case for the principal axes of buildings and many other types of F I G U R E 6 Correlations of (A) ln 𝜂 and (B) ln 𝜈 between two orthogonal horizontal orientations. Solid lines represent empirical data and dashed lines in (B) represent estimates obtained with the regression model using Equation (7) structures. These correlations are shown in Figure 6 for different periods, which shows that both are relatively constant throughout the range of 𝜙.…”

“…[4] Although using measures of central tendency such as RotD50 or the geometric mean of the spectral ordinates of the two as-recorded horizontal components may be adequate for earthquake-resistant design purposes if the ground motion directionality is small, its use becomes questionable if the directionality is large. [5,6] For example, in 1-s oscillators, the intensity in the orientation of maximum response is, on average, approximately 55% larger than the one occurring in the perpendicular direction, [7] therefore ground motion directionality is not small and requires more attention than the one that has been given in the past.…”

Directionality and polarization of response spectral ordinates in the 2023 Kahramanmaras, Türkiye earthquake doublet

“…This finding is significant since it means that the probability distribution of the orientation of maximum intensity is not uniform as previously thought and that it can be estimated from the geographic location of the site relative to the location of the epicenter. Poulos and Miranda's (2023) motivation for examining the orientation of maximum response with respect to the transverse orientation was that S waves from theoretical double couple point sources in a homogeneous medium exhibit polarization transverse to the direction of propagation. In their study, they used the epicenter as the location of the point source.…”

“…The orientation of maximum intensity for 5%-damped linear elastic oscillators subjected to the ground motions, as well as their spatial distribution, is investigated. The work of Poulos and Miranda (2023) is extended by investigating the orientation of maximum response with respect to the transverse orientation of a line segment connecting a station and the surface projection of the point of maximum slip. That is, the point of maximum slip is treated as the point source for radiation patterns, and its ability to predict the orientation of maximum intensity for the Tu¨rkiye doublet is investigated.…”

An algorithm for spectrally matching bi-directional ground motions to a target RotD100 spectrum while maintaining the radial spectral acceleration pattern

“…RotD100) are substantially larger than the median intensity (i.e. RotD50 or GMRotI50; Huang et al, 2008; Poulos et al, 2022; Poulos and Miranda, 2022a), the values of the seismic design parameters of many codes are all defined in terms of RotD100 in the horizontal plane (e.g. ASCE/SEI 7-16, 2016; Federal Emergency Management Agency (FEMA) P-2082-1, 2020; International Building Code (IBC), 2018).…”