Abstract:
Rotational ground motion is an important factor affecting structural torsional response, rocking response, and earthquake-induced damage. Previous studies indicate that three translational components alone cannot fully describe seismic wavefield motion and its engineering effects. Rotational components provide supplementary information for ground-motion characterization, structural response analysis, and seismic performance assessment. However, because rotational observation instruments and available observational data have long been limited, existing ground motion studies have mainly focused on the three translational components, and the characteristics of rotational ground-motion records remain relatively less understood. In recent years, advances in collocated translational-rotational observation techniques have made it possible to obtain six-component ground-motion records and have provided an observational basis for investigating the characteristics of rotational ground motion using measured data. Accordingly, this study uses collocated translational-rotational observations to analyze the characteristics of rotational ground motion in terms of record quality, peak parameters, response spectral features, and empirical prediction models.
A six-component ground motion dataset was compiled from the Garner Valley Downhole Array (GVDA) in southern California, USA, and the ACAN/ROAN stations on Kefalonia Island, Greece. The dataset contains 349 records: 130 from the GVDA array, with local magnitudes of ML3.0−7.2, a maximum source-to-site distance of about 207 km, and a site vS30 of about 280 m/s; and 219 from the ACAN/ROAN stations, with local magnitudes of ML1.9−5.0, a maximum source-to-site distance of about 59 km, and a site vS30 of about 250 m/s. Each record includes three translational acceleration components and three rotational angular velocity components.
A consistent preprocessing and quality-control procedure was applied. Signal and noise windows were defined, and their Fourier amplitude spectra were calculated. The signal-to-noise ratio (SNR) was obtained from the spectral ratio between signal and noise. The frequency band satisfying SNR>3 was defined as the usable bandwidth, from which the filter cutoff frequencies were determined. The SNR analysis indicates that rotational records have a significantly narrower usable bandwidth than translational records and exhibit lower SNRs in the low-frequency range. The high-pass cutoff frequency fHP of translational records decreases with increasing magnitude, whereas the fHP values of rotational records are higher and show no clear magnitude dependence. This suggests that increasing magnitude has a limited effect on improving the low-frequency SNR of rotational components, mainly because rotational motions have smaller amplitudes and are more strongly affected by instrumental and environmental noise.
Peak rotational velocity (PRV) and peak ground acceleration (PGA) were selected as representative intensity measures of rotational and translational ground motions, respectively. This choice is supported by the fact that rotational angular velocity is related to the spatial variation of the translational wavefield and can be theoretically linked to translational acceleration under simplified wave-propagation conditions. The statistical correlation between PRV and PGA was then analyzed in logarithmic coordinates. Regression analysis shows a clear linear correlation between PRV and PGA in both datasets, indicating a relatively stable statistical relationship between rotational and translational peak parameters.
The response spectral characteristics of rotational ground motion were examined using a rotational single-degree-of-freedom system. The 5%-damped rotational angular acceleration response spectra were computed and compared with translational acceleration response spectra. The two types of spectra differ in both peak period and spectral shape. In the EW and NS directions, the median peak period of the rotational spectra is about 0.05 s, shorter than that of the translational spectra, about 0.08−0.09 s. This indicates that horizontal rotational response is mainly controlled by short-period components. In contrast, the dominant periods of the UD translational component and the rotational component about the vertical axis are relatively close. Typical records also show that the rotational response spectra have narrower plateau regions, with peak responses concentrated in the short-period range. For translational spectra, the UD component is generally weaker than the horizontal components, whereas the three rotational components have more comparable spectral amplitudes.
An empirical prediction model for PRV was developed with reference to conventional ground-motion prediction equations. Local magnitude ML and source-to-site distance R were used as the main explanatory variables. Because the rotational records were obtained from only two stations with similar site conditions, no separate site term was introduced. Regression analyses for PRVz, PRVH(t), and PRVall(t) show that the models generally describe the dependence of PRV on magnitude and distance, with R2 values greater than 0.6. The predicted PRV values decrease with increasing distance, indicating a distance-attenuation trend. However, because of the limited sample size, restricted magnitude-distance distribution, and small number of stations, relatively large scatter remains in the rotational peak parameters, and the empirical prediction of rotational ground motion is still subject to uncertainty.
In summary, based on the six-component records from the GVDA array and the ACAN/ROAN stations, this study analyzed the record quality, peak parameters, and response spectral characteristics of translational and rotational ground motions, as well as empirical prediction models for peak rotational velocity. Because no site term is included, their applicability is mainly limited to site conditions and magnitude-distance ranges similar to those covered by the present dataset. Future studies should include more six-component records and further consider site, path, and near-fault effects. The results provide a reference for rotational ground-motion processing, seismic input determination, and seismic performance assessment of structures when rotational effects are considered.