Amplitude Effects on First-Mode Periods and Damping Ratios: A Data-Driven Study
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This study summarizes the findings of a systematic investigation into the amplitude dependency of first-mode periods and damping ratios using a large dataset of instrumented buildings. We analyze seismic responses from 63 buildings in California with four or more earthquake records between 1971 and 2024, applying system identification techniques to estimate the buildings’ dynamic properties across varying excitation levels. Additionally, we examine four buildings in Chile, which provide over 500 earthquake data points, offering a dense sampling of modal properties across a wide range of structural response amplitudes due to the country’s high seismicity. We use a time-domain prediction error method (PEM) and stochastic subspace identification (SSI-MOESP) to analyze seismic response data. For ambient vibrations, we employ the Frequency Domain Decomposition (FDD) method for mode shapes and periods, and the Random Decrement technique to estimate damping ratios. Amplitude is quantified using the peak roof drift ratio (PRDR). Regression analysis reveals that both periods and damping ratios increase with PRDR up to approximately 10-4. Beyond this threshold, these parameters tend to increase at a lower rate and stabilize at a PRDR value of approximately 10-3. Comparisons with ambient vibration data show that initial periods range 0.75 to 1.00 times those estimated at the PRDR threshold of 10-4, while damping ratios range from 0.30 to 0.80 times the corresponding values. The results of this study provide statistically significant, empirical evidence of amplitude-dependent first-mode modal properties, with implications for structural modeling, seismic assessment of existing structures, seismic response prediction, and performance-based earthquake engineering.