In performance-based earthquake engineering, a large number of ground-motion time histories are needed for analyzing the distribution of dynamic response of nonlinear systems. However, actual recorded ground motions are often limited. Especially, recorded motions at design levels are very rare, and may not be sufficient for characterizing structural responses. As an alternative approach, ground motions can be simulated using stochastic methods. One of such examples is a recent work by Yamamoto and Baker (2013), who use wavelet packet transform to model complex time-varying earthquake ground motions. The wavelet-packet based model demonstrates great promise in a variety of earthquake engineering applications.

This dissertation further develops the wavelet-packet based model t...[ Read more ]

In performance-based earthquake engineering, a large number of ground-motion time histories are needed for analyzing the distribution of dynamic response of nonlinear systems. However, actual recorded ground motions are often limited. Especially, recorded motions at design levels are very rare, and may not be sufficient for characterizing structural responses. As an alternative approach, ground motions can be simulated using stochastic methods. One of such examples is a recent work by Yamamoto and Baker (2013), who use wavelet packet transform to model complex time-varying earthquake ground motions. The wavelet-packet based model demonstrates great promise in a variety of earthquake engineering applications.

This dissertation further develops the wavelet-packet based model to generate spatially distributed ground-motion time histories, which can preserve the natural variability and spatial correlation of ground-motion waveforms. The ground-motion spatial correlation is particularly important for analysing spatially distributed structures, as well as hazard analysis and loss estimation in a regional scale. Based on the wavelet-packet characterization, spatial cross-correlations of wavelet-packet parameters are determined through geostatistical analysis of regionalized ground-motion data from California, Japan, Mexico and Taiwan. The geostatistical analysis of ground-motion data from different regions reveals significant dependence of the correlation structure on regional site conditions, which leads to the development of a region-specific correlation model parameterized by the correlation range of V_s30 in each region. In general, the spatial cross-correlations of wavelet-packet parameters are stronger if the correlation range of V_s30 in that region is greater. The present model can be used to stochastically simulate spatially correlated ground-motion waveforms on a regional scale for future earthquakes. The model can also be used to conditionally simulate time histories of historical earthquakes at unmeasured sites. Using the developed spatial cross-correlation model, ground-motion time histories can be synthesized at unmeasured locations through cokriging estimation of wavelet-packet parameters in the neighborhood. As part of this study, case studies are conducted using the Northridge and Chi-Chi earthquake data. The model capability is verified in blind tests by comparing simulated time histories with the actual recorded data.

The second part of this dissertation develops a wavelet-packet based ground-motion simulation and modification technique to generate energy-compatible and spectrum-compatible (ECSC) synthetic motions. The ECSC method significantly advances traditional ground motion modification approaches, because it generates time series that not only match target spectral accelerations, but also match other important ground motion features not considered in traditional approaches, such as the total energy and its temporal accumulation, as well as ground-motion duration. One-to-one comparison between the ECSC simulated motions and actual recorded motions demonstrates great similarity in a variety of ground motion intensity measures, including acceleration, velocity, displacement time histories, energy content, frequency content and duration. The performance of the ECSC motions is also systematically validated using simple elasto-plastic hysteretic systems, Newmark displacement and sliding mass models. These extensive numerical simulations demonstrate that the ECSC ground motions can accurately predict nonlinear response of these systems. The method has great potential to be used in time history analyses of nonlinear systems in performance-based earthquake engineering design.