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Stochastic Modeling and Simulation of Ground Motions for Performance-Based Earthquake Engineering


A site-based fully-nonstationary stochastic model for strong earthquake ground motion is developed. The model employs filtering of a discretized whit-noise process. Nonstationarity is achieved by modulating the intensity and varying the filter properties in time. The formulation has the important advantage of separating the temporal and spectral nonstationary characteristics of the process, thereby allowing flexibility and ease in modeling and parameter estimation. The model is fitted to recorded ground motions by matching a set of statistical characteristics, including the mean-square intensity, the mean zero-level up-crossing rate, and a measure of the bandwidth, all expressed as functions of time. These characteristics represent the evolving intensity and time-varying frequency content of the ground motion. Post-processing by a second filter assures zero residual velocity and displacement, and improves the match to response spectral ordinates for long periods.

The proposed stochastic model is employed to develop a method for generating an ensemble of synthetic ground motion time-histories for specified earthquake and site characteristics. The stochastic model is fitted to a large number of recorded ground motions taken from the PEER NGA database. Strong ground motions recorded on firm ground with source-to-site distance of at least 10 km are selected. Fitting to recorded ground motions results in sample observations of the stochastic model parameters. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source-to-site distance and the site shear-wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate an ensemble of synthetic ground motions. The resulting synthetic accelerations as well as corresponding velocity and displacement time-histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions.

The method of ground motion simulation for specified earthquake and site characteristics is extended to simulate orthogonal horizontal ground motion components. Two stochastic processes are considered, each representing one component. Assuming statistical independence between the underlying white-noise processes, the two horizontal components are simulated on a set of orthogonal principal axes, along which the components are statistically uncorrelated. A database of principal component ground motion pairs is developed by rotating the as-recorded horizontal ground motion component pairs into their principal axes. The stochastic model is fitted to the recorded motions in the principal component database. Using the resulting sample observations for the model parameters, regression models are developed to empirically relate each model parameter to the earthquake and site characteristics. Correlations between parameters of the two ground motion components are empirically determined. Given earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters for the two horizontal ground motion components. Each set of these model parameter realizations along with two statistically independent white-noise processes are used in the stochastic model to generate an orthogonal pair of horizontal ground motion components along the principal axes. The simulated components, while being statistically independent, have overall characteristics, i.e., evolution of intensity and frequency content, that are similar to each other in the same way that the characteristics of a pair of real recorded ground motion components along their principal axes are similar. The simulated principal components may be rotated into any desired direction, such as the coordinate axes of a structure, through a simple orthogonal transformation.

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