Keywords: envelope function, random vibration theory, NGA database, nonstationary seismic model, seismic response spectra, stochastic simulation.

In this chapter, a method for developing stochastic response spectra and predicting the earthquake signal generated at a site on the basis of random vibration theory is proposed. The approach evaluates the maximum structural response, namely the response spectrum, without requiring the use of repeated time history analyses, but directly obtaining the peak response of a single degree of freedom system subject to a stochastic process which represents a given earthquake. For this purpose a nonstationary stochastic model for the ground motion is developed. This is defined by a deterministic temporal function and a set of parameters that describe, respectively, the evolution of the amplitude during an earthquake and the frequency content of the record. The value of the parameters of the envelope amplitude modulation function can be determined on the basis of the information contained in a subset of the PEER (Pacific Earthquake Engineering Research Center) NGA project strong-motion database of accelerograms. In this way, it is possible to formulate some relations between the stochastic model parameters and seismological parameters. The procedure consists of selecting a seismological scenario for the target site, simulation of strong ground-motions caused by the scenario earthquake and formulation of the probabilistic response spectra, namely the seismologically-based stochastic response spectra (SSRS). The proposed method is able to predict the amplitudes of the peaks of the response, which may be useful in assessing the potential for damage of an earthquake.

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