Defining equivalent stationary PSDF to account for nonstationarity of earthquake ground motion

This paper presents three approaches to defining the stationary power spectrum density function (PSDF) of strong ground acceleration, for prediction of structural response corresponding to the strong-motion stationary part of the input excitation. The first approach defines the PSDF in terms of the Fourier amplitude spectrum and a stationary duration of ground acceleration. The PSDF obtained by this approach predicts accurately the response of structures with low to intermediate natural periods. In the second approach, we introduce the concept of stationary duration of response, which is defined as a function of the natural period and damping ratio of the oscillator. Using this approach, it is possible to get accurate estimates of response amplitudes for the broad range of natural periods. However, it is not convenient in practical applications to deal with several stationary durations for a given input excitation. Further, to evaluate these durations it is necessary to specify both the Fourier and the response spectra of ground accelerations; whereas the common engineering practice is to specify the response spectrum only. Therefore, the third approach suggests the use of the response ‘spectrum compatible’ PSDF. The paper presents several improvements in the general methodology used for this purpose. The improvements mainly relate to using more accurate peak factors and to using the transient nature of response. The spectrum compatible PSDFs, as evaluated in the present study, provide realistic specification of strong ground motion for stochastic seismic response analyses of structures.