Synthesis of Non-Stationary Seismic Waves Based on Phase Difference Spectrum and Its Application

A synthetic method of multi-dimensional and multi-point non-stationary seismic waves (MMNSWs) based on phase difference spectrum is proposed to simulate the non-stationarity and multi-dimensionality of real ground motions in hope to overcome the deficiencies of the traditional trigonometric series method, such as the arbitrariness in selection of the envelope function and loss of non-stationarity feature in frequency domain. First, the traveling wave effect, coherence effect, local site effect and multi-dimensional property of ground motions are modelled using the random field theory. Then, the phase difference spectrum is determined and used to characterize the non-stationarity of intensity and frequency of ground motions. Finally, the synthetic non-stationary ground motions are applied to an actual bridge for seismic analysis, and the generated dynamic responses are compared with the equivalent response spectrum obtained by response spectrum method. Results show that the MMNSWs generated based on phase difference spectrum does not need the envelope function to control the waveform of seismic waves, and hence can exclude the arbitrariness of artificial selection of the intensity envelope function. Since it has taken into account the relevance and multidimensionality of seismic ground motions, the proposed method is better than the traditional trigonometric series method for synthesis of ground motions. In addition, the results generated by the proposed method are basically consistent with those by the traditional response spectrum method. The difference between the values of shear force and bending moment at two pier bottoms, calculated by the response spectrum method, is in the range of 10% and 17%, respectively, while the difference is less than 9% and 12%, respectively, by the proposed method.