Spectral Relative Motion of Two Structures due to Seismic Travel Waves

Abstract

This paper proposes a spectral difference method to estimate the maximum relative displacement between adjacent elastic structures subjected to seismic traveling waves. The method, based on random vibration theory, seeks the cross-correlation between the responses of adjacent structures subjected to differential earthquake excitation with time lag. The results of computer simulation with 15 earthquake records show a good agreement between the proposed spectral analysis and time-history analysis. The relations between the maximum relative displacement of adjacent structures and their vibration periods, damping, as well as the time lag of earthquake excitations are clarified using the closed form solution obtained. Time lag of the excitations among adjacent structures alters the correlation and phase of vibration of the adjacent structures. The cross-correlation coefficient explained herein captures this aspect. Its magnitude under nonzero time lag can be very different from that under zero time lag. In some instances, these coefficients can have different signs. This leads to a significant change in the peak relative displacement of adjacent structures. These are especially true when the structures are subjected to surface waves; they rest on soft soils where low wave velocities develop, and their supports are remotely located.