Free vibration of soils during large earthquakes

Free vibration of soils happens frequently during some large earthquakes, perhaps seeming like a paradox. This happens because the energy released from seismic sources in some cases is not stationary in time, allowing relaxation intervals in between without important seismic wave arrivals in which free soil vibration happens. Two techniques to estimate the natural period of the free vibration from accelerograms are presented: autocorrelograms and Fourier spectra. Both techniques sometimes allow measuring higher mode frequencies of the soil for the three first modes as well as modal damping. Free vibration modal periods satisfy the classic 1D equation S-wave theory. The presence of free vibrations corresponds to shear wave soil energy radiation episodes rather than to energy amplification of incoming stationary seismic shear waves suggested by the dynamic soil amplification. These results explain the discrepancies observed between the theoretical soil dynamic amplification and the accelerographic measurement. Observation of free vibration of soils is not always possible, it depends on the duration of the time windows without important seismic waves arrivals compared to the natural period and damping of the soil.