Modal Analysis for Building-Soil Interaction

An approximate method of modal analysis is presented for the earthquake response of linear building-foundation systems. Modal damping is obtained as a formal extension of the classical method of modal analysis and is shown to be equivalent to the energy ratio criterion proposed by Jacobsen. By making use of the modal shapes of the fixed-base superstructure, modal damping in the system is expressed as a weighted sum of the critical damping ratios of the superstructure plus an additional term representing the energy dissipated by the soil. To estimate the accuracy of the suggested method, both analytical and numerical studies are performed. Several examples are included to illustrate the effect of hysteretic soil damping on the system response.