Response variability for a structure with soil–structure interactions and uncertain soil properties

A non-classical modal analysis based formulation is used to quantify the effect of uncertain soil-foundation properties on structural response in seismically excited soil–structure interacting (SSI) systems. This formulation allows the response of the interacting system to be represented as a superposition of the responses of uncoupled modal equations which include an additional random vector to represent the system uncertainties. The method is implemented by an effective Gaussian quadrature integration method to find the frequency-domain stochastic response properties of the SSI systems. Numerical examples of MDOF SSI systems illustrate that the main effect of uncertain soil properties on such SSI systems is to alter the magnitudes of modal response near the system resonant frequencies, rather than to shift the resonant frequencies. When the uncertainty of soil-foundation properties is not negligible, there may be significant variations of the transfer functions for modal response and significant uncertainty about the spectral density of structural response may occur near the system’s resonant frequencies.