Response variability of an SSI system with uncertain structural and soil properties

A non-classical modal-analysis-based formulation including an additional random vector to represent the system uncertainties is used to quantify the effect of uncertain soil–foundation and superstructure properties on structural response for seismically excited soil–structure interacting (SSI) systems. It is shown that the pertinent equations are essentially the same as those for only soil parameter uncertainty and very similar to those for only structural parameter uncertainty. The method is implemented here by using an effective Gaussian quadrature method to find accurate frequency-domain stochastic response properties of the SSI systems. Numerical examples of multiple-degree-of-freedom SSI systems with quite large parameter uncertainty illustrate that the unconditional spectral density of the structural response is often very similar to that in the absence of uncertainty. However, deterministic variations of parameters may cause large changes in the response spectral density. In particular, when the parameter uncertainty is not negligible, there may be significant uncertainty about the spectral density of structural response near the systemʹs resonant frequencies. It is shown that the effects of uncertainty about multiple parameters can generally be adequately and efficiently approximated by applying a simple first-order second-moment approximation to the results for single-parameter uncertainty.