Variability in seismic response of secondary systems due to uncertain soil properties

A mode acceleration formulation is presented to investigate the variability in the response of a secondary system which is supported on a flexible-base primary system at multiple attachment points. The response functions are considered to be uncertain due to uncertainties in the values of shear wave velocity and Poisson’s ratio of the foundation soil. Both soil parameters are assumed to be statistically independent variables with Gaussian distributions. A numerical study with the help of an example primary-secondary (P–S) system shows that dynamic response should be ignored only for very stiff secondary modes, say > 7 times as stiff as the dominant mode of the primary system, for the proposed formulation to work well. It is also seen that uncertainty in shear wave velocity can be ignored in case of limited soil-structure interaction, while uncertainty in Poisson’s ratio should be considered only when soil damping is sensitive to the Poisson’s ratio and there is significant soil-structure interaction.