Influence of Foundation Flexibility on $R_{\mu }$ and $C_{\mu }$ Factors

Strength-reduction $\left(R_{\mu }\right)$ and displacement-modification $\left(C_{\mu }\right)$ factors have been extensively studied in the past for firm ground, and even for soft soils considering site effects, but always excluding soil–structure interaction. In this work, they are investigated for a single elastoplastic structure with flexible foundation excited by vertically propagating shear waves. The concepts developed earlier for fixed-base yielding systems are extended to account for soil–structure interaction. This is done by use of the simplified reference model and a nonlinear replacement oscillator recently proposed by the writers. Numerical evaluations are conducted for typical system configurations, using the great 1985 Michoacan earthquake recorded at one site representative of the lakebed zone in Mexico City. Results are compared with those corresponding to the fixed-base case. It is found that the site effects observed by other writers for the rigid-base condition are increased or decreased by soil–structure interaction, depending on the period ratio of the structure and site. Finally, it is shown how a site-dependent reduction rule proposed elsewhere for fixed-base systems should be adjusted for interacting systems using the information presented.