Derivation, Validation, and Web Application of Dimensionless Analytical Solutions for Equivalent Period and Damping Ratio of Soil-Foundation-Structure Systems

The paper proposes closed-form solutions to estimate the period lengthening and the damping ratio of buildings considering the effects of the dynamic soil-foundation-structure interaction. They were derived by introducing analytical solutions of the impedance functions in the equation of the displacement of the so-called “replacement oscillator.” The obtained expressions depend on well-established and ad-hoc defined dimensionless parameters and are applicable to several configurations of subsoil and shallow foundations, even accounting for the cross-interaction among footings and the foundation flexibility. The proposed approach was successfully validated against well-known solutions available in literature and against the period and damping ratio experimentally measured on (1) the steel–concrete prototype Europroteas (Greece); and (2) masonry buildings founded on soft clay in the city of Matera (south of Italy). To promote their widespread application, the closed-form solutions were implemented into a web application 0D-In, exploited to execute a sensitivity analysis. The outcomes of this study highlighted that the period increases more significantly for structures founded on flexible or interacting foundations. The soil hysteretic contribution is maximum for rocking prone structures. For ordinary buildings, the radiative damping ratio prevails, due to the considerable length of rectangular footings. Again for ordinary buildings, the effect of the embedment appears of secondary importance both on the period lengthening and on the damping ratio.