An analytical approach to estimate period and damping ratio of buildings founded on soft soil

Analytical closed-form solutions to estimate the effect of soil-structure interaction on the fundamental period and damping ratio of buildings are a useful tool to correctly interpret data of real-time dynamic monitoring of single structures as well as to assess the vulnerability of classes of buildings located on different subsoils. Most of the existing formulae simplify the structure into a single degree of freedom system (SDOF) on a shallow circular footing resting on a half-space. Nevertheless, reliable equivalence criteria to assimilate a multi-DOF building to a SDOF, a foundation grid system to a single circular footing, as well as a layered soil profile to a half space, are still not trivial. The application of the analytical formulae to more complex foundation systems require the direct calculation of the foundation impedance functions that may be onerous and too long in the above-described applications. This paper re-elaborates the analytical impedance functions and the derivation of the fundamental period and foundation damping ratio proposed in the literature and adopted by seismic design codes, to obtain solutions in which period and damping directly depend on dimensionless ratios expressing the soil-structure relative stiffness and mass, the structural slenderness and the foundation embedment. The obtained formulae were applied to five masonry buildings located on shallow covers of soft clay in Southern Italy, where the natural periods were experimentally measured.