Filtering action of embedded massive foundations: new analytical expressions and evidence from 2 instrumented buildings

This paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half-space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a quasi-kinematic interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width-to-embedment depth ratio, and the foundation-to-soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free-field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation-to-free-field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation-to-soil mass density and foundation width-to-embedment depth ratios.