On the filtering effect induced by embedded foundations

The seismic performance of structures is usually evaluated under a fixed base assumption, by applying a base slab input motion equal to the free-field motion, i.e. neglecting the dynamic interaction between the structure, the foundation and the foundation soil. Soil-structure interaction results from both kinematic effects, whereby a foundation with no mass modifies the input motion solely by its stiffness, and inertial effects, as the motion of the foundation is further modified as a result of the inertia actions in the structure-foundation system. Numerical, experimental, and theoretical studies have shown that kinematic interaction can have significant effects on the dynamic behaviour of embedded foundations and that the motion of the foundation may differ from that in free-field conditions, depending on the frequency content of the earthquake, the geometry of the problem, and the ratio of the stiffness of the foundation and of the soil. This paper deals with the filtering effect induced by embedded foundations on the input motion transmitted to the structure. The relevant parameters, described through three kinematic interaction factors, are obtained by dimensional analysis of the problem. Based on the results of 2D finite difference analyses and of a simplified 1D theoretical model, it can be shown that these interaction factors depend both on the ratio between the depth of embedment of the foundation and wavelength of the input signal (ωH/V_S ) and on the aspect ratio of the foundation ( B/H ). Simplified expressions to compute the interaction factors in practice are proposed.