An analytical solution for the filtering effect of piles in two-layer soil

The aim of this work is to investigate the kinematic response of a floating pile (either free- or fixed-head) embedded in a two-layer soil subjected to upward-propagating seismic waves. Closed form analytical solutions are provided for the kinematic interaction factors, based on a Beam-on-Dynamic-Winkler-foundation (BDWF) model properly adjusted for the problem at hand. For the fixed-head pile case, a simplified solution to assess the pile-to-soil acceleration ratio is provided adopting the concept of average soil motion over an effective pile length. The proposed solutions compare well with rigorous elastodynamic Finite-Element analysis. Insight is given into the interpretation of the mechanisms regulating the reduction of design spectra as function of structural period. Finally, as an outcome of a wide parametric study, ready-to-use formulae are proposed for a rapid assessment of the pile-induced spectral reduction.