Modal and nodal impedance functions for truncated semi-infinite soil domains

A general methodology for numerically extracting the impedance functions of flexible soil-foundation interfaces (SFIs) in both physical (nodal) and modal domains is provided, which can also be applied to any truncated semi-infinite elastic media. A recently developed finite element method that features perfectly matched layers as absorbing boundary conditions is used to compute the wave responses within the semi-infinite soil domain. Using this tool, the impedance functions are obtained by prescribing the known nodal or modal displacement along the SFI and computing the corresponding reactions. The modal approach has the advantage of only computing the impedance functions for the most important mode shapes that control the behavior of the interface with a reduced computational cost. The accuracy of the proposed method is investigated through forced-vibration analysis of a strip foundation on surface of an elastic half-space. It is found that reduced-order modal impedance matrices can be as accurate as their nodal counterparts as long as a set of appropriate mode shapes is retained. Moreover, depending on the type of the applied loading and its frequency content, higher (flexible) mode shapes will be activated, and therefore, the substructure methods that are based on rigid or winkler-type impedance functions may predict the actual response of the foundation poorly.