An inerter-based lumped-parameter model using improved legendre polynomials for time-domain analysis of soil-structure interaction

The foundation impedances describing dynamic soil-structure interaction (SSI) are frequency-dependent, rendering the utilization of impedance challenging for time-domain analysis of structural dynamic responses. A lumped-parameter model (LPM) composed of frequency-independent spring, damper, and inerter is proposed to represent the frequency-dependent characteristics of dynamic impedance, thereby facilitating direct time-domain seismic analysis of structures under SSI effects. On the basis of the orthogonality of the improved complex Legendre polynomials, the dynamic impedance of the foundation is approximated through the least-squares curve fitting technique. Subsequent partial fraction decomposition of these polynomial expressions allows their equivalent representation as assemblies of first and second-order discrete mechanical elements, which are used to identify the coefficients of the mechanical components in the LPM. Numerical examples indicate that the proposed model achieves a more accurate representation of the frequency-dependent foundation impedance with fewer components, by employing improved Legendre polynomials rather than ordinary power polynomials. Additionally, because the proposed LPM is formulated without mass elements, it avoids the fundamental flaw where spurious inertial forces arising from base motion distort the true seismic input. Finally, the accuracy of the proposed LPM is validated through seismic response comparisons with benchmark SSI models, followed by its further application to the seismic response analysis of nonlinear superstructures.