Analysis of soil-foundation-structure interaction based on a novel lumped parameter model with improved Legendre polynomials

A lumped parameter model (LPM) adopting frequency independent spring, damper and inerter is developed in this work. It can effectively characterise frequency-dependent impedance within the time domain, thus supporting direct time-domain seismic analysis for structures with soil structure interaction (SSI) effects incorporated. The ratio of the improved Legendre polynomials is used to represent the dynamic impedance of the foundation. by defining the error function, the correlation constant coefficient is obtained by using least square method. The ratios of the improved Legendre polynomials are decomposed into partial fraction expansions and equated to first and second order discrete element models. Comparison with existing LPMs shows that the present model can express the dynamic impedance of various foundation types by using a small number of elements. The low-order improved Legendre polynomials exactly capture the frequency-dependent variation of the elastic half-space solution across a wide band. Additionally, the proposed LPM is constructed without mass elements, thereby avoiding the intrinsic issue wherein pseudo inertial forces generated by base motion corrupt the genuine seismic excitation. Numerical examples are adopted to verify and compare the time-history responses of the soil-foundation-structure system subjected to seismic excitations. Meanwhile, the applicability of the proposed model to nonlinear structural systems is further investigated.