Accuracy controllable time-domain difference approach to calculate foundation resisting force

Interaction forces between foundation and structure isone of key problems in nonlinear dynamic response analysis of structuresaccounting for soil-structure dynamic interaction. Currently there are twokinds of method dealing with it: one is the direct integrity analysisapproach, the other is time-domain substructure approach. Because of farless computational cost comparison to the former, time-domain substructureapproach is very important in engineering field. The fact that foundationimpedance complexly vary with frequency makes the calculation of time-domainfoundation resisting force time-consuming. To simplify the calculation oftime-domain foundation resisting force, many lumped-parameter models havebeen proposed. Lumped-parameter model reflects the singular component offoundation impedance which is not square integrable and correspond tosimultaneous effect. Nevertheless the regular component can't be reflectedaccurately, which correspond to time-delay effect and be square integrable.Time-domain recursive model proposed by Safak (2006) used for representingtime-domain foundation resisting force can simulate the regular component offoundation impedance. But the whole essential of foundation impedance cannot be reflected in this model because the corresponding filter function hasintrinsically limitation at Nyquist frequency. Thus, time-domain foundationresisting force can not be simulated accurately. Combining lumped-parametermodel and time-domain difference recursive filter model, a time-domaindifference approach of accuracy controllable foundation resisting force isproposed. Numerical examples results demonstrate that the proposed procedurecan perfectly fit the frequency dependent impedance in interested frequencyband.