Lumped-parameter model of foundations based on complex Chebyshev polynomial fraction

This paper uses the complex Chebyshev polynomials to develop the lumped-parameter (L-P) model of foundations. The method is an important extension to the approach adopting polynomials to model the dynamic properties of the foundation. Using the complex Chebyshev polynomials can reduce the unexpected wiggling in the foundation modeling, which inevitably occurs if using the simple polynomials of high degree. In the present analysis, the normalized flexibility function of foundation is expressed in terms of complex Chebyshev polynomial fraction. Through the partial-fraction expansion the complex Chebyshev polynomial fraction is decomposed into two sets of basic discrete-element models. The parameters in the models are obtained through the least-square curve-fitting to the available analytical or on-site measurement results. The accuracy and validity of the L-P model is validated through the applications to the surface circular foundations, embedded square foundations and pile group foundations, respectively. It is shown that in general the present model has better accuracy and needs fewer parameters than the existing L-P models.