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Nested Lumped-Parameter Model for Foundation with Strongly Frequency-dependent Impedance

A nested lumped-parameter model (LPM) consisting of frequency-independent springs and dashpots is proposed to represent the foundation-soil dynamic system with strongly frequency-dependent impedance in time domain. Due to the convergence and robustness of the complex Chebyshev polynomial, it is used to approximate the dynamic flexibility of the foundation by least-square curve-fitting technique. The comparisons with existing LPMs show that the present model can express the impedance by using a small number of elements and reduce oscillation of the solution appearing in simple polynomial approximations. Finally, several examples of foundations with irregular geometries are presented to show the application of nested LPMs.