Consistent lumped‐parameter models for unbounded soil: Physical representation

A systematic procedure to develop a consistent lumped‐parameter model with real frequency‐independent coefficients to represent the unbounded soil is developed. Each (modelled) dynamic‐stiffness coefficient in the frequency domain is approximated as a ratio of two polynomials, which is then formulated as a partial‐fraction expansion. Each of these terms is represented by a discrete model, which is the building block of the lumped‐parameter model. A second‐order term, for example, leads to a discrete model with springs and dampers with two internal degrees of freedom, corresponding to two first‐order differential equations, or, alternatively, results in a discrete model with springs, dampers and a mass with one internal degree of freedom, corresponding to one second‐order differential equation. The lumped‐parameter model can easily be incorporated in a general‐purpose structural dynamics program working in the time domain, whereby the structure can even be non‐linear. A thorough evaluation shows that highly accurate results are achieved, even for dynamic systems with a cutoff frequency.