Consistent lumped‐parameter models for unbounded soil: Frequency‐independent stiffness, damping and mass matrices

A systematic procedure to develop consistent (symmetric) stiffness, damping and mass matrices with real coefficients to represent any unbounded soil is developed. These property matrices are based on the lumped‐parameter models of Reference 1. Either stiffness and damping matrices corresponding to first‐order differential equations involving the internal degrees of freedom and those on the structure‐soil interface result or, alternatively, in addition mass matrices are introduced, corresponding to second‐order differential equations, which reduce the number of internal degrees of freedom by a factor 2. The stiffness, damping and mass matrices can easily be incorporated in a general‐purpose structural dynamics program working in the time domain, whereby the structure can even be non‐linear.