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 Refernce 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.