Simple lumped-parameter models of foundation using mass-spring-dashpot oscillators

Simple lumped-parameter models are developed in this study for generally re presenting the horizontal, vertical, rocking and torsional vibrations of ri gid foundations. A spring and a dashpot are first attached in parallel to a mass to constitute a single-degree-of-freedom oscillator. Depending on the requirement of accuracy, the lumped-parameter model is then designed to co nsist of one or several oscillators connected in series. In addition, a new expression for the dynamic compliance function, instead of the conventiona l expression for the dynamic impedance function, is adopted in this researc h to improve accuracy. The effectiveness of these models is demonstrated fo r various cases including surface square foundations, surface circular foun dations and embedded square foundations, It is found that the performance o f the new models is better in approximating translational foundation vibrat ions than in cases of rotational foundation vibration. Compared with the ot her existing lumped-parameter models, the models proposed in this paper hav e advantages in requiring fewer parameters and featuring a more systematic expansion.