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

Simple lumped-parameter models are developed in this study for generally representing the horizontal, vertical, rocking and torsional vibrations of rigid 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 consist of one or several oscillators connected in series. In addition, a new expression for the dynamic compliance function, instead of the conventional expression for the dynamic impedance function, is adopted in this research to improve accuracy. The effectiveness of these models is demonstrated for various cases including surface square foundations, surface circular foundations and embedded square foundations, It is found that the performance of the new models is better in approximating translational foundation vibrations than in cases of rotational foundation vibration. Compared with the other existing lumped-parameter models, the models proposed in this paper have advantages in requiring fewer parameters and featuring a more systematic expansion.