Simplified Model for Vertical Vibrations of Surface Foundations

A simplified model for simulating unbounded soil in the vertical vibration problems of surface foundations is presented. The model comprises a mass, a spring, and a dashpot without any internal degree of freedom. By considering three equivalent criteria, a group of equivalent models is established for a foundation-soil system. An optimal equivalent model is then determined to represent the best simplified model. The parameters of the optimal equivalent model may be obtained by a much easier and more direct method than the optimization technique used by existing models. The dynamic responses of the foundation-soil system using the optimal equivalent models are also compared with those obtained by the half-space theory and by the existing lumped-parameter models. The optimal equivalent model is found to have more accurate results than existing discrete models especially for responses at resonant frequencies. This proposed method may be easily applied to practical problems involving soil-structure interaction such as machine foundation vibration and seismic structural analysis.