As an alternative to rigorous boundary-element solutions, simple physical models can be used to determine e.g. the interaction force-displacement relationship (dynamic stiffness) of foundations and the seismic effective foundation input motion. Translational and rotational cones and their corresponding lumped-parameter models together with simple one-dimensional wave patterns in the horizontal plane allow surface, embedded and pile foundations even for a layered site to be analyzed and thus form a major step towards developing a strength-of-materials approach to foundation - vibration analysis. The analysis can mostly be performed directly in the time domain. The physical models provide physical insight which is often obscured by the mathematical complexity of rigorous solutions, offer simplicity in application as well as in the physics and in the rigorous mathematical solution of the physical model, are sufficiently general to enable reasonably complicated practical cases to be solved, exhibit adequate accuracy, allow physical features to be demonstrated and offer the potential for generalizations
