| Abstract: | Strong shaking of structures during large earthquakes may result in some cases in partial separation of the base of the structure from the foundation. A simplified problem of this type, the dynamic response of a rocking rigid block allowed to uplift, is examined here. Two foundation models are considered: the Winkler foundation and the much simpler ‘two-spring’ foundation. It is shown that an equivalence between these two models can be established, so that one can work with the much simpler two-spring foundation. Simple solutions of the equations of motion are developed and simplified methods of analysis are proposed. In general, uplift leads to a softer vibrating system which behaves non-linearly, although the response is composed of a sequence of linear responses. As a result the apparent rocking period increases with the amount of lift-off. The corresponding apparent ratio of critical damping decreases, in general, with the amplitude of the response. Compared to the case without lift-off, the response of the system may increase or decrease because of the uplift, depending on the excitation and the parameters of the system. |
