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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.
Psycharis et al. (Sat,) studied this question.