Dynamic behavior of rocking structures allowed to uplift

Abstract

Strong shaking of structures during large earthquakes may result in some cases in partial separation of the base of the structure from the sail. This phenomenon of uplifting, which can affect the dynamic behavior of the structure significantly, even if the amount of uplift is small, is examined in this thesis. First the case of a rocking rigid block is investigated and then more complicated, flexible superstructures are introduced. Two foundation models which permit uplift are considered: the Winkler foundation and the much simpler "two-spring" foundation. Several energy dissipating mechanisms are also introduced into these models. It is shown that an equivalence between these two models for the foundation can be established, so that one can always work with the much simpler two-spring foundation. In this way complete analytical solutions can be derived in most cases. Moreover, simple approximate methods for the calculation of the apparent fundamental period of the rocking system are developed and simplified methods of analysis are proposed. In general, uplift leads to a softer vibrating system which behaves nonlinearly, although the response is composed of a sequence of linear responses. As a result, the apparent fundamental resonant frequency of the uplifting system is always less than the fundamental resonant frequency of both the soil-structure interacting system, in which lift-off is not allowed, and the superstructure itself. The second and higher resonant frequencies of the superstructure, however, are not affected significantly by lift-off. For damped foundations, the ratio of critical damping associated with the apparent fundamental mode decreases, in general, with the amount of lift-off. These effects of uplift on the dynamic properties of the rocking system can alter the response of the structure significantly during an earthquake. Nevertheless, it cannot be said a priori whether they are favorable to the behavior or not; this depends on the parameters of the system and the time history of the excitation.

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