SummaryThis paper assesses the seismic fragility of single degree of freedom rocking structures within a probabilistic framework. The focus is on slender rigid structures that exhibit negative stiffness during rocking. The analysis considers ground motions with near‐fault characteristics, either solely coherent pulses or synthetic ground motions that include, in addition, a stochastic high‐frequency component. The study offers normalized fragility curves that estimate the overturning tendency, as well as the peak response rotation of a rocking structure. It shows that the use of bivariate intensity measures (IMs) can lead to superior fragility curves compared with conventional univariate IMs. Regardless, the study advocates the use of dimensionless–orientationless IMs that offer an approximately ‘universal’ description of rocking behavior/fragility, a normalized description almost indifferent to the amplitude and the predominant frequency of the excitation or the size and the slenderness of the rocking structure. Importantly, the analysis unveils hidden order in rocking response. There exists a critical peak ground acceleration, below and above which, peak rocking response scales differently. In particular, when the structure does not overturn, the peak rotation follows approximately a biplanar pattern with respect to the intensity and the predominant frequency of the excitation. Finally, the analysis verifies that rocking overturning depends primarily on the velocity characteristics of the ground motion. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, the dynamic response of the rocking block subjected to base excitation is revisited. The goal is to offer new closed-form solutions and original similarity laws that shed light on the fundamental aspects of the rocking block. The focus is on the transient dynamics of the rocking block under finite-duration excitations. An alternative way to describe the response of the rocking block, informative of the behaviour of rocking structures under excitations of different intensity, is offered. In the process, limitations of standard dimensional analysis, related to the orientations of the involved physical quantities, are revealed. The proposed dimensionless and orientationless groups condense the response and offer a lucid depiction of the rocking phenomenon. When expressed in the appropriate dimensionless-orientationless groups, the rocking response becomes perfectly self-similar for slender blocks (within the small rotations range) and practically self-similar for non-slender blocks (larger rotations). Using this formulation, the nonlinear and non-smooth rocking response to pulse-type ground motion can be directly determined, and need only be scaled by the intensity and frequency of the excitation.

SUMMARY Predicting the rocking response of structures to ground motion is important for assessment of existing structures, which may be vulnerable to uplift and overturning, as well as for designs which employ rocking as a means of seismic isolation. However, the majority of studies utilize a single rocking block to characterize rocking motion. In this paper, a methodology is proposed to derive equivalence between the single rocking block and various rocking mechanisms, yielding a set of fundamental rocking parameters. Specific structures that have exact dynamic equivalence with a single rocking block, are first reviewed. Subsequently, approximate equivalence between single and multiple block mechanisms is achieved through local linearization of the relevant equations of motion. The approximation error associated with linearization is quantified for three essential mechanisms, providing a measure of the confidence with which the proposed methodology can be applied. Copyright © 2014 John Wiley & Sons, Ltd.