A Probabilistic Investigation of the Toppling of Rigid Bodies Experiencing 3D Ground Motions

Abstract eng:
A rigid body, whose shear connection with its base is achieved through friction, exhibits a complex non linear response when subjected to ground motions. This response, generally characterized as rocking, involves a combination of pure rotations with respect to a corner point, sliding and uplift, i.e., time instances in which the body is completely airborne. Previous studies, making the assumptions of rigid base, no sliding, no uplift and planar motion, have highlighted the sensitivity of the rocking response to details of the ground motions. In this study, a rigid body on deformable base is subjected to spectrum compatible artificial time histories and scaled earthquake records and the probability of the body overturning is determined. The dependence of the overturning risk of a rocking body on the dimensions, ground deformability, coefficient of friction, three dimensional earthquake input and base aspect ratio, are highlighted with use of suitable two dimensional and three dimensional Winkler models that take sliding, uplift and geometric non linearities fully into account. The suitability of the existing spectral compatible time history-generation methods is examined, for use in estimating the risk related to the strongly nonlinear behavior of rocking objects.

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