A preliminary investigation of methods for generating fragility curves for rocking bodies

For reasons related to functionality, mobility, or as recently has been suggested to improve dynamic performance, several structural and non-structural elements are let to experience large rotations and displacements when subjected to ground excitations. This overall behavior can be characterized as rocking. Recently, the interest in the behavior of rocking elements subjected to ground motions has increased. This is partly due to the importance of the rocking bodies themselves, for example museum artifacts and monuments are irreplaceable, while hospital equipment is of paramount importance to post-seismic response, partly due to the fact that advances in technology have allowed for key elements of infrastructure to become more mobile, such as large super-computer units, and finally also due to the realization that a large part of the cost during earthquakes is attributed to non-structural elements. Characterizing the risk of these elements subjected to ground motions is therefore of increasing importance. However, the dynamic response of rocking elements during ground motions is strongly non-linear and the mode of failure of these objects is, unlike typical civil engineering applications, not related to exceeding a stress- but a displacement -or rotations - limit. Consequently, several of the existing methodologies to study the risk associated of structures are not applicable, as they usually are focused on systems that are geometrically linear and whose failure is associated with fracture or yield. A remedy for this is to study the risk associated to rocking bodies using the more general approach of creating probability of failure curves. The latter approach requires the use of time histories compatible with some measure of intensity as an input to the deterministic models. For this purpose there are several alternatives: stochastic methods able to generate synthetic time histories, such as the Spectral Representation method, methods based on selecting or scaling existing recorded ground motions based on their compatibility to an intensity measure, and numerical data driven approaches able to generate new time histories based on a set of selected time histories. Each of the previous methods has properties which may be more or less advantageous when applied to the problem of rocking. This work will focus on generating ground records compatible with a seismological intensity measure, the magnitude of the earthquake, for the purpose of generating probability of failure curves for rocking bodies. The effects of biaxial versus uniaxial input will be examined highlighting the importance of making use of the notion of principal axes. Based on this conclusions a methodology for creating probability of failure curves for rocking bodies will be proposed