Seismic response distribution expressions for on-ground rigid rocking blocks under ordinary ground motions.

Predictive relationships are offered for the response of on-ground 2D rigid blocks undergoing rocking. Among others, this is pertinent to (a) modern or classical antiquity structures that utilize rocking as a seismic protection mechanism and (b) freestanding contents (e.g., cabinets, bookcases, museum artefacts) located on the ground or lower floors of stiff buildings. Blocks of varying dimensions were subjected to a full range assessment of seismic response under increasing intensity levels of ordinary (no-pulse, no-long-duration) ground motions, parameterized by peak ground acceleration or velocity. Both response and intensity were normalized, allowing the fitting of general-purpose parametric expressions to determine the mean and dispersion of response for an arbitrary block of interest. These can be utilized in the same way as conventional strength-ratio/ductility/period relationships of yielding oscillators, to enable the rapid assessment or design of simple rocking systems.