Towards a design framework for rocking structures

A methodology is presented for the seismic assessment of overturning safety of rocking structures, including single blocks, multi-block columns, and arches. The proposed methodology does not require nonlinear dynamic analysis, and it can enable the development of an efficient, prescriptive design procedure for rocking structures.

The rocking behavior under earthquake excitations is analyzed both analytically and numerically, and fundamental, physics-based relationships between natural records and analytically-derived single- and double-pulse excitations are highlighted through the introduction of two key parameters: the impulse duration and the impulse-moment duration. Using these rocking parameters, the simplified overturning acceleration response spectrum (OAS) is defined, where overturning safety is expressed through a limit to the normalized peak ground acceleration as a function of the frequency parameter (𝑝) that characterizes the structure. The OAS can be approximated through the envelope of a uniform minimum threshold and two curves proportional to 1/𝑝 and 1/𝑝2.

The accuracy of the simplified OAS curves is illustrated using a set of 100 ground motion records that include time histories from both near-field and far-field events. When location-specific design curves are determined, engineers may assess rocking structures using only the block characteristics, eliminating the need for time–history analyses. The analogy between this approach and conventional response spectrum analysis for elastic–plastic structures is also demonstrated.