Towards physically justified, site-specific overturningacceleration response spectra

Abstract

A methodology is presented for the seismic assessment and design of rocking structures, including single blocks, multi-block columns, and arches, without the need for nonlinear dynamic analysis. The proposed approach provides a standardized workflow to specify location-specific rocking parameters based on real earthquake records, which can be applied as a practical design tool. The rocking behavior under earthquake excitations is analyzed both analytically and numerically, and fundamental relationships between natural records and simple synthetic pulses are highlighted through the introduction of two key parameters: the impulse duration ($t_\mathrm{I}$) and the impulse-moment duration ($t_\mathrm{M}$). Using these parameters, the simplified \textit{overturning acceleration response spectrum} (OAS) is defined, which normalizes peak ground acceleration by the block's minimum acceleration threshold ($a_\mathrm{p,min}$) and plots it against the frequency parameter ($p$). The OAS can be accurately represented by three simple curves—a constant, one proportional to $1/p$, and one approximately proportional to $1/p^2$—which delineate the stable, overturning without impact, and overturning after impact conditions.The method is validated with 100 near-field and far-field earthquake records, showing that the simplified OAS curves provide a robust estimate of seismic demands at a given location. By providing location-specific design curves, the proposed methodology enables engineers to assess or design rocking structures using only the block characteristics ($p$ and $a_\mathrm{p,min}$), eliminating the need for time-history analyses. A numerical example further illustrates the analogy between this approach and conventional response spectrum analysis for elastic–plastic structures.

Keywords: overturning acceleration spectrum, rocking characteristics, seismicrocking response, rocking-based design method, site-specific rocking parameters