Predictive relationships are offered for the response of on-ground 2D rigid blocks undergoing rocking. Among others, this is pertinent to (1) modern or classical antiquity structures that utilize rocking as a seismic protection mechanism and (2) freestanding contents (e.g., cabinets, bookcases, and museum artifacts) 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 and 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 strengthratio/ductility/period relationships of yielding oscillators, to enable the rapid assessment or design of simple rocking systems.

The seismic response assessment of rocking systems via Incremental Dynamic Analysis (IDA) is investigated, focusing on the issues that arise in the analysis and postprocessing stages. Rocking IDA curves generally differ from those of hysteretic structural systems due to (i) the frequent appearance of resurrections; (ii) their highly weaving non-monotonic behavior; and (iii) their overall high variability. Hence, including or ignoring analysis results above the first resurrection level, deriving statistics given a response level versus an intensity measure level, as well as selecting an adequate number of ground motion records and runs per record, become challenging issues with non-trivial impact on the probabilistic characterization of rocking response. This necessitates a fresh view on analysis choices and post-processing techniques, aiming to assure the accuracy and fidelity of rocking IDA results. As an example, the effect of different choices and techniques are showcased on two-dimensional rigid blocks that are assumed to represent simplified models of monolithic ancient columns of different slenderness.

The influence of the vertical component of ground motion is investigated for assessing the distribution of the seismic response of unanchored rigid blocks. Multiple stripes of site‐hazard‐consistent ground motions are employed for calculating the seismic response of rigid rocking blocks with and without the inclusion of the vertical component. The comparison of the resulting response is being made both for single records and full suites, employing a paired record versus an ensemble‐statistics comparison, respectively. It is shown that on a single record basis, the vertical component may have a non‐negligible but highly variable influence on the rocking response, sometimes detrimental, sometimes beneficial. Still, when considering any large ensemble of records, the effect becomes statistically insignificant, except for the very specific case of rocking uplift for stocky blocks. To this end, for cases where the appearance of uplift is associated with damage, closed‐form expressions are proposed to modify the lognormal fragility function of rocking initiation given the block slenderness and the ratio of the peak vertical over the peak horizontal ground acceleration.

Analytical expressions are proposed for predicting the rocking response of rigid freestanding building contents subjected to seismic-induced floor excitations. The study considers a wide range of rigid block geometries and seismic floor acceleration histories that were recorded during actual earthquakes in instrumented Californian buildings, so as to cover, in a fully probabilistic manner, the entire spectrum of potential pure rocking responses, i.e. from the initiation of rocking up to the block overturning. Contrary to past observations on anchored building contents (prior to any failure in their anchorage system that could alter their response and mode of failure), it is shown that the response of free-standing blocks is not influenced by the predominant period of the supporting structure. The proposed set of equations can be utilised for estimating the response statistics and consequently for undertaking an analytical seismic fragility assessment on rocking building contents.

The parametric representation of rocking fragilities is statistically investigated. Initially, the potential normalization of the rocking parameters to reduce the problem's dimensionality is tackled by undertaking comparisons both on a single‐record and a sample‐of‐records basis. It is found that the slenderness angle can be normalized out when probabilistically considering the rocking response of simple rocking blocks with the same semi‐diagonal length. Then, the robustness of the lognormal distribution for characterizing the rocking motion is investigated. Sets of pulse‐like and ordinary ground motions are employed to test the lognormal fit for the full range of rocking response when the peak ground acceleration or the peak ground velocity are employed as intensity measures. In both cases, the lognormal distribution offers an adequate, but often imperfect, baseline model of the rocking fragility curves. Instead, a shifted lognormal that accounts for the absence of response below the rocking initiation intensity is an enhanced solution that can form the basis for offering simplified response model surrogates.