Statistical property parameterization of simple rocking block response

Abstract

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.

Intensity measures as interfacing variables versus response proxies: The case of rigid rocking blocks

“…In other words, the two IM-Ps can be designated as moderately sufficient when compared to the examined IM-Vs; yet, it is their inefficiency in tandem with the lack of available GMPEs that make them unsuitable when the goal is to assess the vulnerability of rocking systems. The same observations about the (in)efficiency of the two examined IM-Ps hold if block slenderness adjustment is employed instead of record scaling, as proposed by Lachanas et al (2023). 62 Then the two IM-Ps may show somewhat reduced 𝛽 IM values close to overturning but still not low enough to be considered as acceptable IM-V choices.…”

“…Where better, block‐specific results are needed, a variant of $$\textit{Avg}{S}_{\textit{agm}}$$ (preferably with a period range optimized in postprocessing), will generally offer better performance. Τhe results presented in Figure 4 are calculated per Equation () and they will be the same if each IM is employed with its dimensionless form 31,62 since the standard deviation of the natural logarithm is unaffected by the multiplication or the division of the data by a constant.…”

Effect of ground motion processing and filtering on the response of rocking structures

“…Such a statistical approach is not only applied to rocking structures: Riddell and Newmark 94 produced inelastic spectra for yielding structures based on statistics on ensembles of excitations. In fact, this approach is consistent with the fundamental seismic design problem, which involves computing the response to a set of ground motions, rather than to an individual one 95‐103 …”

“…In fact, this approach is consistent with the fundamental seismic design problem, which involves computing the response to a set of ground motions, rather than to an individual one. [95][96][97][98][99][100][101][102][103] For an ensemble of ground motions to be useful, in this paper all ground motions were scaled to the same PGV. PGV was used as an intensity measure, as it performs better than PGA or PGD for rocking structures.…”

Seismic damage evaluation of unanchored nonstructural components under combined effects of horizontal and vertical near‐fault ground motions

“…The influence of block size on its rocking demands under horizontal excitations was highlighted in previous studies (e.g., 36,37 ). In addition to the slender block in Table 4, four more slender blocks with different geometry (i.e., Case 1.1 and Case 1.4 in Table 5) are considered to probe the block size effect on rocking demands under bidirectional inputs.…”