The influence of the vertical component of ground motion on the probabilistic treatment of the rocking response of free‐standing blocks

Abstract

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.

Statistical property parameterization of simple rocking block response

“…The first and stricter comparison is made on a paired‐record basis. [ 38 ] In the context of medical studies, this corresponds to supplying the tested medicine versus a placebo (or two different α values) to identical twins (or records). Specifically, after the analysis with the full set of 86 ground motions for the 5×3 blocks of Table 1, a paired one‐by‐one record comparison is employed between blocks with the same p but different α.…”

“…This ensemble‐statistics comparison is considered looser than the previous one since it considers a statistics‐to‐statistics comparison instead of the more rigorous record‐to‐record comparison. [ 38 ] Essentially, the 16/50/84 IDA fractiles are computed on an EDP given IM (EDP|IM) basis and then the results per frequency case are plotted together in the dimensionless IM‐EDP axes. As presented in Figure 8, only small differences are captured for all the p ‐cases and all quantiles considered.…”

“…The present work is part of a broader study [31,[37][38][39][40] that aims to investigate in detail the seismic response standardization for the case of rigid rocking blocks. By this, we mean (i) the provision of a standard parametric distribution for probabilistically representing rocking response, and (ii) the provision of simplified expressions to capture the distribution parameters.…”

Hazard consistent record selection procedures accounting for horizontal and vertical components of the ground motion: Application to liquid storage tanks

“…Indeed, there are examples of structural systems where neglecting the effect of the vertical component may not be warranted. Such examples include, but are not limited to, reinforced concrete precast structures, 15 dams, [16][17][18] nuclear power plant units, 19 cylindrical fluid containers, 20 silos, 21 rocking systems, 22,23 non-structural elements 24,25 (e.g. suspended ceilings), base-isolated buildings, 26 reinforced concrete (RC) frame buildings, 27,28 masonry buildings, 29,30 bridges, 31 highway overcrossings 32,33 and building contents sensitive to rocking, sliding or overturning.…”

Seismic response distribution expressions for rocking building contents under ordinary ground motions

“…The effect of vertical floor excitation on the rocking components was disregarded in view of past findings (e.g. Makris and Kampas, 2016;Linde et al, 2020) that it is negligible for almost all practical applications, especially when adopting a probabilistic treatment (Lachanas et al, 2022a).…”