Intensity measures, fragility analysis and dimensionality reduction of rocking under far‐field ground motions

Abstract

Problems for which it is impossible to make a precise causal prediction are commonly tackled with statistical analysis. Although fairly simple, the problem of a rocking block on a rigid base subjected to seismic excitation exhibits a fascinating, complex response, making it extremely difficult to validate numerical models against experimental results, thus calling for a statistical approach. In this context, this paper statistically studies the rocking behaviour of rigid blocks, excited by synthetic far‐field ground motions. A total of 50 million analyses are performed, considering rocking blocks of height ranging from 1 to 20 m and slenderness angle ranging from 0.1 to 0.35 rad. The results are used to explore the performance of different ground motion intensity measures (IMs), in terms of their ability to predict the maximum rocking rotation. By comparing the efficiency, sufficiency and proficiency of the IMs, it is found that the peak ground velocity (PGV) performs optimally. Then, fragility curves are constructed using different IMs, concluding again that the PGV is the most efficient IM. Impressively, the fragility curves for different block sizes collapse to a single curve, if a non‐dimensional IM that involves PGV and the block geometry is used. Finally, the results produced on the basis of far‐field synthetic motions are compared to results based on recorded ground motions.

A multi‐level approach to predict the seismic response of rigid rocking structures using artificial neural networks

“…Rocking is particularly sensitive to characteristics of the ground excitation. 16,17 Psycharis et al 18 illustrated the importance of peak ground velocity (PGV) over peak ground acceleration (PGA) to rocking response; similar results were later found in Sieber et al 19 Dimitrakopoulos and Paraskeva 20 highlighted the contribution of PGV and a combination of PGA with a frequency characteristic (PGA/PGV) to rocking amplitude. Later, Petrone et al 21 and Lachanas et al 22 verified the importance of PGV and PGA to the overturning of slender and stocky rocking structures, respectively.…”

“…Psycharis et al 18 . illustrated the importance of peak ground velocity ( PGV ) over peak ground acceleration ( PGA ) to rocking response; similar results were later found in Sieber et al 19 . Dimitrakopoulos and Paraskeva 20 highlighted the contribution of PGV and a combination of PGA with a frequency characteristic ( PGA / PGV ) to rocking amplitude.…”

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

“…Most recent literature has expanded to incorporate explicit testing to validate candidate IMs. For example, Giouvanidis and Dimitrakopoulos 33 tested multiple IMs for simple rocking blocks, based on amplitude, frequency, duration, or energy characteristics of the ground motion; Pappas et al 34 tested the efficiency of PGA and PGV for a monolithic 3D rocking column; Kavvadias et al 35 proposed two IMs for rocking blocks based on the rocking rotation and the angular velocity spectra; Bantilas et al 36 investigated IMs for rocking podium structures; Shokrabadi and Burton 37 tested IMs for two rocking lateral-load resisting systems; more recently, Sieber et al 38 investigated simple rocking blocks, proposing the…”

“…column; Kavvadias et al 35 proposed two IMs for rocking blocks based on the rocking rotation and the angular velocity spectra; Bantilas et al 36 investigated IMs for rocking podium structures; Shokrabadi and Burton 37 tested IMs for two rocking lateral-load resisting systems; more recently, Sieber et al 38 investigated simple rocking blocks, proposing the universal use of PGV for predicting non-trivial angles of rotation. In many of the above studies, the findings may be fully applicable for IM-P usage, but it remains to be seen whether (and to what extent) they are applicable for an IM-V, especially given the fact that risk estimates may be heavily influenced by the IM selection.…”

“…proposed two IMs for rocking blocks based on the rocking rotation and the angular velocity spectra; Bantilas et al 36 . investigated IMs for rocking podium structures; Shokrabadi and Burton 37 tested IMs for two rocking lateral‐load resisting systems; more recently, Sieber et al 38 . investigated simple rocking blocks, proposing the universal use of PGV for predicting non‐trivial angles of rotation.…”