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.