Efficiency of Seismic Intensity Measures for the Overturning Fragility Analysis of Rocking Rigid Blocks

The overturning fragility of free-standing rigid blocks under earthquake excitation is investigated to explore how seismic input and block geometry govern the rocking outcome. A large cloud dataset of rocking responses is generated by dynamic simulations using Housner's model for rocking. A lognormal fragility model, with median and dispersion parameters estimated by maximum likelihood, is then employed to characterize the overturning probability conditioned on a scalar intensity measure (IM) of seismic severity. A novel definition of efficiency is proposed to identify IMs that exhibit high predictive capability of the rocking outcome when a lognormal fragility model is employed. Robust metrics are introduced for quantitative assessment, thereby avoiding the potential misinterpretation that can arise from the usual use of the dispersion fragility parameter alone. Among a broad set of classical IMs, it is confirmed that velocity-based ones result the most efficient, with peak ground velocity delivering optimal calibration-discrimination trade-off. In a broader perspective, the proposed procedure provides a reliable methodological framework for assessing the efficiency of IMs in categorical seismic fragility analysis.