Seismic fragility of rigid rocking structures: optimal intensity measures by a deep learning approach
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The rocking motion of free-standing rigid blocks under dynamic excitation has attracted growing interest in seismic engineering for predicting the behavior of ancient masonry constructions, historical monuments, and unanchored contents in modern buildings. The single-block rocking problem was first formulated by Housner, who derived the smooth-motion equation (assuming no bounce or slide) and the coefficient of restitution for perfectly inelastic, instantaneous corner impacts. Later studies have shown that the block seismic vulnerability decreases as the block size increases and gets worse for low-frequency earthquakes. Although the highly nonlinear, non-smooth nature of rocking motion makes exact time-history predictions virtually impossible, the Housner model is reliable when interpreted probabilistically. Fragility curves, quantifying the probability that the rocking angle exceeds a specified limit-state threshold for a given seismic intensity measure, have thus become a key tool for assessing the block seismic vulnerability. Considering rocking-initiation and overturning limit states of slender blocks via lognormal fragility models, it has been proven that the most efficient intensity measures, i.e., those most strongly correlated with the rocking response, are those capturing velocity or frequency-content information of ground motions. Recently, an artificial neural network approach has been employed to predict the block response based on structural parameters and ground motion characteristics. The present work introduces an innovative deep learning framework for evaluating the overturning seismic fragility of rigid rocking blocks. By revisiting intensity-measure efficiency, data-driven architectures are designed to process ground-motion records and extract optimal intensity measures consistent with the adopted lognormal fragility model.