Seismic Overturning Fragility Analysis for Rigid Blocks Subjected to Floor Motions

This paper investigates the seismic rocking-overturning fragility of freestanding rigid blocks subjected to one-sine acceleration pulses from a probabilistic perspective. An equivalent single-degree-of-freedom (SDOF) model with a bespoke discrete damper is used to simulate the responses of four blocks with varying geometries under excitation with various characteristics. The simulation results are used to perform an overturning fragility analysis and evaluate the performance of various intensity measures (IMs). An IM strip, referred to as a hybrid strip, can be observed in the analysis, within which both safe rocking and overturning occur. For IM values outside of the hybrid strip, there exists a clear distinction between these two states. In this study, we introduce the hybrid ratio, a parameter that can estimate the size of the hybrid strip of different IMs. The hybrid ratio is defined as the combination of two ratios of hybrid strip width and the two IM strip widths corresponding to safe rocking and overturning, respectively. The effect of the different analysis strip widths is also examined in the overturning fragility analysis. The results suggest that the IM determined by excitation magnitude, frequency, and block geometry parameters demonstrates its superiority compared with some well-known IMs by having the smallest hybrid ratio and coefficient of variation, as well as good robustness of the overturning fragility curves against the change of the analysis strip width.