Hysteretic energy-based state-dependent fragility for ground motion sequences

A framework to derive state‐dependent fragility relationships of structures subjected to ground‐motion sequences (e.g. mainshock‐aftershock (MS‐AS) or triggered earthquakes) is proposed. The hysteretic energy dissipated in the sequence is adopted as the main demand parameter, as it is a cumulative measure monotonically increasing with the length of the excitation. For a structure subjected to earthquake‐induced ground motions, it is not possible to define a closed‐form representation of the hysteretic energy as a function of the peak deformation. However, based on theoretical considerations, the hysteretic energy‐peak deformation trend is discussed, highlighting that (a) the significant duration of the ground motion explains the variability of the hysteretic energy for a given peak deformation; (b) the hysteretic energy dissipated in an AS decreases (for a given AS peak displacement) if the peak displacement in the MS increases. A vector‐valued probabilistic seismic demand model consistent with these considerations is proposed in the form of a surface relating the hysteretic energy in the sequence to the peak deformation in the MS and a ground‐motion intensity measure of the AS. This is calibrated via sequential cloud‐based time‐history analyses. The framework is demonstrated for 14 reinforced concrete frame buildings with different height, plastic mechanisms, and infill distributions. The results show the feasibility of the proposed approach, effectively capturing damage accumulation without inconsistencies in the obtained statistical model. The framework may be used for risk‐assessment applications explicitly incorporating ground‐motion sequences. The hysteretic energy versus peak deformation relationship may also be exploited in problems involving long‐duration ground motions or soft soils.