Identifying Optimal Intensity Measures for Predicting Damage Potential of Mainshock–Aftershock Sequences

Large earthquakes are followed by a sequence of aftershocks. Therefore, a reasonable prediction of damage potential caused by mainshock (MS)–aftershock (AS) sequences is important in seismic risk assessment. This paper comprehensively examines the interdependence between earthquake intensity measures (IMs) and structural damage under MS–AS sequences to identify optimal IMs for predicting the MS–AS damage potential. To do this, four categories of IMs are considered to represent the characteristics of a specific MS–AS sequence, including mainshock IMs, aftershock IMs (i.e., IMMS and IMAS, respectively), and two newly proposed IMs through taking an entire MS–AS sequence as one nominal ground motion (i.e., IM1MS–AS), or determining the ratio of IMAS to IMMS (i.e., IM2MS–AS), respectively. The single-degree-of-freedom systems with varying hysteretic behaviors are subjected to 662 real MS–AS sequences to estimate structural damage in terms the Park–Ang damage index. The intensities in terms of IMMS, IMAS, and IM1MS–AS are correlated with the accumulative damage of structures (i.e., DI1MS–AS). Moreover, the ratio (i.e., DI2MS–AS) of the AS-induced damage increment to the MS-induced damage is related to IM2MS–AS. The results show that IM2MS–AS exhibits significantly better performance than IMMS, IMAS, and IM1MS–AS for predicting the MS–AS damage potential, due to its high interdependence with DI2MS–AS. Among the considered 22 classic IMs, Arias intensity, root-square velocity, and peak ground displacement are respectively the optimal acceleration-, velocity-, and displacement-related IMs to formulate IM2MS–AS. Finally, two empirical equations are proposed to predict the correlations between IM2MS–AS and DI2MS–AS in the entire structural period range.