## 1 Introduction  
Past large earthquake events, such as the 1999 Chi-Chi earthquake [1], the 2008 Wenchuan earthquake [2], and the 2011 Tohoku earthquake [3] have shown that structures located in seismically active regions are commonly exposed to sequential-type excitations during a strong earthquake event. The cascading effects of mainshock (MS) and the following aftershocks (AS) could lead to a significant accumulation of structural damage, which tends to make a structure vulnerable to severe damage and even collapse. Nevertheless, current seismic design codes usually consider the design earthquake as a single event only, yet neglecting the detrimental effects caused by MS-AS sequences. Therefore, it is important to estimate the cumulative damage of structures under MS-AS sequences in an appropriate way, for accurately evaluating their dynamic performance subjected to a major earthquake event. In recent years, numerous studies have been conducted to evaluate structural damage caused by MS-AS sequences using single-degree-of-freedom (SDOF) systems. These studies could be traced back to [PERSON] [4] who first examined the inelastic response of a SDOF system under a specific MS-AS sequence consisting of one MS and two ASs. It was reported that the ASs could lead to a significant increase in structural inelastic deformation and energy dissipation. After that, various structural performance indicators, e.g., peak displacement response [5; 6; 7], behavior factor [8; 9], ductility demand [8; 10; 11; 12; 13], input energy [14], damage index [15], and collapse capacity [16], have been adopted to examine the AS effect by subjecting SDOF systems to a suite of real [11; 12] or artificial [8; 9; 10; 11; 15; 16] MS-AS sequences. Recently, multiple degree of free dom systems (MDOFs) have been used to investigate the structural damage caused by MS-AS sequences; the studied structures include steel frames [17] bare and infilled reinforced concrete frames [18; 19; 20], wood structures [21], equipped structures [22], bridges [23] and other kind of structure [24]. The aforementioned studies compare the structural damage under MSs alone and MS-AS sequences, showing the significant effect of aftershocks on structural performance under earthquakes. Accurate prediction of the damage potential of an earthquake has always been a well concerned issue in earthquake engineering [25]. To estimate the earthquake damage potential, it is necessary to introduce two intermediate variables, one representing the strength or severity of the earthquake and the other describing the actual damage or destructiveness due to the earthquake. Therefore, investigation of the interdependence between the earthquake intensity measures (IMs) and the structural damages plays a core role in the prediction of earthquake damage potential. An IM with a close dependence on structural damage can well reflect the damage potential of an earthquake. In recent years, different IMs have been linked with various structural damage indices to examine their correlation levels [26; 27; 28; 29; 30; 31; 32]. These studies have reported that the correlation between IMs and structural damage is affected by many factors, including the near- or far-fault ground motions [33; 34], dimensionality of earthquake inputs [35; 36], structural properties [37], and structural damage indicators adopted [38]. Due to the complex characteristics of ground motions, no IM alone can be regarded as the optimal one for assessing earthquake damage potential. Recently, several advanced IMs have been developed by combining classic IMs together to improve the capability of predicting damage potential [39; 40; 41]. In the studies stated above, however, the focus is mostly attached on the damage potential of single earthquake events without accounting for the effect of sequential earthquakes. In other words, the damage potential for the MS-AS sequences has not been paid adequate attention as that for the MSs alone. Recently, [PERSON] et al. [42] and [PERSON] et al.