## 1 Introduction  
Many seismic regions worldwide observe a sequence of earthquakes and result in aggravation in terms of damage and fatality, because it is almost impossible to restore structural capacity when seismic events are ongoing. For example, the 2015 Gorkha earthquake in Nepal started on 25 April 2015 (Mw 7.8), and more than 300 aftershocks of local magnitude greater than 4 were recorded until 2019. The mainshock was followed by a magnitude 6.9 event within an hour, by a magnitude 6.7 event on 26 April, and the strongest aftershock occurred on 12 May 2015 (Mw 7.3). Between 25 April and 12 May, the seismic events were so intense that hardly any occupants could enter their houses. Figure 1 shows an example of damage due to the mainshock and the first major aftershock, as well as after the 12 May aftershock of the 2015 Gorkha earthquake in Nepal. Figure 1a shows that the damage grade is D3, whereas, after the 12 May event, the damage grade is D5 per the EMS-98 damage scale [1]. Similar cases of damage caused by the mainshock-aftershock sequence were reported during the 1934 Nepal-Bihar earthquake and the 1833 Nepal earthquake [2]. Foreshocks were not reported during either of the events; however, the 1988 earthquake in eastern Nepal was preceded by a strong foreshock [3]. So far, all the notable earthquakes that originated in the Main Central Thrust (MCT) have shown mainshock-aftershock sequencing; whereas the 1988 Udaypur earthquake that originated from the Main Frontal Thrust (MFT) depicted foreshock-mainshock-aftershock sequence. Similar tectonic activities were reported during the 2016 Central Italy earthquake sequence. On24 August 2016, a magnitude 6.1 foreshock was followed by a magnitude 6.5 event on 30 October 2016 during the central Italy earthquake sequence. Further details regarding damage and vulnerability due to the Central Italy earthquake sequence can be found elsewhere (see, e.g., [4]). Quantification of seismic vulnerability of structures and infrastructures is either confined to a single event or mainshock-aftershock regimes only. Fragility functions are widely used to quantify seismic vulnerability [5]. Similarly, index-based vulnerability analysis is also gaining momentum because this system is faster than analytical approaches [6]. Seismic strengthening in the time window between the mainshock and aftershock or foreshock and mainshock events is almost impossible, thus damage incurred to structures and infrastructures persists until the next event(s), leading to damage aggravation to collapse. Thus, the studies that report a single event or mainshock-aftershock regimes could only underestimate seismic vulnerability, especially in the regions where seismic sequences are expected. [PERSON] and [PERSON] [7] analyzed seismic fragility of low-rise steel moment-resisting frame buildings under single and multiple earthquakes. They concluded that the post-mainshock damage has no significant role in the aftershock resistance capacity. [PERSON] and [PERSON] [8] performed fragility assessment of aging reinforced concrete (RC) buildings under the mainshock-aftershock sequence. They concluded that conventional building codes are highly conservative in assuring seismic safety of RC buildings under earthquake sequence. For ordinary moment-resisting frame RC buildings, a gradual reduction in aftershock collapse capacity was reported under increased mainshock damage level [9]. [PERSON] et al. [10] found an increase in seismic vulnerability of RC buildings when subject to aftershocks. They considered the in-plane and out-of-plane behavior of infill walls [11] and found that the bare frame model results in conservatively higher vulnerability than the infill frame. [PERSON] et al. [12] estimated the damage accumulation of nearly 53% and 134% for mainshock and mainshock-aftershock sequences for 100 years probability for Naples, Italy.