## 3 Results and Discussion  
Based on the spectral displacement demands obtained from nonlinear time history analysis using the seven foreshocks, foreshock fragility functions for low-rise SMRF buildings were created, as shown in Figure 8. As can be seen in Figure 8, the slight damage (D1) tendency rapidly increased after 0.4 g. For example, at 1 g, the exceedance probability of D1 is 60%. Since the foreshock did not induce higher damage states, foreshock fragility function is created only for D1 damage state. After completing foreshock time history analysis, we deployed mainshock time history continuing the analysis, and obtained displacements for respective mainshock time histories. Thus, the spectral displacements were achieved as the combined displacements due to foreshock and mainshock time histories. We constructed fragility functions for combined displacement demands for the four damage states, as shown in Figure 9. When mainshock time history is deployed, vulnerability of low-rise SMRF buildings is found to be significantly increased. For instance, D1 is initiated at \(\sim\)0.18 g, D2 at \(\sim\)0.25 g, D3 at \(\sim\)0.35 g, and D4 is initiated at 0.4 g. Figure 9 highlights that at 1 g, exceedance probabilities of D1, D2, D3, and D4 are, respectively, 95%, 70%, 45%, and 20%. This indicates that if the foreshock-mainshock sequence is considered, the exceedance probability of D4 is 18% higher than that for the foreshock-only scenario. On the contrary, the discrepancy in D1 is \(\sim\)35%. Similarly, D2 and D3 are the most fluctuated damage states when foreshock-mainshock sequence is considered. Hinge formation will be rapid when post-foreshock analysis is deployed; thus, D2 and D3 should have experienced more fluctuation. When foreshock-mainshocksequence is considered, low-rise SMRF buildings have 100% exceedance probability to D1 after 1.4 g. At the same spectral acceleration, D4 has 50% exceedance probability. We also performed post-aftershock-mainshock sequence time history analysis, deploying respective aftershocks to obtain displacement demand due to foreshock-mainshock-aftershock sequence. The fragility functions for the four damage states due to foreshock-mainshock-aftershock sequence are plotted in Figure 10. Figure 10 highlights that vulnerability of a low-rise SMRF building is increased after the introduction of aftershock time  
Figure 8: Foreshock fragility functions for low-rise SMRF buildings. Figure 9: Foreshock and mainshock fragility functions for low-rise SMRF buildings. history. However, the increase in vulnerability is lower in the post-mainshock compared to the increase in the post-foreshock scenario. When aftershock is included, exceedance probabilities of D1, D2, D3, and D4 are, respectively, 98%, 80%, 55%, and 30% at 1 g spectral acceleration. Additionally, initiation of each damage state occurred at lower spectral acceleration value when compared to foreshock-mainshock sequence. As existing seismic codes do not comply with the seismotectonics that usually result in earthquake sequence, the comparison between fragility functions due to foreshock only, foreshock-mainshock sequence, and foreshock-mainshock-aftershock sequence, as plotted in Figure 11, clearly depict that vulnerability will be undeniably increased while adding one more strong motion. Post-aftershock sequence or post-mainshock sequence analysis are found to be further critical as highlighted by a notable increase in the probability of exceedance in each damage state. Figure 11 quantifies the variation in exceedance probabilities for each damage state in the case of foreshock, foreshock-mainshock, and foreshock-mainshock-aftershock scenarios, which is rare, if not absent, in the existing literature. The mainshock may govern the majority of hinge mechanisms so that the increase in vulnerability due to aftershocks is found to be somehow steady.