## 2 Mainshock-Aftershock Sequences  
Previous studies [24; 25; 26] have shown that the characteristics, such as amplitudes, duration, and frequency contents, of the mainshock are seismologically distinct from those of their aftershocks. These distinctions originate from physical mechanisms governing stress redistribution and fault zone adjustments following the mainshock rupture. Crucially, such physics-based correlations between mainshocks and aftershocks are inherently difficult to replicate in artificial sequences generated through repeated scaling or stochastic superposition methods [29; 30]. Empirical evidence highlights systematic flaws in synthetic approaches. [PERSON] and [PERSON] [29] and [PERSON] and [PERSON] [30] demonstrated that synthetic sequences artificially enforce spectral compatibility between aftershocks and mainshock-damaged structures, thereby triggering unphysical resonance effects. Such computational artifacts evidently amplify structural responses compared to real sequences, distorting risk evaluations. To overcome these limitations, this study intentionally adopts as-recorded sequences. It should be noted that while individual as-recorded sequences exhibit scatter due to natural seismological variability, their collective behavior adheres to deterministic physical principles. The statistics of mainshock and aftershock scenarios indicate that, in general, a strong mainshock triggers a series of aftershocks with smaller magnitudes. However, a portion of the aftershock ground motion has not been recorded at that time for numerous reasons (e.g., seismometer failure, shock too slight to be detected), thus resulting in the as-recorded dataset being incomplete [30]. In addition, a strong aftershock is more inclined to aggravate the damage to the structure than a small aftershock [39; 40]. For simplicity, this study mainly focuses on the case of the mainshock with the strongest aftershock, hereafter referred to as the mainshock-aftershock sequence. In this investigation, the mainshock-aftershock sequences are selected from the Pacific Earthquake Engineering Research Center (PEER) ground motion database [47]. All earthquake records meet the following criteria: (1) the moment-magnitude (\(M_{\rm w}\)) of the mainshock is no less than 5.5, and the \(M_{\rm w}\) of the aftershock is no less than 5.0; (2) the peak ground acceleration (\(PGA\)) of the mainshock is no less than 0.10 g, and the \(PGA\) of the aftershock is no less than 0.05 g; (3) ground motions recorded on soft soil sites (i.e., the average shear-wave velocity \(v_{\rm s,30}\) is no less than 180 m/s in the upper 30 m of the site profile) or exhibiting distinct velocity pulse characteristics are excluded; (4) recording stations are located in free-field sites or within first-floor low-rise buildings where soil-structure interaction effects can be neglected. According to the aforementioned criteria, an ensemble of 144 mainshock-aftershock sequences (considering both horizontal components) recorded from 12 earthquake events is selected in this study. Each sequence comprises a mainshock paired with its predominant aftershock. The details of all seismic sequences, including \(v_{\rm s,30}\), \(M_{\rm w}\), \(PGA\), distances to horizontal projection of rupture (\(R_{\rm rup}\)) and peak ground velocity (\(PGV\)), are summarized in Appendix A. To precisely determine residual displacements under seismic sequences, a 50 s zero-acceleration interval is inserted both between the mainshock-aftershock transition and at the sequence termination. This ensures that structural vibrations fully subside before displacement measurements. Figure 1 illustrates three samples of as-recorded mainshockaftershock sequences (the 1972 Managua earthquake, the 1983 Coalinga earthquake, and the 1994 Northridge earthquake) after padding zero-acceleration time history. Using the processed earthquake sequences, the nonlinear time-history analysis (NTHA) can be performed to calculate the residual displacement response.