Mainshock Aftershock Research Articles

Characterization of Swarm and Mainshock–Aftershock Behavior in Puerto Rico

Abstract The recent Indios, Puerto Rico earthquake sequence has drawn attention, as the increased seismicity rate in this area was unprecedented. The sequence began on 28 December 2019, caused a 6.4 magnitude earthquake on 7 January 2020, and remained active over a year later. This sequence fits the nominal definition of an earthquake swarm in that it had an abrupt onset, a sustained high rate of seismicity without a clear triggering mainshock or evidence for Omori decay, and a lack of adherence to Bath’s law. However, the sequence also had several prominent mainshock–aftershock (MS–AS) sequences embedded within it. We applied three-station waveform cross correlation to the early part of this sequence using the Puerto Rico Seismic Network (PRSN) catalog as templates, which confirmed the mixture of swarm and MS–AS patterns. In an effort to place this intriguing sequence in the context of the previous seismicity in Puerto Rico, we investigated the existence of swarms and MS–AS sequences recorded by the PRSN since 1987 by identifying sequences with increased seismicity rate when compared to the background rate. About 59 sequences were manually verified and characterized into swarms or MS–AS. We found that 58% of the sequences follow traditional swarm patterns and 14% adhere to traditional MS–AS behavior, whereas 29% of the sequences have a mixture of both swarm and MS–AS behaviors. These findings suggest that it is not unusual for the Indios sequence to have a mixture of both the characteristics. In addition, the detection of many swarms distributed over a broad area of the subduction interface indicates stress heterogeneity and low-coupling consistent with prior studies indicating that the potential for a magnitude ∼8 megathrust earthquake along the Puerto Rico trench is unlikely.

Analysis of the 2021 Semangko Bay Earthquake Sequence in Southern Sumatra, Indonesia, Using Broadband Seismic Network Data

Abstract Beginning on 30 June 2021, hundreds of earthquakes were detected beneath Semangko Bay in southernmost Sumatra, which is located adjacent to the Sunda Strait, a narrow sea passage that separates the islands of Java and Sumatra. A number of these earthquakes were large enough to be felt by people living in the city of Lampung, some 100 km to the east. In terms of magnitude and temporal distribution, the earthquakes did not follow a typical mainshock–aftershock sequence because the onset was marked by a cluster of five earthquakes with local magnitudes that ranged between 4.2 and 4.6, followed by a rapid decay in the number of detected events. We have relocated 254 of the 258 earthquakes that were recorded between 30 June and 14 July 2021, with a local magnitude range between ML 0.9 and 4.6, using the double-difference relocation method (hypoDD); focal mechanisms were also determined for a subset of events with a magnitude >4. Our results show that the seismicity pattern and focal mechanism solutions are more consistent with a multiple event episode caused by the rupture of several antithetic faults that have a similar strike to the west Semangko fault in southernmost Sumatra rather than a single fault plane. These faults appear to be part of a small graben system located beneath Semangko Bay, which was likely activated by ongoing extension in the Sunda Strait.

Seismic vulnerability assessment of tall pier bridges under mainshock-aftershock-like earthquake sequences using vector-valued intensity measure

In most current seismic investigations on bridges with tall piers, only mainshock actions are considered without incorporating the effect of mainshock-aftershock (MA) sequences. This paper investigates the seismic fragility and the associated direct financial losses of tall pier bridges subjected to MA sequences using the vector-based intensity measure considering both main- and after-shocks. Numerical model of a typical RC tall pier bridge is developed and validated through shake table test results. Nonlinear time-history analyses are extensively conducted to obtain the seismic responses of the bridge under MA sequences, which are further utilized for the development of fragility surfaces. The analytical results show that in the MA sequences, the contribution of the aftershocks to the peak structural seismic demands is basically negligible unless their intensities exceeding critical values. While the structural vulnerabilities increase with both the intensities of main- and after-shocks, the role of mainshocks is observed more substantial. On the other hand, however, by totally neglecting the effect of the aftershocks, the failure probability and financial loss of the tall bridge would be underestimated, particularly when strong aftershocks occur following mainshocks.

Seismic behavior of RC moment resisting structures with concrete shear wall under mainshock–aftershock seismic sequences

A structure may be subject to several aftershocks after a mainshock. In many seismic design provisions, the effect of the seismic sequences is either not directly considered or has been underestimated. This study examined the seismic behavior of reinforced concrete (RC) moment-resisting structures with concrete shear walls under seismic sequences. Two three-dimensional structures of short and medium height were designed and analyzed under seven real mainshock–aftershock seismic sequences. The models were loaded and designed according to the Iranian seismic code (4th ed.; Standard No. 2800) and ACI-318. The structures were analyzed using the nonlinear explicit finite element method. The maximum displacement, inter-story drift ratio, residual displacement, and ratio of aftershock PGA to mainshock PGA were investigated and assessed. Because of the high lateral stiffness of the shear walls in addition to their completely elastic behavior, the aftershocks did not increase the inter-story drift ratio or relative displacement in the short structure model. The medium height model under the seismic sequences showed a significant growth in the relative displacement (roughly 25% in some cases), inter-story drift ratio, plastic strain, and residual displacement (42.22% growth on average) compared to the structure that was only subjected to the mainshock. Remarkably, in some cases, the aftershock doubled the residual displacement. Unlike the moment-resisting frames under seismic sequences, the models showed no significant growth in the drift ratio with an increase in height. Assessments indicated that the ratio of aftershock PGA to mainshock PGA is a determinative parameter for structural behavior under seismic sequences, such that high values of this ratio (> 0.6) caused significant increases in the residual and relative displacements.

The Seismogenic Structure of the 2017 Mw 6.9 Milin, Tibet, Earthquake: A Possible Newly Active Fault at the Eastern Himalayan Syntaxis

AbstractOn 18 November 2017, an Mw 6.9 earthquake occurred in Milin, Tibet, with the epicenter at the top of the Namche Barwa syntaxis. This event did not produce surface ruptures, and its seismogenic structure remains unclear or controversial. Using the locations of the Milin mainshock and aftershocks, locations of regional small earthquakes and focal mechanism solutions from 2007 to 2009, this work analyzed the causative fault and tectonic setting of the Milin earthquake and assessed the regional seismic risk. The results suggest that the seismogenic structure of the Milin earthquake was a secondary fault, the southern branch of the XiXingla fault (XXLF). Within 28 hr after the mainshock, the aftershocks of the Milin event spread northeastward to the secondary north branch fault of the XXLF and the secondary south branch fault of the Palong–Pangxin fault. Across the top of the Namche Barwa syntaxis (Namche Barwa block) and the Chayu block in the southeast, an earthquake dense belt (EDB) has developed. This EDB has similar deep structures beneath the two blocks, in which several northeast-dipping structural planes exit, and different portions of the EDB imply a unified tectonic stress field. Combining these data with the foreshock–mainshock–aftershock data for the 1950 Mw 8.6 Chayu, Tibet, earthquake, we speculate that the structural planes produced by the EDB at depth in the two blocks have already been connected or tended to connect, resulting in a new fault system trending northwest and approximately 280 km long. The 2017 Mw 6.9 Milin earthquake occurred at the northwestern end of this fault system. At present, the development stage, maturity, and fine structure of this new fault system remain unclear but should receive additional attention. Based on its maximum rupture area, this new fault system is capable of generating an Mw 7.7 earthquake in the future.

Experimental investigation on the damage accumulation of reinforced concrete columns under mainshock‐aftershock sequences

AbstractThis paper presents the details and results of shaking table tests conducted on six 1/3‐scaled reinforced concrete columns subjected to mainshock‐aftershock (MSAS) ground motions. For each of the two subsets distinguished by the axial compression ratio in the test matrix, one column specimen was subjected to a standard cyclic loading protocol, whereas the second specimen was subjected to a mainshock ground motion record followed by a standard cyclic loading protocol. The third specimen was subjected to MSAS ground motion records followed by a standard cyclic loading protocol. The cyclic loading protocol was used to examine the degradation of the seismic capacity of the specimens. The intensity of the aftershock ground motion record was 0.68 times that of the mainshock ground motion record. The test results indicated that the damage accumulation of columns induced by the MSAS sequence is significant in the shaking table tests, and the MSAS‐induced maximum displacement of the specimen with an axial compression ratio of 0.4 was approximately twice as large as that induced by mainshock only. In comparison with the mainshock only case, the aftershock further reduced the structural strength and stiffness of the specimens by 9% and 7%, respectively. The ductility of the specimens tended to decrease with the increase of damage. The damage accumulation of the column with a higher axial compression ratio was more serious than that observed in a column with a lower axial compression ratio.

ETAS-Approach Accounting for Short-Term Incompleteness of Earthquake Catalogs

ABSTRACT The epidemic-type aftershock sequence (ETAS) model is a powerful statistical model to explain and forecast the spatiotemporal evolution of seismicity. However, its parameter estimation can be strongly biased by catalog deficiencies, particularly short-term incompleteness related to missing events in phases of high-seismic activity. Recent studies have shown that these short-term fluctuations of the completeness magnitude can be explained by the blindness of detection algorithms after earthquakes, preventing the detection of events with a smaller magnitude. Based on this assumption, I derive a direct relation between the true and detectable seismicity rate and magnitude distributions, respectively. These relations only include one additional parameter, the so-called blind time Tb, and lead to a closed-form maximum-likelihood formulation to estimate the ETAS parameters directly accounting for varying completeness. Tests using synthetic simulations show that the true parameters can be resolved from incomplete catalogs. Finally, I apply the new model to California’s most prominent mainshock–aftershock sequences in the last decades. The results show that the model leads to superior fits with Tb decreasing with time, indicating improved detection algorithms. The estimated parameters significantly differ from the estimation with the standard approach, indicating higher b-values and larger trigger potentials than previously thought.

Development of fragility surfaces for reinforced concrete buildings under mainshock‐aftershock sequences

AbstractA single intensity measure (IM) is commonly used to develop fragility curves for structures subjected to mainshock‐aftershock (MS‐AS) scenarios. This study aims to propose a framework to develop MS‐AS fragility surfaces by characterizing the MS‐AS sequences with two IMs. To do this, the well‐known Park & Ang damage index, which increases monotonically with the ground motion duration, is adopted to represent the accumulative structural damage during sequential excitations. The MS‐AS accumulative damage of structures is thus represented by the combination of the initial damage caused by MS and the incremental damage caused by AS. Based on total probability theorem, the process of assessing MS‐AS fragility is consequently divided into two parts, namely the MS fragility assessment and the AS fragility assessment, respectively, where the cases of dynamic instability are considered. The proposed framework is illustrated using a typical four‐story reinforced concrete frame building. The peak ground velocity values of both MS and AS are taken as the representative IMs for the MS‐AS sequences. The fragility results for MS only and MS‐AS sequences are compared to scrutinize the effects of AS on structural damage. It is found that the MS‐AS sequence can cause significantly larger exceedance probabilities of limit states compared to the MS only. The MS‐AS sequence also leads to a reduction of the MS‐AS fragility median conditioned on a given AS intensity. Such reduction increases with the increase of the AS intensity.

Prediction of spectral accelerations of aftershock ground motion with deep learning method

Ground motion prediction equations (GMPEs) are crucial for the seismic hazard analysis of infrastructures. Currently, nearly all GMPEs are designed to predict only mainshock; in addition, they are generally based on a pre-assumed function form for data fitting. Historical earthquake records show that the mainshock (MS) is always followed by several aftershocks (ASs), aggravating the structural damage caused by the MS. The direct application of the traditional earthquake-oriented GMPE to predict ASs may not properly reflect their spectral characteristics and relationship with the MS. All pre-defined functions are generally low-order functions, i.e., they include limited number of variables. The newly emerged deep learning method is a powerful tool for revealing and presenting correlations among high-dimensional variables. Thus, the deep learning method was used as a GMPE to predict the spectral accelerations (Sa) of aftershocks in this study. Two popular networks (the deep neural network (DNN) and conditional generative adversarial network (CGAN)) were adopted to build the prediction model. Eight seismic variables and Sa of the mainshock at 21 periods were used as inputs for the deep learning model, and the Sa of the aftershocks at 21 periods were the outputs. A total of 503 sets of MS–AS records were used to develop the model, and the prediction results were compared with real data and that obtained by traditional GMPEs. The comparisons indicated that the deep learning model is a promising tool for predicting the Sa of aftershocks, and the CGAN model is slightly better than the DNN model because of the former's random nature in the generation of new data.

Comparative Study on Seismic Fragility Assessment of Self-Centering Energy-Absorbing Dual Rocking Core versus Buckling Restrained Braced Systems under Mainshock–Aftershock Sequences

AbstractA strong mainshock may cause several aftershocks within a short interval. These aftershocks can make buildings damaged during the mainshock more vulnerable to collapse. Hence, it is critica...

An investigation of the structural nonlinearity effects on the building seismic risk assessment under mainshock–aftershock sequences in Tehran metro city

This research attempts to investigate the effects of neglecting the nonlinear behavior of structures on the estimated seismic risk assessment of buildings under mainshock–aftershock (MA) sequences. In this regard, the Tehran metro city is selected as a building site due to its high seismicity level. Three separate 5-, 10-, and 15-story buildings are considered and designed based on international design codes. The earthquake hazard scenarios containing mainshock–aftershock sequences are modeled randomly using a synthetic stochastic methodology for this region. Next, by implementing the Monte Carlo simulation method, buildings performances are obtained for a large number of different scenarios, and consequently, the lifetime direct losses imposed on the buildings are evaluated. To investigate the effect of structural nonlinearity, the described process is performed in two distinct scenarios: one of them assumes that the buildings behave linearly, while the other one allows the structures to respond nonlinearly. Finally, the level of dependency of calculated lifetime seismic risk to this parameter and also the contribution of different sources of losses, including physical damage, business interruption, and casualty losses, are investigated considering the aftershocks effect.

Near-Fault Monitoring Reveals Combined Seismic and Slow Activation of a Fault Branch within the Istanbul–Marmara Seismic Gap in Northwest Turkey

Abstract Various geophysical observations show that seismic and aseismic slip on a fault may occur concurrently. We analyze microseismicity recordings from a temporary near-fault seismic network and borehole strainmeter data from the eastern Marmara region in northwest Turkey to track seismic and aseismic deformation around the hypocentral region of an Mw 4.5 earthquake in 2018. A slow transient is observed that lasted about 30 days starting at the time of the Mw 4.5 event. We study about 1200 microseismic events that occurred during 417 days after the Mw 4.5 event around the mainshock fault rupture. The seismicity reveals a strong temporal clustering, including four episodic seismic sequences, each containing more than 30 events per day. Seismicity from the first two sequences displayed typical characteristics driven by aseismic slip and/or fluids, such as the activation of a broader region around the mainshock and swarm-like topology. The third and fourth sequences correspond to typical mainshock–aftershock sequences. These observations suggest that slow slip and potentially fluid diffusion along the fault plane could have controlled the seismicity during the initial 150 days following the Mw 4.5 event. In contrast, stress redistribution and breaking of remaining asperities may have caused the activity after the initial 150 days. Our observation from a newly installed combined dense seismic and borehole strainmeter network follows an earlier observation of a slow transient occurring in conjunction with enhanced local seismic moment release in the same region. This suggests a frequent interaction of seismic and aseismic slip in the Istanbul–Marmara seismic gap.

Probabilistic demand models and fragilities for reinforced concrete frame structures subject to mainshock-aftershock sequences

This paper presents a formulation for developing seismic demand models and estimating fragilities for reinforced concrete (RC) structures under mainshocks (MSs) only and mainshock-aftershock (MS-AS) sequences. The demand model for the MS only is a function of the MS intensity, while the model for the MS-AS sequence is a function of two variables, one describing the MS and one describing the AS. A Bayesian method is used to calibrate the demand models. The demand models are then used to estimate the fragility of RC structures. Predictive fragility curves are developed to include the uncertainties in the model parameters estimated by Bayesian approach, and confidence bounds of the fragility curves are developed to separate the effects of the uncertainty in the model parameters from the other sources of uncertainties. The proposed formulation is illustrated using a typical five-story RC frame building. The results show that the fragility curves for MS only tend to significantly underestimate the fragility curves for MS-AS sequences. Also, the uncertainty in the fragilities for the MS-AS sequence is, as expected, larger than that considering only the MS.

Seismic Reflection Images of Possible Mantle-Fluid Conduits and Basal Erosion in the 2011 Tohoku Earthquake Rupture Area

Multi-channel seismic reflection and sub-bottom profiling data reveal landward-dipping normal faults as potential conduits for mantle-derived fluids in the coseismic slip area of the 2011 Tohoku earthquake (Mw9.0). Normal faults below the helium isotope anomaly sites appear to develop through the forearc crust (i.e., the seafloor sedimentary section and Cretaceous basement) and to evolve to lower dip angles as extension progresses deeper, potentially extending down to the mantle wedge, despite their intermittently continuous reflections. The faults are characterized by high-amplitude, reverse-polarity reflections within the Cretaceous basement. Moreover, deep extension of the faults connecting to a low-velocity region spreading from the Cretaceous basement into the mantle wedge across the forearc Moho suggests that the faults are overpressured by local filling with mantle-derived fluids. The locations of the normal faults are roughly consistent with aftershocks of the 2011 Tohoku earthquake, which show normal-faulting focal mechanisms. The 2011 Tohoku mainshock and subsequent aftershocks can lead the pre-existing normal faults to be reactive and more permeable so that locally trapped mantle fluids can migrate up to the seafloor through fault fracture zones. The reactivated normal faults may be an indicator of shallow coseismic slip to the trench. Locally elevated fluid pressures can decrease the effective normal stress for the fault plane, facilitating easier slip along the fault and local tsunami. The landward-dipping normal faults developing from the seafloor down into the Cretaceous basement are predominant in the middle slope region of the forearc. A possible shear zone with high-amplitude, reverse-polarity reflections above the plate interface, which is almost localized to the middle slope region, suggests more intense basal erosion of the overlying plate in that region.

Fault‐Valve Behavior Estimated From Intensive Foreshocks and Aftershocks of the 2017 M 5.3 Kagoshima Bay Earthquake Sequence, Kyushu, Southern Japan

AbstractDetermining fluid migration and pore pressure change within the Earth is key to understand earthquake occurrences. We investigated the spatiotemporal characteristics of the intense foreshocks and aftershocks of the 2017 ML 5.3 earthquake in Kagoshima Bay, Kyushu, southern Japan, to examine the physical processes governing this earthquake sequence. Our relocated hypocenters show the foreshocks moved on a sharply defined plane with a steep dip. The mainshock rupture initiated at the edge of the foreshock seismic gap. The size of the foreshock seismic gap is comparable to that of the mainshock estimated from the source corner frequency, suggesting this seismic gap corresponds to the large slip region of the mainshock. The aftershocks migrated upward along several steeply dipped planes with a seismicity pattern that deviated from the typical mainshock–aftershock type. This deviation of seismicity pattern, together with the hypocenter migrations, suggests aseismic processes, such as pore pressure migration and aseismic slip, affected this earthquake sequence. We established the following hypothesis. First, fluids originating from the subducting slab migrated upward and intruded into the fault plane, reducing the fault strength and causing the foreshock sequence and potentially aseismic slip. Second, the mainshock rupture occurred due to the decreased fault strength and the increased shear stress in an area with relatively high strength. Third, pore pressure increase associated with post‐failure fluid discharge caused the upward aftershock migration. These observations are consistent with the fault‐valve model and show the importance of fluid movement at depth not only in earthquake swarms but also in foreshock–mainshock–aftershock sequences.

Seismic vulnerability assessment of ageing reinforced concrete structures under real mainshock-aftershock ground motions

Ageing structures located in moderate to high seismicity regions are exposed to multiple natural stressors during their lifetime. Large earthquake events coupled with environmental aggressive agents increase the progressive failure probability of these structures. The accumulated damage during the main earthquake event might be exacerbated by its following aftershocks. This might result in catastrophic failure of these structures, and consequently, result in several socio-economic losses. Taking such progressive deterioration mechanism into consideration, the current study presents a framework to assess the vulnerability of ageing Reinforced Concrete (RC) frames subject to real Mainshock-Aftershock (MS-AS) ground motion sequences. Employing an advanced fibre-based finite element modelling technique, the nonlinear static and dynamic behaviour of a case-study RC frame with various ages is simulated under 48 real MS-AS record pairs. Quantifying corrosion-variant damage states, the age-specific fragility curves are developed for the considered structure under both single MS events and MS-AS sequences. It was found that the severely corroded RC frames are most likely to collapse before the second event comes up. Moreover, results show that the PGA ratio of AS to MS plays a critical role in seismic vulnerability assessment of highly corrosion-damaged RC frames.

The Productivity of Cascadia Aftershock Sequences

ABSTRACTThis study addresses questions about the productivity of Cascadia mainshock–aftershock sequences using earthquake catalogs produced by the Geological Survey of Canada and the Pacific Northwest Seismic Network. Questions concern the likelihood that future moderate to large intermediate depth intraslab earthquakes in Cascadia would have as few detectable aftershocks as those documented since 1949. More broadly, for Cascadia, we consider if aftershock productivities vary spatially, if they are outliers among global subduction zones, and if they are consistent with a physical model in which aftershocks are clock-advanced versions of tectonically driven background seismicity. A practical motivation for this study is to assess the likely accuracy of aftershock forecasts based on productivities derived from global data that are now being issued routinely by the U.S. Geological Survey. For this reason, we estimated productivity following the identical procedures used in those forecasts and described in Page et al. (2016). Results indicate that in Cascadia we can say that the next intermediate depth intraslab earthquake will likely have just a few detectable aftershocks and that aftershock productivity appears to be an outlier among global subduction zones, with rates that on average are lower by more than half, except for mainshocks in the upper plate. Our results are consistent with a clock-advance model; productivities may be related to the proximity of mainshocks to a population of seismogenic fault patches and correlate with background seismicity rates. The latter and a clear correlation between productivities with mainshock depth indicate that both factors may have predictive value for aftershock forecasting.

The Productivity of Cascadia Aftershock Sequences

ABSTRACT This study addresses questions about the productivity of Cascadia mainshock–aftershock sequences using earthquake catalogs produced by the Geological Survey of Canada and the Pacific Northwest Seismic Network. Questions concern the likelihood that future moderate to large intermediate depth intraslab earthquakes in Cascadia would have as few detectable aftershocks as those documented since 1949. More broadly, for Cascadia, we consider if aftershock productivities vary spatially, if they are outliers among global subduction zones, and if they are consistent with a physical model in which aftershocks are clock-advanced versions of tectonically driven background seismicity. A practical motivation for this study is to assess the likely accuracy of aftershock forecasts based on productivities derived from global data that are now being issued routinely by the U.S. Geological Survey. For this reason, we estimated productivity following the identical procedures used in those forecasts and described in Page et al. (2016). Results indicate that in Cascadia we can say that the next intermediate depth intraslab earthquake will likely have just a few detectable aftershocks and that aftershock productivity appears to be an outlier among global subduction zones, with rates that on average are lower by more than half, except for mainshocks in the upper plate. Our results are consistent with a clock-advance model; productivities may be related to the proximity of mainshocks to a population of seismogenic fault patches and correlate with background seismicity rates. The latter and a clear correlation between productivities with mainshock depth indicate that both factors may have predictive value for aftershock forecasting.

Seismic collapse assessment of steel plate shear walls considering the mainshock–aftershock effects

This study evaluates the effect of mainshock–aftershock sequences on the collapse of steel plate shear wall (SPSW) systems. For this purpose, three 9-, 14- and 20-story SPSWs are selected considering the practical range of heights used in this system. After numerical modeling of the structures, they are initially subjected to static-pushover analyses to evaluate their plastic behavior in large inelasticity regions. The incremental dynamic analysis is subsequently performed to capture the collapse capacity of the structures under aftershock excitations preceded by mainshocks that pose various levels of damage expressed in terms of maximum inter-story drift (MID). Evaluation of the median collapse capacities under aftershock excitations exhibit the same reduction ratios at similar mainshock MIDs for the different structures. This reduction is predicted via a quadratic polynomial for given mainshock MID values. Investigation of the mainshock-aftershock effects on distribution of the MIDs and maximum ductility demands at the collapse state shows that the prior mainshock damage mainly affects the collapse capacity by consuming the energy-absorption capacity of the infill plates, thus causing strength deterioration. Irrespective of the mainshock damage level, the structures were found to collapse when their first-story columns reach a threshold softening level.

Mainshock–aftershock low-cycle fatigue damage evaluation of performance-based optimally designed steel moment frames

Considering the widespread damages of connections in steel moment frame (SMF) structures due to destructive earthquakes, seismic assessment of these structures for cumulative low-cycle fatigue (LCF) is of utmost importance and must be carefully taken into account in the design process of SMFs. To calculate the LCF damage index for SMFs, the Palmgren-Miner’s rule is applied on the history of relative drift of the stories based on non-linear response history analysis and existing experimental fatigue curves. On the other hand, repeated earthquakes strongly affect the inelastic response of structures and can increase building vulnerability. Therefore, the primary objective of this study is to numerically assess the mainshock-aftershock LCF damage index for performance-based optimally designed SMFs. Two illustrative design examples of 6- and 12-story SMFs are presented and designed for optimal initial and total costs in the context of performance-based design. The LCF damage index is evaluated for these structures by conducting nonlinear response-history analysis for a suite of real strong multiple earthquakes. The results showed that the optimally designed SMFs are highly vulnerable against LCF damage due to mainshock-aftershock seismic sequences. Subsequently, a simple procedure is proposed to increase the safety of optimally designed SMFs against the LCF damage. To this end, performance-based optimization process is performed for 6- and 12-story SMFs by considering higher seismic confidence levels and the results demonstrate the effectiveness of this strategy in controlling the LCF damage of SMFs caused by seismic sequences.