Mainshock–aftershock seismic fragility assessment of civil structures: A state-of-the-art review
Abstract
Sequential seismic events occur worldwide, which impose significant threats to the safety and serviceability of Civil infrastructure, especially buildings and bridges. Fragility functions are imperative to support decision-making tools for potential seismic risk identification and its impact on structural performance during sequential earthquakes. The increasing number of publications shows a notable increase in interest among researchers and the scientific community in this domain. This study presents a systematic review of available resources and techniques for structural performance and fragility evaluation subjected to mainshock–aftershock seismic loading. Efforts have been made to focus on the salient features of various approaches rather than criticizing the mathematical frameworks and associated analysis approaches. Existing knowledge related to the effect of sequential seismic loading on buildings and bridge infrastructures and their fragility estimates is presented concisely. The paper concludes by detailing the opportunities for future developments in the fragility analysis of Civil infrastructure under sequential seismic hazard. This would encourage stakeholders and decision-makers to put into practice their applications for risk mitigation, recovery planning, and well-informed decision-making.
1 INTRODUCTION
Sequential seismic events trigger around the globe where complex tectonic settings exist. In the past several decades, despite the rapid advancement in the knowledge about seismic risk and assessment, the existing seismic design guidelines have overlooked the effect of sequential seismic loading. However, many of the historical major seismic events, such as 1994 Northridge (USA), the 1999 Kocaeli (Turkey), 2011 Tohoku (Japan) and Christchurch (New Zealand), 1997 Umbria–Marche and the 2012 Emilia (Italy), and the more recent 2023 Turkey–Syria earthquakes were followed by significant aftershocks, increasing the damage level, and even some of the structures were pushed to the collapse state.1 The mainshock-damaged structures may not be capable of withstanding the strong aftershock excitation and, therefore, are associated with a higher risk of damage and even collapse.
During sequential seismic events, the collapse of many structures has been reported. Capacity degradation in terms of stiffness and strength loss in the mainshock event makes it more susceptible to aftershock loading. During Umbria–Marche 1997, two sequential mainshocks (M 5.5 and 5.9) were followed by another aftershock of magnitude 5.5 within a month after the mainshocks. Many of the buildings survived the first shock yet got severely damaged in the following aftershocks.2 After the Chi-Chi (1999) earthquake in Taiwan, China, more than 30,000 aftershocks were recorded within 3 months. A mainshock (M 7.6) was followed by the largest aftershock (M 6.5), which resulted in the collapse of many structures that had already withstood the mainshock. A total of more than 8500 buildings were destroyed, and around 6200 buildings were significantly damaged.3 In 1999 the Kocaela and Sakarya regions in Turkey, many of the buildings were damaged during the first shock (M 7.4), which were further pushed to the collapse state by the later event.4 Similarly, the following aftershock in 2011 (M 6.2) after the September 2010 mainshock (M 7.1) severely damaged many buildings in Christchurch city with a total death toll of approximately 180 inhabitants. However, in the following aftershock, less damage was observed in June (M 6.0) and December (M 6.0) 2011, respectively.5 The great Tohoku earthquake in 2011 (M 9.0) jolted the eastern part of Japan, followed by a significant number of aftershocks with large magnitude, resulting in the collapse of many structures. The Wenchuan earthquake (2008) of magnitude 7.9, with approximately eight aftershocks having a magnitude of 6.0–6.5, led to an increase in damage accumulation and even a complete collapse of the structures that already faced a mainshock.6 During the Chile earthquake of magnitude 8.8 in 2010, many aftershocks were reported, which significantly amplified the level of damage in the mainshock-survived structures. Likewise, during the 2016 Kumamoto earthquake (Japan), many structures were pushed into a severe plastic stage, where a foreshock of magnitude 6.0 was followed by two stronger aftershocks having a magnitude of 6.0 and 7.0, respectively. Similarly, in Central Italy (2016),7 Napa (2014) Nepal,8 Alaska (2018),9 and Turkey–Syria (2023),10 many of the mainshock-damaged structures were severely damaged and many turned into rubbles.
As alluded to above, Civil infrastructure is highly expected to experience multiple seismic shocks during their service life. To mitigate the socioeconomic and associated losses, performance evaluation and strengthening of existing bridges and building infrastructure prone to sequential seismic loading are imperative for decision-makers. For the preseismic planning and postseismic response of structures, the probabilistic seismic risk assessment of bridges and buildings is critical, requiring the development of fragility functions. The vast majority of buildings and bridge infrastructure are not designed according to seismic guidelines around the world.11-14 These deficiencies demand the reconsideration of important factors, including (i) the degree of vulnerability of these nonseismically designed infrastructures, (ii) the associated economic impact and loss, and (iii) the selection and prioritization of the performance upgradation along with risk mitigation techniques. The diversity in design approaches, guidelines, and construction practices makes it difficult to adopt a single methodology that applies to different structures around the world. The uncertainties arising from material, structural, and regional variations in seismic characteristics resulted in different approaches to better predicting the seismic vulnerability of Civil structures. Although these different methodologies target a specific purpose and adopt different frameworks, the main objective is to evaluate the seismic response to ensure structural safety and infrastructure management for better decision-making in the aftermath of seismic disaster events.
This study aims to provide a comprehensive review of the existing approaches and highlights a recent trend in the seismic performance evaluation of Civil infrastructure, specifically focusing on buildings and bridges, subjected to sequential seismic events. This paper illustrates a concise and thorough summary, features, and state-of-the-art review of different approaches proposed for sequential seismic loading and structural performance evaluation systematically based on existing literature. To begin with, the importance of sequential seismic events in the structural performance evaluation is reviewed. The following sections describe the concept of fragility functions as a basis for the mainshock–aftershock (MSAS) fragility estimation. This part provides a detailed description of the MSAS fragility analysis of bridges and building structures. The next part of the review summarizes different approaches for the MSAS ground-motion pair selection and appropriate seismic intensity measure (IM) and demand parameter selection for MSAS fragility estimation. The review concludes by summarizing the progress so far that has been made while accounting for critical issues of structural vulnerability, including the effect of strengthening, aging and deterioration, geometrical irregularities, ground motion directionality, and so on. An attempt has been made to cover most of the related aspects in the title domain, making it a comprehensive study yet not an exhaustive study. To the best of the authors' knowledge, no such state-of-the-art study has been conducted so far that summarizes the structural performance of bridges and buildings subjected to sequential seismic loading.
2 SIGNIFICANCE OF SEQUENTIAL SEISMIC LOADING
Structures are prone to accumulation of damage during sequential seismic loading and need to be properly designed to withstand more than a single seismic event in their service life. Current seismic codes for Civil structures allow for appropriate ductility, stiffness, and strength to withstand rare, less frequent, and frequent seismic loads for collapse prevention, critical damage protection, and serviceability limit states, respectively. The seismic vulnerability assessment and performance evaluation of Civil infrastructure can be used to quantify the potential loss associated with prospective catastrophic seismic events. Performance evaluation and design strategies for designing and upgrading critical components in the existing infrastructure will help reduce the likelihood of life and economic loss during high-intensity seismic events. During the last three decades, the assessment of seismic vulnerability and performance of critical infrastructure subjected to sequential seismic events became a topic of research interest, which provides a basis for managing retrofit prioritization and action-oriented mitigation decisions. Figure 1 shows the statistics of research publications in the past few decades related to structural performance subjected to sequential seismic events. An increasing trend in the publication rate shows the growing interest in research and the scientific community in this field. More than 180 well-reputed journals have been published since 2000, which are selected from different refereed journals (Appendix A).
A significant increase in the number of publications was made after 2008, where the number of publications in just 2 years (2009–2010) was almost equal to the total number of publications in the past 7 years (2001–2008). In the period 2019–2021, the number of publications was 31, which exceeded in 2022–2023 to 35, and many more are expected to be published in the following months. These growing indices confirm the growing interest of the research community and Civil infrastructure-related industry stakeholders to look after the existing infrastructure performance and vulnerability quantification under sequential seismic events around the globe.
3 FRAGILITY ANALYSIS CONCEPT
Following the seismic risk assessment framework proposed by Whitman et al.21 the Applied Technological Council (ATC) and Federal Emergency Management Agency (FEMA) push forward the concept and formulation of fragility functions from the application perspective. In 1997, the Hazard United Sates (HAZUS) was developed as a risk assessment tool, which was then extended to multiple hazard scenarios, including earthquakes, hurricanes, and floods.22
Several approaches are proposed in the literature for the derivation of fragility function, which are explicitly applicable to system vulnerability assessment.23-25 These methods are broadly classified as expert-based judgment, empirical, experimental, and analytical approaches as presented in Table 1. The expert-based fragility models involve questioning the field experts to determine the probable estimate of damage in the aftermath of any seismic event.15 In this method, the experts provide their opinion of exceeding each limit state, which makes it possible to develop the fragility curves for each limit state over a range of demand intensity. Since this method is more subjective, very often the judgments are biased and consist of several uncertainties which are not taken into consideration in the final fragility models. Such factors negatively affect the reliability and applicability of judgmental fragility functions. The empirical methods comprise postearthquake structural damage data and field observation reports.26-29 The empirical fragility curves are more realistic; however, it does not apply to general scenarios and is usually associated with a large degree of uncertainty. The lack of consistency in the definition of the limit states and field observation by the inspection teams considerably reduces the reliability of this approach. The analytical methods are based on a simulation that typically relies on numerical structural models to simulate the seismic response of structures. This is commonly adopted when there is no adequate damage data available. The most commonly adopted approaches include elastic spectral analysis, nonlinear static analysis, nonlinear time history analysis (NTHA), incremental dynamic analysis (IDA), and probabilistic seismic demand modeling with the Bayesian approach.18, 20, 30-43 The analytical methods are more reliable and less biased and can consider all types of uncertainties in the analysis. Contrary, this approach is computationally expensive and time-consuming, requiring the definition of the quantitative limit states and selection of the probability distribution functions for the uncertain parameters, which is an additional source of uncertainty. Furthermore, the selection of an appropriate analysis technique is a challenging issue in numerical analysis. The mathematical description of the analytical models facilitates the computational environment for regional risk and resilience quantification, like, HAZUS22 and REDARS.44
| Fragility development method | Features | Drawbacks |
|---|---|---|
| Professional/expert judgment | Easy and simple to implement. Different factors can be considered simultaneously. |
Depending on professional expertise. Highly subjective. Less reliable and biased. |
| Experimental | Consider the actual damage behavior. | Insufficient data. On the basis of qualitative definitions of different damage states. |
| Empirical | Shows the actual vulnerability and real picture of structural performance. | Lack of sufficient data. Deterministic in nature. Poor damage observations. |
| Analytical | Enhanced reliability. Minimal bias. Cope with all types of uncertainties. |
Computationally expensive. Defining the damage states. Selection of appropriate analysis technique. Selection of appropriate probability distribution functions. |
4 MSAS FRAGILITY ANALYSIS
Due to damage accumulation in subsequent seismic events, structural vulnerability aggravates, and the combined effect of sequential loading will be higher than the one caused by mainshock or aftershocks only. Figure 2 illustrates a typical fragility profile for a single seismic event and MSAS sequence. The damage induced by potential aftershocks is not considered explicitly in seismic risk and vulnerability assessment. However, considerable research has been conducted in the past two decades to take into account the additional damage accumulation associated with aftershocks in the seismic vulnerability frameworks. The available guidelines for mainshock-damaged structures are based on performance limits ranging from the onset of damage to complete collapse, where the seismic behavior is assessed by performing a nonlinear static analysis on the prior damaged structure. A synopsis of available studies on MSAS fragility assessment of bridges and buildings infrastructure is presented in Table 2.
| Structural system | Demand parameters | Intensity measure | Reference |
|---|---|---|---|
| Bridge pier | Shear strain demand, flexural deformation | Sa | 46 |
| Displacement ductility | Sa | 47, 48 | |
| Peak drift | PGA | 49 | |
| Peak ductility demand | PGA | 50 | |
| Peak drift | Sa, T1 | 51, 52 | |
| Park and Ang damage index | PGA | 53 | |
| Drift ratio | PGA | 54 | |
| Drift, curvature | Sa, 1.0 | 55 | |
| Displacement ductility | PGA | 56 | |
| Curvature ductility | PGV | 57 | |
| Drift ratio and modified bridge damage index | Sa, T1 | 58 | |
| Park and Ang damage index | PGA | 59 | |
| Bridge pier, bearing, and system | Peak curvature, peak displacement | PGA | 60 |
| RC bridge pier, bearing, abutment, and system | Displacement ductility | PGA | 61 |
| Bridge pier and system | Displacement ductility | Sa, T1 | 62 |
| Precast bridge | Peak displacement at midspan | Sa, T1 | 63 |
| Wood frame | Interstory drift ratio | Sa, 0.3 | 64 |
| Peak drift | Sa | 65 | |
| Story drift | Sa | 66 | |
| RC frame | Interstory drift ratio | Sa, 2.0 | 67 |
| Peak shear strain, interstory drift ratio | Sa, T1 | 68 | |
| Interstory drift ratio | Sdi | 69 | |
| Story drift ratio, peak floor acceleration | Sa, T1 | 70 | |
| Drift | PGA | 71 | |
| Interstory drift ratio | CAV | 72 | |
| Park and Ang damage index | Sa | 73 | |
| Inter story drift | Sa | 74 | |
| Drift ratio | Sa | 75 | |
| Interstory drift ratio | Sa | 76 | |
| Park and Ang damage index | PGV | 77 | |
| Modified Park and Ang damage index | Sa, avg | 78 | |
| Maximum interstory displacement | Modified acceleration spectrum intensity | 79 | |
| Drift ratio | PGA | 80 | |
| Park and Ang damage index | PGA | 81 | |
| Park and Ang damage index | PGV | 82 | |
| Cumulative hysteretic energy | Sa, avg | 83, 84 | |
| RC column | Drift ratio | Sa | 85 |
| Steel frame | Drift ratio | PGA, Sa, CAV | 86 |
| Residual drift ratio | Sa | 87 | |
| Interstory drift ratio | Sa, T1 | 88, 89 | |
| Masonry buildings | Interstory drift ratio | PGA | 90 |
| RC frame with masonry infill | Interstory drift ratio | PGA | 91 |
| Interstory drift ratio | Sa, T1 | 92 |
- Abbreviations: CAV, cumulative absolute velocity; MSAS, mainshock–aftershock; PGA, peak ground acceleration; PGV, peak ground velocity; RC, reinforced concrete; Sa, spectral acceleration.
For the aftershock fragility analysis, mostly the NTHA or IDA is employed with the initial damage state (IDS) associated with the mainshocks.1, 93, 94 The NTHA is the most reliable fragility estimation method despite being the most computationally expensive and employed by many researchers.35, 95-97 This method involves a realistic ground motion suit and can readily estimate the probability of being in a particular DS from the closed form, considering the damage level induced by the mainshock. The basic procedure is graphically illustrated in Figure 3. Using a suitable ground motion data set, the NTHA is performed for each mainshock-damaged bridge sample with a predefined IDS, and the peak response of components is monitored for aftershock-probabilistic seismic demand model (AS-PSDM) generation used in the aftershock fragility estimation. This approach is more realistic because the ground motions are applied as recorded. However, it does not provide the conditioned-specific aftershock performance of the structure.
Due to the large number of ground motions required for the NTHA, the IDA, which is a special type of NTHA, has been put forward. In this method, the ground motions are linearly scaled, and a series of aftershock analyses are performed at different intensity levels. Typically, this method is mostly employed for aftershock collapse probability estimation.81 This method can be applied in two ways: (1) scaling the MS part to induce a known damage level followed by an unscaled AS excitation1 and (2) scaling the MS until a known damage level is induced, followed by AS scaling until complete collapse of the structure is reached.81, 98 The incrementation can be performed for MS only or both parts of the sequence, depending on the final objective of the analysis. In the first type of framework, the IDSs are defined based on the correlation between visible damage and component response from extensive full-scale experiments of columns.1 The different possible damage mechanisms are incorporated in the numerical model for the full-scale structure and subjected to the scaled mainshock until a specified response is achieved. For the aftershock response estimation, the aftershock hazard suit is applied without any scaling, and the fragility models are derived based on different initial mainshock-DSs. This framework has been implemented for California's old reinforced concrete (RC) frame structures. However, it does not guarantee to push the structure until the collapse point. For the complete collapsed criteria, the second approach is most commonly employed, which is primarily based on double IDA. Like the first approach, initially, the mainshock is scaled at different intensities to induce reference damage in the structure. In the following step, aftershocks are intensified until the complete collapse criteria are met. Using piecewise regression, the probabilistic seismic demand surface is established for final fragility estimation. The validity of this framework has been evaluated for multistory RC frame structures.81, 98, 99 Although both of the frameworks are effective in aftershock fragility estimation, they suffer from a major limitation of excessive scaling of the MS or AS or both parts, especially when the recorded seismic hazard suit contains significantly low-intensity records.
4.1 Bridge infrastructure
Several researchers developed the fragility functions for highway bridges by explicitly taking into account the MSAS hazard.46-49, 100 Alessandri et al.49 evaluated the seismic risk of mainshock-damaged bridges further subjected to aftershocks to decide on traffic operation after seismic hazard. The aftershock hazard using Omori's law and the fragility function of the bridge at different DSs are convolved to calculate the risk level. The proposed method combines the numerical analysis results with the in situ information for better decision-making. This method is applied to an existing RC bridge for efficiency evaluation. Franchin and Pinto46 used the fragility functions to know the state of the bridge in a probabilistic way until the collapse of the structure. On the basis of the aftershock fragility estimates, decision-based criteria are proposed for the operation of bridge structures in the aftermath of a mainshock event which is based on the comparative estimate of the collapse risk of mainshock-damage and preshock risk of the pristine bridge structure. It was revealed that after a certain threshold time limit after the mainshock, the bridge operation can be resumed when the level of risk reduces to an acceptable range.
Wang et al.58 performed back-to-back IDA to calculate the aftershock fragility conditioned on different levels of postmainshock DS using a modified Bracci damage index (MBDI). This index takes into integration the multiple factors associated with cumulative damage and the deteriorating modeling technique in an analytical manner. The performance of the proposed index is compared with the traditional drift ratio parameter for the aftershocks. A higher probability of exhibiting severe damage in the aftershock event was demonstrated, provided that higher damage is sustained in the mainshock event. Similarly, Wang et al.59 evaluated the fragility of the RC bridge pier by considering the effect of aftershocks on different damage structures with varying periods and the damage of aftershocks at different magnitudes using the Park and Ang damage index. Results demonstrated that the additional damage caused by aftershocks gradually decreases with the increase of axial compression ratio in different DSs. Increasing the reinforcement ratio can significantly reduce the damage probability of columns. However, the fragility performance of columns by increasing the reinforcement ratio gradually decreases with the increase in the axial compression ratio. The effect of aftershocks on the exceeding probability is lower in columns with a small axial compression ratio.
Another study put forward a mainshock-integrated aftershock fragility assessment framework for a bridge structure, which empirically encodes the mainshock-associated damage into the traditional fragility estimation framework.56 The fragility models incorporate the probability of collapse due to the mainshock and the effect of the variable aftershocks conditioned on the mainshock. Results show that the traditional framework will overestimate the fragility of the bridge. However, due to the added parameter accounting for the mainshock effect, the modified framework yield fits well with the lognormal functions, which accurately estimate the MSAS sequence fragility functions. Similarly, Ghosh et al.53 proposed a probabilistic framework to predict the damage accumulation in highway bridges under sequential seismic loading. Linear and multilinear seismic demand models were developed for single and multishocks during the service life of bridge structures. The mainshocks and their occurrence rate were considered probabilistically throughout the lifetime of the structure, whereas the aftershocks hazard was considered following a time window of 365 days after the mainshock. A significant increase in the damage index is revealed for repeated shocks within the service life of the structural system. The interaction of seismic excitation directionality and the variation in bridge geometry is crucial for understanding the bridge's complex dynamic response in assessing structural safety. Some excitation directions may lead to different damage modes, which are not the same if subjected to conventional excitation practices along the longitudinal and transverse bridge directions.101 Omranian et al.55 evaluated the seismic performance of skew bridges under MSAS sequence using fragility functions. The fragility characteristics only under mainshock were found to be very conservative. Additionally, the degree of vulnerability increased with the increase in the skew angle. The fragilities obtained based on aftershock and excitation orientation effects are found to be more vulnerable than predicted by the HAZUS. This study focused on the response of the column without accounting for the rest of the major components. A study by Pang and Wu60 investigated the effect of MSAS sequence on bridge components and system fragility using a set of 75 real sequential seismic records. The probabilistic seismic demand models (PSDMs) developed for mainshock only and MSAS sequences show an increase in the structural response parameter, eventually leading to high fragility demand for the MSAS case, both for the component and bridge system. The study suggests that bridge system vulnerability assessment should be made while accounting for all the vulnerable components.
Dong and Frangopol50 put forward a probabilistic framework for seismic fragility and resilience assessment of bridges under MSAS sequential loading by adopting an single degree of freedom (SDOF) system. The repair loss and functionality evaluation is based on a set of DSs that are mutually exclusive and collectively exhaustive. The repair loss and time-dependent functionality are assessed, and it was demonstrated that the aftershocks will significantly affect these indicators for the resilience evaluation. The proposed framework can support the decision-making process for planning the postevent retrofit selection and prioritization while reducing the social and economic impact associated with the MSAS sequence. Similarly, Chen et al.57 investigated the seismic fragility and the associated direct financial losses of tall pier bridges subjected to MSAS sequences. An experimentally validated pier model was considered in this study. For the sequential seismic data set, a randomized approach was followed, which considered the aftershock part of the sequence from the same seismic data set following an appropriate statistical sampling technique. A bilinear trend was observed in the intensity measure-engineering demand parameter response for the cases when conditioned on the mainshock intensities. This is true for cases where the response associated with the mainshock is more dominant than the aftershock counterpart. Unlike previous studies, results show that the contribution of the aftershocks to the peak structural seismic demands is insignificant unless their intensities exceed critical values. While structural vulnerabilities increase, with both the intensities of main- and aftershocks, the role of mainshocks is observed to be more substantial.
4.2 Building infrastructure
4.2.1 RC frames
Buildings comprise a huge fraction of built infrastructure and are equally susceptible to seismic hazard aftershocks as bridges. Different researchers quantified the seismic resilience and vulnerability of frame structures under different conditions.67, 69-71, 74 Raghunandan et al.69 estimated the residual capacity of the mainshock-damaged structure dynamically by subjecting the structure to a suite of ground-motion time histories. Each mainshock is scaled so that it induces a specific damage level in the structure, followed by the aftershock scaling. The residual capacity is calculated as the spectral acceleration corresponding to the onset of the limit state. Results show that for slight damage in the mainshock, the collapse capacity will not be affected by the aftershocks. However, it will significantly drop for the mainshock-moderately damaged structures. These findings suggest that the increase in vulnerability associated with the aftershock is dependent on the initial state of the structure after the mainshock hit. Therefore, the relative difference between slight damage and extensive collapse state for the aftershock shows a nonuniform increase in damage progression.
Similarly, Song et al.81 proposed a fragility surfaces development framework considering double IDA for stepwise regression seismic demand model of MSAS sequence. The developed PSDM follows a bilinear trend with an increasing trend in the dispersion term, which illustrates the relative impact of scaling low-magnitude aftershocks. The fragility contour lines depict that a larger IM of mainshock or aftershock leads to a decreased IM demand required for the same DS, however, the mainshock generally causes more damage compared with the aftershock for the same intensity level. Farivarrad and Estekanchi80 evaluated the seismic performance of multistory frame structures subjected to MSAS seismic sequences by applying the endurance time method for synthetic seismic records. For the aftershock damage prediction associated with intensity, the interactional curves in terms of intensity levels were developed for residual drift capacity and structural performance. It is revealed that the residual structural state due to the mainshock has a considerable impact on the final state of the studied structures. To make a reliable conclusion, it is essential to consider the cumulative response of the structure subjected to MSAS seismic sequences. It was suggested that seismic hazards defined by PBEE must include the probability of aftershocks.
Moshref et al.85 assessed the residual capacity of RC columns subjected to mainshock loading using visual indicators and residual drift. For the sequential seismic analysis, the mainshock ground motion from FEMA P695 was replicated as aftershocks. The maximum and residual drift ratios are correlated after the IDA, followed by the fragility derivation for the MSAS scenario. Permanent displacement and visual damage indicators were considered to develop the fragility curves for mainshock-damage columns. The key conclusion drawn from this study revealed that stiffness degradation is primarily due to severe damage level, and therefore the residual deformation is not an appropriate parameter for describing the performance of the columns. Similarly, Hosseinpour and Abdelnaby74 developed fragility functions for different story frame structures using sequential loading. It was found that the aftershock-only fragility is very low due to lower duration and lower range of frequencies. However, considering the cumulative damage from the previous mainshock, the aftershock fragility shows a higher probability of exceedance for all the limit states and intensities. Another study by Abdelnaby71 investigated the effect of repeated earthquake loading on multistory frame structures using the real seismic data from the Tohoku, Japan earthquake, in terms of fragility functions. The effect of aftershock fragility as a function of story height is assessed. The results are compared for mainshock only and MSAS cases and it was concluded that the aftershocks have a high damage potential. The low-rise structure shows high vulnerability with increasing the intensity of seismic motion for all the considered limit states, whereas the mid and high-rise structures are less prone to the negative impact of aftershocks in the life safety and near-collapse limit states. An important highlight of this study is aftershock fragility for the same set of structures under different regional aftershock hazards, including Japan, Chili, and New Zealand. The difference is more prominent in the higher DSs, where Chili seismic hazard is the most demanding followed by New Zealand compared with the Japanese data set. This illustrates the importance of considering regional-specific hazards in the aftershock fragility assessment rather than relying on data that might underestimate the fragility results. Wen et al.73 introduce a vulnerability assessment framework for MSAS sequential loading on the structure. It was reported that an aftershock can alter the mainshock fragility by more than 15%, depending on the level of damage observed in the mainshock. The response is presented in terms of typical deformation-based parameters as well as hysteretic energy (EH). For the sequential seismic excitation, the increase in deformation was less significant compared with the increase in cumulative EH, illustrating the energy-based damage index is more effective than the deformation-based damage index in reflecting the additional damage caused by aftershocks. Another study described the PSDMs and fragility estimates for the mainshock and MSAS sequential loading cases.78 Unlike the mainshock demand model case, aftershock fragility estimation is a function of two variables, one describing the mainshock and one describing the aftershock. Bayesian approach is employed to calibrate the proposed demand models using simulation data considering both mainshock and MSAS sequence records and fragility functions corresponding to different limit states were developed. A higher margin of uncertainty is observed for the MSAS fragility case.
The sequential seismic hazard directly affects the seismic resiliency of a system, which describes the recovery of the system after a disastrous event. Wen et al.76 evaluated the loss in resilience due to aftershocks for RC structures, considering the recovery time and pre-event functionality of the system. The replacement threshold is employed for engineering application and decision-making. Their study demonstrated that the aftershocks could increase the resilience loss concerning the mainshock alone. Also, aftershocks tend to increase the seismic demand of structures concerning mainshock only, and structures under the MSAS sequence tend to attain larger damage levels than mainshock only. Therefore, the probability of exceeding a given limit state is higher for the MSAS sequence than for mainshock only. Di Sarno99 carried out a detailed parametric analysis of multiple seismic events on the performance of RC structures by employing an inelastic constant ductility acceleration, displacement, and force reduction factor spectra for real seismic data. The normalized strength spectrum revealed a triple-fold increase in the force demand for the seismic sequence. It was concluded that the adequacy of degrading hysteretic models is crucial for the reliable inelastic performance evaluation of structures. Further, the modification in strength and deformation capacity is recommended for nonseismically designed structures under sequential seismic hazards.
4.2.2 Steel frame structures
Steel structures are more vulnerable to fatigue cracking at critical locations due to repeated shocks. Veismoradi et al.87 investigated the seismic collapse risk of buckling restrained multistory frames under MSAS sequential loading using fragility functions. A probabilistic framework is introduced, which takes into consideration the effect of postmainshock permanent drift and the upcoming aftershock per annum. It was reported that the aftershocks are more severe and increase the collapse fragility when the structure already suffers a large magnitude of residual displacement (RD). The increase in the annual probability of reaching the limit states associated with aftershocks depends on the intensity of the aftershock, as well as the damage caused by the corresponding mainshock. Similarly, Di Sarno and Wu86 evaluated the nonseismically designed steel frames under repeated seismic shocks. To have reliable fragility estimates, the state-dependent fragility functions were considered for cases: no damage, slight and moderate damage. The results demonstrated that slight postdamage has negligible influence on the residual structural capacity. However, the moderate postdamage fragility case was more pronounced. For cases where the damage increment due to aftershocks is negligible, it is due to the frame model exhibiting severe hardening and weaving behavior in the IDA. This results in the failure of frames at higher IMs compared with undamaged cases. This study also suggests that if the mainshock-associated damage is slight, the aftershock analysis can consider the undamaged state for postquake analysis. Whereas for cases with moderate damage, the postquake excitation must consider the reduced capacity of the structure by simply reducing the material properties using the reduction factors.
Similarly, Saed and Balomenos88 proposed a framework for performance evaluation of corroded steel frame structure, and the fragility surfaces were developed for both mainshock and aftershock intensity by employing nine real MSAS records. In the analysis, 10–50 years of corrosion accumulation is considered for examining its impact on the fragility of frame models over service life. Results show a remarkable increase in seismic fragility for the extreme limit states. The MSAS sequences increased the exceedance probability of limit states compared with the mainshock-only scenario. Furthermore, by increasing the aftershock intensity, the probabilities increased for a given mainshock intensity, which further exacerbates the increase in frame height due to the rapid development of an inelastic response mechanism. A study by Park et al.102 proposed a methodology to calculate the aftershock fragility of postmainshock-damaged steel moment-resisting frame buildings, by selecting artificial critical sequences causing the vulnerability of the building to aftershocks. This study primarily uses an inverse approach to select a limited number of aftershocks that are responsible for pushing the structures to extreme DSs to be used as an indicator for retrofit design as per the predicted damaged structural response corresponding to various performance levels. Li and Ellingwood94 investigated the cumulative damage in steel frame structures following a mainshock using a probabilistic framework. The structural response and probabilistic DSs were developed using an enhanced uncoupled modal response history analysis method. It was revealed that the aftershock characteristics have a significant effect on the damage pattern progression. Further, the aftershocks have a high probability of causing considerable cumulative damage if the mainshock causes initial significant damage. Li et al.45 studied the collapse fragility of special moment-resistant frame (SMRF) buildings subjected to MSAS sequences considering different seismic excitation scenarios. The key findings suggest that no matter how the seismic sequence is generated, the collapse limit state is sensitive to the DS sustained due to the mainshock. Further, for different mainshock scenarios, the aftershock fragility is remarkably different in the higher DS. This can be attributed to the difference in spectral contents. Another study investigated the influence of MSAS sequences on the seismic fragility and economic performance of typical self-centering steel braced-frames employing posttension tendon-based self-centering braces.89 The collapse probability due to aftershocks significantly increased, further leading to a more than 22% increase in the expected losses over 50 years of the target structures. Moreover, the residual deformation parameter is reported to be more sensitive to aftershocks compared with peak absolute floor acceleration responses.
Iervolino et al.103 argued that for structural life cycle assessment, it is imperative to account for the built-up of seismic losses associated with multiple earthquakes. If the classical probabilistic seismic hazard analysis (PSHA) is replaced by the aftershock PSHA in the PBEE framework, the Markovian model is equally applicable to the multiple aftershocks from a given mainshock. This model is further extended to account for the damage accumulation at the same time within any MSAS sequence as well as among multiple seismic sequences. This is validated through a series of multistory RC steel frames designed for different hazard levels in Italy. The back-to-back IDA is employed for computing state-dependent fragility functions for calibrating the Markov models. Results show that for different hazard sites, the median IM causes a transition between any two DSs, increasing with the increase in seismic hazard.
4.2.3 Masonry and wood structures
Most of the low-rise residential buildings are made up of masonry and wood, which are equally susceptible to sequential seismic events, like, the other lifeline structures. Considering the MSAS hazard, an analytical method for maximum story drift estimation is proposed for masonry structures by Zhang et al.90 Using a parametric approach, the effect of aftershock intensity, site classes, story count, and mortar strength was evaluated under MSAS seismic loading. Overall, the effect of aftershocks on masonry structures in the plastic phase is more distinct than that in the elastic phase. Fragility functions are derived considering uncertainties in ground motion and structural properties. It was reported that aftershock collapse probability will increase by more than 30% for the mainshock-damaged structures. The probability of exceeding the collapse limit can increase by 32.2% when aftershocks have equal intensity as the mainshock. Following the reconnaissance of the destructive 2010–2011 Canterbury earthquake, many of the nonductile masonry buildings had suffered from moderate to major damage due to a sustained initial slight damage level associated with the mainshock. Fikri and Ingham92 demonstrated that these buildings can be highly vulnerable in an aftershock, with further damage potentially occurring at a smaller intensity of earthquake shaking than was experienced in the mainshock. In contrast, the increase in seismic fragility to cause building collapse due to aftershocks was found to be insignificant. The aftershocks lead to an increase in the interstory drift ratio for the considered models. Furthermore, the selection of the MSAS sequence was demonstrated to highly influence the collapse occurrence probability.
For wooden structures, Goda and Salami64 investigated the aftershock effects using fragility functions by employing real MSAS sequences. The inelastic seismic response curve showed an increase of 5%–20% in structural response for medium DS. They revealed that the primary parameters for a combined increase in damage level are large magnitude aftershock, smaller aftershock distance, and large aftershock PGA characteristics. Additionally, the greater aftershock response spectra at some periods are also a main driving factor for increasing damage levels. Nazari et al.66 proposed a methodology for the development of calibrated wood frame structures' fragility considering the aftershock effect. It is observed that the fragility curves for collapse risk have a similar shape for the MSAS sequences for different levels of the mainshock. For the mainshock-survived structure, the aftershock collapse risk is not critical for engineered wood frame structures. The findings suggest that for structures where the primary goal is focused on life safety, the consideration of aftershock hazards in strength-based design is not critical. However, for tall wooden structures, where the collapse criteria are not solely based on strength, the aftershocks become more crucial and must be considered in the design phase. Another study by the same authors investigated the sensitivity of collapse probability to the MSAS sequence intensity.65 Results show an increase in the collapse fragility with an increase in the mainshock magnitude, while decreases with source-to-site distances. This study showed that for a reasonable aftershock magnitude and aftershock source-to-site distribution, the spatial sensitivity of collapse fragility is more affected by aftershock magnitude distribution.
5 SEISMIC HAZARD AND STRUCTURAL CAPACITY PARAMETERS FOR MSAS FRAGILITY
Fragility functions are derived by convolving the PSDMs against the structural limit state corresponding to different DSs. The selection of seismic hazard suits and the definition of structural response parameters are important in developing fragility relationships, which are briefly outlined in this section.
5.1 Selection of MSAS sequence for dynamic analysis
The selection of a consistent sequential seismic loading protocol is imperative for reliable structural analysis and risk quantification. Different researchers have used different approaches for sequential ground motion pairing for nonlinear dynamic analysis. Being the simplest approach, the mainshock–mainshock (MSMS) approach considers the ground motion pairs based on the mainshock event only.1, 66, 69, 104-107 The second ground motion in this type of loading sequence may be a different record from the mainshock database or a scaled or unscaled version of the original mainshock. Another approach is the targeted-mainshock–mainshock (TG-MSMS), in which the second mainshock in a pair closely matches the aftershock characteristics motion, including larger rupture distance and lower magnitude than the first mainshock.105, 108 The same sequence–mainshock–aftershock (SS-MSAS) approach takes the first and second records from the mainshocks and aftershocks of the same sequence (e.g., Tohoku earthquake mainshocks and Tohoku earthquake aftershocks).73, 108-111 In the different sequences of the mainshock–aftershock (DS-MSAS) approach, the first and second ground motions are taken from two different mainshock and aftershock sequences (e.g., Tohoku mainshocks and Kumamoto aftershocks).
Several factors affect the aftershock ground motion characteristics conditioning upon the mainshock occurrence. Aftershocks are usually smaller in magnitude considering the implications of source and path.112 Also, the same site will have larger source-to-site distances compared with the parental mainshock due to a smaller rupture area. Evidence of a mild correlation between MSASs attributes belonging to the same sequence has been reported, even when the source and path differences are considered.113 Considering these points, Shokrabadi et al.75 concluded that the SS-MSAS pairs are ideal for sequential analysis due to their capability of capturing these attributes naturally.
Limited researchers evaluated the differences in dynamic responses of structures considering MSMS and MSAS sequences. Goda108 quantified the ductility demands imposed by MSMS and SS-MSAS sequences from the Japanese seismic database. The former sequence was selected based on Omori's law to match the aftershock magnitude distribution.114 This approach is equivalent to TG-MSMS without considering the difference in rupture distances. Goda115 evaluated the seismic performance of wooden frame structures subjected to MSMS and SS-MSAS sequences. The MSMS sequence used the same record for the second waveform as the first one. Results revealed a higher collapse probability for structure compared with the SS-MSAS sequence. Similar findings were reported by another study for steel frame structures.110 Collectively, these studies show that the MSMS sequence is more vulnerability demanding compared with the MSAS sequence, which captures the attributes of the second waveform more accurately.
Shokrabadi et al.75 investigated the effect of MSMS pairing on structural collapse performance. The significance of the correlation between mainshock and aftershock concerning structural response is evaluated using the SS-MSAS and DS-MSAS sequences. Also, the response is investigated for TG-MSMS and SS-MSAS sequences to propose an alternative for aftershock selection from the available database. Results demonstrated that due to systematic differences in the frequency contents of both records, the MSMS sequence potentially overestimates the structural response and the associated risk compared with MSAS sequence pairs. The correlation between event terms of mainshock and aftershock ground motions recorded from the same sequence is found to have a significant impact on the maximum story drift ratio. On the basis of their study, the use of SS-MSAS record sets is recommended, which places a premium on documentation of aftershock ground motions following major events.
Another important point regarding the selection of aftershocks is related to its impact on structural response compared with the mainshock. For the state-dependent PSDMs, studies have shown the crossover problem of fragility.1, 116 Some of the selected seismic records might result in a lower structural response compared with the single mainshock event only. Technically this is not an indicator of decreasing damage level, instead, it is related to changes in the dynamic characteristics of the structure. Establishing a PSDM based on these results leads to a crossover of the fragility models for the undamaged and state-dependent damaged structures, as shown in Figure 4. This will mislead the damageability evaluation of the structure with the impression that the damaged structure is less vulnerable than the undamaged one for the given ground motion intensity. To cope with this limitation, studies proposed the bilinear approximation of the PSDMs for a better fit to the observed data.1, 116-118
5.2 Engineering demand parameters (EDPs) and IM for MSAS fragility evaluation
An important aspect of fragility formulation is defining the appropriate limit state that describes the varying levels of damage for the bridge components and bridge system. In literature, most of the studies consider four different levels of limit states, namely, slight, moderate, extensive, and complete, for which the qualitative definitions are proposed and described by HAZUS.22 For quantitative analysis, these definitions are taken into consideration by associating an appropriate numerical value, which closely describes the behavior of any limit states at the onset of reaching the damage level considered. The governing response quantities are considered in the response evaluation known as EDPs. For different structural systems, different EDPs can be used due to the difference in design and serviceability requirements. Several EDP choices are adopted by different researchers for seismic response evaluation. For instance, residual drift,87 maximum interstory drift,70, 79, 92 and maximum inelastic displacement (MD)105 are a few of the most used EDPs as they reflect the extreme response of the structure under seismic action. For the mainshock-damaged structure, Freddi et al.119 argued that the interstory drift-related EDP is not sufficient to assess the seismic response and fragility for follow-up seismic events. Further, most of the existing bridge and building infrastructures might not comply with the recent seismic design requirements in displacement or drift-related limit states, therefore the usability of these limit states may vary from case to case for the existing infrastructures.
Park and Ang120 developed a damage index based on the energy dissipation capacity and ductility demand of the structure. This index considers the combination of classical deformation-based parameters along with the strength and stiffness degradation behavior of the structure in terms of EH. Zhai et al.121 reported that the Park–Ang damage index could be employed for damage evaluation by investigating aftershock damage through SDOF inelastic systems. Similarly, Kumar and Gardoni47, 48 quantified the structural degradation due to sequential seismic damage in probabilistic terms using the Park–Ang damage index, and the corresponding fragility functions were developed. Other studies also validated the Park–Ang and its modified versions as the best choice of EDP selection due to the combined consideration of displacement and EH dissipation in sequential seismic events.53, 77, 78, 122, 123
Amiri, Di Sarno, and Garakaninezhad124 investigated the correlation between nonspectral and cumulative-based earthquake IMs and different EDPs of schematized structures in terms of efficiency and sufficiency under varying input loading directions. Structural performance is expressed as MD, maximum inelastic absolute acceleration (MA), RD, and EH. Extensive parametric analyses revealed that the MD, MA, EH, and RD of regular systems are the most appropriate demand parameters.
Several researchers have used different demand parameters for bridge structures, for instance, the MBDI,58 drift,51, 52, 54, 55 displacement ductility ratio,61, 62 curvature ductility,55, 57 bearing displacement,60, 61 and abutment displacement61 are a few to list to describe the damage. Similarly, for RC frame structures, the commonly adopted EDPs include the Park–Ang damage index,78, 81, 82 interstory drift ratio,67, 70, 75, 92, 125 and drift.74 The drift-related EDP is also extended to steel frames86 and wood frame structures.66 For different structures, Table 3 summarizes the demand parameters and their threshold values corresponding to different limit states, used by different researchers for MSAS fragility assessment.
| Structural system | Demand parameter | Limit states values | Reference | |||
|---|---|---|---|---|---|---|
| Slight | Moderate | Extensive | Collapse | |||
| Bridge pier | Park and Ang index | 0.25 | 0.4 | 0.8 | 1 | 59 |
| 0.1 | 0.25 | 0.4 | 1 | 53 | ||
| Modified Bracci damage index | 0.02 | 0.21 | 0.57 | 1 | 58 | |
| Drift ratio | 0.33 | 0.57 | 0.76 | 0.94 | 58 | |
| Drift | 0.7 | 1.5 | 2.5 | 5 | 51, 52, 54, 55 | |
| 0.003 | 0.01 | 0.02 | — | 49 | ||
| Displacement ductility ratio | 2.25 | 2.9 | 4.6 | 5 | 62 | |
| 1 | 1.2 | 1.48 | 4.48 | 61 | ||
| 1 | 1.2 | 1.76 | 4.76 | 50 | ||
| Curvature ductility | 1.29 | 2.1 | 3.52 | 5.24 | 57 | |
| 1 | 2 | 3.5 | 5 | 55 | ||
| 1.4 | 2.5 | 3.7 | 5.85 | 60 | ||
| Bridge bearing | Displacement (mm) | 37 | 104 | 136 | 187 | 61 |
| 20 | 100 | 150 | 200 | 60 | ||
| Bridge Abutment | Displacement (mm) | 25 | 50 | 100 | 150 | 61 |
| RC frame | Park and Ang index | 0.1 | 0.2 | 0.5 | 1 | 77, 78, 81, 82 |
| 0.11 | 0.4 | 0.77 | >0.77 | 73 | ||
| Inter story drift ratio (%) | 0.15 | 0.4 | 1 | 1.75 | 92 | |
| 1.06 | 1.87 | 2.30 | — | 79 | ||
| 0.2–0.3 | 0.8 | 2 | 4.21–5.32 | 70 | ||
| — | 1 | 2 | 4 | 72, 76, 126 | ||
| 1 | 2 | 2.75 | 5 | 75 | ||
| 0.5 | 0.8 | 2 | 5.95 | 68 | ||
| Drift | 0.2 | 0.5 | 1.5 | 2.5 | 74 | |
| RC frame isolation bearing | Shear strain (%) | 120 | 160 | 200 | 250 | 68 |
| Wood frame | Drift | 1 | 2 | 4.5 | 7 | 65, 66 |
| Masonry structure | Inter story drift ratio (%) | 0.08 | 0.13 | 0.26 | 0.39 | 90 |
| Steel frame | Residual drift | 0.25 | 0.75 | 1.25 | >1.25 | 87 |
| Inter story drift ratio (%) | 0.2 | 0.5 | 1 | 4 | 88 | |
| 0.2 | 0.5 | 1 | 2 | 89 | ||
| Drift | 0.04–0.06 | 0.32–0.70 | 2.41–3.60 | — | 86 | |
- Abbreviations: MSAS, mainshock–aftershock; RC, reinforced concrete.
The MSAS fragility function for a particular DS is expressed in terms of ground motion IM. Several studies are available regarding the optimal IM selection for single seismic event fragility estimation, which is equally applicable to sequential seismic fragility estimation approach provided that the chosen IM to measure the fragility for mainshock only and MSAS sequence must be easily quantifiable for the earthquake characteristics and be representative of the damage potential of earthquakes.126 Since the early time of fragility formulation, different opinions have been available. In the ATC-1315 documentation, the Modified Mercalli scale is adopted, while the spectral acceleration corresponding to the fundamental mode, was preferred by the FEMA-695.127 Different researchers have utilized different alternatives for the choice of an IM selection, including peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), spectral acceleration (Sa), and Arias intensity are few among to mention.
A generic criterion was devised for the selection of an optimum IM, which is based on efficiency, sufficiency, and computability indices.128 Mackie and Stojadinović20 proposed another selection criteria based on the relative magnitude of uncertainty error estimation in the demand models. According to that, the ideal IM should be the most practical, efficient, sufficient, robust, and effective. They investigated a total of 65 IMs, classified into three classes, and it was concluded that spectral acceleration and spectral displacement at the fundamental mode are the most appropriate IMs. Gardoni et al.129 recommended Sa as a better predictor than PGA for various EDPs. An average value of spectral acceleration over a range of periods is also recommended for higher accuracy in demand model estimation.130, 131 A fractional order IM has been proposed for the PSDM by another study,132 which is based on the SDOF system with fractional response and damping and combining the peak ground response with the spectral acceleration at 0.2 and 1.0 s. However, this IM is not more useful in risk evaluation due to the nonavailability of the hazard curves for the fractional order of the IMs. Another study by Amiri, Di Sarno, and Garakaninezhad124 revealed the optimal IMs in terms of efficiency and sufficiency are squared velocity, root mean square of acceleration, root square velocity, and squared velocity. Contrary, PGA has been recommended as the optimum IM based on the cumulative index of efficiency, sufficiency, and practicality.133 It is worth mentioning that the appropriateness of the IM choices selection is highly sensitive to the ground motion suits considered, for which the detail highlights can be found in Padgett and DesRoches133 The choice of different IMs used for MSAS fragility estimation by different researchers for bridges and buildings can be found in Table 2.
6 MSAS FRAGILITY ANALYSIS CONSIDERING SPECIAL CONDITIONS
6.1 Variation in MSAS fragility due to seismic strengthening
Most of the available studies on MSAS fragility assessment are focused on as-built infrastructure. MSAS fragility curves can also be used for assessing the retrofit measure and its optimality among the available retrofit strategies. Fakharifar et al.51, 52 comprehensively assessed the seismic collapse capacity and fragility of mainshock-damaged highway bridges with different retrofit schemes (FRP, conventional thick steel, and hybrid jacket). The severe damage due to the mainshock significantly jeopardizes the postevent resilience of the bridge pier. The fragilities of the unrepaired and repaired bridge largely deviate from each other under the extensive and collapse DSs. The FRP jacketing outperforms in enhancing the seismic collapse capacity of the bridge pier compared with the steel jacket. For illustration purposes, Figure 5A shows fragility curves for the as-built and retrofitted structures showing the comparative effectiveness of different strengthening schemes for seismic vulnerability mitigation. A study by Huang and Andrawes134 indicated an improvement as high as 117% in bridge overall performance subjected to strong MSAS sequences by applying Shape Memory Alloy (SMA) confinement to piers. Similarly, Omranian et al.135 investigated the seismic damage and fragility functions for the as-built and retrofitted bridges subjected to the MSAS sequence. FRP confinement has a more significant effect on the seismic performance of the bridge particularly in the higher levels of DS, such as severe and complete. Jeon et al.54 proposed a framework for aftershock fragility estimation, which can quantify the cumulative damage of the bridge under the MSAS sequence and the effectiveness of the steel and fiber-reinforced-polymer jackets as a repair scheme following a mainshock event. Fragility results show that the CFRP retrofitting scheme is less effective than the steel jacketing. However, the relative difference is lower than 5% for the considered limit states and IDSs, and therefore either of the options can be effectively adopted for retrofit upgradation. Additionally, the effectiveness of steel jacketing is evaluated for the abutments, which outperformed in vulnerability mitigation in the transverse direction than in the longitudinal direction.
Similarly, Han et al.68 investigated the seismic performance of RC nonductile frames subjected to MSAS sequence with hypothetical base isolation used as a retrofitting scheme. The study revealed that base isolation can greatly reduce seismic vulnerability for higher damage levels. Shafaei and Naderpour136 evaluated the seismic fragility of FRP retrofitted multistory RC frame structures subjected to MSAS sequence and reported that the retrofit scheme is effective in enhancing the seismic collapse fragility of the structure. While the retrofitting resulted in collapse capacity elevation of the structure, the reduction in collapse capacities due to different mainshocks associated damage levels is independent of the structural inherent ductility and strength capacity. This reduction in capacity was attributed to the structural inherent inelastic behavior due to concrete cracking and steel yielding. Another study assessed the MSAS seismic vulnerability of RC frame structures retrofitted with hybrid dampers and the performance was compared with the retrofitted structures.137 The retrofitted structures show better performance in terms of the median collapse capacity and seismic fragility compared with the unretrofitted ones. Ghasemi et al.138 evaluated the seismic performance of RC frames under sequential-type loading with SMA and Ultrahigh-Performance Steel Fiber Reinforced Concrete (UHPSFRC). Outperforming results were reported, showing the effectiveness of using these retrofit strategies in reducing transient and residual drifts and enhancing the functionality of structures in both mainshock and aftershock.
6.2 Effect of material deterioration and aging on MSAS fragility
Deterioration due to aging significantly alters the seismic performance of structures. The effect of aging and capacity degradation has been overlooked by practitioners and the relevant stakeholders for a long time. There have been several studies available focusing on the aging consideration of bridges and buildings' seismic performance evaluation. However, very limited studies accounted for deterioration phenomena in MSAS fragility estimation.61, 79, 82, 88 The effect of corrosion with aging in conjunction with repeated shocks is investigated on the fragility of RC structure.79 Corrosion is considered only for fully and partially exposed beams and columns, and it was revealed that the structure will experience a significant reduction in global seismic capacity and hence increase in seismic fragility for each limit state, which becomes more detrimental for the sequential seismic loading, as shown in Figure 5B.
A study by Afsar Dizaj et al.139 proposed a framework for seismic vulnerability assessment of aging RC frames subject to real MSAS ground motion sequences. Corrosion-variant pushover analyses are performed on a case-study RC frame with various corrosion damage levels to quantify the corrosion-variant demand limit states. It was reported that the collapse probability is higher under the MSAS sequences. Furthermore, for severely corroded RC structures due to aging, the failure mode will change to brittle due to a reduction in reinforcement area, even only under MS. Zhou et al.82 carried out the seismic resilience assessment for the corroded RC aging buildings under MSAS loading. A vector-valued approach is employed to evaluate the structural fragility under different levels of corrosion rate. The fragility and resilience curves are then developed for the uncorroded and corroded RC frame cases under mainshocks alone and MSAS sequences, and it was reported that the coupling effect due to both corrosion and aftershocks led to a more significant reduction in the structural resilience than the individual effect due to either corrosion or aftershocks and therefore should be considered simultaneously for resilience evaluation. Similarly, Saed and Balomenos88 proposed a framework for performance evaluation of corroded RC frame structure, and the fragility surfaces were developed for both mainshock and aftershock hazards. Results show that corrosion and aftershocks may significantly affect seismic fragility, especially for the extreme limit states. For a four-story frame, the average probability of exceeding the collapse limit state increased by approximately 10% as the building experienced 50-year corrosion exposure.
Likewise, Di Sarno and Amiri140 investigated the effect of structural deterioration on period elongation under MSAS sequence for RC structures schematized as SDOF systems. The time shift ratio was investigated under various conditions, including stiffness degradation and damage accumulation. Results show that period elongation is insignificantly affected by the stiffness degradation ratio. For short to moderate-period structures, period elongation is directly proportional to the accumulated damage, while for flexible structures the effect is less pronounced. More recently, the aftershock seismic risk assessment of the aging petrochemical unit was investigated.141 The impact of aftershocks with and without considering the corrosion damage was considered. A slight increase in the aftershock fragility was reported in the absence of corrosion, whereas the presence of corrosion aggravates the damage and loss associated risk by more than double fold. This illustrates the increase in seismic risk due to loss in the effective mass of the structure in seismic-prone regions.
Liang et al.61 investigated the seismic time-varying fragility of offshore bridges considering material deterioration in the entire life cycle. It was concluded that the exceeding probability of bridges under different DSs increases with the extension of service time and the increase in ground motion intensity. Material deterioration with aging further aggravates the seismic response and fragility of bridge components and systems, therefore both factors should be considered in the seismic performance evaluation of such structures. For bridge structures, Panchireddi and Ghosh142 investigated the cumulative vulnerability of highway bridges subjected to multiple mainshocks. A comparison of damage index exceedance probabilities between the nondeteriorating and aging case-study bridge revealed a significant impact of corrosion deterioration on the seismic vulnerability for multiple earthquake events. Similarly, Cui, Alipour, and Shafei143 found that multiple earthquake events expedite the corrosion process with aging, and therefore, negatively influence the vulnerability of RC bridge piers.
6.3 Effect of skewness and scouring on MSAS fragility of bridges
Skewed bridges are commonly incorporated in multilevel highway interchanges and have the potential for significant damage in comparison with straight bridges under earthquake events.144 Omranian et al.55 investigated RC bridge fragility under various skew configurations. Results revealed that models with more skewness have a higher vulnerability, which is further aggravated by aftershocks, as shown in Figure 5C. Results were compared with the HAZUS criteria and suggested that the aftershocks effect should be considered for a more accurate fragility assessment. Garakaninezhad et al.145 investigated the seismic performance of a 60° skewed bridge in California under the MSAS sequence. It was revealed that the nonlinear response may increase by approximately 66% due to the combined consideration of skewness and incidence loading direction.
The seismic performance of structures can be significantly altered by the combined action of scouring and seismic loading. Pandikkadavath et al.62 investigated the seismic vulnerability of bridges subjected to sequential loading and local scouring. Results demonstrated that the two-span bridges are more vulnerable than the three-span bridges for all the DSs. The variation in vulnerability is high for low return period flooding events. Similarly, Jithiya et al.146 investigated RC bridge pier under the combined action of MSAS loading and scouring, while accounting for soil structure interaction. Results were compared for the absence and presence of flood-induced scour, and it was concluded that a high fragility demand would be imposed due to the scouring-related capacity loss.
6.4 Effect of variation in ground motion directionality on MSAS fragility
The selection of ground motions is one of the key building blocks in the fragility assessment framework. The effect of ground motion directionality on the seismic response of a bridge is extensively investigated by Garakaninezhad et al.145 Using a bidirectional MSAS sequential loading scheme, the nonlinear response of the bridge was evaluated. It was concluded that accounting for the incidence loading direction of the mainshock, and the corresponding aftershock significantly alters the seismic performance of the bridge. Similarly, Omranian et al.55 investigated the seismic fragility of skewed bridges under varying input loading directions. Results revealed a pronounced effect on the vulnerability of bridges, and exclusive consideration of this parameter can underestimate the seismic vulnerability in skew bridges, as shown in Figure 5D. An excitation direction of about 60° with respect to the longitudinal axis of the deck caused maximum probability of failure. The accuracy of the results was evaluated by comparing them with the HAZUS model.
Di Sarno and Pugliese79 evaluated the relative differences between successive incident angles on various seismic responses of nonlinear SDOF systems. The mean maximum normalized responses of all the combinations of MSAS incidence angles were considered. It was concluded that short-period structures are more vulnerable to sequential loading if there is a considerable difference in the incidence angles for the MSAS sequence. The findings revealed that critical structural response might come from taking into account the relative differences of successive incidence angles in sequential earthquakes. Consequently, it is imperative to rotate the aftershock and mainshock at distinct angles for reliable seismic evaluation of structures. Similarly, another study revealed that the effect of ground motion rotation is significant for MSAS sequences and can exceed 25% for the considered demand parameters.147
7 CONTRIBUTIONS, LIMITATIONS, AND RECOMMENDATIONS FOR FUTURE DEVELOPMENT
By consolidating the research trends and methodologies employed, this paper identified the gaps in current approaches, particularly with respect to how MSAS events impact the overall structural vulnerability and resilience compared with standalone earthquakes. This study provides an influential pathway for future research direction and seismic risk assessment practices by enhancing focus on sequential seismic risk in fragility derivation. The current emphasis is on the single event-based performance estimation, which may underestimate the already damaged structure for the following aftershocks. This study encourages developing new methodologies and their experimental validation for explicitly considering the cumulative damage in structure due to mainshocks. Another important aspect of this review suggests the integration of aftershock consequences in the seismic design codes for enhancing structural resilience in seismically active regions by considering rigorous assessment criteria accounting for damage accumulation during the service life of the intended designed structures. The need for the aftershocks to be treated in a probabilistic manner in the seismic risk assessment framework like the standalone event is also highlighted. This will ensure an informed seismic risk performance evaluation framework for disaster mitigation, better preparedness, and postdisaster recovery plan.
The studies so far being reviewed in this article are suffering from major limitations, specifically related to guidelines or methodologies that are applicable on a regional scale. There exist studies that consider the seismic risk assessment of infrastructure at a regional scale, however, are limited to single standalone seismic events only. The current existing model may not capture the multiseismic hazard at a regional scale, especially when dealing with all the basic lifeline elements. There is a dire need to develop sequential fragility models that are equally applicable at an expanded regional level for better allocation of resources and disaster response strategies and related decision-making. These extended fragility models should consider the aftershock seismicity of the selected region in a probabilistic way for better predictability of the sequential hazard and reliable model development for resilient-regional planning of the lifeline infrastructure. This, in turn, is related to another challenge of data availability for aftershocks at a regional level. The global seismic databases often lack sequential seismic records, especially in regions where there are no or limited seismic stations installed, leading to high uncertainty in aftershock hazard prediction. The applicability of the aftershock fragility also suffers if they are considered independent events for simplification in the fragility derivation framework. To cope with this, a thorough study of the regional aftershock seismicity might be a major challenge for practitioners.
Although there exists a wide variety of studies focusing on vulnerability analysis of structures subjected to sequential seismic hazards, there is scope for significant improvement in the title domain. In broader terms, demand and capacity are the key parameters in the fragility estimation framework. For building structures, most often displacement-based EDPs are utilized to describe the damaged state of a structural system and hence for fragility derivation. However, seismic energy imparted to the system may cause damage beyond physical deformation. Therefore, for sequential seismic analysis, it is imperative to account for dissipated-energy-based EDP along with correlated physical-damage-based EDP for more accurate structural DS representation and, hence, reliable fragility estimates. Besides, the optimality of the IM for fragility derivation is crucial for enhanced EDP-IM correlation and reduced uncertainties. Different indices are used to evaluate this optimality and have been incorporated into the classical fragility derivation by several researchers. However, for the aftershocks hazard suit, most of the studies have not dealt with this issue and relied solely on the mainshock suit. The degree of uncertainty in the sequential fragility functions can be reduced to a possible minimum by considering the optimality of IM associated with the aftershock in combination with the mainshock hazard suit.
In general, very few studies have considered the effect of uncertainty quantification in capacity and limit state definitions, especially when the structure already suffers the first shock. The analytical approaches are highly capable of uncertainty treatment and progressing it throughout the fragility framework in a probabilistic manner to get a more reliable structural performance estimate. However, in the case of sequential loading, the uncertainty parameters need to be updated for the following loading case and require an integrated framework. Additionally, the selection of seismic sequence is a potential source of uncertainty in fragility derivation which has been rarely addressed so far. The directionality effect associated with each ground motion in the MSAS sequence can significantly alter the dynamic characteristics of structures and should be considered in a probabilistic way.
For bridge infrastructure, most of the available studies focus on the MSAS fragility of piers only and subsequently, the whole bridge performance is approximated based on this single component only. However, different components of the bridge are equally exposed to the impact of sequential seismic loading and collectively describe the structural performance. The existing frameworks should be extended to account for all the vulnerable components in MSAS fragility estimates in a probabilistic domain. Further, for MSAS fragility estimation, structural performance is monitored using a global EDP, like, drift ratio. However, different components may respond in different ways in the nonlinear range, and therefore, it is important to develop a correlation of the component's local EDPs with the structural system's global EDPs for reliable fragility estimates.
Emphasis should be given to the implementation of soil–structure interaction as a potential variable in structural safety and sequential fragility estimation. There exist limited studies related to the effect of scouring on MSAS bridge performance. Most of the approaches applied so far employed a simplified model for the foundation's behavior. A more advanced modeling approach is needed to account for the scour geometry, the variation in scoured soil properties, the hydraulic actions as well as the potential damage modes for a portfolio of bridges. In literature, insignificant attention has been paid to the structural performance of geometrically complex and irregular structures (e.g., curved bridges, multideck bridges, and irregular buildings) under sequential seismic hazards. The interaction of sequential seismic loading with such structures may result in a more complex dynamic response and needs to be investigated for seismic risk and loss mitigation.
This study topic has a lot to be considered for future research development. For instance, the integration of existing risk assessment framework to account for aftershocks for regional fragility model derivation. Additionally, for improved urban-level resiliency, the interaction between different existing lifeline infrastructures should be considered in future studies. The potential hazards that might amplify the seismic regional vulnerability should be considered following a comprehensive approach for understanding the spatial distribution of damage for different lifeline elements and facilities. Future studies should also focus on developing comprehensive validation strategies by incorporating long-term seismic monitoring data of real multiple structure classes for ensuring the adoption of validated models in seismic codes and retrofitting practices. Although this section provides a brief description of possible future developments for reliable sequential fragility estimates, further studies along with detailed examples are required to adequately assess their implementation in the fragility framework.
8 CONCLUSIONS
A detailed state-of-the-art review is presented for the fragility assessment of bridges and building infrastructure subjected to sequential seismic hazard. Considering recent strong earthquake events, mainshock-damaged structures have shown to be more vulnerable, threatening the life and operation safety of Civil infrastructure. The estimation of vulnerability increase for the mainshock-damaged structures plays a significant role in assessing potential losses to facilitate crucial decision-making, such as emergency response mobilization, inspection priority, and recovery decision. The objective of this paper is to provide insight into the significance and the current approaches for MSAS structural performance evaluation and its application in fragility estimation. Fragility functions, being a major part of the seismic risk assessment framework, allow the decision- and policy-makers to cope with risk mitigation and infrastructure management in a probabilistic domain. This study summarized the available approaches for MSAS fragility functions estimation for bridges and building infrastructure and extended to account for different scenarios, including retrofitting, deterioration due to aging, skewness, scouring, and variation in seismic incidence angle. Even though fragility functions are imperative in seismic performance assessment of structures under sequential seismic hazard, it has not been properly integrated into the available design guidelines for seismic performance evaluation associated with varying magnitude of seismic hazard in the aftermath of mainshock event. Despite the availability of a wide variety of literature related to structural performance and fragility evaluation of different structures under sequential seismic loading, still there is a scope for future development. More research in this domain is required to facilitate well-informed, consistent, and rigorous risk and resilience assessments of the Civil infrastructure, which will aid in the development of adaptation, mitigation, and recovery strategies for successive seismic hazards.
ACKNOWLEDGMENTS
The first author gratefully acknowledges the financial support from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
CONFLICTS OF INTEREST
The authors declare no conflicts of interest.
APPENDIX A: LIST OF RELEVANT JOURNALS REFERRED TO IN THIS STUDY
Journal of Engineering Mechanics, ASCE
Journal of Structural Engineering, ASCE
Journal of Bridge Engineering, ASCE
ACI Structural Journal
Journal of Earthquake Engineering
Journal of Performance of Constructed Facilities
Journal of Building Engineering
International Journal of Concrete Structures and Materials
Structure and Infrastructure Engineering, Maintenance, Management, Life-Cycle Design, and Performance
Computer-Aided Civil and Infrastructure Engineering
International Journal of Reliability and Safety
Bulletin of Earthquake Engineering
Soil Dynamics and Earthquake Engineering
Earthquake Engineering and Structural Dynamics
Engineering Structures
Structures
Structure and Infrastructure Engineering
Earthquake and Structures
Earthquake Spectra
Advances in Civil Engineering
Advances in Structural Engineering
Structural Safety
Reliability Engineering and System Safety
Computer and Structures
Earthquake Engineering and Engineering Vibration
