Framework of aftershock fragility assessment–case studies: older California reinforced concrete building frames

Current seismic design codes and damage estimation tools neglect the influence of successive events on structures. However, recent earthquakes have demonstrated that structures damaged during an initial event (mainshock) are more vulnerable to severe damage and collapse during a subsequent event (aftershock). This increased vulnerability to damage translates to increased likelihood of loss of use, property, and life. Thus, a reliable risk assessment tool is required that characterizes the risk of the undamaged structure subjected to an initial event and the risk of the damaged structure under subsequent events. In this paper, a framework for development of aftershock fragilities is presented; these aftershock fragilities define the likelihood that a building damaged during a mainshock will exhibit a given damage state following one or more aftershocks. Thus, the framework provides a method for characterizing the risk associated with damage accumulation in the structure. The framework includes the following: (i) creation of a numerical model of the structure; (ii) characterization of building damage states; (iii) generation of a suite of mainshock–aftershocks; (iv) mainshock–aftershock analyses; and (v) development of aftershock fragility curves using probabilistic aftershock demand models, defined as a linear regression of aftershock demand–intensity pairs in a logarithmic space, and damage‐state prediction models. The framework is not limited to a specific structure type but requires numerical models defining structural response and linking structural response with damage. In the current study, non‐ductile RC frames (low‐rise, mid‐rise, and high‐rise) are selected as case studies for the application of the framework. Copyright © 2015 John Wiley & Sons, Ltd.     

A performance‐based framework for adaptive seismic aftershock risk assessment

Operative seismic aftershock risk forecasting can be particularly useful for rapid decision‐making in the presence of an ongoing sequence. In such a context, limit state first‐excursion probabilities (risk) for the forecasting interval (a day) can represent the potential for progressive state of damage in a structure. This work lays out a performance‐based framework for adaptive aftershock risk assessment in the immediate post‐mainshock environment. A time‐dependent structural performance variable is adopted in order to measure the cumulative damage in a structure. A set of event‐dependent fragility curves as a function of the first‐mode spectral acceleration for a prescribed limit state is calculated by employing back‐to‐back nonlinear dynamic analyses. An epidemic‐type aftershock sequence model is employed for estimating the spatio‐temporal evolution of aftershocks. The event‐dependent fragility curves for a given limit state are then integrated together with the probability distribution of aftershock spectral acceleration based on the epidemic‐type aftershock sequence aftershock hazard. The daily probability of limit state first‐excursion is finally calculated as a weighted combination of the sequence of limit state probabilities conditioned on the number of aftershocks. As a numerical example, daily aftershock risk is calculated for the L'Aquila 2009 aftershock sequence (central Italy). A representative three‐story reinforced concrete frame with infill panels, which has cyclic strength and stiffness degradation, is used in order to evaluate the progressive damage. It is observed that the proposed framework leads to a sound forecasting of limit state first‐excursion in the structure for two limit states of significant damage and near collapse. Copyright © 2014 John Wiley & Sons, Ltd.     

Post‐repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes

In light of recent earthquakes, structures damaged during an initial seismic event (mainshock) may be more vulnerable to severe damage and collapse during a subsequent event (aftershock). In this paper, a framework for the development of aftershock fragilities is presented; these aftershock fragilities define the likelihood that a bridge damaged during an initial event will exhibit a given damage state following one or more subsequent events. The framework is capable of (i) quantifying the cumulative damage of unrepaired bridges subjected to mainshock–aftershock sequences (effect of multiple earthquakes) and (ii) evaluating the effectiveness of column repair schemes such as steel and fiber‐reinforced‐polymer jackets (post‐repair effect of jackets). To achieve this aim, the numerical model of repaired columns is validated using existing experimental results. A non‐seismically designed bridge is chosen as a case study and is modeled for three numerical bridge models: a damaged (but unrepaired) bridge model, and two bridge models with columns repaired with steel and fiber‐reinforced polymer jackets. A series of back‐to‐back dynamic analyses under successive earthquakes are performed for each level of existing damage. Using simulated results, failure probabilities of components for multiple limit states are computed for each bridge model and then are used to evaluate the relative vulnerability of components associated with cumulative damage and column repair. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic risk assessment considering cumulative damage due to aftershocks

Calculating the limit state (LS) exceedance probability for a structure considering the main seismic event and the triggered aftershocks (AS) is complicated both by the time‐dependent rate of aftershock occurrence and also by the cumulative damage caused by the sequence of events. Taking advantage of a methodology developed previously by the authors for post‐mainshock (MS) risk assessment, the LS probability due to a sequence of mainshock and the triggered aftershocks is calculated for a given aftershock forecasting time window. The proposed formulation takes into account both the time‐dependent rate of aftershock occurrence and also the damage accumulation due to the triggered aftershocks. It is demonstrated that an existing reinforced concrete moment‐resisting frame with infills subjected to the main event and the triggered sequence exceeds the near‐collapse LS. On the other hand, the structure does not reach the onset of near‐collapse LS when the effect of triggered aftershocks is not considered. It is shown, based on simplifying assumptions, that the derived formulation yields asymptotically to the same Poisson‐type functional form used when the cumulative damage is not being considered. This leads to a range of approximate solutions by substituting the fragilities calculated for intact, MS‐damaged, and MS‐plus‐one‐AS‐damaged structures in the asymptotic simplified formulation. The latter two approximate solutions provide good agreement with the derived formulation. Even when the fragility of intact structure is employed, the approximate solution (considering only the time‐dependent rate of aftershock occurrence) leads to higher risk estimates compared with those obtained based on only the mainshock. Copyright © 2016 John Wiley & Sons, Ltd.     

Building service life economic loss assessment under sequential seismic events

Aftershocks have been shown to exacerbate earthquake‐induced financial losses by causing further damage to structural and nonstructural components in buildings that have already been affected by a mainshock event and increasing the duration of disrupted functionality. Whereas seismic loss assessment under isolated events has been addressed thoroughly in previous studies, comparatively less has been accomplished in the area of loss assessment under sequences of mainshock‐aftershock ground motions. The main objective of the current study is to formulate a comprehensive framework for quantifying financial losses under sequential seismic events. The proposed framework is capable of accounting for the uncertainties in the state of structure due to accumulation of earthquake‐induced damage, the time‐dependent nature of seismic hazard in the post‐mainshock environment, and the uncertainties in the occurrence of mainshock and aftershock events. Application of the proposed framework to a 4‐story reinforced concrete moment frame shows that consideration of aftershocks could increase lifecycle earthquake‐induced losses by up to 30% compared with mainshock‐only assessments.     

Closed‐form aftershock reliability of damage‐cumulating elastic‐perfectly‐plastic systems

Major earthquakes (i.e., mainshocks) typically trigger a sequence of lower magnitude events clustered both in time and space. Recent advances of seismic hazard analysis stochastically model aftershock occurrence (given the main event) as a nonhomogeneous Poisson process with rate that decays in time as a negative power law. Risk management in the post‐event emergency phase has to deal with this short‐term seismicity. In fact, because the structural systems of interest might have suffered some damage in the mainshock, possibly worsened by damaging aftershocks, the failure risk may be large until the intensity of the sequence reduces or the structure is repaired. At the state‐of‐the‐art, the quantitative assessment of aftershock risk is aimed at building tagging, that is, to regulate occupancy. The study, on the basis of age‐dependent stochastic processes, derived closed‐form approximations for the aftershock reliability of simple nonevolutionary elastic‐perfectly‐plastic damage‐cumulating systems, conditional on different information about the structure. Results show that, in the case hypotheses apply, the developed models may represent a basis for handy tools enabling risk‐informed tagging by stakeholders and decision makers. Copyright © 2013 John Wiley & Sons, Ltd.     

Spatiotemporal seismic hazard and risk assessment of M9.0 megathrust earthquake sequences of wood‐frame houses in Victoria,British Columbia,Canada

Megathrust earthquake sequences, comprising mainshocks and triggered aftershocks along the subduction interface and in the overriding crust, can impact multiple buildings and infrastructure in a city. The time between the mainshocks and aftershocks usually is too short to retrofit the structures; therefore, moderate‐size aftershocks can cause additional damage. To have a better understanding of the impact of aftershocks on city‐wide seismic risk assessment, a new simulation framework of spatiotemporal seismic hazard and risk assessment of future M9.0 sequences in the Cascadia subduction zone is developed. The simulation framework consists of an epidemic‐type aftershock sequence (ETAS) model, ground‐motion model, and state‐dependent seismic fragility model. The spatiotemporal ETAS model is modified to characterise aftershocks of large and anisotropic M9.0 mainshock ruptures. To account for damage accumulation of wood‐frame houses due to aftershocks in Victoria, British Columbia, Canada, state‐dependent fragility curves are implemented. The new simulation framework can be used for quasi‐real‐time aftershock hazard and risk assessments and city‐wide post‐event risk management.     

考虑主余震作用下的核岛厂房结构易损性研究

一次强震常伴随着多次余震作用,且时间间隔较短.研究表明,主震诱发的系列余震会对原有结构造成进一步的累积损伤.核岛厂房结构作为核反应堆的最后一道防线,其在服役期间可能遭受主震和余震的累积作用.参考我国现行规范,定义了四类性能水准(PL)和三种极限状态(LS),以混凝土最大应变作为结构破坏指数(DI),以谱加速度Sa作为地...     

Record selection for aftershock incremental dynamic analysis

The back‐to‐back application of mainshock records as aftershock is often considered in conducting aftershock incremental dynamic analysis. In such an approach, the characteristics of mainshock records are considered to be similar to those of major aftershock records within the same mainshock–aftershock sequences. The underlying assumption is that the characteristics of selected mainshocks, other than those used for record selection, are not significant in the assessment of structural responses. A case study is set up to investigate the effects of aftershock record selection on the collapse vulnerability assessment. The numerical results for a specific wood‐frame structure indicate that the aftershock fragility can be affected by the aftershock record characteristics, particularly response spectral shape. Copyright © 2014 John Wiley & Sons, Ltd.     

Damage spectra for the mainshock–aftershock sequence-type ground motions

Strong aftershocks have the potential to increase the damage state of the structures due to the damage accumulation. This paper investigates the damage spectra for the mainshock–aftershock sequence-type ground motions with Park–Ang damage index. A method of simulating the mainshock–aftershock sequence-type ground motions is proposed based on the modified form of Bath's law and NGA ground motion prediction equation. The damage spectra are computed using the recorded and simulated sequence-type ground motions, and the effects of period of vibration, strength reduction factor, site condition, seismic sequence, damping ratio and post-yield stiffness on damage spectra are studied statistically. The results indicate that the effect of aftershock on structural damage is significant and recorded sequence-type ground motions may underestimate the damage of long-period structures due to the incompleteness of dataset. A simplified equation is proposed to facilitate the application of damage spectra in the seismic practice for mainshock–aftershock sequence-type ground motions.     

Seismic analyses of a RCC building under mainshock–aftershock seismic sequences

A large mainshock may trigger numerous aftershocks within a short period, and nuclear power plant (NPP) structures have the probability to be exposed to mainshock–aftershock seismic sequences. However, the researchers focused on seismic analyses of reinforced concrete containment (RCC) buildings under only mainshocks. The aim of this paper is to thoroughly investigate the dynamic responses of a RCC building under mainshock–aftershock seismic sequences. For that purpose, 10 as-recorded mainshock–aftershock seismic sequences with two horizontal components are considered in this study, and a typical three-dimensional RCC model subjected to the selected as-recorded seismic sequences is established. Peak ground accelerations (PGAs) of mainshocks equal to 0.3 g (safe shutdown earthquake load-SSE load) are considered in this paper. The results indicate that aftershocks have a significant effect on the responses of the RCC in terms of maximum top accelerations, maximum top displacements and accumulated damage. Furthermore, in order to preserve the RCC from large damage under repeated earthquakes, local damage and global damage indices are suggested as limitations under only mainshocks.     

Aftershock collapse vulnerability assessment of reinforced concrete frame structures

In a seismically active region, structures may be subjected to multiple earthquakes, due to mainshock–aftershock phenomena or other sequences, leaving no time for repair or retrofit between the events. This study quantifies the aftershock vulnerability of four modern ductile reinforced concrete (RC) framed buildings in California by conducting incremental dynamic analysis of nonlinear MDOF analytical models. Based on the nonlinear dynamic analysis results, collapse and damage fragility curves are generated for intact and damaged buildings. If the building is not severely damaged in the mainshock, its collapse capacity is unaffected in the aftershock. However, if the building is extensively damaged in the mainshock, there is a significant reduction in its collapse capacity in the aftershock. For example, if an RC frame experiences 4% or more interstory drift in the mainshock, the median capacity to resist aftershock shaking is reduced by about 40%. The study also evaluates the effectiveness of different measures of physical damage observed in the mainshock‐damaged buildings for predicting the reduction in collapse capacity of the damaged building in subsequent aftershocks. These physical damage indicators for the building are chosen such that they quantify the qualitative red tagging (unsafe for occupation) criteria employed in post‐earthquake evaluation of RC frames. The results indicated that damage indicators related to the drift experienced by the damaged building best predicted the reduced aftershock collapse capacities for these ductile structures. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic fragility assessment on the post-mainshock damaged shield building considering aftershock duration and damage ratio

In general, historical earthquake events have shown that a strong mainshock might trigger several aftershocks, which can cause additional damage and seismic risk to the structures. This work tries to investigate the aftershock duration on seismic fragility of the shield building in consideration of initial damage. For this purpose, a three-dimensional finite element model of shield building is established using a concrete damage plastic model. A series of mainshock-aftershock sequences with different durations are selected and scaled to match the target spectrum. A damage ratio of tensile damage is developed to evaluate the additional damage caused by mainshock and aftershocks. Aftershocks with three durations, namely, 20 s, 40 s, and 60 s, are used to study the effect of initial damage levels and aftershock durations on the accumulative damage and seismic fragility of the shield building. The results indicate that those aftershocks with longer durations may wreak more worse cumulative damage to the post-mainshock damaged structure and significantly affect the probability of exceedance. It is also indicated that the initial damage levels have a significant impact on the fragility curves of the shield building. This work can directly incorporate the influence of mainshock-damaged states into the fragility assessment for Nuclear Power Plant.

     

Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences

A large mainshock may trigger numerous aftershocks within a short period, and large aftershocks have the potential to cause additional cumulative damage to structures. This paper investigates the effects and potential of aftershocks on the accumulated damage of concrete gravity dams. For that purpose, 30 as-recorded mainshock–aftershock seismic sequences are considered in this study, and a typical two-dimensional gravity dam model subjected to the selected as-recorded seismic sequences is modeled. A Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is selected for the concrete material. This model is used to evaluate the nonlinear dynamic response and the seismic damage process of Koyna dam under mainshock–aftershock seismic sequences. According to the characteristics of the cracking damage development, the local and global damage indices are both established to study the influence of strong aftershocks on the cumulative damage of concrete gravity dams. From the results of this investigation, it is found that the as-recorded sequences of ground motions have a significant effect on the accumulated damage and on the design of concrete gravity dams.     

Post‐quake decision analysis using dynamic programming

We introduce a general decision analysis procedure based on stochastic dynamic programming in the post‐quake aftershock environment. The damage sustained by the building due to the mainsheet, the time‐varying aftershock rates and the potential for further damage progression in the post‐quake environment are all factors taken into consideration in the proposed methodology. This procedure enables the optimal decision after the mainshock to be selected based on the minimization of expected financial losses, subject to a constraint on a minimal level of individual life‐safety, using a consistent probabilistic framework to explicitly quantify the uncertainties in the variables. Copyright © 2008 John Wiley & Sons, Ltd.     

Cumulative damage effects of mainshock-aftershock sequences on RC-frame structures

Frequent aftershocks often follow a strong mainshock. They can significantly increase cumulative damage to a structure. A model of a five-story reinforced concrete frame structure was designed and a nonlinear mathematical model of the structure was developed to investigate the damage states resulting from different mainshock-aftershock sequences. Mainshock-aftershock sequences consisting of one of three recorded mainshocks combined with one of five recorded aftershocks were created for input to the mathematical model. Inelastic energy dissipation and the Park-Ang damage index were used as measures of cumulative damage to the structure. The results demonstrate that consideration of only the single mainshock ground motion in seismic building design can result in the design and construction of unsafe buildings. Total cumulative damage to a structure is caused by the combination of damage states resulting from the mainshock and the aftershock(s).     

Effects of aftershocks on peak ductility demand due to strong ground motion records from shallow crustal earthquakes

Aftershocks induced by a large mainshock can cause additional damage to structures and infrastructure, hampering building reoccupation and restoration activities in a post‐disaster situation. To assess the nonlinear damage potential due to aftershocks, this study investigates the effects of aftershocks by using real as well as artificially generated mainshock–aftershock sequences. The real mainshock–aftershock sequences are constructed from the Pacific Earthquake Engineering Research Center—Next Generation Attenuation database for worldwide shallow crustal earthquakes; however, they are deemed to be incomplete because of missing records. To supplement incomplete real dataset, artificial sequences are generated on the basis of the generalized Omori's law, and a suitable aftershock record selection procedure is then devised to simulate time‐series data for mainshock–aftershock sequences. The results from nonlinear dynamic analysis of inelastic single‐degree‐of‐freedom systems using real and artificial sequences indicate that the incremental effects of aftershocks on peak ductility demand using the real sequences are relatively minor and that peak ductility demand estimates based on the generalized Omori's law are greater, particularly in the upper tail, than those for the real sequences. The results based on the generalized Omori's law also suggest that the aftershock effects based on the real sequences might underestimate the aftershock impact because of the incompleteness of the real dataset. Copyright © 2012 John Wiley & Sons, Ltd.     

The partitioning of radiated energy and the largest aftershock of seismic sequences occurred in the northeastern Italy and western Slovenia

We analyzed the most relevant seismic sequences that occurred from 1977 to 2007 in the Friuli-Venezia Giulia region (northeastern Italy) and western Slovenia. The eight aftershock sequences were triggered by low- to moderate-magnitude earthquakes with mainshock duration magnitude ranging from 3.7 to 5.6. The b-value of the Gutenberg–Richter law varies from 0.8 to 1.1. The modified Omori’s modeling of the sequences evidences values of the p exponent ranging from 0.8 to 1.0. Using the Reasenberg and Jones (Science 243:1173–1176, 1989; Science 265:1251–1252, 1994) approach, we computed the probabilistic estimate of the aftershock rates and the largest aftershock in given time intervals. The difference in magnitude between the mainshock and the largest aftershock is calculated according to the modified Båth law and using an approach that considers the partitioning of the radiated seismic energy between mainshock and aftershocks. The partitioning of the radiated seismic energy appears to play a significant role in the evolution of the sequences. We define the parameter R _ES as the ratio between the radiated seismic energy of the mainshock and the summation of the seismic energy radiated by the aftershocks. The difference in magnitude between the mainshock and the largest aftershock, calculated with the parameter R _ES, agrees well with the observed difference. In most sequences, the parameter R _ES decreases very quickly until the occurrence of the largest aftershock and then becomes constant. By analyzing the values of R _ES during the early hours following the mainshock, we found that the R _ES values after 24 h are well related to the final ones, calculated on the whole sequence, and to the differences in magnitude between the mainshock and the largest aftershock.     

主-余震作用下框架-核心筒错层隔震结构地震响应分析

新型错层隔震结构是基础隔震和层间隔震体系发展而来的一种新型隔震结构。强主震发生后会伴随着大量的余震出现,余震会使结构造成更大损伤。研究新型错层隔震结构分别在单独主震和主-余震作用下结构的变形与损伤,采用ETABS有限元软件建立某24层框架-核心筒结构模型进行非线性时程响应分析。结果表明：主-余震作用下,新型错层隔震结构的核心筒损伤主要集中在框架隔震层和核心筒隔震层之间,框架的塑性铰集中在框架隔震层以下部分,框架隔震层角柱支座的滞回曲线饱满且比核心筒隔震层角部隔震支座耗能好。新型错层隔震结构的最大隔震层位移均出现在框架隔震层。在余震作用下,新型错层隔震结构的损伤会显著增加。框架隔震层以上框架部分和以下框架部分以及核心筒的损伤分别增加8%、10%和19.80%。余震对隔震层的影响更大,框架隔震层和核心筒隔震层的层间位移分别增加78.70%和60.54%。