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S_a作为地震动强度指标(IM),提出一种考虑主余震序列作用下核岛厂房结构的易损性评估方法。选取PEER数据库地震记录,采用增量动力分析方法,给出了AP1000核岛厂房在420条主余震序列地震作用下的易损性曲线。定量分析了主震强度和主余震谱加速度比对核岛厂房结构易损性的影响。结果表明:核岛厂房的超越概率随着余震强度的增大而增大;余震在主震对结构损伤的基础上会加重核岛厂房的附加损伤;随着主余震谱加速度比从0.5增加到1.0时,核岛厂房结构破坏状态超越概率提高了10%～40%。     

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.     

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.     

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.     

Aftershock seismic assessment taking into account postmainshock residual drifts

This paper introduces and evaluates a methodology for the aftershock seismic assessment of buildings taking explicitly into account residual drift demands after the mainshock (i.e., postmainshock residual interstory drifts, RIDR_o). The methodology is applied to a testbed four‐story steel moment‐resisting building designed with modern seismic design provisions when subjected to a set of near‐fault mainshock–aftershock seismic sequences that induce five levels of RIDR_o. Once the postmainshock residual drift is induced to the building model, a postmainshock incremental dynamic analysis is performed under each aftershock to obtain its collapse capacity and its capacity associated to demolition (i.e., the capacity to reach or exceed a 2% residual drift). The effect of additional sources of stiffness and strength (i.e., interior gravity frames and slab contribution) and the polarity of the aftershocks are examined in this study. Results of this investigation show that the collapse potential under aftershocks strongly depends on the modeling approach (i.e., the aftershock collapse potential is modified when additional sources of lateral stiffness and strength are included in the analytical model). Furthermore, it is demonstrated that the aftershock capacity associated to demolition (i.e., the aftershock collapse capacity associated to a residual interstory drift that leads to an imminent demolition) is lower than that of the aftershock collapse capacity, which mean that this parameter should be a better measure of the building residual capacity against aftershocks. Copyright © 2014 John Wiley & Sons, Ltd.     

A probabilistic framework for quantification of aftershock ground‐motion hazard in California: Methodology and parametric study

This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Seismic damage accumulation in multiple mainshock–aftershock sequences

Earthquakes are generally clustered, both in time and space. Conventionally, each cluster is made of foreshocks, the mainshock, and aftershocks. Seismic damage can possibly accumulate because of the effects of multiple earthquakes in one cluster and/or because the structure is unrepaired between different clusters. Typically, the performance-based earthquake engineering (PBEE) framework neglects seismic damage accumulation. This is because (i) probabilistic seismic hazard analysis (PSHA) only refers to mainshocks and (ii) classical fragility curves represent the failure probability in one event, of given intensity, only. However, for life cycle assessment, it can be necessary to account for the build-up of seismic losses because of damage in multiple events. It has been already demonstrated that a Markovian model (i.e., a Markov chain), accounting for damage accumulation in multiple mainshocks, can be calibrated by maintaining PSHA from the classical PBEE framework and replacing structural fragility with a set of state-dependent fragility curves. In fact, the Markov chain also works when damage accumulates in multiple aftershocks from a single mainshock of known magnitude and location, if aftershock PSHA replaces classical PSHA. Herein, this model is extended further, developing a Markovian model that accounts, at the same time, for damage accumulation: (i) within any mainshock–aftershock seismic sequence and (ii) among multiple sequences. The model is illustrated through applications to a series of six-story reinforced concrete moment-resisting frame buildings designed for three sites with different seismic hazard levels in Italy. The time-variant reliability assessment results are compared with the classical PBEE approach and the accumulation model that only considers mainshocks, so as to address the relevance of aftershocks for life cycle assessment.     

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.     

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.     

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).     

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.     

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.     

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.     

Inelastic seismic demand estimation of wood-frame houses subjected to mainshock-aftershock sequences

An active aftershock sequence, triggered by a large mainshock, can cause major destruction to urban cities. It is important to quantify the aftershock effects in terms of nonlinear responses of realistic structural models. For this purpose, this study investigates the aftershock effects on seismic fragility of conventional wood-frame houses in south-western British Columbia, Canada, using an extensive set of real mainshock-aftershock earthquake records. For inelastic seismic demand estimation, cloud analysis and incremental dynamic analysis are considered. A series of nonlinear dynamic analyses are carried out by considering different seismic input cases and different analysis approaches. The analysis results indicate that consideration of aftershocks leads to 5–20 % increase of the median inelastic seismic demand curves when a moderate degree of structural response is induced. The findings of this investigation facilitate the extension of the existing approaches for inelastic seismic demand estimation to incorporate the aftershock effects.     

强余震的灾害评估

极震区的烈度分布是由主震和大余震产生的。最重的地震灾区为余震区，其范围可由震级与地震区烈度的统计关系求得。在震级与震中烈度关系中，初期余震的烈度略高于主震，晚期强余震的烈度比主震的低。不同烈度对建筑物的损害程度可通过烈度与损失率曲线进行评估。强余震和后续强震的人口伤亡比主震轻。     

The M<Subscript>W</Subscript> 4.5 Vallorcine (French Alps) earthquake of 8 September 2005 and its complex aftershock sequence

On 8 September 2005 a moderate M_W 4.5 earthquake occurred in the north-western Alps midway between Chamonix (France) and Martigny (Switzerland). The focal mechanism corresponds to a right-lateral strike-slip on a N60°E fault plane. The foreshock–mainshock–aftershock sequence is investigated on the basis of data recorded by a temporary network of 28 stations deployed for 1 month just after the mainshock, and data from permanent, regional seismic networks. Absolute and relative locations of more than 400 events are obtained with a mean uncertainty of approximately 0.2 km. Small foreshocks, the mainshock, and early and late aftershocks are located relative to the main aftershock set. The seismic sequence exhibits a surprisingly complex structure, with at least five clusters on distinct fault planes. The main elongated cluster agrees with the location of the mainshock, its hypocenter being 4.3 km below sea level. We discuss the relationship between the right-lateral fault beneath the Loriaz peak (the source of the Vallorcine event), the nearby normal Remuaz fault, and the regional seismotectonic stress field.     

余震序列的时空特征ht

研究我国东部9次余震序列的总体特征得到:余震频度符合 n=n1t-h关系;频度和强度随时间衰减较慢;最大地震后3、4天内发生的余震所勾划的余震区常常比最终余震区小;多数余震分布在地壳中5至10公里的深度上.一些强余震前的中小余震时空分布有下述特征:（1）强余震前几天至十几天,余震序列的频度偏离正常衰减值;（2）强余震前有中小余震震中向下一次强余震的震中附近扩展或形成空区的现象;（3）强余震前震级序列出现缺震现象;（4）余震序列有准周期性.上述特性预示其后将发生强余震,同时表明强余震有类似于大地震的孕震过程.种种现象还表明余震序列在时间和空间上可能是由主震的直接余震和强余震的次级余震相互叠加所组成的.最后将某些特性和岩石试验结果进行了比较和讨论.      

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.     

Aftershock risk assessment and the decision to open traffic on bridges

Critical issues in emergency management after a seismic event are assessing the functionality of the main infrastructures (hospitals, road network, etc.) and deciding on their usability just after the mainshock. The use of a pure analytical tool to assess the aftershock risk of a structure can be contrasted with the limited time available to make a decision about the usability of a structure. For this reason, this paper presents a method for evaluating post‐earthquake bridge practicability based on a rational combination of information derived from numerical analyses and in situ inspections. In particular, we propose an effective tool to speed up the decision‐making process involved in evaluating the seismic risk of mainshock‐damaged bridges in the context of aftershocks. The risk is calculated by combining the aftershock hazard using the Omori law and the fragility curves of the structure, which are calculated using the regression analysis of a sample of results obtained with data randomly generated by the Latin Hypercube Sampling technique and updated based on the results of in situ inspection. Different decision criteria regarding the practicability of bridges are discussed, and a new criterion is proposed. This tool was applied to an old highway RC viaduct. There are two main findings, including the high sensitivity to Bayesian updating (especially when the damage predicted by numerical analysis does not match the real damage) and the criteria used to decide when re‐open bridges to traffic. Copyright © 2013 John Wiley & Sons, Ltd.