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.     

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.     

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.     

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.     

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.     

Stochastic procedure for the simulation of synthetic main shock‐aftershock ground motion sequences

According to the current seismic codes, structures are designed to resist the first damaging earthquake during their service life. However, after a strong main shock, a structure may still face damaging aftershocks. The main shock‐aftershock sequence may result in major damage and eventually the collapse of a structure. Current studies on seismic hazard mainly focus on the modeling and simulation of main shocks. This paper proposes a 3‐step procedure to generate main shock‐aftershock sequences of pairs of horizontal components of a ground motion at a site of interest. The first step generates ground motions for the main shock using either a source‐based or site‐based model. The second step generates sequences of aftershocks' magnitudes, locations, and times of occurrence using either a fault‐based or seismicity‐based model. The third step simulates pairs of ground motion components using a new empirical model proposed in this paper. We develop prediction equations for the controlling parameters of a ground motion model, where the predictors are the site condition and the aftershock characteristics from the second step. The coefficients in the prediction equations and the correlation between the model parameters (of the 2 horizontal components of 1 record and of several records in 1 sequence) are estimated using a database of aftershock accelerograms. A backward stepwise deletion method is used to simplify the initial candidate prediction equations and avoid overfitting the data. The procedure, based on easily identifiable engineering parameters, is a useful tool to incorporate effects of aftershocks into seismic analysis and design.     

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.     

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.     

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.     

2013年芦山MS7.0地震序列参数的早期 特征: 传染型余震序列模型计算结果

为考察2013年4月20日芦山M_S7.0地震震后序列参数的早期特征, 利用“传染型余震序列”(ETAS)模型和最大似然法进行了参数估计. 设定截止震级M_c=M_L2.0, 拟合时段为震后0.31—24.12天, 计算获得α=1.89, p=1.22, 同时利用最大似然法估计获得b=0.72. 与中国大陆地区其它中强震的余震序列参数的比较表明, 芦山M_S7.0地震序列参数表现为触发次级余震的能力较弱和序列衰减速率较快的特征, 反映出余震区相对较高的应力水平. 为检测结果的稳定性, 设定不同的截止震级M_c以及不同的拟合截止时间, 分别进行参数拟合和参数标准差估计. 结果表明, M_c的选取对α值影响明显, 对p值影响则较小. 此外, 震后10天内获得的参数拟合结果随时间变化较为明显, 而其后各参数变化总体较为平稳.      

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.

     

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.     

地震危险性评价中余震活动的影响--以邢台余震区为例

目前通用的地震危险性模型在确定有关地震活动性参数时都强调删除余震,其理由是因为所应用的地震活动模型是泊松模型。但是在现实的地震灾害中,有些是因为余震活动所引起的。忽略余震活动的影响,可能会低估某些区域的地震危险。本文提出考虑余震活动的地震危险性分析模型,并从此模型出发,以邢台地震为例,对余震区内、余震区边界和余震区外等场点计算了考虑余震活动的地震危险性结果,同时,在原有模型的基础上,只改变余震区所处的潜在震源区的地震年发生率,计算相同场点的地震危险性结果,并把这两个结果与不考虑余震活动的结果进行比较,在此基础上讨论在某些区域考虑余震活动的必要性。     

Comparison of the spatial distribution of ground motion between main shocks and strong aftershocks

Using the ground motion attenuation relation, we calculated and compared the effective peak acceleration (EPA) generated by main shocks and their strong aftershocks of 21 earthquake sequences with MS≥7 occurred in Chinese mainland and offing of China during 1966~2002. The result shows that EPA of strong aftershocks usually exceed that of main shock for 76.2% earthquake sequences and EPA of more than 50% strong aftershocks are greatly lar-ger than that of main shocks in large area, which suggests that it is necessary to take damage produced by strong aftershock into account in the probabilistic seismic hazard analysis and the seismic design.     

基于ETAS模型对青海地区余震预测效能评估的研究

为系统评估青海地区余震短期发生率的预测效能,以及构建适合地震活动特点的余震早期预测策略和预测指标体系,利用国际上当前较为前沿的时间序列ETAS模型和"瘦化算法"对青海地区2009年以来的8个地震的早期余震序列参数进行拟合,并利用N-test检验方法对预测结果进行回溯性的效能评估。研究表明:ETAS模型和"瘦化算法"对青海地区的余震发生率具有很好的预测能力,建议采用3天的预测时间窗,且对序列早期阶段进行应用,或可取得"最佳"的预测效果。     

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.      

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.     

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.