考虑主余震序列作用的砌体结构易损性分析

鉴于我国砌体结构抗震面临的严峻形势,以及主余震序列作用下砌体结构易损性研究存在的不足,以汶川地震中1栋典型砌体房屋为依托,开展考虑主余震序列作用的砌体结构易损性研究。首先,建立了结构的三维有限元模型,并从结构动力特性与损伤等方面验证了模型的合理性; 其次,选取整体损伤耗能作为结构性能参数,并给出了对应不同破坏等级的结构整体损伤耗能界限值; 最后,基于IDA方法对结构进行了不同主余震序列作用下的易损性分析。结果表明:相对于层间位移角,整体损伤耗能更适用于描述余震对结构的累积损伤效应; 随着结构主震损伤程度的加深,余震对结构造成的影响越明显,且主余震序列作用下结构呈现出比主震单独作用下高一个破坏等级的趋势; 当ΔPGA小于0.6时,结构的极限状态超越概率最大增幅不超过10%,此时余震的影响较小; 当ΔPGA大于0.6时,结构的极限状态超越概率最大增幅可达到33.1%,此时余震的影响较大。     

考虑主余震作用的近海桥墩时变地震易损性分析

基于OpenSEES平台,以某近海刚构桥桥墩为例,选取符合场地类型的地震波,并根据地震记录构造主余震序列。运用"能力需求比"分析方法建立不同服役时间节点桥墩控制截面在不同损伤状态条件下的地震易损性曲线,研究氯离子侵蚀和主余震序列对桥墩抗震性能的影响。结果表明:同一损伤状态的超越概率随着服役时间延长和PGA增大而不断变大,且随着损伤状态等级提高,超越概率逐渐降低。轻微损伤状态下,主余震序列对桥墩易损性影响较小;中等损伤、严重破坏和完全倒塌状态下,同一服役期,考虑主余震序列作用下桥墩的超越概率相比于仅考虑主震作用明显增大。     

主余震作用下高强钢筋混凝土框架的易损性分析

为研究主余震作用下配置高强钢筋的RC框架结构的抗震性能,根据相同设计指标和"等强代换"的原则,设计了三榀六层四跨的钢筋混凝土框架,纵向受力钢筋的强度等级分别为HRB400、HRB500和HRB600。通过OpenSees平台进行有限元建模,将最大层间位移角作为结构损伤指标,反应地震作用的结构响应。选取15条地震加速度时程,通过重复法构造人工主余震序列并进行IDA分析,得到结构在不同强度的主余震序列作用下的地震易损性曲线。结果表明:主震PGA越大,余震的最大层间位移角越大,结构达到各极限状态的概率越高。对比配置不同钢筋强度的三榀框架的计算结果,可知"等强代换"原则下,相同主余震序列作用时,钢筋强度的提高对结构抗倒塌性能有不利影响,但影响有限。     

主余震序列型地震动作用下RC框架结构损伤耗能研究

强震发生后通常伴随着余震，余震的发生会加重结构损伤甚至引发倒塌。为了量化研究主余震序列型地震动对结构损伤的影响，以一栋3层钢筋混凝土框架结构为研究对象，选取了10条实际的主余震记录作为地震动输入，采用ABAQUS非线性有限元软件对该框架结构进行非线性动力时程分析，并依据结构局部和整体损伤耗能指标来评价主余震序列型地震动对框架结构累积损伤的影响。研究结果表明:序列地震会加剧结构底层柱的局部损伤耗能，特别是对底层中柱的影响更加明显；序列地震作用下的结构整体损伤耗能平均值相对于单主震作用下增加约30%；当余震与主震的第一周期谱加速度指标的比值Sa （T₁）_余震/Sa （T₁）_主震较大时，序列地震对结构损伤需求的影响更为显著。     

最不利主余震序列型地震动作用下RC框架结构易损性研究

余震的发生会造成结构的累积损伤，不同类型的主余震序列地震动对结构的影响有所差异。鉴于此，以主震卓越周期小于或接近余震卓越周期为基本原则，确定了最不利主余震序列地震动。选择4层RC框架结构为研究对象，在增量动力分析的基础上，定义了4个性能水平，以此来研究该结构的易损性。依据破坏状态概率和震害指数，得到7度多遇、7度设防和7度罕遇地震的易损性指数。研究结果表明:依据我国规范设计的RC框架结构的4个性能水平的量化指标限值依次为1/495、1/263、1/108和1/45，余震的出现会加剧结构的破坏状态。当以易损性指数作为评价指标时，可认为该结构能够满足小震不坏、中震可修和大震不倒的抗震设防目标。     

主余震作用下山地掉层框架结构的易损性分析

一次强震过后通常伴有多次余震发生,由于主震和其后续余震之间的间隔时间较短,使得主震损伤结构未能得到及时修复而进一步遭受余震作用,产生“二次损伤”。山地结构的受力性能与普通结构有显著差别。参考我国现行规范设计了具有代表性的3个不同掉层数与掉跨数的山地掉层框架结构及1个普通平地框架结构,采用增量动力分析方法,以Park-Ang损伤指数作为结构响应参数DM,以PGA作为地震动强度参数IM,给出了掉层结构以及平地结构在主余震作用下的易损性曲线,对比分析了掉层结构与平地结构的易损性,研究了余震对各结构易损性的附加影响。基于抗倒塌储备系数(CMR)评价了结构的抗倒塌能力,比较了各结构的抗震倒塌安全储备。结果表明:余震会提高结构的超越概率,且随着余震强度的提高,超越概率越大;掉层结构的超越概率更高,且掉层数与掉跨数对结构地震易损性的影响较大;与平地结构相比,山地掉层结构抗倒塌储备系数较小,抗倒塌安全储备较低。对于掉层结构,掉跨数与掉层数的增加均会降低结构的抗倒塌安全储备,且掉层数对CMR的影响更大。     

主余震下近海钢筋混凝土桥墩全寿命抗震分析

我国近海桥梁具有服役期长、工作环境恶劣并且面临较高的地震作用风险等特点。本文分析了全寿命周期内高性能混凝土中氯离子腐蚀作用,采用10组相同台站记录的实际主余震记录构造出新的主余震地震序列,利用增量动力分析(IDA)和地震易损性方法分析了主余震地震序列和氯离子腐蚀对桥墩抗震性能的影响。分析结果表明:在轻微破坏状态下,服役时间和地震序列对桥墩地震易损性影响不大;在中等破坏、严重破坏和完全破坏状态下,服役时间和地震序列作用均对桥墩地震易损性有很大影响,桥墩更容易进入危险状态。     

主余震作用下钢框架-中心支撑结构抗震性能分析

为研究余震对钢框架-中心支撑结构抗震性能的影响，以钢框架-拉链柱式中心支撑结构和传统钢框架-人字形中心支撑结构为例，基于增量动力分析方法，对2种结构在主余震、主震作用下进行地震易损性分析。对比了2种结构地震易损性差异，根据抗倒塌储备系数评价了2种结构的抗倒塌性能。结果表明：余震会增加结构的地震易损性，其影响程度随着地震动强度的变大而增加；与人字形中心支撑结构相比，拉链柱式中心支撑结构在高强度地震下处于重度损伤和倒塌2种极限状态时的失效概率更低，抗倒塌储备系数更大，抗倒塌性能更优。     

基于能量的主余震作用下RC框架损伤与震后性能评估

地震发生后，震损结构能否承受强余震是震害调查与灾后重建中的重要问题。因此，准确评估主余震造成的结构损伤以及评估主震后震损结构的剩余倒塌能力至关重要。采用基于能量的地震损伤指标对结构损伤进行评估，以能量谱作为工程需求参数，再通过引入震损结构模型对结构在主余震作用下的累积损伤进行评估，建立主余震作用下结构整体损伤评估理论框架。然后，基于I_V损伤指数对主余震下的结构损伤进行量化，得到震损结构的倒塌能力曲线，并确定结构剩余承受强余震的能力。以6层3跨钢筋混凝土(reinforced concrete, RC)框架结构为例进行分析，结果表明：地震能量损伤指标法物理意义明确，可以从能量角度快速评价主余震下结构损伤；震损结构的剩余倒塌能力随着主震强度增加而逐渐降低；对于案例结构而言，主震下结构损伤小于0.32时可以认为震损结构是安全的可以承受强余震，介于0.32～0.52之间时，需要对震损结构加固修复，以保障余震安全。     

考虑非结构构件损伤的钢筋混凝土框架建筑多维地震易损性分析

基于单一指标的传统地震易损性分析忽略了非结构构件损伤对建筑抗震性能的影响。首先基于多维性能极限状态理论建立了三维性能极限状态方程,并对几种特殊情况下的三维阈值曲面进行了讨论。进而以最大层间位移角作为整体结构与位移敏感型非结构构件的性能指标,以峰值楼面加速度作为加速度敏感型非结构构件的性能指标,对建筑的结构损伤和非结构损伤进行描述。考虑各性能指标之间的相关性和各性能指标所对应的极限状态阈值的不确定性,建立了建筑在地震作用下的三维性能极限状态的超越概率函数。最后,采用Open Sees有限元软件对一7层钢筋混凝土框架填充墙建筑进行增量动力分析,得到其各性能水平下的地震易损性曲线。分析结果表明,当忽略非结构构件损伤时,各性能极限状态的超越概率均降低,从而高估了建筑剩余功能水平,进而导致低估建筑的损失。在考虑各性能指标的极限状态阈值的不确定性时,对任一性能极限状态,不同变异系数取值下的易损性曲线会出现交点,在交点之前超越概率随着变异系数的增大而增大,交点之后则随着变异系数的增大而减小。在考虑性能指标间的相关性时,对任一性能极限状态,超越概率随着相关系数的减小而增大。另外,性能指标阈值的不确定性与性能指标间的相关性对地震易损性的影响随着性能水平的提高而逐渐降低,且对低性能水平下建筑地震易损性有明显影响。     

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.     

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 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.     

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.     

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.     

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.     

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.     

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%。