主余震序列作用下钢筋混凝土框架结构损伤分析

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”。为此,以一栋5层按我国相关设计规范设计的钢筋混凝土框架结构为研究对象,对主余震序列对结构造成累积损伤及余震对结构造成的增量损伤进行了研究。选取75条真实主震及其余震记录构成序列型地震动输入。同时,采用真实主余震序列中的主震记录,分别采用重复法和随机法两种人工余震构造方法,构造两组人工主余震序列作为地震输入。采用改进的Park-Ang损伤指数作为结构损伤指标,对结构在主震及其在真实和人工主余震序列作用的损伤进行计算,并对余震产生的结构增量损伤进行评估。进一步以峰值加速度、谱加速度、Arias强度作为主震和余震强度参数,研究了余震与主震强度比与余震增量损伤之间的相互关系。分析结果表明：基于随机法的人工主余震序列会对结构造成最显著的增量损伤;采用余震和主震强度比可以较好地预测余震增量损伤的显著性。     

基于分步调幅法的钢筋混凝土结构主余震易损性曲面分析

传统主余震易损性分析多采用仅考虑主震强度或余震强度的标量式易损性函数，所获得的易损性曲线无法全面反映主、余震强度对结构抗震性能的综合影响。为解决这一问题，提出了一种同时包含主、余震强度的主余震易损性曲面分析方法。通过对主余震序列进行主、余震分步调幅，获得包含不同主、余震强度组合的主余震序列输入。通过分步拟合，构建同时包含主、余震强度的主余震需求模型，生成主余震易损性曲面，并进一步计算获得具有不同危险性水平的主、余震强度所对应的主余震易损性指数。以一栋按我国规范设计的钢筋混凝土框架结构为例，采用所提出方法进行了主余震易损性曲面分析。分析结果表明：所提出方法可以有效地生成结构的主余震易损性曲面，给定主震危险性水平而提升余震危险性水平或给定余震危险性水平而提升主震危险性水平，均可带来结构主余震易损性指数的提高，且后者引起的主余震易损性指数提高幅度更为显著，证明了主震作用在主余震易损性分析中的主导地位。     

主余震序列作用下屈曲约束支撑框架易损性分析

主震引发的多次强余震可能导致屈曲约束支撑(BRB)在地震作用下发生疲劳破坏。BRB突然失效可能使主震引起的微小损伤加剧,引发结构倒塌。因此,有必要考虑余震对BRB构件和BRBF结构的影响。通过增量动力方法,对考虑BRB疲劳性能的屈曲约束支撑框架(BRBF)进行易损性分析,对比了在单独主震和主余震序列作用下BRBF结构的地震易损性差异。结果表明,在高强度主余震序列作用下,BRBF结构的失效概率显著增加,对其性能要求更高。此外,分别以峰值层间位移角和残余峰值层间位移角作为需求参数指标,对比分析了BRBF结构在主余震序列作用下的易损性差别。结果表明,以残余峰值层间位移角为参数指标时,对结构性能要求更严格。     

主余震序列作用对剪力墙结构动力响应影响分析

为了研究主余震序列作用对高层剪力墙结构动力响应的影响,以某超高层作为研究基础建立了其动力弹塑性分析模型,开展了相关研究工作。选取10个真实主余震序列作用事件,构造了14条主余震序列作用作为输入的地震荷载;以PGA、PGV、PGA/PGV等作为表征地震动强度的指标,计算了结构在主余震序列作用及仅主震作用下的结构塑性耗能、最大残余层间位移角的增量损伤比及Karl Pearson相关系数;分析了主余震序列作用下结构塑性耗能及最大残余层间位移角的特点和地震动强度指标与增量损伤比的相关性。结果表明,主余震序列作用加剧了结构损伤,其塑性耗能增量平均达24%～28%;主余震序列作用下结构最大残余层间位移角有可能增大,也有可能减少。基于塑性耗能的结构主余震增量损伤比与PGV、SED、S_I等速度相关的地震动强度表征指标均表现出了较强的相关性,可考虑作为选择和调整主余震序列作用地震波的指标;基于最大残余层间位移角的结构主余震增量损伤比则与地震动强度指标相关性较弱。     

多塔斜拉桥在主震-余震序列波下地震位移研究北大核心

桥梁等结构在遭受地震时,总是会历经前震、主震与余震等一系列地震波动。余震的存在可能会使结构的地震需求超过主震时期,可以说余震对于结构安全有着不可忽略的影响。建立有限元模型,对常规摩擦支座的减隔振体系桥梁结构输入主震-余震序列波,得到墩梁相对位移时程,通过对比分析结构在主震作用下、在余震单独作用下以及在主震-余震序列波作用下支座位移之间的差别,来研究强余震对结构位移峰值以及残余位移的影响。分析研究表明:强余震在很大程度上影响了结构的位移峰值以及残余位移,在抗震设计中余震的作用是不可忽视的,在地震波输入时,应当考虑主震余震序列波。     

考虑余震影响的RC框架结构抗震设计方法

历史地震表明强余震会进一步增大结构的破坏程度甚至使其倒塌，但是我国乃至世界上的所有抗震设计规范均只考虑主震作用而没有直接考虑余震影响。为提出能有效考虑余震影响的抗震设计方法，文章基于主余震设计谱和主震设计谱共设计了12个钢筋混凝土(RC)框架结构。选取50条实际主余震地震动对所有结构进行增量动力分析进而得到结构倒塌易损性，对比分析了主余震、主震影响区域结构的倒塌储备系数CMR，发现仅采用设计谱进行弹性设计会使得主余震影响区域结构的CMR会小于主震影响区域结构。为实现主余震、主震影响区域结构的倒塌储备等效，首先给出了以基本周期T1为变量的Sa, 50% collapse预测公式，然后推导了结构倒塌储备等效方程，并结合设计谱进行数值求解，最后给出了倒塌储备等效条件下以主震影响区域结构基本周期T1,M为变量的主余震影响区域结构基本周期T1,A预测公式，综合使用该预测公式和主余震设计谱可以实现主余震、主震影响区域结构的倒塌储备等效。     

主余震序列地震作用下一级抗震预应力型钢混凝土空腹桁架转换层框架结构抗震性能研究

基于"三道防线抗震设防"的设计方法,以2榀8度(0.2g)设防区的上抬层数不同的一级抗震预应力型钢混凝土(PSRC)空腹桁架转换层框架结构为研究对象,完成了罕遇烈度水准下不同余震主震强度比■的系列弹塑性时程分析。然后,通过层间位移角、转动能力需求比和损伤指数等多个性能指标,对构件、防线以及结构整体等不同层次的抗震性能和损伤状况进行研究。结果表明:在主震及主余震序列地震作用下,结构均未发生整体破坏,当余震较强时,以损伤指数计算的个别上抬框架梁出现局部破坏;结构后续两道防线的损伤明显小于第一道防线,形成主要以第一道防线内梁铰耗能的"梁柱混合出铰机制","三道防线抗震设防"的设计原则得以实现;余震作用下,结构的整体损伤指数显著增加,且"二次损伤"明显;较大余震下,转换柱出铰普遍,甚至出现"层侧移机制",应加强转换柱柱端弯矩增大措施。     

主余震下增量动力时程分析及主震易损性分析

以3层钢筋混凝土框架填充墙结构为研究对象,将调幅后的主震与余震串联,对结构进行主余震作用下的增量动力时程分析(IDA分析),并探讨了仅考虑主震作用下的部分样本的易损性,对日后钢筋混凝土框架—填充墙结构的震害评估及安全性能评定提供了依据。     

考虑主余震序列的高墩刚构桥地震易损性分析

基于主震和余震的统计关系以及多性能极限状态的相关性理论,提出了考虑主余震序列的桥梁系统地震易损性评估方法。该方法可以较全面地考虑余震对桥梁地震易损性分析的影响,同时又可避免用桥墩局部易损性代替系统易损性产生的较大误差。以一座典型双肢薄壁高墩高构桥为例,建立了其考虑余震作用的系统地震易损性曲线,并将结果与仅考虑主震作用的易损性曲线对比。结果表明:评估高墩刚构桥地震易损性时,宜考虑主余震序列,否则将高估其在各级地震下的抗震性能,此现象对严重损伤、完全破坏情形尤为明显;主震震级越大,余震对高墩刚构桥地震易损性影响越强烈;即使高墩刚构桥在主震中仅发生轻微损伤,但在余震中倒塌的可能性仍然很高。     

考虑余震影响的结构抗震设计实用方法

本文利用文献１中给了贩主震震级与余震震级之间的统计关系，并基于地震动能量等效的方法，将主震和多次余震等效为一次地震。然后从现行抗震规范出发，提出了考虑余震影响的结构抗震设计实用方法。最后给出了算例。     

Vulnerability assessment of a high‐rise building subjected to mainshock–aftershock sequences

Strong aftershocks have the potential to further aggravate the damage state of structures, and much less attention has been given to the seismic vulnerability of high‐rise buildings than that of low‐ to medium‐rise buildings. This study assesses the seismic vulnerability of a 32‐storey frame–core tube building by performing the incremental dynamic analysis on the material‐based three‐dimensional numerical model. A storey damage model based on the material damage is developed using the weighted average method. Eighteen recorded mainshock–aftershock sequences, whose mainshock records match the target spectrum, are selected. The results indicate that the developed stroey damage model can effectively reflect the additional damage induced by aftershocks. Strong aftershocks have high potential to change the location of weak storeys. Notably, shifts of weak storeys are observed in more than 30% of aftershocks with relative spectral acceleration of 0.8. As the mainshock‐induced damage state becomes more severe, the mainshock‐damaged building becomes increasingly fragile to the aftershock excitation and more sensitive to aftershock intensities. The probability of exceeding severe damage state increases from 35.3% to 62.1% due to the effects of strong aftershocks. The results in this study can provide supports to the seismic resilience assessment of this high‐rise building.     

Seismic design requirements for reinforced concrete piers considering aftershock-induced seismic hazard

The main purpose of this study is to develop an estimation procedure of seismic design level setting for reinforced concrete (RC) piers considering aftershock-induced seismic hazards. This work develops an assessment method of the seismic hazards induced by aftershocks and takes an example of the Chi–Chi Earthquake in Taiwan. The number of aftershocks is assumed to follow the modified Gutenberg–Richter law with lower and upper bounds when analysing the cumulative density function of the magnitude of the aftershock within a specified post-mainshock period for the earthquake. Additionally, this work considers the spatial uncertainty in the hypocentres of aftershocks to assess the aftershock-induced seismic hazards. Fragility curves and residual factors of damaged RC piers are used in the transition probability matrix of Markov Chain model for considering the cumulative damage induced by aftershocks by incorporating uncertainty into aftershock events, as well as into structural capacity and residual factors corresponding to a specified damage state, the exceedance probabilities for various damage states can be estimated using Markov Chain model and Monte Carlo Simulation. Finally, in the case study, the proposed procedure is used to determine the important factor in the preliminary seismic design of typical RC piers for the Chi–Chi Earthquake in Taiwan.     

Seismic capacity assessment of postmainshock damaged containment structures using nonlinear incremental dynamic analysis

This paper investigates the structural performance and seismic capacity of the postmainshock damaged containment structure through the incremental dynamic analysis (IDA). To evaluate the seismic capacity with minimum uncertainty, the damage measure (DM) and intensity measure (IM) for IDA curves are selected in term of the coefficient of variation. The IDA using mainshock records is implemented to examine the seismic damage process of a containment structure and determine key damage states. The static cyclic loading analysis and aftershock IDA are also conducted on mainshock‐damaged containment structures to investigate the effect of initial damage states on the dynamic characteristics of structures. Finally, based on IDA results, limit states of a containment structure are defined using a generalized multidimensional limit‐state function that allows considering the dependence between the mainshock‐damaged level and residual seismic capacity. These proposed bidimensional limit‐state functions can be used in the fragility analysis and risk assessment of containment structures under mainshock–aftershock, which can improve the accuracy of seismic assessment.     

Seismic vulnerability assessment of process towers using fragility curves

This study focuses on the seismic vulnerability assessment of process towers. A 96‐m process tower, located at the Shazand Refinery, is considered for a case study sample. The vulnerability of this structure is expressed with the development of fragility curves, which provide the probability of exceeding a prescribed level of damage for a wide range of ground motion intensities. The methodology of developing fragility curves for process towers is shown. The developed fragility curves can be very useful for emergency management agencies and insurance companies wishing to estimate the overall loss after an earthquake. The vulnerability of nonstructural equipments of tower is also assessed in subsequent step. To model the process tower with its base details, a nonlinear finite element model is generated. It was found that the fragility curves should be developed for external pressure condition because it is more critical state of loading. The results show that the damage to the process tower occurs in the shell; and the other types of damages, i.e. yielding of anchor bolts, structural damage to foundation and overturning of tower, do not occur. Copyright © 2013 John Wiley & Sons, Ltd.     

Fragility Assessment Model of Building Structures Using Characteristics of Artificial Aftershock Motions

Any additional loads applied to a damaged structure can aggravate its instability and thus, the impact of successive earthquakes need to be considered. This study proposed a quantitative assessment model for the fragility of a damaged structure subjected to aftershock. Mean period and the strong motion duration were considered as characteristics of earthquake motions. Simulation models of two reinforced concrete structures and one steel structure were selected to examine the applicability of the model. Based on the suggested fragility and residual deformation coefficients, critical earthquake sequences for each structure were identified. The proposed model was efficient in selecting critical earthquake sequences by using the limited number of aftershocks, and these sequences are expected to be useful indicators in the establishment of a retrofit plan according to the predicted structural response and target performance levels.     

Building life-cycle cost analysis due to mainshock and aftershock occurrences

The objective of this paper is to develop formal stochastic expected financial loss estimation models over the lifetime of the building due to mainshocks and their subsequent aftershock sequences. Mainshocks are typically modeled as a homogeneous Poisson process with constant mean rate of occurrence, while the resulting aftershocks are modeled as a nonhomogeneous Poisson process with random magnitudes which has parameters (mainshock magnitude, m_m, and location) that are conditional on the random mainshock. The initial model to compute expected losses is the simplified homogeneous Poisson mainshock process and nonhomogeneous Poisson aftershock process with “immediate” repair of the building to the initial building state. We then develop a more general Markov and semi-Markov framework where we consider both Poisson and renewal processes for modeling mainshock occurrences with various building damage progression scenarios. Finally, we will incorporate the random aftershock losses into pre-mainshock financial loss estimation. The ability to compute the expected building life-cycle cost due to both mainshocks and aftershocks will be useful as an input to seismic decision making (both post- and pre-mainshock).     

有损伤压弯构件的恢复力试验研究及其应用

本文通过三组钢筋混凝土压弯构件模型的振动台主余震模拟试验和周期性抗震静力试验，初步给出了建立有损伤压弯构件恢复力骨架曲线的一般方法，并在此基础上就不同情况具体给出了随机主余震作用下结构层恢复力骨架曲线的建立步骤，从而为结构在主余震作用下的随机反应分析奠定了基础。最后，通过算例分析，得出了余震对结构破坏的影响。     

考虑倒塌概率修正的钢筋混凝土框架结构地震易损性分析

为研究倒塌概率对非倒塌极限状态的影响,提出了考虑倒塌概率修正的结构地震易损性分析方法。基于全概率定理,将结构极限状态划分为倒塌状态和非倒塌状态两类,若结构发生倒塌则认为结构发生非倒塌极限状态破坏的概率为100%。考虑倒塌概率修正的地震易损性分析方法包含直接方法和间接方法,其中,直接方法是直接对传统地震易损性函数进行修正,而间接方法仅修正地震易损性函数中的概率地震需求参数。以4榀不同高度不同设防烈度的钢筋混凝土平面框架结构作为研究对象,选择100条实际地震动记录作为输入,分别采用直接方法和间接方法开展考虑倒塌概率修正的地震易损性分析。结果表明：倒塌概率对轻微破坏和中等破坏极限状态的影响较小,而对严重破坏极限状态的影响较大;在地震动强度较小时,两种方法对地震易损性的修正结果相差较小;随着地震动强度的提高,两种方法对地震易损性修正结果的差距逐渐增大。     

基于地震易损性解析函数的概率地震风险应用研究

在采用全概率方法的基于性能的地震工程研究中,定量反映地震作用和工程结构中存在的不确定性是研究的关键。利用地震易损性和地震风险的概率解析函数,针对一栋按我国相关规范设计的五层三跨钢筋混凝土框架结构进行了地震易损性分析和风险评估。采用100条实际地震动作为输入以考虑地震动的不确定性,提出了基于控制变换拉丁超立方体抽样技术的随机Pushover方法以考虑结构不确定性对其抗震能力的影响。结果表明：算例结构在50年内发生完全破坏的概率不超过2%,发生严重破坏的概率不超过10%,发生轻微破坏的概率基本不超过63.2%,基本满足我国“小震不坏、中震可修、大震不倒”的三水准要求。