【作者】 于晓辉；

【导师】 王光远； 吕大刚；

【作者基本信息】 哈尔滨工业大学 ， 工程力学， 2012， 博士

【摘要】 近年来，以控制地震风险和地震损失为目标的新一代基于性能地震工程（Performance-Based Earthquake Engineering, PBEE）正成为国际地震工程领域的研究热点。由于地震灾害和工程结构本身均具有强烈的随机性和不确定性，因此美国太平洋地震工程研究中心（Pacific Earthquake Engineering ResearchCenter, PEER）提出了基于全概率表达式的新一代PBEE概率决策框架。该框架以概率地震风险为研究目标，将概率地震危险性、概率地震易损性和概率地震损失作为主要研究内容。为了适应基于性能地震工程（PBEE）的发展趋势，我国编制完成了《建筑工程抗震性态设计通则（试用）》。最新颁布的《建筑抗震设计规范GB50010-2010》也在构件层次提出了基于性能的抗震设计方法。但是，上述文献均采用的是第一代确定性的基于性能的抗震设计思想，基于全概率的PBEE在我国尚未得到广泛的研究。此外，2008年汶川特大地震也启示我们：即使按现行抗震规范进行设计的结构，在发生超过预期的罕遇地震甚至“巨震”时也有发生倒塌的可能性。因此，对按现行规范设计的结构进行地震安全与风险评估，对于进行科学的抗震加固和防震减灾规划具有重要的理论和实际意义。基于上述原因，本文以按我国规范设计的钢筋混凝土框架结构为研究对象，以概率地震风险为研究目的，以概率地震易损性为主要研究内容，从不确定性传递的角度，采用解析函数和高效随机模拟方法，对概率地震易损性和风险分析进行了理论和应用研究。本文的主要研究内容如下：1)按照我国规范，设计了23个不同高度、不同设防烈度的钢筋混凝土框架结构作为“索引原型（index achetype）结构”，并在OpenSees中对结构进行了有限元建模。通过与钢筋混凝土构件（柱）和结构整体的实验结果对比，验证了本文所建立OpenSees模型的合理性。2)将降维积分与Nataf变换相结合，提出了一种考虑随机变量边缘分布和相关性信息的点估计法，并提出了一种新的灵敏度参数。通过三个数值算例研究表明：本文提出的点估计法的精度满足要求，提出的灵敏度参数可以合理地描述随机变量在标准正态空间的变化对模型反应的影响。3)选取了100条实际地震动作为输入，对60个地震动强度参数和6个结构反应参数进行了地震动强度参数的概率评价。分别采用云图法和条带法建立了单体结构的概率地震需求模型，验证了地震需求与地震动强度之间对数线性关系的合理性。针对传统概率地震需求模型无法考虑倒塌状态对地震需求影响的缺点，提出了考虑倒塌状态的概率地震需求模型修正方法。提出了群体结构概率地震需求分析的云图-条带法，建立了群体结构的概率地震需求模型。4)提出了在结构Pushover曲线上定义非倒塌极限状态阈值的构件-整体混合损伤控制原则。考虑结构不确定性的影响，基于本文提出的点估计法，提出了一种随机Pushover方法来进行非倒塌极限状态的概率抗震能力分析。考虑地震动和结构不确定性的影响，提出了基于均值一次二阶矩法（MVFOSM）的随机增量动力分析（IDA）方法，以评估强震作用下结构的概率抗倒塌能力。采用随机Pushover方法和随机IDA方法，建立了23个索引原型结构的概率抗震能力模型。基于单体结构概率抗震能力分析结果，统计获得了群体结构的抗震能力概率分布特征，并对本文定义的四种极限状态阈值进行了概率评价。5)证明了基于地震动强度和基于结构位移的概率地震易损性函数的一致性。从不确定性传递的角度，推导了考虑本质不确定性的概率地震需求易损性和概率地震损伤易损性的解析函数，以及考虑知识不确定性的概率地震易损性点估计和区间估计解析函数，并获得了概率地震易损性点估计函数的置信度水平。利用解析概率地震易损性函数，得到了索引原型结构的地震易损性曲线，并计算了结构的极限状态和破坏状态失效概率。提出了一种定量描述结构地震安全的指标：安全裕度比，并对索引原型结构在不同极限状态下的安全裕度进行了概率评价。生成了与HAZUS软件相容的地震易损性曲线，并与HAZUS软件建议的地震易损性曲线进行了对比分析。对传统的地震易损性模型进行了考虑倒塌状态的模型修正。进行了群体结构的概率地震易损性分析，并与单体结构的地震易损性曲线进行了对比分析。6)基于概率地震易损性函数，采用经典的幂指数形式的概率危险性函数，推导了考虑本质和知识不确定性的概率地震风险的解析函数。在概率地震易损性分析的基础上，采用概率地震风险解析函数，分别在地震需求和地震损伤层次进行了索引原型结构的概率地震风险分析。为评估按我国规范设计的钢筋混凝土框架结构的地震概率安全水平，进一步计算了索引原型结构在使用期（50年）内的失效概率。根据群体结构的概率地震易损性分析结果，进一步进行了群体结构的概率地震风险分析。更多还原

【Abstract】 In recent years, the new generation of performance-based earthquakeengineering (PBEE) aimed at controlling seismic risk and earthquake loss hasbecome one of world-wide research hot topics in the community of earthquakeengineering. Due to the strong randomness and uncertainties in earthquake srongmotions and engineering structures, the Pacific Earthquake Engineering ResearchCenter (PEER) proposed a fully probabilistic risk-informed decision framework forthe new generation of PBEE. In this PEER’s PBEE framework, probabilistic seismicrisk is defined as the seismic performance objective, which includes three mainbuilding blocks: probabilistic seismic hazard, probabilistic seismic fragility, andprobabilistic seismic loss.To adapt to the development trend of PBEE, a pilot edition of “general rule forperformance-based seismic design of buildings” was firstly published in2004inChina. Moreover, the new edition of the Chinese Seismic Design Code of Buildings(GB50010-2010) also carried out a performance-based seismic design method at thelevels of structural elements. However, both of the above important codes employedthe first generation of performance-based seismic design methodology. In fact, thenew generation of fully probabilistic PBEE has not been widely studied and appliedin China. In addition, the great Wenchuan earthquake in2008indicates us that eventhough the structures are designed according to the current seismic code, they arestill probable to collapse in face of unpredicted rare earthquakes or even “hugeearthquakes”. Therefore, it’s reasonable to evaluate seismic risk and safety ofcode-conforming structures. The assessment of seismic risk and safety for structurescan help make rational decisions on seismic retrofitting of structures and disastermitigation planning. Based on the above considerations, in this thesis, theassessment of probabilistic seismic fragility and risk for Chinese code-conformingreinforced concrete (RC) frame structures in the framework of new-generationPBEE is taken as research objective. From the viewpoint of uncertainty propagation,the analytical functions are derived for probabilistic seismic fragilty and risk. Usingthe derived analytical functions and highly effective simulation techniques, theprobabilities of seismic fragility, risk, and safety of Chinese code-conforming RCframe structures are systematically evaluated. The main contents are summarized asfollows:1) Twenty-three RC frame buildings with different fortification intensities andstoreys are designed according to Chinese codes as the “index archetype structures”. These structures are modeled in the platform OpenSees. Through comparing withthe test data of RC elements (columns) and a global structure, the OpenSees modelsare verified and validated to be adequate to describe the nonlinear behavior of theindex archetype structures.2) An advanced point estimate method incorportating marginal distributionsand correlation information of basic random variables is put forward by combiningdimension-reduction integration with Nataf transformation. In the presentedapproach, a new sensitivity factor is proposed. Through three numerical examples, itis illustrated that the developed method has adequate accuracy to estimate probilitymoments of model outputs. Moreover, the presented sensitivity factor is valid toanalyze the influences of the variation of random variables in the standard normalspace on the outputs of nonlinear complex models.3) One hundred real ground motion records are selected as inputs toprobabilistically evaluate the earthquake intensity measures through relating60intensity measures vs.6structural response parameters. The probabilistic seismicdemand models (PSDMs) for individual buildings are built by both cloud-methodand stripe-method, and the rationality of the log-linearity relationships betweenseismic demand and earthquake intensity is furhter verified. Since the conventionalPSDM cannot incorporate the case of collapse, a modified PSDM consideringcollapse case is presented. A new cloud-stripe method is developed for probabilisticseismic demand analysis for group buidlings, and the PSDM for group structures isbuilt up by the new approach.4) The first three non-collapse limit states (i.e. minor damage, moderatedamage, and severe damage) are identified from the pushover curves of structureswith a local-global hybrid damage controlling criterion. Considering the effects ofstructural random parameters on seismic capacity of buildings, a random pushoveranalysis approach with the advanced point estimate method is developed forprobabilistic seismic capacity analysis (PSCA) of non-collapse limit states ofstructures. To consider the effects of both randomness in structural parameters anduncertainty in earthquake strong motions on seismic collapse capacity of structures,a random incremental dynamic analysis (IDA) approach based on mean value firstorther second moment (MVFOSM) is developed for PSCA of collapse state ofstructures. The probabilistic seismic capacity models for23index archetypebuildings are built by the random pushover analysis approach and the random IDAmethod. Then, the probabilistic seismic capacity models for group structures arefitted from the PSCA results for all the index archetype structures. In addition, thethreshold values for the four limit states determined in this study areprobabilistically evaluated.5) The consistence between the intensity-based and displacement-based seismic fragility functions is proved. From the viewpoint of uncertainty propagation,the analytical formulations for probabilistic seismic demand and damge fragilityfunctions considering aleatory uncertainty are derived, and the point and intervalestimate functions of seismic fragility considering epistemic uncetianty are furthergiven. Then the interval confidence level of the point estimate function of seismicfragility is obtained. Using these analytical fragility functions, the seismic fragilitycurves for the index archetype structures are generated. Then the failureprobabilities of various limit states and damage states are calculated for all thearchetype structures from the obtained seismic fragility curves. A new index tomeasure structural safety named as “safety marginal ratio (SMR)” is proposed toevaluate the safety margins of the index archetype structures at various limit states.The HAZUS-compatible seismic fragility curves are generated, and compared withthe recommended seismic fragility curves in HAZUS. Considering the case ofcollapse, the conventional seismic fragility functions are modified. Seismic fragilityanalysis is further carried out for group structures, and then the generated seismicfragility curves for group structures are compared with those for each indexarchetype building.6) Incorporationg the generally used power-law seismic hazard function, theprobabilistic seismic risk functions considering both aleatory and epistemicuncetianties are derived based on the developed analytical fragility functions. Usingthese analytical functions, the probabilistic seismic risks of the index archetypestructures are evaluated at the levels of both seismic demand and seismic damage,based on the results of probabilistic seismic fragility analysis. To evaluate theprobabilistic safety of Chinese code-conforming RC frame structures, the failureprobabilities during the service life (50years) are further computed for the indexarchetype structures. Based on the calculated probabilistic seismic fragilities ofgroup structures, the probabilistic seismic risks for group structures are furtherevaluated.更多还原