主余震序列作用下钢筋混凝土框架结构的多元联合易损性研究

Aftershocks will increase the structural damage induced by the mainshock and consequently promote its failure possibility. However there isn’t the seismic design method considering the effect of aftershocks in the current domestic and foreign seismic design codes. In addition, there are rare studies about the influence of aftershocks on seismic safety of existed structures. To deal with this problem, this project takes the widely located reinforced concrete (RC) frame structures in our country as the research objective. Shaking table test and numerical simulation are both used as research tools. The real mainshock-aftershock sequences involving strong aftershocks are selected as the inputting ground motions. Using the principles of statistics, the most optimum earthquake intensity parameter of the mainshock and that of the aftershock are selected as the vector-form intensity measure of the mainshock-aftershock sequence. Copula theory is adopted to consider the failure criteria incorporating the maximum displacement together with the residual displacement. The uncertainty parameters that have significant effects on structural performance are taken into account. The multivariate joint statistical relations with inputting multivariate earthquake intensities of mainshock-aftershock sequences and outputting multivariate damages of structures are derived, and then the structural failure probabilities exceeding different damage states are calculated under different intensities of mainshock-aftershock sequences. Finally, the multivariate joint seismic fragility model conditioned on mainshock-aftershock sequences is derived. Based on this model, the influence of aftershocks on the residual safety of the mainshock-damaged structure is estimated from two viewpoints, i.e., increase damage probability and safety margin. The study results in this project can provide supports for the decisions to design new buildings and to retrofit old buildings with considering aftershocks.

余震将加剧结构的主震损伤，增大结构的失效可能，但是目前国内外抗震规范尚未有针对余震的抗震设计方法，对于余震对既有结构安全影响的相关研究也比较匮乏。为此，本项目以我国量大面广的钢筋混凝土框架结构为研究对象，以振动台试验和数值模拟作为研究手段，挑选含较强余震的主余震序列作为地震动输入，基于统计学原则选择最优主震强度参数和最优余震强度参数组合作为主余震序列的向量式强度参数，基于Copula理论联合考虑结构最大变形和残余变形的失效准则，考虑对结构性能影响显著的不确定性因素，建立主余震序列的多元地震强度与结构的多元损伤之间的概率关系，计算结构在不同主余震强度下发生各级破坏状态的失效概率，获得结构在主余震序列作用下的多元联合地震易损性模型，进一步从增量损伤概率及安全裕度两个角度对余震对震损结构剩余安全的影响进行评估，从而为考虑余震影响的新建结构抗震设计和既有结构抗震评定与加固提供决策支持。

大量的地震历史资料表明：大部分强震过后都伴随有多次余震的发生，其中，多数伴有较大强度的强余震。余震的发生将加剧主震损伤效应，导致主震损伤结构产生明显的增量损伤，对人员生命安全造成更大的威胁。然而，现行抗震规范中却未考虑余震对结构的潜在影响。为了合理评估主余震序列作用下结构的抗震性能，本项目以地震易损性为评估手段，以我国钢筋混凝土框架结构为主要研究目标，开展了钢筋混凝土框架结构在主余震序列作用下的地震易损性分析。主要研究成果可以总结为以下6点：1) 开展了钢筋混凝土框架结构在主余震序列作用下的振动台试验；2) 分别从非线性单自由度体系和非线性多自由度体系（钢筋混凝土框架结构）两个角度，对主余震序列作用下的结构增量损伤进行了研究；3) 提出了一种可以同时考虑主震和余震强度的主余震序列作用下结构多元概率地震需求分析的分步条带法，并将其用于建立钢筋混凝土框架结构在主余震序列作用下的多元概率地震需求模型；4) 分别计算了非线性单自由度体系的抗主余震序列倒塌能力和主震损伤钢筋混凝土框架结构的抗余震倒塌能力；5) 提出了一种基于Copula理论的主余震序列作用下钢筋混凝土框架结构的多元联合易损性分析方法，并从失效概率和易损性指数两个角度开展了基于易损性的钢筋混凝土框架结构抗主余震序列的安全评估；6) 基于已有的强震数据库，采用Copula理论对主震和余震反应谱之间的相关性进行了研究，并提出了一种余震条件均值谱的预测方法。上述研究成果将有助于工程人员合理评估结构的“二次抗震能力”，并将为考虑余震影响的新建结构抗震设计和既有结构抗震评定与加固提供决策支持。

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