结构抗震可靠度二种简化解析表达式的一致性证明

Verification of consistency of two simplified analytical formulations for structural seismic reliability

结构抗震可靠度分析的解析求解一直是结构可靠度领域和地震工程领域研究者们的追求目标。解析表达式不仅有利于简化结构抗震可靠度分析这个极端困难的工作,而且也有利于进行基于可靠度的结构概率抗震性能设计与评定。从全概率定理的两种不同表达式出发,介绍了国际上流行的两种结构抗震可靠度解析表达式,过去一直认为这是两种理论基础不同的表达式。本文通过对地震易损性函数关系的解析推导,揭示了若干重要关系,证明了两种表达式的一致性。

Analytical solutions for seismic reliability analysis of structures have been the pursued objectives of many researchers in the communities of structural reliability and earthquake engineering for a long time. Analytical formulations can not only simplify the tedious and difficult process of seismic reliability analysis of structures but also favor the probabilistic performance - based seismic design and assessment of structures. In this study, two state-ofthe-art analytical formulations for structural seismic reliability are introduced from the two different aspects of total probability theorem （TPT）. It was considered that the two formulations were different in the theoretical foundation in the past. However, this study verifies the consistency of the two formulations via the analytical derivation of the seismic fragility function, in which some important relationships are found.