基于Copula理论的混凝土受压#br#本构全曲线参数相关性研究

混凝土本构关系全曲线是混凝土结构在地震作用下的非线性行为乃至倒塌全过程分析的关键基础。然而，现有试验方法一般仅给出强度和弹性模量2个参数、且不能合理刻画基本参数之间的相关性，不足以确立混凝土本构关系全曲线。文章基于混凝土损伤本构模型，利用混凝土受压本构关系全曲线试验数据，采用最佳平方逼近准则和遗传算法，对混凝土的抗压强度、峰值应变、弹性模量和下降段参数进行识别。进而，对这些参数的边缘分布和参数间的相关性进行研究。通过拟合优度检验，给出最优边缘分布和Copula相关结构模型。在此基础上，采用条件抽样法生成具有相关性的参数样本，由此生成计算本构全曲线。对比研究表明，只有合理地考虑混凝土参数间的相关性，才能获得均值和标准差均与试验结果符合较好的混凝土本构关系全曲线样本。文章的研究工作以期为混凝土结构非线性分析提供合理基础。

Research on the dependence between parameters in complete stress-strain#br#constitutive curve of concrete based on copula theory#br#

The complete constitutive relationship curve of concrete is the key basis for the analysis of nonlinear behavior and the collapse process of concrete structures under earthquakes. However, the existing experimental measures only yield the strength and the modulus of elasticity of concrete, and the correlation between them is not reasonably quantified. This is inadequate for the determination of complete constitutive relationship curve of concrete. Based on the damage constitutive model of concrete, the compressive strength, peak strain, modulus of elasticity and the parameter of descent stage are identified from the tested data of complete uni-axial compressive stress-strain curves of concrete by adopting the best square approximation criterion and the genetic algorithmFurthermore, the marginal distribution of the above parameters and the dependence between them are studied. The optimal marginal distribution and Copula model are determined by the goodness-of-fit test. Furthermore, the conditional sampling method is employed to generate samples of the 4 probabilistically dependent parameters to construct the calculated constitutive curves. The results show that only when the probabilistical dependence between the constitutive parameters of concrete are reasonably characterized, can the mean and standard deviation of the complete compressive stress-strain curves agree well with the test results. The investigation will provide a reasonable basis for the nonlinear response analysis of concrete structures.