Copula-Based Quantification of Probabilistic Dependence Configurations of Material Parameters in Damage Constitutive Modeling of Concrete

Abstract

The constitutive model of concrete is the key basis for nonlinear analysis of concrete structures under disastrous dynamic actions, e.g., earthquakes. The material parameters of the constitutive model of concrete are essentially probabilistically dependent. However, in practice, it is mostly assumed that these parameters are either independent or perfectly dependent. In the present paper, the quantification of probabilistic dependence configurations between random material parameters and their effects on stochastic structural responses are investigated. Based on the ample amount of data from tested complete curves of compressive stress-strain relationships of concrete with different strength grades, the parameters in the damage constitutive model of concrete are samplewise identified. Further, the probabilistic dependence configurations are studied based on copula theory, which is also considered as a data-mining tool. The complete constitutive curves of concrete are generated according to the obtained dependence configurations and marginal distributions. Then, combined with the probability density evolution method, the stochastic response analysis of concrete structures is carried out. The analysis results show that the dependence among the strength, peak strain, and the parameter of the descendent segment cannot be ignored. Due to the constraint of dependence configurations, the distribution characteristics of the generated point set are substantially consistent with the tested results, and the generated complete stress-strain curves agree well with the tested curves at both the level of sample and the level of second-order moments. In addition, no abnormal complete stress-strain curves, e.g., those with low strength and sharp descendent segment, which are unlikely to occur in the test, are generated. The dependence configuration of the parameters of concrete has considerable effects on the response and reliability of concrete structures, and may even lead to the change of overall structural failure mode. Consequently, ignoring the probabilistic dependence of material parameters may yield misleading results for decision making. Problems to be further studied are also discussed.