A hierarchy model for the uncertainty quantification of spatial variability in the constitutive parameters of concrete in structures

摘要

In engineering practice, the compressive strength of concrete of the same strength grade at different positions of a structure is usually treated either as perfectly correlated or as completely independent random variables. However, due to the common factors affecting the randomness, e.g., the mix proportion, placing, consolidating, curing, etc., such treatment is unreasonable and consequently the results may be misleading. In this paper, a hierarchy model is adopted to describe the variability of the constitutive parameters of concrete in a structure. In this model, the total variability of the constitutive parameters of concrete in a structure is separated according to the contributing factors on four hierarchies: the hierarchy of structure, of floor, of component and of representative volume element (RVE). By this model, the correlation between components and that between floors can be captured. In addition, based on a large number of test complete compressive stress-strain curves, the copulabased joint probability distribution of the constitutive parameters of concrete crossing multiple strength grades is given. Combining this joint distribution with the hierarchy model, the compressive constitutive parameters of concrete in a reinforced concrete (RC) structure can be obtained. Then the stochastic response analysis of a 6story RC frame subjected to seismic ground motion is conducted. The results show that the variability of concrete on the hierarchy of floor has a non-negligible impact on the structural response, whereas the variability of concrete on the hierarchy of component and that of RVE may be ignored. In addition, it is found that only considering the variability of concrete on the hierarchy of structure will underestimate the variability of structural response and seriously overestimate the reliability of structure. On the contrary, considering the variability of concrete in a structure by the independent identically distribution is unreasonable and will lead to large errors in the variability of structural response and reliability.