A probabilistic upscaling of microstructural randomness in modeling mesoscale elastic properties of concrete

Abstract

We present a modeling framework for propagating the uncertainty, stemming from random heterogeneity of concrete microstructure, to its mesoscale elastic properties at the level of statistical volume element. The microstructure of concrete is modeled as a three-phase composite, consisting of aggregates (inclusions) in mortar (matrix), and interfacial transition zone (ITZ), a thin high porosity zone surrounding aggregates. There is inherent randomness in the composition and mechanical properties of these constituents, which in turn causes spatial heterogeneity in the local material behavior. We present a statistical characterization process to quantify the uncertainty associated with local aggregate volume fraction and aggregate size distribution. We then adopt and test a probabilistic model based on the random matrix theory and maximum entropy principle to construct a stochastic description for bounded apparent elasticity tensors at the mesoscale level, in which the bounds are obtained through a computational calibration process based on the theory of micromechanics and numerical homogenization. The framework provides an efficient way to model and simulate the local statistical fluctuations of material properties that are linked to phenomena occurring at the subscale level of heterogeneity.