Investigation of the unbiased probabilistic behavior of the fiber-reinforced concrete's elastic moduli using stochastic micromechanical approach

The probabilistic behavior of the fiber-reinforced concrete is usually represented by the common probability density functions, which will lead to the biased results. This study aims to develop a stochastic multiphase micromechanical framework with Legendre orthogonal polynomial to investigate the unbiased probabilistic behavior of the fiber-reinforced concrete's moduli. The different phase volume fractions are analytically calculated based on the aggregate grading and the material's effective properties are quantitatively reached by employing the multilevel micromechanical homogenization schemes. The Monte Carlo simulations are adopted to attain the different order moments of fiber-reinforced concrete's effective properties, with which the unbiased probability density functions are reached by using the Legendre orthogonal polynomial approximations and the linear transformations. Numerical examples indicate that the proposed framework is accurate and computationally efficient to characterize the fiber-reinforced concrete's probabilistic behavior.