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.

中文翻译：

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使用随机微机械方法研究纤维增强混凝土弹性模量的无偏概率行为

纤维增强混凝土的概率行为通常用常见的概率密度函数表示，这会导致结果有偏差。本研究旨在开发具有勒让德正交多项式的随机多相微机械框架，以研究纤维增强混凝土模量的无偏概率行为。基于骨料级配分析计算不同相体积分数，并通过采用多级微机械均化方案定量达到材料的有效性能。采用蒙特卡罗模拟得到纤维混凝土有效性能的不同阶矩，通过使用勒让德正交多项式近似和线性变换，可以达到无偏概率密度函数。数值例子表明，所提出的框架准确且计算效率高，可以表征纤维增强混凝土的概率行为。