A Legendre polynomial-based stochastic micromechanical framework is proposed to quantify the unbiased probabilistic behavior for the unsaturated concrete repaired by the electrochemical deposition method (EDM). By following the authors’ previous works, a deterministic micromechanical model with new multilevel homogenization scheme for the repaired unsaturated concrete is presented based on the material’s microstructures. With the stochastic descriptions for the microstructures of the repaired unsaturated concrete, the deterministic framework is extended to stochastic. The unbiased probabilistic behavior of the repaired concrete is reached by incorporating the Legendre polynomial approximations and the Monte Carlo simulations. The predictions herein are then compared with the available experimental data, existing models and the commonly used probability density functions, which indicate that the presented stochastic micromechanical framework is capable of characterizing the EDM healing process for unsaturated concrete considering the material’s random microstructure. Finally, the statistical effects of the deposition products and unsaturated pores are discussed.

中文翻译：

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基于Legendre多项式的EDM修复非饱和混凝土的随机微力学模型

提出了一种基于勒让德多项式的随机微力学框架，以量化通过电化学沉积法（EDM）修复的非饱和混凝土的无偏概率行为。通过遵循作者先前的工作，基于材料的微观结构，提出了一种具有新的多级均质化方案的修复性不饱和混凝土确定性微力学模型。通过对修复后的不饱和混凝土的微观结构进行随机描述，确定性框架扩展到了随机模型。通过合并勒让德多项式逼近和蒙特卡洛模拟，可以达到修复后混凝土的无偏概率性。然后将此处的预测与可用的实验数据进行比较，现有模型和常用的概率密度函数，这表明考虑到材料的随机微观结构，所提出的随机微力学框架能够表征非饱和混凝土的EDM修复过程。最后，讨论了沉积产物和不饱和孔隙的统计作用。