Through upscaling from the hydration products to a macroscopic composite, a multi-scale framework is proposed to predict the effective properties of ultra-high-performance concrete (UHPC) with different reaction degrees. In this framework, the hydration of Portland cement and the pozzolanic reaction of silica fume (SF) are taken into consideration. Different length scale representative volume elements are used to describe the material's hierarchical microstructures. The constituents’ volume fractions at different length scales are analytically calculated by the reaction degrees of Portland cement and SF. Multi-scale and multi-level homogenisation schemes are adopted to quantitatively relate the microstructures to the macroscopic properties. The numerical results showed that estimations of existing hydration models can be obtained as special cases of the proposed model. By comparison with experimental data and results estimated in previous work, it was found that the proposed multi-scaling approaches are capable of predicting the macroscopic behaviour of UHPC with different reaction degrees.

中文翻译：

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基于反应度的超高性能混凝土有效性能多尺度预测

通过从水化产物放大到宏观复合材料，提出了一个多尺度框架来预测具有不同反应程度的超高性能混凝土（UHPC）的有效性能。在此框架中，考虑了硅酸盐水泥的水化和硅粉 (SF) 的火山灰反应。不同长度尺度的代表性体积元素用于描述材料的分层微观结构。不同长度尺度下组分的体积分数通过硅酸盐水泥与SF的反应程度解析计算。采用多尺度、多层次的均质化方案，将微观结构与宏观性能定量联系起来。数值结果表明，现有水化模型的估计可以作为所提出模型的特例获得。通过与先前工作中估计的实验数据和结果进行比较，发现所提出的多尺度方法能够预测具有不同反应程度的 UHPC 的宏观行为。