Chun-Hui He, Chao Liu

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All mechanical properties of a porous medium depend upon its fractal dimensions, however, how to measure the fractal dimensions is still an open issue. This paper adopts the two-scale fractal theory to calculate fast and effectively the fractal dimensions of a porous concrete. Of the concrete's properties that have been fascinating engineers and scientists, by far the most perplexing is the effects of its porosity and pore size on concrete's strength. Though there were many ad hoc empirical formulae for predicting the strength, much deviation arose for practical applications. Here a dimensionless model and the fractal theory are adopted to insight theoretically into the effects, and for the first time ever, some physically relative and mathematically reliable formulations are proposed. Additionally nano/micro particles’ size and distribution can also be used for theoretical prediction of the concrete’s strength, it shows that the boundary-induced force occurs when the particles tend to micro/nanoscales. The present theory sheds new light on the optimal design of various functional concretes.


Two-scale fractal, Geometric potential, Dimensionless analysis, Hall-Petch effect, Porosity

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