Discussion: A fractal model for simulating the formation of microcracks in the fracture process zone and a theoretical explanation of the size effect of the fracture energy of concrete

A fractal model is presented for simulating the formation of microcracks in the fracture process zone of concrete. The model is used to calculate the fractal dimension D of a network of microcracks. It is found that the branching angle of microcracks can greatly affect the value of D, and a lower value of D can be expected for high-strength concrete than for normal-strength concrete. In the light of fractal theory, a formula for calculating the total area of the fracture surface. including the area of microcracks, is proposed. The size effect of the fracture energy of cement-based materials is explained and the quantitative relationship between the fracture energy Gf, the surface energy of the concrete γs, the fractal dimension of the network of microcracks Dc, and the height of the ligament of the concrete specimen H is established as Gf = 2γsC″HDc−1 (where C″ is a constant). Using this formula. the fra ctal dimension Dc, of the network of microcracks in high-strength and normal-strength concrete was det...

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