Three-dimensional fractal analysis of microstructural morphologies in concrete

The fracture process in concrete cannot be properly understood in an Euclidean framework, due to its complex morphology at the micro- and meso-level. The inherent flaws interact through a multi-scale process, leading to self-a ne fracture surfaces. Furthermore, the network of microcracks possesses non-Euclidean geometrical properties. A new experimental equipment has been developed, which allows the entire fracture surface, or any plane cross section, to be digitised and analysed. This represents an important progress with respect to the study of mono-dimensional pro les. In this paper, the 3D algorithms developed for evaluating the fractal dimension of surfaces and stress-carrying sections are described. The invasive fractal character of the fracture surfaces is con rmed. Moreover, the lacunar fractal character of the stress-carrying cross sections, a priori assumed by Carpinteri (1994), is proved experimentally.