Fractal analysis of damage detected in concrete structural elements under loading

In Civil Engineering materials subjected to stress or strain states a quantitative evaluation of damage is of great importance due to the critical character of this phenomenon, which at a certain point suddenly turns into a catastrophic failure. An effective damage assessment criterion is represented by the statistical analysis of the amplitude distribution of acoustic emission (AE) signals emerging from the growing microcracks. The amplitudes of such signals are distributed according to the Gutenberg–Richter (GR) law and characterised through the b-value which decreases systematically with damage growth. On the other hand, the damage process is also characterised by the progressive coalescence of microcracks to form fracture surfaces. Geometrically the fractal dimension D of the damaged domain is expected to decrease from an initial value comprised between 2 and 3 towards a final value nearly equal to 2. The b-value and the fractal analysis, are here applied to two case studies of concrete specimens loaded up to failure, and the obtained results are compared and discussed. In particular, we emphasize that a single fractal dimension does not adequately describe a crack network, since two damaged domains with the same fractal dimension could have significantly different properties.