Concrete is a man-made material containing a particulate filler designed on the basis of a sieve curve. In case of river aggregate, the particles are approximately spherical and smoothtextured. The particle-matrix interface is mostly the weakest chain link in the mechanical system. This implies damage evolution to start at particle-matrix interfaces. In case of direct tension, these interface cracks will be on average perpendicular to the loading direction. In case of direct compression, they will be parallel to the loading direction. A single fracture surface is formed in tension and a series of fracture surfaces in compression. They are the result of crack concentration within a process zone, in which the engineering crack closely meanders around a dividing plane. This allows to model these fracture surfaces on different resolution levels. It is shown, using stereological notions, that the very phenomenon is of a non-ideal fractal nature. Estimates for fractal dimension of fracture surfaces in concretes based on sieve curves at the border of the practical range are found to closely match experimental data reported in the literature.