Fractals, statistics and size-scale effects on concrete strength

The size-scale effects on concrete strength are a very important topic in engineering design. In recent years, the scientific community dedicated great efforts in order to gain a precise description of this phenomenon and to highlight the physical mechanisms that lie behind it. Aim of this paper is to review the fundamentals of the fractal approach (Carpinteri, 1994b), which has recently been at the centre of a scientific debate, and to revisit in detail its connections with statistics. The most recurrent criticisms against the fractal interpretation of the size-scale effects will be rejected and theoretical results regarding the link between fractals and statistics will be also confirmed by numerical simulations.