A stereological analysis of aggregate grading and size effect on concrete tensile strength

One of the most important topics in solid mechanics is the study of the so-called size effects, whose importance has been widely recognised during the last decades. Size effects are particularly strong in quasi-brittle (i.e., concrete-like) materials. In this paper we focus our attention on the tensile strength decrease associated with the size of concrete structures. An original explanation of this well-known size effect was proposed by the first Author based on the assumption of a fractal-like damage localisation at the mesostructural level. This hypothesis leads to a multifractal scaling law (MFSL) for concrete tensile strength. The present contribution provides a scaling law for concrete tensile strength based on its aggregate size distribution. Since the weakest link in normal strength concrete is represented by the interface between the cementitious matrix and the aggregates, it seems reasonable to look for a relationship between the aggregate grading and the material strength. Based on the hypothesis that the strength depends on the largest flaw, we compute the strength of a concrete specimen as a function of its size. Differently from other statistical approaches, we use a truncated distribution (namely the Füller distribution) in order to describe realistically the flaw population inside the specimen. Calculating the distribution of the largest flaw size by means of statistics of extremes, and relating it to the specimen size, we obtain a scaling law for concrete tensile strength whose trend strictly agrees with the MFSL. Finally, we pay particular attention to the computation of the power law exponent characterising the strength scaling at the smallest sizes and present a comparison with available experimental data.