Size effect on flexural strength of notched and un-notched concrete and rock specimens by Finite Fracture Mechanics

Size effect in quasi-brittle material cannot be described simply by Linear Elastic Fracture Mechanics, which moreover is limited to cracked geometries. In the present paper we apply Finite Fracture Mechanics to determine the size effect on the flexural strength of notched and un-notched quasi-brittle material specimens under quasi -static mode I loadings. Although the framework is general, special attention is paid on the Three Point Bending and Semi-Circular Bending test geometries. The scaling of flexural strength is of particular interest for concrete and concrete-like materials because of the large variation from laboratory to real structural sizes. Theoretical predictions are discussed and compared with several experimental data from the literature, related to both concrete and rock specimens. The excellent matching with the experimental data proves the soundness of the Finite Fracture Mechanics approach, even more valuable because of its simplicity: just two shape functions are needed to determine the scaling of the flexural strength (or of the nominal fracture toughness) for a given geometrical shape.