Boundary effect model for size effect on fracture of quasi-brittle materials

Size effects on the specific fracture energy GF and the nominal strength σN of notched concrete specimens are studied together in this paper. The size independent GF for very large specimens is compared with the asymptotic limit of the fracture energy predicted by size effect models using σN. This comparison provides a useful assessment on the validity of different size effect models as it is known that the asymptotic limit of GF for very large specimens is a size-independent material constant and is higher than the size dependent GF measured from small specimens. The size effect model presented in this study considers the influence of specimen boundaries and shows that specimen boundary conditions can significantly influence the quasi-brittle fracture behaviour of concrete, which is responsible for the apparent size effect. It is shown that the controlling factor for the size effect is the ratio of crack versus crack-tip fracture process zone, or un-cracked ligament versus the fracture process zone, whichever is smaller, rather than the specimen size. Experimental results available in the literature are used to substantiate this size effect mechanism.