Size effect and boundary conditions in the brazilian test: theoretical analysis

Splitting strength determined in the Brazilian test is assumed to be a property independent of size and uniquely related to the intrinsic material strength. However, as was experimentally demonstrated by various authors, the splitting strength depends on the specimen size. In this paper, the size effect in the Brazilian test is analyzed theoretically using a nonlinear fracture model based on cohesive crack concepts and the results obtained are compared with the classical strength limit approach. Two important variables are studied: the load-bearing strip and the geometry of the specimen. From the numerical results a closed form expression is proposed, dependent on the width of the bearing strip and on geometry. The results confirm that splitting strength decreases with the specimen size, tending towards an asymptotic solution for large size specimens. Within the size range analyzed (0.1 m to 2.5 m diameter for typical concrete) the splitting strength can vary by up to 25% in cylindrical specimens and by up to 35% in prismatic square section specimens, although this size effect is strongly dependent on the load-bearing strip. For widths of bearing strip smaller than 4% of the specimen diameter, the effect of the specimen size is negligible and the splitting strength approaches the tensile strength for any practical specimen size.