Deterministic size effect in the strength of cracked concrete structures

This paper is concerned with identifying and quantifying the deterministic (as opposed to statistical) size effect in the strength of cracked concrete structures that is believed to be a result of stress discontinuities introduced by the cracks. For this, the strength of geometrically similar pre-cracked specimens of varying sizes made from three concrete mixes is measured in three-point bend and wedge splitting geometries. The true, size-independent specific fracture energy and the corresponding tension softening diagram of each of the three mixes are independently established in order to exclude their influence on the strength size effect. The test results show that the deterministic strength size effect weakens as the size of the crack reduces. This is confirmed by theoretical/computational studies based on the fictitious crack model in the range of sizes tested in the laboratory. The theoretical/computational model has been extended beyond this limited range to include cracked concrete structures in the size range 1 : 80. The computational results have been fitted by a simple strength size effect formula with appropriate asymptotic behaviour at both size extremes. The three unknown coefficients in this formula depend only on the size of the crack and they can be obtained by conducting tests on geometrically similar specimens of any shape but of varying sizes that can be conveniently handled in a laboratory. The three material properties of the concrete mix appearing in this formula, namely the Young modulus E, the direct tensile strength ft and the size-independent specific fracture energy GF must be independently measured.