Fractals, Fractures, and Size Effects in Concrete

Correlation between fractal dimensions and fracture properties in cementitious material is reported. Wedge splitting tests of specimens as much as 1.52 m (5 ft) long and having 7.62‐cm (3‐in.) maximum size aggregate were first performed to determine fracture toughness KIc and fracture energy GF. Subsequently, one of the split parts was mapped using a profilometer to provide detailed one‐dimensional profiles. Finally, the fractal dimension of the profiles was determined by a specially developed computer program. The fracture surfaces are fractal over the measured range of scales, and the fractal dimension is independent of crack trajectory. There is a weak correlation between the fracture properties and the fractal dimensions. The implications of the fractal nature of the cracked surfaces on the fracture energy GF are discussed, as is the relationship between a fractal analysis and the size effect law