Fractal dimension––a measure of fracture roughness and toughness of concrete

The quantitative description of rough surfaces and interfaces has been an important challenge for many years. This paper addresses the potential application of fractal geometry to characterize the fracture surface and to determine whether there is any correlation between fracture properties and the roughness of the fracture surface. Fractured surfaces of three different size wedge-splitting specimens, dimensions varying from (width×total depth×thickness) 420×420×50 mm to 1680×1680×200 mm with four different maximum aggregate sizes of 9.5, 19, 38, and 76 mm, were analyzed using a modified slit-island technique. It was found that fractal dimension, i.e., roughness, increases with an increase in both specimen and maximum aggregate size. A clear correlation exists between roughness (fractal dimension) and fracture toughness: the tougher the material, the higher the fractal dimension.