FRACTAL DIMENSION AS A MEASURE OF ROUGHNESS OF CONCRETE FRACTURE TRAJECTORIES

In this article, fractal characterization of concrete and mortar fracture trajectories is carried out. These trajectories were either sectioned from a replica of the fracture surface, profiled from a digitized image of the fracture surface, or generated via fractional Brownian motion simulation. Compact tension fractured concrete specimens with three different maximum aggregate sizes (d(max) = 4.7, 18.8, and 37.5 mm) and a projected fracture area (ligament area) of 125 x 367.5 mm were analyzed. Two methods, step divider and variogram, were utilized to evaluate the fractal dimension of the fracture trajectories. The fractal dimensions of concrete fracture trajectories calculated using these methods were in the range of 1.07 to 1.25. The variogram method yielded higher values than the step divider method. Synthetic profiles generated via fractional integrals of Brownian motion showed a good visual similarity to the actual fracture profiles.