Fractal cracking of concrete: Parameterization of spatial diffusion

Concrete cracks on the tension face of beams in uniaxial bending are interpreted as a non-Fickian diffusive phenomenon resulting from a self-affine random fractal process. It is shown how a complete spatial description of the cracking geometry can be found from experimental data using both a (Hurst) scaling exponent and a diffusion-type coefficient. Once determined experimentally, these parameters are used to synthesize cracking patterns using fractional Brownian motion functions. In addition, it is shown how an effective Fokker-Planck diffusion equation can be used to describe the spatial geometry of the cracking.