Similarity properties of demineralization and degradation of cracked porous materials

The paper analyze the similarity properties of demineralization processes in cracked porous materials, coupled with diffusive and advective mass transfer through fractures. The aim is to find out, whether, when and how fractures accelerate or magnify the overall chemical degradation process. A dimensional analysis of a simplified dissolution process around a fracture channel reveals different self-similar properties for diffusion and advection dominated mass transport in the fracture. For a pure diffusive transport, the fracture degradation length develops with the quadratic root of time; while it evolves with the square root of time when advection dominates. These asymptotic behaviors are confirmed by model-based simulations of ‘realʹ calcium leaching in cracked cement-based materials. It is shown, that a diffusion dominated mass transport in a fracture does not significantly accelerate the overall chemical degradation, since the one-dimensional-degradation through the porous material catches up with the initially faster diffusion through the fracture. In turn, advection dominated mass transfer in fractures can significantly accelerate the overall calcium depletion for ‘highʹ fluid velocities in the fracture. Finally, diffusive dominated mass transport in a crack network may also accelerate the calcium leaching process for small values of crack spacing factors. A rough analytical solution for estimating this effect of a crack network is derived and validated through model-based simulations.