The analysis of the effect of cracks on the acceleration of the calcium leaching process of cement-based materials has been pursued. During the last period we have introduced a modeling accounting for the high diffusivity of fractures in comparison with the weak solid material diffusivity. It has been shown through dimensional and asymptotic analysis that small fractures do not significantly accelerate the material aging process. This important result for the overall structural aging kinetics of containment structure has been developed. If it is now obvious that a pure diffusive mass transport in a cracked material is not a significant source of calcium leaching acceleration, less appears to be known on the material chemical degradation due to an arrival of pure water through the material fractures. When penetrating the material, the pure water may effectively induce an important leaching since the calcium present in the fracture can be evacuated at high velocity by the water flow. This mass transport phenomenon of calcium transported by the water flux is referred to as a convective (or advective) mass transport.