Matching permeability law from diffuse damage to discontinuous crack opening

Experimental tests prove strong interaction between mechanical state and transport properties of concrete. In order to describe such interaction, relations either between damage (related to diffuse microcracking) and permeability or between macrocrack opening and permeability are applied. However none of these relations based on continuum and discontinuum approaches of concrete behaviour modelling, are able to represent by a unique relation the permeability evolution throughout the fracture process. Therefore, we propose to define a new relation matching the existing ones in the limit cases. At first, by means of a simple analytical approach we relate the crack opening with the state variable of the non local damage model. Then, using this variable substitution, the relation of permeability evolution with crack opening is reported to damage variable. Both relations of the evolution of permeability are thus reported to damage and can be weighted by the damage variable to form a single relation between permeability and damage presumed to be valid for diffuse damage state and discontinuous macrocracking. In order to emphasize influence of the matching law on structural response, we run finite element simulations of a Brazilian splitting test. In conclusion, numerical tendencies are similar to observed ones on experimental results.