Permeability due to the Increase of Damage in Concrete: From Diffuse to Localized Damage Distributions

Experimental tests exhibit a strong interaction between material damage and transport properties of concrete. There are at least two asymptotic cases where some theoretical modeling exists: in the case of diffuse cracking, the material permeability should be controlled by damage, e.g., by the decrease of average stiffness due to microcracking. In the case of localized microcracking, and after a macrocrack has formed, permeability should be controlled by a power function of the crack opening (Poiseuille flow). For quasi-brittle materials with evolving microstructure due to mechanical loads, a transition regime on the evolution of permeability between these two asymptotic cases is expected. In this contribution, we define a relationship between permeability and damage that is consistent with the two above configurations. One of the key issues is to relate the crack opening to the state variables in the continuum approach, so that the two asymptotic cases are expressed in the same variable system and can be matched. A simplified approach is used for this purpose. The permeability law is then derived using a mixing formula that weights each asymptotic regime with damage. To illustrate the influence of the matching law on structural response, finite-element simulations of a Brazilian splitting test and a comparison with existing test data are presented.