A meso-macro numerical approach for crack-induced diffusivity evolution in concrete

In this paper, the authors present a meso-macro numerical approach in order to determine macroscopic diffusivity tensors in heterogeneous quasi-brittle materials such as concrete. The meso-structure is based on a two-phase 3D representation of heterogeneous materials with stiff aggregates embedded in a mortar matrix. In order to take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field of those finite elements containing more than a single material. In addition, a strong discontinuity is also added to take into account the crack formation and evolution. The mesoscale coupling with the mass transport part is based on Fick's Law with a modified diffusion coefficient accounting for crack opening and aggregates. Then, by means of an homogenization procedure some macro values for the macroscopic diffusivity tensor are computed. The main original contribution of this paper is that the macroscopic diffusivity tensor integrates more complex features. Such features coming as a by-product results of the meso-macro analysis such as the cracking process - including evolution from diffuse cracks in the bulk to localized macro-crack(s) -, tortuosity of the crack's path, induced-anisotropy and presence of aggregates. The defined tensor is used afterwards in order to estimate the service-life of concrete structures, including the effect of the cracking and the internal meso structure.