A separation of scales homogenization analysis for the modelling of calcium leaching in concrete

Calcium leaching in concrete is highly influenced by the presence of aggregates. We present in this work a modelling framework of calcium leaching which accounts for this fact. Starting from the microscopic point of view, the method consists of the derivation of the macroscopic equation governing the average concentration field in the equivalent medium as well as the determination of the macroscopic transport parameters. In fact, the homogenization method used in this work is based on a separation of scales approach and allows to estimate the diffusion and the tortuosity tensors to be introduced in the macroscopic formulation of the mass conservation of calcium in the liquid phase. In this first attempt, we show that these estimates depend strongly on the morphological parameters of the microstructure which represent the geometry of the domain occupied by the phase in which the diffusion process takes place. The problem of numerically integrating the equations at hand is addressed within the context of the finite element method. Finally, numerical simulations are compared with our experimental results on cement paste, mortar and concrete.