Numerical modelling of the healing process induced by carbonation of a single crack in concrete structures: Theoretical formulation and Embedded Finite Element Method implementation

We consider a model for reactive flows which describes the healing process induced by carbonation of a single crack in concrete structures. The aim of this paper is to study the complex interplay between advection-diffusion mechanisms in a crack-matrix system combined with different chemical reactions taking place (dissolution/precipitation). Carbonated water is first injected through a crack. Then, a diffusion process of calcium ions (Ca2+ ) takes place from the porous matrix to the crack due to the existing calcium ions concentration gradient. Finally, those calcium and carbonates ions (CO32−) from the percolating solution react to form a calcite (CaCO3) layer responsible for the healing of the crack. The developed model takes the form of transport-reaction partial differential equations for both crack and porous matrix. From numerical point of view these equations are discretized by means of the Embedded Finite Element Method (E-FEM). The E-FEM allows to use meshes not necessarily matching the physical interface, defined herein as the crack, while retaining the accuracy of the classical finite element approach. This is achieved by introducing a weak discontinuity in the calcium ions concentration field for finite elements where the crack is present. A numerical solving strategy is presented to efficiently resolve the FE problem both in terms of calcium and carbonate concentration field variables and weak discontinuity parameters. In addition, an analytical model for the computation of the calcite layer width, resulting in the healing process, is suggested. Finally, considering the dependence of the diffusivity and permeability coefficients on the width of the calcite, a coupled model arises for the numerical modelling of the healing process induced by carbonation in a crack.