In the current research, a mathematical model for the post-damage improvement of the carbonated blast furnace slag cement (BFSC) exposed to accelerated carbonation is constructed. The study is embedded within the framework of investigating the effect of using lightweight expanded clay aggregate, which is incorporated into the impregnation of the sodium mono-fluorophosphate (Na-MFP) solution. The model of the self-healing process is built under the assumption that the position of the carbonation front changes in time where the rate of diffusion of Na-MFP into the carbonated cement matrix and the reaction rates of the free phosphate and fluorophosphate with the components of the cement are comparable to the speed of the carbonation front under accelerated carbonation conditions. The model is based on an initial-boundary value problem for a system of partial differential equations which is solved using a Galerkin finite element method. The results obtained are discussed and generalized to a three-dimensional case.