Modeling of damage in cement-based materials subjected to external sulfate attack. I: Formulation

A chemomechanical mathematical model is presented to simulate the response of concrete exposed to external sulfate solutions. The model is based on the diffusion-reaction approach, and several mechanisms for the reaction of calcium aluminates with sulfates to form expansive ettringite are considered. Fick's second law is assumed for diffusion of the sulfate ions. A second-order chemical reaction between reacting calcium aluminates and ingressing sulfates depletes the sulfate concentration. The products of the second-order reaction between the aluminates and sulfates are chosen among several competing mechanisms, and a rule-of-mixtures approach is used to relate the expansive nature of the products with the prescribed specific gravity of the compounds. It is furthermore assumed that the crystallization pressure of products of reaction results in a bulk expansion of the solid. The constitutive response of the matrix and the expansive stresses are calculated from the imposed volumetric strain. Microcracks are initiated when the strength of the matrix is reached, leading to changes in the diffusivity and a reduction in the elastic properties of the matrix. The variation of diffusivity is linked to the scalar damage parameter due to cracking of the matrix. Due to the changes in the diffusivity, the problem is treated as a moving boundary problem, and a methodology is proposed to adapt the solution of the 1D case to the 2D problem of a prismatic specimen. Theoretical expansion-time responses are obtained and compared with a variety of data available in the literature.