Modeling of damage in cement-based materials subjected to external sulfate attack. I: Formulation
01 Aug 2003-Journal of Materials in Civil Engineering (American Society of Civil Engineers)-Vol. 15, Iss: 4, pp 305-313
TL;DR: In this article, a second-order chemical reaction between reacting calcium aluminates and ingressing sulfates depletes the sulfate concentration, leading to changes in the diffusivity and a reduction in the elastic properties of the matrix.
Abstract: 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.
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TL;DR: In this paper, a leaching and external sulphate attack on concrete lead to dissolution of hydration products, mainly portlandite, and in case of ingress of sulphate ions to formation of expansive products such as gypsum and ettringite.
308 citations
TL;DR: In this paper, a refinement of the crystallization pressure hypothesis was proposed to explain sulfate related expansion, and it was shown that expansion is related to the transformation of monosulfate crystals embedded in the C-S-H to ettringite.
200 citations
TL;DR: In this paper, a conceptual graphical analysis is proposed to relate the degree of surface deterioration and mineralogical composition of attacked surface to the main variables of external sulfate attack: water/cementitious material ratio, limestone content and C 3 A content of the cement.
193 citations
TL;DR: In this article, a model for degradation of concrete exposed to external sulfate attack at the meso-level is presented, which is based on the systematic use of zero-thickness interface elements equipped with fracture-based constitutive laws.
Abstract: In this paper we focus on the external sulfate attack on concrete specimens at the meso-level. There is nowadays a renewed interest in rationally describing the mechanisms behind expansive processes leading to cracking and spalling of concrete exposed to sulfate solutions. A model is presented for degradation of concrete exposed to external sulfate attack at the meso-level, i.e. representing explicitly in the simulations the main heterogeneities of the material. A previously developed mesomechanical approach has been coupled with a diffusion–reaction analysis at the same scale. It is based on the systematic use of zero-thickness interface elements equipped with fracture-based constitutive laws, and the effect of discrete cracks on the transport of ions is explicitly accounted for. The main results obtained agree qualitatively and quantitatively well with experimental observations in terms of ettringite penetration depth, expansions, crack patterns and spalling effects.
186 citations
TL;DR: In this paper, a numerical methodology is proposed to simulate the degradation of cementitious materials under external sulfate attack, which includes diffusion of ions in and out of the structure, chemical reactions which lead to dissolution and precipitation of solids, and mechanical damage accumulation using a continuum damage mechanics approach.
Abstract: A numerical methodology is proposed in this paper to simulate the degradation of cementitious materials under external sulfate attack. The methodology includes diffusion of ions in and out of the structure, chemical reactions which lead to dissolution and precipitation of solids, and mechanical damage accumulation using a continuum damage mechanics approach. Diffusion of ions is assumed to occur under a concentration gradient as well as under a chemical activity gradient. Chemical reactions are assumed to occur under a local equilibrium condition which is considered to be valid for diffusion controlled reaction mechanisms. A macro-scale representation of mechanical damage is used in this model which reflects the cracking state of the structure. The mechanical and diffusion properties are modified at each time step based on the accumulated damage. The model is calibrated and validated using experimental results obtained from the literature. The usefulness of the model in evaluating the mineralogical evolution and mechanical deterioration of the structure is demonstrated.
157 citations
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