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11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver and A. Huerta (Eds) A BIPHASE MODEL FOR CONCRETE SUBJECT TO SULFATE ATTACK NICOLA CEFIS AND CLAUDIA COMI Department of Civil and Environmental Engineering Politecnico di Milano P.zza Leonardo da Vinci 32, 20133 Milano e-mail: nicola.cefis@polimi.it, claudia.comi@polimi.it web page: http://www.dica.polimi.it Key words: Concrete, Damage, Porous Media, Sulfate attack Abstract. In the present paper we focus on the numerical simulation of degradation in concrete due to the development of secondary ettringite in the hardened material (delayed ettringite formation or DEF). This chemical reaction, causing expansion and microcracking of the material, can occur due to an external or internal sulfate attack. A chemical-diffusion model allows for the computation of the amount of expansive products of the reaction. The concrete affected by DEF is then represented as a two-phase material made of a solid skeleton and an expanding phase, which exerts a pressure capable of damaging the concrete surrounding the reactive sites. The model is validated on the basis of experimental data on cement mortar specimens reported in the literature. 1 INTRODUCTION The delayed ettringite formation is one of the phenomena which may cause swelling and severe microcracking in concrete. This expansive chemical reaction takes place between the reacting calcium aluminates of the cement paste and the sulfates (already present in the material or coming from the environment) and can occur in massive structures where the temperature at early age is large [1] and/or in concrete structures in contact to external sulfate solutions (e.g nuclear waste deposits or tunnels in contact with sulfate- rich soils [2]). In those situations, the durability analysis requires two main ingredients: a proper diffusion-reaction model, for the computation of the amount of expansive reaction products, and a mechanical model for the prediction of swelling and material degradation. In [3] a detailed formulation of the reactive diffusion model is provided, while a sim- plified empirical relation is used to compute the damage of the material. In [4] a meso- mechanical approach, describing micro-cracks formation with zero-thickness interface el- ements, coupled with a diffusion-reaction analysis is proposed. 1 Nicola Cefis and Claudia Comi In this paper we implement the formulation of the reactive-diffusion problem developed in [3] to compute the sulfate and aluminates concentrations and the amount of formed ettringite. Following a weakly coupled approach, similar to that proposed in [5], [6] for concrete affected by the alkali-silica reaction, the ettringite content is assumed as the input variable for a subsequent chemo-elastic damage analysis. In the framework of the Biot’s theory [7], the material is represented as a two-phase medium: the solid skeleton and the expansive reaction products. The mechanical degradation is described by a phenomenological isotropic damage model. The reactive-diffusion model is first applied to compute the ettringite formation in cement mortar specimens subject to external sulfate attack and the influence of the de- pletion of aluminates on the sulfates diffusion is studied. Then, to assess the capability of the chemo-damage model to account for the influence of different stress conditions on the expansion induced by the DEF, the tests reported in [8] on restrained specimens cured at high temperature and subject to internal sulfate attack are simulated. 2 REACTION-DIFFUSION MODEL When concrete is in contact with sulfate solutions, sulfate ions diffuse into the cement paste and different chemical reactions can occur. According to several Authors (see e.g [3], [9]) the most relevant reactions can be divided into two sets: first the penetrated sulfates react with the available portlandite to form gypsum (CSH2 ), then the gypsum reacts with the different calcium aluminate phases of the cement paste to form ettringite C6 AS 3 H32 (using the usual cement chemistry notation C ≡ CaO, A ≡ Al2 O3 , S ≡ SO3 , H ≡ H2 O ). As proposed in [3], all the chemical reactions leading to delayed ettringite formation are lumped in a single expression as Ceq + q · S −→ C6 AS 3 H32 (1) P3 where Ceq = i=1 γi Pi is an equivalent grouping of the reacting calcium aluminates (P1 = C4 AH13 , P2 = C4 ASH12 , P3 = C3 A) and q den

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