Concrete modelling for expertise of structures affected by alkali aggregate reaction E. Grimal a , A. Sellier b , S. Multon b, ⁎, Y. Le Pape c , E. Bourdarot a a Electricité de France, Centre d'Ingénierie Hydraulique, EDF-CIH Technolac, 73373 Le Bourget du Lac Cedex, France b Université de Toulouse, UPS, INSA, LMDC (Laboratoire Matériaux et Durabilité des Constructions), 135, avenue de Rangueil, F-31 077 Toulouse Cedex 04, France c Electricité de France, Recherches & Développements, Dept. MMC,-avenue des Renardières-Ecuelles, F-77818 Moret-sur-Loing Cedex, France abstract article info Article history: Received 16 October 2008 Accepted 10 September 2009 Keywords: Alkali Aggregate Reaction (C) Durability (C) Modeling (E) Structure Expertise Alkali aggregate reaction (AAR) affects numerous civil engineering structures and causes irreversible expansion and cracking. In order to control the safety level and the maintenance cost of its hydraulic dams, Electricité de France (EDF) must reach better comprehension and better prediction of the expansion phenomena. For this purpose, EDF has developed a numerical model based on the finite element method in order to assess the mechanical behaviour of damaged structures. The model takes the following phenomena into account: concrete creep, the stress induced by the formation of AAR gel and the mechanical damage. A rheological model was developed to assess the coupling between the different phenomena (creep, AAR and anisotropic damage). Experimental results were used to test the model. The results show the capability of the model to predict the experimental behaviour of beams subjected to AAR. In order to obtain such prediction, it is necessary to take all the phenomena occurring in the concrete into consideration. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Alkali aggregate reaction (AAR) affects numerous civil engineering structures and causes irreversible expansion and cracking. AAR is a chemical reaction between the reactive siliceous phases of aggregates and alkalis of the cement. The aggregate swelling (due to its cracking) and the product of the reaction (gel) leads to the apparition of a swelling pressure causing expansion and cracking. The consequences are a decrease in the functional capacities of civil engineering structures such as hydraulic dams. “Electricité de France” (EDF) needs better prediction of the phenomena to assess the safety level and the maintenance costs of its dams. Therefore, a numerical model integrated in a finite element com- puter code was developed by EDF and LMDC to calculate the behaviours of AAR-affected structures. Previous research had been carried out to develop mechanical modelling of AAR [2–7]. With the same assumption of the effect of the pressure induced by the AAR gel on the concrete considered as a porous medium, the purpose of the modelling was to add the effect of the delayed strains (creep), drying shrinkage and anisotropic damage into the constitutive laws. One of the aims is to quantify both anisotropy and amplitude of the swelling and damage due to AAR. A rheological model was thus developed to assess the coupling between the three main phenomena: creep, AAR and anisotropic damage. Recent experimental results [8–10] were simulated to check the model robustness. First, the model is presented; then the behaviours of various reinforced concrete beams damaged by AAR and stored in different moisture and loading conditions [8–10] are reproduced. Finally, results are discussed regarding the model assumptions. 2. Model description The main developments contributed by this model concern interac- tions between AAR gel and long-term strain (creep) [11] on the one hand, and the swelling anisotropy induced by oriented cracking on the other hand. Particular attention is also paid to modelling the effects of moisture both on AAR and long-term strain (creep and shrinkage). In consequence, the AAR swelling depends on all these elementary phenomena. Acker [12] suggested that the basic creep of concrete was mainly due to the C–S–H behaviour (C–S–H sliding) but also to micro diffusion of water leading to consolidation phenomena. Recent experimental evidence proposed by Bernard [13] confirms this assumption. Therefore, a Visco-Elasto-Plastic (VEP) anisotropic damage model including chemical AAR pressure has been developed. In order to model C–S–H sliding and consolidation, the model is separated into two levels: - The first, rheological, level (VEP in Fig. 1) is based on a division of the strain and stress state in a spherical part (module VEP s in Fig. 2(a)) and a deviatoric part (module VEP d in Fig. 2(b)). The response of the C–S–H structure under hydrostatic stress (consolidation) is mod- elled by the spherical part while the deviatoric part accounts for the C–S–H sliding (without volumetric change) under shear stress. - The second plastic level (VD t in Fig. 1) allows large strains encountered in AAR problems to be modelled. It is linked to an anisotropic AAR traction damage model. Cement and Concrete Research 40 (2010) 502–507 ⁎ Corresponding author. E-mail address: multon@insa-toulouse.fr (S. Multon). 0008-8846/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.cemconres.2009.09.007 Contents lists available at ScienceDirect Cement and Concrete Research journal homepage: http://ees.elsevier.com/CEMCON/default.asp