# Chemo-Mechanical Model for the Expansion of Concrete due to Alkali Silica Reaction
## 1 Introduction  
Alkali-silica reaction (ASR) is a gradual and deleterious reaction between the reactive silica in concrete aggregates and the alkaline pore solution of concrete. The reaction starts from the progressive attack of siloxane networks in aggregates by hydroxide ions. The dissolved silica binds with alkali ions to generate alkali silicate, called the pre-expansion gel (basic ASR gel) with a significant sorptivity. In the presence of moisture, the basic ASR gel swells significantly by absorbing water. The expansive pressure caused by the swelling gel will be loaded on the solid skeleton of concrete. This leads to damage in concrete and expansion [1; 2]. Numerous models were developed for the simulation of ASR damage as summarized in References [3; 4]. Those include theoretical approaches emphasized on the reaction mechanism [5; 6], mesoscale models to explain the mechanism of deterioration [7; 8; 9; 10] and macroscale models to combine the chemical reaction kinetics and mechanical constitutive laws to predict the behavior of ASR-affected concrete at structural scale [11; 12; 13; 14; 15]. [PERSON] and [PERSON] [5] proposed a reaction kinetics of ASR governed by a Stefan type diffusion of alkali-rich water into reactive aggregates. They were able to explain the size effect of ASR damage depending on the size of reactive aggregates. The imbibition of alkali-rich water was considered as the driving force of gel swelling [16; 17; 18]. The overall ASR process was modeled by using the mass balance of moisture. The role of alkali was rather simplified in those models [5; 17; 18]. The role of alkali was well discussed by [PERSON] et al. 's model [19; 20]. Alkali transport and consumption were modeled in a multi-scale approach. The formation of the gel by the ASR reaction was driven by the alkali concentration in the pore solution. They were able to capture the effect of thedecreased alkali in the pore solution, which was caused by alkali binding in the gel and alkali leaching out of specimens. Both alkali and moisture play crucial roles during the reaction process. Alkali reacts with reactive silica to produce the basic form of gel which is believed to be non-expansive without water imbibition to the gel [5; 18]. Once moisture is imbibed to the gel, the gel swells to produce pressure to the surrounding solid skeleton causing expansion and damage. During the ASR reaction, the consumption and transportation of alkali and moisture take in place simultaneously. The variations in alkali and water content may lead to different behaviors of ASR. Moreover, the above mentioned models are suitable to only the situation that alkali ions are charge-balanced by hydroxide ions. For the alkali ions charge-balanced by other anions, for instance, chloride ions from NaCl. It would not form the basic gel because the pH is too low to break the siloxane network. However, if the chloride ions supplied by sodium chloride get bound in Friedel salt, hydroxyl ions released to keep charge-balance result in high pH [21]. An experimental study was carried out [22] to investigate the effect of sodium chloride on ASR. When specimens were immersed in high pH solution, i.e., NaOH, the expansion caused by ASR was increased dramatically by extra NaCl. The chemical composition analysis of ASR products showed that the extra NaCl increased the Na/Si ratio of ASR gel. According to References [23; 24], such a kind of gel with a high Na/Si ratio has a high expansibility, causing high expansion. Therefore, alkali charge-balanced by hydroxyl ions and other anions should be considered separately. Although the basic gel is formed by the alkali charge-balanced by hydroxyl ions, the expansibility of the gel is influenced by the total amount of sodium in the pore solution, i.e., the alkali charge-balanced by other anions, i.e., chloride ions as mentioned above. In this paper, 'alkali' refers to only the part of alkali charge-balanced by hydroxyl ions as the default definition. Portland cement is the main source of alkali.