A mathematical model for the kinetics of the alkali–silica chemical reaction

• Published in: Cement and concrete research Vol. 68; pp. 184 - 195
• Main Authors: Saouma, Victor E., Martin, Ruth A., Hariri-Ardebili, Mohammad A., Katayama, Tetsuya
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2015
• Subjects: Cements; Chemical reactions; Concretes; Diffusion; Evolution; Long-Term Performance; Mathematical analysis; Mathematical models; Petrography; Reaction kinetics; Reaction rate; Temporal logic; Long-Term Performance; Reaction rate; Petrography
• ISSN: 0008-8846; 1873-3948
• DOI: 10.1016/j.cemconres.2014.10.021

Starting from the chain of three chemical reactions which characterize the alkali–silica reaction (ASR), this paper attempts to develop a mathematical framework through which the reaction kinetics can be better understood. A petrographic support is given to better understand the physical implications of these equations, and to provide a reasonable support for the choice of the reaction rates. First an analytical solution is sought. Though one was not found, three new conservation laws were derived. Then a numerical solution is applied, and important observations are made. First, and foremost, the role of water is confirmed, and then the outcome of the reaction when different concentrations of alkali and silica are used is derived. Finally, the temporal evolution of the expansive gel formation is contrasted with both macro-kinetics model, and diffusion based meta-model for the concrete expansions are compared.