Mathematical model for kinetics of alkali-silica reaction in concrete

Vast though the literature on the chemistry of the alkali-silica reaction (ASR) in concrete has become, a comprehensive mathematical model allowing quantitative predictions seems lacking. The present study attempts a step toward this goal. While two distinct problems must be dealt with, namely, (1) the kinetics of the chemical reaction with the associated diffusion processes and (2) fracture mechanics of the damage process, only the former is addressed here. The analysis is focused on the recent attempts by C. Meyers and W. Jin to incorporate ground waste glass (mainly, bottle glass) into concrete. With minor adjustment, though, the model can be applied to ASR in natural aggregates as well. A characteristic unit cubic cell of concrete containing one spherical glass particle is analyzed. A spherical layer of basic ASR gel grows radially inward into the particle, controlled by diffusion of water toward the reaction front. Modification of the solution for the case of mineral aggregates with veins of silica is also indicated. Imbibition of additional water from the adjacent capillary pores, which causes swelling of the gel, is described as a second diffusion process, limited by the development of pressure due to resistance of concrete to expansion. The water used up to form the basic ASR gel and imbibed to cause its swelling appears as a sink term in the non-linear diffusion equation for the global water transport through a concrete structure. The differential equations are integrated numerically. The study of the effects of various parameters provides improved understanding of the ASR, and specially the effect of glass particle size. Full prediction will require measurements of some parameters of the reaction processes.