Mathematical model for kinetics of alkali–silica reaction in concrete

Abstract

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 adjustments, 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 especially the effect of glass particle size. Full prediction will require measurements of some parameters of the reaction processes. D

Alkali–silica reaction: Current understanding of the reaction mechanisms and the knowledge gaps

“…In this view, the observed differences in reactivity of different size particles is due to the time needed to diffuse OH-to the reactive sites, which may be in the interior of aggregates [72]. A related model proposed by Bažant and Steffens [79] suggests that the swelling pressure of the ASR gel strongly depends on the size of reactive aggregates and is maximum at some intermediate particle size. Another theory is that the effects observed can be explained by fracture mechanics.…”

“…The analytical model from Bažant and Steffens [79] assume that the kinetics of ASR is driven by the diffusion of the alkalis to the aggregates, and that the reaction occurs at the aggregate surface. Homogenization techniques are then employed to derive the macroscopic swelling [79,209].…”

“…Homogenization techniques are then employed to derive the macroscopic swelling [79,209]. This model does not however produce reasonable predictions of the free expansion of the laboratory samples in most cases.…”

Chemo‐hygro‐mechanical modelling and numerical simulation of concrete deterioration caused by alkali‐silica reaction

“…Reference [13]. The ASR model proposed by Ba$ z zant and Steffens [2] is based on the idea, that the imbibition of water generates a pressure in the gel, which pushes the gel to permeate the pores in the cement paste located very near the surface of the aggregate particles. A macroscopic expansion is initiated only when the volume of the gel exceeds the accessible pore volume resulting in a pressurization of the interfacial transition zone.…”

“…A mesoscopic approach involves the analysis of a single representative aggregate particle and its vicinity, whereby the kinetics of the chemical and diffusional processes involved are described on the scale of the aggregates, see e.g. Reference [2]. On the other hand, in a macroscopic approach concrete is described at the scale of laboratory specimens, see e.g.…”