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

Abstract 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.

[1]  Catherine Larive,et al.  Apports combinés de l'expérimentation et de la modélisation à la compréhension de l'Alcali-réaction et de ses effets mécaniques , 1998 .

[2]  T. Katayama.  Diagnosis of Alkali-Aggregate Reaction - Polarizing Microscopy and SEM-EDS Analysis , 2010 .

[3]  T. C. Powers,et al.  An Interpretation of Some Published Researches on the Alkali-Aggregate ReactionPart 1-The Chemical Reactions and Mechanism of Expansion , 1955 .

[4]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[5]  S. Chatterji,et al.  Chemistry of alkali–silica reaction and testing of aggregates , 2005 .

[6]  Alexander Steffens,et al.  Mathematical model for kinetics of alkali-silica reaction in concrete , 2000 .

[7]  T. Ichikawa,et al.  Modified model of alkali-silica reaction , 2007 .

[8]  Alain Ehrlacher,et al.  A computational linear elastic fracture mechanics-based model for alkali–silica reaction , 2012 .

[9]  Victor E. Saouma,et al.  Constitutive Model for Alkali-Aggregate Reactions , 2006 .

[10]  Alain B. Giorla,et al.  Modelling of Alkali-Silica Reaction under Multi-Axial Load , 2013 .

[11]  L. Glasser,et al.  The chemistry of ‘alkali-aggregate’ reaction , 1981 .

[12]  Marc-André Bérubé,et al.  Laboratory assessment of alkali contribution by aggregates to concrete and application to concrete structures affected by alkali-silica reactivity , 2002 .

[13]  Y. Xia,et al.  A Mathematical Model for the Pessimum Size Effect of ASR in Concrete , 2003 .

[14]  James H. Espenson,et al.  Chemical kinetics and reaction mechanisms , 1981 .

[15]  Sidney Diamond,et al.  Alkali release from feldspars into pore solutions , 2003 .

[16]  Victor E. Saouma,et al.  Chemo-Mechanical Micromodel for Alkali-Silica Reaction , 2013 .

[17]  Claudia Comi,et al.  Two-phase damage modeling of concrete affected by alkali–silica reaction under variable temperature and humidity conditions , 2012 .

[18]  Stéphane Multon,et al.  Effect of applied stresses on alkalisilica reaction-induced expansions , 2006 .

[19]  R Dron,et al.  THERMODYNAMIC AND KINETIC APPROACH TO THE ALKALI-SILICA REACTION. PART 1. CONCEPTS , 1992 .

[20]  Mohsen Ben Haha.  Mechanical effects of alkali silica reaction in concrete studied by SEM-image analysis , 2006 .

[21]  T. Uomoto,et al.  Analytical Study Concerning Prediction of Concrete Expansion Due to Alkali-Silica Reaction , 1994, "SP-145: Durability of Concrete -- Proceedings Third CANMET - ACI International Conference, Nice, France 1994".

[22]  Dent Classer,et al.  The Chemistry of Alkali-Aggregate Reactions , 1981 .

[23]  B. Capra,et al.  Modeling of Induced Mechanical Effects of Alkali-Aggregate Reactions , 1998 .

[24]  Karen Scrivener,et al.  Micro-mechanical modelling of alkali–silica-reaction-induced degradation using the AMIE framework , 2010 .

[25]  V. M. Malhotra,et al.  Durability of Concrete , 2011 .