Modeling alkali–silica reaction in non-isothermal, partially saturated cement based materials

A mathematical model of combined action of hygro-thermal, chemical and mechanical loads is proposed to describe chemical degradation of cement based materials due to ASR and cracking due to material stresses. The model is based on mechanics of multiphase reactive porous media and isotropic damage theory. The mass-, energy- and momentum balance equations, as well as constitutive and physical relationships necessary for modelling the ASR in variable hygro-thermal conditions, are developed. Material shrinkage/swelling is modelled by means of effective stresses, with evolving solid surface fraction and sorption isotherms. Both the ASR reaction extent and the strain caused by it are described in a rate form. The ASR expansion is modelled as an imposed strain, depending on both the material temperature and humidity, considering effect of both gel aging and ASR initiation phase. A method for numerical solution of the model equations with the finite element and finite differences methods is presented. The proposed mathematical model is validated by comparing the simulation results with some published experimental data concerning hygro-thermal processes and ASR expansion of concrete specimens in different hygro-thermal conditions, both constant and variable in time.