An RVE-Based Multi-Scale Approach for Concrete Affected by Alkali–Silica Reaction

The alkali-silica reaction (ASR) is a deleterious reaction that occurs in cementitious mixtures like concrete due to the combination of the alkaline solution of the cement paste with the amorphous silica of the aggregates. As a consequence of this reaction a gel is generated that expands through water absorption, leading to pore filling and pore pressure increment. Experimentally, the consequences of ASR are observed in both the micro-cracking path around the aggregate and the stiffness reduction of the overall skeleton or solid phase. To get a proper prediction of the aforementioned effect, it is necessary to consider the kinetics of the chemical reaction and its effect on the mechanical behavior. In this paper, the ASR is modeled introducing a variable that quantifies its progress through a first order kinetic law. This variable affects the volumetric component of the Helmholtz free energy which now shall account for the chemo-mechanical behavior of the material. Thus, an additional term is introduced in the microscopic free energy density related to the chemical reaction process. The proposed free energy equation is implemented in a thermodynamically consistent multi-scale framework accounting for the chemo-mechanical degradation of the micro-structure due to the volumetric expansion of the gel. The cement mortar constitutive relation is reformulated using Biot’s poromechanics theory to include the pore pressure in the mechanical description, and a damage model to reproduce the solid phase degradation. Finally, some numerical examples showing the potential of the presented formulation are discussed.