A multi-scale poromechanical model of damage induced by Delayed Ettringite Formation (DEF) as a consequence of progression of micro-cracks at the fine aggregate scale is developed. The aim is to link the DEF-induced expansion at both the microscopic and macroscopic scales to the loss of stiffness of the mortar and the increase of its diffusion coefficient. At the microscopic scale, mortar is assumed to be constituted of three phases: cement paste, sand and micro-cracks. Damage is assumed to be driven by a free expansion of cement paste due to ettringite crystallization pressures in small capillary pores, at a lower scale. The corresponding homogenised poroelastic properties are estimated along with the diffusion coefficient by resorting either to a Mori-Tanaka scheme or to a self-consistent scheme, as a function of paste and aggregate properties as well as on the density of micro-cracks. The latter is assumed to be an evolving internal variable in order to model DEF-induced damage in the mortar. As the DEF-induced expansive free strain in the cement paste is restrained by the sand particles, internal stresses arise in the mortar. The corresponding free energy can be partially released by an increase in the micro-cracks density by analogy with the energy restitution rate of linear elastic fracture mechanics. The role of the damage criterion adopted on the thermodynamic force associated with micro-cracks density increase is investigated.
Micromechanical modelling of damage induced by delayedettringite formation in concrete
