Multi-Scale Chemo-Mechanical Modeling of Eco-Self-Compacting Concrete Incorporating Recycled Glass Powder

We present a mechanistic multiscale framework for the joint analysis of mechanical performance and durability of eco-designed self-compacting concrete incorporating recycled glass powder. At the microscale, the cementitious matrix is described as a hierarchical composite comprising calcium-silicate-hydrate (C-S-H), portlandite (CH), and finely ground glass, with explicit physico-chemical interactions between these phases. The pozzolanic reactivity of the glass is modeled by a kinetic law that links the local consumption of portlandite to the specific surface area of the glass particles, thereby inducing controlled microstructural densification and an evolution of the connected porosity. On the mechanical side, an operator-based homogenization scheme of Mori-Tanaka type relates the effective elasticity tensor to the intrinsic properties of the constituent phases and to the glass volume fraction. On the transport side, durability is addressed through a diffusion-reaction model in which the effective diffusivity depends explicitly on the evolving porosity, thus capturing the permeability reduction induced by the pozzolanic reaction. These ingredients are coupled into a multiphysics-multiscale system in which the glass volume fraction ${？}_g$ appears as a design parameter. The precise mathematical problem considered is the characterization of an optimal glass content through an objective functional $F\left({？}_g\right)=\alpha E_{\text{eff}}\left({？}_g\right)？\beta D_{\text{eff}}\left({？}_g\right)$ , which balances effective stiffness $E_{\text{eff}}$ against effective diffusivity $D_{\text{eff}}$ for prescribed positive weights