TITLE:
Multi-Scale Chemo-Mechanical Modeling of Eco-Self-Compacting Concrete Incorporating Recycled Glass Powder
AUTHORS:
Maingha Ronald Rigain, Odi Enyegue Thierry, Langola Olivier, Abanda André, Kenmogne Fabien, Kikmo Wilba Christophe, Koffi Djanna Francis Lénine
KEYWORDS:
Multiscale Modeling, Chemo-Mechanical Coupling, Recycled Glass Powder, Durability of Cementitious Materials, Homogenization, Physics-Informed Surrogates, Optimization of Composite Microstructures
JOURNAL NAME:
Journal of Materials Science and Chemical Engineering,
Vol.14 No.8,
August
17,
2026
ABSTRACT: 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
ϕ
g
appears as a design parameter. The precise mathematical problem considered is the characterization of an optimal glass content through an objective functional
F(
ϕ
g
)=α
E
eff
(
ϕ
g
)−β
D
eff
(
ϕ
g
)
, which balances effective stiffness
E
eff
against effective diffusivity
D
eff
for prescribed positive weights
α,β
. Under explicit structural assumptions on the maps
ϕ
g
↦
E
eff
(
ϕ
g
)
and
ϕ
g
↦
D
eff
(
ϕ
g
)
(monotonicity, concavity/convexity, and endpoint behaviour), we prove that F is strictly concave on the admissible interval
[
0,
ϕ
crit
]
and admits a unique critical point
ϕ
g
opt
∈
(
0,
ϕ
crit
)
, which is the unique global maximizer of F. This result establishes, in a mathematically precise sense, the existence and uniqueness of an optimal recycled glass volume fraction that achieves a well-defined trade-off between mechanical reinforcement and mitigation of diffusive degradation. Numerical simulations of the coupled chemo-microstructural-transport-mechanical problem illustrate the qualitative behaviour predicted by the analysis and exhibit the same optimality structure, thereby providing a coherent numerical counterpart to the theoretical result. Beyond its intrinsic predictive capabilities, the proposed model offers a structured, operator-based formulation that can serve both as a tool for the rational design of sustainable concretes and as a physics-based prior in data-driven frameworks. In particular, the governing equations and homogenized operators can be embedded as constraints or inductive biases in transfer-learning or domain-adaptation settings, and the effective laws
D
eff
(
ϕ
p
)
and
ℂ
eff
(
ϕ
p
)
constitute natural targets for interpretable surrogate models constructed via symbolic regression, explainable machine learning, or Kolmogorov-Arnold-type networks. This opens a pathway toward quantitatively reliable, computationally efficient, and physically consistent design tools for next-generation eco-efficient cementitious composites, and provides a clear roadmap for integrating future experimental calibration and hybrid computational strategies to obtain quantitative predictions for
C
CH
(
t
)
,
ϕ
p
(
t
)
,
D
eff
(
t
)
, and
E
eff
(
t
)
.