Predicting cement microstructure and mechanical properties in hydrating cement paste with a Phase-Field model

TL;DR

This work develops an adapted Phase-Field model to predict the microstructure evolution during cement hydration by revising the free-energy landscape and introducing distinct equilibrium constants for dissolution and precipitation. The three coupled fields ($\text{C3S}$, $\text{CSH}$, and $c$) evolve under tilted free energies $Ed$ and $Ep$, governed by $\partial C3S/\partial t$, $\partial CSH/\partial t$, and $\partial c/\partial t$ equations, and mass conservation constraints, yielding hydration-driven porosity and smooth phase interfaces. The resulting hydrated microstructures are used in a computational homogenization scheme to predict elastic moduli, with PF predictions showing close agreement with experimental trends and outperforming semi-empirical cellular-automata approaches that overestimate porosity. The study demonstrates a thermodynamically consistent link between hydration chemistry, microstructure formation, and mechanical response, and discusses extensions to 3D and multiphysics couplings for broader cementitious material applications.

Abstract

Predicting the evolving microstructure of hydrating cement is essential for understanding and modeling its mechanical property development. Physics-based continuum approaches offer a rigorous framework for capturing the thermodynamics of dissolution and precipitation processes at the microstructural scale. In this work, we present an adapted Phase-Field (PF) model for cement hydration that resolves key physical inconsistencies in existing PF formulations by introducing a revised free-energy potential and distinct equilibrium constants for clinker dissolution and hydrate precipitation. The resulting PF framework reproduces microstructural evolution, yielding realistic porosity levels and continuous phase boundaries in close agreement with experimental observations. The predicted hydrated microstructures are subsequently used in a computational homogenization scheme to evaluate the elastic response of the material. The PF-derived mechanical properties show good agreement with experimental trends, supporting the ability of the proposed framework to consistently link hydration chemistry, microstructure formation, and the resulting mechanical response.

Figures (16)

• Figure 1: Scheme of the hydration process considered.
• Figure 2: Free energy $f_{\eta}$ and its derivative $\partial f_{\eta}$.
• Figure 3: Example of tilted free energy $f_{C3S}+Ed(c, {C3S})$ (in red), the dissolution is favored ($c<c_{eq,\,C3S}$).
• Figure 4: Example of tilted free energy $f_{CSH}+Ep(c, {CSH})$ (in blue), the precipitation is favored ($c>c_{eq,\,CSH}$).
• Figure 5: Evolution of the microstructure during the hydration process.