A reaction model for cement solidification: Evolving the C-S-H packing density at the micrometer-scale

Cement paste is a multiphase material of complex chemistry, of which 60% by volume is typically composed of calcium-silicate-hydrates (C-S-H), the phase that lends the material its strength and stiffness. Moreover, it has been shown that the C-S-H phase is a dispersion of nanometer-sized particles that are characterized by an attractive-repulsive potential and densify in course of the hydration reaction. Herein, we model the nucleation and growth of the nanoparticles as a continuous density field subject to a reaction equation. Using this phase-field approach, we aim to reduce the parameter space present in similar hydration models and create a vehicle to upscale mechanical information from the nanometer-scale to the micrometer-scale. Despite the apparent simplification of the physics at play, we readily reproduce the cement paste reaction kinetics and microtexture-functions of temperature, coarseness of the calcium-silicate source particles, and initial water-to-cement ratio-, and vet them against experimental observations. Presenting results for two-dimensional simulations, we achieve excellent agreement with measurements of hydration heat curves, pore-chord-length and solid-chord-length density functions, distributions of low- and high-density C-S-H products, and elasticity.