Cement hydration from hours to centuries controlled by diffusion through barrier shells of C-S-H

Saeed Rahimi-Aghdam, Zdeněk P. Bažant*, M. J. Abdolhosseini Qomi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


Although a few good models for cement hydration exist, they have some limitations. Some do not take into account the complete range of variation of pore relative humidity and temperature, and apply over durations limited from up a few months to up to about a year. The ones that are applicable for long durations are either computationally too intensive for use in finite element programs or predict the hydration to terminate after few months. However, recent tests of autogenous shrinkage and swelling in water imply that the hydration may continue, at decaying rate, for decades, provided that a not too low relative pore humidity (above 0.7) persists for a long time, as expected for the cores of thick concrete structural members. Therefore, and because design lifetimes of over hundred years are required for large concrete structures, a new hydration model for a hundred year lifespan and beyond is developed. The new model considers that, after the first day of hydration, the remnants of anhydrous cement grains, gradually consumed by hydration, are enveloped by contiguous, gradually thickening, spherical barrier shells of calcium-silicate hydrate (C-S-H). The hydration progress is controlled by transport of water from capillary pores through the barrier shells toward the interface with anhydrous cement. The transport is driven by a difference of humidity, defined by equivalence with the difference in chemical potential of water. Although, during the period of 4–24 h, the C-S-H forms discontinuous nano-globules around the cement grain, an equivalent barrier shell control was formulated for this period, too, for ease and effectiveness of calculation. The entire model is calibrated and validated by published test data on the evolution of hydration degree for various cement types, particle size distributions, water-cement ratios and temperatures. Computationally, this model is sufficiently effective for calculating the evolution of hydration degree (or aging) at every integration point of every finite element in a large structure.

Original languageEnglish (US)
Pages (from-to)211-224
Number of pages14
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Feb 1 2017


  • Aging of concrete
  • Calcium silicate hydrate
  • Cement particle size
  • Diffusion barrier
  • Effective diffusivity
  • Hydration modeling
  • Relative humidity
  • Temperature
  • Water-to-cement ratio

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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