A three-dimensional hydration and microstructure model for portland cement has been developed and preliminarily validated against experimental data. For input, the model requires the particle size distribution and a set of SEM/X-ray images for the cement of interest. With this information, a three-dimensional representation of the cement particles in water is constructed which matches the following characteristics of the input information: 1) the particle size distribution, 2) the individual phase volume fractions, and 3) the individual phase surface fractions which are in contact with porosity (water). Additionally, the cement particles may be either flocculated or dispersed during this construction process to better represent real cement-water systems.
Starting with the constructed three-dimensional cement particle image, a computer model based on a set of cellular-automata-like rules has been developed for simulating the hydration reactions that occur between cement and water. The model accounts for the major reactions of the cement clinker phases (tricalcium silicate, dicalcium silicate, tricalcium aluminate, and tetracalcium aluminoferrite) and gypsum. Reaction stoichiometries and reactant and product physical properties (molar volume, density, and heat of formation) have been taken from the available literature or obtained from calibration against experimental data. In addition to representing the microstructural evolution which occurs during hydration, the model also provides quantitative information on the amount of hydration which has occurred, the heat which would be released under isothermal conditions, and the amount of chemical shrinkage which would occur.
To validate the model, experimental studies have been conducted on Cements 115 and 116 issued in 1995 by the Cement and Concrete Reference Laboratory (CCRL) at NIST. At 25 ºC, non-evaporable water content, heat release via isothermal microcalorimetry, and chemical shrinkage have been measured at three different w/c ratios (0.3, 0.4, and 0.45). The first of these can be converted to a degree of hydration by normalization by the value measured for fully hydrated samples of each of the two cements. The three experimental measurements exhibit good agreement with one another over the range of w/c ratios studied. The kinetic (dispersion) models of Knudsen have been utilized to fit the non-evaporable water content vs. time for times up to 90 days. The parabolic dispersion model has been found to provide the best overall fit to the experimental data, with a relatively constant induction time for the two cements and three w/c ratios.
Using the fitted parabolic dispersion models, the model results have been calibrated to the experimental data. For Cements 115 and 116, a single set of parameters can be used to relate model cycles to real time via an equation of the form: time = t0 + B*cycles2. With this calibration, the agreement between model and experimental degrees of hydration, heat releases, and chemical shrinkages is in general excellent. In adddition, based on the gel-space ratio theory of Powers and Brownyard, the hydration model has been used to predict the 7 and 28-day compressive strengths of ASTM C109 mortar cubes from the measured 3-day strengths and the calibrated hydration kinetics. The predictions have been found to lie well within the standard deviation of the CCRL interlaboratory testing program, suggesting one promising engineering application of the three-dimensional cement hydration and microstructure program.
In the future, efforts will concentrate on extending these results to other temperatures and calibrating the incorporation of silica fume into the microstructure model.