Temperature-variable C-S-H Stoichiometry

It is well known that the pore structure of cement paste is a function of the temperature under which the hydration occurs [22]. One likely explanation for this effect is that the density of the C-S-H gel that forms is a function of temperature, with the general tendency to form a denser gel at higher temperatures. A denser gel would be consistent with the observed increase in and coarsening of the capillary porosity in the paste with increasing hydration temperature. Based on chemical shrinkage measurements and other data compiled by Geiker [23], version 2.0 of CEMHYD3D contains the following two functions to describe the relationships between molar volume (molarv) and temperature and between water content (watercon- the molar ratio of H to S in C-S-H) and temperature, respectively:

$$molarv[C\!\!-\!\!S\!\!-\!\!H] = 1000. \times (108. - 8. \times \frac{T-20}{80-20})\ mm^3/mol$$ (3)

$$watercon[C\!\!-\!\!S\!\!-\!\!H] = 4.0 - 1.3 \times \frac{T-20}{80-20}$$ (4)

where T is the hydration temperature in degrees Celsius. These equations result in the following predicted chemical shrinkages for the hydration of C₃S: 0.082 g H₂O / g C₃S at 5 ºC, 0.067 at 20 ºC, 0.034 at 50 ºC, and 0.0 at 80 ºC. The hydration model should be used with caution for hydration temperatures above 80 ºC, as little experimental data is available above this temperature and phases such as ettringite are generally unstable above 70 ºC, anyway. It should be noted that while the model varies the H/S molar ratio of the C-S-H with temperature, a constant molar ratio of C/S is assumed regardless of temperature, since the data of Bentur et al. [22] appears inconclusive in this area.