Degree of Hydration

To examine the agreement between CEMHYD3D predictions and measured degrees of hydration, the w/c = 0.35 cement pastes cured under saturated conditions at 20 ºC were first selected. The measured and CEMHYD3D predictions for degree of hydration are provided in Figure 3, and it can be seen that there is nearly perfect agreement between the experimental results from two different sets of specimens (A and B) and those predicted by CEMHYD3D, using the cycle/time conversion factor of 0.00027 h/cycle². For the sealed curing results also shown in Figure 3, it is observed that the CEMHYD3D model underpredicts the hydration achieved in the real specimens at later ages.

Next, the influence of curing temperature on the achieved degree of hydration was examined by considering the w/c = 0.35 cement paste cured at 40 ºC. It has previously been observed that calcium silicate and cement pastes cured at higher temperatures exhibit a coarser pore structure, perhaps due to the formation of a denser calcium silicate hydrate gel (C-S-H) layer around the cement particles.^{17, 18} To attempt to better incorporate this effect into version 3.0 of the CEMHYD3D software, a parameter that influences the distance that "diffusing C-S-H" species are located from the initial cement particle surfaces was varied from its version 2.0 fixed value of 8 (elements) down to 1. In CEMHYD3D,^{5, 15} when elements (voxels) of tricalcium silicate or dicalcium silicate are selected for dissolution, the selected element of the original silicate is removed, an element of "diffusing C-S-H" is created at a porosity element immediately adjacent to the dissolution site and, as needed to maintain the appropriate volume stoichiometry of the hydration reactions, an additional element of diffusing C-S-H is placed at a random location near the original dissolution source, specifically within a 2n x 2n x 2n cubic (box) volume centered at the dissolution source element. The diffusing C-S-H elements then undergo a random walk diffusion process within the available capillary porosity until precipitating on a solid surface. Decreasing the value of n should indirectly result in a denser layer of C-S-H elements being formed around the unhydrated cement particle cores, leading to a coarser capillary porosity and likely a reduction in the hydration achieved at longer times as well. In version 2.0 of CEMHYD3D, n had a fixed value of 8, while in version 3.0, the value of n has been made to be a function of temperature as described further below. The results for the predicted degree of hydration as a function of n are shown in Figure 4. Based on these results, the C-S-H location parameter was set to be a linear function of temperature with a value of 3 for all (further) 40 ºC hydration simulations, while maintaining a value of 8 for the 20 ºC simulations using:

where Max and int represent the maximum and integer functions, respectively. The influence of n on the percolation properties of the capillary porosity will be presented subsequently. As shown in Figure 5, n = 3 also provides a good fit of the CEMHYD3D model to the experimental data obtained for the w/c = 0.35 cement pastes cured under sealed conditions at 40 ºC.

Equivalent hydration plots for the w/c = 0.435 and w/c = 0.45 cement pastes are provided in Figures 6 and 7, respectively. For these higher w/c ratios, a much smaller influence of saturation (sealed vs. saturated) is observed, as sufficient initial water is present to continue the hydration in the sealed samples even as chemical shrinkage and self-desiccation occur. ⁷ For all four cases shown in Figures 6 and 7, the agreement between the experimental measurements and the CEMHYD3D predictions appears reasonable.

Results for the much denser w/c = 0.25 cement pastes are presented in Figures 8 and 9. While the sealed hydration predictions of CEMHYD3D are reasonable for both curing temperatures, the saturated results are surprising in that the LOI-based measured degrees of hydration are much greater than the CEMHYD3D model predictions at later ages, particularly for the 40 ºC curing. These experimental values even significantly exceed the nominal value for the expected ultimate degree of hydration in a w/c = 0.25 cement paste of about 0.25/0.36 = 0.694. As noted previously by Hansen,¹⁹ it appears that low w/c cement pastes cured at higher temperatures have an inherently higher amount of chemically bound (or at least nonevaporable) water than conventional w/c pastes. When the C-S-H is restricted to form in very confined spaces, it appears that while its physically bound water per unit hydration may decrease, its chemically bound water increases, as has also been observed for DSP (densified with small particles) w/cm = 0.18 blended cement pastes hydrated at 23 ºC under "saturated" conditions by Lu et al.²⁰ Conversely, for w/c = 0.33 pastes of tricalcium silicate, Odler and Skalny have observed that the chemically bound water content per unit hydration (measured directly by x-ray diffraction) actually decreases with hydration time for sealed hydration either at 25 ºC or 50 ºC.²¹ Thus, while past measurements have indicated that for w/c = 0.3 to w/c = 0.45 cement pastes, LOI-based degrees of hydration are in good agreement with both isothermal calorimetry and chemical shrinkage measurements,⁵ for w/c = 0.25 and lower cement pastes, particularly when cured at higher temperatures, non-evaporable water content may no longer be a reliable measure of achieved hydration at later ages, as has already been noted for cement pastes with pozzolanic additions.^{22, 23}

Figure 4. Measured and CEMHYD3D predicted degree of hydration for w/c = 0.35 cement paste cured at 40 ºC under saturated conditions, as a function of the local box size used for C-S-H precipitation (B1− n = 1 voxel to B8− n = 8 voxels).

Figure 9. Measured and CEMHYD3D predicted degrees of hydration for w/c = 0.25 cement pastes cured at 40 ºC.