Powers’ model for hydrating cement paste provides an effective means of addressing the first question [16]. If for a given concrete mixture, one desires to provide enough water to compensate for the maximum expected chemical shrinkage and maintain saturated conditions in the hydrating cement paste, the mass of water needed per cubic meter of concrete (Mw in kilograms of water per cubic meter of concrete) is given by a simple product of the concrete mixture cement factor (Cf in kilograms of cement per cubic meter of concrete), the expected chemical shrinkage per unit mass of cement at 100 % hydration (CS in kilograms of water per kilogram of cement), and the cement’s maximum expected degree of hydration (αmax) [17, 18]:
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(3) |
For w/c < 0.36, the maximum expected degree of hydration under saturated conditions is given by (w/c)/0.36. For higher w/c ratios, one can either apply equation (3) directly with a maximum expected degree of hydration of 1.0 [17] or calculate the water needed to provide for complete hydration of the cement particles, while allowing for the formation of empty pores within the hydrating microstructure [18]; the two approaches are illustrated graphically in Figure 9. An optimum approach likely lies somewhere between these two extremes.
The actual chemical shrinkage is a function of cement composition and curing temperature [19, 20, 21]. The chemical shrinkage computed for each projected hydration reaction (silicates and aluminates) depends strongly on the assumed molar volumes and specific gravities. Thus, references [19, 20, 21] all arrive at slightly different coefficients for the different hydration reactions, even when the same molar reaction stoichiometry is considered.
An additional concern to how much water is needed is how much water is available in the water reservoirs (LWA or SAP). While SAPs generally release nearly all of their water at relatively high relative humidities [18], different LWAs vary greatly in what fraction of their total water content is "easily" released (Chapters 2-4 of this report). When converting from a volume of water needed to a volume or mass of water reservoirs needed, this availability of the internal water must be given proper consideration as well [18, 21, 22].
Figure 9: Internal water needed to maintain hydration (saturation) in cement paste, with chemical shrinkage, CS=0.065 [21].