Knowing how much internal curing water is needed and how far the water can reasonably travel within the cement paste, the final piece of the puzzle is how the water reservoirs are distributed in the three-dimensional concrete microstructure. A proper analogy for this question is that of the protected paste volume concept for air-entrained concrete [17, 27]. Instead of being interested in what fraction of the cement paste is within a given distance of an air void, here we are concerned with what fraction of the cement paste is within a given distance of a water reservoir. This analogy may actually apply in both directions, as empty water reservoirs may serve as an effective air entrainment system [17, 18].
A three-dimensional hard core/soft shell microstructure model can be conveniently applied to determining the "protected" paste volume as a function of distance from a water reservoir (LWA or SAP). Such a model has been developed at NIST and is available for free downloading at http://ciks.cbt.nist.gov/cmml.html [28]. Similar models have been employed by other research groups [26]. Basically, a three-dimensional volume of concrete is represented as a continuum three-dimensional cube filled with solid aggregate (or SAP) particles. Both particles that supply water and those that do not are considered in the most general formulation of the computer model. Generally, in models of this type, water absorption by the normal weight aggregates is not considered, thus representing a worst-case scenario with regards to internal water curing. The "hard core" particles are placed at random locations from largest to smallest such that they do not overlap one another. Water reservoir particles are then surrounded by "soft shells" of various thicknesses and the volume fraction of the matrix cement paste as a function of shell thickness is computed using systematic 3-D point sampling [28]. The general output of the model consists of a table of the protected paste volume as a function of distance from the water reservoir surface and a two-dimensional color-coded image illustrating the availability of water within the concrete microstructure. Typical results are provided in Figure 11 and Table II for a concrete with 70 % aggregates by volume and replacement of 20 % of the fine aggregates by water reservoirs. In this example, 100 % of the cement paste is within 1.0 mm of a water reservoir surface (a relevant distance for early and middle age curing) and 98 % of the cement paste is within 0.5 mm (a more relevant distance for later age curing) [21].
Figure 11: Example two-dimensional image (1.6 cm x 1.6 cm) from a portion of an internal water curing simulation [21].
| Table II: "Protected Paste" Volume vs. Distance from the Water Reservoir Surfaces | |
|---|---|
|
Distance from Water Reservoir Surface (mm) |
Protected Paste Fraction |
|
0.02 |
0.046 |
|
0.05 |
0.128 |
|
0.1 |
0.280 |
|
0.2 | Table II: "Protected Paste" Volume vs. Distance from the Water
Reservoir Surfaces
0.563 |
|
0.5 |
0.978 |
|
1.0 |
1.000 |
Lu and Torquato have developed analytical equations for this same quantity that are strictly applicable for two-phase systems [29]. Concrete with internal water curing is at least a three-phase system, consisting of matrix (cement paste), water reservoirs (LWA or SAP), and normal weight aggregates. Bentz and Snyder [17] have shown that a simple modification of the Lu and Torquato equations to account for the normal weight aggregate volume fraction provides results in reasonable agreement with the three-dimensional simulations for distances up to several hundred micrometers, while Zhutovsky et al. [26] showed that the modified analytical predictions are less accurate when larger flow distances of several millimeters are considered.
As illustrated by Reinhardt and Mönnig [30], models such as DuCom [6] can allow an even more detailed modeling of the water distribution within a concrete with internal water curing. Figure 12 shows an example of the water distribution (in units of kg/m3) in a system with a single initially saturated water reservoir particle in its center (water reservoir volume fraction of 15 % and cement paste w/c=0.33). The top side of the cube (z direction) was open to the atmosphere (20 ºC and 65 % RH). The water content is clearly higher in the vicinity of the water reservoir. As illustrated in Figure 13, this results in a concurrent increase in the achieved degree of hydration after 14 d of curing, relative to a system with no internal water curing.
Figure 12: Water distribution in units of kg/m3 simulated with the DuCom model [6, 30].
Figure 13: Degree of hydration vs. saturated lightweight aggregate content of 3-D DuCom microstructures after 14 d [6, 30] of hydration under sealed, one open surface, or two open surface curing conditions with w/c=0.33.