The measured changes in internal RH with hydration time are provided in Figure 2. The measured internal RH is a function of temperature, and is projected to be about 3 % higher at 30 ºC than at 20 ºC [13]. After initial equilibrium of the sensors was achieved, the RH decreases with hydration time. This is a direct consequence of the creation of empty pores within the specimens hydrating under sealed conditions. The Kelvin equation describes the relationship between the size of these pores and the internal RH (assuming cylindrical pores and a contact angle of zero degrees between the pore solution and the pore walls) [14]:
where γ is the surface tension of the pore solution, Vm is its molar volume, r is the radius of the largest water-filled pore (or the smallest empty pore), R is the universal gas constant, and T is the absolute temperature. The introduction of either LWA or SAP will alter the size of the pores being emptied due to self-desiccation (hydration) of the paste. The largest water-filled pores empty first as the surrounding cement paste hydrates [15]. The effect can be observed in Figure 2. For the mixtures with an internal supply of water (either LWA or SAP), the RH remains higher than in the reference mixture throughout the course of the hydration, only falling to about 95 % after 12 d of hydration, as the larger pores in the LWA or the expanded SAP particles empty instead of the smaller capillary pores in the hydrating cement paste. According to equation 1, the emptying of these larger pores (higher values of r) will result in higher RH values, as is observed experimentally.
Figure 2. Measured internal RH vs. time for the various mortars during sealed hydration at 30 ºC.
The water menisci created during self-desiccation will induce capillary stresses in the pore solution and therefore on the solid network containing the pore solution. Assuming a cylindrical pore geometry, the tensile stress in the pore solution, #963;cap, is given by [14]:
where all other terms have been defined above.
The shrinkage strain of a partially saturated porous medium due to these capillary stresses in the water-filled pores can be estimated as [16, 17]:
where ε is the shrinkage (negative strain), S is the degree of saturation (0 to 1) or volume fraction of water-filled pores, K is the bulk modulus of elasticity of the porous material, and Ks is the bulk modulus of the solid framework within the porous material. This equation is only approximate for a partially-saturated visco-elastic material such as hydrating cement paste, but still provides insight into the physical mechanism of autogenous shrinkage and the importance of various physical parameters.
The measured autogenous deformations for the various mixtures are provided in Figure 3. The use of internal curing (by providing a supply of free water) is seen to be a highly effective means of mitigating autogenous shrinkage. Each of the three internal curing mixtures (LWA08, LWA20, and SAP) either significantly reduces or eliminates the measured autogenous shrinkage. Because it provides the most extra curing water, the LWA20 mixture totally eliminates autogenous shrinkage, resulting instead in a small autogenous expansion, perhaps due to ettringite formation and/or swelling of the cement hydration products due to water absorption.
Figure 3. Measured autogenous deformation vs. time for the various mortars during sealed hydration at 30 ºC.
A comparison of the distribution (availability) of internal curing water in the three different mortars with internal curing has been undertaken using the NIST 3-D hard core-soft shell (HCSS) computer model of "water" distribution within mortar [18, 19], based on the measured particle size distributions for the sand, LWA, and SAP (expanded) particles. The relative proximity of the hydrating cement paste to the internal water sources (LWA or SAP) is illustrated in Figure 4.
Figure 4. Computer modeling of fraction of paste vs. distance from a low-density aggregate or SAP particle surface.
Because of the low permeability of high-performance cement paste, self-desiccation is completely prevented only within 100 µm from an internal curing source. Thus, according to the paste proximity plot provided in Figure 4, the mortar LWA20 should be protected, while the mortars LWA08 and SAP should undergo self-desiccation, at least locally, in agreement with the measured autogenous deformations shown in Figure 3. This is also illustrated in Figure 5, which shows 2-D images generated from the 3-D HCSS microstructures of the mortars LWA08, LWA20 and SAP, including sand, LWA or SAP, and the proximity of the hydrating paste to the LWA/SAP surfaces (paste < = 100 µm from LWA or SAP, or paste > 100 µm from LWA or SAP).
While the SAP and LWA08 mortars contain basically the same quantity of 'extra' water (Table 1), the SAP mortar is more efficient in reducing autogenous shrinkage at later ages (Figure 3), most likely due to the more homogeneous distribution of the extra curing water within the three-dimensional mortar microstructure (Figure 5c vs. Figure 5a). At earlier ages (< 5 d), SAP and LWA08 perform equivalently with respect to autogenous deformation (Figure 3), as the internal curing water is able to travel distances greater than 100 µm within the more porous, higher permeability 'early-age' cement paste. Photos of polished sections of the mortars LWA20 and SAP are given in Figure 6. The spatial distribution of the LWA and SAP (voids) in the actual images of the mortars compare reasonably well with their respective simulated color 2-D images in Figure 5.
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Figure 5. Computer modeling of the distribution of phases. a: 8 % replacement (the white "unprotected" paste is 97 % percolated in 3-D) b: 20 % replacement of sand by low-density aggregates and c: 0.4 % addition of SAP particles (the white paste is 83 % percolated in 3-D). Color code: Red- sand, yellow- LWA or SAP, white- paste > 100 µm from LWA or SAP, blue- paste within 100 µm from LWA or SAP. Each 2-D image is 10 mm x 10 mm in size.
Finally, the results of the compressive strength testing are provided in Figure 7. The measured proportional gains in compressive strength between 7 d and later ages (27 d to 29 d) can be linked to the internal RH data presented in Figure 2. It is consistently observed that for those specimens where a higher internal RH is maintained during this time period, a greater gain in compressive strength is found. This is a natural consequence of the linkages between moisture availability, hydration rates, and strength development. It is well known that hydration proceeds at a reduced rate as the specimen internal RH is decreased [20, 21, 22]. This highlights a possible secondary benefit of internal curing in addition to the primary reduction in autogenous deformation, namely the achievement of an increased degree of hydration and a potentially higher compressive strength (and lower permeability/diffusivity) under sealed curing conditions. The increased degree of hydration may not always lead to an increase in compressive strength for the mortar or concrete specimens, as the increased strength of the cement paste binder may be offset by the increased porosity of the composite as a whole (due to the internal porosity of the low-density aggregates or the hollow voids introduced by the SAP particles). In practice, the influence of specimen RH on measured compressive strength presents an additional complication [9, 23].
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b) 
Figure 6. 2-D microstructures for the a) LWA mortar with 20 % mass replacement (LWA20) and the b) SAP mortar systems. Polished specimens, optical microscope with a field width of 15 mm.
Figure 7. Compressive strength development for the various mortars during sealed hydration at 30 ºC.