3. Results and Discussion
Figure 1- Initial 2-D images from experimental and model systems: a) real system (285 µm by 285 µm), b) model system with spherical particles, and c) model system with real particle shapes (200 µm by 200 µm).
a) 
b) 
c) 
Figure 1 presents two-dimensional images from the initial starting microstructures for the real cement paste and for two model cement pastes generated with spherical and real particle shapes, respectively. The ability to generate starting three-dimensional microstructures based on real particle shapes is a recent addition to the VCCTL software [12]. Initially, attempts were made to model the cement paste using a 100 x 100 x 100 microstructure model. However, this resulted in a system with too fine of cement particles (as indicated by the more rapid decay of the normalized correlation function in Fig. 2), relative to the real 300 x 300 x 300 microstructure. Increasing the system size to 2003 allowed for a truer representation of the "larger" cement particles (maximum diameter = 65 µm) present in the starting cement 133 microstructure, and resulted in a correlation function that basically overlaps the one measured on the real starting microstructure. While the correlation functions for the 2003 microstructures based on spherical and real-shaped particles both basically overlap that obtained for the real system (Fig. 3), a more visually pleasant agreement is observed between the real system and the model system based on real particle shapes in Fig. 1.
Figure 2- Measured normalized correlation functions for initial real and model microstructures showing the influence of model system size.
Next, the microstructures following
hydration are considered.Figure 4 shows
the two-dimensional images for the unhydrated cement particles in the real and model
microstructures, while their normalized correlation functions are provided in
Fig. 5. A good agreement between both
the visual images and their correlation functions is observed.
There is an indication that the particles in
the model system are "rougher" in both the visual image and in the higher
initial slope of the correlation function in Fig. 5. This is most likely due to the pixel-based
nature and inherent finite resolution of the CEMHYD3D model where individual
voxels dissolve, diffuse, and react within the available pore space
[2]. In
Fig. 5, no substantial difference is
observed between the normalized correlation functions for the two model
systems based on spherical and real particle shapes. This observation also holds true for the
results to be subsequently presented for the hydration products and capillary
pores, indicating that the use of
spherical as opposed to real-shaped particles appears to have a negligible
influence on the resultant microstructures in the CEMHYD3D model. Thus, it seems to be much more important to
adequately capture the particle size distribution of the particles
(Fig. 2) than
their specific shapes. In this regard,
it is worth noting that spherical particles are typically assumed in the
derivation of a particle size distribution from either experimental light
scattering or sieve measurements.
Figure 3- Measured normalized correlation functions for initial real and model microstructures showing the influence of model particle shape.
Surprisingly, the correlation distance, defined as how long it takes the normalized correlation function to decay to a value near 0, is actually larger in all three of the hydrated microstructures (Fig. 5) than in the initial microstructures (Fig. 3). The physical explanation of this seemingly perplexing behavior is that many of the smaller cement particles have completely hydrated, so that the unhydrated particle correlation functions in the hydrated systems are dominated by the remaining "larger" cement particles.
The two-dimensional images and normalized correlation functions for all of the hydration products are presented in Figures 6 and 7, respectively. Once again, reasonable agreement is observed between the real and model microstructures. The corresponding figures for the capillary porosity phase are provided in Figures 8 and 9. Observing the normalized correlation functions in Fig. 9, there is some indication that the capillary porosity in the model system may be slightly finer than that in the real microstructure. This porosity would be even finer if the model were executed under saturated as opposed to sealed conditions. As indicated by the grey (empty) pores in Fig. 8, a substantial contribution to the "coarse" porosity in the hydrated microstructure is the presence of these large pores that are the first to empty under sealed curing conditions, due to self-desiccation. This observation points out the importance of proper curing of higher w/c concretes, as well as lower w/c ones, to avoid the formation of large empty pores that may remain throughout the lifetime of the material. A further analysis was performed on the connectivity or percolation of the capillary porosity in the real and model microstructures [13]. Percolated porosity fractions of 98 % [7] and 85 % were measured for the real and model systems, respectively, further indicating the similarity between the real and simulated microstructures.
Figure 4- 2-D images from experimental and model hydrated systems showing remaining unhydrated cement particles: a) real system, b) model system with real particle shapes.
| a) | 
| b) | > |
Figure 5- Measured normalized correlation functions for hydrated real and model microstructures for the remaining cement particles.
Figure 6- 2-D images from experimental and model hydrated systems showing hydration products: a) real system, b) model system with real particle shapes.
Figure 7- Measured normalized correlation functions for hydrated real and model microstructures for all of the hydration products.
Figure 8- 2-D images from experimental and model hydrated systems showing capillary porosity (in black): a) real system, b) model system (empty pores in grey).
Figure 9 - Measured normalized correlation functions for hydrated real and model microstructures for the capillary porosity (water-filled and empty).
Figure 10- 2-D images from experimental and model hydrated systems showing calcium hydroxide (in white): a) real system, b) model system with a high nucleation probability for CH, and c) model system with a 100X lower nucleation probability for CH.
While it is difficult to distinguish individual hydration product phases in the real microstructure, attempts were made to isolate the calcium hydroxide (CH) phase for a visual comparison. The greylevel histogram for the real microstructure was analyzed and a threshold selected to give a CH volume fraction that matched that expected for the measured amount of hydration (about 12 %), after the "false" CH rims around each hydrating cement particle were removed by a simple 3-D erosion algorithm. Figure 10a provides a two-dimensional image of the "segmented" CH. Model representations of the CH distribution are provided in Figures 10b and 10c for two choices for the parameter that controls the nucleation of CH crystals within the CEMHYD3D microstructure model. Clearly, the lower value for this parameter gives the better visual agreement with the experimental data.
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