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The cement, specifically tricalcium silicate, hydration model utilized in this research has been described in detail elsewhere [6,7] so that only the salient features will be outlined here. The cement powder to be modelled is represented by non-overlapping digitized spheres following the particle size distribution (PSD) measured on actual cement samples. In this study, we have employed the PSDs given in Ref. [8] to examine cements with median particle diameters of 10, 20, and 30 µm. To minimize finite size effects, periodic boundaries are used during particle placement, such that a particle which extends outside of one face of our 3-D computational volume is completed into the opposite side of the system. In these simulations, each pixel element represents 1 µm3 in volume and the total system size including a single flat plate aggregate is either 450 x 220 x 220 or 600 x 220 x 220 pixels. The thickness of the single aggregate is adjusted so that in the computational cube, the appropriate ratio of "interfacial zone" (within the interfacial transition zone (ITZ) thickness) to "bulk" (outside the ITZ thickness) cement paste is obtained, as determined using the concrete microstructure model described below. The cement particles are placed in order of size from largest to smallest at random locations in the 3-D microstructure such that they do not overlap one another or the aggregate particle.
After initial particle placement, a simple cellular automaton model is utilized to model the hydration reactions between tricalcium silicate and water [9]. Cement pixels in contact with water dissolve at random, diffuse within the pore space, and react to form calcium hydroxide crystals in the pore space and calcium silicate hydrate gel (C-S-H) on the surfaces of the original cement particles and previously deposited C-S-H. For these studies, the aggregate is considered inert and does not participate in the hydration reactions. After the user-specified volume fraction of the initial cement has reacted, known as the degree of hydration, the microstructure can be quantified by determining the porosity present as a function of distance from the aggregate surface. Initially, after particle placement, the interfacial transition zone region contains a higher w/c ratio (more porosity) than the bulk paste due to the inefficient packing of the cement particles (the so-called "wall effect"). During hydration, the porosity is reduced throughout, but still remains higher in the ITZ regions. Thus, these regions will typically have a higher diffusivity than the bulk paste regions. Once porosity has been quantified, relative diffusivity (D/Do ) as a function of distance from the aggregate surface, x, can be estimated using the relationship established in Ref. [10]:
where relative diffusivity is defined as the ratio of the diffusivity of
ions in the material of interest relative to their value in bulk water,
(x) is
the porosity fraction at a distance x, and H is the Heaviside
function
having a value of 1 when > 0.18 and a value of 0 otherwise.
