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Cement and Mineral Admixture Particles

The microstructural model used to simulate the interfacial zone has been described in detail elsewhere [7,11,12]. Within the model, space (volume) is represented as a series of discrete cubic elements, called pixels, arranged on a simple cubic lattice. For the simulations presented in this paper, this three-dimensional lattice is 200 x 200 x 200, for a total of eight million pixels. Each pixel represents a volume element occupied by a single phase of the concrete microstructure and is approximately 1 cubic micrometer in volume. For these simulations, relevant phases are water-filled porosity, cement, C-S-H, CH, pozzolanic C-S-H (C-S-H produced from the pozzolanic reaction of CH with silica fume), silica fume, and aggregate. Entrained air is not considered in the model, but should not affect the results of this study.

In the model, portland cement is considered to be composed entirely of C₃S. This simplification has not limited the model's applicability, however, as it has been applied successfully to i) computing the continuity of the capillary porosity and other phases in portland cement as a function of the degree of hydration [12], ii) characterizing the cement paste- aggregate interface in portland-cement concrete with and without mineral admixtures [7,8], and iii) calculating diffusion coefficients for cement pastes as a function of w/c ratio and [13]. Although the hydration chemistry of portland cement is certainly more complicated than that of C₃S, it is the spatial (geometrical and topological) arrangement of solid and pore phases that will determine most performance properties of cement paste, such as strength, diffusivity, or permeability. Justification that this physical microstructural model accurately represents these spatial properties of portland cement pastes as well as C3S pastes is based on the volume stoichiometry of the hydration reactions and has been given previously [8,12].

To begin a simulation, a starting microstructure is created. For simulation of interfacial zones, a 100 x 100 x 100 pixel cubic aggregate is placed in the center of the 200 x 200 x 200 pixel model. In these studies, the aggregate is considered to be inert so that neither C-S-H nor CH may precipitate on its surface. Next, a water-to-solids (w/s) ratio, where solids includes the cement and silica fume but not the aggregate, and silica fume volume concentration are specified and the needed number of cement and admixture particles are placed inside the 200³ pixel hydration volume. The cement and mineral admixtures particles are not allowed to overlap the aggregate or each other and are placed at random locations as it is assumed that the water content of the system is always such that a true dispersion can be achieved. For low w/s ratios and systems containing silica fume, water reducing agents or superplasticizers might be required to achieve this dispersion.

Cement particles are modelled as digitized spheres having two different diameters, 21 and 11 pixels respectively. Thus, on the basis of scale, the aggregate must be considered as a sand particle, as it is five to ten times larger than the cement particles. Similar results would be obtained with larger aggregate particles, as it is the size of the cement particles that controls the interfacial zone properties, as long as the aggregate particles are much larger than the cement particles. The cement particles are placed using periodic boundary conditions to reduce any artificial edge effects. Thus, if a cement particle is placed so that any part of it projects outside the model volume, that part is "wrapped around" to the opposite side of the volume. The silica fume particles are modelled as fine one-pixel elements, roughly equivalent to a one micrometer cube. The silica fume particles are placed at random in the remaining unoccupied locations throughout the 3-D microstructure after the aggregate and cement particles have been placed. Silica fume concentrations are assigned to be either 10 or 20% by weight of total solids. Assuming specific gravities of 3.2 for cement and 2.2 for silica fume, these mass concentrations correspond to 13.9 and 26.7 on a volume basis of total initial solids.