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List of Figures

• Figure 1: Showing concrete at four different length scales: upper left is concrete, upper right is mortar, lower left is cement paste, lower right is C-S-H.
• Figure 2: Showing processed and segmented SEM images of four kinds of portland cement particles. Each phase in the cement is identified by a unique color. The random microstructural differences between particles in the same cement, and between particles in different cements, is readily apparent.
• Figure 3: Showing four stages of hydration in a microstructural model of C₃S hydration. The degrees of hydration are: top left--0, top right--20 %, bottom left--50%, bottom right--87%. Red=unreacted cement, blue=CH, yellow=C-S-H, and black= porosity.
• Figure 4: Showing the capillary porosity remaining at the set point, for several experimental and model cement pastes involving different initial cement particle configurations, as a function of the w/c ratio of the cement paste.
• Figure 5: Showing the fraction of the capillary pore space that is part of a percolated (continuous) cluster, for several different water:cement ratio cement pastes as a function of degree of hydration.
• Figure 6: Showing the fraction of the capillary pore space that is part of a percolated (continuous) cluster, for several different water:cement ratio cement pastes as a function of capillary porosity.
• Figure 7: Showing the electrical conductivity of the cement paste at -40^oC, plotted vs. the volume fraction of C-S-H. The solid symbols are model results, and the open symbols represent experimental values.
• Figure 8: Showing cement paste conductivity results, normalized by the pore fluid conductivity, for an 0.5 w/c cement paste as a function of the capillary porosity.
• Figure 9: Showing model data for the diffusivity for several different w/c ratio cement pastes, normalized by the free water diffusivity, all plotted vs. capillary porosity.
• Figure 10: Showing experimental and model results for how the relative diffusivity changes as the amount of CH leached away increases.
• Figure 11: Showing a slice of a three dimensional model of mortar, with four aggregate diameters ranging between 0.5 and 3 millimeters. The four colors (dark blue, light blue, green, and red, indicate, from small to large, the four aggregate sizes used. The interfacial transition zone is shown as yellow.
• Figure 12: Showing slices of two different three dimensional concrete models, with spherical and ellipsoidal shaped aggregate particles. Aggregates are white, bulk cement paste is gray, and the interfacial transition zones are black.
• Figure 13: Showing the volume fractions of the hard cores and the soft shells when the soft shell phase has just percolated, for monosize spherical hard core particless. The solid lines are from an effective medium theory described later in the text.
• Figure 14: Showing the fraction of the total interfacial zone volume that is a part of a percolated (continuous) cluster as a function of aggregate volume fraction and for several interfacial zone thicknesses.
• Figure 15: Showing the fraction of the total cement paste volume fraction that lies within a given distance from an aggregate surface, for a mortar with a sand volume fraction of 0.552, and a concrete with an aggregate volume fraction of 0.646.
• Figure 16: The exact initial slope of the conductivity, in the limit of dilute sand concentration, is shown as a function of _s/_p for the four size model mortar.
• Figure 17: Composite conductivity for the four size model mortar is plotted vs. the interfacial zone conductivity. [Both are normalized by bulk paste conductivity.] The solid dots are the random walk data; also shown are the effective medium results (SC=self consistent and D=differential).
• Figure 18: Composite conductivities (calculated by random walk simulations) for the random model are shown as a function of sand concentration for three values of the interfacial zone conductivity. Also shown are the predictions of the SC and D-EMT calculations, with the same normalization as in the previous figure.
• Figure 19: The exact initial slope of the conductivity, in the limit of dilute sand concentration, is shown as a function of σ_s/σ_p for a typical mortar and a typical concrete aggregate particle size distribution.
• Figure 20: Two-dimensional slices from three-dimensional model microstructures of the C-S-H gel at the scale of nanometers. The left image is of the micro model (25 nm by 25 nm), and the right image is of the macro model (250 nm by 250 nm). White=solid, black=pore.

EXECUTIVE SUMMARY

Concrete is a complex composite material. It has random microstructure at length scales ranging from nanometers to millimeters. The calcium silicate gel phase is a random composite at the nanometer scale, cement paste has complex microstructure at the micrometer scale, and the random arrangement of aggregates (rocks, sand) in concrete makes it a random composite at the millimeter scale. This multi-length scale, random microstructure can be approximately described using computer models, whose results are interpreted via percolation theory and composite theory.

First concrete and percolation theory ideas are introduced. Cement paste, at the micrometer scale, is then considered. The basic digital-image-based cement hydration model is introduced. Percolation ideas are then applied to understand model and experimental results for the set point (solids percolation), capillary pore space percolation, calcium silicate gel percolation, cement paste pore size, cement paste diffusivity, and calcium hydroxide percolation (leaching).

Next, the microstructure of mortar and concrete is considered, using the hard core/soft shell percolation model. The percolation of the interfacial transition zone phase is studied, and its importance to the transport properties of concrete explained. Using these percolation ideas, the diffusivity/conductivity of concrete can be approximately mapped out.

Finally, after presenting a computer model for the nanostructure of calcium silicate gel, and studying its transport properties, the elements of a multi-scale model for the diffusivity/conductivity of concrete are presented. The report ends with a summary of results.