Percolation theory considers the "connectedness" of a phase or multiple phases across a microstructure [24]. Formalized by Hammersley in the 1950's [25], it provides a technical basis for quantifying apparently random microstructures. Cement-based materials are essentially unique from a percolation standpoint, in that the percolation characteristics of several different phases influence properties [5,6,26,27]: the commonly measured "set point" is a measure of the percolation of the solids in a hydrating cement paste system, the percolation/depercolation of the capillary porosity dominates the transport properties of these materials, and the percolation of calcium hydroxide can have a large influence on their durability [5,28]. A common measure of percolation is the fraction of a phase that is part of a connected pathway across a microstructure. In a three-dimensional unit cube system, this would mean that portion of a phase which is connected (via a pathway totally remaining in the phase) to two opposing faces of the microstructure. For digital images, this quantity can be easily assessed using a simple "burning algorithm" [24,27]. An important item to note is that the percolation characteristics of a system are quite different in two and three dimensions. In three dimensions, a much smaller volume fraction of a phase (such as about 20%) can achieve percolation than in two dimensions (where 45-60% may be required).