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### 3. Percolation Properties of the Pore Space

As cement hydration progresses, the pore space is gradually being filled, because the factor T is greater than one. The connectivity of the pore space as a function of hydration is a percolation problem. In this paper the term "pore space" refers to capillary pore space, the water-filled space between the cement particles and their reaction products that is left over from the original cement-water mixture. There are nanometer-scale pores in the C-S-H surface product material, which form continuous pathways, called gel pores. However, transport properties are dominated by the much larger capillary pores as long as they percolate, i.e., form a continuous pathway. If the capillary pores close off, however, then transport must be dominated by the much smaller C-S-H gel micropores. There is no sharp size cut- off between capillary and gel pores. The capillary pores are considered to have a size ranging from hundreds of micrometers down to tens of nanometers, with the upper end of the C-S-H gel pore size distribution overlapping the lower end of the capillary pore size range [11].

Since the microstructural model is represented as a digital image, there is an underlying lattice in the structure of the model. Therefore, all the computational techniques developed for lattice percolation problems can be carried over to analyze digitized continuum structures like the cement paste model. For instance, the fraction of the pore space that is part of the percolating cluster is easily determined using a "burning algorithm" [20].

Recent work using the microstructural model [13] has shown that the capillary pore space of cement paste does have a percolation threshold, at a capillary porosity of about 18%, or c = 0.18. This threshold c is independent of the initial porosity or water:cement ratio [13]. Also, the C-S-H surface product phase itself has a percolation threshold, and changes from discontinuous to continuous at a volume fraction of about 17%. The close agreement of the two thresholds with a conjecture by Scher and Zallen [21] as to the value of a "universal" continuum percolation threshold of 16% in 3-d has been noted and discussed [13]. For typical w/c ratios, the C-S-H phase percolates quite early in the hydration process, and is continuous simultaneously with the capillary pore space.

The percolation theory-based description of the dependence of diffusivity on cement paste microstructure will be discussed more fully in section 6.

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