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Computer simulation methods

The algorithms for simulation of microstructure and computation of electrical conductivity have been described in detail elsewhere [2]. Briefly, a cellular automaton-type digital- image-based algorithm has been developed to simulate the microstructural development of cement paste during hydration. The degree of hydration of the cement paste microstructure is varied systematically, and the capillary porosity is measured directly by counting pixels. Once a three- dimensional microstructure has been built up in the computer, Laplace's equation is solved for the structure using a finite-difference technique and a conjugate gradient method [2]. This is formally equivalent to setting up and solving a random conductor network in the model image, with the values of the conductances assigned appropriately [12].

Figure 1 shows a two-dimensional section of such a network, with the highest conductance bonds being drawn the thickest. The pore fluid conductivity is normalized to unity, so that a conductance of 1 is assigned to adjacent pairs of pixels representing capillary pore space. This means that the computed bulk conductivity will be given in units of σ_o, so that σ = Γ. Since the C-S-H gel phase contains very fine continuous micropores, it is assigned a finite but much smaller conductance of 0.0025. This number has been calibrated by experimental chloride diffusivities measured for 28-day or older samples [2]. In the time range studied in this paper, the conductivity is dominated by the capillary pore space, so that the exact value of the conductivity assigned to the C-S-H phase would have only minor effects on the results. All measured capillary porosities were greater than 28%, which is well above the percolation threshold of 18% [11]. Interfaces between phases are assigned intermediate conductances [2], as is shown in Fig. 1 by the intermediate thickness bonds.