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Pade approximants can be employed [32,33] to describe the conductivity of porous sandstone rocks where the sand grains have a thin clay coating that has a higher conductivity than the electrolytic pore fluid. This is a situation analogous to the mortar and concrete conductivity problem being studied here. The Pade approximant in this case is a ratio of a quadratic polynomial to a linear polynomial,

where x = σs / σp . The parameters a, b, c, and d are given by combinations of four well-defined parameters F, Λ, f, and λ which are defined in terms of two limits of the effective conductivity [33].

The first limit, in which the interfacial zone is only slightly more (or slightly less) conductive than the bulk cement paste matrix, σs / σp → 1, is given exactly by perturbation theory as [33]

where 1/F is the ratio of the conductivity of the mortar to the conductivity of the bulk paste when σs / σp = 1, and Λ is a pore scale length parameter calculated in terms of the electric fields associated with the σs = σp problem [33]. When σs / σp = 1, σ / σp = 1/F, and when σs / σp is close to 1, Eq. (16) is linear in σs / σp with a slope given by the ratio 2h/(FΛ) [33].

The second limit is when the conductivity of the interfacial zone is much larger than that of the bulk cement paste, σs / σp >> 1. Assuming that the interfacial zones percolate, the composite conductivity in this limit is given by perturbation theory as [33]

where f and λ are additional length parameters defined in terms of the solutions of the σp = 0 and σs = 1 problem [33]. Fitting Eq. (16) to Eqs. (17) and (18) gives the four unknown coefficients a, b, c, and d.

Next: Conductivity Results Up: Computational Methods Previous: Effective medium theory