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Hydraulic Conductivity Related to Porosity and Swelling of Soil¹

ABSTRACT

The hydraulic conductivity factor in Darcy's equation for viscous flow is analyzed in terms of a modified Kozeny equation. The modifications include a correction for swelling, and the replacement of the cubic exponent of the porosity term by an exponent varying between 0 and 3. The choice depends on the interplay between surface and volume of soil pores, as determined by flocculation-dispersion conditions. Swelling is calculated from the theory of the diffuse double layer. A theoretical analysis of experimental results on the hydraulic conductivity of two soils for percolants of variable concentration and composition showed that a single value for the electrical potential parameter sufficed to match theoretical with experimental data when the concentration of the percolant ranged from 10 to 100 meq/liter. Taking into account effects of pore size, pore density, effective porosity, and flow matrix on the hydraulic conductivity, the above has been explained in terms of expansive swelling of smaller pores at the expense of larger ones. A number of published studies have been analyzed in the light of the theory proposed. The relevance of the theory with regard to the alleged contrast between grain and pore models of soil has been considered.

¹ Contribution from the US Soils Laboratory, and the US Water Conservation Laboratory, Soil and Water Conservation Research Division, ARS, USDA, Beltsville, Md. and Phoenix, Ariz., respectively.

² Research Soil Scientists at Beltsville, Phoenix, and Beltsville, respectively. The authors are indebted to G. H. Bolt, State Agricultural University of the Netherlands, for his guidance in solving equation [4] in this paper.

Received for publication May 20, 1968. Accepted for publication September 6, 1968.