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Hydraulic Conductivity of Soils: Unified Approach to the Statistical Models¹

ABSTRACT

Conceptual theory of the hydraulic conductivity of unsaturated porous media is presented. This analysis permits us to derive systematically the models of R. C. Childs and N. Collis George (1950), M. R. J. Wyllie and G. H. F. Gardner (1958) and Y. Mualem (1976) as well as other existing and new versions, from some common statistical principles.

The resulting formulas of unsaturated hydraulic conductivity can be classified into three categories: (i) universal formulas independent of the soil type which result from extremely simplifying assumptions; (ii) formulas with one degree of freedom, and (iii) formulas with two degrees of freedom. The latter two types of equations result from accounting for the correlation between pores and the tortuosity of flow path. These formulas can be adjusted to soil type to represent better the variability of soil properties and increase the accuracy of the predicted hydraulic conductivity. However, in this stage it is a potential advantage only. Empirical study should be followed in order to derive the optimal methods of estimating the unknown parameters.

¹ Contribution from the Hydrology and Water Resource Program, Faculty of Civil Engineering, Colo. State Univ., Fort Collins, CO 80523. Supported by funds provided by the National Science Foundation under Grant ENG-7611542.

² Senior Research Associate, Colo. State Univ., and Professor, Tel-Aviv Univ., Israel, respectively.

Received for publication August 19, 1977. Accepted for publication February 13, 1978.

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