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Theory and Measurement of Anisotropic Air Permeability in Soil¹

ABSTRACT

Three fundamental theorems on the movement of air through anisotropic soil are stated. New and simple proofs for two of the theorems are given; proof for one is referred to in the literature. On the basis of these theorems, formulas are derived for converting, to horizontal and vertical permeabilities, air flow measurements, previously reported in the literature, on soil clods. It is shown that the reported values of anisotropic permeabilities are apparent values, and that these apparent values depart considerably, in certain cases, from the correct values. As an extreme example, the reported ratio of the apparent horizontal to apparent vertical permeability for clod samples of Clarion soil, is 2.09, whereas the corrected ratio is 13.0. One particularly interesting general result of the theory is that an apparent value of the vertical permeability is, in fact, the geometric mean of the vertical and horizontal permeabilities of the sample. It is finally shown that the arithmetric mean of the apparent vertical and apparent horizontal permeability does not deviate greatly from the arithmetic mean of the true horizontal and true vertical permeability, the deviation being, for the Clarion sample, only 24%.

¹ Journal Paper No. J-2628 of the Iowa Agr. Exp. Sta., Ames, Iowa, Project 998. Contribution of the Department of Agronomy. Presented before Div. I, Soil Science Society of America, Dallas, Tex., Nov. 17, 1953.

² Graduate student, and Professor of Soils and Physics. The senior author, who is now Research Officer for the Water Conservation and Irrigation Commission, Leeton, New South Wales, Australia, Gratefully acknowledges receipt of an International Fellowship from Iowa State College, also, a United States Government Fulbright Grant for travel from and to the Netherlands.

Received for publication November 1, 1954.