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Some Theoretical Aspects of the Flow of Water in Unsaturated Soils¹

ABSTRACT

The validity of Darcy's law in unsaturated media and the assumptions made in its use are discussed. The relationship of the permeability coefficient in Darcy's law to various soil parameters is briefly considered, the total soil moisture potential is defined, and its components discussed. By use of the equation of continuity and Darcy's law, an equation of flow is derived, and the general problem of obtaining solutions of this equation is outlined. The special mathematical difficulties encountered when the permeability is considered as a function of the moisture content or the capillary potential are also indicated. A numerical solution of the flow equation for a semi-infinite system is given, using a functional relationship between the permeability and the moisture content, and the phenomenon of a wetting front is shown to be indicated.

¹ Part of a thesis submitted to the Graduate School of Cornell University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The author acknowledges with appreciation the assistance of Prof. M. B. Russell, who supervised his studies. Presented before Sections I and VI, Soil Science Society of America, State College, Pa., August 30, 1951.

² Former Graduate Assistant, Agronomy Department, Cornell University, Ithaca, N. Y. Now Research Engineer, Schlumberger Well Surveying Corp., Ridgefield, Conn.