Steady Infiltration From Buried Point Sources and Spherical Cavities

Abstract

Steady infiltration in two-and three-dimensional systems has been treated classically as a process of saturated flow with a free surface. The series this paper initiates deals with the generally unsaturated flow regimes set up by prolonged infiltration into regions with no shallow ambient water table. The analysis is simpler than the classical one in the sense that it does not involve a free surface. With hydraulic conductivity represented by an exponential function of moisture potential, the nonlinear equation for •teady flow is transformed into a linear equation which is formally equivalent to that for diffusion in a moving medium. The fundamental point source solution is explored and is used as the basis of an analysis of steady infiltration from spherical cavities. For cavities of small (dimensionless) radius, the infiltration rate is determined almost wholly by capillarity; on the other hand, gravity distorts the pattern of moisture distribution stro,ngly, even when the cavity radius is small. (This is the first of a planned series of papers by the author and R. A. Wooding on steady infiltration in two-and three-dimensional systems of various geometries relevant to. problems of infiltration and seepage arising in hydrology and irrigation technology. This development of the mathematical physics of infiltration in two and three dimensions is made possible by a device for the quasilinearization of the general equation describing steady water movement in unsaturated soils and porous materials [Philip, 1966b; 1967; 1968a, b]. Before turning to the specific problems of infiltration from spherical cavities, we first outline the basis of the method of analysis to be used in the series. QUASILINEARIZATION 0F STEADY INFILTRATION EQUATION Applying the continuity requirement to Darcy's law for an unsaturated homogeneous soil or porous medium [Richards, 1931; Childs and Collis-Geowe, 19'50; Klute, 19'52] yields the steady flow equation = o where K is the hydraulic conductivity, and ß is the total potential. We use potentials based on unit weight of water, em (of water) being a suitable unit. The convenient unit for K is then cm see-L ß comprises moisture (capillary) po-tential i and the gravitational component --z, where z is the vertical ordinate, taken positive downwards. Equation 1 then becomes 1039

A Hypersingular Boundary Integral Equation for a Class of Problems Concerning Infiltration from Periodic Channels

“…The normal flux over the surface of the channel is chosen to be constant F = −V 0 . From the definition of the dimensionless variables in equation (7) and using the value of α given by Philip [3] (that is α = 0.002 cm −1 ) and letting the reference length L = 100 cm it follows that αL = 0.2 and therefore…”

“…For example steady infiltration problems of this type have been considered by Philip [1][2][3], Wooding [4], Raats [5,6], Zachmann and Thomas [7], Pullan and Collins [8] and Batu [9,10] while time dependent problems have been solved by Lomen and Warrick [11] and Warrick [12]. These authors all consider infiltration through a uniform homogeneous soil.…”

“…where h is the soil water potential and α is an empirical constant that provides a measure of the relative significance of gravity and capillarity for water movement in the soil (see Philip [3] ). The matric flux potential Θ is related to the hydraulic conductivity by the equation…”

Overview of Selected Soil Pore Water Extraction Methods for the Determination of Potentially Toxic Elements in Contaminated Soils: Operational and Technical Aspects

“…Fine soils, where capillarity dominates, have small -values; coarse soils where gravity effects control water transport have larger -values (Phillip, 1968).…”

Evaluating the Effects of Mulch and Irrigation Amount on Soil Water Distribution and Root Zone Water Balance Using HYDRUS-2D

“…The soil moisture pattern under drip irrigation has been studied using empirical, analytical, and numerical models in the past decades [22][23][24][25][26][27][28]. HYDRUS-2D is a hydrologic model that simulates water, heat, and solute movements in 2D and 3D variably saturated porous media [29,30].…”