Unsaturated hydraulic conductivity was measured using four different methods. Tension permeameters were used to measure unsaturated hydraulic conductivity in the field, using a single disc method, which depends on the measurements of sorptivity, steady state flow rate, initial and final water content (White and Perroux, 1987, 1989). Also, a double disc method was used which utilizes Wooding's (1968) equation for two different disc radii at the same tension for steady state flow rates. Undisturbed and disturbed soil cores were used to measure unsaturated hydraulic conductivity in the lab, using water retention curves with van Genuchten's equations. There were no significant differences in the mean of hydraulic conductivity between single and double disc methods in all the tensions used (0, 5, 10 and 15 cm). There were significant differences between the field methods and undisturbed soil cores in zero cm tension, and disturbed soil cores in 10 and 15 cm tension. The effect of land preparation on the unsaturated hydraulic conductivity was studied using the double disc method. Tilling has significant effects on the unsaturated hydraulic conductivity at all tensions used. The spatial variation of unsaturated hydraulic conductivity and steady state flow in different tensions using the double disc method was studied. We found exponential variogram models for unsaturated hydraulic conductivity at 5, 10 and 15 cm tensions and a random model for zero cm tension. Also, exponential models were best fitted for steady state flow corresponding to pores radii of 0.03 - 0.015 cm, 0.015 - 0.010 cm and steady state flow at 10 cm tension. A Michaelis-Menton model was used for steady state flow at 5 cm and 15 cm tension. Disc permeameters were also used to add 5 cm depth of water, bromide and dye solution at 0, 5, 10 and 15 cm tensions with three replicates. A comparison was made between field data and simulated model under the same boundary and initial conditions as in the field. Results showed that the water and bromide move deeper than the prediction of the simulated model in all tensions used. The differences were larger between simulated model and field data for both water and bromide concentrations in the lower tension and smaller in the higher tension as a result of elimination of some preferential flow paths. An equation was developed for cumulative infiltration valid for both small and large time. The parameters calculated using the developed equation closely matched the measured infiltration, and fit better than a three term series similar to the Philip equation for one-dimensional flow.

This dissertation develops analytical expressions for the effective hydraulic conductivity Kₑ of a three-dimensional porous medium bounded by two parallel planes of infinite extent separated by a distance 2a. Head varies randomly along each boundary about a uniform mean value. The log hydraulic conductivity Y forms a homogeneous, statistically anisotropic random field having a variance σᵧ² and principal integral scales λ₁, λ₂, λ₃. Flow is uniform in the mean parallel to the principal coordinate χ₁. A solution is first derived for mildly nonuniform media with σᵧ² ≪ 1 via an approximate form of the 1993 residual flux theory by Neuman and Orr. It is then extended to strongly nonuniform media with arbitrarily large σᵧ² by invoking the Landau-Lifshitz conjecture as Kₑ = KG exp {σᵧ² [1/2 — (D + S)]} . Here, K(G) is the geometric mean of hydraulic conductivities and D and S are domain and surface integrals, respectively. Based on a rigorous limiting analysis we show that when the length scale ratio p = a / λ₁ → 0, Kₑ is equal to the arithmetic mean hydraulic conductivity K(A). This supports the theoretical finding of Neuman and Orr and the numerical result by Desbarats. When ρ → ∞ we obtain expressions for Kₑ that have been previously derived in the stochastic literature for infinite flow domains. For strongly anisotropic media with integral scale ratios ε₂ = λ₂ / λ₁ and ε₃ = λ₃ / λ₁ equal to each other and tending to zero or infinity ( ) i 0) we obtain the closed form solution Kₑ = K(G) exp {σᵧ²[exp(—p) — 0 .5]} . The latter reduces to K(A) when ρ → 0 and tends to the harmonic mean K(H) as ρ → ∞. One can think of the case ε₂ = ε₃ = 0 as mean flow along parallel channels having mutually uncorrelated hydraulic conductivities, and of the case ε₂ = ε₃ → ∞ as mean flow normal to layers having uniform hydraulic conductivities. For statistically isotropic media we show numerically that Kₑ equals K(A) when ρ = 0.01; when ρ ≥ 4, Kₑ = K(G) exp(σᵧ²/6) the three-dimensional infinite domain solution. Our results support the analytical finding of Rubin and Dagan, and predict and explain all related bounded domain numerical results. Finally, contrary to Dagan's assertion, we show that for small ρ boundary effects are extremely important; the absolute value of the surface integral S equals the value of the domain integral D.

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Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1984. / Bibliography: leaves [187]-199. / Microfiche. / xvii, 199 leaves, bound ill. 29 cm

Thesis (M.S. - Hydrology and Water Resources)--University of Arizona. / Includes bibliographical references.

Thesis (Ph. D. - Hydrology and Water Resources)--University of Arizona. / Includes bibliographical references.

Thesis (Ph. D. - Hydrology and Water Resources)--University of Arizona, 1986. / Includes bibliographical references (leaves 174-179).