Effective Parameters for Unsaturated Flow

Wildenschild, Dorthe.  Characterization of Unsaturated Hydraulic Parameters for Homogeneous and
Heterogeneous Soils.  Ph.D. Technical University of Denmark, Department of Hydrodynamics and Water Resources. Lyngby 1996.

Abstract: Two-dimensional unsaturated flow and transport through heterogeneous sand was investigated under controlled laboratory conditions. The unsaturated hydraulic conductivity of five homogeneous sands and three heterogeneous systems composed of these five sands was measured using a steady state flux controlled method. The heterogeneous sand systems were established in a laboratory tank for three realizations of random distributions of the homogeneous sands comprising a system of 207 grid cells. The water flux was controlled at the upper boundary, while a suction was applied at the lower boundary such that on the average a uniform pressure profile was established and gravity flowapplied. Solute breakthrough curves measured at discrete points in the tank using time domain reflectometry, as well as dye tracer paths, showed that flow and transport took place in a very tortuous pattern where several grid cells were completely bypassed. The degree of tortuosity appeared to be dependent on the degree of saturation, as the tortuosity increased with decreasing saturation. Despite the tortuous flow patterns, we found that the effective unsaturated hydraulic conductivity as well as the retention curves for the three realizations of the heterogeneous sand were quite similar, thus suggesting that this type of heterogeneous flow system can be treated as an equivalent  homogeneous medium characterized by effective parameters.

Wildenschild, D. ; Jensen, K. H. 1999 Laboratory investigations of effective flow behavior in unsaturated heterogeneous sands.  Water Resour. Res. Vol. 35 , No. 1 , p. 17.

 Abstract:

The concept of effective parameters has been introduced in recent years to represent the spatial variability of natural soils in numerical simulation models. In the present study, effective hydraulic properties of unsaturated flow were investigated for the case of a two-dimensional heterogeneous laboratory tank. Hydraulic parameter estimates obtained from simple statistical averages, inverse procedures, and a stochastic theory were compared to effective retention and hydraulic conductivity characteristics measured for the whole tank at steady state. The applicability of the effective parameter estimates was investigated by comparing transient flow events monitored in the laboratory tank with

simulated results based on those estimates. Capillary suction measurements were simulated reasonably well using several straightforward arithmetic and geometric statistical averaging approaches, whereas most averaging approaches simulated too slow a response in the outflow rate. An alternative approach involving a combination of arithmetic and geometric averaging of the measured values more closely simulated the observed relatively fast changes in outflow rate. Generally, the simulations based on the measurements of effective properties performed quite well, indicating that the fundamental concept of effective parameters may be valid for this type of heterogeneous soil system.

Wildenschild, D. ; Jensen, K. H. 1999. Numerical modeling of observed effective flow behavior in unsaturated heterogeneous sands. Water Resour. Res. Vol. 35 , No. 1 , p. 29.