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Comparison of the Glover Solution with the Simultaneous-Equations Approach for Measuring Hydraulic Conductivity

Dep. of Soil Science, North Carolina State Univ., Raleigh, NC 27695-7619

*Corresponding author.

ABSTRACT

The Glover solution and the simultaneous-equations approach have been suggested for determining the saturated hydraulic conductivity (K_s) of the vadose zone by the constant-head well permeameter technique. The objective of this paper is to examine the two procedures and discuss the uncertainty associated with calculating K_s by the simultaneous-equations approach (referred to as K_fs) as compared with using the Glover solution. Two flow regions are identified with the constant heights of water, H₁ and H₂ (H₂ > H₁), at the bottom of an auger hole of radius r during measurements of steady state flow rates, Q₁ and Q₂. The K_s's over the distances H₁ (lower region), H₂ – H₁ (upper region), and H₂ (entire wetted zone) at the bottom of the hole are designated as K_sl, K_su, and K_sc, respectively. Using the Glover solution for calculating K_sl and K_sc for a homogeneous and isotropic medium, an equation is developed for calculating K_su based on Q₁, H₁, Q₂, H₂, and r. This equation is found to be very similar to the equation for calculating K_fs by simultaneous-equations approach. It is shown that K_sl > K_sc whenever the K_fs value is negative. Conversely, the matric flux potential calculated by the simultaneous-equations approach (_m) is negative only when K_sc > K_sl. This is significant because, in the simultaneous-equations approach, the K_fs value will not be acceptable when _m is negative. The Glover solution (i.e., equation to calculate K_sc or K_sl) is applicable to both homogeneous and heterogeneous soils and does not yield a negative value, whereas the simultaneous-equations approach can only yield reliable results for homogeneous and isotropic media.

Contribution from the Dep. of Soil Science, North Carolina State Univ. Paper no. 11742 of the Journal Series of the North Carolina Agric. Res. Serv., Raleigh, NC 27695-7643.

Received for publication August 9, 1988.