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Shape Factors for Seepage into Pits¹

ABSTRACT

In the field "pit-bailing" method, saturated hydraulic conductivity below a water table is determined from the rate of rise of water in a pit. The relationship between the rate of rise and the soil hydraulic conductivity is expressed as a shape factor. Shape factors are presented here for pits with length/radius ratio ranging from 0 to 2, for pits ranging from empty to 0.9 full, and for impermeable-barrier and very permeable source lower boundary conditions at various distances below the pit. The calculated shape factors are extrapolated to the situation of a pit in an effectively infinitely deep uniform soil. Shape factors for pits of a given fullness with a source or a semi-infinite lower boundary condition are found to decrease and then increase as the length/radius ratio of the pit increases, reaching a minimum typically when this ratio is between 0.2 and 0.5 for the semi-infinite case. This trend is investigated to determine whether it is due to calculation errors for extreme geometries or is due to real phenomena. That the trend exists is found by examining analytical solutions to two situations—a pit fully penetrating to an impermeable barrier and a disk in semi-infinite space.

¹ Supported in part by project no. 15-0356 of the Illinois Agric. Exp. Stn.

² Associate Professor of Agronomy and Professor of Mathematics, respectively.

Received for publication December 20, 1982. Accepted for publication August 25, 1983.