Does the Darcy–Buckingham Law Apply to Flow through Unsaturated Porous Rock?

Abstract

The Darcy–Buckingham (DB) law, critical to the prediction of unsaturated flow, is widely used but has rarely been experimentally tested, and therefore may not be adequate in certain conditions. Failure of this law would imply that the unsaturated hydraulic conductivity is not constant for a given water content, as assumed in nearly all subsurface flow models. This study aims to test the DB law on unsaturated porous rock, complementing the few previous tests, all done on soils. Two lithotypes of calcareous porous rocks were tested. The quasi-steady centrifuge method was used to measure the flux density for different centrifugal driving forces while maintaining essentially constant water content, as required. Any deviations from the direct proportionality of the measured flux and the applied force would indicate a violation of the DB law. Our results show that, for the tested rocks and conditions, no physical phenomena occurred to cause a failure of the DB law.