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.

Simulating preferential flow and snowmelt partitioning in seasonally frozen hillslopes

“…The use of Darcy‐Buckingham and capillary‐bundle assumptions, like that of the Richards equation‐VG model used here, have been criticized for not being the most physically realistic representation of flow in macropores, as opposed to alternate kinematic wave and viscous film flow descriptions (Beven & Germann, 2013; Jarvis et al, 2016; Mohammed et al, 2018). Nonetheless, the Darcy‐Buckingham formulation has been shown to be valid and acceptable for simulating macropore flow (Turturro et al, 2020), and more importantly for this study, Richards equation‐VG models have the utility to consider preferential flow in multiple spatial directions (Aguilar‐López et al, 2020; Bishop et al, 2015).…”

“…Nonetheless, the Darcy-Buckingham formulation has been shown to be valid and acceptable for simulating macropore flow (Turturro et al, 2020), and more importantly for this study, Richards equation-VG models have the utility to consider preferential flow in multiple spatial directions (Aguilar-L opez et al, 2020;Bishop et al, 2015).…”

通过多种实验方法利用人工降雨进行优先流的探测与定量化

“…The resulting increase of hydraulic conductivity draws more water to flow in that material, increasing this effect to generate preferential flow. As well as layered systems, this effect is common in such features as sand-filled karst sinkholes (Truss et al 2007), sediment-filled fractures (Wealthall et al 2001) as in the case of fractured limestones (Cherubini et al 2008), and cement and or matrix material in which the lithoclasts constituting porous carbonate rock are very wet and conductive (Turturro et al 2020). These mechanisms are crucial to lateral flow at large scales and are a major cause of longdistance flow in the unsaturated zone (Nimmo et al 2002).…”

Advances in Environmental Hydraulics

“…Three contributions are about hyporheic fluxes: two field studies investigated these fluxes at a small river confluence [17] and the effects of such fluxes on the macroinvertebrate community [18], while their relationship with the bioturbation activity of macroinvertebrates was studied in laboratory [19]. The last two articles addressed the accuracy of groundwater flux measurement using a seepage meter in the laboratory [20] and the experimental validation of the Darcy-Buckingham (DB) law in unsaturated porous rocks [21]. The research articles apply theoretical, field, laboratory, and numerical methods to address their scientific questions, which are related both to classical EH themes and to broad and important morphological and ecological issues of natural water systems.…”

“…The Darcy-Buckingham (DB) law, i.e., direct proportionality between the flux through a porous medium and the net force that drives it, is widely applied in subsurface hydrology but has rarely been experimentally tested, particularly under unsaturated conditions. Complementary to the few previous tests performed on soils, Turturro et al [21] tested the DB law on two lithotypes of unsaturated calcareous porous rocks. The quasi-steady centrifuge method was used to measure the flux density for different centrifugal driving forces while maintaining essentially constant water content.…”