On the porous‐continuum modeling of gravity‐driven fingers in unsaturated materials: Extension of standard theory with a hold‐back‐pile‐up effect

Eliassi, Mehdi; Glass, Robert J.

doi:10.1029/2001wr001131

Cited by 58 publications

(80 citation statements)

References 74 publications

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“…However, the authors do not think that the hysteresis in the h-q relationship explains the saturated finger tips and the drainage behind it, which brings an upward negative pressure and a growth of fingers. It has recently been recognized that the general theory of Richards' equation is insufficient for predicting finger flow [de Rooij, 2000;Glass, 2001, Wang et al, 2003;Jury et al, 2003], and additional terms to Richards' equation have been proposed for expressing mathematically the nonmonotonic moisture profiles [Eliassi and Glass, 2002]. Since Richards' equation is a combination of equation (1) and the mass conservation equation, and mass conservation is universal for any flow, we think that the inability of Richards' equation to predict the occurrence of fingers stems from the inadequacy of applying equation (1) across the wetting front in materials that exhibit finger flow.…”

Section: Introductionmentioning

confidence: 99%

Unexpected water content profiles under flux‐limited one‐dimensional downward infiltration in initially dry granular media

Shiozawa

Fujimaki

2004

Water Resources Research

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[1] Distinct water-content profiles, having saturated q-bumps at and immediately behind wetting fronts, were observed in narrow columns (9 mm ID) of homogeneous air-dried glass beads under downward one-dimensional infiltration with applied water fluxes at lower than the saturated hydraulic conductivity. The infiltrating water content profiles and the position of the wetting front as a function of time were also calculated based on Richards' equation using an independently measured hydraulic conductivity function K(q), and water retention characteristic q(h), of the drainage process, and by applying a pressure boundary condition, h we , which is almost atmospheric pressure, at the moving wetting front. The good agreement between the calculated profiles and the observed confirms that the dynamic water entry pressure h we (where q(h we ) is the saturated water content), does exist for air-dried glass beads, although it is in contradiction to the modern theory of unsaturated water flow in porous media. This physical property of dry media creates an upward negative pressure profile behind the wetting front that would inevitably produce finger flow if the column diameter were larger. At the wetting front, the water content and pressure should be completely discontinuous at the level of pore size, and hence Darcy's equation cannot be applied across the interface between the air-dried and saturated media.

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Section: Introductionmentioning

confidence: 99%

Unexpected water content profiles under flux‐limited one‐dimensional downward infiltration in initially dry granular media

Shiozawa

Fujimaki

2004

Water Resources Research

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“…A strong motivation for these studies were mathematical results excluding the existence of overshoot profiles for the traditional Richards equation from hydrology (Nieber 1996;Otto 1996Otto , 1997Geiger and Durnford 2000;Glass 2001, 2002;Egorov et al 2003;DiCarlo 2005DiCarlo , 2013Duijn et al 2007;Juanes 2008, 2009). It has been conjectured that new theoretical approaches might be unavoidable (Eliassi and Glass 2002;Duijn et al 2007Duijn et al , 2013Juanes 2008, 2009;Hilfer et al 2012;Nieber et al 2005) to reconcile theory and experiment. On the other hand, a recent investigation (Hilfer and Steinle 2014) has uncovered the existence of saturation overshoot profiles within the traditional theory in the hyperbolic limit, while the Richards equation represents a special parabolic limit.…”

Section: Introductionmentioning

confidence: 99%

Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

et al. 2016

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Motivated by observations of saturation overshoot, this article investigates generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations resulting from a flux function of high symmetry. All boundary resp. limit value problems of the travelling wave ansatz, which lead to smooth travelling wave solutions, are systematically explored. A complete, visually and computationally useful representation of the five-dimensional manifold connecting wave velocities and boundary resp. limit data is found by using methods from dynamical systems theory. The travelling waves exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is given to the non-monotonic profiles. The stability of the travelling waves is studied by numerically solving the full system of the partial differential equations with an efficient and accurate adaptive moving grid solver.

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“…However, since that theory also predicts an infinite wetting front velocity at t ¼ 0 [Philip, 1959], it can be expected to exhibit inconsistencies similar to the ones in the classical GA approach, particularly during the early stage of infiltration. It would be interesting to test emerging theories for variably saturated two-fluid flow in porous media that account for a dynamic capillary pressure [Gray and Hassanizadeh, 1991;Eliassi and Glass, 2002;Hassanizadeh et al, 2002;Cueto-Felgueroso and Juanes, 2009;Hilpert, 2012] and that can also model saturation overshoot at an infiltration front.…”

Section: Discussion and Summarymentioning

confidence: 99%

Dynamic capillary pressure during water infiltration: Experiments and Green‐Ampt modeling

Pellichero¹,

Glantz²,

Burns³

et al. 2012

Water Resources Research

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[1] In a recent study by Hsu and Hilpert (2011), the Green-Ampt (GA) model for water infiltration was modified to account for a dynamic capillary pressure that depends on the wetting front velocity. In that study, the only transient flow, to which the modified GA approach was compared, was capillary rise. In this paper, transient downward infiltration experiments were performed using three different ponding depths. We demonstrated that infiltration can be effectively modeled using the modified GA approach. The parameters of the dynamic capillary pressure relationship were fitted and independent of the ponding depth. Furthermore, the experimental data could not be described accurately at early times with the classical GA approach. This was particularly evident when plotting the product between the Darcy velocity and the wetting front position against the wetting front position. In these plots, the initial unphysical infinite rate of infiltration, that occurs in the classical GA model, appears to be a primary element of inaccuracy. It was furthermore verified that the limited ability of the classical GA approach to describe the experimental data is not related to inertial forces arising during the initial phase of infiltration.

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On the porous‐continuum modeling of gravity‐driven fingers in unsaturated materials: Extension of standard theory with a hold‐back‐pile‐up effect

Cited by 58 publications

References 74 publications

Unexpected water content profiles under flux‐limited one‐dimensional downward infiltration in initially dry granular media

Unexpected water content profiles under flux‐limited one‐dimensional downward infiltration in initially dry granular media

Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

Dynamic capillary pressure during water infiltration: Experiments and Green‐Ampt modeling

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