Nonmonotonic moisture profile as a solution of Richards' equation for soils with conductivity hysteresis

Kacimov, A. R.; Yakimov, N. D.

doi:10.1016/s0309-1708(97)00030-4

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…Over the last 40 years, gravity‐driven fingering (GDF) within water‐wettable porous materials has been observed and studied in many laboratory and field experiments [e.g., Palmquist and Johnson , 1960, 1962; Tabuchi , 1961; Peck , 1965; Hill and Parlange , 1972; Raats , 1973; White et al , 1976, 1977; Diment and Watson , 1985; Glass et al , 1988, 1989a, 1989d, 1990; Baker and Hillel , 1990; Selker et al , 1992a, 1992c; Lu et al , 1994; Liu et al , 1994a, 1994b; Nicholl et al , 1994; Babel et al , 1995; Hendrickx and Yao , 1996; Yao and Hendrickx , 1996; Selker and Schroth , 1998; Wang et al , 1998a, 1998b; Nissen et al , 1999; Geiger and Durnford , 2000; Sililo and Tellam , 2000; Yao and Hendrickx , 2001]. Additionally, a number of investigations have focused on theoretical aspects of this phenomenon and its simulation using a variety of approaches [e.g., Philip , 1975; Parlange and Hill , 1976; Diment et al , 1982; Diment and Watson , 1983; Tamai et al , 1987; Hillel and Baker , 1988; Glass et al , 1989b, 1989c, 1991; Selker et al , 1992b; Chang et al , 1994; Chen and Neuman , 1996; Neumann and Chen , 1996; Glass and Yarrington , 1996; Nieber , 1996; Kapoor , 1996; Babel et al , 1997; Kacimov and Yakimov , 1998; Wang et al , 1998c; Geiger and Durnford , 2000; Ursino , 2000; Benson , 2001; Du et al , 2001].…”

Section: Introductionmentioning

confidence: 99%

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

Eliassi

Glass

2002

Water Resources Research

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[1] The traditional Richards equation (RE) in combination with standard monotonic properties (constitutive relations and hysteretic equations of state) has been shown to lack critical physics required to model gravity-driven fingering (GDF). We extend the RE with an experimentally observed hold-back-pile-up (HBPU) effect not captured in the standard porous-continuum RE formulation. We postulate the HBPU effect is tied to wetting front sharpness and can be mathematically formulated in a variety of ways to include hypodiffusive, hyperbolic, and mixed spatial-temporal forms involving respectively a Laplacian, a second-order derivative in time, and a Laplacian of a first-order derivative in time of the state variables. For each, we can infer an extended flux relation comprised of the Darcy-Buckingham flux plus an additional component due to the HBPU effect. Extended flux relations that are mathematically similar to each can be found in the single-phase and multiphase flow literature, however, all with very different underlying conceptualizations of the possible physics.INDEX TERMS: 1866 Hydrology: Soil moisture; 1875 Hydrology: Unsaturated zone; 1829 Hydrology: Groundwater hydrology; KEYWORDS: wetting front instability, gravity-driven fingers, nonmonotonicity, extended porous media theory, hypodiffusive and hyperbolic flux relations, dynamic capillary pressure Citation: Eliassi, M., and R. J. Glass, On the porous-continuum modeling of gravity-driven fingers in unsaturated materials: Extension of standard theory with a hold-back-pile-up effect, Water Resour.

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Section: Introductionmentioning

confidence: 99%

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

Eliassi

Glass

2002

Water Resources Research

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“…which is again a contradiction I Remark 5.3. Some engineering papers (see, for instance, Poulovassilis and Tzimas [20], Kacimov and Yakimov [10], and the references therein) account for hysteresis even in the relation between hydraulic conductivity and saturation, which in this paper is represented as in Figure 3 (without hysteresis). These hysteretic effects are however much less evident than the ones in the s versus u relation.…”

Section: Jomentioning

confidence: 98%

Hysteresis in Filtration through Porous Media

Bagagiolo¹,

Visintin²

2000

Z. Anal. Anwend.

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We study an evolution problem for filtration through porous media, accounting for hysteresis in the saturation versus pressure constitutive relation. We provide a weak formulation of the problem, assuming that the memory effect in the constitutive relation consists not only of a rate-independent component but also of a rate-dependent one. We prove an existence result, which also applies to the case where the hysteresis operator is of Preisach-type.

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“…However, many parameters are needed and these parameters may hinder the development of analytical solutions considering hysteresis. Although Kacimov and Yakimov (1998) put forward a hysteretic loop, the model does not involve hysteretic relationship between water content and pore-water pressure. The smooth hysteretic SWCCs of arbitrary wetting/drying paths are presented by Li (2005).…”

Section: Pedroso and Williams Model (2010)mentioning

confidence: 99%

Incorporating hysteresis in one-dimensional seepage modeling in unsaturated soils

Huang

2011

KSCE J Civ Eng

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To understand better the influence of soil-water characteristic hysteresis on rainfall infiltration and pore-water pressure distributions in unsaturated soils, an analytical solution to the one-dimensional governing partial differential equation considering hysteresis is derived using a Fourier integral transformation. The analytical solution considers time-dependent and arbitrary initial pore-water pressure distributions, as well as a time-varying rainfall flux process at the ground surface. An exponential function is used to represent the hysteretic Soil-Water Characteristic Curve (SWCC) and the relationship between hydraulic conductivity and pore-water pressure. The calculated results demonstrate that the critical point, the intersection between wetting and drying domains in one-dimensional unsaturated seepage, is influenced by many factors. The hysteresis in soil-water characteristics is an important factor in infiltration process influencing the pore-water pressure profiles in unsaturated soils. The effects of hysteretic parameters on pore-water pressure profiles are also analyzed. The value of α in the hysteresis model is found to be the most significant factor influencing the pore pressure distributions.

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Nonmonotonic moisture profile as a solution of Richards' equation for soils with conductivity hysteresis

Cited by 9 publications

References 15 publications

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

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

Hysteresis in Filtration through Porous Media

Incorporating hysteresis in one-dimensional seepage modeling in unsaturated soils

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