A Mathematical Treatment of Infiltration from a Line Source into an Inclined Porous Medium

Zachmann, David W.

doi:10.2136/sssaj1978.03615995004200050004x

Cited by 11 publications

(7 citation statements)

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“…It has connections with Philip [1971] and Raats [1972]. Zachmann [1978] and Philip [1988] developed certain solutions for quasi-linear sources in regions with sloping boundaries, and we relate those studies to the present results in section 10.…”

Section: Many Results In Multidimensional Steady Unsaturated Flow Arementioning

confidence: 89%

“…It is instructive to compare the labor for such a calculation with that needed by Zachmann [1978] results close to sources, whereas the present methods apply in both near and far fields.…”

Section: Sources At and Beneath A Slopingmentioning

confidence: 99%

“…(65) Zachmann [1978] did not recognize explicitly this limit on solutions of this type. For point sources the problem is not so severe.…”

Section: Figures 6 and 7 Are Comparable With Those Of Zachmann [1978]mentioning

confidence: 99%

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Steady infiltration flows with sloping boundaries

Philip¹,

Knight²

1997

Water Resources Research

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Section: Many Results In Multidimensional Steady Unsaturated Flow Arementioning

confidence: 89%

“…It is instructive to compare the labor for such a calculation with that needed by Zachmann [1978] results close to sources, whereas the present methods apply in both near and far fields.…”

Section: Sources At and Beneath A Slopingmentioning

confidence: 99%

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Steady infiltration flows with sloping boundaries

Philip¹,

Knight²

1997

Water Resources Research

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“…Batu's solution for the single strip source is rather formal, given in terms of a Fourier integral, and numerical evaluation is performed only for aL = 0.2 and 0.5. These investigations are also based on the quasilinear assumption, and the sources are described by specifying the strength of the line source [Raats, 1970;Zachmann, 1978] or the infiltration rate on the strip [Batu, 1978]. These specifiedinfiltration problems can also be formulated in terms of a stream function, as shown by Raats [1970]; Batu [1980] and Batu and Gardner [ 1978] present solutions for periodic strip sources with nonuniform infiltration formulated in this way.…”

Section: K(o) = Ks Exp (A½) ½-< 0 (1)mentioning

confidence: 99%

“…However, Philip [ 1984b], points out the danger of specifying the problem solely in kinematic terms, which can lead to physically untenable solutions if the flow dynamics are not considered in tandem. Zachmann [1978] considered infiltration from a line source into an inclined porous layer and presents series solutions for moisture potential and a stream function.…”

Section: K(o) = Ks Exp (A½) ½-< 0 (1)mentioning

confidence: 99%

The steady distribution of moisture beneath a two‐dimensional surface source

Martinez¹,

McTigue²

1991

Water Resources Research

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The steady distribution of moisture beneath a two-dimensional strip source is analyzed by applying the quasi-linear approximation. The source is described by specifying either the moisture content or the infiltration rate. A water table is specified at some depth D below the surface, the depth varying from shallow to semi-infinite. Numerical solutions are determined, via the boundary integral equation method, as a function of the material inverse sorptive length a, the width of the strip source 2L, and the depth to the water table. The moisture introduced at the source is broadly spread below the surface when aL << 1, for which absorption by capillary forces is dominant over gravity-induced flow. Conversely, the distribution becomes fingerlike along the vertical when aL >> 1, where gravity is dominant over absorption. For a source described by specifying the moisture content, the presence of a water table at finite depth influences the infiltration through the source when aD is less than about 4; infiltration rates obtained assuming the water table depth is semi-infinite are of sufficient accuracy for greater values of aD. When the source is described by a specified infiltration flux, the maximum allowable value of this flux for which the material beneath the source remains unsaturated is determined as a function of nondimensional sorptive number and depth to the water table.specification for hydraulic conductivity the Kirchhoff transformation renders a linear field equation for a potential, which is equivalent to the relative permeability. This approach is referred to as a quasi-linear analysis after Philip [1968], who has vigorously pursued this approximation (see, for example, Philip [1969, 1984a, 1989a], Waechter and Philip [1985], and Philip et al. [1989a, b] and references therein). Some further discussion of this approximation for hydraulic conductivity in general and for representation of volcanic tuffs can be found in the paper by Martinez and McTigue [1991].Our purpose here is to investigate the steady distribution of moisture beneath a strip source as a function of the material inverse sorptive length a, a term coined by Waechter and Philip [ 1985], and the depth to the water table, D. Localized surface sources arise due to topographic relief or from shallow ponds [Wooding, 1968;Weir, 1986]. The distribution of moisture introduced from natural ponds and gullies, which collect and retain moisture, is of concern for subsurface waste disposal. The current problem is prototypical of such problems involving steady surface infiltration and reveals the subsurface redistribution of the moisture as a function of the type of porous material. The problem is also relevant to the redistribution of surface moisture introduced Paper number 9 ! WR00437. 0043-1397/91/91WR-00437505.00 for irrigation (e.g., drip systems) or for dust control (e.g., road watering) in arid regions. For all the aforementioned applications the steady problem will define the maximum extent of wetting about the surface source, with the applied ...

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Analysis of three-dimensional groundwater flow in the near-surface layer of a small watershed

Watanabe

1988

Journal of Hydrology

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A Mathematical Treatment of Infiltration from a Line Source into an Inclined Porous Medium

Cited by 11 publications

References 0 publications

Steady infiltration flows with sloping boundaries

Steady infiltration flows with sloping boundaries

The steady distribution of moisture beneath a two‐dimensional surface source

Analysis of three-dimensional groundwater flow in the near-surface layer of a small watershed

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