KFU. Card publication. Phreatic seepage around a rectilinear cutoff wall: the Zhukovsky-Vedernikov-Polubarinova-Kochina dispute revisited

KAZAN
FEDERAL UNIVERSITY

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- 中文
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PHREATIC SEEPAGE AROUND A RECTILINEAR CUTOFF WALL: THE ZHUKOVSKY-VEDERNIKOV-POLUBARINOVA-KOCHINA DISPUTE REVISITED

Form of presentation

Articles in international journals and collections

Year of publication

2023

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Authors, employees of KFU

Obnosov Yuriy Viktorovich, author

Other authors

Kacimov Anvar Rashidovich, author

Bibliographic description in the original language

Anvar Kacimov, Yurii Obnosov Phreatic seepage around a rectilinear cutoff wall: the Zhukovsky-Vedernikov-Polubarinova-Kochina dispute revisited. Advances in Water Resources (Elsevier), 173(2023) 104367 (pp.1-12), DOI: 10.1016/j.advwatres.2023.104367 (WoS IF=4.51, Q1)

Annotation

The problem of steady 2-D potential Darcian flow from a flat-bottomed reservoir of a coffer or other type of dam, separated from an empty tailwater by an impermeable vertical sheet piling, is one of the pillars in groundwater hydrology and soil mechanics. Analytical solutions to this problem are presented in the books by Forchheimer, Zhukovsky, Vedernikov, Polubarinova-Kochina, Harr, among others. For the case of seepage with a phreatic line, descending from the downstream face of the cutoff, the formulae presented in classical textbooks - despite the simplicity of conformal mappings of the complex potential quarter-plane onto the Zhukovsky half-strip - have lacunae and flaws. We discuss and clean the mismatch in the abovementioned formulae. The classical analytical solutions in the textbooks deal with the regime of no backwater, for which the magnitude of the specific discharge vector at infinity coincides with hydraulic conductivity of the soil. We obtain a general solution for most general flows with backwater, for which the specific discharge at infinity is zero and the free surface has an inflection point in the physical plane. The capillary fringe in the hodograph domain is imaged by a circular cut. The pressure head infinitely deep under the cutoff-wall is infinite. A circular tetragon in the hodograph domain is conformally mapped onto the quadrant in the complex potential plane via a reference plane. In the case with backwater, one extra condition is needed to fix a mathematical solution. For this purpose, the location of a point on the free surface is fixed. Mathematically, two affixes in the reference plane are found by solving a system of two nonlinear equations (in the no backwater case, only one affix is found and one equation is solved). We also examine flow with a phreatic line in a low-permeable layer (e.g. concrete apron of a dam) with an Λ-shaped topology of streamlines, bounded from the left by a cutoff. Seepage from a dam reservoir through a subjacent highly-permeable alluvium induces the pore water motion in the upper layer. A Hilbert boundary-value problem is solved for the complex potential in this cell. In the Kirkham-Brock type boundary condition along the interface between the two layers, the horizontal component of the specific discharge is constant. Phreatic surfaces rising on the downstream face of the cutoff caps Λ-shaped streamlines, which turn around a hinge point on the interface between two layers of contrasting permeability.

Keywords

cutoff wall, phreatic surface, 2-D seepage, analytical solution by complex potential-hodograph method, Hilbert?s boundary-value problem

The name of the journal

ADV WATER RESOUR

URL

https://doi.org/10.1016/j.advwatres.2023.104367

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=276514&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Obnosov Yuriy Viktorovich	ru_RU
dc.contributor.author	Kacimov Anvar Rashidovich	ru_RU
dc.date.accessioned	2023-01-01T00:00:00Z	ru_RU
dc.date.available	2023-01-01T00:00:00Z	ru_RU
dc.date.issued	2023	ru_RU
dc.identifier.citation	Anvar Kacimov, Yurii Obnosov Phreatic seepage around a rectilinear cutoff wall: the Zhukovsky-Vedernikov-Polubarinova-Kochina dispute revisited. Advances in Water Resources (Elsevier), 173(2023) 104367 (pp.1-12), DOI: 10.1016/j.advwatres.2023.104367 (WoS IF=4.51, Q1)	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=276514&p_lang=2	ru_RU
dc.description.abstract	ADV WATER RESOUR	ru_RU
dc.description.abstract	The problem of steady 2-D potential Darcian flow from a flat-bottomed reservoir of a coffer or other type of dam, separated from an empty tailwater by an impermeable vertical sheet piling, is one of the pillars in groundwater hydrology and soil mechanics. Analytical solutions to this problem are presented in the books by Forchheimer, Zhukovsky, Vedernikov, Polubarinova-Kochina, Harr, among others. For the case of seepage with a phreatic line, descending from the downstream face of the cutoff, the formulae presented in classical textbooks - despite the simplicity of conformal mappings of the complex potential quarter-plane onto the Zhukovsky half-strip - have lacunae and flaws. We discuss and clean the mismatch in the abovementioned formulae. The classical analytical solutions in the textbooks deal with the regime of no backwater, for which the magnitude of the specific discharge vector at infinity coincides with hydraulic conductivity of the soil. We obtain a general solution for most general flows with backwater, for which the specific discharge at infinity is zero and the free surface has an inflection point in the physical plane. The capillary fringe in the hodograph domain is imaged by a circular cut. The pressure head infinitely deep under the cutoff-wall is infinite. A circular tetragon in the hodograph domain is conformally mapped onto the quadrant in the complex potential plane via a reference plane. In the case with backwater, one extra condition is needed to fix a mathematical solution. For this purpose, the location of a point on the free surface is fixed. Mathematically, two affixes in the reference plane are found by solving a system of two nonlinear equations (in the no backwater case, only one affix is found and one equation is solved). We also examine flow with a phreatic line in a low-permeable layer (e.g. concrete apron of a dam) with an Λ-shaped topology of streamlines, bounded from the left by a cutoff. Seepage from a dam reservoir through a subjacent highly-permeable alluvium induces the pore water motion in the upper layer. A Hilbert boundary-value problem is solved for the complex potential in this cell. In the Kirkham-Brock type boundary condition along the interface between the two layers, the horizontal component of the specific discharge is constant. Phreatic surfaces rising on the downstream face of the cutoff caps Λ-shaped streamlines, which turn around a hinge point on the interface between two layers of contrasting permeability.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	cutoff wall	ru_RU
dc.subject	phreatic surface	ru_RU
dc.subject	2-D seepage	ru_RU
dc.subject	analytical solution by complex potential-hodograph method	ru_RU
dc.subject	Hilbert?s boundary-value problem	ru_RU
dc.title	Phreatic seepage around a rectilinear cutoff wall: the Zhukovsky-Vedernikov-Polubarinova-Kochina dispute revisited	ru_RU
dc.type	Articles in international journals and collections	ru_RU