Size and shape of steady seawater intrusion and sharp-interface wedge

The polubarinova-kochina analytical solution to the dam problem revisited

A. R. Kacimov, Y. V. Obnosov

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Rescaling of the geometrical sizes and the value of hydraulic conductivity in the classical problem of steady two-dimensional (2D) potential seepage through a rectangular earth dam with an empty tailwater is shown to result in a mathematically equivalent problem of seawater intrusion with a sharp interface into a confined horizontal aquifer, which discharges fresh groundwater to the sea through a vertical segment of the beach. The shape of the interface, the vertical and horizontal sizes of the static intrusion wedge, and its cross-sectional area are written in an explicit form, using the Polubarinova-Kochina formulas, rectified. The densities of the two liquids and the aquifers' hydraulic conductivity and thickness, as well as the incident hydraulic gradient serve as input parameters. With reduction of the incident groundwater gradient far upstream from the intrusion zone (due to, e.g., freshwater abstraction by wells), the sizes of the wedge rapidly increase. The analytical solution has been validated with recent sand tank experiments.

Original languageEnglish
Article number6016005
JournalJournal of Hydrologic Engineering
Volume21
Issue number8
DOIs
Publication statusPublished - Aug 1 2016

Fingerprint

Salt water intrusion
Hydraulic conductivity
Aquifers
Dams
Groundwater
dam
seawater
Embankment dams
hydraulic conductivity
Seepage
Beaches
aquifer
earth dam
Sand
groundwater
Hydraulics
seepage
Liquids
beach
hydraulics

Keywords

  • Earth dam problem
  • Exact solution
  • Seawater intrusion
  • Sharp-interface model
  • Steady potential phreatic flow

ASJC Scopus subject areas

  • Environmental Chemistry
  • Civil and Structural Engineering
  • Water Science and Technology
  • Environmental Science(all)

Cite this

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abstract = "Rescaling of the geometrical sizes and the value of hydraulic conductivity in the classical problem of steady two-dimensional (2D) potential seepage through a rectangular earth dam with an empty tailwater is shown to result in a mathematically equivalent problem of seawater intrusion with a sharp interface into a confined horizontal aquifer, which discharges fresh groundwater to the sea through a vertical segment of the beach. The shape of the interface, the vertical and horizontal sizes of the static intrusion wedge, and its cross-sectional area are written in an explicit form, using the Polubarinova-Kochina formulas, rectified. The densities of the two liquids and the aquifers' hydraulic conductivity and thickness, as well as the incident hydraulic gradient serve as input parameters. With reduction of the incident groundwater gradient far upstream from the intrusion zone (due to, e.g., freshwater abstraction by wells), the sizes of the wedge rapidly increase. The analytical solution has been validated with recent sand tank experiments.",
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N2 - Rescaling of the geometrical sizes and the value of hydraulic conductivity in the classical problem of steady two-dimensional (2D) potential seepage through a rectangular earth dam with an empty tailwater is shown to result in a mathematically equivalent problem of seawater intrusion with a sharp interface into a confined horizontal aquifer, which discharges fresh groundwater to the sea through a vertical segment of the beach. The shape of the interface, the vertical and horizontal sizes of the static intrusion wedge, and its cross-sectional area are written in an explicit form, using the Polubarinova-Kochina formulas, rectified. The densities of the two liquids and the aquifers' hydraulic conductivity and thickness, as well as the incident hydraulic gradient serve as input parameters. With reduction of the incident groundwater gradient far upstream from the intrusion zone (due to, e.g., freshwater abstraction by wells), the sizes of the wedge rapidly increase. The analytical solution has been validated with recent sand tank experiments.

AB - Rescaling of the geometrical sizes and the value of hydraulic conductivity in the classical problem of steady two-dimensional (2D) potential seepage through a rectangular earth dam with an empty tailwater is shown to result in a mathematically equivalent problem of seawater intrusion with a sharp interface into a confined horizontal aquifer, which discharges fresh groundwater to the sea through a vertical segment of the beach. The shape of the interface, the vertical and horizontal sizes of the static intrusion wedge, and its cross-sectional area are written in an explicit form, using the Polubarinova-Kochina formulas, rectified. The densities of the two liquids and the aquifers' hydraulic conductivity and thickness, as well as the incident hydraulic gradient serve as input parameters. With reduction of the incident groundwater gradient far upstream from the intrusion zone (due to, e.g., freshwater abstraction by wells), the sizes of the wedge rapidly increase. The analytical solution has been validated with recent sand tank experiments.

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KW - Steady potential phreatic flow

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