Phreatic seepage flow through an earth dam with an impeding strip

New mathematical models are developed and corresponding boundary value problems are analytically and numerically solved for Darcian flows in earth (rock)–filled dams, which have a vertical impermeable barrier on the downstream slope. For saturated flow, a 2-D potential model considers a free boundar...

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Veröffentlicht in:Computational geosciences 2020-02, Vol.24 (1), p.17-35
Hauptverfasser: Kacimov, A. R., Yakimov, N. D., Šimůnek, J.
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Šimůnek, J.
description New mathematical models are developed and corresponding boundary value problems are analytically and numerically solved for Darcian flows in earth (rock)–filled dams, which have a vertical impermeable barrier on the downstream slope. For saturated flow, a 2-D potential model considers a free boundary problem to Laplace’s equation with a traveling-wave phreatic line generated by a linear drawup of a water level in the dam reservoir. The barrier re-directs seepage from purely horizontal (a seepage face outlet) to purely vertical (a no-flow boundary). An alternative model is also used for a hydraulic approximation of a 3-D steady flow when the barrier is only a partial obstruction to seepage. The Poisson equation is solved with respect to Strack’s potential, which predicts the position of the phreatic surface and hydraulic gradient in the dam body. Simulations with HYDRUS, a FEM-code for solving Richards’ PDE, i.e., saturated-unsaturated flows without free boundaries, are carried out for both 2-D and 3-D regimes in rectangular and hexagonal domains. The Barenblatt and Kalashnikov closed-form analytical solutions in non-capillarity soils are compared with the HYDRUS results. Analytical and numerical solutions match well when soil capillarity is minor. The found distributions of the Darcian velocity, the pore pressure, and total hydraulic heads in the vicinity of the barrier corroborate serious concerns about a high risk to the structural stability of the dam due to seepage. The modeling results are related to a “forensic” review of the recent collapse of the spillway of the Oroville Dam, CA, USA.
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D.</creatorcontrib><creatorcontrib>Šimůnek, J.</creatorcontrib><title>Phreatic seepage flow through an earth dam with an impeding strip</title><title>Computational geosciences</title><addtitle>Comput Geosci</addtitle><description>New mathematical models are developed and corresponding boundary value problems are analytically and numerically solved for Darcian flows in earth (rock)–filled dams, which have a vertical impermeable barrier on the downstream slope. For saturated flow, a 2-D potential model considers a free boundary problem to Laplace’s equation with a traveling-wave phreatic line generated by a linear drawup of a water level in the dam reservoir. The barrier re-directs seepage from purely horizontal (a seepage face outlet) to purely vertical (a no-flow boundary). An alternative model is also used for a hydraulic approximation of a 3-D steady flow when the barrier is only a partial obstruction to seepage. The Poisson equation is solved with respect to Strack’s potential, which predicts the position of the phreatic surface and hydraulic gradient in the dam body. Simulations with HYDRUS, a FEM-code for solving Richards’ PDE, i.e., saturated-unsaturated flows without free boundaries, are carried out for both 2-D and 3-D regimes in rectangular and hexagonal domains. The Barenblatt and Kalashnikov closed-form analytical solutions in non-capillarity soils are compared with the HYDRUS results. Analytical and numerical solutions match well when soil capillarity is minor. The found distributions of the Darcian velocity, the pore pressure, and total hydraulic heads in the vicinity of the barrier corroborate serious concerns about a high risk to the structural stability of the dam due to seepage. 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R.</au><au>Yakimov, N. D.</au><au>Šimůnek, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Phreatic seepage flow through an earth dam with an impeding strip</atitle><jtitle>Computational geosciences</jtitle><stitle>Comput Geosci</stitle><date>2020-02-01</date><risdate>2020</risdate><volume>24</volume><issue>1</issue><spage>17</spage><epage>35</epage><pages>17-35</pages><issn>1420-0597</issn><eissn>1573-1499</eissn><abstract>New mathematical models are developed and corresponding boundary value problems are analytically and numerically solved for Darcian flows in earth (rock)–filled dams, which have a vertical impermeable barrier on the downstream slope. For saturated flow, a 2-D potential model considers a free boundary problem to Laplace’s equation with a traveling-wave phreatic line generated by a linear drawup of a water level in the dam reservoir. 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subjects Approximation
Boundary value problems
Capillarity
Computational fluid dynamics
Computer simulation
Dam stability
Dams
Earth
Earth and Environmental Science
Earth dams
Earth Sciences
Exact solutions
Finite element method
Forensic science
Free boundaries
Geotechnical Engineering & Applied Earth Sciences
Hydraulic gradient
Hydraulics
Hydrogeology
Mathematical Modeling and Industrial Mathematics
Mathematical models
Original Paper
Poisson equation
Pore pressure
Pore water pressure
Pressure head
Saturated flow
Seepage
Seepage lines
Soil
Soil Science & Conservation
Spillways
Steady flow
Structural stability
Three dimensional flow
Two dimensional flow
Two dimensional models
Unsaturated flow
Water levels
title Phreatic seepage flow through an earth dam with an impeding strip
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