TY - JOUR

T1 - Phreatic seepage flow through an earth dam with an impeding strip

AU - Kacimov, A. R.

AU - Yakimov, N. D.

AU - Šimůnek, J.

N1 - Funding Information:
AK was supported by SQU, grant IG/AGR/SWAE/14/02. Critique and recommendations by an Associate Editor and anonymous referee are highly appreciated.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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.

AB - 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.

KW - 2-,3-D transient seepage with a phreatic surface

KW - Richards’ equation

KW - analytical models

KW - earth dams

KW - fields of pore pressure head

KW - heaving and suffusion

KW - water content and velocity

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U2 - 10.1007/s10596-019-09879-8

DO - 10.1007/s10596-019-09879-8

M3 - Article

AN - SCOPUS:85077387683

SN - 1420-0597

VL - 24

SP - 17

EP - 35

JO - Computational Geosciences

JF - Computational Geosciences

IS - 1

ER -