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 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

Minimizing Evaporation by Optimal Layering of Topsoil: Revisiting Ovsinsky's Smart Mulching-Tillage Technology Via Gardner-Warrick's Unsaturated Analytical Model and HYDRUS

Ovsinsky (1899, https://www.rulit.me/books/novaya-sistema-zemledeliya-read-193251-1.html) suggested and tested a water conserving soil no-till technology for rain-snow-fed field crops in a semiarid environment in southern Russia. We model Ovsynsky's unsaturated flow fragment, in which 1-D steady evaporation and evapotranspiration through a two-layered soil from a horizontal static water table to a dry soil surface takes place. Gardner's exponential and algebraic functions are used for the unsaturated hydraulic conductivity-suction head relations. The vertical evaporation flux depends on the dyads and triads (correspondingly) of the parameters of these functions, for example, the saturated hydraulic conductivity and the sorptive number of the two layers. The flux, as a function of the relative thickness of the upper stratum, is analytically found from the solution of one or two nonlinear equations. This relation can be nonmonotonic and exhibits either a minimum or maximum depending on whether this stratum is coarser or finer than the subjacent stratum fed from a horizontal isobar. HYDRUS-1D simulations confirm these extrema. This explains the experimental results from the literature on mulching/tillage/soil crusting-sealing, which can increase, decrease, or have no impact on evaporation from a shallow water table. Alterations of the soil's homogeneity to reduce evaporation losses can improve the hydrological balance of soil profiles

Steady Flow from an Array of Subsurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited

Kornev’s (Subsurface irrigation, Selhozgiz, Moscow-Leningrad, 1935) subsurface irrigation with a periodic array of emitting porous pipes is analytically modeled as a steady potential Darcian flow from a line source generating a phreatic surface. The hodograph method is used. The complex potential strip is mapped onto the triangle of the inverted hodograph. An analogy with the Deemter (Theoretische en numerieke behandeling van ontwaterings-en infiltratie stromings problemen (in Dutch). Theoretical and numerical treatment of flow problems connected to drainage and irrigation. Ph.D. dissertation, Delft University of Technology, 1950) drainage problem and Kidder (J Appl Phys 27(8):867–869, 1956) free-surface flow toward an array of oil wells underlain by a “wavy” oil–water interface is drawn. For a half-period of Kornev’s flow, the “wavy” phreatic surface has an inflection point. The “waviness” of the phreatic surface is controlled by the spacing between emitters, the strength of line sources, and the pipe pressure and radius. Numerical modeling with HYDRUS involved two factors which constrained the saturated–unsaturated flow: the positive pressure head at the outlet of the modeled domain and lateral no-flow boundaries, with a qualitative corroboration of analytical solutions for potential (fully saturated) and purely unsaturated flows. HYDRUS is also applied to a generalized Philip’s regime of an unsaturated flow past a subterranean hole, which is impermeable at its top and leaks at the bottom

Minimizing Evaporation by Optimal Layering of Topsoil: Revisiting Ovsinsky's Smart Mulching-Tillage Technology Via Gardner-Warrick's Unsaturated Analytical Model and HYDRUS

©2019. American Geophysical Union. All Rights Reserved. Ovsinsky (1899, https://www.rulit.me/books/novaya-sistema-zemledeliya-read-193251-1.html) suggested and tested a water conserving soil no-till technology for rain-snow-fed field crops in a semiarid environment in southern Russia. We model Ovsynsky's unsaturated flow fragment, in which 1-D steady evaporation and evapotranspiration through a two-layered soil from a horizontal static water table to a dry soil surface takes place. Gardner's exponential and algebraic functions are used for the unsaturated hydraulic conductivity-suction head relations. The vertical evaporation flux depends on the dyads and triads (correspondingly) of the parameters of these functions, for example, the saturated hydraulic conductivity and the sorptive number of the two layers. The flux, as a function of the relative thickness of the upper stratum, is analytically found from the solution of one or two nonlinear equations. This relation can be nonmonotonic and exhibits either a minimum or maximum depending on whether this stratum is coarser or finer than the subjacent stratum fed from a horizontal isobar. HYDRUS-1D simulations confirm these extrema. This explains the experimental results from the literature on mulching/tillage/soil crusting-sealing, which can increase, decrease, or have no impact on evaporation from a shallow water table. Alterations of the soil's homogeneity to reduce evaporation losses can improve the hydrological balance of soil profiles

Steady Flow from an Array of Subsurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited

Kornev’s (Subsurface irrigation, Selhozgiz, Moscow-Leningrad, 1935) subsurface irrigation with a periodic array of emitting porous pipes is analytically modeled as a steady potential Darcian flow from a line source generating a phreatic surface. The hodograph method is used. The complex potential strip is mapped onto the triangle of the inverted hodograph. An analogy with the Deemter (Theoretische en numerieke behandeling van ontwaterings-en infiltratie stromings problemen (in Dutch). Theoretical and numerical treatment of flow problems connected to drainage and irrigation. Ph.D. dissertation, Delft University of Technology, 1950) drainage problem and Kidder (J Appl Phys 27(8):867–869, 1956) free-surface flow toward an array of oil wells underlain by a “wavy” oil–water interface is drawn. For a half-period of Kornev’s flow, the “wavy” phreatic surface has an inflection point. The “waviness” of the phreatic surface is controlled by the spacing between emitters, the strength of line sources, and the pipe pressure and radius. Numerical modeling with HYDRUS involved two factors which constrained the saturated–unsaturated flow: the positive pressure head at the outlet of the modeled domain and lateral no-flow boundaries, with a qualitative corroboration of analytical solutions for potential (fully saturated) and purely unsaturated flows. HYDRUS is also applied to a generalized Philip’s regime of an unsaturated flow past a subterranean hole, which is impermeable at its top and leaks at the bottom