TY - JOUR

T1 - Analytical traveling-wave solutions and HYDRUS modeling of wet wedges propagating into dry soils

T2 - Barenblatt's regime for Boussinesq's equation generalized

AU - Kacimov, A. R.

AU - Šimůnek, J.

N1 - Funding Information:
This work was supported by the Sultan Qaboos University via the grant DR/RG/17 . Helpful comments of three anonymous referees are appreciated.
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2021/7

Y1 - 2021/7

N2 - The classical Barenblatt solution of an initial-boundary value problem (IBVP) to the parabolic Boussinesq equation, which gives a rectangular triangle of full saturation, propagating from a reservoir into an adjacent porous bank with a vertical slope, is shown to coincide with a solution of IBVP to the elliptic Laplace equation with a phreatic surface along which both isobaricity and kinematic conditions are exactly met. For an arbitrary bank slope, a saturated wedge, which propagates (translates) into dry soil, is also explicitly found. The analytical solutions favorably compare with the results of HYDRUS-2D modeling, i.e., with the FEM solutions of the same IBVPs to the Richards equation. Applications to geotechnical engineering of dykes subject to the impact of flash floods are discussed by comparisons of phreatic lines, loci of the fronts, isobars, equipotential contours, vector fields of Darcian velocity, isotachs, and streamlines in the three models. For example, it is shown that a rapid drawup of the reservoir level induces hydraulic gradients, which may cause seepage-induced erosion of the porous medium, in particular, lessivage.

AB - The classical Barenblatt solution of an initial-boundary value problem (IBVP) to the parabolic Boussinesq equation, which gives a rectangular triangle of full saturation, propagating from a reservoir into an adjacent porous bank with a vertical slope, is shown to coincide with a solution of IBVP to the elliptic Laplace equation with a phreatic surface along which both isobaricity and kinematic conditions are exactly met. For an arbitrary bank slope, a saturated wedge, which propagates (translates) into dry soil, is also explicitly found. The analytical solutions favorably compare with the results of HYDRUS-2D modeling, i.e., with the FEM solutions of the same IBVPs to the Richards equation. Applications to geotechnical engineering of dykes subject to the impact of flash floods are discussed by comparisons of phreatic lines, loci of the fronts, isobars, equipotential contours, vector fields of Darcian velocity, isotachs, and streamlines in the three models. For example, it is shown that a rapid drawup of the reservoir level induces hydraulic gradients, which may cause seepage-induced erosion of the porous medium, in particular, lessivage.

KW - Dry dike subject to seepage from a reservoir with a water level rising at a constant rate

KW - Isobars-streamlines-isotachs in HYDRUS

KW - Similarity solution

KW - Transient complex potential

KW - Translating phreatic surface

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U2 - 10.1016/j.jhydrol.2021.126413

DO - 10.1016/j.jhydrol.2021.126413

M3 - Article

AN - SCOPUS:85107812534

SN - 0022-1694

VL - 598

JO - Journal of Hydrology

JF - Journal of Hydrology

M1 - 126413

ER -