Analytical traveling-wave solutions and HYDRUS modeling of wet wedges propagating into dry soils: Barenblatt's regime for Boussinesq's equation generalized

A. R. Kacimov*, J. Šimůnek

*Corresponding author for this work

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1 Citation (Scopus)


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.

Original languageEnglish
Article number126413
JournalJournal of Hydrology
Publication statusPublished - Jul 2021
Externally publishedYes


  • Dry dike subject to seepage from a reservoir with a water level rising at a constant rate
  • Isobars-streamlines-isotachs in HYDRUS
  • Similarity solution
  • Transient complex potential
  • Translating phreatic surface

ASJC Scopus subject areas

  • Water Science and Technology

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