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Solving the Problem of Groundwater Flow in an Inundated Massif with Vertical Drains

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Abstract

The earlier solutions of the problem of groundwater flow in an inundated rock massif with vertically drains (drain trenches) are represented by extremely complex mathematical relationships in complex variables which make them difficult to use in applied problems. A new approximate-hydromechanical solution of the problem was obtained with the use of velocity hodograph and the presentation of model relationships in elementary functions, which coincides with the exact data in boundary points and which are in almost complete agreement (⪡1%) with the results of exact calculations by V.V. Vedernikov for special cases. For the first time, a picture of the field of full flow velocities was analytically constructed in the form of an isotach family for the given inundated massif with drains, showing the heterogeneous character of velocity distribution in it at the presence of water in the drain. Groundwater flow diagrams are also presented for boundary lines (in particular, in comparison with the case when there is no water in the drain), along with plots of flow functions and heads.

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Funding

The study was carried out under the subjects of Governmental Orders to IAMA KBSC RAS (122041800015-8) and WPI RAS (FMWZ-2022-0001).

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Kabardin-Balkar Scientific Center, Russian Academy of Sciences (IAMA KBSC RAS), 360000, Nal’chik, KBR, Russia

    K. N. Anakhaev

  2. Water Problems Institute, Russian Academy of Sciences (WPI RAS), 119333, Moscow, Russia

    K. N. Anakhaev, V. V. Belikov & N. M. Borisova

  3. Russian University of Transport (RUT (MIIT)), 127994, Moscow, Russia

    Kh. K. Anakhaeva

Authors
  1. K. N. Anakhaev
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  2. V. V. Belikov
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  3. Kh. K. Anakhaeva
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  4. N. M. Borisova
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Correspondence to N. M. Borisova.

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Anakhaev, K.N., Belikov, V.V., Anakhaeva, K.K. et al. Solving the Problem of Groundwater Flow in an Inundated Massif with Vertical Drains. Water Resour 50, 392–399 (2023). https://doi.org/10.1134/S0097807823030028

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  • DOI: https://doi.org/10.1134/S0097807823030028

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