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An Exact Semi-Inverse Solution for the Family of Geophysical Problems of a Draining Slope

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Abstract

One of the main causes of the appearance of dangerous geophysical slope phenomena is water saturation of slopes and the negative hydrodynamic impact of a stream of underground waters on them. In this work, an exact semi-inverse hydromechanical solution for a family of geophysical problems of a draining slope is obtained based on the theory of functions of a complex variable. Using the method of consecutive conformal mappings, an analytical interrelation between areas of complex potential and N.E. Zhukovskii’s complex is established. The interrelation allows one to determine all the necessary parameters of the filtration area. An example of calculation with the determination of aquifuge lines, seepage area, depression surface, and lines of flow and equipotential lines with construction of an orthogonal and quadratic hydrodynamic grid of the filtration flow seeping the draining slope is presented. A short estimate of the filtration effect on the suffusion and landslide stability of the soil body of the draining slope is given.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Kabardino-Balkarian Science Center, Russian Academy of Sciences, 360000, Nalchik, Kabardino-Balkar Republic, Russia

    K. N. Anakhaev

  2. Water Problems Institute, Russian Academy of Sciences, 119333, Moscow, Russia

    K. N. Anakhaev & V. V. Belikov

Authors
  1. K. N. Anakhaev
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  2. V. V. Belikov
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Correspondence to K. N. Anakhaev or V. V. Belikov.

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Translated by A. Nikol’skii

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Anakhaev, K.N., Belikov, V.V. An Exact Semi-Inverse Solution for the Family of Geophysical Problems of a Draining Slope. Dokl. Phys. 65, 26–30 (2020). https://doi.org/10.1134/S1028335820010048

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  • DOI: https://doi.org/10.1134/S1028335820010048

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