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Journal of Mathematical Sciences

, Volume 160, Issue 4, pp 525–535 | Cite as

Numerical solution of a one-dimensional problem of filtration consolidation of saline soils in a nonisothermal regime

  • A. P. Vlasyuk
  • P. M. Martynyuk
  • O. R. Fursovych
Article
  • 29 Downloads

A mathematical model of a problem of filtration consolidation of saline soils in a nonisothermal regime with allowance for the presence of salts in the liquid and solid phases is constructed. A numerical solution of the corresponding one-dimensional boundary-value problem is found by the method of finite differences. As an example, we investigate a problem of filtration consolidation of a massif of clay soil of finite thickness. Results of numerical investigations and their analysis are presented.

Keywords

Saline Soil Pressure Head Filtration Coefficient Pore Liquid Mass Exchange Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    I. V. Arkhangel’skii, “Change of the geological environment in construction and operation of nuclear power plants,” Geoékologiya, No. 4, 310–313 (1999).Google Scholar
  2. 2.
    N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods [in Russian], BINOM, Laboratoriya Znanii, Moscow (2004).Google Scholar
  3. 3.
    V. M. Bulavats’kyi, Yu. G. Kryvonis, and V. V. Skopets’kyi, Nonclassical Mathematical Models of Heat and Mass Transfer Processes [in Ukrainian], Naukova Dumka, Kiev (2005).Google Scholar
  4. 4.
    A. P. Vlasyuk and O. V. Zherebyat’ev, “Filtration consolidation of clay soils in the presence of mass transfer of salts,” Visn. Ukr. Derzh. Akad. Vodn. Hospod., Issue 1, Part 1, 40–43 (1998).Google Scholar
  5. 5.
    A. P. Vlasyuk and M. T. Kuzlo, “Experimental investigations of some filtration parameters of salt solutions in sandy soils,” Melior. Vodne Hospod., Issue 87, 43–46 (2000).Google Scholar
  6. 6.
    A. P. Vlasyuk and P. M. Martynyuk, Mathematical Modeling of Consolidation of Soils in the Process of Filtration of Salt Solutions [in Ukrainian], Vydavnytstvo UDUVGP, Rivne (2004).Google Scholar
  7. 7.
    A. P. Vlasyuk and P. M. Martynyuk, “Filtration consolidation of a soil massif in the base of a water-development works in the presence of salt transfer,” Visn. L’viv. Univ. Ser. Prykl. Matem. Inform., Issue 5, 68–74 (2002).Google Scholar
  8. 8.
    A. P. Vlasyuk and P. M. Martynyuk, “Filtration consolidation of a soil massive in the presence of soil transfer in a nonisothermal regime,” Visn. L’viv. Univ. Ser. Prykl. Matem. Inform., Issue 7, 138–147 (2003).Google Scholar
  9. 9.
    A. P. Vlasyuk and P. M. Martynyuk, “Numerical solution of a class of problems encountered in the theory of filtration consolidation,” Dop. Nats. Akad. Nauk Ukrainy, No. 12, 65–72 (2000).Google Scholar
  10. 10.
    A. P. Vlasyuk and P. M. Martynyuk, “Numerical modeling with stabilized schemes of the finite element method of the filtration consolidation of a body of a plain earth dam with consideration for heat and mass transfer,” Mat. Metody Fiz.-Mekh. Polya, 48, No. 2, 59–70 (2005).MATHGoogle Scholar
  11. 11.
    A. P. Vlasyuk and P. M. Martynyuk, “Numerical solution of a two-dimensional problem of filtration consolidation of a soil massif in the presence of transfer of soils in a nonisothermal regime,” Visn. L’viv. Univ. Ser. Prykl. Mat. Inform., Issue 11, 148–159, (2006).Google Scholar
  12. 12.
    A. P. Vlasyuk, P. M. Martynyuk, and O. R. Fursovych, “Mathematical modeling of filtration consolidation of soils in the presence of mass exchange processes,” Visn. Nats. Univ. Vodn. Hospod. Pryrodokor., Issue 1, 236–244 (2006).Google Scholar
  13. 13.
    A. A. Zubkov, O. V. Makarova, V. V. Danilov, et al., “Technogenic processes in sandy collector beds in burial of liquid radioactive wastes,” Geoékologiya, No. 2, 133–144 (2002).Google Scholar
  14. 14.
    P. L. Ivanov, Soils and Bases of Water-Development Works. Mechanics of Soils [in Russian], Vysshaya Shkola, Moscow (1991).Google Scholar
  15. 15.
    V. I. Lavrik and N. A. Nikiforovich, Investigation of Convective Mass Transfer in Two-Dimensional Filtration of Underground Water under Conditions of Mass Exchange. Preprint [in Russian], Institute of Mathematics, Kiev (1982).Google Scholar
  16. 16.
    I. I. Lyashko, L. I. Demchenko, and G. E. Mistetskii, Numerical Solution of Problems of Heat and Mass Transfer in Porous Media [in Russian], Naukova Dumka, Kiev (1991).Google Scholar
  17. 17.
    P. M. Martynyuk, “On taking into account the presence of dissolved salts in pore water in mathematical modeling of consolidation of soils,” Visn. Kyiv. Univer. Ser. Fiz.-Mat. Nauky, Issue 2, 168–174 (2003).Google Scholar
  18. 18.
    N. N. Verigina (editor), Methods of Predicting the Salt Regime of Soils and Underground Water [in Russian], Kolos, Moscow (1979).Google Scholar
  19. 19.
    A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).Google Scholar
  20. 20.
    A. A. Samarskii and V. S. Nikolaev, Methods of Solution of Mesh Equations [in Russian], Nauka, Moscow (1978).Google Scholar
  21. 21.
    V. V. Skopets’kyi and V. M. Bulavats’kyi, “Mathematical modeling of some processes of filtration consolidation of massifs saturated with salt solutions,” Dop. Nats. Akad. Nauk Ukrainy, No. 8, 55–61 (2005).Google Scholar
  22. 22.
    V. A. Florin, Fundamentals of Mechanics of Soils [in Russian], Vol. 2, Gosstroiizdat, Moscow (1961).Google Scholar
  23. 23.
    A. V. Shostak and O. I. Fialko, “Influence of temperature of the compressibility and consolidation of clay soils,” Visn. Kyivs’k. Univ. Ser. Heoloh., Issue 15, 47–49 (1997).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • A. P. Vlasyuk
    • 1
  • P. M. Martynyuk
    • 1
  • O. R. Fursovych
    • 1
  1. 1.National University of Water Management and Natural Resources ApplicationRivneUkraine

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