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

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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.

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References

  1. I. V. Arkhangel’skii, “Change of the geological environment in construction and operation of nuclear power plants,” Geoékologiya, No. 4, 310–313 (1999).

  2. N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods [in Russian], BINOM, Laboratoriya Znanii, Moscow (2004).

    Google Scholar 

  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. 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).

  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. 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. 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).

  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).

  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).

  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).

    MATH  Google Scholar 

  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).

  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. 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).

  14. P. L. Ivanov, Soils and Bases of Water-Development Works. Mechanics of Soils [in Russian], Vysshaya Shkola, Moscow (1991).

    Google Scholar 

  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. 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. 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).

  18. N. N. Verigina (editor), Methods of Predicting the Salt Regime of Soils and Underground Water [in Russian], Kolos, Moscow (1979).

    Google Scholar 

  19. A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  20. A. A. Samarskii and V. S. Nikolaev, Methods of Solution of Mesh Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  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. V. A. Florin, Fundamentals of Mechanics of Soils [in Russian], Vol. 2, Gosstroiizdat, Moscow (1961).

    Google Scholar 

  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).

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 197–204, January–March, 2008.

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Vlasyuk, A.P., Martynyuk, P.M. & Fursovych, O.R. Numerical solution of a one-dimensional problem of filtration consolidation of saline soils in a nonisothermal regime. J Math Sci 160, 525–535 (2009). https://doi.org/10.1007/s10958-009-9518-8

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