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Mathematical Simulation of Humidification of Earth on a Slope and Calculation of Its Safety Factor

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Journal of Engineering Physics and Thermophysics Aims and scope

This paper presents a mathematical model of the simultaneous processes of moisture, heat, and salt transfer in a porous medium, as well as a pattern of calculation of earth stability on a slope depending on the above factors and nonlinear dependences on them of the strength characteristics of the earth. The corresponding boundary-value problem has been solved by the method of radial basis functions. A comparison has been made between the results of numerical experiments showing the relationship between the change in the value of the safety factor and the position of the slip curve depending on the heat, salt, and moisture transfer.

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References

  1. State Standard GOST V.1.1-3-97. Engineering Protection of Territories, Buildings, and Structures from Landslides and Avalanches. General Principles [in Russian], Gosbud Ukrainy, Kiev (1998).

  2. State Standard GOST A.2.1-1-2008. Engineering Surveys for Construction [in Russian], Minregionbud Ukrainy, Kiev (2008).

  3. State Standard GOST V.1.1-25-2009. Protection from Dangerous Geological Processes. Basic Principles of Design [in Russian], Minist. Vopr. ZhKKh Ukrainy, Kiev (2008).

  4. N. N. Maslov, Soil Mechanics in the Practice of Construction (Landslides and Measures) [in Russian], Stroiizdat, Moscow (1977).

    Google Scholar 

  5. A. W. Bishop and N. Morgenstern, Stability coefficients for earth slopes, Geotechnique, 10, No. 4, 164−169 (1960).

    Article  Google Scholar 

  6. J. Krahn, Stability Modeling with SLOPE. An Engineering Methodology, 1st edn., revision 1, GEO-SLOPE International Ltd., Calgary, Alberta (2004).

  7. E. Spencer, A method of analysis of the stability of embankments assuming parallel interslice forces, Geotechnique, 17, No. 1, 11–26 (1967).

    Article  Google Scholar 

  8. N. R. Morgenstern and V. E. Price, A numerical method for solving the equations of stability of general slip surfaces, Comput. J., 9, Issue 4, 388−393 (1967).

    Article  Google Scholar 

  9. V. G. Fedorovskii and S. V. Kurilo, Method to calculate the stability of hillsides and slopes, Geoékologiya, No. 6, 95−106 (1997).

    Google Scholar 

  10. Ya. H. Huang, Stability Analysis of Earth Slopes [Russian translation], Stroiizdat, Moscow (1988).

    Google Scholar 

  11. P. L. Ivanov, Soils and Foundations of Hydrotechnical Structures. Soil Mechanics, Textbook for Special Hydrotechnical Universities [in Russian], Vysshaya Shkola, Moscow (1991).

    Google Scholar 

  12. S. B. Omuraliev, Influence of moisture content on the strength properties of loamy soils at in-plane shear, Vestn. Kyrgyzsko-Rossiiskogo Slavyansk. Univ., No. 7, 19–23 (2006).

    Google Scholar 

  13. O. S. Kovrov, Estimation of the effect of hydrogeological characteristics of soils on the stability of natural slopes to predict landslides, Ékol. Bezop., No. 1, 72–76 (2013).

    Google Scholar 

  14. T. V. Kutya and P. M. Martynyuk, Mathematical simulation of the wetting of the slope earth as a result of a nonramming pipeline with account for the processes of heat and salt transfer, in: Physicomathematical Modeling and Information Technologies, Issue 19, 107−115 (2014).

  15. V. P. Petrukhin, Building Properties of Salted and Cemented Soils [in Russian], Stroiizdat, Moscow (1980).

    Google Scholar 

  16. O. R. Michuta, Mathematical simulation of the effect of multicomponent chemical solutions and nonisothermal conditions on the processes of soil consolidation in a two-dimensional case, Mat. Komp. Modelir., Ser. Tekh. Nauki, Issue 6, 143−153 (2012).

    Google Scholar 

  17. T. V. Pham and D. J. Fredlund, The application of dynamic programming to slope stability analyses, Can. Geotech. J., No. 40, 830–847 (2003).

    Article  Google Scholar 

  18. J.-G. Caputo and Y. A. Stepanyants, Front solutions of Richards′ equation, Transp. Porous Media, 74, Issue 1, 1−20 (2007).

    Article  MathSciNet  Google Scholar 

  19. Feike J. Leij, Walter B. Russell, and Scott M. Lesch, Closed form expressions for water retention and conductivity data, Ground Water, 35, No. 5, 848–858 (1997).

    Article  Google Scholar 

  20. P. N. Vabishchevich and A. O. Daniyarov, Mathematical simulation of the wetting of the aeration zone under the conditions of a high position of ground waters, Mat. Modelir., 6, No. 11, 11−24 (1994).

    MATH  Google Scholar 

  21. A. P. Vlasyuk and P. M. Martynyuk, Numerical Solution of the Problems of Consolidation and Filtrational Breakup of Soils under the Conditions of Heat and Mass Transfer by the Method of Radial-Basis Functions [in Russian], Nats. Univ. Vodn. Khoz. Prodov., Rovno (2010).

  22. E. A. Vlasova, V. S. Zarubin, and G. N. Kuvyrkin, Approximate Methods of Mathematical Physics [in Russian], Izd. Moskovsk. Gos. Tekhn. Univ. im. N. É. Baumana, Moscow (2001).

  23. E. J. Kansa, Multiquadrics — a scattered data approximation scheme with application to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations, Comput. Math. Appl., 19, Nos. 8–9, 147−161 (1990).

    Article  MathSciNet  Google Scholar 

  24. V. M. Kolodyazhnyi and O. Yu. Lisina, Numerical schemes of solving boundary-value problems on the basis of meshless methods using radial basis functions and atomic radial basis functions, Probl. Mashinostr., 13, No. 4, 49–56 (2010).

    Google Scholar 

  25. A. P. Vlasyuk and P. M. Martynyuk, Mathematical Simulation of Consolidation of Soils in Filtration of Salt Solutions under Nonisothermal Conditions [in Russian], Nats. Univ. Vodn. Khoz. Prodov., Rovno (2008).

    Google Scholar 

  26. F. P. Vasil’ev, Optimization Methods [in Russian], Faktorial Press, Moscow (2002).

    Google Scholar 

  27. I. V. Beiko, P. M. Zin’ko, and A. G. Nakonechnyi, Optimization Problems, Methods, and Algorithms [in Russian], Nats. Univ. Vodn. Khoz. Prodov., Rovno (2011).

  28. G. Yilmaz, The effects of temperature on the characteristics of kaolinite and bentonite, Sci. Res. Essays, 6, No. 9, 1928–1939 (2011).

    Article  Google Scholar 

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Authors and Affiliations

  1. National University of Water Management and Nature Use, 11 Sobornaya Str, Rovno, 33000, Ukraine

    T. V. Kutya & P. N. Martynyuk

Authors
  1. T. V. Kutya
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  2. P. N. Martynyuk
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Correspondence to T. V. Kutya.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 5, pp. 1256–1265, September–October, 2018.

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Kutya, T.V., Martynyuk, P.N. Mathematical Simulation of Humidification of Earth on a Slope and Calculation of Its Safety Factor. J Eng Phys Thermophy 91, 1189–1198 (2018). https://doi.org/10.1007/s10891-018-1848-2

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  • DOI: https://doi.org/10.1007/s10891-018-1848-2

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