NUMERICAL INVESTIGATION OF PRESSURE HEAD JUMP
VALUES ON A THIN INCLUSION IN ONE-DIMENSIONAL
NON-LINEAR SOIL MOUSTURE TRANSPORT PROBLEM
Petro M. Martyniuk1, Olha R. Michuta2, Oksana V. Ulianchuk-Martyniuk3, Mykola T. Kuzlo4
1,2,3,4National University of Water
and Environmental Engineering
Rivne, UKRAINE

Abstract

A non-linear process of moisture transport in the soil containing thin inclusions has been investigated. The corresponding one-dimensional boundary value problem has been solved numerically with the finite element method. By means of numerical experiments the differences in pressure head jump values have been presented in the case of various conjugation conditions - classical and modified ones.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 4
Year: 2018

DOI: 10.12732/ijam.v31i4.10

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] L. Di Matteo, C. Pauselli, D. Valigi, M. Ercoli, M. Rossi, G. Guerra, C. Cambi, R. Ricco, G. Vinti, Reliability of water content estimation by profile probe and its effect on slope stability, Landslides, 15, No 1 (2018), 173-180.
  2. [2] D.-J. Wang, H.-M. Tang, Y.-H. Zhang, C.-D. Li, L. Huang, An improved approach for evaluating the time-dependent stability of colluvial landslides during intense rainfall, Environmental Earth Sciences, 76 (2017), 321.
  3. [3] K.M. Sample-Lord, C.D. Shackelford, Membrane behavior for unsaturated bentonite barriers, In: Geo-Congress 2014 (2014), 1900-1909.
  4. [4] F.M. Azad, D.W. Airey, R.K. Rowe, A. El-Zein, Laboratory investigation of moisture content redistribution on the base of double composite liner systems, In: 6th International Congress on Environmental Geotechnics, New Delhi, India (2010), 354-359.
  5. [5] P.M. Martyniuk, M.T. Kuzlo, S.K. Matus, T.P. Tsvietkova, Mathematical model of nonisothermal moisture transference in the form of water and vapor in soils in the case of chemical internal erosion, Far East J. of Mathematical Sciences, 102, No 12 (2017), 3211-3221.
  6. [6] A.P. Vlasyuk, T.P. Tsvetkova, Mathematical simulation of the transport of salt in the case of filtration and moisture transfer in saturated–unsaturated soils in a moistening regime, J. of Engineering Physics and Thermophysics, 88, No 5 (2015), 1062-1073.
  7. [7] N. Ivanchuk, P.Martynyuk, T. Tsvetkova, O.Michuta, Mathematical modeling and computer simulation of the filtration processes in earth dams, Eastern-European J. of Enterprise Technologies, 86, No 2/6 (2017), 63-69.
  8. [8] A.Ya. Bomba, S.V. Yaroshchak, Complex approach to modeling of twophase filtration processes under control conditions, J. of Mathematical Sci- ences, 184, No 1 (2012), 56-68.
  9. [9] I.V. Sergienko, V.V. Skopetskyi, V.S. Deineka, Mathematical Modeling and Research of Processes in Heterogeneous Environments, Naukova Dumka, Kiev (1991) (in Russian).
  10. [10] I.V. Sergienko, V.S. Deineka, Optimal Control of Distributed Systems With Conjugation Conditions, Kluwer Academic Publishers, New York (2005).
  11. [11] S.I. Lyashko, D.A. Nomirovskii, The generalized solvability and optimization of parabolic systems in domains with thin low-permeable inclusions, Cybernetics and Systems Analysis, 39, No 5 (2003), 737-745.
  12. [12] D.A. Nomirovskii, Generalized solvability of parabolic systems with nonhomogeneous transmission conditions of nonideal contact type, Differential Equations, 40, No 10 (2004), 1467-1477.
  13. [13] D.A. Nomirovskii, Generalized solvability and optimization of a parabolic system with a discontinuous solution, J. of Differential Equations, 233, No 1 (2007), 1-21.
  14. [14] D.A. Nomirovskii, O.I. Vostrikov, Generalized statements and properties of models of transport processes in domains with cuts, Cybernetics and Systems Analysis, 52, No 6 (2016), 931-942.
  15. [15] M.T. van Genuchten, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, No 5 (1980), 892-898.
  16. [16] J. Simunek, M.T. van Genuchten, M. Sejna, Recent developments and applications of the HYDRUS computer software packages, Vadose Zone J., 15 (2016), 1-25.
  17. [17] V. Herus, O. Stepanchenko, P. Martyniuk, O. Michuta, Two-dimensional problem concerning contact suffusion interplay on the filtration consolidation processes of heterogeneous soils, International J. of Pure and Appl. Math., 11, No 2 (2017), 407-418.