Have a personal or library account? Click to login
Modelling the Unsteady Flow of Water into a Partly Saturated Soil Cover

Modelling the Unsteady Flow of Water into a Partly Saturated Soil

Modelling in Civil Environmental Engineering
Volume 15 (2019): Issue 4 (December 2019)
By: Benyelles Zoheir,  Abdeldjalil Zadjaoui and  Bekkouche Abdelmalek  
Open Access
|Feb 2020

References

  1. [1] Vachaud G. (1968). Contribution à l’étude des problèmes d’écoulement en milieux poreux non saturés. PhD Thesis, Faculty of Sciences, University of Grenoble, 159 p.
    Search in Google ScholarBack to article
  2. [2] Ed Diny S. (1993). Etude expérimentale des transferts hydriques et du comportement mécanique d’un limon non saturé. Thesis of the INPL-National Polytechnic Institute of Lorraine. Nancy, 177p.
    Search in Google ScholarBack to article
  3. [3] Childs, E. C. (1969). An introduction to the physical basis of soil water phenomena. New York-London: J. Wiley and Sons. Inc. https://DOI.org/10.1180/claymin.1969.008.2.1310.1180/claymin.1969.008.2.13
    Search in Google ScholarBack to article
  4. [4] Olsen Harold W. (1966) Darcy’s law in saturated kaolinite. Water Resources Research. 2 (2).p. 287–295. https://DOI.org/10.1029/WR002i002p0028710.1029/WR002i002p00287
    Search in Google ScholarBack to article
  5. [5] Buckingham E. (1931). Studies on the movement of soil moisture. Bulletin 38. USDA Bureau of Soils. 30 Washington. DC. 1907.
    Search in Google ScholarBack to article
  6. [6] Richards L.A. Capillary conduction of s through porous medium. Physics 1, 318-333 https://DOI.org/10.1063/1.174501010.1063/1.1745010
    Search in Google ScholarBack to article
  7. [7] Childs, E.C. and Collis-George G.N. (1950). The permeability of porous materials. Proceeding of the Royal Society of London Series A 201. 392-405. https://DOI.org/10.1098/rspa.1950.006810.1098/rspa.1950.0068
    Search in Google ScholarBack to article
  8. [8] Philip J. R. (1955). The concept of diffusion applied to soil water. Proc. Nat. Acad. Sci. India 24A, pp.93-104. https://Doi.org/10.1016/0016-7061(74)90021-410.1016/0016-7061(74)90021-4
    Search in Google ScholarBack to article
  9. [9] Bruce R.R. and Klute A. (1956). The measurement of soil water diffusivity. Soil Science Society of American Proceeding. Vol. 20, p.458-462. Doi:10.2136/sssaj1956.03615995002000040004x10.2136/sssaj1956.03615995002000040004x
    Search in Google ScholarBack to article
  10. [10] Philip J. R. (1957). The theory of infiltration: 1. the infiltration equation and its solution. Soil Sci., Vol. 83, pp.345-357. DOI: 10.1097/00010694-200606001-0000910.1097/00010694-200606001-00009
    Search in Google ScholarBack to article
  11. [11] Philip J. R. (1957). The theory of infiltration: 2. the profile infinity. Soil Sci., Vol. 83, pp.435-448. 1957b.10.1097/00010694-195706000-00003
    Search in Google ScholarBack to article
  12. [12] Morel-Seytoux, H.J., Billica, J.A. (1985). A Two-Phase Numerical Model for Prediction of Infiltration: Applications to a Semi-Infinite Soil Column. Water Resources Research. 21(4), p. 607-615. 1985a https://DOI.org/10.1029/WR021i004p0060710.1029/WR021i004p00607
    Search in Google ScholarBack to article
  13. [13] Morel-Seytoux, H.J., Billica, J.A. (1985). A Two-Phase Numerical model for prediction of infiltration: case of an impervious bottom. Water Resources Research, 21(9), p. 1389-1396. 1985b. https://DOI.org/10.1029/WR021i009p0138910.1029/WR021i009p01389
    Search in Google ScholarBack to article
  14. [14] Hoffmann M. R. (2003). Macroscopic equations for flow in unsaturated porous media. Ph.D. dissertation, Washington University. 2003.
    Search in Google ScholarBack to article
  15. [15] Ju S. H. and Kung K. J. S. (1997). Mass types, element orders and solution schemes for Richards’equation. Computers and Geosciences, 23(2), 175–187.https://DOI.org/10.1016/S0098-3004(97)85440-410.1016/S0098-3004(97)85440-4
    Search in Google ScholarBack to article
  16. [16] Arampatzis G., Tzimopoulos C., Sakellariou-Makrantonaki M. and Yannopoulos S. (2001). Estimation of unsaturated flow in layered soils with the finite control volume method. Irrig. Drain, 50, pp. 349–358, 2001. 10.1002/ird.3110.1002/ird.31
    Search in Google ScholarBack to article
  17. [17] Nasseri M. Shaghaghian MR., Daneshbod Y. (2008). An analytic solution of water transport in unsaturated porous media. Journal of Porous Media. 11(6). DOI: 10.1615/JPorMedia.v11.i6.6010.1615/JPorMedia.v11.i6.60
    Search in Google ScholarBack to article
  18. [18] Kavetski D., Binning P. and Sloan S. W. (2002). Non-iterative time stepping schemes with adaptive truncation error control for the solution of Richards’ equation. Adv. Wat. Res. 38(10), 1211–1220. https://DOI.org/10.1029/2001WR00072010.1029/2001WR000720
    Search in Google ScholarBack to article
  19. [19] Haverkamp R. (1983). Solving the equation for the infiltration of water into the soil. Analytical and numerical approaches. PhD thesis ESE-Physical Sciences: Univ. Scientific and Medical and National Polytechnic Institute of Grenoble, 240 pages.
    Search in Google ScholarBack to article
  20. [20] Humbert P. (1984). Application of finite element method for flow in porous media. LPC newsletter, No. 132, p. 21-37. 1984.
    Search in Google ScholarBack to article
  21. [21] Baca R. G., Chung J. N. and Mulla D. J. (1997). Mixed transform finite element method for solving the nonlinear equation for flow in variably saturated porous media. Int. J. Numer. Method. Fluid. 24, 441–455.https://DOI.org/10.1002/(SICI)1097-0363(19970315)24:5<441::AID-FLD501>3.0.CO;2-910.1002/(SICI)1097-0363(19970315)24:5<441::AID-FLD501>3.0.CO;2-9
    Search in Google ScholarBack to article
  22. [22] Bergamaschi L. and Putti, M. (1999). Mixed finite element and Newton-type linearizations for the solution of Richards’ equation. Int. J. Numer. Method. Eng., 45, 1025–1046. https://DOI.org/10.1002/(SICI)1097-0207(19990720)45:8%3C1025::AID-NME615%3E3.0.CO;2-G10.1002/(SICI)1097-0207(19990720)45:8<1025::AID-NME615>3.0.CO;2-G
    Search in Google ScholarBack to article
  23. [23] Kormi T. (2003). Modélisation numérique du gonflement des argiles non saturées. PhD Thesis, National School of Bridges and Roads, Paris, 153 pages. 2003.
    Search in Google ScholarBack to article
  24. [24] Ross PJ. (2003). Modeling soil water and solute transport – fast, simplified numerical solutions. Agr. J., 95, 1352–1361. DOI: 10.2134/agronj2003.135210.2134/agronj2003.1352
    Search in Google ScholarBack to article
  25. [25] Brooks R.H., Corey A.T. (1964). Hydraulic properties of porous media. Hydrology Paper, 3, Colorado State University, Fort Collins, 24 p.
    Search in Google ScholarBack to article
  26. [26] Varado N., Braud I., Ross P. J. and Haverkamp R. (2006). Assessment of an efficient numerical solution of the 1D Richards equation on bare soil. J. Hydrol., 323, 244–257. DOI: 10.1016/j.jhydrol.2005.07.05210.1016/j.jhydrol.2005.07.052
    Search in Google ScholarBack to article
  27. [27] Basha, H. A. (1999). Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resour. Res., 25(1), 75–93. https://DOI.org/10.1029/1998WR90001510.1029/1998WR900015
    Search in Google ScholarBack to article
  28. [28] Farthing M. W., Kees C. E., Coffey T. S., Kelley C. T. and Miller C. T. (2003). Efficient steady state solution techniques for variably saturated groundwater flow. Adv. Water Resour., 26(8), 15 833–849. DOI:10.1016/S0309-1708(03)00076-9.10.1016/S0309-1708(03)00076-9
    Search in Google ScholarBack to article
  29. [29] Bunsri T., Sivakumar M., and Hagare D. (2008). Numerical modeling of tracer transport in unsaturated porous media. J. Appl. Fluid Mech., 1(1), 62–70. https://DOI.org/10.1007/s11242-013-0138-x10.1007/s11242-013-0138-x
    Search in Google ScholarBack to article
  30. [30] Witelski T.P. (1997). Perturbation analysis for wetting front in Richards’equation. Transport Porous Med. 27, pp. 121–134. DOI: 10.1023/A:100651300912510.1023/A:1006513009125
    Search in Google ScholarBack to article
  31. [31] Zadjaoui A. (2009). Etude du transfert hydrique dans les sols non saturés: échange sol – atmosphère. PhD Thesis. Department of Civil Engineering, University of Tlemcen. Algeria.
    Search in Google ScholarBack to article
  32. [32] Zadjaoui A. and Houmadi Y. (2019). Theoretical and experimental aspects of flow tests in situ, Algérie équipement, 28 (60), 61-69.
    Search in Google ScholarBack to article
  33. [33] Kevorkian J. and Cole J. D. (1996). Multiple Scale and Singular Perturbation Methods. Springer-Verlag. New York. DOI: 10.1007/978-1-4612-3968-010.1007/978-1-4612-3968-0
    Search in Google ScholarBack to article
  34. [34] Nayfeh A. H. (1973). Perturbation Methods. John Wiley & Sons, New York. 1973. DOI:10.1002/978352761760910.1002/9783527617609
    Search in Google ScholarBack to article
  35. [35] Nayfeh A. H. and Mook D. T. (1979). Nonlinear Oscillations. John Wiley & Sons, New York. DOI:10.1002/978352761758610.1002/9783527617586
    Search in Google ScholarBack to article
  36. [36] He, J.H. Homotopy perturbation technique. Comput. Meth. Applied Mech. Eng., 178 (3-4): 257-262. https://DOI.org/10.1016/S0045-7825(99)00018-310.1016/S0045-7825(99)00018-3
    Search in Google ScholarBack to article
  37. [37] He, J.H. (2006). New interpretation of homotopy perturbation method. Int. J. Mod. Phys. B., 20 (18): 2561-2568. https://DOI.org/10.1142/S021797920603481910.1142/S0217979206034819
    Search in Google ScholarBack to article
  38. [38] Barari A., Omidvar M., Ghotbi A. R. and Ganji D. D. (2008). Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations. Acta Appl. Math. 104, 161–171. https://DOI.org/10.1007/s10440-008-9248-910.1007/s10440-008-9248-9
    Search in Google ScholarBack to article
  39. [39] Barari A., Ghotbi A. R., Farrokhzad F. and Ganji D. D.(2008). Variational iteration method and Homotopy-perturbation method for solving different types of wave equations. J. Appl. Sci., 8, 15 120–126. 2008b. DOI: 10.3923/jas.2008.120.12610.3923/jas.2008.120.126
    Search in Google ScholarBack to article
  40. [40] Ghotbi A. R., Avaei A., Barari A. and Mohammadzade M. A. (2008). Assessment of He’s homotopy perturbation method in Burgers and coupled Burgers’ equations. J. Appl. Sci., 8, 322–327. 2008a. DOI: 10.3923/jas.2008.322.32710.3923/jas.2008.322.327
    Search in Google ScholarBack to article
  41. [41] Ghotbi A. R., Barari A., and Ganji D. D. (2008). Solving ratio-dependent predator–prey system with constant effort harvesting using homotopy perturbation method. J. Math. Prob. Eng.http://dx.DOI.org/10.1155/2008/94542010.1155/2008/945420
    Search in Google ScholarBack to article
  42. [42] He, J.H. (1999). Variational iteration method: A kind of nonlinear analytical technique: Sorne examples. Int. Non!. Mech., 344: 699-708. DOI:10.1016/S0020-7462(98)00048-110.1016/S0020-7462(98)00048-1
    Search in Google ScholarBack to article
  43. [43] He, J.H. (2000). Variational iteration rnethod for autonomous ordinary differential systems. Applied Math. Comput., 114 (2-3): 115-123. https://DOI.org/10.1016/S0096-3003(99)00104-610.1016/S0096-3003(99)00104-6
    Search in Google ScholarBack to article
  44. [44] Momani S. and Abuasad S. (2006). Application of He’s variational iteration method to Helmholtz equation. Chaos Soliton Fract. 27. p. 1119–1123. DOI: 10.1016/j.chaos.2005.04.11310.1016/j.chaos.2005.04.113
    Search in Google ScholarBack to article
  45. [45] Sweilam N. H. and Khader M. M. (2007). Variational iteration method for one dimensional nonlinear thermo-elasticity. Chaos Soliton Fract., 32, 145–149. http://dx.DOI.org/10.1016/j.chaos.2005.11.02810.1016/j.chaos.2005.11.028
    Search in Google ScholarBack to article
  46. [46] Barari A., Omidvar M., Ganji D. D. and Tahmasebi Poor A. (2008). An Approximate solution for boundary value problems in structural engineering and fluid mechanics. J. Math. Problems Eng. 1–13. http://dx.DOI.org/10.1155/2008/39410310.1155/2008/394103
    Search in Google ScholarBack to article
  47. [47] Asgari A., Bagheripourb M.H., Mollazadehb M. (2011). A generalized analytical solution for a nonlinear infiltration equation using the exp-function method. Scientia Iranica, Transactions A: Civil Engineering; 18 pp. 28–35. https://DOI.org/10.1016/j.scient.2011.03.00410.1016/j.scient.2011.03.004
    Search in Google ScholarBack to article
  48. [48] Shahrokhabadi S., Vahedifard F. and Bhatia M. (2017). A Fast-Convergence Solution for Modeling Transient Flow in Variably Saturated Soils Using the Isogeometric Analysis. Geotechnical Frontiers. GSP 280. Pp. 756-765. DOI: 10.1061/9780784480472.08010.1061/9780784480472.080
    Search in Google ScholarBack to article
  49. [49] Lu, N., and Godt, J. W. (2013). Hillslope hydrology and stability. Cambridge University Press.https://DOI.org/10.1017/CBO9781139108164.00110.1017/CBO9781139108164.001
    Search in Google ScholarBack to article
  50. [50] Griffiths, D. V., Lu, N. (2005). Unsaturated slope stability analysis with steady infiltration or evaporation using elasto-plastic finite elements. Int. J. Num. Anal. Methods. Geomech, 29(3), 249-267. https://DOI.org/10.1002/nag.41310.1002/nag.413
    Search in Google ScholarBack to article
  51. [51] Vahedifard F., Leshchinsky D., Mortezaei K., Lu N. (2016). Effective stress-based limit-equilibrium analysis for homogeneous unsaturated slopes. Inter. J. Geom.16 (6). D4016003. DOI/10.1061/(ASCE)GM.1943-5622.000055410.1061/(ASCE)GM.1943-5622.0000554
    Search in Google ScholarBack to article
  52. [52] Vahedifard F., Mortezaei K., Leshchinsky B.A. (2016). Role of suction stress on service state behavior of geosynthetic-reinforced soil structures. Trans. Geotechnics, 8. p. 45-56. DOI: 10.1016/j.trgeo.2016.02.00210.1016/j.trgeo.2016.02.002
    Search in Google ScholarBack to article
  53. [53] Vanapalli S.K., Mohamed F.M.O. (2007). Bearing capacity of model footings in unsaturated soils. Experimental unsaturated soil mechanics, 483-493. 2007. https://DOI.org/10.1007/3-540-69873-6_4810.1007/3-540-69873-6_48
    Search in Google ScholarBack to article
  54. [54] Vahedifard F, Robinson JD. (2015). Unified method for estimating the ultimate bearing capacity of shallow foundations in variably saturated soils under steady flow. Journal of Geotechnical and Geoenvironmental Engineering 142 (4). p.04015095. DOI: 10.1061/(ASCE)GT.1943-5606.000144510.1061/(ASCE)GT.1943-5606.0001445
    Search in Google ScholarBack to article
  55. [55] Vahedifard F., Leshchinsky BA., Mortezaei K., Lu N. (2015). Active earth pressures for unsaturated retaining structures. J. Geot. and Geoe. Eng. 141 (11). p.04015048. DOI: 10.1061/(ASCE)GT.1943-5606.000135610.1061/(ASCE)GT.1943-5606.0001356
    Search in Google ScholarBack to article
  56. [56] Lipnikova K., Moultona D. and Svyatskiya D. (2016). New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation. Adv. Wat. Res. DOI: 10.1016/j.advwatres.2016.04.01610.1016/j.advwatres.2016.04.016
    Search in Google ScholarBack to article
  57. [57] Ould Amy M., J.P. Magnan. (1965). Numerical modeling of flow and deformation in earth dams constructed on soft soils. Series “Studies and research LPC” series Geotechnics, No. 10. 145p. 1991
    Search in Google ScholarBack to article
  58. [58] Liakopoulos, A.C. Theoretical solution of unsteady unsaturated flow problem in soils. Bull. Intern. Assoc. Sci. Hydrology. Vol. 10, pp. 5-39.10.1080/02626666509493368
    Search in Google ScholarBack to article
  59. [59] H. R. Thomas, Y. He, M. R. Sansom, C. L. W. Li. (1996). On the development of a model of the thermo-mechanical-hydraulic behavior of unsaturated soils, Engineering Geology, Volume 41, Issues 1–4, Pages 197-218. https://DOI.org/10.1016/0013-7952(95)00033-X10.1016/0013-7952(95)00033-X
    Search in Google ScholarBack to article
  60. [60] Benyelles Z. (1988). Modelling the flow of water into a partly saturated soil. Thesis of Master of Science by Research, 299 pages, University College, Cardiff; United Kingdom.
    Search in Google ScholarBack to article
  61. [61] Narasimhan, T.N. (1979). The significant of the storage parameter in saturated–unsaturated groundwater flow. Water Resources Res. 1-53 pp569-575. https://DOI.org/10.1029/WR015i003p0056910.1029/WR015i003p00569
    Search in Google ScholarBack to article
DOI: https://doi.org/10.2478/mmce-2019-0010 | Journal eISSN: 2784-1391
Journal RSS Feed
Language: English
Page range: 18 - 30
Published on: Feb 27, 2020
Published by: Technical University of Civil Engineering of Bucharest
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Keywords:
Flow,
Unsaturated porous media,
Modelling,
FEM
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2020 Benyelles Zoheir, Abdeldjalil Zadjaoui, Bekkouche Abdelmalek, published by Technical University of Civil Engineering of Bucharest
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Previous articleVolume 15 (2019): Issue 4 (December 2019)