1. bookVolumen 15 (2019): Heft 4 (December 2019)
12 Apr 2013
4 Hefte pro Jahr
Uneingeschränkter Zugang

Modelling the Unsteady Flow of Water into a Partly Saturated Soil

Online veröffentlicht: 27 Feb 2020
Volumen & Heft: Volumen 15 (2019) - Heft 4 (December 2019)
Seitenbereich: 18 - 30
12 Apr 2013
4 Hefte pro Jahr

[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 Scholar

[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 Scholar

[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.1969.008.2.13Search in Google Scholar

[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/WR002i002p00287Search in Google Scholar

[5] Buckingham E. (1931). Studies on the movement of soil moisture. Bulletin 38. USDA Bureau of Soils. 30 Washington. DC. 1907.Search in Google Scholar

[6] Richards L.A. Capillary conduction of s through porous medium. Physics 1, 318-333 https://DOI.org/10.1063/1.174501010.1063/1.1745010Search in Google Scholar

[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.1950.0068Search in Google Scholar

[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)90021-4Search in Google Scholar

[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/sssaj1956.03615995002000040004xSearch in Google Scholar

[10] Philip J. R. (1957). The theory of infiltration: 1. the infiltration equation and its solution. Soil Sci., Vol. 83, pp.345-357. DOI: 10.1097/00010694-200606001-0000910.1097/00010694-200606001-00009Search in Google Scholar

[11] Philip J. R. (1957). The theory of infiltration: 2. the profile infinity. Soil Sci., Vol. 83, pp.435-448. 1957b.Search in Google Scholar

[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/WR021i004p00607Search in Google Scholar

[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/WR021i009p01389Search in Google Scholar

[14] Hoffmann M. R. (2003). Macroscopic equations for flow in unsaturated porous media. Ph.D. dissertation, Washington University. 2003.Search in Google Scholar

[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)85440-4Search in Google Scholar

[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.31Search in Google Scholar

[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.i6.60Search in Google Scholar

[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/10.1029/2001WR00072010.1029/2001WR000720Search in Google Scholar

[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 Scholar

[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 Scholar

[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;2-9Search in Google Scholar

[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-GSearch in Google Scholar

[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 Scholar

[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/agronj2003.1352Search in Google Scholar

[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 Scholar

[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.2005.07.052Search in Google Scholar

[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/10.1029/1998WR90001510.1029/1998WR900015Search in Google Scholar

[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)00076-9Search in Google Scholar

[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-xSearch in Google Scholar

[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:1006513009125Search in Google Scholar

[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 Scholar

[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 Scholar

[33] Kevorkian J. and Cole J. D. (1996). Multiple Scale and Singular Perturbation Methods. Springer-Verlag. New York. DOI: 10.1007/978-1-4612-3968-010.1007/978-1-4612-3968-0Search in Google Scholar

[34] Nayfeh A. H. (1973). Perturbation Methods. John Wiley & Sons, New York. 1973. DOI:10.1002/978352761760910.1002/9783527617609Search in Google Scholar

[35] Nayfeh A. H. and Mook D. T. (1979). Nonlinear Oscillations. John Wiley & Sons, New York. DOI:10.1002/978352761758610.1002/9783527617586Search in Google Scholar

[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)00018-3Search in Google Scholar

[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/S0217979206034819Search in Google Scholar

[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/s10440-008-9248-9Search in Google Scholar

[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.2008.120.126Search in Google Scholar

[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.2008.322.327Search in Google Scholar

[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/10.1155/2008/94542010.1155/2008/945420Search in Google Scholar

[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)00048-1Search in Google Scholar

[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)00104-6Search in Google Scholar

[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.2005.04.113Search in Google Scholar

[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.2005.11.028Search in Google Scholar

[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/10.1155/2008/39410310.1155/2008/394103Search in Google Scholar

[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.2011.03.004Search in Google Scholar

[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: 10.1061/9780784480472.08010.1061/9780784480472.080Search in Google Scholar

[49] Lu, N., and Godt, J. W. (2013). Hillslope hydrology and stability. Cambridge University Press.https://DOI.org/10.1017/CBO9781139108164.00110.1017/CBO9781139108164.001Search in Google Scholar

[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.413Search in Google Scholar

[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.1943-5622.0000554Search in Google Scholar

[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.2016.02.002Search in Google Scholar

[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_48Search in Google Scholar

[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.1943-5606.0001445Search in Google Scholar

[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.1943-5606.0001356Search in Google Scholar

[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.2016.04.016Search in Google Scholar

[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. 1991Search in Google Scholar

[58] Liakopoulos, A.C. Theoretical solution of unsteady unsaturated flow problem in soils. Bull. Intern. Assoc. Sci. Hydrology. Vol. 10, pp. 5-39.10.1080/02626666509493368Search in Google Scholar

[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-XSearch in Google Scholar

[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 Scholar

[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/WR015i003p00569Search in Google Scholar

Empfohlene Artikel von Trend MD

Planen Sie Ihre Fernkonferenz mit Scienceendo