Effects of Gravity and Hysteresis on 1D Unsaturated Infiltration

  • Lizhou WuEmail author
  • Runqiu Huang
  • Xu Li


Unsaturated infiltration is significant in a wide range of engineering applications including rainfall-induced landslides (Zhan et al. 2013). The spatial and temporal evolution of flow in an unsaturated medium involves a governing partial differential equation that is expressed by the Richards’ equation (1931).


  1. Basha HA (1999) Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resour Res 35(1):75–83Google Scholar
  2. Basha HA (2011) Infiltration models for semi-infinite soil profile. Water Resour Res 47:W08516Google Scholar
  3. Broadbridge P, White I (1988) Constant rate rainfall infiltration: a versatile nonlinear model. 1. Analytic solution. Water Resour Res 24(1):145–154. Scholar
  4. Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Hydrology, Paper No. 3. Colorado State University, Fort Collins, ColoradoGoogle Scholar
  5. Chen JM, Tan YC, Chen CH, Parlange JY (2001a) Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes. Water Resour Res 37(4):1091–1093CrossRefGoogle Scholar
  6. Chen JM, Tan YC, Chen CH (2001b) Multidimensional infiltration with arbitrary surface fluxes. J Irrig Drain Eng (ASCE) 127(6):370–377CrossRefGoogle Scholar
  7. Chen JM, Tan YC, Chen CH (2003) Analytical solutions of one-dimensional infiltration before and after ponding. Hydrol Process 17(4):815–822CrossRefGoogle Scholar
  8. Chen JM, Tan YC (2005) Analytical solutions of infiltration process under ponding irrigation. Hydrol Process 19(18):3593–3602CrossRefGoogle Scholar
  9. Dane JH, Wierenga PJ (1975) Effect of hysteresis on the prediction of infiltration, redistribution and drainage of water in layered soil. J Hydrol 25(3–4):229–242CrossRefGoogle Scholar
  10. Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. Wiley, New YorkCrossRefGoogle Scholar
  11. Gardner WR (1958) Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci 85:228–232CrossRefGoogle Scholar
  12. Gillham RW, Klute A, Heerman DF (1976) Hydraulic properties of a porous medium: measurement and empirical representation. Soil Sci Soc Am J 40(2):203–207CrossRefGoogle Scholar
  13. Haines WB (1930) Studies in the physical properties of soil. V. The hysteresis effect in capillary properties and the modes of water distribution associated therewith. J Agric Sci 20:97–116CrossRefGoogle Scholar
  14. Hank RJ, Klute A, Bresler E (1969) A numerical method for estimating infiltration redistribution, drainage, and evaporation of water from soil. Water Resour Res 13:992–998Google Scholar
  15. Hillel D (1998) Environmental soil physics. Academic, New YorkGoogle Scholar
  16. Hills RGB, Hudson IP, Wierenga PJ (1989) Modeling one-dimensional infiltration into very dry soils. Water Resour Res 25:1271–1282CrossRefGoogle Scholar
  17. Hogarth W, Hopmans J, Parlange JY, Haverkamp R (1988) Application of a simple soil-water hysteresis model. J Hydrol 98(1–2):21–29CrossRefGoogle Scholar
  18. Hogarth WL, Parlange JY, Norbury J (1992) Addendum to “First integrals of the infiltration equation”. Soil Sci 154:341–343CrossRefGoogle Scholar
  19. Jaynes DB (1985) Comparison of soil–water hysteresis models. J Hydrol 75:287–299CrossRefGoogle Scholar
  20. Kacimov AR, Yakimov ND (1998) Nonmonotonic moisture profile as a solution of Richards’ equation for soils with conductivity hysteresis. Adv Water Resour 21(8):691–696CrossRefGoogle Scholar
  21. Kawai K, Karube D, Kato S (2000) The model of water retention curve considering effects of void ratio. In: Proceedings Asian conference on unsaturated soils, pp 329–334Google Scholar
  22. Kim JM (2000) A fully coupled finite element analysis of water-table fluctuation and land deformation in partially saturated soils due to surface loading. Int J Numer Meth Eng 49:1101–1119zbMATHCrossRefGoogle Scholar
  23. Klausner Y (1991) Fundamentals of continuum mechanics of soils. Springer, New YorkCrossRefGoogle Scholar
  24. Kool JB, Parker JC (1987) Development and evaluation of closed-form expressions for hysteretic hydraulic properties. Water Resour Res 23(1):105–114CrossRefGoogle Scholar
  25. Li XS (2005) Modelling of hysteresis response for arbitrary wetting/drying paths. Comput Geotech 32(2):133–137CrossRefGoogle Scholar
  26. Likos WJ, Lu N (2004) Hysteresis of capillary stress in unsaturated granular soil. J Eng Mech ASCE 130(6):646–655CrossRefGoogle Scholar
  27. Mualem Y (1974) A conceptual model of hysteresis. Water Resour Res 10:514–520CrossRefGoogle Scholar
  28. Mualem Y (1984) Prediction of the soil boundary wetting curve. Soil Sci 137:379–389CrossRefGoogle Scholar
  29. Nimmo JR (1992) Semi-empirical model of soil water hysteresis. Soil Sci Soc Am J 56:1723–1730CrossRefGoogle Scholar
  30. Ozisik M (1989) Boundary value problems of heat conduction. Dover, New York, pp 85–87Google Scholar
  31. Parlange JY, Barry DA, Parlange MB, Hogarth WL, Haverkamp R, Ross PJ, Ling L, Steenhuis TS (1997) New approximate analytical technique to solve Richards equation for arbitrary surface boundary conditions. Water Resour Res 33:903–906CrossRefGoogle Scholar
  32. Pedroso DM, Williams DJ (2010) A novel approach for modelling soil-water characteristic curves with hysteresis. Comput Geotech 37(3):374–380CrossRefGoogle Scholar
  33. Pham HQ, Fredlund DG, Barbour SL (2003) A practical hysteresis model for the soil-water characteristic curve for soils with negligible volume change. Geotechnique 53(2):293–298CrossRefGoogle Scholar
  34. Philip JR (1964) Similarity hypothesis for capillary hysteresis in porous materials. J Geophys Res 69(8):1553–1562CrossRefGoogle Scholar
  35. Raats PAC (1970) Steady infiltration from line sources and furrows. Soil Sci Soc Am J 34(5):709–714CrossRefGoogle Scholar
  36. Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics (NY) 1:318–333zbMATHCrossRefGoogle Scholar
  37. Russo D, Jury WA, Butters GL (1989) Numerical analysis of solute transport during transient irrigation. 1. The effect of hysteresis and profile heterogeneity. Water Resour Res 25(10):2109–2118CrossRefGoogle Scholar
  38. Srivastava R, Yeh TCJ (1991) Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils. Water Resour Res 27(5):753–762CrossRefGoogle Scholar
  39. Staple WJ (1969) Comparison of computed and measured moisture redistribution following infiltration. Soil Sci Soc Am Proc 33:840–847CrossRefGoogle Scholar
  40. Tan YC, Ma KC, Chen CH et al (2009) A numerical model of infiltration processes for hysteretic flow coupled with mass conservation. Irrig Drain 58(3):366–380CrossRefGoogle Scholar
  41. Topp GC (1971) Soil-water hysteresis: the domain theory extended to pore interaction conditions. Soil Sci Soc Am Proc 33:219–225CrossRefGoogle Scholar
  42. Tracy FT (2006) Clean two- and three-dimensional analytical solutions of Richards’ equation for testing numerical solvers. Water Resour Res 42:W08503CrossRefGoogle Scholar
  43. Van Genuchten MT (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898CrossRefGoogle Scholar
  44. Warrick AW, Islas A, Lomen DO (1991) An analytical solution to Richards’ equation for time-varying infiltration. Water Resour Res 27(5):763–766CrossRefGoogle Scholar
  45. Wu LZ, Zhang LM (2009) Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils. Int J Numer Anal Meth Geomech 33:773–790zbMATHCrossRefGoogle Scholar
  46. Wu LZ, Zhang LM, Huang RQ (2012) Analytical solution to 1D coupled water infiltration and deformation in two-layer unsaturated soils. Int J Numer Anal Meth Geomech 36:798–816CrossRefGoogle Scholar
  47. Wu LZ, Zhang LM, Li X (2016a) One-dimensional coupled infiltration and deformation in unsaturated soils subjected to varying rainfall. Int J Geomech 16(2). Scholar
  48. Wu LZ, Selvadurai APS, Zhang LM, Huang RQ, Huang J (2016b) Poro-mechanical coupling influences on potential for rainfall-induced shallow landslides in unsaturated soils. Adv Water Resour 98:114–121CrossRefGoogle Scholar
  49. Zhan TLT, Jia GW, Chen YM, Fredlund DG, Li H (2013) An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis. Int J Numer Anal Met 37(12):1737–1760CrossRefGoogle Scholar
  50. Zhang LL, Zhang LM, Tang WH (2005) Rainfall-induced slope failure considering variability of soil properties. Geotechnique 55(2):183–188CrossRefGoogle Scholar
  51. Zhu JT, Mohanty BP (2002) Analytical solutions for steady state vertical infiltration. Water Resour Res 38(8):1145CrossRefGoogle Scholar

Copyright information

© Science Press  2020

Authors and Affiliations

  1. 1.College of Environment and Civil EngineeringChengdu University of TechnologyChengduChina
  2. 2.Chengdu University of TechnologyChengduChina
  3. 3.School of Civil EngineeringBeijing Jiaotong UniversityBeijingChina

Personalised recommendations