Analytical Solution to 1D Coupled Infiltration and Deformation in Unsaturated Porous Media

  • Lizhou WuEmail author
  • Runqiu Huang
  • Xu Li


Unsaturated flow is important in a wide range of engineering applications such as rainfall, irrigation, nuclear waste disposal, and rainfall-induced landslides (Inverson 2000; Wu et al. 2016).


  1. Basha HA (1999) Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resour Res 35(1):75–83CrossRefGoogle Scholar
  2. Basha HA (2000) Multidimensional linearized nonsteady infiltration toward a shallow water table. Water Resour Res 36(9):2567–2573CrossRefGoogle Scholar
  3. Basha HA (2011) Infiltration models for semi-infinite soil profile. Water Resour Res 47(8):192–198CrossRefGoogle Scholar
  4. Broadbridge P, White I (1988) Constant rate rainfall infiltration: a versatile nonlinear model. I. Analytical solution. Water Resour Res 24(1):145–154CrossRefGoogle Scholar
  5. Chen JM, Tan Y, Chen CH (2001) Multidimensional infiltration with arbitrary surface fluxes. J Irrig Drain Eng 127(6):370–377CrossRefGoogle Scholar
  6. Chen JM, Tan YC, Chen CH (2003) Analytical solutions of one-dimensional infiltration before and after ponding. Hydrol Process 17(4):815–822CrossRefGoogle Scholar
  7. Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. Wiley, New YorkCrossRefGoogle Scholar
  8. Gardner WR (1958) Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci 85(4):228–232CrossRefGoogle Scholar
  9. Hillel D (1998) Environmental soil physics. Academic, New YorkGoogle Scholar
  10. Hogarth WL, Parlange JY, Norbury J (1992) Addendum to “First integrals of the infiltration equation”. Soil Sci 154(5):341–343CrossRefGoogle Scholar
  11. Iverson RM (2000) Landslide triggering by rain infiltration. Water Resour Res 36(7):1897–1910CrossRefGoogle Scholar
  12. 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(9):1101–1119zbMATHCrossRefGoogle Scholar
  13. Lloret A, Gens A, Batlle F, Alonso EE (1987) Flow and deformation analysis of partially saturated soils. In: Proceedings 9th European conference on soil mechanics, Dublin, vol 2, pp 565–568Google Scholar
  14. Ozisik M (1989) Boundary value problems of heat conduction. Dover, New York, pp 85–87Google Scholar
  15. Parlange JY (1972) Theory of water movement in soils: VIII. One dimensional infiltration with constant flux at the surface. Soil Sci 114:1–4CrossRefGoogle Scholar
  16. Parlange JY, Barry DA, Parlange MB et al (1997) New approximate analytical technique to solve Richards equation for arbitrary surface boundary conditions. Water Resour Res 33:903–906CrossRefGoogle Scholar
  17. PDE Solutions Inc. (2004) FlexPDE user guide. PDE Solutions Inc., Antioch, CAGoogle Scholar
  18. Pereira JHF (1996) Numerical analysis of the mechanical behavior of collapsing earth dams during first reservoir filling. PhD thesis, University of Saskatchewan, CanadaGoogle Scholar
  19. Pullan AJ (1990) The quasilinear approximation for unsaturated porous media flow. Water Resour Res 26(6):1219–1234CrossRefGoogle Scholar
  20. Raats PAC (1970) Steady infiltration from line sources and furrows. Soil Sci Soc Am J 34(5):709–714CrossRefGoogle Scholar
  21. Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1(5):318–333zbMATHCrossRefGoogle Scholar
  22. Smiles DE, Raats PAC (2004) Swelling and shrinking soils. In: Hillel D (ed) Encyclopedia of soils in the environment, vol 4. Elsevier, pp 115–124Google Scholar
  23. Srivastava R, Yeh TCJ (1991) Analytical solutions for one dimension, transient infiltration toward the water table in homogeneous and layered soils. Water Resour Res 27(5):753–762CrossRefGoogle Scholar
  24. Tracy FT (2006) Clean two- and three-dimensional analytical solutions of Richards’ equation for testing numerical solvers. Water Resour Res 42(8):W08503CrossRefGoogle Scholar
  25. Tsai TL, Wang JK (2011) Examination of influences of rainfall patterns on shallow landslides due to dissipation of matric suction. Environ Earth Sci 63(1):65–75CrossRefGoogle Scholar
  26. Van Genuchten MT (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898CrossRefGoogle Scholar
  27. 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
  28. Wu LZ, Zhang LM (2009) Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils. Int J Numer Anal Met 33(6):773–790zbMATHCrossRefGoogle Scholar
  29. 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 Met 36:798–816CrossRefGoogle Scholar
  30. Wu LZ, Zhang LM, Li X (2016) One-dimensional coupled infiltration and deformation in unsaturated soils subjected to varying rainfall. Int J Geomech 16(2):06015004CrossRefGoogle Scholar
  31. Zhan TLT, Ng CWW (2004) Analytical analysis of rainfall infiltration mechanism in unsaturated soils. Int J Geomech 4(4):273–284CrossRefGoogle Scholar
  32. 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
  33. Zhang LM, Li X (2010) Micro-porosity structure of coarse granular soils. J Geotech Geoenviron 136(10):1425–1436CrossRefGoogle Scholar
  34. Zhang LL, Zhang LM, Tang WH (2005) Rainfall-induced slope failure considering variability of soil properties. Geotechnique 55(2):183–188CrossRefGoogle 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