2D Infiltration in Unsaturated Porous Media

  • Lizhou WuEmail author
  • Runqiu Huang
  • Xu Li


Coupling between water infiltration and mechanical deformation in partially saturated porous media is central to many natural and man-made systems in civil and environmental engineering. During water infiltration, the pore-water pressure is redistributed, on one hand, by the hydraulic properties of the partially saturated soil including retention characteristics and permeability, and, on the other hand, by the external loading due to climate conditions (rainfall intensity, duration, and evapo-transpiration rate).


  1. Alonso EE, Gens A, Delahaye CH (2003) Influence of rainfall on the deformation and stability of a slope in overconsolidated clays: a case study. Hydrogeol J 11:174–192CrossRefGoogle Scholar
  2. Basha HA (1999) Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resour Res 35(1):75–83CrossRefGoogle Scholar
  3. Basha HA (2000) Multidimensional linearized nonsteady infiltration toward a shallow water table. Water Resour Res 36:2567–2573CrossRefGoogle Scholar
  4. Basha HA, Selvadurai APS (1998) Heat-induced moisture transport in the vicinity of a spherical heat source. Int J Numer Anal Met 22(12):969–981zbMATHCrossRefGoogle Scholar
  5. Bettess P (1977) Infinite elements. Int J Numer Meth Eng 11(1):53–64zbMATHCrossRefGoogle Scholar
  6. Casini F (2012) Deformation induced by wetting: a simple model. Can Geotech J 49(8):954–960CrossRefGoogle Scholar
  7. Castelblanco JM, Delage P, Pereira J, Cui Y (2011) Some aspects of the compression and collapse behaviour of an unsaturated natural loess. Géotechnique Letters 1(2):17–22CrossRefGoogle Scholar
  8. Chen JM, Tan YC, Chen CH, Parlange JY (2001) Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes. Water Resour Res 37(4):1091–1093CrossRefGoogle Scholar
  9. Cho SE, Lee SR (2001) Instability of unsaturated soil slopes due to infiltration. Comput Geotech 28:185–208CrossRefGoogle Scholar
  10. Dakshanamurthy V, Fredlund DG, Rahardjo H (1984) Coupled three-dimensional consolidation theory of unsaturated porous media. In: Proceedings of the international conference on expansive soils, Adelaide, Australia, pp 99–103Google Scholar
  11. Davis RO, Selvadurai APS (1996) Elasticity and geomechanics. Cambridge University Press, Cambridge, UKGoogle Scholar
  12. Davis RO, Selvadurai APS (2002) Plasticity and geomechanics. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  13. Davis RO, Selvadurai APS (2004) Plasticity and geomechanics. Cambridge University Press, UKGoogle Scholar
  14. Desai CS, Siriwardane HJ (1984) Constitutive laws for engineering materials with emphasis on geologic materials. Prentice-Hall, LondonzbMATHGoogle Scholar
  15. Ehlers W, Graf T, Ammann M (2004) Deformation and localization analysis of partially saturated soil. Comput Method Appl M 193:2885–2910zbMATHCrossRefGoogle Scholar
  16. Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. Wiley, New YorkCrossRefGoogle Scholar
  17. Garcia E, Oka F, Kimoto S (2011) Numerical analysis of a one-dimensional infiltration problem in unsaturated soil by a seepage-deformation coupled method. Int J Numer Anal Met 35(5):544–568zbMATHCrossRefGoogle Scholar
  18. Gardner WR (1958a) Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci 85:228–232CrossRefGoogle Scholar
  19. Gardner WR (1958b) Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci 85:228–232CrossRefGoogle Scholar
  20. Griffiths DV, Lu N (2005) Unsaturated slope stability analysis with steady infiltration or evaporation using elasto-plastic finite elements. Int J Numer Anal Met 29:249–267zbMATHCrossRefGoogle Scholar
  21. Kangro R, Nicolaides R (2000) Far field boundary conditions for Black-Scholes equations. SIAM J Numer Anal 38(4):1357–1368MathSciNetzbMATHCrossRefGoogle Scholar
  22. Khalili N, Zargarbashi S (2010) Influence of hydraulic hysteresis on effective stress in unsaturated soils. Géotechnique 60(9):729–734CrossRefGoogle Scholar
  23. 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
  24. Lu N, Godt JW, Wu DT (2010) A closed-form equation for effective stress in unsaturated soil. Water Resour Res. Scholar
  25. Mansuco C, Jommi C, D’Onza F (Eds) (2012) Unsaturated soils: research and applications, vols 1 and 2. Springer, BerlinGoogle Scholar
  26. McKee CR, Bumb AC (1984) The importance of unsaturated flow parameters in designing a hazardous waste site. In: Hazardous waste and environmental emergencies (Hazardous materials control research institute national conference). Houston, TX, 12–14 March 1984, Silver Sping, Md, pp 50–58Google Scholar
  27. Mualem Y (1976) A new model for predicting the conductivity of unsaturated porous media. Water Resour Res 12:513–522CrossRefGoogle Scholar
  28. Oka F, Kimoto S, Takada N (2010) A seepage-deformation coupled analysis of an unsaturated river embankment using a multiphase elasto-viscoplastic theory. Soils Found 50(4):483–494CrossRefGoogle Scholar
  29. Ozisik M (1989) Boundary value problems of heat conduction. Dover, New YorkGoogle Scholar
  30. Pietruszczak S (2010) Fundamentals of plasticity in geomechanics. CRC Press, Boca Raton, FLzbMATHGoogle Scholar
  31. Rotisciani GM, Sciarra G, Casini F, Desideri A (2015) Hydro-mechanical response of collapsible soils under different infiltration events. Int J Numer Anal Meth Geomech 39(11):1212–1234CrossRefGoogle Scholar
  32. Rotisciani GM, Casini F, Desideri A, Sciarra G (2017) Hydro-mechanical behavior of an embankment during inundation. Can Geotech J 54(3):348–358CrossRefGoogle Scholar
  33. Schofield AN, Wroth P (1968) Critical state soil mechanics. McGraw-Hill, New YorkGoogle Scholar
  34. Selvadurai APS (2000) Partial differential equations in mechanics. In: Fundamentals, Laplace’s equation, diffusion equation and wave equation, vol 2. Springer, BerlinCrossRefGoogle Scholar
  35. Selvadurai APS (2003) Intake shape factors for entry points in porous media with transversely isotropic hydraulic conductivity. Int J Geomech 3:152–159MathSciNetCrossRefGoogle Scholar
  36. Selvadurai APS, Suvorov AP (2012) Boundary heating of poroelastic and poro-elastoplastic spheres. Proc R Soc A-Math Phys 468:2779–2806. Scholar
  37. Selvadurai APS, Suvorov AP (2014) Thermo-poromechanics of a fluid filled cavity in a fluid-saturated geomaterial. Proc R Soc A-Math Phy 470:1471–2946. Scholar
  38. Selvadurai APS, Suvorov AP, Selvadurai PA (2014) Thermo-hydro-mechanical processes in fractured rock formations during glacial advance. Geosci Model Dev Disc 7:7352–7394Google Scholar
  39. Sillers WS, Fredlund DG (2001) Statistical assessment of soil-water characteristic curve models for geotechnical engineering. Can Geotech J 38(6):1297–1313CrossRefGoogle Scholar
  40. Srivastava R, Yeh TCJ (1991) Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soils. Water Resour Res 27:753–762CrossRefGoogle Scholar
  41. Thorel L, Ferber V, Caicedo B, Khokhar I (2011) Physical modelling of wetting-induced collapse in embankment base. Géotechnique 61(5):409–420CrossRefGoogle Scholar
  42. van Genuchten MY (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898CrossRefGoogle Scholar
  43. Wu LZ, Selvadurai APS (2016) Rainfall infiltration-induced groundwater table rise in an unsaturated porous medium. Environ Earth Sci 75(2):1–11Google Scholar
  44. Wu LZ, Zhang LM (2009) Analytical solution to 1D coupled water infiltration and deformation in unsaturated soils. Int J Numer Anal Meth Geomech 33(6):773–790zbMATHCrossRefGoogle Scholar
  45. 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 36:798–816.CrossRefGoogle Scholar
  46. Wu LZ, Selvadurai APS, Huang RQ (2013) Two-dimensional coupled hydromechanical modeling of water infitration into a transversely isotropic unsaturated soil region. Vadose Zone J 12(4)CrossRefGoogle Scholar
  47. Wu LZ, Sun P, Huang RQ (2017a) Analytical analysis of partially saturated infiltration coupled with deformation in a semi-infinite region. Int J Geomech 17(6):06016040CrossRefGoogle Scholar
  48. Wu LZ, Zhang LM, Zhou Y, Li BE (2017b) Analysis of multi-phase coupled seepage and stability in anisotropic slopes under rainfall condition. Environ Earth Sci 76(14):469CrossRefGoogle Scholar
  49. Yang YB, Hung HH (2001) A 2.5D finite/infinite element approach for modelling visco-elastic bodies subjected to moving loads. Int J Numer Meth Eng 51(11):1317–1336zbMATHCrossRefGoogle Scholar
  50. Zhan TLT, Ng CWW (2004) Analytical analysis of rainfall infiltration mechanism in unsaturated soils. Int J Geomech 4:273–284CrossRefGoogle Scholar
  51. 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 Meth Geomech 37(12):1737–1760CrossRefGoogle Scholar

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© 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

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