Skip to main content
SpringerLink
Log in

Predicting Hysteresis of the Water Retention Curve from Basic Properties of Granular Soils

  • Original paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

The water retention curve (WRC), which represents the relationship between volumetric water content (θ) and suction (ψ), is required to analyze the hydro-geotechnical response of unsaturated soils. The laboratory (or field) determination of the WRC can however be time consuming and difficult to conduct. A practical alternative, particularly useful at the preliminary stages of a project, is to estimate the WRC using a predictive model based on basic geotechnical properties that are easy to obtain. One common limitation of such predictive models is due to hysteresis effects, which are not taken into account by most of these models. The authors present in this paper an extended version of the Modified Kovács (MK) predictive model that incorporates hysteresis of the WRC along different paths, including the main wetting and drying curves and the wetting and drying scanning curves for granular soils. The model formulation is presented, and predictions are compared to experimental data obtained on different granular soils. The results show a good agreement for the main and scanning curves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Abbreviations

α:

Parameter in the van Genuchten model

ψ:

Suction head

θ:

Volumetric water content

ψ1 :

Suction head at the inversion point

θ1d (ψ):

Volumetric water content in the drying scanning curve

θ1w (ψ):

Volumetric water content in the wetting scanning curve

ψ a :

Air entry value (or AEV)

θ a :

Volumetric water content associated with the AEV

β d :

Contact angle during the drying process

θ d (ψ):

Volumetric water content in the main drying curve

θ d (ψ1):

Volumetric water content in the main drying curve at the inversion point

ψ resMK :

Residual suction head (corresponding to the residual water content)

θ r :

Residual volumetric water content

θ s :

Saturated volumetric water content

β w :

Contact angle during the wetting process

θ w (ψ):

Volumetric water content in the main wetting curve

θ w (ψ1):

Volumetric water content in the main wetting curve at the inversion point

a c :

Adhesion coefficient

AEV:

Air entry value

C U :

Coefficient of uniformity

D 10 :

Diameter at 10 % passing on the cumulative grain-size distribution

D 60 :

Diameter at 60 % passing on the cumulative grain-size distribution

e :

Void ratio

h co :

Equivalent capillary rise

h cod :

Equivalent capillary rise for the drying process

h cow :

Equivalent capillary rise for the wetting process

k u :

Hydraulic conductivity

m MK :

Pore size distribution parameter in the MK model (−)

MDC:

Main drying curve

MK :

Modified Kovács model

MK h :

Modified Kovács model with hysteresis effect

MWC:

Main wetting curve

n :

Porosity

DSC:

Drying scanning curve

PF:

Pedotranfer function

WSC:

Wetting scanning curve

r :

Channel radius

R :

Pore radius

S a :

Adhesion component of the degree of saturation

S c :

Capillary component of the degree of saturation

S r :

Degree of saturation

WRC:

Water retention curve

References

  • Ahuja R, Naneyj W, Williamrs D (1985) Estimating soil water characteristics from simpler properties or limited data. Soil Sci Soc Am J 49:1100–1105

    Article  Google Scholar 

  • Araujo YC, Toledo PG, Leon V, Gonzalez HY (1995) Wettability of silane-treated glass slides as determined from X-ray photoelectron spectroscopy. J Col Int Sci 176:485–490

    Google Scholar 

  • Arya LM, Paris JF (1981) A physico-empirical model to predict the soil moisture-characteristic from particle size distribution and bulk density data. Soil Sci Soc Am J 45:1023–1030

    Article  Google Scholar 

  • Aubertin M, Ricard JF, Chapuis RP (1998) A predictive model for the water retention curve: application to tailings from hard-rock mines. Can Geotech J 45:55–68 (with Erratum…)

    Article  Google Scholar 

  • Aubertin M, Mbonimpa M, Bussière B, Chapuis RP (2003) A model to predict the water retention curve from basic geotechnical properties. Can Geotech J 40:1104–1122

    Article  Google Scholar 

  • Bachman J, Horton R, Grant SA, van der-Ploeg R (2002) Temperature dependence of water retention curves for wettable and water-repellent soils. Soil Sci Soc Am J 66:44–52

    Article  Google Scholar 

  • Bouma J (1989) Using soil survey for quantitative land evaluation. Adv Soil Sci 9:177–213

    Article  Google Scholar 

  • Bouwer H (1966) Rapid field measurement of the air entry value and hydraulic conductivity of soils as significant parameters in flow system analysis. Water Resour Res 2:729–738

    Article  Google Scholar 

  • Bradford SA, Leij FJ (1995) Fractional wettability effects on scaling two and three-fluid capillary pressure-saturation relations. Environ Sci Tech 29:1446–1455

    Article  Google Scholar 

  • Brooks RH, Corey AJ (1964) Hydraulic proprieties of porous media. Hydrolo Pap 3 Colo State Univ Fort Collins

  • Bustos C, Toledo PG (2003) Pore-level modeling of gas and condensate flow in two- and three-dimensional pore networks. Pore size distribution effects on the relative permeability of gas and condensate. Transp Porous Media 53:281–315

    Article  Google Scholar 

  • Coasne B, Gubbins K, Pellenq RJM (2005) Domain theory for capillary condensation hysteresis. Phys Rev B 72:4304

    Article  Google Scholar 

  • Davis DD, Horton R, Heitman JL, Ren TS (2009) Wettability and hysteresis effects on water sorption in relatively dry soil. Soil Sci Soc Am J 73:1947–1951

    Article  Google Scholar 

  • Delage P, Cui YJ (2000) L’eau dans les sols non saturés. Tech de l’ingénieur 1:1–20

    Google Scholar 

  • Don Scott H (2000) Soil physic: agricultural and environmental applications. Iowa State University Press, Iowa

    Google Scholar 

  • Flynn D, McNamara H, O’Kane P, Pokrovskii A (2004) Application of the preisach model to soil-moisture hysteresis. BCRI Preprint 15, 2003. http://www.bcri.ucc.ie/ BCRI_15.pdf to be included in a book “Science of Hysteresis”, edited by Giorgio Bertotti and I. Mayergoyz

  • Fredlund DG, Houston SL (2009) Protocol for the assessment of unsaturated soil properties in geotechnical engineering practice. Can Geotech J 46:694–707

    Article  Google Scholar 

  • Gillham RW, Klute A, Heerman DF (1976) Hydraulic properties of a porous medium: measurement and empirical representation. Soil Sci Soc Am J 40:203–207

    Article  Google Scholar 

  • Gupta SC, Larson WE (1979) Estimating soil-water retention characteristics from particle size distribution, organic matter percent, and bulk density. Water Resour Res 15:1633–1635

    Article  Google Scholar 

  • Haines WB (1930) Studies in the physical proprieties of soil: V. The hysteresis effect in capillary proprieties, and the modes of moisture distribution associated therewith. J Agri Sci 20:97–116

    Article  Google Scholar 

  • Haverkamp R, Parlange JY (1986) Predicting the water retention curve from particle-size distribution: 1. Sandy soils without organic matter. Soil Sci 142:325–339

    Article  Google Scholar 

  • Haverkamp R, Reggiani P (2002) Physically based water retention prediction models [property transfer models], In: Dane JH, Topp GC (eds) Methods of soil analysis, part 4—physical methods: Soil science society of america book series no. 5, Madison, Wis., Soil Science Society of America, pp 762–777, 781–782

  • Haverkamp R, Zammit C, Bouraoui F (1998) Grizzly soil data bank, base de données de paramètres caractéristiques des sols. LTHE, Grenoble

    Google Scholar 

  • Haverkamp R, Reggiani P, Ross PJ, Parlange JY (2002) Soil water hysteresis prediction model based on theory and geometric scaling. In: Raats PAC, Smiles D, Warrick A (eds) Environmental mechanics: Water, mass and energy transfert in the biosphere. Geophysical Monograph 129. American Geophysical Union, Washington, DC, pp 213–246

  • Hillel D (1980) Fundamentals of soil physics. Academic Press Inc., New York, p 413

    Google Scholar 

  • Hillel D (1998) Environmental soil physics. Academic Press Inc., San Diego, p 771

  • Hillel D, Mottes J (1966) Effect of plate impedance, wetting method, and aging on soil moisture retention. Soil Sci 102:135–140

    Article  Google Scholar 

  • Huang M, Lee Barbour S, Elshorbagy A, Zettl JD, Si BC (2011) Infiltration and drainage processes in multi-layered coarse soils. Can J Soil Sci 91:169–183

    Google Scholar 

  • Hoa NT, Gaudu R, Thirriot C (1977) Influence of the hysteresis effect on transient flows in saturated-unsaturated porous media. Water Resour Res 13:992–996

    Article  Google Scholar 

  • Ishakoglu A, Baytas AF (2004) The influence of contact angle on capillary pressure–saturation relations in a porous medium including various liquids. Int J Eng Sci 43:744–755

    Article  Google Scholar 

  • Jaynes DB (1992) Estimating hysteresis in the soil water retention function. Proceedings of the international workshop on indirect methods for estimating the hydraulic proprieties of unsaturated soils. University of California, Riverside, CA, pp 219–232

    Google Scholar 

  • Jury WA, Gardner WR, Gardner WH (1991) Simulation diffusion in a Boolean model of soil pores. Eur J Soil Sci 45:483–491

    Google Scholar 

  • Kaluarachchi J, Parker JC (1989) An efficient finite element method for modeling multiphase flow. Water Resour Res 25:43–54

    Article  Google Scholar 

  • Klausser Y (1991) Fundamentals of continuum mechanics of soils. Springer, New York

    Book  Google Scholar 

  • Kool JB, Parker JC (1987) Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties. Water Resour Res 23:105–114

    Article  Google Scholar 

  • Kovács C (1981) Seepage hydraulics. Elsevier, Amsterdam

    Google Scholar 

  • Kumar S, Malik RS (1990) Verification of quick capillary rise approach for determining pore geometrical characteristics in soils of varying texture. Soil Sci 150:883–888

    Article  Google Scholar 

  • Leij FJ, Alves WJ, van Genuchten MTh, Williams JR (1996) The UNSODA-unsaturated soil hydraulic database. User’s Manual Version 1.0. Report EPA/600/R-96/095. National Risk Management Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency, Cincinnati, OH

  • Letey J, Osborn J, Pelishek RE (1962) Measurement of liquid-solid contact angles in soil and sand. J Geotech Geoenviron Eng 123:1118–1126

    Google Scholar 

  • Likos W, Lu N (2002) Hysteresis of capillary cohesion in unsaturated soils. In: Proceeding of 15th ASCE Engineering Mechanics Conference, June 2–5, 2002, Columbia University, New York, NY

  • Maqsoud A, Bussière B, Aubertin M (2002) L’hystérésis des sols non saturés utilisés dans les recouvrements avec effet de barrières capillaires. Proceedings of the 55th Canadian Geotechnical Conference—3rd Joint IAH-CNC/CGS: Ground and Water: Theory to practice, Niagara Falls, Ontario, Canada, pp 181–188

  • Maqsoud A, Bussière B, Mbonimpa M, Aubertin M. (2004) Hysteresis effects on the water retention curve: A comparison between laboratory results and predictive models. 5th Joint IAH-CNC and CGS Groundwater Specialty Conference, 57th Canadian Geotechnical Conference, Quebec, Quebec, Canada, 23-27 October 2004. Session 3A, H21.175, pp 8–15. CD-ROM

  • Marshall TJ, Holmes JW, Rose CW (1996) Soil physics, 3rd edn. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Mbonimpa M, Aubertin M, Chapuis RP, Bussière B (2000) Développement de fonctions hydriques utilisant les propriétés géotechniques de base. 1st Joint IAH-CNC and CGS Groundwater Specialty Conference. Montreal, pp 343–350

  • Mbonimpa M, Aubertin M, Maqsoud A, Bussière B (2006) A predictive model for the water retention curve of deformable clayey soils. J Geotech Geoenviron Eng ASCE 132:1121–1132

    Article  Google Scholar 

  • Miller EE, Miller RD (1956) Physical theory for capillary flow phenomena. J Appl Phys 27:324–332

    Article  Google Scholar 

  • Mitchel RJ, Mayer AS (1998) The significance of hysteresis in modeling solute transport in unsaturated porous media. Soil Sci Soc Am J 62:1506–1512

    Article  Google Scholar 

  • Morrow NR (1975) The effects of surface roughness on contact angle with special reference to petroleum recovery. J Can Petrol Technol 14:42–53

    Google Scholar 

  • Moseley WA, Dhir VK (1996) Capillary pressure-saturation relations in porous media including the effect of wettability. J Hydrol 178:33

    Article  Google Scholar 

  • Mualem Y (1976) A catalogue of the hydraulic properties of unsaturated soils. Technion, Israel Institute of Technology, Research Project 442, Haifa, Israel

  • Mualem Y (1984) A modified dependent-domain theory of hysteresis. Soil Sci 137:283–291

    Article  Google Scholar 

  • Mualem Y, Beriozkin A (2009) General scaling rules of the hysteretic water retention function based on Mualem’s domain theory. Eur J Soil Sci 60:652–661

    Article  Google Scholar 

  • Naasz R, Michel JC, Charpentier S (2008) Water repellency of organic growing media related to hysteretic water retention properties. Eur J Soil Sci 59:165

    Article  Google Scholar 

  • Nemes A, Rawls WJ (2004) Soil texture and particle-size distribution as input to estimate soil hydraulic properties. In: Pachepsky Y, Rawls WJ (eds) Development of pedotransfer functions in soil hydrology. Elsevier, Amsterdam

    Google Scholar 

  • Peng XR, Horn R (2007) Anisotropic shrinkage and swelling of some organic and inorganic soils. Eur J Soil Sci 58:98–107

    Article  Google Scholar 

  • Poulovassilis A (1962) Hysteresis of pore water, and application of concept of independent domains. Soil Sci 93:405–412

    Article  Google Scholar 

  • Rawls WJ, Rakensiek DL (1982) Estimating soil water retention from soil properties. J Irrig Drain Div ASCE 108:166–171

    Google Scholar 

  • Si BC, Kachanoski RC (2000) Unified solution for infiltration and drainage with hysteresis: theory and field test. Soil Sci Soc Am J 64:30–36

    Article  Google Scholar 

  • Simunek J, van Genuchten MTh, Sejna M (1998) The Hydrus-1D software package for simulating the one-dimensional movement of water, heat and multiple solutes in variability-saturated media. Version 3.0. Department of Environmental Sciences, University of California Riverside, CA

  • Suciu CV, Iwatsubo T, Yaguchi K, Ikenaga M (2005) Novel and global approach of the complex and interconnected phenomena related to the contact line movement past a solid surface from hydrophobized silica gel. J Colloid Interface Sci 283:196–214

    Article  Google Scholar 

  • Tyler SW, Wheatcraft SW (1989) Application of fractal mathematics to soil water retention estimation. Soil Sci Soc Am J 53:987–996

    Article  Google Scholar 

  • Ustohal P, Stauffer F, Dracos T (1998) Measurements and modelling of hydraulic characteristics of unsaturated porous media with mixed wettability. J Contam Hydrol 33:5–37

    Article  Google Scholar 

  • Vereecken H, Maes J, Feyen J, Darius P (1989) Estimating the soil moisture retention characteristic from texture, bulk density and carbon content. Soil Sci 148:389–403

    Article  Google Scholar 

  • Wang XD, Peng XF, Lu JF, Liu T, Wang BX (2004) Contact angle hysteresis on rough surfaces. Heat Transf Asian Res 33:201–210

    Google Scholar 

  • Wang Z, Feyen J, Nielsen DR, van Genuchten MTh (1997) Two-phase flow infiltration equation accounting for air entrapment effects. Water Resour Res 33:2759–2767

    Article  Google Scholar 

  • Whitmore AP, Heinen M (1999) The effect of hysteresis on microbial activity in computer simulation models. Soil Sci Soc Am J 63:1101–1105

    Article  Google Scholar 

  • Yang H, Rahardjo H, Leong EC, Fredlund DG (2004) Factors affecting drying and wetting soil-water characteristic curves of sandy soils. Can Geotech J 41:908–920

    Article  Google Scholar 

  • Zhang Q, Werner AD, Aviyanto RF, Hutson JL (2009) Influence of soil moisture hysteresis on the functioning of capillary barriers. Hydrol Process 23:1369–1375

    Article  Google Scholar 

Download references

Acknowledgments

This study was funded by NSERC and by the participants in the Industrial Polytechnique-UQAT Chair on Environmental and Mine Wastes Management (www.polymtl.ca/enviro-geremi).

Author information

Authors and Affiliations

  1. Department of Applied Sciences, Industrial NSERC Polytechnique-UQAT Chair in Environment and Mine Wastes Management, Université du Québec en Abitibi-Témiscamingue, 445 University Blvd, Rouyn-Noranda, QC, J9X 5E4, Canada

    Abdelkabir Maqsoud, Bruno Bussière & Mamert Mbonimpa

  2. Departement of Civil, Geological and Mining Engineering, Industrial NSERC Polytechnique-UQAT Chair in Environment and Mine Wastes Management, École Polytechnique de Montréal, P.O.Box 6079, Stn Centre-ville, Montreal, QC, H3C 3A7, Canada

    Michel Aubertin

Authors
  1. Abdelkabir Maqsoud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruno Bussière
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michel Aubertin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mamert Mbonimpa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdelkabir Maqsoud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maqsoud, A., Bussière, B., Aubertin, M. et al. Predicting Hysteresis of the Water Retention Curve from Basic Properties of Granular Soils. Geotech Geol Eng 30, 1147–1159 (2012). https://doi.org/10.1007/s10706-012-9529-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-012-9529-y

Keywords

Search

Navigation