Acta Geotechnica

, Volume 12, Issue 1, pp 67–83 | Cite as

Contact angle mechanical influence in wet granular soils

  • Jérôme DuriezEmail author
  • Richard Wan
Research Paper


We investigate the macroscopic mechanical influence of the local liquid–solid contact angle that governs the fluid distribution in granular soils under unsaturated conditions. To this end, a discrete element method (DEM)-based implementation that accommodates for any contact angle is proposed and applied to an idealized granular material in the pendular regime. The DEM model includes resultant capillary forces as well as a comprehensive description of the capillary bridges (volume, surface, orientation tensor) by solving the Laplace–Young equation in a general case, instead of using any unnecessary phenomenological relation. Macroscale mechanical simulations for different constant contact angle values reveal that granular assemblies are less sensitive to unsaturated conditions for higher contact angles, which is in line with the contact angle influence at the microscopic capillary bridge scale. The contribution of the fluid mixture to the total stresses of the wet soil, the so-called capillary stresses, indeed decreases according to the contact angle. Thus, the increase in apparent shear strength due to unsaturated conditions is reduced for higher contact angles. As such, the classical assumption of perfect wetting (zero contact angle) appears to be non-conservative.


Contact (wetting) angle Capillary (suction) stresses Capillary bridge Discrete element method (DEM) Laplace–Young equation 



This work is supported by the Natural Science and Engineering Research Council of Canada and Foundation Computer Modelling Group within the framework of a Government-Industry Partnership (NSERC-CRD) Grant towards the fundamental understanding of complex multiphasic granular media.


  1. 1.
    Alonso E, Pereira JM, Vaunat J, Olivella S (2010) A microstructurally based effective stress for unsaturated soils. Géotechnique 60(12):913–925. doi: 10.1680/geot.8.P.002 CrossRefGoogle Scholar
  2. 2.
    Bachmann J, Horton R, van der Ploeg RR, Woche S (2000) Modified sessile drop method for assessing initial soil-water contact angle of sandy soil. Soil Sci Soc Am J 64(2):564–567. doi: 10.2136/sssaj2000.642564x CrossRefGoogle Scholar
  3. 3.
    Bathurst RJ, Rothenburg L (1990) Observations on stress-force-fabric relationships in idealized granular materials. Mech Mater 9(1):65–80CrossRefGoogle Scholar
  4. 4.
    Bishop AW, Blight GE (1963) Some aspects of effective stress in saturated and partly saturated soils. Géotechnique 13:177–197CrossRefGoogle Scholar
  5. 5.
    Bisschop FRD, Rigole WJ (1982) A physical model for liquid capillary bridges between adsorptive solid spheres: The nodoid of Plateau. J Colloid Interface Sci 88(1):117–128. doi: 10.1016/0021-9797(82)90161-8 CrossRefGoogle Scholar
  6. 6.
    Chateau X, Dormieux L (1995) Homogenization of a non-saturated porous medium: Hill’s lemma and applications. CR Acad Sci Paris Série II 320:627–634zbMATHGoogle Scholar
  7. 7.
    Chateau X, Moucheront P, Pitois O (2002) Micromechanics of unsaturated granular media. J Eng Mech 128(8):856–863. doi: 10.1061/(ASCE)0733-9399(2002)128:8(856) CrossRefGoogle Scholar
  8. 8.
    Chenu C, Le Bissonnais Y, Arrouays D (2000) Organic matter influence on clay wettability and soil aggregate stability. Soil Sci Soc Am J 64(4):1479–1486. doi: 10.2136/sssaj2000.6441479x CrossRefGoogle Scholar
  9. 9.
    Czachor H (2006) Modelling the effect of pore structure and wetting angles on capillary rise in soils having different wettabilities. J Hydrol 328(34):604–613. doi: 10.1016/j.jhydrol.2006.01.003 CrossRefGoogle Scholar
  10. 10.
    Duriez J, Wan R (2015) Effective stress in unsaturated granular materials: micromechanical insights. In: coupled problems in science and engineering VI, pp 1232–1242Google Scholar
  11. 11.
    Fisher RA (1926) On the capillary forces in an ideal soil; correction of formulae given by W. B. Haines. J Agric Sci 16:492–505. doi: 10.1017/S0021859600007838 CrossRefGoogle Scholar
  12. 12.
    Fredlund DG, Morgenstern NR (1977) Stress state variables for unsaturated soils. J Geotech Eng Div 103(GT5):447–466Google Scholar
  13. 13.
    Gili JA, Alonso EE (2002) Microstructural deformation mechanisms of unsaturated granular soils. Int J Numer Anal Meth Geomech 26(5):433–468. doi: 10.1002/nag.206 CrossRefzbMATHGoogle Scholar
  14. 14.
    Gladkyy A, Schwarze R (2014) Comparison of different capillary bridge models for application in the discrete element method. Granular Matter 16(6):911–920. doi: 10.1007/s10035-014-0527-z CrossRefGoogle Scholar
  15. 15.
    Gray WG, Schrefler BA (2007) Analysis of the solid phase stress tensor in multiphase porous media. Int J Numer Anal Meth Geomech 31(4):541–581. doi: 10.1002/nag.541 CrossRefzbMATHGoogle Scholar
  16. 16.
    Haines WB (1925) Studies in the physical properties of soils: II. A note on the cohesion developed by capillary forces in an ideal soil. J Agric Sci 15:529–535. doi: 10.1017/S0021859600082460 CrossRefGoogle Scholar
  17. 17.
    Hotta K, Takeda K, Iinoya K (1974) The capillary binding force of a liquid bridge. Powder Technol 10(45):231–242. doi: 10.1016/0032-5910(74)85047-3 CrossRefGoogle Scholar
  18. 18.
    Lechman J, Lu N (2008) Capillary force and water retention between two uneven-sized particles. J Eng Mech 134(5):374–384. doi: 10.1061/(ASCE)0733-9399(2008)134:5(374) CrossRefGoogle Scholar
  19. 19.
    Lian G, Thornton C, Adams MJ (1993) A theoretical study of the liquid bridge forces between two rigid spherical bodies. J Colloid Interface Sci 161(1):138–147. doi: 10.1006/jcis.1993.1452 CrossRefGoogle Scholar
  20. 20.
    Liu Z, Yu X, Wan L (2016) Capillary rise method for the measurement of the contact angle of soils. Acta Geotech 11(1):21–35. doi: 10.1007/s11440-014-0352-x CrossRefGoogle Scholar
  21. 21.
    Love A (1927) A treatise on the mathematical theory of elasticity. Cambridge University Press, CambridgezbMATHGoogle Scholar
  22. 22.
    Lowry BJ, Steen PH (1995) Capillary surfaces: Stability from families of equilibria with application to the liquid bridge. Proc R Soc Lond Math Phys Eng Sci 449(1937):411–439. doi: 10.1098/rspa.1995.0051 CrossRefzbMATHGoogle Scholar
  23. 23.
    Lu N, Likos W (2006) Suction stress characteristic curve for unsaturated soil. J Geotech Geoenviron Eng 132(2):131–142. doi: 10.1061/(ASCE)1090-0241(2006)132:2(131) CrossRefGoogle Scholar
  24. 24.
    Mani R, Kadau D, Herrmann HJ (2013) Liquid migration in sheared unsaturated granular media. Granular Matter 15(4):447–454. doi: 10.1007/s10035-012-0387-3 CrossRefGoogle Scholar
  25. 25.
    Mani R, Semprebon C, Kadau D, Herrmann HJ, Brinkmann M, Herminghaus S (2015) Role of contact-angle hysteresis for fluid transport in wet granular matter. Phys Rev E 91:042,204. doi: 10.1103/PhysRevE.91.042204 MathSciNetCrossRefGoogle Scholar
  26. 26.
    Melnikov K, Wittel FK, Herrmann HJ (2016) Micro-mechanical failure analysis of wet granular matter. Acta Geotech 11(3):539–548. doi: 10.1007/s11440-016-0465-5 CrossRefGoogle Scholar
  27. 27.
    Molenkamp F, Nazemi AH (2003) Interactions between two rough spheres, water bridge and water vapour. Géotechnique 53(2):255–264. doi: 10.1680/geot.2003.53.2.255 CrossRefGoogle Scholar
  28. 28.
    Padday JF, Pitt AR (1973) The stability of axisymmetric menisci. Philos Trans R Soc Lond Math Phys Eng Sci 275(1253):489–528. doi: 10.1098/rsta.1973.0113 CrossRefGoogle Scholar
  29. 29.
    Pierrat P, Agrawal DK, Caram HS (1998) Effect of moisture on the yield locus of granular materials: theory of shift. Powder Technol 99(3):220–227. doi: 10.1016/S0032-5910(98)00111-9 CrossRefGoogle Scholar
  30. 30.
    Richefeu V, El Youssoufi MS, Radjaï F (2006) Shear strength properties of wet granular materials. Phys Rev E. doi: 10.1103/PhysRevE.73.051304 Google Scholar
  31. 31.
    Richefeu V, Radjaï F, El Youssoufi M (2006) Stress transmission in wet granular materials. Eur Phys J E 21(4):359–369. doi: 10.1140/epje/i2006-10077-1 CrossRefGoogle Scholar
  32. 32.
    Scheel M, Seemann R, Brinkmann M, Di Michiel M, Sheppard A, Breidenbach B, Herminghaus S (2008) Morphological clues to wet granular pile stability. Nat Mater 7(3):189–193. doi: 10.1038/nmat2117 CrossRefGoogle Scholar
  33. 33.
    Scholtès L, Chareyre B, Nicot F, Darve F (2009) Micromechanics of granular materials with capillary effects. Int J Eng Sci 47(1):64–75. doi: 10.1016/j.ijengsci.2008.07.002 MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Soulié F, Cherblanc F, El Youssoufi M, Saix C (2006) Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials. Int J Numer Anal Meth Geomech 30(3):213–228. doi: 10.1002/nag.476 CrossRefzbMATHGoogle Scholar
  35. 35.
    Than V, Khamseh S, Tang A, Pereira JM, F., FC, Roux JN Basic mechanical properties of wet granular materials: A DEM study. Journal of Engineering Mechanics 0(0):C4016,001 (0). doi: 10.1061/(ASCE)EM.1943-7889.0001043
  36. 36.
    Šmilauer V, Catalano E, Chareyre B, Dorofeenko S, Duriez J, Gladky A, Kozicki J, Modenese C, Scholtès L, Sibille L, Stránský J, Thoeni K (2010) Yade Documentation, 1st edn. The Yade Project.
  37. 37.
    Wan R, Duriez J, Darve F (2015) A tensorial description of stresses in triphasic granular materials with interfaces. Geomech Energy Environ 4:73–87. doi: 10.1016/j.gete.2015.11.004 CrossRefGoogle Scholar
  38. 38.
    Wan R, Khosravani S, Pouragha M (2014) Micromechanical analysis of force transport in wet granular soils. Vadose Zone J 13(5):1–12. doi: 10.2136/vzj2013.06.0113 Google Scholar
  39. 39.
    Wang K, Sun W (2015) Anisotropy of a tensorial Bishop’s coefficient for wetted granular materials. J Eng Mech 0(0):B4015,004. doi: 10.1061/(ASCE)EM.1943-7889.0001005 CrossRefGoogle Scholar
  40. 40.
    Weber J (1966) Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents. Bull de liaison des Ponts et Chaussées 20:1–20Google Scholar
  41. 41.
    Willett CD, Adams MJ, Johnson SA, Seville JPK (2000) Capillary bridges between two spherical bodies. Langmuir 16(24):9396–9405. doi: 10.1021/la000657y CrossRefGoogle Scholar
  42. 42.
    Yunus Y, Vincens E, Cambou B (2010) Numerical local analysis of relevant internal variables for constitutive modelling of granular materials. Int J Numer Anal Meth Geomech 34(11):1101–1123. doi: 10.1002/nag.845 zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of CalgaryCalgaryCanada

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