Skip to main content
SpringerLink
Log in

Effect of Pore-Water Surface Tension on Tensile Strength of Unsaturated Sand

  • Original Paper
  • Published:
Indian Geotechnical Journal Aims and scope Submit manuscript

Abstract

Tensile behaviour of unsaturated sand was investigated both experimentally and theoretically. A custom-built direct tension apparatus was employed to perform direct tension tests on unsaturated sand specimens at different saturations levels and packing dry density. An attempt was made to understand the effect of surface tension of wetting liquid and loading rate on the tensile strength. The magnitude of the tensile strength was found to be dependent on saturation, dry density, loading rate and type of wetting liquid used. It was found that the tensile strength decreases, as the surface tension of the wetting liquid decreases and rate of loading increases; however, the decrease in tensile strength was found to be not proportional to the reduction in the surface tension and unsaturated specimens mobilize higher tensile strength than suggested by the capillary tube model. The experimental results were also compared with the predicted results from two theoretical tensile strength models: the micro-mechanical and the macro-mechanical models. Results predicted using the micro-mechanical model agreed well with the experimental results, but only at lower degree of saturation values. On the other hand, the macro-mechanical model followed the experimental trend for the entire range of saturation reasonably well. At reduced surface tension, both the models under-predicted the experimental results significantly.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

\( \alpha \) :

Contact angle (degrees)

\( \alpha^{\prime} \) :

Inverse of air-entry value [(N/m2)−1]

\( \theta \) :

Filling angle (degrees)

\( \rho_{l} \) :

Density of the liquid (g/cm3)

\( \rho_{s} \) :

Density of the solid (g/cm3)

\( \sigma \) :

Normal stress (N/m2)

\( \sigma^{\prime} \) :

Effective stress (N/m2)

\( \sigma^{s} \) :

Suction stress (N/m2)

\( \sigma_{tc} \) :

Tensile strength in capillary state (N/m2)

\( \sigma_{tf} \) :

Tensile strength in funicular state (N/m2)

\( \sigma_{ti} \) :

Isotropic tensile strength (N/m2)

\( \sigma_{tp} \) :

Tensile strength in pendular state (N/m2)

\( \sigma_{tu} \) :

Uniaxial tensile strength (N/m2)

\( \tau \) :

Shear stress (N/m2)

\( \phi \) :

Internal friction angle (degrees)

\( \varPsi \) :

Matric suction (N/m2)

\( a/d \) :

Particle separation distance ratio

\( a^{\prime} \) :

Schubert’s model parameter

C :

Cohesion (N/m2)

\( d \) :

Diameter of idealized sand particle (Rumpf’s model) (mm)

\( e \) :

Void ratio

\( F_{c} \) :

Force component due to pressure difference across liquid bridge (N)

\( F_{s} \) :

Force component due to surface tension (N)

\( F_{t} \) :

Total bonding force due to surface tension and pressure difference across liquid bridge (N)

\( G_{s} \) :

Specific gravity

\( k \) :

Co-ordination number

\( m_{s} \) :

Mass of the solid (kg)

\( m_{l} \) :

Mass of the liquid (kg)

\( n \) :

Pore-size distribution factor

n p :

Porosity

\( P_{c} \) :

Capillary pressure (N/m2)

\( r,h \) :

Radii of the curvature describing the liquid bridge (Rumpf’s model) (mm)

\( r^{*} ,h^{*} \) :

Dimensionless radii of the curvature describing the water bridge (Rumpf’s model)

\( S \) :

Degree of saturation

\( S_{c} \) :

Capillary saturation

\( S_{e} \) :

Effective or normalized saturation

\( S_{r} \) :

Residual saturation

\( T_{s} \) :

Surface tension (mN/m)

\( u_{a} \) :

Pore-air pressure (N/m2)

\( u_{w} \) :

Pore-water pressure (N/m2)

\( V_{bridge} \) :

Volume of the liquid bridge (mm3)

\( V_{l} \) :

Volume of the liquid (mm3)

\( V_{s} \) :

Volume of the solid (mm3)

\( w \) :

Gravimetric water content

References

  1. Lu N, Kim T-H, Sture S, Likos WJ (2009) Tensile strength of unsaturated sand. J Geotech Geoenviron Eng 135(12):1410–1419

    Google Scholar 

  2. Lu N, Wu B, Tan CP (2007) Tensile strength characteristics of unsaturated sands. J Geotech Geoenviron Eng 133(2):144–154

    Article  Google Scholar 

  3. Fredlund DG, Morgenstern NR, Widger RA (1978) The shear strength of unsaturated soils. Can Geotech J 15(3):313–321

    Article  Google Scholar 

  4. Vanapalli S, Fredlund D, Pufahl D, Clifton A (1996) Model for the prediction of shear strength with respect to soil suction. Can Geotech J 33(3):379–392

    Article  Google Scholar 

  5. Khalili N, Geiser F, Blight G (2004) Effective stress in unsaturated soils: review with new evidence. Int J Geomech 4(2):115–126

    Article  Google Scholar 

  6. Lu N, Likos WJ (2004) Unsaturated soil mechanics. Wiley, New York

    Google Scholar 

  7. Heibrock G, Zeh R, Witt K (2005) Tensile strength of compacted clays. In: Schanz T (ed) Unsaturated soils: Experimental studies. Springer, Berlin pp 395–412

  8. Fredlund D, Xing A, Huang S (1994) Predicting the permeability function for unsaturated soils using the soilwater characteristic curve. Can Geotech J 31(4):533–546

    Article  Google Scholar 

  9. Al-Hussaini MM, Townsend FC (1973) Tensile testing of soils: a literature review. U.S. Army Engineer Waterways Experiment Station, Soils and Pavement Laboratory, Vicksburg, Mississippi

    Google Scholar 

  10. Snyder VA, Miller RD (1985) Tensile strength of unsaturated soils. Soil Sci Soc Am J 49(1):58–65

    Article  Google Scholar 

  11. Leavell DA, Peters JF (1987) Uniaxial tensile test for soil. Technical report GL-87-10. Department of the Army, Waterways Experiment Station, U.S. Army Corps of Engineers, Vicksburg, Mississippi

  12. Kim T-H (2001) Moisture-induced tensile strength and cohesion in sand PhD. thesis. University of Colorado, Boulder

  13. Tamrakar SB, Mitachi T, Toyosawa Y, Itoh K (2005) Tensile strength of compacted and saturated soils using newly developed tensile strength apparatus. Soils Found 45(6):103–111

    Article  Google Scholar 

  14. Lu N, Wu B, Tan C (2005) A tensile strength apparatus for cohesionless soils. In: A. Tarantino, et al (ed) Paper presented at the Advanced Experimental Unsaturated Soil Mechanics, Trento, Italy, pp 105–110

  15. Griffiths D, Lu N (2005) Unsaturated slope stability analysis with steady infiltration or evaporation using elasto-plastic finite elements. Int J Numer Anal Meth Geomech 29(3):249–267

    Article  MATH  Google Scholar 

  16. Perkins SW (1991) Modeling of regolith structure interaction in extraterrestrial constructed facilities. University of Colorado, PhD thesis. Boulder, Columbia

  17. Goulding RB (2006) Tensile strength, shear strength and effective stress for unsaturated sand. PhD thesis. University of Missouri, Columbia

  18. Bishop AW (1959) The principles of effective stress. Teknisk Ukeblad 39:859–863

    Google Scholar 

  19. Rumpf H (1961) The strength of granules and agglomerates. Paper presented at the Agglomeration, New York

  20. Lambe T, Whitman R (1969) Soil mechanics. Wiley, New York

    Google Scholar 

  21. Schubert H (1975) Tensile strength of agglomerates. Powder Technol 11(2):107–119

    Article  Google Scholar 

  22. Schubert H, Herrmann W, Rumpf H (1975) Deformation behaviour of agglomerates under tensile stress. Powder Technol 11(2):121–131

    Article  Google Scholar 

  23. Peirrat P, Caram HS (1997) Tensile strength of wet granular materials. Powder Technol 91(2):81–93

    Google Scholar 

  24. Karube D, Kawai K (2001) The role of pore water in the mechanical behavior of unsaturated soils. Geotech Geol Eng 19(3–4):211–241

    Article  Google Scholar 

  25. Molenkamp F, Nazemi AH (2003) Interactions between two rough spheres, water bridge and water vapour. Géotechnique 53(2):255–264

    Article  Google Scholar 

  26. Lu N, Likos WJ (2006) Suction stress characteristic curve for unsaturated soil. J Geotech Geoenviron Eng 132(2):131–141

    Article  Google Scholar 

  27. Bear J (1972) Dynamics of fluids in porous media. American Elsevier, New York

    MATH  Google Scholar 

  28. Smith JE (1995) The effect of concentration dependent surface tension on vadose zone flow and transport, PhD thesis. University of Waterloo, Canada

  29. Henry E, Smith J, Warrick A (1999) Solubility effects on surfactant-induced unsaturated flow through porous media. J Hydrol 223(3):164–174

    Article  Google Scholar 

  30. Smith JE, Gillham RW (1999) Effects of solute concentration–dependent surface tension on unsaturated flow: laboratory sand column experiments. Water Resour Res 35(4):973–982

    Article  Google Scholar 

  31. Henry E, Smith J, Warrick A (2001) Surfactant effects on unsaturated flow in porous media with hysteresis: horizontal column experiments and numerical modeling. J Hydrol 245(1):73–88

    Article  Google Scholar 

  32. Or D, Tuller M (2005) Capillarity. In: Hillel D (ed) Encyclopedia of Soils in the Environment. Elsevier, Amsterdam, pp 155–164

  33. Cho GC, Santamarina JC (2001) Unsaturated particulate materials—particle-level studies. J Geotech Geoenviron Eng 127(1):84–96

    Article  Google Scholar 

  34. Kim T-H, Sture S (2008) Capillary-induced tensile strength in unsaturated sands. Can Geotech J 45(5):726–737. doi:10.1139/t08-017

    Article  Google Scholar 

  35. Pietsch W, Rumpf H (1967) Haftkraft, kapillardruck, flüssigkeitsvolumen und grenzwinkel einer flüssigkeitsbrücke zwischen zwei kugeln. Chem Ing Tech 39(15):885–893

    Article  Google Scholar 

  36. Schubert H (1984) Capillary forces-modeling and application in particulate technology. Powder Technol 37(1):105–116

    Article  Google Scholar 

  37. Terzaghi K (1943) Theoretical soil mechanics. Wiley, New York

    Book  Google Scholar 

  38. Fredlund DG, Morgenstern NR (1977) Stress state variables for unsaturated soils. J Geotech Geoenviron Eng 103(GT5):447–466

    Google Scholar 

  39. van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898

    Article  Google Scholar 

  40. BASF (2008) Petrochemicals - n-BUTANOL (Technical Leaflet). BASF SE, Ludwigshafen. http://www.solvents.basf.com/portal/load/fid228768/n_Butanol_e_03_08.pdf. Accessed 1 January 2016

  41. Bashir R (2007) Quantification of surfactant induced unsaturated flow in the vadose zone, PhD thesis. McMaster University, Hamilton, Ontario, Canada

  42. Mikulitsch AW, Gudehus G (1995) Uniaxial tension, biaxial loading and wetting tests on Loess. In: Alonso EE, Delages P (eds) Proceeding of the 1st international conference on unsaturated soils, Paris, France 1995. A.A. Balkema, Rotterdam, pp 45–150

    Google Scholar 

  43. Kim T-H, Sture S (2004) Effect of moisture on attraction force in beach sand. Mar Georesour Geotechnol 22(1–2):33–47

    Article  Google Scholar 

  44. Conway JH, Sloane NJA (1988) Sphere packings, lattices and groups. Grundlehren der mathematischen Wissenschaften 290. Springer, New York

    Book  Google Scholar 

  45. Sture S, Costes NC, Batiste SN, Lankton MR, AlShibli KA, Jeremic B, Swanson RA, Frank M (1998) Mechanics of granular materials at low effective stresses. J Aerosp Eng 11(3):67–72

    Article  Google Scholar 

  46. Bikerman JJ (1970) Physical Surfaces. In: Loebl EM (ed) Physical Chemistry. Academic, San Diego

    Google Scholar 

Download references

Acknowledgments

The authors wish to thank Mr. Peter Koudys and Prof. Dieter Stolle of McMaster University for their kind help with the manufacturing of the equipment used in the research presented in this paper. The first author acknowledges the financial assistance provided by NSERC, York University, and MITACS for his Masters studies at York University.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, York University, Toronto, ON, Canada

    Prateek Jindal, Jitendra Sharma & Rashid Bashir

Authors
  1. Prateek Jindal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jitendra Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rashid Bashir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jitendra Sharma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jindal, P., Sharma, J. & Bashir, R. Effect of Pore-Water Surface Tension on Tensile Strength of Unsaturated Sand. Indian Geotech J 46, 276–290 (2016). https://doi.org/10.1007/s40098-016-0184-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40098-016-0184-8

Keywords

Search

Navigation