Technical Papers
Oct 16, 2014

Fractal Representation for Effective Stress of Unsaturated Soils

Publication: International Journal of Geomechanics
Volume 15, Issue 6

Abstract

Bishop’s effective stress equation for unsaturated soils was abandoned for some time because of the difficulties in estimating the value of parameter χ. Only recently has it been recognized that the use of Bishop’s stress equation can lead to simpler and more realistic constitutive models for unsaturated soils. Based on the analysis of the equilibrium of solid particles, it was possible to establish an analytical expression for Bishop’s parameter χ from soil pore structure. It is shown that quantitative predictions of shear strength and volume change in unsaturated soils can be made using the effective stress concept.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The National Nature Science Foundation of China (Grant No.41272318) is acknowledged for its financial support. Ahment H. Aydilek, Associate Professor of the Department of Civil and Environmental Engineering, University of Maryland is also acknowledged for his kind help.

References

Alonso, E. E., Pereira, J.-M., Vaunat, J., and Olivella, S. (2010). “A microstructurally based effective stress for unsaturated soils.” Géotechnique, 60(12), 913–925.
Avnir, D., Farin, D., and Pfeifer, P. (1984). “Molecular fractal surfaces.” Nature, 308(Mar), 261–263.
Bishop, A. W. (1959). “The principle of effective stress.” Teknisk Ukeblad., 106, 859–863.
Bishop, A. W., and Blight, G. E. (1963). “Some aspects of effective stress in saturated and partly saturated soils.” Géotechnique, 13(3), 177–197.
Blight, G. E. (1967). “Effective stress evaluation for unsaturated soils.” J. Soil Mech. and Found. Div., 93(2), 125–148.
Bolzon, G., Schrefler, B. A., and Zienkiewicz, O. C. (1996). “Elastoplastic soil constitutive laws generalized to partially saturated states.” Géotechnique, 46(2), 279–289.
Burland, J. B. (1965). “Some aspects of the mechanical behaviour of partly saturated soils.” Moisture equilibria and moisture changes in the soils beneath covered areas, G. D. Aitchison, ed., Butterworth, Sydney, Australia, 270–278.
Butterfield, R. (1979). “A natural compression law for soils (an advance on elogp).” Géotechnique, 29(4), 469–480.
Chen, Z. H., Xie, D. Y., and Wang, Y. S. (1994). “Effective stress in unsaturated soils.” Chin. Geotech. Eng., 16(3), 62–69.
Coleman, J. D. (1962). “Stress-strain relations for partially saturated soils.” Géotechnique, 12(4), 348–350.
Cunningham, M. R., Ridley, A. M., Dineen, K., and Burland, J. B. (2003). “The mechanical behaviour of a reconstituted unsaturated silty clay.” Géotechnique, 53(2), 183–194.
Donald, I. B. (1956). “Shear strength measurements in unsaturated noncohesive soils with negative pore water pressure.” Proc., 2nd Australia-New Zealand Conf. on Soil Mechanics and Foundation Engineering, New Zealand Institution of Engineers, Wellington, New Zealand, 200–205.
Fredlund, D. G., and Morgenstern, N. R. (1977). “Stress state variables for unsaturated soils.” ABB Rev., 103(5), 447–466.
Futai, M. M., Almeida, M. S. S., and Lacerda, W. A. (2006). “The shear strength of unsaturated tropical soil in Ouro Preto, Brazil.” Proc., 4th Int. Conf. on Unsaturated Soils, Geotechnical special publication 147, G. A. Miller, C. E. Zapata, S. L. Houston, and D. G. Fredlund, eds., ASCE, Reston, VA, 1200–1211.
Gens, A., and Alonso, E. E. (1992). “A framework for the behaviour of unsaturated expansive clays.” Can. Geotech. J., 29(6), 1013–1032.
Hashiguchi, K. (1995). “On the linear relations of Vlnp and lnvlnp for isotropic consolidation of soils.” Int. J. Numer. Anal. Methods Geomech., 19(5), 367–376.
Jennings, J. E. B., and Burland, J. B. (1962). “Limitations to the use of effective stresses in partly saturated soils.” Géotechnique, 12(2), 125–144.
Khalili, N., Geiser, F., and Blight, G. E. (2004). “Effective stress in unsaturated soils: Review with new evidence.” Int. J. Geomech., 115–126.
Khalili, N., and Khabbaz, M. H. (1998). “A unique relationship for χ for the determination of the shear strength of unsaturated soils.” Géotechnique, 48(5), 681–687.
Lee, I.-M., Sung, S.-G., and Cho, G.-C. (2005). “Effect of stress state on the unsaturated shear strength of a weathered granite.” Can. Geotech. J., 42(2), 624–631.
Lloret, A., Villar, M. V., Sánchez, M., Gens, A., Pintado, X., and Alonso, E. E. (2003). “Mechanical behaviour of heavily compacted bentonite under high suction changes.” Géotechnique, 53(1), 27–40.
Lu, N. (2008). “Is matric suction a stress variable?” J. Geotech. Geoenviron. Eng., 899–905.
Mandelbrot, B. B. (1982). The fractal geometry of nature, Freeman, San Francisco.
Mitchell, J. K. (1976). Fundamentals of soil behavior, Wiley, New York.
Öberg, A. L., and Sällfors, G. (1997). “Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve.” Geotech. Test. J., 20(1), 40–48.
Rahardjo, H., Indrawan, I. G. B., Leong, E. C., and Yong, W. K. (2008). “Effects of coarse-grained material on hydraulic properties and shear strength of top soil.” Eng. Geol., 101(3–4), 165–173.
Röhm, S. A., and Vilar, O. M. (1995). “Shear strength of an unsaturated sandy soil.” Proc., 1st Int. Conf. on Unsaturated Soils, E. E. Alonso and P. Delage, eds., Vol. 1, Balkema, Rotterdam, Netherlands, 31–38.
Rojas, E. (2008). “Equivalent stress equation for unsaturated soils. I: Equivalent stress.” Int. J. Geomech., 285–290.
Sołowski, W. T., and Sloan, S. W. (2014). “Equivalent stress approach in creation of elastoplastic constitutive models for unsaturated soils.” Int. J. Geomech., 04014041.
Sun, D., Sheng, D., Li, X., and Sloan, S. W. (2008). “Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions.” Comput. Geotech., 35(6), 845–852.
Terzaghi, K. (1936). “The shear resistance of unsaturated soil.” Proc., 1st Int. Conf. on Soil Mechanics and Foundation Engineering, Harvard Printing Office, Cambridge, MA, 54–56.
Vanapalli, S. K., Fredlund, D. E., Pufahl, D. E., and Clifton, A. W. (1996). “Model for the prediction of shear strength with respect to soil suction.” Can. Geotech. J., 33(3), 379–392.
Wheeler, S. J., and Karube, D. (1995). “Constitutive modeling.” Proc., 1st Int Conf. on Unsaturated Soils, E. E. Alonso and P. Delage, eds., Balkema, Rotterdam, Netherlands.
Wheeler, S. J., Sharma, R. S., and Buisson, M. S. R. (2003). “Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils.” Géotechnique, 53(1), 41–54.
Xu, Y. F. (2004). “Fractal approach to unsaturated shear strength.” J. Geotech. Geoenviron. Eng., 264–273.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 15Issue 6December 2015

History

Received: Sep 3, 2013
Accepted: Sep 2, 2014
Published online: Oct 16, 2014
Published in print: Dec 1, 2015

Permissions

Request permissions for this article.

Authors

Affiliations

Professor, Dept. of Civil Engineering, Shanghai Jiao Tong Univ., Shanghai 200240, China (corresponding author). E-mail: [email protected]
Ling Cao
Ph.D. Candidate, Dept. of Civil Engineering, Shanghai Jiao Tong Univ., Shanghai 200240, China.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share