Exponential Equation for Predicting Shear Strength Envelope of Unsaturated Soils
Publication: International Journal of Geomechanics
Volume 19, Issue 7
Abstract
An exponential equation is introduced to predict the nonlinear variation of shear strength with matric suction for unsaturated soils. The proposed equation involves three constant parameters, two of which are effective shear strength parameters (i.e., ϕ′ and c′). The third parameter is the maximum capillary cohesion, , which is the maximum possible increase in shear strength due to matric suction. A procedure for the determination of from the soil-water characteristic curve (SWCC) is devised. The proposed equation is validated through a series of constant-suction consolidated drained triaxial tests conducted on specimens reconstituted by isotropic consolidation from the slurry state. In addition, the validity of the equation is investigated by applying it to the test results of five other soils that were available in the literature for the low-suction range (i.e., up to 1,500 kPa). A comparative study on the prediction of shear strength was carried out between the proposed equation and six other shear strength equations found in the literature. The results show that the proposed equation provides reliable predictions of the shear strength of unsaturated soils when the shear strength converges to an asymptotic value at the residual water content.
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References
Ahmadi-Naghadeh, R. 2016. “Hydro-mechanical behavior of unsaturated specimens isotropically reconstituted from slurry and compacted specimens.” Ph.D. thesis, Middle East Technical Univ.
Ahmadi-Naghadeh, R., and N. K. Toker. 2017. “Volume change measurement in triaxial tests by monitoring cell fluid volume based on viscoelastic behavior of the test setup.” Geotech. Test. J. 40 (4): 683–697.
Ahmadi-Naghadeh, R., and N. K. Toker. 2018. “A new isotropic specimen preparation method from slurry for both saturated and unsaturated triaxial testing of a low-plasticity silt.” Geotech. Test. J. 42 (4): GTJ20170269. https://doi.org/10.1520/GTJ20170269.
Al Aqtash, U., and P. Bandini. 2015. “Prediction of unsaturated shear strength of an adobe soil from the soil–water characteristic curve.” Constr. Build. Mater. 98: 892–899. https://doi.org/10.1016/j.conbuildmat.2015.07.188.
Bao, C., B. Gong, and L. Zhan. 1998. “Properties of unsaturated soils and slope stability of expansive soils, keynote lecture.” In Proc., 2nd Int. Conf. on Unsaturated Soils (UNSAT 98), 71–98. Beijing: International Academic.
Bishop, A. 1959. “The principle of effective stress.” Teknisk Ukeblad 106 (39): 859–863.
Bishop, A. W., I. Alpan, G. E. Blight, and I. B. Donald. 1960. “Factors controlling the strength of partially saturated cohesive soils.” In Proc., Research Conf. on Shear Strength of Cohesive Soils, 503–532. Reston, VA: ASCE.
Bishop, A. W., and I. B. Donald. 1961. “The experimental study of partly saturated soil in the triaxial apparatus.” In 5th Int. Conf. on Soil Mechanics and Foundation Engineering, 13–21. Paris: Dunod.
Brooks, R. H., and A. T. Corey. 1964. Hydraulic properties of porous media. Hydrology Paper No. 3. Fort Collins, CO: Colorado State Univ.
Cunningham, M. R., A. M. Ridley, K. Dineen, and J. B. Burland. 2003. “The mechanical behaviour of a reconstituted unsaturated silty clay.” Géotechnique 53 (2): 183–194. https://doi.org/10.1680/geot.2003.53.2.183.
Escario, V., and J. F. T. Jucá. 1989. “Strength and deformation of partly saturated soils.” In Vol. 2 of Proc., 12th Int. Conf. on Soil Mechanics and Foundation Engineering, 43–46. Boca Raton, FL: CRC.
Fredlund, D. G. 1975. “A diffused air volume indicator for unsaturated soils.” Can. Geotech. J. 12 (4): 533–539. https://doi.org/10.1139/t75-061.
Fredlund, D. G., and N. R. Morgenstern. 1977. “Stress state variables for saturated and unsaturated soils.” J. Geotech. Eng. Div. 103 (5): 447–466.
Fredlund, D. G., N. R. Morgenstern, and R. A. Widger. 1978. “The shear strength of unsaturated soils.” Can. Geotech. J. 15 (3): 313–321. https://doi.org/10.1139/t78-029.
Fredlund, D. G., G. W. Wilson, and S. L. Barbour. 2001. “Unsaturated soil mechanics and property assessment.” In Geotechnical and geoenvironmental engineering handbook, edited by R. K. Rowe, 107–146. Berlin: Springer.
Fredlund, D. G., and A. Xing. 1994. “Equations for the soil-water characteristic curve.” Can. Geotech. J. 31 (4): 521–532. https://doi.org/10.1139/t94-061.
Fredlund, D. G., A. Xing, M. D. Fredlund, and S. L. Barbour. 1996. “The relationship of the unsaturated soil shear to the soil-water characteristic curve.” Can. Geotech. J. 33 (3): 440–448. https://doi.org/10.1139/t96-065.
Gan, J. K. M., D. G. Fredlund, and H. Rahardjo. 1988. “Determination of the shear strength parameters of an unsaturated soil using the direct shear test.” Can. Geotech. J. 25 (3): 500–510. https://doi.org/10.1139/t88-055.
Garven, E. A., and S. K. Vanapalli. 2006. “Evaluation of empirical procedures for predicting the shear strength of unsaturated soils.” In Proc., 4th Int. Conf. on Unsaturated Soils 2006, 2570–2581. Reston, VA: ASCE.
Goh, S. G. 2012. “Hysteresis effects on mechanical behaviour of unsaturated soils.” Ph.D. thesis, School of Civil and Environmental Engineering, Nanyang Technological Univ.
Hilf, J. W. 1956. “An investigation of pore-water pressure in compacted cohesive soils.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Colorado.
Jennings, J. E. B., and J. B. Burland. 1962. “Limitations to the use of effective stresses in partly saturated soils.” Géotechnique 12 (2): 125–144. https://doi.org/10.1680/geot.1962.12.2.125.
Karube, D., S. Kato, M. Honda, and K. Tsurugasaki. 1997. “The relationship between shearing characteristics and the composition of pore-water in unsaturated soil.” Doboku Gakkai Ronbunshu 1997 (575): 49–58. https://doi.org/10.2208/jscej.1997.575_49.
Kayadelen, C., M. A. Tekinsoy, and T. Taşkıran. 2007. “Influence of matric suction on shear strength behavior of a residual clayey soil.” Environ. Geol. 53 (4): 891–901. https://doi.org/10.1007/s00254-007-0701-2.
Khalili, N., F. Geiser, and G. E. Blight. 2004. “Effective stress in unsaturated soils: A review with new evidence.” Int. J. Geomech. 4 (2): 115–126. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:2(115).
Khalili, N., and M. Khabbaz. 1998. “A unique relationship for χ for the determination of the shear strength of unsaturated soils.” Géotechnique 48 (5): 681–687. https://doi.org/10.1680/geot.1998.48.5.681.
Lee, I. M., S. G. Sung, and G. C. Cho. 2005. “Effect of stress state on the unsaturated shear strength of a weathered granite.” Can. Geotech. J. 42 (2): 624–631. https://doi.org/10.1139/t04-091.
Lu, N., and W. J. Likos. 2004. Unsaturated soil mechanics. Hoboken, NJ: Wiley.
Melgarejo Corredor, M. L. 2004. “Laboratory and numerical investigations of soil retention curves.” Ph.D. thesis, Imperial College London.
Miao, L., S. Liu, and Y. Lai. 2002. “Research of soil–water characteristics and shear strength features of Nanyang expansive soil.” Eng. Geol. 65 (4): 261–267. https://doi.org/10.1016/S0013-7952(01)00136-3.
Montanez, J. E. C. 2002. “Suction and volume changes of compacted sand-bentonite mixtures.” Ph.D. thesis, Univ. of London.
Nash, J. E., and J. V. Sutcliffe. 1970. “River flow forecasting through conceptual models part I—A discussion of principles.” J. Hydrol. 10 (3): 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.
Nishimura, T., S. H. Mydin, S. Ogawa, Y. Endou, and H. Toyota. 1997. “Constitutive surface for unsaturated soils.” In Proc., Prefailure Deformation Characteristics of Geomaterials (IS-NAGOYA 97), 425–430. Rotterdam, Netherlands: A. A. Balkema.
Öberg, A., and G. Sällfors. 1997. “Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve.” Geotech. Test. J. 20 (1): 40–48. https://doi.org/10.1520/GTJ11419J.
Oloo, S. Y., and D. G. Fredlund. 1996. “A method for determination of ϕb for statically compacted soils.” Can. Geotech. J. 33 (2): 272–280. https://doi.org/10.1139/t96-006.
Patil, U. D., L. R. Hoyos, and A. J. Puppala. 2016a. “Modeling essential elastoplastic features of compacted silty sand via suction-controlled triaxial testing.” Int. J. Geomech. 16 (6): D4016012. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000726.
Patil, U. D., L. R. Hoyos, and A. J. Puppala. 2016b. “Characterization of compacted silty sand using a double-walled triaxial cell with fully automated relative-humidity control.” Geotech. Test. J. 39 (5): 742–756. https://doi.org/10.1520/GTJ20150156.
Patil, U. D., A. J. Puppala, L. R. Hoyos, and A. Pedarla. 2017. “Modeling critical-state shear strength behavior of compacted silty sand via suction-controlled triaxial testing.” Eng. Geol. 231: 21–33. https://doi.org/10.1016/j.enggeo.2017.10.011.
Rassam, D. W., and F. Cook. 2002. “Predicting the shear strength envelope of unsaturated soils.” Geotech. Test. J. 25 (2): 215–220. https://doi.org/10.1520/GTJ11365J.
Rojas, E. 2008a. “Equivalent stress equation for unsaturated soils. I: Equivalent stress.” Int. J. Geomech. 8 (5): 285–290. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:5(285).
Rojas, E. 2008b. “Equivalent stress equation for unsaturated soils. II: Solid-porous model.” Int. J. Geomech. 8 (5): 291–299. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:5(291).
Tekinsoy, M. A., C. Kayadelen, M. S. Keskin, and M. Söylemez. 2004. “An equation for predicting shear strength envelope with respect to matric suction.” Comput. Geotech. 31 (7): 589–593. https://doi.org/10.1016/j.compgeo.2004.08.001.
Terzaghi, K. 1925. Erdbaumechanik auf bodenphysikalischer grundlage. Leipzig, Germany: Franz Deuticke.
Terzaghi, K. 1936. “The shearing resistance of saturated soils and the angle between the planes of shear.” In Vol. 1 of Proc., Int. Conf. on Soil Mechanics and Foundation Engineering, 54–56. Cambridge, MA: Harvard University Press.
Thu, T. M. 2006. “Shear strength and volume change relationship for an unsaturated soil.” Ph.D. thesis, School of Civil and Environmental Engineering, Nanyang Technological Univ.
Vanapalli, S. K. 1994. “Simple test procedures and their interpretation in evaluating the shear strength of unsaturated soils.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Saskatchewan.
Vanapalli, S. K., and D. G. Fredlund. 2000. “Comparison of different procedures to predict unsaturated soil shear strength.” In Proc., Geo-Denver 2000: Advanced in Unsaturated Geotechnics, 195–209. Reston, VA: ASCE.
Vanapalli, S. K., D. G. Fredlund, D. E. Pufahl, and A. W. Clifton. 1996. “Model for the prediction of shear strength with respect to soil suction.” Can. Geotech. J. 33 (3): 379–392. https://doi.org/10.1139/t96-060.
Vilar, O. M. 2006. “A simplified procedure to estimate the shear strength envelope of unsaturated soils.” Can. Geotech. J. 43 (10): 1088–1095. https://doi.org/10.1139/t06-055.
White, N. F., H. R. Duke, D. K. Sunada, and A. T. Corey. 1970. “Physics of desaturation in porous materials.” J. Irrig. Drain. Div. 96 (2): 165–191.
Xu, Y. F. 2004. “Fractal approach to unsaturated shear strength.” J. Geotech. Geoenviron. Eng. 130 (3): 264–273. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:3(264).
Xu, Y. F., and L. Cao. 2015. “Fractal representation of effective stress of unsaturated soils.” Int. J. Geomech. 15 (6): 04014098. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000446.
Zargarbashi, S., and N. Khalili. 2011. “Discussion of ‘Shear Strength Equations for Unsaturated Soil under Drying and Wetting’ by Goh Shin Guan, Harianto Rahardjo, and Leong Eng Choon.” J. Geotech. Geoenviron. Eng. 137 (12): 1310–1313. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000455.
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© 2019 American Society of Civil Engineers.
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Received: Apr 11, 2018
Accepted: Dec 31, 2018
Published online: Apr 16, 2019
Published in print: Jul 1, 2019
Discussion open until: Sep 16, 2019
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