Water Retention Curve with Different Void Ratios over a Wide Suction Range and Its Application to Shear Strength
Publication: International Journal of Geomechanics
Volume 22, Issue 8
Abstract
Shear strength (τ) analysis has received considerable attention, because of its importance when designing various geotechnical structures, such as tunnels, retaining walls, shallow foundations, and slopes. Predicting the unsaturated τ from water retention curves (WRCs) is an existing method. The validity of this method for the prediction of unsaturated τ over a wide suction (ψ) range has been discussed by several researchers. However, the existing method ignores the influence of void ratio (e), which plays a strong part in the water holding capacity and the τ analysis of unsaturated soils. Therefore, according to an existing WRC equation that distinguishes capillary water and adsorbed water, a new WRC equation was proposed to consider the effect of e on the water holding capacity. In addition, using the e dependent WRC, a new method that predicted the τ of unsaturated silts or silty clays at various e over a wide ψ range (that included the residual zone) was proposed. The prediction of τ by the proposed method produced better predictions for experimental data than that of the existing method.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (U2034204, 52078031), the Beijing Natural Science Foundation (8202038), the Fundamental Research Funds for the Central Universities (2020JBM048, 2020CZ002), and the China State Construction Engineering Corporation (CSCEC-2019-Z-09).
Notation
The following symbols are used in this paper:
- b
- parameter that describes the effect of void ratio on ψc;
- c′
- effective cohesion of saturated soil;
- e
- actual void ratio;
- e0
- reference void ratio;
- erfc()
- complementary error function;
- M
- slope of critical state line;
- Ms
- slope of failure line when ψ > ψmax;
- p′
- effective mean stress;
- pn
- net mean stress;
- q
- deviator stress;
- qmax
- deviator stress that corresponds to maximum effective stress;
- Sr
- degree of saturation;
- Sra
- adsorptive component of degree of saturation;
- Src
- capillary component of degree of saturation;
- ζ
- standard deviation of logtransformed soil pore radius;
- θ0
- adsorptive volumetric water content when ψ = 1 kPa (i.e., does not consider capillary condensation);
- θs
- saturated volumetric water content;
- σ′
- effective normal stress;
- σn
- net normal stress;
- τ
- shear strength;
- τmax
- shear strength that corresponds to maximum effective stress;
- ϕ′
- effective angle of internal friction of saturated soil;
- ϕs
- angle of internal friction when ψ > ψmax;
- χ
- unsaturated effective stress parameter;
- χmax
- effective stress parameter that corresponds to maximum effective stress;
- ψ
- suction;
- ψc
- suction that corresponds to the median pore radius at e;
- ψc0
- suction that corresponds to the median pore radius at e0;
- ψd
- suction at oven dryness; and
- ψmax
- suction that corresponds to maximum effective stress.
References
Alonso, E. E., J.-M. Pereira, J. Vaunat, and S. Olivella. 2010. “A microstructurally based effective stress for unsaturated soils.” Géotechnique 60 (12): 913–925. https://doi.org/10.1680/geot.8.P.002.
Brooks, R. H., and A. T. Corey. 1964. Hydraulic properties of porous media, Hydrology Paper No. 3. Fort Collins, CO: Colorado State Univ.
Brunauer, S., P. H. Emmett, and E. Teller. 1938. “Adsorption of gases in multimolecular layers.” J. Am. Chem. Soc. 60 (2): 309–319. https://doi.org/10.1021/ja01269a023.
Campbell, G. S., J. D. Jungbauer, S. Shiozawa, and R. D. Hungerford. 1993. “A one-parameter equation for water sorption isotherms of soils.” Soil Sci. 156 (5): 302–305. https://doi.org/10.1097/00010694-199311000-00002.
Campbell, G. S., and S. Shiozawa. 1992. “Prediction of hydraulic properties of soils using particle-size distribution and bulk density data.” In Indirect methods for estimating the hydraulic properties of unsaturated soils, edited by M. T. van Genuchten, F. J. Leij, and L. J. Lund, 317–328. Riverside, CA: USDA, U.S. Salinity Laboratory.
Chen, Y., H. Lin, R. Cao, and C. Zhang. 2021. “Slope stability analysis considering different contributions of shear strength parameters.” Int. J. Geomech. 21 (3): 04020265. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001937.
Fayer, M. J., and C. S. Simmons. 1995. “Modified soil water retention functions for all matric suctions.” Water Resour. Res. 31 (5): 1233–1238. https://doi.org/10.1029/95WR00173.
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 strength to the soil-water characteristic curve.” Can. Geotech. J. 33 (3): 440–448. https://doi.org/10.1139/t96-065.
Gao, Y., D. Sun, A. Zhou, and J. Li. 2020. “Predicting shear strength of unsaturated soils over wide suction range.” Int. J. Geomech. 20 (2): 04019175. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001555.
Gao, Y., D. Sun, A. Zhou, and J. Li. 2018. “Effect of stress state on soil–water retention and its application on the strength prediction.” Géotechnique Lett. 8 (4): 324–329. https://doi.org/10.1680/jgele.18.00159.
Gao, Y., D. Sun, Z. Zhu, and Y. Xu. 2019. “Hydromechanical behavior of unsaturated soil with different initial densities over a wide suction range.” Acta Geotech. 14 (2): 417–428. https://doi.org/10.1007/s11440-018-0662-5.
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 Soil, Geotechnical Special Publication 147, edited by G. A. Miller, C. E. Zapata, S. L. Houston, and D. G. Fredlund, 2570–2592. Reston, VA: ASCE.
Hou, C., and X. Yang. 2021. “Three-dimensional face stability of tunnels in unsaturated soils with nonlinear soil strength.” Int. J. Geomech. 21 (4): 06021006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001916.
Khalili, N., and M. H. 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.
Khlosi, M., W. M. Cornelis, A. Douaik, M. T. van Genuchten, and D. Gabriels. 2008. “Performance evaluation of models that describe the soil water retention curve between saturation and oven dryness.” Vadose Zone J. 7 (1): 87–96. https://doi.org/10.2136/vzj2007.0099.
Khlosi, M., W. M. Cornelis, D. Gabriels, and G. Sin. 2006. “Simple modification to describe the soil water retention curve between saturation and oven dryness.” Water Resour. Res. 42 (11): W11501. https://doi.org/10.1029/2005WR004699.
Konrad, J.-M., and M. Lebeau. 2015. “Capillary-based effective stress formulation for predicting shear strength of unsaturated soils.” Can. Geotech. J. 52 (12): 2067–2076. https://doi.org/10.1139/cgj-2014-0300.
Kosugi, K. 1996. “Lognormal distribution model for unsaturated soil hydraulic properties.” Water Resour. Res. 32 (9): 2697–2703. https://doi.org/10.1029/96WR01776.
Kosugi, K. 1999. “General model for unsaturated hydraulic conductivity for soils with lognormal pore-size distribution.” Soil Sci. Soc. Am. J. 63 (2): 270–277. https://doi.org/10.2136/sssaj1999.03615995006300020003x.
Lu, N. 2016. “Generalized soil water retention equation for adsorption and capillarity.” J. Geotech. Geoenviron. Eng. 142 (10): 04016051. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001524.
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.
Ng, C. W. W., H. Sadeghi, and F. Jafarzadeh. 2017. “Compression and shear strength characteristics of compacted loess at high suctions.” Can. Geotech. J. 54 (5): 690–699. https://doi.org/10.1139/cgj-2016-0347.
Oh, S., and N. Lu. 2015. “Slope stability analysis under unsaturated conditions: Case studies of rainfall-induced failure of cut slopes.” Eng. Geol. 184: 96–103. https://doi.org/10.1016/j.enggeo.2014.11.007.
Rosone, M., C. Farulla, and A. Ferrari. 2016. “Shear strength of a compacted scaly clay in variable saturation conditions.” Acta Geotech. 11 (1): 37–50. https://doi.org/10.1007/s11440-015-0379-7.
Salager, S., M. Nuth, A. Ferrari, and L. Laloui. 2013. “Investigation into water retention behaviour of deformable soils.” Can. Geotech. J. 50 (2): 200–208. https://doi.org/10.1139/cgj-2011-0409.
Sheng, D., A. Zhou, and D. G. Fredlund. 2011. “Shear strength criteria for unsaturated soils.” Geotech. Geol. Eng. 29 (2): 145–159. https://doi.org/10.1007/s10706-009-9276-x.
Sun, C., J. Chai, T. Luo, Z. Xu, X. Chen, Y. Qin, and B. Ma. 2021. “Nonlinear Shear-strength reduction technique for stability analysis of uniform cohesive slopes with a general nonlinear failure criterion.” Int. J. Geomech. 21 (1): 06020033. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001885.
Sun, D., H. Matsuoka, Y.-P. Yao, and W. Ichihara. 2000. “An elasto-plastic model for unsaturated soil in three-dimensional stresses.” Soils Found. 40 (3): 17–28. https://doi.org/10.3208/sandf.40.3_17.
Sun, D., D. Sheng, and Y. Xu. 2007. “Collapse behaviour of unsaturated compacted soil with different initial densities.” Can. Geotech. J. 44 (6): 673–686. https://doi.org/10.1139/t07-023.
Tang, Y., H. A. Taiebat, and A. R. Russell. 2017. “Bearing capacity of shallow foundations in unsaturated soil considering hydraulic hysteresis and three drainage conditions.” Int. J. Geomech. 17 (6): 04016142. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000845.
Tekinsoy, M. A., C. Kayadelen, M. S. Keskin, and M. Soylemez. 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.
Vanapalli, S. K., D. G. Fredlund, and D. E. Pufahl. 1999. “The influence of soil structure and stress history on the soil-water characteristics of a compacted till.” Géotechnique 49 (2): 143–159. https://doi.org/10.1680/geot.1999.49.2.143.
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.
Van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Zhang, C.-g., X.-d. Chen, and W. Fan. 2016. “Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity.” J. Cent. South Univ. 23 (4): 944–954. https://doi.org/10.1007/s11771-016-3142-9.
Zhou, A., R. Huang, and D. Sheng. 2016. “Capillary water retention curve and shear strength of unsaturated soils.” Can. Geotech. J. 53 (6): 974–987. https://doi.org/10.1139/cgj-2015-0322.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 8 • August 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 28, 2021
Accepted: Mar 28, 2022
Published online: Jun 1, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 1, 2022
Authors
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.