Coupled Hydro-Mechanical Elastoplastic Constitutive Model for Unsaturated Sands and Silts. I: Formulation
Publication: International Journal of Geomechanics
Volume 12, Issue 3
Abstract
Unsaturated soils are three-phase porous media consisting of a solid skeleton, pore water, and pore air. The behavior of unsaturated soils is strongly influenced by the matric suction (pore air pressure minus the pore water pressure). Soil water characteristic curves (SWCCs) describe the relationship between matric suction and water content in unsaturated soils and, therefore, capture the hydro-behavior of soils. SWCCs show hysteretic behavior that not only depends on the wetting or drying history of the soil, but also on the stress-strain history (mechanical behavior) of a soil. The hydro-behavior of unsaturated soils, on the other hand, influences the mechanical behavior through matric suction. To predict the behavior of unsaturated soils, a hysteretic SWCC model is proposed based on the bounding surface plasticity concept. The model for hysteretic SWCCs is then incorporated into a constitutive model for unsaturated sands and silts in the general stress space. The resulting model is a comprehensive constitutive model that accounts for the coupling effects between hydro- and mechanical behavior of unsaturated sands and silts in the general stress space. The numerical integration of the constitutive equations and model calibration and validation are presented in a companion paper.
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Acknowledgments
This work was supported by the U.S. National Science Foundation (Grant No. CMS-0301457) and the Oklahoma Center for the Advancement of Science and Technology (Project No. AR081-045).
References
Alonso, E. E., Gens, A., and Josa, A. (1990). “A constitutive model for partially saturated soils.” Geotechnique, 40(3), 405–430.GTNQA8
Bishop, A. W. (1959). “The principle of effective stress.” Tek. Ukebl., TUGEAJ106(39), 113–143.
Borja, R. I. (2006). “On the mechanical energy and effective stress in saturated and unsaturated porous continua.” Int. J. Solids Struct., 43(6), 1764–1786.IJSOAD
Chen, L. X., Miller, G. A., and Kibbey, T. C. G. (2007). “Rapid pseudo-static measurement of hysteretic capillary pressure-saturation relationships in unconsolidated porous media.” ASTM Geotech. Test. J.GTJODJ, 30(6), 1–10.
Cheng, J. T., Pyrak-Nolte, L. J., Nolte, D. D., and Giordano, N. J. (2004). “Linking pressure and saturation through interfacial areas in porous media.” Geophys. Res. Lett., 31(8), L08502-.GPRLAJ
Croney, D. (1952). “The movement and distribution of water in soils.” Geotechnique, 3(1), 1–16.GTNQA8
Croney, D., Coleman, D. J., and Black, W. P. M. (1958). “Movement and distribution of water in soil in relation to highway design and performance.” Highway Research Board Special Rep. No. 40, Highway Research Board, Washington, DC, 226–252.
Dafalias, Y. F. (1986). “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.” J. Eng. Mech.JENMDT, 112(9), 966–987.
Dafalias, Y. F., and Manzari, M. T. (2004). “Simple plasticity sand model accounting for fabric change effects.” J. Eng. Mech.JENMDT, 130(6), 622–634.
Dafalias, Y. F., Papadimitriou, A. G., and Li, X. S. (2004). “Sand plasticity model accounting for inherent fabric anisotropy.” J. Eng. Mech.JENMDT, 130(11), 1319–1333.
Dafalias, Y. F., and Popov, E. P. (1976). “Plastic internal variables formalism of cyclic plasticity.” J. Appl. Mech., 43(4), 645–651.JAMCAV
Dangla, P., Malinsky, L., and Coussy, O. (1997). “Plasticity and imbibition-drainage curves for unsaturated soils: A unified approach.” Proc., 6th Int. Conf. on Numerical Models in Geomechanics, Montreal, Balkema, Rotterdam, Netherlands, 141–146.
Farias, M. M., Pinheiro, M., and Neto, M. P. C. (2006). “An elastoplastic model for unsaturated soils under general three-dimensional conditions.” Soil Found., 46(5), 613–628.
Feng, M., and Fredlund, D. G. (1999). “Hysteretic influence associated with thermal conductivity sensor measurements.” From Theory to the Practice of Unsaturated Soil Mechanics, Proc., 52nd Canadian Geotechnical Conf. and Unsaturated Soil Group, Regina, 651–657.
Geiser, F., Laloui, L., and Vulliet, L. (2006). “Elasto-plasticity of unsaturated soils: Laboratory test results on a remoulded silt.” Soil Found., 46(5), 545–556.
Gillham, R. W., Klute, A., and Heermann, D. F. (1976). “Hydraulic properties of a porous medium: Measurement and empirical representation.” Soil Sci. Soc. Am. J.SSSJD4, 40(2), 203–207.
Hassanizadeh, S. M., and Gray, W. G. (1993). “Thermodynamic basis of capillary pressure in porous media.” Water Resour. Res., 29(10), 3389–3405.WRERAQ
Held, R. J., and Celia, M. A. (2001). “Modeling support of functional relationships between capillary pressure, saturation, interfacial area and common lines.” Adv. Water Resour., 24(3–4), 325–343.AWREDI
Houlsby, G. T. (1997). “The work input to an unsaturated granular material.” Geotechnique, 47(1), 193–196.GTNQA8
Khalili, N., Habte, M. A., and Zargarbashi, S. (2008). “A fully coupled flow deformation model for cyclic analysis of unsaturated soils including hydraulic and mechanical hystereses.” Comput. Geotech., 35(6), 872–889.CGEOEU
Khalili, N., Witt, R., Laloui, L., Vulliet, L., and Koliji, A. (2005). “Effective stress in double porous media with two immiscible fluids.” Geophys. Res. Lett., 32(15), L15309.GPRLAJ
Kohgo, Y. (2008). “A hysteresis model of soil water retention curves based on bounding surface concept.” Soil Found., 48(5), 633–640.
Li, X. S. (1997). “Modeling of dilative shear failure.” J. Geotech. Geoenviron. Eng., 123(7), 609–616.JGGEFK
Li, X. S. (2003). “Effective stress in unsaturated soil: A microstructural analysis.” Geotechnique, 53(2), 273–277.GTNQA8
Li, X. S. (2005). “Modelling of hysteresis response for arbitrary wetting/drying paths.” Comput. Geotech., 32(2), 133–137.CGEOEU
Li, X. S. (2007a). “Thermodynamics-based constitutive framework for unsaturated soils. 1: Theory.” Geotechnique, 57(5), 411–422.GTNQA8
Li, X. S. (2007b). “Thermodynamics-based constitutive framework for unsaturated soils. 2: A basic triaxial model.” Geotechnique, 57(5), 423–435.GTNQA8
Liu, C. (2009). “A coupled hydraulic-mechanical elastoplastic constitutive model for unsaturated sands and silts.” Ph.D. dissertation, Univ. of Oklahoma, Norman, OK.
Liu, C., and Muraleetharan, K. K. (2006). “Description of soil water characteristic curves using the bounding surface plasticity theory.” Proc., 4th Int. Conf. on Unsaturated Soils, GSP No. 147, Vol. 2, Miller, G. A., Zapata, C. E., Houston, S. L. and Fredlund, D. G., eds., Geo-Institute, ASCE, Carefree, AZ, 2432–2440.
Loret, B., and Khalili, N. (2000). “A three-phase model for unsaturated soils.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 24(11), 893–927.
Maâtouk, A., Leroueil, S., and La Rochelle, P. (1995). “Yielding and critical state of a collapsible unsaturated silty soil.” Geotechnique, 45(3), 465–477.GTNQA8
Manzari, M. T., and Dafalias, Y. F. (1997). “A critical state two-surface plasticity model for sands.” Geotechnique, 47(2), 255–272.GTNQA8
Manzari, M. T., and Prachathananukit, R. (2001). “On integration of a cyclic soil plasticity model.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 25(6), 525–549.
Miller, G. A., Khoury, C. N., Muraleetharan, K. K., Liu, C., and Kibbey, T. C. G. (2008). “Effects of soil skeleton deformations on hysteretic soil water characteristic curves: experiments and simulations.” Water Resour. Res., 44, W00C06.WRERAQ
Morrow, N. R. (1970). “Physics and thermodynamics of capillary action in porous media.” Ind. Eng. Chem., 62(6), 32–56.IECHAD
Muraleetharan, K. K., Liu, C., Wei, C. F., Kibbey, T. C. G., and Chen, L. (2009). “An elastoplastic framework for coupling hydraulic and mechanical behavior of unsaturated soils.” Int. J. Plast., 25(3), 473–490.IJPLER
Murray, E. J. (2002). “An equation of state for unsaturated soils.” Can. Geotech. J.CGJOAH, 39(1), 125–140.
Nova, R., and Wood, M. D. (1979). “A constitutive model for sand in triaxial compression.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 3(3), 255–278.
Pham, H. Q., Fredlund, D. G., and Barbour, S. L. (2003). “A practical hysteresis model for the soil-water characteristic curve for soils with negligible volume change.” Geotechnique, 53(2), 293–298.GTNQA8
Rampino, C., Mancuso, C., and Vinale, F. (2000). “Experimental behaviour and modeling of an unsaturated compacted soil.” Can. Geotech. J.CGJOAH, 37(4), 748–763.
Reeves, P. C., and Celia, M. A. (1996). “A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale model.” Water Resour. Res., 32(8), 2345–2358.WRERAQ
Rojas, E., and Rojas, F. (2005). “Modeling hysteresis of the soil-water characteristic curve.” Soil Found., 45(3), 135–145.
Sheng, D., Sloan, S. W., and Gens, A. (2004). “A constitutive model for unsaturated soils: Thermomechanical and computational aspects.” Comput. Mech., 33(6), 453–465.
Sivakumar, V. (1993). “A critical state framework for unsaturated soil.” Ph.D. dissertation, Univ. of Sheffield, UK.
Taiebat, M., and Dafalias, Y. F. (2008). “SANISAND: Simple anisotropic and plasticity model.” Int. J. Numer. Anal. Methods Geomech.IJNGDZ, 32(8), 915–948.
Terzaghi, K. (1936). “The shear resistance of saturated soils and the angle between the planes of shear.” Proc., 1st Int. Conf. on Soil Mechanics and Foundation Engineering, Vol. 1, 54–56.
Thu, T. M., Rahardjo, H., and Leong, E. C. (2007). “Elastoplastic model for unsaturated soil with incorporation of the soil-water characteristic curve.” Can. Geotech. J.CGJOAH, 44(1), 67–77.
Vaunat, J., Romero, E., and Jommi, C. (2000). “An elastoplastic hydro-mechanical model for unsaturated soils.” Experimental evidence and theoretical approaches in unsaturated soils, Tarantino, A. and Mancuso, C., eds., Balkema, Rotterdam, Netherlands, 121–138.
Wei, C., and Dewoolkar, M. M. (2006). “Formulation of capillary hysteresis with internal state variables.” Water Resour. Res., 42(7), W07405.WRERAQ
Wei, C., and Muraleetharan, K. K. (2002a). “A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity.” Int. J. Eng. Sci., 40(16), 1807–1833.IJESAN
Wei, C., and Muraleetharan, K. K. (2002b). “A continuum theory of porous media saturated by multiple immiscible fluids: II. Lagrangian description and variational structure.” Int. J. Eng. Sci., 40(16), 1835–1854.IJESAN
Wheeler, S. J., Sharma, R. S., and Buisson, M. S. R. (2003). “Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils.” Geotechnique, 53(1), 41–54.GTNQA8
Wood, M. D., Belkheir, K., and Liu, D. F. (1994). “Strain softening and state parameters for sand modelling.” Geotechnique, 44(2), 335–339.GTNQA8
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Information
Published In
International Journal of Geomechanics
Volume 12 • Issue 3 • June 2012
Pages: 239 - 247
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jul 28, 2010
Accepted: May 19, 2011
Published online: May 23, 2011
Published in print: Jun 1, 2012
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