Simple Yield Surface Expressions Appropriate for Soil Plasticity
Publication: International Journal of Geomechanics
Volume 10, Issue 4
Abstract
The objective of this paper is to present a number of simple, practical, and useful analytical expressions of a yield surface for geomaterials. In classical plasticity, the analytical expression of a yield surface defines the locus of points in stress space at which plastic flow initiates, and the corresponding function must depend on direct and mixed invariants of stress and tensor-valued internal variables. One single function describes a yield surface in order to avoid singularities and computational difficulties arising from the use of multiple functions representing intersecting surfaces in stress space that are often used for cap-type models in soil plasticity. The presented functions are conveniently subdivided in three main categories depending on the type of analytical expression used, and they all describe properly closed yield surfaces which are continuous and convex. The internal variables in these functions can be used in order to address classical plasticity features such as isotropic and kinematic hardening, the latter in the form of rotational hardening. The effects of parameters on the shape of yield surfaces are clearly demonstrated and illustrated for all functions in triaxial stress space. The generalization of these functions to the multiaxial stress space is presented using a consistent method such that if one applies triaxial loading conditions on the multiaxial expressions, the triaxial ones are retrieved. Finally, the appropriateness of the yield functions in regards to the soil type is discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Argyris, J. H., Faust, G., Szimmat, J., Warnke, E. P., and Willam, K. J. (1974). “Recent developments in the finite element analysis of prestressed concrete reactor vessels.” Nucl. Eng. Des., 28(1), 42–75.
Collins, I. F. (2002). “Associated and non-associated aspects of the constitutive laws for coupled elastic/plastic materials.” Int. J. Geomech., 2(2), 259–267.
Collins, I. F., and Hilder, T. (2002). “A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests.” Int. J. Numer. Analyt. Meth. Geomech., 26(13), 1313–1347.
Collins, I. F., and Houlsby, G. T. (1997). “Application of thermomechanical principles to the modelling of geotechnical materials.” Proc. R. Soc. London, Ser. A, 453, 1975–2001.
Collins, I. F., and Kelly, P. A. (2002). “A thermomechanical analysis of a family of soil models.” Geotechnique, 52(7), 507–518.
Dafalias, Y. F. (1986). “An anisotropic critical state soil plasticity model.” Mech. Res. Commun., 13(6), 341–347.
Dafalias, Y. F. (1987). “An anisotropic critical state clay plasticity model.” Proc., 2nd Int. Conf. on Constitutive Laws for Engineering Materials, C. S. Desai, E. Krempl, P. Kiousis, and T. Kundu, eds., Vol. I, Elsevier Science, New York, 513–521.
Desai, C. S. (1980). “A general basis for yield, failure and potential functions in plasticity.” Int. J. Numer. Analyt. Meth. Geomech., 4(4), 361–375.
Desai, C. S., Somasundaram, S., and Frantziskonis, G. (1986). “A hierarchical approach for constitutive modelling of geologic materials.” Int. J. Numer. Analyt. Meth. Geomech., 10(3), 225–257.
Houlsby, G. T. (1981). “A study of plasticity theories and their application to soils.” Ph.D. thesis, Univ. of Cambridge, Cambridge, U.K.
Houlsby, G. T. (1982). “A derivation of the small-strain incremental theory of plasticity from thermodynamics.” Proc., IUTAM Conf. on Deformation and Failure of Granular Materials, Taylor and Francis, Delft, The Netherlands, 109–118.
Kavvadas, M. J. (1982). “Non-linear consolidation around driven piles in clays.” Sc.D. thesis, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
Korhonen, K. H., and Lojander, M. (1987). “Yielding of perno clay.” Constitutive Laws for Engineering materials: Theory and Applications, Proc., 2nd IC, C. S. Desai, et al., eds., Vol. II, Elsevier Science, New York, 1249–1255.
Lawrence, J. D. (1972). A catalog of special plane curves, Dover, New York.
Manzari, M. T., and Dafalias, Y. F. (1997). “A critical state two-surface plasticity model for sands.” Geotechnique, 47(2), 255–272.
Modaressi, H., Laloui, L., and Aubry, D. (1994). “Thermodynamical approach for Camclay-family models with Roscoe-type dilatancy rules.” Int. J. Numer. Analyt. Meth. Geomech., 18, 133–138.
Newson, T. A., and Davies, M. C. R. (1996). “A rotational hardening constitutive model for anisotropically consolidated clay.” Soils Found., 36(3), 13–20.
Pestana, J. M., and Whittle, A. J. (1999). “Formulation of a unified constitutive model for clays and sands.” Int. J. Numer. Analyt. Meth. Geomech., 23(12), 1215–1243.
Roscoe, K. H., and Burland, J. B. (1968). “On the generalized stress-strain behaviour of wet clay.” Engineering plasticity, Cambridge University Press, Cambridge, U.K., 553–609.
Taiebat, M., and Dafalias, Y. F. (2008). “SANISAND: simple anisotropic sand plasticity model.” Int. J. Numer. Analyt. Meth. Geomech., 32(8), 915–948.
Thevanayagam, S., and Chameau, J. L. (1992). “Modelling anisotropy of clays at critical state.” J. Eng. Mech., 118(4), 786–806.
Wheeler, S. J., Karstunen, M., and Näätänen, A. (1999). “Anisotropic hardening model for normally consolidated soft clays.” Numerical Models in Geomechanics, Proc., NUMOG VII, G. N. Pande, S. Pietruszczak, and H. F. Schweiger, eds., Vol. II, Balkema, Rotterdam, The Netherlands, 33–40.
Wheeler, S. J., Näätänen, A., Karstunen, M., and Lojander, M. (2003). “An anisotropic elastoplastic model for soft clays.” Can. Geotech. J., 40, 403–418.
Whittle, A. J., and Kavvadas, M. J. (1994). “Formulation of MIT-E3 constitutive model for overconsolidated clays.” J. Geotech. Eng., 120(1), 173–198.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Dec 5, 2008
Accepted: Jan 12, 2010
Published online: Jan 15, 2010
Published in print: Aug 2010
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.