Anisotropic Hardening Plasticity Model for Sands
Publication: Journal of Geotechnical Engineering
Volume 117, Issue 6
Abstract
An anisotropic hardening plasticity model based on the concept of bounding‐surface plasticity is formulated for prediction of the three‐dimensional stress‐strain‐volume‐change behavior of sand. The model employs the anisotropic invariants of the second‐order stress and rotational tensors as a formalism to account for the material anisotropy. The rotational tensor is linked to the fabric ellipsoid of particulate sand. The model is shown to satisfy the objectivity requirement from the form‐invariance principle. Twelve material constants required in the model can be determined from triaxial experiments. A study of the three‐dimensional behavior of Hostun sand serves as a basis for evaluating the capability of the model. Overall, the model's predictions are acceptable and can capture the variations of soil behavior with the rotation of principal stress direction and the relative magnitude of intermediate principal stress.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aboim, C. A., and Roth, W. H. (1982). “Bounding surface plasticity theory applied to cyclic loading of sand.” Proc., Int. Symp. on Numerical Models in Geomechanics, Zurich, Switzerland, Balkema, Rotterdam, The Netherlands, 65–72.
2.
Anandarajah, A., and Dafalias, Y. F. (1986). “Bounding surface plasticity. Ill: application to anisotropic cohesive soils.” J. Engrg. Mech., ASCE, 112(12), 1292–1318.
3.
Baker, R., and Desai, C. S. (1984). “Induced anisotropy during plastic straining.” Int. J. Numer. Anal. Methods Geomech., 8, 167–185.
4.
Banerjee, P. K., and Yousif, N. B. (1986). “A plasticity model for the mechanical behaviour of anisotropically consolidated clays.” Int. J. Numer. Anal. Methods Geomech., 10, 521–541.
5.
Bardet, J. P. (1986). “Bounding surface plasticity model for sands.” J. Engrg. Mech., ASCE, 112(11), 1198–1215.
6.
Dafalias, Y. S. (1975). “On cyclic and anisotropic plasticity,” thesis presented to the University of California, at Berkeley, California, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
7.
Dafalias, Y. F., and Popov, E. P. (1975). “A model of nonlinear hardening materials for complex loading.” Acta Mechanica, 21, 173–192.
8.
Dafalias, Y. F., and Popov, E. P. (1976). “Plastic internal variables formalism of cyclic plasticity.” J. Appl. Mech. Trans. ASME, 43, 645–651.
9.
Dafalias, Y. F., and Herrmann, L. R. (1982). “Bounding surface formulation of soil plasticity.” Proc. Soil Mechanics—Transient and Cyclic Loads, G. N. Pande and O. C. Zienkiewicz, eds., John Wiley and Sons, Chichester, U.K.
10.
Dafalias, Y. F. (1986). “Bounding surface plasticity. I: mathematical foundation and hypoplasticity.” J. Engrg. Mech., ASCE, 112(9), 966–987.
11.
DeNatale, J. S. (1982). “Calibration of the bounding surface plasticity model by multivariate optimization,” thesis, presented to the University of California, Davis, California, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
12.
Desai, C. S., Somasundaram, S., and Frantziskonis, G. (1986). “A hierarchical approach for constitutive modeling of geologic materials.” Int. J. Numer. Anal. Methods Geomech., 10, 225–257.
13.
Ghaboussi, J., and Momen, H. (1982). “Modeling and analysis of cyclic behaviour of sands.” Proc. Soil Mechanics—Transient and Cyclic Loads, G. N. Pande and O. C. Zienkiewicz, eds., John Wiley and Sons, Chichester, U.K.
14.
Hashiguchi, K. (1979). “Constitutive equations of granular media with anisotropic hardening.” Proc. of the Third Int. Conf. on Numerical Methods in the Geome‐chanics, Aachen, Germany, 435–439.
15.
Hights, D. W., Gems, A., and Symes, M. J. (1983). “The development of a new hollow cylinder apparatus for investigating the effect of principal stress rotation in soils.” Geotechnique, 33(4), 335–383.
16.
Kavvads, M. J. (1983). “A constitutive model for clays based on non‐associated anisotropic elasto‐plasticity.” Proc. of the Int. Conf. on Constitutive Laws for Engineering Materials—Theory and Application, Tucson, Ariz., 263–270.
17.
Krieg, R. D. (1975). “A practical two‐surface plasticity theory.” J. Appl. Mech. Trans. ASME, E42, 641–646.
18.
Lanier, J., and Zitouni, Z. (1989). “Development of a data base using the Grenoble true triaxial apparatus.” Proc. Int. Workshop on Constitutive Equations for Granular, Non‐Cohesive Soils, A. Saada and G. Bianchini, eds., 47–60.
19.
Liu, I. S. (1982). “On representation of anisotropic invariants.” Int. J. Engrg. Sci., 20, 1099–1109.
20.
McVay, M., and Taesiri, Y. (1985). “Cyclic behaviour of pavement base materials.” J. Geotech. Engrg., 111(1), 1–17.
21.
Ochiai, H., and Lade, P. V. (1983). “Three‐dimensional behavior of sand with anisotropic fabric.” J. Geotech. Engrg., ASCE, 109(10), 1313–1328.
22.
Oda, M., Konishi, J., and Nemat‐Nasser, S. (1980). “Some experimentally based fundamental results on the mechanical behaviour of granular materials.” Geotechnique, 30(4), 479–495.
23.
Pastor, M., Zienkiewicz, O. C., and Leung, K. H. (1985). “Simple model for transient soil loading in earthquake analysis. II. non‐associative model for sands.” Int. J. Numer. Anal. Methods Geomech., 9, 447–498.
24.
Pietruszczak, S., and Mroz, Z. (1983). “On hardening anisotropy of ^‐consolidated clays.” Int. J. Numer. Anal. Methods Geomech., 7, 19–38.
25.
Pietruszczak, S., and Stolle, D. F. E. (1987). “Modelling of sand behaviour under earthquake excitation.” Int. J. Numer. Anal. Methods Geomech., 11, 221–240.
26.
Poorooshasb, H. D., and Pietruszczak, S. (1985). “On yielding and flow of sand, a generalized two‐surface model.” Comput. Geotech., 1(1), 33–58.
27.
Prevost, J. H. (1985). “A simple plasticity theory for frictional cohesionless soils.” Soil Dyn. Earthquake Engrg., 4(1), 9–17.
28.
Saada, A., and Puccini, P. (1989). “The development of a data base using the Case hollow cylinder apparatus.” Proc. Int. Workshop on Constitutive Equations for Granular, Non‐Cohesive Soils, A. Saada and G. Bianchini, eds., 33–40.
29.
Saada, A., and Bianchini, G. (1989). “Constitutive equations for granular, nonco‐hesive soils.” A. Saade and G. Bianchini, eds., A. A. Balkema, Rotterdam, The Netherlands.
30.
Shaw, H. L. (1990). “An anisotropic hardening elasto‐plasticity model for particulate media,” thesis presented to the University of Akron, at Akron, Ohio, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
31.
Smith, G. F. (1971). “On isotropic functions of symmetric tensors, skewed‐sym‐metric tensors and vectors.” Int. J. Engrg. Sci., 9, 889–916.
32.
Spencer, A. J. M. (1972). “Theory of invariants.” Continuum Physics, 1, A. C. Eringen, ed., Academic Press, New York, N.Y., 239–353.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 117 • Issue 6 • June 1991
Pages: 913 - 933
Copyright
Copyright © 1991 ASCE.
History
Published online: Jun 1, 1991
Published in print: Jun 1991
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.