Multiaxial Cyclic Plasticity Model for Clays
Publication: Journal of Geotechnical Engineering
Volume 120, Issue 6
Abstract
A total stress‐based bounding surface plasticity model for clays is developed to accommodate multiaxial stress reversals. The model is constructed based on the idea of a vanishing elastic region undergoing pure translation inside a bounding surface, and an interpolation function for hardening modulus which varies with stress distance of the elastic region from the unloading point. Central to the development of the model are the general criteria for loading and unloading, which are phrased based upon the simple argument that with continued loading the hardening modulus should decrease monotonically with deformation. Combined with numerical integration of the elastoplastic constitutive equations in a form suitable for a robust computer implementation, the model is applied to cohesive soils undergoing undrained stress reversals and cyclic loading. With a suitable choice of the interpolation function for the hardening modulus, it is shown that existing one‐dimensional nonlinear laws for soils can be replicated, such as the hyperbolic, exponential, the Davidenkov, and even the Ramberg‐Osgood models. Specifically, the appropriateness of the exponential hardening function for cohesive soils is investigated and its parameters determined for some clays and silts for use in dynamic soil‐structure interaction modeling.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Achenbach, J. D. (1987). Wave propagation in elastic solids. 1st Ed., North‐Holland, Amsterdam, The Netherlands.
2.
Borja, R. I. (1991a). “Composite Newton‐PCG and quasi‐Newton iterations for nonlinear consolidation.” Comp. Methods Appl. Mech. Engrg., 86(1), 27–60.
3.
Borja, R. I. (1991b). “Modeling the monotonic and cyclic viscoplastic soil behavior.” Proc., 2nd Int. Conf. Recent Advances Geotech. Earthquake Engrg. Soil Dyn., Vol. 1, S. Prakash, ed., 37–40.
4.
Borja, R. I., Wu, W. H., and Smith, H. A. (1992). “Nonlinear vertical vibration of rectangular foundations.” Proc., 10th World Conf. on Earthquake Engrg., A. A. Balkema, Rotterdam, The Netherlands, 1537–1542.
5.
Borja, R. I., Wu, W. H., and Smith, H. A. (1993). “Nonlinear response of vertically oscillating rigid foundations.” J. Geotech. Engrg., ASCE, 119(5), 893–911.
6.
Borja, R. I., Wu, W‐H., Amies, A. P., and Smith, H. A. (1994). “Nonlinear lateral, rocking, and torsional vibration of rigid foundations.” J. Geotech. Engrg., ASCE, 120(3), 491–513.
7.
Dafalias, Y. F., and Popov, E. P. (1977). “Cyclic loading for materials with a vanishing elastic region.” Nuclear Engrg. and Des., 41, North‐Holland, Amsterdam, The Netherlands, 293–302.
8.
Dafalias, Y. F., and Herrmann, L. R. (1982). “Bounding surface formulation of soil plasticity: Chapter 10” Soil mechanics—transient and cyclic loads, G. N. Pande and O. C. Zienkiewicz, eds., John Wiley, New York, N.Y.
9.
Georgiannou, V. N., Rampello, S., and Silvestri, F. (1991). “Static and dynamic measurements of undrained stiffness on natural overconsolidated clays.” Proc., 10th Eur. Conf. on Soil Mech. and Found. Engrg., 91–95.
10.
Hardin, B. O., and Drnevich, V. P. (1972). “Shear modulus and damping in soils: design equations and curves.” J. Soil Mech. and Found. Div., ASCE, 98(7), 667–692.
11.
Hughes, T. J. R. (1982). “Stress‐point algorithm for a pressure‐sensitive multiple‐yield‐surface plasticity theory,” Rep. UCJD‐19339, Lawrence Livermore Laboratory, Livermore, Calif.
12.
Kondner, R. L. (1963). “Hyperbolic stress‐strain response: cohesive soils.” J. Soil Mech. and Found. Div., ASCE, 89(1), 115–143.
13.
Krieg, R. D., and Key, S. W. (1976). “Implementation of a time‐independent plasticity theory into structural computer programs.” Constitutive equations in visco‐plasticity: computational and engineering aspects, J. A. Stricklin and K. J. Saczalski, eds., ASME, New York, N.Y.
14.
Martin, P. P., and Seed, H. B. (1982). “One‐dimensional dynamic ground response analyses.” J. Geotech. Engrg. Div., ASCE, 108(7), 935–952.
15.
Mróz, Z. (1967). “On the description of anisotropic work‐hardening.” J. Mech. Phys. Solids, 15, 163–175.
16.
Mróz, Z., Norris, V. A., and Zienkiewicz, O. C. (1979). “Application of an anisotropic hardening model in the analysis of elastoplastic deformation of soils.” Géotechnique, London, England, 29(1), 1–34.
17.
Ortiz, M., and Popov, E. P. (1985). “Accuracy and stability of integration algorithms for elastoplastic constitutive relations.” Int. J. for Numerical Methods in Engrg. 21, 1561–1576.
18.
Prager, W. (1956). “A new method of analyzing stresses and strains in work‐hardening plastic solids.” J. Appl. Mech., 78(Dec), 493–496.
19.
Prevost, J. H. (1977). “Mathematical modelling of monotonic and cyclic undrained clay behaviour.” Int. J. Num. Analyt. Methods Geomech., 1(2), 195–216.
20.
Ramberg, W., and Osgood, W. T. (1943). “Description of stress‐strain curves by three parameters,” Tech. Note 902, National Advisory Committee for Aeronautics.
21.
Salah‐mars, S., and Kavazanjian, E. Jr. (1992). “A virtual surface concept for nested yield surface plasticity.” Int. J. Num. Analyt. Methods Geomech., 16, 779–796.
22.
Seed, H. B., and Idriss, I. M. (1970). “Soil moduli and damping factors for dynamic response analysis,” Earthquake Engineering Res. Rep. No. EERC 70‐10, University of Calif., Berkeley, Calif.
23.
Streeter, V. L., Wylie, E. B., and Richart, F. E. Jr. (1974). “Soil motion computations by characteristics method.” J. Geotech. Engrg. Div., ASCE, 100(3), 247–263.
24.
Tang, H. T., Tang, Y. K., and Stepp, J. C. (1990). “Lotung large‐scale seismic experiment and soil‐structure interaction method validation.” Nuclear Engrg. and Des., 123, 197–412.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jan 4, 1993
Published online: Jun 1, 1994
Published in print: Jun 1994
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.