General Stress‐Dependent Elastic Moduli for Cross‐Anisotropic Soils
Publication: Journal of Geotechnical Engineering
Volume 119, Issue 10
Abstract
A new general nonlinear model for the dependence of the elastic moduli of a cross‐anisotropic soil on the stress state is presented. In agreement with experimental evidence, the model considers that the Young's modulus, the shear modulus and the bulk modulus of soil depend on the stress state, while the three Poisson's ratios are practically constant. The expressions for the stress dependence of the moduli are derived in a rigorous way by considering the conservation of energy during a cycle of loading along any arbitrary closed stress path, assuming purely elastic behavior. For the special case of isotropic soil, the model reduces to an earlier solution, developed by Lade and Nelson in 1987. A parametric study elucidates the effects of normal stresses, deviatoric stresses, Poisson's ratios, and degree of cross anisotropy on the elastic behavior of soil. Furthermore, simulations of undrained triaxial compression tests demonstrate that anisotropy may have a substantial effect on the development of excess pore‐water pressure and the direction of the stress path.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Arthur, J. R. F., and Menzies, B. K. (1972). “Inherent anisotropy in sand.” Geotechnique, London, England, 22(1), 115–129.
2.
Atkinson, J. H. (1975). “Anisotropic elastic deformations in laboratory tests on undisturbed London clay.” Geotechnique, London, England, 25(2), 357–384.
3.
Dakoulas, P., and Sun, Y. (1992). “Fine Ottawa sand: experimental behavior and theoretical predictions.” J. Geotech. Engrg., ASCE, 118(12), 1906–1923.
4.
El Hosri, M. S. (1984). “Contribution a l'etude des proprietes macanique des materiaux.” These d'Etat, University of Paris VI, Paris, France (in French).
5.
Gazetas, G. (1982). “Stress and displacement in cross‐anisotropic soils.” J. Geotech. Engrg. Div., ASCE, 108(4), 532–553.
6.
Gerrard, C. M. (1977). “Background to mathematical modeling in geomechanics: the roles of fabric and stress‐history.” Finite elements in geomechanics, John Wiley and Sons, Inc., New York, N.Y., 33–120.
7.
Graham, J., and Houlsby, G. T. (1983). “Anisotropic elasticity of a natural clay.” Geotechnique, London, England, 33(2), 165–180.
8.
Hardin, B. O. (1978). “The natural of stress‐strain behavior for soils.” Proc., Spec. Conf. Earthquake Engrg. Soil Dynamics, ASCE, New York, N.Y., Vol. 1, 3–90.
9.
Hardin, B. O., and Black, W. L. (1968). “Vibration modulus of normally consolidated clay.” J. Soil Mech. and Found. Div., ASCE, 94(2), 353–369.
10.
Hardin, B. O., and Black, W. L. (1969). “Closure to ‘Vibration modulus of normally consolidated clay.’” J. Soil Mech. and Found. Div., ASCE, 95(11), 1531–1537.
11.
Hooper, J. A. (1975). “Elastic settlement of a circular raft in adhesive contact with a transversely isotropic medium.” Geotechnique, London, England, 25(4), 691–711.
12.
Kirkgard, M. M., and Lade, P. V. (1991). “Anisotropy of normally consolidated San Francisco Bay mud.” Geotech. Testing J., 14(3), 231–246.
13.
Kirkpatrick, W. M., and Rennie, I. A. (1972). “Directional properties of consoliated kaolin.” Geotechnique, London, England, 22(1), 166–169.
14.
Lade, P. V., and Nelson, R. B. (1987). “Modeling the elastic behavior of granular maerials.” Int. J. for Numerical and Analytical Methods in Geomech., 11(5), 521–542.
15.
Lekhnitskii, S. G. (1963). Theory of elasticity of an anisotropic body. Holden‐Day, San Francisco, Calif.
16.
Loret, B. (1985). “On the choice of elastic parameters for sand.” Int. J. for Numerical and Analytical Methods in Geomech., 9(3), 285–292.
17.
Love, A. E. H. (1927). A treatise on the mathematical theory of elasticity. Cambridge University Press, Cambridge, England.
18.
Pickering, D. J. (1970). “Anisotropic elastic parameters for soil.” Geotechnique, London, England, 20(3), 271–276.
19.
Saada, A. S., and Ou, C. D. (1973). “Stress‐strain relations and failure of anisotropic clays.” J. Geotech. Engrg. Div., ASCE, 99(12), 1091–1111.
20.
Seed, H. B., Wong, R. T., Idriss, I. M., and Tokimatsu, K. (1984). “Moduli and damping factors for dynamic analyses of cohesionless soils.” Rep. No. UBC/EERC‐84/14, University of California, Berkeley, Calif.
21.
Yamada, Y., and Ishihara, K. (1979). “Anisotropic deformation characteristics of sand under three dimensional stress conditions.” Soils and Found., 19(2), 79–94.
22.
Yokota, K., and Konno, M., (1980). “Dynamic Poisson's ratio of soil.” Proc., 7th World Conf. Earthquake Engrg., Istanbul, Turkey, 3, 475–478.
23.
Yong, R. N., and Silvestri, V. (1979). “Anisotropic behavior of a sensitive clay.” Can. Geotech. J., 16(2), 335–350.
24.
Yu, S. (1992). “Experimental investigation and constitutive modeling of marine clay.” PhD thesis, Rice University, Houston, Tex.
25.
Ward, W. H., Samuels, S. G., and Gutler, M. E. (1959). “Further studies of the properties of London clay.” Geotechnique, London, England, 9(2), 321–344.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 119 • Issue 10 • October 1993
Pages: 1568 - 1586
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Aug 7, 1992
Published online: Oct 1, 1993
Published in print: Oct 1993
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.