Plane Strain Constitutive Equations for Soils
Publication: Journal of Geotechnical Engineering
Volume 109, Issue 3
Abstract
An attempt is made to clarify certain aspects of the modeling of behavior of particulate materials. The issues are presented in terms of an incremental Hooke's law. The formulation accounts at least partially for the effects of inherent and stress‐induced anisotropy and for the effects of direction and rotation of the stress increment vector. Arguments are presented to indicate that plane strain in particulate materials is approximately two‐dimensional, with in‐plane normal stresses and longitudinal strains uncoupled from out‐ofplane stress. Particulate materials exhibit stress‐path‐induced anisotropy as well as stress‐magnitude‐induced anisotropy. A given particulate material may be cross‐anisotropic in triaxial compression but two‐dimensional in plane strain. Hooke's law is used as a vehicle for presentation of the issues because of its familiarity to geotechnical engineers and its continued use in practice.
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References
1.
Arthur, J. R. F., Chua, K. S., Dunstan, T., and Rodriguez del C., J. I., “Principal Stress Rotation: A Missing Parameter,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 106, No. GT4, Apr., 1980, pp. 419–433.
2.
Drnevich, V. P., “Constrained and Shear Moduli for Finite Elements,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, No. GT5, May, 1975, pp. 459–473.
3.
Duncan, J. M., and Chang, C. Y., “Nonlinear Analysis of Stress and Strain in Soils,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 96, No. SM5, Sept., 1970, pp. 1629–1653.
4.
Duncan, J. M., and Clough, G. W., “Finite Element Analyses of Port Allen Lock,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM8, Aug., 1971, pp. 1053–1068.
5.
Hardin, B. O., “Effects of Strain Amplitude on the Shear Modulus of Soils,” Technical Report No. AFWL‐TR‐72‐201, Air Force Weapons Laboratory, Albuquerque, N.M., Mar., 1973.
6.
Hardin, B. O., discussion of “Anisotropic Shear Modulus due to Stress Anisotropy,” by Stephen K. Roesler, Journal of the Geotechnical Engineering Division, ASCE, Vol. 106, No. GT8, Aug., 1980, pp. 956–958.
7.
Hardin, B. O., “The Nature of Stress‐Strain Behavior for Soils,” presented at the 1978, ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, held at Pasadena, Calif.
8.
Hardin, B. O., “Plane Strain Constitutive Equations for Soils and Rock Masses,” Soil Mechanics Series No. 30, Department of Civil Engineering, University of Koutchy, Feb., 1982.
9.
Hardin, B. O., and Drnevich, V. P., “Shear Modulus and Damping in Soils: Design Equations and Curves,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SM7, July, 1972, pp. 667–692.
10.
Hendron, A. J., Jr., “The Behavior of Sand in One‐Dimensional Compression,” thesis, presented to the University of Illinois, at Urbana, Ill., in 1963, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
11.
Iwan, W. D., “On a Class of Models for the Yielding Behavior of Continuous and Composite Systems,” Journal of Applied Mechanics, American Society of Mechanical Engineers, Vol. 34, Sept., 1967, pp. 612–617.
12.
Jaky, J., “The Coefficient of Earth Pressure at Rest,” Journal of the Society of Hungarian Architects and Engineers, 1944, pp. 355–358.
13.
Kondner, R. L., “Hyperbolic Stress‐Strain Response: Cohesive Soils,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 89, No. SM1, Feb., 1963, pp. 115–143.
14.
Masing, G., “Eigenspannungen and Verfestigung beim Messing,” Proceedings, 2nd International Congress of Applied Mechanics, Zurich, Switzerland, 1926.
15.
Mayne, P. W., and Kulhawy, F. H., “‐OCR Relationships in Soil,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 108, No. GT6, June, 1982, pp. 851–872.
16.
Newmark, N. M., and Rosenblueth, E., “Fundamentals of Earthquake Engineering,” Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1971, pp. 162–163.
17.
Ramberg, W., and Osgood, W. T., “Description of Stress‐Strain Curves by Three Parameters,” Technical Note 902, NACA, 1943.
18.
Rowe, P. W., “The Stress‐Dilatancy Relation for Static Equilibrium of an Assembly of Particles in Contact,” Proceedings of the Royal Society of London, Series A, Vol. 269, 1962, pp. 500–527.
19.
Schmertmann, J. H., “The Undisturbed Consolidation Behavior of Clay,” Transactions, ASCE, Vol. 120, 1955, pp. 1201–1227.
20.
Sokolnikoff, I. S., “Mathematical Theory of Elasticity,” 2nd ed., McGraw‐Hill Book Co., Inc., New York, N.Y., 1956, p. 63.
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Copyright © 1983 ASCE.
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Published online: Mar 1, 1983
Published in print: Mar 1983
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