Yield Function for Soil with Anisotropic Fabric
Publication: Journal of Engineering Mechanics
Volume 115, Issue 1
Abstract
A fabric tensor for three‐dimensional assemblies of granular soils is introduced as an index showing the anisotropy due to the preferred orientation of constituent particles and is actually determined by using data derived from a material science approach of soils. Using the fabric tensor, a Drucker‐Prager type of yield function is extended so as to take into account the anisotropic yielding behavior of granular soils. Plane strain tests on Toyoura sand are analyzed with a result that the anisotropic shear strength is well fitted by the extended Drucker‐Prager yield function. Based on this, it is concluded that this study provides a step to link the material science approach of soils, in which the spatial arrangement of particles and associated voids plays an important role, to the continuum theory of plasticity.
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References
1.
Baker, R., and Desai, C. S. (1984). “Induced anisotropy during plastic straining.” Int. J. Num. Anal. Meth. in Geomech., 8(2), 167–185.
2.
Baltov, A., and Sawczuk, A. (1965). “A rule of anisotropic hardening.” Acta Mech., 1, 81–92.
3.
Barden, L., and Khayatt, A. L. (1966). “Incremental strain rate ratio and strength of sand in the triaxial test.” Geotech., 16(4), 338–357.
4.
Bazant, Z. P., and Kim, J. K. (1986). “Creep of anisotropic clay: Microplane model.” J. Geotech. Engrg., ASCE, 114(4), 458–475.
5.
Casagrande, A., and Carillo, N. (1944). “Shear failure of anisotropic materials.” Proc. Boston Soc. Civ. Engrs., 31, 74–87.
6.
Chen, W. F., and Saleeb, A. F. (1982). Constitutive equations for engineering materials: Elasticity and modeling. John Wiley and Sons, Inc., New York, N.Y.
7.
Cowin, S. C. (1985). “The relationship between the elasticity tensor and the fabric tensor.” Mech. Mat., 4, 1–11.
8.
Cowin, S. C., and Satake, T. (1978). Continuum mechanical and statistical approaches in the mechanics of granular materials. Gakujutsu Bunken Fukyu‐Kai, Tokyo, Japan.
9.
Curray, J. R. (1956). “Analysis of two‐dimensional orientation data.” J. Geol., 64, 117–131.
10.
Desai, C. S., and Siriwardane, H. J. (1984). Constitutive laws for engineering materials with emphasis on geologic materials. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
11.
Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plastic analysis of limit design.” Quart. Appl. Math., 10(2), 157–165.
12.
Feda, J. (1982). Mechanics of particulate materials. Elsevier Scientific Publishing Co., Amsterdam, The Netherlands.
13.
Ghaboussi, J., and Momen, H. (1984). “Plasticity model for inherently anisotropic behaviour of sand.” Int. J. Num. Meth. in Geomech., 8, 1–17.
14.
Hill, R. (1948). “A theory of yielding and plastic flow of anisotropic metals.” Proc. Royal Soc. London. Series A, 193.
15.
Hill, R. (1956). The mechanical theory of plasticity. Oxford Univ. Press, London, England.
16.
Jenkins, J. T., and Satake, M. (1983). Mechanics of granular materials: New models and constitutive relations. Studies Appl. Mech. 7. Elsevier Scientific Publishing Co., Amsterdam, The Netherlands.
17.
Kanatani, K. (1983). “Characterization of structural anisotropy by fabric tensors and their statistical test.” J. Jap. Soc. Soil Mech. Found. Engrg., 23(4), 171–177.
18.
Kanatani, K. (1984). “Distribution of directional data and fabric tensors.” Int. J. Engrg. Sci., 22(2), 149–164.
19.
Lade, P. V., and Duncan, J. M. (1975). “Elastoplastic stress‐strain theory for cohesionless soil.” J. Geotech. Engrg., ASCE, 101(10), 1037–1053.
20.
Mitchell, J. K. (1976). Fundamentals of soils behavior. John Wiley and Sons, Inc., New York, N.Y.
21.
Oda, M. (1981). “Anisotropic strength of cohesionless sands.” J. Geotech. Engrg., ASCE, 107(9), 1219–1231.
22.
Oda, M., Koishikawa, I., and Higuchi, T. (1978). “Experimental study of anisotropic shear strength of sand by plane strain test.” Soils and Found. 18(1), 25–38.
23.
Oda, M., Nemat‐Nasser, S., and Mehrabadi, M. M. (1982). “A statistical study of fabric in a random assembly of spherical granules.” Int. J. Num. Anal. Meth Geomech., 6, 77–94.
24.
Oda, M., Nemat‐Nasser, S., and Konishi, J. (1985). “Stress‐induced anisotropy in granular masses.” Soils and Found. 25(3), 85–97.
25.
Pariseau, W. G. (1968). “Plasticity theory for anisotropic rocks and soils.” Proc. 19th Symp. on Rock Mechanics, Austin, Tex., 267–295.
26.
Reinicke, K. M., and Ralston, T. D. (1977). “Plastic limit analysis with an anisotropic, parabolic yield function.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 14, 147–154.
27.
Salencon, J. (1974). Application of the theory of plasticity in soil mechanics. John Wiley and Sons, Inc., New York, N.Y.
28.
Satake, M. (1982). “Fabric tensor in granular materials.” Deformation and failure P. A. Vermeer and H. J. Luger, eds. Balkema, Rotterdam 63–68.
29.
Tatsuoka, F., Sakamoto, N., Kawamura, T., and Fukushima, S. (1986). “Strength and deformation characteristics of sand in plane strain compression at extremely low pressures.” Soils and Found., 26(1), 65–84.
30.
Truesdell, C., and Noll, W. (1965). “The non‐linear field theories of continuum,” Encyclopedia of physics, 3(1), Springer‐Verlag, Berlin.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 115 • Issue 1 • January 1989
Pages: 89 - 104
Copyright
Copyright © 1989 ASCE.
History
Published online: Jan 1, 1989
Published in print: Jan 1989
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