Modeling Cross Anisotropy in Granular Materials
Publication: Journal of Engineering Mechanics
Volume 133, Issue 8
Abstract
A constitutive model has been developed to capture the behavior of cross-anisotropic frictional materials. The elastoplastic, single hardening model for isotropic materials serves as the basic framework. Based on the experimental results of cross-anisotropic sands in isotropic compression tests, the principal stress coordinate system is rotated such that the model operates isotropically within the rotated framework. Experimental plastic work contours on the octahedral plane are plotted for a series of true triaxial tests on dense Santa Monica Beach sand to study the effects of cross anisotropy on the evolution of yield surfaces. The amount of rotation of the yield and plastic potential surfaces decreases to zero (isotropic state) with loading. The model is constructed for cases where the principal stress and material symmetry axes are collinear and no significant rotation of principal stresses occur. The model incorporates fourteen parameters that can be determined from simple experiments, such as isotropic compression, drained triaxial compression, and triaxial extension tests. A series of true triaxial and isotropic compression tests on dense Santa Monica Beach sand are used as a basis for verification of the capabilities of the proposed model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was supported by the National Science Foundation under Grant Nos. MSS 9119272/MSS 9396271 and CMS 0096341. Grateful appreciation is expressed for this support.
References
Abelev, A. V. (2001). “Cross-anisotropic behavior of granular materials under three-dimensional loading conditions.” Ph.D. thesis, Johns Hopkins Univ., Baltimore, Md.
Abelev, A. V., and Lade, P. V. (2003). “Effects of cross anisotropy on three-dimensional behavior of sand. I: Stress–strain behavior and shear banding.” J. Eng. Mech., 129(2), 160–166.
Abelev, A. V., and Lade, P. V. (2004). “Characterization of failure in cross-anisotropic soils.” J. Eng. Mech., 130(5), 599–606.
Anandarajah, A. M., and Dafalias, Y. F. (1985). “Anisotropic hardening bounding surface constitutive model for clays.” Proc., 5th Int. Conf. Num. Meth. Geomech., Balkema, Rotterdam, The Netherlands, 267–275.
Anandarajah, A. M., and Dafalias, Y. F. (1986). “Bounding surface plasticity. III: Application to anisotropic cohesive soils.” J. Eng. Mech., 112(2), 1292–1318.
Arthur, J. R. F., and Menzies, B. K. (1972). “Inherent anisotropy in a sand.” Geotechnique, 22(1), 115–128.
Bazant, Z. P., Ansal, A. M., and Krizek, R. J. (1979). “Viscoplasticity of transversely isotropic clays.” J. Engrg. Mech. Div., 105(4), 549–565.
Bazant, Z. P., Caner, F. C., Carol, I., Adley, M. D., and Akers, S. A. (2000). “Microplane model M4 for concrete. I: Formulation with work-conjugate deviatoric stress.” J. Eng. Mech., 126(9), 944–953.
Bazant, Z. P., and Prat, P. C. (1987). “Creep of anisotropic clay: New microplane model.” J. Eng. Mech., 113(7), 1050–1064.
Boehler, J. P., and Sawczuk, A. (1977). “On yielding of oriented solids.” Acta Mech., 27, 185–206.
Carol, I., Jirasek, M., and Bazant, Z. (2001). “A thermodynamically consistent approach to microplane theory. Part I. Free energy and consistent microplane stresses.” Int. J. Solids Struct., 38, 2921–2931.
Casagrande, A., and Carillo, N. (1944). “Shear failure of anisotropic materials.” J. Boston Soc. Civ. Eng., 31(4), 74–87.
Crouch, R. S., and Wolf, J. P. (1995). “On a three-dimensional anisotropic plasticity model for soil.” Geotechnique, 45(2), 301–305.
Dafalias, Y. F. (1987). “An anisotropic critical state clay plasticity model.” Constitutive laws for engineering materials: Theory and applications, C. S. Desai et al., eds., 513–521.
El-Sohby, M. A., and Andrews, K. Z. (1973). “Experimental examination of sand anisotropy.” Proc., 8th Int. Conf. Soil Mech., 1, 103–109.
Ghaboussi, J., and Momen, H. (1984). “Plasticity model for inherently anisotropic behavior of sands.” Int. J. Numer. Analyt. Meth. Geomech., 8(1), 1–17.
Gutta, S. K. (2003). “Modeling large three-dimensional stress reversals in cross-anisotropic sands.” Ph.D. thesis, Univ. of Delaware, Newark, Del.
Inel, S., and Lade, P. V. (1997). “Rotational kinematic hardening model for sand. Part II: Characteristic work hardening law and predictions.” Comput. Geotech., 21(3), 217–234.
Iwan, W. D. (1967). “On a class of models for the yielding behavior of continuous and composite systems.” J. Appl. Mech., 34, 612–617.
Kavvadas, M. J. (1983). “A constitutive model for clays based on non-associative elasto-plasticity.” Proc., Int. Conf. Constitutive Laws for Engineering Materials: Theory and Applications, Elsevier, New York, 263–270.
Kim, M. K., and Lade, P. V. (1988). “Single hardening constitutive model for frictional materials. I. Plastic potential function.” Comput. Geotech., 5, 307–324.
Kirkgard, M. M., and Lade, P. V. (1991). “Anisotropy of normally consolidated San Francisco Bay mud.” Geotech. Test. J., 14(3), 231–246.
Kirkgard, M. M., and Lade, P. V. (1993). “Anisotropic three-dimensional behavior of a normally consolidated clay.” Can. Geotech. J., 30, 848–858.
Lade, P. V. (1977). “Elastoplastic stress-strain theory for cohesionless soil with curved yield surfaces.” Int. J. Solids Struct., 13, 1019–1035.
Lade, P. V. (1990). “Single-hardening model with application to NC clay.” J. Geotech. Engrg., 116(3), 394–414.
Lade, P. V., and Abelev, A. V. (2003). “Effects of cross anisotropy on three-dimensional behavior of sand. II: Volume change behavior and failure.” J. Eng. Mech., 129(2), 167–174.
Lade, P. V., and Abelev, A. V. (2005). “Characterization of cross-anisotropic soil deposits from isotropic compression tests.” Soils Found., accepted.
Lade, P. V., and Inel, S. (1997). “Rotational kinematic hardening model for sand. Part I: Concept of rotating yield and plastic potential surfaces.” Comput. Geotech., 21(3), 183–216.
Lade, P. V., and Kim, M. K. (1988a). “Single hardening constitutive model for frictional materials. II. Yield criterion and plastic work contours.” Comput. Geotech., 6, 13–29.
Lade, P. V., and Kim, M. K. (1988b). “Single hardening constitutive model for frictional materials. III. Comparisons with experimental data.” Comput. Geotech., 6, 31–47.
Lade, P. V., and Nelson, R. B. (1987). “Modeling the elastic behavior of granular materials.” Int. J. Numer. Analyt. Meth. Geomech., 11, 512–524.
Lewin, P. I., Yamada, Y., and Ishihara, K. (1982). “Correlated drained and undrained 3D tests on loose sand.” Proc., IUTAM Conf. Deformation and Failure of Granular Materials, Balkema, Rotterdam, The Netherlands, 419–429.
Li, X. S., and Dafalias, Y. F. (2002). “Constitutive modeling of inherently anisotropic sand behavior.” J. Geotech. Geoenviron. Eng., 128(10), 868–880.
Liang, R. Y., and Ma, F. (1992a). “Anisotropic plasticity model for undrained behavior of clays. I: Theory.” J. Geotech. Engrg., 118(2), 229–245.
Liang, R. Y., and Ma, F. (1992b). “Anisotropic plasticity model for undrained behavior of clays. II: Verification.” J. Geotech. Engrg., 118(2), 246–265.
Ling, H. I., Yue, D., Kaliakin, V. N., and Themelis, N. J. (2002). “Anisotropic elastoplastic bounding surface model for cohesive soils.” J. Eng. Mech., 128(7), 748–758.
Mahmood, A., and Mitchell, J. K. (1974). “Fabric-property relationship in fine granular materials.” Clay Miner., 22(516), 397–408.
Mahmood, A., Mitchell, J. K., and Lindblom, U. (1976). “Effect of specimen preparation method on grain arrangement and compressibility in sand.” Soil Specimen Prep. Lab. Testing, ASTM STP 599, West Conshohocken, Pa., 169–192.
Masad, E., and Muhunthan, B. (2000). “Three-dimensional characterization and simulation of anisotropic soil fabric.” J. Geotech. Geoenviron. Eng., 126(3), 199–207.
Matsuoka, H., and Ishizaki, H. (1981). “Deformation and strength of anisotropic soil.” Proc., Int. Conf. Soil Mech. Found. Eng., 1, 699–702.
Mroz, Z. (1967). “On the description of anisotropic work hardening.” J. Mech. Phys. Solids, 15, 163–175.
Nakata, Y., Hyodo, M., Murata, H., and Yasufuku, N. (1998). “Flow deformation of sands subjected to principal stress rotation.” Soils Found., 38(2), 115–128.
Nova, R., and Sacchi, G. (1982). “A model of the stress-strain relationship of the orthotropic geologic media.” J. Mec. Theor. Appl., 1(6), 927–949.
Ochiai, H., and Lade, P. V. (1983). “Three-dimensional behavior of sand with anisotropic fabric.” J. Geotech. Engrg., 109(10), 1313–1328.
Oda, M. (1972a). “Initial fabrics and their relations to mechanical properties of granular materials.” Soils Found., 12(1), 17–36.
Oda, M. (1972b). “The mechanism of fabric changes during compressional deformation of sand.” Soils Found., 12(2), 1–18.
Oda, M. (1981). “Anisotropic strength of cohesionless sands.” J. Geotech. Engrg. Div., 107(9), 1219–1231.
Oda, M., and Nakayama, H. (1988). “Introduction of inherent anisotropy of soils in the yield function.” Micromechanics of Granular Materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, 81–90.
Oda, M., and Nakayama, H. (1989). “Yield function for soil with anisotropic fabric.” J. Eng. Mech., 115(1), 89–104.
Oka, F., Kimoto, S., Kobayashi, H., and Adachi, T. (2002). “Anisotropic behavior of soft sedimentary rock and a constitutive model.” Soils Found., 42(5), 59–70.
Pande, G. N., and Sharma, K. G. (1981). “Time-dependent multilaminate model for clay—A numerical study of the influence of rotation of principal stress axes.” Proc., Implementation of Computer Procedures and Stress–Strain Laws in Geotech. Engrg., Vol. II, Acorn Press, Durham, N.C., 575–590.
Pande, G. N., and Xiong, W. (1982). “An improved multilaminate model of jointed rock masses.” Proc., Int. Symp. on Numer. Models in Geomech., R. Dungar, G. N. Pande, and G. A. Studer, eds., Balkema, Rotterdam, The Netherlands, 218–226.
Pietruszczak, S., and Pande, G. N. (2001). “Description of soil anisotropy based on multi-laminate framework.” Int. J. Numer. Analyt. Meth. Geomech., 25(2), 197–206.
Prevost, J. H. (1977). “Mathematical modeling of monotonic and cyclic undrained clay behavior.” Int. J. Numer. Analyt. Meth. Geomech., 1, 195–216.
Prevost, J. H. (1978). “Plasticity theory for soil stress–strain behavior.” J. Engrg. Mech. Div., 104(5), 1117–1194.
Prevost, J. H. (1982). “Two-surface versus multi-surface plasticity theories: A critical assessment.” Int. J. Numer. Analyt. Meth. Geomech., 6, 323–328.
Shapiro, S., and Yamamuro, J. A. (2003). “Effects of silt on three-dimensional stress-strain behavior of loose sand.” J. Geotech. Geoenviron. Eng., 129(1), 1–11.
Tobita, Y. (1989). “Fabric tensors.” Mechanics of Granular Materials, Report from TC13, Int. Soc. of Soil Mechanics and Foundation Engineering, M. Satake, ed., Rio De Janeiro, 6–9.
Wong, R. K. S., and Arthur, J. R. F. (1985). “Induced and inherent anisotropy in sand.” Geotechnique, 35(4), 471–481.
Yamada, Y., and Ishihara, K. (1979). “Anisotropic deformation characteristics of sand under three dimensional stress conditions.” Soils Found., 19(2), 79–94.
Yamada, Y., and Ishihara, K. (1981). “Undrained deformation characteristics of loose sand under three-dimensional stress conditions.” Soils Found., 21(1), 97–107.
Yoshimine, M., Ishihara, K., and Vargas, W. (1998). “Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand.” Soils Found., 38(3), 179–188.
Yu, S., and Dakoulas, P. (1993). “General stress-dependent elastic moduli for cross-anisotropic soils.” J. Geotech. Engrg., 119(10), 1568–1586.
Zienkiewicz, O. C., and Pande, G. N. (1977). “Time-dependent multi-laminate model of rocks—A numerical study of deformation and failure of rock masses.” Int. J. Numer. Analyt. Meth. Geomech., 1, 219–247.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: Jul 30, 2003
Accepted: Oct 10, 2006
Published online: Aug 1, 2007
Published in print: Aug 2007
Notes
Note. Associate Editor: Yunping Xi
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.