Elastoplastic Model for Clay with Microstructural Consideration
Publication: Journal of Engineering Mechanics
Volume 135, Issue 9
Abstract
Clay material can be considered as a collection of clusters, which interact with each other mainly through mechanical forces. From this point of view, clay is modeled by analogy to granular material in this paper. An elastoplastic stress-strain relationship for clay is derived by using the granular mechanics approach developed in previous studies for sand. However, unlike sand, clay deformation is generated not only by the mobilizing but also by compressing clusters. Thus, in addition to the Mohr-Coulomb’s plastic shear sliding and a dilatancy type flow rule, a plastic normal deformation has been modeled for two clusters in compression. The overall stress-strain relationship can then be obtained from the mobilization and compressing of clusters through a static hypothesis of the macro-micro relations. The predictions are compared with the experimental results for clay under both drained and undrained triaxial loading conditions. Three different types of clay, including remolded and natural clay, have been selected to evaluate the model’s performance. The comparisons verify that this model is capable of accurately reproducing the overall behavior of clay, which accounts for the influence of key parameters such as void ratio and mean stress. A section of this paper is devoted to show the model’s capability of considering the influence of inherent anisotropy on the stress-strain response under undrained triaxial loading conditions.
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References
Batdorf, S. B., and Budianski, B. (1949). “A mathematical theory of plasticity based on concept of slip,” NACA Tech Note 1871.
Bazant, Z. P., and Oh, B. H. (1986). “Efficient numerical integration on the surface of a sphere.” J. Appl. Math. Mech., 66(1), 37–49.
Bazant, Z. P., Xiang, Y., Adley, M. D., Prat, P. C., and Akers, S. A. (1996). “Microplane model for concrete. II: Data delocalization and verification.” J. Eng. Mech., 122(3), 255–262.
Biarez, J., and Hicher, P. Y. (1994). Elementary mechanics of soil behaviour, Balkema, Rotterdam, The Netherlands, 208.
Biarez, J., and Hicher, P. Y. (2008). “Mechanisms of soil deformation.” Constitutive modeling of soils and rocks, P. Y. Hicher and J. F. Shao, eds., Wiley, New York, 31–71.
Chang, C. S. (1988). “Micromechanical modeling of constructive relations for granular material.” Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, 271–279.
Chang, C. S., Chao, S. C., and Chang, Y. (1995). “Estimates of mechanical properties of granulates with anisotropic random packing structure.” Int. J. Solids Struct., 32(14), 1989–2008.
Chang, C. S., and Gao, J. (1995). “Second-gradient constitutive theory for granular material with random packing structure.” Int. J. Solids Struct., 32(16), 2279–2293.
Chang, C. S., and Hicher, P. -Y. (2005). “An elastic-plastic model for granular materials with microstructural consideration.” Int. J. Solids Struct., 42, 4258–4277.
Chang, C. S., Kabir, M., and Chang, Y. (1992a). “Micromechanics modelling for the stress strain behavior of granular soil—II: Evaluation.” J. Geotech. Engrg., 118(12), 1975–1994.
Chang, C. S., and Liao, C. (1990). “Constitutive relations for particulate medium with the effect of particle rotation.” Int. J. Solids Struct., 26, 437–453.
Chang, C. S., and Misra, A. (1990). “Application of uniform strain theory to heterogeneous granular solids.” J. Eng. Mech., 116(10), 2310–2328.
Chang, C. S., Misra, A., and Acheampon, K. (1992b). “Elastoplastic deformation of granulates with frictional contacts.” J. Eng. Mech., 118(8), 1692–1708.
Chang, C. S., Misra, A., and Weeraratne, S. P. (1989a). “A slip mechanism based constitutive model for granular soils.” J. Eng. Mech., 115(4), 790–807.
Chang, C. S., Sundaram, S. S., and Misra, A. (1989b). “Initial moduli of particulate mass with frictional contacts.” Int. J. Numer. Analyt. Meth. Geomech., 13(6), 626–641.
Christofferson, J., Mehrabadi, M. M., and Nemat-Nassar, S. (1981). “A micromechanical description on granular material behavior.” ASME J. Appl. Mech., 48, 339–344.
Delley, B. (1996). “High order integration schemes on the unit sphere.” J. Comput. Chem., 17(9), 1152–1155.
Emeriault, F., and Cambou, B. (1996). “Micromechanical modeling of anisotropic nonlinear elasticity of granular medium.” Int. J. Solids Struct., 33(18), 2591–2607.
Hicher, P. Y. (2001). “Microstructure influence on soil behaviour at small strains.” Pre-failure deformation characteristics of geomaterials, M. Jamiolkowski, R. Lancellotta, and D. Lo Presti, eds., Swets and Zeitlinger, Lisse, The Netherlands, 2, 1291–1297.
Hicher, P. Y., Wahyudi, H.and Tessier, D. (2000). “Microstructural analysis of inherent and induced anisotropy in clay.” Mech. Cohesive-Frict. Mater., 5(5), 341–371.
Jenkins, J. T. (1988). “Volume change in small strain axisymmetric deformations of a granular material.” Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, 143–152.
Jenkins, J. T., and Strack, O. D. L. (1993). “Mean-field inelastic behavior of random arrays of identical spheres.” Mech. Mater., 16, 25–33.
Kirkgard, M. M., and Lade, P. V. (1991). “Anisotropy of normally consolidated San Francisco bay mud.” Geotech. Test. J., 14(3), 231–246.
Kruyt, N. P., and Rothenburg, L. (2002). “Micromechanical bounds for the effective elastic moduli of granular materials.” Int. J. Solids Struct., 39(2), 311–324.
Lebedev, V. I. (1976). “Quadratures on the sphere.” Zh. Vychisl. Mat. Mat. Fiz., 16, 294–306.
Lebedev, V. I. (1977). “Quadrature formulas of orders 25–59 for the sphere.” Sib. Math. J., 18, 132–142.
Liao, C. L., Chan, T. C., Suiker, A. S. J., and Chang, C. S. (2000). “Pressure-dependent elastic moduli of granular assemblies.” Int. J. Numer. Analyt. Meth. Geomech., 24, 265–279.
Liao, C. L., Chang, T. P., Young, D., and Chang, C. S. (1997). “Stress-strain relationship for granular materials bases on hypothesis of best fit.” Int. J. Solids Struct., 34(31–32), 4087–4100.
Matsuoka, H., and Takeda, K. (1980). “A stress-strain relationship for granular materials derived from microscopic shear mechanisms.” Soils Found., 20(3), 45–58.
Mindlin, R. D. (1969). “Microstructure in linear elasticity.” Arch. Ration. Mech. Anal., 16, 51–78.
Oda, M. (1977). “Coordination number and its relation to shear strength of granular material.” Soils Found., 17(2), 29–42.
Ortiz, M., Pinsky, P. M., and Taylor, R. L. (1983). “Operator split methods for the numerical solution of the elastoplastic dynamic problem.” Comput. Methods Appl. Mech. Eng., 39, 137–157.
Pande, G. N., and Sharma, K. G. (1982). “Multi-laminate model of clays-a numerical evaluation of the influence of rotation of the principal stress axis.” Proc., Symp. on Implementation of Computer Procedures and Stress-Strain Laws in Geotechnical Engineering, C. S. Desai and S. K. Saxena, eds., Acorn, Durham, N.C., 575–590.
Rothenburg, L., and Selvadurai, A. P. S. (1981). “Micromechanical definitions of the Cauchy stress tensor for particular media.” Mechanics of structured media, A. P. S. Selvadurai, ed., Elsevier, Amsterdam, 469–486.
Rowe, P. W. (1962). “The stress-dilatancy relations for static equilibrium of an assembly of particles in contact.” Proc. R. Soc. London, Ser. A, 269, 500–527.
Simo, J. C., and Hughes, T. J. R. (1998). Computational inelasticity, Springer, New York.
Suiker, A. S. J., and Chang, C. S. (2004). “Modelling failure and deformation of an assembly of spheres with frictional contacts.” J. Eng. Mech., 130(3), 283–293.
Taylor, D. W. (1948). Fundamentals of soil mechanics, Wiley, NewYork.
Walton, K. (1987). “The effective elastic moduli of a random packing of spheres.” J. Mech. Phys. Solids, 35, 213–226.
Zervoyanis, C. (1982). “Etude synthétique des propriétés mécaniques des argiles et des sables sur chemin oedométrique et triaxial de revolution.” Thèse de Docteur-Ingénieur, Ecole Centrale de Paris (in French).
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Received: Jun 24, 2008
Accepted: Nov 30, 2008
Published online: Aug 14, 2009
Published in print: Sep 2009
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