Evaluation of Two Homogenization Techniques for Modeling the Elastic Behavior of Granular Materials
Publication: Journal of Engineering Mechanics
Volume 131, Issue 11
Abstract
This paper discusses the capabilities of two homogenization techniques to accurately represent the elastic behavior of granular materials considered as assemblies of randomly distributed particles. The stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations, using two different homogenization methods, namely the kinematic method and the static method. The numerical predictions obtained by these two homogenization techniques are compared to results obtained during experimental studies on different granular materials. Relations between elastic constants of the assembly, interparticle properties, and fabric parameters are discussed, as well as the capabilities of the models to take into account inherent and stress-induced anisotropy for different stress conditions.
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References
Bellotti, R., Jamiolkowski, M., Lo Presti, D. C. F., and O’Neil, D. A. (1996). “Anisotropy of small strain stiffness in Ticino Sand.” Geotechnique, 46(1), 115–131.
Biarez, J., and Hicher, P.-Y. (1994). Elementary mechanics of soil behaviour, Balkema, Rotterdam, 200.
Cambou, B., Dubujet, P., Emeriault, F., and Sidoroff, F. (1995). “Homogenization for granular materials.” Eur. J. Mech. A/Solids, 14(2), 255–276.
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., and Gao, J. (1996). “Kinematic and static hypotheses for constitutive modeling of granulates considering particle rotation.” Acta Mech., 115(1–4), 213–229.
Chang, C. S., and Liao, C. L. (1994). “Estimates of elastic modulus for media of randomly packed granules, Part 2.” Appl. Mech. Rev., 47(1), 197–206.
Chang, C. S., and Misra, A. (1990).“Application of uniform strain theory to heterogeneous granular solids,” J. Eng. Mech., ASCE. 116(10), 2310–2328.
Chang, C. S., Sundaram, S. S., and Misra, A. (1989). “Initial moduli of particulated mass with frictional contacts.” Int. J. Numer. Analyt. Meth. Geomech., 13(6), 629–644.
Geoffroy, H., Di Benedetto, H., Duttine, A., and Sauzeat, C. (2003). “Dynamic and cyclic loading on sands: Results and modelling for general stress-strain conditions.” 3rd Int. Symposium on Deformation Characteristics of Geomaterials, ISLyon’03, Balkema, Roterdam.
Hardin, B. O., and Black, W. L. (1966). “Sand stiffness under various triaxial stresses.” J. Soil Mech. Found. Div., 92(1), 27–42.
Hardin, B. O., and Drnevich, V. P. (1972). “Shear modulus and damping in soils: Measurements and parameter effects (Terzaghi Lecture).” J. Soil Mech. Found. Div., 98(6), 603–624.
Hicher, P.-Y. (1996). “Elastic properties of soils.” J. Geotech. Eng., 122(8), 641–648.
Hicher, P.-Y. (1998). “Experimental behaviour of granular materials.” Behaviour of granular materials, B. Cambou, ed., SpringerWien, New York, 1–97.
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 & Zellinger, Lisse, 1291–1297.
Hoque, E., and Tatsuoka, F. (1998). “Anisotropy in elastic deformation of granular materials.” Soils Found., 38(1), 163–179.
Iwasaki, T., and Tatsuoka, F. (1977). “Effects of grain size and grading on dynamic shear moduli of sands.” Soils Found., 17(3), 19–35.
Jenkins, J. T. (1988). “Volume change in small strain axisymmetric deformations of a granular material. In: Micromechanics of granular materials,” M. Satake and J. T. Jenkins, eds., Elsevier, Amsterdam, 143–152.
Jiang, G.-L., Tatsuoka, F., Fora, A., and Koseki, J. (1997). “Inherent and stress-state-induced anisotropy in very small strain stiffness of a sandy gravel.” Geotechnique, 47(3), 509–521.
Kuwano, R., and Jardine, R. (2002). “On the applicability of cross-anisotropic elasticity to granular materials at very small strains.” Geotechnique, 52(10), 727–749.
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. H., and Chang, C. S. (1997). “Stress-strain relationships for granular materials based on the hypothesis of best fit.” Int. J. Solids Struct., 34, 4087–4100.
Mindlin, R. D. and Deresiewicz, H. (1953). “Elastic spheres in contact under varying oblique forces.” ASME Trans. J. Appl. Mech., 20, 327–344.
Rothenburg, L., and Bathurst, R. J. (1989). “Analytical study of induced anisotropy in idealized granular materials.” Geotechnique, 39(4), 601–614.
Skoglund, G. R., Cunny, R. W., and Marcuson, W. F. (1976). “Evaluation of resonant column test devices.” J. Geotech. Eng. Div., Am. Soc. Civ. Eng., 102(11), 1147–1158.
Walton, K. (1987). “The effective elastic moduli of a random packing of spheres.” J. Mech. Phys. Solids, 35, 213–226.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 11 • November 2005
Pages: 1184 - 1194
Copyright
© 2005 ASCE.
History
Received: Sep 7, 2004
Accepted: Dec 28, 2004
Published online: Nov 1, 2005
Published in print: Nov 2005
Notes
Note. Associate Editor: Jin Y. Ooi
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