Modelling the elastic behaviour of granular materials
Tóm tắt
A review of the literature indicates that the elastic behaviour of granular materials is isotropic and that Poissony's ratio is constant, whereas Young's Modulus, the bulk modulus and the shear modulus vary with the mean normal stress and the deviatoric stress. A nonlinear, isotropic model for the elastic behaviour is developed on the basis of theoretical considerations involving the principle of conservation of energy. Energy is therefore neither generated not dissipated in closed‐loop stress paths or in closed‐loop strain paths. The framework for the model consists of Hooke's law, in which Poission's ratio is constant and Young's modulus is expressed as a power function invlving the first invariat of the stress tensor and the second invariant of the deviatoric stress tensor. The characteristics of the model are described, and the accuracy is evaluated by comparison with experimental results from triaxial tests and three‐dimensional cubical triaxial tests with a variety of stress paths. Parameter determination from unloading–reloading cycles in conventional triaxial compression tests is demonstrated, typical parameter values are given for granular materials and extension of the model to soils with effective cohesion is described.
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Tài liệu tham khảo
Lade P. V., 1982, Large stress reversals in triaxial tests on sand, Proc. 4th Int. Conf. Num. Meth. Geomech., Edmonton, Canada, 1, 171
Wilson G., 1948, A contribution to the study of the elastic properties of sand, Proc. 2nd Int. Conf. Soil Mech. Found. Eng. Rotterdam, 1, 197
Mindlin R. D., 1949, Compliance of elastic bodies in contact, J. Appl. Mech., Trans. A. S. M. E., 71, A‐259, 10.1115/1.4009973
Mindlin R. D., 1953, Elastic spheres in contact under varying oblique forces, J. Appl. Mech., Trans. A. S. M. E., 75, A‐327, 10.1115/1.4010702
Duffy J., 1957, Stress–strain relations and vibrations of a granular medium, J. Appl. Mech., A. S. M. E., 24, 585, 10.1115/1.4011605
Jacobson B., 1957, Some fundamental properties of sand, Proc. 4th Int. Conf. Soil Mech. Found. Eng., 1, 167
O. U.JanaradananandA. N.Harkauli ‘Rebound characteristics of cohesionless soils’ Proc. 2nd Asian Regional Conf. Soil Mech. Found. Eng. Japan 1963 pp.1–4.
Janbu N., 1963, Soil compressibility as determined by odometer and triaxial tests, Proc. European Conf. Soil Mech. Found Eng., Wiesbaden, 1, 19
Makhlouf H. M., 1965, Factors influencing the modulus of elasticity of dry sand, Proc. 6th Int. Conf. Soil Mech. Found. Eng., Montreal, 1, 298
Ko H.‐Y., 1967, Deformation of sand in hydrostatic compression, J. Soil Mech. Found. Div., A. S. C. E., 93, 137, 10.1061/JSFEAQ.0000964
Ko H.‐Y., 1967, Deformation of sand in shear, J. Soil Mech. Found. Div., A. S. C. E., 93, 283, 10.1061/JSFEAQ.0001024
Duncan J. M., 1970, Nonlinear analysis of stress and strain in soils, J. Soil Mech. Found. Div., A. S. C. E., 96, 1629, 10.1061/JSFEAQ.0001458
K. S.WongandJ. M.Duncan ‘Hyperbolic stress–strain parameters for nonlinear finite element analyses of stresses and movements in soil masses’ Geot. Eng. Report No. TE 74‐3 Dept. of Civ. Eng. Univ. of Calif. Berkeley (1974).
Hardin B. O., 1969, Closure to ‘Vibration modulus of normally consolidated clay, J. Soil Mech. Found. Div., A. S. C. E., 95, 1531, 10.1061/JSFEAQ.0001364
Hardin B. O., 1978, Proc. Spec. Conf. Earthquake Eng. Soil Dyn., 3
P. W.Rowe ‘Theoretical meaning and observed values of deformation parameters for soil’ Proc. Roscoe Memorial Symp. Stress–strain Behavior of Soils pp.143–194(1971).
Coon M. D., 1971, Recoverable deformation of cohesionless soils, J. Soil Mech. Found. Div., A. S. C. E., 97, 375, 10.1061/JSFEAQ.0001548
Desai C. S., 1984, Constitiutive Laws for Engineering Materials
Krizek R. J., 1977, Fabric effects on strength and deformation of kaolin clay, Proc. 9th Int. Conf. Soil Mech. Found. Eng., 1, 169
Yokota K., 1980, Dynamic Poisson's ratio of soil, Proc. 7th World Conf. Earthquake Eng., Istanbul, 3, 475
M. S.El Hosri ‘Contribution a l'etude des proprietes mecanique des materiaux’ These d'Etat Univ. Paris VI France (1984).
Lade P. V., 1973, Cubical triaxial tests on cohesionless soil, J. Soil Mech. Found. Div., A. S. C. E., 99, 793, 10.1061/JSFEAQ.0001934
Lade P. V., 1982, Three‐parameter failure criterion for concrete, J. Eng. Mech. Div., A. S. C. E., 108, 850, 10.1061/JMCEA3.0002874
Lade P. V., 1984, Mechanics of Engineering Materials, 385
P. V.Lade H. L.JessbergerandN.Diekmann ‘Stress–Strian and volumetric behavior of frozen soil’ Proc. 2nd Int. Symp. Ground Freezing Trondheim 1980 pp.48–64.