Journal of the Korean Geotechnical Society (한국지반공학회논문집)

Korean Geotechnical Society (한국지반공학회)
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Elastic-plastic Micromechanics Modeling of Cross-anisotropic Granular Soils: I. Formulation

직교 이방적 사질토의 미시역학적 탄소성 모델링: I. 정식화

  • Published : 2007.03.31
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Abstract

A micromechanics-based model to simulate the elastic and elastic-plastic behavior of granular soils is developed. The model accounts for the fabric anisotropy represented by the statistical parameter of the spatial distribution of contact normals, the evolution of fabric anisotropy as a function of stress ratio, the continuous change of the co-ordination number relating to the void ratio, and the elastic and elastic-plastic microscopic contact stiffness. Using the experimental data for metallic materials, the elastic-plastic contact stiffness is derived as a power function of the normal contact force as well as the contact force initiating the yielding of contact bodies. To quantitatively assess microscopic model parameters, approximate solutions of cross-anisotropic elastic moduli are derived in terms of the micromechanical parameters.

본 연구에서는 사질토의 탄성 및 탄소성 거동을 모사하기 위한 미시역학 기반의 구성 모델을 개발하였다. 개발 모델은 접촉 방향의 공간 분포를 통계적으로 처리한 조직 이방성, 응력비에 따른 조직 이방성의 변화, 간극비 변화에 따른 접촉점 수의 변화, 그리고 미시적 탄성-탄소성 접촉 강성을 고려하였다. 금속 재료에 대한 시험결과를 이용하여 미시적 탄소성 접촉 강성 모델을 수직 접촉력과 입자의 항복 접촉력에 대한 거듭제곱 함수의 형태로 유도하였다. 모델 변수를 정량적으로 평가하기 위해 직교 이방 탄성 계수의 근사식을 유도하였다.

Keywords

References

  1. Adams, G. G., and Nosonovsky, M. (2000), 'Contact modeling forces', Tribology international, 33, 431-442 https://doi.org/10.1016/S0301-679X(00)00063-3
  2. Bazant, Z. P., Caner, F. c., Carol, L, Adley, M. D., and Akers, S. A. (2000), 'Microplane model M4 for concrete. I: Formulation with work-conjugate deviatoric stress', Journal of Engineering Mechanics-ASCE, 126(9), 944-953 https://doi.org/10.1061/(ASCE)0733-9399(2000)126:9(944)
  3. Chang, C. S., Chao, S. J., and Chang, Y. (1995), 'Estimates of Elastic-Moduli for Granular Material with Anisotropic Random Packing Structure', International Journal of Solids and Structures, 32(14), 1989-2008 https://doi.org/10.1016/0020-7683(94)00225-L
  4. Chang, C. S., and Gao, J. (1996), 'Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation', Acta Mechanica, 115(1-4), 213-229 https://doi.org/10.1007/BF01187424
  5. Chang, C. S., Misra, A., and Sundaram, S. S. (1991), 'Properties of granular packings under low amplitude cyclic loading', Soil Dynamics and Earthquake Engineering, 10(4), 201-211 https://doi.org/10.1016/0267-7261(91)90034-W
  6. Chang, C. S., Sundaram, S. S., and Misra, A. (1989), 'Initial Moduli of Particulated Mass with Frictional Contacts', International Journal for Numerical and Analytical Methods in Geomechanics, 13(6), 629-644 https://doi.org/10.1002/nag.1610130605
  7. Christoffersen, J., Mehrabadi, M. M., and Nematnasser, S. (1981), 'A Micromechanical Description of Granular Material Behavior', Journal of Applied Mechanics-Transactions of the Asme, 48(2), 339-344 https://doi.org/10.1115/1.3157619
  8. Cundall, P. A., and Strack, O. D. L. (1979), 'Discrete NumericalModel for Granular Assemblies', Geotechnique, 29(1), 47-65 https://doi.org/10.1680/geot.1979.29.1.47
  9. Darve, F., and Nicot, F. (2005), 'On incremental non-linearity in granular media: phenomenological and multi-scale views (Part I)', International Journal for Numerical and Analytical Methods in Geomechanics, 29(14), 1387-1409 https://doi.org/10.1002/nag.466
  10. Einav, I., and Puzrin, A. M. (2004), 'Continuous hyperplastic critical state (CHCS) model Derivation', International Journal of Solids and Structures, 41(1), 199-226 https://doi.org/10.1016/j.ijsolstr.2003.09.012
  11. Emeriault, F., and Cambou, B. (1996), 'Micromechanical modelling of anisotropic non-linear elasticity of granular medium', International Journal of Solids and Structures, 33(18), 2591-2607 https://doi.org/10.1016/0020-7683(95)00170-0
  12. Emeriault, F., and Chang, C. S. (1997), 'Interparticle forces and displacements in granular materials', Computers and Geotechnics, 20(3-4), 223-244 https://doi.org/10.1016/S0266-352X(97)00004-9
  13. Fang, H. L. (2003), 'A state-dependent multi-mechanism model for sands', Geotechnique, 53(4), 407-420 https://doi.org/10.1680/geot.53.4.407.37320
  14. Goddard, J. D. (1990), 'Nonlinear Elasticity and Pressure-Dependent Wave Speeds in Granular Media', Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 430(1878), 105-131
  15. Hertz, H. (1882), 'Uber die Beruhrung fester elastischer Korper (On the contact of elastic solids)', Journal of reine und angewandte mathematik, 92, 156-171
  16. Hicher, P. Y., and Chang, C. S. (2005), 'Evaluation of two homogenization techniques for modeling the elastic behavior of granular materials', Journal of Engineering Mechanics-ASCE, 131(11), 1184-1194 https://doi.org/10.1061/(ASCE)0733-9399(2005)131:11(1184)
  17. Jager, J. (1999), 'Uniaxial deformation of a random packing of particles', Archive of Applied Mechanics, 69(3), 181-203 https://doi.org/10.1007/s004190050213
  18. Johnson, K. L. (1985), Contact mechanics, Cambridge University Press, Cambridge
  19. lung, Y. H., Chung, C. K., and Finno, R. J. (2004), 'Development of nonlinear cross-anisotropic model for the pre-failure deformation of geomaterials', Computers and Geotechnics, 31(2), 89-102 https://doi.org/10.1016/j.compgeo.2004.01.002
  20. Kuwano, R., and Jardine, R. J. (2002), 'On the applicability of cross-anisotropic elasticity to granular materials at very small strains', Geotechnique, 52(10), 727-749 https://doi.org/10.1680/geot.52.10.727.38848
  21. Liao, C. L., Chan, T. C., Suiker, A. S. J., and Chang, C. S. (2000), 'Pressure-dependent elastic moduli of granular assemblies', International Journal for Numerical and Analytical Methods in Geomechanics, 24(3), 265-279 https://doi.org/10.1002/(SICI)1096-9853(200003)24:3<265::AID-NAG65>3.0.CO;2-X
  22. Liao, C. L., Chang, T. P., Young, D. H., and Chang, C. S. (1997), 'Stress-strain relationship for granular materials based on the hypothesis of best fit', International Journal of Solids and Structures, 34(31-32), 4087-4100 https://doi.org/10.1016/0020-7683(95)00287-1
  23. Love, A. E. H. (1927), A Treatise of the mathematical theory of elasticity, Cambridge university press, Cambridge, UK
  24. Madadi, M., Tsoungui, O., Latzel, M., and Luding, S. (2004), 'On the fabric tensor of polydisperse granular materials in 2D', International Journal of Solids and Structures, 41(9-10), 2563-2580 https://doi.org/10.1016/j.ijsolstr.2003.12.005
  25. Mehrabadi, M. M., Nematnasser, S., and Oda, M. (1982), 'On Statistical Description of Stress and Fabric in Granular-Materials', International Journal for Numerical and Analytical Methods in Geomechanics, 6(1), 95-108 https://doi.org/10.1002/nag.1610060107
  26. Mindlin, R. D. (1949), 'Comliance of elastic bodies in contact', Journal of applied mechanics, 16, 259-270
  27. Mindlin, R. D., and Deresiewicz, H. (1953), 'Elastic spheres in contact under varying oblique forces', Journal of applied mechanics, ASME, 20(3), 327-344
  28. Mulhearn, T. O. (1959), 'Deformation of metals by Vickers-type pyramidal indenters', J. Mech. Physics Solids, 7, 85-92 https://doi.org/10.1016/0022-5096(59)90013-4
  29. Nicot, F., and Darve, F. (2006), 'Micro-mechanical investigation of material instability in granular assemblies', International Journal of Solids and Structures, 43(11-12), 3569-3595 https://doi.org/10.1016/j.ijsolstr.2005.07.008
  30. Oda, M., Nematnasser, S., and Mehrabadi, M. M. (1982), 'A Statistical Study of Fabric in a Random Assembly of Spherical Granules', International Journal for Numerical and Analytical Methods in Geomechanics, 6(1), 77-94 https://doi.org/10.1002/nag.1610060106
  31. Ouadfel, H., and Rothenburg, L. (2001), 'Stress-force-fabric' relationship for assemblies of ellipsoids', Mechanics of Materials, 33(4), 201-221 https://doi.org/10.1016/S0167-6636(00)00057-0
  32. Pestana, J. M., Whittle, A. J., and Salvati, L. A. (2002), 'Evaluation of a constitutive model for clays and sands: Part I - sand behaviour', International Journal for Numerical and Analytical Methods in Geomechanics, 26(11), 1097-1121 https://doi.org/10.1002/nag.237
  33. Puzrin, A. M., and Burland, J. B. (2000), 'Kinematic hardening plasticity formulation of small strain behaviour of soils', International Journal for Numerical and Analytical Methods in Geomechanics, 24(9), 753-781 https://doi.org/10.1002/1096-9853(20000810)24:9<753::AID-NAG97>3.0.CO;2-2
  34. Samuels, L. E., and Mulhearn, T. O. (1956), 'The deformation zone associated with indentation hardness impressions', J. Mech. Physics Solids, 5, 125-130 https://doi.org/10.1016/0022-5096(57)90056-X
  35. Stallebrass, S. E., and Taylor, R. N. (1997), 'The development and evaluation of a constitutive model for the prediction of ground movements in overconsolidated clay', Geotechnique, 47(2), 235-253 https://doi.org/10.1680/geot.1997.47.2.235
  36. Walton, O. R., and Braun, R. L. (1986), 'Viscosity, granulartemperature, and stress calculations for shearing assemblies of inelastic, friction disks', Journal of rheology, 30(5), 949-980 https://doi.org/10.1122/1.549893
  37. Yimsiri, S., and Soga, K. (2000), 'Micrornechanics-based stress-strain behaviour of soils at small strains', Geotechnique, 50(5), 559-571 https://doi.org/10.1680/geot.2000.50.5.559
  38. Yu, P., and Richart, F. E., Jr. (1984), 'Stress ratio effects on shear modulus of dry sands', Journal of Geotechnical Engineering, 110(3), 331-345 https://doi.org/10.1061/(ASCE)0733-9410(1984)110:3(331)