KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
권호 표지
DOI QR코드

DOI QR Code

A Constitutive Model for Rotation of Principal Stress Axes during Direct Simple Shear Deformation

직접단순전단변형에 따른 주응력 방향의 회전을 고려한 구성모델

  • 박성식 (원광대학교 공과대학 토목환경도시공학부) ;
  • 이종천 (원광대학교 공과대학 토목환경도시공학부)
  • Received : 2007.10.04
  • Accepted : 2007.11.12
  • Published : 2008.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

A constitutive model, which can simulate the effect of principal stress rotation associated with direct simple shear test, is proposed in this study. The model is based on two mobilized planes. The plastic strains occur from the two mobilized planes, and depend on stress state, and they are added. The first plane is a plane of maximum shear stress, which rotates about the horizontal axis, and the second plane is a horizontal plane which is spatially fixed. The second plane is used to consider the effect of principal stress rotation on simple shear tests under different stress states. The soil skeleton behavior observed in drained simple shear tests is captured in the model. This constitutive model is incorporated into the dynamic coupled stress-flow finite difference program FLAC. The model is first calibrated with drained simple shear tests on loose Fraser River sand. The measured shear stress and volume change are partially induced by principal stress rotation and compared with model calculations. The model is verified by comparing predicted and measured settlements due to rigid footing resting on loose sands. Settlements predicted by the proposed model were very similar to measured settlements. Mohr-Coulomb model can not consider the effect of principal stress rotation and its prediction was only 20% of measured settlements.

본 논문에서는 직접단순전단변형으로 발생하는 주응력 방향의 회전에 의한 소성변형을 고려할 수 있는 구성모델을 제안하였다. 이 모델은 두 개의 응력면에서 발생하는 응력상태의 변화를 이용하여 각 응력면의 소성변형률을 계산하였다. 두 개의 응력면에서 계산된 소성변형률을 합산하여 전체 소성변형률을 구하였다. 첫번째 응력면은 최대전단응력면을 나타내며 이 응력면은 응력변화에 따라 수평방향을 기준으로 회전한다. 두번째 응력면은 수평방향으로 고정된 수평면을 나타낸다. 초기 수직응력과 수평응력이 서로 다른 상태에 있는 직접단순전단시험의 공시체에서 전단변형으로 발생하는 주응력 방향의 회전현상을 두번째 응력면에 작용하는 응력상태를 이용하여 모델링하였다. 본 모델의 구성관계식은 전단변형으로 인한 흙의 골격변화 즉 체적변화를 수식화하였으며 응력-물의 상관관계를 동시에 묘사할 수 있는 FLAC을 이용하여 모델링하였다. 느슨한 Fraser River 모래의 배수 직접단순전단시험에서 발생하는 전단응력과 체적변화는 주응력 방향의 회전에 따른 소성변형을 포함하고 있으므로 이를 계산하여 구성모델을 검증하였다. 느슨한 모래 지반에 놓인 강성기초의 하중 증가에 따라 발생하는 지반침하를 주응력 방향의 회전을 고려하여 예측하였을 때 실제 계측된 침하량과 유사한 결과를 얻었다. 주응력 방향의 회전을 고려하지 않고 Mohr-Coulomb모델을 이용하여 계산된 침하량은 실제 침하량 또는 제안된 모델이 예측한 침하량의 약 20%정도에 해당하였다.

Keywords

References

  1. 오사키(1958) 건축지반조사법(일본어), 옴출판사
  2. Arthur, J. R. F., Chua, K. S., Dunstan, T., and Rodriguez del C. J. I.(1980) Principal stress rotation: a missing parameter. Journal of the Geotechnical Engineering Division, Vol. 106(GT4), pp. 419-433
  3. Arthur, J.R.F., Chua, K.S., and Dunstan, T. (1977) Induced anisotropy in a sand. Geotechnique, Vol. 27, No. 1, pp. 13-30 https://doi.org/10.1680/geot.1977.27.1.13
  4. Burland, J. B. and Burbidge, M. C. (1985) Settlement of foundations on sand and gravel. Proc. Inst. Civ. Engrs., 78, Part 1, pp. 1325-1381
  5. Cudny, M. and Vermeer, P.A. (2004) On the modelling of anisotropy and destructuration of soft clays within the multi-laminate framework. Computers and Geomechanics, Vol. 31, No. 1, pp. 1-22 https://doi.org/10.1016/j.compgeo.2003.12.001
  6. Hill, R. (1950) The mathematical theory of plasticity. Oxford University Press, New York
  7. Ishihara, K. and Towhata, I. (1983) Sand response to cyclic rotation of principal stress direction as induced by wave loads. Soils and Foundations, Vol. 23, No. 4, pp. 11-26 https://doi.org/10.3208/sandf1972.23.4_11
  8. Itasca (2000) FLAC, version 4.0. Itasca Consulting Group Inc., Minneapolis
  9. Kabilamany, K. and Ishihara, K. (1991) Cyclic behaviour of sand by the multiple shear mechanism model. Soil Dynamics and Earthquake Engineering, Vol. 10, No. 2, pp. 74-83 https://doi.org/10.1016/0267-7261(91)90037-Z
  10. Leroueil, S. and Hight, D.W. (2003) Behaviour and properties of natural soils and soft rocks. Characterisation and Engineering Properties of Natural Soils, Edited by Tan, T. S., Phoon, K. K., Hight, D. W. and Leroueil, S., Vol. 1, pp. 29-254
  11. Miura, K. (1985) Study on the deformation behaviour of anisotropic sand under principal stress axes rotation. Ph. D Thesis, Hokkaido University, Japan
  12. Negussey, D., Wijewickreme, D., and Vaid, Y.P. (1988) Constant volume friction angle of granular materials. Canadian Geotechnical Journal, Vol. 25, No. 1, pp. 50-55 https://doi.org/10.1139/t88-006
  13. Pande, G. N. and Sharma, K. G. (1983) Multi-laminate model of clays-a numerical evaluation of the influence of rotation of the principal stress axes. Int. Journal for Numerical and Analytical Methods in Geomechanics, 7, pp. 397-418 https://doi.org/10.1002/nag.1610070404
  14. Park, S.-S. (2005) A Two Mobilized-plane model and its application for soil liquefaction analysis. Ph.D. Thesis, Department of Civil Engineering, University of British Columbia, Canada
  15. Prevost, J.H. (1985) A simple plasticity theory for frictional cohesionless soils. Soil Dynamics and Earthquake Engineering, Vol. 4, No. 1, pp. 9-17 https://doi.org/10.1016/0261-7277(85)90030-0
  16. Sayao, A.S.F. (1989) Behaviour of sand under general stress paths in the hollow cylinder torsional device. Ph.D. Thesis, Department of Civil Engineering, University of British Columbia, Canada
  17. Seed, H.B., Wong, R.T., Idriss, I.M., and Tokimatsu, K. (1986) Moduli and damping factors for dynamic analyses of cohesionless soils. Journal of Geotechnical Engineering, Vol. 112, No. 11, pp. 1016-1032 https://doi.org/10.1061/(ASCE)0733-9410(1986)112:11(1016)
  18. Skempton, A.W. (1986) Standard penetration test procedures and the effects in sands of overburden pressure, relative density, particle size, ageing and overconsolidation. Geotechnique, Vol. 36, No. 3, pp. 425-447 https://doi.org/10.1680/geot.1986.36.3.425
  19. Sture, S., Budiman, J.S., Ontuna, A.K., and Ko, H.-Y. (1987) Directional shear cell experiments on a dry cohesionless soil. Geotechnical Testing Journal, Vol. 10, No. 2, pp. 71-79 https://doi.org/10.1520/GTJ10935J
  20. Symes, M.J., Gens, A., and Hight, D.W. (1988) Drained principal stress rotation in saturated sand. Geotechnique, Vol. 38, No. 1, pp. 59-81 https://doi.org/10.1680/geot.1988.38.1.59
  21. Symes, M.J., Hight, D.W., and Gens, A. (1982) Investigating anisotropy and the effects of principal stress rotation and of the intermediate principal stress using a hollow cylinder. Deformation and Failure of Granular Materials, International Union of Theoretical and Applied Mechanics Symposium, Balkema, pp. 441-449
  22. Wijewickreme, D. and Vaid, Y.P. (1993) Behaviour of loose sand under simultaneous increase in stress ratio and principal stress rotation. Canadian Geotechnical Journal, Vol. 30, No. 6, pp. 953-964 https://doi.org/10.1139/t93-093