Prediction of Strength for Transversely Isotopic Rock Based on Critical Plane Approach

임계면법을 이용한 횡등방성 암석의 강도 예측

  • 이연규 (군산대학교 해양시스템공학)
  • Published : 2007.04.30

Abstract

Based on the critical plane approach, a methodology far predicting the anisotropic strength ot transversely isotropic rock is Proposed. It is assumed that the rock failure is governed by Hoek-Brown failure criterion. In order to establish an anisotropic failure function, Mohr envelope equivalent to the original Hoek-Brown criterion is used and the strength parameters m, s are expressed as scalar functions of orientation. The conjugate gradient method, which is one of the robust optimization techniques, is applied to the failure function for searching the orientation giving the maximum value of the anisotropic function. While most of the existing anisotropic strength models can be applied only when the stress condition is the same as that of conventional triaxial compression test, the proposed model can be applied to the general 3-dimensional stress conditions. Through the simulation of triaxial compression tests for transversely isotropic rock sample, the validity of the proposed method is investigated by comparing the predicted triaxial strengths and inclinations of failure plane.

임계면법을 적용하여 횡등방성 암석의 강도이방성을 해석하는 방법을 제안하였다. 암석의 파괴는 Hoek-Brown 파괴기준을 따르는 것으로 가정하였다. Hoek-Brown의 경험적 파괴기준식에 대응되는 Mohr 포착선식을 이용하고 강도상수인 m과 s를 방향에 따른 스칼라 함수로 정의하여 이방성 파괴함수를 구성하였다. 이방성 파괴함수를 최대고 하는 임계면의 방향을 찾기 위하여 직접 최적화기법의 하나인 공액구배법을 적용하였다. 횡등방성 안석에 대한 기존 이방성 강도모델이 대부분 삼축압축실험과 동일한 응력조건에서만 적용할 수 있는데 반하여 이 연구에서 제안된 방법은 일반적인 3차원 응력조건에도 쉽게 적용할 수 있다는 장점을 가지고 있다. 삼축압축실험의 모사를 통하여 얻어진 삼축압축강도와 파괴면의 경사에 분석을 통하여 제안된 방법의 적합성을 검토하였다.

Keywords

References

  1. Jaeger, J.C., 1960, Shear failure of anisotropic rocks. Geologic Magazine, 97, 65-72 https://doi.org/10.1017/S0016756800061100
  2. Donath, F.A., 1964, Strength variation and deformation behavior in anisotropic rock. In 'State of stress in the Earth's crust', W.R. Judd (Ed.), 281-298
  3. Horino, F.G. and M.L. Ellickson, 1970, A method of estimating strength of rock containing planes of weakness. U.S. Bureau of Mines Report of Investigation, R.I. 7449
  4. Hoek, E. 1983, Strength of jointed rock masses. Geotechnique, 33(3), 187-223 https://doi.org/10.1680/geot.1983.33.3.187
  5. Hoek, E., and E.T. Brown, 1980, Underground excavations in rock. London: Institution of Mining and Metallurgy
  6. Kanatani, K.-I., 1984, Distribution of directional data and fabric tensors. lnt. J. Engng Sci., 22, 149-164 https://doi.org/10.1016/0020-7225(84)90090-9
  7. McLamore, R. and K.E. Gray, 1967, The mechanical behaviour of anisotropic sedimentary rocks. Trans. Am. Soc. Mech. Engrs Series B, 62-76
  8. Pietruszczak, S. and Z. Mroz, 2001, On failure criteria for anisotropic cohesive-frictional materials. Int. J. Numer. Anal. Meth. Goemech. 25, 509-524 https://doi.org/10.1002/nag.141
  9. Pietruszczak, S., D. Lydzba, and J.F. Shao, 2002, Modelling of inherent anisotropy in sedimentary rocks. Int. J. Solids Struct. 39, 637-648 https://doi.org/10.1016/S0020-7683(01)00110-X
  10. Press, W.H., S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, 1992, Numerical recipes in Fortran. Cambridge University Press
  11. Ushaksaraei, R. and S. Pietruszczak, 2002, Failure criterion for structural masonry based on critical plane approach. J. Eng. Mech. 128(7), 769-778 https://doi.org/10.1061/(ASCE)0733-9399(2002)128:7(769)