Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
권호 표지

A Study on the Estimation of Diameter Distribution and Volumetric Frequency of Joint Discs Using the Least Square Method

최소자승법을 이용한 원판형 절리의 직경분포와 체적빈도 추정에 관한 연구

  • 송재준 (서울대학교 지구환경시스템공학부)
  • Published : 2005.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

An estimation technique of the joint diameter distribution using the least square method is suggested. When utilizing the technique by Song and Lee, the diameter distribution would be obtained only from the trace length distribution defined in an infinite window after the trace length distribution is estimated from the contained trace length distribution. With the new technique, however, the diameter distribution can be directly obtained from the sample histogram of the contained trace lengths. Compared with the previous technique, it shows a more accurate result for small sizes of joint samples and provides the joint geometry parameter of volumetric frequency. Verification of this new technique was completed by using Monte Carlo simulations.

이 연구에서는 최소자승법을 이용하여 절리의 직경분포를 추정하는 방법을 개발하였다. 이전에 Song and Lee가 제안한 방법에서는 현장에서 조사한 양끝내포선(contained trace) 분포로부터 무한 조사창에서 정의되는 절리선(joint trace) 길이 분포를 먼저 구하고 이 후에 직경분포를 구하게 된다. 그러나 새로 제안한 방법을 사용하면 중간 추정과정없이 현장에서 얻은 양끝내포선 분포로부터 바로 절리의 직경분포를 구할 수 있다. 이전의 방법과 비교할 때 새로 제안된 방법은 표본의 크기가 작을 때 조금 더 높은 추정정밀도를 보이며, 직경분포를 추정하는 과정에서 절리의 기하학적 파라미터의 하나인 체적빈도(volumetric frequency)도 제공한다. 새로운 추정법의 검증을 위해 Monte Carlo 시뮬레이션을 적용하였다.

Keywords

References

  1. Baecher, G.B., HH Einstein and N.A. Lanney, 1977, Statistical description of rock properties and sampling. 18th U.S. Symposium on Rock Mechanics, 1-8
  2. Baecher, G.B. and N.A. Lanney, 1978, Trace length biases in joint surveys. 19th U.S. Symposium on Rock Mechanics, Vol. 1, 56-65
  3. Dienes, J.K., 1979, On the inference of crack statistics from observations on an outcropping. 20th U.S. Symposium on Rock Mechanics, Austin, Texas, 259-63
  4. Kulatilake, P.H.S.W. and T.H. Wu, 1986, Relation between discontinuity size and trace length. 27th U.S. Symposium on Rock Mechanics, Tuscaloosa, Alabama, 130-133
  5. Lyman, G.J., 2003, Rock fracrure mean trace length estimation and confidence interval calculation using maximum likelihood methods, Int. J. Rock Mech. Min. Sci., 40.6, 825-832 https://doi.org/10.1016/S1365-1609(03)00043-1
  6. Mauldon, M., 1998, Estimating mean fracture trace length and density from observations in convex windows. Rock Mechanics and Rock Engineering, 31.4, 201-216 https://doi.org/10.1007/s006030050021
  7. Pahl, P.J., 1981, Estimating the mean length of discontinuity traces. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 18, 221-8 https://doi.org/10.1016/0148-9062(81)90976-1
  8. Priest, S.D., 1993, Discontinuity analysis for rock engineering. London: Chapman & Hall
  9. Priest, S.D. and J. Hudson, 1981, Estimation of discontinuity spacing and trace length using scanline surveys. Int. J. Rock Mech. Sci. & Geomech. Abstr., Vol. 18, 183-97 https://doi.org/10.1016/0148-9062(81)90973-6
  10. Song, U. and C.I. Lee, 2001, Estimation of joint length distribution using window sampling. Int. J. Rock Mech. & Min. Sci., Vol. 38, 519-528 https://doi.org/10.1016/S1365-1609(01)00018-1
  11. Villaescusa, E. and E.T. Brown, 1992, Maximum likelihood estimation of joint size from trace length measurements. Rock Mechanics and Rock Engineering, Vol. 25, 67-87 https://doi.org/10.1007/BF01040513
  12. Warburton, P.M., 1980, A stereological interpretation of joint trace data. Int. J. Rock Mech. Min. Sci & Geomech. Abstr, Vol. 17, 181-190 https://doi.org/10.1016/0148-9062(80)91084-0
  13. Zhang, L. and H.H. Einstein, 1998, Estimating the mean trace length of rock discontinuities. Rock Mechanics and Rock Engineering, 31. 4, 217-235 https://doi.org/10.1007/s006030050022