메뉴 건너뛰기




Volumn 43, Issue 6, 2006, Pages 877-893

Inference of discontinuity trace length distributions using statistical graphical models

Author keywords

Discontinuity size; EM algorithm; Fracture network; Maximum likelihood

Indexed keywords

ALGORITHMS; FRACTURE MECHANICS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; RANDOM PROCESSES; STATISTICAL METHODS;

EID: 33744506085     PISSN: 13651609     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijrmms.2005.12.008     Document Type: Article
Times cited : (45)

References (67)
  • 3
    • 85154621968 scopus 로고    scopus 로고
    • ISRM. Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Mining Sci Geomech Abstracts 1978;15(6):319-68.
  • 4
    • 85154552585 scopus 로고    scopus 로고
    • Priest SD. The collection and analysis of discontinuity orientation data for engineering design, with examples. In: Hudson JA, editor. Comprehensive rock engineering; principles, practice & projects: rock testing and site characterization. Oxford: Pergamon Press; 1993. p. 167-92.
  • 5
    • 85154545337 scopus 로고    scopus 로고
    • La Pointe PR. Pattern analysis and simulation of joints for rock engineering. In: Hudson JA, editor. Comprehensive rock engineering. volume 3-rock testing and site characterization. Oxford: Pergamon Press; 1993. p. 215-39.
  • 6
    • 0023834736 scopus 로고
    • Characterizing rock joint geometry with joint system models
    • Dershowitz W.S., and Einstein H.H. Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21 1 (1988) 21-51
    • (1988) Rock Mech Rock Eng , vol.21 , Issue.1 , pp. 21-51
    • Dershowitz, W.S.1    Einstein, H.H.2
  • 7
    • 0027560892 scopus 로고
    • Stochastic three dimensional joint size, intensity and system modelling and a validation to an area in Stripa Mine, Sweden
    • Kulatilake P.H.S.W., Wathugala D.N., and Stephansson O. Stochastic three dimensional joint size, intensity and system modelling and a validation to an area in Stripa Mine, Sweden. Soils Foundations 33 1 (1993) 55-70
    • (1993) Soils Foundations , vol.33 , Issue.1 , pp. 55-70
    • Kulatilake, P.H.S.W.1    Wathugala, D.N.2    Stephansson, O.3
  • 8
    • 0036464928 scopus 로고    scopus 로고
    • Geologic stochastic modeling and connectivity assessment of fracture systems in the Boston area
    • Meyer T., and Einstein H.H. Geologic stochastic modeling and connectivity assessment of fracture systems in the Boston area. Rock Mech Rock Eng 35 1 (2002) 23-44
    • (2002) Rock Mech Rock Eng , vol.35 , Issue.1 , pp. 23-44
    • Meyer, T.1    Einstein, H.H.2
  • 10
    • 0019242168 scopus 로고
    • Stereological interpretation of joint trace data: influence of joint shape and implications for geological surveys
    • Warburton P.M. Stereological interpretation of joint trace data: influence of joint shape and implications for geological surveys. Int J Rock Mech Mining Sci Geomech Abstracts 17 6 (1980) 305-316
    • (1980) Int J Rock Mech Mining Sci Geomech Abstracts , vol.17 , Issue.6 , pp. 305-316
    • Warburton, P.M.1
  • 12
    • 0036528987 scopus 로고    scopus 로고
    • Derivation of parent fracture population statistics from trace length measurements of fractal fracture populations
    • La Pointe P.R. Derivation of parent fracture population statistics from trace length measurements of fractal fracture populations. Int J Rock Mech Mining Sci 39 (2002) 381-388
    • (2002) Int J Rock Mech Mining Sci , vol.39 , pp. 381-388
    • La Pointe, P.R.1
  • 13
    • 0742305761 scopus 로고    scopus 로고
    • Stereological and other methods applied to rock joint size estimation-does Crofton's theorem apply?
    • Lyman G.J. Stereological and other methods applied to rock joint size estimation-does Crofton's theorem apply?. Math Geol 35 1 (2003) 9-23
    • (2003) Math Geol , vol.35 , Issue.1 , pp. 9-23
    • Lyman, G.J.1
  • 14
    • 0036698032 scopus 로고    scopus 로고
    • Stereological relationship between trace length and size distribution of elliptical discontinuities
    • Zhang L., Einstein H.H., and Dershowitz W.S. Stereological relationship between trace length and size distribution of elliptical discontinuities. Géotechnique 52 6 (2002) 419-433
    • (2002) Géotechnique , vol.52 , Issue.6 , pp. 419-433
    • Zhang, L.1    Einstein, H.H.2    Dershowitz, W.S.3
  • 15
    • 10444227186 scopus 로고    scopus 로고
    • Determination of discontinuity size distributions from scanline data
    • Priest S.D. Determination of discontinuity size distributions from scanline data. Rock Mech Rock Eng 37 5 (2004) 347-368
    • (2004) Rock Mech Rock Eng , vol.37 , Issue.5 , pp. 347-368
    • Priest, S.D.1
  • 16
    • 84888960509 scopus 로고
    • Sources of errors in joint surveys
    • Terzaghi R.D. Sources of errors in joint surveys. Geotechnique 15 (1965) 287-304
    • (1965) Geotechnique , vol.15 , pp. 287-304
    • Terzaghi, R.D.1
  • 17
    • 0032182859 scopus 로고    scopus 로고
    • Estimating the mean trace length of rock discontinuities
    • Zhang L., and Einstein H.H. Estimating the mean trace length of rock discontinuities. Rock Mech Rock Eng 31 4 (1998) 217-235
    • (1998) Rock Mech Rock Eng , vol.31 , Issue.4 , pp. 217-235
    • Zhang, L.1    Einstein, H.H.2
  • 18
    • 0001815888 scopus 로고
    • Maximum likelihood estimation of joint size from trace length measurements
    • Villaescusa E., and Brown E.T. Maximum likelihood estimation of joint size from trace length measurements. Rock Mech Rock Eng 25 2 (1992) 67-87
    • (1992) Rock Mech Rock Eng , vol.25 , Issue.2 , pp. 67-87
    • Villaescusa, E.1    Brown, E.T.2
  • 19
    • 0021505792 scopus 로고
    • Estimation of mean trace length of discontinuities
    • Kulatilake P.H.S.W., and Wu T.H. Estimation of mean trace length of discontinuities. Rock Mech Rock Eng 17 4 (1984) 243-253
    • (1984) Rock Mech Rock Eng , vol.17 , Issue.4 , pp. 243-253
    • Kulatilake, P.H.S.W.1    Wu, T.H.2
  • 20
    • 0035361644 scopus 로고    scopus 로고
    • Estimation of joint length distribution using window sampling
    • Song J.J., and Lee C.I. Estimation of joint length distribution using window sampling. Int J Rock Mech Mining Sci 38 4 (2001) 519-528
    • (2001) Int J Rock Mech Mining Sci , vol.38 , Issue.4 , pp. 519-528
    • Song, J.J.1    Lee, C.I.2
  • 21
    • 0033940091 scopus 로고    scopus 로고
    • Estimating the intensity of rock discontinuities
    • Zhang L.Y., and Einstein H.H. Estimating the intensity of rock discontinuities. Int J Rock Mech Mining Sci 37 5 (2000) 819-837
    • (2000) Int J Rock Mech Mining Sci , vol.37 , Issue.5 , pp. 819-837
    • Zhang, L.Y.1    Einstein, H.H.2
  • 22
    • 0036521661 scopus 로고    scopus 로고
    • Statistical model for structure of jointed rock mass
    • Wu F., and Wang S. Statistical model for structure of jointed rock mass. Géotechnique 52 2 (2002) 137-140
    • (2002) Géotechnique , vol.52 , Issue.2 , pp. 137-140
    • Wu, F.1    Wang, S.2
  • 23
    • 0001107658 scopus 로고
    • Censoring and edge effects in areal and line transect sampling of rock joint traces
    • Laslett G.M. Censoring and edge effects in areal and line transect sampling of rock joint traces. J Int Assoc Math Geol 14 7 (1982) 125-140
    • (1982) J Int Assoc Math Geol , vol.14 , Issue.7 , pp. 125-140
    • Laslett, G.M.1
  • 24
    • 85154571087 scopus 로고    scopus 로고
    • Laubach S, Marrett R, Olson J. New directions in fracture characterization. The leading edge 2000. p. 704-11. [Also available at http://www.beg.texas.edu/indassoc/fraccity/public/documents/TLE%Fractures.pdf].
  • 25
    • 0019574303 scopus 로고
    • Estimating the mean length of discontinuity traces
    • Pahl P.J. Estimating the mean length of discontinuity traces. Int J Rock Mech Mining Sci Geomech Abstracts 18 3 (1981) 221-228
    • (1981) Int J Rock Mech Mining Sci Geomech Abstracts , vol.18 , Issue.3 , pp. 221-228
    • Pahl, P.J.1
  • 26
    • 0032182827 scopus 로고    scopus 로고
    • Estimating mean fracture trace length and density from observations in convex windows
    • Mauldon M. Estimating mean fracture trace length and density from observations in convex windows. Rock Mech Rock Eng 31 4 (1998) 201-216
    • (1998) Rock Mech Rock Eng , vol.31 , Issue.4 , pp. 201-216
    • Mauldon, M.1
  • 28
    • 85154581041 scopus 로고    scopus 로고
    • Einstein HH. Modern developments in discontinuity analysis-the persistence-discontinuity problem. In: Hudson JA, editor. Comprehensive rock engineering, volume 3-rock testing and site characterization. New York: Pergamon Press; 1993. p. 215-39.
  • 29
    • 0141457344 scopus 로고    scopus 로고
    • Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods
    • Lyman G.J. Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods. Int J Rock Mech Mining Sci 40 (2003) 825-832
    • (2003) Int J Rock Mech Mining Sci , vol.40 , pp. 825-832
    • Lyman, G.J.1
  • 30
    • 85154578657 scopus 로고    scopus 로고
    • Jimenez-Rodriguez R, Sitar N, Bartlett PL. Maximum likelihood estimation of trace length distribution parameters using the EM algorithm. In: Barla G, Barla M, editors. Prediction, analysis and design in geomechanical applications: proceedings of the eleventh international conference on computer methods and advances in geomechanics (IACMAG-2005), vol. 1. Bologna: Pàtron Editore; 2005. p. 619-26.
  • 31
    • 85154569309 scopus 로고    scopus 로고
    • Jimenez-Rodriguez R, Sitar N, Chacón J. Caracterización de discontinuidades en macizos rocosos mediante modelos gráficos probabilísticos [Characterization of discontinuities in rock masses by means of probabilistic graphical models]. In: Pérez Aparicio J, Rodríguez Ferrán A, Martins J, Gallego R, César de Sá J, editors. Métodos Numéricos en Ingeniería 2005 [Numerical Methods in Eng 2005]. Barcelona: SEMNI, Sociedad Española de Métodos Numéricos en Ingeniería; 2005. p. 222. Extended abstract in Proceedings; full paper in CD-Rom.
  • 33
    • 0034770763 scopus 로고    scopus 로고
    • Data acquisition in engineering geology. An improvement of acquisition methods for geotechnical rock mass parameters
    • Fasching A., Gaich A., and Schubert W. Data acquisition in engineering geology. An improvement of acquisition methods for geotechnical rock mass parameters. Felsbau 19 5 (2001) 93-101
    • (2001) Felsbau , vol.19 , Issue.5 , pp. 93-101
    • Fasching, A.1    Gaich, A.2    Schubert, W.3
  • 34
    • 0141568945 scopus 로고    scopus 로고
    • Discontinuity trace map construction using photographs of rock exposures
    • Lemy F., and Hadjigeorgiou J. Discontinuity trace map construction using photographs of rock exposures. Int J Rock Mech Mining Sci 40 6 (2003) 903-917
    • (2003) Int J Rock Mech Mining Sci , vol.40 , Issue.6 , pp. 903-917
    • Lemy, F.1    Hadjigeorgiou, J.2
  • 35
    • 0038680611 scopus 로고    scopus 로고
    • An evaluation of image analysis algorithms for constructing discontinuity trace maps
    • Hadjigeorgiou J., Lemy F., Côté P., and Maldague X. An evaluation of image analysis algorithms for constructing discontinuity trace maps. Rock Mech Rock Eng 36 2 (2003) 163-179
    • (2003) Rock Mech Rock Eng , vol.36 , Issue.2 , pp. 163-179
    • Hadjigeorgiou, J.1    Lemy, F.2    Côté, P.3    Maldague, X.4
  • 36
    • 85154607967 scopus 로고    scopus 로고
    • Chan LY. Application of block theory and simulation techniques to optimum design of rock excavations. Ph.D. thesis, University of California, Berkeley; 1987.
  • 38
    • 84984819313 scopus 로고
    • Predicting the number of dimensions of key blocks of an excavation using block theory and joint statistics
    • Farmer I.W., Daemen J.J.K., Desai C.S., Glass C.E., and Neuman S.P. (Eds), A.A. Balkema, Rotterdam
    • Chan L.Y., and Goodman R.E. Predicting the number of dimensions of key blocks of an excavation using block theory and joint statistics. In: Farmer I.W., Daemen J.J.K., Desai C.S., Glass C.E., and Neuman S.P. (Eds). Rock mechanics; proceedings of the 28th U.S. symposium (1987), A.A. Balkema, Rotterdam 81-87
    • (1987) Rock mechanics; proceedings of the 28th U.S. symposium , pp. 81-87
    • Chan, L.Y.1    Goodman, R.E.2
  • 41
    • 0035492503 scopus 로고    scopus 로고
    • Stability analysis of rock blocks around a tunnel using a statistical joint modeling technique
    • Song J.J., Lee C.I., and Seto M. Stability analysis of rock blocks around a tunnel using a statistical joint modeling technique. Tunnelling Underground Space Technol 16 4 (2001) 341-351
    • (2001) Tunnelling Underground Space Technol , vol.16 , Issue.4 , pp. 341-351
    • Song, J.J.1    Lee, C.I.2    Seto, M.3
  • 42
    • 0002066763 scopus 로고
    • Fractal geometry of two-dimensional fracture networks at Yucca Mountain, Southwestern Nevada
    • Stephansson O. (Ed), Centek, Lulea, Sweden
    • Barton C., and Larsen E. Fractal geometry of two-dimensional fracture networks at Yucca Mountain, Southwestern Nevada. In: Stephansson O. (Ed). Proceedings of the international symposium on fundamentals of rock joints (1985), Centek, Lulea, Sweden 77-84
    • (1985) Proceedings of the international symposium on fundamentals of rock joints , pp. 77-84
    • Barton, C.1    Larsen, E.2
  • 44
    • 0031412438 scopus 로고    scopus 로고
    • Box fractal dimension as a measure of statistical homogeneity of jointed rock masses
    • Kulatilake P., Fiedler R., and Panda B.B. Box fractal dimension as a measure of statistical homogeneity of jointed rock masses. Engineering Geology 48 3-4 (1997) 217-229
    • (1997) Engineering Geology , vol.48 , Issue.3-4 , pp. 217-229
    • Kulatilake, P.1    Fiedler, R.2    Panda, B.B.3
  • 45
    • 0031252104 scopus 로고    scopus 로고
    • Scaling and connectivity of joint systems in sandstones from western Norway
    • Odling N. Scaling and connectivity of joint systems in sandstones from western Norway. J Struct Geol 19 10 (1997) 1257-1271
    • (1997) J Struct Geol , vol.19 , Issue.10 , pp. 1257-1271
    • Odling, N.1
  • 46
    • 0033625887 scopus 로고    scopus 로고
    • Fractal analysis of joint patterns in granite
    • Ehlen J. Fractal analysis of joint patterns in granite. Int J Rock Mech Mining Sci 37 6 (2000) 909-922
    • (2000) Int J Rock Mech Mining Sci , vol.37 , Issue.6 , pp. 909-922
    • Ehlen, J.1
  • 47
    • 0019574773 scopus 로고
    • Estimation of discontinuity spacing and trace length using scanline surveys
    • Priest S.D., and Hudson J.A. Estimation of discontinuity spacing and trace length using scanline surveys. Int J Rock Mech Mining Sci Geomech Abstracts 18 3 (1981) 183-197
    • (1981) Int J Rock Mech Mining Sci Geomech Abstracts , vol.18 , Issue.3 , pp. 183-197
    • Priest, S.D.1    Hudson, J.A.2
  • 48
    • 0035054058 scopus 로고    scopus 로고
    • Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces
    • Mauldon M., Dunne W.M., and Rohrbaugh M.B. Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces. J Struct Geol 23 2-3 (2001) 247-258
    • (2001) J Struct Geol , vol.23 , Issue.2-3 , pp. 247-258
    • Mauldon, M.1    Dunne, W.M.2    Rohrbaugh, M.B.3
  • 49
    • 0021505159 scopus 로고
    • Sampling bias on orientation of discontinuities
    • Kulatilake P.H.S.W., and Wu T.H. Sampling bias on orientation of discontinuities. Rock Mech Rock Eng 17 4 (1984) 215-232
    • (1984) Rock Mech Rock Eng , vol.17 , Issue.4 , pp. 215-232
    • Kulatilake, P.H.S.W.1    Wu, T.H.2
  • 50
    • 0025570686 scopus 로고
    • A general procedure to correct sampling bias on joint orientation using a vector approach
    • Wathugala D.N., Kulatilake P.H.S.W., Wathugala G.W., and Stephansson O. A general procedure to correct sampling bias on joint orientation using a vector approach. Comput Geotech 10 (1990) 1-31
    • (1990) Comput Geotech , vol.10 , pp. 1-31
    • Wathugala, D.N.1    Kulatilake, P.H.S.W.2    Wathugala, G.W.3    Stephansson, O.4
  • 51
    • 0031185778 scopus 로고    scopus 로고
    • Fracture sampling on a cylinder: from scanlines to boreholes and tunnels
    • Mauldon M., and Mauldon J.G. Fracture sampling on a cylinder: from scanlines to boreholes and tunnels. Rock Mech Rock Eng 30 3 (1997) 129-144
    • (1997) Rock Mech Rock Eng , vol.30 , Issue.3 , pp. 129-144
    • Mauldon, M.1    Mauldon, J.G.2
  • 52
    • 0001457258 scopus 로고
    • The survival curve under monotone density constraints with applications to two-dimensional line segment processes
    • Laslett G.M. The survival curve under monotone density constraints with applications to two-dimensional line segment processes. Biometrika 69 1 (1982) 153-160
    • (1982) Biometrika , vol.69 , Issue.1 , pp. 153-160
    • Laslett, G.M.1
  • 53
    • 85154571081 scopus 로고    scopus 로고
    • Starzec P. Characterisation and modeling of discontinuous rock mass: geostatistical interpretation of seismic response to fracture occurrence, discrete fracture network modeling and stability predictions for underground excavations. Ph.D. thesis, Chalmers University of Technology; 2001.
  • 54
    • 0002774978 scopus 로고
    • Some sampling problems in technology
    • Johnson N.L., and Smith Jr. H. (Eds), Wiley, New York
    • Cox D.R. Some sampling problems in technology. In: Johnson N.L., and Smith Jr. H. (Eds). New developments in survey sampling (1969), Wiley, New York 506-527
    • (1969) New developments in survey sampling , pp. 506-527
    • Cox, D.R.1
  • 55
    • 0021404166 scopus 로고
    • Mixture densities, maximum likelihood and the EM algorithm
    • Redner R.A., and Walker H.F. Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev 26 2 (1984) 195-239
    • (1984) SIAM Rev , vol.26 , Issue.2 , pp. 195-239
    • Redner, R.A.1    Walker, H.F.2
  • 56
    • 85154579626 scopus 로고    scopus 로고
    • Jordan MI. An introduction to probabilistic graphical models, 2003. (unpublished manuscript). Department of Statistics. University of California, Berkeley.
  • 57
    • 2342533082 scopus 로고    scopus 로고
    • On convergence properties of the EM algorithm for Gaussian mixtures
    • Xu L., and Jordan M.I. On convergence properties of the EM algorithm for Gaussian mixtures. Neural Comput 8 1 (1996) 129-151
    • (1996) Neural Comput , vol.8 , Issue.1 , pp. 129-151
    • Xu, L.1    Jordan, M.I.2
  • 58
    • 0002629270 scopus 로고
    • Maximum likelihood from incomplete data via the EM algorithm
    • Dempster A.P., Laird N.M., and Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc (B) 39 1 (1977) 1-38
    • (1977) J R Stat Soc (B) , vol.39 , Issue.1 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 60
    • 85154590533 scopus 로고    scopus 로고
    • Jimenez-Rodriguez R, Sitar N. Maximum likelihood inference of discontinuity trace lengths based on observations at rock outcrops. GeoEngineering Report, Department of Civil and Environmental Engineering, University of California, Berkeley; 2005, in preparation.
  • 62
    • 0001927585 scopus 로고
    • On information and sufficiency
    • Kullback S., and Leibler R.A. On information and sufficiency. Ann Math Stat 22 1 (1951) 79-86
    • (1951) Ann Math Stat , vol.22 , Issue.1 , pp. 79-86
    • Kullback, S.1    Leibler, R.A.2
  • 63
    • 0001381164 scopus 로고
    • Estimating the components of a mixture of normal distributions
    • Day N.E. Estimating the components of a mixture of normal distributions. Biometrika 56 3 (1969) 463-474
    • (1969) Biometrika , vol.56 , Issue.3 , pp. 463-474
    • Day, N.E.1
  • 64
    • 85154567646 scopus 로고    scopus 로고
    • e colloque GRETSI, (Vannes, France); 1999. p. 259-62.
  • 65
    • 0034356155 scopus 로고    scopus 로고
    • Smooth estimates of normal mixtures
    • Tong B., and Viele K. Smooth estimates of normal mixtures. Cana J Stat 28 3 (2000) 551-561
    • (2000) Cana J Stat , vol.28 , Issue.3 , pp. 551-561
    • Tong, B.1    Viele, K.2
  • 66
    • 0001354471 scopus 로고
    • A constrained formulation of maximum-likelihood estimation for normal mixture distributions
    • Hathaway R.J. A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Ann Stat 13 2 (1985) 795-800
    • (1985) Ann Stat , vol.13 , Issue.2 , pp. 795-800
    • Hathaway, R.J.1
  • 67
    • 0023856093 scopus 로고
    • Parameter estimation for finite mixture distributions
    • Davenport J.W., Bezdek J.C., and Hathaway R.J. Parameter estimation for finite mixture distributions. Comput Math Appl 15 10 (1988) 819-828
    • (1988) Comput Math Appl , vol.15 , Issue.10 , pp. 819-828
    • Davenport, J.W.1    Bezdek, J.C.2    Hathaway, R.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.