A Study of Density Analysis and Automatic Clustering Algorithm of Fracture Orientation Data

Kunchai Lee; Bryan Kim; Myungkyu Song; Sean Lee

doi:10.7474/TUS.2025.35.4.431

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2025 Vol.35, Issue 4 Preview Page Next Page

Original Article

A Study of Density Analysis and Automatic Clustering Algorithm of Fracture Orientation Data 균열 방향성 자료의 밀도 분석 및 자동 군집화 알고리즘 연구

31 August 2025. pp. 431-459

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Abstract

The orientation of fractures distributed within rock masses is an important factor that affects the behavior of rock masses. Therefore, the orientation data of the borehole images measured in the field are data that must be closely analyzed in engineering activities targeting rock masses. These fractures can be classified into clusters with similar orientations, and the representative characteristics of fractures in each cluster are used to reflect the influence of the fractures on the behavior of the rock mass in engineering analysis. In this study, the orientation data obtained from the borehole image were used to automatically cluster the fractures distributed in the target rock mass, and the results were visualized to present the distribution and statistical characteristics of the fractures in the rock mass. In this process, the Fisher mixture model method was developed as an automatic clustering algorithm based on Fisher distribution, and several alternatives for rational and efficient setting of initial parameters were presented.

Keywords

Orientation

Fracture set

Automatic clustering

Fisher mixture model

Density contour

암반 내에 분포하는 균열의 방향성은 암반의 거동에 영향을 미치는 중요한 요소이다. 따라서 현장에서 측정된 균열의 방향성 자료는 암반을 대상으로 하는 공학 활동에서 면밀히 분석되어야 하는 자료이다. 이러한 균열들은 유사한 방향을 갖는 군집들로 분류될 수 있으며, 각 균열군의 대표 특성은 공학적 분석에서 균열이 암반의 거동에 미치는 영향을 반영하는 데 사용된다. 본 연구에서는 시추공 영상에서 얻은 방향성 자료를 이용하여 대상 암반에 분포하는 균열들을 자동으로 군집화하고, 이를 시각화하여 암반 내 균열의 분포 및 통계적 특성을 제시하였다. 이 과정에서 피셔 분포에 기반한 자동 군집화 알고리즘인 피셔혼합모델 알고리즘을 개발하고, 초기 매개변수의 합리적이고 효율적인 설정을 위한 여러 대안을 제시하였다.

키워드

방향성

균열군

자동군집화

피셔혼합모델

밀도 등고선

References

Bishop, C.M., 2006, Pattern recognition and machine learning. Information Science and Statistics. Springer Science+Business Media, LLC, New York.

Chilès, J.P. and Marsily, G.D., 1993, Flow and Contaminant Transport in Fractured Rock, chapter 4 - Stochastic Models of Fracture Systems and Their Use in Flow and Transport Modeling, Elsevier, pp. 169-236.

10.1016/B978-0-12-083980-3.50008-5

Fisher, R., 1953, Dispersion on a sphere. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 217(1130), 295-305.

10.1098/rspa.1953.0064

Géron, A., 2019, Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd Edition. O’Reilly Media, Incorporated.

Hammah, R. and Curran, J., 1998, Fuzzy cluster algorithm for the automatic identification of joint sets. International Journal of Rock Mechanics and Mining Sciences, 35(7), 889-905.

10.1016/S0148-9062(98)00011-4

Hutchinson, E.B., Rutecki, P.A., Alexander, A.L., and Sutula, T.P., 2012, Fisher statistics for analysis of diffusion tensor directional information. Journal of Neuroscience Methods, 206(1), 40-45.

10.1016/j.jneumeth.2012.02.00422342971PMC3314136

Jung, Y.B. and Jeon, S., 2003, Fuzzy Clustering Method for the Identification of Joint Sets. Tunn Undergr Space, 13(4), 294-303.

Kamb, W.B., 1959, Ice petrofabric observations from blue glacier, washington, in relation to theory and experiment. Journal of Geophysical Research, 64(11), 1891-1909.

10.1029/JZ064i011p01891

Marcotte, D. and Henry, E., 2002, Automatic joint set clustering using a mixture of bivariate normal distributions. International Journal of Rock Mechanics and Mining Sciences, 39(3), 323-334.

10.1016/S1365-1609(02)00033-3

McFadden, P.L., 1980, The best estimate of fisher’s precision parameter κ. Geophysical Journal International, 60(3), 397-407.

10.1111/j.1365-246X.1980.tb04816.x

Ojeda, P., Elmo, D., Rogers, S., and Brzovic, A., 2023, Discrete fracture network (dfn) analysis to quantify the reliability of borehole-derived volumetric fracture intensity. Geosciences, 13(6), 187.

10.3390/geosciences13060187

Priest, S. and Hudson, J., 1976, Discontinuity spacings in rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 13(5), 135-148.

10.1016/0148-9062(76)90818-4

Priest, S.D., 1985, Hemispherical projection methods in rock mechanics. Allen [and] Unwin, London.

Priest, S.D., 1993, Discontinuity analysis for rock engineering. Chapman & Hall, London.

10.1007/978-94-011-1498-1

Robin, P.Y.F. and Jowett, E.C., 1986, Computerized density contouring and statistical evaluation of orientation data using counting circles and continuous weighting functions. Tectonophysics, 121(2), 207-223.

10.1016/0040-1951(86)90044-2

Ruan, Y., Liu, W., Wang, T., Chen, J., Zhou, X., and Sun, Y., 2023, Dominant partitioning of discontinuities of rock masses based on dbscan algorithm. Applied Sciences, 13(15), 8917.

10.3390/app13158917

Vollmer, F.W., 1995, C program for automatic contouring of spherical orientation data using a modified kamb method. Computers & Geosciences, 21(1), 31-49.

10.1016/0098-3004(94)00058-3

Watson, G.S., 1966, The statistics of orientation data. The Journal of Geology, 74(5), Part 2, 786-797.

10.1086/627211

Zimmerman, R.W. and Paluszny, A., 2023, Fluid Flow in Fractured Rocks. Wiley.

10.1002/9781119248040

Information

Publisher :Korean Society for Rock Mechanics and Rock Engineering
Publisher(Ko) :한국암반공학회
Journal Title :Tunnel and Underground Space
Journal Title(Ko) :터널과 지하공간
Volume : 35
No :4
Pages :431-459
Received Date : 2025-07-23
Revised Date : 2025-08-20
Accepted Date : 2025-08-20
DOI :https://doi.org/10.7474/TUS.2025.35.4.431

Tunnel and Underground SpaceISSN:1225-1275(Print) 2287-1748(Online)한국암반공학회

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