Abstract
Identification of rock discontinuity sets is essential for each studied jointed rock slope, and is also an initial step in many existing methods for rock slope stability analysis. This paper presents a new hierarchical agglomerative clustering method using modified agglomerative nesting (MAGNES) algorithm for automatically partitioning discontinuity sets. It is an orientation-based clustering method, and different linkage criteria (single, complete, and average) are incorporated for merging two closest clusters. The performance of MAGNES is tested using a complicate artificial data set, Shanley and Mahtab’s data set, and a real data set from unmanned aerial vehicle (UAV) survey. In addition, the clustering results of four other well-recognized clustering methods are also chosen as comparisons. It shows that the single linkage criterion is inapposite for partitioning orientations and the complete linkage criterion is not robust. Only MAGNES using average linkage criterion (MAGNES_AVG) shows good performance for detecting discontinuity sets. Generally, the main discrepancies among the clustering results lie mainly in the poles at the boundary of two adjacent joint sets. Considering the real data sets are characterized by “ground truth,” the artificial data set with known classification labels is used to further test which method performs better. The number of misclassification points is adopted as an evaluation index, and MAGNES_AVG performs best in partitioning the poles at the boundary of adjacent joint sets. Another advantage of the proposed algorithm is that it is independent of initial parameters, which is user-friendly.
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References
Abellán A, Oppikofer T, Jaboyedoff M, Rosser NJ, Lim M, Lato MJ (2014) Terrestrial laser scanning of rock slope instabilities. Earth Surf Process Landf 39:80–97. https://doi.org/10.1002/esp.3493
Assali P, Grussenmeyer P, Villemin T, Pollet N, Viguier F (2014) Surveying and modeling of rock discontinuities by terrestrial laser scanning and photogrammetry: semi-automatic approaches for linear outcrop inspection. J Struct Geol 66:102–114. https://doi.org/10.1016/j.jsg.2014.05.014
Battulwar R, Zare-Naghadehi M, Emami E, Sattarvand J (2021) A state-of-the-art review of automated extraction of rock mass discontinuity characteristics using three-dimensional surface models. J Rock Mech Geotech Eng 13:920–936. https://doi.org/10.1016/j.jrmge.2021.01.008
Bemis SP, Micklethwaite S, Turner D, James MR, Akciz S, Thiele ST, Bangash HA (2014) Ground-based and UAV-based photogrammetry: A multi-scale, high-resolution mapping tool for structural geology and paleoseismology. J Struct Geol 69:163–178. https://doi.org/10.1016/j.jsg.2014.10.007
Cai M, Wang P, Zhao K, Zhang D (2005) Fuzzy C-means cluster analysis based on genetic algorithm for automatic identification of joint sets. Chin J Rock Mech Eng 24:371–376. https://doi.org/10.3321/j.issn:1000-6915.2005.03.002 (In Chinese with English abstract)
Chen J (2001) 3-D network numerical modeling technique for random discontinuities of rock mass. Chin J Geotech Eng 23:397–402. https://doi.org/10.3321/j.issn:1000-4548.2001.04.003 (In Chinese with English abstract)
Chen J, Zhu H, Li X (2016) Automatic extraction of discontinuity orientation from rock mass surface 3D point cloud. Comput Geosci 95:18–31. https://doi.org/10.1016/j.cageo.2016.06.015
Day WHE, Edelsbrunner H (1984) Efficient algorithms for agglomerative hierarchical clustering methods. J Classif 1:7–24. https://doi.org/10.1007/BF01890115
Ding Q, Huang R, Wang F, Chen JP, Wang C, Zhang X (2018) Multi-parameter dominant grouping of discontinuities in rock mass using improved ISODATA algorithm. Math Probl Eng 5619404:1–10. https://doi.org/10.1155/2018/5619404
Emmendorfer RL, Canuto AMP (2021) A generalized average linkage criterion for Hierarchical Agglomerative Clustering. Appl Soft Comput J 100:106990. https://doi.org/10.1016/j.asoc.2020.106990
Feng QH, Röshoff K (2004) In-situ mapping and documentation of rock faces using a full-coverage 3-D laser scanning technique. Int J Rock Mech Min Sci 41:139–144. https://doi.org/10.1016/j.ijrmms.2004.03.032
Ferrero AM, Forlani G, Roncella R, Voyat HI (2009) Advanced geostructural survey methods applied to rock mass characterization. Rock Mech Rock Eng 42:631–665. https://doi.org/10.1007/s00603-008-0010-4
Fisher N (1987) Statistical analysis of spherical data. Cambridge University Press, London
Gao F, Chen D, Zhou K, Niu W, Liu H (2018) A fast clustering method for identifying rock discontinuity sets. KSCE J Civ Eng 23:556–566. https://doi.org/10.1007/s12205-018-1244-7
Ge Y, Tang H, Xia D, Wang L, Zhao B, Teaway JW, Chen H, Zhou T (2018) Automated measurements of discontinuity geometric properties from a 3D-point cloud based on a modified region growing algorithm. Eng Geol 242:44–54. https://doi.org/10.1016/j.enggeo.2018.05.007
Gigli G, Casagli N (2011) Semi-automatic extraction of rock mass structural data from high resolution LIDAR point clouds. Int J Rock Mech Min Sci 48:187–198. https://doi.org/10.1016/j.ijrmms.2010.11.009
Gomes RK, Oliveira LPL, Gonzaga LJ, Tognoli FMW, Veronez MR, Souza MK (2016) An algorithm for automatic detection and orientation estimation of planar structures in LiDAR-scanned outcrops. Comput Geosci 90:170–178. https://doi.org/10.1016/j.cageo.2016.02.011
Goodman RE, Shi GH (1985) Block theory and its application to rock engineering. Prentice-Hall, New Jersey
Hammah RE, Curran JH (1998) Fuzzy cluster algorithm for the automatic identification of joint sets. Int J Rock Mech Min Sci 35:889–905. https://doi.org/10.1016/S0148-9062(98)00011-4
Hammah RE, Curran JH (1999) On distance measures for the Fuzzy K-means algorithm for joint data. Rock Mech Rock Eng 32:1–27. https://doi.org/10.1007/s006030050041
Han X, Chen J, Wang Q, Li Y, Zhang W, Yu T (2016) A 3D fracture network model for the undisturbed rock mass at the Songta dam site based on small samples. Rock Mech Rock Eng 49:611–619. https://doi.org/10.1007/s00603-015-0747-5
Haneberg WC (2008) Using close range terrestrial digital photogrammetry for 3-D rock slope modeling and discontinuity mapping in the United States. Bull Eng Geol Environ 67:457–469. https://doi.org/10.1007/s10064-008-0157-y
Harrison JP (1992) Fuzzy objective functions applied to the analysis of discontinuity orientation data. In: Hudson JA (ed) Rock characterization. Thomas Telford, British Geotechnical Society, London, pp 25–30
Hassani M, Seidl T (2016) Using internal evaluation measures to validate the quality of diverse stream clustering algorithms. Vietnam J Comput Sci 4:171–183. https://doi.org/10.1007/s40595-016-0086-9
Hoek E, Bray J (1981) Rock slope engineering. The Institution of Mining and Metallurgy, London
ISRM (1978) Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Min Sci 15(6):319–368. https://doi.org/10.1016/0148-9062(79)91476-1
Jain AK (2010) Data clustering: 50 years beyond K-means. Pattern Recognit Lett 31:651–666. https://doi.org/10.1016/j.patrec.2009.09.011
Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31:264–323. https://doi.org/10.1145/331499.331504
Jimenez R (2007) Fuzzy spectral clustering for identification of rock discontinuity sets. Rock Mech Rock Eng 41:929–939. https://doi.org/10.1007/s00603-007-0155-6
Jimenez-Rodriguez R, Sitar N (2006) A spectral method for clustering of rock discontinuity sets. Int J Rock Mech Min Sci 43:1052–1061. https://doi.org/10.1016/j.ijrmms.2006.02.003
Klose CD, Seo S, Obermayer K (2005) A new clustering approach for partitioning directional data. Int J Rock Mech Min Sci 42:315–321. https://doi.org/10.1016/j.ijrmms.2004.08.011
Kong D, Wu F, Saroglou C (2020) Automatic identification and characterization of discontinuities in rock masses from 3D point clouds. Eng Geol 265:105442. https://doi.org/10.1016/j.enggeo.2019.105442
Kulatilake PHSW, Wang L, Tang H, Liang Y (2011) Evaluation of rock slope stability for Yujian River dam site by kinematic and block theory analyses. Comput Geotech 38:846–860. https://doi.org/10.1016/j.compgeo.2011.05.004
Li X, Chen Z, Chen J, Zhu H (2019) Automatic characterization of rock mass discontinuities using 3D point clouds. Eng Geol 259:105131. https://doi.org/10.1016/j.enggeo.2019.05.008
Li Y, Wang Q, Chen J, Xu L, Song S (2015) K-means algorithm based on particle swarm optimization for the identification of rock discontinuity sets. Rock Mech Rock Eng 48:375–385. https://doi.org/10.1007/s00603-014-0569-x
Liu J, Zhao XD, Xu ZH (2017a) Identification of rock discontinuity sets based on a modified affinity propagation algorithm. Int J Rock Mech Min Sci 94:32–42. https://doi.org/10.1016/j.ijrmms.2017.02.012
Liu T, Deng J, Zheng J, Zheng L, Zhang Z, Zheng H (2017b) A new semi-deterministic block theory method with digital photogrammetry for stability analysis of a high rock slope in China. Eng Geol 216:76–89. https://doi.org/10.1016/j.enggeo.2016.11.012
Lu C, Cai C (2019) Challenges and countermeasures for construction safety during the Sichuan-Tibet railway project. Eng 5:833–838. https://doi.org/10.1016/j.eng.2019.06.007
Ma GW, Xu ZH, Zhang W, Li SC (2014) An enriched K-means clustering method for grouping fractures with meliorated initial centers. Arab J Geosci 8:1881–1893. https://doi.org/10.1007/s12517-014-1379-x
Mah J, Samson C, McKinnon SD (2011) 3D laser imaging for joint orientation analysis. Int J Rock Mech Min Sci 48:932–941. https://doi.org/10.1016/j.ijrmms.2011.04.010
Mahtab MA, Yegulalp TM (1982) A rejection criterion for definition of clusters in orientation data. In: Goodman RE, Heuze FE (eds) Proceedings of the 22nd US Symposium Rock Mechanics, Berkeley, California, August 1982. American Institute of Mining Metallurgy and Petroleum Engineers, New York, pp 116–123. https://doi.org/10.1016/0148-9062(83)91604-2
Maulik U, Bandyopadhyay S (2002) Performance evaluation of some clustering algorithms and validity indices. IEEE Trans Pattern Anal Mach Intell 24:1650–1654. https://doi.org/10.1109/TPAMI.2002.1114856
Obregon C, Mitri H (2019) Probabilistic approach for open pit bench slope stability analysis - a mine case study. Int J Min Sci Technol 29:629–640. https://doi.org/10.1016/j.ijmst.2019.06.017
Omran MGH, Engelbrecht AP, Salman A (2007) An overview of clustering methods. Intell Data Anal 11:583–605. https://doi.org/10.3233/ida-2007-11602
Park HJ, Lee JH, Kim KM, Um JG (2016) Assessment of rock slope stability using gis-based probabilistic kinematic analysis. Eng Geol 203:56–69. https://doi.org/10.1016/j.enggeo.2015.08.021
Priest SD (1993) Discontinuity Analysis for Rock Engineering. Chapman & Hall. https://doi.org/10.1016/0926-9851(93)90044-Y
Riquelme AJ, Abellán A, Tomás R, Jaboyedoff M (2014) A new approach for semi-automatic rock mass joints recognition from 3D point clouds. Comput Geosci 68:38–52. https://doi.org/10.1016/j.cageo.2014.03.014
Roncella R, Forlani G (2005) Extraction of planar patches from point clouds to retrieve dip and dip direction of rock discontinuities. ISPRS WG III/3, III/4, V/3 Workshop “Laser Scanning 2005.” Enschede, the Netherlands, pp 162–167
Shanley RJ, Mahtab MA (1976) Delineation and analysis of clusters in orientation data. Math Geol 8:9–23. https://doi.org/10.1007/BF01039681
Song S, Wang Q, Chen J, Li Y, Zhang W, Ruan Y (2017) Fuzzy C-means clustering analysis based on quantum particle swarm optimization algorithm for the grouping of rock discontinuity sets. KSCE J Civ Eng 21:1115–1122. https://doi.org/10.1007/s12205-016-1223-9
Sturzenegger M, Stead D (2009) Close-range terrestrial digital photogrammetry and terrestrial laser scanning for discontinuity characterization on rock cuts. Eng Geol 106:163–182. https://doi.org/10.1016/j.enggeo.2009.03.004
Vasuki Y, Holden EJ, Kovesi P, Micklethwaite S (2014) Semi-automatic mapping of geological Structures using UAV-based photogrammetric data: an image analysis approach. Comput Geosci 69:22–32. https://doi.org/10.1016/j.cageo.2014.04.012
Wang X, Zou L, Shen X, Ren Y, Qin Y (2017) A region-growing approach for automatic outcrop fracture extraction from a three-dimensional point cloud. Comput Geosci 99:100–106. https://doi.org/10.1016/j.cageo.2016.11.002
Watson GS, Williams EJ (1956) On the construction of significance tests on the circle and the sphere. Biom 43:344–352. https://doi.org/10.2307/2332913
Xu LM, Chen JP, Wang Q, Zhou FJ (2013) Fuzzy C-means cluster analysis based on mutative scale chaos optimization algorithm for the grouping of discontinuity sets. Rock Mech Rock Eng 46:189–198. https://doi.org/10.1007/s00603-012-0244-z
Xu R, Wunsch D (2005) Survey of clustering algorithms. IEEE Trans Neural Netw 16:645–678. https://doi.org/10.1109/TNN.2005.845141
Yan J, Chen J, Li Y, Li Z, Zhang Y, Zhou X, Qaiser M, Liu J, Wang Z (2021) Kinematic-based failure angle analysis for discontinuity-controlled rock slope instabilities: a case study of Ren Yi Peak Cluster in Fusong County, China. Nat Hazards 111:2281–2296. https://doi.org/10.1007/s11069-021-05137-2
Zhan J, Chen J, Xu P, Zhang W, Han X, Zhou X (2017a) Automatic identification of rock fracture sets using finite mixture models. Math Geosci 49:1021–1056. https://doi.org/10.1007/s11004-017-9702-1
Zhan J, Xu P, Chen J, Wang Q, Zhang W, Han X (2017b) Comprehensive characterization and clustering of orientation data: a case study from the Songta dam site, China. Eng Geol 225:3–18. https://doi.org/10.1016/j.enggeo.2017.01.010
Zhang W, Chen JP, Liu C, Huang R, Li M, Zhang Y (2012) Determination of geometrical and structural representative volume elements at the Baihetan dam site. Rock Mech Rock Eng 45:409–419. https://doi.org/10.1007/s00603-011-0191-0
Zhao M (2020) Rock structure information acquisition based on UAV photogrammetry. Jilin University (Master thesis, in Chinese with English abstract)
Zhou S, Xu Z, Liu F (2016) Method for determining the optimal number of clusters based on agglomerative hierarchical clustering. IEEE Trans Neural Netw Learn Syst 28:3007–3017. https://doi.org/10.1109/TNNLS.2016.2608001
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The authors would like to thank the editor and anonymous reviewers for their comments and suggestions which helped a lot in making this paper better.
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This work was supported by the National Natural Science Foundation of China (Grant No. 41941017, U1702241) and the National Key Research and Development Program of China (Grant No. 2018YFC1505301).
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Yan, J., Chen, J., Zhan, J. et al. Automatic identification of rock discontinuity sets using modified agglomerative nesting algorithm. Bull Eng Geol Environ 81, 229 (2022). https://doi.org/10.1007/s10064-022-02724-w
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DOI: https://doi.org/10.1007/s10064-022-02724-w