Automatic Mapping of Discontinuity Persistence on Rock Masses Using 3D Point Clouds


Finding new ways to quantify discontinuity persistence values in rock masses in an automatic or semi-automatic manner is a considerable challenge, as an alternative to the use of traditional methods based on measuring patches or traces with tapes. Remote sensing techniques potentially provide new ways of analysing visible data from the rock mass. This work presents a methodology for the automatic mapping of discontinuity persistence on rock masses, using 3D point clouds. The method proposed herein starts by clustering points that belong to patches of a given discontinuity. Coplanar clusters are then merged into a single group of points. Persistence is measured in the directions of the dip and strike for each coplanar set of points, resulting in the extraction of the length of the maximum chord and the area of the convex hull. The proposed approach is implemented in a graphic interface with open source software. Three case studies are utilized to illustrate the methodology: (1) small-scale laboratory setup consisting of a regular distribution of cubes with similar dimensions, (2) more complex geometry consisting of a real rock mass surface in an excavated cavern and (3) slope with persistent sub-vertical discontinuities. Results presented good agreement with field measurements, validating the methodology. Complexities and difficulties related to the method (e.g., natural discontinuity waviness) are reported and discussed. An assessment on the applicability of the method to the 3D point cloud is also presented. Utilization of remote sensing data for a more objective characterization of the persistence of planar discontinuities affecting rock masses is highlighted herein.

This is a preview of subscription content, access via your institution.

Fig. 1

Modified from (Hudson and Priest 1983)

Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16



Density based scan


Discontinuity set


Discontinuity set extractor


Effective instantaneous field of view


Ground penetrating radar


High definition surveying


International Society for Rock Mechanics and Rock Engineering


Joint (wall) compressive strength


Joint (wall) Roughness coefficient


Kernel density estimation


Light detection and ranging


Root-mean-square error


Structure from Motion


Terrestrial laser scanner

a i :

Area of the ith discontinuity in a 3D region of volume V

a Ri :

Area of the discontinuity i within region R

A :

First parameter of the general form of the equation of a plane

A R :

Total area of the region

B :

Second parameter of the general form of the equation of a plane

C h :

Convex hull



D :

Fourth parameter of the general form of the equation of a plane

I :

Intensity of discontinuities within a rock mass

J :


k :

Numerical parameter that controls the sensitivity of the merging process of coplanar clusters

K :

Discontinuity persistence

m :


n :

Number of data

O :

Origin of a Cartesian coordinate system

P :


R :

Region of a plane

s :

Normal spacing

V :

Volume of a region

x :

First coordinate of a point in a Cartesian coordinate system

X :

Set of points

y :

Second coordinate of a point in a Cartesian coordinate system

z :

Third coordinate of a point in a Cartesian coordinate system

α :

Dip direction angle of a discontinuity set

β :

Dip angle of a discontinuity set

λ :

Mean trace termination or persistence frequency

µ :

Mean of point-plane distances

σ :

Standard deviation of the distances point-plane distances


  1. Abellán A, Derron M-H, Jaboyedoff M (2016) ‘Use of 3D point clouds in geohazards’ special issue: current challenges and future trends. Remote Sens 8:130.

    Article  Google Scholar 

  2. Alameda P (2014) Aplicación de nuevas metodologías de adquisición de datos para el análisis de estabilidad de taludes: casos de estudio en materiales foliados de la Cordillera Bética. University of Granada, Spain

    Google Scholar 

  3. Assali P, Grussenmeyer P, Villemin T, Pollet N, Viguier F (2016) Solid images for geostructural mapping and key block modeling of rock discontinuities. Comput Geosci 89:21–31.

    Article  Google Scholar 

  4. Baecher GB (1983) Statistical analysis of rock mass fracturing. J Int Assoc Math Geol 15:329–348.

    Article  Google Scholar 

  5. Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10:1–54

    Article  Google Scholar 

  6. Botev ZI, Grotowski JF, Kroese DP (2010) Kernel density estimation via diffusion. Ann Stat 38:2916–2957.

    Article  Google Scholar 

  7. Cano M, Tomás R (2013) Characterization of the instability mechanisms affecting slopes on carbonatic Flysch: Alicante (SE Spain), case study. Eng Geol 156:68–91.

    Article  Google Scholar 

  8. Chen N, Kemeny J, Jiang Q, Pan Z (2017) Automatic extraction of blocks from 3D point clouds of fractured rock. Comput Geosci 109:149–161.

    Article  Google Scholar 

  9. Dershowitz WS (1985) Rock joint systems. Ph. D. Thesis, Massachusetts Institute of Technology

  10. Dershowitz WS, Einstein HH (1988) Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21:21–51.

    Article  Google Scholar 

  11. Einstein HH, Veneziano D, Baecher GB, O’Reilly KJ (1983) The effect of discontinuity persistence on rock slope stability. Int J Rock Mech Min Sci Geomech Abstr 20:227–236.

    Article  Google Scholar 

  12. Ester M, Kriegel H, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Simoudis E, Han J, Fayyad U (eds) Second international conference on knowledge discovery and data mining. AAAI Press, Portland, Oregon, pp 226–231

    Google Scholar 

  13. García-Sellés D, Falivene O, Arbués P, Gratacos O, Tavani S, Muñoz JA (2011) Supervised identification and reconstruction of near-planar geological surfaces from terrestrial laser scanning. Comput Geosci 37:1584–1594.

    Article  Google Scholar 

  14. 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.

    Article  Google Scholar 

  15. Goodman RE (1989) Introduction to rock mechanics, 2nd edn. Wiley, New York

    Google Scholar 

  16. Haneberg W (2007) Directional roughness profiles from three-dimensional photogrammetric or laser scanner point clouds. In: Eberhardt E, Stead D, Morrison T (eds) Rock mechanics: meeting society’s challenges and demands. Taylor & Francis, Vancouver, pp 101–106

    Chapter  Google Scholar 

  17. 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.

    Article  Google Scholar 

  18. Hudson JA, Priest SD (1983) Discontinuity frequency in rock masses. Int J Rock Mech Min Sci 20:73–89.

    Article  Google Scholar 

  19. Humair F, Abellán A, Carrea D, Matasci B, Epard J-L, Jaboyedoff M (2015) Geological layers detection and characterisation using high resolution 3D point clouds: example of a box-fold in the Swiss Jura Mountains. Eur J Remote Sens 48:541–568.

    Article  Google Scholar 

  20. International Society for Rock Mechanics (1978) International society for rock mechanics commission on standardization of laboratory and field tests: Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Min Sci Geomech Abstr 15:319–368.

    Article  Google Scholar 

  21. Jaboyedoff M, Metzger R, Oppikofer T, Couture R, Derron M-.H, Locat J, Turmel D (2007) New insight techniques to analyze rock-slope relief using DEM and 3D-imaging cloud points: COLTOP-3D software. In: Francis T (ed) Rock mechanics: Meeting Society’s challenges and demands. Proceedings of the 1st Canada—U.S. Rock Mechanics Symposium,Vancouver, Canada, May 27–31, 2007. pp 61–68

  22. Jaboyedoff M, Oppikofer T, Abellán A, Derron M-. Loye HM-H, Metzger A, Pedrazzini R A (2012) Use of LIDAR in landslide investigations: a review. Nat hazards 61:5–28.

    Article  Google Scholar 

  23. Jordá Bordehore L, Riquelme A, Cano M, Tomás R (2017) Comparing manual and remote sensing field discontinuity collection used in kinematic stability assessment of failed rock slopes. Int J Rock Mech Min Sci 97:24–32.

    Article  Google Scholar 

  24. Khoshelham K, Altundag D, Ngan-Tillard D, Menenti M (2011) Influence of range measurement noise on roughness characterization of rock surfaces using terrestrial laser scanning. Int J Rock Mech Min Sci 48:1215–1223.

    Article  Google Scholar 

  25. Kurz TH, Buckley SJ, Howell JA, Schneider D (2011) Integration of panoramic hyperspectral imaging with terrestrial lidar data. Photogramm Rec 26:212–228.

    Article  Google Scholar 

  26. Lai P, Samson C, Bose P (2014) Surface roughness of rock faces through the curvature of triangulated meshes. Comput Geosci 70:229–237.

    Article  Google Scholar 

  27. Lato MJ, Bevan G, Fergusson M (2012) Gigapixel imaging and photogrammetry: development of a new long range remote imaging technique. Remote Sens 4:3006–3021.

    Article  Google Scholar 

  28. Lato MJ, Kemeny J, Harrap RM, Bevan G (2013) Rock bench: Establishing a common repository and standards for assessing rockmass characteristics using LiDAR and photogrammetry. Comput Geosci 50:106–114.

    Article  Google Scholar 

  29. Leica (2016) Cyclone v9.1

  30. Leica Geosystems AG (2011) Leica ScanStation C10 data sheet. Heerbrugg, Switzerland

    Google Scholar 

  31. Lichti DD, Jamtsho S (2006) Angular resolution of terrestrial laser scanners. Photogramm Rec 21:141–160.

    Article  Google Scholar 

  32. Longoni L, Arosio D, Scaioni M, Papini M, Zanzi L, Roncella R, Brambilla D (2012) Surface and subsurface non-invasive investigations to improve the characterization of a fractured rock mass. J Geophys Eng 9:461–472.

    Article  Google Scholar 

  33. Mauldon M (1994) Intersection probabilities of impersistent joints. Int J Rock Mech Min Sci 31:107–115.

    Article  Google Scholar 

  34. Micheletti N, Chandler JH, Lane SN (2015) Investigating the geomorphological potential of freely available and accessible structure-from-motion photogrammetry using a smartphone. Earth Surf Process Landforms 40:473–486.

    Article  Google Scholar 

  35. Oppikofer T, Jaboyedoff M, Blikra L, Derron M-, Metzger H R (2009) Characterization and monitoring of the Åknes rockslide using terrestrial laser scanning. Nat Hazards Earth Syst Sci 9:1003–1019.

    Article  Google Scholar 

  36. Oppikofer T, Jaboyedoff M, Pedrazzini A, Derron M-, Blikra H L (2011) Detailed DEM analysis of a rockslide scar to characterize the basal sliding surface of active rockslides. J Geophys Res Earth Surf.

    Article  Google Scholar 

  37. Ortega OJ, Marrett RA, Laubach SE (2006) A scale-independent approach to fracture intensity and average spacing measurement. Am Assoc Pet Geol Bull 90:193–208.

    Article  Google Scholar 

  38. Park HJ, West TR, Woo I (2005) Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA. Eng Geol 79:230–250.

    Article  Google Scholar 

  39. Priest SD, Hudson JA (1981) Estimation of discontinuity spacing and trace length using scanline surveys. Int J Rock Mech Min Sci 18:183–197.

    Article  Google Scholar 

  40. Rahman Z, Slob S, Hack HRGK. (2006) Deriving roughness characteristics of rock mass discontinuities from terrestrial laser scan data. In: Proceedings of 10th IAEG congress: engineering geology for tomorrow’s cities, Nottingham, United Kingdom. pp 1–12

  41. RIEGL (2017) RIEGL VZ-6000 3D very long range terrestrial laser scanner with online waveform processing terrestrial laser scanning

  42. 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.

    Article  Google Scholar 

  43. Riquelme A, Abellán A, Tomás R (2015) Discontinuity spacing analysis in rock masses using 3D point clouds. Eng Geol 195:185–195.

    Article  Google Scholar 

  44. Riquelme A, Tomás R, Cano M, Abellán A, Tomás R, Abellán A (2016) Using open-source software for extracting geomechanical parameters of a rock mass from 3D point clouds: discontinuity Set Extractor and SMRTool. In: Ulusay R, Aydan Ö, Gerçek H, Hindistan M, Tuncay E (eds) Rock mechanics & rock engineering: from the past to the future. CRC Press, Taylor & Francies Group, London, pp 1091–1096

    Chapter  Google Scholar 

  45. Riquelme A, Ferrer B, Mas D (2017) Use of high-quality and common commercial mirrors for scanning close-range surfaces using 3D laser scanners: a laboratory experiment. Remote Sens 9:1152.

    Article  Google Scholar 

  46. Ruiz-Carulla R, Corominas J, Mavrouli O (2017) A fractal fragmentation model for rockfalls. Landslides 14:875–889.

    Article  Google Scholar 

  47. Shang J, Hencher SR, West LJ, Handley K (2017) Forensic excavation of rock masses: a technique to investigate discontinuity persistence. Rock Mech Rock Eng 50:2911–2928.

    Article  Google Scholar 

  48. Slob S, Turner AK, Bruining J, Hack HRGK (2010) Automated rock mass characterisation using 3-D terrestrial laser scanning. TU Delft, Delft University of Technology, Delft

    Google Scholar 

  49. Sturzenegger M, Stead D (2009a) Close-range terrestrial digital photogrammetry and terrestrial laser scanning for discontinuity characterization on rock cuts. Eng Geol 106:163–182.

    Article  Google Scholar 

  50. Sturzenegger M, Stead D (2009b) Quantifying discontinuity orientation and persistence on high mountain rock slopes and large landslides using terrestrial remote sensing techniques. Nat Hazards Earth Syst Sci 9:267–287

    Article  Google Scholar 

  51. Sturzenegger M, Yan M, Stead D, Elmo D (2007) Application And Limitations of Ground-based Laser Scanning In Rock Slope Characterization. In: Eberhardt E, Stead D, Morrison T (eds) 1st Canada—U.S. Rock Mechanics Symposium. American Rock Mechanics Association, Vancouver, Canada, pp 29–36

    Chapter  Google Scholar 

  52. Sturzenegger M, Stead D, Elmo D (2011) Terrestrial remote sensing-based estimation of mean trace length, trace intensity and block size/shape. Eng Geol 119:96–111.

    Article  Google Scholar 

  53. Tatone BSA, Grasselli G (2010) A new 2D discontinuity roughness parameter and its correlation with JRC. Int J Rock Mech Min Sci 47:1391–1400.

    Article  Google Scholar 

  54. Teledyne Optech Incorporated (2017) ILRIS-LR terrestrial laser scanner. Canada

  55. Tuckey Z, Stead D (2016) Improvements to field and remote sensing methods for mapping discontinuity persistence and intact rock bridges in rock slopes. Eng Geol 208:136–153.

    Article  Google Scholar 

  56. Ullman S (1979) The interpretation of visual motion. Massachusetts Inst of Technology Pr, Cambridge

    Google Scholar 

  57. Vaskou P (2016) Structural characterization of faults and fractures in underground works. In: Ulusay R, Aydan O, Gerçek H, Hindistan MA, Tuncay E (eds) Rock mechanics and rock engineering: from the past to the future. CRC Press, Boca Raton, pp 99–104

    Chapter  Google Scholar 

  58. Vivas J, Hunt C, Stead D, Allen DM, Elmo D (2015) Characterising groundwater in rock slopes using a combined remote sensing—numerical modelling approach. In: 13th ISRM Int. Congr. Rock Mech

  59. Vöge M, Lato MJ, Diederichs MS (2013) Automated rockmass discontinuity mapping from 3-dimensional surface data. Eng Geol 164:155–162.

    Article  Google Scholar 

  60. 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.

    Article  Google Scholar 

  61. Zhang L (2006) Rock discontinuities. In: Zhang L (eds) Engineering properties of rocks, 4th edn. Elsevier, Amsterdam, pp 226–230

    Google Scholar 

  62. Zhang L, Einstein HH (2000) Estimating the intensity of rock discontinuities. Int J Rock Mech Min Sci 37:819–837.

    Article  Google Scholar 

Download references


This work was partially funded by the University of Alicante (vigrob-157 Project, GRE14-04 Project and GRE15-19 Project), the Spanish Ministry of Economy, Industry and Competitiveness (MINECO), the State Agency of Research (AEI) and the European Funds for Regional Development (FEDER) (projects TEC2017-85244-C2-1-P and TIN2014-55413-C2-2-P) and the Spanish Ministry of Education, Culture and Sport (project PRX17/00439). A. Abellán would like to acknowledge the support received from the H2020 Program of the European Commission under the Marie Skłodowska-Curie Individual Fellowship [MSCA-IF-2015-705215].

Author information



Corresponding author

Correspondence to Adrián Riquelme.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Riquelme, A., Tomás, R., Cano, M. et al. Automatic Mapping of Discontinuity Persistence on Rock Masses Using 3D Point Clouds. Rock Mech Rock Eng 51, 3005–3028 (2018).

Download citation


  • Persistence
  • Rock mass
  • Characterization
  • 3D point clouds
  • Photogrammetry
  • LiDAR
  • Automatic extraction