Rock Mechanics and Rock Engineering

, Volume 51, Issue 10, pp 3005–3028 | Cite as

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

  • Adrián RiquelmeEmail author
  • Roberto Tomás
  • Miguel Cano
  • José Luis Pastor
  • Antonio Abellán
Original Paper


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.


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



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

List of symbols


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


Area of the discontinuity i within region R


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


Total area of the region


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


Convex hull




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


Intensity of discontinuities within a rock mass




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


Discontinuity persistence




Number of data


Origin of a Cartesian coordinate system




Region of a plane


Normal spacing


Volume of a region


First coordinate of a point in a Cartesian coordinate system


Set of points


Second coordinate of a point in a Cartesian coordinate system


Third coordinate of a point in a Cartesian coordinate system

Greek letters


Dip direction angle of a discontinuity set


Dip angle of a discontinuity set


Mean trace termination or persistence frequency


Mean of point-plane distances


Standard deviation of the distances point-plane distances



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].


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of AlicanteAlicanteSpain
  2. 2.Institute of Applied Geosciences, School of Earth and EnvironmentUniversity of LeedsLeedsUK

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