Abstract
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.
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Modified from (Hudson and Priest 1983)
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Abbreviations
- DBSCAN:
-
Density based scan
- DS:
-
Discontinuity set
- DSE:
-
Discontinuity set extractor
- EIFOV:
-
Effective instantaneous field of view
- GPR:
-
Ground penetrating radar
- HDS:
-
High definition surveying
- ISRM:
-
International Society for Rock Mechanics and Rock Engineering
- JCS:
-
Joint (wall) compressive strength
- JRC:
-
Joint (wall) Roughness coefficient
- KDE:
-
Kernel density estimation
- LiDAR:
-
Light detection and ranging
- RMSE:
-
Root-mean-square error
- SfM:
-
Structure from Motion
- TLS:
-
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
- Cl:
-
Cluster
- D :
-
Fourth parameter of the general form of the equation of a plane
- I :
-
Intensity of discontinuities within a rock mass
- J :
-
Discontinuity
- k :
-
Numerical parameter that controls the sensitivity of the merging process of coplanar clusters
- K :
-
Discontinuity persistence
- m :
-
Mean
- n :
-
Number of data
- O :
-
Origin of a Cartesian coordinate system
- P :
-
Point
- 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
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Acknowledgements
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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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). https://doi.org/10.1007/s00603-018-1519-9
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DOI: https://doi.org/10.1007/s00603-018-1519-9