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Integrating discontinuity trace and facet orientation Measurements for improved discontinuity data analysis
International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
Integrating discontinuity trace and facet orientation Measurements for improved discontinuity data analysis Norbert H. Maerz a,n, James N. Otoo b a b
Missouri University of Science and Technology, Rolla, MO 65409-0660, USA Chevron North America Exploration and Production, Houston, TX, USA
art ic l e i nf o Article history: Received 10 September 2013 Received in revised form 28 August 2014 Accepted 31 August 2014
1. Introduction
2. LiDAR and optical imaging of discontinuities
Discontinuities, which are ubiquitous in most rock masses, influence the engineering properties and behaviors of all but the weakest of rock types [1–5]. Thus, the properties of the discontinuities become of prime importance when dealing with rock masses [6]. The orientation of the discontinuities is arguably the most important property in many instances. The analysis of discontinuity data basically involves building models that represent the discontinuities. These models are in most cases based on the fact that geological processes usually generate one or more (typically at least three) clusters of nearly parallel discontinuities in a rock mass. Discontinuities manifest themselves in rock cuts and outcropping as fracture surfaces ‘facets’ that can be measured by LiDAR (Light Detecting and Ranging) or fracture ‘traces’ that can be measured from optical imaging methods (Fig. 1; [7–10]). Measurements of the orientation of facets are recorded in terms of dip direction and dip angle. Traces, however, are recorded with trend and plunge, which unlike facet measurement, are a two dimensional measurement that represents the intersection of the fracture surface with a rock cut/outcrop surface. This paper presents geometrical methods of integrating facet orientations measured from LiDAR point cloud data and trace orientations measured from optical images for better characterization of systematic discontinuity orientations.
Facets can be detected using LiDAR techniques. The point cloud produced by a laser scanner is searched for a region of co-planar points, and using any three non-linear points from this region one can determine the orientation solving the classic three-point problem [10]. Thus, a geometric plane can be fitted to the entire section of the point cloud that comprises that region [7]. Alternatively, several three-point orientations can be calculated to reduce or assess uncertainty. The assemblage of fracture traces can be optically imaged, and their (2-D) orientation can be measured by optically imaging the rock cut, using appropriate image processing filters like a canny edge detector [11] to isolate the lines of intersection, and measuring their orientation. Photogrammetry software, including Sirovision, ShapeMatrix3D, and AdamTech, allows users to measure orientations of traces [12–16].
n
Corresponding author. Tel.: þ 1 573 341 6714; fax: þ 1 573 341 4368. E-mail addresses: [email protected] (N.H. Maerz), [email protected] (J.N. Otoo). http://dx.doi.org/10.1016/j.ijrmms.2014.08.016 1365-1609/& 2014 Elsevier Ltd. All rights reserved.
3. Combining LiDAR and optical imaging measurements The general principle behind combining facet 3-D orientations and trace 2-D orientations on a vertical rock cut is based on the fact that both 3-D facet orientations (LiDAR measured) and 2-D trace orientations (optically measured) can be clustered into their respective sets with mean orientations (dip direction/dip angle, and azimuth/plunge). Additionally all 2-D traces lie on, and define, the intersection of two planar discontinuities (the plane of the rock cut face and the discontinuity plane associated with that trace). While we do not know what that 3-D orientation of the discontinuity represented by a particular trace is, we can test geometrically if a given trace vector is parallel to a given
N.H. Maerz, J.N. Otoo / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
discontinuity surface (set). If so, it belongs to the same set, and vice versa. This methodology is inconclusive in situations where traces belong to a set or sets of unexposed facets.
301
3.1. Principle demonstration A simple demonstration of the principle is presented using Fig. 2(a) and (b). Fig. 2(a) highlights the facet measurements, and Fig. 2(b) adds the trace measurements. Both the facets and traces are identified with a set number. In this case the set numbers of the facets and set numbers of the traces were made to correspond with each other for the purposes of this demonstration.
3.2. Combining trace and facet measurements The two methods by which 3-D facets orientations can be combined to yield 2-D trace orientation are the stereonet and the vector dot product approaches.
Fig. 1. Rock cut showing both fracture trace (red line) and facet (cyan polygon) [7].
3.2.1. Stereonet approach A stereonet can be used to determine which facet and trace orientations go together by plotting the great circle of the facet orientation and the vector of the trace orientation. If the trace belongs to the same set as the facet, i.e. the trace sits on the same plane as that of the facet, then the trace vector will fall on the great circle of the facet (give or take measurement error and natural orientation variability) on a stereonet. If the vector terminates on the great circle then the trace and the facet are co-planar, and belong to the same set (Fig. 3). Using all of the trace and facet information in Fig. 3, it can be established for the case of all four sets that the trace vectors terminate on the great circle of the facet for each set (Fig. 4).
Fig. 2. (a) Test rock cut with facets measured in terms of dip direction/dip angle. Each color represents a different set (Magenta set 1, Green set 2, Yellow set 3, Blue set 4). (b) Test rock cut with both traces and facets, traces were measured in terms of dip azimuth and plunge. The colors of the traces correspond to the colors of the facets (Magenta set 1, Green set 2, Yellow set 3, Blue set 4). The red colored traces do not have a corresponding facet.
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N.H. Maerz, J.N. Otoo / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
Fig. 3. Vector of trace terminating on great circle of facet showing that the two are co-planar, and belong to the same set.
Fig. 4. Vectors of traces (arrows) terminating on great circles of facets (each set shown in different colors) illustrates the principle.
Table 1 Matrix of angles between unit normals of all facet sets and unit trace vectors of all trace sets. The diagonal elements show angles of close to 901, which means that trace vector falls on the facet surface.
3.2.2. Vector dot product approach The same result can be determined by taking the dot product of the trace unit vector and the facet unit normal vector. Similarly to the stereonet method, if the trace belongs to the same set as the facet, i.e. the trace sits on the same plane as that of the facet, then using the equation for the angle between two lines, if the angle of the trace vector and facet unit normal vector is 901 or very close to
901, then the trace is contained within the plane of the facet. This can be determined by the following equation: cos φ ¼ TF
ð1Þ
where T is the trace unit vector, and F is the facet unit normal vector.
N.H. Maerz, J.N. Otoo / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
In the example above, a matrix of angle calculations can be made showing the relationship between the traces and facets for each of the sets (Table 1).
4. Summary and conclusion Discontinuity orientations are important for stability and other geological analysis, but manual measurements have shortcomings. LiDAR (facet) measurements can be done; however, LiDAR cannot measure traces. Optical imaging, on the other hand, can measure traces (2-D), but not facets. This paper shows that traces and facets can be linked together by the use of geometrical analysis.
Acknowledgments The authors would like to thank the National Science Foundation, USA, for sponsoring this work. This work is supported in part by NSF CMMI Award #0856420 and #0856206. References [1] Maerz N.H. Photo analysis of rock fabric Ph.D. dissertation, Ontario, Canada: University of Waterloo; 1990. [2] Priest SD. Discontinuity analysis for rock engineering. London: Chapman and Hall; 1993. [3] Scheidegger AE. The enigma of jointing. Riv Ital Geofis 1978;5:1–4.
303
[4] Hudson JA, Hudson JL. Establishing potential behavioral modes of rock engineering systems by computer simulation of interaction matrix energy flux. Int J Rock Mech Min Sci 1993;30:457–68. [5] Hudson JA, Priest JP. Discontinuities and rock mass geometry. Int J Rock Mech Min Sci 1979;16:339–62. [6] Bieniawski ZT. Engineering rock mass classification. New York: Wiley; 1989. [7] Otoo JN, Maerz NH, Li X, Duan, Y 3-D discontinuity orientations using combined optical imaging and LiDAR techniques. In: Proceedings of the 45th US rock mechanics symposium, San Francisco, 26–29 June, 2011. p. 9–14. [8] Otoo JN, Maerz NH, Li X, Duan Y. Verification of a 3-D LiDAR viewer for discontinuity orientations. Rock Mech Rock Eng 2013;46:543–54. [9] Kemeny J, Post R. Estimating three-dimensional rock discontinuity orientation from digital images of fracture traces. Comput Geosci 2003;29(1):65–77. [10] Maerz NH, Youssef AM, Otoo JN, Kassebaum TJ, Duan Y. A simple method for measuring discontinuity orientations from terrestrial LiDAR images. Environ Eng Geosci 2013;19:185–94. [11] Canny J. A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 1986;8:679–98. [12] Haneberg WC, Norrish NI, Findley DP Digital outcrop characterization for 3-D structural mapping and rock slope design along interstate 90 new snoqualmie pass, Washington. In: Proceedings of the 57th annual highway geology symposium, Breckenridge, 27–29 September 2006. p. 146–60. [13] Haneberg WC. Using close range terrestrial digital photogrammetry for 3D rock slope modeling and discontinuity mapping in the United States. Bull Eng Geol Environ 2008;67(4):457–69. [14] Birch JS Using 3DM analyst mine mapping suite for rock face characterization. In: Proceedings of the 41st US rock mechanics symposium, Golden, Colorado, 17–21 June, 2006. p. 13–32. [15] Gaich A, Potsch M, Schubert W Basics and applications of 3D imaging systems with conventional and high resolution camaras. In: Proceedings of the 41st US rock mechanics symposium, Golden, Colorado, 17–21 June, 2006. p. 33–48. [16] Gates WCB, Haneberg WC Comparison of standard structural mapping results to 3-D photogrammetric model results: boundary transformer banks rockfall mitigation project. In: Proceedings of the 46th US Rock mechanics/geomechanics symposium, Chicago, 24-27 June, 2012. p. 1–5.
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
Integrating discontinuity trace and facet orientation Measurements for improved discontinuity data analysis Norbert H. Maerz a,n, James N. Otoo b a b
Missouri University of Science and Technology, Rolla, MO 65409-0660, USA Chevron North America Exploration and Production, Houston, TX, USA
art ic l e i nf o Article history: Received 10 September 2013 Received in revised form 28 August 2014 Accepted 31 August 2014
1. Introduction
2. LiDAR and optical imaging of discontinuities
Discontinuities, which are ubiquitous in most rock masses, influence the engineering properties and behaviors of all but the weakest of rock types [1–5]. Thus, the properties of the discontinuities become of prime importance when dealing with rock masses [6]. The orientation of the discontinuities is arguably the most important property in many instances. The analysis of discontinuity data basically involves building models that represent the discontinuities. These models are in most cases based on the fact that geological processes usually generate one or more (typically at least three) clusters of nearly parallel discontinuities in a rock mass. Discontinuities manifest themselves in rock cuts and outcropping as fracture surfaces ‘facets’ that can be measured by LiDAR (Light Detecting and Ranging) or fracture ‘traces’ that can be measured from optical imaging methods (Fig. 1; [7–10]). Measurements of the orientation of facets are recorded in terms of dip direction and dip angle. Traces, however, are recorded with trend and plunge, which unlike facet measurement, are a two dimensional measurement that represents the intersection of the fracture surface with a rock cut/outcrop surface. This paper presents geometrical methods of integrating facet orientations measured from LiDAR point cloud data and trace orientations measured from optical images for better characterization of systematic discontinuity orientations.
Facets can be detected using LiDAR techniques. The point cloud produced by a laser scanner is searched for a region of co-planar points, and using any three non-linear points from this region one can determine the orientation solving the classic three-point problem [10]. Thus, a geometric plane can be fitted to the entire section of the point cloud that comprises that region [7]. Alternatively, several three-point orientations can be calculated to reduce or assess uncertainty. The assemblage of fracture traces can be optically imaged, and their (2-D) orientation can be measured by optically imaging the rock cut, using appropriate image processing filters like a canny edge detector [11] to isolate the lines of intersection, and measuring their orientation. Photogrammetry software, including Sirovision, ShapeMatrix3D, and AdamTech, allows users to measure orientations of traces [12–16].
n
Corresponding author. Tel.: þ 1 573 341 6714; fax: þ 1 573 341 4368. E-mail addresses: [email protected] (N.H. Maerz), [email protected] (J.N. Otoo). http://dx.doi.org/10.1016/j.ijrmms.2014.08.016 1365-1609/& 2014 Elsevier Ltd. All rights reserved.
3. Combining LiDAR and optical imaging measurements The general principle behind combining facet 3-D orientations and trace 2-D orientations on a vertical rock cut is based on the fact that both 3-D facet orientations (LiDAR measured) and 2-D trace orientations (optically measured) can be clustered into their respective sets with mean orientations (dip direction/dip angle, and azimuth/plunge). Additionally all 2-D traces lie on, and define, the intersection of two planar discontinuities (the plane of the rock cut face and the discontinuity plane associated with that trace). While we do not know what that 3-D orientation of the discontinuity represented by a particular trace is, we can test geometrically if a given trace vector is parallel to a given
N.H. Maerz, J.N. Otoo / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
discontinuity surface (set). If so, it belongs to the same set, and vice versa. This methodology is inconclusive in situations where traces belong to a set or sets of unexposed facets.
301
3.1. Principle demonstration A simple demonstration of the principle is presented using Fig. 2(a) and (b). Fig. 2(a) highlights the facet measurements, and Fig. 2(b) adds the trace measurements. Both the facets and traces are identified with a set number. In this case the set numbers of the facets and set numbers of the traces were made to correspond with each other for the purposes of this demonstration.
3.2. Combining trace and facet measurements The two methods by which 3-D facets orientations can be combined to yield 2-D trace orientation are the stereonet and the vector dot product approaches.
Fig. 1. Rock cut showing both fracture trace (red line) and facet (cyan polygon) [7].
3.2.1. Stereonet approach A stereonet can be used to determine which facet and trace orientations go together by plotting the great circle of the facet orientation and the vector of the trace orientation. If the trace belongs to the same set as the facet, i.e. the trace sits on the same plane as that of the facet, then the trace vector will fall on the great circle of the facet (give or take measurement error and natural orientation variability) on a stereonet. If the vector terminates on the great circle then the trace and the facet are co-planar, and belong to the same set (Fig. 3). Using all of the trace and facet information in Fig. 3, it can be established for the case of all four sets that the trace vectors terminate on the great circle of the facet for each set (Fig. 4).
Fig. 2. (a) Test rock cut with facets measured in terms of dip direction/dip angle. Each color represents a different set (Magenta set 1, Green set 2, Yellow set 3, Blue set 4). (b) Test rock cut with both traces and facets, traces were measured in terms of dip azimuth and plunge. The colors of the traces correspond to the colors of the facets (Magenta set 1, Green set 2, Yellow set 3, Blue set 4). The red colored traces do not have a corresponding facet.
302
N.H. Maerz, J.N. Otoo / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
Fig. 3. Vector of trace terminating on great circle of facet showing that the two are co-planar, and belong to the same set.
Fig. 4. Vectors of traces (arrows) terminating on great circles of facets (each set shown in different colors) illustrates the principle.
Table 1 Matrix of angles between unit normals of all facet sets and unit trace vectors of all trace sets. The diagonal elements show angles of close to 901, which means that trace vector falls on the facet surface.
3.2.2. Vector dot product approach The same result can be determined by taking the dot product of the trace unit vector and the facet unit normal vector. Similarly to the stereonet method, if the trace belongs to the same set as the facet, i.e. the trace sits on the same plane as that of the facet, then using the equation for the angle between two lines, if the angle of the trace vector and facet unit normal vector is 901 or very close to
901, then the trace is contained within the plane of the facet. This can be determined by the following equation: cos φ ¼ TF
ð1Þ
where T is the trace unit vector, and F is the facet unit normal vector.
N.H. Maerz, J.N. Otoo / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 300–303
In the example above, a matrix of angle calculations can be made showing the relationship between the traces and facets for each of the sets (Table 1).
4. Summary and conclusion Discontinuity orientations are important for stability and other geological analysis, but manual measurements have shortcomings. LiDAR (facet) measurements can be done; however, LiDAR cannot measure traces. Optical imaging, on the other hand, can measure traces (2-D), but not facets. This paper shows that traces and facets can be linked together by the use of geometrical analysis.
Acknowledgments The authors would like to thank the National Science Foundation, USA, for sponsoring this work. This work is supported in part by NSF CMMI Award #0856420 and #0856206. References [1] Maerz N.H. Photo analysis of rock fabric Ph.D. dissertation, Ontario, Canada: University of Waterloo; 1990. [2] Priest SD. Discontinuity analysis for rock engineering. London: Chapman and Hall; 1993. [3] Scheidegger AE. The enigma of jointing. Riv Ital Geofis 1978;5:1–4.
303
[4] Hudson JA, Hudson JL. Establishing potential behavioral modes of rock engineering systems by computer simulation of interaction matrix energy flux. Int J Rock Mech Min Sci 1993;30:457–68. [5] Hudson JA, Priest JP. Discontinuities and rock mass geometry. Int J Rock Mech Min Sci 1979;16:339–62. [6] Bieniawski ZT. Engineering rock mass classification. New York: Wiley; 1989. [7] Otoo JN, Maerz NH, Li X, Duan, Y 3-D discontinuity orientations using combined optical imaging and LiDAR techniques. In: Proceedings of the 45th US rock mechanics symposium, San Francisco, 26–29 June, 2011. p. 9–14. [8] Otoo JN, Maerz NH, Li X, Duan Y. Verification of a 3-D LiDAR viewer for discontinuity orientations. Rock Mech Rock Eng 2013;46:543–54. [9] Kemeny J, Post R. Estimating three-dimensional rock discontinuity orientation from digital images of fracture traces. Comput Geosci 2003;29(1):65–77. [10] Maerz NH, Youssef AM, Otoo JN, Kassebaum TJ, Duan Y. A simple method for measuring discontinuity orientations from terrestrial LiDAR images. Environ Eng Geosci 2013;19:185–94. [11] Canny J. A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 1986;8:679–98. [12] Haneberg WC, Norrish NI, Findley DP Digital outcrop characterization for 3-D structural mapping and rock slope design along interstate 90 new snoqualmie pass, Washington. In: Proceedings of the 57th annual highway geology symposium, Breckenridge, 27–29 September 2006. p. 146–60. [13] Haneberg WC. Using close range terrestrial digital photogrammetry for 3D rock slope modeling and discontinuity mapping in the United States. Bull Eng Geol Environ 2008;67(4):457–69. [14] Birch JS Using 3DM analyst mine mapping suite for rock face characterization. In: Proceedings of the 41st US rock mechanics symposium, Golden, Colorado, 17–21 June, 2006. p. 13–32. [15] Gaich A, Potsch M, Schubert W Basics and applications of 3D imaging systems with conventional and high resolution camaras. In: Proceedings of the 41st US rock mechanics symposium, Golden, Colorado, 17–21 June, 2006. p. 33–48. [16] Gates WCB, Haneberg WC Comparison of standard structural mapping results to 3-D photogrammetric model results: boundary transformer banks rockfall mitigation project. In: Proceedings of the 46th US Rock mechanics/geomechanics symposium, Chicago, 24-27 June, 2012. p. 1–5.