Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. Method for Automated Discontinuity Analysis of Rock Slopes with Three-Dimensional Laser Scanning Siefko Slob, Bart van Knapen, Robert Hack, Keith Turner, and John Kemeny Three-dimensional (3D) laser scanning data can be used to characterize discontinuous rock masses in an unbiased, rapid, and accurate manner. With 3D laser scanning, it is now possible to measure rock faces whose access is restricted or rock slopes along highways or railway lines where working conditions are hazardous. The proposed method is less expensive than traditional manual survey and analysis methods. Laser scanning is a relatively new surveying technique that yields a so-called point cloud set of data; every single point represents a point in 3D space of the scanned rock surface. Because the density of the point cloud can be high (on the order of 5 mm to 1 em), it allows for an accurate reconstruction of the original rock surface in the form of a 3D interpolated and meshed surface using different interpolation techniques. Through geometric analysis of this 3D mesh and plotting of the facet orientations in a polar plot, it is possible to observe clusters that represent different rock mass discontinuity sets. With fuzzy k-means clustering algorithms, individual discontinuity sets can be outlined automatically, and the mean orientations of these identified sets can be computed. Assuming a Fisher's distribution, the facet outliers can be removed subsequently. Finally, discontinuity set spacings can be calculated as well. • Erroneous data are introduced because of sampling difficulties (e.g., choice of sampling method, human bias, instrument error). • Safety risks are often considerable. Often field measurements are carried out at the base of existing slopes; during quarry, tunneling, or mining operations; or along busy highways or railway tracks. • Direct access to rock faces is often difficult or impossible. Apart from these practical problems, manual field survey methods are also time-consuming, labor-intensive, and costly. The use of laser scanning in combination with an automated discontinuity analysis, has several advantages over the traditional manual field survey methods: • Laser scanning data can be used as a basis for a cheaper, more objective, and more precise and accurate method of determining discontinuity orientations. • Laser scanning surveys can be carried out rapidly (in minutes) and at some distance (4 to 800 m) from the actual site in a controlled environment, which minimizes safety risks. • Laser scanning techniques allow surveys of rock faces up to several hundreds of meters away from the operator, so that discontinuity properties of inaccessible spots can be obtained, which was previously impossible to do. In rock mass characterization, the analysis of discontinuity properties is important because it determines, to a large extent, the mechanical behavior of the rock mass (J). Most civil and mining engineering works that deal with rock masses require a good understanding of the discontinuities (joints bedding planes and fractures) in the rock mass. It is therefore important to determine properties such as orientations, roughness, and spacing of the different discontinuity sets. Discontinuity properties of a rock mass can be measured in the field using standardized methods, such as scan line surveys or cell mapping (2, 3). Both systems have their respective advantages and disadvantages, but all manual field survey methods have several disadvantages in common (4): The idea of obtaining discontinuity information from an exposed rock mass through remote sensing is not new. Analogue stereo photogrammetric techniques already allow the measurement of orientations of individual discontinuities (5). More recently, applications have been developed that use digital imagery and data processing instead. Basic photogrammetric principles combined with pattern recognition routines allow the user to create three-dimensional (3D) models of virtually any object (6). In the field of rock mechanics, applications have been developed that make use of this technique (7, 8). These applications, however, require time-consuming data processing to arrive at the final 3D model and still require manual outlining of discontinuity surfaces to calculate orientations. With photogrammetric techniques, it is also necessary to measure in several control points within the scene to arrive at a proper 3D model. Feng eta!. (9) demonstrated that it is also possible to use a nonreftector total station to measure fracture orientations. Although good results were obtained, the amount of data points that can be acquired is limited, and the manual operation of the total station still requires a large amount of time and effort on site. A few recent publications demonstrate the possibility of determining discontinuity orientations from single digital S. Slob. and R. Hack, International Institute for Geo-lnformation Sciences and Earth Observation [ITCJ, P.O. Box 6, 7500 AA Enschede, Netherlands. B. van Knapen, Delft University of Technology, Faculty of CiTG, Mijnbouwstraat 12, 262B EB Delft, Netherlands. K. Turner. Department of Geology and Geological Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, CO BD401-1 BB7. J. Kemeny, Department of Mining and Geological Engineering, University of Arizona, Tucson, AZ B5721. Transportation Research Record: Journal of the Transportation Research Board, No. 1913, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp. 1B7-194. 187 Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. Transportation Research Record 1913 188 images on the basis of fracture traces and advocate the combined used of laser scan data with digital imagery (4, /0). Three-D terrestrial laser scanning is a relatively new, but already revolutionary, surveying technique. The main advantage overphotogrammetric techniques is that a 3D data model is generated in real time. Different laser scanning systems exist, but the technique used outdoors for geodetic surveying or for measuring large civil engineering structures is usually the time-of-flight or laser range finding technique. These scanners have a laser diode that sends a pulsed laser beam to the scanned object (11 ). The pulsed laser beam moves through a rapidly changing elevation and azimuth angle of a rotating or oscillating mirror inside the instrument. The pulse is diffusely reflected by the surface of the object it hits, and part of the light is returned to the receiver. The time that the laser light needs to travel from the laser diode to the object surface and back is measured very precisely. Knowing the speed of light, the distance from the scanner to the object can be computed. With the azimuth and angle of the beam, the position of each reflection point can then be calculated. The laser scan survey yields a digital data set, which is essentially a dense point cloud, in which each point is represented by a coordinate in 3D space (X, Y, and Z, relative to the scanner's position). With this data, the 3D geometry of any scanned object or scene can be analyzed. Very large and complex objects can be scanned from different positions. Most software programs used to capture the survey data allow it to merge the different surveys into a single point cloud. In this way, the shadow areas of surveys can be complemented with scans in which the previously hidden areas can be "seen" by the laser beam. The most important advantage of the laser scanning method is that a very high point density can be achieved-up to 5 mm resolution or larger. Therefore, the shape of the surveyed object or scene can be modeled with a very high resolution, precision, and accuracy in three dimensions. Laser scanning can measure objects and scenes up to a distance of nearly 800 m, under ideal conditions. In realworld situations, however, distances on the order of 50 to 100m are more typical. The method is also fast: A full 360° scan can be carried out with the latest models in less than 4 min. Most laser scanners fit on a regular surveying tripod and can have a laptop or palmtop computer attached to operate the scanner and to store the survey data. It should be noted, however, that the developments in laser scanning technology go very fast, and some of the specifications given here may already be outdated by the time this paper is published. DATA QUALITY ISSUES Currently, a number of 3D laser scanning devices are on the market from different manufacturers that use the ranging principle (e.g., LeicaCyrax, Riegl, Trimble-Mensi, and Optech-Ilris). A typical field setup of a 3D laser scanner is shown in Figure 1. The underlying principles of the different laser scanners are essentially the same, but the quality of the data generated may vary between manufacturers and models. The most important data quality parameters are as follows: • Resolution. The resolution is the minimum distance between measured points (typically on the order of 5 mm to 1 em), depending on the range to the object and size of the object (see laser beam divergence). It determines what level of detail can be recognized from the scanned scene or object. • Accuracy and precision. This parameter determines how well the data represent the actual geometry of the scanned scene of object. FIGURE 1 Typical fiald satup of Issar scanner IOptech 30 llris scanner 13011. Umbrella kaeps scanner cool and allows usar to read display. As mentioned earlier, the laser scanner measures the time of flight of the laser beam. Because the time differences are so small, there is a limit to the precision with which time of flight can be measured. This basically results in an error of the range measurement, which can be on the order of 25 to 10 mm for a single shot or 15 to 5 mm for averaged multiple shot measurements (12). Range precision is independent of the distance to the object. • Scanning speed. Scanning speed has drastically improved over the years with improved hardware and improved data storage techniques. Depending on the scanner type, resolution, and size of the object or scene, scanning speeds can range between a few minutes to half an hour. • Laser beam divergence. A laser beam is never perfectly parallel but always has a certain amount of divergence. For example, a laser beam the size of a small dot (15 mm) at around 20m may be the size of a large dish (30 em) at 100m distance (3 mrad). Obviously, this results in an averaging of the measurement over a larger area. It also decreases the amount of reflected energy and thus limits the range at which objects or scenes can be scanned. Recent laser scanners however, have improved drastically in beam divergence, which may now be down to 0.25 mrad (25 mm per 100 m)(l2). DATA PROCESSING Geometric Correction of Data The laser data are, in principle, georeferenced to their own coordinate system, relative to the scanner's position [often the scanner's position is defined as the origin, (0,0,0)]. If it is needed to integrate the data into existing databases in computer-aided design or geographic information systems, for example, then the data must be referenced to a regional or a local grid system. Most laser scanning systems allow real-time or posterior georeferencing of the point cloud data by using reflectors that have premeasured coordinates. The reflectors can be surveyed-in with a total station or a differential Global Positioning System. Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. Slob. van Knapen, Hack, Turner, and Kemeny However, when using laser scan data to measure discontinuity properties, it is not strictly necessary to georeference the entire data set to a local or regional grid or coordinate system. For the measurement of discontinuity orientations, the only requirement is to reorient the data relative to the true north and to make sure that the data are level. In other words, the X, Y, and Z coordinates should be referenced such that, for example, the f-axis represents the true north-south direction, the X-axis represents the true east-west direction, and Z represents the actual elevation. For a slope stability analysis, it is merely necessary to know the relative orientation of joints and bedding planes compared with the actual slope orientation and geometry. The same applies to quarry and tunnel operations, where the block size and block stability is of key importance, which does not require an absolute georeferencing. Most of the time, the direction in which the scan is being made (where the laser beam has angle 0 and azimuth 0) is considered the Y direction (or false north) and X and Z the (false) easting and (false) elevation, respectively .If the scanner (on a tripod) is leveled perfectly horizontal, and the bearing (true north) of the scanner can be measured, it is possible to apply a simple rotation to the data set to make it orient to the true north. Of course, it is a crude way of reorienting that depends entirely on the precision with which the bearing of the scanner can be measured and the accuracy with which the scanner can be leveled. However, the relative accuracy remains intact. It can be expected that laser scanners in the future will be equipped with a built-in leveling device, an electronic compass, and a differential global positioning system so that instant relative or even absolute georeferencing can be achieved. For a very accurate georeferencing to a global or local grid, additional geodetic measurements will still be needed. In some cases, the laser scanner cannot be oriented horizontally, for instance, when a scan must be made at an angle to capture the top of a steep and high rock face. It this case, the point cloud data set cannot merely be rotated but has to undergo a more complex transformation. In this scenario, the scanned scene must have some reference information. For example, two fiat boards can be placed in the scan or on the rock face (in the case study described further in this paper, these were two 60- x 60-cm white plywood boards; see Figure 2). The orientation of these boards can be measured with a regular geological field compass (typically only up to 1° precision). Because the boards appear in the data set, the orientation according to the scanner's coordinate system can be calculated, and these can subsequently be compared with the true orientation. Transformation parameters can then be computed to reorient the entire data set. It should be emphasized that even though the accuracy of the transformation may not be very high with this method, the precision of the data remains intact. Surface Reconstruction It is not possible to derive valuable information on the basis of the point cloud data alone. Point cloud data can only be visualized, which gives the user a very good visual impression of the scanned object (see Figure 3). However, to analyze the surface of the object it represents, the point cloud data must be interpolated and reconstructed as a 3D surface model. Three-D surface reconstruction algorithms can be divided roughly into polygonal and parametric techniques. An example of polygonal techniques is 3D Delaunay triangulation, which creates irregular, triangular patches using simple linear interpolation between the points 189 FIGURE 2 Carboniferous mate-siltstones with wall-davalopad discontinuities. Part of slope !outlined with rectangular boxl is used in this paper to demonstrate methodology. Inset shows detail of the outlined area, which is approximately 1.5 x 2.0 m. in 3D space. Examples of applications that use 3D Delaunay surface triangulation on point clouds are Cocone (13, I 4) and Points2Polys (15). Examples of parametric techniques and applications are NonUniform Rational B-Splines (NURBS) or Radial Basis Functions (RBFs) (16, 17), which use parametric functions to define surface patches. Parametric techniques create more natural looking surfaces and more accurate representations and interpolates in areas with missing data. Parametric techniques however, require more computing power than polygonal interpolation techniques. Polygonal interpolation techniques work well on laser scan data sets when the spatial resolution is relatively small compared with the laser's range error. Delaunay 3D triangulation resulted for instance in an apparently visually correct reconstructed surface. If, however, the data density of the point cloud is relatively high compared with the error, the Delaunay interpolation gives poor results. For instance, if an object is scanned with a resolution of 5 mm, although the position error is in the order of 10 mm, the Delaunay routine interpolates linearly between neighboring points. It is not difficult to imagine that the interpolated surface is more influenced by the error than by the overall trend. This problem can be overcome by undersampling the point cloud data or decreasing the scanner's resolution. The RBF parametric interpolation technique overcomes this problem without having to undersample or use a low scanning resolution. It uses poly harmonic RBFs to reconstruct smooth, manifold surfaces from (noisy) point cloud data, and it can repair incomplete meshes (17). This technique allows fast reconstruction of surfaces, even on the basis of millions of points-something that was not possible before. Polyharmonic spline functions result in smooth interpolations. The technique is well suited to reconstruct surfaces from nonuniformly sampled data. If there are missing data or "holes," they are filled and the surfaces are extrapolated smoothly. Another advantage of this method is that it can handle noisy laser scan data well. Noise from the surfaces can be smoothed out using different techniques, which is demonstrated in Carr et al. (16). The functional representation of an RBF is in effect a solid model, which means that gradients Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. Transportation Research Record 1 91 3 190 FIGURE 3 30 visualization of entire point cloud !with the software Fx, beta version 1.0 from Split Engineering 129)1 of scan made of slope in Figure 2. Reflected laser intensities are shown in grayscale (i.e., white is high reflection and black is low reflection!. and surface normals can be determined analytically. This allows the user to create uniform meshes, which has advantages for mesh simplification and remeshing applications (17). DATA ANALYSIS measurement, comparable to an individual manual orientation measurement made for each discontinuity set in a traditional way with a geological field compass. In many cases, this assumption may not be valid. If, for instance, surfaces in the outcrop are formed by fractures through intact rock or if the surfaces have been affected by weathering, these surfaces are Stereo or Polar Plotting of Individual Facets of Reconstructed Rock Surface After the surface reconstruction, the geometry of the rock face is now represented by hundreds of thousands to millions of triangles or facets. Each individual facet has three nodes or points that are defined in 3D (X, Y, Z) space. In case of a surface reconstructed by using polygonal techniques (such as Delaunay triangulation), each node is the actual original laser scan point, because a linear interpolation is used. In case of a surface reconstruction using parametric techniques, each node is part of the computed polynomial meshed surface and thus no longer represents an original laser scan point (see Figure 4). Because the 3D coordinates of each node are known, it is possible, through the application of basic geometric rules, to determine the orientation for each facet or the normal of each facet (18. 19). The assumption is that most surfaces in a discontinuous rock outcrop are actually formed by the internal discontinuity structure of the rock mass. In this case, each facet represents in fact a single orientation (a) (b) FIGURE 4 lsl 30 visualization of original point cloud data showing high density of data 15 mm resolution! and 'fuzzy' character of original data caused by influence of positioning error 1±1 cml; lbl points of faoats that have been meshed by using parametric FastRBF method. When compared with original date, it is evident that the fuzzy character is removed and that more detail can ba observed. Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. 191 Slob, van Knapen, Hack, Turner, and Kemeny not characteristic for a specific discontinuity. If much rubble, scree, or soil is present in the rock outcrop, this will of course also affect the outcome of the analysis. However, the underlying hypothesis remains valid, which is that if discontinuity sets are clearly visible in the rock outcrop, it will also be possible to observe trends in the data. If trends can be observed in the data, it should then also be possible to statistically define them, even if the data contain noise. By plotting the orientations of all individual facets in a stereo or polar plot, the trends in the data can be visualized and recognized in the form of clusters (19). After the hypothesis, each cluster therefore represents a different discontinuity set. Because of the high density of the laser data, it is possible to have hundreds of thousands to millions of facets for a single rock outcrop. Consequently, these data will provide a solid basis for statistical analyses (clustering techniques) to obtain the discontinuity information contained in the laser scan data of the exposed rock mass. This clustering technique is explained in the following section. An automated clustering was applied to eliminate the human bias as much as possible. 'I' (a) Identification of Joint Sets by Using Clustering Techniques For the automatic clustering of discontinuity sets, the adjusted fuzzy k-means clustering method is used, as suggested by Hammah and Curran (20). The disadvantage of this method is that an initial guess of the number of clusters must be made, which again introduces human bias. However, the number of sets closest to reality can be determined with the aid of validity indices, like those proposed by Xie and Beni (21) and Gath and Geva (22). One major advantage is that this algorithm can be improved through the use of quantifiable discontinuity properties, such as spacing or joint roughness (23). The clustering algorithm is based on a "soft" classification scheme (i.e., it includes all facet orientations). This means that cluster outliers are not removed. To reduce the presence of this noise and to allow for a better rock surface analysis, a proper rejection criterion for the delineation of discontinuity sets needs to be found (24). The mean orientation of each cluster plays a key role in determining a cluster distribution and should therefore be known with great accuracy. This can be achieved by an appropriate clustering method in combination with a weighting factor or by simplifying the mesh. Simplification of the mesh can be done by grouping of adjoining triangles with similar orientations and merging them into larger facets. The larger a facet becomes after the simplification, the more it represents an actual discontinuity plane. All approaches that can lead to a proper delineation of each cluster boundary are based on the assumption that the distribution pattern is that of the so-called Fisher distribution (25) (i.e., a circular concentration around the mean). Fisher distributions have been observed in many of the stereo plots from the laser scan data, and it appears to be a justified theory. In this study, Fisher's k-value was used in an iterative process of increasing subcluster size. Because a higher Fisher's k or concentration parameter K corresponds to a relatively dense distribution, the highest value found for any subset should mark the boundary of the entire cluster. The difference in variance of the mean orientation between two subsequent subsets produces a comparable result. This (simple form of) F-test (26, 27) is used to delimit the cluster boundaries (see Figure 5). Fisher's model as a probability density function further allows for the determination of the frequency of orientations on a unit sphere (3, 26, 28). It also indicates the variance ofthe mean orientation. Both parameters can serve as a factor to delimit the different clusters by (b) FIGURE 5 !al Polar plot of ell orientations of individual facets in 3D surface model. Clusters end cluster centers ere identified with fuzzy k-meens method. Facets belonging to different discontinuity sets receives different color. All facets ere classified, as well as the obvious outliers in the cluster, which may belong to nondiscontinuity surfaces. Refer to Table 1 for legend to statistics. lbl Polar plot showing only those facets that fulfill Is simple type ofl F-test !2, Bl. This is being used ass first pragmatic approach to delimit cluster boundaries. All outliers have been removed. using critical cone angles or frequencies as a threshold value. Another approach is to test for equivalence between two subsets originating from one cluster, determined by a pooled F-test statistic (27). Determination of Discontinuity Spacing Distributions Another very important aspect in rock mass characterization is the determination of discontinuity set spacing and spacing distribution. Together with the orientation of the discontinuity sets, this aspect determines the variation in size and shape of the blocks that make up the fabric of the rock mass. For most engineering applications dealing with rock masses, this is crucial information. By separating the individual discontinuity sets and surfaces from the entire data Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. Transportation Research Record 1913 192 set, it becomes possible to analyze these surfaces in 3D space and subsequently to derive the distances (spacings) between them. IMPLEMENTATION OF DATA ANALYSIS To carry out the data processing and data analysis steps described in the previous sections, a number of computer scripts have been written with Matlab as a programming platform. The advantages of Matlab are that it is well suited to process large amounts of data, it provides good visualization routines, and it does not require extensive programming experience. An additional advantage is that the FastRBF routines to reconstruct surfaces are available as Matlab toolboxes so that all processing and analysis routines can be integrated easily. The processing and analysis steps are listed in the following sections and are illustrated in the figures included in this paper. Other software is currently under development by Split Engineering LLC (29) that made use of generally the same concepts as described in this paper. For demonstration purposes, a small part of rock slope was singled out that has well-developed discontinuities (see Figure 2). This data set was processed and analyzed using the described method. This rock slope was scanned with Optech's ILRIS-3D Intelligent Laser Ranging and Imaging System (30). The location of the slope is in Spain, along road TP7101 between False! and Bellmunt, Priorat District, Catalan Province. The rock mass consists of meta-siltstones of Carboniferous age. Data-Processing Steps 1. Import raw (X, Y, Z) point cloud data (see Figure 3). 2. Crop data if desired (see Figure 4). 3. Reorient data using rotation or transformation. 4. Reconstruct surface with parametric interpolation (using the FastRBF toolbox) (see Figure 6). 5. Visualize the meshed surface in Matlab. 6. Export surface data to generic OBJ (Wavefront) or Virtual Reality Modeling Language data formats for visualization and exchange purposes. Data Analysis Steps 7. Calculate orientation of facets. 8. Plot all facet orientations in a stereo net. 9. Perform cluster analysis using the fuzzy k-means method (for results, please refer to Table 1). 10. Visualize different clusters in a stereonet by coloring of the different cluster regions (see Figure 5). 11. Apply the colors of the different cluster regions to the 3D meshed surface to verify visually whether the automated clustering result is as expected (see Figure 6). 12. Remove cluster outliers, recalculate mean set orientation (see Figure 5), and visualize results in a stereo net (see Figure 5). 13. Reapply the colors of the different cluster regions to the 3D meshed surface to verify visually whether the delineated clusters really outline the "real" discontinuity sets (see Figure 7). 14. Model each individual joint plane and visualize them (see Figure 7). 15. Calculate discontinuity spacings within each set (see Table I). COST-BENEFIT ANALYSIS An example is given that illustrates the advantages in time and costs of discontinuity analysis on the basis of laser scan survey data over a traditional analysis. The data are from an actual case study described by Monte (31). This study was on a section of roadway of US-93, which is a major commercial route between Phoenix, Arizona, and Las Vegas, Nevada. The Arizona Department of Transportation contracted URS Corporation (URS) in 2003 to complete a geotechnical investigation for widening of a 5.6-km stretch ofUS-93. This section of roadway, located between Wickenburg, Arizona, and Interstate 40, traverses through granite and basin fill and floodplain deposits. The traditional survey and analysis required the following: • Cell mapping, 350 joint orientation measurements, two people for2 days; • Processing and making graphs of the data, one person for 2 days; • Tota16 person days (with overhead, assume $1,000 per day); and Yellow (a) (b) FIGURE 6 lal 30 rendering of the reconstructed rock surface with the FestRBF method. Artificial lighting has been used to emphasize visible structures and amount of detail. !bl Recolored 30 surface model with color assigned to four different discontinuity clusters as shown in Figure 5. All surfaces are being classified, as well as surfaces that are clearly nondiacontlnuity surfaces. Apparent are clear outlining of bedding lin yellow) and orthogonal joint set lin radl. Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. Slob, van Knapen, Hack, Turner, and Kemeny TABLE 1 193 Summary Statistics Before Outlier Removal Discontinuity Set Number After Outlier Removal Set Spacing Statistics Number of Facets Mean Orientation Fisher's K-Yaluc Number of Facets Mean Orientation Set I blue 69,445 233/04 10.87 62,684 233/05 Set 2 red 50,855 306/34 8.56 34,081 304/36 Set 3 yellow 83,494 144/47 23.04 67,336 144/48 Set 4 purple 88,662 205/20 23.33 69,855 206/20 Fisher's K-Value Mean Normal Set Spacing Dimension of Set j_ to Orientation 16.37 8.20cm 147.59em 60.33 20.29em 162.28 em 50.27 7.03 em 161.65 em 42.04 4.13 em 58.10em The data file contains 292,456 facets originating from 147,425 points. • Share of equipment and software costs $250 C;; 0th of actual cost of Brunton, stereonet, software, and so forth). The total cost was approximately $6,250 (mostly personnel). A laser scan survey with automatic software analysis would require the following: • Field scanning (six scans) and digital imaging, one person for I day; • Data processing: 0.5 to 1 day; • Scanner rental: $1 ,500; • Share of other field equipment (camera, etc.), $200; and • Share of software costs, $1,500 (assume Y; 0th of actual cost of $15,000 for data processing software). The total cost is $4,700-$5,200 (one-third personnel, two-thirds equipment and software). The conclusion that can be drawn from this comparative study is that laser scan-based survey and automated analysis can be considerably faster and less labor-intensive and, therefore, cheaper than traditional survey and analysis. If the laser scan equipment and software are also used on a more routine basis, rental and share costs will likely become even lower. Developments of this new technique, like all other new information and communication technology techniques, are very rapid. The capabilities of current laser scanners are greatly improved compared with the first generation, but the price of a system has remained the same or is even becoming less, because larger numbers are being produced and sold. CONCLUSIONS 3D laser scanning data can be used as input in a computer-based method to • Model rock slopes at high detail and with high accuracy in three dimensions with parametric surface reconstruction techniques; • Determine the orientations of discontinuity sets in an outcropping discontinuous rock mass from this modeled rock surface without physical access to the slope; • Automate the cluster analysis using fuzzy k-means clustering; • Remove cluster outliers assuming Fisher's distribution; • Visualize the results in stereo or polar plots; and • Visualize the results in the 3D surface model. The advantages of the method described in this paper are as follows: • No physical access is needed to or near the rock surface to measure discontinuity orientations, which has obvious advantages in terms of safety. Yellow (a) (b) FIGURE 7 Cal Recolored version of 30 surface model with color assigned to different discontinuity clusters in Figure 5a. All facets that do not fulfill F-test (see Figure 5b,J have not been colored and are shown in grey. It is evident that only "real" discontinuity surfaces have now been classified and colored. Compare with Figure Sb. (b) individual discontinuity planes of Set 2 (red! and Set 3 (yellow!, modeled as linear trend surfaces. From calculating distances between the individual surfaces, joint set spacing can be computed. Slob, S., Van Knapen, B., Hack, R., Turner, K., Kemeny, J., 2005. Method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. Transportation Research Record: Journal of the Transportation Research Board; Geology and Properties of Earth Materials. 1913 (2005). DOI: 10.3141/1913-18. ISSN: 0361-1981. pp. 187-194. 194 • Inaccessible rock faces can now be analyzed; particularly for slope stability and block size analysis, this has obvious advantages. • The human bias in determining rock mass discontinuities is mostly removed. • More discontinuity data can be gathered than in using traditional (manual) techniques, which allows proper application of statistical tools. • Higher accuracy of the orientation measurements can be achieved. There are three parts to accuracy: 1. Accuracy of measurement of strike and dip; 2. Much better statistical sampling, therefore, more accurate joint sets and properties of each set; and 3. Measuring the average orientation of a fracture rather than the specific location where the Brunton compass is placed. • Laser scanning also can assist other aspects of a geotechnical project. An important example is that an accurate survey of the geometry of a slope is realized, which can be integrated with other geometric elements, such as drainage ditches, road surface in a computer-aided design, or geographic information system. • It is faster, less labor-intensive, and, therefore, cheaper than traditional surveying. ACKNOWLEDGMENTS This research was funded by ITC's internal research budget within the framework of the HiRES 3D research program. Split Engineering LCC supplied the Ilris laser scanner for use during the fieldwork in Spain and the beta version of the Fx software. REFERENCES 1. Bieniawski, Z. T. Engineering Rock Mass Classification. John Wiley and Sons, New York, 1989. 2. Priest, S. D., and J. A. Hudson. Estimation of Discontinuity Spacing and Trace Length Using Scanline Surveys, International Journal of Rock Mechanics and Mining Sciences & Geomechanics, Vol. 18, 1981, pp. 183-197. 3. Priest, S.D. Discontinuity Analysis for Rock Engineering. 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