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Terrestrial laser scanning used to determine the geometry of a granite boulder for stability analysis purposes
Geomorphology 106 (2009) 271–277
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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / g e o m o r p h
Terrestrial laser scanning used to determine the geometry of a granite boulder for stability analysis purposes J. Armesto, C. Ordóñez ⁎, L. Alejano, P. Arias Department of Natural Resources and Environmental Engineering, School of Mining, University of Vigo, 36310 Vigo, Spain
a r t i c l e
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Article history: Received 4 September 2008 Received in revised form 12 November 2008 Accepted 13 November 2008 Available online 19 November 2008 Keywords: Granite boulder Terrestrial laser scanning 3D digital model Safety factor
a b s t r a c t In this paper we analyze the use of terrestrial laser scanning (TLS) technologies to determine the geometric features of a granite boulder. Accurate determination of these features is a key to performing a reliable stability analysis of the boulder. TLS has been demonstrated to have important advantages over traditional measurement techniques—such as, for example, direct methods based on the use of tapes or indirect methods such as topography or closerange photogrammetry. TLS equipment enables thousands of points to be accurately measured in minutes. In our study TLS-measured points were used to model the surface of a boulder. Geometric parameters were then calculated, namely, centre of gravity, volume of the boulder and dimensions of the boulder contact area with the ground. Taking into account mechanical and environmental factors, these parameters were used to calculate the safety factor of the boulder against toppling and sliding. Our results show that, when seismic activity in the region is taken into consideration, the boulder is borderline stable–unstable. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The evaluation and management of natural risks requires an analysis of the geomorphological processes associated with rockfalls and landslides, particularly in mountainous regions with existing or planned infrastructures or installations affecting humans. Highresolution digital elevation models (DEMs), obtained by means of aerial photography, and light detection and ranging (LIDAR) systems (Chang et al., 2005; Roncella et al., 2005; Schulz, 2007) are increasingly being used to conduct stability analyses of rock slopes, to model and simulate fall paths and to manage geomorphological risk. The main drawback of these techniques, however, is that they are not applicable to vertical slopes or freestanding boulders, as the aerial perspective prevents sufficient data being obtained for the slope or boulder support area. Land-based techniques that can be used to measure rocks and slopes are basically traditional topography, close-range photogrammetry and terrestrial laser scanning (TLS). Total-station measurement depends greatly on the skill of the operator in terms of both capturing a sufficient number of points and selecting suitable points to faithfully represent the surface of the rock or slope. Close-range photogrammetry is limited by the difficulty of obtaining data for areas where obstacles prevent the filming necessary to obtain stereoscopic pairs. One such example is filming in wooded areas. TLS, however, is a relatively new technique that is becoming increasingly popular in geomorphological studies of vertical slopes and freestanding ⁎ Corresponding author. Tel.: +34 986814052; fax: +34 986812201. E-mail address: [email protected] (C. Ordóñez). 0169-555X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2008.11.005
boulders. Compared with other techniques, TLS systems offer a number of advantages, such as noncontact acquisition of the threedimensional (3D) geometry for the entire uncovered surface of an object, high-density data capture (clouds of millions of points), great measuring accuracy, and a rapid acquisition rate. The combination of accuracy, speed and range in a single instrument has led to the use of TLS systems in fields as different as 3D modelling for the reconstruction of archaeological and other cultural assets (Guidi et al., 2004), forensic anthropology (Bolliger et al., 2008), the modelling and analysis of structure stability (Arias et al., 2007), etc. In terms of TLS applications to geomorphological analysis, of particular note is the research by Abellán et al. (2006), describing TLS generation of a detailed DEM from clouds of points measured for a test area in the Spanish Pyrenees with a view to creating an inventory of slopes and simulating landslide paths and speeds. In Ghirotti and Genevois (2007), TLS data were used to capture a detailed topographical image of a mountain slope in the Italian Apennines and to analyse its stability by means of simulations in which GSI (Geological Strength Index) values were varied according to the Hoek and Brown (1997) model. Bauer et al. (2005) described a methodology for measuring slopes using TLS and automatically processing point clouds in order to detect changes in unstable surfaces. Other works of note– by Runqiu and Xiujun (2008) and Feng and Roshoff (2004)–described long-range TLS data capture processes, the registration of clouds of points and the creation of 3-D models of slopes and banks, all aimed at ascertaining geomorphological parameters such as fracture angles, directions, spacing, surface textures, etc. All these works coincide in pointing to the potential of TLS for geomorphological studies.
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In this article we describe a methodology based on using TLS to acquire clouds of points and aimed at generating the geometry of the 3-D surface and obtaining cross sections of a boulder. The resulting 3D model enabled us to determine the centre of gravity and to calculate the dimensions of the support surface and the volume of the boulder. This information, combined with data on the mechanical characteristics of the rock and on a series of external factors, enabled us to determine whether the boulder was unstable and required steps to prevent possible toppling or sliding. 2. Methods
made from the same position will thus be based on the same coordinate system. For cases where more than one scan is made, the projected coordinate system (PCS) is arbitrary, and the geographic coordinate system (GCS) refers to geodesic or cartographic coordinates. The process of transforming point coordinates from the SOCS to the PCS or GCS is called alignment or registration (described below). The PCS can be leveled either by using the scanner's self-leveling function (if equipped with one) and establishing GCP control points for known coordinates, or by determining the system axes in the cloud of points. Topographic methods using GPS or total station, supported by a national geodetic network, are required to establish the GCS.
2.1. TLS measurement The TLS surveying procedure applied to the measurement, dimensioning and stability analysis of the boulder was structured as follows: -
Scan project planning. Data acquisition. Data processing (registration). Post-processing (triangulation and dimensioning). Stability analysis.
2.1.1. Scan project planning Long-range TLS measurement is based on the emission of a laser beam with a wavelength in the optical or near infrared domains that affect an object directly. The distance from the point of emission to the surface is obtained by calculating the flight time of the signal. The distance measurement system is combined with a baffle plate which aims the beam in the direction of the surface to be measured. The horizontal and vertical angles that correspond to each emitted pulse are determined by coders. Thus, a spherical coordinate system centered on the scanner is defined from which Cartesian coordinates (X, Y, Z) are obtained for any point measured on the surface of the object. To obtain adequate data for the object to be measured, the acquisition project should be planned considering the following issues: - Location and number of stations. Two issues are key, namely, minimizing the number of stations (with a view to optimizing scanning time and accuracy) and ensuring that scanned areas overlap so that the entire surface is covered. - Occlusions. We need to be remember that all that is visible to the operator from the scanning position will be recorded in the scan, and likewise, whatever is not visible will be excluded. Any object that intervenes between the scanner and the surface to be measured will reflect the beam before it reaches the surface. The object will consequently cast a shadow on the surface whose size will be directly proportional to the proximity of the scanner. This problem is resolved by making an inspection of the objects in the vicinity of the planned scan positions. Special attention should be paid to detecting occlusions caused by convexities and concavities in the rock. - Resolution. Most TLS systems allow angular resolution to be configured for a specific spatial resolution for the scanned surface by combining greater distances with higher resolutions and shorter distances with lower resolutions. This combination is only limited, firstly, by the maximum angular resolution of the instrument, the beam width (the beam footprint on the object should not be wider than the angular step width) and the expected detail in the modeling of the object surface. - Reference system. Three coordinate systems coexist in scanned measurements. Firstly, the scanner's own coordinate system (SOCS) defines coordinates for each position of the instrument with respect to its optical centre. All 3D clouds of points for scans
2.1.2. Data acquisition Two scans were made from each scan position. The first scan, called the overview scan, was based on a minimum-resolution (angular interval of 0.2°) scan of the entire field of vision (360° with respect to the Z axis and 80° for vertical amplitude). The second highresolution scan was of an area including the surface to be scanned and selected from a two-dimensional (2D) view of the first scan. When modelling a rock with a more or less regular surface (like the Penedo da Sobreira boulder), an angular interval giving a resolution of 2–5 cm can be considered sufficient. Generated in real time for each scan and for each point were spherical coordinates R, φ, θ and the corresponding Cartesian coordinates, X, Y, Z (whose coordinate system is centered on the scanner). The Cartesian coordinates were obtained from the spherical coordinates as X =R · sin θ · cos φ, Y =R · sin θ · sin φ, Z =R· cos θ. Also obtained for each point was a measure of laser reflection from the surface, which depends, among other factors, on the physical characteristics of the surface and the incidence angle (Boehler and Marbs, 2003). 2.1.3. Data processing: registration To align the clouds of points in a common coordinate system, we used the iterative closest point (ICP) algorithm, which enables two surfaces, S and S, to be aligned in the same system. This process consists, essentially, of the following: - For a given surface S, when a deformation function, F: Mp = F(P), with known parameters is applied to the surface it produces a model Ms of the surface. With P as a point in S, for each point Mp in Ms, we next look for the nearest P′ in the surface S. - A cost function is established in which P and P′ are known, whereas the parameters for the deformation F are assumed to be unknown. To obtain the new deformation parameters, cost is minimized to the point at which the termination criterion is satisfied. The surfaces Si are defined for each scan by applying triangulation to the registered point cloud (details can be found in Besl and McKay, 1992). In our case the procedure consisted of dividing each scan, in the θ–φ plane, into square cells, the length of whose sides was established on the basis of the angular resolution established for the scan. For each cell an adjustment plane was calculated from the cell's points. If point deviation was excessive, the points in the cell were considered not to belong to the same plane; the cell was thus subdivided and each subcell was processed repeating the same procedure. 2.1.4. Post-processing: triangulation and dimensioning The point cloud was manually divided into the required classes: boulder, support area and surroundings. The boulder and the ground were triangulated using flat triangulation and the quadratic least squares (QLS) plane, respectively, and the surroundings were eliminated. A triangulated mesh of the support area for the boulder was generated by establishing a regular mesh on the projection plane in such a way that, for each grid, the QLS plane was determined for points
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measured on the terrain surface. If point deviation was excessive, this was interpreted as points not being co-planar; the grid was thus further divided and the same procedure was repeated. The parameters to be configured in each case were maximum admissible deviation, maximum edge length, reference plane, mesh resolution, and the angle between the vector normal to the estimated plane and the vector normal to the reference plane. Note that if the ground is covered with vegetation, mesh grids measuring 0.5–1 m should be used, as small grid sizes produce irregular meshes that model the vegetation rather than the ground surface. The boulder was triangulated in sections using Delaunay 2D triangulation applied to the viewing plane. The following parameters were configured manually: - Maximum edge length, which defines the maximum length of the edge of each triangle. - Maximum angle, which limits the angle between two beams originating in the SOCS and terminating in the vertices of a triangle edge, thereby limiting the length of the edge. From the triangulated meshes for the terrain and the boulder, we obtained, cross sections and longitudinal sections reflecting the three main boulder directions (see the definition of these directions below). For dimensioning purposes, a cross-sectional plane was defined. A comparison plane was also defined, with respect to which two semivolumes were calculated as the sum of the volume of the prisms with their base in the comparison plane and their other extreme in a mesh triangle. The difference between the fill and cut semi-volumes represented the total volume of the boulder. 2.2. Stability analysis The basic rock mechanics data were obtained from density tests on granite samples from the Penedo da Sobreira boulder and from joint data obtained in situ. Rock joints were characterised according to the Barton strength criteria (Barton, 1973, 1976) and the recommendations of the International Society of Rock Mechanics (Brown, 1981). Special attention was given to correctly estimating the JRC (joint roughness coefficient) and r & R (Schmidt hammer rebounds on weathered and fresh rock surfaces). In granites, removal of the overburden results in three perpendicular sets of joints and weakness orientations (Mabbutt, 1961; GCO, 1987). In quarrying terminology, the weakness planes are called the rift, grain and hardway planes (Taboada et al., 2005), which determine the geomorphology of many granite outcrops all over the world and guide granite quarrying operations. The rift plane is sub-horizontal and is the plane of least resistance. The grain plane is vertical (perpendicular to the grain) and produces a poorer break in the rock. Finally, the hardway plane, which is vertical and orthogonal to the rift and grain planes, is the minimum weakness plane. Once we had information on the geometric and rock mechanic properties of the boulder, together with the average rainfall and seismic intensity in the area, we were ready to carry out a stability analysis of the boulder. Two types of instability mechanism were considered (Fig. 1): sliding and toppling (Goodman and Bray, 1977; Sagaseta, 1986; Bobet, 1999). 2.2.1. Stability against sliding Sliding stability takes account of plane failure (sliding in a single plane), a mechanism studied by Hoek and Bray (1977). Stability depends on the safety factor, which is the ratio of stabilising forces to destabilising forces acting on the block. Taking into account water and seismic pressures, the safety factor can be expressed (Hoek and Bray, 1977) as follows: SFSL =
ðW cos β − αW sin β − U ÞtgΦpeak W sin β + αW cos β
ð1Þ
Fig. 1. Instability mechanisms: sliding (left) and toppling (right).
where W: weight of the boulder (KN); U: total water pressure (KN); α: pseudo-seismic contribution coefficient; β: terrain slope (degrees) and: Φpeak friction angle (degrees). The peak friction angle, Φpeak, is calculated from factors obtained from joint data, according to the formula by Barton and Bandis (1990): JCSn Φpeak = /r + JRCn · log10 σn 0 /r = /b − 20 + 20 · ðr = RÞ
ð2Þ ð3Þ
where: ϕr ϕb JRCn JCSn σn
friction residual angle basic friction angle joint roughness coefficient corrected by scale joint compressive strength corrected by scale normal tension
Water pressure depends on the boulder contact surface area, A, the height of the water column at its centre, h, and specific weight of water, γw, according to the following expression: U=
1 Ahγ w 3
ð4Þ
2.2.2. Stability against toppling Rock slope instability from toppling in quarries, road cuts or natural slopes is quite frequent, and a number of actual cases have already been studied (Alejano and Alonso, 2005; Alejano et al., 2006). The basic idea underlying the toppling of a block boulder is that it will remain stable as long as the projection of the vector representing the weight falls within its base. This is why knowledge of the geometry of a block is of paramount importance in correctly assessing block stability. Extending this simple concept, the safety factor against toppling can be calculated as the ratio of stabilizing movements to overturning movements. An overall knowledge of the geometry of a boulder is therefore of paramount importance in order to be able to correctly assess its stability.
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In our case, various sections of the boulder were considered given that the 3-D effects were important. The boulder was thus divided into three main sections–one central (A) and two lateral (B and B′) sections–so as to take into account the stabilizing effect of the side zones. Two external sections were not accounted for in the toppling calculations for two reasons: firstly, their significance is low, and secondly, excluding them renders the approach more conservative. In general, we sought a balance between simplicity and accuracy in calculating the moments. The sections are illustrated in the plan view of the boulder depicted in Fig. 2. The general expression of the safety factor against toppling for each of the three main sections is given as follows (Alejano et al., 2006): SFTOP =
MSTABILIZING ðW cos βÞd = MOVERTURNING ðW sin βÞh + Ut + αWm
ð5Þ
where d and h, t and m are the moments arm lengths, for the dry case U = 0 and for the non-seismic case α = 0.
not moved, among the local people (and especially those living in houses located roughly 300 m below the boulder) a perception exists that the rock has moved. In fact, this research was inspired by an invitation from the local council to perform a hazard assessment of the stability of the boulder and to determine the possible consequences if it toppled. Two physical characteristics of the geographic area where the boulder is located were considered for the stability analysis: rainfall and seismic activity. Local maps show a maximum rainfall of 200 L/m2 in 24 h for a return period of 50 years (Ministerio de Medio Ambiente, 2000). This level of rainfall could well produce water pressure at the boulder base and produce a water head at its centre of up to 2 m. On the other hand, information was also gathered on the earthquakes occurring in or near the area in recent decades. The most powerful earthquake, with an intensity of 3.3 on the Richter scale, occurred in 1998 near the village of Mondariz, 15 km from the boulder location. Because an equivalent vibration would generate horizontal accelerations of just under 0.04 g in the boulder zone, a pseudo-seismic analysis can be considered to be a realistic approach in this case.
3. Case study 3.2. TLS 3-D modelling and dimensioning of the boulder 3.1. Boulder characteristics In many parts of the world, including Galicia (NW Spain), granite landscapes are strewn with granite boulders (Ollier, 1978; Le Pera and Sorriso-Vallor, 2000; Migon, 2006) that are the result of spheroidal weathering and a combination of physical and chemical weathering (Ollier, 1977). This process creates rounded boulders and also contributes to creating domed monoliths. One such boulder, locally called Penedo da Sobreira, was the object of this study (Fig. 3). Although comparison of the boulder location at present with that obtained from aerial photographs in 1956 seems to indicate that it has
The equipment used for this research to determine the boulder dimensions was a Riegl LMS-Z390i 3-D time-of-flight (TOF) laser scanner. This device measures distances in a range of 1.5 to 400 m, with a nominal accuracy of 6 mm to 50 m in normal illumination and reflectivity conditions. The laser is infrared and has a wavelength of between 0.7 and 2 μm. The viewing field has 80° vertical angle and 360° horizontally. The minimum and maximum angular resolutions are 0.2° and 0.002°, respectively; and the point measurement rate ranges between 8000 and 11,000 points/second. The beam divergence is 0.3 mrad, equivalent to 30 mm/100 m range. The software used for
Fig. 2. Plan view of the boulder, scan positions and surroundings for 5 m equidistant contour curves. Cross-sections of the granite boulder used to perform the instability analysis are also shown.
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Fig. 3. View of the Penedo da Sobreira granite boulder from below.
registration and alignment for the clouds of points was RiSCAN PRO Software by Riegl© (Riegel, 2008). The possible locations for the scanner were limited by the topography of the site where the granite boulder was located. Access from the south is by a narrow passageway measuring 1 m wide at its narrowest part (the space between the slope and the boulder). Two scanner positions were established at each end of this passageway: one on a waist-high rock, and the other on a platform of earth created for the purpose. Other positions were established on the road north of the rock so as to optimise visibility of the rock. The inclination sensors of the scanner were used to level the cloud of points. In the data acquisition phase, two scans were made from each scan position. The overview scan was done for the entire field of vision (360° with respect to the Z axis and 80° of vertical amplitude) at the minimum-resolution (angular interval 0.2°). For the second highresolution scan, an area is selected from a 2D view that includes the surface to be scanned (Fig. 4). The horizontal and vertical angular step width was established as 0.05° after considering the aim of maximum surface detail, beam divergence and laser-to-object distance. This distance ranged from a few meters for the northern stations to 25 m for the road stations. The resulting clouds of points were irregular grids of points, at a distance of 0.5 cm for the densest areas, and 30– 50 cm for the top of the boulder, where visibility was limited due to slope and accessibility. Of the four scan positions, the fine scan for the third scan position had to be discarded, however, as it was affected by a dense fog. Scanning took some 50 m, although some 2 h in total was spent on traveling, assembly and measurement. A standard deviation for error of 31 mm was obtained in the alignment of the three clouds of points by means of ICP. The final clouds of points obtained contained 1,612,831 points, 881,583 of which corresponded to the immediate surroundings and the support terrain for the boulder, and 91,661 to the surface of the boulder. Triangulated meshes were generated from the clouds of points. This mesh yielded 2-D longitudinal sections and cross sections of the supported boulder and the terrain. In addition to 2-D and 3-D graphic outputs, the coordinates for each point were exported so that stability could be calculated. In order to dimension the boulder, the cloud was divided into two. Two triangulations were generated for each half, obtaining the total
volume with respect to the same external plane by calculating the difference between each half (as explained above). The final volume was 2230 m3. An estimate of error in computation of the boulder volume was obtained as a function of the distance measurement error given by the calibration specifications of the Riegl LMS Z390i laser scanner, resulting in an estimated error of 1%. 3.3. Stability analysis Rock samples were collected and cut into cylindrical specimens that were tested for density and the basal friction angle—the two basic rock mechanics properties essential to stability analysis. The average density obtained was 2.59 g/cm3 (2.59 t/m3) and the average basic friction angle, ϕb, was 33°, obtained from tilt tests as suggested by Stimpson (1981). It was observed that the rift planes in the area dip around 30°, basically coinciding with the slope where the granite boulder is located. Joints parallel to the rift planes were thus sought and characterized in the field.
Fig. 4. Three-dimensional view of a cloud of points for the front of the boulder (north) and surroundings.
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The values measured and calculated for each of the parameters in Eq. (1) were as follows: W U α β Φpeak
56,680 KN 907.09 KN 41° 30° 41°
Both weight and water pressure are given as force units, in other words, the boulder mass was multiplied by gravity acceleration and pressure was multiplied by the contact area. For these values we obtained safety factors for stability (Eq. (1)) of SFSL = 1.51 for the boulder with no water or seismic forces in play, and of SFSL = 1.35 for the boulder under water pressure and during the strongest recorded earthquake (the worst case scenario). These values for the natural slope indicate stability, and so it can be safely asserted that the granite boulder is not likely to slide. In this analysis, it was considered that sliding would be likely to occur on the contact surface as characterized by the Barton and Bandis (1990) equations, based on the assumption that the surface was flat, rough in texture, without fill and reflected the terrain slope. Underlying this assumption is the desire to make a conservative estimate, in other words, an estimate that would err on the side of safety. As for the toppling stability analysis–Eq. (5)–several calculations were made for the different possible circumstances of the boulder. For dry and non-seismic conditions, the safety factor against toppling, SFTOP, was calculated as 1.11, indicating that the boulder was stable. If water pressure in the base were accounted for, as would be the case in extremely rainy periods, the factor of safety dropped to 1.09, again indicating stability. If the boulder experienced a horizontal acceleration of 0.04 g–representing the strongest earthquake likely in the area–then the factor of safety was 1.00 (0.9998), which indicates a borderline stable–unstable scenario. The results obtained indicate that instability arising from sliding on the support surface is very unlikely. However, in the worst possible case, the boulder could well topple. 4. Conclusions This article describes a methodology for applying a long-range 3-D laser-scanning system to the measurement, modelling and analysis of the stability of large boulders. Stability analysis of a supported rock requires that both its entire surface and the support areas be modelled. Furthermore, if access to the boulder is limited, terrestrial measurement techniques are realistically the only feasible technique that can be used. Compared to conventional terrestrial techniques (topography and photogrammetry), TLS systems have the advantage that they do not rely on an operator's criterion for the selection of the boulder surface points to be measured; the operator, in fact, only has to configure the angular resolution of the scan. Another advantage is that TLS systems enable a far greater volume of points to be captured than traditional techniques. TLS systems also provide Cartesian coordinates in real time. Registration of the point clouds and the meshing enable graphic outputs to be obtained in conventional formats and also the volume to be calculated to a high level of precision. The fact that the boulder in our case study had another boulder nearby and vegetation all round made it more practical to use TLS rather than close-range photogrammetry. The geometry for the boulder enabled us to determine its weight, center of gravity and contact area with the terrain. This information, combined with data obtained for the terrain and from the laboratory tests on the mechanical properties of the contact area, enabled us to conclude that, in the most unfavorable water pressure and seismic acceleration circumstances, the boulder would be stable against sliding but could only be considered borderline stable against
toppling. For this reason it would be advisable to make regular checks of the boulder to ensure that it had not moved, for which TLS would be the most suitable system. Another option would be to take some steps to prevent the boulder rolling down the slope; for instance, by anchoring the boulder behind or supporting it in the front. Acknowledgement The financial support of the National Secretary of Universities and Research of the Spanish Ministry of Science and Education (Grant No BIA2006-10259) is gratefully acknowledged. References Abellán, A., Vilaplana, J.M., Martínez, J., 2006. Application of a long-range Terrestrial Laser Scanner to a detailed rockfall study at Vall de Núria (Eastern Pyrenees, Spain). Engineering Geology 88, 136–148. Alejano, L.R., Alonso, E., 2005. Application of the shear and tensile strength reduction technique to obtain factor of safety of toppling and footwall rock slopes. In: Konecky (Ed.), Proceeding of the ISRM Conf. on Rock Mechanics. EUROCK 2005. 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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / g e o m o r p h
Terrestrial laser scanning used to determine the geometry of a granite boulder for stability analysis purposes J. Armesto, C. Ordóñez ⁎, L. Alejano, P. Arias Department of Natural Resources and Environmental Engineering, School of Mining, University of Vigo, 36310 Vigo, Spain
a r t i c l e
i n f o
Article history: Received 4 September 2008 Received in revised form 12 November 2008 Accepted 13 November 2008 Available online 19 November 2008 Keywords: Granite boulder Terrestrial laser scanning 3D digital model Safety factor
a b s t r a c t In this paper we analyze the use of terrestrial laser scanning (TLS) technologies to determine the geometric features of a granite boulder. Accurate determination of these features is a key to performing a reliable stability analysis of the boulder. TLS has been demonstrated to have important advantages over traditional measurement techniques—such as, for example, direct methods based on the use of tapes or indirect methods such as topography or closerange photogrammetry. TLS equipment enables thousands of points to be accurately measured in minutes. In our study TLS-measured points were used to model the surface of a boulder. Geometric parameters were then calculated, namely, centre of gravity, volume of the boulder and dimensions of the boulder contact area with the ground. Taking into account mechanical and environmental factors, these parameters were used to calculate the safety factor of the boulder against toppling and sliding. Our results show that, when seismic activity in the region is taken into consideration, the boulder is borderline stable–unstable. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The evaluation and management of natural risks requires an analysis of the geomorphological processes associated with rockfalls and landslides, particularly in mountainous regions with existing or planned infrastructures or installations affecting humans. Highresolution digital elevation models (DEMs), obtained by means of aerial photography, and light detection and ranging (LIDAR) systems (Chang et al., 2005; Roncella et al., 2005; Schulz, 2007) are increasingly being used to conduct stability analyses of rock slopes, to model and simulate fall paths and to manage geomorphological risk. The main drawback of these techniques, however, is that they are not applicable to vertical slopes or freestanding boulders, as the aerial perspective prevents sufficient data being obtained for the slope or boulder support area. Land-based techniques that can be used to measure rocks and slopes are basically traditional topography, close-range photogrammetry and terrestrial laser scanning (TLS). Total-station measurement depends greatly on the skill of the operator in terms of both capturing a sufficient number of points and selecting suitable points to faithfully represent the surface of the rock or slope. Close-range photogrammetry is limited by the difficulty of obtaining data for areas where obstacles prevent the filming necessary to obtain stereoscopic pairs. One such example is filming in wooded areas. TLS, however, is a relatively new technique that is becoming increasingly popular in geomorphological studies of vertical slopes and freestanding ⁎ Corresponding author. Tel.: +34 986814052; fax: +34 986812201. E-mail address: [email protected] (C. Ordóñez). 0169-555X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2008.11.005
boulders. Compared with other techniques, TLS systems offer a number of advantages, such as noncontact acquisition of the threedimensional (3D) geometry for the entire uncovered surface of an object, high-density data capture (clouds of millions of points), great measuring accuracy, and a rapid acquisition rate. The combination of accuracy, speed and range in a single instrument has led to the use of TLS systems in fields as different as 3D modelling for the reconstruction of archaeological and other cultural assets (Guidi et al., 2004), forensic anthropology (Bolliger et al., 2008), the modelling and analysis of structure stability (Arias et al., 2007), etc. In terms of TLS applications to geomorphological analysis, of particular note is the research by Abellán et al. (2006), describing TLS generation of a detailed DEM from clouds of points measured for a test area in the Spanish Pyrenees with a view to creating an inventory of slopes and simulating landslide paths and speeds. In Ghirotti and Genevois (2007), TLS data were used to capture a detailed topographical image of a mountain slope in the Italian Apennines and to analyse its stability by means of simulations in which GSI (Geological Strength Index) values were varied according to the Hoek and Brown (1997) model. Bauer et al. (2005) described a methodology for measuring slopes using TLS and automatically processing point clouds in order to detect changes in unstable surfaces. Other works of note– by Runqiu and Xiujun (2008) and Feng and Roshoff (2004)–described long-range TLS data capture processes, the registration of clouds of points and the creation of 3-D models of slopes and banks, all aimed at ascertaining geomorphological parameters such as fracture angles, directions, spacing, surface textures, etc. All these works coincide in pointing to the potential of TLS for geomorphological studies.
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In this article we describe a methodology based on using TLS to acquire clouds of points and aimed at generating the geometry of the 3-D surface and obtaining cross sections of a boulder. The resulting 3D model enabled us to determine the centre of gravity and to calculate the dimensions of the support surface and the volume of the boulder. This information, combined with data on the mechanical characteristics of the rock and on a series of external factors, enabled us to determine whether the boulder was unstable and required steps to prevent possible toppling or sliding. 2. Methods
made from the same position will thus be based on the same coordinate system. For cases where more than one scan is made, the projected coordinate system (PCS) is arbitrary, and the geographic coordinate system (GCS) refers to geodesic or cartographic coordinates. The process of transforming point coordinates from the SOCS to the PCS or GCS is called alignment or registration (described below). The PCS can be leveled either by using the scanner's self-leveling function (if equipped with one) and establishing GCP control points for known coordinates, or by determining the system axes in the cloud of points. Topographic methods using GPS or total station, supported by a national geodetic network, are required to establish the GCS.
2.1. TLS measurement The TLS surveying procedure applied to the measurement, dimensioning and stability analysis of the boulder was structured as follows: -
Scan project planning. Data acquisition. Data processing (registration). Post-processing (triangulation and dimensioning). Stability analysis.
2.1.1. Scan project planning Long-range TLS measurement is based on the emission of a laser beam with a wavelength in the optical or near infrared domains that affect an object directly. The distance from the point of emission to the surface is obtained by calculating the flight time of the signal. The distance measurement system is combined with a baffle plate which aims the beam in the direction of the surface to be measured. The horizontal and vertical angles that correspond to each emitted pulse are determined by coders. Thus, a spherical coordinate system centered on the scanner is defined from which Cartesian coordinates (X, Y, Z) are obtained for any point measured on the surface of the object. To obtain adequate data for the object to be measured, the acquisition project should be planned considering the following issues: - Location and number of stations. Two issues are key, namely, minimizing the number of stations (with a view to optimizing scanning time and accuracy) and ensuring that scanned areas overlap so that the entire surface is covered. - Occlusions. We need to be remember that all that is visible to the operator from the scanning position will be recorded in the scan, and likewise, whatever is not visible will be excluded. Any object that intervenes between the scanner and the surface to be measured will reflect the beam before it reaches the surface. The object will consequently cast a shadow on the surface whose size will be directly proportional to the proximity of the scanner. This problem is resolved by making an inspection of the objects in the vicinity of the planned scan positions. Special attention should be paid to detecting occlusions caused by convexities and concavities in the rock. - Resolution. Most TLS systems allow angular resolution to be configured for a specific spatial resolution for the scanned surface by combining greater distances with higher resolutions and shorter distances with lower resolutions. This combination is only limited, firstly, by the maximum angular resolution of the instrument, the beam width (the beam footprint on the object should not be wider than the angular step width) and the expected detail in the modeling of the object surface. - Reference system. Three coordinate systems coexist in scanned measurements. Firstly, the scanner's own coordinate system (SOCS) defines coordinates for each position of the instrument with respect to its optical centre. All 3D clouds of points for scans
2.1.2. Data acquisition Two scans were made from each scan position. The first scan, called the overview scan, was based on a minimum-resolution (angular interval of 0.2°) scan of the entire field of vision (360° with respect to the Z axis and 80° for vertical amplitude). The second highresolution scan was of an area including the surface to be scanned and selected from a two-dimensional (2D) view of the first scan. When modelling a rock with a more or less regular surface (like the Penedo da Sobreira boulder), an angular interval giving a resolution of 2–5 cm can be considered sufficient. Generated in real time for each scan and for each point were spherical coordinates R, φ, θ and the corresponding Cartesian coordinates, X, Y, Z (whose coordinate system is centered on the scanner). The Cartesian coordinates were obtained from the spherical coordinates as X =R · sin θ · cos φ, Y =R · sin θ · sin φ, Z =R· cos θ. Also obtained for each point was a measure of laser reflection from the surface, which depends, among other factors, on the physical characteristics of the surface and the incidence angle (Boehler and Marbs, 2003). 2.1.3. Data processing: registration To align the clouds of points in a common coordinate system, we used the iterative closest point (ICP) algorithm, which enables two surfaces, S and S, to be aligned in the same system. This process consists, essentially, of the following: - For a given surface S, when a deformation function, F: Mp = F(P), with known parameters is applied to the surface it produces a model Ms of the surface. With P as a point in S, for each point Mp in Ms, we next look for the nearest P′ in the surface S. - A cost function is established in which P and P′ are known, whereas the parameters for the deformation F are assumed to be unknown. To obtain the new deformation parameters, cost is minimized to the point at which the termination criterion is satisfied. The surfaces Si are defined for each scan by applying triangulation to the registered point cloud (details can be found in Besl and McKay, 1992). In our case the procedure consisted of dividing each scan, in the θ–φ plane, into square cells, the length of whose sides was established on the basis of the angular resolution established for the scan. For each cell an adjustment plane was calculated from the cell's points. If point deviation was excessive, the points in the cell were considered not to belong to the same plane; the cell was thus subdivided and each subcell was processed repeating the same procedure. 2.1.4. Post-processing: triangulation and dimensioning The point cloud was manually divided into the required classes: boulder, support area and surroundings. The boulder and the ground were triangulated using flat triangulation and the quadratic least squares (QLS) plane, respectively, and the surroundings were eliminated. A triangulated mesh of the support area for the boulder was generated by establishing a regular mesh on the projection plane in such a way that, for each grid, the QLS plane was determined for points
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measured on the terrain surface. If point deviation was excessive, this was interpreted as points not being co-planar; the grid was thus further divided and the same procedure was repeated. The parameters to be configured in each case were maximum admissible deviation, maximum edge length, reference plane, mesh resolution, and the angle between the vector normal to the estimated plane and the vector normal to the reference plane. Note that if the ground is covered with vegetation, mesh grids measuring 0.5–1 m should be used, as small grid sizes produce irregular meshes that model the vegetation rather than the ground surface. The boulder was triangulated in sections using Delaunay 2D triangulation applied to the viewing plane. The following parameters were configured manually: - Maximum edge length, which defines the maximum length of the edge of each triangle. - Maximum angle, which limits the angle between two beams originating in the SOCS and terminating in the vertices of a triangle edge, thereby limiting the length of the edge. From the triangulated meshes for the terrain and the boulder, we obtained, cross sections and longitudinal sections reflecting the three main boulder directions (see the definition of these directions below). For dimensioning purposes, a cross-sectional plane was defined. A comparison plane was also defined, with respect to which two semivolumes were calculated as the sum of the volume of the prisms with their base in the comparison plane and their other extreme in a mesh triangle. The difference between the fill and cut semi-volumes represented the total volume of the boulder. 2.2. Stability analysis The basic rock mechanics data were obtained from density tests on granite samples from the Penedo da Sobreira boulder and from joint data obtained in situ. Rock joints were characterised according to the Barton strength criteria (Barton, 1973, 1976) and the recommendations of the International Society of Rock Mechanics (Brown, 1981). Special attention was given to correctly estimating the JRC (joint roughness coefficient) and r & R (Schmidt hammer rebounds on weathered and fresh rock surfaces). In granites, removal of the overburden results in three perpendicular sets of joints and weakness orientations (Mabbutt, 1961; GCO, 1987). In quarrying terminology, the weakness planes are called the rift, grain and hardway planes (Taboada et al., 2005), which determine the geomorphology of many granite outcrops all over the world and guide granite quarrying operations. The rift plane is sub-horizontal and is the plane of least resistance. The grain plane is vertical (perpendicular to the grain) and produces a poorer break in the rock. Finally, the hardway plane, which is vertical and orthogonal to the rift and grain planes, is the minimum weakness plane. Once we had information on the geometric and rock mechanic properties of the boulder, together with the average rainfall and seismic intensity in the area, we were ready to carry out a stability analysis of the boulder. Two types of instability mechanism were considered (Fig. 1): sliding and toppling (Goodman and Bray, 1977; Sagaseta, 1986; Bobet, 1999). 2.2.1. Stability against sliding Sliding stability takes account of plane failure (sliding in a single plane), a mechanism studied by Hoek and Bray (1977). Stability depends on the safety factor, which is the ratio of stabilising forces to destabilising forces acting on the block. Taking into account water and seismic pressures, the safety factor can be expressed (Hoek and Bray, 1977) as follows: SFSL =
ðW cos β − αW sin β − U ÞtgΦpeak W sin β + αW cos β
ð1Þ
Fig. 1. Instability mechanisms: sliding (left) and toppling (right).
where W: weight of the boulder (KN); U: total water pressure (KN); α: pseudo-seismic contribution coefficient; β: terrain slope (degrees) and: Φpeak friction angle (degrees). The peak friction angle, Φpeak, is calculated from factors obtained from joint data, according to the formula by Barton and Bandis (1990): JCSn Φpeak = /r + JRCn · log10 σn 0 /r = /b − 20 + 20 · ðr = RÞ
ð2Þ ð3Þ
where: ϕr ϕb JRCn JCSn σn
friction residual angle basic friction angle joint roughness coefficient corrected by scale joint compressive strength corrected by scale normal tension
Water pressure depends on the boulder contact surface area, A, the height of the water column at its centre, h, and specific weight of water, γw, according to the following expression: U=
1 Ahγ w 3
ð4Þ
2.2.2. Stability against toppling Rock slope instability from toppling in quarries, road cuts or natural slopes is quite frequent, and a number of actual cases have already been studied (Alejano and Alonso, 2005; Alejano et al., 2006). The basic idea underlying the toppling of a block boulder is that it will remain stable as long as the projection of the vector representing the weight falls within its base. This is why knowledge of the geometry of a block is of paramount importance in correctly assessing block stability. Extending this simple concept, the safety factor against toppling can be calculated as the ratio of stabilizing movements to overturning movements. An overall knowledge of the geometry of a boulder is therefore of paramount importance in order to be able to correctly assess its stability.
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In our case, various sections of the boulder were considered given that the 3-D effects were important. The boulder was thus divided into three main sections–one central (A) and two lateral (B and B′) sections–so as to take into account the stabilizing effect of the side zones. Two external sections were not accounted for in the toppling calculations for two reasons: firstly, their significance is low, and secondly, excluding them renders the approach more conservative. In general, we sought a balance between simplicity and accuracy in calculating the moments. The sections are illustrated in the plan view of the boulder depicted in Fig. 2. The general expression of the safety factor against toppling for each of the three main sections is given as follows (Alejano et al., 2006): SFTOP =
MSTABILIZING ðW cos βÞd = MOVERTURNING ðW sin βÞh + Ut + αWm
ð5Þ
where d and h, t and m are the moments arm lengths, for the dry case U = 0 and for the non-seismic case α = 0.
not moved, among the local people (and especially those living in houses located roughly 300 m below the boulder) a perception exists that the rock has moved. In fact, this research was inspired by an invitation from the local council to perform a hazard assessment of the stability of the boulder and to determine the possible consequences if it toppled. Two physical characteristics of the geographic area where the boulder is located were considered for the stability analysis: rainfall and seismic activity. Local maps show a maximum rainfall of 200 L/m2 in 24 h for a return period of 50 years (Ministerio de Medio Ambiente, 2000). This level of rainfall could well produce water pressure at the boulder base and produce a water head at its centre of up to 2 m. On the other hand, information was also gathered on the earthquakes occurring in or near the area in recent decades. The most powerful earthquake, with an intensity of 3.3 on the Richter scale, occurred in 1998 near the village of Mondariz, 15 km from the boulder location. Because an equivalent vibration would generate horizontal accelerations of just under 0.04 g in the boulder zone, a pseudo-seismic analysis can be considered to be a realistic approach in this case.
3. Case study 3.2. TLS 3-D modelling and dimensioning of the boulder 3.1. Boulder characteristics In many parts of the world, including Galicia (NW Spain), granite landscapes are strewn with granite boulders (Ollier, 1978; Le Pera and Sorriso-Vallor, 2000; Migon, 2006) that are the result of spheroidal weathering and a combination of physical and chemical weathering (Ollier, 1977). This process creates rounded boulders and also contributes to creating domed monoliths. One such boulder, locally called Penedo da Sobreira, was the object of this study (Fig. 3). Although comparison of the boulder location at present with that obtained from aerial photographs in 1956 seems to indicate that it has
The equipment used for this research to determine the boulder dimensions was a Riegl LMS-Z390i 3-D time-of-flight (TOF) laser scanner. This device measures distances in a range of 1.5 to 400 m, with a nominal accuracy of 6 mm to 50 m in normal illumination and reflectivity conditions. The laser is infrared and has a wavelength of between 0.7 and 2 μm. The viewing field has 80° vertical angle and 360° horizontally. The minimum and maximum angular resolutions are 0.2° and 0.002°, respectively; and the point measurement rate ranges between 8000 and 11,000 points/second. The beam divergence is 0.3 mrad, equivalent to 30 mm/100 m range. The software used for
Fig. 2. Plan view of the boulder, scan positions and surroundings for 5 m equidistant contour curves. Cross-sections of the granite boulder used to perform the instability analysis are also shown.
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Fig. 3. View of the Penedo da Sobreira granite boulder from below.
registration and alignment for the clouds of points was RiSCAN PRO Software by Riegl© (Riegel, 2008). The possible locations for the scanner were limited by the topography of the site where the granite boulder was located. Access from the south is by a narrow passageway measuring 1 m wide at its narrowest part (the space between the slope and the boulder). Two scanner positions were established at each end of this passageway: one on a waist-high rock, and the other on a platform of earth created for the purpose. Other positions were established on the road north of the rock so as to optimise visibility of the rock. The inclination sensors of the scanner were used to level the cloud of points. In the data acquisition phase, two scans were made from each scan position. The overview scan was done for the entire field of vision (360° with respect to the Z axis and 80° of vertical amplitude) at the minimum-resolution (angular interval 0.2°). For the second highresolution scan, an area is selected from a 2D view that includes the surface to be scanned (Fig. 4). The horizontal and vertical angular step width was established as 0.05° after considering the aim of maximum surface detail, beam divergence and laser-to-object distance. This distance ranged from a few meters for the northern stations to 25 m for the road stations. The resulting clouds of points were irregular grids of points, at a distance of 0.5 cm for the densest areas, and 30– 50 cm for the top of the boulder, where visibility was limited due to slope and accessibility. Of the four scan positions, the fine scan for the third scan position had to be discarded, however, as it was affected by a dense fog. Scanning took some 50 m, although some 2 h in total was spent on traveling, assembly and measurement. A standard deviation for error of 31 mm was obtained in the alignment of the three clouds of points by means of ICP. The final clouds of points obtained contained 1,612,831 points, 881,583 of which corresponded to the immediate surroundings and the support terrain for the boulder, and 91,661 to the surface of the boulder. Triangulated meshes were generated from the clouds of points. This mesh yielded 2-D longitudinal sections and cross sections of the supported boulder and the terrain. In addition to 2-D and 3-D graphic outputs, the coordinates for each point were exported so that stability could be calculated. In order to dimension the boulder, the cloud was divided into two. Two triangulations were generated for each half, obtaining the total
volume with respect to the same external plane by calculating the difference between each half (as explained above). The final volume was 2230 m3. An estimate of error in computation of the boulder volume was obtained as a function of the distance measurement error given by the calibration specifications of the Riegl LMS Z390i laser scanner, resulting in an estimated error of 1%. 3.3. Stability analysis Rock samples were collected and cut into cylindrical specimens that were tested for density and the basal friction angle—the two basic rock mechanics properties essential to stability analysis. The average density obtained was 2.59 g/cm3 (2.59 t/m3) and the average basic friction angle, ϕb, was 33°, obtained from tilt tests as suggested by Stimpson (1981). It was observed that the rift planes in the area dip around 30°, basically coinciding with the slope where the granite boulder is located. Joints parallel to the rift planes were thus sought and characterized in the field.
Fig. 4. Three-dimensional view of a cloud of points for the front of the boulder (north) and surroundings.
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The values measured and calculated for each of the parameters in Eq. (1) were as follows: W U α β Φpeak
56,680 KN 907.09 KN 41° 30° 41°
Both weight and water pressure are given as force units, in other words, the boulder mass was multiplied by gravity acceleration and pressure was multiplied by the contact area. For these values we obtained safety factors for stability (Eq. (1)) of SFSL = 1.51 for the boulder with no water or seismic forces in play, and of SFSL = 1.35 for the boulder under water pressure and during the strongest recorded earthquake (the worst case scenario). These values for the natural slope indicate stability, and so it can be safely asserted that the granite boulder is not likely to slide. In this analysis, it was considered that sliding would be likely to occur on the contact surface as characterized by the Barton and Bandis (1990) equations, based on the assumption that the surface was flat, rough in texture, without fill and reflected the terrain slope. Underlying this assumption is the desire to make a conservative estimate, in other words, an estimate that would err on the side of safety. As for the toppling stability analysis–Eq. (5)–several calculations were made for the different possible circumstances of the boulder. For dry and non-seismic conditions, the safety factor against toppling, SFTOP, was calculated as 1.11, indicating that the boulder was stable. If water pressure in the base were accounted for, as would be the case in extremely rainy periods, the factor of safety dropped to 1.09, again indicating stability. If the boulder experienced a horizontal acceleration of 0.04 g–representing the strongest earthquake likely in the area–then the factor of safety was 1.00 (0.9998), which indicates a borderline stable–unstable scenario. The results obtained indicate that instability arising from sliding on the support surface is very unlikely. However, in the worst possible case, the boulder could well topple. 4. Conclusions This article describes a methodology for applying a long-range 3-D laser-scanning system to the measurement, modelling and analysis of the stability of large boulders. Stability analysis of a supported rock requires that both its entire surface and the support areas be modelled. Furthermore, if access to the boulder is limited, terrestrial measurement techniques are realistically the only feasible technique that can be used. Compared to conventional terrestrial techniques (topography and photogrammetry), TLS systems have the advantage that they do not rely on an operator's criterion for the selection of the boulder surface points to be measured; the operator, in fact, only has to configure the angular resolution of the scan. Another advantage is that TLS systems enable a far greater volume of points to be captured than traditional techniques. TLS systems also provide Cartesian coordinates in real time. Registration of the point clouds and the meshing enable graphic outputs to be obtained in conventional formats and also the volume to be calculated to a high level of precision. The fact that the boulder in our case study had another boulder nearby and vegetation all round made it more practical to use TLS rather than close-range photogrammetry. The geometry for the boulder enabled us to determine its weight, center of gravity and contact area with the terrain. This information, combined with data obtained for the terrain and from the laboratory tests on the mechanical properties of the contact area, enabled us to conclude that, in the most unfavorable water pressure and seismic acceleration circumstances, the boulder would be stable against sliding but could only be considered borderline stable against
toppling. For this reason it would be advisable to make regular checks of the boulder to ensure that it had not moved, for which TLS would be the most suitable system. Another option would be to take some steps to prevent the boulder rolling down the slope; for instance, by anchoring the boulder behind or supporting it in the front. Acknowledgement The financial support of the National Secretary of Universities and Research of the Spanish Ministry of Science and Education (Grant No BIA2006-10259) is gratefully acknowledged. References Abellán, A., Vilaplana, J.M., Martínez, J., 2006. Application of a long-range Terrestrial Laser Scanner to a detailed rockfall study at Vall de Núria (Eastern Pyrenees, Spain). Engineering Geology 88, 136–148. Alejano, L.R., Alonso, E., 2005. Application of the shear and tensile strength reduction technique to obtain factor of safety of toppling and footwall rock slopes. In: Konecky (Ed.), Proceeding of the ISRM Conf. on Rock Mechanics. EUROCK 2005. 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