Magnitude–frequency relation for rockfall scars using a Terrestrial Laser Scanner

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Engineering Geology 145–146 (2012) 50–64

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Engineering Geology

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Magnitude–frequency relation for rockfall scars using a Terrestrial Laser Scanner

Dulcis Santana a, Jordi Corominas a,⁎, Olga Mavrouli a, David Garcia-Sellés b

a Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, Barcelona, UPC, Spainb Department of Geodynamics and Geophysics, University of Barcelona, Spain

⁎ Corresponding author.E-mail address: jordi.corominas@upc.edu (J. Coromi

a b s t r a c t

Article history:Received 22 July 2011Received in revised form 25 June 2012Accepted 2 July 2012Available online 13 July 2012

Keywords:Terrestrial Laser ScanningRockfallMagnitude-FrequencyDiscontinuity surfaceRockfall volumeScar

The analysis of the three-dimensional rockfall scar geometry provides clues for the understanding of the fail-ure mechanisms acting on cliffs, of the conditioning factors, and on the frequency of the events. In this paper, asupervised step-by-step methodology is presented for establishing the statistical magnitude–frequency rela-tion of rockfall scar volumes, using a point cloud from Terrestrial Laser Scanner (TLS) data. The methodologyincludes a procedure for identifying discontinuity surfaces, calculating the areas of those which are exposed,and the height of rockfall scars. In the estimation of the rockfall scar volume a key issue is the considerationof the minimum spacing of the discontinuity sets to differentiate between step-path surfaces and undulatedones. Having obtained the distributions of both the basal area and height of the scar across the slope, the vol-ume of the rockfall scars is calculated stochastically by multiplication of these two parameters by means of aMonte Carlo simulation. Both distributions of the basal area and of the rockfall scar volume are found to bepower-law, with the exponent b ranging from 0.9 to 1.2. The relation obtained might be used as a first ap-proach of rockfall magnitude–frequency curves in large cliffs.

1. Introduction

Cliffs are morphological features frequently found in shorelinesand mountain ranges. They form steep rock faces that recede contin-ually by erosion and slope instability as most active degradationprocesses. In alpine environments rockfalls are the predominant evo-lutionary mechanism of cliffs (Whalley et al., 1983; Flageollet andWeber, 1996). Rockfalls are masses of any size detached from asteep rock face that descend rapidly mostly through the air by freefall, sliding, bouncing or rolling (Varnes, 1978; Cruden and Varnes,1996).

Lithology, stratigraphy and structure exert strong control on thegeometry and the temporal evolution of cliffs (Hampton et al.,2004). The study of rock face features allows the understanding ofthe mechanisms that cause cliff degradation and instability. Surfacecharacteristics of joints daylighting in the rock outcrop affect theirshear strength (Patton, 1966; Barton, 1976) while the spatial arrange-ment of both the slope face and the discontinuities configures the fail-ure mode. The latter are typically included as input parameters forkinematical and stability analyses of rock slopes (Hoek and Bray,1981; Goodman, 1989). The potential for future instability of cliffsmay be also assessed and rated based on several measurable param-eters observable in rock mass exposures such as the rock strength,

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geologic structure, joint spacing, weathering stage, among others(Pierson et al., 1990; Rouiller et al., 1998; Budetta, 2004; Jaboyedoffet al., 2004b). The reader is referred to Pantelidis (2011) for a recentreview of the most used rock mass instability indexes.

Traditional surveying methods employed for the characterizationof the rock mass discontinuities, their location, orientation, persis-tence, and spacing, include scan-line or cell mapping methods(Priest and Hudson, 1981; Priest, 1993). Manual field discontinuitysurveys are however time consuming and they are often affectedby systematic and human errors (Ewan et al., 1983; Herda, 1999).Furthermore, steep and often unstable profile of the rock face oftenrenders data acquisition both unsafe and unfeasible (Sturzeneggerand Stead, 2009).

In the last decade, Terrestrial Laser Scanner (TLS) applications havebecome a common surveying technique for characterization of the rockmass exposures. Explicit information on the performance of TLS can befound in Slob and Hack (2004), Slob et al. (2005) and Shi et al. (2009).Its increasing use is due to its capability to provide quickly and easily,digital data of high accuracy and precision. TLS may capture informa-tion from inacessible outcrops, and acquire large data sets which canbe readily treated. The main applications for the assessment of the in-stability of a rock face may be summarized in the following (Kemenyand Turner, 2008; Jaboyedoff et al., 2010): the reconstruction of the to-pography and generation of DEM (Abellan et al., 2006; Agarwal et al.,2006); the identification and characterization of discontinuity setsand of their spacing (Feng and Röshoff, 2004; Jaboyedoff et al., 2004b,

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2008; Slob et al., 2005; Gaich et al., 2006; Poropat, 2006; Coggan et al.,2007; Lato et al., 2009; Sturzenegger and Stead, 2009); the determina-tion of the size and spatial distribution of potentially unstable rockmass volumes (Jaboyedoff et al., 2009; Sturzenegger et al., 2011); thedetection and measurement of rock face displacements (Rosser et al.,2007; Oppikofer et al., 2008; Abellan et al., 2009; Oppikofer et al.,2009); obtaining the spatial distribution and magnitude of rockfallsevents (Abellan et al., 2006; Rosser et al., 2007; Lim et al., 2010); andmonitoring of cliff erosion and quantification of the retreat rate(Rosser et al., 2005; Abellan et al., 2011; Young et al., 2011).

The observation of geometrical features of the rock face causedby the detachment of rock masses may provide clues for the under-standing of the instability mechanisms affecting the rock mass,their conditioning parameters, and the temporal evolution of theslope profile. TLS has been used to identify and locate recent rock-fall scars and missing rock volumes from the cliff faces based onthe analysis of sequential scans (Abellan et al., 2006; Oppikofer etal., 2009; Lim et al., 2010; Kenner et al., 2011). The density distribu-tion of rockfall scars is a measure of the rockfall activity and may beused for estimating cliff recession rates. In particular, the number ofboth rockfall scars and potentially movable blocks has been taken asa qualitative measure of the frequency of rockfalls (Copons andVilaplana, 2008).

The distribution of the rockfall scars on the cliff face is an indicatorof the rockfall activity over the last hundreds or thousands of years. Inthis paper, we present a methodology to obtain a statistical distribu-tion of the volumes of rockfall scars from a cliff using a point cloudcaptured by a TLS. We combine recently developedmethods for filter-ing and segmentation of the point cloud to extract planar surfaces,identify the main joint sets present in the rock face, calculate thearea of the exposed discontinuity surfaces, and the volume of the de-tached rock masses. This is a supervised procedure including a fewsemi-automated steps that can be applied to a large rock wall expo-sure. We also implement our own method to refine and validate theplane orientations used to define the joint sets.

2. Estimating volumes of rockfall events and rockfall scars

A rockfall scar is a rupture surface on a vertical cliff resulting fromone or several rockfall events. Its state of freshness is often an indica-tion of the scar age. Colors of the scars generated by recent rockfallsare bright. In temperate and alpine environments, scars tend to dark-en shortly after their generation, so some time after the occurrence ofthe rockfall event, the scar color starts vanishing and eventually itcould be hardly differentiated from those existing previously.

The volume of rockfall events occurring between successive TLSscans can be easily measured. Accurate estimate of the volume ofthe detached rock mass can be obtained by subtracting DEMs orby computing the volume between point clouds prepared beforeand after the rock fall event (Abellan et al., 2011; Deline et al.,2011). When the original topography is not available or has notenough resolution, volumes of rockfall events of a known age havebeen calculated by reconstructing the pre-existing topographyover a TLS-scan generated DEM with the support of photographstaken before the detachment of the rock mass (Ravanel andDeline, 2008). Oppikofer et al. (2009) were able to detect scars onthe slope face that are formed by the sliding planes involved. Thepre-rockfall event topography was reconstructed by fitting planesaround the scars using the commercial software Polyworks V.10and the Sloping Local Base Level SLBL method (Jaboyedoff et al.,2004a). In this case, rockfall volume distribution was establishedfor a limited number of scars.

Uncertainties in the computed volume come primarily from theresolution and errors associated to the TLS equipment, selectedmethodology, distance to the target area, and to the generation ofthe DEM (Mikos et al., 2005; Abellan et al., 2009; Dunning et al.,

2010; Jaboyedoff et al., 2010). However, when the pre-rockfall topog-raphy of the slope is lacking, main uncertainties in volume computa-tion derive from the assumptions made for its reconstruction andthe nature of the rockfall events. Measurement of the rockfall scar vol-ume does not yield the volume of the rockfall events that generatedthe scar although both volumes are related to some extent. Rockfallscars are the result of the detachment of rock masses from the rockface in either one or multiple events. The detachment of an initialrock mass may induce further instability in the slope and the rockfallscar may enlarge and retrogress by successive failures. Eyewitness ac-counts describing historical rockfalls indicate that minor detachmentsmay be noticed before and after a main event (Deline et al., 2011). Aparadigmatic example is the Randa rockfall of 1991 (Noverraz andBonnard, 1992; Sartori et al., 2003). On April 18 a rockfall was pro-duced by breaking up of about 22 mio m3 from the rock face over a pe-riod of several hours. The day after, a mass of about 100,000 cm3 ofrock fell again. Finally, another large rockfall of about 7 mio m3 oc-curred on May 9. Frequent minor rockfalls were noticed severalweeks before and after the main failures.

Sequential scans taken at either monthly or annual intervals (Lim etal., 2010; Abellan et al., 2011; Young et al., 2011) are able to provide ac-curate distributions of rockfall scar volumes. Most of them are probablythe result of single rockfall events but the possibility that some scarscould be the result of several consecutive rock mass detachments can-not be completely disregarded. Consequently, rockfall scar volumesmust be considered as an upper envelop of the rockfall volumes thathave originated them.

In this work we present a procedure to calculate the rockfall scarvolumes distribution in a large cliff face. To calculate the size of the de-tached rock masses from the scars we must consider the pre-existingtopography. Here, it has been assumed that the cliff recedes followinga slope equilibriummodel (De Lange andMoon, 2005) which is parallelto the initial slope profile. According to this, large failures changing sig-nificantly the original profile such as a step path rock mass failure arenot considered. The volume of the rockfall scar is thus approximatedby the volume of the prism whose faces are the basal discontinuity sur-face of the scar and two other intersecting discontinuity planes thatquite often behave as tension cracks (Fig. 1). The basic assumption inthe considered case is that detachment of rock volumes from theslope face is mostly governed by the existing discontinuity sets andthat rockfall scars on cliffs are formed by intersecting discontinuities.The detachment is produced by the initial displacement of a rock blockresting on the basal surface by either sliding (planar failure) or topplinguntil it is detached from the rockwall. The volumes corresponding to thescars are calculated probabilistically by multiplying a random sample ofthe basal sliding area of the detached rockmass and scar height distribu-tions, using a Monte Carlo simulation. The details of the methodologyfollowed are given in the next section.

3. Methods

The methodology to obtain the volume distribution of the existingscars on the outcrop from a TLS point cloud involves 6 main steps,which are resumed in Fig. 2.

It consists in a supervised procedure, including some automatedsub-steps (1, 3 and 4). Being a step-by-step procedure, it favoursthe reproducibility of the results, and consequently their objectivityand reliability.

3.1. Step 1: plane fitting at each point and calculation of normal vectorsand of the plane's attributes

After obtaining the point cloud of a slope using a TLS, the first stepof the proposed procedure aims at the visualization of it and the ac-quirement of preliminary information for the dip and dip directionof the topographic surface at each point. To enable accurate surface

Fig. 1. Rockfall scar formed by three intersecting joint sets, defining a prism. The detached block is resting on a basal discontinuity surface (C). (h) is the height of the rockfall scar.

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reconstruction of the topography from a 3D composite point cloud,usually various datasets have to be obtained from independent viewdirections. Then, the alignment of the scans is achieved first by a

Fig. 2. Flow chart for the identification and calcula

preliminary alignment, which consists in identifying common pointson the different point clouds, and then by an automated procedurewhich is carried-out to minimize the alignment errors and to

tion of the areas and volumes of rockfall scars.

optimize the point clouds' overlay (Besl and McKay, 1992; Chen andMedioni, 1992; Abellan et al., 2006; Oppikofer et al., 2009).

For every single point of the point cloud, a plane is then fitted byregression to the points that are comprised within a sphere around it,having a user-defined radius. A minimum number of points includedin the sphere are fixed to ensure the exclusion of isolated points. Thefitting is based on the moment-of-inertia method and it is performedusing the SELF-software. Details on this can be found at Garcia-Selléset al. (2009, 2011).

For every plane corresponding to a point, some parameters are eval-uated which include the normal vector to the point (its components)and the collinearity and coplanarity indices, K and M, respectively(Figure 3). Both these values are indicative of the quality of the fittedplane. Their calculation is described analytically at Fernandez et al.(2004); Woodcock (1977) and Garcia-Sellés et al. (2011).

3.2. Step 2: identification of discontinuity sets

The characterization of discontinuity sets can be realized eitherusing fitting planes (Jaboyedoff et al., 2004b; Fernandez, 2005;Abellan et al., 2006; Oppikofer et al., 2008; Sturzenegger and Stead,2009) or creating Triangulated Irregular Network (hereafter TIN) sur-faces as elements of the plane orientations (Feng et al., 2001; Slob etal., 2002; Kemeny and Post, 2003; Lato et al., 2009). Here, for theidentification of discontinuity sets, the first approach is used.

Step 2 involves the grouping of the points of the point cloud intoclasses that then are grouped to form the discontinuity sets. Everyclass is composed by points which normal vectors have a maximumangular deviation among them, so as to share the same exposed sur-face (discontinuity plane) on the slope. The classification is mademanually by observation of the point cloud using the Gocad software(Earth Decision Sciences, http://www.earthdecision.com). The pointcloud is rotated in several directions to facilitate the visual check ofthe variability in angular deviation of the normal vectors betweenneighbouring points. The determination of points that belong into agiven class is resolved considering the consistency of the plane atti-tude and, in this way, point classes are identified.

Fig. 3. K is the collinearity index, the larger theK-value, the better thepoints arefittedon a line.M

Points corresponding to vegetation or other terrain irregularitiesand noise are found not to comply with the constraints for plane qual-ity with reference to M and K (step 1) or not to belong to any pointclass (step 2). These points are filtered using utilities of Gocad.

If the exposed discontinuity surfaces were flat and smooth, thepoint classes would directly delineate discontinuity sets. However,in reality, discontinuity surfaces vary in undulation and roughnessand as a result they may be composed by several point classes. An ex-ample is shown in Fig. 4. Thus, to obtain the characteristics of themain discontinuity sets across the slope, the point classes that corre-spond to every set have to be determined. A methodology was devel-oped to this purpose, which is described in the following.

All point classes are overlaid on photographs of the rocky out-crop (Figure 4). Empty areas are ought to missing points due tovegetation or filtering of data noise. A point class is consideredto belong to a single discontinuity set. To check how point classesare joined to form discontinuity sets a “co-existence matrix” isprepared for some representative, sample areas of the slope. The“co-existence matrix”, is used to measure the simultaneous occur-rence of two point classes on the same discontinuity surface of theslope, and it is calculated by the ratio of the number of times thattwo given point classes are overlaid on surfaces of the same dis-continuity set, to the total number of times that one of thesetwo is encountered at the selected sampling areas of the slope(Table 1). Using this matrix, all combinations of the point classesare checked in pairs. If the percentage of co-existence of two clas-ses is higher than a fixed percentage for the selected sample, thenit is assumed that these classes belong to the same discontinuityset. This threshold can be established based on photos or in situverifications. It was found that co-existing point classes on sur-faces that were visually confirmed to belong to the same disconti-nuity set, coincide at a percentage of 25% or higher. In this way,combinations of point classes belonging to the same discontinuityset are identified, although the properties of the latter have notbeen calculated, so far.

It has to be highlighted that the number of points or point classesbelonging to the same discontinuity set is not indicative of whether

is the coplanarity index, the smaller theM-value, thebetter thepoints arefitted on a plane.

Fig. 4. Discontinuity surfaces (on the left) may be composed by several point classes (on the right, with different colors), depending on their undulation and roughness.

Table 1Co-existence matrix of the point classes on scars.

A 100% Count (A∩B)/Count A∗100%a

B Count (A∩B)/Count B∗100%a 100%

a A, B: point classes.

Fig. 5. Distance (D) and angular (α) tolerance criterion for determining whether twoneighbouring points pertaining to the same discontinuity set are coplanar or not. Twopoints will be assigned to the same plane if their difference in height for several combina-tions of D andα, is smaller than theminimumdiscontinuity spacing (s) defined for this set.

that set is a predominant one or not. Few large discontinuity surfacesmay result into the same number of points on a stereogram with a lotof small surfaces, which are usually those that define the predomi-nant discontinuity sets on a slope.

3.3. Step 3: generation of discontinuity surfaces

The next step of the procedure is the generation of the discontinuitysurfaces. This consists in creating a plane surface mesh from the pointcloud data, separately for every group of point classes belonging to thesame discontinuity set. Algorithms for the extraction of surfaces frompoint clouds of buildings and other objects have been presentedamong others by Biosca and Lerma (2008), Awwad et al. (2010) andVosselman et al. (2004). However, not always is taken into consider-ation with sufficient precision the fact that most discontinuity surfacespresent certain undulation and roughness. Neighbouring points maylay at a different height either because the discontinuity surface isundulated or because they belong to different parallel planes of thesame discontinuity set. Thus here, to overcome this uncertainty, a co-planarity criterion is established for the association of neighbouringpoints to the same or different planes. In the second case, the two differ-ent surfaces will be staggered and separated a height, greater than theminimum spacing (s) of the respective set (Figure 5). The establishmentof the minimum spacing for the discontinuities is necessary to proceed.For given values of it, it is possible to define different pairs of lengths (D)and angles (α) of the lines linking two neighbouring points (for exam-ple, X and Y) that will constraint two points lying on the same surface.The minimum spacing can be evaluated either by field survey or usingmore sophisticated techniques as the one presented in this paper forthe case-study. It practically consists in an iterative process for thecalculation of the three afore-mentioned parameters, s, D and α. Ateach iteration, the generated surfaces are checked and the parametersare optimized to avoid over-segmentation or under-segmentationafter comparison with photo samples. The checking can be appliedautomatically, for all the groups of point classes belonging to the samediscontinuity set, using the program SELF, where the parameters αand D are introduced manually. In this way, all points belonging to the

same surface are identified and the discontinuity surface is generatedby fitting a plane on them using planar regression.

3.4. Step 4: calculation of areas and heights

As afore-mentioned, all scar volumes are defined by three surfacesthat correspond to three intersecting discontinuity sets (Figure 1). Thefirst one is the basal plane (C) of the detached rock mass that createdthe scar in the past, and the other two, (A) and (B) are the quasi-orthogonal bounding planes. So, at this step, it has to be decidedwhich sets define the basal plane and which ones the tension cracks.

To this purpose, kinematic analysis using stereonets may be per-formed for different failure mechanisms, according to Markland (1972).

The developedmethodology is to be applied at massive scale, acrossan entire slope. So both basal discontinuity areas and heights (definedby the intersection line of tension crack surfaces) should be calculatedmassively. An algorithm developed by the authors was used to this pur-pose. The algorithmwas programmed onVisual Basic language. The dis-continuity surfaces are discretized into grid cells of a fixed mesh size.The maximum dimensions of width (ΔX′max) and length (ΔY′max) arecalculated, as shown in Fig. 6.ΔX′max is themaximumdistance betweenpoints, along the plane's strike, and ΔY′max the one along its dip direc-tion, both measured locally on each plane. The total areas for thebases are yielded by the sum of areas of cells that do contain points.

Fig. 6. A) Projection of points belonging to a scar on its respective plane; B) scar area estimation by grid meshing.

Because of the large number of scars on a slope, determining theirheight manually is at present unfeasible with our available tools. Toovercome this restriction, the distribution of the scar height acrossthe slope is estimated indirectly, based on the following assumption:for a given scar, the two bounding planes (A and B) share a commonedge between them, which is their intersection line. For quasi-orthogonal planes, the height of a scar is given by the length of the in-tersection line; otherwise the latter must be corrected accordingly. Allplanes A and B in the study area must then have a common frequencydistribution for either widths or lengths, which is the frequency dis-tribution of their intersection line. Given the repeatability of the in-teraction pattern between discontinuity sets this step leads to theacquirement of the range (including up and down limits) and the dis-tribution of scar heights across the slope, which will be used for theprobabilistic volume calculation at the following step.

It is highlighted that the height of the rockfall scar often coincideswith the spacing of the plane C. But in some cases it may consist ofseveral spacing distances. Fig. 7 illustrates an example.

3.5. Step 5: verification of scar surface generation

The identification of discontinuity sets at step 2 was based on ob-servations of sample areas. To improve the process robustness, it hasto be verified whether local observations are representative of theentire slope. At this point, after the generation of the discontinuity

Fig. 7. Scar with a height (h) including se

surfaces and the calculation of their area and height, the grouping ofpoint classes can be verified for the entire slope. This is what thisstep is used for.

The merging of point classes for the generation of discontinuity sur-faces at step 2 can be verified based on this criterion: if merging of twoor more point classes is correct, when comparing the size of the gener-ated surfaces before and after it, the number of small surfaces must de-crease while that one of large surfaces must increase (Figure 8). This isbecause the increase in the area of the scars is ought tomerging of pointclasses that belong to contiguous surfaces. If planes of point classes arenot contiguous the size of the exposed discontinuity surfaces will notincrease (these point classes belong, in fact, to different discontinuitysets.). To apply the criterion, steps 4 and 5 should be repeated for differ-ent combinations ofmergedpoint classes. After this step, for the verifieddiscontinuity sets, the generation of scars and the calculation of theirareas and heights is finalized.

3.6. Step 6: calculation of scar volumes

For the calculations, the missing volumes from the scars are as-sumed to be right or oblique prisms. Their volume is the product ofthe area of the base (basal surface area) and the distance betweenthe two base faces (height). In the case of a non-right prism the realheight is the perpendicular distance between the two bases and thecalculated height at step 4 should be corrected accordingly.

veral discontinuity spacings (s1+s2).

AREA (A) + AREA (B)

AREA (A U B)

REDUCTION OF SMALLAREAS

INCREASE OF LARGEAREAS

Fig. 8. Checking the suitability of merging point classes: if contiguous classes aremerged to form larger surfaces then the number of small surfaces must decrease andconversely the number of large surfaces must increase.

Table 2Main discontinuity sets of the Forat Negre and Borrassica slopes identified withscanlines performed at their bottom.

Given the large quantity of rockfall scars on the slope face, the calcu-lation of scars volumes is not made individually at every scar, but mas-sively. A stochastic approach that employs theMonte Carlomethodwasadopted. The input variables are the scar area and height. Probabilitydensity functions are fitted to each one of them and random samplesare created. The distribution of volumes is obtained from the productof areas and heights for all the samples. For this statistical elaboration,the software EasyFit by Mathwave may be used.

Discontinuity set Dip direction Dip Relative frequency (%)

F1 54 59 19.5F2 320 54 6.2F3 157 56 9.0F4A 247 45 6.2F4B 266 64 14.0F5 182 47 6.0F6 192 85 7.0F7 141 89 30.0

4. Case study

This methodology was applied to a pilot zone at the slope of theSolà d'Andorra and in particular at Forat Negre and Borrassica, inthe Principality of Andorra, Eastern Pyrenees. This small countryborders on Spain to the South and France to the North (Figure 9).

The study area is a steep slope originated by the excavation of thePleistocene glaciers. The outcrop is made of granodiorites, which are

Fig. 9. (A) Location of the pilot zone in the Solà d'Andorra (upper left in yellow). (B) Partiashown in red with the situation of the scanlines in green. Numbers in red inside boxes are

intensely fractured as the result of the Alpine and Hercynian orogen-eses (Bouchez and Gleizes, 1995).

The site is affected by numerous rockfalls that interact withhuman settlements, which have extended up to the slopes duringthe last sixty years. Talus deposits accumulate at the bottom of theslope, which are composed of boulders with volumes ranging in sizefrom 0.5 to 270 m3 (Copons, 2007). Further description of the studysite may be found in Copons (2004) and Corominas et al. (2005).

4.1. Field work

In order to carry out a comparison with the TLS results, thefracture pattern of the rock mass was characterized using thescanline sampling methodology (Priest and Hudson, 1981). Sevenscanlines were performed with a total length of 72 m. Different ex-posures were mapped to avoid orientation bias (ISRM, 1978;Priest, 1993). This sampling method was only applied to the bot-tom of the walls because of the difficult access to the higher out-crops. The results are shown in Table 2 and Fig. 10 and will becompared with those obtained by applying the described method-ology from the TLS data.

l view of the Forat Negre and Borrassica slopes. (C) Boundaries of the scanned cliff arethe locations of the scan stations.

Fig. 10. Main discontinuity sets of the Forat Negre and Borrassica slopes identified with scanlines performed at their bottom.

Fig. 11. The aligned point cloud of Forat Negre and Borrassica slopes. Light colors cor-respond to rock outcrops and dark to vegetation.

4.2. Procedure followed

The TLS equipment used is the ILRIS-3D (OPTECH), with an accu-racy of 0.7 cm at ranges of 100 m and a maximum range of 700 menabling us to obtain 2000 points per second (www.Ilris3D.com).Further information about this equipment is found in Abellan et al.(2006), Garcia-Sellés et al. (2009), Garcia-Sellés et al. (2011).

A series of scans from five different positions was carried out tocover the entire zone of interest. To this end, a relative positioningGPS technique using nets such as the CatNet from the InstitutCartogràfic de Catalunya was used. Coordinates of all the positionswere determined and the merging of the point clouds wasperformed. The alignment was carried out with the ImAlign mod-ule of Polyworks (Innovmetric Software, http://www.innovmetric.com) (Figure 11).

A total of 15 scans were performed that allowed scanning an area of22,000 m2 with 22,121,604 points. The density of the point cloud guar-anties avoiding problems related to low resolution (Sturzenegger andStead, 2009).

Planes were fitted at each point, for a sphere radius smallerthan 0.25 m, and normal vectors were calculated, using the SEFLsoftware. The criteria for accepting the planes were: M equal orgreater than 3.5 and K less than 1.2. A minimum of 6 points wasestablished for the definition of a plane. Since the discontinuitysets will be eventually verified (step 5), the selected criteria areless restrictive than those proposed in Fernandez (2005) for intersectionpoints of a geological surface and the topography (e.g. joints, faults,planes…).

Next, using Gocad tools, 30 point classes were obtained out of thepoint cloud (Table 3 and Figure 12).

A sample of 375 discontinuity surfaces was selected from photosof the study-area, and for each surface we overlaid the point classes

(Figure 13). Table 4 indicatively shows an extract from the co-existencematrix, built with this data. Coincidence of two point classes higherthan 25% is interpreted as they are laying on the same surface andbelonging to the same discontinuity set. This threshold was selectedparticularly for this case study, after photo validation.

Next, we generated the discontinuity surfaces. To optimize the pa-rameters s, D, and α, we performed a sensitivity analysis for D and α

Table 3Orientation of point classes identified with the TLS.

Point class Dipdirection

Dip Point class Dipdirection

Min Max Min Max Min Max Min Max

1 31 86 50 86 16 150 170 50 602 1 30 60 90 17 140 165 65 753 352 358 50 90 18 167 184 80 904 320 350 75 90 19 120 145 40 605 320 350 37 75 20 140 165 75 906 300 320 75 90 21 109 140 72 907 300 320 40 75 22 85 110 35 908 275 300 50 75 23 220 245 70 909 275 300 75 90 24 120 145 55 9010 245 275 50 90 25 100 150 25 4011 180 220 30 55 26 150 170 16 3512 180 220 55 70 27 172 185 52 6013 185 220 70 90 28 220 245 55 9014 172 220 30 55 29 165 184 60 7015 167 184 72 80 30 150 170 35 50

using s values between 0.1 and 0.3. Checking was performed by plot-ting the results on a CAD environment and by analyzing the generat-ed surfaces for the selected parameters (see Figures 15 and 16). It wasobserved that over-segmentation can be avoided for angles α greaterthan 6°and under-segmentation for s up to 0.25 m. For values of αlower than this threshold, small surfaces are generated and partiallysuperimposed over bigger ones, as for example the surfaces P1 to P4that, in reality, comprise points belonging to a common surface, P of

Fig. 12. Orientation of point clas

Fig. 14a. Instead, for s larger than 0.25 m, the generated surfaces arefar more persistent than those corresponding to reality, with plungesthat significantly deviate from those of the point class segments(Figure 14b).

The undulation of the discontinuity surfaces at Forat Negre andBorrassica slopes has usually amplitudes less than 0.1 m and excep-tionally up to few decimeters. On the other hand, the minimumobserved spacing in the field and with TLS images is 0.1 m. Thiscan be seen in Fig. 15 which presents measurements of the normaldistance for 784 contiguous surfaces from the same discontinuityset F1, with the software Rhinoceros®. Consequently, for values be-tween 0.1 m and 0.25 m, there exists some overlapping betweenundulation and spacing, and considering this we selected a spacingof 0.2 m, as discriminant value for generating discontinuity surfaces.This means that two contiguous parallel surfaces of the samediscontinuity set separated less than 0.2 m (orthogonal distance)will be considered the same surface, and will be merged. Similar is-sues for the distribution of spacing have also been discussed byOppikofer et al. (2011).

Taking into account the afore-mentioned checks for the parame-ters D and α, for s=0.2 m, the thresholds of D=1 m and α=11.5°were finally chosen for the surface generation. An additional restric-tion was the minimum number of points contained in the calculateddiscontinuity surfaces, which was taken to be 6. In this way, 22,112individual discontinuity surfaces were identified.

To verify that the point classes have been correctly merged, thecumulative frequency-area relation of scar surfaces was calculated,before and after the merge (Figure 16). When the comparison be-tween both frequency distributions was showing an increase in the

ses identified with the TLS.

Fig. 13. Point cloud with different colors that correspond to different point classes (left) and identification of them on the numbered discontinuity surfaces (right).

Table 4Extract from the co-existence matrix showing the percentage of each point class shar-ing discontinuity surfaces with other classes.

Point class Point class

1 2 3 4a 4b 6a 6b

1 100 13 0 0 0 0 02 17 100 8 0 0 0 03 0 25 100 25 0 0 04a 0 0 3 100 68 46 544b 0 0 0 81 100 48 716a 0 0 0 71 63 100 836b 0 0 0 65 71 65 100

number of large areas and a decrease in the number of small ones,merging was considered successful. Otherwise the discontinuity setswere redefined.

A total of 8 discontinuity sets have been identified at the ForatNegre and Borrassica slopes. The areas of all exposed discontinuity

Fig. 14. (a) Plan view of the discontinuity surfaces generated with angles less than 6°: four sua single surface P; (b) section view of the fitted plane accepting spacings larger than 0.25 m:an unrealistically persistent surface (under-segmentation).

surfaces daylighting in the rock face were calculated, as well.Table 5 and Fig. 17 show the dip direction and dip angle for eachset, the relative frequency of the respective encountered areas, andtheir mean and maximum area. The surface areas range from 0.1 m2

to 236.3 m3 (the latter, for F3 discontinuity set). The most frequentsets are F3, F7 and F1.

It was observed that the discontinuity sets obtained by field datadiffer slightly from those obtained with TLS. Stereograms of TLSdata show that F2 is not as frequent as indicated by field data. More-over, the set F8 appears frequently for TLS data whereas it is hardlyidentified with field data. The mismatches are due to:

(a) The number of measured planes: the planes counted in situ(164) are an order of magnitude lower than those countedusing TLS.

(b) Field measurements were made at outcrops located at thebottom of the slopes while the TLS point cloud is captured forthe entire slope.

rfaces (P1 to P4) are generated (over-segmentation) that actually should correspond tothe generated plane plunges with a different angle than the point class segments giving

Fig. 15. Spacing measured directly on the plane model. A total of 22,112 exposed surfaces were identified on a slope surface of 22,000 m2.

Fig. 16. Conditions for accepting (A) or rejecting (B) the merging of point classes.

4.3. Calculated rockfall volumes

The kinematical analysis using the Markland test on the slopes ofthe study area (Figure 18) indicated that F3 and F5 sets define

Table 5Joint sets and the main features detected with TLS data.

Discontinuityset

Dip direction/dip

Relative frequency(%)

Maximumarea

Averagearea

(m2) (m2)

F1 56/63 13.5 121.6 0.3F3 155/57 25.7 236.3 0.7F4A 256/66 1.4 11.6 0.4F4B 283/75 2.7 20.3 0.4F5 187/54 17.7 144.4 0.7F6 187/75 9.1 23.8 0.5F7 155/87 21.5 213.7 0.5F8 92/57 4.2 34.6 0.4

potential planar failure as predominant type of initiation failurefor rockfalls in the slopes of Forat Negre and Borrassica. This is con-firmed by the historical rockfalls recorded in the area (Copons,2004).

Accordingly, the calculation of the volumes of the rockfall scarshas been made considering F3 and F5 as basal planes of the detachedrock masses. Because either wedge or toppling failures are rare in thepilot area, no other basal planes were considered. F1 and F7 are thediscontinuity sets that usually bound the detached blocks (tensioncracks) and were used to calculate the scar height (the length ofintersection line between F1 and F7) of the rockfall scar.

Basal plane areas were found to be well fitted by a Log-Pearson IIIdistribution and scar heights by a General Extreme Value one. Addi-tionally it was observed that basal plane areas follow a power-lawdistribution with exponents varying between 0.9 and 1.2 for the dif-ferent discontinuity sets.

Scar volumes were assumed to be prismatic. For oblique prisms,Palmstrom (2005) showed that for angles between the height and

Fig. 17. Joint sets and their main features detected with TLS data.

the base face, of 60° or more, the inaccuracy imposed by a simplifiedmeasurement that considers angles of 90° is limited. So, for obliqueangles between discontinuities, more than 60°, which is also observedfor the study area, discontinuities can be assumed to be orthogonaland no correction is needed. The scar volume is then the product ofthe basal surface with the height of the scar.

The scar volume distribution was obtained probabilistically usinga Monte Carlo simulation. The volumes were calculated as the prod-uct of 5000 random samples, with the variables of area and height

Fig. 18. F3 and F5 define potential planar failure. The adjacent tension cracks are the sa

following the afore-mentioned distributions, and they were foundto be well fitted by the inverse power-law (Figure 19).

F v > Vð Þ ¼ 1919 v−0:9

where, F is the cumulative frequency and v the volume in cubicmeters.

me for both basal sets F1 and F7 and the slope face orientation is shown in green.

Fig. 19.Magnitude–volume of scars found with TLS data. At the upper left is written theequation of the power law function fitted through the volumes greater than 0.25 m3.

Nevertheless, a roll over effect (Stark and Hovius, 2001; Guzzettiet al., 2002) is observed in the volume distribution, for volumesbelow 0.75 m3, thus the magnitude - frequency relation is best fittedat volumes larger than 0.25 m3. Rollover effects has been also ob-served for landslide inventories by Pelletier et al. (1997), Hungret al. (2008), Guthrie and Evans (2004a, 2004b, 2007), Hovius et al.(2000), and Turcotte et al. (2002) who suggested the censoring ofthe small landslides sizes by under-sampling or physiographic re-strictions. The TLS-based procedure prevents from under-samplingsmall (less than 0.75 m3) scar volumes and therefore no censoring ef-fect is expected. The resolution of the technique allows the detectionof areas and spacings as small as 0.1 m2 and 0.2 m respectively,which corresponds to volumes as small as 0.02 m3. Because of this,the rollover shown in Fig. 19 must have another explanation and isprobably ought to the existent fracture patterns rather than to cen-soring effects related to low-precision.

The obtained scar volumes have amagnitude that ranges from low tomoderate. Asmentioned before, the volumes of the rockfall scars may bethe result of one or several rockfall events and must be considered asan upper envelop of rockfall event volumes. On the other hand, thedetachment of large rock masses through step-path or differentlyoriented discontinuity surfaces has not been considered in their calcula-tion. Consequently, this scar volume distribution probably overestimatesthe rockfall volume distribution, although it might underestimate theoccurrence of large rockfall masses.

In spite of this, we compared the rockfall scar volume distributionfor Andorra with rockfall volume distributions suggested in earlier

Table 6

Author Site Method

Hungr et al.(1999)a

British Columbia rail andhighway routes,Canada

Rail and highwayinventories

Rousseau(1999) a

Mahaval,La Reunión

Instrumentalmeasurements

Dussauge-Peisseret al.(2002) a

Upper Arly Gorges,French Alps

Historical data

Grenoble, French AlpsYosemite Valley, California

Malamud et al.(2004)

Umbria-Marché Rockfalls due to1997 earthquake

Yosemite, California Historical data(Wieczorek et al.1998)

Grenoble, French Alps Historical data (RTM, 19

a taken from Dussauge-Peisser et al. (2002).

works, keeping in mind that the variability of the results might beought to differences in the methods used related to data collection,binning, and plotting. It was found that in some cases, the b value isgreater (Hungr et al., 1999; Dussauge-Peisser et al., 2002; Guzzettiet al., 2002; Dussauge et al., 2003) but, in other cases, it is quite sim-ilar (Rousseau, 1999; Malamud et al., 2004) (Table 6). There are au-thors that consider that b is closely dependent on the lithology andthe fracturation level (Hungr et al., 1999; Dussauge et al., 2003). Al-though several hypotheses may be considered, the high b value forthe scar volumes that we have found, in comparison with thesuggested b values for rockfall volumes of Table 6 might be attributedto the fact that a step-path surface is not included as a whole in an in-dividual rockfall scar. With our methodology, if the basal surface ofthe failure is staggered, each step will be interpreted as an indepen-dent rockfall scar.

Brunetti et al. (2009) and Van Den Eeckhaut et al. (2007) list manyof the power law exponents (b) reported in the literature.

5. Conclusions

A supervised methodology has been proposed for the detection ofdiscontinuity surfaces and the calculation of missing volumescorresponding to scars from past rockfalls on a rock cliff, using TLSdata. It is a step-by-step supervised procedure that employs quantita-tive criteria, and thus offering results with reduced uncertainties. Theproposed procedure which is based on the use of TLS data overcomespotential restrictions of access to the rock outcrop. It can be appliedfor the assessment of the distribution of the areas and volumes ofscars at a massive scale on a slope cliff. Additionally, using a MonteCarlo approach it overcomes the difficulty of the point-to-point calcu-lation of scar missing volumes in order to get their distribution, whichis practically unfeasible for slope faces formed by dense rockfall scarspopulation.

Certain issues presenting complexitieswere faced and solved duringthe development of the afore-mentioned procedure, which involve: theconsideration that point classes of similar dip and dip directionmay be-long to different discontinuity sets, the incorporation of restrictionsbased on the local parameters of undulation and spacing used for gen-erating discontinuity surfaces, the calculation of the rockfall scar areasand heights and the stochastic calculation of the volume distributionacross the slope.

The application of theprocedure to ForatNegre andBorrassica, delin-eated 8 main discontinuity sets. Although small differences exist, theidentified discontinuity sets from the proposed methodology showedgood agreement with those from the field data, which indicates a goodreliability of the method. The observed mismatch can be attributed tothe abundance of information using TLS data in contrast with possibleunder-sampling of field data due to non accessible areas.

Geological setting N b

Massive felsic rock, road cuts 389 0.43Massive felsic rock, road cuts 123 0.4Jointed metamorphic, rock, road cuts 64 0.7Jointed metamorphic, rock, road cuts 122 0.65Single natural basaltic cliff 370 1

Metamorphic andsedimentary rocks

59 0.45±0.15

Calcareous cliffs 87 0.41±0.11Granitic cliffs 101 0.46±0.11

157 1.07

Granitic 135 1.07

97) Calcareous 89 1.07

For scars larger than 0.25 m3, the obtained scar volumes in ForatNegre and Borrassica can be fitted by a power-law distributionwhere the value of the exponent b is 0.9 and maximum scar volumesobtained reach up to a few thousands of cubic meters. Although thereis not a direct relation between the magnitude–frequency of the rock-fall scars and the rockfall events (given that a rockfall may consist invarious scars or a scar in various rockfalls), both distributions arefound to follow a power-law. Additionally, the calculated value ofthe exponent b, for the magnitude–frequency of scar volumes, is sim-ilar to the value that is indicated by some authors for the magnitude–frequency of rockfall events. This suggests, that in case rockfall inven-tories are not available, the magnitude–frequency of the rockfall scarsmight be alternatively considered, if the following assumptions canbe made: (a) the volume of the rockfall is given by the volume ofthe scar in the cliff face; (b) failures of large rock masses slidingover step-path discontinuity planes are considered only for spacingssmaller than a defined threshold (20 cm in our case-study) and pro-vided that these planes are contiguous.

A roll-over effect was observed for volumes smaller than 0.75 m3,which needs further investigation. Given the precision of the method,undersampling does not seem to be the cause (Stark and Hovius,2001; Guzzetti et al., 2002).

Acknowledgments

The authors would like to acknowledge the funding of the MarieCurie European Reintegration Grant (ERG) “RISK-LESS: Quantitativevulnerability assessment for the evaluation of landslide risk in inhabitedareas” (FP7, contract number 268180) and from the project Big Risk,funded by the Spanish Ministry of Science and Innovation. Field workwas partly financed by the project CGL2006-06596 (DALMASA) withcontract number BIA2008-06614, by the Spanish Ministry of Scienceand Technology.

References

Abellan, A., Vilaplana, J.M., Martinez, J., 2006. Application of a long-range terrestriallaser scanner to a detailed rockfall study at Vall de Nuria (Eastern Pyrenees,Spain). Engineering Geology 88, 136–148.

Abellan, A., Jaboyedoff, M., Oppikofer, T., Vilaplana, J.M., 2009. Detection of millimetricdeformation using a terrestrial laser scanner: experiment and application to rock-fall event. Natural Hazards and Earth System Sciences 9, 365–372.

Abellan, A., Vilaplana, J.M., Calvet, J., García-Sellés, D., Asensio, E., 2011. Rockfall monitoringby Terrestrial Laser Scanning— case study of the basaltic rock face at Castellfollit de laRoca (Catalonia, Spain). Natural Hazards and Earth System Sciences 11, 829–841.

Agarwal, P.K., Arge, L., Danner, A., 2006. From point cloud to grid DEM: a scalable approach.In: Reidl, A., Kainz, W., Elmes, G. (Eds.), Progress in Spatial Data Handling, 12th Interna-tional Symposium on Spatial Data Handling. Springer.

Awwad, T.M., Zhu, Q., Du, Z., Zhang, Y., 2010. An improved segmentation approach forplanar surfaces from unstructured 3D point clouds. The Photogrammetric Record25–129, 5–23.

Barton, N., 1976. The shear strength of rock and rock joints. International Journal ofRock Mechanics and Mining Sciences and Geomechanics Abstracts 13 (9),255–279.

Besl, P.J., McKay, N.D., 1992. A method for registration of 3-D shapes. IEEE Transactionson Pattern Recognition and Machine Intelligence 14 (2), 239–256.

Biosca, J.M., Lerma, J.L., 2008. Unsupervised robust planar segmentation of terrestriallaser scanner point clouds based on fuzzy clustering methods. ISPRS Journal ofPhotogrammetry and Remote Sensing 63 (1), 84–98.

Bouchez, J.L., Gleizes, G., 1995. Two stage deformation of the Mont-Louis-Andorra granitepluton (Variscan Pyrenees) inferred from magnetic susceptibility anisotropy. Journalof the Geological Society 152, 669–679 (Proc Natl Acad Sci USA 19, 2530–2537).

Brunetti, M.T., Guzzetti, F., Rossi, M., 2009. Probability distributions of landslide vol-umes, Nonlinear Processes in Geophysics 16, 179–188.

Budetta, P., 2004. Assessment of rockfall risk along roads. Natural Hazards and EarthSystem Sciences 4, 71–81.

Chen, Y., Medioni, G., 1992. Object modelling by registration of multiple range images.Image and Vision Computing 10 (3), 145–155.

Coggan, J.S., Wetherelt, A., Gwynn, X.P., Flynn, Z.N., 2007. Comparison of hand mappingwith remote data capture systems for effective rock mass characterization. Proc.11th Congress of ISRM, Lisbon, Portugal.

Copons, R., 2004. Avaluació de la perillositat de caigudes de blocs rocosos al Solàd'Andorra la Vella. Tesis doctoral, Dpt. de Geodinàmica i Geofísica, Universitat deBarcelona.

Copons, R., 2007. Avaluació de la perillositat de caigudes de blocs rocosos alSolàd'Andorra la Vella. Monografies del CENMA.

Copons, R., Vilaplana, J.M., 2008. Rockfall susceptibility zoning at a large scale: fromgeomorphological inventory to preliminary land use planning. Engineering Geology102, 142–151.

Corominas, J., Copons, R., Moya, J., Vilaplana, J.M., Altimir, J., Amigó, J., 2005. Quantitativeassessment of the residual risk in a rockfall protected area. Landslides 2, 343–357.

Cruden, D.M., Varnes, D.J., 1996. Landslide types and processes. In: Turner, A.K.,Schuster, R.L. (Eds.), Landslides Investigation and Mitigation: National ResearchCouncil, Transportation Research Board, Special Report, 247, pp. 36–75.

De Lange, W.P., Moon, V.G., 2005. Estimating long-term cliff recession rates from shoreplatform widths. Engineering Geology 80, 292–301.

Deline, P., Alberto, W., Broccolato, M., Hungr, O., Noetzli, J., Ravanel, L., Tamburini, A.,2011. The December 2008 Crammont rock avalanche, Mont Blanc massif area,Italy. Natural Hazards and Earth System Sciences 11, 3307–3318.

Dunning, S.A., Rosser, N.J., Massey, C.I., 2010. The integration of terrestrial laser scanningand numerical modelling in landslide investigations. Quarterly Journal of EngineeringGeology & Hydrogeology 43, 233–247.

Dussauge, C., Grasso, J.-R., Helmstetter, A., 2003. Statistical analysis of rockfall volumedistributions. Journal of Geophysical Research 108 (B6), 2286.

Dussauge-Peisser, A., Helmstetter, A., Grasso, J.-R., Hanz, D., Desvarreux, P., Jeannin, M.,Giraud, A., 2002. Probabilistic approach to rockfall hazard assessment: potential ofhistorical data analysis. Natural Hazards and Earth System Sciences 2, 15–26.

EasyFit, t. Mathwave — data analysis and simulation http://www.mathwave.com.Ewan, V.J., West, G., Temporal, J., 1983. Variation in measuring rock joints fro tunnelling.

Tunnels and Tunnelling 15 (4), 15:18.Feng, Q.H., Röshoff, K., 2004. In-situ mapping and documentation of rock faces using a full

coverage 3-D laser scanning technique. International Journal of Rock Mechanics andMining Science 41 (3).

Feng, Q., Sjögren, P., Stephansson, O., Jing, L., 2001. Measuring fracture orientation atexposed rock faces by using a non-reflector total station. Engineering Geology59, 133–146.

Fernandez, O., 2005. Obtaining a best fitting plane through 3D georeferenced data.Journal of Structural Geology 27, 855–858.

Fernandez, O., Muñoz, J.A., Arbués, P., Falivene, O., Marzo, M., 2004. Three-dimensionalreconstruction of geological surfaces: an example of growth strata and turbiditesystems from the Ainsa basin (Pyrenees, Spain). American Association of PetroleumGeologists Bulletin 88, 1049–1068.

Flageollet, J.C., Weber, D., 1996. Fall. In: Dikau, R., Brunsden, D., Schrott, L., Ibsen, M.L.(Eds.), Landslide Recognition—Identification, Movement and Causes. John Wiley,Chichester, pp. 13–28.

Gaich, A., Pötsch, M., Schubert, W., 2006. Acquisition and assessment of geometric rockmass feature by true 3D images. Proc. 41st U.S. Symp. on RockMech. Golden Colorado,pp. 17–21.

Garcia-Sellés, D., Arbués, P., Falivene, O., Gratacos, O., Tavanil, S., Muñoz, J., 2009.Metodologia para la caracterización automática de las estructuras geológicas apartir de datos LIDAR (CIMNE). VII Simposio Nacional sobre Taludes y Laderasinestables. Barcelona. Spain.

Garcia-Sellés, D., Arbués, P., Falivene, O., Gratacos, O., Tavanil, S., Muñoz, J.A., 2011.Supervised identification and reconstruction of near-planar geological surfacesfrom terrestrial laser scanning. Computers & Geosciences 37, 1584–1594 (Availableonline in www.elsevier.com/locate/cageo).

Gocad, d. Earth Decision Sciences. http://www.earthdecision.com.Goodman, R.E., 1989. Introduction to RockMechanics. JohnWiley & Sons, New York. 561 pp.Guthrie, R.H., Evans, S.G., 2004a. Analysis of landslide frequencies and characteristics in

a natural system, coastal British Columbia. Earth Surface Processes and Landforms29, 1321–1339.

Guthrie, R.H., Evans, S.G., 2004b. Magnitude and frequency of landslides triggered by astorm event, Loughborough Inlet, British Columbia. Natural Hazards and EarthSystem Sciences 4, 475–483.

Guthrie, R.H., Evans, S.G., 2007. Work, persistence, and formative events: the geomorphicimpact of landslides. Geomorphology 88, 266–275.

Guzzetti, F., Malamud, B.D., Turcotte, D.L., Reichenbach, P., 2002. Power-law correlationsof landslide areas in Central Italy. Earth and Planetary Science Letters 195, 169–183.

Hampton, M.A., Griggs, G.B., Edil, T.B., Guy, D.E., Kelley, J.T., Komar, P.D., Mickelson,D.M., Shipman, H.M., 2004. Processes that govern the formation and evolution ofcoastal cliffs. U.S. Geological Survey Professional Paper 1693, 7–38.

Herda, H.H.W., 1999. Strike standard deviation for shallow‐dipping rock fracture sets.Rock Mechanics and Rock Engineering 32, 241–255.

Hoek, E., Bray, J.W., 1981. Rock Slope Engineering Institution of Mining and Metallurgy,London.

Hovius, N., Stark, C.P., Hao-Tsu, C., Jiun-Chuan, L., 2000. Supply and removal of sedi-ment in a landslide-dominated mountain belt: Central Range, Taiwan. Journal ofGeology 108, 73–89.

Hungr, O., Evans, S.G., Hazzard, J., 1999. Magnitude and frequency of rock falls and rockslides along the main transportation corridors of southwestern British Columbia.Canadian Geotechnical Journal 36 (2), 224–238.

Hungr, O., McDougall, S., Wise, M., Cullen, M., 2008. Magnitude–frequency relation-ships of debris flows and debris avalanches in relation to slope relief. Geomorphol-ogy 96, 355–365.

ISRM, 1978. Commission on standardization of laboratory and field tests. Suggestedmethods for the quantitative description of discontinuities in rock masses. Interna-tional Journal of Rock Mechanics and Mining Sciences and Geomechanics 15 (6),319–368.

Jaboyedoff, M., Baillifard, F., Couture, R., Locat, J., Locat, P., 2004a. Toward preliminary haz-ard assessment using DEM topographic analysis and simple mechanical modeling by

means of sloping local base level. In: Lacerda, W.A., Ehrlich, M., Fontoura, A.B., Sayao,A. (Eds.), Landslides Evaluation and Stabilization. Balkema, pp. 199–205.

Jaboyedoff, M., Baillifard, F., Philippossian, F., Rouiller, J.D., 2004b. Assessing fractureoccurrence using weighted fracturing density a step towards estimating rock insta-bility hazard. Natural Hazards and Earth System Sciences 4, 83–93.

Jaboyedoff, M., Pedrazzini, A., Horton, P., Loye, A., Surace, I., 2008. Preliminary slopemass movements susceptibility mapping using LIDAR DEM. Proceedings of 61thCanadian Geotechnical Conference, pp. 419–426.

Jaboyedoff, M., Réjean Couture, R., Locat, P., 2009. Structural analysis of Turtle Moun-tain (Alberta) using digital elevation model: toward a progressive failure. Geomor-phology 5–16.

Jaboyedoff, M., Oppikofer, T., Abellan, A., Derron, M.-H., Loye, A., Metzger, R., Pedrazzini,A., 2010. Use of LIDAR in landslide investigations: a review. Natural Hazards 61, 5–28.

Kemeny, J., Post, R., 2003. Estimating three-dimensional rock discontinuity orientationfrom digital images of fracture traces. Computers & Geosciences 29, 65–77.

Kemeny, J., Turner, K., 2008. Ground based LIDAR. Rock slope mapping and assessment.Technical Report of the Central Federal Lands Highway Division US Department ofTransportation FHWA-CFL/TD-08-006 (www.iaeg.info).

Kenner, R., Philips, M., Danioth, C., Denier, C., Thee, P., Zgraggen, A., 2011. Investigation ofrock and ice loss in a recently deglaciated mountain rock wall using terrestrial laserscanning: Gemsstock, Swiss Alps. Cold Regions Science and Technology 67, 157–164.

Lato, M., Diederichs, M., Hutchinson, D.J., Harrap, R., 2009. Optimization of LiDAR scan-ning and processing for automated structural evaluation of discontinuities in rockmasses. International Journal of Rock Mechanics and Mining Science 46, 194–199.

Lim, M., Rosser, N.J., Allison, R.J., Petley, D.N., 2010. Erosional processes in the hard rockcoastal cliffs at Staithes, North Yorkshire. Geomorphology 114, 12–21.

Malamud, B., Turcotte, L., Guzzetti, F., Reichenbach, P., 2004. Landslide inventories andtheir statistical properties. Earth Surface Processes and Landforms 687–711, 29.

Markland, J.T., 1972. A Useful Technique for Estimating the Stability of Rock SlopesWhen the Rigid Wedge Slide Type of Failure is Expected. Imperial College RockMechanics Research Reprints. n. 19.

Mikos, M., Vidmar, A., Brilly, M., 2005. Using a laser measurement system for monitor-ing morphological changes on the Strug rock fall, Slovenia. Natural Hazards andEarth System Sciences 5, 143–153.

Noverraz, F., Bonnard, C., 1992. L' écroulement rocheux de Randa, près de Zermatt. In:Bell, D.H. (Ed.), Landslides. : Proceedings of the 6th International Symposium, 1.Balkema, Rotterdam, pp. 165–170.

Oppikofer, T., Jaboyedoff, M., Keusen, H.R., 2008. Collapse at the eastern Eiger flank inthe Swiss Alps. Nature Geoscience 1, 531–535.

Oppikofer, T., Jaboyedoff, M., Blikra, L., Derron, M.H., 2009. Characterization and mon-itoring of the Aknes rockslide using terrestrial laser scanning. Natural Hazardsand Earth System Sciences 9, 1643–1653.

Oppikofer, T., Jaboyedoff, M., Pedrazzini, A., Derron, M.-H., Blikra, L.H., 2011. DetailedDEM analysis of a rockslide scar to improve the basal failure surface model ofactive rockslides. Journal of Geophysical Research 116.

Palmstrom, A., 2005. Measurement of and correlations between block size and rock qual-ity designation (RQD). Tunelling and Underground Space Technology 20, 362–377.

Pantelidis, L., 2011. A critical review of highway slope instability risk assessment sys-tems. Bulletin of Engineering Geology and the Environment 70 (3), 395–400.

Patton, F.D., 1966. Multiple modes of shear failure in rock. Proc. 1st Congr. ISRM, Lisbon,1966, I, pp. 509–513.

Pelletier, J.D., Malamud, B.D., Blodgett, T., Turcotte, D.L., 1997. Scale-invariance of soilmoisture variability and its implications for the frequency-size distribution oflandslides. Engineering Geology 48, 255–268.

Pierson, L.A., Davis, S.A., Van Vickler, R., 1990. Rock-fall Hazard Rating System Imple-mentation Manual. Federal Highway Administration (FHWA). Report FHWA —

OR-EG-90-01. FHWA, U.S. Department of Transportation, p. 80.Polyworks, s. (Innovmetric Software) http://www.innovmetric.com.Poropat, G.V., 2006. Remote 3D mapping of rock mass structure. In: Tonon, F.,

Kottenstette, J. (Eds.), Laser and Photogrammetric Methods for Rock Face Charac-terization, ARMA, pp. 63–75.

Priest, S.D., 1993. Discontinuity Analysis for Rock Engineering. Chapman and Hall, London.473 pp.

Priest, S.D., Hudson, J.A., 1981. Estimation of discontinuity spacing and trace lengthusing scan line surveys. International Journal of Rock Mechanics and MiningSciences and Geomechanics Abstracts 18, 183–197.

Ravanel, L., Deline, P., 2008. La face ouest des Drus (massif du Mont Blanc): évolutionde l'instabilité d'une paroi rocheuse dans la haute montagne alpine depuis la fin

du Petit Age Glaciaire. Géomorphologie: Relief, Processus, Environnement 4,261–272.

Rosser, N.J., Petley, D.N., Lim, M., Dunning, S.A., Allison, R.J., 2005. Terrestrial laser scan-ning for monitoring the process of hard rock coastal cliff erosion. Quarterly Journalof Engineering Geology & Hydrogeology 38, 363–375.

Rosser, N., Lim, M., Petley, D., Dunning, S., Allison, R., 2007. Patterns of precursory rock-fall prior to slope failure. Journal of Geophysical Research 112, F04014, http://dx.doi.org/10.1029/2006JF000642.

Rouiller, J.D., Jaboyedoff, M., Marro, J.D., Philippossian, F., Mamin, M., 1998. Pentesinstables dans le Pennique valaisan. Rapport final du Programme National deRecherche PNR 31/CREALP, vol. 98. vdf Hochschulverlag AG and ETH, Zürich. 239pp.

Rousseau, N., 1999. Study of seismic signals associated with rockfalls at 2 sites on theReunion Island (Mahavek Cascade and Souffriére cavity) - Ph.D thesis, Inst. dePhys. du Globe de Paris.

RTM, 1997. Inventaire des mouvements rocheux, Secteur de Grenoble. Service deRestauration des terrains en Montagne, 38, Grenoble, France.

Sartori, M., Baillifard, F., Jaboyedoff, M., Rouiller, J.D., 2003. Kinematics of the 1991Randa rockslides (Valais, Switzerland). Natural Hazards and Earth System Sciences3, 423–433.

SEFL (Surface Extraction from LIDAR), Institut de recerca GEOMODELS.Shi, G., Cheng, X., Guan, Y., Li, Q., 2009. Best distance of terrestrial 3D laser scanning

point cloud registration. Journal of Jiangsu University - Natural Science Edition,30 (2), 197–200.

Slob, S., Hack, H.R.G.K., 2004. 3D terrestrial laser scanning as a new field measurementand monitoring technique. In: Hack, Robert, RafigAzzam, Charlier, Robert (Eds.),Engineering Geology for Infrastructure Planning in Europe. A European Perspec-tive. Springer Verlag, pp. 179–190.

Slob, S., Hack, H.R.G.K., Turner, A.K., 2002. An approach to automate discontinuity mea-surements of rock faces using laser scanning techniques. In: Dinid da Gama, C.,Riberia e Sousa, L. (Eds.), Proceedings of ISRM EUROCK 2002. 25–28 November2002. Sociedade Portuguesa de Geotecnia, Funchal, Portugal, pp. 87–94.

Slob, S., Hack, H.R.G.K., Van Knapen, B., Turner, K., Kemeny, J., 2005. A method for auto-mated discontinuity analysis of rock slopes with three — dimensional laser scan-ning. Transportation Research Record: Journal of the Transportation ResearchBoard 1913, 187–194.

Stark, C.P., Hovius, N., 2001. The characterization of landslide size distributions. Geo-physical Research Letters 28 (6), 1091–1109.

Sturzenegger, M., Stead, D., 2009. Quantifying discontinuity orientation and persis-tence on high mountain rock slopes and large landslides using terrestrial remotesensing techniques. Natural Hazards and Earth System Sciences 9, 267–287.

Sturzenegger, M., Stead, D., Elmo, D., 2011. Terrestrial remote sensing-based estimationof mean trace length, trace intensity and block size/shape. Engineering Geology119, 96–111.

Turcotte, D.L., Malamud, B.D., Guzzetti, F., Reichenbach, P., 2002. Self-organization, thecascade model, and natural hazards. Proceedings of the National Academy of Sci-ences of the United States of America 19 (99 (Suppl. 1)), 2530–2537.

Van Den Eeckhaut, M., Poesen, J., Govers, G., Verstraeten, G., Demoulin, A., 2007. Char-acteristics of the size distribution of recent and historical landslides in a populatedhilly region. Earth and Planetary Science Letters 256, 588–603.

Varnes, D.J., 1978. Slope movement types and processes. Landslides: analysis and con-trol. Transportation Research Board Special Report 176, 11–33.

Vosselman, B., Gorte, B.G.H., Sithole, G., Rabbani, T., 2004. Recognising structure in laserscanner point clouds. The International Archives of the Photogrammetry, RemoteSensing and Spatial Information Sciences 46 (Part 8/W2), 33–38.

Whalley, W.B., Douglas, G.R., Jónsonn, A., 1983. The magnitude and frequency of largerockslides in Iceland in the postglacial, Geografiska Annaler. 65 A, 99–110.

Wieczorek, G.F., Morrissey, M.M., Iovine, G., Godt, J., 1998. Rock fall Hazards in theYosemite Valley. US Geological Survey, Open File Report. 98–467.

Woodcock, N.H., 1977. Specification of fabric shapes using an eigenvalues method.Geological Society of America Bulletin 88, 1231–1236.

Young, A.P., Guza, R.T., O'Relly, W.C., Flick, R.E., Gutiérrez, R., 2011. Short-term retreatstatistics of a slowly eroding coastal cliff. Natural Hazards and Earth System Sci-ences 11, 205–217.

Magnitude–frequency relation for rockfall scars using a Terrestrial Laser Scanner

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