Skip to main content
SpringerLink
Log in

Size Distribution for Potentially Unstable Rock Masses and In Situ Rock Blocks Using LIDAR-Generated Digital Elevation Models

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

In this paper, two analytical procedures which are independent from the existence of empirical data are presented for the calculation of (1) the size distribution of potentially unstable rock masses that expresses the potential rockfall size distribution, including big volumes corresponding to potential rare events with low susceptibility of failure and (2) the in situ block distribution on the slope face. Two approaches are, respectively, used. The first one involves the detection of kinematically unstable surfaces on a digital elevation model (DEM) and on orthophotos and the calculation of the volumes resting on them. For the second one the in situ block volumes formed by the intersection of the existing discontinuity sets are calculated using a high-resolution DEM. The procedures are presented through an application example at the country of Andorra and in particular at the chute of Forat Negre. The results from the first procedure indicate that it is kinematically possible to have mobilized volumes of some thousands of cubic meters; however, these are considered rare events with low susceptibility of failure. The size distribution of potentially unstable rock masses for big volume events was well fitted by a power law with an exponent of −0.5. The in situ block distribution on the slope face from the second procedure, assuming three types of intersection between the joints of the existing discontinuity sets and two extreme cases of discontinuity persistence, was also found to follow a power law, but with an exponent of −1.3. The comparison with the observed in the field block volume distribution on the slope face indicates that in reality discontinuities have a very high persistence and that considering only their visible trace length overestimates volumes, which is conservative.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Abellán A, Vilaplana JN, Martínez J (2006) Application of a long-range Terrestrial Laser Scanner to a detailed rockfall study at Vall de Núria (Eastern Pyenees, Spain). Eng Geol 88:136–148

    Article  Google Scholar 

  • Abellán A, Jaboyedoff M, Oppikofer T, Vilaplana JM (2009) Detection of millimetric deformation using a terrestrial laser scanner: experiment and application to a rockfall event. Nat Hazards Earth Syst Sci 9:365–372

    Article  Google Scholar 

  • Aler J, Du Mouza J, Arnould M (1996) Measurement of the fragmentation efficiency of rock mass blasting and its mining applications. Int J Rock Mech Min Sci Geomech 33(2):125–139

    Article  Google Scholar 

  • Barton N (2013) Shear strength criteria for rock, rock joints, rock fill and rock masses: Problems and some solutions. J Rock Mech Geotech, Eng. JRMGE Wuhan Elsevier 5:249–261

  • Becker J, Stewart C, Radke RJ (2009) LiDAR inpainting from a single image. IEEE 12th International Conference on Computer Vision. Proceedings of International Conference on 3-D Digital Imaging and Modeling (3DIM)

  • Birch J S (2006) Using 3DM Analyst mine mapping suite for rock face characterization. In Tonon F, Kottenstette J (ed). Laser and photogrammetric methods for rock face characterization ARMA, 13–32

  • Chau KT, Wong RHC, Wu JJ (2002) Coefficient of restitution and rotational motions of rockfall impacts. Int J Rock Mech Min Sci 39:69–77

    Article  Google Scholar 

  • Coggan J S, Wetherelt A, Gwynn XP, Flynn ZN (2007) Comparison of hand-mapping with remote data capture systems for effective rock mass characterization. Proceedings of the 11th Congress of ISRM, Lisbon, Portugal

  • Copons R (2004) Avaluació de la perillositat de caigudes de blocs a Andorra la Vella (Principat d’Andorra) Ph.D. thesis. UB Barcelona

  • Corominas J, Mavrouli O (2013) Estimation quantitative du risque (QRA) pour les bâtiments lié aux éboulements rocheux progrès et défis. Les dangers naturels en Suisse: pratique et développements. In Comptes rendus de la deuxième Journée de Rencontre sur les Dangers Naturels (Université de Lausanne, 18 février 2011). Mémoire de la Société vaudoise des Sciences naturelles. (Ed) Nicolet P, Derron M-H, Jaboyedoff M. 25:229–242

  • Corominas J, Mavrouli O, Moya J (2012) Simplified approach for obtaining the block volume distribution of fragmental rockfalls. ISL-NASL 2012. 11th International & 2nd North American Symposium on Landslides. 3–8 June Banff: CRC Press. Taylor & Francies Group. 1159–1164

  • Crosta G, Agliardi F (2003) A methodology for physically based rockfall hazard assessment. Nat Hazard Earth Syst Sci 3:407–422

    Article  Google Scholar 

  • Cruden DM, Hungr O (1986) The debris of the Frank Slide and theories of rockslide–avalanche mobility. Can J Earth Sci 23(3):425–432

    Article  Google Scholar 

  • Cruden DM, Varnes DJ (1996) Landslide types and processes. In Turner AK, Shuster RL (Eds) Landslides: Investigation and Mitigation. Transp Res Board. Spec Rep 247:36–75

  • Délèze JY, Jaboyedoff M, Baillifard F, Rouiller JD (2003) Mattercliff-software for the analysis of spatial distribution of discontinuities in cliffs. EGS-AGU-EUG Joint Assembly, Nice, France, April 2003. Geophys Res Abstr 5:03384

    Google Scholar 

  • Derron MH, Blikra L, Jaboyedoff M (2005) Preliminary assessment of landslide and rockfall hazards using a DEM (Oppstadhornet, Norway). Nat Hazards Earth Syst Sci. 285–292

  • Di Luzio E, Bianchi Fasani G, Bretscheider A (2013) Potential rockfalls and analysis of slope dynamics in the Palatine Aarchaeological area (Rome, Italy) Geologica Acta, vol 11, N 2, June 2013, 245–264

  • Dorren LKA, Domaas U, Kronholm K, Labiouse V (2011) Methods for predicting rockfall trajectories and run-out zones. In: Lambert S, Nicot F (eds). Rockfall engineering. ISTE Ltd./Wiley, 143–173

  • Dussauge-Peisser A, Helmstetter C, Grasso JR, Hantz D, Desvarreux P, Jeannin M, Giraud A (2002) Probabilistic approach to rockfall hazard assessment: potential of historical data analysis. Nat Hazards Earth Syst Sci 2:15–26

    Article  Google Scholar 

  • Elmouttie M, Poropat G (2011) A method to estimate in situ block size distribution. Rock Mech Rock Eng 37:529–535

    Google Scholar 

  • Evans S, Hungr O (1993) The assessment of rockfall hazard at the base of talus slopes. Can Geotech J 30:620–636

    Article  Google Scholar 

  • Evans SG, Clague JJ, Woodsworth GJ (1989) The pandemonium creek rock Avalanche, British Columbia. Can Geotech J 26(3):427–446

    Article  Google Scholar 

  • Gaich A, Poetsch M, Schubert W (2006) Acquisition and assessment of geometric rock mass feature by true 3D images, in: Proceedings of the 41st U.S. Symposium on rock mechanics (USRNS). 17–21 June, Golden, Colorado

  • Gates W, Ortiz L, Florez R (2005) Analysis of Rockfall and Blasting Backbreak Problems, US 550, Molas Pass, CO. 40th U.S. Symposium on Rock Mechanics (USRMS), June 25–29, Anchorage, Alaska

  • Grasselli G (2001) Shear Strength of Rock Joints Based on Quantified Surface Description, Ph.D. dissertation, Ecole Polytechnique Fédérale de Lausanne

  • Guerin A, Hantz D, Rossetti1 J- P, Jaboyedoff M (2014) Estimating rockfall frequency in a mountain limestone cliff using terrestrial laser scanner Nat. Hazards Earth Syst. Sci. Discuss. 2: 123–135 (under review)

  • Guzzetti F, Reichenbach P, Wieczorek GF (2003) Rockfall hazard and risk assessment in the Yosemite Valley California, USA. Nat Hazards Earth Syst Sci 3:491–503

    Article  Google Scholar 

  • Hack HRGK (1998) Slope stability probability classification, SSPC. ITC publications no 43. Delft

  • Hantz D (2011) Quantitative assessment of diffuse rock fall hazard along a cliff foot. Nat Hazards Earth Syst Sci 11:1303–1309

    Article  Google Scholar 

  • Hoek E, Bray J (1981) Rock slope engineering. The Institution of Mining and Metallurgy, London

    Google Scholar 

  • Hsü KJ, Kenneth J (1975) Catastrophic Debris Streams (Sturzstroms) Generated by Rockfalls. Geol Soc Am Bull 86(1):129–140

    Article  Google Scholar 

  • Hungr O, Evans SG, Hazzard J (1999) Magnitude and frequency of rock falls and rock slides along the main transportation corridors of southwestern British Columbia. Can Geotech J 36(2):224–238

    Article  Google Scholar 

  • Hungr O, Leroueil S, Picarelli L (2014) The Varnes classification of landslide types, an update. Landslides 11(2):167–194

    Article  Google Scholar 

  • Jaboyedoff M, Philippossian F, Mamin M, Marro C, Rouiller JD (1996) Distribution spatiale des discontinuités dans une falaise. Rapport de travail PNR31, VDF Publisher, Zürich. pp 90

  • Jaboyedoff M, Baillifard F, Hantz D, Heidenreich B, Mazzoccola D (2001) Terminologie. In: Carere K, Ratto S (ed) Prévention des mouvements de versants et des instabilités de falaises. Zanolini FE. 48–57

  • Jaboyedoff M, Baillifard F, Philippossian F, Rouiller JD (2004) Assessing fracture occurrence using “weighted fracturing density”: a step towards estimating rock instability hazard. Nat Hazards Earth Syst Sci 4:83–93

    Article  Google Scholar 

  • Jaboyedoff M, Dudt JP, Labiouse V (2005) An attempt to refine rockfall hazard zoning based on the kinetic energy frequency and fragmentation degree. Nat Hazards Earth Syst Sci 5:621–632

    Article  Google Scholar 

  • Jaboyedoff M, Metzger R, Oppikofer T, Couture R, Derron MH, Locat J, Turmel D (2007) New insight techniques to analyze rock-slope relief using DEM and 3D-imaging cloud points: COLTOP-3D software. In: Eberhardt E, Stead D, Morrison T (ed) Rock mechanics: meeting society’s challenges and demands vol 1 Taylor & Francis 61–68

  • Jaboyedoff M, Couture R, Locat P (2009) Structural analysis of Turtle Mountain (Alberta) using digital elevation model: toward a progressive failure. Geomorphology 103:5–16

    Article  Google Scholar 

  • Jaboyedoff M, Oppikofer T, Abellan A, Derron MH, Loye A, Metzger R, Pedrazzini A (2012) Use of LIDAR in landslide investigations: an overview. Nat Hazards 61:5–28

    Article  Google Scholar 

  • Kemeny J, Post R (2003) Estimating Three-Dimensional Rock Discontinuity Orientation from Digital Images of Fracture Traces. Comput Geosci 29(1):65–77

    Article  Google Scholar 

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

  • Kemeny J, Norton B, Turner K (2006) Rock slope stability analysis utilizing ground-based LiDAR and digital image processing. Felsbau 24:8–16

    Google Scholar 

  • Kim BH, Cai M, Kaiser PK, Yang HS (2007) Estimation of block sizes for rock masses with non-persistent joints. Rock Mech Rock Eng 40(2):169–192

    Article  Google Scholar 

  • Krishna C, Devkota J, Eun H, Gyo-Won K (2009) Characteristics of discontinuity spacing of Yeongdeok granite. Geosci J 13(2):161–165

    Article  Google Scholar 

  • Kulatilake PHSW, Chen J, Teng J, Pan G, Shufang X (1995) Discontinuity network modelling of the rock mass around a tunnel close to the proposed permanent shiplock area of the three gorges dam site in China. Proceedings od 35th U S Rock Mechanics Symposium (Ed) Daemen and Schultz. 807–812

  • Lato M, Hutchinson J, Diederichs M, Ball D, Harrap R (2009) Engineering monitoring of rockfall hazards along transportation corridors: using mobile terrestrial LiDAR. Nat Hazards Earth Syst Sci 9:935–946

    Article  Google Scholar 

  • Lizotte YC, Scoble MJ (1994) Geological control over blast fragmentation. Can Min Metall Bull 87(983):57–71

    Google Scholar 

  • Locat P, Couture R, Locat J, Leroueil S, Jaboyedoff M (2006) Fragmentation energy in rock avalanches. Can J Geotech 43:830–851

    Article  Google Scholar 

  • Lu P, Latham JP (1999) Developments in the assessment of in situ block size distributions for rock masses. Rock Mech Rock Eng 32:29–49

    Article  Google Scholar 

  • Markland JT (1972) A useful technique for estimating the stability of rock slopes when the rigid wedge slide type of failure is expected. Imperial College Rock Mechanics. Res Repr 19:10

    Google Scholar 

  • Metzger R, Jaboyedoff M, Oppikofer T, Viero A, Galgaro A (2009) Coltop3D: a new software for structural analysis with high resolution 3D point clouds and DEM. Frontiers + innovation CSPG CSEG CWLS convention, Calgary

    Google Scholar 

  • Moya J, Corominas J, Pérez Arcas J, Baeza C (2010) Tree-ring based assessment of rockfall frequency on talus slopes at Solà d’Andorra, Eastern Pyrenees. Geomorphology 118:393–408

    Article  Google Scholar 

  • Nocilla N, Evangelista A, Scotto di Santolo A (2009) Fragmentation during rock falls: Two Italian case studies of hard and soft rocks. Rock Mech Rock Eng 42:815–833. doi:10.1007/s00603-008-0006-0

    Article  Google Scholar 

  • Oppikofer T (2009) Detection analysis and monitoring of slope movements by high-resolution digital elevation models. PhD thesis. Istitute of Geomatics and Analysis of Risks. Faculty of Geosciences and Environments. University of Lausanne. Switzerland

  • Oppikofer T, Jaboyedoff M, Blikra LH, Derron MH, Metzger R (2009) Characterization and monitoring of the Åknes rockslide using terrestrial laser scanning. Nat Hazards Earth Sys Sci 9:1003–1019

    Article  Google Scholar 

  • Palmstrom A (2005) Measurement of and correlations between block size and rock quality designation (RQD) tunelling and underground. Space Technol 20:362–377

    Article  Google Scholar 

  • Poropat GV (2006) Remote 3D mapping of rock mass structure. In: Tonon F, Kottenstette J (ed) Laser and photogrammetric methods for rock face characterization ARMA, 63–75

  • Priest SD, Hudson JA (1981) Estimation of discontinuity spacing and trace length using scan line surveys. Int J Rock Mech Min Sci Geomech Abstr 18:183–197

    Article  Google Scholar 

  • Rohmer J, Dewez T (2012) What if the power-law model did not apply for the prediction of very large rockfall events? Geophys Res Abstr, vol 14 EGU2012-2397

  • Santana D, Corominas J, Mavrouli O, Garcia-Sellés D (2012) Magnitude–frequency relation for rockfall scars using a Terrestrial Laser Scanner. Eng Geol 145–146:50–64

    Article  Google Scholar 

  • Scholtès L, Donzé F-V (2012) Modelling progressive failure in fractured rock masses using a 3D discrete element method. Int J Rock Mech Min Sci 52:18–30

    Article  Google Scholar 

  • Slob S, Hack R (2004) 3D terrestrial laser scanning as a new field measurement and monitoring techniques. Engineering geology for infrastructure planning in Europe: a European perspective. Lectures Notes in Earth Sciences. Springer, Berlin 104:179–189

  • Slob S, Hack R, van Knapen B, Kemeny J (2005) A method for automated discontinuity analysis of rock slopes with 3D laser scanning. Proceedings of the Transportation Research Board (TRB) 84th Annual Meeting. Washington

  • Sornette D (2002) Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth. Proc Natl Acad Sci U S A 99(1):2522–2529

    Article  Google Scholar 

  • Sturzenegger M, Stead D (2009) Quantifying discontinuity orientation and persistence on high mountain rock slopes and large landslides using terrestrial remote sensing techniques. Nat Hazard Earth Syst Sci 9(2):267–287

    Article  Google Scholar 

  • Turner K, Kemeny J (2005) A method for automated discontinuity analysis of rock slopes with three-dimensional laser scanning. In: Transportation research record: journal of the transportation research board. 1913:187–194

  • Varnes DJ (1958) Landslide types and processes. In: Eckel EB (Ed) Landslides and Engineering Practice. Highway Research Board Special Report 29. NAS‐NRC Publication 544, Washington, 20–47

  • Varnes DJ (1978) Slope movement types and processes. In: Schuster RL, Krizek RJ (ed), Landslides, analysis and control. Transportation Research Board Sp. Rep. No. 176, Nat Acad oi Sci:11–33

  • Wallis PF, King MS (1981) Discontinuity spacings in a crystalline rock. Int J Rock Mech Min Sci 17:63–66

    Article  Google Scholar 

  • Wang Y, Tonon F (2010) Discrete element modeling of rock upon Impact in rock fall analysis. Rock Mech Rock Eng 44(1):23–35

    Article  Google Scholar 

  • Zhang ZX, Kou SQ, Jiang LG, Lindqvist PA (2000) Effects of loading rate on rock fracture: fracture characteristics and energy partitioning. Int J Rock Mech Min Sci 37:745–762

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Marie Curie Research and Training Network “Mountain Risks” funded by the European Commission (2007–2010, Contract MCRTN-35098) and by the Government of Andorra (Edicte de 10/04/2013, BOPA nº18 17/04/2014). The authors would like to thank A. Loye, A. Pedrazzini, and C. Longchamp for their support in the preparation of this work.

Author information

Authors and Affiliations

  1. Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, 08034, Barcelona, Spain

    O. Mavrouli & J. Corominas

  2. Centre de recherche sur l’environnement terrestre Faculté des géosciences et de l’environnement, University of Lausanne, 1015, Lausanne, Switzerland

    M. Jaboyedoff

  3. International Centre for Numerical Methods in Engineering, CIMNE, 08034, Barcelona, Spain

    O. Mavrouli

Authors
  1. O. Mavrouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Corominas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Jaboyedoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Mavrouli.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mavrouli, O., Corominas, J. & Jaboyedoff, M. Size Distribution for Potentially Unstable Rock Masses and In Situ Rock Blocks Using LIDAR-Generated Digital Elevation Models. Rock Mech Rock Eng 48, 1589–1604 (2015). https://doi.org/10.1007/s00603-014-0647-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-014-0647-0

Keywords

Search

Navigation