, Volume 15, Issue 5, pp 829–845 | Cite as

Magnitude and frequency relations: are there geological constraints to the rockfall size?

  • Jordi CorominasEmail author
  • Olga Mavrouli
  • Roger Ruiz-Carulla
Original Paper


There exists a transition between rockfalls, large rock mass failures, and rock avalanches. The magnitude and frequency relations (M/F) of the slope failure are increasingly used to assess the hazard level. The management of the rockfall risk requires the knowledge of the frequency of the events but also defining the worst case scenario, which is the one associated to the maximum expected (credible) rockfall event. The analysis of the volume distribution of the historical rockfall events in the slopes of the Solà d’Andorra during the last 50 years shows that they can be fitted to a power law. We argue that the extrapolation of the F-M relations far beyond the historical data is not appropriate in this case. Neither geomorphological evidences of past events nor the size of the potentially unstable rock masses identified in the slope support the occurrence of the large rockfall/rock avalanche volumes predicted by the power law. We have observed that the stability of the slope at the Solà is controlled by the presence of two sets of unfavorably dipping joints (F3, F5) that act as basal sliding planes of the detachable rock masses. The area of the basal sliding planes outcropping at the rockfall scars was measured with a terrestrial laser scanner. The distribution of the areas of the basal planes may be also fitted to a power law that shows a truncation for values bigger than 50 m2 and a maximum exposed surface of 200 m2. The analysis of the geological structure of the rock mass at the Solà d’Andorra makes us conclude that the size of the failures is controlled by the fracture pattern and that the maximum size of the failure is constrained. Two sets of steeply dipping faults (F1 and F7) interrupt the other joint sets and prevent the formation of continuous failure surfaces (F3 and F5). We conclude that due to the structural control, large slope failures in Andorra are not randomly distributed thus confirming the findings in other mountain ranges.


Rockfalls Magnitude and frequency relations Solà d’Andorra Maximum Credible Event 



This work has been carried out with the support of the fellowship to the third author and within the framework of the research project Rockmodels financed by the Spanish Ministry of Economy and Competitiveness  and the European Regional Development's funds (FEDER), (BIA2016-75668-P) and by the Government of Andorra (Edicte de 10/04/2013, BOPA n°18 17/04/2014). We thank the Parc Nacional d’Aigüestortes i Estany de Sant Maurici for the support provided for the survey with TLS at Pala Morrano slope.


  1. Abbruzzese JM, Sauthier C, Labiouse V (2009) Considerations on Swiss methodologies for rock fall hazard mapping based on trajectory modelling. Nat Hazards Earth Syst Sci 9:1095–1109CrossRefGoogle Scholar
  2. Agliardi F, Crosta G, Zanchi A (2001) Structural constraints on deep-seated slope deformation kinematics. Eng Geol 59:83–102CrossRefGoogle Scholar
  3. Agliardi F, Crosta GB, Frattini P (2009a) Integrating rockfall risk assessment and countermeasure design by 3D modelling techniques. Nat Hazards Earth Syst Sci 9:1059–1073CrossRefGoogle Scholar
  4. Agliardi F, Crosta GB, Zanchi A, Ravazzi C (2009b) Onset and timing of deep-seated gravitational slope deformations in the eastern Alps, Italy. Geomorphology 103:113–129CrossRefGoogle Scholar
  5. Ambrosi C, Crosta GB (2006) Large sackung along major tectonic features in the Central Italian Alps. Eng Geol 83:183–200CrossRefGoogle Scholar
  6. Amigó J, Altimir J, Copons R (2001) Verificación de los resultados del modelo de simulación Eurobloc a partir de casos reales de caídas de bloques rocosos. V Simposio Nacional sobre Taludes y Laderas Inestables Madrid Vol 2: 653–663Google Scholar
  7. Badger TC (2002) Fracturing within anticlines and its kinematic control on slope stability. Environ Eng Geosci VIII:19–33Google Scholar
  8. Ballantyne CK (2002) Paraglacial geomorphology. Quat Sci Rev 21:1935–2017CrossRefGoogle Scholar
  9. Ballantyne CK, Stone JO (2004) The Beinn Alligin rock avalanche, NW Scotland: Cosmogenic 10Be dating, interpretation and significance. The Holocene 14:448–453CrossRefGoogle Scholar
  10. Barlow J, Lim M, Rosser N, Petley D, Brain M, Norman E, Geer M (2012) Modeling cliff erosion using negative power law scaling of rockfalls. Geomorphology 139:416–424CrossRefGoogle Scholar
  11. Barton N, Bandis S (1982) Effects of block size on the shear behavior of jointed rock. The 23rd U.S Symposium on Rock Mechanics. Berkeley, California, pp 739–760Google Scholar
  12. Böhme M, Oppikofer T, Jaboyedoff M, Hermanns RJ, Derron MH (2015) Analyses of past and present rock slope instabilities in a fjord valley: implications for hazard estimations. Geomorphology 248:464–474CrossRefGoogle Scholar
  13. Bonnet E, Bour O, Odling NE, Davy P, Main I, Cowie P, Berkowitz B (2001) Scaling of fracture systems in geological media. Reviews in. Geophysics 39:347–383CrossRefGoogle Scholar
  14. Bourrier F, Dorren L, Hungr O (2013) The use of ballistic trajectory and granular flow models in predicting rockfall propagation. Earth Surf Process Landf 38:435–440CrossRefGoogle Scholar
  15. Brardinon F, Church M (2004) Representing the landslide magnitude–frequency relation: Capilano River Basin, British Columbia. Earth Surf Process Landf 29:115–124CrossRefGoogle Scholar
  16. Brideau MA, Yan M, Stead D (2009) The role of tectonic damage and brittle rock fracture in the development of large rock slope failures. Geomorphology 103:30–49CrossRefGoogle Scholar
  17. Brundl M, Romang HE, Bischof N, Rheinberger CM (2009) The risk concept and its application in natural hazard risk management in Switzerland. Nat Hazards Earth Syst Sci 9:801–813CrossRefGoogle Scholar
  18. Burbank DW, Leland J, Fielding E, Anderson RS, Brozovic RS, Reid MR, Duncan C (1996) Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas. Nature 379:505–510CrossRefGoogle Scholar
  19. Cascini L, Bonnard C, Corominas J, Jibson R, Montero-Olarte J (2005) Landslide hazard and risk zoning for urban planning and development. State of the art report (SOA7). In: Hungr O, Fell R, Couture R, Eberthardt E (eds) Proceedings of the international conference on “landslide risk management”, Vancouver (Canada). Taylor and Francis, London, pp 199–235Google Scholar
  20. Cave JAS, Ballantyne CK (2016) Catastrophic rock-slope failures in NW Scotland: quantitative analysis and implications. Scott Geogr J 132:185–209CrossRefGoogle Scholar
  21. Chau KT, Wong RCH, Liu J, Lee CF (2003) Rockfall hazard analysis for Hong Kong based on rockfall inventory. Rock Mech Rock Eng 36:383–408CrossRefGoogle Scholar
  22. Clarke BA, Burbank DW (2010) Bedrock fracturing, threshold hillslopes and limit to the magnitude of landslides. Earth Planet Sci Lett 297:577–586CrossRefGoogle Scholar
  23. Copons R (2007) Avaluació de la perillositat de caigudes de blocs rocosos al Solà d'Andorra la Vella. Monografies del CENMAGoogle Scholar
  24. Copons R, Altimir J, Amigó J, Vilaplana JM (2001) Medotología Eurobloc para el estudio y protección de caídas de bloques rocosos. Principado de Andorra V Simposio Nacional sobre Taludes y Laderas Inestables Madrid 2:665–676Google Scholar
  25. Copons R, Vilaplana JM, Corominas J, Altimir J, Amigó J (2004) Rockfall risk management in high-density urban areas. The Andorran experience. In: Glade T, Anderson M, Crozier MJ (eds) Landslide hazard and risk. John Wiley and Sons, Chichester, pp 675–698Google Scholar
  26. Corominas J (1996) The angle of reach as a mobility index for small and large landslides. Can Geotech J 33:260–271CrossRefGoogle Scholar
  27. Corominas J (2007) Experience on landslide risk management in the Eastern Pyrenees (Spain and Andorra): achievements and challenges. In: Ho K, Li V (eds) The 2007 International Forum on Landslide Disaster Management. Hong Kong. The Hong Kong Institution of Engineers, vol 1, pp 49–70Google Scholar
  28. Corominas J, Moya J (2008) A review of assessing landslide frequency for hazard zoning purposes. Eng Geol 102:193–213CrossRefGoogle Scholar
  29. Corominas J, Copons R, Vilaplana JM, Altimir J, Amigó J (2003) Integrated landslide susceptibility analysis and hazard assessment in the principality of Andorra. Nat Hazards 30:421–435CrossRefGoogle Scholar
  30. Corominas J, Copons R, Moya J, Vilaplana JM, Altimir J, Amigó J (2005) Quantitative assessment of the residual risk in a rock fall protected area. Landslides 2:343–357CrossRefGoogle Scholar
  31. Corominas J, van Westen C, Frattini P, Cascini L, Malet JP, Fotopoulou S, Catani F, Van Den Eeckhaut M, Mavrouli O, Agliardi F, Pitilakis K, Winter MG, Pastor M, Ferlisi S, Tofani V, Hervás J, Smith JT (2014) Recommendations for the quantitative analysis of landslide risk. Bull Eng Geol Environ 73:209–263Google Scholar
  32. Corominas J, Mavrouli O, Ruiz-Carulla R (2017) Rockfall occurrence and fragmentation. In Sassa K, Mikos M, Yin Y (eds) Advancing culture of living with landslides, Springer,. 1:75–97.
  33. Crosta GB, Frattini P, Agliardi F (2013) Deep seated gravitational slope deformations in the European Alps. Tectonophysics 605:13–33CrossRefGoogle Scholar
  34. Crosta GB, Hermanns RL, Dehls J, Lari S, Sepulveda S (2016) Rock avalanches clusters along the northern Chile coastal scarp. Geomorphology.
  35. Cruden DM (1975) Major rock slides in the Rockies. Can Geotech J 13:8–20CrossRefGoogle Scholar
  36. Cruden DM (1985) Rock slope movements in the Canadian Cordillera. Can Geotech J 22:528–540CrossRefGoogle Scholar
  37. Cruden DM, Hu XQ (1993) Exhausting and steady state models for predicting landslide hazards in the Canadian Rocky Mountains. Geomorphology 8:279–285CrossRefGoogle Scholar
  38. Cruden DM, Varnes DJ (1996) Landslide types and processes. In: Landslides investigation and mitigation, A. K. Turner and R. L. Schuster, eds.: National Research Council, Transportation Research Board, Special Report 247, pp 36–75Google Scholar
  39. Davies TR, McSaveney MJ (2002) Dynamic simulation of the motion of fragmenting rock avalanches. Canadian Geotechical. Journal 39:789–798Google Scholar
  40. Delaney KB, Evans SG (2015) The 2000 Yigong landslide (Tibetian Plateau), rockslide- dammed lake and outburst flood: review, remote sensing analysis and process modeling. Geomorphology 246:377–393CrossRefGoogle Scholar
  41. Dussauge C, Grasso JR, Helmstetter A (2003) Statistical analysis of rockfall volume distributions: implications for rockfall dynamics. J Geophys Res 108(B6):2286CrossRefGoogle Scholar
  42. Dussauge-Peisser A, Helmstetter A, Grasso JR, Hanz D, Desvarreux P, Jeannin M, Giraud A (2002) Probabilistic approach to rockfall hazard assessment: potential of historical data analysis. Nat Hazards Earth Syst Sci 2:15–26CrossRefGoogle Scholar
  43. Eberhardt E, Stead D, Coggan JS (2004) Numerical analysis of initiation and progressive failure in natural rock slopes—the 1991 Randa rockslide. Int. J. Rock Mech. Mining. Sciences 41:69–87Google Scholar
  44. Escalé J (2001) La nova llei d’ordenament territorial a Andorra. In La Gestió dels Riscos naturals. Primeres Jornades CRECIT, Andorra la Vella Google Scholar
  45. Evans SG, Clague JJ (1988) Catastrophic rock avalanches in glacial environments. In: Bonnard C (ed) 5th International Symposium on Landslides, Lausanne, Switzerland, 2, pp 1153–1158Google Scholar
  46. Evans S, Hungr O (1993) The assessment of rockfall hazard at the base of talus slopes. Can Geotech J 30:620–636CrossRefGoogle Scholar
  47. Evans SG, Bishop NF, Smoll LF, Murillo PV, Delaney KB, Oliver-Smith A (2009) A reexamination of the mechanism and human impact of catastrophic mass flows originating on Nevado Huascarán, Cordillera Blanca, Peru, in 1962 and 1970. Eng Geol 108:96–118CrossRefGoogle Scholar
  48. Fell R, Corominas J, Ch B, Cascini L, Leroi E, Savage WZ, (on behalf of the JTC-1 Joint Technical Committee on Landslides and Engineered Slopes) (2008) Guidelines for landslide susceptibility, hazard and risk zoning for land use planning. Eng Geol 102:85–98CrossRefGoogle Scholar
  49. Ganerød GV, Grøneng G, Rønning JS, Dalsegg E, Elvebakk H, Tønnesen JF, Kveldsvik V, Eiken T, Blikra LH, Braathen A (2008) Geological model of the Åknes rockslide, western Norway. Eng Geol 102:1–18CrossRefGoogle Scholar
  50. Gigli G, Frodella W, Garfagnoli F, Morelli S, Mugnai F, Menna F, Casagli N (2014) 3-D geomechanical rock mass characterization for the evaluation of rockslide susceptibility scenarios. Landslides 11:131–140CrossRefGoogle Scholar
  51. Guthrie R, Evans SG (2004) Analysis of landslide frequencies and characteristics in a natural system. Coastal British Columbia. Earth Surf Process Landf 29:1321–1339CrossRefGoogle Scholar
  52. Gutiérrez-Rodríguez MC, Turu V (2013) Hidrogeología de un valle glaciar: el caso de la cubeta de Andorra (Pririneos Orientales). Parte 1: datos geoquímicos. X Simposio de Hidrogeología Granada
  53. Guttemberg B, Richter CF (1954) Seismicity of earth and associated phenomena, 2nd edn. Princeton University Press, Princeton, NJGoogle Scholar
  54. Guzzetti F, Cardinali M, Reichenbach P (1996) The influence of structural setting and lithology on landslide type and pattern. Environ Eng Geosci 2:531–555CrossRefGoogle Scholar
  55. Guzzetti F, Malamud BD, Turcotte DL, Reichenbach P (2002) Power-law correlations of landslide areas in Central Italy. Earth Planet Sci Lett 195:169–183CrossRefGoogle Scholar
  56. Guzzetti F, Reichenbach P, Wieczorek GF (2003) Rockfall hazard and risk assessment in the Yosemite Valley, California, USA. Nat Hazards Earth Syst Sci 3:491–503CrossRefGoogle Scholar
  57. Guzzetti F, Ardizzone F, Cardinali M, Rossi M, Valigi D (2009) Landslide volumes and landslide mobilization rates in Umbria, central Italy. Earth Planet Sci Lett 279:222–229CrossRefGoogle Scholar
  58. Hergarten S (2012) Topography-based modeling of large rockfalls and application to hazard assessment. Geophys Res Lett 39:L13402. CrossRefGoogle Scholar
  59. Hermanns RL, Strecker MR (1999) Structural and lithological controls on large Quaternay rock avalanches (sturzstroms) in arid northwestern Argentina. Geol Soc Am Bull 111:934–948CrossRefGoogle Scholar
  60. Hermanns RL, Niedermann S, Ivy-Ochs S, Kubik PW (2004) Rock avalanching into a landslide dammed lake causing multiple dam failure in Las Conchas valley (NW Argentina)—evidence from surface exposure dating and stratigraphic analyses. Landslides 1:113–122CrossRefGoogle Scholar
  61. Hewitt K (2002) Styles of rock-avalanche depositional complexes conditioned by very rugged terrain, Karakoram Himalaya, Pakistan. In: Evans SG, DeGraff JV (eds) Catastrophic landslides: effects, occurrence, and mechanisms 15:345–377Google Scholar
  62. Hewitt K, Clague JJ, Orwin JF (2008) Legacies of catastrophic rock slope failures in mountain landscapes. Earth Sci Rev 87:1–38CrossRefGoogle Scholar
  63. Ho KKS (2004) Recent advances in geotechnology for slope stabilization and landslide mitigation—perpective from Hong Kong. In: Lacerda WA, Ehrlich M, Fontoura SAB, Sayao ASF (eds) Landslides: Evaluation and Stabilization, vol 2. Taylor and Francis, London, pp 1507–1560Google Scholar
  64. Hovius N, Stark CP, Allen PA (1997) Supply and removal of sediment in a landslide-dominated mountain belt: Central Range, Taiwan. J Geol 108:73–89CrossRefGoogle Scholar
  65. Hsü KJ (1978) Albert Heim: observations of landslides and relevance to modern interpretations. In: Voight B (ed) Rockslides and avalanches; 1, natural phenomena. Elsevier, Amsterdam, pp 70–93Google Scholar
  66. 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 36:224–238CrossRefGoogle Scholar
  67. Hungr O, Leroueil S, Picarelli L (2014) The Varnes classification of landslides types, an update. Landslides 11:167–194CrossRefGoogle Scholar
  68. Jarman D (2006) Large rock slope failures in the highlands of Scotland: characterisation, causes and spatial distribution. Eng Geol 83:161–182CrossRefGoogle Scholar
  69. Jarman D, Calvet M, Corominas J, Delmas M, Gunnell Y (2014) Large-scale rock slope failures in the eastern Pyrenees: identifying a sparse but significant population in paraglacial and parafluvial contexts. Geogr Ann A 96(3):357–391CrossRefGoogle Scholar
  70. Kakimi T (1980) Magnitude frequency relation for displacement of minor faults and its significance in crustal deformation. Bull Geol Soc Jpn 31:467–487Google Scholar
  71. Keller B (2017) Massive rock slope failure in Central Switzerland: history, geologic–geomorphological predisposition, types and triggers, and resulting risks. Landslides.
  72. Klar A, Aharonov E, Kalderon-Asael B, Katz O (2011) Analytical and observational relations between landslide volume and surface area. J Geophys Res 116:1–10CrossRefGoogle Scholar
  73. Korup O, Clague JJ, Hermanns RL, Hewitt K, Strom AL, Weidinger JT (2007) Giant landslides, topography and erosion. Earth Planet Sci Lett 261:578–589CrossRefGoogle Scholar
  74. Lari S, Frattini P, Crosta GB (2014) A probabilistic approach for landslide hazard analysis. Eng Geol 182:3–14CrossRefGoogle Scholar
  75. Li ZH, Huang HW, Xue YD, Yin J (2009) Risk assessment of rockfall hazards on highways. Georisk 3:147–154Google Scholar
  76. Malamud BD, Turcotte DL, Guzzetti F (2004) Landslide inventories and their statistical properties. Earth Surf Process Landf 29:687–711CrossRefGoogle Scholar
  77. Marques FMSF (2008) Magnitude-frequency of sea cliff instabilities. Nat Hazards Earth Syst Sci 8:1161–1171CrossRefGoogle Scholar
  78. Massironi M, Bistacchi A, Dal Piaz GV, Monopoli B, Schiavo A (2003) Structural control on mass-movement evolution: a case study from the Vizza Valley, Italian Eastern Alps. Eclogae Geol Helv 96:85–98Google Scholar
  79. Mavrouli O, Corominas J (2017) Comparing rockfall scar volumes and kinematically detachable rock masses. Eng Geol 219:64–73CrossRefGoogle Scholar
  80. Mavrouli O, Corominas J, Jaboyedoff M (2015) Size distribution for potentially unstable rock masses and in-situ rock blocks using LIDAR generated digital elevation models. Rock Mech Rock Eng 48:1589–1604CrossRefGoogle Scholar
  81. McColl ST (2012) Paraglacial rock-slope stability. Geomorphology 153-154:1–16CrossRefGoogle Scholar
  82. Pedrazzini A, Humair F, Jaboyedoff M, Tonini M (2016) Characterisation and spatial distributionof gravitational slope deformation in the Upper Rhone catchment (Western Swiss Alps). Landslides 13:259–277CrossRefGoogle Scholar
  83. Picarelli L, Oboni F, Evans SG, Mostyn G, Fell R (2005) Hazard characterization and quantification. In: Hungr O, Fell R, Couture R, Eberthardt E(eds) Landslide risk management, Taylor and Francis, London. pp 27–61Google Scholar
  84. Pickering G, Bull JM, Sanderson DJ (1995) Sampling power-law distributions. Tectonophysics 248:1–20CrossRefGoogle Scholar
  85. Rochet L (1987) Application des modeles numeriques de propagation a l’etude des eboulements rocheux. Bull Lab Ponts et Chaussées 150(151):84–95Google Scholar
  86. Rosser N, Lim M, Petley D, Dumming S, Allison R (2007) Patterns of precursory rockfall prior to slope failure. J Geophys Res 112:F04014CrossRefGoogle Scholar
  87. Rossi M, Witt A, Guzzetti F, Malamud BD, Peruccacci S (2010) Analysis of historical landslide time series in the Emilia-Romagna region, northern Italy. Earth Surf Process Landf 35:1123–1137CrossRefGoogle Scholar
  88. Royán MJ, Abellán A, Jaboyedoff M, Vilaplana JM, Calvet J (2014) Spatio-temporal analysis of rockfall pre-failure deformation using terrestrial LiDAR. Landslides 11:697–709CrossRefGoogle Scholar
  89. Royán MJ, Abellán A, Vilaplana JM (2015) Progressive failure leading to the 3 December 2013 rockfall at Puigcercós scarp (Catalonia, Spain). Landslides 12:585–595CrossRefGoogle Scholar
  90. Santana D, Corominas J, Mavrouli O, Garcia-Selles D (2012) Magnitude-frequency relation for rockfalls using a terrestrial laser scanner. Eng Geol 145–146:50–64CrossRefGoogle Scholar
  91. Scheidegger AE (1973) On the prediction of reach and velocity of catastrophic landslides. Rock Mech 5:231–236CrossRefGoogle Scholar
  92. Selby MJ (1980) A rock mass strength classification ofr geomorphic processes: with tests from Antartica and New Zealand. Zeits. Fur Geomorphologie 24:31–51Google Scholar
  93. Selby MJ (1992) Hillslope materials and processes. University Press, OxfordGoogle Scholar
  94. Shang Y, Yang Z, Li L, Liu D, Liao Q, Wang Y (2003) A super-large landslide in Tibet in 2000: background, occurrence, disaster, and origin. Geomorphology 54:225–243CrossRefGoogle Scholar
  95. Soeters R, Van Westen CJ (1996) Slope instability, recognition, analysis and zonation. In: Turner AT, Schuster RL (eds) Landslides—investigation and mitigation, Transportation Research Board Special Report No 247. National Academy Press, Washington DC, pp 129–177Google Scholar
  96. Stark CP, Hovius N (2001) The characterization of the landslide size distributions. Geoph. Res Lett 28:1091–1094CrossRefGoogle Scholar
  97. Stead D, Wolter A (2015) A critical review of rock slope failure mechanisms: the importance of structural geology. J Struct Geol 74:1–23CrossRefGoogle Scholar
  98. Strom A (2015) Clustering of large bedrock landslides and recurrent slope failure: implications for lands seismic hazard assessment of the Tien Shan – Djungaria region. International. J Geohazards Environ 1:110–121CrossRefGoogle Scholar
  99. Sturzenegger M, Stead D (2012) The Palliser Rockslide, Canadian Rocky Mountains: characterization and modeling of a stepped failure surface. Geomorphology 138:145–161CrossRefGoogle Scholar
  100. Swain RE, England JF Jr, Bullard KL, Raff DA (2006) Guidelines for evaluating hydrologic hazards, U.S. Department of Interior, Bureau of Reclamation, Denver, CO, 83 pGoogle Scholar
  101. Turner AK, Jayaprakash GP (2012) Introduction. In: Turner AK, Schuster RL (eds) Rockfall characterization and control. Transportation Research Board. National Academy of Sciences, Whasington D.C., pp 3–20Google Scholar
  102. Turu V, Boulton G, Ros X, Peña, JL, Martí C, Bordonau J, Serrano E, Sancho C, Constante A, Pous J, González JJ, Palomar J, Herrero R, García JM (2007) Structure des grands bassins glaciaires dans le nord de la Péninsule Ibérique: comparaison entre les vallées d’Andorre (Pyerénées orientales), du Gállego (Pyrénées centrales) et du Trueba (Chaîne Cantabrique); Quaternaire, vol. 184, 309–325
  103. Turu V, Calvet M, Bordonau J, Gunnell Y, Delmas M, Vilaplana JM, Jalut G (2016) Did Pyrenean glaciers dance to the beat of global climatic events? Evidence from the Würmian sequence stratigraphy of an ice-dammed paleolake depocentre in Andorra. In: Quaternary glaciation in the Mediterranean region. Geological Society, Special Publication. London. 433Google Scholar
  104. UN/ISDR (2004) Living with risk: a global review of disaster reduction initiative. United Nations Publication, GenevaGoogle Scholar
  105. USBR (2015) Best practices in dam and levee safety risk analysis. Version 4.0 USBR, USACE.
  106. Voight B, Pariseau WG (1978) Rockslides and avalanches: an introduction. In: Voight B (ed) Rockslides and avalanches, 1 natural phenomena. Elsevier, NY, pp 1–67Google Scholar
  107. Wang X, Frattini P, Crosta G, Zhang L, Agliardi F, Lari S, Yang Z (2014) Uncertainty assessment in quantitative rockfall risk assessment. Landslides 11:711–722CrossRefGoogle Scholar
  108. Whalley WB, Douglas GR, Jonsson A (1983) The magnitude and frequency of large rockslides in Iceland in the postglacial. Geogr Ann 65A:99–110CrossRefGoogle Scholar
  109. Willenberg H, Löw S, Eberhardt E, Evans KF, Spillman T, Heinke B, Maurer H, Green AG (2008) Internal structure and deformation of an unstable crystalline rock mass above Randa (Switzerland): part I e internal structure from integrated geological and geophysical investigations. Eng. Geology 101:1–14Google Scholar
  110. Wolman MG, Miller JP (1960) Magnitude and frequency of forces in geomorphic processes. J Geol 68:54–74CrossRefGoogle Scholar
  111. Wolter A, Stead D, Clague JJ (2014) A morphologic characterisation of the 1963 Vajont Slide, Italy, using long-range terrestrial photogrammetry. Geomorphology 206:147–164CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Division of Geotechnical Engineering and Geosciences, Department of Civil and Environmental EngineeringUniversitat Politècnica de Catalunya, BarcelonaTechBarcelonaSpain
  2. 2.University of TwenteEnschedeThe Netherlands

Personalised recommendations