Articles | Volume 10, issue 2
https://doi.org/10.5194/esurf-10-165-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-10-165-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The landslide velocity
Shiva P. Pudasaini
CORRESPONDING AUTHOR
Chair of Landslide Research, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany
Institute of Geosciences, Geophysics Section, University of Bonn,
Meckenheimer Allee 176, 53115 Bonn, Germany
Michael Krautblatter
Chair of Landslide Research, Technical University of Munich, Arcisstraße 21, 80333 Munich, Germany
Related authors
Martin Mergili, Hanna Pfeffer, Andreas Kellerer-Pirklbauer, Christian Zangerl, and Shiva Prasad Pudasaini
EGUsphere, https://doi.org/10.5194/egusphere-2025-213, https://doi.org/10.5194/egusphere-2025-213, 2025
Short summary
Short summary
We present a new version of the landslide model r.avaflow. It includes a model where different materials move on top of each other instead of mixing; a model supporting the entire range from block sliding to flowing; a model for slow-moving processes; and an interface for virtual reality visualization. Based on the results for four case studies we conclude that, at the moment, our enhancements are very useful for visualization of landslides for awareness building and environmental education.
Shiva P. Pudasaini
Earth Surf. Dynam. Discuss., https://doi.org/10.5194/esurf-2022-31, https://doi.org/10.5194/esurf-2022-31, 2022
Preprint withdrawn
Short summary
Short summary
New analytical landslide velocity solutions are unified with existing solutions, provide a complete picture of landslide with accelerating & decelerating movements through entire track. Initially ascending & descending fronts result in strikingly contrasting deposition lengths. Time & space evolution with initial peaks of variable strengths lead to a spectacular propagation pattern. Numerical solutions can be replaced by cost-effective, analytical solutions, offering great practical advantages.
Benjamin Jacobs, Mohamed Ismael, Mostafa Ezzy, Markus Keuschnig, Alexander Mendler, Johanna Kieser, Michael Krautblatter, Christian U. Grosse, and Hany Helal
EGUsphere, https://doi.org/10.5194/egusphere-2025-2007, https://doi.org/10.5194/egusphere-2025-2007, 2025
This preprint is open for discussion and under review for Earth Surface Dynamics (ESurf).
Short summary
Short summary
The Mortuary Temple of Hatshepsut is one of the key heritage sites in Egypt but potentially threatened by rockfalls from a 100 m high limestone cliff. We transferred established monitoring techniques from mountainous (alpine) environments to this major cultural heritage site and test their performance in a historically sensitive desert environment. Our study shows the first event and impact analysis of rockfalls at the Temple of Hatshepsut, providing vital data towards future risk assessment.
Riccardo Scandroglio, Samuel Weber, Till Rehm, and Michael Krautblatter
Earth Surf. Dynam., 13, 295–314, https://doi.org/10.5194/esurf-13-295-2025, https://doi.org/10.5194/esurf-13-295-2025, 2025
Short summary
Short summary
Despite the critical role of water in alpine regions, its presence in bedrock is frequently neglected. This research examines the dynamics of water in fractures using 1 decade of measurements from a tunnel 50 m underground. We provide new insights into alpine groundwater dynamics, revealing that up to 800 L d-1 can flow in one fracture during extreme events. These quantities can saturate the fractures, enhance hydraulic conductivity, and generate pressures that destabilize slopes.
Samuel Weber, Jan Beutel, Michael Dietze, Alexander Bast, Robert Kenner, Marcia Phillips, Johannes Leinauer, Simon Mühlbauer, Felix Pfluger, and Michael Krautblatter
EGUsphere, https://doi.org/10.5194/egusphere-2025-1151, https://doi.org/10.5194/egusphere-2025-1151, 2025
Short summary
Short summary
On 13 June 2023, a freestanding rock pillar on the Matterhorn Hörnligrat ridge collapsed after years of weakening. Our study explores how seasonal temperature changes and water infiltration into frozen rock contributed to its failure. By combining field data, lab tests, and modeling, we reveal how warming permafrost increases rockfall risks. Our findings highlight the need for multi-method monitoring and modeling to understand rock slope failure and its links to climate change.
Martin Mergili, Hanna Pfeffer, Andreas Kellerer-Pirklbauer, Christian Zangerl, and Shiva Prasad Pudasaini
EGUsphere, https://doi.org/10.5194/egusphere-2025-213, https://doi.org/10.5194/egusphere-2025-213, 2025
Short summary
Short summary
We present a new version of the landslide model r.avaflow. It includes a model where different materials move on top of each other instead of mixing; a model supporting the entire range from block sliding to flowing; a model for slow-moving processes; and an interface for virtual reality visualization. Based on the results for four case studies we conclude that, at the moment, our enhancements are very useful for visualization of landslides for awareness building and environmental education.
Maike Offer, Samuel Weber, Michael Krautblatter, Ingo Hartmeyer, and Markus Keuschnig
The Cryosphere, 19, 485–506, https://doi.org/10.5194/tc-19-485-2025, https://doi.org/10.5194/tc-19-485-2025, 2025
Short summary
Short summary
We present a unique long-term dataset of measurements of borehole temperature, repeated electrical resistivity tomography, and piezometric pressure to investigate the complex seasonal water flow in permafrost rockwalls. Our joint analysis shows that permafrost rocks are subjected to enhanced pressurised water flow during the thaw period, resulting in push-like warming events and long-lasting rock temperature regime changes.
Felix Pfluger, Samuel Weber, Joseph Steinhauser, Christian Zangerl, Christine Fey, Johannes Fürst, and Michael Krautblatter
Earth Surf. Dynam., 13, 41–70, https://doi.org/10.5194/esurf-13-41-2025, https://doi.org/10.5194/esurf-13-41-2025, 2025
Short summary
Short summary
Our study explores permafrost–glacier interactions with a focus on their implications for preparing or triggering high-volume rock slope failures. Using the Bliggspitze rock slide as a case study, we demonstrate a new type of rock slope failure mechanism triggered by the uplift of the cold–warm dividing line in polythermal alpine glaciers, a widespread and currently under-explored phenomenon in alpine environments worldwide.
Johannes Leinauer, Michael Dietze, Sibylle Knapp, Riccardo Scandroglio, Maximilian Jokel, and Michael Krautblatter
Earth Surf. Dynam., 12, 1027–1048, https://doi.org/10.5194/esurf-12-1027-2024, https://doi.org/10.5194/esurf-12-1027-2024, 2024
Short summary
Short summary
Massive rock slope failures are a significant alpine hazard and change the Earth's surface. Therefore, we must understand what controls the preparation of such events. By correlating 4 years of slope displacements with meteorological and seismic data, we found that water from rain and snowmelt is the most important driver. Our approach is applicable to similar sites and indicates where future climatic changes, e.g. in rain intensity and frequency, may alter the preparation of slope failure.
Natalie Barbosa, Johannes Leinauer, Juilson Jubanski, Michael Dietze, Ulrich Münzer, Florian Siegert, and Michael Krautblatter
Earth Surf. Dynam., 12, 249–269, https://doi.org/10.5194/esurf-12-249-2024, https://doi.org/10.5194/esurf-12-249-2024, 2024
Short summary
Short summary
Massive sediment pulses in catchments are a key alpine multi-risk component. Combining high-resolution aerial imagery and seismic information, we decipher a multi-stage >130.000 m³ rockfall and subsequent sediment pulses over 4 years, reflecting sediment deposition up to 10 m, redistribution in the basin, and finally debouchure to the outlet. This study provides generic information on spatial and temporal patterns of massive sediment pulses in highly charged alpine catchments.
Sibylle Knapp, Michael Schwenk, and Michael Krautblatter
Earth Surf. Dynam., 10, 1185–1193, https://doi.org/10.5194/esurf-10-1185-2022, https://doi.org/10.5194/esurf-10-1185-2022, 2022
Short summary
Short summary
The Flims area in the Swiss Alps has fascinated the researchers with its complex geological history ever since. Especially the order of events related to the Tamins and Flims rockslides has long been debated. This paper presents novel results based on up to 160 m deep geophysical profiles, which show onlaps of the Bonaduz Formation onto the Tamins deposits (Ils Aults) and thus indicate that the Tamins rockslide occurred first. The consecutive evolution of this landscape is shown in four phases.
Shiva P. Pudasaini
Earth Surf. Dynam. Discuss., https://doi.org/10.5194/esurf-2022-31, https://doi.org/10.5194/esurf-2022-31, 2022
Preprint withdrawn
Short summary
Short summary
New analytical landslide velocity solutions are unified with existing solutions, provide a complete picture of landslide with accelerating & decelerating movements through entire track. Initially ascending & descending fronts result in strikingly contrasting deposition lengths. Time & space evolution with initial peaks of variable strengths lead to a spectacular propagation pattern. Numerical solutions can be replaced by cost-effective, analytical solutions, offering great practical advantages.
Bernd Etzelmüller, Justyna Czekirda, Florence Magnin, Pierre-Allain Duvillard, Ludovic Ravanel, Emanuelle Malet, Andreas Aspaas, Lene Kristensen, Ingrid Skrede, Gudrun D. Majala, Benjamin Jacobs, Johannes Leinauer, Christian Hauck, Christin Hilbich, Martina Böhme, Reginald Hermanns, Harald Ø. Eriksen, Tom Rune Lauknes, Michael Krautblatter, and Sebastian Westermann
Earth Surf. Dynam., 10, 97–129, https://doi.org/10.5194/esurf-10-97-2022, https://doi.org/10.5194/esurf-10-97-2022, 2022
Short summary
Short summary
This paper is a multi-authored study documenting the possible existence of permafrost in permanently monitored rockslides in Norway for the first time by combining a multitude of field data, including geophysical surveys in rock walls. The paper discusses the possible role of thermal regime and rockslide movement, and it evaluates the possible impact of atmospheric warming on rockslide dynamics in Norwegian mountains.
Carolin Kiefer, Patrick Oswald, Jasper Moernaut, Stefano Claudio Fabbri, Christoph Mayr, Michael Strasser, and Michael Krautblatter
Earth Surf. Dynam., 9, 1481–1503, https://doi.org/10.5194/esurf-9-1481-2021, https://doi.org/10.5194/esurf-9-1481-2021, 2021
Short summary
Short summary
This study provides amphibious investigations of debris flow fans (DFFs). We characterize active DFFs, combining laser scan and sonar surveys at Plansee. We discover a 4000-year debris flow record in sediment cores, providing evidence for a 7-fold debris flow frequency increase in the 20th and 21st centuries, coincident with 2-fold enhanced rainstorm activity in the northern European Alps. Our results indicate climate change as being the main factor controlling debris flow activity.
Philipp Mamot, Samuel Weber, Saskia Eppinger, and Michael Krautblatter
Earth Surf. Dynam., 9, 1125–1151, https://doi.org/10.5194/esurf-9-1125-2021, https://doi.org/10.5194/esurf-9-1125-2021, 2021
Short summary
Short summary
The mechanical response of permafrost degradation on high-mountain rock slope stability has not been calculated in a numerical model yet. We present the first approach for a model with thermal and mechanical input data derived from laboratory and field work, and existing concepts. This is applied to a test site at the Zugspitze, Germany. A numerical sensitivity analysis provides the first critical stability thresholds related to the rock temperature, slope angle and fracture network orientation.
Doris Hermle, Markus Keuschnig, Ingo Hartmeyer, Robert Delleske, and Michael Krautblatter
Nat. Hazards Earth Syst. Sci., 21, 2753–2772, https://doi.org/10.5194/nhess-21-2753-2021, https://doi.org/10.5194/nhess-21-2753-2021, 2021
Short summary
Short summary
Multispectral remote sensing imagery enables landslide detection and monitoring, but its applicability to time-critical early warning is rarely studied. We present a concept to operationalise its use for landslide early warning, aiming to extend lead time. We tested PlanetScope and unmanned aerial system images on a complex mass movement and compared processing times to historic benchmarks. Acquired data are within the forecasting window, indicating the feasibility for landslide early warning.
Michael Krautblatter, Lutz Schirrmeister, and Josefine Lenz
Polarforschung, 89, 69–71, https://doi.org/10.5194/polf-89-69-2021, https://doi.org/10.5194/polf-89-69-2021, 2021
Ingo Hartmeyer, Robert Delleske, Markus Keuschnig, Michael Krautblatter, Andreas Lang, Lothar Schrott, and Jan-Christoph Otto
Earth Surf. Dynam., 8, 729–751, https://doi.org/10.5194/esurf-8-729-2020, https://doi.org/10.5194/esurf-8-729-2020, 2020
Short summary
Short summary
Climate warming is causing significant ice surface lowering even in the uppermost parts of alpine glaciers. Using terrestrial lidar, we quantify rockfall in freshly exposed cirque walls. During 6-year monitoring (2011–2017), an extensive dataset was established and over 600 rockfall events identified. Drastically increased rockfall activity following ice retreat can clearly be observed as 60 % of the rockfall volume detached from less than 10 m above the glacier surface.
Ingo Hartmeyer, Markus Keuschnig, Robert Delleske, Michael Krautblatter, Andreas Lang, Lothar Schrott, Günther Prasicek, and Jan-Christoph Otto
Earth Surf. Dynam., 8, 753–768, https://doi.org/10.5194/esurf-8-753-2020, https://doi.org/10.5194/esurf-8-753-2020, 2020
Short summary
Short summary
Rockfall size and frequency in two deglaciating cirques in the Central Alps, Austria, is analysed based on 6-year rockwall monitoring with terrestrial lidar (2011–2017). The erosion rates derived from this dataset are very high due to a frequent occurrence of large rockfalls in freshly deglaciated areas. The results obtained are important for rockfall hazard assessments, as, in rockwalls affected by glacier retreat, historical rockfall patterns are not good predictors of future events.
Cited articles
Baselt, I., de Oliveira, G. Q., Fischer, J.-T., and Pudasaini, S. P.: Evolution of stony debris flows in laboratory experiments, Geomorphology, 372, 107431, https://doi.org/10.1016/j.geomorph.2020.107431, 2021.
Berger, C., McArdell, B. W., and Schlunegger, F.: Direct measurement of
channel erosion by debris flows, Illgraben, Switzerland, J. Geophys. Res.-Earth, 116, F01002, https://doi.org/10.1029/2010JF001722, 2011.
Bertini, L., Cancrini, N., and Jona-Lasinio, G.: The Stochastic Burgers Equation, Commun. Math. Phys., 165, 211–232, 1994.
Burgers, J. M.: A mathematical model illustrating the theory of turbulence, in: Advances in Applied Mechanics, edited by: von Mises, R. and von Karman, T., Academic Press Inc., New York, 171–199, https://doi.org/10.1016/S0065-2156(08)70100-5, 1948.
Cascini, L., Cuomo, S., Pastor, M., Sorbino, G., and Piciullo, L.: SPH run-out modelling of channelized landslides of the flow type, Geomorphology, 214, 502–513, 2014.
Chalfen, M. and Niemiec, A.: Analytical and numerical solution of Saint-Venant equations, J. Hydrol., 86, 1–13, 1986.
Christen, M., Bartelt, P., and Gruber, U.: AVAL-1D: an avalanche dynamics program for the practice, in: Vol. 2, 1st congress “Interpraevent
in the Pacific Rim”, Conference proceedings “Protection of habitat against floods, debris flows and avalanches”, 14–18 October 2002, Matsumoto, Japan,, 715–725, https://www.dora.lib4ri.ch/wsl/islandora/object/wsl:17895 (last access: 6 March 2022), 2002.
Christen, M., Kowalski, J., and Bartelt, P.: Ramms: numerical simulation
of dense snow avalanches in three-dimensional terrain, Cold Reg. Sci. Technol., 63, 1–14, 2010.
Cole, J. D.: On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math., 9, 225–236, 1951.
Cui, P., Zeng, C., and Lei, Y.: Experimental analysis on the impact force of viscous debris flow, Earth Surf. Proc. Land., 40, 1644–1655, 2015.
Cuomo, S., Pastor, M., Capobianco, V., and Cascini, L.: Modelling the space time evolution of bed entrainment for flow-like landslides, Eng. Geol., 212, 10–20, 2016.
de Haas, T. and van Woerkom, T.: Bed scour by debris flows: experimental investigation of effects of debris flow composition, Earth Surf. Proc. Land., 41, 1951–1966, 2016.
de Haas, T., Nijland, W., de Jong, S. M., and McArdell, B. W.: How memory
effects, check dams, and channel geometry control erosion and deposition by debris flows, Scient. Rep., 10, 14024, https://doi.org/10.1038/s41598-020-71016-8, 2020.
Di Cristo, C., Iervolino, M., and Vacca, A.: Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis, J. Hydrol., 559, 585–595, 2018.
Dietrich, A. and Krautblatter, M.: Deciphering controls for debris-flow
erosion derived from a liDAR-recorded extreme event and a calibrated numerical model (Rossbichelbach, Germany), Earth Surf. Proc. Land., 44, 1346–1361, 2019.
Dowling, C. A. and Santi, P. M.: Debris flows and their toll on human life: a global analysis of debris-flow fatalities from 1950 to 2011, Nat. Hazards, 71, 203–227, 2014.
Erismann, T. H. and Abele, G.: Dynamics of Rockslides and Rockfalls, Springer, New York, ISBN 978-3-662-04639-5, 2001.
Evans, S. G., Bishop, N. F., Smoll, L. F., Murillo, P. V., Delaney, K. B., and Oliver-Smith, A.: A re-examination of the mechanism and human impact of catastrophic mass flows originating on Nevado Huascaran, Cordillera Blanca, Peru in 1962 and 1970, Eng. Geol., 108, 96–118, 2009.
Faraoni, V.: Helmoltz problem for the Riccati equation from an analogous Friedmann equation, Eur. Phys. J. C, 82, 13, https://doi.org/10.1140/epjc/s10052-021-09966-0, 2022.
Faug, T.: Depth-averaged analytic solutions for free-surface granular flows impacting rigid walls down inclines, Phys. Rev. E, 92, 062310, https://doi.org/10.1103/PhysRevE.92.062310, 2015.
Faug, T., Chanut, B., Beguin, R., Naaim, M., Thibert, E., and Baraudi, D.:
A simple analytical model for pressure on obstacles induced by snow avalanches, Ann. Glaciol., 51, 1–8, 2010.
Frank, F., McArdell, B. W., Huggel, C., and Vieli, A.: The importance of entrainment and bulking on debris flow runout modeling: examples from the Swiss Alps, Nat. Hazards Earth Syst. Sci., 15, 2569–2583, https://doi.org/10.5194/nhess-15-2569-2015, 2015.
Gauer, P.: Considerations on scaling behavior in avalanche flow along cycloidal and parabolic tracks, Cold Reg. Sci. Technol., 151, 34–46, 2018.
Ghosh Hajra, S., Kandel, S., and Pudasaini, S. P.: Optimal systems of Lie
subalgebras for a two-phase mass flow, Int. J. Non-Lin. Mech., 88, 109–121, 2017.
Ghosh Hajra, S., Kandel, S., and Pudasaini, S. P.: On analytical solutions of a two-phase mass flow model, Nonlin. Anal. Real World Appl., 41, 412–427, 2018.
Gubler, H.: Comparison of three models of avalanche dynamics, Ann. Glaciol., 13, 82–89, 1989.
Havens, S., Marshall, H.-P., Johnson, J. B., and Nicholson, B.: Calculating the velocity of a fast-moving snow avalanche using an infrasound array, Geophys. Res. Lett., 41, 6191–6198, 2014.
Highland, L. M. and Bobrowsky, P.: The landslide handbook – A guide to understanding landslides: Reston, Virginia, US Geological Survey Circular 1325, US Gelogical Survey, p. 129, https://pubs.usgs.gov/circ/1325/ (last access: 6 March 2022), 2008.
Hopf, E.: The partial differential equation , Comm. Pure Appl. Math., 3, 201–230, 1950.
Huggel, C., Zgraggen-Oswald, S., Haeberli, W., Kääb, A., Polkvoj, A., Galushkin, I., and Evans, S. G.: The 2002 rock/ice avalanche at Kolka/Karmadon, Russian Caucasus: assessment of extraordinary avalanche formation and mobility, and application of QuickBird satellite imagery, Nat. Hazards Earth Syst. Sci., 5, 173–187, https://doi.org/10.5194/nhess-5-173-2005, 2005.
Iverson, R. M., Reid, M. E., Logan, M., Lahusen, R. G., Godt, J. W., and Griswold, J. P.: Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment, Nat. Geosci., 4, 116–121, 2011.
Iverson, R. M. and Ouyang, C.: Entrainment of bed material by earth-surface mass flows: review and reformulation of depth-integrated theory, Rev. Geophys., 53, 27–58, 2015.
Johannesson, T., Gauer, P., Issler, D., and Lied, K.: The Design of Avalanche Protection Dams, Recent Practical and Theoretical Developments, edited by: Barbolini, M., Domaas, U., Harbitz, C. B., Johannesson, T., Gauer, P., Issler, D., Lied, K., Faug, T., and Naaim, M., European Commision, Directorate General for Research, ISBN 978-92-79-08885-8, 2009.
Kattel, P., Khattri, K., Pokhrel, P., Kafle, J., Tuladhar, B., and Pudasaini, S.,: Simulating glacial lake outburst floods with a two-phase mass flow model, Ann. Glaciol., 57, 349–358, 2016.
Kattel, P., Kafle, J., Fischer, J.-T., Mergili, M., Tuladhar, B. M., and
Pudasaini, S. P.: Interaction of two-phase debris flow with obstacles, Eng. Geol., 242, 197–217, 2018.
Körner, H. J.: The Energy-Line Method in the Mechanics of avalanches, J. Glaciol., 26, 501–505, 1980.
Lanzoni, S., Gregoretti, C., and Stancanelli, L. M.: Coarse-grained debris flow dynamics on erodible beds, J. Geophys. Res.-Earth, 122, 592–614, 2017.
Le, L. and Pitman, E. B.: A model for granular flows over an erodible surface, SIAM J. Appl. Math., 70, 1407–1427, 2009.
Li, P., Hu, K., and Wang, X.: Debris flow entrainment rates in non-uniform channels with convex and concave slopes, J. Hydraul. Res., 56, 1–12, 2017.
Liu, W., Yang, Z., and He, S.: Modeling the landslide-generated debris flow from formation to propagation and run-out by considering the effect of vegetation, Landslides, 18, 43–58, 2021.
Lu, P. Y., Yang, X. G., Xu, F. G., Hou, T. X., and Zhou, J. W.: An analysis of the entrainment effect of dry debris avalanches on loose bed materials, SpringerPlus, 5, 1621, https://doi.org/10.1186/s40064-016-3272-4, 2016.
McClung, D. M.: Derivation of Voellmy's Maximum Speed and Run-Out Estimates from a Centre-of-Mass Model, J. Glaciol., 29, 350–352, 1983.
McCoy, S. W., Kean, J. W., Coe, J. A., Tucker, G. E., Staley, D. M., and
Wasklewicz, T. A.: Sediment entrainment by debris flows: In situ measurements from the headwaters of a steep catchment, J. Geophys. Res., 117, F03016, https://doi.org/10.1029/2011JF002278, 2012.
McDougall, S. and Hungr, O.: Dynamic modelling of entrainment in rapid
landslides, Can. Geotech. J., 42, 1437–1448, 2005.
Medina, V., Hürlimann, M., and Bateman, A.: Application of FLATModel, a
2D finite volume code, to debris flows in the northeastern part of the Iberian Peninsula, Landslides, 5, 127–142, 2008.
Mergili, M., Fischer, J.-T., Krenn, J., and Pudasaini, S. P.: r.avaflow v1, an advanced open-source computational framework for the propagation and interaction of two-phase mass flows, Geosci. Model Dev., 10, 553–569, https://doi.org/10.5194/gmd-10-553-2017, 2017.
Mergili, M., Emmer, A., Juricova, A., Cochachin, A., Fischer, J.-T., Huggel, C., and Pudasaini, S. P.: How well can we simulate complex hydro-geomorphic process chains? The 2012 multi-lake outburst flood in the Santa Cruz Valley (Cordillera Blanca, Peru), Earth Surf. Proc. Land., 43,
1373–1389, 2018.
Mergili, M., Pudasaini, S. P., Emmer, A., Fischer, J.-T., Cochachin, A., and Frey, H.: Reconstruction of the 1941 GLOF process chain at Lake Palcacocha (Cordillera Blanca, Peru), Hydrol. Earth Syst. Sci., 24, 93–114, https://doi.org/10.5194/hess-24-93-2020, 2020a.
Mergili, M., Jaboyedoff, M., Pullarello, J., and Pudasaini, S. P.: Back calculation of the 2017 Piz Cengalo–Bondo landslide cascade with r.avaflow: what we can do and what we can learn, Nat. Hazards Earth Syst. Sci., 20, 505–520, https://doi.org/10.5194/nhess-20-505-2020, 2020b.
Montecinos, G. I.: Analytic solutions for the Burgers equation with source terms, arXiv preprint: 1503.09079v1, 2015.
Nadjafikhah, M.: Exact solution of generalized inviscid Burgers' equation, arXiv preprint: 0908.3601v1, 2009.
Parez, S. and Aharonov, E.: Long runout landslides: a solution from granular mechanics, Front. Phys., 3, 80, https://doi.org/10.3389/fphy.2015.00080, 2015.
Perla, R., Cheng, T. T., and McClung, D. M.: A two-parameter model for snow-avalanche motion, J. Glaciol., 26, 197–207, 1980.
Pilvar, M., Pouraghniaei, M. J., and Shakibaeinia, A.: Two-dimensional sub-aerial, submerged, and transitional granular slides, Phys. Fluids, 31, 113303, https://doi.org/10.1063/1.5121881, 2019.
Pudasaini, S. P.: Some exact solutions for debris and avalanche flows, Phys. Fluids, 23, 043301, https://doi.org/10.1063/1.3570532, 2011.
Pudasaini, S. P.: A general two-phase debris flow model, J. Geophys. Res., 117, F03010, https://doi.org/10.1029/2011JF002186, 2012.
Pudasaini, S. P.: A novel description of fluid flow in porous and debris materials, Eng. Geol., 202, 62–73, 2016.
Pudasaini, S. P.: A full description of generalized drag in mixture mass flows, Eng. Geol., 265, 105429, https://doi.org/10.1016/j.enggeo.2019.105429, 2020.
Pudasaini, S. P. and Fischer, J.-T.: A mechanical erosion model for two-phase mass flows, Int. J. Multiphase Flow, 132, 103416, https://doi.org/10.1016/j.ijmultiphaseflow.2020.103416, 2020.
Pudasaini, S. P. and Hutter, K.: Avalanche Dynamics: Dynamics of Rapid Flows of Dense Granular Avalanches, Springer, Berlin, New York, ISBN 978-3-540-32687-8, 2007.
Pudasaini, S. P. and Krautblatter, M.: The mechanics of landslide mobility with erosion, Nat. Commun., 12, 6793, https://doi.org/10.1038/s41467-021-26959-5, 2021a.
Pudasaini, S. P. and Krautblatter, M.: The Landslide Velocity, arxiv: preprint,
https://arxiv.org/pdf/2103.10939.pdf (last access: 7 March 2022), 2021b.
Pudasaini, S. P. and Mergili, M.: A multi-phase mass flow model, J. Geophys. Res.-Earth, 124, 2920–2942, 2019.
Pudasaini, S. P. and Miller, S. A.: The hypermobility of huge landslides and avalanches, Eng. Geol., 157, 124–132, 2013.
Pudasaini, S. P., Ghosh Hajra, S., Kandel, S., and Khattri, K. B.: Analytical
solutions to a nonlinear diffusion-advection equation, Z. Angew. Math. Phys., 69, 150, https://doi.org/10.1007/s00033-018-1042-6, 2018.
Qiao, C., Ou, G., and Pan, H.: Numerical modelling of the long runout character of 2015 Shenzhen landslide with a general two-phase mass flow model, Bull. Eng. Geol. Environ. 78, 3281–3294, 2019.
Razis, D., Kanellopoulos, G., and der Weele, K.: The granular monoclinal
wave, J. Fluid Mech., 843, 810–846, 2018.
Rui, Y. and Yin, M.: An Analytical Solution for the Run-Out of Submarine Debris Flows, Mar. Geod., 42, 246–262, 2019.
Saingier, G., Deboeuf, S., and Lagree, P.-Y.: On the front shape of an inertial granular flow down a rough incline, Phys. Fluids, 28, 053302,
https://doi.org/10.1063/1.4948401, 2016.
Salm, B.: Contribution to avalanche dynamics, in: IAHS Publ. No. 69, International Symposium on Scientific Aspects of Snow and Ice Avalanches, 1965, Davos, 199–214, 1966.
Schaerer, P. A.: Friction coefficients and speed of flowing avalanches, in: IAHS-AISH Pub. 114, Snow Mechanics: Proceedings of the Grindelwald Symposium, April 1974, Int. Assoc. Sci. Hydro., 425–432, https://nrc-publications.canada.ca/fra/voir/td/?id=1d89f442-5be5-4c1c-bf84-ff3877e07189 (last access: 6 March 2022), 1975.
Scheidegger, A. E.: On the Prediction of the Reach and Velocity of Catastrophic Landslides, Rock Mech., 5, 231–236, 1973.
Schürch, P., Densmore, A. L., Rosser, N. J., and McArdell, B. W.: Dynamic controls on erosion and deposition on debris-flow fans, Geology, 39, 827–830, 2011.
Shugar, D. H., Jacquemart, M., Shean, D., et al.: A massive rock and ice avalanche caused the 2021 disaster at Chamoli, Indian Himalaya, Science, 373, 300–306, 2021.
Tai, Y.-C., Gray, J. M. N. T., Hutter, K., and Noelle, S.: Flow of dense
avalanches past obstructions, Ann. Glaciol., 32, 281–284, 2001.
Tai, Y.-C., Noelle, S., Gray, J. M. N. T., and Hutter, K.: Shock-capturing and front-tracking methods for granular avalanches, J. Comput. Phys., 175, 269–301, 2002.
Theule, J. I., Liebault, F., Laigle, D., Loye, A., and Jaboyedoff, M.: Channel scour and fill by debris flows and bedload transport, Geomorphology, 243, 92–105, 2015.
Voellmy, A.: Über die Zerstörungskraft von Lawinen, in:
Schweizerische Bauzeitung, Jahrg. 73, Ht. 12., 159–162; Ht. 15, 212–217;
Ht. 17, 246–249: Ht. 19, 280–285, On the destructive force of avalanches,
Translation No. 2, Alta, Avalanche Study Center, USDA, Forest Service, 1955.
Walter, F., Amann, S., Kos, A., Kenner. R., Phillips, M., de Preux, A., Huss, M., Tognacca, C., Clinton, J., Diehl, T., and Bonanomi, Y.: Direct observations of a three million cubic meter rock‐slope collapse with almost immediate initiation of ensuing debris flows, Geomorphology, 351, 106933, https://doi.org/10.1016/j.geomorph.2019.106933, 2020.
Short summary
We present the first physics-based general landslide velocity model incorporating internal deformation and external forces. Voellmy–inviscid Burgers' equations are specifications of the novel advective–dissipative system. Unified analytical solutions constitute a new foundation of landslide velocity, providing key information to instantly estimate impact forces and describe breaking waves and folding, revealing that landslide dynamics are architectured by advection and reigned by forcing.
We present the first physics-based general landslide velocity model incorporating internal...