# Shallow Landslides and Rockfalls Velocity Assessment at Regional Scale: A Methodology Based on a Morphometric Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Heim Method

#### 2.3. Input Data Preparation and Elaboration

- (1)
- L’—horizontal distance of each point within the landslide from the top;
- (2)
- Tanβ—tangent of the propagation angle (constant for each landslide);
- (3)
- G—vertical distance between the top and the energy line, G = L’ × tanβ;
- (4)
- Q
_{2}—height of the energy line, Q_{2}= Qmax–G; - (5)
- k—kinetic load, k = Q
_{2}—landslide point elevation (DEM).

## 3. Results

#### Validation of the Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Cruden, D.M. A Simple Definition of a Landslide. Bull. Int. Assoc. Eng. Geol.
**1991**, 43, 27–29. [Google Scholar] [CrossRef] - Nadim, F.; Kjekstad, O.; Peduzzi, P.; Herold, C.; Jaedicke, C. Global Landslide and Avalanche Hotspots. Landslides
**2006**, 3, 159–173. [Google Scholar] [CrossRef] - Cruden, D.M.; Varnes, D.J. Landslides Types and Processes. Landslide: Investigation and Mitigation, Transportation Research Board; Natural Academy Press: Washington, DC, USA, 1994. [Google Scholar]
- Hürlimann, M.; Rickenmann, D.; Medina, V.; Bateman, A. Evaluation of Approaches to Calculate Debris-Flow Parameters for Hazard Assessment. Eng. Geol.
**2008**, 102, 152–163. [Google Scholar] [CrossRef] - Jakob, M.; Stein, D.; Ulmi, M. Vulnerability of Buildings to Debris Flow Impact. Nat. Hazards
**2012**, 60, 241–261. [Google Scholar] [CrossRef] - Tofani, V.; Del Ventisette, C.; Moretti, S.; Casagli, N. Integration of Remote Sensing Techniques for Intensity Zonation within a Landslide Area: A Case Study in the Northern Apennines, Italy. Remote Sens.
**2014**, 6, 907–924. [Google Scholar] [CrossRef] [Green Version] - Solari, L.; Bianchini, S.; Franceschini, R.; Barra, A.; Monserrat, O.; Thuegaz, P.; Bertolo, D.; Crosetto, M.; Catani, F. Satellite Interferometric Data for Landslide Intensity Evaluation in Mountainous Regions. Int. J. Appl. Earth Obs. Geoinf.
**2020**, 87, 102028. [Google Scholar] [CrossRef] - Kim, M.-I.; Kwak, J.-H. Assessment of Building Vulnerability with Varying Distances from Outlet Considering Impact Force of Debris Flow and Building Resistance. Water
**2020**, 12, 2021. [Google Scholar] [CrossRef] - Novellino, A.; Cesarano, M.; Cappelletti, P.; Di Martire, D.; Di Napoli, M.; Ramondini, M.; Sowter, A.; Calcaterra, D. Slow-Moving Landslide Risk Assessment Combining Machine Learning and InSAR Techniques. Catena
**2021**, 203, 105317. [Google Scholar] [CrossRef] - Arattano, M.; Marchi, L. Measurements of Debris Flow Velocity through Cross-Correlation of Instrumentation Data. Nat. Hazards Earth Syst. Sci.
**2005**, 5, 137–142. [Google Scholar] [CrossRef] [Green Version] - Dorren, L.K.A.; Berger, F.; le Hir, C.; Mermin, E.; Tardif, P. Mechanisms, Effects and Management Implications of Rockfall in Forests. For. Ecol. Manag.
**2005**, 215, 183–195. [Google Scholar] [CrossRef] - Bardi, F.; Raspini, F.; Frodella, W.; Lombardi, L.; Nocentini, M.; Gigli, G.; Morelli, S.; Corsini, A.; Casagli, N. Monitoring the Rapid-Moving Reactivation of Earth Flows by Means of GB-InSAR: The April 2013 Capriglio Landslide (Northern Appennines, Italy). Remote Sens.
**2017**, 9, 165. [Google Scholar] [CrossRef] [Green Version] - Duncan, J.M. State of the art: Limit equilibrium and finite-element analysis of slopes. J. Geotech. Eng.
**1996**, 122, 577–596. [Google Scholar] [CrossRef] - Pastor, M.; Blanc, T.; Haddad, B.; Petrone, S.; Sanchez Morles, M.; Drempetic, V.; Issler, D.; Crosta, G.B.; Cascini, L.; Sorbino, G.; et al. Application of a SPH Depth-Integrated Model to Landslide Run-out Analysis. Landslides
**2014**, 11, 793–812. [Google Scholar] [CrossRef] [Green Version] - Lan, H.; Derek Martin, C.; Lim, C.H. RockFall Analyst: A GIS Extension for Three-Dimensional and Spatially Distributed Rockfall Hazard Modeling. Comput. Geosci.
**2007**, 33, 262–279. [Google Scholar] [CrossRef] - Hungr, O. A Model for the Runout Analysis of Rapid Flow Slides, Debris Flows, and Avalanches. Can. Geotech. J.
**1995**, 32, 610–623. [Google Scholar] [CrossRef] - Wichmann, V. The Gravitational Process Path (GPP) Model (v1.0)–A GIS-Basedsimulation Framework for Gravitational Processes. Geosci. Model Dev.
**2017**, 10, 3309–3327. [Google Scholar] [CrossRef] [Green Version] - Prochaska, A.B.; Santi, P.M.; Higgins, J.D.; Cannon, S.H. A study of methods to estimate debris flow velocity. Landslides
**2008**, 5, 431–444. [Google Scholar] [CrossRef] - Carlà, T.; Intrieri, E.; Di Traglia, F.; Nolesini, T.; Gigli, G.; Casagli, N. Guidelines on the Use of Inverse Velocity Method as a Tool for Setting Alarm Thresholds and Forecasting Landslides and Structure Collapses. Landslides
**2017**, 14, 517–534. [Google Scholar] [CrossRef] [Green Version] - Corominas, J.; van Westen, C.; Frattini, P.; Cascini, L.; Malet, J.-P.; Fotopoulou, S.; Catani, F.; Van Den Eeckhaut, M.; Mavrouli, O.; Agliardi, F.; et al. Recommendations for the Quantitative Analysis of Landslide Risk. Bull. Eng. Geol. Environ.
**2014**, 73, 209–263. [Google Scholar] [CrossRef] - Fell, R.; Corominas, J.; Bonnard, C.; Cascini, L.; Leroi, E.; Savage, W.Z. Guidelines for landslide susceptibility, hazard and risk zoning for land-use planning. Eng. Geol.
**2008**, 102, 99–111. [Google Scholar] [CrossRef] [Green Version] - Pudasaini, S.P.; Krautblatter, M. The Landslide Velocity. Earth Surf. Dyn.
**2022**, 10, 165–189. [Google Scholar] [CrossRef] - Bayer, B.; Simoni, A.; Mulas, M.; Corsini, A.; Schmidt, D. Deformation Responses of Slow Moving Landslides to Seasonal Rainfall in the Northern Apennines, Measured by InSAR. Geomorphology
**2018**, 308, 293–306. [Google Scholar] [CrossRef] - Raspini, F.; Bianchini, S.; Ciampalini, A.; Del Soldato, M.; Solari, L.; Novali, F.; Del Conte, S.; Rucci, A.; Ferretti, A.; Casagli, N. Continuous, Semi-Automatic Monitoring of Ground Deformation Using Sentinel-1 Satellites. Sci. Rep.
**2018**, 8, 7253. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Crippa, C.; Valbuzzi, E.; Frattini, P.; Crosta, G.B.; Spreafico, M.C.; Agliardi, F. Semi-Automated Regional Classification of the Style of Activity of Slow Rock-Slope Deformations Using PS InSAR and SqueeSAR Velocity Data. Landslides
**2021**, 18, 2445–2463. [Google Scholar] [CrossRef] - Pawluszek-Filipiak, K.; Borkowski, A.; Motagh, M. Multi-Temporal Landslide Activity Investigation by Spaceborne SAR Interferometry: The case study of Polish Carpathians. Remote Sens. Appl. Soc. Environ.
**2021**, 24, 100629. [Google Scholar] [CrossRef] - Heim, A. Bergsturz und Menschenleben; Fretz und Wasmuth: Zurich, Switzerland, 1932. [Google Scholar]
- Cignetti, M.; Manconi, A.; Manunta, M.; Giordan, D.; De Luca, C.; Allasia, P.; Ardizzone, F. Taking Advantage of the ESA G-POD Service to Study Ground Deformation Processes in High Mountain Areas: A Valle d’Aosta Case Study, Northern Italy. Remote Sens.
**2016**, 8, 852. [Google Scholar] [CrossRef] [Green Version] - Ratto, S.; Giardino, M.; Giordan, D.; Alberto, W.; Armand, M. Carta dei Fenomeni Franosi della Valle d’Aosta; Tipografia Valdostana: Aosta, Italy, 2007. [Google Scholar]
- Trigila, A.; Iadanza, C.; Guerrieri, L. The IFFI Project (Italian Landslide Inventory): Methodology and Results. Guidelines for Mapping Areas at Risk of Landslides in Europe; APAT: Rome, Italy, 2007; pp. 15–18. [Google Scholar] [CrossRef]
- Trigila, A.; Iadanza, C. Landslides in Italy. Special Report; Italian National Institute for Environmental Protection and Research (ISPRA): Rome, Italy, 2008.
- Ratto, S.; Bonetto, F.; Comoglio, C. The October 2000 Flooding in Valle d’Aosta (Italy): Event Description and Land Planning Measures for the Risk Mitigation. Int. J. River Basin Manag.
**2003**, 1, 105–116. [Google Scholar] [CrossRef] - Giardino, M.; Giordan, D.; Ambrogio, S.G.I.S. Technologies for Data Collection, Management and Visualization of Large Slope Instabilities: Two Applications in the Western Italian Alps. Nat. Hazards Earth Syst. Sci.
**2004**, 4, 197–211. [Google Scholar] [CrossRef] - Cossart, E.; Braucher, R.; Fort, M.; Bourlès, D.L.; Carcaillet, J. Slope Instability in Relation to Glacial Debuttressing in Alpine Areas (Upper Durance Catchment, Southeastern France): Evidence from Field Data and 10Be Cosmic Ray Exposure Ages. Geomorphology
**2008**, 95, 3–26. [Google Scholar] [CrossRef] - Martinotti, G.; Giordan, D.; Giardino, M.; Ratto, S. Controlling Factors for Deep-Seated Gravitational Slope Deformation (DSGSD) in the Aosta Valley (NW Alps, Italy). Geol. Soc. Lond. Spec. Publ.
**2011**, 351, 113–131. [Google Scholar] [CrossRef] - Crosta, G.B.; Frattini, P.; Agliardi, F. Deep Seated Gravitational Slope Deformations in the European Alps. Tectonophysics
**2013**, 605, 13–33. [Google Scholar] [CrossRef] - Canuti, P.; Casagli, N. Considerazioni sulla Valutazione del Rischio di Frana. Fenomeni Franosi e Centri Abitati. Atti del Convegno di Bologna; Consiglio Nazionale delle Ricerche: Rome, Italy, 1996.
- Tarquini, S.; Nannipieri, L. The 10 M-Resolution TINITALY DEM as a Trans-Disciplinary Basis for the Analysis of the Italian Territory: Current Trends and New Perspectives. Geomorphology
**2017**, 281, 108–115. [Google Scholar] [CrossRef] - Jahn, J. Entwaldung und Steinschlag. In Proceedings of the International Congress Interpraevent, Graz, Austria, 4–8 July 1988; Volume 1, pp. 185–198. [Google Scholar]
- Zinggeler, A. Steinschlagsimulation in Gebirgswa Ldern: Modellierung der Relevanten Teilprozesse. Master’s Thesis, University of Bern, Bern, Switzerland, 1990; p. 116. [Google Scholar]
- Gsteiger, P. Steinschlagschutzwald. Ein Beitrag zur Abgrenzung, Beurteilung und Bewirtschaftung. Schweiz. Z. Forstwes.
**1993**, 144, 115–132. [Google Scholar] - Doche, O. Etude Experimentale de Chutes de Blocs en Forêt. In Cemagref Doc. 97/0898; Cemagref/Institut des Sciences et Techniques de Grenoble (ISTG): Grenoble, France, 1997; p. 130. [Google Scholar]
- Perret, S.; Dolf, F.; Kienholz, H. Rockfalls into Forests: Analysis and Simulation of Rockfall Trajectories -Considerations with Respect to Mountainous Forests in Switzerland. Landslides
**2004**, 1, 123–130. [Google Scholar] [CrossRef] - Iverson, R.M. The Physics of Debris Flows. Rev. Geophys.
**1997**, 35, 245–296. [Google Scholar] [CrossRef] [Green Version] - Rickenmann, D. Empirical relationships for debris flows. Nat. Hazards
**1999**, 19, 47–77. [Google Scholar] [CrossRef] - Goetz, J.; Kohrs, R.; Parra Hormazábal, E.; Bustos Morales, M.; Belén Araneda Riquelme, M.; Henríquez, C.; Brenning, A. Optimizing and Validating the Gravitational Process Path Model Forregional Debris-Flow Runout Modelling. Nat. Hazards Earth Syst. Sci.
**2021**, 21, 2543–2562. [Google Scholar] [CrossRef] - Perla, R.; Cheng, T.T.; McClung, D.M. A two-parameter model of snow-avalanche motion. J. Glaciol.
**1980**, 26, 197–207. [Google Scholar] [CrossRef] [Green Version] - Salvatici, T.; Tofani, V.; Rossi, G.; D’Ambrosio, M.; Tacconi Stefanelli, C.; Masi, E.B.; Rosi, A.; Pazzi, V.; Vannocci, P.; Petrolo, M.; et al. Application of a physically based model to forecast shallow landslides at a regional scale. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 1919–1935. [Google Scholar] [CrossRef] [Green Version] - D’Ambrosio, M.; Tofani, V.; Rossi, G.; Salvatici, T.; Tacconi Stefanelli, C.; Rosi, A.; Masi, E.B.; Pazzi, V.; Vannocci, P.; Catani, F.; et al. Application of regional physically-based landslide early warning model: Tuning of the input parameters and validation of the results. In EGU General Assembly Conference Abstracts; EGU: Munich, Germany, 2017; p. 13712. [Google Scholar]
- Hungr, O. Dynamics of Rapid Landslides. In Progress in Landslide Science; Springer: Berlin/Heidelberg, Germany, 2007; pp. 47–57. [Google Scholar] [CrossRef]
- Bellugi, D.G.; Milledge, D.G.; Cuffey, K.M.; Dietrich, W.E.; Larsen, L.G. Controls on the size distributions of shallow landslides. Proc. Natl. Acad. Sci. USA
**2021**, 118, e2021855118. [Google Scholar] [CrossRef]

**Figure 1.**Litho-technical map of the Valle d’Aosta Region, Italy, distributed by regional authorities.

**Figure 3.**Slide model of a landslide; CM = centre of mass of the displaced body; u = potential energy; k = kinetic load; w = work of the friction forces; φ

_{a}= apparent angle of friction (tan φ

_{a}= (1 − r

_{u})tan φ’, where r

_{u}represents the ratio of water pressure to total vertical lithostatic pressure) (modified from Canuti and Casagli [37]).

**Figure 4.**Graphical representation of a generic landslide based on the Heim Energy Line method; the parameters obtained with a specific Matlab routine are indicated.

**Figure 5.**Velocity values of a shallow landslide obtained by a Matlab code based on the Heim method. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory.

**Figure 6.**Velocity values of a rockfall obtained by a Matlab code based on the Heim method. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory.

**Figure 7.**Velocity values of the shallow landslide, shown in Figure 5, obtained by the GPP model. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory.

**Figure 8.**Velocity values of a rockfall, shown in Figure 7, obtained by the GPP model. The continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory.

**Figure 9.**Other examples of the application of the proposed method and GPP model. (

**a**) Velocity values of a shallow landslide obtained by a Matlab code based on the Heim method; (

**b**) velocity values of the same shallow landslide shown in (

**a**) obtained by the GPP model; (

**c**) velocity values of a rockfall obtained by a Matlab code based on Heim method; (

**d**) velocity values of the same rockfall shown in (

**c**) obtained by the GPP model. In all the figures, the continuous black line corresponds to the landslide boundary, and the black point to the release reference point according to the IFFI inventory.

**Figure 10.**Graph of correlation between the proposed method and GPP model maximum velocity values for ten selected rockfalls. Each point shown in the graph represents the maximum velocity value of a rockfall computed with the two methods.

**Figure 11.**Graph of correlation between the proposed method and GPP model maximum velocity values for ten selected shallow landslides. Each point shown in the graph represents the maximum velocity value of a shallow landslide computed with the two methods.

**Figure 12.**Boxplots of the velocity values of the selected sample of rockfalls. The full-colour boxplots refer to the proposed method velocity values, and the dashed ones to the GPP velocity values. The colours correspond to those used in Figure 10. The boxplot consists of a box, delimited by the first and third quartiles, with the median value reported inside, and two whiskers that connect the box to the minimum and maximum value.

**Figure 13.**Boxplots of the velocity values of the selected sample of shallow landslides. The full-colour boxplots refer to the proposed method velocity values, and the dashed ones to the GPP velocity values. The colours correspond to those used in Figure 11. The boxplot consists of a box, delimited by the first and third quartiles, with the median value reported inside, and two whiskers that connect the box to the minimum and maximum value.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Marinelli, A.; Medici, C.; Rosi, A.; Tofani, V.; Bianchini, S.; Casagli, N.
Shallow Landslides and Rockfalls Velocity Assessment at Regional Scale: A Methodology Based on a Morphometric Approach. *Geosciences* **2022**, *12*, 177.
https://doi.org/10.3390/geosciences12040177

**AMA Style**

Marinelli A, Medici C, Rosi A, Tofani V, Bianchini S, Casagli N.
Shallow Landslides and Rockfalls Velocity Assessment at Regional Scale: A Methodology Based on a Morphometric Approach. *Geosciences*. 2022; 12(4):177.
https://doi.org/10.3390/geosciences12040177

**Chicago/Turabian Style**

Marinelli, Antonella, Camilla Medici, Ascanio Rosi, Veronica Tofani, Silvia Bianchini, and Nicola Casagli.
2022. "Shallow Landslides and Rockfalls Velocity Assessment at Regional Scale: A Methodology Based on a Morphometric Approach" *Geosciences* 12, no. 4: 177.
https://doi.org/10.3390/geosciences12040177