# Determination of Hazard Due to Debris Flows

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

^{3}m

^{3}), frequency of debris flow occurrence scaled to the times per century (%), drainage basin area (km

^{2}), main channel length (km), drainage basin relief (km), drainage density (km/km

^{2}), and active main channel proportion (%). To calculate the H index, a sum is made of the results obtained by assigning each of these seven parameters a value between 0 and 1 via transformation functions.

## 2. Intensity of Debris Flows

#### Debris Flow Intensity Index

_{DF}, proposed by [36], was selected since it can represent the forces that generate damage and, therefore, can be correlated with infrastructure damage. This index is calculated according to the following expression:

_{DF}is the Debris Flow Intensity Index (m

^{3}/s

^{2}), d

_{max}is the maximum flow depth (m), and V

_{max}is the maximum flow velocity (m/s).

## 3. Materials and Methods

#### 3.1. Phase I: Determination of the Hazard Due to Debris Flows in Rural Areas

_{DF}is calculated in each pixel by means of Equation (1) for all the return periods analyzed.

_{DF}is obtained for each return period, in order to obtain a single value in each pixel, the following equation must be applied, which is similar to that of the mathematical expectation, with the difference that exceedance probabilities are used instead of occurrence probabilities.

_{min}up to n for T

_{max}; T

_{min}is the lowest return period from which the I

_{DF}is calculated; T

_{max}is the longest return period analyzed; and ${I}_{{DF}_{Ti}}$ is the Debris Flow Intensity Index corresponding to return period i.

_{min}value can correspond to the return period from which the flood begins or to the return period from which debris flows begin to have a considerable impact on the territory. The selection of the criterion to be applied will depend on the quantity and quality of information available and on expert judgment.

_{DF}than less frequent events, the value of T

_{min}must be obtained with the greatest possible certainty in order to avoid overestimating or underestimating the value of this parameter [38].

_{max}, can lead to an overestimation of the impact of the event since it could not be representative of the material transported and the precise estimation of the D

_{max}that could be transported is complex, it is recommended to use the D

_{90}as a representative size of the blocks that could be mobilized, considering that the D

_{90}corresponds to a diameter such that 90% of the diameters of the transported sediments are smaller than this value.

#### 3.2. Phase II: Determination of Hazard in Urban Areas, Urban Expansion Areas, and Areas Classified as High and Medium Hazards in Rural Areas

_{DF}(such as sediment particle size) to perform a hazard classification [37].

_{DF}value is obtained, which increases as the frequency of occurrence of the events decreases. Using this information, a hazard curve is constructed for each pixel, taking the I

_{DF}values as the ordinate axis and the corresponding return periods as the abscissa axis. For each pixel involved in the flow, a curve similar to the one presented in Figure 1 is obtained. If, in some pixels, the number of I

_{DF}values is insufficient to plot a curve, it is suggested to carry out additional return period modeling in order to complement this information.

_{DF}is greater than 5 m

^{3}/s

^{2}. In the present methodology, high-frequency events were defined as those corresponding to return periods of 30 and 100 years. The value of 30 years was adopted because, in some countries, such as Colombia, it is the return period used for the design of works to protect agricultural areas against floods, and the period of 100 years was adopted because, in some countries, such as Spain, Mexico, and Colombia, it is a reference value for the determination of flood hazard and risk.

_{DF}of 5 m

^{3}/s

^{2}must be interpolated from the hazard curve plotted in each pixel.

_{DF}takes values higher than 25 m

^{3}/s

^{2}. The event corresponding to the 500-year return period was established as an event of low frequency of occurrence because it is taken as a reference in some countries, such as Spain and Colombia, for the determination of the flood hazard and risk.

_{DF}value corresponding to the 500-year return period must be determined in each pixel by means of the hazard curve, and then the hazard level must be established according to the classification presented in Table 3.

## 4. Application to a Case Study

#### 4.1. Characterization of the Study Area

^{2}and an average slope of 28%. It has an average discharge of 10.90 m

^{3}/s and a bimodal rainfall regime with two rainy periods (March to May and October to December) and two periods of moderate rainfall (January to February and June to September). The average annual precipitation of the basin fluctuates between approximately 3500 mm in the upper part and approximately 2200 mm in the lower part. In its basin are the municipality of Jamundí and the southern part of the municipality of Cali [47]. The municipality of Jamundí, which could be seriously affected by a debris flow of the Jamundí River, has a population of 131,000 people, of which approximately 80% live in the urban area [48].

#### 4.2. Input Information to the Mathematical Models

#### 4.2.1. Digital Terrain Elevation Models DEM

#### 4.2.2. Hydrological Information

#### 4.2.3. Sedimentological Information

#### 4.2.4. Rheological Characteristics of the Flow

^{−2}poises, α2 = 1.81 × 10

^{−1}dynes/cm

^{2}, β1 = 22.1, and β2 = 25.7 [50].

#### 4.3. Phase I: Determination of the Hazard in the Rural Area

_{DF}values were calculated at each pixel for all modeled events. Figure 8a shows the I

_{DF}calculated for the event corresponding to the 500-year return period. Subsequently, by means of Equation (2), taking as the T

_{min}value the return period from which the flood begins and based on the I

_{DF}obtained for each of the events analyzed, the combined I

_{DF}value was obtained for each pixel. Figure 8b shows the combined I

_{DF}calculated in the Jamundí River basin.

_{90}value of the sediments that could be mobilized by the debris flows. Figure 9 presents the distribution of the D

_{90}diameter of the sediments in the Jamundí River watershed, which was obtained via information collected in field campaigns carried out by [49].

_{DF}and D

_{90}values are integrated for each pixel according to the criteria established in Table 1. This procedure allows the classification of the hazard as high, medium, or low in all points of the territory. Figure 10 shows the zoning of the hazard due to debris flows in the Jamundí River watershed at a scale of 1:25,000. According to the results obtained, almost the entire rural area of the watershed presents a low hazard level; only a few small sectors restricted mainly to the watercourses present medium and high hazard levels.

#### 4.4. Phase II: Determination of Hazards in Urban Areas, Urban Expansion Areas, and Areas Classified as High and Medium Hazards in Rural Areas

_{DF}in the flooded pixels was calculated. From this information, for each pixel, a hazard curve that relates the probability of occurrence of debris flow with its corresponding I

_{DF}was interpolated, taking into account that in each pixel, there are as many I

_{DF}as events that flood it. A minimum number of 6 points was established to plot these curves. During the plotting of the curves, it was found that in most cases, the best fit to the points obtained was reached with polynomial equations of degree 2.

_{DF}of 5 m

^{3}/s

^{2}would have been established. According to Table 2, if this period is less than 30 years, the hazard is classified as high; if it is between 30 and 100 years, the hazard is medium, and if it is greater than 100 years, the hazard is low. Figure 12a shows the hazard zoning considering this criterion.

_{DF}for the event with a return period of 500 years was determined. According to Table 3, if this I

_{DF}is less than 1 m

^{3}/s

^{2}, the hazard is low; if it is between 1 and 25 m

^{3}/s

^{2}, the hazard is medium, and if it is greater than 25 m

^{3}/s

^{2}, the hazard is high. Figure 12b shows the zoning of the territory considering this criterion.

## 5. Discussion

_{DF}flow intensity indexes equal to or greater than 5 m

^{3}/s

^{2}and the potential to cause partial structural damage to homes and other exposed buildings. There could also be debris flows corresponding to return periods of 500 years or more with flow intensity indexes equal to or greater than 25 m

^{3}/s

^{2}, which would have the potential to cause severe structural damage.

_{DF}equal to or greater than 1 m

^{3}/s

^{2}and less than 25 m

^{3}/s

^{2}. There could also be events with return periods between 30 years and 100 years that reach I

_{DF}values of 5 m

^{3}/s

^{2}. It is considered that events of these magnitudes put people’s lives at risk and forced them to evacuate their homes.

_{DF}equal to or greater than 5 m

^{3}/s

^{2}may occur, which have the potential to cause damage to homes and other exposed buildings. Floods with a return period of 500 years would probably cause slight structural damage and/or some sedimentation since they would have a flow intensity index equal to or less than 1 m

^{3}/s

^{2}.

## 6. Conclusions

_{DF}, which is calculated from the maximum depths and velocities of debris flows corresponding to different return periods. The hydrodynamic characteristics of the flow must be estimated via mathematical modeling performed using models that consider the non-Newtonian flow rheology and the volumes of sediments that could be incorporated into the flow.

_{DF}, which is an empirical parameter. These values were derived from the consequences of several debris flows around the world. In order to increase the level of certainty of the adopted values, it is necessary to expand and permanently update the number of events analyzed for the definition of the I

_{DF}and the sediment size. This greater certainty in the adopted reference values would allow an increase in the level of accuracy of the zoning of the territory.

_{DF}would reach values that are associated with severe structural damage. Events with a high frequency of occurrence reach I

_{DF}values associated with structural damage considered relatively minor.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rickenmann, D.; Zimmermann, M. The 1987 debris flows in Switzerland: Documentation and analyses. Geomorphology
**1993**, 8, 175–189. [Google Scholar] [CrossRef] - Papathoma-Köhle, M.; Gems, B.; Sturm, M.; Fuchs, S. Matrices, curves and indicators: A review of approaches to assess physical vulnerability to debris flows. Earth Sci. Rev.
**2017**, 171, 272–288. [Google Scholar] [CrossRef] - Bernard, M.; Gregoretti, C. The use of rain gauge measurements and radar data for the model-based prediction of runoff-generated debris-flow occurrence in early warning systems. Water Resour.
**2021**, 57, e2020WR027893. [Google Scholar] [CrossRef] - Huang, Y.; Sun, J.; Zhu, C. Mechanism and Prevention of Debris Flow Disaster. Water
**2022**, 14, 1143. [Google Scholar] [CrossRef] - Koutroulis, A.; Tsanis, I. A method for estimating flash flood peak discharge in a Poorly Gauged Basin: Case Study for the 13–14 January 1994 Flood, Giofiros Basin, Crete, Greece. J. Hydrol.
**2010**, 385, 150–164. [Google Scholar] [CrossRef] - 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] - Dowling, C.A.; Santi, P.M. Debris flows and their toll on human life: A global analysis of debris flow fatalities from 1950 to 2011. Nat. Hazards
**2014**, 71, 203–227. [Google Scholar] [CrossRef] - Rheinberger, H.E.; Romang, M. Bründl. Proportional loss functions for debris flow events. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 2147–2156. [Google Scholar] [CrossRef] - Aristizábal, E.; Arango, M.I.; Garcia, I.K. Definición y clasificación de las avenidas torrenciales y su impacto en los Andes colombianos. Cuad. Geogr. Rev. Colomb. Geogr.
**2020**, 29, 242–258. [Google Scholar] [CrossRef] - Wieczorek, G.F.; Larsen, M.C.; Eaton, L.S.; Morgan, B.A.; Blair, J.L. Debris-Flow and Flooding Hazards Associated with the December 1999 Storm in Coastal Venezuela and Strategies for Mitigation. U.S. Geological Survey Open File Report 01-0144 2001. pp. 1–31. Available online: https://pubs.usgs.gov/of/2001/ofr-01-0144/ (accessed on 14 July 2023).
- Imaizumi, F.; Osanai, N.; Kato, S.; Koike, M.; Kosugi, K.; Sakai, Y.; Sakaguchi, H.; Satofuka, Y.; Takayama, S.; Tanaka, T.; et al. Debris flow disaster in Atami, Japan, in July 2021. Int. J. Eros. Control Eng.
**2022**, 15, 1–6. [Google Scholar] [CrossRef] - Westra, S.; Fowler, H.J.; Evans, J.P.; Alexander, L.V.; Berg, P.; Johnson, F.; Kendon, E.J.; Lenderink, G.; Roberts, N.M. Future changes to the intensity and frequency of short-duration extreme rainfall. Rev. Geophys.
**2014**, 52, 522–555. [Google Scholar] [CrossRef] - Chen, H.-W.; Chen, C.Y. Warning Models for Landslide and Channelized Debris Flow under Climate Change Conditions in Taiwan. Water
**2022**, 14, 695. [Google Scholar] [CrossRef] - Cabral, V.C.; Reis, F.; Veloso, V.; Ogura, A.; Zarfl, C. A multi-step hazard assessment for debris-flow prone areas influenced by hydroclimatic events. Eng. Geol.
**2023**, 313, 106961. [Google Scholar] [CrossRef] - Nery, T.D. O uso de parametros morfometricos como potencial indicador a ocorrencia de fluxos de detritos no litoral norte de Sao Paulo. Geosul
**2017**, 32, 179–200. [Google Scholar] [CrossRef] - Correa, C.V.S.; Reis, F.A.G.V.; Giordano, L.C.; Cabral, V.C.; Gramani, M.F.; Gabelini, B.M.; Duz, B.G.; Veloso, V.Q. Assessment of the potentiality to the debris-flow occurrence from physiographic and morphometrics parameters: A case study in Santo Antonio Basin (Caraguatatuba, Sao Paulo State, Brazil). Anu. Inst. Geocienc.
**2021**, 44, 1–14. [Google Scholar] [CrossRef] - Petracheck, A.; Kienholtz, H. Hazard assessment and mapping of mountains risks in Switzerland. In Debris Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, 1st ed.; Rickenmann, D., Chen, C.-L., Eds.; Millpress Science Publishers: Rotterdam, The Netherlands, 2003; Volume 1, pp. 23–28. [Google Scholar]
- Chang, C.; Lin, P.; Tsai, C. Estimation of sediment volume of debris flow caused by extreme rainfall in Taiwan. Eng. Geol.
**2011**, 123, 83–90. [Google Scholar] [CrossRef] - Cabral, V.C.; Reis, F.A.G.V.; D’Affonseca, F.M.; Lucia, A.; dos Santos Correa, C.V.; Veloso, V.; Gramani, M.F.; Ogura, A.T.; Lazaretti, A.F.; Vemado, F.; et al. Characterization of a landslide-triggered debris flow at a rainforest-covered mountain region in Brazil. Nat. Hazards
**2021**, 108, 3021–3043. [Google Scholar] [CrossRef] - Yang, Z.; Zhao, X.; Chen, M.; Zhang, J.; Yang, Y.; Chen, W.; Bai, X.; Wang, M.; Wu, Q. Characteristics, Dynamic Analyses and Hazard Assessment of Debris Flows in Niumiangou Valley of Wenchuan County. Appl. Sci.
**2023**, 13, 1161. [Google Scholar] [CrossRef] - Wang, J.; Yang, S.; Ou, G.; Gong, Q.; Yuan, S. Debris flow hazard assessment by combining numerical simulation and land utilization. Bull. Eng. Geol. Environ.
**2018**, 77, 13–27. [Google Scholar] [CrossRef] - Veloso, V.Q.; Reis, F.A.V.G.; Cabral, V.; Zaine, J.E.; dos Santos Corrêa, C.V.; Gramani, M.F.; Kuhn, C.E. Hazard assessment of debris-flow-prone watersheds in Cubatão, São Paulo State, Brazil. Nat. Hazards
**2023**, 116, 3119–3138. [Google Scholar] [CrossRef] - Zhang, S.; Sun, P.; Zhang, Y.; Ren, J.; Wang, H. Hazard Zonation and Risk Assessment of a Debris Flow under Different Rainfall Condition in Wudu District, Gansu Province, Northwest China. Water
**2022**, 14, 2680. [Google Scholar] [CrossRef] - Cabral, V.C.; Reis, F.A.G.V.; Mendoza, C.M.; Oliveira, A. Model-based assessment of shallow landslide susceptibility at a petrochemical site in Brazil. Rev. Brasil. Geomorfol.
**2022**, 23, 1394–1419. [Google Scholar] [CrossRef] - Iverson, R.M.; Reid, M.E.; Logan, M.; LaHusen, R.G.; Godt, J.W.; Griswold, J.P. Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment. Nat. Geosci.
**2011**, 4, 116–121. [Google Scholar] [CrossRef] - Cao, C.; Zhang, W.; Chen, J.; Shan, B.; Song, S.; Zhan, J. Quantitative estimation of debris flow source materials by integrating multi-source data: A case study. Eng. Geol.
**2021**, 29, 106222. [Google Scholar] [CrossRef] - Hungr, O.; McDougall, S.; Bovis, M. Entrainment of material by debris flows. In Debris-Flow Hazards and Related Phenomena, 1st ed.; Springer Praxis Books; Chen, C.-L., Major, J.J., Eds.; Springer: Berlin, Germany, 2005; Volume 1, pp. 135–158. [Google Scholar] [CrossRef]
- Santi, P.M.; Dewolfe, V.G.; Higgins, J.D.; Cannon, S.H.; Gartner, J.E. Sources of debris flow material in burned areas. Geomorphology
**2008**, 96, 310–321. [Google Scholar] [CrossRef] - Hürlimann, M.; Rickenmann, D.; Graf, C. Field and monitoring data of debris-flow events in the Swiss Alps. Can. Geotech. J.
**2003**, 40, 161–175. [Google Scholar] [CrossRef] - Rickenmann, D. Runout prediction methods. In Debris-Flow Hazards and Related Phenomena, 1st ed.; Springer Praxis Books; Chen, C.-L., Major, J.J., Eds.; Springer: Berlin, Germany, 2005; Volume 1, pp. 305–321. [Google Scholar] [CrossRef]
- Shanmugam, G. Submarine fans: A critical retrospective (1950–2015). J. Palaeogeogr.
**2016**, 5, 110–184. [Google Scholar] [CrossRef] - What Is a Landslide and What Causes One? Available online: https://www.usgs.gov/faqs/what-a-landslide-and-what-causes-one?qt-news_science_products=0#qt-news_science_products (accessed on 4 July 2023).
- Yang, Z.; Wang, L.; Qiao, J.; Uchimura, T.; Wang, L. Application and verification of a multivariate real-time early warning method for rainfall-induced landslides: Implication for evolution of landslide-generated debris flows. Landslides
**2020**, 17, 2409–2419. [Google Scholar] [CrossRef] - Hsu, Y.-C.; Liu, K.-F. Combining TRIGRS and DEBRIS-2D Models for the Simulation of a Rainfall Infiltration Induced Shallow Landslide and Subsequent Debris Flow. Water
**2019**, 11, 890. [Google Scholar] [CrossRef] - Zanchetta, G.; Sulpizio, R.; Pareschi, M.T.; Leoni, F.M.; Santacroce, R. Characteristics of 5–6 May 1998 volcaniclastic debris flows in the Sarno area. J. Volcanol. Geotherm. Res.
**2004**, 133, 377–393. [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] - Ramos, A.M.; Reyes, A.A.; Munevar, M.A.; Ruiz, G.L.; Machuca, S.V.; Rangel, M.S.; Prada, L.F.; Cabrera, M.A.; Rodríguez, C.E.; Escobar, N.; et al. Guía Metodológica Para Zonificación de Amenaza por Avenidas Torrenciales; Servicio Geológico Colombiano y Pontificia Universidad Javeriana: Bogotá, Colombia, 2021. [Google Scholar]
- Bocanegra, R.A.; Francés, F. Assessing the risk of vehicle instability due to flooding. J. Flood Risk Manag.
**2021**, 14, e12738. [Google Scholar] [CrossRef] - Sepe, C.; Calcaterra, D.; Di Martire, D.; Fusco, F.; Tufano, R.; Vitale Ea Guerriero, L. Triggering conditions and propagation of the December 2019 Palma Campania landslide: Implications for residual hazard estimation at recurrent landslide sites. Eng. Geol.
**2023**, 322, 107177. [Google Scholar] [CrossRef] - Bardou, E.; Ancey, C.; Bonnard, C.; Vulliet, L. Classification of debris-flow deposits for hazard assessment in alpine areas. In Proceedings of the 3th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, Davos, Switzerland, 10–12 September 2003; Available online: http://infoscience.epfl.ch/record/94551 (accessed on 18 July 2023).
- He, S.; Liu, W.; Li, X. Prediction of impact force of debris flow based on distribution and size of particles. Environ. Earth Sci.
**2016**, 75, 298–305. [Google Scholar] [CrossRef] - Cui, Y.; Choi, C.E.; Liu, L.H.D.; Ng, C.W.W. Effects of particle size of mono-disperse granular flows impacting a rigid barrier. Nat. Hazards
**2018**, 91, 1179–1201. [Google Scholar] [CrossRef] - Carr, A.P. Sediment size classification. In Beaches and Coastal Geology. Encyclopedia of Earth Sciences Series, 1st ed.; Schwartz, M., Ed.; Springer: New York, NY, USA, 2014; Volume 1, pp. 738–740. [Google Scholar] [CrossRef]
- Liang, Y.; Xiong, F. Quantification of debris flow vulnerability of typical bridge substructure based on impact force simulation. Geomat. Nat. Hazards Risk
**2019**, 10, 1839–1862. [Google Scholar] [CrossRef] - Chehade, R.; Chevalier, B.; Dedecker, F.; Breul, P.; Thouret, J.-C. Effect of Boulder Size on Debris Flow Impact Pressure Using a CFD-DEM Numerical Model. Geosciences
**2022**, 12, 188. [Google Scholar] [CrossRef] - De Hass, T.; van Woerkom, T. Bed scour by debris flows: Experimental investigation of effects of debris-flow composition. Earth Surf. Process. Landf.
**2016**, 41, 1951–1966. [Google Scholar] [CrossRef] - Corporación Autónoma Regional del Valle del Cauca—Universidad del Valle. Caracterización de los Ríos Tributarios del Río Cauca—Tramo Salvajina—La Virginia 2000. Santiago de Cali, Colombia. Available online: https://ecopedia.cvc.gov.co/agua/aguas-superficiales/caracterizacion-del-rio-cauca-y-tributarios-tramo-salvajina-la-virginia (accessed on 14 July 2023).
- Departamento Administrativo Nacional de Estadística (DANE). La Información del DANE: Candelaria, Jamundí, Palmira, Yumbo—Valle del Cauca 2020. Available online: https://129.80.70.228/files/investigaciones/planes-desarrollo-territorial/100320-Info-Alcaldias-Candelaria-Yumbo-Jamund%C3%AD-Palmira.pdf (accessed on 8 April 2022).
- Servicio Geológico Colombiano—Universidad del Valle. Zonificación de amenaza por avenidas torrenciales en Jamundí departamento del Valle del Cauca a escala 1:2000 2021. Santiago de Cali—Colombia. Available online: https://libros.sgc.gov.co/index.php/editorial/catalog/book/75 (accessed on 8 April 2022).
- O’Brien, J.S.; Julien, P.Y. Physical properties and mechanics of Hyperconcentrated sediment flows. In Proceedings of the Delineation of Landslides, Flash Flood, and Debris Flow Hazards, Logan, UT, USA, 14–15 June 1984. [Google Scholar]
- Sanchez, A.; Gibson, S.; Ackerman, C.; Floyd, I. 1D and 2D Debris Flow Modeling with HEC-RAS. In Proceedings of the EGU General Assembly Conference Abstracts 2020, Online, 4–8 May 2020. EGU2020-11752. [Google Scholar] [CrossRef]

**Figure 2.**Flow chart of the procedure to be implemented to determine the hazard due to debris flows.

**Figure 4.**Digital elevation model generated at a scale of 1:2000, including the Jamundí River basin. Source: [49].

**Figure 5.**Temporal distribution of multiannual average precipitation recorded at four stations located in the Jamundí River basin. Source: [49].

**Figure 6.**Hydrographs of floods introduced in the upstream boundary of the mathematical model of the Jamundí River basin. Source: [49].

**Figure 7.**Results of the mathematical modeling at 1:25,000 scale of the debris flows with a 500-year return period: (

**a**) maximum depths; (

**b**) maximum velocities.

**Figure 8.**Debris Flow Intensity Index, I

_{DF}, obtained using the results of mathematical modeling at a scale of 1:25,000: (

**a**) I

_{DF}for the debris flow with a return period of 500 years; (

**b**) combined I

_{DF}.

**Figure 9.**Distribution of the D

_{90}diameter of the sediments in the Jamundí River watershed. Source: [49].

**Figure 10.**Zoning of the hazard at a scale of 1:25,000 due to debris flows in the Jamundí River basin.

**Figure 11.**Results of the mathematical modeling at a scale of 1:2000 of the debris flow with a return period of 500 years: (

**a**) maximum depths; (

**b**) maximum velocities.

**Figure 12.**Zoning at a scale of 1:2000 of the debris flow hazard in the lower part of the Jamundí River basin: (

**a**) zoning obtained from the determination of the return period corresponding to an I

_{DF}de 5 m

^{3}/s

^{2}; (

**b**) zoning obtained from the I

_{DF}calculation corresponding to an event with a return period of 500 years; (

**c**) definitive zoning of the hazard.

**Table 1.**Classification of the hazard due to debris flows according to the Debris Flow Intensity Index, I

_{DF}, and the D

_{90}of the sediments that could be mobilized.

D_{90} (m) | Hazard Due to Debris Flows | ||
---|---|---|---|

Combined Debris Flow Intensity Index I_{DF} (m^{3}/s^{2}) | |||

0–1 | 1–50 | >50 | |

0–0.5 | Low | Medium | Medium |

0.5–1.0 | Medium | High | High |

>1.0 m | Improbable | High | High |

**Table 2.**Hazard classification by debris flows of high frequency of occurrence based on the I

_{DF}and the return period.

Range of the Return Period Corresponding to the I_{DF} = 5 m^{3}/s^{2}(Years) | Hazard Classification |
---|---|

≤30 | High |

30 < T < 100 | Medium |

≥100 | Low |

**Table 3.**Hazard classification due to debris flows with low frequency of occurrence based on the I

_{DF}of the event with return period of 500 years.

Range of the I_{DF} Corresponding to the Event with a Return Period of 500 Years(m ^{3}/s^{2}) | Hazard Classification |
---|---|

<1 | Low |

1–25 | Medium |

>25 | High |

Return Period (Years) (m ^{3}/s^{2}) | Sediment Volume Accumulated at the Upstream Boundary (10 ^{6} m^{3}) |
---|---|

2.33 | 0.00 |

5 | 0.14 |

10 | 0.30 |

25 | 0.55 |

50 | 0.79 |

75 | 0.96 |

100 | 1.05 |

200 | 1.43 |

300 | 1.56 |

400 | 1.74 |

500 | 1.84 |

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## Share and Cite

**MDPI and ACS Style**

Bocanegra, R.A.; Ramírez, C.A.; Salcedo, E.d.J.; Villegas, M.P.L.
Determination of Hazard Due to Debris Flows. *Water* **2023**, *15*, 4057.
https://doi.org/10.3390/w15234057

**AMA Style**

Bocanegra RA, Ramírez CA, Salcedo EdJ, Villegas MPL.
Determination of Hazard Due to Debris Flows. *Water*. 2023; 15(23):4057.
https://doi.org/10.3390/w15234057

**Chicago/Turabian Style**

Bocanegra, Ricardo A., Carlos A. Ramírez, Elkin de J. Salcedo, and María Paula Lorza Villegas.
2023. "Determination of Hazard Due to Debris Flows" *Water* 15, no. 23: 4057.
https://doi.org/10.3390/w15234057