# Numerical Simulation of Debris Flow and Driftwood with Entrainment of Sediment

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{3}[15,19,62]; however, the exact data of the initial debris flow at the trigger time are still unknown. Therefore, in this study, we assumed that the initial volume of the debris flow was 4250 m

^{3}, in line with the literature [15,22,62], which indicated that 10 times the volume (42,500 m

^{3}) of the final debris-flow was generated from the initial debris-flow. We also set four initial points on the upper basin of the Raemian APT, as shown in Figure 1. However, if the characteristics of the initial debris-area were changed in the simulation, the final debris-volume by entrainment erosion would consequently be changed. Nevertheless, we believe that the study of such estimations should be addressed in future work because, in the present study, we focused on numerical methods and reproducibility. Thus, a technique for the detailed estimation of initial debris-characteristics was neglected in the present study.

#### 2.2. Computational Model

#### 2.2.1. Debris-Flow Model

^{2}), $H$ is water-surface elevation, $h$ is water depth, ${D}_{x}$ and ${D}_{y}$ are turbulence terms in the Cartesian coordinate, and ${\rho}_{t}$ is the mixed density. In this study, ${\rho}_{t}=\sigma C+\left(1-C\right)$, $\beta $ is the momentum ratio of the debris flow (1.25) [20], $\sigma $ is the density of the sediment, $\rho $ is the density of water, $C$ is the concentration of the mixed sediment of the debris flow, and ${C}_{*}$ is the maximum concentration of the mixed sediment of the debris flow.

#### 2.2.2. Bottom Shear-Stress of Debris Flow

#### 2.2.3. Entrainment Erosion

#### 2.3. Driftwood Generation Model

#### 2.4. Calculation Procedure

#### 2.5. Computational Conditions

^{2}digital elevation map (DEM) is used for the computational domain by preprocessing with a digital topographic map of Mt. Umyeon (1:5000, NGII [69]).

^{2}. Herein, obstacles were processed on the computational grid, based on the numerical topographical map for urban buildings.

^{2}. We selected the 3 m

^{2}grid size by trial and error of various grid sizes. From the observation data that were captured by CCTV, the inundated depth near the structure was 12 m, and the flow velocity was 28 m/s. In particular, the inundated depth of 12 m is significantly clear among the observations (as shown in Figure 1). Based on these data, we ran the simulation with various grid sizes (ranging from 1.5 to 6 m

^{2}). Although the obstacle shapes of building structures were reproduced well for all grid sizes, the inundated depth was considerably lower (less than 7 m) when the grid size was smaller than 3 m

^{2}. This is because the grid size induced different flow paths from the observation data [62]. When the grid size was larger than 3 m

^{2}, the inundation depth was less than 8 m. In particular, owing to the low resolution of the grid, the obstacle shape was indicated differently from the building structure in the study area, causing different flow vector patterns. Thus, we employed the 3 m

^{2}grid size, and accordingly, the shape of buildings in urban areas was able to be sufficiently reflected in the computational domain. Furthermore, the maximum flooding-height near the Raemian APT could be reproduced in the simulation. As the maximum erosion-depth of the debris flow was observed to be 3 m, this was also applied to the numerical simulation [55].

^{1/3}) in the computational domain, as proposed by Kim et al. [15]. This value is validated in official reports verified by several research institutes, such as the ministry offices and national institutes of Korea [62], which conducted studies on Mt. Umyeon.

^{3}, and the density of the sediment in the debris flow was 2000 kg/m

^{3}[15,62]. The size of the driftwood was the length, diameter, and density of trees in the forest, as shown in Table 1, in line with the report on the additional supplementary investigation of the causes of the Umyeon Mt. landslide [62].

^{−2}as measured in the report [62].

## 3. Results

#### 3.1. Model Reproducibility

^{3}, respectively. The debris flow damaged the Raemian APT up to the fourth floor (12 m). Therefore, we employed this value to verify the maximum flooded height. In addition, the debris volume of Table 3 includes the driftwood volume for driftwood in forest and urban areas.

^{3}in Run1.

^{3}, which is similar to the initial debris volume (4250 m

^{3}). In all the simulation cases, the inflowing velocity is less than the observed velocity. Moreover, both velocities differ partially at 12 m of height. The debris volume of all the simulations is also smaller than the observation data, except for Run1 (43,892 m

^{3}).

^{3}, and the driftwood volumes are 802 and 3814 m

^{3}, respectively. Accordingly, the proportions of the driftwood volume to the debris flow in Runs4 and 5 are 2 and 10%, respectively, as the forest density of Run5 is 5 times larger than that of Run4. As the wood diameter of Run6 is 5 times larger than that of Run4, no driftwood is generated, owing to an increase in the critical modulus, due to the larger diameter. All the simulation cases with driftwood (Run4–6) exhibited smaller impact heights than that of Run2. Compared with Run2, Runs4–5 do not indicate significant tendencies in the inflowing velocity and the debris volume, except for the impact height.

#### 3.2. Time Changes in Simulation Results

#### 3.3. Final Patterns of Entrainment Erosion

^{2}) and deposition (25,538 m

^{2}). In addition, the debris volume is 43,892 m

^{2}, which is the largest value among all the simulations (Figure 7). In the case of flow with driftwood, Run4 shows the largest erosion (39,668 m

^{2}) and deposition (19,807 m

^{2}) areas (Figure 8d), and Run5 shows the largest erosion (32,264 m

^{3}) and deposition (5732 m

^{3}) volumes (Figure 8e). Run3 (Figure 8c) indicates the smallest values among the flow-without-driftwood cases (Run1–3), in terms of the values of areas and volumes. As Run7 is not an entrainment erosion case, no volume or area were observed on the erosion and deposition (Figure 7).

## 4. Discussion

#### 4.1. Patterns of Entrainment Erosion with Forest

#### 4.2. Effect of Characterized Forest and Driftwood on Debris Flow

#### 4.3. Vulnerability Analysis by Impulse Stress

^{−2}= kPa), which evaluates the magnitude of the impact due to the debris flow, as expressed in Equation (30):

#### 4.4. Model Limits

#### 4.4.1. Model Reproducibility

#### 4.4.2. Model Sensitivity by Sediment Size

#### 4.4.3. Applicability of Empirical Parameters

#### 4.4.4. Two-Dimensional Plane Structured Flow of the Model

#### 4.4.5. Wood Collision

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Korea Institute of Geoscience And Mineral Resources (KIGAM). Development of QRA system and damage mitigation technology of landslides. Research report, Office for Government Policy Coordination. KIGAM
**2006**, TRKO200500002717, 1–360. (In Korean) [Google Scholar] - The Donga Ilbo. 2022. Available online: https://www.donga.com (accessed on 1 September 2022). (In Korean).
- Lee, M.; Kim, Y. Movement and deposition characteristics of debris flow according to rheological factors. J. Korean Soc. Agric. Eng.
**2013**, 29, 19–27. (In Korean) [Google Scholar] - O’Brien, J.S.; Julien, P.Y. Physical properties and mechanics of hyper-concentrated sediment flows. In Proceedings of the Specialty Conference on Delineation of Landslide, Flash Flood and Debris Flow Hazard in Utah, Logan, UT, USA, 14–15 June 1984; Utah State University: Logan, UT, USA, 1985; pp. 260–279. [Google Scholar]
- Iverson, R.M.; Ried, M.E.; LaHusen, R.G. Debris-flow mobilization from landslides. Annu. Rev. Earth Planet. Sci.
**1997**, 25, 85–138. [Google Scholar] [CrossRef] - Jeong, S. Rheological models for describing fine-laden debris flows: Grain-size effect. J. Korean Geotech. Soc.
**2011**, 27, 49–61. (In Korean) [Google Scholar] [CrossRef] [Green Version] - Iverson, R.M. The debris-flow rheology myth. In Debris Flow Hazards Mitigation: Mechanics, Prediction and Assessment; Rickenmann, R., Chen, C.L., Eds.; Millpress: Bethlehem, PA, USA, 2003; pp. 303–314. [Google Scholar]
- O’Brien, J.S.; Julien, P.Y.; Fullerton, W.T. Two dimensional water flood and mudflow simulation. J. Hydraul. Engrg. ASCE
**1993**, 119, 244–261. [Google Scholar] [CrossRef] - Beguería, S.; Van Asch, T.W.J.; Malet, J.-P.; Gröndahl, S. A GIS-based numerical model for simulating the kinematics of mud and debris flows over complex terrain. Nat. Hazards Earth Syst. Sci.
**2009**, 9, 1897–1909. [Google Scholar] [CrossRef] [Green Version] - Blanc, T.; Pastor, M. Numerical simulation of debris flows with the 2D–SPH depth integrated model. In Proceedings of the EGU General Assembly Conference Abstracts, Vienna, Austria, 19–24 April 2009; p. 1978. [Google Scholar]
- Mergili, M.; Fellin, W.; Moreiras, S.M.; Stötter, J. Simulation of debris flows in the Central Andes based on open source GIS: Possibilities, limitations, and parameter sensitivity. Nat. Hazards
**2012**, 61, 1051–1081. [Google Scholar] [CrossRef] [Green Version] - Imran, J.; Parker, G.; Locat, J.; Lee, H. 1D numerical model of muddy subaqueous and subaerial debris flows. J. Hydraul. Eng. ASCE
**2000**, 127, 959–968. [Google Scholar] [CrossRef] - Shrestha, B.B.; Nakagawa, H.; Kawaike, K.; Baba, Y. Numerical simulation on debris-flow deposition and erosion processes upstream of a check dam with experimental verification. Annu. Disaster Prev. Res. Inst.
**2008**, 51, 613–624. [Google Scholar] - D’Aniello, A.; Cozzolino, L.; Cimorelli, L.; Morte, R.D.; Pianese, D. A numerical model for the simulation of debris flow triggering, propagation and arrest. Nat. Hazards
**2015**, 75, 1403–1433. [Google Scholar] [CrossRef] - Kim, S.; Paik, J.; Kim, K. Run-out modeling of debris flows in Mt. Umyeon using FLO-2D. J. Korean Soc. Civ. Eng.
**2013**, 33, 965–974. (In Korean) [Google Scholar] - Hsu, S.M.; Chiou, L.B.; Lin, G.F.; Chao, C.H.; Wen, H.Y.; Ku, C.Y. Applications of simulation technique on debris-flow hazard zone delineation: A case study in Hualien County, Taiwan. Nat. Hazards Earth Syst. Sci.
**2010**, 10, 535–545. [Google Scholar] [CrossRef] [Green Version] - Hussin, H.Y.; Quan Luna, B.; van Westen, C.J.; Christen, M.; Malet, J.-P.; van Asch, T.W.J. Parameterization of a numerical 2-D debris flow model with entrainment: A case study of the Faucon catchment, Southern French Alps. Nat. Hazards Earth Syst. Sci.
**2012**, 12, 3075–3090. [Google Scholar] [CrossRef] [Green Version] - An, H.; Kim, M.; Lee, G.; Kim, Y.; Lim, H. Estimation of the area of sediment deposition by debris flow using a physical-based modeling approach. Quat. Int.
**2019**, 503, 59–69. [Google Scholar] [CrossRef] - Lee, S.; An, H.; Kim, M.; Lim, H.; Kim, Y. A Simple Deposition Model for Debris Flow Simulation Considering the Erosion–Entrainment–Deposition Process. Remote Sens.
**2022**, 14, 1904. [Google Scholar] [CrossRef] - Takahashi, T.; Nakagawa, H.; Harada, T.; Yamashiki, Y. Routing debris flows with particle segregation. J. Hydraul. Eng. ASCE
**1992**, 118, 1490–1507. [Google Scholar] [CrossRef] - Shieh, C.L.; Jan, C.D.; Tsai, Y.F. A numerical simulation of debris flow and its application. Nat. Hazards
**1996**, 13, 39–54. [Google Scholar] [CrossRef] - Ghilardi, P.; Natale, L.; Savi, F. Modeling debris flow propagation and deposition. Phys. Chem. Earth
**2001**, 26, 651–656. [Google Scholar] [CrossRef] - Mambretti, S.; Larcan, E.; Wrachien, D.D. Theoretical and experimental analysis of debris flow: Rheology and two-phase modeling. Irrig. Drain.
**2008**, 57, 555–570. [Google Scholar] [CrossRef] - Brufau, P.; Garcia-Navarro, P.; Ghilardi, P.; Natale, L.; Savi, F. 1D mathematical modelling of debris flow. J. Hydraul. Res.
**2000**, 38, 435–446. [Google Scholar] [CrossRef] - Jan, C.D. A study on the numerical modeling of debris flow. In Proceedings of the 1997 1st International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, San Francisco, CA, USA, 7–9 August 1997; pp. 717–726. [Google Scholar]
- Jin, M.; Fread, D.L. 1D routing of mud/debris flow using NWS FLDWAV model. In Proceedings of the First Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, San Francisco, CA, USA, 7–9 August 1997; pp. 687–696. [Google Scholar]
- Laigle, D.; Coussot, P. Numerical modeling of mudflows. J. Hydraul. Eng.
**1997**, 123, 617–623. [Google Scholar] [CrossRef] - Locat, J. Normalized rheological behavior of fine muds and their flow properties in a pseudoplastic regime. In Proceedings of the First Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, San Francisco, CA, USA, 7–9 August 1997; pp. 260–269. [Google Scholar]
- Takahashi, T. Debris Flow. Monograph Series of IAHR; Routledge & CRC Press Balkema: New York, NY, USA, 1991; pp. 1–165. [Google Scholar]
- Remaître, A.; Malet, J.-P.; Maquaire, O.; Ancey, C.; Locat, J. Flow behaviour and runout modelling of a complex debris flow in a clay-shale basin. Earth Surf. Process. Landf.
**2005**, 30, 479–488. [Google Scholar] [CrossRef] - Shrestha, B.; Nakagawa, H.; Kawaike, K.; Baba, Y.; Zhang, H. Driftwood deposition from debris flows at slit-check dams and fans. Nat. Hazards
**2012**, 61, 577–602. [Google Scholar] [CrossRef] - Hasanpour, A.; Istrati, D.; Bukcle, I. Coupled SPH–FEM modeling of tsunami-borne large debris flow and impact on coastal structures. J. Mar. Sci.
**2021**, 9, 1068. [Google Scholar] [CrossRef] - Istrati, D.; Hasanpour, A. Advanced numerical modelling of large debris impact on piers during extreme flood events. In Proceedings of the 7th IAHR Europe Congress, Athens, Greece, 7–9 September 2022. [Google Scholar]
- Haehnel, R.B.; Daly, S.F. Maximum impact force of woody debris on floodplain structures. J. Hydraul. Eng.
**2004**, 130, 112–120. [Google Scholar] [CrossRef] - Hasanpour, A.; Istrati, D.; Bukcle, I. Multi-physics modeling of tsunami debris impact on bridge decks. In Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure, Athens, Greece, 5–7 July 2022. [Google Scholar]
- Oudenbroek, K.; Naderi, N.; Bricker, J.D.; Yang, Y.; Van der Veen, C.; Uijttewaal, W.; Moriguchi, S.; Jonkman, S.N. Hydrodynamic and debris-damming failure of bridge decks and piers in steady flow. Geosciences
**2018**, 8, 409. [Google Scholar] [CrossRef] [Green Version] - Istrati, D.; Hasanpour, A.; Buckle, I. Numerical investigation of tsunami-borne debris damming loads on a coastal bridge. In Proceedings of the 17 World Conference on Earthquake Engineering, Sendai, Japan, 13–18 September 2020. [Google Scholar]
- Ruiz-Villanueva, V.; Bladé, E.; Sánchez-Juny, M.; Marti-Cardona, B.; Díez-Herrero, A.; Bodoque, J.M. Two-dimensional numerical modeling of wood transport. J. Hydroinform.
**2014**, 16, 1077–1096. [Google Scholar] [CrossRef] - Ruiz-Villanueva, V.; Gamberini, C.; Bladé, E.; Stoffel, M.; Bertoldi, W. Numerical Modeling of Instream Wood Transport, Deposition, and Accumulation in Braided Morphologies Under Unsteady Conditions: Sensitivity and High-Resolution Quantitative Model Validation. Water Resour. Res.
**2020**, 56, e2019WR026221. [Google Scholar] [CrossRef] - Kang, T.; Kimura, I.; Shimizu, Y. Numerical simulation of large wood deposition patterns and responses of bed morphology in a braided river using large wood dynamics model. Earth Surf. Process. Landf.
**2020**, 45, 962–977. [Google Scholar] [CrossRef] - Kang, T.; Kimura, I.; Onda, S. Application of Computational Modeling for Large Wood Dynamics with Collisions on Moveable Channel Beds. Adv. Water Resour.
**2021**, 152, 103912. [Google Scholar] [CrossRef] - Persi, E.; Petaccia, G.; Sibilla, S.; Brufau, P.; García-Navarro, P. Calibration of a dynamic Eulerian-lagrangian model for the computation of wood cylinders transport in shallow water flow. J. Hydroinf.
**2019**, 21, 164–179. [Google Scholar] [CrossRef] - Leonardi, A. Numerical simulation of debris flow and interaction between flow and obstacle via DEM. Doctoral Dissertation, ETH Zurich, Zürich, Switzerland, 2015. [Google Scholar]
- Nakagawa, H.; Takahashi, T.; Ikeguchi, M. Driftwood behavior by overland flood flows. J. Hydrosci. Hydraul. Eng. JSCE
**1994**, 12, 31–39. (In Japanese) [Google Scholar] - Nakagawa, H.; Inoue, K.; Ikeguchi, M.; Tsubono, T. Behavior of driftwood and the process of its damming up. J. Hydrosci. Hydraul. Eng. JSCE
**1995**, 13, 55–67. (In Japanese) [Google Scholar] - Gotoh, H.; Sakai, T.; Hayashi, M. Lagrangian model of drift-timbers induced flood by using moving particle semi-implicit model. J. Hydrosci. Hydraul. Eng. JSCE
**2002**, 20, 95–102. [Google Scholar] - Ikari, H.; Gotoh, H.; Sumi, T. Computational mechanics of a blocking of gateless bottom outlet by drift woods. Annu. J. Hydraul. Eng. JSCE
**2006**, 50, 793–798, (In Japanese with English abstract). [Google Scholar] [CrossRef] - Shimizu, Y.; Osada, K. Numerical simulation on the driftwood behavior in open-channel flows by using distinct element method. In Proceedings of the 8th International Conference on Hydro-Science and Engineering (ICHE-8), Nagoya, Japan, 9–11 September 2008. [Google Scholar]
- Eggertsson, O. Mackenzie river driftwood—A dendrochronological study. Arctic
**1994**, 47, 128–136. [Google Scholar] [CrossRef] [Green Version] - Braudrick, C.A.; Grant, G.E.; Ishikawa, Y.; Ikeda, H. Dynamics of wood transport in streams: A flume experiment. Earth Surf. Process. Landf.
**1997**, 22, 669–683. [Google Scholar] [CrossRef] - Abbe, T.B.; Montgomery, D.R. Patterns and processes of wood debris accumulation in the Queets river basin, Washington. Geomorphology
**2003**, 51, 81–107. [Google Scholar] [CrossRef] - Comiti, F.; Andreoli, A.; Lenzi, M.A.; Mao, L. Spatial density and characteristics of woody debris in five mountain rivers of the Dolamites (Italian Alps). Geomorphology
**2006**, 78, 44–63. [Google Scholar] [CrossRef] - Bochhiola, D.; Rulli, M.C.; Rosso, R. Transport of large woody debris in the presence of obstacles. Geomorphology
**2006**, 76, 166–178. [Google Scholar] [CrossRef] - Rickenmann, D.; Laigle, D.; McArdell, B.W.; Hübl, J. Comparison of 2D debris-flow simulation models with field events. Comput. Geosci.
**2006**, 10, 241–264. [Google Scholar] [CrossRef] [Green Version] - Crosta, G.B.; Imposimato, S.; Roddeman, D. Numerical modelling of entrainment/ deposition in rock and debris-avalanches. Eng. Geol. Mech. Veloc. Large Landslides
**2009**, 109, 135–145. [Google Scholar] [CrossRef] - D’Ambrosio, D.; Di Gregorio, S.; Iovine, G. Simulating debris flows through a hexagonal cellular automata model: SCIDDICA S3–hex. Nat. Hazards Earth Syst. Sci.
**2003**, 3, 545–559. [Google Scholar] [CrossRef] [Green Version] - Medina, V.; Hürlimann, M.; Bateman, A. Application of FLATModel, a 2D finite volume code, to debris flows in the northeastern part of the Iberian Peninsula. Landslides
**2008**, 5, 127–142. [Google Scholar] [CrossRef] - Hungr, O.; McDougall, S. Two numerical models for landslide dynamic analysis. Comput. Geosci.
**2009**, 35, 978–992. [Google Scholar] [CrossRef] - Pastor, M.; Haddad, B.; Sorbino, G.; Cuomo, S.; Drempetic, V. A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. Int. J. Numer. Anal. Methods Geomech.
**2009**, 33, 143–172. [Google Scholar] [CrossRef] - Shimizu, Y.; Suzuki, E.; Kawamura, S.; Inoue, T.; Iwasaki, T.; Hamaki, M.; Omura, K.; Kakegawa, E. Nays2D Flood solver manual. Int. River Interface Coop.
**2015**. [Google Scholar] - International River Interface Cooperative (iRIC). 2022. Available online: http://i-ric.org/en (accessed on 1 September 2022).
- Seoul City. Research contract report: Addition and Complement causes survey of Mt, vol.2011 Woomyeon landslide. Res. Rep.
**2014**, 51-6110000-000649-01, 1–46. (In Korean) [Google Scholar] - Yonhapnews. 2011. Available online: https://www.yna.co.kr (accessed on 1 September 2022). (In Korean).
- Sisain. 2011. Available online: https://www.sisain.co.kr (accessed on 1 September 2022). (In Korean).
- Kang, T.; Kimura, I. Computational modeling for large wood dynamics with root wad and anisotropic bed friction in shallow flows. Adv. Water Resour.
**2018**, 121, 419–431. [Google Scholar] [CrossRef] - Kimura, I.; Kitanozo, K. Effects of the driftwood Richardson number and applicability of a 3D-2D model to heavy wood jamming around obstacles. Environ. Fluid Mech.
**2020**, 20, 503–525. [Google Scholar] [CrossRef] - Hasanpour, A.; Istrati, D. Reducing extreme flooding loads on essential facilities via elevated structures. In Proceedings of the ASCE Lifelines Conference, Los Angeles, CA, USA, 31 January–4 February 2022. [Google Scholar]
- United States Department of Agriculture. Wood Handbook; Department of Agriculture: Washington, DC, USA, 2010. [Google Scholar]
- National Geographic Information Institute (NGII). Mt. Umyon Digital Topographical Map 2022. Available online: https://www.ngii.go.kr (accessed on 1 September 2022). (In Korean)

**Figure 2.**Driftwood generation model (${M}_{s}$ is critical moment of perpendicularly cantilevered wood; ${M}_{w}$ is moment acting on the stem of the wood body).

**Figure 10.**Spatial patterns of trees and driftwood (note that in the case of the overturned and fixed trees, the debris will be able to flow above the tree after the height of the debris flow exceeds the diameter of the fallen tree).

**Figure 12.**Impulse stress at the target area 1 (see Figure 1).

Parameter | Value (Unit) | Parameter | Value (Unit) |
---|---|---|---|

Initial debris flow volume | 4250 (m^{3}) | Critical bending stress of wood breaking | 45 (MPa) |

Advection of concentration | Upwind | Critical bending stress of wood deformation | 8 (MPa) |

Turbulence model | Zero equation | Advection of flow | TVD-MUSCL |

Computational domain | 0.6 (width) $\times $ 0.8 (length) (km^{2}) | Uniform grid size | 3 $\times $ 3 (m^{2}) |

Resolution of topography | 1 $\times $ 1 (m^{2}) | Manning roughness coefficient | 0.04 (s/m^{1/3}) |

Angle of repose | 25 (degree) | Simulation time | 120 (s) |

Density of water | 1000 (kg/m^{3}) | Density of forest of study area | 6000 (0.06 m^{2}) |

Density of tree | 800 (kg/m^{3}) | Mean stem-length of wood | 10.3 (m) |

Static-friction coefficient of driftwood | 0.9 | Mean stem-diameter of wood | 0.28 (m) |

Rolling friction coefficient of driftwood | 0.4 | Kinematic friction coefficient of driftwood | 0.6 |

Concentration of sediment–water mixture | 0.4 | Max. concentration | 0.55 |

Limitative concentration | 0.5 | Density of sediment | 2000 (kg/m^{3}) |

Time step | 0.01 (s) | Max. erosion depth | 3 (m) |

Erosion ratio | 0.001 | Deposition ratio | 0.01 |

No. | Sediment Size (mm) | Wood Diameter of Forest (m) | Driftwood Generation | Density of Forest (Tree Number/m ^{2}) | Remarks |
---|---|---|---|---|---|

Run1 | 0.75 | - | N | - | Small diameter |

Run2 | 1 | - | N | - | Standard |

Run3 | 1.25 | - | N | - | Large diameter |

Run4 | 1 | 0.231 | Y | 0.06 | Run2 with driftwood |

Run5 | 1 | 0.231 | Y | 0.3 | Forest density $\times $5 |

Run6 | 1 | 1.155 | Y | 0.06 | Stem diameter $\times $5 |

Run7 | 1 | - | N | - | No-entrainment erosion |

Case | Impact Height ^{(1)}(m) | Inflowing Velocity ^{(2)} (m/s) | Final Debris Volume ^{(3)}(m ^{3}) | Driftwood Volume (m ^{3}) |
---|---|---|---|---|

Observation | 12.0 | 28.0 | 42,500 | - |

Run1 | 5.3 | 16.5 | 43,892 | - |

Run2 | 12.9 | 20.4 | 36,653 | - |

Run3 | 12.4 | 22.1 | 30,403 | - |

Run4 | 11.9 | 20.5 | 32,843 (32,041, without driftwood) | 802 |

Run5 | 10.1 | 19.2 | 38,775 (35,591, without driftwood) | 3814 |

Run6 | 8.5 | 20.1 | 34,441 | 0 |

Run7 | 0.8 | 14.3 | 4775 | - |

No. | Height Acc. (-) | Velocity Acc. (-) | Debris Vol. Acc. (-) | Mean Acc. Value (-) |
---|---|---|---|---|

Run1 | 0.44 | 0.59 | 0.97 | 0.67 |

Run2 | 0.93 | 0.73 | 0.86 | 0.84 |

Run3 | 0.97 | 0.79 | 0.72 | 0.82 |

Run4 | 0.99 | 0.73 | 0.77 | 0.83 |

Run5 | 0.84 | 0.69 | 0.91 | 0.81 |

Run6 | 0.71 | 0.72 | 0.81 | 0.75 |

Run7 | 0.07 | 0.51 | 0.11 | 0.23 |

No. | Concentration of Sediment–Water Mixture (m^{3}/m^{3}) | Impact Velocity at Target Area 1 (m/s) | Water Density (kg/m ^{3}) | Sediment Density (kg/m^{3}) | Impulse Stress (kPa) |
---|---|---|---|---|---|

Run1 | 0.45 | 16.4 | 1000 | 2000 | 389.9 |

Run2 | 0.48 | 19.8 | 1000 | 2000 | 580.2 |

Run3 | 0.42 | 21.5 | 1000 | 2000 | 656.3 |

Run4 | 0.47 | 18.4 | 1000 | 2000 | 497.6 |

Run5 | 0.39 | 19.2 | 1000 | 2000 | 514.2 |

Run6 | 0.49 | 20.8 | 1000 | 2000 | 644.6 |

Run7 | 0 | 0.95 | 1000 | 2000 | 0.9 |

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Kang, T.; Jang, C.-L.; Kimura, I.; Lee, N.
Numerical Simulation of Debris Flow and Driftwood with Entrainment of Sediment. *Water* **2022**, *14*, 3673.
https://doi.org/10.3390/w14223673

**AMA Style**

Kang T, Jang C-L, Kimura I, Lee N.
Numerical Simulation of Debris Flow and Driftwood with Entrainment of Sediment. *Water*. 2022; 14(22):3673.
https://doi.org/10.3390/w14223673

**Chicago/Turabian Style**

Kang, Taeun, Chang-Lae Jang, Ichiro Kimura, and Namjoo Lee.
2022. "Numerical Simulation of Debris Flow and Driftwood with Entrainment of Sediment" *Water* 14, no. 22: 3673.
https://doi.org/10.3390/w14223673