# 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

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**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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**MDPI and ACS Style**

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