# Numerical Investigation on the Kinetic Characteristics of the Yigong Debris Flow in Tibet, China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geological Setting and Debris Flow Features

#### 2.1. Geological Setting

#### 2.2. Debris Flow Features

^{8}m

^{3}geomaterials slid down along the gully for about 3 min [36,37], and the sliding direction is around 225°. The horizontal runout distance is about 8000 m, and the vertical dropdown is about 3330 m from its source area at 5520 m to its sediment fan at 2190 m. Deduced from seismic surveillance data, the maximum velocity of the debris flow is higher than 100 m/s, and the average velocity is about 40 m/s [40,41].

^{2}. The elevation of the debris flow top is about 5360 m, and the lowest elevation of the deposit area is about 2200 m. The slope at both sides of the Zhamunong gully are very steep. Figure 4 shows the path profile of this debris flow. In this figure, the original slope surface (blue dashed line) and the present slope surface (green solid line) are from [42]. As shown in Figure 4, the debris flow could be identified by three major zones: source zone, propagation zone, and deposit zone. The characteristics of the three zones are described below.

#### 2.2.1. Source Zone

^{2}. The elevation of the source area sharply decreased from 5360 to 3750 m, with a slope angle of 40.0°. This area was covered by thick glaciers almost all year round. The source area was wedge-shaped, wide at the top and narrow at the bottom. It poured down along the creek bed at a high speed.

#### 2.2.2. Propagation Zone

^{2}. The axial length of this zone is about 3200 m, and the width ranges from 780 to 1500 m. The elevation of this zone ranges from 3790 to 2840 m, with a height difference of 950 m. The average slope of this zone is about 16.0°, which was much gentler than that of the source zone. Many boulders are distributed in the gully. Most of these are angular with a diameter of over 0.5 m.

#### 2.2.3. Deposit Zone

^{6}m

^{2}, and the average depth of sediment is about 50 m [3]. Due to the high motion velocity, the debris flow flushed into the Yigong river and formed a huge dam and an extensive dammed lake. The location of the lake is shown in Figure 2. The length of the trumpet-shaped dam is about 4.6 km, the maximum width is 3.0 km, and the dam height is 60–120 m. The dam sloped at 5° at the upstream side and 8° at the downstream side [35]. After the dam formation, water level of the Yigong lake continuously rose at a rate of about 1 m/day, which flooded the Yigong tea farm, schools, and villages surrounding the barrier lake. On 10 June 2000, the dam failed and resulted in devastating flooding, which destroyed farms, villages, bridges, and highways along its route. In recent years, the loose sediment was eroded by water from the Zhamunong gully and formed a debris fan in the Yigong river channel.

## 3. Numerical Model

#### 3.1. SPH Algorithm

_{d}is a normalization factor in two- and three-dimensional space, α

_{d}= 15/7 πh

^{2}and 3/2 πh

^{3}, respectively. R is the normalized distance between particles i and j, defined as R = r/h. Here, r is the distance between particles i and j.

_{0}is the reference density which can be measured through laboratory tests. c

_{s}is the sound speed at the reference density, which can be set equal to ten times the maximum velocity [51]. γ is the exponent of the equation of state and is usually set to 7.0 for a good simulation of geomaterial flow behavior [52].

#### 3.2. SPH Model of the Yigong Debris Flow

#### 3.2.1. Material Model

_{y}is the yield shear stress, which is commonly defined as the Mohr–Coulomb yield criterion with the cohesion c and frictional angle φ [29,59]. p is the pressure which can be obtained by Equation (3). D and D

_{Π}are the strain rate and its second invariant.

#### 3.2.2. Boundary Treatment

_{0}plus the density increment dρ. The density increment dρ can be obtained according to the mass conservation equation, as shown in Equation (1). k is the free surface parameter. When the particle is identified as a free boundary particle, then zero pressure is applied.

#### 3.2.3. OpenMP Parallelism

#### 3.2.4. Time Integration

**X**,

**V**, and

**a**are the displacement, velocity, and acceleration field, respectively.

## 4. Kinetic Characteristics of the Yigong Debris Flow

#### 4.1. Two-Dimensional Modeling

^{3}. The strength characteristics of the debris flow mass were studied through a series of high-speed ring shear tests and rotary shear tests in the previous studies [61,62]. According to the test results, the values of the c and φ of the geomaterial can be approximately set to be 10 kPa and 20°, respectively. The selection of dynamic viscosity η is often challenging. In the previous simulation, Bingham model was widely used to simulate debris flows considering a range of dynamic viscosities from 20 to 500 Pa·s [29,63,64]. The sound speed c

_{s}is set to be 10 v

_{max}(v

_{max}is the maximum velocity). The parameter γ in the equation of state is set to be 7.0 for a good simulation of geomaterial flow behavior.

_{2}relative error norm in the deposition depth, ε

_{L}

_{2}, was evaluated using the following equation:

#### 4.2. Three-Dimensional Modeling

^{8}m

^{3}. The number of particles along the vertical direction varies in different positions according to the depth of the sliding surface at that position. The strength parameters used in 3D simulation are the same as those used in 2D model. Based on this model, the numerical modeling of the Yigong debris flow motion across 3D terrain is conducted, and the results are shown in Figure 10. The color of the particles in the figures represents the sliding velocity. After slope failure, the debris flow mass goes through an acceleration process since the slope is quite steep in the source area. The maximum sliding velocity is about 98.4 m/s, which appears at 47.5 s after the slope failure. Afterwards, the debris flow mass slows down gradually due to the friction and the collision during the propagation. Finally, the debris flow mass crashes into a mountain on the opposite bank of Yigong river and then blocks the river channel. The whole motion process takes about 200 s, and the final depositions of the debris flow mass on the runout path are shown in Figure 10g. Figure 11 shows the Yigong debris flow deposition. The red dashed line is the simulated debris flow deposition, with the area of 4.76 km

^{2}, which is close to the measured data 5.0 km

^{2}[37]. The maximum length and width of the deposition belt are 4.62 and 2.84 km, respectively, which are close to the observed values of 4.60 and 3.0 km, and its shape is basically in agreement with the observed shape (blue solid line in Figure 11).

#### 4.3. Analysis of Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Path profile of the Yigong debris flow (based on [42]).

Case | Rheological Parameters of Debris Flow | Relative Error Norm | ||
---|---|---|---|---|

η (Pa·s) | c (kPa) | φ (°) | ε_{L}_{2} | |

1 | 200 | 0 | 5 | 0.235 |

2 | 200 | 0 | 10 | 0.227 |

3 | 200 | 0 | 20 | 0.205 |

4 | 200 | 10 | 10 | 0.174 |

5 | 200 | 20 | 20 | 0.183 |

6 | 100 | 10 | 20 | 0.243 |

7 | 400 | 10 | 20 | 0.267 |

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**MDPI and ACS Style**

Dai, Z.; Xu, K.; Wang, F.; Yang, H.; Qin, S.
Numerical Investigation on the Kinetic Characteristics of the Yigong Debris Flow in Tibet, China. *Water* **2021**, *13*, 1076.
https://doi.org/10.3390/w13081076

**AMA Style**

Dai Z, Xu K, Wang F, Yang H, Qin S.
Numerical Investigation on the Kinetic Characteristics of the Yigong Debris Flow in Tibet, China. *Water*. 2021; 13(8):1076.
https://doi.org/10.3390/w13081076

**Chicago/Turabian Style**

Dai, Zili, Kai Xu, Fawu Wang, Hufeng Yang, and Shiwei Qin.
2021. "Numerical Investigation on the Kinetic Characteristics of the Yigong Debris Flow in Tibet, China" *Water* 13, no. 8: 1076.
https://doi.org/10.3390/w13081076