# 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

- Zou, Q.; Cui, P.; Jiang, H.; Wang, J.; Li, C.; Zhou, B. Analysis of regional river blocking by debris flows in response to climate change. Sci. Total Environ.
**2020**, 741, 140262. [Google Scholar] [CrossRef] [PubMed] - Huang, R.Q. Large-scale landslides and their sliding mechanisms in China since the 20th century. Chin. J. Rock Mech. Eng.
**2007**, 26, 433–454, (In Chinese with English abstract). [Google Scholar] - Shang, Y.J.; Yue, Z.Q.; Yang, Z.F.; Wang, Y.C.; Liu, D.A. Addressing severe slope failure hazards along Sichuan-Tibet highway in southwestern China. Epis. Newsmag. Int. Union Geol. Sci.
**2003**, 26, 94–104. [Google Scholar] - Zou, Z.X.; Tang, H.M.; Xiong, C.R.; Su, A.J.; Criss, R.E. Kinetic characteristics of debris flows as exemplified by field investigations and discrete element simulation of the catastrophic Jiweishan rockslide, China. Geomorphology
**2017**, 295, 1–15. [Google Scholar] [CrossRef] - Leonardi, A.; Pirulli, M. Analysis of the load exerted by debris flows on filter barriers: Comparison between numerical results and field measurements. Comput. Geotech.
**2020**, 118, 103311. [Google Scholar] [CrossRef] - Liu, S.L.; Zhang, J.C.; Cheng, X.; Wang, W.B.; Jiang, H.T. Gradation and Rheological Characteristics of Glacial Debris Flow along the Kangding-Linzhi Section of Sichuan-Tibet Railway. Adv. Civ. Eng.
**2020**, 2020, 8886137. [Google Scholar] - Chang, M.; Liu, Y.; Zhou, C.; Che, H.X. Hazard assessment of a catastrophic mine waste debris flow of Hou Gully, Shimian, China. Eng. Geol.
**2020**, 275, 105733. [Google Scholar] [CrossRef] - Ma, C.; Deng, J.Y.; Wang, R. Analysis of the triggering conditions and erosion of a runoff-triggered debris flow in Miyun County, Beijing, China. Landslides
**2018**, 15, 2475–2485. [Google Scholar] [CrossRef] - Xiong, J.; Tang, C.; Chen, M.; Zhang, X.Z.; Shi, Q.Y.; Gong, L.F. Activity characteristics and enlightenment of the debris flow triggered by the rainstorm on 20 August 2019 in Wenchuan County, China. Bull. Eng. Geol. Environ.
**2021**, 80, 873–888. [Google Scholar] [CrossRef] - Fannin, R.J.; Wise, M.P. An empirical-statistical model for debris flow travel distance. Can. Geotech. J.
**2001**, 38, 982–994. [Google Scholar] [CrossRef] - Tang, C.; Zhu, J.; Chang, M.; Ding, J.; Qi, X. An empirical-statistical model for predicting debris-flow runout zones in the Wenchuan earthquake area. Quat. Int.
**2012**, 250, 63–73. [Google Scholar] [CrossRef] - Huang, J.; Hales, T.C.; Huang, R.Q.; Ju, N.P.; Li, Q.; Huang, Y. A hybrid machine-learning model to estimate potential debris-flow volumes. Geomorphology
**2020**, 367, 107333. [Google Scholar] [CrossRef] - Fang, Q.S.; Tang, C.; Chen, Z.H.; Wang, S.Y.; Yang, T. A calculation method for predicting the runout volume of dam-break and non-dam-break debris flows in the Wenchuan earthquake area. Geomorphology
**2019**, 327, 201–214. [Google Scholar] [CrossRef] - Zhou, G.G.D.; Li, S.; Song, D.R.; Choi, C.E.; Chen, X.Q. Depositional mechanisms and morphology of debris flow: Physical modelling. Landslides
**2019**, 16, 315–332. [Google Scholar] [CrossRef] - Wang, D.P.; Chen, Z.; He, S.M.; Chen, K.J.; Liu, F.M.; Li, M.Q. Physical model experiments of dynamic interaction between debris flow and bridge pier model. Rock Soil Mech.
**2019**, 40, 3363–3372. [Google Scholar] - Tan, D.Y.; Yin, J.H.; Qin, J.Q.; Zhu, Z.H.; Feng, W.Q. Experimental study on impact and deposition behaviours of multiple surges of channelized debris flow on a flexible barrier. Landslides
**2020**, 17, 1577–1589. [Google Scholar] [CrossRef] - Brighenti, R.; Spaggiari, L.; Segalini, A.; Savi, R.; Capparelli, G. Debris flow impact on a flexible barrier: Laboratory flume experiments and force-based mechanical model validation. Nat. Hazards
**2021**, 106, 735–756. [Google Scholar] [CrossRef] - Bowman, E.T.; Laue, J.; Imre, B.; Springman, S.M. Experimental modelling of debris flow behaviour using a geotechnical centrifuge. Can. Geotech. J.
**2010**, 47, 742–762. [Google Scholar] [CrossRef] - Milne, F.D.; Brown, M.J.; Knappett, J.A.; Davies, M.C.R. Centrifuge modelling of hillslope debris flow initiation. Catena
**2012**, 92, 162–171. [Google Scholar] [CrossRef] - Zhou, J.W.; Cui, P.; Yang, X.G. Dynamic process analysis for the initiation and movement of the Donghekou landslide-debris flow triggered by the Wenchuan earthquake. J. Asian Earth Sci.
**2013**, 76, 70–84. [Google Scholar] [CrossRef] - Chen, R.D.; Liu, X.N.; Cao, S.Y.; Guo, Z.X. Numerical simulation of deposit in confluence zone of debris flow and mainstream. Sci. China Technol. Sci.
**2011**, 54, 2618–2628. [Google Scholar] [CrossRef] - Cascini, L.; Cuomo, S.; Pastor, M.; Rendina, I. SPH-FDM propagation and pore water pressure modelling for debris flows in flume tests. Eng. Geol.
**2016**, 213, 74–83. [Google Scholar] [CrossRef] - Shen, W.; Li, T.L.; Li, P.; Lei, Y.L. Numerical assessment for the efficiencies of check dams in debris flow gullies: A case study. Comput. Geotech.
**2020**, 122, 103541. [Google Scholar] [CrossRef] - Lei, M.; Yang, P.; Wang, Y.K.; Wang, X.K. Numerical analyses of the influence of baffles on the dynamics of debris flow in a gully. Arab. J. Geosci.
**2020**, 13, 1052. [Google Scholar] [CrossRef] - Zhou, G.G.D.; Du, J.H.; Song, D.R.; Choi, C.E.; Hu, H.S.; Jiang, C.H. Numerical study of granular debris flow run-up against slit dams by discrete element method. Landslides
**2020**, 17, 585–595. [Google Scholar] [CrossRef] - Zhou, X.Y.; Sun, D.A.; Xu, Y.F. A new thermal analysis model with three heat conduction layers in the nuclear waste repository. Nucl. Eng. Des.
**2021**, 317, 110929. [Google Scholar] [CrossRef] - Zhou, J.; Li, Y.X.; Jia, M.C.; Li, C.N. Numerical Simulation of Failure Behavior of Granular Debris Flows Based on Flume Model Tests. Sci. World J.
**2013**, 2013, 603130. [Google Scholar] [CrossRef][Green Version] - Dai, Z.L.; Huang, Y.; Cheng, H.L.; Xu, Q. SPH model for fluid–structure interaction and its application to debris flow impact estimation. Landslides
**2017**, 14, 917–928. [Google Scholar] [CrossRef] - Huang, Y.; Cheng, H.L.; Dai, Z.L.; Xu, Q.; Liu, F.; Sawada, K.; Moriguchi, S.; Yashima, A. SPH-based numerical simulation of catastrophic debris flows after the 2008 Wenchuan earthquake. Bull. Eng. Geol. Environ.
**2015**, 74, 1137–1151. [Google Scholar] [CrossRef] - Coussot, P.; Piau, J.M. A large-scale field coaxial cylinder rheometer for the study of the rheology of natural coarse suspensions. J. Rheol.
**1995**, 39, 105–124. [Google Scholar] [CrossRef] - Pellegrino, A.M.; Di Santolo, A.S.; Schippa, L. The sphere drag rheometer: A new instrument for analysing mud and debris flow materials. Int. J. Geomate
**2016**, 11, 2512–2519. [Google Scholar] [CrossRef] - Pellegrino, A.M.; Scotto di Santolo, A.; Schippa, L. An integrated procedure to evaluate rheological parameters to model debris flows. Eng. Geol.
**2015**, 196, 88–98. [Google Scholar] [CrossRef] - Portilla, M.; Chevalier, G.; Hürlimann, M. Description and analysis of the debris flows occurred during 2008 in the Eastern Pyrenees. Nat. Hazards Earth Syst. Sci.
**2010**, 10, 1635–1645. [Google Scholar] [CrossRef][Green Version] - Han, Z.; Su, B.; Li, Y.; Wang, W.; Wang, W.; Huang, J.; Chen, G. Numerical simulation of debris-flow behavior based on the SPH method incorporating the Herschel-Bulkley-Papanastasiou rheology model. Eng. Geol.
**2019**, 255, 26–36. [Google Scholar] [CrossRef] - Wang, Z.; You, Y.; Zhang, G.; Feng, T.; Liu, J.; Lv, X.; Wang, D. Superelevation analysis of the debris flow curve in Xiedi gully, China. Bull. Eng. Geol. Environ.
**2021**, 80, 967–978. [Google Scholar] [CrossRef] - Xu, Q.; Shang, Y.; van Asch, T.; Wang, S.; Zhang, Z.; Dong, X. Observations from the large, rapid Yigong rock slide—debris avalanche, southeast Tibet. Can. Geotech. J.
**2012**, 49, 589–606. [Google Scholar] [CrossRef] - Shang, Y.J.; Yang, Z.F.; Li, L.H.; Liu, D.; Liao, Q.L.; Wang, Y.C. A super-large landslide in Tibet in 2000: Background, occurrence, disaster, and origin. Geomorphology
**2003**, 4, 225–243. [Google Scholar] [CrossRef] - Zhou, J.W.; Cui, P.; Hao, M.H. Comprehensive analyses of the initiation and entrainment processes of the 2000 Yigong catastrophic landslide in Tibet, China. Landslides
**2016**, 13, 39–54. [Google Scholar] [CrossRef] - Lee, H.Y.; Chung, S.L.; Wang, J.R.; Wen, D.J.; Lo, C.H.; Yang, T.F.; Zhang, Y.; Xie, Y.; Lee, T.Y.; Wu, G.; et al. Miocene Jiali faulting and its implications for Tibetan tectonic evolution. Earth Planet. Sci. Lett.
**2003**, 205, 185–194. [Google Scholar] [CrossRef][Green Version] - Kang, C.; Chan, D.; Su, F.; Cui, P. Runout and entrainment analysis of an extremely large rock avalanche—A case study of Yigong, Tibet, China. Landslides
**2017**, 14, 123–139. [Google Scholar] [CrossRef] - Li, J.; Chen, N.S.; Zhao, Y.D.; Liu, M.; Wang, W.Y. A catastrophic landslide triggered debris flow in China’s Yigong: Factors, dynamic processes, and tendency. Earth Sci. Res. J.
**2020**, 24, 71–82. [Google Scholar] [CrossRef][Green Version] - Yin, Y.P. Characteristics of Bomi–Yigong huge high speed landslide in Tibet and the research on disaster prevention. Hydrogeol. Eng. Geol.
**2000**, 4, 8–11, (In Chinese with English abstract). [Google Scholar] - Gingold, R.A.; Monaghan, J.J. Smoothed particle hydrodynamics: Theory and application to non-spherial stars. Mon. Not. R. Astron. Soc.
**1977**, 181, 375–389. [Google Scholar] [CrossRef] - Dai, Z.L.; Huang, Y.; Cheng, H.L.; Xu, Q. 3D numerical modeling using smoothed particle hydrodynamics of flow-like landslide propagation triggered by the 2008 Wenchuan earthquake. Eng. Geol.
**2014**, 180, 21–33. [Google Scholar] [CrossRef] - Dai, Z.L.; Huang, Y.; Xu, Q. A hydraulic soil erosion model based on a weakly compressible smoothed particle hydrodynamics method. Bull. Eng. Geol. Environ.
**2019**, 78, 5853–5864. [Google Scholar] [CrossRef] - Jamalabadi, M.Y.A. Frequency analysis and control of sloshing coupled by elastic walls and foundation with smoothed particle hydrodynamics method. J. Sound Vib.
**2020**, 476, 115310. [Google Scholar] [CrossRef] - Price, D.J.; Laibe, G. A solution to the overdamping problem when simulating dust-gas mixtures with smoothed particle hydrodynamics. Mon. Not. R. Astron. Soc.
**2020**, 495, 3929–3934. [Google Scholar] [CrossRef] - Ma, C.; Iijima, K.; Oka, M. Nonlinear waves in a floating thin elastic plate, predicted by a coupled SPH and FEM simulation and by an analytical solution. Ocean Eng.
**2020**, 204, 107243. [Google Scholar] [CrossRef] - Liu, M.B.; Liu, G.R. Smoothed particle hydrodynamics (SPH): An overview and recent developments. Arch. Comput. Methods Eng.
**2010**, 17, 25–76. [Google Scholar] [CrossRef][Green Version] - Monaghan, J.J.; Gingold, R.A. Shock simulation by the particle method SPH. J. Comput. Phys.
**1983**, 52, 374–389. [Google Scholar] [CrossRef] - Zheng, B.; Chen, Z. A multiphase smoothed particle hydrodynamics model with lower numerical diffusion. J. Comput. Phys.
**2019**, 382, 177–201. [Google Scholar] [CrossRef] - Zhang, W.J.; Ji, J.; Gao, Y.F. SPH-based analysis of the post-failure flow behavior for soft and hard interbedded earth slope. Eng. Geol.
**2020**, 267, 105446. [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] - 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] - Wang, W.; Chen, G.Q.; Han, Z.; Zhou, S.H.; Zhang, H. 3d numerical simulation of debris-flow motion using sph method incorporating non-newtonian fluid behavior. Nat. Hazards
**2016**, 81, 1981–1998. [Google Scholar] [CrossRef] - Fávero Neto, A.H.; Askarinejad, A.; Springman, S.M.; Borja, R.I. Simulation of debris flow on an instrumented test slope using an updated Lagrangian continuum particle method. Acta Geotech.
**2020**, 15, 2757–2777. [Google Scholar] [CrossRef] - Schippa, L.; Pavan, S. Numerical modelling of catastrophic events produced by mud or debris flows. Int. J. Saf. Secur. Eng.
**2011**, 1, 403–423. [Google Scholar] [CrossRef] - Chen, H.; Lee, C.F. Runout analysis of slurry flows with Bingham model. J. Geotech. Geoenviron. Eng.
**2002**, 128, 1032–1042. [Google Scholar] [CrossRef] - Dai, Z.L.; Wang, F.W.; Huang, Y.; Song, K.; Iio, A. SPH-based numerical modeling for the post-failure behavior of the landslides triggered by the 2016 Kumamoto earthquake. Geoenviron. Disasters
**2016**, 3, 1–14. [Google Scholar] [CrossRef][Green Version] - Li, P.; Shen, W.; Hou, X.; Li, T. Numerical simulation of the propagation process of a rapid flow-like landslide considering bed entrainment: A case study. Eng. Geol.
**2019**, 263, 105287. [Google Scholar] [CrossRef] - Wang, Y.F.; Dong, J.J.; Cheng, Q.G. Velocity-dependent frictional weakening of large rock avalanche basal facies: Implications for rock avalanche hypermobility? J. Geophys. Res. Solid Earth
**2017**, 122, 1648–1676. [Google Scholar] [CrossRef] - Hu, M.J.; Pan, H.L.; Zhu, C.Q.; Wang, F.W. High-speed ring shear tests to study the motion and acceleration processes of the Yigong landslide. J. Mt. Sci.
**2015**, 12, 1534–1541. [Google Scholar] [CrossRef] - Marr, J.G.; Elverhøi, A.; Harbitz, C.; Imran, J.; Harff, P. Numerical simulation of mud-rich subaqueous debris flows on the glacially active margins of the Svalbard–Barents Sea. Mar. Geol.
**2002**, 188, 351–364. [Google Scholar] [CrossRef] - Beguerı´a, S.; Van Asch, T.W.J.; Malet, J.P.; Gro¨ndahl, 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] - Zhou, C.H.; Yue, Z.Q.; Lee, C.F.; Zhu, B.Q.; Wang, Z.H. Satellite image analysis of a huge landslide at Yi Gong, Tibet, China. Q. J. Eng. Geol. Hydrogeol.
**2001**, 34, 325–332. [Google Scholar] [CrossRef][Green Version]

**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 |

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

© 2021 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**

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