# Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Tremendous Yigong Landslide

^{2}and its volume was approximately 300 million m

^{3}. Subsequently, the water level of Yigong Lake rose at a rate of approximately 0.5 m/day and showed an increasing trend. By 24 May, the measured inflow according to the ADCP method was 518 m

^{3}/s. At that time, the water level of the lake increased at a rate of about 1.0 m/day, and the storage capacity was nearly 1.07 × 10

^{9}m

^{3}. In addition, as the occurrence time of the Yigong landslide coincided with the peak period of ice and snow melt, the water level at the Yigong barrier lake rose continuously, with a maximum daily increase of more than 100 million m

^{3}. Overall, the scale and harm of the Yigong landslide were both large (ranking third in the world).

#### 2.2. Emergency Responses of Yigong Landslide

#### 2.3. Calculus Application

## 3. Results and Analysis

#### 3.1. Theoretical Analysis of Barrier Lake Formation

#### 3.2. Theoretical Description of Main-Stream Volume Variation

_{i}. Water level showed a power function relation with time. When a series of emergency measures are taken, the increased water volume in the main channel becomes equal to the reduced water volume in the barrier lake. Therefore, the total main channel volume change is equal to the sum of the volume change of the barrier lake in every short time period, which can be expressed by Equation (5). Here, the area of the barrier lake at t is expressed as S

_{t}while the water level over time is expressed as H(t).

_{t}:

_{i}is a constant coefficient that is negative under a drainage state; the parameter k

_{N}is the average value of k

_{i}in a measurable time length; and T

_{0}=0 and T

_{N}=T represent the starting point and ending point of the measurable time length, respectively. The interval from T

_{N}to T

_{N+1}indicates the time period to be estimated.

_{i}to T

_{i+1}, the volume change can be expressed as.

_{i}to T

_{i+1}).

#### 3.3. Theoretical Description of Emergency Measures

#### 3.3.1. Excavation of Diversion Channels

_{0}and the bottom elevation is Z

_{s}. The bottom width of the trapezoid is b and the slope is m. In addition, the water level of the barrier lake over time can be expressed as dH(t). The bottom elevation of the division channel over time can be expressed as dZ

_{s}(t). The water level in the division channel during the discharge process is H′ which can be expressed as:

_{0}represents atmospheric pressure on the surface of the barrier lake, p

_{1}represents atmospheric pressure on the side of the dam breach, v

_{0}represents the flow velocity in the barrier lake, v represents the flow velocity at the dam breach, H′ indicates the height difference between barrier lake and dam breach, which equals to the water level of division channels. The atmospheric pressure on the lake surfaces equals to that of the dam breach, so there is p

_{0}= p

_{1}, and the resulting flow velocity equals the well-known Torricelli’s law.

_{d}is the final breach height, as shown in Figure 9. According to the physical and geometric relations, there is:

#### 3.3.2. Implementation of Engineering Blasting

_{a}and v

_{b}, respectively. In addition, the water depths of two verticals are h

_{a}and h

_{b}, respectively. As the water depth of these two vertical lines are different, the parameters v

_{a}and v

_{b}represent different weights. The water depth of a differential unit dx is ${\mathrm{h}}_{\mathrm{a}}+\left({\mathrm{h}}_{\mathrm{b}}{-\mathrm{h}}_{\mathrm{a}}\right){\mathrm{x}/\mathrm{L}}_{0}$ while the flow velocity is ${\mathrm{v}}_{\mathrm{a}}+\left({\mathrm{v}}_{\mathrm{b}}{-\mathrm{v}}_{\mathrm{a}}\right){\mathrm{x}/\mathrm{L}}_{0},$ so the flow discharge over the length L

_{0}can be expressed as:

_{0}can be obtained. Therefore, if the flow velocity and water depth are measured at some time points like (e.g., t

_{1}, ${\text{}\mathrm{t}}_{1}+\Delta \mathrm{t}$, ${\text{}\mathrm{t}}_{1}+2\Delta \mathrm{t}$, ${\mathrm{t}}_{1}+(\mathrm{n}-1)\Delta \mathrm{t}$) are measured, the flow discharge ${\mathrm{Q}}_{{\mathrm{L}}_{0}{\mathrm{t}}_{1}}$, ${\mathrm{Q}}_{{\mathrm{L}}_{0}{\mathrm{t}}_{1}+\Delta \mathrm{t}}$, ${\mathrm{Q}}_{{\mathrm{L}}_{0}{\mathrm{t}}_{1}+2\Delta \mathrm{t}}$, ${\mathrm{Q}}_{{\mathrm{L}}_{0}{\mathrm{t}}_{1}+(\mathrm{n}-1)\Delta \mathrm{t}}$ can be calculated. After taking blasting measures, the flow discharge and the amount of overflow both increase, indicating that this variation process over time can also be regarded as an accumulation of emergency response effects over a certain length L

_{0}. There is:

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Chen, S.J.; Chen, Z.Y.; Tao, R.; Yu, S.; Xu, W.J.; Zhou, X.B.; Zhou, Z.D. Emergency Response and Back Analysis of the Failures of Earthquake Triggered Cascade Landslide Dams on the Mianyuan River, China. Nat. Hazards Rev.
**2018**, 19, 05018005. [Google Scholar] [CrossRef] - Shi, Z.M.; Wang, Y.Q.; Peng, M.; Guan, S.G.; Chen, J.F. Landslide dam de-formation analysis under aftershocks using large-scale shaking table tests measured by video grammetric technique. Eng. Geol.
**2015**, 186, 68–78. [Google Scholar] [CrossRef] - Zhou, G.G.D.; Zhou, M.J.; Shrestha, M.S.; Song, D.R.; Choi, C.E.; Cui, K.F.E.; Peng, M.; Shi, Z.M.; Zhu, X.H.; Chen, H.Y. Experimental investigation on the longitudinal evolution of landslide dam breaching and outburst floods. Geomorphology
**2019**, 334, 29–43. [Google Scholar] [CrossRef] - Cao, Z.; Yue, Z.; Pender, G. Landslide dam 1failure and flood hydraulics. Part-II: Coupled theoretical modeling. Nat. Hazards
**2011**, 59, 1021–1045. [Google Scholar] [CrossRef] - Zhang, L.M.; Peng, M.; Xu, Y. Assessing risks of breaching of earth dams and natural landslide dams. In Proceedings of the Indian Geotechnical Conference-2010, Mumbai, India, 16–18 December 2010. [Google Scholar]
- Zhao, W.Y.; Chen, X.Q.; You, Y.; Chen, J.G. Dam-break characteristics of landslide dams with different types of open channel discharge sections. Environ. Earth Sci.
**2015**, 74, 1–10. [Google Scholar] [CrossRef] - Clague, J.J.; Evans, S.G. A review of catastrophic drainage of moraine-dammed lakes in British Columbia. Quat. Sci. Rev.
**2000**, 19, 1763–1783. [Google Scholar] [CrossRef] - Liu, M.; Zhang, Y.; Tian, S.F.; Chen, N.S.; Rahman, M.M.; Iqbal, J. The effects of loose deposits on debris flow processes in the Aizi Valley, southwest China. J. Mt. Sci. Engl.
**2019**, 17, 156–172. [Google Scholar] [CrossRef] - Zhang, L.; Xiao, T.; Jian, H.; Chen, C. Erosion-based analysis of breaching of Baige landslide dams on the Jinsha River, China, in 2018. Landslides
**2019**, 16, 1965–1979. [Google Scholar] [CrossRef] - Wu, L.; Deng, H.; Huang, R.; Zhang, L.M.; Guo, X.G.; Zhou, Y. Evolution of lakes created by landslide dams and the role of dam erosion: A case study of the Jiajun landslide on the Dadu River, China. Quatern. Int.
**2019**, 503A, 41–50. [Google Scholar] [CrossRef] - Sassa, K.; Tsuchiya, S.; Fukuoka, H.; Mikos, M.; Doan, L. Landslides: Review of achievements in the second 5-year period (2009–2013). Landslides
**2015**, 12, 213–223. [Google Scholar] [CrossRef] - Van, T.P.; Sassa, K.; Takara, K.; Dang, K.; Luong, L.H.; Ha, N.D. Formation process of two massive dams following rainfall-induced deep-seated rapid landslide failures in the Kii Peninsula of Japan. Landslides
**2018**, 15, 1761–1778. [Google Scholar] - Paliaga, G.; Faccini, F.; Luino, F.; Turconi, L.; Bobrowsky, P. Geomorphic processes and risk related to a large landslide dam in a highly urbanized Mediterranean catchment (Genova, Italy). Geomorphology
**2019**, 327, 48–61. [Google Scholar] [CrossRef] - Korup, O. Geomorphic hazard assessment of landslide dams in South Westland, New Zealand: Fundamental problems and approaches. Geomorphology
**2005**, 66, 167–188. [Google Scholar] [CrossRef] - Costa, J.E.; Schuster, R.L. The formation and failure of natural dams. Geol. Soc. Am. Bull.
**1988**, 100, 1054–1068. [Google Scholar] [CrossRef] - Wang, F.; Dai, Z.; Okeke, C.A.U.; Mitani, Y.; Yang, H. Experimental study to identify premonitory factors of landslide dam failures. Eng. Geol.
**2018**, 232, 123–134. [Google Scholar] [CrossRef] - Wang, B.; Zhang, J.M.; Chen, Y.L.; Peng, Y.; Liu, X.; Liu, W.J. Comparison of measured dam-break flood waves in triangular and rectangular channels. J. Hydrol.
**2019**, 575, 690–703. [Google Scholar] [CrossRef] - Zhou, G.G.; Cui, P.; Zhu, X.H. A preliminary study of the failure mechanisms of cascading landslide dams. Int. J. Sediment. Res.
**2016**, 30, 223–234. [Google Scholar] [CrossRef] - Nian, T.K.; Wu, H.; Li, D.Y. Experimental investigation on the formation process of landslide dams and a criterion of river blockage. Landslides
**2020**, 17, 2547–2562. [Google Scholar] [CrossRef] - Li, D.; Nian, T.; Wu, H.; Wang, F.W.; Zheng, L. A predictive model for the geometry of landslide dams in V-shaped valleys. Bull. Eng. Geol. Environ.
**2020**, 79, 1–14. [Google Scholar] [CrossRef] - Shrestha, B.B.; Nakagawa, H. Hazard assessment of the formation and failure of the Sunkoshi landslide dam in Nepal. Nat. Hazards
**2016**, 82, 2029–2049. [Google Scholar] [CrossRef] - Gong, X.L.; Chen, K.T.; Chen, X.Q.; You, Y.; Chen, J.G.; Zhao, W.Y.; Liang, J. Characteristics of a Debris Flow Disaster and Its Mitigation Countermeasures in Zechawa Gully, Jiuzhaigou Valley, China. Water
**2020**, 12, 1256. [Google Scholar] [CrossRef] - Jiang, X.; Wei, Y. Erosion characteristics of outburst floods on channel beds under the conditions of different natural dam downstream slope angles. Landslides
**2020**, 17, 1823–1834. [Google Scholar] [CrossRef] - Xu, Q.; Fan, X.M.; Huang, R.Q.; Westen, C.V. Landslide dams triggered by the wenchuan earthquake, Sichuan Province, south west China. Bull. Eng. Geol. Environ.
**2009**, 68, 373–386. [Google Scholar] [CrossRef] - Zhao, T.; Dai, F.; Xu, N.W. Coupled DEM-CFD investigation on the formation of landslide dams in narrow rivers. Landslides
**2017**, 14, 189–201. [Google Scholar] [CrossRef][Green Version] - Wang, W.; Chen, G.; Zhang, Y.; Zheng, L.; Zhang, H. Dynamic simulation of landslide dam behavior considering kinematic characteristics using a coupled DDA-SPH method. Eng. Anal. Bound. Elem.
**2017**, 80, 172–183. [Google Scholar] [CrossRef] - Seyedashraf, O.; Mehrabi, M.; Akhtari, A. Novel approach for dam break flow modeling using computational Intelligence. J. Hydrol.
**2018**, 559, 1028–1038. [Google Scholar] [CrossRef] - Stefanelli, C.T.; Casagli, N.; Catani, F. Landslide damming hazard susceptibility maps: A new GIS-based procedure for risk management. Landslides
**2020**, 17, 1635–1648. [Google Scholar] [CrossRef][Green Version] - Rohan, T.J.; Wondolowski, N.; Shelef, E. Landslide susceptibility analysis based on citizen reports. Earth. Surf. Proc. Land.
**2021**, 46, 791–803. [Google Scholar] [CrossRef] - Wu, H.; Nian, T.K.; Chen, G.Q.; Zhao, W.; Li, D.Y. Laboratory-scale investigation of the 3-D geometry of landslide dams in a U-shaped valley. Eng. Geol.
**2020**, 265, 105428. [Google Scholar] [CrossRef] - Dabiri, Z.; Hlbling, D.; Abad, L.; Helgason, K.J.; Samundsson, P.; Tiede, D. Assessment of Landslide-Induced Geomorphological Changes in Hítardalur Valley, Iceland, Using Sentinel-1 and Sentinel-2 Data. Appl. Sci.
**2020**, 10, 5848. [Google Scholar] [CrossRef] - Chen, L.C.; Yang, H.Q.; Song, K.L.; Huang, W.; Ren, X.H.; Xu, H. Failure mechanisms and characteristics of the Zhongbao landslide at Liujing Village, Wulong, China. Landslides
**2021**, 18, 1445–1457. [Google Scholar] [CrossRef] - Wang, H.; Liu, S.; Xu, W. Numerical investigation on the sliding process and deposit feature of an earthquake-induced landslide: A case study. Landslides
**2020**, 17, 2671–2682. [Google Scholar] [CrossRef] - Guo, X.J.; Cui, P.; Li, Y.; Zou, Q.; Kong, Y.D. The formation and development of debris flows in large watersheds after the 2008 Wenchuan Earthquake. Landslides
**2016**, 13, 25–37. [Google Scholar] [CrossRef] - Tian, S.; Chen, N.; Wu, H.; Yang, C.Y.; Zhong, Z.; Rahman, M. New insights into the occurrence of the baige landslide along the jinsha river in tibet. Landslides
**2020**, 17, 1207–1216. [Google Scholar] [CrossRef] - Xu, C.; Cui, Y.; Xu, X.; Bao, P.P.; Fu, G.; Jiang, W.L. An anthropogenic landslide dammed the songmai river, a tributary of the jinsha river in southwestern china. Nat. Hazards
**2019**, 99, 599–608. [Google Scholar] [CrossRef] - Song, K.; Wang, F.W.; Zuo, Q.J.; Huang, B.L.; Mao, W.W.; Zheng, H. Successful disaster management of the July 2020 Shaziba landslide triggered by heavy rainfall in Mazhe Village, Enshi City, Hubei Province, China. Landslides
**2020**, 1–5. [Google Scholar] [CrossRef] - Junichi, K.; Naoki, I. Outline of measures for sediment disaster by the sabo department of mlit, japan. Landslides
**2020**, 17, 2503–2513. [Google Scholar] [CrossRef] - Fan, X.; Xu, Q.; Alonso-Rodriguez, A.; Subramanian, S.S.; Li, W.L.; Zheng, G.; Dong, X.J.; Huang, R.Q. Successive landsliding and damming of the Jinsha river in eastern Tibet, China: Prime investigation, early warning, and emergency response. Landslides
**2019**, 16, 1003–1020. [Google Scholar] [CrossRef] - Xu, Y.; He, L.J.; Zhang, L.X. Engineering measures for emergency disposal and analysis on typical cases of barrier lakes. Eps. Water Res. Hydropwer. Info.
**2021**, 42, 49–54. (In Chinese) [Google Scholar] - Lanzoni, S.; Gregoretti, C.; Stancanelli, L.M. Coarse-grained debris flow dynamics on erodible beds. J. Geophys. Res.
**2017**, 122, 592–614. [Google Scholar] [CrossRef] - Chen, C.; Zhang, L.M.; Xiao, T.; He, J. Barrier lake bursting and flood routing in the Yarlung Tsangpo Grand Canyon in October 2018. J. Hydrol.
**2020**, 583, 124603. [Google Scholar] [CrossRef] - Abdedou, A.; Soulaïmania, A.; Tchamen, G.W. Uncertainty propagation of dam break flow using the stochastic nonintrusive B-splines Bézier elements-based method. J. Hydrol.
**2020**, 590, 125342. [Google Scholar] [CrossRef] - Wang, H.; Zhou, Y.; Wang, S.X.; Wang, F.T. Coupled model constructed to simulate the landslide dam flood discharge: A case study of baige landslide dam, jinsha river. Front. Earth Sci.
**2020**, 14, 63–76. [Google Scholar] [CrossRef] - Liang, G.; Wang, Z.; Zhang, G.G.; Wang, L.L. Two huge landslides that took place in quick succession within a month at the same location of Jinsha River. Landslides
**2019**, 16, 1059–1062. [Google Scholar] [CrossRef] - Liu, N.; Ysng, Q.G.; Chen, Q.G. Hazard Mitigation for Barrier Lakes; Changjiang Press: Wuhan, China, 2016; pp. 240–266. [Google Scholar]
- Begam, S.; Sen, D.; Dey, S. Moraine dam breach and glacial lake outburst flood generation by physical and numerical models. J. Hydrol.
**2018**, 563, 694–710. [Google Scholar] [CrossRef] - Hardesty, S.; Shen, X.; Nikolopoulos, E.; Anagnostou, E. A numerical framework for evaluating flood inundation hazard under different dam operation scenarios—A case study in Naugatuck river. Water
**2018**, 10, 1798. [Google Scholar] [CrossRef][Green Version] - Evans, S.G.; Hermanns, R.L.; Schuster, R.L.; Strom, A. Natural and Artificial Rockslide Dams; Springer: Berlin, Germany, 2011. [Google Scholar]

**Figure 2.**Localization and number of publications on barrier lakes, and the corresponding cluster analysis in the last 20 years. (Note: Different colors represent different research topics; the lines represent the co-citation relationship; the larger the node is, the more frequently the keywords appear in the research).

**Figure 5.**The calculus theory in the research on barrier lakes. (

**a**) The area segmentation in a rectangle and a f curve. (

**b**) The area segmentation under the main channel streamflow curve of Yigong barrier lake.

**Figure 10.**Calculation of partial flow discharge in the blasting process based on calculus theory. (

**a**) The depth-measuring verticals of varying cross sections at diversion channels. (

**b**) Two depth-measuring vertical of two cross sections.

**Figure 12.**The modelling results of HEC-RAS. (

**a**) The variation curve of breach width b and flow velocity v with time. (

**b**) Water depth and velocity distribution after dam break.

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**

Wang, J.; Tan, G.; Shu, C.; Zhang, C.; Wang, R.; Han, S.; Yang, Q. Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation. *Water* **2021**, *13*, 2506.
https://doi.org/10.3390/w13182506

**AMA Style**

Wang J, Tan G, Shu C, Zhang C, Wang R, Han S, Yang Q. Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation. *Water*. 2021; 13(18):2506.
https://doi.org/10.3390/w13182506

**Chicago/Turabian Style**

Wang, Jingwen, Guangming Tan, Caiwen Shu, Chong Zhang, Rui Wang, Shasha Han, and Qigui Yang. 2021. "Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation" *Water* 13, no. 18: 2506.
https://doi.org/10.3390/w13182506