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Enhancement of semi-theoretical models for predicting peak discharges in breached embankment dams

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Abstract

During the application of semi-theoretical models to predict peak discharges for breached embankment dams, it is often encountered to be lack of necessary model parameters such as breach height. In order to solve this deficiency and improve the application of the semi-theoretical models for estimating the peak discharge, a mathematical relation is proposed to predict the breach height (Hb) using the water depth above breach bottom (Hw) based on a subset of a composite database (72 historical dam failures). The breach height relation has a high coefficient of determination (R2) when it is applied in the composite database. Using the prediction by the breach height relation as a substitute for the observation, these semi-theoretical models used here produce similar results in terms of both prediction accuracy and uncertainty. Moreover, the dispersion of the flood peak discharge predicted by forecasting models is weakened and the skewness is improved by adopting the breach height relation. Therefore, the application of semi-theoretical models to predict peak discharges can be improved obviously. So, it is found that the breach height using the proposed relation can be a satisfactory substitute when the observed value of Hb is unavailable in a dam failure. Besides, the prediction accuracy will decrease slightly with the increase of database, but the decrease is limited. It should be noted that the proposed breach height relation is only suitable for predicting the height of embankment dam breach in principle.

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Abbreviations

B avg :

Average width of the final breach

E l :

Embankment length

E w :

Average embankment width

e i :

Individual prediction error

e m :

Mean prediction error in logarithmic scale

g :

Gravitational acceleration

H b :

Breach height

H d :

Dam height

H w :

Water depth above breach bottom at time of failure

IQR :

Interquartile range

K m :

Factor accounting for failure mode

k :

Vertical erosion rate of the breach

M l :

Breach left-slope ratio

M r :

Breach right-slope ratio

m :

Average breach side-slope ratio

Q p :

Peak outflow

Q pmax :

Maximum possible peak discharge

Q pri :

ith predicted peak discharge

Q obi :

ith observed peak discharge

Q obm :

Mean of the observed peak discharges

Q1, Q3 :

Upper and lower quartiles

Q 2 :

Median

q :

Combinative parameter of the cross-section

R 2 :

Coefficient of determination

RRMSE :

Relative root mean square error

S e :

Standard deviation of the errors

T f :

Breach formation time

V s :

Reservoir storage

V w :

Volume of water stored above breach bottom at time of failure

W :

Characteristic parameter of the flow depth

α 0 :

Exponent of the level reservoir-volume curve

α, β :

Coefficients in Froehlich’s formula

η :

Dimensionless parameter in formula of Walder and O’Connor

υ e :

Characteristic velocity in formula of De Lorenzo and Macchione

σ :

Standard error of prediction

ζ :

Coefficient in formula of Wang et al.

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Acknowledgements

The first author would like to thank for the National Key Research and Development Program of China (Grant No: 2018YFC1505000), the financial support of National Natural Science Foundation of China (Grant No: 51879179) and the Sichuan Provincial Youth Science and Technology Innovation Research Team Special Funding Project (No: 2019JDTD0007). The sixth author would like to thank for the financial support of National Natural Science Foundation of China (Grant No: 51579166).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    Bo Wang, Wenjun Liu, Jianmin Zhang, Yunliang Chen, Chao Wu, Yong Peng, Zhenyu Wu, Xin Liu & Sha Yang

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  1. Bo Wang
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Wang, B., Liu, W., Zhang, J. et al. Enhancement of semi-theoretical models for predicting peak discharges in breached embankment dams. Environ Fluid Mech 20, 885–904 (2020). https://doi.org/10.1007/s10652-019-09730-9

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