A simplified mathematical model for the dam-breach hydrograph for three reservoir geometries following a sudden full dam
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A simplified mathematical model for the dam‑breach hydrograph for three reservoir geometries following a sudden full dam break Hui Hu1 · Jianfeng Zhang1 · Tao Li1 · Jie Yang1 Received: 16 April 2018 / Accepted: 24 April 2020 © Springer Nature B.V. 2020
Abstract The prediction of dam-break water flow at dam site is essential to reduce the potential for loss of damage in the downstream floodplain. In this study, the influence of reservoir shapes (rectangular, trapezoidal and triangular wedge) on dam-break discharge hydrographs at a dam site was investigated to estimate the peak discharge and discharge hydrograph quickly. By assuming instantaneous and complete breaches to simplify the discharge process, a formula for the peak discharge and a simple analytical solution to the entire discharge hydrograph following a dam break at the dam site were generated. The discharge hydrograph at the dam site derived by the proposed mathematical model was validated through a comparison with the results calculated by the numerical simulation and other existing approaches. The outflow discharges calculated by both the mathematical and numerical model was very similar under the conditions of the three different reservoir shapes. The overall discharge hydrograph shape was mainly influenced by the length of the reservoir, while the magnitude of the outflow discharge was primarily affected by the initial water depth. Keywords Instantaneous dam break · Peak discharge · Discharge hydrograph · Reservoir shape · A simple analytical solution
* Tao Li [email protected] Hui Hu [email protected] Jianfeng Zhang [email protected] Jie Yang [email protected] 1
State Key Laboratory Base of Eco‑Hydraulic Engineering in Arid Area, School of Water Resources and Hydropower, Xi’an University of Technology, Xi’an 710048, China
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Natural Hazards
1 Introduction A sudden dam break followed by a flood released instantaneously from a reservoir can cause catastrophic effects and pose significant natural hazards downstream (Costa 1985; Pektas and Erdik 2014). The key issues are the water flow at the dam site and the flood routing downstream. Given that the water flow process at the dam site is the upper boundary of downstream cross sections, it is essential to deal with the problem of the discharge variations at the dam site (Peng and Zhang 2012). A variety of hydrological, hydraulic, geomorphological and geometric factors affect the outflow characteristics at the breach. There are nonetheless great uncertainties involved in the problem (Hooshyaripor et al. 2014). The significant and effective role of the reservoirs geometry on the main features of dam-break flows, i.e., the peak discharge and the time variations of the discharge hydrograph, was demonstrated in Taher-Shamsi et al. (2003), Lobovsky et al. (2014) and Hooshyaripor and Tahershamsi (2015). Moreover, in practice, precise and fast calculation of dambreak floods for complicated types of rapidly varying unsteady flows will precisely prevent breaks of dams and ef
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