Sensitivity Analysis of Rock-Fill Dam Break Flood on Different Dam Break Durations

The dam break pattern of rock-fill dams is normally gradual failure. This kind of dam failure is caused by seepage piping or overtopping, in which dam crest overflow is more common. The dam breach expansion process shall depend comprehensively on the structure pattern, material property of dam, and damsite cross sectional topography. And the break duration has a significant impact on the magnitude of break flood and the counter-measures for excess-standard flood. Take the Karot Hydropower Project constructed on the Jhelum River in Pakistan as an example, the dam break mathematical model is set up to ana-lyze the sensitivity of damsite discharge process, downstream highest flood water surface profile and flood peak appearance time to dam break duration. The results show that: with the increase of dam break duration, damsite peak discharge is decreased sharply, flood peak appearance time extends, on-way highest water levels below Karot dam are lowered significantly, and some settlement places below Karot dam can avoid being inundated until the break duration reaches a critical value. If encountering probable maximum flood, the dam break occurs when the reservoir water level reaches dam top EL, some measures can be taken to extend the break duration, so as to effectively reduce the loss of downstream flood. The research results will help to understand the relationship mechanism between rock-fill dam break flood and break duration and provide a scientific basis or some solutions for optimization design of dam and counter-measures of dam break flood.


Introduction
Earth-rock or rock-fill dam is the most widely used dam type in reservoirs and dams. Taking China as an example, in 2018, it had nearly 100,000 reservoirs and dams, of which earth-rock dams accounted for more than 95% [1] [2]. Compared with other dam types, earth-rock dams have suffered the most from natural disasters such as earthquakes and over-standard floods, and the damage degree is also more serious [3]. In recent years, with global climate change, the probability of dam failure caused by extreme weather has greatly increased [4]. From 1954 to 2017, a total of 3529 reservoir dams broke out in China, and in 2018, there were 12 more dam failures [5], of which dams below 30 m accounted for about 88% of the total dam failures [6]. These dam breaches have caused serious losses to the lives and property safety of the people downstream. Therefore, it is necessary to deeply study the collapse mechanism and break process of earth-rock dams.
Earth-rock dam failure mechanism and simulation of the failure process are the basis of dam-break disaster assessment and emergency treatment. After decades of research and exploration, domestic and foreign scholars have systematically revealed the failure mechanism of earth-rock dams under the action of different hazard factors, developed various mathematical models of dam breaks and obtained a series of innovative results, which provides theoretical support for improving prediction accuracy of dam break flood disaster [7]. Dam break patterns include sudden whole failure (or break) and gradual failure, the latter is further divided into gradual whole failure and gradual local failure, and the former (or also known as instantaneous break) normally occurs on gravity dam or arch dam, with very short break time; the gradual failure normally happens at the rock-fill dam, earth-rock dam and other types as well as earth-rock cofferdam [8] [9] [10]. The failure of rock-fill dam is caused by seepage piping or overtopping, in which dam crest overflow is more common, the type of dam breach can be approximated as rectangular or trapezoid, and the final size shall depend comprehensively on the material property of dam and damsite cross sectional topography [10] [11]. The Physical models should be used as supplement and calibration of Numerical models [12]. Some studies found that the vegetation and dam break shape play an important role in dam break flood wave [13]. Rock-fill dam break flood analysis is a very important basic work in early warning and emergency rescue work, and the accuracy of dam breach flood prediction can directly affect the formulation and implementation of emergency treatment plans; among them, the prediction of dam break durations is a prerequisite for risk assessment and emergency response [14]. According to relevant research, rock-fill dam break flood is sensitive for dam break duration, and the break duration has a significant impact on the magnitude of break flood and the counter-measures for excess-standard flood [15] [16].
Therefore, it is necessary to carry out in-depth research on the sensitivity of rock-fill dam break flood on different dam break durations, revealing the relationship between rock-fill dam break flood and break duration.

Study Area
Taking the Karot Hydropower Project constructed on the Jhelum River in Pa- Karot Hydropower Project is located in the Jhelum River in Pakistan, as shown in Figure 1. It's a Class II large (2)

2) Section Module
Section module contains three parts: river channel section data, Karot Dam level-volume curve, and Mangla reservoir level-volume curve, the latter two parts are mainly used to simulate dam-retained channel storage volume.   Level-volume curve of upstream reservoir of Karot Dam: The break flood of Karot dam consists of two parts, one part comes from upstream channel inflow and the other part is flood formed by sudden release of reservoir capacity retained by the dam, the latter is related to channel retained water volume above dam. The level-storage relation curve of Karot dam is simulated by adding storage area to the dam upstream section.
Downstream Mangla Reservoir level-volume curve: The reservoir capacity of Mangla Hydropower Station consists of 7 parts: upper Jhelum River, lower Jhelum River, Kanshi River, Poonch River, Mangla reservoir area, Khad reservoir area and Jari reservoir area. The water level-storage (area) of Mangla Hydropower Station is shown in Figure 4. The channel storage capacity is directly simulated for the former three parts based on measured section data, the storage capacity at different water levels is composed of channel segment storage capacity comprising adjacent channel section, and pyramid frustum cubature formula is applied for approximate calculation, as shown in Formula (1). Storage capacity of the latter four parts is obtained from Mangla Hydropower Station total storage capacity deducted from storage capacity of the former three parts at relevant water levels. Level-storage relation curve of Poonch River, Mangla reservoir area, Khad reservoir area and Jari reservoir area is simulated by adding storage area to dam upstream BX37 section.
( ) where, V is the total storage capacity of upper Jhelum River and lower Jhelum  Discharge structures: Discharge structures are considered for dam break flood simulation. Spillway in structure module adopts discharge capacity curve generalization, as shown in Figure 5, before dam break, spillway discharge flood; after dam break, flood overflow dam body while spillway discharge is not considered.

Computational Conditions and Schemes
After the occurrence of Karot dam break, its influence on the lower reach is re-     Initial water level: Initial water level of Karot break model is considered as NPL 461 m, initial water level between Karot damsite and Mangla damsite is considered as NPL 378.56 m of Mangla hydropower station; for the river reach with bed elevation higher than 378.56 m, its initial water level is considered according to the initial water level of adjacent river sections and the slope of river.

Results
Karot Hydropower Station is a Class II large (2) hydro project; its water retaining structure is an asphalt concrete core rockfill dam. According to Karot dam break modelling results in "Feasibility Study of 720 MW Karot Hydropower Project", the full breach formation time is 2 hours. This report has used standard values of the breach parameters. No discussion is made to uncertainty of the parameters. The estimation of the breach parameters can have a significant effect on the final peak discharge at the dam site so an understating of the uncertainty is important. According to the dam break data of the same type dam, the dam break durations are generally longer than 5.5 h. Therefore, the model should be rerun for at least one more breach time, to test the sensitivity to this parameter. Depending on the result of this sensitivity check, more robust conclusions could be made, or the model could be rerun for other values to gain a better understating of the likely impacts. In

Sensitivity Analysis of Peak Discharge
Under the condition of different dam break durations, damsite discharge process is as shown in Figure 9; damsite peak discharge is as shown in Figure 10. It can be seen that: after the dam break, the peak discharge at the Karot damsite is   When the dam break duration is shorter than 2 h, the damsite peak discharge is declined rapidly with the increase of breach failure time, and when the dam break duration is longer than 9 h, the damsite peak discharge is increased insignificantly.
The peak discharge of dam break flood within the range of 40 km downstream of dam is attenuated quickly, as shown in Figure 11. When the dam break dura-

Sensitivity Analysis of Downstream Highest Flood Water Surface Profile
Under the condition of different dam break durations, the highest flood water surface profile from Karot damsite to Mangla damsite is as shown in Figure 12. Open Journal of Safety Science and Technology It can be seen that: When the dam break duration increases from 1 h to 14 h, the on-way highest water level from Karot damsite to Mangla damsite is lowered by 0.22 -21.48 m, and the lowering of water level is mainly located in the reaches from 1 to 40 km below Karot dam. When the dam break duration is shorter than 6 h, the highest flood water surface profile is declined rapidly with the increase of breach failure time, and when the dam break duration is longer than 9 h, the highest flood water surface profile is increased insignificantly.

Sensitivity Analysis of Flood Peak Appearance Time
When the dam break duration is 2 h, the discharge process of on-way typical section at downstream of dam after the Karot dam break is as shown in Figure   13. It can be seen that: after the dam break, the flood peak transmits quickly. It

Sensitivity Analysis of Submerged Real Objects
Under the condition of different dam break durations, the submerged real objects below Karot dam are as shown in Figure 14 and Table 1. It can be seen that: When the dam break duration is 2 h, the submerged real objects are 2 Figure 11. On-way peak discharge along downstream of dam after dam break.

Conclusions
According to the rock-fill dam break flood sensitivity check results, the conclusions can be drawn: Karot damsite flood will exceed the spillway flood releasing capacity, the reservoir is pre-discharged to ensure dam safety; when it is forecasted that Karot damsite flood may possibly lead to dam break, we should immediately organize personnel for evacuation; as it takes a short time dam break flood spreading to downstream Mangla damsite, Mangla Hydropower Station has no time to con-Open Journal of Safety Science and Technology duct pre-discharge upon Karot dam break; it is therefore suggested to strengthen flood early warning forecast and discharging flood in advance when it is forecast that upstream Azad Pattan Hydrological Station has occurred super-standard flood.