Modelling and Impact Analysis of Combined Dam Failure of Small Tandem Reservoir Groups in Hilly Areas

Numerous small reservoirs in hilly areas play a significant role in flood control and profit-making in the basin, but there is also a risk of dam failure when encountering special circumstances such as excessive flooding, which may cause large losses downstream. In this paper, we take the small reservoirs in Shandong Province as the research object, analyze the hydraulic topology of three types of tandem reservoirs, generalize the shape of the breach by using the transient lateral local one-break to the end, calculate the dam-break flooding process by using the quadratic parabolic method, and simulate the dam-break by using the MIKE21 model based on the principle of the two-dimensional incompressible Reynolds mean stress equation for the incompressible fluid, and analyze the peak flow under various combinations of dam-break flow by setting various combinations of the number of dam-breaks and the timing of dam-break simulation. By setting various combinations of dam failure numbers and timing, we analyzed the changing rules of peak dam failure flow, inundation area and other elements under various combinations, and sought the most unfavorable combinations and parameters such as the timing of dam failure, and the results of the analyses can provide technical support for the assessment of the risk of dam failure in the tandem reservoirs in the hilly area and the risk correspondence.


Introduction
For the past few years, climate anomalies and frequency of unusual weather events have occurred more often than not, and the rainfall distribution in time and space has been severely uneven, with many places experiencing record rainfall.Reservoirs, as an engineering measure for flood control and disaster mitigation as well as profit generation, play a crucial role in protecting downstream safety and irrigating downstream farmland, and are an important infrastructure for safeguarding regional economic and social development [1].
Because reservoir dam failure floods are unpredictable and often occur suddenly, there is little measured information available to study it historically, and its current study is usually achieved using numerical calculations or physical modelling tests [2].The simulation of a cascading dam failure The simulation of cascade dam failure needs to be based on the simulation of single reservoir failure, considering different dam types, the chain response of cascade reservoirs and more complex flood composition.
There have been more results on the dam failure studies of terraced reservoir groups.For example, Chen Chunyan [3] et al, Su Bin [4], Guan Zhiwei [5] and Li Guangjin [6] used numerical computation to simulate the dam failure of the terrace reservoirs; Liu Qinghong [7] et al, Yang Zhongyong [2] et al, He Chengshan [8], and Mihretab G. Tedla [9] et al, respectively, used the DamBreak dam failure model, the MIKE21FM twodimensional hydrodynamic model and the CFD open source software OpenFOAM and HEC-HMS model and HEC-RAS model respectively to simulate the dam failure of a terraced reservoir and analyze the impact characteristics of the terraced reservoir after dam failure; Bullen Emma [10] studied the dam failure model and mapping problems of the reservoirs in Wales; Guo Xinlei [11] et al. developed a numerical simulation platform for the successive failures of a group of reservoirs based on the DB-IWHR model, which can provide a reasonable flood relief for the terraced reservoirs under the extreme operation conditions.The rational flood release scheme is given under extreme operating conditions; Hu Liangming [12] et al. established a continuous dam failure model for earth and rock dams of terraced reservoirs by linking upstream and downstream reservoirs through flood regulation algorithms on the basis of the DB-IWHR model; Li Ping [13] et al. and Lin Pengzhi [14] et al. constructed a Bayesian network model for the successive failures of two reservoirs, and analyzed the probability of dam failure of the terraced reservoirs.
In this paper, three groups of tandem reservoirs in the general hilly area of Shandong Province, namely, "big on top and small on the bottom", "comparable on top and bottom" and "small on top and big on the bottom", are selected, and the same type of dam failure scenarios are set up for each group of reservoirs.The flooding process and inundation under different scenarios are analysed to summarise the flood inundation pattern of dam failure under different topological relationships.

Basic Information about the Study Area
The selected study sites are located in Geshi Town, Ningyang County, Tai'an City, Shandong Province, Nanhuang Town, Rushan City, Weihai City, and Datuan Town, Rongcheng City, Weihai City, all of which are located in the general hilly area.
The three groups of tandem reservoirs selected for this study satisfy the topological relationship of "large above and small below, comparable above and below, and small above and large below", namely, Mazhuang Reservoir and Dongyun Reservoir, Gaojiatun Reservoir and Siqingjiang Reservoir, and Dazhuji Reservoir and Dazhuji Reservoir.The three groups of reservoirs in the study area belong to the general hilly area, where the river specific drop is larger than that in the plains and the flood evolution is fast.The topological relationships of the three selected groups of typical tandem reservoirs cover most of the two tandem reservoir types, and the study of their dam failure floods and inundation impacts can provide a reference for dam failure of other terrace reservoirs in the hilly area.

Calculation of Dam Failure Flow
In this paper, 3 groups of 6 reservoirs dam type are all earth and stone dams, according to "Hydraulic Calculation Manual (Second Edition)", this earth and stone dam breach form using transient lateral local breach treatment.B -Water surface width along the dam axis or length of dam ceiling in case of dam failure (m).

Dam Failure Flow.
Soil and rock dam failure flood calculations select rectangular breach transient lateral local a collapse to the end, due to the breach b is smaller than the dam length B, this breach upstream of the negative wave will have a multi-directional to provide the characteristics of the downstream water discharge, so that the breach of the depth of water increases, the flow also increases.
The maximum flow cannot be calculated directly from the instantaneous total dam failure, but needs to be multiplied by a correction factor greater than 1 . Regarding the index of correction coefficient  , generally take 0.25~0.4,this according to the yellow committee dam failure flood evolution model test data take  = 0.4, that is: 3.1.3.Dam Failure Flood Process.This time, four parabolas were used to generalise the flow process.
Where: K -coefficient, generally take 4 to 5. V --Reservoir dischargeable capacity before dam failure (m³) 2) Preliminarily determine the flow process line based on T , m Q , 0 Q .
Check whether the water volume between the process line and the Q = 0 Q line is equal to the discharge capacity V , if not, adjust the value of T and retry the calculation until they are equal.

Combination of Dam Failure Scenarios and Simulation Results
In order to study the inundation effects of different dam failure flood combinations, four working conditions are set up for each group of typical tandem reservoirs, i.e., "lower failure, upper failure and lower diffusion, upper and lower failures at the same time, and upper failure leading to lower failure", and a total of 12 working conditions are calculated in this paper.

Analysis of the Impact of Upstream Dam Failures on Downstream Reservoirs
When the upstream reservoir breaks the dam will produce a large flood flow, the flood water in the evolution of the downstream process will be attenuated, the flood water evolution to the downstream reservoir when the peak of the flood water and the maximum discharge of the downstream reservoir will be compared to analyse the impact on the downstream reservoir, the data are shown in Table 4.In the first group of tandem reservoirs, for Scenario 2, in the case of a single breach of the upstream Mazhuang Reservoir, the maximum dam breaching flow it generates is 1809m³/s, and when the flood water evolves to the Dongyun Reservoir, the flow rate attenuates to 536m³/s, which is still much larger than the maximum discharge flow of 99.56m³/s in Dongyun Reservoir, and as the incoming water volume is larger than the discharged volume, the water level of the Dongyun Reservoir will rise gradually, because the Mazhuang Because the reservoir capacity of the Mazhuang Reservoir is 2.4 times that of the Dongyun Reservoir, the water level of the Dongyun Reservoir will continue to rise, and when it rises to the crest elevation, it will overflow the dam, which will then lead to a dam failure in the downstream reservoir.
In the second group of tandem reservoirs, for Scenario 6, in the case of a single breach of the upstream Gaojiatun Reservoir, the maximum breaching flow rate generated is 272m³/s.Due to the close proximity of the two reservoirs, after the breaching of the Gaojiatun Reservoir, the floodwaters flow into the Siqingjiang Reservoir, the breaching flow rate of the upstream reservoir is greater than the maximum discharge of the downstream reservoir of 29.03m³/s, and the water level of the Siqingjiang Reservoir will rise gradually, and due to the comparable reservoir capacity of the two reservoirs, the water level of the downstream reservoir must rise to the top elevation of the dam and overflow the dam, which then leads to the breaching of the downstream reservoir.Since the two reservoirs have equal capacity, the water level of the downstream reservoir will rise to the dam crest elevation and overflow the dam, which will lead to the dam failure of the downstream reservoir.
In the third group of tandem reservoirs, for Scenario 10, in the case of a single breach of the upstream Dazhuji Reservoir, it produces a maximum breaching flow of 594 m³/s, and when the flood water evolves into the downstream Dazhuji Reservoir, the flow rate attenuates to 243 m³/s, which is greater than the maximum discharge flow of the downstream reservoirs of 162 m³/s.However, since the upstream reservoirs' capacity is much smaller than that of the downstream reservoirs, the upstream reservoirs will not be empty when the upstream reservoirs empty After that, the water level in the downstream reservoir did not reach the dam crest elevation, and therefore it would not lead to dam failure in the downstream reservoir.

Comparative Analysis of the Impact of a Dam Failure in a Tandem Reservoir Versus a Single Downstream Reservoir Failure
In the three groups of tandem reservoirs selected in this study, all the working conditions show that the dam failure flow, total inundation area, and inundation area under different water depths of the tandem reservoirs are all larger than those of the downstream reservoirs.Which in the reservoir "big up and small down" and "up and down equivalent" when the law is more obvious, when the upstream reservoir is small, the dam failure flow itself is small, when the flood water evolution to the downstream will be much smaller than the downstream dam failure flood, the two flood processes superimposed on the downstream dam failure flood will not have a big difference.flood will not be much difference.The localised inundation areas of the three types of tandem reservoirs under the downstream reservoir single breach and upstream reservoir breach floods leading to downstream reservoir breach scenarios are mapped as follows.

Analysis of the Impact of Dam Failure Timing on Tandem Reservoir Failures
In the three sets of tandem reservoirs in this simulation, when the upstream reservoir is larger, the gap between the simulated dam failure flood flow and inundation area under different dam failure timing is larger, because the dam failure flow generated by the upstream reservoir is large, and although the two reservoirs are far away from each other, the flood peak of the upstream reservoir is still much larger than that of the downstream reservoir dam failure flood when the upstream reservoir flood evolves downstream, which will have a larger gap between the flood process or flood peak when superimposed in a different way with the downstream reservoir dam failure flood.When the upstream and downstream reservoirs are of similar size, the simulated dam failure flood flow and inundation area under different dam failure timing have smaller gaps, because the distance between the two selected reservoirs is small, and there is no big gap between the two sets of flood processes when the upstream reservoir dam failure flood evolves to the downstream and the staggered peak time is short, so there is no big gap between the peaks of the flood and the flood processes, and the resulting inundation impacts are not large.
When the downstream reservoir is larger, there is a small gap between the simulated dam failure peak flow and the inundation area, because the dam failure flow from the upstream reservoir evolves to the downstream reservoir and the dam failure flow from the downstream reservoir is insignificant compared to the dam failure flow from the downstream reservoir, but there is a small gap between the two flooding processes superimposed in different ways, but the total amount of flooding is the same, and the resulting inundation area is basically no gap.There is essentially no difference in the inundation area.Comparison of local inundation for the three types of tandem reservoirs for the simultaneous upstream and downstream reservoir breach scenario and the downstream reservoir breach scenario due to the upstream reservoir breach flood are shown below.

Results and Discussion
From the above analyses of dam failure for various operating conditions, the following results can be obtained: (1) A comparison of the various options shows that the more capacity the reservoir has and the taller the dam site, the higher the dam failure in flow, and the more easily a succession of downstream reservoir failures can occur if there is a graded reservoir downstream.Therefore, among the three groups of tandem reservoirs, the dam failure of both Mazhuang Reservoir and Gaojiatun Reservoir will cause the downstream reservoirs to collapse, but the former will have a greater impact on the downstream, whereas due to the smaller size of the upstream Dazhuji Reservoir, its failure will not have an impact on the downstream reservoirs.
(2) In three sets of dam failure simulations for reservoirs with different magnitude topological relationships, all scenarios show that a continuous failure of upstream and downstream echelon reservoirs produces larger flood peaks, flood processes, and inundation areas, and a more rapid arrival time of the flood front and flood peaks, relative to a single failure of a downstream reservoir.
(3) In this study, for the reservoir relationships of "equal upstream and downstream" and "small upstream and large downstream", there is not much difference in the impacts of dam failure under different timing of dam failure; while when the reservoirs are "large upstream and small downstream", the flood peak, inundated area, flood front and flood arrival time, and inundated area under different water depths are all greater than those of the graded reservoirs that fail at the same time.The flood peak, inundation area, flood front and peak arrival time, and inundation area at different water depths of the downstream reservoir resulting from the upstream dam failure are all larger than those for the simultaneous dam failures of the staircase reservoirs.

Conclusion
(1) In this paper, the dam failure flow is calculated according to the Water Resources Calculation Manual, and since the dams under study are all earth and rock dams, the breach is made by transient transverse local one-break-to-the-bottom, and the dam failure flood process line is calculated by the quadratic parabolic method, and simulated by MIKE21 model based on the principle of the Reynolds mean stress equation for two-dimensional incompressible fluid, the simulation of the dam failure of two-dimensional reservoirs based on the method has certain Rationality.
(2) At present, most of the domestic and foreign research on dam failure is aimed at a single dam failure, and in the study of dam failure in terraced reservoirs, the main focus is on the discussion of the dam failure flow process, flood evolution characteristics and inundation characteristics, while this paper takes a different approach to the study of different tandem types of reservoirs dam failure and the evolution of the law, through the setting of a variety of combinations of the number of dams and timing, comparative analysis of various combinations of dam failure under the peak flow, evolutionary time, inundation By setting a variety of combinations of the number and timing of dam failure, comparing and analysing the pattern of change of dam failure flow peak, evolution time, inundation area and other elements under various combinations, we seek the most unfavourable dam failure scheme and tandem type, and the results of the study can provide reference for the flood prevention and mitigation of reservoirs in hilly areas.
(3) This paper does not consider interval floods when simulating dam failure floods, and only two dam failure timing scenarios are considered, and these efforts will continue to be refined in subsequent studies.

Figure 1 .
Figure 1.Location map of tandem reservoirs.

3. 1 . 1 .
Dam Breach Width.The length of the dam break of the earth dam failure b value, the Yellow Committee of the Academy of Water Sciences based on the analysis of the actual information recommended the following calculation method: b -width of ulceration (m); V -Reservoir capacity at dam failure (million m³); H -Depth of water in front of the dam at the time of dam failure (m); k -The coefficients related to the soil quality of the dam have values of approximately 0.65 for clay and 1.3 for loam;

Figure 2 .
Figure 2. Downstream single breach and cascading dam breach inundation maps.

Figure 3 .
Figure 3. Comparative inundation maps for simultaneous and cascading dam failure scenarios.

Table 2 .
Table of quadratic parabolas. m

Table 3 .
Combination of dam failure programmes.

Table 4 .
Downstream reservoir intake and maximum discharge flow data.