Impact of Levee-Breach Width on the Channel–Levee–Floodplain: A Case Study in the Huaihe River Basin, China

Abstract

Breach geometry is one essential feature for flood modelling in the channel–levee–floodplain system. It is hard to accurately predict the breach geometry because of its high uncertainty. However, due to the fact that breach geometry direct impacts the flow through the breach, the water surface profile in the channel and the flood hazard factors within the floodplain are changed with the breach geometry. To explore the impacts of breach width (one feature of the breach geometry) on the channel–levee–floodplain system, we took the Cinan Feiyou Flood Control Protection Area (CNFY-FCPA) in the middle reach of the Huaihe River Basin as the study area. We constructed a coupled 1D-2D hydrodynamic model to simulate the flooding with a series of breach-width scenarios. According to the simulation results of the models, we quantitatively analyzed the impacts of breach width on the inflow through the breach, fluvial flood process, and flood hazard factors in the CNFY-FCPA. The results indicate that (i) the relationship between the peak discharge (and inflow volume) and breach width was approximate to an S-shaped curve, while the peak discharge, inflow volume, and duration per unit width decreased with the wider breach; (ii) the breach caused a decrease in the water surface profile along the entire river sections; and (iii) while the breach width exceeded a certain width, the inundation area was nearly stable without changing with wider breach. The certain width was not the same in different rivers of 300 m in the Yinghe River and of 500 m in the Huaihe River. The research results can provide a scientific basis for flood-control and disaster-reduction decision making.

1. Introduction

The artificial levees encircle the floodplain to the flood control protection area (FCPA, also known as levee flood protection zone) and secure a relatively suitable area for human living when the water stage in the river channel is higher than the hinterland ground. Levees are designed according to a certain design standard based on the requirements of different protection objects (from 20-year to >200-year return flood in China), and the fluvial flood will breach or overtop the levees while exceeding the designed standard [1,2]. The breach geometry characteristics, including the initial breach width, breach growth rate, and final breach width, are important to accurately predict the flood inundation area and map the flood hazard [3,4,5,6,7,8]. However, the breach geometry characteristics are highly uncertain and difficult to predict accurately in advance [7,9,10,11,12,13]. Hypothetical levee-breach (non-existent in reality) scenarios are widely used to pre-simulate the flood hazard factors before a flood comes and are useful for the administrators to make decision in the flood controlling [14]. The breach width used in the flood inundation modelling in References [14,15,16,17,18] adopted a fixed value that was actual in historical floods or hypothesis with an empirical or mathematical method. Regarding the impact of breach width on flood evolution, more attention has been paid to the comparative study of flood hazard factors within FCPA under different breach width scenarios. For example, Su et al. [19] analyzed the impact of the breach width on the arrival time of floods in the lower Yellow River FCPA; and He et al. [20] compared the differences in the flood storage, inundation area, depth with different breach widths in the east of Qingtongxia FCPA in the Yellow River. The flow in the channel and through the breach, as well as other parts of the system, was not fully discussed in [20,21]. The sensitivity analysis of breach width on the channel–levee–floodplain system pointed out that the breach width was a sensitive parameter [5,7], but it did not provide the flow relation with the breach width. In addition, the decrease in the water stage in the river channel due to the breach may reduce the breach possibility in other parts of the levee. While there are higher-level FCPA (i.e., cities) in the basin, a breach at the lower-level FCPA will be initiatively created to reduce the water stage in the river channel [21]. In general, because the levee-breach width is hard to accurately predict before the flood comes, and the breach width determines the water stage in the river and the flood hazard factors within the FCPA, it is necessary to study the impact of the levee-breach width on the channel–levee–floodplain system in advance to provide some useful information for the administrators.

The middle reach of the Huaihe River Basin is one of the most flood-prone and severely affected flood-disaster areas in China because of the highly concentrated and intensive fluvial floods from the upstream, the low discharge capacity through the channel, and the backwater effect by the Hongze Lake in the downstream [22,23]. The fluvial flood in this area has a high probability of flooding, large head difference between the inside and outside of the levee, and long duration of high-water. Levees are important components of the Huaihe River flood control engineering system and play an important role in defending against fluvial flooding. The FCPAs have a higher population and industrial density than the other regions in the basin. Once the levee breaks, it will cause great losses. The levees in the Huaihe River Basin have passively breached in 1950, 1954, 1968, and 1975, and the levee-breach final widths range from 20 m to 500 m. In 1954, the left levee of the Huaihe River at Yushanba breached to 457 m (including three parts), and the inundated area in Cinan Feiyou FCPA by the levee breach was about 1080 km².

This work aimed to analyze the impact of the levee-breach width on the channel–levee–floodplain system. In order to analyze how the breach width impacts the breach flow, a relationship between the breach flow (peak discharge, inflow volume, and inflow duration) and the breach width was built. To analyze how the breach width impacted on the channel and whether there was effective intentional breach width in controlling the river water stage, the degree and range of the river channel influenced by the breach were identified. To check whether flood hazard factors always increased with the wider breach, we identified the flood hazard factors in the FCPA and whether they varied with the breach. We used a one-dimensional–two-dimensional (1D-2D) coupled hydrodynamic model to construct the flood analysis models (Section 2.2). A series of scenarios with different levee-breach widths (combinations with the breach location and the flood magnitude) were set and calculated by the flood analysis models (Section 2.3). The models with scenarios simulated the fluvial flooding in the channels, the flow penetrating through the breached portion, and the flood inundation within the FCPA. Meanwhile, some quantitatively features representing the impact (including the fluvial flooding in the channels, the flow penetrating through the breached portion, and the flood inundation within the FCPA) were extracted from the outputs from the flood analysis models (Section 2.4). Through the comparation of features, we quantitatively analyzed the impact of the levee-breach width on the hydrograph in the river channel, breach, and the FCPA (Section 3 and Section 4). The results would provide a scientific basis for flood controlling and disaster-reduction decision making.

2. Materials and Methods

2.1. Study Area

The study area, named Cinan Feiyou Flood Control Protection Area (CNFY-FCPA), comprises the region that is bordered by the left levees of the Yinghe River, Huaihe River, and Xifeihe River; and the right levee of the Cihuaixinhe River. Location and surroundings of the study area is shown in Figure 1. The total area of the CNFY-FCPA is 2213 km². The left levees of the Yinghe River, Huaihe River are designed to prevent the 100-year return period flood, which have a crest level of 2 m taller than the project flood stages. The right levee of the Cihuaixinhe River (a manmade bypass), made up of the spoil of the bypass excavation, is as wide as several hundred meters. The flood stage in the Yinghe River, Huaihe River, and Xifeihe River is higher than the ground in the CNFY-FCPA, and the fluvial flooding potentially inundates into the CNFY-FCPA through levee breaching or overtopping. The study area is a relatively flat terrain with a 0.005-degree slope from northwest to southeast. The average, maximum, and minimum ground elevation are 25.2 m, 30 m, and 17.5 m, respectively. The crests of threadiness infrastructures, such as railways, highways, and inner river levees, are about 2-to-4 m above the surrounding ground and have a significant impact on the flood routing while levee breaching. The Fuyang Sluice, Zhengyangguan, Lutaizi, Xiashankou, and Xifeihe Sluice are the main stream gauging stations surrounding the area. The Fuyang Sluice and Zhengyangguan are the typical stream gauging stations in the Yinghe River and Huaihe River, with an upstream catchment area of 35,246 km² and 88,630 km². The designed discharge capacity of the reach of the Yinghe River from the Fuyang Sluice to enter the Huiahe River is 3760 m³/s, and the Huaihe River from Zhengyangguan to Guohekou is 10,000 m³/s. The left levee of the Huaihe River had breached at the Yushanba in 1954 as three discontinuous sections, which had a width of 255 m, 202 m, and 102 m, and depth of 4 m to 4.5 m.

2.2. Flood Analysis Model

Figure 2 shows a schematic diagram of the calculation scope of the flood analysis model. A 1D-2D coupled hydrodynamic model was constructed using MIKE FLOOD. The 1D-2D coupled model integrated the 1D model MIKE11 and 2D model MIKE21 into a single coupled system [24]. The unsteady flow of the Yinghe River and Huaihe River was modeled in MIKE11. The flood inundation in the CNFY-FCPA was modeled in MIKE21. The linkage between the MIKE11 river branch (at the levee-breach position) and the MIKE21 cells (some cells nearby the levee-breach position) simulated the flow through the levee breach.

The 1D model used the measured longitudinal and cross-sectional terrain, and the average space between cross-sections was 500 m. The channel roughness, one of the sensitivity parameters in the 1D model [25], was calibrated by typical floods in 2003 and 2007. The maximum difference between the simulated and measured peak water stage was 0.07 m in 2003, and the maximum was 0.04 m in 2007. The calibrated values of the roughness of the riverbed and the beach in the Yinghe River were 0.0225 s/m^1/3 and 0.0375 s/m^1/3; and in the Huaihe River, they were from 0.025 s/m^1/3 to 0.027 s/m^1/3 and from 0.038 s/m^1/3 to 0.042 s/m^1/3. The bed resistance in the 2D model was set according to [26]: land cover of orchards, forest, agriculture, rangeland, and dry land was 0.04 s/m^1/3, 0.04 s/m^1/3, 0.05 s/m^1/3, 0.035 s/m^1/3, and 0.06 s/m^1/3, respectively.

The 2D model used unstructured mesh that could easily handle irregularly shaped inner and outer boundaries [27]. The threadiness infrastructures (the railways, highways, and interior river levees inside of the CNFY-FCPA) were generalized as lines and acted as the inner boundaries along with the outer boundaries in the mesh generating. We preprocessed the DEM and used the spatial interpolation method of adjacent DEM to form new terrain data that could truly reflect the overall trend terrain, eliminating the micro-landforms such as levees, roads, and rivers. The resolution of the DEM and interpolated terrain was 5 m. The micro-landforms (railways, highways, and inner river levees) were simplified as lines, and the holding back of the lines on the flood inundation were similar to a dike. If the water stage within the cell on one side of the dikes was higher than the crest of the dike, flooding overtopped the dike and inundated the other side cell. The number of discrete cells in the 2D model had a significant impact on computational efficiency. To effectively decrease the numerical computation time, the modeling scope in the 2D model was limited to the area below the highest flood stage in the FCPA, and the maximum area of the discrete cell was no more than 0.1 km². The CNFY-FCPA was discrete into 35,214 cells and 18,043 nodes in space.

2.3. Scenarios Setting

Based on factors such as the historical hazards and geological conditions of the levee foundation and river conditions, the Yuanzhai was selected as the representative location for the analysis of the Yinghe River levee-breach flood, and the Yushanba was chosen as the location for the Huaihe River levee-breach flood. Both the Yushanba breach and Yuanzhai breach were hypothetical and did not exist in reality. The Yuanzhai breach was located in the northwest of the FCPA, and the adjacent ground elevation was relatively high. The elevation of the levee crest at Yuanzhai was 34.1 m, the project flood stage was 32.01 m, and the adjacent ground elevation inside the levee was about 28 m. The flood from the breach flowed downstream along the slope within the FCPA and might inundate a large area with a high flow velocity. The Yushanba breach was located in the southeastern part of the low-lying in the FCPA. The elevation of the levee crest at the Yushanba was 27.5 m; the project flood stage was 25.5 m; and the adjacent ground elevation was a relatively low, i.e., 19.3 m. The floodwater from the Yushanba breach progressed against the slope towards the upper end of the FCPA.

The breach shape was assumed to be rectangular and was characterized by its final width, widening rate, and final invert elevation. The theoretical final width of the breach was calculated using the empirical Equation (1) in Reference [28].

B_b = 4.5(lg B)^3.5 + 50,

(1)

where B_b is the final width of the breach, and B is the river width.

The theoretical final width of the Yuanzhai breach was 207 m, and the Yushanba breach was 440 m according to Equation (1). To analyze the impact of the breach width on the flood hazard, the theoretical breach width was used as the intermediate value, with 2 or 3 levels set upwards and downwards. Therefore, the width series of the Yuanzhai breach were set to 10 m, 50 m, 100 m, 200 m, 300 m, 500 m, and 1000 m; and for the Yushanba breach, they were set to 50 m, 100 m, 200 m, 500 m, 1000 m, and 2000 m. Meanwhile, the final invert elevation of each breach was the riverside toe elevation. The breach width along the levee was assumed to form instantaneously, meaning that the initial breach width was equal to the final one. The breach was assumed to form with a fixed speed vertically from the levee crest to the final invert elevation.

To analyze the impact of the breach width on the channel–levee–floodplain system under different flood magnitudes, the Yinghe River 50-year flood, the Yinghe River 100-year flood, the Huaihe River 100-year flood, and the Huaihe River 300-year flood were adopted to represent the flood magnitude. The flood control design standard of the levee and river channel of the Huaihe River was a 100-year flood, and for the Yinghe river, it was a 50-year flood. The designed flood hydrographs were created from the Huaihe River Basin Comprehensive Planning results, which were widely used in the planning and designing of flood control projects in the Huaihe Basin. The hydrographs were unsteady processes and were calculated based on the 1954 flood event. The peak discharge of the 50-year flood and 100-year flood in the Yinghe River was 4580 m³/s and 5961 m³/s. The peak discharge of the 100-year flood and 300-year flood in the Huaihe River was 10,000 m³/s and 14,245 m³/s. The design flood hydrograph at the boundaries is shown in Figure 3.

To sum up, there were 26 scenarios (shown in

Table 1. List of scenarios.

No.	Breach Location	Breach Width/m	Hydrological Condition
1–7	Yuanzhai at the left levee of the Yinghe River	10, 50, 100, 200, 300, 500, 1000	50-year Yinghe River flood
8–14			100-year Yinghe River flood
15–20	Yushanba at the left levee of the Huaihe River	50, 100, 200, 500, 1000, 2000	100-year Huaihe River flood
21–26			300-year Huaihe River flood

) designed based on a combination of the breach location, breach width, and fluvial flood magnitude. In the 1st-to-14th scenario, the breach location was at the Yuanzhai, while the flood magnitude was that of the Yinghe River 50-year flood in the 1st-to-7th scenario and was that of the Yinghe River 100-year flood in the 8th-to-14th scenario. The upper boundaries were the same as those of the design flood hydrograph of the Fuyang Sluice and Zhengyangguan, and the lower boundary was the relationship of stage–discharge at the Xiashankou. In the 15th-to-26th scenario, the breach location was at the Yushanba, with the flood magnitude of the Huaihe River 100-year in the 15th-to-20th scenario and the Huaihe River 300-year in the 21st-to-26th scenario.

2.4. Feature Extraction

From the view of the river-channel–levee–FCPA system, the levee-breach width may affect the flooding process within the subsystem and the linkage of the subsystem, i.e., the inflow through the breach, the fluvial flood, and the flood inundation process within the FCPA. Some quantitative features representing the impact on subsystems were extracted from the outputs from the flood analysis models. Figure 4 shows a sketch of the feature extraction, and the details are as follows:

Firstly, the impact of the breach width on the inflow through the breach was measured by three indexes, i.e., the peak inflow discharge, inflow volume, and inflow duration. They were acquired from the discharge hydrograph of the linkage between the 1D and 2D model. The peak inflow discharge, Q_p, refers to the maximum discharge in the discharge hydrograph. The inflow volume, V, refers to the time-integrated discharge while the discharge was greater than 0. The inflow duration, T_Du refers to the duration when the inflow discharge was greater than 0.

Secondly, the impact of the breach width on the fluvial flooding after the breach formed was measured by two indexes, which were acquired from the outputs of the 1D model. The first index was the decrease in the peak water stage (h_p(non-breach)-h_p(breach)), referring to the difference in the highest water stage along the longitudinal profile between the breach and no-breach scenario and reflecting the impact of the breach on the water surface profile. The second index was the maximum decrease in water stage (Δh_max), at the control nodes, referring to the maximum difference in the water stage at a specific chainage in the river channel between the breach and no-breach scenario and reflecting the maximum impact of the breach on the water stage in the river channel. The control nodes included the cross-section upstream of the breach and hydrological stage-gauging station. Because of the unsteady inflow discharge through the breach, the decrease in the peak water stage and the maximum decrease in water stage appeared asynchronously. Once the breach was formed, on account of the high stage difference between the upstream (in the river) and downstream (in the protected area) of the breach, the inflow through the breach increased sharply, and the water stage in the river channel changed fast, so the maximum decrease in water stage may happen soon after the breach forms. Along with the continuous inflow from the upstream and the decrease in the inflow through the breach, the water stage in the river channel would increase further, and the peak water stage would be larger than the water stage at the time the breach began.

Lastly, the impact of the breach width on the flood inundation process within the FCPA was measured according to three indexes that were constructed according to the spatial distribution of flood hazard characteristics: inundation area, inundation depth, and flood velocity. They were acquired from the outputs of the 2D model and processed by GIS. The first index was the additional inundation area with the larger breach at the specific time. The second index was the inundation depth difference between the large and small breach scenario. The third index was the flood velocity difference between the large and small breach scenario. The difference in flood hazard factors was based on the gradient level of the breach width, subtracting the small breach from the large breach.

3. Results

3.1. Inflow through the Breach

Figure 5 shows how the relationship curves of the peak inflow discharge (and the inflow volume) changed with the breach width, and the curves were approximate to the second half of the S-shapes. The wider the breach, the higher the peak inflow discharge and the larger the inflow volume through the breach; meanwhile, the smaller the breach, the smaller the peak inflow discharge and the inflow volume per unit breach width. When the breach width was less than 200 m, the peak inflow discharge and the inflow volume increased rapidly with the increase in the breach width. When the breach width exceeded 200 m, the rising rates of the peak inflow discharge and the inflow volume slowed down with the increasing breach width. When the breach width was wider than 500 m, the inflow volume of the Huaihe River in the 100-year and 300-year flood scenarios was approximate stabilized at 2.655 billion m³ and 5.320 billion m³.

In the case of the same breach width, both the peak inflow discharge and inflow volume through the breach increased with the magnification of the flood magnitude. This was owed to the higher river flood level and the longer duration of the high-water stage in the larger flood magnitude. The ratio of the inflow volume in the higher river flood level to the smaller flood magnitude was not a constant, and it increased with larger breach widths. The ratios of the 300-year to 100-year flood were 1.76 to 2.01 in the Huaihe River. The ratios of the 100-year to 50-year flood were 1.46 to 1.54 in the Yinghe River.

The larger the breach width, the greater the flood discharge into the breach, resulting in a shorter duration of the influenced high-water stage in the river and a shorter duration of inflow through the breach. For the inflow through the breach at the Yinghe River, when the breach width exceeded 200 m, the duration of the inflow was no longer changed with the breach width, and it stabilized at 17.0 days in the 50-year flood and at 18.58 days in the 100-year flood. For the inflow through the breach at the Huaihe River, when the breach width was wider than 500 m, the duration of the inflow stabilized at 20.46 days in the 100-year flood and 24.92 days in the 300-year flood.

As the breach is large, the flow through the breach can be approximated to a broad crested weir formula and calculated with a standard weir expression (Equation (2)) [24].

$$Q=W·C·{\left(H_{us}-H_w\right)}^k·{\left[1-{\left(\frac{H_{ds}-H_w}{H_{us}-H_w}\right)}^k\right]}^{0.385}$$

(2)

where Q is the discharge through the breach, W is the breach width, C is the weir coefficient, k is the weir exponential coefficient, H_us is the water stage at the channel side, H_ds is the water stage at the floodplain side, and H_w is the weir crest level.

It is intuitively plausible to see from Equation (2) that the discharge is proportional to the width of the breach. However, the discharge and the water level at the floodplain and channel sides are interactive in real time, and the iteratively calculated discharge is not proportional to the breach width anymore. According to the modelling results (Section 3.1), the relation between the flow (peak discharge, volume, and duration) through the breach and breach width is not linear but approximate to the second half of the S-shape in the study area. Because the water stage in the floodplain side rises faster due to the higher discharge in the wider breach, the water head difference between the two sides reduces with a faster speed. Then, although the flow through the breach rises with the breach width, the rising rate is nonlinear. Meanwhile, we can derive that it needs to use an iterative method to simulate the flood process in the channel–levee–floodplain system, and the non-iterative method (e.g., calculating the discharge according to Equation (2), while assuming that the water stage at the floodplain side is fixed) will give a liner discharge with breach width, but that is an erroneous result.

Despite the parallel trend of the relationships between the breach flow and breach width, the relationships are visibly different in different flood magnitudes and rivers. This demonstrates that the breach flow is not only a matter of the breach width but also of the fluvial flood events (peak water stage and duration of the fluvial flood). It is more than necessary that the breach flow is modelled with a specific river and flood event. Meanwhile, we also recognize that, since the breach width is constant, the larger the magnitude of the flood, the higher the flow (peak flow, volume and duration), as well as the peak flow and volume per unit breach width.

3.2. Fluvial Flood after Breaching

Figure 6 shows the stage hydrograph at the cross-section linked to the breach. After the breach formed, the water stages at the cross-section were lower than those of the non-breach scenario, and they even fell in some breach scenarios. As shown in Figure 6a, in the scenarios of the 50-year flood in the Yinghe River and when the breach width exceeds 100 m, during the period from the breach onset time to front of the second flood event coming, the water stages at the chainage were lower than they were at the breach onset time (same as the project water stage). As shown in Figure 6b, in the scenarios of the 100-year flood in the Yinghe River and when the breach width exceeded 200 m, after the breach formed, the water stages fell firstly and rose latterly; also, the falling rate was faster and the rising rate was slower with the wider breach. This was because, the larger the breach, the larger inflow through the breach and the faster the water-stage rising in the inner FCPA, and the water level difference between the upstream and downstream of the breach would more rapidly reduce, resulting in less flood inflow in the later stage. As shown in Figure 6c, in the scenarios of the 100-year flood in the Huaihe River, the water stages fell firstly and rose latterly, and the falling and rising rates were faster with the widening breach. As shown in Figure 6d, in the scenarios of the 300-year flood in the Huaihe River, when the breach width was less than 200 m, the water stages continued to rise, but the rising rate was slower than it was in the non-breach scenario. When the breach width was wider than 500 m, the stages fell firstly and rose latterly, and the falling and rising rates were faster with the wider breach.

Figure 7 shows the maximum decline in the water surface profile in the river channel caused by the breach. From the Figure 7, we can see that the maximum decline values in the all scenarios were positive, indicating that, compared to the non-breach scenario, all water surface profiles declined in various ranges. As the breach became wider or the flood magnitude became larger, the water surface profile in the Yinghe River declined within a larger range. As shown in Figure 7a,b, when the breach was wider than 100 m in the 50-year flood or wider than 300 m in the 100-year flood of the Yinghe River, the maximum decline in the reach from the Fuyang Sluice to the downstream of the breach with 10 km did not increase with the wider breach. As shown in Figure 6c, in the scenarios of the Huaihe River 100-year flood, the maximum decline was roughly the same in the upper reach from the Zhengyangguan to the downstream of the breach with 47.4 km, and it was obviously different in the rest breach. This is because the time of the peak water stage was the first moment after the breach formed in the upper reach, and not the first moment in the rest reach. The record of the peak water stage in the upper reach was the same value, and it was different in the rest reach. As shown in Figure 7d, in the Huaihe River 300-year flood scenarios, the water surface stage in the Huaihe River declined in the order of 100 m, 50 m, 200 m, 500 m, 1000 m, and 2000 m of the breach width, instead of the gradient of the breach width.

3.3. Flood Hazard Factors in Flood Control Protection Area

Figure 8 shows the spatial distribution of the flood inundation areas under a series of breach widths. As the breach widened, with the exception of the inundation area by the smaller breach, the additional area on the periphery was inundated by the wider breach. Moreover, the additional area in the Yinghe River flood (shown in Figure 7a,b) was more obvious than that in the Huaihe River flood (Figure 7c,d). The breach width was only 10 m in the Yinghe River 50-year flood, and flooding from the breach inundated 271 km² of land in the FCPA. When the breach width reached 50 m, the inundation area expanded to 695 km². When the breach width exceeded 300 m, the inundation area was essentially the same, with an area of 1230 km² to 1305 km². With the same breach width, the inundation area by the Yinghe River 100-year flood was larger than that in the Yinghe River 50-year flood. When the breach width exceeded 500 m, the inundation area by the Yinghe River was up to 1590 km² to 1647 km². However, the additional area created by breach widening was relatively small in the Huaihe River flood. In the Huaihe River 100-year flood scenarios, when the breach width was less than 1000 m, the inundation area was 851 km² to 923 km², and the additional parts created by breach widening were relatively small; the inundation area was up to 1105 km² as the breach widened to 2000 m. In the Huaihe River 300-year flood scenario, the inundation area was 1105 km² as the breach width became 2000 m; when the breach wider than 200 m, the inundation area remained stable at 1601 km² to 1699 km².

The flood hazard factors, such as inundation depth, flow velocity, and inundation time within the FCPA, increased with the wider breach. The inundation area by the large breach included two parts, i.e., the inundation area of the small breach scenario and additional inundation area. The flood hazard factors within the inundation area of the small breach scenario generally increased in a large breach scenario.

Table 2. Difference of the flood hazard characteristic induced by the breach width in the Yinghe River 100-year flood.

Breach Width/m		Increment of Inundation Depth/m		Increment of Flow Velocity/(m/s)		Increment of Inundation Time/d
Small Breach	Large Breach	Within the Inundation Area by Small Breach	Additional Inundation Area of Large Breach	Within the Inundation Area by Small Breach	Additional Inundation Area of Large Breach	Within the Inundation Area by Small Breach
10	50	0.68	0.91	0.06	0.11	6.30
50	100	0.33	1.29	0.03	0.10	2.72
100	200	0.42	0.42	0.03	0.06	1.93
200	300	0.16	0.23	0.01	0.04	0.96
300	500	0.08	0.10	0.01	0.05	0.51
500	1000	0.03	0.06	0.00	0.04	0.22

lists the difference of the flood hazard factors induced by the wider breach width in the Yinghe River 100-year flood event. When the breach widened from 10 m to 50 m, within the inundation area of the 10 m breach width (347 km²), the inundation depth averagely increased by 0.68 m, the flow velocity averagely increased by 0.06 m/s, and the inundation time averagely extended by 6.3 days. The average inundation depth within the additional inundation area by the 50 m breach width was 0.91 m, and the average flow velocity was 0.11 m/s. When the breach width exceeded 300 m, the increasing trend of flood risk factors within the inundation range of the small breach scheme gradually slowed down.

4. Discussion

4.1. Range of Influenced by the Breach in the River Channel

The breach causes a decrease in the peak water surface profile in the river channel, affecting the entire river section modeled by the flood analysis model [29]. The influence range by the breach is not only the channel downstream of the breach but also the upstream. The upstream channel water stage drops due to the new pathway provided by the breach, and the discharge capacity is enhanced in the same stage compared with the non-breach [30,31,32]. The downstream channel water stage drops due to the breach dividing part of the floodwaters, thus reducing the discharge by this channel. The maximum decrease along the channel is not always located at the cross-section near the breach. This is not consistent with the findings in Reference [33]. This may be caused by the river channels’ geomorphology and the hydrological condition, which needs further research.

4.2. Turning Point of Breach Width in the Effective Restricting of the Inundation Area

The breach width is one of the key breach geometry features in determining the inundation area of the breach [3,4,5,6,7,8]. As the breach becomes wider, the inundation area expands, but the rate of expansion reduces. There is a turning point for the breach width in the relationship between the inundation area and the breach width. When the breach width is below the point, the inundation area obviously increases with the wider breach. However, when the breach width is equal to the point, the inundation area is nearly stable and does not change with the wider breach. Because of the existence of the critical breach width, administrators should pay more attention to the breach width and take effective measures to control the widening rate of the breach after the breach forms. When the breach width is wider than the critical one, the measures that are used to control the breach width have a limited effect in the inundation area of the FCPA. The critical breach width is not the same in different rivers; for instance, it is 300 m in the Yinghe River and of 500 m in the Huaihe River. Therefore, it is necessary that the critical breach width be analyzed according to the location of the breach, the flood process of the river, and the topography of the FCPA rather be taken as a uniform value for all rivers.

4.3. Effective Intentional Breach Width

The presence of levees does not completely eliminate the risk of inundation of flood-prone areas [2]. Every levee is constructed to cope with a given maximum flood magnitude, above which flow will overtop or breach the levee and flow into the FCPA. If the flood exceeding the flood control capacity hits the basin, a levee breach will be intentionally created on the lower-level FCPA to reduce the water stage in the river and to ensure the safety of the downstream city [21]. According to the Huai River Flood Control Scheme, CNFY-FCPA may need to intentionally breach the levee to reduce the water stage in the Huaihe River and ensure the safety of the higher-level flood protection areas (e.g., the Cinan Feizuo FCPA, Huainan City, and Bengbu City, as shown in Figure 1a). When the breach width exceeds 500 m in the Huaihe 300-year flood event, the maximum decrease in the surface profile is very limited with a wider breach. Therefore, to reduce the amount of the post-disaster reconstruction of the intentional breach, measures controlling the breach width should not be undertaken until the breach width exceeds 500 m. Meanwhile, the inundation area of breakwater floods expands and gradually stabilizes with the wider breach, and the growth rate decreases with the increase in the breach width. When the Huaihe River encounters excessive floods and needs to intentionally break the levee of the Huaihe River, the width of the opening should not exceed 500 m.

5. Conclusions

We constructed coupled 1D-2D hydrodynamic models to simulate the flooding in the channel–levee–floodplain system with a series of breach-width scenarios. The parameters of the hydrodynamic model were calibrated with measured flood water stages. To draw the relationship between the breach width and its impact, a series of breach widths were reasonably set to 6 or 7 levels, and the median width was calculated by using an empirical formula. Some quantitative features, representing the flow in all subsystems, were extracted from the outputs of models. After comparing the features, we quantitatively analyzed the impact of the breach width on the flow through the breach, fluvial flood process, and flood hazard factors in the CNFY-FCPA. The results indicated the following: (1) The relationship between the peak discharge (and inflow volume) and breach width was approximate to an S-shaped curve, while the peak discharge, inflow volume, and duration per unit width decreased with the wider breach. (2) The breach caused a decrease in the water surface profile of the river and affected the entire river sections modeled in the flood analysis model. The research results could provide a scientific basis for flood-control and disaster-reduction decision making.