Introduction

Floods are high frequency natural disasters that result in a wide range of hazards which seriously threaten the social stability and economic development of countries worldwide. Reservoirs are buildings that play an important role in floods control and regulation. At present, China has built more than 98,800 dams, the highest number in the world, with various types of reservoirs. However, over time, many reservoirs have faced difficulty in avoiding dilapidation and aging, leading to the emergence of numerous damaged and dangerous reservoirs. From 1954 to 2019, the total number of dam failures in China was 3,541, with an annual average of 53.7 dam failures1. The causes of dam failure include flood overtopping, dam quality problems, and improper management, among which flood overtopping accounts for more than 50%2. As global warming worsens, extreme rainfall continues to increase and intensify3,4, exacerbating the disastrous nature of floods5 Once a dam failure occurs in the upstream reservoir of a city under extreme rainfall, the resulting dam failure flooding superimposed on urban flooding has much destructive power than natural flooding, affecting economic development and social stability. Therefore, it is of great practical importance to consider the dam failure of urban reservoirs during extreme rainfall.

Against the background of global warming, various types of extreme rainfall events have occurred frequently in recent years, and rainfall is an important factor that leads to flooding. Once triggered, the dam failure of urban reservoirs seriously threatens the safety of people’s lives and property. Therefore, correctly recognizing the characteristics of production and sink flow is an important task for simulating dam failure in urban reservoirs under extreme rainfall6. In recent decades, numerous scholars have conducted in-depth and systematic studies on dam failures. Ying et al.7 investigated the use of differential forms such as windward, TVD, and control volume methods, in the numerical simulation of dam failure flood evolution in a 1D open channel. Lai et al.8 proposed a computationally efficient hybrid finite volume and finite difference method for the numerical solution of St. Venant’s equations in a 1D open-channel flow. Pramanik9, Amir10, and Pilotti et al.11 investigated algorithms for high-precision river cross sections based on a high-precision digital terrain model, improving its efficiency and computational accuracy. Hervouet12 proposed a new parallel computational method to improve the computational efficiency of 2D models. Singh13, Begnudelli14, and Mao et al.15 used accurate segmentations of wet and dry interfaces to manage the topography and complex flow patterns of dam failure floods and investigated the differential formats of windward, center, and Godunov to solve 2D shallow-water equations. Swartenbroekx et al.16 divided a flood into two parts and built a 2D flood evolution numerical model, where the upper model was set as clear water, and the lower model was constructed to contain the riverbed evolution and sediment transport processes. Yang Z W, Liu W M, Garcia-Castellanos D et al.17 highlight that the hydraulics of high-magnitude outburst floods and sediment transport play crucial roles in reshaping canyon geomorphology. Ruan H C, Chen H Y, Chen X Q et al.18 proposed an innovative approach of using flexible protecting net (FPN) to control the outburst discharge of the landslide dam based on failure machnism, to prevent landslide dam outburst flood. Kumar V, Gupta V, Jamir I et al.19 considered the increase in average annual rainfall to go into the potential landslide damming process in dam sizing and dam stability assessment. Currently, Many experimental studies have been conducted on dam failure mechanisms and flood evolution after transient failure. Reservoir dam failures are complex and involve several factors. Most of the dam failure flood studies are based on a single flood as the object of study, considering the evolution of the riverbed, sediment transport, and other factors. Rainfall is an important factor contributing to flooding. Extreme rainfall can lead to a rapid increase in the amount of water flowing into a reservoir within a short period of time, leading to a rapid rise in reservoir levels and an increased risk of exceeding safe design standards. There are fewer studies on dam failure in urban reservoirs under extreme rainfall. However, studies on dam failures superimposed on other disaster flood evolution processes are scarce. Therefore, considering dam failures in urban reservoirs during extreme rainfall is of great practical significance.This study used observed data from the heavy rainfall event in Zhengzhou on July 20, 2021, with Jiangang Reservoir in Zhengzhou as the study site. Flood evolution simulation analyses were carried out for different scenarios of rainfall and flooding processes under three working conditions: rainfall only, dam failure only and dam failure coupled with rainfall, to characterize the flood response due to dam failure under different rainfall conditions. Hydraulic element support was provided for flood vulnerability evaluation and Urban flood disaster control.

Methods

Study area

The Jiangang Reservoir is a medium-sized reservoir with urban flood control and water supply functions located in the upper reaches of the Jialu River in the Huaihe River Basin. The control basin area of the reservoir is 113 km2, and the length of the main stream is 28.4 km2. The total capacity of the reservoir is 60,704,100 m3, and the utilizable capacity of the reservoir is 47,910,000 m3. The elevation at the top of the dam, which is 34 m high, is 158.52 m, and the maximum height of the top of the dam is 8.4 m. From top to bottom, the headwater slopes of the dams are 1:3.0, 1:3.5, and 1:2.0, and it is bermed with dry-laid concrete blocks. The backwater slopes are 1:2.5, 1:2.75, and 1:3.0 from top to bottom, and also bermed with dry-laid blocks. The reservoir is located in the upstream of Zhengzhou City. Downstream of the reservoir, 6 km away, are the Beijing-Guangzhou Railway, Longhai Railway, city power plant, water plant, and other water supply and energy facilities, where flood control ___location is important. Reservoir level to improve the first class. The design flood standard was for individuals over 100 years old. The calibration flood standard was one over 5000 years, as shown in Fig. 1.

Fig. 1
figure 1

Location Map of Jiangang Reservoir. The ___location map was created with the software ArcGIS 10.8. (https://www.arcgis.com).

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Chicago rain pattern method

The Chicago rain patterns model is a classical distributed rainfall intensity model typically used for short-duration rainfall events. It can generate rainfall process lines based on specific design rainfall return periods and durations. Additionally, the model allows for the adjustment of rainfall intensity curves according to different design return periods, making it particularly beneficial for applications considering extreme weather.The Chicago Rain Patterns method demonstrates high accuracy in estimating design rainfall intensities, especially when employing standard design rainfall curves.

The Chicago rain pattern method was used to derive the storm design process. Its rain model is based on the storm intensity formula20, which mainly solves for average rainfall intensity and designs the extreme value of the rain peak of the storm. The Chicago rain model uses the integrated rain peak ___location coefficient to reflect the ___location of the rain peak. Therefore, determining the integrated peak ___location coefficient r is a prerequisite for the Chicago rain model. Based on the ___location of the peak, rainfall can be divided into two periods: before and after the peak. The storm intensity was calculated using Eqs. (1)– (3).

$${r_i}=\frac{{{t_i}}}{{{T_i}}}$$
(1)
$$r=\frac{{\sum\limits_{i} {{t_i}} \times {T_i}}}{{\sum\limits_{i} {{T_i}} }}$$
(2)
$$i=\frac{A}{{{{\left( {t+b} \right)}^n}}}$$
(3)

where i is the design storm intensity, a is the hourly rain rate, t is the time, b is the time parameter, and n is the storm attenuation index. The total rainfall duration is assumed to be \(\:{t}_{z}\), the total rainfall is \(\:{H}_{z}\); the pre- and post-peak rainfall durations are \(\:{t}_{a1}\:\)and \(\:{t}_{a2}\), respectively; the pre- and post-peak instantaneous rainfall intensities are \(\:{I}_{a1}\) and \(\:{I}_{a2}\), respectively; and the cumulative rainfall is \(\:{H}_{a1},\:\:{H}_{a2}\). The results are shown in Eq. (4) and Eq. (5).

$${t_{a1}}={t_z} \times t$$
(4)
$${t_{a2}}={t_z} \times (1 - r)$$
(5)

The pre- and post-peak average rainfall intensities were calculated using the above equation, and the results are shown in Eqs. (6) and (7).

$${i_{a1}}=\frac{{{r^n}A}}{{{{\left( {t+rb} \right)}^n}}}$$
(6)
$${i_{a2}}=\frac{{{{\left( {1 - r} \right)}^n}A}}{{{{\left[ {t+\left( {1 - r} \right)b} \right]}^n}}}$$
(7)

The instantaneous rain intensity equation was derived as follows:

$${I_{a1}}=\frac{{\left( {1 - n} \right){r^n}A}}{{{{\left( {t+rb} \right)}^n}}}+\frac{{nb{r^{n+1}}A}}{{{{\left( {t+rb} \right)}^{n+1}}}}$$
(8)
$${I_{a2}}=\frac{{(1 - n){{(1 - r)}^n}A}}{{{{\left[ {t+\left( {1 - r} \right)b} \right]}^n}}}+\frac{{nb{{\left( {1 - r} \right)}^{n+1}}A}}{{{{\left[ {t+\left( {1 - r} \right)b} \right]}^{n+1}}}}$$
(9)

Finally, the rainfall accumulation process is represented by Eqs. (10) and (11).

$${H_{a1}}={H_z}\left\{ {r - \left( {r - \frac{t}{{{t_z}}}} \right){{\left[ {1 - \frac{t}{{r\left( {{t_z}+b} \right)}}} \right]}^{ - n}}} \right\}$$
(10)
$${H_{a2}}={H_z}\left\{ {r+\left( {\frac{t}{{{t_z}}} - r} \right){{\left[ {1+\frac{{t - {t_z}}}{{(1 - r)({t_z}+b)}}} \right]}^{ - n}}} \right\}$$
(11)

Rainfall type is often represented by the rainfall peak ___location coefficient as its characteristic value21,22,23. The rainfall peak ___location coefficient r refers to the entire rainfall during the peak of the time period and the total duration of the rainfall ratio. It characterizes the field of the maximum rainfall appearing in the ___location, as shown in Eq. (12):

$$r=\frac{{{U_{\hbox{max} }}}}{U}$$
(12)

where r is the rain peak ___location coefficient, Umax is the period when the rain peak occurs, and U is the total rainfall duration.

Based on the peak ___location coefficient, rainfall processes can be qualitatively classified into three types: forward, centered, and backward24. Using the three-year (2016–2018) rainfall data of the study area, we determined that the study area was dominated by the single-peak rainfall type. The overflow and inundation under the single-peak rainfall type are higher than those under the uniform and double-peak rainfall types. Therefore, the three single-peak rainfall types were generalized by combining the Chicago rainfall type and the long-calendar-time rainstorm formula of the Beijing Institute of Technology using the annual maximum method. The formula for a long -calendar rainstorm is given by Eq. (13)25,26,27,28.

$$q=\frac{{2479.78(1+0.963\log P)}}{{{{(t+15.3)}^{0.775}}}}$$
(13)

where q is rainfall, P is the return period, and t is time.

To select the appropriate rain peak ___location coefficients, this study combined the long- calendar- time Chicago Eqs. 2028,29. Three coefficients were selected for the forward, centered, and reverse rainfall processes. The generalized rainfall process for t = 12 h was calculated, as shown in Figs. 2, 3 and 4.

Fig. 2
figure 2

Schematic diagram of the bias-front rain pattern generalization.

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Fig. 3
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Schematic diagram of the centered rain type generalization.

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Fig. 4
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Schematic diagram of the deviated rain pattern generalization.

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Through a comparative analysis25,26,30,31, the final selection was a biased forward rain peak position coefficient of r = 0.2, centered rain peak position coefficient of r = 0.45, and backward rain peak position coefficient of r = 0.75.

Determination of the design stormwater process

Calculation of output and sink flows

According to the characteristics of the watershed in which the Jiangang Reservoir is located, the data, past experiences, and design requirements. The rainstorm runoff correlation diagram method was used to calculate production flow and deduce the designed net rainfall for the study area32,33. Taking representative and unfavorable conditions as the main principles, very heavy rainfall in Zhengzhou was chosen as the typical rainstorm working condition. Rainstorm data measured from 8:00 a.m. on July 20 to 8:00 a.m. on July 21 were used as the basis. In addition, the rainfall–runoff relationship curves in the Atlas of Designed Storm Floods for Small- and Medium-Sized Watersheds in Henan Province were combined to derive the designed net rainfall for that period, as shown in Fig. 5.

Fig. 5
figure 5

Comparison of storm and design net rainfall from July 20, 8 a.m. to July 21, 8 a.m.

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The unit line method was used for convergence calculation34. Based on the measured rainfall and runoff data of the Changzhuang Reservoir, which was adjacent to the study area, from 8:00 am on July 20 to 8:00 am on July 21 at the Zhengzhou National Meteorological Station, the convergence unit lines in the study area were determined using linear programming. The depth of runoff in the unit line was controlled at 10 mm, which indicated that the calculation of the surface runoff process was basically the same as that of the measured surface runoff process. The shapes of the flood process lines are relatively similar. The trends of rising and receding floods were similar. The simulated flow values for each period were consistent with the measured flow values. The calculation error for the flood flow was 1.8%. This meets the standard hydrological forecasting specification that the calculation error must be less than 20% of the measured flood flow value, which has been proven feasible. A comparison of the calculation results is presented in Fig. 6.

Fig. 6
figure 6

Comparison of reservoir control basin flows from July 20, 8 a.m. to July 21, 8 a.m.

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Different rainfall types

Combining the Chicago rain type and long-calendar storm equations, the rainfall duration was set to t = 24 h and the return period to p = 5000. The design rainfall processes for the different rainfall patterns are shown in Fig. 7. Based on the characteristics of production and sink flow in the study area,

the corresponding design flood process was deduced, as shown in Fig. 8.

Fig. 7
figure 7

Comparison of rainfall processes for different rainfall designs at P = 5000 and t = 24 h.

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Fig. 8
figure 8

Comparison of design flood process for different rainfall patterns at P = 5000 and t = 24 h.

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The total rainfall of the different rain types at P = 5000 and t = 24 h was approximately 345.5 mm, which was relatively concentrated. Figure 8. shows that at t = 5, 11, and 18 h, the maximum rainfall reached 101.18, 127.37, and 115.26 mm is reached for the forward rain type, centered rain type, and backward rain type, respectively. As shown in Fig. 9, the three rainfall types reach their flood peaks at t = 7, 13, and 20 h with 373.1, 410.5, and 417.8 m3/s, respectively. The flood peak lagged behind the rain peak by approximately 2 h, and the flooding process gradually weakened as the heavy rainfall trend weakened. Therefore, the more the rainfall peak lags behind, the larger and later the flood peak of the flood process is formed, which is unfavorable for water conservancy projects.

Different recurrence periods

The recurrence period was set as p = 100, p = 1000, and p = 5000, with a rainfall peak ___location coefficient of r = 0.2 and a rainfall duration t = 24 h. Combining the Chicago rain type and long- duration storm formula, the design rainfall processes for different recurrence periods are shown in Fig. 9. Based on the characteristics of the production and sinks in the study area, the corresponding design flood process was deduced, as shown in Fig. 10.

Fig. 9
figure 9

Comparison of rainfall processes for different return periods at r = 0.2 and t = 24 h.

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Fig. 10
figure 10

Comparison of design flood process for different return periods at r = 0.2 and t = 24 h.

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As shown in Fig. 9, when r = 0.2 and t = 24 h, the rainfall is concentrated at 221.57, 294.49, and 345.46 mm for the different recurrence periods. The maximum rainfall was reached at t = 5 h. As the recurrence period for the same rain type and rainfall duration increases, the rain peak and total rainfall also increases.

As shown in Fig. 10, the total duration of the flooding process was 34 h. A flood peak was observed at t = 7 h. The design rainfall and flood process for different return periods indicate that the longer the return period, the more intense the storm, and the greater the flood volume and flood peak. The flood peak lagged the rainfall peak by approximately 2 h. These conditions are unfavorable for water conservancy projects.

Different rainfall duration

Rainfall durations of t = 12 h and t = 24 h were selected, and the rainfall peak ___location coefficient of r = 0.2 and recurrence period of p = 5000 were set. Combined with the Chicago rain-type and long-calendar storm formulas, the design rainfall process for the different rainfall calendars is shown in Fig. 11. Based on the aforementioned characteristics of the production and catchment flows in the study area, the corresponding design flood process was deduced, as shown in Fig. 12.

Fig. 11
figure 11

Comparison of rainfall processes for different calendar times at r = 0.2 and p = 5000.

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Fig. 12
figure 12

Comparison of design flood processes for different calendar times at r = 0.2 and p = 5000.

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As shown in Fig. 11, when r = 0.2 and p = 5000, the total rainfall is 293.2 mm at a rainfall duration of t = 12 h, and the maximum rainfall of 100.1 mm was reached at t = 3 h. The rainfall at t = 24 h was 345.46 mm, reaching a maximum of 101.2 mm at t = 5 h, which was relatively concentrated. As the rainfall duration increased for the same rain type and recurrence period, the total rainfall increased.

As shown in Fig. 12, the total duration of the flood process at a rainfall duration of t = 12 h is 22 h, and at t = 5 h, the flood peak reaches 252.7 m3/s, with a flood volume of 2241.9 m3/s. When the rainfall duration is t = 24 h, the total duration of the flooding process is 34 h, and the flood peak reaches 373.1 m3/s at t = 7 h, with a flood volume of 2699.9 m3/s; the flood peak lags behind the rain peak by about 2 h. The design rainfall and flood processes for different rainfall calendars show that the longer the rainfall period, the larger the total rainfall, and the larger the flood volume and flood peaks, which are unfavorable for water conservancy projects.

Model parameter

Data sources and preprocessing

Topographic data were obtained from NASA with a DEM resolution of 12.5 m × 12.5 m. Land use data were obtained from the GlobeLand30 global surface coverage data with a spatial resolution of 30 m. The downloaded DEMs were processed using ArcGIS 10.7 to obtain the DEMs of the study area. HEC-RAS 6.0 was used as the platform, and the coordinate system used was WGS1984 UTM Zone 49 N. The main dam of Jiangang Reservoir is an earth-rock dam, and Jiangang Reservoir was set up to gradually break the dam owing to overtopping. The dam- related parameters are input into the HEC-RAS, and the formula was selected, in which we obtained a trapezoidal breach. The width of the lower bottom of the breach was 123 m, and the slopes of the left- and right- sloping sides were 0.5. The values of the related river roads were refined using the HEC-RAS custom area roughness setting. The relationship between the water level and storage capacity of the Jiangang Reservoir is presented in Fig. 13.

Fig. 13
figure 13

Relationship chart of water level and storage capacity in Jiangang Reservoir.

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Roughness settings

The surface roughness in the floodplain of the dam failure flood varies greatly. Therefore, it is necessary to set the surface roughness, and the value of roughness directly affects the calculation results. In this paper, based on the land use data, the roughness of different land use types is set separately, and the roughness distribution map is made and imported into HEC-RAS. The roughness distribution map is made and imported into HEC-RAS. The local terrain was refined using linear objects. At other locations, the calculated grid size was set to 100 m × 100 m. The values of the related river roads were refined using the HEC-RAS custom area roughness setting, as shown in Table 1.

Table 1 Ground roughness value.
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Flood Severity indicators

Indicators of flood severity were used to measure the extent of damage in the study area. Flood severity simulation data were extracted using ArcGIS vectors for dam failure- only and dam failure coupled with rainfall scenarios under the three rainfall types. The dam- failure flood severity SD reflects the extent of flood damage to public and social properties within the flood risk area35,36,37. The dam-failure flood severity can be expressed as the product of the water depth D (m) in the study area and the flood flow velocity V (m/s) at the corresponding point, as shown in Eq. (14):

$${S_D}=D \times V$$
(14)

Flood levels were categorized into five classes based on empirical methods commonly used at home and abroad, as shown in Table 238.

Results

HEC-RAS is used to simulate the flow dynamics in rivers, reservoirs, and dam breach floods. For complex terrains and flow patterns, the two-dimensional model provides more accurate information on water levels and velocity distributions. HEC-RAS can accurately simulate the evolution of dam breach floods, particularly in modeling dam failure and downstream flood routing, including flow velocities, water level fluctuations, and flood inundation areas.The rainfall and flooding processes of the three rainfall types were imported into a 2D model constructed based on HEC-RAS for dam-failure coupled rainfall. Flood evolution simulations were performed for rainfall- only, dam failure-only, and dam failure-coupled rainfall. The simulation results of the water depth, flow rate, and flood severity under different conditions were obtained.

The settings for the three working conditions were as follows in Table 2. (1) Rainfall- only scenario: only rainfall boundary conditions were set in the study area, and flooding was simulated in the area downstream of the reservoir due to rainfall. (2) Dam failure- only scenario: the reservoir overflows and breaks during the incoming flood, and the downstream area of the reservoir was not affected by rainfall. (3) Dam-break coupling rainfall scenario: rainfall and flood processes started at the same time. During a flood, the reservoir overtopped and broke the dam, and the downstream area of the reservoir simultaneously experienced waterlogging due to rainfall.

Table 2 The settings for the three working conditions.
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Simulation analysis of dam failure under different rainfall patterns

The comparison results of the simulation of maximum water depth, flow velocity, and flood severity distribution in the study area under the three working conditions, with a rain peak ___location coefficient of r = 0.2, r = 0.45, and r = 0.75 are shown in Figs. 14, 15, 16, 17, 18 and 19, and Figs. 20, 21 and 22, respectively.

Fig. 14
figure 14

Simulation of maximum water depth distributions at r = 0.2 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 15
figure 15

Simulation of maximum flow velocity distributions at r = 0.2 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 16
figure 16

Simulation of distribution of severity of the maximum flood at r = 0.2 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 17
figure 17

Simulation of maximum water depth distributions at r = 0.45 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 18
figure 18

Simulation of maximum flow velocity distributions at r = 0.45 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 19
figure 19

Simulation of the maximum flood severity distributions at r = 0.45 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 20
figure 20

Simulation of maximum water depth distributions at r = 0.75 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 21
figure 21

Simulation of maximum flow velocity distributions at r = 0.75 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 22
figure 22

Simulation of the maximum flood severity distributions at r = 0.75 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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When the rain peak ___location coefficient was r = 0.2, the maximum flow rate of the breach was 20362.5 m3/s at t = 8.67 h. At r = 0.45, it was 20521.6 m3/s at t = 13.5 h, and at r = 0.75, it was 20832.4 m3/s at t = 19.17 h. Moreover, the three rain types reached the flood peaks at t = 7 h, t = 13 h and t = 20 h respectively, indicating that the difference between the flood peak time and maximum flow rate of the breach was approximately1 h. and that that the flood peaks were closely related to the breaching speed of the reservoir. In addition, the rain peak ___location coefficient at r = 0.2 reacheds the maximum flow 4.83 h earlier at r = 0.45. The rain peak ___location coefficient reached the maximum flow 10.5 h earlier at r = 0.75. This indicates that the more forward the rain pattern, the faster the dam failure rate of the reservoir, and the shorter the time for flood disaster warning and emergency evacuation of the downstream urban population.

Simulation analysis of dam failure under different recurrence periods

Considering the catastrophic rainstorm event in Zhengzhou, Henan Province, on July 20, 2021, and the increasing frequency of extreme events due to climate change, there is a need to elevate flood design standards for recurrence intervals. In core urban areas and regions with critical infrastructure, design standards should be based on 100-year, 1000-year, or even 5000-year recurrence intervals.

The simulation results of the distribution of the maximum water depth, flow velocity, and flood severity in the study area under the three conditions of rainfall- only, dam failure- only, and dam failure-coupled rainfall at the return period p = 100, p = 1000, and p = 5000 are shown in Figs. 23, 24, 25, 26, 27 and 28, and Figs. 29, 30 and 31, respectively.

Fig. 23
figure 23

Simulation of maximum water depth distributions at p = 100 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 24
figure 24

Simulation of maximum flow velocity distributions at p = 100 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 25
figure 25

Simulation of maximum flood severity distribution at p = 100 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 26
figure 26

Simulation of maximum water depth distributions at p = 1000 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 27
figure 27

Simulation of maximum flow velocity distributions at p = 1000 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 28
figure 28

Simulation of maximum flood severity distribution at p = 1000 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 29
figure 29

Simulation of maximum water depth distributions at p = 5000 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 30
figure 30

Simulation of maximum flow velocity distributions at p = 5000 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 31
figure 31

Simulation of maximum flood severity distribution at p = 5000 for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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The simulation results show that when p = 100, the breach reached a maximum flow rate of 19,853.7 m3/s at t = 10 h. At p = 1000, it was 2,002.3 m3/s at t = 9.17 h, and at p = 5000, it was 20,362.5 m3/s at t = 8.67 h. The maximum flow rate was 0.5 h earlier at p = 5000 than at p = 1000, and 1.33 h earlier than that at p = 100. This shows that the longer the reproduction period, the faster the rate of collapse. Because of the longer return period, rainfall and flood flow increased, thereby accelerating the breach. By this point, the population downstream should be engaging in emergency evacuation actions.

Simulation analysis of rainfall flooding process and dam failure at different rainfall durations

The simulation results for the maximum water depth, flow velocity, and flood severity distribution in the study area under three conditions for a rainfall duration of t = 12 h and t = 24 h are shown in Figs. 32, 33, 34, 35, 36 and 37, respectively.

Fig. 32
figure 32

Simulation of maximum water depth distribution at t = 12 h for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 33
figure 33

Comparison of simulation of maximum flow velocity distribution at t = 12 h for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 34
figure 34

Simulation of maximum flood severity distribution at t = 12 h for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 35
figure 35

Simulation of maximum water depth distribution at t = 24 h for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 36
figure 36

Simulation of maximum flow velocity distributions at t = 24 h for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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Fig. 37
figure 37

Simulation of maximum flood severity distribution at t = 24 h for the (a) rainfall-only, (b) dam failure-only, and (c) dam failure-coupled rainfall conditions.

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At t = 12 h, the maximum flow rate of the breach reached 19,853.7 m3/s at t = 6.45 h, and at t = 24 h, it reached 20028.3 m3/s at t = 8.97 h. The maximum flow rate was 2.5 h earlier with the rainfall duration of t = 12 h than with t = 24 h. This shows that as the rainfall duration decreases, the rainfall and flood peaks advance, and the collapse speed accelerates. However, the longer the rainfall duration, the larger the total rainfall and flood volume.

Discussion

Dam failure flood severity under different rainfall types

The flood severity in Table 3 was divided into five classes: extremely low, low, moderate, high, and very high. The results of the comparison of the flood severity classifications for dam failure- only and dam failure- coupled rainfall for the two conditions of the three rainfall types are shown in Figs. 38, 39 and 40. The area of each grade was counted, as shown in Table 4.

Table 3 Classification of floods.
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Table 4 Area of each flood severity class for each condition under different rainfall patterns.
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Fig. 38
figure 38

Comparison of flood severity classes at r = 0.2. (a) Dam failure-only condition (b) Dam failure-coupled rainfall.

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Fig. 39
figure 39

Comparison of flood severity classes at r = 0.45. (a) Dam failure-only condition (b) Dam failure-coupled rainfall.

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Fig. 40
figure 40

Comparison of flood severity classes at r = 0.75. (a) Dam failure-only condition (b) Dam failure-coupled rainfall.

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  1. (1)

    Based on the simulation, the overall average severity of flooding in the study area under the dam failure-only scenario is moderate, while that of the dam failure- coupled rainfall scenario was at a lower level owing to the large inundation area. The more anterior the rainfall pattern, the faster the rate of reservoir failure, and the greater the extent of inundation and severity of flooding under the dam failure-only and dam failure-coupled rainfall scenarios. In terms of rainfall peak ___location coefficients r = 0.2, r = 0.45, and r = 0.75, the proportion of the overall affected area for each level of dam failure severity was approximately the same as that for the dam failure-only scenario:40.5%, 38.5%, 6%, 6.5%, and 8.5%, respectively. Flood severity was greater on both sides of the river around the channel, with a gradual decrease in flood severity downstream of the channel. As shown in Table 4, in the dam failure coupled rainfall scenario, the areas with medium, high and very high flood severity ratings were 24.92 km2, 25.03 km2 and 25.30 km2 under the three rain types, and the areas with low and very low flood severity ratings were 289.83 km2, 290.9 km2 and 292.67 km2 under the three rain types, indicating that the increase of the area with higher flood severity ratings was smaller and the increase of the area with lower flood severity ratings was larger. This indicates that under the coupled dam failure rainfall scenario, the increase in the area with higher flood severity level is smaller while the increase in the area with lower flood severity level is larger as the rain type is more backward. Therefore, in conditions of high flood severity, the inundation area is significantly larger than in conditions of lower flood severity. As rainfall patterns become more extreme, the inundation area gradually expands. However, in cases of high flood severity, the increase in inundation area is relatively modest. Conversely, for lower flood severity conditions, the increase in inundation area is substantial. With the continuous superposition of subsequent floods, the larger the flood flow, the larger the affected area. Compared with the dam failure-only scenario, the increase in the area in the higher flood severity class for the dam failure- coupled rainfall scenario was smaller. The increase in the area of the lower flood severity class was greater. This was approximately 3.7 times more than the increase in the area in the higher flood severity class.

Overall, the inundation area of the study area for the dam failure-coupled rainfall scenario increased by approximately 200 km2 compared with the dam failure-only scenario. The difference in the affected area between the dam failure-only and the dam failure-coupled rainfall scenarios for dam failure flood severities of moderate, high, and very high was small. This is because the areas with moderate, high, and very high severity of dam failure floods are on both sides of the upstream channel. The inundation floods created by rainfall converge downstream of the city with topography and have less impact on areas with higher flood severity. The increased inundation extent in the dam failure-coupled rainfall scenario at a higher level of flood severity was mainly located downstream of the river channel. Inundation due to rainfall increases the water depth at flood-prone points; consequently, the flood severity level increases. The dam failure-only and dam failure-coupled rainfall scenarios largely differed in terms of the lower dam-failure flood severity levels for the different rainfall patterns. The area affected at the lower level under the dam failure-coupled rainfall scenario was approximately 3.2 times that under the dam failure-only scenario because the area affected by rainfall in the study area was much larger than that affected by dam failure. However, the inundation flood water created by rainfall was deeper and flowed less; therefore, the flood severity of most of the inundation areas was lower. Based on the above analysis, the extent of inundation under both conditions increased as the rain type became backward. The increase was small, but the rain type was closely related to the dam failure time. When the rain type was biased forward, the reservoir dam failure time increased, and the flood warning time became shorter. Therefore, the more forward the rain pattern, the more unfavorable it is for the reservoir.

Dam failure flood severity under different recurrence periods

Flood severity simulation data were vectorially extracted using ArcGIS for both the dam failure-only and dam failure-coupled rainfall scenarios under the three return periods. The natural breakpoint method was used to grade the flood severity for each case, as listed in Table 3. The results of the comparison of the flood severity classification for both the dam failure- only and dam failure-coupled rainfall conditions for the three return periods are shown in Figs. 41, 42 and 43. The area for each classification was calculated, as shown in Table 5.

Table 5 Area of each class of flood severity for the two operating conditions under different return periods.
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Fig. 41
figure 41

Flood severity ratings at p = 100. (a) Dam failure only condition (b) Dam failure coupled rainfall condition.

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Fig. 42
figure 42

Comparison of flood severity ratings at p = 1000. (a) Dam failure only condition (b) Dam failure coupled rainfall condition.

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Fig. 43
figure 43

Flood severity ratings at p = 5000. (a) Dam failure only condition (b) Dam failure coupled rainfall condition.

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As shown in Table 5, the inundation area for the dam failure- only scenario increased by 7 km2 for the return period p = 5000 compared with p = 1000, and 4.09 km2 compared with p = 100, indicating that the rainfall and flood peaks increased with the increase in the return period, as well as the inundation area. The increase in the area at a higher level of flood severity was smaller for the dam failure- coupled rainfall scenario compared with the dam failure-only scenario, and greater for a lower flood severity class. Moreover, as the return period increased, the area affected by each flood severity class also increased. The increase in the inundation area for the dam failure-coupled rainfall case for the return period of p = 5000 was 46.28 km2 compared with p = 1000. The increase in the inundation area for the rainfall type r = 0.45 is 15.28 km2, which indicates that the inundation area of the flood increases gradually with the increase in the return period. The increase in the inundation area was more significant compared with the dam failure-only condition, in which the increase in the inundation area was mainly due to rainfall.

Under a dam failure-coupled rainfall scenario, flood severity was greater on both sides of the river channel, and the severity of the floods downstream of the river channel gradually decreased. The difference in the affected area between the dam failure-only scenario and the dam failure- coupled rainfall scenario under different return periods was small for the moderate, high, and very high severity floods. This is because areas with moderate, high, and very high dam failure flood severity are on both sides of the upstream channel. The floods caused by rainfall converged downstream of the city with the terrain, which had less impact on areas with higher flood severity. The dam failure- coupled rainfall scenario had a higher level of flood severity, and the increased inundation range was mainly located downstream of the river channel. Inundation due to rainfall increases the water depth at flood-prone points, and flood severity increases accordingly. The difference between the dam failure- only and the dam failure-coupled rainfall scenarios at a lower level of flood severity was large for different return periods. This difference increased with an increase in the reproductive period because the amount of rainfall and the inundation range increased. In summary, the flood severity on both sides of the river was higher in the dam failure- only condition for the return periods p = 100, p = 1000, and p = 5000. Flood severity gradually decreases downstream of the river.

Dam failure flood severity under different rainfall duration

The comparison results of the flood severity classifications for the dam failure-only and dam failure-coupled rainfall scenarios under the two rainfall calendars are shown in Figs. 44 and 45. The area of each class was determined with Table 3. The area of each class was counted, as shown in Table 6.

Table 6 Area of flood severity classes for each condition at different calendar times.
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Fig. 44
figure 44

Comparison of flood severity ratings at t = 12 h. (a) Dam failure only condition (b) Dam failure coupled rainfall condition.

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Fig. 45
figure 45

Comparison of flood severity classes at t = 24 h. (a) Dam failure-only condition (b) Dam failure-coupled rainfall condition.

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Based on Table 6, the inundation range of rainfall type at t = 24 h for the dam failure-only condition increases by 4.72 km2 or approximately 4.5%, compared with that at t = 12 h. This shows that with an increase in the rainfall duration, the larger the flood peak and flood volume; the inundation range of the flood gradually increased, and the affected range also increased. The increase in the area at the lower flood severity level was greater. In addition, the inundation area for the dam failure-coupled rainfall scenario with a rainfall duration of t = 24 h increased by 18.6 km2 or approximately 17%, compared with t = 12 h, indicating that the increase in the area of the lower flood severity class was smaller in the dam failure-coupled rainfall scenario than in the dam failure-only scenario. In contrast, the increase in the area of the lower flood severity class was larger. When the rainfall duration was t = 12 h and t = 24 h, the inundation area of the dam failure-coupled rainfall condition under the two rainfall durations increases by 191.93 km2 and 205.81 km2, respectively, compared with the dam failure-only condition. The areas with moderate, high, and extremely high severity of flooding because of dam failure are on both sides of the river around the upstream channel, and the inundation floodwater formed by rainfall converges downstream of the city along with the topography, which has less impact on the area of flood severity at higher severity levels. The areas with higher severity levels were less affected. The increased extent of flood severity under the dam failure-coupled rainfall scenario was mainly located downstream of the river channel. Internal flooding due to rainfall increases the water depth at flood- prone locations and consequently increases flood severity. The dam failure-only and dam failure-coupled rainfall scenarios significantly differed in terms of the lower severity of dam- failure floods for different rainfall durations. Because the area affected by rainfall in the study area was much larger than the area affected by dam failure, the water depth and flow velocity of the inundated flood water formed by rainfall were smaller; thus, the flood severity of most of the inundated area was lower.

Overall, the flood severity was higher on both sides of the river around the channel under the dam failure-only condition at rainfall durations of t = 12 h and t = 24 h, and the severity of flooding downstream of the river gradually decreased. From the above analysis, it can be concluded that, with an increase in rainfall duration, the inundation range under both conditions increases, with a smaller increase under the dam failure-only condition and a larger increase under the dam failure-coupled rainfall condition. Therefore, the greater the increase in the rainfall duration, the more unfavorable it becomes.

Conclusions

In this study, the rainfall type, return period, and rainfall duration were comprehensively considered in the construction of the spatial and temporal rainfall distributions and flood processes for the different scenarios. Numerical rainfall-only, dam failure-only, and dam failure-coupled rainfall simulations were performed for each rainfall process. ArcGIS was used as the platform to extract the simulated data, and the flood severities under different working conditions were hierarchically compared. The flood characteristics of urban reservoir dam failures under different rainfall conditions were analyzed to determine the most unfavorable working conditions, which were rain type r = 0.2, return period p = 5000, and rainfall duration t = 24 h. The main conclusions are as follows.

  1. 1.

    As the rainfall pattern became more backward, the recurrence period and rainfall duration increased, as well as the flood peak and flood volume which was more unfavorable for a reservoir.

  2. 2.

    The more anterior the rain pattern, the faster the failure of the reservoir. The higher the flood volume, the faster the reservoir breaks.

  3. 3.

    As the rainfall pattern became backward and the recurrence period and rainfall duration increased, the extent of inundation increased for both the dam failure-only and dam failure-coupled rainfall scenarios. The increase was smaller for those in higher flood severity classes and greater for lower flood severity classes.

  4. 4.

    The inundation ranges f for dam failure-only and dam failure-coupled rainfall differed considerably. The difference in their extent was more constant for different rainfall patterns. However, the total rainfall increased with the recurrence period and rainfall duration, as well as the difference between the inundation ranges under both conditions.

Due to the generalization of the model to the actual situation, the simulation results may differ from the actual situation. HEC-RAS is primarily designed to simulate surface flow of rivers and floods. Whereas urban subsurface drainage systems may play an important role in dam failure simulations, HEC-RAS is limited in its ability to handle these subsurface systems.However, the qualitative conclusions based on the comparison are of some reference significance. In the future, the underground pipe network distribution can be further simulated with the urban pipe network data to do a more in-depth analysis of the urban rainfall flooding modle. HEC-RAS is primarily designed to simulate surface flow of rivers and floods. Whereas urban subsurface drainage systems may play an important role in dam failure simulations, HEC-RAS is limited in its ability to handle these subsurface systems.