Study on Flood Control Safety Evaluation Based on Composite Risk Model

The process of dam design up to the management of dam operation involves many uncertain factors, such as hydrologic, hydraulic and flood control factors, which cause risks for the flood control safety of dams. This study presents an integrated probabilistic framework that combines Monte Carlo Simulation and a flood control risk model. Results show that the highest flood level of 1000-year return periods of the Zhelin Reservoir exceeds the designed flood level. However, the overtopping risk probability is small because super safe elevation is considered in the crest elevation design of the earth dam. 5 Sensitivity analysis indicates that flood peak flow, line type hydrological factors and flood control level are more sensitive than hydraulic factors. When many factors are considered, the comprehensive risk rate is small because of the positive and negative effects of these factors. Numerical experiments indicate that hydrology and flood control level influence the estimated maximum water level more than hydraulics does. Because of these uncertain factors, it is necessary to consider super safe elevation in dam planning and design. And pay attention to the sensitive factor of flood control level in reservoir management 10 and operation.

The discharge capacity of flood control structures is designed according to the design flood of a specific return period. In practice, the design flood is usually estimated by the frequency analysis using observed runoff data. However, in areas where there is no runoff data or insufficient runoff data, the design flood is generally estimated by adopting a design rainstorm data of a specific return period through the hydrological and hydraulic routing. Using the design flood, the various characteristic water levels from the hydraulic model can be obtained for determining the scale or size of flood control hydraulic structures, such as the crest elevation of dam. However, many uncertainties in the estimation of floods are caused due to imperfect of 30 calculation procedure, incomplete data and randomness of flood (Smith and Ward 1998). This may lead to the actual failure probability of the flood exceeding the design value resulting in potential destruction of the flood control structure. Therefore, it is necessary to carry out flood risk analysis for the hydraulic structures. Tung (1985) evaluated the reliability of hydraulic structures using a model comprehensively consider the hydrological and hydraulic uncertainties. Lee and Mays (1986) analyzed the failure probability of reservoir flood control due to the hydraulic uncertainty factors roughness coefficient of Manning's 35 equation. Apel et al. (2007) proposed dynamic probabilistic model was applied to explore the influence of dike breaches on flood frequency distribution along rivers. The proposed method based on actual flooding data used Monte Carlo framework to simulate the whole flood process and quantify the flood risk, rather than hypothetical scenarios.
The aforementioned research primarily focuses on the influence of single factor (hydrological and hydraulic uncertainties) for the risk analysis of hydraulic structures. The risk analysis model proposed herein not only takes into account single factors 40 (hydrological, hydraulic, and flood control level) but also composited these uncertainties factors to explore the reliability of the flood control structures of reservoir dams. Since reservoirs and levees are widely used to protect watershed areas from being flooded, this study focuses on a risk analysis for the flood-control ability of reservoir dams in order to calculate the failure probability of the water level exceeding the dam crest elevation. This study evaluates the risk of the maximum water level exceeding the dam crest elevation of the reservoir using the advanced Monte Carlo Simulation. The model requires a 45 corresponding functional relationship between the maximum water level and the hydrological, hydraulic, and flood control level factors, which must be established using integrated probabilistic framework that combines Monte Carlo Simulation and a flood control risk model. This study analyzes the sensitivity of the hydrology, hydraulics, and flood control level uncertainty factors as related to the flood-control capacity of dams along the Xiuhe River, and evaluates the performance of the typical flood and their impact on the flood-control ability of the dam system using the proposed risk analysis model. m, and the rain collection area is 9340 km 2 . The Zhelin Reservoir is the largest earth dam reservoir in China, with a total capacity of 7.9×10 9 m 3 , flood control capacity of 3.2 ×10 9 m 3 , and irrigation storage of 3.44 ×10 9 m 3 . It is a large water conservancy and hydropower project with comprehensive benefits of flood control, irrigation, shipping and development of aquatic products. The design flood for the flood-control hydraulic structures in the Zhelin Reservoir is 1‰(1000-year return 60 periods, design peak flow of 18250 m 3 /s), and the standard of checking is 0.1‰(10000-year return periods, design peak flow of 22900 m 3 /s). On the basis of these standards, the designed flood level is 70.13 m, checking flood level is 73.01 m, and crest elevation is 73.5 m. The design flood level is calculated on the basis of flow data and rainstorm data of 1954-1958 and the data of Historical Extraordinary Flood. During this period, the reservoir construction is in its early stage, and the length of the hydrological data was short. Dams that were designed and built decades ago may not meet current design standards 65 that reflect our improved knowledge of extreme flood events (Byungil Kim 2017). Although dams may decrease the frequency of flooding, they may exacerbate the hazards of flooding (NRC 2012). Therefore, the scale of The Zhelin Reservoir is large, and its safety is particularly important. Whether the standard of flood control hydraulic structures in the reservoir reaches the design requirements, and whether a certain risk of flood control safety exists in the reservoir should be analyzed and evaluated.

Data sources 70
The raw data source utilized in this research includes the statistical data of flood peak flow (1901, 1931 and 1953-2010 years) from the hydrologic station (

85
It is necessary to generate random numbers of the random variables with known distribution types using Monte Carlo method to simulate failure probability. Then, the distribution type is transformed into a random parameter according to the distribution function of the random variable. Taking the random number of peak flow as an example, the specific methods and steps are as follows: (1)The peak flow of natural river obeys the distribution of Pearson type III (P-III) (Dong and Wang 2003). The peak discharge 90 series upstream of the reservoir with the distribution of P-III (Formula 1) is fitted according to the available data. The mean value, variance, variation coefficient and skewness coefficient of the statistical parameters are calculated. where, And Γ(α) represents Γdistribution,x represents mean value, C v represents coefficient of variation, C s represents coefficient of skewness.
(2)The methods of generating random numbers include multiplicative congruence method and mixed residual method. Especially, multiplicative congruence method is widely used because of its' excellent statistical characteristics. The pseudorandom numbers of (0, 1) distributed in this paper are obtained by multiplicative congruence method. The homogeneity test and inde-100 pendence test have been carried out, and the results are satisfactory.
(3)The Q m random series of flood peak will be obtained by the transformation method. According to the typical flood, the flood process series can be calculated by the same frequency amplification method, and then the random flood data can be obtained. water level rising over the dam crest, which is named as the classical risk. In order to study the quantitative estimation formula of dam flood control safety risk the type of risk must be identified in advance. The classical risk is adopted in this study. Wu and Yang (2011) indicated that the risk for reservoir flood control analysis can be expressed as follows:

Risk analysis of dam flood control
where P r (·) refers to overtopping probability that system loading (L) is greater than the resistance (R). For the flood control ability of the dam, L and R can be, respectively, the maximum water level and the crown elevation of the dam, and Eq. 3 can be rewritten as, where Z max represents the maximum water level, and H dam represents the height of the dam crown. M refers to total number of random tests, S refers to times of Z max >H dam

Generation of uncertainty factors
Theoretically, the hydrological, hydraulic, and flood control level factors have different physical and statistical characteristics.
As a result, this study generates the uncertainty factors using the Monte Carlo simulation based on their physical and statistical 125 properties. The generation of the uncertainty factors is described below.

Hydrological uncertainty factors
Flood is a very complex dynamic stochastic process, usually described by flood characteristics such as flood peak, flood volume and flood hydrograph.

Hydraulic uncertainty factors 140
The main hydraulic uncertainties factors of flood risk are form and size of spillway structure, and uncertainty of discharge coefficient because of coefficients of hydraulic structures (weir coefficient and tube flow coefficient). Through the statistical analysis of many scholars it is thought that most of the errors caused by these uncertainties are normal distribution (Yang 1999).
Based on the hydraulic model test results, the study assumes that the total discharge capacity of the flood discharge facilities varies from 95% to 105% of the design discharge capacity. A correction coefficient of flow is introduced, λ 2 (λ 2 = 0.95 ∼ 1.05, 145 λ 2 obeys normal distribution). That can be expressed as follows: where, Q dis . represents the actual discharge of reservoir. Q des . represents the design outflow of reservoir.