Risk assessment of cascade reservoir dams is not only the key to ensure the safety of the basin, but also the objective requirement of dam risk management. Based on the development status of cascade reservoirs in China, the complexity of dam risk management of cascade reservoirs compared with a single reservoir was analyzed. By reviewing the advances on the studies of dam risk in cascade reservoirs, this paper summarized their limitations in terms of scientificity and practicability. Moreover, some concepts and methods were proposed on the risk assessment of cascade reservoirs: (1) The dam risk of a cascade reservoir was decomposed into own risk and additional risk, the consequence of its dam breach was decomposed into direct loss and potential loss, and an influence coefficient was defined to reflect the risk transmission and superposition degree among cascade reservoirs; (2) The related concepts and formulas for the calculation of dam risk probability and consequence of cascade reservoirs were proposed, which realized the transition of dam risk assessment method from a single reservoir to cascade reservoirs; (3) A project rank classification method for cascade reservoirs was proposed, which took into account not only the project scale and benefits in socioeconomic development, but also the successive dam breaches possibility and consequences. This study is of great significance to clarify the focus of future research and promote the practical application of dam risk management in cascade reservoirs.@en

Because of the uncertainty regarding the potential loss of life, it is difficult to use societal life risk criteria for dams established based on existing methods and the related research. Based on existing dam safety standards, dam safety conditions, and the opinions of the public on dam risks, an innovative methodology, i.e. P–P curve, was proposed to establish societal life risk criteria for dams. The annual probability of dam failure, population at risk, and dam height, which have the most significant and direct impacts on the potential loss of life, were selected as the basic indices. Taking China as an example, societal life risk criteria for the dams of five types of reservoirs were established; in these criteria, the heights of 30 m and 70 m were proposed as the bases for upgrading the risk criteria for the dams of small-type reservoirs, medium-type and large (2)-type reservoirs, respectively. The proposed methodology was designed to be more practical in determining the risk levels for dams because the values of the basic indices are considerably easier to determine than those of risk criteria based on the existing methods.@en

Because of the uncertainty regarding the potential loss of life, it is difficult to use societal life risk criteria for dams established based on existing methods and the related research. Based on existing dam safety standards, dam safety conditions, and the opinions of the public on dam risks, an innovative methodology, i.e. P–P curve, was proposed to establish societal life risk criteria for dams. The annual probability of dam failure, population at risk, and dam height, which have the most significant and direct impacts on the potential loss of life, were selected as the basic indices. Taking China as an example, societal life risk criteria for the dams of five types of reservoirs were established; in these criteria, the heights of 30 m and 70 m were proposed as the bases for upgrading the risk criteria for the dams of small-type reservoirs, medium-type and large (2)-type reservoirs, respectively. The proposed methodology was designed to be more practical in determining the risk levels for dams because the values of the basic indices are considerably easier to determine than those of risk criteria based on the existing methods.@en

Because of the risk transmission and superposition among dams in cascade reservoirs, the analysis and probability calculation of dam risk become more complex compared with a single reservoir. By analyzing the main risk sources and actionmechanisms, the disaster-causing factors, disaster-transmitting body and disaster-bearing body in the cascade reservoirs system were determined. By defining the influence coefficient (IC) to express the transmission and superposition degree of dam risk among cascade reservoirs, dam risk was divided into two parts: own risk (OR) and additional risk (AR). On this basis, the relevant concepts and equations for the calculation of the dam risk probability of cascade reservoirs were proposed. The numerical simulation was carried out to quantify the IC, and a Bayesian network analysis model was constructed to calculate the OR. Finally, taking five cascade reservoir dams in the Dadu River basin as examples, the value of their ORs, ARs and risk probabilities were calculated, and thereafter the weakest cascade, controlling cascade and general cascade in the system were divided. The proposed methodology realizes an effective connection with the dam risk calculation method of a single reservoir, which can provide a reference for the risk assessment and management of cascade reservoirs in the basin.@en

The benefits of water resource utilization include social benefits, economic benefits, and ecological environmental benefits, so it is difficult to evaluate them comprehensively by adopting the traditional cost-income analysis method. Catastrophe evaluation method, which majors in dealing with uncertain problems, evaluates system synthetically based on the internal mechanism of the system. It calcu-lates the evaluation value of the system in the condition that the relative importance of the indexes is determined and the exact weights are unknown. In this paper, the comprehensive evaluation model of water resources utilization benefits is established based on the catastrophe evaluation method. Moreover, the method which embodies the important roles of various benefits effectively is applied to evaluate the comprehensive benefits of different water resources utilization schemes from 2000 to 2005 in Zhengzhou City of China. The results show that the method has good flexibility and provides a new idea for a comprehensive evaluation of water resources utilization benefits.@en

Cascade reservoirs are essential in water resource utilization, flood control, and disaster mitigation. They have been built in several rivers worldwide. The rank classification for cascade reservoirs has significant practical implications for resource distribution decisions and risk management strategies and is also essential for ensuring the security of the basin. Internationally, reservoirs are typically classified based on project scale and dam failure consequences, whereas the risk transmission and superposition effect renders the classification method of reservoirs not directly applicable to cascade reservoirs. Therefore, to address this issue, this study proposed a rank classification method for cascade reservoirs. First, based on the scale, benefits, and risk consequences of dam failure, an index system for the rank classification of cascade reservoirs was established. Second, by constructing social risk criteria for cascade reservoirs and establishing a link among “project rank-reliability index-annual failure probability,” the allowable dam failure losses for different project ranks were determined. Thereafter, considering risk transmission and superposition, the rank classification standard and index quantification method for cascade reservoirs were proposed. Finally, five cascade reservoirs were selected for a feasibility study. The proposed method provides a supplement to the current rank classification standard of water conservancy projects in China and can also serve as a reference for risk assessment and classification management of cascade reservoirs in other countries.@en

Compared with a single reservoir, the risk in cascade reservoirs has the transmission and superposition effect, which increases the complexity of its risk consequence assessment. In view of this problem, the direct consequence (DC) and potential consequence (PC) were defined as two parts of the dam breach risk consequence of cascade reservoirs. The upstream dam-break flood inundation line and the downstream reservoir land acquisition line were taken as the upper and lower boundaries of the assessment space, which made the risk consequence assessment more intuitive and further improved its scientificity and practicability. Subsequently, the conditional probability of downstream dam breach under the upstream dam-break flood was determined to quantify the risk transmission and superposition. On this basis, the relevant concepts and formulas for calculating the dam breach risk consequence in cascade reservoirs were proposed. Taking five cascade reservoirs as examples, the risk consequences of each cascade dam breach were evaluated. The results show that the proposed method is effective in assessing the risk consequence of dam breach in cascade reservoirs and is more in line with the connotation of dam risk management, which can provide reference for the design and risk control of cascade reservoirs.@en

Dam breach has catastrophic consequences for human lives and economy. In previous studies, empirical models are often, to a limited extent, due to the inadequacy of historical dam breach events. Physical models, which focus on simulating human behavior during floods, are not suitable for fast analysis of a large number of dams due to the complexities of many key parameters. Therefore, this paper proposes a method for fast evaluation of potential consequences of dam breach. Eight main indices, i.e., capacity of reservoir (CR), dam height (HD), population at risk (PR), economy at risk (ER), understanding of dam breach (UB), industry type (TI), warning time (TW), and building vulnerability (VB), are selected to establish an evaluation index system. A catastrophe evaluation method is introduced to establish an evaluation model for potential consequences of dam breach based on the indices which are divided into five grades according to the relevant standards and guidelines. Validation of the method by twelve historical dam breach events shows a good accuracy. The method is applied to evaluate potential consequences of dam breach of Jiangang Reservoir in Henan Province, China. It is estimated that loss of life in the worst scenario is between that of Hengjiang Reservoir and that of Shimantan Reservoir dam breach, of which fatalities are 941 and 2717, respectively, showing that risk management measures should be taken to reduce the risk of potential loss of life.@en

Despite the rapid development of risk analysis in dam engineering, there is a relative absence of research on the environmental impact of dam break. As a systematic theory, set pair analysis has a good effect in dealing with uncertainties, although the result is relatively rough and easy to distort. A connection degree of five grades and a generalized set of potential are introduced to improve traditional set pair analysis. Combined with the index system, the evaluation model of the environmental impact of dam break is established, which is based on generalized set pair analysis. Taking Sheheji Reservoir dam as an example, a comparison of evaluation results of fuzzy mathematics theory and generalized set pair analysis is made, which verifies the scientificity and practicability of the method proposed in this paper. The results show that the evaluation grade of the environmental impact of dam break at Sheheji Reservoir is serious, and appropriate management measures should be taken to reduce the risk.@en

Despite the fact that the Bayesian network has great advantages in logical reasoning and calculation compared with the other traditional risk analysis methods, there are still obvious shortcomings in the study of dynamic risk. The risk factors of the earth-rock dam breach are complex, which vary with time during the operation period. Static risk analysis, limited to a specific period of time, cannot meet the needs of comprehensive assessment and early warning. By introducing time factors, a dynamic Bayesian network model was established to study the dynamic characteristics of dam-breach probability. Combined with the calculation of the conditional probability of nodes based on the Leaky Noisy-Or gate extended model, the reasoning results of Bayesian networks were modified by updating the data of different time nodes. Taking an earth-rock dam as an example, the results show that it has less possibility to breach and keep stable along the time axis. Moreover, the factors with vulnerability and instability were found effective, which could provide guidance for dam risk management.@en

The internal mechanism affecting life loss caused by a dam-break flood is complicated. On the basis of analyzing the risk formation path, a risk evaluation indicator system was established which included the hazards, exposure and vulnerability factors. Variable Fuzzy Sets theory was introduced into the risk evaluation of life loss risk grades and applied to eight collapsed dams in China. According to the sequence of the risk grades of these dams, the evaluation result was mainly consistent with the actual mortality ranking sequence, showing that the model could be effectively applied to the risk evaluation of life loss in dam-break events. Aimed at the problem of large differences in the downstream population distribution of dams in China, this manuscript suggested that 10,000 people should be the basis for the grouping operation of dams in the risk evaluation. These Variable Fuzzy evaluation models and grouping suggestions could help stakeholders to allocate the funds for dam reinforcement more accurately and provide a scientific basis for the study of dam-break life loss and dam risk management.@en

The environmental impact of dam breach has the features of complexity and uncertainty. There is a lack of systematic and comprehensive research on the environmental impact of dam breach in China. Considering such fuzziness of environment evaluation and the lack of precise data, this work chooses the method of multi-index comprehensive evaluation. Targeting to solve the uncertainty problem of weight calculation and evaluation model, this work introduces the statistic cloud theory to calculate the weight and variable fuzzy set theory to evaluate the environmental impact. We select seven environmental impact factors, including channel morphology, vegetation coverage, water and soil environment, biodiversity, human ecology, and industrial pollution, are selected to construct the evaluation index system and construct the value standard of them. The models are applied to the dam of Shaheji Reservoir in China. The results show that the environmental impact degree of the reservoir member an extremely serious grade mostly, reaching 0.589. Compared with the evaluation results already done, the result of the proposed models shows that the models are reasonable and scientific, which provides a new method for environmental impact assessment of dam breach considering the uncertainty feature of the environment.@en

The key to simulating the mechanical properties of earth-rockfill dam materials is selecting a reasonable constitutive model. The traditional constitutive model targets specific earth-rockfill dam materials and involves many hypotheses in theory, resulting in large common errors in applications. The Pastor-Zienkiewicz model (P-Z model) based on generalized plastic mechanics theory has a strict theoretical base, but it involves many parameters. Moreover, the determination of parameter a entails high discreteness because of experimental conditions, and this discreteness influences the accuracy of simulation analysis. The mechanical properties of earth-rockfill dam materials were simulated using the P-Z model in this study to optimize parameter a of the model and decrease its discreteness. First, conventional triaxial shear test results of earth-rock materials were denoised with the empirical mode decomposition method. Second, a method to optimize parameter a was proposed by using cloud theory. Lastly, a numerical simulation analysis of the triaxial shearing test was performed with the optimized P-Z model. Research results demonstrate that the entropy error and hyper entropy error rates of the triaxial shearing test data decline by 35% and 67%, respectively, and the cloud droplet range of parameter a is narrowed by 32%. The discreteness of the values decreases significantly. The simulation calculation results are consistent with the test results, thereby confirming the reasonability of the proposed parameter optimization method. The optimized P-Z model can simulate the mechanical properties of earth-rockfill dam materials accurately. This study can provide a theoretical reference for finite element simulation analysis of earth-rockfill dam structures.@en

Both hydrodynamic factors and social factors have large impacts on the loss of life caused by dam failure. Relatively large uncertainty intervals of the influencing factors lead to changes in the potential loss of life. Based on an analysis of the formation mechanism of loss of life, the influencing factors were identified. Combined with interval theory, a method for calculating loss of life and determining the impacts of the influencing factors on loss of life was proposed. The intervals of the exposure rate of the population at risk and the mortality of the exposed population, which are impacted by the major influencing factors such as the flood severity, warning time, understanding of dam failure, and building vulnerability, were recommended. Furthermore, a range of correction coefficients caused by the minor influencing factors, such as the dam failure time, rescue ability, and age distribution, was analyzed. The proposed method was validated by analyzing the losses of life in 21 flooded regions after 10 dam failure events and 2 flash river floods, in which the intervals of the estimated results all contained the actual loss of life. In addition, the ratios of the upper bounds to the corresponding lower bounds of the intervals were all less than 10, which is in accordance with the characteristic that the results of different existing methods vary within an order of magnitude. This is the first work that pays careful attention to the uncertainty intervals of loss of life estimates, and the proposed method effectively determined the severity of the potential loss of life caused by dam failure. @en

Both hydrodynamic factors and social factors have large impacts on the loss of life caused by dam failure. Relatively large uncertainty intervals of the influencing factors lead to changes in the potential loss of life. Based on an analysis of the formation mechanism of loss of life, the influencing factors were identified. Combined with interval theory, a method for calculating loss of life and determining the impacts of the influencing factors on loss of life was proposed. The intervals of the exposure rate of the population at risk and the mortality of the exposed population, which are impacted by the major influencing factors such as the flood severity, warning time, understanding of dam failure, and building vulnerability, were recommended. Furthermore, a range of correction coefficients caused by the minor influencing factors, such as the dam failure time, rescue ability, and age distribution, was analyzed. The proposed method was validated by analyzing the losses of life in 21 flooded regions after 10 dam failure events and 2 flash river floods, in which the intervals of the estimated results all contained the actual loss of life. In addition, the ratios of the upper bounds to the corresponding lower bounds of the intervals were all less than 10, which is in accordance with the characteristic that the results of different existing methods vary within an order of magnitude. This is the first work that pays careful attention to the uncertainty intervals of loss of life estimates, and the proposed method effectively determined the severity of the potential loss of life caused by dam failure. @en

The evaluation of the benefits of urban water resource utilization, which include supporting life and industrial and agricultural production, is important for decision-making and policy formulation in urban water management. However, since life cannot be quantified in terms of economic value, it is difficult for traditional economic analysis methods to comprehensively evaluate the benefits of urban water resource utilization. Output per unit water and the proportion of water to resource inputs were proposed to evaluate these benefits. An evaluation index system was established based on catastrophe theory, which evaluates the system under the condition that the relative importance of indices is determined and the exact weights are unknown. Emergy theory, which reflects the process of energy conversion, was introduced to analyze various benefits of urban water resource utilization. By applying these methods to evaluate these benefits in Zhengzhou, China, the author verified the rationality of the proposed methods, providing new ideas to evaluate these benefits.@en

The evaluation of the benefits of urban water resource utilization, which include supporting life and industrial and agricultural production, is important for decision-making and policy formulation in urban water management. However, since life cannot be quantified in terms of economic value, it is difficult for traditional economic analysis methods to comprehensively evaluate the benefits of urban water resource utilization. Output per unit water and the proportion of water to resource inputs were proposed to evaluate these benefits. An evaluation index system was established based on catastrophe theory, which evaluates the system under the condition that the relative importance of indices is determined and the exact weights are unknown. Emergy theory, which reflects the process of energy conversion, was introduced to analyze various benefits of urban water resource utilization. By applying these methods to evaluate these benefits in Zhengzhou, China, the author verified the rationality of the proposed methods, providing new ideas to evaluate these benefits.@en

Risk consequences analysis of dam breach is fundamental to risk assessment of reservoir dams. Multiple influencing factors and complex mechanisms lead to great differences between the analysis results of different research methods and the actual consequences. It is suggested that risk consequences can be divided into three basic categories: loss of life, economic loss and environmental impact, based on their definitions. According to the analysis of research achievements and applications abroad, the development trend that physical model based on disaster-causing mechanism takes place of empirical model based on historical data is clarified. Based on the analysis of research status of dam breach risk consequences assessment in China, both advantages and disadvantages of three main research methods, i.e. analysis based on empirical model and disaster-causing mechanism, semi-quantitative evaluation and superposition calculation of regional losses, are clarified in terms of accuracy and practicability. It is proposed that the risk consequences research and practical application can be improved in four aspects, i.e., strengthening the analysis of disaster-causing mechanism, paying attention to the combination of accuracy and practicability, emphasizing the important roles of non-engineering measures and improving the research constantly during application.@en

Risk consequences analysis of dam breach is fundamental to risk assessment of reservoir dams. Multiple influencing factors and complex mechanisms lead to great differences between the analysis results of different research methods and the actual consequences. It is suggested that risk consequences can be divided into three basic categories: loss of life, economic loss and environmental impact, based on their definitions. According to the analysis of research achievements and applications abroad, the development trend that physical model based on disaster-causing mechanism takes place of empirical model based on historical data is clarified. Based on the analysis of research status of dam breach risk consequences assessment in China, both advantages and disadvantages of three main research methods, i.e. analysis based on empirical model and disaster-causing mechanism, semi-quantitative evaluation and superposition calculation of regional losses, are clarified in terms of accuracy and practicability. It is proposed that the risk consequences research and practical application can be improved in four aspects, i.e., strengthening the analysis of disaster-causing mechanism, paying attention to the combination of accuracy and practicability, emphasizing the important roles of non-engineering measures and improving the research constantly during application.@en

Uncertainty is inevitable in the safety monitoring and evaluation process of earth-rock dam. Such uncertainty makes the accurate reflection of the running status of earth-rock dams of traditional safety assessment results impossible. Thus, this study proposed a safety assessment model of earth-rock dams based on the combination weighting method of ideal point and the cloud theory model. The proposed model was used to scientifically solve the uncertainty during the safety assessment of earth-rock dams. Real and reliable weights of indexes were determined using the combination weighting method based on the ideal point. Then, the safety evaluation grade ranges of each evaluation index were divided on the basis of the measured data. These grade ranges were "softened" by combining cloud theory. The proposed safety assessment model was applied to an earth-rock dam in the reservoir of a pumped storage station in Tai'an City, Shandong Province, China. Results demonstrate that: (1) the proposed model can effectively solve fuzzy and random problems during the safety assessment of earth-rock dams, and (2) the results show that the safety of the investigated earth-rock dam is in a normal running state. This outcome reflects the actual conditions of the earth-rock dam. The proposed model provides references in the diagnosis and decision making in the earth-rock dam management department.@en