When a dam breaks, huge floods will be generated that may inundate urban areas, enterprises, farmlands, and infrastructure and cause giant economic losses. Economic risk criteria are a kind of basis for determining dam risk levels and to decide whether risk control measures should be taken or not. However, compared to loss-of-life risk criteria, much fewer economic risk criteria for dams have been proposed and implemented for two main reasons: (a) The ability of most areas to endure economic losses caused by dam breach changes over time because of the constant development of their economic levels; and (b) Economic development levels in an area are distinct from the levels in other areas, resulting in significant differences in the ability of different areas to endure economic losses caused by a dam breach. Therefore, an equivalent economic scale (EES) that indicates the relative economic level of an area to the whole country in a given period of time is a preferred measure. It was shown in this paper that EES has much more stable values than do ordinary economic measures; therefore, it was taken as the basic index for establishing economic risk criteria. Furthermore, due to the distinct economic loss rates of different industries, the index of industrial economic contribution (IEC) was introduced to determine the correction coefficient to modify the ESS to reflect the potential economic loss of the area to be evaluated. This is the first research that pays careful attention to the change of ability to endure economic losses, in which the established economic risk criteria are applicable over a relatively long time and for different areas based on the consideration of the relative level of the economy and the industrial economic contribution.

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.

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.

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.

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 (C_R), dam height (H_D), population at risk (P_R), economy at risk (E_R), understanding of dam breach (U_B), industry type (T_I), warning time (T_W), and building vulnerability (V_B), 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.