1. Introduction
Dams play extremely important roles in flood control, water supply, hydropower generation, irrigation, navigation, and recreation benefits. However, because of the storage of water and inundation, huge potential energy is generated and has a great threat to the downstream [
1]. Dam breach produces a large number of destructive floods and results in losses of life (LOLs) and economy [
2,
3,
4]. Despite the increasing safety of dams due to improved engineering knowledge and better construction quality, a full non-risk guarantee is not possible and an accident can occur, triggered by natural hazards, human actions, or loss of strength capacity of the dam due to its age [
5]. In recent years, there have been many serious dam breach accidents [
6]. By 24 July 2018, at least 20 people had been killed and more than 100 were missing in the floods caused by the collapse of an under-construction dam, which is part of the Xe-Pian Xe-Namnoy hydroelectric power project in Southeast Laos. Twenty people were killed and eight were missing because of the dam breach of Sheyuegou Reservoir in Xinjiang, China on 1 August 2018. Consequently, the risk consequences of dam breach have always attracted the attention of researchers.
Originally, empirical models, which are based on historical events, were established to evaluate consequences of dam breach. Brown and Graham (1988) provided a conceptual model of variables influencing the LOL from dam failure and a method for predicting LOL based on the size of the population at risk (
PR) from failure and the amount of warning time (
TW) available for that population [
7]. DeKay and McClelland (1993) proposed an expression for LOL in terms of warning time (
TW) and population at risk (
PR). The forcefulness of the floods was derived from the historical records of dam breach and flash flood cases via logistic regression [
8]. These studies are often, to a limited extent, based on empirical data of historical flood events, most of which are of low availability, resulting in low accuracy in most applications.
Thereafter, multiple physical models were established, which focus on simulating human behavior during floods. Assaf and Hartford (2002) developed a virtual reality approach (BC Hydro’s Life Safety Model (LSM)) to deal with the problems of failure consequence analysis and emergency planning that are not amenable to resolution through existing analysis techniques, which is undergoing continued development [
9]. Aboelata and Bowles (2008) demonstrated the deterministic uncertainty modes of calculation model of LOL named LIFESim, which was sponsored by the U.S. Army Corps of Engineers (USACE), the Australian National Committee on Large Dams (ANCOLD), and the U.S. Bureau of Reclamation (USBR), for a small community for the sunny-day breach of a large dam [
10]. Jonkman et al. (2008) developed new mortality functions for the estimation of LOL caused by the floods of low-lying areas protected by flood defenses [
11]. Serrano-Lombillo et al. (2012) classified different types of consequences of dam breach and discussed available methods for their estimation and how these results can be incorporated into a risk model in a quantitative risk analysis [
12]. Peng and Zhang (2012) presented a new human risk analysis model (HURAM) using Bayesian networks for estimating human risks due to dam breach floods [
13]. Sun et al. (2014) and Zhou et al. (2014) proposed a methodology containing a combined weight method and the Technique for Order of Preference by Similarity to Ideal Solution for risk ranking of dangerous reservoirs due to its logical consideration of scalar values that simultaneously account for both the best and worst alternatives [
14,
15]. Cleary et al. (2015) used several failure scenarios to predict consequences in terms of downstream inundation and damage [
16]. Li et al. (2018) established a new coupling evaluation model combined with the set pair analysis and variable fuzzy set theory, based on the analysis of hazards, exposure, and vulnerability [
17]. Magilligan et al. (2019) used detailed field sampling and systematic image analysis to document the immediate and sustained geomorphic adjustments at four failed dams within the urbanized Gills Creek watershed [
18]. In general, before deciding the methodology to use, it is necessary to analyze the available data, in order to apply it correctly. Dam breach floods, which are influenced by a continually changing and complex environment, are characterized by sudden occurrence, rapid expansion, and urgent response [
19]. The uncertainties of various factors lead to significant differences in the analysis results of various methods [
2]. However, the key factors and their relative importance in determining consequences caused by dam breach, which have been analyzed in these methods, are quite meaningful to establish a faster or more accurate evaluation model.
Recently, comprehensive evaluation models have begun in prosperity. Wang et al. (2011) developed a fuzzy hierarchy synthesis evaluation model for dam failure, combined with weight analysis of influencing factors by means of the analytic hierarchy process (AHP) [
20]. Zhang and Tan (2014) established a comprehensive risk assessment system of dam flood overtopping based on the synthesis of probability of dam failure and corresponding LOLs and economy [
21]. Liu et al. (2014) proposed a rapid method for floods loss assessment based on a neural network ensemble [
22]. Huang et al. (2017) put forward a new calculation method for estimating LOL based on selecting 14 dam failure cases in China as the basic data by three-dimensional stratified sampling, balancing spatial, vertical elevation, and temporal representations, as well as considering various conditions of the dam collapse [
23]. Li et al. (2019) introduced the variable fuzzy set theory into the risk evaluation of life loss risk grades [
4]. Based on the detailed analysis of impacts on LOL caused by all kinds of influencing factors, severity of consequences caused by dam breach are calculated, which are effective supplements to the above quantitative fatality analysis. However, due to the complex calculation processes and the difficulties in determining accurate values of all influencing factors, it is quite difficult for engineers to judge the potential consequences of dam breach quickly by these methods.
Therefore, a method for fast evaluation of potential consequences caused by dam breach is proposed. Eight indices, which originate from risk sources, risk pathways, and risk receptors and are easy to obtain, are selected and standardized based on their relevant importance in the severity of potential consequences. Furthermore, a catastrophe evaluation method is used to calculate risk values of dam breach consequence, guiding dam risk management.
4. Discussion
According to
Figure 3, catastrophe evaluation results of dam breach consequences of Sheyuegou Reservoir and Gouhou Reservoir are obviously inconsistent with the trend of actual LOL of the other 10 validation reservoirs. However, this situation is caused by specific dam failure conditions. Due to partial damage, instead of not total breach, severity of LOL of Sheyuegou Reservoir is relatively less than the evaluation result which is based on total dam breach. There is a big difference between the distribution of population at the risk of Gouhou Reservoir and the other reservoirs. The floods caused by Gouhou Dam breach did not arrive at the nearest resident area, which was 13 kilometers away from the dam, until 1.5 hours later. Therefore, severity of the floods has been greatly reduced, and the corresponding LOL is relatively less than expected.
According to
Table 5 and
Figure 3, the order of severity of LOL of the other 10 validation reservoirs dam breach from high to low is Banqiao, Shimantan, Hengjiang, Liujiatai, Longtun, Lijiazui, Dongkoumiao, Shijiagou, Xiaomeigang, and Shenjiakeng Reservoirs in catastrophe evaluation results whereas, in statistics, that is Banqiao, Shimantan, Liujiatai, Hengjiang, Longtun, Lijiazui, Dongkoumiao, Shijiagou, Xiaomeigang, and Shenjiakeng Reservoirs. The results are extremely similar in spite of the difference on Hengjiang and Liujiatai Reservoirs, of which LOLs are 941 and 937, respectively. However, there is certain uncertainty around the most probable LOL caused by dam breach, due to complexities in floods and society. Thus, disparity of four fatalities does not demonstrate the difference in consequences. Therefore, the method proposed in this study can be effectively applied to fast evaluation of dam breach consequences.
Compared with the conventional methods, which analyze consequences of dam breach based on the calculation of depth, velocity, and rise rate of floods that constantly change at different downstream locations of the dam, the method proposed in this paper can effectively identify the severity of consequences based on some fundamental parameters which are easy to be obtained. The method is best for the reservoir dams which have limited downstream data. Furthermore, it can be used for fast evaluation of risk consequences of a large number of reservoir dams effectively, costing significantly less money and time than the conventional methods.
The severity of potential LOL can be determined according to the evaluation results in
Figure 3. Understanding of dam breach (
UB) and warning time (
TW), which have close relations to daily dam management, are analyzed with the implementation of the proposed method. According to
Figure 4, the consequence of Jiangang Reservoir dam breach (0.900) in the condition of
UB = vague/unknown and
TW = 0 h is between that of Hengjiang Reservoir (0.894) and that of Shimantan Reservoir (0.908), of which fatalities are 941 and 2517, respectively. Nevertheless, the consequence of Jiangang Reservoir dam breach (0.835) in the condition of
UB = medium and
TW = 6 h is between that of Shijiagou Reservoir (0.829) and that of Dongkoumiao Reservoir (0.840), of which fatalities are 81 and 186, respectively. Therefore, risk management measures, which focus on improving understanding of dam breach (
UB) and warning time (
TW), should be taken in Jiangang Reservoir management to reduce potential LOL caused by dam breach.
Accuracy of the proposed method in this paper is greatly influenced by the index system, due to the fact that the importance of the variables should be reduced from left to right in the catastrophe evaluation method. However, there are differences between main functions of different reservoirs, and between standards and guidelines in different countries. Therefore, the selection and treatment of indices should be adjusted correspondingly according to specific circumstances to ensure scientific nature and practicability of the method. In addition, terrain significantly enhances destructive force of floods caused by dam breach in Alpine Canyon areas, which is not taken into consideration in this research. Therefore, the potential consequences of dam breach in Alpine Canyon areas should be analyzed specifically based on floods simulation.
5. Conclusions
Floods caused by dam breach have been of increasing concern to safety engineers and decision makers. The existing methods for the estimation of consequences were reviewed, which are not applicable to fast evaluation of potential consequences caused by dam breach, especially not for a large number of dams. Therefore, a fast evaluation method was proposed based on catastrophe theory. Combined with the characteristics of catastrophe theory, principles for selecting indices were determined. Then, eight indices, which influence potential consequences significantly and easy to be obtained, were selected to establish an evaluation index system according to their relative importance, and were divided into five grades, i.e., slight, general, moderate, serious, and extremely serious, according to China’s dam management standards and guidelines. Twelve historical dam breach events were adopted for validation, which verifies the accuracy of the method. Taking Jiangang Reservoir as an example, potential LOLs in various conditions were demonstrated, which provides references and bases for dam risk management.