Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
International Journal of Environmental Research and Public Health Article Risk Analysis of Earth-Rock Dam Failures Based on Fuzzy Event Tree Method 1 , 2 , 3 1 , 2 , 3 , 1 , 2 , 3 1 , 2 , 3 Xiao Fu , Chong-Shi Gu *, Huai-Zhi Su and Xiang-Nan Qin State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; fuxiaohhu@163.com (X.F.); su_huaizhi@hhu.edu.cn (H.-Z.S.); Qin_xn@163.com (X.-N.Q.) National Engineering Research Center of Water Resources Efﬁcient Utilization and Engineering Safety, Hohai University, Nanjing 210098, China College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China * Correspondence: csgu@hhu.edu.cn Received: 12 March 2018; Accepted: 26 April 2018; Published: 29 April 2018 Abstract: Earth-rock dams make up a large proportion of the dams in China, and their failures can induce great risks. In this paper, the risks associated with earth-rock dam failure are analyzed from two aspects: the probability of a dam failure and the resulting life loss. An event tree analysis method based on fuzzy set theory is proposed to calculate the dam failure probability. The life loss associated with dam failure is summarized and reﬁned to be suitable for Chinese dams from previous studies. The proposed method and model are applied to one reservoir dam in Jiangxi province. Both engineering and non-engineering measures are proposed to reduce the risk. The risk analysis of the dam failure has essential signiﬁcance for reducing dam failure probability and improving dam risk management level. Keywords: earth-rock dam; risk analysis; dam failure probability; life loss; ETA method; fuzzy set theory 1. Introduction Earth-rock dams account for more than 90% of all of the 90,000 reservoirs in China, among which nearly 30,000 reservoirs are in operation with defects. The primary problem for decision-makers to solve is how to protect the safety of reservoirs and use the nation’s most limited funds to reinforce the most in-need reservoirs [1]. The use of risk analysis to manage these dams has become an urgent problem in the dam industry [2–4]. Dam failure is a low-probability social catastrophic factor, which is extremely harmful. There are great numbers of downstream residents of reservoirs in China. The life loss will be great and intolerable once a dam is damaged. According to statistics, the annual average dam failure rate in China is 8.761 10 . In the 20th century, the average annual dam failure rate of the world was 2.0 10 , regardless of war-related reasons, which means the probability of dam failure in China is relatively high [5]. A number of studies are dedicated to investigating dam failures. Hartford et al. [6] provided a contemporary description of evolving techniques for risk-based dam safety management. They presented some new approaches (e.g., ETA method and comprehensive sections on consequence analysis), which are necessary for the estimation of risk and the planning of emergency preparedness. Rong-Yong and Zong-Kun et al. [7,8] analyzed the overﬂow fuzzy risk on earth dams, which makes the calculation of dam failure probability more reasonable. Graham [9] conducted an extensive evaluation of dam failures and the factors that contributed to loss of life. Masskant [10] found that the consideration of the exact spatial distribution of population growth is essential for reliable estimation of future risk of ﬂooding. Int. J. Environ. Res. Public Health 2018, 15, 886; doi:10.3390/ijerph15050886 www.mdpi.com/journal/ijerph Int. J. Environ. Res. Public Health 2018, 15, 886 2 of 22 This paper mainly focuses on the risk analysis of earth-rock dams from the probability and life loss model of the dam failure [11–13]. In the aspect of dam failure probability, the traditional probability calculation only considers the randomness of the event occurrence and depends on the experience of the experts, but the factors that affect the dam failure are often complicated and fuzzy [14]. Therefore, an event tree analysis (ETA) method based on fuzzy set theory is proposed. Dam failure may cause heavy fatalities, property damage, and environmental deterioration. After calculating the dam failure probability, we also need to analyze the possible life loss caused by the dam failure and establish a life loss assessment model which is suitable for China, so as to serve the dam risk analysis and management. The establishment of a dam failure probability and a dam failure life loss model is of great signiﬁcance to reduce the failure risk, improve the ability to deal with sudden break time, reduce life loss, and improve the management level of dams. 2. Causes, Modes and Paths of Dam Failure Obviously, analysis of dam failures is of critical importance for disasters prevention and mitigation. Hence, an insightful understanding of the characteristics of dam failures (e.g., failure causes, modes, and paths) is needed [15,16]. In different countries and regions, the characteristics and laws of dam failure patterns and dam failure possibilities are different. Therefore, dam failure history information in a certain region is of particular signiﬁcance for the risk analysis of dams in this region. Through the statistical analysis of the history of dam breakage cases, summarizing the causes and modes of dam failure is highly necessary for reservoir dam risk assessment and emergency measures [17]. 2.1. Statistical Analysis of Dam Failure Data At present, many countries in the world have a large number of reservoir dams. Among them, many dams have caused heavy loss of life due to dam failure, as shown in Table 1 [18,19]. These dam failure events have shocked the world and should be studied in-depth. Table 1. Several famous large dam failure events and deaths in the world. 6 3 Dam Name Country Year of Accident Dam Type Reservoir Volume (10 m ) Deaths Mohne Dam German 1943 Gravity dam 134.0 1200 Malpasset Dam France 1959 Arch dam 15.0 421 Vaiont Dam Italy 1963 Arch dam 169.0 2000 Buffalo Creek Dam USA 1972 Tailings dam 49.8 125 Machhu II Dam India 1979 Earth dam 101.0 3000 Shakidor Dam Pakistan 2005 Earth-rock dam - 135 Situ Gintung Dam Indonesia 2009 Earth-rock dam 2.0 100 Since the 1960s, there have been many serious dam failure events in China [20], as shown in Table 2. We should investigate the dam failure events that have caused heavy loss of life, clarify the situation of life loss, and summarize its rules. It can be used for signiﬁcant reference to estimate the fatalities reasonably and to reduce life loss in the future. Int. J. Environ. Res. Public Health 2018, 15, 886 3 of 22 Int. J. Environ. Res. Public Health 2018, 15, x 3 of 22 Table 2. Several large dam failure events and deaths in China. Table 2. Several large dam failure events and deaths in China. Reservoir Volume Dam Name Location Date Dam Type Deaths 6 3 Reservoir Volume (10 m ) Dam Name Location Date Dam Type Deaths 6 3 (10 m ) Longtun Dam Suizhong, Liaoning province 1959.7.22 Clay sloping core dam 30.0 707 Longtun Dam Suizhong, Liaoning province 1959.7.22 Clay sloping core dam 30.0 707 Liujiatai Dam Yixian, Hebei province 1963.8.8 Clay core wall dam 40.5 943 Liujiatai Dam Yixian, Hebei province 1963.8.8 Clay core wall dam 40.5 943 Hengjiang Dam Jiexi, Guangdong province 1970.9.15 Homogeneous earth dam 78.8 941 Hengjiang Dam Jiexi, Guangdong province 1970.9.15 Homogeneous earth dam 78.8 941 Lijiaju Dam Zhuanglang, Gansu province 1973.4.29 Homogeneous earth dam 1.1 580 Banqiao Lijiaju D Dam am ZhLuoyang, uanglang,Henan Gansupr povince rovince 197 1975.8.8 3.4.29 Homo Clay geneo cor us e ea wall rthdam dam 1492.0 .1 580 22,564 Shimantan Dam Wugang, Henan province 1975.8.8 Homogeneous earth dam 91.8 Banqiao Dam Luoyang, Henan province 1975.8.8 Clay core wall dam 492.0 22,564 Gouhou Dam Gonghe, Qinghai province 1993.8.27 Concrete-faced rock-ﬁll dam 3.0 400 Shimantan Dam Wugang, Henan province 1975.8.8 Homogeneous earth dam 91.8 Gouhou Dam Gonghe, Qinghai province 1993.8.27 Concrete-faced rock-fill dam 3.0 400 According to the statistics in [21], the dam failure cases comprise earth dams, concrete dams, According to the statistics in [21], the dam failure cases comprise earth dams, concrete dams, masonry dams, rockﬁll dams, and so on. Figure 1 compares the percentages of these types of dams in masonry dams, rockfill dams, and so on. Figure 1 compares the percentages of these types of dams the world (excluding China) and in China. It clearly shows that the majority of cases are earth-rock in the world (excluding China) and in China. It clearly shows that the majority of cases are earth-rock dams, which account for 70.0% of dams in the world (excluding China) and 93.9% in China. Therefore, dams, which account for 70.0% of dams in the world (excluding China) and 93.9% in China. Therefore, this paper chooses an earth-rock dam for failure analysis. this paper chooses an earth-rock dam for failure analysis. Figure 1. Statistics of dam types of the world (excluding China) and China. Figure 1. Statistics of dam types of the world (excluding China) and China. Earth-rock dam, one of the oldest dame types, generally refers to a dam that is constructed with Earth-rock dam, one of the oldest dame types, generally refers to a dam that is constructed with local soil, stone, or mixture through throwing and rolling, etc. Such a dam has various risks in the local soil, stone, or mixture through throwing and rolling, etc. Such a dam has various risks in the operation, while dam failure is the most critical. Due to the complexity of the hydrogeographical operation, while dam failure is the most critical. Due to the complexity of the hydrogeographical environment, meteorology, hydrodynamic forces and structure of the dam, many factors can lead to environment, meteorology, hydrodynamic forces and structure of the dam, many factors can lead to dam failure. Therefore, it is very important to study the causes, modes, and paths in the earth-rock dam failure. Therefore, it is very important to study the causes, modes, and paths in the earth-rock dam failure probability calculation. dam failure probability calculation. 2.2. Causes and Modes of Earth-Rock Dam Failure 2.2. Causes and Modes of Earth-Rock Dam Failure The earth-rock dam is the dam type with the largest number of calamities and highest dam The earth-rock dam is the dam type with the largest number of calamities and highest dam failure failure rate. According to the failure mechanism, these can be divided into several types: lack of flood rate. According to the failure mechanism, these can be divided into several types: lack of ﬂood control control capacity, insufficient structural stability, seepage damage, and several other conditions. The capacity, insufﬁcient structural stability, seepage damage, and several other conditions. The main main failure modes are dam foundation failure, overtopping, slope instability, spillway failure , and failure modes are dam foundation failure, overtopping, slope instability, spillway failure, and internal internal erosion, as shown in Figure 2 [22–25]. erosion, as shown in Figure 2 [22–25]. Spillway Spillway Dam Crest Dam Crest Dam Crest Dam Crest Dam Crest Dam Crest Int. J. Environ. Res. Public Health 2018, 15, 886 4 of 22 Int. J. Environ. Res. Public Health 2018, 15, x 4 of 22 Int. J. Environ. Res. Public Health 2018, 15, x 4 of 22 FOUNDATION FAILURE Superelevation Leakage in Cross waves foundation Core Weir FOUNDATION FAILURE Superelevation Obstructions Leakage in Cross waves Bulking foundation Core Weir OVERTOPPING Obstructions Flow concentration Surface Erosion Bulking OVERTOPPING SPILLWAY FAILURE Core Flow concentration Surface Erosion INTERNAL EROSION SPILLWAY FAILURE SLOPE Core Crack in core Water level INSTABILIITY Inadequate filter Rapid drawdown Leakage INTERNAL EROSION Core Core SLOPE Crack in core Water level INSTABILIITY Inadequate filter Rapid drawdown Leakage Core Core Figure 2. Several failure modes of earth-rock dams. Figure 2. Several failure modes of earth-rock dams. 3. Establishment of Analysis Models Figure 2. Several failure modes of earth-rock dams. 3. Establishment of Analysis Models 3.1. Event Tree Analysis (ETA) 3. Establishment of Analysis Models 3.1. Event Tree Analysis (ETA) Event tree analysis (ETA) is a logic method, either qualitative and quantitative, that is used to Event tree analysis (ETA) is a logic method, either qualitative and quantitative, that is used to 3.1. Event Tree Analysis (ETA) identify possible outcomes. ETA is widely used as a ‘pre-accident’ analysis technique that examines identify the possible systems ioutcomes. n place, whiET ch A wo is ulwidely d prevent used accias dent a ‘pr pre-accident’ ecursors from analysis developi techn ng in ique to acc that idents examines . It can the Event tree analysis (ETA) is a logic method, either qualitative and quantitative, that is used to systems alsoin bplace, e usedwhich as a ‘po would st-accpr ident’ event anaccident alysis tecpr hnecursors ique that fr id om enti developing fies conseque into nceaccidents. s of an accIt idcan ent also identify possible outcomes. ETA is widely used as a ‘pre-accident’ analysis technique that examines sequence. The application of the ETA method in dam safety, where accident initiation is postulated, be used as a ‘post-accident’ analysis technique that identiﬁes consequences of an accident sequence. the systems in place, which would prevent accident precursors from developing into accidents. It can is used to illustrate how various subsequent events and scenarios evolve [26]. The application also be usedof as the a ‘po ETA st-method accident’ in andam alysis safety techn,iq wher ue th eat accident identifies initiation consequeis nce ps ostulated, of an acciis dent used to The risk analysis of dams with the ETA method is based on a condition or load condition. By sequence. The application of the ETA method in dam safety, where accident initiation is postulated, illustrate how various subsequent events and scenarios evolve [26]. using the tracing method, the various elements of the dam and how the failure happened under the is used to illustrate how various subsequent events and scenarios evolve [26]. The risk analysis of dams with the ETA method is based on a condition or load condition. By using load condition are logically analyzed. Thus, the estimation of overall dam failure probability is The risk analysis of dams with the ETA method is based on a condition or load condition. By the tracing method, the various elements of the dam and how the failure happened under the load available. The ETA method is constructed as shown in Figure 3, which attempts to generate all the using the tracing method, the various elements of the dam and how the failure happened under the condition are logically analyzed. Thus, the estimation of overall dam failure probability is available. resultant events caused by some excitation events such as earthquake, flood, and internal defect: load condition are logically analyzed. Thus, the estimation of overall dam failure probability is The ETA method is constructed as shown in Figure 3, which attempts to generate all the resultant available. The ETA method is constructed as shown in Figure 3, which attempts to generate all the events caused by some excitation events such as earthquake, ﬂood, and internal defect: resultant events caused by some excitation events such as earthquake, flood, and internal defect: Success status 2 Success status 1 Node Success status 2 Failure status 2 Success status 1 Node Fired event Node Failure status 2 Success status 3 Fired event Node Failure status 1 Node Success status 3 Failure status 3 Failure status 1 Node Figure 3. Event tree analysis of dam failure. Failure status 3 The ETA method provides a logical and graphical means to illustrate the sequence of events Figure 3. Event tree analysis of dam failure. Figure 3. Event tree analysis of dam failure. from an initiating event to the complete set of possible outcomes. The risk analysis of dam failure with the ETA method can help us to not only understand the overall process of the system change The ETA method provides a logical and graphical means to illustrate the sequence of events and identify possible accidents in advance, but also take measures to effectively avoid or reduce the The fromET an A in method itiating ev prent ovides to tha e logical complete and set graphical of possible means outcoto mes. illustrate The riskthe ana sequence lysis of da of m events failure from with the ETA method can help us to not only understand the overall process of the system change an initiating event to the complete set of possible outcomes. The risk analysis of dam failure with the and identify possible accidents in advance, but also take measures to effectively avoid or reduce the ETA method can help us to not only understand the overall process of the system change and identify possible accidents in advance, but also take measures to effectively avoid or reduce the incidence of accidents. According to the frequency of each risk factor occurrence, the probability of dam failure can be calculated. Dam crest Dam crest Int. J. Environ. Res. Public Health 2018, 15, 886 5 of 22 However, the ETA method sometimes has less objective basis in estimating the probability of the event in every link of dam failure development. There is little historical data available for reference, most of which requires the experience of experts. The factors affecting dam failure are complicated and often fuzzy. In view of this, this paper also takes the fuzzy set theory into consideration to analyze the risk of earth-rock dam failure. 3.2. Fuzzy Set Theory The concept of fuzzy set was proposed by Zadeh in 1965. The fuzzy set denotes the set of characteristic things with uncertain boundary [27]. For a fuzzy set A on the ﬁnal ﬁeld X, there is a m (x) 2 [0, 1] corresponding to 8x 2 A. m (x) is the membership degree of x to A and m is the A A A membership function of fuzzy set A. 3.2.1. Concept of Fuzzy Numbers Fuzzy numbers are used to deal with some fuzzy and inaccurate information, such as the “very likely” and “unlikely” language used by experts in the risk analysis of earth-rock dams which need to be quantiﬁed with fuzzy numbers combined with membership functions. In this paper, fuzzy numbers are divided into triangular fuzzy numbers and trapezoidal fuzzy numbers [28,29]. A triangular fuzzy number is expressed as A = (a, b, c), whose membership function is > 0; x a (x a)/(b a) a < x b m (x) = (1) >(c x)/(c a) b < x c 0 x > c A trapezoidal fuzzy number is expressed as A = (a, b, c, d), whose membership function is 0; x a (x a)/(b a); a < x b m (x) = (2) 1; b < x c (d x)/(d c); c < x d 0; x > d 3.2.2. Operation of Fuzzy Numbers For a given number 8l 2 [0, 1], the l-cut of fuzzy set A and B can be expressed as l l l A = fxjx 2 R, m lg = [a , b ] 1 1 (3) l l l B = fxjx 2 R, m lg = [a , b ] 2 2 Then the operation between fuzzy sets can be achieved by their l-cut sets: l l l l l l A(+)B = A + B = [a + a , b + b ] 1 2 1 2 l l l l l l A()B = A B = [a a , b b ] 1 2 1 2 (4) l l l l l l A()B = A B = [a a , b b ] 1 2 1 2 l l l l l l A()B = A B = [a a , b b ] 1 2 1 2 3.2.3. Non-Fuzziﬁcation of Fuzzy Language of Experts For the ETA of dam failure, experts often use fuzzy language for qualitative evaluation. Usually, we need to transform the fuzzy language of experts into quantitative analysis and then evaluate the Int. J. Environ. Res. Public Health 2018, 15, x 6 of 22 3.2.3. Non-Fuzzification of Fuzzy Language of Experts Int. J. Environ. Res. Public Health 2018, 15, 886 6 of 22 For the ETA of dam failure, experts often use fuzzy language for qualitative evaluation. Usually, we need to transform the fuzzy language of experts into quantitative analysis and then evaluate the safety of reservoir dams comprehensively. For the probability of dam failure, the fuzzy language can safety of reservoir dams comprehensively. For the probability of dam failure, the fuzzy language can be divided into seven types: ’Extremely unlikely’, ’Very unlikely’, ’Less likely’, ’Uncertain’, ’ be divided into seven types: ‘Extremely unlikely’, ‘Very unlikely’, ‘Less likely’, ‘Uncertain’, ‘Likely’, Likely’, ’Very Likely’, and ’Extremely Likely’. The fuzzy numbers and corresponding -cut sets of ‘Very Likely’, and ‘Extremely Likely’. The fuzzy numbers and corresponding l-cut sets of them are them are expressed in Table 3 [30]: expressed in Table 3 [30]: Table 3. Fuzzy numbers and corresponding -cut sets of fuzzy language. Table 3. Fuzzy numbers and corresponding l-cut sets of fuzzy language. Fuzzy Language Fuzzy Number -Cut Set Fuzzy Language Fuzzy Number l-Cut Set f (0,0， 0.1) f (0,0.1 0.1) Extremely unlikely l Extremely unlikely f = (0, 0, 0.1) f = (0,0.1l + 0.1) f (0.1， 0.2， 0.3) Very unlikely f (0.1 0.1,0.1 0.3) Very unlikely f = (0.1, 0.2, 0.3) f = (0.1l + 0.1,0.1l + 0.3) f (0.2， 0.3， 0.4,0.5) Less likely f (0.1 0.2,0.1 0.5) Less likely f = (0.2, 0.3, 0.4, 0.5) f = (0.1l + 0.2,0.1l + 0.5) f (0.4,0.5， 0.6) Uncertain f (0.1 0.4,0.1 0.6) Uncertain f = (0.4, 0.5, 0.6) f = (0.1l + 0.4,0.1l + 0.6) f (0.5， 0.6， 0.7,0.8) f (0.1 0.5,0.1 0.8) Likely Likely f = (0.5, 0.6, 0.7, 0.8) f = (0.1l + 0.5,0.1l + 0.8) l Very likely f = (0.7, 0.8, 0.9) f (0.7， 0.8,0.9) f = (0.1l + 0.7,0.1l + 0.9) Very likely f (0.1 0.7,0.1 0.9) Extremely Likely f = (0.8, 0.9, 1.0) f = (0.1l + 0.8, 1) f (0.8,0.9， 1.0) Extremely Likely f (0.1 0.8,1) The The m membership embership f function unction is is ex expr pres essed sed i in n Figur Figure e 4 4:: Figure 4. Membership function of fuzzy language. Figure 4. Membership function of fuzzy language. Meanwhile, in the process of organizing experts’ empowerment analysis, it is also necessary to Meanwhile, in the process of organizing experts’ empowerment analysis, it is also necessary to analyze the credibility of different experts. In this paper, the credibility of the expert, also known as analyze the credibility of different experts. In this paper, the credibility of the expert, also known as the the weight of experts, is expressed as α (0 α 1). α 1 represents the expert being the most trusted weight of experts, is expressed as a (0 < a < 1). a = 1 represents the expert being the most trusted and α 0 represents the expert being the least trusted. In this paper, the credibility of the expert is and a = 0 represents the expert being the least trusted. In this paper, the credibility of the expert is determined from four aspects: educational degree, professional title, professional direction, and determined from four aspects: educational degree, professional title, professional direction, and length length of service. The criteria for determining the credibility of an expert are shown in Table 4: of service. The criteria for determining the credibility of an expert are shown in Table 4: Table 4. Criteria for determining the credibility of an expert. Table 4. Criteria for determining the credibility of an expert. Educational Degree Professional Title Aspects Doctor Master Bachelor Senior Medium-grade Junior Educational Degree Professional Title Scoring Aspects [8,10] [7,9] [6,8] [8,10] [7,10] [5,7] Doctor Master Bachelor Senior Medium-grade Junior range Professional direction Length of service Scoring range [8,10] [7,9] [6,8] [8,10] [7,10] [5,7] Aspects Hydraulic structure Hydropower Civil >20a 10a~20a <10a Professional direction Length of service engineering engineering Engineering Scoring Aspects Hydraulic structure Hydropower Civil [7,10] [5,10] [5,8] [8,10] [5,7] [4,6] >20a 10a~20a <10a range engineering engineering Engineering Scoring range [7,10] [5,10] [5,8] [8,10] [5,7] [4,6] Int. J. Environ. Res. Public Health 2018, 15, 886 7 of 22 If b (j =1,2,3,4) is used to represent the evaluation scores of experts in four aspects: educational degree, professional title, professional direction and length of service, the credibility of each expert can be expressed as follows: a = b /40 (5) i å j j=1 3.2.4. Integral Value Method of Non-Fuzziﬁcation for Fuzzy Number After obtaining the corresponding l-cut sets of fuzzy numbers, the integral value method proposed by Liou is used to calculate the fuzzy numbers [31]. I = a I ( A) + (1 a) I ( A) (6) R L where a is the index of optimism, a 2 [0, 1]. I ( A) and I ( A) are the inverse function of left and right L R integral values of A respectively. 1 0.9 I ( A) = 0.5 l ( A)Dl + l ( A)Dl å å L u u l=0.1 l=0 (7) 1 0.9 I ( A) = 0.5 l ( A)Dl + l ( A)Dl å å R l l l=0.1 l=0 where l ( A) and l ( A) is upper bound and lower bound of l-cut sets of A. The upper and lower u l bounds of the fuzzy number A are respectively corresponding to a = 0 and a = 1. The value of the fuzzy number is representative when a = 0.5. 3.3. Application of Dam Failure Risk Analysis The application of the ETA method based on fuzzy set theory in dam failure risk analysis of an earth-rock dam can be summed up in the following steps [32]: (1) In view of the probable dam-breaking event, analyze the various accident paths and the accident links of the dam and establish the event tree structure chart. (2) Calculate the probability of dam failure for all dam-breaking paths under each load condition. Invite experts to carry out a qualitative assessment of the accident. By using the ETA method of fuzzy set theory, the expert qualitative language is converted into quantitative value. The probability of each failure link in the accident path is obtained. Finally, the probability value of the dam in a burst mode is obtained by multiplying the probabilities of each failure link. The conditional probability of each link in a burst mode is p(i, j, k), i = 1, 2, ..., m; j = 1, 2, , n; k = 1, 2, ..., s. where i is the reservoir water level load, j is the failure mode and k represents for each aspect. Then, the probability of burst under the I type load and j type failure mode is P(i, j) = p(i, j, k) (8) k=1 (3) Under the same load, the failure mode of the dam can be independent, at which time the deMorgan law can be used to calculate the burst probability under the same load. P( A + A + + A ) = 1 (1 P ) (9) i1 i2 im i j j=1 (4) Repeat the above steps for different loads on the dam to obtain all possible dam-breaking paths and their probabilities under all possible load conditions. Assuming that the dam failures under Int. J. Environ. Res. Public Health 2018, 15, 886 8 of 22 different loads are independent of each other, the probability of the dam collapse under all different loading conditions is added, that is, the total dam probability of the dam is obtained. P = P(1) + P(2) + + P(n) (10) 3.4. Estimation Model of Dam Failure Life Loss Evaluating the consequences of a dam failure is extremely important in the dam safety study. Dam failure can cause catastrophic losses such as life loss, property loss, environmental loss, and so on. The most important part is the loss of life. This paper focuses on estimating fatalities of a dam failure. The estimation of dam failure life loss is affected by many factors [9]. Among these are cause and type of dam failure; number of people at risk; severity of dam break ﬂood; timeliness of dam failure warnings; occurrence time of dam failure; ease of evacuation. Graham summarized the seven basic steps to evaluate the dam failure life loss, which are still widely used at present. Ke-fa et al. [33,34] conducted an in-depth discussion and analysis on a large amount of data of eight dam failures that have occurred in the history of China. They summarized the basic law of the loss of life and proposed a life loss estimation method, which is suitable for Chinese conditions. In this paper, based on this method, combined with the actual situation of the studied reservoir, the potential loss of life caused by the dam failure will be evaluated. 3.4.1. Estimation Model Parameters of Dam Failure Life Loss Dam-break loss of life is a result of complex factors, usually divided into population at risk (P ), severity degree of dam break ﬂood (S ), occurrence time of dam failure, warning time (W ), AR D T and understanding of P to S . AR D (1) Population at risk (P ) AR Population at risk refers to the number of people in the area covered by the dam-breaking ﬂood. The larger the total population at risk is, and the closer it is to the dam site and main channel, the greater the resulting loss of life will be. P can be determined by survey statistics and population AR registration data: P = P (11) AR å AR where i means a residential area and P means population of the residential area. ARi When considering the P , other factors such as population composition, living environment, AR escape route, and emergency rescue capability should also be taken into consideration in order to obtain more appropriate results. (2) Severity degree of dam failure ﬂood (S ) S refers to the damage degree of dam failure ﬂood to the downstream residents and buildings, which is related to dam type, storage capacity, and discharging ﬂow. S is usually represented by the D V value of the water depth and the velocity of a section: Low severity, D V < 1.0 m /s 2 2 S = Medium severity, 1.0 m /s D V 4.0 m /s (12) : 2 High severity, D V > 4.0 m /s (3) Warning time (W ) Warning time refers to the time from the moment of the dam failure warning to the time when the downstream masses retreated after receiving the instruction. It has an important inﬂuence on the amount of loss of life. W can generally be divided into three categories: T Int. J. Environ. Res. Public Health 2018, 15, 886 9 of 22 Little warning, W < 0.25 h < T Partly warning, 0.25 h W 1.0 h (13) Full warning W > 1.0 h (4) Occurrence time (O ) Occurrence time of dam failure has a signiﬁcant impact on the P and W . According to the AR T weather, occurrence time can be divided into sunny and rainy days; according to the time of day, it can be divided into daytime and night; according to the season, it can be divided into winter and summer. O is very important in the evaluation of life loss. If the dam break occurs on sunny days the trafﬁc will be better; during the daytime, it is more easily found by the staff; if the dam break occurs in summer, it is good for the evacuation of P . AR (5) Understanding of P to S (U ) AR D D Understanding of S for P will affect the success rate of rescue methods, which is an important D AR aspect in estimation of in dam failure life loss. U can be divided into two types: (1) U is fuzzy: D D the population at risk cannot understand the severity degree of the dam break ﬂood when they get the warning and they do not know the necessity, measure, and path of escape. (2) U is explicit: the population at risk can understand the severity degree of the dam break ﬂood clearly and can take the necessary measures of escape clearly. 3.4.2. Calculation of Estimation Model of Dam Failure Life Loss Based on the Graham method and combined with the situation of dams in China, this paper adopts the method of estimating the loss of life of dam failure in China proposed by Lei [33]. This calculation model mainly considers three parts: the number of population at risk (P ), AR the risk mortality rate suitable for China f, and the corresponding correction coefﬁcient w. The formula is as follows: L = w P f (14) OL AR where the value of f is determined according to Table 5. Table 5. Risk mortality rate suitable for China f. S W (h) U D T D Recommended Average Recommended Range Fuzzy 0.7500 0.3000~1.0000 <0.25 Explicit 0.2500 0.1000~0.5000 Fuzzy 0.2000 0.0500~0.4000 High 0.25~1.0 Explicit 0.0100 0.0050~0.0200 Fuzzy 0.1800 0.0100~0.3000 >1.0 Explicit 0.0005 0.0000~0.0010 Fuzzy 0.5000 0.1000~0.8000 <0.25 Explicit 0.0750 0.0200~0.1200 Fuzzy 0.1300 0.0150~0.2700 Medium 0.25~1.0 Explicit 0.0008 0.0005~0.0020 Fuzzy 0.0500 0.0100~0.1000 >1.0 Explicit 0.0004 0.0002~0.0010 Fuzzy 0.0300 0.0100~0.0500 <0.25 Explicit 0.0100 0.0000~0.0200 Fuzzy 0.0070 0.0000~0.0150 Low 0.25~1.0 Explicit 0.0006 0.0000~0.0010 Fuzzy 0.0003 0.0000~0.0006 >1.0 Explicit 0.0002 0.0000~0.0004 1:1.67 1:1.78 1:2.29 1:2.75 Int. J. Environ. Res. Public Health 2018, 15, x 10 of 22 Fuzzy 0.0070 0.0000~0.0150 0.25~1.0 Explicit 0.0006 0.0000~0.0010 Fuzzy 0.0003 0.0000~0.0006 >1.0 Int. J. Environ. Res. Public Health 2018, 15, 886 10 of 22 Explicit 0.0002 0.0000~0.0004 Remarks: when it is sunny daytime, the upper limit is recommended and when it is rainy night, Remarks: when it is sunny daytime, the upper limit is recommended and when it is rainy night, the lower limit is recommended. the lower limit is recommended. 4. Engineering Examples 4. Engineering Examples 4.1. Project Introduction 4.1. Project Introduction 4.1.1. Project Overview 4.1.1. Project Overview Located in the upper reaches of the Zhangjiang River, Ganzhou city, Jiangxi province, a Located in the upper reaches of the Zhangjiang River, Ganzhou city, Jiangxi province, hydropower project is large (2) type of water conservancy project dominated by flood control [35]. a hydropower project is large (2) type of water conservancy project dominated by ﬂood control [35]. 8 3 8 3 Reservoir total capacity is 1.19 × 10 m at the normal pool level of 220.00 m. The checked flood level Reservoir total capacity is 1.19 10 m at the normal pool level of 220.00 m. The checked ﬂood level is 223.70 m and dead water level is 209.00 m. is 223.70 m and dead water level is 209.00 m. In March 2004, the dam was identified as a third-type dam, which would be reinforced in 2008. In March 2004, the dam was identiﬁed as a third-type dam, which would be reinforced in 2008. This paper analyzed the probability of dam failure and the life loss model based on the data before This paper analyzed the probability of dam failure and the life loss model based on the data before the the reinforcement work, aiming to analyze the risk of dam failure before reinforcement and to improve reinforcement work, aiming to analyze the risk of dam failure before reinforcement and to improve the the safety management level. This analysis will provide a significant reference for other dam analyses. safety management level. This analysis will provide a signiﬁcant reference for other dam analyses. The layout plan of the reservoir project is shown in Figure 5: The layout plan of the reservoir project is shown in Figure 5: CHINA M ain dam Figure 5. Layout plan of the reservoir project. Figure 5. Layout plan of the reservoir project. The dam is a roller thick clay core earth dam with a crest elevation of 226.0 m, a maximum dam The dam is a roller thick clay core earth dam with a crest elevation of 226.0 m, a maximum dam height of 36.0 m, a crest width of 5.0 m, and a crest length of 177.0 m. The dam typical cross-section height of 36.0 m, a crest width of 5.0 m, and a crest length of 177.0 m. The dam typical cross-section structure dimensions are shown in Figure 6. Int. J. Environ. Res. Public Health 2018, 15, x 11 of 22 structure dimensions are shown in Figure 6. 226.00 Exceptional flood level 223.70 Design flood level 222.29 220.00 Nomal reservoir level 213.00 207.00 201.00 201.00 Clay core wall Cofferdam Crushed stone soil 195.00 and Clayey fine sand 189.74 Figure 6. Typical cross-section structure dimensions of the dam. Figure 6. Typical cross-section structure dimensions of the dam. 4.1.2. Main Problems of the Dam (1) Main dam: Severe leakage in the dam body, prominent by-pass seepage, severely weathered slope protection rock with the danger of landslide. (2) Auxiliary dam: Existence of permeable layer because of the deficient foundation clearance, the probability of infiltration and damage of left bank, weak anti-seepage function of inclined wall. (3) Spillway: Serious erosion, cracks and tendons in the spillway pier and concrete shaft of the spillway, seriously deterioration of gates and electrical facilities. 4.2. Analysis of Dam Failure Probability 4.2.1. Dam Failure Modes and Paths According to former data, the failure of earth-rock dams in China is mainly based on three conditions: (1) Failure of the dam structures caused by the water load in non-flood season, such as seepage failure; (2) Serious floods in flood season which cause dam collapse, suc h as overtopping, seepage damage, slope landslides, and so on; (3) The dam collapse caused by an earthquake, such as seepage damage, structural failure, and so on. As for the dam area reference, the basic earthquake intensity is less than 6 degrees in this area. This paper does not consider the dam failure caused by the earthquake load according to the relevant norms. Aiming at the dam failure caused by the water load in flood season and non-flood season, this paper screens and analyzes all the dam failure modes and get the main failure modes and damage paths as follows [36–38]: (1) Non-flood season load Leakage of main dam foundation–Piping–Manual intervention–Invalidation of intervention– dam failure; Leakage of auxiliary dam foundation–Piping–Manual intervention –Invalidation of intervention–dam failure; By-pass seepage of auxiliary dam shoulder–Piping–Manual intervention–Invalidation of intervention–dam failure; (2) Flood season load Flood–Leakage of main dam foundation–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–Leakage of auxiliary dam foundation–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–By-pass seepage of auxiliary dam shoulder–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–By-pass seepage of auxiliary dam sloping core–Piping–Manual intervention– Invalidation of intervention–dam failure; Flood–Failure of spillway structure–Breach expanded–Manual intervention–Invalidation of intervention–dam failure; 1:3.26 1:3.00 Spillway 1:2.48 1:2.67 Au xilia r y d am Factor y b u ild in g 1:2.00 Diver sion tu n n el 1:1.50 100 Int. J. Environ. Res. Public Health 2018, 15, 886 11 of 22 4.1.2. Main Problems of the Dam (1) Main dam: Severe leakage in the dam body, prominent by-pass seepage, severely weathered slope protection rock with the danger of landslide. (2) Auxiliary dam: Existence of permeable layer because of the deﬁcient foundation clearance, the probability of inﬁltration and damage of left bank, weak anti-seepage function of inclined wall. (3) Spillway: Serious erosion, cracks and tendons in the spillway pier and concrete shaft of the spillway, seriously deterioration of gates and electrical facilities. 4.2. Analysis of Dam Failure Probability 4.2.1. Dam Failure Modes and Paths According to former data, the failure of earth-rock dams in China is mainly based on three conditions: (1) Failure of the dam structures caused by the water load in non-ﬂood season, such as seepage failure; (2) Serious ﬂoods in ﬂood season which cause dam collapse, such as overtopping, seepage damage, slope landslides, and so on; (3) The dam collapse caused by an earthquake, such as seepage damage, structural failure, and so on. As for the dam area reference, the basic earthquake intensity is less than 6 degrees in this area. This paper does not consider the dam failure caused by the earthquake load according to the relevant norms. Aiming at the dam failure caused by the water load in ﬂood season and non-ﬂood season, this paper screens and analyzes all the dam failure modes and get the main failure modes and damage paths as follows [36–38]: (1) Non-ﬂood season load Leakage of main dam foundation–Piping–Manual intervention–Invalidation of intervention–dam failure; Leakage of auxiliary dam foundation–Piping–Manual intervention–Invalidation of intervention–dam failure; By-pass seepage of auxiliary dam shoulder–Piping–Manual intervention–Invalidation of intervention–dam failure; (2) Flood season load Flood–Leakage of main dam foundation–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–Leakage of auxiliary dam foundation–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–By-pass seepage of auxiliary dam shoulder–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–By-pass seepage of auxiliary dam sloping core–Piping–Manual intervention–Invalidation of intervention–dam failure; Flood–Failure of spillway structure–Breach expanded–Manual intervention–Invalidation of intervention–dam failure; 4.2.2. Calculation of Dam Failure Probability The reservoir is designed according to the 500-year ﬂood (P = 0.2%) and checked according to the 5000-year ﬂood (P = 0.02%). When we select the characteristic load value of the dam, we select the normal water level 220.00 m as the non-ﬂood load value with the frequency of 1.0 and the check ﬂood level 223.70 m as the ﬂood load with the frequency of 0.02%. The key to estimating the risk rate of dam failure by using the ETA method of fuzzy set theory is to calculate the probability of each link accident. Int. J. Environ. Res. Public Health 2018, 15, x 12 of 22 4.2.2. Calculation of Dam Failure Probability The reservoir is designed according to the 500-year flood (P = 0.2%) and checked according to the 5000-year flood (P = 0.02%). When we select the characteristic load value of the dam, we select the Int. J. Environ. Res. Public Health 2018, 15, 886 12 of 22 normal water level 220.00 m as the non-flood load value with the frequency of 1.0 and the check flood level 223.70 m as the flood load with the frequency of 0.02%. The key to estimating the risk rate of dam failure by using the ETA method of fuzzy set theory According to the dam failure mode and the dam break path, the event tree of the dam failure is is to calculate the probability of each link accident. constructed.AThis ccordpaper ing to th takes e dam the failcase ure m of odthe e anpiping d the daof m b the reaauxiliary k path, the dam event shoulder tree of the under dam faithe lure condition is constructed. This paper takes the case of the piping of the auxiliary dam shoulder under the condition of 223.70 m water level in ﬂood season as an example. of 223.70 m water level in flood season as an example. Combined with the judgment of ﬁve experts (E1, E2, E3, E4, E5), the probabilities of each part of Combined with the judgment of five experts (E1, E2, E3, E4, E5), the probabilities of each part of dam failure under this condition are calculated in Figure 7. dam failure under this condition are calculated in Figure 7. Manual intervention D4 Developed Dam failure D3 D5 Large Leak No continued D2 Manual No No intervention Occurrence D7 Developed Dam failure D1 D6 D8 Piping of Dam Slight Leak No Shoulder continued No No No Figure 7. Piping of auxiliary dam shoulder event tree in the flood season. Figure 7. Piping of auxiliary dam shoulder event tree in the ﬂood season. The five experts respectively evaluated D1, D2, D3, D4, D5, D6, D7, and D8 of each link of the piping event tree of the auxiliary dam shoulder [39]. The fuzzy probabilities are shown in Table 6. The ﬁve experts respectively evaluated D1, D2, D3, D4, D5, D6, D7, and D8 of each link of the piping event tree of the auxiliary dam shoulder [39]. The fuzzy probabilities are shown in Table 6. Table 6. Experts’ judgments of piping of auxiliary dam shoulder in the flood season. E1 E2 E3 E4 E5 Table 6. Experts’ judgments of piping of auxiliary dam shoulder in the ﬂood season. D1 Uncertain Likely Uncertain Likely Uncertain D2 Likely Uncertain Uncertain Likely Uncertain E1 E2 E3 E4 E5 D3 Uncertain Uncertain Uncertain Likely Less likely D1 Uncertain Likely Uncertain Likely Uncertain D4 Likely Uncertain Likely Uncertain Uncertain D2 Likely Uncertain Uncertain Likely Uncertain D5 Likely Likely Very likely Likely Uncertain D3 Uncertain Uncertain Uncertain Likely Less likely D4 Likely D6 Less likely Uncertain Uncertain UncLikely ertain Less likUncertain ely Uncertain Uncertain D5 Likely Likely Very likely Likely Uncertain D7 Uncertain Less likely Less likely Less likely Less likely D6 Less likely Uncertain Uncertain Less likely Uncertain D8 Less likely Very unlikely Very unlikely Very unlikely Very unlikely D7 Uncertain Less likely Less likely Less likely Less likely D8 Less likely Very unlikely Very unlikely Very unlikely Very unlikely Considering that different experts have different understandings of the actual operation status of the dam, there are differences among experts in terms of their level of knowledge, professional standards, personal experience ability, and other factors. In order to reduce the influence of expert Considering that different experts have different understandings of the actual operation status subjectivity on the calculation results, this paper uses the weight coefficient of five experts to revise of the dam, there are differences among experts in terms of their level of knowledge, professional the evaluation and get the final evaluation results [40]. standards, personal experience ability, and other factors. In order to reduce the inﬂuence of expert subjectivity on the calculation results, this paper uses the weight coefﬁcient of ﬁve experts to revise the evaluation and get the ﬁnal evaluation results [40]. w E i j i j j=1 P = (15) i j j=1 where P represents result of the expert’s comprehensive evaluation of event i, w represents the i i j weighting coefﬁcient of the event i of the j-th expert’s evaluation, and E represents the evaluation ij result of the i-th event by the j-th expert. Int. J. Environ. Res. Public Health 2018, 15, 886 13 of 22 The weight coefﬁcient of experts can be calculated by 1~9 scale judgment matrix, and the judgment matrix must meet the consistency requirement, otherwise it should be rebuilt. The judgment matrix of experts are shown in Table 7. Table 7. Judgment matrix of experts. Weight Coefﬁcient w Experts E1 E2 E3 E4 E5 ij E1 1 3 4 2 1/2 0.283 E2 1/3 1 2 4 1/3 0.168 E3 1/4 1/2 1 3 1/2 0.123 E4 1/2 1/4 1/3 1 1/3 0.073 E5 2 3 2 3 1 0.353 The estimated values of the fuzzy numbers in each link of the auxiliary dam shoulder are respectively: P = 0.283E + 0.168E + 0.123E + 0.073E + 0.353E = (0.1l + 0.424,0.1l + 0.648) 11 12 13 14 15 P = (0.1l + 0.436,0.1l + 0.671) P = (0.1l + 0.337,0.1l + 0.579) P = (0.1l + 0.441,0.1l + 0.681) P = (0.1l + 0.489,0.1l + 0.742) P = (0.1l + 0.329,0.1l + 0.564) P = (0.1l + 0.257,0.1l + 0.528) P = (0.1l + 0.164,0.1l + 0.427) The calculation result is substituted by the Formulas (6) and (7) to calculate the fuzzy numbers. By adopting the integral value method proposed by Liou to calculate the fuzzy numbers, the fuzzy probability of each link of the auxiliary dam shoulder is obtained. Where a = 0 and a = 1 respectively correspond to the upper and lower bounds of the fuzzy numbers of the failure probability P and P . When a = 0.5, the calculated value obtained is the probability value P of the accident link. The following Table 8 is available: Table 8. Probabilities of each accident of the auxiliary dam shoulder. Event D1 D2 D3 D4 D5 D6 D7 D8 P 0.536 0.553 0.458 0.561 0.616 0.447 0.392 0.295 P 0.474 0.486 0.387 0.491 0.539 0.379 0.307 0.214 P 0.598 0.621 0.529 0.631 0.692 0.514 0.478 0.377 The probability of the auxiliary dam shoulder failure is: P = P + P = P P P P P + P (1 P )P P P = 0.059 Large D1 D2 D3 D4 D5 D1 D2 D6 D7 D8 Slight Considering the occurrence frequency of a ﬂood season load of 223.70 m water level is 0.02%, the risk rate of the earth-rock dam with the water level of 223.70 m in the ﬂood season and the dam failure occurring is: f P = 0.059 0.0002 = 1.18 10 Int. J. Environ. Res. Public Health 2018, 15, x 14 of 22 Int. J. Environ. Res. Public Health 2018, 15, x 14 of 22 Considering the occurrence frequency of a flood season load of 223.70 m water level is 0.02%, Considering the occurrence frequency of a flood season load of 223.70 m water level is 0.02%, the risk rate of the earth-rock dam with the water level of 223.70 m in the flood season and the dam the risk rate of the earth-rock dam with the water level of 223.70 m in the flood season and the dam failure occurring is: failure occurring is: Int. J. Environ. Res. Public Health 2018, 15, 886 14 of 22 5 f P 0.059 0.0002 1.18 10 5 f P 0.059 0.0002 1.18 10 4.2.3. Calculation of Dam Failure under Different Load Conditions 4.2.3. Calculation of Dam Failure under Different Load Conditions 4.2.3. Calculation of Dam Failure under Different Load Conditions According to the method above, the dam failure probabilities occurring under other conditions According to the method above, the dam failure probabilities occurring under other conditions According to the method above, the dam failure probabilities occurring under other conditions can be obtained, which are shown in Figures 8–15. can be obtained, which are shown in Figure 8 to Figure 15. can be obtained, which are shown in Figure 8 to Figure 15. Manual Manual intervention intervention Dam P=3.79E-05 Dam Developed failure P=3.79E-05 Developed 21.1% failure 5.0% 21.1% 55.3% Large Leak 5.0% 55.3% No Large Leak continued No continued 13.0% 13.0% No No Manual No No Manual intervention Occurrence intervention Occurrence Dam P=2.09E-05 Developed Dam 5.0% failure Developed P=2.09E-05 5.0% failure 1.0% 5.0% Piping of Dam Slight Leak 1.0% 5.0% No Piping of Dam Slight Leak Foundation continued No Foundation continued 87.0% 8.8% 87.0% 8.8% No No No No No No Figure 8. Piping of main dam foundation event tree in the non-flood season. Figure 8. Piping of main dam foundation event tree in the non-ﬂood season. Figure 8. Piping of main dam foundation event tree in the non-flood season. Manual Manual intervention intervention Dam P=1.63E-05 Dam Developed failure P=1.63E-05 Developed 41.6% failure 12.9% 12.2% 41.6% Large Leak 12.9% 12.2% No Large Leak continued No continued 5.0% 5.0% No No Manual No Manual No intervention Occurrence intervention Occurrence Dam P=2.55E-06 Developed Dam 5.0% failure Developed P=2.55E-06 5.0% failure 1.0% 5.0% Piping of Dam Slight Leak 1.0% 5.0% No Piping of Dam Slight Leak Foundation continued No Foundation continued 95.0% 10.7% 95.0% 10.7% No No No No No No Figure 9. Piping of auxiliary dam foundation event tree in the non-flood season. Figure 9. Piping of auxiliary dam foundation event tree in the non-flood season. Figure 9. Piping of auxiliary dam foundation event tree in the non-ﬂood season. Int. J. Environ. Res. Public Health 2018, 15, x 15 of 22 Manual intervention Dam P=1.11E-05 Developed failure 39.7% 13.0% 8.6% Large Leak No continued 5.0% No Manual No intervention Occurrence Dam Developed P=2.09E-06 5.0% failure 1.0% 5.0% Piping of Dam Slight Leak No Shoulder continued 95.0% 8.8% No No No Figure 10. Piping of auxiliary dam shoulder event tree in the non-flood season. Figure 10. Piping of auxiliary dam shoulder event tree in the non-ﬂood season. Manual intervention Dam P=6.23E-02 Developed failure 55.3% 52.5% 64.3% Large Leak No continued 53.6% No No Manual intervention Occurrence Dam Developed P=1.49E-03 62.2% failure 8.6% 25.3% Piping of Dam Slight Leak No Foundation continued 46.4% 23.6% No No No Figure 11. Piping of main dam foundation event tree in the flood season. Manual intervention Dam P=2.77E-02 Developed failure 42.8% 53.6% 63.2% Large Leak No continued 42.1% No Manual No intervention Occurrence Dam Developed P=4.27E-03 45.4% failure 10.5% 37.8% Piping of Dam Slight Leak No Foundation continued 57.9% 41.1% No No No Figure 12. Piping of auxiliary dam foundation event tree in the flood season. Int. J. Environ. Res. Public Health 2018, 15, x 15 of 22 Int. J. Environ. Res. Public Health 2018, 15, x 15 of 22 MM anu anu al al initn et re ve rve ntn ion tion Dam Dam P=1.11E-05 P=1.11E-05 Developed Developed fai fai lulru ere 39.7% 39.7% 1313 .0% .0% 8.6 8% .6% Lar Lar gege L L eak eak No No con con tin tiu ne u ded 5.0 5% .0% No No No No MM an an ual u al initn et re ve rve ntn ion tion OO ccc ucru rr er necn ece Dam Dam Developed P= P2 = .09 2.09 E-E 06 -06 Developed 5.0 5% .0% failure failure 1.0% 1.0% 5.0 5% .0% PiPi pip nig ng ofof D am Dam SlS igh ligh t L t L eak eak No No Sh Sou hou ldle d rer con con tin tiu ne u ded 9595 .0% .0% 8.8% 8.8% No No No No No No Int. J. Environ. Res. Public Health 2018, 15, 886 15 of 22 Fig Fig ure ure 1 0 1.0 P . ipi Pipi ng n g o f oa f uxi auxi lia lira y r y da da mm sh sh oulder oulder ev ev en en t ttr t ee ree inin th te h e n o nn o-n flo -flo od od sese aso aso n.n . MM anu anu al al initn et re ve rve ntn ion tion Dam Dam P=6.23E-02 P=6.23E-02 De D ve eve lop lop eded failure failure 5555 .3% .3% 5252 .5% .5% 6464 .3% .3% Large Leak Large Leak No No con con tin tiu ne u ded 5353 .6% .6% No No No No MM an an ual u al initn et re ve rve ntn ion tion OO ccc ucru rr er necn ece Dam Dam P=1.49E-03 Developed P=1.49E-03 Developed 6262 .2% .2% failure failure 8.6% 8.6% 2525 .3% .3% PiPi pip nig ng ofof D am Dam SlS igh ligh t L t L eak eak No No Fou Fou nd nat dat ion ion con con tin tiu ne u ded 46.4% 46.4% 2323 .6% .6% No No No No No No Figure 11. Piping of main dam foundation event tree in the flood season. Figure 11. Piping of main dam foundation event tree in the flood season. Figure 11. Piping of main dam foundation event tree in the ﬂood season. MM anu anu al al intervention intervention Dam Dam P=2.77E-02 P=2.77E-02 Developed Developed faiflai ur lu ere 42.8% 42.8% 5353 .6% .6% 63.2% 63.2% Lar Lar gege L L eak eak No No con con tin tu in eu ded 4242 .1% .1% No No No MM anan ual u al No intervention intervention Occurrence Occurrence Dam Dam P= P 4= .27 4.27 E-E 03 -03 De D ve eve lop lop eded 45.4% 45.4% faiflai ur lu ere 10.5% 10.5% 3737 .8% .8% Pip Pi in pg inof g of D am Dam SliS gh ligh t L t L eak eak No No Fou Fou ndn at diat on ion continued continued 5757 .9% .9% 41.1% 41.1% No No No No No No Int. J. Environ. Res. Public Health 2018, 15, x 16 of 22 Figure 12. Piping of auxiliary dam foundation event tree in the flood season. Fig Figure ure 1 12. 2. P Piping iping o of f a auxiliary uxiliary da dam m fo foundation undation ev event ent ttr ree ee in in tthe he flo ﬂood od se season. ason. Manual intervention Dam P=4.69E-02 Developed failure 56.1% 61.6% 45.8% Large Leak No continued 55.3% No No Manual intervention Occurrence Dam P=1.23E-02 Developed 53.6% failure 29.5% 44.7% Piping of Dam Slight Leak No Shoulder continued 44.7% 39.2% No No No Figure 13. Piping of auxiliary dam shoulder event tree in the flood season. Figure 13. Piping of auxiliary dam shoulder event tree in the ﬂood season. Manual intervention Dam P=9.84E-03 Developed failure 55.3% 40.5% 31.1% Large Leak No continued 36.5% No No Manual intervention Occurrence Dam P=1.22E-03 Developed 38.6% failure 12.8% 13.9% Piping of Slight Leak No Sloping Core continued 63.5% 27.9% No No No Figure 14. Piping of sloping core event tree in the flood season. Manual 59.5% intervention Dam Developed P=4.53E-03 failure Breach 43.9% No expanded 46.4% No 30.6% No No Occurrence Upstream Manual 12.2% Landslide 71.7% intervention 68.6% 66.8% Developed Failure of Breach Dam 75.6% P=2.10E-02 Spillway unexpanded failure No No structure 69.4% Downstream Manual No Landslide intervention 69.6% 33.2% Developed Dam No 65.7% P=8.46E-03 65.7% failure No No Figure 15. Failure of spillway structure core event tree in the flood season. InItn . t J.. J En . En viv ron iron . R . es. Res. Pub Pub licl iHea c Hea lth lt 2 h0 2 10 81 , 8 15 , 15 , x, x 1616 o fo f 22 22 MM anu anu al al intin er tve erve ntin on tion Dam Dam P= P 4= .69 4.69 E-E 02 -02 De D ve eve lop lop eded faiflai ur lu ere 5656 .1% .1% 6161 .6% .6% 4545 .8% .8% Lar Lar gege L L eak eak No No con con tin tu in eu ded 5555 .3% .3% No No No No MM anan ual u al intin er tve erve ntin on tion Oc O cu cc ru re rn re cn ece Dam Dam P= P 1= .23 1.23 E-E 02 -02 De D ve eve lope lope d d 5353 .6% .6% faiflai ur lu ere 2929 .5% .5% 4444 .7% .7% Pip Pi in pg inof g of D am Dam SliS ght light L L eak eak No No ShS ou hou lde ld rer con con tin tu in eu ded 4444 .7% .7% 3939 .2% .2% No No No No No No Int. J. Environ. Res. Public Health 2018, 15, 886 16 of 22 Fig Fig ure ure 1 3 1.3 P . ipi Pipi ng n g o f oa f uxi auxi lia lira y r y da da mm sh so hulder oulder ev ev en en t ttr t ee ree inin th te h e flo flo od od sese aso aso n.n . MM anu anu al al intin er tve erve ntin on tion Dam Dam P= P 9= .84 9.84 E-E 03 -03 De D ve eve lop lop eded faiflai ur lu ere 5555 .3% .3% 4040 .5% .5% 3131 .1% .1% Lar Lar gege L L eak eak No No con con tin tu in eu ded 3636 .5% .5% No No No No MM anan ual u al intin er tve erve ntin on tion Oc O cu cc ru re rn re cn ece Dam Dam P= P 1= .22 1.22 E-E 03 -03 De D ve eve lope lope d d 3838 .6% .6% faiflai ur lu ere 1212 .8% .8% 1313 .9% .9% Pip Pi in pg inof g of SliS ght light L L eak eak No No Slop Slop ing C ing C oror e e con con tin tu in eu ded 6363 .5% .5% 2727 .9% .9% No No No No No No Fig Fig ure ure 1 4 1.4 P . ipi Pipi ng n g o f osl f sl opin opin g g cor cor e e ev ev en en t ttr t ee ree inin th te he flo flo od od sese aso aso n.n . Figure 14. Piping of sloping core event tree in the ﬂood season. Ma M na un au l al 5959 .5% .5% inte inr te ve rn ve tin oti non DaD m a m DeD ve elv oep lo ep ded P= P 4= .53 4.53 E-E 03 -03 faifa luir lu e re BrB ea rc eh ac h 4343 .9% .9% NoNo exp ex ap na dn ed ded 4646 .4% .4% 3030 .6% .6% NoNo NoNo NoNo OcO cu cr cu re rn re ce nce Up U str pse tr am ea m Ma M na un au l al 1212 .2% .2% LaLa ndn sld id sle ide 7171 .7% .7% inte inr te ve rn ve tin oti non 6868 .6% .6% 6666 .8% .8% DeD ve elv oep lo ep ded FaF ila uir lu e r oef of BrBr eac eh ac h DaD m a m 7575 .6% .6% P= P 2= .10 2.10 E-E 02 -02 unu en xp ex ap na dn ed ded Spi Spi llw ll aw y ay faifa luir lu e re NoNo NoNo strsu tr cu tu cr tu e re 6969 .4% .4% DoD wo n w str nsetr am ea m Ma M na un au l al NoNo LaLa ndn sld id sle ide inte inr te ve rn ve tin oti non 6969 .6% .6% 3333 .2% .2% DeD ve elv oep lo ep ded DaD m a m NoNo 6565 .7% .7% P= P 8= .46 8.46 E-E 03 -03 faifa luir lu e re 6565 .7% .7% NoNo NoNo Figure 15. Failure of spillway structure core event tree in the ﬂood season. Fig Fig ure ure 1 5 1.5 F . a Fil aure ilure o f ospi f spi llw llw ay a y st st ruc ruc ture ture c o cro e re ev ev en en t ttr t ee ree inin th te h e flo flo od od sese aso aso n.n . According to the above ETA method based on fuzzy set theory, we can summarize the dam failure probabilities under non-ﬂood season and ﬂood season load in Table 9: Table 9. Dam failure probabilities summary. Failure Load Failure Mode and Parts Frequency f f P Percentage Probability P 5 5 Piping of main dam foundation 100% 4.00 10 4.00 10 34.54% non-ﬂood season 5 5 Piping of auxiliary dam foundation 100% 1.88 10 1.88 10 16.23% (220.00 m) 5 5 Piping of auxiliary dam shoulder 100% 1.32 10 1.32 10 11.40% 2 5 Piping of main dam foundation 0.02% 6.38 10 1.28 10 11.05% 2 5 Piping of auxiliary dam foundation 0.02% 5.93 10 1.18 10 10.28% ﬂood season 2 5 Piping of auxiliary dam shoulder 0.02% 5.03 10 1.01 10 8.72% (233.70 m) 2 6 Piping of sloping core 0.02% 1.91% 1.11 10 2.21 10 2 6 Failure of spillway structure 0.02% 3.40 10 6.80 10 5.87% Total 1.16 10 The probability of the dam failure is 1.16 10 , which is higher than the maximum probability of collapse estimated by the Bureau of Reclamation 10 ; thus, measures should be taken to reduce the failure probability. Table 9 shows that the main dam failure mode is the main dam foundation piping and the auxiliary dam foundation piping. The analysis results are consistent with the actual conditions Int. J. Environ. Res. Public Health 2018, 15, 886 17 of 22 of the dam. In view of the analysis results, we should focus on strengthening the reinforcement of main dam foundation and auxiliary dam foundation. During the ﬂood season, strengthening the monitoring of ﬂood data and paying attention to the reinforcement of the spillway are necessary. 4.3. Estimation Model of Dam Failure Life Loss Dayu County, a total area of 1367.63 km , administers 11 townships. In 2006, the county’s resident population was 291,969, with an average population density of 214 persons/km . The population and the buildings are dense. 4.3.1. Determination of Inﬂuencing Factors (1) Population at risk (P ) AR First, identify the population at risk (P ). According to the ﬂooding range of dam break ﬂoods, AR the following Table 10 is obtained according to the government statistics on the population distribution of the submerged area. Among them, the number of P in the daytime and night are different; AR the impact factors are 0.5 and 0.8 respectively. Table 10. P of the submerged area. AR Administrative Region Households Population P (Daytime) P (Night) AR AR Fujiang township 1261 4727 2363 3782 Nan’an town 18,727 65,735 32,868 52,588 Total 19,988 70,462 35,232 56,370 (2) Severity degree of dam break ﬂood (S ) Calculate the average D V value of the submerging range’s administrative area, as shown in the following Table 11: Table 11. Average D V value and corresponding S . Administrative Region D V (m /s) S Fujiang township 14.48 High Nan’an town 11.26 High (3) Warning time (W ) The calculated area is relatively small, with only Fujiang township and Nan’an Town. Modern communications are more developed. Therefore, it is assumed that the ﬂood warning time (W ) is the same, divided into: 0~0.25 h, 0.25 ~1.0 h, and beyond 1.0 h. (4) Occurrence time (O ) This simulated dam break occurs only in the daytime and night conditions, and other conditions such as weather and season are temporarily not taken into consideration. (5) Understanding of P to S (U ) AR D D The understanding of P to S (U ) is shown is Table 12. AR D D Table 12. Understanding of P to S (U ). AR D D Warning Time 0~0.25 h 0.25~1.0 h >1.0 h Daytime Fuzzy Explicit Explicit Night Fuzzy Fuzzy Explicit Int. J. Environ. Res. Public Health 2018, 15, 886 18 of 22 4.3.2. Estimation of Dam Failure Life Loss The formula of estimation of dam failure loss of life (L ) is as follows: OL L = w P f (16) OL AR where f is according to the Figure 5. For the dam considered in this paper, the corresponding correction coefﬁcient w is as follows according to the relevant information, which is shown in Table 13. Table 13. Corresponding correction coefﬁcient w . Warning Time 0~0.25 h 0.25~1.0 h >1.0 h Daytime 0.80 0.60 0.40 Night 0.80 0.65 0.50 Then, we can make the estimation according the formula above. The results of the estimation of dam failure loss life are shown below. Table 14. Estimated dam failure loss of life when W = 0~0.25 h. Administrative Region Fujiang Township Nan’an Town DV (m /s) 14.48 11.26 S High High W 0~0.25 h 0~0.25 h P 2363 32,868 AR U Fuzzy Fuzzy Daytime F 0.30 0.30 w 0.80 0.80 L 567 7888 OL P 3782 52,588 AR U Fuzzy Fuzzy Night F 0.70 0.70 w 0.80 0.80 L 2118 29,449 OL Table 15. Estimated dam failure loss of life when W = 0.25~1.0 h. Administrative Region Fujiang Township Nan’an Town 14.48 11.26 DV(m /s) S High High W 0.25~1.0 h 0.25~1.0 h P 2363 32,868 AR U Explicit Explicit Daytime f 0.01 0.01 w 0.6 0.6 L 14 197 OL P 3782 52,588 AR U Fuzzy Fuzzy Night f 0.2 0.2 w 0.65 0.65 L 492 6836 OL Int. J. Environ. Res. Public Health 2018, 15, 886 19 of 22 Table 16. Estimated dam failure loss of life when W > 1.0 h. Administrative Region Fujiang Township Nan’an Town DV(m /s) 14.48 11.26 S High High W >1.0 h >1.0 h P 2363 32,868 AR U Explicit Explicit Daytime f 0.001 0.001 w 0.4 0.4 L 1 13 OL P 3782 52,588 AR U Explicit Explicit Night f 0.001 0.001 w 0.5 0.5 L 2 26 OL In general, Table 17. Estimated dam failure loss of life. w 0~0.25 h 0.25~1.0 h >1.0 h Daytime 8455 211 14 OL Night 31,567 7328 28 Combined with the calculation results from 3.2, the dam has a 1.16 10 probability of dam failure. The possible loss of life in this case is estimated as shown in Table 18. As can be seen from the Tables 14–18, the life loss (L )of dam failure is most affected by the OL warning time (W ), and the occurrence time (daytime or night) also has great inﬂuence. Therefore, the dam workers should strengthen safety monitoring (especially in ﬂood season) and improve the warning time. It is highly necessary to ensure W is longer than one hour, which can signiﬁcantly reduce the loss of life of dam failure. According to the social risk standard F-N reference map of China reservoir dams, the calculated risk of life loss is higher than 1.1 10 , which is an intolerable risk. So the dam reinforcement project should also be carried out, which is consistent with the 3.2 research conclusion. Table 18. Possible loss of life of the dam failure estimated. w 0~0.25 h 0.25~1.0 h >1.0 h 1 2 3 Daytime 9.79 10 2.44 10 1.62 10 OL 1 3 Night 3.66 8.49 10 3.24 10 In the event that dam engineering facilities cannot be changed and dam-breaking ﬂoods cannot be perfectly predicted, we need to strengthen the management of non-engineering measures in order to reduce the dam failure life loss. Some suggested actions below can be taken into consideration: (1) Evacuate residents in times of ﬂood season and minimize the risk to the population; (2) Strengthen the monitoring work (especially in the ﬂood season), improve the capability of early warning of dam breakage, and increase the warning time, which must be more than one hour; (3) Strengthen the liaison among downstream residents to ensure smooth communication; (4) Improve the level of contingency plans, ensure the availability of trafﬁc in the submerged area and enhance the rescue capability after dam failure. Int. J. Environ. Res. Public Health 2018, 15, 886 20 of 22 5. Conclusions This paper conducted the risk analysis of an earth-rock dam failure, which involves several complicated factors. Based on the analyzed results, the following can be concluded. (1) After considering various factors affecting the dam safety, a new model with the ETA method based on fuzzy set theory is proposed for the dam failure analysis, and good results were achieved. By using the ETA method, the probability of each link of dam failure mode can be clearly evaluated. Combined with fuzzy set theory, experienced experts are invited to carry out the evaluation and analysis. The main failure modes of the dam in non-ﬂood season are the main dam and auxiliary dam piping, and in ﬂood season the spillway failure needs to be considered. The project reinforcement should be carried out in a targeted manner. (2) After considering other scholars’ estimation model of life loss, population at risk (P ), severity AR degree of dam break ﬂood (S ), warning time (W ), occurrence time (O ) and understanding of D T T P to S (U ) are taken into consideration as well as the corresponding correction coefﬁcient w. AR D D The new estimation model is applied to a speciﬁc project and the expected dam failure life loss exceeds the standard requirements. Some non-engineering measures are proposed with a view of reducing the dam failure life loss. In summary, the dam risk is already at a high stage. It is highly necessary to reinforce the project in addition to strengthening the ﬂood season monitoring and raising the warning time. The dam failure risk analysis model proposed in this paper has been successfully applied to a speciﬁc water conservancy project and achieved good results. For other dams, the analysis model can also be applied to improve the operation of dam management. Author Contributions: All authors named on the manuscript have made a signiﬁcant contribution to this work. X.F. contributed to the conception of the study; C.-S.G. contributed signiﬁcantly to analysis and manuscript preparation; X.F. performed the data analysis and wrote the manuscript; H.-Z.S. and X.-N.Q. helped perform the analysis with constructive discussions. Acknowledgments: This work was supported by National Key R&D Program of China (2016YFC0401601, 2017YFC0804607), National Natural Science Foundation of China (Grant Nos. 51739003, 51479054, 51779086, 51579086, 51379068, 51579083, 51579085, 51609074), Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions ( YS11001), Jiangsu Natural Science Foundation (Grant No. BK20160872), Special Project Funded of National Key Laboratory(20145027612, 20165042112), Key R&D Program of Guangxi (AB17195074), Central University Basic Research Project (2017B11114), the Fundamental Research Funds for the Central Universities (Grant No. 2017B617X14), Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant Nos. KYCX17_0424, KYZZ16_0283). Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Yang, M.; Qian, X.; Zhang, Y.; Sheng, J.; Shen, D.; Ge, Y. Spatial Multicriteria Decision Analysis of Flood Risks in Aging-Dam Management in China: A Framework and Case Study. Int. J. Environ.l Res. Public Health 2011, 8, 1368–1387. [CrossRef] [PubMed] 2. Hall, J.W.; Sayers, P.B.; Dawson, R.J. National-scale Assessment of Current and Future Flood Risk in England and Wales. Nat. Hazards 2005, 36, 147–164. [CrossRef] 3. Balmforth, N.J.; Von Hardenberg, J.; Provenzale, A.; Zammett, R. Dam breaking by wave-induced erosional incision. J. Geophys. Res. Earth Surf. 2008, 113, 1–12. [CrossRef] 4. Passey, M.; Bennett, T.; Zielinski, A.; Donnelly, C.R. Dam safety management plans: A conceptual framework for risk-informed decision making in ontario. In Proceedings of the Canadian Dam Association Association Canadienne Des Barrages Dam Safety, Banff, AB, Canada, 4–9 October 2014. 5. Singh, V.P. Dam Breach Modeling Technology; Springer: Houten, The Netherlands, 1996. 6. Hartford, D.N.; Baecher, G.B. Risk and Uncertainty in Dam Safety; Thomas Telford Ltd.: London, UK, 2004; pp. 185–215. 7. Rong-Yong, M.A.; Huang, H.Y.; Liao, X.T. Analysis of overﬂow fuzzy risk on earth dam. J. Saf. Environ. 2004, 4, 15–18. Int. J. Environ. Res. Public Health 2018, 15, 886 21 of 22 8. Zong-Kun, L.I. Analysis of seepage failure fuzzy risk on earth dams. Dam Saf. 2007, 1, 17–20. 9. Graham, W.J. A Procedure for Estimating Loss of Life Caused by Dam Failure. Dam Saf. Ofﬁce US Bur. Reclam. 1999, 6, 262. 10. Maaskant, B.; Jonkman, S.N.; Bouwer, L.M. Future risk of ﬂooding: An analysis of changes in potential loss of life in South Holland (The Netherlands). Environ. Sci. Policy 2009, 12, 157–169. [CrossRef] 11. Escuder-Bueno, I.; Mazzà, G.; Morales-Torres, A.; Castillo-Rodríguez, J.T. Computational Aspects of Dam Risk Analysis: Findings and Challenges. Engineering 2016, 2, 319–324. [CrossRef] 12. Liu, Z.Q.; Nadim, F.; Eidsvig, U.K.; Lacasse, S. Reassessment of Dam Safety Using Bayesian Network. Geo-Risk 2017, 2016, 168–177. 13. MccClelland, D.M; Bowles, D.S. Estimating Life Loss for Dam Safety Risk Assessment-a Review and New Approach; Institute for Water Resources US Army Corps of Engineers: Alexandria, VA, USA, 2002. 14. Tsakiris, G.; Spiliotis, M. Embankment Dam Break: Uncertainty of Outﬂow Based on Fuzzy Representation of Breach Formation Parameters; IOS Press: Amsterdam, The Netherlands, 2014; pp. 2365–2378. 15. Altarejosgarcía, L.; Escuderbueno, I.; Moralestorres, A. Advances on the Failure Analysis of the Dam— Foundation Interface of Concrete Dams. Materials 2015, 8, 8255–8278. [CrossRef] [PubMed] 16. Chen, Z. Analysis of the existing situations and problems in failure risk evaluation of high arch dams. J. Hydroelectr. Eng. 2010, 29, 70–75. 17. You, L.; Li, C.; Min, X.; Xiaolei, T. Review of Dam-break Research of Earth-rock Dam Combining with Dam Safety Management. Procedia Eng. 2012, 28, 382–388. [CrossRef] 18. Wishart, J.S. Overtopping Breaching of Rock-Avalanche Dams. Master ’s Thesis, University of Canterbury Civil Engineering, Canterbury, UK, 2007. 19. Sharma, R.P.; Kumar, A. Case Histories of Earthen Dam Failures; International Conference on Case Histories in Geotechnical Engineering: Chicago, IL, USA, 2013. 20. Xie, J.B.; Sun, D.Y. Statistics of dam failures in China and analysis on failure causations. Water Resour. Hydropower Eng. 2009, 40, 124–128. 21. Zhang, L.M.; Xu, Y.; Jia, J.S. Analysis of earth dam failures: A database approach. Georisk Assess. Manag. Risk Eng. Syst. Geohazards 2009, 3, 184–189. [CrossRef] 22. Imbrogno, D.F. Analysis of Dam Failures and Development of a Dam Safety Evaluation Program. Doctoral Dissertation, The Ohio State University, Columbus, OH, USA, 2014. 23. Pyayt, A.L.; Kozionov, A.P.; Mokhov, I.I.; Lang, B.; Meijer, R.J.; Krzhizhanovskaya, V.V.; Sloot, P. Time-frequency methods for structural health monitoring. Sensors 2014, 14, 5147–5173. [CrossRef] [PubMed] 24. Luo, Y.; Chen, L.; Xu, M.; Huang, J. Breaking mode of cohesive homogeneous earth-rock-ﬁll dam by overtopping ﬂow. Nat. Hazards 2014, 74, 527–540. [CrossRef] 25. Foster, M.; Fell, R.; Spannagle, M. The statistics of embankment dam failures and accidents. Can. Geotech. J. 2000, 37, 1000–1024. [CrossRef] 26. Baecher, G.B. Uncertainty in dam safety risk analysis. Georisk Assess. Manag. Risk Eng. Syst. Geohazards 2016, 10, 92–108. [CrossRef] 27. Elmazoghi, H.G. Fuzzy algorithm for estimating average breach widths of embankment dams. Nat. Hazards 2013, 68, 229–248. [CrossRef] 28. Huang, L.; Huang, J.; Wang, W. The Sustainable Development Assessment of Reservoir Resettlement Based on a BP Neural Network. Int. J. Environ. Res. Public Health 2018, 15, 146. [CrossRef] [PubMed] 29. Arunraj, N.S.; Mandal, S.; Maiti, J. Modeling uncertainty in risk assessment: An integrated approach with fuzzy set theory and Monte Carlo simulation. Accid. Anal. Prev. 2013, 55, 242–255. [CrossRef] [PubMed] 30. Wang, Y.; Zhang, J.; Guo, E.; Sun, Z. Fuzzy Comprehensive Evaluation-Based Disaster Risk Assessment of Desertiﬁcation in Horqin Sand Land, China. Int. J. Environ. Res. Public Health 2015, 12, 1703–1725. [CrossRef] [PubMed] 31. Liou, T.S.; Wang, M.J.J. Ranking fuzzy numbers with integral value. Fuzzy Sets Syst. 1992, 50, 247–255. [CrossRef] 32. Abdollahzadeh, G.; Rastgoo, S. Risk Assessment in Bridge Construction Projects Using Fault Tree and Event Tree Analysis Methods Based on Fuzzy Logic. ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B Mech. Eng. 2015, 1, 600–603. [CrossRef] 33. Lei, L.I.; Zhou, K.F. Methods for evaluation of life loss induced by dam failure. Adv. Sci. Technol. Water Resour. 2006, 26, 76–80. Int. J. Environ. Res. Public Health 2018, 15, 886 22 of 22 34. Zhou, K.F.; Lei, L.I.; Sheng, J.B. Evaluation model of loss of life due to dam breach in China. J. Saf. Environ. 2007, 7, 145–149. 35. Dong, J.; Wu, H.; Fu, Q. Dam-break ﬂood calculation and risk assessment of Youluokou Reservoir. South-to-North Water Transf. Water Sci. Technol. 2014, 12, 189–191. 36. Redaelli, M. Estimating the probability of piping-induced breaching of flood embankments. Geotech. Saf. Risk 2011, 567–575. 37. Pham, H.T.; Oo, H.Z.; Jing, C. Stability of Slope and Seepage Analysis in Earth Dam Using Numerical Finite Element Model. Study Civ. Eng. Arch. 2013, 2, 104–108. 38. Sachpazis, C. Detailed Slope Stability Analysis and Assessment of the Original Carsington Earth Embankment Dam Failure in the UK. Electron. J. Geotech. Eng. 2013, 18, 6021–6060. 39. Dong, J.; Wu, H.; FU, Q. Possible failure mode analysis for a dam based on event tree analysis methodology. Yangtze River 2013, 44, 72–75. 40. Hu, Q.; Xu, S.; Liu, Y. Application of improved fuzzy fault tree method in earth-rock dam failure risk assessment. J. Nanchang Inst. Technol. 2013, 32, 72–75. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
International Journal of Environmental Research and Public Health – Pubmed Central
Published: Apr 29, 2018
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.