A Method for Fast Evaluation of Potential Consequences of Dam Breach

Delft University of Technology

A method for fast evaluation of potential consequences of dam breach

Ge, Wei; Jiao, Yutie; Sun, Heqiang; Li, Zongkun; Zhang, Hexiang; Zheng, Yan; Guo, Xinyan; Zhang, Zhaosheng; van Gelder, P. H.A.J.M. DOI 10.3390/w11112224 Publication date 2019 Document Version Final published version Published in Water (Switzerland)

Citation (APA) Ge, W., Jiao, Y., Sun, H., Li, Z., Zhang, H., Zheng, Y., Guo, X., Zhang, Z., & van Gelder, P. H. A. J. M. (2019). A method for fast evaluation of potential consequences of dam breach. Water (Switzerland), 11(11), [2224]. https://doi.org/10.3390/w11112224 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above.

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Article A Method for Fast Evaluation of Potential Consequences of Dam Breach

Wei Ge 1,2,* , Yutie Jiao 1, Heqiang Sun 1, Zongkun Li 1, Hexiang Zhang 1, Yan Zheng 1, Xinyan Guo 1, Zhaosheng Zhang 3 and P.H.A.J.M. van Gelder 2

1 School of Water Conservancy Engineering, Zhengzhou University, Zhengzhou 450001, China; [email protected] (Y.J.); [email protected] (H.S.); [email protected] (Z.L.); [email protected] (H.Z.); [email protected] (Y.Z.); [email protected] (X.G.) 2 Safety and Security Science Group (S3 G), Faculty of Technology, Policy and Management, Delft University of Technology, 2628 BX Delft, The Netherlands; [email protected] 3 Henan Qianping Reservoir Construction Administration, Zhengzhou 450003, China; [email protected] * Correspondence: [email protected] or [email protected]; Tel.: +31-15-278-1776

Received: 22 August 2019; Accepted: 23 October 2019; Published: 25 October 2019

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

Keywords: dam breach; consequences; life; economy; catastrophe evaluation

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 [2–4]. 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

Water 2019, 11, 2224; doi:10.3390/w11112224 www.mdpi.com/journal/water Water 2019, 11, 2224 2 of 12

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]. Water 2019, 11, x FOR PEER REVIEW 3 of 11 Water 2019, 11, x FOR PEER REVIEW 3 of 11 influencing factors, severity of consequences caused by dam breach are calculated, which are Water 2019,, 11,, xx FORFOR PEERPEER REVIEWREVIEW 3 of 11 Watereffectiveinfluencing2019, 11 , supplement 2224 factors, severitys to the ofabove consequences quantitative caused fatality by analysis. dam breach However, are calculat due toed, the which complex3 of 12 are calculation processes and the difficulties in determining accurate values of all influencing factors, it influencinginfluencingeffective supplement factors, factors, severity severitys to the of ofabove consequences consequences quantitative caused caused fatality by by analysis. dam dam breach breach However, are are calculat due toed, the which complex are is quite difficult for engineers to judge the potential consequences of dam breach quickly by these Basedeffectivecalculation on the supplement detailedprocesses analysis sand toto thethe of difficultiesabove impacts quantitative on in LOL determining caused fatality by a ccurate all analysis. kinds values of However, influencing of all influencingdue factors, to the severity factors, complex it methods. ofcalculationis consequences quite difficult processes caused for engineers and by dam the difficulties breachto judge are the in calculated, determiningpotential which consequence accurate are eff ectivevaluess of dam supplements of allbreach influencing quickly to the factors, by above the seit Therefore, a method for fast evaluation of potential consequences caused by dam breach is quantitativeisismethods. quitequite difficultdifficult fatality forfor analysis. engineersengineers However, toto judgejudge due thethe to thepotential complex consequence calculations processes of dam breach and the quickly difficulties by th inese proposed. Eight indices, which originate from risk sources, risk pathways, and risk receptors and are determiningmethods.Therefore, accurate a method values for of all fast influencing evaluation factors, of potential it is quite consequences difficult for caused engineers by dam to judge breach the is easy to obtain, are selected and standardized based on their relevant importance in the severity of potentialproposed.Therefore, consequences Eight a indices method of, dam which for breach fast originate evaluation quickly from by risk of these potential sources, methods. risk consequences pathways, caused and risk by receptors dam breach and are isis potential consequences. Furthermore, a catastrophe evaluation method is used to calculate risk proposed.easyTherefore, to obtain Eightight a, are method indicesindices selected,, which forwhich and fast originate standardized evaluation from of riskbased potential sources, on their consequences risk relevant pathways, importance caused and risk by receptorsin dam thebreach severity and is are of values of dam breach consequence, guiding dam risk management. proposed.easypotential to obtain Eight consequences.,, indices, areare selectedselected which Furthermore, andand originate standardizedstandardized froma catastrophe risk basedbased sources, onon evaluation theirtheir risk pathways,relevantrelevant met hodimportanceimportance and is risk used receptors inin to the the calculate severityseverity and are risk ofof easypotentialvalues to obtain, of dam consequences. are breach selected consequence Furthermore, and standardized, guiding a catastrophe baseddam risk on management. their evaluation relevant met importancehod is used in theto calculate severity ofrisk 2. Materials and Methods potentialvalues of consequences. dam breach Furthermore,consequence,, aguidingguiding catastrophe damdam evaluationriskrisk management.management. method is used to calculate risk values of2. dam Materials breach consequence,and Methods guiding dam risk management. 2.1. Catastrophe Evaluation Method 2. Materials and Methods 2.2.1. Materials Catastrophe and MethodsEvaluation Method 2.1.1. Catastrophe Theory 2.1. Catastrophe Evaluation Method 2.1.2.1.1. CatastropheThe Catastrophe French Evaluation mathematicianTheory Method Rene Thom systematically expounded catastrophe theory in 2.1.1.“Stability Catastrophe of Structure Theory and Morphogenesis” [24]. Catastrophe theory, which was originated from the 2.1.1. CatastropheThe French Theory mathematician Rene Thom systematically expounded catastrophe theory in Whitney singularity theory of smooth mapping and the Poincare–Andronov–Hopf bifurcation “StabilityThe Frenchof Structure mathematician and Morphogenesis Rene Thom” [24 ]. systematically Catastrophe theory, expounded which was catastrophe originated theor fromy the in theoryThe French of dynamic mathematician systems, Renewas Thomused to systematically supervise the expounded transition catastrophe of a system theory from in one “Stability state to “WhitneyStabilitytability of singularityof Structuretructure theoryandand M orphogenesis of smooth mapping” [2[24]].. CatastropheCatastrophe and the Poincaretheory,theory, whichwhich–Andronov was originated–Hopf bifurcation from the ofanother Structure when and control Morphogenesis” variables are [24]. changed. Catastrophe By studying theory, whichthe change was originatedof minimum from value the of Whitney the state Whitneytheory of singularity dynamic systems, theory ofwas smooth used to mapping supervise and the the transition Poincare of– Andronov a system – fromHopf one bifurcation state to singularityfunction theory(potential of smooth function) mapping F(x), the and characteristics the Poincare–Andronov–Hopf of the discontinuous bifurcation change theory state ofthat dynamic near the theorytheoryanother of of when dynamic dynamic control systems, systems, variables was are used changed. to supervise By studying the transitionthe change of of aminimum system from value one of the state state to systems,critical waspoint used can be to det superviseermined. the transition of a system from one state to another when control anotherfunction when (potential control function) variables F( xare), the changed. characteristics By studying of the the discontinuous change of minimum change state value that of thenear state the variables are changed. By studying the change of minimum value of the state function (potential functionfunctioncritical point (potential(potential can be function)function) determined. F((x), ), thethe characteristicscharacteristics ofof thethe discontinuousdiscontinuous changechange statestate thatthat nearnear thethe function)2.1.2. CommonF(x), the Catastrophe characteristics Evaluation of the discontinuous Model change state that near the critical point can critical point can be determined. be determined. 2.1.2.A Common catastrophe Catastrophe evaluation Evaluation method quantifies Model the relative importance of indices according to the 2.1.2. Common Catastrophe Evaluation Model 2.1.2.2.1.2.internal CommonA Common c atastrophecontradictions Catastrophe Catastrophe evaluation and Evaluation mechanismsEvaluation method Model quantifies Model in normalization the relative equations importance of the of system,indices accordingand reduces to the subjectiveinternalA c atastrophecontradictions factors in evaluation the and evaluation mechanisms method process quantifies in effectively.normalization the relative The equations method importance has of thebeen of system,indices widely accordingand used reduces in several to the AA catastrophe catastrophe evaluation evaluation method method quantifies quantifies the the relative relative importance importance of of indices indices according according to to the the researchinternalsubjective contradictionsfield factorss, including in the and evaluation water mechanisms resources process in effectively.normalization assessment The[25,26 equations method], mapping has of thebeen floods system, widely susceptibility and used reduces in several [2 the7], internalinternal contradictions contradictions and and mechanisms mechanisms in in normalization normalization equations equations of of the the system, system, and and reduces reduces the the safetysubjectiveresearch analysis field factorss, includingof in railway the evaluation water system resources sprocess [28], andeffectively. assessment quantitative The[25,26 method analysis], mapping has o beenf a floods non widely- equilibrium susceptibility used in several phase [27], subjectivesubjective factors factors in in the the evaluation evaluation process process eff effectively.ectively. The The method method has has been been widely widely used used in in several several transitionresearchsafety analysis field processs, includingof [ 29 railway]. water system resourcess [28], and assessment quantitative [25,26 analysis], mapping of a floods non- equilibrium susceptibility phase [27], researchresearch fields, field includings, including water water resources resources assessment assessment [25,26 ],[25,26 mapping], mapping floods susceptibility floods susceptibility [27], safety [27], safetytransitionThom analysis process Rene of(2018) [ 29 railway]. pointed system outs that[28 ]when, and controlquantitative variables analysis are less of thana non four,-equilibrium there are phaseseven analysissafety of analysis railway ofsystems railway [28 system], ands quantitative[28], and quantitative analysis of analysis a non-equilibrium of a non-equilibrium phase transition phase formstransitionThom of potentialprocess Rene (2018) [ 29 function]. pointed at most out that[30] .when The typescontrol of variables mutation arewhich less correspondthan four, there to these are seven processtransition [29]. process [29]. potentialformsThom of potentialfuncti Reneons (2018) functionare calledpointed at primary most out that[3 0catastrophe] .when The typescontrols, includingof variables mutation folding, arewhich less cusp, correspondthan swallowtail, four, there to these arebutterfly, seven ThomThom Rene Rene (2018) (2018) pointed pointed out out that that when when control control variables variables are less are than less four, than there four, are there seven are forms seven ellipticalformspotential of potentialfuncti umbilicalons functionare point, called hyperbolic at primary most [3 0catastrophe umbilical]. The types points, includingof , mutation and parabolicfolding, which cusp, correspond umbilicus. swallowtail, Theto these firstbutterfly, seven four offorms potential of potential function at function most [ 30 at]. most The types[30]. The of mutation types of which mutation correspond which correspond to these seven to these potential seven catastrophepotentialelliptical functi umbilical modelsons areare point, calledcommonly hyperbolic primary used, catastrophe umbilical as shown pointsin, includingTable, and 1. parabolicfolding, cusp, umbilicus. swallowtail, The firstbutterfly, four functionspotential are functi calledons primary are called catastrophes, primary catastrophe includings, folding, including cusp, folding, swallowtail, cusp, swallowtail, butterfly, elliptical butterfly, ellipticalcatastrophe umbilical models are point, commonly hyperbolic used, umbilical as shown pointin Table, and 1. parabolic umbilicus. The first four umbilicalelliptical point, umbilical hyperbolic point, umbilical hyperbolic point, umbilical and parabolic point umbilicus., and parabolic The first umbilicus. four catastrophe The first models four catastrophe models are commonlyTable used,1. Common as shownly used in catastrophe Table 1. models. arecatastrophe commonly models used, as are shown commonly in Table used,1. as shown in Table 1. Type Table 1. CommonSketch mlyap used catastrophe models.Potential function Table 1. Commonly used catastrophe models. Type TableTable 1. Commonly1. CommonSketch mly used apused catastrophe catastrophe models. models.Potential function Type Sketch map Potential ffunction Type Sketch Map Potential Function Folding catastrophe F(x) = x3/3 + ax FoldingFolding catastrophe catastrophe F(Fx()x )== x3x/33/3 ++ axax 3 FoldingCusp catastrophe catastrophe F(x)F =(x x)4 =/4 x +3 /3 ax +2/2 ax + bx CuspCusp catastrophe catastrophe F(Fx()Fx )=(x= x) 4x=/44 /x 4+/3+ ax ax+2 /22ax/2 + + bxbx 4 2 SwallowtailCusp catastrophe catastrophe F(x)F =((x x)) 5 =/5 x +4/4/4 ax +3 /3 ax +2/2/2 bx +2 /2bx + cx Swallowtail catastrophe F(x) = 5x5/5 + ax3 3/3 + bx2 2/2 + cx SwallowtailButterfly catastrophe catastrophe F(x)F =((x x)) 6 =/6 x +5/5/5 ax +4 /4 ax +3/3/3 bx +3 /3 bx +2/2/2 cx +2/2 cx + dx Swallowtail catastrophe F(x)6 = x5/5 +4 ax3/3 +3 bx2/2 +2 cx ButterflyButterfly catastrophe catastrophe F((Fx())x =) =x6x/6/66/ 6+ +axax4/4/44/ 4+ + bxbx3/3/33/ 3 ++ cxcx2/2/22/2 ++ dxdx In Butterfly a catastrophe catastrophe model, all critical points of the potentialF(x) = x function6/6 + ax4/4 F +(x bx) are3/3 + combined cx2/2 + dx into a balancedInIn a a catastrophe catastrophe surface. By model, model, solving all all the critical critical first derivativepoints points of of thethe of potential function function, F ( the(x)) are are equilibrium combined combined surface into into a a In a catastrophe model, all critical points of the potential function F(x) are combined into a balancedequationIn a cancatastrophesurface. be attained. By model, solving Then all the, criticalthe first bifurcation derivative points of set, the of which potential reflects functionfunction, the relationship F the(x) are equilibrium combined between surface into state a balanced surface. By solving the first derivative of potential function, the equilibrium surface equation equationbalancedvariables canand surface. becontrol attained. By variables, solving Then thecan,, thethe firstbe bifurcation bifurcation obtained, derivative and set, set, of the which which potential corresponding reflects reflects function, the the normalization relationship relationship the equilibrium between betweenequations surface state state can

variablesbe derived. and control variables, can be obtained, and thethe corresponding normalization equations can be derived.

Water 2019, 11, 2224 4 of 12 can be attained. Then, the bifurcation set, which reﬂects the relationship between state variables and control variables, can be obtained, and the corresponding normalization equations can be derived. Water The2019, 11 respective, x FOR PEER normalization REVIEW equations of the three catastrophe types—cusp catastrophe,4 of 11 swallowtail catastrophe, and butterﬂy catastrophe, which are most widely used, are as follows: The respective normalization equations of the three catastrophe types—cusp catastrophe, 1/2 1/3 swallowtail catastrophe, and butterfly catastrophexa = a , ,x whichb = b are most widely used, are as follows: (1) xa = a1/2, xb = b1/3 （1） x = a1/2, x = b1/3, x = c1/4 (2) xa = a1/a, xb = b1/3,b xc = c1/4 c （2）

a 1/2 b1/2 1/3 c 1/31/4 d 1/1/54 1/5 （） x = axa =, xa = b, xb, =x b= c , x, cx= =c d , xd = d 3(3) The normalization equations convert different types of qualitative states of control variables into Thethe same normalization type of comparable equations convert qualitative diﬀerent states. types Then of,qualitative the catastrophe states evaluation of control variables value of intothe thesystem same can type be ofobtained comparable by recursive qualitative calculation states. Then,of the the potential catastrophe function. evaluation value of the system can be obtained by recursive calculation of the potential function. 2.2. Consequences Evaluation of Dam Breach 2.2. Consequences Evaluation of Dam Breach

2.2.1. Principles for Indices Identification Identification (1)(1) IndependenceIndependence ofof indicesindices Many indices indices are are interrelated, interrelated, which which have have negative negative influences influences on evaluation on evaluation results. In results. addition, In notaddition, all the not factors all the directly factors aff directlyect the consequencesaffect the consequences of dam breach. of dam Some breach. demonstrate Some demonstrate their influences their throughinfluences the through other factors the other [11 ].factors Therefore, [11]. Therefore, basic indices basic or indices direct indices or direct should indices be should selected be based selected on clarifyingbased on clarifying the interaction the interaction mechanism mechanism among them. among them. (2)(2) EEffectivenessffectiveness ofof indicesindices Some indices indices have have great great uncertainties, uncertainties of which, of which conditions conditions or probabilities or probabilities are hard to are determine hard to determine before dam breach occurs, e.g., dam breach time and the weather during dam breach. before dam breach occurs, e.g., dam breach time and the weather during dam breach. These indices These indices are unable to be predicted or be controlled by management measures, meaning lack of are unable to be predicted or be controlled by management measures, meaning lack of effectiveness effectiveness for risk management. The existing research results also point out that the above factors for risk management. The existing research results also point out that the above factors are of low are of low importance [23]. importance [23]. (3)(3) PracticabilityPracticability ofof indicesindices Some indicesindices cooperatecooperate with with each each other other to to result result in consequences.in consequences. For For example, example, water water depth depth and and flow velocity reflect severity of dam breach floods, which are difficult to determine. However, flow velocity reflect severity of dam breach floods, which are difficult to determine. However, capacity capacity of reservoir (CR) and dam height (HD), which affect the two indices directly, are more of reservoir (CR) and dam height (HD), which affect the two indices directly, are more intuitive and intuitive and easier to be obtained, meaning more practicability. easier to be obtained, meaning more practicability. (4) Combination of quantity and quality (4) Combination of quantity and quality As known to all, some indices are easy to be quantified, whereas the others are not, e.g., As known to all, some indices are easy to be quantified, whereas the others are not, e.g., understanding of dam breach (UB). Therefore, both quantity indices and quality indices should be understanding of dam breach (UB). Therefore, both quantity indices and quality indices should be analyzed comprehensively to evaluate the consequences. analyzed comprehensively to evaluate the consequences.

2.2.2. Evaluation Index System Combined with with the the theory theory of ofdisaster disaster science science [17], [17] the, main the main objects objects of dam of breach dam canbreach be dividedcan be intodivided three into categories: three categories: risk sources, risk sources, risk pathways, risk pathways and risk, and receptors. risk receptors Therefore,. Therefore, indices indices of dam of breachdam breach consequences consequences can be can identiﬁed be identified from threefrom categoriesthree categories based inbased a logical in a logical process process of dam of breach dam consequences,breach consequences as shown, as inshown Figure in1 Figure. 1.

Breach Affect Cause Dam Floods Object Consequences

Figure 1. Logical process of dam breach consequences.

(1) Risk sources Severity of dam breach is mainly reflected on water depth, flow velocity, and rise rate of floods. However, due to topography and difference in distance from the dam site, there are countless values of the indices. Despite differences with respect to their temporal and geographical situations, the major factors that have determined the LOL in those historical flood events seem to be similar [11].

Water 2019, 11, 2224 5 of 12

(1) Risk sources Severity of dam breach is mainly reflected on water depth, flow velocity, and rise rate of floods. However, due to topography and difference in distance from the dam site, there are countless values of the indices. Despite differences with respect to their temporal and geographical situations, the major factorsWater 2019 that, 11 have, x FOR determined PEER REVIEW the LOL in those historical flood events seem to be similar [11]. Therefore,5 of 11 basic indices of capacity of reservoir (CR) and dam height (HD) are selected to characterize the severity Therefore, basic indices of capacity of reservoir (CR) and dam height (HD) are selected to characterize of dam breach floods, i.e., risk sources. the severity of dam breach floods, i.e., risk sources. (2) Risk pathways (2) Risk pathways For a certain dam, the key factors which affect the loss rate of dam breach are warning time (TW) For a certain dam, the key factors which affect the loss rate of dam breach are warning time (TW) and building vulnerability (VB)[11]. Waring time (TW) is the time span between issued warning and and building vulnerability (VB) [11]. Waring time (TW) is the time span between issued warning and the dam-breaching moment (i.e., warning initiation time or lead time). Building vulnerability (VB) the dam-breaching moment (i.e., warning initiation time or lead time). Building vulnerability (VB) mainly depends on the material and form of the building. Generally, the higher buildings provide mainly depends on the material and form of the building. Generally, the higher buildings provide safer shelter for people in floods. safer shelter for people in floods. (3) Risk receptors (3) Risk receptors a. Loss of life (LOL) a. Loss of life (LOL) Population at risk (PR) is the main direct influencing factor of LOL. Understanding of dam breach Population at risk (PR) is the main direct influencing factor of LOL. Understanding of dam (UB) directly affects self-rescue and emergency evacuation, thus affecting mortality caused by dam breach (UB) directly affects self-rescue and emergency evacuation, thus affecting mortality caused by breach floods. dam breach floods. b. Loss of economy (LOE) b. Loss of economy (LOE) Economy at risk (ER) is the main direct influencing factor of LOE. Due to difference in vulnerability, Economy at risk (ER) is the main direct influencing factor of LOE. Due to difference in industry types (TI), i.e., agriculture, industry, and services, have great influences on LOE. In addition, vulnerability, industry types (TI), i.e., agriculture, industry, and services, have great influences on LOE is significantly less sensitive to warning time (TW) than LOL. LOE. In addition, LOE is significantly less sensitive to warning time (TW) than LOL. Therefore, an evaluation index system of dam breach consequences is established, as shown in Therefore, an evaluation index system of dam breach consequences is established, as shown in Figure2. Figure 2.

Evaluation of dam breach consequences

Loss of life Loss of economy

Risk pathways Risk pathways Risk

Risk receptors Risk receptors Risk

Risk sources Risk sources Risk

Populationat risk

vulnerability vulnerability vulnerability

Understanding of

dambrea

Economy at Economy risk

r r

W W

ndustry types types ndustry

eservoir eservoir

D D

C C

arning time arningtime arningtime

B B

apacity of apacity of

amheight amheight

uilding uilding

( (

(

H H

T T

P E

W W

R R

D D

)

) ) )

( (

C C

(

( (

R R

V V

) ) ) )

B B

) )

FigureFigure 2.2. EvaluationEvaluation indexindex systemsystem ofof damdam breachbreach consequences.consequences.

2.2.3. Standardization of Indices In order to facilitate analysis, the indices can be divided into five grades on average [14], i.e., {slight; general; moderate; serious; extremely serious} ∈ {[0,0.2); [0.2,0.4); [0.4,0.6); [0.6,0.8); [0.8,1]}. There are great differences in the characteristics of impact indices of dam breach consequences in different countries. Taking China as an example, values and standardization of indices are analyzed. Dam height (HD), which is a certain value, is one of the most important factors of dam breach consequences. Generally, the consequences of dam breach will be extremely serious in the case of HD of ≥100 m. Therefore, standardization of dam height (HD) is shown in Equation (1):

Water 2019, 11, 2224 6 of 12

2.2.3. Standardization of Indices In order to facilitate analysis, the indices can be divided into five grades on average [14], i.e., {slight; general; moderate; serious; extremely serious} {[0,0.2); [0.2,0.4); [0.4,0.6); [0.6,0.8); [0.8,1]}. ∈ There are great differences in the characteristics of impact indices of dam breach consequences in different countries. Taking China as an example, values and standardization of indices are analyzed. Dam height (HD), which is a certain value, is one of the most important factors of dam breach consequences. Generally, the consequences of dam breach will be extremely serious in the case of HD of 100 m. Therefore, standardization of dam height (H ) is shown in Equation (4): ≥ D

( HD 100 0 < HD < 100 RHD = . (4) 1 HD 100 ≥

Some indices are in a certain range (e.g., warning time (TW)), of which standard values can be calculated by interpolation according to the thresholds of corresponding severity. While the others are qualitative (e.g., understanding of dam breach (UB)), of which standard values can be determined artificially according to experience and engineering practice on the basis of determining the severity level firstly. China has categorized its dams into five types: small type II, small type I, medium type, large type II, and large type I, based on the capacity of their reservoirs [31]. According to “standards for flood control” in China, population in protection and equivalent economic scale in protection of different types of reservoirs are prescribed [32]. Generally, population in protection, which is protected from floods by dams, equals to population at risk (PR). The equivalent economic scale, instead of absolute amount of economy, is proposed to reflect economy at risk (ER), ensuring that the standards are applicable under the constantly developing economic environment. The equivalent economic scale is determined by population in protection, per capita gross domestic product (GDP) of the protected areas, and per capita GDP of the whole country in the same period, as shown in Equation (5):

Equivalent economic scale = Population in protection per capita GDP of the × (5) protected areas per capita GDP of the whole country in the same period. ÷ Main characteristics of reservoirs at all types in China are shown in Table2.

Table 2. Main characteristics of reservoirs at all types in China.

Characteristics Small Type II Small Type I Medium Type Large Type II Large Type I C /million m3 [0.1,1) [1,10) [10,100) [100,1000) [1000, ) R ∞ P /million person [0,0.05) [0.05,0.2) [0.2,0.5) [0.5,1.5) [1.5, ) R ∞ E /million person [0,0.1) [0.1,0.4) [0.4,1.0) [1.0,3.0) [3.0, ) R ∞

According to the impact on the severity of risk consequences, understanding of dam breach (UB) and warning time (TW) can also be divided into five grades [13,23]. Different types of buildings, such as adobe, brick, brick-concrete, reinforced concrete, and high-rise (built of reinforced concrete) buildings, provide different shelters for population at risk due to their different vulnerabilities in floods caused by dam breach [11,33]. Because of the specific characteristics of different types of industry (TI), the order of sensitivity to flood damage from high to low is agriculture, industry, and services. Therefore, the corresponding grades of relevant indices are shown in Table3. Water 2019, 11, 2224 7 of 12

Table 3. Corresponding grades of relevant indices.

Extremely Serious Indices Slight [0,0.2) General [0.2,0.4) Moderate [0.4,0.6) Serious [0.6,0.8) [0.8,1] C /million m3 [0.1,1) [1,10) [10,100) [100,1000) [1000, ) R ∞ P /million person [0,0.05) [0.05,0.2) [0.2,0.5) [0.5,1.5) [1.5, ) R ∞ UB precise medium general vague unknown T /h [6, ) [3,6) [1,3) [0.25,1) [0,0.25) W ∞ VB high-rise reinforced concrete brick-concrete brick adobe E /million person [0,0.1) [0.1,0.4) [0.4,1.0) [1.0,3.0) [3.0, ) R ∞ TI services services–industry industry industry–agriculture agriculture

2.3. Evaluation Procedures (1) Deﬁning the values of all indices based on statistics and on-site investigation. (2) Standardizing the indices according to their characteristics.

“The-bigger-the-better” indices and “the-smaller-the-better” indices can be standardized, respectively, by: ri rmin Ri = − , (6) rmax r − min rmax ri Ri = − , (7) rmax r − min where Ri is the standard value of index i; ri is the initial value of index i; rmax and rmin are the maximum and minimum values of all indices, respectively.

(3) Calculating the catastrophe value hierarchically by using the recursive method according to the corresponding mutation types.

3. Results

3.1. Validation of the Method The outcomes of the proposed method are compared with 12 historical dam breach events in China. Due to the lack of statistical data on LOE, only severity evaluation of LOL is applied. Relevant parameters of the 12 reservoirs are shown in Table4.

Table 4. Relevant parameters of the 12 reservoirs.

3 Reservoir Province Year CR/Million m HD/m PR/person UB TW/h VB Longtun Liaoning 1959 30.00 9.5 35,428 vague 0.00 adobe Liujiatai Hebei 1960 40.54 35.9 64,941 vague 1.00 adobe Hengjiang Guangdong 1970 78.79 48.4 70,000 precise/medium 0.25 brick/adobe Dongkoumiao Zhejiang 1971 2.55 21.5 4700 vague 0.00 brick/adobe Lijiazui Gansu 1973 1.45 25.0 2000 vague 0.00 adobe Shijiagou Gansu 1973 0.856 28.6 300 vague 0.40 adobe Shimantan Henan 1975 91.80 25.0 204,490 medium/general 0.00 adobe Banqiao Henan 1975 492.00 24.5 402,500 medium/general 0.00 adobe Gouhou Qinghai 1993 3.30 71.0 3060 vague 0.00 brick/adobe Xiaomeigang Hubei 1995 0.14 10.9 1400 vague 0.00 brick/adobe Shenjiakeng Zhejiang 2012 0.24 28.5 300 medium 0.00 brick-concrete Sheyuegou Xinjiang 2018 6.78 37.7 5600 precise/medium 0.00 brick-concrete

Based on the cusp catastrophe model, the swallowtail catastrophe model, the above evaluation index system, and evaluation results, which reﬂect the severity of LOL caused by dam breach, of the 12 reservoirs are obtained. In addition, statistics of LOL of the validation dams breach are adopted for comparison, as shown in Table5. Water 2019, 11, 2224 8 of 12

Table 5. Severity evaluation and statistics of loss of life of dam breach.

Item Longtun Liujiatai Hengjiang Dongkoumiao Lijiazui Shijiagou Statistics/person 707 943 941 186 580 81 Evaluation 0.868 0.893 0.894 0.840 0.841 0.829 results Item Shimantan Banqiao Gouhou Xiaomeigang Shenjiakeng Sheyuegou Statistics/person 2517 19701 320 34 11 28 Evaluation 0.908 0.921 0.870 0.774 0.771 0.821 results Water 2019, 11, x FOR PEER REVIEW 8 of 11

3.2. Implementation of the Method Jiangang Reservoir, which locates in the southwest of Zhengzhou C Cityity of China, has a capacity 3 of 60.7041 million m3 and an earth earth-rock-rock dam with a height of 37.1 m, and protects almost 0.2 million citizens. Potential Potential LOLLOL of of Jiangang Jiangang Reservoir Reservoir dam dam breach breach under under ﬁve conditions five conditions is analyzed, is analyzed, as shown as inshown Table in6. Table 6. Table 6. Potential loss of life of Jiangang Reservoir dam breach under ﬁve conditions. Table 6. Potential loss of life of Jiangang Reservoir dam breach under five conditions. Item Jiangang 1 Jiangang 2 Jiangang 3 Jiangang 4 Jiangang 5 Item Jiangang 1 Jiangang 2 Jiangang 3 Jiangang 4 Jiangang 5 U vague/unknown vague/unknown medium medium medium B UB vague/unknown vague/unknown medium medium medium TW/h 0 1 0 1 6 TW/h 0 1 0 1 6 Evaluation results 0.900 0.887 0.880 0.867 0.835 Evaluation results 0.900 0.887 0.880 0.867 0.835

Evaluation results of dam breach of the 12 validationvalidation reservoirs and JiangangJiangang Reservoirs are shown in FiguresFigures3 3 and and4 .4.

Figure 3. Evaluation results of dam breach of the validation reservoirs. reservoirs. * *** Loss Loss of of life life is plotted on a logarithmiclogarithmic scale.scale.

Figure 4. Evaluation results of dam breach of Jiangang Reservoir and some validation reservoirs.

Water 2019, 11, x FOR PEER REVIEW 8 of 11

3.2. Implementation of the Method Jiangang Reservoir, which locates in the southwest of Zhengzhou City of China, has a capacity of 60.7041 million m3 and an earth-rock dam with a height of 37.1 m, and protects almost 0.2 million citizens. Potential LOL of Jiangang Reservoir dam breach under five conditions is analyzed, as shown in Table 6.

Table 6. Potential loss of life of Jiangang Reservoir dam breach under five conditions.

Item Jiangang 1 Jiangang 2 Jiangang 3 Jiangang 4 Jiangang 5 UB vague/unknown vague/unknown medium medium medium TW/h 0 1 0 1 6 Evaluation results 0.900 0.887 0.880 0.867 0.835

Evaluation results of dam breach of the 12 validation reservoirs and Jiangang Reservoirs are shown in Figures 3 and 4.

WaterFigure2019, 11 3., 2224 Evaluation results of dam breach of the validation reservoirs. ** Loss of life is plotted on a 9 of 12 logarithmic scale.

FigureFigure 4. 4. EvaluationEvaluation results results of of dam dam breach breach of of Jiangang Jiangang Reservoir Reservoir and and some some validati validationon reservoirs. reservoirs.

4. Discussion According to Figure3, 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 Table5 and Figure3, 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 Figure3. 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 Figure4, 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), Water 2019, 11, 2224 10 of 12 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.

Author Contributions: Conceptualization, W.G. and Z.L.; methodology, W.G.; validation, Y.J., H.S., and Y.Z.; formal analysis, H.Z. and X.G.; investigation, X.G. and Z.Z.; writing of original draft preparation, W.G. and H.S.; writing of review and editing, Y.J., W.G., and H.Z.; supervision, P.H.A.J.M.v.G.; funding acquisition, W.G. and Z.L. Funding: This research was funded by the National Natural Science Foundation of China (grant No. 51679222, 51709239, and 51379192), the China Postdoctoral Science Foundation (grant No. 2018M632809), the China Study Abroad Foundation (grant No.201808410536), the Science and Technology Project of Henan Province of China (grant No. 182102311070), the Key Project of Science and Technology Research of Education Department of Henan Province of China (grant No. 18A570007), and the Science and Technology Project of Water Conservancy of Henan Province of China (grant No. GG201813). Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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