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Safety and Reliability for Managing Risk – Guedes Soares & Zio (eds)© 2006 Taylor & Francis Group, London, ISBN 0-415-41620-5

Safety of coastal defences and flood risk analysis

C.V. Mai1,2, P.H.A.J.M. van Gelder1 & J.K. Vrijling1

1 Delft University of Technology, Delft, Netherlands2 Hanoi Water Resources University, Hanoi, Vietnam

ABSTRACT: This paper is aimed at safety assessment of coastal flood defences and investigation of floodrisk for coastal regions. Firstly, a general safety assessment procedure of coastal defences is performed byapplying reliability analysis, which includes steps of identification of failure modes by various possible failuremechanisms, statistic description of hydraulic loads and resistance of the coastal defences and calculation ofthe failure probability. Secondly, overview of risk analysis of coastal defence system is followed, in which dueto possible failures of the system, loss of life, economic, environmental, cultural losses and further intangiblescan occur. It is necessary to determine the question if safe is safe enough and figure out acceptable risk levels.Acceptable risk is strongly related with the acceptable probability of failure and the acceptable amount of damagesand losses. The state of the art in risk analysis will be reviewed and discussed. Application of the reliability andrisk analysis to case studies of Vietnam coastal flood defences is investigated.

1 INTRODUCTION

1.1 Background

Sea dikes are the most important coastal structuresalong the coastlines of Vietnam and many other coastsaround the world which have their low-lying areasbehind. The main function of sea dikes is to protectlow-lying coastal areas which are highly vulnerable tocoastal flooding. In general the design of these coastalstructures is based on purely deterministic or quasi-deterministic approaches. The design water level ofsuch structures is normally based on the maximumwave run-up or on acceptable overtopping rates underextreme storm surge conditions. Due to the fact thatthe coastal structures are usually under impacts ofmany natural phenomena and processes which hap-pens randomly both by time, space, their intensityand amplitude, therefore the deterministic approachessame to not bring closer proper outcomes. In addi-tion, geotechnical related failure modes of sea dikesare often disregarded and/or not properly accountedfor in the design process.

Probabilistic approach with reliability and riskbased design concepts have been increasingly pro-posed and applied in the lasts few years (see e.g.the concept, method and application in Bakker &Vrijling 1980; Vrijling et al., 1998; Voortman 2002;and Oumeraci et al., 2001). The probabilistic methodallows designers take into account the uncertaintiesof the input parameters and treat them as the randomvariables. Moreover, probabilistic models describe

possible failure modes for various types of hydraulicand coastal structures. Even though, application ofthese methods is still limited to the simple cases orjust to a couple of failure mechanisms. Especially indeveloping countries as Vietnam these methods is justintroduced as a new modern design approach whichhas few applications. Implementation of probabilis-tic design and risk analysis to Vietnamese situation offlood defence and coastal protection is therefore neces-sary. The implementation methods can also be appliedfor the cases of other developing countries.

Nevertheless, before go into detailed analyses andapplications of probabilistic approach in the field ofcoastal defence structures, it is strongly necessary tohave an overview on understanding of the methods.Study on physical processes of loading and the phys-ical failure mechanisms of the coastal structures arealso large important to have a proper view before estab-lishing a probabilistic models for these issues. Theseneed a broad research effort in near futures. This paperjust presents some initial results of applying reliabil-ity and risk based approach for Vietnamese coastaldefence situation.

1.2 Fluvial flood and coastal defences in Vietnam

Vietnam is affected regularly by substantial sufferingdue to floods. The most severe floods occur duringhigh river discharges and during, and shortly after,typhoons. The typhoons are accompanied by torrentialrains causing flash floods which regularly submerge

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low-lying areas.The deltaic coastal area to a distance ofabout 20 km behind the sea dikes is threatened in par-ticular because of the combined occurrence of stormsurge from the sea and high river discharge at hightides. As a result of these severe loads and the ratherlow safety level of the present dikes, the water defensesystem ofVietnam fails regularly. Since 1996,Vietnamwas affected by several flood disasters, each of thoseresponsible for the loss of hundreds of lives and con-siderable damage to infrastructure, crops, rice paddy,fishing boats and trawlers, houses, schools, hospitals,etc.. The total material damage of the flood disastersin these years exceeded USD 500 million, which dam-age was accompanied by the loss of almost over 1000lives. The flood disasters occurred in North Vietnam(1996 and 2005), in SouthVietnam (1997) as well as inthe Central provinces (1998, 2005). Most floods wereinitiated by typhoons and occurred in the coastal zone.

The relative low safety level of theVietnamese dikeswas noticed in 1996 during two visits of Dutch mis-sions to Vietnam. Most designs of the Vietnamesesea and river dikes are based on loads with returnperiod 20 years or even shorter periods. Comparedto the Dutch standard (return periods 3000 to 10000year) these return periods are very small. Besidesthis fact the Dutch mission marked most Vietnamesedike designs as poor and disputable (Vrijling & Hauer2000). Designs are not always based on the right for-mulae, hydraulic boundary conditions are not alwaysbased on proper statistics (for example design waterlevel and wind set up are not always treated as twoindependent phenomena), failure mechanisms whichdiffer from overtopping are often neglected, no atten-tion is given to length effects, monitoring and timelyrepair of small damages is often at a poor level, etc.As a result the true probability of failure (probabilitythat the load is larger than or equaled to the resistanceof the flood defence system) of the Vietnamese waterdefense system may exceed the design frequency.Although designed to fail only once in 20 year thiswater defense system might well fail almost every year.The experiences in last 10 years support this assertion.

1.3 Damrey typhoon and its consequences

The Damrey typhoon (named in Vietnam as Storm No.7) is considered the most vigorous in the last 50 years.With wind force near to the storm center at Beaufortscale 12 (118 to 133 km per hour) and the wind gustingabove Beaufort Scale 12, the typhoon was forecastedto affect all coastal provinces of Vietnam from QuangNinh to Da Nang. The typhoon was forecasted to bevery dangerous, particularly to the sea dike system,serves to protect hundreds thousands of people, ricefields and aquaculture production areas along the coastof Vietnam. By 5.00 AM on 27 September the windforce rose from Beaufort scale 7-8 to scale 12 (133 km

Figure 1. Consequence of the Damrey typhoon SEP 2005.

per hour) hitting provinces from Hai Phong to ThanhHoa as the typhoon moved in a west to northwest direc-tion. The typhoon caused high storm surges, whichcoincided with high tide so they were amplified.

The wave run up was as high as 3–4 meters, highstorm surge in combination with high tide led to toomuch overtopping of sea water at sea dikes in almostall affected provinces. It broke certain sea dike sec-tions in Hai Hau district in Nam Dinh province andHau Loc district in Thanh Hoa. The total damage wasenormous; 25 km of sea dikes were broken and nearlytotally destroyed. In Nam Dinh a stretch of 800 m seadikes was completely washed out.

The seawater penetrating the inland by 3–4 km incoastal provinces and the following flash floods inupland areas have destroyed at least 1,194 houses anddamaged another 11,576. More than 130,000 ha of ricefields have been submerged and damaged, most ofwhich could not been harvested before the typhoon.Severe damage occurred to transport and electricityinfrastructure and particularly the irrigation systems.According to the rapid assessment of Disaster Man-agement Working Group the direct damage estimateas of 28 September is USD 430 million.

2 OVERVIEW OF PROBABILISTIC APPROACHIN FLOOD DEFENCES

Since the last few decades the awareness grew that theprobability of exceedance of the design water level, thedesign frequency or the return period is not a good pre-dictor of the true probability of flooding. Normally thedike crest exceeds the design water level by some mea-sure, thus the probability of overtopping is smaller thanthe design frequency. But some parts of the dike mayalready be critically loaded before the design waterlevel is reached. There are more failure mechanismsthat can lead to flooding of the polder than overtop-ping. Another danger is that water discharge structures(e.g. sluices, gates, ship logs…) are not functionedwell in time before the high water moment. Moreoverthe length of a dike ring has a considerable influence.A chain is as strong as the weakest link. So a singleweak spot determines the actual safety of an entire dikering. Due to this so called length effect the probabilityof failure of a dike ring depends on the length of this

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Figure 2. Flood defence system and its elements presentedin a fault tree (CUR, 1988).

too much

instability ofprotected ele.

scour

instability oftoe structure

System failure -Inundation

instability ofdike's slope

damage of

erosion ofinner slopes

dike crest

overtopping

outer slopes

inner slopesinstability of

instability of

piping

rupturing

sand flow

outer slopes

armour layerdamage of

armour layerinstability of

erosion of

failure offilter layers

Failure ofdike section i

Figure 3. A dike section as a series system of failure modes.

ring as well. In a practical case the probability of fail-ure of an entire dike ring may exceed the probabilityof failure of a single section by for example a factor10 or higher. More extensive description can be foundin Vrijling et al., 1993.

The probabilistic approach aims to determine thetrue probability of flooding of a polder and to judgeits acceptability in view of the consequences.As a startthe entire water defence system of the polder is stud-ied. Typically this system contains sea dikes, dunes,river levees, sluices, pumping stations, high hills, etc.(Figure 2). In principle the failure and breach of anyof these elements leads to flooding of the polder. Theprobability of flooding results from the probabilitiesof failure of all these elements.

Within a longer element e.g. a dike of some kilo-meters length, several independent sections can bedivided. Each section may fail due to various possi-ble failure mechanisms like overtopping, sliding ofouter or inner slope, piping, erosion of the protectedouter slope, ship collision, dike’s toe instability, etc..The relation between the failure mechanisms in a sec-tion and the unwanted consequence flooding can beschematised with a fault-tree (Figure 3).

The failure probabilities of the mechanisms are cal-culated using the methods of the modern reliabilitytheory, like Level III or Level II methods.

In the reliability calculations all uncertainties aretaken into account. Three classes of uncertainties

Table 1. Example table of overall probability of flooding.

Section Overtopping Piping Etc. Total

dike 1.1 p1.1 (overtopp.) p1.1 (piping) p1.1(etc.) p1.1(all)dike 1.2 p1.2 (overtopp.) p1.2 (piping) p1.2(etc.) p1.2(all)etc. … … … …dune pdune(overtop.) pdune(piping) pdune(etc.) pdune(all)sluice psluice(overtop.) psluice(piping) psluice(etc.) psluice(all)total pall(overtop.) pall(piping) pall(etc.) pall(all)

are distinguished: The intrinsic uncertainty is char-acteristic for natural phenomena; Model uncertaintydescribes the imperfection of the engineering modelsin predicting the behaviour of river courses, dikes andstructures; Statistical uncertainty is caused by the lackof data. More extensive discussion see also van Gelder1999.

Because all uncertainties are included in the calcu-lations of the failure probability the latter is not singlya property of the physical reality but also of the humanknowledge of the system. The consequence is that thesafety of a dike system as expressed by the calculatedprobability of flooding can be improved by increasingour knowledge as well, apart from strengthening theweakest elements in this system. All calculated proba-bilities of failure can be presented in a form of Table 1.

The last column of the table shows immediatelywhich element or section has the largest contribution tothe probability of flooding of the polder under study.Inspection of the related row reveals which mecha-nism will most likely be the cause. Thus a sequenceof measures can be defined which at first will quicklyimprove the probability of flooding but later runs intodiminishing returns.

2.1 Reliability analysis of a multi-elements system

Quantification of the probability of system failurestarts with the definition of reliability functions for allfailure modes in the lowest level of the fault tree. Asfrom literatures, the general form of reliability func-tion of component ith of the system can be simplywritten by Bakker & Vrijling (1980):

In which Ri and Si are multivariate functions whichstand for strength and load, respectively and bothconcerned with stochastic variables. The probabilitydensity function of Zi given by fZi(X).Then the prob-ability of failure of the element ith which has the limitstate function Zi is:

In reality Zi may be a function of number of stochasticvariables X1, X2, . . . ,Xn , as both the “load”, Si, and

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the “strength”, Ri, and may depend on more than onevariable. In order to perform a level II calculation, thefirst order reliability methods (FORM) is used. In theFORM analysis, the failure surface Z(Xj) = 0 atthe design point X ∗

j is approximated by by the hyper-plane normal to the vector X ∗

j (Rackwitk, 1977).By using Taylor expansion the failure function islinearised and after the linearisation it can be stated as:

Zlini : Linearized reliability function of Zi in {X ∗

j }; ( ∂Z∂X )

Xj = X ∗j gradient vector at the design point X ∗

j , deter-mined by partial derivative of Zj with respect to Xjevaluate in Xj = X ∗

j .The mean value and standard deviation of Zlin

i are:

If mean values X1∗ = µ(Xj ), …, X ∗

n = µ(Xn) aresituated, a so called mean value approximation ofthe probability of failure is obtained. If the failureboundary is nonlinear, a better approximation can beachieved by linearization of the reliability function ata design point. The design point is defined as the pointon the failure boundary in which the joint probabilitydensity is maxima. Therefore the design point can beobtained by:

where, reliability index and influence factor of vari-able number jth to failure probability of element ithcan be determined by:

A more general form of a reliability function thatcovers a large number of cases is given by:

where R is the resistance of the component, S is theloading on the component, z is a vector of design vari-ables describing among others the structural geometryof the component and X is a vector of load of randomvariables.

The occurrence of the failure mode described byequation (9) is indicated by negative values of the reli-ability function. If fx(X ) denotes the joint probability

distribution of random input boundaries. The proba-bility of occurrence of every failure mode is given by:

The overall failure probability of a dike sectionnumber ith is given by:

where (Z1 < 0; Z2 < 0; … Zi < 0;… Zm < 0) denotesat least one of m failure mechanisms occurs.

The fundamental lower and upper bounds in thislevel II approach are approximated by:

For more narrower bounds with better approximationit is suggested to use Ditlevsen bound (see Ditlevsen1979).

2.2 Discussions

Following the above background, there are two essen-tial probabilistic approach based models can beapplied and developed conceptually:

1) Probabilistic assessment of safety level: If thegeometry of every component is known and thejoint probability distribution of load and strengthvariables is quantified, the probability of failure ofthe system of flood defences can be found. Thiscan be applied for technical management purpose todetermination of safety levels of the existing systemand to find out the weakest point of the system.

2) Reliability-based design model: very often thequestion is, however, reversed for a design purpose.For a pre-defined failure probability (e.g. given anacceptable level of probability of flooding for a cer-tain location) a geometry of the structure needs tobe found in order to fulfill the design requirementin combination with minimisation of the construc-tion cost of the system. For a fixed value of theprobability of failure, the set of acceptable designalternatives is conceptually given by (12a). In orderto find the unique solution the cost optimisationhas to be accounted for as show in (12b). The opti-mal design geometry can be found mathematicallyby the following equation system (see Voortman,2002):

where Pf ,max denotes the maximum acceptableprobability of system failure; I denotes the directcost of the system.

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Generation of geometry alternative

Calculation of failure probability

Pf <Pmax(opt.)

Estimation of RT =f(Pf) Estimation of I

true

false

Total costs

Search for the lowest cost solution

Figure 4. General reliability-based design of coastaldefences.

However, it is noted that in this model the total costis considered only direct investment cost. It is possibleto include also maintenance/ repair costs in the opti-misation.The reliability-based optimisation model canbe modified by (13):

In this case, I is the initial investment cost and RTis the maintenance/repair cost during the total servicelifetime of the structures,T.The investment cost can beestimated based on given geometry while the later termcan be expressed through the failure probability of theeach consider alternative. Again the minimum point oftotal construction cost in space of failure probabilityis searched. This procedure of the “reliability-basedoptimisation” is illustrated in Figure 4.

3 DUTCH EXPERIENCES ON RISKANALYSIS OF FLOOD DEFENCES

3.1 Overview

The modern probabilistic approach aims to give pro-tection when the risks are felt to be high. Risk isdefined as the probability of a disaster e.g. a floodrelated to the consequences. As long as the modernapproach is not firmly embedded in society, the ideaof acceptable risk may be quite suddenly influencedby a single spectacular accident or incident like 1953flood disaster in the Netherlands, tsunami disaster inThailand, Indonesia, Sri Lanka 2004, Katrina in NewOrleans, USA 2005, Damrey in Vietnam 2005, etc.These could be the starting or turning point of anynew safety policy establishment.

The estimation of the consequences of a flood con-stitutes a central element in the modern approach. Mostprobably society will look to the total damage causedby the occurrence of a flood. This comprises a numberof casualties, material and economic damage as wellas the loss of or harm to immaterial values like worksof art and amenity. Even the loss of trust in the waterdefense system is a serious, but difficult to quantifythe effect.

However for practical reasons the notion of risk ina societal context is often reduced to total number ofcasualties using a definition as “the relation betweenfrequency and the number of people suffering from aspecified level of harm in a given population from therealisation of specified hazards”. If the specified levelof harm is limited to loss of life, the societal risk may bemodelled by the frequency of exceedance curve of thenumber of deaths, also called the FN-curve (see moredetail in Vrijling et al., 1998). When the probabilitiesof flooding of any polder are calculated the questionof if the polder safe enough may arise. The answer forthis question can only come from a broad judgement ofthe cost of improving the defences against the reduc-tion of the probability of flooding related to the scaleof the damage. This judgement is political in essence,because the costs as well as the benefits contain manyaspects that may be valued quite differently by differ-ent parties. Dike improvement costs money, land area,cultural heritage and amenity.

Obviously, if dike improvement is relatively expen-sive a higher probability of flooding will be accepted.On the other hand if the consequence of flooding isrelatively substantial one will aim for a smaller prob-ability. Moreover, the environmental consequences offlooding and the potential effects on nature and cul-tural heritage should also play an increasing role inassessing the required scale of flood protection. Theimage of the country as a safe place to live, works, andinvest is finally at stake. This justifies a fundamentalreassessment of the acceptability of the flood risks inview of the costs of improvement.

From literatures, the acceptance of risk should bestudied from the three different points of view in rela-tion to the estimation of the consequences of flooding.The first point of view is the assessment by the individ-ual. Attempts to model this are not feasible, thereforeit is proposed to look to the preferences revealed inthe accident statistics.The fact, that the actual personalrisk levels connected to various activities show statisti-cal stability over the years and are approximately equalfor the Western countries, indicate a consistent patternof preferences. The probability of losing one’s life innormal daily activities such as driving a car or workingin a factory appears to be one or two orders of magni-tude lower than the overall probability of dying. Onlya purely voluntary activity such as mountaineeringentails a higher risk (see Vrijling et al., 1998).

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Apart from a slightly downward trend of the deathrisks presented (due to technical progress), it seemspermissible to use them as a basis for decisions withregard to the personally acceptable probability offailure, by means of the equation below:

where Pd|fi denotes the probability of being killed inthe accident event. In this expression the policy factorβi varies with the degree of voluntariness (see Vrijlinget al, 1998). For the safety of dikes a βi-value of 1.0 to0.1 is thought to be applicable.

Another point of view concerns the assessment bysociety. The judgment of the societal risk due to acertain activity should be made on a national level.The determination of the socially acceptable level ofrisk assumes also that the accident statistics reflectthe result of a social process of risk appraisal andthat a standard can be derived from them. In additionto that the formula should account for risk aversionin a society. Relatively frequent small accidents aremore easily accepted than one single rare accident withlarge consequences like a flood, although the expectednumber of casualties is equal for both cases. The stan-dard deviation of the number of casualties reflects thisdifference. Risk aversion can be represented math-ematically by adding the desired multiple k of thestandard deviation to the mathematical expectation ofthe total number of deaths, E(Ndi) before the situationis tested against the norm of βi.100 casualties for theNetherlands:

where: k = risk aversion index.To determine the mathematical expectation and the

standard deviation of the total number of deaths occur-ring annually in the context of activity i, it is necessaryto take into account the number of independent placesNAi where the activity under consideration is carriedout.

The translation of the nationally acceptable levelof risk to a risk criterion for one single installationor polder where an activity takes place depends onthe distribution type of the number of casualties foraccidents of the activity under consideration. In orderto relate the new local risk criterion to the commonshape of a FN-curve, the following type is preferred:

where x is the number of casualties in a year, FNdij (x)is the distribution function of the number of casualties(probability of less than x casualties in a year) and Ci

-ln(Pf)

Cos

t

PV(Pf*S)

I

Q: total cost

-ln(Pfopt.)

Opt. point

Min

cost

Figure 5. CBA in risk-based design (Vrijling et al., 1993).

is a constant, which depends on the activity i underconsideration.

The problem of the acceptable level of risk can bealso formulated in a way of economic optimal basedon cost benefit analysis (CBA). The expenditure Ifor a safer system is equated with the gain made bythe decreasing present value of the risk. The conceptscheme is shown in Figure 5. The optimal level ofsafety indicated by Pf−opt corresponds to the point ofminimal cost:

where Q refers to the total cost, PV is the present valueoperator and S refers to the total damage in case offailure.

Cost-benefit analysis in principle is limited to quan-tifiable aspects of the decision with all consequencesof flooding are measured in monetary terms. In real-ity, there are several dimensions of flooding risk thatcan in principle be quantified, but not necessarily inmonetary terms. An important aspect that falls in thisgroup is the risk of loss of life due to flooding. Further-more, it is observed that disastrous events become lessacceptable to the general public if the magnitude ofthe consequences is larger. This behaviour is referredto as risk aversion.

One way to deal with monetary and non-monetaryaspects of flood protection is to define constraints onthe solution space, which limits the range of accept-able flooding probabilities to values that are deemedacceptable in the light of the non-monetary conse-quences of flooding. Observed risk aversion may beincluded in the definition of the constraint (Vrijlinget al., 1995, 1998).

Another way to include monetary and non-monetary aspects of flood protection is by applicationof the Life Quality Method, proposed by Nathwani

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et al., 1997. In this method, decisions concerning riskare judged using a social indicator called the Life Qual-ity Index (LQI), which combines the effects of thedecision on the life expectancy at birth and the grossdomestic product per capita. From a practical pointof view, this is a convenient method since the proper-ties of the life quality model may be established fromobserved values of the properties of society. Howeverthe validity of this approach model is very hard toverify.

3.2 Discussions

Reliability-based design depends on the availabilityof a pre-defined failure probability requirement. In asituation where acceptable safety levels are definedin regulation (e.g. pre-defined design frequency), themethods outlined in the previous section are sufficientto obtain a cost-effective design that fulfils the require-ments. In some cases, the required failure probabilityis not yet defined. For instance the case when a designis made for a situation where no regulation is avail-able or when an analysis is performed in a process ofdefining/redefining required safety levels.

From the review of risk analysis in previous section,the acceptable probability of failure can be definedby comparing the cost of protection to a characteristicvalue of the consequences of flooding. In a purely eco-nomic sense this leads to risk-based cost-benefit analy-sis. Applications in coastal engineering in the Westerncountries have been published by Bakker & Vrijling(1980), Burcharth et al., (1995),Voortman et al., (1998,1999, 2001 and 2002), Vrijling et al., (1998). In risk-based design, a model is established that provides ameasure of the effectiveness of the protection systemas a function of its failure probability. The two maincomponents of such a model are the cost of protectionand a characteristic value of the consequences of flood-ing, both as a function of the probability of failure.

Actually, forVietnamese situation of flood defencesand coastal protection, the safety levels were set bydesign frequencies which varied by locations andimportance of the elements. It is known as a fixedvalues and indicated in National Design Standards(e.g. for provincial sea dike is 1/20 years, river dike1/25 years). These safety levels were selected approx-imately 30 years ago. There is no clear explanation ofthese selections. And it is not updated as the changesof social economic situation occasionally. Currently,there is not any framework of establishing actual safetylevels for flood defences and coastal protection.There-fore it is necessary to derive and implement such aframework of risk analysis and risk-based design forVietnamese situation. The combination of the con-strained cost benefit analysis and LQI models issuggested to use, which will account for developingcharacteristic (e.g. fast economic growth but limitedinitial investment). The results should be compared

with that from other approaches like FN-curves fromstatistical and/or loss of life model. This will be treatedas a task of further study.

4 IMPLEMENTING RELIABILITY &RISK ANALYSIS INTO VIETNAMESESITUATION

4.1 Example of Hai Phong dike ring – lengtheffect

The present situation of flood defences in Vietnam iswell indicated in Section 1.2.Apart from that all designare made in two dimensions without paying attentionto the third one: the system length.

This section focuses on importance of the conse-quences of the two dimensional dike design approach.A simple example shows the influence of systemlength effects at Haiphong sea dikes.

The Haiphong dike ring consists of 47 km. Thisdike ring may be subdivided in 47 independent sec-tions with identical length. Each section is constructedaccording to a design which is based on loads withreturn period 20 years. Suppose the probability offailure of a section truly reflects this return period:probability of failure section = Pf ,sect = 1/20 = 0.05year−1. This probability is the minimum probabilityof failure of the entire dike ring, which refers to thecase of full correlation of all sections. In this case allsections should fail simultaneously. However practicalexperience shows that all sections of a dike ring neverfail simultaneously: failure occurs to the weakest sec-tion(s) only. Therefore failure of the dike ring dependson the behaviour of the weakest section. The dike ringshould be conceived as a series system of n = 47 inde-pendent elements.The maximum probability of failureof such a series system may be calculated conform:

This maximum probability Pf ,ring = 0.9102, which isapproximately equal to a return period of 1 year,applies to the hypothetical situation of perfect inde-pendence of all elements. In most cases this situationdiffers from reality too. Although strength parametersas crest height and geotechnical properties of a sectionmight well be uncorrelated in the case of the cho-sen length scale 1000 meters, the hydraulic load willprobably be more or less the same for adjacent sec-tions. Therefore the probabilities of failure of adjacentsections are often still somehow correlated.

Taking into account the correlation due to hydraulicloads a more proper upper bound for Pf ,ring wasestimated at (Vrijling & Hauer 2000):

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where n refers to the number of sections of the dikering under consideration. It should be noted that thisresult belongs to a specific case, the formula aboveshould not be conceived as a theoretical result for allkinds of situations. However the starting-points of thisexample are rather common and therefore the formulamight well apply to a Vietnamese situation too. Inthat case the upper bound of the probability of fail-ure of the dike ring in the Vietnamese example mightbe Pf ,ring ≤ (0,05/1.1)*(1.036 + 0.064*47) = 0.1850,which probability corresponds with a return period1/0.0.185 ≈ 5.5 year. This return period might well bethe true return period of failure of the Haiphong dikering.

As far the example only concerned the possibil-ity of overtopping of sections. Some sections mighthave failed earlier as a result of other failure mecha-nisms too. Therefore the return period of failure mightbe even smaller than 5.5 year. In case of a dike ringconsisting of both sea dikes and river dikes and inde-pendent load characteristics of the rivers and the seathe value Pf ,ring ≈ 0.185 might be an optimistic value.Taking it all in all the true frequency of failure of thedike ring as a whole might well exceed the design fre-quency of a two dimensional section by a factor 10. Forthe Vietnamese situation a factor of at least 5 (prefer-ably 10) should be adopted for the choice of the designfrequency.

Besides of the length effect, the true frequency offlooding depends on the total number of dike rings inViet Nam too. The probability of flooding in a countrywill increase according as the number of dike ringsincreases. This effect may be considered in the sameway as the length effect.The more dike rings in a coun-try, the more severe the requirements should be to thesafety level of each dike ring on its own.

4.2 Example of Namdinh sea defence system

4.2.1 Present situation and protection strategyThe NamDinh Province constitutes part of the RedRiver Delta in Northern part of Vietnam. The totallength of Namdinh coastline is about 90 km sufferingfrom severe erosion and serious damages of coastaldefences. This can be considered as the representativefor coastal problems in the region. The coastline ismainly protected by dikes and revetments.

The failure of the sea dikes and revetments occursfrequently due to actions of severe typhoons, strongwaves in combination of high tides while their designparameters were not sufficient. Moreover due to theaction of waves and currents the foreshore erosion hasoccurred seriously which also leads to the collapse ofdikes and the revetments.

In response the central and local authorities haveundertaken some efforts in order to restrain the pos-sible adverse consequences and as future defensive

Figure 6. Schematization of Namdinh sea dike system.

measures, some sections of new sea dikes had beenbuilt. However, such efforts still remain limited toreactive and temporary measures.

The dike system is characteristically positioned asshown in Figure 6 with two defensive lines and sepa-rated section by section with sub-crossing dikes. Whena breach takes place at the main dikes, the sub-crossingdikes can limit flooding areas and the second dikes willbe a new first line of the system. The distance betweentwo defensive lines is about 200 meters.

Due to budget constrains, lack of information on thesea boundary conditions and suitable design method-ology as well as strategic and long-term solutions, thedike system was usually designed and constructed inpoor conditions.As the consequence, the system couldbe destroyed once in every 10 years. Therefore the costof dike maintenance is finally very extensive. Statis-tically, for maintenance of Namdinh sea dikes systemit is represented nearly 95 percent of the total coastaldefence budget of Vietnam.

4.2.2 Possible failure mechanismsNamdinh sea dikes are selected in this study as themost typical sea defence system in Northern Vietnam.Possible failure mechanisms of Namdinh sea dikes arevarious. For more detail on failure description, see alsoin Mai et al., 2004. Due to lack of information and timelimited, in this paper, the following dominant failuremodes are discussed:

1 – overtopping; 2 – instability of slope protection;3 – geotechnical instability of inner and outer slope; 4– scour induced dike failure and; and 5 – piping.

Hypothesis: The failure of the dike system will notoccur if all dike sections, which are consecutive andforming the dike system, are stable. For a dike sectionthe failure may occur since there will be presented oneof any failure mechanisms. The fault tree of the dikes,in this case, is shown similarly on Figure 3.

4.2.3 Reliability analysisFollows the method given above, the reliability ofNamdinh sea dike system is conducted from reliabil-ity analysis of all dike sections. For each of those theconsideration is taken of five given possible failuremechanisms. The reliability functions of these failuremechanisms are given in Table 2. Statistic descriptionof related variables are listed in appendix table. Using

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Table 2. Limit state functions of related failuremechanisms.

F.M. Limit state function Criteria based

1 Z = Zc − Zmax =Zc − (MHWL + Surge + 2% Run-upS.L.Rise + Z2%)Zc − (MHWL + Surge + 1 l/s/m overtopS.L.Rise + Zq)

2 Z = (Hs/�D)R − (Hs/�D)SZ = {φ*�*D} − Pilarczyk’sHs*(tan α/SQRT(S0))b/cos α

Z = {8.7*P0.18*(S/N0.5)0.2* Van der Meer’s*(tan α/SQRT(S0)) − 0.5} −{Hs/�/D}

3 Z = SF − 1 Bishop’s4 Z = hprotected − hscour holes Summer & Fredsoe5 Z1 = ρc*g*d − ρw*g*�H Ruptured criteria

Z2 = m*Lt/c − �H Bligh’s criteria

Table 3. Failure probability of Namdinh sea dikes.

Failure mode\case Old dikes Actual dikes

a. Dikes with slope protection by rock revetment:Overtop overflowing 0.4740 0.0474Armour failure 0.4730 0.0157Sliding Outer Sl 3.1E-5 3.1E-5Sliding inner Sl 0.005709 0.005709Piping 3.0E-12 3.0E-12Scour depth exceed 0.068 0.068Upper bound Pf 0.96 0.14

b. Dikes with slope protection by block revetment:Overtop overflowing 0.6320 0.0464Armour failure 0.1320 0.0123Sliding Outer Sl 3.1E-5 3.1E-5Sliding inner Sl 0.005709 0.005709Piping 3.0E-12 3.0E-12Scour depth exceed 0.068 0.068Upper bound Pf 0.78 0.13

FORM these reliability functions given the results inTable 3. Extensive description of the failure mech-anism, statistical load and strength boundaries andformulation of reliability functions can be found inMay 2004.

4.2.4 Reliability-based design valuesTotal length of Namdinh sea dikes is 90 kilometers.Total number of sections is 30, with each section lengthof 3000 meters. Design frequency of whole system canbe obtained from the actual sea dike design standard ofVietnam: p = 1/20 = 0.05. Applying equation (18) thefailure probability of a single section is determined:Pfsec. = 0.0186 <=>1/55 years.

Assuming that proportion of every failure mech-anisms contributes to the total failure probability of

Table 4. Design values of interested parameters permechanism.

F.M. ArmourDesign value Overt. failure Sliding Scour

Contrib.sec. 40 45 0.004 0.5 14failure (%)Failure Prob 0.0074 0.00837 10−7 6.10−4 0.0026[year−1]Parameter Zcrest[m] Dn50[m] m1[-] m2[-] hscour[m]Design value 8.60 0.95 3.65 2.92 1.34

a section is similar to the previous case. The failureprobability of each failure mechanism can be derivedfrom Pfsec.. Since acceptable probability of the fail-ure is known, applying reliability-based approach, thedesign parameter can be determined.

In this case, Pfsec. = 0.0186, the design values ofinterested parameters are obtained in Table 4.

5 DISCUSSIONS

Most of the existing design of sea dikes and revetmentsin Vietnam were based on the old design methods(standards), which no longer be used nowadays, andwere constructed under poor conditions of execu-tion, quality control, investment and management.Thefuture effect of boundary condition was normally notaccount for (e.g. increase in water depth due to fore-shore erosion and morphological changes, occurrenceof scour holes, settlement of dike body and sea levelrise, etc…).As the result the design load boundary wasunderestimated. The strength of the dikes is insuffi-cient to the actual condition. Consequently, the failuresof sea dikes often occur even with lower design storms.

The failure probability of the old dikes in Namd-inh, which were applied old design codes, is very highat 96%. This means that the old dike could be fault1/0.96 ≥ 1 time per year. This is unacceptable safetylevel by any safety regulations. Obviously, the dikeswere constructed from 2-dimensional design with lowdesign frequency (1/20 years) of which the lengtheffect were not taken into account. If this would beaccount for, the design frequency of each dike sec-tion should be decrease to Pfsec. = 0.0186 accordingto (18). It corresponds to return period of about 55years (instead of 20 years) for Namdinh case. There-fore the risk of the old system is increased by factor 3.For the coming design of Namdinh dikes, if the designfrequency of inundation due to dike failure is p(%),then the design frequency of every section should be atmost of one third of p(%).The actual dikes were designwith return period of 20 years. However the probabil-ity of inundation due to dike failure is given muchhigher, about p = 0.14 (see Table 3). This corresponds

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to failure occurrence of once in 7 years instead of0.05 = 1/20 years.

The failures of the sea dikes mostly cause byovertopping and/or instability of armour layer and sub-sequently by scour induced failures. The probabilitiesof failure of the dikes due to slopes sliding and pipingmodes are relatively small comparing to others.

The probabilistic results in this example are com-parable in good way with the results from determin-istic assessment. Reasonably, this exacts that what ishappening at Namdinh dikes in the last few years.

Conceptually, the design values of some interestedparameters are given from reliability based-design forthe similarly boundary conditions. However these arejust determined by a simplified model which takeninto account only two random variables. For moreproper results a sophisticated reliability model shouldbe applied and need more further studies.

6 CONCLUSIONS ANDRECOMMENDATIONS

This study reviews partially existing methods of relia-bility and risk based approaches which applied in thefield of flood defences and coastal protection.The reli-ability analysis starts with a fault tree at the lowestlevel. Overall failure probability of the system is cal-culated at the top level of the tree. The reliability baseddesign is an essential design tool for flood defence andcoastal protection when having a pre-defined failureprobability and the geometry of the structure needsto be found in order to fulfill the design requirementin combination with minimisation of the constructioncost of the system. On the other hand, if the geome-try of every component of the flood defence systemis known and the joint probability distribution of loadand strength variables is quantified, the probability offailure of the system can be found. This can be appliedfor technical management purpose to determination ofsafety levels of any existing system and to find out theweaker/weakest points of the system.

Additionally in risk-based design the effectivenessof the protection system as a function of its failureprobability can be modeled.The two main componentsof the model are the cost of protection and a character-istic value of the consequences of flooding, both as afunction of the probability of failure. This model couldbe a powerful tool supporting decision process to set(or re-set) the safety levels of protection in relation toinvestment levels and acceptable consequences for anyscale of protection system.

Application of reliability and risk analysis in theseexample cases given interesting results. Regarding tothe case of Namdinh coastal protection, followed thereliability based approach with its specific fault tree,the actual relative low safety level of the whole system

were figured out. Analysis shows that the failure mayoccur once every year at the existing old-design dikesections and about 7 years with the actual dikes. Thissafety levels are unacceptable with Vietnamese actualdesign codes (once in every 20 years). The effect ofsystem length to probability of failure was clearly indi-cated by the case of Hai Phong dike ring. From thatone can realize that with 2-dimensional design (no con-sideration of system length) the actual safety level ofwhole system may reduce by factor 10 or more!

Reliability and risk analysis in the field of flooddefence and coastal protection has been developed/developing effectively in some developed countries.Applying this modern approach in the same fieldin developing countries, therefore, should be imple-mented. Especially for the country where the safetylevels of the actual flood protection are relatively lowand safety regulations are not usually clear defined. Ageneral framework of implementation of state of theart is thus important. Specific reliability and risk basedmodels should be developed in those countries whichshould account for some developing characteristics(e.g. limited initial investment, cheaper man power,fast economic growing) and some limitations of dataavailability, lack of modern construction equipments,poor professional knowledge etc. This may becomean interesting topic for the future researches. Beside,extensive studies on determination of sea boundaries,interaction between them and the coastal defensivesystem as well as descriptions of their failure mech-anisms in relations to their physical processes shouldalso be carried out.

REFERENCES

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Burcharth, H.F., Sørensen, J.D. & Christiani, E. 1995. Appli-cation of reliability analysis for optimal design of verticalwall breakwaters. Proceedings of the International Con-ference on Coastal and Port Engineering in DevelopingCountries (COPEDEC).

Central committee for flood and typhoon 1996. Announce-ment on typhoon No. 2. Hanoi, 23rd August 1996.

CUR 1988. Probabilistic design of flood defences. Gouda,Netherlands.

Disaster management working group (DMWG)- JointAssessment of Disaster needs 2005. Rapid Needs Assess-ment in Thanh Hoa, Ninh Binh and Nam Dinh provinces,hit by typhoon Damrey (STORM No. 7), 28–29 September2005.

Ditlevsen, O. 1979. Narrow reliability bounds for structuralsystems. Journal of Structural Mechanics, pp. 453–472.

Gelder, P.H.A.J.M. van 1999. Statistical Methods for theRisk-based design of Civil Structures. PhD-thesis. DelftUniversity of Technology 1999.

Mai, C.V. 2004. Safety assessment of sea dike in Vietnam,M.Sc-thesis. Unesco-IHE, Delft, The Netherlands, 2004.

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Mai, C.V. & Pilarczyk, K.W. 2005, Safety aspect of sea dikesin Vietnam-A Namdinh case study. Conference Proceed-ing of International Symposium on Stochastic Hydraulics.IAHR Paseo Bajo Virgen del Puerto 3, 28005 Madrid,Spain 2005.

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Oumerarci, H. Allsop, N.W.H., Groot, M.B. de, Crouch,R., Vrijling, J.k., Kortenhaus, A. & Voortman, H.G.2001, Probabilistic design tools for vertical breakwaters,Balkema, Rotterdam, 2001.

Pilarczyk, K.W. 1998. Dikes and revetments, Design,maintenance and safety assessment. Rijkswaterstaat,A.A.Balkema/Rotterdam/Brookfield, 1998.

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Voortman, H.G. 2002. Risk-based design of large-scaleflood defence systems. PhD-thesis. Delft University ofTechnology.

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Vrijling J.K. & Hauer M. 2000. Probabilistic design and riskanalysis of water defenses in relation to the Vietnamesewater defense system. Delft University of Technologyand Delft Cluster.

Vrijling, J.K., Hengel, van W. & Houben, R.J. 1998. Accept-able risk as a basic for design. Journal of ReliabilityEngineering and System Safety: pp 141–150. Elsevier1998.

Vrijling, J.K., Hengel, van W. & Houben, R.J. 1995, A frame-work for risk evaluation, Jounal of Hazadous Materials43, pages 245–261.

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Appendix: Statistical description of related random variables.

MeanNot. Description Unit Dist. value Std. dev.

φ Empirical factor -Pilarczyk – Norm 5 0.5ϕ Friction angle o Nor nom 20

ρc Saturated density of subsoil kG/m3 Deter 1800γsat. Soil unit weight (saturated) kN/m3 Nor nom 5%γunsat. Soil unit weight (unsaturated) kN/m3 Nor nom 5%ρw Water density kG/m3 Deter 10318.7 Model factor – norm 8.7 5%a Safety free board – Norm 0.5 0.05A Wave loads on outer slope kN Nor nom 50b Power factor – Norm 0.65 0.15B Transportation load on dike’s crest kN Nor 100 10C Cohesion kN/m2 Nor nom 5%cB Bligh constant – Deter 15cos α Cosine of slope angle – Norm 0.97 5%D Required block thickness/rock size m Deter nomd Thickness of the top layer m Norm 3.5 0.2Hs Wave height at toe of the dikes (1/20 years) m Lognor 2.0 0.35k Permeability m/s Deter. nomK� Reduction factor for slope roughness m Norm Nom 0.05Kp Transformed coefficient % of wave exceedance m deter 1.65 –Kw Coefficient of wind effect – deter 1 –Lk Seepage path length m Norm 48 5m Cotangent of slope angle – Norm 4 0.15md Model factor – Norm 1.67 0.33MHWL High tidal level (+MSL) m Norm 2.29 0.071N Number of storms – Deter 7000P Permeability factor – Norm 0.2 0.05S Initial damage level – Deter 2S0 Wave steepness – Deter 0.02SL.rise Sea level rise m Norm 0.1 0.05Surge Incr. W.level by storm m Weil 1.0 0.2tan α Tangent of slope angle – Norm 0.25 5%Tm Wave mean period s Deter nomZbed Design water level m Norm nom 0.2Zinland Inland water level m Norm 0 0.5

nom : normative value; Norm: Normal distributed; Weil: Weibull distributed; Deter: Deterministics; Lognor: lognormaldistributed.

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