International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Evaluation of decisions to rehabilitate South African dams in terms of the ANCOLD ALARP criterion and… Viljoen, Celeste; Reynolds, Sonel Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20151Evaluation of Decisions to Rehabilitate South African Dams interms of the ANCOLD ALARP Criterion and SWTP for HumanSafetyCeleste ViljoenSenior Lecturer, Dept. of Civil Engineering, Stellenbosch University, South AfricaSonel ReynoldsEngineer, Dept. of Water and Sanitation, South AfricaABSTRACT: Eleven case studies of dam rehabilitation projects in South Africa are evaluated in termsof quantitative risk assessment criteria (ANCOLD, 2003) and Society’s Willingness to Pay (SWTP)(Pandey, et al., 2006). Inspection and design reports on which the decisions to rehabilitate were basedwere made available by the Department of Water and Sanitation, South Africa, from where estimates ofpre- and posterior probabilities of failure, expected loss of human lives as well as cost of rehabilitationwere obtained. In all cases, ANCOLD’s ALARP criterion dictated that the (existing) dams berehabilitated. Only one of the eleven cases requires rehabilitation based on the SWTP criterion.  Theother cases either had a prohibitively high rehabilitation cost, an already low probability of failure priorto rehabilitation or low expected loss of lives in case of failure.1. INTRODUCTIONSouth African and international dam authoritiesbase their decisions to rehabilitate dams onseveral criteria, of which risk to human lives isan important one.  Internationally, the AustralianNational Committee on Large Dams’(ANCOLD’s) risk to human lives criterion,based on the ALARP principle, may beconsidered the most widely accepted. Thiscriterion accepts lower safety levels for existingdams, based on the argument that it isconsiderably more expensive to improve thesafety of existing structures compared to newones (ANCOLD, 2003).Target safety levels, as defined by theProbabilistic Model Code (JCSS, 2001) aresimilarly differentiated based on the relative costof implementing safety measures, with lowersafety levels being accepted when the relativecost is large.  These target safety levels havebeen derived based on monetary optimization(Rackwitz, 2000), while the ANCOLD criteriaare based on engineering judgment and pastexperience.The social acceptability of the structuraldesign in terms of risk to human life is, however,not necessarily guaranteed when relying on theANCOLD life safety criteria or the JCSS targetreliabilities. Figure 1 shows the interactionbetween monetary optimization and anacceptance criterion for risk to life. Within theacceptable region the optimization may beperformed by a private or societal decisionmaker, but the acceptance criterion always has tobe evaluated from a societal point of view. Theacceptance threshold can be defined based on themarginal life saving costs principle, using theLife Quality Index (LQI) net benefit criterion tojudge the efficiency of life saving measures froma societal point of view. Only efficientinvestments into life safety have to be performed,as dictated by the LQI based Society’sWillingness to Pay (SWTP), but higher safetylevels are of course also acceptable and may beaimed at if required by monetary optimization orother considerations. SWTP is a utility function12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20152which may be used to determine the level ofexpenditure into life safety required by society(Pandey, et al., 2006) and applied in this study todetermine the lower bound for acceptableinvestments in dam rehabilitation.  The costeffectiveness of rehabilitation work to provideincreased safety determines whether or not theinvestment is required. Economic optimizationwould often imply higher safety levels thanrequired by SWTP (Rackwitz and Streicher2002, Fisher et.al. 2012).Figure 1: The LQI acceptance criterion as aboundary condition for monetary optimizationThe content of the paper is outlined asfollows: ALARP criteria and their application indecision making regarding dam rehabilitationsare discussed in section 2. In section 3, SWTP isintroduced as a lower bound to acceptableinvestments in dam safety. Data for eleven casesof actual dam rehabilitations that were carriedout in South Africa is provided in section 4.Finally, in section 5 the decisions to rehabilitateare evaluated for these cases in terms of (a)internationally accepted ALARP criteria forexisting dams, (b) the lower bound for acceptablesafety as defined by SWTP. We conclude withshort discussions on the acceptability ofrehabilitation decisions taken, the factors thatinfluence the SWTP boundary and a comparisonof ALARP and SWTP criteria.2. ALARP CRITERIA AND DAMREHABILITATION DECISION MAKINGThe most commonly used format toquantitatively assess risk to human life is againstrisk acceptance criteria, presented as acceptancelines on a Farmer diagram, such as Figure 2.Farmer diagrams have a double-logarithmic scalewith the x-axis representing the number offatalities (N) and the y-axis representing theannual frequency (F) of N or more fatalitiesoccurring (Kroon and Maes, 2008).Risk located below the negligible line maybe regarded as broadly acceptable, while risklocated above the intolerable line should not beaccepted. In between the two criterion lines risksare regarded as tolerable only if they are reducedto be As Low as Reasonably Practicable(ALARP). The joined term "reasonablypracticable" can be interpreted as the degree ofrisk balanced against time, cost and physicaldifficulty of implementing risk reductionmeasures (Melchers, 2001).Figure 2: Illustration of typical implementation ofquantitative risk acceptance criteriaBall and Floyd (1998) presents an overview ofthe development and application of quantitativerisk to human life criteria from the 1960’s to the1990’s, focusing on developments in the UK,Hong Kong and the Netherlands: Acceptancelines are primarily defined by two properties,12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20153namely the intersection with the y-axis and thegradient of the line. The upper limit oftolerability is often set at 10-4 for 10 or morefatalities. The negligible acceptance line tends tobe located two or three factors of 10 (100 or1000) lower on the frequency (F) scale. For somecriteria, such as the criteria developed in HongKong, the acceptance lines are truncatedvertically and thus an upper limit for thepotential loss of life is defined. The gradient ofthe line represents the degree of risk aversion ofthe society (Kroon and Maes, 2008). Riskaversion is the additional public opposition to anevent which kills a large number of people over aseries of smaller events which collectively resultin the same number of fatalities. According toBall and Floyd (1998), most acceptance lineshave negative gradients of between −1 and −2.A gradient of −1, is termed ’risk neutral’, whilea steeper gradient implies risk aversion.Current application of conventionalacceptability criteria for risk to human life ininternational dam safety is reported in "RiskAssessment in Dam Safety Management"(ICOLD, 2005). In this survey the InternationalCommission on Large Dams (ICOLD) collectedresponses from 24 member countries. Of these,nine (Australia, Canada, Czech Republic,Germany, the Netherlands, New Zealand, SouthAfrica, United Kingdom and the USA) explicitlydiscuss risk criteria. Although many countriespresented a view and acknowledge that risk-based tools are useful within dam safety, thereare contradicting opinions on its application andmany countries are hesitant to clearly definequantitative acceptance criteria for risk to humanlife.2.1. ANCOLD CriteriaThe Australian Committee on Large Dams(ANCOLD), proposes risk acceptance criteria fornew and existing dams in their Guidelines onRisk Assessment (ANCOLD, 2003), as shown inFigure 3: The acceptance line for existing damsis one factor of 10 less stringent than for newdams, based on the argument that it isconsiderably more expensive to improve thesafety of existing structures compared to newones, i.e. it is not deemed reasonably practicableto reduce the risk of existing dams to the samelevels as new dams. Also, acceptance lines aretruncated horizontally, because currenttechnology does not allow for the construction ofdams with smaller probabilities of failure.Figure 3: ANCOLD risk acceptance criteria for newand existing dams3. SWTP AS A LOWER BOUND FOR DAMSAFETY3.1. BackgroundSociety’s Willingness to Pay (SWTP) is a utilityfunction which effectively determines the lowerbound for investments in life safety required bysociety (Pandey, et al., 2006). It is based on theLife Quality Index (LQI) which jointly considersthe social indicators of a nation to give a measureof the quality of life of a society (Pandey andNathwani, 2004). In a simple form, the LQI canbe written as = (1)where G represents the Gross Domestic Product(GDP) per person, E the life expectancy at birthand q is a parameter which reflects the trade-offplaced on consumption and the value attached tolength of life. The parameter q depends on thefraction of time spent producing G, and theremaining time, the leisure time, available for theenjoyment of E.12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20154An investment in life safety should lead toan improved life quality. A small change in theLQI due to the implementation of a safetymeasure is shown as= + (2)where dG corresponds to the monetary cost ofimplementing the project (negative), dE thechange in the life expectancy due to a change inthe risk associated with the project and K = 1/q.The LQI net benefit criterion requires thatan investment into life safety, which influencesboth G and E, should lead to a positive change inthe LQI, i.e. dL/L≥0 . SWTP defines the lowerboundary for acceptable decisions and may beobtained as the exact value (dL/L = 0) ofEquation 2:−dG ≥ SWTP = GK ≈ GKC dμ (3)Society requires that an investment, −dG, into alife-saving activity should at least be equal to theSWTP for a marginal increase in life expectancy(Fischer, et al., 2011). The parameter dE/E maynot always be easily quantified and instead itmay be calculated as the product of the mortalitychange (dμ) and a demographic constant (Cx).The demographic constant takes age-averagingand discounting into account (Lentz, 2007).3.2. Estimation of SWTPCountry specific values of SWTP may bederived, but South Africa does not conform wellwith the preferences underlying the LQIprinciple, i.e. the joint development of health andlife safety (life expectancy at birth), economy(GDP per person) and the necessary time to work(described by q as the ratio of work time toleisure time) .In this study the Earth value for SWTP(ESWTP) (Faber and Virgüez-Rodriguez, 2011)was used, assuming a 3% time preference ratefor consumption and a uniform mortalityreduction scheme. The ESWTP of $US517,000/life amounts to R 4.048 million/life,based on the average R/$ exchange rate for theperiod 2006 to 2011, during which time the damrehabilitations described in section 4 werecarried out.3.3. SWTP in dam safetySWTP dictates that investments should be madeinto all life saving measures which areconsidered efficient by society, i.e. where thecost per marginal life saved is less than theSWTP threshold. In the dam rehabilitationprojects considered here, rehabilitations wouldbe efficient (and required) if∆∆ ≤ (4)where ∆ is the annualized cost of rehabilitationover the design life and ∆ is the correspondingreduction in annual expected loss of life.  Thereduction in annual expected loss of life ∆ isrealized based on the reduction in the annualprobability of dam failure achieved throughrehabilitation, multiplied by the estimated loss oflife (LL) in case of dam failure∆N = p , − p , . LL (5)The South African Department of Water andSanitation (DWS) assumes the annual probabilityof dam failure after it has been rehabilitatedP , to be between 10-5 and 10-6 per year,equivalent to a well-engineered dam with noknown deficiencies (Oosthuizen et al., 2002).For a given rehabilitation investment to beconsidered efficient, a minimum reduction ∆ inthe expected loss of human lives are required(Eq.4). Equation 5 then implies that arehabilitation investment may be consideredinefficient because;a) the achieved reduction in the probability ofdam failure is too small. This may in turn bedue to an ineffective rehabilitation strategy,or because the initial probability of failure isalready small.b) the expected number of lost lives (LOL) incase of failure is already so low that achange in failure probability does little toimprove the expected ∆12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20155For a given dam rehabilitation project, with∆C, p , and p , known, a threshold valueLL may be calculated, which can be usedtogether with p , to locate an FN-SWTP-criterion line on the Farmer diagram, assuming arisk neutral gradient of one. For such a project, ifthe expected LL in case of dam failure is morethan the threshold value (LL ) therehabilitation project is required by society.Section 5.2 details this assessment for elevendam projects.4. CASE STUDIESA 2004/05 the South African Department ofWater Affairs study concluded that 166 of the314 government owned dams was in need ofrehabilitation. The study prompted spending onrehabilitations that amounted to over R1.5 billionby 2012 with 19 dams being rehabilitated in full(Segers, 2012). Initial inspection reports andrehabilitation design reports were made availablefor eleven of these and is used here as casestudies.Table 1: Estimated risk to human life for dams priorto rehabilitationDamEstimatednumber oflost lives( )Priorprobabilityof failure( , )Min Max Min MaxBospoort (Sluiceopen) 9 13 1e-3 1e-2Bospoort (Sluice fail) 9 13 1e-2 1e-1Klein Maricopoort 3 5 1e-4 1e-3Toleni 2 3 5e-4 5e-3Lakeside 200 400 2e-4 2e-3Vaalkop 35 350 2e-5 2e-4Rust de Winter 13 13 5e-5 5e-4Makotswane 5 8 3e-4 3e-3Kromellenboog 18 19 2e-4 2e-3Albert Falls 100 170 1e-4 1e-3Glen Brock 21 29 1e-3 1e-2Wentzel 156 312 1e-3 1e-2DWA estimates of the initial probability offailure P , and loss of life (LL) in case ofdam failure were obtained as intervals fromDWA dam safety inspection reports, as shown inTable 1. Note that for Bospoort Dam twoscenarios were considered in the DWA riskanalysis, namely 1a) sluice gates functionnormally during dam failure, and 1b) sluice gatefailure.Rehabilitation design reports provided theestimated total costs of safety improvements,which were annualized over a 50 year design lifeat an interest rate of 7%, as detailed in Table 2.Table 2: Estimated cost of rehabilitationDamEstimatedcost ofrehabilitationAnnualisedcost ofrehabilitation(Rm/yr)Bospoort R 84 342 000 R 6.11mKlein Maricopoort R 39 330 000 R 2.85mToleni R 23 662 000 R 1.71mLakeside R 25 194 000 R 1.83mVaalkop R 24 225 000 R 1.76mRust de Winter R 21 318 000 R 1.54mMakotswane R 16 956 000 R 1.23mKromellenboog R 19 157 000 R 1.39mAlbert Falls R 16 530 000 R 1.20mGlen Brock R 17 600 000 R 1.28mWentzel R 14 250 000 R 1.03m5. EVALUATION OF REHABILITATIONDECISIONS5.1. Comparison to ANCOLD criteriaRisk to human life was estimated by DWS foreleven dams in need of rehabilitation, as detailedby the intervals reported in Table 1. These prior-to-rehabilitation intervals can be used to positionthe eleven South African dams on the ANCOLDFN-criteria graph, so that each project is depictedby a block, as shown on Figure 4.Figure 4 can be used to evaluate theseprojects in terms of the ANCOLD acceptabilitycriteria. It is clear that, according to ANCOLD,the decisions to rehabilitate are justified as noneof the dams adhered to acceptable risk levels forexisting dams prior to rehabilitation.12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20156Figure 4: DWA rehabilitation projects compared to ANCOLD FN-criteria as well as to their project specificFN-SWTP-criteria lines5.2. Comparison to SWTP criteriaFN-SWTP-criterion lines were generated foreach of the eleven case studies, based on theprocedure described in Section 3.3.  Accordingly,it can be seen in Figure 4 that most of therehabilitations were not required by society.Based on the average cost per marginal life saved(∆ ∆ ), only the rehabilitation of Wentzel dam(11) is required by society.  Table 3 provides theaverage cost per marginal life for the eleven casestudies, ranging from R 0.8 million up to R 1 308million per marginal life.Of course, it should be reiterated here thateven when dam rehabilitation work is notrequired by society, it may still be consideredbased on economic, environmental, or otherconsiderations in addition to safety.The position of each criterion line dependsonly on the rehabilitation cost and SWTP.Criterion lines would become more stringentwith increased SWTP or decreased rehabilitationcost.  Correspondingly, the most stringent FN-SWTP-criterion is associated with Wentzel Dam,which has the lowest annualized rehabilitationcost, while the least stringent FN-SWTP-criterion is associated with Bospoort Dam, whichhas the highest annualized rehabilitation cost.It is interesting to note that, for Bospoort Dam,the FN-SWTP lines intersect the vertical axis at apositive value, which would imply that at theserehabilitation cost levels, society deems morethan one expected death per annum acceptable.At very high values of expected loss of life, the12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20157SWTP lower bound would require higher safetylevels than currently accepted by ANCOLD.Table 3: Average cost per marginal life savedthrough dam rehabilitation projectsDam Average ∆(lives/year) Marginal lifecost∆ ∆(R/life)Bospoort 6.04e-2 R 101m6.05e-1 R 10mKlein Maricopoort 2.18e-3 R 1 308mToleni 6.86e-3 R 250mLakeside 3.28e-1 R 5.6mVaalkop 2.01e-2 R 87mRust de Winter 3.50e-3 R 441mMakotswane 1.07e-2 R 115mKromellenboog 2.02e-2 R 69mAlbert Falls 7.35e-2 R 16mGlen Brock 1.37e-1 R 9mWentzel 1.29e-0 R 0.8m6. CONCLUSIONSThe decisions to rehabilitate eleven SouthAfrican dams were evaluated.  The decisions arejustified by comparison to ANCOLD riskacceptance criteria.  However, SWTP indicatesthat only one of the eleven rehabilitations wasrequired by society, with the SWTP thresholdlocated two to three factors of 10 (100 or 1000)higher on the frequency (F) scale than theANCOLD acceptance line for existing structures.The position of the FN-SWTP-criterion is damdependant and influenced primarily by the costof rehabilitation works and the SWTP value.Societal requirements for rehabilitation are thenlargely influenced by the initial probability offailure of the dam and the expected number oflost lives in case of failure.  This in turn impliesthat a rehabilitation investment may beconsidered inefficient because the achievedreduction in the probability of dam failure is toosmall, typically because the initial probability offailure is already fairly small; or because theexpected number of lost lives in case of failure isalready so low that a change in failureprobability does little to further reduce theexpected number of lost lives.In addition to life safety and economicconsiderations, the South African Department ofWater Affairs also considered socio-economic,social and environmental impacts in theirdecision to rehabilitate (Reynolds, 2013).Surprisingly however, the cost of rehabilitationworks does not form part of their decision. If andhow this cost should be included in the decisionframework needs consideration.7. ACKNOWLEDGEMENTSDWS is gratefully acknowledged for theirfinancial support and for providing the inspectionand design reports on dam rehabilitations.8. REFERENCESANCOLD (2003). “Guidelines on Risk Assessment”,Australian Committee on Large Dams.Ball, D.J. and Floyd, P.J. (1998). Societal Risks.Tech. Rep., Health and Safety Executive,United Kingdom.Faber, M.H. and Virgüez-Rodriguez, E. (2011).Supporting decisions on global health and lifesafety investments. Applications of Statistics andProbability in Civil Engineering.Fisher, K., Barnardo-Viljoen, C., and Faber, M. H.(2012), “Deriving target reliabilities from theLQI”, LQI symposium in Kgs. Lyngby,Denmark.ICOLD (2005). Risk Assessment – In Dam SafetyManagement, Bulletin 130. Tech. Rep.,International Committee on Large Dams.JCSS, Probabilistic Model Code: Part 1 - Basis ofDesign, Joint Committee of Structural Safety,Editor. 2001.Kroon, I.B. and Maes, A. (2008). TheoreticalFramework for Risk Assessment andEvaluation. Tech. Rep., Joint Committee ofStructural Safety (JCSS).Lentz, A., Acceptability of Civil EngineeringDecisions Involving Human Consequences,PhD thesis; Lehrstuhl für Massivbau derTechnischen Universität München. 2007,Technischen Universität München. p. 158.Melchers, R.E. (2001). On the ALARP approach torisk management. Reliability Engineering andSystem Safety, vol. 71, pp. 201–208.12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20158Oosthuizen, C., Elges, H.F.W.K. and Hattingh, L.C.(2002). Risk-based Rehabilitation of Dams. In:Proceedings 6th International Conference onConservation and Rehabilitation. 11-13November 2002,Madrid, Spain.Pandey, M.D. and Nathwani, J.S., 2004. Life qualityindex for the estimation of societal willingness-to-pay for safety. Structural Safety, 26(2), 181–199.Pandey, M., Nathwani, J., and Lind, N. (2006), “Thederivation and calibration of the life-qualityindex (LQI) from economic principles”,Structural Safety, 28(4), 341–360.Pandey, M., Nathwani, J., Lind, N. (2006). “Thederivation and calibration of the life-qualityindex (LQI) from economic principles”,Structural Safety, 28(4), 341–360.Rackwitz, R. (2000) Optimization — the basis ofcode-making and reliability verification.Structural Safety, 22(1): 27-60.Rackwitz, R. and Streicher, H. (2002). “Optimizationand target reliabilities”. JCSS Workshop onReliability Based Code Calibration.Reynolds, S. (2013). “Evaluating the decision criteriafor the prioritization of South African dams forrehabilitation in terms of risk to human lives”,M.Sc.Eng thesis, University of Stellenbosch,South Africa.

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