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

Economic optimization considerations in South African dam rehabilitations 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, 20151Economic Optimization Considerations in South African DamRehabilitationsCeleste ViljoenSenior Lecturer, Dept. of Civil Engineering, Stellenbosch University, South AfricaSonel ReynoldsEngineer, Dept. of Water and Sanitation, South AfricaABSTRACT: Economic optimization is applied to eleven case studies of actual dam rehabilitationprojects in South Africa. The optimization includes the cost of rehabilitation and damage- andcompensation costs for lives lost in case of dam failure. Economic motivation for the existence of thefacility is excluded from the optimization. Five of the eleven cases would require rehabilitation basedon economic optimization.  The other cases either had a prohibitively high rehabilitation cost, analready low probability of failure prior to rehabilitation or low expected loss of lives in case of failure.Costs to improve safety for the different cases was typically between ZAR 0.5 and 5 million perpercentage reduction in the probability of failure over a 50 year design life, but could be as high asR50m/%.  A high cost per percentage reduction is typically associated with dams that already had a lowprobability of failure prior to rehabilitation. Interesting to note when the outcome is compared to otherrehabilitation decision criteria is that ANCOLD’s ALARP criterion dictated that in all of the elevencases the dams be rehabilitated, while only one of the eleven cases would require rehabilitation basedon the Society’s Willingness to Pay utility function (Reynolds, 2013).  Surprisingly, the cost ofrehabilitation works is not considered as part of the South African Department of Water andSanitation’s (DWS's) decision framework. Rational incorporation of this cost needs consideration.1. INTRODUCTIONSouth African and international dam authoritiesbase their decisions to rehabilitate dams onseveral criteria, of which risk to human lives isan important one. The economic efficiency of theproposed rehabilitation work seems to be oflesser importance and is often not explicitlyconsidered. Ideally, these should beappropriately weighted in the decision process.This paper takes a first step towardsformulating how this may be possible, by firstapplying economic optimization principles toeleven case studies of actual dam rehabilitationprojects, comparing these economically feasibledecisions to what would be arrived at byalternative decision models, and discussing theinfluence of various contributing factors in thedecision framework.2. BACKGROUNDInternationally, the Australian NationalCommittee on Large Dams’ (ANCOLD’s) risk tohuman lives criterion, based on the ALARPprinciple, may be considered the most widelyaccepted decision criterion to motivaterehabilitation.  This criterion accepts lowersafety levels for existing dams, based on theargument that it is considerably more expensiveto improve the safety of existing structurescompared to new ones (ANCOLD, 2003).Society’s Willingness to Pay (SWTP) is autility function which may be used to determinethe acceptable level of expenditure into lifesafety required by society (Pandey, et al., 2006).The cost effectiveness of rehabilitation work toprovide increased safety determines whether theinvestment is required.12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20152Investments for improved safety could alsobe made for economic reasons.  Economicoptimization would often imply higher safetylevels than required by SWTP (Rackwitz andStreicher, 2002; Fisher, 2012).In addition to life safety and economicconsiderations, the South African Department ofWater and Sanitation also considers socio-economic, social and environmental impacts intheir decision to rehabilitate. Surprisinglyhowever, the cost of rehabilitation works is notconsidered.The eleven case studies considered here aredam rehabilitation projects carried out between2006 and 2011 by the Department of Water andSanitation (DWS) within South Africa.Inspection and design reports on which thedecisions to rehabilitate were based were madeavailable by DWS, from where estimates of pre-and posterior probabilities of failure, loss ofhuman lives and damage in case of failure, aswell as cost of rehabilitation were available.3. MONETARY NET BENEFIT OFREHABILITATIONFor typical engineering facilities the monetarynet benefit function is expressed by Rackwitz(2002) as( ) = ( ) − ( ) − ( ) (1)In the case of a rehabilitation project, ( ) is thebenefit derived from the extended existence ofthe facility, C(p) is the cost of rehabilitationworks, D(p) is the change in the expected cost offailure of the facility and p is the vector of allsafety relevant factors particular to therehabilitation project under consideration.It is assumed here that rehabilitation doesnot extend the useful life of the facility, so B(p)is assumed to be zero, i.e. economic motivationsfor the existence of the facility is excluded fromthe optimization.Rehabilitation should generally lead to alowered probability of failure P of the facility,resulting in a reduction in the expected cost offailure.  Thus, D(p) should be negative,calculated as shown in Section 3.1 (Eq. ( ) =( ) − ( ) (5) and making apositive contribution to the net benefit Z(p).Positive net benefit ( ) impliesrehabilitation alternatives that are economicallyfeasible.  In this study eleven actual damrehabilitations are assessed to determine whetheror not the decisions to rehabilitate were justifiedfrom an economic perspective.3.1. Expected cost of failureDirect- and indirect economic losses in case ofdam failure are estimated as part of SouthAfrican dam safety evaluations. Direct economiclosses could include the damage to the structure,loss of agriculture and the costs of emergencyrelief, while the indirect economic losses couldinclude the loss of future benefits of the facility(Oosthuizen, 2002). The number of lost humanlives ( ) is also estimated as part of each damsafety evaluation.According to Lentz (2007) compensation forlost lives should be included in the cost offailure. The Societal Value of a Statistical Life(SVSL) may be used as an estimate ofappropriate compensation for a lost life, based onsocietal preferences. The societal preferencesreferred to here are those underlying the LifeQuality Index (LQI) principle as defined byPandey, et al. (2006), i.e. the joint developmentof health and life safety (life expectancy at birth),economy (GDP per person) and the necessarytime to work.Faber and Virguez-Rodrigues (2011) estimatesan Earth value for SVSL ( ) based onobservations from 71 countries, representingmore than 70% of the Earth population.  Theof $US 629,000 used in this work isbased on a rate of time preference forconsumption of 3% (Arrow, 1995) and a uniformmortality reduction scheme. It is converted toSouth African Rands at the average R7.83/$exchange rate for the period under consideration.The total cost of failure c is determined bycombining the components above as follows= + + . (2)12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20153Table 1: Dam failure cost- and probability estimates from the relevant dam safety evaluation reportsDamEstimated economic cost of failure Estimatednumber of lostlives( )Priorprobability offailure( ( )) Year ofestimate( )Direct( ) Indirect( )Min Max Min Max Min Max Min MaxBospoort (Sluice open) R 3m R 6m R 30m R 60m 9 13 1e-3 1e-2 2005Bospoort (Sluice fail) R 3m R 6m R 30m R 60m 9 13 1e-2 1e-1 2005Klein Maricopoort R 3.9m R 39m R 3m R 3m 3 5 1e-4 1e-3 1999Toleni R 0.06m R 0.6m R 0.6m R 5.8m 2 3 5e-4 5e-3 2000Lakeside R 6.7m R 67m R 67m R 671m 200 400 2e-4 2e-3 1999Vaalkop R 15m R 150m R 150m R 1500m 35 350 2e-5 2e-4 2000Rust de Winter R 2.1m R 21m R 21m R 209m 13 13 5e-5 5e-4 1994Makotswane R 1.6m R 18m R 16m R 180m 5 8 3e-4 3e-3 2005Kromellenboog R 70m R 700m R 700m R 7000m 18 19 2e-4 2e-3 2005Albert Falls R 20m R 40m R 60m R 2000m 100 170 1e-4 1e-3 2004Glen Brock R 5m R 10m R 20m R 40m 21 29 1e-3 1e-2 2006Wentzel R 0.55m R 5.5m R 5.5m R 55m 156 312 1e-3 1e-2 1994The failure probability in year is the product ofthe annual probability of failure and theprobability that no dam failure occurred up toyear , thus= 1 − (3)The expected cost of failure is thendetermined from( ) = ∑ ( )( ) (4)where the discount rate is taken as 3% (Arrow,1995) and the remaining service life of therehabilitated facility is assumed to be 50 years.The change in the expected cost of failure ofthe facility is computed as( ) = ( ) − ( ) (5)where is acknowledged that rehabilitationwill improve the safety features of the dam, thusimproving the probability of failure from its priorvalue ( ) to its post rehabilitation value( ) , that respectively feeds intoEquation 4.The estimates of losses and ( ) aresummarized in Table 1, as determined from thevarious dam safety evaluations for the elevencase studies.According to Oosthuizen (2002) it may beassumed that the probability of failure afterrehabilitation ( ) may be assumed to beequivalent to that of a new dam, i.e. between1 and 1 .3.2. Cost of rehabilitationOnce a decision to rehabilitate has been reached,the design of suitable rehabilitation works willcommence. It is only at this stage that a costestimate for C(p) becomes available, as providedin Table 2.Table 2: Estimated cost of rehabilitationDamEstimated costofrehabilitation( ) Year ofestimate( )Rehabili-tationcomplete( )Bospoort R 84 342 000 2007 2009KleinMaricopoort R 39 330 000 2008 2011Toleni R 23 662 000 2007 2010Lakeside R 25 194 000 2008 2009Vaalkop R 24 225 000 2006 2007Rust de Winter R 21 318 000 2008 2010Makotswane R 16 956 000 2006 2008Kromellenboog R 19 157 000 2008 2009Albert Falls R 16 530 000 2008 2010Glen Brock R 17 600 000 2009 2010Wentzel R 14 250 000 2007 200812th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20154It is interesting to note therefore that thecost of rehabilitation is not considered by theSouth African Department of Water andSanitation as part of their decision to rehabilitate.3.3. Time value of moneyEstimates of the different cost componentsmentioned in Sections 3.1 and 3.2 above aremade at different times during the decisionprocess, as indicated in Figure 1 and Tables 1and 2.Figure 1: Timeline for dam rehabilitation projectAll cost components ( , , and( )) are discounted to their worth in the year inwhich rehabilitation works are completed ( ),using basic economic principles, so that= (1 + ) (6)where is the year in which the relevant costcomponent was estimated.  An inflation rateof = 5% was used as appropriate for SouthAfrica.3.4. ResultsThe net benefit Z(p) as per Equation 1 wascalculated for each of the eleven dams.However, since bands of possible values wereestimated for several of the input parameters asindicated by the min/max columns in Table 1,three estimates of net benefit were made for eachdam, namely a best case (B), worst case (W) andaverage (A). The best case net benefit Z (p) wasestimated using maximum estimates forp (p ) and c with the minimum estimate forp (p ) , to obtain a maximum estimate forD(p) . Conversely, the worst case net benefitZ (p) was estimated using minimum estimatesfor p (p ) and c with the maximum estimatefor p (p ), to obtain a minimum estimate forD(p).  The average net benefit Z (p) was takenas the average of the two cases above.The estimates for Z(p) are provided inTable 3. Positive net benefits Z(p) arehighlighted and imply rehabilitation alternativesthat are economically feasible.Table 3: Estimated net benefitDamNet BenefitBest caseZ (p) Worst caseZ (p) AverageZ (p)Bospoort(Sluice open) -R 62m -R 91m -R 77mBospoort(Sluice fail) R 16m -R 75m -R 29mKleinMaricopoort -R 25m -R 45m -R 35mToleni -R 24m -R 27m -R 26mLakeside R 126m -R 21m R 52mVaalkop -R 6m -R 25m -R 16mRust de Winter -R 16m -R 23m -R 20mMakotswane R 1m -R 18m -R 9mKromellenboog R 462m -R 15m R 224mAlbert Falls R 74m -R 17m R 28mGlen Brock R 25m -R 15m R 5mWentzel R 335m R 4m R 170mOnly five of the eleven dams requirerehabilitation based on the average expected netbenefit, with Wentzel dam being the only one forwhich rehabilitation is feasible even for the worstcase estimate of net benefit.The cases for which rehabilitation was notdeemed feasible either had a prohibitively highrehabilitation cost, an already low probability offailure prior to rehabilitation or low estimatedloss of lives in case of failure. In the case ofKromellenboog dam, the high economic losses incase of failure contributed significantly to itsrehabilitation being economically feasible, inspite of fairly low values for p (p ) and .It should be noted that rehabilitationprojects will often extend the remaining useful12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20155life of a facility.  This benefit ( ) was ignoredin this study, but will of course increase themonetary net benefit of such a project, thusmaking it more likely to be economicallyfeasible.3.5. Comparison to other criteria3.5.1. 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 2: The acceptable annual probability offailure for existing dams is ten times lessstringent than for new dams, based on theargument that it is considerably more expensiveto improve the safety of existing structurescompared to new ones, i.e. it is not deemedreasonably practicable to reduce the risk ofexisting dams to the same levels as new dams.Also, acceptance lines are truncated horizontally,because current technology does not allow forthe construction of dams with smallerprobabilities of failure.Target safety levels for buildings, as definedby the Probabilistic Model Code (JCSS, 2001)are similarly differentiated based on the relativecost of implementing safety measures, withlower safety levels being accepted when therelative cost is large.  These target safety levelshave been derived based on monetaryoptimization (Rackwitz and Streicher, 2000),while the ANCOLD criteria are based onengineering judgment and past experience.The eleven South African dams are alsoshown on Figure 2, positioned based on theirprior-to-rehabilitation data. Each block ishighlighted in accordance with the findings ofTable 3, i.e. the darker the highlight, the moreeconomically feasible the rehabilitation.It is clear that the decisions to rehabilitatewere justified based on the ANCOLD safetycriteria. Rehabilitation will decrease the dams’annual probabilities of failure, thus loweringeach block to a position between 1 and 1 ,which would make them acceptable in terms ofthe ANCOLD criteria.The ANCOLD criteria do not seem toresemble target safety levels that correspond toeconomically optimum values, although theinclusion of realistic estimates for ( ) maybring these closer.  It may be useful to derivetarget safety levels based on monetaryoptimization for dams, similar to what was donefor buildings by Rackwitz and Streicher (2000).From Figure 2 it seems that rehabilitationbased on economic optimization becomesdifficult to justify for dams with an annualprobability of failure lower than ≤ 1 , orwith consequences of failure of less than fifteenlives.3.5.2. SWTP criteriaThe social acceptability of the structure in termsof risk to human life is not necessarilyguaranteed when relying on the ANCOLD lifesafety criteria or the JCSS target reliabilities.The acceptance threshold can be definedbased on the marginal life saving costs principle,using the Life Quality Index (LQI) net benefitcriterion to judge the efficiency of life savingmeasures from a societal point of view.  Onlyefficient investments into life safety have to beperformed, as dictated by the LQI-basedSociety’s Willingness to Pay (SWTP), but highersafety levels are of course also acceptable andmay be aimed at if required by monetaryoptimization or other considerations.The SWTP utility function (Pandey, et al.,2006) is applied by Reynolds (2013) 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 optimization would often implyhigher safety levels than required by SWTP(Rackwitz and Streicher, 2002; Fisher,2012) and this is confirmed here:Only Wentzel dam required rehabilitationbased on SWTP (Reynolds, 2013).12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20156Figure 2: South African dam rehabilitation projects overlaid on ANCOLD safety criteria4. REHABILITATION EFFICIENCYThe ANCOLD criteria acknowledges the factthat safety improvements for existing structuresare less cost efficient than for new structures.  Anattempt is made here to quantify the costefficiency of typical rehabilitation measures byconsidering the eleven South African casestudies.The rehabilitation costs were normalizedwith respect to the change in the 50 yearprobability of dam failure , achieved throughrehabilitation, where, = 1 − (1 − ) (7)Since DWS provide a range (min, max) estimaterespectively of the initial- and final annualprobability of failure, the average value for eachwas used here.Table 4 reports the cost per percentagereduction in the probability of dam failure over a50 year remaining service life, for the elevencases.  The normalized cost varies typicallybetween R0.5m- and R5m per percentage, butcould be as high as R 50m/%.  A high cost perpercentage reduction is typically associated withdams that already had a low probability of failureprior to rehabilitation.The wide range of normalized rehabilitationcosts show that even within existing dams,significant differences exist in the costeffectiveness of rehabilitation measures.  Thecurrent ANCOLD differentiation between “new”and “existing” structures aim to account for thedifference in cost effectiveness of rehabilitation12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20157measures, but it may be prudent to refine thisdifferentiation in risk acceptance criteria tosomething that can be better quantified.Table 4: Normalised cost of rehabilitationDamCost ofrehabili-tation( ) Changein ,∆ ,Normalised costof rehabilitation( ).∆ ,Bospoort R 93m 2.41e-1 R 3.9m/%Bospoort R 93m 9.41e-1 R 1.0m/%KleinMaricopoort R 46m 2.69e-2R 17.0m/%Toleni R 27m 1.28e-1 R 2.1m/%Lakeside R 26m 5.33e-2 R 5.0m/%Vaalkop R 25m 5.21e-3 R 48.8m/%Rust de Winter R 24m 1.34e-2 R 17.6m/%Makotswane R 19m 7.90e-2 R 2.4m/%Kromellenboog R 20m 5.33e-2 R 3.8m/%Albert Falls R 18m 2.69e-2 R 6.8m/%Glen Brock R 18m 2.41e-1 R 0.8m/%Wentzel R 15m 2.63e-1 R 0.6m/%5. CONCLUSIONSOnly five of the eleven dams requirerehabilitation based on the average expected neteconomic benefit. The cases for whichrehabilitation was not deemed feasible either hada prohibitively high rehabilitation cost, analready low probability of failure prior torehabilitation or low estimated loss of lives incase of failure.The cost effectiveness of rehabilitations, asmeasured by the cost of rehabilitation perpercentage reduction of the 50 year probabilityof failure, varied between R0.5m/% and R5m/%,but could be as high as R 50m/%. A high costper percentage reduction is typically associatedwith dams that already had a low probability offailure prior to rehabilitation.These are indications that current decisioncriteria for the rehabilitation of existing damsmay be too stringent, leading to rehabilitation ofdams which are neither economically feasible,nor required by society from a safety perspective.However, rehabilitation projects willinevitably also extend the remaining useful lifeof a facility.  This benefit was excluded in thisstudy, but will of course increase the monetarynet benefit of such a project, thus making it morelikely to be economically feasible.Rackwitz and Streicher (2002) determinedtarget reliability levels for typical bridge- andbuilding structures based on principles ofeconomic optimization and using simplifiedload- and resistance models to estimateprobabilities of failure.  It may be useful toconduct a similar exercise for dam structures.6. ACKNOWLEDGEMENTSDWS is gratefully acknowledged for theirfinancial support and for providing the inspectionand design reports on dam rehabilitations.7. REFERENCESArrow, K.J. (1995). Intergenerational equity and therate of discount in long-term social investment.Technical Report, Stanford University,Department of Economics.ANCOLD (2003). “Guidelines on Risk Assessment”,Australian Committee on Large Dams.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.Oosthuizen, C. (2000). Risk-Based Dam SafetyAssessment in South Africa. Proceedings of the20th ICOLD Congress, 5:19-22.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. 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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