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

Value of information in retrofitting of flood defenses Schweckendiek, T. (Timo); Vrouwenvelder, A. C. W. M. (Ton) Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Value of Information in Retrofitting of Flood DefensesT. (Timo) SchweckendiekLecturer, Dept. of Hydraulic Engineering, Delft Univ. of Technology, Delft, NetherlandsSr. researcher/consultant, unit Geo-engineering, Deltares, Delft, NetherlandsA.C.W.M. (Ton) VrouwenvelderProfessor, Dept. of Structural Engineering, Delft Univ. of Technology, Delft, NetherlandsSr. expert, Dept. of Structural Reliability, TNO, Delft, NetherlandsABSTRACT: Dikes and levees play a crucial role in flood protection. The main causes of levee failuresare of geotechnical nature; geotechnical failure modes are also the main contributors to the probability offailure of flood defences due to the typically large uncertainties in ground conditions. Hence, informationon ground conditions and soil properties is crucial in safety assessments and retrofitting designs of levees.The present paper demonstrates how we can reduce these uncertainties and how we can provide input forrational decision making on investments in monitoring and site investigation. If working in a frameworkwith an explicit target reliability, the value of such information can be expressed in terms of the savingsthat can be achieved in retrofitting costs. The key ingredients of the approach are Bayesian posterioranalysis for reliability updating by incorporating the information from various sources and Bayesian(pre-posterior) decision analysis for estimating the uncertainty and expected values of the consequencesand costs of the considered decision options. The optimal strategy is the one with the least expectedcost to meet the pre-set reliability target (e.g. by a safety standard). Several examples and case studiesaddressing different sources of information, such as field observations and piezometer monitoring duringfloods or site investigation by Cone Penetration Tests (CPT), illustrate the impact of reliability updatingand suggest that investments in inspection and monitoring are often worthwhile, especially when the prioruncertainties are large.1. INTRODUCTIONWhat is a sensible investment in site investigationand monitoring for flood defences which have beenassessed to be unsafe and, consequently, need to beretrofitted? Practitioners as well as researchers havebeen struggling with this question for a long time.Though we know that acquiring additional informa-tion, especially on geotechnical properties, helpsus to reduce uncertainties and, hence, to come upwith more appropriate safety assessments and de-sign, it is hard to quantify the value of informationor the return on investment with the deterministicor semi-probabilistic codes of practice currently ap-plied in most places. On the other hand, Eurocodeor the envisaged revision of Dutch safety standardsfor flood defences (Deltaprogramma, 2014) provideopenings to work with target reliabilities, enablingus to work in a fully probabilistic fashion.1.1. ObjectivesThe main objective of present paper is to demon-strate how the value of information of site inves-tigation and monitoring of flood defences can bequantified in order to support decision making insafety assessment and retrofitting situations wherethe safety requirement is formulated as target relia-bility (i.e. an acceptable annual probability of fail-ure).As there are several sources of information to beemployed, we also aim to provide an overview ofthe types of information and the way they can beused to update the reliability and how their value ofinformation can be quantified.Ultimately, application of the presented approach112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015in levee retrofitting projects should lead to opti-mized retrofitting designs and to a reduction of thecosts to keep flood defense systems safe (i.e. meettheir reliability targets).1.2. ScopeAs the field of flood defences is wide in termsof hazards (e.g. coast, rivers, lakes), structures andfailure mechanisms, we will focus on one specificapplication after discussing the general frameworkfor the sake of illustration, namely the failure modebackward internal erosion for river levees (in theremainder called "piping"). In the Dutch flood riskanalysis project VNK2 (Jongejan et al., 2013), pip-ing was identified as the main contributing mecha-nism to the probability of breaching of river leveesand to the associated flood risk. Hence, it is of par-ticular practical relevance.The starting point for the approach is a leveewhich does not meet its target reliability for the fail-ure mode piping. The decision options consideredare essentially (a) to reduce uncertainty by acquir-ing and/or incorporating additional information, (b)to take physical reinforcement measures (e.g. pip-ing berms or seepage screens) or (c) a combinationof both.1.3. OutlineThe application of Bayesian posterior and deci-sion analysis to the problem at hand is discussed insection 2, as well as how the envisaged applicationrelates to applications reported earlier in the litera-ture. Section 3 briefly recaps two sources of infor-mation related to observations during flood load-ing, namely (visual) field observations and moni-tored pore water pressures, and demonstrates theimpact of such observations of the probability offailure. Section 4 elaborates on a novel applicationof posterior and decision analysis on the mappingof the blanket layer on the landside of the levee bymeans of Cone Penetration Testing (CPT), wherethe thickness of the blanket is treated as a two-dimensional random field.2. BAYESIAN DECISION ANALYSIS FORLEVEE RETROFITTINGMany structures world-wide approach their de-sign life time and there is a growing demand forassessment of existing structures. Hence, it is sur-prising that also in the literature we increasinglysee contributions on structural (re-)assessment, dataassimilation and reliability updating, both in termsof method development as well as in applications.This section provides a concise overview of re-cent developments in geotechnical engineering and,more specifically, with respect to flood defences.2.1. Bayesian posterior analysisThe basis for incorporating additional informa-tion in a reliability analysis is Bayesian posterioranalysis (or Bayesian Updating), which is based onBayes’ rule (Bayes, 1763):P(F |ε) = P(F ∩ ε)P(ε) =P(ε|F)P(F)P(ε) (1)where P(F |ε) is the posterior or updated probabil-ity of failure F , conditional on the observation ε . Instructural reliability problems, typically the failureset is defined in terms of the performance functiong through F ≡ {g(x) < 0}, in which x representsthe vector of random variables.Recent examples of Bayesian reliability updatingin the literature are Ching and Hsieh (2006) who de-scribe a way of using Monte-Carlo simulation forupdating the reliability of monitored geotechnicalsystems, Zhang et al. (2011) who update the prob-ability of an embankment by incorporating site-specific performance information (e.g. survival ofa load) and Schweckendiek et al. (2014) as wellas Schweckendiek and Vrouwenvelder (2013), bothconsidering reliability updating for levees with re-spect to internal backward erosion (piping).Besides direct reliability updating there are nu-merous reports of applications of Bayesian updat-ing to reduce uncertainties in soil properties, mostnotably due to its pioneering nature Tang (1971)and more recently Zhang et al. (2004) as well asChing and Phoon (2012).Furthermore, Straub (2014) describes howBayesian Updating (and value of information anal-ysis) can be done in a computationally efficientmanner using standard techniques from structuralreliability analysis.212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20152.2. Target reliability constraintsMost commonly in real-life designs or decisionson the scope of site investigation and monitoringfor assessment and design purposes, we do nothave the opportunity to apply full-fledged risk anal-yses and risk acceptance criteria directly. How-ever, modern codes of practice such as Eurocodeor the envisaged Dutch safety standards for flooddefences (Schweckendiek et al., 2012) provide uswith risk-motivated target reliability levels, whichallows us to apply probabilistic approaches at least.As will be shown in the remainder, a probabilis-tic approach enables us to express the value of in-formation through expected costs, which would bevirtually impossible or largely arbitrary in a semi-probabilistic setting.Working with target reliabilities means that theprobability of failure of the structure in questionneeds to comply with the target probability of fail-ure pT , P(F) ≤ pT , or for the posterior probabilityof failure:P(F |ε)≤ pT (2)Notice that different codes of practice may workswith different reference periods. Whereas Eu-rocode uses the design life time, the Dutch safetystandards for flood defences are based on annualprobabilities.2.3. Bayesian decision analysisBayesian decision analysis enables us to com-pare different decision options in terms of their ex-pected utility. For risk-neutral decision makers theoptimal decision boils down to be the one with theminimum expected cost.For flood defenses that have to comply with a tar-get reliability as defined in the previous section thatmeans that the total cost of the decision options usu-ally consists of investments in uncertainty reduction(e.g. site investigation, monitoring) and the cost ofretrofitting to bring the structure up to the reliabilitytarget. If we opt for measures to reduce uncertaintyfirst, the retrofitting is based on the posterior knowl-edge (i.e. probabilities), as illustrated in Figure 1.More formally, the optimal pre-posterior (i.e. ex-pected future) retrofitting cost Cr are obtained by:E[C′′r (Ψ)] =∫minΩCr(Ω, f (x|ε)) f (ε|Ψ)dε (3)Figure 1: Decision tree for safety assessment andretrofitting of flood defenses.s.t. P(F |ε)≤ pTwhere Ω is the set of retrofitting design variables,f (x|ε) is the posterior distribution of the randomvariables and f (ε|Ψ) =∫f (ε|Ψ,x) f (x)dx is theprior distribution of the evidence conditional on theinvestigation parameters Ψ. For a more thouroughelaboration refer to Schweckendiek (2014).2.4. Value of InformationUsing the definition of minimum pre-posteriorcost from the previous section (Eq. 3), we can ex-press the value of information in different ways.Following the commonly used concepts (Straub,2014), the value of information of inspection andmonitoring can, in the contemplated assessmentand re-design situation, be expressed in terms ofthe difference in (expected) cost of the assesseddecision option and the retrofitting cost with priorknowledge (i.e. without acquiring and incorporat-ing more data):VoI(Ψ) =C′r−E[C′′r (Ψ)] (4)where C′r is the retrofitting cost for the cost-optimaldesign based on prior knowledge:C′r =∫minΩCr(Ω, f (x)) f (x)dx (5)s.t. P(F)≤ pTConsequently, a (pre-posterior) benefit-cost ratio(BCR) can be defined as the ratio of the VoI andthe investment cost Cs in reducing uncertainty:BCR(Ψ) =VoI(Ψ)Cs=C′r−E[C′′r (Ψ)]Cs(6)312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Recent examples of applications of VoI conceptsfrom related disciplines are described in Faber et al.(2000), Straub and Faber (2004), Corotis et al.(2005), Thoens and Faber (2013) or Garre andFriis-Hansen (2013).The following sections will provide examples ofnew observations can be incorporated in the re-liability of a levee with respect to internal back-ward erosion, including considerations of cost-effectiveness using the definitions above.3. SURVIVED FLOODSA valuable source of information for geotechni-cal failure mechanisms of levees are survived loadevents, i.e. extreme floods.3.1. Field observationsField observations during heavy loading likeseepage or sand boils are signs of bad performance,because they indicate the initiation of (partial) fail-ure mechanisms such as uplift or heave. Schweck-endiek et al. (2014) describe how reliability updat-ing for this type of observations can be done in aBayesian framework using the same performancefunctions as for the (prior) reliability analysis itself,considering the observation as if the flood were aload test. Figure 2 illustrates the impact such obser-vations can have on the fragility curves (probabilityof failure conditional on the river water level) for anobserved sand boil.1 2 3 4 5 600.20.40.60.81h [m+REF]f h(h), F h c,i(h), Fh c,i|ε(h)  uplift prioruplift posteriorheave priorheave posteriorpiping priorpiping posteriorfailure priorfailure posteriorh (PDF)Figure 2: Prior and posterior fragility curves of a leveewith respect to uplift, heave and piping as function ofthe river water level according to a case study from theNetherlands (Schweckendiek, 2014)Not only observing partial failure can be usedfor reliability updating purposes, also (partial) sur-vival similarly contains valuable information, re-sulting in an increase of reliability. Schweckendiek(2014) concludes that changes in probability of fail-ure of one order of magnitude are not uncommon,depending on the magnitude of (reducible) prior un-certainty.Apart from the effort that goes into the reliabilityupdating analysis itself, there is virtually no cost in-volved in this type of observation. Hence, the valueof information can hardly be expressed here in prac-tical terms. On the other hand, it is obvious that theinformation should be used, if available.3.2. Monitored pore water pressuresSimilar to the visual observations, we can usemonitoring of the pore pressure response to floodloading (ideally at potential exit points for piping,see Fig. 3) for reliability updating and, hence, influ-encing the investment cost in retrofitting measures.Figure 3: Illustration of the uplift (partial) failuremechanism and the potential exit point where instal-lation of piezometers to monitor the pore pressure re-sponse to flood loading is most effective.Compared to the inequality type of informationprovided by observations partial failure or survival,the challenge here is the treatment of equality typeof information. Straub (2011) provides and elegantsolution for this problem using standard structuralreliability analysis methods, as also illustrated byPapaioannou et al. (2014). Schweckendiek (2014)discusses the application to uplift, heave and piping(backward erosion). The impact of incorporatingthe monitoring information is similar to field obser-vation and can bring about changes of a factor 10both ways.Schweckendiek and Vrouwenvelder (2013)demonstrate pre-posterior analysis for a simplifiedexample, investigating the cost-effectiveness ofsuch installing piezometers for monitoring the412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015pore pressure response to flood loading. Ourconclusion was that the VoI (i.e. difference inexpected cost) was considerable and that due to thefact that monitoring costs are typically orders ofmagnitude lower than retrofitting costs, even smallsavings the the retrofitting design lead to ratherhigh benefit-cost ratios (in the example the BCRwas roughly 30).Similar conclusions are drawn in Schweckendiek(2014) for a case study in the Netherlands, in whichnot only uncertainties in ground properties are con-sidered, but also the uncertainty in the stratificationthough so-called subsoil scenarios. Figure 4 illus-trates that the pre-posterior distribution of the reli-ability index (for the combined failure mechanismof uplift, heave and piping; black continuous line)can be quite wide due to the large prior uncertain-ties in the relevant ground properties and the strat-ification. The red vertical line in Figure 4 is the0 1 2 3 4 500.511.52βprobability density  uplift posterioruplift priorheave posteriorheave priorpiping posteriorpiping priorfailure posteriorfailure priortarget (βT)Figure 4: Density plots of pre-posterior realisations ofposterior reliability indices for four subsoil scenarioswith a random future water level and measurement er-ror (1 year of monitoring), from Schweckendiek (2014).reliability target in the case study. The probabilityof exceeding the target reliability after incorporat-ing the next year’s flood’s response was 5% in thecase study. That meant a potential saving of mil-lions of Euro investment in retrofitting with a 5%probability (because retrofitting wouldn’t be neces-sary at all), implying expected savings in the orderof 105 Euro versus investments in the order of 104Euro. That in turn, according to the definitions insection 2.4, implies a VoI in the order of 105 Euroand a BCR of roughly 10.It needs to be mentioned that the fact that theremay be a waiting time until the next significantflood was neglected here. It can be easily incor-porated in the decision analysis by accounting forthe probability of a relevant observation in the con-sidered monitoring period. Depending on the localconditions, taking this effect into account can sig-nificantly reduce the cost-effectiveness.4. SITE INVESTIGATIONSeveral approaches to support decisions ingeotechnical site investigation planning have beenreported in the literature (Baecher, 1979; Halimand Tang, 1990; Elkateb et al., 2003; Meriaux andRoyet, 2007; Goldsworthy et al., 2007), but none ofthem actually quantifies the value of information inmonetary terms.4.1. Anomaly detectionSchweckendiek et al. (2011) do provide a frame-work similar to the concepts presented in thepresent paper and illustrates the value of informa-tion of soundings (e.g. CPT) to detect adverse ge-ological details under a levee, at the same time op-timizing the site investigation parameters (i.e. thesounding distance).50 100 150 2000100200300400500600ds [m]Cost [kE]  Cr = CbermCs|DCs|¬ DE[Cs]ds*Figure 5: Anomaly detection example from Schweck-endiek (2014) - costs as a function of the soundinginterval. The light-grey line shows the total cost ofretrofitting and site investigation, provided no anomalyis detected. The dashed black line is the expected costincluding the probability of detection.The black dashed line in Figure 5 shows the ex-pected total cost (site investigation plus retrofitting)as function of the sounding distance, where thesoundings are targeted at finding an adverse geolog-ical detail of uncertain width (mean 50 m, standarddeviation 15 m). The optimum is found at the low-est expected cost (black circle). The example again512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Figure 6: Computational framework for the optimisation of site investigation (SI) parameters for a levee involvingmodelling the spatial variability of properties by means of random fields. After Schweckendiek (2014). Notice thatβ is the prior reliability and βT is the reliability target.shows a high VoI (i.e. difference between the blackcircle and the continuous black line) and BCR andat the same time it illustrates the existence of a min-imum amount of site investigation in a frameworkwith a target reliability (at the jump of the expectedcost).4.2. Example: Blanket thicknessSimilar to anomaly detection, VoI-concepts, op-timization of site investigation parameters and de-cision analysis can also be applied to more sophis-ticated problems. Schweckendiek (2014) appliedpre-posterior analysis to a problem of levee reli-ability with respect to piping, particularly to theinvestigation of the blanket thickness on the land-side of the levee, which was modelled as a two-dimensional random field. As illustrated in Figure 6The regular sounding grid was optimized by simu-lating the inspection outcome based on prior knowl-edge, the results of which where then used to de-termine the posterior reliability using conditionedrandom fields and, subsequently the width of thelandside berm was designed for the levee to meetthe target reliability using posterior properties.Figure 7 shows the expected total cost (site in-vestigation and retrofitting) for different configura-tions of the search grid. From the results could beconcluded that in the particular case study, one rowof soundings in the levee with a sounding distanceof roughly 300 m would be optimal (which wasroughly the horizontal auto-correlation distance ofthe blanket thickness). Also in this example, theVoI of site investigation exceeded the cost of thesoundings, implying a positive benefit-cost ratio.For details refer to Schweckendiek (2014).5. CONCLUSIONSThe proposed framework for assessing the cost-effectiveness of investments to reduce uncertaintiesworks with a target reliability. The optimal strategyis defined as the one with the least expected costs toreach a pre-set reliability target. The (costs of) con-612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20150 100 200 300 4003600380040004200440046004800sounding distance dCPT [m]expected total cost [kEuro]  one rowdCPT,x = 50m100m200mFigure 7: Expected total cost (site investigation plus retrofitting) according to case study from Schweckendiek(2014). The horizontal axis depicts the sounding distance in the landside blanket in longitudinal direction of thelevee and the different lines represent different transversal distances of a second row of soundings from the leveetoe line (see legend).sequences are only treated implicitly through thesafety standard (i.e. reliability target). Such an ap-proach has the advantage that it is more accessibleto practitioners than a fully risk-based approach, asconsidering the consequences of failure explicitly isusually cumbersome and beyond the experience ofthe designing engineers. Furthermore, safety stan-dards are often motivated not only economically butalso through loss-of-life considerations, which areeven more difficult to assess explicitly.On the other hand, the proposed framework has asignificant drawback compared to a fully risk-basedapproach. As demonstrated in several of the ref-erenced examples and case studies, the incentivesin the approach can lead to sub-optimal decisions.The reason is that there is no award for incorporat-ing "unfavourable observations" (i.e. leading to adecrease in reliability), because they lead to no de-crease or even an increase in retrofitting cost. Froma risk point of view, even buying unfavourable evi-dence can pay off, as the increased risk can then bereduced by measures. In the presented frameworkthat is not the case.Despite this drawback, the approach can bea useful tool for practitioners for optimizing in-vestments in site investigation and monitoring forgeotechnical problems and for comparing differentstrategies. Overall, the referenced examples andcases show that the value of information can be veryhigh, if the prior uncertainties are large, as is verytypical in geotechnical engineering.Future work should focus on the combination ofmultiple sources of information and on the analysisof staged strategies. Furthermore, little is knownabout which portion of the uncertainties faced inthe assessments is reducible and which is not, espe-cially when it comes to model uncertainty.6. REFERENCESBaecher, G. B. (1979). “Analyzing Exploration Strate-gies. Site Characterization and Exploration.” Reportno., Massachusetts Institute of Technology.Bayes, T. (1763). “An Essay towards solving a Prob-lem in the Doctrine of Chances.” Biometrika, 45, 293–315.Ching, J. and Hsieh, Y.-H. (2006). “Updating Reliabil-ity of Instrumented Geotechnical Systems Via SimpleMonte Carlo Simulation.” Journal of GeoEngineer-ing, 1(2), 71–78.Ching, J. and Phoon, K. K. 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