Risk analysis during tunnel construction using Bayesian NetworksPorto Mctro case study.docx

Risk analysis during tunnel construction using Bayesian NetworksPorto Mctro case study.docx

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RiskanalysisduringtunnelconstructionusingBayesianNetworksPortoMctrocasestudy

TunnellingandUndergroundSpaceTechnology27（2012）86–100

ContentslistsavailableatSciVerseScienceDirect

TunnellingandUndergroundSpaceTechnology

journalhomepage:

www.elsevier.com/locate/tust

RiskanalysisduringtunnelconstructionusingBayesianNetworks:

PortoMetrocasestudy

RitaL.Sousa,HerbertH.Einstein⇑

Dept.ofCivilandEnvironmentalEngineering,MassachusettsInstituteofTechnology,Cambridge,USA

articleinfo

Articlehistory:

Received16December2010

Receivedinrevisedform15July2011

Accepted17July2011

Availableonline27August2011

Keywords:

RiskTunneling

BayesianNetworks

abstract

Thispaperpresentsamethodologytosystematicallyassessandmanagetherisksassociatedwithtunnelconstruction.Themethodologyconsistsofcombiningageologicpredictionmodelthatallowsonetopre-dictgeologyaheadofthetunnelconstruction,withaconstructionstrategydecisionmodelthatallowsonetochooseamongstdifferentconstructionstrategiestheonethatleadstominimumrisk.Thismodelusedtunnelboringmachineperformancedatatorelatetoandpredictgeology.BothmodelsarebasedonBayesianNetworksbecauseoftheirabilitytocombinedomainknowledgewithdata,encodedependen-ciesamongvariables,andtheirabilitytolearncausalrelationships.Thecombinedgeologicprediction–constructionstrategydecisionmodelwasappliedtoacase,thePortoMetro,inPortugal.Theresultsofthegeologicpredictionmodelwereingoodagreementwiththeobservedgeology,andtheresultsoftheconstructionstrategydecisionsupportmodelwereingoodagreementwiththeconstructionmethodsused.Verysignificantistheabilityofthemodeltopredictchangesingeologyandconsequentlyrequiredchangesinconstructionstrategy.Thisriskassessmentmethodologyprovidesapowerfultoolwithwhichplannersandengineerscansystematicallyassessandmitigatetheinherentrisksassociatedwithtunnel

construction.

2011ElsevierLtd.Allrightsreserved.

1.Introduction

Thereisanintrinsicriskassociatedwithtunnelconstructionbecauseofthelimitedaprioriknowledgeoftheexistingsubsur-faceconditions.Althoughthemajorityoftunnelconstructionpro-jectshavebeencompletedsafelytherehavebeenseveralincidentsinvarioustunnelingprojectsthathaveresultedindelays,costoverruns,andinafewcasesmoresignificantconsequencessuchasinjuryandlossoflife.Itisthereforeimportanttosystematicallyassessandmanagetherisksassociatedwithtunnelconstruction.Adetaileddatabaseofaccidentsthatoccurredduringtunnelcon-structionwascreatedbySousa（2010）.Thedatabasecontains

204casesallaroundtheworldwithdifferentconstructionmeth-odsanddifferenttypesofaccidents.Theaccidentcaseswereobtainedfromthetechnicalliterature,newspapersandcorrespon-dencewithexpertsinthetunnelingdomain.

Knowledgerepresentationsystems（orknowledgebasedsys-tems）anddecisionanalysistechniqueswerebothdevelopedtofacilitateandimprovethedecisionmakingprocess.KnowledgerepresentationsystemsusevariouscomputationaltechniquesofAI（artificialintelligence）forrepresentationofhumanknowledge

⇑Correspondingauthor.Address:

70MassachusettsAve.,Room1-342,Cam-bridgeMA02139,USA.Tel.:

+16172533598;fax:

+16172536044.

E-mailaddress:

einstein@mit.edu（H.H.Einstein）.

andinference.Decisionanalysisusesdecisiontheoryprinciplessupplementedbyjudgmentpsychology（Henrion,1991）.Bothemergedfromresearchdoneinthe1940sregardingdevelopmentoftechniquesforproblemsolvinganddecisionmaking.JohnvonNeumannandOscarMorgensten,whointroducedgametheoryin

‘‘GamesandEconomicBehavior’’（1944）,hadatremendousimpactonresearchindecisiontheory.

Althoughthetwofieldshavecommonroots,sincethentheyhavetakendifferentpaths.Morerecentlytherehasbeenaresur-genceofinterestbymanyAIresearchersintheapplicationofprob-abilitytheory,decisiontheoryandanalysistoseveralproblemsinAI,resultinginthedevelopmentofBayesianNetworksandinflu-encediagrams,anextensionofBayesianNetworksdesignedtoincludedecisionvariablesandutilities.The1960ssawtheemer-genceofdecisionanalysiswiththeuseofsubjectiveexpectedutil-ityandBayesianstatistics.HowardRaiffa,RobertSchlaifer,andJohnPrattatHarvard,andRonaldHowardatStanfordemergedasleadersintheseareas.ForinstanceRaiffaandSchlaifer’sAppliedStatisticalDecisionTheory（1961）providedadetailedmathemati-caltreatmentofdecisionanalysisfocusingprimarilyonBayesianstatisticalmodels.Prattetal.（1964）developedbasicdecisionanal-ysis.whileEskesenetal.（2004）andHartfordandBaecher（2004）providegoodsummariesonthedifferenttechniques（faulttrees,decisiontrees,etc.）thatcanbeusedtoassessandmanageriskintunneling.

0886-7798/$-seefrontmatter2011ElsevierLtd.Allrightsreserved.doi:

10.1016/j.tust.2011.07.003

Variouscommercialandresearchsoftwareforriskanalysisdur-ingtunnelconstructionhavebeendevelopedovertheyears,themostimportantofwhichistheDAT（DecisionAidsforTunneling）,developedatMITincollaborationwithEPFL（EcolePolytechniqueFédéraledeLausanne）.TheDATarebasedonaninteractivepro-gramthatusesprobabilisticmodelingoftheconstructionprocesstoanalyzetheeffectsofgeotechnicaluncertaintiesandconstruc-tionuncertaintiesonconstructioncostsandtime.（Dudtetal.,

2000;Einstein,2002）However,themajorityofexistingriskanaly-sissystems,includingtheDAT,dealonlywiththeeffectsofran-dom（‘‘common’’）geologicalandconstructionuncertaintiesontimeandcostofconstruction.Thereareothersourcesofrisks,notconsideredinthesesystems,whicharerelatedtospecificgeo-technicalscenariosthatcanhavesubstantialconsequencesonthetunnelprocess,eveniftheirprobabilityofoccurrenceislow.

Thispaperattemptstoaddresstheissueofspecificgeotechnicalriskbyfirstdevelopingamethodologythatallowsonetoidentifymajorsourcesofgeotechnicalrisks,eventhosewithlowprobabil-ity,inthecontextofaparticularprojectandthenperformingaquantitativeriskanalysistoidentifythe‘‘optimal’’constructionstrategies,where‘‘optimal’’referstominimumrisk.Forthatpur-poseadecisionsupportsystemframeworkfordeterminingthe

‘‘optimal’’（minimumrisk）constructionmethodforagiventunnel

Fig.1.BayesianNetworkexample.

therelationsbetweenvariables.Inthisexamplethearrowfrom

CtoB2meansthatChasadirectinfluenceonB2.

Specifically,aBayesianNetworkisacompactandgraphicalrep-resentationofajointdistribution,basedonsomesimplifyingassumptionsthatsomevariablesareconditionallyindependentofothers.AsaresultthejointprobabilityofaBayesianNetworkoverthevariablesU={X1,...,Xn},representedbythechainrulecanbesimplifiedfrom:

n

Y

alignmentwasdeveloped.Thedecisionsupportsystemconsistsoftwomodels:

ageologicpredictionmodel,andaconstructionstrat-egydecisionmodel.BothmodelsarebasedontheBayesianNet-

PðUÞ¼

i

to

PðXijx1;...;xi1Þ

worktechnique,andwhencombinedallowonetodeterminethe

PðUÞ¼QnPðX¼xjparentsðXÞÞ,where‘‘parents（X）’’isthe

‘optimal’tunnelconstructionstrategies.Thedecisionmodelcon-

i

parentsetof

iiii

Xi.

tainsanupdatingcomponent,byincludinginformationfromthe

excavatedtunnelsections.Thissystemwasimplementedinarealtunnelproject,thePortoMetroinPortugal.

2.BackgroundonBayesianNetworks

BayesianNetworksaregraphicalrepresentationsofknowledgeforreasoningunderuncertainty.Theycanbeusedatanystageofariskanalysis,andmaysubstitutebothfaulttreesandeventtreesinlogicaltreeanalysis.Whilecommoncauseormoregeneraldepen-dencyphenomenaposesignificantcomplicationsinclassicalfaulttreeanalysis,thisisnotthecasewithBayesianNetworks.Theyareinfactdesignedtofacilitatethemodelingofsuchdependen-cies.Becauseofwhathasbeenstated,BayesianNetworksprovideagoodtoolfordecisionanalysis,includingprioranalysis,posterioranalysisandpre-posterioranalysis.Furthermore,theycanbeex-tendedtoinfluencediagrams,includingdecisionandutilitynodesinordertoexplicitlymodeladecisionproblem.

ABayesianNetworkisaconcisegraphicalrepresentationofthe

jointprobabilityofthedomainthatisbeingrepresentedbythe

ItisthispropertythatmakesBayesianNetworksaverypower-fultoolforrepresentingdomainsunderuncertainty,allowingonetostoreandcomputethejointandmarginaldistributionsmoreefficiently.

InordertoobtainresultsfromBayesianNetworksonedoesinference.ThisconsistsofcomputinganswerstoqueriesmadetotheBayesianNetwork.Thetwomostcommontypesofqueriesare:

–Aprioriprobabilitydistributionofavariable

PðAÞ¼X...XPðX1;...;Xk;AÞð1Þ

X1Xk

whereAisthequery-variableandX1toXkaretheremainingvariablesofthenetwork.Thistypeofquerycanbeusedduringthedesignphaseofatunnelforexampletoassesstheproba-bilityoffailureunderdesignconditions（geology,hydrology,etc.）.

–Posteriordistributionofvariablesgivenevidence

（observations）

PðA;eÞ

randomvariables,consistingof（RusselandNorvig,2003）: