Importance ranking of parameter uncertainties in geo-hazard assessments

191 Pages·2016·8.67 MB·English

by  Jeremy Rohmer

Importance ranking of parameter uncertainties in
geo-hazard assessments
Jeremy Rohmer
To cite this version:
Jeremy Rohmer. Importance ranking of parameter uncertainties in geo-hazard assessments.
Modeling and Simulation. Universit´e de Lorraine, 2015. English. <tel-01319716>
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UNIVERSITE DE LORRAINE
Ecole Nationale Supérieure des Mines de Nancy
Laboratoire GeoRessources
Ecole Doctorale RP2E

THESE

Présentée en vue du grade de

DOCTEUR DE L’UNIVERSITE DE LORRAINE
en Génie Civil-Hydrosystèmes-Géotechnique

Par

Jérémy ROHMER

Importance ranking of parameter uncertainties
in geo-hazard assessments
Analyse de sensibilité des incertitudes paramétriques
dans les évaluations d’aléas géotechniques

le 16 Novembre 2015

Devant le jury composé de

Michael OBERGUGGENBERGER– University of Innsbruck – Austria Rapporteur
Michael BEER – University of Liverpool – UK Rapporteur
Anne GEGOUT-PETIT – Université de Lorraine – France Examinateur
Gilles GRANDJEAN – BRGM – France Examinateur
Thierry VERDEL – Université de Lorraine – France Directeur de thèse
Jack-Pierre PIGUET – Université de Lorraine – France Co-directeur de thèse

Acknowledgements
IthankT.VerdelandJ.-P.Piguet(Uni.Lorraine)foracceptingtosupervisethisPhDthesis.I
amverygratefultomyco-authors,C.Baudrit(INRA),E.Foerster(CEA),A.Nachbaur(BRGM)
andT.Verdel(Uni.Lorraine),fortheconstructiveworkandfruitfuldiscussionswhichledto
thepublicationssupportingthepresentmanuscript.
IalsothanktheBRGMdirectorateof"RisksandPrevention"division(J.L.Foucher,H.Fabriol
andG.Grandjean)forsupportingmy"personalandprofessional"project.
IamalsogratefultoD.Guyonnet(BRGM/ENAG)andG.Grandjean(BRGM)forintroducing
metoFuzzysetsandnewuncertaintytheoriesandO.Sedan(BRGM)forhisveryvaluable
adviceonpractical/operationalaspectsofnaturalriskassessments.
Lastbutnotleast,Iamverygratefultomyfamily(Julia,myparents,myparentsinlawand
mysisterinlaw)forsupportingme.SpecialthankstotheFrenchtraincompanySNCFforits
repetitivedelays,whichletmeenoughtimeforwritingthismanuscript.
Orleans,16November2015 J.Rohmer.
i

Technical Summary
Thecentraltopicofthepresentthesisisthetreatmentofepistemicuncertaintyingeo-hazard
assessments(likelandslide,earthquake,etc.).Contrarytoaleatoryuncertainty(akarandom-
ness,variability),epistemicuncertaintycanbereducedthroughadditionalmeasurements
(labtests,insiteexperiments,etc.)ormodelling(e.g.,throughnumericalsimulations)orextra
researchefforts.Amongthedifferenttypesofepistemicuncertainties,wefocusedhereonthe
parametricone:thiscorrespondstotheincompleteknowledgeofthecorrectsettingofthe
inputparameters(likevaluesofsoilproperties)ofthemodelsupportingthegeo-hazardas-
sessment.Apossibleoptiontomanagethistypeofuncertaintyisthroughsensitivityanalysis:
1.identifythecontributionofthedifferentinputparametersintheuncertaintyonthefinal
hazardoutcome;2.rankthemintermsofimportance;3.decideaccordinglytheallocationof
additionalcharacterisationstudies.
Forthispurpose,variance-basedglobalsensitivityanalysis(VBSA)isapowerfulprocedure,
whichallows:i.incorporatingtheeffectoftherangeoftheinputvariationandofthenatureof
theprobabilitydistribution(normal,uniform,etc.);ii.exploringthesensitivityoverthewhole
rangeofvariation(i.e.inaglobalmanner)oftheinputrandomvariables;iii.fullyaccounting
forpossibleinteractionsamongthem;andiv.providingaquantitativemeasureofsensitivity
withoutintroducingaprioriassumptionsonthemodel’smathematicalstructure(i.e.model-
free).Themostimportantsourcesofparameteruncertaintycanthenbeidentified(usingthe
maineffects)aswellastheparametersofnegligibleinfluence(usingthetotaleffects).Besides,
somekeyattributesofthemodelbehaviourcanbeidentified(usingthesumofthemain
effects).Yet,totheauthor’sbestknowledge,thiskindofanalysishasrarelybeenconducted
inthedomainofgeo-hazardassessments. Thiscanbeexplainedbythespecificitiesofthe
domainofgeo-hazardassessments,whichimposeconsideringseveralconstraints,whichare
atthecoreofthepresentwork.
Mostnumericalmodelssupportinggeo-hazardassessmentshavemoderate-to-highcompu-
tationtime(typicallyseveralminutes,evenhours),eitherbecausetheyarelarge-scale(e.g.,
landslidesusceptibilityassessmentatthespatialscaleofavalley),orbecausetheunderlying
processesaredifficulttobenumericallysolved(e.g.,complexelastoplasticrheologylawlike
theHujeuxmodeldescribingthecomplexcoupledhydromechanicalbehaviourofaslipsur-
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TechnicalSummary
face).Despitetheextensiveresearchworkontheoptimizationofthecomputationalgorithms,
VBSAremainscomputationallyintensive,asitimposestorunalargenumberofsimulations(>
1,000).Inthiscontext,VBSAcanbemadepossibleviathecombinationwithmeta-modelling
techniques. Thistechnique consistsinreplacingthe long-runningnumerical model by a
mathematicalapproximationreferredtoas“meta-model”(alsonamed“responsesurface”,
or“surrogatemodel”),whichcorrespondstoafunctionconstructedusingafewcomputer
experiments(typically50-100,i.e.alimitednumberoftimeconsumingsimulations),andaims
atreproducingthebehaviourofthe“true”modelinthedomainofmodelinputparameters
andatpredictingthemodelresponseswithanegligiblecomputationtimecost.
TheapplicabilityofthecombinationVBSAandmeta-modelswasdemonstratedusingthe
model developed by Laloui and co-authors at EPFL (Lausanne) for studying the Swiss La
Frasse landslide. We focused on the sensitivity of the surface displacements to the seven
parametersoftheHujeuxlawassignedtotheslipsurface.Inthiscase,asinglesimulationtook
4daysofcalculation. Ontheotherhand,evaluatingthemaineffects(firstordersensitivity
indices)shouldrequire>1,000differentsimulations,whichisherehardlyfeasibleusingthe
numerical simulator. Thiscomputationburden was alleviated using akriging-type meta-
modelconstructedusing30differentsimulations.Furthermore,theimpactofthemeta-model
error(i.e.theadditionaluncertaintyintroducedbecausethetruesimulatorwasreplacedby
anapproximation)wasdiscussedbytreatingtheproblemundertheBayesianformalism.This
allowedassigningconfidenceintervalstothederivedsensitivitymeasures:theimportance
rankingcouldthenbedoneaccountingforthelimitedknowledgeonthe“true”simulator(i.e.
throughonly30differentlong-runningsimulations),henceincreasingtheconfidenceinthe
analysis.Totheauthor’sbestknowledge,theapplicationofsuchkindsoftechniqueisoriginal
inthedomainoflandslideriskassessment.
ThesecondlimitationofVBSAisrelatedtothenatureoftheparameters(inputoroutput):
theyarescalar. Yet,inthedomainofgeo-hazard,parametersareoftenfunctional,i.e. they
arecomplexfunctionsoftimeorspace(orboth).Thismeansthatparameterscanbevectors
withpossiblehighdimension(typically100-1,000).Forinstance,theoutputsoftheLaFrasse
modelcorrespondtotemporalcurvesofthedisplacements(discreditedin300steps)atany
nodesofthemesh,i.e. theoutputsarevectorsofsize300atanyspatiallocation. Another
exampleisthespatialdistributionofhydraulicconductivitiesofasoilformation.Focusing
firstonthefunctionaloutputcase,amethodologytocarryoutdynamic(global)sensitivity
analysisoflandslidemodelswasdescribedcombining:1.basissetexpansiontoreducethedi-
mensionalityofthefunctionalmodeloutput;2.extractionofthedominantmodesofvariation
intheoverallstructureofthetemporalevolution;3.meta-modellingtechniquestoachievethe
computation,usingalimitednumberofsimulations,ofthesensitivityindicesassociatedto
eachofthemodesofvariation.Thesewereinterpretedbyadoptingtheperspectiveoftherisk
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TechnicalSummary
practitionerinthefollowingfashion:“identifyingtheproperties,whichinfluencethemostthe
possibleoccurrenceofadestabilizationphase(acceleration)overthewholetimeduration
oronaparticulartimeinterval”.However,alimitationwasunderlined,namelythephysical
interpretationofthedominantmodesofvariation,especiallycomparedtothetraditional
time-varyingVBSA(moreeasilyinterpretable,butalsointractableforverylongtimeseries).
Basedonthestudyonthefunctionaloutput,theapplicabilityoftheproposedmethodology
wasalsoinvestigatedforthecaseoffunctionalinputsusingasanexample,arandomfield
assignedtotheheterogeneousporosityofasoilformation.
Finally, a third limitation of VBSA is related to the representation of uncertainty. By con-
struction,VBSAreliesontools/proceduresoftheprobabilisticsetting.Yet,inthedomainof
geo-hazardassessments,thevalidityofthisapproachcanbedebatable,becausedataareoften
scarce,incompleteorimprecise.Inthiscontext,themajorcriticismsavailableintheliterature
againstthesystematicuseofprobabilityinsuchsituationswerereviewed.Onthisbasis,the
useofaflexibleuncertaintyrepresentationtoolwasinvestigated,namelyFuzzySetstohandle
differentsituationsofepistemicuncertainty.Foreachsituation,examplesofrealcasesinthe
contextofgeo-hazardassessmentswereused:
• Vagueness due to the use of qualitative statements. The application of Fuzzy Sets
wasillustratedinthecontextofsusceptibilityassessmentofabandonedunderground
structures.Inparticular,itisshownhowtheso-called“thresholdeffect”canbehandled
whentheexpertdefinesclassesofhazard/susceptibility;
• Reasoningwithvagueconcepts.ThisishandledusingFuzzyLogic.Thisisillustrated
withthetreatmentofimprecisionassociatedtotheinventoryofassetsatriskinthe
contextofseismicriskanalysis;
• Imprecision.Thisishandledbydefiningpossibilitydistributions,whichhaveastrong
linkwithFuzzySets. Thisisillustratedwiththerepresentationofuncertaintyonthe
amplificationfactoroflithologicalsiteeffectsinthecontextofseismicriskanalysis;
• Imprecisionontheparametersofaprobabilisticmodel.Thisishandledinthesetting
offuzzyrandomvariables.Thisisillustratedusingaprobabilisticdamageassessment
modelinthecontextofseismicriskanalysis,namelytheRISK-UE,level1model.
Onthisbasis,theissueofsensitivityanalysisconsideringamixtureofrandomnessandimpre-
cisionwasaddressed.Basedonaliteraturereview,amajorlimitationwasoutlined,namely
thecomputationtimecost:newtoolsforuncertaintyrepresentationbasicallyrelyoninterval-
valuedtools,theuncertaintypropagationtheninvolvesoptimisationprocedure,whichcan
behighlycomputationallyintensive. Inthiscontext,anadaptationofthecontributionto
failureprobabilityplotof[LiandLu,2013],tobothhandleprobabilisticandpossibilisticin-
formationwasproposed.Theanalysiscanbeconductedinapost-processingstep,i.e.using
onlythesamplesofrandomintervalsandofrandomnumbersnecessaryforthepropagation
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TechnicalSummary
phase, henceatnoextracomputationalcost. Besides, itallowsplacingonthesamelevel
randomandimpreciseparameters,i.e.itallowsthecomparisonoftheircontributioninthe
probabilityoffailuresothatconcreteactionsfromariskmanagementperspectivecanbe
decidedaccordingly.Theapplicabilityofthiseasy-to-usetoolwasdemonstratedusingreal
cases,whereitisquestionabletouseprobabilitiestotreatuncertainty.Thefirstapplication
casecorrespondstostabilityanalysisofsteepslopes.Themainimpreciseparametersinthis
casearethetensioncrack’sheightlocatedintheupperpartofthecliffandthetoeheight.The
secondonecorrespondstothestabilityanalysisofanabandonedundergroundquarry,where
theextractionratiowasimprecisebecauseitcouldonlybeestimatedwithgreatdifficulties
(duetotheparticulargeometryofthequarry).Finally,athirdexamplewasused,namelythe
stabilityanalysisofaminepillarpresentingthinlayersofclay,whosepropertiesaredifficultto
evaluateinpractice.Thislastexampleimposedtorelyonmeta-modellingtechniquestoease
thejointuncertaintypropagationphaseusingthelong-runningmechanicalnumericalcode.
Insummary, thepresentworkshouldbeseenasanefforttohandleepistemicparameter
uncertaintiesingeo-hazardassessments.First,theachievementisofmethodologicalnature
(methodologyforconductingVBSAusinglongrunningsimulators,methodologyforconduct-
ingVBSAadaptedtofunctionaloutputs,methodologyforconductingsensitivityanalysiswhen
bothimprecisionandrandomnessarepresent).Thismethodologicalworktakesadvantagesof
therecentadvancesinthestatisticalcommunity(VBSA,basissetexpansion,FuzzySets,Fuzzy
randomvariables,hybridpropagation,etc.)toanswerpracticalquestions(whatdrivestheun-
certaintyontheresultsofthehazardassessment?Howtoconductmultiplesimulationswhen
thesimulationcodetakesonehourtoberun?Howshouldtheuncertaintybetreatedwhen
theonlypiecesofinformationavailablerestricttovaguestatementsandafewquantitative
estimates?).Agreatattentionhasbeenpaidtoinvestigatetheapplicabilityofeachproposed
technique/procedurei.e.byhighlightingtheprosandconsthroughtheconfrontationtoreal
cases.Thisconstitutesthesecondachievementofthepresentwork.
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