by Anton Biryukov A thesis submitted in conformity with the requirements for the degree of Master

66 Pages·2015·8.34 MB·English

SIMULATED GEOPHYSICAL MONITORING OF RADIOACTIVE WASTE REPOSITORY BARRIERS
by
AntonBiryukov
Athesissubmittedinconformitywiththerequirements
forthedegreeofMasterofAppliedScience
GraduateDepartmentofCivilEngineering
UniversityofToronto
(cid:13)c Copyright2015byAntonBiryukov
Abstract
Simulatedgeophysicalmonitoringofradioactivewasterepositorybarriers
AntonBiryukov
MasterofAppliedScience
GraduateDepartmentofCivilEngineering
UniversityofToronto
2015
Estimationofattenuationoftheelasticwavesinclaysandhighclay-contentrocksisimportantforthequality
of geophysical methods relying on processing the recorded waveforms. Time-lapse imaging is planned to be
employed for monitoring of the condition of high-radioactive waste repositories. Engineers can analyze and
optimizeconfigurationofthemonitoringsystemusingnumericalmodellingtools. Thereliabilityofmodeling
requirespropercalibration. Thepurposeofthisthesisisthreefold: (i)proposeacalibrationmethodologyforthe
wavepropagationtoolsbasedontheexperimentaldata,(ii)estimatetheattenuationinbentoniteasafunctionof
temperatureandwatercontent,and(iii)investigatethefeasibilityofactivesonicmonitoringoftheengineered
barriers. The results suggest that pronounced inelastic behavior of bentonite has to be taken into account in
geophysicalmodelingandanalysis. Therepository–scalemodelsconfirmthatactivesonicmonitoringiscapableof
depictingphysicalchangesinthebentonitebarrier.
ii
Acknowledgements
My “mission - MASc thesis” would never be accomplished without support and encouragement from many
individualsacrosstheglobe,towhomIwouldliketoexpressmywholeheartedgratitude. Firstofall,Iwould
liketothankmysupervisors,Prof. GiovanniGrasselliandDr. NicolaTisatofortheirguidance,professionalism,
support,andsenseofhumor. OnoneofmanycoldRussianwinterdays,ProfessorGrasselliofferedmeawonderful
opportunitytostudyrockmechanicsandgeophysicsunderhissupervisionatonethebestuniversitiesintheworld,
and in no doubts the best GeoGroup on campus. Back then I would never believe that professors can be any
informalandsofriendly. wouldalsoliketothankNicolaforhis(i)endlesspatienceandpoolofknowledge,that
hiskindlysharedwithmeeverytimeIhadquestionsIwasunabletoresolve,(ii)never-endingenthusiasmand
creativity,(iii)experimentalistexperiencehewouldalwaysshare. Ihavenevermetsuchinspirationalpeoplebefore
andamlookingforwardtocontinuemypathwithintheItalianteamoneday.
Iwouldalsoliketothankmydearresearchbuddies,withoutwhommystayintheUniversityandinCanada
would be less entertaining and productive. Thank you, Simon Gerrard Edmund Harvey, Qi Zhao and Paola
Miglietta,forallthetimewespenttogetherarguing,solvingproblems,TAing,playinghockey,drinkingcoffee,
proofreadingeachotherwritingandhavinggreattimeoutsidetheUniversitywalls. ThankstoDr. ScottBriggsfor
hisadvice,languageandwordethymologysupport,aswellasperiodicallecturesonhowtosetupthenetworks
andserversproperly,andoccasionaldiscussionsonvarioustopics. IsincerelyappreciateallthetimeSimonandQi
spentlisteningtomycurses,complainsandstillmanagingtostayclosefriendsandsticktogether.
Asweknow,allworkandnoplaymakesJackadullboy. ThankstomycolleaguesintheDepartmentand
CEGSAfororganizingsocialeventsandentertainingmeinthehardtimes.
IwouldalsoliketothankProfessorBerndMilkereitandRaminSalehfortheircontinuousgeophysicalsupport
andassociateddiscussion,andinvitingmetoKEGS.SpecialthanksgotoProfessorKarlPetersonforhiskindness
andhelpingmeduringmyfirstdaysasaninternationalstudentinCanada. Icandefinitelyclaimthatunderhis
supervisionIbenefitedfrommyTAhoursmore,thantheundergraduatestudents. Imanagedtolearnmoreabout
microscopy,concretematerialsand...plumbing;whoknowswhatkindofknowledgemightbeofusetomorrow?...
Finally,Iwouldliketoexpressmygratitudetomyparents,mysisterandmydearLizafortheirconstantlove,
support,andencouragement. Theyalwaysmotivatedmetogrowandforcedmetolooktowardsmylifewitha
positiveandoptimisticattitude,whichcarriedmethroughmanydifficulties.
Last,butnotleast,I’dliketothankmyfriendsfromMoscowInstituteofPhysicsandTechnology,whoremained
closenomatterhowmuchtimeandspaceseparatedus: Iwillalwaysfeelstrongbondsbetweenus“phystechs”,
thebondsthatcansustainanypoliticalconflicts. IappreciatethesupportandmotivationfromEugeneGrebennikov
bothbeforeandaftermyarrivalinCanada,withoutwhomthisadventurewouldprobablyneverhappen.
iii
Contents
1 Introduction 2
1.1 Basicsofwavepropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 1Dcase: extensional(bar)waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 2Dand3Dcases: compressionalandshearbodywaves . . . . . . . . . . . . . . . . . . . 3
1.2 Wavesinviscoelasticmedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Fluidsaturationeffects: empiricalandheuristicalmethods . . . . . . . . . . . . . . . . . 5
1.2.2 Linearviscoelasticity: dispersionandattenuation . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Numericalmodellingofwavepropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Generaloverviewofnumericalmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 GeneralconceptsofFD,FEM,SEMandBEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 FiniteDifferenceMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.2 FiniteElementandSpectralElementMethod . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.3 BoundaryElementMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Chaptersummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Workflowtonumericallyreproducelaboratoryultrasonicdatasets 14
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Laboratorysetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Numericalsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3 Reasonsforcalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.4 Calibrationmethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 IterativecalibrationoftheexperimentalsetupforS-waves . . . . . . . . . . . . . . . . . 19
2.4.2 Subdomainmodelupscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.3 WetmontmorilloniteS-waveattenuationestimation . . . . . . . . . . . . . . . . . . . . . 21
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 AppendixA:Goodnessoffit(GOF)functionestimation . . . . . . . . . . . . . . . . . . . . . . 25
2.8 AppendixB:Barwaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.9 AppendixC:Errorsofthecalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
iv
3 Attenuationofbentonite. Monitoringofnuclearwasterepositories 29
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Laboratoryandnumericalsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.2 Attenuationmodellingmechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.3 Iterationprocedurestructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.4 GOFevaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.5 Repository-scalemodelsimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.1 Attenuationestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.2 ModifiedGTSframeworksimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5.1 EffectsoftemperatureandwatercontentonQ andQ . . . . . . . . . . . . . . . . . . . 45
p s
3.5.2 UncertaintyinQvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.5.3 Implicationsonrepository-scalemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Concludingremarksandfuturework 50
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Bibliography 52
v
List of Tables
2.1 Materialparametersusedinnumericalsimulations . . . . . . . . . . . . . . . . . . . . . . . . . 17
vi
List of Figures
1.1 Wavepropagationphenomenoninaperfectlyelasticrod. . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Hysterisisloop. Theredlineshowstheidealstress-strainpathfollowedbyapurelyelasticmaterial.
Thegreenpathisfollowedbyarealmaterial. Thedifferencebetweentheareasunderloadingand
unloadingcurvesdescribestheenergylossesduringthecycle. . . . . . . . . . . . . . . . . . . . 5
1.3 Fundamental mechanical elements comprising the mechanical models employed to represent
viscoelasticmaterials: a)aspringandb)adashpot. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Kelvin-Voigtmechanicalmodel(a)withassociatednormalizedvelocityandattenutioncurves(b). 8
1.5 ThepropagationoftheRickerwaveletthroughtheelasticrodswith(a)andwithouttheanelastic
Kelvin-Voigtintrusion(b). Theintrusiondomainisshowninred. Thesuccessionofsnapshots
showsthewavefieldintherodatcorrespondingtimeslices.Reddashedlineindicatesthereflections
offtheintrusion.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 (a)SchematicdiagramoftheultrasonicfacilityemployedintheexperimentstomeasureV and
p
V ;(b)asubdomainusedforiterativecalibration;(c)aphotooftheultrasonicfacilityinafully
s
assembledstate;and(d)normalizedsignalsenttotheemitter.. . . . . . . . . . . . . . . . . . . . 16
2.2 (a)TheGOFdistributionasafunctionoftheK andK and(b,c,d)numericaltracescorrespond-
s p
ingto“no-sample”modelwithvariousvelocitymodels. Greensquaresandredtrianglesshow
analyticallypredictedP-andS-wavearrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Numericaltracescorrespondingtosubdomain(a)andfull-size(b)models. Theoverlapbetween
thetraces(c)lendsvaliditytothevaluesofK andK obtainedthroughmodelingonthesubdomain. 20
p s
2.4 Anexampleof“constantQ-spectrum”attenuationmodelemployedinthemodelscorrespondingto
(a)Q=6and(b)itsGSLSdiagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5 TheGOFdistributionasafunctionoftheQ andQ (a)andnumericaltracescorrespondingto
p s
viscoelastic(b,c)andaquasi-elastic(d,Q =300)simulationsinbentonite. Greensquaresand
s
redtrianglesshowanalyticallypredictedP-andS-wavearrivals,respectively . . . . . . . . . . . 22
2.6 Theroadmapofthecalibrationprocedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7 IllustrationofGOFevaluation: user-definedreferencepointsandcorrespondingnumericalpeaks
areshownbybluesquaresandredcircles,respectively. Theprojectionofformerandlatterontime
axisresultsintosetsofT andT respectively . . . . . . . . . . . . . . . . . . . . . . . . 26
i,exp i,num
2.8 NumericaltracescorrespondingtoS-waveandP-waveexperimentsinbounded/unboundedmodels
(a,b,respectively)andP-wavesimulationcorrespondingtocalibrated“no-sample”model. Red
circles,greentrianglesandbluesquaresshowanalyticallypredictedP-,bar,andS-wavearrivals,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
vii
3.1 (a)SchematicdiagramoftheultrasonicfacilityemployedintheexperimentstomeasureV and
p
V and used for iterative attenuation estimation (b) Material parameters used in the numerical
s
simulations. Theelasticmodulianddensityofbentonitevarywiththetemperatureanditswater
content (Tisato and Marelli [2013]); therefore we provide the range of values for V , V , and
p s
densityρthatwereassignedduringattenuationestimation. (c)Normalizedinputsignalsenttothe
emitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 (a) 1 asafunctionoffrequencyapproximatesconstantQ=25in1kHz–1MHzbandwidth.
Q(f)
Notethatthesignalspectrumremainswithinthesetfrequencyrangeatanycrosssectionofthe
setup(only4areshownforclarity). (b)Themechanicalrepresentationoflinearviscoelasticmodel
(inlet)andcorrespondingdispersionofS-wavevelocity. . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Goodness-of-Fitevaluationmethodology: a)pairedpeaksanalysis,shownforapairofanumerical
andexperimental;b)peakslopecomparisonandc)crosscorrelationofnumericalandexperimental
seismogramnormalizedbyautocorrelationofexperimentaltrace . . . . . . . . . . . . . . . . . . 37
3.4 Schematic diagram of the GTS tunnel, modified after Marelli et al. [2010]. The canister with
borosilicateHLRW-glassmatrixisplacedinthetunnelandisolatedfromthehostrockbybentonite
filling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 GOF estimation plots (a) and numerical traces (b,c,d) corresponding to a bentonite sample of
W = 20%,T = 40◦ C. Cold and hot colors indicate low and high values of GOF metric,
c
respectively. ThelocationsofP-andS-wavearrivalshownbygreensquaresandredtriangles,
respectively,indicatethefidelityofnumericalmodeltopropagatethesignalatconstantapparent
velocityV usingdispersionmodelswithdifferentrelaxationfrequenciesandinputvelocities
apparent
V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
corr
3.6 DistributionofQ andQ inbentoniteasafunctionoftemperatureandwatercontent: a)Q (W )
p s p c
andQ (W )atT =50,b)interpolatedQ (T,W )andQ (T,W )surfaceplots. . . . . . . . . . 41
s c p c s c
3.7 (a) Schematic diagram of the tunnel cross section A and monitoring system, the viscoelastic
parametersofthematerialsemployed(Table)and(b)seismograms,correspondingtomodelled
bentonitephysicalconditions(cases). Thereceiversareindicatedasblacktriangles,thesource
locationisshowninreddiamond. Thetablesummarizestheviscoelasticparametersthatwere
assignedtobentoniteonacase-by-casebasis. Forbetterwaveformcomparison,themainsignal
arrivalsforreceivers#9and#10areshown. Seismictracesarecolor-codedbasedonthephysical
conditions(modelingcase)theyreferto. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.8 (a) Schematic diagram of the tunnel cross section B and monitoring system, the viscoelastic
parametersofthematerialsemployed(Table)and(b)seismograms,correspondingtomodelled
bentonite physical conditions (cases).The receivers are indicated as black triangles, the source
locationisshowninreddiamond. Thetablesummarizestheviscoelasticparametersthatwere
assignedtobentoniteonacase-by-casebasis. Seismictracesarecolor-codedbasedonthephysical
conditions(modelingcase)theyreferto. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.9 PseudocolorplotforreceiverqualitymatrixR,correspondingtofourreceiversemployedinthe
crosssectionAmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.10 PseudocolorplotforreceiverqualitymatrixR,correspondingtofourreceiversemployedinthe
crosssectionBmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
viii
Preamble
Thepresentthesishasbeenpreparedasacollectionoftwojournalarticlesfocusedontheestimationofviscoelastic
properties of bentonite and monitoring of high-level radioactive waste (HLRW) repositories. However, at the
momentofthesissubmission,onlyChapter2hasbeensubmittedandisinpressinascientificjournal. Bothtopics
arestudiednumerically. Theinvestigationaimsat:
• proposingamethodologytocalibratethenumericaltoolsforaccuratereproductionoflaboratoryexperiments;
• presentingatechniquetonumericallyestimateattenuationinthematerialofinterestbasedonlaboratory
data;
• providingasolid“foundation”foranumericaltoolthatenablessimulationsoftheactiveseismicmonitoring
intheHLRWrepositories.
Chapter1servesasanintroductiontothefundamentalsofwavepropagationtheory,thatisinthebasisofthis
thesis,suppliedwiththeequationsandconceptsgoverningthepropagationofwavesinbothidealizedelasticmedia
andmediawithdissipation. Abriefoverviewofthenumericaltools,simulatingwavepropagation,isprovidedat
theendofthechapter.
Chapter2presentsastep-by-stepguideforthecalibrationofnumericaltoolsbasedoniterativeprocedure
appliedtothelaboratorydataonultrasonicwavepropagationinbentonite. Varyingtheinputvelocitymodel,we
attempttoeliminatetheuncertaintyintheinputvaluesanddelayscausedbytheimperfectionsofthesetup. The
proposedcalibrationmethodologyissomewhatuniversalandinprinciplecanbeappliedtonumericaltoolsof
differentconstitutionandemploydatafromvariousultrasonicexperimentalsetups(publishedinJournalofRock
MechanicsandGeotechnicalEngineering,1,no. 5,1–9).
Chapter3proposesamethodologyofestimatingqualityfactorsinbentoniteusingforwardmodelingiterative
procedure.Thefirststepwastoexaminethedependenceoftheattenuationonthetemperatureandthewater-content
ofbentonite. Thesecondstepwastoassessthereliabilityoftheproposedactiveseismicmonitoringroutineby
modelingthewavepropagationatfull-scalerepositorymodel,incorporatingviscoelasticpropertiesofbentonite(to
besubmittedtoGeophysicalJournalInternational).
Chapter4summarizesthemainfindingsofthethesisandprovidesanoutlookonpossiblefutureresearchpaths
thatcouldimproveourknowledgeaboutattenuationmechanismsinlowpermeabilityclaysandtheusabilityof
seismicmonitoringofradioactivewasterepositories.
1
Chapter 1
Introduction
1.1 Basics of wave propagation
Thissectionprovidesabriefexplanationoftheequationsandconceptsthatgovernthepropagationofelasticwaves.
Initially, a perfect elastic material that represents the ideal case in which no elastic energy is lost, is assumed.
Furtherdissipationmechanismsthatpartiallyabsorbpropagatingenergywillbeintroducedtomodelmorerealistic
materialbehavior.
Starting from a simplified, one-dimensional (1D) linear elastic model, it will be demonstrated that low-
amplitude,dynamicallyappliedstressestravelintheelasticmediumatafinitespeed(wavevelocity). Asanext
step,thetheorywillbeappliedtothree-dimensional(3D)case,andthewaveequationforfullyelasticwaveswill
beconstructed. Itwillbeshownthattwotypesofsolutionsarepossible,correspondingtocompressional(P)and
shear(S)waves,andwillderivetheequationsfortheirvelocities. Thesolepurposeofthesectionistointroduce
thereaderwiththeprinciplesdescribingthewavepropagationwithoutintroducingthecomplicationsthatarisedue
totheimperfectionsandtheviolationofassumptions.
1.1.1 1Dcase: extensional(bar)waves
Figure1.1: Wavepropagationphenomenoninaperfectlyelasticrod.
Consideraslenderelasticrodofagivencross-sectionalshapethatisuniformalongtherodaxis(x-direction,
2