Dpartmenet fdral de lenvironnement, des transports, de lnergie et de la communication DETEC Ofiice fdral de lnergie OFEN D:\SecureDATA\Forschungsprogramme\TP0067 F-Wasserkraft\01 laufend\P103095 Design of pressure tunnels and shafts\V154103 Design of pressure tunnels and shafts\Berichte\Titelseite Rapports annuel 2009.doc Rapport annuel 2009 Dimensionnement des galeries et puits blinds Design of steel lined pressure tunnels and shafts D:\SecureDATA\Forschungsprogramme\TP0067 F-Wasserkraft\01 laufend\P103095 Design of pressure tunnels and shafts\V154103 Design of pressure tunnels and shafts\Berichte\Titelseite Rapports annuel 2009.doc Mandant: Office fdral de lnergie OFEN Programme de recherche Force hydraulique CH-3003 Berne www.bfe.admin.chCofinancement: Competence Center for Energy and Mobility CCEM-CH, CH-5232 Villigen PSI Mandataire: Ecole Polytechnique Fdrale de Lausanne EPFL Laboratoire de Constructions Hydrauliques LCH Station 18 CH-1015 Lausannelchwww.epfl.chAuteurs: Fadi Hachem, EPFL-LCH, fadi.hachem@epfl.chProf. Dr. Anton Schleiss, EPFL-LCH, anton.schleiss@epfl.ch Responsable de domaine de lOFEN: Dr. Michael MoserChef de programme de lOFEN: Dr. Klaus Jorde Numro du contrat et du projet de lOFEN: 154103 / 103095 Lauteur de ce rapport porte seul la responsabilit de son contenu et de ses conclusions. ii Table of content Sommaireiii1. Recall12. Practical relevance of this research13. State-of-the-art and gaps of knowledge23.1 State-of-the-art23.2 Remaining gaps of knowledge24. An overview of the research plan and the main project objectives35. Physical scaled model46. Prototype measurements67. Theoretical model68. Project timetable79. Follow-up of the project810. Bibliography811. Appendices8List of Figures Figure1.1:PartnersandmainobjectivesofHydroNetprojectconsortium 1Figure4.1:Mainobjectivesoftheresearchproject 4Figure5.1:Schemeofthephysicalscaledmodel 5Figure5.2:Detailedschemeofthetestpipeandmeasuringsensors 5Figure6.1:GeneralplanviewofGrimselIIpowerplant 6Figure7.1:Crosssectionofthetheoreticalmodelofpressurizedsteellinedtunnels 7Figure8.1:Projecttimetableschedule 7

iii Sommaire Lafortedemandedelnergiedepointeoffreuneoccasionuniqueauxproducteurs hydro-lectriquessuissespouraugmenterlacapacitdeproductiondeleursusines.Les centraleshydro-lectriquesdoiventoprerdesvitessesvariablesassurantlquilibre production-demandeavecefficacit,flexibilitetscurit.Parconsquent,lesprojetsde pompage-turbinageontgagnd'importancemajeurcarilspermettentun approvisionnementdnergiedepointeenfaisantcirculerleseauxentredeuxrservoirs amont et aval situs des altitudes diffrentes. Danslebutdoptimiserlecomportement des amnagements hydro-lectriques et plus particulirementlesamnagementdepompage-turbinage,unconsortiumtechnique nommHydroNetatmisenplacepourdfinirunenouvellemthodologiepourle dimensionnement,lafabrication,lopration,lauscultationetlecontrledescentrales hydro-lectriques. Ce consortium permettra doffrir de nouvelles ides la technologie de productionhydro-lectriqueetdemaintenirlapositionprivilgiedelaSuissedansce domaine ainsi que dans l'exportation de la haute technologie. Lerlecldegniecivildansceconsortiumsersumedansledimensionnement, lauscultation et le contrle des galeries et puits blinds en se proccupant essentiellement de la scurit de ces ouvrages. La scurit d'une centrale hydro-lectrique est primordiale car ce type damnagement doit tre dimensionner pour remplir son rle pour une dure de service pas moins que 90 ans. L'optimisation des rgles de dimensionnement et la proposition de nouvelles mthodes de contrle et dauscultation des galeries et puits blinds constituent le sujet de cette thse. Uneattentionparticulireseraconsacrel'interactionstructure-fluideainsiqula propagationdesondesacoustiquesdansleauetdanslesrochesavoisinantes. Ltablissementetlexploitationdunmodlephysiquechellerduiteainsique lanalyse des mesures effectues sur prototype permettra dtablir des nouveaux modles thoriquesdelinteractionfluide-structuresuitedesfluctuationsdepressions provoquesparlescoupsdeblier.Ilseraensuitepossiblededvelopperdesnouvelles mthodes et procdures de dimensionnement pour les puits blinds. Ces mthodes seront basessurlecomportementcontraintes-dformationsduchemisageenacieren considrant linteraction entre les diffrentes composantes de la structure savoir; lacier, le bton et le rocher. Les rsultats de ces analyses reprsentent une cible cruciale en Suisse suite la rupture du puits blinds de lamnagement hydro-lectrique de Cleuson-Dixence endcembre2000.Uneruptureprovoqueparledveloppementetlapropagationdes micro-fissures dans les soudures de l'acier du blindage. Depuis1980,aucunerecherchefondamentalen'apastmenedanslecadrede dimensionnementdespuitsblindsconsidrantlinteractionaveclerocher.Le comportementreldelastructurecomposeenacier,btonetrochern'estpasencore totalement compris surtout leffet des svres coups de bliers sur le comportement de la structureencourtetlongdureainsiquesurlascuritdublindage.Apriori,des modles en lments finis existent actuellement mais ils ne sont pas calibrs d la dficit desdonnesmesuressurprototype.Cesmesuresnesontpassouventdisponibles,etsi elles existent, elles sont inaccessibles pour les travaux de recherche. Ledimensionnementetlanalysedelascuritdesgaleriesetpuitsblindsbasssur l'idedegarderlacontrainteadmissibledansleblindageau-dessousdelalimite iv dlasticitdelacierutilissontdevenusinsuffisantsdepuislutilisationfrquentedes aciers de blindage haute rsistance. Ce type dacier possde un risque de rupture fragile plus lev que les aciers ordinaires relativement ductiles. Lestudesantrieuresontmontrqu'iln'yaaucuneraisonpoursinquiterdu problme de fatigue du blindage en aciers ductiles. Nanmoins, cette conclusion peut tre critiquequandl'acierhautersistanceestutiliscommeblindagepourlespuitsdes amnagementshydro-lectriquesdehautechuteetdanslescentralesdepompage-turbinage. Dans ces dernires, les amplitudes des fluctuations de pression sont plus faibles maispossdentunefrquenceplusleveconduisantainsiunnombreconsidrablede cycles de contrainte. Ce projet de recherche vise dvelopper de nouvelles et innovatrices directives pour le dimensionnementdesgaleriesettunnelsblinds.Elletraiteraprincipalement,dansle cadre dune thse, les points suivants: 1-Etude de littrature, qui indiquera les paramtres principaux d'intrt du problme et les pistes conqurir. 2-Basesthoriques,dontlebutprincipalestdedcrirelaphysiquederrireles diffrents phnomnes. 3-Mesuressurprototype,olepuitsblindsd'unecentralelectriquedepompage-turbinage sera quip par des instruments de mesure non-intrusifs. Les rsultats de cesmesurespermettrontdecomprendrelecomportementdublindageetdeses lments principaux. 4-Modlisationphysiquechellerduite,d'uneconduiteenacierenrobepardu btonoupardautresmatriaux.Descoupsdeblierserontcrssousdes conditions aux limites bien contrles et sous des oprations de vanne de fermeture bien dfinies. 5-Analyse des mesures effectues sur prototype, qui seront utiliss pour vrifier les modles thoriques et pour calibrer les modles en lments finis. 6-Dveloppementdemodlethorique,bassurl'analysedesrsultatsdesessais dcrivant la rponse de la structure des pressions internes transitoires svres. 7-Nouvellesdirectivesdedimensionnement,pourleblindagedesgaleriesetpuits en acier haute rsistance soumis aux variations de pression hydrauliques internes svres. 8-Rapport de thse et publications scientifiques. Cerapportdcritbrivementlesobjectifs principauxdelathseetrsumelestravaux effectus durant la priode entre aot 2008 et aot 2009. Mots cls :Centraleshydro-lectriquesdepompage-turbinage,dimensionnementdespuits blinds, structure compose, pression interne transitoire, mcanique de rupture fragile etfatigue,mesuressurprototype,propagationdesondes,directivesde dimensionnement. FADI HACHEM LCH EPFL - 1 -1.Recall Modern power plants are expected to operate at variable speed in a wide range of output powerwithimprovedefficiency,flexibilityandsafety.Therefore,thepumpedstorage powergenerationhasgainedinimportancesinceitallowsstoringandgenerating electricitytosupplyhighpeakdemandsbymovingwaterbackandforthbetween reservoirs at different elevations. A projectconsortium,called HydroNet (Modern Methodologies for Design, Manufacturing and Operation of Pumped-Storage Power Plant) (Figure 1.1) has been built aiming to converge towardsaconsistentstandardizedmethodologyfordesign,manufacturing,operation, monitoring and control of pumped storage power plants in order to give new impulsions inthehydropowertechnologyandmaintainthestrongpositionofSwitzerlandinpeak hydropower production as well as in the exportation of high valued technology. One of the civil engineering field involved in this consortium is the design and control of pressurized shafts and tunnels with a special focus on safety. Since 1980's, no significant fundamentalresearchhasbeenperformedaimingtointegratedesignwithinteraction betweenwater,steelliningandrockmass.Theresultsoftheseinvestigationsstandfora crucialtargetinSwitzerlandsincethecollapseoftheshallowburiedpressureshaftof Cleuson-Dixence hydropower plant in December 2000. Figure1.1:PartnersandmainobjectivesofHydroNetprojectconsortium2.Practical relevance of this research This research project will end to some practical applications, mainly: 1- Newdesignguidelinesforthesteeltunnellinersusinghigh-strengthsteeland subjected to severe internal hydraulic pressure fluctuations. 2- Developmentofnewtheoreticalmodelbasedontheanalysisofthetestresults describing the structure response during severe hydraulic transients. HYDRODYNAMIC(EPFL - LMH)ELECTRICITY(EPFL - LME)(EPFL - LCH)ECOLOGY ISSUES CIVIL ENGINEERING(EAWAG)OPTIMUM DESIGN AND OPERATION OF PUMPED STORAGE POWER PLANTSCivil engineering Sedimentation Pressurized waterwaysControl & MonitoringRotor-Stator Flow induced Unsteady behaviour & hydro acousticControl & MonitoringDownstream ecologicaleffects of particlesPhysical & Chemicalchange of particlesMotor-Generator optimizationTransient Behaviour (SIMSEN-UMP MonitoringControl strategies for variable speedCONTROL & MONITORING- Instrumentation of existing power plant- Data collection and storage- Signal processing data mining- Validation of monitoring methods- Predictive maintenance- Non-intrusive instrumentation- Profitability optimization (Economy)HydroNet FADI HACHEM LCH EPFL - 2 - 3- Relevant monitoring methods for steel liner tunnels and shafts using non-intrusive instrumentation.Thesemethodswilldetectsomespecificphysicalmeasurandsneededtopredictmaintenanceworksthatminimizetheriskofacatastrophic failure of the structure. 3.State-of-the-art and gaps of knowledge 3.1State-of-the-art TheState-of-the-art,hasbeenalreadypreparedbasedonanextensiveliteraturereviewof theessentialdesignrequirementsandfieldsrelatedtothesteelliningstructure(referto theDemandedesubside(2008)ReportaddressedtoOFEN).Tounderstandthe behaviourofsuchcompositestructure,adiscussionhasbeendoneonthematerials propertiesandthewaythatmayinfluencetheresistanceofthestructure.Itwasshown thattheactualdesignisbaseduponthesameconceptofanycompositestructurewhere the need for a full understanding of the behaviour of its three composing materials: Steel, Concrete and Rock is essential for any attempt for design. It is known that the steel lining mustcarryloadswithoutexcessiveyieldingorruptureandthatthegeologicaland geotechnicalparametersofthehostedrockarethekeyissuefordeterminingtheload sharing ratios between the composite materials of the steel lining system. 3.2Remaining gaps of knowledge Throughanextensiveliteraturestudy,adetailreviewoftheavailabledesignrulesfor pressurizedsteellinertunnelsandshaftshasshownthatresearchanddesignhasbeen conducted mainly during the period of construction of hydropower plant in Europe until the1980's.Since then,nosignificant fundamental research has been performed aiming to integrate design with interaction between lining and rock mass. The true behaviour of combined steel-concrete-rock linings is not yet fully understood, especiallytheinfluenceofseveretransientflowphenomena,suchaswaterhammer effects, on the short and long term structural behaviour and safety of the lining.Theexistingdesignmethodshavebeenbasedontheideaofkeepingtheallowable stress in steel liner below yielding point with respect to a certain requirements concerning properties of the steel used (e.g. ductility) and some construction details and tolerances to minimizestressraiserpoints.Designingandsafetyassessmentofthesestructuresbased ontheexistingmethodshavebecomeinsufficientsincerecentlyveryhighstrengthsteel liners are used with a high risk of brittle failure. Previousstudieshaveshownthattherearenoreasonforconcernwithregardtothe fatigue strength of the ductile steel linings. Nevertheless, this conclusion can be criticized when high-strength steel is used in high-head hydropower plant and in pumping-storage schemes where pressure waves of smaller amplitudes but of high frequencies can lead to a very high number of stress cycles. It is well known that water hammer phenomenon forces the steel liner shell to vibrate. Thesevibrationscreateacousticwavesinwaterandpressurewavesinthesurrounding rock mass. These waves have not been measured before, even so, they can carry precious informationabouttheresponseofthetunneltotransientpressurefluctuations.By FADI HACHEM LCH EPFL - 3 - processingthemeasuredwavesignals,itisexpectedtoassesstheequivalentelastic properties of the steel lined tunnel or shaft. Theactualdesigncriteriaandmethodsforloadsharingcalculationsforsteellined pressuretunnelsandshaft,aswellas,theactualgapsofknowledgehavebeenreviewed anddiscussedin(HachemandSchleiss,2009).Thispaperisjointedtothisreportin Appendix A.1. 4.Anoverviewoftheresearchplanandthemainproject objectives TheresearchplanofthisprojecthasbeensubmittedtotheDirectoroftheDoctoral Program in Structures EPFL in the 8th of august 2008. It was accepted by the dean of the doctoral school of the EPFL in the 22nd of august 2008.Thehydraulic-mechanicalinteractionbetweenwater,steel,concreteandrockwillbe investigatedindetail.Thiswillallowbetterassessingofthetechnicalpotentialof pressurizedwaterwaystosatisfyfuturepracticalapplicationsofhydropowerschemes submittedtoseveremarketconstraints,includingmultipledailyopeningsandclosings manoeuvres in the power house due to peak load demands. The research project mainly focus on the following subtasks : 1-Literaturestudy,inwhichtheavailabledesignrulesforpressurizedsteellinings waterwaysandthecoupledbehaviourandloadsharingcalculationofthe composite structure have been reviewed. 2-Theoreticalbases,thatmayincludetheoryonfracturemechanicsofsteeland fluid-structure interaction and wave propagation in water, in the steel liner and in thesurroundingrockmedia.Themaingoalistotheoreticallydescribethemain physics behind the different phenomena in question. 3-Prototypemeasurements,thatwillbeperformedonthepressurizedshaftof GrimselIIpowerplantinSwitzerland.Theshaftwillbeequippedwithnon-intrusiveinstrumentstoacquireprototypemeasurementsneededforcalibration and verification of the theoretical model of the lining and its main elements. 4-Physical scaled modelling, which consists of a test conduit made of several pieces ofdifferenttypeofmaterials(steel,PVCandaluminium)wherewaterhammer phenomenonwillbecreatedundercontrolledboundaryconditionsandgate operation.Thepropagationofpressurewavesinwater,inthepipewalland throughthepipescoverwillbemeasuredandprocessedfordifferentconduit layouts and configurations. 5-Analysisofmodelandprototypemeasurements,thatwillbeusedtoverify theoretical developments and to calibrate finite element models. 6-Developmentoftheoreticalmodelbasedontheanalysisofthetestresults describing the structure response during severe hydraulic transients. 7-Newdesignguidelinesforsteeltunnellinersusinghigh-strengthsteeland subjected to severe internal hydraulic pressure fluctuations. 8-Dissertation report and scientific publications The main objectives of this research project are summarized in Figure 4.1. FADI HACHEM LCH EPFL - 4 - Figure4.1:Mainobjectivesoftheresearchproject5.Physical scaled model Inpurposetounderstandthecomplexproblemrelatedtowavespropagation,aphysical scaledmodelisnowunderconstruction(Figure 5.1).Itwillbeequippedtobeableto producewaterhammershockwavesunderawellcontrolledboundaryconditionsand gate operation. Inadditiontothetraditionalphysicalmeasurementsneededtostudythistypeof problem (e.g. water flow, pressure transducers, etc.), the model will be equipped with twohydrophones and five geophones sensors that are able to capture pressure waves in water andwavespropagatingalongandtransmittedoutwardthepipeswallandcover.The measured signals will be processed and studied in time and frequency domains trying to relate them to the elastic properties of the pipe. Differentconfigurationswillbeexaminedbychangingsystematicallythepositionof thesteelconduitflangesandbyreplacingandchangingthepositionofconduitpieces made of other type of materials. Figure5.2showsamoredetailedviewofthetestpipescheme.Theconstruction drawingsoftheinstallationandthedifferenttestpipeconfigurationstobestudiedare given in Appendix A.2. TestswillstartbyinthemiddleofSeptember2009attheLaboratoryofHydraulic Machines(LMH)wherethephysicalmodelisbuilt.Atotalofabout40to45 configurations(seeAppendixA.2)havetobetestedandanalyzed.Thetestcampaignis expected to end in April 2010. New designguidelines Development of a theoretical model c onsidering theFluid-Structure Interactionunder transient pressureUsing fracturemechanics to assess the response of high-strength steel used as linerNon-intrusive monitoring & Control methodsTo detect hot spots in the structure during transients Elasticity deteriorationUsing test results from a physical scaled model set -up Prototype measurements Grimsel siteFADI HACHEM LCH EPFL - 5 - Figure 5.1 : Scheme of the physical scaled model Figure 5.2 : Detailed scheme of the test pipe and measuring sensors The test pipeWater suppl ysystemFl ow meterMai n reservoi rPumpFl ow di recti onAi r chamberShut-off valve(L=7000 ; di=150 ; ts=4.5)STEEL CONDUIT TEST MODEL(DN=150)SHUT-OFFVALVE AIR VESSELSTEEL CONDUIT TEST MODEL(L=7 m , di=150 mm , ts=4.5 mm)GEOPHONEPRESSURE TRANSDUCERSHYDROPHONEHYDROPHONEFADI HACHEM LCH EPFL - 6 - 6.Prototype measurements The pressurized shaft of the high-pressure side of the pumping-storage hydropower plant of Grimsel II in Switzerland (Figure 6.1) will be equipped with pressure sensors, geophones and hydrophones sensors allowing the performance of prototype-scaled measurements of theliningresponseanditsmainelements.Detailedanalysisofresultsandcomparison with the theoretical model will be performed to verify its adequacy and efficiency. Based on the analysis of the test results, adaptation and optimization of the theoretical modelwillbeperformedtodescribethecoupledbehaviourofwater-steel-concreteand rock system during severe hydraulic transients. Figure 6.1 : General plan view of Grimsel II power plant After several site investigations, the actual sensing equipments (position, performance, dataacquisitionsystem,etc.)havebeenidentifiedandneedsforotherormorepowerful equipments have been clarified (see Appendix A.3). The one-year measurement campaign is planned to start by the end of September 2009. 7.Theoretical model AFluid-StructureInteraction(FSI)theoreticalmodelwithaxisymmetricalbehaviourand longitudinalmotionisactuallyunderpreparation(Figure7.1).Thismodelcandetectthe compressionalwatermodeinwaterandtheradialandaxialpropagationmodesinthe steel liner and in the far field rock zone. Thetime-dependentstressdiagrams,resultingfromtheFSIproblem,willbeusedas inputforthedeterministicandprobabilisticfracturemechanicsmodelsofsteelliners.A finite element model will be build and results will be compared with those obtained from thetheoreticalmodel.Thephysicalandprototypemeasurementswillbeusedfor calibration and verifications. The final results may be used to adapt some existing design procedures in aeronautical field, nuclear power plants and long span steel bridges to steel liners design. FADI HACHEM LCH EPFL - 7 - Figure 7.1 : Cross section of the theoretical model of pressurized steel lined tunnels 8.Project timetable The time schedule of the different project phases can be given as follows : Figure 8.1 : Project timetable schedule Backfill concreteClose field rock zoneFar field rock zoneSteel liner( ) i t x/ci [u, v, p] = [u(r), v(r), p (r)] e Initial gapSeriesofSprings, Dashpotsand additional Masses (Kelvin model)FADI HACHEM LCH EPFL - 8 - 9.Follow-up of the projectBesidethefollowing-upbythedirectorofthisresearchwork,Prof.AntonSchleiss,this researchprojectissupervisedcloselybytheseniorresearchassociates,DrErikBollaert andDrJean-LouisBoillat.Accordingly,progressmeetingsareplannedregularly,every five to six weeks, with the research project director and the senior research associates. One to two times a year, the progress state of the project will be presented as an internal conferencesatLCH(oneconferencehasbeengivenonthe7thofNovember2008andthe secondwilltakeplaceonthe4thofSeptember2009).Furthermore,twointermediate reportsattheendofthefirstandthesecondyearwillbeprepared(thefirstreporthas been submitted in August 2008). IntheframeworkofthemultidisciplinaryCCEM-project,periodicalsessions(2per year)willbeorganizedtoshareinformationandtodiscusstheprogressoftheproject (three technical meetings have took place until now). 10.BibliographyDemandedesubsidelOFEN(2008).Projetderecherche,Dimensionnementdesgalerieset puits blinds. Laboratoire de Constructions Hydrauliques (LCH). Hachem,F.andSchleiss,A.(2009).Thedesignofsteel-linedpressuretunnelsandshafts. International Journal on Hydropower & Dams, 16(3):142-151. 11.Appendices A.1The state-of-the-art of the design of steel-lined pressure tunnels and shafts. A.2The construction drawings and test configurations of the physical scaled model. A.3Sensing requirements for the prototype measurements. FADI HACHEM LCH EPFL - 9 - A.1 The state-of-the-art of the design of steel-lined pressure tunnels and shafts Steel-lined pressure shafts and tunnels in rock arethekeystructuresofhydroelectricpowerplants.Becauseofthehigherpeakenergydemands,hydroplantshavetooperateunderroughconditionsas regards the output power with improved efficiency,flexibilityandsafety.Therefore,thedevelopmentofnewdesignguidelinesforpressurizedwaterwaysys-temsisrequired,basedonthedetailedstress-strainbehaviourofthelining,andtakingintoaccountacombinationofdifferentmaterialssuchashighstrengthsteel,concreteandrock.Theimportanceofsuchnewguidelineshasbeenunderlinedbythecol-lapseoftheshallowpressureshaftattheCleuson-DixencehydroplantinSwitzerland,inDecember2000.Since the 1980s, no significant fundamental researchhas been carried out regarding the interaction betweensteellinersandthesurroundingrockmass.Thetruebehaviourofcombinedsteel-concrete-rockliningsisnotyetfullyunderstood,especiallytheinfluenceofseveretransientflowphenomena,suchaswaterham-mereffects,ontheshort-andlong-termstructuralbehaviour and the safety of the lining. Powerful finiteelement models do exist, but they are rarely calibratedbecause of the lack of prototype measurements.This paper gives an overview of existing methods forloadsharingcalculationsanddesignguidelinesforsteel-linedpressuretunnelsandshaftsunderinternalwaterpressure.Adistinctioncanbemadebetweencalculations for axisymetrical isotropic and anisotrop-icrockmassessurroundingtheliner.Highstrengthsteel is more and more often used for steel liners. Forsuch steel, design methods based on yielding strengthcan be questioned. Also, gaps in knowledge are iden-tified and future research is suggested based on frac-turemechanicstheory,aswellastheassessmentofwaterhammer-inducedacousticwavesinwaterandpressure waves in the surrounding rock mass.1. Current design criteria for steel linersBasic criteria for the design of steel-lined sections oftunnelsandshaftsasrecommendedbySchleiss[19881] are:(A) working stress and deformation of the steel liner; and,(B) load-bearing capacity of the rock massCondition AThisreferstothebehaviourofthesteelliner,andincludes:A1. stability of the steel liner under external water pressure;A2. limiting working stresses in the steel liner; and,A3. limiting local deformation of steel liner (crack bridging).Condition A1In accordance with normal practice, a factor of safetyof 1.5 against buckling should be adopted. If the act-ing external water pressure is based, because of a lackoffielddata,onveryconservativeassumptions,asafety factor of between 1.15 and 1.30 is sufficient. Inthe case of a sandwich lining, the compressive stress-es in inner concrete ring should be well below the ulti-matestrengthoftheconcrete(thesafetyfactorsapplied in the different codes vary from 1.8 to 2.5).Condition A2The stresses in the steel liner are derived based on thecompatibilityoftheradialdisplacementsofthesteeland rock at their boundary, as transmitted by the back-fillconcrete.Loadsharingbetweensteellinerandrockshouldbedeterminedbytakingintoaccountacrackedbackfillconcrete(notangentialstressescanbe transmitted) and the effect of a crack stress-relievedrock zone. Condition A3 The steel liner must be able to bridge any cracks in thebackfillconcretewhichdevelopunderinternalpres-sure.Since,forreasonsofsymmetry,aminimumoftwocrackswilloccur,themaximumexpectedwidthof the cracks will be equal to the half of the total cir-cumferentialdeformationoftherockmassunderinternal pressure. This condition only comes into playfor very thin steel liners as in case of sandwich liningswithsteelmembraneswherethicknessarenotgov-erned by buckling.Condition BThepurposeofthisconditionis,ontheonehand,tocheck the load sharing assumed for Condition A2 and,ontheotherhand,toguaranteesufficientsecurityagainstrockmassfailure.Themaximumrockmassparticipationisequaltothemechanicalpressuredeveloped at the boundary between the steel liner (orbackfill concrete) and the rock at which the rock canno longer share the load. In principle, this limited loadsharingisreachedassoonasthemaximumtensilestressesintherockmasscausedbythatboundarypressureexceedthenaturalstressesintherockmass(in a plan perpendicular to tunnel axis).142 Hydropower & DamsIssue Three, 2009The design of steel-linedpressure tunnels and shaftsF. E. Hachem and A. J. Schleiss, Laboratory of Hydraulic Constructions, EPFL, SwitzerlandThe state-of-the-art of the design criteria and the methods for load sharing calculations for steel linedpressure tunnels and shafts is reviewed here. The design methods mainly based on allowable stresses in thesteel liner can be questioned if high strength steel is used. After addressing the problematic nature of suchsteel, the author outlines the application of fracture mechanics theory in the design of steel liners. A newresearch project is briefly described, where the acoustic signal of waterhammer will be used to access thestructural stiffness of steel lined pressure tunnels and shafts.In the following, the design criteria for internal waterpressure are discussed more in detail.2. Load sharing between the steel linerand surrounding rock mass2.1 Radial symmetric calculation modelThedeterminationoftheloadsharingbetweenthesteel lining, the backfill concrete and the surroundingrockmassisnormallybasedonelastictheory.Theradial deformation of the steel liner is put equal to theradialdeformationofthebackfillconcreteandtherock mass in the so-called compatibility condition ofdeformations.For the calculation of the load sharing, five differentzones are considered (see Fig. 1): 1. Steel lining, which is in direct contact with the pres-surizedwater.Itprovidesanimperviousmembraneand carries a certain part of the internal pressure pi.2. Initial gap, between steel and backfill concrete. Thesteellinerwillshrinkasaresultofthecontactwithcoldwater,leavingasmallgapDr0 betweenthetwomaterials. A typical value of Dr0 equal to 0.25 of ri isoftenusedindesigncorrespondingtoatemperaturedecrease of 20oC. The gap caused by the shrinkage ofthebackfillconcreteisnormallyfilledbygroutingbefore the pressure shaft or tunnel is put into operation.3. Concrete,asabackfillbetweenthesteellinerandthe excavated rock. Having a tensile strength of about1 to 2 MPa, the backfill concrete is normally fissuredunder internal pressure and cannot transmit tangentialstresses.4.Crackedrockzone,whichcorrespondstothedis-turbed part of the rock mass as a result of excavationmethodsandofthechangeinthestressfieldaroundtunnel. Being cracked, this part of the rock mass can-not transfer tensile stresses. The external radius rf andthemodulusofelasticityEcrm forthisdisturbedzonearethetwomostimportantparameterstobedeter-mined for the design. The external radius rf of the dis-turbed rock is normally estimated atbetween one andfive times the excavated tunnel radius ra [Brekke andRipley, 19872]. Nishida et al. [19823] have shown thatformechanicalexcavationbytunnelboringmachine(TBM),rf wasroughly0.3m,andforexcavationbydrill and blast, rf was roughly 0.5 to 1.3 m, both mea-suredin5mdiametertunnelincrystallinerock.Therefore, for good rock conditions, values of rf high-er than 1.0 to 1.5 times ra are considered as very con-servative. Schleiss [19881] suggested 0.5 to 1.0 m fortunnels excavated by (TBM) and 1.0 to 2.0 m for drilland blast.5.Soundrockzone.Thisnon-disturbedzoneisassumedasahomogeneous,isotropicandelasticmaterialhavingameanelasticdeformationmodulusErm thatcanbemeasuredin-situorestimatedforexample by the Hoek-Brown method [Hoek, 20064] orbyRMR orQ indexes[Bieniawski,19735]and[Gurocak et al., 20076].2.2 Solving the compatibility condition2.2.1 Analytical methodsOnthebasisofthecompatibilityofdeformations,Table 1 illustrates approaches for the calculation of theload transfer suggested by various authors. The maindifferencesbetweentheseapproachesarisefromassumptionsregardingthebackfillconcrete(crackedoruncracked),theextensionofthedisturbedrockzone as well as the annular gap.Theeffectontherockmassparticipationandthepresence of an annular gap can change the results sig-nificantly. For example, increasing the outer radius ofthedisturbedrockzonefrom2ra to5ra decreasesthepercentage of the load transferred to rock from 45 to20percent.Decreasingthemodulusofelasticityofthe disturbed rock mass, having an outer radius of 3ra,from 75 to 50 per cent of Erm decreases the load trans-ferred percentage from 40 to 35 per cent.2.2.2 Graphical methodsSeveral authors have developed graphs for the designof steel liners [Nicolopolous, 19837].Seeber [19758] suggested a graphical solution of thecompatibilityconditionofdeformationsatthesteel-rock interface. Its application is illustrated in the lowerpressuretunneloftheNorthForkStanislausriverhydroelectric project. In this project, Schleiss [19881]enhancedSeeber-diagramtotakeintoaccounttherockconfinementandthecrackbridgingcriteriainisotropic rock mass. Once the internal water pressurehasbeenfittedbetweentheworkinglineoftherockmass (upper right quadrant of Fig. 2) and the workingline of the steel liner (lower right quadrant), the strainandhoopstressinthesteellinercanbeobtaineddirectly as well as the load sharing between the steelliner and the concrete-rock system.Therequiredeffectivedepthofcover(upperleftquadrant) and the crack bridging criteria (lower rightquadrant) will be discussed later.Hydropower & DamsIssue Three, 2009 143Fig. 1. Calculation model for steel liners with axisymetricalbehaviour.Fig. 2. Seeberdesign diagramincluding maximumrock massparticipationcriterion [Schleiss,19881].144 Hydropower & DamsIssue Three, 2009Table 1 : Load transfer calculation techniques for tunnel steel linings under internal pressuresReferenceSteel-Concrete-Rock systemRemarksCompatability of deformationsSteel =Backfill concrete +Cracked rock zone +Sound rock zone +Annual gap, Drq-Tche [194932][(ps.ri2)/(Es.t)].(l-v2)[(pc.rc)/Ec].(l-vc2).ln(ra/rc)[(pc.rc)/Erm].(l-vs2).ln(rf/ra)[(pc.rc)/Erm].(l-vs2).(l+vt)Not considered-Brekke [19872]after Gumensky(ps.ri2)/(Es.t)Treated as intact rockTreated as intact rock[(pc.rc)/Erm].(l+vs)Not considered-and Chu (1948)Vaughn [195633](ps.ri2)/(Es.t)[(pc.rc)/Ec].(l-vc2).ln(ra/rc)[(pc.rc)/Erm].(l-vr2).ln(rf/ra)[(pc.rc)/Erm].[(z2+rf2)/(z2-rf2)/(z2-rf2)+vr]kpri.w.DTkpis the ratio of plasticc to elasticdeformation of rockBrekke [19872]after Patterson et al(ps.ri2)/(Es.t)(pc/Ec).[(ra2-rc2)/(2ra)](pc.rc/Erm).[(rf2-ra2)/(2.ra.rf)][(pc.rc)/Erm].(l+vr)0.0003.ri-(195)]Brekke [19872] afterMoody (1959)(ps.ri2)/(Es.t)(pc+prl).(ra-rc)/(2.Ec)Treated as intact rock[(pc.rc)/Rrm].(l+vr)Considered butformulated-Brekke [19872] afterLaufer and [(ps.ri2)/(Es.t)].(l-vs2)Treated as intact rockTreated as intact rock[(pc.rc)/Erm].(l+vt)0.0003.ri-Seeber [196126]Brekke [19872]after Ramos and(pr.ri2)/(Es.t)Treated as disturbed rock[(pc.rc)/Erm].ln(rf/ra)[(pc.rc)/Erm].(l+vs)0.0002.ri-Abrams (1968)Brekke [19872]after Kruse (1970)[(ps.ri2)/Es.t)].(1-vs2)[(pc.rc)/Ec].ln(ra/rc)[(pc.rc)/Erm].ln(rf/ra)[(pc.rc)/Erm].(l+vr)0.0001.ri-Brekke [19872] afterJacobsen (1977)[(ps.ri2)/(Es.t)].(l-vs2)Treated as intact rock[(pc.rc)/Erm].ln(rf/ra)[(pc.rc)/Erm].(l+vs)0.0005.ri-Schleiss [19881](ps.ri)/Es.t)[(pc.rc)/Ec].(l-vc2).ln(ra/rc)[(pc.rc)/Erm].(l-vr2).ln(rf/ra)[(pc.rc)/Erm].(l+vr)0.00025.ri-Moore [198934][(ps.ri2)/Es.t)].(l-vs2)[(pc.rc)/Ec].ln(ra/rc)[(pc.rc)/Ecrm].ln(rf/ra)[(pc.rc)/Erm].(l+vr)ri.w.DT; and it isEcrm= 50 to 75%nil in tropicalof Erm[Eskilsson, 199935]and semi-tropicalEM 1110-2-2901[199718][(ps.ri2)/(Es.t)].(l-vs2)[(pc.rc)/Ec].ln(ra/rc)[(pc.rc)/Ecrm].ln(rf/ra)[(pc.rc)/Erm].(l+vr)ri.w.DT-2.2.3 Numerical methodsIftherockbehaviourisanisotropicandinhomoge-neousaroundthetunnel,analyticalsolutionsarenotavailableanymoreandnumericalmethodsasfiniteelement approaches have to be used.2.3 Anisotropic rock mass behaviourIfthebehaviouroftherockmassisanisotropic(forexample,bedding,foliation,jointing,andsoon)thecircumferentialstressesinthesteellinerscanvaryconsiderably.Aroughestimationisoftenusedforaxisymetrical rock mass behaviour by using an over-allrockmassstiffnessequaltotheminimumvaluethattherockcanhave[BrekkeandRipley,19872].Nevertheless,withsuchanapproach,thenon-axisy-metrical deformation of the steel liner is not taken intoaccount.Eristov [19679and 196810] has studied the behaviourofpressuretunnelliningsinanisotropic,orthotropicelasticmediabydividingthelininginton beamele-ments. He established an analytical system that givesthe total radial deformation at q angle, Dr(q), along thelinerperimeterasafunctionoftheinternalpressure,thesteellinercharacteristicsandtheelasticreactioncoefficients of the rock mass kx and ky (kx < ky) mea-sured in two perpendicular directions x and y. A rela-tionshiphasbeenalsogiventoestimatethereactioncoefficients of the rock mass in the q direction.These relationships can be written, according to Fig.3, as follows:... [2.1]where:... [2.2]... [2.3]... [2.4]and n is the number of beam elements of the steel linerhaving the length of DS.It should be mentioned that Eristov's method is sim-ilartotheFiniteElementAnalysisdescribedinUSArmy Manual [199711]. In this Manual, the radial andtangentialspringstiffnesses(elasticreactioncoeffi-cients)areestimated,fora2-Dcalculationmodel,from equations (2.5) and (2.6).... [2.5]... [2.6]wherea isthearcdefiningthebeamelements,inradians:3. Assessment of the maximum rockmass participationThecalculationtechniquessolvingthecompatibilitycondition for load transfer assume directly a full loadsharingwiththerock.Therefore,thequestionisforwhichminimumrockcoverfullloadsharingcanbeadmitted.It is clear that for a tunnel or shaft situated very closetothegroundsurfaceortotheundergroundcavernsandchambers,thesteellininghastobedesignedforfull internal pressures without taking into account loadtransfer to the rock. For regions with low rock cover,thecapacityoftherockmasstowithstandthepres-sures transmitted from the steel lining is usually deter-mined by in-situ stress measurements (hydraulic jack-ingorfracturingandovercoring).Often,whentherockcoverisbelow20ri [Schleiss,19881and19922]no load sharing is considered. In the Indian Standards[199613],noloadsharingistakenintoaccountiftheoverburdenweightislessthan40percentverticallyand 120 per cent horizontally compared with the inter-nal water pressure under normal loading conditions.ThelefthandsideofFig.2showsthemaximumrockmassparticipationcurvecalculatedbySchleissas a function of overburden rock. This curve has beenimplemented in the design diagram for the lower pres-sure tunnel of the North Fork Stanislaus river hydro-electric project. A safety factor of SF = 2.0 was used.Inassessingadequateconfinement,mostofthedesigners use static head considering only the upsurgewater levels in the surge tank. The best way to assessthe maximum rock mass participation is to measure in-situ rock stresses in boreholes near the future tunnel orshaft.Sincesuchmeasurementsarenotalwaysavail-able, the rock mass participation can be estimated fromoverburden as the Fig. 2. Nevertheless, an assumptionof the ratio between the minimum horizontal stress andthe overburden has to be made (k0 value).Ithastobenotedthattheminimumprimarystresscanbelowerthantheonecausedbytheoverburdenmeasuredperpendiculartotherocksurfaceforsteepslopes [Seeber, 198514]. When measuring the perpen-dicular distance to the rock surface, protruding ridgesand noses do not affect the stress in the rock masses inavalleyside,andshouldthereforebeneglected.Simplifiedtopographicmapswithsmoothcontourlines, drawn inside such protruding features, should bedrawn [Broch, 198415].4. Crack bridgingSeeber[19758]proposedacrackbridgingcriteriasince the liner must be able to bridge the cracks in thebackfillconcrete.Inthemostcriticalcase,onlytwocrackscanoccurinthebackfillconcrete.Tobridgethesecrackssafely,Seeberstatedthatthesteelwallthicknessmustbeatleastequalorhigherthanthecrackwidthinastratifiedrockmasshavingdistinctelasticity modulus in both directions, parallel and per-pendiculartostratifications.So,thecrackbridgingcriteriawithoutconsideringasafetyfactor,wasdefined by:... [4.1]whereus istheradialdeformationandri theinternalradius of the liner.Hydropower & DamsIssue Three, 2009 145Fig. 3. Calculationmodel accordingto Eristov (1967,1968) for steelliners inanisotropic rockmass. At left: non-axisymetricdeformation ofsteel liner, in themiddle: elasticreactions of thesteel liner and atright: elasticreaction forcesbetween steel linerand rock.AccordingtoSchleiss[19881],forisotropicbehav-iouroftherockmass,thedeformationus leadstoauniformincreaseofthesteellinerperimeter.Forasafetyfactorequalto2.0,thecrackbridgingcriteriabecomes:... [4.2]InthelowerrightquadrantofFig.2,thiscrackbridgingcriteriaisimplementedinthedesigndia-gram. For a detailed assessment of the crack bridging crite-ria, Seeber and Danzl [198816] defined a critical ratio(df max/t)crit ,wheredfmax isthewidthofthelargestcrackinbackfillconcrete,takingintoconsiderationthe properties of steel, the friction coefficient betweensteellinerandconcrete,msc aswellas,theinternalpressure and the internal radius to steel thickness ratio(ri/t).Theyproposedarelationhipfor(dfmax/t)crit inanisotropic stratified rocks as follows:... [4.3]where:... [4.4]and, fm and em are respectively the maximum strengthand the corresponding strain of steel used.5. Comparison of recommendationsand codes for the design of steel liners5.1 Loads and load combinationsIn Europe, the C.E.C.T. [198017] recommendations havebeen developed for the design and construction of steel-lined tunnels and shafts. The US Army Manuals [199511and 199718] give recommendations for design of perma-nentsteellinings.TheIndianStandards[199613]treatthe subject of the structure design of steel lining.Forthedesignofpenstocksandsteellinedtunnels,the allowable stress method is used in which all loads(both dead and live loads) have a load factor equal to1. Loads include: Construction loads (handling, erecting, and so on) Live loads (earthquake) Dead loads (weight of the structure and rock loads) Intermittent loads (filling and drainage of tunnel) Service loads that are divided to:(1) Maximum static head minus the head losses plusthe waterhammer and surge during load rejection when all units are operating with normal governor closure time(2) Minimum static head minus the waterhammer and down surge occurring when all units operate from speed no load to full load acceptance(3) The head at transient maximum surge. Emergency loads which include:(1) Maximum static head plus waterhammer and surge during partial gate closure in critical time of (2L/a) seconds at maximum rate with the cushioning stroke being inoperative in one unit(2) Same as No1 but with the cushioning stroke being inoperative in all units. Exceptional loads including:(1) Unforeseen operation that produce instantaneouschanges in the flow rate(2) Rapid closure of turbine gates in less than (2L/a)seconds for maximum flow rate(3) Rhythmic opening and closing of the turbine gates when complete cycle of gate operation is per-formed in (4L/a) seconds.The combinations of loads adopted by different rec-ommendations are given in Table 2.The waterhammer or overpressure calculated by theelasticwatercolumntheory[Parmakian,196319andJaeger,197720],isingeneralassumedtobelinearlydistributedalongthedevelopedlengthoftheshaft,betweentheconnectionpointoftheshaftwiththesurgetankorwiththewaterintakeandthenearestdownstream closing gate.146 Hydropower & DamsIssue Three, 2009Table 2: Loads and load combinations (normal, intermittent, emergency and exceptional) for steel lining design, according to the three recommendations: CECT [1980], USACE Manual [1995] and Indian standards [1996]Loads Loading combinationsNormal Intermittent Emergency ExceptionalConstruction X XLive X X XDead X X X X X X X X X X X X X X X XIntermittent XService No. 1 X X XService No. 2 X XService No. 3 X XEmergency No. 1 XEmergency No. 2 XExceptional No. 1 XExceptional No. 2 XExceptional No. 3 XConsidered in the recommendationC.E.C.T. O O O O O O OEM 1110-2-3001 O O O O O O OIndian Standards O O O O O O O5.2 Equivalent and allowable stresses in steel linersAccordingtoC.E.C.T.[198017]andasgeneralrule,steelstressesaredividedintoprimaryandsecondarystresses.Theprimarystressesinduceddeformationsincrease with the loads even after the yield strength isexceeded. Secondary stresses are local stresses wheredeformationstoptoincreaseswithforceswhentheelasticlimitofthematerialusedisreached.Forcir-cumferentialortangentialstressesinsteelliner,pri-mary stresses are those caused by the internal pressuretaking into consideration the initial gap and the resis-tance of the hosted rock, if it is considered. In longitu-dinaldirection,primarystressesoccurasaresultofPoissonseffectofthecircumferentialstressesandcaused by friction.According to C.E.C.T. [198017], at least for primarystresses, all calculations have to be made in the elasticrange. The equivalent stress in the steel, seq is evalu-ated after combining longitudinal and circumferentialstresses with the Hencky-Von Mises theory in triaxialstate of stresses according to the relationhip:... [5.1]Inplanestresscondition(ss3 =0),Eq.(6.1)becomes:... [5.2]Theequivalentstressshouldnotbehigherthantheallowable stress at any point of the steel liner. In Table3, ratios of the allowable steel stresses to yield or ten-sile strengths as recommended in different sources aregiven.Itcanbenoticedthatforeachloadcombina-tion, these ratios are different if the internal pressure isshared or not with the rock mass.6. Problematic nature of high strength steel6.1 Historical development of the steelstrengthThe development of new steel grades was always dri-venbythedemandofhavingoptimalmechanicalcharacteristics for different uses. To increase the yieldstrengthofsteel,alloyingcarbonandmanganesehassome adverse effects on the weldability of the steel. Asecondpossibilityistheheattreatmentwherefine-grained structure is obtained with a better toughness.An updated version of the historical context of rolledsteelproductstakenfrom[SamuelssonandSchrter,200521] is shown in Fig. 4.Until1950,steelwhichistodayknownasS355J2accordingtoEN10025,wasconsideredasahighstrength steel. From the 1960s, the application of theQuenchingandTemperingprocessforsteelgradesbegan.Today,thisprocessgivessteelgradeswithyielding strength up to 1100 MPa and more, althoughonly grades up to 960 MPa yield stress are standard-ized.Inthe1970s,theThermo-Mechanicalrollingprocess was developed. This process produces gradesup to 960 MPa with better welding performance thansteels produced by (QT). 6.2 Requirement for yield to tensile strength ratioMost of the design codes define an upper limit of theyieldtotensilestrengthratio.Normally,theyieldstrength considered in the design should not be higherthan 80 per cent (for steel plates thicker than 50 mm)andthan90percent(forthinnersteelplates)ofthetensilestrength.Thislimitationpenalizestheuseofhighstrengthsteelsinstructuralapplications.Ithasbeen shown that this limitation is not relevant becausethetoughnessisindependentoftheyieldtotensilestrength ratio [Langenberg et al., 200022]. 6.3 Ductility and toughnessThetoughnessistheabilityofamaterialtoabsorbenergy prior to fracture. The larger the area under thestress-strain curve, the tougher the material is. In gen-eral,thetoughnessdecreaseswithincreasingyieldstrength of steels.Hydropower & DamsIssue Three, 2009 147Table 3: Allowable stresses in terms of what is used by some organizations and codesLoad combinationOganizationNormal Intermittent Emergency Exceptionalstandard ReferenceWithout With Without With Without With Without Withrock mass participation rock mass participation rock mass participation rock mass participation%fy %fu %fy %fu %fy %fu %fy %fu %fy %fu %fy %fu %fy %fu %fy %fuAISI Brekke after AISI 100 67C.E.C.T.C.E.C.T. (1980) 91 50 100 68-100 56PG&E Brekke after PGE 100 67 67 33SCE Brekke after SCEUSACE EM 1110-2-3001 50 25 67 33 100 50USBR Brekke after USACE 100 67Indian Standards IS (1995) 60 33 90 67 67 40 100 90 60 100 100Fig. 4. Historicaldevelopment ofyield strength forrolled steelproducts.High toughness and low carbon equivalent values inductile steel allow for lower welding preheat temper-atures,whichinturn,resultinlesshardeningandreduced tendency of cold cracking. 6.4 Hydrogen induced crackingThecoldcrackingordelayedcrackingisoneofthemostcommonandseriousproblemsencounteredinweldings of high strength steel. It can occur in the heataffectedzone(HAZ)andinfusionzone(FZ)oftheweldings. Tests have shown that hydrogen absorptioncanreach7ml/100gunderweldingwithoutusingshieldingmaterials(forexampleinertandsemi-inertgases, blanket of granular fusible flux of limes, silicaand so on). It can be reduced to 2 ml/100 g by usingsuitable shielding materials.6.5 Corrosion and stress corrosion crackingIn the presence of oxygen and water, or under certainsoilandelectricalconditions,refinedirontendstoreturntoitsmorestableform,ionoxide(rust).Thisreversion is an electrochemical natural process inher-ent to steel [AWWA, 200423]. Tensilestresses,cyclicstressesorhighfrequencyvibrations acting combined with a corrosive environ-mentcanenhanceoracceleratethedeteriorationofsteelknownasthephenomenonofstresscorrosioncracking. For high strength steel, the stress corrosioncrackingisasortofweakeningcausedbyhydrogenpenetratingintocracksanddiffusingfromthecracktipstowardthematerial. TheoriginofthishydrogencanbeH2 gasmolecules,waterordissociatedH2Smolecules.Thehydrogeninteractswiththemicro-fracturefacilitatingthereinitiationandpropagation.High strength steels and their weldings are sensitive tosuch phenomenon in presence of water and humidity.6.6 Fatigue loading and fatigue processFluctuations of internal pressures and potential struc-turalvibrationsofthesteellinerareconsideredasfatigue loading. The consequence is time variation oftheworkingstressesinthestructure.Fatiguefailuresare avoided by ensuring that all critical features, suchaslongitudinalweldingsofthesteelliner,haveanadequatefatiguestrength.Themostwidelymethodused at the design stage, is based on the plot of stress(S) against the number of cycles to failure (N), whichis known as an S-N curve for the relevant detail classof the weldings [Maddox, 199124].Tagwerker[198025]hasstudiedpressureoscillationsinthepowerconduitsofthreehydropowerstationsproducingpeak-load.Basedonanumberofloadcycles up to 1000 cycles per year, and for ductile steellinerswithayieldstrengthequalto520MPa,itwasconcluded that such oscillating loads are of no concernregarding fatigue strength of the linings. Nevertheless,Seeber [198514and 198526] pointed out that it was notthesomewhathigherstaticinternalwaterpressurescausedbysurgetankoscillationwhichwastheprob-lem in some peak-load hydro plants, but rather the highfrequencyofthedynamicwaterpressurescausedbywaterhammer with smaller amplitudes.It is also known that the fatigue strengths of weldeddetails are independent of the tensile properties of thesteel. As a consequence, the S-N design curves are alsocommon to high strength steels welded satisfactory.Infact,thevalidityofS-N curvesforhighstrengthsteel was explained by Maddox [199124] and BarsomandRolfe[199927]inreferringtotheinitiationandpropagation of fatigue cracks. It was observed that thetensile strength of steel has little effect on the rate ofpropagationofacrack.Unweldedspecimensshowabenefit from increases in tensile strength as a result ofthe existence of crack initiation, or incubation periodsinadditiontothatrequiredforpropagation.Onthecontrary,weldedspecimenshaveaconstantfatiguestrength,determinedessentiallybythepropagationphenomenonalone.Suchbehaviourisrelatedtothepresenceofpre-existingcracklikeflaws,suchashydrogen inherent intrusions, for which in fact, crackinitiation has been achieved.Weldedhighstrengthsteel,therefore,offersnointrinsic advantage in term of fatigue strength. On thecontrary,theremaybeahighernumberofpotentialcracksandflawsinthewelds.Theriskofhavingcracks that propagate beyond the critical size is there-fore higher.6.7 Corrosion fatigueThefatiguedesignrulesarenormallybasedonthetestdataobtainedindryairatambienttemperature.Therefore,theydonotconsidercorrosionwhichmayhave a significant influence on allowable fatigue stresses.In fact, cracks accelerate corrosive attack. If the fluc-tuatingstressesarehighenoughtopropagatefatiguecracks from stress concentrations, corrosive reactionsmayacceleratetheirgrowth.Thus,thecorrosionfatigue strength of a welded joint can be smaller thanthat under dry conditions. Furthermore, localized cor-rosiveattackatstressconcentrationsandsurfacedefects can increase the severity of the stress concen-tration and produce fatigue cracks.7. Application of fracture mechanicstheory to the steel liner design7.1 The deterministic approachInanunflawedmember,thetraditionaldesignofasteelstructureundertensilestressesisbasedonthe148 Hydropower & DamsIssue Three, 2009Fig. 5. Calculationresults of an exampleusing the traditionaland the fracturemechanics designapproach. The upperfigure shows thevariation of therequired steel linerthickness and theweight of steel lineras a function of theyield strength of thesteel. The lowerfigure depicts thevariation of theallowable tensilesteel against theyield strength.Examples inputsare: pi = 18 MPa, ri= 1.9 m, SafetyFactors againstyielding and againstbrittle fracture = 2.0,ac = 25.4 mm andac/2c = 0.2criteria of preventing yielding by keeping the drivingstressseq belowtheresistancestressfy. Accordingly,forstructurescontaininginitialcracks,thestressintensity factor, KI is a calculated driving factor whichmust be kept below the resistance factor KIC to preventbrittle fracture.Forsteelliners,crack-likedefectsareoftenpresentbut designers normally assume that, if a steel of suffi-cient ductility is used, local yielding occurs and redis-tributesstressesinthevicinityofstressraisers.Thislocal yielding may not occur in high strength steel andtherefore,theriskofabrittlefailurewillincrease.Crack-like defects are normally considered in moderndesign when high strength steel is used in the structureof nuclear powerplants, long span steel bridges and intheaeronauticalindustry.Theselectionofmaterialsandallowablestresslevelsisbasedonthefactthatdiscontinuitiesmaybepresentormayinitiateandpropagate under cyclic loads or stress corrosion crack-ing.Therefore,crackssizecanreachacriticalvaluewhere KI becomes larger than KIC producing the brit-tle failure of the steel.The use of high strength steel liner using thick weld-edplatesinhydropowerplantstogetherwiththeincrease of the dynamic pressures, lead to a higher riskof potential cracks in the steel liner weldings and thus,an increasing of the risk of brittle failure.To illustrate the use of the fracture mechanics theoryfor selecting an appropriate material for the steel liner,thecalculationresultsofanexample[BarsomandRolfe, 199927] are given in Fig. 5. An internal pressureof180barsandalinerradiusof1.9mareassumed.No load sharing with the surrounding rock is consid-ered.Thesafetyfactoragainstyieldingandbrittlefracture of 2.0 is considered. An external surface flawwith a depth ac equal to 25.4 mm and a depth to lengthratio of 0.2 is assumed as the maximum crack size thatcouldnotbedetectedandrepairedduringsteellinerinspections.Theminimumsteellinerthicknessforhandling purposes is considered equal to 25.4 mm.Theresultsshowthattherequiredsteellinerthick-nessusingthefracturemechanicstheoryincreaseswith the increase of the yielding strength of the steel.Forthesametheory,theallowabletensilestress,fsdecreases when the yielding strength increases. Fig. 5showsthatforsteelyieldstrengthhigherthan900MPa and for steels with relatively low values of KIC,thefracturemechanicstheorybecomescriticalwhenfracture is a possible mode of failure.7.2 The probabilistic approachTheresidualdispersionwithrandomdistributionsoflattice defects in steel plates and weldings confirm therandomnatureofsuchmaterialdamages.Thus,aprobabilisticratherthanadeterministicapproachshould be used in the modern design of steel liners.ProbabilisticFractureMechanics(PFM)iswelldevelopedinthenuclearandaeronauticalindustries[BesunerandTetelman,197728;Provan,198729;Nicholson and Ni, 199730]. It should be also applied tosteel liners of pressure tunnels built with welded highstrengthsteelandloadedbyhighdynamicpressurefluctuations with high number of stress cycles.The keystone of the PFM approach is a deterministicengineeringmodelofoneormoresystemfailuremodes combined with assumed or proposed statisticalvariationsofcontrollingparametersexpressedascumulative Probability Distribution Functions (PDF).ThebasisofPFMisthesimpleaxiomthatagivenmodeoffailureevent(E)willoccurwhenthestresssw associated with the failure mode exceeds the modegoverningstrengthsf.Theprobabilityoffailureaccording to mode (E) is given by:... [7.1]where the strength margin Y is:... [7.2]with i = 1, , nx, depends on input variables (of num-bernx)thataffectcomponentstressorstrengthorboth, and G is a concise deterministic summary of allpriorengineeringexperience,modelsandassump-tions. The xi are the values of the controlling parame-ters described as a random variables Xi with cumula-tivedistributionfunctionsassumedtobeknownandrepresented by:... [7.3]Thesolutionofequations(7.2)and(7.3)toobtainPDF(Y)inEq.(7.1)maybedoneinclosed-formforsimplecasesorbyusingnumericalsolution,suchasthe Monte-Carlo (MC) simulation, if the PDF(xi) andG(xi) distributions are complicated.Ifitisassumedthattheequivalentstressseq,theyielding strength fy and the brittle fracture strength ffof a steel liner can be represented by normal distribu-tioncurves[BesunerandTetelman,197727afterOsgood],failureoccursbytheyieldingmode(Ey)(Yy= fy - seq < 0) or by the fracture mode (Ef) (Yf = ff-se