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Analyzing Uncertainty in Civil Engineering PDF

243 Pages·2005·4.688 MB·English
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W. Fellin · H. Lessmann · M. Oberguggenberger · R. Vieider (Eds.) Analyzing Uncertainty in Civil Engineering Wolfgang Fellin · Heimo Lessmann Michael Oberguggenberger · Robert Vieider (Eds.) Analyzing Uncertainty in Civil Engineering With 157 Figures and 23 Tables Editors a.o. Univ.-Prof. Dipl.-Ing. Dr. WolfgangFellin Institutfu¨rGeotechnikundTunnelbau Universita¨tInnsbruck Technikerstr. 13 6020Innsbruck Austria em. Univ.-Prof. Dipl.-Ing. HeimoLessmann Starkenbu¨hel304 6073Sistrans Austria a.o. Univ.-Prof. Dr. MichaelOberguggenberger Institutfu¨rTechnischeMathematik, GeometrieundBauinformatik Universita¨tInnsbruck Technikerstr. 13 6020Innsbruck Austria Dipl.-Ing. RobertVieider VieiderIngenieurGmbH Rebschulweg1/E 39052KalternanderWeinstraße Italy ISBN3-540-22246-4 SpringerBerlinHeidelbergNewYork LibraryofCongressControlNumber: 2004112073 Thisworkissubjecttocopyright. Allrightsarereserved, whetherthewholeorpartofthe materialisconcerned, specificallytherightsoftranslation, reprinting, reuseofillustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplicationofthispublicationorpartsthereofispermittedonlyundertheprovisions oftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionfor usemustalwaysbeobtainedfromSpringer-Verlag. Violationsareliabletoprosecutionunder GermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springeronline.com (cid:1)c Springer-VerlagBerlinHeidelberg2005 PrintedinGermany Theuseofgeneraldescriptivenames,registerednames,trademarks,etc. inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Typesetting: Dataconversionbytheauthors. FinalprocessingbyPTP-BerlinProtago-TeX-ProductionGmbH,Germany Cover-Design: medionetAG,Berlin Printedonacid-freepaper 62/3020Yu-543210 Preface Thisvolumeaddressestheissueofuncertaintyincivilengineeringfromdesign to construction. Failures do occur in practice. Attributing them to a residual risk or a faulty execution of the project does not properly cover the range of causes. A closer scrutiny of the design, the engineering model, the data, the soil-structure-interactionandthe modelassumptions is required.Usually,the uncertaintiesininitialandboundaryconditionsaswellasmaterialparameters are abundant. Current engineering practice often leaves these issues aside, despite the fact that new scientific tools have been developed in the past decades that allow a rational description of uncertainties of all kinds, from model uncertainty to data uncertainty. It is the aim of this volume to have a critical look at current engineering risk concepts in order to raise awareness of uncertainty in numerical compu- tations, shortcomings of a strictly probabilistic safety concept, geotechnical modelsoffailuremechanismsandtheirimplicationsforconstructionmanage- ment,execution,andthejuristicquestionastowhohastotakeresponsibility. Inaddition,anumberofthenewproceduresformodellinguncertaintyareex- plained. Our central claim is that doubts and uncertainties must be openly ad- dressed in the design process. This contrasts certain tendencies in the engi- neering community that, though incorporating uncertainties by one or the other way in the modelling process, claim to being able to control them. In our view, it is beyond question that a mathematical/numerical for- malization is needed to provide a proper understanding of the effects of the inherent uncertainties of a project. Available information from experience, in situmeasurements,laboratorytests,previousprojectsandexpertassessments should be taken into account. Combining this with the engineering model(s) - and a critical questioning of the underlying assumptions -, insight is gener- ated into the possible behavior, pitfalls and risks that might be encountered at the construction site. In this way workable and comprehensible solutions are reached that can be communicated and provide the relevant information for all participants in a complex project. This approach is the opposite of an algorithm that would provide single numbers pretending to characterize the risks of a project in an absolute way (likesafetymarginsorfailureprobabilities).Suchmagicnumbersdonotexist. Instead of seducing the designing engineer into believing that risks are under VI Preface control, we emphasize that understanding the behavior of the engineering systemis the centraltaskandthekeyto responsibledecisionsinviewofrisks and imponderables. The bookis the resultofacollaborateeffortofmathematicians,engineers and construction managers who met regularly in a post graduate seminar at the University of Innsbruck during the past years. It contains contributions thatshedlightonthecentraltheme outlinedabovefromvariousperspectives and thus subsumes the state of discussion arrivedat by the participants over thoseyears.Exceptforthreereprintsoffoundationalpapers,allcontributions are new and have been written for the purpose of this collection. Thebookstartswiththreepapersongeotechnics.Thefirsttwoarticlesby Fellin address the problem of assessment of soil parameters and the ambigu- ity of safety definition in geotechnics. The third paper by Oberguggenberger and Fellin demonstrates the high sensitivity of the failure probability on the choice of input distribution. This sets the stage for the theoretically oriented paper by Oberguggenberger providing a survey of available models of uncer- tainty and how they can be implemented in numerical computations. The mathematical foundations are complemented by the following paper of Fetz describing how the joint uncertainty in multi-parameter models can be in- corporated. Next, Ostermann addresses the issue of sensitivity analysis and how it is performed numerically. This is followed by a reprint of a paper by Herle discussing the resultof benchmark studies. Predictions of deformations obtainedbydifferentgeotechniciansandnumericalmethodsinthesameprob- lem are seen to deviate dramatically from each other. Lehar et al. present an ultimate load analysis of pile-supported buried pipelines, showing the exten- sive interplay between modelling, laboratory testing and numerical analysis which is necessary to arrive at a conclusive description of the performance of the pipes. The paper by Lessmann and Vieider turns to the implications of the geotechnical model uncertainty to construction management. It discusses the type of information the construction manager would need as well as the question of responsibility in face of large model uncertainties. The following paper by Oberguggenberger and Russo compares various uncertainty models (probability,fuzzy sets,stochasticprocesses)atthe handofthe simple exam- ple of an elastically bedded beam, while the article by Oberguggenberger on queueing models ventures into a similar comparison of methods in a theme relevant for project planning. The book is completed by a reprint of a survey articleshowinghowfuzzysetscanbeusedtodescribeuncertaintythroughout civil engineering. Innsbruck, Wolfgang Fellin May 2004 Heimo Lessmann Michael Oberguggenberger Robert Vieider Contents Assessment of characteristic shear strength parameters of soil and its implication in geotechnical design Wolfgang Fellin.................................................. 1 1 Characteristic values of soil parameters ......................... 1 2 Example .................................................... 6 3 Influence on design ........................................... 9 4 Conclusions.................................................. 13 References ...................................................... 14 Ambiguity of safety definition in geotechnical models Wolfgang Fellin.................................................. 17 1 Slope stability of a vertical slope ............................... 17 2 Various safety definitions ...................................... 19 3 Different geotechnical models .................................. 27 4 Sensitivity analysis ........................................... 28 5 Conclusion .................................................. 30 References ...................................................... 31 The fuzziness and sensitivity of failure probabilities Michael Oberguggenberger, Wolfgang Fellin.......................... 33 1 Introduction ................................................. 33 2 Probabilistic modeling ........................................ 34 3 Sensitivity of failure probabilities: two examples.................. 36 4 Robust alternatives........................................... 44 5 Conclusion .................................................. 48 References ...................................................... 48 The mathematics of uncertainty: models, methods and interpretations Michael Oberguggenberger ......................................... 51 1 Introduction ................................................. 51 2 Definitions .................................................. 53 VIII Contents 3 Semantics ................................................... 57 4 Axiomatics .................................................. 63 5 Numerics.................................................... 64 6 The multivariate case ......................................... 66 References ...................................................... 67 Multi-parameter models: rules and computational methods for combining uncertainties Thomas Fetz .................................................... 73 1 Introduction ................................................. 73 2 Random sets and sets of probability measures.................... 74 3 Numerical example ........................................... 77 4 Types of independence ........................................ 82 5 Sets of joint probability measures generated by random sets ....... 85 6 The different cases............................................ 87 7 Numerical results for Examples 1, 2, 3, 4 and Conclusion .......... 96 References ...................................................... 98 Sensitivity analysis Alexander Ostermann ............................................101 1 Introduction .................................................101 2 Mathematical background .....................................102 3 Analytic vs. numerical differentiation ...........................104 4 Examples ...................................................106 5 Conclusions..................................................114 References ......................................................114 Difficulties related to numerical predictions of deformations Ivo Herle .......................................................115 1 Introduction .................................................115 2 Predictions vs. measurements ..................................116 3 Constitutive model ...........................................118 4 Mathematical and numerical aspects............................123 5 Concluding remarks ..........................................124 References ......................................................125 FE ultimate load analyses of pile-supported pipelines - tackling uncertainty in a real design problem Hermann Lehar, Gert Niederwanger, Gu¨nter Hofstetter ...............129 1 Introduction .................................................129 2 Pilot study ..................................................131 3 Laboratory tests .............................................133 4 Numerical model of the pile-supported pipeline ..................147 5 On-site measurements.........................................155 6 Design ......................................................158 7 Conclusions..................................................161 Contents IX References ......................................................162 The Implications of Geotechnical Model Uncertainty for Construction Management Heimo Lessmann, Robert Vieider ..................................165 1 The “last”...................................................165 2 The soil / building interaction .................................166 3 The computational model .....................................172 4 Safety.......................................................174 5 The probabilistic approach ....................................176 6 Information for the site engineer ...............................178 7 Conclusion ..................................................178 References ......................................................181 Fuzzy, probabilistic and stochastic modelling of an elastically bedded beam Michael Oberguggenberger, Francesco Russo .........................183 1 Introduction .................................................183 2 The elastically bedded beam...................................184 3 Fuzzy and probabilistic modelling ..............................185 4 Stochastic modelling..........................................189 5 Summary and Conclusions.....................................195 References ......................................................195 Queueing modelswith fuzzy data in construction management Michael Oberguggenberger .........................................197 1 Introduction .................................................197 2 The fuzzy parameter probabilistic queueing model................199 3 Fuzzy service and return times .................................204 References ......................................................208 Fuzzy models in geotechnical engineering and construction management Thomas Fetz, Johannes J¨ager, David Ko¨ll, Gu¨nther Krenn, Heimo Lessmann, Michael Oberguggenberger, Rudolf F. Stark ................211 1 Introduction .................................................211 2 Fuzzy sets ...................................................213 3 An application of fuzzy set theory in geotechnical engineering......215 4 Fuzzy differential equations....................................225 5 Fuzzy data analysis in project planning .........................227 References ......................................................238 Authors .......................................................241 Assessment of characteristic shear strength parameters of soil and its implication in geotechnical design Wolfgang Fellin Institut fu¨r Geotechnik und Tunnelbau,Universit¨at Innsbruck Summary. The characteristic shear strength parameters of soil are obviously de- cisiveforthegeotechnical design.Characteristic parameters aredefinedascautious estimates of the soil parameters affecting the limit state. It is shown how geotech- nical engineers interpret this cautious estimate. Dueto theinherent lack of data in geotechnicalinvestigations thereisalwaysacertaindegreeofsubjectivityinassess- ing the characteristic soil parameters. The range of characteristic shear parameters assignedtothesamesetoflaboratoryexperimentsby90geotechnicalengineershas been used to design a spread foundation. The resulting geometrical dimensions are remarkably different. It is concluded that geotechnical calculations are rather esti- mates than exact predictions. Thus for intricate geotechnical projects a sensitivity analysisshouldbeperformedtofindoutcriticalscenarios.Furthermoreacontinuous appraisal of thesoil properties during theconstruction process is indispensable. 1 Characteristic values of soil parameters 1.1 Definition European geotechnical engineers proposed a definition of the characteristic value of soil or rock parameters given in EC 7: ”The characteristic value of a soil or rock parameter shall be selected asacautiousestimateofthevalueaffectingtheoccurrenceofthelimit state.” [4, 2.4.3(5)] Failure in soils is generally relatedwith localisationof strains in shear bands. Therefore, simple geotechnical limit state analyses are based on assuming shear surfaces,e.g., the calculationof stability of slopes using a defined shear surface,seeFig.2.Thusthevalueaffectingthelimitstateistheshearstrength of the soil. The shear strength in the failure surfaces is usually modelled by theMohr-Coulombfailurecriterionτ =c+σ·tanϕ,withthe stressσ acting f normal to the shear surface. The validity of this model will not be discussed here, it should only be mentioned that it is not applicable in all cases. 2 Wolfgang Fellin Assuming that the Mohr-Coulomb failure criterion is an appropriate model, the parameters whose distributions we have to analyse are the fric- tion coefficient µ=tanϕ and the cohesion c. In the limit state1 the shear strength is mobilised over the whole length of the shear surface. Accounting for this is usually done in the way as EC 7 proposes: ”The extent of the zone of ground governing the behaviour of a geotechnical structure at a limit state is usually much larger than the extent of the zone in a soil or rock test and consequently the governing parameter is often a mean value over a certain surface or volume of the ground. The characteristic value is a cautious estimate of this mean value. ...” [4, 2.4.3(6)] 1.2 Intuitive Model Averyinstructivemodeltoexplainthisideawaspresentedin[6].Weconsider the base friction of n equally weighted blocks on a horizontalsoil surface, see Fig. 1. The blocks are pushed by the horizontal force H. The total weight of theblocksisW.EachblockhastheweightofW/nandthefrictioncoefficient µ . i H µ i 1 2 3 n Fig. 1. Equally weighted blocks pushed by a horizontal force on a horizontal soil surface. Eachblock i contributes to the resistance µ W/n. For a constant pushing i force H all blocks act together. Thus the total resisting force is (cid:1)n (cid:1)n W 1 µ =W µ =Wµ. i n n i i=1 i=1 The limit state function for slip is therefore g :=µW −H . 1 Strictly spoken thisis only truein critical state.

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