Analyzing Uncertainty in Civil Engineering

243 Pages·2005·4.688 MB·English

by  Wolfgang Fellin, Heimo Lessmann, Michael Oberguggenberger, Robert Vieider

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
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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.