Table Of ContentRisk Engineering
Dirk Proske
Bridge Collapse
Frequencies
versus Failure
Probabilities
Risk Engineering
Series editor
Dirk Proske, Vienna, Austria
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Dirk Proske
Bridge Collapse Frequencies
versus Failure Probabilities
With 29 Tables and 90 Figures
123
DirkProske
University of Natural Resourcesand
LifeSciences
Vienna
Austria
ISSN 2195-433X ISSN 2195-4348 (electronic)
Risk Engineering
ISBN978-3-319-73832-1 ISBN978-3-319-73833-8 (eBook)
https://doi.org/10.1007/978-3-319-73833-8
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For Beatrix and Rolf
Contents
1 Objective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Terms and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Definition of the Term “Bridge” . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Definition of the Term “Collapse” . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Definition of the Term “Cause”. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Definition of the Term “Bridge Collapse Frequency” . . . . . . . . . 8
2.6 Definition of the Term “Failure Probability”. . . . . . . . . . . . . . . . 9
2.7 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Categorization of Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Structural Systems of Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 Construction Material of Bridges. . . . . . . . . . . . . . . . . . . . . . . . 18
4.4 Construction Method of Bridges . . . . . . . . . . . . . . . . . . . . . . . . 20
4.5 Age Distribution of Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Measures of Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2 Probability of Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2.1 Unconditional Probability of Failure . . . . . . . . . . . . . . . . 28
5.2.2 Conditional Probability of Failure. . . . . . . . . . . . . . . . . . 29
vii
viii Contents
5.3 Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3.2 Mortality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3.3 Fatal Accident Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3.4 F-N-Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.3.5 Lost Life Years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.4 Target Probability of Failure Values . . . . . . . . . . . . . . . . . . . . . 36
5.5 Correction of Probability of Failure . . . . . . . . . . . . . . . . . . . . . . 43
5.5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.5.2 Correlation Consideration. . . . . . . . . . . . . . . . . . . . . . . . 45
5.5.3 Human Error Consideration . . . . . . . . . . . . . . . . . . . . . . 48
5.5.4 Structural Determinacy. . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.5.5 Maintenance and Deterioration . . . . . . . . . . . . . . . . . . . . 54
5.5.6 Actual Loads and New Loads. . . . . . . . . . . . . . . . . . . . . 55
5.5.7 Structural Probabilities of Failure . . . . . . . . . . . . . . . . . . 57
5.6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6 Collapse Frequencies of Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Data Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3 Number of Bridges Worldwide . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.4 Collapse Frequency of Bridges . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.5 Time-Dependency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.6 Causes of Damages and Conclusions. . . . . . . . . . . . . . . . . . . . . 78
6.6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.6.2 Bridge Location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.6.3 Bridge Collapse Fluctuation . . . . . . . . . . . . . . . . . . . . . . 89
6.6.4 Bridge Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.6.5 Bridge Structural System . . . . . . . . . . . . . . . . . . . . . . . . 96
6.6.6 Bridge Age Distribution. . . . . . . . . . . . . . . . . . . . . . . . . 97
6.7 Prediction of Future Collapse Frequencies . . . . . . . . . . . . . . . . . 99
6.8 Comparison of Target Values and Failure Probabilities. . . . . . . . 104
6.9 Further Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.10 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 125
Chapter 1
Objective
Probably more than a billion structures exist on earth including several million
bridges.Thesuccessofthetechnicalproduct“structures”isnotonlybasedonthe
gained large improvement of the quality of life for humans including protection
againstenvironmentalhazardsandconditionsandsecurity,itisalsostronglyrelated
totheoutstandingsafetyofthestructuresitself.
Structuresareprobablyoneoftheearliesttechnicalproductsproducedbymankind
(Figs.1.1and1.2).ThecodeofHammurabibyimposingharshpunishmenttobuilders
of collapsing structures shows that the safety of structures has been an important
issuesincethousandsofyears.Thetoolstoensureandprovideasufficientsafetyof
structureshaveevolvedoverthistime,forarchbridgesseeProskeandvanGelder
(2009).
Todaythereexistdifferentnumericalparameterstoevaluatethesafetyofstruc-
tures.Oneoftheseparametersisthe“probabilityoffailure”ofastructure.Theterm
probabilityoffailureandfailureprobabilityofstructuresrespectivelycanbefound
inalargenumberofscientificpublications,booksorcodesofpractice.Thecomputa-
tionoftheprobabilityoffailureofstructures,andspecificallybridges,isperhapsnot
dailybusiness,butstate-of-the-artandhasbeencarriedoutinnumerouscases[just
seetheconferenceproceedingsoftheInternationalConferenceonStructuralSafety
& Reliability (ICOSSAR), International Conference on Applications of Statistics
andProbabilityinCivilEngineering(ICASP),EuropeanSafetyandReliabilityCon-
ference(ESREL)andInternationalProbabilisticWorkshopseries(IPW)].Ifwehave
computedtheprobabilityoffailureinsomanycasesweshouldbeabletocompare
thesetheoreticalvalueswiththeobservation,thecollapsefrequency.
However, such comparisons of the probability of failure with the frequency of
collapse are not common in structural engineering, they do not exist for bridges.
In many codes and books it is argued that these two parameters can not directly
becomparedduetotheirindividuallimitations.Thisargumentissurprisingsincein
otherindustriessuchastheNuclearPowerIndustrysuchcomparisonsarecarriedout
(Proske2016)andareoftenanissueofpublicdiscussionrelatedtothequalityofthe
models.Evenfurther,ourmodelsshouldalwaysbecomparabletorealityandtoreal
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D.Proske,BridgeCollapseFrequenciesversusFailureProbabilities,RiskEngineering,
https://doi.org/10.1007/978-3-319-73833-8_1
2 1 Objective
Fig.1.1 Reconstruction of a typical pile dwelling around 4000 B.C in Switzerland (Seengen)
(PictureD.Proske)
Fig.1.2 Gizapyramidcomplexbuildaround2500B.C.(PictureD.Proske)
worldobservationsrespectivelywhichwouldinourcasebethefrequencyofcollapse.
If our models are neither based, nor compared nor confirmed by observations, we
developmodelsandparameterswhichareneitherusefulnorverifiable.Wehaveto
