Risk Engineering Dirk Proske Bridge Collapse Frequencies versus Failure Probabilities Risk Engineering Series editor Dirk Proske, Vienna, Austria The Springer Book Series Risk Engineering can be considered as a starting point, looking from different views at Risks in Science, Engineering and Society. The book series publishes intense and detailed discussions of the various types of risks, causalities and risk assessment procedures. Although the book series is rooted in engineering, it goes beyond the thematic limitation, since decisions related to risks are never based on technical information alone. Therefore issues of “perceived safety and security” or “risk judgment” are compulsory when discussing technical risks, natural hazards, (environmental) health and social risks. One may argue that social risks are not related to technical risks, however it is well known that social risks are the highest risks for humans and are therefore immanent in all risk trade-offs. The book series tries to cover the discussion of all aspects of risks, hereby crossing the borders of scientific areas. More information about this series at http://www.springer.com/series/11582 Dirk Proske Bridge Collapse Frequencies versus Failure Probabilities With 29 Tables and 90 Figures 123 Dirk Proske University of Natural Resources and Life Sciences Vienna Austria ISSN 2195-433X ISSN 2195-4348 (electronic) Risk Engineering ISBN 978-3-319-73832-1 ISBN 978-3-319-73833-8 (eBook) https://doi.org/10.1007/978-3-319-73833-8 Library of Congress Control Number: 2017963976 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. 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Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland 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. The success of the technical product “structures” is not only based on the gained large improvement of the quality of life for humans including protection against environmental hazards and conditions and security, it is also strongly related to the outstanding safety of the structures itself. Structures are probably one of the earliest technical products produced by mankind (Figs. 1.1 and 1.2). The code of Hammurabi by imposing harsh punishment to builders of collapsing structures shows that the safety of structures has been an important issue since thousands of years. The tools to ensure and provide a sufficient safety of structures have evolved over this time, for arch bridges see Proske and van Gelder (2009). Today there exist different numerical parameters to evaluate the safety of struc- tures. One of these parameters is the “probability of failure” of a structure. The term probability of failure and failure probability of structures respectively can be found in a large number of scientific publications, books or codes of practice. The computa- tion of the probability of failure of structures, and specifically bridges, is perhaps not daily business, but state-of-the-art and has been carried out in numerous cases [just see the conference proceedings of the International Conference on Structural Safety & Reliability (ICOSSAR), International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP), European Safety and Reliability Con- ference (ESREL) and International Probabilistic Workshop series (IPW)]. If we have computed the probability of failure in so many cases we should be able to compare these theoretical values with the observation, the collapse frequency. 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 be compared due to their individual limitations. This argument is surprising since in other industries such as the Nuclear Power Industry such comparisons are carried out (Proske 2016) and are often an issue of public discussion related to the quality of the models. Even further, our models should always be comparable to reality and to real © Springer International Publishing AG, part of Springer Nature 2018 1 D. Proske, Bridge Collapse Frequencies versus Failure Probabilities, Risk Engineering,