kth royal institute of technology Licentiate Thesis in Structural Engineering and Bridges Reliability-based fatigue assessment of existing steel bridges RUOQI WANG Stockholm, Sweden 2020 Reliability-based fatigue assessment of existing steel bridges RUOQI WANG Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defence for the Degree of Licentiate of Engineering on Friday the 13th November 2020, at 1:00 p.m. in M108, Brinellvägen 23, Stockholm. Licentiate Thesis in Structural Engineering and Bridges KTH Royal Institute of Technology Stockholm, Sweden 2020 © Ruoqi Wang ISBN 978-91-7873-663-8 TRITA-ABE-DLT-2031 Printed by: Universitetsservice US-AB, Sweden 2020 Abstract Fatigue is among the most critical forms of deterioration damage that occurs to steel bridges. It causes a decline of the safety level of bridges over time. Therefore, the performance of steel bridges, which may be seriously affected by fatigue, should be assessed and predicted. There are several levels of uncertainty involved in the crack initiation and propagation process; therefore the probabilistic methods can provide a better estimation of fatigue lives than deterministic methods. When there are recurring similar details which may have correlation with each other and be regarded as a system, there are distinct advantages to analyze them from a system reliability perspective. It allows the engineer to identify the importance of an individual detail or the interaction between details with respect to the overall performance of the system. The main aim of this licentiate thesis is to evaluate probabilistic methods for re- liability assessment of steel bridges, from both a single detail level and a system level. For single details, an efficient simulation technique is desired. The widely applied Monte Carlo simulation method provides accurate estimation, however, is very time-consuming. The Subset simulation method is investigated as an alterna- tive and it shows great feasibility in dealing with a multi-dimensional limit state function and nonlinear crack propagation. For larger systems, the spatial correla- tion is considered between details. An equicorrelation-based modelling approach has been proposed as supplement to common simulation techniques to estimate the system reliability analytically and significantly reduce the simulation time. With correlation considered, the information of one accessible detail could be used to predict the status of the system. While reliability analysis aims for a specific safety level, risk analysis aims to find the most optimal solution. With consequences considered, a risk-based decision support framework is formulated for the selected system, which is presented as a decision tree. It reveals that the decisions based on reliability assessment can be different from those based on risk analysis, since they have different objective criteria. Keywords: Fatigue, steel bridges, reliability analysis, spatial correlation, risk anal- ysis, Monte Carlo simulation i Sammanfattning Utmattning är en av de mest allvarliga nedbrytningsmekanismer som stålbroar utsätts för. Den orsakar en försämrad säkerhet för broar över tid. Därav måste stålbroars tillförlitlighet, som kan påverkas allvarligt på grund av utmattning, bedö- mas och förutsägas. Flera olika nivåer av osäkerheter är involverade i initiering och propagering av utmattningssprickor, varför sannolikhetsbaserade metoder kan ge en bättre uppskattning av utmattningslivslängden än deterministiska metoder. När liknande detaljer återkommer i en konstruktion och med korrelation mellan varandra kan dessa betraktas som ett system, för vilket tillförlitlighetsmetoder på systemnivå kan utnyttjas.. Det gör det möjligt för ingenjören att identifiera bety- delsen av en individuell detalj eller interaktionen mellan detaljer med avseende på systemets totala tillförlitlighet. Det huvudsakliga syftet med denna licentiatuppsats är att utvärdera sannolikhets- baserade metoder för uppskattning av stålbroars tillförlitlighet, både med avseende på enskilda detaljer och på systemnivå. För enskilda detaljer eftersträvas en tidsef- fektiv simuleringsteknik. Den allmänt tillämpade Monte Carlo-simuleringsmetoden ger en robust uppskattning, men är mycket tidskrävande. Subset-simuleringsmetoden undersöks som ett alternativ och den visar stor potential när det gäller att hantera en flerdimensionell gränsfunktion och en olinjär sprickpropageringsmodell. På sys- temnivå beaktas den rumsliga korrelationen mellan detaljer. En modelleringsmetod baserad på konstant korrelation mellan detaljer har föreslagits som komplement till vanliga simuleringstekniker för att uppskatta tillförlitligheten analytiskt och av- sevärt minska simuleringstiden. Genom att utnyttja korrelationen kan information om en tillgänglig detalj användas för att förutsäga systemets status. Medan en tillförlitlighetsanalys bedöms mot en specifik säkerhetsnivå används risk- analysen för att hitta den mest optimala åtgärden. Genom att beakta konsekvenser har ett riskbaserat verktyg för beslutsstöd föreslagits och presenterats i form av ett beslutsträd. Resultaten visar att besluten baserade på tillförlitlighet kan skilja sig från de som baseras på en uppskattad risk, eftersom metoderna har olika målfunk- tioner. Nyckelord: Utmattning, stålbroar, tillförlitlighet, rumslig korrelation, riskanalys, Monte Carlo-simulering iii Preface The research work presented in this thesis was carried out at the Department of Civil and Architectural Engineering, KTH Royal Institute of Technology, Stockholm. It has been appreciatively financed by the KTH Railway Group. I would like to express my most sincere gratitude towards my supervisors, Asso- ciate Professor John Leander and Professor Raid Karoumi for their guidance and continuous support. Special thanks go to Dr. Johan Spross for taking the time to review this thesis and providing valuable comments. I would also like to thank my colleagues and friends at the Division of Structural Engineering and Bridges. They shared their knowledge with me, offered their sup- port, and make my studies full of joy. Last but not least, I would like to thank my parents for their endless love and firm support. Stockholm, November 2020 Ruoqi Wang v Publications The current thesis is based on the work presented in the following publications, labelled Paper I-III. Paper I Wang, R., Leander, J., and Karoumi, R. (2019). Comparison of simulation methods applied to steel bridge reliability evaluations. Proceedings of the 13th International Conference on Applications of Statistics and Probability in Civil Engineering. Paper II Wang, R., Leander, J., and Karoumi, R. (2020). Fatigue reliability assessment of steel bridges considering spatial correlation in system evaluation. Submitted for review. Paper III Wang, R., Leander, J., and Karoumi, R. (2020). Risk analysis fordecisionsupport—acasestudy on fatigue assessment of a steel bridge. Proceedings of the 30th European Safety and Relia- bility Conference and the 15th Probabilistic Safety Assessment and Management Conference. The planning of the papers, the major part of the analyses and of the writing has been performed by Wang. The monitored stress data was supplied by the second co-author and is a result of the work presented in Leander (2018). The co-authors have participated in the planning of the work and contributed to the papers with comments and revisions. vii Contents Preface v Publications vii 1 Introduction 1 1.1 Background ................................ 1 1.2 Aims and scope .............................. 3 1.3 Scientific contribution .......................... 4 1.4 Outline of the thesis ........................... 5 2 Reliability analysis 7 2.1 Deterministic methods .......................... 8 2.2 Probabilistic methods .......................... 10 2.3 Risk analysis ............................... 15 2.4 System reliability assessment ...................... 16 3 Risk analysis 21 3.1 Risk analysis methods .......................... 22 3.2 Risk-based decision-making methods .................. 28 3.3 A theoretical model for fatigue assessment . .............. 31 4 Summary of appended papers 35 5 Concluding remarks 39 5.1Discussion................................. 39 5.2 Conclusions ................................ 40 5.3 Further research ............................. 41 References 43 Paper I 51 Paper II 61 Paper III 93 ix Chapter 1 Introduction Fatigue is among the most critical forms of deterioration damage that occurs to steel bridges. It is usually causing a decline of the safety level over time due to repeated or varying loading. The deterioration process consists of initiation and propagation of cracks, which often accumulate in an invisible way and may eventually trigger different levels of consequences. A closure of the bridge for maintenance will lead to inevitable traffic disturbance and bring much inconvenience to the travelers and transport operators. More severely, a bridge collapse may induce fatalities as well as economic loss. Therefore, the performance of steel bridges, which may be seriously affected by fatigue, should be assessed and predicted. An adequate safety level should be guar- anteed by combining theoretical assessment, maintenance and regularly-arranged inspections. It is motivated by economic as well as environmental reasons. An early repair compared to a catastrophic failure will save much material and minimize the construction impact, which is environmentally sustainable. 1.1 Background Structural reliability