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PART III Reliability of existing structures

PART III Reliability of existing structures. Reasons for assessment 1/4. Reasons for assessment 2/4. Troubling condition of a structure. The evidence of deterioration Damage following an extreme load event (vehicular impact, fire, extreme wind, earthquake, etc.)

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PART III Reliability of existing structures

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  1. PART III Reliability of existing structures Erasmus program, Valencia 2010

  2. Reasons for assessment 1/4 Erasmus program, Valencia 2010

  3. Reasons for assessment 2/4 Troubling condition of a structure • The evidence of deterioration • Damage following an extreme load event (vehicular impact, fire, extreme wind, earthquake, etc.) • A clearly inadequate serviceability Railway bridge, 1955, Sweden Erasmus program, Valencia 2010

  4. Reasons for assessment 3/4 Issues related to design, construction, use • Change of tenancy or use including increased loads • Discovery of design or construction errors • Concern about quality of building materials or workmanship • Deviations from the original project *prEN 1991-1-1: 2001 E. Actions on structures … Erasmus program, Valencia 2010

  5. Reasons for assessment 4/4 Issues related to service life of structure • Expiry of design working life (DWL) and estimation of residual life • Extension of the working life on the basis of an earlier assessment of the structure *prEN 1990: 2001 E. Eurocode - Basis of structural design … Erasmus program, Valencia 2010

  6. Assessment process 1/4 Decision analysis Erasmus program, Valencia 2010

  7. Assessment process 2/4 Simplified flowchart* *http://www.sustainablebridges.net Erasmus program, Valencia 2010

  8. Assessment process 3/4 Utilisation of on-site data Erasmus program, Valencia 2010

  9. Assessment process 4/4 Bayesian probabilistic assessment of structures Erasmus program, Valencia 2010

  10. Updating probabilistic information 1/10 Bayes theorem Erasmus program, Valencia 2010

  11. Updating probabilistic information 2/10 Bayesian updating of random variables Erasmus program, Valencia 2010

  12. Updating probabilistic information 3/10 Bayes theorem for densities Erasmus program, Valencia 2010

  13. Updating probabilistic information 4/10 Example of pre-stressed railway sleepers (i/vii) (1) Doubt about deficient concrete strength (2) Core samples are taken (3) Tests are carried out Small-size sample of core strengths:x = {x1, x2, x3, x4} Erasmus program, Valencia 2010

  14. Updating probabilistic information 5/10 Example of pre-stressed railway sleepers (ii/vii) Compressive concrete strength of sleeperX~N(μ, σ) θ = ( μ = unknown, σ =17.1 MPa) Prior distribution of μ:μ~ N(μ, σ) = N(100 MPa, 10 MPa) Erasmus program, Valencia 2010

  15. Updating probabilistic information 6/10 Example of pre-stressed railway sleepers (iii/vii) New information: 10 tests on concrete cores (n = 10) (MPa) Erasmus program, Valencia 2010

  16. Updating probabilistic information 7/10 Example of pre-stressed railway sleepers (iv/vii) Posterior distrib. of μ:μ~ N(μ, σ) = N(107 MPa, 4.76 MPa) Erasmus program, Valencia 2010

  17. Updating probabilistic information 8/10 Example of pre-stressed railway sleepers (v/vii) Erasmus program, Valencia 2010

  18. Updating probabilistic information 9/10 Example of pre-stressed railway sleepers (vi/vii) Updated (predictive distribuiton of the concrete strength X: X~ N(μ, σ) = N(107 MPa, 17.8 MPa) Erasmus program, Valencia 2010

  19. Updating probabilistic information 10/10 Example of pre-stressed railway sleepers (vii/vii) Original and predictive densities of the compressive strength 5th percentile: 77.7 MPa 5th percentile: 71.9 MPa Erasmus program, Valencia 2010

  20. Updating event probabilities Bayes theorem A high degree of dependence between the eventsg(X)  0andh(X) * 0will produce an updated failure probability. Erasmus program, Valencia 2010

  21. Updating by proof loading 1/3 Example of bridge structure Erasmus program, Valencia 2010

  22. Updating by proof loading 2/3 Updated (truncated) model of resistance Erasmus program, Valencia 2010

  23. Updating by proof loading 3/3 Updating of reliability Limit state function: The event of withstanding the load test: The updated probability of failure: Erasmus program, Valencia 2010

  24. Updating by revision of the limit state 1/2 Recommended distributions of model uncertainties* *JCSS Probabilistic model code. JCSS, 2000. Erasmus program, Valencia 2010

  25. Updating by revision of the limit state 1/2 Expressions of model uncertainties h(x) = g(x,x) h(x) = x g(x) h(x) = x + g(x) Model uncertainties account for:  Random effects which are neglected in the model g(x) Simplification in the mathematical relations Measurement errors *JCSS Probabilistic model code. JCSS, 2000. Erasmus program, Valencia 2010

  26. Safety of existing structures Target reliabilities & tolerable failure probabilities According to ISO 13822* * ISO 13822. Bases for design of structures – Assessment of existing structures. ISO, Geneva, 2001. Erasmus program, Valencia 2010

  27. Bibliography • Diamanditis, D. (2001) Probabilistic assessment of existing structures. A publication of JCSS. The publishing company of RILEM: Geneve. • Faber, M.H. (2000) Reliability based assessment of existing structures. Prog. Struct. Engng. Mater., 2: 247-253. • Melchers, R.E. (1999) Structural reliability analysis and prediction, Wiley: Chichester etc. • Zhang, R., Mahadevan, S. (2000) Model uncertainty and Bayesian updating in reliability-based inspection. Structural Safety, 22: 145-160. • Zhang, R., Mahadevan, S. (2001) Reliability-based reassessment of corrosion fatigue life. Structural Safety, 23: 77-91. Erasmus program, Valencia 2010

  28. THE END OF PART III Thanks for attention! Egidijus R. Vaidogas Vilnius Gediminas technical university Vilnius, Lithuania erv@st.vgtu.lt http://e-stud.vgtu.lt/darb/4722 Erasmus program, Valencia 2010

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