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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

Erasmus program, Valencia 2010

reasons for assessment 1 4
Reasons for assessment 1/4

Erasmus program, Valencia 2010

reasons for assessment 2 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.)
  • A clearly inadequate serviceability

Railway bridge, 1955, Sweden

Erasmus program, Valencia 2010

reasons for assessment 3 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

reasons for assessment 4 4
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

assessment process 1 4
Assessment process 1/4

Decision analysis

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assessment process 2 4
Assessment process 2/4

Simplified flowchart*

*http://www.sustainablebridges.net

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assessment process 3 4
Assessment process 3/4

Utilisation of on-site data

Erasmus program, Valencia 2010

assessment process 4 4
Assessment process 4/4

Bayesian probabilistic assessment of structures

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updating probabilistic information 1 10
Updating probabilistic information 1/10

Bayes theorem

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updating probabilistic information 2 10
Updating probabilistic information 2/10

Bayesian updating of random variables

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updating probabilistic information 3 10
Updating probabilistic information 3/10

Bayes theorem for densities

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updating probabilistic information 4 10
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

updating probabilistic information 5 10
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

updating probabilistic information 6 10
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

updating probabilistic information 7 10
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

updating probabilistic information 8 10
Updating probabilistic information 8/10

Example of pre-stressed railway sleepers (v/vii)

Erasmus program, Valencia 2010

updating probabilistic information 9 10
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

updating probabilistic information 10 10
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

updating event probabilities
Updating event probabilities

Bayes theorem

A high degree of dependence between the eventsg(X)  0andh(X) * 0will produce an updated failure probability.

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updating by proof loading 1 3
Updating by proof loading 1/3

Example of bridge structure

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updating by proof loading 2 3
Updating by proof loading 2/3

Updated (truncated) model of resistance

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updating by proof loading 3 3
Updating by proof loading 3/3

Updating of reliability

Limit state function:

The event of withstanding the load test:

The updated probability of failure:

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updating by revision of the limit state 1 2
Updating by revision of the limit state 1/2

Recommended distributions of model uncertainties*

*JCSS Probabilistic model code. JCSS, 2000.

Erasmus program, Valencia 2010

updating by revision of the limit state 1 225
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

safety of existing structures
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

bibliography
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

the end of part iii
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