Reliability-based assessment of existing structures. General background. Why do we need to assess reliability of an existing structure?

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1 Reliability-based assessment of existing structures Fredrik Carlsson Sven Thelandersson General background The value of existing built infrastructure in the developed world is tremendous It is becoming increasingly older since much were built the decades after World war 2. Accelerating development in society requires changes in use and reconstruction High economic incentive if existing facilities can be used longer and be utilised for new needs. Structural Engineering - Lund University 1 Structural Engineering - Lund University 2 Example: Bridges in the European railway network Age of bridges < 20 years 11% years 22 % years 32 % >100 years 35 % Type of bridges Concrete 23 % Metallic 21 % Arches (mostly masonry) 41 % Composite (steel/concrete) 14 % Why do we need to assess reliability of an existing structure? Deviations from the original project description Indications from periodic investigation of its state Doubts about safety due to evidence of damage Unusual incidents during use (e.g. vehicle impact, fire, earthquakes) Inadequate serviceability Discovery of design or construction errors Planned change of use of the structure Expiry of residual service life based on earlier assessment of the structure Source: EU-project Sustainable bridges Structural Engineering - Lund University 3 Structural Engineering - Lund University 4 1

2 Residual service life - definition General features in assessment of existing structures β The safety is usually first verified with standard methods based on deterministic code rules. β target t 0 t now Safe Unsafe Time If this indicates that safety is not sufficient, there are three alternative ti decisions i 1. Perform more detailed analysis and investigation of the structure 2. Strengthen the structure Usually the cheapest alternative if sufficient safety can be verified Residual service life 3. Demolish and replace the structure Structural Engineering - Lund University 5 Structural Engineering - Lund University 6 Relative cost to increase safety For a new structure the additional cost to increase safety is low (e.g add some reinforcement) For an existing structure this cost is usually very high One could argue that the target reliability could be set lower in that case, but this is usually not possible for political reasons Structural Engineering - Lund University 7 JCSS Target Reliability Indices (per year) Relative safety cost high medium small Low consequences of failure β = 3.1 moderate consequences of failure β = 3.3 high consequences of failure β = ( P F 10 ) ( P F 510 ) ( P F 10 ) β = 3.7 β = 4.2 β = ( P F 10 ) ( P F 10 ) ( P F 510 ) β = 4.2 β = 4.4 β = ( P F 10 ) ( P F 510 ) ( P F 10 ) 2

3 Assessment procedure in three phases Faber (2001) Structural Engineering - Lund University 9 Reliability-based assessment is often employed in the third phase Advantages and possibilities by use of probabilistic methods for assessment of safety for existing structures 1. Makes it possible to successively introduce specific information about the particular structure* into the analysis. 2. Gives a measure of safety for the structure, which can be used as a basis for decision about the future of the structure. 3. Sensitivity analyses shows the importance of different factors. 4. Usually less conservative than generic code rules *Information in structural codes is intended to be valid for all possible structures on the market Structural Engineering - Lund University 10 Bayesian probabilistic reassessment of structures Example reinforcement bars s R s Suppose that we need to increase the capacity of the reinforcement with 10 %! Structural Engineering - Lund University 11 Structural Engineering - Lund University 12 3

4 Prior decision analysis Posterior decision analysis The first step is to evaluate the capacity based on available first hand (a priori) information (e.g. generic information about the actual material quality). An a priori probabilistic model for the yield strength of the steel can be formulated on this basis. If this is not sufficient further investigations may be performed to update the information. A number of tests of the material is performed and the probabilistic model describing the yield strength is updated. The analysis based on the new information may show that the reliability is sufficient or not. This type of analys is referred to as a posterior decision analysis since it is performed after new information has been obtained This first step is called prior decision analysis Structural Engineering - Lund University 13 Structural Engineering - Lund University 14 Pre-posterior decision analysis As a tool for planning the investigations to update the information a so called pre-posterior analysis can be made. The idea is to perform a posterior analysis before the tests are performed, assuming that the results are in line with the prior information. In this analysis all costs for strengthening, tests, etc. are considered, given that the requirement for reliability is fulfilled. The result is used as a basis to decide about investigation plans and other measures to be taken. Risk-based decision analysis C=0*y+1*8=8 Mil. Sfr C=0.0018*6.55+0,9982 *2=2,01 Mil. Sfr C=0,0036*4,55+0,9964 *0=16,38 Mil. Sfr Faber (2001) Structural Engineering - Lund University 15 Structural Engineering - Lund University 16 4

5 Information which may be used to update the reliability of a structure The fact that the structure has survived so far Tests of the structural materials in the structure Geometrical measures Damage D and deterioration ti Proof loading Static and dynamic response to controlled loading Structural Engineering - Lund University 17 Bayesian updating of material properties Ffy 1,00 0,80 0,60 0,40 0,20 0, fy [MPA] Statistical methods are available to update probability distribution functions based on new test information Can be found in e.g. JCSS-publication: Probabilistic assessment of existing structures. Ed. by Diamantides D. Can be purchased through Structural Engineering - Lund University 18 Prior Post Probabilistic updating based on proof loading Updating based on indirect information Utilization of information not originating from the structure itself to upgrade the reliability. This is possible if the information is correlated to the structure through common loading, correlated materials or degradation process. Based on conditional probability Structural Engineering - Lund University 19 Structural Engineering - Lund University 20 5

6 Updating based on inspections example fatigue of steel with inspection of crack propagation Example: Öland bridge (from Fredrik Carlsson) Completed1969 Length: 6 km B=180 kn Four lanes (two in each direction) Updating at each inspection conditional on no crack found Structural Engineering - Lund University 21 Kantbal Mittlinj Kantbal Critical section: Moment capacity of cantilever slabs Structural Engineering - Lund University 22 Material properties Load model A/B Kritiskt φ10c300 Ks40 φ12c300 Ks60 φ16c300 Ks60 φ12c300 Ks60 φ12c300 Ks From drawings: Rebars: Ks40 and Ks60 Concrete: K φ10c300 Ks40 φ10c300 Ks Information is needed about properties of old material qualities A= axle pressure B=boogie pressure Structural Engineering - Lund University 23 Structural Engineering - Lund University 24 6

7 C f fst As st Z = C f fst A s d st C f bf 2 st cc Limit state function ( C + M ) ( C + M ) ( C M ) M G G M B B M T 0,22B ε a 0,22B ε a 0,66B ε a M T = = = b r + 2,6 2 eff 3 3I ,6 3 4I1a Structural Engineering - Lund University 25 T Basic random variables Variabel Symbol Fördelning Medelvärde Standardav. Tryckhållfasthet fcc Lognormal 47,5 MPa 7,6 MPa betong: Drag hållfasthet fst Lognormal 667,6 MPa 30 MPa armering: Armeringsarea: As Konstant 1,80*10 m /m Effektiv höjd: d Lognormal 0,238 m 0,01 m Bredden: b Konstant 1,0 m - Moment av MG Normal 29,2 knm/m 1,5 knm/m egentyngd: Moment av MB Normal 128kNm/m 12,8 13kNm/m 1,3 beläggning: Boogietryck: B Normal Beräknas 0,05B Dynamisk ε Normal 1,07 0,07 förstoringsfaktor: Hävarm: a Normal* 2,085 0,24 m Tröghetsmoment: I1 Konstant 6,92*10 m Tröghetsmoment: I2 Konstant 2,25*10 m Modell osäkerhet C fst Lognormal 1,0 0,05 armering: Modell osäkerhet C fcc Lognormal 1,0 0,05 betong: Modell osäkerhet C MG Normal 0 1,5 egentyngd: Modell osäkerhet C MB Normal 0 0,65 beläggning: Modell osäkerhet C MT Normal 1,0 0,05 trafiklast: Structural Engineering - Lund University 26 Results Sensitivities COMREL was used to calculate reliability index and sensitivities and the allowable boogie pressure corresponding to target reliability = 4,75 was determined to 0,5 0,4 0,3 0,2 B= 603 kn This can be compared with the allowable boogie pressure determined from standard code-based classification, which was -värden 01 0,1 0 Cf st d f st f cc Cf cc CMB MB CMG MG a CMT B e -0,1-0,2-0,3-0,4 B code = 408 kn -0,5 Grundvariabler Structural Engineering - Lund University 27 Structural Engineering - Lund University 28 7

8 Possible improvements of the results through additional information More accurate control of rebar positions Improved knowledge about yield strength of rebars Transversal positions of heavy vehicles Improved knowledge of vehicle widths Improved knowledge about dynamic amplification factor (Proof loading) Structural Engineering - Lund University 29 Fredrik has later investigated a number of critical sections for the Öland bridge and verified axle and boogie pressures for the bridge to the satisfaction of the bridge owner Vägverket. This has saved a lot of money which could be spent on traffic safety elsewhere. Thank You!! Structural Engineering - Lund University 30 8

RELIABILITY ASSESSMENT OF EXISTING STRUCTURES

1. Introduction RELIABILITY ASSESSMENT OF EXISTING STRUCTURES EN Eurocodes, presently being implemented into the system of national standards nearly in the whole Europe, are particularly intended for the