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Rackwitz – Symposium Nov. 2006
Potential and Limits of Probabilistic Service Life Design Peter Schießl
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Bild 57: Rißstellen mit Querschnittsminderungen (infolge Korrosionsabtragungen) ΔF > 0,5 %. Mittlere Querschnittsminderungen ΔF > 0,5 % und Anteil dieser Rißstellen bezogen auf alle Rißstellen. Rippentorstahl Ø 8 mm
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The History:
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1978 CEB –Task group Durability 1982 CEB Bulletin 148 – St-A-R-Durability 1989 CEB Bulletin 182 – Design Guide 1997 CEB Bulletin 238 – New Approach to Durability Design 1999 Brite EURAM Research Project “DURACRETE” 2002 fib Task Group 5.6 2006 fib Bulletin 34
– MCSLD
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Probabilistic Service Life design
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Involves statistics and reliability. It was a main objective to establish a methodology as close as possible to structural design fib TG 5.6 has therefore chosen the package of standards associated with Eurocode-0 / Eurocode-2 as the main references As the new fib Model Code 2006 shapes, the elements will be implemented into this framework.
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Model Code for Service Life Design (MC SLD)
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Gives “Principles” that have to be obeyed Gives “Application rules” as informative examples on sufficiently verified methods Chapter 1 2 3 4 5
Introduction/General Basis of Design Verification of Service Life Design Execution and Quality Control Maintenance and Condition Control
Annex A Management of reliability for SLD Annex B Full probabilistic design models
d βσ
Z
σ
R
R
βσ
Z
σ
Z
σ
F
F
Z
pf
r, f, z
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Model Code on Service Life Design
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assumptions
1
terms of definitions other administrative provisions
2
design criteria full probabilistic design
3
probabilistic models -resistances -loads/exposure -geometry limit states
partial factor design
deemed to satisfy design
avoidance of deterioration
design values -characteristic values -partial safety factors -combination factors
exposure classes
exposure classes
design equations
design provisions
design provisions
design / verifications project specification for material selection and execution maintenance plan inspection / monitoring plan
4
quality plan for execution (optional) inspection of execution
5
maintenance
in case of non-conformity with the performance criteria, the structure becomes either obsolete or subject to a redesign
principles of service life
condition control during service life
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Safety concept, structural design
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P {failure} = P {R - S < 0} < P target RC/γR - Sc . γs > 0 RC: load bearing capacity based on characteristics values γR: partial safety factor (resistance) SC: characteristic value of the influence of loading γS: partial safety factor (stress/load)
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Safety concept, durability design
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P {failure} T= P {R - S < 0} T< P target RC/γR - Sc . γs > 0
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Safety concept, durability design
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P {failure} T= P {R - S < 0} T< P target RC/γR - Sc . γs > 0 Example
RC: concrete cover c SC: ingress of chloride front
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Design criterion: cover > depassivation depth RC , SC
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Elaboration of Service Life Design BRITE-EURAM project „DURACRETE“
RC,T
RC(t)
SC,T
SC(t)
SC(t) 0
T
exposure period in [a] November 2006
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New design concept - Basis and terms of the safety concept -
Z = R - S
(Env.) Load Resistance Reliability
pf = Φ ( -
σZ
σS
σR
μS
β . σZ
R
S 0
σZ
μR
r, s
Z
pf 0
µZ
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β . σZ
μZ
) = Φ (- β ), with µ Z = µ R - µ S , σ Z =
z
σ R2 + σ S2
Reliability Index Φ ( . ) Normal Distribution Failure Probability
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Basic deterioration model (reinforcement corrosion)
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Degree of deterioation 4
Ultimate Limit State (ULS)
3 2 1
Time t [a]
Reliability index β ~ 1.5
Limit States
~ 4.2
1
Depassivation of reinforcement
2
Formation of cracks
3
Spalling
4
Failure
Reinforcement corrosion (Deterioration period)
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Example: Westerschelde - Tunnel - NL
Cross Section
Longitudinal Section Ring: 1
2
3
4
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Ring 2
180°
"Tübbing" 0,45 m 270°
90° joints 0° = 360° 11,00 m
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Geometry of Prefabricated Tunnel-Ring Element
Xc (joint)
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Chlorid attack (Cl-)
xc
xc Carbonation (CO2) eventually chloride attack (Cl-)
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Example: Westerschelde - Tunnel - NL
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Requirement of the owner: Tender document: Agreement between owner and contractor:
Service Life 100a Design for depassivation as a serviceability limit state β ≥ 1,8
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Material Model (Chloride Diffusion)
Ccrit = CSN 1- erf
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xc to n 2 Do • M • t • t
c : critical corrosion initiating chloride content Ccrit crit cSN : chloride concentration at the surface C xc
: concrete cover
Do
: chloride migration coefficient
M
: model factor
tt o o tt
: reference age : service life November 2006
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List of parameters for SLD – Limit State 1, Depassivation
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Parameter
Unit
µ
s
Distribution type
Xc -concrete cover
[mm]
50
5
Beta*
Do -Cl-migration coefficient
[ 10-12 m2/s]
4,75
0,71
ND
0,70
0,10
ND
Ccrit -critical Chloride content [M.-%/Binder] n-aging factor
[-]
0,60
0,07
ND
Kt -factor -test conditions
[-]
1,00
-
D
Ke -factor-environment
[-]
1,00
0,10
ND
Kc -factor-execution
[-]
1,00
0,20
ND
CSN c(Cl-) - concrete surface
[M.-%/Binder]
4,00
0,050
ND
to -time of testing
[a]
0,0767
-
D
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Result of Serve Life Design (Limit State 1 - Depassivation)
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β in [-] 3,6 3,4
β
= 3,488
pf
= 0,0002
3,2 3,0
β
= 2,561
pf
= 0,0053
2,8
β
= 2,255
pf
= 0,0126
2,6 2,4
β
= 1,951
2,2
pf
= 0,0255
2,0 1,8 20
30
40
50
60
70
80
90
100 t in [a]
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Update of SLD during Service Life Degree of deterioation Ultimate Limit State (ULS)
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4
3 2 1
Design Assumptions rel. to - actions - resistance
After construction - Knowledge of quality achieved - Measurement of model parameters - reduction model uncertainty
Time t [a]
After depassivation - determination of corrosion rate
Before depassivation - determination of interaction between action and resistance → Measurement of the depassivation front
Improvement of service life prediction November 2006
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Example: Olympic Tower
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Level 291,0 m
Level 192,6 m Level 160,0 m
Top
Platform for visitors
Antenna platforms
Inspection area
Level 0,0 m
Ground
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Resistance variable: concrete cover
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dc = dc,measured + ε
dc: geometrical variable (concrete cover) dc,measured: measured concrete cover ε: error term (uncertainty of the non destructive measuring device)
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Stress variable: carbonation depth
⎛ t0 ⎞ − 1 x c (t) = 2 ⋅ k e ⋅ k c ⋅ (k t ⋅ R ACC,0 + ε t ) ⋅ ΔCS ⋅ t ⋅ ⎜ ⎟ ⎜ t ⎟ ⎝ ⎠ xc(t): k e: kc: RACC,0-1: kt, εt: ΔCS: t: W: pSR: ToW:
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w
Carbonation depth at time t f(RH) – RH function f(t curing) – Curing function Inverse of the carbonation resistance Test method translation factors CO2-concentration of the ambient air Time in service f(t, pSR, ToW) – Wetting function Probability of surfaces subjected to driving rain in dependency to their orientation Time of wetness
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Update: comparison a-priori/a-posterior
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Orientation East, level 8 m above ground 0.07
reliability index β [-]
6.0
probability of occurance a-posterior
reliability index, a-priori reliability index, a-posterior
5.0
0.06 0.05
4.0
0.04
3.0
0.03
2.0
0.02
1.0
0.01
0.0
0.00 100
0
20
40 33 inspection
60
80
failure probablility pf [%]
7.0
time of exposure [a] November 2006
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Example: Parking Deck Allianz-Arena
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Parking deck Highway A 9 Allianz-Arena
Bus parking
Highway A 995
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Example: Parking Deck Allianz-Arena
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Parking deck
pedestrian area
Level 3 Level 2 Level 1 Level 0
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Example: Parking Deck Allianz-Arena
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Coating zones
coated surface (cracked zone, bending zone)
uncoated surface
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Example: Parking Deck Allianz-Arena
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Design principle: S-1: Cl- on coated cracks
S-1: Cl- on uncoated concrete
R-2: Concrete cover plus monitoring R-1: Coating plus regulary inspection/maintenance November 2006
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Example: Parking Deck Allianz-Arena – Uncoated Area
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Example: Parking Deck Allianz-Arena - Column
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Example: Parking Deck Allianz-Arena
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Updating procedure (monitoring)
cabels to measuring instrument
time of exposure cathode anodes
reinforcement
cathode (precious metal)
anodes (reinforcement steel)
front of depassivation
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Example: Parking Deck Allianz-Arena Updating procedure
β [-]
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β [-]
pf [-]
pf [-] reliability β
A-Priori reliability
a-priori calculation a-posterior calculation
0.15
A-Posterior
failure probability
failure probability pf
1.0
a-priori calculation a-posterior calculation
t [a] 50
t [a]
xdep. [mm]
Expected information from the sensors (slope assumed)
n = 30
tinsp.
t [a] November 2006
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Test Methods for the Material Resistance Basic requirement for SLD
Chloride diffusion resistance Lab-testing: Rapid migration test
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Simple and reproducible measurement of the decisive material resistance parameters in the lab and at the site
At the site: Electrolytic resistance Wenner-Probe
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Interrelation between DCl- and Electrolytic Resistance
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Migrationcoefficient DCI,M [10-12 m² / s] 100,0
w/(z + 0,5 f) = 0,50 ohne und mit SFA Lagerung: Beton: 20 °C/80 % r. F. Mörtel: Wasser 20 °C
10,0
1,0 28 d 91 d 365 d
0,1 100
1000
10000
100000
Elektrolytic resistance [Ohm] November 2006
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Testing Concept of Concrete Quality
Potential diffusion resistance of cementes Deff, cement
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Interrelation between cement and conrete property Deff,concr. = Deff, cem. × f(concr.)
Potential concrete quality Deff, concrete Concrete quality in the structure Deff, structure
Requirement for execution
Measured concrete properties
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Testing Concept of Concrete Quality
Potential diffusion resistance of cementes Deff eff, cement
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Interrelation between cement and conrete property Deff D eff,concr. = Deff eff, cem. × f(concr.)
Potential concrete quality Deff, eff concrete Concrete quality in the structure Deff eff, structure Measured concrete properties
Requirement for execution
Deff eff
→ fc !
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Conclusion 1
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SLD on a probabilistic basis applicable for depassivation in uncracked concrete Design procedure with partial safety factors exists → DURACRETE, fib Tg 5.6 Only a design concept on a probabilistic basic is able to consider material variations, variation of actions and model uncertainties SLD ready for standardisation in the next generation of Standards (EN, ISO) → fib Tg 5.6 has prepared a ModelCode for Service Life Design (fib - Bulletin, Jan 06) November 2006
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Conclusion 2 – other Deterioration Mechanisms
Reinforcement corrosion in the region of cracks
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Further developement of deterioration models, quantification by research DFG Forschergruppe
Dissolving chemical attack
Design examples exist
Sulphate attack ASR
For the time being: Design strategy A
Frost - Frost deicing salt
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