Post on 02-Jan-2020
CONTROL OF CRACKING FOR CONCRETE BRIDGES -THE PERFORMANCE OF CALCULATION MODELS
Dr.-Ing. Lars Eckfeldt
Civil Engineering. Institute of Concrete Structures
7th International Conference on Short and Medium Span Bridges
Montreal, 23th August 2006
TU Dresden, 31.08.2006 Control of Cracking– Performance of Calculation Models
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0 Cracks-the intro from Calgary, Alta
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170 NDPin29
Nat.Annexes
+NCCI
ENV
01 Setting
Timeline
EN 1992-1-1 Bridge: EN 1992-2
< 1993 2005
Various National Standards
FIP/CEBModelcode 90
Experience
2001 2010
EN 1990 Basis of Design
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01 Setting
SLS-Bridges(Serviceability Limit States)
Ed ≤ Cd →(wlim;wmax;...)
crack width control(primary cracking)
-min.reinforcement-stress limitations
crack width control(loading)
deflection control
Durabilityconcerns(cover,
detailing)
-verification withsuitable models
ULS-(detailing)
-not span dependent !
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01 Setting
SLS-Bridges(Serviceability Limit States)
Ed ≤ Cd →(wlim;wmax;...)
crack width control(primary cracking)
-min.reinforcement-stress limitations
crack width control(loading)
deflection control
Durabilityconcerns(cover,
detailing)
-verification withsuitable models
ULS-(detailing)
-not span dependent !
Ambitious objectives:-servicelife: 50 →100 years∴→wlim= 0.2 mm∴→demands on c (cover) are higher
... contradicting ?!
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01 Setting
NDP – National Determined Parameters:
Concrete Bridges – Example from EN 1992-2
7.3.4 Calculation of crack widths(101) The evaluation of crack width may be performed using recognised methods.
Note: Details of recognised methods for crack width control may be found in a Country’s National Annex. The recommended method is that in EN 1992-1–1 clause 7.3.4.
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02 Model background
“classic” cracking approach – based on bond (Tepfers)
A crack occurs if σctreaches fct(x).
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02 Assessment
o m r m
2(w /2) ww 2S s
⇒ =→ = ⋅ Δε = ⋅ Δε
Basic assumption:
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02 Assessment
Simplified resistance model
steelstress
cones
strut
ties back
bond action stress
reduced
accumulatingcover stress
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03 Special Problems
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04 General Assumption
ct t s
ct c,eff,loc b b o s s
ct c,eff,loc b b o s,cr s
b b ct
s b
s,cr ct c,eff,loc s ct s,ef
s,cro
F F F
A ( d ) S A
cracking:f A ( d ) S A
where : k f
A d ² / 4
f A / A f /
2S 2
= ≤
↓σ ⋅ = τ ⋅ π ⋅ ⋅ ≤ σ ⋅
⋅ = τ ⋅ π ⋅ ⋅ ≈ σ ⋅
τ = ⋅
= π ⋅
σ ≈ ⋅ = ρ
σ ⋅ π∴ = bd ²⋅
b
/ 4
(τ ⋅ π bd⋅cts,cr b
b ct
fd
2 k f)
σ ⋅= →
⋅ ⋅s,ef b
b ct
/ d
2 k f
ρ ⋅
⋅ ⋅
bo
b s,ef
d2S
2 k∴ =
⋅ ⋅ ρ
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04 Standard models
The FIP/CEB(fib)-Modelcode 1990
Pre-calculated characteristic crack widths wk
s t ct,eff s,ef e s,efbk lim
s,ef s
k f / (1 )dw w
3.6 E
⎛ ⎞ σ − ⋅ ρ ⋅ + α ⋅ ρ⎛ ⎞= ⋅ ≤⎜ ⎟ ⎜ ⎟⎜ ⎟⋅ ρ ⎝ ⎠⎝ ⎠
s t s,efb3 1 1 2 4
s,ef s
ect,eff s,efk
k f / (1 )dw k c k k k
E
⎛ ⎞ σ − ⋅ ρ ⋅ + α ⋅ ρ⎛ ⎞= ⋅ + ⋅ ⋅ ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ρ ⎝ ⎠⎝ ⎠
The recommended Eurocode 2-method
in a more familiar look (strong MC 78-roots?)
s t s,efb1
T B s,ef s
ect,eff s,efk
k f / (1 )dw 1.7 2c
(5 ;10 ) E
⎛ ⎞ σ − ⋅ ρ ⋅ + α ⋅ ρ⎛ ⎞= ⋅ + ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟⋅ ρ ⎝ ⎠⎝ ⎠
Δεm∼
srm
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04 Situation
Conditions:-exposition XD 2(deicing salts)-structural classS 3
∴→Σc ≥ 55 mm
Cross - section
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04 Situation
Cross - section
Conditions:-exposition XD 2(deicing salts)-structural classS 3∴→Σc ≥ 55 mm
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05 Objectives
Semi-empirical approaches need calibration :
1. For 95% of test data wm,test: wm,test < wk,cal
2. For 75% of test data wmax,test:wmax,test < wk,cal
3. For 95% of test data wmax,test: wmax,test < 1.25·wk,cal
It implicates that the prediction performance of wk,cal israther accurate limiting the range of characteristic crack widths narowly around the predictions.
Compare this conclusion to reality!
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05 Objectives
Comparison with w/sr = const.
allows for conclusion of the expected performance of wcal
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05 Objectives
Comparison with w/sr = const.
allows for conclusion of the expected performance of wcal
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05 Objectives
Comparison with w/sr = const.
allows for conclusion of the expected performance of wcal
4.Economic rule recommended
For 90%...95% of wk,cal: 0.8 wk,test< wk,cal < 1.5 wk,test
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06 Randomization-enabling other analysis
Often available larger [wm,test; wm,cal] datasets in diagramsrelate to certain cracking models – but they refer to characteristic loading only.
Situations with varying loads can be assessed by modifying(randomizing) the characteristic data according to an assumed loading system and probability distribution.
Gk Qk,ir r 1Σ+ =
Gk
Qk,i
" "-LS " " " " " "r 0.5 ; 0.6 ; 0.7r 0.5 0.4 0.3
Loadsystem Footbridge Railwaybridge Roadbridge
Σ
⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⇒⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠
Gk: mean value of a small varying load distributionQk,i:k-quantile of a Gumbel- or a bimodal distribution
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06 Randomization-enabling other analysis
Example: Distribution of lorry trafic on highway bridges
from Research Report: Bestimmung von Kombinationsbeiwerten und –regeln für Einwirkungen auf Brücken. Sukhov, Sedlacek, Novak et al.
k-valueBonus
Reality ?
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06 Randomization-enabling other analysis
Randomization-Methods are described within the paper.
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06 Randomization-enabling other analysis
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06 Other Analysis
Obtained results: for restraints
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06 Other Analysis
Obtained results: for restraints
k m
s t ct,eff s,ef e s,efbk
s,ef s
Sensible adjustments ?!MC 90: w /w =1.25
k f / (1 )dw
3.1.2...1.
68
E
⎛ ⎞ σ − ⋅ ρ ⋅ + α ⋅ ρ⎛ ⎞= ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟⋅ ρ ⎝ ⎠⎝ ⎠
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06 Other Analysis
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07 Model adjustments
As result of the extensive analysis, to meet requirementsserious model improvements are helpful and necessary:
1. Modify the approach to Ac,eff decisevily and ρs,ef respectively
2. Define the bond resistance dependent on the coversize
Suggestion: Model Eckfeldt
s t s,cr,loc s,ef,locbk b,lim r
b,lim s,ef,loc s
k [ ( )]dw 1.57 k c
2 k E
⎛ ⎞ σ − ⋅ σ = ρ⎛ ⎞= ⋅ + ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟⋅ ⋅ ρ ⎝ ⎠⎝ ⎠
f
rk,cals
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07 Model adjustments
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07 Performance after adjustments
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08 Reliability Checks-Background
s(E) z
2 2z
r
r s
m m m−β = =
σσ + σ
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08 Reliability Checks-Background
r
rk,cal,i rm,test,i k,cal,i m,test,i
rm,test,i m,test,i
/test,i cal-test (s ; w),i
z ( /test)
z ( /test)
An approach towards a limit state function:z =( /test)
s -s w -w;
s w
mß=
Δ
Δ
Δ
Δ
⇔
∴σ
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08 Reliability Checks
Competitive models only deserve acception if results meet the reliability objective (ß-index) that is defined by EC 0.
(s(E) in SLS-"translation" sz
2 2 2 2z
calculated design( )
test result)criteriar cd
r s c s
m m m mm− −β = = ⎯⎯⎯⎯⎯⎯⎯⎯→ =
σσ + σ σ + σ
w,cal,class w,test,class sr,cal,class sr,test,class
2 2 2 2w,cal,class w,test,class sr,cal,class sr,test,class
crackm m m m
width orcontrol
− −→
σ + σ σ + σ
A more stabile solution yields if:
r
rk,cal,i rm,test,i k,cal,i m,test,i
rm,test,i m,test,i/test,i cal-test (s ; w),i
z ( /test)
z ( /test)
s -s w -wz =( /test) ;
s w
mß=
Δ
Δ
Δ
Δ ⇒
∴σ
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08 Reliability Checks
z zmβ ⋅ σ =
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08 Reliability Checks-Background
ß-index and failure probability pf→ EC 0 Basis of Design
Relation between ß and pf (1 year reference)
SLS, for non-reversibledeformation
ULS
Recommendation for minimum ß-indexes
Reliability class Minimum ß - indexesreference time 1 year reference time 50 years
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08 Reliability Checks-Background
ß-index and failure probability pf→ EC 0 Basis of Design
Relation between ß and pf (1 year reference)
SLS, for non-reversibledeformation
ULS
Table is valid for structures of reliability class (RC) 2.
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9 Reliability approach
-Available datasets (being representative samples) are seen as representing the population, they form a virtual populationespecially the sr-dataset with geometric information adhered.
-The resampling method is derived from cross-validation(multicross-validation) methods to respect the given data.
-For drawing (re-) samples, the sample size of √n was chosen.
-The representative data were ordered to the (w;2So)mean,test-data
-Difficult: to divide reversible and non-reversible deformation→conserv. assumption, there are always non-reversible byeffects.
-Analysis done is done by drawing random samples out of this virtual population – the statistic method is resampling.
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08 Reliability Checks
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10 Conclusions
Judgements on site:
Stay tolerant !!
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10 Conclusions
Judgements on site:
Stay tolerant !!
k;0.80 k;0.98w w→
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1. If parameters ρs,ef and kb could be revised the „classic approach“ would improve the prediction performance of srk(=2So,k) and wk.
10 Conclusions
2. Models in general should be made more understoodable and never loaded with expectations they cannot bear.
-by attaching performance characteristics
3. Testing and comparing with available test data – Modernizedatasets (gain time scale, restraints and geometric information).
4. Needed : Probabilistic ready bond models for a complexerparametric research
Stay tolerant while judging crack width exceedings on sitebecause of random influences!!