control of cracking for concrete bridges...concrete bridges – example from en 1992-2 7.3.4...

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

OHP 2 of 40

0 Cracks-the intro from Calgary, Alta


OHP 3 of 40

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


OHP 4 of 40

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 !


OHP 5 of 40

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 ?!


OHP 6 of 40

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


OHP 12 of 40

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




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05 Objectives



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


OHP 20 of 40


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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Randomization-Methods are described within the paper.


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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


OHP 30 of 40


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


OHP 31 of 40

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


OHP 32 of 40


z zmβ ⋅ σ =


OHP 33 of 40


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


OHP 34 of 40


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.


OHP 35 of 40

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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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!!


OHP 40 of 40

11 Appendix

Front

Back

The new model´s core can be placed on a beer coaster. (by friendly permisson of the staff of the „Grizzly Paw“, Canmore, Alta

control of cracking for concrete bridges...concrete bridges – example from en 1992-2 7.3.4...

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