fib symposium 2013 presentation on "early-age thermal–shrinkage crack formation in bridge...

Early-age thermal–shrinkage crack formationin bridge abutmentsExperiences and modelling

Prof. DSc. Eng. Kazimierz FLAGADsc. Eng. Barbara KLEMCZAK, SUT prof.MSc. Eng. Agnieszka KNOPPIK-WRÓBEL

Cracow University of Technology, Cracow, PolandSilesian University of Technology, Gliwice, Poland

Agenda

1 Development of cracks in abutmentsEarly-age crackingCracking pattern in abutments

2 Modelling of early-age crackingAnalytical modelNumerical model

3 Analysis of WA-465 abutmentAnalytic approachNumerical approach

4 Conclusions

Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment

Conclusions

Early-age crackingCracking pattern in abutments

Hydration temperatures

Typical bridge abutmentmassive element, m = S/V ' 2.0m−1

Internal self-heatingalmost adiabatic conditions,∆T = 30÷ 40◦C

Temperature and humidity changesthermal & shrinkage strains

Restraint of deformationthermal & shrinkage stresses

Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments


Conclusions


Restraint stresses

Figure 1 : Heating phase – expansion.



Conclusions


Restraint stresses

Figure 2 : Cooling phase – contraction.



Conclusions


Cracking of abutments at Gliwice-Sośnica Interchange

Figure 3 : The view of Gliwice–Sośnica Interchange,southern Poland



Conclusions


Gliwice-Sośnica Interchange

Figure 4 : Cracking pattern in WA-465 abutment, Gliwice–Sośnica Interchange.



Conclusions


Cracking of bridge frame structures at A4 motorway

Figure 5 : The view of A4 motorway Tarnów–Rzeszów,south-eastern Poland



Conclusions


Cracking of bridge frame structures at A4 motorway

Figure 6 : Cracking pattern in WA-142 wall, Tarnów–Rzeszów A4 motorway.Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments


Conclusions

Analytical modelNumerical model

Modelling strategy

Modelling methods

analytical numerical



Conclusions


Modelling strategy

Modelling methods

analytical

numerical



Conclusions


Modelling strategy

Modelling methods

analytical numerical



Conclusions


Thermal–moisture analysis

Max. internal temperatureTint = Tp + χ∆Tadiab

Mean max. temperatureTm = Tint − 1

3 (Tint − Tsur )

Temperature change∆T = γ (Tm − Ta)

Thermal strain∆εT = αT∆T

Total shrinkage strainεcs = εcd + εca

εcd , εcd – acc. to EC2

Differential strain

∆εcs = εIIcs(t II)−[εIcs(t I + t II)− εIcs(t I)

]I – element I, foundationII – element II, wall



Conclusions


Thermal–shrinkage stress analysis

Figure 7 : Thermal–shrinkage stresses at expansion at the height of the cenerline.

τp =Ac · (∆εt + ∆εcs) · Ecm,eff (t)

0.5 · lz · b≤ τp = 0.5 ·

√fcm · fctm

T2 = 0.5 · τp · lz · b



Conclusions



Figure 8 : Thermal–shrinkage stresses at contraction at the height of the cenerline.

τp =Ac · (∆εt + ∆εcs) · Ecm,eff (t)

0.5 · lz · b≤ τp = 0.5 ·

√fcm · fctm

T2 = 0.5 · τp · lz · b



Conclusions



1 phenomenological model2 decoupling of thermal–moisture and mechanical fields3 full coupling of thermal and moisture fields:

T = div(αTT gradT + αTW gradc) +1

cbρqv

c = div(αWW gradc + αWT gradT )− Kqv4 thermal–shrinkage strains – volumetric strains calculated based

on predetermined temperature and humidity change:

dεn =[dεnx dεny dεnz 0 0 0

]dεnx = dεny = dεnz = αT dT + αW dW



Conclusions



1 phenomenological model

2 decoupling of thermal–moisture and mechanical fields3 full coupling of thermal and moisture fields:


cbρqv







Conclusions



1 phenomenological model2 decoupling of thermal–moisture and mechanical fields

3 full coupling of thermal and moisture fields:


cbρqv







Conclusions





cbρqv

c = div(αWW gradc + αWT gradT )− Kqv

4 thermal–shrinkage strains – volumetric strains calculated basedon predetermined temperature and humidity change:





Conclusions





cbρqv







Conclusions



1 stress state determined under the assumption thatthermal–moisture strains have distort character

2 viscoelasto–viscoplastic material model of concrete:

Figure 9 : Failure surface development.

failure surface

stress path

τoct

τoct

τoct

f

σm

Figure 10 : Damage intensity factor.

damage intensity factor

sl =τoctτ foct



Conclusions


Thermal–shrinkage stress analysis1 stress state determined under the assumption that

thermal–moisture strains have distort character

2 viscoelasto–viscoplastic material model of concrete:


failure surface

stress path

τoct

τoct

τoct

f

σm



sl =τoctτ foct



Conclusions


Thermal–shrinkage stress analysis1 stress state determined under the assumption that

thermal–moisture strains have distort character2 viscoelasto–viscoplastic material model of concrete:


failure surface

stress path

τoct

τoct

τoct

f

σm



sl =τoctτ foct



Conclusions


Implementation

pre-processor & post-processordata preparation & presentationwith ParaView

processorTEMWILthermal–moisture fieldsMAFEM_VEVPstress analysis



Conclusions

Analytic approachNumerical approach

Basic caseconcrete class C30/37, steel class BSt500Scement type CEM I 42.5N, 365 kg/m3,ambient temperature Tz = 4◦C, initial temperature of concrete Tp = 18◦C,wooden formwork of 1.8 cm plywood removed after 7 days,no insulation, protection of top surface with PE foil.

Figure 11 : Geometry and finite element mesh of analysed abutment.



Conclusions


Thermal strains

max. self-heating temperatureTint = 52.6◦C, Tsur = 15.0◦C

mean temperature in sectionTm = 40.0◦C

temperature difference∆Tstem = 36◦C, ∆T = 21.7◦C

thermal strain∆εT = 2.17 · 10−4

Figure 12 : Temerature distribution insectin acc. to Schmidt’s method.



Conclusions


Shrinkage strains

strain in foundation beforeexecution of stem: t I = 15 daysεIcs(t I) = 0.27 · 10−4

strain in foundation and stem 7days after execution of stem:t I + t II = 22 daysεIcs(t I + t II) = 0.31 · 10−4,εIIcs(t II) = 0.21 · 10−4

differential shrinkage strain∆εcs = 0.17 · 10−4

εI – strain in foundationεII – strain in stem wall

Figure 13 : Graphical interpretation ofstrain development in abutment.



Conclusions


Stresses and cracking

bond force at the jointT2 = 25.29MN

stressesσ|h=0 = 9.09MPaσ|h=Hc = −4.84MPa

height of crackfctm = fctm(7 days)hcrack = 3.84m ' 0.5Hc

Figure 14 : Graphical interpretation of crackheight determination.



Conclusions





Conclusions


Stresses



Conclusions


Damage intensity/Cracking

(a) interior (b) surface

Figure 15 : Damage intensity maps (cracking in black).



Conclusions

Conclusions

1 results from analytic and numerical analysis comply with thepractical observations,

2 simplified engineering model can be helpful in the preliminaryrisk assessment,

3 detailed analysis of the phenomena requires the use ofnumerical methods,

4 numerical analysis allows to determine thermal, moisture andstress state as well as possible damage of the structure in thewhole time of concrete curing.


The research was done as a part of the project N N506 043440“Numerical prediction of cracking risk and methods of its reductionin massive and medium-thick concrete structures”, funded by PolishNational Science Centre.

Co-author, A. Knoppik-Wróbel is a scholar under the project„SWIFT“ POKL.08.02.01-24-005/10 co-financed by European Unionunder the European Social Fund.

fib symposium 2013 presentation on "early-age thermal–shrinkage crack formation in bridge...

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