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
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
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
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
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Early-age crackingCracking pattern in abutments
Restraint stresses
Figure 1 : Heating phase – expansion.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Early-age crackingCracking pattern in abutments
Restraint stresses
Figure 2 : Cooling phase – contraction.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Early-age crackingCracking pattern in abutments
Cracking of abutments at Gliwice-Sośnica Interchange
Figure 3 : The view of Gliwice–Sośnica Interchange,southern Poland
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Early-age crackingCracking pattern in abutments
Gliwice-Sośnica Interchange
Figure 4 : Cracking pattern in WA-465 abutment, Gliwice–Sośnica Interchange.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Early-age crackingCracking pattern in abutments
Cracking of bridge frame structures at A4 motorway
Figure 5 : The view of A4 motorway Tarnów–Rzeszów,south-eastern Poland
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Early-age crackingCracking pattern in abutments
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
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Modelling strategy
Modelling methods
analytical numerical
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Modelling strategy
Modelling methods
analytical
numerical
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Modelling strategy
Modelling methods
analytical numerical
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–shrinkage stress analysis
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–moisture analysis
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–moisture analysis
1 phenomenological model
2 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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–moisture analysis
1 phenomenological model2 decoupling of thermal–moisture and mechanical fields
3 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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–moisture analysis
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 )− Kqv
4 thermal–shrinkage strains – volumetric strains calculated basedon predetermined temperature and humidity change:
dεn =[dεnx dεny dεnz 0 0 0
]dεnx = dεny = dεnz = αT dT + αW dW
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–moisture analysis
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–shrinkage stress analysis
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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–shrinkage stress analysis1 stress state determined under the assumption that
thermal–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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–shrinkage stress analysis1 stress state determined under the assumption that
thermal–moisture strains have distort character2 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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Thermal–shrinkage stress analysis1 stress state determined under the assumption that
thermal–moisture strains have distort character2 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
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytical modelNumerical model
Implementation
pre-processor & post-processordata preparation & presentationwith ParaView
processorTEMWILthermal–moisture fieldsMAFEM_VEVPstress analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytic approachNumerical approach
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytic approachNumerical approach
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytic approachNumerical approach
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytic approachNumerical approach
Thermal–moisture analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytic approachNumerical approach
Stresses
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
Conclusions
Analytic approachNumerical approach
Damage intensity/Cracking
(a) interior (b) surface
Figure 15 : Damage intensity maps (cracking in black).
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
Development of cracks in abutmentsModelling of early-age crackingAnalysis of WA-465 abutment
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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments
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.
Top Related