Full text available: https://www.researchgate.net/publication/236171819_Early-age_thermalshrinkage_crack_formation_in_bridge_abutments._Experiences_and_modelling?ev=prf_pub

1. Early-age thermal–shrinkage crack formation
in bridge abutments
Experiences and modelling
Prof. DSc. Eng. Kazimierz FLAGA
Dsc. Eng. Barbara KLEMCZAK, SUT prof.
MSc. Eng. Agnieszka KNOPPIK-WRÓBEL
Cracow University of Technology, Cracow, Poland
Silesian University of Technology, Gliwice, Poland

2. Agenda
1 Development of cracks in abutments
Early-age cracking
Cracking pattern in abutments
2 Modelling of early-age cracking
Analytical model
Numerical model
3 Analysis of WA-465 abutment
Analytic approach
Numerical approach
4 Conclusions

3. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking pattern in abutments
Hydration temperatures
Typical bridge abutment
massive element, m = S/V 2.0m−1
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

4. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking pattern in abutments
Hydration temperatures
Typical bridge abutment
massive element, m = S/V 2.0m−1
Internal self-heating
almost adiabatic conditions,
∆T = 30 ÷ 40◦C
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

5. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking pattern in abutments
Hydration temperatures
Typical bridge abutment
massive element, m = S/V 2.0m−1
Internal self-heating
almost adiabatic conditions,
∆T = 30 ÷ 40◦C
Temperature and humidity changes
thermal & shrinkage strains
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

6. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking pattern in abutments
Hydration temperatures
Typical bridge abutment
massive element, m = S/V 2.0m−1
Internal self-heating
almost adiabatic conditions,
∆T = 30 ÷ 40◦C
Temperature and humidity changes
thermal & shrinkage strains
Restraint of deformation
thermal & shrinkage stresses
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

7. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking pattern in abutments
Restraint stresses
Figure 1 : Heating phase – expansion.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

8. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking pattern in abutments
Restraint stresses
Figure 2 : Cooling phase – contraction.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

9. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking 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

10. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking 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

11. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking 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

12. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Early-age cracking
Cracking 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

13. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Modelling strategy
Modelling methods

14. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Modelling strategy
Modelling methods
analytical

15. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Modelling strategy
Modelling methods
analytical numerical
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

16. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

17. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Max. internal temperature
Tint = Tp + χ∆Tadiab
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

18. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Max. internal temperature
Tint = Tp + χ∆Tadiab
Mean max. temperature
Tm = Tint − 1
3 (Tint − Tsur )
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

19. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Max. internal temperature
Tint = Tp + χ∆Tadiab
Mean max. temperature
Tm = Tint − 1
3 (Tint − Tsur )
Temperature change
∆T = γ (Tm − Ta)
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

20. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Max. internal temperature
Tint = Tp + χ∆Tadiab
Mean max. temperature
Tm = Tint − 1
3 (Tint − Tsur )
Temperature change
∆T = γ (Tm − Ta)
Thermal strain
∆εT = αT ∆T
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

21. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Max. internal temperature
Tint = Tp + χ∆Tadiab
Mean max. temperature
Tm = Tint − 1
3 (Tint − Tsur )
Temperature change
∆T = γ (Tm − Ta)
Thermal strain
∆εT = αT ∆T
Total shrinkage strain
εcs = εcd + εca
εcd , εcd – acc. to EC2
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

22. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Max. internal temperature
Tint = Tp + χ∆Tadiab
Mean max. temperature
Tm = Tint − 1
3 (Tint − Tsur )
Temperature change
∆T = γ (Tm − Ta)
Thermal strain
∆εT = αT ∆T
Total shrinkage strain
εcs = εcd + εca
εcd , εcd – acc. to EC2
Differential strain
∆εcs = εII
cs(tII) − εI
cs(tI + tII) − εI
cs(tI)
I – element I, foundation
II – element II, wall
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

23. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–shrinkage stress analysis
Figure 7 : Thermal–shrinkage stresses at expansion at the height of the cenerline.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

24. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical 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

25. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

26. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
1 phenomenological model
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

27. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
1 phenomenological model
2 decoupling of thermal–moisture and mechanical fields
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

28. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
1 phenomenological model
2 decoupling of thermal–moisture and mechanical fields
3 full coupling of thermal and moisture fields:
˙T = div(αTT gradT + αTW gradc) +
1
cbρ
qv
˙c = div(αWW gradc + αWT gradT) − Kqv
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

29. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–moisture analysis
1 phenomenological model
2 decoupling of thermal–moisture and mechanical fields
3 full coupling of thermal and moisture fields:
˙T = div(αTT gradT + αTW gradc) +
1
cbρ
qv
˙c = div(αWW gradc + αWT gradT) − Kqv
4 thermal–shrinkage strains – volumetric strains calculated based
on predetermined temperature and humidity change:
dεn
= dεn
x dεn
y dεn
z 0 0 0
dεn
x = dεn
y = dεn
z = αT dT + αW dW
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

30. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–shrinkage stress analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

31. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–shrinkage stress analysis
1 stress state determined under the assumption that
thermal–moisture strains have distort character
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

32. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–shrinkage stress analysis
1 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.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

33. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Thermal–shrinkage stress analysis
1 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
oct
oct
oct
f
m
Figure 10 : Damage intensity factor.
damage intensity factor
sl =
τoct
τf
oct
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

34. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytical model
Numerical model
Implementation
pre-processor & post-processor
data preparation & presentation
with ParaView
processor
TEMWIL
thermal–moisture fields
MAFEM_VEVP
stress analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

35. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical approach
Basic case
concrete class C30/37, steel class BSt500S
cement 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

36. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical approach
Thermal strains
max. self-heating temperature
Tint = 52.6◦C, Tsur = 15.0◦C
mean temperature in section
Tm = 40.0◦C
temperature difference
∆Tstem = 36◦C, ∆T = 21.7◦C
thermal strain
∆εT = 2.17 · 10−4
Figure 12 : Temerature distribution in
sectin acc. to Schmidt’s method.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

37. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical approach
Shrinkage strains
strain in foundation before
execution of stem: tI = 15 days
εI
cs(tI) = 0.27 · 10−4
strain in foundation and stem 7
days after execution of stem:
tI + tII = 22 days
εI
cs(tI + tII) = 0.31 · 10−4,
εII
cs(tII) = 0.21 · 10−4
differential shrinkage strain
∆εcs = 0.17 · 10−4
εI – strain in foundation
εII – strain in stem wall
Figure 13 : Graphical interpretation of
strain development in abutment.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

38. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical approach
Stresses and cracking
bond force at the joint
T2 = 25.29MN
stresses
σ|h=0 = 9.09MPa
σ|h=Hc = −4.84MPa
height of crack
fctm = fctm(7 days)
hcrack = 3.84m 0.5Hc
Figure 14 : Graphical interpretation of crack
height determination.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

39. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical approach
Thermal–moisture analysis
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

40. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical approach
Stresses
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

41. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Analytic approach
Numerical 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

42. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Conclusions
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

43. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Conclusions
1 results from analytic and numerical analysis comply with the
practical observations,
2 simplified engineering model can be helpful in the preliminary
risk assessment,
3 detailed analysis of the phenomena requires the use of
numerical methods,
4 numerical analysis allows to determine thermal, moisture and
stress state as well as possible damage of the structure in the
whole time of concrete curing.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

44. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Conclusions
1 results from analytic and numerical analysis comply with the
practical observations,
2 simplified engineering model can be helpful in the preliminary
risk assessment,
3 detailed analysis of the phenomena requires the use of
numerical methods,
4 numerical analysis allows to determine thermal, moisture and
stress state as well as possible damage of the structure in the
whole time of concrete curing.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

45. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Conclusions
1 results from analytic and numerical analysis comply with the
practical observations,
2 simplified engineering model can be helpful in the preliminary
risk assessment,
3 detailed analysis of the phenomena requires the use of
numerical methods,
4 numerical analysis allows to determine thermal, moisture and
stress state as well as possible damage of the structure in the
whole time of concrete curing.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

46. Development of cracks in abutments
Modelling of early-age cracking
Analysis of WA-465 abutment
Conclusions
Conclusions
1 results from analytic and numerical analysis comply with the
practical observations,
2 simplified engineering model can be helpful in the preliminary
risk assessment,
3 detailed analysis of the phenomena requires the use of
numerical methods,
4 numerical analysis allows to determine thermal, moisture and
stress state as well as possible damage of the structure in the
whole time of concrete curing.
Agnieszka Knoppik-Wróbel Early-age cracking in bridge abutments

47. The research was done as a part of the project N N506 043440
“Numerical prediction of cracking risk and methods of its reduction
in massive and medium-thick concrete structures”, funded by Polish
National 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 Union
under the European Social Fund.