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1. Cracking risk in early-age RC walls
MSc. Eng. Agnieszka KNOPPIK-WRÓBEL
Silesian University of Technology, Gliwice, Poland
Faculty of Civil Engineering
Department of Structural Engineering
Karlsruhe, 22-25 July 2012

2. Agenda
1 Development of cracks in RC walls
Thermal–shrinkage cracking
Factors of influence
2 Numerical model
Thermal and moisture analysis
Thermal–shrinkage strains
Stress analysis
Implementation
3 Analysis of RC wall
Thermal–moisture analysis
Stress analysis
Damage intensity analysis
4 Parametric study
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
5 Conclusions

3. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Thermal–moisture effects
Figure 1: Hoover Dam, USA
concrete
water + cement + aggregate
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

4. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Thermal–moisture effects
Figure 1: Hoover Dam, USA
concrete
water + cement + aggregate
cement hydration
highly exothermic process
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

5. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Thermal–moisture effects
Figure 1: Hoover Dam, USA
concrete
water + cement + aggregate
cement hydration
highly exothermic process
heat and moisture transport
temperature and moisture gradients
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

6. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Thermal–moisture effects
Figure 1: Hoover Dam, USA
concrete
water + cement + aggregate
cement hydration
highly exothermic process
heat and moisture transport
temperature and moisture gradients
stresses
thermal–shrinkage stresses in structure
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

7. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Internal restraint vs. external restraint
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

8. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Internal restraint vs. external restraint
internal restraint
result of temperature and
moisture gradients within
the element
self-induced stresses
predominant: massive structures
block foundations
gravity dams
massive retaining walls
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

9. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Internal restraint vs. external restraint
internal restraint
result of temperature and
moisture gradients within
the element
self-induced stresses
predominant: massive structures
block foundations
gravity dams
massive retaining walls
external restraint
limitation of deformation by
mature concrete of previously
cast layers
restraint stresses
predominant: restrained structures
tank walls
nuclear containment walls
bridge abutments
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

10. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Cracking pattern in RC walls
Figure 2: Cracking pattern observed in a real RC wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

11. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Cracking pattern in RC walls
h
1/3-2/3h
hh
l
21
cr
2
cr lcr
wk,max
wk,max
Figure 3: Typical cracking pattern in RC wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

12. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Factors affecting the risk of early-age cracking
Factors contributing to the complex process of thermal–shrinkage
cracking of RC walls:
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

13. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Factors affecting the risk of early-age cracking
Factors contributing to the complex process of thermal–shrinkage
cracking of RC walls:
1 thermal properties of concrete dependent on concrete mix
composition
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

14. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Factors affecting the risk of early-age cracking
Factors contributing to the complex process of thermal–shrinkage
cracking of RC walls:
1 thermal properties of concrete dependent on concrete mix
composition
2 conditions during casting and curing of concrete
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

15. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Factors affecting the risk of early-age cracking
Factors contributing to the complex process of thermal–shrinkage
cracking of RC walls:
1 thermal properties of concrete dependent on concrete mix
composition
2 conditions during casting and curing of concrete
3 technology of concreting
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

16. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Factors affecting the risk of early-age cracking
Factors contributing to the complex process of thermal–shrinkage
cracking of RC walls:
1 thermal properties of concrete dependent on concrete mix
composition
2 conditions during casting and curing of concrete
3 technology of concreting
4 environmental conditions
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

17. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–shrinkage cracking
Factors of influence
Factors affecting the risk of early-age cracking
Factors contributing to the complex process of thermal–shrinkage
cracking of RC walls:
1 thermal properties of concrete dependent on concrete mix
composition
2 conditions during casting and curing of concrete
3 technology of concreting
4 environmental conditions
5 dimensions and geometry of concrete structure
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

18. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal and moisture analysis
Thermal–shrinkage strains
Stress analysis
Implementation
General assumptions
1 phenomenological model
full coupling of thermal and moisture fields
decoupling of thermal–moisture and mechanical fields
2 stress state determined under the assumption that
thermal–moisture strains have distort character
3 viscoelasto–viscoplastic material model of concrete
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

19. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal and moisture analysis
Thermal–shrinkage strains
Stress analysis
Implementation
Thermal and moisture analysis
Coupled thermal–moisture equations
˙T = div(αTT gradT + αTW gradc) +
1
cbρ
qv
˙c = div(αWW gradc + αWT gradT) − Kqv
Initial conditions
T(xi , t = 0) = Tp(xi , 0)
c(xi , t = 0) = cp(xi , 0)
Boundary conditions
nT
(αTT gradT + αTW gradc) + ˜q = 0
nT
(αWW gradc + αWT gradT) + ˜η = 0
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

20. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal and moisture analysis
Thermal–shrinkage strains
Stress analysis
Implementation
Thermal–shrinkage strains
Imposed thermal–shrinkage strains εεεn:
volumetric strains
dεεεn
= dεn
x dεn
y dεn
z 0 0 0
calculated based on predetermined temperature and humidity
dεn
x = dεn
y = dεn
z = αT dT + αW dW
W = f (c)
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

21. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal and moisture analysis
Thermal–shrinkage strains
Stress analysis
Implementation
Stress analysis
viscoelastic area
˙σσσ = Dve
(˙εεε − ˙εεεn
− ˙εεεc
)
viscoelasto–viscoplastic area
˙σσσ = Dve
(˙εεε − ˙εεεn
− ˙εεεc
− ˙εεεvp
)
failure surface
stress path
oct
oct
oct
f
m
Figure 4: Damage intensity factor.
possibility of crack occurrence
sl =
τoct
τf
oct
Figure 5: Failure surface development.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

22. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal and moisture analysis
Thermal–shrinkage strains
Stress analysis
Implementation
Implementation
pre-processor & post-processor
data preparation & presentation
with ParaView
processor
TEMWIL
thermal–moisture fields
MAFEM_YOUNG
stress analysis
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

23. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–moisture analysis
Stress analysis
Damage intensity analysis
Basic case
concrete class C30/37, steel class RB400
cement type CEM I 42.5R, 375 kg/m3,
ambient temperature Tz = 25◦C, initial temperature of concrete Tp = 25◦C,
wooden formwork of 1.8 cm plywood removed after 28 days,
no insulation, protection of top surface with foil.
20.0 m
0.7m
4.0m
4.0 m
0.7 m
Z
Y
X
Figure 6: Geometry and finite element mesh of analysed wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

24. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–moisture analysis
Stress analysis
Damage intensity analysis
Thermal fields
40
45
50
55
ature [°C]
interior
surface
20
25
30
35
0 2 4 6 8 10 12 14 16 18 20
tempera
time [days]
Figure 7: Temperature development in time.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

25. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–moisture analysis
Stress analysis
Damage intensity analysis
Moisture fields
15
16
17
18
ontent (x100)
3/m3]
interior
surface
12
13
14
0 2 4 6 8 10 12 14 16 18 20
moisture co
[m3
time [days]
Figure 8: Moisture content development in time.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

26. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–moisture analysis
Stress analysis
Damage intensity analysis
Stress development & deformations
0.6
1.2
1.8
MPa]
interior
surface
‐1.8
‐1.2
‐0.6
0.0
0 2 4 6 8 10 12 14 16 18 20
stress [M
time [days]
Figure 9: Stress development in time.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

27. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Thermal–moisture analysis
Stress analysis
Damage intensity analysis
Stress distribution & damage intensity
-0,7
-0,2
0,3
0,8
1,3
1,8
2,3
2,8
3,3
3,8
-2,5 -1,5 -0,5 0,5 1,5 2,5
height[m]
stress [MPa]
interior
surface
Figure 10: Distribution of stress at the height of the wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

28. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Chosen factors
Influence of the following parameters analysed:
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

29. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Chosen factors
Influence of the following parameters analysed:
1 ambient temperature and temperature difference
Tz = Tp = 25◦
C (basic), 20◦
C or 15◦
C
pre-cooling by 5◦
C or 10◦
C
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

30. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Chosen factors
Influence of the following parameters analysed:
1 ambient temperature and temperature difference
Tz = Tp = 25◦
C (basic), 20◦
C or 15◦
C
pre-cooling by 5◦
C or 10◦
C
2 time of formwork removal
after 28 days (basic)
after 3 days
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

31. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Chosen factors
Influence of the following parameters analysed:
1 ambient temperature and temperature difference
Tz = Tp = 25◦
C (basic), 20◦
C or 15◦
C
pre-cooling by 5◦
C or 10◦
C
2 time of formwork removal
after 28 days (basic)
after 3 days
3 concrete mix composition (type and amount of cement)
CEM I 42.5R 375 kg (basic), 325 kg or 425 kg
CEM II B-S 42.5N, CEM III/A 42.5N or CEM V/A 32.5R
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

32. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Damage intensity maps (after 20 days) comparison
(a)Tz =Tp=15◦
C (b)Tz =Tp=20◦
C (c)Tz =Tp=25◦
C
Figure 11: Damage intensity maps in the interior of the wall (ambient temperature).
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

33. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Damage intensity maps (after 20 days) comparison
(a)Tz =Tp=15◦
C (b)Tz =Tp=20◦
C (c)Tz =Tp=25◦
C
Figure 11: Damage intensity maps in the interior of the wall (ambient temperature).
(a)Tz =25◦
C, Tp=25◦
C (b)Tz =25◦
C, Tp=20◦
C (c)Tz =25◦
C, Tp=15◦
C
Figure 12: Damage intensity maps in the interior of the wall (temp. difference).
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

34. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Maximum damage intensity factor comparison
0.53
0 37
0.54
0 39
0.57
0 39
0.45 0.45 0.470.5
0.6
0.7
0.8
0.9
1.0
tensity factor
interior
surface
0.37
0.23
0.39
0.25
0.39
0.26
0.32
0.22
0.34
0.23
0.34
0.23
0.0
0.1
0.2
0.3
0.4
damage int
Figure 13: Influence of ambient temperature and temperature difference on damage
intensity factor.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

35. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Damage intensity maps (after 20 days) comparison
(a)Tz =Tp=25◦
C, 28 days (b)Tz =Tp=25◦
C, 3 days
Figure 14: Damage intensity maps in the interior of the wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

36. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Damage intensity maps (after 20 days) comparison
(a)Tz =Tp=25◦
C, 28 days (b)Tz =Tp=25◦
C, 3 days
Figure 14: Damage intensity maps in the interior of the wall.
(a)Tz =Tp=25◦
C, 28 days (b)Tz =Tp=25◦
C, 3 days
Figure 15: Damage intensity maps on the surface of the wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

37. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Maximum damage intensity factor comparison
0.53 0.56 0.54 0.57 0.57 0.59
0.45
0.79
0.45
0.79
0.47
0.81
0.5
0.6
0.7
0.8
0.9
1.0
tensity factor
interior
surface
0.0
0.1
0.2
0.3
0.4
damage in
Figure 16: Influence of time of formwork removal on damage intensity factor.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

38. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Hydration heat of cements
200
250
300
350
ration, [J/g]
0
50
100
150
0 10 20 30 40 50 60 70 80
heat of hydr
time, [h]
CEM I 42,5R
CEM II/B‐S 42,5N
CEM III/A 42,5N
CEM V/A (S‐V) 32,5R
Figure 17: Development of hydration heat of different types of cements.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

39. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Damage intensity maps (after 20 days) comparison
(a)CEM I 325kg/m3
(b)CEM I 375kg/m3
(c)CEM I 425kg/m3
(d)CEM II 375kg/m3
(e)CEM III 375kg/m3
(f)CEM V 375kg/m3
Figure 18: Damage intensity maps in the interior of the wall.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

40. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Influence of ambient temperature and temperature difference
Influence of time of formwork removal
Influence of concrete mix composition
Maximum damage intensity factor comparison
0.49
0.57
0.64
0.53
0.57
0.490.47
0.52
0 44 0.470 5
0.6
0.7
0.8
0.9
1.0
ensity factor
interior
surface
0.40
0.44
0.41
0.0
0.1
0.2
0.3
0.4
0.5
CEM I 42.5R
325kg/m3
CEM I 42.5R
375kg/m3
CEM I 42.5R
425kg/m3
CEM II B‐S 42.5N
375kg/m3
CEM III/A 42.5N
375kg/m3
CEM V/A 32.5R
375kg/m3
damage inte
Figure 19: Influence of concrete mix composition on damage intensity factor.
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

41. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Research importance
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

42. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Research importance
Importance
need to ensure desired service life and function of the
structure
on-going examination of early-age cracking problem
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

43. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Research importance
Importance
need to ensure desired service life and function of the
structure
on-going examination of early-age cracking problem
Numerical model
qualitatively and quantitatively proper results
conformation with present knowledge and experience
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

44. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Research importance
Importance
need to ensure desired service life and function of the
structure
on-going examination of early-age cracking problem
Numerical model
qualitatively and quantitatively proper results
conformation with present knowledge and experience
Contribution
multi-parameter numerical model of thermal–moisture effects in
early-age concrete and its implementation
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

45. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Discussion of results
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

46. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Discussion of results
Technology and curing conditions
moderate ambient temperatures
positive influence of initial cooling
surface cracking risk if formwork removed early
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

47. Development of cracks in RC walls
Numerical model
Analysis of RC wall
Parametric study
Conclusions
Discussion of results
Technology and curing conditions
moderate ambient temperatures
positive influence of initial cooling
surface cracking risk if formwork removed early
Concrete mix composition
low-heat cements: lower hydration temperatures vs. lower
rate of strength development
Agnieszka Knoppik-Wróbel Cracking risk in early-age RC walls

48. 9th fib International PhD Symposium in Civil Engineering
22–25 July 2012
Karlsruhe Institute of Technology, Germany