1. Moisture Diffusion and Long-term Deformation of Concrete
KAIST Civil and Environmental Engineering
Jin-Keun KIM

2. Moisture diffusion of concrete Prediction of long-term deformation
Index
Moisture diffusion of concrete
Prediction of long-term deformation
Researches in KAIST

3. Moisture diffusion of concrete
Definition of the diffusion
Diffusion is the net movement of a substance (e.g., an atom, ion or molecule) from a region of high concentration to a region of low concentration. This is also referred to as the movement of a substance down a concentration gradient.

4. Moisture diffusion of concrete
Fick’s first law of diffusion
J : diffusion flux
D : diffusion coefficient or diffusivity (m2/s)
c : concentration
For steady state,
For unsteady state,

5. Moisture diffusion of concrete
Moisture diffusion equation
For pore relative humidity
Diffusion coefficient
For pore moisture content

6. Moisture diffusion of concrete
The effect of relative humidity and temperature on the diffusion coefficient
Relationship between relative humidity and diffusion coefficient
Relationship between temperature and diffusion coefficient

7. Moisture diffusion of concrete
Moisture diffusion coefficient suggested in CEB-FIP(‘90)
For isotherm condition
D1 : diffusion coefficient when h = 1.0
D0 : diffusion coefficient when h = 0
: D0 /D1
hc : diffusion coefficient when D (h) = 0.5D1
n : exponent
h : pore relative humidity
D1,0 = (m2/hr)
fck0 = 10 MPa
fck = fcm-8 MPa

8. Moisture diffusion of concrete
Moisture diffusion coefficient suggested by Bazant
( )

9. Moisture diffusion of concrete
Moisture diffusion coefficient by Mihashi
D1 : diffusion coefficient at saturated condition (h=1) and 20oC
U : activation energy
R : gas constant
, hc, n, N1, N2 : material constants depending on the mixture and curing condition

10. Moisture diffusion of concrete
Boundary condition
: environmental humidity
: surface humidity
Surface factor equation suggested by Sakata
Equivalent thickness by Bazant
around 0.75 mm

11. Moisture diffusion of concrete
Moisture diffusion of concrete → Change of internal humidity
⇒ Change of mechanical properties : Compressive strength,
Modulus of elasticity
Change of long-term deformation : Creep and shrinkage
Differential drying shrinkage ⇒ shrinkage crack

12. Differential drying shrinkage
Cause
moisture content difference at every position in the concrete by the moisture diffusion

13. Compressive strength (MPa) Cement content (kgf/m3)
Differential drying shrinkage - example
Slab
Analysis parameters
- Fixed end, Free end
- Thickness (h) : 0.2, 0.4, 0.8 m
- Ambient humidity : 30, 50, 80 %
Concrete
Compressive strength (MPa) 24
Cement content (kgf/m3)
300
Water content (kgf/m3)
180
Free end
Fixed end

14. Differential drying shrinkage - example
Humidity versus depth of slab – Ambient humidity is 30%
H = 0.2m
H = 0.4m
H = 0.8m

15. Differential drying shrinkage - example
Humidity versus depth of slab – Ambient humidity is 50%
H = 0.2m
H = 0.4m
H = 0.8m

16. Differential drying shrinkage - example
Humidity versus depth of slab – Ambient humidity is 80%
H = 0.2m
H = 0.4m
H = 0.8m

17. Differential drying shrinkage - example
Stress versus depth of slab
– Ambient humidity is 30%
H = 0.2m
H = 0.4m
H = 0.8m

18. Differential drying shrinkage - example
Stress versus depth of slab
– Ambient humidity is 50%
H = 0.2m
H = 0.4m
H = 0.8m

19. Differential drying shrinkage - example
Stress versus depth of slab
– Ambient humidity is 80%
H = 0.2m
H = 0.4m
H = 0.8m

20. Differential drying shrinkage - example
Strain versus time – Free end
Ambient humidity : 30%
Ambient humidity : 50%
Ambient humidity : 80%

21. Differential drying shrinkage - example
Stress versus depth of slab
– Ambient humidity is 30%
H = 0.2m
H = 0.4m
H = 0.8m

22. Differential drying shrinkage - example
Stress versus depth of slab
– Ambient humidity is 50%
H = 0.2m
H = 0.4m
H = 0.8m

23. Differential drying shrinkage - example
Stress versus depth of slab
– Ambient humidity is 80%
H = 0.2m
H = 0.4m
H = 0.8m

24. Importance of prediction of long-term deformation
Column shortening in high-rise building
Prestress loss in the PS structures
Long-term deformation in beam and slab
Expansion and reduction of the crack width
Re-distribution of stress between steel and concrete in RC member

25. Researches in KAIST Autogenous shrinkage and basic creep
Creep of concrete under multi-axial stresses
Differential drying shrinkage
Study on column shortening

26. + Autogenous shrinkage and basic creep Existing basic creep model
high strength and/or
early age concrete
elastic + creep deformation +
autogenous shrinkage
autogenous shrinkage
separation from basic creep model
Basic creep of concrete is creep deformation produced under applied stress without moisture migration to the atmosphere.
Autogenous shrinkage of concrete is a phenomenon that concrete contracts itself without change of weight and temperature of concrete.
Basic creep strain measured from conventional basic creep test contains autogenous shrinkage.
So current basic creep model based on conventional basic creep test data contains elastic and creep deformation dependent on applied stress, and autogenous shrinkage. Whether this autogenous shrinkage depends on applied stress or not will be revealed in this study.
Up to now this autogenous shrinkage has been ignored in basic creep model. In case of ordinary strength concrete or hardened concrete, autogenous shrinkage is small, so current basic creep model is applicable to these kinds of concrete.
But nowadays, the use of high strength concrete whose autogenous shrinkage cannot be ignorable increases in construction sites.
So, to develop a basic creep model applicable to high strength or early age concrete, this autogenous shrinkage has to be separated from current basic creep model.
So the objective of this study is to show the necessity of a new basic creep model considering autogenous shrinkage effect on basic creep model.
Applicability of basic creep model should be checked !

27. Autogenous shrinkage and basic creep
Test 1 : Autogenous shrinkage and basic creep test for various w/c ratios
Tested for four different types of concrete mix
Variables
autogenous shrinkage test : w/c ratios - 30, 40, 50, and 60%
basic creep test : w/c ratios - 30, 40, 50, and 60%
: loading ages - 1, 3, 7, and 28 days
Concrete mix proportions
W/C
(%)
unit weight (kgf/m3) Ad W C S G 30
175
583
591
999
1.0% 40
438
687
1031
0.6% 50
350
752
0.3% 60
292
849
1030
0.1%
Next I’ll talk about test program performed in this study.
To obtain previously mentioned real basic creep, autogenous shrinkage and basic creep test for various W/C ratios were performed in this study.
Test was performed for four different types of concrete mix.
Test variable of autogenous shrinkage test is water cement ratio such 30, 40, 50 and 60%.
Test variable of basic creep test is water cement ratio, and loading ages,
This table shows concrete mix proportions for four water cement ratios.

28. Autogenous shrinkage and basic creep
Test 2 : Autogenous shrinkage and basic creep test for various applied load
Tested for w/c ratio 30% at 1 day age
Variables
basic creep test : applied load levels – 0.1, 0.2, 0.3, and 0.4fc’
In this study, autogenous shrinkage and basic creep test for various applied load
were performed to verify the applicability of basic creep model and effect autogenous shrinkage on basic creep of concrete.
Test was performed for water cement ratio 30% at 1day age.
Test variable of basic creep test is applied load levels such as 10, 20 ,30, and 40 percent of compressive strength of concrete at 1day.
In autogenous shrinkage test, prism and cylinder specimens were used as shown in this picture.
There were no remarkable differences of autogenous shrinkage between two cases.
In basic creep test, four applied load were measured from each load cell equipped to each testing device as shown in this picture.
Autogenous shrinkage test
Basic creep test for four stress levels

29. Autogenous shrinkage and basic creep
Autogenous shrinkage test
Autogenous shrinkage drastically increases at early ages.
Early age stage
Hardening stage
Next I’ll talk about the test results.
This graph shows autogenous shrinkage strains for four water cement ratios.
From this figure, we can see that autogenous shrinkage increases as water cement ratio decreases and the amount of that is remarkable especially for water cement ratio 30%.
Measured autogenous shrinkage strains

30. Autogenous shrinkage and basic creep
Apparent and real basic creep
autogenous shrinkage from t’ to t
elastic strain
real basic creep
apparent basic creep
Next I’ll introduce apparent and real basic creep defined in this study.
This figure shows basic creep strain measured from basic creep test under applied stress sigma zero loading at age t’.
In this study apparent basic creep is defined as total strain measured from basic creep test shown as this line in this figure. So this apparent basic creep contains elastic, creep, and autogenous shrinkage strain.
On the other hand, real basic creep shown as this line can be obtained by excluding autogenous shrinkage from apparent basic creep. .

31. Autogenous shrinkage and basic creep
Basic creep test for various w/c ratios
The difference between real and apparent creep compliance function
is clearly visible in case of loading at 1 and 3 days.
t’ = 1 day
t’ = 1 day
t’ = 3 days
t’ = 3 days
t’ = 7 days
t’ = 7 days
t’ = 28 days .
t’ = 28 days
Next I’ show test results of basic creep test for four water cement ratios.
This is the case of water cement ratio 30%, this is for 40%.
In this graph, black line means apparent basic creep compliance, and red line means real basic creep compliance obtained from previous method.
From these results we can see that the differences between real and apparent creep compliance are obvious in case of loading at 1 and 3 days.
Apparent and real basic creep compliance functions with age

32. Autogenous shrinkage and basic creep
Basic creep test for four applied load levels
t’ = 1 day, W/C = 30%
fc’ = 23MPa
t’ = 1 day, W/C = 30%
fc’ = 23MPa .
This is test results of basic creep test for four applied load levels.
This figure shows total strain including autogenous shrinkage, and this figure shows total strain excluding autogenous shrinkage.
Total strain including and excluding autogenous shrinkage

33. Autogenous shrinkage and basic creep
The comparison of apparent and real basic creep
Real basic creep can be obtained from conventional basic creep tests by simply subtracting the autogenous shrinkage in a stress-free state.
This graph shows total strain excluding autogenous shrinkage with applied load.
In this graph, this red line passing through the origin and this point passes other two points.
This means this real creep compliance is independent on applied stress.
So this equation is true.
On the other hand, we can see that these three points have linear relationship in previous and this graph.
This means autogenous shrinkage is independent of applied stress.
From these conclusions, we can see that this equation using real creep compliace is true !
Apparent and real basic creep compliance functions with age

34. Creep of concrete under multiaxial stresses
Concrete is generally subjected to multiaxial stresses in many structures.
Multiaxial Stress
Uniaxial Stress
매스콘크리트, 원자력 격납구조물의 이방향프리스트레스 부재,
내진설계에 의해 횡보강재가 많이 사용된 기둥 등 많은 구조물에서
콘크리트는 다축응력 상태에 놓이게 됩니다.
기존의 연구는 일축응력상태를 대상으로
크리프 특성을 규명하고자 하는 데 치중했으며,
메커니즘, 수학모델, 예측모델 등의 개발이 이루어져왔습니다.
그러나 다축응력 상태에 대한 연구는 매우 부족했으며,
연구결과들도 서로 일치하지 않아, 다축응력 상태의 크리프 특성은 아직까지
명확히 규명되어 있지 않습니다.

35. Creep of concrete under multiaxial stresses
Experimental apparatus
이 그림은 2축응력과 3축응력을 가하지 위해 제작된 실험장치를 나타낸 것입니다.
일정한 하중을 유지하기 위해 유압펌프, 유압게이지를 전자제어장치에 연결하여 시간에 따라 실린더 내에 일정한 유압이 작용하도록 하였습니다.
Biaxial stress state
Triaxial stress state

36. Creep of concrete under multiaxial stresses
Creep Poisson’s ratio CI
CII
CIII
초기의 급격한 변화는 실험결과에 민감하기 때문이다.
0.15~0.20사이로 분포
fluctuation of creep Poisson’s ratio with time, it is difficult to distinguish whether these values are increasing, decreasing or remaining constant with time.
Time(days)

37. Creep of concrete under multiaxial stresses
Effective creep Poisson’s ratio CI
CII
CIII
삼축응력 상태의 effective Poisson’s ratio가 이축응력상태의 포아송 비보다 작게 나타났으며, CI 콘크리트의 경우 CII, 와 CIII 콘크리트에 비 작은 값을 보였습니다. 전체적으로 about 0.16 to 0.2.
Time(days)

38. Creep of concrete under multiaxial stresses
Volumetric components of stress and creep strain CI
CII
CIII
Multi-axial creep deformation of concrete under multi-axial stresses can be interpreted in terms of the superimposed volumetric and deviatoric components of strain and stress.
This figure shows the volumetric stresses and creep strains at 1, 4, 7, 28 days after initial loading. The volumetric stresses and strains were obtained from these equations. The volumetric stresses were linearly proportional to volumetric creep strains and the linear relationship remained with time. It can be shown that the volumetric stresses and creep strains had the same relationship even though the stress combinations applied to the specimens were different.

39. Creep of concrete under multiaxial stresses
Deviatoric components of stress and creep strain CI
CII
CIII
This figure shows the relationship between deviatoric stresses and deviatoric creep strains. The deviatoric stresses and the deviatoric creep strains also had the linear relationship. The linearity of volumetric components and deviatoric components remained with time and multi-axial creep can be analyzed with this linear property. In second analytical study, this linearity will be used.

40. Differential drying shirnkage
Measurement of RH
Specimen

41. Differential drying shirnkage
Experimental results
Relative humidity at each point with time (t0 = 3 days)
w/c = 0.28
w/c = 0. 40
w/c = 0.68

42. Differential drying shirnkage
부등건조수축
Differential drying shirnkage
Experimental results
Relative humidity at each point with time (t0 = 28 days)
w/c = 0.28
w/c = 0. 40
w/c = 0.68

43. Differential drying shirnkage
부등건조수축
Differential drying shirnkage
Experimental results
Shrinkage strain at each point with time (t0 = 3 days)
w/c = 0.28
w/c = 0. 40
w/c = 0.68

44. Differential drying shirnkage
부등건조수축
Differential drying shirnkage
Experimental results
Shrinkage strain at each point with time (t0 = 3 days)
w/c = 0.28
w/c = 0. 40
w/c = 0.68

45. Importance of the study
Study on column shortening
Importance of the study
Differential column shortening
Serviceability and safety problems
Demands for reasonable prediction of shortening
Crack
Distortion of wall
Exterior column
Interior column
Deformation of anchor of elevator

46. Needs of prediction of column shortening in SRC columns
Study on column shortening
Needs of prediction of column shortening in SRC columns

47. Characteristic of SRC columns and analysis procedures
Study on column shortening
Characteristic of SRC columns and analysis procedures
d𝜀 𝑠ℎ = 𝑘 𝑠ℎ dℎ
𝜀 𝑠ℎ : drying shrinkage
ℎ : relative humidity
at a point in the section H1 H2
H1 > H2 H3 H4
H3 < H4
H : Relative humidity
𝑘 𝑠ℎ = 𝜀 𝑠 0 𝑔 𝑠 (𝑡) d 𝑓 𝑠 (ℎ) d ℎ
: ultimate shrinkage
𝑓 𝑠 (ℎ) = 1− ℎ 3

48. Study on column shortening
Analysis program
Analysis of moisture diffusion
Relative humidity distribution in concrete
Calculate initial strain and curvature at time 𝒕 𝟎
Calculate free shrinkage strain and creep strain at each location of concrete
Calculate the restraining stress
Calculate the restraining resultants
Calculate the strain at a reference point 0 and curvature at time t
Calculate the strain at each location and stress at time t

49. Differential drying shrinkage analysis result
Study on column shortening
Differential drying shrinkage analysis result
60cm each side, covering depth 10cm
w/c = 0.3
Environmental condition : 20℃, 65%
Plain H
Cross

50. Study on long-term deformation depending on the finishing materials
Study on column shortening
Study on long-term deformation depending on the finishing materials
w/c = 0.3
Environmental condition : 20℃, 40%
Finishing material : oil-paint, water-paint, waterproofer
[Drying shinkage]
[Creep]

51. Study on column shortening
Gradual development of the global stiffness matrix
sequence 1

52. Study on column shortening
Gradual development of the global stiffness matrix
sequence 1
sequence 2

53. Study on column shortening
Gradual development of the global stiffness matrix
sequence 1
sequence 2
sequence 3

54. Study on column shortening
Gradual development of the global stiffness matrix
sequence 1
sequence 2
sequence 3
sequence 4

55. Study on column shortening
Gradual development of the global stiffness matrix
sequence 1
sequence 2
sequence 3
sequence 4
sequence 5

56. Study on column shortening
Gradual development of the global stiffness matrix
sequence 1
sequence 2
sequence 3
sequence 4
sequence 5
sequence 6

57. Study on column shortening
Result of column shortening analysis
C214
C216
C236
Modeled part
Overall trend of analysis result
coincide with measured data
Because of the lack of
construction information
and accuracy of measurement,
errors exist.

58. Thank you 