21

WORK OF JCI COMMITTEE ON AUTOGENOUS SHRINKAGE Ei-ichi Tazawa*1, Ryoichi Sato*2, Etsuo Sakai*3 and Shingo Miyazawa*4 *1 Professor Emeritus, Hiroshima University, Japan *2 Hiroshima University, Japan *3 Tokyo Institute of Technology, Japan *4 Ashikaga Institute of Technology, Japan 1. Introduction Shrinkage of hardened concrete due to cement hydration, which is not caused by evaporation or temperature change, is known as autogenous shrinkage. The phrase "autogenous shrinkage" was used by C. G. Lyman more than sixty years ago[1]. Since autogenous shrinkage of ordinary concrete is much less than drying shrinkage, it has been thought that autogenous shrinkage could be ignored from engineering point of view. However, it has been recently proved that autogenous shrinkage can be so large as to be a cause of cracking in high-strength concrete structures. Therefore, many studies have been carried out for the last decade especially in Europe and Japan. Technical Committee on Autogenous Shrinkage was set up in 1995 by Japan Concrete Institute (JCI). The JCI Committee investigated (1) definition of autogenous shrinkage, (2) testing methods for autogenous shrinkage, stress and cracking, (3) mechanism and prediction of autogenous shrinkage and (4) prediction of shrinkage induced stress and cracking. In this report, the activities of the JCI Committee are summarized. The details of the activities were reported at International Workshop on Autogenous Shrinkage of Concrete (AUTOSHRINK'98) held in 1998[2].

2. Terminology The JCI Committee proposed the definition of autogenous shrinkage and other related technical terms, such as autogenous expansion, chemical shrinkage, self desiccation and subsidence. In this chapter, the terminology is quoted from the JCI Committee report[2].

22

Autogenous shrinkage Autogenous shrinkage is the macroscopic volume reduction of cementitious

materials when cement hydrates after initial setting. Autogenous shrinkage does

not include the volume change due to loss or ingress of substances, temperature

variation, application of an external force and restraint.

Autogenous shrinkage can be expressed as the percentage of volume reduction

“autogenous shrinkage ratio” or one dimensional length change “autogenous

shrinkage strain”.

Note: The phenomenon of macroscopic volume reduction of cement paste, mortar and concrete caused by chemical shrinkage is referred as autogenous shrinkage. When autogenous shrinkage is measured, the initial length (volume) of specimens should be measured at the time of initial setting. Although autogenous shrinkage is essentially a three dimensional phenomenon, autogenous shrinkage strain (εas ) is described as linear strain. When ordinary concrete is subjected to drying, water evaporation results in drying shrinkage. In large structural elements made of concrete, temperature variation due to heat of hydration results in thermal strain. Under these conditions where the mass and the temperature of concrete are changed, the strain which has been obtained as drying shrinkage strain or thermal strain includes autogenous shrinkage strain under the corresponding temperature conditions. Volume change that is generated when concrete is still fresh should be excluded in order to define autogenous shrinkage. Since autogenous shrinkage is generally used for prediction of cracking, the strain generated in a period when cementitious material is fresh is excluded. Therefore, the time of initial setting of cement is specified as the start point of autogenous shrinkage measurement.

Autogenous expansion

Autogenous expansion is the macroscopic volume increase of cementitious

materials when cement hydrates after initial setting. Autogenous expansion does

not include volume change due to loss or ingress of substances, temperature

variation, application of an external force and restraint.

Autogenous expansion can be expressed as the percentage of the volume

increase “autogenous expansion ratio” or one dimensional length change

“autogenous expansion strain”. Autogenous volume change

Autogenous volume change includes autogenous shrinkage and autogenous

expansion.

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Chemical shrinkage

Chemical shrinkage is the phenomenon in which the absolute volume of hydration

products is less than the total volume of unhydrated cement and water before

hydration. Chemical shrinkage is described by the following equation. (Notation in

the equation is shown in Fig. 1)

（ＶＣ＋ＶＷ ）－Ｖｈｙ

Ｓｈｙ＝ ――――――――― ×100 (1)

ＶＣｉ＋ＶＷｉ

Shy: chemical shrinkage ratio (%)

Vci: volume of cement before mixing

Vc : volume of hydrated cement

Vwi: volume of water before mixing

Vw : volume of reacted water

Vhy: volume of hydration products Note: When hardened cement paste is considered as a composite of solid phase (unhydrated cement and hydration products), liquid phase (unhydrated water) and gas phase (air bubbles existing after mixing and the voids created by hydration), chemical shrinkage is considered to be the reduction of absolute volume of reactants, i.e. solids phase plus liquid phase. On the other hand, autogenous shrinkage is considered to be the reduction of the external volume since solid skeleton is formed. After the skeleton of hydration products develops in the absence of an external source of water, the progress of hydration results in the formation of additional voids in hardened microstructure of cement. Therefore, the macroscopic volume reduction, i.e. the autogenous shrinkage, is much less than the chemical shrinkage. The relation between autogenous shrinkage and chemical shrinkage of cement paste without evaporation and any external source of water is schematically shown in Fig.2 and also described as eq.(2). Ｓｈｙ≒ＳＰ＋Ｓａｓ＋ΔＳｈｙ (2) where,

Sas: autogenous shrinkage ratio(%) ΔShy: chemical shrinkage ratio at the time of initial setting(%) Sp : the ratio of the volume of voids created by hydration to the volume of hardened cement paste(%)

In eq.(2), right and left sides are not explicitly equal each other. This is because the initial volume for calculating chemical shrinkage (Shy) is specified as the volume of the mixture at the end of mixing, on the other hand, that for autogenous shrinkage (Sas) is specified as

24

the volume at the initial setting. Since the term ΔShy in the eq.(2) is very small, Ｓｈｙ is approximated by the following equation for practical purpose. Ｓｈｙ≒ＳＰ＋Ｓａｓ (3)

Autogenous shrinkage

Chemical shrinkage Void due to hydration

Age

Vol

ume

redu

ctio

n

Initi

al se

ttin

g

Chemical shrinkage at initial settiing

Fina

l set

ting

Fig. 2 Relation between chemical shrinkage and autogenous shrinkage

Fig. 1 Notation in eq.(1)

Before mixing After hydration

Chemical shrinkage ＶＣｉ

ＶＷｉ

ＶＣ

ＶＷ Ｖｈｙ

Unhydrated cement

Unreacted water

25

The relation between autogenous shrinkage ratio and autogenous shrinkage strain is described as the following equation. Ｓａｓ＝300εａｓ (4) where, εａｓ: autogenous shrinkage strain When the effect of gravity is not negligible, length change in the horizontal direction of cementitious material is different from that in the vertical direction. The relation between chemical shrinkage and length change in the horizontal direction is schematically shown in Fig. 3. The relation between chemical shrinkage and length change in the vertical direction is shown in Fig. 4(a) for mixtures without bleeding and Fig. 4(b) for mixtures with bleeding.

Fig. 3 Relation between chemical shrinkage and autogenous shrinkage in the horizontal direction where,

Ｗ： unhydrated water ＷＢ： bleeding water Ｃ： unhydrated cement

Ｗ Ｃ At casting

Ｗ Ｃ Ｈ y At initial setting

Autogenous shrinkage

Chemical shrinkage

Ｗ ＰＣ Ｈ y After hardening

26

Autogenous shrinkage

Ｈ y

Chemical shrinkage

ＷＷＷ

Ｃ

Ｐ

ＣＣ Ｈ y

Subsidence

Chemical shrinkage

At casting At initial setting after hardening

(a) without bleeding

At casting At initial setting After hardening

(b) with bleeding

Chemical shrinkage

Ｈ y

ＷＢ

Ｗ Ｗ Ｗ

Ｃ

Ｐ

Ｃ Ｃ Ｈ y

Subsidence

Autogenous shrinkage

Chemical shrinkage

Fig. 4 Relation between chemical shrinkage and autogenous shrinkage in the vertical direction

27

Ｈ y： hydration products Ｐ： voids generated by hydration

Self desiccation

Hardened cement paste can be subjected to drying due to consumption of

capillary water in the progress of cement hydration. When this phenomenon

happens it is called as self desiccation.

Note: When the voids (P) created by hydration is not supplied with water from the surrounding environment, the hardened cementitious material can be substantially drying without evaporation. This phenomenon is called self desiccation. If a specimen with dense microstructures or a large cross section is used, water can penetrate into only the surface layer of the specimen even under water curing. Then the central part of the specimen can be subjected to self desiccation.

Subsidence

Vertical length change in cementitious materials before initial setting, which is

caused by bleeding, chemical shrinkage and so on, is called subsidence.

Note: In case of fresh concrete, in which the skeleton of hydration products has not been formed, cement particles are re-arranged by the effect of gravity as chemical shrinkage proceeds, then macroscopic shrinkage occurs in the vertical direction. Therefore, subsidence of concrete is caused not only by the difference in specific gravities of water and solid particles, which is manifested by bleeding, but also by chemical shrinkage. 3. Factors affecting autogenous shrinkage In this chapter, the factors affecting autogenous shrinkage such as type of cement, type of mineral admixtures, water-cement ratio and volume concentration of aggregate are described.

(1) Type of cement Autogenous shrinkage of cement paste with various types of cement is shown in Fig.5. It can be seen that autogenous shrinkage is strongly dependent on the type of cement. It should be noticed that this is not the case in drying shrinkage. Autogenous shrinkage of moderate heat Portland cement(M) and low heat Portland cement(L) is much less than ordinary Portland cement(N). It is assumed that autogenous shrinkage of cement paste

28

can be described by the following equation.

εp(t) ＝ a･αC3S(t)･(C3S%)＋b･αC2S(t)･(C2S%)＋c･αC3A(t)･(C3A%) ＋d･αC4AF(t)･(C4AF%)＋e･(Blaine)＋f (5) where

εp(t) is autogenous shrinkage of cement paste (×10-6) αi(t) is degree of hydration of compound i (%) t is age ( i %) is content of compound i (%) i is mineral compound (Blaine) is Blaine fineness of cement (cm2/g) a, b, c, d, e and f are constants

Constant a, b, c, d, e and f were determined from regression analysis using experimental data, and it is proved that the coefficients c and d, which correspond to C3A and C4AF, are much larger than those corresponding to C2S and C3S by one or two orders. This suggests that autogenous shrinkage depends on the hydrations of C3A and C4AF. Calculated autogenous shrinkage by this equation is compared with the observed values as shown in Fig.6. Calculated values are roughly the same as the observed ones, and it can be said that autogenous shrinkage of cement paste with different type of cement can be predicted by the mineral composition of cement. (2) Mineral admixture The effect of blast furnace slag on autogenous shrinkage of cement paste is shown in Fig.7. Autogenous shrinkage is slightly decreased by addition of blast furnace slag with low Blaine fineness. On the other hand, it is increased by addition of blast furnace slag with high Blaine fineness especially at large replacement ratios. Some experimental researches show that autogenous shrinkage is decreased by addition of fly ash, and is increased by addition of silica fume.

(3) Water-cement ratio Autogenous shrinkage of cement pastes with different water-cement ratio is shown in Fig.8. Autogenous shrinkage increases with decreasing water-cement ratio. For the cement paste with water-binder ratio of 0.17 containing silica fume, more than 4000 micro strain is observed at the age of 1 month. Furthermore, autogenous shrinkage of cement pastes with low water-cement ratio increases more rapidly at early ages than those with higher water-cement ratio. The test data for concrete is shown in Fig.9. Autogenous shrinkage increases with decrease in water-cement ratio, which is the same result as for cement pastes.

(4) Volume concentration of aggregate Autogenous shrinkage occurs mainly in cement paste, so shrinkage of concrete decreases

29

with increase in volume concentration of aggregate. In case of drying shrinkage, the effect of volume concentration of aggregate has been estimated from composite models, for example, series model (eq.(6)), parallel model (eq.(7)) and Hobbs’ model (eq.(8))[3].

apc V−= 1εε (6)

)EE(VV

paa

apc 11

1−+

−=εε (7)

)KK(VK/K)KK)(V(

paapa

paapc 11

11−++

+−=εε (8)

where cε is autogenous shrinkage of concrete pε is autogenous shrinkage of cement paste aV is volume concentration of aggregate pK is bulk modulus of elasticity of cement paste aK is bulk modulus of elasticity of aggregate

)(/EK υ213 −= , υ is Poisson’s ratio, E is modulus of elasticity

Autogenous shrinkage of mortar and concrete with different volume concentration of aggregate is shown in Fig.10. It can be seen that these composite models are also applicable to autogenous shrinkage of concrete.

4. Relation between autogenous shrinkage and other volume changes Autogenous shrinkage generally does not occur by itself. Other kinds of volume changes usually occur at the same time in concrete structures. The relationship between autogenous shrinkage and other kinds of volume changes, such as thermal strain, drying shrinkage and swelling, are summarized.

(1) Thermal strain As concrete temperature changes with time in massive concrete structures, autogenous shrinkage strain and thermal strain occurs simultaneously. It is desirable to obtain both types of shrinkage separately in order to calculate shrinkage-induced stress. Test data for autogenous shrinkage of concrete under different constant temperatures, 20℃, 40℃ and 60℃, are shown in Fig.11. Autogenous shrinkage increases more rapidity at higher temperature, therefore, the data are plot against effective age based on maturity concept in this figure. The three curves can be roughly presented as a single curve. Then autogenous shrinkage under varying temperature can be determined based on effective age. It has been reported, however, that maturity concept is not applicable to some kinds of concrete.

30

(2) Drying shrinkage When concrete is subjected to drying after curing, drying shrinkage occurs simultaneously with autogenous shrinkage. The relationship between water-cement ratio and three kinds of shrinkage; drying shrinkage, autogenous shrinkage and the total shrinkage is shown in Fig.12. In this figure, drying shrinkage is determined by subtracting autogenous shrinkage of sealed specimen from the total shrinkage of dried specimen. In case of high water-cement ratio, most part of shrinkage is drying shrinkage. On the other hand, in case of low water-cement ratio, autogenous shrinkage is much larger than drying shrinkage. Shrinkage of concrete with water-cement ratio of 0.2 is shown in Fig.13, where the specimens were subjected to drying at different relative humidity after 7 days of sealed curing. In case of low relative humidity, shrinkage is observed due to evaporation. In case of high relative humidity, on the other hand, expansion is observed due to moisture movement from the environment into the specimen. This is because internal relative humidity of high-strength concrete may be lower than external relative humidity. Therefore, properties of drying shrinkage of high-strength concrete are quite different from those of ordinary concrete.

(3) Swelling Length change of cement paste with different water-cement ratio during water curing is shown in Fig.14. Cross section of the specimen is 40x40mm, and water-cement ratio is varied as 0.3, 0.23 and 0.17. Cement paste with water-cement ratio of 0.3 gradually increases its length. On the other hand, cement pastes with water-cement ratio of 0.23 and 0.17 decreases its length even if they are stored in water. Length change of cement paste with 0.3 water-cement ratio during water curing is shown in Fig.15. Cross section of the specimen is varied as 20x20mm, 40x40mm and 100x100mm. Shrinkage is observed in the specimen with larger dimensions even in water. This may be because curing water permeates only into the exterior part of the specimen and the interior part is subjected to self-desiccation. Therefore, the volume change of high-strength concrete is influenced by both swelling and autogenous shrinkage which simultaneously occur in a cross section. 5. Methods to reduce autogenous shrinkage As previously mentioned, using cement with a higher C2S content and lower C3A and C4AF contents is very effective to reduce autogenous shrinkage. In order to obtain the design strength at 28 days, water-cement ratio of low heat cement concrete should be slightly less than that of normal cement concrete, therefore autogenous shrinkage can be slightly decreased by using low heat cement. If the design strength is specified at 91 days, water-cement ratio of low heat cement concrete may be much higher, which means autogenous shrinkage will be considerably decreased.

31

Increasing SO3 content in cement up to 5 % significantly decreases autogenous shrinkage without decrease in compressive and flexural strength[4]. Addition of fiber such as steel fiber and vinylon fiber is also effective to reduce both autogenous shrinkage and tensile strength of concrete[5]. It has been proved that various types of admixtures are effective to reduce autogenous shrinkage. Some shrinkage reducing agents, which reduce the surface tension of capillary water, are effective to reduce autogenous shrinkage. Effect of expansive admixtures of CSH type (E1) and CaO type (E2, E3) on autogenous shrinkage is shown in Fig.16. Expansion is observed at early ages and then shrinkage is observed under sealed condition. The effect of a water-repellent powder on autogenous shrinkage is shown in Fig.17. Water-repellent powder is also effective to reduce autogenous shrinkage. This may be because addition of this kind of powder increases the contact angle between cement hydrate and capillary water, and then decreases the capillary tension. Autogenous shrinkage of light-weight aggregate concrete decreases with increase in moisture content of aggregate[6]. In case of boiled light-weight aggregate, even slight expansion was observed. This phenomenon has been explained by moisture movement from the aggregate particles to the surrounding cement paste. The effect of curing method on length change of expansive concrete is shown in Fig.18 [7]. The concrete specimens cured in pressurized water at high temperature (180 ℃ and 1 MPa for 6 hours) expands more than twice as much as ordinary autoclaved concrete. Furthermore, when the specimens are subjected to different environmental conditions, in water, sealed and dried, no volume change is observed in any environments in case of pressurized water curing. 6. Prediction model for autogenous shrinkage It is important to predict autogenous shrinkage strain precisely in order to control cracking and to predict long-term behaviors of high-strength concrete structures. The ultimate value and the development with time of autogenous shrinkage are dependent on water-cement ratio. On the basis of experimental data, JCI Technical Committee has proposed a prediction model for autogenous shrinkage of concrete[2].

εc(t)＝γεc0(w/b)β(t)×10-6 (9)

where,

For 0.2≦w/b≦0.5: εc0(w/b)＝3070exp{－7.2(w/b)} (10) For 0.5＜w/b: εc0(w/b)＝80 (11)

32

β(t)＝[1－exp{－a(t－t0)b｝] (12) εc(t) is autogenous shrinkage of concrete at age t γ is a coefficient to describe the effect of cement type (γ=1.0 for ordinary Portland cement) εc0(w/b) is the ultimate autogenous shrinkage

β(t) is a coefficient to describe the development of autogenous shrinkage with time w/b is water-binder ratio a and b are constants t is age in day t0 is initial setting time in day

If concrete temperature is not 20℃, t and t0 are modified with eq. (13)[8]

t, t0＝ ∑=

+

−n

i ii T/)t(T

.expt1 0273

40006513∆

∆ ･ (13)

where, it∆ is the number of days where a temperature T (℃) prevails

)t(T i∆ is the temperature during the time period it∆ , T0=1℃

This model consists of the ultimate value of autogenous shrinkage εc0 and the function to describe the development of autogenous shrinkage with time β(t), and the coefficient γ to describe the effect of cement and admixture. Effect of temperature on autogenous shrinkage is taken into account by using effective age which has been proposed by CEB-FIP[8]. This model is valid for concretes with water-cement ratio ranging from 0.20 to 0.6 and with normal volume concentration of aggregate, at an environmental temperature ranging from 20℃ to 60℃. The relation between observed and calculated values of autogenous shrinkage of concretes with normal Portland cement is shown in Fig.19. The calculated values have good agreement with the observed values.

7. Prediction of autogenous shrinkage stress The factors affecting autogenous shrinkage stress due to external restraint are the amount of autogenous shrinkage, elastic modulus and creep, which are basically the same as those affecting thermal stress and drying shrinkage stress. In this chapter, the applicability of step-by-step method[9] to calculation of autogenous shrinkage stress is investigated. The concept of stress analysis by the step-by-step method is shown in Fig.20. This method enables to estimate rapid development of stress and stress relaxation due to creep. Autogenous shrinkage stress was calculated on the assumption of linear strain distribution through the cross section. The equations for Young's modulus and creep coefficient of concrete which are applicable to the age before 1 day have been proposed in order to take

33

account of their rapid developments at early ages[2]. Autogenous shrinkage stress was measured and calculated by the step-by-step method for a reinforced concrete column (850x850x2200mm) with reinforcement ratio of 2.97%. Belite-rich cement and 10 % of silica fume were used and compressive strength at 28 days was 110N/mm2. Autogenous shrinkage measured with plain concrete with the same cross section as the RC column was approximately 600x10-6 at 3 days. Observed and calculated values of autogenous shrinkage stress are shown in Fig.21. It is proved that the step-by-step method based on the superposition principle accurately evaluates autogenous shrinkage stress due to reinforcement restraint, in which stress due to temperature distribution in a cross section is neglected References 1. C.G.Lyman, 'Shrinkage and internal stress' in 'Growth and Movement in Portland

Cement Concrete', (Oxford University Press, London, 1934) 25-45. 2. Japan Concrete Institute, 'Committee Report, Autogenous Shrinkage of Concrete',

edited by E. Tazawa, E & FN SPON (1999) 3-62. 3. D.W. Hobbs, 'Influence of aggregate restraint on the shrinkage of concrete', Journal of

ACI, Vol.71, No.9 (1974) 445-450. 4. S.Miyazawa, T. Kuroi and E. Tazawa, 'Influence of chemical composition and

particle size of cement on autogenous shrinkage', Second International Conference on Engineering Materials, JSCE and CSCE (2001) (to be published)

5. S.Miyazawa, T.Kuroi and H.Shimomura, 'Effect of fiber on autogenous shrinkage stress of high-strength cement mortar', The Sidney Diamond Symposium, The American Ceramic Society (1998) 179-190.

6. K.Kohno, T.Okamoto, Y.Ishikawa and A.Kodama, 'Effect of curing on shrinkage of concrete using artificial lightweight aggregate', Proceedings of the Japan Concrete Institute, Vol.22. No.2 (2000) 241-246.

7. E.Tazawa, K.Kawai and K.Miyaguchi, 'Expansive concrete curing in pressurized water at high temperature', Cement & Concrete Composites, 22 (2000) 121-126.

8. CEB-FIP model code (1990) 9. R. Sato, M. Xu, and Y. Yan, 'Stress of high-strength concrete due to autogenous

shrinkage combined with hydration heat of cement', ACI's International SP.172-44 (1997) 837-852.

34

Fig.5 Autogenous shrinkage of cement paste with different type of cement (W/C=0.30)

Fig.6 Relationship between calculated and observed autogenous shrinkage of cement paste (W/C=0.30)

500

1000

0

Obs

erve

d au

toge

nous

shri

nkag

e (×

10-6

)

Calculated autogenous shrinkage (× 10-6)

▲□

○

★

☆

△

◇

★★

★

□□

□

▲

▲▲◇

◇

◇

△△

△○

○

○

☆

☆

☆

W/C=0.30

Age: 7, 14, 28, 70 daysOriginal length :24 hours from casting

500 1000

500

1000

0

Obs

erve

d au

toge

nous

shri

nkag

e (×

10-6

)

Calculated autogenous shrinkage (× 10-6)

▲□

○

★

☆

△

◇

★★

★

□□

□

▲

▲▲◇

◇

◇

△△

△○

○

○

☆

☆

☆

W/C=0.30

▲□

○

★

☆

△

◇

★★

★

□□

□

▲

▲▲◇

◇

◇

△△

△○

○

○

☆

☆

☆

W/C=0.30

Age: 7, 14, 28, 70 daysOriginal length :24 hours from casting

500 1000

10001

2 4 100

-1000

2000

1000

10001

2 4 7 100

-1000

2000

1000

LOG

NB

A

MS

WN

H

0

0 1000

12 4

10100

2000

1000

10001

2 4 7 100

2000

1000 A

utog

enou

s shr

inka

ge (x

10-6

)

LOG

NB

A

Age (days)

MS

WN

H

0

0

Age (days)

35

Fig.7 Effect of blast furnace slag on autogenous shrinkage of cement paste (W/(C+BS)=0.40)

Fig.8 Effect of water-cement ratio on autogenous shrinkage of cement paste

0

500

1000

1500

2000

0 20 40 60 80 100

BS/(C +BS) (%)

Autogenous shrinkage (x10

-6)

3380cm 2/g

4060cm 2/g

8010cm 2/g

0

1000

2000

3000

4000

5000

Aut

ogen

ous s

hrin

kage

(×10

-6)

Age (day)

1 2

10

100 1000

：40-0-0：30-0-0：23-0-0.6：23-10-0.6：17-10-2.0

W/C-SF-SP(%)

36

Fig.9 Effect of water-cement ratio on autogenous shrinkage of concrete

Fig.10 Effect of volume concentration of aggregate on autogenous shrinkage

Fig.11 Effect of temperature on autogenous shrinkage of concrete

0

200

400

600

800

1000

0 20 40 60 80 100

Age (day)

N50-0

N40-0

N30-0

N20-0

N20-10(SF)

N17-10(SF)Autogenous shrinkage (x10-

6)

W/C-SF(%)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Volum e concentration of aggregate

εc/ε

p

Mortar(w/c=0.3, granite)Mortar(w/c=0.3, rhyolite)Concrete(w/c=0.3)Mortar(w/c=0.2, granite)SeriesParallelHobbs

Age: 28 days

-200

0

200

400

600

0 1 10 100

Effective age (days)

Autogenous shrinkage (×

10

-6)

C al.20℃40℃60℃

W /(C +BS)＝0.30BS/(C +BS)＝70%

BS: 8000cm2/g

37

Fig.12 Relationship between water-cement ratio and shrinkage of concrete (60%R.H.)

Fig.13 Effect of relative humidity on shrinkage of concrete (W/C=0.20)

Fig.14 Effect of W/C on length change of cement paste under water (40x40x160mm)

0

200

400

600

800

1000

1200

0.1 0.3 0.5 0.7

W ater-cem ent ratio

Strain (×

10

-6)

total shrinkage

autogenous shrinkage

drying shrinakge

400

-400

-800

Stra

in(×

10-6

)

1

2

7 28 70

Age (day)

30-0-0

23-0-0.6

17-20-2.0

0

W/C-SF-SP(%)

400

-400

-800

Stra

in(×

10-6

)

1

2

7 28 70

Age (day)

30-0-0

23-0-0.6

17-20-2.0

0

W/C-SF-SP(%)

Str

ain

（×

10

-6)

-1200

-1000

-800

-600

-400

-200

0 1 10 100 1000

Age （day）

Sealed

40%RH

60%RH

80%RH

90%RH

W/C=0.20

38

Fig.15 Effect of specimen size on length change of cement paste under water (W/C=0.30)

Fig.16 Effect of expansive admixture on autogenous shrinkage of cement paste (W/C=0.30)

Fig.17 Effect of water-repellent powder on autogenous shrinkage of cement paste (W/C=0.40)

-1200

-800

-400

0

1 10 100 1000

Age (days)

Strain (x10

-6)

0%5%7.5%10%30%

-1200

-800

-400

0

400

800

1 10 100 1000

Age (days)

Strain (x10

-6)

PlainE1E2E3

800

0

-400

400

1 2 7 28

20×20×160mm

40×40×160mm

100×100×400mm

Age (day)St

rain

(×

10-6

)

800

0

-400

400

1 2 7 28

20×20×160mm

40×40×160mm

100×100×400mm

Age (day)St

rain

(×

10-6

)

39

(a) autoclaved curing (b) in pressurized water at high temperature

Fig.18 Effect of curing method on shrinkage of expansive concrete (W/C=0.35)

Fig.19 Relationship between observed and calculated autogenous shrinkage of concrete

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

C alculated value（×10-6）

Measured value（

×10

-6）

O rdinary Portland cem entW /C＝0.2～0.5，20℃

40

Fig.20 Concept of stress analysis by step-by-step method

Fig.21 Autogenous shrinkage stress in a full-sized reinforced concrete column