Prediction Model for Autogenous Prediction Model for Autogenous Shrinkage of Concrete with Different Shrinkage of Concrete with Different

Type of Cement Type of Cement

Shingo MiyazawaShingo MiyazawaDepartment of Civil Engineering, Ashikaga Institute of Technology Department of Civil Engineering, Ashikaga Institute of Technology

Ashikaga, JapanAshikaga, Japan

Ei-ichi TazawaEi-ichi TazawaResearch and Development Initiative, Chuo UniversityResearch and Development Initiative, Chuo University

Tokyo, JapanTokyo, Japan

Autogenous shrinkage should be considered in order to calculate

thermal stress in massive concretelong term deflection in RC memberstime dependent loss of prestressing force

(JSCE,1998)

Prediction of autogenous shrinkage

εc(t) ＝ γ·εc0(w/c)·β(t) (×10-6) (JSCE, 2002)

Ultimate autogenous shrinkage εc0(w/c) ＝ 3070 exp{ － 7.2(w/c)} (0.2≦w/c ＜ 0.5)

80 (0.5≦w/c)

Effect of type of cement : γ=1.0 (OPC) γ ？ (other type of cement) Development of autogenous shrinkage β(t) ＝ 1 － exp{ － a(t － t0)b ｝

 

Prediction Model for autogenous shrinkage of concrete

？ ？

Experimental ProceduresExperimental Procedures

Materials

CementC3S

(%)

C2S

(%)

C3A

(%)

C4AF

(%)

Specific surface

area（ cm2

/g)

w/c

N 54 21 8 8 3280 0.18-0.65H 63 11 8 8 4420M 44 34 4 12 3240 0.22-0.50L 30 52 3 9 3350

• river sand• crushed stone (maximum size: 20mm) • polycarboxylic acid type superplasticizer (w/c 0.18 ～ 0.4)• air-entraining and water-reducing agent (w/c 0.5 ～ 0.65)

Measurement of autogenous shrinkage before demolding (JCI, 1996)

start of measurements : initial set

Measurement of autogenous shrinkage after demolding (JCI, 1996)

Contact gauge

300mm

Measurements: 1 day, 3 days, 7 days, 28 days, ……2 years

Curing: 20℃

Test results (1)Test results (1)

- Effect of type of cement on - Effect of type of cement on autogenous shrinkage -autogenous shrinkage -

Age days（ ）

-1000

-800

-600

-400

-200

00.1 1.0 10.0 100.0 1000.0

Str

ain

×10

（-6

）

N25H25M25L25

Age days（ ）

-1000

-800

-600

-400

-200

0

2000.1 1.0 10.0 100.0 1000.0

N40H40M40L40

Age days（ ）

-1000

-800

-600

-400

-200

0

2000.1 1.0 10.0 100.0 1000.0

N50H50M50L50

Age days（ ）

-1000

-800

-600

-400

-200

00.1 1.0 10.0 100.0 1000.0

Str

ain

×10

（-6

）

N22H22M22L22 w/c=0.22

w/c=0.25 w/c=0.5

w/c=0.4

1000

1 10 100

W/C = 0.3

1000

-2000

-1000

10001

10 100

W/C = 0.3

1000

-2000

-1000

(days)

LO

G

NB

A

MS

WN

H

0

0St

rain

（×

10-6）

Stra

in （

×10

-6）

(days)1000

1 10 100

W/C = 0.3

1000

-2000

-1000

10001

10 100

W/C = 0.3

1000

-2000

-1000

(days)

LO

G

NB

A

MS

WN

H

0

0St

rain

（×

10-6）

Stra

in （

×10

-6）

(days)

Autogenous shrinkage of cement paste with various types of cement　　　　　　　　　　　　　　　　　 (Tazawa & Miyazawa, 1992)　

Mineral compound (%) Cement

C3S C2S C3A C4AF CaSO4 N 49.4 23.9 8.8 9.4 3.40 H 48.4 31.2 2.0 12.2 2.98 M 64.6 9.7 8.8 8.5 4.93 S 58.0 18.5 1.9 13.7 3.91 W 67.2 11.2 11.6 0.6 4.25 O 56.2 20.7 1.8 14.0 3.74 L 27.8 56.3 2.4 7.6 3.74

500

1000

0

Obs

erve

d au

toge

nous

shr

inka

ge (

×10

-6)

Calculated autogenous shrinkage (×10-6)

▲

□

○

★

☆

△

◇

★★

★

□□

□

▲

▲

▲◇

◇

◇

△

△△

○

○

○

☆

☆

☆

W/C=0.30

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

500 1000

εp(t) ＝ A ･ αC3S(t) ･ (C3S%) ＋ B ･ αC2S(t) ･ (C2S%) ＋ C ･ αC3A(t) ･(C3A%)

＋ D ･ αC4AF(t) ･ (C4AF%) ＋ E ･ (Blaine) ＋ F (Tazawa

& Miyazawa, 1992) 　 αi(t) : degree of hydration of mineral compound (%)

(Blaine) : Blaine fineness of cement (cm/g2)A, B, C, D, E and F : constants

Autogenous shrinkage of cement paste at age t (×10-6)

N H M L

γ 1.0 1.2 0.85 0.4

γ ＝－ 0.0042 ･ (C3S%) － 0.0049 ･ (C2S%) ＋ 0.125 ･(C3A%)

　　 ＋ 0.093 ･ (C4AF%) ＋ 0.00015 ･ (Blaine) － 0.90 　

εc(t) ＝ γ·εc0·β(t) (JSCE, 2002)

-1200

-1000

-800

-600

-400

-200

00.10 0.30 0.50 0.70

水セメント比

×

10ひ

ずみ

（-6

）

実測値（シリーズＡ）実測値（シリーズＢ）実測値（シリーズＣ）提案式prEN式土木学会式土木学会式

-1200

-1000

-800

-600

-400

-200

00.10 0.30 0.50 0.70

水セメント比

×

10ひ

ずみ

（-6

）

実測値（シリーズＡ）実測値（シリーズＢ）実測値（シリーズＣ）提案式prEN式土木学会式土木学会式S

trai

n (×

10-6)

Water-cement ratio

N, 91days ○ obs. (Series A) ● obs. (Series B) △ obs. ― ― proposed model - - - pre EN model

水結合材比

-1400

-1200

-1000

-800

-600

-400

-200

00.1 0.3 0.5 0.7

×10

ひず

み（

-6）

H提案式prEN式

Str

ain

Water-cement ratio

● obs. (Series A) ― ― proposed model - - - pre EN model

H, 91days

Str

ain

(×10

-6)

水結合材比

-1400

-1200

-1000

-800

-600

-400

-200

00.1 0.3 0.5 0.7

×10

ひず

み（

-6）

M提案式prEN式

1.1 .水結合材比

-1400

-1200

-1000

-800

-600

-400

-200

00.1 0.3 0.5 0.7

×10

ひず

み（

-6）

M提案式prEN式

1.1 .Water-cement ratio

Str

ain

(×10

-6)

M, 91days

● obs. (Series A) ― ― proposed model - - - pre EN model

水結合材比

-1400

-1200

-1000

-800

-600

-400

-200

00.1 0.3 0.5 0.7

×10

ひず

み（

-6）

L提案式prEN式

Str

ain

(×10

-6)

Water-cement ratio

L, 91days

● obs. (Series A) ― ― proposed model - - - pre EN model

Test results (2)Test results (2)

- Development of autogenous - Development of autogenous shrinkage with time -shrinkage with time -

材齢（日）

-1400

-1200

-1000

-800

-600

-400

-200

0

2000.1 1 10 100

×10

ひず

み（

-6）

N17 N18 N20N22 N25 N30N40 N50 N65

w/c（％）

17

6540

30

22

20

25

Age (days)S

trai

n

Effect of w/c on autogenous shrinkage of concrete (OPC)

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 材齢 （日）

εa

/ε（ｔ

）a

91（）

24.0a 24.0a 68.0b 68.0b

Age (days)

β(t) ＝ 1 － exp ｛－ a （ t － to ） b ｝

w/c=0.40

ε c (t)

/εc (

91)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.10 0.30 0.50 0.70水結合材比

提案式 N

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.10 0.30 0.50 0.70水結合材比

提案式 N

a = 3.27exp{－ 6.83×(w/c)}a = 3.27exp{－ 6.83×(w/c)} b = 0.251exp{2.49×(w/c)}b = 0.251exp{2.49×(w/c)}

　 a 　 b

w/c w/c

● 　 obs.Cement: OPC

● 　 obs.Cement: OPC

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 材齢 （日）

εa

/ε（ｔ

）a

91（）

実測値

提案式

prEN式

w/c=0.18

obs.

proposed

prEN model

Age (days)

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 材齢 （日）

εa

/ε（ｔ

）a

91（）

実測値提案式prEN式土木学会式

w/c=0.30

obs.

proposed

prEN model

JSCE model

Age (days)

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 材齢 （日）

εa

/ε（ｔ

）a

91（）

実測値提案式prEN式土木学会式

obs.

proposed

prEN model

JSCE model

w/c=0.50

Age (days)

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

Age (days)

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

Age (days)

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 材齢 （日）

εa

/ε（ｔ

）a

91（）

実測値提案式prEN式土木学会式

obs.

proposed

prEN model

JSCE model

w/c=0.65

Age (days)

εc(t) ＝ γ·εc0·β(t) (×10-6) (JSCE, 2002)

Ultimate autogenous shrinkage εc0 ＝ 3070exp{ － 7.2(w/c)} (0.2≦w/c ＜ 0.5)

80 (0.5≦w/c)

Effect of type of cement : γ=1.0 (OPC)

Development of autogenous shrinkage β(t) ＝ [1 － exp{ － a(t － t0)b ｝ ]

 

N H M L

γ 1.0 1.2 0.85 0.4

a = 3.27exp{－ 6.83×(w/c)}

b = 0.251exp{2.49×(w/c)}

(Measured by 15 organizations)

-1000

-800

-600

-400

-200

0-1000-800-600-400-2000

H M L BB

Predicted autogenous shrinkage (×10-6)O

bser

ved

auto

geno

us s

hrin

kage

(×

10-6)

LPC NPC MPC LPC

-1000

-800

-600

-400

-200

0-1000-800-600-400-2000

×10ひずみ（ -6 [ ]） 予測値

N[ 28 ]材齢 日

Predicted autogenous shrinkage (×10-6)

Cement : OPC

Age : 28 days

Obs

erve

d au

toge

nous

shr

inka

ge (

×10

-6)

Relation between predicted and observed autogenous shrinkage

Conclusions

1. Autogenous shrinkage of concrete is strongly dependent on type of cement. The coefficient γ in JSCE model, which describes the influence of cement type, has been determined on the basis of mineral composition of cement.

2. Development of autogenous shrinkage with time is dependent on w/c. The coefficients a and b in JSCE model, which describe the development of autogenous shrinkage, have been proposed as functions of w/c.

3. Autogenous shrinkage calculated form the proposed model was compared with the observed values, and it is proved that the model has adequate accuracy for practical purposes.

•予備

(Measured by 15 organizations)

-1000

-800

-600

-400

-200

0-1000-800-600-400-2000

×10ひずみ（ -6 [ ]） 予測値

N[ 28 ]材齢 日

Predicted autogenous shrinkage (×10-6)

Cement : OPC

Age : 28 days

Obs

erve

d au

toge

nous

shr

inka

ge (

×10

-6)

(Measured by 15 organizations)

-1000

-800

-600

-400

-200

0-1000-800-600-400-2000

H M L BB

Predicted autogenous shrinkage (×10-6)

Obs

erve

d au

toge

nous

shr

inka

ge (

×10

-6)

LPC NPC MPC LPC

1000

1 10 100

W/C = 0.3

1000

-2000

-1000

10001

10 100

W/C = 0.3

1000

-2000

-1000

(days)

LO

G

NB

A

MS

WN

H

0

0

Str

ain

（×10

-6）

Str

ain

（×10

-6）

(days)1000

1 10 100

W/C = 0.3

1000

-2000

-1000

10001

10 100

W/C = 0.3

1000

-2000

-1000

(days)

LO

G

NB

A

MS

WN

H

0

0

Str

ain

（×10

-6）

Str

ain

（×10

-6）

(days)

Figure 1 – Influence of cement type on autogenous shrinkage of cement paste.

Mineral compound (%) Cement

C3S C2S C3A C4AF CaSO4 N 49.4 23.9 8.8 9.4 3.40 H 48.4 31.2 2.0 12.2 2.98 M 64.6 9.7 8.8 8.5 4.93 S 58.0 18.5 1.9 13.7 3.91 W 67.2 11.2 11.6 0.6 4.25 O 56.2 20.7 1.8 14.0 3.74 L 27.8 56.3 2.4 7.6 3.74

500

1000

0

Cement

○

△□

◇☆▲★

NHM

S

WOL

Mineral compound (%)

C3S C2S C3A C4AF CaSO4

49.4

48.464.6

58.067.2

56.2

27.8

23.9

31.29.7

18.511.2

20.756.3

8.8

2.08.8

1.9

11.6

1.82.4

9.412.2

8.5

13.7

0.614.0

7.6

3.4

2.984.93

3.91

4.25

3.743.74

Ob

serv

ed a

uto

gen

ous

shri

nk

age

(×

10-6)

Calculated autogenous shrinkage (×10-6)

▲

□

○

★

☆

△

◇

★★

★

□

□

□

▲

▲

▲◇

◇

◇

△

△△

○

○

○

☆

☆

☆

W/C=0.30

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

500 1000

w/c a b0.20 1.2 0.40.23 1.5 0.40.30 0.6 0.50.40 0.1 0.7

0.5-0.6

0.03 0.8

βas(t)＝ 1 ｰ exp｛ｰ a（ｔｰｔo） b｝βas(t)＝ 1 ｰ exp｛ｰ a（ｔｰｔo） b｝