prediction model for autogenous shrinkage of concrete with different type of cement shingo miyazawa...
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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}