HPC of high mechanical strength and good workability can be made by using Portland cement blended with Fly Ash and Slag (fineness GGBS). The two supplementary binders are important to ensure the high performance of concrete.
The influence of the water-cement ratio on the drying shrinkage is slightly small, but the difference still recognizes. Meanwhile, the creep in concrete presents a significant influence of the water-cement ratio.
The effects of fly ash replacement in the early age of hydration are quite negligible. It even can slightly reduce the compressive strength of HPC. However, at the later age, fly ash has some effects to increase compressive strength of HPC because of the continuing hydration of fly ash.
The fly ash replacement in HPC does not significant affect to decrease the shrinkage strain.
HPC with high-volume fly ash even can increase the shrinkage strain. In the other hand, fly ash in HPC with high-volume has a significant affect to creep. However, it shows a negative effect which increases the creep of HPC.
Almost the models to predict the shrinkage and creep of concrete applying for this thesis figure out not really exactly the prediction. This issue can be explained by the different between aggregate strength of Taiwan and other places. This thesis has suggested a modified CCL2001 model with the changing some coefficients in the prediction formulas by trial and error method. The modifications of CCL model are shown as following:
62
( ) 40.0802 172.9723 248.2666 118.64
c
( ) 40.0802 172.9723 248.2666 118.64
c
However, the function of f(x) is very sensitive to the low value of Ec(28)/Ec(7) when this ratio values around 1.1 to 1.2. This is the limitation of this model because the changing of the ratio Ec(28)/Ec(7) around value of 1.1 to 1.2 could lead to great changing of shrinkage prediction.
63
REFERENCES
[1] Henry, G. R., “ACI’s defines High-Performance Concrete,” ACI Technical Activities Committee, 1999.
[2] Neville, A. M., “Properties of Concrete,” Fourth Edition, Longman Group Limited, England, 1995, 844 pp.
[3] Büyüköztürk, O. and L. Denvid, “High Performance Concrete: Fundamentals and Application,” Massachusetts Institute of Technology, 2005.
[4] 林宜賢，「高性能混凝土配比設計研究」，國立成功大學土木工程研究所碩士論 文，民國九十二年。
[5] Mehta, P. and P. J.M. Monteiro, “Concrete Structure, Properties and Materials,”
Prentice- Hall Inc., Englewood-Cliffs, N. J., 1986.
[6] Aiticin, P. C. and A. Neville, “High Performance Concrete Demystified,” Concrete International, Vol. 15, No. 1, PP. 21-26, 1989.
[7] 李修齊(詹穎雯指導)，「高強度混凝土水中磨耗性質之機理探討」，碩士論文，
國立台灣大學土木工程研究所，民國八十六年。
[8] 黃兆龍、洪盟峰，「高性能混凝土」，營建知訊，129期，PP. 5-17，民國八十 二年。
[9] Beshrb, H., A. A. Almusallama, and M. Maslehuddinb, “Effect of coarse aggregate quality on the mechanical properties of high strength concrete,” Construction and Building Materials, PP. 97-103, 2003.
[10] Ozturan, T. and C. Cecen, “Effect of coarse aggregate type on mechanical properties of concretes with different strengths,” Cement and Concrete Research, Vol. 27, PP. 165-170, 1997.
64
[11] Wu, Ke-Ru, B. Chen, W. Yao, and D. Zhang, “Effect of coarse aggregate type on mechanical properties of high-performance concrete,” Cement and Concrete Research, Vol.
31, 2001.
[12] British Standard Method, BS 812.
[13] Amirkhanian, et. al., “The Effect of Igneous Aggregate Source with Various Los Angeles Abrasion Test Values on the Strength of Concrete Mixtures,” Cement Concrete and Aggregates, CCAGDP. , Vol. 14, No. 2, PP. 86-92, Winter, 1992.
[14]「高強度混凝土設計及施工準則初步研究」，內政部建築研究籌備處專題研究計 畫成果報告，PP. 8，民國七十九年。
[15] Mehta, P. K., “Pozzolanic and Cementitious by Products as Mineral Admixtures for Concrete-A Critical Review,” ACI SP-79, PP. 1-46, 1983.
[16] ACI Committee 226, “Silica Fume in Concrete,” ACI Material Journal, 1987.
[17] Takeshi, Y., K. Tsutomu, N. Masateru, and T. Takao, “Pozzolanic reactivity of fly ash - API method and K-value,” Elsevier Ltd., 2006.
[17] Li, J. and P. Tian, “Effect of Slag and Silica Fume on Mechanical Properties of High-Strength Concrete,” Building Materials and Concrete Research Institute, 1997.
[18] ACI Committee 233R, “Slag Cement in Concrete and Mortar,” ACI, 2003.
[19] Steven, H. K., K. Beatrix, and C. P. William, “Design and Control of Concrete Mixtures,” Portland Cement Association, 2003, pp. 307-308.
[20] Malhotra, V. M., A. A. Ramezanianpour, “Fly Ash in Concrete,” CANMET, 1994.
[21] Hau, C., “Analyses and Models of the Autogenous Shrinkage of Hardening Cement Paste, Cem. Con. Res. 25, 1457-1468.
[22] Bazant, Z.P. and L. J. Najjar, “Material Structures,” 5,3-20 (1972)
65
[23] Glanville, W. H. and F. G. Thomas, “Further Investigations on the Creep or Flow of Concrete under Load,” Building Research Tech. No.21.
[24] Freyssinet, E., “Deformation of Concrete,” Magazine of Concrete Research, V.3. No.8, 1951, pp.49-56.
[25] Acker, P., “Superficial shrinkage of Concrete,” Lisbon, pp. 157-162
[26] Tazawa, E. and S. Miyazawa, “Experimental Study on Mechanism of Autogenous Shrinkage of Concrete,” Cem. Con. Res. 25, 1633-1638.
[27] Ouchi, M., M. Hibino, K. Ozawa, and H. Okamura, “A Rational Mix-Design for Mortar in Self-Compacting Concrete,” Proceeding of the Sixth East-Asia-Pacific Conference on Structural Engineering & Construction, Taipei, Taiwan, 1998, pp. 1307-1312.
[28] Ulm, F., “Creep and shrinkage couplings,” Cem. Con. Age. 26, 1687-1692.
[29] Bazant, Z.P. and J. C. Chern, “Strain softening with creep and exponential algorithm,”
J. Eng. Mech. ASCE 111 (EM5), 1985, pp. 391-451.
[30] CEB-FIP Model Code 1990, Final Draft, CEB Bulletin d’Information, No. 203, PP. 2.
27-2. 38, PP. 2. 43-2. 49, 1991.
[31] Gardner N. J., and J. W., Zhao, “Proposed Code Provisions for Shrinkage and Creep,”
Canadian Concrete Conference, 1993.
[32] Bazant, Z. P. and S., Baweja “Justification and Refinements of Model B3 for Concrete Creep and Shrinkage-2. Updating and Theoretical Basis,” Materials and Structures, Vol. 28, PP. 488-495, 1995.
[33] Bazant, Z. P. and S., Baweja, “Justification and Refinements of Model B3 for Concrete Creep and Shrinkage-1. Statistics and Sensitivity,” Materials and Structures, Vol. 28, PP.
415-430, 1995.
[34] Bazant, Z. P. and W. P., Murphy, “Creep and Shrinkage Prediction Model for Analysis and Design of Concrete Structures-Model B3,” Materials and Structures, Vol. 28, PP. 357-365, 1995.
66
[35] Carlos, V. and G. Cristian, “Modeling Portland Blast-Furnace Slag Cement High-Performance Concrete,” ACI Material Journal, September-October, 2004.
[36] American Association of State Highway and Transportation Officials (AASHTO.),
“AASHTO LRFD Bridge Design Specifications. 3rd ed.”, 2004.
[37] 陸景文，「台灣地區混凝土橋梁溫度、彈性應變、潛變及乾縮特性之整合研究
」，博士論文，國立台灣大學土木工程研究所，民國九十年7月。
[38] Lin, Y. K., “A Study on Creep and Shrinkage of HSC Containing High Fineness GGBF Slag,” Master Thesis, National Taiwan University – Civil Engineering Department, 2010.
[39] Hsu, C. A., “The Ultimate Loading Test and Analysis of SCC Prestressed Girder,”
Master Thesis, National Taiwan University – Civil Engineering Department, 2008.
[40] Chen, K. C., “Self-Compacting Concrete and Prestressed Structures Behavior,” Master Thesis, National Taiwan University – Civil Engineering Department, 2004.
[41] Chen, C., “A Study on Mix Proportion Design and Mechanical Behavior of High-Volume Fly Ash Concrete,” Master Thesis, National Taiwan University – Civil Engineering Department, 2010.
[42] Davis, R.E., R. W. Carlson, J. W. Kelly, and H. E. Davis, “Properties of Cements and Concretes Containing Fly Ash,” Journal of the American Concrete Institute, 1937, 33: 577-612.
[43] Munday, J.G.L., L. T. Ong, L. B. Wong, and R. K. Dhir, “Load-Independent Movement in OPC/PFA Concrete,” In Proceedings, International Symposium on the Use of PFA in Concrete, University of Leeds, UK, Apr. 14-16, 1982. pp. 243-261.
[44] Yuan, R.L. and J. E. Cook, “Study of a Class C Fly Ash Concrete,” In Proceeding, 1st International Conference on the Use of Fly Ash, Silica Fume, Slag, and Other Mineral By-products in Concrete, Montebello, PQ, July 31st – Aug. 5th, 1983. Edited by V.M. Malhotra.
American Concrete Institute, Detroit, MI, Special Publication SP-79, pp. 307-319.
67
TABLES AND FIGURES
Table 2-1 Properties of High-Strength Concrete Aggregate requirements.
Properties Affect the reasons Request method
Grading Fine aggregate
68
Table 2-2 Chemical compositions of Pozzolan materials
Chemical name General Cement
Table 3-1 Mix proportion of High-Performance Concrete [38~41]
No Proportion Cement (kg/m3)
69
Table 3-2 Chemical composition of Taiwan Cement type I [38]
Chemical composition Test result
Table 3- 3 Physical properties of Taiwan Cement type I [38]
Test results Physical properties Inspection
Results
Specification values %
I IA
Fineness, specific surface area
m2/kg 352 ≧280 ≧280
Maximum % CNS1163(1986) 7.4
≦12 ≦22
Minimum % - ≧16
Note
70
Table 3-4 Physical and chemical properties of the blast furnace slag [38]
Test items The
results Specifications Test method (CNS)
Table 3-5 Loss on ignition of Fly Ash [39]
Categories LOI(%) Water content (%)
Low-calcium Fly Ash
1 4.461 0.219
2 4.918 0.138
5 4.976 0.193
High-calcium Fly Ash H 7.417 0.619
71
Table 3-6 Chemical compositions and physical properties of Fly ash [39]
Test items
14. Strength activity cement (7day) % of control Min. 75 86.78 84.88 Strength activity cement (7day) % of control Min. 75 97.84 86.03
15. Water Demand Control % Max. 105 96.69 99.17
16. Health degrees (hot swelling test)% Max. 0.80 0.056 0.053 Table 3-7 Physical properties and sieve analysis of Tachia coarse aggregate [38]
Coarse aggregate (Tachia) Sieve size Sieve accumulation
Sieving percentage
Specific gravity = 2.625，L.A. = 19.26%
Saturation water absorption of drying surface aggregate = 0.9%
72
Table 3-8 Physical properties and sieve analysis of East Asia fine aggregate [38]
Fine aggregate Sieve size Sieve accumulation
Sieving percentage Gram Percentage
No. 4 22.13 4.4354 95.5646
No. 8 32.85 11.0194 88.9806
No. 16 67.81 24.6102 75.3898
No. 30 139.06 52.4813 47.5187
No. 50 181.97 88.9526 11.0474
No. 100 47.36 98.4447 1.5553
No. 200 4.35 99.3166 0.68345
Bottom 3.41 100 0
F.M. = 2.8，Specific gravity = 2.47
Saturation water absorption of drying surface aggregate = 2.385%
Table 3-9 Properties of super-plasticizer. [38]
Test Items Specifications
Solid content 14%±5
Gravity 1.07±0. 05
pH 4.5±2
73
Table 3-10 Fresh properties of concrete. [38~41]
No. Mix proportion Flow test (cm) Slump test (cm) Air content (%)
1 W37S20F20 60-70 25 1.5
2 W40S20F20 60-70 25 1.5
3 W40S25F25 60-70 25 1.5
4 W44S18F8 60-70 25 1.5
5 W37S30F16(A) 60-70 25 1.5
6 W37S30F16(B) 60-70 25 1.5
7 W42F0 64.5 25.5 4.2
8 W42F40 50 25 3.2
9 W37F50 62.3 27 3.9
10 W35F40 62.5 27 3.9
11 W31F50 68.5 26 3.8
Table 3-11 Hardening properties of concrete [38~41]
7days 14days 28days 56days 90days
Proportion f’c E(103) f’c E(103) f’c E(103) f’c E(103) f’c E(103) W37S20F20 34.5 23.15 40.8 25.87 47.7 26.91 49.2 29.24 - - W40S20F20 31.0 22.8 37.6 23.86 43.4 26.02 47.1 28.02 - -
W40S25F25 25.8 18.5 31.3 19.33 35.3 21.04 - - - -
W44S18F8 27.65 17.55 32.17 19.71 37.66 22.26 43.84 24.32 47.37 27.16 W37S30F16(A) 26.09 15.49 34.23 17.85 41.19 21.18 47.66 22.85 52.17 25.60 W37S30F16(B) 20.99 13.14 28.73 15.98 39.23 19.71 - - - -
W42F0 30.27 25.39 - - 47.35 25.83 51.49 31.06 53.03 32.57
W42F40 27.46 23.26 - - 44.62 31.14 50.15 31.60 53.24 32.93
W37F50 33.41 26.21 - - 49.38 30.93 53.01 33.68 54.12 33.65
W35F40 33.50 30.25 - - 50.00 30.24 54.61 35.68 59.00 36.05
W31F50 31.29 25.39 - - 51.08 25.71 58.46 29.40 63.79 33.44
(Unit: MPa)
74
Table 4-1 Elastic modulus of concrete and prediction according to CCL model and ACI363 [38]
75
Table 4-2 Elastic modulus of High-Volume fly ash concrete and prediction according to CCL model and ACI363 [38]
Mixture Age
76
Table 4-3 Drying shrinkage strain of OPC and SCC (10-6) [39]
t-t' OPC
W44S18F8
SCC W37S30F16(A) (day) t'=14d t'=28d t'=14d t'=28d
0.001 1.3 0.0 4.6 0.0
0.008 1.3 0.0 4.6 0.0
0.04 2.6 2.0 19.0 2.0
0.06 4.0 5.9 28.0 6.9
0.1 9.9 6.9 31.0 8.9
0.16 11.0 12.0 29.0 11.0
0.25 21.0 13.0 33.0 9.8
0.54 36.0 17.0 49.0 12.0
1 66.0 33.0 81.0 29.0
1.5 90.0 36.0 95.0 36.0
2.5 147.0 63.0 133.0 59.0
4 188.0 100.0 184.0 79.0
6 235.0 148.0 240.0 117.0
10 332.0 217.0 310.0 167.0
16 477.0 305.0 368.0 227.0
25 539.0 390.0 441.0 288.0
33 561.0 448.0 490.0 338.0
56 668.0 560.0 596.0 458.0
90 738.0 614.0 678.0 516.0
365 1002.0 809.0 934.0 783.0
1114 1127.0 905.0 1120.0 955.0
77
Table 4-4 Total creep test [10-6/(kgf/cm2)] [39]
t-t' OPC
W44S18F8
SCC W37S30F16(A) (day) t'=14d t'=28d t'=14d t'=28d
0.001 5.5 4.4 5.9 5.0
0.008 5.6 4.4 6.0 5.0
0.04 5.8 4.4 6.0 5.1
0.06 5.9 4.4 6.1 5.2
0.1 5.9 4.4 6.3 5.1
0.16 6.2 4.5 6.4 5.2
0.25 6.4 4.6 6.7 5.4
0.54 6.8 4.8 7.1 5.7
1 7.1 5.2 7.6 6.1
1.5 7.4 5.6 8.0 6.5
2.5 7.8 5.8 8.4 6.7
4 8.2 6.2 8.9 7.3
6 8.8 6.8 9.5 7.8
10 9.6 7.2 10.3 8.3
16 10.7 7.7 10.8 8.8
25 11.6 8.4 11.5 9.4
33 12.3 8.8 11.8 9.9
56 13.5 9.7 12.4 10.3
90 14.5 10.4 12.9 10.9
365 19.2 13.9 16.8 13.9
1114 21.7 15.9 18.8 16.5
78
Table 4-5 Measured drying shrinkage strain of SCC [38]
t-t’(days)
Drying shrinkage strain (10-6) t’=14 day
W37S20F20 W40S20F20 W40S25F25
0.001 0 0 0
0.05 5 5 0
0.1 8 9 8
0.15 15 15.5 15
1 22 18.5 61
2 31 40 83
3 55 82.5 91
4 75.5 93.5 99
5 90 106.5 120
6 92.5 108.5 127
7 101 118.5 141.5
10 159 187 178
16 192 199.5 231.5
25 229.5 256 265
33 253 267.5 276.5
56 287 312
70 304 330
90
79
Table 4-6 Measured total creep strain of SCC [38]
t-t’(days)
Total creep strain (10-6/MPa) t’=14 day
W37S20F20 W40S20F20 W40S25F25
0.001 37.19 41.17 48.23
Table 4-7 Coefficients of shrinkage and creep prediction formulas [38]
Prediction formula Shrinkage Creep
CEB-FIP 1990 βsc=5 α=0
FIB2000 As literature
CCL K=1
80
Table 4- 8 Relationship between f(x) and hardening properties of concrete
Time (days) 7 28
Ec(28)/Ec(7) f(x) Trial
f(x)
Proportion f’c E(103) f’c E(103)
W37S20F20 34.50 23.15 47.70 26.91 1.162419 0.820235943 1.0
W40S20F20 31.00 22.80 43.40 26.02 1.141228 1.017880952 1.0
W40S25F25 25.80 18.50 35.30 21.04 1.137297 1.058004695 1.0
W44S18F8 27.65 17.55 37.66 22.26 1.268376 0.233527084 0.15
W37S30F16(A) 26.09 15.49 41.19 21.18 1.367334 0.146190261 0.15
W37S30F16(B) 20.99 13.14 39.23 19.71 1.5 0.1571 0.15
81
Figure 2-1 28 Days compressive strength and water-cement ratio diagram [4]
Figure 2-2 Property-strength relation in solids of portland cement mortars with different mix proportions [5]
82
Figure 2-3 Composition of fresh and hardened cement paste at maximum hydration at various w/c values. [6]
Figure 2-4 Coarse aggregate type and Compressive strength diagram [8]
83
Figure 2-5 Relationship between Strength and Aggregate types [10]
Figure 2-6 Relationship between compressive strength and compressive strength of aggregate at different water-cement ratio [11]
84
Figure 2-7 Effect of silica fume on strength of concrete (after Malhotra and Carette 1983)
Figure 2-8 Phase diagram indicating composition of portland cement and blast-furnace slag in the system CaOSiO2-Al2O3 (based on Lea [1971] and Bakker [1983]). [18]
85
Figure 2-9 Diagrammatic model of the types of water associated with the calcium silicate hydrate. [5]
Figure 4-1 Relationship between water-cement ratio and compressive strength of concrete (40% Fly ash replacement)
20 30 40 50 60 70
0 20 40 60 80 100
Compressive strength (MPa)
Time (days) W35F40
W42F40
86
Figure 4-2 Relationship between water-cement ratio and compressive strength of concrete (50% Fly ash replacement)
Figure 4-3 Relationship between water-cement ratio and compressive strength of concrete (SCC)
20 30 40 50 60 70
0 20 40 60 80 100
Compressive strength (MPa)
Time (days) W31F50
W37F50
20 30 40 50 60
0 20 40 60
Compressive strength (MPa)
Time (days) W37S20F20 W40S20F20
87
Figure 4-4 Compressive strength development of concretes containing fly ash [20]
Figure 4-5 Relationship between fly ash replacement and compressive strength of HPC (w/c: 0.42)
20 30 40 50 60
0 20 40 60 80 100
Compressive strength (MPa)
Time (days) W42F0
W42F40
88
Figure 4-6 Typical stress-strain behaviors of cement paste, aggregate, and concrete. [2]
Figure 4-7 Relationship between Elastic modulus and compressive strength of High-Strength Concrete
y = 3.4753x + 6.6945 R² = 0.5745
20 25 30 35 40
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
Elasticity of Modulus (GPa)
Experiment
(MPa)
89
Figure 4-8 Relationship between Elastic modulus and compressive strength of High-Strength Concrete and comparison with ACI363 and CCL model
Figure 4-9 Relationship between Elastic modulus and Compressive strength of Self-Compacting Concrete and comparison with ACI363 and CCL model
y = 3.4753x + 6.6945
Elasticity of Modulus (GPa)
Experiment ACI363 CCL
(MPa)
90
Figure 4-10 Drying shrinkage strain of OPC compare with SCC (exposure at 14d)
Figure 4-11 Drying shrinkage strain of OPC compare with SCC (exposure at 28d)
0
91
Figure 4-12 Creep test comparison between OPC and SCC (loading at 14d)
Figure 4-13 Creep test comparison between OPC and SCC (loading at 28d)
0 5 10 15 20 25
0.001 0.1 10 1000
Creep 10-6/(kgf/cm2)
Time (days) OPC t'=14d
SCC t'=14d
0 2 4 6 8 10 12 14 16 18
0.001 0.1 10 1000
Creep 10-6/(kgf/cm2)
Time (days) OPC t'=28d
SCC t'=28d
92
Figure 4-14 Effect of w/c ratio on shrinkage or creep [5]
Figure 4-15 Relationship between w/c ratio and shrinkage strain of HPC
0 50 100 150 200 250 300 350
0.001 0.01 0.1 1 10 100
Shrinkage strain (10-6)
Log time after exposure (days) W37S20F20
W40S20F20
93
Figure 4-16 Relationship between w/c ratio and creep of HPC
Figure 4-17 Drying shrinkage strain of HPC (14days)
30 40 50 60 70 80
0.001 0.01 0.1 1 10 100
Creep (10-6/MPa)
Log time since loading (days) W37S20F20
W40S20F20
0 50 100 150 200 250 300 350
0.001 0.01 0.1 1 10 100
Shrinkage strain (10-6)
Log time after exposure (days) W40S20F20
W40S25F25 W37S20F20
94
Figure 4-18 Drying shrinkage of concretes incorporating high-calcium fly ash. [20]
Figure 4-19 Drying shrinkage of concretes versus equivalent cement content. [43]
Figure 4-20 - Creep of fly ash concrete. [44]
95
Figure 4-21 Relationship between fly ash replacement and creep property of concrete
Figure 4- 22 Comparison Elastic modulus of concrete at 28days
35 40 45 50 55 60 65 70 75 80
0.001 0.01 0.1 1 10 100
Creep (10-6/MPa)
Log time since loading (days) W40S20F20
W40S25F25
26.91
26.02
21.04 22.26
21.18
19.71
W37S20F20 W40S20F20 W40S25F25
W44S18F8 W37S30F16(A) W37S30F16(B)
96
Figure 4-23 CEB-FIP90 model vs. shrinkage strain test
Figure 4-24 CEB-FIP90 model vs. shrinkage strain test
0
Log time after exposure (days) W37S20F20
Log time after exposure (days) W44S18F8
97
Figure 4-25 GL2000 model vs. shrinkage strain test
Figure 4-26 GL2000 model vs. shrinkage strain test
0
Log time after exposure (days) W37S20F20
Log time after exposure (days) W44S18F8
98
Figure 4-27 B3 model vs. shrinkage strain test
Figure 4-28 B3 model vs. shrinkage strain test
0
Log time after exposure (days) W37S20F20
Log time after exposure (days) W44S18F8
99
Figure 4-29 CCL model vs. shrinkage strain test
Figure 4-30 CCL model vs. shrinkage strain test
0
Log time after exposure (days) W37S20F20
Log time after exposure (days) W44S18F8
100
Figure 4-31 CEB-FIP model vs. Creep test
Figure 4-32 CEB-FIP model vs. Creep test
30
Log time since loading (days) W37S20F20
Log time since loading (days) W44S18F8
101
Figure 4-33 GL2000 model vs. Creep test
Figure 4-34 GL2000 model vs. Creep test
30
Log time since loading (days) W37S20F20
Log time since loading (days) W44S18F8
102
Figure 4-35 B3 model vs. Creep test
Figure 4-36 B3 model vs. Creep test
30
Log time since loading (days) W37S20F20
Log day since loading (days) W44S18F8
103
Figure 4-37 CCL model vs. Creep test
Figure 4-38 CCL model vs. Creep test
30
Log time since loading (days) W37S20F20
Log time since loading (days) W44S18F8
104
Figure 4-39 Original CCL2001 model prediction for shrinkage strain of W37S20F20
Figure 4-40 Original CCL2001 model prediction for shrinkage strain of W40S20F20
0 100 200 300 400 500 600 700 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W37S20F20
CCL model(Original)
0 100 200 300 400 500 600
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W40S20F20
CCL model(Original)
105
Figure 4-41 Original CCL2001 model prediction for shrinkage strain of W40S25F25
Figure 4-42 Original CCL2001 model prediction for shrinkage strain of W44S18F8
0 100 200 300 400 500 600
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W40S25F25
CCL model(Original)
0 200 400 600 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W44S18F8
CCL model(Original)
106
Figure 4-43 Original CCL2001 model prediction for shrinkage strain of W37S30F16(A)
Figure 4-44 Original CCL2001 model prediction for shrinkage strain of W37S30F16(B)
0 200 400 600 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W37S30F16(A)
CCL model(Original)
0 200 400 600 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W37S30F16(B)
CCL model(Original)
107
Figure 4-45 Relationship between f(x) and Ec(28)/Ec(7).
Figure 4-46 Finding function to show the relationship between f(x) and Ec(28)/Ec(7) 0
0.2 0.4 0.6 0.8 1 1.2
1.1 1.2 1.3 1.4 1.5 1.6
f(x)
x=Ec(28)/Ec(7)
Ec(28)/Ec(7)
y = -40.0802x3 + 172.9723x2 - 248.2666x + 118.6400 R² = 0.9631
0 0.2 0.4 0.6 0.8 1 1.2 1.4
1.1 1.2 1.3 1.4 1.5 1.6
y = f(Ec(28)/Ec(7))
x = Ec(28)/Ec(7)
Ec(28)/Ec(7)
108
Figure 4-47 Modified CCL2001 model prediction for shrinkage strain of W37S20F20
Figure 4-48 Modified CCL2001 model prediction for shrinkage strain of W40S20F20
0 100 200 300 400 500 600
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W37S20F20
CCL model(Original) CCL model(modified)
0 100 200 300 400 500 600
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W40S20F20
CCL model(Original) CCL model(modified)
109
Figure 4-49 Modified CCL2001 model prediction for shrinkage strain of W40S25F25
Figure 4-50 Modified CCL2001 model prediction for shrinkage strain of W44S18F8
0 100 200 300 400 500 600
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W40S25F25
CCL model(Original) CCL model(modified)
0 200 400 600 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W44S18F8
CCL model(Original) CCL model(Modified)
110
Figure 4-51 Modified CCL2001 model prediction for shrinkage strain of W37S30F16(A)
Figure 4-52 Modified CCL2001 model prediction for shrinkage strain of W37S30F16(B)
0 200 400 600 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W37S30F16(A)
CCL model(Original) CCL model(Modified)
0 200 400 600 800
0.001 0.01 0.1 1 10 100
Drying shrinkage (10-6)
Log time after exposure (days) W37S30F16(B)
CCL model(Original) CCL model(Modified)
111
Figure 4-53 Comparison between Modified CCL model prediction and Measured Shrinkage
Figure 4-54 Original CCL2001 model prediction for creep of W37S20F20
y = 0.9026x + 27.298 R² = 0.9362
0 100 200 300 400 500 600
0 100 200 300 400 500 600
Predicted Drying Shrinkage (10-6)
Measured Drying Shrinkage (10-6) Test data
20 40 60 80 100 120
0.001 0.01 0.1 1 10 100
Creep (10-6/Mpa)
Log time since loading (days) W37S20F20
CCL model (original)
112
Figure 4-55 Original CCL2001 model prediction for creep of W40S20F20
Figure 4-56 Original CCL2001 model prediction for creep of W40S25F25
20 40 60 80 100 120 140
0.001 0.01 0.1 1 10 100
Creep (10-6/Mpa)
Log time since loading (days) W40S20F20
CCL model (original)
40 60 80 100 120 140 160
0.001 0.01 0.1 1 10 100
Creep (10-6/Mpa)
Log time since loading (days) W40S25F25
CCL model (original)
113
Figure 4-57 Original CCL2001 model prediction for creep of W44S18F8
Figure 4-58 Original CCL2001 model prediction for creep of W37S30F16(A)
30 50 70 90 110 130 150
0.001 0.01 0.1 1 10 100
Creep (10-6/MPa)
Log time since loading (days) W44S18F8
CCL model (original)
30 50 70 90 110 130 150
0.001 0.01 0.1 1 10 100
Total Creep (10-6/MPa)
Log time since loading (days) W37S30F16(A)
CCL model (original)
114
Figure 4-59 Original CCL2001 model prediction for creep of W37S30F16(B)
Figure 4-60 - Modified CCL2001 model prediction for Creep of W37S20F20
30 50 70 90 110 130 150
0.001 0.01 0.1 1 10 100
Total Creep (10-6/MPa)
Log time since loading (days) W37S30F16(B)
CCL model (original)
20 40 60 80 100 120
0.001 0.01 0.1 1 10 100
Creep (10-6/Mpa)
Log time since loading (days) W37S20F20
CCL model (original) CCL model (modified)
115
Figure 4-61 Modified CCL2001 model prediction for Creep of W40S20F20
Figure 4-62 Modified CCL2001 model prediction for Creep of W40S25F25
20 40 60 80 100 120 140
0.001 0.01 0.1 1 10 100
Creep (10-6/Mpa)
Log time since loading (days) W40S20F20
CCL model (original) CCL model (modified)
40 60 80 100 120 140 160
0.001 0.01 0.1 1 10 100
Creep (10-6/Mpa)
Log time since loading (days) W40S25F25
CCL model (original) CCL model (modified)
116
Figure 4-63 Modified CCL2001 model prediction for creep of W44S18F8
Figure 4-64 Modified CCL2001 model prediction for creep of W37S30F16(A)
30 50 70 90 110 130 150
0.001 0.01 0.1 1 10 100
Creep (10-6/MPa)
Log time since loading (days) W44S18F8
CCL model (original) CCL model (modified)
30 50 70 90 110 130 150
0.001 0.01 0.1 1 10 100
Creep (10-6/MPa)
Log time since loading (days) W37S30F16(A)
CCL model (original) CCL model (modified)
117
Figure 4-65 Modified CCL2001 model prediction for creep of W37S30F16(A)
Figure 4- 66 Comparison between Modified CCL model prediction and Measured Creep.
40 60 80 100 120
0.001 0.01 0.1 1 10 100
Creep (10-6/MPa)
Log time since loading (days) W37S30F16(B)
CCL model (original) CCL model (modified)
y = 0.887x + 4.6948 R² = 0.9354
40 60 80 100 120
40 60 80 100 120
Predicted creep (10-6/MPa)
Measured creep (10-6/MPa) Test data