THE UNIVERSITY OF DA NANG
UNIVERSITY OF SCIENCE AND TECHNOLOGY

NGUYEN BA THACH

AN EXPERIMENTAL STUDY ON SHRINKAGE
STRAINS OF CONCRETE IN STANDARD
CLIMATIC CONDITIONS AT GIA LAI

MAJOR

: ENGINEERING MECHANICS

CODE

: 9520101

SUMMARY OF DOCTORAL DISSERTATION IN THE FIELD
OF ENGINEERING

DA NANG - 2019


The work was finished at
University of Science and Technology - The University of Da Nang

Supervisors:
1. Dr. TRUONG HOAI CHINH, Assoc. Prof.
2. Dr. PHAN QUANG MINH, Prof.

Reviewer 1st : …………………………………

where the characteristics of the Central Highlands climate is obvious. These cracks directly affect to the
structures of building. The study on the shrinkage strains of concrete in climatic conditions of Gia Lai
province is essential to support the construction management, design consultancy, construction, using of
concrete materials as well as the application of new technologies for reinforced concrete structures in
the area.
Based on above analyses, the topic of this dissertation is “An experimental study on shrinkage
strains of concrete in standard climatic conditions at Gia Lai”. This is anessential and practical scientific
research project.
2. Objectives of the research
The experimental study systematically collected and built the experimental data on the shrinkage
strain of concrete using local aggregate in standard climatic conditions of Gia Lai province. These data are
basically used to study on the design of reinforced concrete structures at Gia Lai suitably; The experimental
study determined experimental coefficients based on suitable prediction model. As a result, the development
of time-dependent shrinkage strains of concrete in standard climatic conditions at Gia Lai could be predicted;
The experimental study compared the shrinkage strains of concrete in standard and natural climatic
conditions at Gia Lai. As a result, the suitable solutions for restricting shrinkage strains of concrete in the
first period after casting were suggested; The experimental study on shrinkage strains of reinforced concrete
and steel fiber concrete proposed the solutions which could restrict shrinkage strains of concrete
3. Object and scope of the thesis
Object: Time-dependent shrinkage strains of concrete in standard climatic conditions of Gia Lai
province; Effect of reinforced bars and steel fibers on shrinkage strains of concrete.
Scope of Works: Shrinkage strains of concrete without admixtures in standard climatic conditions of
Gia Lai province with specimens: Regular concrete of compressive strength of concrete B22.5 (M300#) with


2
ratios between water and cement (N/X) of 0.40, 0.45, 0.50; Steel fiber reinforced concrete (density of steel
fiber is 40 kg/m3); Reinforced concrete with reinforcement ratio of 1.13%.
4. Methodology
Theoretical research and experimental research.

reducing the shrinkage strains of concrete. Based on these results, the recommendation of reducing the
shrinkage strains of concrete was conducted.

CHAPTER 1
THEORETICAL RESEARCHES ON TIME-DEPENDENT
SHRINKAGE STRAINS OF CONCRETE
1.1. Research background of time-dependent shrinkage strains of concrete in Vietnam and all over


3
the world
Practical researches on time-dependent shrinkage strains of concrete all over the world: The
primary researches were published by many authors such as: Pickett (1956), Lyse (1960), Neville (1970,
1981, 1983, 1990, 1995), Smadi et al (1987), Bažant (1982, 1988, 1994), Tazawa và Miyazawa (1995),
Ojdrovic và Zarghamee, 1996, Mac Gregor, 1997, Gilbert (2001), Acker và Ulm (2001), Swapnil Deshpande
et al (2007). Recently, there are some authors who published their researches such as: Faez Sayahi (2016),
Vasu

Krishna,

Rakesh

Kumar

(2016),

Balaguru,

Caronia


According to GOST 24544-81, the time-dependent shrinkage strain of concrete is determined by
equation (1.1):
∆𝑡
𝛼𝑛 + ∆𝑡
1.7. Analysis of cracks due to shrinkage strain in concrete
𝜀𝑐𝑠 (𝑡) = 𝜀𝑐𝑠 (∞)

(1.1)

Cracking is one of the main reasons of impairment of working ability (including bearing capacity
and utility), resulting in a reduction in the life of the building for concrete and reinforced concrete
construction. Shrinkage is divided into softening shrinkage and strengthening shrinkage (dry shrinkage).
Softening shrinkage occurs within 24 hours (most significant in the first 10 hours) after concreting, when the
strength of concrete is not enough. For concrete materials, two time-dependent shrinkage strains are soft
shrinkage strain and dry shrinkage strain. Because of shrinkage strains, concrete is subjected to tensile stress
which depends on the value of shrinkage strain.


4
1.8. Effect of reinforcement bars in cracked reinforced concrete structures due to shrinkage strain
Because of shrinkage strains, concrete is subjected to tensile stress which depends on the value of
shrinkage strain, while reinforcement bars are in compressive stage. The reinforcement bars reduce the
extension of cracks instead of restricting cracks. In conclusion, the position of reinforcement bars in
reinforced concrete structures are to reduce the development of cracks.
1.9. Conclusion of Chapter 1
Scientists all over the world have been studying the time-dependent shrinkage of concrete for long
time and achieving many important results.
The shrinkage of concrete has been studied over more than a century with several research aspects,
from the basic mechanism of impact shrinkage to several structural problems related to strains.
Based on above analyses of mathematical models for time-dependent shrinkage strains of concrete,



5
Experiment of calculation of shrinkage strains of concrete; Experiment of measurement of restrained
shrinkage of concrete by Restrained Ring Test.
2.4. Materials used in experiments, making specimens, casting and maintenance of specimens
Materials used in experiments: Cement; Stone (1x2); Sand; Water; Steel fiber; Reinforcement bar
12. Fabrication of specimens based on TCVN 3015:1993. Curing specimens based on TCVN 3117:1993
and TCVN 3015:1993.
2.5. Experimental equipmentfor measuring shrinkage strainsof concrete
Climatic cabinet (controlling temperature and humidity according to experimental requirements):
Climatic cabinet is set up at temperature 25±20C, humidity 75±5% during the experiment. These setups
specify the average temperature and humidity of standard climatic conditions of Gia Lai.
Tools for measuring shrinkage strain of concrete: Comparator of MATEST (Italia) manufacture;
Model: C363 KIT.
Dimension of specimens of determination the compressive resistance strength of regular concrete is
15x15x15 cm.
Dimension of specimens of determination the time-dependent compressive strength and young
modulus of concrete is 15x30 cm.
Dimension of specimens of calculation of shrinkage strains of concrete is 10x10x40 cm.
Dimension of Restrained Ring Test tools are 406 mm of outer diameter, 305 mm of inner diameter,
152 mm of height and 12.5 mm of thickness.
2.6. Experimental result
Table 2.1. Experimental results of compressive strength 𝑹đ𝒄
𝒏 (𝟐𝟖) of regular concrete
đ𝒄
The average value 𝑹𝒏 (𝟐𝟖)
(MPa)
No
Symbol

7
days
22.53
21.63
21.10

of M1, M2, M3 specimens
The average value Rn(t), MPa
28
60
90
180
270
days
days
days
days
days
31.14 33.00 33.58 34.26 34.58
29.58 31.48 32.10 32.61 32.85
28.70 30.67 31.29 31.64 31.87

364
days
34.74
33.18
32.09

Standard
deviation

days
days
days
days
days
23.86 32.95 34.82 35.30 35.90 36.22
23.00 31.35 33.23 33.80 34.25 34.49
22.47 30.47 32.47 33.00 33.30 33.51

364
days
36.32
34.74
33.66

Standard
deviation
(STD)
4.46
4.18
4.03


6
Table 2.4. Experimental results of the time-dependent Young Modulus E(t) of regular concrete of
M1, M2, M3 specimens
The average value E(t), MPa
Standard
Specimens Ratio
deviation


Specimens
group

Ratio
(N/X)

MS1
MS2
MS3

0.40
0.45
0.50

7
days
26184
23421
21135

concrete of MS1, MS2, MS3 specimens
The average value E(t), MPa
28
60
90
180
270
days
days

Spec. M2
N/X = 0.45
mM2
M2

Spec. M3
N/X = 0.50
mM3
M3

Temperature Humidity
(t)
(RH)

1
2
3
4
5
6
7
14
21

(%)
0
0.27
0.38
0.45
0.51

50
63
77
90
107
183
243

(%)
0
1.61
2.09
2.25
2.38
2.47
2.52
2.85
3.10

(x10-6)
0
43
63
80
100
117
130
221
284



0.75
0.79
0.90
0.99
1.03
1.07
1.11
1.14

237
273
303
330
357
377
397
407

1.95
2.01
2.05
2.09
2.13
2.16
2.21
2.25

290
330

25.0
25.0
25.0

75
75
75
75
75
75
75
75

84
91

1.17
1.21

423
437

2.28
2.33

477
487

3.55
3.57


25.0
25.0

75
75


7

Date

Spec. M1
N/X = 0.40

Spec. M2
N/X = 0.45

Spec. M3
N/X = 0.50

mM1
(%)

M1
(x10-6)

mM2
(%)


1.33
1.35

487
493

2.45
2.47

537
543

140
147

1.37
1.39

503
507

2.49
2.50

154
168
182
196
224
252

2.79
2.87
2.95

Temperature Humidity
(t)
(RH)
(oC)

(%)

558
568

25.0
25.0

75
75

3.69
3.71

578
584

25.0
25.0

75

3.85
3.91
3.96
4.02
4.10
4.17

618
624
631
638
644
657
670
687
700

25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0

75
75
75

20
0.65
33
0.72
50
0.78
60

Spec. MS2
N/X = 0.45
mMS2
MS2
(%)
(x10-6)
0
0
1.49
23
1.75
33
1.86
47
1.94
67
2.00
80

Spec. MS3
N/X = 0.50
mMS3

75
75
75
75

7
14
21
28
35
42
49
56

0.84
1.00
1.04
1.11
1.16
1.23
1.30
1.34

70
100
123
157
193
229
254

177
213
257
297
333
357
377

25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0

75
75
75
75
75
75
75
75

63
70

1.38

337

2.60
2.67

380
390

3.93
3.97

424
437

25.0
25.0

75
75


8

Date

Spec. MS1
N/X = 0.40

Spec. MS2
N/X = 0.45


2.72
2.75

403
417

4.01
4.04

105
112

1.62
1.64

373
387

2.76
2.78

427
440

119
126

1.66
1.68

2.10
2.17

423
433
447
457
463
470
477
490
503
517
537
551

2.84
2.85
2.88
2.90
2.93
2.98
3.01
3.06
3.11
3.16
3.23
3.31

Temperature Humidity

4.09
4.11

497
507

25.0
25.0

75
75

473
483
497
508
513
520
527
534
541
560
567
593

4.13
4.15
4.17
4.19
4.22

25.0
25.0
25.0

75
75
75
75
75
75
75
75
75
75
75
75

Table 2.8. Experimental results of time-dependent shrinkage strain and mass loss of concrete in
standard climatic conditions of Gia Lai (Group 3 - Reinforced concrete)

Date

1
2
3

Spec. MT1
N/X = 0.40
mMT1
MT1

3.06
23
3.29
30

Temperature Humidity
(t)
(RH)
(oC)
25.0
25.0
25.0

(%)
75
75
75

4
5
6
7
14
21
28
35

1.14
1.22
1.35

143
173

3.43
3.52
3.58
3.62
3.80
3.88
3.94
4.02

47
80
97
110
140
167
193
223

25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0


25.0
25.0

75
75

56
63

1.79
1.82

203
220

2.88
2.92

250
270

4.25
4.29

297
317

25.0
25.0


(%)

MT3
(x10-6)

70
77

1.87
1.90

233
243

2.96
3.01

283
297

4.32
4.36

84
91

1.94
1.96

253

224
252
280
322
364

2.02
2.03
2.05
2.08
2.10
2.12
2.14
2.18
2.22
2.24
2.30
2.35
2.40
2.48
2.55

313
337
350
357
367
383
393
407


327
340

25.0
25.0

75
75

4.40
4.44

353
363

25.0
25.0

75
75

333
347

4.48
4.50

373
393

4.69
4.73
4.76
4.81
4.86
4.92
4.99
5.07

413
427
437
443
457
473
490
507
523
533
547
560
570
587
603

25.0
25.0
25.0
25.0
25.0

Date

Spec. M1
N/X = 0.40
mM1
M1
(%)
(x10-6)

Spec. M2
N/X = 0.45
mM2
M2
(%)
(x10-6)

Spec. M3
N/X = 0.50
mM3
M3
(%)
(x10-6)

Temperature Humidity
(t)
(RH)
(oC)

(%)


1.66
1.76
1.87
1.96
1.99

0
77
96
120
145
168
199
338

0
2.09
2.53
2.70
2.87
2.99
3.06
3.14

0
102
122
154
189
220

2.12
2.18

451
450

3.24
3.39

526
513

24.7
23.5

72
77

35
42

1.16
1.19

384
393

2.26
2.29


(%)

M1
(x10-6)

mM2
(%)

M2
(x10-6)

mM3
(%)

M3
(x10-6)

49
56

1.22
1.25

395
409

2.32
2.36

450

2.51

91
98
105
112
119
126
133
140
147
154
168
182
196
224
252
280
322
364

1.45
1.48
1.50
1.52
1.54
1.56
1.57
1.59
1.61

2.58
2.60
2.62
2.64
2.67
2.68
2.71
2.77
2.79
2.83
2.87
2.89
2.95
3.00
3.05
3.12
3.20

Temperature Humidity
(t)
(RH)
(oC)

(%)

493
498

23.8
22.6


540
555
560
560
587
597
592
613
623
619
636
642
650
647
669
681
676
716

3.81
3.85
3.87
3.88
3.91
3.93
3.95
3.96
3.99
4.01

23.3
22.8
27.6
30.1
23.2
26.7
28.3
23.6
30.5
29.2
31.5
23.5
29.2
28.2
27.4
29.5

77
62
78
83
58
53
82
66
60
80
55
58
51

81
1.05
96

Spec. MS2
N/X = 0.45
mMS2
MS2
(%)
(x10-6)
0
0
1.42
58
1.71
83
1.94
104
2.02
126

Spec. MS3
N/X = 0.50
mMS3
MS3
(%)
(x10-6)
0
0
2.80


111
126

2.12
2.21

143
168

3.51
3.57

189
208

30.7
28.6

52
56

14
21

1.25
1.33

224
296

Spec. MS3
N/X = 0.50

mMS1
(%)

MS1
(x10-6)

mMS2
(%)

MS2
(x10-6)

mMS3
(%)

MS3
(x10-6)

28
35

1.40
1.48

310
310


331
350

2.70
2.75

70
77
84
91
98
105
112
119
126
133
140
147
154
168
182
196
224
252
280
322
364

1.65
1.70

483
500
496
520
527
533
528
557
573
570
610

2.79
2.84
2.88
2.93
2.97
2.99
3.01
3.04
3.06
3.08
3.10
3.12
3.14
3.18
3.22
3.24
3.30
3.35

77

370
413

4.00
4.04

418
460

22.6
26.2

81
63

430
445
453
449
480
490
484
520
530
526
547
560
553


474
487
503
499
524
538
532
564
577
571
601
614
609
643
653
662
658
686
692
693
720

28.8
22.5
30.8
24.3
27.2
23.3
22.8

51
80
56
58
60
55

Table 2.11. Experimental results of time-dependent shrinkage strain and mass loss of concrete in
natural climatic conditions of Gia Lai (Group 3 - Reinforced concrete)

Date

1
2

Spec. MT1
N/X = 0.40
mMT1
MT1
(%)
(x10-6)
0
0
0.89
34

Spec. MT2
N/X = 0.45
mMT2
MT2

4

1.16
1.29

54
70

2.09
2.34

74
90

3.56
3.65

94
115

29.6
29.0

53
55

5
6

1.46


Spec. MT2
N/X = 0.45

Spec. MT3
N/X = 0.50

mMT1
(%)

MT1
(x10-6)

mMT2
(%)

MT2
(x10-6)

mMT3
(%)

MT3
(x10-6)

7
14

1.59
1.65


1.79
1.84

266
270

2.84
2.89

49
56
63
70
77
84
91
98
105
112
119
126
133
140
147
154
168
182
196
224

272
278
283
307
310
320
325
340
356
351
390
404
400
419
438
433
466
474
483
478
503
520
517
554

2.96
3.01
3.06
3.12
3.16

28.6
29.2

56
54

4.01
4.05

378
366

24.7
23.5

72
77

320
324

4.11
4.17

370
355

29.1
23.3


4.33
4.38
4.43
4.48
4.51
4.55
4.56
4.59
4.61
4.63
4.66
4.68
4.70
4.73
4.77
4.81
4.84
4.88
4.93
4.99
5.06
5.14

343
350
380
390
403
421
414

23.2
26.7
28.3
23.6
30.5
29.2
31.5
23.5
29.2
28.2
27.4
29.5

77
81
63
55
89
52
77
62
78
83
58
53
82
66
60
80
55


CH1
11

CH2
11

CH3
11

CH4
11

2.7. Conclusion of Chapter 2
The process of making specimens, casting and maintenance of specimens was carried out based on
the specification of TCVN 3015:1993.
The process of measurement of shrinkage strains was specified in TCVN 3117:1993.


13
The time-dependent compressive strength and Young modulus of concrete of specimens were
measured within 364 days, which includes 7 times of measurement of 7 days, 28 days, 60 days, 90 days, 180
days, 270 days and 364 days. The maximums of compressive strength and Young modulus were observed at
364 days.
The set of specimens for measurement shrinkage strains was keep in climatic cabinet of temperature
0

of 25±2 C and humidity of 75±5% during the experiments.
The measurement of time-dependent shrinkage strains of concrete specimens was carried out after
364 days. The experimental results of shrinkage strain of concrete specimens are the average value of three

60
90
180
270
364
(STD)
days
days
days
days
days
days
days
The suggested results of compressive strength of concrete Rn(t) (Group 1 - Regular concrete)
M1-ĐX
0.40
23.41 31.14 33.08 33.69 34.33 34.55 34.66
4.03
M2-ĐX
0.45
22.24 29.58 31.42 32.01 32.61 32.82 32.92
3.83
M3-ĐX
0.50
21.58 28.70 30.49 31.05 31.64 31.84 31.94
3.71
The suggested results of compressive strength of concrete Rn(t)

Specimens
group

0.40
0.45

24.77
23.57

32.95
31.35

35.00
33.30

35.65
33.92

36.32
34.56

36.55
34.78

36.67
34.89

4.26
4.06

0.50

22.91


suggested results of compressive strength of

concrete Rn(t)

concrete Rn(t)

(Group 1 - Regular concrete)

(Group 2 - Steel fiber reinforced concrete)

3.1.2. Analyzing and evaluating time-dependent Young Modulus E(t) of two groups of concrete (Group 1 Regular concrete; Group 2 - Steel fiber reinforced concrete)
According to the experimental results of time-dependent Young modulus of regular concrete and
steel fiber reinforced concrete, proposing the formulas and the experimental coefficients which indicate the
relation between the Young modulus E(t) and the Young modulus of 28 days based on the total least-squares
method (use the Solver tool in Microft Excel).
𝐸(𝑡) = 𝐸(28)

𝑡
2,24 + (0,92. 𝑡)

(3.2)

Table 3.2. The suggested results of Young Modulus of concrete E(t)
(Group 1 - Regular concrete; Group 2 - Steel fiber reinforced concrete)
The average value E(t), MPa
Standard
deviation
7
28

26786 33215 34695 35152 35621 35781 35863
3256
MS2-ĐX
0.45
24281 30109 31451 31865 32290 32435 32510
2952

Specimens
group

Ratio
(N/X)

MS3-ĐX

0.50

21764

26987

28190

28561

28942

29072

29139

28
days
1.058

Comparativevalue (kR)
60
90
180
days
days
days
1.055
1.051
1.048

0.45
0.50

1.063
1.065

1.060
1.062

1.055
1.059

Specimens
group


days

28
days

Comparativevalue (kE)
60
90
180
days
days
days

0.40
0.45

1.038
1.041

1.037
1.039

1.033
1.037

1.030
1.034

1.028
1.031

EMS2 với EM2
EMS3 với EM3

270
days

364
days

Figure 3.5. The comparision of compressive

Figure 3.6. The comparison of Young Modulus

strength of concrete Rn(t) between Group 1 -

E(t) between Group 1 - Regular concrete and

Regular concrete and Group 2 - Steel fiber

Group 2 - Steel fiber reinforced concrete

reinforced concrete


16
3.3. Determination of the experimental coefficients which predictthe time-dependent shrinkage strains
of concrete (Group 1 - Regular concrete) in standard climatic conditions of Gia Lai according to
Russian Standard GOST 24544-81
Table 3.5. Values of experimentalcoefficientscalculated according to GOST 24544-81 of concrete
specimens (Group 1 - Regular concrete)

714.68
755.51

54.01
41.41
35.85

- The formula for predicting of the shrinkage strains of regular concrete specimens M1 which have
ratio of N/X of 0.40:
𝑡
(3.3)
54,01 + 𝑡
- The formula for predicting of the shrinkage strains of regular concrete specimens M2 which have
𝜀𝑐𝑠 (𝑡) = 693,52. 10−6

ratio of N/X of 0.45:
𝑡
(3.4)
41,41 + 𝑡
- The formula for predicting of the shrinkage strains of regular concrete specimens M3 which have
𝜀𝑐𝑠 (𝑡) = 714,68. 10−6

ratio of N/X of 0.50:
𝜀𝑐𝑠 (𝑡) = 755,51. 10−6

𝑡
35,85 + 𝑡

(3.5)



concrete specimens of Group 1 - Regular concrete

shrinkage strains and mass loss of concrete
specimens of Group 1 - Regular concrete

3.5.2. Effect of ratio N/X on shrinkage strains of concrete specimens of group 2

Figure 3.13. Time-dependent shrinkage strains of

Figure 3.14. Relation between time-dependent

concrete specimens of Group 2 - Steel fiber

shrinkage strains and mass loss of concrete

reinforced concrete

specimens of Group 2 - Steel fiber reinforced
concrete


18
3.5.3. Effect of ratio N/X on shrinkage strains of concrete specimens of group 3

Figure 3.15. Time-dependent shrinkage strains of

Figure 3.16. Relation between time-dependent

concrete specimens of Group 3 - Reinforced

different ratio of N/X in standard and natural climatic conditions of Gia Lai


19

Figure 3.19. Time-dependent shrinkage strains of

Figure 3.20. Time-dependent shrinkage strains of

concrete specimens of Group 1 in standard and

concrete specimens of Group 2 in standard and

natural climatic conditions of Gia Lai

natural climatic conditions of Gia Lai

Figure 3.21. Time-dependent shrinkage strains of concrete specimens of Group 3 in standard and
natural climatic conditions of Gia Lai
3.7.2. Comparison of shrinkage strains of three groups of concrete with the different concrete mix design,
same ratio of N/X in standard and natural climatic conditions of Gia Lai

Figure 3.22. Time-dependent shrinkage strains of

Figure 3.23. Time-dependent shrinkage strains of

concrete specimens of three groups with ratio of

concrete specimens of three groups with ratio of


M1-ĐKTN/M1-ĐKC
0.00
2.32
1.89
1.87
1.86
1.86
1.86
1.86
1.85
1.60

N/X = 0.45
M2-ĐKTN/M2-ĐKC
0.00
2.33
1.91
1.90
1.88
1.87
1.86
1.85
1.86
1.55

N/X = 0.50
M3-ĐKTN/M3-ĐKC
0.00
2.36
1.93

1.09

63
70
77
84
91
98
105
112
119
126

1.12
1.13
1.12
1.12
1.12
1.10
1.09
1.07
1.11
1.10

1.14
1.13
1.13
1.13
1.11
1.11

147
154
168
182
196
224
252
280

N/X = 0.40
M1-ĐKTN/M1-ĐKC
1.09
1.10
1.07
1.10
1.10
1.10
1.08
1.09
1.09

N/X = 0.45
M2-ĐKTN/M2-ĐKC
1.11
1.11
1.09
1.11
1.11
1.11
1.09

concrete and Group 3 - Reinforced concrete with same ratio of N/X innatural climatic conditions of
Gia Lai
Table 3.6. The results of shrinkage strains of concrete of Group 1 - Regular concrete, Group 2 - Steel
fiber reinforced concrete and Group 3 - Reinforced concrete with same ratio of N/X in natural climatic
conditions of Gia Lai

1
2
3
4
5
6
7
14
21
28

N/X=0.40
M1/ MS1
0.00
1.34
1.15
1.16
1.16
1.17
1.18
1.19
1.21
1.22


1.30
1.35
1.37
1.38
1.38
1.39
1.40
1.43

N/X=0.45
M2 / MT2
0.00
1.54
1.30
1.34
1.36
1.37
1.38
1.39
1.40
1.42

N/X=0.50
M3 / MT3
0.00
1.51
1.29
1.33
1.35
1.36

1.19

1.21
1.17
1.17
1.19
1.17
1.17
1.16
1.16

1.44
1.46
1.45
1.47
1.49
1.46
1.47
1.48

1.45
1.44
1.44
1.45
1.47
1.46
1.45
1.44

1.41

112

1.14
1.17

1.14
1.16

1.14
1.14

1.39
1.44

1.37
1.39

1.34
1.35

Date


22

119
126
133
140
147

M3 / MS3
1.12
1.11
1.12
1.11
1.10
1.10
1.08
1.07
1.07

N/X=0.40
M1/ MT1
1.34
1.33
1.33
1.31
1.27
1.28
1.24
1.23
1.22

N/X=0.45
M2 / MT2
1.33
1.30
1.30
1.28
1.26

1.22

1.22
1.18

1.17
1.14

280
322

1.10
1.15

1.09
1.09

1.07
1.06

1.21
1.26

1.18
1.18

1.15
1.14

364

3.11. Conclusion of Chapter 3
• Based on the experimental data, the parameters of prediction of time-dependent compressive
strength and Young modulus of concrete and steel fiber reinforced concrete were determined.
• Based on the shrinkage strains experimental dataof concretes which have 0.4, 0.45 and 0.5 of
ratio between water and cement in concrete mix design, the catalogue of ultimate shrinkage strain cs(∞) and
the parameter n depending on the ratio between water and cement was established. As a result, the
shrinkage strains of regular concrete cs(t) at arbitrary time were proposed used as below:
𝑡
𝜀𝑐𝑠 (𝑡) = 𝜀𝑐𝑠 (∞)
𝛼𝑛 + 𝑡
• Equations of (3.3), (3.4) and (3.5) used the reliable experimental factors, so the results were in
high agreement with the results of model of prediction of shrinkage using Australian Standard AS 3600 in
tropical climatic zone.


23
• The results of shrinkage strains of concrete in standard climatic conditions of Gia Lai are:
- Shrinkage strains of concrete depends on climatic conditions and ratio of N/X dramatically.
- After 21 days of concrete casting, the shrinkage strains of concrete of natural climatic conditions of
Gia Lai province are around twice times than that of standard climatic conditions. The incremental
coefficient of shrinkage strains kmt considering the fluctuation of humidity in natural climatic conditions of
Gia Lai is:
kmt = 1.86 when t ≤ 21 days
kmt =1.10 when t > 21 days
- Using steel fiber reinforced concrete with ratio of steel fiber of 40 (kg/m3) decrease the shrinkage
strains of concrete of around 1.15 to 1.20 times mainly in 21 first days after casting. The efficiency decreases
when ratio of N/X increases.
- Using reinforced concrete with ratio of reinforcement bar of 1.13% decrease the shrinkage strains
of concrete of around 1.30 to 1.40 times mainly in 21 first days after casting. The efficiency decreases when
ratio of N/X increases.

3. The shrinkage strains of regular concrete in standard and natural climatic conditions at Gia Lai
𝜀𝑐𝑠 (𝑡) = 755,51. 10−6

were compared. Based on the experimental results, after 21 days of concrete casting, the shrinkage strains of
concrete of natural climatic conditions-dry season of Gia Lai province are around twice times than that of