Nghiên cứu thực nghiệm biến dạng co ngót của bê tông trong điều kiện khí hậu chuẩn tại gia lai tt tiếng anh

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 : …………………………………

Reviewer 2nd: …………………………………
Reviewer 3rd: …………………………………

This dissertation was examinedby the Committeeat The University of Da Nang on … of …, 20…

For the details of the dissertation, please contact:
- Information and Library Center, University of Da Nang.
- National Library of Viet Nam.


1

INTRODUCTION
1. Motivation and thematic framework
Scientists all over the world have been studying the time-dependent shrinkage of concrete for long
time and achieving many important results. There are many scientific research projects, many scientific
articles in prestigious magazines which introducethe research results of shrinkage strains. The contents of
researches include: Study on shrinkage strain of new concrete material; Research on the solutions of
reducing shrinkage strains (using of admixtures, new materials, etc.). The researchers conducted these
studies based on the experimental measurements of the shrinkage strains of concrete materials.
Currently, the prediction for shrinkage is mainly depended on the Foreign Standards which have less
reliable estimationin risks and different temperature climatic conditions. The current standards of developed
countries, such as Eurocode European Standard (EC2, 1992), British Standard 8110 (BS 8110, 1997),
Standard CEB-FIP 1990 (CEB 1990), American Standard (ACI-209), Australian Standards 3600 (AS 3600),
Forecast model of Russian Concrete Institute, Russian Standard (GOST 24544-81), present the details of the
experimental works on measuring shrinkage strains of concrete.
There are a few researches of experimental shrinkage in Vietnam currently, and the experimental
data are not systematic. The determination of shrinkage strains for regular concrete without admixtures does
not have specific experimental data which correspond to several climatic conditions of difference zones.
The crack due to shrinkage strains occurs commonly in construction works in Gia Lai province

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.

5. Science and practical significance
Science Significance: The thesis has studied the time-dependent shrinkage strains of concrete in the
standard and natural climatic conditions of Gia Lai province. The experimental coefficients which are used
to predict the time-dependent shrinkage strains of concrete are determined. As a result, the thesis supports
the recommendations for researching the response of reinforced concrete structures considering the
shrinkage strains.
Practical Significance: The time-dependent shrinkage strains of concrete in standard and natural
climatic conditions of Gia Lai province are determined by the experimental results of this thesis. These
results provide a set of data on shrinkage strain of concrete which are used to support the analysis reinforced
concrete structures considering the shrinkage strains. Consequently, the recommendations of reducing the
crack of concrete structures and reinforced concrete structurewere proposed.
6. Organization of the thesis
The thesis comprises three chapters which are described as follow:
Chapter 1: Theoretical researches on time-dependent shrinkage strains of concrete
Chapter 2: An experimental study on shrinkage strains of concrete in climatic conditions at Gia Lai
Chapter 3: To analyze and evaluate the experimental results
7. Novelty of the thesis
• The thesis built the experimental data on the shrinkage strain of concrete using local aggregate in
climatic conditions of Gia Lai province. These data are used in practical design of reinforced concrete
structures.
• The thesis conducted experimental study on the shrinkage of concrete in 364 days with several
specimens of the ratio between water and cement (N/X) of 0.40, 0.45 and 0.50 in standard climatic
conditions of Gia Lai province (temperature of 25±20C and humidity of 75±5%). The results of experiment
are used to predict time-dependent shrinkage strains of concrete in standard climatic conditions of Gia Lai
province.
• The thesis conducted the experimental study on the comparison of the development of shrinkage
strain of concrete between the standard and the natural climatic conditions of Gia Lai province. Based on the
experimental results, 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 thesis conducted the experimental study on the effect of steel fibers and steel bars on

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

David,

Roda

Andrés

(2017),

Jun Yang, Qiang Wang, Yuqi Zhou (2017), Karagüler, Yatağan (2018), Safiuddin, Kaish, Woon, Raman
(2018).
Practical researches on time-dependent shrinkage strains of concrete in Vietnam: The research on
shrinkage deformation of concrete can include a number of authors such as: Le Van Thuong (1993), Hoang
Quang Nhu (2007), Cao Duy Khoi, Ngo Hoang Quan (2012), Nguyen Ngoc Binh, Nguyen Trung Hieu
(2012; 2015), Tran Ngoc Long (2016).
1.2. Time-dependent shrinkage strains of concrete
Shrinkage is a time-dependent strain of concrete associated with the loss of moisture that occurs at
different stages in the life of the concrete. It is independent with loading.
1.3. Mechanism of shrinkage
True shrinkage mechanism: Capillary shrinkage; Chemical shrinkage; Dry shrinkage.
Nominal shrinkage mechanism: Crack effect; Geometrical effect.
1.4. Factors affecting shrinkage
Internal factors: Aggregate; Cement; Ratio between water and cement; Chemical admixtures;
Dimension and shape of specimens.
External factors: Curing method; Temperature; Relative humidity.
1.5. The models of time-dependent shrinkage strains of concrete
Main models for estimating time-dependent shrinkage strains of concrete in several standards
include: Russian Standard GOST 24544-81, Prediction Model of Russian Concrete Institute, Australian
Standards AS 3600, American Standard ACI 209R-92, British Standard BS 8110, European Standard CEBFIP 2010, European Standard Eurocode 2 and model B3.
1.6. Prediction formulations for time-dependent shrinkage strain of concretebased on the experimental
resultsaccording to Russian standard GOST 24544-81

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,

main factors which affect to shrinkage strains of concrete material includes: concrete mix method (type of
cement, ratio of fine aggregate, ratio between water and cement, etc.), dimension and shape of structures,
relative humidity of environment. The suitable concrete mix design is important to reduce shrinkage strains
of concrete.
Currently, the researches on shrinkage strains of concrete are few in climatic conditions of Gia Lai
province. There have been not experimental data of shrinkage strains for regular concrete without
admixtures in Vietnam Standard. Therefore, the research of determination of shrinkage strains of concrete
is essential, and the topic of this thesis is determined.

CHAPTER 2
AN EXPERIMENTAL STUDY ON SHRINKAGE STRAINS OF
CONCRETE IN CLIMATIC CONDITIONS AT GIA LAI
2.1. Climatic characteristics at Gia Lai
Standard climatic conditions at Gia Lai: According to Pleiku City Metering Station of the Central
Highlands Hydrometeorological Agency, the average annual temperature is 230C-270C. The average annual
humidity is 70%-80%. There fore, the standard temperature is 25±20C and the standard humidity is 75±50C.
Natural climatic conditions at Gia Lai: The temperature and humidity in Environmental Laboratory
are observed during the experiments. The temperature changes from 22.50C to 31.50C, while the range of
humidity is 51% to 89%.
2.2. Objectives of experiments
Based on the set of experimental data results: Assessingthe effect of ratio of water and cement (N/X)
on the shrinkage strains of regular concrete, steel fiber reinforced concrete and reinforced concrete;
Evaluating the time-dependent shrinkage strains of regular concrete, steel fiber reinforced concrete and
reinforced concrete in standard and natural climatic conditions of Gia Lai; Assessing the restriction of
cracking due to shrinkage strain of concrete with steel fibers and reinforcement bars; proposing the
experimental coefficients to determine time-dependent compressive strength, Young modulus and shrinkage
strains of concrete.
2.3. Experiment
Experiments of determination the compressive resistance strength of concrete regard to shrinkage
strain; Experiment of determination of time-dependent compressive strength and young modulus 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

Note
28 days
1
M1
31.52
Ratio of N/X = 0.40 (Regular concrete)
2
M2
30.68
Ratio of N/X = 0.45 (Regular concrete)
3
M3
29.05
Ratio of N/X = 0.50 (Regular concrete)
Table 2.2. Experimental results of the time-dependent compressive strength Rn(t) of regular concrete

Specimens
group

Ratio
(N/X)

M1
M2
M3

0.40
0.45
0.50

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

(STD)
4.34
4.09
3.93

Table 2.3. Experimental results of the time-dependent compressive strength Rn(t) of steel fiber

Specimens
group

Ratio
(N/X)

MS1
MS2
MS3

0.40
0.45
0.50

reinforced concrete of MS1, MS2, MS3 specimens
The average value Rn(t), MPa
7
28
60
90
180
270
days

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

7
28
60
90
180
270
364
group
(N/X)
(STD)
days
days
days
days
days
days
days
M1
0.40
25225 32045 33164 33528 33830 34031 34432
3221
M2
0.45
22501 28988 30143 30396 30731 31042 31488
3112
M3
0.50
20281 25931 27018 27262 27432 27749 27999
2709
Table 2.5. Experimental results of the time-dependent Young Modulus E(t) of steel fiber reinforced

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

days
days
days
33215 34258 34537 34787 34943
30109 31244 31425 31698 31952
26987 28085 28250 28341 28618

364
days
35300
32352
28840

Standard
deviation
(STD)
3215
3120
2730

Table 2.6. Experimental results of time-dependent shrinkage strain and mass loss of concrete in
standard climatic conditions of Gia Lai (Group 1 - Regular concrete)

Date

Spec. M1
N/X = 0.40
mM1
M1

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

0.57
0.61
0.69
0.72

(x10-6)
0
23
37
50
60
70
80
143
193

(%)
0
0.78
1.19
1.35
1.50
1.61
1.69
1.89
1.93

(x10-6)
0
33

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

(oC)
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0

(%)
75
75
75
75
75
75
75
75
75

28
35
42
49
56
63
70
77

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

363
390
410
430
447
463

3.15
3.22
3.31
3.37
3.41
3.44
3.48
3.52

337
378
408
434
458
478
494
508

25.0
25.0
25.0
25.0
25.0

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

521
531

25.0
25.0

75
75

98
105

1.24
1.26

450
453

2.36
2.38

500
507

3.60
3.62

541
553

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
(%)

M2
(x10-6)

mM3
(%)

M3
(x10-6)

112
119

1.28
1.30

470
473

2.41
2.43

523
527

3.65
3.67

126
133

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

280
322
364

1.40
1.43
1.47
1.50
1.56
1.61
1.67
1.75
1.84

517
523
530
537
550
563
577
603
610

2.53
2.56
2.60
2.63
2.68
2.74

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

75

553
563

3.73
3.74

598
608

25.0
25.0

75
75

567
573
580
587
593
607
620
633
653

3.76
3.79
3.82

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

75
75
75
75
75
75

Table 2.7. Experimental results of time-dependent shrinkage strain and mass loss of concrete in
standard climatic conditions of Gia Lai (Group 2 - Steel fiber reinforced concrete)

Date

1
2
3
4
5
6

Spec. MS1
N/X = 0.40
mMS1
MS1
(%)
(x10-6)
0
0
0.35
13
0.52

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

MS3
(%)
(x10-6)
0
0
2.58
33
2.75
47
2.89
63
3.03
90
3.18
107

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

(%)
75
75

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

278

2.05
2.18
2.21
2.24
2.28
2.34
2.43
2.47

97
140
173
210
251
282
311
330

3.29
3.42
3.49
3.57
3.64
3.69
3.75
3.81

120

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

1.43

297
313

2.51
2.56

350
366

3.85
3.89

397
410

25.0
25.0

75
75

77
84

1.50
1.53

323

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

Spec. MS3
N/X = 0.50

mMS1
(%)

MS1
(x10-6)

mMS2
(%)

MS2
(x10-6)

mMS3
(%)

MS3
(x10-6)

91
98

1.57
1.60

353
367

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

403
417

2.80
2.82

133
140
147
154
168
182
196
224
252
280
322
364

1.70
1.71
1.73
1.75
1.79
1.83
1.86
1.91
1.96
2.03

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

(t)
(RH)
(oC)

(%)

447
457

25.0
25.0

75
75

4.06
4.07

473
484

25.0
25.0

75
75

457
467

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

4.26
4.29
4.34
4.39
4.45
4.53
4.60

514
527
540
557
570
579
586
596
604
613
637
651

25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0

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

(%)
(x10-6)
0
0
0.65
7
0.98
12

Spec. MT2
N/X = 0.45
mMT2
MT2
(%)
(x10-6)
0
0
2.05
13
2.26
17

Spec. MT3
N/X = 0.50
mMT3
MT3
(%)
(x10-6)
0
0

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

1.40
1.50
1.56
1.61
1.67

20
37
43
53
77
93
110
130

2.34
2.40
2.44
2.47
2.55
2.64
2.68
2.73

30
57
70
87
111
123

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

75
75
75
75
75
75
75
75

42
49

1.70
1.75

157
183

2.79
2.84

200
233

4.14
4.21

257
280

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

75
75


9

Date

Spec. MT1
N/X = 0.40

Spec. MT2
N/X = 0.45

Spec. MT3
N/X = 0.50

mMT1
(%)

MT1
(x10-6)

mMT2
(%)

MT2
(x10-6)

mMT3

(%)

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

273

3.05
3.09

304
321

98
105

1.98
2.00

287
297

3.13
3.15

112
119
126
133
140
147
154
168
182
196

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

413
423
433
447
463
477
497

3.17
3.19
3.21
3.23
3.25
3.27
3.29
3.34
3.38
3.40
3.46
3.52
3.57
3.65
3.73

Temperature Humidity
(t)
(RH)
(oC)

(%)

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

25.0
25.0

75
75

357
380
397
403
413
430
440
457
463
470
483
500
513
523
534

4.53
4.54
4.57
4.58
4.60
4.62
4.65

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

25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0
25.0

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

Table 2.9. Experimental results of time-dependent shrinkage strain and mass loss of concrete in
natural climatic conditions of Gia Lai (Group 1 - Regular concrete)

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
2
3
4
5
6
7
14

0
0.20
0.43
0.50
0.59
0.68
0.79
0.79

0
53
70
94
112
130
149
266

0
1.21
1.43

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

242
410

28.8
28.2
29.6
29.0
31.2
30.7
28.6
29.2

56
57
53
55
51
52
56
54

21
28

1.03
1.10

357
379

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

463
465

3.49
3.53

523
508

29.1
23.3

61
70


10

Date

Spec. M1
N/X = 0.40

Spec. M2
N/X = 0.45

Spec. M3
N/X = 0.50

mM1

(%)

M1
(x10-6)

mM2
(%)

M2
(x10-6)

mM3
(%)

M3
(x10-6)

49
56

1.22
1.25

395
409

2.32
2.36

450

449

3.58
3.61

63
70

1.28
1.32

423
447

2.39
2.43

490
507

77
84

1.37
1.40

457
473

2.47

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

1.63
1.68
1.72
1.74
1.79
1.84
1.90
1.97
2.06

488
497
494
504
523
537
532
550
558
553
576
582
589
595
613
629
653
664

2.55

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

77
81

3.66
3.70

537
553

26.2
28.8

63
55

523
537

3.74
3.78

567
583

22.5
30.8

89
52

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

4.05
4.10
4.13
4.18
4.23
4.28
4.36
4.43

585
595
613
609
630
643
638
667
677
672
693
700
708
704
727
737
732
767

24.3
27.2

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

80
56
58
60
55

Table 2.10. Experimental results of time-dependent shrinkage strain and mass loss of concrete in
natural climatic conditions of Gia Lai (Group 2 - Steel fiber reinforced concrete)

Date

1
2
3
4
5

Spec. MS1
N/X = 0.40
mMS1
MS1
(%)
(x10-6)
0
0
0.52
40
0.77
61
0.89

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

78
3.12
107
3.26
135
3.40
165

Temperature Humidity
(t)
(RH)
(oC)
28.8
28.2
29.6
29.0
31.2

(%)
56
57
53
55
51

6
7

1.11
1.20

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

2.25
2.37

287
375

3.64
3.76

348
443

29.2
24.7

54
72


11

Date

Spec. MS1
N/X = 0.40

Spec. MS2
N/X = 0.45

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

2.48
2.56

373
376

3.81
3.85

42
49

1.51
1.54

314
318

2.62
2.66

382
373

56
63

1.58
1.61

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

1.74
1.78
1.82
1.84
1.86
1.88
1.90
1.91
1.94
1.96
1.98
2.03
2.07
2.09
2.14
2.19
2.25
2.32
2.39

368
377
390
386
420
433
429
457
470
464

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

3.41
3.48
3.56

Temperature Humidity
(t)
(RH)
(oC)

(%)

426
433

23.5
29.1

77
61

3.91
3.96

436
420

23.3
23.8

70

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

580
587
593
587
607
623
619
660

4.09
4.13
4.17
4.21
4.26
4.28
4.30
4.33
4.35
4.37
4.39
4.41
4.43
4.48
4.51
4.57
4.62
4.67
4.72
4.80
4.87

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

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

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

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

(%)
(x10-6)
0
0
1.80
50

Spec. MT3
N/X = 0.50
mMT3
MT3
(%)
(x10-6)
0
0
3.26
67

Temperature Humidity
(t)
(RH)
(oC)
28.8
28.2

(%)
56
57

3

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

1.56

82
94

2.41
2.51

107
123

3.76
3.84

140
162

31.2
30.7

51
52


12

Date

Spec. MT1
N/X = 0.40

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

108
192

2.60
2.64

144
244

3.90
3.96

21
28

1.70
1.74

255
265

2.72
2.76

323
316

35
42

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

252
280
322
364

1.87
1.92
1.96
2.01
2.04
2.08
2.13
2.16
2.17
2.19
2.21
2.23
2.25
2.27
2.29
2.30
2.34
2.38
2.40
2.45
2.50
2.56
2.64
2.72

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

3.21
3.25
3.30
3.31
3.33
3.36
3.38
3.40
3.42
3.44
3.46
3.51
3.55
3.57
3.63
3.68
3.74
3.81
3.89

Temperature Humidity
(t)
(RH)
(oC)

(%)

179
298

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

61
70

312
310
333
347
360
372
364
397
410
404
443
460
456
478
493
490
523
532
539
532
567
577
573
600

4.22
4.28

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

442
457
450
493
507
503
530
544
541
579
596
607
602
636
643
640
673

23.8
22.6
26.2
28.8
22.5
30.8
24.3
27.2
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
81
63
55
89
52
77
62
78
83
58
53
82
66
60
80
55

58
51
80
56
58
60
55

Table 2.12. Date of beginning ofobserved cracks in concrete specimens of Restrained Ring Test
Regular concrete
(BTT)

Specimen type
Time of
crack appearance
Date

CH1
6

CH2
6

CH3
6

Reinforced concrete fiber steel
(BTCST)
CH4
6

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

specimens. In the date of 364 of measurement, the experimental results of shrinkage strains of concrete were
from 610x10-6 to 700x10-6. Those resultsare quite high.
Experimental results of Restrained Ring Test indicated that the steel fiber had important role in
restriction of crack due to shrinkage. The steel fiber not only slow down the crack formation process but also
reduce the expansion of crack. As a result, the possibility of using steel fiber in reinforced concrete
structures, especially floor of industrial builds, floor of bridges, etc. to restrict the crack of concrete due to
shrinkage strains is high.

CHAPTER 3
TO ANALYZE AND EVALUATE THE EXPERIMENTAL
RESULTS
3.1. Analyzing and evaluating time-dependent compressive strength Rn(t) and Young Modulus E(t) of
two groups of concrete in natural climatic conditions (Group 1 - Regular concrete; Group 2 - Steel
fiber reinforced concrete)
3.1.1. Analyzing and evaluating time-dependent compressive strength Rn(t) of two groups of concrete
(Group 1 - Regular concrete; Group 2 - Steel fiber reinforced concrete)
According to the experimental results of time-dependent compressive strength of regular concrete
and steel fiber reinforced concrete, proposing the formulas and the experimental coefficients which indicate
the relation between the compressive strength Rn(t) and the compressive strength of 28 days based on thetotal
least-squares method (use the Solver tool in Microft Excel).
𝑡
𝑅𝑛 (𝑡) = 𝑅𝑛 (28)
3,08 + (0,89. 𝑡)
Table 3.1. The suggested results of compressive strength of concrete Rn(t)
(Group 1 - Regular concrete; Group 2 - Steel fiber reinforced concrete)
The average value Rn(t), MPa
Standard
deviation
7
28

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

Ratio
(N/X)

(3.1)


14
The average value Rn(t), MPa
7
28
60
90
180
270
days
days
days
days
days
days
(Group 2 - Steel fiber reinforced concrete)

364
days

Standard
deviation
(STD)

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

30.47

32.37

32.97

33.59

33.80

33.91

3.94

Specimens
group

Ratio
(N/X)

MS1-ĐX
MS2-ĐX
MS3-ĐX

Figure 3.1. The experimental results and

Figure 3.2. The experimental results and

suggested results of compressive strength of

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

60
90
180
270
364
(STD)
days
days
days
days
days
days
days
The suggested results of Young Modulus of concrete E(t) (Group 1 - Regular concrete)
M1-ĐX
0.40
25843 32045 33473 33914 34367 34520 34600
3142
M2-ĐX
0.45
23377 28988 30280 30679 31088 31227 31299
2842
M3-ĐX
0.50
20912 25931 27087 27443 27810 27934 27999
2542
The suggested results of Young Modulus of concrete E(t)
(Group 2 - Steel fiber reinforced concrete)
MS1-ĐX
0.40

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

2646


15

Figure 3.3. The experimental results and

Figure 3.4. The experimental results and

suggested results of Young Modulus of concrete

suggested results of Young Modulus of concrete

E(t) (Group 1- Regular concrete)

E(t) (Group 2 - Steel fiber reinforced concrete)

3.2. Comparison of time-dependent compressive strength Rn(t) and Young Modulus E(t) of two groups
of concrete in natural climatic conditions (Group 1 - Regular concrete; Group 2 - Steel fiber
reinforced concrete)
Table 3.3. The results of compressive strength of concrete Rn(t) between
Group 1 - Regular concrete and Group 2 - Steel fiber reinforced concrete

0.40

7
days
1.059

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

Ratio
(N/X)

RMS1 với RM1
RMS2 với RM2
RMS3 với RM3

1.053
1.055

1.050
1.052

270
days
1.047

364
days
1.046

1.050
1.052

1.047
1.049

Table 3.4. The results of Young Modulus E(t) between
Group 1 - Regular concrete and Group 2 - Steel fiber reinforced concrete
7

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

1.027
1.029

1.025
1.027

0.50

1.042

1.041

1.040

1.036

1.033

1.031

1.030

Specimens
group

Ratio
(N/X)

EMS1 với EM1

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)

Spec.
M1
M2
M3

𝑋̅

𝑌̅

𝑆12

𝑆22

𝑚1,2

𝑟

𝐵

𝐴

107,97 0,2336 9001.32 0.019 12.9791 0.99976 0.0014 0.0779
107,97 0,2090 9001.32 0.018 12.5949 0.99982 0.0014 0.0579
107,97 0,1904 9001.32 0.016 11.9143 0.99966 0.0013 0.0474

𝜀𝑐𝑠 (∞) (x10−6 )

𝛼𝑛

693.52

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)

Figure 3.7. Experiment and suggested results of

Figure 3.8. Experiment and suggested results of

time-dependent shrinkage strains of regular

time-dependent shrinkage strains of regular

concrete specimens M1

concrete specimens M2

Figure 3.9. Experiment and suggested results of time-dependent shrinkage strains of regular concrete
specimens M3


17
3.4. Comparison between the suggested prediction and Australian Standard AS 3600 and Forecast
model of Russian Concrete Institute

Figure 3.10. The shrinkage strain results of suggested prediction and AS 3600 and Forecast model of
Russian Concrete Institute
3.5. Evaluation of effect of ratio between water and cement N/X on shrinkage strains of 03 concrete
groups in standard climatic conditions of Gia Lai (Group 1 - Regular concrete; Group 2 - Steel fiber
reinforced concrete; Group 3 - Reinforced concrete)
3.5.1. Effect of ratio N/X on shrinkage strains of concrete specimens of group 1

Figure 3.11. Time-dependent shrinkage strains of

Figure 3.12. Relation between time-dependent

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

shrinkage strains and mass loss of concrete

concrete

specimens of Group 3 - Reinforced concrete

3.5.4. Evaluating effect of ration N/X on shrinkage strains of concrete (Group 1 - Regular concrete;
Group 2 - Steel fiber reinforced concrete; Group 3 - Reinforced concrete)
N/X ratio affects to the shrinkage strains of concrete dramatically. Increasing the ratio of N/X will
increase shrinkage strains of concrete. The possibility of crack in concrete structures depending on those
strains is high.
Dehydration of concrete depending on evaporation and hydration of cement is high in the early days
after concreting. Mass loss of concrete due to dehydration is proportional to shrinkage strain of concrete;
Reducing ratio of N/X is one of solutions to reduce the shrinkage strain of concrete. This should be
considered in the design process of concrete mix.
3.6. Shrinkage strains of concrete of Group 1 - Regular concrete, Group 2 - Steel fiber reinforced
concrete and Group 3 - Reinforced concrete in standard climatic conditions of Gia Lai

Figure 3.17. Time-dependent shrinkage strains of

Figure 3.18. Time-dependent shrinkage strains of

concrete specimens of Group 1 and Group 2

concrete specimens of Group 1 and Group 3

3.7. Shrinkage strains of concrete of Group 1 - Regular concrete, Group 2 - Steel fiber reinforced
concrete and Group 3 - Reinforced concrete in standard and natural climatic conditions of Gia Lai
3.7.1. Comparison of shrinkage strains of three groups of concrete with the same concrete mix design,

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

N/X of 0.4 in standard and natural climatic

N/X of 0.45 in standard and natural climatic

conditions of Gia Lai

conditions of Gia Lai


20

Figure 3.24. Time-dependent shrinkage strains of concrete specimens of three groups with ratio of N/X
of 0.50 in standard and natural climatic conditions of Gia Lai
3.8. Shrinkage strains of concrete of Group 1 - Regular concrete with same concrete mix design, same
ratio of N/X in standard and natural climatic conditions of Gia Lai
Table 3.6. The results of Shrinkage strains of concrete of Group 1 - Regular concrete with same
concrete mix design, same ratio of N/X in natural climatic conditions and standard of Gia Lai

1
2
3
4
5
6
7
14
21
28

N/X = 0.40

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

1.92
1.89
1.88
1.86
1.86
1.85
1.52

35
42

1.41
1.30

1.40
1.28

1.38
1.25

49
56

1.20
1.15

1.15
1.10

1.14

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

1.10
1.07
1.11
1.11

1.12
1.12
1.12
1.12
1.10
1.10
1.11
1.09
1.11
1.11

133

1.08

1.09

1.09

Date


21

140

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

1.10
1.10

N/X = 0.50
M3-ĐKTN/M3-ĐKC
1.12
1.11
1.09
1.11
1.11
1.11
1.09
1.11
1.10

322
364

1.08
1.09

1.07
1.10

1.07
1.10

Date

3.9. 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 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

N/X=0.45
M2 / MS2
0.00
1.33
1.15
1.15
1.15
1.17
1.18
1.18
1.20
1.21

N/X=0.50
M3 / MS3
0.00
1.30
1.14
1.14
1.15
1.16
1.16
1.18
1.19
1.20

N/X=0.40
M1/ MT1
0.00
1.57

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

1.35
1.38
1.39
1.40

35
42
49
56
63
70
77
84

1.24
1.25
1.24
1.24
1.21
1.21
1.21
1.21

1.23
1.22
1.21
1.21
1.19
1.18
1.18

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

1.43
1.44
1.42
1.41
1.42
1.41
1.38

91
98

1.26
1.18

1.20
1.16

1.17
1.14

1.50
1.46

1.48
1.40

1.41
1.35

105

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

154
168
182
196

N/X=0.40
M1/ MS1
1.14
1.14
1.15
1.14
1.12
1.11
1.11
1.10
1.11

N/X=0.45
M2 / MS2
1.13
1.13
1.13
1.12
1.11
1.12
1.10
1.09
1.10

N/X=0.50

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

1.26
1.22
1.21
1.21

N/X=0.50
M3 / MT3
1.28
1.27
1.27
1.26
1.24
1.24
1.20
1.17
1.17

224
252

1.13
1.10

1.10
1.10

1.07
1.06

1.24

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

1.09

1.08

1.07

1.20

1.19

1.14

Date

3.10. Evaluating the experimental results of shrinkage strains of regular concrete specimens and steel
fiber reinforced concrete specimens by Restrained Ring Test with ratio of N/X of 0.40

Figure 3.25. Time-dependent of strains of steel

Figure 3.26. Time-dependent of strains of steel

ring in case of regular concrete with ratio of N/X

ring in case of steel fiber reinforced concrete

of 0.40

with ratio of N/X of 0.40

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.

- After 21 days of casting, effect of steel fiber and reinforcement bar is smaller than the beginning
period of casting.

CONCLUSIONS AND RECOMMENDATIONS
1. Conclusions
The summaries of the thesis “An experimental study on shrinkage strains of concrete in standard
climatic conditions at Gia Lai” are listed below:
1. The thesis built the experimental data on the shrinkage strain of concrete using local aggregate in
climatic conditions of Gia Lai province. These data are used in practical design of reinforced concrete
structures.
2. The shrinkage of concrete in 364 days with several specimens of the ratio between water and
cement (N/X) of 0.40, 0.45 and 0.50 in standard climatic conditions of Gia Lai province (temperature of
25±20C and humidity of 75±5%) were measured. The results of experiment are used to determine the
experimental coefficients which could predict time-dependent shrinkage strains of regular concrete of
compressive strength of concrete B22.5 (M300#) in standard climatic conditions of Gia Lai province.
- With the ratio of N/X of 0.40:
𝜀𝑐𝑠 (𝑡) = 693,52. 10−6

𝑡
54,01 + 𝑡

- With the ratio of N/X of 0.45:
𝜀𝑐𝑠 (𝑡) = 714,68. 10−6

𝑡
41,41 + 𝑡

- With the ratio of N/X of 0.50:
𝑡
35,85 + 𝑡

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