水和反応モデルに基づく膨張コンクリートの力学的性質及び中性化深さの予測に関する研究
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言語: English
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公開日: 2021-06-23
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キーワード (En):作成者: グェン, ダック ヴァン
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https://doi.org/10.15118/00010396

Predicting Mechanical Properties andCarbonation Depth of Expansive Concrete Basedon Hydration Reaction Model
水和反応モデルに基づく膨張コンクリートの力学的性質及び中性化深さの予測に関する研究byNguyen Duc Van

A Dissertation Submitted in Partial Fulfillmentof the Requirements for the Degree ofDoctor of Philosophy

Division of Engineering
MURORAN INSTITUTE OF TECHNOLOGY
March 2021i

Abstract
Although expansive additives have been widely used to efficiently reduce shrinkage cracking in concrete,
little research has been undertaken to model the hydration reaction of cement and expansive additive blends
and to predict the properties and durability of expansive concrete.

In this study, a numerical model to simulate the hydration reaction of cement paste containing expansive
additive at an early age is proposed and then the compressive strength, carbonation depth, and expansion
strain of expansive concrete are predicted based on the hydration reaction model. Additionally, theinfluence of restrained conditions on the mechanical properties and durability such as frost resistance andcarbonation resistance are also investigated in this research. Using the proposed model, this study predicted
the hydration degree, rate of heat evolution, gel/space ratio, amount of calcium silicate hydroxide (CSH),
calcium hydroxide (CH), ettringite of hardening cement-expansive additive paste, and porosity of expansive
concrete. For the experimental investigation, the rate of heat evolution test, under-water weighing test,
length change ratio test, expansion strain test, compressive strength test, mercury intrusion porosimetry test,
freezing-thawing test and accelerated carbonation test were performed to verify the proposed model andpredicting equation. From the relationship between the gel/space ratio and compressive strength, anequation was deduced for the prediction of the development of compressive strength of expansive concrete.
Considering the diffusion of CO2 in a gaseous phase into the concrete pore and the reaction of CO2 with
CH and CSH, a mathematic model was proposed to predict the carbonation depth of expansive concrete. A
hypothesis was described to predict the expansion strain through a model of the volumetric change of
expansive concrete calculated by combining the formation of ettringite, influence coefficient of shrinkage,
and restraint degree coefficient.

For verification of the model and predicting equation, the results indicated good agreement of the calculated
data with the measured data. Furthermore, this work also found that the model parameters (in the hydration
reaction model) can be represented as a function of the mineral composition of the cement. A coefficient
was deduced to find the satisfactory value for predicted results (in predicting compressive strength). A
restraint degree coefficient was found to build an equation for predicting the expansion strain of expansive
concrete under restrained conditions. The results demonstrate that the proposed model and equation are
effective and useful in predicting the hydration, mechanical properties, and carbonation depth of expansive
concrete.

ii

Table of Contents
Abstract ........................................................................................................................................................ ii
Table of Contents ...................................................................................................................................... iii
List of Tables............................................................................................................................................. vii
List of Figures .......................................................................................................................................... viii
List of Chemical Notations ....................................................................................................................... xi
CHAPTER 1 INTRODUCTION .............................................................................................................. 2
1.1 Background ............................................................................................................................................ 2
1.2 Expansive additive.................................................................................................................................. 3
1.2.1 Type of expansive additive .............................................................................................................. 3
1.2.2 Hydration of expansive additive ...................................................................................................... 3
1.2.3 Mechanism of reduction in shrinkage crack using expansive additive ........................................... 4
1.3 Previous research .................................................................................................................................... 5
1.3.1 Influence of restrained condition on properties of expansive concrete ........................................... 5
1.3.2 Hydration reaction model ................................................................................................................ 6
1.3.3 Predicting the compressive strength .............................................................................................. 10
1.3.4 Predicting the carbonation depth ................................................................................................... 12
1.3.5 Predicting the expansion strain...................................................................................................... 13
1.4 Objective of Research........................................................................................................................... 15
1.5 Outline of thesis.................................................................................................................................... 16
References .................................................................................................................................................. 18
CHAPTER 2 MATERIAL AND EXPERIMENTAL INVESTIGATION .......................................... 22
2.1 Introduction .......................................................................................................................................... 22
2.2 Material ................................................................................................................................................ 24
2.2.1 Ordinary Portland Cement............................................................................................................. 24
2.2.2 Expansive Additive ....................................................................................................................... 24
2.2.3 Aggregate ...................................................................................................................................... 24
2.2.4 Admixtures .................................................................................................................................... 24
2.2.5 Water ............................................................................................................................................. 25
iii

2.3 Experimental Design ............................................................................................................................ 26
2.3.1 Design of Paste .............................................................................................................................. 26
2.3.2 Design of Concrete ........................................................................................................................ 26
2.4 Experimental Method ........................................................................................................................... 27
2.4.1 Cement Paste and Cement Paste mixed with Expansive Additive ................................................ 27
2.4.1.1 Calorimetry Test ..................................................................................................................... 27
2.4.1.2 Under-Water Weighing Test .................................................................................................. 28
2.4.1.3 Compressive Strength............................................................................................................. 29
2.4.2 Cement Concrete and Expansive Concrete ................................................................................... 29
2.4.2.1 Workability Test ..................................................................................................................... 29
2.4.2.2 Mercury Intrusion Porosimetry Test ...................................................................................... 29
2.4.2.3 Compressive Strength Test ..................................................................................................... 30
2.4.2.4 Length Change Ratio and Expansion Strain Test ................................................................... 30
2.4.2.5 Underwater Weighing Test..................................................................................................... 31
2.4.2.5 Accelerated Carbonation Test ................................................................................................ 31
2.4.2.6 Freezing - Thawing Test......................................................................................................... 32
2.5 Results and Discussion ......................................................................................................................... 33
2.5.1 Heat Evolution and Hydration Degree .......................................................................................... 33
2.5.2 Workability of concrete ................................................................................................................. 34
2.5.2 Porosity.......................................................................................................................................... 35
2.5.2.1 Paste ....................................................................................................................................... 35
2.5.2.2 Concrete.................................................................................................................................. 35
2.5.3 Compressive Strength.................................................................................................................... 38
2.5.3.1 Paste ....................................................................................................................................... 38
2.5.3.2 Concrete.................................................................................................................................. 39
2.5.4 Length Change Ratio and Expansion Strain .................................................................................. 40
2.5.5 Carbonation Depth ........................................................................................................................ 42
2.5.6 Frost Resistance............................................................................................................................. 43
2.6 Conclusion ............................................................................................................................................ 45
References .................................................................................................................................................. 46iv

CHAPTER 3 MODELING EARLY AGE THE HYDRATION OF CEMENT PASTE MIXED WITH
EXPANSIVE ADDITIVE ........................................................................................................................ 49
3.1 Introduction .......................................................................................................................................... 49
3.2 Hydration model ................................................................................................................................... 51
3.2.1 Model equation .............................................................................................................................. 51
3.2.2 Effect of mineral composition on the model parameters ............................................................... 55
3.3 Results and Discussion ......................................................................................................................... 57
3.3.1 Relationship between mineral composition and model parameters .............................................. 57
3.3.2 Verification of hydration model .................................................................................................... 59
3.4 Conclusion ............................................................................................................................................ 62
References .................................................................................................................................................. 63
CHAPTER 4 PREDICTING THE COMPESSIVE STRENGTH OF EXPANSIVE CONCRETE
BASED ON THE HYDRATION MODEL ............................................................................................ 67
4.1 Introduction .......................................................................................................................................... 67
4.2 Predicting the compressive strength ..................................................................................................... 69
4.2.1 Gel/space ratio ............................................................................................................................... 69
4.2.2 Relationship between cement paste strength and concrete strength .............................................. 70
4.3 Results and Discussion ......................................................................................................................... 72
4.3.1 Relationship between compressive strength of cement paste and gel/space ratio ......................... 72
4.3.2 Relationship between conversion coefficient and gel/space ratio ................................................. 73
4.4 Conclusions .......................................................................................................................................... 75
References .................................................................................................................................................. 76
CHAPTER 5 PREDICTING CARBONATION DEPTH OF EXPANSIVE CONCRETE BASED ON
HYDRATION REACTION MODEL..................................................................................................... 78
5.1 Introduction .......................................................................................................................................... 78
5.2 Predicting carbonation depth ................................................................................................................ 80
5.2.1 Calcium hydroxide ........................................................................................................................ 81
5.2.2 Calcium Silicate hydroxide ........................................................................................................... 83
5.2.3 Effective diffusion of CO2 in concrete and porosity of concrete................................................... 84
5.3 Results and Discussion ......................................................................................................................... 86v

5.3.1 Amount of calcium hydroxide and calcium silicate hydroxide ..................................................... 86
5.3.2 Porosity of concrete ....................................................................................................................... 88
5.3.3 Verification of prediction equation. .............................................................................................. 88
5.4 Conclusions .......................................................................................................................................... 90
References .................................................................................................................................................. 91
CHAPTER 6 PREDICTING EXPANSION STRAIN OF EXPANSIVE CONCRETE BASED ON
HYDRATION REACTION MODEL..................................................................................................... 94
6.1 Introduction .......................................................................................................................................... 94
6.2 Predicting expansion strain .................................................................................................................. 96
6.2.1 Production of ettringite .................................................................................................................. 96
6.2.2 Modeling of expansion strain ........................................................................................................ 97
6.3 Results and Discussion ......................................................................................................................... 99
6.3.1 Amount of ettringite ...................................................................................................................... 99
6.3.2 Verification of prediction equation ............................................................................................. 100
6.4 Conclusions ........................................................................................................................................ 103
References ................................................................................................................................................ 104
CHAPTER 7 CONCLUSIONS AND FUTURE WORK .................................................................... 106
7.1 Conclusions ........................................................................................................................................ 106
7.2 Future Works ...................................................................................................................................... 107
Acknowledgments .................................................................................................................................... 108

vi

List of Tables

Table 1.1 Type of expansive additive according to ACI standards [1.9] ..................................................... 3
Table 1.2 Hydration Reaction Model ........................................................................................................... 6
Table 2.1 Chemical composition and physical properties of materials ...................................................... 24
Table 2.2 Composition of materials ........................................................................................................... 24
Table 2.3 Properties of Aggregates ............................................................................................................ 25
Table 2.4 Mix Proportions.......................................................................................................................... 26
Table 2.5 Mix proportions .......................................................................................................................... 27
Table 2.6 Specification of MMC-511SV6 ................................................................................................. 28
Table 2.7 Test results of fresh concrete ...................................................................................................... 35
Table 2.8 Critical pore entry diameter (nm) ............................................................................................... 37
Table 2.9 Carbonation depth of concrete (mm).......................................................................................... 43
Table 3.1 Relative contribution of clinker compounds to heat of hydration (J/g) ...................................... 54
Table 3.2 Model parameters of Eqs. (3.9a)–(3.9d) at 20 ℃ ....................................................................... 57
Table 3.3 Equations showing relationship between mineral composition and model parameters ............. 59
Table 3.4 Coefficients for Arrhenius’ law.................................................................................................. 60
Table 5.1 Molar weight and molar volume of the main compounds found in Portland cement andPortland-based binders. .............................................................................................................................. 82
Table 5.2 Molar volume differences [5.8] .................................................................................................. 85
Table 5.3 Coefficient of predicting equation .............................................................................................. 89vii

List of Figures

Figure 1.1 Mechanism of reduction in shrinkage cracking using the EX. ................................................... 4
Figure 1.2 Schematic of relationship between mortar strength and expansion of the EX [1.13] ................. 4
Figure 1.3 Type of restrained condition ....................................................................................................... 5
Figure 1.4 Schematic of restrained condition ............................................................................................... 5
Figure 1.5 Compressive strength ratio of expansive concrete by restraining [1.14] .................................... 6
Figure 1.6 C-CBM model............................................................................................................................. 7
Figure 1.7 HYMOSTRUC model. ............................................................................................................... 8
Figure 1.8 Embedding of particles in the outer shell of hydrating particles [1.23]. ..................................... 8
Figure 1.9 The hydrating C3S particle at time t (Navi and Pignat model).................................................... 9
Figure 1.10 CEMHYD3D Model. ................................................................................................................ 9
Figure 1.11 Relationship between strength and gel/space ratio with different mix proposition [1.30]...... 11
Figure 1.12 Schematic of volumetric change of cement paste containing expansive additive [1.5]. ......... 13
Figure 1.13 Schematic of expansion strain and autogenous shrinkage strain [1.43]. ................................. 14
Figure 1.14 Framework of this thesis ......................................................................................................... 17
Figure 2.1 Plan process of Chapter 2 ......................................................................................................... 23
Figure 2.2 Isothermal Calorimetry Apparatus (MMC-511SV6) ................................................................ 28
Figure 2.3 Schematic of the underwater weighing test .............................................................................. 29
Figure 2.4 Schematic of the restrained mold for testing the pore structure and restrained compressive
strength ....................................................................................................................................................... 30
Figure 2.5 Schematic of the specimens measuring 100 × 100 × 400 mm3: (a) free condition and (b)restrained condition according to the JIS A 6202. ..................................................................................... 31
Figure 2.6 Schematic of the specimens measuring 75 × 75 × 400 mm3: (a) free condition and (b) restrained
condition. .................................................................................................................................................... 31
Figure 2.7 Accelerated Carbonation Chamber ........................................................................................... 31
Figure 2.8 Freezing-Thawing chamber ...................................................................................................... 32
Figure 2.9 Heat evolution: (a) w/b 0.3 and (b) w/b 0.5 .............................................................................. 33
Figure 2.10 Degree of hydration: (a) w/b 0.3 and (b) w/b 0.5.................................................................... 33
Figure 2.11 Rates of heat evolution of cement with and without EX against time at different curing
temperatures: (a) OPC100, (b) EX5, and (c) EX10.................................................................................... 34
Figure 2.12 Total porosity of hardened paste with different w/b ratios ..................................................... 35
Figure 2.13 Effect of the triaxial restrained condition on the pore size distribution of the cement andexpansive mortar under the restrained and unrestrained conditions with different w/b ratios: (a, b, c) test
results of OPC, EX20, and EX40 with w/b 0.3, respectively; and (d, e, f) test results of OPC, EX20, andEX40 with w/b 0.5, respectively. ............................................................................................................... 37
Figure 2.14 Schematic of the effect of chemical stress on the pore structure: (a) free condition and (b)triaxial restrained condition. ....................................................................................................................... 37
Figure 2.15 Relationship between the total porosity and EX contents under the unrestrained and triaxial
restrained conditions: (a) w/b ratio of 0.3 and (b) w/b ratio of 0.5 ............................................................ 38
viii

Figure 2.16 Compressive strength of Portland cement and cement-EX paste of different w/b ratio ......... 39
Figure 2.17 Relationship between the EX content and compressive strength of concrete under theunrestrained and restrained conditions: (a) w/b ratio of 0.3 and (b) w/b ratio of 0.5. ................................ 40
Figure 2.18 Length change ratio of concrete: (a, d) results of the sample measuring 75×75×400 mm3; (b,e) results of the sample measuring 100×100×400 mm3 (free standard); and (c, f) results of the sample
measuring 100×100×400 mm3 (JIS A 6202)............................................................................................. 41
Figure 2.19 Expansion strain of concrete: (a, d) test results of the sample measuring 75×75×400 mm3; (b,e) test results of the sample measuring 100×100×400 mm3 (free standard); and (c, f) test results of thesample measuring 100×100×400 mm3 (JIS A 6202) ................................................................................ 42
Figure 2.20 Comparison of the RDMs of cement and expansive concrete under the restrained andunrestrained conditions: (a) w/b ratio of 0.3 and (b) w/b ratio of 0.5. ....................................................... 44
Figure 3.1 Flow chart ................................................................................................................................. 50
Figure 3.2 Schematic of hydration reaction of a single OPC or EX particle.............................................. 51
Figure 3.3 Maximum amount of heat liberated by OPC and cement–EX blends. ..................................... 54
Figure 3.4 Hydration degree of mineral compositions [3.38]. ................................................................... 56
Figure 3.5 Changes detected in phase composition of the OPC paste at different periods of OPC hydration[3.39]. ......................................................................................................................................................... 56
Figure 3.6 Relationship between mineral composition and model parameters at w/b 0.3: (a) relationshipbetween B and C3S, (b) relationship between D and (C3A + C2S), and (c) relationship between kr and (C3S
+ C3A) at 20℃, respectively. ...................................................................................................................... 57
Figure 3.7 Relationship between mineral composition and model parameters at w/b 0.5: (a), (b), and (c)relationship between B and C3S at 5℃, 20℃, and 40℃, respectively; (d), (c), and (e) relationship between
D and (C3A + C2S) at 5℃, 20℃, and 40℃, respectively; (g), (h), and (i) relationship between kr and (C3S
+ C3A) at 5℃, 20℃, and 40℃, respectively. .............................................................................................. 58
Figure 3.8 Comparison of calculated and measured rates of heat evolution at 20 ℃: (a) OPC100, (b) EX5,(c) EX10, (d) EX15, and (e) EX20. ............................................................................................................ 60
Figure 3.9 Calculated and measured hydration degrees of cement with and without EX at 5℃, 20℃, and 40℃ at w/b 0.5: (a) OPC100, (b) EX5, and EX10. ........................................................................................ 61
Figure 3.10 Total comparison of calculated and measured hydration degrees........................................... 61
Figure 4.1 Flow chart ................................................................................................................................. 68
Figure 4.2 Unit volume of concrete [4.12] ................................................................................................. 70
Figure 4.3 Cross section S1-S2 [4.12] ......................................................................................................... 70
Figure 4.4 Schematic of damage of concrete: (a) normal concrete, (b) high strength concrete ................. 71
Figure 4.5 Gel/space ratio and compressive strength of OPC and EX pastes: (a) Portland cement paste, (b)Cement-EX paste........................................................................................................................................ 72
Figure 4.6 Fitting the calculated data to the Powers [20] data. .................................................................. 73
Figure 4.7 Relationship between ω and gel/space ratio. ............................................................................ 73
Figure 4.8 Relationship between compressive strength and gel/space ratio of expansive concrete. .......... 73
Figure 5.1 Flow chart ................................................................................................................................. 79
Figure 5.2 Comparison of calculated data and measured data of the amount of CH from OPC and EX... 86
Figure 5.3 Amount of calcium hydroxide .................................................................................................. 87
Figure 5.4 Amount of calcium silicate hydroxide ...................................................................................... 87ix

Figure 5.5 Comparison of calculated data and measured data of concrete porosity and paste .................. 88
Figure 5.6 Comparison of calculated data and measured data of carbonation depth of concrete .............. 89
Figure 6.1 Flow chart ................................................................................................................................. 95
Figure 6.2 Schematic of volumetric change of expansive concrete ........................................................... 97
Figure 6.3 Comparison of predicted data and measured data of ettringite content .................................... 99
Figure 6.4 Actual amount of ettringite ..................................................................................................... 100
Figure 6.5 Comparison of experimental data [6.10] and calculated data (according to Eq. 6.12). .......... 100
Figure 6.6 Time-dependent β coefficient ................................................................................................ 101
Figure 6.7 Comparison of author’s data (under restrained condition) and Choi’s data (unrestrained
condition) ................................................................................................................................................. 101
Figure 6.8 Comparison of predicted data and measured data................................................................... 102

xList of Chemical Notations

Compounds

Notation

Calcium dioxide (CaO)C

Silicon oxide (Si2O)

S

Alumina oxide (Al2O3)

A

Iron oxide (Fe2O3)

F

Sulfur oxide (SO3)S̅

Water (H2O)

H

Carbon dioxide (CO2)C̅

Tricalcium silicate (3CaO.SiO2)C3 S

Dicalcium silicate (2CaO.SiO2)C2 S

Tricalcium aluminate (3CaO.Al2O3)

C3 A

Tetracalcium aluminate (4CaO.Al2O3 Fe2O3)

C4 AF

Calcium sulfoaluminate (Ye’elimite)

C4 A3 S̅

(4CaO.Al2O3.3SO3)
Anhydrite (CaSO4)

CS̅

Gypsum (CaSO4.2H2O)CS̅H2Calcium silicate hydrate (3CaO.SiO2.H2O)

CSH

Calcium hydroxide Ca(OH)2

CH

Ettringite (6CaO.Al2O3.3SO3.32H2O)

C6 AS̅3 H32

Monosulfate (4CaO.Al2O3.SO3.10H2O)

C4 AS̅H10xi

CHAPTER 1
INTRODUCTION

1CHAPTER 1 INTRODUCTION
1.1 Background
Concrete is one of the construction materials and is the single most widely used throughout the work due
to its unique advantages such as high durability, high resistance to nature, and low cost. However, there aremany factors that affect the quality of concrete, where drying shrinkage is one of the unfavorable propertiesof concrete. Under the restrained conditions, the drying shrinkage causes an increase in tensile stress leading
to cracking, which dramatically affects the durability, architectural aesthetics, and service lifetime of thebuilding. Using the admixtures as one solution to prevent the crack caused by the drying shrinkage such as
expansive additive, shrinkage reducing agent, and limestone powder.

Nowadays, expansive concrete is widely used as an efficient way to either reduce and eliminate shrinkage
cracking. Expansive concrete is made by mixing the expansive additive with cement, water, aggregate(coarse and fine), and other admixtures, which increases the volume of concrete. The action of expanding
concrete is due to the production of ettringite or calcium hydroxide from the hydration reaction of expansive
additive with water [1.1]. In order to investigate the effect of expansive additive on the quality of concrete,
most previous studies have been carried out based on the experimental investigations. Thus, a question isposed here that is possible through a certain factor to build up a model to predict the change as well as thedevelopment of expansive concrete properties. From there, it is possible to evaluate the quality of theconcrete.

There are lots of researches [1.2-1.5] reported that hydration reaction of ordinary Portland cement (OPC)(or cement-based materials) is very important to be estimated since there is a great relation of hydration
with the microstructure of hardening cement-based materials, the development of strength, the carbonation,
the volumetric change and the expansion strain of concrete as well. It also means these properties ofconcrete could be predicted based on the hydration reaction of cement (or cement-based materials).
Therefore, in this study, a numerical model was proposed for simulation of the hydration reaction of cement
paste containing the expansive additive and then predicting the mechanical properties and carbonation
depth of expansive concrete based on its relationship with the hydration reaction of cement-expansive
additive (cement-EX) blends.

2

1.2 Expansive additive
1.2.1 Type of expansive additive
According to JIS A 6202 [1.7], an expansive additive (EX) is an admixture mixed with OPC and water,
producing the ettringite and calcium hydroxide (CH) from hydration reaction, which makes the concrete or
mortar expand. In Japan, the expansive additive has been made with the use of expansive cement, which ismanufactured by mixing expansive admixtures with concrete [1.8]. Therefore, expansive concretes of theJapanese type are widely used not only in shrinkage-compensating concrete but also in chemical prestressed
concrete which positively utilizes the expansibility of them. The expansive additive is divided into the
ettringite type and limestone type. Recently, the expansive additive combining ettringite type and limestone
type has been used.
Unlike the expansive concrete that developed in Japan. According to ACI standards [1.9], the expansive
cement is divided into four types as given in Table 1.1.

Type

Table 1.1 Type of expansive additive according to ACI standards [1.9]Compounds
Hydration products

K TypeCalcium sulfoaluminate (4CaO.3Al2O3.SO3)

Ettringite

Gypsum (CaSO4)
Lime (CaO)
S TypeTricalcium aluminate (3CaO. Al2O3)

Ettringite

Gypsum (CaSO4)
M TypeAluminous cement CaO.Al2O3

Ettringite

Gypsum (CaSO4)
O TypeLime (CaO)

Calcium hydroxide

1.2.2 Hydration of expansive additive
The main hydration products of expansive additive are the ettringite and CH [1.10]. The chemical reactionsof the expansive additive are described as shown in Eqs. (1.1a) and (1.1b).
C + H → CH

Eq. (1.1a)

6C + C4 A3 S̅ + 8CS̅ + 96H → C6 AS̅̅̅3 H32

Eq. (1.1b)

However, by the XRD quantitative analysis, Morioka et al. [1.11, 1.12] reported that the hydration productsof EX are not only Ettringite and CH, but also calcium sulfate (CaSO4.2H2O) and monosulphate (AFm)were observed. The results indicated that in the early stage of the reaction, the free-lime reacted faster thanthe hydration of Hauyne anhydrite. The results were also found that 2-2.5 molar of ettringite and gel were
produced by 1 molar of Hauyne.
31.2.3 Mechanism of reduction in shrinkage crack using expansive additive
Figure 1.1 shows the mechanism of reduction in shrinkage crack using the expansive additive. In the caseof Portland cement concrete, tensile stress is generated by restraining shrinkage and cracks develop if tensilestress exceeds tensile strength.
For expansive concrete, concrete mixed with an expansive additive that expands on the early age by theformation of ettringite and calcium hydroxide. The compressive force is introduced into the concrete by the
restrained condition during expansion. Subsequent tensile stress caused by the drying shrinkage will reducethese stresses. A residual compression will remain in the concrete, minimizing the risk of shrinkage
cracking.
M. Morioka [1.13] reported that to provide expansion effectively, the expansive additive should react inthe effective expansion periods which are periods II and III. The expansion is not useful with period I in
the fresh state, while expansive strain becomes small in period IV once sufficient strength has developed.
Figure 1.2 shows the relationship between mortar strength and expansion of expansive additive.

Figure 1.1 Mechanism of reduction in shrinkage cracking using the EX.

Figure 1.2 Schematic of relationship between mortar strength and expansion of the EX [1.13]

4

1.3 Previous research
1.3.1 Influence of restrained condition on properties of expansive concrete
In concrete structure, the restrained condition divided into two types (see Figure 1.3): Internal restraint due
to either reinforcement or aggregate; External restraint by some adjacent structural elements such as beam,column, etc.

RESTRAINTED CONDITION

Internal

Reinforcement

External

Adjacent structural elements:
Beam, Column,

Aggregate

Figure 1.3 Type of restrained condition

In order to evaluate the effect of restrained conditions on the properties of expansive concrete, Nguyen etal. [1.14] reported that the compressive strength of expansive concrete was enhanced by the restrained
conditions. However, the authors have mostly focused on the horizontal restrained condition (it called
uniaxial), as shown in Figure 1.4. In an actuarial concrete structure, the concrete could be restrained bythree directions (triaxial). Therefore, it is interesting to consider the effect of the restrained condition inthree directions.

Other directions?

Horizontal

Figure 1.4 Schematic of restrained condition [1.14]

Tsuji et al. [1.15] have studied the effect of the triaxial restrained condition on the properties of expansive
additive. The results showed that the compressive strength of expansive concrete higher than that of cement
concrete around 30%-50% under triaxial restrained conditions. However, the dosage of EX was a high level
about 80 and 90 kg of 1 m3 of concrete. Meanwhile, 20 kg of 1 m3 of concrete is as a standard amount ofexpansive additive [1.16].
5

Figure 1.5 Compressive strength ratio of expansive concrete by restraining [1.15]

Also, consider the effect of the confinement, Harada [1.17] found that the frost resistance of concrete could
be enhanced by the confinement. It concluded that under the restrained condition the mechanical propertiesof expansive concrete could be improved.

1.3.2 Hydration reaction modelOver the past few decades, several models have been built and developed to simulate the hydration reactionof cement or cement-based materials using various approaches, as shown in Table 1.2.

Table 1.2 Hydration Reaction Model
Hydration Reaction Model

Authors

TOMOSAWA’S MODEL

Fuminori Tomosawa(1997)The University of TokyoHYMOSTRUC

K. van Breugel(1991)

Delft University of Technology

DUCOM

Koichi Maekawa(1996)The University of Tokyo
Bentz and Garboczi

CEMHYD3D

National Institute of Standards and Technology
Ippei Maruyama

C-CBM (2003)

The University of Tokyo

In 1974, Tomosawa [1.18] proposed a kinetic model of Portland cement hydration. Based on Tomosawa’s
model, Maruyama [1.19] has developed and proposed a model of Portland cement hydration. In this model,
the volumetric changes of the cement particle, the chemically bound, and physically bound water were6

considered. Figure 1.6 shows the C-CBM model [1.19, 1.20] with three types of mode, “Mode 1” is thestate that the cement particle does not make contact with the surfaces of the cell, “Mode 2” is the state thatthe cement particle starts to make contact with surfaces of cell and the contacted parts have a circular shape,and “Mode 3” is the state that the cement particle makes contact with the surface of cell widely and thecontacted parts are connected each other.

Water and pore

t=0

CementPoret=Hydration productt= +Figure 1.6 C-CBM model [1.19, 1.20].
Park [1.21] designed a microstructural hydration model of Portland cement that considered the reductionin the hydration rate that occurs due to the interfacial area of contact between the free water and thehydration products. A hydration model of slag-cement blends was proposed by Wang [1.22], this model
has considered the production of calcium hydroxide in cement hydration and its consumption in the slag
reaction.
Mongkhon Narmluk et al. [1.23] investigated the effect of fly ash on the hydration kinetics of cement in
low water to binder (w/b) fly ash-cement at different curing temperatures using the modified shrinkingcore model. The results show that, at 20℃ and 35℃, the fly ash retards the hydration of cement in the early
period, but accelerates the hydration of cement in the later period. However, at 50℃, the fly ash retards thehydration of the cement at a later period when using high replacement ratios.
K. van Breugel [1.2] built a computer-based model, called HYMOSTRUC, the acronym for HYdration,
MOrphology and STRUCture formation as shown in Figure 1.7, where grey color is unhydrated cement,
the red color is inner hydration products, and the yellow color is outer hydration products. This model has
been presented for the kinetics of hydration and structural formation of cement-based materials. The
hydrating cement particles are represented as expanding spheres to be shown in Figure 1.8. The model cansimulate the development of properties of cement-based materials such as the development of hydrationand microstructure, the volume changes of the hardened cement pastes, and the effect of geometricalchanges of the microstructure on the creep of the hardened concrete.

7Figure 1.7 HYMOSTRUC model [1.2].

Figure 1.8 Embedding of particles in the outer shell of hydrating particles [1.24].

Based on the HYMOSTRUC model, Xian Liu et al. [1.25] have developed a computational materials model
to simulate the formation of microstructure in materials containing limestone powder. He reported that withthe proceeding of hydration the limestone powder has a decreasing influence on the microstructure andcould obstruct somewhat the formation of a denser microstructure at later hydration stage.
Maekawa et al. [1.26] have modeled the concrete performance that covers microstructure, hydration,
temperature, moisture content, state of equilibrium, mechanical strength, and volumetric change through a
computational simulation model called DuCOM (Durability of Concrete Model).
P. Navi and C. Pignat [1.27] developed a 3-D computer model for simulating the hydration andmicrostructure development of C3S pastes with or without small inert grains during hydration based on“Integrated Particles Kinetics Model”. In this research, the pore volume and the contact surfaces between
8the hydrated particles and the inert grains are calculated. The influences of the inert grains on the overall
degree of hydration and the total contact surfaces, and on the setting time of the hydrated cement are shown.
He reported that when 1 cm3 C3S dissolves, it produces 1.7 cm3 CSH and 0.6 cm3 CH. The part of CSH isdivided into two parts: 1 cm3 inner CSH and 0.7 cm3 outer CSH as shown in Figure 1.9.

Figure 1.9 The hydrating C3S particle at time t (Navi and Pignat model [1.27]).

The computer model CEMHYD3D was originally developed in NIST by Bentz and Garboczi to represent
the hydration process of Portland cement two-dimensionally. D.P. Bentz [1.28] has simulated the Portland
cement hydration and microstructure development using a three-dimensional computer model as shown in
Figure 1.10. The computer model was used to simulate the development of microstructure, hydration degree,
and to predict the compressive strength. Based on CEMHYD3D, D.P. Benzt [1.29] modeled the influenceof limestone filler on cement hydration. In this paper, the CEMHYD3D computer model has been modified
to consider the influence of limestone substitutions, the effects of various limestone substitutions onachieved a degree of hydration, microstructure, and strength development was predicted.

Figure 1.10 CEMHYD3D model [1.28].

9

Chen Wei [1.30] simulated the hydration of Portland cement paste using Van Eijk’s Model. In this research,
the computer model CEMHYD3D is extended based on the version developed by Van Eijk for simulating
the hydration of slag cement. The author reported that the extended model is able to simulate the hydration
process of slag cement paste in a precise way and can be used to predict various properties of the hydrating
paste. In addition, the simulated microstructure can be used to evaluate some durability-related propertiesof slag cement concrete.

1.3.3 Predicting the compressive strength
In general, there exists a fundamental inverse relationship between porosity and strength of solids [1.31].
This relationship can be described by the expression.
𝑆 = 𝑆0 ∙ 𝑒 −𝑘𝑝

Eq. (1.2)

where
S is strength of the material which has a given porosity p;
𝑆0 is intrinsic strength at zero porosity;
k is constant.
In addition, many studies also have reported the relationship between the gel/space ratio and strength [1.31,
1.32]. A gel/space ratio is defined as the ratio of the volume of the hydrated cement paste to the sum of thevolumes of hydrated cement and of the capillary pore, also called the amount of solid fraction in the system,
which is therefore equal to 1-porosity [1.31]. Powers [1.31] found that the 28-day compressive strength 𝑓𝑐
of three different mortar mixture was related to the gel/space ratio. Figure 1.11 shows the relationshipbetween the compressive strength and gel/space ratio. From this figure, he suggested a compressive strength
equation as a function of gel/space ratio as shown in Eq. (1.3).
𝑓𝑐 = 243𝑥𝐶3

Eq. (1.3)

where
𝑥𝑐 is the gel/space ratio, 243 is the value of intrinsic strength of mortar at zero porosity.

10Figure 1.11 Relationship between strength and gel/space ratio with different mix proposition[1.31].
Ryshkewitch [1.33] and Schiller [1.34] have suggested an equation as shown in Eqs. (1.4) and (1.5) thatshow the relationship between the strength and porosity of low porosity case.
𝑓𝑐 = 𝑓0 ∙ 𝑒 −𝐵𝑃

Eq. (1.4)

𝑓𝑐 = 𝐶 ∙ ln⁡(𝑃𝑐𝑟 /𝑃)

Eq. (1.5)

where,
𝑓𝑐 is the compressive strength of a hardened cement paste;
P is the porosity;
𝑓0 is the strength of the hardened cement paste at zero porosity;
𝑃𝑐𝑟 is the porosity of the hardened cement paste at zero strength;
B and C are material constants.

Based on the equation of Ryshkewitch and Schiller, Choi et al. [1.16] have assumed that the developmentof compressive strength of cement paste with an expansive additive was closely related to the pore volume
based on the results of the existing studies as shown in equation (1.6) and (1.7). The coefficient of eachporosity was referred to the existing studies of Maruyama [1.19] and Katsura [1.35].
𝑓𝑐 = 182 ∙ 𝑒 −5.215𝑃 : 0.3 > 𝑃

Eq. (1.6)

𝑓𝑐 = 73 ∙ ln⁡(0.523/𝑃): 0.3 ≤ 𝑃

Eq. (1.7)

Similar to the suggestion of Powers, Wang X.Y. [1.36] evaluated the compressive strength of PortlandLimestone cement by using the gel/space ratio, 𝑥𝑓𝑐 , of concrete can be calculated as follows:

11

𝑥𝐶 =

2.06(1/𝜌𝐶 ) 𝐶 𝐶0
(1/𝜌𝐶 ) 𝐶 𝐶0 + 𝑊0

Eq. (1.8)

where𝜌𝐶 is specific gravity of cement;
𝐶 is hydration degree;

𝐶0 and 𝑊0 are the mass fractions of OPC and water in the mix proportions, respectively.
2.06 is the volume increase rate of OPC paste or also known that 1 ml of hydrated cement occupies
2.06 ml [1.37].

Lam L. et al. [1.32] introduced a model to describe the relationship between the w/c ratio and the degree ofhydration and the gel/space ratio of high-volume fly ash/cement systems. The gel/space ratio of Fly ash –Cement (FC) paste, evaluated based on the proposed model, were found to be consistent with the gel/spaceratio of Portland cement (PC) paste in terms of the relationship with compressive strength. However, thehydration degree of FC and PC paste was obtained by determining the non-evaporable water content.
The relationship between compressive strength and porosity for porous concrete was investigated by Lian
C. et al. [1.38] through a new model, which was derived from Griffith’s theory. The predicted results show
a better agreement with the experimental data for porous concrete.

1.3.4 Predicting the carbonation depth
Papadakis et al. [1.39, 1.40] described the physicochemical processes of concrete carbonation, thenproposed and developed a simple mathematical model for the evolution of carbonation in time. The
chemical reaction of carbonation and parameters such as the ambient concentration of CO2, the molar
concentrations of the carbonate constituents (CH and CSH), and the effective diffusivity of CO2 incarbonated concrete were considered in the mathematical model, as described in Eq. (1.9) and (1.10).

2De,CO2 [CO2 ]0
xc = √
・√t[CH] + 3[CSH]
a

εc
RH b
De,CO2 = A ()) (1 −
C
P
W
100
+
+
ρc ρp ρw

where,xc (cm) is the carbonation depth;t (week) is the time to expose specimen in carbonation condition;
De,CO2 (m2/s) is the effective diffusivity of CO2 in carbonated concrete;[CO2 ]0 (％) is the CO2 content in the ambient air at the concrete surface, [CO2 ]0 = 5%;
12Eq. (1.9)

Eq. (1.10)

[CH] and [CSH] (mol) are the molar concentrations of Portlandite and Calcium silicate hydrate;
RH (%) is the ambient relative humidity;
ρc , ρp , and ρw (kg/m3) are the density of cement, supplementary cementing materials, and water,
respectively;
C, P, and W is the cement, supplementary cementing materials (silica fume or fly ash) and water content
in 1 m3 of fresh concrete;εc (%) is the porosity of concrete.
Based on the mathematical model for the evolution of concrete carbonation and combined the numericalmodel for the hydration reaction, X-Y Wang et al. [1.41] proposed a numerical model that can predict the
carbonation of concrete containing the low-calcium fly ash. In this model, the parameters were calculated
by considering the time dependence of the hydration reaction of cement.

1.3.5 Predicting the expansion strain
Choi et al. [1.5] modeled the volumetric change of concrete mixed with an expansive additive by the balance
between the shrinkage of OPC and the expansion of the expansive additive, as shown in Figure 1.12. By
assuming that the shrinkage of cement is caused by the capillary tension and taking into account the
behavior of the moisture inside the pore structure and the pore size distribution of hardened cement paste,
the shrinkage of cement was modeled. Meanwhile, the expansion of the EX was modeled by considering
the volumetric change of the EX-particles caused by an increase in the outermost layer of particles of thehydration products that were formed at an early age.

Figure 1.12 Schematic of volumetric change of cement paste containing expansive additive [1.5].

Similar to the assuming of Choi et al. [1.5], Miyazawa [1.42] reported that the expansion strain of expansive
concrete was modeled by considering the expansion strain of the expansive additive and autogenous
shrinkage of cement, as described in Figure 1.13.

13

Figure 1.13 Schematic of expansion strain and autogenous shrinkage strain [1.43].

14

1.4 Objective of Research
The aim of the research is to model the hydration reaction of cement paste mixed with an expansive additiveat an early age and then predict the mechanical properties and carbonation of expansive concrete based on
the hydration reaction model.
From these aims, the objectives of the research in this thesis can be listed as follows:•

To propose a numerical model to simulate the early age hydration reaction of cement paste mixed
with expansive additive.

•

To propose an equation for the prediction of the development of compressive strength of
expansive concrete.

•

To predict the expansion strain of expansive concrete.

•

To predict the carbonation depth of expansive concrete.

15

1.5 Outline of thesis
The research framework of this thesis is presented in Figure 1.14. The thesis is organized into 7 chapters,
and the contents are briefly summarized as follows:

Chapter 1 covers the introduction, including the background of the research, information of expansive
additive, previous researches, and the objective of the research.

Chapter 2 contains materials used and experimental investigation in this work. The results of this chapter
will be used to verify the results of the proposed model and predicting equation in this research. Especially,
the effect of restrained conditions on the mechanical properties, carbonation resistance, and frost resistanceof expansive concrete is also presented in this chapter.

Chapter 3 presents a hydration model that describes the hydration reaction that occurs when the expansive
additive is mixed with cement at an early stage. The effect of curing temperature on the model parameters
is considered. Besides, the relationship between the model parameters and the compound of cement isdeduced and explained in detail.

Chapter 4 presents an equation to predict the compressive strength of expansive additive by considering
the gel/space ratio and compressive strength. The relationship between the compressive strength of cement
pastes and concrete is discussed. A conversion coefficient is deduced to find a satisfactory value forpredicted data.

Chapter 5 deals with the mathematical model for predicting the carbonation depth of cement concrete andexpansive concrete. The value of parameters in this model will be calculated based on the hydration reaction
model.

Chapter 6 focuses on the production of ettringite and calcium hydroxide from the hydration reaction ofboth cement and expansive additive. This is the main key for predicting the expansion strain of expansive
concrete. Besides that, the balance between the shrinkage of cement and the expansion of expansive additive
is considered. The coefficient of the restraint degree is discussed and used as a parameter in this model.

Chapter 7 summarizes the main findings of the research and suggestion for future works are presented.

16

Chapter 1 Introduction
Background, previous research, objective of research, thesis outline

Chapter 2 Materials and Experiments• Material used; Mix proportions; Testing;• Effect of restrained condition on mechanical properties, frost resistance and carbonation resistance of expansive concrete;• Results and Discussion

Chapter 3 Modeling the early age the hydration reaction of cement paste mixed with expansive additive• Hydration model• Effect of curing temperature on model parameters• The relationship between model parameters and compound of cement

Chapter 4 Predicting thecompressive strength of expansive
concrete based on hydration
reaction model• Gel/space ratio• The relationship between strengthof cement and concrete• Predicting equation

Chapter 5 Predicting thecarbonation depth of expansive
concrete based on hydration
reaction model• Mathematic model• Relationship between model
parameters and hydration model

Chapter 6 Predicting the expansion
strain of expansive concrete basedon hydration reaction model• Amount of CH and CSH• Balance of shrinkage of cement
and expansion of EX• Predicting equation

Chapter 7 Conclusions
Conclusions; Future works

Figure 1.14 Framework of this thesis

17References[1.1] Recommended practice for expansive concrete, Concrete library of JSCE No.23 (1994).
[1.2] K. van Breugel, Simulation of hydration and formation of structure in hardening cement-basedmaterials. Doctoral thesis, Delft University of Technology (1991).
[1.3] X. Liu, G. Ye, G. De Schutter, Simulation of the microstructure formation in hardening selfcompacting cement paste containing limestone powder as filler via computer-based model, Materials andStructures 46 (2013) pp 1861-1879.
[1.4] X-Y. Wang, H-S. Lee, Model for predicting the carbonation depth of concrete containing lowcalcium fly ash, Construction and Building Materials 23 (2009) pp 725-733.
[1.5] Choi H., Choi H., Lim M., Noguchi T., Kitagaki R., Modeling of volume changes of concrete mixed
with expansive additives, Construction and Building Materials 75 (2015), pp 266-274.
[1.6] Choi H., Noguchi T., Modeling of Mechanical Properties of Concrete Mixed with Expansive
Additive. International Journal of Concrete Structures and Materials, Vol.9, No.4, pp.391-399, December
2015.
[1.7]. JIS A 6202, Expansive Additive for Concrete (Amendment 1), Japanese Industrial Standard
Committee (2008).
[1.8] Nagataki S., Gomi H., Expansive admixtures (mainly etrringite), Cement and Concrete Composites,
20, pp 163-170, 1998.
[1.9] ACI Committee 223: Expansive cement concretes - Present state of knowledge. ACI Journal, pp.
583-610, August 1970.
[1.10] Hyeonggil Choi, A study on the macro prediction of shrinkage-reduction behavior in concrete
using expansive additive. Doctoral thesis, The university of Tokyo (2013). (in Japanese)[1.11] M. Morioka, H. Hagiwara, E. Sakai, M. Daimon, Hydration reaction of thecalciumshulphoaluminate-type expansive additive, Cement and Science and Concrete Technology 52(1998) pp 2-7. (in Japanese).
[1.12] M. Morioka, H. Hagiwara, J-K. Kang, Y. Ohba, E. Sakai, M. Daimon, Hydration ofCalciumsulphoaluminate type expansive containing excess free-lime, Journal of the society of inorganic
material, Japan 7 (2000) pp 99-106.
[1.13] T. Higuchi, M. Eguchi, M. Morioka, E. Sakai, Hydration and properties of expansive additive
treated high temperature carbonation. Cement and Concrete Research. 64 (2014), pp.11-16.
[1.14] Nguyen T.B.T.; Chatchawan R.; Saengsoy W.; Tangtermsirikul S.; Sugiyama T. Influences ofdifferent types of fly ash and confinement on performances of expansive mortars and concretes, Constr.
Build. Mater. 2019, 209, 176-186.
[1.15] Y. Tsuji, H. Maruyama, A fundamental study on effect of restraint method on mechanicalproperties of expansive concrete. Proceedings of the 6th Annual Conference on Concrete Engineering,
1984, 86, 341-344.
[1.16] H. Choi, T. Noguchi, Modeling of Mechanical Properties of Concrete Mixed with Expansive
Additive, International Journal of Concrete Structure and Materials, Vol.9, No.4, December 2015,
pp.391-399.
[1.17] A. Harada, Effect of rebar restraint on the length change of freeze-thaw behavior and deteriorationof frost damage of concrete structure. Master’s thesis (2007), Muroran Institute of Technology.
18

[1.18] Tomosawa F., Hydration Model of Cement, Cement Technology Annual Report 28 pp.53-57,
1974.
[1.19] Maruyama I., Time dependent property of cement-based materials on the basis of microstructure
mechanics, Doctorate Thesis University of Tokyo, Japan, March 2003 (in Japanese).
[1.20] Maruyama I., Matsushita T., Noguchi T., Numerical modeling of Portland cement hydration.
International RILEM symposium on concrete modelling- CONMOD’08 (2008) Delft, the Netherlands.
[1.21] Park, K.B., Jee, N.Y., Yoon, I.S., Lee, H.S., Prediction of Temperature Distribution in HighStrength Concrete Using Hydration Model, ACI Materials Journal (2008) 105:180-186.
[1.22] Wang, X.Y., Lee, H.S., Park, K.B., Kim, J.J., Golden, J.S., “A Multi-Phase Kinetic Model to
Simulate Hydration of Slag-Cement Blends,” Cement and Concrete Composite 32 (2010).
[1.23] Narmluuk, M., Nawa, T., Effect of Fly Ash on the Kinetics of Portland Cement Hydration at
Different Curing Temperatures, Cement and Concrete Research 41 (2011) 579-589.
[1.24] Lossier, H., The self-stressing of concrete by expanding cements, 1948.
[1.25] Xian Liu, Guang Y., Geert D. S., Yong Y., Simulation of the microstructure Formation inHardening Self-Compacting Cement Paste Containing Limestone Powder as Filler via Computer-Based
Model. Materials and Structures, 46 (11), pp. 1861-1897, 2013.
[1.26] Maekawa et al., Koichi Maekawa, Rajesh Chaube and Toshiharu Kishi. Modelling of Concrete
Performance: Hydration, Microstructure Formation and Mass Transport, 1999.
[1.27] P. Navi, C.Pignat, Simulation of cement hydration and the connectivity of capillary pore space,
Advanced Cement Based Material 4 (2) (1996) 58-67.
[1.28] D.P. Bentz, Three-dimensional computer simulation of cement hydration and microstructuredevelopment J Am Ceram Soc, 80 (1) (1997), pp. 3-21.
[1.29] D.P. Benzt, Modeling the influence of limestone filler on cement hydration using CEMHYD3D,
Cement and Concrete Composites, Vol. 28, Issue 2, Feb 2006, pages 124-129.
[1.30] Chen Wei, Hydration of slag cement: Theory, Modeling and Application, (Doctorate thesis) The
University of Twente, January 2007.
[1.30] [1.31] P. Kumar Mehta, Paulo J. M. Monteiro, “Concrete: Microstructure, Properties, andMaterials,” Fourth Edition.
[1.32] Lam L., Wong Y.L., Poon C.S., Degree of hydration and gel/space ratio of high-volume fly
ash/cement systems. Cement and Concrete Research 30 (2000) 747-756.
[1.33] Ryshkewitch, E. (1953). Composition and strength of porous sintered alumina and zirconia.
Journal of the American Ceramic Society, 36, 65–68.
[1.34] Schiller, K. K. (1958). Mechanical properties of non-metallic materials (pp. 35–50). London, UK:
Butterworths[1.35] Katsura O., Morimoto J., Nawa T., A Model of Strength development considering hydration of
cement. Proceeding of the Japan Concrete Institute, 39, 109-114.
[1.36] Wang, Modeling of Hydration, Compressive Strength, and Carbonation of Portland-Limestone
Cement (PLC) Concrete. Materials, 10, 115, 2017.
[1.37] A. M. Neville, “Properties of Concrete”, Fourth Edition.

19[1.38] Lian C., Zhuge Y., Beecham S., The Relationship Between Porosity and Strength for Porous
Concrete. Construction and Building Materials, 25, pp 4294-4298, 2011.
[1.39] V.G. Papadakis, M.N. Fardis, C.G. Vayenas, Effect of composition, environmental factors andcement-lime mortar coating on concrete carbonation. Materials and Structures 25 (1992) pp 293-304.
[1.40] V. G. Papadakis, Effect of supplementary cementing materials on concrete resistance against
carbonation a chloride ingress. Cement and Concrete Research Volume 30, (2000) pp 291-299.
[1.41] X.Y. Wang, H.S. Lee, A model for predicting the carbonation depth of concrete containing lowcalcium fly ash. Construction and Building Materials 23 (2009) pp 725-733.
[1.42] Shingo Miyazawa, JCI-RILEM International Workshop, Concrack5, April 24-26, 2017, Japan

20

CHAPTER 2
MATERIALS AND EXPERIMENTALINVESTIGATION

21

CHAPTER 2 MATERIAL AND EXPERIMENTAL INVESTIGATION

2.1 Introduction
Concrete has a major unfavorable property, which is drying shrinkage [2.1]. The cracks caused by drying
shrinkage leads to reduced strength and durability and increased risk of corrosion. To address this problem,
expansive concrete is widely used to efficiently prevent the shrinkage cracks. Expansive concrete is
nowadays made in two ways. The first method is using expansive cement to make expansive concrete. The
second approach is using an expansive additive as a cement replacement material to make expansive
concrete. The latter method has been widely used in Japan and Thailand [2.2]. According to the American
Concrete Institute standard [2.3], three kinds of expansive cement are available: K, M, and S types.
According to the JIS A 6202 [4], an expansive additive is an admixture that reacts with water and makes
the concrete expand due to the production of ettringite and calcium hydroxide from the hydration reaction.
Expansive concrete has been applied to slabs, pavements, shrinkage-compensating concrete structures, etc.
[2.5]. Considerable laboratory research on the mechanical properties and durability of expansive concrete
has been undertaken. However, these experiments were performed under unrestrained (free) conditions(e.g., compressive strength, accelerated carbonation, and freezing–thawing tests). In an actual concrete
structure, the expansive concrete is usually restrained by reinforcement, connecting members, foundation,etc. Therefore, the behavior of expansive concrete under restrained conditions must be investigated in alaboratory.
Several studies were conducted to investigate the effect of restrained conditions on the expansive concrete
properties. Tsuji et al. [2.6] reported that the compressive strength of expansive concrete was higher thanthat of cement concrete by approximately 30%-50% under a restrained condition. The amount of expansive
additive (EX) was used at a high level, which was approximately 80 kg/m 3 of concrete. However, as astandard amount in Japan, EX is known as 20 kg/m3 of concrete. Similar to the results reported by Nguyen
et al. [2.2], Tsuji et al. [2.6] also reported that the compressive strength of expansive concrete could be
improved by confinement. However, the expansive concrete confinement was only restrained by thehorizontal directions and did not consider the vertical directions. Considering the effect of restrained
conditions, Harada [2.7] found that the frost resistance of the restrained concrete was enhanced comparedto that of the unrestrained conditions for cement concrete. Furthermore, Colin et al. [2.8] found a decreasein the size of the large pores of expansive cement paste under uniaxial restrained conditions. Note that mostof these works only focused on the mechanical behavior of expansive concrete under uniaxial restrained
conditions. Meanwhile, an experimental study on the effect of both uniaxial and triaxial restrained
conditions on the mechanical properties and durability of expansive concrete has not yet been established.
The aim of this chapter are: firstly, to presents the information of materials, mix proportions of pates andconcrete, and test method, which were used in this study; secondly, to understand the effect of expansive
additive on the properties of paste and concrete and use the results of this chapter as a way to verify thecalculated data that will be presented in Chapter 3, Chapter 4 and Chapter 5; finally, to investigate the effect22

of a restrained condition on the mechanical properties, carbonation depth, and frost resistance of expansive
concrete at different water-binder (w/b) ratios and grasp these effects to obtain a correct assessment of theexperiments on expansive concrete in a laboratory.
Chapter 2Materials and Experimental Investigation

Materials, Mix Proportions, Test Methods

PastesConcrete➢ Isothermal Calorimetry➢ Under-water Weighing➢ Compressive strength➢ Workability➢ Under-Water Weighing➢ MIP➢ Compressive Strength➢ Length change ratio and Expansion strain➢ Accelerated Carbonation➢ Freeze and Thaw
Investigating the effect of restrained condition

Results and Discussion

Conclusion

Figure 2.1 Plan process of Chapter 223

2.2 Material
2.2.1 Ordinary Portland Cement
In this study, Ordinary Portland Cement (OPC) was used as compliance with Japanese Industrial Standards(JIS) and was introduced into the matrix in pastes and concrete. Table 2.1 shows the chemical compositions
and physical properties of OPC. Table 2.2 shows the mineral composition of OPC. The composition of
OPC were calculated using the Bogue equation [2.9], as shown in Eqs. (2.1a) - (2.1d).
C3 S = 4.07(CaO) − 7.60(SiO2 ) − 6.72(Al2 O3 ) − 1.43(Fe2 O3 ) − 2.85(SO2 )(Eq. 2.1a)

C2 S = 2.87(SiO2 ) − 0.75(3CaO. SiO2 )(Eq. 2.1b)

C3 A = 2.65(Al2 O3 ) − 1.69(Fe2 O3 )(Eq. 2.1c)

C4 AF = 3.04(Fe2 O3 )(Eq. 2.1d)Material
OPC
EX

Table 2.1 Chemical composition and physical properties of materials
Chemical composition (mass, %)Density(g/cm3)
SiO2
Al2O3
Fe2O3
CaO
MgO
SO3

Blain
(cm2/g)

21.4
1.8

3.15
3.05

3490
3260

5.5
5.4

2.9
0.9

64.3
67.0

1.5
-

2.0
19.6

Table 2.2 Composition of materials
Composition, (mass,%)
Material
OPC
EX

C3S (%)

C2S (%)C3A (%)

C4AF (%)

f-CaO

Ye’elimite

CaSO4

50.33
-

23.41
8.0

9.51
-

8.92
3.3

45.4

9.2

31.4

2.2.2 Expansive Additive
Calcium Sulphoaluminate (CSA) – type expansive additive (EX) was used in this study. The chemicalcomposition and physical properties, and composition of expansive additive are given in Table 2.1 andTable 2.2, respectively. The composition of EX (see Table 2.2) were obtained from the report made by
Takayuki Higuchi et al. [2.10].

2.2.3 Aggregate
For concrete mixes, the JIS standard aggregate (coarse and fine aggregates) was used in this research. The
properties of the fine and coarse aggregates are given in Table 2.3.

2.2.4 Admixtures
An AE water-reducing agent (Master Pozzolith No. 70), high-performance water-reducing agents, and an
AE agent (Master Air 404) were used to control the concrete workability and air content.

24

2.2.5 Water
Tap water of Muroran Institute of Technology was used as the mixing water for paste and concrete in this
work.

Tests

Table 2.3 Properties of Aggregates
Aggregates
Fine

CoarseSieve Analysis% PassingNo. of Sieve (mm)
5

100

2.5

93

1.2

72

0.6

46

0.3

20

0.15
Fine Modulus

3
2.5

-

Density (g/cm3)

2.68

2.68

Absorption (%)

1.78

2.17

25

Maximum size: 20 mm

2.3 Experimental Design
2.3.1 Design of Paste
For cement and cement-expansive additive (cement-EX) paste, two series of the sample were considered.
The mixture proportions for each were summarized in Table 2.4. In series 1, the EX replacement levels
were 0%, 5%, 10%, 15%, 20%, and 100%. The water-to-binder (w/b) ratios were 0.3 and 0.5. The energy
generated during the hydration of OPC and cement–EX was measured using a multi-micro calorimeter(MMC-511 SV) at 20 °C for 72 h and these values were used to determine the hydration reaction rate. In
order to evaluate the effect of the curing temperature on the hydration reaction model, the energies
generated during the hydration of OPC100, EX5, and EX10 were also measured at different curing
temperatures (5, 20, and 40 °C) at w/b 0.5. In series 2, the blended cement mixes contained 0% and 5% EX
cement replacement by weight; the w/b ratios were 0.3, 0.4, and 0.5. The gel/space ratio was calculated
from the porosity of OPC and the cement–EX paste, wherein the porosity was determined by underwater
weighing. A compressive strength test was conducted to determine the compressive strength of the cement
paste and the cement–EX paste.
Table 2.4 Mix Proportions
OPC
(%)

EX
(%)

EX0*

100

0

EX5*

95

5

EX10*

90

10

EX15

85

15

EX20

80

20

EX100

0

100

EX0

100

0

Samples

Series 1

Series 2
EX5

95

5

w/b

CuringTemperature(℃)

Experiments

0.3,
0.5*

5*,
20,
40*,

Isothermal calorimetry

0.3,
0.4, 0.5

20

Under-water weighing
Compressive strength

Note: * denotes the heat evolution of OPC100, EX5, and EX10 were determined at curing temperatures of
5 and 40℃ for w/b 0.5.

2.3.2 Design of Concrete
For cement concrete and expansive concrete, the mix concrete proportions are given in Table 2.5. Cement
concrete and expansive concrete were prepared with water-binder ratios (w/b) of 0.3 and 0.5, which was
divided into two series, respectively. The amount of EX replacing the binder was 0, 20, and 40 kg/m 3. For
concrete mixes with w/b 0.3, in order to control the slump, flow, and air content, the high-performance26

water-reducing agents, and an AE agent (Master Air 404) were used with the dosage of 1.2% and 0.001%
by weight of binder, respectively. The concrete samples were used for the tests on the length change ratio,
expansion strain, underwater weighing, compressive strength, accelerated carbonation and freeze-thaw.
The mortar samples were used to determine the pore size distribution using the MIP test, which wereobtained by separating the coarse aggregates from the fresh concrete by wet sieving (5 mm sieve).

Series

Sym.

w/b

W

OPC
Series 1

Series 2

Table 2.5 Mix proportions
Unit weight, kg/m3
Admixtures
C
EX
S
A
583

-

563

20

EX40

543

40

OPC

370

-

350

20

EX20

EX20

0.3

0.5

EX40

175

185

330

616

981

Experiments

SP8SV

Workability,(Bx1.2%)

Length change ratio,

Master air 404

Expansion strain,(Bx0.001%)

Under-water weighing,Compressive strength,

No. 70855

959(250 ml/B = 100

Accelerated carbonation,
Freeze-thaw

kg)

40

2.4 Experimental Method
2.4.1 Cement Paste and Cement Paste mixed with Expansive Additive
2.4.1.1 Calorimetry Test
The hydration of cement-based materials is an important characteristic. To investigate the hydration processof cement-based materials, isothermal calorimetry, semi-adiabatic calorimetry, or solution calorimetry
method can be used for different purposes. Isothermal calorimetry is a useful method for determining theheat production rate and the developed heat during cement hydration. It may be used for different purposes:
to determine the total heat of hydration; to determine the rate of heat evolution; as a general tool toinvestigate the hydration process of cement.
In this study, an isothermal calorimeter (MMC-511SV6) from TOKYO RIKO as shown in Figure 2.2 wasused to measure the rate of heat evolution of OPC paste and Cement-EX paste at 30-second intervals. The
specification of MMC-511SV6 is shown in Table 2.6.

27

Figure 2.2 Isothermal Calorimetry Apparatus (MMC-511SV6)
Table 2.6 Specification of MMC-511SV6
Specifications
Measurement temperature ranges

5°C~60°C

Detector

Thermo-module approximately 52mV/°C

Calorimetric detection sensitivity

Approximately 0.16μV/μW

Measurement channel

1~6 点

Baseline drift±1μV/5°C・24h（8.5μW）

Calibrated calorie supply

25μW~0.8W Continuously variable supply

Stirring

0~114r.p.m. Continuously variable stirring

Data Measurement

Analyze the data recorded on the graphic recorder card using acomputer

2.4.1.2 Under-Water Weighing Test
Many studies [2.2], [2.11], [2.12] used the MIP test to determine the total porosity of mortar and concrete.
However, the MIP test cannot measure a pore size (diameter) smaller than 3 nm [2.8, 2.13]. Meanwhile,
the gel pore diameter ranges from 1 nm to 10 nm [2.13]. Therefore, the underwater weighing (Figure 2.3)
test was used herein to determine the satisfactory value of the total porosity of concrete. The preparation of
the total-porosity test samples was similar to that for the MIP sample test. After being vacuum freeze-driedfor 24 h, the cube samples were immersed in water and continued to be kept in a vacuum chamber for 24
h. The masses of the cube samples were determined under the water in a saturated surface-dry condition
and after drying at 105⁡℃ for 24 h. The total porosity was calculated as follows:𝜌𝑏
𝑉𝑡 = (1 −) × 100%
𝜌𝑡𝑟
28(Eq. 2.2)

Put equipment s
water and reset di(Eq. 2.3)
zero

𝑚𝑜𝑣𝑒𝑛
𝜌𝑏 =
𝑚𝑓𝑙𝑜𝑎𝑡𝜌𝑡 =𝑚𝑜𝑣𝑒𝑛
𝑚𝑜𝑣𝑒𝑛 − 𝑚𝑤𝑎𝑡𝑒𝑟(Eq. 2.4)

where 𝑉𝑡 is the total porosity (%); 𝜌𝑏 is the bulk density (g/cm3); 𝜌𝑡𝑟 is the true density (g/cm3); 𝑚𝑜𝑣𝑒𝑛 is
Put equipment submerged in

Drop the samp

the sample mass after drying at 105 ℃; 𝑚𝑓𝑙𝑜𝑎𝑡 is the sample mass intheandfloating
conditionwater
reset digitalscales (g);to 𝑚𝑤𝑎𝑡𝑒𝑟 =equipment andzerobuoyancy of t

Drop the samples into theequipment and measure thebuoyancy of the sample.

Remove the eincluding the sam
hook and measu
them𝑚𝑡 − 𝑚𝑎𝑝 is the mass of sample under water (g); 𝑚𝑡 is the mass of the equipment and sample under water(g); and 𝑚𝑎𝑝 is the mass of the equipment under water (g).
Put equipment submerged inwater and reset digital scales tozero

Put equipment submergedin water and reset digitalscales to zero.

Fig.4 Under-water weighting
Drop the samples into theRemove the equipment
equipment and measure theincluding the samples from theRemove hookthe equipment
Drop themasssamplesinto
the in theof thesamplesand measure the mass of
including the sample
from andthe samples.
equipment andmeasurethefloating
condition.
equipment
hook and measure the mass
buoyancy of the sample.
them.

Figure 2.3 Schematic of the underwater weighing test

Fig.4 Under-water weighting method

The ages and curing condition were 1-day, 3-day, 7-day, 14-day and 28-day, and under-water curingcondition.
2.4.1.3 Compressive Strength

Remove the equipment
including the sample from thehook and measure the mass
them.

weightingCompressive strength Fig.4
testsUnder-water
were conducted
onmethod
paste samples according to JIS A 1108 [2.14] withdimensions 40×40×160 mm3 at 1-day, 3-day, 7-day, 14-day, and 28-day of under-water curing condition.

2.4.2 Cement Concrete and Expansive Concrete
2.4.2.1 Workability Test
For workability of concrete mixes, the slump, slump flow and air content of concrete were carried out
according to JIS A 1101 [2.15], JIS A 1150 [2.16], and JIS A 1128 [2.17], respectively.
2.4.2.2 Mercury Intrusion Porosimetry Test
The interfacial transition zone is well known to have a significant effect on the pore size distribution of thehardened concrete. The MIP test was conducted on the mortar samples herein to address this problem. The
samples were obtained by separating the coarse aggregates from the fresh concrete by wet sieving (5 mmsieve). The unrestrained mortar was cast in prism molds measuring 40×40×160 mm3 and demolded after
1 day. Sealed curing was then performed in a room at a temperature of 20℃ and relative humidity of 60%.
On the contrary, the restrained mortar was cast into the designed molds (Figure 2.4). At the test ages, themortars were cut into small 5×5×5 mm3 cubes and soaked in ethanol for 1 week prior to being vacuum
freeze-dried for 24 h to stop the hydration. The mortar samples for this test were randomly selected.
29

A

A
A-A

Schematicofofthe
restrained
moldfor fortesting
restrained
FigureFig.1
2.4 Schematic
restrainedmoldtesting
the pore structure and restrained
compressive strength.
compressive strength

2.4.2.3 Compressive Strength Test
The compressive strength was measured on ∅100 × 200 mm cylinders at different conditions (i.e.,
unrestrained and restrained conditions) to evaluate the effect of the restrained condition on the compressive
strength of concrete. The unrestrained concrete was demolded 24 h after casting and covered by a plastic
sheet to cure at 20℃ and 60% relative humidity until the time of the test. For the restrained condition,
Nguyen et al. [2.2] designed a cube mold measuring 100×100×100 mm3, which was restrained using two
steel bars to connect with a steel plate at the specimens’ ends. However, these molds could only confine
the concrete in one direction (i.e., horizontal direction) and did not consider the vertical direction. To
address this limitation, the concrete was cast in the steel molds to restraint three directions. The verticaldirection was restrained by connecting the two-steel plate using four steel bars (Figure 2.4). Both theunrestrained and restrained compressive strengths were tested in accordance with JIS A 1108 [2.14] at 3, 7,
and 28 days.
2.4.2.4 Length Change Ratio and Expansion Strain Test
The length change ratio and expansion strain of concrete tests were performed under both free andrestrained conditions. For the free condition, the free expansion of concrete was conducted in accordancewith the JIS A 1129 [2.18]. For this test, steel prisms measuring 100×100×400 mm3 and 75×75×400 mm3
were used. The specimens were demolded at 24 h after casting to avoid steel mold confinement. An
embedded strain gauge was installed into the center of the unstrained specimens to measure the expansion
strain for the free condition (Figures 2.5a and 2.6a). For the restrained condition, the concrete was cast into
the restrained molds according to the JIS A 6202 [2.4] (Figure 2.5b). A strain gauge was attached on the
top and bottom surface of the rebar at the center of the specimen. A data logger was used to immediately
record the strains of the unrestrained and restrained concrete after casting.

30

Embedded strain gauge

Embedded strain gauge

Gauge

Gauge

75

100

400

400

(a)

(a)
Strain gauge

Rebar ∅ 11mm

Strain gauge

Rebar⁡∅6 mm

75

100

400

398
Steel plate

(b)

(b)

Figure 2.5 Schematic of the specimens measuring

Figure 2.6 Schematic of the specimens

100 × 100 × 400 mm3: (a) free condition and (b)measuring 75 × 75 × 400 mm3: (a) free condition

restrained condition according to the JIS A 6202.

and (b) restrained condition.

2.4.2.5 Underwater Weighing Test
The total porosity of mortar and concrete were carried out at 28 days with the same as method in section
2.3.1.2.
2.4.2.5 Accelerated Carbonation Test
The accelerated carbonation test was conducted in accordance with JIS A 1153 [2.19] to measure thecarbonation depth of all the concrete mixtures measuring 100×100×400 mm3. The carbonation depth wasmeasured by spraying a phenolphthalein solution on the test surface after 13 weeks of exposure to an
accelerated carbonation condition (ambient temperature: 20±2℃; CO2 concentration: 5±0.2%; and relative
humidity: 60±5%). Figure 2.7 shows the accelerated carbonation chamber.

Figure 2.7 Accelerated Carbonation Chamber31

2.4.2.6 Freezing - Thawing Test
In this test, the frost resistance of concrete was determined according to the JIS A 1148 [2.20] withdimensions of 75×75×400 mm3. The fundamental transverse frequency and the mass loss change of thespecimens were measured within 300 cycles. The resistance of concrete to freeze–thaw was evaluated by
calculating the value of the relative dynamic modulus of elasticity (RDM), as given in Eq. (4). The
specimens are often considered as frost damage when the RDM value is less than 60%. Figure 2.8 shows
the testing freezing-thawing system.
𝑓𝑛2
𝑃𝑛 = ( 2 ) × 100%𝑓0

(Eq. 2.5)

Figure 2.8 Freezing-Thawing chamber

32

2.5 Results and Discussion
2.5.1 Heat Evolution and Hydration Degree
Figure 2.9, Figure 2.10 show the rate of heat evolution and degree of hydration of the OPC paste and thecement–EX paste with diffident of w/b ratio 0.3 and 0.5 cured at 20 °C, respectively. According to thesefigures, the rate of heat evolution for EX100 at all ages were higher than those of the OPC paste and cement–
EX paste. The degrees of hydration were approximately 0.5, 0.6 and 0.78, 0.8 for OPC100 and EX100 for
w/b 0.3 and w/b 0.5, respectively. For the cement–EX paste, the degree of hydration increased withincreasing EX replacement. The results demonstrated that the presence of the expansive additive contributes
to increase in the heat of hydration, consistent with the results reported by Choi et al. [2.21]. Thisphenomenon arose due to the contribution 𝐶4 𝐴𝐹 and free lime (𝑓𝑟𝐶) to the heat of hydration.

70

70

Rate of heat evolution, j/g.hr

Rate of heat evolution, J/g.hr

w/b 0.3

(a)
60
50
40
OPC100
EX10
EX20

30

EX5
EX15
EX100

20

10

(b)

w/b 0.5

60
50

40
OPC100
EX10
EX20

30

EX5
EX15
EX100

20
10

0

0
0

12

24

36
48
Time, h

60

0

72

12

24
36
Time, h

48

60

72

Figure 2.9 Heat evolution: (a) w/b 0.3 and (b) w/b 0.5
1

1

(a)

Degree of Hydration

Degree of hydration

0.8
0.6

0.4
0.2

OPC100
EX10
EX20

12

24

36
Time, h48

60

w/b 0.5

0.8

0.6
0.4
0.2

EX5
EX15
EX100

OPC100
EX10
EX20

EX5
EX15
EX100

36
48
Time, h

60

0

0
0

(b)

w/b 0.3

72

0

12

24

Figure 2.10 Degree of hydration: (a) w/b 0.3 and (b) w/b 0.5

3372

The results for the rate of heat evolution for OPC100, EX5, and EX10 paste at 5℃ , 20℃, and 40℃ are
presented in Figure 2.11. A higher curing temperature leads to faster heat evolution for all samples. The
total heat evolution of the EX10 was higher than that of EX5 and OPC100.
Our experimental results demonstrate that the curing temperature had a significant effect on the hydration
reaction of cement and cement–EX blends. This is similar to the results reported by Maruyama [2.22], whoshowed the results of the heat liberation rate of cement in isothermal conditions. In addition, because of theformation of more ettringite, highly exothermic properties (high and broadened first peak, shorter induction
period, and lower second peak) were observed. This observation is consistent with the finding of W. NocunWczelik [2.23]. However, this may also be explained by the hydration reaction of the mineral content.
Specifically, give a certain curing temperature, the second peak becomes lower with increasing amounts ofEX (see Fig. 2.11a-c). This is due to a decrease in the amount of C3S phase, which leads to lower heat
evolution for the cement-EX paste in the acceleration period. The effect of the phase composition of the
OPC at different periods of OPC hydration is presented in Chapter 3.
70

60

OPC100

50
40
5℃

30

20 ℃
40 ℃

20

70

(b)

60

EX5

50

40
5℃

30

20℃
40℃

20

10

10

0

12

24

36
Time, h

48

60

72

EX10

50
40
5℃

30

20℃
40℃

20
10

0

0

(c)

60
Rate of heat evolution J/g h(a)Rate of heat evolution, J/g h

Rate of heat evolution, J/g h

70

0
0

12

24

36
Time, h

48

60

72

0

12

24

36
Time, h

48

60

72

Figure 2.11 Rates of heat evolution of cement with and without EX against time at different
curing temperatures: (a) OPC100, (b) EX5, and (c) EX10.

2.5.2 Workability of concrete
Table 2.7 presents the test results of the fresh non-expansive and expansive concrete. The slump, flow, andair content results were obtained in accordance with the JIS A 1101 [2.15], JIS A 1150 [2.16], and JIS A
1128 [2.17], respectively. Table 1 shows that the slump and the flow of concrete were almost the same forall samples in the two series. The tendency was also seen in the air content results for concrete with w/b
0.5. Meanwhile, the air content of the fresh concrete with w/b 0.3 slightly increased when the amount ofexpansive additive was increased. These tendencies were similar to those reported by M. Tsuji et al. [2.6],
who showed the results of a new test method for the restrained expansion of expansive concrete.

34

Table 2.7 Test results of fresh concrete
Slump
(cm)

Flow
(cm)

Air content
(%)

-

66

4.7

-

65.5

5.5

EX40

-

66

5.8

OPC

20

-

4.8

19.4

-

4.9

19.5

-

4.9

Samplew/b

OPC
Series 1

EX20

Series 2

0.3

EX20

0.5

EX40

2.5.2 Porosity
2.5.2.1 Paste
Figure 2.12 compares the results of total porosity of the hardened cement paste containing the expansive
additive with the w/b ratio of 0.3, 0.4, and 0.5. The results indicated that the total porosity for all sample
slight decreases with time. This is due to the formation of hydration products (C-S-H, ettringite) fills into
the pore in the paste. It means the pore structures of the pastes are dense with the hydration process.
Additionally, the results also showed that the total porosity is lower with the lower w/b ratio. This may
explain why decreasing the w/b ratio increases the compressive strength of hardened paste.

Total porosity, %

70
60
50

40
30

20
10
0
0

7

w/b50-OPC
w/b40-EX5

14Age, dayw/b50-EX5
w/b30-OPC

2128

w/b40-OPC
w/b30-EX5

Figure 2.12 Total porosity of hardened paste with different w/b ratios

2.5.2.2 Concretea) Pore structure
Figure 2.13 shows the test results of the pore size distribution of the cement mortar (OPC sample) and the
expansive mortar (EX20 and EX40) with w/b 0.3 and 0.5 obtained by the MIP test at 28 days. The pore35

size distribution curves of the control mortar sample (OPC sample) typically exhibited at least two sharp
peaks for w/b 0.3 and 0.5. The first one laid less than 10 nm, while the second corresponded to a diameterof approximately 20–50 nm. The first peak that laid less than 10 nm was difficult to observe in the expansive
mortar. The results showed that the pore diameter corresponding to the highest peak in the differential curveslightly decreased with the addition of the expansive additives for both w/b 0.3 and 0.5. When comparing
different w/b ratios, these pore diameters increased with a higher w/b ratio. For the EX40 sample with bothw/b 0.3 and 0.5, the rounded peak appeared in the pore size ranging from 100 to 1000 nm, indicating that
the EX-addition affected the pore diameter of 100–1000 nm. However, the effect of the restrained conditionon this pore diameter range was not observed.
The concept of a critical pore entry diameter was considered to evaluate the influence of the restrained
condition on the pore size distribution of the control and expansive mortar samples. Scrivener et al. [2.24]
reported that the critical pore entry diameter is the pore diameter, where the steepest slope of the cumulative
curve is recorded. The critical pore entry diameter is the pore diameter that corresponds to the highest peakof the differential curve. Table 2.8 shows the test results of the critical pore entry diameter. Under the samew/b ratio, the critical pore entry diameter increased with the increasing amount of EX. The critical pore
entry diameter was decreased by the restrained condition. In other words, under the restrained conditions,the pore diameter tended to become finer, which may be explained by the hypotheses below.
The first hypothesis is relevant to the formation of the ettringite crystal when the expansive additive reacts
with water, which will fill the microspore in the cement–expansive paste matrix. This phenomenon leads
to a denser pore structure. This hypothesis was also reported by Van et al. [2.25] and Nguyen et al. [2.2].
For the second hypothesis, the pore size distribution of the restrained sample shifts to a finer region becauseof the chemical stress effect [2.6]. The expansive force is caused by the EX hydration that makes the pore
diameter become smaller by the constraining pressure of the external constraining restrained mold (e.g.,framework) (Figure 2.14).

36

EX20_unrestrained
EX20_restrained

OPC_unrestrained
OPC_restrained
Differential pore volume (cc/g)

0.30

0.30

0.30

OPC - w/b 0.3

EX40 - w/b 0.3

EX20 - w/b 0.3

0.25

0.25

0.25

0.20

0.20

0.20

0.15

0.15

0.15

0.10

0.10

0.10

0.05

0.05

0.05

0.00
1

Differential pore volume (cc/g)

EX40_unrestrained
EX40_restrained

10

0.00
1000 10000
1

100
(a)

0.30

10

100
(b)

0.00
1000 10000
1

EX20 - w/b 0.5
0.25

0.25

0.20

0.20

0.20

0.15

0.15

0.15

0.10

0.10

0.10

0.05

0.05

0.05

10

0.00
1000 10000
1

100

Pore diameter (nm)(d)

1000 10000

EX40 - w/b 0.5

0.25

1

100
(c)

0.30

0.30
OPC - w/b 0.5

0.00

10

10

100

0.00
1
1000 10000

10

100

1000 10000

Pore diameter (nm)(f)

Pore diameter (nm)(e)

Figure 2.13 Effect of the triaxial restrained condition on the pore size distribution of the cement andexpansive mortar under the restrained and unrestrained conditions with different w/b ratios: (a, b,c) test results of OPC, EX20, and EX40 with w/b 0.3, respectively; and (d, e, f) test results of OPC,
EX20, and EX40 with w/b 0.5, respectively.
Table 2.8 Critical pore entry diameter (nm)Samplew/b 0.3

w/b 0.5

Unrestrained

Restrained

Unrestrained

Restrained

OPC

28.11

24.28

35.95

33.28

EX20

30.77

26.05

33.89

33.89

EX40

28.26

26.24

48.38

40.81

Volumetric change
Expansion force

Compression force

(a)

Pore
Hydration products
Unhydrated EX
Restrained mold(b)

Figure 2.14 Schematic of the effect of chemical stress on the pore structure: (a) free condition and(b) triaxial restrained condition.
37b) Total porosity
The under-water weighing test was used herein to determine the total porosity of concrete under the free
and triaxial restrained conditions. Figure 2.15 illustrates the total porosity results for different concrete
mixtures at 28 days. Consequently, the total porosity slightly increased as the amount of EX increased. This
result is consistent with the findings of Choi et al. [2.21], who reported that the volume of the capillary pore
increases with the increasing EX addition. The total porosity of the concrete with and without EX at the
w/b ratio of 0.5 was higher than that at the w/b ratio of 0.3. The total porosity of the restrained sample at
the w/b ratio of 0.5 was approximately 3% and 21% less than that of the unrestrained samples for EX20and EX40, respectively. In other words, the pore structure of the expansive concrete was denser under the
restrained condition. However, this tendency was not observed for EX40 at the w/b ratio of 0.3, which canbe attributed to the higher concrete stiffness at a lower w/b ratio making the concrete expand more hardly,
thereby leading to a decrease in the effect of the restrained condition. In conclusion, observing the effect of
the restrained condition on the total porosity was easier with a lower stiffness in the expansive concrete.

20

unrestrained
25
w/b 0.3
20

15

15

10

10

5

5

0

0

Total porosity (%)

25

OPC

EX20

(a)

restrained
w/b 0.5

OPC

EX40

Samples

EX20

EX40

(b)

Figure 2.15 Relationship between the total porosity and EX contents under the unrestrained andtriaxial restrained conditions: (a) w/b ratio of 0.3 and (b) w/b ratio of 0.5

2.5.3 Compressive Strength
2.5.3.1 Paste
Figure 2.16 shows the compressive strength test results of the cement paste with and without expansive
additive with different w/b ratio of 0.3, 0.4, and 0.5. It can be seen that the compressive strength of all
samples increases with increasing the curing time. It was also observed that with the lower w/b ratio gave
the higher compressive strength of cement and cement-EX paste. These tendencies are consistent with thegeneral knowledge of the compressive strength development of cement-based materials. In addition, theresults indicated that the presence of EX leads to a decrease in the compressive strength of cement-EX paste
when compared to that of Portland cement paste at 3, 7, 14 and 28 days. However, at 1day, the results
showed an opposite trend, the compressive strength of cement-EX paste higher than that of cement paste.
38

This may be explained as follows: As mentioned previously, the mixture was cast into the prism steel moldand removed from the mold after 24 hours to cure under water until the day of testing (3, 7, 14, and 28days). Meanwhile, at 1day, the compressive strength test was carried out immediately after removing thesample from the mold. In other words, the condition of the samples at 1 day and the other days wererestrained and unrestrained (free) condition, respectively. Furthermore, under the restrained condition,
compressive stress will be created on the inside of the specimen by the expansion of EX particle, it is known
as a chemical prestressing concrete. This may be the main reason to lead to strength enhancement. Therefore,
it can be concluded that the compressive strength of cement-EX paste is enhanced by the restrained
condition. This conclusion is consistent with the results of previous studies [2.1], [2.1].

Compressive strength, MPa

120

100
80
60
40
20

0
1
w/b50-OPC
w/b40-EX5

3

7Age, dayw/b50-EX5
w/b30-OPC

1428
w/b40-OPC
w/b30-EX5

Figure 2.16 Compressive strength of Portland cement and cement-EX paste of different w/b ratio

2.5.3.2 Concrete
The compressive strengths of cement and expansive concrete were tested under the restrained andunrestrained conditions. Figure 2.17 illustrates the compressive strength results of all the concrete mixturesat ages of 3, 7, and 28 days of sealed curing age. The strength values were the average of three test samples.
Figure 10 shows that the compressive strength of concrete varied between 45 MPa to 130 MPa and 20 MPa
to 53 MPa for the w/b ratios of 0.3 and 0.5, respectively. The compressive strength of concrete slightly
decreased with the increasing amount of EX because the total porosity increased with the increasing EX
addition, which decreased the compressive strength. This result is consistent with those of the previous
studies [2.21], [2.25], [2.26], which showed that the compressive strength decreases as the total porosity
increases. The compressive strength of concrete at the w/b ratio of 0.3 was not enhanced by the restrained
condition. This phenomenon was also found in the results of OPC and EX20 at the w/b ratio of 0.5. However,
the effect of the restrained condition on the compressive strength was clearly observed for EX40 at the w/b
39

ratio of 0.5. The results indicate that the compressive strength of the restrained concrete was 12% larger
than that of the unrestrained concrete and was approximately similar to that of EX20 at 28 days. The results
also imply that at an early age of 3 days, the EX40 restrained concrete showed a larger compressive strengththan both EX20 restrained and unrestrained concrete. This result is possibly caused by the decrease in the
total porosity of the expansive concrete (Figure 2.15b) under the confinement condition, which led to its
higher strength. These results demonstrate that the compressive strength of the expansive concrete was
improved under the restrained conditions as the amount of EX increased to 40 kg/m3. The conclusion
corresponded to the results of Nagataki et al. [2.27], who studied the relations among unit expansive
additive content, compressive strength, and restrained expansion rate.

Compressive strength（N/mm2)

3 days_unrestrained
3 days_restrained

7 days_unrestrained
7 days_restrained

140

60

120

50

100

40

80

28 days_unrestrained
28 days_restrained

30

60

20

40
20

10

w/b 0.3

0

0

20
(a)

w/b 0.500
20
40
Amount of expansive additive (kg)(b)

40

Figure 2.17 Relationship between the EX-content and compressive strength of concrete under theunrestrained and restrained conditions: (a) w/b ratio of 0.3 and (b) w/b ratio of 0.5.

2.5.4 Length Change Ratio and Expansion Strain
Figure 2.18 presents the length change ratio of the cement and expansive concrete with different w/b ratios
and types of retrained conditions. In the case of w/b 0.3 (Figures 2.13a-2.13c), an insignificant effect of therestrained condition was observed on the length change ratio of both cement and expansive concrete.
Moreover, these results indicate that the length change ratio increased when the expansive additive dosage
was increased. These tendencies were found in the test results of w/b 0.5 (Figures 2.13d-2.13f). However,
the effect of the restrained condition on the length change ratio was observed in the case of w/b 0.5,
especially for EX40. The length change ratio of the restrained concrete was smaller than that of theunrestrained concrete and was clearly observed when the amount of the expansive additive reached 40
kg/m3. When different restrained conditions were considered (free standard, JIS A 6202), the expansive
concrete sample was tested following the JIS A 6202. It showed the smallest length change, which wascaused by the restraint of the steel bars inside it and the two steel plates at both its ends. Meanwhile, the40

expansive concrete sample was tested according to the free standard, which was restrained by reinforcement.
The expansive concrete with w/b 0.3 had a smaller length change ratio compared to the expansive concretewith w/b 0.5. This result may be explained by the concrete stiffness. The concrete with w/b 0.5 had a smaller
stiffness that led to a higher expansion of the concrete containing the expansive additive. This explanationis consistent with the hypothesis reported by Nguyen et al. [2.2].
OPC_unrestrained
OPC_restrained
0.10

Length change ratio (%)

0.10

w/b 0.3

0.08

EX40_unrestrained
EX40_restrained

EX20_unrestrained
EX20_restrained

0.10

w/b 0.3

0.08

0.06

0.06

0.06

0.04

0.04

0.04

0.02

0.02

0.02

0.00

0.00

0.00

-0.02

-0.02

-0.02

-0.04

-0.04
0

7

14

21

-0.04

0

28

7

(a)
Length change ratio (%)

0.10
0.08

14

21

28

0

(d)

w/b 0.5

0.10

(e)

0.08

0.06

0.04

0.04

0.04

0.02

0.02

0.02

0.00

0.00

0.00

-0.02

-0.02

-0.02

-0.04

-0.04

14

21

28

21

w/b 0.5

28

(f)

0.08

0.06

7

14

(c)

0.06

0

7

(b)
0.10

w/b 0.5

w/b 0.3

0.08

-0.04
0

7

Age (days)

14

21

28

0

Age (days)

(d)

(c)

7

14

21

28

Age, days(f)Figure 2.18 Length change ratio of concrete: (a, d) results of the sample measuring 75×75×400 mm3;(b, e) results of the sample measuring 100×100×400 mm3 (free standard); and (c, f) results of thesample measuring 100×100×400 mm3 (JIS A 6202)

Figure 2.19 shows the expansion strain of the non-expansive and expansive concrete with different w/b
ratios and types of restrained conditions. The expansion strain tendency was similar to the length change
ratio of concrete (Figure 2.18). However, unlike in the test results of the length change ratio of concretewith w/b 0.3, the effect of the restrained condition on the expansion strain of the expansive concrete wasobserved, which may be attributed to the different testing positions. Meanwhile, the length change of thesample was determined by measuring the change of the whole sample. The expansion strain test was
performed on the inside of a sample. Relevant to the expansion strain of EX40 with different types ofrestrained conditions (Figures 2.19e and 2.19f), the expansion strain of concrete restrained by the JIS A
6202 was higher than that restrained by the free standard. The higher expansion strain of EX40 by the JIS
41method can be explained as follows: the expansion strain of concrete was determined by the strain gauge
attached to the steel bar surface at the center of the specimen to measure the steel bar strain. In other words,
the steel bar expanded (shrunk) with the expansion (or shrinking) of concrete. Therefore, when the
expansive concrete was restrained by the JIS method, the effect of the expansion force on the steel bar was
higher than that on the steel bar of free standard.
The results demonstrate that the expansive concrete expansion could be restrained by restraining a subject,such as a rebar. The rebar ratios and the degree of restraint could also affect the expansive concrete
expansion. This study focused on a uniaxial restrained condition for the expansion strain test. Hence,
studying the influence of the degree of restraint on the expansive concrete expansion will be very interestingin the future.

OPC_unrestrained
OPC_restrained
Expansion strain (µm)

2000

EX20_unrestrained
EX20_restrained

2000

w/b 0.3

2000

w/b 0.3

1600

1600

1600

1200

1200

1200

800

800

800

400

400

400

0

0

0

-400

-400
0

7

14

21

2000

7

14

21

28

0

2000

2000

w/b 0.5

1600

1600

1200

1200

1200

800

800

800

400

400

400

0

0

0

-400

28

21

28

14
21
Age (days)(f)28

w/b 0.5

-400

-400
14
21
Age (days)
(d)

14
(c)

1600

7

7

(b)

w/b 0.50

w/b 0.3

-400
0

28

(a)

Expansion strain (µm)

EX40_unrestrained
EX40_restrained

0

7

14
21
Age (days)
(e)

28

0

7

Figure 2.19 Expansion strain of concrete: (a, d) test results of the sample measuring 75×75×400 mm3;(b, e) test results of the sample measuring 100×100×400 mm3 (free standard); and (c, f) test results ofthe sample measuring 100×100×400 mm3 (JIS A 6202)

2.5.5 Carbonation Depth
The carbonation depth of concrete with and without expansive additive at different w/b ratios was measured
through the phenolphthalein test exposed in the controlled condition (temperature: 20℃; relative humidity:
60%; and CO2 concentration: 5%) for 13 weeks (Table 2.8). The concrete carbonation depth results were42the average of 18 to 20 measurements from the exposed surface. The test results indicated that concrete
was not carbonated under a w/b ratio of 0.3 compared with that under a w/b ratio of 0.5. This result may be
attributed to the compact structure of the concrete at the lower w/b ratio. The concrete carbonation depth
increased with the increasing w/b ratio. This observation is consistent with that reported by Singh et al.
[2.28]. At the w/b ratio of 0.5, the carbonation depth increased with the addition of the expansive additive.
However, comparing the different restrained conditions, the carbonation depth of the restrained condition
was smaller than that of the free condition. This result can be explained by the denser structure of therestrained concrete caused by the compressed pore in the concrete by the chemical prestress effect. Thisphenomenon was discussed in Section 2.4.2.2.
The results demonstrate that the carbonation resistance of the expansive concrete was enhanced by
restraining. The concrete carbonation specimen was made under the uniaxial restrained condition. As
mentioned, the chemical prestress effect made the pore structure of the expansive concrete denser under
the restrained conditions. Nagataki et al. [2.27] also reported that the chemical prestress effect greatly
depends on many factors, such as kind of cement, w/b ratio, curing method, reinforcing rebar ratio, anddegree of restraint. Therefore, in the future, more investigations are necessary to find the influence of thesefactors on the chemical prestress effect in expansive concrete.

Table 2.9 Carbonation depth of concrete (mm)Samplew/b 0.3

w/b 0.5

Unrestrained

Restrained

Unrestrained

Restrained

OPC

0

0

1.15

0.95

EX20

0

0

2.90

1.78

EX40

0

0

3.60

2.80

2.5.6 Frost Resistance
Figure 2.15 shows a comparison of the RDMs of the Portland cement and expansive concrete under the
restrained and unrestrained conditions at the w/b of 0.3 and 0.5. The values of the result were the averageof two test samples.
The RDM decreased with the increasing amount of expansive additive in both the restrained andunrestrained conditions. The results demonstrate that the presence of EX led to a reduction of the frost
resistance of concrete, especially for the unrestrained concrete. This result is consistent with that of theprevious study [2.29] and may be explained by the formation of the micro-cracks caused by the expansionof the EX-hydration under the free conditions. When evaluating the effect of the restrained condition of the
frost resistance of concrete, the results indicated that for the w/b ratio of 0.3, the restrained concretes had ahigher RDM than the unrestrained concretes because the RDMs of OPC, EX20, and EX40 wereapproximately 80% and 87% at 300 cycles. For the w/b ratio of 0.5, observing the change of the RDM of43

the OPC and EX20 was difficult. However, the expansive concrete (EX40) showed early frost damage withan RDM below 80% at 12 freezing–thawing cycles and below 60% at 100 cycles under free condition.
Meanwhile, the RDM of EX40 was below 60% at 190 cycles under the restrained condition.
The results conclude that the frost resistance of the expansive concrete was enhanced by the restrained
conditions at the lower w/b ratio. Furthermore, a previous study [2.7] found that under the triaxial restraint,
the frost resistance of the Portland cement concrete was better than that of the uniaxial restrained concrete.
According to this conclusion, the present research may be extended in the future by investigating theinfluence of the degree of restraint on the frost resistance of expansive concrete, especially the triaxial

Relative dynamic modulus of elasticity (%)

restraint.

OPC_unrestrained
OPC_restrained

EX20_unrestrained
EX20_restrained

100

100

80

80

60

60

40

40

20

EX40_unrestrained
EX40_restrained

20
w/b 0.3

0

0

100

200
(a)

w/b 0.50300
0Cycles of freeze-thaw

100

200

300

(b)

Figure 2.20 Comparison of the RDMs of cement and expansive concrete under the restrained andunrestrained conditions: (a) w/b ratio of 0.3 and (b) w/b ratio of 0.5.

44

2.6 Conclusion
1)

The heat evolution of cement paste increases with increasing the addition of EX and increasingof curing temperature.

2)

The presence of EX led to an increase in the total porosity of cement paste and concrete.
However, that of expansive concrete was decreased by the restraining when the amount of EX
was 40 kg/m3 of concrete at a w/b ratio of 0.5. This is the reason why the compressive strengthof the expansive concrete was enhanced under the restrained conditions when the amount of
the expansive additive reached 40 kg/m3 of concrete.

3)

Under the restrained condition, the pore size distribution of the expansive mortar shifted to asmaller size.

4)

The concrete expansion increased with the increasing amount of EX. The length change ratio
and expansion strain of concrete with and without an expansive additive could be controlled
by the restrained condition.

5)

The concrete carbonation depth was not observed at the w/b ratio of 0.3. For the w/b of 0.5, thecarbonation resistance of the expansive concrete was improved by restraining.

6)

It is essential considering the effect of the restrained conditions in evaluating the various
experimental results of the expansive concrete with a large expansive additive dosage (i.e., over
20 kg/m3 concrete) or concrete combining EX with other cement replacement materials (e.g.,
fly ash and blast furnace slag).

45

References[2.1] Lam N.T.; Sahamitmongkol R.; Tangtermsirikul S. Expansion and compressive strength of concretewith expansive additive”, Res. Dev. J. 2008, 9, 2, 40-49.
[2.2] Nguyen T.B.T.; Chatchawan R.; Saengsoy W.; Tangtermsirikul S.; Sugiyama T. Influences ofdifferent types of fly ash and confinement on performances of expansive mortars and concretes, Constr.
Build. Mater. 2019, 209, 176-186.
[2.3] ACI Committee 223 “Expansive cement concretes - Present state of knowledge”, ACI J. Aug-1970,
583-610.
[2.4] Japanese Industrial Standard Committee. Expansive additive for concrete (Amendment 1), JIS A 62022008.
[2.5] Sidney M.L. Section 5 - Calculations relating to concrete and masonry. In Construction calculations
manual, 1st ed.; Elsevier Science: Elsevier Ltd., Netherlands, 2012; pp. 211-264.
[2.6] Tsuji Y.; Maruyama H.; A fundamental study on effect of restraint method on mechanical propertiesof expansive concrete. Proceedings of the 6th Annual Conference on Concrete Engineering, 1984, 86, 341344.
[2.7] Harada A. Influence of reinforcement restraint on the length change and frost damage during freezingthawing action in structural concrete. Master Thesis, Muroran Institute of Technology, Japan, March-2011.
[2.8] Lobo C.; Cohen M.D. Pore structure development in type K expansive cement pastes. Cem. Concr.
Res. 1991, 21, issues 2-3, 229-241.
[2.9] A.M. Neville, Properties of Concrete, fifth ed., Prentice Hall, Pearson, Harlow, England.
[2.10] T. Higuchi, M. Eguchi, M. Morioka, E. Sakai, Hydration and Properties of Expansive Additive
Treated High Temperature Carbonation, Cement and Concrete Research 64 (2014) 11-16.
[2.11] Shen J.; Xu Q. Effect of moisture content and porosity on compressive strength of concrete duringdrying at 105℃. Constr. Build. Mater. 2019, 195, 19-27.
[2.12] Beaudoin J.J. Porosity measurement of some hydrated cementitious systems by high pressure
mercury intrusion-microstructural limitations. Cem. Concr. Res. 1979, 9, issue 6, 771-781.
[2.13] Aligizaki K.K. Pore Structure of Cement-Based Material: Testing, Interpretation and Requirements,
1st ed.; CRC Press: Taylor & Francis, American, 2005.
[2.14] Japanese Industrial Standard Committee. Method of test for compressive strength of concrete, JIS A
1108-2018.
[2.15] Japanese Industrial Standard Committee. Method of test for slump of concrete. JIS A 1101-2005.
[2.16] Japanese Industrial Standard Committee. Method of test for slump flow of concrete. JIS A 11502007.
[2.17] Japanese Industrial Standard Committee. Method of test for air content of fresh concrete by pressure
method. JIS A 1128-2019.
[2.18] Japanese Industrial Standard Committee. Methods measurement for length change of mortar andconcrete-Part 3: Method with dial gauge, JIS A 1129, 2010.
46

[2.19] Japanese Industrial Standard Committee. Method of accelerated carbonation test for concrete. JIS
A 1153-2012.
[2.20] Japanese Industrial Standard Committee. Method of test for resistance of concrete of freezing andthawing, JIS A 1148-2010[2.21] H. Choi, M. Lim, H. Choi, T. Noguchi, R. Kitagaki. Modelling of creep of concrete mixed withexpansive additives. Magazine of Concrete Research, 2015, 67 (7), pp.335-348.
[2.22] I. Maruyama, Time Dependent Property of Cement-Based Materials on the Basis of MicroMechanics, Ph.D. Thesis, University of Tokyo, Japan, March 2003 (in Japanese).
[2.23] W. Nocun-Wczelik, A. Stok, Z. Konik, Heat evolution in hydrating expansive cement systems. J
Therm Anal Calorim. 101 (2010), pp. 527-532.
[2.24] Scrivener K.; Snellings R.; Lothenbach B. A practical guide to microstructural analysis of
cementitious materials, 1st ed.; CRC Press: Boca Raton, America, 2016.
[2.25] Van N.D., Choi H.; Hama Y. Modeling early age hydration reaction and predicting compressive
strength of cement paste mixed with expansive additive. Constr. Build. Mater. 2019, 223, 994-1007.
[2.26] Kim Y.Y.; Lee K.M.; Bang J.W.; Kwon S.J. Effect of w/c ratio on durability and porosity in cement
mortar with constant cement amount. Ad. Mater. Sci. Eng. 2014, 2014, Article ID 273460.
[2.27] Nagataki S.; Gomi H. Expansive admixtures (mainly ettringite). Cem. Concr. Com. 1998, 20, 163170.
[2.28] Singh N.; Singh S.P. Reviewing the Carbonation Resistance of Concrete. J. Mater. Eng. Struc. 2016,
3, 35-57.
[2.29] Makoto S.; Kentoro S.; Yoshihiko H.; Ryoetsu Y. Frost Resistance of Expansive Concrete, Japan
Society of Civil Engineers 67th Annual Academic Lecture, 2012 (in Japanese).

47

CHAPTER 3
MODELING EARLY AGE THE HYDRATION OF
CEMENT PASTE MIXED WITH EXPANSIVE
ADDITIVE

48

CHAPTER 3 MODELING EARLY AGE THE HYDRATION OF CEMENT PASTE MIXEDWITH EXPANSIVE ADDITIVE
3.1 Introduction
An expansive additive (EX) is an admixture that reacts when mixed with cement and water: the expansive
concrete expands due to the production of ettringite or calcium hydroxide arising from a hydration reaction[3.1]. EX is commonly used in concrete to reduce cracks resulting from drying shrinkage. There is a strong
relationship between the hydration reaction of cement–expansive additive (cement–EX) blends and the heat
evolution, strength development, and volumetric changes of the material, all of which lead to the crackingof hardened concrete. Therefore, it is necessary to study the hydration of cement–EX blends rigorously.
However, this hydration process is more complicated than the hydration process of ordinary Portland
cement (OPC) because of the co-occurrence of both OPC and EX hydration processes.
To investigate the hydration kinetics of cement, over the past few decades, a number of studies have been
conducted to model cement hydration in order to grasp the time-dependent properties of cement-basedmaterials [3.2]. In a recent study, Tomosawa [3.3] proposed a hydration model to estimate the rate of heat
evolution in the hydration of OPC. The model simulates the hydration process using a single kinetic
equation. Based on Tomosawa’s model, a hydration model of OPC was developed by Maruyama [3.4],
where the volumetric changes of cement particles, chemically bound water, and physically bound water
were considered. Maekawa et al. [3.5], [3.6] proposed a multicomponent model for the heat of hydrationof Portland cement. The hydration rate was controlled by evaluating the temperature dependence, hydrationlevel, and free water consumption. However, the models proposed so far [3.2], [3.3], [3.4], [3.5], [3.6] only
focus on simulating the hydration reaction of a single cement particle. Therefore, a model that could
simulate both the hydration of cement and the reaction of mineral admixtures is essential.
Several models that simulate the hydration of cement taking into account the reaction of mineral admixtures
have been reported. Schindler et al. [3.7] proposed a hydration model for predicting the heat evolution of
cementitious materials. The proposed model focuses on the effects of the chemical composition of cement,
cement fineness, mixture proportions, and supplementary cementing materials (SCMs). Riding et al. [3.8]
presented an empirical model for calculating the heat evolution owing to the hydration of concrete mixtures.
The model takes into account the effects of cement chemistry, aggregate type, water–cement ratio, SCMs,
chemical admixture type and dosage, and temperature of hydration. Based on results of isothermal
microcalorimetry experiments, De Schutter [3.9], [3.10] also proposed a general kinetic hydration modelof Portland cement and slag-blended cement. Merzouki et al. [3.11] proposed a kinetic hydration model tosimulate the hydration of cement paste containing blast furnace slag by considering the production of
calcium hydration in cement hydration and its consumption by slag hydration. Based on an experimental
study, Tanaka et al. [3.12] proposed a method for estimating the adiabatic temperature rise in concrete madewith blast furnace slag-blended cement. In addition, Park et al. [3.13] designed a microstructural hydration
model of Portland cement considering the reduction in the hydration rate that occurs due to the interfacial
area of contact between the free water and hydration products. Furthermore, a hydration model of slag–49

cement blends was proposed by Xiao-Young et al. [3.14]. In this model, the production of calcium
hydroxide in cement hydration and its consumption in slag reaction were considered. Narmluk and Nawa
[3.15] investigated the effects of fly ash on the hydration kinetics of cement for low water to binder fly ash–cement mixtures at different curing temperatures using a modified shrinking-core model. It should be notedthat most of the general models have simulated the hydration reaction of cement paste containing blast
furnace slag and fly ash. Meanwhile, information about the degree of hydration of cement containing
expansive additives is still limited. Specifically, a simulation model for the hydration of cement mixed withEX has not yet been established.
In this study, therefore, a simulation model was proposed for the hydration reaction of cement paste blended
with an expansive additive. The degree of hydration and rate of heat evolution of cement paste containing
expansive additive was obtained from the proposed hydration model. Subsequently, the experimental andcalculated results were compared to validate the proposed model. Figure 3.1 shows a flow chart
representing the work undertaken.

Chapter 3
Modeling early age of the hydration of cement paste mixed with expansive additive
Modeling
Effect of curing
temperature

Hydration
heat ofclinker

Input parameter

Bogue
calculation

Chapter 2
Experimental

Isothermal
calorimetry
C4 AF

C3A
C3S

Output parameter

C2S

Previous
studies

Energy generated
during the hydrationof OPC and EX
Equation modelCalculation of
maximum amount ofheat released

Degree of hydration

Degree of hydration
Comparison

Conclusion

Figure 3.1 Flow chart50

3.2 Hydration model
3.2.1 Model equation
Inner and Outerhydration products layer

Protective layer

𝑡

𝑟𝑡

𝑟0

Cement or EX
particle
t=0

𝑟𝑡

Water
t=

t=

+

Figure 3.2 Schematic of hydration reaction of a single OPC or EX particle.

Based on the shrinking-core model, a fundamental hydration equation was proposed by Tomosawa [3.3]and developed by Maruyama [3.4] to simulate the hydration reaction of single cement particles. In themodel introduced in [3.3] and [3.4], three coefficients were considered: 𝑘𝑑 is the reaction coefficient in the
induction period, 𝐷𝑒 is the coefficient of effective diffusion of water through the hydration product layer(C–S–H gel), and 𝑘𝑟 is the coefficient of the reaction rate of cement.
Referring to previous studies [3.2], [3.3], [3.4] that describe the hydration model of OPC, hydrationof the cement–EX paste was modeled as shown in Eq. (3.1). In Eq. (3.1), we modified the calculation ofsome parameters to make it more suitable for simulating the hydration reaction of cement containing an
expansive additive, as shown in Eq. (3), (4) (5), and (9). In order to simplify the hydration process, thecement and EX particles were simply assumed to be spherical in shape; a schematic representing thehydration reaction of a single OPC and EX particle is shown in Figure 3.2. The hydration reaction occurs
immediately when water comes into contact with the OPC or EX particle and creates a protective film.
After some time, the hydration product is generated. According to the shrinking-core model [3.16], thehydration reaction can be divided into three stages: (a) diffusion of water throughout the protective film
surrounding the OPC or EX particle to the surface of the solid, (b) penetration and diffusion of water
through the outer and inner hydration product layers to the surface of the unreacted OPC or EX particle,
and (c) reaction of water with OPC or EX at this reaction surface.
𝑑
3𝐶𝑤∞
=
×(
𝑑
(𝛾 + 𝑊𝑎,𝑔 )𝜌𝐵 𝑟02

1
1

2/3 +
𝑘𝑑 𝑟0 0

where

−1/3
− (2 −
0𝐷𝑒

is the hydration degree of cement–EX blends;

−1/3
0)

)
+

1

( Eq. 3.1)

2/3
𝑘𝑟 𝑟0 00 is the non-hydration degree; 𝑟0 is the averageradius of the initial OPC and EX particles (mm), as shown in Eq. (3.2) [3.17], [3.18]; 𝑆𝐵 is the average
specific surface area of OPC and EX (mm2/g) as indicated in Eq. (3.3); 𝑆𝑂𝑃𝐶 and 𝑆𝐸𝑋 are the specificsurface areas of OPC and EX (mm2/g), respectively; (𝛾 + 𝑊𝑎,𝑔 ) is the total chemically and physically51

bound water in the cement–EX blends (g) as described in Eq. (3.4); 𝛾 is the average chemically boundwater in cement–EX blends (g);⁡𝑊𝑎,𝑔 is the average physically bound water in the cement–EX blends (g);𝜌𝐵 is the average specific gravity of OPC and EX; 𝐶𝑤∞ is the amount of water in the outer region of the CS-H gel (%). 𝑘𝑑 and 𝑘𝑟 are coefficients for the reaction (mm/h); 𝐷𝑒 is the effective diffusion coefficient ofwater in the gel (mm2/h).
r0 =3
S B × ρB

SB = SOPC ∙(Eq. 3.2)

C0
EX 0+ SEX ∙
C0 + EX 0
C0 + EX0(γ + Wa,g ) = 0.42 ∙(Eq. 3.3)

C0
EX 0+ 0.48 ∙C0 + EX 0
C0 + EX 0(Eq. 3.4)

In Eqs. (3)–(5), 𝐶0 and 𝐸𝑋0 are the mass fractions of the OPC and EX in the mixed sample, respectively.
The reaction coefficient 𝑘𝑑 [3.19], [3.20], [3.21] is assumed to be a function of the hydration degree (mm/h),
as shown in Eq. (3.5), where 𝐵 (mm/h) and 𝐶 (mm/h) are the rate-determining coefficients; 𝐵 controls therate of protective film formation and 𝐶 controls the rate of protective film decay [3.15], and 𝑟𝑡 is the averageradius of an unhydrated OPC and EX particle (mm).
kd =

B
1.5

+ C(r0 − rt )4(Eq. 3.5)

The effective diffusion coefficient of water 𝐷𝑒 (mm2/h) [3.20], [3.21], [3.22], [3.23] in the gel, assumed to
be a function of the degree of hydration, is shown in Eq. (3.6). Here, 𝐷𝑒0 is the initial diffusion coefficientof water in the gel (mm2/h).
1

De = De0 ln⁡(α)(Eq. 3.6)

The amount of water in the outer region of the C–S–H gel is expressed as a function of the degreeof hydration, as shown in Eqs. (3.7) and (3.8). 𝐶𝑤∞ is also described as decrease in the amount of available
water in the capillary pores [3.14], [3.15]. This implies that the amount of available water will decrease
when the cement and EX react with water to create the hydration product layer. In this work, therefore, it
was necessary to consider the decrease in the amount of available water, caused by the cement and EX
reactions. Theoretically [3.24], at complete hydration, 1 g of cement chemically binds with approximately
0.23 g of water during the cement hydration reactions and 0.19 g of physically bound gel water.
For the OPC paste, the 𝐶𝑤∞ [3.14], [3.15] can be determined using the following equation:
Cw∞ =w0 − 0.42C0 OPC
w0(Eq. 3.7)

where 0.42 represents the total chemically and physically bound water,⁡𝑤0 is the mass fraction of water inthe mixed sample, and

𝑂𝑃𝐶 is the degree of hydration of OPC.

52

The physically bound water is called evaporable water, which is calculated by drying the specimen in anoven at 105 °C for 24 h. The chemically bound water, also called non-evaporable water, is determined byheating the specimen at approximately 1000 °C for approximately 30 min. The loss of weight in the sample
from 105 °C to approximately 1000 °C was interpreted to be the loss of chemically bond water [3.25],[3.21].
According to the experimental results, the total chemically bound water and physically bound water of EX
was 0.48 g. Therefore, for cement–EX blends, the 𝐶𝑤∞ is determined by the following equation:
Cw∞ =
where

w0 − 0.42C0 OPC − 0.48EX0 EX
w0(Eq. 3.8)

𝐸𝑋 is the degree of hydration of EX.

The effect of the curing temperature on these coefficients was assumed to follow Arrhenius’ law as shownin Eqs. (9a)–(9d) [3.3], [3.4], [3.14], [3.15]:
B = B20 exp⁡(−β1 (1/T − 1/293)(Eq. 3.9a)

C = C20 exp⁡(−β2 (1/T − 1/293)(Eq. 3.9b)

De = De20 exp⁡(−β3 (1/T − 1/293)(Eq. 3.9c)

k r = k r20 exp⁡(−E/R(1/T − 1/293)(Eq. 3.9d)

where 𝛽1 , 𝛽2 , 𝛽3 ,⁡ and 𝐸/ are temperature sensitivity coefficients and 𝐵20 (mm/h), 𝐶20 (mm/h), 𝐷𝑒20(mm2/h) , and 𝑘𝑟20 (mm/h) are the values of 𝐵 , 𝐶 , 𝐷𝑒 , and 𝑘𝑟 at 20 °C (293K), respectively. In theseexperiments, the curing temperatures were 5, 20, and 40 °C; the values of⁡𝐵 , 𝐶 , 𝐷𝑒 , and 𝑘𝑟 varied for
different curing temperatures.
Van Breugel [3.8], [3.26] assumed that the degree of cement hydration was proportional to the heatreleased, as shown in Eq. (3.10), where Q (t) (J/g) is the heat released at time t and Q max (J/g) is the totalheat available for the blended cement hydration reaction.
(t) =

Q (t)
Q max

(Eq. 3.10)

The maximum heat released by the OPC and EX mixture at complete hydration can be determinedby the following equation [3.8], [3.26]:
Q (OPC⁡or⁡EX) = q1 . (%C3 S) + q2 . (%C2 S) + q3 . (%C3 A) + q4 . (%C4 AF) + q5 . (%frC)+ q 6 . (%MgO)(Eq. 3.11)

where 𝑞1 , 𝑞2 , 𝑞3 , 𝑞4 , 𝑞5 , and 𝑞6 denote the heat evolved for each composition (J/g), predicted by Van
Breugel’s study [3.26] and listed in Table 4. %𝐶3 𝑆, %𝐶2 𝑆 , %𝐶3 𝐴, %𝐶4 𝐴𝐹 , %𝑓𝑟𝐶 , and %𝑀𝑔𝑂 are themineral compositions of cement obtained by the Bogue calculation and shown in Table 2.2 (see Chapter 2).
53

Table 3.1 Relative contribution of clinker compounds to heat of hydration (J/g)
q1
q2
q3
q4
q5
Author
%C3 S
%C2 S
%C3 A
%C4 AF
%frC

q6
%MgO

570

260

840

125

-

-

Bogue [3.28]

500

260

866

125

-

-

Wm. Lerch et al. [3.29]

500

260

866

420

1166

850

Thorvaldson [3.30]

-

-

-

1166

-

-

Chatharin [3.31]

500

251

1340

420

1172

-

Adam [3.32]

-

-

500

170

840

-

Newkirk [3.33]

560

1360

300

-

-

-

Maximum amount of heat liberation, J/g

Woods [3.27]

700
600

500
400

300
200

100
0

OPC

EX5

EX10

EX15

EX20

EX100

Figure 3.3 Maximum amount of heat liberated by OPC and cement–EX blends.
Based on Eq. (Eq. 3.11), the maximum heat of hydration of OPC and cement–EX blends was determined.
Results are shown schematically in Figure 3.3; as can be seen, the maximum heat hydration of OPC andcement–EX blends increased with the addition of expansive additives. In order to determine the maximum
amounts of heat liberated by OPC, Maruyama [3.19] has used the heat of hydration of the constituents ofWoods. However, because of the expansive additive containing a large amount of free lime (𝑓𝑟𝐶) [3.34],[3.35], the relative contribution to the heat of hydration of the free line needed to be considered in Eq. (3.11).
In this study, therefore, the heats of hydration of the constituents of Wm Lerch et al. (see Table 3.1) wereused to calculate the maximum heat of hydration. Our calculated results correspond to the finding of Choi
[3.36].
According to Eq. (3.10), the hydration degree of the cement–EX blends is defined as the ratio between theheat released at time t to the maximum amount of heat released at complete hydration. 𝑄𝑡 is determinedusing the isothermal calorimetry method and 𝑄𝑚𝑎𝑥 is calculated using the following equation:54

Q (max) = Q OPC ∙C0
EX 0+ Q EX ∙C0 + EX 0
C0 + EX 0(Eq. 3.12)

where 𝑄𝑂𝑃𝐶 and 𝑄𝐸𝑋 are the maximum amounts of heat released by the OPC and EX (J/g), respectively.
Note that 𝑄𝑂𝑃𝐶 and 𝑄𝐸𝑋 are calculated from Eq. (3.11).

3.2.2 Effect of mineral composition on the model parameters
Previous studies [3.4], [3.37] reported a relationship between the model parameters 𝐵, 𝐷,⁡𝐶, and 𝑘𝑟 and thecement component (𝐶3 𝑆, 𝐶3 𝐴, and 𝐶2 𝑆). However, the detailed reasons for explaining these relationships
were not established. Therefore, in this section, the relationship between the mineral composition and model
parameters was deduced on the basis of the degree of hydration of the composition and the least-squares
method. In addition, we have also discussed why the model parameters have a relation with the mineralcomposition of the cement.
Odler [3.38] determined the hydration degree of the mineral composition as a function of hydration time(see Figure 3.4), demonstrating that the hydration of C3A and C4AF began immediately after the initial
contact of the OPC or EX with water. The hydration of C3S started after approximately 2 h, and that of C2Sstarted at around 30 h. In addition, Jansen [3.39] suggested a typical calorimetric curve for the rate of heat
evolution of cement-based materials (see Figure 3.5). In this figure, the hydration process comprised four
periods: the initial period, induction period (also called the dormant period), acceleration period, anddeceleration period. In the initial period, C3A and C4AF began to undergo the reaction; during the induction
and acceleration periods, the hydration of C3S occurred; finally, during the deceleration period, C2S began
to undergo its reaction and the C3A reaction speed increased. Furthermore, in this study, the least-squares
method was used to determine the value of model parameters. Fitting the experimental results to the modelusing the least-squares method showed that B20 and D20 had an effect on the induction period anddeceleration period, respectively. On the other hand, kr20 had an effect on both the acceleration anddeceleration periods.
From this information, the relationship between the mineral composition and the model parameters wasdeduced. The parameters 𝐵, 𝐷, and 𝑘𝑟 showed a relationship with the 𝐶3 𝑆, (𝐶3 𝐴 + 𝐶2 𝑆), and (𝐶3 𝑆 + 𝐶3 𝐴)
phase, respectively. In other words, the model parameters can be represented as a function of thecomponents of the cement.

55

50
40

C3S

30

Heat Flow

Progress of hydration (%)

60

C3A

20
C4 AF

10
C2S

0

0.01

0.1

1
10
Hydration time, h

100

1000

Hydration time, hFigure 3.4 Hydration degree of mineral

Figure 3.5 Changes detected in phasecompositions [3.38].

composition of the OPC paste at different
periods of OPC hydration [3.39].

56

3.3 Results and Discussion
3.3.1 Relationship between mineral composition and model parameters
Model parameters determined using the least-squares method are shown in Table 3.2 for a w/b of 0.3 and0.5 at 20 ℃. C20 is 1×109 for the OPC paste without expansive additive replacements and 5×108 for 5, 10,15, and 20% expansive additive replacement contents. For EX100, the C20 are 5×1011 at w/b 0.3 and 0.5,
respectively. The other model parameters varied with the EX replacement content: B and D increased and𝑘𝑟 decreased with the addition of the expansive additive. In addition, the dependence of model parameters
𝐵, 𝐷, and 𝑘𝑟 on the mineral compositions of cement at different curing temperature is shown in Figure 3.6
and Figure 3.7 for w/b 0.3 and w/b 0.5, respectively. 𝐵 and 𝐷 decreased and 𝑘𝑟 increased with increasing
mineral content. However, an effect of the curing temperature on the tendency noted for these relationships
was not observed. The results showed that the relationship between the model parameters and the mineralcomposition was approximately linear with a good correlation (approximately 0.9).
Table 3.2 Model parameters of Eqs. (3.9a)–(3.9d) at 20 ℃
𝐵20
𝐶20
𝐷20
𝑘𝑟20
SampleR2

OPC1003.6E-11

1.0E+92.5E-11

6.6E-80.96

EX5

8.0E-115.0E+85.8E-11

6.3E-80.89

EX101.3E-105.0E+88.5E-11

5.8E-80.96

EX15

1.7E-105.0E+8

1.2E-10

5.7E-80.95

EX20

2.4E-105.0E+8

1.7E-10

5.6E-8

0.87

EX100

1.2E-125E+118.00E-7

8.85E-8

0.71

OPC1003.6E-11

1.0E+92.5E-11

6.8E-80.89

EX5

1.0E-105.0E+85.8E-11

6.0E-80.92

EX10

1.5E-105.0E+81.0E-105.0E-80.93

EX15

2.0E-105.0E+8

1.8E-10

5.2E-80.97

EX20

2.6E-105.0E+83.0E-105.0E-8

0.96

EX100

3.6E-85.0E+11

3.0E-10

1.25E-7

0.94

w/b

0.3

0.5

30

7

20

y = -2.1044x + 109.07
R² = 0.9909

20

15
10

y = 0.0915x + 1.0455
R² = 0.9135

15
kr x 10-8 mm/h

D x 10-11 mm2 /h

B x 10-11 mm/h25

y = -2.1385x + 72.52
R² = 0.9864
10

6

5

5

5
0

0
40

45

50

55

4
25

30

35

+

3.6-(a) B and C3 S at 20℃

EX10

EX5

50

55

60

+

3.6-(b) D and C3 A + C2 S at 20℃
OPC10045EX153.6-(c) D and C3 S + C3 Aat 20℃
EX20Figure 3.6 Relationship between mineral composition and model parameters at w/b 0.3: (a)relationship between B and C3S, (b) relationship between D and (C3A + C2S), and (c) relationshipbetween kr and (C3S + C3A) at 20℃, respectively.

57

30

30

℃

25

30

y = -2.2526x + 117.22
R² = 0.9979

℃

℃

25

25

y = -2.3157x + 120.51
R² = 0.9979

/

15

15

10

10

10

5

5

5

𝑩 ×⁡

−

15

0

0

0
40

45

50

40

55

3.7-(a) B and C3 S at 5℃
℃

40

55

/

45

50

3.7-(c) B and C3 S at 40℃
℃

℃
600

y = -4.0826x + 134.22
R² = 0.9316

25
20

y = -89.566x + 2929.5
R² = 0.9466

450

15

300

10

0.6

150

5
0.0

0
25

30
+

35

0
25

3.7-(d) D and C3 A + C2 S at 5℃

30
+

35

25

3.7-(e) D and C3 A + C2 S at 20℃

8

30
+

35

3.7-(f) D and C3 A + C2 S at 40℃

8

8

7

7

℃

y = 0.1083x - 0.455
R² = 0.7649

−

𝒌𝒓 ×⁡

,

/

℃
7

6
5

55

750

30

y = -0.2929x + 9.7134
R² = 0.9008

,
−

50

3.7-(b) B and C3 S at 20℃

1.8

𝑫 ×⁡

45

35

2.4

1.2

y = -2.3927x + 124.51
R² = 0.9979

20

,

20

20

6

6
5

5

4

4

4

45

50

+

A

55

3.7-(g) D and C3 S + C3 A at 5℃60

y = 0.2175x - 5.9305
R² = 0.7299℃

y = 0.1548x - 2.7845
R² = 0.7806

45

50

+

55

60

45

A

3.7-(h) D and C3 S + C3 A at 20℃
OPC100

EX5

EX10

EX15

50

+

A

55

60

3.7-(i) D and C3 S + C3 A at 40℃
EX20

Figure 3.7 Relationship between mineral composition and model parameters at w/b 0.5: (a), (b),and (c) relationship between 𝑩 and C3S at 5℃, 20℃, and 40℃, respectively; (d), (c), and (e)relationship between 𝑫 and (C3A + C2S) at 5℃, 20℃, and 40℃, respectively; (g), (h), and (i)relationship between 𝒌𝒓 and (C3S + C3A) at 5℃, 20℃, and 40℃, respectively.
The results reported here demonstrate that the proposed suggestion can effectively explain the relationshipbetween the model parameters and the mineral compositions, as explained in Section 3.3.2. Based on Eqs.
(9a)–(9d), these relationships as a function of the mineral composition are shown in Table 3.3. Maruyama[3.4] suggested the parameters 𝐷 and 𝑘𝑟 to be functions of 𝐶3 𝑆 and (𝐶3 𝑆 + 𝐶3 𝐴), respectively. These
relationships were also proposed in a previous work reported by Wang [3.44], who reported that 𝐵, 𝐶, 𝐷,
and 𝑘𝑟 show a relationship with (𝐶3 𝑆 + 𝐶3 𝐴), 𝐶3 𝑆, 𝐶2 𝑆, and 𝐶3 𝑆, respectively. However, unlike in previous
studies [4,44], in this study, 𝐵, 𝐷, and 𝑘𝑟 were seen to be functions of 𝐶3 𝑆, (𝐶3 𝐴 + 𝐶2 𝑆), and (𝐶3 𝑆 + 𝐶3 𝐴),
respectively. The difference between previous studies [3.4] and [3.44] and our investigation arises fromseveral factors. One factor is the materials used in the current study. Another factor may be the method todetermine the model parameters and the experimental method. As shown in Table 3.3, the parameter 𝐶 was
not dependent on the cement component. The results also indicated that the value of 𝐶 increased onincreasing the curing temperature. A previous study [3.15] reported that 𝐶 controls the rate of protective
film decay. Therefore, it can be concluded that increasing the curing temperature leads to the rate of58

protective film decay becoming faster. In other words, the higher curing temperature leads to a fasterhydration reaction of cement and cement–EX paste. This conclusion is consistent with our results.
Table 3.3 Equations showing relationship between mineral composition and model parameters
Temperature
Equations
B = (−2.25 × (C3 S% + 117.2) × 10−11(22b)k r = (0.11 × (C3 S% + C3 A%) − 0.45) × 10−8(22c)

D = (−0.29 × (C3 A% + C2 S%) + 9.7) × 10

5℃

(22a)
−11

OPC case: C = 2.0E+8; EX case: C = 0.5E+8
B = (−2.10 × C3 S% + 109.1) × 10−11

(23a)

w/b

D = (−3.14 × (C3 A% + C2 S%) + 72.5) × 10−11

(23b)

0.3

k r = (0.09 × (C3 S% + C3 A%) − 1.04) × 10−8(23c)

OPC case: C = 1.0E+9; EX case: C = 5.0E+8; (EX100: C = 5E+11)

20 ℃

B = (−2.32 × (C3 S% + 120.5) × 10−11

(24a)

w/b

D = (−4.08 × (C3 A% + C2 S%) + 134.2) × 10−11

(24b)

0.5

k r = (0.15 × (C3 S% + C3 A%) − 2.7) × 10−8(24c)

OPC case: C = 1.0E+9; EX case: C = 5.0E+8; (EX100: C = 5E+11)

40 ℃

B = (−2.39 × (C3 S% + 124.5) × 10−11(25a)

D = (−89.57 × (C3 A% + C2 S%) + 2929.5) × 10−11(25b)k r = (0.21 × (C3 S% + C3 A%) − 5.9) × 10−8(25c)

OPC case: C = 67E+8; EX case: C = 68E+8

3.3.2 Verification of hydration model
As mentioned previously, the aim of this study was to propose a simulation model for the hydration reactionof cement–EX blends. In this section, therefore, first, to verify the heat evolution using the proposed model,
experiments were performed using isothermal calorimetry at a curing temperature of 20⁡℃. A comparisonof the measured and the calculated rate of heat evolution for OPC100 and cement–EX pastes (EX5, EX10,
EX15, and EX20) at w/b 0.5 is illustrated in Figure 3.8. The figure shows that the calculated andexperimental results were in good agreement for all the samples. Furthermore, to verify the applicability ofthe proposed model and the effectiveness of Eqs. 3.9(a)-3.9(d), we measured and predicted the degrees ofhydration for OPC100, EX5, and EX10 at different curing temperatures of 5 ℃, 20 ℃, and 40 ℃ with aw/b of 0.5, as illustrated in Figure 3.9. As shown in Figure 3.9, a higher curing temperature led to an
accelerated degree of hydration. At the same curing temperature, the hydration degree increased with theaddition of the EX replacement ratio at 72 h. The values of the temperature sensitivity coefficients for
Arrhenius’ law were obtained and are listed in Table 3.4. Good agreement between the calculated results
and the measured results is evident here, as well. Finally, to evaluate the applicability of our model, a totalcomparison of the calculated and measured hydration degrees of all samples with a w/b of 0.3 and 0.5 at59

curing temperatures of 5 ℃, 20 ℃, and 40 ℃ is shown in Figure 3.10. Most of the points fall within theaccuracy limit lines.
Based on the results of the verification of the proposed model, we confirmed that our model shows good
applicability for cement–EX blends and a wide range of curing temperatures. In addition, previous studies[3.4], [3.26], and [3.37] have shown that the hydration reaction of cement-based materials shows arelationship with properties of concrete such as its compressive strength, chemical shrinkage, volumetricchange, and carbonation depth. Therefore, it is very useful to use our model to predict the mechanicalproperties and durability of expansive concrete. In order to prove our suggestion, in this study, thecompressive strength of expansive concrete was predicted using our model through the gel/space ratio,
which will be discussed next chapter.
20

20

15

EX5

(b)

Calculated

15

Calculated

Measured10

Rate of heat evolution, J/g h

OPC100(a)

Rate of heat evolution, J/g h

Measured

10

5

0

5

12

24

36
Time, h

48

60

72

Calculated

15

Measured
10

5

0
0

12

24

36
Time, h

20

48

60

0

72

12

24

36
Time, h

48

60

72

20

EX15

(d)
Rate of heat evolution, j/g h

EX10

(c)

0

0

Rate of heat evolution, J/g h

Rate of heat evolution, J/g h20

Calculated

15

Measured
10

5

0

(e)

EX20

Calculated

15

Measured
10

5

0
0

12

24

36
Time, h

48

60

72

0

12

24

36
Time, h

48

60

72

Figure 3.8 Comparison of calculated and measured rates of heat evolution at 20 ℃: (a) OPC100, (b)EX5, (c) EX10, (d) EX15, and (e) EX20.

SampleTable 3.4 Coefficients for Arrhenius’ law
𝛽1 (K)𝛽2 (K)
𝛽3 (K)

OPC100

150

8700

11000

600

EX5

150

12000

14000

60

EX10

150

12000

14000

60

60

E/R (K)

(a)(b)

OPC100(c)

EX5Degree of hydration

Degree of hydration

0.6

0.6

0.4

0.4
0.2

12

24

36
Time, h

48

60

72

0.4

0

0
0

0.6

0.2

0.2

0

EX10

0.8

0.8

0.8
Degree of hydration

1

1

1

0

12

24

36
Time, h

48

60

72

0

Calculated 5C

Calculated 20C

Calculated 40C

Measured 5C

Measured 20C

Measured 40C

12

24

36
Time,h48

60

72

Figure 3.9 Calculated and measured hydration degrees of cement with and without EX at 5℃, 20℃,
and 40 ℃ at w/b 0.5: (a) OPC100, (b) EX5, and EX10.

1±20% Accuracy limits line

Measured data, α

0.8

0.6

0.4

0.2

0
0

0.2

0.4
0.6
Calculated data, α0.8Figure 3.10 Total comparison of calculated and measured hydration degrees.

61

1

3.4 Conclusion
A numerical model is proposed to simulate the hydration reaction of cement paste containing expansive
additive at an early age. In order to test the accuracy of the proposed model, the predicted results from themodel for cement–EX blends were compared with experimental results. The results from the proposedmodel were in good agreement with experimental results and so the model proposed here can be applied tothe simulation of the hydration reaction of cement containing an expansive additive. Furthermore, thepresent study found that the hydration parameters 𝐵, 𝐷, and 𝑘𝑟 have a relationship with the 𝐶3 𝑆, (𝐶3 𝐴 +𝐶2 𝑆), and (𝐶3 𝑆 + 𝐶3 𝐴) phase, respectively.

62

References[3.1] Recommended Practice for Expansive Concrete, Concrete Library of JSCE No.23, June 1994.
[3.2] I. Maruyama, T. Matsushita, T. Noguchi, 2008. Numerical modeling of Portland cement hydration,
International RILEM Symposium on Concrete Modeling-CONMOD’08 26-28 May 2008, Delft, The
Netherlands.
[3.3] F. Tomasawa, Development of a kinetic model for hydration of cement, in Proceeding of the 10th
International Congress Chemistry of Cement, Gothenburg, Sweden, 2-6 June 1997; Chandra, S., Ed.; pp.
51-58.
[3.4] I. Maruyama, Time Dependent Property of Cement-Based Materials on the Basis of Micro-Mechanics,
Ph.D. Thesis, University of Tokyo, Japan, March 2003 (in Japanese).
[3.5] K. Maekawa, R. Chaube, T. Kishi, Modeling of Concrete Performance: Hydration, Microstructure
Formation and Mass Transport. London, New York: Routledge; 1998.
[3.6] K. Maekawa, T. Ishida, Modeling of structural performances under coupled environmental andweather actions. Materials and Structures. 35 (2002) pp. 591–602.
[3.7] K.A. Schindler, J.K. Folliard, Heat of hydration models for cementitious materials. ACI Materials
Journal. 102 (1) (2005), pp. 24–22.
[3.8] K.A. Riding, J.L. Poole, K.J. Folliard, M.C.G. Juenger, A.K. Schindeler, Modeling hydration of
cementitious systems. ACI Materials Journal. 109 (2) (2012), pp. 225–234.
[3.9] G. De Schutter, Hydration and temperature development of concrete made with blast-furnace slag
cement. Cement and Concrete Research. 29 (1) (1999), pp. 143–149.
[3.10] G. De Schutter, Fundamental study of early age concrete behavior as a basis for durable concrete
structures. Materials and Structures. 35 (2002), pp. 15–21.
[3.11] T. Merzouki, M. Bouasker, N. El H. Khalifa, P. Mounanga, Contribution to the modeling of
hydration and chemical shrinkage of slag-blended cement at early age. Construction and Building Materials.
44 (2013), pp. 368–380.
[3.12] S. Tanaka, K. Inoue, Y. Shioyama, R. Tomita, Methods of estimating heat of hydration andtemperature rise in blast furnace slag blended cement. ACI Materials Journal. 92 (1995), pp. 429–436.
[3.13] K.B. Park, N.Y. Jee, I.S. Yoon, H.S. Lee, Prediction of temperature distribution in high-strength
concrete using hydration model. ACI Materials Journal. 105 (2008), pp. 180–186.
[3.14] X.Y. Wang, H.S. Lee, K.B. Park, J.J. Kim, J.S. Golden, A multi-phase kinetic model to simulate
hydration of slag-cement blends. Cement and Concrete Composite. 32 (2010), pp. 468–477.
[3.15] M. Narmluuk, T. Nawa, Effect of fly ash on the kinetics of Portland cement hydration at different
curing temperatures. Cement and Concrete Research. 41 (2011), pp. 579–589.
[3.16] O. Levenspiel, Chemical Reaction Engineering, Third Edition. John Wiley & Sons, Inc. (1999).
[3.17] K.B. Park, T. Noguchi, J. Plawsky, Modeling of hydration reaction using neural networks to predict
the average properties of cement paste. Cement and Concrete Research. 35 (2005), pp. 1676-1684.
https://doi.org/10.1016/j.cemconres.2004.08.004.
63

[3.18] H. Sugiyama, Y. Masuda, Prediction of temperature rise of concrete member using mathematicalmodel for cement hydration and microstructure formation. J. Struct. Constr. Eng., AIJ. 73 (623) (2008), pp.
[3.19] I. Maruyama, T. Noguchi, T. Matsushita, Hydration model of Portland cement. J. Struct. Constr.
Eng., AIJ. (593) (2005), pp. 1–8 (in Japanese). https://doi.org/10.3130/aijs.70.1_7.
[3.20] X.Y. Wang, H.S. Lee, Simulation of a temperature rise in concrete incorporating fly ash or slag.
Materials and Structures. 43 (2010), pp. 737–754. https://doi.org/10.1617/s11527-009-9525-8.
[3.21] X.Y. Wang, H.S. Lee, Modeling of hydration kinetic in cement based materials considering theeffects of curing temperature and applied pressure. Construction and Building Materials. 28 (2012), pp. 1–
13.
[3.22] H.S. Lee, X.Y. Wang, L.N. Zhang, K.T. Koh, Analysis of the optimum usage of slag for thecompressive strength of concrete. Materials. 8 (2015), pp. 1213–1229. https://doi.org/10.3390/ma8031213.
[3.23] W.J. Fan, X.Y. Wang, K.B. Park, Evaluation of the chemical and mechanical properties of hardening
high-calcium

fly

ash

blendedconcrete.

Materials.

8(2015),

pp.

5933–5952.

https://doi.org/10.3390/ma8095282.
[3.24] K.K. Aligizaki, Pore structure of cement-based materials: testing, interpretation and requirements.
Modern Concrete Technology. Taylor & Francis (2006).
[3.25] L. Lam, Y.L. Wong, C.S. Poon, Degree of hydration and gel/space ratio of high-volume fly
ash/cement systems. Cement and Concrete Research. 30 (2000), pp. 747–756.
[3.26] K. van Breugel, Simulation of Hydration and Formation of Structure in Hardening Cement-BasedMaterials, Ph.D. Thesis, Delft, The Netherlands (1991).
[3.27] H. Woods, H.H. Steinour, and H.R. Starke. Effect of composition of Portland cement on heat evolved
duringhardening.

Industrial&

Engineering

Chemisty.

24

(11)

(1932)

pp.

1207-1214.

https://doi:10.1021/ie50275a002.
[3.28] R.H. Bouge. Calculation of the compounds in Portland cement. Industrial & Engineering Chemistry
Analytical Edition. 1 (4) (1929), pp. 192-197. https://doi:10.1021/ac50068a006.
[3.29] Wm. Lerch and R.H. Bogue, Heat of hydration of Portland cement pastes. Part of Bureau ofStandards Journal of Research. 12 (1934), pp. 645-664.
https://nvlpubs.nist.gov/nistpubs/jres/12/jresv12n5p645_A2b.pdf.
[3.30] T. Thorvaldson, W. G. Brown, C.R.Peaker, Studies on the thermochemistry of the compounds
occurring in the system CaO-Al2O3-SiO2. IV. The heat of solution of tricalcium aluminate and its hydrates
in hydrochloric acid. (1930), pp. 3927-3936. https://doi:10.1021/ja01373a024.
[3.31] P. Catharin, Heat of hydration and strength development. BETONWERK+ FERTIGTEILTECHNIK. 99 (1978), p.539-544.
[3.32] L.D. Adam, The measurement of very early hydration reactions of portland cement clinker by athermoelectric conduction calorimeter. Cement and Concrete Research 6 (1976), pp. 293-307.
https://doi.org/10.1016/0008-8846(76)90127-7.
[3.33] T.F. Newkirk, in 3rd ISCC, London (1952), pp 151-168.
64

[3.34] A. Hori, M. Takahashi, Y. Tsuzi, M. Harada, Fundamental properties of concrete using low added
expansive additive. Proceeding of the Japan Concrete Institute. 24 (1) (2002) (in Japanese).
[3.35] T. Higuchi, M. Eguchi, M. Morioka, E. Sakai, Hydration and properties of expansive additive treatedhigh temperature carbonation. Cement and Concrete Research. 64 (2014), pp.11-16.
[3.36] H. Choi, T. Noguchi, Modeling of mechanical properties of concrete mixed with expansive additive,
International Journal of Concrete Structures and Materials. 9 (4) (2015), pp. 391–399.
[3.37] X.Y. Wang, Modeling of hydration, compressive strength, and carbonation of Portland-Limestone
Cement (PLC) concrete. Materials. 10 (2017), pp. 115.
[3.38] I. Odler (1998). Hydration, setting and hardening of portland cement, in P. Hewlett (ed.), Lea’s
chemistry of cement and concrete, 4th edn, Arnold, London, U.K., pp. 241–297.
[3.39] D. Jansen, F. Goetz-Neunhoeffer, C. Stabler, J. Neubauer, A remastered external standard method
applied to the quantification of early OPC hydration. Cement and Concrete Research. 41 (2011), pp. 602–
608.

65

CHAPTER 4PREDICTING THE COMPESSIVE STRENGTH OFEXPANSIVE CONCRETE BASED ON THE
HYDRATION MODEL

66

CHAPTER 4 PREDICTING THE COMPESSIVE STRENGTH OF EXPANSIVE CONCRETE
BASED ON THE HYDRATION MODEL
4.1 Introduction
Concrete is widely used in the world as a building material with many outstanding features such as highstrength and durability, low cost, and so on. Although there are many kinds of strength (compressive
strength, flexural strength, etc.), compressive strength is commonly considered to evaluate the quality ofconcrete because strength is directly related to the structure of hydrated cement paste [4.1]. It is wellknown that the water-cement (w/c) ratio has affected the compressive strength. However, at any w/c ratio,
the strength depends on the hydration degree of cement and its chemical and physical properties [4.1].
Therefore, the hydration process of cement or cement-based material has a relationship with thedevelopment of compressive strength of concrete. The other words, the compressive strength development
could be predicted through the hydration reaction of cementitious systems.
In order to predict the compressive strength of concrete, many studies [4.2], [4.3], [4.4], and [4.5] havereported a relationship between the compressive strength and the pore volume and predicted thecompressive strength through these relations. Choi et al. [4.6] modeled the compressive strength and elastic
modulus of a hardened cement paste mixed with expansive additives and validated the model byconsidering the pore structure of a hardened cement paste based on the hydration. Furthermore, Powers[4.7] found that the compressive strength was related to the gel/space ratio and suggested a compressive
strength equation as a function of the gel/space ratio. Lam et al. [4.8] introduced a model to describe therelationship between the gel/space ratio and the compressive strength. The results showed that the gel/spaceratio of the fly ash–cement paste was consistent with that of the OPC paste in terms of the relationship withthe compressive strength. In addition, considering the gel/space ratio, Wang [4.9] evaluated thedevelopment of the compressive strength of ultra-high-performance concrete using a blended cement
hydration model employing Powers’ strength theory. The abovementioned studies [4.2], [4.3-4.9] indicatedthat it is possible to predict the development of the compressive strength of concrete through Powers’
strength theory considering the gel/space ratio. However, these studies have mostly focused on themechanical properties of Portland cement, fly ash–cement, and slag–cement blends; few investigations havestudied the properties of expansive concrete. Moreover, applying the hydration model to predict themechanical properties and durability of expansive concrete has not been studied specifically.
As mentioned above, Powers [20] suggested a strength theory that determined a relationship between thecompressive strength of Portland cement concrete and gel/space ratio through experimental data. The
analysis herein is also based on the theory suggested above but we apply it to expansive concreteconsidering the contribution of cement hydration and expansive additive reaction. In this case, thecompressive strength of expansive concrete was predicted from the strength of cement paste and thecharacteristics of aggregates, and the gel/space ratio was obtained from the proposed hydration model.
Figure 4.1 shows a flow chart representing the work undertaken. In order to predict the compressive strength,
using Powers’ Strength theory, the relationship between the gel/space ratio and the compressive strength67

of paste was deduced. Then, a relationship between the gel/space ratio and compressive strength of concrete
was suggested.

Chapter 4
Prediction of Compressive Strength of Expansive Concrete
Chapter 3
Hydration Model

Chapter 2
Experimental

Gel/space ratio

Gel/space ratio

Compressive strength
Volume increase rateof gelHardened Paste
𝑓𝑐 = 𝐴𝑥 𝑛
Characteristics ofaggregate

Aggregate strength

Powers’ Strength
TheoryOPC

Concrete=

Volume of aggregate

A = 234 (Mpa), n = 3
EX
A =? (Mpa), n =?

Figure 4.1 Flow chart684.2 Predicting the compressive strength
4.2.1 Gel/space ratio
In general, there exists a fundamental inverse relationship between the porosity and the strength of solids[4.1047]. Choi et al. [4.6] assumed that the strength development of a cement paste mixed with an expansive
additive is closely related to the pore volume based on the results of existing studies. Wang [4.11] reported
that the compressive strength depends on the gel/space ratio determined from the cement hydration and w/b
ratio. A gel/space ratio is defined as the ratio of the volume of the hydrated cement paste to the sum of thevolumes of the hydrated cement and the capillary pore. This ratio is also called the amount of solid fractionin the system and is therefore equal to 1-porosity [4.10].
In this section, we describe the relationship between the concrete strength and the gel/space ratio for
concrete with a 5% EX replacement content. The concrete strength was investigated by considering thecement paste strength, the characteristics of the aggregate, and an original coefficient 𝜔. Gel/space ratio
was calculated from the proposed model.
The gel/space ratio of Portland cement paste 𝑥𝑐 [4.1] can be described by the following expression:𝑥𝐶 =2.06(1/𝜌𝐶 ) 𝐶 𝐶0
(1/𝜌𝐶 ) 𝐶 𝐶0 + 𝑊0

Eq. (4.1)

where ρC is the specific gravity of cement; 2.06 is the volume increase rate of the OPC paste based on theunderstanding that 1 mL of hydrated cement occupies 2.06 mL of volume [4.1], [4.10]; and𝐶 is the degreeof hydration of the OPC paste.
For the Portland cement paste, Powers [4.1] found that the 28-day compressive strength 𝑓𝑐 of three different
mixtures was related to the gel/space ratio, as shown in Eq. (4.2):
𝑓𝑐 = 𝐴𝑥𝐶𝑛

Eq. (4.2)

where 𝑥𝑐 is the gel/space ratio; A is the intrinsic strength of materials at zero porosity (MPa); and n is anexponent.
For the compressive strength of concrete, Powers [4.1] found the values of A and n to be 234 MPa and 3,
respectively.
For the cement–EX paste, the compressive strength can be predicted using Powers’ Strength theory as
follows:𝑛𝑓𝐶−𝐸𝑋 = 𝐴𝑥𝐶−𝐸𝑋

Eq. (4.3)

where fC-EX is compressive strength of the cement–EX blend; A is the intrinsic strength of the cement–EX
blend at zero porosity (MPa); and n is an exponent.
In Eq. (4.3), 𝑥𝐶−𝐸𝑋 is the gel/space ratio, which can be calculated using Eq. (4.4). Choi et al. [4.6] proposeda volume increase rate of 3.34 for the EX paste. Therefore, the gel/space ratio of the EX paste must be
adjusted as follows:69

𝑥𝐶−𝐸𝑋 =2.06(1/𝜌𝑐 ) 𝑐 𝐶0 + 3.34(1/𝜌𝐸𝑋 ) 𝐸𝑋 𝐸𝑋0(1/𝜌𝑐 ) 𝑐 𝐶0 + (1/𝜌𝐸𝑋 ) 𝐸𝑋 𝐸𝑋0 + 𝑊0

Eq. (4.4)

where xC-EX is the gel/space ratio of the cement–EX paste; ρEX is the specific gravity of EX; and 3.34 is thevolume increase rate of the EX paste [4.6].

4.2.2 Relationship between cement paste strength and concrete strength
The relationship between the cement paste and concrete strength was investigated through a model
developed by Upendra [4.12]. In this model, the author considered a unit volume of concrete in the form ofa prism (or cylinder) as shown in Figure 4.2. The cylinder of concrete has a unit area of cross-section asshown in Figure 4.3. Assuming that the volume of the cylinder of the aggregate is Va, the deformation
behavior of such a model can be determined by assuming the following:•

The stress applied to the concrete cylinder does not vary along the depth of the layer AA1D1D or
BB1C1C;•For the combined material (aggregate and matrix) BB1C1C, the strain in the direction of application ofstress is the same as the strains in the aggregate and in the matrix.

Paste

S1

A1

A

B1

B

Compression
1 − 𝑉𝑎
2

𝑉𝑎

1
C1

C

D1

D

Aggregates

1 − 𝑉𝑎2

S2

Figure 4.2 Unit volume of concrete [4.12].

1 − 𝑉𝑎2𝑉𝑎

1 − 𝑉𝑎2

Figure 4.3 Cross section S1-S2 [4.12].

The elastic strain of concrete [48] is𝜀𝑐 = 𝜀𝑝 (1 − √𝑉𝑎 ) + 𝜀𝑎 . √𝑉𝑎

Eq. (4.5)

where 𝜀𝑐 , 𝜀𝑝 , and 𝜀𝑎 (N/mm2) are given by
𝜀𝑐 =

𝑓𝑐
𝑓𝑐
𝑓𝑐
; 𝜀𝑝 =;⁡𝜀𝑎 = ⁡𝐸𝑐
𝐸𝑝𝐸𝑎

Eq. (4.6-a)

70

𝑓𝑝
𝑓𝑐
𝑓𝑎
=
=
𝐸𝑐 𝐸𝑝 𝐸𝑎

Eq. (4.6-b)

Combining Eqs. (4.5) and (4.6-a, b), the compressive strength of concrete is expressed as
𝑓𝑐 = 𝑓𝑝 (1 − √𝑉𝑎 ) + 𝑓𝑎 . √𝑉𝑎

Eq. (4.7)

where 𝑓𝑐 , 𝑓𝑝 , and 𝑓𝑎 are the compressive strengths of the concrete, paste, and aggregate (MPa), respectively;
𝑉𝑎 is the volume of aggregate (%).
Based on Eq. (4.7), however, the aggregate strength has a strong effect on the compressive strength of
concrete. This means that the compressive strength of concrete mainly depends upon the compressive
strength of aggregates; the strength deterioration of concrete is more than or equal to that of the aggregates.
In fact, however, there are two damaged concrete cases, as the compressive strength test is carried out asshown in Figure 4.4. In the first case, the compressive strength of cement paste is less than that of aggregates
and the damage only occurs in the cement paste. In the second case, the compressive strength of the cement
paste is more than or equal to that of the aggregates and the damage would occur in the cement pastes aswell as in the aggregates.
Therefore, to determine a satisfactory value for the predicted result that is consistent with the results in thisstudy, a coefficient should be deduced, which can be written as 𝜔.
The prediction equation can be rewritten as:
𝑓𝑐 = {𝑓𝑝 (1 − √𝑉𝑎 ) + 𝑓𝑎 . √𝑉𝑎 } ∙ 𝜔

Eq. (4.8)

P

P

CracksAggregate

Paste
𝑓𝑝

𝑓𝑎

𝑓𝑝

4.4-(a) Damage of normal concrete𝑓𝑎4.4-(b) Damage of high strength concrete

𝑓𝑝 : Compressive strength of cement paste
𝑓𝑎 : Compressive strength of aggregates
Figure 4.4 Schematic of damage of concrete: (a) normal concrete, (b) high strength concrete714.3 Results and Discussion
4.3.1 Relationship between compressive strength of cement paste and gel/space ratio
In this section, to predict the compressive strength of expansive concrete, the dependence of compressive
strength of cement paste on the gel/space ratio with and without EX was determined. The relationshipbetween the gel/space ratio and the compressive strength of OPC and EX pastes are shown in Figure 4.5.
The gel/space ratio correlates with the compressive strength for coefficient correlations of 0.72 and 0.82
for the OPC and EX5 samples, respectively. According to Eq. (4.2) and the results, the compressive strength
can be expressed as:
For OPC paste:

𝑓𝑐 = 250𝑥 3.16

Eq. (4.9)

For EX paste:

𝑓𝐸𝑋 = 454𝑥 3.99

Eq. (4.10)
150

(a)

OPC100Compressive Strength, N/mm2

Compressive Strength, N/mm2

150

y = 250.05x3.1598
R² = 0.7281

100

(b)
y = 454.4x3.9919
R² = 0.824

100

50

0

EX

50

0
0

0.2

0.4
0.6
Gel/Space ratio

0.8

1

0

0.2

0.4
0.6
Gel/Space ratio

0.8

1

Figure 4.5 Gel/space ratio and compressive strength of OPC and EX pastes: (a) Portland cement
paste, (b) Cement-EX paste.

According to the results, for a given gel/space ratio, the cement–EX paste shows higher compressive
strength than that of the cement paste. This is possibly due to the effect of the pore structure of the cement–
EX paste on the strength enhancement. The formation of ettringite crystals will fill the pores in the cement–
EX paste matrix, which leads to a denser pore structure. This result is in agreement with the previous findingof Nguyen. et al [4.13], who studied the effect of expansive additive on the total porosity of mortars. They
found that the total porosity of expansive mortar is smaller than that of non-expansive mortar. This is thereason for the higher intrinsic strength of the cement–EX paste at zero porosity when compared to that of
cement paste (see Eqs. (4.9), (4.10)).

72

4.3.2 Relationship between conversion coefficient and gel/space ratio

2100

Compressive strength, N/

120

80
60
40
Powers [20]20

Calculated
0

0

0.5
Gel/space ratio

1

Figure 4.6 Fitting the calculated data to the Powers [20] data.
0.5
y = 1.1449x - 0.4412
R² = 0.9871

𝜔 coefficient

0.4
0.3
0.2
0.1

0
0

0.5
Gel/space ratio

1

Figure 4.7 Relationship between 𝝎 and gel/space ratio.

Compressive Strength, N/

2

150
120

y = 253.33x2.6942
R² = 0.8383

90

60
30
0
0

0.2

0.4
0.6
Gel/space ratio

0.8

1

Figure 4.8 Relationship between compressive strength and gel/space ratio of expansive concrete.
73

In this part of the study, the compressive strength of expansive concrete was calculated from the strengthof the cement–EX paste, characteristics of the aggregate, and the value of 𝜔 using Eq. (4.8), as presented
in Section 4.2.2. The gel/space ratio was calculated from the proposed model through Eq. (4.4).
By fitting the calculated data to the Powers [4.1], [4.7], [4.10] data using the least-squares method, the valueof the 𝜔 coefficient could be calculated. Figure 4.6 shows the fitting results. Furthermore, the relationshipbetween the value of the coefficient 𝜔 and the gel/space ratio was also evaluated, as shown in Figure 4.7.
The 𝜔 coefficient correlated linearly with the gel/space ratio with a high correlation coefficient of 0.98 (seeFigure 4.7). It was also evident that the 𝜔 coefficient can be represented as a function of the gel/space ratio
and is given by𝜔 = 1.1449𝑥 − 0.4412

Eq. (4.11)

where 𝑥 is the gel/space ratio.
Combining the value of the 𝜔 coefficient and Eq. (21), the relationship between the compressive strengthof concrete and the gel/space ratio was evaluated for wEX5, as shown in Figure 4.8. The figure shows thatthe gel/space ratio data correlates with the predicted compressive strength. As mentioned above, Powers[4.1], [4.7], [4.10] suggested a relationship, given by 𝑓𝑐 =234𝑥 3 , between the compressive strength of
concrete and the gel/space ratio for OPC. Similar to the suggestion of Powers, we suggest a relationshipbetween the compressive strength of expansive concrete and the gel/space ratio, which can be given as:
2.69
𝑓𝐶−𝐸𝑋 =253𝑥𝐶−𝐸𝑋

Eq. (4.12)

In Eq. (28), the value of intrinsic strength A is 253 MPa and n is 2.69 for expansive concrete. As shown in
Figure 4.8, give a certain gel/space ratio, the compressive strength of expansive concrete is higher than thatof Portland cement concrete. This result is consistent with the experimental results reported previously[4.14]. Thus, the proposed model has been proven to be able to estimate the gel/space ratio of cement–EX
pastes and capable of modeling the compressive strength of expansive concrete. However, our prediction
is only applicable for expansive concrete with 5% of expansive additive, which is known as a standard
amount (20kg/m3) of expansive additive for expansive concrete in Japan. In fact, we have considered awide range of expansive additives such as 10%, 15%, and 20% expansive additive replacement by weight.
However, experimental results indicated that a large amount of expansive additive will increase thevolumetric change of sample under unconfined conditions, which causes many internal and surface cracks.
This strongly affects the total porosity and compressive strength of the cement–EX paste. In other words,
the total porosity increases for a larger amount of expansive additive under unconfined conditions. Thistendency was also found in the study reported by Choi et al. [4.6].

74

4.4 Conclusions
1) The gel/space ratio of cement–EX blends was calculated by applying the proposed model. An
original⁡𝜔 coefficient was deduced to find a satisfactory value for predicted results, called theconversion coefficient.
2) The compressive strength of expansive concrete was predicted by considering the cement–EX paste
strength, characteristics of the aggregate, and the conversion coefficient. Using Powers’ strength
theory, an equation showing dependence of the compressive strength of expansive concrete on thegel/space ratio of expansive additive was deduced with A = 253 and n = 2.69.

75

References[4.1] A.M. Neville, Properties of Concrete, 5th ed. Harlow, England: Prentice Hall, Pearson.
[4.2] F. Tomasawa, Development of a kinetic model for hydration of cement, in Proceeding of the 10th
International Congress Chemistry of Cement, Gothenburg, Sweden, 2-6 June 1997; Chandra, S., Ed.; pp.
51-58.
[4.3] E. Ryshkewithch, Composition and strength of porous sintered alumina and zirconia. Journal of theAmerican Ceramic Society. 36 (1953), pp. 65–68.
[4.4] K.K. Schiller, Mechanical properties of non-metallic materials. London, UK: Butterworths. (1958)
pp. 35–50.
[4.5] C. Lian, Y. Zhuge, S. Beecham, The relationship between porosity and strength for porous concrete.
Construction and Building Materials. 25 (2011), pp. 4294–4298.
[4.6] H. Choi, T. Noguchi, Modeling of mechanical properties of concrete mixed with expansive additive,
International Journal of Concrete Structures and Materials. 9 (4) (2015), pp. 391–399.
[4.7] T.C. Powers, Structure and physical properties of hardened Portland cement paste. Journal American
Ceramic Society. 41 (1958), pp.1–6.
[4.8] L. Lam, Y.L. Wong, C.S. Poon, Degree of hydration and gel/space ratio of high-volume fly ash/cement
systems. Cement and Concrete Research. 30 (2000), pp. 747–756.
[4.9] X.Y. Wang. Properties prediction of ultra-high performance concrete using blended cement hydration
model. Construction and Building Materials.
[47] [4.10] P.K. Mehta, P.J.M. Monteiro, Concrete: Microstructure, Properties, and Materials, Fourth
Edition. New York: McGraw-Hill Education.
[44] [4.11] X.Y. Wang, Modeling of hydration, compressive strength, and carbonation of PortlandLimestone Cement (PLC) concrete. Materials. 10 (2017), pp. 115.
[48] [4.12] J.C. Upendra, The effect of the elastic modulus of the aggregate on the elastic modulus, creep
and creep recovery of concrete. Magazine of Concrete Research. 16 (48) (1964), pp 129-138.
[51] [4.13] T.B.T. Nguyen, R. Chatchawan, W. Saengsoy, S. Tangtermsirikul, T. Sugiyama. Influences ofdifferent types of fly ash and confinement of performances of expansive mortars and concrete. Construction
and Building Material 209 (2019) pp.176-186.
[52] [4.14] D.T. Nguyen, R. Sahamitmogkol, L.N. Trong, S. Tongaroonsri, S. Tangtermsirikul. Predictionof shrinkage cracking age of concrete with and without expansive additive. Songklanakarin J. Sci. Technol.
32 (5), pp469-480, Sep-Oct. 2010.

76

CHAPTER 5
PREDICTING CARBONATION DEPTH OFEXPANSIVE CONCRETE BASED ON
HYDRATION REACTION MODEL

77

CHAPTER 5 PREDICTING CARBONATION DEPTH OF EXPANSIVE CONCRETE BASEDON HYDRATION REACTION MODEL
5.1 Introduction
Expansive concrete has been used as an efficient way to prevent and minimize cracking caused by drying
shrinkage in concrete structures such as slabs, pavements, etc. [5.1, 5.2]. The expansion is generated by the
production of ettringite and calcium hydroxide (CH) from the hydration reaction of expansive additive withwater [5.2]. Concrete mixed with expansive additive (EX) that will expand in the first few days of its life,
and a prestress is induced in concrete to offset or reduce tensile stress caused by drying shrinkage when the
expansion of expansive concrete has been restrained by a restraining object such as embedded steel
reinforcement.
It is well-known that the steel reinforcement in concrete is protected from corrosion by a thin oxide layer
forms on the steel and prevents metal atoms from dissolving due to the alkaline environment of concretewith high pH (pH of 12 to 13). One of the factors that enhance the corrosion of the steel embedded is
cracking [5.3]. As the cracks in the surface of concrete or mortar are present, the CO2 gaseous from theatmosphere may move towards the inner zones of concrete, then neutralize the alkalinity of concrete, whichleads to the pH of the pore water in a concrete decrease to a low value of 9. The passive layer on the steel
surface is no longer stable and corrosion can take place [5.3, 5.4]. Therefore, the effect of the carbonationon the service like time of concrete structure with or without supplement cementing materials (SCM) suchas fly ash, blast-furnace slag, and expansive additive (EX) as well must be considered.
Several experimental researches [5.5, 5.6] were studied to investigate the influence of carbonation on theproperties and microstructure of expansive concrete. Sakai et al. [5.5] reported that no differences were
found in the carbonation depth and the compressive strength between expansive concrete and cement
concrete. However, Tu Liuqing et al. [5.6] also reported that replacing Portland cement with fly ash andexpansive additive increases the carbonation rate of concrete. This result is not consistent with the findingof Sakai et al. [5.5]. Meanwhile, Papadakis [5.7-5.9] was the first to propose and develop a fundamental
mathematical model for the physicochemical process involved in the carbonation of Portland cement
concrete and concrete containing SCM. This model considered both concrete composition andenvironmental factors. However, in this model [1], the calculating equation of parameters did not consider
the hydration dependence of cement. Because the production of calcium hydroxide (CH) and calcium
silicate hydroxide (C-S-H) depends on the hydration degree of cement and SCM. Therefore, a mathematicalmodel that could predict the carbonation depth of concrete considering the hydration dependence of cement
is essential. Wang and Lee [5.10] have proposed a numerical model for predicting the carbonation depth of
concrete containing the low-calcium fly ash. The hydration reaction of cement compounds was consideredin this model.
It notes that the above studies [5.5-5.10] have a deal with the carbonation of expansive concrete inexperimental and predicting the carbonation depth of cement concrete and concrete mixed with the SCM;
there is no research that proposed a numerical model for predicting the carbonation of expansive additive.
78

In this study, therefore, the mathematic model was proposed and developed to predict the carbonation depthof concrete mixed with expansive additive. The parameters such as CH, C-S-H content, and porosity ofconcrete were calculated by considering the hydration dependence of both Portland cement and EX.
Subsequently, the measured data and calculated data were compared to validate the proposed model. Figure
5.1 shows a flow chart representing the work undertaken.

Chapter 5
Predicting Carbonation Depth of Expansive Additive Based On Hydration Model
Chapter 3
Hydration Model

Takayuki
Higuchi’s data

Chapter 2
Experimental

Papadakis’s coefficenceMix proportions

Materials compositions

Air content*(in fresh concrete)Comparison

The amount ofCH and CSH

Comparison
Porosity

Porosity

Effective diffusivity of CO2

Prediction Equation

Comparison
Calculated data

Figure 5.1 Flow chart

79

Measured data5.2 Predicting carbonation depth
The main carbonation reaction in concrete or mortar is usually described by the carbonated of calcium
hydroxide as shown in the Eq. (5.1a). Besides Ca(OH)2 , the carbonation of C-S-H is also possible [5.3][5.9], [5.10], [5.11], [5.12], [5.13], 5.14] (see Eq. 5.1b).
Ca(OH)2 + ⁡ CO2 ⁡ → CaCO3 + H2 O

Eq. (5.1a)

3CaO. 2SiO2 . 3H2 O + 3CO2 → (3CaCO3 . 2SiO2 . 3H2 O)

Eq. (5.1b)

For predicting the carbonation depth of concrete, a fundamental and comprehensive reaction engineeringmodel of the process of the concrete carbonation was developed and experimentally verified by Papadakis
et al. [5.7], [5.15], as shown in Eq. (5.2). This model considered the diffusion of CO2 in a gaseous phase
into concrete pore, its dissolution in the aqueous film of these pores, the dissolution of solid Ca(OH)2 inpore water, its ultimate reaction with the dissolved CO2, and the reaction of CO2 with C-S-H and with someunhydrated phases of cement.
2De,CO2 [CO2 ]0
xc = √
・√t[CH] + 3[CSH]

Eq. (5.2)

where,xc (cm) is the carbonation depth;t (week) is the time to expose specimen in carbonation condition;
De,CO2 (m2/s) is the effective diffusivity of CO2 in carbonated concrete;[CO2 ]0 (％) is the CO2 content in the ambient air at the concrete surface, [CO2 ]0 = 5%;[CH] and [CSH] (mol) are the molar concentrations of Portlandite and Calcium silicate hydrate.
In this study, the carbonation depth of expansive concrete is predicted by using Eq. (5.2). However, someparameters in Eq. (5.2) are modified to make it more suitable for predicting the carbonation depth of
concrete mixed with expansive additive, as described in the next parts in detail.
In Eq. 5.1, the calcium hydroxide reacting is produced by hydration of the calcium silicate compounds ofthe cement [5.3], [5.11]. In this study, concrete was mixed with an expansive additive as a replacement
material. Therefore, the calcium hydroxide reacting here is also produced by the hydration of free-CaO andthe calcium silicate compounds of the expansive additive. Similar to the production of the calcium
hydroxide, the production of the calcium silicate hydroxide reacting in Eq. (5.2) is not only from thehydration cement but also from the hydration of expansive additive.
The hydration of Portland cement is a series of complex reactions of the cement compounds. In this study,
however, the hydration reactions of ordinary Portland cement are described by the Eqs. (5.3-5.6) [5.9], [5.9][5.13], [5.14].
2C3 S + 6H → C3 S2 H3 + 3CH

Eq. (5.3)

2C2 S + 4H → C3 S2 H3 + CH

Eq. (5.4)

2C3 A + CS̅H2 ⁡ + 10H → C4 AS̅H12

Eq. (5.5)80

C4 AF + 2CH + 10H → C6 AFH12

Eq. (5.6)

Meanwhile, the hydration reactions of the expansive additive are described by Eqs. (5.7-5.10) [5.16], [5.17].
C + ⁡H⁡ → CH

Eq. (5.7)

6CH + C4 A3 S̅ + 8CaSO4 + 90H → (3CaO. Al2 O3 3. CaSO4 . 32H2 O)

Eq. (5.8)

2C2 S + 4H → C3 S2 H3 + CH

Eq. (5.9)

C4 AF + 2CH + 10H → C6 AFH12

Eq. (5.10)

In order to calculate the amount of CH and C-S-H, the method of calculating the molar mass of an elementin chemistry is performed using the equation as shown in Eq. (5.11).
n=Eq. (5.11)

M

where,
n is the molar mass of an element (mol);m is the amount of an element (g);M is the relative formula mass.
An example was carried out to explain the method. Example: Calculating the amount of CaO from 4g Ca?
Firstly, the reaction of Ca and oxygen are described by following equation:
2Ca + ⁡ O2 ⁡ → 2CaO

Eq. (5.12)

From reaction Eq. (5.12), with 1 mol of Ca create 1mol CaO. According to Eq. (5.11), the number of molesof Ca equal to the amount of Ca divided by the relative formula mass of Ca, which is 0.1 mol. Therefore,
the number of moles of CaO is 0.1. The amount of CaO is

CaO = nCaO × MCaO = 0.1 × 56 = 5.6⁡(g).

5.2.1 Calcium hydroxide
In this study, the CH content is calculated by considering the production and consumption of CH from thehydration reaction of cement and expansive additive through the Eqs. (5.3-5.10). From the Eqs. (5.3-5.10),
the number of moles of CH isnCH = nCH[Eq.⁡⁡(5.3)] + nCH[Eq.⁡⁡(5.4)] − nCH[Eq.⁡⁡(5.6)] + nCH[Eq.⁡⁡(5.7)] − nCH[Eq.⁡⁡(5.8)]+ nCH[Eq.⁡⁡(5.9)] − nCH[Eq.⁡⁡(5.10)]
CH = nCH × MCH

Eq. (5.13)
Eq. (5.14)

3 fCOPC
3S
×C
2 MC3 S

Eq. (5.15a)

1 fCOPC
2S
nEq.⁡⁡(5.4) =×C
2 MC2 S

Eq. (5.15b)

nEq.⁡⁡(5.3) =nEq.⁡⁡(5.6) = 2
nEq.⁡⁡(5.7) =

fCOPC
4 AF

×C

Eq. (5.15c)

EX
fCaO
× EX
MCaO

Eq. (5.15d)

MC4 AF

81

EX
fYe
′ el.
× EX
MYe′ el.

Eq. (5.15e)

1 fCEX
2S
× EX
2 MC2 S

Eq. (5.15f)

fCEX
4 AF
× EX
MC4 AF

Eq. (5.15g)

nEq.⁡⁡(5.8) = 6
nEq.⁡⁡(5.9) =nEq.⁡⁡(5.10) = 2
where,

n𝐶𝐻 is the number moles of calcium hydroxide (mol);nEq.⁡⁡(5.3) , nEq.⁡⁡(5.4) , nEq.⁡⁡(5.6) , nEq.⁡⁡(5.7) , nEq.⁡⁡(5.8) , nEq.⁡⁡(5.9) and⁡nEq.⁡⁡(5.10) are the number of moles ofcalcium hydroxide according to the chemical equation (5.3), (5.4), (5.6), (5.7), (5.8), (5.9), and (5.10),
respectively, as indicated in Eq. (5.15a-5.15g);
CH is the amount of calcium hydroxide (g);MCH , MC3 S , MC2 S , MC4 AF , MCaO and MYe′ el. are the relative formula mass of CH, cement and expansive
additive compound, respectively. The values are given in Table 5.1;
C and EX are the weigth of cement and expansive additive in the mix proportion.

Table 5.1 Molar weight and molar volume of the main compounds found in Portland cement andPortland-based binders.
Molar weight
CompoundDensity3-3

Molar volume
363

10 (kg/mol)

10 (kg/m )10 (m /gmol)

C3 S

228.30

3.20

71.34

C2 S

172.22

3.30

52.19

C3 A

270.18

3.03

89.17

C4 AF

485.96

3.77

128.90CS̅H2

172.17

2.32

74.21

H

18.02

1.00

18.02

CH

74.10

2.24

33.08

C3 S2 H3

342.41

2.28

150

C4 AS̅H12

622.51

1.95

319.24C4 AH13560.472.06

272.07

C3 A・3CS̅・H32

1255.131.78

705.13

C6 AFH12814.312.65

307.87

C8 AFS̅2 H24

1302.44

2.3

560

C8 AFH26

1178.29

2.3

500

Ye’elimite (C4 A3 S̅)

610

-

-

82

CC̅

100.09

2.71

36.93

C

56.08

3.32

16.89

S

60.08

2.20

27.28

A

101.96

4.00

25.49

F

159.69

5.24

30.48

S̅

80.07

-

-

However, the presented equations of number moles and amount of CH (see Eq. (5.13) and Eq. (5.14)) are
the values when the hydration degree of cement (or cement-EX blend) is equal to 1 ( 𝑚𝑎𝑥 = 1). To evaluate
time dependent on the production of CH, the hydration degree of cement and expansive additive isconsidered. The degree of hydration of cement and cement-EX blend was modeled by the numerical model,
which was discussed in Chapter 3. The number moles of CH are rewritten
ntCH = (nCH[Eq.⁡⁡(5.3)] + nCH[Eq.⁡⁡(5.4)] − nCH[Eq.⁡⁡(5.6)] ) ×

OPC + (nCH[Eq.⁡⁡(5.7)]− nCH[Eq.⁡⁡(5.8)] + nCH[Eq.⁡⁡(5.9)] − nCH[Eq.⁡⁡(5.10)] ) ×

Eq. (5.16)EXtt
CH = nCH × MCH

Eq. (5.17)

where,
ntCH (mol) and
OPC andt
CH (g) are the number moles and the amount of CH at time t, respectively;

EX are the hydration degree of cement and expansive additive.

5.2.2 Calcium Silicate hydroxide
Similar to the method of calculating the amount of CH, the amount of C-S-H is also calculated by balancing
the production and consumption of CH in the hydration reactions of cement and expansive additive (seeEqs. (5.3-5.10). According to Eqs. (5.3-5.10), the number moles of C-S-H isnCSH = nCSH[Eq.⁡⁡(5.3)] + nCSH[Eq.⁡⁡(5.4)] + nCSH[Eq.⁡⁡(5.9)]

Eq. (5.18)

1 fCOPC
3S
×C
2 MC3 S

Eq. (5.19a)

1 fCOPC
2S
nCSH[Eq.⁡⁡(5.4)] =×C
2 MC2 S

Eq. (5.19b)

1 fCEX
2S
× EX
2 MC2 S

Eq. (5.19c)

nCSH[Eq.⁡⁡(5.3)] =nCSH[Eq.⁡⁡(5.9)] =where,
nCSH is the total number moles of C-S-H;

nCSH[Eq.⁡⁡(5.3)] , nCSH[Eq.⁡⁡(5.4)] , and nCSH[Eq.⁡⁡(5.9)] (mol) are the number moles of C-S-S according to Eq.
(5.3), (5.4), and (5.9), respectively, as shown in Eqs. (5.19a-5.19b)
The amount of C-S-H is
CSH = nCSH × MCSH

83

Eq. (5.20)

where,CSH (g) is the amount of C-S-H;

MCSH (g) is the relative formula mass of C-S-H (see Table 5.1).
At time t, the total number moles and amount of C-S-H is written
ntCSH = (nCSH[Eq.⁡⁡(5.3)] + nCSH[Eq.⁡⁡(5.4)] ) ×

OPC + nCSH[Eq.⁡⁡(5.9)] ×tt
CSH = nCSH × MCSH

ntCSH (mol) andEX

Eq. (5.21)
Eq. (5.22)t
CSH (g) are the number moles and the amount of C-S-H at time t, respectively.

5.2.3 Effective diffusion of CO2 in concrete and porosity of concrete
Papadakis et al. [5.17] reported that the effective diffusivity of CO2 depends on the volume, the structure,and the degree of saturation of the pores in concrete (or mortar). It has been measured using a WickKallenbach type of apparatus [5.8] and represented as a function of porosity, the composition of concrete,
and the ambient relative humidity, as shown in Eq. (5.23).
a

εc
RH b
De,CO2 = A ()) (1 −
C
P
W
100
+
+
ρc ρp ρw

Eq. (5.23)

where,
De,CO2 (m2/s) is the effective diffusivity of CO2;
RH (%) is the ambient relative humidity;
ρc , ρp , and ρw (kg/m3) are the density of cement, supplementary cementing materials, and water,
respectively;
C, P, and W is the cement, supplementary cementing materials (silica fume or fly ash) and water content
in 1 m3 of fresh concrete;εc (%) is the porosity of concrete as shown in Eq. (5.24) [5.9].
W

εc = εair+ρ - εh - εp - εcarw

Eq. (5.24)

where,
εair (%) is the volume fraction of entrapped or entrained air in concrete;
εh , εp , and εcar are the porosity reductions due to hydration of Portland cement, pozzolanic activity, andcarbonation, respectively. Papadakis suggested that the porosity reduction due to pozzolanic activity isalmost zero [5.9]. The εh and εcar are given by Eqs. (5.25) and (5.26), respectively [5.5], [5.11]:
εh = fC3 S ̅̅̅̅̅̅
VC3 S + fC2 S ̅̅̅̅̅̅
VC2 S + fC3 A ̅̅̅̅̅̅
VC3 A + fC4 AF ̅̅̅̅̅̅̅
VC4 AF

Eq. (5.25)

εcar = nCH ̅̅̅̅̅
VCH + nCSH ̅̅̅̅̅̅
VCSH

Eq. (5.26)

where,
̅̅̅̅̅̅
VC3 S, ̅̅̅̅̅̅
VC2 S, ̅̅̅̅̅̅
VC3 A , ̅̅̅̅̅̅̅
VC4AF , ̅̅̅̅̅VCH, and ̅̅̅̅̅̅
VCSH and are differences in volumes between the solid
reactants and solid products, respectively (see Table 5.2) (m3/mol).
nCH and nCSH are the molar volume of CH and C-S-H.
84

Table 5.2 Molar volume differences [5.8]
Unit

C3 S

C2 S

C3 A

C4 AF

CH

C-S-H

53.28

39.35

155.86

220

3.85

15.39

̅ x 10−6,
V3

m /molThe parameters A, a, and b are 1.64*10-6, 1.8, and 2.2 respectively, obtained from regression analysis ofexperimental data for 0.5<w/c<0.8 [5.11]. Papadakis [5.11] also reported that the diffusion parametervalues were changed by the w/b ratios.
Based on Papadakis’s equation, the effective diffusivity of CO2 in concrete mixed with expansive additiveis described in Eq. 5.27.
aDe,CO2 = A (

εc
RH b
)
) (1 −
C
E
W
100
+
+
ρc ρEX ρw

Eq. (5.27)

where,E (kg/m3) is the expansive additive content in 1 m3 of fresh concrete;ρEX (kg/m3) is the expansive additive density;
The parameter A, a, and b are obtained by fitting data in this study.
In this study, the porosity of cement concrete and expansive concrete is calculated by considering the timedependent of hydration reaction, are given in Eqs. (28) and (29):εh = (fC3 S ̅̅̅̅̅̅
VC3 S + fC2 S ̅̅̅̅̅̅
VC2 S + fC3 A ̅̅̅̅̅̅
VC3 A + fC4 AF ̅̅̅̅̅̅̅
VC4 AF ) ×(fC3 S ̅̅̅̅̅̅
VC3 S +fC4 AF ̅̅̅̅̅̅̅
VC4 AF )EX ex
εcar = ntCH ̅̅̅̅̅
VCH + ntCSH ̅̅̅̅̅̅
VCSH

OPC +

Eq. (5.25)
Eq. (5.26)

where,
ntCH and ntCSH are the molar volume of CH and C-S-H at time t, as described in Eqs. (5.16) and (5.21).

85

5.3 Results and Discussion
5.3.1 Amount of calcium hydroxide and calcium silicate hydroxide
As mentioned above, the aim of this chapter is to predict the carbonation depth of cement concrete andexpansive concrete. It is known that the main reactions of the carbonation process in concrete are thereaction of calcium hydroxide (CH) and CaO in the calcium silicate hydroxide (C-S-H) compound of
hardened cement with CO2 into calcium carbonate. Hence, it is very important to calculate the amount ofCH and C-S-H. Therefore, to verify the present equation, a comparison between the predicted results andexperimental results is shown in Figure 5.2. The present equation was validated using data from Takayuki[5.18] and Zhang [5.19]. For experimental results, the CH content of these studies was obtained bydetermining the mass loss in the temperature range of 350-500℃ using the TG-DTA and TGA apparatus.
It can be seen in Figure 5.2 that the experimental results and predicted results have a good relationship due
to most of the data are within the confidence limits line (±10%). The results of verification suggest that thepresent equation is useful for predicting the CH and C-S-H content from the hydration of OPC and EX.
100
+10%

Measured data, %

80

60

-10%

40

20
Series6
CH from OPC
CH from EX
Series7
0
0

20

40
60
Cacluated data,%

80

100

Figure 5.2 Comparison of calculated data and measured data of the amount of CH from OPC
and EX

The prediction results of the calcium hydroxide contents are shown in Figure 5.3 at different w/b ratios.
The CH content of all samples increases with time for both w/b ratios. Results showed that the CH content
increases with the addition of the expansive additive. It is well-known that the production of CH from thehydration of EX is the hydration reaction of free-CaO and from the hydration of OPC is the hydration
reaction of cement composition (C3S and C2S). In this study, the amount of free CaO is about 45.4 % of themass (see Chapter 2). Therefore, this is due to the high content of free CaO in expansive additive, which
directly related to the production of CH. The CH content are approximately 98, 105 and 112 kg/m3, and 70,
78, and 85 kg/m3 at w/b 0.3 and w/b 0.5, respectively. The value of CH content herein is calculated by using
the present equation combining the mix proportion of concrete. The results also indicated that the CH86content of samples at lower w/b ratio is large than that of samples at higher w/b ratio. This may be explainedby the amount of cement at w/b of 0.3. According to the mix proportions (see chapter 2), the amount of
cement is 583 kg/m3 and 370 kg/m3 at w/b of 0.3 and 0.5, respectively. Therefore, the higher amount of
cement is the reason why the CH content of the sample at w/b 0.3 larger than that of the sample at w/b 0.5.
120

120

w/b 0.5

w/b 0.3
100
Amount of CH, kg

Amount of CH, kg

100
80
60
40
20

80
60
40
20

OPC

EX20

OPC

EX40

0

EX20

EX40

0
0

24

48

72
96
Time, h

120

144

168

0

24

48

72
96
Time, h

(a)

120

144

168

(b)

Figure 5.3 Amount of calcium hydroxide

Figure 5.4 shows the predicted data of the amount of calcium silicate hydroxide of cement and expansive
concrete at different w/b ratios. With the time of hydration, the amount of C-S-H tendency was similar to
the CH content of concrete. However, unlike in the predicted data of the CH content, the amount of C-S-H
decreased when the expansive additive dosage was increased. These tendencies were found in both w/b
ratios of 0.3 and 0.5. The C-S-H is the main hydration product of the hydration process of cement, theproduction of C-S-H depends on the cement content in 1 cubic meter of concrete. Therefore, when the
expansive additive addition increased, the amount of cement was decreased. The decrease in cement dosage
leads to a decrease in the amount of C-S-H. This is explaining the tendency that was reported above.

200

200

w/b 0.5150

150
Amount of CSH, kg

Amount of CSH, kg

w/b 0.3

100

50

100

50
OPC

EX20

EX40

OPC

0

EX20

EX40

0

0

24

48

72
96
Time, h

120

144

168

0

24

48

72
96
Time, h(a)(b)

Figure 5.4 Amount of calcium silicate hydroxide
87

120

144

168

5.3.2 Porosity of concrete
One of the important factors to predict the carbonation depth of concrete is porosity (total porosity). The
same as other parameters, to verify the predicting equation for calculating the porosity content, acomparison between measured data and predicted data of porosity of concrete and cement paste is illustrated
in Figure 5.5. For experiment data, the porosity of concrete and cement paste with and without expansive
additive was determined by under-water weighing (discussion in Chapter 2). The testing times are 28-day
and 1-day, 3-day, 7day, 14-day, and 28 days for concrete and cement paste, respectively. The results showedthat most of the data are within in confidence limit line (±10). It concludes that the present equation here
can be applied to predicting the porosity of concrete and cement paste mixed with expansive additive.

100
+10%

Measured data, %

80

60

40

-10%

20

0
0

20

w/b 0.5_OPC paste
w/b 0.3_EX20 paste
w/b 0.5_EX40 con.
w/b 0.3_EX40 con.

40
60
Cacluated data,%
w/b 0.5_EX20 paste
w/b 0.5_OPC con.
w/b 0.3_OPC con.

80

100

w/b 0.3_OPC paste
w/b 0.5_EX20 con.
w/b 0.3_EX20 con.

Figure 5.5 Comparison of calculated data and measured data of concrete porosity and paste

5.3.3 Verification of prediction equation.
The value of coefficients in Eq. (5.27) is given in Table 5.1. The coefficients A and c increased with theaddition of the expansive additive, which leads to the value of the effective diffusivity of CO2 in carbonatedconcrete (De,CO2 ) increased. In other words, the diffusion of CO2 gas through concrete becomes easier. Thisis maybe explained the hydration of expansive additive in concrete generates the capillary pore more thanthat of Portland cement. The effect of the dosage of the expansive additive on the capillary pore wasdiscussed in chapter 2. This result is in agreement with the previous finding of Papadakis [5.11], whoreported that the addition of supplementary cementing materials may further promote the pore88

disconnection. The results have also shown that the decrease in A and c when the w/b ratio was lower. Thisis due to the development of a disconnected pore system, which will lead to low transport rates [5.20].
According to Eq. (5.27), the coefficient d directly related to the environment humidity of the testing
condition (unchanged 60%). Unlike coefficients A and a, therefore, the value of coefficient b is not changed
with different w/b ratios and the addition of EX. These results also consistent with the previous results[5.11]. Finally, the comparison between the prediction results and experimental results is shown in Figure5.6. As shown in Figure 5.6, the prediction results are in agreement with the experiment results. It concluded
that the present equation is useful for predicting the carbonation depth of expansive concrete.
As mentioned above, combining the hydration reaction equation and the hydration model the hydration
products were calculated. It means from this way the amount of ettringite is also calculated. It is wellknown that the production of ettringite and calcium hydroxide are directly related to the expansion of
expansive concrete. In other words, the expansion of expansive concrete could be predicted by calculating
the production process of ettringite and calcium hydroxide. This will be discussed in the next chapter.
SampleTable 5.3 Coefficient of predicting equation
A
a
b

w/b

OPC

3.5E-06

1.6

2.2

EX

6.70E-06

3.2

2.2

OPC

4.95E-06

1.8

2.2

6.50E-04

2.5

2.2

RH, %

CO2, %

60

5

0.3

0.5
EX

OPC-w/b 0.5

EX20-w/b 0.5

EX40-w/b 0.5

OPC-w/b 0.3

EX20-w/b 0.3

EX40-w/b 0.3

23
Cacluated data (mm)45Measured data (mm)

4

3

2

1

0
0

1

5

Figure 5.6 Comparison of calculated data and measured data of carbonation depth of concrete895.4 Conclusions
This study proposed a numerical model for predicting the carbonation depth of concrete mixed withexpansive additive. The amount of CH, C-S-H, and total porosity of concrete were calculated with the timeof hydration reaction of cement and expansive additive based on the hydration model. In order to test theaccuracy of the proposed model, the prediction results and experiment results were compared. The results
indicated that prediction results were in good agreement with experimental results and so the model
proposed here can be applied to calculate the CH, C-S-H content, porosity, and the carbonation depth of
expansive concrete.

90References[5.1] J.J. Brooks, Chapter 6 shrinkage of concrete, Concrete and Masonry Movements (2015) pp 137-185.
[5.2] Recommended practice for expansive concrete, Concrete library of JSCE No.23 (1994).
[5.3] A.M. Neville, Properties of Concrete, 5th ed. Harlow, England: Prentice Hall, Pearson.
[5.4] M. Criado, Chapter 13-The corrosion behavior of reinforced steel embedded in alkali-activated mortar.
Handbook of Alkali-Activated Cement, Mortars and Concrete (2015) pp333-372.
[5.5] E. Sakai, K. Kosuge, S. Teramura, K. Nakagawa, Carbonation of Expansive Concrete and Change of
Hydration Products, ACI symposium paper 126 (1991) 989-1000.
[5.6] T. Liuqing, S. Zhonghe, C. Wei, X. Wenbing, M. Juntao, Effect of carbonation on the microstructureof concrete containing fly ash and expansive admixture. Advanced Materials Research Vol. 347-353 (2011)
pp 4074-4080.
[5.7] V.G. Papadakis, C.G. Vayenas, M.N. Fardis, Fundamental modeling and experimental investigationof concrete carbonation, ACI Mater J 88 (1991) pp 363–373.
[5.8] V.G. Paparakis, C.G. Vayenas, M.N. Fardis, Physical and chemical characteristics affecting the
durability of concrete. ACI materials journal, Technical paper, title no. 88-M24 (1991) pp 186-196.
[5.9] V.G. Papadakis, Experimental investigation and theoretical modeling of silica fume activity inconcrete. Cement and Concrete Research 29 (1) (1999) pp 79–86.
[5.10] X.Y. Wang, H.S. Lee, A model for predicting the carbonation depth of concrete containing lowcalcium fly ash. Construction and Building Materials 23 (2009) pp 725-733.
[5.11] V. G. Papadakis, Effect of supplementary cementing materials on concrete resistance against
carbonation a chloride ingress. Cement and Concrete Research Volume 30, (2000) pp 291-299.
[5.12] M.A. Peter, A. Muntean, S.A Meier, M. Bohm, Competition of several carbonation reactions in
concrete: A parametric study. Cement and Concrete Research 38 (2008) pp 1385-1393.
[5.13] V.G. Papadakis, Effect of fly ash on Portland cement systems. Part I: lowcalcium fly ash. Cement
and Concrete Research 29 (11) (1999) pp 1727–36.
[5.14] V.G. Papadakis, Effect of fly ash on Portland cement systems. Part II: high calcium fly ash. Cement
and Concrete Research 30 (10) (2000) pp 1647–54.
[5.15] V.G. Papadakis, M.N. Fardis, C.G. Vayenas, Effect of composition, environmental factors andcement-lime mortar coating on concrete carbonation. Materials and Structures 25 (1992) pp 293-304.
[5.16] H. Choi, A study on the macro prediction of shrinkage-reduction behavior in concrete using
expansive additive. Doctoral thesis, the university of Tokyo 2013.
[5.17] M. Morioka, H. Hagiwara, E. Sakai, M. Daimon, Hydration reaction of the calciumsulphoaluminatetype expansive additive. Cement Science and Concrete Technology, No.52 1998 pp 2-7.
[5.18] T. Higuichi, M. Eguchi, M. Morioka, E. Sakai. Hydration and properties of expansive additive
treated high temperature carbonation. Cement and Concrete Research 64 (2014) pp 11-16.

91

[5.19] Zh. Y. Rong, K. X. Ming, L. Z. Chen, L. Z. Bao, Z. Qing, D. B. Qin, X. Feng, Influence oftriethanolmine on the hydration product of portlandite in cement paste and the mechanism. Cement andConcrete Research 87 (2016) pp 64-76.
[5.11] V. G. Papadakis, Effect of supplementary cementing materials on concrete resistance against
carbonation an chloride ingress. Cement and Concrete Research Volume 30, (2000) pp 291-299.
[5.20] F. Young, Sulfate attack, Concrete International 20 (1998) 7.

92

CHAPTER 6
PREDICTING EXPANSION STRAIN OF
EXPANSIVE CONCRETE BASED ON
HYDRATION REACTION MODEL

93

CHAPTER 6 PREDICTING EXPANSION STRAIN OF EXPANSIVE CONCRETE BASED ON
HYDRATION REACTION MODEL
6.1 Introduction
In concrete structures, Portland cement is used as a binder that binds the other materials together. The
shrinkage of cement caused by the loss of water from the concrete during environmental exposure, leading
to cracks in concrete. Because these cracks will directly affect the durability and strength of concrete,
minimizing their formation to guarantee the serviceability of concrete structure is essential [6.1-6.2]. To
address this problem, the application of the expansive additive is well-known as an effective way to reduceshrinkage and can enhance the density of cement concrete structures [6.3]. Thus, it has been widely applied
to many kinds of concrete structures (slab, pavement, etc.) [6.4].

The expansive additive can increase the volume of concrete by the expansion of ettringite and calcium
hydroxide generated in cement paste in the hydration process. To model the volumetric change of expansive
concrete, Choi et al. [6.5] suggested a method that takes into account the balance between the shrinkage of
cement and the expansion of expansive additive. In this modeling, the expansion of EX was modeled byconsidering an increase in the outermost radius of the EX-particles of the hydration products. The shrinkage
of cement was modeled by considering the pore diameter distribution and the thermodynamic equilibrium
state of the moisture. Miyazawa [6.6] also reported that the expansion strain of expansive concrete is thebalance of the expansion strain of expansive additive and the autogenous shrinkage of cement.

The aim of this chapter is to model the expansion strain of expansive concrete, which also considers the
expansion of EX and shrinkage of cement. The expansion of expansive concrete was calculated byconsidering the production of CH and ettringite in expansive concrete. A parameter that describes the effectof the shrinkage of cement was deduced by considering the relationship between the calculated data andexperimental data. Because the model was built for expansive concrete under the unrestrained condition, a
coefficient was proposed to find predicted data for expansive concrete under the restrained condition.
Figure 6.1 shows a flow chart of this chapter.

94

Chapter 6
Predicting Expansion Strain of Expansive Concrete Based On Hydration Model

Chapter 2
Experimental

Takayuki’s data

Chapter 3
Hydration Model

Chapter 5
CH content (%)

Ettringite content (%)

Mix proportion

Comparison

Amount of CH and
Etrringite (kg)Physical properties
of EX
Expansion rate
Restraint degree
Expansion strain（µm）

Comparison

Effect of shrinkage of cement
Expansion strain（µm）

Figure 6.1 Flow chart956.2 Predicting expansion strain
6.2.1 Production of ettringite
As discussed in Chapter 5 that the hydration products of expansive additive are the CH and ettringite. The
reaction of expansive additive with water is described by Eqs. (5.7-5.10) in chapter 5. However, Morioka
et al. [6.7] found that the hydration products of expansive additive are not only CH and ettringite but also
gypsum (CS̅H2 ) and monosulfate (C4 AS̅H10 ) using the XRD quantitative analysis. The gypsum was
generated from the hydration of anhydrite, as shown in Eq. (6.5). Nagataki et al. [6.8] reported that the
ettringite and monosulfate were generated as the SO3/Al2O3 ratio was about 3 and 1, respectively. And inprevious research [6.7], the authors explained that the formation of the monosulfate is due to the SO3/Al2O3
ratio was 2.18. It concludes that the formation of the monosulfate depends entirely on the SO3/Al2O3 ratio.
In this study, the SO3/Al2O3 ratio is over 3 (see Table 2.1 in Chapter 2), therefore, there is no the monosulfate
in the hydration products of EX. Additionally, Higuchi et al. [6.9] also found the C2S and C4AF in thecomposition of EX. For these reasons, the hydration of expansive are shown as follows:
C + ⁡H⁡ → CH

Eq. (6.1)

6CH + C4 A3 S̅ + 8CaSO4 + 90H → 3(CaO. Al2 O3 3. CaSO4 . 32H2 O)

Eq. (6.2)

2C2 S + 4H → C3 S2 H3 + CH

Eq. (6.3)

C4 AF + 2CH + 10H → C6 AFH12

Eq. (6.4)

CS̅ + 2𝐻 → CS̅H2

Eq. (6.5)

As shown in Eqs. (6.1-6.5), the reaction of CH, ye’elimite, and anhydrite is related to the formation of
ettringite. However, the CH and anhydrite are also involved in other reactions (see Eq. (6.4) and Eq. (6.5).
Therefore, in this case, the formation of ettringite is closely related to the hydration of ye’elimite. The otherwords, the amount of ettringite will be calculated by considering the hydration of ye’elimite based on thehydration reaction of expansive additive. It notes that the ettringite is also produced from the hydration
reaction of cement, but produced ettringite will convert to the monosulfate at an early age. Furthermore,
Yamamoto et al. [6.10] reported that the formation of CH and ettringite from cement hydration, which was
not a role play in the expansion. Therefore, in this study, the ettringite was formed from the hydration of
cement, which is not considered as a factor of the expansion of expansive concrete.
Similar to calculating method of CH and CSH content in Chapter 5, the number moles and ettringite content
are calculated, as shown in Eq. (6.6) and Eq. (6.7):

ntEtt = 3

fYe′ el. ×EX ×
MYe′ el.

tt
Ett = nEtt × MEtt96

EX

Eq. (6.6)
Eq. (6.7)

where,fYe′ el. (%) is the mass fraction of ye’elimite;
EX is the hydration degree of EX;

EX (kg) is the dosage of EX;
MYe′ el. (g/mol) is the relative formula mass of ye’elimite;
ntEtt (mol) is the moles of ettringite;t
Ett (g) is the amount of ettringite.

6.2.2 Modeling of expansion strain
To model the expansion strain of expansive concrete, it is important to identify the volume change ofconcrete. The volume change of concrete is caused by an increase in the formation of CH and ettringite
with the time of hydration. In this study, by assuming that the concrete mixed with the expansive additive
will be expanded with the directions (x-y-z) under free condition, as described in Figure 6.2. From thisassumption, the volume of concrete the expansive additive isV0 = 1⁡(

3)

Eq. (6.8)

V0+α = (1 + 2x)3 (3)

Eq. (6.9)

where,
V0 and V0+α (m3) are the volume of concrete at t = 0 and t =;x is the expansion strain (μ ).

A
1
1

ｙ

1

ｘ

Volume of concrete

1

ｚ

A

1

A-A

Figure 6.2 Schematic of volumetric change of expansive concrete

The volumetric change of expansive additive is also the volume of CH and ettringite generated in thehardened paste, as indicated in Eq. (6.10)

97

VEttringte+CH = V0+α − V0 = (1 + 2x)3 − 1
VEttringte+CH =ettringite

ρettringite+

CH

Eq. (6.10)
Eq. (6.11)

ρCH

where,
VEttringte+CH is the volume of etrringite and CH, as described in Eq. (6.11).
ρettringite and ρCH (g/cm3) are the density of ettringite (1.7 g/cm3) and CH (2.24 g/m3).

Thus, expansion strain is3

𝑥 =√𝑉𝐸𝑡𝑡𝑟𝑖𝑛𝑔𝑡𝑒+𝐶𝐻 + 1 − 1
2Eq. (6.12)

In this study, the author is only focusing on the expansion strain of expansive concrete by calculating thevolume of CH and ettringite. However, the shrinkage of cement also occurs in expansive concrete. This isdiscussed in Chapter 1. Therefore, to find a satisfactory value for predicted results, a coefficient is deduced,
called 𝛽 the coefficient of shrinkage effect. The value of 𝛽 is calculated by considering the relationshipbetween predicted data and the experimental data [6.11]. So, the 𝛽 can be represented as a function of time.
The expansion strain is3

𝑥 =√𝑉𝐸𝑡𝑡𝑟𝑖𝑛𝑔𝑡𝑒+𝐶𝐻 + 1 − 1× ⁡𝛽⁡2Eq. (6.13)

As mentioned above that the present model here is applied for concrete without restrained condition effect.
In this study, despite the expansion strain of expansive concrete was measured immediately after theconcrete is cast into the mold, the experimental sample was removed from the mold after one day. At thesame time, the expansion also begins when EX mixed with cement and water. Therefore, during that one
day, the expansive concrete will be affected by the restraint caused by the mold. On the other hand, for
expansive concrete, the experimental measurement of expansion strain is performed under restrained
conditions according to JIS A 6202 [6.12]. To address this problem, a coefficient that expresses the effectof restrained condition on the expansion strain of expansive concrete is needed, called 𝛿 the restraint degree
coefficient. The 𝛿 coefficient is obtained by comparing the restrained and unrestrained expansion strain,
which will be discussed in the next section in detail.
Thus, now the expansion strain is:3

𝑥 =√𝑉𝐸𝑡𝑡𝑟𝑖𝑛𝑔𝑡𝑒+𝐶𝐻 + 1 − 1× ⁡𝛽 × ⁡δ
298

Eq. (6.14)

6.3 Results and Discussion
6.3.1 Amount of ettringite
To verify the calculating equation of ettringite content, a comparison between the predicted data andmeasured data was performed, as shown in Figure 6.3. In this Figure, the calculated data was obtained by
combining Eq. (6.6) and (6.7), the measured data was obtained by Rietveld analysis of the XRD patterns[6.9]. The figure shows that the calculated and experimental data were in good agreement. It demonstrates
that the proposed equation is effective in calculating the ettringite content was generated by the hydrationof EX. Furthermore, this also confirms that the hypothesis about the relationship between the content of
ettringite generated and the reaction of ye’elimite is correct.

100

Ettringite+10%

Measured data, %

80
60

-10%

40
20
0

0

20

40
60
Cacluated data,%

80

100

Figure 6.3 Comparison of predicted data and measured data of ettringite content

The actual ettringite is obtained by the mix proportion of concrete (see Chapter 2), as indicated in Figure
6.4. As can be seen, the amount of ettringite in the EX40 sample was higher than that of EX20 at all ages.
At 7 days, the ettringite amounts were approximately 2.2 and 5 kg in 1 m 3 of concrete. This may be
explained by the dosage of EX used in 1 m3 of concrete, it means the amount of ettringite increased when
the dosage of EX increased. As mentioned above, in this study, the author did not consider the formationof ettringite from the hydration of cement. Therefore, there was only the ettringite amount that was
generated by the hydration of EX.

99

Amount of Ettringite, kg

6
5
4
3
2
1

Series1
EX20

EX40
Series2

72
96
Time, h

120

0
0

24

48

144

168

Figure 6.4 Actual amount of ettringite

6.3.2 Verification of prediction equation
The 𝛽 coefficient was determined by considering the relationship between the experimental results [6.11]
and the calculated data from Eq. (6.12). The comparison of experimental results and calculated data isshown in Figure 6.5.

Exp. data

Predicted data

2

5

Expansion strain, 10-6

600
500
400

300
200
100

0
0

1

3
4
Time, days

6

7

Figure 6.5 Comparison of experimental data [6.11] and calculated data (according to Eq. 6.12).

100Figure 6.6 shows the relationship between the value of the 𝛽 coefficient and time. The 𝛽 coefficientcorrelated with the time with a high correlation coefficient of 0.96. Thus, the 𝛽 coefficient can be
represented as a function of time and is given by:
β = 0.9881𝑒 −0.067t ⁡ (0.6 ≤ β ≤ 1 and 0 ≤ t ≤ 7)

Eq. (6.14)

1.6
1.4
y = 0.9881e-0.067x
R² = 0.6022

β coefficient

1.2
1
0.8

0.6
0.4
0.2
0
0

2

4
Time, days

6

8

Figure 6.6 Time-dependent 𝛃 coefficient
While the β was a time-dependent coefficient, 𝛿 was a constant. The value of 𝛿 coefficient was obtainedby comparing the previous results [6.11] and the results of this study (see chapter 2), as shown in Figure
6.7. According to this figure, the value of the 𝛿 coefficient was approximately 0.42.
400

Expansion strain, 10-6

350
300
250

200
150

Author’s data

100

Choi’s data [10]50Restraint degree

0
0

1

2

3
4
Time, days

5

6

7

Figure 6.7 Comparison of author’s data (under restrained condition) and Choi’s data [6.11](unrestrained condition)

101Thus, the expansion strain of expansive additive can be written as follows:

x=

3 𝑉

√ 𝐸𝑡𝑡𝑟𝑖𝑛𝑔𝑡𝑒+𝐶𝐻 +1−1
× 0.9881𝑒 −0.067t × ⁡0.42 (0 ≤ t ≤ 7)
2

Eq. (6.15)

From Eq. (6.15), the expansion strain of expansive concrete under restrained conditions was calculated andcompared with measured results (JIS A 6202) as shown in Figure 6.8. The results show that the predicteddata was approximately equal to the experimental results. The results reported here demonstrate that the
proposed equation is effective and useful in predicting the expansion strain of expansive concrete under the
restrained conditions with w/b 0.5 and the dosage of EX is 20 kg/m3 of concrete. However, the Eq (6.15)
was built from fitting the experimental data and model data to obtain the value and time-dependent equationof β and 𝛿 is perhaps the biggest limitation to accurately model. Therefore, in the future, in order to addressthese limitations, a behavior mechanism of cement shrinkage should be proposed to explain the present
expansion model of expansive concrete in detail. Furthermore, the experiments of expansive concrete under
different restrained conditions need to carry out to find the excellent value of the 𝛿 coefficient.

Exp. data

Predicted data

180

Expansive strain, 10-6

160
140
120
100
80
60
40
20
0

1

2

3

7

Time, days

Figure 6.8 Comparison of predicted data and measured data102

6.4 Conclusions
A hypothesis supporting the expansion of expansive concrete under free conditions was described. An
equation was proposed to predict the expansion strain of expansive concrete under restrained conditions byconsidering the formation of ettringite from hydration reaction of expansive additive, shrinkage of cement,
and restraining factor. Especially, the ettringite was calculated based on the hydration reaction model. A
comparison between calculated data and experimental data of expansion strain was performed that showed
the agreement. It demonstrates that the proposed equation is useful for predicting the expansion strain of
expansive concrete under restraining.

103

References[6.1] Architectural Institute of Japan (AIJ), Recommendations for practice of crack control in reinforced
concrete buildings (design and construction); 2006.
[6.2] Japan Concrete Institute (JCI), Research committee report on shrinkage of concrete; 2010.
[6.3] Chapter 4-Cement, Building materials in civil engineering. Woodhead publishing series in civil andstructural engineering (2011) pp 46-80.
[6.4] J.J. Brooks, Chapter 6-Shrinkage of concrete, Concrete and Masonry Movements (2015) pp 137-185.
[6.5] H. Choi, H. Choi, M. Lim, T. Noguchi, R. Kitagaki, Modeling of volume changes of concrete mixed
with expansive additives, Construction and Building Materials 75 (2015), pp 266-274.
[6.6] Shingo Miyazawa, JCI-RILEM International Workshop, Concrack5, April 24-26, 2017, Japan.
[6.7] M. Morioka, H. Hagiwara, E. Sakai, and M. Daimon, Hydration reaction of thecalciumsulphoaluminate-type expansive additive. Cement Science and Concrete Technology, No.52,1998.
[6.8] Nagataki S., Gomi H., Expansive admixtures (mainly etrringite), Cement and Concrete Composites,
20, pp 163-170, 1998.
[6.9] T. Higuchi, M. Eguchi, M. Morioka, E. Sakai, Hydration and properties of expansive additive treatedhigh temperature carbonation. Cement and Concrete Research. 64 (2014), pp.11-16.
[6.10] K. Yamamoto, M. Morioka, E. Sakai and M. Daimon, Expansion mechanism of cement added withexpansive additive. Concrete Research and Technology, Vol.14, No.3, Sep. 2003.
[6.11] Hyeonggil Choi, A study on the macro prediction of shrinkage-reduction behavior in concrete using
expansive additive, Doctoral Thesis, University of Tokyo, 2013.
[6.12] Japanese Industrial Standard Committee. Expansive additive for concrete (Amendment 1), JIS A
6202-2008.

104

CHAPTER 7
CONCLUSIONS AND FUTURE WORKS

105

CHAPTER 7 CONCLUSIONS AND FUTURE WORK
7.1 Conclusions
In this study, by using a mathematical equation the hydration reaction of cement pastes containing the
expansive additive was modeled. Based on the hydration reaction model, the compressive strength,carbonation depth, and expansion strain of expansive concrete were predicted. In order to verify the modeland predicted data, several experiments on the properties and durability of expansive concrete were carriedout. Especially, the influence of restrained conditions on these properties was also experimentallyinvestigated in this study. There are some conclusions obtained from the results in this study as follows:1.

Under the restrained condition, the compressive strength, frost resistance, carbonation
resistance of expansive concrete was improved. This phenomenon is observed when the dosageof expansive additives used reached about 40 kg/m3.

2.

By considering three processes: Diffusion of water through the protective layer surrounding
the particle to the surface of the cement; Penetration and diffusion of water through the blanket
of hydration product to the surface of the unreacted core; And the reaction of water with cement
or EX at this reaction surface, a numerical model was proposed to simulate the hydration
reaction of cement paste containing expansive additive at an early age.

3.

The gel/space ratio of cement-EX paste was calculated by considering the hydration of cement
and expansive additive based on the hydration reaction model. Using Powers’ strength theory,an equation showing the dependence of the compressive strength of expansive concrete on thegel/space ratio of cement-EX paste was proposed with the value of A and n are 253 and 2.69,
respectively.

4.

The amount of CH and CSH generated from the hydration of cement and EX were calculated
based on the hydration reaction model. A mathematical equation describing the carbonation of
expansive concrete was proposed to predict the carbonation depth.

5.

A hypothesis describing the expansion of concrete containing the expansive concrete wasdeduced. By considering the balance of expansion of expansive and shrinkage of cement andrestraining factor, a mathematical equation was proposed to predict the expansion strain of
expansive concrete under restrained conditions.

106

7.2 Future Works
1. As mentioned in the Introduction chapter, the hydration reaction of cement (or cement-basedmaterials) is related to many properties of concrete, in addition to the properties described in the
study, there are also other properties such as pore structure and so on. Therefore, it is interesting tofind out the relationship between pore structure and hydration reaction of cement. From there, it ispossible to model the pore structure of cement concrete as well as expansive concrete.
2. Regarding the hydration reaction model and predicting carbonation depth, the model parameters
were calculated by the last-squared method that is also known as a fitting method. Therefore, to be
more persuasive, it is necessary to study and use other methods in calculating the coefficients suchas machine learning.
3. One of the important factors that directly affect the quality and durability of concrete is the curingconditions such as temperature and humidity. In this study, the effect of temperature on thehydration of the cement and expansive additive was considered. It is therefore interesting to extend
the research to predict the properties of concrete based on the hydration model and take into accountthe effects of the curing conditions on these properties.
4. Regarding predicting the expansion strain, the effect of shrinkage of cement was investigated bycomparison of experimental data and calculated data. Using the hydration reaction model to predict
the shrinkage of cement is interesting in the next study. It is essential to find the effect of the w/b
ratio on the parameter in order to extend the predicting equation.

107

ACKNOWLEDGMENTS

I wish to express my sincere appreciation to those who have contributed to this thesis and supported me in
one way or the other during this amazing journey.

My deep gratitude goes first to Prof. Yukio Hama, my supervisor for his patience, motivation, caring, andimmense knowledge. He has been always there to help, guide me in all the time of research, writing ofjournal, and this thesis as well. I am very grateful to him for his comments and plans to solve problems
encountered in doing research through the Lab’s seminars and discussions.

My sincere thanks also go to Assoc. Prof. Hyeonggil Choi who is my co-advisor. The door to Assoc. Prof.
Choi's office was always open whenever I ran into a trouble spot or had a hard question not only about mymaster thesis but also my doctoral thesis. I have always felt motivated to continue solving research problems
after having long discussions with him.

My gratitude extends to Dr. Jihoon Kim who has given helpful advice, discussions, suggestions, guidance,and encouragement during the seminar presentations in our laboratory.

Besides my advisor, I would like to thank the rest of my thesis committee: Prof. Mitsuo Mizoguchi, Assoc.
Prof. Noriyuki Sugata, Assoc. Prof. Yuya Takase, for their insightful comments, encouragement, andconstructive suggestions which have helped me significantly to improve the quality of my research.
A big “Thank you!” also goes out to all the students in my laboratory, who are always willing to help mein the process of doing experiments as well as responsible for organizing activities for the laboratory.
Thanks also go to Ms. Matsumura, Mr. Takai, and Ms. Kuroiwa, who were my partner for providing mewith unfailing support. In particular, I am grateful to Dr. Kim Junho and Dr. Nguyen Xuan Quy for helping
and enlightening me on how to write and review a scientific paper. Without their precious support, it would
not be possible to conduct this research.

As an international student, I would like to thank all the members of the Office of the Center forInternational Relations for their full support not only for me but also for my family to help me achieve mygoals. In particular, I must show my gratitude to Mr. Inoya and his family for their whole-hearted support
while we are living in Muroran as our friends.

I would also like to thank my Vietnamese friends and all international friends for their friendship and forsharing with me their best wishes. In particular, I am also very grateful to Dr. Tran Vinh Ha in the Nihonshu
team who always willing to give me a lot of advice not only in scientific research but also in everyday life.

108

Last but not the least, I would like to extend my heartfelt thanks and love to my whole family for providing
me with unfailing support throughout my years of study and through the process of researching. I am deeply
grateful to my parents, my parents in law, and my brother for trusting and encouraging me to achieve mygoals in my research career. And finally, I would like to acknowledge the most important persons in mylife – my wife, Luong Thi Mui, and my daughter, Nguyen Mai Khanh Vy for always being there for me,
encouraging me, and always being my motivation to get through the toughest times during the Ph.D course.

Muroran, March 2021
Nguyen Duc Van

109