STRENGTH MODEL FOR MORTAR BASED ON HYDRATION HEAT …

STRENGTH MODEL FOR MORTAR BASED ON

HYDRATION HEAT AND MICROSTRUCTURE DEVELOPMENTS

Virak HAN1, Soty ROS1 and Hiroshi SHIMA2

1Dept. of Infrastructure Systems Eng., Kochi University of Technology (185 Miyanokuchi, Tosayamada, Kami City, Kochi 782-8502, Japan)

E-mail: [email protected] 2Fellow of JSCE, Professor, Dept. of Infrastructure Systems Eng., Kochi University of Technology

(185 Miyanokuchi, Tosayamada, Kami City, Kochi 782-8502, Japan) E-mail: [email protected]

This paper presents a strength model for Portland cement mortar with and without partial replacement mineral powders, limestone filler, blast furnace slag, and fly ash. The model was developed based on hy-dration heats and microstructure developments. The investigation was conducted on cylindrical mortar specimens with different water-to-cement ratios, different types of cements, and different curing condi-tions. The compressive strength of mortar was found to have a linear relationship with the ratio of hydration heat coupled with the porosity. Consequently, a strength model for mortar compressive strength, which is a summation of all heat-pore components multiplied by their own strength contribution factors, was estab-lished. The calculations of compressive strength using the proposed model agreed well with the experi-mental results in terms of cement paste, mortar, and concrete. Key Words : compressive strength, effective porosity, hydration heat, Portland cement mortar

1. INTRODUCTION

It is generally accepted that strength developments of cement paste, mortar, and concrete are controlled by the developments of microstructures and the hy-dration heats of constituent minerals in the mixes. Therefore, knowledge of the microstructures and the hydration heat developments is significant for the development of a strength prediction model.

Accordingly, a hydration heat model for cement based on the multi-component concept of constituent minerals and a multi-component model for hydration heat of concrete based on cement mineral compounds were developed and proposed1), 2), 3). Some types of mineral powders, namely limestone filler, blast fur-nace slag, fly ash, and silica fume were also produced as partial replacements for cement. These types of mineral powders were purposely used to improve the workability and the consistency of the mixes, and thereby improve strength. Consequently, many studies have been conducted to quantify the effects of these types of mineral powders on the properties of the fresh and the hardened cement paste4), 5), 6), 7), 8), mortar9), 10), 11), 12), 13), and concrete14), 15), 16), 17).

Moreover, several models for blended cement and mortar with the presence of partial replacement mineral powders effect have been developed and proposed. In 1996, a multi-component model for hydration heat of blended cement with blast furnace slag and fly ash was proposed by Kishi and Maekawa18). Then, in 2004, a model for the hydration heat-generating process of blended cement with sil-ica fume was proposed by Otabe and Kishi19). Addi-tionally, Suzuki et al.20) also introduced an equation to quantify the generation process of hydration heat of cement in concrete by considering the adiabatic temperature rise, the activation energy of cement, and the limit of degree of hydration. Moreover, the hydration heats of mortar constituents can be calcu-lated by means of the multi-component heat model of Kishi21) introduced in 2005.

Particularly, a strength development model for concrete based on the increase of degree of hydration was previously proposed by Kato and Kishi22) in 1994. The model was developed by taking into ac-count the mix proportions, the curing conditions, and the age of the concrete. Furthermore, in 2006, Kishi and Otabe23) also proposed a strength model by

Journal of JSCE, Vol. 1, 366-378, 2013

366

quantifying outside hydration volume and capillary pores.

However, a strength model for cement paste, mortar, and concrete using Portland cement with and without partial replacement mineral powders based on the hydration heats and the microstructure de-velopments has not yet been identified. Therefore, this study aimed to introduce a strength prediction model for cement paste, mortar, and concrete fol-lowing the fundamental theories of microstructure developments and the multi-component hydration developments3), 18).

2. EXPERIMENT (1) Materials

This study focused on three types of Portland ce-ment: low-heat Portland cement (LH), high-early- strength Portland cement (HES), and ordinary Port-land cement (OPC). The mineral compositions of the cements are summarized in Table 1. Moreover, three types of partial replacement mineral powders, lime-stone filler (LS), blast furnace slag (SG), and fly ash (FA) were also used to examine their strength con-tributions in the mixes. Their specific gravity, fine-ness modulus, and primary mineral compositions are given in Table 2.

Additionally, the water content in the sand was maintained to be the same as the SSD water content (the inside absorbed water with dry surface) to avoid changes in the mix proportions. Meanwhile, the superplasticizer (SP) used in the mixes was made of Poly-carboxylate compounds whose pH and density were 9 and 1.04 g/cm3, respectively. (2) Ideal mixes

Prior to the main mixes for strength model de-velopment, an investigation on the sand content ef-fect, SP dosage effect, and mixing time duration ef-fect have been conducted to identify the ideal mixes that lead to high cement dispersion and maximum compressive strength of mortar24). It was found that SP dosage of 1% and mixing time duration of 10 minutes were the optimum dosage and mixing time duration, respectively24). Consequently, the ideal mixes were made for all cylindrical mortar speci-mens whose compressive strengths were utilized in the strength model development. Particularly, the names of the mixes were given according to the percentage of water-to-cement ratio and curing con-ditions as shown in Table 3, Table 4 and Table 5. (3) Mixing procedures

The mixer is a fixed cylinder that consists of three spatulas, which can turn around the axis of the cyl-inder. Before mixing, the materials were dosed and

kept with covers to prevent evaporation or desicca-tion. Twenty percent of water volume was mixed with the admixture and introduced into the mixes separately from another 80% of water volume. To compensate for the effect of material consumption by the apparatuses, a plastering mix with the same mix proportions as the main mix was first carried out.

The mixing sequence was then orderly performed. First of all, sand and partial replacement mineral powder were uniformly introduced into the mixer and blended for 30 seconds. Then 80% of the water volume was added and the blending was continued

Table 1 Properties of Portland cements.

Mineral types Percentage by weight

LH HES OPC C3S 28 63 58 C2S 53 11 15.5 C3A 3 9 11.4

C4AF 10 8 7.6 Specific gravity (g/cm3) 3.24 3.13 3.13 Surface area in (cm2/g) 3280 4770 3400

Table 2 Properties of mineral powder.

LS FA (II)* Slag CaCO3 (%) 95.0 - - CaO (%) - 3.27 43.37SiO2 (%) - 45.0 33.58Al2O3 (%) - 24.99 15.09

Specific gravity (g/cm3) 2.7 2.36 2.91 Fineness modulus (g/m2) 3530 3410 3930 * Fly ash type II, Japanese product

Table 3 Tested fc’ of LH mortar specimens.

Mix name 7 days(MPa)

14 days

(MPa) 28 days(MPa)

91 days(MPa)

045wc-wet 27.8 42.5 61.3 83.1 045wc-seal 33.9 45.3 56.5 78.1 060wc-seal 13.4 - 36.3 - 060wc-wet 13.9 23.4 38.7 50.3 030wc-seal 57.0 - 82.0 - 030wc-wet 59.0 77.3 100.2 116.4

Table 4 Tested fc’ of OPC mortar specimens.


14 days

(MPa) 28 days(MPa)

91 days(MPa)

060wc-wet 33.7 39.9 46.5 51.6 045wc-wet 54.9 62.5 72.0 77.1 030wc-seal 75.5 83.8 91.7 96.2 030wc-wet 84.3 91.7 100.4 108.3

Table 5 Tested fc’ of HES mortar specimens.


14 days

(MPa) 28 days(MPa)

91 days(MPa)

060wc-seal 36.8 40.6 44.4 47.2 045wc-seal 57.0 62.4 67.6 69.7 030wc-seal 85.6 93.0 96.9 97.7

030wc-wet 90.7 96.4 104.7 111.9

367

for 60 seconds. Subsequently, the blending was stopped for 15 seconds to rub the spatulas and the admixture was introduced together with 20% of the water volume. Finally, the blending was continued until it reached 10 minutes of mixing time duration.

(4) Curing

Three cylindrical specimens of 100 mm diameter and 200 mm height were sampled per age of strength. The specimens were divided into two groups and were cured under different curing conditions. The first group was cured in a temperature-controlled room with a relative humidity of 60% and a temper-ature of 20oC (called seal-cured or seal). Meanwhile, another group was cured in a water tank with con-stant temperature of 20oC (called wet-cured or wet). All specimens of both groups were cured until the age of testing.

(5) Compressive strength test

The compressive strength tests were performed on the cylindrical specimens at the age of 7, 14, 28, and 91 days following a method of test for compressive strength of concrete of JIS A 1108. The same pro-cedures for hardened concrete testing were also made for hardened mortar testing. Shimadzu Testing Ma-chine was used to test the compressive strength fc’. In case of 100×200 mm cylindrical specimen is tested, the machine can give a maximum stress of 127 MPa. During the test, a constant stress of 0.21 MPa/sec, which is within the range recommended by ASTM C 39 standards, was applied on the mortar specimens until failure.

3. MODELING OF MORTAR COMPRES-

SIVE STRENGTH (1) Development of mortar compressive strength

The values of fc’ in the cylindrical mortar speci-mens were sorted according to the types of cement and the partial replacement of mineral powder used in the mixes, as listed in Table 3, Table 4, Table 5, Table 6, Table 7, and Table 8.

Based on the experimental results, fc’ of LH mor-tars developed relatively slow at early age as com-pared with the HES and OPC mortars. However, it can be observed in the case of 030wc-wet mortars listed in Table 3, Table 4 and Table 5 that an almost equivalent fc’ was obtained among the mortars with the three types of Portland cement at the older age of 28 and 91 days. These results manifested the prop-erties of LH cement of slowing down the degree of hydration in the mixes at early age and compensating for the strength at older age. Meanwhile, it may be an additional evidence that fc’ of LH mortars kept in-creasing even after 28 days as shown in Fig.1 and

Table 3. The aim of this research was to develop a model

for fc’ of mortars by quantifying the strength contri-butions of the critical controlling parameters in the mixes.

(2) Development of strength model

In this study, the hydration heat values of each cement compound were calculated by means of the multi-component heat model of Kishi21), while those of the pore components were calculated by means of the microstructure model of Maekawa et al.26).

Consequently, the heat-pore components of the specimens of LH, HES, and OPC mortars were ob-tained and summarized in Table 9, Table 10, and Table 11, respectively. Fig.2 and Fig.3, respectively, shows the developments of porosities and hydration heats of each component of LH mortars with w/c = 0.3. Meanwhile, the integration of multi-component heat and microstructure models are illustrated in Fig.4.

Table 6 Tested fc’ of mortars with SG replacement.

Mix name 7th

(MPa) 14th

(MPa) 28th

(MPa)91st

(MPa)045wcSG20-wet 22.0 38.5 59.9 83.94060wcSG20-seal 11.9 20.6 36.3 55.10030wcSG60-seal 40.7 53.4 66.0 77.48030wcSG20-seal 49.40 67.27 80.08 94.17

Table 7 Tested fc’ of mortars with FA replacement.

Mix name 7th

(MPa) 14th

(MPa) 28th

(MPa)91st

(MPa)045wcFA20-wet 18.8 32.8 52.1 79.3060wcFA20-wet 7.9 13.9 27.8 52.1030wcFA20-seal 45.6 60.7 78.2 96.4030wcFA20-wet 40.9 58.1 79.9 111.2

Table 8 Tested fc’ of mortars with LS replacement.

Mix Name 7th

(MPa) 14th

(MPa) 28th

(MPa)91st

(MPa)030wcLS20 51.35 - 84.35 - 045wcLS20 20.67 33.15 45.73 69.24060wcLS20 12.06 16.24 26.26 42.78

Fig.1 Development of fc’ of LH mortar with w/c=0.3.

0

20

40

60

80

100

120

140

0 14 28 42 56 70 84 98

Com

pres

sive

str

engt

h (M

Pa)

Age (day)

Tested

368

It can be observed in Fig.2 that the interlayer and gel porosities seemed to be constant after 21 days; however, the capillary, the effective or kinematics porosities, and the total porosities kept decreasing until the age of 91 days. According to some re-searchers, fc’ is inversely proportional to porosity while the interlayer pore has very little effect on the strength25). It can be observed further in Fig.3 that C2S and C3S seemed to give more hydration heats than C3A and C4AF. However, the hydration heats given by the four compounds had been considered in the strength prediction model. It was because the strength of cement had been reported to depend on the basis of its pure compounds, C2S, C3S, C3A and C4AF25). These compounds control the rate of evo-lution of the heat of hydration of cement, and con-sequently the strength of cement. Moreover, the products of the hydration reaction of cement consist of a solid and a pore system. This pore system highly influences the strength of mortar and concrete25).

In addition, Kato and Kishi22) focused on only the strength contribution of C2S and C3S by considering that the contributions of C3A and C4AF are negli-gibly small. However, their model was found to un-derestimate the tested strengths of mortar for all types of cement, LH, OPC, and HES in this study.

Therefore, the strength model should be a function of the hydration heat H given by the four components of cement and the specific type of porosity P as ex-pressed in equation (1a). Meanwhile, g(P, H) in equation (1a) is a function in which the specific type of porosity and hydration heat are expressed as given in equation (1b):

HPgfc ,'

(1a)

HPIPPIHPg ,

(1b) where fc' : concrete compressive strength, mortar or paste; P : specific type of porosity;

H : unit total hydration heat of cement chemical compound (H = ΣaiHi), while ai is the strength contribution factor of the ith cement compound and Hi is the heat of hydration given by the ith compound; and

PI : initial porosity. Since the initial porosity is equal to the initial total

volume of water Vw, PI could be replaced by Vw and

Fig.2 Development of porosities of different types, w/c=0.3, wet.

Fig.3 Development of hydration heat of different compounds,

w/c=0.3, wet.

Fig.4 Integration of multi-component heat and microstructure models.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 14 28 42 56 70 84 98P

oros

ity

(m3 )

Age (day)

Interlayer GelCapillary EffectiveTotal

0

10

20

30

40

0 14 28 42 56 70 84 98

Hyd

ratio

n he

at (

Mca

l/m3 )

Age (day)

C3A C4AFC2S C3S

Microstructure Model26)

Hydration Heat of C2S, C3S, C3A, C4AF, Slag, FA

Degree of hydration

Porosity: interlayer , gel and capillary porosity

Effective porosity (EP)

Strength Prediction Model

Multi-component Heat Model21)

369

Table 9 Calculated data of LH mortars.

w/c Curing Age

(days) fc’

(MPa) Hi (Mcal/m3) Pore volume (m3)

C3A C4AF C2S C3S TP (Vw) Interlayer GP CP EP

0.3

Seal 7 57 5.04 7.67 8.40 28.46 0.308 0.040 0.044 0.153 0.19728 81 5.45 8.61 14.65 30.28 0.308 0.051 0.056 0.111 0.167

Wet

7 59 5.32 8.11 8.40 30.21 0.308 0.042 0.046 0.147 0.19314 77.3 5.72 9.04 12.95 31.69 0.308 0.050 0.055 0.115 0.1728 100.2 5.98 9.63 16.93 32.56 0.308 0.057 0.063 0.089 0.15291 116.4 6.27 10.28 21.07 33.44 0.308 0.063 0.070 0.062 0.132

0.45

Wet

7 33.9 3.98 5.96 5.95 22.71 0.328 0.031 0.034 0.209 0.24314 45.3 4.35 6.92 9.22 23.68 0.328 0.037 0.041 0.185 0.22628 56.5 4.55 7.47 12.95 24.10 0.328 0.043 0.047 0.162 0.20991 78.1 4.71 7.90 17.74 24.34 0.328 0.050 0.055 0.134 0.189

Seal

7 27.8 4.03 5.98 5.95 23.08 0.328 0.031 0.034 0.207 0.24114 42.5 4.46 7.10 9.22 24.02 0.328 0.037 0.041 0.183 0.22428 61.3 4.67 7.73 13.07 24.32 0.328 0.043 0.048 0.159 0.20791 83.1 4.78 8.11 19.34 24.41 0.328 0.052 0.058 0.124 0.182

0.6

Seal 7 13.4 2.98 4.40 4.37 17.19 0.321 0.023 0.025 0.232 0.25728 36.3 3.48 5.80 9.61 17.92 0.321 0.032 0.035 0.197 0.232

Wet

7 13.9 2.99 4.40 4.37 17.26 0.321 0.023 0.025 0.232 0.25714 23.4 3.36 5.31 6.77 17.85 0.321 0.028 0.031 0.214 0.24528 38.7 3.50 5.85 9.61 17.93 0.321 0.032 0.036 0.196 0.23291 50.3 3.53 6.03 15.17 17.93 0.321 0.040 0.044 0.166 0.21

Table 10 Calculated data of OPC mortars.

w/c Curing Age

(days) fc’



0.3

Seal

7 75.48 15.56 4.84 4.19 44.09 0.304 0.047 0.057 0.106 0.16314 83.82 16.08 5.05 4.58 46.39 0.304 0.050 0.060 0.095 0.15528 91.68 16.51 5.21 4.85 48.14 0.304 0.052 0.063 0.086 0.14991 96.18 17.05 5.42 5.16 50.21 0.304 0.054 0.065 0.077 0.142

Wet

7 84.25 17.15 5.35 4.79 50.72 0.304 0.054 0.065 0.077 0.14214 91.74 18.11 5.74 5.43 54.10 0.304 0.058 0.070 0.060 0.13 28 100.42 18.89 6.05 5.91 56.65 0.304 0.061 0.074 0.047 0.12191 108.32 19.96 6.46 6.53 59.83 0.304 0.065 0.079 0.031 0.11

0.45 Wet

7 54.90 14.15 4.34 3.80 43.08 0.323 0.045 0.055 0.133 0.18814 62.48 15.44 4.94 4.86 46.26 0.323 0.050 0.061 0.113 0.17428 71.98 16.30 5.34 5.59 48.03 0.323 0.053 0.064 0.100 0.16491 77.05 17.18 5.77 6.35 49.48 0.323 0.056 0.068 0.088 0.156

0.6 Wet

7 33.70 10.82 3.25 2.80 33.36 0.317 0.035 0.042 0.171 0.21314 39.85 12.10 3.88 3.77 35.78 0.317 0.039 0.047 0.153 0.2 28 46.53 12.68 4.23 4.53 36.48 0.317 0.041 0.050 0.144 0.19491 51.56 12.92 4.41 5.00 36.64 0.317 0.042 0.051 0.140 0.191

Table 11 Calculated data of HES mortars.

w/c Curing Age

(days) fc’



0.3

Wet

7 85.60 11.12 5.13 3.06 49.28 0.305 0.048 0.058 0.107 0.16514 92.95 11.54 5.31 3.35 51.76 0.305 0.051 0.061 0.096 0.15728 96.90 11.89 5.48 3.55 53.73 0.305 0.053 0.063 0.088 0.15191 97.67 12.36 5.69 3.80 56.15 0.305 0.055 0.066 0.078 0.144

Seal

7 90.65 12.47 5.68 3.54 56.50 0.305 0.055 0.066 0.078 0.14414 96.39 13.17 6.01 3.98 59.93 0.305 0.059 0.070 0.063 0.13328 104.74 13.79 6.31 4.33 62.69 0.305 0.062 0.074 0.051 0.12591 111.87 14.66 6.73 4.79 66.31 0.305 0.066 0.078 0.034 0.112

0.45 Seal

7 57.01 9.78 4.40 2.79 44.39 0.315 0.043 0.052 0.137 0.18914 62.24 10.42 4.74 3.26 46.94 0.315 0.046 0.055 0.125 0.18 28 67.61 10.93 5.01 3.61 48.80 0.315 0.049 0.058 0.115 0.17391 69.67 11.61 5.38 4.05 50.97 0.315 0.051 0.061 0.104 0.165

0.6 Seal

7 36.78 8.23 3.68 2.28 37.00 0.317 0.036 0.043 0.169 0.21214 40.62 8.80 4.04 2.87 38.68 0.317 0.039 0.046 0.158 0.20428 44.42 9.13 4.26 3.23 39.47 0.317 0.040 0.048 0.152 0.2 91 47.20 9.35 4.43 3.52 39.83 0.317 0.041 0.049 0.148 0.197

370

equation (1a) could be expressed as follows:

HVPVf ww'

c (2)

It can be seen in equation (2) that fc’ is a function

of three main parameters Vw, P and H. It might be questionable why P and H were separated as two parameters when these properties are both associated with the degree of hydration. It has been known that under the same hydration heat, the porosity in mortar changes with the content of w/c. Meanwhile, under the same degree of hydration, the hydration heat changes with the type of cement. These phenomena imply that P and H are controlled not only by the degree of hydration but also by the type of cement and the w/c. That explains why P and H were sepa-rated as two parameters as expressed in equation (1) to represent their role in the strength development.

Additionally, it has been addressed that strength is not only affected by porosity but also by pore size distribution25). It is because pore size distribution controls the stress distribution and the stress con-centration in mortar25). Moreover, with the same porosity, cement paste with smaller pores generally gives higher strength as compared with that with larger pores25). Another previous report also stated that the effect of pores smaller than 20 nm in diam-eter was found to be negligible27). That was the rea-son why the porosity of some specific pore sizes has been focused27).

As expressed in equation (2), the parameter P should be represented by a specific porosity type that has significant effect on the development of the strength of mortar. The porosity type might be gel pore (GP), capillary pore (CP), effective or kine-matic pore (EP), or total pore (TP), while EP repre-sents the interconnected pores through which water can circulate, (EP = GP + CP). The values of GP, CP, EP, and TP of the specimens were calculated by means of the microstructure model of Maekawa et al.26) and listed in Table 9, Table 10, and Table 11.

To select the most suitable porosity type to intro-duce into equation (2), two steps of the investigation were performed: (1) the developments of fc’ with pore components, GP, CP, EP, TP, (Vw–GP)/Vw, (Vw–CP)/Vw, (Vw–EP)/Vw, and (Vw–TP)/Vw; and (2) the developments of fc’ with heat-pore components, Hi×(Vw – GP)/Vw, Hi×(Vw – CP)/Vw, Hi×(Vw – EP)/Vw,

and Hi×(Vw – TP)/Vw while Hi include HC2S, HC3S, HC4A, and HC4AF. Consequently, EP was found to be the most suitable porosity type to be introduced into the strength model for equation (2). It was because fc’ was found to develop linearly with (Vw – EP)/Vw and with Hi×(Vw – EP)/Vw for all cement types of mortars as illustrated in Fig.5(b) and Fig.6, Fig.7

(a) fc’ and EP

(b) fc’ and (Vw-EP)/Vw

Fig.5 Developments of fc' and microstructure developments.

(a) HC2S×(Vw-EP)/Vw and HC3S×(Vw-EP)/Vw

(b) HC3A×(Vw-EP)/Vw and HC4AS×(Vw-EP)/Vw

Fig.6 Development of fc' with Hi×(Vw-EP)/Vw in the case of LH

cement.

R² = 0.9686R² = 0.9937R² = 0.9469

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1

f c' (

MP

a)

EP

LH mortarsOPC mortarsHES mortars

R² = 0.9911

R² = 0.9959

R² = 0.9208

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1f c

' (M

Pa)

(Vw-EP)/Vw


R² = 0.947R² = 0.9142

0

20

40

60

80

100

120

140

0 10 20 30 40 50

f c' (

MP

a)

Hi×(Vw-EP)/Vw

C2SC3S

R² = 0.9487R² = 0.9719

0

20

40

60

80

100

120

140

0 3 6 9 12 15

f c' (

MP

a)

Hi×(Vw-EP)/Vw

C3A

C4AF

371



Fig.7 Development of fc' with Hi×(Vw-EP)/Vw in the case of OPC cement.

and Fig.8, respectively. Meanwhile, the inverse proportion between fc’ and EP shown in Fig.5(a) also supported that EP was significant to be considered in the strength model. Accordingly, equation (2) could be represented as follows:

HVEPVf ww

'c

(3a)

or iiww

'c HVEPVf

(3b)

As shown in Fig.5(a) and Fig.5(b), the correlation

between EP and the compressive strength of mortar seemed to be high enough. However, the authors tried to introduce a new correlation between fc’ and heat-pore components, which they believed would also give a good strength prediction model for all types of cement mortars and concretes. As a result, the applicability of this correlation has been con-firmed in this study.

Additionally, it is generally accepted that CP is the appropriate pore type controlling strength. However, based on authors’ experimental data, as illustrated in Fig. 9, substituting CP into equation (2) or equation (3a), the linearity between fc’ and heat-pore compo-nents was found to have low correlation especially for OPC and HES mortars. Meanwhile, it can be seen in Fig.6, Fig.7 and Fig.8 that when EP was used, fc’



Fig.8 Development of fc' with Hi×(Vw-EP)/Vw in the case of HES cement.

Fig.9 fc' and heat-pore components using CP.

of mortar developed linearly with the heat-pore components with high correlation for individual heat of hydration of chemical compound consisting in the cement. By substituting the hydration heats given by all cement compositions, equation (3b) can be rep-resented by equation (4) as follows:

ACSCSC HαHαHαVEPVf 333221ww

'c (

)44 AFCHα (4)

where α1, α2, α3 and α4 are the constants repre-

senting the strength contribution factor of HC2S, HC3S, HC3A, and HC4AF, respectively. The exact value of α1,

R² = 0.9177R² = 0.9887

0

20

40

60

80

100

120

0 10 20 30 40 50

f c' (

MP

a)

Hi×(Vw-EP)/Vw

C2SC3S

R² = 0.9929

R² = 0.98610

20

40

60

80

100

120

0 3 6 9 12 15

f c' (

MP

a)

Hi×(Vw-EP)/Vw

C3AC4AF

R² = 0.9159R² = 0.9872

0

20

40

60

80

100

120

140

0 10 20 30 40 50

f c' (

MP

a)

Hi×(Vw-EP)/Vw

C2SC3S

R² = 0.9839R² = 0.9798

0

20

40

60

80

100

120

140

0 3 6 9 12 15f c

' (M

Pa)

Hi×(Vw-EP)/Vw

C3AC4AF

R² = 0.9765

R² = 0.8973

R² = 0.8847

0

20

40

60

80

100

120

140

0 20 40 60 80 100

f c' (

MP

a)

ΣHi×(Vw-CP)/Vw


372

α2, α3 and α4 were calculated by means of the ex-perimental data for the tested strength at 14, 28, and 91 days age as listed in Table 12.

Therefore, the compressive strength model for mortar for LH, OPC, and HES cement mortars was proposed for different ages as follows:

ACSCSC HHHVEPVf 332ww'14.c 2.10.11.6(

)7.22 4 AFCH (5a)


)5.13 4 AFCH (5b)

ACSCSC HHHVEPVf 332ww'91c. 16.08.12(

)11 4 AFCH (5c)

The accuracy of the proposed model was exam-

ined by the comparisons between fc’ obtained from the experimental results and the calculation results by means of equations (5a), (5b) and (5c). It can be ob-served in Fig.10 that the proposed equations could precisely predict fc’ with the means value of tested strength to predicted strength ratios of 1.02.

On the other hand, the authors’ proposed equations were also compared with the proposed model of Kato and Kishi22) whose equations were given as follows:

FLSGSCSC dQdQdQdQdf 4027402523

'c (6a)

iii dwdQ (6b)

where wi is the ith clinker mineral in powder-to-water ratio by weight in the mix; and dβi is the incremental increase in the degree of hydration of ith clinker mineral component.

Table 12 Contributive coefficients of mineral compounds.

Age C3A C4AF C2S C3S

14 1.2 22.7 -6.1 1.0 28 -0.08 13.5 0.6 1.73 91 -0.16 11.2 2.1 1.8

Consequently, the authors’ proposed equation was found to better fit the test results for all types of ce-ment as illustrated in Fig.11(a), Fig.11(b) and Fig.11(c).

(3) Change in strength contribution of mineral

compounds As listed in Table 12, the strength contributive

coefficients of each mineral compound calculated at different ages were different. It is true that when a cement particle reacts with water, the reaction starts from its surface and spreads inwards, while the par-ticle expands outwards as illustrated in Fig.12.

Fig.10 Prediction of strength of Portland cements using the

proposed model.

Fig.12 Cement particle under reaction with water.

(a) LH Mortars (b) OPC Mortars (c) HES Mortars

Fig.11 Tested strengths and predicted strengths of mortars with different types of cement.

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Tes

ted

stre

ngth

(M

Pa)

Modeled strength (MPa)

Age

Expansion Younger

Unhydrated + WATER = Old hydrated

New hydrated

Cement Expanding hydrates

0

20

40

60

80

100

120

0 20 40 60 80 100

f c' (

MP

a)

Age (days)

Tested strengthKato and Kishi's model Authors' model

0

20

40

60

80

100

120

0 20 40 60 80 100

f c' (

MP

a)

Age (days)


0

20

40

60

80

100

120

0 20 40 60 80 100

f c' (

MP

a)

Age (days)


373

This would mean that at an age of curing, the cement particles consist of both old and young hydrates de-pending on the degree of hydration. Since the degree of hydration was different, the strength contribution factor of each mineral compound was also different at each age of curing.

Moreover, as shown in Table 12, the strength contribution of C3A is positive at early ages and negative at older ages. According to Bogue28), the pure compounds of C2S, C3S, C3A and C4AF have positive strength contribution. However, these compounds can have interaction effect between themselves and result in a negative strength contri-bution. Blaine et al.29) also reported that C3A has a positive strength contribution up to 7 or 28 days but negative strength contribution at older age.

According to Neville25), C3A contributes to the strength of the cement paste at one to three days, and possibly longer, but causes retrogression at an ad-vanced age, particularly in cements with a high C3A or (C3A+C4AF) content. Moreover, when hardened cement paste is attacked by sulfates, expansion due to the formation of calcium sulfoaluminate from C3A may result in a disruption of the hardened paste25). These mechanisms also demonstrated the negative effect of C3A on strength found in this study.

The changes in C3A strength contributions could be due to the hydrate fracture mechanism of the compounds. During the hydration, the hydrated structures are composed of Portlandite CH and cal-cium silicate hydrate CSH with the presence of small amount of Alumino ferrite tri (Aft) and Alumino ferrite mono (AFm). Based on a fractographic study of hydrated Portland cement by Dalgleish and Pratt30), the young paste interparticle fracture occurs through the developing gel and around the rigid inclusions of CH with some amount of AFt and AFm. Meanwhile, while the cement paste is maturing, CH crystals form a massive structure and result in a tortuous path of an interparticle crack.

Alternatively, CSH becomes denser and develops higher strength, leading to a fracturing energy similar to that of CH cleavage. Moreover, the failure in mature paste occurs along a relatively straight path through an extensive CH region and a dense massive CSH. Simultaneously, AFt and AFm grows in an isolated porosity. This suggests that the strength of young paste is strongly controlled by CH, AFt and AFm. However, the strength of older paste is strongly controlled by CH and CSH. The growth of AFt and AFm in an isolated porosity formed low-density regions where the fine-particle gel structure had retained its initial fibrous morpholo-gy30), which might express the negative contribution of C3A to mortar compressive strength at older age.

4. MODEL APPLICABILITY IN THE CASE OF POWDER REPLACEMENT

(1) Limestone powder contributions

Cement mortars in which 20% of the weight of cement contents were replaced by LS replacement powder were produced. Their tested compressive strengths are listed in Table 8. To examine the ap-plicability of the authors’ proposed strength model to the prediction of the compressive strength of mortars with LS replacement powder, the calculation results using equation (5) were plotted against the tested fc’ of the mortars with LS. It can be observed in Fig.13 that equation (5) underestimated fc’ of the mortar when LS replacement was introduced into the mixes. This would imply that the authors’ proposed strength model could not be applied to the mixture containing limestone filler.

Nevertheless, the underestimations of equation (5) could be because this equation introduced only the strength contributions of the mineral compounds of cement, while the contribution of LS replacement whose content was 20% of the weight of cement contents in the mix was neglected.

It has been known that LS is not totally reactive but its physical and chemical properties have an effect on fc’. Physically, LS plays a role as filler between the clinker grains. Meanwhile, the additional surface area provided by the LS particles may provide sites for the nucleation and the growth of hydration products. Both the increase of hydrates and the presence of LS as filler are exactly contributive to strength. Furthermore, the improvement of strength due to the addition of LS replacement was confirmed by the research results in other literatures7), 10), 25).

Based on the experimental results of Barker and Cory7), the size and the distribution of Ca(OH)2 de-posits in cement paste were both influenced by the presences of LS replacement. Larger regions of

Fig.13 Strength underestimation of equation (5) in the case of LS

replacement of 20% of weight of cement content.

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Tes

ted

stre

ngth

(M

Pa)


Mortar with LS

374

Ca(OH)2 were unevenly distributed throughout the limestone-filled paste as compared with the previous OPC.

Moreover, the addition of LS replacement in amounts of 5% or 25% could increase the rate of hydration of C3S, and thus increased strength7). According to Tsivilis et al.10), the total porosity and the carbonation depth in mortar decreased when LS replacement was introduced into the mixes. Similarly, LS reacted with monosulfate and resulted in mono-carboaluminate and mono-sulfoaluminate25). The reaction took place to an extent depending on the LS replacement dosage. Meanwhile, fc’ of mortar could be affected by the modifications of the hydra-tion products.

Therefore, it can be said that the strength contri-bution of LS filler should be also introduced into equation (5) for more accurate predictions of fc’ of mixture with LS filler, which will be the next target of this study.

(2) Slag and fly ash contributions

The applicability of equation (5) was also exam-ined in the case of mixture with blast furnace slag (SG) or with fly ash (FA). Accordingly, two series of cylindrical mortar specimens with SG replacement (SG mortar) and FA replacement (FA mortar) were investigated. Moreover, in the FA mortar as shown in Table 7, 20% of the weight of cement content was replaced by FA, while 20% and 60% of the weight of cement content were replaced by SG in the case of SG mortars. As listed in Table 6, different dosages of SG, 20% and 60%, were used for SG mortars with water-to-paste ratio of 0.3 (w/p = 0.3), while only 20% of SG replacement were used for SG mortars with w/p = 0.45 and 0.6. The tested fc’ of SG mortars and FA mortars, respectively, are summarized in Table 6 and Table 7.

Furthermore, equation (5) was also used to predict fc’ of FA mortars and SG mortar for comparison with the tested fc’. As shown in Fig. 14, equation (5) was also found to underestimate fc’ of FA mortars and SG mortars. This was also because equation (5) did not introduce the strength contribution of FA and SG.

It has been confirmed that the catalysts produced by cement could have reacted with SG and FA. This reaction produced hydration products similar to the pure cement paste and resulted in a reduction of Ca(OH)2 in the mortar. According to O’Flasherty and Mangat31), SG and FA were found to react with ce-ment by binding Ca(OH)2 with free silica by a pozzolanic reaction forming a non-soluble structure. Similar reports were also given by Karim et al.13), Papadakis and Tsimas15), Memon et al.16), and Chindaprasirt and Rukzon32). Moreover, Toutanji et al.17) and the ACI Committee33) stated that the

Fig.14 Prediction of strength of SG and FA mixes using the

proposed model for equation (5).

strength, permeability, flow, and cohesive charac-teristics of mortars can be typically improved by means of SG and FA. According to Prinya et al.8), the increase in FA content in cement paste led to a de-crease in pore size distribution and the average pore diameter in the paste, and thus to improved strength.

Thus, the findings in this study would confirm that the strength contribution of SG and FA should be also introduced into equation (5) for better prediction of fc’ of mixtures with SG and FA, which will be the next target of this study. 5. PREDICTION FOR OTHER DATA

The additional data were obtained from the UBE-Mitsubishi Cement Corporation consisting of standard mortars, normal and high-strength concretes using Portland cements, LH cement, OPC cement, MH (Medium-heat cement) and HES (High-Early- Strength cement). In addition, the data from the Su-mitomo Osaka cement consisted of some standard mortars using five different LH cement and HES cements.

The proposed strength model expressed in equa-tion (5) was used to calculate fc’ of mortar, normal concrete, and high-strength concrete for comparison with data from other sources. Fig.15, Fig.16 and Fig.17 show the comparison of fc’ of mortars, high strength concretes, and normal concretes, respec-tively. It can be observed that the predicted strength calculated by means of equation (5) seems to have a linear relationship with those of other sources’ data. These results suggest that fc’ of cement paste, mortar, and concrete has a linear relationship with the couple heat-pore component expressed in equation (5).

Moreover, the means ratio of the tested strengths to the calculated strengths was found to be 1.3, 1.46, and 1.5 for the mortars, the high-strength concretes, and the normal concretes, respectively. These results indicated that equation (5) underestimated fc’ of other

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Tes

ted

stre

ngth

(M

Pa)


Mortar with FAMortar with SG

375

sources’ data. Therefore, the investigation was ex-tended to the properties of the materials used by UBE and Sumitomo. As shown in Table 13, the properties of their materials properties are different from those used by the authors. That could explain why the predicted strength was lower than the tested strength of the external sources’ data.

Moreover, the authors’ proposed strength model might have underestimated fc’ of normal concrete obtained from other source as shown in Fig.17 due to the presence of coarse aggregate in the concrete. According to previous studies, fc’ of concrete de-pends on w/c, cement-to-aggregate ratio, degree of compaction, bond between mortar and aggregate, and grading, strength and size of the aggregate34), 35). Generally, the crack in normal concrete takes place along the cement paste-aggregate interfacial zone, while its strength depends on the integrity of the mortar and the nature of the coarse aggregate36).

Furthermore, for a given w/c, the type of aggregate was found to control the strength, stiffness, and fracture energy of concrete37), 38). The findings of other researchers mentioned above clarified why the variation coefficient (accuracy) in Fig.17 seemed to be large. Additionally, the authors’ model did not take into account the effect of the aggregate type on the development of fc’. Therefore, it was reasonable that less accuracy was obtained when the proposed model was used to predict fc’ of concretes with dif-ferent types of aggregates. However, as shown in Fig.10, the proposed strength model could precisely predict the compressive strength of mortars.

However, it seems questionable that the authors’ proposed model, which was developed based on cement mortar, was found to underestimate the compressive strength of concrete from other sources. According to Stock et al.39), at a constant wa-ter/cement ratio of 0.5, a gradual decrease of fc’ was observed when the volume of aggregate as a per-centage of the total volume was increased from zero to 20. In addition, the different Young’s modulus between aggregates and cement mortars induce a stress concentration in the concrete under compres-sion, which is most susceptible to cracking25).

On the other hand, according to Kaplan40), the compressive strength of concrete was found to be

Fig.15 fc’ of mortar by means of equation (5) and the tested fc’ from Sumitomo and UBE.

Fig.16 fc’ of high-strength concrete by means of Eq. (5) and the

tested fc’ from UBE.

Fig.17 fc’ of normal concrete by means of Eq. (5) and the tested

fc’ from UBE.

Table 13 Material properties used by UBE and Sumitomo.

Dispersion Own data External sources Maximum dispersion Unknown dispersion

Aggregate volume (m3)

0.37 (w/c=0.3) 0.47 (w/c=0.45) 0.52 (w/c=0.6)

0.567 (Standard mortar) 0.7-0.71 (Normal concrete) 0.63-0.67 (High-strength concrete)

Aggregate type Mountainous Unknown

Specific gravity 2.59 2.63

y = 1.3148xR² = 0.8901

0

15

30

45

60

75

90

0 20 40 60 80

Tes

ted

stre

ngth

(M

Pa)


Test

Prediction slope

y = 1.4627xR² = 0.8584

0

20

40

60

80

100

120

0 20 40 60 80

Tes

ted

stre

ngth

(M

Pa)


UBEPrediction slope

y = 1.4988xR² = 0.8448

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Tes

ted

stre

ngth

(M

Pa)


Normal ConcretePrediction slope

376

higher than that of mortar. He indicated that the mechanical interlocking of the coarse aggregate contributes to the strength of concrete in compression. Similarly, Walker and Bloem41) found that with the same w/c of 0.65, the strengths of mortars at 3 days, 7 days, and 28 days were found to be lower than those of concretes due to the greater amount of entrapped air in mortars. Additionally, Singh42) reported that at a water/cement ratio, the increase of aggre-gate/cement ratio results in an improvement of compressive strength. He mentioned that in certain cases, a larger amount of aggregate absorbs a greater quantity of water, which leads to a reduction of the effective water/cement ratio. 6. CONCLUSIONS

The following conclusions can be derived from

this study: 1) The compressive strength of cement, mortar, and concrete was found to have a linear relationship with the hydration heat coupled with the effective poros-ity. 2) The strength contributions of Portland cement mineral compounds were found to change with time. Meanwhile, the strength contribution of C3A was found to be positive at early age (younger than 20 days) and negative at older age (older than 20 days). 3) The effective porosity was found to be the suitable porosity type to express the hydration heat of cement compositions in the strength model. 4) The strength model for Portland cement mortars was proposed to be:


)7.22 4 AFCH


)5.13 4 AFCH

ACSCSC HHHVEPVf 332ww'91.c 16.08.12(

)11 4 AFCH

5) The authors’ proposed strength model was found to underestimate fc’ of mortars when 20% of the weight of cement content in mortar was replaced by LS, SG or FA. It implied that the strength contribu-tion of LS, SG, and FA should be introduced in the proposed strength prediction model to get more ac-curate strength prediction.

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multi-component concept of constituent minerals, Master Thesis Submitted to Department of Civil Engineering, the University of Tokyo, 1992.

2) Kishi, T., Ozawa, K. and Maekawa, K.: Multi-component

model for hydration heat of concrete based on cement mineral compounds, Proceeding of the JCI, Vol. 15, No.1, pp. 1211-1216, 1993.

3) Kishi, T. and Maekawa, K.: Multi-component model for hydration heat of Portland cement, Journal of Materials, Concrete Structures and Pavements, JSCE, Vol. 526, No.29 pp. 97-109, November 1995.

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6) Padakis, V. G.: Effect of fly ash on Portland cement sys-tems: Part II. High-calcium fly ash, Cement and Concrete Research, Vol. 30, pp. 1647-1654, 2000.

7) Barker, A. P. and Cory, H. P.: The Early Hydration of Limestone-Filled Cements, Blended Cements in Construc-tion, R. N. Swamy, Ed., Elsevier, pp. 107-124, 1991.

8) Prinya, C., Chai, J. and Theerawat, S.: Effect of fly ash fineness on compressive strength and pore size of blended cement paste, Cement & Concrete Composites, Vol. 27, pp. 425-428, 2005.

9) Erdogdu, K. and Tucker, P.: Effect of fly ash particle size on strength of Portland cement fly ash mortars, Cement and Concrete Research, Vol. 28, pp. 1217-1222, 1998.

10) Tsivilis, S., Batis, G., Chaniotakis, E., Grigoriakis, G. and Theodossis, D.: Properties and behavior of limestone ce-ment concrete and mortar, Cement and Concrete Research, Vol. 30, No. 10, pp. 1679-1683, 2000.

11) Li, G. and Wu, X.: Influence of fly ash and its mean particle size on certain engineering properties of cement composite mortars, Cement and Concrete Research, Vol. 35, pp. 1128-1134, 2005.

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13) Karim, M. R., Zain, M. F. M., Jamil, M., Lai, F. C. and Islam, M. N.: Strength development of mortar and concrete containing fly ash: A review, International Journal of the Physical Sciences, Vo. 6, No. 17, pp. 4137-4153, 2011.

14) Thomasa, M. D. A., Shehataa, M. H., Shashiprakasha, S. G., Hopkinsb, D. S. and Cailb, K.: Use of ternary cementitious systems containing silica fume and fly ash in concrete, Cement and Concrete Research, Vol. 29, pp. 1207-1214, 1999.

15) Papadakis, V. G. and Tsimas, S.: Supplementary cementing materials in concrete: Part I: efficiency and design, Cement and Concrete Research, Vol. 32, No. 10, pp. 1525-1532, 2002.

16) Memon, A. H., Radin, S. S., Zain, M. F. M. and Trottier, J. F.: Effect of mineral and chemical admixtures on high-strength concrete in seawater, Cement and Concrete Research, Vol. 32, pp. 373-377, 2002.

17) Toutanji, H., Delatte, N., Aggoun, S., Duval, R. and Danson, A.: Effect of supplementary cementitious materials on the compressive strength and durability of short-term cured concrete, Cement and Concrete Research, Vol. 34, No. 2, pp. 311-319, 2004.

18) Kishi, T. and Maekawa, K.: Multi-component model for hydration heat of blended cement with blast slag and fly ash, Journal of Materials, Concrete Structures and Pavements, JSCE, Vol. 33, No. 550, pp. 131-143, November 1996.

19) Otabe, Y. and Kishi, T.: Modeling hydration heat generating process of blended cement with Silica Fume, Proceedings

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of annual meeting of JCI, Vol. 26, No. 1, pp. 555-560, 2004. 20) Suzuki, Y., Harada, Y., Maekawa, K. and Tsuji, Y.: Quan-

tification of hydration-heat generation process of cement in concrete, Concrete Library of JSCE, Vol. 16, pp. 111-124, 1990.

21) Kishi, T.: Multi-component heat calculation code, 2005. 22) Kato, Y. and Kishi, T.: Strength development model for

concrete in early ages based on hydration of constituent mineral, Proceeding of the JCI, Vol. 16, No. 1, pp. 503-508, 1994.

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27) Sersale, R., Cioffi, G. and Zenone, F.: Relationship between gypsum content, porosity, and strength of cement, Cement and Concrete Research, Vol. 21, No. 1, pp. 120-126, 1991.

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29) Blaine, R. L., Arni, H. T. and Defore, M. R.: Interrelations between Cement and Concrete Properties, Part III, U.S. Department of Commerce, National Bureau of Standards, BSS 8, 1968.

30) Dalgleish, B. J. and Pratt, P. L.: Fractographic Studies of Microstructural Development in Hydrated Portland Ce-ment, Journal of Material Science, Vol. 17, pp. 2199-2207, 1982.

31) O’Flaherty, F. J. and Mangat, P. S.: Influence of constitu-ents on the properties of self-compacting repair materials. In: A Skarendahl and Ö Petersson (ed.), Proceedings of the First International RILEM Symposium, pp. 263-274, 1999.

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33) ACI Committee 233: Slag Cement in Concrete and Mortar, ACI 233R-03, 233R1-233R19, March 28, 2003.

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(Received May 15, 2013)

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STRENGTH MODEL FOR MORTAR BASED ON HYDRATION HEAT …