SCIENCE CHINA Technological Sciences

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*Corresponding author (email: sunwei@seu.edu.cn)

• RESEARCH PAPER • June 2012 Vol.55 No.6: 1515–1522

doi: 10.1007/s11431-011-4737-x

Numerical calculation and influencing factors of the volume fraction of interfacial transition zone in concrete

SUN GuoWen, SUN Wei*, ZHANG YunSheng & LIU ZhiYong

Jiangsu Key Laboratory of Construction Materials, Southeast University, Nanjing 211189, China

Received March 26, 2011; accepted October 19, 2011; published online January 19, 2012

The determination of volume fraction of interfacial transition zone (ITZ) is very important for investigating the quantitative relationship between the microstructure and macroscopical property of concrete. In this paper, based on Lu and Torquato’s most nearest surface distribution function, a calculating process of volume fraction of ITZ is given in detail according to the actual sieve curve in concrete. Then, quantitative formulas are put forward to measure the influencing factors on the ITZ vol-ume fraction. In order to validate the given model, the volume fractions of ITZ obtained by numerical calculation are compared with those by computer simulation. The results show that the two are in good agreement. The order of the factors influencing the ITZ volume fraction is the ITZ thickness, the volume fraction of aggregate and the maximum aggregate diameter for Fuller gradation in turn. The ITZ volume fraction obtained from the equal volume fraction (EVF) gradation is always larger than that from the Fuller gradation for a given volume fraction of aggregate.

concrete, interfacial transition zone (ITZ), volume fraction, Fuller distribution, equal volume fraction distribution (EVF), sieve curve

Citation: Sun G W, Sun W, Zhang Y S, et al. Numerical calculation and influencing factors of the volume fraction of interfacial transition zone in concrete. Sci China Tech Sci, 2012, 55: 15151522, doi: 10.1007/s11431-011-4737-x

1 Introduction

It is well known that the microstructure of cement paste in the vicinity of an aggregate differs from that of bulk cement paste and that of neat hydrated cement paste [1]. This spe-cial microstructure is called the interfacial transition zone (ITZ), and the “wall” effect of aggregate is the main reason for its formation [2, 3]. Therefore, the porosity, water-ce- ment ratio and degree of hydration of the ITZ are much higher than those of the bulk cement paste. The volume fraction of ITZ which is obtained by backscattered electron imaging makes up some 20%–30% of the total paste vol-ume in a typical concrete [4]. This means that the ITZ in concrete could have a significant influence on its properties

such as the transport [5–7] and mechanical [8–11] proper-ties.

The determination of volume fraction of ITZ in concrete has been studied a lot by scientists in terms of computer simulation technology. For example, Garboczi and Bentz [2] took a way of the random point sampling, and Zheng et al. [12] did numerical simulation of concrete mesostructure and combined Monte-Carlo numerical integration method, while Garboczi et al. [8], Sun et al. [9], and Yang et al. [10] adopted the approximate method of the surface area of the aggregates multiplied by the uniform thickness of the ITZ layers, in which the ITZ thickness mainly depends on the median size of the cement grains rather than on the aggre-gate size [13]. The former two methods can obtain compar-atively accurate results, but they are time-consuming. The third method brought large errors due to lack of considering the overlapping degree of ITZ layers between neighboring

1516 Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6

aggregates. Therefore, it is more useful if the analytical so-lution can be directly obtained to calculate the volume frac-tion of ITZ. Fortunately, the nearest surface distribution function in physics presented by Lu and Torquato [14] has provided the choice.

The research objective of this paper is to give a simple numerical method considering the overlap degree of ITZ layers to obtain the volume fraction of ITZ based on Tor-quato’s most nearest surface distribution function. Further-more, quantitative formulas are put forward to measure the influencing factors on the ITZ volume fraction, and the volume fraction of aggregates, the interface thickness, the maximum aggregate diameter and the aggregate gradation are discussed. Finally, according to the actual sieve curve of aggregates in concrete, the results of numerical calculation for ITZ are compared with those by using computer simula-tion.

2 Formula for interfacial transition zone vol-ume

Based on the statistical geometry of composites, Lu and Torquato [14] have derived a theory of the nearest-surface distribution functions, which can be used to predict the ITZ volume fraction in concrete [2]. The concrete is modeled as a three-phase composite at the mesoscopic scale, as de-scribed in Figure 1, namely the spherical aggregate parti-cles, the interfacial transition zone and the bulk cement paste. In Lu and Torquato’s theory [14], the overlap be-tween the ITZ layers has been fully taken into account, so the prediction of the ITZ volume fraction is accurate not only for small ITZ thickness (tITZ), but also for all values of tITZ. The volume fraction of ITZ(VITZ) is expressed as

2 3ITZ a a V ITZ ITZ ITZ1 (1 )exp ( ) ,V V V N ct dt gt (1)

where

2

a

4,

1

Rc

V

(1a)

22

V2

a a

84,

1 (1 )

NR RdV V

(1b)

2 32 22 2

V V2 3

a a a

16 644,

3(1 ) 3(1 ) 27(1 )

N A NRR R RgV V V

(1c)

where NV is the total number of particles per unit volume and Va is the volume fraction of aggregates in the concrete; indicates an average over the aggregate size distribution. A is a coefficient that has different values (0, 2, or 3) ac-cording to the analytical approximation chosen in the theory [14]; c, d and g are determined in terms of the number av-erages of the particle radius and the squared particle radius.

Figure 1 Schematic diagram of the overlap of ITZ layers in concrete.

As can be seen from eq. (1), the factors influencing the ITZ volume fraction are the aggregate gradation, the volume fraction of aggregate, the maximum aggregate diameter and the ITZ thickness. For a given concrete mixture, materials density and a sieve analysis, these variables are known or can be determined.

3 Applying theoretical solutions to the concrete for Fuller and EVF gradation

The aggregates in actual concrete are expressed in terms of the mass fraction passing or retained by a certain sieve size. If the aggregates of different sizes have the same density, the mass fraction is equivalent to volume fraction. There-fore, according to eq. (1), to quantitatively obtain the ITZ volume fraction, the volume-based probability density of aggregate must be converted into the number-based proba-bility density function. The method is given in this paper.

Here, FV (D), fV (D), and fN (D) are used to represent the volume-based accumulative probability function, the vol- ume-based probability density function and the num- ber-based probability density function of spherical aggre- gate particles, respectively, where D, V and N are the diam-eter, volume and number of arbitrary spherical aggregate particles, respectively. The mutual relationship of the three functions is given in details.

fV (D) can be obtained by differentiating FV (D) with re-spect to D as follows:

VV V

d ( )( ) ( ) .

d

F Df D F D

D (2)

If the diameter of spherical aggregate particles varies from D-dD/2 to D+dD/2, the volume-based probability den- sity function is determined. Then, the number of spherical aggregate particles in the scope of D±dD/2 is given by

V

3

( )d( )d .

6

f D Dn D D

D

(3)

Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6 1517

And then, the total number of spherical aggregate parti-cles is determined by

max max

min min

V

3

( )d( )d .

6

D D

D D

f D Dn D D

D

(4)

So, the number-based probability function of spherical ag- gregate particle is given by

max max

min min

3V

N3

V

( )d( )d( )d .

( )d ( )dD D

D D

D f D Dn D Df D D

n D D D f D D

(5)

Of course, for the spherical aggregates, eq. (5) can also be expressed as follows:

min maxN 1

max min

( ) ,( )

n n

n n n

nD Df D

D D D

(6)

where n is a coefficient indicating the type of aggregate gradation. n equal to 2.5 and 3.0 represent the lower and upper bounds of aggregate gradations, respectively, denot-ing the Fuller gradation and the equal volume fraction (EVF) gradation [15]. From a mathematical point of view, the two kinds of gradation mentioned above are continuous distribu-tion functions and the ITZ volume fraction can be directly calculated. For example, the calculating process of Fuller aggregates gradation by applying eqs. (2)–(5) to eq. (1) is described as follows.

The cumulative volume probability of aggregate for Fuller gradation is given by

minV

max min

( ) ,D D

F DD D

(7)

where FV(D) is the cumulative volume probability of the aggregate and D is the diameter of spherical aggregate par-ticles, which varies from the minimum Dmin to the maxi-mum Dmax. Dmin is set to be 0.15 mm in this paper. The volume probability density function of aggregate particles is obtained by substituting eq. (7) into eq. (2) as follows:

V

max min

1 1( ) d .

2( )f D D

D D D

(8)

By substituting eq. (8) into eq. (5), the number based proba-bility density function of aggregate particles can be obtained as

72.5 2.5

max min 2N 2.5 2.5

max min

5( ) .

2( )

D Df D D

D D

(9)

Similarly, the number based probability density function of aggregate particles for EVF gradation can be given by

3 3

4max minN 3 3

max min

3( ) .

3( )

D Df D D

D D

(10)

According to the classical theory of probability and as-suming that the radius of spherical aggregate particles is R, the k order moment of fN (D) about the origin for continuous distribution function, Rk, is expressed as

max

min

d .2

kDk

D

DR f D D

(11)

For the spherical aggregates, substitution of eq. (5) into eq. (11) yields

3 3min max max min

3 3max min

min max min max

max min

3 (ln ln ), 3,

8( )

( ), for other cases.

2 ( )( )

k

k n n k

k n n

D D D Dn k

D DR

n D D D D

n k D D

(12)

Apparently, the first, second and third orders of fN (D) about the origin for Fuller gradation are

2.5 2.5

1 min max min max2.5 2.5max min

5( ),

6( )

D D D DR

D D

(13a)

2 2.5 2.5 2

2 min max min max2.5 2.5max min

5( ),

4( )

D D D DR

D D

(13b)

2.5 3 3 2.5

3 min max min max2.5 2.5max min

5( ).

8( )

D D D DR

D D

(13c)

Obviously, 12 R , 2R and 34

3R represent the

average diameter, area and volume of spherical aggregate particle in concrete, respectively. Therefore, the total ag-gregate particles number per unit volume of concrete, NV, is equal to

aV 3

3.

4

VN

R

(14)

Substituting eq. (13c) into eq. (14), the total aggregate particles number per unit volume of concrete for Fuller, NV is given by

2.5 2.5

a max minV 2.5 3 3 2.5

min max min max

6 ( ).

5 ( )

V D DN

D D D D

(15)

Similarly, for EVF gradation, NV is given by:

3 3

a max minV 3 3

min max max min

2 ( ).

(ln ln )

V D DN

D D D D

(16)

According to the derivation mentioned above, eqs. (13) and (15) are substituted into eq. (1), and the calculated re-sults of the volume fraction of ITZ for Fuller gradation are described in Figure 2, where aggregate particle sizes range from 0.l5 to 20 mm, and ITZ thicknesses (tITZ) are equal to 10, 30, 50 and 80 m. The difference between Figures 1(a),

1518 Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6

Figure 2 Comparison of VITZ between simulation result and theoretical value.

(b) and (c) lies in constant A value in eq. (1), where small circles denote the experimental values. As can be seen from Figure 1, there is little influence of A value on the calculated results of the ITZ volume fraction. Of course, A = 0 is al-ways the best choice to use, which is in line with Garboezi and Bentz’s results [2]. Therefore, to investigate the influ-ence of four factors mentioned above on the ITZ volume fraction, the value of A is adopted as 0 in the fourth section. In addition, it can be seen that from Figure 2, the ITZ vol-ume fraction increases with the increase of tITZ for a given volume fraction of aggregate (Va), but when tITZ and Va are greater than 50 m and 0.7, respectively, the ITZ volume fraction in concrete gradually decreases. This fact implies that the ITZ volume fraction mainly depends on the relative size of tITZ and Va for a given aggregate gradation. Which one will have a greater impact on the ITZ volume fraction? This will be analyzed in next section.

4 Factors influencing on the volume fraction of ITZ in concrete

As mentioned above, the ITZ volume fraction mainly de-pends on the aggregate gradation, aggregate volume fraction, the maximum aggregate diameter and ITZ thickness. Therefore, the effects of the four factors need to be quanti-tatively analyzed. The differentiation result of eq. (1) can be directly used to investigate the influence of ITZ thickness and aggregate volume fraction on VITZ. Take the aggregate for Fuller gradation for example to illustrate the four fac-tors.

Substitution of eq. (14) into eq. (1) yields

2 3aITZ a a ITZ ITZ ITZ3

31 1 exp .

4

VV V V ct dt gt

R

(17)

4.1 Effect of the ITZ thickness on the ITZ volume fraction

The derivation of tITZ in eq. (17) yields

2aITZa ITZ ITZ3

2 3aITZ ITZ ITZ3

31 2 3

4

3exp ( ) .

4

VVV c dt gt

t R

Vct dt gt

R

(18)

As for the influence of tITZ on the VITZ, we assume that Dmin=0.15 mm and Dmax=20 mm. According to eq. (18), the relationship of change rate between ∂VITZ/∂tITZ and tITZ is shown in Figure 3 for the Fuller gradation. As can be seen from Figure 3, the VITZ increases almost linearly with the increase of tITZ in some scope of the volume fraction of ag-gregate (Va). However, when the Va is greater than 0.7, the VITZ gradually drops with the growth of tITZ. The main rea-son is that the overlapping degree between the ITZ of neighboring aggregate particles is dependent mainly on tITZ and the average surface-to-surface distance between aggre-gates. As a rule, the larger the tITZ is, the smaller the average surface-to-surface distance is, therefore, the larger the over-lapping degree of ITZ is. So, for a given average sur-face-to-surface distance, i.e., for a given Va, increasing tITZ can increase the overlapping degree between the ITZ of neighboring aggregate particles and hence reduce the VITZ.

Figure 3 Influence of tITZ on VITZ.

Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6 1519

4.2 Effect of the volume fraction of aggregate on the ITZ volume fraction

The derivative of Va in eq. (17) yields

2 3ITZITZ ITZ ITZ3

a

3exp 1 1 ( )

4a

VB V ct dt gt

V R

2 3aITZ ITZ ITZ3

3 exp ,

4 a a a

V c d gt t t B

V V VR

(19)

where

2 3aITZ ITZ ITZ3

3,

4

VB ct dt gt

R (19a)

2

2a a

4,

1

Rc

V V

(19b)

22V

2 3a aa

164,

(1 )1

N RRd

V VV

(19c)

2 32 2 2 2V V

2 3 4a a aa

32 644.

3(1 ) 9(1 )3 1

N R R A N RRg

V V VV

(19d)

As for the effect of Va on the VITZ, we assume that Dmin=0.15 mm and Dmax=20 mm. Based on eq. (19), the relationship of change rate between ∂VITZ/∂Va and Va is demonstrated in Figure 4 for the Fuller gradation. As can be seen from Figure 4, when Va is lesser than 0.7, the rate of change between ∂VITZ/∂Va and Va is approximately linear. This fact implies that the influence of Va on the VITZ is rela-tively small in some scope of tITZ. However, when Va is greater than 0.7, the VITZ gradually decreases. For example, when tITZ=80 m, the VITZ at Va=0.7 decreases by 13.42% with respect to that at Va=0.8. The fact shows that the over-lapping degree of ITZ between neighboring aggregates clearly increases, which causes decrease of the VITZ. At the same time, it can be found from the change value of vertical coordinates in Figures 3 and 4 that the influence of tITZ is more than that of Va on the VITZ.

4.3 Effect of the maximum aggregate diameter on ITZ volume fraction

As for the effect of the maximum aggregate diameter (Dmax) on the VITZ, we assume that tITZ=30 m, Dmin=0.15 mm and Dmax=5, 10, 20 and 25 mm, respectively. The results are exhibited in Figure 5 for the Fuller gradation, which clearly shows that the VITZ decreases with the increase of Dmax. Es-pecially, when Dmax increases from 5 to 25 mm, the VITZ decreases by 55.67%, 55.16%, 53.73% and 46.55% for a given value of Va at 0.2, 0.4, 0.6 and 0.8, respectively. The

Figure 4 Influence of Va on VITZ.

Figure 5 Influence of aggregate diameter on VITZ.

reason for this is that the aggregate surface area decreases relatively as the maximum aggregate diameter increases, which will lead to the growth of VITZ. Of course, the VITZ increases with the increase of Va for a given value of Dmax, which can be seen from Figure 5, too.

4.4 Effect of the aggregate gradation on the volume fraction of ITZ

The effect of the aggregate gradation on the volume fraction of ITZ (VITZ) is shown in Figure 6 for the Fuller gradation and the EVF gradation, where tITZ =30 m, Dmin=0.15 mm and Dmax = 20 mm. As can be seen from Figure 6, the VITZ in concrete for EVF gradation is always larger than that with the Fuller gradation for a given Va. The main reason is that there are more small aggregate particles included in the EVF gradation [14], which makes the ITZ volume fraction in concrete with the EVF gradation larger than that with the Fuller gradation for a given Va. This fact implies that the aggregate gradation also has a significant influence on VITZ. In addition, it is of interest to note that when the volume

1520 Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6

Figure 6 Influence of aggregate gradation on VITZ.

fraction of aggregate increases to about 0.7, the VITZ is up to peak and then decreases gradually. This can be explained as follows. Firstly, if the overlap of ITZ between neighboring aggregates is ignored, the VITZ approximately equals the surface area of aggregate multiplied by tITZ. Therefore, when Va increases, the surface area of aggregate accordingly increases, which leads to the growth of the VITZ. Secondly, the average surface-to-surface distance between aggregates decreases with the increase of Va, which gives rise to the increase of the overlapping degree between neighboring aggregates, and therefore the ITZ volume fraction decreases. These facts illustrate that Va has two opposite effects. When the former effect is larger than the latter, the VITZ will in-crease, and vice versa.

Based on the above analysis, it can be seen that the most important factor influencing the ITZ volume fraction for Fuller gradation is the ITZ thickness. For example, when Va =0.8, the ITZ volume fraction at tITZ =30 m increases by 200% with respect to that at tITZ=10 m. The second factor is the volume fraction of aggregate. By comparison, the ITZ volume fraction at Va =0.3 increases by 143% with respect to that at Va=0.8 for tITZ=30 m. The least influencing factor is the maximum aggregate diameter. When Va=0.8 and tITZ=30 m, the VITZ at Dmax=25 mm increases by 46.55% with respect to that at Dmax=5 mm.

The results mentioned above illustrate that the most ef-fective way of improving ITZ is to reduce the ITZ thickness. Therefore, the most economical way is adding fine mineral admixtures to concrete to optimize particle diameter of ce-mentitious materials or reducing the water/cement ratio. In addition, Figure 6 also reveals that actual aggregate should approximately close in upon Fuller distribution as soon as possible by optimizing aggregate gradation.

5 Applying theoretical solutions to actual con-crete

A typical sieve analysis is expressed in terms of the mass

fraction passing or retained by a certain sieve size in actual concrete. As a rule, several important parameters such as di, M, and Ci characterize aggregate gradation, where Ci is volume fraction of aggregates retained on some sieve that has a diameter between di and di+1, di<di+1, M is the total number of sieves used, and the sum of Ci over the M sieves equals 1. If aggregates of different sizes have the same den-sity, the mass fraction is equivalent to the volume fraction. But this kind of sieve analysis is volume-based interval probability or volume-based interval cumulative probability. From a mathematical point of view, this size distribution of aggregate is the form of discrete function. So, applying eq. (1) to calculate the ITZ volume fraction should be based on reasonable assumptions for every level of aggregates in sieves. The size distribution of aggregate is also considered as uniformly by volume within each sieve in this paper, which is easy to handle analytically, and is physically rea-sonable [2]. The detailed calculated process is presented in this paper.

If aggregate is uniformly distributed by volume within a sieve, then the volume-based probability density function of aggregate in concrete expressed by the range (V, V+dV), contained in the ith sieve, is given by

1

d( )d .i

i i

C Vp V V

V V

(20)

If a spherical aggregate particle volume is expressed by V, then by substituting eq. (20) into eq. (3) the number proba-bility of particles in the range (V, V+dV) is given by

1

d( )d .

( )i

i i

C Vn V V

V V V

(21)

So, within the range (Vi, Vi+1), the number probability of aggregates is as follows:

a

1

d( )d ,

( )i

i i

V C Vn V V

V V V

(22)

where Va is the volume fraction of aggregates per unit vol-ume of concrete. If NV is the total number of aggregate par-ticles used per concrete volume, the total number probabil-ity density function of spherical aggregate particles within the range (Vi, Vi+1) is given by

a

V 1

d( )d .

( )i

i i

V C Vn V V

N V V V

(23)

According to the expression of sieve curve, using V=D3/6 and dV =D2dD/2, the equivalent formula of eq. (23) is

1

a3 3

V 1

18 d( )d .

( )i

i i

V C D Dn D D

N D D

(24)

Thus, in terms of classical probability theory, integrating over each sieve’s endpoint and summing over each sieve for

Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6 1521

eq. (25) is equal to 1 for this expression, i.e.,

1

1

( )d 1.i

i

M D

Di

n D D

(25)

This normalization determines the value of NV as

a 1V 3 3

1 1

18ln .

( )

Mi i

i ii i

V C DN

DD D

(26)

And then, substitution eq. (24) into eq. (11), the average number density of aggregate is given by

1 1a

3 31 V 1

18d .

( )

i

i

M Dn ni

Di i i

V CD D D

N D D

(27)

Clearly,

a 1

3 31 V 1

18,

( )

Mi i i

i i i

V C D DD

N D D

(27a)

2 2

a 123 3

1 V 1

9.

( )

Mi i i

i i i

V C D DD

N D D

(27b)

In this way, according to the sieve curve, the volume fraction of ITZ in concrete can be obtained by substituting eqs. (26) and (27) into eq. (1), where D=2R and D2= 4R2. The actual aggregate size distribution is shown in Figure 7, where three types of sand were used to calculate the volume fraction of ITZ, corresponding to coarse, me-dium and fine siliceous sand, and their fineness modulus were 3.53, 2.61 and 1.80, respectively. Usually, the ITZ is not uniform. Nevertheless, for the sake of modeling, the ITZ is considered as a uniform region that has a certain thick-ness. Therefore, according to the size distribution of aggre-gate in Figure 7, where the ITZ thickness is assumed 15 m and volume fraction of aggregate (Va) ranges from 30 per-cent to 80 percent, the calculated results are listed in Table 1. From Table 1, it can be seen that numerical results are in accordance with the computer simulation results by using Zheng’s approach [12]. Considering numerical results cal-culated in this paper as accurate values, the deviation be-tween numerical and simulation results is about 3 percent in

Table 1. This fact indicates that the aggregate assumption mentioned above is reasonable.

6 Conclusions

1) The volume fraction of ITZ in concrete increases with the increase of the interface thickness and with the decrease of the maximum aggregate diameter.

2) The volume fraction of aggregate (Va) has two oppo-site effects on the ITZ volume fraction. When Va is less than 0.7, the ITZ volume fraction increases with the growth of Va. On the contrary, when it is beyond the value of 0.7, the av-erage surface-to-surface distance between aggregates de-creases with the increase of Va, which gives rise to increase of the overlapping degree of ITZ layers, and therefore the ITZ volume fraction decreases.

3) The aggregate gradation has a significant influence on the ITZ volume fraction. The equal volume fraction (EVF) gradation is always larger than that with the Fuller gradation for a given volume fraction of aggregate.

4) The order for factors to influence the ITZ volume fraction is the ITZ thickness, volume fraction of aggregate, and the maximum aggregate diameter for Fuller gradation in turn.

Figure 7 Aggregate size distributions.

Table 1 Numerical and simulation results of volume fraction of ITZ

Va Numerical results (%) Simulation results (%) Deviation (%)

Coarse Medium Fine Coarse Medium Fine Coarse Medium Fine

0.3 3.24 5.67 8.67 3.19 5.51 8.36 1.54 2.82 3.58

0.4 4.31 7.51 11.42 4.20 7.20 10.83 2.55 4.13 5.17

0.5 5.37 9.30 13.99 5.16 9.04 13.42 3.91 2.80 4.07

0.6 6.39 10.94 16.18 6.03 10.35 15.67 5.63 5.39 3.15

0.7 7.33 12.28 17.48 6.95 11.91 16.47 5.18 3.01 5.78

0.8 8.02 12.66 16.45 7.69 11.97 16.20 4.11 5.45 1.52

1522 Sun G W, et al. Sci China Tech Sci June (2012) Vol.55 No.6

5) An actual aggregate size distribution is considered as uniform distribution by volume within each sieve, and the proposed approximate treatment is simple and of highly accurate degree to calculate the ITZ volume fraction.

This work was supported by the National Basic Research Program of Chi-na (“973” Project) (Grant No. 2009CB623200) and the National High-Tech Research and Development Program of China (“863” Pro-ject)( Grant No. 2008AA030794).

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