Evaluating the distance between particles in fresh cement ......from PSD, and density measured according to ASTM C188 [21] of cement fractions were summarized in Table 3. According

Construction and Building Materials 142 (2017) 109–116

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Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

Evaluating the distance between particles in fresh cement paste basedon the yield stress and particle size

http://dx.doi.org/10.1016/j.conbuildmat.2017.03.0550950-0618/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: School of Materials Science and Engineering, SouthChina University of Technology, 510640 Guangzhou, China.

E-mail address: [email protected] (T. Zhang).

Yiqun Guo a, Tongsheng Zhang a,b,⇑, Jiangxiong Wei a,b, Qijun Yu a,b, Shixi Ouyang c

a School of Materials Science and Engineering, South China University of Technology, 510640 Guangzhou, ChinabGuangdong Low Carbon Technologies Engineering Center for Building Materials, 510640 Guangzhou, ChinacChina Building Materials Academy, 10024 Beijing, China

h i g h l i g h t s

� The coarser particles needed larger kto achieve same yield stress of paste.

� The relationships between yieldstress and k were established.

� k in binary-cement pastes wasevaluated in consideration of particlesize.

� Reliability of the evaluation of k wasvalidated experimentally.

� This paper gives a deeper insight intoinitial packing and bridging ofparticles.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 December 2016Received in revised form 16 February 2017Accepted 9 March 2017

Keywords:Distance between particlesFresh cement pasteYield stressParticle sizeSolid volume concentration

a b s t r a c t

The distance between particles (k) plays a key role in the flowability of fresh cement pastes. k given inavailable literatures is an average value and independent with the particle size. Actually, coarse particlesin cement paste need a larger k to achieve same yield stress compared with fine particles. In the presentstudy, relationship between yield stress and k for single-fraction cement pastes was established by intro-ducing an exponential-type function. Then the function was theoretically deduced to evaluate k inbinary-fraction cement pastes. For cement pastes with yield stress of 30 Pa, distance between coarse par-ticle (48.51 lm) and fine particle (6.63 lm) was 5.00 lm, while distance between mid-sized particle(20.27 lm) and fine particle (6.63 lm) was only 2.57 lm. Finally, the reliability of k in binary-fractioncement paste was experimentally validated. This method can be applied in multi-fraction cement pastes,and k in consideration of particle size will give a deeper insight in the flowability and microstructuraldevelopment of cement pastes.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

The workability of fresh concrete, which is one of the concernsin engineering applications, is driven by the flowability (or rheo-logical properties) of fresh cement paste (the fluid phase of con-crete). Fresh cement paste mainly consists of water and cementparticles, and its flowability generally attributes to the initial

Nomenclature

PSD particle size distributionH-B model Herschel-Bulkley modelD50 volume median diameter (lm)k distance between particles (lm)kf distance between particles in fine-fraction cement paste

(lm)kc distance between particles in coarse-fraction cement

paste (lm)Tw water coating thickness (lm)Twf water coating thickness of fine particles in binary-

fraction cement paste (lm)Twc water coating thickness of coarse particles in binary-

fraction cement paste (lm)SSA specific surface area (m2/cm3)SSAf specific surface area of fine fraction (m2/cm3)SSAc specific surface area of coarse fraction (m2/cm3)qp wet density of cement paste (g/cm3)qc density of cement (g/cm3)qw density of water (g/cm3)

Mt total weight of container and cement paste (g)Mc weight of container (g)Vc volume of container (cm3)s shear stress (Pa)sc yield stress (Pa)y shear rate (s�1)We Volume of excess water (cm3/cm3)Ww volume ratio of water to cement (dimensionless)u solid volume concentration of cement paste (dimen-

sionless)um maximum solid volume concentration of cement paste

(dimensionless)Vm minimum void ratio (dimensionless)l size ratio of finer fraction to coarser fraction in binary-

fraction cement (dimensionless)XL volume proportion of coarser fraction in binary-fraction

cement (dimensionless)k,n coefficients of H-B model (dimensionless)

110 Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116

packing of particles in fresh cement paste. Compared with thepacking of dry particles (particles are assumed to be contactedwith their neighbor ones as shown in Fig. 1), the voids among par-ticles in cement paste are filled up by part of water (filling water),then particles are separated by the residual water (excess water)[1,2]. Thus particles in cement paste do not directly contact withtheir neighbor particles, and the water coated around particlescontributes greatly to the fluidity of fresh cement paste [3–6].

Many attempts have been made to evaluate the rheologicalproperties from the initial packing of particles in fresh cementpaste. For instance, the yield stress of cement paste can be pre-dicted from the solid volume concentration (u) of cement pastesby the YODEL based on first principles, in which particle size distri-bution (PSD), inter-particle forces, and microstructural featureswere taken into account [7,8]. Bentz reported that the relationshipbetween yield stress and particle number density (the number ofparticles in unit volume of powder) shows a percolation-type trend[9]. Silva presented the yield stress of cement paste increases withthe decrease of particle size [10], while Ferraris pointed out that

Fig. 1. The packing of dry particles.

yield stress increases and then drops with the decrease of particlesize, and the yield stress reaches maximum value when the meansize of particles equals to 5.7 lm [11].

Actually, major factors influencing the yield stress of freshcement pastes, such as particle size, particle number density, solidvolume concentration, etc. can be attributed to the distancebetween particles (k) in fresh cement paste. A larger k generallymeans more water coated around particles, which provides betterlubrication and eventually contributes to the flowability of freshcement paste. For fresh cement pastes with same flowability, smallk is beneficial to the cluster and bridging of hydration products anddensification of microstructure [12,13], and then contributes tostrength development and deformation resistance [14], especiallyat very early age. Therefore, beside the flowability of fresh cementpaste, the mechanical properties and volume stability of cementpaste during hardening are subject to k either.

Ferraris introduced the distance between aggregates in concreteand pointed out that higher torque is necessary for maintainingconstant rotation speed of the plate when the distance betweenaggregates is decreasing [15]. Thus, there must be a similar rela-tionship between k and rheological properties of cement paste. Itis observed that the yield stress of fresh cement paste is propor-tional to k [16]. Commonly, k is calculated from u of cement pasteand the specific surface area of particles in cement paste [17,18].

u ¼ qp � qw

qc � qwð1Þ

where, qp is the wet density of cement paste (g/cm3), qc and qw arethe densities of cement and water (g/cm3), respectively.

For the maximum solid volume concentration (um) of cementpaste, the corresponding minimum void ratio (Vm) is defined byEq. (2):

Vm ¼ 1�um

umð2Þ

The volume of excess water (We) can be evaluated by the fol-lowing equation:

We ¼ Ww � Vm ð3Þwhere,Ww is the volume ratio of water to cement, which can be cal-culated from u.

Fig. 3. The packing of particles with varied Tw.

Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116 111

Consequently, the water coating thickness (Tw) is obtained by:

Tw ¼ We

Að4Þ

where, A is the surface area of particles in unit volume of cementpaste.

Then k in cement paste can be calculated by Eq. (5):

k ¼ Tw � 2 ð5ÞObviously, it is assumed that k is independent with the size of

cement particle in the above calculation, indicating particles withdifferent size have equal Twork (average value) as shown inFig. 2. In fact, coarser particles needs larger k to achieve sameflowability compared with finer particles (Fig. 3) [19]. Since thePSD of Portland cement generally lies in the range of 1–80 lm, kin cement paste certainly varies with the size of cement particles.Therefore, it is irrational to use an average k to describe the rheo-logical properties of fresh cement pastes.

In present study, the relationship between yield stress and k forsingle-fraction cement paste was established in consideration ofthe size of cement particle, and then described by anexponential-type function. The function was theoretically deducedto evaluate k in binary-fraction cement pastes based on the yieldstress and particle size. By taking into account the size of cementparticles, k calculated by present method will give a deeper insightin the flowability and microstructural development of cementpastes from the viewpoint of initial particle packing and particle-to-particle bridging.

2. Experimental

2.1. Preparation of cement pastes

The chemical and mineral compositions (calculated by Boguemethod [20]) of Portland cement used in this study were listedin Table 1 and Table 2, respectively. By changing the operationalparameters of an air classifier (such as air flow rate, feed rate,and rotor speed), Portland cement was classified into four frac-tions, then the PSD of each fraction was determined by laserdiffraction method (Malvern Mastersizer 2000, refractive index ofdispersant (ethyl alcohol): 1.32 and obscuration: 12.4%). Sincethe cement particles merely distributed in a narrow range asshown in Fig. 4, the volume median diameter (D50) was taken asthe mean size of the cement fraction. The D50 and SSA calculated

Fig. 2. The packing of particles with equal Tw.

from PSD, and density measured according to ASTM C188 [21] ofcement fractions were summarized in Table 3.

According to the mix proportions listed in Table 4, each cementfraction was blended with water into a homogenous paste as spec-ified in ASTM C305 [22].

2.2. The solid volume concentration of cement pastes

Fresh cement paste was added into a cylinder-shaped container(U 55.0 mm � 50.0 mm), and 60 s vibration was applied to ensurethe exhaust of air voids, then the excess paste was removed by astraight edge. The wet density of cement paste can be calculatedby Eq. (6):

qp ¼Mt �Mc

Vcð6Þ

where, Vc is the volume of container (cm3); Mt is the total weight ofcontainer and paste (g); Mc is the weight of container (g).

Three repeated tests were carried out, and the average valuewas selected as the wet density of cement paste (Fig. 5), then uwas calculated by Eq. (1) and plotted in Fig. 6. With the reductionof W/C, u increased and then drops rapidly. Maximum solid vol-ume concentration (um) was achieved at a threshold W/C. Therewas nearly no difference in solid volume concentration when theW/Cs were larger than the corresponding threshold W/Cs. How-ever, the threshold W/Cs of cement pastes decreased and the um

increased with the increase of particle size. For instance, the um

of cement paste prepared by D50 = 48.51 lm fraction as high as0.517, being 9.53% higher than that of the cement paste preparedby D50 = 6.63 lm fraction (0.472).

2.3. The yield stress of cement pastes

The yield stress of cement paste was measured by a shear rate-controlled rheometer (Brookfield R/S plus) equipped with a shearvane (four blades with 20 mm in width and 40 mm in length).The shearing sequence used in rheology test (Fig. 7) consisted oftwo cycles and a rest period. The first cycle, namely pre-shearingcycle, was used for ensuring each sample has achieved an equilib-rium state before rheology test. In this cycle, the shear rateincreased from 0 to 200 s�1 in 25 s and maintained at 200 s�1 for25 s, then decreased to 0 s�1 in subsequent 10 s. After a 10 s restperiod the data-logging cycle was performed, in which the shearrate increased from 0 to 200 s�1 in 100 s and then decreased to

Table 1The chemical composition of Portland cement (%).

SiO2 Al2O3 Fe2O3 CaO MgO K2O Na2O SO3 Others LOI*

21.60 4.35 2.95 63.81 1.76 0.51 0.16 2.06 1.61 1.19

* LOI, loss on ignition.

Table 2The mineral composition of Portland cement* (%)

C3S C2S C3A C4AF CaSO4�2H2O

56.20 19.61 6.54 8.97 3.50

* Calculated by Bogue method [20].

Fig. 4. The particle size distribution of cement fractions (a) Incremental volume vs.particle size, (b) Cumulative volume vs. particle size.

Table 3The densities and specific surface areas of cement fractions.

D50 (lm) 48.51 20.27 9.97 6.63

Specific surface area (m2/cm3) 0.155 0.403 1.066 2.160Density (g/cm3) 3.20 3.12 3.10 3.09

112 Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116

0 s�1 in another 100 s. The down ramp of shear stress-rate curvethat implied more stable rheological information of cement pastewas used for yield stress analysis.

The down ramp of shear stress-rate curve can be described byHerschel-Bulkley (H-B) model, which generally agreed better withthe experimental results [23–25]. The shear stress-rate equationwas given by Eq. (7):

s ¼ sc þ kyn ð7Þwhere s, sc and y are shear stress (Pa), yield stress (Pa) and shearrate (s�1), respectively; k and n are empirical coefficients.

Variation of the yield stress of single-fraction cement pasteswith different W/Cs was shown in Fig. 8. For cement pastes pre-pared by given cement fraction, yield stress decreased with theincrease of W/C. However, yield stress of cement pastes with sameW/C increased significantly as the particle size of cement fractiondecreased. For instance, yield stress of cement pastes with W/Cof 0.5 raised from 14.05 Pa to 75.35 Pa when D50 of cement fractiondropped from 20.27 lm to 9.97 lm.

3. Relationships between sc and k for single-fraction cementpastes

3.1. Selection of um

During the calculation of k, um of cement pastes were generallyobtained by experiments [17,26]. However, at lowW/C, the cementpaste was too thick to exhaust the air voids even the vibration wasapplied, and the agglomeration of cement particles could not beneglected at such a low W/C [27,28]. As shown in Fig. 6, the differ-ence among um of single-fraction cement pastes was about 10%(from 0.472 to 0.517), and um of ordinary Portland cement pasteseven varied from 0.325 to 0.767 in the available literatures[17,19,29]. Thus the deviations of um cannot be ignored.

Although the repulsive electric forces exerted among particlesbrings down the packing density of powder when the particle sizedecreases [30], the influence of repulsive electric forces on thepacking density of cement paste can be neglected due to the watercoated around particles. That is to say, um of cement paste shouldbe independent with the particle size. As the densities of randomloose packing and random close packing of mono-sized sphericalparticles are 0.60 and 0.64, respectively [31], an average value(0.62) is selected as um for all single-fraction cement pastes.

3.2. Calculation of k

k in single-fraction cement pastes was calculated by Eq. (5) andplotted in Fig. 9. For all the cement fractions, k decreased linearlywith the increase of u. For a given u, k dropped significantly withthe decrease of particle size, which can be attributed to the largerspecific surface area of finer cement fractions.

3.3. Relationship between yield stress and k

The relationship between k and yield stress of cement pasteswas illustrated in Fig. 10. The yield stress dropped rapidly and thendecreased gradually with the increase of k. To achieve the sameyield stress, larger k was required for cement paste prepared bycoarser fraction. For example, when yield stress maintained at50 Pa, k in cement pastes prepared by cement fraction with

Table 4Mix proportions of single-fraction cement pastes.

D50

(lm)Water to cement ratio (W/C)

48.51 0.20, 0.23, 0.25, 0.28, 0.30, 0.33, 0.35, 0.38, 0.4020.27 0.23, 0.25, 0.28, 0.30, 0.33, 0.35, 0.38, 0.40, 0.43, 0.45, 0.48, 0.50,

0.539.97 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.706.63 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80

Fig. 5. The wet densities of single-fraction cement pastes with different W/Cs.

Fig. 6. The solid volume concentration of single-fraction cement pastes withdifferent W/Cs.

Fig. 7. Shearing sequence used in rheology test.

Fig. 8. The yield stress of single-fraction cement pastes with different W/Cs.

Fig. 9. The relationship between k and solid volume concentration for single-fraction cement pastes.

Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116 113

D50 = 48.51 lm was 5.87 lm, which was four times as that withD50 = 6.63 lm.

An exponential-type function was introduced by Kwan andMcKinley [32] to describe the relationship between yield stressand the thickness of water coated around particles. Here, the func-tion was employed to establish the relationship between yieldstress and k.

sc ¼ ae�b�k ð8Þ

where, a and b are parameters related to the particle size of cementfractions.

In Eq. (8), a is the ultimate yield stress when k in cement pasteequals to zero (water just fills into the voids among particles, and

particles in cement paste contact with their neighbor ones), and bis the sensitivity of yield stress to the variation of k. The values of aand b for single-fraction cement pastes were listed in Table 5. The

Fig. 10. The relationship between yield stress and k for single-fraction cementpastes.

114 Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116

ultimate yield stress decreased and then increased with theincrease of particle size. For cement paste prepared byD50 = 6.63 lm fraction, the sensitivity of yield stress had a highervalue, indicating that the yield stress of cement paste was moresensitive to finer particles. It is known that yield stress is attributedto friction among particles, which is mainly depended mechanicallocking and contact area [33]. The mechanical locking plays a mainrole in the friction among particles for cement pastes with coarserparticles, while friction among particles is predominated by largercontact area (surface area of particles) for cement pastes with finerparticles. Therefore, ultimate yield stresses of cement pastes pre-pared by both D50 = 6.63 lm and D50 = 48.51 lm fractions arehigher than that by D50 = 9.97 lm.

4. Evaluation of the Dp based on the yield stress of binary-fraction cement pastes

4.1. The relationship between yield stress and k for binary-fractioncement pastes

The flowability of cement paste is generally influenced by therheological properties of liquid, the surface texture of cement par-ticles, and k. For single-fraction cement pastes and binary-fractioncement pastes, no difference in pore solution chemistry (such aspH value, ions concentration) is observed during mixing and rheol-ogy test [34], resulting in same rheological properties of liquid. Andthe surface texture of cement particles is also independent withthe particle size as same crushing and milling procedures areapplied to the same Portland cement. Therefore, it can be inferredthat the yield stress of cement pastes only depend on k, and therelationships between k and yield stress for single-fraction cementpastes can be employed to evaluate k in binary-fraction cementpastes.

For binary-fraction cement pastes, k equals to the sum of watercoating thickness of two neighbor particles, the distance between

Table 5The values of a and b in the exponential-type function.

D50 (lm) a (Pa) b (lm�1)

6.63 419 1.5729.97 303 0.80320.27 465 0.79348.51 5141 0.785

fine and coarse particles in binary-fraction cement paste can becalculated by Eq. (9):

k ¼ Twf þ Twc ¼ 12� ðkf þ kcÞ ð9Þ

where, Twf is the water coating thickness of fine particles in binary-fraction cement paste (lm), and Twc is that of coarse particles (lm).kf is the distance between particles in fine-fraction cement paste(lm), and kc is that in coarse-fraction cement paste (lm).

kf can be calculated by Eq. (10) (the inverse function of Eq. (8)):

kf ¼ � 1bf

lnðscafÞ ð10Þ

where, af (Pa) and bf (lm�1) can be obtained from Table 5.Similarly, kc can also be calculated. Consequently, k in binary-

fraction cement pastes can be calculated by combining Eqs. (9)and (10):

k ¼ �12� 1

bfln

scaf

� �þ 1bc

lnscac

� �� �

¼ � bf þ bc

2bf bclnsc þ bclnaf þ bf lnac

2bf bcð11Þ

To simplify Eq. (11), dimensionless coefficients m and n aredefined as following formulas:

m ¼ � bf lnac þ bclnafbf þ bc

ð12Þ

n ¼ � 2bcbf

bf þ bcð13Þ

Then the relationship between yield stress and k for binary-fraction cement paste can be written as following equation:

sc ¼ em�n�k ð14ÞBy comparing Eq. (8) (for single-fraction cement pastes) and Eq.

(14) (for binary-fraction cement pastes), the two relationshipsobey the same exponential-type function, only the calculation ofparameters shows significant difference. That is to say, the rela-tionships between yield stress and k in cement pastes obey samerule, and can be described by the exponential-type function, theparameters in function only depend on the particle size.

Binary-fraction cement pastes were prepared according to theproportion listed in Table 6, then yield stress was obtained follow-ing the experimental procedure specified in Section 2.3. Based onyield stress shown in Fig. 11, the water coating thickness of parti-cles in binary-fraction cement pastes were calculated according toEq. (14).

Water coating thickness of both fine and coarse particlesincreased with the increase of W/C as shown in Fig. 12. Notably,significant difference in water coating thickness was observed forfine and coarse particles even in same binary-fraction cementpaste. For M2 with W/C of 0.55, the water coating thickness of par-ticle with D50 = 6.67 lm was 1.03 lm, while that of particle withD50 = 48.51 lm was as high as 3.66 lm. Fig. 13 provided the rela-tionships between yield stress and k for binary-fraction cementpastes. Compared with M2 and M3, larger k was needed for M1to achieve same yield stress, as relative coarser particles were used.For instance, when the yield stress equaled to 30 Pa, distancebetween fine and coarse particles in M1 was 5.00 lm, which wasnearly double as that in M3 (2.57 lm).

4.2. Validation of k in binary-fraction cement pastes

The W/C of binary-fraction cement pastes was calculated by kfand kc , then the validation of k was carried out by comparing the

Table 6The mix proportions of binary-fraction cement pastes.

Cement ID D50 (lm) * Density of the mixture (g/cm3) W/C

Coarse Fine

M1 48.51 20.27 3.16 0.30, 0.33, 0.35, 0.38, 0.40, 0.43, 0.45M2 48.51 6.63 3.15 0.30, 0.35, 0.40, 0.45, 0.50, 0.55M3 20.27 6.63 3.11 0.40, 0.45, 0.50, 0.55, 0.60, 0.65

* The volume percentages of both coarse and fine fractions are 50%, respectively.

Fig. 12. The Tw of particles in binary-fraction cement pastes with different W/Cs.

Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116 115

actual W/C andW/C calculated. According to Eq. (15),um of binary-fraction cement pastes can be obtained [35]:

um ¼ 0:64=½1:0� ð0:362� 0:315ðlÞ0:7ÞXL

þ 0:955ðlÞ4ðX2L=ð1� XLÞÞ� ð15Þ

where, l is the mean size ratio of finer fraction to coarser fraction;XL is the volume proportion of coarser fraction in binary mixture.The um of binary-fraction cement pastes calculated were listed inTable 7.

Through combining Eqs. (2) to (6), W/C of binary-fractioncement pastes can be calculated by Eq. (16):

W=C ¼ ½0:25ðkf � SSAf þ kc � SSAcÞ þ 1�um

um� � qw

qcð16Þ

where, SSAf and SSAc are the specific surface areas of fine and coarsecement fractions, respectively.

Fig. 14 showed that the W/C calculated from k in binary-fraction cement pastes increased linearly with the actual W/C,and all data were around the line of equality. Within 10% deviationwas observed due to the low efficiency of air classifier, as particlesin each fraction was regard as mono-sized spheres though it actu-ally presented narrow PSD. Therefore, it is proved that k in binary-fraction cement pastes can be evaluated by the relationshipbetween k and yield stress for single-fraction cement pastes, andk is indeed significantly influenced by the size of cement particle.

According to the above theoretical and experimental analyses, itcan be inferred that k in multi-fraction cement paste can also becalculated by its yield stress and the exponential-type relationshipbetween yield stress and k for each single-fraction cement paste.To sum up, it provided a reliable method to evaluate k in freshmulti-fraction cement pastes, and k in consideration of particle sizewill give a deeper insight in the flowability and microstructuraldevelopment of cement pastes from the viewpoint of initial

Fig. 11. The yield stress of binary-fraction cement pastes with different W/Cs.

Fig. 13. The relationships between yield stress and k for binary-fraction cementpastes.

Table 7The um of binary-fraction cement pastes

Cement ID l XL um

M1 0.418 0.50 0.697M2 0.137 0.748M3 0.327 0.714

particle packing and particle-to-particle bridging, which eventuallyinfluencing the mechanical properties development, volume stabil-ity, and durability of cement-based materials.

Fig. 14. Comparison of actual W/C and W/C calculated from k in binary-fractioncement pastes.

116 Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116

5. Conclusions and prospect

The main conclusions that can be drawn from the present studyare summarized as follows:

(a) It was confirmed that k in single-fraction cement pastesindeed varied significantly with the size of cement particleat given yield stress. Then an exponential-type function(sc ¼ ae�b�k) was introduced to describe the relationshipbetween yield stress and k for single-fraction cement pastes.

(b) The exponential-type function was theoretical deduced andthen employed to evaluate k in binary-fraction cementpastes. For cement pastes with yield stress of 30 Pa, distancebetween coarse particle (48.51 lm) and fine particle(6.63 lm) was 5.00 lm, while distance between mid-sizedparticle (20.27 lm) and fine particle (6.63 lm) was only2.57 lm.

The reliability of k in binary-fraction cement paste was con-firmed by comparing actual W/C and W/C calculated from k. Thismethod can be further applied to multi-fraction cement pastes,and k in consideration of particle size will give a deeper insightin the flowability and microstructural development of cementpastes from the viewpoint of initial particle packing and particle-to-particle bridging.

Acknowledgements

This work was funded by the National Natural Science Founda-tion of China (No. 51302090 and 51272244), Guangdong specialsupport for Youth S&T innovation talents (2015TQ01C312), PearlRiver S&T Nova Program of Guangzhou (201610010098), andNational key research and development program(2016YFB0303502), their financial supports are gratefullyacknowledged.

References

[1] H. Ma, D. Hou, Y. Lu, Z. Li, Two-scale modeling of the capillary network inhydrated cement paste, Constr. Build. Mater. 64 (2014) 11–21.

[2] H. Ma, S. Tang, Z. Li, New pore structure assessment methods for cement paste,J. Mater. Civil Eng. 27 (2) (2013) A4014002.

[3] F. Rosquoët, A. Alexis, A. Khelidj, A. Phelipot, Experimental study of cementgrout: rheological behavior and sedimentation, Cem. Concr. Res. 33 (5) (2003)713–722.

[4] M. Lachemi, K.M.A. Hossain, V. Lambros, P.C. Nkinamubanzi, N. Bouzoubaâ,Performance of new viscosity modifying admixtures in enhancing therheological properties of cement paste, Cem. Concr. Res. 34 (2) (2004) 185–193.

[5] L. Senff, J.A. Labrincha, V.M. Ferreira, D. Hotza, W.L. Repette, Effect of nano-silica on rheology and fresh properties of cement pastes and mortars, Constr.Build. Mater. 23 (7) (2009) 2487–2491.

[6] A. Kashani, R. San Nicolas, G.G. Qiao, J.S.J. Van Deventer, J.L. Provis, Modellingthe yield stress of ternary cement–slag–fly ash pastes based on particle sizedistribution, Powder Technol. 266 (2014) 203–209.

[7] R.J. Flatt, P. Bowen, Yield stress of multimodal powder suspensions: anextension of the YODEL (Yield Stress mODEL), J. Am. Ceram. Soc. 90 (4) (2007)1038–1044.

[8] Z. Toutou, N. Roussel, Multi scale experimental study of concrete rheology:from water scale to gravel scale, Mater. Struct. 39 (2) (2006) 189–199.

[9] D.P. Bentz, C.F. Ferraris, M.A. Galler, A.S. Hansen, J.M. Guynn, Influence ofparticle size distributions on yield stress and viscosity of cement-fly ashpastes, Cem. Concr. Res. 42 (2) (2012) 404–409.

[10] A.P. Silva, A.M. Segadães, D.G. Pinto, L.A. Oliveira, T.C. Devezas, Effect ofparticle size distribution and calcium aluminate cement on the rheologicalbehaviour of all-alumina refractory castables, Powder Technol. 226 (2012)107–113.

[11] C.F. Ferraris, K.H. Obla, R. Hill, The influence of mineral admixtures on therheology of cement paste and concrete, Cem. Concr. Res. 31 (2) (2001) 245–255.

[12] G. Ye, K. Van Breugel, A.L.A. Fraaij, Experimental study and numericalsimulation on the formation of microstructure in cementitious materials atearly age, Cem. Concr. Res. 33 (2) (2003) 233–239.

[13] H. Ma, Z. Li, Realistic pore structure of Portland cement paste: experimentalstudy and numerical simulation, Comput. Concr. 11 (4) (2013) 317–336.

[14] E. Ghiasvand, A.A. Ramezanianpour, A.M. Ramezanianpour, Influence ofgrinding method and particle size distribution on the properties of Portland-limestone cements, Mater. Struct. 48 (5) (2015) 1273–1283.

[15] C.F. Ferraris, J.M. Gaidis, Connection between the rheology of concrete andrheology of cement paste, ACI Mater. J. 89 (4) (1992) 388–393.

[16] K. Vance, A. Kumar, G. Sant, N. Neithalath, The rheological properties of ternarybinders containing Portland cement, limestone, and metakaolin or fly ash,Cem. Concr. Res. 52 (2013) 196–207.

[17] A.K.H. Kwan, L.G. Li, Combined effects of water film thickness and paste filmthickness on rheology of mortar, Mater. Struct. 45 (9) (2012) 1359–1374.

[18] L.G. Li, A.K.H. Kwan, Effects of superplasticizer type on packing density, waterfilm thickness and flowability of cementitious paste, Constr. Build. Mater. 86(2015) 113–119.

[19] T. Zhang, Q. Yu, J. Wei, P. Zhang, P. Chen, A gap-graded particle size distributionfor blended cements: analytical approach and experimental validation,Powder Technol. 214 (2) (2011) 259–268.

[20] R.H. Bogue, Calculation of the compounds in Portland cement, Ind. Eng. Chem.1 (4) (1929) 192–197.

[21] ASTM C188, Standard Test Method for Density of Hydraulic Cement, ASTMInternational, West Conshohocken, 2015.

[22] ASTM C305, Standard Practice for Mechanical Mixing of Hydraulic CementPastes and Mortars of Plastic Consistency, ASTM International, WestConshohocken, 2014.

[23] J.J. Chen, A.K.H. Kwan, Superfine cement for improving packing density,rheology and strength of cement paste, Cem. Concr. Compos. 34 (1) (2012) 1–10.

[24] L.D. Schwartzentruber, R.L. Roy, J. Cordin, Rheological behaviour of freshcement pastes formulated from a self-compacting concrete (SCC), Cem. Concr.Res. 36 (7) (2006) 1203–1213.

[25] P.F.G. Banfill, O. Rodríguez, M.I. Sánchez de Rojas, M. Frías, Effect of activationconditions of a kaolinite based waste on rheology of blended cement pastes,Cem. Concr. Res. 39 (2009) 843–848.

[26] A.K.H. Kwan, H.H.C. Wong, Effects of packing density, excess water and solidsurface area on flowability of cement paste, Adv. Cem. Res. 20 (1) (2008) 1–11.

[27] H. Ma, Z. Li, Multi-aggregate approach for modeling interfacial transition zonein concrete, ACI Mater. J. 111 (2) (2014) 189–200.

[28] H. Ma, D. Hou, Z. Li, Two-scale modeling of transport properties of cementpaste: formation factor, electrical conductivity and chloride diffusivity, Comp.Mater. Sci. 110 (2015) 270–280.

[29] W.W.S. Fung, A.K.H. Kwan, Role of water film thickness in rheology of CSFmortar, Cem. Concr. Compos. 32 (4) (2010) 255–264.

[30] B. Bournonville, P. Coussot, X. Château, Modification du Modèle de Farris Pourla Prise en Compte des Interactions Géométriques d’un Mélange Polydispersede Particules, Rhéologie 7 (2004) 1–8.

[31] X. Château, Particle packing and the rheology of concrete, in: Understandingthe Rheology of Concrete, Woodhead Publishing, 2012, pp. 117–143.

[32] A.K.H. Kwan, M. McKinley, Effects of limestone fines on water film thickness,paste film thickness and performance of mortar, Powder Technol. 261 (2014)33–41.

[33] W.W.S. Fung, A.K.H. Kwan, Effect of particle interlock on flow of aggregatethrough opening, Powder Technol. 253 (2014) 198–206.

[34] E. Berodier, Impact of the supplementary cementitious materials on thekinetics and microstructural development of cement hydration PhD Thesis,EPFL, Lausanne, Switzerland, 2015.

[35] S. Yerazunis, S.W. Cornell, B. Wintner, Dense random packing of binarymixtures of spheres, Nature 207 (1965) 835–837.