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

Construction and Building Materials 142 (2017) 109–116

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Evaluating the distance between particles in fresh cement paste based on the yield stress and particle size 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, China Guangdong Low Carbon Technologies Engineering Center for Building Materials, 510640 Guangzhou, China c China Building Materials Academy, 10024 Beijing, China b

h i g h l i g h t s

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


The coarser particles needed larger k

to achieve same yield stress of paste.
The relationships between yield

stress and k were established.
k in binary-cement pastes was

evaluated in consideration of particle size.
Reliability of the evaluation of k was validated experimentally.
This paper gives a deeper insight into initial packing and bridging of particles.

a r t i c l e

i n f o

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

Keywords: Distance between particles Fresh cement paste Yield stress Particle size Solid 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 in available literatures is an average value and independent with the particle size. Actually, coarse particles in cement paste need a larger k to achieve same yield stress compared with fine particles. In the present study, relationship between yield stress and k for single-fraction cement pastes was established by introducing an exponential-type function. Then the function was theoretically deduced to evaluate k in binary-fraction cement pastes. For cement pastes with yield stress of 30 Pa, distance between coarse particle (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-fraction cement 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 microstructural development of cement pastes. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction

⇑ Corresponding author at: School of Materials Science and Engineering, South China University of Technology, 510640 Guangzhou, China. E-mail address: [email protected] (T. Zhang). http://dx.doi.org/10.1016/j.conbuildmat.2017.03.055 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

The workability of fresh concrete, which is one of the concerns in engineering applications, is driven by the flowability (or rheological properties) of fresh cement paste (the fluid phase of concrete). Fresh cement paste mainly consists of water and cement particles, and its flowability generally attributes to the initial

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Nomenclature PSD particle size distribution H-B model Herschel-Bulkley model D50 volume median diameter (lm) k distance between particles (lm) kf distance between particles in fine-fraction cement paste (lm) distance between particles in coarse-fraction cement kc paste (lm) Tw water coating thickness (lm) Twf water coating thickness of fine particles in binaryfraction cement paste (lm) Twc water coating thickness of coarse particles in binaryfraction cement paste (lm) SSA specific surface area (m2/cm3) specific surface area of fine fraction (m2/cm3) SSAf 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)

packing of particles in fresh cement paste. Compared with the packing of dry particles (particles are assumed to be contacted with their neighbor ones as shown in Fig. 1), the voids among particles 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 with their neighbor particles, and the water coated around particles contributes greatly to the fluidity of fresh cement paste [3–6]. Many attempts have been made to evaluate the rheological properties from the initial packing of particles in fresh cement paste. For instance, the yield stress of cement paste can be predicted from the solid volume concentration (u) of cement pastes by the YODEL based on first principles, in which particle size distribution (PSD), inter-particle forces, and microstructural features were taken into account [7,8]. Bentz reported that the relationship between yield stress and particle number density (the number of particles in unit volume of powder) shows a percolation-type trend [9]. Silva presented the yield stress of cement paste increases with the decrease of particle size [10], while Ferraris pointed out that

Mt Mc Vc

total weight of container and cement paste (g) weight of container (g) volume of container (cm3) shear stress (Pa) yield stress (Pa) shear rate (s1) Volume of excess water (cm3/cm3) volume ratio of water to cement (dimensionless) solid volume concentration of cement paste (dimensionless) maximum solid volume concentration of cement paste (dimensionless) minimum void ratio (dimensionless) size ratio of finer fraction to coarser fraction in binaryfraction cement (dimensionless) volume proportion of coarser fraction in binary-fraction cement (dimensionless) coefficients of H-B model (dimensionless)

s sc

y We Ww u um Vm

l

XL k,n

yield stress increases and then drops with the decrease of particle size, and the yield stress reaches maximum value when the mean size of particles equals to 5.7 lm [11]. Actually, major factors influencing the yield stress of fresh cement pastes, such as particle size, particle number density, solid volume concentration, etc. can be attributed to the distance between particles (k) in fresh cement paste. A larger k generally means more water coated around particles, which provides better lubrication and eventually contributes to the flowability of fresh cement paste. For fresh cement pastes with same flowability, small k is beneficial to the cluster and bridging of hydration products and densification of microstructure [12,13], and then contributes to strength development and deformation resistance [14], especially at very early age. Therefore, beside the flowability of fresh cement paste, the mechanical properties and volume stability of cement paste during hardening are subject to k either. Ferraris introduced the distance between aggregates in concrete and pointed out that higher torque is necessary for maintaining constant rotation speed of the plate when the distance between aggregates is decreasing [15]. Thus, there must be a similar relationship between k and rheological properties of cement paste. It is observed that the yield stress of fresh cement paste is proportional to k [16]. Commonly, k is calculated from u of cement paste and the specific surface area of particles in cement paste [17,18].

u¼

qp  qw qc  qw

ð1Þ

where, qp is the wet density of cement paste (g/cm3), qc and qw are the densities of cement and water (g/cm3), respectively. For the maximum solid volume concentration (um ) of cement paste, the corresponding minimum void ratio (V m ) is defined by Eq. (2):

Vm ¼

1  um

um

ð2Þ

The volume of excess water (W e ) can be evaluated by the following equation:

We ¼ Ww  Vm Fig. 1. The packing of dry particles.

ð3Þ

where, W w is the volume ratio of water to cement, which can be calculated from u.

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111

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

Tw ¼

We A

ð4Þ

where, A is the surface area of particles in unit volume of cement paste. Then k in cement paste can be calculated by Eq. (5):

k ¼ Tw  2

ð5Þ

Obviously, it is assumed that k is independent with the size of cement particle in the above calculation, indicating particles with different size have equal T w ork (average value) as shown in Fig. 2. In fact, coarser particles needs larger k to achieve same flowability compared with finer particles (Fig. 3) [19]. Since the PSD of Portland cement generally lies in the range of 1–80 lm, k in cement paste certainly varies with the size of cement particles. Therefore, it is irrational to use an average k to describe the rheological properties of fresh cement pastes. In present study, the relationship between yield stress and k for single-fraction cement paste was established in consideration of the size of cement particle, and then described by an exponential-type function. The function was theoretically deduced to evaluate k in binary-fraction cement pastes based on the yield stress and particle size. By taking into account the size of cement particles, k calculated by present method will give a deeper insight in the flowability and microstructural development of cement pastes from the viewpoint of initial particle packing and particleto-particle bridging. 2. Experimental 2.1. Preparation of cement pastes The chemical and mineral compositions (calculated by Bogue method [20]) of Portland cement used in this study were listed in Table 1 and Table 2, respectively. By changing the operational parameters of an air classifier (such as air flow rate, feed rate, and rotor speed), Portland cement was classified into four fractions, then the PSD of each fraction was determined by laser diffraction method (Malvern Mastersizer 2000, refractive index of dispersant (ethyl alcohol): 1.32 and obscuration: 12.4%). Since the cement particles merely distributed in a narrow range as shown in Fig. 4, the volume median diameter (D50) was taken as the mean size of the cement fraction. The D50 and SSA calculated

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

from PSD, and density measured according to ASTM C188 [21] of cement fractions were summarized in Table 3. According to the mix proportions listed in Table 4, each cement fraction was blended with water into a homogenous paste as specified 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 ensure the exhaust of air voids, then the excess paste was removed by a straight edge. The wet density of cement paste can be calculated by Eq. (6):

qp ¼

Mt  Mc Vc

ð6Þ

where, V c is the volume of container (cm3); M t is the total weight of container and paste (g); Mc is the weight of container (g). Three repeated tests were carried out, and the average value was selected as the wet density of cement paste (Fig. 5), then u was calculated by Eq. (1) and plotted in Fig. 6. With the reduction of W/C, u increased and then drops rapidly. Maximum solid volume concentration (um ) was achieved at a threshold W/C. There was nearly no difference in solid volume concentration when the W/Cs were larger than the corresponding threshold W/Cs. However, 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 as 0.517, being 9.53% higher than that of the cement paste prepared by D50 = 6.63 lm fraction (0.472). 2.3. The yield stress of cement pastes

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

The yield stress of cement paste was measured by a shear ratecontrolled rheometer (Brookfield R/S plus) equipped with a shear vane (four blades with 20 mm in width and 40 mm in length). The shearing sequence used in rheology test (Fig. 7) consisted of two cycles and a rest period. The first cycle, namely pre-shearing cycle, was used for ensuring each sample has achieved an equilibrium state before rheology test. In this cycle, the shear rate increased from 0 to 200 s1 in 25 s and maintained at 200 s1 for 25 s, then decreased to 0 s1 in subsequent 10 s. After a 10 s rest period the data-logging cycle was performed, in which the shear rate increased from 0 to 200 s1 in 100 s and then decreased to

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Table 1 The 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 2 The mineral composition of Portland cement* (%)

*

C3S

C2S

C3A

C4AF

CaSO42H2O

56.20

19.61

6.54

8.97

3.50

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

s ¼ sc þ kyn

Calculated by Bogue method [20].

ð7Þ

where s, sc and y are shear stress (Pa), yield stress (Pa) and shear rate (s1), respectively; k and n are empirical coefficients. Variation of the yield stress of single-fraction cement pastes with different W/Cs was shown in Fig. 8. For cement pastes prepared by given cement fraction, yield stress decreased with the increase of W/C. However, yield stress of cement pastes with same W/C increased significantly as the particle size of cement fraction decreased. For instance, yield stress of cement pastes with W/C of 0.5 raised from 14.05 Pa to 75.35 Pa when D50 of cement fraction dropped from 20.27 lm to 9.97 lm. 3. Relationships between sc and k for single-fraction cement pastes 3.1. Selection of um During the calculation of k, um of cement pastes were generally obtained by experiments [17,26]. However, at low W/C, the cement paste was too thick to exhaust the air voids even the vibration was applied, and the agglomeration of cement particles could not be neglected at such a low W/C [27,28]. As shown in Fig. 6, the difference among um of single-fraction cement pastes was about 10% (from 0.472 to 0.517), and um of ordinary Portland cement pastes even 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 particles brings down the packing density of powder when the particle size decreases [30], the influence of repulsive electric forces on the packing density of cement paste can be neglected due to the water coated around particles. That is to say, um of cement paste should be independent with the particle size. As the densities of random loose packing and random close packing of mono-sized spherical particles 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 Fig. 4. The particle size distribution of cement fractions (a) Incremental volume vs. particle size, (b) Cumulative volume vs. particle size.

Table 3 The densities and specific surface areas of cement fractions. D50 (lm)

48.51

20.27

9.97

6.63

Specific surface area (m2/cm3) Density (g/cm3)

0.155 3.20

0.403 3.12

1.066 3.10

2.160 3.09

0 s1 in another 100 s. The down ramp of shear stress-rate curve that implied more stable rheological information of cement paste was used for yield stress analysis.

k in single-fraction cement pastes was calculated by Eq. (5) and plotted in Fig. 9. For all the cement fractions, k decreased linearly with the increase of u. For a given u, k dropped significantly with the decrease of particle size, which can be attributed to the larger specific surface area of finer cement fractions. 3.3. Relationship between yield stress and k The relationship between k and yield stress of cement pastes was illustrated in Fig. 10. The yield stress dropped rapidly and then decreased gradually with the increase of k. To achieve the same yield stress, larger k was required for cement paste prepared by coarser fraction. For example, when yield stress maintained at 50 Pa, k in cement pastes prepared by cement fraction with

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Table 4 Mix proportions of single-fraction cement pastes. D50 (lm)

Water to cement ratio (W/C)

48.51 20.27

0.20, 0.23, 0.53 0.25, 0.25,

9.97 6.63

0.23, 0.25, 0.28, 0.30, 0.33, 0.35, 0.38, 0.40 0.25, 0.28, 0.30, 0.33, 0.35, 0.38, 0.40, 0.43, 0.45, 0.48, 0.50, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80

Fig. 7. Shearing sequence used in rheology test.

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

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

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

D50 = 48.51 lm was 5.87 lm, which was four times as that with D50 = 6.63 lm. An exponential-type function was introduced by Kwan and McKinley [32] to describe the relationship between yield stress and the thickness of water coated around particles. Here, the function was employed to establish the relationship between yield stress and k.

ð8Þ

Fig. 9. The relationship between k and solid volume concentration for singlefraction cement pastes.

where, a and b are parameters related to the particle size of cement fractions. In Eq. (8), a is the ultimate yield stress when k in cement paste equals to zero (water just fills into the voids among particles, and

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

sc ¼ aebk

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

k ¼ T wf þ T wc ¼

1  ðkf þ kc Þ 2

ð9Þ

where, T wf is the water coating thickness of fine particles in binaryfraction cement paste (lm), and T wc 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 

1 sc lnð Þ bf af

ð10Þ

where, af (Pa) and bf (lm1) can be obtained from Table 5. Similarly, kc can also be calculated. Consequently, k in binaryfraction cement pastes can be calculated by combining Eqs. (9) and (10): Fig. 10. The relationship between yield stress and k for single-fraction cement pastes.

     1 1 sc 1 sc þ ln k¼  ln 2 bf bc af ac ¼

ultimate yield stress decreased and then increased with the increase of particle size. For cement paste prepared by D50 = 6.63 lm fraction, the sensitivity of yield stress had a higher value, indicating that the yield stress of cement paste was more sensitive to finer particles. It is known that yield stress is attributed to friction among particles, which is mainly depended mechanical locking and contact area [33]. The mechanical locking plays a main role in the friction among particles for cement pastes with coarser particles, while friction among particles is predominated by larger contact area (surface area of particles) for cement pastes with finer particles. Therefore, ultimate yield stresses of cement pastes prepared by both D50 = 6.63 lm and D50 = 48.51 lm fractions are higher than that by D50 = 9.97 lm. 4. Evaluation of the Dp based on the yield stress of binaryfraction cement pastes 4.1. The relationship between yield stress and k for binary-fraction cement pastes The flowability of cement paste is generally influenced by the rheological properties of liquid, the surface texture of cement particles, and k. For single-fraction cement pastes and binary-fraction cement pastes, no difference in pore solution chemistry (such as pH value, ions concentration) is observed during mixing and rheology test [34], resulting in same rheological properties of liquid. And the surface texture of cement particles is also independent with the particle size as same crushing and milling procedures are applied to the same Portland cement. Therefore, it can be inferred that the yield stress of cement pastes only depend on k, and the relationships between k and yield stress for single-fraction cement pastes can be employed to evaluate k in binary-fraction cement pastes. For binary-fraction cement pastes, k equals to the sum of water coating thickness of two neighbor particles, the distance between

Table 5 The values of a and b in the exponential-type function. D50 (lm)

a (Pa)

b (lm1)

6.63 9.97 20.27 48.51

419 303 465 5141

1.572 0.803 0.793 0.785

bf þ bc bc lnaf þ bf lnac lnsc þ 2bf bc 2bf bc

ð11Þ

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

bf lnac þ bc lnaf bf þ bc

ð12Þ

2bc bf bf þ bc

ð13Þ

m¼

n¼

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

sc ¼ emnk

ð14Þ

By comparing Eq. (8) (for single-fraction cement pastes) and Eq. (14) (for binary-fraction cement pastes), the two relationships obey the same exponential-type function, only the calculation of parameters shows significant difference. That is to say, the relationships between yield stress and k in cement pastes obey same rule, and can be described by the exponential-type function, the parameters in function only depend on the particle size. Binary-fraction cement pastes were prepared according to the proportion listed in Table 6, then yield stress was obtained following the experimental procedure specified in Section 2.3. Based on yield stress shown in Fig. 11, the water coating thickness of particles in binary-fraction cement pastes were calculated according to Eq. (14). Water coating thickness of both fine and coarse particles increased with the increase of W/C as shown in Fig. 12. Notably, significant difference in water coating thickness was observed for fine and coarse particles even in same binary-fraction cement paste. For M2 with W/C of 0.55, the water coating thickness of particle with D50 = 6.67 lm was 1.03 lm, while that of particle with D50 = 48.51 lm was as high as 3.66 lm. Fig. 13 provided the relationships between yield stress and k for binary-fraction cement pastes. Compared with M2 and M3, larger k was needed for M1 to achieve same yield stress, as relative coarser particles were used. For instance, when the yield stress equaled to 30 Pa, distance between fine and coarse particles in M1 was 5.00 lm, which was nearly 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 kf and kc , then the validation of k was carried out by comparing the

115

Y. Guo et al. / Construction and Building Materials 142 (2017) 109–116 Table 6 The mix proportions of binary-fraction cement pastes. Cement ID

M1 M2 M3 *

D50 (lm)

*

Coarse

Fine

48.51 48.51 20.27

20.27 6.63 6.63

Density of the mixture (g/cm3)

W/C

3.16 3.15 3.11

0.30, 0.33, 0.35, 0.38, 0.40, 0.43, 0.45 0.30, 0.35, 0.40, 0.45, 0.50, 0.55 0.40, 0.45, 0.50, 0.55, 0.60, 0.65

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

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

um ¼ 0:64=½1:0  ð0:362  0:315ðlÞ0:7 ÞX L þ 0:955ðlÞ4 ðX 2L =ð1  X L ÞÞ

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 in Table 7. Through combining Eqs. (2) to (6), W/C of binary-fraction cement pastes can be calculated by Eq. (16):

W=C ¼ ½0:25ðkf  SSAf þ kc  SSAc Þ þ

1  um

um



qw qc

ð16Þ

where, SSAf and SSAc are the specific surface areas of fine and coarse cement fractions, respectively. Fig. 14 showed that the W/C calculated from k in binaryfraction cement pastes increased linearly with the actual W/C, and all data were around the line of equality. Within 10% deviation was observed due to the low efficiency of air classifier, as particles in each fraction was regard as mono-sized spheres though it actually presented narrow PSD. Therefore, it is proved that k in binaryfraction cement pastes can be evaluated by the relationship between k and yield stress for single-fraction cement pastes, and k is indeed significantly influenced by the size of cement particle. According to the above theoretical and experimental analyses, it can be inferred that k in multi-fraction cement paste can also be calculated by its yield stress and the exponential-type relationship between yield stress and k for each single-fraction cement paste. To sum up, it provided a reliable method to evaluate k in fresh multi-fraction cement pastes, and k in consideration of particle size will give a deeper insight in the flowability and microstructural development of cement pastes from the viewpoint of initial

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

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

Table 7 The um of binary-fraction cement pastes

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

Cement ID

l

XL

um

M1 M2 M3

0.418 0.137 0.327

0.50

0.697 0.748 0.714

particle packing and particle-to-particle bridging, which eventually influencing the mechanical properties development, volume stability, and durability of cement-based materials.

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

5. Conclusions and prospect The main conclusions that can be drawn from the present study are summarized as follows: (a) It was confirmed that k in single-fraction cement pastes indeed varied significantly with the size of cement particle at given yield stress. Then an exponential-type function (sc ¼ aebk ) was introduced to describe the relationship between yield stress and k for single-fraction cement pastes. (b) The exponential-type function was theoretical deduced and then employed to evaluate k in binary-fraction cement pastes. For cement pastes with yield stress of 30 Pa, distance between coarse particle (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. The reliability of k in binary-fraction cement paste was confirmed by comparing actual W/C and W/C calculated from k. This method can be further applied to multi-fraction cement pastes, and k in consideration of particle size will give a deeper insight in the flowability and microstructural development of cement pastes from the viewpoint of initial particle packing and particleto-particle bridging. Acknowledgements This work was funded by the National Natural Science Foundation of China (No. 51302090 and 51272244), Guangdong special support for Youth S&T innovation talents (2015TQ01C312), Pearl River S&T Nova Program of Guangzhou (201610010098), and National key research and development program (2016YFB0303502), their financial supports are gratefully acknowledged. References [1] H. Ma, D. Hou, Y. Lu, Z. Li, Two-scale modeling of the capillary network in hydrated 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 cement grout: 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 the rheological 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 nanosilica 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, Modelling the yield stress of ternary cement–slag–fly ash pastes based on particle size distribution, Powder Technol. 266 (2014) 203–209. [7] R.J. Flatt, P. Bowen, Yield stress of multimodal powder suspensions: an extension 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 of particle size distributions on yield stress and viscosity of cement-fly ash pastes, 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 of particle size distribution and calcium aluminate cement on the rheological behaviour 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 the rheology 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 numerical simulation on the formation of microstructure in cementitious materials at early age, Cem. Concr. Res. 33 (2) (2003) 233–239. [13] H. Ma, Z. Li, Realistic pore structure of Portland cement paste: experimental study and numerical simulation, Comput. Concr. 11 (4) (2013) 317–336. [14] E. Ghiasvand, A.A. Ramezanianpour, A.M. Ramezanianpour, Influence of grinding method and particle size distribution on the properties of Portlandlimestone cements, Mater. Struct. 48 (5) (2015) 1273–1283. [15] C.F. Ferraris, J.M. Gaidis, Connection between the rheology of concrete and rheology of cement paste, ACI Mater. J. 89 (4) (1992) 388–393. [16] K. Vance, A. Kumar, G. Sant, N. Neithalath, The rheological properties of ternary binders 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 film thickness 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, water film 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 distribution for 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, ASTM International, West Conshohocken, 2015. [22] ASTM C305, Standard Practice for Mechanical Mixing of Hydraulic Cement Pastes and Mortars of Plastic Consistency, ASTM International, West Conshohocken, 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 fresh cement 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 activation conditions 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 solid surface 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 zone in concrete, ACI Mater. J. 111 (2) (2014) 189–200. [28] H. Ma, D. Hou, Z. Li, Two-scale modeling of transport properties of cement paste: 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 CSF mortar, Cem. Concr. Compos. 32 (4) (2010) 255–264. [30] B. Bournonville, P. Coussot, X. Château, Modification du Modèle de Farris Pour la Prise en Compte des Interactions Géométriques d’un Mélange Polydisperse de Particules, Rhéologie 7 (2004) 1–8. [31] X. Château, Particle packing and the rheology of concrete, in: Understanding the 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 aggregate through opening, Powder Technol. 253 (2014) 198–206. [34] E. Berodier, Impact of the supplementary cementitious materials on the kinetics and microstructural development of cement hydration PhD Thesis, EPFL, Lausanne, Switzerland, 2015. [35] S. Yerazunis, S.W. Cornell, B. Wintner, Dense random packing of binary mixtures of spheres, Nature 207 (1965) 835–837.