CONCRETE LIBRARY OF JSCE NO. 29, EUNE 1997
EFFECT OF POWDE G-ERACTE ON PASTE FIQW
(Translation from Proceedings of JSCE, No.544/V-32, August 1996)
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Haj ime OKAMURA
The objective of this study is to propose a method for estimating water
retaining factor and flow factor, which are powder properties that affect paste
fluidity-, from the particle size distribution, the particle shape, and the
hydration properties of the cement. The results obtained are as follows. The
water retaining factor is proportional to a product of an index representing
particle size and an index representing the form of the particle size
distribution, and the constant of proportionality represents the pa_rticle shape
and hyfiation properties. The flow factor is proportional to the product of an
index representing particle size and an index representing particle shape or the
hydration properties , and a constant term represents the surface state of the
powder assuming a proportionality constant to be invariant.
Key Vvbrds: paste, powder, water retaining factor, flow factor
particle size distribution, particle shape
Yoshinobu EDAMATSU is a research engineer at the Cement/Concrete Research
Laboratory of Sumitomo Osaka Cement CO. , LTD. , Osaka, Japan. His research
interests include problems concerning mix design for self -compacting concrete.
He is a member of the JSCE.
Kouj i SHIMOKAWA is a reseuch engineer at the Tsukuba Concrete
Laboratory of Fuj isawa Pharmaceutical CO. , LTD. , Ibaraki, Japan.
Research
Hajime OKAMURA is a professor in the Department of Civil Engineering at the
University of Tokyo, Tokyo, Japan. For the past twelve years he has studied
self-compacting high-performance concrete. He is a Fellow of the JSCE.
—249—
1
. Introduction
The powdered materials,
such as cement and blast-furnace
smallest solid particles
to concrete composite materials.
the size distribution
and shape of these powder particles
concrete fluidity.
slag, contribute
the
It is well knownthat
have an influence on
It has already been shown that the powder properties
can be quantitatively
represented by the water retaining
factor or flow factor[1]
[2] [3].
The water
retaining
factor is the maximumvolumetric water-powder ratio at which the
relative flow area of the paste remains 0,.or the ratio at which the paste just
begins to deform. The flow factor is the volumetric water-powder ratio required
to increase the relative flow area by a unit quantity;
it is equivalent to the
deformability
of the paste when the water-powder ratio is above the water
retaining factor.
The water retaining factor and flow factor are obtained from flow tests on paste
in the absence of vibration[1].
Certain characteristics,
such as particle
size
distribution,
are used as indexes for powder quality
control. If the water
retaining factor and flow factor could be estimated from these characteristics,
powders suitable for self-compacting high-performance concrete could be produced.
This would enable a more rational mix design system for such concrete[1].
The objective
of this
study is to propose a method for estimating
water
retaining
factor and flow factor from powder characteristics.
To this end, we
clarify
the relation between powder characteristics
and water retaining factor
and flow factor.
Incidentally,
particularly
this
study
tiny particles,
2. Characteristics
deals with general
such as silica-fume,
powders, so powders with
are not covered.
of powders
Five moderate heat Portland cements of different
brands and production lots,
four limestone powders, two types of blast-furnace
slag of different
particle
size distributions,
and fly ash were used. These powders are used to produce
self-compacting concrete. The particle-size
distribution
and particle
shape of
each powder is described below.
2. 1 Particle
size distribution
The particle
size distribution
of each powder is shown in Figs.l,
2, and 3.
Measurements were made with a laser-diffraction
measuring instrument which
measures scatter;
the Cilasl064
made by Cilas company. Methanol was used to
disperse the powders, and dispersion was ensured by applying ultrasonic
waves
for 60 seconds before tasting
measurements.
These figures were drawn from cumulative values of particle
The method used to plot them is described.
size
distribution.
©Counted particle
sizes are chosen at regular logarithmic
intervals.
Here,
particle
sizes is increased from 0.17 nm in logarithmic
steps such that each
size was double the previous one.
©The cumulative count at each particle
size was obtained from the measurement
value. Here, the cumulative count placing between two inarching measurement
250 -
35
30
BS60
25
£ . 25
(D
20
"I
20
~ 15
.2
15
0
.01
0. 1
1
Particle
10
100
1000
/
FA
0 .01
0. 1
Fig.2 Particle
(blast-furnace
values was obtained frcm a straight
line approximation of two measurement
values.
LS180
©The value between marching particle
sizes.
was calculated
frcm
the
cumulative values.
LS60
0
1000
100
size ( p. m)
size
slag
.01
distribution
and fly ash)
100
0 .1
Particle
sizes.
Fig.
are
10
LS40a
© The values were plotted
in the
figure,
as the particle
size is in
logarithmic
steps. Here, the particle
size which corresponds to the value
was central between marching particle
(D The
two marching
values
connected by the spline function[4].
1
Particle
size ( ju m)
Fig. l Particle
size distribution
(moderate heat Portland cement)
BS40
1000
size ( n m)
3 Particle
size distribution
( limestone powder)
Certain characteristics
of these particle
size distributions
are discussed here.
Despite different
brands and production lots of these moderate heat Portland
cement, the overall form of the particle
size distributions
do not differ.
The
peak occurs at about 30 /zm. The gradient on the smaller particle
size of the
peak is gentle,
but the other side is steep. These are hardly any particles
coarser than 100 //m nor fine particles
less than 0.1 //m.
The distribution
of blast-furnace
slag is similar to that of moderate heat
Portland cement, with only one peak. But because blast-furnace
slag has its own
fineness characteristics,
the actual particle
sizes are different.
(The fineness
of BS60 is 6,010 cm2/g; and that of BS40 is 4,370 cm2/g.) There are no coarse
particles
above 100 /zm, but there are more fine particles
less than 0.1 ^m than
in moderate heat Portland cement.
The form of the fly ash distribution
is also similar to that of moderate heat
Portland cement. The peak for fly ash is, however, larger than for the cement,
at about 55 /zm. Fly ash contains a lot of coarse particles
larger than 100 //m.
The limestone powders are of two characteristic
types. One has only a single
peak, as with the moderate heat Portland cement. The other has two peaks. This
great difference
in distribution
results from differing
production methods used
for the different
brands. Limestone powder can vary considerable in particle
-251 -
Phot.l Particle
shape
(moderate heat Portland cement)
Phot. 3 Particle
(blast-furnace
shape
slag)
Phot.2 Particle
shape
( limestone
powder )
Phot, 4. Particle
(fly
ash)
shape
size distribution
even when the fineness is similar.
On the other hand, the peak
position
may be different
even when the form is similar.
This result
from a
difference
in fineness.
(The fineness of LS40a is 4,660 cm2/g; LS40b is 4,770
cm2/g; LS60 is 6,440 cm2/g; and LS180 is 18,000
cm2/g. ) Limestone powder contains
fine particles
down to less than 0.1 //m in larger quantities
than in moderate
heat Portland cement. LS40a contains a larger proportion
of coarse particles
more than 100 /zm.
2.2
Particle
shape
Typical
photographs
Phot.l,
2,
3,
and
showing particle
shape,
as taken with
an SEM, are shown in
4.
Moderate heat Portland cement and limestone powder particles
are extremely
unevenpolyhedrons, and the in surfaces are not very angular. Blast-furnace slag
particles
are moreangular and sharper than those of other powders, and the in
surface is irregular but smooth. Fly ash includes a lot of globular particles.
3
. Basic equation of paste flow
A linear relation between the relative flow area (Eq. (l) ) as calculated
from the
paste flow and the volumetric water-powder ratio has already been made
clear[2][3].
The paste flow is given by the basic equation Eq.(2),
and is
determined by the flow factor and water retaining factor, both properties
of the
powder, and by the volumetric water-powder ratio. (Fig.4)
rp-f-S-V
uooj
-252-
-i
(1)
Table 1 Properties
p ar t i c le
T yp e
o f
p ow d e r
s iz e
fa c t o r
(PF
m a x im u m
o f
of powders
v a l u e
p a rt ic l e
d is t r ib u t i o n
sh ap e
f a ct o r
f a ct o r
(HF )
(S F )
s iz e
d i s t r ib u t i o n
(h )
w at e r
re t a i n in g
fa c t o r
E q .(6 )
t e s t
M C l
1 .1 0
0 .32
1 .0 3
0 .8 8
1 .0 0
1 .00
m o de r a t e
M C 2
1 .l l
0 .31
1 .01
0 .8 6
0 .9 6
0 .96
he a t
M C 3
1 .0 9
0 .31
1 .01
0 .8 5
0 .9 4
0 .94
M C 4
1 .0 9
0 .30
0 .9 9
0 .9 2
0 .9 9
0 .99
M C 5
1 .0 9
0 .31
1 .0 1
0 .9 0
0 .9 8
0 .98
B S 4 0
1 .2 4
0 .2 2
0 .8 5
0 .9 5
0 .97
B S 60
1 .32
0 .2 6
0 .92
1 .1 0
1 .08
B P l
1 .30
0 .2 5
0 .9 1
1 .0 7
1 .07
B P 2
1 .2 5
0 .2 2
0 .8 6
0 .9 8
0 .99
L S 4 0 a
1 .2 0
0 .1 5
0 .7 0
0 .7 1
0 .67
L S 4 0b
1 .31
0 .31
1 .01
0 .9 9
0 .87
l im e s t on e
L S 60
1 .1 7
0 .1 7
0 .7 5
0 .8 3
0 .83
po w d e r
L S 1 8 0
1 .5 4
0 .30
0 .9 9
1 .2 9
1 .4 9
B P 3
1 .4 7
0 .2 7
0 .94
1 .1 7
1 .2 3
B P 4
1 .2 7
0 .1 8
0 .7 7
0 .8 2
0 .7 8
1 .0 5
0 .2 2
0 .8 6
0 .5 4
0 .5 4
P o rt la n d
c em e n t
b la st fu r n a ce
s la g
fl y
a sh
0 .91
0 .8 4
0 .61
*1: BP1 and BP2 are blended powders in which BS40 was blended with BS60.
blending
ratios
are as follows : BP1,
BS40:BS60=20:80;
BP2,
BS40:BS60=80:20.
*2: BP3 and BP4 are blended powders in which LS40a was blended with LS180.
blending
ratios
are as follows : BP3,
LS40a:LS180=20:80;
BP4,
LS40a:LS180=80:20.
Vw
--=Ep.rp+pP
Vp
(2)
The
The
Vw/Vp
Where rp is the relative
flow area, Fp is the
value of the paste flow (mm) in the absence of
vibration,
Vw is the volumetric ratio of water
in the paste, Vp is the volumetric ratio of
powder in the paste, Ep is the flow factor of
the powder, and £p is the water retaining factor
of the powder.
The flow factor
represents
the degree of
Fig.4 Basic equation
of
deformation of the paste after deforming it. The
paste
flow
water retaining factor is the volumetric waterpowder ratio when the paste begins to deform.
Therefore, the amount of water needed to gain a
certain relative
flow area decreases with these factors,
The smaller these
factors are, the better properties of powders are evaluated.
4
. Water retailing
factor
The water retaining
factor, which represents the volumetric water-powder ratio
when the paste begins to deform, is a powder property that affects
paste
fluidity;
it differs with the type of powder as shown in Table 1. Therefore, the
differences
of the water retaining factor with the characteristics
of powders
253 -
are considered.
It is generally
accepted that the characteristics
of the particle
size
distribution
of a powder influence the fluidity
of a paste made with that powder.
With similar
powders, of equal fineness,
the fluidity
of the pastes is
influenced by the form of the particle
size distribution.
On the other hand, if
the distribution
is equal, the fluidity
is influenced by powder fineness. That
is, the fluidity
of pastes made with similar
powders is influenced by the
average diameter of the particles
and the form of the particle
size
distribution[5].
Thus, the characteristics
of the particle size distribution
can
be represented numerically,
allowing the relation
between the water retaining
factor and these characteristics
to be clarified.
A number of functions to represent the characteristics
distribution
have been proposed. In this study, to simplify
the particle
size factor shown in Bq. (3) was used.
PF= Jp(x).
pf0(x)
of particle
size
the calculations,
(3)
pf0(x)dx
=1.65-Q.5Log(x)
(pfO(x)
^O)
(4)
Where PF is the particle
size factor, pfO(x)
is the standard particle
factor, p(x) is the particle size distribution
curve, and x is the particle
size
size
Um).
The particle
size factor can be calculated by integrating
the standard particle
size factor
(Eq.(4),
Fig.5),
and the particle
size distribution
curve as
described above in "2. Characteristics
of powders. " This factor is equivalent to
powder fineness. The particle
size factors of the powders are shown in Table 1.
Particle size factor increases with falling
particle
size.
A standard particle
size factor was developed as follows. Water retention has a
close relation with the fineness,. since the water is retained on the surface of
powder particles
or sand particles.
Fineness is in inverse proportion to
particle
size, as the solid line in Fig.6 shows. Whenthe particle
size is small,
however, it appears larger as a result of cohesion[6].
Therefore, the relation
between particle
size and fineness is shown by the dotted line in Fig.6.
o 2.5
Influence
of cohesion
N
2 .0
pfO(x)=1.
CO
65-0.5
Log(x)
o
CD 1 .5
r
1.0
CO
Q.
"S
ra
0.5
73
2 o.o
'
0.1
1
10
100
1000
1 0000
Log (particle
Particle
size (/*m)
Fig. 5 Relation between particle
s ize
and
standard
particle
size factor
size)
Fig. 6 Relation between particle
size and fineness
-254 -
1.6
S
1.4
MC
>O : B S
A A
LF AS
t
ra
4-
1.2
c
-E 1.0
co
ca
B- 0.8
5 0.6
==
nA
0 .9
L S 180
&
*>
L S 40b
I
I
1.0
1.1
I
I
1.2
Particle
L S 40a
I
1.3
size
1.4
I
1.5
1 .6
Particle size
factor
Fig. 7 Relation between particle
size
factor
and water
retaining factor
Fig.8
Maximumvalue of particle
size distribution
Thus, as a first approximation, the relation between the logarithm, of particle
size and fineness was made proportional.
The constant proportionality
and the
constant in Eq. (4) were set up such that the straight
line goes through certain
points as shown in Fig.5. These points were plotted from the average particle
size of moderate heat. Portland cement, limestone powder (LS180) , and Fuji river
sand, taking the water retaining
factors as standard particle
size factors. The
particle
size distributions
of these powders were of analogous form. Because of
representing equally the fineness of powder by the value blaine, these water
retaining factors, which had a close relation with the fineness, was substituted
for blaine. For the particle sizes greater than 2,000 jum, the standard particle
size factor was set to 0. The reason for this was that the restraint
amongsuch
particles
was strong, the apparent water retaining factor due to this restraint
was greater than the water retention of the particle
surface.
Figure 7 shows the relation between particle
size factor and water retaining
factor. The water retaining factor increases with particle
size factor, or with
decreasing particle
size. Even though the particle
size factors of limestone
powders LS40a and LS40b are approximately equal, their water retaining factors
are very different.
As shown in Fig.3,
this results from a difference
in the
form of the particle size distribution.
Incidentally,
the open symbols in Fig.7
represent blended powders consisting of BS40 with BS60 as well as LS40a with
LS180. Open symbols represent these blended powders throughout this text. The
blending ratios are shownin the notation of Table 1.
To represent the form of the particle
size distribution,
the maximum
value on
the particle
size distribution
curve, as shown in Fig.8, was used. The maximum
value for each powder is shown in Table 1. It decreases with increasing width of
the particle
size distribution.
Figure 9 shows the relation between maximum
value of particle
size distribution
and water retaining
factor.
The water retaining
factor increases with the
maximumvalue of particle
size distribution,
or decreasing
width of the
distribution.
Even though the maximumvalues for LS40a and LS40b are
approximately equal, their water retaining
factors are very different.
This is
caused by the very different
the particle
size factors of these powders, as
shown in Fig.7. Thus, the water retaining factor is influenced by the average
particle
size and also the form of the particle size distribution.
Therefore,
if
the multiple
of the
particle
255 -
size
factor
and the distribution
l.b
ｧ
1 .4
1 .6
A XAo
FLBM ASC
t.
¥ L S 1 80
1.4
1.2
03
H- 1 .2
c
.E 1 .0
CO
｣ 0 .8
1.0
0ｫ
** x
0.8
0.6
¥
0.4
CO
3:
0 .6
L S 40b
I
n A
0 .1 0
0.1
5
0.20
Maximumvalue of particle
I
0.25
0.2
I
0.30
: Eq.(6)
0.0
0.35
0.6
0.8
Particle
size distribution
Fig. 9 Relation between maximum
value of particle
size
distribution
and water
retaining
factor
1.0
size factor
1.2
1.4
X distribution
1.6
1.8
factor
Fig. 10 Relation between characteristic
of particle
size distribution
and water retaining
factor
factor is treated as a property of the particle
size distribution,
it is
proportional to the water retaining factor in the case of the same material, as
shownin Fig.10. Here, the distribution
factor is the square root of a quotient
which is divided 'the maximumvalue of the particle
size distribution
by 0.3,
which is the same as for moderate heat Portland cement (Bq.(5),
Table 1). The
distribution
factor is a relative
index for comparing the particle
size
distribution
of moderate heat Portland cement, as the standard powder, with that
of another powder. The proportional
relation between the property of particle
size distribution
and the water retaining factor is shown by Eq. (6),
and the
calculated constant of proportionality
for each powder is given in Table 1.
(5)
)3p = SF-PF-HF
(6)
Where HF is the distribution
factor, h is the maximumvalue of particle
size
distribution,
j3 p is the water retaining
factor of the powder, PF is the
particle size factor, and SF is the shape factor.
The constant of proportionality
differs with the type of powder, and represents
the particle
shape and the powder's degree of activation.
Accordingly,
it is
defined as the shape factor of a powder. The shape factor of fly ash, which has
a spherical
shape, is small, while that of blast-furnace
slag, which has an
angular shape, is large. Though the particle
shape and the surface state of
moderate heat Portland cement are similar to those of limestone powder, its
shape factor is larger. This is a result of the greater surface area and the
consumption of water by the hydration of ettringite.
Because the degree of
hydration differs,
however, with the amountof C3A or gypsum, and with the form
of the gypsum, in the moderate heat Portland cement, the shape factor varies.
Figure ll shows the relation
between the particle
size distribution
and the
water retaining factor of powders in which moderate heat Portland cement has
been blended with admixtures : blast-furnace
slag, limestone powder, and fly ash.
The water retaining
factors of these powders are shown in Table 2. The
-256-
Table 2 Properties
v o l um et r i c
T yp e
r a t io o f
a d m ix t u r e
of
p ow de r
to
b l en d e d
p ar t i c le
size
fa c t o r
of blended
m a x im u m
v a lu e o f
powders
d i s tr ib ut io n
p ar t i c l e
s iz e
d i s t r ib u t i o n
(h )
s h ap e
fa c t
a c r or
HP )
t e s t/ Eq .(8 )
0 .9 6
0 .9 6
1 .0 0
0 .97
0 .9 9
1 .0 2
0 .9 7
0 .97
1 .0 2
1 .0 5
0 .8 5
0 .92
0 .97
0 .9 7
1 .0 0
0 .2 7
0 .9 5
0 .8 6
0 .91
0 .9 2
1 .0 2
1 .1 6
0 .2 0
0 .8 2
0 .8 6
0 .7 9
0 .8 1
1 .0 3
0 .8
1 .1 8
0 .1 7
0 .7 4
0 .8 8
0 .7 3
0 .7 8
1 .0 6
1 .0
1 .2 0
0 .1 5
0 .7 0
0 .7 9
0 .67
0 .6 7
1 .0 0
0 .2
1 .0 9
0 .2 8
0 .9 7
0 .82
0 .8 8
0 .8 8
1 .0 0
0 .6
1 .0 7
0 .2 4
0 .8 9
0 .7 5
0 .71
0 .7 2
1 .0 1
0 .8
1 .0 6
0 .2 2
0 .8 6
0 .7 0
0 .6 3
0 .6 4
1 .0 2
1 .0
1 .0 5
0 .2 2
0 .8 6
0 .6 1
0 .54
0 .5 4
1 .0 0
1 .l l
0 .3 1
1 .0 1
0 .8 6
0 .9 6
0 .9 6
1 .0 0
0 .2
1 .1 3
0 .2 8
0 .9 7
0 .87
0 .6
1 .1 8
0 .2 4
0 .9 0
0 .92
0 .8
1 .2 1
0 .2 3
0 .8 7
1 .0
1 .2 4
0 .2 2
0 .2
1 .1 2
l im es t o ne
0 .6
p ow de r
s l ag
f ly
a sh
m o d e r at e
P or t l a nd
fa c t or
test
p ow d e r
f ur n a c e
r e t a in in g
fa c t
actor
(S F )
E q . (8 )
(P F )
b l a st -
water
h e at
c em en t
(M C 2 )
admixtures
volumetric
0.8
to
were blended
in
ratios of 0.2, 0.6, or
the
blended
powder
1 .2
(Eq.(7)).
«
1.0
*£**
y
Vad
ad= Vad +Vc
--dx
.5
(7)
0.8
A,'"
*
'
- 0.6
O
_
A
Where yad is the volumetric ratio
of admixture to blended powder,
Vc is the volumetric ratio of
moderate heat Portland cement,
and Vad is the volumetric ratio
of the admixture.
:
A:
D:
BSLS
FA
: MC+BS
MC+LS
MC+FA
0.4
0 .8
Particle
0.9
1.0
size factor x distribution
1.1
1.2
factor
Fig. ll Relation between characteristic
of particle
size distribution
and water retaining
factor
(blended
powder with two types
of powder)
The particle
size factor of the
blended powder is proportional
to
the volumetric ratio of admixture
to
blended
powder.
The
di stribution
factor ,
however,
falls below a straight
line connecting moderate heat Portland cement and the
admixture, as shown in Fig.12.
This means that the characteristics
of the
particle size distribution
are improved by blending.
In Fig.12,
the point where the volumetric ratio of admixture to blended powder
is 0 is the value for moderate heat Portland cement, while where it is 1
represents the value for the admixture. Therefore, the water retaining factor of
blended powder in Fig.ll
should fall bellow a dashed line connecting moderate
heat portland cement and admixture. In fact, however, the water retaining factor
is above the value plotted on the dashed line. This is caused by an increase in
the hydration speed of moderate heat Portland cement as more admixture is added.
-257-
1.2
¥ .<L
x;
O:
A:
D:
|1'1
o
£ 1.0;
MC
BS
LS
FA
X : M
O : B
: L
D : F
1 .1
1 .0
C
S
S
A
o
0 .9
4-
| 0.9
"-- O
0 .8
-Q
CO
w
0 .7
A -~
"
0.8
CO
5 0.7
- * - ,.
I
n K
Volumetric
0.2
D
0 .6
0.6
0.0
D
"" - _
0.4
ratio of admixture
0.6
0.8
to blended
1.0
0.0
Volumetric
powder
Fig. 12 Relation between volumetric
rat io
of
admixture
to
b l ended
powder
and
distribution
factor
I
0.2
I
I
0.4
I
I
I
I
0.6
0.8
ratio of admixture to blended
1.0
powder
Fig. 13 Relation between volumetric
rat io
of
admixture
to
blended powder and shape
f actor
Generally, when ordinary Portland cement has been blended with blast-furnace
slag, fly ash, or limestone powder, the hydration speed of the cement is assumed
to decrease. However, the hydration of interstitial
materials
in the cement
during mixing, or within a few minutes of adding the water, accelerates[7]
[8].
Therefore, the shape factor of a blended powder calculated by Eq. (6) is bigger
than the value plotted on a straight
line connecting the shape factors of the
two powders, as shown in Fig.13.
It is assumed that the difference between the
two values increases with the volumetric ratio of admixture to blended powder,
since the hydration speed of moderate heat Portland cement increases with the
volumetric ratio of admixture.
In order to calculate the water retaining factor for a blended powder by Bq. (6),
whenblast-furnace slag, limestone powder . or fly ash is used as the admixture,
the shape factor of moderate heat
Portland
cement needs to be set
appropriately ,
according
to
the
1.0
volumetric ratio of the admixture.
o
Whenmoderate heat Portland cement is
blended with another powder, the water
retaining
factor
of the admixture
remains
constant
whatever
the
volumetric ratio of the admixture, as
shown in Fig.14.
Therefore,
the
volumetric ratio
of admixture to
blended powder should be proportional
to the volumetric ratio of water to
blended powder, namely the water
retaining factor of the blended powder.
As shown in Fig,15,
however, the water
retaining
factor is higher than the
values falling
on a straight
line
connecting the two water retaining
factors.
As mentioned, this results
from the influence of the admixture on
the hydration rate of moderate heat
Portland cement. When fly ash is
-258-
T
o 0.9
r
est result
0.7
to 0.6
0 .5
0
0. 1
0.2
0.3
0.4
0.5
Volumetric ratio of limestone powder
Fig. 14 Relation between volumetric
ratio
of limestone
powder
and its
water retaining
f actor
(obtained
from a paste test
of powder in which moderate
heat Portland
cement was
b l ended
with
l imes tone
powder)
1 .2
U E fl
H
o
_
A:
à":
Q __ _ __ ?
1 .0
cO )
.E
..A
" -- ,
1
à"à"à"
A
S 3
x - M C
0 -6
E l
CO
m
in<3~1
o .8
CO
n
aCD
｣
=s - . A
EU ; 一 > ,
A
ｫ
: BS
LS
FA
1 .0
-a
à"-'
O : B S
A : L S
D : F A
I
I
r¥A
0.0
Volumetric
0.2
I
I
0.4
I
I
0.6
I
I
0.8
ratio of admixture to blended
I
0.9
1.0
0.0
powder
Volumetric
Fig. 15 Relation between volumetric
rat io
of
admixture
to
blended powder and water
retaining
factor
0.2
0.4
ratio of admixture
0.6
0.8
to blended
1.0
powder
Fig. 16 Comparison between test
result
of
water
retaining
factor
and
calculation
by Eq. (8)
blended,
the influence
is little,
and the volumetric ratio of admixture
blended powder is approximately proportional
to the water retaining
factor.
to
On the other hand, when blast-furnace
slag or limestone powder is added, the
volumetric ratio of admixture to blended powder can be regarded as approximately
proportional
to the water retaining
factor only if the volumetric ratio of
admixture to blended powder is small ( yad is below 0.6).
Therefore, as shown in Fig.16, when the volumetric ratio of admixture to blended
powder is small, the water retaining
factor of the admixture can be calculated
by Eq. (8) from the water retaining factor of the blended powder and the blending
ratio.
jSp = j8c+ (j8ad -jSc)
- ^d
(8)
Where jSp is the water retaining
factor of the blended powder, /3c is the water
retaining
factor of moderate heat Portland cement, jS ad is the water retaining
factor of the admixture, and y ad is the volumetric ratio of admixture to
blended powder.
5. Flow factor
In flow tests on paste, the flow factor, which represents the ease of paste
deformation, is a property of the powder that affects the fluidity
of the paste.
It differs
with the type of powder, as shown in Table 3. Accordingly,
such
differences
of the flow factor with the characteristics
of powders are
considered.
The flow factor is determined by the contact probability
amongthe particles
and
by the degree of contact friction.
The contact probability
depends on the number
of particles
which exist per unit volume of paste. Therefore, it is higher when
the particle
size is small. The degree of contact friction
when the particles
comeinto contact depends on the shape of the particles
and the in surface state.
The relation
between particle
size factor,
which indicates
the contact
probability
among the particles,
and the flow factor is shown in Fig.17.
The
flow factor increases with particle
size factor. In the case of the same
-259-
0.25
0.25
0.20
0.20
o
S
«
o
3 0.15
TO
|
0.15
f
:Eq.(9
4-
4-
0.10
|
0.10
LJ_
Ll_
0.05
0.05
0 .00
0 .00
1
.0
1.1
1.2
Particle
1.3
1.4
1 .5
0 .4
1.6
Fig.18
Fig. 17 Relation between particle
s ize
factor
and flow
fa ctor
material,
the flow factor
increas es
with
fal l ing
particle
size. The degree of
this increase differs
with
the type of powder. This
difference
is attributable
to particle
shape or its
surface state.
Therefore, flow factor was
indicated the relation with
the product of shape factor
calculated by Bq. (6) and the
particle
size
factor,
as
shown in
Fig.18.
The
flow
factor,
except in the case
of blast-furnace
slag,
is
approximately
proportional
to this
product.
Blastfurnace slag differs
from
the other powders because
its surface is smooth and
glassy. On the other hand,
the
contact
friction
of
moderate
heat
Portland
cement is strong,
because
needles of ettringite
are
formed on its
surface by
hydration.
In this
case,
however, the influence
of
hydration is included in the
shape factor.
0.6
0.8
Particle
size factor
po w d e r
1.4
1 .6
of powders
p a r t i c le
o f
1.2
shape factor
Relation between flow factor
and product of particle
size
factor and shape factor
Table 3 Properties
Type
1.0
size factorx
size
fa c t or
sh a p e
f lo w
f a ct o r
fa c to r
(P F
(S F )
E q . (9 )
t e st
MCl
1 .1 0
0 .8 8
0 .1 0
0 .1 0
m od e r a t e
MC2
1 .l l
0 .8 6
0 .1 0
0 .1 0
he a t
MC 3
1 .0 9
0 .8 5
0 .0 9
0 .0 9
MC4
1 .0 9
0 .9 2
0 .l l
0 .0 9
MC 5
1 .0 9
0 .9 0
0 .1 0
0 .0 9
BS40
1 .2 4
0 .0 9
0 .0 9
B S 60
1 .32
0 .1 0
0 .l l
BPl
1 .30
0 .1 0
0 .1 0
BP2
1 .25
0 .1 0
0 .0 9
L S 4 0a
1 .20
0 .1 0
0 .0 9
L S 4 0b
1 .31
0 .0 8
0 .0 7
l im e s t o n e
LS 60
1 .17
0 .1 4
0 .1 5
p ow de r
LS180
1 .54
0 .2 3
0 .2 4
P o rt l a n d
c em e n t
b l a st fu r n a ce
s la g
f ly
0 .9 1
0 .84
BP3
1 .47
0 .1 8
0 .2 2
BP4
1 .27
0 .l l
0 .0 9
0 .02
0 .0 3
ash
1 .0 5
0 .61
*1: BP1 and BP2 are blended powders in which BS40
was blended with BS60. The blending
ratios
are as
follows
:
BS40:BS60=80:20.
BP1,
BS40
:BS60=20
: 80;
BP2,
*2:
BP3 and BP4 are blended
powders
in which
LS40a was blended
with LS180.
The blending
ratios
are
as
follows:
BP3,
LS40a:LS180=20:80;
BP4,
LS40a:LSl80=80
:20.
This relation
between flow
factor and the above product is indicated
by Eq.(9).
In this
study,
the
proportional
factor A in Bq. (9) is 0.24,
and is constant. The fixed number B is
an index representing
the state of the particle
surface. It is smaller for a
smoother surface. The value for blast-furnace
slag is -0.18,
but the other
powders are -0.13. The fixed numbers A and B were chosen to give best agreement
between experimental values and calculated values using Eq. (9 ).
-260-
0 .2 5
0 .2 5
A
A
0 .2 0
0 .2 0
E9
o
0 .15
A
: BM SC
A A
: L S
: F A
0 .15
A
CO
M-
CO
40 .10
<X P
-A
x
0 .10
: M C
o
x* '
u_
Ll_
O
: B S
A A
: L S
I
: F A
I
0 .0 5
I
n nn
0.8
I
I
1.0
I
I
1.2
1.4
Particle size factor x distribution
1.6
(9)
0.1
5
0.20
0.25
0.30
0.35
of the
Fig. 20 Relation
between maximum
value of particle
size
distribution
and flow
factor
0 .25
x
: MC
à"O:
BS
AA:
LS
à" : FA
0.20
0.15
à"
the state
0
Maximumvalue of particle size distribution
Where PF is the particle
size factor,
SF is the shape factor,
A is a fixed
number (in this study, 0.24),
and B is
an index representing
particle surface.
n nn
0.1
factor
Fig. 19 Relation
between characteristic
of particle
size distribution
and flow factor
Ep=A-PF-SF+B
A
0 .0 5
0.10
Figure 19 shows, as in the case of
water retaining
factor,
the relation
between the flow factor
and the
characteristics
of the particle
size
distribution.
The relation between the
flow factor of limestone powder and
the characteristic
of the particle
size distribution
is not correlative.
This
is
because of a lack
of
correlation between the flow factor of
limestone powder and the maximum
value
of particle
size
distribution,
as
o
a
o
S
xO
0.05
0.00
0.4
0.8
1.0
1.2
1.4
1
Waterretaining factor
Fig. 21 Relation between water
retaining
factor
and
flow factor
0 .20
x
à"
A
à"
shown in Fig.20.
The flow factor is determined by the
average particle
size,
the particle
shape, and the surface state of the
particle.
Therefore,
as shown in
Fig.21,
the correlation
between flow
factor and water retaining
factor is
not very strong.
0.6
0 .15
MC
BS
LS
FA
O:
A:
D:
MC+BS
MC+LS
MC+FA
0 .10
0 .05
0 .00
Figure 22 shows the relation
between
flow factor
and the product
of
particle
size factor and shape factor
for blended powders, where moderate
heat Portland cement is blended with
an admixture:
blast-furnace
slag,
limestone powder, and fly ash (Table
4).
These admixtures were blended in
-261 -
0.5
0.7
0.9
1.1
1.3
Particle size factor x shape factor
Fig.22
Relation between flow factor
and product
of
particle
siz e
factor
and
shape
fa ctor
(blended
powder with two
types of powder)
0 .12
0 .00
0.0
0.2
Volumetric
0.4
ratio of admixture
0.6
0.8
to blended
1.0
Volumetric
The
flow
factors
of
blended powders consisting
of moderate heat Portland
cement with
l imestone
powder or fly ash can be
represented by Eq. (9) with
the fixed number B set at
-0.13,
as with the simple
use of these powders. The
flow factor of the blend
containing
blast-furnace
slag
can
al so
be
represented by Eq.(9).
In
this
case, however, the
fixed number B needs to be
chosen according
to the
ratio
of
blast -furnace
Table 4 Properties
Ty p e
o f
p ow d er
r a t io o f
a dm ix t ur e
t o b l en d e d
b l a st f ur n a c e
s l a g
l im e s t o n e
p ow d er
a s h
m od e r a te
shown
in
Fig.23,
in
fl ow
P o rt
l an d
0.8
to blended
1.0
powder
powders
fa c to r
E g . (1 0 )
t e s t
te st / Eq .(1 0 )
0 .2
0 .1 0
0 .0 9
0 .9 0
0 .6
0 .0 9
0 .0 9
1 .0 0
0 .8
0 .0 9
0 .0 8
0 .8 9
1 .0
0 .0 9
0 .0 9
1 .0 0
0 .2
0 .0 9
0 .0 9
1 .0 0
0 .6
0 .0 9
0 .0 9
1 .0 0
0 .8 -
0 .09
0 .0 9
1 .0 0
1 .0
0 .09
0 .0 9
1 .0 0
0 .2
0 .08
0 .0 9
1 .1 3
0 .6
0 .06
0 .0 6
1 .0 0
0 .8
0 .05
0 .0 5
1 .0 0
1 .0
0 .03
0 .0 3
1 .0 0
0 .1 0
0 .1 0
1 .0 0
p ow de r
f ly
0.6
of blended
v o l um e t r i c
slag.
As
0.4
ratio of admixture
Fig. 24 Relation between volumetric
rat io
of
admixture
to
blended powder and product
of particle
size factor and
shape factor
Fig. 23 Relation between volumetric
rat io
of
admixture
to
blended
powder and flow
f a ctor
volumetric ratios of 0.2,
0.6, or 0.8 to the blended
powder.
0.2
0 .0
powder
h e at
c em e n t
(M C 2 )
case of a blended powder
of moderate heat Portland
cement with limestone powder or fly ash, the flow factor is proportional to the
volumetric ratio of admixture to blended powder. This is because the relation
between the volumetric ratio of admixture to blended powder and the product of
particle
size factor and shape factor for the blended powder resembles the
relation between the volumetric ratio of admixture to blended powder and the
flow factor,
as shown in Fig.24.
Therefore, the flow factor of such a blended powder is determined
factor of each admixture and its blending ratio (Eq. (10),
Table 4).
Ep = Ec+(Ead-Ec)
- >ad
by the
flow
(10)
262
Where Ep is the flow factor of blended powder, EC is the flow factor of moderate
heat Portland cement, Ead is the flow factor of the admixture, and yad is the
volumetric ratio of the admixture to blended powder.
6. Conclusion
In this study, a method is proposed for estimating the water retaining
factor
and flow factor of powders using the particle
size distribution,
the particle
shape, and the hydration property of the cement.
The results
can be summarized as follows.
(1) Taking as a characteristic
value of the powder particle size distribution
a
value obtained by multiplying
the particle
size factor by the distribution
factor, it was clarified
that the water retaining factor of a particular
type of
powder is proportional to this characteristic
value.
(2) When the constant of proportionality
in the
factor and the characteristic
value is defined
that the shape factor differs with the type of
particle
shape and hydration properties of the
relation between water retaining
as the shape factor, it was found
powder, and is determined by the
cement.
(3) The flow factor increases in proportion with the product of the particle
size factor and the shape factor. Assuming the proportionality
constant to be
invariant,
it was clarified
that it is an index representing the state of the
surface of the particles.
(4) The water retaining
factor of a blended powder in which moderate heat
Portland cement was blended with blast-furnace
slag, limestone powder, or fly
ash can be calculated from the particle
size distribution
characteristic
value
by setting the shape factor of moderate heat Portland cement in accordance with
the volumetric blending ratio of the admixture.
Incidentally,
when the volumetric ratio of admixture to blended powder is below
0.6, the water retaining factor of the blended powder can be approximated by the
water retaining factor of the admixture and the blending ratio.
(5) The flow factor of a blended powder in which moderate heat Portland cement
was blended with limestone powder or fly ash can be calculated,
as with the
simple use of these powders, from the particle size factor and the shape factor.
Also, it can be calculated
from the flow factor of the admixture and the
blending ratio.
The flow factor of a blended powder containing blast-furnace
calculated
by setting
the constant term in the equation
blending ratio of the blast-furnace slag.
slag can also be
according to the
Acknowledgements
The authors would like to thank Dr. KazumasaOzawa, Associate Professor in the
Department of Civil Engineering at the University of Tokyo, for his helpful
suggestions
and Mr. Hideki
Endou of NIHON CEMENTCo. , LTD. for his
the experimental work and for taking the SEMphotographs.
-263-
assistance
in
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