Critical Grain Size of Fine Aggregates in the View of the Rheology of Mortar
International Journal of Concrete Structures and Materials
Critical Grain Size of Fine Aggregates in the View of the Rheology of Mortar
Jae Hong Kim
Jin Hyun Lee
The aim of this research was to investigate the validity of the Krieger-Dougherty model as a quantitative model to predict the viscosity of mortar depending on various aggregate sizes. The Krieger-Dougherty model reportedly predicted the viscosity of a suspension, which includes cement-based materials. Concrete or mortar incorporates natural resources, such as sand and gravel, referred to as aggregates, which can make up as much as 80% of the mixture by volume. Cement paste is a suspending medium at fresh state and then becomes a binder to link the aggregate after its hydration. Both the viscosity of the suspending medium and the characteristics of the aggregates, therefore, control the viscosity of the cement-based materials. In this research, various sizes and gradations of fine aggregate samples were prepared. Workability and rheological properties were measured using fresh-state mortar samples and incorporating the various-sized fine aggregates. Yield stress and viscosity measurements were obtained by using a rheometer. Based on the packing density of each fine aggregate sample, the viscosity of the mortar was predicted with the Krieger-Dougherty model. In addition, further adjustments were made to determine the water absorption of fine aggregates and was transferred from successful experiment to simulation for more accurate prediction. It was also determined that both yield stress and viscosity increase when the fine aggregate mean size decreases throughout the mix. However, when the mean size of the fine aggregates is bigger than 0.7 mm, the yield stress is not affected by the size of the fine aggregate. Additionally, if aggregate grains get smaller up to 0.3 mm, their water absorption is critical to the rheological behavior.
mortar; rheology; viscosity; fine aggregate; grain size; Krieger-Dougherty equation
Viscosity is defined as resistance to flow of fluid under
shear stress and taken as the ratio between the shear stress
and shear rate
(George and Qureshi 2013)
. Viscosity helps
prevent segregation during handling processes such as
delivering, and placing for cementitious materials such as
mortar or concrete
. In a concrete mixture, the
segregation of coarse aggregate is dominated by the
viscosity of mortar. To achieve a high performance on its
strength and durability, securing the viscosity for a
stable mix becomes more important. On the other hand, an
unstable supply of river sand and gravel due to the depletion
of natural resources results in the use of various types of
coarse and fine aggregates, which include crushed,
manufactured, recycled, or marine aggregates. Their physical
properties including shape, size, texture, and grading
including micro-fines can vary significantly from the
reference state of aggregates that originated in a river. Even
though they marginally satisfy the standard of aggregates, its
poor quality causes difficulty in mix proportioning
et al. 1990; Goltermann and Johansen 1997)
. Also the
physical properties of the aggregate affect the performance
of concrete and especially dominate workability in its fresh
(Erdog˘an and Fowler 2005; Westerholm et al. 2008;
Nanthagopalan and Santhanam 2011; Wallevik and Wallevik
2011; Quiroga and Fowler 2004; Mahmoodzadeh and
. Therefore, evaluating the aggregate effect on the
viscosity of freshly mixed cementitious materials allows us
to control and guide the selection of the proper type of
Based on the idea of coarse aggregates suspended in
mortar, the viscosity of mortar dominates the segregation
resistance and rheological behavior of the concrete mixture.
Predicting viscosity of mortar, composed of fine aggregate
and cement paste goes back to the principles behind
aggregate particles suspended in cement paste
(Erdem et al. 2010;
Hidalgo et al. 2009; Toutou and Roussel 2006)
. This study
analyzes the size effect of fine aggregates on the viscosity of
the mortar. For this portion of the study we tested
monosized sands with 10 different diameters, which were mixed
with a constant proportioning ratio. Blending the mono-sized
sands required gap grading and controlled packing density of
(Goltermann and Johansen 1997; Park et al.
. The second research objective focuses on the effect of
packing density and the associated rheological properties of
the mortar samples. The third objective is to determine the
effect of aggregates size on their water absorption and the
subsequent viscosity of mortar mixtures.
2. Materials and Sample Preparation
2.1 Mortar Samples
The fine aggregate used was natural river sand, which had
various particle size distributions. A control sample was
made up of natural river sand generally used for concrete
mix proportioning. Table 1 reports the sieve test results
obtained by ASTM C136
(ASTM International 2006)
the grading curve was within the recommendation range for
concrete mix. The mean size and fineness modulus of the
control sand sample were 0.71 mm and 2.39, respectively.
The specific gravity was 2.60. The other samples were
prepared by controlling the size of sand grains. Two sets of
sieves were used for this experiment: (1) A set of sieves from
ASTM C136 standard, reported in Table 1, and (2) a set of
sieves for further detail analysis with opening sizes of
2.00 mm (No. 10), 0.85 mm (No. 20), 0.43 mm (No. 40),
0.25 mm (No. 60), and 0.15 mm (No. 100). The two sets of
sieves handled 10 different size sand samples. The
monosize sand samples were prepared with retained sand on each
sieve following the test for each set of sieves. For instance,
using the ASTM C136 sieve set, the mean size of the sand
sample retained on No. 16 sieve was calculated by averaging
the opening sizes of the No. 8 sieve and No. 16 sieve, which
determined a mean size of 1.77 mm and an error bound of
±0.59 mm. The sand samples prepared with two sets of
sieves are summarized in Table 2 with the samples’
fundamental properties. G samples were composed mono-sized
grains having a mean designated mean size. M 1.33, M 1.04
and M 0.66 samples were produced by mixing (1) G 1.77
and G 0.89; (2) G 1.77, G 0.89 and G 0.45; and (2) G 0.89
and G 0.45, respectively. They were mixed using a ratio of
1:1 or 1:1:1 by mass.
Depending on the gradation of sand samples, packing
density varies, and a mixed sand sample is expected to have
a higher packing density. The packing density is the main
factor used to determine the viscosity in the Krieger–
(Wildemuth and Williams 1984;
. For mortar, under this research scope, in which
the mortar is a suspension of fine aggregate to cement paste,
the packing density of each dried sand sample was measured
by following method:
1. Fill the fine aggregate sample in a 1-L steel cylinder and
measure its weight. The fine aggregate sample should
then be fully packed using a rubber hammer and the
2. Calculate the volume of the fine aggregate sample by
dividing the weight measured from the previous step by
the density of the fine aggregates. The volume occupied
by the fine aggregates, per unit volume, would be the
packing density. Consequently, the maximum fillable
volume ratio of fine aggregates can be obtained for each
sample. The measured packing density value of each
sample is summarized in Table 2.
The densest packing of uniform spheres is given by
closedpacking microstructures. Face centered cubic (FCC) or
hexagonal close packing (HCP) generates the highest packing
density, p/3H2 = 0.74. In contrast,
Song et al. (2008)
analytically determined that random close packing (irregular or
jammed packing) does not exceed the value of 0.634. The
experiment in this study corresponds to the case, and the
margin of the spherical diameter in Table 2 addresses the
excess of jammed packing. With a margin larger than
±0.2 mm, G 1.77, G 1.43, G 0.89 and G 0.64 exceeded the
maximum jammed packing. Thus, the mixed samples and the
river sand certainly increased the packing beyond the limit.
The sieve test required oven-dried sand samples; however,
when the sand sample is mixed with cement paste as a
mortar, the oven-dried sand sample absorbs the mixing
water. Hence, it was necessary to determine the absorption
rate to calculate the saturated but surface dry (SSD)
condition of each sample. Furthermore, since smaller sizes of fine
aggregates have higher specific surface areas, fine aggregate
samples with the smaller mean size absorbed more water
than the larger fine aggregates. This relates to the solid
concentration of mortar and its need for a water-to-cement
ratio. When this ratio is properly applied, it gives the mortar
a higher yield stress and viscosity. The absorption ratio of
each fine aggregate sample was evaluated based on ASTM
(ASTM International 2015)
. Table 2 lists the fine
aggregate samples’ absorption rates. The absorption ratio
increased as the mean size of the fine aggregate sample
decreased, as expected. Notably, for G 0.34, about 7.26% of
the highest absorption was observed.
For all mortar mixtures, the mix proportion was manually
selected to show a rheological behavior sensitive to the
aggregate condition. The water-to-cement ratio and
sand-tocement ratio were fixed to 0.45 and 1.2, respectively. The
volume fractions of water, cement, and sand were then
0.366, 0.259, and 0.375, respectively. Commercially
available ordinary Portland cement was used, which is equivalent
to the Type I cement of ASTM C150
. According to the information provided by the
manufacturer, the specific gravity of the cement was 3.14 and the
Blaine value was 335 m2/kg. The chemical composition of
the cement used is shown in Table 3. A high-range
waterreducing admixture (HRWRA) was added to remove yield
stress effect from mini slump flow and channel flow tests of
the samples. The HRWRA dosage was 0.6% by cement
mass, and was a polycarboxylate-based solution with a solid
content of 22%. Additionally, to prevent excessive bleeding,
0.1% by cement weight of viscosity modifying admixture
(VMA) was added. All used chemical admixtures are
commercially available products in South Korea. For mortar
mixing, a 5 L planetary mortar mixer was used. Figure 1
shows the mixing protocol. As the first step, all materials
were placed in a mixing bowl and mixed at the first (low)
speed for 2 min. When resting for 1 min and during this
interval, the materials on side of the mixing bowl was
scraped down by a scraper. For the final mixing, the
materials were mixed at the second speed for 2 min
following discharge and prepared for testing within 4 min.
Hence the mortar samples were tested 9 min after water
contact with the cement.
3. Tests Results
3.1 Workability of the Mortar Samples
To evaluate the workability of fresh state mortar
depending on the sand size, mini-slump flow test and channel flow
test were conducted. Basically, the mini-slump flow test was
executed with the same method of ASTM C1611
, but a smaller cone mold was used for
the mortar consistency test. The dimension of the
minislump cone is 70 mm-diameter at the top and 100
mm-diameter at the bottom with a height of 50 mm. The channel
flow test measure the one-sided flow of a cube sample
having 100 mm on each side
(Kim et al. 2014, 2015, 2017)
For both tests, the measured data was (1) flowing distance
and (2) the time duration until flowing stopped.
Table 4 reports the results of the mini-slump flow and the
channel flow methods, where the fine aggregate size effects
on the mortar workability is found. Generally, as the mean
size of fine aggregate decreased, both final flow distance and
stoppage time duration also decreased. This trend was
confirmed within a lower range of 0.89 mm (the mean particle
size of G 0.89), and no clear trend was observed with coarser
particles. For mixed fine aggregate samples, the undisturbed
workability was also found on the M 1.33 and M 1.04
samples which have a bigger mean size of fine aggregate
than G 0.89. Meanwhile, M 0.66 achieved a smaller mean
size, a higher mini-slump flow and a longer stoppage time,
as expected. Therefore, it is concluded that because the fine
aggregates consist of smaller particles, the fluidity is
decreased, so viscosity (defined as the invert of fluidity in
rheology) increased. Note that no matter what the mean size
of the fine aggregates, the well-graded fine aggregates can
have a good fluidity and a high resistance to aggregate
segregation. Additionally, the fine aggregate samples
composed of a bigger mean size (1.43 mm or mean particle size
of G 1.43), are susceptible to segregation due to their
homogeneous grading even though they had a higher
minislump flow indicating good workability.
3.2 Rheology of the Mortar Samples
To measure the rheological properties of the mortar
samples, their flow curves were measured using a commercial
rheometer from Thermo Scientific Inc. with a building
materials cell (BMC) unit. Generally, a rotational viscometer
(or rheometer) measures torque during rotation of a coaxial
cylinder rotor. In the case of mortar, however, a larger size of
fine aggregate causes a slip on the surface of the cylinder
rotor and the inner wall of the outer cylinder (cup), which
sometimes results in plug flow around the rotor. The BMC
used in this study had a vane rotor and slits on the inner wall
to prevent slip and plug flow. Figure 2 shows the structure
and dimension of rotational viscometer. The inner diameter
of the cylinder was 74 mm, and the rotating diameter of the
vane was 50 mm. The sample was filled to about 130 mm in
height and the torque was measured at programmed
rotational speeds. The programmed rotational speed protocol is
as follows: The rotational speed was increased by 0.8
rotation per second (rps) increments until it reached 8.0 rps.
Each rotational speed stage was maintained for five seconds.
After reaching 8.0 rps, the rotational speed was decreased by
0.8 rps increments until 0 rps. From these step-up and
stepdown protocols, two flow curves (up curve, and down curve)
(Ferron et al. 2007)
. In this study scope, there
was no difference between up and down curves, which
means there was no thixotropy within 2 min of the
measuring period cessation.
The BMC used in this research had a wide-gap cylindrical
geometry; thus, a linear shear rate on the radial direction
could not be applied on the measured samples. Furthermore,
a Bingham fluid like the mortar samples in the zero-shearing
zone can occur near the wall of the cylinder. In this case, the
(Koehler and Fowler 2004)
separately considers whether the sample in the viscometer flowed
for the entire range or the sample in the viscometer only
partially flowed. When a Bingham fluid flows for the entire
range, the relation between torque and rotational speed is
expressed as follows:
X ¼ 8p2hlp
where X is the rotational speed (rps), T is the torque
measured (N m), h is the height of the vane, R1 is the radius
of the vane, and R2 is the inner radius of the cylinder. The
yield stress and plastic viscosity of the Bingham fluid model
is then obtained from the slope and x-intercept of Eq. (1).
The existence of dead zone (no shear flow) near the inner
wall of the container changes the relationship as follows:
X ¼ 8p2hlp
Figure 3 shows the flow curves of four representative
samples. In the graph, the points are the rheological
measurements at each rotational speed, and the dashed lines
show the applicable results of the Reiner–Riwlin equation
for the case of partial shear flow. The rheological parameters
of yield stress and viscosity, evaluated by Eqs. (1) and (2)
are compared in Fig. 4. Assuming shear flow occurred
during entire range of the sample, Eq. (1) gave a slightly
lower yield stress and higher viscosity values than those
given by Eq. (2), which calculated a partial shear flow in the
sample. Further, the difference between two evaluations
increased when a sample had a higher yield stress. The
difference caused by the partial shear flow was maximized
with G 0.34 showing the highest yield stress. Here, the shear
flow range is considered within 29 mm of the center radius
compared with the 37 mm inner radius of the container (29/
37 = 78% in radius). The rotational radius was calculated
by R2 ¼ pffiTffiffiffi=ffiffi2ffiffipffiffiffihffiffisffiffiffiyffi at 0.8 rps (0.064 N m). The other
mortar samples had an effective radius within a range of less
than 85% of the inner diameter of the container, where the
differences of the two model equations are negligible.
Therefore, Eq. (2) was applied to evaluate the rheological
parameters of the G 0.34 sample only. To further analyze the
mortar samples, the rheological properties of the base
cement paste (interstitial fluid for the mortar suspensions)
were additionally measured. The sample adopts the same
mix proportion as the mortar samples, but fine aggregates
were excluded (w/cm = 0.45, HRWRA = 0.6% and
VMA = 0.1%). As a result, the base cement paste sample
showed a low viscosity compared to the mortar samples and
a negligible yield stress. Applying a Newtonian fluid model
evaluated its viscosity at 0.37 Pa s.
Figure 5 shows the influence of fine aggregate size on the
yield stress and plastic viscosity of the mortar samples. The
round points show the G sample data to be consistent with
approximately mono-sized sand, and the triangle points
show the M sample data. Regardless of the grading
characteristic, the plastic viscosity gradually increases with the
smaller mean size of the fine aggregates. The trend, however,
disappears when the mean size exceeds 0.7 mm. All mortar
samples showed zero yield stress and 1.7 Pa s viscosity
when the mean size of the fine aggregates was larger than
0.7 mm. The trend for the yield stress was also similar. That
shows the tendency of a mortar sample incorporating fine
aggregates bigger than a certain size to show rheological
properties independent of its grading characteristics. The
effect of fine aggregates on the resultant rheological
behavior is controlled only by its content in mix proportion,
which is also related to the workability test (Sect. 3.1)
results: No influence of mean size was found on the
minislump flow when the sample mean size was bigger than
0.89 mm (see samples G 1.77, G 1.43 and G 0.89).
The Krieger–Dougherty model
(Krieger and Dougherty
1959; Roussel et al. 2010)
predicts the viscosity of the
suspension using solid volume fraction, packing density and
the intrinsic viscosity of particles:
g ¼ gs 1 þ /m
where g is the viscosity of suspension, gs is the viscosity of
the interstitial fluid, / is the volume fraction of the particles,
/m is the packing density, and ½g is the intrinsic viscosity.
This model obviously shows the increased viscosity with
increased solid volume fraction
(Wildemuth and Williams
. In this research, the solid volume fraction of the
mortar samples is applied at 0.4. The volume fraction of fine
aggregates and the packing density of fine aggregates were
measured as previously described. The intrinsic viscosity of
½g in Eq. (1) was 2.5 assuming the shape of individual fine
aggregate particles as non-colloidal spheres. Table 5
calculates the viscosity values of mortar and the differences
between calculated value and measured value based on the
cement paste viscosity where g0 = 0.37 Pa s described in
The difference is within 10% excluding samples G 0.64
and G 0.34. Still it is needed to discuss the high error of G
0.64. It should be noted that its measured viscosity is out of
trend, which strongly points to measurement error. Sample G
0.34 showed extremely high viscosity, which caused the
estimation to lose its accuracy. Water absorption of fines
reportedly maximizes with smaller particles, which will be
discussed in the next paragraph. The other samples can be
explained by the Krieger–Dougherty equation, which is also
valid for the mixed sample case. Measurement of wet
packing, contrary to the dry packing adopted in this study, is
expected to decrease the difference because the
hydrodynamic properties of grains are not consistent when they are
floating in a suspended medium
(Kwan et al. 2012)
Additionally, as a possible factor, the chemical admixtures used in
this research are affected by changing packing density under
wet conditions, which induces errors between predicted
viscosity and dry packing density. For better prediction,
although the wet packing conditions of suspension should be
evaluated with the influence of chemical admixtures, as per
Bentz et al. (2012)
, it is difficult to evaluate the influence of
superplasticizers on packing conditions of suspensions.
Furthermore, according to
Wallevik and Wallevik (2011)
superplasticizer is considered to only affect yield stress of
cement paste; furthermore, VMA changes the medium of the
suspension rather than the particles. Although this theoretical
background as per
Quiroga and Fowler (2004)
et al. (2012)
may not follow a prescribed methodology in a
practical aspect, this research agrees with their findings that
the addition of chemical admixtures to the samples can be
considered a factor causing prediction error.
The viscosity estimation error for G 0.34 was
approximately 63% in Table 5, and the sample gave the highest
water absorption—more than double that of the other
samples—as reported in Table 2. The following experiment was
designed to verify that the water absorption generates error
of the viscosity estimation. Two samples, G 0.45 and G 0.34,
were compared. The difference in their water absorption was
3.50%, but their packing densities were very similar, 0.633
and 0.626, respectively. Simply adding 3.50% absorbed
water to the S60 sample allows it to maintain same solid
volume fraction as G 0.45. After the absorption rate was
corrected for G 0.34, the value in parentheses, the rheology
parameters and difference to the predicted values were added
in Table 5. The prediction of rheological properties was
possible at 0.34 mm of the fine aggregate sample size, while
the workability difference was observed as smaller than
0.89 mm of the fine aggregate sample size. Therefore, it can
be concluded that workability decreases with decreasing
particle mean size and is only influenced by water absorption
in a range from 0.34 to 0.89 mm. Considering the water
absorption effect keeps the Krieger–Dougherty model valid,
the hydrodynamic state of the mortar samples is consistent in
the range of aggregate size.
The effect of the aggregates size, excluding the effect of
their water absorption, can be analyzed based on a loosening
phenomenon on the packing state. Cement paste, the
interstitial fluid for the mortar samples, is not a liquid matter but
another suspension at a micro-scale. The maximum particle
size of Portland cement is less than 75 lm in a dry state, and
its remained the same on a 45 lm-sieve making it practically
less than 10% by mass. The cement particles place in
between the aggregate particles results in the loosening
effect on the packing of aggregates; hence, the packing
density decreases. Applying the compressive packing model
de Larrard and Sedran (2002
) allows us to
consider the loosening effect, and consequent packing
density for d1-dominant packing, which is calculated as
1 y2 1
where the loosening coefficient of aij = H(1 - (1 - dj/
di)1.02). The parameters b1, b2, b3,… are the packing density
of each class of particles having the diameter of d1, d2, d3,…,
respectively, and their mutual volume fractions are given by
y1, y2, y3,…, respectively. Note that the mutual volume
fractions were defined the volume fraction of each-class
particles divided by the total volume fraction of all particles.
The mono-sized sand first takes the largest class of
particles, d1, and then the following classes of d2, d3,…, are
reserved for cement particles classified in its dimension.
Their packing densities can be assumed as constant,
bi = 0.634 (theoretical value for random packing), because
the packing density of mono-sized sand with a mean size of
less than 1 mm, from G 0.89 to G 0.34 in this study, was
within ±1.5% error. Thus, the b-ratio in the denominator
cancels out with the value of 1. In addition, only the packing
of sand is investigated here; then, getting rid of the packing
effect of cement particles gives
/m ¼ 1 þ y2a12 þ y3a13 þ y4a14 þ
ffi b1ð1 y2a12 y3a13 y4a14
which is finally approximated by the binominal expansion.
The loosening effect from the di-sized cement particle is
yia1i 9 100% decrease in the packing density of sand. If
d2sized particles take the remaining cement amount on the
45 lm-sieve, which is 4% of the total cement mass as an
example, the volume fraction of d2-sized particles is 0.0104
from that of the total cement amount (0.259). The value of y2
is then given by 0.0104/(0.0104 ? 0.375) = 0.0398 with
the volume fraction of sand (0.375). The coefficient becomes
a12 = H(1 - (1 - 0.132)1.02) = 0.367 with d2/
d1 = 0.045/0.34 = 0.132. Finally, the loosening effect of
cement particles larger than 45 lm decreases 1.46% of the
packing density. The decrease is within the range of
fluctuation when the packing density of sand was measured.
Therefore, the mortar sample incorporating the smallest sand
particles (0.34 mm) was possibly predicted with the
Krieger–Dougherty equation. If fine sand having the size of
0.1 mm is used, the loosening effect doubles and the original
Krieger–Dougherty equation would lose its predicting
accuracy. The loosening effect is expected to be maximized
if a mix (1) incorporates finer sand or (2) uses coarser
cement, showing a lower percentage passing on a 45
sieve. Figure 6 shows the result of the parametric study
calculating the loosening effect, where three plots assumes
the passing percentage on a 45 lm-sieve by 94, 90 or 86%.
In this research, the rheological properties of fresh state
mortar were evaluated depending on various mean sizes of
fine aggregate, and the rheological properties were predicted
using the Krieger–Dougherty model. This paper’s research
experiment results can be summarized as follows;
1. Mini-slump and channel flow of mortar showed
decreased flowing distance and reaching time with
smaller fine aggregate grains. The workability change
according to the dimension of aggregates can be related
to the relationship between viscosity and the mean size
of the fine aggregate sample.
2. The relation of torque-rotational speed can be analyzed
with the Reiner–Rivlin model for quantitative
expression of yield stress and viscosity of fresh-state mortar.
From the analysis, as the mean size of the fine aggregate
decreased, yield stress and viscosity of the fresh state
mortar increased. However, the size of the fine
aggregate did not influence the yield stress when the
aggregate size exceeded 0.70 mm.
3. The Krieger–Dougherty model allows prediction of the
viscosity of mortar, and the viscosity of mortar can be
decreased with low packing density of fine aggregate.
The packing density was increased from single-sized
gradation to multi-sized gradation because of filling
effect of various size particles.
4. Smaller grains of fine aggregates showed higher
adsorption per unit mass. For air-dried conditions, since
the mortar including the fine aggregate with higher
absorption rate decreases water-to-cement ratio, yield
stress and viscosity of the mortar can be increased. From
the absorption rate measurement, when the mean size of
the fine aggregate sample is higher than 0.34 mm (S60),
the absorption rate of the fine aggregate is remarkably
increased as the mean size of the fine aggregate is
increased. In this case, compensating the absorption
ratio provided a more accurate prediction of viscosity
with the Krieger–Dougherty model.
5. Therefore, by using the method suggested in this
research, the viscosity of a given mortar can be
predicted by measuring the viscosity of cement paste
and packing density of fine aggregate. This indicates
that accurate prediction of the rheological behavior of
mortar is possible by conducting a packing density test
of various fine aggregate types.
This research was supported by Basic Science Research
Program through the National Research Foundation of
Korea (NRF) funded by the Ministry of Science, ICT and
Future Planning (NRF-2015R1A1A1A05001382).
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