146902 1403-2727-ijcee-ijens

International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 14 No: 03 25
146902-1403-2727-IJCEE-IJENS © June 2014 IJENS
I J E N S
An Economical and Time Saving Procedure for
Concrete Dosing
Danilo A. Bomfim, Walter Libardi and and João B. Baldo*
Universidade Federal de São Carlos
Departamento de Engenharia de Materiais
Via Washington Luiz km 235 - São Carlos – SP – 13565-905 – Brazil
*
Corresponding author – e-mail – baldo@power.ufscar.br
Abstract-- In this work it is presented a simple method for
Portland cement concrete dosing procedure. It is based on
particle packing first principles together with a concise way of
treating separately the needs for admixture water for each
individual concrete constituent (coarse, medium and fine
aggregates and the cement), as well as to the void content. The
procedure is also supported by a specific mixing sequence of the
raw materials. The verification of the model efficiency, was made
by comparing the strength development at various ages of
concrete specimens produced by means of the new dosing
procedure, with that presented by conventional portland cement
concrete specified for 35MPa  5,076 psi of compressive strength,
using the Brazilian Portland Cement Association (ABCP)
method. After 28 days, the new dosing method provided a
concrete with average compressive strength value of 54MPa 
7,832 psi. Conversely the one produced under ABCP method
reached an average compressive strength of 43MPa  6,236 psi at
the same age, containing however 30% higher cement content.
Index Term-- Concrete, dosing, concrete composition, concrete
strength
1. INTRODUCTION
Considering the urging need for competitiveness and natural
resources preservation, even the apparently simple operation
of structural Portland cement concrete dosing, appears as a
great challenge to those dedicated to the production of cement
containing composites. Several standardized and supposedly
optimized dosing procedures, have been proposed either by
government institutes or builders associations. Nevertheless,
most of them are neither efficient nor friendly, being difficult
to put into practice by the average technical personnel, under
routine work. The art of concrete dosing is a practice
involving the search for low cost/benefit ratio of materials,
equipment and labor involved. At the same time, the structural
elements design pre-conditions has to comply with building
codes requirements. In spite of the intricacies at the
microscopic level not yet fully revealed, structural civil
cement concrete is considered a simple material because of the
much abuse it stands without failing that easily. Concrete is
made by mixing appropriate amounts of coarse, medium and
fine natural aggregates, together with a cementitious hydraulic
binder (portland cement) and water [1]. The rheological and
setting properties of concrete, are dictated by its chemical and
mineralogical composition, particulate size distribution, the
relative volume fractions of its constituents and the
water/cement ratio. It is a common practice to add to the
concrete batch, special admixtures (solid or liquid), which will
act mostly on the paste, in order to promote workability,
control of setting time and flow properties. Among the most
important special additives are the mineral admixtures (fumed
silica, fly ash) and functional chemicals called plasticizers,
superplasticizers, retardants and accelerators [2,3]. These last
chemicals in certain situations can be deleterious to some
properties of the hardened concrete.
The hardened concrete microstructure is constituted by three
main phases. The first is comprised by the coarse and medium
aggregates, which are embedded in the second rigid phase,
made of fine aggregates and the hydrated cement, generally
called the matrix. A third boundary phase appearing in the
nearest vicinity of aggregates is called transition zone. In spite
of its slimness (50 m  0.002 in), the transition zone plays a
decisive role on the ultimate strength of the concrete and its
properties depend strongly on the way the aggregate interacts
with the products formed by the dissolution and re-
crystallization of the cement particles. Nevertheless, the level
of relative density or the void volume fraction in every
concrete, is also a very important parameter controlling its
strength and durability. As a result there is a need for a dosing
procedure based on the packing efficiency of the concrete
components.
Normally the production of a concrete starts with the choice of
raw materials and their characterization. The components are
selected to support a set of predetermined desired properties
(final strength, cement consumption, slump). Once the
materials and the target properties are set, volumetric or mass
relations of the constituents for the formulation of the final
concrete batch are determined, using specific procedures.
Among the concrete constituents, the cement is of highest cost
in addition to the environmental impact upon its production,
turning it worthwhile to find ways to decrease its contents in
the batch, without altering (when possible) the targeted final
properties. These features were taken into consideration, in the
formulation of the new concrete dosing method presented in
this work.
Research Significance
Most of the recommendations or procedures for concrete
dosing are based on a somewhat arbitrary choice of
coarse/fine aggregate ratio and the cement content is
determined as well by means of the targeted final strength,
water/cement ratio and the desired slump [4]. These
procedures are most of the time tiresome and hard to follow
even by skilled technical staff. Using a different route, the new

I J E N S
concrete dosing method proposed in this work, is based on
first principles of particle packing presented by seminal
models [5,6,7]. The main objective is to provide concretes
with lower cement content and high strength levels, using a
new approach to determine the concrete constituents
proportions, mixing water content and the components mixing
sequence. The eventual variability of the components particle
size distribution and moisture content particularly the sand and
coarse aggregate, can be detected by two simple procedures;
drying and solid constituents tap density measurement, such
that the whole batch composition can be promptly corrected.
2. THE FUNDAMENTALS OF PARTICLES PACKING
The fundamental basis for dense packing of particulate
materials, considers the filling of interstices resulting from the
successive packing of smaller particles into the interstices left
by previously packed larger ones. In essence, this follows a
fractal concept, through the consideration that the sequential
packing of particles each time of smaller sizes, creates ever
decreasing self similar structures of empty spaces. If particles
larger than the available interstices are introduced in the
system, the packing efficiency is decreased. In addition to the
fractal logic, a mixing order must also be considered for the
accomplishment of an optimized dense packing of particulate
material.
Among the several parameters which affect the packing
efficiency of a mix made from different particulate materials,
the most important are the packing density of each individual
set of particles composing the global particulate system, the
shape, the size ratio and the width of size distribution of each
set of particles. In addition, particles of large aspect ratio and
of rugged surface, are more difficult to flow and sensitive to
agglomeration, leading to a reduction in the density of the
system at the same time requiring more paste and mixing
energy. As a result a larger content of the lubrication medium
(water and/or paste) is needed in order to provide a minimum
paste thickness for the flow to start. However, the excess
water compromises the final strength and durability of the
concrete.
With respect to the shape of particles, if it deviates too much
from an ideal spherical shape, the coordination number of
each particle in the particulate system bed decreases, leading
to a lower packing density as shown in Figure 1 [8]. Another
factor that contributes for the maximum packing of a bed of
particles, is the size ratio (R) among the several constituents
(coarse, medium and fine) average size. In portland cement
concrete for example, the size ratio between the coarse
aggregate particles and the cement particles, can be of the
order of 380 to 1. This fact characterizes a huge particle size
gap between the largest and the smallest components. As a
result, if the whole grain size distribution is not optimized in
order to smooth out a little this gap, the coarse aggregates will
be seen as obstacles for the fine ones, giving rise to what is
known as the “wall effect”. The main implication of this
phenomenon is that mixing water, tends to be locally
concentrated at the coarse aggregates surfaces and will not
migrate towards the concrete free surface. As the water
cement ratio in this region is much larger than in the rest of
the matrix, a weak porous transition zone in the hardened
concrete will be created, affecting negatively the concrete
ultimate strength.
2.1 -The Discrete Particle Packing Model (Furnas Model)
In the Furnas seminal particle packing model [6], the particles
are considered of spherical shape and distributed in various
groups of mono-dispersed or discrete particles (of the same
diameter), successively smaller in diameter. The objective
consists on the packing of a unit mass of the solid particulate
in a minimum volume of a certain container of fixed total
volume. The interstices left by the packing of the bigger
particles is filled by successively smaller sized groups of
particles. The Packing efficiency PF (corresponding to the
packed particles true volume divided by the volume they
occupy in the container), will depend on the number of groups
of particles used and the size ratio among each successive
group. The efficient packing of a blend of different sized
particle groups, is reached when the size discriminator (R) has
a direct relation to the aperture of the new interstices, which
are created every time a group fills the interstices left by a
previously packed larger sized group. Experimentally it has
been found that R must be bigger than 5. Using this procedure
for an infinitely large number of size groups, it results in the
complete filling of the interstices. In this case PF reaches the
value of 1, meaning a complete filling of space or zero voids
left. We may conclude that for the blending of different size
groups, there will be one particular proportioning of their
quantities, which leads to the most efficient packing (PFmax)
of their mixture. In the Furnas model it is assumed that the
volumetric void fraction (Vf) left by the packing of each group
of discrete spherical particles is the same. Their individual
packing efficiencies (considered separately) are assumed to be
equal to 50% (which is not true in practice).
The packing efficiency of each group of discrete particles can
be written as follows:
PFi = 1 – Vfi = (bi/ti) (1)
Where Vfi is the volumetric void fraction of a fixed mass of
particles of the component i. This volume represents the one
that is left, after a fixed mass of particles is packed by tapping
(vibration) in a container of fixed total volume. The tapping
density bi is obtained by dividing the mass of particles by the
volume they occupy after vibration packing of the component
i in a container. The term ti is the true density (real density)
of component i.
For a mixture of n groups of discrete sized particles, provided
that R>5, the following relationship applies [9]:
PFmix = PF1 + (1-PF1)PF2 + ….(1-PF1) (1-PF2)…(1-PFn-
1).PFn (2)
Where PFi (i =1 to n) is the individual packing efficiency
from the largest to the smallest particles in the whole
particulate size distribution.
If we assume that Vf1 = Vf2 = Vf3 = …. Vfn = Vf, then

I J E N S
PFmix = 1 – (Vf) n
(3)
If the number of group sizes, each time smaller by a factor R,
is infinitely large (n) then PFmix = PFmax = 1, because
Vf
n
0 [10].
Based on the above, for a mixture of coarse medium and fine
spheres, forming three groups sizes like the ones in a concrete
composed of coarse aggregate+ sand + cement, the optimized
packing of the mixture is given by
PFmix = PFc+(1-PFc) PFm+ (1-PFc)(1-PFm) PFf (4)
Where PFc is the packing efficiency of the coarse particles,
PFm is the packing efficiency of the medium particles and PFf
is the packing efficiency of the fine particles.
Based on Equation 3, the volumetric void fraction left in the
mix is given by:
Vfmix= 1 – PFmix (5)
The volumetric contribution of each size group (Vi), for a unit
of mass of the total mix (Wf’s
) can be determined by the
following relationships:
V1 = PF11 (6)
V2 = (1 - PF1).PF2 .2 (7)
V3 = (1 - PF1). (1 – PF2).PF3. 3 (8)
Where I, 2 and 3 are the respective specific density (with
respect to the water true density) of each set of particles, for
example of three components involved in the whole mixture.
By using these last relationships the volume fractions
contributions of each group (fVi), for an improved packing of a
unit mass of mixture of n groups sizes, can be determined as
follows:














n
i
i
i
Vi
V
V
f
1
(9)
In other words, the respective volume fractions of each dry
component can be calculated through the following equations.
fV1= V1 / Vtotal (10)
fV2 = V2 / Vtotal (11)
fV3= V3 / Vtotal (12)
fVn = Vn/Vtottal . (13)
Where Vtotal = V1 + V2 + V3 + …..+ Vn. For a three
component system like in a portland cement concrete, fV1, fV2
and fV3 are the volume fractions of the coarse aggregates, sand
and the cement respectively in a unit volume of a mixture of
the three different components.
2.2 - The Volumetric Dosing Ratio
The volumetric dosing ratio (Vri) of each component can
finally be determined by normalizing the volume fractions fVi
with respect to the smallest value in the set (dividing by the
smallest fVi).

 n
i
vi
vi
f
f
1
riV (14)
This will give the volume ratios : Vr1 : Vr2 : Vr3 ; …: Vrn for
the components in the whole mixture. The volume ratios can
be transformed into mass ratios by using the true density of
each of the particulate size group, and the individual mass of
each dry material can be determined.
From the previous considerations, it can be seen that the
maximum packing efficiency, depends on the proportioning of
particle sets and their particle size ratio. It will reach the limit
of 1 when the number of groups is infinite and the individual
packing efficiencies of the groups are high and the differences
in size ratio (R) for each successive group is large (R>5).
Examples of the effect of size ratios on the tapping density of
three sets of spherical particles is shown in Table I [9]. It can
be seen that particular combinations of size ratios are
necessary for the optimized packing of a three size fractions
particulate system bed. In this manner for a ternary mixture of
coarse medium and fine spherical particles, good packing
efficiency (PFmix  0.850) will be attained if their average
size differences for coarse, medium and fine particles follows
a size ranking in the order of ; 25:5:1.
3 - THE FORMULATION OF THE NEW CONCRETE
DOSING METHOD
The population of defects in a hardened concrete body is the
result of a deficient packing of its constituents, excess of
mixing water and/or over air entrainment as well as by un-
appropriate mixing and placing conditions.
The proposed method of this work aims, first of all, the
packing optimization of the particulate materials used in a
concrete batch (cement, coarse, medium and fine sized
aggregates). It is a must to take indirectly into account, by
measuring the respective tapping density, the effects of shape
and ratio size on the packing efficiency. In addition, because
of its lubricating effects and contribution to the aggregates
relative movements, in this proposed method, the water
complementarily to its cement hydrating function is also
considered to be part of the packing conditions. This is
because water will fill voids also. In this manner the global
participation of the water in a concrete batch can be analyzed

I J E N S
by parcels. In Figure 2, it is shown a flow chart of the new
proposed concrete dosing framework.
The final dosing can be either in volumetric or mass terms. In
this last case the true density is used to transform in mass
fraction instead of volume fractions.
The starting point of the method, is to consider the concrete as
composed of three sets of non isometric dry particulate
material. The main data base to be gathered is the evaluation
of their individual tapping densities (i) and also knowing in
advance the respective true density of each component (ti),
which can be found in minerals handbooks or in producers
catalogs. In Figure 3, it is shown schematically the
determination of the tap density of the constituent raw
materials of the concrete batch.
The respective tapping density of each chosen component, is
determined by pouring a fixed mass (for example 1kg  2.2 lb)
of the particulate material, into a graduated cylindrical
container. The graduated container diameter must be at least
20 times the largest particle diameter in the component under
tapping density evaluation. The system is vibrated in a
vibratory table for 15 seconds under 2mm  0.080in amplitude
and 60 Hz of frequency. After vibration, the final apparent
volume occupied by the material is visually evaluated against
the graduated container marks. The tapping density is
calculated by dividing the material mass by the occupied
volume after tapping. The packing efficiency of each
component (PFi), can be calculated by using the true density
of the particular component. These values are applied to
Equation 1 and Equations 6 to 14, in order to determine the
volume fractions of the dry ingredients (cement, sand and
coarse aggregates) that will compose the final batch.
3.1 Mixing Water Determination Procedure
In this new proposed concrete dosing method, the mixing
water is divided into four distinct quantities or parcels. Each
will be separately determined based on the behavior of each
raw material with respect to the water and also in accordance
to the desired workability (slump). All the raw materials
should be previously dried before to proceed in this part of the
procedure (12 hours at 110C 166F).
The first quantity (P1) is the water volume necessary to
hydrate the cement quantity, which depends on the chemical
and mineralogical composition of the cement. This quantity
can be determined by the following relation.
P1 = Vrc.c h (15)
Where Vrc is the cement volume ratio (Eq. 14) to be added to
the whole mix, h is the water mass fraction necessary for its
hydration and c is the cement true density. The quantity h can
be obtained from the cement producer.
The second water quantity (P2) is the water volume relative to
the sand saturation. It is known that a dry sand quantity
absorbs approximately 4wt% of water through its pores till
saturation and swelling. The mass of this type of water can be
evaluated as shown in Equation 16.
P2 = 0.04. Vrs s (16)
Where Vrs is the dry sand volume ratio (Eq. 14) to be added to
the whole concrete mix and s is the sand true density.
The third water quantity (P3) is the volume of water required
to wet the coarse aggregate surface and also that absorbed by
its open porosity. The absolute evaluation of his amount is
difficult to do, because it involves a previous knowledge of
the coarse aggregate specific surface area (m2
/g). In addition it
must be assumed that a monolayer of water molecules is
enough to wet that surface. In order to bypass this difficulty a
reasonably good approximation can be done, by weighing a
certain dry mass (Md) of the coarse aggregate, immersing it in
water for 12 hours and measuring its saturated weight (Ms)
after rolling the saturated coarse aggregates in a wet cloth. The
difference between the saturated weight and the dry weight
divided by the dry weight, is an approximate measure of the
water mass fraction involved in the absorption and surface
wetting of the coarse aggregate. This water mass fraction
(Wca) relative to dry aggregate weight, can be calculated by
Equation 17 and the water parcel (P3) is given by Equation 18.
Wda = [(Ms-Md)/Md] (17)
P3 = Wca.Vrca ca (18)
Where Vrca is the volume ratio of coarse aggregate (Eq. 14) to
be used in the mix proportioning. Wca is the amount of
absorption and wetting water of the coarse aggregate, and ca
is the coarse aggregate specific density .The same procedure
as above, could be applied to the determination of the water
quantity P2.
The fourth water quantity (P4) is the water required to give
workability and lubrication to the concrete mass. This amount
should theoretically be equal to the volume of empty spaces
left by the packing of the dry materials. However, at the same
time the minimum paste thickness requirement must be taken
into consideration. Considering the water density of 1g/cc, its
volume fraction (Vw) relative to the voids left by the unit of
mass of dry material in the mix, can be calculated by means of
Equation 19 and its quantity (P4) by Equation 20.
Vw= (1-Pfmix) (19)
P4 = Vw. H2O (20)
Where H2O is the water true density at the measurement
temperature.
The summation of P1, P2, P3 and P4 gives the total amount of
water to be added to the concrete total dry mass. In order to
avoid over-watering of the mix, it is important to notice that in
the case that the coarse aggregates and/or the sand are already
wet, their moisture content must be previously determined, by
drying, and taken into account in the determination of the
quantities P2 and P3.
3.2 - Mixing Sequence

I J E N S
Another very important step in the dosing of concrete is the
mixing order of its components. The mixing order affects
directly the concrete slump, placing energy, concrete final
density and surface finishing. In this study an optimized
mixing order in order to provide the above requirements was
developed as shown in the flow chart of Figure 4.
It is important to work with raw materials free of
contaminations and as dry as possible. After the calculations
relative to the amounts of each component is done, the
following mixing order is applied:
3.3 - Mixing Step 1
In this step, the aim is to prepare the coarse aggregate surface
to produce a strong transition zone. In this case all of the
coarse aggregate amount, is initially dry mixed for 3 minutes
with 10% of the cement total quantity. Next, the water
quantity P3 is added and the mixing is proceeded additionally
during 5 minutes. This is called Mixture 1.
3.4 - Mixing Step 2
To the Mixture 1 prepared as above, it is added (under mixing)
all the sand quantity of the concrete mix plus the water
quantity P2. The mixing time of Step 2 is of the order of 5
minutes. In this step the aim is to provide the filling of the
interstices left by the coarse aggregates, beginning the packing
of the mixture. This is called Mixture 2.
3.5 - Mixing Step 3
To the Mixture 2 prepared as above it is added sequentially
(under constant mixing) the rest of the cement plus the water
quantity P1. This is called Mixture 3. The total mixing time of
this step is of the order of 8 minutes. The aim of this step is to
fill the interstices left on Step 2, with the cement paste
increasing the packing density of the whole mix.
3.6 - Mixing Step 4
To the Mixture 3 prepared as above it is added the water
quantity P4, and the mixing is continued for 5 minutes. In this
case the final portion of the mixing water is used to give
workability and lubricity to the mix.
4 - EXPERIMENTAL VERIFICATION OF THE
PROPOSED DOSING METHOD
The verification of the proposed model efficiency, was made
by comparing the strength development at various ages of
concrete specimens produced by means of the new dosing
procedure, with that presented by concrete specimens
specified for 35MPa  5,076 psi of compressive strength,
produced with the same raw materials under the Brazilian
Portland Cement Association (ABCP) procedure, which is of
widespread use in Brazil and bears some similarity with
ASTM. The specimens in both cases were produced, without
special additives, using easily available commercial raw
materials such as basalt coarse aggregates, river sand and
ordinary Portland cement.
4.1 - The Materials
The materials used to prepare the two concretes by using the
two different methods, were the same and are specified below.
4.2 - Cement
The cement used to prepare the two concrete compositions
was of ordinary type with mineral admixtures, produced in
Brazil by Itau Cement Company. Its general chemical
characteristics are presented in Table II.
4.3 - Coarse Aggregate
The coarse aggregate used in this study was a crushed and
screened basalt mined in the vicinity of the city of Campinas
in the State of São Paulo whose compressive strength is of the
order of 60MPa  8,702 psi. The grain size distribution of the
coarse aggregate was in the range from 9 to 19mm. Its true
density was 2.72g/cm3
 169.80 lb/ft3
and water absorption of
0.5wt%.
4.4 - Sand
The sand used to produce the concretes was a washed river
sand from the Mogi Guaçu river in the State of Sao Paulo. The
sand was dried in a laboratory drier to a final moisture content
of 2wt%. Its determined specific gravity by Helium
picnometry was of 2.64g/cm3
 164.81 lb/cft. Its grain size
distribution was 97% between 0.15mm  0.0060in and 4.8mm
 0.190in as shown in Figure 5.
As it can be seen the grain size distribution of the sand used in
this investigation, indicates it is a medium type sand,
following the Brazilian Standard NBR- 7217/82 (equivalent to
ASTM C144) superior and inferior limits as shown in Figure
5.
5 - THE CONCRETE DOSING PROCEDURE
The dosing of the concrete using the new developed procedure
was based on the equations presented earlier in this paper. The
respective tapping densities (i) and packing factors (i/t) of
each component are shown in Table III.
The determination of the volume contributions of each dry
constituent for a unit mass of the total mixture, was made
through the use of the data of Table III applied to Equations 6
to 14 as follows.
Vca = PFca . ca = 0.565 . 2.72 = 1.537
Vs = ( 1 – PFca ). PFs . s = ( 1 – 0.565 ) . 0.686 . 2.65 =
0.791
Vc = ( 1 – PFca ) . ( 1 – PFs ) . PFc . c = ( 1 – 0.565 ) . ( 1 –
0.686 ) . 0.529 . 3.09 = 0.227
Where:
Vca is the coarse aggregate volumetric contribution in the mix.
Vs is the sand volumetric contribution in the mix
Vc is the cement volumetric contribution in the mix.
The total volume per unit mass of the dry solids mixture is
given by:
Vtotal = Vi = ( 1. 537 + 0.791 + 0.227 ) = 2.555

I J E N S
In this case the densities are the specific densities (normalized
with respect to the water density of 1g/cm3
 0.0163 lb/cft at
25C).
The respective volume fractions in percentage, of each dry
constituent can also be calculated by applying the data above
to Equations 10, 11 and 12 resulting in:
f Vca= (Vca / vtotal) . 100= (1.537 / 2.555).100 = 60.15 %
f Vs = (Vs / vtotal ) . 100 = (0.791 / 2.555).100 = 30.96 %
f Vc = (Vc / Vtotal) . 100= (0.227 / 2.555).100= 8.89 %
Applying the data of Table III to Equation 2 it results that the
solids packing fraction in the dry mix is given by:
PFmix = 0.565 + [ (1 – 0.565 ) . 0.686 ] + [(1 – 0.565 ) . (1 –
0.686 ) . 0.529 ] = 0.936
Consequently the volume fraction percentage of voids left in
the dry mix is :
Vvmix= ( 1 – PFmix) . 100 = ( 1 – 0.936) = 6.45%
By dividing the volume fractions of the dry components by the
volume fraction of the cement, it will result in the volumetric
dosing (Eq. 14) of the components in terms of volume ratio of
Cement (Vrc), volume ratio of Sand (Vrs) and volume ratio of
Coarse Aggregate (Vrca). The volumetric dosing for an unit
mass of the dry the mix is given by:
Vrc : Vrs : Vrca = 1.00 : 3.49 : 6.77
The above ratios express how the dry solids are dosed
volumetrically for the whole concrete mix.
What is need to be done next, is the calculation of the water
volume ratios (Pi) using Equations 15, 16, 18 and 20. The
water quantities for the volumetric dosing calculated above are
determined as follows:
Quantity P1
P1= Vc.c . h = 1.00 . 3.09 . 0.12 = 0.371
Quantity P2
P2 = Sab Vs s= 0,05 . 3.485 . 2.65 = 0.462
Where Sab is the sand water absorption
Quantity P3
P3 = CAab x Vca. ca= 0.005 . 6.71 . 2.72 = 0.091
Where CAab is the coarse aggregate water absorption.
Finally the quantity P4 is calculated as follows:
Quantity P4
P4 = (1-PFmix) .VT . pH2O = 0.0645 . 1.556 . 1 = 0.1
By summing up the Pi
´s
the total water ratio X is given by:
X = 0.371 + 0.462 + 0.091 + 0.1 = 1.024
In this manner the final dosage in mass basis, normalized with
respect to the cement content, can be expressed by the ratios
respectively in terms of ; Cement : Sand : Coarse aggregate;
Mixing water as follows:
(Vrc.c/.c) : (Vrs. .s/.c : (Vrca.ca/.c) ; (X. .H2O/.c)
(1.3.09/3.09) : (3.49.2.65/3.09) : (6.77. 2.72/3.09) ;
(1.024.1/3.09)
Which results in the final batch mass proportions of:
1,00 : 2.99 : 5.95 ; 0.33
In order to verify comparatively the efficiency of the new
concrete dosing procedure (in terms of strength development
only), two concrete compositions using the same raw
materials were prepared. One (F-01) using the proposed
method, and the other (A-01) using the Brazilian Portland
Cement Association (ABCP) concrete dosing procedure,
which is of wide spread use in Brazil.
5.1 - Specimens Preparation
Twenty cylindrical specimens of 15cm  5.91in diameter and
30cm  11.82in in height, of each composition, were prepared
following the procedures of each method and molded in a
vibratory table (60 Hz and 2mm  0.08in oscillation
amplitude). The specimens were moist cured for 48 hours in
the mold. After demolding the specimens were cured under
Ca(OH)2 saturated water during 7, 14 and 28 days. After each
curing period 5 specimens of each composition were tested in
a moist condition, under compression, in an universal testing
machine (Instron Model – 5500-R).
6. EXPERIMENTAL RESULT
In Table IV it is shown the raw materials quantities used in the
compositions prepared following the two different dosing
procedures. Some physical characteristics of both mixtures in
the wet and hardened conditions were also evaluated. I can be
noticed that for similar slumps and under a much smaller
water/cement ratio, the degree of densification of the
specimens prepared using the new proposed dosing procedure,
is substantially higher than the one obtained using the
traditional ABCP procedure. In addition the cement quantity
used by the new method is about 50% less than that of the
ABCP last dosing method.
6.1 - Compressive Strength
The results of compressive strength after different ages
obtained for the two compositions, are shown in Figure 5. It is
quite clear that, irrespective of the age, the compressive
strength values obtained for the composition prepared using
the new procedure, are substantially bigger than the ones
obtained with the composition prepared by the ABCP method.
In addition, the compressive strength values presented by the
composition F-01 are impressive, considering its much lower
cement content than that used in the specimens prepared under
the ABCP method (A-01) .
Naked eye observations of fracture surfaces of specimens of
both compositions indicated that the crack propagation in the
specimens prepared using the new procedure was eminently

I J E N S
intragranular in nature. On the other hand the fracture
propagation path of specimens prepared by the traditional
method was eminently intergranular. This fact indicates that
the interface aggregate/matrix was much stronger for the
composition F-01, which also contributed to its higher
compressive strength.
7. CONCLUSION
1 – The new proposed concrete dosing procedure and mixing
order was very effective on promoting an optimization of the
mechanical strength of a common Portland cement concrete
using much less cement and a lower water to cement ratio than
those of a concrete designed to a fck = 35MPa  5,076 psi
compressive strength, under the traditional Brazilian Portland
Cement Association procedure. In addition the, the slump was
kept under acceptable value and the rheological characteristic
tixotropy, important for molding under vibration, was
improved.
2 – The implementation of the new proposed concrete dosing
procedure is friendly, and fast. Its simple data gathering
procedure and processing characteristics, make it a powerful
tool for reformulation of concrete mixes whenever raw
materials characteristics change.
3 – The new procedure is easy to implement and can be done
by any technical people involved in its calculations.
4 – The method is very economic and leads to the attainment
of high packing efficiency of the raw materials, using low
cement quantities.
5 – Any variability of the packing characteristics of the
components is detected by the tapping density measurement
and the proportions are automatically corrected during the
sequential calculations.
ACKNOWLEDGEMENTS
The authors wish to thank to the CAPES for the Fellowship of
one of the authors (Danilo A. Bomfim) and to
FAPESP/CEPID/CMDMC for the research funding.
REFERENCES
[1] Mehta, P. K. and Monteiro, P. J. M. –“ Concrete Structure
Properties and Materials” – 2nd
edition - Editora Pini, São Paulo,
1994.(in Portuguese).
[2] Ramachandran, V. S. – “ Concrete Admixtures Handbook –
Properties, Science and Technology “ – Noyes Publications, New
Jersey , 1995.
[3] Bentur, A. and Cohen, M. D. – “ Effect of Condensed Silica Fume
on the Microstructure of The Interfacial Zone in Portland Cement
Mortars” – J. Am. Ceram. Society , vol.70 1987 …..
[4] Neville, A. M. –“ Properties of Concrete” – Pitman Publishing,
London, 1975
[5] Westman, A. E. R. and Hugill, H. R. – “ The Packing of Particles”
– J. Am. Ceram. Soc. 13 (1930) 767-779.
[6] Furnas, C.C. – “ Relation Between Specific Volume, Voids and
Size Compositions in Systems of Broken Solids of Mixed Sizes “ –
US Bureau of Mines Reports of Investigations vol. 1894 (1928).
[7] Andreasen, A.H. M. –“ Zur Kennits des Mahlgutes” –
Kolloidchemiche Beiheffe” – 27 (1928) 349-388.
[8] German, R. M. – “ Particle packing Characteristics” – 1st
edition,
Metal Powder Industries Federation Publication, Princeton, 1989.
[9] German, R. M. – “ The Role of particle Packing density in Powder
Injection Molding” – In Brookes, C. A., Reviews in Powder
Metallurgy and Physical Ceramics, 5 (1992) 81-110.
[10] Zheng, J. , Johnson, P. F. and Reed, J. S. – “ Improved equation of
the Continuous particle Size distribution for Dense packing” – J.
Am. Ceram. Society 73 (1990) 1392-1398.
[11] Hu, C., Larrard, F. –“Rheological Testing and Modeling of Fresh
High Performance Concrete”- Materials and Structures 18 (1995)
1-7.
Biographical Sketch of Authors
Danilo A. Bomfim – MS. In Materials Engineering from Universidade
Federal de São Carlos – presently at Saint Gobain Ceramic and Plastics –
Vinhedo – SP - Brazil.
Walter Libardi – Professor of Strength of Materials - Ph.D. in Structural
Engineering - from Escola de Engenharia de São Carlos – USP – São Carlos
– SP – Brazil
JOÃO B. BALDO – PROFESSOR OF CERAMICS- PH.D. IN
MATERIALS SCIENCE AND ENGINEERING FROM THE
UNIVERSITY OF WASHINGTON – SEATTLE - USA
Table I
Size ratios and volumetric percentage of three sets of spherically shaped particles of discrete (one and only size) sizes, for optimized packing of three sets of
particles.
Size Ratios
(R)
% Fine % Medium % Coarse % Relative Density
1:7:49 11,0 14,0 75,0 95,0
1:100:10000 10,0 23,4 66,6 91,6
1:7:77 10,0 23,0 67,0 90,0

I J E N S
Table II
General Characteristics of the cement used in the comparative study
Chemical Analysis
SiO2 (wt%) 15.00
Al2O3 (wt%) 4.26
Fe2O3 (wt%) 2.47
CaO (wt%) 59.05
MgO (wt%) 5.60
K2O (wt%) 1.00
Na2O (wt%) 0.17
SO3 (wt%) 3.06
CO2 (wt%) 1.01
Loss of Ignition (wt%) 4.58
Insoluble Residues (wt%) 3.80
True Density (g/cm3
)/(lb/cft) 3.09/192.91
Table III
Tapping densities (i) and packing efficiency (i/t) for each of the materials used.
Material mass (kg)/(lb) Vol as poured
( liters )/(cft)
Vol after tapping
(liters)/(cft)
i ( g / cm3
)
(lb/cft)
PFi = (i/t)
Basalt
Aggregate
1.000/2.20 0.800/0.02825 0.650/0.02295 1.54/96.14 PFca = 0.565
River Sand 1.000/2.20 0.600/0.02119 0.550/0.01942 1.82/113.62 PFs = 0.686
Cement 1.000/2.20 0.890/0.03143 0.600/0.02119 1.67/104.25 PFc = 0.529
Table IV
Batches of the two Concretes formulated using the two different dosing procedures. The batch F-01 was produced under the new developed procedure, while
batch A-01 was produced under the ABCP procedure.
F-01 (water/cement = 0,35) A-01 (water/cement = 0,40)
Matrix volume (%) 42 Matrix volume (%) 57
Cement (kg / m3
)
(lb/cft)
254
15.86
Cement (kg / m3
)
(lb/cft)
356
22.22
Sand (kg / m3
)
(lb/cft)
747
46.63
Sand(kg / m3
)
(lb/cft)
848
52.94
Total mixing water (kg / m3
) (lb/cft) 89
5.56
Total mixing water(kg / m3
)
(lb/cft)
142
8.86
Coarse aggregate (kg / m3
)
(lb/cft)
1491
93.08
Coarse aggregate(kg / m3
)
(lb/cft)
1032
64.43
Slump (mm)
(in)
30
11.81
Slump (mm)
(in)
32
12.60
Density (g / cm3
)
(lb/cft)
2,64
164.81
Density (g / cm3
)
(lb/cft)
2,20
137.34
Relative density (%) 98,51 Relative density (%) 78,90

I J E N S
Fig. 1. The effect of particle shape on the packing efficiency of a bed of particles [8]
Fig. 2. Flow Chart for the New Dosing Procedure. (For the mixing order see Figure 4).

I J E N S
Fig. 3. Scheme of the individual concrete components tapping density measurement (a) Volume occupied by the as poured individual concrete component (b)
Volume occupied by the individual concrete component after vibration (15 seconds 60 Hz 2mm amplitude).
Fig. 4. Flow chart of the developed mixing sequence of the components for the concrete preparation.
0
20
40
60
80
100
120
0 1 2 3 4 5 6 7 8 9 10
C
u
m
u
la
tiv
e
M
a
s
s
(w
t%
)
Sieve Aperture (mm)
Superior Limit
This Study
Inferior Limit

I J E N S
Fig. 5. Grain Size distribution of the river sand used in this investigation together with the superior and inferior limits of concrete sands established by the
Brazilian Standard NBR–7127/82 (equivalent to ASTM C144).
Fig. 6. Compressive Strength values obtained for the compositions F-01 and A-01 at the ages of; 7, 14 and 28 days .
Strength versus Curing Age
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30
Curing Age (days)
Strength(MPa)
Sample F-01
Sample A-01

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