Packing density of cementitious materials: part 1—measurement using a wet packing method

ORIGINAL ARTICLE

Packing density of cementitious materials:part 1—measurement using a wet packing method

Henry H. C. Wong Æ Albert K. H. Kwan

Received: 3 March 2007 / Accepted: 29 May 2007 / Published online: 19 June 2007

� RILEM 2007

Abstract The packing characteristics of the cemen-

titious materials have great influence on the perfor-

mance of a concrete mix, but there is so far no

generally accepted method of measurement. Herein, a

new method, called the wet packing method, is

developed. It mixes the cementitious materials with

water and then measures the apparent density and

voids content of the resulting mixture at varying

water/cementitious materials ratio to characterise the

packing behaviour of the cementitious materials.

Trial mixing and testing revealed that the mixing

procedure is crucial to the success of the test method.

To ensure thorough mixing within a reasonable time,

a special mixing procedure is adopted. Using this

method, the packing characteristics of pure cement

and blended cementitious materials under different

conditions have been measured. Based on the results

so obtained, it is advocated that the packing density

and water demand should be measured directly using

a wet packing method rather than indirectly by any

consistence test because the water content at any

preset consistence is not necessarily the same as the

minimum water content needed to fill up the voids.

Some useful applications of the new method are

illustrated in Part 2 of this paper.

Keywords Cementitious materials � Consistence �Packing density � Water demand

1 Introduction

Early in the 1960s, Powers [1] had suggested that we

could imagine a concrete mixture to be composed of

aggregate and cement paste. As conceived by Powers,

the cement paste has to first fill up the voids between

aggregate particles and the ‘‘excess’’ paste will then

disperse the aggregate particles to produce a thin

coating of paste surrounding each aggregate particle

for lubricating the concrete mix. In general, the

higher the packing density of the aggregate is, the

smaller will be the volume of voids to be filled and

the larger will be the amount of excess paste for

lubrication. Hence, a higher packing density could at

a fixed paste volume, lead to a better workability and

for a given workability, lead to a reduced paste

demand. Following the geometric similarity princi-

ple, the packing density of the cementitious materials

should have a similar effect; an increase in packing

density of the cementitious materials should improve

the flowability of the paste and/or reduce the water

demand.

In 1994, by maximising the packing density of the

cementitious materials using a packing model,

H. H. C. Wong � A. K. H. Kwan (&)

Department of Civil Engineering, The University of Hong

Kong, Pokfulam Road, Hong Kong, Hong Kong SAR,

China

e-mail: [email protected]

H. H. C. Wong

e-mail: [email protected]

Materials and Structures (2008) 41:689–701

DOI 10.1617/s11527-007-9274-5

DeLarrard and Sedran [2] had reduced the water/

cementitious materials (W/CM) ratio to as low as 0.14

by weight and thereby achieved concrete strengths of

165–236 MPa. One year later in 1995, by maximising

the packing of all granular materials in the concrete

mix using the same packing model and also applying

other advanced production techniques, Richard and

Cheyrezy [3] had achieved concrete strengths in the

order of 200–800 MPa. Besides reducing the W/CM

ratio to increase strength, such strategy may also be

employed without reducing the W/CM ratio to

increase workability. In 1996, Sedran et al. [4] had

applied the packing theory to the design of self-

consolidating concrete and based on the successful

outcome concluded that the performance optimisation

of concrete is mainly a matter of improving the

packing density of its granular skeleton.

Subsequently, Lange et al. [5] showed that

improving the packing density of the cementitious

materials by blending ordinary cement with a finer

blast furnace slag based cement could significantly

reduce the water demand and enhance the overall

properties of the mortar produced. More recently,

Jones et al. [6] studied both theoretically and

experimentally the effectiveness of different types

of fillers in minimizing the voids content of the

cementitious materials. It was found that the effec-

tiveness of the fillers is dependent on whether a

superplasticiser is present and that in general finer

fillers are more effective especially when a super-

plasticiser has been added to disperse the particles

and reduce agglomeration.

The concept of particle packing is useful also in

other fields of engineering [7] and throughout the

years has advanced to a high degree of sophistication.

However, although a number of theoretical packing

models have been developed, accurate measurement

of the packing density of very fine materials, such as

the cementitious materials used in concrete, has

remained a difficult task. The packing density of

cementitious materials has been measured in terms of

the water demand arbitrarily taken as the water

content required for a certain consistence, but such

water content is not really the same as that needed for

filling up the voids. Moreover, since there may be air

entrapped, the packing density evaluated just from

the water demand may not be accurate. A review of

the existing methods of packing density measurement

is given in the next section. Apart from the review,

the present study aims to develop a new method that

could overcome the afore-mentioned problems.

2 Existing methods of packing density

measurement

The existing methods may be broadly classified into

direct methods that determine the packing density

directly from the bulk density of the packed particles

and indirect methods that determine the packing

density indirectly by consistence tests. They do not

yield the same results and in fact are measuring

different parameters. Details of these methods are

reviewed in the following.

2.1 Direct methods

The British Standard BS 812: Part 2: 1995 [8] has

specified a dry packing method for measuring the

bulk density of aggregate, from which the voids

content and packing density may be determined.

There are two versions, one for coarse aggregate

under uncompacted or compacted conditions and the

other for filler under compacted condition. This

methodology is widely used also in the field of

powder technology. However, Svarovsky [9] warned

that the bulk density of a powder is very much

dependent on the state of compaction and it must be

explicitly stated whether the bulk density measured is

the aerated, poured, tapped or compacted bulk

density. Moreover, the exact treatment to be applied

to the powder sample has to be standardized as this

could affect the test results and their interpretation.

Another major problem with dry packing is that

with decreasing particle size, the adhesion phenom-

ena arising from Van der Waals and electrostatic

forces between the particles become more and more

important, causing agglomeration that increases the

voids content [10]. According to Pietsch [11], the

critical size is approximately 100 mm. At a smaller

size, the ratio of inter-particle force to gravity is

greater than unity and agglomeration is likely to be

significant. That is why the packing behaviour of fine

particles is different from that of coarse particles. In

general, the dry packing method would tend to

overestimate the voids content and underestimate the

packing density of fine particles.

690 Materials and Structures (2008) 41:689–701

The authors have actually applied the dry packing

method to cementitious materials and found that the

measured packing density results were unreasonably

low compared to those obtained using the proposed

wet packing method (the comparison will be pre-

sented later in this paper). Serious agglomeration was

observed during dry packing and thus unless this

problem has been completely resolved, the dry

packing method is not suitable for measuring the

packing density of cementitious materials, of which

the grain sizes are generally smaller than 100 mm.

2.2 Indirect methods

Virtually all the indirect methods measure the voids

content of a sample of cementitious materials in

terms of the water demand taken as the minimum

water content needed for the cementitious materials

to form a paste and achieve a certain consistence.

Such practice is based on the faith that for any

cementitious materials, there is a minimum water

content for the formation of a paste and at this

minimum water content, the voids content is also

minimum. In many cases, it is further assumed that

there is no air entrapped in the paste and so the

volume occupied by this minimum water content may

be taken as the minimum voids content of the

cementitious materials from which the packing

density may be evaluated.

The simplest way of measuring the water demand

is to follow the standard consistence test, as specified

in BS EN 196: Part 3: 1995 [12] or other recognized

standards. In the standard consistence test, the Vicat

apparatus is used and the consistence of the paste is

measured in terms of the penetration depth of the

plunger. To further simplify the test, the change of

penetration depth with water content is not fully

explored and only the water content at which the

penetration depth is equal to 34 ± 1 mm is arbitrarily

taken as the water content for standard consistence. It

is assumed that this water content for standard

consistence is the same as the water demand of the

cementitious materials.

Different researchers measured the water demand

in different ways. Lange et al. [5] used the standard

consistence test method without adding any plasti-

ciser or superplasticiser. Jones et al. [6] carried out

standard consistence tests both with and without

superplasticiser added and obtained for each mixture

of cementitious materials, two water demand values,

one without any superplasticiser added and the other

with a certain dosage of superplasticiser added. Their

results revealed that the water demand was dependent

on the presence of superplasticiser and that the water

demand measured with a superplasticiser added

generally agreed better with the theoretical packing

model.

Whilst adopting the standard consistence test as

specified in BS EN 196 for determining the water

demand, Dewar [13] suggested to allow for an air

content of say 1.5% in the paste when evaluating the

voids content of the cementitious materials. Bigas

and Gallias [14] also followed the standard consis-

tence test method of BS EN 196 but instead of

assuming an arbitrary value of air content in the paste

actually measured the apparent density of the paste to

allow for the presence of air. Since the effect of the

air content on the bulk volume of the paste has been

taken into account, their method of determining the

voids content and packing density should be more

accurate than the other methods.

On the other hand, DeLarrard [15] suggested to

measure the water demand without going through the

standard consistence test. He took the water demand

as the minimum water content for producing a thick

paste and assumed that any water content lower than

this minimum will only yield a humid soil. He also

advised that if any admixture with plasticising prop-

erties is to be used in the concrete mix, then the water

demand should be measured with the same dosage of

admixture added. In his method, the water demand is

simply measured by mixing the cementitious materi-

als with different amounts of water and finding the

water content that gives a consistence intermediate

between a humid soil and a thick paste. Without any

mechanical and quantitative measure, the consistence

of the paste has to be determined by manual judgment.

After the water demand is measured, the voids content

and packing density are evaluated with the air content

in the paste assumed to be zero.

Experience with the water demand tests indicated

that the mixing process during preparation of the

paste is more efficient for compacting the fine

particles than the normal combination of vibration

and pressure applied during dry packing and that as a

result the packing density achieved in a paste is

generally higher than that in a dry packed form.

Moreover, with the addition of a superplasticiser,

Materials and Structures (2008) 41:689–701 691

which disperses the particles and reduces agglomer-

ation, the packing density would be even higher.

Overall, the wet mixing method should yield higher

and more reliable packing density results than the dry

packing method.

However, the indirect methods are not without

problems. Firstly, the water demand has been taken as

the water content at a certain arbitrarily chosen level

of consistence but there is so far no evidence to prove

that at such consistence level, the water content is just

enough to fill up the voids. Secondly, as pointed out

by Iveson et al. [16], liquid-bound granules can exist

in different states of liquid saturation. In the pendular

state, the particles are held together by liquid bridges

at their contact points. In the capillary state, the

granules are saturated with surface liquid drawn back

into the voids under capillary action. Between these,

there is a transitional funicular state in which the

voids are not fully saturated. Since the transition from

pendular to capillary state (in the present context, this

corresponds to transition from a humid soil to a thick

paste) is gradual and not clear-cut, it is difficult to

judge whether the capillary state, at which the liquid

is just enough to fill up the voids, has been reached.

Thirdly, the air content in the paste is often neglected,

resulting in underestimation of the voids content and

overestimation of the packing density.

Having considered the above, it may be concluded

that the water content at a certain fixed consistence is

not a good measure of the voids content of cemen-

titious materials. It is an important parameter in its

own right but should not be used to evaluate the

packing performance of cementitious materials. To

measure the voids content and packing density of

cementitious materials, a new method not relying on

consistence measurement is needed, as presented in

the next section.

3 Proposed method of packing density

measurement

3.1 Definitions of terms

At the outset, the terms used to describe the packing

behaviour of cementitious materials are defined to

avoid misunderstanding, as different researchers are

using different terms with different definitions caus-

ing a lot of confusion.

In a bulk volume of granular material, the voids

are the interstitial space between the solid particles.

The voids content (denoted by e) is defined as the

ratio of the volume of voids to the bulk volume of the

granular material, while the voids ratio (denoted by u)

is defined as the ratio of the volume of voids to the

solid volume of the granular material. They are inter-

related by the following equation:

e ¼ u

1 þ uð1Þ

The voids may be filled with water or air or both. The

water content (denoted by ew) is defined as the ratio

of the volume of water to the bulk volume of the

granular material and the water ratio (denoted by uw)

is defined as the ratio of the volume of water to the

solid volume of the granular material. On the other

hand, the air content (denoted by ea) is defined as the

ratio of the volume of air to the bulk volume of the

granular material and the air ratio (denoted by ua) is

defined as the ratio of the volume of air to the solid

volume of the granular material. They are related to

each other by:

ew ¼uw

1 þ uw þ ua

ð2Þ

ea ¼ua

1 þ uw þ ua

ð3Þ

The solid concentration of the granular material

(denoted by /) is defined as the ratio of the solid

volume of the granular material to the bulk volume of

the granular material. It may be evaluated using the

following equation:

/ ¼ 1� e ¼ 1

1 þ uð4Þ

3.2 Development of the proposed wet packing

method

The proposed method has the following characteristics:

(1) It is a wet packing method. In other words, it

mixes the given cementitious materials with

water to form water-bound granules, from which

the voids content and solid concentration are

measured.


(2) It does not rely on any consistence observation

or measurement. Instead, the W/CM ratio is

varied and the resulting voids content and solid

concentration are determined by measuring the

apparent density of the granules.

(3) Since the voids content and solid concentration

are evaluated from the apparent density, the air

content is automatically taken into account. In

fact, the air content may also be evaluated for

analysis.

(4) The mixing procedure, which has been found

during trials to be crucial to the success of the

method, is specially designed. Conventional

mixing procedure requires a long time to

achieve thorough mixing when the water con-

tent is low and/or very fine materials are dealt

with. The mixing procedure adopted herein

would allow thorough mixing to be achieved

within a much shorter time.

During the development of the proposed method,

several mixing procedures had been tried. At the

beginning, the mixing procedure in BS EN 196 was

followed. As per BS EN 196, the cement and water

were added in a single batch into the mixing bowl and

then the mixture was stirred for 3 min. However, it

was found that this mixing procedure worked well

only when the water ratio was higher than 0.6. At a

lower water ratio, the mixing time of 3 min was found

to be insufficient. With the mixing time extended, it

was revealed that the consistence would improve with

time up to a certain limit. Very often, the mixture

remained for a long time in the form of discrete

water-bound granules with dry surfaces and it was

only when the mixing time was considerably pro-

longed then the granules eventually coalesced

together to form a thick paste. When the cement

was blended with very fine materials such as

condensed silica fume, the required mixing time

was even longer and could be as long as 60 min.

Hand mixing had also been tried but the situation was

no better.

As explained by Iveson et al. [16], when mixing a

powder and water together, the following processes

take place: ‘‘wetting and nucleation’’, and ‘‘consol-

idation and growth’’. During wetting and nucleation,

the water distribution is initially very poor and only

discrete water-bound granules are formed. The pores

inside the granules are saturated but the surfaces

remain dry. Later on, consolidation and growth occur,

as the ‘‘excess’’ water in the mixture, if any, wets the

surfaces of the granules or the water inside the

granules are squeezed to the surfaces to facilitate

coalescence of the granules together. When the water

content is high such that there is excess water to wet

the surfaces of the granules, the consolidation and

growth process is quite fast resulting in the formation

of a slurry or paste within minutes. However, when the

water content is low, the coalescence will be depen-

dent mainly on the water-squeezing process, which is

in general very slow [17], leading to a much longer

mixing time required for forming a paste. The reason

why the mixing of finer materials and water together

takes a longer time is that the squeezing of water

through finer pores requires more energy and time.

To overcome the above problem, the authors have

adopted the strategy of avoiding the slow water-

squeezing process by keeping the mixture saturated

most of the time. When under-saturated, the granules

are not easy to be deformed or intermixed with each

other because of the capillary forces that give them

strength [16]. However, when saturated or over-

saturated, such strength is lost [18] and thorough

mixing can be achieved quite easily and quickly. To

keep the mixture saturated as far as possible, the

powder is added bit by bit instead of in a single batch

to the water during mixing. By so doing, at the

beginning, a slurry is formed. Then, as more powder

is added, the slurry is turned into an over-saturated

paste. When further powder is added by spreading it

evenly to the paste, the powder is very soon wetted

and intermixed with the paste. As the degree of

saturation gradually drops, the mixing becomes more

difficult but the total time needed is still much shorter

than that required when the conventional mixing

method of adding all the powder in a single batch is

used. The authors have tried different ways of adding

the powder to the water and arrived at the conclusion

that the best way is to first add one half of the powder

to the water to form a slurry and then add the

remaining half in four equal portions. The testing

procedure so developed is presented in the following.

3.3 Testing procedures

The packing density is not the same as the solid

concentration, which varies with the W/CM ratio.


When the W/CM ratio is relatively high, the solid

particles are dispersed in the water, resulting in a

solid concentration that decreases as the W/CM ratio

increases. On the other hand, when the W/CM ratio is

relatively low, the water content is not sufficient to

thoroughly mix with the solid particles to form a

paste, resulting in a solid concentration that decreases

as the W/CM ratio decreases. There is an optimum

W/CM ratio at which maximum solid concentration

is achieved. The maximum solid concentration,

which occurs when the particles are tightly packed

against each other, is taken as the packing density of

the granular material. Therefore, to determine the

packing density, it is necessary to carry out the wet

packing tests at different W/CM ratios over a range

wide enough to cover the optimum W/CM ratio. With

no previous test data to help decide on an appropriate

range, it is suggested to start at a W/CM ratio by

volume of 1.0 for the first test and then successively

reduce the W/CM ratio for further tests until the solid

concentration has reached a maximum value and then

dropped. It should be noted that the W/CM ratio by

volume is the same as the water ratio uw. All W/CM

ratios referred to hereafter are by volume.

The procedures of the proposed test method are

described below (note: all equipment used are the

same as those specified in BS EN 196: Parts 1–3):

(1) Set the W/CM ratio at which the wet packing

test is to be carried out. Weigh the required

quantities of water, cementitious materials and

superplasticiser (if any) and dose each ingredi-

ent into a separate container.

(2) If the cementitious materials consist of several

different materials blended together, pre-mix

the materials in dry for 2 min.

(3) Add all the water into the mixing bowl.

(4) Add half of the cementitious materials and

superplasticiser into the mixing bowl and run

the mixer at low speed for 3 min.

(5) Divide the remaining cementitious materials

and superplasticiser into four equal portions.

Add the remaining cementitious materials and

superplasticiser into the mixing bowl one

portion at a time and after each addition run

the mixer at low speed for 3 min.

(6) Transfer the mixture to a cylindrical mould and

fill the mould to excess. If compaction is to be

applied, apply compaction at this stage. Remove

the excess with a straight edge and weigh the

amount of paste in the mould.

(7) If so desired, the consistence of the paste may

be measured at this stage using the Vicat

apparatus. It should be noted however that the

consistence results will not be used to calculate

the packing density.

(8) Repeat steps (1) to (7) at successively lower W/

CM ratios until the maximum solid concentra-

tion, i.e. the packing density, has been found.

From the test results so obtained, the voids ratio, air

ratio and solid concentration may be determined as

depicted in the following. Let the mass and volume of

paste in the mould be M and V, respectively (the mould

used by the authors is of 62 mm diameter · 60 mm

height but any other mould of similar size may also be

used). If the cementitious materials consist of several

different materials denoted by a, b, c and so forth, the

solid volume of the cementitious materials Vc and the

volume of the water Vw in the mould may be worked

out from the following equations:

Vc ¼M

qwuw þ qaRa þ qbRb þ qcRcð5Þ

Vw ¼ uw Vc ð6Þ

in which qw is the density of water, qa, qb and qc are

the solid densities of a, b and c, and Ra, Rb and Rc are

the volumetric ratios of a, b and c to the total

cementitious materials. Having obtained Vc and Vw,

the voids ratio u, air ratio ua and solid concentration

/ may be determined as:

u ¼ V � Vcð Þ=Vc ð7Þ

ua ¼ V � Vc � Vwð Þ=Vc ð8Þ

/ ¼ Vc=V ð9Þ

4 Results and discussions

4.1 Materials

Three types of cementitious materials, namely,

ordinary Portland cement (OPC), pulverised fuel


ash (PFA) and condensed silica fume (CSF), were

used in the experiments. The OPC was a commonly

used cement, which had been tested to comply with

BS 12: 1996. The PFA was a classified ash, which

had been tested to comply with BS 3892: Part 1:

1982. The CSF was imported from Norway and

according to the supplier, it complied with ASTM C

1240-03. Their particle densities had been measured

in accordance with BS 812: Part 2: 1995 as 3110 kg/

m3, 2329 kg/m3 and 2202 kg/m3, respectively. The

particle size distributions of the OPC and PFA had

been measured by the laser diffraction method, as

depicted in Fig. 1. The particle size distribution of the

CSF had not been measured but according to the

supplier, the mean particle size of the CSF was about

0.15 mm.

Where required, a superplasticiser (SP) was added

during the tests. The SP used was a polycarboxylate-

based admixture. It has a solid mass content of 20%

and a relative density of 1.03. According to the

supplier, the normal dosage of this SP, measured in

terms of liquid mass, should be 0.5–3.0% by mass of

cement, but a higher dosage may also be used if

proven to be satisfactory by trial mixing. As the OPC,

PFA and CSF have different densities and it is the

solid volume rather than the mass that is more

important, the SP dosage is expressed in terms of the

liquid mass of SP per unit solid volume of the

cementitious material. The standard dosage of SP

(denoted by 1 · SP) used in this study was 93.3 kg/m3

(corresponding to the upper limit of the normal

dosage recommended by the supplier). Double dos-

age (denoted by 2 · SP) and triple dosage (denoted

by 3 · SP) were also used in some of the tests to

investigate the effects of SP dosage.

4.2 Presentation and interpretation of test results

During the tests, the apparent density (for voids ratio

and solid concentration evaluation) and the penetra-

tion depth (for consistence evaluation) of the paste

were measured. The results are presented in Fig. 2 by

plotting the voids ratio and penetration depth against

the W/CM ratio. In the voids ratio graph, a straight

line entitled ‘‘ea = 0’’ is drawn. This line is an

0

20

40

60

80

100

1 10 100

Particle size (µm)

Cum

ulat

ive

volu

me

(%)

PFA

OPC

Fig. 1 Particle size distributions of OPC and PFA

W/CM ratio by volume

Voi

ds r

atio

umin

uwb

ua

ε a = 0

uw


Pene

trat

ion

dept

h (m

m)

34 mm

u ws

Fig. 2 Presentation and interpretation of test results


equality line because ea = 0 when u = uw. The actual

air ratio ua (given by ua = u�uw) may be obtained as

the vertical distance between the voids ratio curve

and the ‘‘ea = 0’’ line. Several important parameters

can be obtained from the curves plotted. From the

lowest point of the voids ratio curve, the minimum

voids ratio umin and the basic water ratio uwb (the

water ratio yielding minimum voids ratio) can be

determined. From the penetration depth curve, the

water ratio at standard consistence uws can be

obtained. For many years, umin, uwb and uws have

been treated by many researchers as equivalent.

However, it will be shown from the test results that

they are not the same and should not be mixed up.

4.3 Packing of OPC

The test results for OPC with no SP or 1 · SP added

are presented in Fig. 3. From the results for OPC with

no SP added, it can be seen that at high W/CM ratio,

the voids ratio curve followed closely the ‘‘ea = 0’’

line indicating that the air content was then negligibly

small. As the W/CM ratio was reduced to lower than

0.900, the voids ratio curve started deviating from the

‘‘ea = 0’’ line because the air ratio had began to

increase. When the W/CM ratio reached 0.846, the air

ratio increased to around 2%. Further reduction of the

W/CM ratio to the basic water ratio of 0.750 yielded

a minimum voids ratio of 0.831 and a maximum solid

concentration of 0.546. At a W/CM ratio lower than

the basic water ratio, no paste could be formed and as

a result the voids ratio became very large. On the

other hand, the penetration depth results revealed that

the water ratio at standard consistence was 0.958.

The corresponding results for OPC with 1 · SP

added are similar in general trend to those for OPC

with no SP added. The major differences are that with

SP added, the basic water ratio changed from 0.750 to

0.525, the minimum voids ratio decreased from 0.831

to 0.607, the maximum solid concentration increased

from 0.546 to 0.622, while the water ratio at standard

consistence decreased from 0.958 to 0.554. These

changes demonstrated the effectiveness of the SP in

dispersing the cement particles. However, it should

be noted that regardless of whether SP has been

added, the basic water ratio is substantially lower

than the minimum voids ratio. In fact, at the basic

water ratio, the air content is quite large and the

water content is not sufficient to fill up the voids.

Furthermore, the water ratio at standard consistence

is quite different from the basic water ratio or the

minimum voids ratio. In other words, the water ratio

at standard consistence, which has long been used to

determine the water demand, is not really the same as

the minimum water ratio at which the water content is

just sufficient to fill up the voids.

4.4 Effects of SP dosage

Figure 4 shows the test results for OPC with different

dosages of SP added. It can be seen from these results

that when the dosage was increased from 1 · SP to

2 · SP, the basic water ratio changed from 0.525 to

0.480, the minimum voids ratio decreased from 0.607

0.4

0.6

0.8

1.0

1.2

0.4 0.6 0.8 1.0 1.2


Voi

ds r

atio

OPC (no SP)OPC (1xSP)

εa = 0

0

10

20

30

40

0.4 0.6 0.8 1.0 1.2


Pene

trat

ion

dept

h (m

m)

OPC (no SP)

OPC (1xSP)

Fig. 3 Test results for OPC with no SP or 1 · SP added


to 0.567 and the maximum solid concentration (i.e.

the packing density) increased from 0.622 to 0.638,

but when the dosage was further increased to 3 · SP,

the packing behaviour of the paste remained more or

less the same. From these values, it may be worked

out that the packing density increased only by 3%

when the dosage of SP was doubled or even tripled.

Hence, the addition of a higher dosage of SP than the

standard dosage (1 · SP) provided little further

improvement in packing performance and the stan-

dard dosage was already quite close to the saturation

dosage. It can also be seen from these results that

regardless of the SP dosage, the basic water ratio is

always substantially lower than the minimum voids

ratio whereas the water ratio at standard consistence

is neither equal to the basic water ratio nor equal to

the minimum voids ratio.

4.5 Effects of compaction

In order to investigate the effects of compaction, a

series of tests was carried out with each cement-water

mixture compacted by vibration before its apparent

density and penetration depth were measured. The

compaction was applied by filling the cement-water

mixture into the mould of the Vicat apparatus in four

equal layers and vibrating the mould after adding

each layer. The vibration was carried out by mount-

ing the mould onto the vibration machine, which was

normally used for compacting mortar cubes in

compliance with BS 4550: Part 3: 1978 [19], and

running the motor of the machine each time for

exactly 30 s.

The test results so obtained for OPC with 1 · SP

added and with or without compaction applied are

compared in Fig. 5. At W/CM ratio higher than 0.700,

the effect of compaction was insignificant because

even without compaction the paste was saturated with

little air inside. When the W/CM ratio was decreased

to around 0.600 or lower, the compaction started to

take effect as more air tended to be entrapped in the

paste during mixing. After the compaction was

applied, the apparent density of the paste was

increased and the voids ratio decreased. It had also

been observed that at W/CM ratio lower than 0.500,

the cement-water mixture appeared more like a non-

cohesive soil before compaction and was turned into a

cohesive paste after compaction. At the end, the

compaction demonstrated its effectiveness by reduc-

ing the basic water ratio from 0.525 to 0.450 and the

minimum voids ratio from 0.607 to 0.508, and

increasing the packing density from 0.622 to 0.663.

From Fig. 5, it can also be seen that along with the

reduction in voids ratio, there was also a reduction in

penetration depth after compaction. This was due to

densification of the solid particles, which increased

the penetration resistance. As a result, the water ratio

at standard consistence was increased from 0.554 to

0.589.

4.6 Effects of blending with PFA or CSF

To demonstrate the usefulness of the new test

method, another series of tests was carried out to

0.4

0.5

0.6

0.7

0.8

0.4 0.5 0.6 0.7 0.8


Voi

ds r

atio

OPC (1xSP)OPC (2xSP)OPC (3xSP)

εa = 0

0

10

20

30

40

0.4 0.5 0.6 0.7 0.8


Pene

trat

ion

dept

h (m

m)

OPC (1xSP)OPC (2xSP)OPC (3xSP)

Fig. 4 Test results for OPC with different dosages of SP added


evaluate the effects of blending OPC with PFA or

CSF. Two cementitious materials mixtures have been

prepared, one containing 75% OPC plus 25% PFA

and the other containing 85% OPC plus 15% CSF (all

percentages are by volume). The SP dosage was fixed

at 1 · SP, while the W/CM ratio by volume was

varied from 0.800 to lower than the basic water ratio.

The test results so obtained are compared to those for

pure OPC with the same SP dosage in Fig. 6.

It is evident from the comparison that blending

OPC with either PFA or CSF could at all W/CM

ratios significantly decrease the voids ratio. With

25% of the OPC replaced by an equal volume of

PFA, the minimum voids ratio decreased from 0.607

to 0.558 (8% decrease) and the packing density

increased from 0.622 to 0.642 (3% increase). On the

other hand, with 15% of the OPC replaced by an

equal volume of CSF, the minimum voids ratio

decreased from 0.607 to 0.422 (30% decrease) and

the packing density increased from 0.622 to 0.703

(13% increase). The improvement in packing density

may be attributed partly to the filling effect of PFA

and CSF, which reduces the voids volume by filling

up the gaps between the OPC particles, and partly to

the spherical shape of the PFA and CSF particles,

which allows better packing to be achieved [20, 21].

CSF is more effective than PFA in improving the

packing density because of the greater filling effect

arising from its ultra-high fineness.

0.4

0.5

0.6

0.7

0.8

0.4 0.5 0.6 0.7 0.8


Voi

ds r

atio

OPC (no compaction)OPC (compaction)

εa = 0

0

10

20

30

40

0.4 0.5 0.6 0.7 0.8


Pene

trat

ion

dept

h (m

m)

OPC (no compaction)OPC (compaction)

Fig. 5 Test results for OPC with or without compaction

applied

0.3

0.4

0.5

0.6

0.7

0.8

0.3 0.4 0.5 0.6 0.7 0.8


Voi

ds r

atio

Pure OPC75%OPC+25%PFA

85%OPC+15%CSF

εa = 0

0

10

20

30

40

0.3 0.4 0.5 0.6 0.7 0.8


Pene

trat

ion

dept

h (m

m)

Pure OPC75%OPC+25%PFA85%OPC+15%CSF

Fig. 6 Test results for blended cementitious materials


However, the improvement in packing density

would not be apparent if the dry packing method was

used to determine the packing density. The packing

densities of pure OPC and the (75% OPC + 25%

PFA) and (85% OPC + 15% CSF) mixtures have also

been measured by the dry packing method. During

dry packing, the specified proportions of OPC, PFA

and CSF were pre-mixed and then filled into a 45 mm

diameter · 45 mm height cylindrical mould in five

successive layers, each tapped 40 times by a 10 mm

diameter rod. After tapping, the mixture inside the

mould was weighed for determination of packing

density. The results so obtained are compared to

those by the proposed wet packing method in Table 1,

from which it can be seen that the packing densities

measured by the dry packing method are far too low

and that the increase in packing density by blending

OPC with CSF would not be revealed by the dry

packing method. Aggregation, coating and caking,

which are signs of strong inter-particle force and

agglomeration [11], were observed during dry pack-

ing. It may thus be inferred that agglomeration was

the main reason for the low packing densities

obtained by the dry packing method.

4.7 Significance of umin, uwb and uws

Table 2 summaries the various values of umin, uwb

and uws obtained in the present study. It is evident

that these three ratios are not the same. The minimum

voids ratio umin is of importance because it may be

used to evaluate the packing density of the given

mixture of cementitious materials. The basic water

ratio uwb is the optimum W/CM ratio at which the

voids ratio is minimum. Since the corresponding air

ratio ua is not equal to zero, the basic water ratio must

not be taken as the minimum water ratio at which the

water is just sufficient to fill up the voids.

From Figs. 3–6, it can be seen that, in general, at a

W/CM ratio lower than the minimum voids ratio umin,

there would be a significant amount of air voids

inside the paste but at a W/CM ratio just slightly

higher than the minimum voids ratio umin, the amount

of air voids inside the paste would become insignif-

icant (as revealed by the variation of the air ratio ua

with the W/CM ratio). Hence, the minimum voids

ratio umin may also be taken as the minimum water

ratio at which the water content is just sufficient to fill

up the voids. In fact, the minimum voids ratio umin

should be regarded as the absolute minimum W/CM

ratio to be used in concrete mix design because a W/

CM ratio lower than this would lead to an unaccept-

ably large air content.

The water ratio at standard consistence uws has

long been used to determine the water demand.

However, it is quite different from both the basic

water ratio and the minimum voids ratio. Further-

more, in the case of OPC with 1 · SP added, the

compaction applied reduced the basic water ratio and

the minimum voids ratio but at the same time

increased the water ratio at standard consistence.

Hence, the water ratio at standard consistence cannot

be a physically true measure of the minimum voids

ratio or the minimum water ratio.

5 Conclusions

The existing methods of measuring the packing

density of cementitious materials have been reviewed

and their problems identified. It was found that the

dry packing methods are afflicted by agglomeration

while the common practice in the wet mixing

Table 1 Packing densities measured by dry and wet packing

methods

Mix proportions Dry packing

method (with

tapping applied)

Wet packing method

(with 1 · SP added

but no compaction

applied)

Pure OPC 0.514 0.622

75% OPC

+ 25% PFA

0.539 0.642

85% OPC

+ 15% CSF

0.480 0.703

Table 2 Summary of voids ratio and water ratio results

Cementitious mixture umin uwb uws

OPC (no SP) 0.831 0.750 0.958

OPC (1 · SP) 0.607 0.525 0.554

OPC (2 · SP) 0.567 0.480 0.505

OPC (3 · SP) 0.574 0.480 0.483

OPC (1 · SP and compaction) 0.508 0.450 0.589

75% OPC + 25% PFA (1 · SP) 0.558 0.458 0.473

85% OPC + 15% CSF (1 · SP) 0.422 0.358 0.401


methods of determining the water demand as the

water content at a certain preset consistence is not

really appropriate. To resolve these and other prob-

lems, a new method, which is a wet packing method

not relying on consistence measurement, has been

developed. It mixes the cementitious materials with

water at different water/cementitious materials ratios,

determines the voids ratio and solid concentration of

each resulting mixture by measuring its apparent

density rather than consistence, and takes the max-

imum solid concentration achieved as the packing

density of the cementitious materials. A special

mixing procedure of adding the cementitious mate-

rials bit by bit to the water so as to keep the mixture

saturated as far as possible is adopted to ensure

thorough mixing within a reasonable time.

The new method has been applied to study the

basic packing behaviour of a common cement, the

effects of superplasticiser dosage, the effects of

compaction and the effects of blending cement with

pulverised fuel ash or condensed silica fume. From

the test results, the basic water ratios, the minimum

voids ratios and the water ratios at standard consis-

tence of the various cementitious materials under

different conditions have been obtained. These

revealed that the basic water ratio, the minimum

voids ratio and the water ratio at standard consistence

are not the same. Generally, the basic water ratio is

substantially lower than the minimum voids ratio.

This is because at the basic water ratio, there is

always some air in the paste (i.e. the paste is not

saturated). More importantly, the minimum voids

ratio may be taken as the minimum water ratio at

which the water is just sufficient to fill up the voids.

Lastly, since there is no logical relation between the

water ratio at standard consistence and the minimum

voids ratio, the traditional practice of determining the

water demand from the water ratio at standard

consistence is incorrect and should be abandoned.

The wet packing tests conducted herein have

shown quantitatively in a correct manner for the first

time (to the best of the authors’ knowledge) the actual

increase in packing density that could be achieved by

blending cement with either pulverised fuel ash or

condensed silica fume. Further studies on triple

blending of cement, pulverised fuel ash and con-

densed silica fume, and on how the flow of the

cement paste could be improved by maximising the

packing density of the cementitious materials have

also been carried out, as reported in Part 2 of the

paper.

Acknowledgement The work described in this paper was

fully supported by a grant from the Research Grants Council of

the Hong Kong Special Administrative Region, China (Project

No. HKU 7139/05E).

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Documents

Packing density of cementitious materials: part 1—measurement using a wet packing method