THE EFFECT OF MICROSTRUCTURE
ON THE PROPERTIES
OF FOAMED CONCRETE
MASTER OF ENGINEERING (STRUCTURAL ENGINEERING)
In the
FACULTY OF ENGINEERING
UNIVERSITY OF PRETORIA
© University of Pretoria
THE EFFECT OF MICROSTRUCTURE
ON THE PROPERTIES
OF FOAMED CONCRETE
Foamed
consisting
concrete
is produced
when a foaming
agent
IS
added
to cement-based
of cement, water, cement e;\.1ender and filler. This lightweight
can contribute
development
significantly
to uplift
of infrastnlchlre.
disadvantaged
conununities
building
when
To achieve this goal, in depth research
slurry,
material
used during
the
into the stmchlral
properties of the material is essential.
Since 1992 tests to determine struchlral properties of foamed concrete have been conducted at
the University of Pretoria. The results show that the compressive
strength of foamed concrete
is a function of age, ash/cement ratio and porosity and for a given porosity and age there is an
optimum
ash content, resulting
in the maximum
compressive
strength.
The focus of this
research is therefore on foamed concrete mixhlfes with target densities varying between 700
kglm3 and 1500 kg/mJ where the question that needed to be answered is: what is the influence
of the microstnlchlre
on the physical and stmchlral properties of these mixhlres?
The study is restricted to the effect of the microstmchlre
properties
on the relation between the physical
(such as density, ash / cement ratio and porosity),
and the stnlchrral
property
(compressive strength) of foamed concrete.
In order to evaluate the influence of the microstnlchlre
to develop parameters
to explain
on these relationships
and quantity the microstnlchlre
it was necessary
of foamed concrete.
An
image processing
parameters
and analysis system was applied to deyelop the air-void size distribution
and the air-void spacing parameters.
These parameters were used to represent the
microstmcture
(entrained air-void stmchlre) of the foamed concrete mixhrres. It was therefore
now possible
to plot graphs showing
the effect of the microstmchlre
on the physical and
struchlral properties of foamed concrete.
It was established
that the 28-day
dry densities
distribution.
In him the air-void size distribution
and 28-day
compressive
strength
of foamed
influence on the spacing of air-voids
have an influence
on the air-void
size
has an influence on the average % porosities
concrete.
The 28-day dry del!sities haye no
and in turn the spacing of the air-voids does not have
any influence on the average % porosity and 28-day compressive strength.
Skuimbeton
word vervaardig
deur 'n sh.l.limmiddel by sement, water en sementaanvuller
te
voeg. Hierdie liggewig beton kan met welslae gebmik word in die opbou van infra stmk.1uur
by minder
bevoorregte
gemeenskappe.
Om hierdie doel te bereik
is dit nodig
om die
stmkturele eienskappe van die boumateriaal te ondersoek.
Sedert 1992 word daar by die Universiteit van Pretoria navorsing gedoen oor die stmh.1urele
eienskappe "an skuimbeton.
van die shlimbeton,
Daar is gevind dat die dmksterkte
'n funksie is van die ouderdom
die as / sement verhouding en die porositeit. Die maksimum dmksterkte
by "n spesifieke ouderdom van die sh.l.limbeton \\ord verkry by 'n optimlml as hoeveelheid in
die mengsel.
Die doel van hierdie navorsing
is om te bepaal of die mikro-stmkhutr
skuimbetol1 enige invloed het op die fisiese en strukhlrele einskappe van die materiaal.
mengsels
van
Slegs
met teiken digthede hlssen 700 kg/m3 en 1500 kg/m3 word beshldeer in hierdie
navorsing.
Die Shldie word beperk tot die effek van die mikro-stmkhutr
op die fisiese eienskappe
sement verhoudil1g, digtheid en porositeit) en stmh.turele eienskappe (28 dae dmksterkte)
(as /
van
die spesifieke mengsels.
"n Fotografiese
beeld prossesering
en analitiese stelsel is gebmik om parameters te ontwikkel
om die mikro-struh.111ur van skuimbeton
te h.wantitiseer. Twee parameters
is ontwikkel,
die
eel1 om die verdeling van die grote van die ingemengde lug borrels aan te dlli en die ander een
om die spaslenng
van die ingemengde
hierdie parameters
die mikro-stmktuur
om die effek van die mikro-stmktuur
lug borrels in die mengsel aan -te dui.
van skuimbeton verteenwoordig
Aangesien
was dit nou moontlik
op die fisiese- en stmkturele eienskappe van sJ...l.limbeton
te bepaal.
Die resultate
van die studie dui aan dat die 28-dae droe digtheid wel 'n invloed het op die
verdeling van die grote van die lug borrels. Die verdeling van die grote van die lug borrels het
weer 'n effek op die gemiddelde porositeit
en 28-dae dmk sterkte. Die 28-dae droe digtheid
het geen invloed op die spasiering van die lug borrels en die die spasiering van die lug borrels
op sy beurt het ook nie 'n invloed op die gemiddelde porositeit en 28-dae dmk sterkte nie.
I wish to express my appreciation
to the following organisations
and persons \vho made this
dissertation possible:
Mr. D. Mostert
Mr. 1. Pretorius
Mrs. 1. Callanan
Miss B. Le Roux
Miss G. Veldman
PersOlUlel of the concrete
laboratory
of the Civil Engineering
depamnent
of the
University of Pretoria.
•
My family, especially my husband and two children for their encouragement
sacrifices they made.
•
To my creator.
and all the
l.
INTRODUCTION
1.1
Background
1.2
Objectives of stl1dy
1.3
Scope of study
1.4
Study methodology
1.5
Organisation
of dissertation
Introduction
Material composition
3.2
2.2.1
Cement paste
2-1
2.2.2
Foam
2-3
Material properties
2-6
2.3.1
Relation between density and compressive strength
2-7
2.3 2
Relation between density and porosity
2-8
2.3.3
Relation between porosity and compressive strength
2-8
2.3.4
Effect of ash content porosity and age on compressive strength
2-11
Microstmcture
2-12
Conclusions
2-15
Methods for measurement of air-void parameters in air-entrained
hardened concrete
3.2.1
Linear traverse method
3.2.1.1 Air-void stmcture parameters
3.2.2
Modified point-count method
3-5
3.2.3
Image analysis in conjunction with linear traverse method
3-5
3.2.4
Image processing method
3-6
3.2.4.1 Air-void stmctllfe parameters
3-10
3.3
Rosin-Ranunler
3.4
Conclusions
3-12
4.
EXPERIMENT AL PROCEDURE
4-1
4.1
Introduction
4-1
4.2
Composition of foamed concrete mi:-..1ures
4-2
4.3
Density
4-2
4.4
Compressive strength
4-3
4.5
Air-void stmcture
4-3
4.6
distribution function
3-7
4.5.1
Image analysis
4-3
4.5.2
Sample preparation
4-5
4.5.3
Identification of air-voids
4-7
4-9
Porosity
4.6.1
Apparatlls
4-9
4.6.2
Experimental procedure
4-10
Mixtures
Results
Introduction
Air-void shape
Air-void size distribution
6.3.1
Air-void size distribution parameters
6.3.1.1 Rosin-Rammler
air-void diameter distribution
parameters
6-7
Air-void spacing
6-11
Conclusions
6-16
6.5.1
Air-void shape
6-16
6.5.2
Air-void size and size distribution
6-16
Introduction
7-1
Effect of density on air-void stmcture
7-1
7.2.1
Air-void size distribution
7-1
7.2.2
Air-void spacing
7-4
Effect of ash / cement ratio on air-void stmcture
7-5
7.3.1
Air-void size distribution
7-5
7.3.2
Air-void spacing
7-6
Effect of air-void stmchlre on porosity
7-7
7.4.1
Air-void size distribution
7-7
7.4.2
Air-void spacing
7-8
Effect of air-void struchrre on compressive strength
7-9
7.5.1
Air-void size distribution
7-9
7.5.2
Air-void spacing
7-13
Effect of air-void stmchlre on predicted long term
compressive strength
7-13
Conclusions
7-16
Conclusions
Reconunendations
APPENDIX
A
Air-void size distribution of mixes
APPENDIX
B
Exponential fit for cumulative percentage oversize airvoid diameters of mixhlres
APPENDIX
C
Modified Rosin-Rarllinler void distribution of mixes
APPENDIX
D
Macro in micros oft. excel for calculation of void spacing
APPENDIX
E
Air-void spacing distribution of mixes
APPENDIX
F
Exponential fit for cumulative percentage oversize airvoid spacing of mixtures
Smumary of exponential fits for the cumulative
for specific ash! cement ratios
%, {)versize graphs
of foamed concrete mi.\1ures
5-2
Table 5.1:
Composition
Table 5.2:
Volume ratios of mixtures
5-3
Table 5.3:
Densities of mi.\1ures
5-4
Table 5.4:
Porosity and 28-day compressive strength of mixtures
5-5
Table 6.1:
x- and
Y -chords to determine shape of air-voids
6-3
Table 6.2:
Fitted functions of oversize air-void diameter distribution
6-8
Table 6.3:
Rosin-Ranunler
6-10
Table 6.4:
Fitted function and parameters of oversize air-void diameter
air-void size distribution parameters
distribution
6-12
Fitted functions and air-void spacing parameters
6-17
Fitted functions for the relationship between the 28-day dry
density and the 28-day compressive strength
Fitted functions for the relationship bel\\'een the average
% porosity and the 28-day compressive strength
7-11
Predicted compressive strengths of mixtures after 365 days
7-15
Figure 2.1:
Orientation of organic ions in water (Kreij gee 1967)
Figure 2.2:
Scheme of the interactions between cement, air, water
and molecules of foaming agent (Kreijger, 1967)
Simple model of the composition of foamed concrete
as used in the investigation by (Hoff, 1972)
Dimensional range of pores in hardened air entrained
cement paste (Gowripalan,
1990 and Uchikawa, 1991)
Figure 3.1:
Distribution of traverse lines on the surface test specimen
Figure 3.2:
Detennination
of chord lengths and lengths in paste on
traverse line
Size distribution of air-voids in fresh air entrained
concrete (Nasser and Singh, 1995)
Diagrammatic representation
of Rosin- Ranunler
distribution function (Wainwright and Olonmsogo,
1999)
Figure 4.1:
Image analysis system
4-4
Figure 4.2:
Diamond saw used for cutting of specimens
4-5
Figure 4.3:
Preparation and alignment of specimens
4-6
Figure 4.4:
Wet grounding of test surfaces of specimens
4-6
Figure 4.5:
Image of foamed concrete as seen on computer monitor
4-7
Figure 4.6:
Manually traced air-voids as seen on computer monitor
4-8
Figure 4.7:
Arrangement of vaCUlun sahlration apparatus
4-10
Figure 6.1:
Determination of x-and y-cord of air-voids in images
6-2
Figure 6.2:
Shape of air-voids
6-4
Figure 6.3:
Histogram of x-chord / y-chord ratios of air-voids with
diameters smaller than 300 ~lIn
6-4
Figure 6.4:
Typical air-void size distributions
6-6
Figure 6.5:
Exponential fit for cumulative percentage oversize air-voids
6-7
Figure 6.6:
Rosin-Ranunler
6-9
distribution graph.
Foamed concrete is one of few building materials combining good mechanical
strength
with low themlal
extensively
improving
material
conductivity
and ease of application.
to reduce the "veight of precast concrete building
the insulating
properties
contribute
significantly
units and also
of these units. This lightweight
when used during the development
to uplift disadvantaged
of infrastructme
communities.
It is used
building
can therefore
To achieve this
goal, in depth research into the structural properties of the material is essential.
Foamed concrete is produced when a foaming agent is added to cement-based
slurry, consisting
of cement, water, cement extender and filler. The foaming
agent, consisting
of hydrolized protiens is diluted with water and aerated to
create the foam (Neville,
1987).
The cement paste sets around the foam
bubbles
and when the foam begins to degenerate,
strength
to maintain
persentage
the paste has sufficient
its shape armmd the void. To ensme that the desired
of air is entrained in the mixture, pre-foaming,
where the foaming
agent is aerated before being added to the mixture, is recommended
(Kearsley,
1996).
Cost is always a major factor in the development
of infrastruchlre.
can be designed to use fly ash as a cement replacement
strength and minimizing
Mi;\.1ures
thereby optimizing
cost. Fly ash is readily available at low cost in South
Africa (Kriiger, 1998).
Since 1992 tests to determine structural properties
been conducted
compressive
at ilie University
of Pretoria.
of foamed concrete have
The results
showed that the
strength of foamed concrete is a function of age, ash / cement
ratio and porosity and for a given porosity and age there is an optimum ash
content, resulting
in the maximum compressive
strength.
All the tests were
conducted on foanled concrete mixtures with target densities higher than 1000
3
kg/m
.
In addition the effect of the microstnlchlre
properties
1999).
of these spesific mixhrres
(air-void structure) on the
was found to be minimal
(Kearsley,
The focus of this research is on foamed concrete miJl.1ures-.vith target densities
varying between 700 kg/m3 and 1500 kg/m3 where the question that needs to
be answered is: what is the influence of the microstmcture
on the physical and
structural properties of these mixtures'?
•
Detenl1ine the influence
of the physical
properties
of foamed concrete
mixtures with target densities varying between 700 kg/m3 and 1500 kg/m3
on the stmctural properties of these mixtures.
•
Develop parameters to explain and quantifY the microstmcture
of foamed
•
Detemline
of foamed
the effect of the microstmcture
on the properties
concrete miJl.1ures with target densities varying between
700 kg/m3 and
1500 kg/m3.
•
Determine the possible influence of the microstructure
on the optimum ash
content of the mixhlres with target densities varying between 700 kg/m3
and 1500 kg/m3•
The scope of this investigation
using rapid hardening
African pre-foaming
3
2 kg/m
covers foamed concrete mixmres manufachlred
Portland cement, unclassified
agent "Foamtech"
consisting
ash (pozz-fill),
a South
of hydrolyzed protiens and
of chopped 6.7 Dtex fibrillated polypropylene
fibers (12 mm long).
Only one source of each material is used in this project and no inert filler (such
as sand) is used in any of the mixhrres. A cost analysis for design miJl.1ures
does not form part of the investigation.
The pore stmchlre
of foamed concrete consists
entrained air-voids and entrapped air-voids.
of gel and capillary pores,
For the scope of this shldy only
the entrained air-void stmctme is identified to represents the microstmcture
of
foamed concrete. The influence therefore of the gel and capillary pores as well
as the entrapped air-voids on the properties of foamed concrete is not covered
by this research.
The study is restricted to the effect of the microstmcture on the 28-day dry
density, ash / cement ratio, average % porosity and the 28-day compressive
strength of the foamed concrete mixtures. The detennination of the influence
of the microstruchlre on the shrinkage, creep, water absorption, permeability,
ultimate strength, durability and vollUne stability of the mixtures is therefore
beyond the scope of tllis investigation. The effect of the method of casting and
the curing of the foamed concrete mi~tures on microstruchlre is not covered by
this research.
Foamed concrete mixhlres with different ash / cement ratios (zero to four) and
different target densities between 700 kg/m3 and 1500 kg/m3 were used in this
investigation. A pre-foamed protein based foaming agent was used for the
mixhlres to ensure predictable densities.
The physical properties (28-day dry density and average % porosity) as well as
a spesific structural property (the 28-day compressive strength) of the foamed
concrete mixhlres were obtained first, before the relationsllips between these
properties were detemlined.
In order to evaluate the influence of the microstructure on these relationships it
was
necessary
to
develop
parameters
to
explain
and
quantifY the
microstruchlre of foamed concrete. An image processing and analysis system
was applied to develop the air-void size distribution parameters and the airvoid spacing parameters. These parameters were used to represent the
microstructure (entrained air-void structure) of the foamed concrete mixtures.
It was tllerefore now possible to plot graphs showing the effect of the
microstruchlre on the physical and structural properties of foamed concrete.
•
The composition
and material properties
of foamed co"ncrete are discussed
in Chapter 2 and the most important physical and structural properties are
identified.
•
The methods of measurement
of air-yoid parameters
as used for hardened
conventional concrete are evaluated in Chapter 3.
•
In Chapter 4 the experimental procedure is discussed.
•
The results are listed in Chapter 5.
•
In
Chapter
6
the
air-void
structure
parameters
(the
air-void
Size
distribution and the air-void spacing) are developed.
•
The
influence
of the
microstmcture
on the
physical
and
stmctural
properties is evaluated in Chapter 7.
•
Chapter 8 contains the conclusions and the recommendations
•
References are given in Chapter 9.
•
Various results are provided in the different appendices. These appendices
are referred to in the main body of the dissertation.
of the study.
Lightweight concrete's density is appreciably lower than the usual range of
concretes made with normal weight aggregates. Three types of lightweight
concrete are produced namely (Neville, 1987):
a)
Lightweight aggregate concrete
b)
Aerated concrete: Foamed - or Gas concrete
c)
No-fines concrete
In essence, the decrease in density of the concrete in each type is obtained by
the presence of voids either in the aggregate or in the mortar or in the openings
between the coarse aggregate particles (Neville, 1987).
This study is only concerned with aerated concrete in particular foamed
concrete, which is produced by introducing large voids (O.Olmm to l.Omm) in
size, into the cement paste. The cement paste consists of cement, water and
cement replacement. Depending on the required properties it can be produced
with or without lightweight aggregate such as sand, stone dust, fine gravel etc.
(Taylor, 1974). The introduction of the voids is achieved by adding foam to
the mixture. A foaming agent consisting of hydrolized proteins is diluted with
water and aerated to fonn the foam.
The aim of this research is to investigate the microstmchlre of the material as
the primary factor influencing the relationship between the physical properties
and the struchrral properties of foamed concrete. In this chapter the
composition of the material and the relationships between the physical
properties and the structural properties of foamed concrete are evaluated.
Factory made steam-cured foamed concrete was first successfully produced in
1928 using cement as a basic binding material. Subsequently, countries like
USSR,
USA and Germany developed
binding
materials,
depending
new teclmologies- based on different
on their availability
and their relative
costs.
Maximmll economy would result if lime is used as the base since lime is the
cheapest
binding
material,
but studies
done at Ennore,
cement in the binder is necessary to optimize
Madras
show that
setting time. As a result, at
Ennore, Madras only a portion of the cement was replaced by fly ash, a waste
product from the Basin Bridge powerhouse nearby (Chitharanjan,
During the manufacturing
the air-bubbles
1978).
of the product the cement paste starts setting around
and when the foanl begins to degenerate
after approximately
three quarters of an hour, the paste must have sufficient strength to maintain its
shape arOlmd the air-void (Kearsley 1996). Using a combination
of cement and
fly ash the required strength of the cement paste can be attained if the free
CaO content in the binder available for chemical reaction can be maintained.
In other words the CaO in the fly ash is used to augment the reduction of CaO
in the binder because of the removal of a portion of cement. Cement contains
active lime in the form of CaO, which varies from 55 to 65 percent, and its
activity
varies ''lith
Chitharanjan
the quality
(Chitharanjan,
of cement
1978)
at the time of use. Therefore
concluded
that
a theoretical
prediction
regarding the optimum percent of fly ash cannot be made, the optimum can
only be reached experimentally.
The use of a lightweight
aggregate, for example sand, as filler in the mixture
will also influence the optimum percentage of fly ash. The filler will increase
the silica content of the paste and that will change the final hydration product,
namely
the
(Chitharanjan,
calcilU11 silicate
hydrates
known
as
crystalline
tobermorite
1978).
It was found by Chitharanjan
Bridge powerhouse
(Chitharanj an, 1978) that the optimum
fly ash content for the maximum
Basin
strength with minimlU11
density and moisture content is 40 percent by weight of the specific binder.
The replacement of cement with fly ash did not keep the quality of the foamed
concrete the same, but in fact it improved the quality.
In large areas of South Africa fly ash is available at low cost and according to
Kearsley (Kearsley,
1999) the South African fly ash (pozz-fill - unclassified
ash) can be llsed as a cement replacement in foamed concrete with no negative
effect on the properties.
Although the rate of gain in strength is reduced by
use of large volumes of ash, up to 67 % of the cement can be replaced by ash
without any significant reductions in long-term strength.
The
composition
of the mi;\.1ure used
by Kearsley
(Kearsley,
1999) to
determine the optimmn ash / cement ratio is Portland cement, South African
fly ash and foam manufactured
an optimum
ash content, resulting
given porosity.
developed
with a pre-foaming
A compressive
in the highest compressive
strength
for this type of mixhlres
theoretically.
agent. There seems to be
model
to predict
It was found that this optimum
strength for a
(as discussed
in 2.3.4)
the optimmn
is
ash content
ash content increases with an
increase in age.
Foamed
concrete
is more sensitive
to water content than normal concrete.
Concrete nonnally has a certain water demand to obtain a required workability
and the strength of the concrete decreases as the water-cement
(Neville,
1987). For foamed concrete workability
ratio increases
is not a problem but if the
water in the mix.1ure is not sufficient for initial reaction of the cement paste,
the cement withdraws
water from the foam, causing rapid degeneration of the
foam. If too much water is added, segregation takes place, causing a variation
in density (Kearsley, 1996).
Kearsley (Kearsley,
1996) did research on the optimum water/cement ratio for
all the different foam contents and fOlmd that it is in the region of 0.38 when
no fly ash was added. When South African fly ash was used in the binder the
required water/cement ratio increased as the fly ash/cement ratio increased.
The density of the foamed concrete is a nmction of the volume of foam that is
added to the cement
entrained
paste.
To ensure that the desired
in the mix.1ure, pre-foaming,
percentage
air is
,•.here the foaming agent is aerated
before being added to the mixhlre, is used (Kearsley, 1996).
The aerated foaming agent, on mixing with the cement-based
slurry entrains a
controlled quantity of air in unifoilll1y dispersed discreet cavities. These voids
are typically spherical with diameters from 0.01 mm to Ul mm and are closely
spaced being not more than 0.4 nun apart (Neville, 1987).
The foaming agent is surface active, which means that the molecules when
placed into water are capable of splitting themselves into ions (see figure 2.1).
The organic ions are built up of a long organic chain, which is lillcharged, and
an electrically charged part or the polar part. As water can be considered to
consist of dipoles, the polar part of the organic ion will be attracted by that part
of the water molecule, which has an opposite charge (Kreijger, 1967).
The chain is always pushed out of the water; this being hydrophobic (water
hating) and the polar group is attracted to the water this being hydrophilic
(water loving). If the polar part is charged positive, one speaks of a cat-ion: if
it is charged negative, of an an-ion. Next to these two groups there are organic
molecules, which can be presented also as a dipole (see figure 2.1). These are
called non-ionic. (Kreij ger, 1967).
The net result when mlxmg the foam, water and cement paste is that the
foaming agent molecules orient themselves at any air / water interface thereby
stabilizing
themselves.
The surface of the cement particles is made
hydrophobic by the admixture and by means of the carbon chains the airbubbles adhere to the cement particles and the sand grains. This combined
effect stabilizes the air bubbles, which is the best condition for a regular
distribution throughout the mixture (see figure 2.2) (Kreijger, 1967).
The pressure difference between the inside and outside of an air bubble
given by the following relationship (Uchikawa, 1991):
M
=
pressure difference between inside and outside of air-void
r
= surface tension
D
=
bubble diameter
IS
cation
anion
organic chain
air
'Water
~---
'Water
dipoles
~ __
---~
----~
nonionic
•
L
-
~
0
cationic
•c •
'of
L
••••L
anionic
.-
c.
'of
polar part
of U-.e ion
':-
co·
'of
•
Mionic sur(<<.~
¥t
~
~
1M1!;ef, cement
Airbvbblti djell to c~
"99"'9"'"
IvWotW:
and
IU'r.ac.~-=tM
~(
IUt'r~-aetM
~t
hrdn::ipo'w1.ic:
og.-.lw+;"' ••••••• _
..,hich m
hyd"'l,M.
~rs_.tedrnlln~t
A"bubbl•• ilOt..led frcm C*'Ml\l
OIITWftl
...._.j.u..
N"l'l~.
T
~iJ
~~
.,f~~
L
...t~'of
Figure 2.2: Scheme ofthe interactions between cement, air, water and molecules of
foaming agent (Kreijger, 1967).
From equation 2.1 it is clear that small bubbles require the air in the bubble to
be at a higher pressure than larger bubbles, and therefore there is a strong
tendency for small bubbles to join to form larger bubbles to lower the airpressure in the bubbles. The foaming agent is based on materials, which will
lower the surface tension, and therefore it becomes easier to form smaller
bubbles. The foaming agent also helps to maintain the bubble by slightly
increasing viscosity and by fomling a stabilized skin to the bubble.
The air-bubbles just after forming are not filled with products of hydration
because they are separate from the capillary pore system in the cement paste as
gel can only form in water (Neville, 1987).
The foaming agent is one of the most important elements of the material. A
good quality foaming agent and therefore one which has the ability to form a
stabilized skin to the air-bubbles will guarantee an evenly distributed air-void
system.
In order to evaluate the relations between the physical properties and the
structural properties of foamed concrete these properties have to be identified.
When lrndertaking the design of a foamed concrete mixture, a target casting
density is detemlined and the dry density of the mixture is the most important
factor affecting the properties of the mixture (Kearsley, 1999). The density is
therefore identified as an important physical property that has to be
investigated.
According to Kearsley (Kearsley, 1999) porosity, ash / cement ratio, and age
are also variables. which will influence the structural characteristics of foamed
concrete.
Strength, durability, impermeability and volume stability are the most
important stmctural characteristics of concrete. Nevertheless strength usually
gives an overall picture of the quality of concrete and it is directly related to
the struchlre of the cement paste (Neville, 1987). Therefore in the rest of this
investigation only the compreSSive strength will be use as the struchlral
property indicating the quality of foamed concrete.
The required target casting density can be determined by using chosen water I
cement
(w/c)
and sand I cement
(sic)
ratios (ACI, 1975) and the relative
densities of the materials the mass of the cement and the volume of foam that
should be added to obtain the required density. By assuming that
VI liters of
foam should be added per cubic meter of foamed concrete and that the cement
content of the mixture is
x kg/m3
the following equations can be used for
calculatrng the achlal mixhlre compositions:
1000
x
xslc
+ xw / c + -+ VI
RDc
RD,
= --
RDf
Relative density offoam
RDc
Relative density of cement
RDs
Relative density of sand
In mixtures where the sand has been replaced by ash an ash / cement ratio (a/c)
is used instead of the sand I cement ratio and the relative density of sand is
replaced with the relative density of ash (Kearsley, 1999).
From these equations it's clear that the density of foamed concrete is directly
related to the percentage foam that is added to the slurry. The maximum.
compressive strength of the material decreases as the foam content increases
(Kearsley, 1997).
According to Vine-Lott (Vine-Lott, 1985) the compressive strength of foamed
concrete is an inverse function of the density of the material. This relationship
between density and compressive strength is exponential, the value of the
exponent varying \vith the size and distribution of the air-voids.
The porosity of a porous material is defined as the fraction of its bulk volume
occupied by voids therefore the porosity of foamed concrete is defined as the
relative volume of pores or voids in the cement paste.
Kearsley (Kearsley, 1999) found that porosity is largely dependent on the dry
density and not on ash type or ash content. The porosity of foamed concrete as
a function of dry densities between 800 kg/m3 and 2000 kg/m3 can best be
described using the following equation:
P -- 1866 )Yd
-0.844
p
porosity (%)
Yd
dry density (kg/m3)
Several equations have been suggested to express the relationship between
porosity and strength of porous solids. According to Fagerlund and Romer
(Fager1und, 1973 and Romer, 1985) the following equation can be used
successfully to express the relationship between porosity and strength of
cement paste:
P
=
porosity
n
=
empirical constant
Hoff
(Hoff,
compressive
1972)
investigated
the
relationship
between
porosity
strength of foamed concrete. The foamed concrete
was made using only Portland
cement, water, and preformed
and
investigated
foam, which
provided the air, content. Foamed concrete can be shown by the simple model
in figure 2.3 as being composed
of air, evaporable
water, non-evaporable
water and· cement. As such, foamed concrete can be considered
as a cement
paste with a large void content or high porosity and equation 2.5 can be used
to express the relationship between porosity and strength.
Hoff (Hoff, 1972) defined the theoretical porosity as the fractional portion of
the total volume
that is air plus
evaporable
water.
From
weight-volume
considerations, the porosity can be expressed as follows:
P
= 1 __ d_c(_1 _+ _0._2_0p_c_)
(l +k)peYw
VT
ENTRAINED
AND
ENTRAPPED
AIR
VA
EVAPORABLE
WATER
Yew
Vv
TH EORETICAL
POROSITY,
n
= Vv =
VA
VT
NONEVAPORABLE
WATER
Vnw
CEMENT
Figure 2.3: Simple model of the composition
investi2ation by (Hoff, 1972).
Vs
Vc
of foamed concrete
as used in the
+ Yew
VT
Substituting
this equation for porosity in the strength-pofClsity equation 2.5 for
cement paste will give the following expression:
(J
n
oc
=
de
(J0
d
(-_C-r
l+k
empirical constant
=
concrete density
These equations only hold tme for foamed concrete containing only air, water
and cement. Kearsley (Kearsley, 1999) made modifications
that the theoretical
to equation 2.6 so
porosity of mi.\.1ures containing ash could be detennined.
The water binder ratio and the binder specific gravity were used in equation
2.6, where the tenn binder is defined as all the cementitious
material in the
mixhlre. The binder specific gravity is calculated by dividing the total binder
weight by the total binder volume. The theoretical porosity of foamed concrete
mixhlres
containing
a cement extender,
one year after casting
expressed by the following equation (Kearsley, 1999):
P =1- dc(1+0.2Pb)
(l + k)pbr"
is therefore.
Effect
of ash content,
porosity
and age on compressive
strength
The compressive
and therefore
compressive
strength of foamed concrete is not only a function of porosity
dry density
strength
but also of mixhlfe
of foamed
concrete
age and ash content.
is represented
The
by the following
equation (Kearsley, 1999):
Ie
compressive strength (MPa)
t
time since casting (days)
P
ale
porosity (as a fraction)
a j1and A.
ash / cement ratio (by weight)
constants
Kearsley (Kearsley,
1999) detennined
and A.) for pulverized
different values for the constants
fuel ash (Pfa)
and pozz-fil
(unclassified
(a j1
fly ash)
respectively (see Table 2.1).
For the scope of this research only South African pozz-fil (unclassified
fly ash)
is used as a cement extender.
Although high fly ash content results in a reduction in compressive
strength at
early ages, the long-tenn strength (say after one year) is improved by replacing
up to 75 % of the cement (by weight) with ash.
Pfa
Pozz-tiII
a
3.7
3.7
/31
24.91
/32
52.89
56.78
/33
-12.27
-14.31
,1,1
172.8
,1,2
-196.0
-229.7
).3
34.02
46.04
Constant
I
23.74
i
176.9
I
The 365 day strengths for mix.1ures with dry densities between 800 kg/m3 and
2000 kg/m3 indicate an optimum ash content with maximum strength obtained
at ash / cement ratios in the region of 1.5 (Kearsley, 1999).
It is clear that the physical properties (dry density, porosity and ash content) as
\vell as the age have an influence on the structural
strength).
The
question
arises,
what
concrete has on these properties?
effect
property
(compressive
the microstruchlre
of foamed
The same porosity as well as density can be
achieved for many small air-voids or for fewer larger air-voids in the mixhlre;
therefore the air-void stmcture may influence these properties.
Compressive
strength of nonnal concrete appears to depend not so much on
the chemical
composition
as on the physical
struchrre
of the products
hydration of cement and on their relative voltmletric proportions.
it is the presence of flaws, discontinuities
of
In particular,
and pores that influence the strength
of the concrete (Neville, 1987).
Olonmsogo
material,
(Olonmsogo,
pre-detennined
distribution,
the strength
1990) stated that the pore stmcture of a cementitious
by
its
porosity,
is a very important micro-stmctural
of the material.
The properties
mean
radius
characteristic
are dependent
distribution of the pores within the hardened cement paste.
and
pore
size
as it influences
mainly
on the
The pore stmchlre of air-entrained
cement paste consists- of water - and air-
voids as shown in Figure 2.4. The water voids comprises of the gel pore space
corresponding
to the space between the C-S-H layers and the capillary pore
space whose fonnation
pastes.
depends on the evaporation
The capillary
specimens.
pores remain unfilled
with hydrates
Hence the different mixhlre preparation
well as curing conditions
(time, temperahlre,
of the water used in the
in the hardened
(w/c ratio, compaction) as
relative hlilllidity) and type of
cement used are all parameters influencing the gel- and capillary pore stmcture
of the paste (Atzeni, 1987).
The air-voids include the entrained air formed by the air-entraining
agent and
the entrapped air as a result of the mixing process (Uchikawa, 1991).
The gel pore shapes are usually represented as platy cylindrical however, the
hydraulic radius can also represent it. The shape of the capillary pores is also
cylindrical but with small contractions and enlargements
shown in figure 2.4 (Cebeci,
1980). Meanwhile
along their lengths as
the shape of air-voids
spherical or polyhedral resembling spherical (Uchikawa, 1991).
l\
1\
,I~---'
\J
Gel
pores
Ions
..,
S~-
Capillary
pores
02-
000
aIr
bubbles
~,
er-
Entrained
e:>
--
-
-
Entrapped
air voids
laI'ger than
3
. /1\
,
-4
10
-3
10
-1
10
\
10 ..•../1\._--'
:2
3
10
10
Figure 2.4: Dimensional range of pores in hardened air entrained cement paste
(Gowripalan, 1990 and Uchikawa, 1991),
are
Odler and Rossler (Odler and Rossler, 1985) correlate compressive strength of
hardened cement pastes with gel- and capillary pore distribution
by means of
the following equation:
Correlation
results showed however that some of the constants were negative,
implying paradoxically,
that increased porosity enhanced strength. This can be
explained by the fact that as hydration progresses there is a greater number of
smaller size pores. As a result, for certain curing times the smaller size ranges
appear
to increase
strengths
and because
are higher
different approach
correlating
of the greater munber of hydrated phases,
too. It is for this reason that (Atzeni,
1987) used a
for taking into aCCOtult the effect of pore distribution
by
strength with an original parameter, nanled the 'mean distribution
radius', defined as follO\·\,s:
abmptly above the threshold of 10
(r m)
distribution
parameter
compressive
strength properties
does
!Un.
not
According to (Atzeni, 1987) the pore
give
an
adequate
correlation
of
of hardened cement pastes. Therefore Atzeni
Compressive
incorporates
strength
is
directly
proportional
the fraction of gel and capillary
to
a
parameter,
which
pores, the mean distribution
radius of these pores and the characteristic strength of the cement paste.
Cebeci (Cebeci, 1981) investigated
structure
introduces
of hardened
cement
the effect of air entrairunent
paste
and
found
that
on the pore
air-entraining
the large air-voids and does not alter the characteristic
struchlre of hardened cement paste appreciably.
the other hand fOlmd that at high porosities
only
fine pore
Kearsley (Kearsley,
1999) on
(low target densities) of foamed
concrete the calculated paste porosity is higher than the porosity of the cement
paste containing no foam. It is therefore possible that some of the water added
to mixtures as part of the foam is increasing the effective water / binder ratio
in other words changing the gel and capillary
pore stmchlre
of the paste
sUITOlmding the entrained air- voids. The assumption can be made that the gel
and capillary pore stmcrure as well as the air-void
stmcture
will have an
influence on the properties of foamed concrete.
The air-void stmcture of foamed concrete is for the scope of this investigation
identified
as the more important
micro-stmchlral
characteristic
and will be
investigated in chapter three.
•
The density of foamed concrete is directly related to the percentage
foam
that is added to the slurry.
•
The compressive strength of foamed concrete is an inverse flmction of the
density of the material.
•
Compressive
strength of foamed concrete
IS
a function of ash content,
porosity and mixhlre age (physical properties).
•
There seems to be an optimum
ash content,
compressive strength for a given porosity.
resulting
111
the highest
•
The
air-void
stmchlre
is a very important
infl uencing the properties of foamed concrete.
micro-struchlral
property
The air-void structure of foamed concrete is identified as one of the most
important micro-properties influencing the properties of- foamed concrete. In
search of a way to describe the air-void stmcture of foamed concrete, the
methods of detennination of the air-void parameters for air-entrained hardened
concrete are evaluated in this chapter.
Stereo10gy is the fOlmdation of image analysis. It represents the mathematical
methods for reconstmcting the three-dimensional parameters defining the
struchrre from measurements obtained on sections of the stmchlre (Chan,
1987).
The following methods for measurement of air-void parameters in airentrained concrete are based on stereology as well as the fact that the essential
feahlre of entrained air-voids, is that they are spherical and, therefore, circular
in section, whereas other feahlres will generally be irregular in shape.
METHODS
FOR
MEASUREMENT
OF
AIR-VOID
PARAMETERS IN AIR-ENTRAINED HARDENED CONCRETE
The American Standard Test Method (ASTM C 457, 1990) and the ne"v
European Standard (prEN, 1993) describe a linear traverse method for
measurement of air-void parameters.
According to this method, cubes or cylinders of minimum dimension 150
ll1ll1
are cast from the air-entrained concrete Imder investigation. The samples are
sectioned, such that the cut surfaces are perpendicular to the sample face that
was uppennost during manufachrre, to produce specimens for analysis.
The approximate dimensions of the specimens are 150
ll1ll1.
ll1ll1
x 100
ll1ll1 X
40
The largest face of these prisms is then grolmd to produce a smooth flat
surface finish. The surface is further prepared in such a .vay that the voids are
highlighted with a white powder and the rest of the matrix is inked black for
microscopic investigation.
The prepared specimen is mounted Imder a stereoscopic microscope with a
magnification of 100 x +/- 10 x. Using the linear-traverse method, the air-void
structure is examined by scamting the specimen along a series of traverse lines
mnning parallel to the original free upper surface during manufachlre (see
figure 3.1).
Traverse lines
at 6 mm
separation
The number of air-voids intersected by the traverse lines is recorded, as are the
individual chord lengths of the traverse across the air-voids. The traverse
length through paste and the total length of traverse are also recorded (see
figure 3.2). These recorded data are then analysed according to the
stereological linear analysis of Rosiwell. According to this analysis the areal
fraction and consequently the volmlle fraction can be approximated by the
intercept length fraction (Chan, 1987).
With the results of this analysis the air-void stmcture is described by means of
the following parameters:
a)
Total air content. The proportion of the total volmue of concrete
taken up by air-voids expressed as a percentage by volmne. Willis
(Willis, 1949) derived the following equation to determine the air
content by chord intercept measmements:
Where:
n
=
the munber of bubbles intersected per Imit length of traverse.
o
b)
Specific
surt'ace
of
entrained
air.
A
calculated
parameter
representing the total surface area of air-voids divided by their volmue
(bolmdary area of air-voids per unit vohune of air). According to
4
a=-
7
The equations for air content and specific surface are applicable to any
system of spherical dispersoids whether the system is made up of
single or multisized spheres.
c)
Spacing factor. The calculation of this parameter aSSlilllesthat all airvoids present are of unifonll size and are evenly distributed through
the cement paste. It is distributed
volume
such that the-model
of air per unit volume of concrete
has the same
and the same specific
surface of air bubbles as the system of random sized bubbles.
Each
hypothetical air-void is centrally imbedded in a cement paste cube.
The spacing factor is the distance from the comer of the cube to the
surface of the sphere 01ypothetical air-void) and can be calculated by
knowing
the spesific
surface of entrained
air, air-void
content and
cement paste content of the specimen (Chan, 1987).
d)
Air-void
size distIibution.
The European standard (prEN 1993) use
the chord lengths to calculate the distribution
of the number of air-
void diameters within the cement paste.
During the linear traverse method only those air-voids intercepted
the traverse
line will be counted in the chord distribution;
by
a large
number will not be intercepted
and are therefore not included in the
chord distribution.
in
Calculations
means to estimating
(prEN 1993) Annex A provide a
the total number of voids from those intercepted
by means of a statistical analysis.
A graphical
representation
of the distribution
can be obtained
by
plotting the volume of air attributable to each size of void, either as a
volume percentage
of the cement paste or as a proportion
of the total
air content.
e)
Micro-air
content.
A calculated
parameter
representing
the aIr
content attributed to air-voids of 0.3 mm dianleter or less.
The
determination
of
all
these
parameters
was
developed
before
the
teclmology of image analysis exists. None of these factors has been proven to
give an exact measure of the desired quantity (Willis,
1949). The calculations
of the spacing factor for example inadequately assume uniform sized air-voids
and neglect aggregates
between the air-voids.
and therefore it is not representative
of the distances
Equation 2.1 gives the pressure difference between the inside and outside of an
air bubble. According to (Uchikawa, 1991) if the assumption is made that the
outside pressure is atmospheric pressure and
r is
to be the surface tension of
water the minimum diameter of an air-void is approximately 30 urn. The
maximum diameter of air-voids is 1 nun and the pores with diameters greater
than 1 mm is defined as large entrapped air. The pores smaller than 30 lUnare
defined as gel- and capillary pores. According to Wilk & Dobrolubov (Wilk &
Dobrolubov, 1984) perfectly batched and mixed air-entrained concrete of high
durability contains well-distributed spherical voids with diameters varying
between 20 and 300 micrometer. The micro air paranleter therefore does not
represent a specific classification of pore type in the mixture, but indicates the
quality of air entraining.
The American Standard Test Method (ASTM C 457, 1990) also describes a
modified point-cOlUltmethod for the measurement of the air-void parameters.
The preparation of the specimens is the same as for the linear traverse method.
For this method the air-void stmcture is examined by scanning it along a
regular imaginary grid system of points at which stops are made to determine
the composition of the matrix.
The linear distance between stops, the number of stops in air-voids and paste
are recorded. These recorded data are analysed by the stereology point analysis
of Glagolev and Thomson. According to this analysis the areal fraction and
therefore the volume fraction can be evaluated by the fraction of points (Chan,
1987).
The same air-void paranleters as for the linear-traverse method are determined'
by the recorded data and they are used to describe the air-void system.
Cahill (Cahill, 1994) developed a method where image acquisition and
analysis are used in conjunction with the linear traverse method to determine
the air-void system. It comprises a motorised X-V stage, a microscope with
focus control, a high- resolution monochrome camera, a motor control box and
the Kontron IBAS Image Analysis system.
The specimens are prepared in the same way as for the ASTM - and European
methods (ASTM C 457, 1990 and prEN, 1993).
The traverse of the camera
over the polished surface of the concrete mimics the linear traverse method.
Each of the images produced by the camera is analysed by placing it on a fine
grid. The system examines every square, a number representing
numerical
its place on a
scale ranging from 0 (black) to 255 (pure white) via intermediate
numbers representing
shades of grey. The image is then acquired and llily void
within the image is identified solely on the criterion of intensity of grey value.
All occurrences of grey value above a threshold of e.g. 220 are assumed part
of a void llild are turned white. The background
values 220 or below, is
converted to black, so producing a binary black/white
image. Once the image
has been digitised and acquired in this way, the information is stored and can
be analysed mathematically.
A traverse line is placed across an image and the
overlap of the traverse line with any air-void yields chord intercepts. The void
chords are measured and the method of calculation
taken
directly
previously
from the European
in paragraph
Standard
of air-void parameters
(prEN,
3.2.1.1 these parameters
1993).
is
As discussed
do not represent the actual
quantities desired.
Nasser llild Singh (Nasser llild Singh, 1995) developed a new apparatus
method
concrete.
system,
to
detennine
the air-void
characteristics
The apparatus
consists
of an electronic
computer
and image processing
software.
of fresh
video
and
and hardened
cmnera,
The method
lighting
consists
of
video images taken of the concrete surface to be tested and these are analyzed
to determine air-void parameters. It takes a short period of time to perform the
test compared to the traditional standard methods.
There is no need to prepare the concrete surfaces of the specimens while using
tlus method. The first step in the method is to expose the specimen to the video
camera,
which is set to magnifY the image 30 times. Next the camera is
focused and the image is monitored so as to obtain the best possible picture of
the concrete surface, which can be stored in the apparatlls
for inunediate
or
future statistical analysis.
Image processing
feahlres
from
identification
software is used to identitY, extract, and measure different
a frozen
video
image.
The
principal
behind
the air-void
is that air-voids are darker than other feahrres in the image and
can be assigned
a very low value of gray scale. The air-voids
are selected
having the same gray scale range. The software routines can calculate the area
of the selected air-voids, their x-y coordinates and their diameters.
The image processing method of Nasser and Singh (Nasser and Singh, 1995)
uses the calculated air-void area to determine the air-void diameter.
Air-void diameter
{4A
= ~-;;-
Where:
A
=
area of void.
By using the image processing method of Nasser and Singh the data of the airvoids
are recorded.
Standard
(prEN,
The air-void
parameters
as defmed
1993) can then be calculated
by the Ellfopean
by exporting
the data to a
spreadsheet that contains the required geometric fommlae for calculations.
The fact that the software
calculate
routines
of the image
the area of the selected air-voids,
processmg
method
their x-y coordinates
can
and their
diameters and then export it to a spreadsheet ensures the exact measurement of
the achlal quantity of the air-void parameters.
•
Specific smface of entrained air
•
Spacing factor
•
Air-void size distribution
This parameter does not give an accurate indication of the percentage air in the
mixhlre, because it does not take the gel and capillary pores into consideration.
The
achtal
porosity
of the mixhlres
can be detemuned
by the vacuum
sahlration method as discussed in chapter 4 paragraph 4.4.
According to equation 3.2 the spec!fic area of the air-voids
= ----
4
Diameter
This parameter is only dependent on the diameter of the air-void and therefore
the diameter of the air-void as such can be used to evaluate relations between
the properties of the mixhlres and the microstmchlre.
A spacing factor defined as the distance from the center of an air-void to the
center of the nearest air-void in the neighborhood
is developed. The center to
center spacing between any two air-voids is given by:
Xl,2
=
x - coordinates of air-voids
Yl,2 = Y - coordinates of air-voids
If the spacing factor
aggregate
is calculated
in this manner
content between the air-voids
are not taken into account. In other
words this spacing factor is not representative
distances
betw'een the air-voids.
investigation has to be developed.
the paste content and
of the minimum or maximum
A representative
spacing
factor for this
Nasser and Singh (Nasser and Singh, 1995) obtained a histogram
of the
diameters of the air-voids and their size distribution from the exported data
(see figure 3.3). The average diameter as determined from the histogram
is
used to represent the group of the individual values of the diameters of the airvoids. The question arises if this average diameter is really representative
of
the size distribution?
All these parameters are based on the essential feature that entrained air-voids
are spherical and therefore circular in section. With the data obtained from the
image processing method the shape of the air-voids can be determined and the
circularity therefore be tested.
120
/
100
i)' 80
c:
CIl
::l
~
u.
• • • • • • • • • •
I Frequency
•
60
I
100%
80%
60%
Cumulative
Frequency
40%
40
20%
20
0
a
0
~
~ ~
000
80
~
0
8 ~ ~ l;jI ~ lD ~ Oi
d d d d d d d d
to
~
~
~
0
0
0
•
C'i
0
0%
~
~ ~
000
Air-void size In mm
Figure 3.3: Size distribution
Singh, 1995)
of air-voids in fresh air entrained
concrete (Nasser and
In searching
description
for a parameter,
which
will provide
of the air-void size distribution
a more representative
than proposed
by Nasser
and
Singh, the Rosin - Rammler distribution flillction was investigated.
From a probability
size distribution
point of Yiew Rosin and Ranunler investigated
of crushed coal and developed a function that describes the
distribution as (Olonmsogo.
Rosin
the particle
1990):
b
:=
fineness characteristic measure of the material being analyzed.
n
=
a measure of the range of particle sizes.
and Ranunler
also found that the function
does not only apply to
crushed coal but also to various other powered materials.
Where:
The weight flUlctionflx} is denoted as RR.
1
InIn(-)
RR
= nOn x -In xo)
Equation 3.7 describes a straight line plot vvith a coordinate system made up of
a log scale abscissa
for the particle size x, and an ordinate with a double
logaritlun of the reciprocal of the residue RR. The slope of the straight line is
n and the line intercept the horizontal axis at a value describing the particle
size x (Olomnsogo,
representation
1990).
A hypothetical
of the particle
example
size distribution
of the diagranmlatic
by the Rosin
-
Rammler
distribution ftmction is shown in figure 3.4.
?
;;::.
.!i (36.8"h)
.!i
~
;;::.
.!i (36.8"1.)
.!i
Figure 3.4: Diagrammatic representation
(Wainwright and Olorunsogo, 1999).
of Rosin-Rammler
distribution
Figure 3.4 (a) shows the typical particle size distribution
function
of four different
samples having the same n and different xo' This illustration
shows that the
sample
ranges
represented
distribution
by the four plots
might
have similar
of size
(denoted by equal n) but with possible varying degrees of fineness
(indicated by the various
xo)' The sample represented by plot 1 being the
finest and the one represented
by plot 4 the coarsest of the four. Similarly,
figure 3.4 (b) illustrates a situation whereby the four samples might be of the
same fineness (because of the same
xo) but possibly with different size ranges
Defining
the air-voids
used to provide
as circular particles
this distribution
an easy means of describing
function can be
the air-void size distribution
quanti tati vely.
•
From the literature reviewed it can be concluded that the air-void stmcture
can best be detennined by the image processing and analysis method.
•
The air-void stmcture of foamed concrete can fully be described by means
of the shape of the air-voids, distances between air-voids and the air-void
size distribution.
•
The Rosin-Ranunler
providing
distribution
an easy means
quantitatively.
function can be evaluated as a method
of describing
the air-void
size distribution
Literature review indicates that by replacing percentages of cement with fly
ash the properties of the cement paste in foamed concrete can be enhanced.
Foamed concrete mixhrres with different ash/cement ratios and different target
densities are therefore used in this investigation. A pre-foamed protein based
foaming agent is used for the mixhlres to ensure predictable densities
(Kearsley 1996).
All materials used in this research are produced in South Africa and a single
source of the different materials "vas used.
This chapter describes the different methods used to determine the physical
properties (the density, porosity and the air-void struchlre) as well as a specific
struchrral property (the compressive strength) of the foamed concrete
mixhlres.
The vacuum saturation method is used to determine the achial porosity of the
foamed concrete test specimens.
An image processing and analysis system was used to determine the air-void
struchrre parameters. At present it proved to be the most accurate method. The
apparahls differ slightly from the apparatus used by Nasser and Singh (Nasser
and Singh, 1995) in that a high-resolution monochrome camera was used
instead of an electronic video camera.
The foamed concrete used in tllis research is produced lUlder controlled
conditions from cement, fly ash, water and a pre-foamed protein based
foaming agent.
The cement used is rapid hardening Portland cement from PPC, Herculus,
Pretoria. The cement can be classified as CEM I 42,5R according to the South
African Specification SABS EVN 197- 1:1992. Unclassified ash (pozz-fill) is
obtained in bulk from Letabo and used as a cement ex.1ender.
The foaming agent used is "Foamtech", consisting of hydrolyzed protiens and
it's manufactured in South Africa. The foaming agent is diluted with water in a
ratio of 1:40 and then aerated to a density of70 kg/m3.
It was not the aim of this investigation to establish the effect of fibers on the
properties of foamed concrete and therefore 2 kg/m3 of chopped 6.7 Dtex
fibrillated polypropylene fibers (12 mm long) were used in all the mixtures.
Research at the University of Pretoria showed that these fibers do not
influence the compressive strength of foanled concrete but do have a
significant effect on the tensile strength offoamed concrete (Kearsley, 1997).
The test specimens (cubes) cast for this study have a dimension of 100-mm x
100-nml x 100-nml. The initial density of the specimens as measured during
manufacturing is the casting density and it can be compared with the design
density or in other words the target density.
Test specimens are de-moulded within 24 hours of casting and the de-mould
density of each specimen is detennined. After de-moulding, each specimen is
wrapped in plastic and cured in constant temperature room (22
0
C) and 60 %
relative humidity for 28 days.
The density of each speCimen is agam determined after 28 days and this
density is called the 28-day test density.
For the measurement
of the 28-day dry density one specimen in every batch is
cured for 28 days in the constant temperahlre room. There after the cube is
'weighed to determine the testing density. The cube is then placed in an oven at
a temperature
of 100
0
C for another 7 days and the dry density is then
determined.
The 100-mm test cubes were cast in steel moulds and de-moulded
hours. Then it was wrapped in pol}1hene wrapping
temperature room (22
0
after ± 24
and kept in a constant
C) and 60 % relative humidity, up to the day of testing.
The cubes were cmshed on a more sensitive press, (with a 50 MPa capacity),
than usually used for nornIaI concrete.
Three cubes from the same mixture of
foamed concrete were cmshed and the average of the three results is used to
define the strength of the mix.ture. The compressive strength were recorded to
the nearest 0.1 MPa (Kearsley, 1999).
The image processing
and analysis system used in this research is shown in
Figure 4.1.
It consists
of a high-resolution
microscope
and computer with the image analysis software "Optimate
The microscope
manually
has a movable
monochrome camera connected to an optical
X, Y stage and by moving
in both the X and Y directions,
representative
5 .21".
the specimen
images
of the
specimen are collected.
The software
has a function "Area Morphometry"
(Optimate
5.21 Utilities
menu) which allows the collection of data of a randomly selected image (or
section of the specimen).
A sub-flUlction allows the defining of smaller areas
of the image to be investigated by using a pointing device e.g. a mouse to trace
the perimeter of such an area, which will then be displayed on the monitor.
Holding down the primary mouse button and following the perimeter of the
area performs the trace. The trace will be displayed on the computer monitor
as a thin red line.
The data of every defmed area in the image is stored and analyzed separately.
The output data is presented and stored in an ASCn file for use by any data
processing computer program.
The output data of the encircled areas of a specific image consist of the total
area in calibration units, total length of perimeter in calibration units, x - and y
position of area centroid. The circularity, longest axis in calibration
width perpendicular
units,
to longest axis, mean and standard deviation of the grey
value of the pixels enclosed by the area are also part of the output data
(Optimum 5.21 Utilities menu).
An extra cube for every mixture was cast for microscopic analysis purposes.
Slices of the cube of between
12-mm and 15-mm thick are cut using a
diamond saw (See Figure 4.2). The slices are cut perpendicular to the original
free surface after which every slice is again cut in quarters. The dimensions of
the specimens
are 50-mm x 50-mm x 12-15-mm. The alignment
of the
specimens is kept the same throughout the whole experiment (See Figure 4.3).
The intended test surfaces of the specimens are wet ground using sandpaper
with a 180 and 600 grit respectively, to produce a smooth flat surface (See
Figure 4.4).
The specimens are cleaned with compressed air to remove any residue and
prepared in the oven at 50°C to ensure a dry surface for microscopic analysis
(Visagie, M. 1997).
lOOxlOOx12-15 mm
slice
lOOxlOOxlOO
mm cube
Four specimens each 50x50x12-15
mm
According to the method used for identification
Standard
(PrEN
480-II: 1993), the concrete
of air-voids
by the European
surface is first inked black to
reduce contrast between aggregate and paste and allowed to dry. Working
a
white zinc paste into the voids highlights them. Air-voids in foamed concrete
is closer together than in nonnal
concrete and therefore tms method is not
suitable for foamed concrete as not all the air-voids are filled with the paste.
In this shldy, no specific method was used to accentlwte the contrast between
air-voids and cement paste. The focus of the optical microscope
until the cement paste was in focus and all the air-voids
computor monitor. TillS contrast is considered
was adjusted
are blurred on the
to be sufficient to distinguish
between air-voids and cement paste.
Figure 4.5 shows the typical images produced by the canlera. The air-voids
can easily be identified. Every one of these images are digitized and stored by
the computer.
..•
~
100 urn
The "Area Morphometry"
ftmction of the software allows the defining of air-
voids in the photo by tracing
the perimeter
of the void on the computor
monitor with the mouse. The trace is displayed
as a tmn red line on the
monitor (See Figure 4.6). The data for every defIned area in. the photo is stored
and analyzed separately.
•••
••
100 urn
y
Lx
Each photograph
that was taken represented
an area 1954 J..tmwide and 1872
J..tmhigh. Twenty photos of each mixture were analyzed resulting in more than
250 air-voids counted per mixhne.
Air-voids
were counted with diameters between
10 J..tmand a 1000 J..tm.By
setting the boundaries it was ensured that only entrained air-voids was counted
and not entrapped air or gel pores.
The output data of the software is presented and stored in an ASCII fIle. An
extract of part of the fIle is shown in Table 4.1. The count is the number of air-'
voids counted in a spesifIc photo. The area is the total area of a spesifIc airvoid in (J..tmi units. The perimeter is the length in J..tmof the red line indicated
on the computor monitor. The next two columns are the x- and y coordinates
of the centroid of each air-void.
Count
Area
Perimeter
X· Position
y. Position
4
20991.37
577.19
64.3
1117.08
30543.43
685.76
977.05
758.38
12658.85
463.64
557.97
755.42
8
2
6
34692.92
789.81
1267.8
593.96
4481.82
271.67
700.51
1132.35
1082.13
7015.42
368.07
512.13
9109.98
366.93
985.75
1042.1
260921
641.91
704.35
954.54
2847.63
227.92
922.69
821.08
17543.11
512.65
1415.72
703.62
137915
1567.1
281.09
600.62
40711.36
761.77
1402.32
199.35
2091.51
184.93
267.94
375.39
21116.37
586.9
798.62
151.87
15786.97
503.82
1179.44
912.46
8347.76
352.81
1429.51
917.84
12594.82
444.64
1374.66
720.46
27064.69
651.57
1183.64
689.18
5756.24
296.34
1177.62
130.71
There are different methods, which can be used to determine the actual
porosity of concrete. According to Gaafer (Gaafer, 1995) the porosity that is
calculated using the mercury porosimetry technique is always lower than that
determined from the vacuum saturation technique. As foamed concrete
contains relatively large percentage voids, that might not be easily accessible
to water, (Kearsley, 1999) decided to use the vacuum saturation apparatus as
developed by Cabrera and LYlllisdaleat the University of Leeds to determine
the porosity of foamed concrete.
The apparatus as developed by Cabrera and LYlllisdale at the University of
Leeds (Gaafer, B.A. 1995) is used to determine the porosity of the
mixhlretures. Figure 4.7 shows the arrangement of the apparatus.
2. Vacuum pump
3. Three - way valve, to be connected to the desiccator
4. Bottle made from pyrex.
5. De-aerator
6. Tubing
The 50-mm x 50-mm x 12-15-mm specImens
used for the microscopic
analysis was also used for this test. The samples were dried at 100
0
C until all
the evaporable water had evaporated and the weight had stabilized.
The dried samples were placed in the desiccator and the valve to the vacuum
pump was opened. The samples were placed under vacuum for at least three
hours; thereafter the valve to the bottle was opened to fill the dissicator with
de-aired, distilled water. It was filled with water up to 300 mm above sample
level and the vacuum pump was used for another three hours. At this stage the
valve to the atmosphere was opened to provide extra pressure which pushes
water into the pores of the samples. The samples remaino::d lUlder water over
night and the next day the saturated samples were weighed in air and water.
The porosity was calculated with the following fOIDllIla (Gaafer, 1995):
P
= (wsat -
W
(w - W
sat
)
dry
wat
* 100
)
P
=
Vacuum sahlration porosity (%)
Wwt
=
Weight in air of sahlrated sample
Thirty foamed concrete mi:\1ures with different ash/cement ratios and target
densities varying between 700 kg/m3 and 1500 kg/m3 are used in this
investigation. Ash/cement ratios of zero, one, two, three and four are used to
be able to detennine the effect thereof on the properties of the mixtures. The
compositions of the mi:\1ures are listed in Table 5.1. The water/cement,
ash/cement and water/binder ratios as indicated in Table 5.1 are weight ratios
and the binder content is taken as the sum of the cement and the ash. The
volumetric proportional composition of each mi:\1urecan be seen in Table 5.2.
The values of the different densities measured (as explained in Chapter 4) for
every mixture is listed in Table 5.3.
Table 5.4 shows the porosity and the 28-day cube compressive strength of
each mixture. The 28-day test and dry densities are listed with the porosity and
the cube strength. The porosity as shown in the table presents the average
value of the porosity of two samples tested for each mixture with the vacuum
sahlration method as described in the previous chapter. Each 28-day
compressive strength value presents the average of three cubes tested for every
mixhlfe.
Mix
number
Ash!
Cement
ratio
Water!
Cement
ratio
Water!
Binder
ratio
Composition
of mixture
per (m3)
Target
densiy'
(kg!m)
cement
(kg)
ash
(kg)
water
(I)
foam
(I)
fibers
(kg)
1
0
0.33
0.33
1500
1112
0
367
278
2
2
0
0.33
0.33
1200
879
0
290
429
2
3
0
0.33
033
1000
723
0
239
530
2
4
0
0.33
0.33
900
645
0
213
580
2
5
0
0.33
0.33
800
567
0
187
631
2
6
0
0.33
0.33
700
490
0
162
681
2
7
1
0.58
0.29
1500
574
574
334
221
2
8
1
0.58
0.29
1200
454
454
264
384
2
9
1
0.58
0.29
1000
373
373
219
492
2
10
1
0.58
0.29
900
333
333
195
546
2
11
1
0.58
0.29
800
294
294
173
598
2
12
1
0.58
0.29
700
252
252
149
654
2
13
2
0.87
0.29
1500
383
765
336
192
2
14
2
0.87
0.29
1200
302
605
266
361
2
15
2
0.87
0.29
1000
249
498
219
474
2
16
2
0.87
0.29
900
222
444
195
530
2
17
2
0.87
0.29
800
195
391
172
587
2
18
2
0.87
0.29
700
168
337
148
643
2
19
3
1.17
0.28
1500
291
873
320
189
2
20
3
1.17
0.28
1200
230
690
253
358
2
21
3
1.17
0.28
1000
189
568
208
472
2
22
3
1.17
0.28
900
169
507
186
528
2
23
3
1.17
0.28
800
149
446
163
585
2
24
3
1.17
0.28
700
128
385
141
641
2
25
4
1.6
0.27
1500
234
936
314
184
2
26
4
1.6
0.27
1200
185
740
248
355
2
27
4
1.6
0.27
1000
152
609
204
469
2
28
4
1.6
0.27
900
136
544
182
526
2
29
4
1.6
0.27
800
120
478
160
583
2
30
4
1.6
0.27
700
103
413
138
640
2
Composition
Water!
Cement
Ratio
(by
weight)
Water!
Binder
ratio
(by
weight)
1
0
0.33
0.33
2
0
0.33
3
0
4
Mix
number
Ash!
Cement
ratio
Target
densi7.
(kg!m)
of mixture
(per Volume)
cement
ash
water
foam
fibers
(%)
(%)
(%)
(%)
(%)
1500
35.3
0.0
36.7
27.8
0.2
0.33
1200
27.9
0.0
29.0
42.9
0.2
0.33
0.33
1000
23.0
0.0
23.9
53.0
0.2
0
0.33
0.33
900
20.5
0.0
21.3
58.0
0.2
5
0
0.33
0.33
800
18.0
0.0
18.7
63.1
0.2
6
0
0.33
0.33
700
15.5
0.0
16.2
68.1
0.2
7
1
0.58
0.29
1500
18.2
26.1
33.4
22.1
0.2
8
1
0.58
0.29
1200
14.4
20.6
26.4
38.4
0.2
9
1
0.58
0.29
1000
11.8
16.9
21.9
49.2
0.2
10
1
0.58
0.29
900
10.6
15.1
19.5
54.6
0.2
11
1
0.58
0.29
800
9.3
13.4
17.3
59.8
0.2
12
1
0.58
0.29
700
8.0
11.5
14.9
65.4
0.2
13
2
0.87
0.29
1500
12.1
34.8
33.6
19.2
0.2
14
2
0.87
0.29
1200
9.6
27.5
26.6
36.1
0.2
15
2
0.87
0.29
1000
7.9
22.6
21.9
47.4
0.2
16
2
0.87
0.29
900
7.0
20.2
19.5
53.0
0.2
17
2
0.87
0.29
800
6.2
17.8
17.2
58.7
0.2
18
2
0.87
0.29
700
5.3
15.3
14.8
64.3
0.2
19
3
1.17
0.28
1500
9.2
39.7
32.0
18.9
0.2
20
3
1.17
0.28
1200
7.3
31.4
25.3
35.8
0.2
21
3
1.17
0.28
1000
6.0
25.8
20.8
47.2
0.2
22
3
1.17
0.28
900
5.4
23.0
18.6
52.8
0.2
23
3
1.17
0.28
800
4.7
20.3
16.3
58.5
0.2
24
3
1.17
0.28
700
4.1
17.5
14.1
64.1
0.2
25
4
1.6
0.27
1500
7.4
42.6
31.4
18.4
0.2
26
4
1.6
0.27
1200
5.9
33.6
24.8
35.5
0.2
27
4
1.6
0.27
1000
4.8
27.7
20.4
46.9
0.2
28
4
1.6
0.27
900
4.3
24.7
18.2
52.6
0.2
29
4
1.6
0.27
800
3.8
21.7
16.0
58.3
0.2
30
4
1.6
0.27
700
3.3
18.8
13.8
64.0
0.2
Densities
Mix
number
Ashl
Waterl
Cement
ratio
Cement
ratio
Waterl
Binder
ratio
Target
densitx
(kg/m)
Casting
densitx
(kg/m)
De-mould
densitx
(kg/m)
28-day
Test
28-day
Dry
densitx
(kg/m)
densitx
(kg/m)
1
0
0.33
0.33
1500
1488
1465
1460
1223
2
0
0.33
0.33
1200
1199
1200
1197
892
3
0
0.33
0.33
1000
1013
998
994
831
4
0
0.33
0.33
900
897
888
882
741
5
0
0.33
0.33
800
810
788
783
661
6
0
0.33
0.33
700
677
667
657
536
7
1
0.58
0.29
1500
1512
1478
1463
1235
8
1
0.58
0.29
1200
1170
1089
1071
901
9
1
0.58
0.29
1000
1014
1006
989
811
10
1
0.58
0.29
900
906
885
872
735
11
1
0.58
0.29
800
815
788
774
646
12
1
0.58
0.29
700
716
705
694
559
13
2
0.87
0.29
1500
1516
1475
1467
1230
14
2
0.87
0.29
1200
1208
1160
1156
958
15
2
0.87
0.29
1000
1018
995
988
790
16
2
0.87
0.29
900
900
879
865
713
17
2
0.87
0.29
800
788
784
767
612
18
2
0.87
0.29
700
722
707
691
555
19
3
1.17
0.28
1500
1514
1477
1469
1219
20
3
1.17
0.28
1200
1211
1189
1185
958
21
3
1.17
0.28
1000
1041
1016
1012
812
22
3
1.17
0.28
900
901
880
869
697
23
3
1.17
0.28
800
813
802
795
631
24
3
1.17
0.28
700
711
704
691
540
25
4
1.6
0.27
1500
1488
1456
1443
1168
26
4
1.6
0.27
1200
1214
1185
1173
941
27
4
1.6
0.27
1000
1012
994
985
771
28
4
1.6
0.27
900
917
884
875
726
29
4
1.6
0.27
800
797
772
759
689
30
4
1.6
0.27
700
719
687
676
518
28-day
Com
pressive
Strength
(MPa)
Ashl
Cement
ratio
Waterl
Cement
ratio
Waterl
Binder
ratio
Target
densitt:
28-day
Test
densitt:
28-day
Dry
densilJ.
(kg/m)
(kg/m)
(kg/m)
1
0
0.33
0.33
1500
1460
1223
43.5
22.00
2
0
0.33
0.33
1200
1197
892
55.1
9.40
3
0
0.33
0.33
1000
994
831
59.8
7.17
4
0
0.33
0.33
900
882
741
64.8
4.52
5
0
0.33
0.33
800
783
661
68.9
3.30
6
0
0.33
0.33
700
657
536
76.8
2.00
7
1
0.58
0.29
1500
1463
1235
41.7
24.20
8
1
0.58
0.29
1200
1071
901
53.5
6.25
9
1
0.58
0.29
1000
989
811
58.2
4.69
10
1
0.58
0.29
900
872
735
61.9
2.92
11
1
0.58
0.29
800
774
646
70.9
2.29
12
1
0.58
0.29
700
694
559
72.4
1.40
13
2
0.87
0.29
1500
1467
1230
41.9
20.50
14
2
0.87
0.29
1200
1156
958
51.7
5.84
15
2
0.87
0.29
1000
988
790
60.0
3.76
16
2
0.87
0.29
900
865
713
67.8
2.45
17
2
0.87
0.29
800
767
612
71.8
1.47
18
2
0.87
0.29
700
691
555
73.8
1.00
19
3
1.17
0.28
1500
1469
1219
40.7
10.56
20
3
1.17
0.28
1200
1185
958
49.8
5.07
21
3
1.17
0.28
1000
1012
812
55.1
2.43
22
3
1.17
0.28
900
869
697
67.5
1.61
23
3
1.17
0.28
800
795
631
71.3
1.14
24
3
1.17
0.28
700
691
540
72.5
0.72
25
4
1.6
0.27
1500
1443
1168
42.6
6.63
26
4
1.6
0.27
1200
1173
941
56.6
3.53
27
4
1.6
0.27
1000
985
771
60.3
1.71
28
4
1.6
0.27
900
875
726
66.1
1.25
29
4
1.6
0.27
800
759
689
70.7
0.77
30
4
1.6
0.27
700
676
518
74.2
0.53
Mix
number
Porosity
("!o)
The aim of this research is to investigate the microstructure of the material as a
primary factor influencing the relationship between the physical properties
(such as density and porosity), and the struchlral property (compressive
strength) of foamed concrete. In order to evaluate these relationships it was
necessary to develop parameters to explain and quantifY the microstruchlre of
foamed concrete.
Literature review indicated that the air-void struchlre of foamed concrete is
one of the most important micro-properties influencing the properties of the
material. Therefore in this chapter the development of the air-void structure
parameters are discussed.
From the literature it is found that the air-void structure of air-entrained
concrete can be described in terms of the air-void shape, size distribution and
spacing in the cement paste.
The
Rosin-Rammler
distribution
and
the
overSIze air-void
diameter
distribution are investigated to determine parameters for the air-void size
distribution.
The perpendicular distance through the cement paste from one air-void to the
nearest other air-void in the vicinity is used to describe the spacing of the airvoids. Specific parameters for these distances are developed and discussed in
this chapter.
The shape of the air-voids in the mixtures used in this investigation had to be
determined first before parameters could be developed to describe the air-\'oid
structure of foamed concrete.
Twenty photographs
with a target
investigate
density
(and therefore twenty images) were taken from a mixture
of 900 kg/m3 and an ash / cement ratio of two to
the shape and alig1Ullent of the air-voids. The total distance in /-lm
of the cord in the direction of the x-axis through the centroid of the air-void is
taken as the x-cord of the air-void.
The total distance of the cord in the
direction of the y-axis through the centroid of the air-void is taken as the ycord of the air-void
(See Figure
6.1).
The x-cord and the y-cord were
measured for every air-void in an image (See Table 6.1 for all the data).
~
100 urn
The shape of the air-voids can be determined by evaluating the x- and y-cords
of the air-voids. The air-void is circular if the x-cord of the air-void is equal to
the y-cord of the air-void.
In Figure 6.2 the y-cords of the air-voids are plotted as a function of the xcords and there is clearly no orientation
of the air-voids
in the x- or y-
direction. From tllis graph it can also be seen that the air-voids with diameters
smaller
than 300 /-lm have a lligher circularity
diameters greater than 300
~1l11
in section than those with
in section. The most likely reason therefore is
that the air bubbles merge if the diameter of the air-voids become greater than
300 /-lm.
x-chord
y- chord
x- chord
y- chord
x- chord
y- chord
x- chord
y- chord
(urn)
(urn)
(urn)
(urn)
(urn)
(urn)
(urn)
(urn)
63
56
353
390
180
165
223
235
68
64
198
269
125
133
60
53
343
134
108
125
178
193
550
605
300
234
123
140
210
175
235
230
88
124
382
195
140
123
245
265
226
304
354
253
115
120
188
203
337
520
596
233
135
198
396
333
327
45
108
163
153
190
225
205
227
279
93
93
128
148
400
235
225
226
309
265
438
343
190
159
185
156
375
270
163
145
435
378
91
106
493
370
568
208
135
150
444
222
418
398
326
138
185
225
213
224
242
228
185
148
153
155
109
71
238
235
498
383
530
550
395
327
142
105
556
320
243
273
300
295
176
185
60
73
178
185
138
149
99
105
268
275
143
148
93
110
200
263
63
90
488
511
48
97
145
155
113
108
78
134
300
159
160
178
63
85
235
235
255
279
195
275
53
55
270
403
193
231
375
200
833
465
48
60
276
256
128
105
138
163
62
56
140
130
119
155
74
113
125
123
278
273
317
267
626
380
168
145
52
44
498
208
178
165
358
435
230
215
70
110
78
92
141
208
468
I
450
l
900
Air-voids
circular in
section
800
700
E
:l
600
~
500
.,g
400
"E
>-
I
I
••••
t-
•
u
Merging of air-voids
~,,,,,
••
.+.•
300
200
100
I
o
o
~
+
+
I
I
I
I
•
+
•
•
•
•
•
•
300
400
600
500
700
800
900
Figure 6.3 shows the histogram of the x-chord / y-chord ratio of the air-voids
with diameters smaller than 300
~lln.The
air-void is circular if the x-chord / y-
chord ratio equals one. The mean and standard deviation of this histogram was
found
to be 0.96
distribution
Joubert,
and 0.024
respectively.
The probability
with a standard nOffiml variable of two is P
1996). 95.4%
therefore
=
for a normal
0.954 (Van As and
of the x-chord / y-chord ratio values fall
between 0.91 and 1.01. Based on this analysis and data the assumption
made that the majority of air-voids
was
in the foamed concrete mixtures can be
described as circular in section.
30%
,
I
25%
20%
>.
u
c
I_ Frequency
QJ
:l 15%
e-
ll:
u.
10%
5%
I
0%
I
,
I
I
~
I_•
•
Figure 6.3: Histogram of x-chord / y-chord ratios of air-voids with diameters
smaller than 300 flm
1
Using the fact that the air-Yoids are circular in section and assuming that the
air-voids
are perfect spheres, an effective air-void diameter can be calculated
using the measured area from the software output data (Visagie, 1997):
Air-void diameter
The distribution
{4A
= {--;-
of the air-Yoid sizes was detemlined by plotting a histogram
for the calculated air-voids counted in each mixtme. Typical air-void diameter
distributions
are indicated in Figure 6.4 and the histograms plotted for all the
other mixtures are attached in Appendix A. The percentage of the number of
voids is plotted on the vertical axis and the air-void diameters are plotted on
the horizontal
axis. The cumulatiw
persentage distribution
is also plotted on
tlllS graph. The size distribution of air-voids for all the mixtures follows a log
nonnal
distribution
(Visagie,
1997). The cmllulative
distribution
shows the
persentage of the voids that is smaller than a certain diameter.
From Figure 6.4 it appears that for lower densities there is an increase in the
number of larger voids. Parameters had to be developed, in order to quantifY
these differences
in air-void
sizes and to compare the mixtures
with each
other. These parameters ,vill also be used to evaluate the influence of air-void
size distribution on the properties offoamed concrete.
By plotting
cumulative
the
inverse
of the cumulative
percentage
% oversize air-void diameter distribution
distribution,
the
is obtained as shown in
Figure 6.5. ProYision was made for statistical outliers by not taking the five
percent smallest diameters and five percent largest diameters into account. A
cumulative
plot as shown in figure 6.5 was drawn for each mixture
Appendix B).
(see
Mix 3 - Target
density
1000 kg/m3
=
(A/C
0)
100%
10%
90%
9%
8%
80%
~
7%
70%
u
6%
60%
OJ
5%
50%
C"
OJ
4%
40%
3%
30%
>c:
:>
u:
2%
1%
-hi
0%
a
~
"
a
a
~
~
a
(0
a
a
N
(0
N
a
;;:;
a
a
(0
~
(')
Mix 5 - Target
B,'I ,I,'. ' : i , i Ii,
a
(0
'<t
a
U;
a
a
I[l
<0
(0
diameter
density
III , ,n, i I i IIIII
a
(0
(0
a
a
a
t: "- ;;;
(0
a
co
(0
a
0;
a
(um)
800 kg/m3
(AiC
=
0)
100%
90%
8%
80%
7%
70%
~
6%
60%
,:::
5%
C"
OJ
4%
u:
:>
(0
OJ
9%
OJ
:>
E
()
0%
~
10%
>u
c:
:;
10%
Void
~
OJ
:;>
20%
,',a ,.",
(0
~
50%
,,.:·:·:·:·:,:·:3
3%
40%
F re que nc y
--Cumulative
30%
%
OJ
';
:;
E
:>
()
20%
2%
1%
10%
0%
0%
0
0
(0
0
0
(0
~
0
0
(0
N
N
0
;;:;
0
<D
(')
0
~
Void
0
<D
"
0
U;
diameter
0
<D
l{)
0
<0
0
<D
<D
0
r-
0
<D
r-
0
;;;
0
(0
ea
0
0;
0
(0
OJ
~
a
:2:
(urn)
The fitted trendline that best describe the measured values is an exponential,
function. The fitted functions for all the mixtures can be seen in Table 6,2. The
statistical
R-square value for all the mixtures of the exponential fit is bet\veen
0.96 and 0.998. The exponential equation is therefore a tme representation
of
the cumulative % oversize air-void diameter distribution.
Both the constants
in the equation vary with density and ash content and
therefore the constants as such cmmot be used to compare the mih,tures (See
100%
90%
ClJ
N
'iij
...
ClJ
>
0
<ft.
ClJ
.:::
i;j
:;
E
::::l
u
y = 2.0915e-00109x
80%
R2
70%
=
0.9945
60%
i
I!
Cumulative % over-size
•
50%
j-
40%
E,poo. (C"m"l,ti~ %
30%
20%
O~I.
size)
I
I
I
t=:1
H
i
:
10%
0%
0
Defining
the
distribution
air-voids
as
circular
areas
in section
the
Rosin-Ranml1er
function (equation 3.6) can be used to provide a way of describing
the air-void size distribution quantitatively.
The cumulative
% oversize air-void diameter distribution
can be represented
as a Rosin-Ranunler
trendlines fitted for all the mixtures'
distributions
are
representation
of the distributions
The Rosin-Ranunler
exponential
as discussed in 6.3.1
distribution.
cumulative
equations
The reason
is the
% oversize air-void diameter
and
these
equations
are
tme
- see 6.3.1.
air-void SIze distribution
parameters
are listed in Table
6.3 and Figure 6.6 and 6.7 is an example of how the values in the Table were
graph In In (l/y) versus In
derived. The modified Rosil1-Ranunler distribution
is plotted,
with y the fitted nmctions y
cumulative
% oversize
air-void
diameter
=
a
e(bx)
x
(see Table 6.2) for the
distribution
and x the air-void
diameter. A linear trend line and equation is also added to these graphs (see
Figure 6.6). The slope and interception
taken as the n value and In x
0
value respectively
Ranunler nmction. The Rosin-Ranull1er
viewed in Appendix C.
with the horizontal
distribution
axis of the line is
of the modified
Rosin-
for all the mix1ures can be
Target
Fitted Function
v
a e lb,)
Ash!
Cement
ratio
Water!
Cement
ratio
Water!
Binder
ratio
a
b
1
0
0.33
0.33
1500
1.4517
-0.0061
0.9752
2
0
0.33
0.33
1200
3.1625
-0.0137
0.9948
3
0
0.33
0.33
1000
20915
-0.0109
0.9945
4
0
0.33
0.33
900
1.8106
-0.0085
0.9948
5
0
0.33
0.33
800
1.6839
-0.0072
0.9918
6
0
0.33
0.33
700
1.6907
-0.004
0.9881
7
1
0.58
0.29
1500
1.9795
-0.0108
0.9966
8
1
0.58
0.29
1200
2.1509
-0.0109
0.9953
9
1
0.58
0.29
1000
1.954
-0.0095
0.9948
10
1
0.58
0.29
900
1.6416
-0.0073
0.9915
11
1
0.58
0.29
800
1.3041
-0.0053
0.9947
12
1
0.58
0.29
700
1.4722
-0.0043
0.9849
13
2
0.87
0.29
1500
2.5265
-0.0125
0.9936
14
2
0.87
0.29
1200
2.0025
-0.0125
0.9824
15
2
0.87
0.29
1000
1.4143
-0.0071
0.9733
16
2
0.87
0.29
900
2.1091
-0.0072
0.9888
17
2
0.87
0.29
800
1.8165
-0.0056
0.9824
18
2
0.87
0.29
700
1.655
-0.0057
0.9941
19
3
1.17
0.28
1500
2.0551
-0.0117
0.9829
20
3
1.17
0.28
1200
1.7065
-0.0111
0.96
21
3
1.17
0.28
1000
1.6738
-0.0064
0.985
22
3
1.17
0.28
900
1.6455
-0.0056
0.9935
23
3
1.17
028
800
2.1211
-0.0052
0.9756
24
3
1.17
0.28
700
2.04
-0.0035
0.9748
25
4
1.6
0.27
1500
5.333
-0.0183
0.9784
26
4
1.6
0.27
1200
5.01
-0.0168
0.9771
27
4
1.6
0.27
1000
3.2081
-0.0119
0.9899
28
4
1.6
0.27
900
1.61
-0.0052
0.9771
29
4
1.6
0.27
800
2.1105
-0.0071
0.9745
30
4
1.6
0.27
700
1.8457
-0.0041
0.9915
Mixture
number
densilf:
(kg!m)
=
R2
w
.~
VI
Qj
>
0
"*>
0.8
y
=
1.3047x
R'2
QJ
=
- 6.5393
0.9973
Slope (n) = 1.3047
~:J
=
5.012
parameter
(Xc)
In Xo
E 04
:J
Position
=
150 um,
~
.,...
E
E
oJ
0
36.8
% of the air-void
diameters
are greater than the
Xo
value
(position
parameter in !lm) This parameter is an indicator of the void size. The n value
represents
the range of the air-void
diameter
distribution
of the air-void
diameters greater than Xo (See Figure 6.7).
100%
90%
QJ
.~
VI
80%
Qj
>
70%
I
n (slope) indicates the
0
60%
"*.:':
range of the air-void
diameters larger than
50%
Xo
~:J
30%
QJ
E
:J
40%
20%
--Expon.
()
10%
(Cumulative
% over-
size)
0%
0
The values of the slope n and the position parameter
Xo
for all 30 mixtures can
be seen in Table 6.3. The equations for the linear trendline fitted to the RosinRanunler distribution
graph and the statistical R-square value of the linear fit
are also listed in Table 6.3.
Ash!
Water!
Mixture
number Cement Cement
ratio
ratio
Water!
Binder
ratio
Target
densilf:
(kg!m)
Fitted function for
Rosin-Rammler
distribution graph
y
cx + d
=
c
d
R2
Rosin·Rammler
distribution
oarameters
Slope
Position
parameter
n
xo(um)
219
1.183
1
0
0.33
0.33
1500
1.183
-6.3729
0.9993
2
0
0.33
0.33
1200
1.6407
-8.2473
0.9968
152
1.6407
3
0
0.33
0.33
1000
1.3047
-6.5393
0.9973
150
1.3047
4
0
0.33
0.33
900
1.2441
-6.4421
0.9981
176
1.2441
5
0
0.33
0.33
800
1.2117
-6.42
0.9986
198
1.2117
6
0
0.33
0.33
700
1.2918
-7.6459
0.999
372
1.2918
7
1
0.58
0.29
1500
1.3796
-6.9278
0.9984
152
1.3796
8
1
0.58
0.29
1200
1.4213
-7.1877
0.9984
157
1.4213
9
1
0.58
0.29
1000
1.3761
-7.0778
0.9985
171
1.3761
10
1
0.58
0.29
900
1.2794
-6.7807
0.9991
200
1.2794
11
1
0.58
0.29
800
1.1516
-6.2888
0.9996
235
1.1516
12
1
0.58
0.29
700
1.2172
-7.0058
0.9994
316
1.2172
13
2
0.87
0.29
1500
1.5112
-7.5665
0.9978
149
1.5112
14
2
0.87
0.29
1200
1.389
-6.7821
0.9984
132
1.389
15
2
0.87
0.29
1000
1.1973
-6.259
0.9994
186
1.1973
16
2
0.87
0.29
900
1.416
-7.7351
0.9984
236
1.416
17
2
0.87
0.29
800
1.333
-7.5034
0.9987
278
1.333
18
2
0.87
0.29
700
1.2818
-7.1157
0.999
258
1.2818
19
3
1.17
0.28
1500
1.4084
-6.9932
0.9983
143
1.4084
20
3
1.17
0.28
1200
1.3063
-6.411
0.9989
134
1.3063
21
3
1.17
0.28
1000
1.2918
-7.0329
0.999
231
1.2918
22
3
1.17
0.28
900
1.2811
-7.1319
0.999
262
1.2811
23
3
1.17
0.28
800
1.4198
-8.2239
0.9982
328
1.4198
24
3
1.17
0.28
700
1.4341
-8.8538
0.9986
480
1.4341
25
4
1.6
0.27
1500
1.9269
-9.5447
0.9955
142
1.9269
26
4
1.6
0.27
1200
1.8923
-9.4934
0.9956
151
1.8923
27
4
1.6
0.27
1000
1.6425
-8.493
0.9973
176
1.6425
28
4
1.6
0.27
900
1.2676
-7.1315
0.9991
277
1.2676
29
4
1.6
0.27
800
1.4194
-7.7762
0.9982
240
1.4194
30
4
1.6
0.27
700
1.341
-7.9768
0.9987
383
1.341
The corresponding
50 % oversize air-void diameter (D50) in I-lm can be read
from the exponential
fit graph
(see Figure
6.8). This diameter
gives an
indication of the average void size of each mih1ure. In the same way the 10 %
oversize air- void diameter
(D 10), which shows the difference in number of
larger voids in each mixture.
The values of the oversize air-void diameter
distribution parameters (D50) and (D 10) can be seen in Table 6.4. These
parameters can be compared for different mixture compositions.
100%
90%
y
QJ
.!::!
(/)
(jj
>
0
<f.
QJ
.:::
80%
2.0915e'00109x
R2
70%
=
0.9945
60%
50%
40%
E
::J
30%
E
::J
20%
u
=
--
Expon. (Cumulative % over
size)
10%
0%
0
100
10501
200
300
1010
I
The shape and size of the air-voids can not be the only aspects describing the
air-void stTIlcture because the thickness of the paste arolmd the air-voids may
also have an influence on the properties of the material. Based on the principle
that a chain is only as strong as its weakest link, the minimum paste thickness
around each air-void was established (Kearsley, 1999).
The perpendicular
distance through the cement paste from one air-void to the
nearest other air-void in the vicinity is used to describe the spacing of the airvoids in other words the minimLUll paste thickness for each air-void - see the
microscopic image in Figure 6.9.
Mixture
number
Ash!
Water!
Cement Cement
ratio
ratio
Water!
Binder
ratio
Target
densiv,
(kg!m)
Fitted Function
y
a e Ibx)
=
R2
Oversize air-void
diameter distribution
parameters
D10
D50
(,...m)
(f.lm)
a
b
1
0
0.33
0.33
1500
1.4517
-0.0061
0.9752
175
439
2
0
0.33
0.33
1200
3.1625
-0.0137
0.9948
135
252
3
0
0.33
0.33
1000
2.0915
-0.0109
0.9945
131
279
4
0
0.33
0.33
900
1.8106
-0.0085
0.9948
151
341
5
0
0.33
0.33
800
1.6839
-0.0072
0.9918
169
392
6
0
0.33
0.33
700
1.6907
-0.004
0.9881
305
707
7
1
0.58
0.29
1500
1.9795
-0.0108
0.9966
127
276
8
1
0.58
0.29
1200
2.1509
-0.0109
0.9953
134
282
9
1
0.58
0.29
1000
1.954
-0.0095
0.9948
143
313
10
1
0.58
0.29
900
1.6416
-0.0073
0.9915
163
383
11
1
0.58
0.29
800
1.3041
-0.0053
0.9947
181
485
12
1
0.58
0.29
700
1.4722
-0.0043
0.9849
251
625
13
2
0.87
0.29
1500
2.5265
-0.0125
0.9936
130
258
14
2
0.87
0.29
1200
2.0025
-0.0125
0.9824
111
240
15
2
0.87
0.29
1000
1.4143
-0.0071
0.9733
146
373
16
2
0.87
0.29
900
2.1091
-0.0072
0.9888
200
423
17
2
0.87
0.29
800
1.8165
-0.0056
0.9824
230
518
18
2
0.87
0.29
700
1.655
-0.0057
0.9941
210
492
19
3
1.17
0.28
1500
2.0551
-0.0117
0.9829
121
258
20
3
1.17
0.28
1200
1.7065
-0.0111
0.96
111
256
21
3
1.17
0.28
1000
1.6738
-0.0064
0.985
189
440
22
3
1.17
0.28
900
1.6455
-0.0056
0.9935
213
500
23
3
1.17
0.28
800
2.1211
-0.0052
0.9756
278
587
24
3
1.17
0.28
700
2.04
-9·0035
0.9748
402
862
25
4
1.6
0.27
1500
5.333
-0.0183
0.9784
129
217
26
4
1.6
0.27
1200
501
-0.0168
0.9771
137
233
27
4
1.6
0.27
1000
3.2081
-0.0119
0.9899
156
291
28
4
1.6
0.27
900
1.61
-0.0052
0.9771
225
534
29
4
1.6
0.27
800
2.1105
-0.0071
0.9745
203
430
30
4
1.6
0.27
700
1.8457
-0.0041
0.9915
319
711
Figure 6. 10 which represent
coordinate,
y-coordinate
and
a nucroscoplc
a radius
(R)
Image of tlu'ee air-voids.
represent
each
air-void.
A xThe
coordinates of the centroids of the air-voids are fOlmd in the output data of the
software. The radii were calculated from the measured areas by assuming that
all air-voids are perfect spheres.
..•
~
100 um
The distance (51,2) between void 1 and void 2 can be calculated
usmg the
following equation (Kearsley, 1999):
51,2
=
Xl X2 =
Yl Y2
=
Rd~2
=
Minimum Perpendicular distance between void 1 and void 2.
x-coordinates of void 1 and void 2.
y-coordinates of void 1 and void 2.
radii of void 1 and void 2.
By sequentially replacing the properties of void 2 in Equation 6.1 with each of
the air-voids on the photo the distance behveen void 1 and each of the of the
other voids can be calculated. These distances are compared and the minimmll
distance is recorded as the space between void 1 and its closest neighbor. After
detemlining the minimwn spacing for void I the procedure -can be repeated for
each of the other voids (Kearsley, 1999).
The ASCII file of the photo data as produced by the analysis
every photograph'
taken
\vere imported
into
spreadsheets
software for
using
Microsoft
Excel. A macro was written in Excel (see Appendix D) to take each void and
calculate the thickness of the paste between that void and all the other voids.
The minimum
value calculated
was taken as the minimum
thickness
of the
paste around that spesific void (Kearsley,
1999). The macro as written by
Kearsley was changed for tIus investigation.
A negative minimum value (air-
voids touching each other) is recorded by the macro as zero.
The distribution
spacing)
of the minimum distances between the air-voids
was determined
by plotting
lustograms
for the calculated
spacings cOtU1tedin each mixhrre. A typical distribution
6.11 and the histograms
(the air-void
air-void
is indicated in Figure
plotted for all the other mixhlres
are attached in
Appendix E. The percentage of the number of milumurn distances between airvoids is plotted on the vertical axis to compare the histograms
mixhlres
horizontal
with
each other
and the air-void
axis. The cumulative
frequancy
spacings
of the different
are plotted
% distribution
on the
for the air-void
spacing is also plotted on this graph. The spacing of the air-voids indicated, as
zero on the graph is air-voids touching each other.
20%
100%
18%
90%
16%
80%
~
14%
70%
>-
12%
60%
. 50%
4J
c
" 10%
4J
:J
t::r 8%
.
t..···,·········,
Frequency
4J
u:
~
6%
I --
4%
Cumulative
%
%
H
r-t
1;
III
"5
40%
§
30%
20%
()
2%
10%
0%
0%
0
distribution was used to develop parameters for spacing of air-voids in order to
compare mi:\.'tures.
The inverse of the cumulative frequency % distribution of the air-void spacing
was obtained and an exponential function was fitted for the graph (see Figure
6.12). The exponential
fit for the graphs for all the mixtures can be viewed in
Appendix F. Provision was made for statistical outliers by omitting the top and
bottom 5 %, in other words the 5 % voids with the smallest distance to their
nearest neighbor and the 5 % voids with the largest distance to their nearest
neighbor.
The fitted functions for all the mixtures can be seen in Table 6.5.
The statistical
R-square
value for all the mixtures of the exponential
fit is
bet\veen 0.89 and 0.998 (see Table 6.5). The exponential equation is therefore
a tme representation
of the inverse of the cumulative frequency % distribution.
Both the constants
in the equation vary with density and ash content and
therefore the constants
as such CalUlot be used to compare the miA'tures (See
The median distance bet\veen the air-voids 550 (where 50% of the air-void
spacing are smaller than the value) and 590 distance (where 10 % of the void
spacing are smaller than the value) was calculated for each mixhlre by using
the fitted functions (See Figure 6.12). S50 and S90 are also listed in Table 6.5.
100% ~---------------------------90%
y
80%
=
1 1524e -0.0043x
RZ• = 0.9874
~I-------------~
70%
60%
% over size
I--cumulative
50%
40%
--
30%
Expon.
size)
(Cumulative
% over
20%
10%
0%
o
100
200
IS50
~
•
I
The air-voids in these mixhrres are approximately
circular in section and it
was assmned that the air-voids are perfect spheres, therefore the size of the
air-voids are best described with an effective air-void diameter.
•
The air-void diameter distribution follows a log normal distribution.
•
The Rosin-Ranunler
void size distribution.
indicates
diameters
distribution
parameters
are used to describe the a1r-
It consists of the position parameter (xo), (this value
the air-void diameter in Jlm for which 36.8 % of the air-void
are larger) which gives an indication of the void size. The (n)
value represents
the range of the air-void diameter distribution
void diameters greater than (xo).
of the air-
Water!
Cement
ratio
Water!
Binder
ratio
densitt
(kg!m)
1
a
0.33
0.33
1500
1.2027
-0.0427
0.9874
190
7
2
a
0.33
0.33
1200
1.0481
-0.0134
0.996
60
11
3
a
0.33
0.33
1000
0.9042
-0.017
0.9975
30
a
4
a
0.33
0.33
900
0.9264
-0.0144
0.9953
40
2
5
a
0.33
0.33
800
0.921
-0.0157
0.99
70
2
6
a
0.33
0.33
700
0.9913
-0.0097
0.9889
70
10
7
1
0.58
0.29
1500
1.1256
-0.0056
0.9826
140
40
8
1
0.58
0.29
1200
1.239
-0.0097
0.9862
90
33
9
1
0.58
0.29
1000
1.1769
-0.0102
0.9928
80
26
10
1
0.58
0.29
900
1.081
-0.0072
0.9888
100
25
11
1
0.58
0.29
800
1.1069
-0.0069
0.9412
110
30
12
1
0.58
0.29
700
0.6975
-0.0058
0.963
60
a
13
2
0.87
0.29
1500
1.0495
-0.0043
0.9747
150
36
14
2
0.87
0.29
1200
0.9919
-0.0038
0.9704
180
26
15
2
0,87
0.29
1000
1.2805
-0.0076
0.9911
120
46
16
2
0.87
0.29
900
1.2951
-0.0084
0.9822
110
43
17
2
0.87
0.29
800
1.1853
-0.0091
0.987
90
30
18
2
0.87
0.29
700
1.3375
-0.0096
0.9863
100
41
19
3
1.17
0.28
1500
1.4157
-0.0091
0.9893
110
50
20
3
1.17
0.28
1200
1.2286
-0.0071
0.9853
130
44
21
3
1.17
0,28
1000
1.1899
-0.0085
0.9951
100
33
22
3
1.17
0.28
900
1.3901
-0.0098
0.9658
100
44
23
3
1.17
0.28
800
1.6036
0.00102
0.9718
110
57
24
3
1.17
0.28
700
1.0125
-0.0067
0.9664
100
18
25
4
1.6
0.27
1500
1.6886
-0.0044
0.9501
280
143
26
4
1.6
0.27
1200
1.2471
-0.0079
0.9951
120
41
27
4
1.6
0.27
1000
1.3124
-0.012
0.9784
80
31
28
4
1.6
0.27
900
1.2185
-0.0062
0.984
140
49
29
4
1.6
0.27
800
0.7782
-0.004
0.8923
110
a
30
4
1.6
0.27
700
1.3544
-0.0076
0.9736
130
54
Target
Fitted Function
y
a e Ib,)
Air-void spacing
parameters
Ash!
Cement
ratio
Mixture
number
=
a
2
R
b
550
590
(~)
(~)
•
The oversize air-void diameter distribution parameters (D50) and (DlO)
are developed to quantify the air-void size distribution.
The 50 % oversize
air-void diameter (D50) in llm gives an indication of the average void size
of each mixture. The 10 % oversize air-void diameter (D 10) indicates the
diameter for which only 10 % of the diameters are larger.
•
The perpendicular
distance through the cement paste from one air-void to
the nearest other air-void in the vicinity is used to describe the spacing of
the air-voids.
•
The spacing
parameters
describe
the distances
between
the air-voids
S50 and S90 are developed
between
air-voids.
and S90 indicates
to quantify and
S50 is the median
distance
the value where 10 % of the
distance between the air-voids is smaller than the value.
The aim of this chapter is to investigate the effect of the air-void stmcture
(air-void size distribution and air-void spacing) on the relation between
physical properties (such as density, ash / cement ratio and porosity), and the
structural property (compressive strength) of foamed concrete. The air-void
structure parameters as developed in chapter 6 are used to detennine the
relationships.
Kearsley (1999) has published results of properties of foamed concrete as a
fimction of dry density. In some references (Neopor and L.B. Chemicals,
Product Information sheets) the properties of foamed concrete are related to
the wet density. The relation between the wet and dry density of the mixtures
is a linear relation (see Figure 7.1) and can be used to compare the results
obtained from the different studies.
1500
• Casting
1250
Density
M
o De-mould
E 1000
.t. 28-Day Test density
<
OJ
~
£'
750
III
I::
<II
0
~
500
0
250
0
0
Density
The effect of the 28-day dry density on the air-void size-distribution
seen
in
Figure 7.2
and
distribution parameters
Figure
7.3.
The
Rosin-Ranunler
can be
air-void
size
(as discussed in 6.3 .1.1) are plotted as a ftmction of the
28-day dry density.
600
E
2-
500
0-
?:S
~i
400
:
~
x
.••
x
• "...
0;
E 300
~
l'J
c..
c 200
:E
"
c..0
-_._-_.
! •••
#A
A/C
A/C
= 1
= 2
I
i,xA/C=3'
x
+
I
I
I
I.•
--+--~-,,.•.•
~~~--_.
i
!
"A/C
= 4
";j(
100
0
,
0
200
Figure 7.2: Relation between
position parameter (xo)
:s
.-A-I-C-=-O~
28-day dry density and Rosin-Rammler
+
1.5 .,--~~~~~~~~~~~~~~~~~~~~~~--~~----,
x
f+,
GI
a.
S!
x
•••
.+
"x~.•. " •x+ •
.•.
"
...
X
distribution
"
.A/C = 0
.•.
'.
XII
+
VI
A/C
= 1
: .•• A/C
= 2
: xA/C
= 3
! "A/C
= 4
i
1400
Figul'C 7.3: Relation
slope (11) parameter
between 28-day dl'Y density and Rosin-Rammler
distdbution
The graph in Figure 7.2 indicates that the position parameter (xo) and therefore
the air-void diameters become smaller as the dry density increases.
In Figure 7.3 the slope (n) is plotted as a ftmction of the dry density. From this
graph it seems that the 28-day dry density does not have any influence on the
n value, which represents the range of the air-void diameter distribution of the
air-void diameters greater than the position parameter (xo).
The relevance of the Rosin-Ranmller
air-void size distribution parameters was
evaluated by comparing the fitted flillctions for the cumulative % oversize airvoid diameters
for different 28-day dry densities for a spesific ash / cement
ratio. The flillctions for ash / cement ratios of three are plotted in Figure 7.4.
The rest of the void size distributions can be viewed in Appendix G.
100%
l
I
90%
: __ Dry Density"
_____Dry Density"
OJ
N
'Q;"
70%
>
60%
0
;;"
OJ
>
~
:l
E
:l
0
-----------:
50%
40%
-lIE-
Dry Density
--
Dry Density"
f!
631 kg/m3
----l
540 kg/m3
I
I
--.- Dry Density"
____ Dry Density"
=
I
812 kg/m3
697 kg/m3
1219 kg/m31
958 kg/m3
!
I
I
30%
20%
~
10%
I
I
0%
-+-----~--~
0
100
Figure 7.4: Summary
air-voill diameters
200
of exponential
fitted functions for the cumulative
% oversize
According to Figure 7.4 the position parameter (xo) and therefore the air-void
diameters
increase as the dry density decreases. On the other hand it is clear
that the dry density has a significant
diameters
influence on the range of the air-void
greater than the position parameter (xo).
The mihtures with lower
densities seem to have more of the larger voids but this trend cannot be seen
when comparing the Rosin-Ranulller
The Rosin-Ranmller
representative
air-void
slope (n) parameters.
SIze distribution
of the air-void size distribution
the fact that the Rosin-Ranulller
end of the cumulative
parameters
parameters
are therefore not
of the mixtures. The reason is
are insensitive
towards the tail
% oversize air-void diameter distribution.
In Figure 7.5 the oversize air-void diameter distribution
parameters
(D50)
and (D 10) are planed as a function of the 28-day dry density in order to find
the influence of dry density on the air-void size distribution.
_._---~~
1000
900
800
o:i
'0
"0
C
0
.~
E
I.AJC = oi·
700
~ .0:; ~
I.
A/C
500
i.
A/C
'"
400
I xA/C
I ";KA/C
2- 600
I
(Il
<{
N
(Il
~
'"
>
0
:5
(Il
'0
QJ
E
"'0~
300
= 1i
= 2i
= 31
•
=
41
1
200
100
0
0
between 28-day dry density and air-void size distdbution
Figure 7.5: Relation
parameters
As the 28-day
smaller.
(hy density
At higher densities
increases
the average
void diameters
became
the 10 % largest voids in the mixhlres
become smaller. It is interesting to note that the distribution
also
curves converge.
indicating
that the voids become smaller and more unifornl in size at higher
densities.
The lower 28-day
3
kg/m
dry densities
(between
500 kg/m3 and 1000
do have an influence on the air-void size because the air-bubbles
)
close together just after casting and therefore have the opporhmity
are
to merge
before setting of the paste around the air-voids. A limit is reached at a 28-day
(by density
of 1000 kg/m3, as the data obtained at higher densities do not
display any clear panern.
3
kg/m
It seems that the dry densities
higher than 1000
do not have an influence on the air-void size distribution
air-voids
because the·
are far apart in the paste and therefore do not have the ability to
merge before setting of the paste around the bubbles.
The effect of the 28-day dry density on the air-void spacing can be seen in
Figure 7.6. For mixhlres with dry densities lower than 1000 kg/m3, 90 % of
the spacing distances are larger than 35 11mand 50 '}'(.of the spacing distances
are larger
than
100 I1nL Spacing
distances
increase
for the higher
dry
densities,
I
250 L-
OJ
c
'03
'"c. ~E
Vl :l
<lJ~
N
Vl
'Vi
~
Qj
i
200 I
I
E
550
I
o :0
'" 100 _-------~~~.~~
"tJ
'0 [l.
~
<{
590
50-.-----
••
'
i
•.
400
600
••
800
dry densities
=
xA/C
= 3
2
I
.A/C = 4
I
•
1000
II
1200
1400
between 28-day dry density and oversize air-void
The lower 28-day
A,A/C
I
....,.....+..
•
.
A,,,,,
•••
)(
200
Figure 7.6: Relation
parameters
•
--,----yA,.
;A;.,:
- - - - -x- .•• - ••••
- •. ~
-;----~----_,_--+I
o
x·.
A,
I
o
.A/C =0
.A/C =1
J'
~----~--------------.";x--I
.x
A,
4i 4J 150
>
..
i
don't have any influence
spacing. The higher 28-day (by densities
void spacing but the data obtained
spacing
on the 31r- void
may have an influence on the air-
in this investigation
is not enough to
determine if there is a relation or not
EFFECT
OF
ASH
I
CEMENT
RATIO
ON
AIR-VOID
distribution
parameters
STRUCTURE
In Figure 7,7 the oversize air-void diameter
(D50)
and (D I 0) are plotted as a flU1ction of the ash / cement ratio. Figure 7. 7 shows
the influence of ash / cement ratio on the air-void size distribution
of mixhlres
with target delisities between 1500 kgim3 and 700 kg/m3
The ash / cement ratio has an influence on the air-void size distribution
According to Figure 7.7 the air-void size distribution
range.
range is the narrowest
;~:[ ---------.~----,-/-"~ ~----,~~~·-----------i
I : 1~::k:~::
300
250
200
•.
,-.
I I
:
r------
'--..,
--
i
!
x
-lK'
~-----~-----:I'--
%
150 or,
x
.
.• --___.----100 1..---------i
5~
II
;K
II
A
._n __n_n_-&--------
1000 kg/m3
x900 kg/m3
i
---~,
A
A
%
800 kg/m3
II'.
----,
J:==================:===========================
o
1000 ,------.----------
..----------------~
~I-------
.
900
800 ~I
._._____
I .1500
I
-.-'----e-_-_--_'
I
i
,/
700 •.
/.-
600 !
-----a
I
----~,
I
~
I
x
;~~ ~i---_-_-----------~~-----'-_:---'-~-'t-·-:~~-'
------~
200 r----nnn____
kg/m3
I
~----~
.1200 kg/m3
A 1000 kg/m3
--II :::::::
,-:
~_
.700 kg/m3
100 +-------------------------
o -'------_----_---
FigUl-e 7.7: Relation
parameters
_
between
ash / cement ratio and air-Yoid size distribution
Figure 7.8 shO\\s the effect of the ash / cement ratio on the air-void spacing of
the mixtures
with target
densities
lower than
1200 kg/m3 The minimum
distances bet\yeen the air-yoids are the largest for an ash / cement ratio of (\yo_
Figure 7.8 also shows that for the mixtures \\ith an ash! cement ratios of t\\O
and three, 90 % of the air-voids
are not tonching
each other (minimum
distances between the air-voids are not zero). There is no mathematical
trend
to describe the effect of the ash! cement ratio on the air-void spacing.
200
~-----------~--~---
180
j;
160
,
I
/,-"
I
,
:------l
:;:!E
o ::J
1 40
J
.~ ~
'"
;;Gi
•.
120
~
'" E
e
1 00
+~~~------~- •.---------•-.------------~-_l
>-
I/)
"tl
t:
'"
a.
'"
o
Cl
t:
III
//
_~ ,/
~
fr-
:-------/
I
t~-- ...
-~~---~~-----··-_·-·~----~
...
--~I
i
80
',
--.
I
%
.-
I/) U
'"
a.
VI
60
40
20
a
.•.
t
I.-
I
l
I
~
-.~~------J
i.
~
~-_
.•.
I
-_.__------1 '--------
The porosity of foamed concrete is the sum of the air-voids and the voids in
the paste. The relation between the 28-day dty density and the average
%
porosity can be seen in Figure 7.9.
A power trendline was added to the graph in Fif,'l.1fe7.9 and the equation and
R-square value displayed on the graph. The statistical
R-square value for the
equation is 0.9591 and therefore a relative strong relation exists between dry
density and average % porosi(l' for the mixtures.
>.
70
1
.~ 60
2
~
?fl.
OJ
01
~
OJ
>
<!
50
-l-------~
I
Iy
t---
I
_
=
",A/C
=
=
=
xA/C
= 3
x A/C
=
• A/C
7718.3x-O 7316
R2 = 0.9591
1
I
• A/C
I
40
30
0
1
2
4
20
10 0
0
The relation
porosit)'
results
(see Figure
in an increase
to higher
densities
bet\veen
porosities
lower
% (dry densities
The
spacll1g
7.11. The
porosity
than
the air-void
7.10)
size distribution
indicates
that an increase
in the average % porosity.
for the mixtures
1000 kg/m\
higher
parameters
distances
of the mixtures.
than
with
and average
in the air-void
Wider
porosities
higher
than
3
1000 kg/m
)
the air-void
as a function
air-voids
do not
lead
50 % (dry
than 50
lower
size distribution
of the porosity
have
any
%
diameter
void distributions
For mixt11res ,vith porosities
are plotted
bet\veen
parameters
influence
does
in Figure
on
the
80~'--
D50
~
•
f::-I-~~---Q.
~
_,,======='"';::(============----
H~.·
50 '
40
;K
~<.
•
~ 30
Dry densities>
« 20 -' ---
kg/mJ
I.
I. AIC = 01
-------
~----------------
1llOll
AIC =
11
I il.AIC =
I x AIC =
,
I '%.AIC =
2
31
I
4!
I
10 ~---------------------------__;
o ------------------------------;
Figure 7.10: Relation
'Yo porosity.
between
air-Yoid size distribution
parameters
and average
1
80 ------.-------..----------70 ~.~L+-•.
.£.
.1('%., I
X A
60 ~~~
•.-r-i-·-t
-'-----------------------L.--...:.------------
2
o
ll.
<ft'
50
i·
I
.~X
.1
•
x
----x---- .•.
40 : •
1
SSO
I
20-------1------------------
>
o ----o
• AIC = 1
S90 __
...1
I
10 ----
--------
EFFECT
'%..AIC=4
---------------------------
--- -------------~
!
------------,-----1
100
OF
x AIC = 3
_
------------------_50
=0
•. AIC = 2
1
--X--'I~ ---~x-~4.
~
«
.AIC
-------------------
<lJ
30 _1__
_
'%..
150
AIR-VOID
200
STRUCTURE
250
300
ON
COMPRESSIVE
STRENGTH
The 28-day compressive
sirength
is plotted as a function respectively of the
28-doy dty densil)' and the average % jJorosiry (see Figure 7.12 and 7.13).
i
i
I
~----,
I
i • A/C = 0
41
>
.~ <;'20
I • A/C
i
41 0.
~2
0._
i
~ 515
u 01
c::
A
=
1
A/C = 2
II II
I
I I
Ii
I '
!
>.41
-9 ~
10
co
N
The relation
.wrengrh
between
of foamed
compressive
the 28-day
concrete
dry density
and the 28-day compressive
is an exponential
relationship.
The 28-day
strengrh increases with an increase in the 28-day dry density. The
ash / cement ratio of the mixtures has a specifIC influence on this relationship.
For the same 28-dc~v cfJ:vdensity. the 28-day cornfJressive srrengrh decreases
as the ash / cement ratio increases.
Table 7.1 lists the exponential
the relationship
fitted functions (as shown in Figure 7.12) for
bet\\'een the 28-day dry density and the 28-day compressive
srrengrh for ditTerent ash / cement ratios. The statistical R-square value of the
exponential fit is also listed in Table 7.1.
Tahle
7.1: Fitted functions
28-day compressive
for the relationship
hetween
the 28-day dry density
strength
Mixture
numbers
Ash!
Cement
ratio
Fitted Function
y
a e (bx)*
=
a
R2
b
1-6
0
0.5157
0.0024
0.9769
7-12
1
0.127
0.0036
0.9955
13-18
2
0.0833
0.0038
0.9884
19-24
3
0.0737
0.0035
0.9865
25-30
4
0.0638
0.0033
0.8538
and the
ClJ
.:::
• A/C
= 0
I
.A/C
= 1
I
~
'" 20
ClJ 0..
Q.~
§ :S
u
>,ClJ
.f5
eO
g'
fj;
15
A
Ale = 2
x A/C = 3
10
i
N
;KA/C
= 4
II
I
!
'~'--~
Figure 7.13: Relation
stren!,'1h
between average 'Yo porosity and 28-day compressive
The relation between the average
strength
% porosity
and the 28-day cumpressive
of foamed concrete is also an exponential
cumpressive
relationship.
The 28-day
strength decreases with an increase in the average % porosity.
The ash ! cement ratio of the mi:\.tures also has a specific influence on this
relationship.
For the same average
% porusi~\'.
the 28-day
compressive
strength decreases as the ash! cement ratio increases.
Table 7.2 lists the exponential fitted functions (as shown in Figure 7.13) for
the relationship between the average % porosi~v and the 28-day compressive
strength for different ash! cement ratios. The statistical R-square value of the
exponential fit is also listed in Table 7.2.
Table
7.2: Fitted functions
28-day compressive
for the relationship
between the average
strenl,rth
Mixture
numbers
Ashl
Cement
ratio
Fitted Function
y = a e Ib'l.
a
R'·
b
1-6
0
528.61
-0.073
0.9978
7-12
1
691.7
-0.0849
0.9572
13-18
2
629.96
-00853
0.97
19-24
3
203.79
-0.075
0.9559
25-30
4
249.97
-00813
0.961
% porosity
and the
3
Ash / cement ratios as well as dry densities lo\\er than 1000 kg/1ll have an
effect on the air-void size distribution.
The air-void size distribution
has an
influence on porosities higher than 50 'Yo. On the other hand the dry density,
ash / cement ratio and porosit)
hme a deJinite eifect on the compressive
strength. As a result o[ these facts a relation has to exist between the air-void
size distribution and compressi ve strength of foamed concrete.
The effect of the air-void size distribution on the 28-day compressive
can be detennined
compressive
that smaller
from Figme
7.14.
unifonlled
strengths.
compressive
strengths.
size air-voids
3
1000 kg/m
higher
28-day
not
seem
lower than 1000 kg/1ll3 The air-void
to have
an influence
on
the
strength [or the mixtures with 28-day dry densities
28-day
higher than
It seems that for the mixtures \\ith 28-day dry densities
than 1000 kg/m3
compressive
does
ensure
lead to lower Nf-day cOlnpressive strengths
for mixtures with 28-day dty densities
distribution
in a mixhlre
Larger air-voids in a mi:\.iure give rise to lower 28-day
Wider air-void size distributions
compressive
a decrease in the 28-day
strength 'vvith an increase in void diameter. Figure 7.14 indicates
compressive
size
It displays
strength
it is the composition
of the paste
higher
that determines
strength of the mixture because the air-voids are too far apart to
have an influence on the compressive strenf,rth.
roc.
30
~
.<= 25
C,
c
~~
xA/C
';f.A/C
= 4!
• A/C
.2:
~
c.
=0
=1
=2
= 31
• A/C
20
OJ
::l
the
.•.A/C
15
E 10
o
u
Figurc 7.14: Rclation bctwcen ovcr sizc air-yojd
day comprcssivc strcngth
distribution
parametcrs
and 28-
The spacing parameters
are plotted as a function of the compressive strength
in Figure 7.15. No real relation bet\\een the air-void spacing and the 28-day
compressive
strength can be found. This correlates with the fact that there is
no relation between air-void spacing and the other physical properties of the
mixtures.
EFFECT
OF AIR-VOID
TERM COMPRESSIVE
The measured
detennine
porosities
the 365-days
tllis investigation.
STRUCTURE
ON PREDICTED
LONG
STRENGTH
were used in equation
predicted
compressive
2.11,
strengths
2.12 and 2.13 to
for the mixtures
III
The constants in Table 2.] for pozz-fill were used for these
mixtllfes. All the values of the predicted 3()5-days compressive
strengths for
the mixtures are listed in Table 7.3. The only discrepancy in this table is mix
no 6' s predicted
strength, it is 100\'er than the 28-day compressive
strength.
The measured porosity is vcry high.
-I
30 -, ~~~--~~
,
~
~
I
25 -r-~~ •
::
C,
~
:
-----~-~--I.----.=--------------------I
i
20
S90
!
'
~
10
x,'•
•
U
i;'
q
I
.•••.\
+
••.•..•.. '.
5 .---.~--./---~
xA/C=3ii
I.
I
o
·
• A/C
.------x~~--
~...
-..•..
------_--
o
•
X
.'
_-
A: ••
--..-----~-.-----~~~~
50
Figure 7.15: Relation
compressive
100
between air-void
150
spacing
200
parameters
and the 28-day
"
1 :J
•••.A/C=21:
j,~ • • .•..
-~~~.~~-.-~---~~.-------
"
=
.A/C=
I
co
N
'
.A/C
::li
0 ',I
I
l
§
•
..•..
-----------~~~-·-I
I
~
~t
I
I
....---~/·-------·_
~
> 15
I
I
'.
-i-
= 41
Figure 7.16 indicates
the relation bet\\een
predicted 365-days compressive
the ash / cement ratio and the
strength of the mixtures with target densities
lower than 12()() kg/m'-
From this graph it seems that the optimum ash / cement ratio for this specific
mixhlres
resulting
in the highest predicted 365-day compressive
two. The question
arises
if the microstructure
strength is
has an\' influence
on this
optimum design mixhlre.
For the mixtmes
with 28-day dry densities
air-void size distributions
narrowest
lower than 1000 kg/nl narrower
lead to higher 28-day compressive strengths, but the
air-void size distribution
is found at an ash / cement ratio of two
(see Figure 7.7). It is possible that for a narrow air-void size distribution
particle packing is the best and therefore the long-tenn compressive
the
strength
of the mixture is a maximum.
:: I
20
u
__
.~~~~~~
,
I·
+----
~
__
---:-~o~~g/m;-l
~_,
iI
•
-- ,_.---~-----
---,~---,
I
I
I
.•. 1000 kg/m3
I
I
•
151~~~~~~~~~~~...
~~~--~~~~~~-----1
I
10
•••
t=----~~~~~~~~~~--~---___..:~~~~~-j
I
5+
l~~~,,------~---~-,,----,
*
o
Figure 7.16: EtTect of ash / cement ratio on the 365-day predicted
strength
compressive
cement ratio of two for mixtures with 28-da,v (by densities lower than 1000
kg/m3 (see Figure 7.8). From literature (Neville,
1987 and Kearsley,
1999)
when ash is added to cement paste initially the gain in strength is caused by
the hydration of the cement and the ash acts as filler. As time passes, the ash
starts contributing
to\\"ards the strength, an increasing percentage of the ash
starts acting as a cement - extender.
Mix nr
AlC ratio
Target
density
(kg/m')
28-day
Com
pressive
Strength
(MPa)
A.
Jl
Measured
t
porosity
365-day
Predicted
Strength
(MPa)
1
0
1500
22.00
176.9
23.74
0.44
365
38.23
2
0
1200
9.40
176.9
23.74
0.55
365
16.45
3
0
1000
7.17
176.9
23.74
0.60
365
10.92
4
0
900
452
176.9
23.74
0.65
365
6.63
5
0
800
3.30
176.9
23.74
0.70
365
3.68
6
0
700
2.00
176.9
23.74
077
365
1.42 •
7
1
1500
24.20
-6.76
66.21
0.42
365
52.14
8
1
1200
6.25
-6.76
66.21
0.54
365
22.55
9
1
1000
4.69
-6.76
66.21
0.60
365
12.94
10
1
900
2.92
-6.76
66.21
0.65
365
7.89
11
1
800
2.29
-6.76
66.21
0.71
365
3.94
12
1
700
1.40
-6.76
66.21
0.75
365
2.27
13
2
1500
20.50
-98.34
80.06
0.42
365
50.25
14
2
1200
5.84
-98.34
80.06
0.52
365
25.28
15
2
1000
3.76
-98.34
80.06
0.59
365
13.81
16
2
900
2.45
-98.34
80.06
0.65
365
7.69
17
2
800
1.47
-98.34
80.06
0.70
365
4.35
18
2
700
1.00
-98.34
80.06
0.74
365
2.65
19
3
1500
10.56
-97.84
65.29
0.41
365
41.51
20
3
1200
5.07
-97.84
6529
0.50
365
22.44
21
3
1000
2.43
-97.84
65.29
0.60
365
9.68
22
3
900
1.61
-97.84
65.29
0.68
365
4.49
23
3
800
1.14
-97.84
65.29
0.71
365
2.85
24
3
700
0.72
-97.84
65.29
0.73
365
2.42
25
4
1500
6.63
-5.26
21.9
0.43
365
15.88
26
4
1200
3.53
-5.26
21.9
0.57
365
5.64
27
4
1000
1.71
-5.26
21.9
0.60
365
4.08
28
4
900
1.25
-5.26
21.9
0.66
365
2.27
29
4
800
0.77
-5.26
21.9
0.71
365
1.33
30
4
700
0.53
-5.26
21.9
0.74
365
0.82
*
The 365-day predicted strength is lower than the 28-day compressive
possible that the equations
densi ties and no ash added.
2.l1,
strength. It is
2.12 and 2.13 are not valid for mixtures vvith low
Based on the principle
mixtures
that a chain is as strong as its· weakest
with a maximum
cement paste around the air-voids
link, the
(mininmm air-
void spacing) can develop the strongest links over a period oftime.
It seems that
the microstruchlre
(air-void
size distribution
and air-void
spacing) has an influence on the long-term strengths of foamed concrete. No
mathematical
relationship
is possible with the existing data therefore further
research is necessary.
From the litera hire review it is found that the relationship
between the density
and compressive
strength of foamed concrete is an exponential
with the power
varying
with the size and distribution
relationship
of the air-voids.
Table 7.1 shows that the power for the mixhnes with an ash / cement ratio of
two is an optimum (0.0038).
In the light of the prevIOus paragraphs
between
it seems that the exponent
exponential
relationship
the 28-day
compressive
strength can be an indicator of the microstructure
distribution
and air-void
spacing)
dry density
of the mixhlres.
and the 28-day
Evaluation
result in a prediction
strength)
•
because
mixhlre.
in the relations
Also in this area
air-void size distribution
can therefore
it is not representative
further
parameters
of the air-void
with the
and the largest
of the optimum design (highest 365-day
for the specific
The Rosin-Rammler
of the exponents
(air-void size
The exponent
highest value indicates the narrowest air-void size distribution
air-void spacing.
of the
compressive
research
is
cannot be used.
size distribution
of the
mixhlres.
•
The 28-day compressive
strength increases with an increase in the 28-day
dry density. The relation is an exponential relation. For the same 28-day
dry density, the 28-day compressive strength decreases as the ash / cement
ratio increases.
•
The relation between the average % porosity and the 28-day compressive
strength of foamed concrete is also an exponential
relationship.
The 28-
day compressive
porosity.
strength
with a decrease- in the average 'Yo
increases
For the same average
'Yo porosity,
the 28-day
compressive
strength decreases as the ash / cement ratio increases.
•
The 28-day dry densities bet\\"een 500 and 1000 kg/m3 have an influence
on the air-void size distribution.
The void diameters became smaller as the
dry density increases.
•
3
It seems (for 28-day dry densities higher than 1000 kg/m
size distribution
)
the air-void
is nol inf1uenced by density. A possible reason therefore
is the fact that the air-voids in these mixtures are far apart in the paste and
do not haw
the ability to merge before setting of the paste around the
bubbles.
•
The air-void size distribution
3
and 1000 kg/m
compressive
porosity
for mixtures with dry densities between 500
has an int1uence on the average % porosities and 28-day
strength
of foamed
and a decrease
concrete.
It displays
in the 28-day compressive
an increase
strength
111
with an
increase in void diameter.
•
It seems that (for the mixtures \vith 28-day dry densities higher than 1000
kg/m3) it is the composition
of the paste that detennines the compressive
strength of the mixture and not the air-void size distribution.
A possible
reason therefore is that the air-'·oids are too far apart in the paste to have
an influence on the 28-day compressive strength.
•
The 28-day dry densities between 500 and lOOO kg/m3 have no influence
on the spacing of air-voids. The higher 28-day dry densities may have an
influence
on
investigation
•
the
air-void
spacing
but
the
data
obtained
in
this
is not enough to detennine if there is a relation or not.
The spacing of the air-voids does not seem to have any int1uence on the
porosity and 28-day compressive strength.
•
The optimum ash / cement ratio for this specific mixtures resulting in the
highest predicted 365-day compressive strength is two.
•
The
narro,,·est
air-void
size
distribution
and the maX1l11lUnair-void
spacing are tound at an ash / cement ratio of two.
•
It seems that the power of the exponential
dcnsit\·
and
microstructure
mixtures.
the compressIve
(air-void
strength
size distribution
relationship
between the dry
can be an indication
and air-void
spacing)
of the
of the
The influence of the physical properties on the stmctural properties of the foamed
concrete mi:\.iures, as investigated in this research maybe summarized as follows:
•
ll1e 28-day dry density and the 28-day compressIve
strength of foamed
concrete are related by an exponential relationship. ll1e 28-day compressive
strength increases with an increase in the 28-day dry density.
•
ll1e average % porosity and the 28-day compressive
concrete
are also
related
by an exponential
strength of foamed
relationship.
The
28-day
compressive strength increases with a decrease in the average % porosity
•
ll1e 28-day compressive strength reduces with increased ash / cement ratio.
ll1is is, however, not the ultimate strength and it is anticipated that with
proper curing the strength of the mi"1ures \vith high ash contents will increase
significantly after more than 28 days.
An image analysis system \vas used to developed the following paran1eters to
explain and quantify the microstmcture (air-void stmcture) of foamed concrete in
order to evaluate the influence of the microstmcture
on the properties of the
mi",1ures with low target densities:
•
ll1e shape of most of the air-voids in these mi:\.1ures is approximately circular
in section and the assumption is made that the air-voids are perfect spheres,
therefore the size of the air-\'oids are best described with an effective air-void
diameter.
•
ll1e Rosin-Rammler distribution function is evaluated and it does not provide
parameters that describe the air-void size distribution quantitatively.
•
ll1e oversize
oir-\!oid
diClmeter distribution
pClrometers
(D50 and DIO) are
developed to quantii')' the air-void size distribution. ll1e 50 % oversize air\oid diameter (D50) gives an indication of the average void size of each
mi"iure. ll1e 10 % oversize air-\oid diameter parameter (DlO) indicates the
diameter of the air-voids for which only 10 % of the diameters are larger.
•
The perpendicular distance through the cement paste from one air-void to the
nearest other air-void in the vicinity is used to describe the spacing of the airvoids.
•
The spacing parameters (550 and 590) are developed to quantify and describe
the distances between air-voids. (550) is the median distance between the airvoids and (590) indicates the value for which 10 % of the void distances are
smaller.
The effect of the air-void stmcture on the properties of foamed concrete mixtures
with low target densities may be summarized as follows:
•
(For 28-day dry densities between 500 and 1000 kg/m3) the air-void SIze
distribution is influenced by density. The void diameters become larger as the
dry density decreases.
•
It seems (for 28-day dry densities higher than 1000 kg/m3) the air-void size
distribution is not influenced by density. A possible reason therefore is the fact
that the air-voids in these mixtures are far apart in the paste and do not have
the ability to merge before setting of the paste around the bubbles.
•
The air-void size distribution (for mixtures with dry densities between 500 and
1000 kg/m3)
has
an influence
on the
average
porosities
and 28-day
compressive strength of foamed concrete. The average air-void size increases
with increased porosity and this decreased the 28-day compressive strength.
•
It seems that the air-void size distribution (for the mixtures with 28-day dry
densities higher than 1000 kg/m3) has no influence on the average porosities
and 28-day compressive strength of foamed concrete. The air-voids are too far
apart in the paste to have an influence on the properties of these mixtures. It
seems that the composition of the paste detemlines the 28-day compressive
strength of these mixtures.
•
At low densities (between 500 and 1000 kg/m3) the 28-day dry density has no
influence on the spacing of air-voids. The higher 28-day dry densities may
have an influence on the air-void spacing but the data obtained in this
investigation is not conclusive.
•
The spacing of the air-voids does not have any influence on the average
porosity or the 28-day compressive strength.
TIle possible
compressive
int1uence of the air-void
stmcture on the predicted
long-tenn
strength of the foamed concrete mi\.1ures with low dry densities
(between 500 and 1000 kg/ m3) is as follows:
•
It seems that for ideal cured foamed concrete mi\.1ures, \vith the narrowest airvoid size distribution and the largest air-void spacing will ensure the highest
365-day compressive strength.
•
It seems that the po\ver of the exponential relationship between the 28-day dry
density and the 2S-day compressive
strength can be an indicator of the
microstmcture (air-void size distribution and air-void spacing) of the mi\.1ures.
TIle power with the highest value indicates the narrowest air-void size
distribution and the largest air-void spacing. Evaluation of the exponents in
the relations can therefore result in a prediction of the optimum design
(highest 365-day compressive strength) for the specific mi\.1ure.
TIlis research was executed USlllg single source materials and the effect of the
different cement, ash and foam sources on the properties of foamed concrete with
target densities lower than 1500 kg/m3 should be investigated.
Further research is necessary on the int1uence of the microstmcture on foamed
concrete mi\.1ures with dry densities higher than 1000 kg/m3
In this study no specific method was used to prepare the samples for microscopic
analysis. Further research is needed into sample preparation to accentuate the
contrast between air-voids and cement paste in order to simplit)r and speed up the
image analysis.
TIle inf1uence of the gel and capillary pores as well as the entrapped air-voids on
the properties of foamed concrete needs investigation.
Only the 28-day properties
properties
of these
mi:-..1ures need further
there is a mathematical
compressive
of the mi:-..1:ureswere obtained
relation
betwcen
il1\'estigation
the air-void
strength of the foamed concrete mi:-..1:ures.
in this study. Long-term
in order to detenlline
structurc
if
and the long-term
ACI Committee 523. 1975. Guide for Cellular Concretes Above 50 pcf, and
for Aggregate Concretes Above 50 pcf
with Compressive Strengths Less
Than 2500 psi. ACI Journal, Febmary 1975, Title no. 72-7, pp. 50-66.
ASTM
1990. Standard Test Method for Microscopical determination of
Parameters of the Air-void System in Hardened Concrete. ASTM Annual
Book, Vol 04.02.
Atzeni, C. Massidda, L. and Sanna, U. 1987. Effect of pore distribution on
the strength of hardend cement pastes. Pore structure and materials
properties, Proceedings of the first intemational RILEM congress, Vol 1, first
ed. Chapman and Hall Ltd, London and New York, pp 195-202
Cahill, J. Dolan, J.e. and Inward,
P.W. 1994, The identification and
measurement of entrained air in concrete using image analysis. Petrography
of cementitious materials, ASTM STP 1215, Sharon M. Dehayes and David
Stark, Eds., American Society for Testing and Materials, Philadelphia,
pp
111-124
Cebeci,
6.z. 1981. Pore stmchlre of air-entrained hardened cement paste.
Cement and concrete research. Volume 11, 1981. pp. 257-265
Chan, S.L. 1987. Applications of stereological and image analytical methods
for concrete testing. Pore structure and materials properties, Proceedings of
the first intemational RILEM congress, Vol 1, first ed. Chapman and Hall
Ltd, London and New York, pp 111-118.
Chitharanjan,
N. Ramal<rishnan, V.S. and Ganesan, S. October 1978. A
new production teclmology for the manufacture of cellular concrete. Indian
concrete Journal, pp. 266-271.
Fagerlund,
G. 1973. Strength and porosity of concrete. Pore Structure
Proceedings of the Intemational RILEM Symposium, Prague, 1973, Part 2,
pp.D51-073.
Gaafer,
B.A. 1995. The effect of envirorullental
of concrete. PhD thesis, University of Leeds.
and water penneability
Gowripalan,
curing condition on the gas
N. Cabrera,
J.G.
Cusens,
A.R.
and
Wainwright,
P.J.
Febmmy 1990. Effect of curing on Durability. Concrete International.pp.4754.
Hotl,
G.e.
1972. Porosity-Strength
Considirations
for Cellular
Concrete.
Cement and Concrete Research. Volume 2, 1972, pp. 91-100.
Kearsley,
E.P.
1996. The use of foamcrete for affordable
third world countries.
development
in
Proceedings conference on concrete in service of
mankind (Congress on appropriate concrete technology), Dundee, UK, 1996.
E & FN Spon, London, UK, pp. 233 - 243
E.P. The use of Foamcrete in Southem Africa, Proceedings of the
Kearsley,
Third CANMETIACI International Conference on High Performance
Concrete, Kuala LtU11Pur,Malaysia, December 1997. American Concrete
Institute, 1997, pp. 919 - 934.
Kearsley,
E.P. 1999. The effect of high volumes of lmgraded fly ash on the
properties offoamed concrete, 1999, PhD thesis, University of Leeds.
Kreijger,
agents
P.e.
and
1967. Action of air-entraining
the
difference
between
them.
agents
and water-reducing
Topic II: Physico-chemical
principles of the action of the admixtures with various cements and concretes.
Proceedings
of the intemational
RILEM
symposium
on admixtures
for
mortar and concrete, Brussels, 1967, pp 33-37
Kriiger,
E 1998. Guides on the use of South African fly ash as a cement
extender. Guide I An Overview. The South African Coal Ash Association
(SACAA), 1998, P 5
Nasser,
KW.
detenllining
and
Singh,
B.P.
the air-void parameters
1995. A new method and apparatus
in fresh and hardened
Neville symposium on concrete technology, 1995, pp. 239-256
for
concrete. Adam
Neopor System GMBH. Neopor light\veight Cellu1ar- Concrete. Product
Information
sheer, Niirtingen, Gennany
Neville, A.M. Brooks, J.J. 1987. Concrete technology,
First ed. Longman
Group, UK Limited. pp. 95.127, 291,357
O(ller, 1. and RoJHer, IVI. 1985. Investigations on the Relationship between
Porosity, Struchlre and Strength of Hydrated Portland Cement Pastes. II
Effect of Porestmcture and of degree of hydration. Cement and Concrete
Research. Volume 15, pp 401-410.
01orunsogo,
F.T.
1990. Effect of particle size distribution of ground
granulated blast nmlace slag on some properties of slag cement mortar. PhD
thesis, University of Leeds.
PrEN 480-11:1993, Admixtures for concrete, mortar and grout - Test
methods - Detennination of air void characteristics in hardened concrete.
European standard.
Romer, M. and O(ller, 1. 1985. Investigations on the Relationship between
Porosity, Stmchlre and Strength of Hydrated Portland Cement Pastes. I Effect
of Porosity. Cement and Concrete Research. Volume 15, pp 320-330.
Taylor, W.H. Febmary 1974. The production, properties and uses of foamed
concrete. Precast Concrete. pp. 83-96
Uchikawa, H. Uchida, S. and Hanehara,
S. April/June 1991. Measuring
method of pore stmcture in hardened cement paste, mortar and concrete. Il
Cemento. Vo1mne88, no 2: pp 67-90
Van As, S.c. and Joubel1, H.S. 1996. Applied
Statistics
For Engineers.
Department of Civil Engineering University of Pretoria. Edition 1996. pp
6-10 - 6-12
Vine-Lott,
K.
November
1985.
Production
of
'foam'
concrete by
microcomputer. Concrete. pp. 12-14
Visagie, M. 1997. The effect of microstructure on the properties of foamed
concrete. Proceedings
0/ the young concrete engineers' and technologists
conference, Midrand, SA, pp. 101-109
Wainwright, P.J. and Olorunsogo, F.T. 1999. Effects of PSD of GGBS on
some durability properties of slag cement mortars. Journal of the South
African Institution of Civil Engineering. Volume 41, Number 1 First Quarter
1999. pp 9-17
Wilk, W. and Dobro1ubov,
G. 1984. Microscopic Quality Control of
Concrete during Construction. Proceedings
of the Sixth International
Conference on the Microscopic, Albuquerque, 1984, pp. 330-343.
Willis, T.F. 1949. Discussion of "The atr requirement of frost-resistant
concrete" by T.c. Powers. Proceedings Highway Research Board. Vo1mue
29, Bulletin No. 33, Portland Cement Assn. pp. 203-211
APPENDIX A
AIR-VOID
SIZE DISTRIBUTION
OF MIXES
10%
9%
8%
~
>.
u
c
QI
:J
0-
~
u.
7%
i
6% L
5%
4%
3%
2%
1%
0%
11111111111
0
0
l()
0
C)
0
<'l
0
0
r--
0
<'l
<'l
l()
N
N
0
r-<'l
0
0
~
l()
0
C)
""
""
0
<'l
l()
0
r-l()
Void diameter
0
<D
0
l()
<D
0
C)
<D
0
0
r-r--
<'l
r--
0
co
0
l()
co
0
C)
co
0
<'l
C)
(urn)
100%
90%
80%
70%
~
I 60%
50%
...
--.-----------~---I,I0'''C«~
J:;:;;:-;-" ...~
Frequency %
40%
%,
-~------------I--Cumulative
300;'0
.:m;~~~~~~:k-~-i~-;---.·.+T·.~m--=::-...---~~~~ ~~~
o
0
0
~ m
a
a
0
M
~
~
~
~
N
a
0
a
0
0
0
M
~
~
~
01
M
~
~
~
N
N
M
M
~
~
~
~
~
ill ill W
m
~
0
0
0
0
0
0
m
a
0
M
~
~
~
a
~
ro
0
~
co
0
m
co
0
M
m
0
~
01
100%
~90%
---!- 80%
70%
~-----_.--------~
~---------~
60%
~----._------------~
50%
i
-r~·.·.·.·.·.·.·.·1 Frequency %
--Cumulative
40%
30%
%
20%
------------------------~
10%
I
0
0
l()
0
C)
0
<'l
0
r--
0
0
l()
N
N
0
C)
N
0
<'l
<'l
0
r-<'l
0
~
0
l()
0
C)
""
""
0
<'l
l()
Void diameter
4--t+t-H--pJa,
'II"
0
0
l()
<D
r--
0
l()
(urn)
<D
0
C)
<D
0
<'l
r--
i
:':1
0
r-r--
··llillllllll'.IIII·
00000
0%
,-
LO
01
("')
,.....
co
co
co
m
m
100%
10%
--~-.--------~
9%
90%
8%
80%
7%
70%
>.
u
c
6%
60%
r'" r
4%
~
'"
5%
LL
3%
~
".:.:.:.:.:
.....
,Frequency
~
---.------------------------~,
2%
~~~+,-~--.,-.j
1'1'
0%
0
0
to
0
:=
0
to
0
0
N
N
0
to
0
0
M
V
to
C;;
I
0
to
...,.
0':
ro.
40%
,30%
I
20%
----------------~i
1%
10%
g%
C umu I'alive
--
50%
j
0
0
0
000
l()
10
ffi
to
l;:;
11IIII1I
1111,'
o
;::
co
~
0
ffi
o
~
CJ)
0
to
CJ)
10%
,I 0%
fl!'
o
~
-~~-~------
+1
~
,
__
~
100%
~_ ..
90%
80%
i,
700/0
I
lll'~
lmilliWii~wjd~~-.,tl,~,a,
I,
I,D,I II-~'
a a
~
~N
0
0
m m
N
N
a
M
M
0
~
M
0
~
~
0
0
m m
~
~
0
M
m
0
~
m
II: II "
:r~:~~a~~e% ~
I·!
, I ' I I III'
Mix 6 - Target density 700 kg/m3
(AiC = 0)
--- -~-
-1-------------
~g- 5%t=
6%
4% ,---
U:
3%
2%
1%
0%
~~~
~
---'1
I
I
90%
I
[;'
8
100%
8% -' -----.------------.-
I
'"
:;
~
~
10% ------------9% ~----------------
7%
~
50%
~~~
III I I I ' II II III I I •• ' ,,~
a 0 a 000
0 000
m m M ~ ~ m m M ~
w w w ~ ~ ro ro ro m m
~
cf!.
600/0
-------~I
80%
~ 70%
~ 60%
-+
--------H
50%
~
>
~
:;
)~~I~~~alJr-t,;,~~ri
1t~~
o a 0 0 0 0 a 0 0 a a 0 a a 0 a 000
m
m m M ~ ~ m m M ~ ~ m m M ~ co~m m M ~ 0
N N M M ~ ~ ~ m m w w w ~ ~
ro ro m m ~
10%
90%
8%
80%
;!.
>0u
c
OJ
::J
7%
~
4%
C"
u..
100%
T
9%
70%
------------------------~i
6%
60%
50%
-------------------------i-
5%
,
,
3%
r---f-
, F re que nc y
--Cumulative
40%
30%
%
20%
2%
1%
0%
0
0
CD
0
~
~
0
CD
0
N
0
0
CD
N
M
0
o
c.o
0
:;r
CD
<'l
""f
l[)
10%
.a, 1111
:11:1,1"",,:1"111111'
0
0
,....
CD
000
.,....
CD
l[)
ill
to
!'
i,:
I i 11111
00000
.,.... <.D
.,.... (!)
r---. •...... co
co
1
III
0%
<.D
,0'>
en
r--I
10%
_________________
9%
.~
100%
90%
._____i
I
8%
80%
7%
70%
6%
5%
4%
-~--F-r-e-q-u-e-n-c-y--n
3%
,-----
--
- ------------------
--
Cum ulative %
2%
1%
~"n~rr~O)-~~~,
. , -~~, , -,
t+c+t+++d++--,
.t\IllUl.IJJ!L,-~p,
0%
~
N
~
M
~
0
M
~
I. I, II I,
~
0
""f
~
,.
,
H-tlll
,
A11II11
-+
50%
40:,(,
q~~~
,
:
60%
II
.11
1~%
0 ~
g ~ ~
~ •......
g ~ ~
~ ~~
W
co ~
m
l[)
r------·------------------··-·-·-----·-~·--·-------·-----------------------------1
Mix 9 .. Target
density1000
kg/m3
(A/C
= 1)
10%
~
,
>0u
c
OJ
::J
g-
u:
100%
9%
90%
8%
80%
7%
70%
60%
;!.
~
50%
40%
~
::J
6%
5%
--.----------.------
_____
,,_.
__..
4%
-------.---
._____ -------'---it·,·,·,·,·,·,·" Frequency
_____________
3%
--Cumulative
2%
I
30%
§
u
I
I'
I
%
20%
1%
llJJll~tr;[J,fi"",
0%
0
~
I
.
0
CD
0
;::
0
0
~ N
CD
0
CD
N
a
...--
a
to
a
,....
ill
.,....
("')
(")
'O;j"
"'f
\J1
000
vO_i~ia
10%
11II H++- II" I'
0
0
c.o
l{)
.,....
to
m_e_t_e_r
~~_)
0%
(0
{Q
J
l
:
I
10%
90%
8%
80%
7%
70%
"•.
6%
60%
5%
50%
u:
4%
0"
>.
u
•.
:J
CT
I
100%
9%
•.
0<
~
'"
:;
E
:J
u
3%
2%
1%
10%
0%
0%
a
a
CD
a
~
~
a
CD
a
a
CD
N
---------~---------±'
10%
9%
----------------------
8%
-
7%
.
~L
I
60%
6%
5%
50%
4%
--Cumulative
2%
0%
----~------ -
""~l,
--
40%
Frequency
10·,·,·,·,·,·,·,·,
3%
1%
100%
90%
80%
70%
----,
30%
%
20%
10%
1111''l,::t
llJlJ-JL,-,.JLJl,+JlJllLJl-~
0%
,-------------------------_._---------------------
i
I
I
!
10%
100%
9%
90%
8%
80%
7%
70%
6%
60%
5%
50%
4%
3%
2%
1%
0%
- t:= Frequency
~·Whv:-~,,=::::I
;~:
o
a
a
0
a
0
0
C;;
~
~
~
U)
fR
CD ti5
Void
L____________
40%
30%
-------------------
diameter
a
000
~
~
0
co ~
0
0
en ~
~
~
__ ._. __
(urn)
_
._
I
~I'
-;- 100%
10%
9%
8%
I
~
7%
6%
<II
:J
5%
~
4%
3%
>.
u
c
t::r
u..
~:
! 70%
~_. -~--------
-. ----~----
-, 1......-..•.•-....-.1F-r-e-q-u-e-n-c-y--~
: ~-
a
CD
a
;::
a
CD
a
N
a
CD
N
u:
40%
30%
20%
%
J
I
--------------------
---------------t
~------------------------------:
~--~.------
7%
6%
5%
4%
3%
__
~
~: 10-:-:-:-:-:-:-:1
. 11",.
a
CD
a
a
CD
a
N
a
CD
N
a
a
~
c;:;
%
a
~
r::
co
I
20%
~~%
.II.~
·,1,111;',1,1",·
a
a
CD
co
60%
50%
40%
30%
Frequency
! ~-Cumulative
2%
1%
0%
100%
90%
80%
70%
-------~I
i
a
~~%
c;:;
---.-.----------
9%
8%
~
Cum ulative
a
10%
<II
:J
60%
%
~
>.
u
c
---:
-----------------------150
2%
1%
0%
~
90%
80%
,
.~~-------~-~~------'-
a
~
Q)
Mix 15 - T a r~-e-t-d-~-n-si~~-0-0-0-k-g-l-m-3-(A-I-C-=-2-)---------~li
10%
9%
8%
~ 7%
6%
'"'
u
c
<II
5%
100%
90%
80%
~
:J
~
u..
4%
3%
't·:.-·:-:-:-:-:·!
: --
2%
1%
0%
n n
III
a
a
CD
a
;::
a
CD
I·
:
n
Cum ulative % i
I111
A,,·
111111111:
a _o(um)
o~_o
__ o
diameter
o
70%
~
60%
50%
~
o__ o
__ o__ o__
"",_~o
I
i
II
:J
E
30%>
c3
10%
[ 0%
.,
:§
40%
20%
~ ~ w ~ ~ ~ ro ~ m ~ ~
Void
----------~-----------~---
111111",·.
Frequency
.
I
I
I
JII
100%
10%
90%
9%
80%
8%
---------------------,
7%
>u
c:
::J
6%
~
, u.
4%
'"
70%
--------------------~
60%
-------------
5% -'-
t-
-----------------
"., ..,.,Frequency
------------
3%
50%
--Cumulative
-~
40%
I,
30%
%
20%
2%
1%
0%
10%
.11"i:
l'III::il
;::::
_________________
.
diameter
<Xl
<Xl
Q)
i:
II
~~~~*
o
Void
IIII1111
0%
:2
Q)
,i
(um)
J
100%
10%
9%
_---------------~
.-------------'-
90%
80%
8%
~
I
>u
c:
::J
----'-
6%
'"
i g-
5%
I
3%
u:
70%
7%
f-l30%
--Cumulative
--------------~-T
%
0
0
(!)
I
0
;:
0
(!)
0
0
N
N
(!)
0
;;;
I
r
----i
~=---II-fi-~b
,M)JJJ,nJ~tL'"tJ llJL I",~.n"",l~
0%
I
=:::mFrequency
___________
1%
II
:~~
---------~------~~
4%
2%
I
60%
20%
10%
0%
~ ~ § ~ ~ ~ ill ~ ~ ~ ~ ~ ~
j
I
I
'-------
1----------------------------------------------Mix 18 - Target
I
density
8%
~
>u
c:
::J
'g-"
u:
7%
6%
5%
~
1
(A/C
=
2)
··~;:;;:==:=::::::::::::=====1'
10%
9%
700 kg/m3
~--.----------~~
t-
100%
90%
80%
~ 70%
~
--.------.--------------------------~t:~:~.~ I
::J
I
§
~~-~d~=--c"m"r,,,w%~:!~
4%
--------
3%
2%
---------
----.-----------,-,-".-,.,.)
Frequency---'--t
40%
0
1%
0%
'"''
0
0
(!)
0
;:
0
(!)
,
""'"
.~
N
~
~
~
~
~
~
ffi
~
~
l
____________________
lit
..,.40*,
:11111:'
0
V_O_i_d
__
d_i_a_m_e
__
te_r {_u_m_
~
~
~
~
~
~
j
I
i
J
100%
, 90%
10%
9%
80%
8%
~
>.
u
l:
------
6%
QI
5%
"<T
~
4%
u..
-----------~
7%
70%
--------------------;
60%
--------------------~
50%
1--+ 40%
1--+
,-,.,.,.-,.;-,-'
Frequency
3%
--
Cum ulative
~~~-~~~~-_I
2%
%
I
i
20%
10%
1%
--:~
o
0
0%
0
0
en
0
;::
0
en
0
N
0
en
N
0
C;;
0
en
C')
0
~
0
en
en
en
"
~~~~ *
~
r--
:2
100%
c 90%
________
9%
-+
8%
----------------
7%
.. -------------
>.
u
6%
QI
5%
-----------------~
4%
________
l:
"<T
~
u..
0%
"1111.11111111111111
10%
~
---------
60%
3%
50%
-_J t·,,·,·,·,-,·,l
40%
Frequency
l--Cumulative
30%
%
20%
10%
1%
0%
:++++--t-.- ,
Ii
0
0
en
0
;::
0
en
0
0
N
N
en
0
C;;
0
en
C')
0
~
Void
0
en
"
0
0
0
LO
L"l
CD
'"
diameter
0
en
'"
0
;:::
I'
0
0
r--
10
en
III ~I , I I'll
000
to
co
II ~, 1I ,
~
.,.... to
Ol
Ol
(um)
10%
9%
8%
>.
u
l:
7%
6%
QI
5%
"~
4%
<T
u..
80%
70%
-------------------------------
2%
~
30%
"' "
3%
, Frequency
:,--Cumulative
%
2%
1%
0%
, i : :
0
0
en
0
;::
0
en
0
0
N
N
en
0
C;;
0
~
0
en
"
0
LO
0
'"
l[)
0
CD
0
en
en
0
;:::
0
r--
en
0
10
J"
0
en
co
1,
1
0
en
0
:2
0%
10%
9%
~-'~---~--------------~~----------=--=--=--=--=--=--=--=-=
8%
---------_;?::
7%
-----.--------
5%
4%
-.
---------'
3%
-;
2%
1%
-"-""-""'-""'-"-F-re-q-u-e-n-c-y--,',
40%
~
30%
; -Cum ulative % I
:
20%
-'- 10%
1'111111"
I
0%
70%
60%
50%
--~--------------------------------
6%
,
~~~%
0
@
~
@
~
11:,1'
0%
i
~ ~ ~
l ~
__
. _
-_._---_
.._-~--=~=----=-------~~;,
-------------------------.-------=====~~
'1~
1:~
I~
>.
i
I
u.
I
6%
100%
... ---------------
60%
-------------
50%
3%
2%
I
1%
I
L_' _
o_o_Yo_o
@__
~__
@
~__ ~.__ ~__
diameter
~,__Void
~__.__ ~_
(um)
---_ .. _---------_.--------------_.-
i
I
'
100%
10%
90%
I
I ~ ~:~ ,-------------------.
I ~
I
80%
50%
40%
---I-iE -: ~~e~~~a~~:e
j ~:~
=
2%
30%
~~o~
JL 1l,.!L _ ~~lJJl
0%
0
~
~
~
~
~
~
~
~
Void
I ---~~--
%
-. ":I~n-fl- - ----Ljn~a_-U
1%
'
70%
60%
-------.-------~
6%
-------------------
~
~
:iameter
~
~
~
(um)
-------------------------
0 Vo
100%
10%
~
>.
u
c:
OJ
::l
C"
OJ
!
u:
9%
90%
8%
80%
7%
70%
6%
, 60%
5%
4%
,
3%
--Cumulative
-~-~_-----
10%
0
CD
0
;:
0
CD
0
N
, 100%
--------+
90%
80%
---.-----------------1.
8%
~
!
'----;- 20%
0%
9%
u.
i
0%
10%
C"
%
1%
0
>.
u
c:
OJ
::l
Frequency
! I""""';""'j
2%
~
t 50%
h
40%
r---\- 30%
I
---------+
7%
-----------------------~!-
6%
-t
5%
4%
Cum ulative
I --
50%
40%
I
I·,·,-,·,·,.;·,·j Frequency
!
3%
70%
60%
30%
%
20%
2%
1%
10%
.A-h+++HhJ
0%
0
0
CD
0
;:
0
CD
0
N
0
0
CD
N
I----~----- Mix
M
27·
0
CD
C')
0
~
Target
0
CD
""
0
0
0
Iii
l[)
<0
CD
density1000
'11111
0
0
(0
(0
kg/m3
0
r::.
(0
11111111
0
0
00
"-
(AiC
=
CD
co
!
0%
II 111II1I
'lit
o
0
~
CD
(J)
(J)
4)
10%
____
9%
>.
u
c:
I
70%
6%
60%
50%
5%
C"
OJ
4%
-------------------------~
3%
------------------~
u:
80%
7%
OJ
::l
100%
90%
~t
-------------~
8%
~
.
40%
I
~FrequencY
H'
' 30%
20%
'--cumUlatlve3%~
2%
,
--------~-
1%
10%
~~~-~.~
0%
0
0
CD
0
;:
0
(0
0
N
0
CD
N
0
M
~
~
0%
~
l5
(J)
~
:2
____
10%
-------
9%
=======:::=======--=-~,
100%
90%
-----~~------------------------
8%
80%
7%
70%
6%
60%
5%
4%
!
~,-
r--+
!
I
1%
JE-,-.,.-..,~,~,~~-, ~1~:~
0%
... '., ..
3%
2%
t"""""""Frequency
11',1.
---,-+~,.,,:.
~
~
ffi
~
~
~
~
~~L
~
~
~
1
~
, ~
,
Void
diameter
(urn)
,_,
,,
10%
8%
0%
V_O_i_d_d_ia_m_e_t,e_r_l_u_m_
------------~---~~
_________________
9%
','
-C'm ""iw
~
,
I 100%
--------'-1
t--------
90%
---------------~I
80%
7%
70%
6%
60%
5% I
4%
3%
2%
I
50%
40%
L--
1%
~j---
0%
0
0
<D
0
~
~
0
<D
0
L __ ~_,
N
0
<D
N
0
;;:;
0
<D
<'l
0
;;;:
Void
0
<D
'"
0
Iii
0
<D
0
lD
diameter
--~--_
(!)
(urn)
..
0
<D
<D
0
r:::.
0
<D
"-
0
;;;
0
<D
co
0
Oi
0
<D
en
E!
0
::2
I
J
APPENDIX 8
EXPONENTIAL
FIT FOR CUMULATIVE
VOID DIAMETERS
PERCENTAGE
OF MIXTURES
OVERSIZE AIR-
100% ~-------------~~--~--~--~~~~~--~~~~~~~~90%
i
!Y= 1.4517e-00061xi
80%
l..... R2
=
0.9752
~I -----
70%
60%
50%
40%
30%
I
20%
10%
0%
-,-i ~~~,-~~~~~~-~~~~~--,~~~~~~~~~~,-~~~~~----.,
100%
90%
80%
-~~--:;
=
3.1625e·o-013h~-------
--------~-_-_--~~~_-_-_-_.-_-_-
R = 0.9948
70%
60%
'-+-Cumulative
50%
40%
--
~~~
t==-30%
0% t-----.----r---~
!
-_-~_.-
2
.0
100
200
rir
% over size
Expon. (Cumulative
% over size)
-----------------.------------~~~~~T---~----~~_-~~~~~~~-~~-
300
L
400
500
Void diameter
600
700
800
900
1000
(um)
-~---~~~-
-------~~~------~~-
~------~~~~~--~~~-~~------~------~-~,
Mix 3 - Target density 1000 kg/m3
(AlC
= 0)
i
100%
<ll
.~
tIl
~
<ll
>
0
~
<ll
>
~
:J
E
:J
u
90%
Y= 2.0915e·00109XI~~~~_~~_~~~_~~
R2 = 0.9945
80%
70%
60%
__
--+--Cumulative
50%
40%
~~------~---~~-~:
30%
20%
10%
0%
0
--
~_~_
% over size
Expon. (Cumulative
% over size)
tJ'
,
I
I
100%
90% "_ ..
<II
N
"in
80%
:u
70%
0
;f!.
60%
>
<II
..,>
!!!
:J
E
:J
(J
-r----
----r
y
= 1.8106e-00085' ~i
~-\--1
2
R
=
0.9948
---------------------~
r--
~
---=~~~~-~=========~I
-I
I
50%
f----1
__
Cumulative % over size
--Ex
pan. (Cumulative % over
size)
I
40% I
!
30% -l!
~
LJ
20%
10%
0%
0
~::I ~---_:~x~:~~;==Y80~-:9~~~-~~~:-O-)--------~
r------------I
100% \
~
"in
~
o
~
~
I
5
90% t---\------80%
70%-----J
+
----I
y = 1.6839e-00072'
R2
=
0.9918
r---------------J
60%
50%
40%
============~D
.
I
-.-Cumulative
~---------------.--.
__
% over size
Ex pan. (Cumulative % over
E
30% 1-----
0
:~~ ~_;--~~-_-1-0.~0~~~~2~0~0~~~·~~~"'_3-0.-0-~~~_~~_0_0
__
5_0_0_-_---_6_:C:O--8-0-0-~:~
-----------
Void
,
size)
diameter
I
I
i--I
,--j
__'0_'o_0_J'
(um)
--------
100%
80%
T
:u
70%
t--
0
60% L_____
90%
<II
N
"in
>
~
<II
>
.~
:;
E
:J
(J
50%
40%
30%
20%
I
1--I
__
---II
Iy = 1.6907e-0004'
I
R2 = 0.9881
--'----.------------.---
~---------------~~========~--==-~---~
•...
~
.
i
Cumulative % over size
I
-~~
1I~____________
___
--Expon.
(Cumulative % overl--
s_iz_e_l
10%
0% ,-----------,------ ---------.---~--r--___,_---~--
_
i
I
I
100%
.,
N
'iij
t
>
0
.,
~
>
~
:;
E
::J
u
I
90%
Iy
-~.
80%
= 1 9795e·oO'08'!
:
70%
~2_=_0_9966
~I
i
--------------.-------j
_I
~
!
H
----_._---~=~~==~========,--_.--'
60%
----+--Cumulative
50%
40%
--Expon.
size)
30%
% over size
(Cumulative
% overl
I
J
20%
10%
I
-'-,
0%
0
100%
1
.,
N
'iij
t
>
~
50%
40%
:;
30%
E
::J
= 2.150ge·0
;
0'09'.,
.._._.
R2 = 0.9953
________
.:::
u
,-
70%
60%
1il
~y
80%
0
.,
.--_-_-=-.~=j
90%
----+--Cumulative
---------'--Expon.
% over size
(Cumulative
% over
size)
--
-"'~.-------_.--------
20%
10%
j
I
-------_._~-•.......-----------_.
0%
0
-------1
i
100%
.,
N
"iij
t
>
90%
y = 1.954e·o.009S'
80%
70%
0
60%
+----
~
50%
~-
40%
1-
.,
>
~::J
E
::J
u
30%
~
--Expon.
size)
I
I
0%
--~
I
20%
10%
~I
R2 = 0.9948
._-----_._-------_.
I
0
100
(Cumulative
% over
100%
90%
11I
y = 1 .6416e"o0073':
.
R' = 0.9915
80%
N
"iij
~
>
0
~
"'iii::
~! ~~~~~~~~-~~~~--~~~-
70%
60%
I
~
+
50%
11I
40%
::l
30%
E
::l
20%
()
10%
--Ex
pan. (Cumulative
size)
% over
~---,,------=-_._-----=---=---=---=---=--=--=--=-_.
-,--~~~~~~-,~,....
••••
~-~~~-~~~~~~-
!
~--~---_.-
0%
i
0
_~~~~~~
100%
I
y=1.3041e-00053,
80%
N
"iij
"-
70%
>
0
60%
~
50%
I
11I
11I
"..,>
:;
'"
E
::l
20%
()
10%
0%
I
.
= ~~:~_-~_
---
-----------+--Cumulative
40%
30%
R'
-~~--~-------._--~--~~~~-~.
~
T
!
--Expon.
I
i
% over size
I
(Cumulative % over~!
------j
size)
__ =~~---------===---n1i
_-~_~~~_---0
l
~~~~~~~~~~_.---.-.J
-~0~~--==~==--=~
90%
11I
~~
·_~_,_________............,__--r~-------,-----,
--._~.,~
1000
100
100%
11I
N
";;;
~
>
0
~
11I
>
i
iii
90% ~--80%
R'=
70%
50% -~~~-.-~--40% -. -~-~~~-
:;
30% ~~~~~~~--
I
E
::l
20% .-----------------.~-
I
10%
0%
0.9849
H
~~~~~~-------------~-~--=="-~
I
--
60%
,I
()
y = 1.4722e-00043'
~~~~~--------
+~~~~-~~~~----~~-~~--I
o
-.-
Cumulative % over size
--
Expon. (Cumulative % over size) ~
--~-~----------1
•
•••
700
...;
i
800
900
1000
,---------
100%
90%
<lJ
N
'in
ID
0
60%
<l'
50%
<lJ
.~
:;
E
:l
()
R: = 0.9936
~:------------------~
________
70%
>
>
y = 2.5265e-O 0125, ,
80%
J~----------
---------
___________
----+-Cumulative
---_~
% over size
_~'!
i
40%
------------Expon.
(Cumulative % over~
size)
30%
20%
10%
0%
0
~
.
.
i
---------.J
-------------..
-------- ··------1
Mix 14 - Target
density
1200 kg/m3
(AiC = 2)
---,
100%
------------~-Ii
90%
<lJ
N
'in
ID
>
0
<l'
<lJ
...,>
~:l
E
:l
()
y = 2.0025e-0012S'
R2 = 09824
80%
_________
70%
----------------1
----------------------~---
-----------J
I
60%
j
50%
40%
-L
20%
0%
•.• ~..
(Cumulative % over~.
size)
~
--_ ..~._--
~-~,"------
-----l
~----------_.-
!
Cumulative % over size
I--Expon.
30%
10%
•
~----------
i
---------~
0
Void
dia meter
(urn)
__________
1-------Mix 15 - Target
density
100%
90%
<lJ
N
'in
ID
>
0
60%
50%
<lJ
E
:l
()
=
70%
<l'
.>.,
'"
:;
y = 1.4143e-00071'i
R2
0.9733
80%
40%
30%
20%
10%
0%
i,
,
0
__
----l
I
1000 kg/m3
--.J
--.
--------···------~l
=__2_)
,
_~AlC
I
p~F~~~'~;~::,:,~'::Okg/m3
,I
1
100%
90%
<II
'"
'iij
80%
<;
70%
0
>
60%
~
50%
<II
,~
n;
40%
:J
30%
E
:J
u
20%
10%
0%
:.\
R2
+---~~~~.~
=
0 9888
J1
I
t=--- \~ __~_~~ ~
~---------~~==--C-==-__
~-~
+-~~~---~~
-+--Cumulative
----------;--Expon.
I
% over size
I
---1
,
100
200
400
500
600
diameter
Void
_._~~~~~_.~~~~~_~
700
800
900
1000
(urn)
dia meter
~
(um)
.
~_
__ .~_-_._-------_._----_~~~~~_._~~_-,
._-------_.
t== ~-==
I
--1
300
Void
~--_~_-
I
---i
,.-----=-==----
"
I
~
(Cumulative % over~~-~
size)
o
I~'
I
lAIC = 2
I
90%
<II
'"
'iij
•...
<II
>
80%
70%
0
60%
~
50%
<II
>
.~
40%
:J
30%
E
:J
u
20%
10%
0%
,-
-
y
=
1 655e'0 0057, ,
R2 = 0 9941
t--:=\ ==
~I ~~-_-_-_-
_---~~-
r~--=~~-.~~--_~~~..-~'~--~-=--=-===~-_-_;1:
i-+--Cumula~lve
% oversize
.----~-=--~~~-==-----=1
~~~.~c_u_m~u_la_t_lv_e_%
__o_v_e_r
1=---=~
I
o
,
----\--
100
I
200
300
400
500
600
700
800
900
1000
100%
90%
"
80%
a;
70%
N
'Vi
>
0
~
">
.~
:;
E
"
u
60%
_~
50%
40%
30%
20%
10%
I---+-Cumulative % oversize
----J
I
I
--------i--Expon.
i
(Cumulative % over~
-~-------------i
i
__ ~-=--==~L=.-==-~~----==----_=--=-~~
size)
I
e--------------i
i
0%
0
60_0
Void dia meter (um)
,-----------_.
_._~---_._------
------_._-~_.
~7_0_0
._8_0_0
__
9_0_0
__
1_0
__
'0_0 ~
__ ._------------
----------------------------------------._._-------_.------_._,._._-~
100%
"
N
'Vi
a;
70%
60%
~
50%
>
"
>
';J
~
"E
u
"
,
80%
0
I
I
--------------------------------1
90%
i
----'-----_._-------_._
-----,--+--~Cum-u-Ia-tive--%
40%
i
.. _._---------------~
-----------~l=_Expon,
(Cumulative% oversize)
30%
20%
Ii
I~
oversize
--=---=----~~----I
10%
0%
0
r~--~---100%
90%
"
80%
a;
70%
0
60%
N
'Vi
>
~
"
>
~
"
u
"
E
50%
'..
L~_
4-~~~IY-=
~_=
I~
--J
.
-~
I
~---=---~~===--
-1,67-38-e-0-0064-'
098~-.l--
--I--Cumulative
II--Expon.
I
% oversize
LJ
(Cumulative % overl~
40%
_i~~~
,
30%
-;--~~-----_.~....-;~---==-~~-==
20%
10%
0%
_______
I
-rL__
i
,
\;
.
---------L_s_iZ_e_)
Void dia meter (um)
I
:-----j
I
100%
<lJ
N
'Vi
a;
>
0
~
<lJ
.::
ro
90%
y = 1.6455e'0 0056'.
__ .~
R2 0.9935
i----.--~--~--
~
----j
=
80%
70%
i -+-
60%
50%
H
Cumulative % over size
--,-
~xpon.
(Cumulative % over size) "~,
40%
:;
30%
E
:J
u
20%
10%
0%
-----~._----------j
~------~-------------~-----_--,--_____J
1000
0
100%
l
----
----~---r-----
90%
y
80%
70%
60%
---
J
--
---------------1
~-
--.=:,-+-Cumulatlve
---
I
-------------1
I-
R2 = 0 9756
--~_~. __~_f--~.
----~
50% ;-~-----40%
=2
1211e-00052<
-------
-. -
Expon
0
---J
-=--=--=-.--~---:...--- - -,
Voover SIZe
I
~-~
(Cumulative % over size)
:i
.~~--~---=-~-:::-==:--=~-~=::'::::==:=--====-..j
30%
1---------
20%
'
j,
--------~
~------
---------
10%
0%
I
]'
-
I
1000
---~
100%
90%
80%
70%
T-----t==i
~
--
.---------,y
= 2.04e-o,0035x;
.-----
R2
= 0.9748
'
60%
50%
j
40%
30%
1
.
-------------
c--~---~-------_.~j
'-+-i --:--
I
I
Cumulative % over size
Expon. (Cumulative
% over size)
_-oj'
------.--------
~~:1======================--------------~--0%
~I---------,_·_-~--,-~·--.
~
---.
-------=-~
--------~-------------I
1000
100%
I
90%
'"
80%
~
70%
>
60%
N
'Iii
'"
0
;l.
~'"
'"
:;
E
::l
u
~
,y
:
= 5.333e-0
0183,
R2 = 09784
I
------~~-
i
I
i---+-Cumulative
50%
iI--Expon.
i
size)
40%
30%
U
% oversize
(Cumulative % overl
LJ:
H
I
20%
I
10%
0%
0
l
100%
90%
80%
70% ---60%
IY
= 5.01e-o016e,
" R2
----------
!
i
= 0.9771
I
----------j
-----------i--.-Cumulative
1--
50%
40%
f~
% over size
Expon. (Cumulative % over size)
==
~
I
30%
20%
10% -
I
--.-----------
0% ---~--_----_---------_---_--_--_---.
M;,27 - T"g'!d',,;ly
1000'g/m3 lAIC = 4}
-==--==_=J .
100%
90%
'"
N
'Iii
:;;
>
0
;l.
'"
.~
co
:;
E
::l
u
~
-~~F-~-2081~--OO~-'-;,~~~-~-------
~~-=-~______-----------==1
80%
L__
70%
60%
~~~======~==~,
---------c=1
,----+----Cumulative% oversize
50%
----,(
li __
i
40%
I
I--Expon.
30%
L__size)
I
i
20%
3.
0%
0
Void diameter
-----
I
I
I
(Cumulative % over
10%
L
~
60_0_ -.--7-°:°---:-8:°_°:
(um)
•__
9:0:0_
1000
I
I
I
100%
90%
1IJ
N
'ijj
t
>
0
~
1IJ
>
.~
:;
E
:J
u
80%
70%
60%
50%
40%
1--Expon.
.
size)
30%
(Cumulative
% overh
:~,
~~.
20%
10%
0%
0
100%
90%
1IJ
N
y = 2.11 05e-00071X i
80%
t
>
0
~
1IJ
>
.~
:;
E
:J
u
70%
~
I
R2 = 0.9745
'ijj
!
60%
: _-Cumulative
--~~~~~~-i
50%
_~
40%
% over size
I
-----1
30%
20%
I
~--_.~
I
i
!
I--Expon.
s iz e)
(Cumulative
% over
G
f-~--1
L==-=-==--------J-------J
10%
0%
0
I
'-
100%
1IJ
.Nl/l-
90%
y
-~
80%
I
----~
70%-j--
~
:~:~ !=t==~~='----~~----~------~~---~---~
~
40%
I ~
~~:~
1.8457e·0004":
R2
I
t
=
=
L'
.J
~......
~-~~~~~~~
------
i
~-~~~~~~~~~~~~~-'
0.9915
-.=-
Cu~ ulative
l--E.xpon.
-
~
size)
I u ':~!-ol
% ove r s~
(Cumulative
,
~
% overh
~l
~
100
200
300
400
Void
~--~~~~~~~~~~~~~~~~--~~~--~~~~~~~~~~~~~~
500
diameter
600
(um)
700
800
900
1
1000
APPENDIX C
MODIFIED
ROSIN-RAMMLER
VOID DISTRIBUTION
OF MIXES
~
N
·Iii
a;
>
0
0.8
.,
~
>
y
=
1.183x - 6.3729
R'2 = 0.9993
Slope
~::l
(n) = 1.183
(In Xo)
E
0.4
::l
2
=
5.387
Position parameter
(Xo)
~----------------'
=
220 um ,
E
E
c--
~
N
·Iii
a;
>
0
.,
~
!
0.8
y = 1.6407x - 8.2473
R'2 = 0.9968
>
Slope
.~
Jp""',, ,,,,m""'
In (Xo)
::l
E
::l
(n) = 1.6407
0.4
2
~
=
5.027
(Xo)'
)""~
_
E
E
~
N
·Iii
a;
>
0
~.,
0.8
y = 13047x
- 65393
R'2 = 09973
Slope (n) = 1 3047
,
InXo=5012
I
,Position
parameter
(Xo) = 150 um ~
£
E
::l
E
!2"
0.4
E
.=
0
0
_
~
'0;
~
••>
~
••>
N
0
0.8
y = 1.2441x - 64421
R'2 = 09981
Slope (n)=
1 2441
(InXo)=5.178
'Position parameter (XO) = 175 um!
"".!l!
::l
E
::l
~
a
4
I
.=
.=
Q)
N
'in
Q;
>
0
';f!.
y
0.8
1
m7~2-------:
=
R'2
<U
>
0.9986
Slope (n)
~
:;
E
:J
=
Position
0.4
= 1.2117
= 5.298
(Xo) =
(In Xo)
parameter
I
200 um
I
!2
~
.::
.::
a
a
~
1.2
'in
Q;
>
1-
o
~
0.8
,~
=
1.298x - 7.6459
Slope (n)
'"
:;
E 0.4
:J
-----~---....:Position
!2
~
c:
c:
y
R'2 = 0.999
••
0
o
=
1.298
(In Xo) = 5.9188
parameter (Xo) = 370 um~--"
a;N
·Vi
:v
>
0
~
y = 1.3796x ·6.9278
RA2 = 0.9984
Slope (n) = 1.3796
(In Xo) = 5.021
Position parameter (Xo) = 150 um
0.8
>
'"
:;
.~
E 0.4
::l
!:2
~
.::
.::
a;N
·Vi
:v
>
0
~
0.8
y
!:2
1.4213x·
RA2
>
'"
.~
:;
E
::l
=
Slope
Position
0.4
=
7.1877
0.9984
(n) = 1.4213
(In Xo)
= 5.057
parameter
(Xo)
=
160 um
.::
.::
0
0
a;N
·Vi
~
>
'"
o
~
0.8
y = 1.3761x
RA2
Slope
=
(n)
·7.0778
0.9985
=
1.3761
(InXo)=5.143
~ Position
param eler (Xo)
I
=
170 um
OJ
N
'jji
~
>
0
~
0.8
Q)
-I
Y = 12794;~
.~
:;
E
::J
~
~
(InXo)=5.3
parameter (Xo)
I
---lPosition
0.4
6780~-
I
R'2 = 0.9991
Slope (n) = 1.2794
>
= 200 um
I
E
E
OJ
N
'iij
~
>
0
?t-
.'",
0.8
Y = 1.1516x
I
Q)
.>
'I
:;
E
::J
~
~
~Position
0.4
L-. __
.
- 6.2888
~! ---
R'2 = 0.9996
'I
Slope (n) = 1.1516
(InXo)=5.46
!
parameter
(Xo)
.
I
= 240 um ~i ----'
.. _.---
E
E
OJ
N
'jji
~
>
~Q)~
0.8.----J
Y = 1.2172x
j
:;5
.~
~
-b
I
0.4
_ .. --
-7.0056
R'2 = 0.9994
Slope
(n) = 12172
I
I
(In Xo) = 5.7555
Position parameter (Xo) = 320 um~: ----_
--------------"
.. ----
W
N
·tii
a;
>
0
~
0.8
y = 1.5112x
>
.~
"3
E
I
:l
~
-=
-=
- 7.5665
=
R'2
0.9978
Slope (n)=
1.5112
QI
In (Xo)
'Position
0.4
= 50069
parameter
(Xo)
=
150;
0
0
~ 1.2
·tii
a;
>
o
y = 1.389x - 6.7821
R'2 = 0.9984
QI
>
ro
Slope (n) = 1.389
i
:l
E 0.4
:l
-~~!
=
(In Xo)
4.88
Position parameter (Xo) = 130 um ~~~~~~-------
~
~
.E
0
o
W
N
·tii
a;
>
o 0.8-
y
~
=
1.1973x
R'2
Slope
=
(n) = 1.1973
=
Position
- 6.259
0.9994
(In Xo)
5.227
param eter (Xo) = 190 um
I-----.----.-------~
OJ
N
'0;
t;;
>
0
;;'!-
0.8
'"
>
.~
:;
E 0.4
:J
y = 1.416x - 7.7351
R'2 = 0.9984
Slope (n) = 1.416
(In Xo) = 5.64
Position parameter (Xo) = 240 um
S2
~
.E
.E
OJ
N
'0;
•..
'">
0
;;'!-
0.8
y = 1.3333x -7.5034
R'2 = 0.9987
Slope (n) = 1.3333
(In Xo) = 5.628
'"
>
.~
:;
E
:J
0.4
S2
~
cosition
,
parameter.~~_c~L:.!_8~~----._-
.E
.E
OJ
N
'0;
t;;
>
0
;;'!-
0.8
'"
.~
>
:;
E
:J
S2
~
.E
.E
0.4
y = 1.2818x - 7.1157--~1
R'2 = 0.999
Slope (n) = 1.2818
i
(In Xo) = 5.551
I
Position parameter (Xo) = 260 um I
~
N
'Vi
Iii
>
0
~
0.8
y
>
=
- 6.9932
0.9983
=
"3
"
!2
~
1.4084x
Slope (n) = 1.4084
(In Xo)
4.965
'~
E
=
RA2
ClJ
0.4
Position
parameter
=
(Xo)
140 um .
E
E
~
N
'Vi
Iii
>
0
~
y = 1.3063x
0.8
>
.~
Slope
"3
E
!2"
- 6.411
RA2 = 0.9989
ClJ
(n) = 1.3063
=
(In Xo)
0.4
Position
parameter
4.9
(Xo)
= 130 um
E
E
~
N
'Vi
Iii
>
0
~
i
0.8
y
>
.~
!2
~"
E
E
1.2918x
Slope
"3
E
=
- 7.0329
RA2 = 0.999
ClJ
0.4
Position
(n)=
1.2918
(In Xo)
= 5.444
parameter
(Xo)
=
230 um
i
i
~.
~
I
N
'in
~
>
0
";!'
0.8
y = 1.2811x
~
::::l
-7.1319
=
R'2
0.999
Slope (n) = 1.2811
.~
:;
E
~.
=
(In Xo)
parameter
Position
0.4
5.567
(Xo)
I
I
=
260 um
I
.E
.E
~
N
'iii
";!'
0.8
y = 1.4198x
>
.~
::::l
E
::::l
- 8.2239
R'2 = 0.9982
Slope (n) = 1.4198
OJ
Position
0.4
(In Xo)
= 5.792
parameter
(Xo)
=
I
330 um,
I
~---,,---,-----'
f2
~
.E
.E
"
~
N
1.2
'iii
~
>
0
~
y
0.8
.~
~
:;
1.4341x - 8.8538
Slope. (n)
I
E 0.4
----~ition
::::l
f2
~
.E
.E
=
R'2 = 0.9986
OJ
0
0
i
I
f2
•...
OJ
>
0
I
=
1.4341
(InXo)=6.173
parameter (Xo)
,
= 480 um j'
Q)
N
'in
Iii
>
0
~
y = 1.9269x
0.8
.<:
Slope
~:>
E
:>
- 9.5447
~----------
R'2 = 0.9955
111
(n)
(In Xo)
0.4
Position
=
parameter
=
1.9269
4.9534
(Xo)
= 140 um
I---
!2
~
E
E
Q)
N
'Vi
Iii
>
0
~
0.8
y = 1.8923x
R'2
111
>
~
E
- 9.4934
l----------I
I
0.9956
Slope (n) = 1.8923
(In Xo) = 5.017
:;
:>
=
Position
0.4
parameter
(Xo)
= 150 um
I
!2
~
E
E
0
I
0
~
In (Void
3
2
Diameter(um))
4
Qj
>
0
~
y
Q)
.:::
~:>
E
:J
!2
~
E
E
OJ
.~
VI
= 1.6425x
- 8.493
R'2 = 0.9973
Slope (n)
= 16425
(InXo)=5.17
R:Jsition pararreter
(Xo)
'I
= 175 um !
5
6__
-.--J
.
7
I
Q)
N
1.2
'jji
:;;
>
0
~
y= 1.2676x -7.1315
R"2 = 09991
0.8
l1J
>
(;j
r-I
Slope (n) = 1.2676
:;
(In Xo) = 5625
!
E 0.4
:J
i
I
I
Position parameter (Xo)
= 280 um
f
S2
~
.E
.E
a
a
Q)
N
1.2
'jji
:;;
>
0
~
y= 1.4194x -7.7762
0.8
R'2 = 0.9982
l1J
.:::
Slope (n)=
(;j
:;
1.4194
(In Xo) = 5.479
E 0.4
'Position parameter (Xo)
:J
= 240 um
I
S2
~
.E
.E
a
a
Q)
.!::! 1.2
1Il
:;;
>
0
~
y = 1.341x - 7.9768
0.8
R'2 = 0.9987
l1J
.:::
I
I
ro
:;
E 0.4
:J
i
(InXo) = 5.948
Position parameter (Xo) = 380 um
L
S2
~
.E
.E
Slope(n)=1.341
a
a
.
,
I
!
f-.--I
APPENDIX D
MACRO IN MICROSOFT
EXCEL FOR CALCULATION
OF VOID SPACING
, distance Macro
, Macro recorded
1999/01/13
by E Kearsley
nr = ActiveCell.Value
While nr > 0
For i = 1 To nr
ActiveCell.Offset(i
- 1, 1) .Range("A1") .Select
xcord = ActiveCell.Value
ActiveCell.Offset(O,
1) .Range("A1") .Select
ycord = ActiveCell.Value
ActiveCell.Offset(O,
1) .Range("A1") .Select
zcord = ActiveCell.Value
ActiveCell.Offset(l
- i, 3) .Range("A1") .Select
ss = 1000
For n = 1 T9 nr
ActiveCell.Offset(n
- 1, -5) .Range("A1") .Select
xx = ActiveCell.Value
Acti veCell. Of fset (0, 1). Range ("A1") .Select
yy = ActiveCell.Value
ActiveCell.Offset(O,
1) .Range("A1") .Select
zz = ActiveCell.Value
ActiveCell.Offset(-n
+ 1, 3) .Range("A1") .Select
temp = Dist(xcord, ycord, zcord, xx, yy, zz)
If i > n Or i < n Then
If temp < ss Then
ss = temp
ActiveCell.Offset(i
- 1, 0) .Range("A1") .Select
ActiveCell.FormulaR1C1
= ss
ActiveCell.Offset(O,
1) .Range("A1") .Select
ActiveCell.FormulaR1C1
= n
ActiveCell.Offset(l
- i, -1) .Range("A1") .Select
Else
End If
Else
End If
Next
ActiveCell.Offset(O,
-6) .Range("Al") .Select
Next
ActiveCell.Offset(nr,
0) .Range("A1") .Select
nr = ActiveCell.Value
Wend
End Sub
Function Dist(xcord, ycord, zcord, xx, yy, zz)
Dist = (Sqr( (xcord - xx) ~ 2 + (ycord - yy) ~ 2) - zcord - zz)
End Function
APPENDIX
E
AIR-VOID SPACING DISTRIBUTION
OF MIXES
~
>u
12%
••
0••u:
10%
8%
6%
4%
2%
0%
c:
:J
100%
90%
20%
18%
16%
14% ,
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
0
lfl
20%
18%
16%
~ 14%
>u 12%
c:
•• 10%
:J
08%
u:•• 6%
4%
2%
0%
70%
1,:.:.:.:.:.:-:.: ...,
0
lfl
0
0
0
lfl
0
0
N
0
lfl
N
0
0
(")
I·"III,
0
lfl
(")
0
0
....
0
lfl
....
"
6°16
E
(5
0
lfl
lfl
0
0
<D
0
lfl
<D
0
0
r---
0
lfl
r---
0
0
co
0
lfl
co
0
0
Ol
0
lfl
Ol
0
0
0
(urn)
100%
90%
80%
20%
18%
16%
~ 14%
() 12%
~ 10%
8%
~
:;
~--T-ar-g-e~-d-e-ns-i-tY-1-00-0-k-9-/~~AlC-=-O-)--------
1~----------~--~-iX-3
0-
~
50%
40%
30%
20%
10%
I
%:
~
60%
0%
0
0
lfl
Void Spacing
~
Frequency %
-------·-------~--Cumulative
0
:J
100%
90%
80%
---------------------~
70%
--~--.====-------------------j
DB
--
Frequency %
Cumulative%
30%
20%
10%
2%
o
o
0
~
a
a
N
0
~
N
0
0
M
" II I III
0
~
M
~, II ; :"rH-H+t-'
0
0
0
0
m 0
~
~
~
IIII I I III
0
0
~
0
~
W
! !
IIII
0
~
W
' , I I I II I II II
0
0
0
0
~
a
~
~
ro
0%
0
~
ro
0
0
m
0
~
m
••
IJ ;~~ I
(5
4%
0%
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L{) 0
f'...
co
If) 0
0>
co
l()
(J')
10%
0%
a
a
0
APPENDIX F
EXPONENTIAL
FIT FOR CUMULATIVE
PERCENTAGE
VOID SPACING OF MIXTURES
OVERSIZE AIR-
100%
OJ
N
90%
'Vi
80%
~
>
70%
0
<f!.
y = 1.1524e'O.0043x
2
R = 0,9874
60%
I-----------------~
50%
.:=
-+-Cumulative
40%
--Expon.
:i
30%
E
20%
OJ
iU
:l
()
% over size
(Cumulative % over size)
10%
0%
0
100%
OJ
N
90%
'Vi
80%
~
>
70%
0
<f!.
OJ
.:=
y = 1.0481 e,00134x
R2 = 0.996
60%
50%
40%
-+-Cumulative
:i
30%
1_- Expon.
:l
20%
iU
E
()
% over size
(Cumulative % over size)
10%
0%
0
100%
OJ
N
90%
'Vi
80%
OJ
70%
0
60%
•...
>
~
y = 0.9042e'o 0173x
R2 = 0.9975
OJ
50%
.~
40%
-+--Cumulative
:i
30%
--
E
20%
>
:l
()
10%
0%
0
% over size
Expon. (Cumulative % over size)
100%
QJ
N
'in
Q;
>
0
<f?
QJ
.2:
~
:;
E
:l
t)
90%
I
Y = 0.9264e·OOl44Xr, ~~~~~~~~~~~~~~~~~~-'-----j
80%
R2 = 0,9953
70%
rj ---------~.-------~-~
60%
50%
40%
30%
20%
Cumulative
Expon. (Cumulative
,
+--
% over size
I-+•--
,
% over size) ~
'
10%
0%
0
100
100%
QJ
N
90%
'in
80%
Q;
>
70%
0
<f?
50%
40%
'"
:;
30%
E
20%
>
:l
t).
= 0.921
e·O.0157x
R2 = 0.99
60%
:;:;
QJ
y
-l-,
-+-
Cumulative
--
Expon. (Cumulative
% over size
% over size)
i
10%
0%
0
100
1000
100%
QJ
N
90%
'in
80%
Q;
>
70%
0
<f?
QJ
y
= 0.9913e·o0097x_~
R2 = 0.9889
__ ~~~~~~~~~~~~~~~_
60%
I
50%
,r,
-+-~~-C~u-m-u-Ia-t-iv-e-Of<-o-o-v-e-r
s-i-ze~~~-~
>
40%
:;
30%
% over size) ~
i
E
20%
I
~
:l
t)
II
. --
Expon. (Cumulative
10%
~
0%
0
I
100%
'Vi
90%
80%
~
o
70%
60%
<lI
N
Iy= 1,1256e-DOO56x~!
-----------------.;
R2 = 0.9826
~.---------,---------.,
I
~
50% ~---
~
:;
§
40%
30%
20%
u
10%
0%
1
---.'------j
--+-
Cumulative % over size
:-1--
~
Expon. (Cumulative % over size) ~
,
!
I
"---------------~
j-------------=~-~_iiii
O~'
I
••---------i
I
---1-0-0--2~0-0--3-0~0---4-00---5-0-0--6-0-0--7-0-0--8-0-0---90-0-'~00~1
L
Void spacing (um)
---------------------------~,---------
!y = 1.23ge-O.0097x~-,-.--'-.
2
R =0.9862
1-
i
-----~=E-C-umulative
------------
% over size
'
L--- E_x_p_on.
(Cumulative Ok over size)
10%
0% +---~--~---~-----~--------------------j
<lI
,~
'"
~
<lI
>
0
';f:.
OJ
,?:
~:J
E
:J
u
100%
90%
80%
l
------.
y = 1.176ge-DOlO2x
R2 = 0.9928
70%
60%
50%
40%
30%
--
20%
10%
0%
0
Expon. (Cumulative % over
size)
100%
IV
N
90%
'iij
80%
:;;
70%
>
0
~
IV
.~
"iO
:;
E
:J
<.>
OOO72x
,Y = 1.081 e·
I R2=0.9888
~;---------------~
l
60%
50%
40%
-+-
Cumulative
--
Expon. (Cumulative
% over size
% over size)
30%
20%
I
10%
0%
0
100%
IV
N
90%
'iij
80%
Y = 1.1 06ge-D·0069x1
:;;
70%
R2 = 0.9412
>
0
~
IV
.~
"iO
60%
50%
I-+- Cumulative
---I --
40%
:;
30%
E
:J
<.>
20%
% over size
Expon. (Cumulative
% over size)
10%
0%
0
100%
IV
.!::!
III
:;;
>
0
~
IV
.~
90%
80%
Y = 0.6975e'OOO56X~
70%
R2 = 0.963
60%
50%
"iO
40%
:;
30%
E
:J
<.>
20%
i
-+-Cumulative
--Expon.
10%
0%
0
% over size
(Cumulative
% over size)
100%
OJ
N
90%
.iij
80%
0;
70%
0
60%
>
~
OJ
50%
:;:
40%
'"
:;
30%
E
:J
u
20%
>
Y = 1.0495e·00043x
~I--------------~
2
R =0.9747
..........- Cumulative
,--
% over size
Expon. (Cumulative
!
% over size) "
10%
0%
i
I
0
1000
100%
90%
Y = 0.991ge.OOO38xll
,I
2
R = 0,9704
.----------------~
50%
----I_+_
40%
--
Cumulative
% over size
Expon. (Cumulative
% over size)
30%
20%
10%
I
0%
1000
100%
OJ
.!::!
90%
VI
80%
Y = 1.2805e-oo~
0;
70%
R2=0,9911
0
60%
>
~
OJ
>
~
:;
E
:J
u
50%
~
..........- Cumulative
40%
--
30%
20%
10%
0%
0
% over size
Expon. (Cumulative
% over size)
100%
Q)
N
'iij
~
>
0
~
Q)
,~
iil
:;
E
:l
(J
90%
80%
70%
,
'y= 1,2951e,o.0084X~I------------------~
I
R2 = 0,9822
I
60%
50%
40%
!
--+--Cumulative
--
% over size
Expon. (Cumulative
% over size)
30%
20%
10%
0%
I
1000
0
Q)
100%
90%
-
N
'iij
~
>
0
~
Q)
,~
iil
:;
E
:l
(J
y
80%E
70% ;
60% i
50%
=
1,1853e'00091X
R2 = 0.987
;--+- Cumulative
40%
: --
% over size
Expon. (Cumulative
% over size)
30%
20%
10%
0%
0
Q)
N
'iij
~
>
0
~
Q)
,~
iil
:;
E
:l
(J
100
100%
90%
y = 1.3375e,o.0096x
80%
70%
R2
60%
50%
40%
= 0.9863
,--+--Cumulative
1--
30%
20%
10%
0%
0
% over size
Expon. (Cumulative
% over size)
100%
QJ
N
90%
'in
80%
QJ
70%
•..
>
0
~
QJ
.2:
10
:;
E
::l
u
-
60%
------j~=_._---c-u-m-u-Ia-t-iv-e-%-o-o-ve-r-s-iz-e---~~
50%
40%
~--
Expon. (Cumulative
% over size) ~
30%
20%
10%
0%
0
100
200
300
400
100%
QJ
N
90%
'in
80%
:;;
>
70%
0
~
QJ
>
10
:;
E
::l
u
Iy = 1 . 2286e-00071XI~--I
__ -----~
-------~
I
R2 = 0.9853
60%
50%
I-+-
Cumulative
40%
!--
Expon. (Cumulative
30%
% over size
% over size)
20%
10%
0%
0
100%
QJ
N
'in
•..
90%
QJ
70%
0
60%
>
~
QJ
,2:
10
:;
E
::l
u
I
'y = 1.189ge-Q
80%
I
o08Sx
2
R = 0.9951
50%
-+-Cumulative
40%
--
30%
20%
10%
0%
0
% over size
Expon. (Cumulative
I
% over size)
100%
QI
90%
N
0Cij
80%
:v
70%
>
0
~
QI
1.3901 eoOOO98x
R2
I
= 0.9658
~I -------------------~
~I
60%
50%
40%
:;
30%
:J
()
=
~
02:
••E
y
i -+--
Series 1
Expon. (Series1)
20%
10%
0%
0
100%
QI
90%
N
'Cij
80%
:v
70%
0
60%
>
~
QI
50%
.2:
40%
••
:;
30%
E
20%
:J
()
y = 1.6036e-00102x
R2
= 0.9718
r-
+-i
-+-
Cumulative
--
Expon. (Cumulative
% over size
% over size)
10%
0%
I
0
100
100%
QI
90%
N
0Cij
80%
:v
70%
>
0
~
QI
>
=
1.0125e-DOO67x'
R2 = 0.9664
60%
50%
.~
40%
:;
30%
E
20%
:J
()
y
-+-Cumulative
--
10%
0%
I
0
% over size
Expon. (Cumulative
% over size)
.,
100%
90%
N
'Vi
80%
Qj
70%
>
0
.,
~
.::
"'
L-----------~!
60%
50%
]---+--Cumulative
40%
"S
30%
E
:J
u
20%
--j --
% over size
Expon. (Cumulative
~
% over size) ~
10%
0%
0
.,
.,...
~.,
.::
100%
1
90%
N
'Vi
>
0
"'
80%
Iy= 1.2471e-00079x_' --------------------
70%
I
2
R =0.9951
60%
-+- Cumulative
50%
40%
"S
30%
E
:J
u
20%
I---------------~
i --
I
% over size
Expon. (Cumulative
% over size)
10%
0%
0
.,
.~
....,
~.,
.::
VI
>
0
"'
100%
90%
80%
y = 1.3124e-o.012x
70%
R2 = 0.9784
60%
50%
I---+-- Cumulative
1--
40%
"S
30%
E
:J
u
20%
10%
0%
0
% over size
Expon. (Cumulative
% over size)
I
100%
CIJ
90%
VI
80%
~
>
70%
.!:!
0
~
CIJ
>
~
:;
E
:l
()
Iy = 1.2185e-QOO62x
I R2 = 0.984
60%
!
-+- Cumulative
50%
40%
--
% over size
Expon. (Cumulative
% over size)
30%
20%
10%
0%
0
100%
CIJ
N
90%
.Iii
80%
~
>
70%
0
~
CIJ
.2:
10
40%
E
20%
= 0.8923
-+-- Cumulative
50%
30%
:l
R2
60%
:;
()
y = 0.7782e-0004X!
% over size
--
Expon. (Cumulative
-+-
Cumulative
--
Expon. (Cumulative
% over size)
10%
0%
0
100%
CIJ
90%
VI
80%
~
70%
0
60% ~
.!:!
>
~
CIJ
>
~
:;
E
:l
()
50%
40%
30%
20%
10%
0%
0
% over size
% over size)
APPENDIX G
SUMMARY OF EXPONENTIAL FITS FOR THE CUMULATIVE %
OVERSIZE GRAPHS FOR SPECIFIC ASH I CEMENT RATIOS
100%
90%
QJ
N
80%
QJ
70%
-+__
0
60%
---*-Dry
50%
40%
---¥-Dry Density = 741 kg/m3
__
Dry Density = 661 kg/m3
30%
___ Dry Density = 536 kg/m3
'Iii
...
>
~
QJ
>
'+'
'"
:;
E
::I
II
Dry Dens ity = 1223 kg/m 3
Dry Density = 892 kg/m3
Density
=
831 kg/m3
-..---:
I
0%
0
100%
90%
'Iii
t
>
80%
0
60%
50%
>
"":;
'"
E
::I
II
-+-Dry
Density = 1235 kg/m3
__
Dry Density = 901 kg/m3
70%
~
QJ
---*-Dry
Density
=
811 kg/m3
40%
---¥-Dry Density = 735 kg/m3
__
Dry Density = 646 kg/m3
30%
___ Dry Density = 559 kg/m3
20%
10%
0%
0
100%
90%
QJ
N
'Iii
t
>
0
~
'.,>
~::I
QJ
E
::I
II
G
20%
10%
QJ
N
~
I !
80%
70%
-+-Dry
Density = 1230 kg/m3
__
Dry Density = 958 kg/m3
60%
---*-Dry
50%
40%
---¥-Dry Density = 713 kg/m3
__
Dry Density = 612 kg/m3
30%
___ Dry Density = 555 kg/m3
20%
10%
0%
0
Density = 790 kg/m3
100%
.,
...,
N
'Iii
>
0
.,
~
.>.,
III
::J
E
::J
u
90%
___ Dry Density = 1219 kg/m3
80%
__
70%
Dry Density = 958 kg/m3
---*-Dry Density = 812 kg/m3
__
Dry Density = 697 kg/m3
60%
50%
-JlE-Dry Density = 631 kg/m3
__ Dry Density = 540 kg/m3
40%
30%
20%
10%
i
0%
0
100%
.,
...,
~.,
N
'ijj
>
0
>
90%
80%
___ Dry Density = 1168 kg/m3
70%
_Dry
60%
---*- Dry Dens ity = 771 kg/m 3
__
Dry Density = 526 kg/m3
50%
.~
40%
:;
30%
E
::J
20%
u
~
Density = 941 kg/m3
I
-JlE-Dry Density = 689 kg/m3
__
Dry Density = 518 kg/m3
10°A,
0%
0
100
200