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1 Introduction

1.1 Background

Insulation is one of the techniques that will always be around. It is a passive

product, once installed it works efficiently, quietly and continually, usually out of sight

enclosed within a structure, a casing or under cladding. Its purpose is to reduce or prevent

the transmission of heat or sound or electricity.

Insulation comes to the fore when the new design of buildings, plant, equipment

or production processes is being considered. It is at this stage that the right specification

must be made, any shortfall in the thickness, or error in the type and application details

will prove costly to rectify at a later date. There are many reasons why professional

engineers, architects and indeed laymen use insulation. They include having to comply

with mandatory legislation i.e. Building Regulations or Standards, to reduce heat

loss/heat gain, to reduce running costs, to control process temperatures, to control surface

temperatures, to reduce the risk of freezing, to provide condensation control, or to reduce

heating plant capacity.

Thermally insulating materials have thus been vital to mankind throughout history.

Their applications are not limited to providing protection of man against extreme

temperatures in their habitats, but they have already been widely used for commercial and

industrial purposes since the industrial revolution in late nineteenth century. For example,

thermal insulators have been employed in cryogenic services to prevent heat gain, such as

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for storage of liquefied natural gas (LNG) at cryogenic temperature of -162.2 oC (see

Figure 1.1) and refrigeration of foodstuffs and storage of liquid hydrogen for aerospace

endeavors. (Cunningham and Roni, 1978)

Figure 1.1: A typical LNG storage tank under construction

They are also needed to prevent heat loss, such as in hot water storage tanks. For

underwater pipes which carry very high temperature crude oil from offshore oil rig to the

processing plants on land, they need to be insulated to prevent seawater from cooling the

oil in these pipes, causing them to become too viscous to flow and as a result not being

able to be transported.

Over the past decades, there has also been an increasing need to develop cost-

effective insulating materials to provide thermal comfort for the inhabitants in buildings.

Due to rising oil prices, measures have been taken to conserve energy used by buildings

to provide thermal comfort. Hence, in many parts of the world, the focus is on energy

efficiency in the design of buildings through more cost-effective thermal insulation

systems. Energy efficiency also addresses the environment concern of green-house gas

emissions that cause global warming.

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In Singapore, the Building and Construction Authority (BCA) has played an

active role throughout the years to help to enhance energy efficiency in buildings by

ensuring that minimum standards in energy efficiency are met. Recently, due to

improvement of technology and better building materials, BCA has replaced the Overall

Thermal Transfer Value (OTTV) with a new standard called the Envelope Thermal

Transfer Value (ETTV). ETTV gives a more accurate correlation with the total heat gain

through a building envelope and, hence, is a more reliable indicator for energy efficiency.

It would replace the current OTTV formulation for envelope. Similarly, the OTTV

formulation for roof would also be replaced with the new Roof Thermal Transfer Value

(RTTV) formulation.

The new ETTV of the building and RTTV of roof with skylights, as determined in

accordance with the formula set out in the “Guidelines on Envelope Thermal Transfer

Value for Buildings” issued by the Commissioner of Building Control, shall not exceed

50 W/m2. However, for roofs without skylights, the U-value cannot exceed the limit

prescribed in Table 1.1 for buildings of the corresponding weight group obtained from

BCA Approved document (October 2004)1. The system analysis approach allows for

flexibility in design without compromising energy efficiency while the requirement on

energy efficient equipment is introduced to ensure that only energy efficient equipment

are used. When compared to the old standards, it is estimated that the new standards on

OTTV, maximum lighting power budget and the efficiency of air-conditioning equipment

could reduce electricity consumption by as much as 24%.

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Table 1.1: Maximum thermal transmittance for roof of air-conditioned building

1.2 Motivation of research

The search for economical and high insulating materials that suit the different

kinds of application mentioned above is still continuing. One prime candidate of a cost-

effective thermal insulation is aerated concrete. Aerated concrete is produced by

introducing air bubbles during the casting process of concrete. There are two main types

of aerated concrete, namely Autoclaved Aerated Concrete (AAC) and foamed concrete.

Autoclaved aerated concrete (AAC) is produced by introducing gas (hydrogen) bubbles

into cement paste or mortar usually made with Portland cement of suitable consistence

using aluminum powder (0.2 % by mass of cement) which reacts with Ca(OH)2 and

alkalis released into solution. The gas bubbles expand the mixture to the required density

after which the concrete is cured either in steam at atmospheric pressure or in steam at

180oC under high pressure in an autoclave.

The air in foamed concrete can be introduced into a mortar or concrete mix using

two methods. The first method is by mixing a pre-formed foam from a foam generator

can be mixed with other constituents in a normal mixer or ready mixed concrete truck.

Second, a synthetic- or protein-based foam-producing admixture can be mixed with the

other mix constituents in a high-shear mixer. The resulting bubbles in the hardened

concrete should be discrete, usually within the size of 0.1 mm to 1 mm.

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AAC has to be factory-made and is used where financial means and other

conditions favor mass production of high-quality products. However, foamed concrete

can be produced at a much lower cost as its main ingredients are readily available and it

can be manufactured on a small scale at construction site, thus saving on transportation

cost of components to the site. Compared to AAC, foamed concrete offers environmental

benefits as it does not require so much fuel energy for high temperature autoclaving.

Foamed concrete uses relatively lower water cement ratio than AAC, so the compressive

strength of foamed concrete can sometimes be higher than AAC. There are also no waste

products and the ingredients are non-hazardous.

Foamed concrete has good mechanical strength, is lightweight and has low

thermal conductivity. It can be produced in a wide range of densities and properties

which can vary to suit particular requirements. Like ordinary concrete, it can easily be

molded to any desired shape or sizes. Foamed concrete can offer a versatile and cost-

effective alternative to other insulation materials. Results from NUS in-house data

showed that energy savings per unit area by using foamed concrete wall (S.G. = 0.8,

thermal conductivity of 0.26 W/m.K) as compared to using convectional concrete wall

(S.G. = 2.4, thermal conductivity of 2.5 W/m.K) is more than 70 %. Thus, it is showed

that foamed concrete can be an effective insulation material to help in energy-saving in

buildings.

Roofing is probably the most widespread application of foamed concrete. (See

Figure 1.2) It is used to provide graded insulation on roof projects beneath waterproofing

membranes. Foamed concrete has two benefits when it is used for roofing. The first

benefit is that it provides a high degree of thermal insulation. The second benefit is that it

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can be used to lay a flat roof to falls, i.e. to provide a slope for drainage. In countries

where roofs are flat and where roof surfaces are used as part of everyday life, foamed

concrete is strong enough to support foot or even vehicular traffic on the roof. Foamed

concrete is also much lighter than slopes made from mortar screeds. This means that a

roof with a slope made of foamed concrete imposes a lower loading on the structure of

the building.

Figure 1.2: Casting foamed concrete as insulating roof deck

Due to the tremendous market for foamed concrete as an insulating material to

meet the rising needs in the building industry and other industries due to its versatility

and economy, continual development and research to understand more about foamed

concrete is required. It would thus be very useful if more information can be known about

how different factors in the mix design of foamed concrete affect its thermal and strength

properties to offer an economical and effective insulation for various applications.

One major concern for the use of an insulating material is its ability to maintain

its low thermal conductivity in the environment it is used. High-porosity materials like

foamed concrete tend to absorb water which will increase its thermal conductivity, thus

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causing the insulating material to lose its effectiveness. One suggestion is to incorporate

polymer into foamed concrete to resist water ingress so as to maintain the effectiveness of

the insulating material during field application. The thermal conductivity of polymer (k ≈

0.19- 0.3 W/m.K) (Weber, 2001) is also much lower than cement paste (k ≈ 0.66 -1.2

W/m.K) (Matiasovsky and Koronthalyova, 2002). Thus, it can be added to foamed

concrete to replace some of the cement content in order to decrease the effective or

resultant thermal conductivity of the resultant material. So far, no record of studies on

properties of polymer-modified foamed concrete could be found in the literature.

However, from several studies that showed improved properties of polymer-modified

normal weight or lightweight concrete, there is reason to believe that adding polymer

might improve the performance of foamed concrete. Thus, it will be interesting to study

the mechanical properties and also thermal conductivity of polymer-modified foamed

concrete in this research study and to discover how this improved material can be

extended to other applications.

Though there is currently some available literature on factors affecting thermal

conductivity of aerated concrete, the majority of the research is focused on AAC. Studies

of thermal conductivity (k) of foamed concrete seem to be fewer in comparison. There

seems to be a lack of comprehensive study on the topic of thermal conductivity for

foamed concrete. Moreover, there are some useful information that are lacking as well in

the literature like the effect of air bubble size (keeping total air content constant) on

thermal conductivity. Thus, in this research study, areas where further studies is

necessary to understand more about this material which is becoming more popular and

widely used will be investigated.

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Hence, this study is undertaken to measure and analyze the thermal conductivity

and some mechanical and thermal properties of foamed concrete in greater detail and also

to find reliable theoretical or numerical models for its prediction. Thermal performance

of foamed concrete which is governed by its thermal conductivity will be studied with

regards to its sensitivity to various factors such as w/c ratio of foamed concrete mix, foam

content and polymer content. The information will provide greater insight to design a

cost-effective foamed concrete mix that is able to achieve its intended purpose with

maximum saving in materials and cost.

Foamed concrete can be applied locally as an insulating material for roofing

systems over the roofs of HDB flats and other flat roof. Lately, secondary roofing slabs

made from ferrocement has been used over the flat roofs of most HDB apartments as part

of the heat insulation system (see Figure 1.3).

However, this secondary roofing system has some disadvantages. For example,

the ferrocement slabs are just mounted on the concrete stumps and thus this system

cannot be applied to apartments in areas where there are strong winds as the slabs can be

blown off easily thus posing a danger to the residents and passer-by. Heat can also be

transferred through these concrete stumps, to give rise to the temperature of the main roof

below. Thus, the effectiveness of the insulation system using ferrocement and air gap for

the roof will be reduced.

Another disadvantage is that after years of deterioration, the strength of the

ferrocement slab will decrease such that it will easily break when someone steps on it.

This again, poses a danger to people who have to go up to the roof due to the nature of

their work. (See Figure 1.4)

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The layer of trapped air between the main and secondary roofs is supposed to

prevent heat transmission to the dwellings below. However, once the ferrocement

secondary roof slab is broken, the insulation provided by the air layer will be ineffective

since heat will be directly transferred to the main roof at the broken portions. Moreover,

the air layer is not strictly adiabatic at the boundaries due to the many openings at the

sides. This may cause heat to be transferred to the main roof through the sides as well.

Hence, the thermal insulation performance of the secondary roofing system may not be as

effective as expected.

These precast ferrocement roof slabs are dense and impermeable to water due to

the high grade of mortar used in their manufacture. Thus, waterproof membranes are

eliminated. However, if there are any holes caused by deterioration of the slabs, or gaps

caused by imperfect workmanship when laying the roof slabs, water may seep through

the building envelope into the building, causing leaking problems to the inhabitants.

Thus, there is a need to come up with more effective roofing systems that suit the

local environmental requirement to replace it. In this research, the feasibility of foamed

concrete as the insulation material for two alternative systems to provide thermal

insulation to the main roof slab will be studied (see Figure 1.5 and Figure 1.6).

Figure 1.3: Sketch of HDB Secondary Roof System

Roofing Slabs

Concrete Stumps

Air Gap Air Gap

Main Roof Level

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Figure 1.4: Picture showing deteriorated roof slab

Figure 1.5: Sketch of the secondary roofing system proposed using low grade foamed concrete

(Alternative A)

Figure 1.6: Sketch of the new roofing system proposed using higher grade foamed concrete

(Alternative B)

Foamed Concrete secondary roofing Slab

Main Roof Level (normal weight concrete)

Foamed Concrete roofing System

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1.3 Objectives and Scope

1.3.1 Objectives

1) To study and understand how various key factors (namely foam content, water-

cement ratio and air void size) affect the thermal conductivity and strength for

different mix designs of foamed concrete.

2) To propose a simplified and user-friendly equation using numerical model (via

FLUENT software) for predicting thermal conductivity of foamed concrete to aid

in the design of foamed concrete mixes for structural and non-structural insulation

purposes, verifying it with current and other researchers’ experimental results and

other analytical models.

3) To investigate the effect of incorporating acrylic polymer into foamed concrete on

its thermal conductivity, mechanical properties and water-resistance property.

4) To investigate the suitability of foamed concrete as an insulation material for

roofing system of buildings to suit local requirements and to propose suitable

design mix of foamed concrete to be used.

1.3.2 Scope of Work

1. To measure the thermal conductivity and some mechanical properties (3-,7-,

28-day compressive strength, flexural strength, splitting tensile strength and

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elastic modulus) of foamed concrete and polymer-modified foamed concrete

with varying foam content, water-cement ratio and polymer content.

2. To investigate the effect of different air bubble size on thermal conductivity of

foamed concrete via numerical models using FLUENT software.

3. To find out the effect of varying foam content and polymer content on the air

bubble sizes using automatic imaging microscopy.

4. To analyze and explain the effect of varying foam content, water-cement ratio

and polymer content in foamed concrete on its thermal conductivity and

mechanical properties.

5. To determine which existing theoretical models can predict the thermal

conductivity of foamed concrete realistically.

6. To investigate the effectiveness of the proposed foamed concrete roofing

systems using (Alternative A and B) suitable mix proportions of foamed

concrete for use on roofs of local buildings.

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2 Literature Review

This chapter describes various topics that are related to the objectives of this

research project. It starts off with the theory of thermal conductivity to understand more

about how heat is conducted in foamed concrete and in polymers. Since polymer-

modified foamed concrete would also be investigated for this research, it would be good

to have a basic background on how heat is transferred in polymers. Thermal resistance of

building insulations will be discussed in order to have a clear understanding of how

insulation works.

The heat flow meter is used to measure the thermal conductivity values of the

concrete specimens and a more detailed description of the apparatus is available in this

chapter as well. Reasons for choosing this apparatus over other equipment will be offered.

A comparison between foamed concrete and other commercially available insulation

material is also presented in this chapter.

There are a few sections devoted to literature review of research works done on

the mechanical and thermal properties of foamed concrete. Information regarding this

material that is still lacking from the literature review is identified. A literature review of

the various theoretical models available to predict thermal conductivity of foamed

concrete is also provided. This section covers a few of the available mathematical

relations for correlating the effective thermal conductivity of a mixture with the thermal

conductivities of the individual components.

Currently, there is no literature available about polymer-modified foamed

concrete. However, there are many studies done for polymer-modified concrete. Thus,

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studying the properties of polymer-modified concrete may give some insights on the

possible effects of incorporating polymer to foamed concrete. The last section of this

chapter will provide more details on flat roofing system used in HDB rooftops. It will

provide some information on its disadvantages and the need to look for alternative

insulation material.

2.1 Thermal conductivity Theory

Thermal conductivity is a material property that plays a key role in all heat

transfer calculations. Heat transfer occurs through three mechanisms, namely conduction,

convection and radiation. Heat is mainly transferred via conduction in solids. Heat

conduction refers to the transport of energy in a medium due to a temperature gradient.

Fourier’s law is given by:

q= -k (dT/dt) (2.1)

where

q = heat flux (W)

k = thermal conductivity (W/m.K)

dT = temperature gradient (K)

dt = thickness of the material (m)

Fourier’s law shows that heat transfer through conduction depends on thermal

conductivity and a temperature gradient. This thermal conductivity is assumed to be

constant. However, it varies with temperature and also moisture content in the material.

The thermal conductivity of a homogeneous material is defined by the Fourier’s law. The

same definition is extended to a heterogeneous material, with the temperature gradient

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being the average value of the temperature gradient over a region large in comparison

with the size of inhomogeneities.

Heat is transported in solid mainly by electron transport and phonon transport.

Electron transport is the dominant transport mechanism in pure metals. Phonons are

defined as the quanta frequency of atomic vibrations. They transfer heat energy through

interactions with themselves and subatomic particles. In metal alloys, both electron and

phonon transport of the heat energy play a significant part. However, in dielectric

materials like polymers and concrete, the dominant way in which heat is conducted is by

phonons.

Bhattacharjee et. al (2004) studied on permeable porosity and thermal

conductivity of construction material. It was reported that most of the ceramics

construction materials such as bricks, blocks and concrete (chemically combined) are

porous in nature. Heat transfer through these materials is a complex process and involves

many components. The most important of these components are: (1) Heat conduction in

solid materials, (2) heat conduction through pore fluid (air or water), (3) convection heat

transfer through pore fluid, (4) radiation from solid surfaces of pores, and (5) evaporation

and condensation in the pores, when they are partially saturated with water. Hence, the

measured thermal conductivity is the amount of heat flow under the unit temperature

gradient for a unit area that encompasses some or all of the above mode of heat transfer

and is effective or equivalent thermal conductivity. These components of heat transfer are

additive but in general not independent.

For a pore diameter smaller than 3 mm, the effect of radiation and convection in

pores can be neglected in comparison with other modes of heat transfer at atmospheric

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pressure and temperature (Luikov, 1980). Thus, at normal ambient condition, the

conduction heat transfer through the solid skeleton and through fluid in the pores are

likely to be the most dominant mechanisms of heat transfer influencing the effective

thermal conductivity of the porous construction materials, when the pores are either

completely dry or fully saturated with water. When the pores are partially saturated,

evaporation condensation of moisture within the pores would also contribute to effective

conductivity significantly.

For a material with reasonably small cells or pores, such as foamed concrete

which contains air voids typically in the range 0.1 to 1 mm, heat transfer due to radiation

and convection within the pores is small and can be neglected or lumped in with the true

conduction component at atmospheric pressure and temperature.

In the case of foamed concrete, air bubbles are incorporated with cement paste to

bring down the thermal conductivity of the final product since air has a low thermal

conductivity. The thermal conductivity of foamed concrete depends on the thermal

conductivity of the solid material (cement paste), as well as the volumetric fraction of the

air or void space. The solid mass/ total volume or the bulk density is a special parameter

of the insulation system. Increasing the bulk density will also increase the thermal

conductivity of foamed concrete.

For materials like polymers, which are extremely long chained molecules that

have repeating units, their thermal conductivities are low as they do not have free

electrons or a regular atomic grid for effective heat transfer through atomic vibration.

Polymers are mostly amorphous (non-crystalline) and it is significantly less crystalline

than other crystalline materials like metals or low-molecular-weight compounds. Thermal

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conductivity has been experimentally shown to increase with increasing crystallinity or

orientation of polymer chains. This can be extrapolated to show that amorphous polymer

will be less conductive than semi-crystalline polymers.

2.2 Thermal resistance of building insulation

2.2.1 Resistance Concept

The rate at which heat flows through a slab of homogenous material under steady-

state conditions is given by:

where:

Q = the resultant heat flow (Watts)

A = the surface area through which the heat flows (m²)

∆T = the temperature difference between the warm and cold sides of the material (K), and

R = the thermal resistance per unit area of the piece of material (m²K/W).

Resistance is usually given as an "R" value which is the resistance of one square

metre of the material subject to a one degree temperature difference. Thus an R value of

a typical fibreglass may be given as R = 2.4, with the implication that it has the units

m²K/Watt. This means that if one takes the area of insulation in square metres

multiplied by the temperature difference in degrees Kelvin and divided by 2.4, one gets

Q = A. ∆Τ

R (2.2)

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the heat flow in Watts. For example, 100 square metres of R2.4 insulation, exposed to a

20°K difference, will pass about 833 Watts.

2.2.2 The U-value

The U-Value is an important concept in building design. It represents the air-to-

air transmittance of an element. This refers to how well an element conducts heat from

one side to the other, which makes it the reciprocal of its thermal resistance. U-value

can be obtained by inverting thermal resistance value of an element.

(2.3)

where RT = total thermal resistance

where Ro = air film resistance of external surface (m2K/W); Ri = air film resistance of

internal surface (m2K/W); K 1, K 2, K n = thermal conductivity of basic material (m2K/W);

b 1, b 2, b n = thickness of basic material (m); Ra = thermal resistance of air space. Table

2.1 shows Ri, Ro and Ra for different scenarios.

The U-Value is a property of a material. Its units are Watts per metre squared

Kelvin (W/m² K). This means that, if a wall material had a U-Value of 1 W/m² K, for

every degree of temperature difference between the inside and outside surface, 1 Watt

of heat energy would flow through each metre squared of its surface.

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Table 2.1: a) Surface film resistance of walls and roofs; b) Air space resistance of walls and roofs (for

air space greater than 100 mm, the Ra for 100 mm should be used)

2.2.3 Thermal resistance of Air Spaces

Heat is transferred across an air space by a combination of conduction,

convection and radiation. Heat transfer by conduction is inversely proportional to depth

of the air space. Convection is mainly dependant on the height of the air space and its

depth. Heat transfer by radiation is relatively independent of both thickness and height,

but is greatly dependent on the reflectivity of the internal surfaces. All three

mechanisms are dependent on surface temperatures. When all three heat transfer

processes occur at the same time, the overall thermal resistance of air spaces, both

reflective and non-reflective, becomes virtually independent of gap depth when it is

greater than around 25mm. (Shirtliffe, 1972)

a b

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2.2.4 Structure of thermal insulators

Commercial insulations generally have two basic structures: a continuous body of

gas that contains a dispersion of solid particles or fibres; and a continuous matrix of solid

material with a random dispersion of gas-filled cavities. For ordinary air spaces with no

heat reflective system, heat is transferred primarily through radiation and convection and

contribution through conduction decreases as the thickness of air spaces increases. With

reflective surface, heat transfer through radiation is greatly reduced. When a small

amount of opaque solid material is distributed throughout an air space, it inhibits heat

transfer by convection and radiation while contributing little to conduction, thereby

raising the value of the thermal resistance of the space as shown in Figure 2.1. Solids

such as glass, rock and plastic that provide little resistance to heat flow can be used in this

way to produce good insulation.

Figure 2.1: Variation of heat transfer across air spaces with thickness, orientation, surface

reflectivity and fibre fill showing size contribution by radiation, conduction and pure convection

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Figure 2.2: Resistance versus thickness for air spaces and wood

The limiting value for a low density, open pore type of insulation is given by the

uppermost curve in Figure 2.2, which represents an ideal situation of heat transfer

through air by conduction only. When thickness of air spaces increases, the resistance

increases. The lowest curve represents the other extreme, which includes the full effect of

radiation and convection. Low density, open pore insulations have resistance versus

thickness curves that lie somewhere between these extremes. (Shirtliffe, 1972)

2.2.5 Effect of Density on Thermal Resistance

The resistance of all types of insulation is strongly dependent on the amount of solid

material present, especially at the low densities that are of practical interest. Figure 2.3

shows how the resistance of 1-inch-thick layers of different materials, measured under a

set of standardized test conditions, varies with density. At very low densities there is so

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little solid material that there is an appreciable amount of heat transfer through the sample

by radiation and some by convection as well. As the proportion of solid material is

increased, these components of heat transfer become quite small until at some point the

increased conduction due to increased amount of solid just matches the reduction due to

decreased convection and radiation. This is the density for maximum resistance. Beyond

this point, resistance decreases slowly as the amount of solid increases. (Shirtliffe, 1972)

Reflective surfaces facing and in contact with insulation can be used to increase

the resistance of low density insulations. If the bounding surfaces of an insulation have a

low emissivity, there will be less heat transfer by radiation and over-all resistance will be

less dependent on density. The dotted curves in Figure 2.3 are examples of the results for

samples with aluminum foil at the surface.

The cost of insulation is dependent on density. Manufacturers tend to market

insulations at densities lower than those that give maximum R per unit thickness because

lower densities give a lower cost per unit of resistance. The range in which most

commercial fibrous insulations are produced is shown in Figure 2.3.

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Figure 2.3: Resistance of 1-inch specimens versus density.

2.3 Steady-state heat conductivity measurements

Thermal conductivity (k) defines a material's ability to transmit heat and is measured in watts per square metre of surface area for a temperature gradient of one Kelvin (K) per unit thickness of one metre, W/m.K. Most thermal conductivity measurements are made under steady-state conditions, which typically take some hours to achieve.

Figure 2.4 shows a schematic diagram of a heat flow meter (HFM) according to ASTM C

518. It establishes steady state unidirectional heat flux through a test specimen between

two parallel plates of constant but different temperatures. It consists of a multi-junction

thermopile formed with the junctions on either side of the specimen to be tested. The heat

flowing through the specimen is measured with calibrated heat flux transducers that are

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in contact with the sample at the plate interface. The thermal conductivity is determined

by the following equation:

where k is a constant known as thermal conductivity of the material; T1 and T2 are the

temperature of the hot and cold plate respectively, T1 > T2; x is the thickness of the

specimen; E is the voltage output of the heat flux sensor and S is the calibration factor of

sensor.

Heat Flux transducer (to data logger)

Figure 2.4: Diagram of a Heat flow meter apparatus

Another widely-used apparatus for measuring thermal conductivity is called the

guarded hot-plate (GHP) according to ASTM C177 as shown in Figure 2.5. It employs a

very similar operating principle as the heat flow meter. It has a guarded heating unit, two

auxiliary heating plates, two cooling units, secondary guarding in the form of edge

k = T1 – T2

xSE (2.4)

Cold Plate

Specimen (with 2-inch thick

Styrofoam insulation)

Hot plate

Heater

Cooling bath

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insulation and a temperature controlled secondary guard. The heat source is positioned in

the center between two samples of the same material. Two samples are used to guarantee

symmetrical heat flow upward and downward, as well as complete absorption of the

heater’s energy by the test samples.

A well-defined power is put into the hot plate during the test. The measurement

temperatures and temperature gradient are adjusted between the heat source and the

auxiliary plates by adjusting the power input into the auxiliary heaters. The guard heater(s)

around the hot plate and the sample set-up guarantee a linear, one-dimensional heat flow

from the hot plate to the auxiliary heaters. The auxiliary heaters are in contact with a heat

sink to ensure heat removal and improved control. By measuring the power input into the

hot plate, the temperature gradient and the thickness of the two samples, the thermal

conductivity can be determined according to the Fourier equation.

Figure 2.5: Diagram of a guarded-hot-plate apparatus

HFM can be easily handled by one person and can give rapid results within a few

hours, and it is applicable to a wide range of test specimen. The set-up can be calibrated

with an NIST standard material with known k-value, thus it can give accurate test results.

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Guarded hot plate has a broader temperature range (-180 to 650 oC) and is an absolute

measurement method which means that no calibration of the unit is necessary. Thus, it

can offer better accuracy. The GHP set-up is however quite cumbersome and would need

at least two people preferably to set up the test.

The results using HFM can be considered as reproducible as those of GHP, albeit

accuracies may be slightly lower than GHP due to heat losses at the edge of the

equipment.

2.4 Insulation Materials

Table 2.2: Thermal conductivity of some common insulation materials

Material

k-value

(W/m.K)

ρd, dry

density

(kg/m3)

Polyurethane foam 0.02 32

Polystyrene 0.037 30

Glass Wool 0.041 65 ~ 160

Polyethylene 0.0348 32 ~ 38

Rock Wool 0.04 40 ~ 130

0.065 300

0.08 400

0.095 500 Foamed concrete

0.115 600

0.194 870 Perlite Concrete 0.28 1315

Vermiculite Concrete 0.1 400

Normal weight concrete with granite 2.6-2.7 2400

Table 2.2 shows the comparison of thermal conductivity between foamed

concrete and other insulation materials and their dry density. Foamed concrete has a wide

range of thermal conductivity depending on its density. For low-density foamed concrete,

their thermal conductivity or k-value are quite low compared to the normal weight and

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heavy weight concrete. Their values are in the same order as some of the commonly-used

thermal insulator in the market. Thus, the potential of using foamed concrete as thermal

insulators is high.

2.5 Properties of foamed concrete

Aerated concrete is relatively homogeneous when compared to normal weight

concrete, as it does not contain coarse aggregate phase. The properties depend mainly on

its microstructure (void-paste system) and composition, which are affected by the type of

binder used, and curing. Aerated concrete is normally envisaged as a good insulation

material; however it can also be utilized for structural usage. Typical mixes are given in

Table 2.3 (Cox and van Dijk, 2002). Typical properties of foamed concrete are shown in

Table 2.4. (Aldridge, 2002)

Further relevant information on the mechanical properties of foamed concrete and

factors affecting its thermal conductivity will be discussed in this section.

Table 2.3: Typical foamed concrete mixes

28

Table 2.4: Typical properties of foamed concrete

2.5.1 Mechanical Properties

2.5.1.1 Compressive strength

Aerated concrete has a lower strength as compared to normal weight concrete due

to the higher amount of voids in the former. The specimen size and shape, method of

pore-formation, direction of loading, age, water content, characteristics of ingredients

used and method of curing are reported to influence the strength of aerated concrete.

Compressive strength can be significantly influenced by the pore structure of the air

pores and the mechanical condition of pore shells. When density is reduced, larger

macropores are formed which leads to a significant drop in compressive strength.

(Narayanan and Ramamurthy, 2000)

Wee et al. (2005) studied on the air void system of foamed concrete and its effect

on mechanical properties. Wee et al. reported that compressive strength of concrete is

controlled by water to cement ratio, because it determines the porosity of cement paste

(Neville, 1997). Compressive strength is also controlled by the size of the existing voids

in the cement paste (Odler and Robler, 1985; Kearsley and Visagie, 1999; Toshio et al.,

29

1991). The result stated in the paper is only applicable for foamed concrete with w/c ratio

of 0.3.

The relationship between strength or modulus to density ratios and spacing factor

as presented in Figure 2.6c indicates that spacing factor also controls the mechanical

properties of foamed concrete produced with the same w/c ratio. When the spacing factor

increases up to 0.04 mm, the corresponding increase in the strength and modulus ratio

was significant. Likewise, as shown in Figure 2.6d, when the spacing factor increases up

to 0.04 mm, the average air void size reduces significantly which thereby contributes to

the significant increase in the strength and modulus ratio. As the spacing factor increases

further from 0.04 to 0.14 mm, the strength and modulus ratio did not increase

significantly. This could be due to the small change in the average air-void size when the

spacing factor increases from 0.04 to 0.14 mm as shown in Figure 2.6c. It is evident that

air void size in combination with the spacing factor significantly governs the mechanical

properties of the foamed concrete. A small air void size in combination with a larger

spacing factor would lead to better mechanical properties and the optimal values of these

factors would result in optimal strength to weight ratio. Figure 2.6d shows the optimal

spacing factor to be 0.04 mm above which, the strength or modulus to density ratios did

not increase significantly. This optimal value was at the transitional air content of 42%

which demarcated the trends of air-void size (Figure 2.6a) and air-void frequency (Figure

2.6b).

Concrete with higher air content tends to result in larger air-voids because of the

proximity of the air-voids, which lead to higher incidence of void coalescing and forming

30

larger air-voids. This observation is more pronounced in concrete with air content of

more than 42%. It is apparent that when the paste content is less than 58%, the average

air-void size increases because there is less cement paste to prevent the air-voids from

coalescing.

Powers (1967) and Mielenz et al. (1958) reported that the coalescence of air-voids

in air entrained concrete may be due to the difference of surface tensions in different size

of bubbles creating difference of pressure. If the water surrounding a small bubble

should become saturated with respect to the pressure in the small bubble, it will become

supersaturated with respect to the water surrounding a large bubble and subsequently one

should expect air to diffuse through the water from a smaller to the larger bubble,

diminishing the smaller and enlarging the larger. This diffusion seems to be more

dominant in lower density mixes which contains lower paste content.

According to Hoff’s (1972) and Kearsley and Wainwright (2001) observations,

the strength of cellular concrete varied with porosity which is directly proportional to the

density. The relationship between dry density versus compressive strength and spacing

factor of the foamed concrete are shown in Figure 2.6d. The compressive strength

increasing with increase in density is well aligned with the trend reported for foamed

concrete by many researchers [ACI Committee 523.3 R-75; McCormick, 1967; Tam et

al., 1981; Fujiwara et al., 1995; Kearsley, 1999; Kearsley and Wainwright, 2001). Figure

2.6e also shows that the spacing factor increases correspondingly as the compressive

strength with an increase in the density. It can also be seen that the rate at which the

compressive strength and the spacing factor increase with density are congruous

31

suggesting that the spacing factor governs the compressive strength for the foamed

concrete made with same w/c ratio. There is a general trend of compressive strength

increasing proportionally with the increasing wet densities for a given w/c ratio, strength

results also depend very much on the test conditions such as the sizes and shapes of

specimens, the moisture content, curing methods and the direction of loading. (Wee, 1997)

Compressive strength of aerated concrete varies inversely with moisture content.

On drying to equilibrium with normal atmosphere, there is an increase in strength and an

even larger increase on complete drying out. Thus, it was recommended that strength

tests be done on materials that have attained equilibrium with the surroundings.

Compressive strength to density ratio of foamed concrete was found to be increased by

using fly ash as a partial/complete replacement for the filler. (Durack and Weiqing, 1998;

Sengupta, 1992; De Rose and Morris, 1999; Giannakou, 2002 )

There are several strength prediction relations that have been proposed to assess

the compressive strength of aerated concrete. For instance, in the case of foamed

concrete, the Feret’s equation (Tam et. al, 1987) relating the strength (S), water–cement

(w/c) and air–cement (a/c) ratios, is given as

S=K[1/(1+(w/c)+(a/c))]n (2.5)

where, K and n are empirical constants. This equation provides a good prediction of

strength. Results showed that the strength of foamed concrete depends on both the water-

cement ratio and the air-cement ratio. The relationship is improved when another term

32

which is the degree of hydration is introduced through Power’s gel/ space ratio concept

into a modified form of Feret’s formula.

Figure 2.6: a) Relationship between air content and air-void size; b) Relationship between air

content and frequency; c) Relationship between average air-void size and spacing factor; d)

Variation of compressive strength or modulus of elasticity density ratio with spacing factor; e)

Relationship between dry density versus compressive strength and spacing factor

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

Ave

rag

e a

ir-v

oid

siz

e (

mm

)

0 10 20 30 40 50 60 70 80

Air content (%)

0 10 20 30 40 50 60 70 80

Air content (%)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Air-v

oid

fre

que

ncy

(1/m

m)

AVS - 0.230

AVS - average air-void size

0.1790.157

0.120

0.112

0.101

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Spacing factor (mm)

0

5

10

15

20

25

30

35

Str

en

gth

or

mo

du

lus t

o d

en

sity

ra

tio Strength - spacing factor

Modulus - spacing factor

a

e

c d

b

0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250

Average air-void size (mm)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Sp

acin

g f

acto

r (m

m)

AC - 11%

26%

41%56%

62%71%

( - 0.6)(0.8)(1.0)

(1.3)

(1.6)

(1.9)AC - air content

( - density)

200 400 600 800 1000 1200 1400 1600 1800 2000

Dry density (kg/m )

0

10

20

30

40

50

60

70

Co

mp

ressiv

e s

tre

ng

th (

MP

a)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Spa

cin

g fa

cto

r (m

m)

3

Strength - density

Spacing factor - density

33

2.5.1.1 Splitting tensile and Flexural strength

Lim (1984) reported that splitting tensile strength for foamed concrete to be at 7

to 12 % of compressive strength and flexural strength lies in the range of 15 to 33 % of

compressive strength. Preliminary Studies were carried out by Wee (1997) on the

properties of foamed concrete with w/c of 0.5, 0.6 and 0.65 and densities varying from

1300, 1600 and 1900 kg/m3 was done. Result shows that flexural and splitting tensile

strength ranged from 0.8 and 2.5 N/mm2 and 0.3-1.2 N/mm2 on the 28th day respectively.

These values were low compared to normal weight concrete. Thus, reinforcing materials

would be needed to increase its flexural capacity in order to ensure easy handling of

foamed concrete on site, especially for thin and long slabs. Splitting tensile strength

according to Wee (1997) was found to be 10 to 13 % of compressive strength and

flexural tensile strength was found to be from 20 to 35 % of compressive strength. The

values reported by Wee (1997) were slightly higher than Lim (1984).

2.5.1.2 Drying Shrinkage

Foamed concrete possesses high drying shrinkage due to the absence of aggregates.

Drying shrinkage increases for decreasing density of foamed concrete. Some of the

typical values of drying shrinkage of foamed concrete can be found in Table 2.3.

Autoclaved aerated concrete has a much lower shrinkage compared to air-cured aerated

concrete. The average drying shrinkage of typical autoclaved aerated concrete is

approximately 0.02 per cent. Shrinkage changes in response to changes in moisture

conditions develop tensile stresses and ultimately lead to cracking in the restrained

product. Rudolph and Valore (1954) commented that the linear drying shrinkage of

34

foamed concrete ranges from 0.3 to 0.6 % as compared to a range of 0.01 to 0.1 % for

AAC.

2.5.2 Thermal conductivity

Foamed concrete has a lower thermal conductivity than conventional concrete.

This is due to the inclusion of air bubbles which have very low thermal conductivity. The

thermal conductivity of foamed concrete is generally accepted as being dependent

primarily on the density. Other factors which affect the thermal conductivity include

moisture content, temperature level, raw materials, pore structure, etc. and will be

discussed further in the later sections. The test method and the apparatus used may have

an influence on the thermal conductivity values. Thus, comparisons between test results

obtained with different methods and equipment should only be made if their influence is

known.

2.5.2.1 Effect of density

The effect of density on thermal performance of aerated concrete was studied

extensively by De Rose and Morris (1999), Loudon (1983), Weigler and Karl (1979) and

Shrivastava (1977). It was found that the higher the density, higher the thermal

conductivity. This is because a denser solid material would propagate heat by conduction

faster as the particles of the solid are more closely packed. Thus at a higher rate of atomic

vibration, collision of the particles (or the transfer of heat energy) takes place faster.

Narayanan and Ramamurthy (2000) commented that thermal conductivity of

aerated concrete is largely a function of density. It does not matter whether the product is

moist cured or autoclaved as far as thermal conductivity is concerned. Rudolph and

35

Valore (1954) also reported similarly that thermal conductivity data from various sources

are in good agreement and are a function of density from 10 to 70 lb per cu ft (160 to

1121 kg/m3), regardless of composition, cell-forming process, or curing and possibly

different types of specimens and test conditions as shown in Figure 2.7.

Figure 2.7: Relationship of thermal conductivity to density for moist-cured and autoclaved cellular

concretes of various compositions and made by various processes. (Data from 17 different sources

and NBS test)

Weigler and Karl (1980) investigated on the properties of structural lightweight

aggregate concrete with reduced density by adding foamed into the concrete mix –

Lighweight aggregate foamed concrete (LAF-concrete). Their intention was to reduce the

density of concrete for load bearing and stiffening structural members and to improve the

thermal insulation properties and thus extend the scope of application of structural

lightweight concrete.

Figure 2.8 shows the thermal conductivity values of LAF-concrete together with

lightweight concretes including foamed concrete. For 20 % of entrained air, the

concrete’s density is reduced by 20 % and the thermal conductivity by 25 %. Compared

36

to other kinds of lightweight concrete of the same compressive strength, LAF-concrete

has a lower thermal conductivity. For a dry density between 700 to 1000 kg/m3, the

highest strength of 5 to 14 MPa were obtained using lightweight aggregates (expanded

clay and expanded shale) with a particle density between 0.6 and 0.9 kg/m3.

Figure 2.8: Thermal conductivity of lightweight-aggregate foamed concrete and various other types

of lightweight concrete at a moisture content of 5 % by volume as a function of the dry density of the

concrete.

2.5.2.2 Effect of moisture

Since moisture will always be present in concretes exposed to the environment

and that moisture would increase the thermal conductivity of concretes, normally a

moisture correction factor is employed to adjust the thermal conductivity obtained from a

particular oven dry density. There are two aspects of moisture correction. Firstly, the

practical moisture content has to be decided and secondly, measured thermal

conductivities have to be multiplied by an appropriate moisture factor to obtain the

thermal conductivity of the practical moisture content.

37

There are a number of moisture correction curve available. The one used in UK is

commonly known as the ‘Jakob’ moisture curve, since it appeared in Jakob’s 1949 book

on Heat transfer. Figure 2.9 compares results on AAC by Jespersen with the Jakob

moisture curve. It was shown that agreement with the Jakob curve is fairly good at

moisture contents above 2 % by volume, below 2 %, agreement is poor. The moisture

correction curve in France is the same as in UK. For the German moisture correction as

described in DIN 52612, it represents a 6 % change in thermal conductivity for each 1 %

change in moisture content by volume. This slope is lesser than that of the Jakob moisture

curve which is about 11 % change in thermal conductivity for 1 % moisture content by

volume in the range of 1 to 5 %. In USA, a different moisture correction curve which is

based on moisture content by weight rather than by volume. Valore, 1980 proposed a

change of 4 to 6 % in thermal conductivity for 1 % change in moisture content by weight.

Figure 2.9: a) The ‘Jakob’ moisture correction; b) Jespersen’s data on thermal conductivity versus

moisture content of AAC at different densities

a b

38

Loudon (1983) did experiments on concrete material of different densities to

investigate whether the moisture correction should be related to moisture content by

volume or by weight. Experimental details are described in Loudon (1983). Loudon

found that Jakob moisture factor over-calculated the thermal conductivity values.

Experimentally-determined moisture factors for AAC correlate better with moisture

content by weight than moisture content by volume. For AAC, a moisture correction of 4

% increase in k value for 1 % increase in moisture content in AAC by weight seemed

appropriate (Figure 2.10).

Lippe (1992) and Laurent and Guerre-Chaley (1995) also found an increasing

trend of k value of AAC as moisture content increases. Kudriashev (1949) who studied

on thermal conductivity values for lime-silica autoclaved cellular concretes (density from

497 to 993 kg/m3) containing different percentages of free moisture and reported a 4 %

increase in thermal conductivity for each percent increase in density due to free moisture.

Whereas, Graf (1949) reported a slightly higher value of 6 % increase in thermal

conductivity value for various cellular concretes for each percent increase in density due

to free moisture. The rationale behind is that some of the air gaps in the solid matrix is

replaced with water and since water has a conductivity of about 25 times that of air, the

thermal conductivity of the concrete increases. Additional heat can also be transferred

across air spaces by an evaporation-condensation process.

39

Figure 2.10: Moisture factor λ / λdry vs moisture content by weight (Loudon, 1983)

2.5.2.3 Effect of mineral Admixture

The addition of fly ash has the effect of decreasing thermal conductivity of

foamed concrete. A 30 % replacement of cement by fly ash was found to decrease k by

12 to 38 % as found by Giannakou and Jones (2002). This was attributed to the lower

density and cenospheric particle morphology of fly ash, which increases the heat flow

path.

De Rose and Morris (1999) studied on the effect of lime and fly ash on the

thermal conductivity of foamed concrete with fixed w/c ratio and fixed density. They

reported that lime and fly ash both had an influence on thermal conductivity. Adding lime

as an additive to the mix increased the k –value. A 10 % addition of fly ash which was

used as a replacement for the cement reduces k –value, following the trend of the results

by Giannakou and Jones (2002) as shown in Figure 2.11.

40

Figure 2.11: Thermal conductivity at fixed w/c ratio and fixed density

2.5.2.4 Effect of pore structure

The pore structure of a material often plays a dominant role in controlling their

useful physical and functional properties including thermal conductivity, and thus is of

importance in the evaluation of performance of the material. Thus, it is important to know

the relations between the pore properties for example the scale, the extent, connectivity of

the pore network in porous materials and other physical and functional properties of the

material. However, the effect of pore structure, size of pores, the shape, the arrangement

of combination of different pore sizes on thermal conductivity of foamed concrete seems

to be lacking.

There are many studies on the factors affecting the effective thermal conductivity

of two-component materials. For example, Meredith and Tobias (1962) who investigated

on analytical models to predict thermal conductivity of a two-component material,

commented that neither the size distribution of the discrete particles in a two-component

material nor the manner in which they are deployed are of consequence if the

concentration of the discrete phase is sufficiently dilute. However, these factors must be

considered if their concentration is increased. This suggests that the effects of discrete

41

particles properties like size distribution and arrangement on effective thermal

conductivity of the two-component material are dependent upon its volume fraction.

Zhang and Liang (1995) who also studied the effective thermal conductivity of

mixed solids materials using numerical analysis found that the effective thermal

conductivity of 2 materials mixed together (one being the discrete phase and the other

being the continuous phase) is dependent upon the volume fraction of the discrete phase,

rather than its size or dimension.

2.5.2.5 Effect of temperature

When the temperature at the hot and cold side of the heat flux meter is increased,

the heat energy being transferred to the particles inside the foamed concrete is increased,

causing more vigorous vibration of the particles and also increases the rate of collision

between particles. Thus, the rate at which heat is conducted through conduction is

increased, resulting in a higher thermal conductivity in specimens which are tested at

higher temperature. The effect of increasing temperature of aerated concrete is to increase

thermal conductivity as observed by Marmoret (1999) and Laurent and Guerre-Chaley

(1995).

2.5.2.6 Effect of age

There is limited literature on the effect of age on the thermal conductivity of

foamed concrete. However, Khan (2002) and Kook et al. (2003) studied the effect of age

on thermal conductivity of a series of specimens (normal weight concrete, cement paste

with gravel, cement mortar and cement paste) which was moist-cured at 20 oC and tested

42

at 3, 7, 14 and 28 days. Their results showed that age hardly affects thermal conductivity

values except at very early age when the cement paste is still hydrating.

2.6 Analytical models to predict thermal conductivity of foamed concrete

In order to ‘design’ an ideal foamed concrete with a suitable thermal conductivity

for its intended purpose, it is essential to know the relation of the effective thermal

conductivity. A great number of analytical models can be used to predict the effective

thermal conductivity of a heterogeneous material exist in the literature. Most theoretical

models are based on certain hypotheses to attempt to depict the physical reality using

simple models with varying accuracy.

Several important factors affect the thermal conductivity of a material. These

include the thermal conductivity of its constituents (discrete and continuous phase), size

and shape, volume fraction, dispersion (degree of mixing) of the discrete phase. Since air

bubbles in foamed concrete are typically spherical and thus isotropic, so their orientation

is not significant. The geometrical structure of the system is important. The following

section will cover the available mathematical formulas in the literature which are used to

correlate the effective thermal conductivity of a mixture with the thermal conductivities

and volume fractions of the individual components. They mainly differ in the

assumptions of their geometrical structures. These available formulas together with their

assumptions and geometrical structures will be compared and their critiques discussed

further here.

43

2.6.1 Series slab and parallel tube model

The most basis model for purposes of analysis of thermal conductivity is that in

which the two components in a mixture are arrayed in alternative parallel layers as shown

in Figure 2.12. If the heat flow is parallel to the layers, the effective thermal conductivity

is given by

(2.6)

where f1 and f2 are the volume fractions of the components having thermal conductivities

λ1 and λ2. If the heat flow is perpendicular to the component layers, the expression of

effective thermal conductivity is given by

(2.7)

These two expressions represent the extreme limits of the true effective thermal

conductivity of a two-component mixture. These limits are shown in Figure 2.13 for the

case of λ1 = 10λ2. Although both of them predict thermal conductivity values

intermediate between the conductivities of the individual components, the conductivity

obtained is very different for the two cases. Thus these limits are of relatively little use

except for laminated materials or unidirectional composite with continuous fibers and are

not suitable for the prediction of thermal conductivity for foamed concrete.

However, from these two simplest models, it is possible to obtain tighter limits for

the thermal conductivity of a two-component mixture by calculating the apparent

effective conductivity.

44

Figure 2.12: Two-phase material with phases distributed as parallel slabs.

Figure 2.13: Effective thermal conductivity of a laminated material with heat flow parallel or

perpendicular to laminations.

Several investigators have represented a disperse second component by a different

geometrical structure, in a cubic array of cubes as shown in Figure 2.14 instead of the

slabs and tubes in Figure 2.12.

Series slabs

As shown in Figure 2.14, the mixture is divided into slabs (A) containing no disperse

second component and into slabs (B) containing both continuous and disperse

45

components. The effective conductivity of the B-slabs is computed, by assuming the

disperse and continuous components act as conductors in parallel. The effective

conductivity of the mixture is computed by taking the A-slabs and the B-slabs in series.

Figure 2.14: Cross-section of the model in which a disperse second phase is considered to be a cubic

array of cubes.

The expression to predict the effective thermal conductivity, λ of a two-component

mixture is given by:

(2.4)

whereby Pa is the fraction of the total area which contains the disperse component of

conductivity λd and (1- Pa) is the fraction of the area which contains the continuous

component of conductivity λc. Pl is the fraction of the total length containing the disperse

46

component. The geometrical assumption of the series slab and parallel tube can be

applied to the dispersions of, for example, fibers or platelets oriented parallel or

perpendicular to the flow of heat.

For a disperse component in the form of cubes or in which cubes may be used to

approximate an isometric discrete component, Equations 2.6 and 2.7 may be recast in

terms of the volumetric fraction of disperse component, which is designated as f. For the

model used, it is easily seen that Pa = f 1/3 and P l = f 2/3; with these substitutions, the forms

usually seen are obtained:

Series Slabs:

(2.8)

Parallel Tubes:

(2.9)

These expressions may look complicated, but the model reduces to the two simple

electrical networks as shown in Figure 2.14. The series-slabs model, always

overestimates the effective thermal conductivity since the continuous component has an

infinite thermal conductivity normal to the principal flow of heat. On the other hand, the

parallel-tubes model effectively assumes that the continuous component has zero thermal

conductivity normal to the principal flow of heat, thus this approach always

underestimates the effective thermal conductivity. Thus, these two methods may not be

47

able to predict the effective thermal conductivity of foamed concrete accurately based on

its models assumed.

2.6.2 Geometric mean model

When a series distribution of the phases and their resistance to heat flow is

assumed, a lower bound effective thermal conductivity of a heterogenous mixture is

obtained. On the other hand, when a parallel distribution is assumed, an upper bound is

obtained. The weighted geometric mean of the constituents’ thermal conductivity

sgsgeff

εελλλ = (2.10)

has been proposed by Woodside and Messmer (1961) as a suitable intermediate between

these two extrema to find a better prediction of the thermal conductivity value. λeff

represents the effective thermal conductivity of the two-component mixture, λg and λs

represent the thermal conductivity and εg and εs represent the volume fractions of the

discrete and continuous phase respectively.

2.6.3 Assad Model

Assad proposes an empirical relationship that is very similar to the geometric

mean equation: the ‘Assad’ equation is

(2.11)

where m = cε and c 1. When c= 1, this equation is identical to the geometric mean

equation. By choice of the average value of m = 0.868ε for clayey aerated concrete (CAC)

and clayey wood concrete (CWC) and m = 0.810ε for autoclaved aerated concrete (AAC),

this model was used to predict the mean effective thermal conductivity within an error of

48

less than ±5 % for CAC and CWC against a higher error of ±20 % for AAC. This model

allows some flexibility to choose an appropriate value for the parameter, m to model the

effective thermal conductivity of a two-phase material. (Goual et al., 1999)

2.6.4 Maxwell model

Maxwell derived an expression for the conductivity of a two-component

dispersion of spherical particles (instead of cubic discrete phase) of conductivity, λd

imbedded in a medium of conductivity λc. λ is the effective thermal conductivity of the

two-component material. Maxwell’s relation can be written in the form:

(2.12)

This expression is rigorously valid for dilute dispersions where the average distance

between dispersed particles is much larger than the particle size and should be accurate

for volume fraction of discrete phase, f ≤ 0.1. Thus, this expression should be suitable for

foamed concrete with volume fraction of the discrete air particles smaller or equal to 0.1.

However, for foamed concrete, the volume fraction of air particles can be significantly

higher than 0.1, thus this expression may not be accurate for concrete with higher foam

content.

2.6.5 Meredith and Tobias Model

For higher concentration of dispersed components, with volume fraction higher

than 0.1, Lord Rayleigh treated the case of uniform spheres arrayed in a cubic lattice

49

distribution. Meredith and Tobias (1962) extended Rayleigh’s derivation by an additional

term and obtained:

(2.13)

Equation 2.13 should be more accurate than Equation 2.12 for values of f from 0.1 up to

π/6 = 0.524, which is the maximum possible value for a cubic array of spheres. For

dispersions which are sufficiently dilute for Equation 2.12 to be valid, neither the size

distribution of the disperse particles nor the manner in which they are deployed are of

consequence. However, these factors must be considered if the concentration of the

dispersed component is increased.

2.6.6 The self-consistent model

Figure 2.15 shows the geometrical model for generalized self consistent scheme

assumed by Kerner (1956). The geometric model consists of a typical inclusion of

spherical shape being imbedded in a concentric spherical matrix shell. The composite

sphere thus obtained was then embedded in a homogeneous and isotropic medium of the

effective thermal conductivity of the composite model. This model is quite different

from the rest of the other models which are either a cubic array of cubes or of spheres.

Concentric model does not restrict the volume fraction of spherical discrete phase

like in the case of Meredith and Tobias model which only allow a maximum volume

fraction of greater than π/6 = 0.524 (which is the maximum possible value for a cubic

array of spheres) to be modeled. Thus, this could be useful to predict the effective

50

thermal conductivity of foamed concrete with very high air content. Moreover, the

spherical geometry assumed by the self-consistent model is consistent with the actual

shape of the air inclusion into foamed concrete. Equation 2.14 shows the formula of the

effective thermal conductivity with respect to the porosity and the thermal conductivity of

the continuous solid medium which is the cement matrix. (Hashin, 1968)

Figure 2.15: Geometrical Model for Generalized Self Consistent Scheme

(2.14)

where is the effective thermal conductivity of the composite material. A typical

spherical particle of arbitrary radius a, consists of material of conductivity k2. The particle

is embedding a concentric matrix shell of unspecified radius ρ, the matrix conductivity

being k1.

Boutin (1996) used the self-consistent method to determine the thermal

conductivity of autoclaved aerated concrete (AAC). He showed that this method is

efficient for autoclaved aerated concrete as its microstructure contains very different-

51

sized pores. His studies showed that the predicted thermal conductivity obtained using

the self-consistent method was reported to be in excellent agreement with the

experimental data.

2.7 Polymer-Modified concrete (PMC)

2.7.1 Background knowledge

Polymer-modified concrete (PMC) is defined as Portland cement and aggregate

combined at the time of mixing with organic polymers that are dispersed or redispersed in

water. This dispersion is called latex, and the organic polymer is a substance composed of

thousands of simple molecules combined into large molecules. These simple molecules

are known as monomers and they go through a reaction called polymerization whereby

they are combined.

A polymer generally contains about 50 % polymer by weight of spherical and

very small (0.01 to 1 microm in diameter) polymer particles held in suspension in water

by surface-active agents. The presence of surface-active particles agents in the latex tends

to incorporate large amounts of entrained air in concrete; therefore, air entraining agents

are usually added to commercial polymer. The spherical polymer molecules and the

entrained air associated with the polymer usually provide excellent workability. Typically,

water/cement ratios are in the range 0.40 to 0.45, and cement contents are of the order

390 to 420 kg/m3. (Kumar M. P. and P.J.M. Monteiro, 1997)

Two processes occur in latex modification of Portland cement mortar and

concrete, namely cement hydration and latex coalescence. Cement hydration generally

occurs first and as the cement particles hydrate and the mixture sets and hardens, the latex

52

particles become concentrated in the void spaces. As water is continuously removed by

cement hydration, evaporation, or both, the latex particles coalesce into a polymer which

is interwoven in the hydrated cement giving a comatrix that coats the aggregate particles

and lines the interstitial voids.

The hardened cement paste is predominantly made up of an agglomerated

structure of calcium silicates, aluminates, and hydroxide bound together by relatively

weak Van der Waal’s forces. The latex being incorporated into the cement paste helps to

reduce rate and extent of moisture movement by blocking the passages whereby

microcracks are formed caused by stresses during drying shrinkage. The latex polymer

film also bridges the microcracks formed and prevents propagation. Thus, tensile strength

and fracture toughness of the polymer-modified concrete is increased. Moreover, the

ingress of fluids like water or soluble salts is hindered due to the passage way of

microcracks being blocked. This naturally increases both the chemical and frost

resistance of concrete.

The optimum degree of polymer modification is usually obtained at about 10 to

20 percent dry latex solids by weight of cement of the mixture. Too low a percent of latex

will not have a significant contribution to the overall properties and not able to harness

the water-reducing effects of the latex, and thus, require more water in the mix for

equivalent workability. This effect of less polymer and more water will degrade the

hardened properties of the mortar and concrete. If too much latex is used, it is not

economical and it can cause excessive air entrainment, and can cause the mixture to act

as a polymer filled with aggregates and cement. (ACI Committee 548)

53

Latexes which are commonly used with hydraulic cements are synthetic

elastomeric polymers like styrene-butadiene rubber (SBR), polychloroprene and

Thermoplastic polymers like polyacrylic ester, styrene-acrylic, vinyl acetate copolymers

and also polyvinyl acetate. There are some improvements in the properties of concrete

being modified by polymer. The final product will have improved bond strength to

concrete substrates, increased flexibility and impact resistance, improved resistance to

ingress of water and dissolved salt and also improved resistance to frost action.

Polymer composition has a significant effect on the properties of the cured

concrete. The effect of various volume fraction of polymer in cement paste and also

formed concrete on thermal conductivity of the materials and the strength and durability

properties will be investigated. Thus, by adding polymer into foamed concrete,

composites which are lightweight, high strength, insulating and weather-resistant can be

produced. Some field applications may include external insulation on concrete block or

cast-in-place roof insulation.

Acrylic latexes have been used for modifying hydraulic cement mixtures for more

than 30 years to improve properties like adhesion, abrasion adhesion, impact strength,

flexural strength, and resistance to permeability. In order to obtain maximum physical

properties, acrylic latex-modified cement mortars should be cured in air. This is because

when latex is allowed to coalesce and form a film through the removal of water, the full

potential of increasing the properties of the mortar is achieved.

2.7.2 Properties of PMC

A review of the literature shows that there has already been much work done to

investigate the properties of polymer-modified mortars and normal weight concrete

54

(Ohama, 1987, Ray et. al, 1994, Afridi et. al, 1994, Mindress et. al, 2003). These studies

show that polymers are added to concrete to improve its workability, drying shrinkage,

strength and durability. There are also reports of properties of polymer-modified

lightweight aggregate concrete (Fontana et al. 1987). However, there are only a few

studies about the use of polymer on lightweight aggregate concrete (LWACs). Reports of

mechanical and thermal properties of foamed concrete with polymer corporated are

almost non-existent. Thus, since information on how polymer will affect the total air

content in foamed concrete which in turn affects the properties of polymer-modified

foamed concrete is lacking, more research in this area is needed.

The compressive strength of LMC is often higher than that of an unmodified

concrete under dry curing conditions because strength continues to develop beyond 28

days. This is attributed not only to the development of the polymer film, but also to the

fact that the polymer inhibits loss of water from latex-modified concrete, LMC. Hence,

the cement can hydrate more completely under these conditions. However, relative

improvements in strength are greater under flexural and tensile loading seen from Table

2.5. Also, LMC has a higher micro strain at failure in tensile loading as shown in Figure

2.20. The greater linearity of the stress-strain curve indicates that more microcracking

occurs prior to failure. It is believed that the polymer films inhibit the propagation of

microcracks because of their high tensile strength. Furthermore, the ability of the film to

form fibrils on rupture provides stress transfer behind the crack tip, thereby reducing

stress concentrations and keeping cracks closed.

2.7.2.1 Mechanical Properties

55

Table 2.5: Mechanical Properties of Latex-modified concrete

Figure 2.16: Tensile stress vs microstrains of polymer-modified concrete with different percentages

of polymer

56

The increased durability of LMC relative to plain concrete can be attributed to

three factors. Firstly, the polymer film lining capillary pore surfaces impedes water

absorption and permeability and prevents the entry of aggressive agents. Secondly, the

improved resistance to tensile cracking reduces the formation of a network of

microcracks that can assist in water transport. When cracks do form, filaments of

polymer, which bridge the cracks, keep them closed. Thirdly, the lower w/c ratio

provides generally improved durability. The air entraining properties of the latex will

naturally provide frost resistance. (Mindress et. al, 2003)

Rossignolo and Agnesini (2002) also studied the mechanical properties of

styrene-butadiene rubber (SBR) modified lightweight aggregate concrete (LWACs). The

main objective of their study is to provide some basic information on the properties of

high performance LWACs using Brazilian LWAs, natural sand, superplasticizer, silica

fume and SBR latex. Properties in the fresh state, compressive strength, splitting tensile

strength, flexural strength, and water absorption of the LWACs were tested. The

inclusion of SBR latex in LWACs decreases the water-(cement and ground granulated

blast furnace slag) [N/(C+S)] ratio.

The compressive strength of SBR-modified LWACs is slightly lower than that of

unmodified LWACs. A decrease in the 7-day compressive strength is, on average, 3.0 %

and 4.4 % at a polymer-cement ratio (P/C, as solid polymer content by mass of cement)

of 5 % and 10 % respectively. This is attributed to an increase in the air content of SBR-

modified LWACs caused by air entrainment.

57

The tensile strength increase is, on average 10 % at a P/C of 5 % and 18 % at a

P/C of 10 %. The flexural strength increase is, on average 16 % at P/C at 5 % and 26 % at

a P/C of 10 %. Such superior properties are attributed mainly to an overall improvement

in cement hydrate-aggregate bond because of a decrease in W/(C+S) and the high tensile

strength of SBR films present in SBR-modified LWACs.

ACI Committee Report 548 reported the strength properties of acrylic-modified

concrete. It was reported that the flexural and tensile strength properties of acrylic-

modified mortar of air-dried specimens are significantly higher than wet-cured specimens

(1 day at 95 % relative humidity plus 6 days immersion in water). Figure 2.17 shows the

flexural modulus (ASTM D 790) of latex-modified mortars as a function of the polymer-

cement ratio by mass. Modification of cement mixtures with acrylic, results in increased

flexibility of the hardened mortar and concrete.

Figure 2.17: Flexural modulus versus acrylic polymer-cement ratio of Portland cement mortar

58

2.7.2.2 Thermal conductivity

There is a major concern of whether concrete, especially lightweight ones have

the ability to maintain its low thermal conductivity in the environment it is used. (Fontana

et al. 1987) Aerated concrete or lightweight concrete is susceptible to water absorption

due to its high porosity. The increase in moisture content within the material has an effect

of increasing the thermal conductivity quite significantly.

There are some recent papers by Ohama (1998) and Fowler (1999) which

reviewed the recent developments and uses of polymer-modified concrete. Polymer was

used to reduce the amount of water absorption in lightweight aggregate concrete so that

their thermal conductivity will not increase due to the intrusion of rain water during its

application. Fontana et al. (1987) have developed lightweight polymer concrete

composites with excellent insulating properties. Lightweight aggregates used are

expanded perlites, glass nodules or hollow alumina silicate microspheres bound together

with unsaturated polyester or epoxy resins.

Expanded perlites are still being used in thermal insulation applications. For

example in India, Keltech Energies Ltd., a leading manufacturer of expanded perlite has

been involved in the manufacture & installation of large perlite concrete blocks for LNG

tanks. Perlite is a natural lightweight siliceous aggregate which is capable of expanding

up to 25 times its original volume upon heating to around 860oC. The large amount of air

voids that are produced in the expansion process is responsible for expanded perlite

excellent insulation property. Glass nodules are also being used currently as loose fill

insulation.

59

These insulating polymer concrete (IPC) with densities of 480 to 960 kg/m3 has

thermal conductivity values ranging from 0.1557 to 0.3287 W/m.K. They have excellent

durability to freezing and thawing due to their low water absorption rate and low

permeability. The compressive strength of the IPC allows it to be used for structural

purposes.

2.7.2.3 Durability

Studies by Rossignolo and Agnesini (2002) show a significant decrease in water

absorption with the inclusion of SBR-latex in unmodified LWACs. The water absorption

of SBR-modified LWACs is, on the average 3.7 % at a P/C of 5 % and 2.3 % at a P/C of

10 %, compared with that of 6.5 % on average for unmodified LWACs.

The decrease in water absorption of SBR-modified LWACs is due to a reduction

in permeability, caused by a reduction in W/(C+S). Such W/(C+S) reduction affects the

gel-space ratio and causes a reduction in the capillary porosity of the system. Polymer

films present in SBR-modified LWAC surfaces also contribute to a reduction in the water

absorption.

ACI Committee Report 548 also reported the durability property of acrylic-

modified concrete. Figure 2.18 shows the results of chloride ion penetration of

unmodified and acrylic latex-modified Portland cement concretes. Adding acrylic to

mortars and concrete can help to reduce permeability of the amount of chloride ion.

60

Figure 2.18: Chloride ion penetration of unmodified and acrylic latex-modified Portland cement

concretes

Studies done by Lim (2005) on water absorption of polymer-modified foamed

concrete is slightly reduced as compared to unmodified ones as shown in Figure 2.19.

The specimens’ densities are the range of 1000 kg/m3, with 50 % foamed content but

polymer content varying from 5- 15 % of cementitious material used. The reduction is

about 4 % for an increase in 5 % polymer content. A decrease in the water absorption of

polymer-modified foamed concrete is attributed mainly to a reduction in permeability,

caused by a reduction in w/c ratio. Such w/c reduction ultimately affects the gel-space

ratio and causes a reduction in the capillary porosity of the system. The water-resistant

performance of foamed concrete modified by acrylic is not as beneficial as expected.

Other additives can be added to foamed concrete reduce the water absorption further.

61

Graph of water absorption vs polymer content

37.7

36.9

34.9

33.5

30

31

32

33

34

35

36

37

38

39

40

0 5 10 15 20

Polymer content (% of cementitious material)

Wa

ter

ab

so

rpti

on

(k

g/m

^3

)

50 % foamedconcrete withpolymer

Figure 2.19: Graph of water absorption of polymer-modified foamed concrete vs polymer content

2.8 Flat roofing systems

A new ferrocement roofing system for HDB blocks has been used to replace the

old practice which consisted of a roofing system consisting of grade 40 reinforced

concrete slab laid at a gradient of 1:50, a layer of waterproof membrane and an elevated

secondary roofing slab. A layer of trapped air between the main and secondary roofs

prevents heat transmission to the dwellings below.

The precast ferrocement roofing slab is made of high grade mortar reinforced with

layers of galvanised fine wire meshes. It is 600 mm x 900 mm and 20 mm thick. It has

good thermal and shrinkage cracking resistance and is also impervious to water

penetration. This material is a thinner and lighter building cladding element with a greater

strength than normal concrete. It is applied in the form of thin secondary roof slabs which

serve to insulate the main roof from intense heat and to drain away rain water (See Figure

2.20).

62

This new roofing system simplifies the overall roof construction process as they

can be installed easily on site. It helps to reduce tedious work of applying a waterproof

membrane on the main roof slabs and also maintenance costs by eliminating the need for

waterproofing membranes. Ferrocement is used as attractive façade features in many of

HDB’s upgrading projects. Its use has also been extended to cladding of service ducts.

Figure 2.20: a) Stools are placed on the main roof to support the secondary roof; b) Trial installation

of ferrocement secondary roof in Sembawang (Singapore)

Numerical studies were done by Chew (2005) using FLUENT software to provide

information on the effectiveness of using different thickness or air gap to provide thermal

insulation for HDB’s secondary roofing system. Chew’s studies showed that air gap may

not necessarily be an effective thermal insulation material for roofing application despite

its low thermal conductivity value. Thicker air gap would lead to the formation of

convection currents. This would in turn bring about the transfer of heat through the bulk

movement of the air particles.

The onset of the convection currents for thicker air gaps could be seen clearly

from the pictures of the streamlines for different air gap thickness in Figures 2.21-2.24.

However, if the air gap layer is too small, though heat transfer by conduction dominates,

the overall amount of heat transferred which is a function of the thickness will still be too

63

high to provide effective thermal insulation. His results have shown that the optimum

thickness of air gap which minimizes the heat transfer is about 160 mm as shown in

Figure 2.25.

The airspace resistance to heat is dependent on not only conduction, but also

convection and radiation in and across the air space. The influencing factors include: a)

thickness of the airspace, b) flow of air in the air space, c) surface properties (emissivity)

and d) direction of heat flow (horizontally or vertically).

For unventilated cavities, thermal resistance increases with increase in cavity

thickness up to a width of 25 m. For larger gaps, convection becomes important and

thermal resistance does not increase.

Figure 2.21: Streamline picture (air gap thickness 10 cm)

Figure 2.22: Streamline picture (air gap thickness 25 cm)

64

Figure 2.23: Streamline picture (air gap thickness 40 cm)

Figure 2.24: Streamline picture (air gap thickness 100 cm)

Besides air, Chew (2005) also analyzed other insulation materials with FLUENT

to find out the heat flux transferred by each material. It was reported that LECA 500

loose fill and foamed concrete with 75 % foam will give the best thermal insulation. For

an insulation thickness of about 25 cm, LECA 500 lightweight concrete can be twice as

effective as air in providing thermal insulation.

Foamed concrete is several times better than air or normal weight concrete in

terms of thermal insulation performance. However, it is important to note that though

foamed concrete with high foam content exhibit excellent thermal insulation property, it

has very low structural strength which makes it only suitable for non-structural

application. For structural usage, the amount of foam in foamed concrete has to be lower.

In Singapore, it is stated that all structural concrete has to be at least grade 30 in CP 65.

65

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30

Thickness of insulation (cm)

He

at F

lux (

W/m

2)

Air (Experimental)

Air (Simulation)

Figure 2.25: Relationship between heat flux and air thickness (using results obtained experimentally

and by simulation using FLUENT)

66

3 Experimental Details

This chapter will focus on giving more information on how the various

experiments were done in the midst of this research project. Information on the

preparation, mix design and designation of the concrete specimens and the properties of

the various constituents of the concrete specimens will be available. The experiments for

this research project are mainly measurement of thermal conductivity, compressive

strength, other mechanical properties of foamed concrete and polymer-modified foamed

concrete and also microscopy study. Thus, details on the thermal conductivity testing

procedures using heat flow meter to investigate the effects of foam content, water-cement

ratio, temperature and polymer content will be described. Experimental procedures like

compressive strength, modulus of elasticity, modulus of rupture, splitting tensile and

microscopy study are also stated in the following sections.

3.1 Materials, casting and curing

Equal portions of Ordinary Portland Cement (OPC) and Ground Granulated Blast

Furnace Slag (GGBFS) were used to form the paste of the foamed concrete. The

chemical composition and physical properties of OPC and GGBFS are given in Table 3.1.

The superplasticiser used for improving workability was Super 20, a ready-to-use

aqueous solution of a modified naphthalene sulfonate and selected highly purified

organic compounds. Super 20 is a low viscosity liquid that contains no chloride and has

been formulated to comply with BS 5075: Part 3: 1985.

67

The polymer used is 100 % acrylic emulsion, which contains 47 % solids by mass.

Its appearance is a milky emulsion and it is non-ionic. Its density at 25oC is 1.06 kg/litre.

Protein-based foaming agent with a specific gravity of 1.1 was used to produce

preformed foam using a foam generator. It cost slightly more than S$3 per litre.

The casting of foamed concrete was done according to ASTM C 796-97. The

ambient temperature during mixing and casting was 27 ± 3o. Immediately after casting

and finishing, the specimens were covered with plastic sheets to avoid direct exposure to

wind and hence minimize evaporation. The covered specimens were kept at the same

temperature until demoulding. After 24 hours, the specimens were demoulded and stored

in the fog room for curing. Concretes were moist-cured in a fog room at 30±2oC and

100% RH for 28 days before using for macrostructure study.

The casting of polymer-modified foamed concrete was done in a similar way as

that of foamed concrete except that acrylic polymer was added to the mixing water of the

mix. OPC and GGBFS were first added to the mixer, followed by mixing water with

acrylic polymer incorporated and lastly, foam and superplasticiser were added in and

mixed well. After casting and finishing, the specimens were also covered with plastic

sheets to avoid rapid hydration during the first 24 hours to avoid surface cracking. The

covered specimens were kept at the same temperature until demoulding. After 24 hours,

the specimens were demoulded.

To obtain maximum physical properties, acrylic latex-modified cement mortars

were cured in air. This procedure is in contrast to unmodified mortar for which optimum

strength properties are achieved by continuous wet-curing. The reason for this difference

is that in order for the latex to beneficially modify the properties of the mixture, it must

68

be allowed to coalesce and form a film. The removal of water is crucial in this film-

forming process. Thus, acrylic latex-modified foamed concrete specimens for this study

were air-cured at room-temperature condition for 28 days before using for macrostructure

study.

Table 3.1: Physical properties and chemical compositions of ordinary Portland cement and ground

granulated blast furnace slag

Composition Specific

gravity

Fineness

(cm2/g),

Blaine

SiO2 Al2O3 Fe2O3 CaO MgO SO3 K2O Na2O

OPC 3.15 3130 20.57 5 3.23 64.3 2.35 2.57 0.7 0.07

GGBS 2.90 4480 32.50 13.80 0.2 42.9 5.8 2 - -

3.2 Mix design and designation

The mix design of the concrete specimens prepared is tabulated in Table 3.2 and

Table 3.3. Mixes are designated according to their types. Five foamed concrete

specimens were represented by Series ‘F’ (F1 to F5), with foam content ranging from 25

% to 70 % and water-cement ratio (w/c) ranging from 0.35 to 0.55. For cement paste,

three specimens of different w/c 0.35, 0.45 and 0.55 were cast, and they are represented

by Series ‘C’ (C1-C3).

Polymer-modified foamed concrete are represented by Series ‘PF’ (PF1-PF6).

Four of them (PF1-PF4) have the same amount of foam content of 50 %, but have

varying contents of polymer, ranging from 5 % to 20 %. P5 and P6, on the other hand,

have the same amount of polymer content of 10 %, but having different foam content of

20 % and 80 % respectively. The series ‘CP’ (CP1-CP4) are cement paste with varying

amount of polymer from 5 % to 20 %.

69

Table 3.2: Mix Design of foamed concrete and cement paste specimens

Mix Designation

Foam content

(%) w/c ratio

Fresh Density (kg/m3)

Cement (kg/m3)

GGBS (kg/m3)

Water (kg/m3)

Foam (kg/m3)

F1 50 0.45 1000 335 335 302 27.6

F2 70 0.45 550 193 193 173 40.6

F3 25 0.45 1440 477 477 429 14.8

F4 50 0.35 1070 385 385 270 27.6

F5 50 0.55 900 297 297 327 27.6

C1 0 0.45 1860 640 640 576 0

C2 0 0.35 1980 734 734 514 0

C3 0 0.55 1760 567 567 624 0

Table 3.3: Mix Design of polymer-modified foamed concrete and cement paste with polymer

specimens

Mix Designation

Foam content

(%) w/c ratio

Fresh Density (kg/m3)

Cement (kg/m3)

GGBS (kg/m3)

Water (kg/m3)

Polymer (kg/m3)

Foam (kg/m3)

PF1 50 0.35 1020 354.4 354.4 230.1 35.4 33.5

PF2 50 0.35 960 342 342 205.2 68.4 33.5

PF3 50 0.35 1000 331 331 182 99.3 33.5

PF4 50 0.35 960 320.5 320.5 160.3 128.2 33.5

PF5 20 0.35 1580 547.5 547.5 328.5 109.5 13.4

PF6 80 0.35 478 137 137 82.2 27.4 53.6

CP1 0 0.35 1940 708.5 708.5 460.5 70.9 0

CP2 0 0.35 1920 684.5 684.5 410.7 136.9 0

CP3 0 0.35 1900 662 662 364.1 198.6 0

CP4 0 0.35 1880 641 641 320.5 256.4 0

3.3 Experimental Procedures

3.3.1 Thermal conductivity

Before the concrete specimens are tested for their thermal conductivity value by

means of the heat flow meter, they are oven dried at a temperature of 105 oC for 24 hours

and cooled for 4-5 hours to let the temperature gradually drops to about room temperature.

Foamed concrete specimens were tested for their thermal conductivity values at age 7

days and 28 days, whereas polymer-modified foamed concrete specimens were tested

70

only at age of 28 days. A picture of the test specimens (300 x 300 x 50 mm) for

measuring thermal conductivity is shown in Figure 3.1.

Figure 3.1: Foamed concrete test specimens for measuring thermal conductivity (300 x 300 x 50 mm)

Due to the many advantages of HFM as mentioned in Chapter 2, this apparatus

will be used for measuring the thermal conductivity values of the specimens in this study.

The heat flow meter apparatus as shown in Figure 3.2 is the main apparatus used in the

determination of thermal conductivity of foamed concrete. It was designed according to

ASTM guideline as described by Wijeysundera et al. (1989). It consists of two metal

plates. The plate having a higher temperature is called the hot plate and the one having a

lower temperature is called the cold plate. The hot plate consists of a brass plate with

heater and the cold plate has a fin-tube heat exchanger built with thick brass plate. The

temperature of the hot plate was maintained by using a water bath with an accuracy of

±0.01 oC.

71

Both heat flux meters on the hot and cold side of the heat flow meter have a

dimension of 100 mm by 100 mm with a thickness of 20 mm. They are used to measure

the heat flux at the surface of the specimen on the top and bottom. The heat flux meters

are positioned in the center of two rubber pads respectively. This is to prevent the

existence of an air gap between the specimen and the plates and also to prevent latent

heat losses from the heat flow meter.

The thermocouples and thermopiles used to measure the temperatures at the top

and bottom surfaces of the specimen are calibrated using master thermometer which is

accurate to ±0.1 oC. A thermopile is an array of thermocouples connected in parallel and

therefore it has higher sensitivity than a single thermocouple. In this study, a 10-junction

thermopile will be used. Calibration data of thermocouple and thermopile is available in

Appendix A. Figure 3.2 shows the schematic drawing of the heat flow meter apparatus

with the cold plate and the hot plate sandwiching the concrete specimens.

The error analysis of the heat flow meter is carried out to estimate how the

various measurements of heat flux, thickness of concrete slab and temperature contribute

to the overall uncertainty in the measurements. The heat flow meter apparatus has an

uncertainty of about ±6 % for the measurement of dry thermal conductivity.

(Wijeysundera et al., 1982) Note that calculation of error analysis of the apparatus is

presented in Appendix A.

72

Figure 3.2: Heat flow meter apparatus with two heat flux transducers and one specimen in between

The information of thermal conductivity of the standard material glasswool is

available for different temperature range and thus the heat flux transducers are calibrated

accordingly to obtain the conversion factor. In this case, there are two heat flux meters,

one on the top and the other at the bottom of the specimen. Assuming that these are

physically identical and have similar outputs, the outputs of the two transducers are

summed and then calibrated as a single transducer apparatus, thus having one common

conversion factor as shown in Table 3.4.

After the thermocouples and thermopiles were carefully placed on the top and

bottom faces of the concrete specimen, the concrete specimen was placed between the

two hot and cold plates. The cold plate was set at 20 oC and the hot was set at 10 oC

higher, which is 30 oC. The experiment was left to run for at least five to six hours to

allow the experimental apparatus to reach steady state. After that, the temperature

difference was obtained from voltage generated by thermopile and the average heat flux

was calculated using the voltages from the cold and hot plates. With known temperature

Specimen

Hot-side Heat flux Transducer Cold-side Heat flux Transducer

Heat flow meter

73

difference, heat flux and thickness of the concrete specimens, the thermal conductivity of

the material can be calculated using the heat transfer equation. The experiment was

repeated by changing the cold plate to 30 oC, 40 oC and 50 oC and the hot side being 10

oC higher than the cold side.

Table 3.4: Calibration of heat flux meters at different temperature ranges

102 (TC cold)

103 (TC hot)

104 (thermo-pile mV)

105 (Flux- cold)-

microV

106 (Flux-hot)-

microV

∆T (thermo-couple)

(103-102)

∆T (thermo-

pile) (deg C)

k from Standard

Data (W/m.K)

Q (W/m2)

Common conversion

factor

20.2 29.4 1.84 472 412 9.2 8.9376 0.03425 12.7547 14.4284

30.2 39.4 1.88 485 434 9.2 9.1285 0.0355 13.5026 14.6927

40.2 49.4 1.91 497 450 9.2 9.2717 0.0366 14.1393 14.9306

50.3 59.5 1.95 509 479 9.2 9.4626 0.0379 14.9430 15.1245

3.3.2 Compressive strength

Compressive strength test was carried out on 100 mm cubes according to BS 1881:

Part 116 (1983). A loading rate of 200 kN per minute was adopted. Three cube specimens

were tested and the average of the three compressive strength values was presented. The

tests were carried out using an Avery-Denison compression machine of 2000 kN capacity

which met the specification stipulated in BS 1881: Part 116 (1983).

The compressive test was conducted on the pure cement paste and foamed

concrete at age 7 and 28 days. As for polymer-modified foamed concrete, the test was

done when the specimens are at the age of 3-days, 7-days and 28-days.

74

3.3.3 Modulus of Elasticity

Modulus of elasticity test was conducted on the standard cylinder of 100 by 200

mm according to BS 1881: Part 121 (1983). The compressive strain was measured with

four transducers. The transducers were mounted in the middle section of the cylinder.

Three specimens were tested and the presented value of modulus of elasticity was

obtained by taking the average. The tests were carried out using the Instron Model 8500

Dynamic Materials Testing System.

3.3.4 Modulus of Rupture

Flexural tests were performed using third point loading test in accordance with BS

1881: Part 118 (1983). The size of the specimens was 100x100x 400 mm3. Three

specimens were tested and the presented value of flexural strength was obtained by

taking the average. The tests were carried out using the Instron Testing System.

3.3.5 Splitting tensile strength

Splitting tensile tests were performed on the standard cylinder of 100 by 200 mm

according to BS 1881: Part 117 (1983). Three specimens were tested and the presented

value of splitting tensile strength was obtained by taking the average.

3.3.6 Microscopy

The samples for microscopy are cuboids of size 70mm by 70mm by 30mm thick

which were cut from a 100 mm cube. The top surface of the cuboids was polished to

attain a smooth surface. In order to get a better contrast for automatic imaging processing,

75

the polished surface was colored by permanent black ink in two perpendicular directions

to ensure that the entire surface was covered with the ink. After the ink dried, white

cement powder was used to fill up the voids on foamed concrete polished surface.

Figure 3.4a shows a sample that was prepared for automatic image analysis to

find out its microscopic properties. The prepared surface was then scanned with a

2400dpi (dots per inch) scanner. This image was analyzed fully automatically by

employing computer software to attain the bubble size distribution in a 60 x 60mm area.

The software is able to identify all circular-shaped air pores from the image and measure

the size of each individual air pores identified. The results can then be collated and the

pore size distribution of the concrete sample can be obtained fairly efficiently.

Air bubbles incorporated into foamed concrete typically have diameter in the

range of 0.1-1 mm. The resolution of the scanner used is 2400dpi. Thus the diameter of

the smallest bubble is represented by 9.45 pixels (> 4 pixels) which can sufficiently

represent the bubble. Particle size analysis of white cement powder shows that the mean

particle size of white cement is 27 µm (sufficiently smaller than the size of air bubbles).

Thus, it is small enough to fill up the air void fully.

To ensure that surface treatment using black marker and white cement will not

distort the air voids on the surface and hence result in inaccurate results, some

verification of the method used was done to provide sufficient confidence for the

obtained results. In one of the tests, two images of the same area were prepared as shown

in Figure 3.3a and c. Figure 3.3a was taken after it was polished and Figure 3.3c was

taken after it was painted black, with the air voids on the polished surface being filled

with white cement. The two images were compared to check whether the voids remained

76

intact after the surface preparation. When the processed image from Figure 3.3d is

superimposed on to the uncoated specimen in Figure 3.3a, it was verified upon

comparison that nearly all the voids remained intact. Thus, the surface treatment process

to get a better contrast can be considered feasible and it will not distort the results

significantly.

Figure 3.3: a) uncoated specimen; b) processed image superposed on to the uncoated specimen as

shown in (a) ; c) coated specimen image with better contrast and d) processed image of (c) using

software

Another verification test was to check whether different types and extent of post-

processing of the same image will significantly affect the results of the pore sizes of the

foamed concrete. Figure 3.4a-c shows the different images being analyzed. These three

images originated from the same image; Figure 3.4a is the original image, Figure 3.4b

has undergone sharpening to get a better contrast in Adobe Photoshop software and

a

c d

b

77

Figure 3.4c has undergone sharpening as well as additional edge processing to the

circular bubbles. By observation, Figure 3.4c shows a reduction in the number of bubbles

after the edge processing as compared to Figure 3.4a and b.

Results from Figure 3.5 show that the results from cutout 1 and cutout 2 are very

similar. This means that increasing the contrast of the original image to cutout 2 will not

affect the results. However, post-processing the original image to cutout 3 will cause the

results of the pore size distribution to deviate from original result. Thus, the other images

to be analyzed will only be sharpened to get a better contrast.

Figure 3.4:a) Cutout (original scanned image), b) Cutout 2, c) Cutout 3

Pore size distribution

-50

0

50

100

150

200

250

0 10 20 30 40 50

Size of air pores

Fre

qu

en

cy

cutout 2

cutout 3

cutout

Figure 3.5: Pore distribution of images which underwent different post-processing

a)

c)

b)

c)

78

The last verification test was to extract a snapshot of the air void selection process

to see whether the software can capture the available air voids. The shaded portions in

Figure 3.6 represent the locations of air voids on one surface of the foamed concrete

specimen. From the snapshot in Figure 3.6, it can be shown that software was able to

select almost all the air voids using circles. Thus, there is much confidence to trust in the

reliability of the method to process the image automatically to count the number of air

bubbles in the area and also to measure the size of the air bubbles.

Figure 3.6: Counting process of image in Figure 3.5d

79

4 Numerical Analysis 4.1 Introduction

In order to come up with an optimized design of foamed concrete with a suitable

thermal conductivity to suit its intended purpose, it is important to know the effect of

thermal conductivity, shape, volume etc. of each component on the effective thermal

conductivity of the mixed system of air bubbles in cement matrix. Appropriate theoretical

models can be a fast way to predict the effective thermal conductivity of mixed solid

materials without having to do the experiments.

Zhang and Liang (1995) did a study on numerical analysis of effective thermal

conductivity of mixed solid materials. They reported that numerical analysis has high

accuracy. It eliminates the need for any hypotheses and it allows effective thermal

conductivity of mixed solid materials with discrete phases of different shapes. They also

reported that the effective thermal conductivity of mixed solid materials is influenced by

the weight (or volume) fraction and the thermal conductivity of individual components in

the materials rather than by the size or dimension of the discrete phase.

The present study aims to verify whether besides thermal conductivity of cement

matrix, the arrangement or space location of air pores, different combinations of pores of

different sizes, shape and size affect the effective thermal conductivity of foamed

concrete. The reason for the study is because the strength of foamed concrete can be

increased by having smaller air bubbles. However, there has been some concern as to

whether by having smaller bubbles will affect the thermal conductivity of foamed

concrete if the amount of air in the foamed concrete is constant.

80

Thus, in this study, the effect of air bubble size (given the same volume fraction

of air bubbles) will be investigated via numerical modeling whereby the geometry and

size of the air bubble can be taken into consideration. Analytical model like self-

consistent model is able predict thermal conductivity of foamed concrete fairly accurately,

however its computation does not include the size of air bubble and also geometry of air

bubble. Thus, numerical method using FLUENT software is selected to carry out the

investigation.

The feasibility of using foamed concrete as an alternative roofing system for HDB

flat roofs will also be investigated by using GAMBIT and FLUENT software. The

relationship of heat flux versus thickness of foamed concrete as an insulator is studied.

4.2 FLUENT

The software used in this study is FLUENT 6.0. It is an unstructured finite

volume CFD (Computational Fluid Dynamics) code which utilizes fundamental mass,

momentum and energy balances to predict fluid flow, heat transfer and other physical

phenomena over a specified domain. CFD enables the user to analyze the impact of

changes to geometry. It complements physical modeling and is thus more cost effective.

Its benefits also include allowing for the investigation of more design options for 2D &

3D arbitrary geometry in less time. It can also provide comprehensive data which is not

easily obtainable from experimental tests. Other than the effect of changes in geometry or

other properties of materials, the cause can be highlighted as well.

“Pre-processing” is the first stage of the CFD investigation and it involves

creating a geometry and internal grid. The grid “discretises” the domain to solve the

81

energy equation. The values of the variables found in the energy equation are calculated

within each cell and thus the accuracy and robustness of the flow solution is dependent

upon how the domain is divided. Smaller elements within the domain can give more

accurate solutions. The boundary type and zone assignment is done at the GAMBIT and

after which the final grid is exported to FLUENT to be solved and post-processed.

FLUENT is a state-of-the-art computer program for modeling fluid flow and heat

transfer in complex geometries. . The pre-processor of FLUENT used is GAMBIT.

FLUENT provides complete mesh flexibility, solving your flow problems with

unstructured meshes that can be generated about complex geometries with relative ease.

Supported mesh types include 2D triangular/quadrilateral, 3D

tetrahedral/hexahedral/pyramid/wedge, and mixed (hybrid) meshes. FLUENT also

allows you to refine or coarsen your grid based on the flow solution. It uses unstructured

Finite Volume method CFD codes and it is an integrated interface for CFD Solver and

Post-processing. All functions required to compute a solution and display the results are

accessible in FLUENT through an interactive, menu-driven interface.

The flow of thermal energy from matter occupying one region in space to matter

occupying a different region in space is known as heat transfer. Heat transfer can occur

by three main methods: conduction, convection, and radiation. Physical models involving

only conduction and/or convection are the simplest, while buoyancy-driven flow, or

natural convection, and radiation models are more complex. Depending on the problem,

FLUENT will solve a variation of the energy equation that takes into account the heat

transfer methods specified. FLUENT is also able to predict heat transfer in periodically

82

repeating geometries, thus greatly reducing the required computational effort in certain

cases.

FLUENT solves the energy equation in the following form:

(4.1)

Where keff is the effective conductivity (k + kt, where kt is the turbulent thermal

conductivity, defined according to the turbulence model being used), and Jj is the

diffusion flux of species j. The first three terms on the right-hand side of Eqn. 4.1

represent energy transfer due to conduction, species diffusion, and viscous dissipation,

respectively. Sh includes the heat of chemical reaction, and any other volumetric heat

sources defined.

In Eqn. 4.1,

(4.2)

where sensible enthalpy is defined for ideal gases as

(4.3)

and for incompressible flows as

83

(4.4)

In Eqn. 4.3 and Eqn. 4.4, Yj is the mass fraction of species j and

(4.5)

where Tref is 298.15 K.

4.3 Thermal conductivity studies

4.3.1 Description of the problem

The effect of size of air bubbles on thermal conductivity of foamed concrete is

investigated by means of the FLUENT software mentioned in Section 4.2. It can be done

by simulating the problem using a cubic model with a spherical shaped air bubble inside.

For this part of the study, the amount of air used is constant at 25 %.

This is a one-dimensional heat flow problem with heat flowing in one direction

from the top to the bottom of the geometry. The sides are at adiabatic condition assuming

that heat does not flow laterally in this case. Assuming the air bubbles are equally spaced

in the cube in an example as shown in Figure 4.1a, we can take advantage of symmetry in

the problem and simplify it by having a smaller domain to reduce computational efforts.

For example in Figure 4.1a, there are 64 air bubbles inside the 3 D cube, it can be divided

into 64 smaller elements with one spherical air bubble inside the cube and only one of

these smaller cubes needs to be solved.

84

Moreover, when air is incorporated into cementitious material during the casting

of foamed concrete and mixed well, from the point of statistics, the material is considered

to be uniform. Thus, the effective thermal conductivity of foamed concrete material is

equal to that of each cubic volume element in Figure 4.1b. The same geometry is scaled

proportionally for different sizes of air bubble to simulate the difference in air bubble size.

Note that the amount of air volume inside the cube remains unchanged. The grid quality

is kept constant for the different cases to make sure that the solutions are not affected by

it.

After the model is set up, numerical analysis is done to find out the effective

thermal conductivity of the model. The effective thermal conductivity of an element is

evaluated by Eqn. 4.6.

)(

.

12 TT

Lqkeff

−= (4.6)

The steady-state heat conduction equation and the respective boundary conditions for the

element are as follow:

(4.7)

85

a) b)

Figure 4.1: a) 3-D geometry of models with 64 bubbles in the cube and b) a cubic volume element for

analysis

4.3.2 Pre-processing

The basic steps in pre-processing is

1) Building up the geometry of the model

2) Generating the mesh

3) Defining boundary type and material type

A geometry to represent foamed concrete structure with air void introduced in

cement matrix is created first and a mesh is generated for the geometry in the GAMBIT

software. The amount of air fraction is 25 %. The mesh generated is then exported to

FLUENT solver. A domain is first defined by specifying a geometry in which the heat

flow is to be solved. In order to solve the heat flow equations in FLUENT to simulate

experimental conditions when determining thermal conductivity, the domain must be

divided into small “control volumes” or “cells”. The values of the heat flow variables are

calculated within each cell. The accuracy and robustness of the heat flow solution is

86

dependent upon how the domain is divided or the grid quality. In order to get accurate

solutions, small variations should occur between cells of the heat flow variable values.

The final step in pre-processing was to define the boundary type and material type.

All the boundaries are assumed to be walls. As for the material type, it was either defined

as a fluid or solid depending on whether air or concrete was used in the analysis.

4.3.3 Post-processing

The data file from GAMBIT was first imported to FLUENT. The first step would

then be to check whether the scale of the model was correct (see Figure 4.2).

Figure 4.2: Checking of model scale

The next step would then be to activate the energy equation and the gravity

function (see Figure 4.3). Before initialization, the boundary conditions (see Figure 4.4)

87

of the walls were set and the material properties defined. The top wall was maintained at

340K while the bottom wall was maintained at 300K. The side walls were assumed to be

adiabatic. Then initialization and iterations were carried out. After the solution converged,

the flux report, temperature and flux contour (see Figure 4.5) could then be generated.

Figure 4.3: Setting the gravity function

88

Figure 4.4: Defining boundary conditions

Figure 4.5: Obtaining the heat flux report

4.3.4 Calibration of the model

Convergence test for different grid quality was done to find out which is the

largest mesh size that can be used without compromising on the accuracy of the solution.

89

Figure 4.6a-d shows the grids for geometry created with decreasing mesh size meaning

that the number of cells is more. At a mesh size of 0.005, there is a convergence of the

solution obtained as shown in Figure 4.7. Thus, this mesh size corresponding to this

geometry size was used in the subsequent models.

a) b)

c) d)

Figure 4.6a-d: FLUENT models with mesh size = 0.01, 0.008, 0.005 and 0.003 respectively

90

Convergence Test of model

0.3815

0.3816

0.3817

0.3818

0.3819

0.382

0.3821

0.3822

0.3823

0.3824

0.3825

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011

Mesh interval size

Th

erm

al c

on

du

cti

vit

y (

W/m

.K)

Figure 4.7: Mesh convergence Test

4.4 Simulation of HDB roofing system using foamed concrete

It is proposed that foamed concrete is used as a material for the roofing system on

the flat roof of HDB flats. Thus, it is necessary to first find out the potential of using

foamed concrete as thermal insulator as compared to using air gap. The performance of

foamed concrete as an insulating roofing system will be investigated in this study via

numerical methods (FLUENT). This problem was considered as a one-dimensional heat

flow problem with heat flowing in one direction from the top to the bottom of the

geometry and the sides are at adiabatic condition assuming that heat does not flow

laterally in this case.

Field measurements were conducted on a rooftop of a local commercial building

by a research done by the building department in National University of Singapore (“A

91

study of Rooftop Gardens in Singapore”, 2002)2. The surface temperatures of a concrete

rooftop at varying local (Singapore) time which are adapted from the field study can be

found in Figure 4.8. The highest surface roof temperature was observed to be 60 oC.

Surface temperature of the roof is affected by amount of solar radiation, air

temperature, humidity and wind. The resultant amount of solar radiation absorbed and

emitted by the roof to raise the temperature of the roof surface is related to the nature of

the surface of the roof. Thus, the design surface temperature of rooftop is dependent on

many factors. The right climatic condition and material properties have to be taken into

account to come out with a realistic design value.

In this study, the worst scenario was considered where the top surface is at 60 oC

and the bottom surface of the roof insulation will be taken to be at a fixed temperature of

20 oC (design temperature of the interior of an air-con room). The properties of Mix F3

(keff = 0.3707, density = 1440 kg/m3) were used to model the roof insulator made of

foamed concrete. The thickness of the two-dimensional rectangular model was varied

from range 7.5 cm to 30 cm. Heat flux produced due to the temperature differential

versus change in thickness of insulation was calculated using the results obtained from

the FLUENT simulation.

92

Graph of surface temperature of rooftop vs local (Singapore) time

0

10

20

30

40

50

60

70

0000-0900 0900-1200 1200-1800 1800-2100 2100-2400

Local (Singapore) time (hrs)

Su

rfa

ce

te

mp

era

ture

of

roo

fto

p (

0C

)

Figure 4.8: Design surface temperature of a typical rooftop at different local (Singapore) time

(adapted from “A study of Rooftop Gardens in Singapore”, 2002)2

93

5 Results and Discussion

In recent years, there is an increasing demand for insulating building materials

like foamed concrete due to the need to cut down on energy wastage. There is a

tremendous market for foamed concrete as an insulating material to meet the rising needs

in the building industry and other industries due to its versatility and economy. Currently,

there is a lack of comprehensive information in the literature for foamed concrete. Thus,

it would be very useful if there is a deeper understanding of what the key factors affecting

its thermal properties and strength properties are. This will aid the end-user to better

design foamed concrete mixes for various applications cost-effectively.

In this chapter, results on effects of key factors like foam content, water-cement

ratio, air void size and polymer content on both the thermal conductivity and strength for

different mix design of foamed concrete and polymer-modified foamed concrete will be

presented. In this study, foam content refers to the amount of foam content designed.

Note that for modeling, keff denotes effective thermal conductivity and it represents the

resultant thermal conductivity of the foamed concrete as a function of thermal

conductivity of cement paste matrix and air bubbles. The results obtained will be

discussed to provide a deeper understanding of these factors in order to fulfill the first

and second objectives of this research project as stated in the introduction in Chapter 1.

The third objective was to propose a model using numerical method (FLUENT

software) for predicting the thermal conductivity of foamed concrete to aid in the design

of cost-effective and innovative mixes for structural and non-structural insulation

purposes. Results from the FLUENT modeling will be presented here. The results from

94

current research and other researchers’ experiments will be used to verify the numerical

results obtained by the proposed model. Analytical models were also used to predict

thermal conductivity of foamed concrete. Results from the various models were used to

compare with the model proposed for this model.

Foamed concrete was proposed for use as a thermal insulating material on flat

roofs of HDB flats or other buildings due to its good insulating property. As discussed in

Chapter 1, there are various disadvantages of the current ferrocement roofing system

using an air layer as a thermal insulator. It was proposed that the insulation system may

be rectified and improved by using an alternative insulating material like foamed concrete

on the flat roofs of HDB flats and other buildings to suit the local requirement. There

would be two mix designs of foamed concrete proposed for foamed concrete insulation

roofing system. This will meet the last objective of this research project as stated in

Chapter One.

5.1 Thermal conductivity

5.1.1 Experimental results for foamed concrete

Thermal conductivity results for the various foamed concrete (w/c ratio varying

from 0.35-0.55 and foam content ranges from 25 to 70 %) and cement paste mixes

measured after 7 and 28 days curing are tabulated in Table 5.1 and Table 5.2 respectively.

The tables show the thermal conductivity results at temperatures ranging from 25- 55 oC.

The description of the sample designation number and the mix design can be found in

Table 3.2. The experimental thermal conductivity data were obtained using heat flow

95

meter using concrete specimens which were oven-dried for 24 hours before testing to

remove the moisture inside.

Table 5.1: Measured thermal conductivity of concrete specimens using heat flow meter after 7 days

Sample W/C ratio

Actual Wet

Specific Gravity

k (W/m.K)

Mean temp: 25

oC

k (W/m.K)

Mean temp: 35 oC

k (W/m.K)

Mean temp: 45 oC

k (W/m.K)

Mean temp: 55 oC

Foam Content

(%)

F4 0.35 1.07 0.2217 0.2265 0.2291 0.2323 50

F1 0.45 1 0.1902 0.1934 0.1964 0.1987 50 Varying w/c ratio

F5 0.55 0.9 0.1832 0.1868 0.1862 0.1911 50

F2 0.45 0.55 0.1228 0.1272 0.1319 0.1348 70

F1 0.45 1 0.1902 0.1934 0.1964 0.1987 50 Varying

foam content F3 0.45 1.44 0.3378 0.3491 0.3533 0.3593 25

C1 0.45 1.86 0.4948 0.5018 0.5104 0.53 0

C2 0.35 1.98 0.5571 0.5689 0.5836 0.599 0

Cement paste

(varying w/c

ratio) C3 0.55 1.76 0.4587 0.4637 0.4776 0.4888 0

Table 5.2: Measured thermal conductivity of concrete specimens using heat flow meter after 28 days

Sample W/C ratio

Actual Wet

Specific Gravity

k (W/m.K)

Mean temp: 25 oC

k (W/m.K)

Mean temp: 35 oC

k (W/m.K)

Mean temp: 45 oC

k (W/m.K)

Mean temp: 55 oC

Increase of k at 25 oC from 7 days to 28 days

% In-crease of k at 25 oC from 7 days to 28 days

Foam Cont-ent (%)

F4 0.35 1.07 0.2509 0.2554 0.2613 0.2653 0.0292 11.65 50

F1 0.45 1 0.2241 0.2246 0.2258 0.2281 0.0339 15.14 50 Varying w/c ratio

F5 0.55 0.9 0.1934 0.1967 0.199 0.2024 0.0102 5.27 50

F2 0.45 0.55 0.1576 0.1637 0.1616 0.1637 0.0348 22.09 70

F1 0.45 1 0.2241 0.2246 0.2258 0.2281 0.0339 15.14 50 Varying

foam content F3 0.45 1.44 0.3707 0.3764 0.39 0.3986 0.0329 8.86 25

C1 0.45 1.86 0.5345 0.5504 0.5633 0.5714 0.0398 7.44 0

C2 0.35 1.98 0.5768 0.5809 0.5894 0.5975 0.0197 3.41 0

Cement paste

(varyiing w/c

ratio) C3 0.55 1.76 0.4845 0.4914 0.5015 0.515 0.0257 5.31 0

Results show that thermal conductivity of cement pastes ranges from 0.4914-

0.5809 W/m.K. Due to the inclusion of air bubbles into cement paste, foamed concrete

96

possesses lower thermal conductivity ranging from 0.1576 to 0.3764 W/m.K. The lowest

thermal conductivity of foamed concrete obtained for this research project is 0.1576

W/m.K at foam content of 70 %. Thermal conductivity of foamed concrete is observed to

be significantly dependent on its density and foam content and less significantly on w/c,

temperature and age. Their effects will be discussed in greater details in subsequent

sections.

5.1.1.1 Effect of density and age

Figure 5.1 shows how thermal conductivity of foamed concrete changes with its

specific gravity. The trend shows that thermal conductivity of concrete is largely

dependent upon the density of the concrete. When density increases, thermal conductivity

increases as well. At higher densities, the amount of solid material present is higher and

the solid particles are more closely packed together. Thus, the rate of collision between

particles (rate of heat transfer) is increased. When the density is lower, there are less solid

particles due to the inclusion of air particles which are spaced much further apart, thus

impeding the rate of conduction which is the dominant heat transfer mechanism. Other

heat transfer mechanism like heat radiation and convection are hindered as well since the

air pores are small, so contributions by them are considered as negligible.

Different density of foamed concrete is used for different applications. Lower

density foamed concrete has lower thermal conductivity and strength properties, and

hence is suitable for insulation purposes. On the other hand, foamed concrete with higher

density can be used for structural purposes due to its higher strength values. However, its

insulation application will be limited since its thermal conductivity is higher.

97

For example, foamed concrete (generally without sand) with density lower than

600 kg/m3 will be suited to be used in roof and floor as insulation against heat and sound

and is applied on rigid floors (i.e. in itself it is not a structural material). It can also used

for tennis courts and interspace filling between brickwork leaves in underground walls,

insulation in hollow blocks and any other filling situation where high insulating

properties are required. For higher density from about 600 to 900 kg/m3, foamed concrete

(normally sand is added) is used for the manufacture of precast blocks and panels for

curtain and partition walls, slabs for false ceilings, thermal insulation and soundproofing

screeds in multi-level residential and commercial buildings.

For more heavy weight foamed concrete with density from 900 to 1200 kg/m3, it

is used in concrete blocks and panels for outer leaves of buildings, architectural

ornamentation as well as partition walls, concrete slabs for roofing and floor screeds.

Foamed concrete with structural strength which is obtained at 1200 to 1600 kg/m3 is used

in precast panels of any dimension for commercial and industrial use, in-situ casting of

walls, garden ornaments and other uses where structural concrete of light weight is an

advantage.

Increasing age of foamed concrete has an increasing effect on its thermal

conductivity as can be observed from Figure 5.1. At a later age, foamed concrete would

have undergone a higher degree of hydration, resulting in denser concrete thus the

thermal conductivity of the material will increases slightly. The percentage increase in

thermal conductivity due to aging seems to be higher for foamed concrete mixes with

higher foam content as shown in table 5.2. Mix F2 which has a high foam content of 70

% showed about 22 % percentage increase in k at 25 oC from 7 to 28 days. This value is

98

relatively higher than for other mixes (C1, F3 and F1) which has the same w/c ratio of

0.45 but with lower foam content.

Comparison of the effects of Specific Gravity on Thermal Conductivity of Foamed

concrete at 7 and 28 days

0.1228

0.1902

0.3378

0.4948

0.1576

0.3707

0.53

0.2241

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

0.3500

0.4000

0.4500

0.5000

0.5500

0.6000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Specific Gravity of Fresh Concrete

Th

erm

alC

on

du

cti

vit

y (

W/m

.K)

25 Deg C (7 days)

25 deg C (28 days)

Figure 5.1: Graph of Thermal conductivity against specific gravity of foamed concrete with w/c= 0.45

at both 7 days and 28 days

5.1.1.2 Effect of foam content or porosity

As foam content in foamed concrete increases, thermal conductivity decreases

quite drastically. This is why foamed concrete can be a good insulator with the addition

of pre-formed foam since air is a poor conductor of heat and thus can help to impede heat

transfer. The addition of 70 % of foam is able to reduce the thermal conductivity by about

70 %, which is quite substantial. The effect on thermal conductivity of foamed concrete

due to foam content can be observed from Figure 5.2. Thermal conductivity of foamed

concrete falls within a band due to an uncertainty of about ±6 % for the heat flow meter

99

apparatus (Wijeysundera et al., 1982), thus the observed parallel trend for results

measured on 28 days may not exist.

In this research, a mix of foamed concrete with 80 % foam content, w/c ratio of

0.35 was attempted to be cast. However, it experienced serious foam collapse and thus

was unable to be cast successfully. Since when a very large amount of foam is added, it

results in an insufficient amount of cement paste to surround the air voids. Coalesce of air

bubbles thus take place. When the air bubbles get bigger after the coalescence, the

tendency for the enlarged bubble to burst during mixing and handling of the mix of

foamed concrete is higher.

Comparison of the effects of foam content on Thermal Conductivity of Foamed concrete

at 7 and 28 days

0.122781233

0.190176337

0.337822347

0.494758305

0.1576

0.2241

0.3707

0.53

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Foam content (%)

Th

erm

al

Co

nd

uc

tiv

ity

(W

/m.K

)

25 Deg C (7 days)

25 deg C (28 days)

Figure 5.2: Graph of Thermal conductivity against foam content at both 7 days and 28 days (w/c =

0.45)

Mix C1

Mix F3

Mix F1

Mix F2

100

5.1.1.3 Effect of w/c ratio

The effect of water-cement ratio (w/c) was also investigated and it was found that

higher w/c ratio results in a lower thermal conductivity of the foamed concrete as seen in

Figure 5.3. The amount of foam content is kept at 50 %, however results of thermal

conductivity of cement matrix (C1, C2 and C3) decreases with increasing w/c ratio as

seen from Table 5.2. Thus, thermal conductivity of foamed concrete is not only

dependent on air void fraction, but also on the thermal conductivity of the cement paste.

Thus, these two parameters, air void ratio and thermal conductivity of cement paste,

would be used to predict thermal conductivity of foamed concrete in analytical models in

later sections.

Cement content decreases with higher w/c ratio. The amount of cement hydration

products will thus be reduced, resulting in less dense material or lesser amount of solid

which are more sparsely-spaced, with interstitial voids as shown in Figure 5.4.

Propagation of heat by conduction decreases as a result of lower rate of particle collision

and thus, transfer heat energy is slowed down.

The trend is very similar to that reported by Kook et al. (2003) who also

investigated the effect of w/c ratio on cement paste. They found that with the addition of

more cement content which means a lower w/c ratio, the thermal conductivity of cement

paste increases. The reason is that cement has a higher thermal conductivity value than

water. The results show that changing w/c ratio of foamed concrete does not have as great

a significant effect on the thermal property as compared to varying foam content.

101

Effects of w/c on Thermal Conductivity of Foamed concrete (50% foam content)

0.2509

0.2241

0.1934

0.2217

0.1902

0.1832

0.17

0.19

0.21

0.23

0.25

0.27

0.3 0.35 0.4 0.45 0.5 0.55 0.6

w/c

Th

erm

al C

on

du

cti

vit

y (

W/m

.K)

28 days

7 days

Figure 5.3: Graph of Thermal conductivity against w/c at 28 days

Figure 5.4: Schematic diagram of cement hydration with different w/c ratio

Mix F4

Mix F1

Mix F5

High thermal conductivity Low thermal conductivity

102

5.1.1.4 Effect of temperature

Figure 5.5 shows the plot of thermal conductivity of the various mixes of foamed

concrete and cement paste (at oven-dried condition) against the mean temperature of

material. The temperature range is from 25 oC to 55 oC. A very slight increasing trend can

be observed from Figure 5.5. However, the increase was not very significant within the

short temperature range which the materials were tested.

When the temperature of the hot side and cold side of the heat flux meter is

increased, the heat energy being transferred to the particles inside the foamed concrete is

increased, causing more vigorous vibration of the particles and also increases the rate of

collision between particles. Thus, the rate at which heat is conducted through conduction

is increased, resulting in a higher thermal conductivity in specimens which are tested at

higher temperature. This increasing trend is consistent with the works of other

researchers like Marmoret (1999) and De Rose and Morris (1999).

Thus, thermal conductivity of foamed concrete may change when it is applied at

different countries. For example, in the desert where the ambient temperature is typically

higher at 45 oC, thermal conductivity of foamed concrete is slightly higher than that of

the same mix of concrete would differ at places with milder temperature of say 25 oC.

This should be taken into consideration when designing foamed concrete as an insulation

material. The increase of thermal conductivity value due to 10 oC increase in temperature

is typically 1-3 % and is seldom higher than 4 %.

103

Comparison of the effects of Temperature on Thermal Conductivity of Foam concrete at

28 days

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

10 15 20 25 30 35 40 45 50 55 60

Mean Temperature (degree Celcius)

Th

erm

al

Co

nd

uc

tivit

y (

W/m

.K)

Mix F1

Mix F2

Mix F3

Mix F4

Mix C1

Mix C2

Mix C3

Figure 5.5: Graph of Thermal conductivity against temperature

5.1.2 Experimental results for foamed concrete with polymer

The results of thermal conductivity for various polymer-modified foamed

concrete and cement paste mixes are tabulated in Table 5.3 measured after 28 days curing.

The description of the sample designation number and the mix design can be found in

Table 3.3 in Chapter 3. Effects of polymer content, foam content and density on thermal

conductivity of polymer-modified foamed concrete will be discussed.

104

Table 5.3: Measured thermal conductivity of polymer-modified concrete specimens using heat flow

meter after 28 days

Mix Designation

Polymer Content

(%)

Foam content

(%) w/c ratio

Fresh Density (kg/m3)

Thermal conductivity, k (W/m.K)

Control 0 50 0.35 1000 0.237

PF1 5 50 0.35 1020 0.232

PF2 10 50 0.35 960 0.226

PF3 15 50 0.35 1000 0.215

PF4 20 50 0.35 960 0.191

PF5 10 20 0.35 1580 0.3909

PF6 10 80 0.35 478 0.1046

CP1 5 0 0.35 1940 0.55

CP2 10 0 0.35 1920 0.535

CP3 15 0 0.35 1900 0.509

CP4 20 0 0.35 1880 0.481

5.1.3 Effect of varying polymer content

Figure 5.6 shows the effect of polymer content on thermal conductivity of

polymer-modified foamed concrete and cement paste. As shown in Figure 5.6, increasing

the amount of polymer will reduce the thermal conductivity of the material slightly. The

effect of polymer to reduce the thermal conductivity of cement paste with no foam added

was observed to be higher than for foamed concrete with 50 % foam content as can be

seen by the gradients of the two equations on Figure 5.6.

105

Graph of thermal conductivity vs polymer content

0.481

0.237 0.2320.226 0.215

0.191

0.577

0.550 0.535

0.509y = -0.0047x + 0.577

y = -0.0022x + 0.2422

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20

polymer content (% by weight of cementitious material content)

th

erm

al

co

nd

ucti

vit

y (

W/m

.K)

50 % foamed concrete

0 % foamed concrete

Mix C2

Mix PF3Mix PF2Mix PF1

Mix Control

Mix CP4

Mix CP3Mix CP2

Mix CP1

Mix PF4

Figure 5.6: Graph of thermal conductivity of foamed concrete against polymer content

Polymer which is added to replace some of the cementitious material in foamed

concrete has a lower thermal conductivity (k ≈ 0.19- 0.3 W/m.K) than cement paste (k ≈

0.66 -1.2 W/m.K). The reduced thermal conductivity could also be due to the additional

air bubbles caused by air entrainment when acrylic polymer is added into the mix. Thus,

adding polymer to foamed concrete helps to lower the overall thermal conductivity of the

polymer-modified foamed concrete.

There is a limit to the amount of foam added into foamed concrete. The higher the

amount of foam, the lesser the amount of cement paste to surround the air voids which

could result in air void coalescence as discussed in Section 5.1.1.2. It was found that a

mix of 80 % foam content, w/c 0.35 and 10 % polymer by weight of cement is cast

106

successfully. Addition of a small amount of polymer can improve the problem of foam

collapse. Initially, however, when a mix of 80 % foam content and w/c ratio of 0.35 was

cast without polymer, it experienced foam collapse. Thus, one benefit of adding acrylic

polymer into foamed concrete is that it allows a greater amount of foam to be added into

foamed concrete. This enables further reduction of its thermal conductivity when a

maximum amount of foam content allowed in foamed concrete is reached. The

effectiveness of foamed concrete as an insulation material can be improved as a much

lower thermal conductivity can be reached by adding a small amount of polymer.

The rationale could be because polymer has smaller particle size than unhydrated

cement particles or hydrated cement products. Polymer consists of long chains of

molecules made up by physical aggregates of smaller molecules united by vague "partial

valences," not true giant molecules held together by chemical bonds. In fact, X-ray

crystallography of polymer fibers revealed unit cells no bigger than those of ordinary

molecules like carbon dioxide or water. Thus, the smaller polymer molecules are able to

maneuver more easily among the air voids and to surround them as compared to cement

particles or hydrated cement products. Thus, the polymer could possibly allow a much

smaller spacing factor of air bubbles to be sustained in foamed concrete of very high

foam content without air void coalescence.

5.1.4 Effect of foam content

Foam content in polymer-modified foamed concrete was varied from 20 to 80 %,

while keeping polymer content constant at 10 %. As the foam content in polymer-

modified foamed concrete increases, thermal conductivity decreases quite drastically as

107

shown in Figure 5.7. The trend is similar to that of foamed concrete. Due to the addition

of 10 % of polymer content (by weight of cement), a material of a high foam content of

80 % resulting in a very low thermal conductivity of 0.1046 W/m.K. measured at 25 oC

can be obtained.

Graph of effective thermal conductivity vs foam content in polymer-modified foamed concrete

0.1046

0.2263

0.5350

0.3909

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90

foam content (% in polymer-modified foamed cocnrete)

Eff

ec

tive

th

erm

al

co

nd

uc

tiv

ity

(W

/m.K

)

10 % polymer content

Figure 5.7: Graph of thermal conductivity of polymer-modified foamed concrete against foam

content

5.2 Simulation Results for effect of air bubble size on thermal conductivity of foamed concrete

Theoretically, the effect of air bubbles size on keff is negligible when it is assumed

that there are only single-sized air bubbles in foamed concrete. Nevertheless, the effect of

air bubble size was investigated using numerical method by means of FLUENT software.

The method of modeling is discussed earlier in Section 4.3 in Chapter 4. The air content

Mix CP2

Mix PF6

Mix PF4

Mix PF5

108

for four types of foamed concrete with differing air bubble size was kept constant at 25 %.

It can be observed from Figure 5.8 that the air bubble diameter has no effect on keff of

material modeled with an air content of 25 % using single-sized air bubbles.

The conclusion that air bubble size does not affect thermal conductivity of foamed

concrete (if air content is kept constant) should only be applicable to air bubbles which

are reasonably small. In other words, the effect of air void size on thermal conductivity of

foamed concrete may be significant for air voids of much larger magnitude than the

typical air bubbles found in foamed concrete due to the additional effect of convection

and radiation. The air bubbles in foamed concrete are usually quite small, in the size of

the range 0.1 to 1 mm. According to Luikov (1980), for a pore diameter smaller than 3

mm in porous material, the effect of radiation and convection in pores can be neglected in

comparison with other modes of heat transfer at atmospheric pressure and temperature.

Heat transfer through radiation and convection within the pores is small and can be

neglected or lumped in with the true conduction component at atmospheric pressure and

temperature. Chew (2005) found that within an air gap of 10 cm thickness (see Figure

2.21), heat transfer through conduction still governs. Heat transfer through an air gap

below the size of 10 cm should be by conduction. Thus, heat transfer due convection and

radiation can be neglected through air bubbles in foamed concrete which are of typically

in the size range of 0.1 to 1 mm.

109

Effect of air bubble size on thermal conductivity of foamed concrete

0.3816

0.3816

0.3816

0.3816

0.3816

0.38140

0.38145

0.38150

0.38155

0.38160

0.38165

0.38170

0.38175

0.38180

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Air bubble diameter size (mm)

Eff

ec

tiv

e t

he

rma

l c

on

du

cti

vit

y o

f fo

am

ed

co

nc

rete

(W

/m.K

)

Figure 5.8: Plot of air bubble diameter against thermal conductivity result from FLUENT

The effect of having different air bubble sizes in foamed concrete on keff was

investigated using FLUENT software as well. Models with mixed-sized spherical air

bubbles of different arrangements are shown in Figure 5.9. The total air content in the

two models was 25 %. The value of thermal conductivity of cement paste used in both

the models was 0.73 W/m.K. Analysis using FLUENT software obtained keff of 0.5205

W/m.K and 0.5325 W/m.K for models shown in Figure 5.9 (b) and (c) respectively.

These two values are very close to the keff of 0.5214 W/m.K obtained from a model with

a single-sized air bubble shown in Figure 5.9 (a). These thermal conductivity values are

tabulated in Table 5.4. The percentage differences between results obtained for the

various models are also tabulated in Table 5.4 and it can be shown that the results do not

110

differ very much. Thus, it shows that that the effect of size and arrangement of air

bubbles in foamed concrete on effective thermal conductivity is not very significant.

a) b) c)

Figure 5.9: FLUENT models with 25 % air content –a) single-sized air bubble; b) mixed-size

spherical air bubbles; c) mixed-size spherical air bubbles with different size combination of air

bubbles.

Table 5.4: Effective thermal conductivity for different types of model obtained by FLUENT analysis

Type of Model Effective Thermal

conductivity, W/m.K.

% difference

from spherical air

bubble

Spherical air bubble model 0.5214 -

Mixed-sized air bubbles model 1

0.5325 2.09

Mixed-sized air bubbles model 2

0.5205 -0.17

keff is observed to be heavily dependent on the volume fraction of air bubbles

(discrete phase) rather than on their sizes for low air content of 25 %. Thus, this implies

that the insulating property of foamed concrete is not compromised even by having

smaller size air bubbles (with same air content) which helps in increasing the strength of

the material. However, this finding might not be able to be extrapolated to foamed

concrete with higher foam content since only a porosity of 25 % was investigated in this

111

study. Modeling of spherical air void of higher air content in a cube was not done due to

geometrical constraint.

Attempts had been made to back up the findings of numerical method with

experimental data by using different-sized bubbles with the same porosity. The method of

varying the average size of air bubbles was suggested to be varied using different foam

density. However, it was found to be hard to control the density of foamed concrete in

that way and moreover, the specimens obtained were of different density. Thus, the

thermal conductivity results obtained would not only be due to the effect of varying the

bubble size, but it would also be interfered by the effect of density. Hence, these attempts

did not work out well.

Other suggestions to vary the size of air bubbles in foamed concrete of the same

porosity would be to use different-sized polystyrene beads. However, due to

unavailability of the materials and lack of time, the tests could not be carried out.

5.3 Models to predict effective thermal conductivity, keff

5.3.1 Multi-variable regression method

A multi-variable regression model is useful for a quick estimation of thermal

conductivity of other design mix of foamed concrete that are within the range of

the experimental results. The statistical model to estimate the thermal

conductivity, k (W/m.K) for foamed concrete, with specific gravity ranging from

0.5 to 2.0, is given by:

112

k28 days = 0.544 – 0.005076x1 – 0.300x2 + 0.000259 x3 (5.1)

where x1 = w/c ratio of the foamed concrete sample

x2 = foamed content of the foamed concrete sample (%)

x3 = temperature of foamed concrete sample (K)

This equation is an empirical model to approximate the thermal performance of

foamed concrete when its w/c ratio, foam content and operating temperature are known.

The predicted values from this empirical model have a percentage root mean square error

of 6.98 %. Figure 5.10 is a scatter plot which compares the experimental thermal

conductivity value with the predicted one using Equation 5.1. The graph shows that the

predicted values provide a reasonable estimate for the corresponding experimental k

values as the correlation coefficient (R-squared value) is 0.9442 which is quite close to 1.

However, it can be observed from Figure 5.10 that Equation 5.1 underestimate thermal

conductivity value of foamed concrete with too low or too high foam content.

113

R2 = 0.9442

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500

Experimental thermal conductivity, k (W/K.m)

Pre

dic

ted

l th

erm

al co

nd

uc

tivit

y, k (

W/K

.m)

Line of Equality

Figure 5.10: Scatter plot illustrating the relationship between the predicted k value using multi-

variable regression method and experimental k value

5.3.2 Analytical models

Analytical models can offer fast results of keff of foamed concrete with varying

foam content and mix proportions by solving equations derived from fundamentals with

certain realistic assumptions. Due to the reasons given in Chapter 2, three models were

chosen to be used for prediction of thermal conductivity of foamed concrete. They are

namely: 1) geometric model, 2) Assad model, and 3) Self-consistent model. However, it

is important to verify the predicted values from these three analytical models chosen with

known experimental values to test which are the ones that can offer close results.

The three analytical models to be tested are calculated by inputting the porosity of

the foamed concrete and also the thermal conductivities of the solid matrix and air. The

114

thermal conductivities of the solid matrix of different water-cement ratio to be used in the

different analytical models are obtained from the experimental results of thermal

conductivity of the pure cement paste, namely Mixes C1, C2 and C3. Thermal

conductivity of air at a temperature of 25 oC is taken to be 0.028 W/m.K.

Table 5.5 shows the calculated results from the analytical models and also the

experimental values of the respective samples at a mean temperature of 25 oC. Figure

5.11 shows the comparison of predicted values of the three different analytical models

with experimental results. Estimation of thermal conductivity values using geometric

model shown in Equation 2.10 was not able to predict thermal conductivity values of

foamed concrete as obtained from the experiments as can be observed from the high

percentage error in Table 5.5.

Table 5.5: Comparison between predictions from analytical models and experimental results

Geometric Model Assad Model Self-consistent

Model

Experimental values (25

Deg C) Sample

air (%)

w/c

k value (W/m.K)

% error

k value (W/m.K)

% error

k value (W/m.K)

% error k value (W/m.K)

Mix F3 25 0.45 0.2494 32.71 0.3373 9.01 0.3647 1.61 0.3707

Mix F1 50 0.45 0.1174 47.62 0.2146 4.23 0.2305 -2.87 0.2241

Mix F2 70 0.45 0.0642 59.24 0.1495 5.13 0.1401 11.08 0.1576

Mix F4 50 0.35 0.1278 49.06 0.2335 6.92 0.2509 0.00 0.2509

Mix F5 50 0.55 0.1171 39.43 0.2067 -6.88 0.2140 -10.64 0.1934

115

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Experimental thermal conductivity, k (W/K.m)

Pre

dic

ted

l th

erm

al co

nd

uc

tivit

y, k (

W/K

.m)

Geometric Model

Assad Model

Self-consistent Model

Line of Equality

Figure 5.11: Comparison of prediction from different analytical models with experimental results

On the other hand, the Assad model (Goual et al., 1999), which is an empirical

relationship that is very similar to the geometric mean equation, was able to obtain

predicted values of thermal conductivity much closer to experimental values. Assad also

found that the results obtained using geometric model was unable to give good

predictions and hence he proposed the Assad model which is given by the relationship as

shown in Equation 2.11. By choice of the average value of m = 0.60ε where c= 0.55 for

foamed concrete, this model was used to predict the mean effective thermal conductivity

within an error of less than ± 9%. This model allows some flexibility to choose an

appropriate value for the parameter, m (= cε) to model the effective thermal conductivity

of a two-phase material. Assad model states that c 1, however in this case, c was taken

to be much lower than 1.

116

The third model used which is the self-consistent model from Equation 2.14 was

also able to predict closely the thermal conductivity of the foamed concrete of different

w/c ratio and also porosity. The errors between the results obtained from self-consistent

model and experimental values are within 11%. The reason that self-consistent model

was a fairly good prediction model could be because it assumes a concentric model that

does not restrict the volume fraction of spherical air bubbles, thus enabling thermal

conductivity with high air content to be predicted closely as well.

Boutin (1996) also used the self-consistent method to determine the thermal

conductivity of autoclaved aerated concrete (AAC). Boutin showed that this method is

efficient for autoclaved aerated concrete as its microstructure contains very different-

sized pores. The predicted thermal conductivity obtained using the self-consistent method

was reported to be in excellent agreement with the experimental data as mentioned in

Section 2.6.6 in Chapter 2. Thus, it showed that self –consistent method can be used to

predict effective thermal conductivity fairly accurately for aerated concrete with macro-

pores like auto-claved aerated concrete and foamed concrete.

5.3.3 Numerical method using FLUENT

Using numerical method allows a different geometry of air bubbles to be

modeled fairly readily to study the shape effect. For example, air bubbles can be modeled

as spheres or cubes in GAMBIT which is the pre-processor of FLUENT. More complex

geometries like effect of having different-sized air bubbles in a model or having air

bubbles arranged in various ways on keff can be analyzed by first modeling in GAMBIT

117

and then analyzing in FLUENT. These more complex geometries may be much harder to

achieve in analytical methods where simpler models are used.

a) b)

c) d)

Figure 5.12: FLUENT models with varying air contents (spherical air bubble) a) 10 %, b) 25 %, c) 35

% and d) 45 %

In Figure 5.12, different volumes of air inside a cement matrix are modeled

using spheres to investigate the effectiveness of using FLUENT to predict thermal

conductivity of foamed concrete with different foam content. However the disadvantage

of modeling air bubbles in a cube as spheres is that there is a maximum amount of air

void allowed due to the limitation of the size of a spherical air bubble inside a cube. Thus,

the maximum foam content used is 45 %. The dimension and properties of the cement

matrix modeled were constant throughout.

Figure 5.13 shows the plot of keff of foamed concrete at different air volume

against thermal conductivity of cement matrix. The keff of foamed concrete cannot be

lower than thermal conductivity of air which was taken as 0.028 W/m.K, which means

that any value of keff which is lower than 0.028 is not meaningful. Thus, the straight lines

118

on the graph in Figure 5.13 have their lowest point imposed at 0.028. The ratios of keff /

thermal conductivity of cement matrix for various air contents were obtained from the

gradients of the functions in Figure 5.13.

When air bubbles are modeled as cubes, higher air contents can be modeled.

Figure 5.14 shows the models of foamed concrete with different air content up to 70 %

being used. For a particular air content used, the thermal conductivity of the cement

matrix used is also varied and analyzed in FLUENT to find out its effect. The result is

plotted in Figure 5.15. To test the effect of modeling different-sized air bubbles in

different geometrical position, analysis is done for the models shown in Figure 5.16.

Effect of thermal conductivity of cement matrix on the effective thermal conductivity of

foamed concrete

y = 0.9039x + 0.0036

y = 0.5773x + 0.0128

y = 0.4573x + 0.0162

y = 0.7019x + 0.0094

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Thermal conductivity of matrix (W/m.K)

Eff

ecti

ve t

herm

al co

nd

ucti

vit

y (W

/m.K

)

35% Foam content

(Spherical air bubble)

0% Foam

content

10% Foam content (Spherical

air bubble)

45% Foam content

(Spherical air bubble)

25% Foam content

(Spherical air bubble)

Figure 5.13: Plot of thermal conductivity of foamed concrete at different air content against thermal

conductivity of cement matrix (where air is modeled as a sphere)

119

a) b)

c) d)

Figure 5.14: FLUENT models with varying air contents (cubic air bubble) a) 10 %, b) 25 %, c) 45 %

and d) 70 %

Effect of thermal conductivity of cement matrix on the effective thermal conductivity of

foamed concrete

y = 0.223x + 0.0218

y = 0.8923x + 0.0042

y = 0.6846x + 0.0102

y = 0.4594x + 0.0161

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Thermal conductivity of matrix (W/m.K)

Eff

ecti

ve t

herm

al co

nd

ucti

vit

y (W

/m.K

)

25% Foam content (cubic

air bubble)

0% Foam

content

10% Foam content (cubic air

bubble)

45% Foam content (cubic

air bubble)

70% Foam content (cubic

air bubble)

Figure 5.15: Plot of thermal conductivity of foamed concrete at different foam content against

thermal conductivity of cement matrix (air is modeled as a cube)

120

a) b) c)

Figure 5.16: FLUENT models with a) 25 % air content using mixed-size spherical air bubbles; b) 25

% air content using mixed-size spherical air bubbles with of different size combination of air

bubbles.c) 35 % air content using mixed-size spherical air bubbles (with the same arrangement of air

bubbles as (a));

The FLUENT analysis results show a decrease of thermal conductivity with an

increase in air content in the cement matrix as plotted in Figure 5.13 and Figure 5.15. It

can be observed that the keff of foamed concrete is linearly related to the thermal

conductivity of cement paste. Thus, the ratio of effective thermal conductivity/ thermal

conductivity of cement matrix for a particular air content will be a constant. The ratio of

effective thermal conductivity of foamed concrete/ thermal conductivity of cement matrix

has been calculated as a function of volume fraction as shown in Figure 5.17. This figure

shows that numerical method employing FLUENT software can be used to predict the keff

of foamed concrete with different foam content quite accurately, especially for foamed

concrete with lower foam content.

For air content of up to 45 %, it was found that both keff obtained using FLUENT

software are very similar for air bubbles modeled as spheres and cubes. Beyond 45 %,

the comparison cannot be made because of the limitation of the volume of spherical air

bubble in a cube. Prediction of thermal conductivity of foamed concrete with air bubbles

modeled as cubes and containing high air contents of 70 % was shown to be slightly

121

lower than the experimental result as shown in Figure 5.17. This could show that when

the volume fraction of the discrete phase of air voids is low (below 45 %), the shape

assumed for the disperse particles is not of consequence.

For the range of air content of up to 35 % investigated, keff of the foamed concrete

models using spherical air bubbles or cubic air bubbles or mixed-sized spherical air

bubbles with different arrangements are very similar as shown in Figure 5.16. The

arrangement or space location of air pores, different combinations of pores of different

sizes; and shape, size and thickness of interporous partition did not appear to affect the

keff of foamed concrete significantly for the range of air content investigated. This implies

that keff is influenced mainly by the volume fraction of the air bubbles instead of by the

arrangement of different combinations of air voids of varying sizes and shape of the air

bubbles.

The curve in Figure 5.17 is the model proposed to correlate effective thermal

conductivity (keff), thermal conductivity of the cement matrix (kmatrix) and percentage

volume of air. It is obtained by using results derived from FLUENT numerical analysis in

this research project. It normalizes effective thermal conductivity by thermal conductivity

of the cement matrix on the y-axis.

Experimental results found in the current research on foamed concrete and

polymer-modified foamed concrete were used to verify the model proposed.

Experimental values were found to fall closely to this curve. Experimental results from

NUS in-house data done on foamed concrete without sand using Guarded Hot Plate

apparatus was also plotted on the same axis. They were also shown to fall reasonably

122

close to the curve. Results from thermal conductivity of litebuilt® foam3 were found to fit

the model proposed.

Analytical models proposed by other researcher to predict keff were also plotted on

the figure. Figure 5.17 shows that results obtained from self-consistent model (Hashin,

1968) and Assad model (Goual et al., 1999) fall closely to the curve that represent the

model proposed. However, results found using the geometric model (Woodside and

Messmer, 1961) fall quite far below the curve, showing that this method underestimated

keff quite significantly.

When volume of percentage of air, ε (%) is near to 100, the value of k/kmatrix

approaches zero since the composite would be mainly air which has the thermal

conductivity value of air of 0.028 W/m.K. that is close to zero. Thermal conductivity

results predicted by analytical models like self-consistent model gave higher values at

very high foam content. However, the proposed model is able to predict thermal

conductivity of foamed concrete more accurately, especially at very high foam content.

Thus, the proposed model which is well-verified by analytical models as well as

experimental data from current and other researches provides a simplified and user-

friendly equation as shown in Figure 5.17. This equation is useful to predict thermal

conductivity of foamed concrete when thermal conductivity of cement matrix and volume

fraction of air is known.

123

k/kmatrix (25 deg C) vs Volume percentage of air

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 10 20 30 40 50 60 70 80 90 100

Volume percentage of air, ε (%)

k/k

matr

ix

Experimental results (foamed concrete without polymer)

Experimental results (foamed concrete with polymer)

Experimental (foamed concrete: NUS in-house results)

Experimental value (litebuilt foam)

FLUENT results (spherical air)

FLUENT results (cubic_air)

FLUENT results (mixed air bubble sizes)

Self-consistent method (Analytical: Hashin, 1968)

Geometric model (Analytical:Woodside and Messmer,1961)

Assad Model (Analytical Model)

Proposed Model

Poly. (Proposed Model)

Figure 5.17: Ratio effective thermal conductivity of foamed concrete/ thermal conductivity of matrix

versus volume fraction of air.

It can also be used in designing work as well. For a certain design k value of

foamed concrete, the designer can decide on a percentage of air to be used and from the

equation, thermal conductivity of the matrix can be obtained. Since relationship of

thermal conductivity of cement matrix and w/c ratio is known from Figure 5.3, w/c ratio

of the design mix can be obtained as well. Thus, design mix of foamed concrete can be

obtained easily to cater for different applications.

5.4 Compressive Strength

Compressive strength results for the various foamed concrete and cement paste

mixes measured after 7 and 28 days curing are tabulated in Table 5.6. The sample

designation number and the mix design can be found in Table 3.2.

124

Table 5.6: 7- and 28- day compressive strength of foamed concrete and cement paste

Mix Designation

Fresh Density (kg/m3)

Compressive strength -7 days (MPa)

Compressive strength -28 days (MPa)

F1 1000 6.59 9.57

F2 550 0.96 1.43

F3 1440 19 29.36

F4 1070 8.43 11.87

F5 9000 4.07 6.14

C1 1860 40.63 57.31

C2 1980 58.08 82.97

C3 1760 33.96 43.59

5.4.1 Effect of density and age

Figure 5.18 shows how compressive strength of foamed concrete changes with its

specific gravity. The trend shows that compressive strength of concrete is highly affected

upon the density of the concrete. When density decreases, compressive strength decreases

as well. This is because compressive strength can be significantly influenced by the pore

structure of the air pores and the mechanical condition of pore shells. When density is

reduced, larger macropores are formed which led to a significant drop in compressive

strength. The increase in compressive strength of foamed concrete from 7 days to 28 days

is about 30 %.

125

Comparison of the effects of Specific Gravity on Compressive Strength of Foamed

concrete at 7 and 28 days

6.59

19.00

40.63

0.96

57.31

29.36

9.57

1.43

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0 0.5 1 1.5 2

Specific Gravity of Fresh Concrete

Co

mp

res

siv

e S

tre

ng

th (

MP

a)

(7 days)

(28 days)

Figure 5.18: Graph of Compressive strength of foamed concrete vs specific gravity of fresh concrete

5.4.2 Effect of foam content

From Figure 5.19 and Figure 5.20, it can be shown that compressive strength of

foamed concrete and polymer-modified foamed concrete decreases with increasing foam

content. Compressive strength of concrete is also highly dependent upon the foam

content of the concrete. When the amount of foam increases, compressive strength

decreases quite drastically. There is less cement paste to surround the air voids thus

causing the air voids to coalesce and the average air void size to increase. Thus, foamed

concrete with high air content would experience higher tendency of coalesce of air-voids,

leading to larger macro pores and a significant drop in compressive strength.

126

Effects of foam content on Compressive strength of Foam concrete (7 and 28 days)

0.96

40.63

9.57

29.36

57.31

6.59

19.00

1.43

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Foam content (%)

Co

mp

res

siv

e S

tre

ng

th (

MP

a)

7 days

28 days

Figure 5.19: Graph of Compressive strength of foamed concrete vs foam content of foamed concrete

Graph of Compressive strength vs foam content

23.99

5.69

1.060

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90

Foam content (%)

Co

mp

res

siv

e s

tre

ng

th (

MP

a)

Foamed concrete with polymercontent of 10 % of cementitiousmaterial

Figure 5.20: Graph of Compressive strength of polymer-modified foamed concrete vs foam content

of foamed concrete

Figure 5.21 shows that air void size increases with foam content in foamed

concrete. It can be observed that the foamed concrete with polymer content of 10 % by

127

weight of cementitious materials has higher air void size than the unmodified foamed

concrete. This explains the trend of lower compressive strength in foamed concrete with

polymer added.

Effect of foam content on average air bubble size

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 20 40 60 80 100

foam content (%)

Avera

ge a

ir v

oid

siz

e (

mm

) No polymer added,

w/c=0.35

Additional polymer

content = 10 % of

cementitious materials,

w/c=0.35

Figure 5.21: Effect of foamed concrete on average air bubble size of foamed concrete

5.4.3 Effect of water-cement ratio

The effect of water-cement ratio on compressive strength was investigated. Figure

5.22 shows that higher w/c ratio brings about a lower compressive strength of the foamed

concrete due to less cement hydration products with lower amount of cement used.

128

Effects of w/c on Compressive strength of Foam concrete (7 and 28 days)

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

w/c ratio

Co

mp

res

siv

e S

tre

ng

th (

MP

a)

7 days

28 days

Figure 5.22: Graph of Compressive strength of foamed concrete vs water-cement ratio of foamed

concrete (50 % foam content used)

5.4.4 Effect of volume fraction of polymer

There is also a slight decreasing trend in compressive strength as the amount of

polymer incorporated into foamed concrete is increased as shown in Figure 5.23. This

could be due to an increase in air void size due to the effect of increasing polymer content

as shown in Figure 5.24. The air void results were obtained by using the microscopy

method as described in Section 3.3.6 in Chapter 3.The compressive strength of acrylic-

modified foamed concrete is slightly lower than that of unmodified foamed concrete. A

decrease in the 28-day compressive strength is, on average, 15.0 % and 20 – 35 % at a

polymer-cement ratio (P/C, as solid polymer content by mass of cement) of 5 % and 10-

20 %.

129

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25

Polymer content (% of cementitious material)

Co

mp

res

siv

e s

tre

ng

th (

MP

a)

Figure 5.23: Graph of Compressive strength of polymer-modified foamed concrete vs polymer

content (50 % foam content used)

Effect of polymer content on average air void size

0.174

0.2210.235

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20

Polymer Content (% of cementitious materials)

Av

era

ge

air

vo

id s

ize

(mm

)

Figure 5.24: Effect of polymer content on average air void size of foamed concrete

5.5 Modulus, Flexural tensile strength, Splitting tensile strength

Inclusion of polymer into foamed concrete has the effect of increasing the

splitting tensile strength and flexural tensile strength. However, Modulus of Elasticity is

130

reduced due to polymer being added. Results are tabulated in Table 5.7 and plotted in

Figures 5.25- 5.29.

Splitting tensile strength was found to be 10 to 18 % of compressive strength and

flexural tensile strength was found to be from 27 to 60 % of compressive strength for

different amount of polymer added. Increase in splitting tensile strength and flexural

strength of foamed concrete caused by adding polymer are attributed mainly to an overall

improvement in cement hydrate bond because of a decrease in w/c ratio and the high

tensile strength of polymer films present in material. Thus, modification of foamed

concrete mixtures with acrylic, results in increased flexibility of the hardened mortar and

concrete. The increase in flexibility of foamed concrete with polymer added can also by

observed by the decrease in modulus of elasticity with increasing amounts of polymer

added.

Table 5.7: Mechanical properties of polymer-modified concrete

Mix Designation

Foam content

(%) w/c ratio

Fresh Density (kg/m3)

Dry Density (kg/m3)

Splitting Tensile Strength (MPa)

Flexural Tensile(MPa)

Modulus of

Elasticity Polymer (kg/m3)

Foam (kg/m3)

PF1 50 0.35 1020 902.10 0.7894 2.0280 5.4600 35.4 33.5

PF2 50 0.35 960 868.41 0.9295 2.9175 3.3400 68.4 33.5

PF3 50 0.35 1000 896.32 0.8902 3.0090 3.1300 99.3 33.5

PF4 50 0.35 960 819.20 1.1533 3.7901 2.4267 128.2 33.5

PF5 20 0.35 1580 1293.51 2.4202 9.2130 2.1567 109.5 13.4

PF6 80 0.35 478 456.64 0.2260 0.5556

Can't be done (too

low) 27.4 53.6

131

2.4202

0.8902

0.2260

0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100

Foam content (%)

Sp

litt

ing

te

ns

ile

str

en

gth

(MP

a)

Foamed concrete with polymercontent of 10 % of cementitiousmaterial

Figure 5.25: Graph of splitting tensile strength of polymer-modified foamed concrete vs foam content

1.1533

0.9295

0.8902

0.7894

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20 25

Polymer content (% of cementitious material)

Sp

litt

ing

te

ns

ile

str

en

gth

(M

Pa

)

50 % foamedconcrete withpolymer

Figure 5.26: Graph of splitting tensile strength of polymer-modified foamed concrete vs polymer

content

132

9.213

2.9175

0.55560

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100

Foam content (%)

Fle

xu

ral

ten

sil

e s

tre

ng

th (

MP

a)

50 % foamed concrete with polymer

Figure 5.27: Graph of flexural tensile strength of polymer-modified foamed concrete vs foam content

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25

Polymer content (% of cementitious material)

Fle

xu

ral

ten

sil

e s

tre

ng

th (

MP

a)

Figure 5.28: Graph of flexural tensile strength of polymer-modified foamed concrete vs polymer

content (50 % foam content used)

133

5.4600

2.1567

3.34003.1300

2.4267

0

1

2

3

4

5

6

0 5 10 15 20 25

Polymer content (% of cementitious material)

Mo

du

lus o

f E

lasti

cit

y (

MP

a)

50 % foamcontent

Figure 5.29: Graph of modulus of elasticity of polymer-modified foamed concrete vs polymer content

5.6 Proposed alternative roofing systems to provide insulation for the flat roofs of HDB flats

5.6.1 Potential of foamed concrete as a roof insulator

As discussed in Chapter 2, using air gap as a thermal insulator for roofing

application may not be as effective as expected even though air has a very low thermal

conductivity of 0.028 W/m.K. Figure 5.30 shows the sketch of the HDB Secondary

Roofing system. The relationship between heat flux and thickness of foamed concrete (F3)

is found via FLUENT simulation as described in Section 4.4. It is superimposed on the

results of heat flux vs thickness of air gap (derived by FLUENT simulation and

experiments using heat flow meter) obtained by Chew (2005) as shown in Figure 5.31.

As can be seen from Figure 5.31, there exists an optimum thickness of air gap which

minimizes heat transfer. On the other hand, heat flux can be reduced further when the

thickness of foamed concrete gets larger and there is no limit like the case of air. Thus, it

134

shows that foamed concrete can be a more potential roof insulator as compared to air gap.

The U-values (thermal transmittance) of the two alternative roofing systems to provide

insulation for the flat roofs of HDB flats or other buildings would be presented in the

following sections.

Figure 5.30: Sketch of HDB Secondary Roofing System

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Thickness of insulation (cm)

He

at

Flu

x (

W/m

2)

Air (Experimental)

Air (Simulation)

Foamed concrete (Simulation)

Figure 5.31: Graph of heat flux vs thickiness of insulation

Ferrocement Roofing Slabs

Air Gap Air Gap

Main Roof Level 120mm Reinforced concrete

Concrete Stump

135

5.6.2 Proposed designs of roofing systems

The proposed designs of the two different alternative roofing systems are

described here. Figure 5.34 shows the results of U-value of each different roofing system

for varying thickness of insulation used. U-value is calculated using the formula given in

Equation 2.3 found in Chapter 2. The data calculated are shown in Appendix B. Two

different alternative roofing systems were investigated. Alternative A (shown in Figure

5.32) consists of a layer of foamed concrete (F3) with k = 0.37 W/m.K., foam content of

25 %, w/c of 0.45 and S.G of 2.5. This grade was chosen in order to comply with the

minimum grade of 30 MPa for structural concrete. The minimum thickness of foamed

concrete need to abide to the U-value of 1.2 W/m2K (value obtained from Table 1.1) is

24.5 cm. It serves as the main roof; there is no normal grade reinforced concrete beneath

it.

Alternative B (shown in Figure 5.33) consists of a layer of foamed concrete

overlaying a 120 mm thick reinforced concrete main roof. The minimum required

strength of foamed concrete used as insulation on roof system is 1.5 kN/m2 (or 1.5 MPa).

Taking into account some factor of safety, the minimum strength can be taken as 3 MPa.

The required strength is quite low because roof tops are generally only subjected to pure

compression and there is no bending. This mix of foamed concrete (with k = 0.19 W/m.K.

and an expected compressive strength of 5 MPa) which consists of 60 % foam content,

w/c of 0.45, S.G of about 0.8 is proposed for Alternative B. The minimum thickness of

foamed concrete for Alternative B roofing system needed to abide to the U-value of 1.2

W/m2K is 10 cm.

136

As shown in Figure 5.34, there is a certain limit to which how low the U-value of

the roofing system using air gap (Figure 5.31) can reach and its U-value exceeded the

required limit of U-value which is set at 1.2 W/m2K. Its U-value can only reach to

minimum of 2.155 W/m2K for roofing system using air gap as an insulator. On the

contrary, U-value can be further reduced for the few proposed alternative roofing systems

using foamed concrete when a larger thickness of foamed concrete is used. Thus, using

air gap as an insulator in roofing systems is not as effective.

Figure 5.32: Sketch of the new roofing system proposed using higher grade foamed concrete

(Alternative A)

Figure 5.33: Sketch of the secondary roofing system proposed using low grade foamed concrete

(Alternative B)

Foamed Concrete secondary roofing Slab

Main Roof Level (normal weight concrete)

B: k = 0.19W/m.K; strength ≈ 5 MPa; S.G.= 0.8

Main Roof Level (foamed concrete)

Foamed Concrete roofing System A: k = 0.37 W/m.K, Strength≈ 30 MPa S.G. = 1.44

137

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

2.80

3.00

3.20

3.40

3.60

3.80

4.00

4.20

4.40

4.60

4.80

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54

Thickness of insulation (cm)

U-v

alu

e (

W/m

2K

)HDB's current: Air gap in between ferrocement slab on top and RC slab below

Proposed Alternative A: Foamed concrete with k= 0.37 W/m.K.

Proposed Alternative B: Foamed concrete with k= 0.19 W/m.K on top of 120mm RC slab

Lightweight aggregate concrete mix with k = 0.8 W/m.K.

B: 11 cm

50 cmA: 24.5 cm

Figure 5.34: Graph of U-values of different roofing systems of an air-conditioned building against

thickness of insulation

The air space resistance, Ra, for air space beyond 100 mm is still 0.174 m2K/W

(Table 2.1b) as stipulated in the guidelines on ETTV of buildings by BCA (extrapolation

is not permitted), thus its thermal resistance did not increase even though a larger

thickness of air gap is used. According to Chew (2005), thermal resistance decreases

when air gap is too large. This is because airspace resistance to heat is dependent on not

only conduction, but also convection and radiation in and across the air space. Thus,

thermal resistance which is the measure of the resistance to heat transferred offered by a

certain component is increased when thickness of air gap is increased. Heat transfer

through conduction governs in the system until the optimum thickness is reached.

When the air gap is larger than the optimum thickness, its effectiveness as an

insulator will be diminished. This is due to the onset of convection currents when the

138

thickness of air gap gets too large as shown in Figures 2.21 to 2.24. The result shown is

derived assuming that there is no movement of air laterally through the air gap. However,

in reality, there can be additional movement of air due to wind through the openings at

the sides or holes caused by deterioration and this could further increase the heat transfer

from the exterior to the interior of the air-conditioned building.

When lightweight aggregate concrete using LECA with k = 0.8 W/ m.K. and S.G.

1.56 (Chew, 2005) was used as the insulation material, the minimum thickness of foamed

concrete needed to abide to the U-value of 1.2 W/m2K is 50 cm. This thickness is twice

the thickness of foamed concrete proposed in Alternative A. Moreover, the S.G of the

lightweight aggregate is much higher than foamed concrete, thus, the dead weight of the

roof would be very high. Using foamed concrete as the insulating material seemed to be a

more viable option on comparison.

Foamed concrete has much strength as an insulating material. The designer using

this material can make use of its good mechanical strength, lightweight property and low

thermal conductivity property to produce a wide range of densities and properties which

can vary to suit particular requirements. It is also a relatively cheaper option as compared

to many other thermal insulators. From the results, it seems that using foamed concrete as

a roofing insulation is feasible and its performance can be even better than using air as an

insulator.

5.6.3 Effect of moisture on design of roofing system

The result in Figure 5.34 is based on oven-dry foamed concrete. However, in

practice, the foamed concrete that will be cast on site will contain a certain percentage of

139

moisture. The thermal conductivity of foamed concrete will increase when it is wet. Since

moisture correction value for thermal conductivity of foamed concrete is not available,

thermal conductivity of each proposed mix is altered based on assumption that the

finding by Loudon (1983) that for every 1 % of moisture content, a moisture correction of

4 % in the keff of autoclaved aerated concrete would apply to foamed concrete.

32

16

29.5

24.5

11

15

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

0 2 4 6 8 10 12

Thickness of insulation (cm)

U-v

alu

e (

W/m

2K

)

Proposed Alternative A: Foamed concrete with k= 0.37 W/m.K.

Proposed Alternative B1: Foamed concrete with k= 0.19 W/m.K on top of 120mm RC slab

Figure 5.35: Effect of moisture content on the minimum required thickness of foamed concrete as

insulation

Thus, Figure 5.35 shows the thickness of insulation required to abide to the U-

value of 1.2 W/m2K that BCA has regulated versus moisture content in foamed concrete.

Since the thickness of foamed concrete needed as insulation is within reasonable limits,

Alternatives A and B can be considered as viable options to overcome the problems of

the roofing system used by HDB lately.

140

6 Conclusion and Recommendations

6.1 Conclusion

In this project, thermal conductivity values and the corresponding compressive

strength values of foamed concrete and also polymer-modified foamed concrete were

determined. The effect of various key factors like foam content, w/c ratio, polymer-

content on these two properties were investigated. This information will be useful to

engineers who need to design suitable structural or non-structural elements such as the

roofing system for which heat insulation is an important consideration. The minimum

thickness of the roof slabs that is required to comply with U-value limits set by BCA was

found. With the mix proportion and dimension of the elements known, the cost can be

well estimated.

Based on the findings for this research study, the following conclusions can be drawn:

1) Increasing the foam content in foamed concrete causes a decrease in the 28-day

compressive strength and also the thermal conductivity.

2) Increasing the water-cement ratio in foamed concrete reduces the 28-day

compressive strength and also the thermal conductivity.

3) Changing the air void size of foamed concrete while keeping the total amount of

air void constant at 25 % does not change its thermal conductivity value based on

numerical study using FLUENT software. Thermal conductivity of foamed

concrete is influenced mainly by the volume fraction of the air bubbles instead of

141

( ) 0098.10135.010425 +−×= − εε

matrixk

k

by the arrangement of different combinations of pores with varying sizes, shape

and size of the air bubbles when the volume fraction is sufficiently low.

4) Insulating property of polymer-modified foamed concrete was improved quite

significantly by almost 20 % when 20 % by weight of cementitious materials was

incorporated in the foamed concrete mix (denoted by PF4) as compared to

unmodified foamed concrete with the same foam content and w/c ratio.

Mechanical properties like splitting tensile strength, flexural strength of polymer-

modified foamed concrete were found to increase quite significantly. Its elastic

modulus decreased, thus allowing more elongation of the material. However,

water resistance was not too significantly increased and compressive strength was

found to be reduced by about 20 %.

5) Adding polymer to foamed concrete which has high foam content can increase the

stability of the air bubbles (or prevent air bubbles from collapsing) and it enables

foamed concrete of very low density to be produced.

6) A simplified and user-friendly equation,

(where k, kmatrix denotes thermal conductivity of foamed concrete and cement

matrix respectively and ε denotes volume percentage of air, %) was derived from

results using numerical analysis (via FLUENT software). It is useful to predict

thermal conductivity of foamed concrete. It was verified by experimental values

obtained in current research and also in other research, as well as values predicted

from two analytical models, namely self-consistent model and Assad model.

7) Foamed concrete is a more viable choice compared to air gap or lightweight

aggregate concrete as an insulation material on roofing systems. Two suitable mix

142

designs and thickness of foamed concrete as alternative roofing systems on top of

HDB or other buildings to replace the ferrocement secondary roofing system

while complying to the U-value of 1.2 W/m2K set by BCA have been investigated

and found feasible as follows:

a) Alternative A which consists of a single 29.5 cm thick layer of high

grade foamed concrete (F3: 25 % foam content, w/c of 0.45, S.G. of 1.44)

with thermal conductivity of 0.44 W/m.K. (assuming moisture content of

5 %) and compressive strength of about 30 MPa.

b) Alternative B which consists of a 15 cm thick layer of lower grade foamed

concrete (60 % foam content, w/c of 0.45, S.G of 0.8) with thermal

conductivity of 0.228 W/m.K. (assuming moisture content of 5 %) and

compressive strength of about 5 MPa on top of a 12 cm thick reinforced

concrete slab.

6.2 Recommendations for Future Research

In this project, the effect of air void size while keeping air void fraction constant

is studied using numerical method only. Experiments can be done to find out the effect to

verify the numerical results found using FLUENT modeling. It can be done by

introducing polystyrene beads of singular size into cement paste to simulate “foamed

concrete with single-sized air bubbles” and testing the thermal conductivity of using

different sizes of polystyrene beads for different concrete specimens.

As moisture will affect the thermal insulation performance of any concrete greatly

during its application, the water resistance performance of the polymer-modified foamed

143

concrete is still not good enough for water-proofing membrane to be eliminated.

However, a higher percentage of polymer of about 30 % or 40 % (weight of cementitious

materials) could be added to foamed concrete to further reduce its water absorption

instead of a maximum of 20 % used in this study. A roofing system which is devoid of

water-proofing membrane can be proposed with a suitable grade of foamed concrete that

has sufficiently high water-resistant capability.

This study deals only with thermal conductivity of foamed concrete and polymer-

modified foamed concrete. Lightweight aggregates like LECA, perlite and vermiculite

could be added into foamed concrete in further research to improve the compressive

strength level and yet not compromise on the thermal conductivity of the lightweight

aggregate foamed concrete.