The thermal conductivity of fibre-reinforced concrete

The thermal conductivity of fibre-reinforced concrete

CEMENT and CONCRETE RESEARCH. Vol. 4, pp. 497-509, 1974. Pergamon Press, Inc. Printed in the United States. THE THERMAL CONDUCTIVITY OF FIBRE-REINFOR...

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CEMENT and CONCRETE RESEARCH. Vol. 4, pp. 497-509, 1974. Pergamon Press, Inc. Printed in the United States.

THE THERMAL CONDUCTIVITY OF FIBRE-REINFORCED CONCRETE

D.J. Cook School of Civil Engineering, University of New South Wales, Sydney, Australia and C. Uher School of Physics, University of New South Wales Sydney, Australia

(Refereed) (Received Oct. 5, 1973; in final form Feb. 28, 1974) ABSTRACT The effect of copper and steel fibre inclusions on the thermal conductivity of mortar and concrete is investigated. The experimental technique is based on the conventional steady-state method using desiccated specimens. The results indicate that copper fibres significantly increase thermal conductivity while steel fibres have a lesser effect. Vibration of the fresh concrete, during specimen manufacture, produces some fibre alignment. As a result, it is found that theoretical methods based on the assumption of a random fibre distribution under-estimate the experimental values. ZUSAMMENFASSUNG Der Einfluss von Einschl~ssen von Kupfer-und Stahlfasern auf die W~rmeleitfahigkeit von M~rtel und Beton wurde untersucht. Die Messungen wurden mit Hilfer der ~blichen station~ren Methode an getrockneten Proben ausgef~hrt. Die Ergebnisse zeigen, dass Kupferfasern die Warmeleitfahigkeit erheblich erh~hen, w~hrend Stahlfasern einer kleinern Einfluss haben. Wenn der frische Beton wahrend der Herstellung der Proben Vibrationen unterworfen wird, richten sich die Fasern einigermassen aus. Dies hat zur Folge, dass theoretische Berechnungen, die auf einer ungeordneten Verteilung beruhen, Kleinere Werte liefern, als den Messungen entspricht.

497

498

Vol. 4, No. 4 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE Introduction In r e c e n t

years,

many

the b e n e f i c i a l

effect

of short d i s p e r s e d

and

flexural

strengths,

of concrete. on fibre

in c o n c r e t e ivity. this

fatigue

Romualdi

concrete, could

suggested

fibres

(4),

on the tensile and d u c t i l i t y

dispersed

to i n c r e a s e

knowledge

shown

in one of the early papers

that r a n d o m l y

also be used

have

fibres

its thermal

conduct-

little w o r k

has been done

is not always

a significant

in

area.

property

thermal

nuclear

conductivity

of concrete,

is important. power

stations,

biological

released

in the

significant

which

shield.

shield

where

structures

such as g r a v i t y

conductivity or c o n t a i n indicated

facilities,

is v e r y d e p e n d e n t

that

that

approximately Since p a p e r was thermal prior

For other

(for the

the o b j e c t to study

to m e a s u r e m e n t . the same

between

fibre

and c o m p a r e d

on w h e t h e r

aspect

content with

and m a s s

the thermal

of that w h e n porous

of fibre

Two types were

and thermal

the m o i s t u r e Jakob

moisture described

m a y be content). in the

to w e i g h t

copper

conductivity

relationships

on equilibrium

and steel,

in c o n c r e t e

Experimental

content

(6)

type and v o l u m e

was dried

placed

and T h o r n e

conductivity

of fibre,

up to 8%.

are a i r - f i l l e d

conductivity

materials,

same v o l u m e t r i c

theoretical

its thermal

by C a m p b e l l - A l l e n

the c o n c r e t e

ratio,

"the flux

Other

supports

the pores

of the i n v e s t i g a t i o n

concentrations

stresses.

m u s t have a

otherwise

and as such

in thermal

the e f f e c t

conductivity,

in v o l u m e

one half

the r e d u c t i o n 65%

thermal

could be s i g n i f i c a n t

furnace

in the dry c o n d i t i o n

20% by volume.

suggested

Research

was about

high

dams.

is a p o r o u s m a t e r i a l

moisture.

of c o n c r e t e

large

is

can cause

is v e r y restricted". stresses

in

by the

of the r a d i a t i o n

of 1.73 W / m ° C

it

indicated,

is a b s o r b e d

that the c o n c r e t e

thermal

launch

where

(5) have

and hence

suggest

are r o c k e t

Concrete

radiation

gradients

attenuated

structures

and Thorne

The e n e r g y

in excess

can be safely

applications

in the form of heat w h i c h

and Thorne

conductivity

concrete

are c e r t a i n

incident

temperature

Campbell-Allen thermal

there

As C a m p b e l l - A l l e n

concrete

with

(1,2,3)

characteristics

and M a n d e l

To the authors'

While

was

investigators

and m o r t a r

relationships

were

obtained

determined

on the

Vol. 4, No. 4

499 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

basis of the t h e r m a l c o n d u c t i v i t y of the c o n s t i t u e n t m a t e r i a l s i.e., m o r t a r and fibre volume. Theory Notation A

A r e a n o r m a l to the heat flow

k

T h e r m a l c o n d u c t i v i t y of c o n c r e t e

km

Thermal c o n d u c t i v i t y of m a t r i x

ka

T h e r m a l c o n d u c t i v i t y of a g g r e g a t e

kll,k22,k33 L M

Cell thermal c o n d u c t i v i t y

in o r t h o g o n a l d i r e c t i o n s

Q

Distance between thermocouples ] - 3 /~ - V m Rate of heat flow

r

T h e r m a l r e s t i v i t y of c o n c r e t e

rll,r22,r33 Vf

Cell thermal r e s t i v i t y in o r t h o g o n a l d i r e c t i o n s

V o l u m e s of fibres per unit v o l u m e of c o n c r e t e

(or

mortar) Vm

V o l u m e of m o r t a r per unit v o l u m e of c o n c r e t e

(or

mortar) Vp

V o l u m e of paste per unit volume of c o n c r e t e

(or

mortar) T1 - T2

Temperature difference between thermocouples

T h e r m a l C o n d u c t i v i t y of C o n c r e t e C o n c r e t e can be c o n s i d e r e d a t w o - p h a s e m a t e r i a l w i t h e i t h e r the a g g r e g a t e

(coarse and fine)

in a c o n t i n u o u s paste phase or

the coarse a g g r e g a t e in a m o r t a r phase. it is p o s s i b l e

W i t h this a s s u m p t i o n

to e x a m i n e the v a r i o u s t h e o r i e s that have been

p r o p o s e d to p r e d i c t the thermal c o n d u c t i v i t y of t w o - p h a s e materials. M a x w e l l p i o n e e r e d the study of the thermal c o n d u c t i v i t y of two-phase materials.

He used p o t e n t i a l t h e o r y to d e r i v e an

e q u a t i o n for e l e c t r i c a l

c o n d u c t i v i t y of r a n d o m l y d i s t r i b u t e d

spheres in a c o n t i n u o u s medium.

By a n a l o g y the thermal c o n d u c t -

ivity of c o n c r e t e can be w r i t t e n

(7) as:

km k

+

2(1

-

V m)

1

=

-

~m)/(1

+

(1)

k

l -

(i - v m)

(l

_

"'" m

~aa )/(l

m

+ --~a )

500

Vol. 4, No. 4 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE An e q u a t i o n

of

similar

Campbell-Allen

and T h o r n e

(8) m e t h o d

lightweight

assumed

for

concrete

discontinuous particles

coarse

Campbell-Allen

11% of From

equation

could

slightly

less

that

i00

(which

conductivity

than

case

of the

and a

aggregate

equation

is:

thermal

the

apparent

conductivity

concretes

they

that M a x w e l l ' s purposes

derived

with

phase,

parameters. only

fibre

fibres

only

the

Their

because concrete

did

on p a r t i c l e

Cheng

the

was

matrix).

components

distribution

and V a c h o n require

of

of the

obtained

knowledge

a

of

provided

arrangement

and

the d i s c r e t e

(12)

however,

and V a c h o n ' s

phase

the m i x t u r e

distribution

spatial

shape

about

continuous

individual

solution,

of the

phase

spatial

not

Maxwell's

concluded

in a c o n c r e t e

of the

Cheng

which

of

relating

a parabolic

model

depend

conductivity

describe

extended They

the d i s c o n t i n u o u s

conductivity

continuous

to T s a o ' s

not

an e q u a t i o n

which

(i0)

particles.

did

for c o p p e r

phase

steel

for

and C r o s s e r

non-spherical

By a s s u m i n g

For

value

for p r e d i c t i o n

to the

bound

coarse

to p r e d i c t

be u s e d

two p h a s e s .

upper

phase

... (2)

also

(ii)

additional

authors

mortar

Their

it w a s

to two p a r a m e t e r s

solution

and E s d o r n ' s

accuracy.

is the

in the

former

the

results

larger

conductivity

able

experimental

conductivity

Tsao

with

their

to i n c l u d e

times

The

lattice.

were

(9) and H a m i l t o n

the

phase

by

Krischer

of a c o n t i n u o u s

in a c u b i c

the

the m i x t u r e

unless

derived

extended

concretes.

aggregate

and T h o r n e

tested.

analysis

been

2 kmk a (i - M) (2M - m 2) + k M + k (i - M) a m

k : km

Fricke

has

(5) who

to c o n s i s t

arranged

to w i t h i n

form

an

assumption.

equation

reduces

to:

k k= 1 The

specific

composite considered

the

problem

containing by L a k k a d ,

the m a t e r i a l cell

m (l.5Vf) ½

... (3) of the

randomly Miatt

to be c o m p o s e d

consisting continuous

of an phase.

and

Parsons

conductivity short (13).

of an a g g r e g a t e

inclusion The

thermal

distributed

cells

of a

fibres They

a fibre,

are

anisotropic

each

surrounded and

been

considered

of cells;

i.e.,

has

their

by

Vol. 4, No. 4

501 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

properties depend on the properties of the matrix and the fibre inclusion.

Upper and lower bounds were derived on the basis

that the composite is statistically isotropic.

The upper bound

is given by: 1 k = ~

{kll + k22 + k331 + 2 I k l l k 2 2 + k22k33 + kllk331 3 3 kll + k22 + k33

...(4)

and the lower bound by 4 I rllr22 + r22r33 + rllr33 I r = ~ rll + r22 + r33

-

i1 3

rll + r22 + r33 3

... (5)

The terms k22 and k33 represent the transverse thermal conductivity of the cell and from symmetry k22 = k33. For k = k22, the thermal conductivity is an absolute lower bound for a composite containing randomly dispersed fibres. k = kll the

Correspondingly when

(the longitudinal thermal conductivity of the cell),

thermal conductivity is an absolute upper bound. Although other approaches have been proposed for two phase

media,

only the theory and equations discussed above appear to be

relevant to fibre concrete. Experimental Measuring Technique There are two main methods of thermal conductivity measurement viz. transient or "probe" methods and the more conventional steady-state methods. and Jaeger theory

The former method is based on the Carslaw

(14) of temperature rise at a fixed point in an

infinite mass resulting from heating by a perfect line source. A detailed description of this method can be found elsewhere (15, 16).

The steady-state method is based on the establishment

of linear heat flow and the measurement of the corresponding thermal gradient.

The thermal conductivity is then determined

from the following: k =

QL A (T 1 - T 2)

... (6)

Each method has certain disadvantages when concrete is

502

Vol. 4, No. 4 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

considered.

With

the probe method,

that

the h e a t i n g

This

is p e r m i s s i b l e

geneous the

element

materials

specimen

will

the

separation

separation

would

practically The there

particle

in this

at t e m p e r a t u r e s

method

above

ambient

in m o i s t m a t e r i a l s

obtain

thermal

with

osmosis

of this

was

cylinder

in a brass

gradients

specimen

(referred

stable

and

was c h o s e n

but

to e l i m i n a t e

equilibrium loses,

the

for by s u s p e n d i n g necessary

as for samples

was a prism, and

37.5 m m

in the plug was The h e a t i n g

and c u r r e n t constant

was b o n d e d

and

thermal secondly

specimen

samples

to p r o d u c e

bonded

in the

similar

to the heat

by m o r e

differential Pairs

long,

cemented

centrally

sink.

The b o t t o m

heat

sink w h i c h

0.5°C per

thermocouples of holes w e r e

were cast

placed

into the hole

to the r e s i s t o r

source.

with

a hole, in one end

plug w i t h a r e s i s t e r

power was d e t e r m i n e d

cooled

than

75 x 75 x 150 mm,

A copper

applied

current

to a w a t e r

temperature

apart.

of

and the air evacuated.

the power

to as the top).

flux.

voltage

accounted

of m o r t a r

Firstly

to

i).

25 mm in d i a m e t e r

heat

cylinder

(17)

previously,

the e f f e c t

method

heat

osmosis

and A p p a r a t u s

The

enclosed

conductivity

to w e i g h t

Firstly,

of time r e q u i r e d

as m e n t i o n e d

the s t e a d y - s t a t e

and m e a s u r i n g

Specimen

not

particularly

thermal

was to study

and c o n d u c t i o n

losses w e r e

temperature

However,

was dried

convection

(see. Fig.

the m e t h o d

insulation

secondly,

two p r e c a u t i o n s .

the s p e c i m e n

Radiation

and

on the t h e r m a l

following

enclosed

thermal

investigation

Accordingly

to reduce

the r e q u i r e d

to m a k e

due to the length

equilibrium.

inclusions

the

size

has two m a i n d i s a d v a n t a g e s .

in o b t a i n i n g

occurs

concrete.

between

of the

9.5 m m m a x i m u m

large

times

the m a t e r i a l

investigation)

sensor.

applicable.

is d i f f i c u l t y

fibre

three

representative

with

be s u f f i c i e n t l y

steady-state

the o b j e c t

otherwise

is

For h e t e r o -

m u s t be at least

For c o n c r e t e

(as was used

to the t e m p e r a t u r e

materials.

not be s t a t i s t i c a l l y

material.

aggregate

be close

for h o m o g e n e o u s

size of the l a r g e s t

the p r o b e s

must

one of the a s s u m p t i o n s

24 hours.

placed

to p r o v i d e

by m e a s u r i n g using

the the

a very

end of the

sample

did not v a r y

in

Copper-constantan

in p r e c a s t

in two a d j a c e n t

holes

50 mm

faces of each

Vol. 4, No. 4

503 THERMAL CONDUCTIVITY, FIBER-REINFORCEDCONCRETE

CURRENT SOURCE

II•CONSTANT 8 II

I|

";

|| ||1|

; ~-

"~"~'B RASS CYLINDER WATER COOLED HEAT SINK FIG. Diagram

Schematic sample. deep,

One

set of holes was

thus m e a s u r i n g

points

in the

ration

two

specimen

given

error

later

pressures time

It was

was

fibre

about

concent-

for thermal

represent

of the a p p a r a t u s

from the

to reach

quoted

25 m m

at two d i f f e r e n t

For each

determinations.

the a v e r a g e

estimated

that

the

5%.

is shown

in Fig.

i.

system u s i n g a r o t a r y pump and w o r k i n g -2 i0 torr w e r e obtained. A typical

of a p p r o x i m a t e l y

required

section.

in this paper

diagram

evacuated

gradient

cast and the v a l u e s

in the v a l u e s

A schematic Air was

cross

were

of four e x p e r i m e n t a l overall

12.5 m m d e e p and the o t h e r

the t h e r m a l

specimens

conductivity

i of A p p a r a t u s

a steady-state

was

eight

hours.

Mix Details The

fibres

in diameter, materials cement,

for the m o r t a r

Nepean

Initially

it was

stiffened

the mix.

copper

in Table

intended

As w o u l d further Beyond

to

0.8 mm,

The c o n s t i t u e n t ordinary

size N e p e a n

Portland gravel.

The

1 below: "dilute"

be expected, addition

the m o r t a r

this

of fibres

a fibre v o l u m e by v i b r a t i o n

for the C1 c o n c r e t e

steel w i r e

were

9.5 mm m a x i m u m

compacted

and

25 nun long.

and c o n c r e t e

are g i v e n

and the

not be p r o p e r l y program

sand and

aggregate.

workability

drawn

and n o m i n a l l y

mix proportions

coarse

used were

action

with reduced

the

significantly

of 4% the m i x could

and the e x p e r i m e n t a l

series was not completed.

A second

504

Vol. 4, No. 4 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE TABLE 1 Mix Proportions

Water/Cement (by weight) Mortar

V

V

m

p

0.50

2.0

1.00

0.52

Concrete

C1

0.50

6.0

0.51

0.27

Concrete

C2

0.44

2.0

0.63

0.50

concrete

- M

Aggregate/Cement (by weight)

series

series was

(C2) w i t h

the

then designed.

incorporated

in this m i x

same paste

Fibre

volumes

and no p r o b l e m s

content

as the m o r t a r

up to 8% w e r e were

encountered

with

compaction. Steel 2, 4 and mixing will

and c o p p e r

8 percent

procedure

fibres,

were placed

was

similar

not be d i s c u s s e d

here.

approximately

24 hours

for 13 days.

T h e y were

until w e i g h t

equilibrium

removed

from the o v e n

to come to a m b i e n t

in v o l u m e

in c o n c r e t e

specimens

casting

then p l a c e d was

and

24 hours

temperature

before

in Ref.

were

The

The 2 and

stripped

stored

in an oven

achieved.

of ½, i,

and mortar.

to that d e s c r i b e d The

after

concentrations

in a fog r o o m at ii0 ° ~ 3°C

specimens

measurement

were

and a l l o w e d

(20 ° + 3°C).

Results The given

thermal

in Table

2.

for the v a r i o u s and 4.

conductivity

Thermal

Comparative

fibre

In these

of the m o r t a r

concentrations

figures,

theoretical

Conductivity

Material

values

TABLE 2 of M o r t a r

and c o n c r e t e s

of thermal are p l o t t e d graphs

conductivity in

using

and C o n c r e t e

Figs.2, equation

Series

Thermal Conductivity (desiccated) (W/m°C)

M

0.862

C1

1.620

C2

1.530

is

3 4

Vol. 4, No. 4

505 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

to Z

EXPERIMENT THEORY ( L A K K A D et a t )

'5"0 . . . . .

.0 t-'

oo

j

==

/

(.J

u

o ;'0 E L

E



~o~er_---

......--'"

St eet 5tee

~t emeXe

~eeeee m~ ~

~------'-I----- r2 3 4

1.o

p-

m

Fibre

I 5

Volume

- : - - . 6

x

t

.... 7

8

(%)

FIG. 2 C o m p a r i s o n of E x p e r i m e n t a l and P r e d i c t e d T h e r m a l C o n d u c t i v i t i e s for M o r t a r Series Iu GI LU tO

tJ

10"0 ,,l,W (u I. u o

EXPERIMENT

~7.5 .D

0

----'-

THEORY ( L A K K A D

et ol.)

E

~ 5"0 3

o

U

0

E

o

E

~,

a-s

Steel

L.

e"

10

-,---T---,---V---,2

3

Fibre

4

5

Volume

(%)

6

FIG. 3 C o m p a r i s o n of E x p e r i m e n t a l and P r e d i c t e d T h e r m a l C o n d u c t i v i t i e s for Cl C o n c r e t e Series

1

I 7

506

Vol. 4, No. 4 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

are

also

shown.

various

fibre

Densities

of the

concentrations

are

three materials given

in T a b l e

at the

3.

TABLE 3 Material Density

Density (Kg/m3)

m

Copper 0

Fibre

½

Volume

1

2

(%)

Steel

4

8

0

Fibre

Ii ~2

Volume

1

2

(%) 4

8

M

1990

2110

2050

2110

2350

2480

2055

2045

2100

2180

2250

2540

Cl

2325

2400

2325

2470

2325

-

2300

2425

2450

-

-

-

C2

2155

2210

2250

2350

2400

2590

2225

2230

2280

2280

2500

2700

Discussion The

addition

of c o p p e r

fibres

concentrations

significantly

of b o t h

and

mortar

is less,

as w o u l d

of c o p p e r

F r o m Figs. values steel

2,

3 and

mortar

is c o i n c i d e n t

with the

(18)

that

shown

randomness

of the

investigation

also

some

orientation.

This was

oriented heat

flow

values

strength.

the

long

determined

The

thermal

as it d r i e s advantage

out,

of

the

of h e a t

experimental on the b a s i s

conductivity

the a d d i t i o n

et al and

stated of

theoretical

fibre

thus

concrete

of s p l i t

and

noticeable

flow would

obviously

of a r a n d o m of c o n c r e t e previously.

fibres must

fibre

from

for

Fibres

in e x c e s s

the

had p r o d u c e d

specimen.

values

Hannant

anisotropy

prisms

vibration

the

equation

destroys

and p r o d u c e s

that

For

it a l s o

Edgington

particularly of

the

and V a c h o n ' s

values.

indicated

sides

as w a s

Cheng

fibres,

conductivity

experimentally.

Examination

in the d i r e c t i o n and g i v e

that

distribution

this

near

seen

obtained

thermal

steel

it can be

vibration

regard

using

of steel.

experimental

with

fibres

to

increase,

conductivity

that

of L a k k a d

fibre

thermal

times

concretes,

that

the

the

i00

4,

volumetric

since

those

and

under-estimates have

The

be e x p e c t e d ,

under-estimate fibre

increased

concrete.

is a p p r o x i m a t e l y

in s m a l l

of

those

thus facilitate

theoretical

distribution.

significantly

decreases

To be of p r a c t i c a l

therefore

increase

the

Vol. 4, No. 4

507 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

10"0

.,a

C..

i

o

E

IJ:

I-.

L

EXPERIMENT . . . . .

THEORY

e't a t )

(LAKKAD

o

>

i

7.5

5.0

__

o 2.5 E

S~e •

t,,.

(u ,,¢:

"-

1-0 , ~ - - , ~ - - - - - - r - - - q 0 1 Z

3

&

i

i

i

5

6

7

Fibre Volume (%) FIG. 4 C o m p a r i s o n of E x p e r i m e n t a l and P r e d i c t e d Thermal C o n d u c t i v i t i e s for C2 C o n c r e t e Series thermal c o n d u c t i v i t y of d e s i c c a t e d c e m e n t s to at least that level w h e r e the c o n c r e t e has a s i g n i f i c a n t v o l u m e t r i c m o i s t u r e content.

The three m a t e r i a l s used in this i n v e s t i g a t i o n ,

t a k e n from the fog r o o m at 14 days after casting, moisture

c o n t e n t s of 22.5%,

series r e s p e c t i v e l y .

Jakob

correction

(6) has s u g g e s t e d that the thermal can be o b t a i n e d by

the dry or d e s i c c a t e d thermal c o n d u c t i v i t y by a factor a p p r o p r i a t e

If C a m p b e l l - A l l e n and T h o r n e ' s c o n c r e t e are used,

to the v o l u m e t r i c m o i s t u r e content. (5) data for m o r t a r and d o l e r i t e

the factors are 1.92,

1.46 and

1.71 for the M, C1 and C2 series r e s p e c t i v e l y . same m u l t i p l y i n g seen

had v o l u m e t r i c

12.8% and 20.8% for the M, C1 and C2

c o n d u c t i v i t y of m o i s t p o r o u s m a t e r i a l s multiplying

when

(from Fig.

To achieve the

factors by the a d d i t i o n of fibres, 4) that for the C2 series,

1% c o p p e r fibres w o u l d be sufficient. be m a d e for the o t h e r series.

it can be

about 6.75% steel and

Similar comparisons

can

It is a p p a r e n t that c o p p e r fibre

i n c l u s i o n s i n c r e a s e the thermal c o n d u c t i v i t y well b e y o n d that of m o i s t c o n c r e t e or mortar.

Steel fibres,

on the o t h e r hand,

p r o d u c e i n c r e a s e s of only 25 - 50% and for g r e a t e r i n c l u s i o n

508

Vol. 4, No. 4 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

concentrations. To i n v e s t i g a t e

the range

and T h o r n e ' s

equation

conductivity

of the m o r t a r

and that

the thermal

3.46 W/m°C. C2 series

apparent thermal

(Equation

2),

was the

conductivity

For the Cl

series,

the ratio was

and the e r r o r

of a p p l i c a t i o n

that E q u a t i o n conductivity

same

assumed

that

the

for both c o n c r e t e

of the N e p e a n

k c a l c / k e x p was

0.92.

associated

it was

of C a m p b e l l - A l l e n

gravel

was

1.01 and for the

In v i e w of the a s s u m p t i o n s

with

the e x p e r i m e n t a l

2 gives

v e r y good

series

values,

estimates

made

it is

of the

of concrete.

Conclusions For the m a t e r i a l s conclusions i.

in this

investigation,

the f o l l o w i n g

can be made:

Metallic

fibre

of m o r t a r greater 2.

tested

inclusions

and concrete.

for copper

Compaction

of thermal

This

fibres

by v i b r a t i o n

the d i r e c t i o n

of heat

than

flow.

steel

as w o u l d

some

conductivity

is s i g n i f i c a n t l y

fibre

As a result

based

under-estimate

the thermal

increase

produces

conductivity

distribution

increase

be expected.

alignment

theoretical

on a r a n d o m

in values

fibre

the e x p e r i m e n t a l

values.

[email protected] The ance w i t h wire

authors

would

like to thank Miss

the c o m p u t i n g

Industries

Pty.

aspects

Ltd.

K. Low for her assist-

of the p r o j e c t

for g e n e r o u s l y

and A u s t r a l i a n

donating

the

steel

fibres.

References i.

S.P. 126

2.

Carson.

C. Ball,

Conc.

Romualdi

6_!i, 657 5•

and J.L.

G. Batson,

J.P.

J. Am.

Conc.

Inst.

Proc.,

68

J. Am.

Conc.

Inst.

Proc.,

68,

(1971).

J. Am. 4.

Rangan.

(1971).

W. Chen 933

3•

Shah and B.V.

Inst.

L. Bailey, Proc.,

and J.A.

69,

Mandel.

E. L a n d e r s 673

and J. Hooks.

(1972).

J. Am.

Conc.

Inst.

Proc.,

(1964).

D. C a m p b e l l - A l l e n

and C.P.

Thorne.

Mag.

Concrete

Res.

Vol. 4, No. 4

509 THERMAL CONDUCTIVITY, FIBER-REINFORCED CONCRETE

15, 6.

39

(1963).

M. Jakob. London

Heat Transfer,

A. Eucken.

8.

O. Krischer

9.

H. Fricke.

i0.

R.L. Hamilton

V.D.I.

Forschungsheft,

and H. Esdorn. Phys.

Rev.,

24,

and O.K.

12.

S.C. Cheng and R.I. Vachon.

13.

S.C.

Ind. Engng.

Lakkad,

Ing Wes.,

Chem.,

Ind. Engng.

53(5),

(1956).

Chem.,

1(3),

395

(1961).

J. Heat Mass Transfer.,

5, 1304

12,

J. Phys.

Press Oxford,

Conduction

England.

of Heat in Solids.

(1959).

E.F.M.

Van der Held and F.G. Van Drunen.

Grav.,

15 865

W. W o o d s i d e

D:

(1972).

H.S. C a r s l a w and J.C. Jaeger.

1688

i, 22

(1924).

B.B. Miatt and B. Parsons.

Phys.,

Clarendon

16.

575

(1932).

(1969).

Appl.

15.

and Hall,

(1963).

G. Tsao.

14.

~, 353

Forsh.

Crosser.

ii.

249

i, p. 91. Chapman

(1949).

7.

187

vol.

Physica's

(1949).

and J.H. Messmer.

J. Appl.

Phys.,

and J.B. Cliffe.

Soil Sci.,

32,

(1961).

17.

W. Woodside

18.

J. Edgington

and D.J.

Hannant.

Mater.

8_~7, 75

Constr.

(1969).

5, 89

(1972).