, 2012

( )

/

.

...

:

.

...

, 2012

( )

/

.

...

:

1. . , . ... ()

2. . , . ...

3. . , . ...

:

1. . , . ... ()

2. . , . ...

3. . , . ...

4. . , . ...

5. . , . . ...

6. . , ...

7. . , ...

. . (. 5343/1932, 202)

,

,

i

,

, . ,

, ,

. ,

, :

.

,

,

. ,

,

.

,

, . ,

K X B (KXB) ,

, ,

, .

(), ,

,

, . ,

(, ..),

, , ,

, ,

, , , .

, ,

,

,

.

,

,

,

- ( ),

- ( ) - (

) .

ii

,

-, ,

,

.

(),

,

.

- - ,

,

, .

,

. ,

,

- ,

. ,

GPRO (Gypsum PROperties). GPRO

.

,

- .

HETRAN (HEat TRansfer ANalysis),

,

, .

HETRAN

,

, . , - HETRAN

-

, GPRO.

iii

-

, ,

. ,

.

. ,

,

,

600 oC.

,

.

,

GPRO

, . GPRO

,

.

,

.

, HETRAN, GPRO,

. HETRAN

,

,

. , HETRAN

,

,

,

.

,

,

. ,

iv

-

, ,

.

,

, ,

- -. ,

.

v

Abstract

Fires in buildings form the main death and destruction cause during fires, despite the fact

that there are not first in frequency. The latter, creates the necessity for controlling and

preventing the fire spread inside buildings, firstly for the safety of human life, and secondly

for the safety of the construction. For that reason, each state establishes fire protection laws

and regulations, which can be distinguished in two main categories: active and passive fire

protection measures. Active fire protection measures aim to trace the fire inside a building, to

inform the inhabitants of the building and to attack the fire, in order to confine it and

finally quench it. On the other hand, passive fire protection measures aim to confine and

delay the fire spread inside of an ablaze building, in order to create enough time for building

evacuation and fire suppression.

Passive fire protection measures compose not only the modern, but also the necessary way

for the fire protection of a construction. On the other hand, Light Weight Construction (LWC)

continuously increases its share in construction due to aesthetic and design versatility, as well

as due to its very good mechanical, thermal, fire and anti-seismic behavior. Dry Wall Systems

(DWS), which are part of LWC systems, are widely used in buildings not only due to their

very good mechanical and anti-seismic behavior, but also due to their very good thermal

behavior under fire conditions. The latter, is mainly due to the fact that the walls (gypsum

boards, cement boards etc.), that DWS consist of, contain water in their crystal structure,

which, under high temperature conditions, is evaporated, absorbing significant heat

quantities from the fire, and thus, delaying the heat transfer through the assembly.

The main goal of this dissertation is the development of specialized computational tools,

in order to accurately predict the variation of the physical properties and the transfer

phenomena inside porous materials (structural elements), which are exposed to different

temperature conditions. Moreover, these computational tools are designed in order to be able

to be combined with detailed Computational Fluid Dynamic (CFD) codes. The frame for the

development of these tools is based on an integrated study, which is presented for the first

time in this dissertation, of the thermal behavior of a structural material which is exposed to

different temperature conditions, and demands the thorough examination of this behavior at

a micro-scale (micro-structure size level), meso-scale (structural element size level) and

macro-scale (building size level) size level.

At first, as part of the micro-scale level study of the thermal behavior of structural

elements, exposed to different temperature conditions, available computational methods

from the open literature, which are used for the determination of the kinetic parameters of

solid state reactions, are programmed. The developed computational tool can be used for post

vi

processing the Differential Scanning Calorimetry (DSC) measurements and for defining the

kinetic parameters of a solid state reaction that may occur when a structural element is

exposed to different temperature conditions.

The connection bond between the micro- and meso-scale size levels, when studying the

thermal behavior of a structural element exposed to different temperature conditions, is the

physical properties of the materials, which compose the element and need to be modeled. For

this purpose, an integrated system of algebraic equations, that defines the physical properties

of a porous material, is presented. In particular, the physical properties that are related to

heat and mass transfer through a porous material are modeled, using this system of

equations, as well as the kinetic parameters, obtained from the micro-scale level analysis. The

above system is programmed and a computational tool named GPRO (Gypsum PROperties)

is developed. GPRO is a general computational tool, which is capable of predicting the

variation of physical properties of a porous material, exposed to different temperature

conditions.

The next step of the integrated study of the thermal behavior of a structural element

exposed to different temperature conditions is the study at a meso-scale level. During this

dissertation, a computational tool, named HETRAN (HEat TRansfer ANalysis), is developed,

in order to predict the thermal behavior of a structural element, composed of multilayer

building materials, exposed to different temperature conditions. HETRAN code has been

developed to fill in the gap in existing computational tools regarding simultaneous heat and

mass transfer in multilayered porous materials, as it solves a system of partial differential

equations, capable of describing the one dimensional simultaneous heat and mass transfer

through porous materials. Finally, the meso-scale HETRAN code, takes into account the effect

of the micro-scale level study, by using the physical properties, obtained from the GPRO

computational tool.

The developed tools are validated and then used in order to simulate the different

physical-chemical processes that take place inside commercial gypsum boards, which are

basic elements of DWS, when they are exposed to high temperatures. Firstly, several DSC

measurements are performed, through which the theoretical background of these processes is

verified. Based on the DSC measurements, a simple system of algebraic equations is

developed, for the determination of the initial composition of a commercial gypsum board

and the energy absorbed or produced at the end of each process. Moreover, the developed

computational tool for the definition of the kinetic parameters of a solid state reaction is used,

in conjunction with the DSC measurements, in order to define the kinetic parameters of the

most important processes that take place inside a gypsum board at temperatures up to 600 oC.

Predictions of each reaction progress are compared with experimental data, revealing an

vii

excellent agreement. It is established that the obtained kinetic parameters can accurately

describe the physical-chemical processes, which take place inside a gypsum board at

temperatures up to 600 oC.

Thereinafter, these kinetic parameters are incorporated into GPRO code in order to

simulate the variation of physical properties of commercial gypsum boards, exposed to

elevated temperatures. The validation of GPRO is performed with experimental data

available from the literature and experimental data measured during the dissertation. Results

showed that the developed computational tool can accurately describe the variation of the

physical properties of a commercial gypsum board, exposed to elevated temperatures, and

confirms that it can be used for parametric studies, in order to improve the physical

properties of a gypsum board.

Finally, HETRAN code is used, in conjunction with GPRO code, in order to simulate the

thermal behavior of commercial gypsum board slabs and assemblies, which are exposed to

elevated temperatures. Predictions of HETRAN code are compared with experimental data

available from the literature, as well as with experimental data measured during the

dissertation, revealing the very good accuracy of the numerical results. Furthermore,

HETRAN code is used in order to assess the effect of several parameters, such as the heat and

mass transfer mechanisms inside the gypsum board porous structure, the heating rate and the

water vapor partial pressure, on the thermal behavior of gypsum boards under high

temperature conditions. Results showed that the developed computational tool can accurately

describe the thermal behavior of a commercial gypsum board or a DWS composed of gypsum

boards under fire conditions. Thus, it contributes not only to the theoretical study of the

different physical-chemical phenomena that take place inside a gypsum board when it is

exposed to elevated temperatures, but also to the design process, parametric study and

optimization of the material.

To sum up, the computational tools, which were developed in this thesis, are capable of

describing the thermal behavior of commercial gypsum boards, at micro- and meso-scale

level. Thus, they can be used in order to give a clear picture of how a gypsum board behaves,

during its exposure to high temperatures conditions.

viii

ix

,

.

2007 2011.

.

, ,

,

.

, ,

.

,

.

, ,

,

.

,

, , ,

, ,

, , ,

,

, ,

.

. ,

, ,

CT-METRE

. ,

-,

. ,

x

,

.

, Dr. Ghazi Wakili, EMPA

Materials Science & Technology,

, .

,

,

.

, ,

, , ,

, .

, .

.

2012

xi

..................................................................................................................................... I

ABSTRACT ..................................................................................................................................... V

................................................................................................................................ IX

..................................................................................................... XI

.................................................................................................... XVII

...................................................................................................... XXVII

.................................................................................................... XXXVII

1 ............................................................................................................................... 1

1.1 ..................................................................................................................... 2

1.2 ..................................................................................................................... 3

1.2.1 ................................................................................................ 4

1.2.2 ................................................................................................... 6

1.3 .................. 8

1.4 ........................................................................ 10

1.5 ................................................................................................ 12

1.6 .................................................................................................. 13

1.7 ....................................................................................................................... 16

2 ... 19

2.1 ................................................................................................................................ 19

2.2 - ................................................................................................................... 21

2.2.1 .................................................................. 22

2.2.1.1 ............................................................. 23

2.2.1.2 ............... 24

2.2.1.3 ........................................... 24

2.2.1.4 ....................... 25

2.2.2 ................................................................................................. 25

2.3 - .................................................................................................................... 26

xii

2.3.1 ................................................................................................... 27

2.3.2 ............................................................................................. 27

2.4 - .................................................................................................................. 28

3 .......................................... 31

3.1 ................................................................................................................................ 31

3.1.1 ............................................................................................................... 32

3.1.2 .................................................................................................... 32

3.1.3 ................................................................... 33

3.2 ........................................................ 35

3.2.1 .................................................................... 37

3.2.1.1 ...................................................................... 38

3.2.1.2 .................................................................................................................. 38

3.2.1.3 ........................................................................................................... 39

3.2.2 .............................................................. 40

3.2.2.1 ............................................................................................................... 41

3.2.2.2 ........................................................................................................ 43

3.2.3 -

................................................................................................ 45

3.2.3.1 .................................................................................. 45

3.2.3.2 ......................................................................................... 46

4 ............................................................................................... 49

4.1 ................................................................................................................................ 49

4.2 ........................................................................................... 50

4.2.1 ........................................................................................................................... 51

4.2.2 .......................................................................................................................... 51

4.2.3 ............................................................................................... 51

4.3 .......................................................................................................... 53

4.3.1 ........................................................................................................ 53

4.3.2 .................................................................................................................. 56

xiii

4.3.3 ........................................................................ 59

4.4 .................................................................................................... 60

4.5 ................................................................................. 60

4.6 ........................................................................ 63

5

.................................................................................... 65

5.1 ................................................................................................................................ 65

5.2

............................................................................................................................................. 67

5.2.1 .......................................................................................... 67

5.2.2 .......................................................... 69

5.2.3 ........................................................................................................... 70

5.3

............................................................................................................. 70

5.3.1 ........................................................................................... 72

5.3.2 .............................................................................................. 73

5.3.3 ......................................................................................... 73

5.4 .............................................................................................................. 73

5.5 HETRAN ................................................................................... 76

5.5.1 ........................................................................................................ 76

5.5.2 ............................................. 77

5.5.3 ................................................................................. 78

5.5.4 ........................................................................................... 79

6 ...... 81

6.1 ................................................................................................................................ 81

6.2 ................................................................................................... 82

6.2.1 .............................................................................................. 84

6.2.2 ................................................................................................ 86

6.3 / ...................... 87

xiv

6.3.1 ....................................................................................................... 88

6.3.2 ....................................................................................... 94

6.3.3 ............................................................................... 111

6.4 ................................................................................................. 120

7

..................................................................................................... 123

7.1 .............................................................................................................................. 123

7.2 .............................................................. 124

7.3 ....................................................................... 127

7.4 .......................................................................................... 128

7.4.1 .............................................................................................. 128

7.4.2 ........................................................................................................... 130

7.5 ................................................................................................. 134

8

..................................................................................................... 137

8.1 .............................................................................................................................. 137

8.2 .............................. 138

8.2.1 .............................................................................................. 138

8.2.2 ................................................................................... 139

8.3 GPRO ....................................................................................... 147

8.3.1 ................................................................................... 151

8.3.2 ........................................................................... 155

8.3.3 .................................................................................................... 156

8.3.4 , , .. 157

8.3.5 ............................................................................................ 159

8.4 ................................................................................................. 163

9

......... 165

9.1 .............................................................................................................................. 165

xv

9.2

........................................................................................................................... 166

9.2.1 ................................................................ 167

9.2.2 ........................................................................................... 168

9.2.2.1 ............................................................................................ 171

9.2.2.2 ............................................................................................. 172

9.2.2.3 ................................................................................. 175

9.3

...................................................... 177

9.3.1 ................................................................ 177

9.3.1.1 ........................................................................................................................... 180

9.3.2 ........................................................................................... 183

9.3.3 ............................................................................... 189

9.4

............................................................................................. 194

9.4.1 ......................................................................... 194

9.4.2 ................................................................ 196

9.4.3 ........................................................................................... 197

9.5 ................................................................................................. 201

10 ......................................................................... 205

10.1 .............................................................................................................................. 205

10.2 .......................................................... 206

10.3 ............................................................................... 208

10.4 ................................................. 210

10.5 ........................................................................................................................ 212

10.5.1 ............................................................... 212

10.5.2 ............................................................................... 212

10.5.3 ......................................................... 213

......................................................................................................................... 215

xvi

I .......................................................................................................................... 233

II ........................................................................................................................ 237

III ....................................................................................................................... 241

IV ....................................................................................................................... 245

V......................................................................................................................... 247

xvii

1

a

A - s-1

fA ..

a

b

iB

fB ..

wB

m-1 s

c

C J kg-1 K-1

0C

1C

fC ..

gC g kg m3

iC

Kc Kozeny

pC J kg-1 K-1

1 .. .

xviii

d m

D m2 s-1

e

E J m-3

aE J mol-1

f ..

f ..

F

.. s-1

0f

cf

f

G

g

,g

h J kg-1

ch W m-2 K

mh m s-1

Ph

j kg s-1 m-2

aEJ s

k W m-1 K-1

K m2

Tk [s-1]

L m

vL ,

2260000

J kg-1

xix

m kg

m / kg s-1

MW kg kmol-1

n

n

N

Dn

FN

GN

LN

Pn

pN m-3

RN

SN

tn

o

p Pa

P Pa

DSCP W kg-1

p

PDF

Pr Prandtl

PSD m-3

q W m-2

Q /

.. m-3

xx

fQ ..

r s-1

2R

gR , 8314 J kmol-1 K-1

S m2

Sc Schmidt

rs %

0,rs

..

1,rs

sats

t s

T K

u m s-1

U m2 K W-1

V m3

w

x m

X

BX m

y

y y()

z z()

0

xxi

m2 s-1

s-1

kg kg-1

H -

J kg-1

t s

m -

kg kg-1

Pa s

kg m-3

Stefan Boltzmann, 5.66910-8 W m-2 K-4

l

aE

g

mix

v

0

ph2

ph3

AH

xxii

air

amb

calc

cav

cbw

CC

CO

cond

conv

cr

CS

cyl

dc

dh

DH

diff

ds

E

ES

eff

eq

exp

f

F

fire

fm

g

xxiii

G

h

HH

i

in

j

kd Knudsen

l

L

m

M

MC

max

md

min

mix

MO

O

out

p

par

pres

pure

r

rad

ref

s

xxiv

S

sl

sp

sph

th

tot

d

CFD Computational Fluid Dynamics

DWS Dry Wall System

GPRO Gypsum PROperties

HETRAN HEat TRansfer ANalysis

KAS Kissinger-Akahira-Sunose

LWC Light Weight Construction

OFW Ozawa-Flynn-Wall

RSS

STR Starink

E

BA -B

xxv

-

-

xxvi

xxvii

1-1 2010 : ) [KARTER

M.J., 2011] ) [FIRE STATISTICS GREAT BRITAIN, 2011] ......................... 3

2-1 ........................................................................ 21

2-2 - : ) )

- .......................................................................................... 22

2-3 ...................... 23

2-4 - ( ) ............................................................ 27

2-5 - ........................................................................................... 29

3-1

: 1) , 2)

3) ............................................................................................................ 34

3-2 ) )

( 3-6)

........................................................................................................................................................ 42

4-1 ) ) ................ 50

4-2 .................................................................... 53

4-3 :

) , ) ) , ................ 55

4-4

............................................................................... 56

4-5

............................................................................................................. 56

4-6 ............................................................................. 57

5-1 ...................................................................................................... 68

5-2 .... 74

5-3 .............................. 75

5-4 ...................................................... 77

5-5 HETRAN ................................. 80

xxviii

6-1 ,

, : )

) ............................................................................................. 89

6-2 : ) ,

)

) ,

, ................. 91

6-3 ( )

( ) ,

40L ( = 2 K MIN-1) : ) )

........................................................................................................................................................ 92

6-4

................................................................................................................................ 93

6-5 : ) , )

)

.............................. 95

6-6 : ) , )

)

(

) ................................................................................. 96

6-7 : ) ( =

5 K MIN-1) ) (=10 K MIN-1) .................... 98

6-8 : ) )

.

(EA,LN(A))

,

................................................................................................................................... 99

6-9

N ,

- : )

(5 K MIN-1)

FRD ) (15 K MIN-1)

STR ........................................................................... 102

xxix

6-10 Y(): )

(

OFW), )

( FRD) )

.............................................................................................................. 103

6-11 - Y()

: ) )

................................................................................................................. 104

6-12 RSS N

: )

) ............................ 106

6-13 ()

(),

,

( 6-8): )

) (

) ..................................................................................................................... 107

6-14 ()

(),

,

( 6-10)

( ) ....... 110

6-15

: )

) .................................................. 113

6-16

( STR) ....................................................................................................... 114

6-17 ()

(),

,

xxx

( 6-14)

( ) ...... 115

6-18

: ) )

......................................................................................... 118

6-19

( STR) ....................................................................................................... 118

6-20 RSS N

................................................................................ 119

6-21 ()

(),

,

,

.... 120

7-1 GKB: ) )

............................................................................................................................................ 124

7-2 ) , ) )

(5MM) ........................................................................................................... 125

7-3 ................................................................... 126

7-4 ) , ) , )

)

........................................................................................................................ 127

7-5 ................................................... 127

7-6 ) CT-METRE

, ) , )

) ..................................................................................... 128

7-7

.................................... 130

7-8 ........................................ 131

7-9 .. 132

xxxi

7-10 ) )

............................................................... 134

8-1

( : MANZELLO ET AL., 2007B) ............................................................ 139

8-2 [JEULIN ET AL., 2001] .......................................... 140

8-3 LC/DC

,

( ) ............................................................................................. 142

8-4

,

.......................................................................................................... 143

8-5 (=300C)

,

( X) ........ 145

8-6 (T=900OC)

,

( X) ........ 146

8-7 ) GKB )

...................................... 149

8-8

1, ,

.......................................................... 151

8-9 : ) )

2,

, 8 ............ 152

8-10 : ) ) ,

1,

, , .... 153

xxxii

8-11 ) ) 1,

,

............................................................................................................................ 154

8-12 ............... 155

8-13 1,

, .............. 156

8-14 1,

, , 156

8-15 1, ,

, ,

: ) , ) , ) )

..................................................................................... 158

8-16 KNUDSEN .......................... 159

8-17 , , 1

: ) , ) , ,

( ), ) ,

, , (

) ) ............. 161

8-18 , ,

1, .................................................................. 162

9-1 ) ISO 834 )

............................................................................................................ 166

9-2 ( GPRO,

80K MIN-1),

: ) , )

) ....................................... 168

9-3 (

HETRAN), ,

( GPRO,

20K MIN-1),

,

[GHAZI WAKILI ET AL., 2007] .......................................................... 170

9-4 (

HETRAN), ,

xxxiii

( GPRO,

20K MIN-1) ,

,

[GHAZI WAKILI ET AL., 2007] .......................................................... 171

9-5 ....... 172

9-6 ( GPRO,

), ,

: ) , ) )

.............................................................................................................................. 173

9-7 (

HETRAN), ,

( GPRO,

), ,

,

[GHAZI WAKILI ET AL., 2007] .......................................................... 174

9-8 (

HETRAN), ,

( GPRO,

80K MIN-1),

,

, [GHAZI WAKILI ET AL., 2007]...................... 176

9-9 ( GPRO,

80K MIN-1),

: ) , )

, ) )

..................................................................................................................................... 179

9-10

................................................................................................................. 183

9-11 (

HETRAN), (

)

, (

GPRO,

80K MIN-1),

, [GHAZI WAKILI ET AL., 2007]...................... 184

xxxiv

9-12

, .............................................................. 185

9-13 : ) -

) ,

, ...................................................................... 186

9-14 : ) , )

) , ,

....................................................................................................................... 187

9-15 : ) , )

) , ,

........................................................................................................................................ 188

9-16 (

) ............................... 190

9-17 ( 10K MIN-1): )

) [PAULIK

ET AL., 1992] ................................................................................................................................. 191

9-18 (

GPRO, 10K MIN-1) (

PAULIK ET AL. [PAULIK ET AL., 1992], 10K MIN-1)

: ) , )

, )

, ) , ) , )

, ) ) ....................... 191

9-19 (

HETRAN),

10K MIN-1,

( GPRO) ( PAULIK

ET AL. [PAULIK ET AL., 1992]) ,

, .................. 193

9-20 ................................................................................................. 195

9-21

........................................................................................................................ 195

9-22 .............................................................................. 197

xxxv

9-23 (

HETRAN), ,

( GPRO,

, 30K MIN-1

FC=1.58),

: ) )

, ....................................................................... 198

9-24 (

HETRAN), ,

( GPRO,

, 30K MIN-1

FC=1.58),

,

: ) ) ,

...................................................................................................... 199

9-25 (

HETRAN), ,

( GPRO,

, 30K MIN-1

FC=1.58),

,

: ) ) ,

........................................................................................................... 200

xxxvi

xxxvii

1-1

2010 ..................................................................................................................... 2

1-2 ................................................ 13

3-1 ................................................................................................. 33

3-2 ( 3-16) ...................... 44

4-1 [HAMMILTON & CROSSER, 1962] .... 50

4-2 A P ............ 54

5-1 ................................ 77

6-1 ................................................................ 89

6-2 ................. 93

6-3 ............................................... 94

6-4

................................................................................................................................... 97

6-5

( 3-20) ............................................................................................................................... 99

6-6 - N

.............................................. 100

6-7 - N

Y() .............................................. 105

6-8

................................................................................... 106

6-9 -

......................................................................................................... 108

6-10

,

............................................................................................................. 109

xxxviii

6-11

,

[BROWN ET AL., 2000] ............................................................................................ 111

6-12

,

[HURST, 1991] ........................................................................................................ 111

6-13

......................................................... 112

6-14

,

............................................................................................................. 114

6-15

................................................................................................................................... 116

6-16

,

....................................................... 119

8-1 ....... 139

8-2 [GHAZI

WAKILI & HUGI, 2009] ................................................................................................................ 140

8-3 ........................................................ 141

8-4 LC/DC .............................. 143

8-5

............................................................................ 146

8-6

................................................................................................ 147

8-7 ............................. 148

8-8 ................. 148

8-9 .............................................................................................. 150

8-10 ............................................................................................ 150

1

1

1

1

, .

,

1050000 [, 2006]. ,

,

. ,

. , ,

[Quintiere, 2006].

.

1%

() [Founti & Cox, 2000, , 2006, Quintiere,

2006]. :

, ,

.

(.. ),

.

2007, 2688340

2

2, 63 3,

5 4.

,

,

.

1.1

,

[Yeoh & Yuen, 2009]. 1-1

,

( ), (.. ),

[Karter, 2011] [Fire

Statistics Great Britain, 2011], 2010. , 1-1,

1-1.

,

, .

, ,

, , ,

. ,

,

,

[, 2006].

1-1 2010

(109)

482000 2755 15420 9.7$

215500 310 1590 1.4$

634000 55 710 0.5$

1331500 3120 17720 11.6$

2 " ". on Line. 28/08/2007.

3 " ". in.gr. 27

2007.

4 "Griechenland atmet auf". n-tv.de. 28/08/2007. 28 2007.

1

3

69600 325 10142 -

32500 44 520 -

216900 19 472 -

319000 388 11134 -

1-1 2010 : ) [Karter M.J., 2011] )

[Fire Statistics Great Britain, 2011]

1.2

,

(). ,

, ,

, .

, :

.. 71/88 ( 32/17.2.1988) .

5905/15/839/1995 ( 611 /12.7.1995)

,

.

.. 6/96 ( 150 13.3.96) .

.. 3/81 .

4

.. 3/81 3/19.1.1981

.

.. 36/95 3/1981

.

,

, [Purkiss,

1996, , 2006]:

,

, , ,

,

(), ,

,

(stability) (integrity)

, , ,

,

: () .

,

() , ,

, .

1.2.1

,

, .

, ,

, , ,

1

5

.

:

(, , ..)

( ,

..)

(sprinklers)

,

(, ..) ..

/

(sprinkler),

(wet), (dry), (preaction), (deluge)

(water spray) (fog)

(foam)

, ,

(halon), ..

( )

( , ..)

6

( ,

)

1.2.2

, ,

.

, , ,

.

, , .

:

.

,

.

:

,

,

, .

, , :

:

,

, . (

) , :

,

(, ..)

,

1

7

:

.

(

):

,

,

..

:

. ( )

, ,

, , ,

:

: ,

.

,

: ,

,

.

: ,

. , 140oC

180oC

:

,

().

,

8

.

:

:

,

.

:

,

1.3

(numerical simulation)

1

9

,

. , (modeling)

. ,

, , .. ,

, .. , ,

,

[, 2000].

,

,

. ,

,

. , ,

,

,

. , ,

,

.

,

, . ,

, ,

[, 2000].

[, 2000, , 2005]. ,

, , ,

.. ,

, , ,

, ,

.. ,

, ,

, , , .. [,

2005]. ()

.

10

1.4

, ()

(light weight constructions) .

,

, ,

,

. (),

, ,

,

[Henkel et al., 2010].

.

, ,

, , ,

[Ghazi Wakili et al., 2007].

(.. ),

( ) .

, ,

.

, ,

,

.

,

,

, .

.

.

,

:

()

1

11

,

.

,

, . ,

,

. ,

,

. ,

, ,

.

,

, . ,

,

,

.

. , ,

.

,

. ,

. ,

,

.

12

1.5

, .

,

, ,

,

.

:

( 4).

-

.

.

( 6).

, , (

), ,

,

( 7).

.

, ,

. , ,

,

, ( 8).

.

.

,

,

( 9).

1

13

1.6

10

. ,

. ,

,

. 2 5

, 6 9

, ,

,

,

.

.

, ,

,

. 1-2 ,

.

1-2

&

2

6

2 2

&

3 4 5

&

&

6 7

8

7

9

2

,

.

14

(-, - -),

.

3

(, ). ,

( , -

) .

, ,

.

, ,

4.

. , ,

,

.

5. ,

,

. ,

, . ,

HETRAN (HEat TRansfer ANalysis)

,

.

6

. ,

,

, . ,

,

,

,

, .

1

15

7

. ,

,

,

.

8

. ,

. ,

GPRO (Gypsum PROperties), 4

6 ,

.

, 7 .

, 9

,

, HETRAN,

GPRO. ,

,

. ,

,

, ,

. ,

, ,

HETRAN

.

10

,

,

,

.

I

. II

16

HETRAN. III

. IV

. , V

, 7 ,

9 .

1.7

:

.. , . , . , .. , . ,

,

, , , 5-8 2007, . 229.

. , . , .,

, 1 , Divani

Caravel, , 21-23 2008, : . 843-854.

. , . , .,

, 1

, Divani Caravel, , 21-23 2008, : . 1473-1484.

. , . , . , . , . ,

, 2008, 6

, , 28 , 2008.

:

D. Kontogeorgos, E. Keramida, M. Founti, Radiative heat transfer modeling of natural gas

diffusion flames, in: Proceedings of 3rd European Combustion Meeting, Chania, Crete,

Greece, 11-13 April 2007.

D. Kontogeorgos, D. Kolaitis, M. Founti, Numerical modeling of heat transfer in gypsum

plasterboards exposed to fire, in: Proceedings of 6th International Conference on Heat

Transfer, Fluid Mechanics and Thermodynamics, Pretoria, South Africa, 27 June to 2 July

2008, paper number: KD1.

1

17

I. Mandilaras, D. Kontogeorgos and M. Founti, Effects of PCMs on Gypsum Board

Properties at Elevated Temperatures, in: Proceedings of 9th IIR Conference on Phase-

Change Materials and Slurries for Refrigeration and Air Conditioning, Sofia, Bulgaria, 29

September to 1 October 2010, p. 123-130.

I. Mandilaras, D. Kontogeorgos and M. Founti, Implementation of the Heat Capacity Method

for Modelling the Thermal Performance of Agglomerate Stones Containing PCM, in:

Proceedings of 9th IIR Conference on Phase-Change Materials and Slurries for

Refrigeration and Air Conditioning, Sofia, Bulgaria, 29 September to 1 October 2010, p.

133-141.

D.A. Kontogeorgos and M.A. Founti, Heat and mass transfer phenomena occurring in a

gypsum board exposed to fire conditions, in: Proceedings of First Middle East Conference on

Smart Monitoring, Assessment and Rehabilitation of Civil Structures, Dubai, UAE, 8 10

February 2011, paper number 160.

:

Kontogeorgos, D.A., Keramida, E.P., Founti, M.A., Assessment of simplified thermal

radiation models for engineering calculations in natural gas fired furnace, Int. J. Heat

Mass Transfer 50 (2007) 5260 5268.

D. Kontogeorgos and M. Founti, Numerical investigation of simultaneous heat and

mass transfer mechanisms occurring in a gypsum board exposed to fire conditions,

Applied Thermal Engineering 30 (2010) 1461-1469.

D. Kontogeorgos, I. Mandilaras and M. Founti, Scrutinizing Gypsum Board Thermal

Performance at Dehydration Temperatures, Journal of Fire Sciences 29 (2010) 111-130.

D. Kontogeorgos, K. Ghazi Wakili, E. Hugi and M. Founti, Heat and moisture transfer

through a steel stud gypsum board assembly exposed to fire, Construction and Building

Materials 26 (2012) 746-754.

D.A. Kontogeorgos and M.A. Founti, Gypsum Board Reaction Kinetics at Elevated

Temperatures, Thermochimica Acta 529 (2012) 6-13.

18

2

19

2

2

2.1

, ,

.

, ,

: 5

.

,

, ,

.

, ,

() . ,

, ,

() [Zalba et al.,

2003]. ,

5 .

20

,

.

, , ,

6 ( ),

, ,

, , [Kaasinen, 1992]. ,

,

[Peippo et al., 1991].

,

, .. ,

. ,

,

, [Novozhilov,

2001]. , ,

,

, ,

.

[Feng et al., 2003 , ,

2006].

, ,

. ,

, , ,

-

, ,

, .

, ,

: -,

- -.

( 2-1).

,

, .

6 ().

2

21

,

,

,

.

.

2-1

2.2 -

- (micro-scale), nm m,

( 2-2).

:

-

.

,

.

,

,

. ,

- , . ,

,

,

( 2-2).

3 ,

4 .

,

22

. ,

. ,

, -

,

6 .

2-2 - : ) ) -

2.2.1

.

/ ,

- ,

. ,

, , , ,

, . , ,

,

, ,

. , -

,

. ,

. ,

(thermal analysis)

(calorimetry),

,

[Haines, 2002].

2

23

, [Mackenzie, 1983,

Hemminger & Sarge, 1998]:

()

,

.

()

- , , ..

.

.

2.2.1.1

[Christian & OReilly,

1985, Skoog & Leary, 1992, Haines, 2002] ( 2-3):

2-3

.

, .

,

(.. , , ).

, ,

, ,

.

24

2.2.1.2

,

[Doyle, 1961, Coats &

Redfern, 1964, Paulik et al., 1992, Haines, 1995, Haines, 2002], ..

,

..

(reproducibility) .

(Sample): ,

.

(Crucible):

. ,

, . ,

.

(Rate of heating):

.

(thermal lag)

. , ,

.

(Atmosphere):

. ,

(.. ) ,

(.. ).

(Mass of the sample):

, . , ,

.

2.2.1.3

()

, .

. , ,

2

25

, ,

.

, ,

.

(), .

,

.

2.2.1.4

() ()

.

, .

, ,

, .

.

,

. , ,

,

. , ,

, ,

.

2.2.2

. ,

.. , ,

..

. , ,

,

.

.

26

.

:

, ,

,

.

, .

, . ,

,

. ,

,

.

,

,

.

2.3 -

- (meso-scale),

,

, ( 2-4).

, ,

7,

. (

/ ),

. :

.

-. ,

7 ,

,

.

2

27

-,

. , ,

,

.

2-4 - ( )

2.3.1

- .

, ( -),

, , ,

. ,

,

,

, . ,

,

,

.

2.3.2

,

-,

, .

28

. ,

, -,

. , -

-.

- .

Navier-Stokes -,

. ,

, ,

-, - ,

, ,

.

2.4 -

- (macro-scale), ,

,

( 2-5). , -

,

, , ,

.

. , ,

- , .

, , -

, , ,

, .

,

, .

2

29

2-5 -

30

3

31

3

3

3.1

,

-

/, .

,

.

: , T, (conversion

fraction), , , P, :

PhfTkdt

dr

3-1

3-1, ,

0 1 (=0 =1

). k(T) (reaction

rate constant), .

f() (reaction model function)

32

. , h(P) (pressure term)

.

3.1.1

.

,

,

/ . ,

[Sestak, 1984, Sestak, 2005, Vyazovkin, 2008].

. ,

,

.

,

3-2 [Burnham et al., 2007].

PnPPh

3-2

(reversible) ,

(AsolidBsolid+Cgas),

.

3-3 [Vyazovkin, 2011], P Peq

, .

eqP

PPh 1

3-3

3.1.2

Arrhenius:

TRE

g

a

AeTk

3-4

A Ea - ,

, Rg .

3

33

3.1.3

, f(),

[Malek, 1992, ,Vyazovkin & Dollimore, 1996, Vyazovkin & Wight, 1999,

Brown, 2001, Vyazovkin et al., 2011]. 3-1

8.

3-1

f() g()

(Power Law)

Pn n(n-1)/n 1/n

(Reaction order)

Rn (1-)n -ln(1-), n=1

[(1-)(1-n)-1]/(n-1), n1

Avrami-Erofeev An n(1-)[-ln(1-)](n-1)/n [-ln(1-)]1/n

-

(One-dimensional

diffusion)

D1 1/2-1 2

-

(Two-dimensional

diffusion)

D2 [-ln(1-)]-1 (1-)ln(1-)+

-

(Three-dimensional

diffusion)

D3 3/2(1-)2/3[1-(1-)1/3]-1 [1-(1-)1/3]2

(Contracting model)

Cn n(1-)(n-1)/n 1-(1-)1/n

n=2, (contracting cylinder)

n=3, (contracting sphere)

, ,

: ,

( ) [Vyazovkin et al., 2011],

, , , d/dt, ,

8 ,

.

34

.

,

. , k(T),

, h(P), 3-1,

,

, f().

, , k(T), ,

f(), ,

, h(P).

3-1

.

3-1

: 1) , 2) 3)

, ,

, ,

(Power Law) ( 3-1). ,

,

. (Reaction Order)

(Diffusion) ( 3-1). , ,

, .

, ,

.

3

35

Avrami-Erofeev ( 3-1)

.

3.2

[Brown et al., 2000]:

( Arrhenius )

, Arrhenius, A Ea

, f(),

. ,

3-1 (Hemminger & Sarge, 1998, Galwey

& Brown, 1999]. , 3-1

, ,

, [Brown et al., 2000].

, ,

[Brown et al., 2000,

Vyazovkin et al., 2011] 3-5:

RN

r

rrdt

dw

dt

d

1

3-5

NR ,

, wr r

, (wr=1, r=).

3-1 :

fAedt

dr

TR

E

g

a

3-6

(differential kinetic methods), :

tTR

E

dteAf

dg g

a

00

3-7

36

(integral kinetic methods). g(),

( 3-1).

, , [Doyle, 1962, Coats & Redfern, 1964, Ozawa, 1965,

Abdel Aziz Khalil, 1982, Elder, 1985, Strydom et al., 1995, Hudson-Lamb et al., 1996, Aybers,

1998, Erdogan et al., 1999, Sanders & Gallagher, 2002, Demir et al., 2003, Seungdo et al., 2004,

Elbeyli & Piskin, 2004].

( 3-6 3-7)

,

[Vyazovkin et al., 2011]. ,

, ()

(),

( ). , ,

,

, ,

9 .

,

, :

(model-fitting method)

(model-free method).

Arrhenius, ,

Arrhenius

. ,

. ,

. ,

,

=0.1-0.9 =0.05-0.95.

9

, .

3

37

.

3.2.1

(model-fit method) ,

.

, Arrhenius

.

,

.

, . ,

: .

Arrhenius (A Ea),

, . ,

, ,

.

,

, ,

Arrhenius.

, ..

() (

). ,

, . , ,

Arrhenius

[Vyazovkin & Dollimore, 1996,

Vyazovkin, 1997, Vyazovkin, & Wight, 1999, Vyazovkin et al., 2011].

10 [Brown et al., 2000, Vyazovkin et al., 2011].

,

10 3-5.

38

.

3.2.1.1

.

,

Arrhenius.

(.. , ,

..).

,

.

,

:

;

(

) (

), ,

.

.

, Ea,

, (. );

: , (.

3.1.3);

, , ,

( 3-1).

3.2.1.2

(linear model-fitting method)

,

( 3-6) .

3

39

3-6

, 1/.

[Vyazovkin et al., 2011]:

oncf 1

3-8

3-8

( 3-1),

c, n o [Perez-Maqueda et al., 2006]. , ,

3-8 3-6

:

TR

EcA

dt

d

g

a

on

ln

1

1ln

3-9

3-9

(

) n

o

.

,

n o.

,

, Ea, ln(cA),

,

. n o

, c, n o

. , c,

- , A. n o

, c A

. , c ,

- , ln(cA)ln(A).

3.2.1.3

(non-linear model-fitting

method)

.

40

Arrhenius, ,

(residual sum of squares), RSS,

,

3-10.

min1

2

exp

N

jcalcjj

yyRSS

3-10

y

, exp calc

, . RSS

( ) .

3.2.2

(model-

free isoconversional method) ,

,

[Friedman, 1964, Ozawa, 1965, Flynn & Wall, 1966].

3-6

, 1/T, :

111

lnlnln

T

f

T

Tk

T

dtd

3-11

.

3-11 , ,

(. =.), f() ,

,

:

g

a

R

E

T

dtd

1

ln

3-12

3-12,

, ,

3

41

11,

, , .

,

,

: (differential isoconversional methods)

(integral isoconversional methods) .

,

( )

(). 3-12,

.

, ,

, =0.05-0.95, 0.05

[Vyazovkin et al., 2011].

,

.

, ,

,

3-6 .

.

,

.

3.2.2.1

Friedman [Friedman, 1964],

3-13:

TR

EAf

dt

d

g

alnln

3-13

3-13 3-6

11 , , ,

.

42

. 3-2

, , , T,

, .

, =0.

ln(d/dt) 1/T ( 3-13), ,

, 3-2.

(ln(d/dt),1/T)

.

( 3.2.2)

.

,

.

3-2 ) )

( 3-6)

,

, , ,

(. 3.2.2.2). , , ,

. ,

(.. ),

, , ,

[Starink,

2003]. ,

[Sbirrazzuoli, 2007]. ,

(.. )

, ()

3

43

. , ,

.

3.2.2.2

3-7.

,

, :

tAeg TRE

g

a

3-14

3-14, 3-16:

TR

E

A

gt

g

alnln

3-15

, , , =0 (

3-2), ln(t) 1/ ( 3-15),

, ,

3-1. (ln(t),1/T)

.

, 3-7

.

(.. Taylor) .

3-7

,

[Starink, 2003]:

TR

ECConst

T g

aiBi

ln

3-16

Bi Ci

3-7. 3-2

3-16, .

Ozawa-Flynn-Wall (OFW) , Kissinger-Akahira-

Sunose (KAS) Starink (STR) .

44

3-2 ( 3-16)

Bi Ci

Ozawa-Flynn-Wall (OFW) 0.00 1.0520 [Ozawa, 1965, Flynn & Wall, 1966]

Kissinger-Akahira-Sunose

(KAS)

2.00 1.0000 [Akahira & Sunose, 1971]

Starink (STR) 1.92 1.0008 [Starink, 2003]

3-7. , , 3-7

[Vyazovkin & Dollimore, 1996, Vyazovkin, 1997, Vyazovkin, 2001].

, , (

)

:

N

i

N

ij ja

iaa

tTEJ

tTEJE

1 ,

,

3-17

i j ,

J12 :

ttTR

E

a dtetTEJg

a

0

,

3-18

3-17

( 3.2.2), ,

, .

3-7

. , ,

[Vyazovkin &

Sbirrazzuoli, 2006, Vyazovkin, 2008],

20-30%,

[Vyazovkin, 2001].

Friedman,

12 J .

3

45

:

t

t

tT

a dttTEJ

-

g

a

R

E-

e,

3-19

3-19 , ,

.

3.2.3 -

,

,

- .

,

3-6.

.

,

3-5, .

. ,

,

- :

.

3.2.3.1

(compensation effect)

(.. ).

,

3-10,

- , Ei Ai, .

(..

), ,

(Ei,Ai).

46

3-20,

[Vyazovkin et al., 2011].

baEA ii ln

3-20

(Ei,Ai)

3-20. ,

(. 3.2.2), Ea,

3-20 - , A ( 3-21),

.

baEA a ln

3-21

- ,

( 3-22)

( 3-23) .

tTR

E

dteAg ga

0

3-22

TR

E

g

a

Aedt

df

1

3-23

3-22 3-23

t (d/dt), ,

, g() f().

g() f() ( 3-1)

.

3.2.3.2

(master plots) :

y() z() [Malek, 1992].

,

(. 3.2.2), y()

z():

3

47

Afedt

dy RT

Ea

3-24

gfTdt

dz

2

3-25

y() z(), , ,

g() f() ( 3-1).

y(), - ,

.

, -

3-26.

max

max2max

TR

E

g

a g

a

efTR

EA

3-26

max

, .

48

4

49

4

4

4.1

, ,

, , ,

.

13 , ,

.

, , ,

, ,

( 4-1). 14

( )

( 4-1).

, .. , , ..

,

- ,

13 , .

14 3.510-4m,

>1m.

50

. , , ,

, ,

.

,

, .

4-1 ) )

4.2

, ,

,

, , :

par

sph

S

S

4-1

. 4-1

[Hammilton & Crosser, 1962].

4-1 [Hammilton & Crosser, 1962]

,

1.00

5:1 0.68

10:1 0.57

, .. [Jeulin et al., 2001],

4

51

, Lcyl dcyl,

[Korte & Brouwers, 2010]. , , ,

4-2.

2

1

1

4

632

cyl

cylcyl

cyl

d

Ld

L

4-2

4.2.1

(porosity)

( ), VF, , V, .

V

VF

4-3

,

4-4, VS

sr .

r

N

s s

s

S

sV

m

V

VV

S

11

V

V

0

1F

4-4

4.2.2

(saturation)

, VL, , VF.

F

Lsat

V

Vs

4-5

4.2.3

(, Probability Density Function) ,

(, Pore Size Distribution) [Assouline &

Rouault, 1997, Rouault & Assouline, 1998].

, [Beck & Schultz, 1972, Collins & Ramirez, 1979,

52

Nakao & Kimura, 1981, Deen et al., 1983, Tam & Tremblay, 1993, Krajewska & Olech, 1996,

Assouline & Rouault, 1997, Rouault & Assouline, 1998],

[Du Bois & Stoupel, 1976, Deen et al., 1983, Aimar et al., 1990, Tam & Tremblay, 1993,

Mochizuki & Zydney, 1993, Assouline & Rouault, 1997, Rouault & Assouline, 1998, Bowen &

Welfoot, 2002], [Mochizuki & Zydney, 1993], ,

Weibull Rayleigh [Deen et al., 1983, Derjani-Bayeh & Rodgers, 2002]

[Wendt et al., 1976, Mason et al., 1980, Wendt & Klein, 1984].

,

, ,

.

,

, ,

[Bowen & Welfoot, 2002, Derjani-

Bayeh & Rodgers, 2002].

4-6, dp,m l

.

2

2

,

2

log

2

1l

mp

p

d

d

lp

p ed

dPDF

4-6

, l,

4-7, , l, dp,th

(maximum pore diameter threshold) .

thp

mpthp

l

l

dC

ddC

C

C

,5

1

2,,

0

21

1

0

210

2

loglog

ln

4-7

dp dp-

dp dp+dp, dp0 4-8.

ppp dPDFNdPSD

4-8

Np

, 4-9.

4

53

max,

min,

max,

min,

p

p

p

p

d

d

ppFp

p

d

d

ppFpF

dddVdPDF

VNdddVdPSDVV

4-9

4.3

:

.

, : ,

.

4.3.1

(tortuosity factor)

, Lsl, , L,

4-10 [Dias et al., 2006, Matyka et al., 2008].

1L

Lsl

4-10

4-2

.

,

: ( 4-11) [Iversen & Jorgensen, 1993, Koponen et al., 1996,

Salem & Chilingarian, 2000, Blondeau et al., 2003], ( 4-12) [Archie, 1942,

54

Millington & Quirk, 1961, Klusacek & Schneider, 1981, Huizenga & Smith, 1986, Zhang &

Bishop, 1994, Mota et al., 1998, Mota et al., 2001, Dias et al., 2006]

( 4-13) [Weissberg, 1963, Ho & Strieder, 1981, Tsai & Strieder, 1986, Comiti & Renaud,

1989, Barrande et al., 2007, Matyka et al., 2008] .

pa

4-11

p

4-12

ln1 p

4-13

4-2 a p

a p

( 4-11)

3 -2 Iversen & Jorgensen, 1993

4 -3 Iversen & Jorgensen, 1993

2.2271 -1.12 Blondeau et al., 2003

( 4-12)

1/3 Millington & Quirk, 1961

0.5 Zhang & Bishop,1994

Mota et al., 1997

0.4 Mota et al., 1998

( 4-13)

0.5 Weissberg, 1963

Ho & Strieder, 1981

1 Tsai & Strieder, 1980

2/3 Tsai & Strieder, 1980

0.86 Comiti & Renaud, 1989

1.66 Barrande et al., 2007

0.77 Matyka et al., 2008

a p

. 4-2 a p

.

4-3

, .

, ,

, . ,

4

55

,

(0 1). ,

,

,

, (, Least Square

Method). .

4-3 : ) , )

) ,

4-4

,

4-14, calc exp

, , N .

N

i

calctote1

2exp

4-14

56

4-4

,

, p=0.601859,

, .

4-5

( 4-13, p=0.601859), .

4-5

4.3.2

(permeability)

.

.

, ,

4

57

, , , Ssp,

[Koponen et al.,

1997, Matyka et al., 2008].

:

2

,

spS

gK

4-15

Kozeny ( 4-16) Kozeny ( 4-17),

[Bear, 1972].

2

3

spKScK

4-16

22

3

spK ScK

4-17

cK Kozeny

(capillaries) ( 4-2),

2 12 [Scheigegger, 1957, Han, 1969, Bear, 1972].

4-6

,

(interconnected

pores) ( 4-6). ,

58

( dead-end pore)

( occluded pore)

( 4-6).

,

(percolation threshold), th , ,

Kozeny.

.

(effective porosity), eff ,

15

[Koponen et al., 1997]:

xxx thefftheffeffeff 12 ,2,3,

4-18

ththx 1 eff,

. : 1 dd effeff 1

0eff th .

, , 4-15 4-16

:

2

3

spK

eff

ScK

4-19

22

3

spK

eff

ScK

4-20

, ,

[Koponen et al., 1997]:

ln,parh

Dsp

d

nS

4-21

15 (>0.6) ,

.

4

59

dh,par=nDVpar/Spar , nD

, Vpar Spar ,

.

,

4-22, Kref=(Vpar/Spar)2/cK.

2

2

ln

effeffrefKK

4-22

(>0.6)

, 4-22 :

2ln

refKK

4-23

,

Kref.

Kref=(dcyl)2/cK.

4.3.3

(diffusion)

, , Knudsen

[Treybal, 1981, Ruthven, 1984, Incropera &

DeWitt, 1985, , 1993, Masel, 1996].

, .

, Knudsen

. ,

,

10-7-10-9 m2/s [Treybal, 1981].

Knudsen

.

Knudsen , ,

,

(effective diffusion coefficient) [, 1993]:

effkdeffmdeff DDD ,,

111

4-24

60

Dmd,eff Dkd,eff

Knudsen, .

4-25 [Weissberg, 1963, Mota et al., 1998, Blondeau et al., 2003]. Dm

.

meffmd DD ,

4-25

Knudsen

4-26 [, 1993].

mfpeffkd udD ,,3

1

4-26

dp uf,m

f, 4-27.

21

,,

8

g

g

mgmfMW

TRuu

4-27

4.4

(effective density) ,

,

, .

,

. , ,

, ( ),

.

r

N

s

s

N

l

l

r

SLeff

sV

mm

sV

mm

V

m

SL

11 0

11

0

4-28

4.5

(effective thermal conductivity)

, , , ,

4

61

, ,

.. [Horai & Simmons, 1969, Hsu et al., 1994, Hsu et al., 1995,

Clauser & Huenges, 1995, Kaviany, 1995]. (..

, ..),

,

, .

( 23 )

. , ,

, ,

,

[Ahmed & Hurst, 1997, Korte & Brouwers, 2010].

Ahmed & Hurst

[Ahmed & Hurst, 1997] ( 4-29), kS, kL kG

, , , ssat

( 4-5), nt ,

.

tttt nnGsatnLsatnSpheff kskskk1

3, 11

4-29

, ,

, ( S-G)

( S-L). ,

4-30 [Somerton et al., 1974].

GSpheffLSpheffsatGSpheffpheff kkskk ,2,,2,,2,3,

4-30

,

[Hamilton & Crosser, 1962, Zehner & Schlunder, 1970, Hsu et al., 1994,

Hsu et al., 1995, Kaviany, 1995, Cernuschi et al., 2004, Carson et al., 2005, Cote & Konrad,

2005, Yu et al., 2006, Do et al., 2007, Cote & Konrad, 2009].

Maxwell [Maxwell, 1873], ,

( )

( ).

[Carson et al.,

62

2005], .

, Maxwell [Hadley, 1986] (

4-31).

12

2112

111

11

2

0

00

0002,

FS

FSFS

FS

FSFpheff

ff

ffkk

4-31

S-F

, kS/kF, 0 (degree of consolidation) f0

.

4-32.

580.0298.0,298.0778.6084.1log

298.00827.0,0827.0154.3405.0log

0827.00,898.4log

0

0

0

4-32

4-33 [Korte &

Brouwers, 2010] 4-34 [Verma et al., 1991].

3

2

12

2

3

20

FS

FSf

4-33

31

3

0ln

FS

f

4-34

,

.

[Burgoyne & Weinberg, 1953, Mathur et al., 1967],

4-35, Xf f.

F

F

N

f f

f

N

f

ffF

k

XkXk

1

1

15.0

4-35

, ,

( 4-36)

( 4-37) ( 4-38)

4

63

[Clauser & Huenges, 1995, Cote & Konrad, 2005].

,

.

SN

s

ssS kXk1

4-36

SN

s s

s

S

k

Xk

1

1

4-37

S

s

N

s

XsS kk

1

4-38

,

. ,

[Kingery et al., 1976, Harmathy, 1988, Ahmed & Hurst, 1997, Szelagowski et

al., 1999, Yu et al., 2006, Do et al., 2007].

, keff,rad, 4-39, G

(2/3 1

).

pradeff dTGk3

, 4

4-39

,

, 4-40.

radeffpheffeff kkk ,3,

4-40

4.6

()

r :

64

rrr rH

dt

dh

4-41

Hr

r, rr r.

:

rrrrr

rrr

r rH

dT

dhrH

dt

dT

dT

dhrH

dt

dh

4-42

4-42 , Cr, r,

(effective specific heat),

:

dTCdh rr

4-43

, ,

:

rrr

rHC

4-44

,

,

[Harmathy, 1983]:

RR N

r

rrref

N

r

rrefeff

rHCCCC

11

4-45

5

65

5

5

5.1

,

, , .

, , ,

, ,

. ,

, , ..,

, -16

,

, .

,

,

, ,

, .

16 ,

.

66

( )

. -

, / ,

,

[Pham, 2006].

.

:

.

,

(

), .

,

, 17. , ,

,

- ,

, ,