Double torsion tests for studying slow crack growth of portland cement mortar

CEMENTand CONCRETERESEARCH. Vol. 10, pp. 833-844, 1980. Printed in the USA. 0008-8846/80/060833-12502.00/0 Copyright (c) 1980 Pergamon Press, Ltd.

DOUBLE TORSION TESTS FOR STUDYING SLOW CRACK GROWTH OF PORTLAND CEMENT MORTAR

M. Wecharatana and S. P. Shah Department of Materials Engineering University of Illinois at Chicago Circle Chicago, Illinois 60680

(Communicated by Z.P. Bazant) (Received Aug. 11, 1980) ABSTRACT For studying slow crack growth in portland cement mortar 32" (812.8 mm) long double torsion specimens were tested. During testing, the loading and reloading compliances, permanent (or inelastic) deformations and crack growth were measured. It was observed that the strain energy release rates calculated from elastic, secant or reloading compliances do not accurately represent the fracture behavior of this material. A modified definition of the strain energy release rate is developed here to include both the elastic and the inelastic strain energy absorbed during crack extension. For this method, in addition to the reloading compliance, the knowledge of the rate of change of permanent deformations with crack growth is necessary. Details of the analytical and experimental procedure are described in this paper. Pour ~tudier la progression lente des fissures dans un mortier de ciment, des 6prouvettes de 32 in. (813 mm) de longueur sont test~es en Double Torsion. La complaisance en chargement-dechargement ainsi que les d~formations r6siduelles et la longueur des fissures ont 6t6 mesur6es durant les essais. On observe que les valeurs du taux de restitution d'6nergie G obtenues des complaisances 61astiques, s6cantes ou de chargement ne sont pas repr6sentatives du comportement de rupture du mat~riau. Une d6finition diff~rente de l'6nergie G est d6velopp6e; elle prend en consideration l'6nergie 61astique ainsi que l'6nergie in~lastique absorb6es durant l'extension des fissures. Les d6tails des essais et la m6thode analytique sont d~crits. Introduction I t has been r e c o g n i z e d t h a t t h e f r a c t u r e o f p o r t l a n d cement c o m p o s i t e s ( m o r t a r , c o n c r e t e and f i b e r r e i n f o r c e d c o n c r e t e ) i s accompanied by a slow c r a c k growth ( 1 - 4 ) . This means t h a t u n l e s s t h e specimen d i m e n s i o n s a r e such t h a t t h e s i z e o f t h e slow c r a c k growth (or m i c r o c r a c k i n g or f r a c t u r e p r o c e s s zone) i s s u b s t a n t i a l l y smaller than the s i z e of the uncracked ligament, the value of the fracture toughness parameters calculated using the usual linear elastic fract u r e mechanics c o n c e p t s w i l l depend on t h e s i z e o f t h e specimen ( 4 - 7 ) . Since 833

834

Vol. I0, No. 6 M. Wecharatana, S.P. Shah

the size of the process zone is likely to be influenced by the size of the inclusions (8) (aggregates, fibers) which in concrete could be about an inch (25.4 mm) long, specimens of a very large size may be necessary to obtain a size-independent fracture parameter. To examine the slow crack growth in portland cement mortar, 32 in. (812.8 mm) long double torsion specimens were used in this study. It has been shown that for the double torsion specimen the elastic strain energy release rate (GI) and the stress-intensity factor (KI) are independent of the crack length (9,10). As a result, it is possible to obtain measurements for several crack lengths from testing a single specimen. Double torsion tests have been recently increasingly used to study the slow crack growth in metals, rocks, ceramics and glasses (11-14). Two studies have also been reported on the use of the double torsion tests on portland cement (15,16). The dimensions of these specimens were much smaller than those reported here. During testing, loading and reloading compliances, permanent deformations upon unloading and crack growth were measured. To calculate the strain energy release rate from the test results it is common to use a compliance calibration technique (2-4). Both the secant and the reloading compliances have been frequently used (17-18). Neither of these metho~were found satisfactory for the type of nonlinear behavior observed in this study. A modified definition of the strain energy release rate and of the corresponding modified compliance is proposed. To evaluate this modified strain energy release rate it is necessary to know the rate of change of the reloading compliance as well as of the permanent deformation upon unloading. In this paper, details of the proposed analysis and the experimental procedure are given in addition to the results of a limited test program. Experiments Specimen Configuration The dimensions of the double torsion specimens used were: 32 in. (812.8 mm) long, 6 in. (152.4 mm) wide, 1.5 in. (38.1 mm) thick for the beam parts (t) and 0.5 in. (12.7 mm) thick at the crack (tn) (Fig. I). Initially the specimen was designed with a groove only on the compression side while the tensile side was kept flat so that the crack propagation can be easily observed. This gave a crack-plane which was one inch thick. Unfortunately, such specimens did not keep crack propagation along the center line even with a premolded or a saw-cut notch. The specimen was redesigned to have grooves on both sides (Fig. i). The crack propagation with these double-grooved specimens was always along the groove. These grooves were triangular with a 3/4 in. (19.1 mm) base and a 1/2 in. (12.7 mm) height (Fig. i). Since with the double-grooved specimens the cracks always initiated and propagated along the groove; no premolded or saw-cut notches were provided. The first measured crack length was considered as an initial crack (a0) in this study. Mix Proportions and Fabrication Four specimens were made with the mix proportions of 1:2:0.5 by weight of cement:sand:water. The cement used was high early strength ASTM Type III cement, and the sand used was a fine silicious sand passing sieve No. i0. The specimens were cast in a closed plexiglas mold. The plexiglas mold were cleaned and oiled before assembling together. The mortar was mixed in a mortar mixer for five minutes before casting it in three layers. The mold was kept on

Vol. lO, No. 6

835 SLOW CRACK GROWTH, DOUBLE TORSION TESTS, MORTAR

152.4mm FREE END ~

MEASURING S

(/3

1

I I

~II,

GROOVES

MEASURIN°~

(W ) ~-Ig.lmm I

I I ~

a

c,/-L

Wm:LOAO,NGAR.

1 "

LENGTH

:CRACK

, :..A. (W)

TH,C.NESS

Jl

tn :THICKNESSIN CRACK PLANE

SECTION (~) - (~)

S " LOAD-LINE DISPLACEMENT

FIG. 1 Specimen Dimensions a table vibrator and vibrated for 40 seconds after casting each layer and after closing the top part of the mold. The specimens were cured for 6 days in an environment with a relative humidity of 100% and 70°F (21°C). They were tested on the seventh day. To faciliate the crack growth measurements, just prior to testing, the specimens were painted along the groove with a white, dye-penetrant developer. Testing Procedure The specimens were tested in an Instron machine with a constant cross head displacement rate of 0.002 in./min. (8.467x10-4 mm/sec.). During testing, the load-line displacement was continuously monitored with a DC-LVDT, the output of which was recorded on an X-Y recorder with an accuracy of 0.005 in./in. To check the symmetry of deformations, a dial gage with an accuracy of 0.0001 in. (2.54 x 10 -3 mm) was used at the other load-point (Fig. 2). The crack was detected and measured on the tensile side by a traveling microscope with a resolution of 0.5 x10 -4 in. (1.27 x 10 -3 mm) (Fig. 2). Before loading, the specimen was supported at the loading-end while the free-end rested on a support hung from the frame which held the moving microscope (Fig. 2). Upon loading to a load of about 200 ibs. (889.6 N) the free end was lifted free of its support (Fig. 2). The details of the support at the loading-end are shown in Figs. 1 and 2. The specimen was supported on a large roller 5 in. (127 mm) long and 1.5 in. (38.1 mm) in diameter (Fig. i). The

836

Vol. I0, No. 6 M. Wecharatana, S.P-. Shah

FIG. 2 Testing Arrangement

roller permitted free rotation of the specimen about its axis. The load was applied through a set of two rollers attached to a thick plate which in turn was connected to the load-cell through an universal joint. The two rollers were 5 in. (127 mm) apart, 2 in. (50.8 mm) long and 0.7 in. (17.78 mm) in diameter. The specimens were loaded up to a predetermined load and then the crosshead displacement was held constant while the specimen was scanned for any crack growth. After the measurements of cracking, the specimen was unloaded. Due to the free-end conditions, the unloading was not continued all the way to a zero load but only down to about 300 Ibs. (1334.4 N). A typical loading, unloading and reloading vs. displacement curves as recorded on the X-Y recorder are shown in Fig. 3.

Vol. lO, No. 6

837 SLOW CRACK GROWTH, DOUBLETORSION TESTS, MORTAR DEFORMATION, 6 ,(mm) o.z 0.3 0.4 0.~

~l I

I

I

I

I

0.6

0.7

I

I -5.0

AI- -I~°I0 09~ ~'~

I000 ,.o.,.o

~ -

°: A I

Orack,e°0th ^/V;

S t o p loadina to m e a s u r e c r o c k growth

_ 4.5

I~

/t

-4.0

80C

.3.5

-

3.0

600 _2.5~ -2.0

~ 400.

d

--I.5 ~

_.1 r ~ ', ' r J r, I' ~

200.

/ /

/ ,

-

t.O

-0.5 / / //j/

r ,

/

~

5 T

I0 I.~ 20 DEFORMATION 5 (in.)xl(~3

25

FIG. 3

Typical Load-Deformation Curves Analysis The basic double torsion analysis is based on the assumption t h a t t h e deflection under the load-point (~) is caused by the elastic torsion of the two identical rectangular bars fixed at the crack-tip. The shear and bending strains of the uncracked portion are neglected. Based on these assumptions, it can be shown that (9,101: C = ~ P

3w 2 a m

(11

~tSG~(tl

where C is the elastic compliance, P is the applied load, a is the length of the crack, W is the beam width, t is the beam thickness, w m is the torsional moment-arm (Fig. 11, G is the elastic shear modulus, and ~(t) is the thickness correction factor whose values were taken from Ref. 10. The elastic strain energy release rate (GI) and the corresponding stress intensity factor (KI) can be given by: p2

dC

p2 dC

GI - 2--T- d a = " T

d-'A

(2)

n

K I = (EGI)½

(3)

where E is the Young's modulus of elasticity and A is the area of the crack plane (A = a • in). Since the quantity dC/da does not contain the term for crack

838

Vol. I0, No. 6

M. Wecharatana, S.P. Shah STRAIGHT MODELSLINE

STRAIN ENERGY RELEASE RATE, G I A)

UNSTABLE LINEAR ELASTIC BRITTLE BEHAVIOR

P

~

ACTUAL CURVE

p

!

QI

.,_,,d.foz~,

gi=

B)

STABLE WITHOUT PLASTIC DEFORMATION. IRREVERSIBLE WORK AREA METHOD.

=

g1 C)

2

P dC 2 dA

gx=

i

8

f ci

P

I

8

I

a_c 2

D)

i

2

I

"dA

RELOADING AND UNLOADING METHOD.

8

p

P..~_P=dCs

2

fixed

Iqr~p

2

dA

STABLE WITH PLASTIC DEFORMATION.

gz = z LdA

p,p, i d a

p

2

I AIHII~C~

s

FIG. 4 Schematic Models for Different Fracture Behavior and Corresponding Strain Energy Release Rates

length (a), it can be seen that the fracture mechanics parameters G I and K I will be independent of the crack length, and will be functions only of the load and specimen dimensions. Modified Strain Energy Release Rate The loading and unloading curves shown in Fig. 3 exhibited a significant amount of permanent (inelastic or plastic) deformations upon unloading. There could be two sources of these inelastic deformations: (i) nonlinear effects due to deformations of the torsion bars, and (2) nonlinear effects associated with the crack growth. It seems reasonable to assume that the primary source of the inelastic deformations is the nonlinear behavior within the process zone and that the material behaves elastically elsewhere. This means that the elastic as well as inelastic energy is absorbed during the slow crack growth and one cannot use Eq. (2) to calculate G I. Four different methods of calculating the strain energy release rate are shown in Fig. 4. If the crack propagation is unstable and if the assumptions of linear elasticity holds, then the classical definition of G I (shaded area in Fig. 4A) is obtained. If the crack propagation is stable and takes place then the definition shown in Fig. 4B is derived. Note that the corresponding compliance for this method is termed the secant compliance (CS = 6/P). This method is also called the quasi-static or the irreversible work-area method

(17).

Vol. I0, No. 6

839 SLOW CRACK GROWTH, DOUBLE TORSION TESTS, MORTAR

To include the permanent deformations many investigators use the reloading (or unloading) compliance (CR) to calculate the strain energy release rate (Fig. 4C). It can be seen that when the strain energy release rate (area shaded with the vertical lines in Fig. 4C) is calculated from the rate of change of the reloading compliance with the crack growth, the inelastic energy release rate is ignored (area shaded with horizontal lines). As a result, this method will underestimate the value of G I. The actual change in the release of energy during the crack extension between neighboring points 1 and 2 is shown as a shaded area in Fig. 4D. The corresponding value of G I can be determined from:

where Pl, P2 are two consecutive loads associated with crack lengths, a I and a2; C R is the reloading compliance and 6p is the permanent deformation. If the loads P1 and P2 are taken sufficiently close then the actual nonlinear curve can be approximated by a series of straight lines. Note that the first term in the parenthesis in Eq. (4) represents the change in the elastic strain energy while the second term represents the change in plastic strain energy. The above equation can be rewritten as:

Ci =

PIP2 2

dC m dA

(5)

where C m is the modified compliance which should be used instead of the elastic compliance in calculating the strain energy release rate for materials which exhibit nonlinear behavior of the type demonstrated here. To calculate the total strain energy release rate using Eq. (4) or (5) one has to determine the rate of change of reloading compliance as well as the rate of change of permanent deformations with crack growth. Results The load-deflection curves of the four mortar specimens are shown in Fig. 5. For simplicity the unloading-reloading parts are not shown. For one of the specimens, the measured crack extensions are noted on the figure. The relation between the permanent deformations and the crack length for these specimens is shown in Fig. 6. A linear regression equation was obtained from the data (Table I). Note that the permanent deformations are obtained by extending the reloading curve to the zero load (Fig. 3). Four different values of compliances are plotted against the crack length (a) in Fig. 7. The secant compliance was calculated simply as the measured deflection divided by the load at the corresponding crack length. The reloading compliance was calculated by measuring the slope of the initial, essentially linear part of the reloading curve (Fig. 3). The modified compliance was calculated from Eq. (5). For a given value of P1 and P2 the area under the shaded curve in Fig. 4D was calculated. This gave the value of G I in Eq. (5). Knowing this, the value of dCm/dA can be calculated. For each crack length a value of the slope of the modified compliance curve was obtained. For small values of crack length it was found that this slope matched the slope of the compliance given by the standard DT theory (Eq. I). As a result the initial value of modified compliance was assumed to be the same as that

840

Vol. I 0 , No. 6 M. Wecharatana, S.P. Shah

DEFORMATION, 6 , ram. 0.2 03 0.4 I I I

o.I I

0.5 I

0.6 I

0.7 I

I00

-4.5

(15.

"

0

(,3.4,)#

8OO-

(,2.37)~ (,o.~ j

1

MORTAR MIx t : 2:0.5 (C:S:W) ~ A Specimen No. I

~

r,~/J(2e'~)\ I

~

~z~::r'_

/

\l

000 D D D 0 0 0

\\

-4.0

No. 2 No. 3 No. 4

-3.5 -30

SO0_

('~ ~ ) Meoenred Crack Length \ \\

~

of SpecimenS= 4 In Inche, ( l i n c h • 25.4 ram. )

~

- Z 5 xZ -2.0

o.

& -I.5

Z

~

--LO

200

--0.5

I 5

0

I I0

15

DEFORMATION ,

6 ,

[

I

20

25

6

in x 1(33

FIG. S Load-Deformation Curves of Four Mortar Specimens

CRACK

LENGTH, o,m.

0.1

0.2

0.3

L

L

I

~4

0.5

0,6

0.7

0-8

I

1

I

I

L

_0.5

r~ DOUBLE TORSION BEAMS TESTS MORTAR Mix 1:2:0.5 mo

(C

: S : W)

-0.4

No. I No. 2 No. 3

_0.3

15 ~ ~ 0 0 0 o o D O0

_~_

Specimen

0

No.

4

_0.2 ,,~o a

I-

o

~

-4

0 O

I 5

I I0

CRACK

(8p,

I 15

LENGTH .

I 20

(3,

nO ~J ~3

o

o

5

_J ft.

o

o_

_0.1

4 2 1 9 X I04

.J ~L

a are in Inches)

I 25

I 30

in

FIG. 6 Permanent Deformation and Crack Growth Relation

Q

Vol. I0, No. 6

841 SLOW CRACK GROWTH, DOUBLE TORSION TESTS, MORTAR

CRACK LENGI'H, a, m. 0.1 I

f

0.2 I

DOUBLE

0.3 I

TORSION

0.4 I

BEAMS

0.5 I

0.6 I

0.7 i

TESTS.

_J6

Mortor 1:2:0.5

Mix

(C:S:W)

vvv

Reloading

eee A ,,,, A

Socant

2

Modified,:l~

ooo o

2O_

/

. ~ , ~ ~ / / ~/ / •.%,/

I

~2 -#: 3

oo

o oo

#~//

E • 2.22 x ,0'.,

K ~_ _ is--

npO

O

'

•

;0

0

_12

~ 4 THEORY

DT

_14

/

/

K _I0

Q ,,~m,e x / / 4~ -8

o/°°

• 0

u

ud ~

~

~

Q"

"/ / / /~O ~/ O--0

C.~ uJ

_6

•

~o

-

•

O

s_

•

•

/

0

/

/

/

,, •

vv.v'v

"

-

~

~

_~-v-~_v_~, v'~v i

5

i

I0

-

•

•

RELOADING

•

v j _v : ~ - - - l r ~ _ ~

.

~

_

v

-4

v

•

_2

•

" i

15

CRACK LENGTH, O ,

I

20

~15 O

in

FIG. 7 Compliance and Crack Growth Relations given by Eq. (i). As the crack became longer, the slope of the modified compliance curve became progressively smaller than the one given by the standard DT theory as can be seen in Fig. 7. The analytical equations obtained by a linear regression analysis of the reloading compliance data and by a nonlinear regression analysis of the modified compliance data are given in Table I. For studying slow crack growth in cementitious composites, R-curve analysis has been used (1,17,18). R-curve is the relationship between the resistance in terms of energy absorbed (GR) and the crack extension (~a). The R-curve analysis of the data is sholm in Fig. 8. The value of G R was calculated for a given crack length using Eq. (4). It can be seen that the resistance curves calculated from either the secant compliance or the reloading compliance underestimated the resistance to crack propagation. As expected, the R-curves for the DT-theory and the modified compliance method are close for small values

842

Vol. I0, No. 6 M. Wecharatana,

S.P. Shah

CRACK EXTENSION, AO. m. 0.1 I

0.2 f

0.3 I

0.4 I

0.5 I

0.6 -I N

gR

'o

1.0

DOUBLE TORSION BEAMS TESTS MORTAR Mix I: 2 : 0 . 5 ( C : S : W )

.E

~z~z~ Sp # o o o Sp # o o o Sp ~: OOo Sp #

,~" 0-8_ cn u~ i--

- 17.5 E

E

I

z

2

3 4

-15.0

c. . ~ ~'°~'(

wi

/

tu 0.6_

/

12.5 ,~ l]c

MODIFIED, c m .

~g|C"

W

0 . 5 5 8 Ib/In

I0.0 ~

>i,i Z m,l Z I-" t./)

J W I1:

0

w n-

-~5

0.4

~ W

-5.0 Secont • Cs

O~

Z UJ Z I1:

/

-2.5

~

RELOADING , C R

llo I'5 CRACK EXTENSION, /~a, in.

~

Is Aa

FIG. 8 Plots of R-Curves

of crack extension. However for the larger values of crack extensions the DTtheory curve (Eq. 2) overestimates the resistance to crack growth. The regression equation for the modified R-curve is shown in Table i. Note that for simplicity only the data points for the modified R-curve are given in Fig. 8. The slow crack growth can also be studied by plotting the stressintensity factor vs. the crack growth velocity (15,16). The stress-intensity factors were calculated from the modified strain energy release rate and using Eq. (3). The crack velocity was calculated from the measured crack extension and the corresponding time between the crack extension measured from the Instron's chart. The plot of K-V curve is shown in Fig. 9. Note that the unstable crack growth occurs at the value of Kic = 1200 lb./in, i/~. (1.3186 MN/m 3/2) which is in good agreement with the value of Glc obtained from the R-curve (Fig. 8). Conclusions i.

A method is developed to extend the concept of linear elastic fracture mechanics to nonlinear material such as portland cement mortar. A modified definition of strain energy release rate is developed to include both the elastic and the inelastic strain energy absorbed during the crack extension.

2.

It was found that the conventional method of calculating fracture from the elastic, secant or reloading compliance may not be accurate for nonlinear materials. For such materials in addition to the reloading compliance a

Vol. I0, No. 6

843 SLOW CRACK GROWTH, DOUBLE TORSION TESTS, MORTAR Stress 0.3 L

Intensity 0.5 I

Factor,

0.7 I

K,

1.0 t

MN/m ~z 1.5 I

2.0 I

3.0 I _5.0

io

G

MORTAR Mix

-4.0

I :2:0.5 0

(C:S:W) 6--

OOO 000

NO. I 2

O OO

4

--3.0

0

5--

E

c

2.0 E

E ~1.5 >"

4--

3_

),

n-o

I.O

©

2_

o

i k

=_ (9

L

i r--KIc" 1200 Ib/in i~l~(I.3186 MN/m 3/2 )

I

i

500

Stress

I

Y

I

I000

Intensity

Factor,

I

2000

o 0 0.5

K

K , Iblin

FIG. 9 K-V Curve

knowledge of the permanent deformations upon unloading is necessary to obtain valid fracture parameters. 3.

For studying the slow crack growth in portland cement mortar, the double torsion specimen developed here was found to be adequate. For these mortars an unstable crack propagation occurred at a crack length of about 12-15 in. (304.8- 381.0 mm) at a value of Gic = 0.558 ib/in° (9.7716x10 -2

N/~). 4.

A plot of the K-V curve indicated a subcritical crack growth followed b~ the rapid crack growth at a value of Kic = 1200 ib/in, i~.(1.3186 MN/m372). This value was in good agreement with the value Gic obtained from the plot of R-curves. Acknowledgements

This research was supported by a grant from the National Science Foundation (ENG 77-23534) to the University of Illinois at Chicago Circle. The research grant is under the supervision of A. E. Naaman and S. P. Shah of the Department of Materials Engineering. References I.

G. Velazco, K. Visalvanich and S. P. Shah, Cement and Concrete Res.,IO, 41

(1980). 2.

J. H. Brown, Magazine of Concrete Res., 24, 185 (1972).

3.

B. Hillemeier and El. K. Hilsdorf, Cement and Concrete Res. ~, 523 (1977).

844

Vol.

I 0 , No. 6

M. Wecharatana, S.P. Shah

TABLE 1 Regression Equations

Regression Equation

Coefficient of Correlation

6p, Permanent Deformation and Crack Length

6p = 2.82714 x 10 -4 a+6.34722 x 10 -4

0.94621

CR, Reloading Compliance and Crack Length

C R = 1.09013x10 -7a+l.10882x10 -6

0.89123

Cm, Modified Compliance and Crack Length

C

0.99215

GR, Strain Energy Release Rate, R-Curve

G R=0.38385 + 1.89948xi0

Relation

Note:

6p . a

. Aa a r e.

m

= 9.84185 x 10 -7 a-4.03886 x i0-9a 2 -2

0.84135

(Aa)

-5.54866 x 10-4(Aa) 2

i n .i n c h e s

CR

Cm a r e

in

in./lbs,

a n d CR i s

in

lbs./ln.

4.

D. J. Cook and G. D. Crookham, Magazine of Concrete Res., 30, 205 (1978).

5.

S. Mindess, Proc. of Eng. Conf. on Cement Production, New Hampshire, June 24-29, 175 (1979).

6.

S. P. Shah, Proc. of Eng. Conf. on Cement Production, New Hampshire, June 24-29, 187 (1979).

7.

P. F. Walsh, Magazine of Concrete Res.,28, 37 (1976).

8.

S. P. Shah and F. J. McGarry, J. Eng. Mech. Div., ASCE, 97, 1663 (1971).

9.

D. P. William and A. G. Evans, J. of Testing and Evaluation, JTEVA I, 264 (1973).

i0.

E. R. F u l l e r ,

ASTM STP 678, 3 (1979).

ii.

B. K. A t k i n s o n , (1979).

12.

A. G. Evans and S. M. Wiederhorn, J. Matls.

13.

M. Matsui, T. Soma and T. Oda, Fracture Mechanics of Ceramics, i, New York, 711 (1978).

14.

F. P. Champomier, ASTM, STP 678, 60 (1979).

15.

A. G. Evans, J. R. C l i f t o n 535 (1976).

16.

J. S. Nadeau, (1974).

17.

Y. W. Mai, J. M a t l s . S c i . ,

18.

J. C. Lenian and A. R. Bunse11, O. Matls.

Int'l

J. Rock Mech. Min. Sci.

& Geomech.,Abstr. 16, 49 Sci.,

2, 270 (1974).

and E. Anderson, Cement and Concrete Res., 6,

S. Mindess and J. H. Hay, J. Amer. Cera. Soc., 57, 51 14, 2091 (1979). Sci.,

14, 321 (1979).