A new approach to the study of the influence of cement fineness on the strength of cement mortars

CEMENT and CONCRETERESEARCH. Vol. 4, pp. 915-923, 1974. Pergamon Press, Inc Printed in the United States.

A NEW APPROACH TO THE STUDY OF THE INFLUENCE OF CEMENT FINENESS ON THE STRENGTH OF CEMENT MORTARS M. H r a s t e D e p a r t m e n t of C h e m i c a l E n g i n e e r i n g , F a c u l t y of T e c h n o l o g y , U n i v e r s i t y of Z a g r e b

A. Bezjak D e p a r t m e n t of C h e m i s t r y , F a c u l t y of P h a r m a c y and B i o c h e m i s t r y , U n i v e r s i t y of Z a g r e b

(Communicated by Z. Sauman) (Received July 30, 1974) ABSTRACT A study is reported on the possibility to determine the influence of particle sizes of c e m e n t on the strength of c e m e n t m o r t a r s by taking into consideration all the particles in a set, under the p r e s u m p t i o n that apart of the independent effect of every particle in the course of hydration there is a simultaneous and intermediate effect of all the particles on the s a m e physical property. The m e t h o d has been applied to c e m e n t of identical chemical and phase composition but different particle size distributions.

Es w i r d ~iber U n t e r s u c h u n g e n b e r i c h t e t , die s i c h m i t d e r Mbglichkeit einer Einflussbestimmung der Teilchengr6ssen auf die F e s t i g k e i t yon Z e m e n t m b r t e l n b e f a s s e n , wobei a l l e Teilchen e i n e r Gruppe imbegriffen sind, unter der Annahme; d a s s a b g e s e h e n yon d e r unabhfingigen Einwirkung j e d e s T e i l c h e n s im Laufe des H y d r a t a t i o n s p r o z e s s e s , auch e i n e s i m u l t a n e g e g e n s e i t i g e Einwirkung a l l e r T e i l c h e n auf d i e s e l b e physikalische Eigenschaft besteht. D i e s e s V e r f a h r e n w u r d e an e i n e m Z e m e n t m i t i d e n t i s c h e r c h e m i s c h e r und P h a s e n z u s a m m e n s e t z u n g , j e d o c h mit v e r s c h i e d e n e n K o r n g r b s s e v e r t e i l u n g e n durchgef~ihrt.

915

916

Vol. 4, No. 6 M. Hraste, A. Bezjak

Introduction It has been customary

s o f a r to

fineness

on the strength

particle

size fractions

the influence Xumerous

exerted

authors

the size between The most

of cement

(1-17)

interpretation

is impossible

to p r o d u c e

cannot be correct.

versus specific

to a c e r t a i n

surface

area

particles

of

to the hydrated

particles.

deficiency .Thus,

it

defined particle

on the influence

of such exclu-

On the other hand the specific

can be characteristic

strength

particles.

the one that explains

with strictly

based

or by

m o s t to t h e f i n a l s t r e n g t h s .

is obviously

a cement

area

cement

imply one or another

so an explanation

area

surface

that cement

by the effect attributed

approaches

surface

have proved

of cement

by the effect of separate

and that of the specific

All the other

sive fractions

mortars

5 a n d 30 }ira c o n t r i b u t e

correct

only,

the influence

by the content of hydrated

t h e g a i n in s t r e n g t h

sizes

express

for the relationship

degree

only.

this relation

fineness

In t h e c a s e o f i n c r e a s e d

is explicable

only by the particle

size distribution. The contribution was therefore Supposing

of definite examined

sizes

within the entire

that the strength

ned by the particle

particle

(S) d e p e n d s

size distribution

to t h e g a i n o f s t r e n g t h set of all particles.

o n a f u n c t i o n H(x) d e t e r m i -

F(x) and the estimated

basic

function [-ICx)(16,18) then

S.fH(x,dx--fF(x) II (x)dx The equation strength entire

is solved

linear

and the content of particles

distribution.However,

effect of definite valid to a certain a better

by applying

insight

the independent

particle

relation

of a definite

the supposition sizes

extent only.

between

the

size within the

of the independent

within the set of all particles It has therefore

into this relationship effect of every

/l/

particle

been concluded

can be obtained, in t h e c o u r s e

if apart

is that of

of the hydra-

Vol. 4, No. 6

917 MORTARS, FINENESS, SIEVE ANALYSIS, STRENGTH

tion process.we

s u p p o s e t h a t t h e r e e x i s t s an i n t e r m e d i a t e

of a l l t h e p a r t i c l e s the

selfsame

on t h e s a m e p h y s i c a l p r o p e r t y

part

supposition is upheld by the probability that by their

effect the particles

of a c e r t a i n s i z e c a n i n c r e a s e

c o n t r i b u t i o n of i n d i v i d u a l p a r t i c l e

c o n n e c t e d w i t h a l l the p a r t i c l e

The i n t e r m e d i a t e

the

of h y d r a t i o n a p a r t i c l e

is not

s i z e s of t h e s e t , but s u r r o u n d e d

sizes only. However,

take by approximation

or decrease

s i z e s to the f o r m a t i o n of s t r e n g t h .

It i s o b v i o u s t h a t d u r i n g t h e p r o c e s s

particular

in t h e c o u r s e of

process. Theoretical

The p r o p o s e d

effect

by

t h e s e t b e i n g a l a r g e one~ w e c a n

t h a t all s i z e s a f f e c t a l l t h e o t h e r s i z e s .

i n f l u e n c e of two e f f e c t s is m a t h e m a t i c a l l y

solved

by the convolution theorem. In t h i s c a s e t h e s t r e n g t h ,

t o o , d e p e n d s on a f u n c t i o n H(x) w h i c h

i n c l u d e s t h e e f f e c t of e v e r y s i n g l e p a r t i c l e f u n c t i o n f(x) a s w e l l a s t h e i n t e r m e d i a t e represented

size expressed

b y the

e f f e c t s of all t h e p a r t i c l e s

b y t h e f u n c t i o n gCx), i . e . :

S ~fH (x)dx.fff

/2/

(y) g ( x - y ) d y d x

The f o r c i n g f u n c t i o n s a r e a d a p t e d to t h e a c t u a l s t a t e b y t a k i n g into account the particle estimated

size distribution

b a s i c f u n c t i o n s [-I(x) a n d ~ ( x ) ~ t h u s :

S,, f

H{x)dx=ffFcy)

It i s not p o s s i b l e to d e t e r m i n e single particle

n (y)F(x-y) ~(x-y)dydx

the intermediate

because a mathematical

a d a p t a b l e to all t h e d i s t r i b u t i o n s that matter

F(x) a n d t h e c o r r e s p o n d i n g

e f f e c t of e v e r y

expression

sufficiently

cannot be formulated

not even a mathematical

expression

/ 3/

and for

for the estimated

918

Vol. z$, No. 6

M. Hraste, A. Bezjak

basic functions [(x) andS(x) , so w e can only e x a m i n e the effect of particle fractions grouped into classes consisting of definite particle sizes~ viz."

S,,y_.~ Y~. < a - < F ( x - y ) > < b > y x-y

if


y

>
x-y

>,, E

/ 4/

xy

xy

To s i m p l i f y

the manner

of notation we change to:

/6/

S-Y~ >-~ A j, K

where:

and < F ( K ) > --weight per cent of particles in classes of definite sizes

Aj,K =

coefficient of m e a n

value denoting the m a x i m u m

effect in the contribution of single classes of definite sizes to the formation of strength J - I,N K,, J,X N,, t o t a l n u m b e r Considering

the fact that cement

size distributions coefficients

of classes.

can be measured,

of the mean

the least

square

mination

of properties

but with different

mortar

value Aj,K.

method,

proceeding

of cement

particle

strengths

it is possible

as well as particle to c a l c u l a t e

the

They have been calculated from

mortars

bv

the experimental

deter-

made

cement,

size distributions.

of the same

Thus obtained

coef-

Vol. 4, No. 6

919 MORTARS, FINENESS, SIEVE ANALYSIS, STRENGTH

f i c i e n t s a r e v a l i d f o r the r e s p e c t i v e identical hydration process.

phase composition

It s h o u l d b e n o t e d t h a t t h e o b t a i n e d

coefficients are closely connected with the manner measurements

a n d the

have been carried

in w h i c h t h e

out a n d it is t h e r e f o r e

to s t a t e the c o n d i t i o n u n d e r w h i c h the p h y s i c a l p r o p e r t i e s

imperative have

been ascertained. The r e l i a b i l i t y f a c t o r R d e f i n e d b v the e x p r e s s i o n accuracy

of t h e a n a l y s i s :

/7/

s h o w s the

n IAj l

i-1 R"

/7/ n

IS.l 1

i,,l where:

n,, n u m b e r of samples A. =elementary deviation, i.e. the difference between i

the experimentally obtained and the calculated value S. (computed by m e a n s of the coefficients 1

Aj, K ) S. = e x p e r i m e n t a l l y 1

determined

physical property

for

the i-th sample.

Experimental

part

The c e m e n t u s e d f o r t h i s w o r k h a d t h e f o l o w i n g c h e m i c a l a n d phase composition:

loss on ignition SiO2

0,4 % 20,3 %

Fe203

2,9 %

AI203

5,9 9/0

Cao

64,4 %

MgO

2,1%

C3S ;~-C2S

56 %

24 %

C3A

9 %

ferrite phase

5 %

920

Vol. 4, No. 6 M. Hraste, A. Bezjak SO 3

2,4 %

Na20

0,6 %

K20

0,8 %

The p h a s e c o m p o s i t i o n w a s d e t e r m i n e d

by X - r a y d i f f r a c t i o n

analysis. By g r i n d i n g the c l i n k e r to d i f f e r e n t f i n e n e s s we o b t a i n e d s a m p l e s on w h i c h the p a r t i c l e s i z e d i s t r i b u t i o n s and s t r e n g t h s w e r e d e t e r m i n e d . The p a r t i c l e s i z e d i s t r i b u t i o n w a s a s c e r t a i n e d by s i e v e a n a l y s i s a c c o r d i n g to DIN 4188 a n d by the s e d i m e n t a t i o n m e t h o d on Bachmann-Sartorius

b a l a n c e . The s t r e n g t h s w e r e t e s t e d in a c c o r -

d a n c e with Y u g o s l a v s t a n d a r d B . C 8 . 0 2 2 - 63 p r e s c r i b i n g

compres-

s i v e and b e n d i n g s t r e n g t h s . F o r the r e q u i r e d classes

c a l c u l a t i o n s the p a r t i c l e s

c o m p r i z i n g the following s i z e s :

3 ( 1 0 - 3 0 }lm), 4 ( 3 0 - 7 0 }lm) a n d

w e r e g r o u p e d into

1(0-5 ~ m ) ,

5(>70 ~m), i.e.

2 ( 5 - 1 0 }~m),

N , , 5 . The l i m i t s

w e r e s e l e c t e d in a c c o r d a n c e w i t h the p r e v i o u s l y a c q u i r e d e x p e r i e n c e . Results and discussion Measurement

v a l u e s f o r the p a r t i c l e s i z e d i s t r i b u t i o n s and s t r e n g t h s

a r e p r e s e n t e d in T a b l e s

1 a n d 2.

To d e t e r m i n e the v a l u e s of c o e f f i c i e n t s A. as p r e s e n t e d in Table 3 ],K i . e . to find out t h e c o n t r i b u t i o n to s t r e n g t h s of d i f f e r e n t c l a s s e s of definite p a r t i c l e s i z e s by their i n t e r m e d i a t e lated the i n t e r m e d i a t e

e f f e c t , we h a v e c a l c u -

e f f e c t of all the c l a s s e s .

M a t h e m a t i c a l l y this

c o n s i s t e d in s o l v i n g a s y s t e m of 35 l i n e a r e q u a t i o n s with 15 u n k n o w n s (N-5).

The s y s t e m w a s s o l v e d b y the l e a s t s q u a r e m e t h o d on the

c o m p u t e r CAE 930. It s h o u l d be e m p h a s i z e d t h a t t h e m e n t i o n e d c o e f f i c i e n t s a r e v a l i d f o r c o n t i n u a l d i s t r i b u t i o n s o n l y w h e n an i n t e r m e d i a t e particles

e f f e c t of all the

is p o s s i b l e a n d o n l y f o r c e m e n t s of a d e f i n e d c h e m i c a l

Vol. 4, No. 6

921 MORTARS, FINENESS, SIEVE ANALYSIS, STRENGTH FABLE

1

Results for Particle Size Distributions Weiqht p e r cent of p a r t i c l e s in s e p a r a t e c l a s s e s Sample 1

2 3 4 3 6 7 8 9 10 1I 12 I3 14 13 16 17 I8 IQ 20 21 22 23 24 25 26 2"¢ 28 29 30 31 32 33 34 33

0-5 ~m 3.0 3.3 4,5 3.5 6.5 7,0 7,5 7,5 I1,0 II.0 12,5 13,0 15,5 13,5 15,5 13,0 17,0 14,5 16,5 9.3 9,0 I0,5 12,0 16,5 3,3 7.0 7,5 6,0 8,0 8,0 7,5 10,0 9,0 II,0 10,0

3-10 ~m 10-30 ~m 30-70 pm )70 ~m 4,0 %0 I0.0 10.5 13.5 1~,5 13.0 18.5 19.5 20.0 1%5 23,3 18,0 21,0 20,0 21,0 15.3 16,0 17,0 I0,3 12,0 15.5 17,5 17,5 I0.0 i3.0 I6,0 14,5 17,0 17,3 26,0 18,0 lq,O 17,5 1%5

20,5 26,0 27.5 31.0 33,0 36,5 35,5 36,0 34,3 34,5 35,0 32,0 33,0 30,5 31,5 31,0 30,3 29,5 28,3 32.0 36,0 37,0 3815 34,5 32,5 36,0 32,5 35,5 36,0 34,0 30,0 38.0 36•0 36,5 37,0

TABLE

17,5 22.5 25,0 27.0 27.0 26.5 26.5 25.5 23,5 23.5 22.0 20,0 20,0 18,5 19,0 lq,O 19.3 18,0 16,5 23,5 30,0 24.5 20,0 20,0 I3,0 32,0 21,5 24.5 22,0 24.0 21,5 22,5 lq,O 20.0 21,0

53.0 3%0 33,0 26.0 20.0 13,5 13,3 12,5 11,3 11.0 11,0 11,5 13,5 14,3 14,0 16,0 17,3 22,0 21,3 21,5 13,0 1215 I2,0 11,5 39,0 22,0 22,3 19,5 17,0 16,5 15,0 11,5 17,0 13,0 12,5

2

Results f o r S t r e n g t h s Strengths Sample

l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 38

(kp/cm 2)

3 days

bending 7 days

28 days

compressive 3 days 7 days 28 days

10.8 24,5 27,3 37,3 44,4 49,8 43,8 46,2 52,2 58.0 54.7 57.9 34.2 60,2 60,3 56,9 56,3 53,7 60,6 31,9 35,6 37,3 38.4 39,1 2%4 43,1 47)1 41~I 53,8 57,5 57,3 53,6 89,6 $9,9 60,4

18,6 33,0 38,5 48,7 55,5 59,2 56,2 55,3 59,9 61,6 64,9 66,6 61,6 64.0 66.0 64,9 64,3 66,8 62,5 42,7 51,3 46,g 48,1 49,9 40,1 53,6 60.3 52,2 60.3 65,8 64,3 64,1 67,7 67,2 69,5

34,5 51,6 51,2 63,8 68,3 68,1 72,3 71,6 73,6 74,8 72,8 86,4 76.4 69,9 71,7 69,6 70,5 77,3 67,7 56,1 66,1 63,5 64,7 70,9 57,4 68,0 " 70+8 72,2 72,5 76,7 87,4 81,0 84,3 7513 76,9

60 106 129 146 174 226 195 213 256 271 293 314 298 312 326 331 316 311 289 126 148 156 16I 198 III 189 210 163 231 269 283 263 283 313 323

89 161 184 233 278 305 29l 306 346 374 364 398 368 393 405 389 388 409 384 206 258 223 221 264 159 239 310 256 324 368 374 375 386 411 419

150 225 254 333 369 403 424 434 455 470 t28 482 451 470 509 488 471 451 445 300 331 353 371 390 253 394 401 363 433 433 466 467 476 490 510

922

Vol. 4, No. 6 M. Hraste, A. Bezjak

TABLE

3

Values for Coefficients A j,

K

Flg,ndi no st r~mqth I daxs J.K

v d,l~s Aj, K

J,K

1, i 0,387 2. 1 I), 348 I, ] O, 1134 1, I 3, 132 4. I ),003 1,2 O, O4 1 4.5 O, 022 3,~ O,Oll 3,5 -0,007 3, ; -0,007 2, ; -0.025 3, I -O.0% 2,2 -O,13b 2, t - 0 . lq5 1.3 -0. tII R-O,06

2~ ,l,tv Aj. K

2. 3

0.35o 1, t 0.30o 1.5 O. 0ST I. I O,0"5 l. I O.02 q 3, I O, 0 2 t 2,5 O. 015 3,5 0,(333 ;,5 -O,O05 1,5 -0,007 1,2 -O,OI~ /, I -0.052 2,2 -O, (1'~5 2,1 -0,23~ 1,3 -O,2~2 R-O,052 C ompressl', 7 days

A5. K

2. ! O, 375 ], I (/.275 I. / (3, I l 2 ;. 1 ),O'~,~ I, 1 O,0')l 2.2 O, {12 I l. 5 0,005 5.5 4 ] , O00 2,3 -1,O35 I. I -0,013 I, I -;1,03(3 4, 5 -0,055 3,~ -O, 1 ~-I 1,2 -0.25o 2. t -},325 Ro0,Ot3

e strenqth

3 da~s J,K Aj, K

J.K

1, I 3,337 2,3 2 , 138 1,1 0,822 1,~ o,6al I, I l), I0~ 1,2 0,3t] I, ~ O. 2q 5 3, ) O,2lq 2,5 O,O07 5.5 -0.015 3,3 -0,232 2.2 -0,712 3. ; +0,876 2.4 -t,370 3,~ -2,~') I R.0,Oql

2,3 3,IIR I, ; 3,0~2 1,3 0,863 1,1 0,7q0 t. t 0 , ll~ t,5 0,051 3,5 -O,OI$ 3.5 -0,033 2.5 -0,073 1,2 -0,2~1 3.] -0.281 3, I -0,3t2 2,2 10,85 } 2,1 -2.1ql 1,3 -2,655 R-0,073

and p h a s e c o m p o s i t i o n .

I,>

Aj l K

28 d i y a J,K

Aj. K

2.1 !. t 1,5 1, i 3.3 I, I 1.5 l, I t,2 3,5 I.~ 2,5

2.283 1, ~,36 0,830 0,~04 O.17O (~, I60 0.0'15 0,OI] -O.OIt -0,0o7 -(),270 -[), 4¢~5

2.2

-O,-C?2

2. t -1,234 !. ~ -1,6}7 R-O,051

The n e g a t i v e s i g n s a r e not to be i n t e r p r e t e d

as denoting groups which decrease

the s t r e n g t h but r a t h e r a s t h o s e

c o n t r i b u t i n g l e s s to the e n t i r e s t r e n g t h and t h e y a r e in fact the r e s u l t of m a t h e m a t i c a l

operations.

from inevitable errors

in the d e t e r m i n a t i o n of the p a r t i c l e s i z e

distribution.

It is v e r y l i k e l y that t h e y d e r i v e

If the s a m e c a l c u l a t i o n w a s a p p l i e d to the r e s u l t s

o b t a i n e d by R i t z m a n n (16) w h o p r e p a r e d d i s p e r s i o n

systems

from

particle size fractions with strictly defined limits,

the n e g a t i v e

s i g n did not p r a c t i c a l l y a p p e a r . The v a l u e s of the c a l c u l a t e d . c o e f f i c i e n t s i n d i c a t e that the i n t e r m e d i a t e e f f e c t of p a r t i c l e s

up to 5 p m with t h o s e of 30 to 70 jam,

a s w e l l a s the e f f e c t of p a r t i c l e s b e t w e e n 5 and 10 Jam and t h o s e of 10 to 30 p m c o n t r i b u t e m o s t to the c o m p r e s s i v e s t r e n g t h s a f t e r 3 and 7 d a y s .

and bending

A s f o r the c o m p r e s s i v e

and b e n d i n g

Vol. 4, No. 6

923

MORTARS, FINENESS, SIEVE ANALYSIS, STRENGTH strengths

a f t e r 28 d a y s the m o s t i m p o r t a n t

effects between particles obtained results

of 5 - 1 0 Jam w i t h t h o s e of 1 0 - 3 0 jam. The

a r e in g o o d a g r e e m e n t

knowledge and can therefore n a t i o n of the m e c h a n i s m

a r e the i n t e r m e d i a t e

w i t h the p r e s e n t

b e t a k e n a s a c o n t r i b u t i o n to t h e e x p l a -

of c e m e n t h a r d e n i n g .

It s h o u l d b e s p e c i a l l y n o t e d t h a t f r o m t h e a s c e r t a i n e d A

J,K ensure

we c a n c a l c u l a t e t h e p a r t i c l e the best or the required

this matter

s t a t e of

a r e in p r o g r e s s .

in the c h e m i c a l a n d p h a s e

size distribution

strength.

coefficients which would

F u r t h e r i n v e s t i g a t i o n on

It is o b v i o u s , h o w e v e r ,

that a change

composition can bring about a change

in the c o e f f i c i e n t s of t h e m e a n v a l u e s s o t h a t a g e n e r a l a p p l i c a t i o n of the p r i n c i p l e is not v e r y s i m p l e • References: 1. H. K~ihl, Z e m e n t ,

18; 1932 ( 1 9 2 9 )

2. A. B. H e l b i g , Z e m e n t ,

1__~9, 237 ( 1 9 3 0 )

3• A. B. H e l b i g • Z e m e n t ,

20, 7 5 ( 1 9 3 1 )

4. H. Kiihl, Z e m e n t ,

2__00, 169 ( 1 9 3 1 )

5. A. E i g e r , T o n i n d . Z t g . , 6

X

C

55~ 1389 ( 1 9 3 5 )

R o c k w o o d , Rock P r o d u c t s ,

7. J . W u h r e r ,

Zement-Kalk-Gips,

52 3,

132 ( 1 9 4 9 ) 148 ( 1 9 5 0 )

8. E. W. S c r i p t u r e S. W. B e n e d i c t , F. J . L i w a n o w i c z , J . A m . Conc.

Inst.,

2__~3~205 ( 1 9 5 1 )

9. A. Rio~ F. V. B a l l a s s i ,

L' Ind. I t a l . del C e m e n t o ~ 2___44,87 ( 1 9 5 1 )

10. K• A i c h i n g e r ,

A• J o r d a n ,

11. N• P. S t e j e r t ,

Cement(URSS)

Zement-Kalk-Gips, , No•3(1954)

12• W• C z e r n i n ~ Z e m e n t - K a l k - G i p s ,

_71160 ( 1 9 5 4 )

13. H. B o e r n e r ,

9~ 153 ( 1 9 5 6 )

Zement-Kalk-Gips,

14. K• B o m k e , Z e m e n t - K a l k - G i p s ~ 15• B• B e k e , Z e m e n t - K a l k - G i p s ~

6--, 87 ( 1 9 5 3 )

S p e c i a l edition~ N o . 6 ~

100

1__~3~ 419 ( 1 9 6 0 )

16• H• R i t z m a n n ~ Z e m e n t - K a l k - G i p s ,

2__J_1, 390 (1968)

17. B. Beke~ L• O p o c z k y ~ E p i t 6 a n y a g ~ 2_~1~ 281 ( 1 9 6 9 ) 18. A. B e z j a k ,

~I. H r a s t e ,

Kern• lnd• ( Z a g r e b ) , 1___99,287 ( 1 9 7 0 )