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Cement and Concrete Research, 2, July 4, pp. 375-386, 1972-07-01
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Factor affecting the Young's modulus - porosity relation of hydrated
portland cement compacts
Feldman, R. F.
https://publications-cnrc.canada.ca/fra/droits
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CEMENT
and CONCRETE RESEARCH.
Vol.
2 ,
p p . 375-386, 1972. Pergamon Press, Inc. Printed in the United S t a t e s .FACTORS AFFECTING YOUNG'S MODULUS
-
POROSITY RELATION O F HYDRATED PORTLANDCEMENT COMPACTS
R. F. F e l d m a n
Division of Building R e s e a r c h , National R e s e a r c h Council of Canada Ottawa 7 , Ontario, Canada
(Communicated by
P .
J .
Sereda)ABSTRACT
Two s e r i e s of c o m p a c t s a r e studied, one d - d r i e d b e f o r e and one a f t e r compaction. M e a s u r e m e n t s of absolute density, helium flow c h a r a c t e r i s t i c s and YoungSs modulus indicate t h a t high p r e s s u r e s c a n f o r c e t h e l a y e r s of d - d r i e d m a t e r i a l c l o s e r t o - g e t h e r , giving a Young's modulus double t h a t displayed when no i n t e r l a y e r w a t e r i s p r e s e n t and identical t o t h a t when s p a c e s a r e occupied by w a t e r molecules. Water c a n r e - e n t e r between t h e l a y e r s , however, and on r e d r y i n g YoungDs modulus i s reduced by 50 p e r cent t o the n o r m a l value f o r t h e d - d r i e d m a t e r i a l . T h e i n t e r l a y e r w a t e r m u s t b e r e g a r d e d a s p a r t of t h e solid.
SOMMAIR,E
Deux s C r i e s d e c o m p a c t s sont e t u d i e e s , l'une I'd-dried" avant l e compactage et l f a u t r e a p r k s . L e s c a l c u l s d e densit6 absolue, l e s c a r a c t e r i s t i q u e s dfCcoulement
3
lfhkliurn e t l e Modulus Young indiquent que l e s h a u t e s p r e s s i o n s peuvent f o r c e r l e s couches d e m a t e r i a u x I'd-dried" e n s e m b l e donnant a i n s i un Modulus Young double d e c e l u i obtenu quand aucune eau e s t prCsente dans l e s e n t r e c o u c h e s et identique3
c e l u i qui e s t obtenu quand l e s e s p a c e s sont occupes p a r d e s moli.cules d'eau. L f e a u peut r C - e n t r e r e n t r e l e s couches, cependant et s u r resCchage, l e Modulus Young e s t r e d u i t p a r 50 p. 100,B
l a v a l e u r n o r m a l e , pour l e matCriau "d-dried". L'eau d'entrecouche peut d t r e c o n s i d e r e e c o m m e f a i s a n t p a r t i e du c o r p s solide.MODULUS OF ELASTICITY, HYDRATED CEMENT, COMPACTS
Vol. 2, No. 4
Introduction
P o r o s i t y i s the m a j o r f a c t o r governing Youngys modulus of e l a s t i c i t y of porous bodies (1, 2), and p r e v i o u s w o r k on hydrated portland cement h a s shown that t h i s m a t e r i a l i s no exception (3, 4, 5). C u r v e s of p o r o s i t y v e r s u s Young's modulus f o r hydrated portland cement s p e c i m e n s p r e p a r e d by p a s t e hydration o r by compaction of bottle hydrated c e m e n t approximately coincide (5).
It h a s a l s o been shown ( 3 ) t h a t i t i s p o s s i b l e t o i n c r e a s e t h e Youngys modulus a t a given p o r o s i t y by allowing complete r e - e n t r a n c e of i n t e r l a y e r
water. It i s recognized
( 6 ,
7, 8 ) t h a t i n t e r l a y e r s p a c e h a s s p e c i a l p r o p e r t i e s ,i n c o n t r a s t with other p o r e s , and a l e s s a r b i t r a r y definition of p o r o s i t y i s r e q u i r e d if it i s t o be u s e d i n c o r r e l a t i o n with o t h e r p r o p e r t i e s . Recently it h a s been d e m o n s t r a t e d (9) t h a t p o r o s i t y of hydrated portland cement c a n be m e a s u r e d by helium pycnometry and t h a t i n t e r l a y e r s p a c e c a n b e excluded by t h i s technique.
This work h a s involved a study of porosity: Young's modulus r e l a - tion of compacts using v a r i o u s techniques whereby t h e i n t e r l a y e r s p a c e configuration m a y b e modified; the widely u s e d exponential m a t h e m a t i c a l e x p r e s s i o n w a s applied in t h i s w o r k f o r c o r r e l a t i n g the data.
E x p e r i m e n t a l M a t e r i a l s
Hydrated cement w a s p r e p a r e d by hydrating a Type I cement in a
rotating bottle a t a w a t e r / c e m e n t r a t i o of 5. 0. Hydration was continued f o r
up t o 28 months and was found t o b e s e n s i b l y complete. When mixing w a s
completed the hydrated cement was f i l t e r e d , d r i e d a t 3270 '0 o v e r a
s a t u r a t e d solution of CaC1 and t h e n s c r e e n e d through a 100-mesh sieve.
2
T h e r e m a i n i n g f r a c t i o n ( m o s t l y C a ( 0 H ) c r y s t a l s ) was ground and r e m i x e d
2
with t h e sieved m a t e r i a l . Compaction
Two s e r i e s of s a m p l e s w e r e m a d e i n t h i s work:
S e r i e s A: Compacts w e r e m a d e f r o m t h e above powdered m a t e r i a l s , which had been d r i e d a t 85°C f o r t h r e e h o u r s in a vacuum c h a m b e r . This had
Vol.
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No. 4
MODULUS OF ELASTI CITY, HYDRATED CEMENT, COMPACTS
p r e v i o u s l y (7) been found t o approximate the d-dried condition. Compacts wer.e f a b r i c a t e d a t nine p r e s s u r e s : 285, 570, 1140, 2850, 4270, 5700, 8540,
2
11,400 and 14, 350 kg/cm i n a gloved box conditioned a t l e s s than 170 RJ3.
T h e s p e c i m e n s w e r e d i s c s 32mm i n d i a m e t e r and 1. 25mm thick. D e t a i l s of the 'compaction p r o c e d u r e h a v e been published e l s e w h e r e (3). Twelve c o m p a c t s w e r e f a b r i c a t e d a t e a c h p r e s s u r e except the two highest, w h e r e nine compacts w e r e f a b r i c a t e d . At a l a t e r d a t e but using t h e s a m e m a t e r i a l , a s i m i l a r s e r i e s w a s p r e p a r e d consisting of t e n c o m p a c t s e a c h a t 570, 5700
2 and 14, 350 kg/cm
.
S e r i e s B: A s e r i e s of compacts was p r e p a r e d a s above, with the hydrated cement d r i e d t o only t h e 3270 RH level. After compaction t h e s e s a m p l e s w e r e d r i e d by heating a t 8 5 ° C until t h e weight l o s s indicated that t h e s a m p l e s w e r e adequately d r i e d with r e s p e c t t o powdered m a t e r i a l . Again a t a l a t e r d a t e
-
and using the s a m e m a t e r i a l , a r e p e a t s e r i e s of 10 c o m p a c t s w a s m a d e a t
P o r o s i t y , Density and Helium Flow M e a s u r e m e n t s
Solid volume m e a s u r e m e n t s w e r e m a d e with a helium c o m p a r i s o n pycnometer and a r e d e s c r i b e d in d e t a i l e l s e w h e r e
(9).
P o r o s i t y w a s c a l - culated f r o m m e a s u r e m e n t of t h e e x t e r n a l g e o m e t r y and t h e solid volume; density was calculated f r o m solid volume and weight.Helium flow m e a s u r e m e n t s a l s o d e s c r i b e d e l s e w h e r e (8) w e r e m a d e 2
on S e r i e s A s a m p l e s compacted a t 520, 5700 and 14,350 kg/cm
,
and onL
S e r i e s B s a m p l e s compacted a t 5700 kg/cm
.
All density and helium flow m e a s u r e m e n t s w e r e m a d e a t t h e d - d r i e d condition.Determination of Young's Modulus of E l a s t i c i t y
Apparatus w a s used that i s d e s c r i b e d e l s e w h e r e (3). The p r o c e d u r e involves t h e m e a s u r i n g of the deflection of a d i s c s p e c i m e n loaded a t i t s
c e n t r e and supported a t t h r e e points located a t the c i r c u m f e r e n c e of a c i r c l e 1 in. in d i a m e t e r . T h e a v e r a g e of five t e s t s w a s c o n s i d e r e d a s Young's modulus f o r any given s e t of conditions.
Rewetting and Sequence of E x p e r i m e n t s
V o l . 2, No. 4 MODULUS OF E L A S T I C I T Y , HYDRATED CEMENT, COMPACTS
After compaction, weight and g e o m e t r y w e r e m e a s u r e d in a gloved
dry-box and t h e s a m p l e s then t r a n s f e r r e d t o the helium pycnometer w h e r e t h e solid volume and helium flow w e r e m e a s u r e d . The s a m p l e s w e r e r e t u r n e d t o t h e dry-box and Young's modulus m e a s u r e m e n t s w e r e taken. At t h i s s t a g e t h e s a m p l e s w e r e placed in a d e s i c c a t o r maintained a t 10070
R H f o r one day, then i m m e r s e d in s a t u r a t e d C a ( 0 H ) solution f o r one month.
2
Subsequently, t h e s a m p l e s w e r e conditioned in a d e s i c c a t o r over t h e
a p p r o p r i a t e s a l t solution f o r 42% RH (3) f o r t h r e e months, when t h e Young's modulus was m e a s u r e d again. S a m p l e s compacted a t 5700 and 14, 350
2
kg/cm w e r e again d - d r i e d and Young's modulus w a s m e a s u r e d f o r t h e third t i m e . The rewetting p r o c e d u r e previously followed w a s repeated and
Young's modulus was m e a s u r e d f o r t h e fourth and l a s t t i m e a f t e r conditioning s a m p l e s t o 42% RH.
The solid volume, density, porosity, h e l i u m flow c h a r a c t e r i s t i c s and Young's modulus of the new S e r i e s A made a t a l a t e r dat,e w e r e
m e a s u r e d i m m e d i a t e l y following f a b r i c a t i o n of the s a m p l e s . No rewetting e x p e r i m e n t s w e r e p e r f o r m e d on t h e s e s a m p l e s .
S e r i e s B, d-dried a f t e r compaction
Solid volume, density, porosity, helium flow c h a r a c t e r i s t i c s and Young's modulus w e r e a l l m e a s u r e d a t the d-dry condition. The rewetting p r o c e d u r e was a l s o followed with t h i s s e r i e s , allowing one month of
exposure in s a t u r a t e d C a ( 0 H ) solution. Young's modulus m e a s u r e m e n t s 2
w e r e m a d e a f t e r s a m p l e s had been conditioned t o 4270 RH.
2
The s a m p l e s compacted a t 5700 kg/cm t h r e e y e a r s l a t e r w e r e only m e a s u r e d f o r Young's modulus a t the d - d r y condition.
R e s u l t s
P o r o s i t y
P o r o s i t y v e r s u s compaction p r e s s u r e s a r e plotted on Fig. 1 a s a semi-log relation. A s observed previously, compaction of m a t e r i a l con-
ditioned a t the higher humidity yields a lower porosity. P o r o s i t i e s a r e a s low a s 7'3% f o r S e r i e s B and 10. 5% f o r S e r i e s A
.
Values a r e tabulated on T a b l e s I and11.
At low p r e s s u r e s , the p o r o s i t i e s f o r t h e two s y s t e m s a r eV o l . 2, No. 4
MODULUS OF ELASTICITY, HYDRATED CEMENT, COMPACTS
quite s i m i l a r , but t h e difference widens a t higher p r e s s u r e s . Any i n t e r l a y e r s p a c e between t h e collapsed s h e e t s of s i l i c a t e s i s not included in t h i s
p o r o s i t y m e a s u r e m e n t , a point that will be elaborated l a t e r .
Density
Variation of density with compaction p r e s s u r e is shown on Fig. 2.
S e r i e s A shows a s t e a d y i n c r e a s e f r o m IZ. 274 a t 285 kg/cm2 t o 2. 395 gm/cc 2 a t 14, 350 kg/cm
.
The new S e r i e s A v a r i e s f r o m 2.293 t o 2. 408 gm/cc L f o r 570 t o 14,350 kg/cm.
FIG, 1 FIG. 2Compaction P r e s s u r e vs P o r o s i t y Density vs Compaction P r e s s u r e
The r e s u l t s f o r S e r i e s B show s o m e s c a t t e r a t t h e higher p r e s s u r e s ,
L
but t h e r e a p p e a r s t o b e l i t t l e i n c r e a s e in density beyond 4200 kg/cm
,
a 2value between 2. 294 and 2. 312 a t 14, 350 kg/cm
.
Thus the s e r i e s in which compaction took p l a c e a f t e r drying shows a much h i g h e r absolute density than t h e s e r i e s d r i e d a f t e r compaction. T h e difference i s not l a r g e at lower p r e s s u r e s .Helium Flow M e a s u r e m e n t s
The r e s u l t s f o r S e r i e s A
,
t h e new s e r i e s in t h e d-dried s t a t e , a r e p r e s e n t e d in Fig. 3. Helium flow d e c r e a s e s with p r e s s u r e of compaction.V o l . 2,
No.
4
MODULUS OF E L A S T I C I T Y , HYDRATED CEMENT, COMPACTS
T A B L E I
YOUNG'S MODULUS DATA F O R S E R I E S A
C o m p a c t i o n
11
E ( d - d r i e d s t a t e ) x k g / c m 2 k g / c m 2 S a n ' 2 ) x 100 2 8 4 . 8 569. 6 5 6 9 . 6 1 1 3 9 . 2 E x 10" k g / c m 2 ( r e w e t t e d and r e t u r n e d t o 42% RH)After about 15 hours the flow r a t e f o r the samples compacted a t 5700 and 14, 350 kg/cm2 i s of the s a m e o r d e r a s the leak r a t e of the apparatus.
Fig. 4 shows a d i r e c t comparison between the helium flow r a t e of two
x (') 2. 09 (') 2. 8 8 (') 4. 8 3 ( 2 ' 9. 43 ("13. 54 ("17. 49 ( 4 ) i 7 . 7 6 (2)25. 35 ("30. 7 3 ("34. 76 (4)35. 1 0 58. 96 53. 04 55. 27 46. 18 T A B L E 11
YOUNG'S MODULUS DATA F O R S E R I E S B
L
samples compacted a t 5700 kg/cm
,
one from S e r i e s A and one from S e r i e sB; densities a r e 2. 374 and 2. 327 gm/cc, respectively. The flow r a t e for
S e r i e s B exceeds by f a r that for S e r i e s A.
C o m p a c t ~ o n P r e s s u r e k g / c m 2 2 8 4 . 8 5 6 9 . 6 1 1 3 9 . 2 2848 4272 5696 5696 8 5 4 4 11392 14346 o 0 . 28 0. 40 1. 0 5 1. 6 3 1. 52 0. 9 0 0 . 7 3 0. 9 9 0. 91 1 . 6 5 1. 27 l 2 12 10 12 2848 4272 5696 5696 8 5 4 4 11392 14346 14346 ( a / x ) x l o o 13. 33 1 3 . 8 9 2 1 . 6 9 1 7 . 2 9 1 1 . 2 3 5. 1 5 4 . 1 1 3. 91 2. 96 4 . 7 5 3. 62 4. 27 11) 10. 12 ( 3 ) 9. 44 ( ' ) 14. 42 ('I Id. 50 ( 3 ) 14. 8 1 ( I ' 1 7 . 2 6 (') 24. 48 (') 29. 1 4 (') 34. 0 0 ( 3 ) 1 7 . 6 8 3 2 . 6 3 d e t e r m i n a t i o n s * N u m b e r s r e p r e s e n t t h e o r d e r i n which d e t e r m i n a t i o n s w e r e m a d e . P o r o s i t y '70 58. 9 4 5 1 . 9 2 4 3 . 9 0 3 0 . 7 0 2 4 . 2 2 1 9 . 7 0 2 1 . 8 0 1 2 . 1 2 8. 92 7 . 1 2 1 . 7 2 (1)':' ( ' ) 2. 61 (') 2. 0 5 ( I ) 4. 33 " N u m b e r s r e p r e s e n t t h e o r d c r i n w h i c h 34. 6 4 2 7 . 9 0 23. 1 4 26. 59 17. 20 1 3 . 0 1 10. 39 1 2 . 6 8 1. 08 0 . 3 3 0. 92 0 . 7 8 1. 17 1 . 0 4 0. 49 0. 9 9 1. 11 1. 34 0. 8 6 1 . 8 1 w e r e m a d e . 12 I 2 I 2 1 0 12 9 9 10 No. of S a m p l e s 12 12 12 12 12 12 10 12 9 9 2 5 . 2 9 3. 2 6 9 . 7 4 5. 41 6. 32 7 . 0 2 2. 8 4 4. 04 3. 8 1 3 . 9 4 4. 8 6 5. 55 0 . 2 2 0 . 3 1 0 . 1 1 0. 28 1 2 . 7 9 1 1 . 8 8 5. 37 6. 46 E - x k g / c m 2 I d - d r i e d s t a t e ) i - X 1 . 2 6 ( I ) 3 . 3 3 ( ' ) 6. 36 (') 1 3 . 3 0 ( ' ) 17. 55 (') 19. 43 (') 20. 15 ( ' ) 17. 6 5 19. 8 2 1 9 . 9 2 0 0. 20 0. 25 0 . 38 0. 6 4 0. 87 0. 57 1. 27 0. 6 9 0 . 8 3 0 . 7 1 E x kg/cm' ( r e w e t t e d and r e t u r n e d t o 42% RH) (a/%) x 100 1 5 . 8 7 7. 51 5. 97 4. 8 1 4. 96 2. 93 6. 3 0 3. 90 4. 1 9 3. 5 4 - x 3. 10 5. 78 (') 8. 61 ("16. 0 4 ( 2 ) 2 ~ . 7 3 ("25. 69 ("33. 60 ( 2 ) 3 7 . 29 (2'39. 3 5 a 0. 28 0. 47 0. 56 0. 59 1. 0 5 1 . 30 1 . 3 4 1. 2 4 1 . 2 2 (a/%) x 100 9. 0 3 8 . 1 3 6 . 50 3. 6 8 5. 07 5. 06 3 . 9 9 3 . 3 3 3 . 1 0
Vol. 2, No. 4
381
MODULUS OF ELASTICITY, HYDRATED CEMENT, COMPACTS
FIG. 3
Helium Inflow for S e r i e s A
3 . 0 0 I I I I I I I
I
0 I I D 1 6 2 0 1 5 1 0 11 4 0TIME, H O U l l
FIG. 4
Helium Inflow -Comparison Between S e r i e s A and B Young's Modulus FIG. 5 Young's Modulus vs P o r o s i t y for, S e r i e s A S e r i e s A
V o l . 2, N o .
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MODULUS OF E L A S T I C I T Y , HYDRATED CEMENT, COMPACTS
p o r o s i t y relation i s r e p r e s e n t e d by t h e upper c u r v e on Fig. 5, a semi-log
plot. It i s l i n e a r f r o m 10 t o 3570 p o r o s i t y and i s s i m i l a r t o the c u r v e s r e p o r t e d by Soroka and S e r e d a (5). T h e c u r v e extrapolates t o 59 x 10 4
2
kg/cm at z e r o porosity; t h i s i s again s i m i l a r t o t h e value taken f r o m t h e r e s u l t s of Soroka and S e r e d a a t about 1070 porosity. (It h a s been shown that p o r o s i t y m e a s u r e m e n t on a d -dried s a m p l e , if done by w a t e r , includes i n t e r
-
l a y e r s p a c e a s porosity. Helium, on t h e o t h e r hand, can exclude t h e s e s p a c e s if t h e a p p r o p r i a t e p r o c e d u r e s a r e used (9). )
E a c h point on Fig. 5 includes Z f 2 levels (approximately 9570
confidence l i m i t s ) and
x
( t h e a r i t h m e t i c m e a n ) i s usually t h e a v e r a g e of twelve s a m p l e s . The number of s a m p l e s t e s t e d , t h e mean, t h e standarddeviation, and t h e coefficient of v a r i a t i o n a r e included in T a b l e I. Up t o 4670 p o r o s i t y the coefficient of v a r i a t i o n does not exceed
6.
570, but i t i s about 1270 f o r t h e l a s t two points, a t 55 and 5970 porosity, respectively. The points f o r t h e s a m p l e s that w e r e rewetted and d r i e d back t o 4270 '0 f a l l a l m o s t exactly on t h e f i r s t c u r v e but t h e coefficient of variation i s about 1270 and higher f o r 2870 p o r o s i t y and higher.F o u r s e t s of compacts w e r e d-dried, giving a m a j o r reduction of Young's modulus a t lower p o r o s i t i e s . At 10. 3970, reduction was f r o m 34.76
4 4 2 4 2
x 10 t o 17. 68 x 10 kg/cm
,
and a t 23. 1470, f r o m 17. 5 t o 14.8 x 10 kg/cm. The s p r e a d d e m o n s t r a t e s a c l e a r s e p a r a t i o n of c u r v e s . T h e o t h e r two points,a t approximately 35 and 46% p o r o s i t y , do not show significant deviation f r o m t h e previous c u r v e , but that a t 46 p e r cent p o r o s i t y shows a v e r y l a r g e coefficient of variation. The s a m p l e s a t 10. 39 and 23. 1470 p o r o s i t y w e r e rewetted and d r i e d back t o 4270 '0. The Young's modulus r e t u r n e d to coincide with t h e points on t h e upper c u r v e , with a low coefficient of variation. F o r example, t h e Young's modulus of the s a m p l e at 10. 3970
4 2
p o r o s i t y changed f r o m 17. 68 x 10 kg/cm i n the d - d r y condition t o 35. 10
4 2 4
x 10 kg/cm
.
T h e initial d - d r y condition was 34. 0 x 10 kg/cm2 and t h e4 2
initial rewetted condition 34.76 x 10 kg/crn
.
The t h r e e new s e r i e s of s a m p l e s , a t approximately 55, 27 and 12.770
p o r o s i t y , fit closely t h e upper c u r v e for t h e f i r s t d - d r y condition. The coefficient of variation of t h e modulus of t h e s e s a m p l e s was r e l a t i v e l y low,
V o l . 2, No.
4
MODULUS OF ELASTICITY, HYDRATED CEMENT, COMPACTS
showing c l e a r l y that t h e s e c h a r a c t e r i s t i c s a r e quite reproducible. S e r i e s B
The Young's modulus-porosity r e l a t i o n f o r S e r i e s B i s p r e s e n t e d on
Fig.
6
and Table 11. The plot i s again a s e m i - l o g and t h e coefficients ofv a r i a t i o n a r e , in general, l e s s than 570 below 5570 porosity. T h e f i r s t d-dried condition i s r e p r e s e n t e d by the lower curve, which i s s i m i l a r t o t h e c u r v e for t h e second d-dried condition of S e r i e s A. Again, t h e r e i s l i t t l e i n c r e a s e in Youngas modulus f r o m 25 t o 770 porosity. A new s e r i e s r e p r e -
sented by one point a t about 2270 ~ o r o s i t y i l l u s t r a t e s f u r t h e r t h e r e p r o d u c i -
bility of t h e c u r v e s . After rewetting and drying t o 4270, Young's modulus i n c r e a s e s over t h e whole p o r o s i t y r a n g e well beyond t h e 9570 confidence l i m i t over m o s t of t h e range. T h e difference in t h e two c u r v e s i s l a r g e a t both ends of t h e p o r o s i t y s c a l e but with a lower coefficient of variation a t
t h e low porosity. The c u r v e f o r t h e rewetted s a m p l e s i s l i n e a r up t o about
4
40% porosity and when extrapolated t o z e r o gives a value of 55 x 10 kg/crn 2
4 2
f o r Young's modulus. T h i s i s s i m i l a r t o t h e value of 59 x 10 kg/cm f o r
t h e f i r s t d-dried and rewetted c u r v e s of S e r i e s A, and indeed t h e whole c u r v e i s s i m i l a r . T h e two c u r v e s a r e plotted together on Fig. 7.
0 1 0 2 0 3 0 4 0 5 0 60
9 6 , P O R O S I T Y
b . P O R O S I T Y
FIG.
6
FIG. 7Young's Modulus vs P o r o s i t y Comparison of Young's Modulus
-
MODULUS OF E L A S T I C I T Y , HYDRATED CEMENT, COMPACTS
Discussion
V o l . 2,
No.
4
T h e s e r e s u l t s show v e r y c l e a r l y that the inclusion of i n t e r l a y e w a t e r molecules i n the s t r u c t u r e of the s i l i c a t e s i n c r e a s e s t h e Young's modulus, i n s o m e c a s e s by over 10070 ( s e e Fig. 6). T h i s h a s been shown
b e f o r e (3), but t h e coefficient of variation in t h e p r e s e n t work i s m u c h lower
than was previously observed. In addition, by compacting t h e m a t e r i a l a f t e r it h a s been d-dried it i s p o s s i b l e t o attain the s a m e high values f o r Young's modulus a s w e r e obtained with i n t e r l a y e r w a t e r p r e s e n t . T h i s o c c u r s a t t h e higher p r e s s u r e s of compaction. Fig. 7 shows t h e s e c u r v e s on the s a m e d i a g r a m . T h e c u r v e f o r S e r i e s A follows t h e c u r v e f o r S e r i e s B without i n t e r l a y e r w a t e r p r e s e n t a t low p r e s s u r e s a s well a s t h e c u r v e for S e r i e s B with i n t e r l a y e r w a t e r p r e s e n t a t high p r e s s u r e s . The
2
t r a n s i t i o n t a k e s p l a c e beyond 4200 kg/cm
.
The density values on Fig. 2show that t h e r e i s no f u r t h e r i n c r e a s e i n density f o r S e r i e s B a f t e r 5600
2
kg/cm
,
and that t h e values f o r S e r i e s A continue t o i n c r e a s e . Heliumflow r e s u l t s show that a s the p r e s s u r e of compaction i s i n c r e a s e d i t i s m o r e difficult f o r helium t o p e n e t r a t e t h e s p a c e s . It s e e m s c l e a r that when compaction o c c u r s a t high p r e s s u r e s with i n t e r l a y e r w a t e r removed t h e l a y e r s a r e f o r c e d c l o s e r together than they a r e when i n t e r l a y e r w a t e r h a s not been removed. T h e high Younges modulus indicates that either s o m e new solid bonds have been established o r t h e s u r f a c e s have been f o r c e d s o c l o s e together that solid-to-solid a t t r a c t i v e f o r c e s contribute t o the higher modulus.
That i n t e r l a y e r w a t e r behaves a s a solid b r i d g e between the l a y e r s i s now apparent, and i t i s c l e a r that t h i s s p a c e cannot b e included a s
porosity, especially s i n c e t h e i n t e r l a y e r w a t e r i s only removed at v e r y low humidities. The equivalent r o l e of t h e w a t e r i s r e - e m p h a s i z e d when
S e r i e s A i s rewetted and Young's modulus r e m a i n s constant, but when t h e s a m p l e s a r e d r i e d again t h e modulii drop t o values s i m i l a r t o t h o s e for S e r i e s B, which h a s a l s o been dried. T h i s m e a n s that, on r e w e t t i n g w a t e r can r e - e n t e r t h e i n t e r l a y e r positions i n s p i t e of t h e fact that t h e l a y e r s a r e c l o s e r together than normal; t h e w a t e r s e e m s t o compensate exactly for any d e c r e a s e i n Young's modulus when t h e l a y e r s move a p a r t . If i n t e r l a y e r
V o l . 2, No.
4
MODULUS OF E L A S T I C I T Y , HYDRATED CEMENT, COMPACTS water i s again removed, the l a y e r s r e v e r t t o a position s i m i l a r t o that in S e r i e s B where drying took place after compaction. This latter position appears to be a m o r e stable state. A second rewetting of S e r i e s A again
returned the Young's modulus t o the original high value. T h e r e a r e thus
t h r e e configurations for the layers:
1) L a y e r s separated, with H 0 molecules occupying the interlayer ~ o s i t i o n s .
2
These molecules play a reinforcing role, giving a high value for Young's modulus.
2 ) Water removed from between the, layers, resulting only in p a r t i a l
collapse. T h e r e i s a reduction in Young's modulus of over 5070 in some cases.
3) Layers p r e s s e d closer together than in configuration ( 2 ) , resulting in a
Young's modulus identical to that of configuration (1).
Increase of Young's modulus owing to compaction of d-dried cement
appears t o take place in such a manner that up to p r e s s u r e s of 4200 kg/cm 2
2
o r 5600 kg/cm the main mechanism i s a reduction of porosity because 2
particles a r e pushed together. Beyond 5600 kg/cm Young's modulus i n - c r e a s e s v e r y little by this p r o c e s s ( s e e Fig. 5, lower c u r v e . ) If t h e i n t e r - layer positions a r e vacant, compaction of the interlayer system occurs at high p r e s s u r e s and Young's modulus continues to increase. This i s
confirmed by density and helium flow measurements. Conclusions
The r o l e of interlayer H 0 molecules i n increasing Young's
2
modulus i s confirmed. If d-dried hydrated cement i s compacted, Young's
modulus values may be obtained identical to those obtained when interlayer water i s present.
T h r e e configurations exist for the layers: 1) H 2 0 molecules between layers;
2 ) l a y e r s ~ a r t i a l l y collapsed and a l l interlayer water removed;
3) layers forced closer to each other by compaction when interlayer water
386 V o l . 2,
No.
4MODULUS OF E L A S T I C I T Y , HYDRATED CEMENT, COMPACTS
I n t e r l a y e r w a t e r a c t s , t h e n , a s i n configuration ( 3 ) and m u s t b e r e - g a r d e d a s p a r t of t h e s o l i d s t r u c t u r e of h y d r a t e d p o r t l a n d c e m e n t . A c k n o w l e d g e m e n t s T h e a u t h o r w i s h e s t o acknowledge t h e v a l u a b l e a s s i s t a n c e of S. Dods i n p e r f o r m i n g e x p e r i m e n t s and g a t h e r i n g d a t a . T h i s p a p e r is a c o n t r i b u t i o n f r o m t h e D i v i s i o n of Building R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l of C a n a d a , and i s p u b l i s h e d w i t h t h e a p p r o v a l of t h e D i r e c t o r of t h e Division. R e f e r e n c e s
1. W. D. K i n g e r y and R. L. Coble, Nat. B u r e a u S t a n d a r d s , Monograph 59,
103-113 ( M a r c h 1963)
2. R. J. S t o k e s , Nat. B u r e a u S t a n d a r d s , M i s c . P u b l . No. 257, 41-72 ( A p r i l 1964).
3. P. J. S e r e d a , R. F. F e l d m a n and E. G. Swenson, Highway R e s . Bd. Spec. Rpt. 90, 58-73 (1966).
4. R.A. H e l m u t h and D.H. T u r k , Highway R e s . B d . , Spec. Rpt. NO. 90, 135-144 (1966). 5. I. S o r o k a and P. J. S e r e d a , P r o c . F i f t h I n t e r n a t . Symp. C h e m . C e m e n t , Tokyo, 1968. P a r t 111, Vol. 111, 67-73 (1969). 6. R. F. F e l d m a n and P. J. S e r e d a , M a t e r i a u x e t C o n s t r u c t i o n , Vol. 1, NO. 61 509 (1968). 7. R. F. F e l d m a n , P r o c .
