Young's modulus of lightweight concretes

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Young's modulus of lightweight concretes

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NATIONAL RESEARCH COUNCIL O F CANADA D I V I S I O N OF B U I L D I N G RESEARCH

YOUNGtS MODULUS O F LIGHTWEIGHT CONCRETES

bs A .G. Davenport Report No. 141 of the Division of B u i l d i n g Research O t t a w a September 1958

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PREFACE

The work d e s c r i b e d i n t h i s r e p o r t was undertaken by t h e a u t h o r a s an assignment t o be c a r r i e d out during t h e

term of a summer appointment. The problem which he so c l e a r l y s e t s out i n h i s opening paragraphs was one which had a r i s e n i n t h e course of e v a l u a t i n g light-weight c o n c r e t e s i n t h e M a t e r i a l s Laboratory of t h e Division. Completion of t h e r e p o r t i n i t s p r e s e n t form was c a r r i e d out subsequently when M r . Davenport r e t u r n e d t o t h e Division t o accept a f u l l - time appointment following p o s t -graduate study.

Non-destructive t e s t i n g techniques such a s t h o s e examined i n t h i s study a r e of g r e a t i n t e r e s t i n t e s t i n g and e v a l u a t i o n work s i n c e t h e y o f f e r t h e p o s s i b i l i t y of p e r i o d i c examination of a s i n g l e specimen throughout t h e course of a n environmental c y c l i n g program. The need t o p r e p a r e a l a r g e number of specimens t o be destroyed one by one a t each t e s t i n t e r v a l i s t h u s avoided, and much time and expense saved. The n o n - d e s t r u c t i v e method must, however, g i v e some u s e f u l c o r r e l a t i o n w i t h t h e p r o p e r t y o r performance f a c t o r being assessed. The information now provided w i l l a s s i s t g r e a t l y i n determining t h e r e l i a n c e which can be placed upon r e s u l t s obtained from t h e techniques i n v e s t i g a t e d when a p p l i e d t o l i g h t -weight c o n c r e t e s .

Ottawa,

September 1958.

N.B. Hutcheon,

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YOUNG'S MODULUS OF LIGHTWEIGHT CONClU3TES

A.G. Davenport

I n r e c e n t years l i g h t and medium weiyht c o n c r e t e s have beoome more and more widely used i n b u i l d i n g , Their m e r i t

l i e s not only i n e f f e c t i v e heat i n s u l a t i o n p r o p e r t i e s , b u t a l s o i n euonomy of handling and high s t r e n g t h t o weight r a t i o .

I n general, t h e s e c o n c r e t e s owe t h e i r l i g h t weight t o a l a r g e number of a i r voids. These lhay be achieved by

introducing gas i n t o the m a t e r i a l e i t h e r by chemical a o t i o n o r by mechanioal means. I n a l l c a s e s t h e proportion of void apace i s high l e a d i n g d i r e c t l y t o the higher moisture absorbency found i n most of t h e s e m a t e r i a l s .

A s the importance of t h e s e l i g h t w e i g h t m a t e r i a l s

i n c r e a s e s s o doe8 t h e need t o t e s t and e v a l u a t e t h e i r s t a b i l i t y and d u r a b i l i t y e s p e c i a l l y under conditions s i m i l a r t o the r i g o u r s of t h e Canadian climate. The most injurious c h a r a c t e r i s t i c s . o f such a climate a r e l i k e l y t o be oyoles of f r e e z i n g and thawing and w e t t i n g and drying. !Che performance of o r d i n a r y concrete and l i g h t w e i g h t c o n c r e t e s must be based, t o a l a r g e e x t e n t , on l a b o r a t o r y t e s t s designed s p e c i f i c a l l y t o reproduce t h e e f f e c t s

of these c l i m a t i c cyoles. Their e f f e c t s on concrete a r e well known; t h e y cause not only oracking and dimensional changes b u t a l s o a d e t e r i o r a t i o n manifested by a change i n e l a s t i c p r o p e r t i e s . Henoe a measurement of the e l a s t i c p r o p e r t i e s i n d i c a t e s g e n e r a l l y

t h e amount o f damage t o the m a t e r i a l caused by repeated c y c l e s of f r e e z i n g and thawing.

It i s i n t h i s type o f t e s t t h a t the dynamic a s opposed t o s t a t i c measurements of the e l a s t i c moduli have come i n t o t h e i r own, There a r e two such methods commonly i n use. The f i r s t c o n s i s t s e s s e n t i a l l y of measuring the v e l o c i t y of an e l a s t i c wave passing through the m a t e r i a l (1). The Young's modulus of t h e m a t e r i a l i s t h e n given by t h e equation

where E

=

Young's modulus

? = the d e n s i t y o f the m a t e r i a l

V = the v e l o c i t y of the wave so found

u = P o i s s o n f s r a t i o

One i n s t r u m e n t with which the v e l o o i t y can be d i r e c t l y measured

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The second method c o n s i s t s of measuring t h e r e s o n a n t frequency of a prism made of t h e m a t e r i a l , by means of an o s c i l l a t o r of v a r i a b l e frequency and a pickup. The Young's modulus when t h e mode of v i b r a t i o n i s l o n g i t u d i n a l i s g i v e n by (2)

E

=

DWn 2

where D i s a o o e f f i c i e n t depending on t h e shape, dimeneiona and mode of v i b r a t i o n of t h e prism

W i s the weight of t h e specimen and n i s t h e r e s o n a n t frequenoy.

A s i m i l a r e x p r e s s i o n e x i s t s f o r t h e t o r s i o n a l modulua.

With o r d i n a r y dense aggregate c o n c r e t e t h e s e methods of t e s t i n g have c e r t a i n advantages: the t e s t s a r e r a p i d and simple and do not i n t e r r u p t f o r long t h e c y c l e s of e i t h e r w e t t i n g and d r y i n g o r f r e e z i n g and thawing t o which t h e samples a r e being

subjected; and t h e a t r a i n a imposed on t h e sample a r e i n f i n i t e s i m a l and cause no damage t o the m a t e r i a l ' s s t r u c t u r e , a s might s t a t i c t e s t s . Conorete i t s e l f i s s u f f i c i e n t l y homogeneous and i s o t r o p i o

(provided t h e sample i s l a r g e enough) t h a t t h e t h e o r e t i c a l

e q u a t i o n s f o r the frequency of a c y l i n d e r o r beam o f homogeneous

i s o t r o p i a m a t e r i a l a p p l y adequately and t h e v a l u e s of the moduli so obtained a r e b o t h c o n s i s t e n t and convincing.

Recently t h e d u r a b i l i t y and s t a b i l i t y of l i g h t w e i g h t m a t e r i e l s have come under d i s c u s s i o n and t h e q u e s t i o n h a s been

asked

-

can dynamic t e s t i n g be used t o t h e same advantage i n t e s t i n g l i g h t w e i g h t m a t e r i a l a a s i t i s i n t e s t i n g o r d i n a r y dense aggregate c o n c r e t e ?

The purpose of t h e experiments d e s c r i b e d i n t h i s paper i s t o answer t h i s question.

One of the major d i f f e r e n c e s i n t h e p r o p e r t i e s of dense and l i g h t w e i g h t c o n c r e t e s i s t h e i r water absorbency; l i g h t w e i g h t c o n c r e t e s absorb up t o twenty times a s much p e r u n i t volume

a s dense aggregate conorete. Since both f r e e z i n g and thawing, w e t t i n g and drying t e s t s i n e v i t a b l y involve the presence of moisture i n l a r g e q u a n t i t i e s , t h e experiments d e s c r i b e d h e r e were almost e n t i r e l y concerned with the a c t i o n of t h i s absorbed water on t h e a p p a r e n t dynamic moduli of t h e m a t e r i a l . S t a t e d more e x p l i c i t l y , t h e q u e s t i o n s t h e s e experiments s e t o u t t o answer a r e :

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1, How does absorbed water a f f e c t the apparent dynamic moduli of l i g h t w e i g h t concretes c a l c u l a t e d from t h e observations, assuming t h a t the m a t e r i a l remains i s o t r o p i c and homogeneous ?

2. I s dynamic t e s t i n g a s u i t a b l e method f o r determining the q u a l i t y of mot s t l i g h t w e i g h t c o n c r e t e s

EXPERIMENTAL PROCEDURE I n t r o d u c t i o n

I n order t o answer t h e s e q u e s t i o n s f o u r t y p i c a l and oommonly used l i g h t w e i g h t concrete m a t e r i a l s were selected. From each of t h e s e m a t e r i a l s e i t h e r e i g h t ( o r t e n ) a c c u r a t e 1 dimensioned t e s t specimens were made, four being 6-in. by 2.f-in. diameter c i r o u l a r c y l i n d e r s and four ( o r a i x ) being 16-in, by 4-in, by

3-in,

beams.

The amount of moisture i n lhe speoimens was c o n t r o l l e d and v a r i e d by vacuum s a t u r a t i o n o r a l t e r n a t i v e l y , by drying i n a room a t a c o n s t a n t 10 per c e n t humidity; thus any d e s i r e d degree of s a t u r a t i o n could be obtained.

The dynamic e l a s t i c moduli f o r eaah specimen and each moisture content were determined by the t m methods of dynamic

t e s t i n g already desaribed: t h e v e l o c i t y of a compression wave was measured; then the resonant frequencies of t h e prismal

specimens were measured i n the l o n g i t u d i n a l t r a n s v e r s e and

torsional modes of v i b r a t i o n , I n o a l c u l a t i n g t h e e l a s t i c moduli from t h e s e measurements it was assumed t h a t t h e equations r e l a t i n g t o homogeneous i s o t r o p i c media were applicable.

S t a t i c t e s t a over a s h o r t range of s t r e s s were a l s o conduoted on the

6-

by 2.8-in, diameter o y l i n d e r s i n order t o determine t h e s t a t i c Young' s modulus corresponding t o the

dynamio modulus f o r each moisture content; t h i s , t o some e x t e n t , provided a r e f e r e n c e t o which the dynamic modulus could be

r e l a t e d o Materials

Since t h r e e of the f o u r m a t e r i a l s used i n these experiments were p r o p r i e t a r y they a r e r e f e r r e d t o by the code l e t t e r s H, A, S and V. Each of these i s now described. Material H

-

This i s an expanded ahale aggregate of b o t h f i n e and coarse grades mixed t o g e t h e r w i t h p o r t l a n d cement i n t h e proportions by weight of per c e n t cement,

37

per c e n t f i n e and 22 p e r c e n t coarse aggregate. The water/cement r a t i o was

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.&

y i e l d i n g a slump on a 12-in. cone o f

l/4

in. The specinlens were very c a r e f u l l y made i n tho l a b o r a t o r y and every p r e c a u t i o n was taken t o ensure uniform c o n s i s t e n c y w i t h i n and b o h o e n

specimens. The boams viero c a s t i n moulds and the c y l i n d e r s oored w i t h a diamond d r i l l from l a r g e r c y l i n d e r s and c u t a t the

ends w i t h a diamond saw. The d r y d e n s i t y of the m a t e r i a l was about 1 0 5 lb/cu f t. Specimens were cured f o r 28 days a t 100 p e r oent R o H . before t e s t i n g . Specimens used i n t h e t e s t were l a b e l l e d :

H-2B)

₁₆

_x

₄

_x

_+in.

beams _H- _{C )}

6-

x

c y l i n d e r s 2.8-in. d i a . M a t e r i a l A

-

This i s a p r o p r i e t a r y c e l l u l a r c o n c r e t e c o n t a i n i n g

a considerable q u a n t i t y o f sand. The m a t e r i a l h a s a c m r a e f i n i s h and each p r e c a s t block ha8 t h e c h a r a c t e r i s t i c of being denser a t t h e bottom than t h e top. This f a c t o r was r e f l e c t e d i n t h e moduli; specimens made from the bottom p a r t of the block y i e l d e d a h i g h e r modulus. Specimens were c u t and cored from p r e c a s t blocks. The dry d e n s i t y of t h e m a t e r i a l was about 80 lb/cu f t .

Specimens used i n t h e experiments were l a b e l l e d :

A-1B ) A-1C )

A - 2 ~ )

16 x

4

x +in. A-2c) 6-in. x 2,8-In. d i a .

beams c y l i n d e r s

A-

*-$I

A- C )

M a t e r i a l S

-

This i s a p r o p r i e t a r y p r e c a s t c e l l u l a r c o n c r e t e which i s autoclaved d u r i n g manufacture w i t h much t h e same

appearance a s foam rubber. Tho d r y d o u s i t y of tho m a t e r i a l was about 34 lb/cu f t . A s w i t h m a t o r i a l A, t h e speclmons were c u t from commercially manufactured blocks. The specimens prepared f o r t h e experiment a were l a b o l l o d :

S-1B) S-1C )

S-2B)

16

x

4

x 3-in. S - 2 ~ ) 6-in. x 2.8-ine d i a .

boams c y l i n d o r s

SL. C )

h f i t e r i a l

--

V

-

This c o n s i s t s of a s t r o n g c o n c r e t o mix c o n t a i n i n g expanded vermiculite as t h e ag,cysgato. Tho sp3cirm1an=l t-;oro m d o i n the l a b o r a t o r y under c a r e f u l c o n t r o l . Tho voluzotric! propor- t i o n - of tha mix wore 1 p a r t c o m n t t o

4

p n r t g oxpanr2ocl v o r m f c u l i t e

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t o n e a r l y 2 p a r t s (1.83) water. The mix i s very sloppy and h a s the appearance and consistency of watery oatmeal porridge.

When the m a t e r i a l d r i e s pores a r e l e f t i n the spaces previously occupied by the excess water. The d r y d e n s i t y of the m a t e r i a l was about

35

lb/cu f t , Specimens were cured 28 days b e f o r e

t e s t i n g , and those used i n the experiments were l a b e l l e d :

V - 1 ~ ) v-2c )

V-2B) V-3C) b i n .

x

2.8-in. dia.

16

x

4 x

+in. V-5C ) c y l i n d e r a

V- bearna V - ~ C

A much weaker mix of v e r m i c u l i t e was a l s o made w i t h 1

p a r t cement t o 8 p a r t s v e r m i c u l i t e

.

Preliminary t e s t a t o o b t a i n t h e dynamic modulus were unsuccessful, however, and t e a t s were discontinued.

Method of S a t u r a t i o n

Specimens were t e s t e d over a s wide a range of moisture c o n t e n t s a s p o s s i b l e . To begin w i t h t h e specimens were d r i e d i n an atmosphere of 10 p e r c e n t R.H. and when t h e i r weights had s t a b i l i z e d they were considered dry; t h i s r e p r e s e n t e d t h e nominal d r y weight, and t h e amount of m a l ~ t u r e introduced t o

t h e specimen was c a l c u l a t e d from it.

To achieve maximum s a t u r a t i o n specimens were placed i n water under vacuum. The apparatus c o n s i s t e d of a 18-in. by 6-in. d i a . c y l i n d r i c a l p l e x i g l a s s c o n t a i n e r connected t o an a s p i r a t o r oapable of maintaining a vacuum of 2 4 in. of mercury. One end of the c y l i n d e r was cemented i n p o s i t i o n and t h e o t h e r end was removable t o allow p l a c i n g of the specimens. Each specimen was placed i n s i d e the c y l i n d e r and covered w i t h water; the end was then replaced and t h e a i r pumped out by t h e a s p i r a t o r . Specimens were under vacuum f o r about 30 minutes, and t h e n l e f t t o soak under atmospheric pressure. Several c y c l e s of t h i s evacuation procedure soinetimes induced the specimens t o absorb g r e a t e r q u a n t i t i e s of water.

After t e s t i n g i n a s a t u r a t e d oondition, the specimens were d r i e d i n s t e p s under room conditions; a t each s t e p they were placed i n sealed polyethylene bags f o r two days ( t o permit t h e moisture t o d i s t r i b u t e i t s e l f evenly) and t e s t e d .

The d i f f e r e n t s a t u r a t e d d e n s i t i e s of the c y l i n d e s s and beams ( ~ a b l e s 111

-

V I ) suggested t h a t t h e r e was probably a moisture g r a d i e n t through t h e specimens which p e r s i s t e d , even

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a f t e r a l l o w i n g two days f o r the m o i s t u r e regime t o s t a b i l i z e . T h i s uneven d i s t r i b u t i o n of m o i s t u r e could a f f e c t t h e inornont of i n e r t i a of the a p o c i m s n , an i m p o r t a n t q u a n t i t y i n t h o c a l c u l a t i o n o .

Dynamic T e s t A p p a r a t u ~

-~

-

---

and Mothod Soniscopo

This a p p a r a t u s e n a b l e s t h e d i r e c t mea suremont of the

r a t e of p r o p a g a t i o n of a n e l a s t i c In?avo (1)

.

A11 e x c i t o r ,

c o n s i s t i n g of a b a t t s r y of p l e z o - o l o c t r i c elements, I s p e r i o d i - c a l l y e x c i t e d by e l e c t r i c impulses. The r e s u l t i n g p u l s o i s t r a n s m i t t e d t o t h e speuimon through a housing f i l l ~ d w i t h o i l and f i t t o d w i t h a r u b b e r diaphragia; t h i s i s p r e s s e d againfit

the f a c e of the sample under t e s t . Tho time lapse between t h e d e p a r t u r e of a n impulgo and i t s a r r i v a l a t a pick-u? f i t t o d a t t h e o t h e r end, i s measwed by o b s e r v i n g the pick-up s i g n a l superiniposod on a time marker on t h e s c r e e n of a c a t h o d e r a y o s o i l l o g r a p h .

A t y p i c a l response s i g n a l on t h o o s c l l l o g r a p h . i s sketched

i n

Fig. 8. The g e n e r a l c h a r a c t e r i s t i c s c o n s i s t of a sharp i n i t i a l paak

-

n o t necessarily of l a r g e amplitude

-

follotved by a n e l t s r of wave p a t t e r n s o f v a r i n and seoniingly chaotic amplitudes; the= represent shear and t o r s

9

ona

$1

waves, surface waves, r e f l e o t e d waves and p o s s i b l y echo waves superimposed on one

a n o t h e r . According t o t h e t h e o r y , however, o n l y t h e v e l o c i t y o f t h e wave f r o n t , i.e., of t h o d i r e o t l o n g i t u d i n a l wave, which

i s r e p r e s e n t e d by t h e f i r s t i n i t i a l peak, i s of i n t e r e s t . The measurements a r e t a k e n i n tmo p a r t s . F i r s t t h e d e l a y due t o r e t a r d a t i o n of t h e e r n i t t o r and pick-up must be measurod, Thls i s done by p l a c i n g t h e r u b b e r diaphragao of t h e e m i t t o r and pick-up f a c e - t o - f a c e and measuring t h e timo

d e l a y of t h e s i g n a l p a s s i n g from one t o t h e o t h o r . The specimen

i s next p l a c e d betrreen t h e two trrjnnduuors and t h o t o t a l timo f o r t h e wave t o t r a v e l t h r o u ~ h t h e spocimon and t h o t r a n s d u c e r s

i s measurod. Tho time t h e wave f r o n t t a k e s t o t r a v e l t h r o u g h t h e specimon i t s e l f i s t h o n t h o d i f f e r o ~ ~ c s b e t n o e n the t c o measurements.

To o n s u r e t h a t t h e p a t h l e n g t h t h r o u g h t h e t r a n s d u c e r s was t h e same, vrith and w i t h o u t t h o apecimona, a j i g nas dovised

t o d e p r e s s t h a d l a p h p a ~ n s e q u a l l y onch ti123. This c o n s i s t o d of

a s l i d i n g c a s e f o r t h e pick-up, h o l d i n p l a c e by a l o n g scron.

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from t h e e m l t t o r l For each monsuremont tho s c r e n was t u r n a d a f i x e d nunbor of times from t h o p o s i t i o n where t h e diaphragms were j u s t i n c o n t a c t . C a l i b r a king i s done w i t h tho diaphragms depressed t h e same nur~lber of s c r e n t u r n s . The screw was t u r n e d enough i n i t l a l l y t o pi-oduco a s t r o n g s i g n a l on t h r j s c r e e n and

i t w a s t h e n kept c o n s t a n t .

C a l i b r a t i o n of tho t i n e marker n n a dons by comparing t h e r e a d i n g i n seconds on t h e d i a l 175th a c a l i b r a t i o n s i g n a l on the screen.

Resonant Frequency

This a g p a r a t u s e n a b l e s t h e r e s o n a n t f r e q u e n c i e s of t h e t h r o e p r i n c i p a l modes of v i b r a t i o n of a prism t o be measured,

namely, t h e l o n g i t u d i n a l , t r a n s v e r s e and t o r a i o n a l o Tho a p p a r a t u s c o n s i s t s of a v a r i a b l e o s c i l l a t o r r a n g i n g from 1 0 t o 10,000 c p s f i t t o d t o a r e o o r d i n g head f o r a phonograph. A t the r e c e i v i n g end t h e a p p a r a t u s c o n s i s t s of a c r y s t a l type pick-up connected t o t h e "Y" p l n t e s on a cathode r a 7 o s c i l l o g r e p h . An a l t e r n a t i n g

p o t e n t i a l i s a p p l i e d t o t h e " X 1 p l a t e s of t h e o s c i l l o g r a p h g i v i n g a h o r i z o n t a l band on t h e s c r e e n , t h e amplitude of whioh i s

p r o p o r t i o n a l t o t h e amplitude of t h e s i g n a l from tho piok-up.

A t a r e s o n a n t frequency of tho spooimen t h e amplitude of tho band on t h e sureen i n c r e a s o s enormously. I n tho c a s e of t h e specimona t e s t e d , t h e pealcs of t h e fundalnontal r e s o n a n t f r e q u e n c i e s were c l e a r l y d e f i n e d i n a l l modos w i t h one excoption. The f r e q u e n c i e s f o r t o r s i o n a l and t r a n s v e r s e modos f o r t h e c a s e of t h e

6-

by 2.8-in d i a

.

c y l i n d e r s prac t i c n l l y c o i n c i d e d o r v e r e c l o s e , depending on tho r e l e v a n t value of dynamic Poissont s r a t i o , This l e d t o a c o n f u s i n g number of "pseudo-peaks" i n t h e nsighbourhood of t h e s e f r e q u a n c i e s . I n o t h o r c a s e s , however, the r e s o n a n t frequencies

oould be e s t i m a t e d t o t h e o r d e r of about 1 p e r c e n t o r more. The p o s i t i o n s used f o r applying t h e e x c i t o r t o o b t a i n t h e d i f f e r e n t modes of e x c i t a t i o n a r e i l l u s t r a t e d

i n

Fig.

9.

I n t h e s e

experiments t h e weights of t h e e x c i t o r and pick-up heads were s u f f i c i e n t t o m a i n t a i n an i n t i m a t e c o n t a c t throughout v i b r a t i o n .

A l t e r n a t i v e equipment t o the o a c i l l o g r a p h f o r d e t e c t i n g t h e pick-up s i g n a l s i s a s e n s i t i v e galvanometer. Reading t h i s

instrument, however, t o n d s t o be much l e s s i n t e r e s t i n g than viewing t h e p a t t e r n s on t h o s c r e e n a s t h e p a t t e r n i t s o l f o f t e n h e l p s t h e o b s e r v e r t o decide whether h i s o b s e r v a t i o n i s r e l e v a n t t o t h e experiment o r whether i t i s , a s was experienced, t h e v i b r a t i o n of a water tap.

(11)

S t a t i c Teot Method C__

Tho spocimons dosigned f o r theso t e s t s mere tho

6-

by 2e8-inr d i a . c y l i n d o r s , Their onds noro c u t a s squarb and plane a3 p o s s i b l e w i t h a diamond nai-1 and, although f a r from i d o a l ,

thoy gave r e a s o n a b l y c o n s i z t o n t r o s u l t s , A s the a d d i t i o n a l refinomont of capping tho spocimons might e a s i l y have a f f o c t e d

t h e dynamic t o s t s i t was n o t dono.

A Baldr~in-Southvrark h y d r a u l i c t e s t i n g machino was used f o r l o a d i n g tho c y l i n d o r s i n co~npression. A s t a n d a r d j i g f o r t e s t i n g 12- by 6-in. d i a . c y l i n d o r s over a n 8-inb gaugo l e n g t h was adapted f o r t o s t i n g t h e

6-

by 2,8-in. d i a , c y l i n d o r s ovor

t h e i r e n t i r o l e n s t h e Tho j l g had a mochanisrn t h a t componsatod f o r e o c e n t r i c s t r a i n i n g and oncrbled a n avorago s t r a i n rnonsurcjmont

over tho e n t i r o circumforonco t o bo rocordod on ono oxtonaomn3tor.

The extensomstor used w a s t h e differential transformor typo which mads i t p o s s i b l e t o r e c o r d a t r o ~ s / a t r a i n curves f o r t h o spocimons on t h e autographic r e c o r d o r of t h o t e s t i n g machino.

Various f a c t o r e provented tho e x a c t r e s u l t s r e q u i r e d from being obtalnod from the s t a t i c t e s t s . The l i m i t a t i o n s o f

the t e s t i n g machinos preventod high m a g n i f i c a t i o n s of nmll

s t r a i n a from boing talren on the drum r e c o r d e r and, h a d , t h e s o been p o s s i b l e , t h o bedding-do:-~n e f f e c t of t h o p l a t e n s of t h e machino on

the c y l i n d e r ends would n o t have j u s t i f i e d t h o i r use. The e f f e c t and e x t e n t of the bodding-dorm can be seen from t21e i n c r e a s e

i n

g r a d i e n t w i t h i n c r e a s o i n s t r e s s on t h e s t r e s s / s t r a i n curves near t h e o r i g i n (Figs. 7, 8,

9 ) .

This c h a r a c t e r i s t i c was u n d e s i r a b l e . I n s t e a d of o b t a i n i n g t h e modulus a t t h e o r i g i n i t was necessary t o be c o n t e n t with the modulus of a f i n i t o p o r t i o n of the curve anay from the o r i g i n which was p r a c t i c a l l y s t r a i g h t , Thosa moduli d i d , hovevar, give reasonably c o n s i s t e n t end conv9.noi.ng r e s u l t s a s can be sson from t h e curves ( F i g s , 7a, b, c ) .

A c e r t a i n amount of the beddin tn e f f e c t was e l i m i n a t e d by l o a d i n g t h e specimen s e v e r a l times

PodoVr

u s u a l l y t h r e e ) u n t i l two i d e n t i c a l p l o t s wero obtained. But f o r t h e 1017 ~ t r e o s e a usod even

t h e f r i c t i o n of t h e b a l l s e a t i n g on tho p l a t o n a f f o c t o d r o s u l t s

i f i t was not c a r e f u l l y a d j u s t e d t o meet t h e c y l i n d e r squarely.

C a l c u l a t i o n s

( a ) Pulse VolociQ

Using t h e exprbaosion a l r o a d y givon i n oquetion (1) f o r

t h e group velclci t y of a n e3.a s t i c viave through n oorai-inf i n i t o , i s o t r o p i c homogeneous niedi~un i s

E

--

-

3 -

( l t - 0.- --.-.-.-- (1.

'-.

.?a

(12)

For 16-in. beams

where : t = pulse time i n set

W

?

= Q 0002205 ~ b / c u in . 1 6 x 4 ~ 3 '

336T

V::'here : Wg = w t i n grams

=

(.002205 l b ) Hence E

-

.002205 x

1.6~

x

1012 dyn 16 x h x j x 3 6 6 . 4

x R x $

Where: R = (1 + a ) ( 1 1_1

-

20) (1

-

a1 F o r

6-

b G 8 - i n . d i e . o y l i n d e r s

v

=

lab in/aec t E = $ x R Values of R a r e t a b u l a t e d f o r

The v a l u e s f o r a used i n t h e c a l a u l e t i o n s of Edm a r e approximately those found by t h e r e s o n a n t frequency technique, f o r t h e r e s p e o t i v e moisture c o n t e n t s . The r e l a t i o n s h i p used f o r c a l c u l a t i n g a is

E

a = r G m l

(13)

TABLE I

( b ) Resonant Freguencx

For the o a l o u l a t i o n of Edyn from the resonant froquoncy of prisms the values of the oonstanta dorived by P i c k e t t ( 2 ) a f t o r

Goons and Timoshonlro. Throe a r e used,

( a ) Longi-tudinal Modo

-

E 2

dsn

=

Whore: E

d3-n

=

dynamlc Younats modulus i n p a l

W a W t of specimen i n grams

Q

n = fundamonto1 rosonant frsquonay

L

D ;..01318 - - a

dZ

f o r o y l i n d ~ r a

=

.OlO35

w

f o r priom

( 6 )

L, b, t e r e length, breadth a n d dcpth of prism. d i s diameter of oylindor

(14)

For

6-

by 2,8-in,

-

d i a c y l i ~ t c l ~ r ~

-

( d ) Transvorso Modo

For 16 by 3 by

k-in.

priona

~3

Edsn

=

.00245 x

7

b t

x

T

x

.002205

x

w g d

p s i

K

Where: T dependo on a end

1

For 3 d n . plano

=

.2

a05

x

10-4

x

T

x

wg.n2 psi K

3 -

L 3.464

x

16

*0542

Where : K r a d i u s of i n e r t i a . For

4.-1n.

plano

(15)

From P i c k e t t @ a ( 2 ) curves o f T a g a i n s t

$

the f o l l o w i n g

a r e obtained:

( e ) Toreionel Mode

For

16

by

3

by

4-in.

beams

a/b

+

b/a Where:

R

=

-

_a

₆

2.52

($12

+ e21 ( 8 ) P 1.282 g

=

g r a v i t a t i o n a l a c c e l e r a t i o n For

6-

by 2.8-in. d i a . a y l i n d e r a In the a a l o u l a t i o n s h e e t s P o i s s o n ~ a r a t i o i s c a l o u l a t e d from the mean value o f E

dyn from the three modea o f v i b r a t i o n and

_E

GdYn by the f o l l o w i n g r e l a t i o n s h i p : e

=

-

1

(16)

Sample T e s t

To e x p l a i n more f u l l y t h e t e s t w o c e d u r e adopted and t h e d e r i v a t i o n of t h e moduli, t h e s e r i e s of experiments conducted

on one specimen i s d i s c u s s e d , The specimen s e l e c t e d f o r d i s c u s s i o n Is S

-

1 C which i s a 2 by 2.8-in. d i a , c y l i n d e r s made of m a t e r i a l S. Some of the t e s t r e s u l t s f o r t h i s specimen a r e given i n Table I1

.

This specimen was l e f t i n a room a t 1 0 per c e n t r e l a t i v e humidity l o n g enough t h a t t h e r e was no f u r t h e r d r y i n g e v i d e n t

from d a i l y weighings. I t s d r y weight was

3 l 4

grams. When t e s t e d dynamically i n l o n g i t u d i n a 1, t r a n s v e r s e and t o r s i o n a l modes i n the manner i n d i u a t e d

i n

Fig.

9

t h e f i r s t n a t u r a l f r e q u e n c i e s were found

t o be 5280, 3080 and 3300 ups r e s p e a t i v e l y . S u b s t i t u t i n g Wg

=

3l.4

and n

=

5280 i n t o e q u a t i o n ( 8 ) g i v e s

=

.222 x

10-4

x

3 4

x 5 2 8 0 ~ ,

= .l94

x

lo6

p s i f o r t h e l o n g i t u d i n a l mode. S u b s t i t u t i n g W g =

3 4

and n

=

3300 o p s i n t o e q u a t i o n

(4)

g i v e s Gdyn

=

.223 x

lon4

x

3 4

x 33002

Henoe Poiaaonta r a t i o i s given by e q u a t i o n

(4)

For t h e o y l i n d e r 1

.117

and hence T

=

2.02. Hence, i n

1

t h e t r a n s v e r s e mode the dynamic Young18 modulua I s o b t a i n e d by

s u b s t i t u t i n g W

=

9.4,

n

=

3080 and T

=

2.02 i n t o e q u a t i o n ( 1 2 ) l3

1:

6

The two v a l u e s o f the mod l u s

,

.I93

x

lo6

and

.l94

x 1 0 are

(17)

The time taken by the f a s t e s t wave t o t r a v e l through the specimen w a s found by means of the nsoniscopew t o be 84.8 micro- aeconda. Using the value of Poissonts r a t i o determined by the resonant frequenu technique, the value of R

=

.818, Substituting

w€J

= 314,

t

=

84.

i!

i n t o equation

( 3 )

gives

6

a208 x 10 psi.

Thia value i s reaorded i n Table 111.

The s t a t i o t e s t yielded the curve shown i n Fig. 7b. whioh i s taken d i r e c t l y from the s t r a i n recorder. The modulus aaloulated over the s t r a i g h t p o r t 1 n of the aurve between a load of 150 l b

₈

and 500 l b i s

.233

x 10 psi.

This ooncludes a l l t e s t a f o r t h i s specimen a t t h i s moisture oontent. The speaimen was then s a t u r a t e d , allowed t o stand f o r

a

f e w days i n a sealed bag aontaining exaess water and again t e s t e d

i n an i d e n t i a a l manner. The speoimen was then dried i n the a i r , allowed t o atand f o r t e n days i n a sealed oontainer t o allow moisture d l a t r i b u t i o n , and again tested. This procedure waa

oontinued u n t i l the specimen was dry again and the modulus i n the dry s t a t e waa measured and recorded a s a check on the value i n i t i a l l y determined.

This was repeated for a l l the specimens of eaoh material and the r e s u l t s were p l o t t e d for eaoh speaimen and the average

(Figs. 1,

3

and

5 )

.

It i s t o be noted t h a t i n a l l oaluulat ion8 the t o t a l weight of the sample including water was used i n the o a l a u l a t i o n of the moduli. Figures 2 and

4

show the changes i n Poiasonfa r a t i o f o r materials A and S respeatively. Figure

6

ahows both the ohanges i n the wave v e l o a i t y aa the moisture content

inareasea, and the velooity of sound i n water*

Tablee I11 t o

VI

reoord the numerical r e a u l t a obtained i n the experiments f o r the dry and s a t u r a t e d conditions; a l l i n t e r - mediary degrees of s a t u r a t i o n a r e omitted but may be abstraoted

froin t b p o i n t s given on the^ graphe.

ANALYSIS

AND

DISCUSSION OF FESULTS Introduo t i o n

I n t h i s eeution the r e s u l t s of these experiments (shown . o a l l y i n ~ i g s . 1 t o

6 )

a r e discussed. AII examination of the

8 ahows t h a t the q u a l i t a t i v e correspondenae between t h e curves

for-eaah apeoimen of each m a t e r i e l l a good; there a r e , however, unexpea ted divergences be tween the moduli de terminsd by the three d i f f e r e n t methods. It i s the purpose now to explain these i n a manner more speaula t i v e than comprehensive.

(18)

D i f f e r e n c e s Betwoen t h e S t a t i c and Dynamic filoduli

The fundamental differences betweon what a r e termed t h e s t a t i c and dynamic moduli l i e i n the amount and r a t e of s t r a i n i n g t h e t t a k e s place. I n t h e dynamic t e s t s t h a t a r e d e s c r i b e d h e r e , the a t r a l n a involved aye almost i n f i n i t e s i m a l and tho r a t e s of a t r a i n i n g a r e i n s t a n t a n e o u s o r a d i a b a t i c , I n t h e s t a t l c t e s t s ,

however, t h e s t r a i n s n e o e s s a r y f o r deterlnScing th3 modul~is a r e i n e v i t a b l y much l a r g e r and t h e r a t e of s t r a i n i n g much slower ( o r i s o t h e r m a l )

-

slow enough t o permit p l a s t i c deformations t o

occur. I f , however, t h i s r a t e of l o a d i n g i n t h e " s t a t i c " t e s t i s i n c r e a s e d and the s t r a i n s decreased t h e modulus t h u s determined should approach i n c r e a s i n g l y c l o s e r t o t h e d namic modulus. For o r d i n a r y dense aggregate c o n c r e t e P h i l l e o

( 3

9

s t a t o d t h i s t o be t h e case: t h e r a t i o of dynamic ( r e s o n a n t ) modulus t o s t a t i c modulus decreased from

1.3

f o r a very slovr l o a d i n g r a t e t o 1.07 f o r t h e f a s t e s t r a t e o b t a i n a b l e . He a l s o found t h a t t h e s e r a t i o s were l e s s f o r a l i g h t e r c o n c r e t e u s i n g a s h a l e aggregate.

These d i f f e r e n o e s probably a r e a l l dependent t o some degree on a oombination of t h e thermal and p l a s t i c p r o p e r t i e s of t h e m a t e r i a l . I n t h e p r e s e n t s e r i e s of experiments t h e d i f f e r e n o e s between tho moduli f o r the v a r i o u s m a t e r i a l s i n t h e d r y s t a t e a l s o a r e n o t very g r e a t ( F i g s . 1,

3,

5 )

and those t h a t do e x i s t a r e probably completely accountad f o r by t h e s e f a c t o r s . They do n o t , however, account f o r t h e l a r g e d i f f e r e n c e s between t h e moduli which a r i s e when t h e moisture i s introduued i n t o t h e specimen.

D i f f e r e n c e s Between t h e Dynamic Moduli

I t i s d i f f i c u l t t o account f o r t h e s e d i f f e r e n o e s . F r o m

Figs. 1,

3

and

5

i t i s e v i d e n t t h a t when moisture i s i n t r o d u c e d i n t o t h e s e specimens the dyanmic "pulsotl modulus d e p a r t s from t h e

"resonant" modulus i n some c a s e s ( m a t e r i e l S f o r example) d r a s t i c a l l y , and t h a t t h e s i m i l a r i t y between t h e moduli which e x i s t e d i n t h e

d r y s t a t e , c e a s e s o The answer t o t h i s must hinge l a r g e l y on the

d i f f e r e n t mechanisms used i n t h e t e s t i n g . On the one hand, t h e modulus determined by measuring the n a t u r a l frequency of a

prism depends on an average moduhis and average weight of a c r o s s - s e c t i o n . I f the m a t e r i a l i s n o t homogeneous tho modulus d e r i v e d from t h e n a t u r a l frequency w i l l s t i l l be an i n d i c a t i o n of t h i s

average modulus f o r t h e con jugato m a t e r i a l . Any d i s c r e p a n o i e s which occur i n t h i s average modulus w i l l be due p r i n c i p a l l y t o two causes: l a r g e changes i n t h e damping c h a r a c t e r i s t i o s of t h e

m a t e r i a l ; and l a r g e changes i n P o i s s o n ' s r a t i o . I t i s c l e a r from t h e equatiions f o r r e s o n a n t frequency

( 5 ,

9 and

13),

however, t h a t t h e l a t t e r cause w i l l only a f f e c t t h e frequency i n t h e t r a n s v e r s e mode. An i n c r e a s e i n e i t h e r t h e damping o r P o i s s o n t s r a t i o w i l l

(19)

and the e l a s t i c modulus. Both t h e s e e f f e c t s w i l l be s l i g h t ( u n l e s s , i n t h e one c a s e , t h e damping i s l a r g e ) . No amplitude measurements were made i n the p r e s e n t experiments and i t i s n o t p o s s i b l e t o s t a t e e i t h e r the magnitude of the damping c o e f f i o i e n t o r t h e changes which may have occurred. I t was n e c e s s a r y there- f o r e , t o assume i n t h e frequency e q u a t i o n s t h a t the damping waa always n e g l i g i b l e .

Except f o r m a t e r i a l A ( F i g , 1) t h e r e s o n a n t moduli f o r the m a t e r i a l s t e s t e d appear t o be f a i r l y c o n s t a n t and i n

comparatively c l o s e agreement with t h e s t a t i c moduli (Figs.

3

and

5 ) .

A p o s s i b l e conclusion i s t h a t t h e r e s o n a n t frequenoy technique g i v e s a s a t i s f a c t o r y i n d i o a t i o n of t h e e l a s t i c

c o n d i t i o n of t h e l a s t two m a t e r i a l s S and V. For m a t e r i a l A

t h e r a p i d i n c r e a s e i n r e s o n a n t modulus w i t h moisture c o n t e n t aompared w i t h the s t a t i c modulus which remains r e l a t i v e l y

conatant (Fig. 1) i s something of a enigma: when the e f f e c t of moisture on t h e p u l s e v e l o c i t y modulus i s considered f u r t h e r t h e behaviour of t h i s m a t e r i a l appears t o be d i s s i m i l a r t o t h a t of e i t h e r m a t e r i a l S o r V. The e x p l a n a t i o n may l i e i n t h e f a o t t h a t m a t e r i a l A i s d i s t i n c t l y g r a n u l a r whereas m a t e r i a l s S and V a r e more s o l i d ma t e r l a l s .

I n c o n t r a d i s t i n c t i o n t o t h e modulus determined by t h e r e s o n a n t frequency technique, t h e "pulse v e l o c i t y " modulus i s

n o t n e c e s s a r i l y a n "average" modulua of t h e m a t e r i a l . The wave whose v e l o c i t y i s measured i s t h e one which t a k e s t h e l e a s t time t o t r a v e r s e the intermediary m a t e r i a l betwoen the e x c i t o c and piok-up. I t i s impossible t o measure a n "average" wave v e l o c i t y

o r t o d l s t i n g u i s h such a wave from the w e l t e r of extraneous echo waves, s h e a r waves, e t c . which f o l l o w i n the wake of t h e f a a t e s t wave.

I n a m a t e r i a l which i s n o t homogeneous, a s i s t h e caae h e r e , i t i s u n l i k e l y t h a t the p a t h taken by t h i s f a s t e s t wave I s a s t r a i g h t l i n e . I n e v i t a b l y i t w i l l t r a v e l mainly through t h e m a t e r i a l through which i t s v e l o c i t y i s f a s t e s t . Thus t h e p u l s e modulus may t e n d t o be n o t i c e a b l y g r e a t e r ; t h i s was found i n a l l c a s e s ( F i g s , 1,

3,

5 ) .

If t h e r e a r e v o i d s i n t h e m a t e r i a l t h e wave must circumvent t h e s e . F'urthermore t h e p a t h taken by t h i s wave w i l l change e v e r y time t h e c o n s t i t u t i o n of the m a t e r i a l changes. Thus t h e f i r s t e f f e c t 0.f the i n t r o d u c t i o n of moiature i n t o the specimen i s t o change t h e p a t h along which the f a s t e s t wave t r a v e l s . The a d d i t i o n of moisture can only s h o r t e n t h i s

p a t h of l e a s t time. This does not mean, however, t h a t tho time taken by t h e f a s t e s t wave t o t r a v e r s e t h i s p a t h i s s h o r t e r ,

because t h e a d d i t i o n a l mass introduoed, o r some of it, a l s o must be a c c e l e r a t e d i n the van of the propagated wave.

(20)

Here, a f u r t h e r quostion a r i s e s . Does t h e a d d i t i o n a l moisture a c c e l e r a t e a s i f i t mere an i n t o g r a l p a r t of t h e

m a t e r i a l ? Probably not s i n c e t h e " e f f e c t i v e i n o s t i a l masstt t o be a c c e l e r a t e d by the wave T s probably l e s s than t h o t o t a l mass of m a t e r i a l and moisture combined* I n a sense tho moisture may "slopt1 around i n t h e void spaceas Also, tho a d d i t i o n of moisture both i n a c t i n g a s a l u b r i c a n t botveen g r a i n s o f the m a t o r i a l and i n t h e a c t i o n of f l u i d p r e s s u r e i n p o r e s and voids may e f f e c t i v e l y i n c r e a s e t h e value of P o i s s o n t s r a t i o of t h e m a t e r i a l a s a whole. This incretise was found during t h e s e experiments a s i n d i c a t e d i n F i g s * 2 and

4,

I f the Young' a modulus and densf t y remain t h e same an i n c r e a s e i n P o i s s o n l s r a t i o would i n c r e s s e t h e v e l o c i t y of t h e wave a s can be seen from e q u a t i o n (1).

Thus, i t may be argued t h a t ,the a d d i t i o n of moisture may have the following e f f e c t s on t h e pulse v e l o c i t y and the modulus

derived from it:

( i ) reduce the p a t h l e n g t h and thua tend t o i n c r e a s e t h e apparent v e l o c i t y of t h e wave and consequently t h e modulua;

( i i ) i n c r e a s e t h e " e f f e o t i v e i n e r t i a l mass" but n o t . b y t h e f u l l amount of the moisture added s i n c e a l l the moisture may not move i n t e g r a l l y w i t h the m a t e r i a l . This mean8 i t may not be necessary f o r a l l the moisture t o be

a c c e l e r a t e d t o permit passage of t h e wave. This would tend t o reduce t h e v e l o c i t y of t h e wave and i n c r e a s e t h e modulus i f the t o t a l mass of m a t e r i a l and moisture were used i n T t s c a m t i o n i n s t e a d of the " e f f e c t i v e

i n e r t i a l mass1' which would be l e s s ;

(iii) i n c r e a s e t h e value of P o i s s o n t s r a t i o ; t h i s tends t o i n c r e a s e the v e l o c i t y .

Figure

6

shows the p u l s e v e l o c i t y changes brought about by the i n t r o d u c t i o n of moisture i n t o t h e m a t e r i a l * M a t e r i a l A

specimens behave d i f f e r e n t l y t o those of m a t e r i a l s V and 9. This

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

q u a l i t a t i v e manner t o e i t h e r of t h e o t h e r two m a t e r i a l s * The f a c t t h s t t h e derived moduli f o r both dynamic methods a r e e s s e n t i a l l y s i m i l a r f o r low moisture c o n t e n t s . ( ~ i g , I ) may i n d i c a t e t h a t the a d d i t i o n of moisture a f f e c t s the mechanism of both measuring

techniques i n a s i m i l a r way. Perhaps t h e I n i t i a l l y absorbed water f i l l s spaces be tween g r a i n boundaries and provides impac t - f r e e and p u r e l y e l a s t i c transmission of a wave v~hlch i s n o t o b t a i n e d i n s t a t i c t e s t s . A t any r a t e t h e m a t t e r i s a n i n t e r e s t i n g s u b j e c t f o r specula t i o n .

(21)

M a t e r i a l s S and V on t h e o t h e r hand i n d i c a t e a g r a d u a l d e c r e a s e i n p u l s e v e l o c i t y w i t h i n c r e a s e i n m o i s t w e c o n t e n t ; t h e modulus shovrs a r a p i d i n c r e a s e , These c h a r a c t e r i s t i c s may w e l l be m a n i f e s t a t i o n s of tho t h r e e e f f e c t s ( i ) ( i i ) ( i i i ) ,

e s p e c i a l l y ( i i ) , I t i s n o t i c e d t h a t t h e v e l o c i t y of sound i n w a t e r i s v e r y c l o s e t o t h a t of t h e m a t e r i a l s i n t h o i r dry s t a t e :

t h i s may have c o n s i d e r a b l e i n f l u e n c e on t h e performance, I t does however i n d i c a t e once moro t h a t the p u l s e v e l o c i t y may n o t be a s u i t a b l e method of t e s t i n g t h i s m a t e r i a l i f moisture i s

p r e s e n t . I n t h e dry s t a t e , however, t h e modulus it y i e l d s , a l t h o u g h s l i g h t l y h i g h e r t h a n e i t h e r t h e s t a t i c o r r e s o n a n t modulus, i s commensurate w i t h both.

CONCLUSIONS

(1) For m a t e r i a l s S and V t h e r e s o n a n t f r e q u e n c y and s t a t i a moduli a r e v e r y c l o s e and v i r t u a l l y c o n s t a n t a t a l l m o i s t u r e

c o n t e n t s . For t h i s r e a s o n t h e r e s o n a n t frequency technique would appear t o be very s u i t a b l e f o r determining t h e appapent e l a s t i c modulus o r c o n d i t i o n of e i t h e r of t h e s e m a t e r i a l s .

(2 For m a t e r i a l A, a l t h o u g h t h e moduli f o r t h e m a t e r i a l i n t h e d r y s t a t e a r e v e r y c l o s e ( t h e p u l s e v e l o c i t y b e i n g g r e a t e r t h a n e i t h e r t h e r e s o n a n t o r t h e s t a t i o modulus and t h e r e s o n a n t b e i n g g r e a t e r t h a n t h e s t a t i c ) t h e a d d i t i o n of m o i s t u r e produoes a wide divergence between the dynamic and s t a t i c moduli. Dynamic t e s t i n g , t h e r e f o r e , may n o t be a s u i t a b l e method f o r t e s t i n g t h i s m a t e r i a l , even though t h e p u l s e v e l o c i t y a p p e a r s t o be s u b s t a n t i a l l y c o n s t a n t once t h e specimen becomes damp.

( 3 )

The behaviour of m a t e r i a l H i s s i m i l a r t o t h a t of o r d i n a r y dense a g g r e g a t e conorete. A s l i g h t r i s e i n t h e dynamio moduli i s r e c o r d e d i n t h e s a t u r a t e d c o n d i t i o n .

(4)

A r e s u l t a l r e a d y found f o r o r d i n a r y dense a g g r e g a t e

c o n c r e t e was found i n t h e s e experiments a l s o . This w a s t h a t the v a l u e of Poissonc s r a t i o ( c a l c u l a t e d from t h e found v a l u e s of

t h e t o r s i o n a l and Youngts moduli u s i n g t h e u s u a l i s o t r o p i c e l a s t i o e q u a t i o n s ) i n c r e a s e s w i t h i n c r e a s e i n m o i s t u r e c o n t e n t

(22)

Ref e r e n ~

1. Parker, W.E. Pulse v e l o c i t y t e s t i n g of concrete.

Proceedings, American S o c i e t y f o r Testing M a t e r i a l s ,

Val.

53,

1953,

P. 1033-1043.

2. P i ~ k e t t , Gerald. Equations f o r computing e l a s t i c c o n s t a n t s from f l e x u r a l and t o r s i o n a l r e s o n a n t f r e q u e n c i e s of v i b r a t i o n of prisms and c y l i n d e r s . Proceedin s,

American S o c i e t y f o r T e s t i n g M a t e r i a l s , Vol.

&5, 1945.

3.

P h i l l e o , ROE. Comparison of r e s u l t s of t h r e e methods f o r determlning Young1 a modulus of e l a s t i c i t y of concrete. Journal of Amerioan Concrote I n s t i t u t e , vol. 26, no.

5,

January

1955.

p.

461-69.

Amerioan S o c i e t y f o r T e s t i n g Materials, Tentative method of t e s t f o r fundamental, t r a n s v e r a e , l o n g i t u d i n a l , and t o r s i o n a l

f r e q u e n c i e s of concrete specimens, ASTM Designation, C-21$-T,

9p

A u s t r i a n Building and Concrete magazine, U l t r a s o n i c t e s t i n g o f m a t e r i a l s w i t h s p e c i a l c o n s i d e r a t i o n o f concrete, March

1955.

Kluge, R.W., M O M . Sparka and E.C. Tuna. Lightweight aggregate

concrete. Journal of t h e American Concrete I n s t i t u t e , vol. 20,

no*

9,

May

1949.

Mitchell, L O J o Some experiences i n dynamic t e s t i n g of m a t e r i a l s . Presented a t annual meeting o f Highway Researoh Board, January 12 t o

15,

1954.

1 6 ~ .

R ,I.L,E.M. S p e c i a l i s s u e on " v i b r a t i o n T e s t i n g of Conoreten.

M O O

15,

August

1953.

Watstein, D. P r o p e r t i e s of conoreto a t h i g h r a t e s o f loading. American S o c i e t y f o r T e s t i n g M a t e r i a l s p r e p r i n t 93b,

1955,

(23)

(24)

TABLE IV

(25)

c D C O . o C 0 m m e N "?'%??

2Z%

%<'%? d d d d O N O d I C O O d 'i's's's d 44'0,'? CUOEON u \ 9 m.0

%

C " . .

3 .

s2s2

<??? 0 0 0 0 o o d m

2"&X

m a

_d922

r'.%'S% d r( 0 0 0 0 P-coco d F ? N ( U 3 m m m m m m o N mmm

%949

d 0 0 0 0 m o 0 0 m e m \o mmm N I C d V W m d o 0 0 r l d r l r l

A

v v v o r l m d N c ~ r l h l l l l

_ga&"***

ICN d 9 C".? d d NIC NCO %2 d m 99 d d

z's!

9'". d m 99 ntw

. .

8 %W

B

2s22

-

i2

m o rn d o T's

28%3-

0 Q'D'O d d e n dlc COO\oco O O Q I C COICICCO m a m a

v.

0 0 0 0 I C s d m m o F?m OICUCUN F2

%$

d&3

m m m m a B d ~ * \ ; f 0 1 1 1 4 4 4 q 4 4 m o m m COO no 3 x 2

s2sc

22%2 d

zss2

?2%2 d

296.3

o AQ-3CO 9 P - 9 I C

M Z %

mlCICm

..

0 . ~ D ~ C O S 9 c o C O 9 d d d d

'?

0 d K

9

a 0 z U 4 .P m +1 Cn R 0 - "4

2:

:

-

₂

U P O Q C m k a Q c-l- rG

.

0 o m m n A N N d C".'".?'". \D I mt-mm o r( . . . a Q

-

K d

3

0 4

"

k

m 9 0 0 0 0 s d m c o M i l

J2sA

tz a 0 0 0 0 m c o a 3 ~

$%in

;

. .

.

d %3

%%

r',?E;'? rl 0 0 0 0 a m \o

2 ~

3 ~

'8. N O 0 o l c m QICCOIC

A m x ~

d k l l l l l--sQ*444 u a I

₃

I C N d 0 d v \ N o . . . H 0 Eld

E"

~ ra l

5

9 I m e n rn W W d P: K I ID we 0 c mmcl 9 I mICICn m N mm K b d o l a c 4 C a

3 2 %

0 5 c A - h Cc

5

rl

5

c

8

.,I

ii

m

....

0 0 0 0 N m N N O O ( U d

a a s x

R I l I I l a'4-444 a

(26)

TABLE V I

(27)

6" x 2 . 8 " DIAM. CYLINDERS 16"x 4 . ~ 3 " BEAMS

GRAMS OF WATER PER CU IN. GRAMS OF WATER PER CU IN.

LEGEND :

-m- RESONANT FREQUENCY

4- PULSE VELOCITY

-*- STATIC

FIGURE I

VARIATION OF YOUNG'S MODULUS FOR MATERIAL A WITH MOISTURE CONTENT DETERMINED BY THREE DIFFERENT METHODS. me * - s L s T ,,,

(28)

F I G U R E 2

2

3

4

5

6 GRAMS OF

WATER PER CU IN.

VARIATION O F

POISSON'S

R A T I O FOR M A T E R I A L A

WITH MOISTURE C O N T E N T ,

(AVERAGE O F

4 -

6'k 2 . 8 ' ' D I A M E T E R C Y L I N D E R S . )

(29)

6" x 2

-

8" DIAM. CY LlNDERS 16" x 4 " x 3" BEAMS

.

"

0 2 4 6 8 1 0 1 2 1 4

GRAMS O F WATER PER CU IN.

0 2 4 6 8 10 12 14 GRAMS OF WATER PER CU IN. LEGEND :

-rn- RESONANT FREQUENCY

-A- PULSE VELOCITY -0- STATIC

FIGURE 3

VARIATION OF YOUNG'S MODULUS FOR MATERIAL S WITH MOISTURE CONTENT DETERMINED BY 3 DIFFERENT METHODS. D 1 R W T C I P Y W L

(30)

m

RESONANT FREQUENCY I // G S /* c

-

m

0 2 4 6 8 10

GRAMS OF WATER PER CU IN.

FIGURE 4

VARIATION OF POISSON'S RATIO WITH

MOISTURE CONTENT.

(31)

6 " x 2 . 8 " DIAMETER CYLINDERS

0 2 4 6 8 10 12 14 16

BEAMS

GRAMS OF WATER PER CU IN. GRAMS OF WATER PER CU IN.

-.-

RESONANT FREQUENCY,

--

PULSE VELOCITY, -*- STATIC

FIGURE 5

VARIATION OF YOUNG'S MODULUS OF MATERIAL V CONCRETE WITH MOISTURE CONTENT DETERMINED BY THREE DIFFERENT METHODS

(32)

2

4

6

8 10

GRAMS

O F

WATER

PER

CU

IN.

LEGEND:

BEAMS

---H---

CYLINDERS

-X-

FIGURE 6

VARIATION O F V E L O C I T Y O F SOUND W I T H

M O I S T U R E C O N T E N T FOR M A T E R I A L A,-

M A T E R I A L S AND M A T E R I A L V.

(33)

FIGURE 7 0 MATERIAL A (MOISTURE CONTENT -DRY) 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 100 0

EACH HORIZONTAL DIVISION = -001"

FIGURE 7 b MATERIAL S (MOISTURE CONTENT - DRY)

6 0 0

0

EACH HORIZONTAL DIVISION = .001"

FIGURE 7c MATERIAL V (MOIST. CONT. 25% SATURATED)

6 0 0

0

EACH HORIZONTAL DIVISION = .OOll'

FIGURE 7 TYPICAL STRESS STRAIN CURVES FOR TEST CYLINDERS. ( 2 . 8 " DIA x 6 *