attenuation of ultrasonic pulse in cement mortar.pdf

7/29/2019 Attenuation of ultrasonic pulse in cement mortar.pdf

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CEMENT and CONCRETE RESEA RCH, Vol. 20, pp. 335-345, 1990. Printed in the USA .0008-8846/90. $3.00+00. Copyright (c) 1990 Pergamon Press plc.

A T T E N U A T I O N O F U L T R A S O N I C P U L S E I N C E M E N T M O R T A R

A B S T R A C T

K . T h a r m a r a t n a m a n d B . S . T a nS c h o o l o f A r c h i t e c t u r eF a c u l t y o f A r c h i t e c t u r e a n d B u i l d i n gN a t i o n a l U n i v e r s i t y o f S i n g a p o r eR e p u b l i c o f S i n g a p o r e 0 51 1

(Refereed)(ReceivedJuly 21; in final form Oct. 12, 1989)

T h e u s e o f u l t r a so n i c p u l s e a t t e n u a t i o n ( U P A ) a s a n o n - d e s t r u c t i v e t e s t i n g p a r a m e t e rt o e v a l u a t e t h e q u a l i ty o f m a t e r i a l i s p r e s e n t e d i n t h i s p a p e r . T h e a t t e n u a t i o n o fu l t r a s o n i c p u l s e is a c o m b i n e d e f f e c t o f t h e g e o m e t r i c d i s p e r s i o n a n d e n e r g yd i s s i p a t i o n . T h e c h a r a c t e r i s t i c o f p u l s e a t t e n u a t i o n w i t h r e s p e c t t o t h e t r a n s m i t t e dp a t h l e n g t h c a n b e r e p r e s e n t e d b y a s i m p l e e q u a t i o n . E x p e r i m e n t s to e x a m i n e t h er e l a t i o n s h i p o f t h e q u a l i t y o f c e m e n t m o r t a r t o p u l s e a t t e n u a t i o n a n d t o p u l s e v e l o c it y( U P V ) a r e p e r f o r m e d . R e s u l t s o f th e e x p e r i m e n t s s h o w t h a t th e p u l s e a t t e n u a t i o nc o r r e la t e w e ll t o c o m p r e s s i v e s t re n g t h o f c em e n t m o r t a r . T h e c o m b i n e d U P A a n dU P V m e t h o d f o r s t r e n g t h e s t i m a t i o n is a l so e v a lu a t e d .

I n t r o d u c t i o nT h e u s e o f n o n - d e s t r u c t i v e t e s ti n g m e t h o d s i n e v a l u a t i n g t h e q u a l i ty o f i n - s i t u c o n c r e t e h a sa c h i e v e d i n c r e a s i n g a c c e p t a n c e i n r e c e n t y e a rs ( 4) . T h e u l t r a s o n i c p u l s e v e l o c i t y ( U P V ) t e c h n i q u ei s o n e o f t h e o f t e n u s e d n o n - d e s t r u c t i v e m e t h o d s . B e s i d e p u l s e v e l o c i t y , a n o t h e r p a r a m e t e ra s s o c i a t e d w i t h t h e p r o p a g a t i o n o f u l t ra s o n i c p u l s e is t h e a t t e n u a t i o n o f t h e p u l s e a m p l i t u d e ( U P A ) .T h e p u l s e a t t e n u a t i o n h a s b e e n s p a r s e l y s t u d i e d i n n o n - d e s t r u c t i v e t e s t i n g . A p r e v i o u s s t u d y ( 5 )i n d i c a t e d t h a t t h e u l tr a s o n i c d a m p i n g , a f o r m o f p u l s e a t t e n u a t i o n , c a n b e c o m b i n e d w i t h p u l s ev e l o c i t y to e s t im a t e t h e s t r e n g t h o f c o n c r e t e . O n e r e c e n t s t u d y ( 6 ) w h i c h u s e s t h e a t t e n u a t i o n o fp u l s e a m p l i t u d e h a s s h o w n t h a t p u l s e a t te n u a t i o n i s m o r e s e n s i t iv e t h a n p u l s e v e l o c i t y in d e t e c t i n gt h e o c c u r r e n c e o f c ra c k g r o w t h i n c o n c r e t e s u n d e r c y c l i c l o a d . T h i s p r e s e n t i n v e s t i g a t i o n s t u d i e st h e r e l a t i o n s h i p b e t w e e n t h e p u l s e a t t e n u a t i o n a n d t h e s t r e n g t h p r o p e r t y o f t h e c e m e n t m o r t a r .T h e m a i n p u r p o s e o f t h is p a p e r i s t o d e m o n s t r a t e t h e p o s s i b i l i t y o f d e t e r m i n i n g a p a r a m e t e rr e p r e s e n t a t i v e o f t h e p u l s e a t t e n u a t i o n a n d s u b s e q u e n t l y , e s t a b l i s h i n g a r e l a t i o n s h i p b e t w e e n t h i sp a r a m e t e r w i t h t h e q u a l i t y o f t h e so l i d m e d i u m . T h e f i r s t p a r t o f t h e p a p e r e x p l a i n s b r i e f l y t h ea t t e n u a t i o n p r o c e s s o f u l t r as o n i c p u ls e p r o p a g a t i o n i n s o l id m e d i u m . T h e l a t e r p a r t d e s c r i b e se x p e r i m e n t s d o n e t o e x a m i n e t h e c h a r a c t e r i s t i c s o f t h e p u l s e a t t e n u a t i o n w i t h r e s p e c t to t h e p a t hl e n g t h a n d a ls o t h e q u a l i t y o f t h e m e d i u m , u s i n g c e m e n t m o r t a r s w i t h d i f f e r e n t s t re n g t h s . C e m e n tm o r t a r m i x t u r e s a r e u s e d t o s t u d y t h e U P A r e s p o n s e in a r e l a t i v e l y m o r e h o m o g e n o u s m a t e r i a l t h a nc o n c r e t e w h i c h i s e s s e n t i a l l y c e m e n t m o r t a r p l u s c o a rs e a g g r e g a te ( g r av e l ) . T h i s s t u d y a i m s t op r o v i d e s o m e b a s i s f o r f u t u r e s t u d i e s o f a t t e n u a t i o n o f u l t r a s o n i c p u l s e i n c o n c r e t e .

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336 K. Tharmaratnam and B.S. Tan Vo l. 20. No. 3

UltrgsQni~; Pulse At tenuat ion In Sol idT h e a t t e n u a t i o n o f t h e s o u n d p r e s s u r e c o n s is t o f t w o c o m p o n e n t s , n a m e l y t h e g e o m e t r i c d i v e r g e n c ea n d t h e e n e r g y d i s s i p a t i o n ( 1 ,2 ) .D i v e r g e n c e o f t h e S o u n d B e a mA s t h e s o u n d b e a m t r a v e ls t h r o u g h t h e s o l id m e d i u m a w a y f r o m t h e s o u rc e , t h e s o u n d b e a m w i l ld i v e r g e f r o m t h e c e n t r e o f t h e b e a m . T h e d i s p e r s i o n ca u s e s l os s o f p u l s e a m p l i t u d e a s t h e a re a o ft h e s o u n d b e a m i s i n c r e a s e d .K r a u t k r a m e r ( 1 ) h a s r e p r e s e n t e d t h e p u ls e a m p l i t u d e b y t h e f o l l o w i n g e q u a t io n :

P d = ] P o 2 S in { ~ r [ . / ( D 2 /4 + r 2 ) - r ] / 5 ) 1 . . .. . ( 1 )w h e r e P d = d i v e r g e d p u l s e a m p l i t u d e a t d i s t a n c e r , P o ffi i n i t i a l p u l s e a m p l i t u d e a t t h e s o u r c e , 6 =w a v e l e n g t h o f t h e s o u n d b e a m , D = d i a m e t e r o f t h e o s c il l a t o r a n d r = d i s t a n c e a w a y f r o m t h es o u r c e . T h e a b o v e e q u a t i o n c a n b e s i m p l i f i e d i f t h e d i s t a n c e is r e l a t i v e l y f a r f r o m t h e s o u r c e , th a ti s r >) D ~ / 4 6 , w h i c h i s c o n s i d e r e d a f a r - f i e l d p r o b l e m :

P d = P o ~" D 2 / 4 6 r ...............................2)

D i s s i p a t i o n o f t h e S o u n d W a v eT h e d i s s i p a t i o n e f f e c t c o n s i s ts o f t w o p r o c e s s e s , n a m e l y s c a t t e ri n g a n d a b s o r p t i o n . S c a t t e r in g i s d u em a i n l y t o t h e n o n - h o m o g e n o u s c o m p o s i t i o n o f th e m e d i u m . T h e s e c o n d p r o c es s , a b s o r p ti o n o fs o u n d w a v e , i s th e a c t u a l l os s o f s o u n d e n e r g y i n t o h e a t e n e r g y , d u e m a i n l y t o th e i n t e r n a l f r i c t i o no f t h e m e d i u m .F o r a p l a n e s i n u s o i d a l w a v e o f s m a l l a m p l i t u d e , t h e a t t e n u a t i o n o f t h e a b o v e t w o d i s s i p a t i n g f a c t o r sa r e fo u n d t o b e e x p o n e n t i a l a n d t h e p u l s e a m p l i t u d e c a n b e a p p r o x i m a t e d b y t h e f o l l o w i n g e q u a t i o n( 1 - 3 ) :

Pa = Po e 'a r . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . 3)w h e r e a ffi a t t e n u a t i o n c o e f f i c i e n t . T h e n a t u r a l l o g a r i t h m o f E q . ( 3 ) g i v e s a r ffi L n ( P a / P o ) . T h i s i st h e t o ta l a t t e n u a t i o n o v e r d i s t a n c e r, a d i m e n s i o n l e s s n u m b e r w h i c h i s e x p r e s s e d i n n a p e r ( N p ) . T h ea t t e n u a t i o n c o e f f i c i e n t , a c a n t h e r e f o r e b e g i v e n i n N p / m m . T h e a t te n u a t i o n c o e f f i c i e n t a isa f f e c t e d b y t h e f r e q u e n c y o f p r o p a g a t i o n . A t p r e s e n t , h o w e v e r , t h i s w i l l n o t b e e x a m i n e d i n th i ss t u d y s i n c e o n l y o n e t y p e o f t r a n s d u c e r ( 5 0 K H z ) w a s u s e d f o r t h e e x p e r i m e n t s .C o m p a r i s o n B e t w e e n D i v e r g e n c e a n d D i s s i p a t i o n F a c t o rF o r q u a l i t y e v a l u a t i o n o f m a t e r i a l s , t h e d i s s i p a t i o n f a c t o r i s c r i t i c a l s i n c e i t i s r e l a t e d t o t h ep r o p e r t i e s o f t h e m i x t u r e . T h e d i v e r g e n c e f a c to r is m a i n l y a g e o m e t r i c p h e n o m e n o n . T h e r e l a t i v ec o n t r i b u t i o n s o f t h e p h e n o m e n a o f d i v e r g e n c e a n d d i s s i p a t i o n t o t h e to t a l a t t e n u a t i o n a r e s h o w ni n T a b l e I .T a b l e I sh o w s t h a t t h e r e l a t i v e im p o r t a n c e o f e a c h f a c t o r d e p e n d s o n t h e p a t h l e n g t h r a n d t h ea t t e n u a t i o n c o e f f i c i e n t a . T h e s e c o n d c o l u m n o f th e ta b l e s h o w s t h a t t h e d i v e r g e n c e f a c t o r fo l l o wt h e i n v e r s e d i s t a n c e la w w h i c h i s d o m i n a n t a t s h o r t e r d i s ta n c e s (< 1 5 0 m m ) b u t g r a d u a l l y b e c o m e sl es s s i g n i f i c a n t f o r l o n g p a t h l e n g th s . H o w e v e r , t h e d i s s i p a t i o n f a c t o r b e c o m e s m o r e p r o m i n e n t a ts h o r t e r d i s t a n c e s w h e n t h e a t t e n u a t i o n c o e f f i c i e n t b e c o m e s h i g h e r .C o m b i n e d U l t r a s o n i c P u l s e A t t e n u a t i o nT h e c o m b i n e d e f f e c t o f b o t h t h e d i v e r g e n c e a n d d i s s i p a t i o n f a c t o r s a r e g i v e n b y t h e f o l l o w i n g


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Vo l. 20, No. 3 Ultrason ic Pulse, Attenuatic~t,Mo rtar, Pulse Velocity 337

T a b l e IC o m p a r i s o n B e t w e e n t h e A t t e n u a t i o n o f D i v e r g e n c e a n d D i s s i p a t i o n L o s s es

P a t hL e n g t h

r D i v e r g e n c e( m m ) P d ( r ) / P d ( 5 0 )

A t t e n u a t e d P u l s e A m p l i t u d e

(%)D i s s i p a t i o n P a ( r ) / P a ( 5 0 ) ( % )F o r A t t e n u a t i o n C o e f f i c i e n t ct ( N p / m )

1 2 3 4 55 0I 0 0 5 0 . 01 5 0 3 3 . 33 0 0 1 6 .74 5 0 I I. I6 0 0 8 . 3I 0 0 0 5 . 0

95.1 90.5 86.1 81.9 77.990.5 81.9 74.1 67.0 60.777 . 9 60 . 7 47 . 2 36 . 8 28 . 767.0 44.9 30.1 20.2 13.557.7 33.3 19.2 11.1 6 .438.7 15.0 5 .8 2 .2 0 .9

e q u a t i o n :P r = P o K c Kd ( l / r ) e " a t . . . .. . .. . .. . .. . .. . .. . . .. 4 )

w h e r e K d = 7r D 2 / 4 6 ( f a r - f i e l d , E q . 2 ) , K c = a t t e n u a t i o n f a c t o r d u e t o c o n t a c t l o s s e s , P r = p u l s ea m p l i t u d e a t d i s t a n c e r f r o m t h e so u r c e . T h e e q u a t i o n f o r t h e n e a r f i e l d ca s es c an b e o b t a i n e d b yi n s e r t i n g E q . ( l ) i n s t e a d o f E q . (2 ) .I n t h e u l t r a s o n i c p u l s e t ra n s m i s s i o n , f u r t h e r l o ss es o f e n e r g y w i l l b e c a u s e d b y t h e i m p e r f e c tc o u p l i n g b e t w e e n t h e t r a n s d u c e r s a n d t h e s p e c i m e n s u r f a c e . T h e f a c t o r K e , i n E q .( 4 ) is t h ea d d i t i o n a l c o n s t a n t i n t r o d u c e d t o a c c o u n t f o r s u ch l o ss e s. I t w a s n o t e d f r o m e x p e r i m e n t a l r e s u lt st h a t th i s c o n s t a n t v a r i e s w i d e l y w i t h r e s p e c t to t he r o u g h n e s s o f t h e s p e c i m e n s u r f a c e . T h u sc o n s i d e r a b l e c a r e n e e d t o b e t a k e n t o e n s u r e a s m o o t h s u r f a c e t h a t p r o v i d e a c o n s i s t e n t K c .D e f i n i t i o n o f t h e P u l s e A t t e n u a t i o n P a r a m e t e rT h e t e r m ' p u l s e a m p l i t u d e ' m e a n s t h e a m p l i t u d e a t t h e c e n t r e o f t h e b e a m s i n c e i t i s t h e m a x i m u ma m p l i t u d e o f t h e b e a m c r o s s - s e c t i o n a n d t h e e a s ie s t t o m e a s u r e i n d i r e c t tr a n s m i s s i o n o f p u l se s . T h ep u l s e a m p l i t u d e o f t h e fi r s t p e a k i s m e a s u r e d f o r t h e d e t e r m i n a t i o n o f a t t e n u a t i o n s i n c e t h e f ir s ta m p l i t u d e i s f r e e f r o m a n y i n t e r f e r e n c e f r o m t h e r e fl e c t e d w a v e s .I n u l t r a s o n i c p u l s e t e s t in g , t h e a m p l i t u d e o f t h e p u l s e i s m e a s u r e d i n v o l t ag e p o t e n t i a l i n s t e a d o fa c o u s t i c p r e s s u r e . T h i s i s d u e t o t h e f a c t t h a t t h e a c o u s t i c p r e s s u r e o f t h e u l t r a s o n i c s o u n d i sd e t e c t e d a s p a r t i c l e s d i s p l a c e m e n t s b y t h e r e c e i v i n g p i e z o e l e c t r i c t r a n s d u c e r , w h i c h c o n v e r t s t h ep h y s i c a l d i s p l a c e m e n t s i n t o v o l ta g e p o t e n ti a l . H o w e v e r , t h e a b o v e a t t e n u a t i o n e q u a t i o n s a r e s t il la p p l i c a b l e s i n c e t h e a m p l i t u d e o f p a r t i c l e d i s p l a c e m e n t i s c l o s e ly r e l a te d t o t h e a m p l i t u d e o f t h ea c o u s t i c p r e s s u r e a n d s i m i l a r l y th e v o l t a g e p o t e n t i a l to t h e p a r t i c l e d i s p l a c e m e n t .T h e u l t r a s o n i c p u l s e a t t e n u a t i o n p a r a m e t e r ( U P A ) u s e d i n th i s s tu d y i s d e f i n e d a s t h e r a t io o f t h ef i r s t p u l se a m p l i t u d e m e a s u r e d a t d i s t a n c e r, o v e r t h e i n i ti a l a m p l i t u d e Po" T h e a m p l i t u d e r a t i o w il lb e d e n o t e d a s , A r = P r / P o ' w h e r e t h e i n i t i a l a m p l i t u d e c a n b e a p p r o x i m a t e d w i t h t h e f i r s t p u l sea m p l i t u d e m e a s u r e d w i t h n o s p e c i m e n b e t w e e n t h e t ra n s d u c e r s . T h i s p u l s e a m p l i t u d e r a t i o is u s e db e c a u s e i t is d i r e c t l y m e a s u r e d i n t e st i n g s , a n d q u i c k a s s e s s m e n t c a n b e d o n e i m m e d i a t e l y a f t e rm e a s u r e m e n t s .

E x n e r i m e n t a l P r o e a m m eT e s t s w e r e c a r r i e d o u t o n c e m e n t m o r t a r s a t tw o s t ag e s . T h e f i r st g r o u p o f m o r t a r m i x e s w a s


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338 K. Tharmaramam and B.S. Tan Vo l. 20, No. 3

e x a m i n e d f o r t h e c h a r a c t e r i s t i c s o f th e u l t r a s o n i c p u ls e a t t e n u a t i o n w i t h r e s p e c t to c h a n g i n g p a t hl e n g th s . A s e c o n d g r o u p o f m i x e s w i t h s im i l a r w o r k a b i l i t y w a s t e st e d fo r t h e c o r r e l a ti o n b e t w e e nt h e s t r e n g t h a n d t h e p u l s e a t t e n u a t i o n . D e t a i l s o f t h e m i x p r o p o r t i o n s a r e g i v e n i n T a b l e I 1.T a b l e I IC e m e n t M o r t a r M i x e s

B a tc h M i x C e m e n t S a n d W / C C o m m e n tC o n t e n I C o n t e n ~ R a t i o( K g / m " ) ( K g / m ~)I I A , I B & I C 2 7 6 t o 1 6 5 9 t o 0 . 9 0 t o L o w t o H i g h6 5 6 1 1 59 0 . 5 0 w o r k a b i l i t yI I I I A , l i B , I I C , 2 4 9 t o 1 6 8 0 t o 1 .0 0 t o M e d i u mI I D , l i E & I I F 4 3 7 1 5 30 0 . 57 w o r k a b i l i t y

S p e c i m e n p r e p a ra t io nC u b e s s p e c i m e n s o f s iz e s 1 0 0 m m a n d 1 5 0 m m w e r e c a s t f o r b o t h s e ts o f m o r t a r m i x e s . B u t t h ins p e c i m e n s o f 1 0 t o 50 m m a n d l o n g s p e c i m e n s o f 3 0 0 m m w e r e a l s o c a s t f o r t h e f i r s t g r o u p o fm o r t a r s . T h e f i n e a g g r e g a t e u s e d is a i r - d r y n a t u r a l s an d c o n f o r m i n g t o t h e f i rs t g r a d i n g z o n e ( BS8 8 2 ). T h e t y p e o f c e m e n t u s e d w a s o r d i n a r y P o r t l a n d c e m e n t a n d a l l m a t e r i a l s w e r e b a t c h e d b yw e i g h t . A l l t h e m i x e s w e r e c o m p a c t e d o n a v i b r a t i n g t a b le t o o b t a i n f u l l y c o m p a c t e d t e s ts p e c i m e n s . T h e s p e c i m e n s w e r e re m o v e d f r o m m o u l d o n e d a y a f t e r c a s t i n g a n d t h e n w a t e r c u re du n t i l a d a y b e f o r e t e s t i n g . S p e c i m e n s w e r e t e s te d a t 2 g - d a y f o r p u l s e a m p l i t u d e , p u l s e v e l o c i t y a n dc o m p r e s s i v e s t r e n g t h .Test in g P r oc ed u r eT w o 5 0 - K H z p i e z o e l e c t r i c t r a n s d u c e r s ( l e a d z i r c o n a t e t i t a n a t e c r y s t a l t y p e ) w e r e u s e d a s t h et r a n s m i t t e r a n d r e c e i v e r o f u l t r a s o n i c v i b r a t i o n s . T h e u l t r a so n i c p u l s e w as g e n e r a te d a t t h ea l t er n a t in g c u r r e n t f r e q u e n c y o f 5 0 H z w i t h a c o m m e r c i al l y av a i la b l e u l tr a s o n i c - s c o p e ( M A R U I ) .A d i g i t a l - s t o r a g e o s c i l l o s co p e w a s u s e d t o d e t e c t t h e t r a n s m i t t e d w a v e s f r o m w h i c h t h e t r a n s m i t t e dt i m e a n d t h e p u l s e a m p l i t u d e s w e r e o b t a i n e d . T h e m e a s u r e m e n t s w e r e t a k e n at t h e m i d - p o i n t o fc u b e s p e c i m e n s a n d i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e c a s t i n g d i r e c t i o n .I n t h e i n i t i a l s t a g e o f t h e e x p e r i m e n t , i t w as f o u n d t h a t l a r g e v a r i a ti o n s i n p u l s e a m p l i t u d e s w e r eo b s e r v e d f o r c u b e s f r o m t h e s a m e m o r t a r m i x w h e n m e a s u r e m e n t s w e r e d o n e o n b a r e m o r t a rs u r f a c e s w i t h g r e a s e a p p l i e d o n as a c o u p l i n g m a t e r i a l . S u b s e q u e n t l y , a t h i n l a y e r (0 . 5 - 1 .0 m m )o f p a r a f f i n w a x w a s c o a t e d t o p r o v i d e a r e l a t i v e l y s m o o t h s u r f a c e i n a d d i t i o n t o a p p l y i n g g r e a s e a st h e c o u p l i n g m a t e r i a l . T h e p u l s e a m p l i t u d e s w e r e o b s e r v e d t o h a v e i n c r e a s e d s u b s t a n t i a l l y , b u tm o r e i m p o r t a n t l y t h e v a r i a ti o n s b e t w e e n c u b e s o f s a m e m o r t a r m i x w e r e g r e a t ly r e d u c e d .

Resu l t s a n d Di sc u ss ionP u l se a t t en u a t ion wi t h r e spec t t o pa t h l en g t hF i g u r e 1 s h o w s t h e r e l a t i o n s h i p b e t w e e n t h e p u l se a m p l i t u d e a n d p a t h l e n g t h f o r t h e m o r t a r m i x e s .T h e m e a s u r e d p u l s e a m p l i t u d e r a t io s a re p l o t t e d t o g e t h e r w i t h a b e s t - f i t l i n e in t h e f o r m o f t h ea t t e n u a t i o n e q u a t i o n , E q . ( 4 ). T h e c o n s t a n t s f o r t h e e q u a t i o n w e r e o b t a i n e d f r o m r e g r e s s io n a n al y s iso f t h e m e a s u r e d d a t a . A l l th e m i x e s sh o w e d v e r y g o o d c o r re l a t i o n b e t w e e n t h e a m p l i t u d e r a t i o an dp a t h l e n g t h w i t h t h e a tt e n u a t i o n e q u a t i o n . T h u s t h e e x p o n e n t i a l d e c r e as e o f p u l s e a m p l i t u d e w i t hr e s p e c t to p a t h l e n g t h c a n b e a p p l i e d t o a c o m p o s i t e o f c e m e n t a n d s a n d m i x t u r e .


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0.70-

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ffi a t t e n u a t i o n c o e f f i c i e n tR - c o r r e l a t i o n c o e f f i c i e n t

F I G . 1The relationship between the amplituderatio and the path length for mortar :(a) IA, (b) IB and (c) IC.

Slight deviations from Eq.(4) for path lengths of less than 30mm are observed in the figures. Thesedeviations are possibly due to the fact that the attenuation equation was simplified for far-fieldproblems only (Sec 2.1). Thus the length of the test specimen should be relatively long ~ 50mm)to avoid this problem. However, very long path length has a disadvantage since the amplitude ofpulse will be small due to attenuation over a long path length. It is dif ficult for the oscilloscope toshow the amplitude difference fo r mixes of different quality. Therefore in the UPA testing ofmaterials the specimen length should be at a moderate range to avoid both extreme problems. Thisrange depends mainly on the properties of the pulse (the far-field criteria) and the attenuationprocess of the testing material.C o r r e l a ti o n s o f P u l s e A t t e n u a t i o n a n d V e l o c i t y w i t h t h e C o m p r e s si v e S t r e n g thThe correlation studies for 100 and 150ram cubes between the 28-day compressive strength, f , with


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340 K. Tharmaramamand B.S. Tan Vol. 20. No. 3

I

t~

I

the pulse ampl itud e ratio are shown in Figure 2. The figures show that the compressive strengthsof cement mortars are related to the ampli tude ratios. The relation ship can be representedapproximately with :

f = a e t~r ......... ......... .. (5)where f is the compressive strength in MPa, A r is the amplitude ratio, and a and b are constants.The correlation coefficients of both 100 and 150ram cubes is 0.876, and the average deviation ofthe calcu lated str ength from the measured s trength are 2.8 and 2.3 MPa ( MN /m m z =N/m m 2 ),respectively.

2 (~d lO0~J~m Cubcs 2 Ib) #50mm Cubes

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FIG. 2Correlation of amplitude ratio with the compressive strength for :(a) 100ram, and (b) 150ram cubes.The corr elation be tween the pulse velocity and compressive strength is also shown in Fig ure 3. Thisrelationship has been studied before (7-9) and the equation most commonly used is :

f -- c eav ....... ....... ....... .... (6)where V is the pulse velocity in km/s , and c and d are constants. In this expe rime nt the correlationcoef fic ient of this relation are 0.906 and 0.908, respectively for 100 and 150ram cubes. The averagedeviation of the calculated strength from the measured strength are 2.6 and 2.7 MPa respectivelyfor 100 and I50mm cubes.Both pulse attenuation and pulse velocity correlations have similar precision in the estimation ofmortar strength. One significan t differe nce between the two correlation is that the percentagechange of pulse atten uati on is of a larger range (.04-.024 / .024 = 67%) than that of the pulsevelocity (4.3-3.4 / 3.4 = 26%), for the corr espo nding change in compressive strength. This impliesthat the pulse attenuation is more sensitive to changes in compressive strength than the pulsevelocity. However there is a higher degree of variabi lity in the measuremen t of pulse attenuation.In the experiment , the coefficient of variation (sample standard deviation / sample average) of theamplitude ratios for cubes of the same mix was within the 10% range, which is higher then the 5%range for the pulse velocities.


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Vol. 20, No. 3 UltrasonicPulse, Attenuation,Mortar, Pulse Velocity 341

3 (a) lOOmm Cubes35 '1"- k = g.~te

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~ 1 tL6

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FIG. 3Correlation of pulse velocity with the compressive strength for :(a) 100ram, and (b) 150ram cubes.

i4 2

C o m b i n e d c o r r e la t i o n o f P u l s e A t te n u a t i o n a n d P u l s e V e l o c i t yStudies (8-10) have indicated that combined correlation of UPV with other parameters, such as thepul l-o ut force and the Rebou nd numb er, can improve the reliability of the prediction ofcompressive strength. A combin ed correlation study was done to examine the possibility ofimprov ing the accuracy of strength estimation using pulse velocity and pulse amplitude ratio. Therelationship selected is in the form of :

f = B e (cv OAr) ......... (7)where B, C, and D are constants. The correlat ion coefficient s are 0.935 and 0.933 respectively forthe 100mm and 150ram cubes. The average devi ation of the measured compressive streng th fromthe strength calculat ed by the relationshi p are 1.9 and 2.1 MPa respectively. The devi ations of this

T a b l e IIICorrelations Coefficients and Constants

Desciption f ffi a e ~ r f ffi c e a v f ffi B e cv OArlOOmm 150mm lOOmm 150mm 100mm 150mm

Constants a : .118 .502 c : .015 .023 B : .020 .052b : 2.05 2.47 d : 1.83 1.72 C : 1.17 1.09D : 0.93 1.13CorrelationCoeff ic ien t R 0.876 0.876 0.908 0.906 0.935 0.933Strength (MPa) 2.7 2.8 2.7 2.6 2.1 1.9Deviat ion (%) 18 18 17 16 14 13


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342 E. Tharrnaramam and B.S. Tan VoL 20, No. 3

4 (a J C o r r e l a t i o n f - A r 4 ( c) C o r r e l a t i o n f - F & A r. 1 5 " 1 5 '

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F I G . 4C o m p a r i s o n b e t w e e n t h e m e a s u r e ds t r e n g t h a n d t h e e s t i m a t e d s t r e n g t hf o r 1 5 0 r am c u b e s u s i n g c o r r e l a t i o n :( a) f - A r , ( b ) f - V , a nd( c ) f V & A r ( c o m b i n e d ) .

c o m b i n e d c o r r e l a t i o n a re l o w e r th a n t h e in d i v i d u a l U P V a n d U P A c o r r e l a t io n s . T a b l e I II s h o w s t h ec o r r e l a t i o n c h a r a c t e r i s t i c s, t h at i s t h e e q u a t i o n c o n s t a n t s , t h e c o r r e l a t i o n c o e f f i c i e n t a n d t h e a v e r a ges t r e n gt h d e v i a t i o n s , f o r b o t h i n d i v id u a l a n d c o m b i n e d m e t h o d s .T h e c o m p a r i s o n b e t w e e n t h e m e a s u r e d a n d c a l c u l a te d s t r e n g t h f o r t h e i n d i v i d u a l a n d c o m b i n e dm e t h o d s a r e s h o w n i n F i gu r e 4 , f o r t h e 1 5 0 r a m c u b e s . T h e f i g u r e s h o w s t h a t e s t i m a t e s o f t h ec o m b i n e d m e t h o d l i e c l o s e r t o t h e e q u i t y l i n e th a n th e i n d i v i d u a l m e t h o d s .T h e A t t e n u a t i o n C o e f f i c i e n t aT h e a t t e n u a t i o n c o e f f i c i e n t r~, t h e t h e o r e ti c a l r e p r e s e n t a t io n ( E q . 4 ) o f p u l s e a t t e n u a t i o n p e r u n i tl e n g t h , c a n b e c a l c u l a te d u s i n g a m p l i t u d e r a t io ( A r ) r e a d i n g s ( a v e r a g e o f 4 s p e c i m e n s ) o f 1 0 0 r a ma n d 1 5 0 r a m c u b e s f r o m e a c h m i x . I f o n e a s s u m e t h a t a a n d K c w e r e t h e s a m e f o r b o t h c u b e s , t h ec o n s t a n t K o i n E q . ( 4 ) c a n b e e l i m i n a t e d a n d s o l v e d f o r a . S u b s e q u e n t s u b s t i t u t i o n i n t o E q . ( 4 ) y i e l d


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Vol. 20, No. 3 Ullxasonic Pulse, Attenuation,Mo rtar, Pulse Velocity 343

T a b l e IVT h e A t t e n u a ti o n C o e f f i c i e n t a

M o r t a rM i x

1 0 0 m m C u b e s 1 5 0 m m C u b e sM e a s u r e d * A t t e n u a t i o n M e a s u r e d *S t r e n g t h C o e f f i c i e n t S t r e n g t hf a f( M P a ) ( N p / m ) ( M P a )

A t t e n u a t i o nC o e f f i c i e n tot( N p / m )I I A 7 .7 5 .1 7 .5 4 .4IIB 9.3 3.4 10.1 .3.5I IC 14.1 3 .3 14.0 3 .4l i D 15.7 2 .4 15.6 2 .3l i e 23 . 0 1 .8 22 . 0 1 .9I I F 28.1 1 .0 26.0 1 .5* a v e r a g e o f 4 c u b e s

t h e c o n s t a n t K c. T h e e x p e r i m e n t a l v a l u e s o f K c ' s w e r e o b s e r v e d t o v a r y s i g n i f i c a n t l y b e t w e e nm i x e s e v e n t h o u g h t h e c o u p l i n g c o n d i t i o n s o f al l t h e s p e c i m e n s w e r e s i m i l a r. T h i s i s b e c a u s e t h ect f o r 1 00 & 1 5 0 m m c u b e s a r e s l i g h t ly d i f f e r e n t e v e n f o r a s a m e m o r t a r m i x . T h e r e f o r e , a c o n s t a n tK c f o r a l l m i x e s ( th e a v e r a g e K c ' s o f a l l m i x e s f r o m t h e p r e v i o u s m e t h o d ) w a s a s s u m e d i n s t e a d , t od e t e r m i n e a f o r e a c h c u b e s iz e o f e a c h m i x .

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F I G . 5R e l a t i o n s h i p b e t w e e n t h e c o r r e l a t io n c o e f f i c i e n ta n d c o m p r e s s i v e s t r e n g t h o f m o r t a r s .

R e s u l t s o f t h i s c a l c u l a t i o n f o r r , a r e s h o w ni n T a b l e IV . T h e c o e f f i c i e n t is s l i g h t l yd i f f e r e n t f o r d i f f e r e n t c u b e s i z e o f t h e s am em i x , b u t g e n e r a l l y , c t i s i n v e r s e l yp r o p o r t i o n a l t o t h e c o m p r e s s i v e s t r e n g t h .T h e c l o s e c o r r e l a t i o n b e t w e e n t h e t w op a r a m e t e r s c a n b e s e e n c l e a r l y i n F i g u r e 5 ,w h e r e a c o r r e l a t i o n c o e f f i c i e n t o f r= 0 .9 5 7i s f o u n d f o r a r e l a t i o n s h i p i n t h ee x p o n e n t i a l f o r m ( f = g e ' h a ) . T h i s c l o sec o r r e l a t i o n s h o w s t h e p o s s i b i l i t y o f u s i n gt h is N D T t e s t in g p a r a m e t e r to d e t e r m i n e t h es t r e n g t h o f m a t e r i a l .I t i s n o t e d t h a t t h e n u m e r i c a l c a l c u l a t i o n o fc t i s v e r y s e n s i t i v e t o t h e c o n s t a n t K c . As l i g h t c h a n g e i n K c c a u s e s a s i g n i f i c a n tc h a n g e i n t~. H e n c e t h e p r a c t i c a l i t y o f u s i n gc~ a s a c o r r e l a t i o n p a r a m e t e r w i t h s t r e n g t h ,w i l l m a i n l y l i e s i n t h e a b i l i t y t o p r o d u c e ac o n s i s t e n t c o n t a c t s u r f a c e a n d t o d e t e r m i n et h e c o n t a c t c o n s t a n t K c a c c u r a t e l y .

T e s t i n g s o f S p e c i m e n s w i t h D i f f e r e n t P a t h L e n g t h sT h e a m p l i t u d e r a t i o c o r r e l a t i o n w i t h s tr e n g t h , e i t h e r i n d i v i d u a l o r c o m b i n e d w i t h U P V , i s o n l ya p p l i c a b l e f o r th e s p e c i f i c l e n g t h at w h i c h t h e c o r r e la t i o n is b a s e d . T h e a - f c o r r e l a t i o n d o e s n o th a s s u c h l i m i t a t i o n s i n c e ct i s n o t d e p e n d e n t o n t h e p a t h l e n g t h . H o w e v e r t h e d i f f i c u l t y i n o b t a i n i n ga c o n s i s t e n t r , , a s d i s c u s s e d e a r l i e r i n s e c t i o n 4 . 4 , m a k e t h e u s e o f ~ - f c o r r e l a t i o n i m p r a c t i c a l .


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344 K. Tharmaramam and B.S. Tan Vo l. 20. No. 3

T h e u s e o f a m p l i t u d e r a t i o - s t r e n g t h c o r r e l a t i o n i n t e s ti n g s p e c i m e n s w i t h d i f f e r e n t p a t h l e n g th s iss t il l p o s s i b l e w i th s o m e a p p r o x i m a t i o n . T h i s i s d o n e b y r e p r e s e n t i n g t h e a m p l i t u d e r a t i o s m e a s u r e da t d i f f e r e n t l e n g t h s w i t h a p p r o x i m a t e d a m p l i t u d e r a t i o s a t a le n g t h f o r w h i c h t h e a m p l i t u d e r a t i o -s t r e n g t h c o r r e l a t i o n w a s b a s e d . T h e a p p r o x i m a t e d a m p l i t u d e r a t io d e r i v e d f r o m E q . (4 ) i s a s f o ll o w :A t , = A r ( r / r ' ) e " = ( r ' ' r ) . .. .. .. .. .. ( 8 )

w h e r e r is th e s p e c i m e n p a t h l e n g t h , r ' i s t h e l e n g t h f o r w h i c h t h e c o r r e l a t i o n w a s b a s e d , A r i s t h em e a s u r e d a m p l i t u d e r a t i o , a n d A t , i s t h e a p p r o x i m a t e d a m p l i t u d e r a t i o . T h i s A t , i s t h e n s u b s t i t u tei n t o t h e o r i g i n a l c o r r e l a t i o n ( E q . 5 o r 7 ) t o f i n d f .S u p p o s e t h a t a a m p l i t u d e r a t i o - s t r e n g t h c o r r e l a t io n f o r a p a r t i c u l a r ty p e o f m i x p r o p o r t i o n w a se s t a b l i s h e d a t 1 5 0 m m , A l s 0 - f , b u t a s p e c i m e n w i t h a d i f f e r e n t p a t h l e n g t h , s a y 1 2 5 m m , i s t o b ee v a l u a t e d . T h e m e a s u r e d a m p l i t u d e r a t i o a t 1 2 5 r a m , A l z 5 c a n n o t u s e t h e A 1 5 0- f c o r r e l a t i o n toe s t i m a t e t h e s t re n g t h . I n s t e a d , t h e a p p r o x i m a t e d A l s 0 f o r t h i s s p e c i m e n i s i n i t i a ll y d e t e r m i n e d f r o mE q . ( 8 ) a n d s u b s e q u e n t l y u s e d t o f i n d t h e s t r e n g t h e s t i m a t e f r o m t h e o r i g i n a l A15o- c o r r e l a t i o n .F o r t h e a b o v e e x a m p l e , t h e c o e f f i c i e n t a n e e d t o b e d e t e r m i n e d o r e s t i m a t e d i n o r d e r t o us e E q .( 8 ).T h i s i s a m a j o r d r a w b a c k f o r t h is m e t h o d s i n c e i t r e q u i r e d a d d i t i o n a l a m p l i t u d e r a t i o m e a s u r e m e n to n a n o t h e r s p e c i m e n o f d i f f e r e n t l e n g t h b u t s i m i l a r q u a l i t y to t h e 1 2 5 ra m s p e c i m e n . O t h e r w i s e , ac a n o n l y b e e s t i m a t e d b a s e d o n p r e v i o u s t e s t s o n s i m i l a r m i x e s , w h i c h w i l l i n t r o d u c e a d d i t i o n a le r r o r s i n t h e s tr e n g t h e v a l u a t i o n . H o w e v e r , t h i s a p p r o x i m a t e m e t h o d i s l es s s e n s i t iv e to v a r i a t i o ni n r, t h a n t h e d i r e c t a - f m e t h o d . A s a m p l e c a l c u l a t i o n f o r c o m p a r i s o n s h o w s t h a t , f o r a 10 0 m ms p e c i m e n , a c h a n g e o f a f r o m 2 t o 3 N p / m c a u se s t h e s t r e n g t h e s t i m a t e f r o m t h e d i r e c t c o r r e l at i o nt o v a r y b y 3 0 % (1 9 . 6 -1 3 . 7 M P a ) , w h e r e a s t h e e s t im a t e f r o m t h e a p p r o x i m a t e a m p l i t u d e r a t iom e t h o d v a r y b y o n l y 1 7 % ( 2 0 . 6 - 1 7 . 2 M P a ) .T h i s a p p r o x i m a t i o n m e t h o d i s a p p l i e d to t h e 1 0 0 m m c u b e s o f m i x e s I I A - I I F . T h e a p p r o x i m a t e1 5 0 r am a m p l i t u d e r a t i o s (A 1 5 0) f o r t h e 1 0 0 ra m c u b e s a r e c a l c u l a t e d ( E q . $ ) u s i n g t h e r , v a l u e sd e t e r m i n e d f r o m e x p e r i m e n t s ( T a b l e I II ) . F i g u r e 6 c o m p a r e s t h e m e a s u r e d s t r e n g t h t o t h e c a l c u l a t e d

6(c0 Co rrelal ion f - Ar 6{b) Approximate Ar Method

A

A 8 a A

v , ! , rI 0 2 e )0I g ~ ' ~ l U ~ (U P = )

/ A/y' s a

10-

5 a& a

0 I 0 Z OI~ '~ ' i1~ ~ 0~)

F I G . 6C o m p a r i s o n b e t w e e n t h e m e a s u r e d s t r e n g t h a n d e s t i m a t e d s t r e n g t h f o r 1 0 0 r a m c u b e s u s i n g( a ) d i r e c t c o r r e l a t i o n , f - A t , a n d ( b ) th e a p p r o x i m a t e d a m p l i t u d e r a ti o m e t h o d .


11/11

Vol. 20, No. 3 Ultrasonic Pulse, Atte~auation, Morta~, Pulse Velocity 345

strength f rom two procedures; this approximate method and the original (Alo 0-f) correlation of the100ram cubes. The calculated strengths are close to the measured strength for both methods. Thisshows that the approximation method is as accurate as the direct At - f correlation.The extrapolation of the amplitude ratio is only applicable for the range of path length examinedso far. Furthe r studies are needed to extend the use of this approximation and the amplitude ratio-strength correlation over a wider range of path length, which is likely to be encountered in the in-situ testings.

C o n c l u s i o nThe major findings from this investigation reported are as follows :1. The attenuation of ultrasonic pulse can be represented by the quantity, Ar , defined as the ratioof the amplitude of the first peak, Pr/Po, with and without specimen respectively. Theamplitude ratio is easily measured together with the pulse velocity in the direct transmissionof ultrasonic pulse.2. The variation of the attenuat ion of ultrasonic pulses with respect to path length can beapproximated using a simple equation (Eq.(4)), for cement mortars.3. The measurement of the pulse attenuation is critically affected by the coupling condition.Therefore , consistency in the transducer coupling is essential for pulse attenuation studies.4. The attenuation of ultrasonic pulse is well correlated with the compressive strength of thecement mortar. However, the correlation is valid for the same path length for which therelationship is based.5. There are two ways of evaluating specimens with different path length : (a) the approximateamplitude ratio method - extrapolate the measured amplitude ratio to a equivalent amplituderatio for a specific length using Eq.(8); or (b) direct correlation of a-f.6. The combined correlation of pulse attenuation and pulse velocity produced good estimationfor strength of cement mortars. Further tests are required to confirm this relationship for

cement mortars with different types of aggregates.7. The use of combined UPA and UPV method as a qualitative non-destructive testing technique,appears possible, for the evaluation of the quality of concrete.R e f e r e n c e s

(1) J. Krau tkramer & H. Kraukramer, Ultrasonic Testing of Material. Third Edition. 0.667,Springer-Verlag, New York (1983).(2) L. Filipczynski, Z. Pawlowski & J. Wehr, Ultrasonic Methods of Testing Materials. p.230,Butterworths, London (1966).(3) H. Kolsky, Stress Waves in Solids. p.213, Dover Publ ication, New York (1963).(4) V.M. Malhotra, In Situ/Nondes tructive Testing of Concrete, SP-82, ACI, Detroit, i(1984).(5) A. Galan , ACI, 64 (10L 678 (1967).(6) V. Fernando & W. Suaris, ACI Material, 84 (3L 185 (1987).(7) J.H. Bungey, The Testing of Concrete in Structures, 0.207, Surrey Universi ty Press, London(1982).(8) A. Samarin & P. Meynink, Concrete International: Design & Const ruction, 3 (3L 25 (1981).(9) I. Facaoru, Proc. Syrup. on Non-Dest ructive Testing of Concrete and Timber, Inst. of CivilEngineers, London, 39 (1969).(10) P. Knaze & P. Beno, RILEM Material and Structure, 17 (99L 207 (1981).(11) Bristish Standard Institution, BS 882, BSI, London, (1973).

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