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Impact resistance of concrete Banthia, Nemkumar P. 1987

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IMPACT RESISTANCE OF CONCRETE by NEMKUMAR P. BANTHIA B . E . , Nagpur U n i v e r s i t y , 1980 M.Tech . , Indian I n s t i t u t e of Technology, 1982 THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of C i v i l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March 1987 © Nemkumar P . B a n t h i a , 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia 1956 Main Mall Vancouver, Canada Department V6T 1Y3 Date DE-6f3/81) A B S T R A C T During i t s s e r v i c e l i f e , a s t r u c t u r e may be s u b j e c t e d to v a r i o u s e n v i r o n m e n t a l and l o a d i n g c o n d i t i o n s . However, i n g e n e r a l , the p r o p e r t i e s determined under one s e t of c o n d i t i o n s may not be used to determine the be h a v i o u r of the m a t e r i a l under a d i f f e r e n t s et of c o n d i t i o n s . For example, i t i s w e l l known t h a t c o n c r e t e i s a s t r a i n r a t e s e n s i t i v e m a t e r i a l ; t h e r e f o r e , i t s p r o p e r t i e s d etermined under c o n v e n t i o n a l s t a t i c l o a d i n g cannot be used t o p r e d i c t the performance of c o n c r e t e s u b j e c t e d t o h i g h s t r a i n r a t e s . The problem i s s e r i o u s because these h i g h s t r a i n r a t e l o a d i n g s a r e a s s o c i a t e d w i t h l a r g e amounts of energy imparted t o the s t r u c t u r e i n a very s h o r t p e r i o d of t i m e , and c o n c r e t e i s a b r i t t l e m a t e r i a l . S i n c e the s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e p r o h i b i t s the use of i t s s t a t i c a l l y determined p r o p e r t i e s i n a s s e s s i n g i t s b e h a v i o u r under dynamic c o n d i t i o n s , h i g h s t r a i n r a t e t e s t s a r e r e q u i r e d . Impact t e s t s were c a r r i e d out on about 500 c o n c r e t e beams. An in s t r u m e n t e d drop weight impact machine was used. The i n s t r u m e n t a t i o n i n c l u d e d s t r a i n gauges mounted i n the s t r i k i n g end of the hammer ( c a l l e d 'the t u p ' ) , and a l s o i n one of the support a n v i l s . In a d d i t i o n , t h r e e a c c e l e r o m e t e r s were mounted a l o n g the l e n g t h of the beam i n order t o o b t a i n the beam response, and a l s o t o enable the i n e r t i a l c o r r e c t i o n t o the observed tup l o a d t o be made. i i Two d i f f e r e n t c o n c r e t e mixes, normal s t r e n g t h w i t h a compressive s t r e n g t h of 42 MPa, and h i g h s t r e n g t h w i t h a compressive s t r e n g t h of 82 MPa, were t e s t e d . The e f f e c t of two t y p e s of f i b r e s , h i g h modulus s t e e l , and low modulus f i b r i l l a t e d p o l y p r o p y l e n e , i n enhancing c o n c r e t e p r o p e r t i e s was i n v e s t i g a t e d . In a d d i t i o n , t e s t s were a l s o conducted on beams w i t h c o n v e n t i o n a l r e i n f o r c e m e n t . Hammer drop h e i g h t s r a n g i n g from 0.15m t o 2.30m were used. S t a t i c t e s t s were conducted on companion specimens f o r a d i r e c t comparison w i t h the dynamic r e s u l t s . In g e n e r a l , i t was found t h a t c o n c r e t e i s a v e r y s t a i n r a t e s e n s i t i v e m a t e r i a l . Both the peak bending l o a d s and the f r a c t u r e e n e r g i e s were h i g h e r under dynamic c o n d i t i o n s than under s t a t i c c o n d i t i o n s . F i b r e s , p a r t i c u l a r l y the s t e e l f i b r e s , were found t o s i g n i f i c a n t l y i n c r e a s e the d u c t i l i t y and the impact r e s i s t a n c e of the com p o s i t e . High s t r e n g t h c o n c r e t e made w i t h m i c r o s i l i c a , i n c e r t a i n c i r c u m s t a n c e s , was found t o behave i n a f a r more b r i t t l e manner than normal s t r e n g t h c o n c r e t e . High speed photography (at 10,000 frames per second) was used t o study the p r o p a g a t i o n of c r a c k s under impact l o a d i n g . In g e n e r a l , the crack v e l o c i t i e s were found t o be f a r lower than the t h e o r e t i c a l c r a c k v e l o c i t i e s . The presence of r e i n f o r c e m e n t , e i t h e r i n the form of f i b r e s , or of c o n t i n u o u s bars was found t o reduce the c r a c k v e l o c i t y . i i i A model was proposed based on a time s t e p i n t e g r a t i o n technique t o e v a l u a t e the response of a beam s u b j e c t e d to an e x t e r n a l impact p u l s e . The model was c a p a b l e of p r e d i c t i n g not o n l y the e x p e r i m e n t a l l y observed n o n - l i n e a r b e h a v i o u r of c o n c r e t e under impact l o a d i n g , but a l s o the more pronounced b r i t t l e behaviour of h i g h s t r e n g t h c o n c r e t e . i v Table of Co n t e n t s 1. INTRODUCTION 1 2. OBJECTIVE AND SCOPE ..5 3. LITERATURE SURVEY 13 4. EXPERIMENTAL PROCEDURES ....40 4 . 1 I n t r o d u c t i o n 40 4.2 Specimen P r e p a r a t i o n 45 4.2.1 Normal S t r e n g t h P l a i n C o n crete Beams ....45 4.2.2 High S t r e n g t h P l a i n Concrete Beams 49 4.2.3 F i b r e R e i n f o r c e d Concrete Beams 50 4.2.4 C o n v e n t i o n a l l y R e i n f o r c e d C o ncrete Beams 51 4.2.5 Notched Beams 51 4.3 T e s t i n g Program 53 4.3.1 S t a t i c T e s t i n g 53 4.3.1.1 F l e x u r a l T e s t s on Beams 53 4.3.1.2 Tension T e s t s on R e i n f o r c i n g Bars 54 4.3.1.3 S t i f f n e s s T e s t on the Rubber Pad 54 4.3.1.4 Compressive S t r e n g t h D e t e r m i n a t i o n from the Broken Halves of the Beams 55 4.3.2 Impact T e s t i n g 56 4.3.2.1 The Impact T e s t i n g Machine 56 4.3.2.2 C a l i b r a t i o n 70 4.3.2.3 A n a l y s i s of the Te s t R e s u l t s ....75 4.3.2.4 The Support R e a c t i o n s 94 5. INERTIAL LOADING IN INSTRUMENTED IMPACT TESTS 98 5.1 I n t r o d u c t i o n 98 5.2 Nature of the I n e r t i a l Load 99 5.3 E x p e r i m e n t a l Observa t ions 102 5.4 The Use of a Rubber Pad 105 5.5 Ins trument ing the Support A n v i l s . . . 1 1 0 PLAIN CONCRETE UNDER IMPACT 112 6.1 I n t r o d u c t i o n 112 6.2 Comparison between the Impact Behaviour of Paste and Concre te Beams 114 6.3 E f f e c t of S t r e s s Rate on P l a i n Normal S t r e n g t h Concre te Beams 119 6.4 E f f e c t of S t r e s s Rate on P l a i n High S trength Concrete Beams 129 6.5 Comparison between Normal S t r e n g t h and High S trength Concre te 134 6.6 E f f e c t of Moment of I n e r t i a 141 6.7 Crack Development in Paste under Impact 143 MODEL ANALYSIS 149 7.1 I n t r o d u c t i o n 149 7.2 Model A - E v a l u a t i o n of Beam Response to an E x t e r n a l Impact Pulse : Energy Balance P r i n c i p l e 1 53 7.2.1 Assumptions 153 7 .2 .2 N o t a t i o n 154 7 .2 .3 E v a l u a t i o n of the K i n e t i c Energy 155 7.2.4 E v a l u a t i o n of the Bending Energy 156 7 .2 .5 The T o t a l Energy 156 7 .2 .6 F i n i t e D i f f e r e n c e Technique 157 7 .2 .7 R e s u l t s 158 7.3 Model B - E v a l u a t i o n of Beam Response to an E x t e r n a l Impact Pulse : S o l u t i o n to the Equat ion of Dynamic E q u i l i b r i u m u s i n g Time Steps 162 v i 7.3.1 The C o n s t i t u t i v e Law for Concre te 163 7.3.2 Time Step A n a l y s i s and the R e s u l t s . . . . . 1 6 5 Appendix - 7.1 E v a l u a t i o n of Beam Response : Beam M o d e l l e d as a S i n g l e Degree of Freedom System 169 Appendix - 7.2 E v a l u a t i o n of Beam Response : Beam M o d e l l e d as a M u l t i Degree of Freedom System 174 Appendix - 7.3 Time Step A n a l y s i s 179 8. ENERGY BALANCE IN INSTRUMENTED IMPACT TESTS 184 8.1 I n t r o d u c t i o n . . . . 1 8 4 8.2 Energy Balance at the Peak Load . . . . . . . . . 1 8 6 8.3 Energy Balance j u s t a f t e r F a i l u r e 194 8.4 The Machine Losses 195 9. NOTCHED BEAMS UNDER IMPACT 201 9.1 I n t r o d u c t i o n 201 9.2 P l a i n and F i b r e R e i n f o r c e d Notched Beams under Impact 202 10. FIBRE REINFORCED CONCRETE UNDER IMPACT 212 10.1 I n t r o d u c t i o n 212 10.2 S t e e l F i b r e R e i n f o r c e d Normal S t r e n g t h Concrete under V a r i a b l e S t r e s s Rate 215 10.3 Po lypropy lene F i b r e R e i n f o r c e d Normal S trength Concrete under V a r i a b l e S t r e s s Rate .220 10.4 Comparison between S t e e l and P o l y p r o p y l e n e F i b r e R e i n f o r c e d Normal S t r e n g t h Concrete . . . . 2 2 4 10.5 E f f e c t of V a r y i n g the S t r e s s Rate i n the Dynamic Range on the Performance of S t e e l F i b r e R e i n f o r c e d Normal S t r e n g t h Concrete . . . . 2 2 7 10.6 S t e e l F i b r e R e i n f o r c e d High S t r e n g t h Concrete under V a r i a b l e S t r e s s Rate 232 10.7 Po lypropy lene F i b r e R e i n f o r c e d High S trength Concrete under V a r i a b l e S t r e s s Rate 236 10.6 Comparison Between F i b r e R e i n f o r c e d Normal St r e n g t h Concrete and F i b r e R e i n f o r c e d High S t r e n g t h Concrete 237 10.9 Crack Development i n S t e e l F i b r e R e i n f o r c e d Normal S t r e n g t h Concrete Under Impact 242 11. CONVENTIONALLY REINFORCED CONCRETE UNDER IMPACT ...244 11.1 I n t r o d u c t i o n 244 11.2 C o n v e n t i o n a l l y R e i n f o r c e d Normal S t r e n g t h Concrete w i t h Deformed R e i n f o r c i n g Bars under V a r i a b l e S t r e s s Rate 245 11.3 The Use of Smooth R e i n f o r c i n g Bars 258 11.4 The Use of Shear Reinforcement 266 11.5 C o n v e n t i o n a l l y R e i n f o r c e d High S t r e n g t h Concrete w i t h Deformed R e i n f o r c i n g Bars under V a r i a b l e S t r e s s Rate, and i t s Comparison w i t h Normal S t r e n g t h Concrete 269 11.6 Crack Development i n C o n v e n t i o n a l l y R e i n f o r c e d High S t r e n g t h C o n c r e t e under Impact ..279 12. CONVENTIONALLY REINFORCED CONCRETE CONTAINING FIBRES UNDER IMPACT 281 12.1 I n t r o d u c t i o n 281 12.2 C o n v e n t i o n a l l y R e i n f o r c e d Normal S t r e n g t h Concrete w i t h P o l y p r o p y l e n e F i b r e s under V a r i a b l e S t r e s s Rate 282 12.3 C o n v e n t i o n a l l y R e i n f o r c e d High S t r e n g t h Concrete w i t h P o l y p r o p y l e n e F i b r e s under V a r i a b l e S t r e s s Rates ..285 12.4 Comparison between C o n v e n t i o n a l l y R e i n f o r c e d Normal S t r e n g t h Concrete w i t h P o l y p r o p y l e n e F i b r e s and C o n v e n t i o n a l l y R e i n f o r c e d High S t r e n g t h Concrete w i t h P o l y p r o p y l e n e F i b r e s ..287 12.5 Pre-damaged Beams 290 CONCLUSIONS 29 5 SCOPE FOR FUTURE WORK 30 6 BIBLIOGRAPHY 308 v i i i LIST OF FIGURES INTRODUCTION OBJECTIVE AND SCOPE LITERATURE SURVEY 3.1 Three d i f f e r e n t ways of de t ermi n i nq the constant "n" ^ ^ 2 g EXPERIMENTAL PROCEDURES 4.1 The Drop Weight Impact T e s t i n g Machine .57 4.2 The dimensions of the machine and the tup . . . . 5 8 4.3 Layout of the Impact T e s t i n g Apparatus 60 4.4 T r i g g e r i n g of the data a c q u i s i t i o n system . . . . 6 2 4.5 The s t r i k i n g end of the hammer or the "Tup" ..63 4.6 The c i r c u i t of the tup 64 4.7 The support a n v i l 65 4.8 The support r e a c t i o n s 66 4.9 The c i r c u i t of the support a n v i l 67 4.10 The accelerometers 68 4.11 The c a l i b r a t i o n of the support and the s t r i k i n g tup 71 4.12 The C a l i b r a t i o n of the Hammer A c c e l e r a t i o n . . . 72 4.13 T y p i c a l output from the f i v e channels of instrumentat ion . . . . . 7 6 4.14 (a) P o s i t i o n s of the a c c e l e r o m e t e r s , (b) A c c e l e r a t i o n d i s t r i b u t i o n , and (c) Genera l i zed i n e r t i a l l o a d 80 4.15 A c c e l e r a t i o n d i s t r i b u t i o n for p l a i n concrete beams 84 4.16 A c c e l e r a t i o n d i s t r i b u t i o n for c o n v e n t i o n a l l y r e i n f o r c e d concre te beams . .85 4.17 (a) Linear a c c e l e r a t i o n d i s t r i b u t i o n , (b) S i n u s o i d a l a c c e l e r a t i o n d i s t r i b u t i o n 86 4.18 (a) Dynamic l oad ing on the beam, (b) Equivalent s t a t i c l o a d i n g 88 ix 4.19 The flow c h a r t of a n a l y s i s 93 4.20 Comparison between the e v a l u a t e d and the observed support r e a c t i o n 94 4.21 A rough check on the v a l i d i t y of the tec h n i q u e used to account f o r I n e r t i a ........96 4.22 The h o r i z o n t a l support r e a c t i o n 97 INERTIAL LOADING IN INSTRUMENTED IMPACT TESTS 5.1 The p e r i o d of i n e r t i a l o s c i l l a t i o n s ....99 5.2 Observed tup and i n e r t i a l l o a d s f o r p l a i n c o n c r e t e 103 5.3 Observed tup and i n e r t i a l l o a d s f o r (a) p l a i n and (b) c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e 104 5.4 E f f e c t of hammer drop h e i g h t on (a) Tup and (b) I n e r t i a l l o a d s 105 5.5 E f f e c t of rubber pad on p l a i n c o n c r e t e beams 108 5.6 E f f e c t of rubber pad on c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams . 110 PLAIN CONCRETE UNDER IMPACT 6.1 Impact behaviour of p a s t e and c o n c r e t e 116 6.2 Impact behaviour of p a s t e and c o n c r e t e upto the peak l o a d 116 6.3 S t a t i c and dynamic l o a d v s . d e f l e c t i o n p l o t s f o r normal s t r e n g t h c o n c r e t e 122 6.4 D e t e r m i n a t i o n of parameter "n" 125 6.5 D e t e r m i n a t i o n of the parameter "n" f o r normal s t r e n g t h c o n c r e t e 126 6.6 Mix w i t h and w i t h o u t m i c r o s i l i c a 129 6.7 D e t e r m i n a t i o n of the parameter "n" f o r h i g h s t r e n g t h c o n c r e t e 133 6.8 Comparison between normal s t r e n g t h and h i g h s t r e n g t h c o n c r e t e 136 6.9 Photograph showing the f r a c t u r e s u r f a c e s f o r h i g h s t r e n g t h and normal s t r e n g t h c o n c r e t e ..137 6.10 The f i n i t e w i d t h zone of m i c r o c r a c k i n g s u r r o u n d i n g a c r a c k ..138 6.11 S t r e s s r a t e s e n s i t i v i t y of h i g h s t r e n g t h c o n c r e t e 140 6.12 Crack development i n p a s t e under impact 145 6.13 (a) Energy absorbed and (b) Crack v e l o c i t y as the c r a c k propagates i n p a s t e 147 MODEL ANALYSIS 7.1 Assumed beam d i s p l a c e m e n t s 154 7.2 F i n i t e d i f f e r e n c e t e c h n i q u e 157 7.3 Energy p r e d i c t i o n s u s i n g Model A 160 7.4 Model p r e d i c t i o n s v s . the e x p e r i m e n t a l f i n d i n g s (Model A) 161 7.5 Model B p r e d i c t i o n s f o r normal s t r e n g t h c o n c r e t e 166 7.6 Model B p r e d i c t i o n s f o r h i g h s t r e n g t h c o n c r e t e 167 7.7 Bending energy a t the peak l o a d (Model B) ...168 A7.1-1 : S i n g l e degree of freedom model 169 A7.1-2 : D e t e r m i n a t i o n of the g e n e r a l i z e d mass 171 A7.2-1 : M u l t i - d e g r e e of freedom model 171 A7.3-1 : S i n g l e degree of freedom model t o e v a l u a t e the beam response u s i n g the Time Step A n a l y s i s 180 ENERGY BALANCE IN INSTRUMENTED IMPACT TESTS 8.1 T y p i c a l tup l o a d v s . time p l o t ..185 8.2 Components of bending energy 188 8.3 Energy balance a t the peak l o a d 190 8.4 Components of bending energy 191 8.5 Energy balance j u s t a f t e r the f a i l u r e 196 8.6 The machine l o s s e s 199 x i 9. NOTCHED BEAMS UNDER IMPACT 9.1 E f f e c t of hammer drop h e i g h t on peak bending l o a d 204 9.2 E f f e c t of hammer drop h e i g h t on e n e r g i e s ....209 9.3 E f f e c t of hammer drop h e i g h t on f r a c t u r e toughness 210 10. FIBRE REINFORCED CONCRETE UNDER IMPACT 10.1 S t a t i c behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 216 10.2 Dynamic behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 217 10.3 S t a t i c and dynamic behaviour of s t e e l f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 219 10.4 S t a t i c behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d normal S t r e n g t h Concrete ...221 10.5 Dynamic behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e ...222 10.6 S t a t i c and dynamic be h a v i o u r of p o l y p r o p y l e n e f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 223 10.7 B e h a v i u r of s t e e l f i b r e r e i n f o r c e d c o n c r e t e at v a r i a b l e s t r e s s r a t e s 228 10.8 S t a t i c behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 233 10.9 Dynamic behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d high s t r e n g t h c o n c r e t e 234 10.10 S t a t i c and dynamic be h a v i o u r of s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e ...235 10.11 S t a t i c behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 237 10.12 Dynamic behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 238 10.13 S t a t i c and dynamic behaviour of p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 240 10.14 Crack development i n s t e e l f i b r e r e i n f o r c e d c o n c r e t e under impact 243 x i i 11. CONVENTIONALLY REINFORCED CONCRETE UNDER IMPACT 1.1 E f f e c t of s t r e s s r a t e on c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e 249 1.2 E f f e c t of hammer drop h e i g h t on (a) peak bending l o a d and (b) f r a c t u r e energy of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e .250 1.3 Energy a t v a r i o u s midspan d e f l e c t i o n s absorbed by c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e beam w i t h deformed bars ...252 1.4 Beam s e c t i o n 253 11.5 T h e o r e t i c a l l y l i m i t i n g and the e x p e r i m e n t a l l y observed moment of r e s i s t a n c e 256 1.6 E f f e c t of hammer drop h e i g h t on (a) peak bending l o a d and (b) f r a c t u r e energy f o r normal s t r e n g t h c o n c r e t e w i t h smooth r e i n f o r c i n g bars 262 1.7 Energy a t v a r i o u s midspan d e f l e c t i o n s f o r beams w i t h smooth bars 263 1.8 Comparison between beams w i t h deformed r e i n f o r c i n g bars and those w i t h smooth r e i n f o r c i n g bars 265 1.9 Comparison between beams w i t h s t i r r u p s and those w i t h o u t s t i r r u p s 268 1.10 Load v s . d e f l e c t i o n p l o t s f o r c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 271 1.11 Comparisons between normal s t r e n g t h and h i g h s t r e n g t h beams 273 1.12 Tup l o a d v s . time p l o t and v e l o c i t y v s . time p l o t f o r h i g h s t r e n g t h c o n c r e t e under 0.5m drop 274 1.13 Tup l o a d v s . time p l o t and v e l o c i t y v s . time p l o t f o r h i g h s t r e n g t h c o n c r e t e under 1.5m drop 274 1.14 Tup l o a d v s . time p l o t and v e l o c i t y v s . time p l o t f o r normal s t r e n g t h c o n c r e t e under 0.5m drop 275 1.15 Tup l o a d v s . time p l o t and v e l o c i t y v s . time p l o t f o r normal s t r e n g t h c o n c r e t e under 1.5m drop 275 x i i i 11.16 Comparison between normal s t r e n g t h and h i g h s t r e n g t h c o n c r e t e 276 11.17 Photographs showing c o n v e n t i o n a l l y r e i n f o r c e d beams a f t e r impact 278 11.18 c r a c k development i n a h i g h s t r e n g t h c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beam .....280 12. CONVENTIONALLY REINFORCED CONCRETE CONTAINING FIBRES UNDER IMPACT 12.1 E f f e c t of adding p o l y p r o p y l e n e f i b r e s t o c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e 283 12.2 E f f e c t of adding p o l y p r o p y l e n e f i b r e s t o c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 286 12.3 Comparison between the e f f e c t of p o l y p r o p y l e n e f i b r e s on c o n v e n t i o n a l l y r e i n f o r c e d normal and h i g h s t r e n g t h c o n c r e t e beams 289 12.4 Photographs showing c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h f i b r e s under impact 293 12.5 Photographs showing c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e w i t h f i b r e s under impact 294 x i v L i s t of Tables 1. INTRODUCTION 2. OBJECTIVE AND SCOPE 3. LITERATURE SURVEY 4. EXPERIMENTAL PROCEDURES 4.1 Types of specimens 46 5. INERTIAL LOADING IN INSTRUMENTED IMPACT TESTS 5.1 E f f e c t of rubber pad on p l a i n c o n c r e t e beams under impact 107 5.2 E f f e c t of rubber pad on c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams under impact 107 6. PLAIN CONCRETE UNDER IMPACT 6.1 Comparison between the dynamic p r o p e r t i e s of paste and c o n c r e t e 115 6.2a S t a t i c b ehaviour of normal s t r e n g t h p l a i n c o n c r e t e beams 120 6.2b Dynamic behaviour of normal s t r e n g t h p l a i n c o n c r e t e beams 121 6.3a S t a t i c b ehaviour of h i g h s t r e n g t h p l a i n c o n c r e t e beams 131 6.3b Dynamic behaviour of h i g h s t r e n g t h p l a i n c o n c r e t e beams 132 6.4a E f f e c t of moment of i n e r t i a on the dynamic behaviour of normal s t r e n g t h c o n c r e t e beams .142 6.4b E f f e c t of moment of i n e r t i a on the dynamic behaviour of h i g h s t r e n g t h c o n c r e t e beams ...142 7. MODEL ANALYSIS 7.1 Beam p r o p e r t i e s f o r the attempted a p p l i c a t i o n of Model A 159 7.2 The c o n s t a n t s i n the c o n s t i t u t i v e law proposed f o r c o n c r e t e 164 8-. ENERGY BALANCE IN INSTRUMENTED IMPACT TESTS 8.1 Energy ba l a n c e at the peak l o a d (normal s t r e n g t h c o n c r e t e 192 8.2 Energy balance at the peak l o a d ( h i g h s t r e n g t h c o n c r e t e 193 8.3 Energy balance j u s t a f t e r f a i l u r e (normal s t r e n g t h c o n c r e t e ^ 197 8.4 Energy balance j u s t a f t e r f a i l u r e ( h i g h s t r e n g t h c o n c r e t e .....198 NOTCHED BEAMS UNDER IMPACT 9.1 Behaviour of notched normal s t r e n g t h c o n c r e t e beams 205 9.2 Behaviour of notched h i g h s t r e n g t h c o n c r e t e beams ...206 9.3 Behaviour of notched normal s t r e n g t h c o n c r e t e beams w i t h p o l y p r o p y l e n e f i b r e s ....207 FIBRE REINFORCED CONCRETE UNDER .IMPACT 10.1 S t a t i c behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 216 10.2 Dynamic behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d normal s t r e n t h c o n c r e t e 217 10.3 e f f e c t of moment of i n e r t i a on s t e e l f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 219 10.4 S t a t i c behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e ...221 10.5 Dynamic behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e ...222 10.6 E f f e c t of moment of i n e r t i a on p o l y p r o p y l e n e f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e ...223 10.7 Dynamic behaviour of s t e e l f i r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e 229 10.8 S t a t i c b ehaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 233 10.9 Dynamic behaviour of p l a i n and s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 234 10.10 E f f e c t of moment of i n e r t i a on s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 235 10.11 S t a t i c behaviour of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 237 xvi 10.12 Dynamic b e h a v i o u r of p l a i n and p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 238 10.13 E f f e c t of moment of i n e r t i a on p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 240 CONVENTIONALLY REINFORCED CONCRETE UNDER IMAPACT 11.1a S t a t i c b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e 246 11.1b Dynamic b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h concrete,w/c r a t i o = 0.4 247 11.1c Dynamic b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h concrete,w/c r a t i o = 0.33 . .. 248 11.2a S t a t i c b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h smooth r e i n f o r c i n g bars 259 11.2b Dynamic b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h smooth r e i n f o r c i n g b a r s , w/c r a t i o =0.4 .....260 11.2c Dynamic b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h smooth r e i n f o r c i n g b a r s , w/c r a t i o = 0.5 ....261 1 U 3 S t a t i c and dynamic behaviour of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h s t i r r u p s 267 11.4 S t a t i c and dynamic behaviour of c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 270 CONVENTIONALLY REINFORCED CONCRETE WITH FIBRES UNDER IMPACT 12.1 S t a t i c and dynamic behaviour of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h p o l p r o p y l e n e f i b r e s 284 12.2 S t a t i c and dynamic behaviour of c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e w i t h p o l y p r o p y l e n e f i b r e s 287 12.3 Dynamic b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d pre-damaged c o n c r e t e beams w i t h and w i t h o u t p o l y p r o p y l e n e f i b r e s 291 x v i i LIST OF SYMBOLS B: Breadth of the beam D: Depth of the beam 1: Suported span of the beam h: Length of the overhanging p o r t i o n of the beam A: The c r o s s - s e c t i o n a l area of the beam D , , D 2 , D 3 : The d i s t a n c e s between the acce l erometers V ^ : Hammer v e l o c i t y m^: Hammer mass a^: Hammer a c c e l e r a t i o n g: E a r t h ' s 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 h : Height of hammer drop P f c : The tup l o a d P^: The g e n e r a l i z e d i n e r t i a l load P^: The g e n e r a l i z e d bending load u 0 : A c c e l e r a t i o n at the centre of the beam u 0 : V e l o c i t y at the centre of the beam u 0 : D e f l e c t i o n at the centre of the beam a^: F a i l u r e s t r e s s a: S t re s s rate e^: F a i l u r e s t r a i n e: S t r a i n rate K I C : C r i t i c a l S t r e s s I n t e n s i t y F a c t o r a: Crack length f u g : Ul t imate t e n s i l e s t rength of s t e e l under s t a t i c load x v i i i f ^ : U l t i m a t e t e n s i l e s t r e n g t h of s t e e l under dynamic l o a d A g: Area of s t e e l i n the s e c t i o n NS: Normal s t r e n g t h c o n c r e t e HS: High s t r e n g t h C o ncrete AE: Energy l o s t by the hammr E g : Energy g a i n e d by the specimen E k e r : R a t a t ^ o n a ^ - k i n e t i c energy i n the specimen E^: Bending energy i n the beam E w o f : W o r k °^ f r a c t u r e energy E : Energy l o s t t o the machine ,. xix ACKNOWLEDGEMENTS F i r s t and foremost, I wish t o thank P r o f . Sidney Mindess, a d e d i c a t e d r e s e a r c h e r , f o r h i s f r i e n d l y s u p p o r t , t a l e n t f o r o r g a n i z a t i o n , and i n v a l u a b l e guidance. H i s c o n s t a n t encouragement as my s u p e r v i s o r was much a p p r e c i a t e d . My next acknowledgement must go t o P r o f . N.D. Nathan f o r h i s u n s t i n t i n g h e l p . I am a l s o very g r a t e f u l to Dr. Arnon Bentur of the Technion, I s r a e l f o r h i s i n v a l u a b l e support and g u i d a n c e . My s p e c i a l thanks a r e a l s o due t o Dr. R.J. Gray, Dr. L . J . G i b s o n , and the l a t e P r o f . J.S. Nadeau.' The e f f o r t s of Mr. C. Town i n p r e p a r i n g the specimens are g r e a t l y a p p r e c i a t e d . I a l s o w i s h t o thank Mr.M. Nazar f o r m a i n t a i n i n g the impact machine, and Mr. G.D. J o l l y and Mr. R.B. Nussbaumer f o r d e s i g n i n g and c o n s t r u c t i n g the data a c q u i s i t i o n system. F i n a l l y , I take t h i s o p p o r t u n i t y t o show my a p p r e c i a t i o n to my w i f e , K a v i t a , f o r her p a t i e n c e and s u p p o r t . xx my parents xxi 1. INTRODUCTION A s t r u c t u r a l e n g i n e e r i s r e q u i r e d t o p r e d i c t the n a t u r e , d u r a t i o n and magnitude of the l o a d i n g on a s t r u c t u r e . On the o t h e r hand, he i s a l s o r e q u i r e d t o know the p r o p e r t i e s of the m a t e r i a l s he i s w o r k i n g w i t h . There a r e a number of t y p e s of l o a d i n g s t o which a s t r u c t u r e can be s u b j e c t e d . L o a d i n g s can be d i v i d e d b r o a d l y i n t o two c a t e g o r i e s : dead l o a d s or q u a s i s t a t i c l o a d s , and suddenly a p p l i e d l o a d s . These a r e g e n e r a l l y r e f e r r e d t o as s t a t i c l o a d i n g and dynamic l o a d i n g , r e s p e c t i v e l y . Load p r e d i c t i o n f o r s t a t i c c o n d i t i o n s i s f a i r l y s t r a i g h t f o r w a r d and does not pose any p a r t i c u l a r problem. But i n the case of dynamic l o a d i n g , the p r e c i s e p r e d i c t i o n of l o a d and i t s v a r i a t i o n w i t h time can be f a i r l y i n v o l v e d . Dynamic l o a d i n g i t s e l f can be s u b d i v i d e d i n t o two c a t e g o r i e s : s i n g l e c y c l e and m u l t i c y c l e . An example of s i n g l e c y c l e dynamic l o a d i n g i s a mass i m p a c t i n g a g a i n s t a s t r u c t u r a l element. However, a s t r u c t u r e u n d e r g o i n g an earthquake would have i t s elements s u b j e c t e d t o m u l t i c y c l e dynamic l o a d i n g . S i n g l e c y c l e dynamic l o a d i n g i s c a l l e d impact l o a d i n g f o r b r e v i t y . There a r e , f u r t h e r , two b a s i c t y p e s of impact l o a d i n g s : s i n g l e p o i n t impact l o a d i n g and d i s t r i b u t e d impact l o a d i n g . A s t r u c t u r e h i t by a m i s s i l e - l i k e o b j e c t would undergo a s i n g l e p o i n t impact, whereas b l a s t s or e x p l o s i o n s would r e s u l t i n a d i s t r i b u t e d impact l o a d . The p r e s e n t work i s co n c e r n e d p r i m a r i l y w i t h s i n g l e p o i n t impact l o a d i n g . 1 2 One b a s i c problem w i t h s i n g l e p o i n t impacts i s the d i f f i c u l t y i n a s s e s s i n g the e x a c t l o a d v e r s u s time h i s t o r y of the impact. As a r e s u l t , energy v a l u e s a r e g e n e r a l l y chosen as the b a s i c v a r i a b l e . The impact r e s i s t a n c e of a m a t e r i a l or a s t r u c t u r e may be d e f i n e d i n terms of the energy the system i s c a p a b l e of a b s o r b i n g b e f o r e f a i l u r e . W h i l e momentum or impulse c o u l d a l s o have been chosen as the b a s i c v a r i a b l e , they can e a s i l y be r e l a t e d t o the energy; the c a l c u l a t i o n of one from the o t h e r i s not d i f f i c u l t . The s i z e and the mass of the i m p a c t i n g body a r e v e r y i m p o r t a n t i n a t y p i c a l impact e v e n t . Three d i s t i n c t s i t u a t i o n s can a r i s e : 1. A v e r y l a r g e o b j e c t s t r u c k by a s m a l l i m p a c t i n g ma s s. 2 . An impact i n v o l v i n g comparable masses. 3. A s m a l l o b j e c t s t r u c k by a l a r g e i m p a c t i n g mass. W h i l e the t h i r d case i s c o m p a r a t i v e l y r a r e , the f i r s t and second c a s e s are o f t e n e n c o u n t e r e d . In the f i r s t c a s e , because of the massiveness of the impacted o b j e c t , damage i s l i m i t e d m a i n l y t o the c o n t a c t zone. In t h e case of comparable masses, however, the response of the impacted mass i s governed by shear and b e n d i n g , and a r e l a t i v e l y l a r g e p o r t i o n of the impacted mass r e a c t s t o the impact. W h i l e t h e case of a s m a l l o b j e c t h i t t i n g a massive t a r g e t has been c o n s i d e r e d by many i n v e s t i g a t o r s , and s o l u t i o n s have been suggested i n the form of e m p i r i c a l f o r m u l a e , the case of impact between comparable masses, t o d a t e , remains 3 u n s o l v e d . On the m a t e r i a l s s i d e , most m a t e r i a l s have been found t o be s t r a i n r a t e s e n s i t i v e , t h u s f u r t h e r c o m p l i c a t i n g t h e whole problem. The degree of s t r a i n r a t e s e n s i t i v i t y depends upon the l o a d i n g system, s u p p o r t c h a r a c t e r i s t i c s , e n v i r o n m e n t a l f a c t o r s , and so on. S i n c e the energy t h a t a s t r u c t u r e i s c a p a b l e of a b s o r b i n g b e f o r e f a i l u r e depends upon i t s m a t e r i a l p r o p e r t i e s , w h i c h , i n the case of impact, depend upon the r a t e of s t r e s s i n g , the problem i s one which cannot be s o l v e d w i t h o u t a thorough knowledge of the m a t e r i a l p r o p e r t i e s . Of a l l of the major m a t e r i a l s of c o n s t r u c t i o n used t o d a y , the b e h a v i o u r of c o n c r e t e under h i g h r a t e s of s t r a i n i s the l e a s t u n d e r s t o o d . The i n h e r e n t l y b r i t t l e n a t u r e of p l a i n c o n c r e t e , i t s extreme weakness i n t e n s i o n , and i t s heterogeneous s t r u c t u r e a r e some of the reasons f o r i t s markedly low impact s t r e n g t h . I t s l a c k of toughness and t e n s i l e s t r e n g t h have meant t h a t i t i s almost always used i n c o n j u n c t i o n w i t h c o n v e n t i o n a l s t e e l r e i n f o r c e m e n t . But the d i s c o v e r y of f i b r e r e i n f o r c e d c o n c r e t e ( f r c ) , and f r c ' s g r e a t l y improved impact r e s i s t a n c e over p l a i n c o n c r e t e , have t r i g g e r e d an i n t e r e s t i n u n d e r s t a n d i n g the impact performance of b o t h f r c and p l a i n c o n c r e t e , s i n c e a p r o p e r u n d e r s t a n d i n g of the composite b e h a v i o u r of f r c c a l l s f o r an u n d e r s t a n d i n g of i t s i n d i v i d u a l components. With p r e s e n t d e s i g n t r e n d s , t h e r e are two reasons f o r the i n c o r p o r a t i o n of f i b r e s i n c e m e n t i t i o u s m a t r i c e s : F i r s t , 4 s i n c e t h e impact r e s i s t a n c e of t h e s e components i s h i g h e r , t h ey can w i t h s t a n d o c c a s i o n a l shocks or o v e r l o a d i n g s w i t h o u t e x t e n s i v e damage. S e c o n d l y , the b e h a v i o u r of f r c under l o a d , which i s c h a r a c t e r i z e d by l a r g e p o s t e l a s t i c d e f o r m a t i o n s , means t h a t f a i l u r e , i f i t o c c u r s a t a l l , g e n e r a l l y does so o n l y a f t e r s u f f i c i e n t w a r n i n g . E x p e r i m e n t a l work, e s p e c i a l l y w i t h i n s t r u m e n t e d impact machines, i s b e i n g c a r r i e d out by s e v e r a l i n v e s t i g a t o r s , but thes e i n s t r u m e n t e d impact t e s t s have i n h e r e n t problems, and the r e s u l t s can be g r o s s l y m i s l e a d i n g i f c a u t i o n i s not e x e r c i s e d i n t h e i r i n t e r p r e t a t i o n . I n e r t i a l l o a d i n g e f f e c t s , energy l o s s p r e d i c t i o n s and so on a r e some of the problems which need c o n s i d e r a t i o n . The b a s i c aim of the p r e s e n t work, t h e r e f o r e , was t o d e v e l o p a v a l i d t e s t i n g t e c h n i q u e f o r t e s t i n g c o n c r e t e under impact, and t o use such a t e c h n i q u e t o e v a l u a t e the impact b e h a v i o u r of c o n c r e t e . The v a r i o u s f a c t o r s t h a t a f f e c t the impact r e s i s t a n c e of c o n c r e t e , and the v a r i o u s r e i n f o r c i n g t e c h n i q u e s t h a t can be made use of i n o r d e r t o enhance i t s impact r e s i s t a c n e were a l s o i n v e s t i g a t e d . 2. OBJECTIVE AND SCOPE C o n c r e t e , w i t h i t s heterogeneous c o m p o s i t i o n and i n e l a s t i c b e h a v i o u r , behaves q u i t e d i f f e r e n t l y from o t h e r m a t e r i a l s such as m e t a l s . The random d i s t r i b u t i o n of f i n e and c o a r s e aggregate p a r t i c l e s throughout the hardened cement m a t r i x and the n o n l i n e a r b e h a v i o u r under l o a d i n g , s e p a r a t e c o n c r e t e from the much more homogeneous m e t a l s . I t i s the v e r y s t r u c t u r e and c o m p o s i t i o n of c o n c r e t e which impart i t s s t r a i n r a t e s e n s i t i v e c h a r a c t e r i s t i c s . The p r e s e n t knowledge of the b e h a v i o u r of c o n c r e t e under h i g h r a t e s t. of l o a d i n g i s inadequate t o e x p l a i n i t s performance as a s t r u c t u r a l m a t e r i a l when s u b j e c t e d t o impact l o a d i n g s . The s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e makes i t improper t o use i t s s t a t i c a l l y d e t e r m i n e d p r o p e r t i e s under h i g h s t r a i n r a t e or impact l o a d i n g . Moreover, the r e s u l t s o b t a i n e d a t low or i n t e r m e d i a t e s t r a i n r a t e s may not be used t o p r e d i c t the b e h a v i o u r under impact l o a d i n g because, (a) no u n i v e r s a l l y a c c e p t e d r u l e e x i s t s f o r such an e x t r a p o l a t i o n , and (b) impact may not be r e g a r d e d s i m p l y as a case of extreme s t r a i n r a t e a p p l i c a t i o n . Not o n l y don't we u n d e r s t a n d p l a i n c o n c r e t e , we c a n ' t even b e g i n t o p r e d i c t the b e h a v i o u r of f i b r e r e i n f o r c e d c o n c r e t e , and of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e a t h i g h s t r e s s r a t e s . H i g h s t r e s s r a t e t e s t i n g of c o n c r e t e n e c e s s i t a t e s a t e s t i n g machine c a p a b l e of g e n e r a t i n g h i g h s t r e s s r a t e s , a method of a c q u i r i n g the d a t a , and f i n a l l y , a v a l i d t e c h n i q u e f o r a n a l y s i n g the t e s t r e s u l t s . An i n s t r u m e n t e d drop weight 5 6 impact machine was d e s i g n e d and c o n s t r u c t e d f o r t h i s purpose as d e s c r i b e d in Chapter 4. Load measurements were made at the p o i n t of the hammer-beam c o n t a c t , and a l s o at one of the s u p p o r t s . Three a c c e l e r o m e t e r s mounted a lon g the l e n g t h of the beam were used to make the i n e r t i a l l o a d c o r r e c t i o n . An a n a l y s i s was deve loped to e v a l u a t e the g e n e r a l i z e d i n e r t i a l l o a d from the a c c e l e r o m e t e r r e a d i n g s . Subsequent e v a l u a t i o n of the "true" or the g e n e r a l i z e d bending l o a d and the f r a c t u r e energy c o u l d be made u s i n g the observed tup l o a d v s . t ime da ta and the i n t e g r a t e d a c c e l e r a t i o n r e c o r d . The support l o a d measurements were compared wi th the e v a l u a t e d g e n e r a l i z e d bending l o a d as a check of the v a l i d i t y of the t e c h n i q u e used in t h i s s tudy f o r i n e r t i a l l o a d c o r r e c t i o n (Chapter 4 ) . C o n s i d e r a b l e s i m p l i f i c a t i o n i s p o s s i b l e in the treatment of the impact data i f some assumptions about the a c c e l e r a t i o n d i s t r i b u t i o n a l o n g the l e n g t h of the beam specimen can be made. In the p r e s e n t work, a c c e l e r a t i o n d i s t r i b u t i o n s were s t u d i e d for p l a i n , f i b r e r e i n f o r c e d , and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams undergo ing impact , and i t i s shown t h a t s imple mathemat i ca l f u n c t i o n s may be used to d e f i n e the a c c e l e r a t i o n d i s t r i b u t i o n a l o n g the l e n g t h of the beam (Chapter 4 ) . Rubber pads between the s t r i k i n g tup and the beam are sometimes used i n order to reduce the i n e r t i a l l o a d o s c i l l a t i o n s . I t has even been suggested t h a t , w i t h the proper pads , the i n e r t i a l l o a d i n g may be e n t i r e l y 7 e l i m i n a t e d . The v a l i d i t y of t h e s e arguments has been examined i n Chapter 5. The t e s t i n g program i n v o l v e d the t e s t i n g of a p p r o x i m a t e l y 350 c o n c r e t e beams under w i d e l y d i f f e r e n t s t r e s s r a t e s . The l o w e s t s t r e s s i n g r a t e chosen was t h a t of q u a s i - s t a t i c t e s t i n g , u s i n g a c o n v e n t i o n a l m e c h a n i c a l t e s t i n g machine; the h i g h e s t s t r e s s i n g r a t e was a c h i e v e d u s i n g the h i g h e s t p o s s i b l e hammer drop h e i g h t i n the impact machine, 2.30m. T h i s gave a range of c r o s s - h e a d v e l o c i t i e s from 4.2x10 m/sec t o about 6.71m/sec. Co n c r e t e i s a conglomerate of randomly d i s t r i b u t e d a g gregate p a r t i c l e s bound t o g e t h e r by h y d r a t e d p o r t l a n d cement. The o v e r a l l p r o p e r t i e s of c o n c r e t e depend upon the p r o p e r t i e s of the p a s t e and on i t s bond w i t h the a g g r e g a t e s . Thus, as a f i r s t s t e p i n the st u d y of the s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e the b e h a v i o u r of p a s t e i t s e l f under impact l o a d i n g was s t u d i e d (Chapter 6 ) . The e f f e c t of s t r e s s r a t e on the b e h a v i o u r of p l a i n c o n c r e t e was a l s o s t u d i e d by s u b j e c t i n g p l a i n c o n c r e t e beams t o s t r e s s r a t e s a s s o c i a t e d w i t h s t a t i c l o a d i n g and tho s e a s s o c i a t e d w i t h impact. The most i m p o r t a n t p r o p e r t i e s s t u d i e d were the s t r e n g t h and the f r a c t u r e energy (Chapter 6 ) . The r o l e of m i c r o s i l i c a ( f i n a l l y d i v i d e d s i l i c a fume) i n i m p r o v i n g the s t a t i c s t r e n g t h of c o n c r e t e i s w e l l known. However, h i g h s t r e n g t h c o n c r e t e i s a l s o known t o be more b r i t t l e than normal s t r e n g t h c o n c r e t e . The e f f e c t of h i g h s t r e n g t h ( a c h i e v e d by the use of m i c r o s i l i c a ) on the 8 p r o p e r t i e s of c o n c r e t e s u b j e c t e d to v a r y i n g s t r e s s r a t e s was i n v e s t i g a t e d . Of p a r t i c u l a r i n t e r e s t was the behav iour of h i g h s t r e n g t h c o n c r e t e beams under the very h i g h s t r e s s r a t e s a s s o c i a t e d wi th impact , and i t s comparison w i t h normal s t r e n g t h c o n c r e t e (Chapter 6 ) . A n a l y t i c a l p r e d i c t i o n of c o n c r e t e behav iour under h i g h s t r e s s r a t e s r e q u i r e s a model and some assumptions r e g a r d i n g i t s b e h a v i o u r . A c o n s t i t u t i v e law for c o n c r e t e w i th the a p p l i e d s t r e s s r a t e as an independent v a r i a b l e was p r o p o s e d . With the proposed c o n s t i t u t i v e law, the behav iour of a beam under an e x t e r n a l l o a d p u l s e was determined u s i n g a s i n g l e degree of freedom model and the time s t ep i n t e g r a t i o n t e c h n i q u e (Chapter 7 ) . The concept of energy b a l a n c e , which has i t s b a s i s in the law of c o n s e r v a t i o n of energy , was examined i n the case of p l a i n c o n c r e t e beams undergo ing impact . The e n e r g i e s l o s t by the hammer up to the peak e x t e r n a l l o a d , and j u s t a f t e r the c o m p l e t i o n of the impact event , were compared to the energy g a i n e d by the beam in v a r i o u s forms. The machine l o s s e s , i f any , were computed (Chapter 8 ) . C o n c r e t e i s a b r i t t l e m a t e r i a l , and as such the s t r e n g t h of a c o n c r e t e element under t e n s i o n or f l e x u r e i s de termined by the s i z e of the l a r g e s t flaw p r e s e n t . S t r e s s e s i n the v i c i n i t y of the t i p of a f law can be expres sed i n terms of b a s i c f r a c t u r e mechanics p a r a m e t e r s . However, the c r i t i c a l v a l u e of the f r a c t u r e toughness (Kj.c^ depends, amongst o ther t h i n g s , upon the r a t e a t which the l o a d i s 9 a p p l i e d . T h i s s t r e s s r a t e dependence of K^^ was i n v e s t i g a t e d f o r normal s t r e n g t h , h i g h s t r e n g t h , and f i b r e r e i n f o r c e d c o n c r e t e u s i n g notched beams s u b j e c t e d to both s t a t i c . and impact l o a d i n g . The common b e l i e f tha t the f i b r e s r e t a r d c r a c k p r o p a g a t i o n . by a c t i n g as c r a c k a r r e s t e r s was a l s o examined (Chapter 9 ) . The use of f i b r e s has proven to be of importance i n improv ing the " d u c t i l i t y " of c o n c r e t e . T h i s d e s i r a b l e c o n t r i b u t i o n of f i b r e s i s p a r t i c u l a r l y welcome i n impact l o a d i n g s i t u a t i o n s , where a l a r g e amount of energy i s suddenly imparted to the s t r u c t u r e , demanding a h i g h energy a b s o r p t i o n c a p a c i t y from i t s e l ements . S t e e l and p o l y p r o p y l e n e f i b r e r e i n f o r c e d beams were s u b j e c t e d to impact and the s t r e n g t h and f r a c t u r e energy v a l u e s thus o b t a i n e d were compared wi th those o b t a i n e d under s t a t i c l o a d i n g . Comparison was a l s o made w i t h beams wi thout f i b r e s (Chapter 10) . The low s t r e n g t h of c o n c r e t e under t e n s i o n has l e d to i t s use a lmost always in c o n j u n c t i o n w i t h r e i n f o r c i n g s t e e l . In s p i t e of the advantages of ad d in g f i b r e s , they cannot r e p l a c e c o n v e n t i o n a l r e i n f o r c i n g b a r s . S t r a t e g i c a l l y p l a c e d r e i n f o r c i n g bars have performed b e t t e r than randomly d i s t r i b u t e d f i b r e s i n terms of both s t r e n g t h and d u c t i l i t y in s t a t i c s i t u a t i o n s . However, v e r y l i t t l e i s known about the performance of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e under impact . To examine t h i s , c o n v e n t i o n a l l y r e i n f o r c e d beams were s u b j e c t e d to impact w i t h v a r y i n g hammer drop h e i g h t s , 10 and t h e i r impact performance was compared w i t h t h e i r s t a t i c p e r f o r m a n c e . Both deformed and smooth r e i n f o r c i n g b a r s were t e s t e d . C o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams made w i t h h i g h s t r e n g t h c o n c r e t e were a l s o t e s t e d (Chapter 11). Confinement has been found t o i n c r e a s e the d u c t i l i t y of c o n c r e t e under s t a t i c l o a d i n g . The e f f e c t of confinement under impact l o a d i n g was examined by c o n f i n i n g c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e u s i n g r e c t a n g u l a r s t i r r u p s , and s u b j e c t i n g the r e s u l t i n g specimens t o both s t a t i c and impact l o a d i n g (Chapter 11). The e f f e c t s of a c o m b i n a t i o n of c o n v e n t i o n a l r e i n f o r c e m e n t and f i b r e r e i n f o r c e m e n t were a l s o s t u d i e d , u s i n g b o t h normal and h i g h s t r e n g t h c o n c r e t e s . Such c o m b i n a t i o n s a re known t o be v e r y e f f e c t i v e i n s t a t i c l o a d i n g , and an attempt was made t o e v a l u a t e t h i s c o m b i n a t i o n under impact l o a d i n g (Chapter 12). A s t r u c t u r a l element i s r e q u i r e d t o c a r r y dead and l i v e s t a t i c l o a d s on a c o n t i n u o u s b a s i s . Thus, i n p r a c t i c e , a t the time of impact the elements w i l l a l r e a d y have been s u b j e c t e d t o s t a t i c l o a d i n g . S i n c e the appearance of t e n s i o n c r a c k s i n c o n c r e t e i s a l l o w e d by most d e s i g n codes, the element may be pre-damaged b e f o r e i t i s s u b j e c t e d t o impact. To check the performance of beams pre-damaged by s t a t i c l o a d i n g , such pre-damaged beams were s u b j e c t e d t o impact and t h e i r performance was compared t o t h a t of undamaged beams. The e f f e c t of f i b r e r e i n f o r c e m e n t on p r e s e r v i n g the i n t e g r i t y of the predamaged beams un d e r g o i n g impact was a l s o 11 s t u d i e d (Chapter 12). The f a i l u r e of c o n c r e t e i s caused by the p r o p a g a t i o n of c r a c k s . Under l o a d , m i c r o - c r a c k s i n the c o n c r e t e grow and c o a l e s c e i n t o m a c r o - c r a c k s t h a t propagate t o cause s e p a r a t i o n . Once u n s t a b l e p r o p a g a t i o n of c r a c k s b e g i n s , t h e be h a v i o u r of the element depends upon the mode i n which the c r a c k p r o p a g a t e s , the v e l o c i t y of the c r a c k , c r a c k b r a n c h i n g , and so on. In the case of impact, s i n c e the e n t i r e event t a k e s p l a c e i n a f r a c t i o n of a second, the p r o p a g a t i o n of the c r a c k cannot be ob s e r v e d w i t h the naked eye. One has t h e r e f o r e t o r e s o r t t o h i g h speed photography t o o b s erve the c r a c k p r o p a g a t i o n . H i g h speed photography was c a r r i e d out u s i n g a motion p i c t u r e camera r u n n i n g a t 10,000 frames per second on h y d r a t e d cement p a s t e , s t e e l f i b r e r e i n f o r c e d c o n c r e t e , and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams. The f i l m s were then viewed frame by frame i n a s m a l l hand v i e w e r t o stu d y the c r a c k p r o p a g a t i o n , c r a c k v e l o c i t i e s , c r a c k b r a n c h i n g , and the c r a c k a r r e s t due t o the presence of the f i b r e s . ( C h a p t e r s 6, 10, and 11). The p r e s e n t s t u d y , t h u s , was d i r e c t e d towards: (a) The development of a v a l i d t e s t i n g method t o t e s t c o n c r e t e beams under impact l o a d i n g , and (b) The assessment of the impact r e s i s t a n c e of p l a i n , f i b r e r e i n f o r c e d , and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams u s i n g such a t e s t i n g method. The output from the t e s t i n g program i s more i n the form of t r e n d s , and l e s s i n the form of b a s i c m a t e r i a l p r o p e r t i e s , a l t h o u g h an attempt has been made t o e v a l u a t e the b a s i c 12 m a t e r i a l p r o p e r t i e s wherever p o s s i b l e . 3. LITERATURE SURVEY  3.1 INTRODUCTION The p o s s i b i l i t y of a s t r u c t u r e b e i n g s u b j e c t e d t o impact, a c c i d e n t a l or o t h e r w i s e , has l o n g been r e c o g n i z e d . A s t r u c t u r e as a whole, or a p a r t i c u l a r s t r u c t u r a l component, c o u l d be c a l l e d upon t o s u s t a i n t he l a r g e amount of energy i m p a r t e d t o i t by a sudden a p p l i c a t i o n of l o a d . In o r d e r t o d e s i g n a s t r u c t u r e f o r dynamic l o a d i n g , we s h o u l d be a b l e t o a s s e s s the energy a b s o r b i n g c a p a c i t y both of the i n d i v i d u a l components of the s t r u c t u r e , and of the e n t i r e s t r u c t u r e i t s e l f . F or example, t o a s s e s s c o r r e c t l y the energy a b s o r p t i o n of a s t r u c t u r e when s u b j e c t e d t o earthquake l o a d i n g , we s h o u l d know the b a s i c m a t e r i a l p r o p e r t i e s a t the s t r a i n r a t e i n q u e s t i o n . In a d d i t i o n t o the m a t e r i a l p r o p e r t i e s , we a l s o need t o know the f a i l u r e mechanisms and the v a r i o u s energy d i s s i p a t i n g mechanisms. U n f o r t u n a t e l y , our knowledge of the b e h a v i o u r of c e m e n t i t i o u s m a t e r i a l s i s s t i l l l a r g l y q u a l i t a t i v e . A l t h o u g h some work a t h i g h s t r a i n r a t e s has been c a r r i e d o u t , the q u a n t i t a t i v e s i d e i s f a r from c l e a r . T h i s may be due t o the wide v a r i a t i o n s o b s e r v e d between d i f f e r e n t e x p e r i m e n t a l i n v e s t i g a t i o n s , which o f t e n r e s u l t i n c o n t r a d i c t o r y c o n c l u s i o n s . Our p r e s e n t knowledge, and c o n s e q u e n t l y our d e s i g n p r a c t i c e as such, a r e s t i l l a t l e a s t p a r t l y e m p i r i c a l i n n a t u r e . I n the absence of a b e t t e r u n d e r s t a n d i n g of the r e a c t i o n of the impacted s t r u c t u r e t o the e x t e r n a l impact l o a d , n o t h i n g can be s a i d w i t h c e r t a i n t y . The s t r e s s 13 1 4 d i s t r i b u t i o n i n an impacted mass of p l a i n c o n c r e t e or f i b r e r e i n f o r c e d c o n c r e t e i s f a r from s i m p l e , due m a i n l y t o the heterogeneous i n t e r n a l s t r u c t u r e , the v a r i a b l e d i s t r i b u t i o n of s t r a i n s , the s t e e p s t r a i n g r a d i e n t s , and the p o o r l y c h a r a c t e r i z e d i n t e r f a c e between the cement and the a g g r e g a t e s . I t i s a l s o worth n o t i n g t h a t i n many i n s t a n c e s a c o r r e c t e s t i m a t i o n of the e x t e r n a l l o a d and i t s v a r i a t i o n w i t h time i s a l s o not p o s s i b l e . The i n p u t l o a d f u n c t i o n , which among o t h e r t h i n g s depends upon the p r e c i s e manner i n which the impacted body a b s o r b s the i n c i d e n t energy and on the r e l a t i v e masses of the b o d i e s c o l l i d i n g , forms an i m p o r t a n t a r e a of s t u d y . The i n p u t i n the form of t h e e x t e r n a l l o a d f u n c t i o n and the o u t p u t , i n the form of t h e s t r u c t u r a l r e s p o n s e , a r e thus h i g h l y i n t e r d e p e n d e n t . M a i n s t o n e and K a v y r c h i n e ( 1 ) , S t r u c k and V o g g e n r e i t e r ( 2 ) , and K a v y r c h i n e and S t r u c k (3) have c i t e d examples of impact and i m p u l s i v e l o a d i n g t h a t may p o s s i b l y o c c u r i n p r a c t i c e and the consequences t h a t may f o l l o w . They have a l s o d e s c r i b e d the problems a s s o c i a t e d w i t h the e v a l u a t i o n of the impact response of s t r u c t u r e s . In the case of impact l o a d i n g , the response of the s t r u c t u r e can be d i v i d e d i n t o two t y p e s : l o c a l response and o v e r a l l response ( 3 ) . Depending on the r e l a t i v e masses of the impacted and the i m p a c t i n g b o d i e s , the o v e r a l l s t r u c t u r a l response may or may not be s i g n i f i c a n t . The case of a v e r y s m a l l o b j e c t h i t t i n g a v e r y l a r g e mass, which i s p a r t i c u l a r l y i n t e r e s t i n g from the m i l i t a r y p o i n t of view, i s a case i n which the l o c a l 15 response i s c r i t i c a l . The N a t i o n a l Defence Research Committee (NDRC) has proposed v a r i o u s e m p i r i c a l formulae t o e s t i m a t e the p e n e t r a t i o n depths (x) f o r the case of nondeformable c y l i n d r i c a l m i s s i l e s i m p a c t i n g c o n c r e t e masses. The g e n e r a l form of the formulae i s x=f(k,W,d,V) (3.1) where k i s a c o n s t a n t , W i s the m i s s i l e w e i g h t , d i s the diameter of the m i s s i l e , and V i s the v e l o c i t y of the m i s s i l e . S l i t e r ( 4 ) found the NDRC formulae t o work s a t i s f a c t o r i l y f o r h i g h v e l o c i t y i m p a c t s ; f o r low v e l o c i t y impacts the observed p e n e t r a t i o n s were much s m a l l e r than the p r e d i c t e d ones. A l s o , these formulae do not a p p l y t o deformable m i s s i l e s ( 4 ) . NDRC formulae do not c o n s i d e r any r e i n f o r c e m e n t p r e s e n t i n the impacted body, thus making the d i f f e r e n t i a t i o n between a r e i n f o r c e d t a r g e t and an u n r e i n f o r c e d t a r g e t an i m p o s s i b i l i t y . V a r i o u s o t h e r i n v e s t i g a t o r s have a l s o p r e s e n t e d independent e m p i r i c a l f o r m u l a e based on t h e i r e x p e r i m e n t a l f i n d i n g s , but a u n i v e r s a l l y a c c e p t e d f o r m u l a does not e x i s t . 16 3.2 IMPACT TESTING So f a r , no r e s u l t s of f u l l s c a l e impact t e s t s on b u i l d i n g s or o t h e r s t r u c t u r e s a r e a v a i l a b l e , but v a r i o u s i n v e s t i g a t o r s have s u b j e c t e d s t r u c t u r a l elements made of c e m e n t i t i o u s m a t e r i a l s ( e . g . , f l e x u r a l members, compre s s i o n members, t e n s i o n members, and s l a b s ) t o dynamic l o a d i n g s . A ttempts were made t o a s c e r t a i n the energy a b s o r b i n g c a p a c i t i e s of the c e m e n t i t i o u s m a t e r i a l s under v a r i a b l e s t r a i n r a t e l o a d i n g s . The v a r i o u s methods employed by the s e i n v e s t i g a t o r s (5,6) i n c l u d e : f r e e f a l l drop weight t e s t s , e x p l o s i v e t e s t s , Charpy or I z o d t e s t s , Hopkinson s p l i t bar t e s t s , and the use of f r a c t u r e mechanics as an a n a l y t i c a l t o o l . U n f o r t u n a t e l y , the e a r l i e r t e s t s of t h i s type were not f u l l y i n s t r u m e n t e d ; i n v e s t i g a t o r s now r e a l i z e t h a t much im p o r t a n t i n f o r m a t i o n can be l o s t i n the absence of prop e r i n s t r u m e n t a t i o n . Most of the s e t e s t s were d i r e c t e d a t f i n d i n g 'work of f r a c t u r e ' v a l u e s , or 'toughness'. Attempts were a l s o made t o o b t a i n the b a s i c m a t e r i a l p r o p e r t i e s , such as the c o n s t i t u t i v e laws i n co m p r e s s i o n or t e n s i o n , c r i t i c a l s t r e s s i n t e n s i t y f a c t o r s , and the c r i t i c a l s t r a i n energy r e l e a s e r a t e s . The e x t e n t t o which u s e f u l i n f o r m a t i o n can be d e r i v e d from t h e s e v a r i a b l e s t r a i n r a t e t e s t s depends upon our g e n e r a l u n d e r s t a n d i n g of the p r o c e s s of l o a d i n g a t h i g h s t r e s s r a t e s and of the energy t r a n s f o r m a t i o n s and d i s s i p a t i o n s o c c u r i n g d u r i n g a t e s t . The da t a o b t a i n e d from an i n s t r u m e n t e d impact t e s t may be v e r y m i s l e a d i n g i f p r o p e r 17 c a u t i o n i n not e x e r c i s e d i n t h e i r i n t e r p r e t a t i o n . The most b a s i c form of i n s t r u m e n t a t i o n p r o v i d e d i n any of thes e i n s t r u m e n t e d impact t e s t s i s the i n s t r u m e n t a t i o n of the s t r i k i n g head or 'tup ' . T h i s form of i n s t r u m e n t a t i o n i s o f t e n supplemented by i n s t r u m e n t e d a n v i l s (specimen s u p p o r t s ) or by i n s t r u m e n t e d specimens. The s t r a i n gauges p r o v i d e d i n the s t r i k i n g head g e n e r a t e a time-base s i g n a l w h i ch, w i t h proper c a l i b r a t i o n , can generate the l o a d v s . time r e c o r d of the impact. T h i s l o a d v s . time r e c o r d of the impact can then be used t o o b t a i n the impulse a c t i n g a g a i n s t the moving t u p , which i n t u r n can be used t o o b t a i n the energy l o s t by the tup ( 7 ) . Other i n f o r m a t i o n o b t a i n a b l e from the l o a d v s . time t r a c e i n c l u d e s the maximum l o a d o c c u r i n g i n an impact, which i s u s e f u l from the s t r e n g t h c a l c u l a t i o n p o i n t of view. Many i n v e s t i g a t o r s have r e a l i z e d t h a t t h e s e t e s t s a r e not f r e e from p a r a s i t i c e f f e c t s such as i n e r t i a l l o a d i n g e f f e c t s . A major p a r t of the tup l o a d , a t the b e g i n n i n g of the impact e v e n t , i s used up i n a c c e l e r a t i n g the specimen from r e s t . Thus, not a l l of the t u p l o a d a c t s upon the specimen as the bending l o a d . T h i s i s termed the " i n e r t i a l l o a d i n g e f f e c t " . C o t t e r e l l ( 8 ) , and l a t e r o t h e r s ( 9 - 1 2 ) , n o t i c e d an i n i t i a l d i s c o n t i n u i t y i n the l o a d v s . time t r a c e s o b t a i n e d from impact t e s t s on m e t a l l i c specimens. T h i s d i s c o n t i n u i t y was e x p l a i n e d by C o t t e r e l l (8) u s i n g e l a s t i c wave t h e o r y . He argued t h a t the compre s s i o n wave i n the s t r i k i n g head i s r e f l e c t e d as a t e n s i o n wave from the f r e e 18 b o u n d a r i e s of the s t r i k e r . Radon and Turner (10) l a t e r found t h a t the n a t u r e of the d i s c o n t i n u i t y o b s e r v e d i n the l o a d v s . time c u r v e s was the same even f o r tups w i t h d i f f e r e n t conf i g u r a t i o n s . A c l e a r p i c t u r e of i n e r t i a l l o a d i n g i s p r e s e n t e d by Sa x t o n , I r e l a n d and S e r v e r (13) and by S e r v e r ( 1 4 ) . The i n e r t i a l l o a d i n g i n the i n s t r u m e n t e d impact t e s t s i s c h a r a c t e r i z e d by o s c i l l a t i o n s about the a c t u a l beam d e f o r m a t i o n l o a d i n the l o a d v s . time c u r v e . The magnitude of t h i s d e v i a t i o n of the apparent t u p l o a d s i g n a l from the a c t u a l beam d e f o r m a t i o n l o a d depends on the masses i n v o l v e d , the v e l o c i t y of impact, the s t i f f n e s s of the c o n t a c t zone, and so on. S e r v e r (14) recommended t h a t r e l i a b l e measurements s h o u l d be made o n l y a f t e r t h r e e o s c i l l a t i o n s of t h i s t y p e . However, i n the case of b r i t t l e m a t e r i a l s such as c o n c r e t e , i t may not be p o s s i b l e t o a v o i d f a i l u r e d u r i n g the f i r s t i n e r t i a l o s c i l l a t i o n . Thus, the g u i d e l i n e s suggested by S e r v e r (14) can not be met. As a r e s u l t , the e n t i r e m e c h a n i c a l response of the beam may be overshadowed by i t s i n e r t i a l r e s p onse. The i n t e r p r e t a t i o n of the t e s t r e s u l t s i n the case of c o n c r e t e , t h u s , may be v e r y d i f f e r e n t from t h a t of m e t a l l i c m a t e r i a l s where the time t o f r a c t u r e i s n o r m a l l y v e r y l o n g . Remedies t o the problem of i n e r t i a l l o a d i n g have been p r e s e n t e d by v a r i o u s i n v e s t i g a t o r s . These remedies may be b r o a d l y c l a s s i f i e d i n t o two c a t e g o r i e s : a n a l y t i c a l and e x p e r i m e n t a l . I t i s worth n o t i n g here t h a t each method has 19 i t s own u n d e r l y i n g and s i m p l i f y i n g a s s u m p t i o n s , and thus no u n i v e r s a l l y a p p l i c a b l e method y e t e x i s t s . Saxton e t a l (13) conducted i n s t r u m e n t e d impact t e s t s on d i f f e r e n t m a t e r i a l s . They r e p o r t e d a l i n e a r dependence of the maximum i n e r t i a l l o a d upon the i n i t i a l v e l o c i t y , and a s y s t e m a t i c i n c r e a s e i n the maximum i n e r t i a l l o a d w i t h an i n c r e a s e i n the a c o u s t i c impedence of the m a t e r i a l t e s t e d . Thus they c o n c l u d e d t h a t the i n i t i a l impact l o a d i s governed by e l e m e n t a r y e l a s t i c wave mechanics. They extended the argument f u r t h e r , by p r o p o s i n g a s e r i e s of t e s t s on s t e e l specimens w i t h known p r o p e r t i e s , t h u s e v a l u a t i n g the t e s t machine parameters i n o r d e r t o e s t i m a t e the i n e r t i a l l o a d f o r any o t h e r m a t e r i a l t o be t e s t e d . The e q u a t i o n s proposed by them a r e t h e r e f o r e r e s t r i c t e d t o t h e i r p a r t i c u l a r machines and i n s t r u m e n t a t i o n . V e n z i , P r i e s t and May (12) m o d e l l e d the beam as h a v i n g pure r o t a t o r y motion and z e r o t r a n s v e r s e s t i f f n e s s . They a l s o assumed t h a t the i n e r t i a l l o a d per u n i t l e n g t h was p r o p o r t i o n a l t o the d i s p l a c e m e n t from the mean p o s i t i o n . They thus d e t e r m i n e d the r e a c t i o n of the tup and the a n v i l s t o t h i s i n e r t i a l l o a d from a knowledge of t h e i r r e s p e c t i v e s p r i n g c o n s t a n t s . Knowing t h e s e r e a c t i o n s , the a c t u a l b ending l o a d was c a l c u l a t e d u s i n g s t a t i c s . Radon and Turner (10) a l s o s u g g ested an approximate c o r r e c t i o n f o r i n e r t i a l l o a d i n i n s t r u m e n t e d impact t e s t s . They assumed t h a t the a c c e l e r a t i o n of each p a r t i c l e i n the beam was a c o n s t a n t w i t h t i m e , as a f u n c t i o n o n l y of i t s 20 p o s i t i o n a l o n g the beam. They o b t a i n e d the i n e r t i a l f o r c e a c t i n g on an i n f i n i t e s i m a l element as a f u n c t i o n of the d i s p l a c e m e n t a t the i n s t a n t of f a i l u r e . Then, c o n s i d e r i n g the problem as one of a beam on e l a s t i c f o u n d a t i o n , w i t h the i n e r t i a l l o a d i n g as the f o u n d a t i o n r e a c t i o n , they s o l v e d f o r the d e f l e c t e d shape as a f u n c t i o n of the t u p l o a d and the o t h e r p h y s i c a l p a r a m e t e r s . Once the d e f l e c t e d shape was known, i t c o u l d be used t o f i n d the bending moment i n the c e n t r e . T h i s was f i n a l l y equated t o the bending moment of a s i m p l y s u p p o r t e d beam and the v a l u e of the a c t u a l bending l o a d was o b t a i n e d . On the e x p e r i m e n t a l s i d e , e v a l u a t i o n and subsequent e l i m i n a t i o n of the p a r a s i t i c e f f e c t s i n v o l v e d r e s o r t i n g t o more s o p h i s t i c a t e d i n s t r u m e n t a t i o n . An e s t i m a t i o n of the a c t u a l bending l o a d on the beam underg o i n g impact was att e m p t e d by Gopalaratnam, Shah, and John ( 1 5 ) , by i n s t r u m e n t i n g the a n v i l s . The d i f f e r e n c e between the r e c o r d e d t u p l o a d and the r e c o r d e d a n v i l l o a d y i e l d e d the i n e r t i a l l o a d on the beam. H i b b e r t (7) t r i e d t o e l i m i n a t e the e f f e c t of i n e r t i a l l o a d i n g from the energy c o m p u t a t i o n s by measuring the k i n e t i c energy a c q u i r e d by the broken h a l v e s of the beam. The Charpy specimens i n H i b b e r t ' s t e s t s were s e c u r e d a t the two ends by means of specimen h o l d e r s and the s e specimen h o l d e r s were a l l o w e d t o r o t a t e a f t e r f r a c t u r e a g a i n s t a s p r i n g and r a t c h e t system. 21 S u a r i s and Shah (16) i n t r o d u c e d a rubber pad between the t u p and the beam and s u b s e q u e n t l y showed t h a t the d i f f e r e n c e between the bending l o a d and the t u p l o a d was reduced because of t h i s m o d i f i c a t i o n t o the t e s t system. The pro c e d u r e adopted by S u a r i s and Shah has two p o i n t s worth n o t i n g . F i r s t , the i n t r o d u c t i o n of the rubber pad s i g n i f i c a n t l y reduced the a p p l i e d s t r a i n r a t e . S e c o n d l y , a l a r g e amount of energy was absorbed i n the e l a s t i c d e f l e c t i o n of the rubber pad, which s h o u l d have been c o n s i d e r e d w h i l e c a l c u l a t i n g the bending energy of the beam. Another major problem t h a t o c c u r s i n i n t e r p r e t i n g r e s u l t s of i n s t r u m e n t e d impact t e s t s i s the problem of the energy b a l a n c e . In an i n s t r u m e n t e d impact t e s t the energy as o b t a i n e d by i n t e g r a t i n g the l o a d v s . time p l o t i s a measure of the t o t a l energy expended by t h e hammer. O b v i o u s l y , not a l l of t h i s energy i s spent i n c r e a t i n g new f r a c t u r e s u r f a c e s . Most of the energy i s consumed i n secondary e f f e c t s . An e x a c t e v a l u a t i o n of t h i s energy l o s s i s i m p o s s i b l e , which means t h a t the energy b a l a n c e e q u a t i o n can never be f u l l y s a t i s f i e d . The g e n e r a l l y a c c e p t e d energy b a l a n c e e q u a t i o n ( 1 7 , 1 8 ) i s , A E 0 = E +E +E • £ + E C+E c (3.2)  s m v i b kpf wof r a f where, A E 0 i s the t o t a l energy o b t a i n e d from the 22 l o a d v s . time r e c o r d , E s ' Em a r e t* i e s t r a ^ n e n e r g i e s i m p a r t e d t o the specimen and the machine, r e s p e c t i v e l y , i s t he v i b r a t i o n a l energy of the specimen, E^p£ i s the k i n e t i c energy p r i o r t o f r a c t u r e of the specimen, Ewof * s t ^ e w o r k °f f r a c t u r e , and E r a f i s the r o t a t i o n a l k i n e t i c energy a f t e r f r a c t u r e . Abe, Chandan and B r a d t (17) attempted an e v a l u t i o n of the t o t a l energy l o s s . The l o a d p o i n t d e f l e c t i o n , o b t a i n e d as the p r o d u c t of the average v e l o c i t y and the t o t a l time t o f r a c t u r e , was used t o e v a l u a t e the t o t a l d e f l e c t i o n a t f r a c t u r e . Knowing the c o m p l i a n c e of the specimen and the maximum l o a d , the c o m p l i a n c e of the hammer c o u l d be c a l c u l a t e d . T h i s c o u l d c o n v e n i e n t l y be used, t h e n , t o e v a l u a t e t h e s t r a i n energy i n the machine. L u e t h (18) and I y e r and M i c l o t (19) have a l s o d e s c r i b e d the method of a p p l y i n g the co m p l i a n c e c o r r e c t i o n t o the measured g r o s s energy v a l u e s . When the energy b a l a n c e concept i s a p p l i e d t o c o n c r e t e , a d d i t i o n a l problems a r i s e . F i r s t of a l l , a c o m p l i a n c e c o r r e c t i o n r e q u i r e s a knowledge of the p r o p e r t i e s of the m a t e r i a l b e i n g t e s t e d a t a h i g h s t r a i n r a t e . For c o n c r e t e our u n d e r s t a n d i n g of t h e s e p r o p e r t i e s i s o n l y ' q u a l i t a t i v e , so the c o m p l i a n c e of the specimen can not be c a l c u l a t e d 23 a c c u r a t e l y . A second problem i n the case of c o n c r e t e , which was not c o n s i d e r e d by the above i n v e s t i g a t o r s , i s the c o m p l i c a t e d n a t u r e of the c o n t a c t zone. W i t h c r u s h i n g o c c u r r i n g i n the c o n t a c t zone, the energy b a l a n c e e q u a t i o n has t o i n c o r p o r a t e an a d d i t i o n a l term, E c r u ' which may be s u b s t a n t i a l but u n f o r t u n a t e l y i s v e r y d i f f i c u l t t o e v a l u a t e . T h i s c r u s h i n g a l s o r e n d e r s the e n t i r e c o m p l i a n c e c o r r e c t i o n p r o c e d u r e d o u b t f u l . One major problem w i t h a p p l y i n g the energy b a l a n c e concept t o c o n c r e t e i s the i n t e r c h a n g e a b i l i t y of the v a r i o u s e n e r g i e s i n v o l v e d . O b v i o u s l y , the s t r a i n energy of the specimen app e a r s , a t l e a s t i n p a r t , as the work of f r a c t u r e . Q u i t e p o s s i b l y some of the s t r a i n energy too i s used t o re a c h the p o s t - f r a c t u r e v e l o c i t y , and some of the k i n e t i c energy t o form the f r a c t u r e s u r f a c e s . With t h i s hazy p i c t u r e on the energy f r o n t , o n l y approximate e v a l u a t i o n s a r e p o s s i b l e w i t h our p r e s e n t u n d e r s t a n d i n g of the problem. 3.3 VARIABLE STRAIN RATE TESTS ON PLAIN CONCRETE B a s i c s t u d i e s of cement p a s t e , of mortar,and of c o n c r e t e have r e v e a l e d the i n h e r e n t l y b r i t t l e n a t u r e of th e s e m a t e r i a l s . To e x a c e r b a t e the s i t u a t i o n , t h e s e cement-based c o n s t r u c t i o n m a t e r i a l s have v e r y low t e n s i l e s t r e n g t h s . The weakness of c o n c r e t e under t e n s i l e s t r e s s , and i t s low f a i l u r e s t r a i n , have meant t h a t c o n c r e t e has a v e r y low toughness; the toughness of some m e t a l s may be al m o s t t h r e e o r d e r s of magnitude h i g h e r than t h a t of 24 c o n c r e t e . Moreover, c o n c r e t e i s s t r a i n r a t e s e n s i t i v e . I t s p r o p e r t i e s were found t o v a r y w i t h s t r e s s a p p l i c a t i o n r a t e s . V a r i a t i o n was found not o n l y between d i f f e r e n t s t r e s s a p p l i c a t i o n r a t e s , but a l s o between v a r i o u s s t r e s s a p p l i c a t i o n systems a t the same s t r e s s r a t e . T h i s has made the problem a l l the more c o m p l i c a t e d . A number of a t t e m p t s have been made t o a s s e s s the b e h a v i o u r of cement-based m a t e r i a l s under v a r y i n g s t r a i n r a t e s . C o n c r e t e , i n the form of c o m p r e s s i o n , t e n s i o n , or f l e x u r a l specimens has been s u b j e c t e d t o i n c r e a s i n g l y h i g h s t r a i n r a t e s , and the v a r i o u s s t r e n g t h and energy v a l u e s d e t e r m i n e d . P o s s i b l y the f i r s t e x p e r i m e n t a l study was t h a t of Abrams (20) i n 1917, who s u b j e c t e d c o n c r e t e c y l i n d e r s t o impact compression l o a d i n g and o b s e r v e d an i n c r e a s e i n the impact s t r e n g t h over the s t a t i c s t r e n g t h . Abrams a l s o o b s e r v e d t h a t the r a t e a t which the f i r s t 88% of the u l t i m a t e l o a d was a p p l i e d d i d not have any e f f e c t on the c o m p r e s s i v e s t r e n g t h . Many o t h e r i n v e s t i g a t o r s have a l s o c o n c l u d e d t h a t a t l e a s t the f i r s t 50% of the l o a d can be a p p l i e d a t any r a t e w i t h o u t a f f e c t i n g the u l t i m a t e s t r e n g t h . W a t s t e i n ( 2 1 ) , by p e r f o r m i n g compression t e s t s on c o n c r e t e a t v a r i a b l e s t r a i n r a t e s (10 ^ t o 10/sec) found t h a t the r a t i o of the dynamic t o the s t a t i c s t r e n g t h was s u b s t a n t i a l l y g r e a t e r than u n i t y . He a l s o o b s e r v e d t h a t t h i s r a t i o f o r s t r o n g c o n c r e t e d i d not d i f f e r much from t h a t f o r weak c o n c r e t e . The f a i l u r e s t r a i n s a t h i g h r a t e s of l o a d i n g 25 were h i g h e r than t h e i r s t a t i c c o u n t e r p a r t s . S i m i l a r l y , the s e c a n t modulus and maximum l o a d were c o n s i d e r a b l y h i g h e r i n the case of h i g h e r s t r a i n r a t e s . Green(22) used the type of cement, the type of c o a r s e a g g r e g a t e , shape of the c o a r s e a g g r e g a t e , c u r i n g c o n d i t i o n s , sand g r a d i n g , mix p r o p o r t i o n and the age of the specimens as the independent v a r i a b l e s i n e v a l u a t i n g the performance of c o n c r e t e a t v a r i a b l e s t r a i n r a t e s . C o n t r a r y t o W a t s t e i n ' s (21) f i n d i n g s , he found t h a t the r a t i o of the impact t o s t a t i c s t r e n g t h i n c r e a s e d w i t h the s t a t i c s t r e n g t h of c o n c r e t e . C o n c r e t e w i t h a n g u l a r a g g r e g a t e s showed a h i g h e r impact s t r e n g t h than the c o n c r e t e w i t h rounded and smooth a g g r e g a t e s . The w a t e r - c u r e d specimens showed h i g h e r impact s t r e n g t h s than the ones t h a t were a i r c u r e d . McNeely and Lash(23) d e t e r m i n e d the e f f e c t of the l o a d i n g r a t e on the t e n s i l e s t r e n g t h of c o n c r e t e . They found a l i n e a r r e l a t i o n s h i p between the modulus of r u p t u r e and the r a t e of l o a d i n g ( R ) , g i v e n by f t = A + B l o g i n R (3.3) where A and B a r e c o n s t a n t s . A t c h l y and F u r r (24) performed compression t e s t s under both s t a t i c and dynamic c o n d i t i o n s a t 0.05 t o 12x10" MPa per s e c . They a l s o found t h a t the c o m p r e s s i v e s t r e n g t h , energy a b s o r p t i o n , s e c a n t modulus and the s t r a i n a t f a i l u r e i n c r e a s e d w i t h an i n c r e a s e i n the s t r a i n r a t e . C o n t r a r y t o W a t s t e i n ' s (21) f i n d i n g s , they found the c o m p r e s s i v e 26 s t r e n g t h and the energy a b s o r p t i o n t o re a c h a c o n s t a n t v a l u e a t h i g h e r r a t e s of l o a d i n g . G o l d s m i t h , Kenner and R i c k e t t s (25) used b a l l i s t i c a l l y suspended Hopkinson s p l i t b a r s t o t e s t c o n c r e t e w i t h d i f f e r e n t a g g r e g a t e s . G r a i n c l e a v a g e i n the aggregate p a r t i c l e s of d i o r i t e was found t o be r e s p o n s i b l e f o r the h i g h energy a b s o r p t i o n c a p a c i t y of c o n c r e t e made u s i n g t h i s a g g r e g a t e . S t r a i n s , when measured f o r exposed a g g r e g a t e s , and f o r the m a t r i x , ( a t the same l o n g i t u d i n a l p o s i t i o n s a l o n g the bar) seemed t o have lower v a l u e s a t the aggregate l o c a t i o n than a t the m a t r i x l o c a t i o n . T h i s s u g g e s t e d t h a t the a g g r e g a t e s were the d e c i d i n g f a c t o r i n the s t i f f n e s s of c o n c r e t e . B i r k i m e r and Lindemann (26) have shown t h a t the c r i t i c a l f r a c t u r e s t r a i n energy t h e o r y p r o v i d e s a m e a n i n g f u l f r a c t u r e c r i t e r i o n . They a l s o found t h a t the c r i t i c a l f r a c t u r e s t r a i n i s d i r e c t l y p r o p o r t i o n a l t o the s t r a i n r a t e r a i s e d t o the o n e - t h i r d power. Hughes and Gregory (27) used "low f r i c t i o n " pads t o reduce the p l a t e n f r i c t i o n i n the case of dynamic compre s s i o n t e s t s on c o n c r e t e p r i s m s . The l o a d column method was used t o d e v e l o p h i g h s t r a i n r a t e s of up t o 30/sec, and a v a l u e of 1.9 was found as the r a t i o of dynamic t o s t a t i c s t r e n g t h . T h i s r a t i o was found t o be l a r g e l y independent of the water-cement r a t i o , age, and cement c o n t e n t , but dependent upon the type of c o a r s e a g g r e g a t e . 27 Sparks and Menzies (28) t e s t e d c o n c r e t e prisms in u n i a x i a l compression under both s t a t i c and f a t i g u e l o a d i n g . The s e n s i t i v i t y of the s t a t i c s t r e n g t h to the r a t e of l o a d i n g was found to be r e l a t e d to the s t i f f n e s s of the aggregate used. Lytag, the l e a s t s t i f f of a l l the aggregates, was found to be the most r a t e s e n s i t i v e ; limestone, the s t i f f e s t aggregate, was found to be the l e a s t r a t e s e n s i t i v e . They a l s o found that t h i s s t r a i n r a t e dependence c o u l d be expressed as a f=C+nlogo (3.4) where o-j i s the f a i l u r e s t r e s s a i s the s t r e s s r a t e . and C and n are c o n s t a n t s . Hughes and Watson (29) t e s t e d c o n c r e t e cubes with v a r y i n g mix p r o p o r t i o n s and two d i f f e r e n t types of coarse aggregates under compressive impact l o a d i n g ( s t r a i n r a t e s up to 17/sec). They found that the u l t i m a t e s t r a i n s decreased with an i n c r e a s e i n the s t r e s s r a t e s , o p p o s i t e to the f i n d i n g s r e p o r t e d i n (24) and (26). T h i s was a t t r i b u t e d to the absence of creep s t r a i n s f o r high s t r a i n r a t e l o a d i n g s . A l s o , the crack propagation path i n the high s t r a i n r a t e t e s t s was much s t r a i g h t e r than that i n the low s t r a i n r a t e t e s t s . Aggregate f a i l u r e s were observed more i n the impact t e s t s than i n the s t a t i c t e s t s . In the s t a t i c t e s t s the crack was found to propagate around the aggregate but never 28 t h r o u g h i t . They c o n s i d e r e d t h i s as the reason f o r the l a r g e energy r e q u i r e m e n t i n the impact t e s t s . The f r a c t u r e mechanics approach t o r a t e of l o a d i n g e f f e c t s i n v o l v e s a c o m b i n a t i o n of the c l a s s i c a l G r i f f i t h t h e o r y w i t h an e m p i r i c a l r e l a t i o n s h i p d e s c r i b i n g the s u b - c r i t i c a l c r a c k growth ( 3 0 ) . A c c o r d i n g t o the concept of s u b - c r i t i c a l c r a c k growth, under a s u s t a i n e d l o a d , a c r a c k of s u b - c r i t i c a l s i z e w i l l e v e n t u a l l y grow t o the c r i t i c a l s i z e , and f a i l u r e w i l l then o c c u r . The v e l o c i t y of such a growing c r a c k i s g i v e n by V=AK I n (3.5) where V i s the c r a c k v e l o c i t y . Kj i s the s t r e s s i n t e n s i t y f a c t o r . . A,n a r e c o n s t a n t s . In the case of r a p i d l o a d i n g , a s u b - c r i t i c a l c r a c k s i m p l y does not have enough time t o grow t o the c r i t i c a l s i z e , and hence the specimen can s u p p o r t a h i g h e r l o a d . The t h r e e d i f f e r e n t ways of d e t e r m i n i n g the c o n s t a n t n i n E q u a t i o n 3.5 a r e g i v e n i n F i g u r e 3.1. F i g u r e 3.1(a) r e p r e s e n t s a c o n s t a n t l o a d t e s t , w i t h aQ the a p p l i e d l o a d c a u s i n g f a i l u r e and T the time t o f a i l u r e . F i g u r e 3.1(b) c o r r e s p o n d s t o the d i r e c t o b s e r v a t i o n of the growing c r a c k and F i g u r e 3.1(c) i s the outcome of a c o n s t a n t r a t e of l o a d i n g t e s t . 29 FIGURE 3.1-Three d i f f e r e n t ways of d e t e r m i n i n g the c o n s t a n t "n" Mindess and Nadeau (31) t r i e d t o compare the s l o p e (n) of the l o g V - l o g K j p l o t , o b t a i n e d from c o n t r o l l e d c r a c k growth i n double t o r s i o n t e s t s , w i t h the s l o p e of the logMOR-logu p l o t ( F i g u r e 3 . 1 ( c ) ) , where u i s the d i s p l a c e m e n t r a t e . They found t h a t n was almost the same i n the case of m o r t a r , but t h a t t h e r e was a d i s c r e p a n c y of a f a c t o r of two f o r the cement p a s t e . They a l s o a n a l y z e d the d a t a o b t a i n e d by the o t h e r i n v e s t i g a t o r s i n o r d e r to f i n d the v a l u e of n i n each c a s e . I t was found t h a t n was l a r g e r f o r compression t e s t s than f o r t e n s i o n and f l e x u r a l t e s t s . Zech and Wittmann (32) a t t e m p t e d t o f i n d the d i s t r i b u t i o n f u n c t i o n of the f l e x u r a l s t r e n g t h of mortars a t v a r y i n g s t r a i n r a t e s . A m i s s i l e f a l l i n g on the f l e x u r a l mortar specimens was employed t o g e n e r a t e s t r a i n r a t e s of 30 about 2/sec. The t h e o r e t i c a l a pproach d e v e l o p e d by M i h a s h i and I z u m i ( 3 3 ) , which r e l a t e s the r a t i o of the dynamic t o s t a t i c s t r e n g t h s t o the r a t e s a t which t h e s e s t r e n g t h s were measured was found t o d e s c r i b e the r e s u l t s s a t i s f a c t o r i l y : <vv-<w < 1 / ( , t' ) > (3-6> where f ^ and f g a r e the dynamic and the s t a t i c s t r e n g t h s , r e s p e c t i v e l y , and a g a r e the dynamic and the s t a t i c s t r e s s r a t e s , r e s p e c t i v e l y , and B i s a m a t e r i a l parameter. The parameter B was found t o i n c r e a s e w i t h an i n c r e a s e i n the s t r e n g t h of c o n c r e t e . Thus s t r o n g e r c o n c r e t e s were p r e d i c t e d t o be l e s s s t r a i n r a t e s e n s i t i v e than weaker ones. Zech and Wittmann (32) a l s o found t h a t the v a r i a b i l i t y was not i n f l u e n c e d by the r a t e of l o a d i n g . S u a r i s and Shah(34) performed i n s t r u m e n t e d v a r i a b l e s t r a i n r a t e t e s t s ( s t r a i n r a t e s from 0.67x10 ^ t o 0.27) on m ortar u s i n g a f l e x u r a l t e s t i n g system. They noted t h a t , i n g e n e r a l , the h i g h e r the s t a t i c f l e x u r a l s t r e n g t h , the lower was the r e l a t i v e i n c r e a s e i n the f l e x u r a l s t r e n g t h w i t h i n c r e a s i n g s t r a i n r a t e . They deduced t h a t on a c o m p a r a t i v e b a s i s , the t e n s i l e response was the most s t r a i n r a t e 31 s e n s i t i v e , the c o m p r e s s i v e response the l e a s t s t r a i n r a t e s e n s i t i v e , w i t h the f l e x u r a l response l y i n g somewhere i n between. They t r i e d t o f i n d the v a l u e of the parameter n i n E q u a t i o n 3.5. However, on the b a s i s of the o b s e r v e d d a t a , they found t h a t n d i d not seem t o be a c o n s t a n t ; r a t h e r , i t d e c r e a s e d w i t h i n c r e a s i n g s t r a i n r a t e . Z i e l i n s k i and R e i n h a r d t (35) and Z i e l i n s k i (36) used the s p l i t Hopkinson bar t e c h n i q u e i n o r d e r t o i n v e s t i g a t e the t e n s i l e s t r e s s - s t r a i n b e h a v i o u r of mortar and c o n c r e t e a t h i g h s t r e s s r a t e s (5000-30000 MPa/sec). They c o n c l u d e d t h a t the remarkable i n c r e a s e i n t-he t e n s i l e s t r e n g t h of c o n c r e t e and mortar a t h i g h s t r e s s r a t e s was due t o the e x t e n s i v e m i c r o c r a c k i n g i n the whole volume of the s t r e s s e d specimen. To support t h i s argument they observed t h a t the u l t i m a t e s t r a i n s a t h i g h e r s t r e s s r a t e s were a l s o h i g h e r . Moreover, the specimens s u b j e c t e d t o h i g h r a t e s of s t r e s s f r a c t u r e d a t more than one p l a c e a l o n g t h e i r l e n g t h s . The d i f f e r e n c e between the impact s t r e n g t h of c o n c r e t e and m o r t a r s was e x p l a i n e d on the b a s i s of the d i r e c t c r a c k a r r e s t i n g a c t i o n of the a g g r e g a t e s . I t was a l s o p o s t u l a t e d t h a t i n the case of v e r y r a p i d l o a d i n g , s i n c e much energy was i n t r o d u c e d i n t o the system i n a s h o r t t i m e , c r a c k s a r e f o r c e d t o d e v e l o p a l o n g the s h o r t e r paths of h i g h e r r e s i s t a n c e , t h r o u g h s t r o n g e r m a t r i x zones and a l s o t h r o u g h some a g g r e g a t e s . A l f o r d (37) s t u d i e d the b e h a v i o u r of a c r a c k , i . e . , i t s v e l o c i t y and i t s p a t h , as the c r a c k approaches a d i s t u r b a n c e 32 (e . g . an aggregate or a v o i d ) . An 'around the aggregate mode' and a 'through the a g g r e g a t e mode' were r e c o g n i z e d f o r c r a c k p r o p a g a t i o n . The main f a c t o r s d e t e r m i n i n g the mode were found t o be the a n g u l a r i t y and the toughness of the a g g r e g a t e s . H i g h speed photography r e s u l t s showed t h a t the o b s e r v e d c r a c k v e l o c i t y was much l e s s than the t h e o r e t i c a l R a y l e i g h wave v e l o c i t y . As a r e s u l t , the dynamic v a l u e of the c r i t i c a l s t r a i n energy r e l e a s e r a t e (G^) was found t o be a p p r o x i m a t e l y the same as the s t a t i c v a l u e ( G ). 3.4 VARIABLE STRAIN RATE TESTS ON FIBRE REINFORCED CONCRETE The poor impact r e s i s t a n c e of p l a i n c o n c r e t e has l e d t o the i n c o r p o r a t i o n of f i b r o u s s u b s t a n c e s i n t o the b a s i c b r i t t l e c e m e n t i t i o u s m a t r i x t o enhance i t s impact performance. I n i t i a l l y , t h e s e f i b r e s were thought t o i n c r e a s e the s t r e n g t h of the c o m p o s i t e , but i t was soon r e a l i z e d t h a t the major advantage i n a d d i n g t h e s e f i b r e s was not i n the enhanced s t r e n g t h , but i n enhanced d u c t i l i t y . T h i s enhanced d u c t i l i t y of the composite may be p a r t i c u l a r l y u s e f u l i n s i t u a t i o n s where a c c i d e n t a l impacts can occur and the energy a b s o r p t i o n c a p a c i t y of the s t r u c t u r e must be c o n s i d e r e d i n d e s i g n . Thus, v a r i o u s i n v e s t i g a t o r s s t a r t e d s t u d y i n g the composite b e h a v i o u r of f i b r o u s c o n c r e t e a t v a r i a b l e s t r a i n r a t e s . Shah and Rangan (38) c o n d u c t e d s t a t i c t e s t s on f i b r e r e i n f o r c e d c o n c r e t e specimens i n t e n s i o n , f l e x u r e , and c o m p r e s s i o n and c o n c l u d e d t h a t t h e b a s i c advantage d e r i v e d 33 from the f i b r e s o c c u r e d o n l y a f t e r the m a t r i x c r a c k e d . Bond s t r e n g t h of f i b r e s was found t o be a v e r y i m p o r t a n t f a c t o r . Naaman and Shah (39) c a r r i e d out p u l l - o u t t e s t s on s t e e l f i b r e r e i n f o r c e d c o n c r e t e i n o r d e r t o s t u d y the e f f e c t of f i b r e o r i e n t a t i o n and f i b r e g r o u p i n g on the peak p u l l - o u t l o a d , t h e u l t i m a t e l o a d and the p u l l - o u t work. They found t h a t the mechanism of f i b r e p u l l - o u t i n the case of s t r a i g h t f i b r e s i s v e r y d i f f e r e n t from the mechanism i n the case of i n c l i n e d f i b r e s . The performance of a group of f i b r e s p u l l i n g out of a m a t r i x c o u l d not always be e s t i m a t e d by knowing the performance of a s i n g l e f i b r e . T h i s was because of the i n c r e a s e d s p a l l i n g and d i s r u p t i o n of the m a t r i x w i t h an i n c r e a s e i n the number of f i b r e s . Thus the e f f i c i e n c y of a group of f i b r e s was l e s s than t h a t of a s i n g l e f i b r e . They f i n a l l y c o n c l u d e d t h a t t h i s e f f e c t s h o u l d be more pronounced i n the case of i n c l i n e d f i b r e s because more m a t r i x c r u s h i n g i s i n v o l v e d i n t h i s c a s e . Kobayashi and Cho (40) c o n s i d e r e d the f l e x u r a l b e h a v i o u r of p o l y e t h y l e n e f i b r e r e i n f o r c e d c o n c r e t e and found the f i b r e s t o be u s e f u l i n i m p r o v i n g the toughness of the c o m p o s i t e . The s t r a i n r a t e s e n s i t i v i t y of the composite was a l s o measured by t h e a u t h o r s . Bhargava and Rehnstrom (41) t e s t e d p l a i n c o n c r e t e , polymer cement c o n c r e t e and p o l y p r o p y l e n e f i b r e r e i n f o r c e d c o n c r e t e under h i g h r a t e s of c o m p r e s s i v e l o a d i n g . They made use of t h e p r i n c i p l e t h a t f o r v i s c o e l a s t i c m a t e r i a l s t h e r e i s an optimum s t r e s s t r a n s m i s s i o n l i m i t . I f the m a t e r i a l i s 34 s u b j e c t e d t o s t r e s s above t h i s l i m i t , the e x c e s s energy i s d i s s i p a t e d i n f r a c t u r e and f a i l u r e , and r e s u l t s i n no i n c r e a s e i n the t r a n s m i t t e d s t r e s s . They found t h a t polymer cement c o n c r e t e had 30-35% h i g h e r dynamic s t r e n g t h s than p l a i n c o n c r e t e . For f i b r e r e i n f o r c e d c o n c r e t e the i n c r e a s e was about 15%. Ramakrishnan e t a l (42) p r e s e n t e d a c o m p a r a t i v e e v a l u a t i o n of two ty p e s of f i b r e s . The performance of s t r a i g h t 25mm l o n g s t e e l f i b r e s was compared t o 50mm l o n g s t e e l f i b r e s w i t h deformed ends. The f i b r e s , h e l d t o g e t h e r by a water s o l u b l e g l u e b e f o r e m i x i n g , were found t o be f r e e from t a n g l i n g or b a l l i n g . Hooked f i b r e s were a l s o found t o produce h i g h e r f l e x u r a l s t r e n g t h , h i g h e r l o a d c a r r y i n g c a p a c i t y , h i g h e r d u c t i l i t y and h i g h e r impact s t r e n g t h . Jamrozy and Swamy(43) d e s c r i b e d t h e i r e x p e r i e n c e w i t h the a p p l i c a t i o n of s t e e l f i b r e r e i n f o r c e d c o n c r e t e i n b u i l d i n g machine f o u n d a t i o n s t h a t were s u b j e c t e d t o impact l o a d i n g . They d e s i g n e d a f r e e f a l l drop weight impact t e s t e r c a p a b l e of r e p e a t e d l y d r o p p i n g a mass on a s t a n d a r d specimen u n t i l a p r e d e t e r m i n e d f a i l u r e c r i t e r i o n was reached. F i b r e s i n g e n e r a l were h e l p f u l i n i n c r e a s i n g the impact performance of c o n c r e t e . The f i b r e volume, f i b r e geometry and f i b r e s i z e were a l l found t o i n f l u e n c e the impact s t r e n g t h . They a l s o found t h a t f o r a g i v e n f i b r e geometry and s i z e , t h e r e e x i s t e d an optimum f i b r e volume, which gave the maximum e f f i c i e n c y . Some a c t u a l f o u n d a t i o n s were i n s t r u m e n t e d , and i t was found t h a t the use of f i b r e r e i n f o r c e d c o n c r e t e was 35 r e a l l y u s e f u l . They a l s o c o n c l u d e d , however, t h a t f i b r e s cannot r e p l a c e c o n v e n t i o n a l r e i n f o r c e m e n t . Radomsky ( 4 4 ) d i s c u s s e d the c o n s t r u c t i o n and the use of a r o t a t i n g impact machine t o i n v e s t i g a t e the impact p r o p e r t i e s of c o n c r e t e r e i n f o r c e d w i t h s t r a i g h t round s t e e l f i b r e s . He c o n c l u d e d t h a t the impact r e s i s t a n c e of t h e s e c o m p o s i t e s i n c r e a s e d w i t h i n c r e a s i n g v e l o c i t y of i mpact, and a l s o w i t h the a n g l e of impact w i t h r e s p e c t t o the f i b r e d i r e c t i o n . O ne-dimensional o r i e n t a t i o n of f i b r e s was found t o g i v e about t w i c e the impact s t r e n g t h of t w o - d i m e n s i o n a l f i b r e o r i e n t a t i o n . A comparison of r o t a t i n g impact machine d a t a w i t h Charpy impact d a t a r e v e a l e d t h a t t h e s e d a t a cannot be compared. T h i s c l e a r l y demonstrates the i n f l u e n c e of the type of machine on the r e s u l t s o b t a i n e d . H i b b e r t (7 ) and H i b b e r t and Hannant ( 4 5 ) used an i n s t r u m e n t e d Charpy impact machine t o study the b e h a v i o u r of f i b r e r e i n f o r c e d c o n c r e t e under impact l o a d i n g . They c a l c u l a t e d the t o t a l energy l o s t by the pendulum from the l o a d v s . time p l o t and a l s o i n d e p e n d e n t l y from the r e s i d u a l pendulum swing. These two v a l u e s were found t o be i n agreement. They a l s o a t t e m p t e d t o c a l c u l a t e t h e energy l o s s e s d u r i n g impact. The k i n e t i c energy of t h e broken h a l v e s of the specimen was d e t e r m i n e d by a l l o w i n g the specimen h o l d e r s t o r o t a t e a f t e r f r a c t u r e a g a i n s t a s p r i n g and r a t c h e t system. On the b a s i s of t h e i r r e s u l t s , they c o n c l u d e d t h a t f o r f i b r e r e i n f o r c e d m a t e r i a l s , the energy absorbed a f t e r the m a t r i x had c r a c k e d was not s u b s t a n t i a l l y 36 d i f f e r e n t under slow f l e x u r e than t h a t o b t a i n e d under impact c o n d i t i o n s . Thus s t r a i n r a t e , t hey c o n c l u d e d , had no e f f e c t on f i b r e - m a t r i x bond p r o p e r t i e s . The m a t r i x f a i l u r e s t r a i n was a l s o found not t o be s e n s i t i v e t o s t r a i n r a t e . These f i n d i n g s , when put t o g e t h e r , i n d i c a t e d t h a t the energy a b s o r b i n g p r o p e r t i e s of f i b r e r e i n f o r c e d c o n c r e t e under impact c o n d i t i o n s c o u l d a l s o be r e a s o n a b l y e s t i m a t e d by p e r f o r m i n g c o n v e n t i o n a l s t a t i c t e s t s and by measuring the a r e a under the l o a d v s . d e f l e c t i o n c u r v e s . The a u t h o r s used a v a r i e t y of s t e e l and p o l y p r o p y l e n e f i b r e s . Amongst the s t e e l f i b r e s , the crimped f i b r e s and the hooked end f i b r e s were found t o be the b e s t . P o l y p r o p y l e n e was not found t o be as e f f e c t i v e as the s t e e l f i b r e s . Gokoz and Naaman (46) c a r r i e d out p u l l - o u t t e s t s on s t e e l , g l a s s and p o l y p r o p y l e n e f i b r e s a t v a r i o u s r a t e s of l o a d i n g from a p o r t l a n d cement mortar m a t r i x . The e n t i r e p r o c e s s of p u l l i n g out i n the case of s t e e l f i b r e s was m o d e l l e d as c o m p r i s i n g a f i r s t peak d e n o t i n g a c o m b i n a t i o n of bond f a i l u r e and f r i c t i o n , a second peak which was o n l y f r i c t i o n dependent, and a f i n a l peak c o r r e s p o n d i n g t o f i n a l t i l t i n g of the specimen due t o the uneven p u l l out r e s i s t a n c e of d i f f e r e n t f i b r e s . S t e e l f i b r e s a t a l l s t r a i n r a t e s were found t o p u l l - o u t , w h i l e the g l a s s f i b r e s were found t o break. W i t h an i n c r e a s e i n the s t r a i n r a t e , the p o l y p r o p y l e n e f i b r e s had an i n c r e a s i n g p e r c e n t a g e of f i b r e s b e i n g p u l l e d o u t . For a l l of the f i b r e s t e s t e d , no s u b s t a n t i a l i n c r e a s e i n the f i r s t peak l o a d w i t h i n c r e a s i n g 37 s t r a i n r a t e was o b s e r v e d . The same was t r u e f o r the second peak. On the energy s i d e , s t e e l and g l a s s f i b r e s d i d not show any change i n the p u l l - o u t energy w i t h c h a n g i n g s t r a i n r a t e . On the o t h e r hand p o l y p r o p y l e n e f i b r e s showed a d r a m a t i c i n c r e a s e i n the p u l l - o u t energy w i t h an i n c r e a s e i n s t r a i n r a t e . Knab and C l i f t o n (47) s t u d i e d the c u m u l a t i v e damage of s t e e l f i b r e r e i n f o r c e d s l a b s s u b j e c t e d t o r e p e a t e d impact. The c r a t e r depth measured r i g h t under the p o i n t of impact was found t o be a good i n d i c a t o r of the c u m u l a t i v e damage. The a d d i t i o n of s t e e l f i b r e s was found t o i n c r e a s e the t o t a l number of blows t o f a i l u r e c o n s i d e r a b l y . S u a r i s and Shah(34) compared the performance of p l a i n c o n c r e t e and p l a i n mortar w i t h t h e i r s t e e l , g l a s s and p o l y p r o p y l e n e f i b r e r e i n f o r c e d c o u n t e r p a r t s . They found t h a t the f l e x u r a l s t r e n g t h (MOR) of both s t e e l and g l a s s f i b r e r e i n f o r c e d m o r t a r s was more s t r a i n r a t e s e n s i t i v e than t h a t of the mortar m a t r i x i t s e l f . P o l y p r o p y l e n e f i b r e r e i n f o r c e d m o r t a r , on the c o n t r a r y , was a p p a r e n t l y not s t r a i n r a t e s e n s i t i v e . The energy a b s o r p t i o n v a l u e s of f i b r e r e i n f o r c e d m ortar w i t h v a r i o u s f i b r e s , s u b j e c t e d t o impact, were found t o be 7 t o 100 t i m e s l a r g e r than those of the u n r e i n f o r c e d m a t r i x . Naaman and Gopalaratnam (48) a l s o s t u d i e d the s t r a i n r a t e s e n s i t i v i t y of s t e e l f i b r e r e i n f o r c e d m o r t a r . They c o n c l u d e d t h a t an i n c r e a s e i n the a s p e c t r a t i o and f i b r e volume, i n g e n e r a l , i n c r e a s e d t h e s t r a i n r a t e s e n s i t i v i t y . 38 The i n c r e a s e i n the composi t e f l e x u r a l s t r e n g t h and energy absorbed w i t h i n c r e a s e d l o a d i n g r a t e was a t t r i b u t e d p r i m a r i l y t o the s t r a i n r a t e s e n s i t i v i t y of the m a t r i x and the p u l l - o u t r e s i s t a n c e of the f i b r e s . Gopalaratnam e t a l ( l 5 ) used a m o d i f i e d i n s t r u m e n t e d Charpy machine f o r t e s t i n g cement based c o m p o s i t e s a t h i g h e r r a t e s of l o a d i n g . They o b s e r v e d an i n c r e a s e of about 60% i n the MOR when the s t r a i n r a t e was i n c r e a s e d from 10 ^/sec t o 0.3/sec. The peak s t r a i n s r e c o r d e d showed an i n c r e a s e a t h i g h e r r a t e s of l o a d i n g . The sec a n t modulus was a l s o found t o i n c r e a s e a t h i g h e r r a t e s of l o a d i n g , which was a t t r i b u t e d t o a d e c r e a s e i n the amount of m i c r o c r a c k i n g a t h i g h e r r a t e s of l o a d i n g . H a r r i s e t a l (49) t e s t e d cement/sand mortar beams r e i n f o r c e d w i t h s h o r t randomly d i s t r i b u t e d f i b r e s of g l a s s , h i g h carbon s t e e l , and m i l d s t e e l i n ben d i n g , and de t e r m i n e d the v a l u e of the work of f r a c t u r e ( 7 ^ ) , and the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r ( K c ) . The c r i t i c a l s t r e s s i n t e n s i t y f a c t o r , which depends upon the peak l o a d o b t a i n e d and the specimen geometry was found t o i n c r e a s e by a f a c t o r of two. The work of f r a c t u r e , on the o t h e r hand, which c o n s i d e r s the e n t i r e l o a d v s . d e f l e c t i o n p l o t , was found t o i n c r e a s e by as much as an or d e r of magnitude, when p l a i n c o n c r e t e was compared w i t h f i b r e r e i n f o r c e d c o n c r e t e . Thus, on the b a s i s of the l i t e r a t u r e s u r v e y , the f o l l o w i n g c o n c l u s i o n s may be made: 39 (a) R e s u l t s o b t a i n e d by the v a r i o u s i n v e s t i g a t o r s a r e o f t e n c o n t r a d i c t o r y . For example, H i b b e r t ( 7 ) has found t h a t the s t r a i n r a t e has no e f f e c t on the p r o p e r t i e s of f i b r e r e i n f o r c e d c o n c r e t e ; most o t h e r s f i n d t h a t t h i s i s not so. (b) No g e n e r a l agreement over the phenomena r e s p o n s i b l e f o r s t r a i n r a t e e f f e c t s e x i s t s . (c) No g e n e r a l agreement over the magnitudes of the obse r v e d e f f e c t s e x i s t s . (d) The e f f e c t s seem t o depend on the type of t e s t and the type of i n t e r p r e t a t i o n . Thus, the n a t u r e of the impact b e h a v i o u r of even a c e m e n t i t i o u s m a t r i x i s not w e l l u n d e r s t o o d , l e t a l o n e the impact b e h a v i o u r of f r c . 4. EXPERIMENTAL PROCEDURES 4.1 INTRODUCTION D e s t r u c t i v e t e s t s on c o n c r e t e have been i n use f o r many y e a r s . However, s t r e n g t h i s not a fundamental m a t e r i a l p r o p e r t y ; i t depends upon how i t i s measured. The m e c h a n i c a l p r o p e r t i e s of c o n c r e t e have been found t o depend upon, amongst o t h e r t h i n g s , the geometry of the specimen, the s t i f f n e s s and type of t e s t i n g machine, l o a d i n g c o n f i g u r a t i o n , m o i s t u r e c o n t e n t , t e m p e r a t u r e , and the r a t e of l o a d i n g . The e f f e c t of the r a t e of l o a d i n g , which was p r o b a b l y f i r s t p o i n t e d out by Abrams(20) i n 1917, has r e c e n t l y become a major a r e a of i n v e s t i g a t i o n . Many i n v e s t i g a t i o n s have r e c e n t l y been c a r r i e d out t o study the r a t e of l o a d i n g , or the s t r e s s r a t e e f f e c t on the p r o p e r t i e s of c o n c r e t e . U n f o r t u n a t e l y , w h i l e f o r the s t a t i c p r o p e r t i e s t h e r e a r e a number of s t a n d a r d t e s t methods, no such s t a n d a r d t e s t method e x i s t s f o r c o n c r e t e under h i g h r a t e s of l o a d i n g , or under dynamic c o n d i t i o n s . H i g h s t r e s s r a t e t e s t i n g on any m a t e r i a l i s based on suddenly i m p a r t i n g a l a r g e amount of energy t o the t e s t specimen. I n most impact machines p o t e n t i a l energy i s s t o r e d i n a s p r i n g , a pendulum, a hammer, or a s i m p l e b a l l , and t h i s s t o r e d energy i s t r a n s f e r r e d t o the specimen over an e x t r e m e l y s h o r t i n t e r v a l of t i m e . The specimen deforms i n response t o t h i s energy t r a n s f e r , l e a d i n g t o the development of h i g h s t r e s s e s i n the specimen over a v e r y s h o r t l e n g t h of 4 0 41 t i m e . B u t , there i s a l i m i t to the amount of energy any m a t e r i a l can absorb as s t r a i n energy b e f o r e f a i l i n g . I f the e x t e r n a l l y a v a i l a b l e energy exceeds t h i s l i m i t , f a i l u r e w i l l r e s u l t . V a r i o u s t e c h n i q u e s have been used to t e s t c o n c r e t e at h i g h s t r e s s r a t e s . The most common a r e : (a) F r e e f a l l drop weight t e s t s ; (b) Work of f r a c t u r e t e s t s ; (c) E x p l o s i v e t e s t s ; (d) H o p k i n s o n ' s S p l i t Bar t e s t ; (e) C h a r p y / I z o d t e s t s ; and (f) F r a c t u r e mechanics t e s t s . In a l l of the above t e s t methods, there i s an attempt to q u a n t i f y the energy r e q u i r e d to ach i eve f a i l u r e . However, because both the f a i l u r e c r i t e r i a and the p h y s i c a l p r o c e s s e s by which f a i l u r e o c c u r s v a r y from t e s t to t e s t , comparisons between any of these t e s t s i s v e r y d i f f i c u l t . In the Charpy t e s t s , a pendulum bob i s used to s t o r e p o t e n t i a l energy , which i s suddenly t r a n s f e r r e d to the specimen when the pendulum i s r e l e a s e d . H i s t o r i c a l l y , the Charpy machine was deve loped p r i m a r i l y f or t e s t i n g m e t a l s . Thus , when t h i s t e s t method i s used for c o n c r e t e , m o d i f i c a t i o n s have to be made. F i r s t , the specimen h o l d e r s have to be m o d i f i e d i n o r d e r to h o l d the much b i g g e r c o n c r e t e spec imens . Another m o d i f i c a t i o n i s i n the form of s t r a i n gauges mounted i n the s t r i k i n g end of the pendulum (7 ) , in the specimen s u p p o r t s , and p o s s i b l y on the specimen 42 i t s e l f . The m o n i t o r i n g of the l o a d d e v e l o p e d i n the i n s t r u m e n t e d pendulum bob p e r m i t s an approach towards the q u a n t i f i c a t i o n of e n e r g i e s . The l o a d v s . time c u r v e thus o b t a i n e d a l s o a l l o w s a c a l c u l a t i o n of the s t r e s s r a t e a c h i e v e d i n a t e s t . ACI Committee 544 (50) has recommended an impact t e s t i n which a 4.5kg s t e e l b a l l i s dropped r e p e a t e d l y t h rough a s t a n d a r d h e i g h t of 457mm (18 i n c h e s ) on a 152.4mm diameter by 63.5mm t h i c k c o n c r e t e t e s t specimen. The number of blows t o a p r e d e t e r m i n e d f a i l u r e c r i t e r i o n i s noted. The number of blows can a l s o be c o n v e r t e d t o an energy v a l u e by m u l t i p l y i n g the energy g i v e n t o the specimen w i t h each blow (20.2 N-m, i n t h i s c ase) by t h e t o t a l number of blows t o f a i l u r e . There a re s e v e r a l major problems w i t h t h i s type of t e s t i n g . The s e l e c t i o n . of the f a i l u r e c r i t e r i o n i s c o m p l e t e l y a r b i t r a r y , and not a l l of the energy goes i n t o the specimen, b e i n g d i s s i p a t e d i n the t e s t d e v i c e i t s e l f . The Hopkinson's s p l i t bar t e c h n i q u e i s o f t e n used as a means of g e n e r a t i n g h i g h s t r e s s r a t e l o a d i n g . B a s i c a l l y , i t c o n s i s t s of two e l a s t i c b a rs . between which the specimen i s sandwiched. An i n c i d e n t s t r e s s p u l s e i s g e n e r a t e d i n the f i r s t e l a s t i c bar and the p u l s e t r a n s m i t t e d t h rough the specimen i s measured a t the second e l a s t i c b a r . Thus, the f o r c e t h a t a c t e d on the specimen can be e v a l u a t e d . T h i s t e c h n i q u e can be used f o r u n i a x i a l c o m p r e s s i v e l o a d i n g (51,52) or u n i a x i a l t e n s i l e l o a d i n g ( 3 6 ) ; s t r e s s r a t e s up t o about 60 MPa/ms can be a c h i e v e d . 43 The work of f r a c t u r e t e s t s c o n d u c t e d u s i n g a c o n v e n t i o n a l s t a t i c machine i n v o l v e s t r e s s i n g a f l e x u r a l specimen a t c o n v e n t i o n a l r a t e s of l o a d i n g and m o n i t o r i n g the l o a d and the l o a d p o i n t d e f l e c t i o n . The energy expended i n c r e a t i n g two new f r a c t u r e s u r f a c e s ( E ^ ) , which i s e q u a l t o the a r e a under the l o a d v s . d e f l e c t i o n p l o t , can then be used t o determine the work of f r a c t u r e 7^, ( 4 . 1 ) where A i s the a r e a of c r o s s s e c t i o n of the specimen. The r e s u l t s o b t a i n e d from such work of f r a c t u r e t e s t s may be used t o p r e d i c t the energy a b s o r p t i o n c a p a b i l i t i e s i n dynamic c o n d i t i o n s o n l y i f the s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e can be i g n o r e d , a v e r y d o u b t f u l a s s u m p t i o n . N e v e r t h e l e s s , such t e s t s may, a t b e s t , p r e d i c t the lower l i m i t on energy a b s o r p t i o n v a l u e s . E x p l o s i v e t e s t s a r e sometimes used t o g e nerate u n i f o r m l y d i s t r i b u t e d dynamic l o a d i n g . The problems o f t e n encountered i n such t e s t s i n c l u d e the u n c e r t a i n t y i n the q u a n t i f i c a t i o n of energy, l o a d s , and the specimen response. F r a c t u r e mechanics has been used as an a n a l y t i c a l t o o l t o p r e d i c t the b e h a v i o u r of c o n c r e t e under h i g h r a t e s of l o a d i n g . However, the s u c c e s s of such a t o o l i s l i m i t e d s i n c e t h e r e i s no u n i v e r s a l agreement over the b a s i c f r a c t u r e mechanics m a t e r i a l c o n s t a n t s , and the c o n s t a n t s 44 t h e m s e l v e s a r e s t r e s s r a t e dependent. In t h i s s t u d y , an i n s t r u m e n t e d drop weight impact machine was used i n o r d e r t o t e s t c o n c r e t e beams a t h i g h s t r e s s r a t e s . T h i s type of machine was c o n s i d e r e d t o be a s u i t a b l e means of t e s t i n g l a r g e specimens of c o n c r e t e under f l e x u r a l impact l o a d i n g . The mass of the hammer was chosen t o be about e i g h t t i m e s the mass of the impacted beam, i n o r d e r t o induce specimen f a i l u r e i n a s i n g l e blow of the hammer. C o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams, which due t o the s t e e l a r e much tougher than p l a i n c o n c r e t e beams c o u l d a l s o be t e s t e d w i t h the same hammer w i t h o u t h a v i n g t o c a r r y out any m o d i f i c a t i o n s t o the machine. 45 4.2 SPECIMEN PREPARATION For the e x p e r i m e n t a l work, p l a i n , f i b r e r e i n f o r c e d , and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams were c a s t . Three d i f f e r e n t s i z e s were chosen; ( l e n g t h x w i d t h x depth) 1525mmx150mmx150mm, 1400mmx1OOmmx125mm, and 1200mmx1OOmmx125mm. The 1500mmx150mmx150mm beams were found t o be t o o heavy and awkward t o h a n d l e . The 1400mmx1OOmmx125mm beams were found t o have a l a r g e segment of the beam o v e r h a n g i n g the s u p p o r t s , which were o n l y 960mm a p a r t . F i n a l l y , most of the beams were made 1200mm x 100mm x 125mm i n s i z e ; a s i z e not d i f f i c u l t t o ' handle and not too l o n g . The cement used was CSA Type 10 normal p o r t l a n d cement ( e q u i v a l e n t t o ASTM type 1 ) . The maximum s i z e of the pea g r a v e l a g g r e g a t e was 10mm. A summary of the specimens p r e p a r e d has been p r e s e n t e d i n T a b l e 4.1. 4.2.1 NORMAL STRENGTH PLAIN CONCRETE BEAMS For the p r o d u c t i o n of normal s t r e n g t h p l a i n c o n c r e t e beams the f o l l o w i n g mix p r o p o r t i o n s , by w e i g h t , were used: w a t e r : c e m e n t : f i n e a g g r e g a t e : c o a r s e a g g r e g a t e = 0.5:1.0:2.0:3.5. In a d d i t i o n , 9.45ml of s u p e r p l a s t i c i z e r (Mighty 150) per kg of cement were added t o the mix. A pan type mixer (0.170m 3 c a p a c i t y ) was used f o r m i x i n g the c o n c r e t e . A l l of the a g g r e g a t e s were p l a c e d i n the mixer and i t was t u r n e d on f o r about one minute. Next the cement, the w a t e r , and the a d d i t i v e s were added. These were then Table 4.1 Types fif Specimens BEAM TYPE Quantity Cast Mix Proportions1 S.plasticizer1 Fibre (%) Strength'(MPa) Designation Paste 10 0.35:1.0 - - - P Normal Strength Plain Concrete 35 0.50:1.0:0.0:2.0:3.5 9.45ml - 42 NS High Strength Plain Concrete 35 0.33:0.86:0.14:1.57:1.04 14.2ml • - 82 HS Normal Strength Steel Fibre Reinforced Concrete 20 . 0.50:1.0:0.0:2.0:3.5 14.2ml 1.5 50 NSSFRC High Strength Steel Fibre Reinforced Concrete 20 0.33:0.86:0.14:1.57:1.04 14.2ml 1.5 82 HSSFRC Normal Strength Polypropylene Fibre Reinforced Concrete 20 0.50:1.0:0.0:2.0:3.5 14.2ml 0.5 49 NSPFRC High Strength Polypropylene Fibre Reinforced Concrete 20 0.33:0.86:0.14:1.57:1.04 14.2ml 0.5 82 HSPFRC Conventionally Reinforced Normal 35 0.40:1.0:0.0:2.0:3.5 0.33:1.0:0.0:2.0:3.5 9.45ml - 49 CRNSC Strength Concrete with Deformed Reinforcing Bars Conventionally 35 0.33:0.86:0.14:1.57:1.04 14.2ml - 82 CRHSC Reinforced High Strength Concrete with Deformed Reinforcing Bars Conventionally 20 0.5:1.0:0.0:2.0:3.5 9.45ml - 42 CRNSC-S Reinforced Normal 0.4:1.0:0.0:2.0:3.5 Strength Concrete with Smooth Reinforcing Bars Conventionally 20 0.4:1.0:0.0:2.0:3.5 9.45ml - 49 CRNSC-ST Reinforced Normal Strength Concrete with Deformed Rebars and Stirrups Conventionally 20 0.40:1.0:0.0:2.0:3.5 14.2ml 0.5 49 CRNSC-P Reinforced Normal Strength Concrete with Polypropylene Fibres Conventionally 20 0.33:0.86:0.14:1.57:1.04 14.2ml 0.5 49 CRHSC-P Reinforced High Strength Concrete with Polypropylene Fibres Normal Strength 20 0.5:1.0:0.0:2.0:3.5 9.45ml - 42 NS-NT Plain with Notch High Strength Plain 20 0.33:0.86:0.14:1.57;1.04 14.2ml - 82 HS-NT with Notch Normal Strength 20 0.5:1.0:0.0:2.0:3.5 14.2ml Plain Concrete with Polypropylene Fibres, Notched 1 Water:CemenfMicrosilica:Fine Aggregate:Coarse Aggregate (by weight). 1 Per kilogram of cement. ' Equivalent Cube Strength obtained by using 125mmxl25mm plates. 49 mixed f o r about 10 m i n u t e s . Once the m i x i n g was completed, the c o n c r e t e was s h o v e l l e d i n t o o i l e d wooden forms i n a s i n g l e l a y e r , and was r o u g h l y compacted w i t h a s h o v e l . P r o p e r compaction was then a c h i e v e d u s i n g an e l e c t r i c immersion v i b r a t o r . Each beam was v i b r a t e d f o r about f i f t e e n seconds a t s i x d i f f e r e n t l o c a t i o n s a l o n g i t s l e n g t h . The forms were then c o v e r e d w i t h p o l y e t h y l e n e s h e e t s . The beams remained i n the forms f o r about 24 h o u r s . At the end of t h i s p e r i o d , the beams were demoulded and t r a n s f e r r e d t o a moi s t room u n t i l t e s t e d . The t e s t ages ranged from about one month t o about one y e a r . On the day of the t e s t i n g , the beams were removed from the m o i s t room and the a c c e l e r o m e t e r l o c a t i o n s were marked. Those marked s p o t s were s u r f a c e d r i e d w i t h a blow d r i e r and c l e a n e d w i t h a w i r e b r u s h . The mounting bases of the a c c e l e r o m e t e r s were then c a r e f u l l y f a s t e n e d t o the beam u s i n g an epoxy a d h e s i v e . The epoxy was a l l o w e d t o dry f o r a minimum p e r i o d of about 15 mi n u t e s , a t the end of which the beams were ready f o r t e s t i n g . 4.2.2 HIGH STRENGTH PLAIN CONCRETE BEAMS H i g h s t r e n g t h p l a i n c o n c r e t e beams were made i n v e r y much the same way as were the normal s t r e n g t h p l a i n c o n c r e t e beams. For the p r o d u c t i o n of h i g h s t r e n g t h c o n c r e t e , 16% m i c r o s i l i c a 1 by weight of the cement was a l s o added, the 1 Produced by Elkem C h e m i c a l s , I n c . , P i t t s b u r g h , P e n n s y l v a n i a . 50 w a t e r / ( c e m e n t + m i c r o s i l i c a ) r a t i o was reduced t o 0.33, and a t r i p l e dose of the s u p e r p l a s t i c i z e r was used. The mix p r o p o r t i o n s were t h e n : w a t e r : c e m e n t : m i c r o s i l i c a : f i n e a g g r e g a t e : c o a r s e a g g r e g a t e = 0.33:0.86:0.14:1.57:1.04 The c a s t i n g and s t o r a g e of the h i g h s t r e n g t h beams was c a r r i e d out i n the same way as f o r the normal s t r e n g t h beams. 4.2.3 FIBRE REINFORCED CONCRETE BEAMS F i b r e r e i n f o r c e d c o n c r e t e beams were made by i n c o r p o r a t i n g s t e e l or p o l y p r o p y l e n e f i b r e s i n t o b o th the normal s t r e n g t h and h i g h s t r e n g t h c o n c r e t e mixes. To produce s t e e l f i b r e r e i n f o r c e d c o n c r e t e , 1.5% by volume of s t e e l f i b r e s were added. These f i b r e s were 50mm l o n g and had t h e i r ends h o o k e d 2 . The f i b r e s were o r i g i n a l l y h e l d t o g e t h e r by a water s o l u b l e s i z i n g , and s p e c i a l c a r e was e x e r c i s e d i n ad d i n g the f i b r e s t o the mix, t o m i n i m i z e b a l l i n g and nonuniform d i s t r i b u t i o n of the f i b r e s t h r o u g h out the body of t he beam. P o l y p r o p y l e n e f i b r e r e i n f o r c e d c o n c r e t e c o n t a i n e d 0.5% by weight of 37mm l o n g f i b r i l l a t e d p o l y p r o p y l e n e f i b r e s 3 . The f i b r e s had a v e r y h i g h water demand and i t pro v e d i m p o s s i b l e , w i t h the t e c h n i q u e d e s c r i b e d above, t o add a h i g h e r volume of f i b r i l l a t e d p o l y p r o p y l e n e f i b r e s t o the 2 Produced by Be k a e r t N.V., Bel g i u m . 3 Produced by F o r t a F i b r e s , I n c . , Grove C i t y , P e n n s y l v a n i a . 51 mix. 4.2.4 CONVENTIONALLY REINFORCED CONCRETE BEAMS The c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams were c a s t w i t h e i t h e r deformed s t e e l r e i n f o r c i n g b a r s or smooth r e i n f o r c i n g b a r s . In the case of the deformed r e i n f o r c i n g b a r s , two 9.52mm ( c r o s s - s e c t i o n a l a r e a = 2x71mm 2) nominal d i a m e t e r deformed s t e e l b a r s were p l a c e d i n the forms so as t o p r o v i d e a c l e a r c o v e r of 25mm from the bottom and the s i d e s of the forms t o the b a r s . The smooth r e i n f o r c i n g b a r s used were a l s o 9.52mm i n dia m e t e r and were p l a c e d i n the forms i n the same way as the deformed b a r s . Some of the r e i n f o r c e d c o n c r e t e beams were p r o v i d e d w i t h 5mm dia m e t e r s t i r r u p s spaced 100mm a p a r t . For the r e i n f o r c e d c o n c r e t e beams, both normal s t r e n g t h and h i g h s t r e n g t h beams, and beams c o n t a i n i n g f i b r e s , were produced, as shown i n T a b l e 4.1. 4.2.5 NOTCHED BEAMS To study the e f f e c t of not c h e s on the dynamic performance of c o n c r e t e , s e v e r a l of the beams made w i t h both normal s t r e n g t h and h i g h s t r e n g t h mixes were no t c h e d . The notches were c u t a t midspan u s i n g a c i r c u l a r diamond c u t t i n g saw; they were 65 t o 70mm deep. The a c t u a l n o t c h depths i n the i n d i v i d u a l beams were measured j u s t b e f o r e the t e s t and were used i n the a n a l y s i s . 53 4.3 TESTING PROGRAM The b a s i c aim of the t e s t i n g program was t o d e v e l o p a v a l i d t e s t i n g t e c h n i q u e t o t e s t c o n c r e t e under impact, and t o i n v e s t i g a t e the e f f e c t of s t r e s s r a t e on the performance of p l a i n , f i b r e r e i n f o r c e d , and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams. The t e s t s c a r r i e d out may be b r o a d l y c l a s s i f i e d i n t o two c a t e g o r i e s : s t a t i c and dynamic. A l l of the t e s t s , s t a t i c or dynamic, were conducted on beams i n a t h r e e p o i n t bending c o n f i g u r a t i o n u s i n g a 960mm span. 4.3.1 STATIC TESTING 4.3.1.1 F l e x u r a l t e s t s on beams The s t a t i c f l e x u r a l t e s t s were c a r r i e d out on a u n i v e r s a l t e s t i n g machine." The beams were s i m p l y s u p p o r t e d on r o l l e r s on a span of 960mm, and the l o a d was a p p l i e d a t midspan. The machine was equipped w i t h a l o a d c e l l c a p a b l e of measuring l o a d s up t o 90 kN. The machine was a l s o e q u i p p e d w i t h an x-y p l o t t e r , w i t h the y c h a n n e l of the p l o t t e r c o n n e c t e d t o the l o a d c e l l and the x c h a n n e l c o n n e c t e d t o a l i n e a r v a r i a b l e d i f f e r e n t i a l t r a n s d u c e r (LVDT) r e a d i n g d e f l e c t i o n s under the l o a d p o i n t . The c r o s s head speed chosen f o r the s t a t i c t e s t i n g was 4.2x10 m/sec. At t h i s r a t e , , i n a t y p i c a l t e s t , i t took about 1 hour t o r e a c h the peak l o a d . Once the l o a d v s . d e f l e c t i o n p l o t s were o b t a i n e d , a p l a n i m e t e r was used t o "B a l d w i n Model GBN, manufactured by Satec Systems, I n c . , USA. 54 measure t h e a r e a under the l o a d v s . d e f l e c t i o n p l o t . T h i s a r e a r e p r e s e n t e d the energy absorbed by the beam. In g e n e r a l , t h r e e specimens of each type were t e s t e d i n t h i s way. 4.3.1.2 Tension t e s t s on r e i n f o r c i n g bars The same u n i v e r s a l t e s t i n g machine was a l s o used t o c a r r y out t e n s i o n t e s t s on both the deformed and smooth r e i n f o r c i n g b a r s used f o r the c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e . A c l i p gauge w i t h an LVDT f i t t e d t o i t was used t o read the s t r a i n over a 50mm gauge l e n g t h . A l o a d v s . di p l a c e m e n t p l o t was o b t a i n e d . The speed of the c r o s s h e a d was m a i n t a i n e d a t about 1mm/minute. The ar e a under the l o a d v s . d i s p l a c e m e n t p l o t t o f a i l u r e was measured w i t h a p l a n i m e t e r . As b e f o r e , t h i s r e p r e s e n t e d the energy r e q u i r e d t o f a i l t he ba r s i n t e n s i o n . The y i e l d s t r e n g t h of the b a r s was found t o be 425 MPa, w h i l e t h e i r u l t i m a t e s t r e n g t h was found t o be 720 MPa. W i t h the u l t i m a t e s t r a i n of 0.12, the energy r e q u i r e d upto f a i l u r e was found t o be 70 MNm/m3 4.3.1.3 S t i f f n e s s t e s t on the rubber pad Some of the dynamic t e s t s were c a r r i e d out w i t h a rubber pad i n between the tup and the beam. T h i s t e c h n i q u e had o r i g i n a l l y been d e v i s e d as a way of e l i m i n a t i n g the i n e r t i a l l o a d i n g e f f e c t s ( 1 6 ) . The B a l d w i n u n i v e r s a l t e s t i n g machine was used f o r t h i s purpose. The l o a d v s . d e f l e c t i o n 55 p l o t f o r the rubber pad i n compression was o b t a i n e d , u s i n g a pad w i t h the di m e n s i o n s of 150mm ( w i d t h ) , 150mm ( b r e a d t h ) , and 50mm ( d e p t h ) . The d e f l e c t i o n s were measured by measuring the movement of the c r o s s head i t s e l f . For such a s o f t m a t e r i a l , t h i s was c o n s i d e r e d t o be a v a l i d t e c h n i q u e f o r d i s p l a c e m e n t measurement. The s t i f f n e s s of the rubber pad was o b t a i n e d by measuring the s l o p e of the l o a d v s . d i s p l a c e m e n t p l o t thus o b t a i n e d . 4.3.1.3 Compressive s t r e n g t h d e t e r m i n a t i o n from broken hal v e s of the beams E q u i v a l e n t cube t e s t s were performed on the h a l v e s of beams broken i n s t a t i c f l e x u r e . Two 125mm x 125mm s t e e l p l a t e s were used on the t o p and the. bottom of the beam l y i n g on i t s 125mm s i d e . Load was a p p l i e d i n a h y d r a u l i c a l l y c o n t r o l l e d t e s t i n g machine u n t i l the c o n c r e t e f a i l e d by c r u s h i n g . 5 6 4.3.2 IMPACT TESTING The impact t e s t i n g was c a r r i e d out u s i n g a drop weight impact machine. The f o l l o w i n g s e c t i o n s p r o v i d e a d e s c r i p t i o n of the machine, the i n s t r u m e n t a t i o n , c a l i b r a t i o n , data a c q u i s i t i o n , and the a n a l y s i s of the t e s t r e s u l t s . 4.3.2.1 The impact t e s t i n g machine a. General principle of a drop weight impact machine A photograph of the ins trumented drop weight impact machine i s shown in F i g u r e 4 .1 ; a d imens ioned sketch i s g iven in F i g u r e 4 .2 . In these types of machines , a hammer w i t h a s u s t a n t i a l mass i s r a i s e d to a c e r t a i n h e i g h t above the specimen. In t h i s p o s i t i o n , the hammer has the p o t e n t i a l energy m^a^h (mass of the hammer x a c c e l e r a t i o n of the hammer under g r a v i t y x h e i g h t to which i t i s r a i s e d ) wi th r e s p e c t to the top s u r f a c e of the spec imen. I f the hammer in t h i s p o s i t i o n i s a l lowed to drop on to the specimen, the p o t e n t i a l energy of the hammer i s c o n v e r t e d to k i n e t i c energy as the hammer f a l l s wi th an a c c e l e r a t i o n a^. (Due to the f r i c t i o n a l f o r c e s in the machine a c t i n g on the hammer, the downward a c c e l e r a t i o n of the hammer i s l e s s than the e a r t h ' s 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 , g ) . J u s t before the hammer s t r i k e s the beam, i t s v e l o c i t y i s g iven by (4.2a) IMPACT HAMMER INSTRUMENTED TUP SPECIMEN SUPPORT F i g u r e 4.1-The Drop Weight Impact T e s t i n g Machine 58 The IMPACT MACHINE F i g u r e 4.2-The Dimensions of the Machine and the Tup At t h i s v e l o c i t y , the hammer has a k i n e t i c energy , 59 2m, (VZa, h ) 2 m,a, h h h (4.2b) When the hammer s t r i k e s the beam, a sudden t r a n s f e r of momentum occurs from the hammer to the beam. As a r e s u l t , the momentum of the hammer d e c r e a s e s . T h i s , in t u r n , r e s u l t s in a l o s s of the hammer k i n e t i c energy , and a c o r r e s p o n d i n g ga in in the beam energy . T h i s t r a n s f e r of energy between the hammer and the beam i s very sudden, and r e s u l t s i n a sudden b u i l d - u p of s t r e s s e s in the beam. In t h i s s t u d y , f i v e channe l s of i n s t r u m e n t a t i o n were p r o v i d e d to monitor the response of the beam to impact . S t r a i n gauges were mounted on the s t r i k i n g end of the hammer ( c a l l e d the ' t u p ' ) and on one of the support a n v i l s , and three a c c e l e r o m e t e r s were mounted a long the l e n g t h of the beam. The s t r a i n gauges in the tup measured the c o n t a c t l o a d between the hammer and the beam, the s t r a i n gauges in the support were des igned to monitor the support r e a c t i o n , and the a c c l e r o m e t e r s were employed to r e c o r d the a c c e l e r a t i o n s in the beam undergoing impact . The time base data were a c q u i r e d by a data a c q u i s i t i o n system based upon an IBM PC. The l ayout of the t e s t i n g se tup i s shown in F i g u r e 4 . 3 . As shown, the hammer i s a t t a c h e d to the h o i s t by means of a H O I S r H A M M E R U T U P - C O L U M N A C C E L E R O M E T E R S I „ B E A L I G H T S O U R C E P H O T O C E L L M A C H I N E C O N T R O L S T R I G G E R I N G P U L S E _ - - ^ H O L E S - M E T A L S T R I P D A T A A C Q U I S I T I O N S Y S T E M P E R S O N A L C O M P U T E R (O/A S T S T E M A C O N T R O L ) • i • i • i . i . i . , .1 ' ' ' 1 > I A • • . . • h« • I i I • i k • • ' • • ' I . . i * • i . • P E D E S T A L F i g u r e 4 .3 -The Layout of the Impact T e s t i n g Se t -up 61 p i n l o c k . The h o i s t can be moved up and down by u s i n g a c h a i n and motor. Once the hammer i s a t the d e s i r e d h e i g h t above the specimen, the pneumatic brakes p r o v i d e d i n the hammer can be a p p l i e d . W i t h t h i s , the hammer "grabs on" t o the columns of the machine. In t h i s p o s i t i o n , the h o i s t can be d e t a c h e d from the hammer. On r e l e a s i n g the pneumatic b r a k e s , t h e hammer f a l l s under g r a v i t y and s t r i k e s the beam, thus g e n e r a t i n g h i g h s t r e s s r a t e l o a d i n g . b. Triggering of the data acquisition system The t r i g g e r i n g of the d a t a a c q u i s i t i o n system, which s h o u l d o c c u r j u s t b e f o r e the hammer h i t s the beam, was a c c o m p l i s h e d by u s i n g a p h o t o c e l l assembly. A s t r i p of m e t a l w i t h h o l e s punched i n i t ran p a r a l l e l t o the columns of the machine as shown i n F i g u r e 4.3. The hammer c a r r i e d a p h o t o c e l l assembly which s l i d a l o n g the me t a l s t r i p as the hammer f e l l upon r e l e a s e . As soon as the p h o t o c e l l assembly reached a h o l e i n the m e t a l s t r i p , the beam of l i g h t f e l l on the p h o t o c e l l t h r ough the h o l e ( F i g u r e 4.4), which t r i g g e r e d the d a t a a c q u i s i t i o n system. c. The tup As t h e t u p ( F i g u r e 4.5), s t r i k e s the beam, the s t r a i n gauges i n the tup r e c o r d the c o n t a c t l o a d . The arrangement of the s t r a i n gauges i n the t u p i s shown i n F i g u r e 4 . 6 ( a ) , and the c i r c u i t diagram i s shown i n F i g u r e 4 . 6 ( b ) . The Light Source 100 100 1 O/ o Netal Strip a Holes •Excitation Output F i g u r e 4 . 4 - T r i g g e r i n g of the Data A c q u i s i t i o n System cn 63 Wheatstone b r i d g e , shown i n F i g u r e 4.6(b) i s b a l a n c e d i n the "no l o a d c o n f i g u r a t i o n " . The 8 s t r a i n gauges are i n s t a l l e d i n two 25 mm diameter c i r c u l a r h o l e s , i n o r d e r t o o b t a i n an a m p l i f i c a t i o n i n the s i g n a l s by making use of the s t r e s s c o n c e n t r a t i o n s a t the bo u n d a r i e s of the h o l e s . The tup was c a l i b r a t e d s t a t i c a l l y u s i n g a h y d r a u l i c a l l y l o a d e d u n i v e r s a l t e s t i n g machine. d.The support anvi I The support a n v i l ( F i g u r e 4.7) was c a p a b l e of r e a d i n g the v e r t i c a l support r e a c t i o n as w e l l as the h o r i z o n t a l F i g u r e 4.5-The s t r i k i n g end of the Hammer, or "Tup" 0<i L J (a) STRAIN GAUGES • TYPE i BONOED RESISTANCE ' 330.0ft ± 0 . 3 % GAGE FACTOR ' 2 . 0 7 1 0 . 3 % TEMPERATURE COEFFICIENT:! 0.1% EXCITATION (b) Figure 4.6-The c i r c u i t of the Tup support reaction (Figure 4 . 8 ) . These two r e a c t i o n s were read separately from the imbalance generated i n two d i f f e r e n t Wheatstone bridges (Figure 4 . 9 ) . These two r e a c t i o n s could be read by the data a c q u i s i t i o n system through two independent channels. The v e r t i c a l r e a c t i o n was read from the s t r a i n gauges mounted in the c i r c u l a r h oles, while the h o r i z o n t a l reaction was read from the s t r a i n gauges mounted in between the two holes (Figure 4 . 9 ) . The s t r a i n gauges reading the v e r t i c a l r e a c t i o n worked on the same p r i n c i p l e as d i d the ones i n the tup'. The bridge reading the h o r i z o n t a l r e a c t i o n , which was balanced i n the no load 65 F i g u r e 4.7-The Support A n v i l c o n f i g u r a t i o n , was thrown out of b a l a n c e w i t h a f i n i t e h o r i z o n t a l l o a d . In the unbalanced s t a t e , the o utput a c r o s s A and B i n F i g u r e 4.9c was p r o p o r t i o n a l t o the magnitude of the h o r i z o n t a l l o a d . I t can be seen from F i g u r e 4.9b and 4.9c t h a t these two c h a n n e l s a c t e d i n d e p e n d e n t l y of each o t h e r . In o t h e r words, the presence of a f i n i t e h o r i z o n t a l l o a d d i d not a f f e c t the b a l a n c e of the b r i d g e r e a d i n g the v e r t i c a l r e a c t i o n , and v i c e v e r s a . C a l i b r a t i o n of the s u p p ort a n v i l was a l s o c a r r i e d out s t a t i c a l l y on a h y d r a u l i c a l l y l o a d e d u n i v e r s a l t e s t i n g machine. 66 Figure 4.8-The Support Reactions e. Accelerometers The accelerometers (Figure 4.10) used were p i e z o e l e c t r i c sensors with a resonant frequency of about 45kHz. 5 With a r e s o l u t i o n of O.Olg, the accelerometers c o u l d read to ±500g and had an overload p r o t e c t i o n of up to 5000g. 'Manufactured by PCB P i e z o t r o n i c s , Inc., B u f f a l o , NewYork. 68 ! I F i g u r e 4.10-The A c c e l e r o m e t e r s / . Acquisition and storage of the data Once the d a t a a c q u i s i t i o n system i s t r i g g e r e d , i t be g i n s t o t r a n s f e r the output from the 5 c h a n n e l s i n t o the computer memory, f o r a p r e s e l e c t e d l e n g t h of t i m e . T h i s l e n g t h of time i s chosen a p p r o p r i a t e l y f o r the exp e c t e d time of the impact event (^15 ms f o r p l a i n and f i b r e r e i n f o r c e d c o n c r e t e , and =*l50ms f o r c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e ) . The f i v e c h a n n e l s were read s i m u l t a n e o u s l y a t 0.2ms i n t e r v a l s . At the end of the e v e n t , the d a t a s t o r e d i n the computer memory a r e w r i t t e n on t o a magnetic d i s c . 69 F i n a l l y , t h e s e data a r e t r a n s f e r r e d t o an Amdahl computer f o r f u r t h e r a n a l y s i s . 70 4.3.2.2 C a l i b r a t i o n a. Cal i brat i on of t he tup The o u t p u t from the s t r a i n gauges i n the t u p was i n the form of v o l t a g e s i g n a l s . To c o n v e r t t h e s e s i g n a l s i n t o l o a d s , c a l i b r a t i o n was needed. A l t h o u g h the t u p was t o be s t r e s s e d d y n a m i c a l l y i n an a c t u a l t e s t , the p r o p e r t i e s of s t e e l under dynamic c o n d i t i o n s were assumed t o be the same as under s t a t i c ones, and so a s t a t i c c a l i b r a t i o n c o u l d be used. The t u p was l o a d e d , i n s t e p s , up t o about 70% of i t s e l a s t i c c a p a c i t y and the output was re a d . F i g u r e 4.11 shows the c a l i b r a t i o n c u r v e . Note from F i g u r e 4.11 t h a t the c a l i b r a t i o n was l i n e a r and the h y s t e r e t i c l o s s was n o n e x i s t a n t . b. Calibration of the support anvil S i m i l a r t o the t u p , the su p p o r t c h a n n e l s were a l s o c a l i b r a t e d s t a t i c a l l y on a h y d r a u l i c a l l y l o a d e d u n i v e r s a l t e s t i n g machine. The c h a n n e l r e a d i n g the v e r t i c a l r e a c t i o n was c a l i b r a t e d by a p p l y i n g a v e r t i c a l l o a d as i n the case of the t u p , and a moment was a p p l i e d t o c a l i b r a t e the h o r i z o n t a l r e a c t i o n c h a n n e l ( F i g u r e 4.8). F i g u r e 4.11 shows the r e s u l t s from t h e c a l i b r a t i o n . As f o r t h e t u p , the c a l i b r a t i o n f o r the support c h a n n e l s was a l s o found t o be l i n e a r , w i t h no h y s t e r e t i c l o s s . 71 72 c. Calibration of the hammer acceleration As mentioned e a r l i e r , the p h o t o c e l l assembly sent out a vo l t a g e s i g n a l , i n the form of a sp i k e , whenever i t i n t e r c e p t e d a hole i n the metal s t r i p . A t y p i c a l output from the p h o t o c e l l assembly i s shown i n Fi g u r e 4.12; the data from the p h o t o c e l l i n d i c a t e d the time r e q u i r e d by the hammer to t r a v e l the d i s t a n c e s between the s u c c e s s i v e h o l e s . I f i t can be assumed that the downward a c c e l e r a t i o n (a^) of the hammer i s constant, and i f we know the time r e q u i r e d to t r a v e l two adjacent segments of len g t h s s, and Fi g u r e 4.12-The C a l i b r a t i o n of the Hammer A c c e l e r a t i o n 73 s 2 ( F i g u r e 4.12), then from the laws of motion, the a c c e l e r a t i o n of the hammer "a^" can be o b t a i n e d as f o l l o w s : Between the f i r s t and the second h o l e , s, = V,At, + 0.5a hAt 2 (4.3) Between the second and the t h i r d h o l e , s 2 = V 2 A t 2 + 0.5a, A t ! (4.4) A l s o , V 2 = V, + avAt, (4.5) t h e r e f o r e , s o l v i n g f o r a, we get 2(s 2 A t i - s t A t 2) a. = (4.6) n A t , A t 2 ( A t , + A t 2 ) I f the h o l e s are e q u a l l y spaced at s, as i s the case i n t h i s study, 2 s ( A t 1 - A t 2 ) a h = (4.7) A ^ A t z f A t T + A t z ) 74 Note t h a t a l l the terms on the r i g h t hand s i d e of Eqn. 4.6 or Eqn. 4.7 can be o b t a i n e d e i t h e r from the output of the p h o t o c e l l , or from p h y s i c a l measurements. Thus the downward a c c e l e r a t i o n can be e v a l u a t e d . I t i s worth m e n t i o n i n g here t h a t the a c c e l e r a t i o n of the hammer was always found t o be l e s s than g (9.81 m / s e c 2 ) . The f r i c t i o n between the columns of the machine and the hammer was thought t o be the reason b e h i n d t h i s d i s c r e p a n c y . The f r i c t i o n was found t o depend upon the c l e a n l i n e s s of the p i l l a r s . An a c c e l e r a t i o n t e s t done r i g h t a f t e r c l e a n i n g the p i l l a r s w i t h acetone r e s u l t e d i n a v a l u e of hammer a c c e l e r a t i o n of 9.60 m/sec 2. On the o t h e r hand, u n c l e a n p i l l a r s , a f t e r r e p e a t e d use, y i e l d e d a c c e l e r a t i o n s as low as 8.64 m/sec 2. T h e r e f o r e , the p i l l a r s were c l e a n e d j u s t b e f o r e e v e r y t e s t and a hammer a c c e l e r a t i o n e q u a l t o 9.60 m/sec 2 was assumed i n the a n a l y s i s . 75 4 . 3 . 2 . 3 A n a l y s i s of the t e s t r e s u l t s The usua l output from the impact t e s t s c a r r i e d out on the c o n c r e t e beams c o n s i s t e d of the tup l o a d , the support l o a d , and the a c c e l e r a t i o n s at three l o c a t i o n s a lon g the l e n g t h of the beam. A l l these data were o b t a i n e d as a f u n c t i o n of t ime . F i g u r e 4.13 shows the f i v e se t s of data o b t a i n e d from the f i v e ins trumented channe l s from a t e s t done on a p l a i n c o n c r e t e beam. S ince the data were a c q u i r e d at 200 microsecond i n t e r v a l s , and s i n c e an impact event took anywhere from 15ms to 150ms, t h i s r e s u l t e d i n s e v e r a l thousand data p o i n t s per t e s t . For the e f f i c i e n t h a n d l i n g of t h i s d a t a , a computer program was w r i t t e n . An a l g o r i t h m of the program i s g iven in S e c t i o n - 4 . 3 . 2 . 3 g . a.The energy lost by the hammer I f the hammer has f a l l e n through a h e i g h t "h" before i t h i t s the beam, then the v e l o c i t y of the hammer j u s t p r i o r to impact i s g iven by E q n . 4 . 2 a . I f t h i s i n s t a n t corresponds to time t = 0 ( F i g . 4.13)., t h e n , Vh(t=0) = V2i^h (4.8) A f t e r the c o n t a c t between the hammer and the beam, an i m p u l s e , g iven by the area under the tup l o a d v s . time p l o t , a c t s on the hammer. From the laws of Newtonian" Mechan ic s , t h i s impulse must be equa l to the change i n the momentum of Figure 4 . 1 3 - T y p i c a l output from the f ive channels of instrumentation 77 the hammer, /P t (t)dt = m h U h (0) - m hU h(t) ( 4 - 9 ) U s i n g Eqn 4.8 and s o l v i n g Eqn 4.9 we g e t , AE(t) = im h[ w2(0) _ y2( t)] (4.10) I f A E ( t ) i s the k i n e t i c energy l o s t by the hammer, then U h (t) = [V2a h h - 1 / P t ( t ) d t ] (4.11 ) h On s u b s t i t u t i n g f o r V h ( 0 ) and v n ( t ) i n E q u a t i o n 4.11, AE(t) = 2-mh[2ahh - (V2ahh - 1 / P t ( t ) d t ) 2 ] (4.12) Thus, a c c o r d i n g t o Eqn. 4.12, at any time t , i f the a r e a under the tup l o a d v s . time p l o t i s known, the energy l o s t by the hammer can be c a l c u l a t e d . As w i l l be seen l a t e r , a l l of t h i s energy l o s t by the hammer may not be t r a n s f e r r e d t o the specimen. Some of the energy, a t l e a s t i n the i n i t i a l 78 p a r t of the impact, i s l o s t t o the t e s t i n g machine i t s e l f ( C hapter 8 ) . b. The generalized bending load The c o n t a c t l o a d between the specimen and the hammer i s not the t r u e bending l o a d on the beam, because of the i n e r t i a l r e a c t i o n of the beam. A p a r t of the tup l o a d i s used t o a c c e l e r a t e the beam from the p o s i t i o n of r e s t . T h i s i n e r t i a l l o a d , c a l l e d the d'Alambert f o r c e , i s d i s c u s s e d i n d e t a i l i n Chapter 5. The i n e r t i a l l o a d must be s u b t r a c t e d from the obser v e d t u p l o a d i n o r d e r t o o b t a i n the a c t u a l bending l o a d on the specimen. V a r i o u s t e c h n i q u e s have been used by v a r i o u s i n v e s t i g a t o r s t o a c c o m p l i s h t h i s (Chapter 5 ) . I n t h i s s t u d y , the a c c e l e r o m e t e r s d a t a were used i n o r d e r t o a p p l y the i n e r t i a l c o r r e c t i o n t o the t u p l o a d . In o r d e r t o a r r i v e a t the t r u e bending (or s t r e s s i n g l o a d ) , i t i s i m p o r t a n t t o u n d e r s t a n d the n a t u r e of the v a r i o u s l o a d s i n q u e s t i o n . The t u p l o a d i s a p o i n t l o a d a c t i n g a t the midspan of the beam, whereas the i n e r t i a l r e a c t i o n of the beam i s body f o r c e d i s t r i b u t e d t h r o u g h o u t the body of the beam. T h i s d i s t r i b u t e d i n e r t i a l l o a d s h o u l d t h e r e f o r e be r e p l a c e d by an e q u i v a l e n t (or g e n e r a l i z e d ) i n e r t i a l l o a d , P ^ ( t ) , which can then be s u b t r a c t e d from the tu p l o a d t o o b t a i n the g e n e r a l i z e d ( t r u e , or e q u i v a l e n t ) bending l o a d P ^ t ) , a c t i n g a t the c e n t r e . As w i l l be shown l a t e r , t h i s g e n e r a l i z e d . b e n d i n g l o a d can then be assumed t o a c t on the beam a t the midspan by i t s e l f , and w i l l p r e d i c t 79 the c o r r e c t e n e r g i e s , midspan moments and s t r e s s e s . As shown i n F i g u r e 4.14, the t h r e e a c c e l e r o m e t e r s a r e p l a c e d at d i s t a n c e s D,, (D,+D 2), and (0.51+h) from the c e n t r e of the beam. I f the a c c e l e r a t i o n s between the a c c e l e r o m e t e r s can be o b t a i n e d by l i n e a r i n t e r p o l a t i o n , i f the a c c e l e r a t i o n s at midspan can be o b t a i n e d by l i n e a r e x t r a p o l a t i o n , and i f . the a c c c e l e r a t i o n d i s t r i b u t i o n can be assumed t o be symmetric about the midspan, then the a c c e l e r a t i o n a t every p o i n t a l o n g the l e n g t h of the beam i s known. I f a segment of the beam, dx, has an a c c e l e r a t i o n u ( x , t ) a t i t s c e n t r e , then the i n e r t i a l f o r c e a c t i n g on i t i s g i v e n by .where p i s the mass d e n s i t y and A i s the a rea of c r o s s s e c t i o n of the beam. In t h i s p o s i t i o n ( F i g u r e 4.14c), l e t the beam be given a v i r t u a l d i s p l a c e m e n t c o m p a t i b l e w i t h i t s c o n s t r a i n t s . Let the v i r t u a l . d i s p l a c e m e n t a t any p o i n t be p r o p o r t i o n a l to the a c c e l e r a t i o n at t h a t p o i n t . I f i i 0 ( t ) , u , ( t ) , u 2 ( t ) , u 3 ( t ) are the a c c e l e r a t i o n s a t the c e n t r e , and a t the three a c c e l e r o m e t e r l o c a t i o n s , r e s p e c t i v e l y , and i f 5 u 0 , S u t , 5 u 2 , and 5u 3 are the c o r r e s p o n d i n g v i r t u a l d i s p l a c e m e n t s , then dl(x,t) = pAdxu(x,t) ( 4 . 1 3 ) 6u, 0 6u ( 4 . 1 4 ) i i(t) u(t) ii(t) 2 u(t) 3 0 F i g u r e 4.14-(a) P o s i t i o n s of the a c c e l e r o m e t e r s (b) A c c e l e r a t i o n d i s t r i b u t i o n and (c) The g e n e r a l i z e d i n e r t i a l Load 81 If the d i s t r i b u t e d i n e r t i a l load i s to be rep l a c e d by a ge n e r a l i z e d i n e r t i a l load in the c e n t r e , then the v i r t u a l work done by the d i s t r i b u t e d i n e r t i a l r e a c t i o n a c t i n g over the d i s t r i b u t e d v i r t u a l displacement should be equal to the v i r t u a l work done by the c e n t r a l l o a d P ^ ( t ) a c t i n g over the v i r t u a l displacement at the c e n t r e , P ^ O S U Q = JpAu(x,t)5u(x)dx + 2/pAu(y,t) 5u(y)dy ( 4 . 1 5 ) On expanding, P . ( t ) 6 u n = 2 O n(t)-G ( t ) 6u n-6u / p f l[Q 0(t)- ° n *] [*V — V — x] dx 1 0 (t)-u (t) / p A [ U l ( t ) x] [6U -1 6u 1~6u 2 x] dx ( 4 . 1 6 ) + /pA[U2(t)-0 o ( t ) - 0 , ( t ) x] [ 6 u 2 - - :] dx + /pA(-1)[u 3(t)- 5 h S y] (-1)[6u 3- 3 h 5 y] where u (t) and 6u are the a c c e l e r a t i o n and the v i r t u a l displacement at the support, r e s p e c t i v e l y . I f the a c c e l e r a t i o n and the v i r t u a l displacement at the support can be assumed to be zero, and i f the beam i s p r i s m a t i c and homogeneous, then Eqn. 4.16 can be s i m p l i f i e d to 1 L U O e u J ^ + l i J ( t ) 6 u D 1 + j U1 3 1 ° 3 U 3 u Q ( t ) P i ( t ) 6 u Q = 2pA 6u QD 1 + 1 u 9 ( t ) 6 U l D 7 + 1 u 1 ( t ) 6 u l D 2 + 1 U2{t] 6 U l D 2 - 2 1 2 l I / , u ^ t ) + 1 u 2 ( t ) 6 u 2 D 3 + 1. u 3('t)6u 3h ( 4 . 1 7 ) 82 E x p r e s s i n g 5u,, 5 u 2 , and 6u 3 i n terms of 5 u 0 u s i n g Eqn. 4.14, and on c a n c e l l i n g 5u 0 on both s i d e s of the e q u a t i o n , we get D P.(t) = 2 PA[ ^ ".T^tr ( " a { t ) + " U 1 ( t ) + V^V 0 5 + 1 °2 ( ~ul(t) + ~u2At) + u (t)u,/t)) j 1 8 ) 3 uQTtT + 3 "T^tT U 2 ( t ) + 3 "T^TtT U3 ( t ) ] Thus, knowing the a c c e l e r a t i o n s a t the c e n t r e and a t the a c c e l e r o m e t e r l o c a t i o n s , and the beam p r o p e r t i e s , the g e n e r a l i z e d i n e r t i a l l o a d can be o b t a i n e d from Eqn. 4.18. Once the g e n e r a l i z e d i n e r t i a l l o a d i s o b t a i n e d , the beam can be modelled as a s i n g l e degree of freeedom system and the g e n e r a l i z e d bending l o a d can be o b t a i n e d from the e q u a t i o n of dynamic e q u i l i b r i u m : P b ( t ) = P t(t) - P.(t) (4.19) c. Acceleration distribution I f the a c c e l e r a t i o n a t any p o i n t a l o n g the l e n g t h of the beam can be ex p r e s s e d as a f u n c t i o n of the a c c e l e r a t i o n a t the c e n t r e , then the e q u a t i o n of v i r t u a l work can be f u r t h e r s i m p l i f i e d . In o t h e r words, i f the a c c e l e r a t i o n s u , ( t ) , u 2 ( t ) , and u 3 ( t ) can be exp r e s s e d as a f u n c t i o n of u 0 ( t ) , then Eqn. 4.18 can be w r i t t e n i n terms of the l o a d p o i n t a c c e l e r a t i o n ( u 0 ( t ) ) a l o n e . S e v e r a l t e s t s conducted on p l a i n , f i b r e r e i n f o r c e d , and c o n v e n t i o n a l l y r e i n f o r c e d beams i n d i c a t e t h a t such a s i m p l i f i c a t i o n i s p o s s i b l e . The observed a c c e l e r a t i o n d i s t r i b u t i o n i n p l a i n and f i b r e r e i n f o r c e d c o n c r e t e i s shown 83 i n F i g u r e 4.15 and th a t f o r c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e i n F i g u r e 4.16. As seen from f i g u r e 4.15, the a c c e l e r a t i o n d i s t r i b u t i o n f o r the p l a i n and f i b r e r e i n f o r c e d c o n c r e t e w i t h o u t c o n v e n t i o n a l r e i n f o r c e m e n t can be approximated as l i n e a r . On the o t h e r hand, the a c c e l e r a t i o n d i s t r i b u t i o n f o r c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e can be approximated as s i n u s o i d a l . W i t h these a p p r o x i m a t i o n s the g e n e r a l i z e d i n e r t i a l l o a d s can be r e c a l c u l a t e d as f o l l o w s : (i) Li near case For the l i n e a r case ( F i g u r e 4.17a), the d i s p l a c e m e n t s can be w r i t t e n a s , 2 u Q(t) . or\) u(x,t) = - — x (between the supports) (4.20) - 2 u n ( t ) u(y,t) = y (overhanging the supports) R e w r i t i n q E a u a t i o n 4.15 f o r t h i s case we have. - r 2 ' G 0 ( t ) X i r 2 6 V i •„ (4.21) P.(t) 6u Q = 2 J P A [ • j ] [ j J dx -2u (t)y -2f iu ny + 2 / PA [ 1 ] [ 5 ] dy once a g a i n , i f the beam i s homogeneous and i s o t r o p i c , Eqn.4.21 can be s i m p l i f i e d t o P.(t) = P A u Q ( t ) 1 + 8 h3 3 3 " I 7 " (4.22) 84 0 75 250 480 ( C E N T E R ) ( A N V I L ) DISTANCE FROM BEAM CENTER , mm F i g u r e 4.15-Acceleration d i s t r i b u t i o n f o r p l a i n concrete beams 1000 -1.5 ms 500 ^SINUSOIDAL DISTRIBUTION 0 1500 i \ o \ ° 0.9ms 1000 \ . -SINUSOIDAL DISTRIBUTION 500 o l \ ? >• 0.5ms 500 -SINUSOIDAL DISTRIBUTION 0 \° 1 Y 0 75 250 480 (CENTER) (ANVIL) DISTANCE FROM B E A M C E N T E R , mm F i g u r e 4.16-Acceleration d i s t r i b u t i o n f o r conventions r e i n f o r c e d c o n c r e t e beams l l y 86 P f ( t ) (b) F i g u r e 4.17-(a) L i n e a r a c c e l e r a t i o n d i s t r i b u t i o n and (b) S i n u s o i d a l a c c e l e r a t i o n d i s t r i b u t i o n Note t h a t the above e x p r e s s i o n can a l s o be o b t a i n e d from the g e n e r a l e x p r e s s i o n (Eqn.4 .18) by e x p r e s s i n g u , ( t ) , u 2 ( t ) , and u 3 ( t ) i n terms of u 0 ( t ) . (ii) Sinusoidal case In t h i s c a s e , the d i s p l a c e m e n t s between the s u p p o r t s a r e assumed t o be s i n u s o i d a l , w h i l e the d i s p l a c e m e n t s on the overhanging p o r t i o n a r e assumed t o be l i n e a r ( F i g u r e 4.17b). A c c o r d i n g l y , u(x,t) = u ( t ) s i n J y i - (between the supports) u(x,t) = - u Q ( t ) ^ (overhanging the supports). R e w r i t i n g E q u a t i o n 4.18 f o r t h i s c a s e , 87 (4.23) P . ( t ) 6 u Q = J PA [ u Q ( t ) s i n - ^ p - ] [ 6 U Q s i n - ^ ] dx + 2/ PA [ - u Q ( t ) [-6u Q Y~ 3 ^ (4.24) For a p r i s m a t i c and homogeneous beam, the above e q u a t i o n can be f u r t h e r s i m p l i f i e d t o (4.25) P.(t) = P A u 0 ( t ) 2 K2 h 3 2 + 31' In a d d i t i o n , Eqn. 4.19 can be used i n b o t h the l i n e a r and i n the s i n u s o i d a l cases t o dete r m i n e the g e n e r a l i z e d bending l o a d . d. Moments and stresses For a beam undergoing impact, the moment a t the c e n t r e can be o b t a i n e d by t a k i n g the moment of a l l the f o r c e s a c t i n g on the beam about the c e n t e r ( F i g u r e 4.18a). The same moment a t the c e n t r e s h o u l d a l s o be p r e d i c t e d i n the e q u i v a l e n t s t a t i c system w i t h the tup l o a d and the i n e r t i a l r e a c t i o n r e p l a c e d by the g e n e r a l i z e d bending l o a d a c t i n g a t the c e n t r e . The case of a l i n e a r a c c e l e r a t i o n d i s t r i b u t i o n w i l l be used t o demonstrate t h i s . I f F^, i s the r e s u l t a n t of the d i s t r i b u t e d i n e r t i a l r e a c t i o n of the beam on the l e f t or 88 1 2h h A h h 1 h (a) (b) F i g u r e 4 . l 8 - ( a ) Dynamic l o a d i n g on the beam and (b) E q u i v a l e n t s t a t i c l o a d i n g the r i g h t h a l f - s p a n , and i f F i 2 i s the r e s u l t a n t of the d i s t r i b u t e d i n e r t i a l r e a c t i o n of the beam on the overhang ( F i g u r e 4.18a), then, F;At) = 4 P A u n ( t ) l (4.26) F 1 2 ( t ) - f p A u n ( t ) h 2 (4.27) From the v e r t i c a l e q u i l i b r i u m of f o r c e s , 89 ^ ( t ) - iP t ( t ) - F . ^ t ) + F . 2 ( t ) (4.28) or, R^t) = iP t ( t ) - i P A u Q ( t ) l + j P Au 0 (t)h 2 JP t(t) - pAuQ(t) [ i - £ 1 ] (4.29) If M 0 ( t ) i s the moment at the c e n t r e , 0 (t) = R l ( t ) | + F . l ( t ) I - F . 2 ( t ) + S u b s t i t u t i n g for R,(t) from Eqn. 4.29, F - , ( t ) from Eqn, 4.26, and F ^ 2 ( t ) from Eqn. 4.27, we get I1n(t) = P t ( t ) i - P Au 0 (t) [ + 2g_ j (4.30) The g e n e r a l i z e d bending load P^(t) can be obtained from Eqn. 4.19, using the g e n r a l i z e d i n e r t i a l load P^(t) obtained from Eqn. 4.22, P b (t) = P t (t) - p Au Q (t) [ £ + - § p - J C4.31 ) 90 I f M 0 ( t ) i s the v a l u e of the moment a t the c e n t r e i n the e e q u i v a l e n t system, t h e n , "eo^ = P b ( t > i With P ^ ( t ) o b t a i n e d from Eqn. 4.31, " e o ^ - P t ^ T . - p A V t ) [ T f + ^ 3 ( 4 ' 3 2 ) On comparing Eqn. 4.30 and Eqn. 4.32 i t can be seen t h a t the moment p r e d i c t e d by the e q u i v a l e n t system (Eqn. 4.32) i s the same as the moment p r e d i c t e d by t h e dynamic a n a l y s i s (Eqn. 4.30). S i n c e the g e n e r a l i z e d bending l o a d p r e d i c t s the c o r r e c t moment a t the c e n t r e i n the e q u i v a l e n t system, i t can be used d i r e c t l y f o r c a l c u l a t i n g the s t r e s s e s and the s t r e n g t h s . The s t r e s s e s i n the beam can be o b t a i n e d from o ( c , t ) = [ P b ( t ) i ] [ £• ] (4.33) where c i s the d i s t a n c e of the f i b r e from the n e u t r a l a x i s and I i s the moment of i n e r t i a . I f i s the modulus of r u p t u r e under the dynamic c o n d i t i o n s t h e n , o = fp I ] D t d b,rnax 4 J 21 (4.34a) 91 F i n a l l y i f i s the extreme f i b r e s t r a i n at the peak bending l o a d P, then, 6 uo,peakD (4.34b) e f = Where, u Q p e a k i s the midspan displacement at the peak l o a d , and D i s the depth of the beam. e. Velocities and Deflections Once the a c c e l e r a t i o n h i s t o r y at any p o i n t along the l e n g t h of the beam i s known, the v e l o c i t y and displacement h i s t o r i e s can be obtained by i n t e g r a t i o n s with respect to time. However, i t i s the v e l o c i t y and the displacement h i s t o r y at the l o a d p o i n t that are of prime concern to us from the poin t of view of a n a l y s i s . The a c c e l e r a t i o n at the c e n t r e u 0 ( t ) , obtained by the l i n e a r e x t r a p o l a t i o n of the measured a c c e l e r a t i o n s , i s used f o r t h i s purpose. I f u 0 ( t ) i s the v e l o c i t y at the c e n t r e , and u 0 ( t ) i s the displacement at the c e n t r e , then, u 0 ( t ) = J U o t U d t (4.35) u 0 ( t ) = / u 0 ( t ) d t (4.36) 92 / . Energy As i n the s t a t i c c ase, the a r e a under the curve of g e n e r a l i z e d bending l o a d (Eqn. 4.19) v s . midspan d i s p l a c e m e n t (Eqn. 4.36) i s a measure of the energy expended i n bending the beam. At the end of the impact event, t h i s area r e p r e s e n t s the f r a c t u r e energy. I f E f a ( t ) i s the bending energy t h e n . E ( t ) = / P b ( t ) du Q (4.37) g. The computer program A computer program was w r i t t e n t o a n a l y s e the data from the impact t e s t s ; the flow c h a r t i s g i v e n i n F i g u r e 4.19. The t e s t data s t o r e d on the magnetic d i s c a r e time based. Thus, the a n a l y s i s s t a r t s a t the i n s t a n t of f i r s t c o n t a c t between the hammer and the beam ( t = 0 ) , and ends a t the p o i n t of f a i l u r e ( t = t ^ ) , when the impact l o a d has f a l l e n back t o ze r o . The output from the program i s i n the form of the energy l o s s h i s t o r y of the hammer(AE(t)), the energy g a i n h i s t o r y of the beam ( E ^ ( t ) ) , and so on. The r e s u l t s can a l s o be o b t a i n e d i n a g r a p h i c a l form. >ata on Mag.Disc\ Loads and Accl. .u.r.t. time, t START 7 .£>/ INPUT Yes V Calculate a h (t) ,U(t) E(t) V Calculate u 0 ( t ) ,u 0(tf u 0 (t) etc. J Calculate P i ( t ) , 1 P.(t) J Calculate E b ( t ) J Calculate Stresses, Strength, etc /Output, .Specimen Info . STOP /Write ± > / y ( t ) , IUrite 7 - £ > / u 0 ( t ) , / /u0(t) etc./ (Urite P,(t) . /Uri te Urite Stresses Strengths Figure 4.19- The Flou Chart of Analysis. 94 4.3.2.4 The support r e a c t i o n a. The vertical reaction As mentioned e a r l i e r , one of the support a n v i l s was a l s o i n s t r u m e n t e d t o read the v e r t i c a l r e a c t i o n at the sup p o r t . T h i s i s a c o m p l e t e l y independent method of c h e c k i n g the v a l i d i t y of E q u a t i o n 4.29, and a l s o p r o v i d e s a check on the o p e r a t i o n of the a c c e l e r o m e t e r s and the s t r a i n gauges i n the t u p . F i g u r e 4.20 shows such a comparison. F i g u r e 4.20 i n d i c a t e d two d i f f e r e n c e s between the r e a c t i o n R , ( t ) 8 EXPERIMENTAL SUPPORT LOAD EVALUATED SUPPORT REACTION \ \ 0 0 2 4 Tine, ms 6 8 10 12 F i g u r e 4.20-Comparison between the e v a l u a t e d and the observed support r e a c t i o n 95 o b t a i n e d by u s i n g Eqn. 4.29, and the measured v e r t i c a l s upport r e a c t i o n . F i r s t , the peak v a l u e of R , ( t ) i s s m a l l e r by about 5-12% than the measured v a l u e . S e c o n d l y , t h e r e i s a phase s h i f t between the two peaks of about 0.2ms, w i t h the measured peak l a g g i n g behind the a n a l y t i c a l peak. Although the reasons behind the u n d e r e s t i m a t i o n of R ^ t ) are not c l e a r , the s h i f t between the two can be a t t r i b u t e d t o the f i n i t e time r e q u i r e d f o r the s t r e s s waves t o t r a v e l from the c e n t r e t o the s u p p o r t . For c o n c r e t e (E=25xl0 9 N/m2, and p =*2400 kg/m 3), the v e l o c i t y of the l o n g i t u d i n a l s t r e s s waves, c, ( g i v e n by c=i/E/p) i s about 3300 m/sec. At t h i s v e l o c i t y , a s t r e s s wave t a k e s about 0.15ms t o t r a v e l from the c e n t r e to the s u p p o r t (a d i s t a n c e of 480 mm). In a d d i t i o n , the sampling i s done at i n t e r v a l s of 0.20ms. The t r a v e l time f o r the s t r e s s waves, the d i s c r e t e s a m p l i n g i n t e r v a l , and the p o s s i b l e uneven c o n t a c t of the beam a t the s u p p o r t s can, t o some e x t e n t a t l e a s t , e x p l a i n t h i s l a g . The r e a c t i o n R 2 ( t ) i n the e q u i v a l e n t s t a t i c system of F i g u r e 4.18b, can be e v a l u a t e d by summing the f o r c e s i n the v e r t i c a l d i r e c t i o n . U s i n g P u . ( t ) from Eqn. 4.31 ( l i n e a r a p p r o x i m a t i o n ) , we g e t , R 2 ( t ) = i P b ( t ) R 2 ( t ) = i P f c ( t ) - p A u Q ( t ) [ - i - + 4h3 (4.38) Zl7 96 A comparison of R,(t) from Eqn. 4.29 and R 2 ( t ) from Eqn. 4.38 shows that they are somewhat d i f f e r e n t . However, f o r the commonly observed peak tup loads and a c c e l e r a t i o n s i n t h i s study, the d i f f e r e n c e between the peaks was l e s s than 6%. Thus, although not s t r i c t l y v a l i d , the measured support r e a c t i o n , when doubled and compared to the g e n e r a l i z e d bending l o a d , can p r o v i d e another check on the technique f o r i n e r t i a l c o r r e c t i o n used here. F i g u r e 4.21 shows such a comparison. The s h i f t between the two peaks can can once again be e x p l a i n e d as above. 161 — , TIME ,msec. F i g u r e 4.21-A rough check on the v a l i d i t y of the technique used here to account f o r i n e r t i a 9 7 b. The horizontal reaction As mentioned e a r l i e r , the i n s t r u m e n t a t i o n i n the support a n v i l was capable of r e c o r d i n g the h o r i z o n t a l r e a c t i o n as w e l l . In the t e s t s performed i n t h i s study, the h o r i z o n t a l r e a c t i o n was always found to be c l o s e to zero. T h i s confirmed the assumption that the beam was simply supported. The h o r i z o n t a l support r e a c t i o n obtained from an impact t e s t done on a p l a i n c o n c r e t e beam has been shown i n F i g u r e 4.22. 2.0 HORIZONTAL SUPPORT REACTION 1 . 5 -TJ o 1.0"" 0 2 4 6 8 Time, ms FIGURE 4.22-The H o r i z o n t a l Support Reaction 5 . INERTIAL LOADING IN INSTRUMENTED IMPACT TESTS  5.1 INTRODUCTION The t e s t i n g of c o n c r e t e a t h i g h s t r a i n r a t e s r e q u i r e s both a t e s t i n g system capab le of p r o d u c i n g h i g h s t r a i n r a t e s , and a v a l i d t echn ique to a n a l y s e the r e s u l t s . N o r m a l l y , impact t e s t s on c o n c r e t e i n compress ion or t e n s i o n do not pose a s e r i o u s problem c o n c e r n i n g the specimen i n e r t i a . However, impact t e s t s on c o n c r e t e beams loaded i n 3 - p o i n t or 4 - p o i n t bending g i v e r i s e to specimen i n e r t i a e f f e c t s which must be c o n s i d e r e d i n the a n a l y s i s . When the in s t rumented tup of the hammer s t r i k e s the beam, the beam suddenly ga ins momentum and the unsupported p a r t of the beam a c c e l e r a t e s in the d i r e c t i o n of the hammer. T h i s g i v e s r i s e to d ' A l a m b e r t f o r c e s , a c t i n g i n a d i r e c t i o n o p p o s i t e to the d i r e c t i o n i n which the beam a c c e l e r a t e s . The s t r a i n gauges in the t u p , s ens ing the c o n t a c t l o a d between hammer and the beam, sense t h i s i n e r t i a l l o a d as w e l l . Thus the tup l o a d c o n s i s t s of the mechan ica l bending l o a d (the s t r e s s i n g l o a d ) , and the l o a d due to the i n e r t i a l r e a c t i o n of the spec imen. The m e c h a n i c a l bending l o a d , which i s the obv ious g o a l of t e s t i n g , can thus be o b t a i n e d from the tup l o a d o n l y i f the " i n e r t i a l r e a c t i o n " of the beam i s known. 98 99 5.2 NATURE OF THE INERTIAL LOAD The n a t u r e of the i n e r t i a l l o a d can be s t be under s t o o d by a s i n g l e degree of freedom model as o u t l i n e d i n Chapter 7 (Appendix-7.1). The a c c e l e r a t i o n s p r e d i c t e d by the model (Eqn.A7.1-8) have been p l o t t e d i n F i g u r e 5.1 a g a i n s t t i m e . The a c c e l e r a t i o n s were o b t a i n e d f o r a p l a i n c o n c r e t e beam s t r u c k by the hammer f a l l i n g t h r o u g h 0.5m. The observed peak tup l o a d was taken e q u a l t o P 0 f and the frequency of the e x t e r n a l l o a d w was det e r m i n e d by the time r e q u i r e d by the C3 C3 ,0 2.0 4.0 6.0 8.0 10.0 TJMF(MS) FIGURE 5 . 1 - P e r i o d of I n e r t i a l O s c i l l a t i o n s 100 tup l o a d t o a t t a i n the peak i n an a c t u a l t e s t . As shown i n F i g u r e 5.1, the a c c e l e r a t i o n s seems t o v a r y s i n u s o i d a l l y w i t h a p e r i o d of about 3.2ms f o r the p l a i n c o n c r e t e beams used i n t h i s s t u d y . S i m i l a r p l o t s can be o b t a i n e d f o r c o n v e n t i o n a l l y r e i n f o r c e d and f i b r e r e i n f o r c e d c o n c r e t e as w e l l ; the n a t u r e of Eqn. A7.1-8 s u g g e s t s t h a t the a c c e l e r a t i o n v a r i a t i o n w i t h r e s p e c t t o time i n t h e s e c a s e s w i l l a l s o be s i n u s o i d a l , but w i t h a d i f f e r e n t p e r i o d than t h a t f o r the p l a i n c o n c r e t e . I n e r t i a l l o a d , which i s the p r o d u c t of the g e n e r a l i z e d mass and the c e n t r a l a c c e l e r a t i o n , t h e r e f o r e i s p r o p o r t i o n a l t o the a c c e l e r a t i o n , and hence has the same p e r i o d as does the a c c e l e r a t i o n . S e r v e r (14) has proposed an e m p i r i c a l e x p r e s s i o n t o p r e d i c t the p e r i o d of i n e r t i a l o s c i l l a t i o n s i n terms of the specimen w i d t h B, specimen t h i c k n e s s D, specimen c o m p l i a n c e C g, and Young's Modulus E: T = 3.36(B/D)(EDC ) 0 , 5 (5.1) S e r v e r a l s o s u g g ested t h a t r e l i a b l e measurements c o u l d be made o n l y a f t e r 3 i n e r t i a l o s c i l l a t i o n s , i . e . , a t any time t g i v e n by, t > 3 T (5.2) Thus a f t e r t h r e e i n e r t i a l o s c i l l a t i o n s , the tup l o a d can be 101 assumed t o be r e p r e s e n t the t r u e m e c h a n i c a l l o a d on the specimen. For d u c t i l e m a t e r i a l s , l i k e m e t a l s , the g u i d e l i n e s s u g g e sted by S e r v e r may be met. However, f o r b r i t t l e m a t e r i a l s , l i k e c o n c r e t e , t h e s e g u i d e l i n e s cannot be met i n g e n e r a l . The b a s i c d i f f e r e n c e between d u c t i l e and b r i t t l e systems i s the time r e q u i r e d by t h e specimens t o f a i l . In the case of d u c t i l e m a t e r i a l s , the specimen u s u a l l y undergoes more than t h r e e i n e r t i a l o s c i l l a t i o n s b e f o r e f a i l i n g . However, i n the case of b r i t t l e m a t e r i a l s , i t may not be p o s s i b l e t o a v o i d f a i l u r e d u r i n g the f i r s t o s c i l l a t i o n ( F i g u r e 5.1). Thus, the whole impact event may not l a s t as l o n g as t h r e e o s c i l l a t i o n s ; the e n t i r e m e c h a n i c a l response of the specimen may ta k e p l a c e w h i l e the specimen i s s t i l l .being a c c e l e r a t e d , and the i n e r t i a l l o a d can c o m p l e t e l y overshadow the t r u e m e c h a n i c a l bending l o a d . For b r i t t l e specimens, t h e r e f o r e , the approach has t o be d i f f e r e n t than f o r d u c t i l e ones. E v a l u a t i o n of the i n e r t i a l l o a d i s p o s s i b l e i n two ways: (1) by a n a l y t i c a l methods as d e s c r i b e d i n Chapter 7; and (2) by e x p e r i m e n t a l l y measuring the a c c e l e r a t i o n s a l o n g the l e n g t h of the beam and then e v a l u a t i n g the g e n e r a l i z e d i n e r t i a l l o a d as d e s c r i b e d i n Chapter 4. The a n a l y t i c a l models, however, do c r e a t e some problems i n the realm of m a t e r i a l t e s t i n g : (a) The a n a l y s i s a p p l i e s o n l y t o e l a s t i c systems. T h i s i m p l i e s t h a t o n l y t h e beam response up t o the peak l o a d can 102 be d e t e r m i n e d w i t h the h e l p of t h e s e models. T h i s might not be of g r e a t c o n c e r n i f c o n c r e t e were an i d e a l l y b r i t t l e m a t e r i a l , and the l o a d s were t o drop suddenly t o zero once the peak had been reached. E x p e r i m e n t a l e v i d e n c e suggests t h a t t h i s i s not t r u e , and the l o a d v s . d i s p l a c e m e n t p l o t i n dynamic c o n d i t i o n s seems t o have a l a r g e post-peak r e g i o n as w e l l . U n f o r t u n a t e l y , t he e l a s t i c a n a l y s i s cannot be a p p l i e d i n t h i s r e g i o n . (b) The dynamic a n a l y s i s r e q u i r e s knowledge of the beam s t i f f n e s s . The e s t i m a t i o n of the beam s t i f f n e s s , i n t u r n , r e q u i r e s knowledge of c o n c r e t e p r o p e r t i e s a t the r e l e v a n t s t r e s s r a t e s . S i n c e c o n c r e t e p r o p e r t i e s a t the h i g h s t r e s s r a t e s a s s o c i a t e d w i t h impact a r e not v e r y w e l l known, the e x a c t e s t i m a t i o n of the s t i f f n e s s of the c o n c r e t e beam i s not p o s s i b l e . 5.3 EXPERIMENTAL OBSERVATIONS I n e r t i a l c o r r e c t i o n s c o u l d have been i g n o r e d i f the " i n e r t i a l r e a c t i o n " p a r t of the tup l o a d was a s m a l l p e r c e n t a g e of the t r u e m e c h a n i c a l bending l o a d . However, e x p e r i m e n t a l e v i d e n c e s u g g e s t s t h a t i n the i n i t i a l p a r t of the impact the i n e r t i a l l o a d can amount t o as much as 60% of the o b s e r v e d tup l o a d . F i g u r e 5.2 shows the i n e r t i a l l o a d v s . time p l o t s f o r t h r e e d i f f e r e n t hammer dro p h e i g h t s , o b t a i n e d i n the case of p l a i n c o n c r e t e beams. F i g u r e 5.3 shows the i n e r t i a l l o a d p l o t t e d a g a i n s t time f o r 103 38 34 30 26 2 22 S 18 O - 1 14 10 6 2 0 — 0 8 16 24 32 4 0 48 56 TIME .msec. FIGURE 5.2-Observed Tup and I n e r t i a l Loads f o r P l a i n C o n c r e t e c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e f o r a hammer drop h e i g h t of 0.5m, For comparison purposes, the r e s u l t s o b t a i n e d f o r a p l a i n c o n c r e t e specimen t e s t e d under 0.5m hammer drop (a d i f f e r e n t specimen than the one shown i n F i g . 5.2) a r e a l s o reproduced i n F i g u r e 5.3. The peak t u p l o a d s and the peak i n e r t i a l l o a d s i n F i g u r e 5.2 f o r p l a i n c o n c r e t e a r e r e p l o t t e d i n F i g u r e s 5.4a and 5.4b, r e s p e c t i v e l y , as a f u n c t i o n of hammer drop h e i g h t . An i n c r e a s e i n t h e drop h e i g h t of the hammer r e s u l t e d i n an i n c r e a s e i n the i n e r t i a l l o a d . An almost l i n e a r v a r i a t i o n was observed ( F i g u r e 5.4b). T h i s i m p l i e s t h a t the 104 5 0 0 0 0 TIME , ms TIME , ms FIGURE 5.3-Observed Tup and I n e r t i a l Loads f o r (a) P l a i n and ( b ) C o n v e n t i o n a l l y R e i n f o r c e d C o n c r e t e c o r r e c t i o n f o r i n e r t i a becomes more and more imp o r t a n t as the s t r a i n r a t e a t which the t e s t i n g i s done i s i n c r e a s e d . S t i f f e r systems seem t o undergo lower a c c e l e r a t i o n s and hence d e v e l o p lower i n e r t i a l l o a d s than do specimens t h a t a r e not as s t i f f . H igh s t r e n g t h p l a i n c o n c r e t e beams, which ar e s t i f f e r than normal s t r e n g t h p l a i n c o n c r e t e beams, were found t o have lower peak i n e r t i a l l o a d s than normal s t r e n g t h p l a i n c o n c r e t e beams t e s t e d under i d e n t i c a l c o n d i t i o n s ( F i g u r e 5.4b). 105 40 32 224 o o 18 8 0 — A 1 1 1 ! ! I I I ! 0 O.I5 0.3 0.45 0.6 0.75 HEIGHT OF HAMMER DROP, m ( a ) 40 32 5 2 4 a < OI8 ---! ! ! ! ! ! ! ! 1 0 0.15 0.3 0.45 0.6 0.75 HEIGHT OF HAMMER DROP, m (b) FIGURE 5 . 4 - E f f e c t of Hammer Drop He ight on (a) Tup and (b) I n e r t i a l Loads for both Normal S t r e n g t h (NS) and High S t r e n g t h (HS) c o n c r e t e 5.4 THE USE OF THE RUBBER PAD One of the suggested e x p e r i m e n t a l methods for e l i m i n a t i n g the i n e r t i a l l o a d i n g i s the use of a rubber pad between the hammer and beam (16) . I t i s argued that, the rubber pad d e l a y s the occurrence of the peak e x t e r n a l l o a d . T h i s g ives s u f f i c i e n t time for the beam to reach the tup v e l o c i t y , and so at the occurrence of the peak e x t e r n a l l o a d , . t h e a c c e l e r a t i o n s and hence the i n e r t i a l load are a b s e n t . Thus, the measured tup l o a d at the peak can be assumed to be the a c t u a l beam bending l o a d . 106 To examine the v a l i d i t y of t h i s t e c h n i q u e , t e s t s were c a r r i e d out on p l a i n and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams w i t h and w i t h o u t a rubber pad i n the system. Hammer drop h e i g h t s r a n g i n g from 0^15m t o 1.0m were used. The e x p e r i m e n t a l l y d etermined a c c e l e r a t i o n s and the i n e r t i a l l o a d s f o r t e s t s done w i t h o u t the rubber pad were compared t o thos e f o r the t e s t s done w i t h the rubber pad i n the system. S i m i l a r comparisons were made between the peak e x t e r n a l l o a d s , peak bending l o a d s , and t h e f r a c t u r e e n e r g i e s . The s t i f f n e s s of the 40mm t h i c k rubber pad used was 2.83 MN/m. In g e n e r a l , i t was found t h a t a l t h o u g h the o c c u r r e n c e of the peak e x t e r n a l l o a d was d e l a y e d w i t h the rubber pad i n the system, the o c c u r r e n c e of the peak beam a c c e l e r a t i o n was a l s o d e l a y e d , and the two o c c u r r e d a t almost the same t i m e . T a b l e s 5.1 and 5.2 and F i g s . 5.5 and 5.6 show the r e s u l t s o b t a i n e d w i t h and w i t h o u t the rubber pad f o r both p l a i n and c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e . The use of the rubber pad r e s u l t e d i n a d e l a y i n the o c c u r r e n c e of the peak tup l o a d , a r e d u c t i o n i n the peak v a l u e of the t u p l o a d , and a l s o i n a r e d u c t i o n i n the peak a c c e l e r a t i o n s a t t a i n e d i n a t e s t . A r e d u c t i o n i n the peak bending l o a d s was a l s o o b s e r v e d . I t was c o n c l u d e d t h a t w i t h the pad i n the system, the a c c e l e r a t i o n s , and hence the i n e r t i a l l o a d s , were reduced. However, i n e r t i a l l o a d s were not c o m p l e t e l y e l i m i n a t e d . I n e r t i a l l o a d i n g , t h u s , appears t o be an i n h e r e n t c h a r a c t e r i s t i c of dynamic t e s t i n g of t h i s k i n d , and cannot Table 5.1 Eflcci of Euilhcr Eaj cn PJaJD Concrete Beams Under Impact Height of Hammer Drop (m) 0.15 m (6)1 0.25m (6)1 0.50m (6)1 Without Pad With Pad Without Pad With Pad Without Pad With Pad Peak Tup Load (N) 19776 12358 25386 12956 37567 14267 Time to Peak (ms) 1.4 9.0 1.2 8.0 0.8 6.0 Peak Acceleration (m/sec2) 1140 766 1340 828 1967 906 Peak Inertial Load (N) 11994 6731 13203 6845 20635 6852 Peak Bending Load (N) 7782 5987 12183 6111 16932 7415 Fracture 25.8 40.0 42.0 41.5 90.1 69.6 Energy (Nm) Table 5.2 Effect of Rubber Pad on Conventionally Reinforced Beams under Impact Height of Hammer Drop (m) 0.5 m (6)1 1.0m (6)1 Without Pad With Pad Without Pad With Pad Peak Tup Load 48071 (N) 43195 63216 51854 Time to Peak 1.80 (ms) 10.6 1.20 7.8 Peak Acceleration 7020 (m/sec!) 681 1321 1054 Peak Inertial 10383 Load (N) 10134 22037 17330 Peak Bending 37688 Load (N) 33061 41179 34524 Fracture Energy 603 (Nm) (to 18mm LPD') 637 666 610 Fracture Energy 934 882 1340 1190 (Nm) (to 36mm LPD') 1 Number of specimens tested. 2 Load Point Deflection. Peak Tup Lead, UN 801 Peak Bending Lead, kN Peak Tup Load, kN a w . £ & s B e s) t-rt O n o n> a 601 110 e a s i l y be e l i m i n a t e d . The d e l a y i n the o c c u r r e n c e of the peak t u p l o a d reduces the s t r a i n r a t e a c h i e v e d i n a t e s t . T h i s was thought t o be the p r o b a b l e reason b e h i n d the reduced peak bending l o a d s o b s e r v e d i n the t e s t s done w i t h the rubber pad i n the system. Reducing the s t i f f n e s s of the c o n t a c t zone d e c r e a s e s the s t r a i n r a t e and hence, t o some e x t e n t a t l e a s t , d e f e a t s the purpose of h i g h s t r a i n r a t e t e s t i n g . In g e n e r a l , the f r a c t u r e energy v a l u e s o b t a i n e d w i t h the rubber pad i n the system were found t o be lower than the ones o b t a i n e d w i t h o u t the pad, w i t h c e r t a i n exceptions.,. I t i s not c l e a r i f the f r a c t u r e e n e r g i e s o b t a i n e d from the t e s t s done w i t h the rubber pad i n the system can be assumed t o be the t r u e beam f r a c t u r e e n e r g i e s , because of the energy a b s o r p t i o n c a p a c i t y of the pad i t s e l f . 5.5 INSTRUMENTING THE SUPPORT ANVILS I n s t r u m e n t a t i o n of the su p p o r t a n v i l s has a l s o been suggested as a way of o b t a i n i n g t h e t r u e m e c h a n i c a l bending l o a d on the specimen (15) (Chapter 4 ) . However as p o i n t e d out i n the p r e v i o u s c h a p t e r , the su p p o r t r e a c t i o n i s not s t r i c t l y e q u a l t o one h a l f of the g e n e r a l i z e d bending l o a d . A l s o , the f i n i t e t i me r e q u i r e d f o r t h e s t r e s s waves t o t r a v e l from t h e beam midspan t o the support causes a l a g between the two l o a d s . However, the d i f f e r e n c e between the magnitudes of the two l o a d s i s not s u b s t a n t i a l (Chapter 4 ) . I n s t r u m e n t i n g the a n v i l i n t h i s s t u d y , p r o v i d e d a rough 111 check on the i n e r t i a l c o r r e c t i o n a p p l i e d t o t h e tup l o a d , and a l s o p r o v i d e d a check on the b e h a v i o u r of the s t r a i n gauges and the a c c e l e r o m e t e r s . 6. P L A I N CONCRETE UNDER IMPACT  6.1 INTRODUCTION S i n g l e c y c l e i m p a c t l o a d i n g on any s t r u c t u r a l e l e m e n t may o c c u r e i t h e r a s a d i s t r i b u t e d t i m e v a r y i n g l o a d due t o a w i n d g u s t o r a i r b l a s t , o r a s a c o n c e n t r a t e d t i m e v a r y i n g p o i n t l o a d a s i n t h e c a s e o f an o b j e c t s t r i k i n g a s t r u c t u r a l member. I n b o t h s i t u a t i o n s , a k n o w l e d g e o f t h e e x a c t v a r i a t i o n o f l o a d w i t h t i m e , a l t h o u g h d e s i r a b l e f r o m t h e d e s i g n p o i n t o f v i e w , i s d i f f i c u l t t o a c q u i r e . I n t h e a b s e n c e o f a p r e c i s e k n o w l e d g e o f t h e l o a d v s . t i m e h i s t o r y o f t h e i m p a c t , i t i s c o n v e n i e n t t o work w i t h " e n e r g y " v a l u e s . I m p a c t , i n most c a s e s , i n v o l v e s an e x t e r n a l a g e n c y c a p a b l e o f i m p a r t i n g e n e r g y t o t h e s t r u c t u r a l e l e m e n t . The e x t e r n a l a g e n c y c o u l d be t h e s h a k i n g g r o u n d u n d e r n e a t h a b u i l d i n g , o r a m i s s i l e f i r e d a t a m i l i t a r y i n s t a l l a t i o n . The s t r u c t u r e , w i t h a l l o f i t s e l e m e n t s , r e s p o n d s t o t h i s e x t e r n a l l y a v a i l a b l e e n e r g y by d e f o r m i n g . S t r e s s e s and s t r a i n s a r e d e v e l o p e d w i t h i n t h e s t r u c t u r e , a n d t h e s t r u c t u r e c o n t i n u e s t o a b s o r b e n e r g y a s s t r a i n e n e r g y . I n t h i s s i t u a t i o n , t h e r e a r e t h r e e p o s s i b i l i t i e s : ( 1 ) A l l o f t h e e x t e r n a l l y a v a i l a b l e e n e r g y may be a b s o r b e d a s s t r a i n e n e r g y w i t h o u t c a u s i n g any damage t o t h e s t r u c t u r e . Once t h e e x t e r n a l l o a d i s r e m o v e d , s u c h a s t r a i n e d s t r u c t u r e w i l l d i s s i p a t e i t s s t r a i n e n e r g y by t h e v a r i o u s d i s s i p a t i o n m e c h a n i s m s , (2 ) An i n t e r m e d i a t e c a s e i n w h i c h t h e s t r u c t u r e i s damaged, b u t c o l l a p s e i s n o t p r e c i p i t a t e d , a n d ( 3 ) The e x t e r n a l l y a v a i l a b l e e n e r g y may be more t h a n t h e maximum 112 1 1.3 s t r a i n energy the s t r u c t u r e or i t s elements can abs o r b w i t h o u t f r a c t u r i n g . F r a c t u r e w i l l i n i t i a t e a t the l o c a t i o n s where the c r i t i c a l s t r e s s e s a r e exceeded, and c o l l a p s e may r e s u l t . I t i s the t h i r d p o s s i b i l i t y t h a t i s of s e r i o u s c o n c e r n i n dynamic l o a d i n g s i t u a t i o n s because of the c a t a s t r o p h i c n a t u r e of f a i l u r e . The f i r s t p o s s i b i l i t y , i n which the s t r u c t u r e remains e l a s t i c d u r i n g t h e whole l o a d i n g h i s t o r y , a l t h o u g h s t r u c t u r a l l y f e a s i b l e , i n v o l v e s h e a v i l y o v e r d e s i g n e d s e c t i o n s , e c o n o m i c a l l y u n a c c e p t a b l e . The problem can be overcome, a t l e a s t i n p a r t , by g i v i n g the s t r u c t u r e added d u c t i l i t y by which the s t r u c t u r e would c o n t i n u e t o deform under the l o a d , a b s o r b i n g the e x t e r n a l energy. A c a t a s t r o p h i c type of f a i l u r e c o u l d , w i t h t h i s added d u c t i l i t y change t o a " y i e l d b e f o r e f a i l " t ype of f a i l u r e . C o n c r e t e , compared t o m e t a l s , absorbs v e r y l i t t l e energy b e f o r e a c a t a s t r o p h i c f a i l u r e r e s u l t s . T h i s mode of f a i l u r e , o c c u r r i n g w i t h o u t much w a r n i n g , can be changed t o some e x t e n t by i n c o r p o r a t i n g f i b r e s , or s t e e l r e i n f o r c i n g b a r s , or b o t h i n t o the m a t r i x . The b e h a v i o u r of the r e s u l t i n g c o m p o s i t e s under dynamic c o n d i t i o n s depends, among o t h e r t h i n g s , upon the way i n which the m a t r i x behaves under t h e s e c o n d i t i o n s . A knowledge of the b e h a v i o u r of p l a i n c o n c r e t e under dynamic c o n d i t i o n s i s t h e r e f o r e e s s e n t i a l , p a r t i c u l a r l y because of the s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e . An account of the the dynamic p r o p e r t i e s of 1 14 hardened cement p a s t e , and p l a i n c o n c r e t e , w i l l be p r e s e n t e d i n t h i s c h a p t e r . The s u c c e e d i n g c h a p t e r s w i l l examine the e f f e c t of ad d i n g f i b r e s , the e f f e c t of ad d i n g c o n v e n t i o n a l s t e e l r e i n f o r c e m e n t , a n d the e f f e c t of add i n g b o t h . 6.2 COMPARISON OF THE IMPACT BEHAVIOUR OF PASTE AND CONCRETE  BEAMS The p r o p e r t i e s of p l a i n c o n c r e t e depend t o q u i t e an e x t e n t on the p r o p e r t i e s of the hardened p a s t e . Hence an u n d e r s t a n d i n g of the be h a v i o u r of c o n c r e t e under h i g h s t r e s s r a t e s i s p o s s i b l e o n l y w i t h an u n d e r s t a n d i n g of the be h a v i o u r of the p a s t e under s i m i l a r c o n d i t i o n s . T h e r e f o r e , i n t h i s s t u d y , t h r e e beams made w i t h pure p a s t e (w/c r a t i o of 0.35) were t e s t e d i n the impact machine. A hammer drop h e i g h t of 0.5m was used. T a b l e 6.1 c o n t a i n s the r e s u l t s of the above t e s t s . The r e s u l t s o b t a i n e d w i t h normal s t r e n g t h c o n c r e t e beams t e s t e d under i d e n t i c a l c o n d i t i o n s have a l s o been t a b u l a t e d f o r com p a r i s o n . F i g u r e 6.1 p r e s e n t s the g e n e r a l n a t u r e of the l o a d v s . d i s p l a c e m e n t p l o t s t o f a i l u r e f o r bo t h p a s t e and normal s t r e n g t h c o n c r e t e . F i g u r e 6.2 p r e s e n t s the p o r t i o n s of l o a d v s . d i s p l a c e m e n t p l o t s p r i o r t o the peak bending l o a d s . I t can be seen from F i g u r e s 6.1 and 6.2 t h a t under impact l o a d i n g , p a s t e appears t o be m a r g i n a l l y weaker than Table 6.1 Comparison between the Dynamic Properties al Paste and Concrete Paste (3)1 Concrete (6)1 Max Min. Mean s Max. Min. Mean s Max. Observed 28793 28093 28428 286 31251 27388 29319 1931 Tup Load (N) Max. Beam 1986 1928 1955 24 1858 1718 1788 70 Accel, (m/sec2) Peak Bending 8470 7462 7819 461 11658 9267 10462 1195 Load (N) Deflection at 479 400 429 35.3 469 384 426 42.5 Peak Bending Load (xlO"6Km) Beam Energy 2.8 2.2 2.5 0.25 4.7 2.6 3.7 1.0 at Peak Bending Load (Nm) Failure Strain 3.11 2.60 2.79 0.23 3.05 2.49 2.77 0.28 (xl<r4) Modulus of 9.8 8.6 9.0 0.53 13.5 10.7 12.0 1.37 Rupture (MPa) Fracture Energy 39.2 30.8 34.9 3.5 47.9 44.5 46.2 1.7 (Nm) lNumber of specimens tested. 116 1 17 c o n c r e t e . The modulus of r u p t u r e (MOR), as d e t e r m i n e d from an e l a s t i c a n a l y s i s (Eqn.4.34a), seems t o be about 30% h i g h e r f o r c o n c r e t e than f o r the p a s t e . The v a l u e s of f r a c t u r e e n e r g i e s i n T a b l e 6.1 i n d i c a t e the more b r i t t l e n a t u r e of the p a s t e compared t o c o n c r e t e . I n t e r e s t i n g l y , the f a i l u r e s t r a i n s , c a l c u l a t e d u s i n g the e l a s t i c a n a l y s i s (Eqn. 4.34b), seem t o have the same v a l u e f o r p a s t e and c o n c r e t e . An i n s p e c t i o n of the f r a c t u r e s u r f a c e s of the broken h a l v e s of the beams i n d i c a t e d t h a t w h i l e the s u r f a c e was v e r y even and smooth f o r the p a s t e , i t was f a i r l y uneven f o r c o n c r e t e . The uneven t f r a c t u r e s u r f a c e suggested t h a t , i n c o n c r e t e , the c r a c k f o l l o w e d a t o r t u o u s p a t h around the a g g r e g a t e s , C o n c r e t e can be c o n s i d e r e d t o be a d i s p e r s i o n of i n e r t a g gregate p a r t i c l e s i n a p a s t e m a t r i x . The bond between the p a s t e and the a g g r e g a t e s i s i n p a r t due t o the m e c h a n i c a l i n t e r l o c k i n g of the a g g r e g a t e s and the p a s t e , and i n p a r t due t o a d h e s i o n . Under s t a t i c l o a d i n g , the p a s t e and c o n c r e t e were found t o be v e r y s i m i l a r i n t h e i r f l e x u r a l s t r e n g t h s . The t r e n d was p r e s e r v e d i n the dynamic s i t u a t i o n as w e l l ( F i g u r e 6.2). The o c c u r r a n c e of almost the same v a l u e of f a i l u r e s t r a i n i n b o t h p a s t e and c o n c r e t e s u g g e s t s t h a t i t may not be a l i m i t i n g s t r e s s but a l i m i t i n g t e n s i l e s t r a i n t h a t d e t e r m i n e s t h e s t r e n g t h of c o n c r e t e a t a p a r t i c u l a r s t r a i n r a t e . The i n c o r p o r a t i o n of a g g r e g a t e s t h a t a r e s t i f f e r than the p a s t e r e s u l t s i n an i n c r e a s e i n the s t i f f n e s s of the r e s u l t i n g c o n c r e t e over t h a t of the p a s t e . Thus, t o a c h i e v e the same l e v e l of s t r a i n b o t h i n c o n c r e t e 118 and i n p a s t e , the e f f e c t i v e s t r e s s i n c o n c r e t e has t o be h i g h e r than t h a t i n the p a s t e . The h i g h e r i n i t i a l e l a s t i c modulus i n the case of c o n c r e t e ( F i g 6.2) s u p p o r t s t h i s argument. Thus, a t the same f a i l u r e s t r a i n , c o n c r e t e can s u p p o r t a h i g h e r l o a d than the p a s t e . Complete f r a c t u r e of the c o n c r e t e r e q u i r e d a h i g h e r energy than f r a c t u r e of the p a s t e . The f r a c t u r e energy, which i s the a r e a under the l o a d v s . d i s p l a c e m e n t p l o t t o f a i l u r e , depends upon the magnitudes of the l o a d s and d i s p l a c e m e n t s . As can be seen from F i g u r e 6.1, f o r the same d i s p l a c e m e n t s , the c o n c r e t e beam c o u l d support m a r g i n a l l y h i g h e r l o a d s than the p a s t e beam. I f the c r a c k i s assumed t o n u c l e a t e a t the peak l o a d , the u n s t a b l e growth of the c r a c k i n c o n c r e t e seems t o r e q u i r e a h i g h e r d r i v i n g f o r c e , i . e . , the c r a c k i n the c o n c r e t e seems t o undergo a h i g h e r r e s i s t a n c e t o i t s growth than t h a t i n the p a s t e . The t o r t u o u s p a t h taken by the c r a c k around the aggregate p a r t i c l e s i n c o n c r e t e , r e s u l t i n g i n l a r g e r a p p a r e n t f r a c t u r e s u r f a c e a r e a , and the s t r a i g h t p a t h taken by the c r a c k i n the p a s t e , r e s u l t i n g i n a smooth f r a c t u r e s u r f a c e , seem t o s u p p o r t t h i s argument. 119 6.3 EFFECT OF STRESS RATE ON PLAIN NORMAL STRENGTH (NS)  CONCRETE BEAMS To s t u d y the e f f e c t of s t r a i n r a t e on normal s t r e n g t h c o n c r e t e , p l a i n c o n c r e t e beams were t e s t e d a t v a r i a b l e s t r a i n r a t e s . Both s t a t i c and dynamic t e s t s were c a r r i e d o u t . The s t a t i c t e s t s were conducted i n a u n i v e r s a l t e s t i n g _ 7 machine, w i t h i t s c r o s s - h e a d moving a t 4x10 m/sec. The dynamic t e s t s were conducted i n the drop weight impact machine. The dynamic t e s t s were c a r r i e d out u s i n g t h r e e d i f f e r e n t hammer dro p h e i g h t s , of 0.15m, 0.25m, and 0.5m. Ta b l e 6.2a shows the r e s u l t s from the s t a t i c t e s t i n g , w h i l e t a b l e 6.2b c o n t a i n s the r e s u l t s from the drop weight impact t e s t s . I t may be seen t h a t the s t r a i n r a t e s imposed on the c o n c r e t e v a r i e d from about 3x10 /sec i n the s t a t i c case t o about 0.5/sec i n the dynamic case w i t h a 0.5m drop. The b e h a v i o u r of c o n c r e t e a t t h e s e extreme r a t e s of s t r a i n i n g i s shown i n the l o a d v s . d e f l e c t i o n p l o t s of F i g u r e 6.3. I t can be seen from F i g u r e 6.3 t h a t upon i n c r e a s i n g the s t r a i n r a t e from 3x10 /sec i n the s t a t i c case t o about 0.5/sec i n the impact range (=* 1.5x10 s t i m e s i n c r e a s e ) , the p r o p e r t i e s of c o n c r e t e seem t o change c o n s i d e r a b l y . Even w i t h i n the dynamic range, a v a r i a t i o n i n the drop h e i g h t of the hammer r e s u l t e d i n a c o n s i d e r a b l e v a r i a t i o n i n the p r o p e r t i e s of c o n c r e t e ( F i g u r e 6.3). In g e n e r a l , i t may be seen t h a t c o n c r e t e i s a v e r y s t r a i n r a t e s e n s i t i v e m a t e r i a l . The main d i f f e r e n c e s between the s t a t i c and dynamic p r o p e r t i e s a r e the i n c r e a s e d s t r e n g t h and the Table 6.2(a) Static Behaviour oi Normal Strength Plain Concrete Beams Static (3)1 Max Min. Mean s Peak Bending Load (N) 6766 6000 6344 306 Deflection at Peak Bending 388 Load (xlO_ 6Km) 289 307 20 Beam Energy at Peak 1.1 Bending Load (Nm) 0.88 1.0 0.08 Failure Strain (xl0~4) 2.7 2.4 2.5 0.17 Modulus of Rupture (MPa) 6.3 5.5 5.9 0.29 Fracture Energy (Nm) 6.5 2.9 5.5 1.5 Mean Strain Rate (/sec) 3xl0"7 Mean Stress Rate 0.0079 (MPa/sec) ^Number of specimens tested. Table 6.2(b) Dynamic behariour a! Wain Mflimal S U M i l u Concrete Height . of Hammer Drop (m) O.I5ra ( « ) ' 0.15m (6)' 0.50ra (7)' Max Min Mean s Mas Min Mean s M a i M m Mean s M a * . Tup 21309 18803 19776 963 29840 21666 25386 3121 37567 35810 36196 677 Load (N) Max. 12957 10512 11306 632 15401 11987 13203 1314 20291 16868 19264 1278 Inertial Load (N) Pea l 9440 7782 8470 604 14668 9178 12183 2401 17727 16452 16932 428 Bending Load (N) Eneigj at 3.5 1.5 2.5 0.7 3.7 2.7 3.0 0.4 9.0 2.2 6.4 2.5 Peak I-oad (Nm) Fracture 30.9 19.1 25.8 4.3 59.6 26.5 42.0 12.4 100.5 87.8 90.1 6.5 Energj (Nm) Modulus of 8.7 7.2 7.8 0.5 13.6 8.5 11.3 2.2 16.4 15.2 15.7 0.4 Rupture ( M P a ) Failure 3.0 2.1 2.7 0.4 3.6 3.0 3.5 0.3 4.0 2.9 3.5 0.4 Strain ( X I o - 4) Mean 3920 8057 19587 Stress Rate (MPa/sec) Me" ».14 0.25 0.44 Strain rale (/sec) 'Number of ipeclmes tested. 1 22 A D E F L E C T I O N , mm F i g u r e 6 . 3 - S t a t i c and Dynamic Load D e f l e c t i o n P l o t s f o r Normal S t r e n g t h C o n c r e t e 1 23 h i g h e r f r a c t u r e e n e r g i e s i n the dynamic case compared t o those i n the s t a t i c c a s e . The d i f f e r e n c e s between the s t a t i c and the dynamic b e h a v i o u r of c o n c r e t e can be e x p l a i n e d on the b a s i s of f r a c t u r e mechanics by a c o m b i n a t i o n of the c l a s s i c a l G r i f f i t h t h e o r y , and the concept of s u b c r i t i c a l c r a c k growth ( s t a t i c f a t i g u e ) . A c c o r d i n g t o the G r i f f i t h t h e o r y , the t i p of a c r a c k or a f l a w i n a l o a d e d continuum i s a p o i n t of s t r e s s c o n c e n t r a t i o n . Even when the nominal s t r e s s i s f a r below the t h e o r e t i c a l s t r e n g t h of the m a t e r i a l , the s t r e s s a t the l e a d i n g edge of the c r a c k may w e l l approach the t h e o r e t i c a l s t r e n g t h and f a i l u r e may r e s u l t . The s t r e s s e s i n the v i c i n i t y of a l o a d e d c r a c k a r e a f u n c t i o n of the nominal s t r e s s , and the c r a c k geometry. The combined e f f e c t of these two parameters can be e x p r e s s e d i n terms of j u s t one parameter, c a l l e d the s t r e s s i n t e n s i t y f a c t o r K j . For a b r i t t l e m a t e r i a l t h e r e e x i s t s a c r i t i c a l v a l u e of the s t r e s s i n t e n s i t y f a c t o r ( Kic^' a m a t e r i a l c o n s t a n t , a t which u n s t a b l e c r a c k growth b e g i n s , l e a d i n g t o a sudden f a i l u r e . A l t h o u g h , L i n e a r E l a s t i c F r a c t u r e Mechanics (LEFM) may not be a s u i t a b l e t o o l f o r a n a l y z i n g the f r a c t u r e b e h a v i o u r of c o n c r e t e ( 3 4 ) , i t s use i n p r e d i c t i n g the s t r e s s r a t e s e n s i t i v i t y of c o n c r e t e i s o f t e n made. In a l o a d e d member the v a l u e of s t r e s s i n t e n s i t y f a c t o r i s g i v e n by Kj = YoVa (6.1) 124 and a t f a i l u r e , K I C = Ya cVlT- (6.2) where Y i s a c o n s t a n t which depends on the specimen geometry, a i s the nominal s t r e s s , and a i s the f l a w l e n g t h ; the s u b s c r i p t c denotes the v a l u e s a t f a i l u r e . Thus, t h e r e e x i s t s a c r i t i c a l c o m b i n a t i o n of the a p p l i e d s t r e s s and the c r a c k l e n g t h t h a t can cause f a i l u r e . A c c o r d i n g t o the concept of s u b c r i t i c a l c r a c k growth, a c r a c k of s u b c r i t i c a l s i z e can grow under a s u b c r i t i c a l s t r e s s by mechanisms such as s t r e s s c o r r o s s i o n ; when i t reaches the c r i t i c a l s i z e ( s a t i s f y i n g E q u a t i o n 6.2) f a i l u r e w i l l o c c u r . The r a t e of s u b c r i t i c a l c r a c k growth has been found t o f o l l o w the f o l l o w i n g e q u a t i o n , V = AK? 1 (6.3) where V i s the c r a c k v e l o c i t y , Kj i s the s t r e s s i n t e n s i t y f a c t o r i n the opening mode, and A, n a r e c o n s t a n t s . The growth of a s u b c r i t i c a l c r a c k o c c u r s a t an i n c r e a s i n g r a t e under a c o n s t a n t nominal s t r e s s as the c r a c k extends ( F i g . 6.4a). I f the l o a d i n g i s v e r y slow, the s u b c r i t i c a l f l a w s have enough time t o grow, t o approach the c r i t i c a l v a l u e , and t o cause f a i l u r e . On the o t h e r hand, v e r y r a p i d l o a d i n g a l l o w s 125 Log * F i g u r e 6 . 4 - T h e parameter "n", d e t e r m i n e d from (a) d i r e c t o b s e r v a t i o n of the c r a c k v e l o c i t y and (b) v a r i a b l e s t r e s s r a t e t e s t s l i t t l e or no time f o r the s u b c r i t i c a l f l a w s t o grow. T h e r e f o r e , the member can s u p p o r t , momentarily a h i g h e r l o a d , g i v i n g an a p p a r e n t l y i n c r e a s e d s t r e n g t h . By how much the s t r e n g t h o b t a i n e d a t one s t r e s s r a t e d i f f e r s from t h a t o b t a i n e d a t some o t h e r s t r e s s r a t e depends the v a l u e of n. The v a l u e of n can be o b t a i n e d as f o l l o w s : l e t , a = s t r e s s r a t e = da dt 1 26 V = c r a c k v e l o c i t y = da dt oa a_ da " V Now, a n d ' Kj = Y c/T T h e r e f o r e , o r , do _2 d a = A Y n o n a n / 2 do = —rx— da A Y n o n a n / 2 o do = n Ca"2 AY da] On i n t e g r a t i n g we g e t , 1 log o f = C + - logo 1 (6.4) where C i s a c o n s t a n t . 1 27 Thus p l o t t i n g l o g a ^ v s . l o g a would produce a s t r a i g h t l i n e p l o t as shown i n F i g u r e 6.4b, w i t h a s l o p e of l/n+1 When the v a l u e s e x p e r i m e n t a l l y o b s e r v e d i n t h i s study f o r normal s t r e n g t h c o n c r e t e a r e p l o t t e d , t h e r e s u l t i n g l o g c j v s . l o g a p l o t l o o k s l i k e the one shown i n F i g u r e 6.5. As can be seen from t h i s p l o t , the i d e a l s t r a i g h t l i n e n a t u r e of the t h e o r e t i c a l p l o t of F i g u r e 6.4b i s not obs e r v e d e x p e r i m e n t a l l y . The ob s e r v e d p l o t s u g g e s t s t h a t w i t h an i n c r e a s e i n the s t r a i n r a t e , the v a l u e of the c o n s t a n t n d e c r e a s e s . S i m i l a r o b s e r v a t i o n s have been r e p o r t e d by S u a r i s and Shah ( 3 4 ) . The n o r m a l l y o b s e r v e d v a l u e s of n, o b t a i n e d by v a r y i n g the s t r a i n r a t e i n a s t r a i n r a t e c o n t r o l l e d t e s t i n g machine, a r e found t o l i e i n the range of 20 t o 50. However, i n the p r e s e n t s t u d y , i n the range of s t r a i n r a t e s a s s o c i a t e d w i t h impact, a v a l u e of n as low as 1.50 was o b s e r v e d . B i r k i m e r (53) has r e p o r t e d a v a l u e as low as n=2.00 under e x t r e m e l y h i g h s t r a i n r a t e s . A r e d u c t i o n i n the" v a l u e of n w i t h an i n c r e a s e i n the s t r a i n r a t e s u g g e s t s a lower s l o p e f o r the l o g V - l o g K j p l o t shown i n F i g u r e 6.4a a t h i g h e r s t r e s s r a t e s . I t has been t a c i t l y assumed i n the above a n a l y s i s t h a t the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r remains the same under d i f f e r e n t s t r a i n r a t e s . However, as w i l l be seen l a t e r , t he c r i t i c a l s t r e s s i n t e n s i t y f a c t o r i t s e l f i n c r e a s e s w i t h the s t r a i n r a t e , f u r t h e r i n c r e a s i n g the s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e a t h i g h s t r a i n r a t e s . 128 1.3., 1.2-1 . Log 6 , HPa/3ec F i g u r e 6 . 5 - D e t e r m i n a t i o n of parameter "n" f o r Normal S t r e n g t h C o n c r e t e 129 6.4 EFFECT OF STRESS RATE ON PLAIN HIGH STRENGTH (HS)  CONCRETE BEAMS In t h i s s t u d y , the h i g h s t r e n g t h c o n c r e t e mix was produced by add i n g EMSAC6 as d e s c r i b e d i n Chapter 4. M i c r o s i l i c a (or s i l i c a fume), i s a by-product of the e l e c t r o m e t a l l u r g i c a l i n d u s t r y . I t p l a y s a double r o l e , f i r s t as a f i l l e r , and then as a p o z z a l a n i c m a t e r i a l which r e a c t s w i t h Ca(OH) 2f a product of h y d r a t i o n . These u l t r a f i n e p a r t i c l e s of s i l i c a (5 nm t o 0.5jLtm) a r e packed i n the i n t e r s t i t i a l spaces between the p o r t l a n d cement c l i n k e r g r a i n s . The d i s p e r s i o n of the t i n y p a r t i c l e s i n the space around and between the cement g r a i n s i s shown i n F i g u r e 6 . 6 . E f f i c i e n t m i x i n g of m i c r o s i l i c a n e c e s s i t a t e s the use of a s u p e r p l a s t i c i z e r . 6 A m i c r o s i l i c a produced by Elkem C h e m i c a l s , I n c . , P i t t s b u r g h , P e n n s y l v a n i a . F i g u r e 6 .6-Mix w i t h o u t ( l e f t ) and w i t h ( r i g h t ) M i c r o s i l i c a 1 30 The i n c r e a s e i n s t r e n g t h due t o the a d d i t i o n of m i c r o s i l i c a may be a t t r i b u t e d i n p a r t t o the e l i m i n a t i o n of the l a r g e r pores and i n p a r t t o the more u n i f o r m d i s t r i b u t i o n of the h y d r a t i o n p r o d u c t s , though the f a c t t h a t the p r o d u c t i o n t e c h n i q u e p e r m i t s a somewhat lower w/c r a t i o i s p r o b a b l y the most i m p o r t a n t f a c t o r . I n t i m a t e d i s p e r s i o n of m i c r o s i l i c a improves the performance of the b i n d e r and improves i t s bond w i t h the a g g r e g a t e p a r t i c l e s and the r e i n f o r c i n g b a r s . The dense m i c r o s t r u c t u r e a l s o l e a d s t o reduced p e r m e a b i l i t y and i n c r e a s e d d u r a b i l i t y . To s t u d y the e f f e c t of s t r a i n r a t e on t h e p r o p e r t i e s of h i g h s t r e n g t h c o n c r e t e (HS), beams were t e s t e d i n t h r e e p o i n t bending i n an i d e n t i c a l manner as the normal s t r e n g t h (NS) beams ( S e c t i o n 6.3). T a b l e 6.3a g i v e s the r e s u l t s of the s t a t i c t e s t s and T a b l e 6.3b g i v e s the r e s u l t s of the impact t e s t i n g , c a r r i e d out a t t h r e e h e i g h t s of hammer drop. I t can be noted from T a b l e s 6.3a and 6.3b t h a t , s i m i l a r t o NS c o n c r e t e , HS c o n c r e t e i s a l s o a v e r y s t r a i n r a t e s e n s i t i v e m a t e r i a l . The main e f f e c t s of i n c r e a s i n g the s t r a i n r a t e a r e i n the i n c r e a s e d s t r e n g t h and i n the i n c r e a s e d f r a c t u r e energy. Based on the d e r i v a t i o n p r e s e n t e d i n S e c t i o n 6.3, a p l o t of l o g a ^ v s . l o g a f o r HS c o n c r e t e i s shown i n F i g u r e 6.7. T h i s p l o t s u g g e s t s t h a t over the range of s t r a i n r a t e s used i n t h i s s t u d y , t h e r e does not e x i s t a unique v a l u e of the parameter n. The v a l u e of n seems t o Table 6.3(a) Static Properties of Plain High strength Concrete Beams Static (4)1 Max Min. Mean s Peak Bending Load (N) 12806 8184 9720 1809 Deflection at Peak Bending 560 Load (xl0"6Xm) 480 500 34 Beam Energy at Peak 3.6 Bending Load (Nm) 2.0 2.5 0.7 Failure Strain (xl0~4) 4.5 3.9 4.1 0.3 Modulus of Rupture (MPa) 11.8 7.6 9.0 1.7 Fracture Energy (Nm) 3.4 2.0 2.8 0.6 Mean Strain Rate (/sec) - 3xl0 - 7 -mean Stress Rate (MPa/sec) - 0.0075 -1Number of specimens tested. T a b l e 6.3(b) D y n a m i c hehanlnur flj E l l i n H i g h S t r e n g t h C o n c r e t e H e i g h t o f H a m m e r D r o p (m) 0.15m ( 6 ) ' 0.2Sra ( 6 ) ' 0 .50m <7)' M a i M i n M e a n s M a x M i n M e a n s M a x M i n M e a n s M a x . T u p 24172 17011 19588 2715 28787 22384 24144 2497 39320 35110 3 6 6 5 2 1725 L o a d ( N ) M a x . 12456 8606 9682 1604 11777 9480 10773 925 19025 16760 17892 1132 I n e r t i a l L o a d ( N ) P e a k 11694 8388 9906 1183 18579 10573 13371 2991 19206 18314 18760 446 B e a d i n g L o a d ( N ) E n e r g y at 2.9 1.8 2.4 0.5 3.0 1.9 2.5 0.4 5.4 3.8 4.6 0.7 P e a k L o a d ( N m ) F r a c t u r e 33.5 20.8 25.1 5.0 43.7 31.0 35 .0 4.7 100.7 57.4 74 .9 18.6 E n e r g j ( N r . ) M o d u l u s o f 10.8 7.8 9.2 1.1 17.2 9.8 12.4 2.8 17.8 16.9 17.4 U.4 R u p t u r e ( M P a ) F a i l u r e 2.6 1.6 2.0 0.4 3.1 1.6 2.4 0.5 3.9 3.1 3.5 0.4 S t r a i n ( X 1 0 - 4 ) M e a n 4584 ' 10316 2 8 9 0 5 S t r e s s R a t e ( M P a / s e c ) M e a n 0.1 • 0.2 0.6 S t r a i n ra te ( / s e c ) 'Number of specimens tested. 133 F i g u r e 6 . 7 - D e t e r m i n a t i o n of parameter "n" f o r High S t r e n g t h Concre te 134 i n c r e a s e w i t h an i n c r e a s e i n the s t r e s s r a t e . S i m i l a r o b s e r v a t i o n s were r e p o r t e d f o r NS c o n c r e t e i n S e c t i o n 6.3. The s l o p e of the h i g h s t r a i n r a t e p o r t i o n of t h e p l o t was found t o c o r r e s p o n d t o a v a l u e of n=2.2. 6.5 COMPARISON BETWEEN NORMAL STRENGTH AND HIGH STRENGTH  CONCRETE The a d d i t i o n of m i c r o s i l i c a seems t o improve the p r o p e r t i e s of c o n c r e t e under s t a t i c l o a d i n g . However, the s u p e r i o r performance of m i c r o s i l i c a c o n c r e t e over normal c o n c r e t e i n s t a t i c s i t u a t i o n s may not n e c e s s a r i l y imply i t s s u p e r i o r i t y i n dynamic s i t u a t i o n s . A comparison of the l o g a ^ v s . l o g a p l o t s ( F i g u r e s 6.5 and 6.7) shows t h a t h i g h s t r e n g t h c o n c r e t e behaves i n almost the same way as does normal s t r e n g t h c o n c r e t e . As mentioned e a r l i e r , the d e v i a t i o n from the e x p e c t e d l i n e a r n a t u r e of the l o g a ^ v s . l o g a p l o t ( F i g u r e 6.4b) i s p r o b a b l y because of the change i n the f r a c t u r e toughness ( K j C ) i t s e l f w i t h a change i n the s t r e s s r a t e . A comparison of the dynamic performance of HS c o n c r e t e w i t h NS c o n c r e t e i s p r e s e n t e d i n F i g u r e s 6.8a, b and c. F i g u r e 6.8a shows the peak bending l o a d s o b t a i n e d f o r the t h r e e drop h e i g h t s and F i g u r e s 6.8b and c show the c o r r e s p o n d i n g v a r i a t i o n s i n the f r a c t u r e energy and the f a i l u r e s t r a i n , r e s p e c t i v e l y . The h i g h e r peak bending l o a d s o b t a i n e d i n the case of HS c o n c r e t e over NS c o n c r e t e f o r a g i v e n drop h e i g h t seem t o suggest t h a t a c o n c r e t e which i s 135 s t r o n g e r i n s t a t i c c o n d i t i o n s i s s t r o n g e r under impact l o a d i n g as w e l l . However, HS c o n c r e t e was a l s o found t o be more b r i t t l e than NS c o n c r e t e f o r a g i v e n drop h e i g h t ( F i g u r e 6.8b), as i n d i c a t e d by i t s reduced f r a c t u r e energy. F i n a l l y , the s t r a i n a t the peak l o a d , r e f e r r e d t o here as the f a i l u r e s t r a i n , which i s p r o p o r t i o n a l t o the d i s p l a c e m e n t a t the peak l o a d , was found t o be h i g h e r f o r NS c o n c r e t e than f o r HS c o n c r e t e a t a g i v e n h e i g h t of hammer drop. I t s h o u l d be noted here t h a t the v a l u e of s t r a i n a t the peak l o a d , o b t a i n e d by u s i n g Eqn. 4.34b, i s a measure of the average s t r a i n o n l y , and does not i n d i c a t e e i t h e r the magnitudes of the s t r a i n s l o c a l l y or the v a r i a t i o n of s t r a i n from one p o i n t t o a n o t h e r . F i g u r e 6.9a shows a photograph of the f r a c t u r e s u r f a c e o b t a i n e d from a NS beam t e s t e d d y n a m i c a l l y . F i g u r e 6.9b shows the c o r r e s p o n d i n g f r a c t u r e s u r f a c e o b t a i n e d w i t h HS c o n c r e t e . I t can be seen t h a t w h i l e the f r a c t u r e s u r f a c e o b t a i n e d w i t h normal s t r e n g t h c o n c r e t e was uneven and w i t h o u t any aggregate f a i l u r e s , the f r a c t u r e s u r f a c e f o r HS c o n c r e t e was smooth and w i t h many aggr e g a t e f a i l u r e s . F a i l u r e s i n b r i t t l e m a t e r i a l s o c c u r due t o the b r e a k i n g of the atomic bonds and the p r o p a g a t i o n of c r a c k s . S i n c e t h e r e i s r e s i s t a n c e t o c r a c k growth, energy has t o be s u p p l i e d f o r c o n t i n u e d c r a c k p r o p a g a t i o n . In the case of an i d e a l l y b r i t t l e m a t e r i a l , the energy consumed d u r i n g a u n i t crack' e x t e n s i o n , c a l l e d the c r a c k growth r e s i s t a n c e R, c o n s i s t s o n l y of the energy r e q u i r e d f o r the b r e a k i n g of the 136 40 32 z * 2 4 < o l 8 B 0 (a) ' I ' l l ' 0 0.15 0.3 0.45 0.6 0.75 HEIGHT OF HAMMER DROP.m 100 ' . 8 0 ->-e ^ 6 0 -hi U l cc 4 0 O < 20 (b) i I 1 l I l I l I 0 0.15 0.3 0.45 0.6 0.75 HEIGHT OF HAMMER DROP.m 0 0.15 0.3 0.45 0.6 0.75 HEIGHT OF HAMMER D R O P . m -F i g u r e 6.8-Comparison between Normal S t r e n g t h and High S t r e n g t h Concrete (a) Peak Bending Load, ( b ) F r a c t u r e Energy, (c) F a i l u r e S t r a i n , 137 F i g u r e 6 . 9-Photographs showing the F r a c t u r e S u r f a c e s o b t a i n e d f o r Normal S t r e n g t h and High S t r e n g t h C o n c r e t e 138 bonds a c r o s s the f r a c t u r e s u r f a c e , and as such i s a c o n s t a n t . Thus, when the s t r a i n energy r e l e a s e d upon u n i t c r a c k e x t e n s i o n i s equal t o the c r a c k r e s i s t a n c e R, c r a c k p r o p a g a t i o n w i l l b e g i n . However, c o n c r e t e i s not an i d e a l l y b r i t t l e m a t e r i a l , and the p r o p a g a t i o n of c r a c k s seems t o be preceded by the f o r m a t i o n of a p r o c e s s zone around the c r a c k t i p . The f o r m a t i o n of t h i s p r o c e s s zone , however, r e q u i r e s energy and thus the c r a c k r e s i s t a n c e i n c o n c r e t e (R) c o n s i s t s not o n l y of the s u r f a c e energy component but a l s o of the m i c r o c r a c k i n g component t h a t o c c u r s i n a zone of w i d t h e as shown i n F i g u r e 6.10, where e i s a p p r o x i m a t e l y e q u a l to the maximum aggregate s i z e i n the case of s t a t i c l o a d i n g . As was shown i n F i g u r e 6.3 and T a b l e 6.2a, even f o r a beam loaded s t a t i c a l l y , the s t r a i n energy accumulated up t o the peak l o a d (=*1.00 Nm) does not seem t o be s u f f i c i e n t t o d r i v e the c r a c k a d i s t a n c e e q u a l t o the depth of . the F i g u r e 6.10-The F i n i t e Width Zone of M i c r o c r a c k i n g That Surrounds a Crack 139 beam. The f i n i t e a r e a under the s t a t i c l o a d v s . d i s p l a c e m e n t p l o t i n the post-peak l o a d r e g i o n s u g g e s t s t h a t t he beam c o n t i n u e s t o abs o r b energy from t h e machine t o a c c o m p l i s h c r a c k growth. T h i s i s t r u e i n s p i t e of the f a c t t h a t the post-peak l o a d energy may have been u n d e r e s t i m a t e d , s i n c e the machine used f o r s t a t i c t e s t i n g was not v e r y s t i f f . Thus, u l t i m a t e l y t he beam r e q u i r e d about 5.5Nm b e f o r e the complete s e p a r a t i o n of the broken h a l v e s . In the case of dynamic l o a d i n g , the same r e a s o n i n g may be used, the o n l y d i f f e r e n c e b e i n g i n the magnitudes of the e n e r g i e s . R e f e r r i n g back t o F i g u r e 6.2 and T a b l e 6.2b (0.5m d r o p ) , w h i l e t he energy t o the peak bending l o a d was o n l y about 6.4Nm, the t o t a l f r a c t u r e energy was found t o be as h i g h as 90Nm. Thus a c r a c k under dynamic l o a d i n g seems t o r e q u i r e more energy t o grow than does a c r a c k under s t a t i c l o a d i n g . The h i g h energy r e q u i r e m e n t i n the post-peak l o a d r e g i o n i n dynamic l o a d i n g p r o b a b l y i s , i n p a r t , a consequence of a wider p r o c e s s zone (53A) or l a r g e r e ( F i g u r e 6.10). However, the exa c t d e t e r m i n a t i o n of the w i d t h of t h e c r a c k e d zone e under dynamic l o a d i n g i s not y e t p o s s i b l e . I n a d d i t i o n , the f r a c t u r e mechanisms may a l s o be d i f f e r e n t under dynamic l o a d i n g . I t i s known t h a t H i g h s t r e n g t h c o n c r e t e e x h i b i t s b e t t e r p a s t e - a g g r e g a t e bond than normal s t r e n g t h c o n c r e t e . I t i s not s u r p r i s i n g t h e r e f o r e t h a t HS c o n c r e t e appears t o undergo l e s s m i c r o c r a c k i n g than normal s t r e n g t h c o n c r e t e . However, as shown i n F i g u r e 6.11 and Tab l e 6.3, dynamic l o a d i n g on HS 1 40 0 I 2 3 4 5 6 7 8 9 IO II 12 DEFLECTION , mm F i g u r e 6.11-Stress Rate S e n s i t i v i t y of H i g h S t r e n g t h C o n c r e t e c o n c r e t e i s a l s o a s s o c i a t e d w i t h the f o r m a t i o n of a m i c r o c r a c k i n g zone which r e s u l t s i n a f i n i t e a r e a under the l o a d v s . d i s p l a c e m e n t p l o t i n the p o s t peak l o a d r e g i o n . In any c a s e , due t o i t s i n c r e a s e d bond q u a l i t y , HS c o n c r e t e i n t h i s study was always found t o be more b r i t t l e than NS c o n c r e t e . 141 6.6 EFFECT OF MOMENT OF INERTIA To study the e f f e c t of the moment of i n e r t i a of the beam on i t s dynamic b e h a v i o r , beams I00mmx125mm i n c r o s s - s e c t i o n were t e s t e d on a 960mm span f i r s t about t h e i r s t r o n g a x i s (I=0.0000162m*), and l a t e r about t h e i r weak a x i s (1=0.0000104m"). The r e s u l t s of these t e s t s are g i v e n i n T a b l e 6.4a for NS c o n c r e t e and in T a b l e 6 .4b for HS c o n c r e t e . The average nominal s t r e s s r a t e s , which were o b t a i n e d by d i v i d i n g the MOR by the time r e q u i r e d to reach the peak, for the same drop h e i g h t of 0.5m, were found to be h i g h e r for the beams t e s t e d about the s t r o n g a x i s than for the beams t e s t e d about t h e i r weak a x i s . Having o b t a i n e d the r e s u l t s at d i f f e r e n t s t r e s s r a t e s , s t r i c t l y s p e a k i n g , they can not be compared. However, s i n c e the s t r e s s r a t e s are not w ide ly d i f f e r e n t , a comparison has been at tempted h e r e . When the v a l u e s of MOR are compared, i t can be seen t h a t , f or both NS and HS c o n c r e t e s , the MORs o b t a i n e d for the beams t e s t e d about the weak a x i s are lower than f o r beams t e s t e d about the s t r o n g a x i s . A l s o , the f r a c t u r e e n e r g i e s f o r the weak a x i s beams are found to be lower than for the s t r o n g a x i s beams. One p o s s i b l e reason behind t h i s may be the d i r e c t i o n i n which the beams were c a s t . A l l of the beams were c a s t w i t h the 125mm s i d e v e r t i c a l . The e l e c t r i c immersion v i b r a t o r used for compact ion a l l o w s the water to b l e e d to the s u r f a c e d u r i n g v i b r a t i o n , r e d u c i n g the w/c r a t i o at the bottom of 142 Table 6.4a Effect pi Mmucnl al immi sm lh£ Jiysamk Behaviour of Normal Strength Concrete I = (4)' 104xl0-7 m4 I = 162x10"7 (7)1 m4 Max Min. Mean s Max. Min. Mean s Peak Bending Load (N) 12608 8589 10550 1483 17727 16452 16932 428 Modulus of Rupture (MPa) 14.5 9.9 12.2 1.7. 16.4 15.2 15.7 0.4 Fracture Energy (Nm) 62.0 49.0 56.0 5.2 100.5 87.8 90.1 6.5 Stress rate (MPa/sec) — — 15212 — 19587 — Eflfid jjf Moment of Inertia on Table 6.4b the Dynamic Behaviour Strength Concrete I = . (4)' 104xl0-7 m' I •= (7)1 164xl0-7 m4 Max Min. Mean S Max. Min. Mean s Peak Bending Load (N) 13660 9799 11250 1464 19206 18314 18760 446 Modulus of Rupture (MPa) 15.7 11.3 13.0 1.7 17.8 17.0 17.4 0.4 Fracture Energy (Nm) 51.0 33.0 40.0 7.2 100.7 57.4 74.9 18.6 Stress - - 21633 - - - 28950 -rate (MPa/sec) 'Number of specimens tested. 143 the beam w h i l e i n c r e a s i n g the w/c r a t i o a t t h e t o p . Thus, one would expect t h a t the beams t e s t e d a l o n g t h e i r s t r o n g a x i s would show h i g h e r MOR v a l u e s and h i g h e r f r a c t u r e e n e r g i e s . 6.7 CRACK DEVELOPMENT IN THE PASTE UNDER IMPACT B r i t t l e f r a c t u r e o c c u r s w i t h the r a p i d p r o p a g a t i o n of a c r a c k i n a lo a d e d continuum. The r a t e a t which the c r a c k p r o p a g a t e s i n a m a t e r i a l seems t o depend not o n l y upon the p r o p e r t i e s of the m a t e r i a l , but a l s o upon the r a t e of l o a d i n g . However, l i t t l e work has been c a r r i e d out so f a r t o measure the v e l o c i t y a t which the c r a c k p r o p a g a t e s i n c e m e n t i t i o u s m a t e r i a l s . Most of the work on c r a c k p r o p a g a t i o n has d e a l t w i t h v e r y low c r a c k v e l o c i t i e s , i n the - 8 — 2 range of 10 m/s t o 10 m/s, o b t a i n e d i n c o n t r o l l e d c r a c k growth s t u d i e s a t v e r y low r a t e s of l o a d i n g . However, a few s t u d i e s have been c a r r i e d out a t h i g h l o a d i n g r a t e s . Bhargava and Rehnstrom (54) l o a d e d c o n c r e t e p r i s m s by d e t o n a t i n g a h i g h e x p l o s i v e i n c o n t a c t w i t h the specimens. U s i n g h i g h speed photography, they found a c r a c k v e l o c i t y i n p l a i n c o n c r e t e of about 180 m/s. T e s t s c a r r i e d out by A l f o r d ( 5 5 ) , a l s o u s i n g h i g h speed photography, showed c r a c k v e l o c i t y i n hardened cement p a s t e s r a n g i n g from 50-160 m/s. He a l s o found the v e l o c i t i e s i n m o r t a r s i n the range of 30-80 m/s. Shah and John (56) m o n i t o r e d c r a c k v e l o c i t i e s i n mortar and c o n c r e t e beams under impact and r e p o r t e d c r a c k v e l o c i t i e s i n the range of I00m/s. Takeda e t 1 44 a l (57) used e x t r e m e l y h i g h l o a d i n g r a t e s , and a s p e c i a l t e s t geometry. They found the c r a c k v e l o c i t y t o be as h i g h as I000m/s. As a p a r t of the p r e s e n t s t u d y , impact t e s t s were c a r r i e d out on beams made w i t h p a s t e u s i n g a 0.50m hammer drop. To m o n i t o r the p r o p a g a t i o n of the c r a c k s d u r i n g the impact t e s t s , a h i g h speed motion p i c t u r e camera was used, r u n n i n g a t a speed of 10,000 frames per second. Thus, s u c c e s s i v e frames r e p r e s e n t an e l a p s e d time of 100 mi c r o s e c o n d s . T h i s time i n t e r v a l was s m a l l enough, compared to the d u r a t i o n of the f r a c t u r e e v e n t , t o p r o v i d e a r e a s o n a b l e r e s o l u t i o n of the c r a c k development. To dete r m i n e the r a t e s of c r a c k growth, the f i l m was viewed frame by frame on a s m a l l hand v i e w e r ; c r a c k l e n g t h was measured d i r e c t l y on the v i e w i n g s c r e e n f o r s u c c e s s i v e frames, p e r m i t t i n g a d i r e c t c a l c u l a t i o n of the c r a c k v e l o c i t y ( a t l e a s t f o r the s u r f a c e t r a c e s of the c r a c k s ) . S i n c e the e x a c t p o s i t i o n of the c r a c k t i p was hard t o judge, the v e l o c i t i e s r e p o r t e d a r e o n l y a p p r o x i m a t e . The c r a c k development f o r the p a s t e i s shown i n F i g u r e 6.12. These f i g u r e s a r e s k e t c h e s showing the c r a c k p a t t e r n at v a r i o u s t i m e s a f t e r the i n i t i a l c o n t a c t between the tup and the specimen. Thus the f i r s t frame c o r r e s p o n d s t o the i n s t a n t of f i r s t hammer and beam c o n t a c t ; a v i s i b l e c r a c k appears t e n frames (1 ms) l a t e r , and so on. The energy as computed from the a r e a under the l o a d v s . d i s p l a c e m e n t p l o t , and the c r a c k v e l o c i t y have been p l o t t e d as a f u n c t i o n of 145 NEAT CEMENT PASTE \ Y 0 10 20 30 Y i f { 40 50 60 70 • '/ 1 •t V' 80 90 100 11 0 B\f-U V V; Vfl 120 130 290 300 VT 6 3 0 720 1200 Crack development as a function of time in a hardened cement paste F i g u r e 6.12 beam subjected to impact loading. The number in each frame represents the time (in units of 0.1 ms) from the f i r s t frame shewn. 146 time i n F i g u r e 6 .13 . A v i s i b l e c r a c k appeared a t about the time t h a t the e x t e r n a l l o a d reached the peak. The c r a c k was a r r e s t e d at t imes and the p r o p a g a t i o n resumed a f t e r every a r r e s t ( F i g u r e 6 . 1 3 b ) . The v e l o c i t i e s p l o t t e d i n F i g u r e 6.13b are those of the c r a c k marked A up to 9 ms (frame 90) . Beyond t h i s t i m e , c r a c k A seemed to have been permanent ly a r r e s t e d . A f t e r 9 ms and up to f a i l u r e , the v e l o c i t i e s of c r a c k B have been p l o t t e d . I t i s i n t e r e s t i n g t o note tha t a l t h o u g h the l o a d had dropped to z e r o at about 11 ms (frame 110), the n u c l e a t i o n and p r o p a g a t i o n of some of the c r a c k s s t i l l c o n t i n u e d beyond t h i s p o i n t . Comparing the 110th frame to the 1200th frame, i t can be seen that new c r a c k s C , D, and E have appeared s i n c e the l o a d dropped to zero i n frame 110. The appearance of a h o r i z o n t a l c r a c k C i n frame 130 i n d i c a t e s tha t the s t r e s s e s are f a r from b e i n g s imple f l e x u r a l s t r e s s e s . The growth of c r a c k E i n the backward d i r e c t i o n (frame 720) a l s o s u p p o r t s the n o t i o n of the complex s t r e s s p a t t e r n w i t h i n the body of the beam undergo ing an impact . The d i s a p p e a r a n c e of c r a c k D between frames 300 and 630 seems to i n d i c a t e the c l o s i n g of a l r e a d y e x i s t i n g c r a c k s due to an u n l o a d i n g or a r e v e r s a l in s t r e s s e s . The permanent a r r e s t of c r a c k A and the appearance of c r a c k C , i n d i c a t e s a c r a c k a r r e s t phenomenon the b a s i s of which i s not yet c l e a r . The p r o p a g a t i o n of the c r a c k i n the post peak l o a d r e g i o n can be d i v i d e d i n t o the f o l l o w i n g t h r e e s tages ( F i g u r e 6 . 1 3 ) . 147 F i g u r e 6.13-(a)Energy absorbed and (b) Crack V e l o c i t y as the Crack propagates i n Paste 1 48 S t a g e - I : The N u c l e a t i o n Stage S t a g e - I I : The Steady S t a t e S t a g e - I l l : The F i n a l Stage As soon as the l o a d r e a c h e s the peak, n u c l e a t i o n o c c u r s . The v e l o c i t y of the c r a c k drops r a p i d l y and l i n e a r l y t o a v a l u e from which a slow e x p o n e n t i a l decay i n c r a c k v e l o c i t y b e g i n s and the c r a c k e n t e r s the second s t a g e . S t a g e - I I , which c o n t i n u e s f o r the l o n g e s t p e r i o d of t i m e , p recedes the f i n a l s t a g e i n which the c r a c k v e l o c i t y r i s e s a g a i n c a u s i n g a s e p a r a t i o n . S t a g e - I , t h a t a c c o u n t s f o r about 50-60% of the t o t a l d i s t a n c e t r a v e l l e d by the c r a c k a l s o a c c o u n t s f o r about 50-60% of the f r a c t u r e energy req u i r e m e n t ( F i g u r e 6.13a). On the o t h e r hand, S t a g e - I l l o c c u r r i n g a t the end of the impact event a c c o u n t s f o r o n l y about 5% of the f r a c t u r e energy. S t a g e - I l l may have i t s b a s i s i n the c o a l e s c e n c e s of the m i c r o c r a c k s a l r e a d y formed i n s t a g e - I and I I i n t o a macro c r a c k a p p e a r i n g i n S t a g e - I l l . The average v e l o c i t y of a p r o p a g a t i n g c r a c k i n p a s t e was found t o be 115 m/sec, and the maximaum v e l o c i t y i n the range of 500-600 m/sec. The average v e l o c i t y of the c r a c k o b s e r v e d here i s o n l y about 5% of the " t h e o r e t i c a l " c r a c k v e l o c i t y ( g i v e n by 0.38v/E/p) i n b r i t t l e m a t e r i a l s ( 5 8 ) . T h i s s u g g e s t s t h a t even the h y d r a t e d cement p a s t e i s not c l a s s i c a l l y b r i t t l e . 7. MODEL ANALYSIS 7.1 INTRODUCTION The b a s i c aim of e x p e r i m e n t a l work on c o n c r e t e i s t o a r r i v e a t a s e t of m a t e r i a l p r o p e r t i e s c a p a b l e of e x p l a i n i n g the e x p e r i m e n t a l l y observed f a c t s . The e n v i r o n m e n t a l c o n d i t i o n s and specimen g e o m e t r i e s used i n l a b o r a t o r y i n v e s t i g a t i o n s may or may not p r e v a i l i n p r a c t i c e . However, the b e h a v i o u r of c o n c r e t e under one s e t of c o n d i t i o n s c a n, t o some e x t e n t a t l e a s t , be used t o p r e d i c t i t s b e h a v i o u r under o t h e r s e t s of c o n d i t i o n s . The i n a b i l i t y t o g e n e r a t e i n the l a b o r a t o r y a l l p o s s i b l e s i t u a t i o n s which may be en c o u n t e r e d i n p r a c t i c e has n o r m a l l y been overcome by the use of m a t h e m a t i c a l models. However, the development of a s u c c e s s f u l model n e c e s s i t a t e s knowledge of the b e h a v i o u r of the m a t e r i a l , and the e f f e c t of v a r i o u s parameters on i t s b e h a v i o u r . Attempts have g e n e r a l l y been made t o determine a se t of fundamental m a t e r i a l p r o p e r t i e s from a l i m i t e d number of e x p e r i m e n t a l o b s e r v a t i o n s . The m a t e r i a l b e h a v i o u r under l o a d , and the mechanisms r e s p o n s i b l e f o r i t s f a i l u r e , a r e two of the parameters needed t o d e s i g n a model. Sometimes, a model may be r e q u i r e d t o d e r i v e u s e f u l i n f o r m a t i o n from the e x p e r i m e n t a l o b s e r v a t i o n s t h e m s e l v e s . I n s t r u m e n t e d impact t e s t s on b r i t t l e m a t e r i a l s can be p l a c e d i n t h i s c a t e g o r y . The l o a d v s . time p u l s e r e c o r d e d by the i n s t r u m e n t e d t u p i n such impact t e s t s i s not the a c t u a l bending l o a d on the t e s t beam. A major p a r t of t h i s c o n t a c t l o a d between the tup and the beam i s the i n e r t i a l l o a d on 149 1 50 the beam. Thus, b e f o r e any u s e f u l i n f o r m a t i o n can be d e r i v e d from such t e s t s , an i n e r t i a l c o r r e c t i o n has t o be p r o v i d e d t o t h e obser v e d t u p l o a d t o a r r i v e a t the a c t u a l bending l o a d . A l t h o u g h some i n v e s t i g a t o r s (15,34) have recommended a d d i t i o n a l i n s t r u m e n t a t i o n t o measure d i r e c t l y the i n e r t i a l l o a d or the a c t u a l bending l o a d , t h e s e t e c h n i q u e s a r e not f r e e from problems: a d d i t i o n a l i n s t r u m e n t a t i o n i s e x p e n s i v e ; some of the s e t e c h n i q u e s may a l t e r t he t e s t c o n d i t i o n s ; and, some assumptions a r e s t i l l n e c e s s a r y t o i n t e r p r e t t h e s e a d d i t i o n a l d a t a . For example, the use of a rubber pad between the t u p and the beam, as d i s c u s s e d i n Chapter 5, can s i g n i f i c a n t l y a l t e r t he s t r a i n r a t e . L i k e w i s e , the assumption of a l i n e a r a c c e l e r a t i o n d i s t r i b u t i o n may not be t r u e i n a l l the c a s e s . Appendices 7.1 and 7.2 p r e s e n t the c l a s s i c a l s o l u t i o n s t o t he problem of a beam s u b j e c t e d t o an i m p u l s e . In Appendix 7.1, the beam has been m o d e l l e d as a s i n g l e degree of freedom system (SDOF) and i n Appendix 7.2, the m u l t i - d e g r e e of freedom (MDOF) s o l u t i o n t o the same problem i s p r e s e n t e d . The e x t e r n a l l o a d p u l s e has been i d e a l i z e d as a s i n e wave i n the s e t r e a t m e n t s . I t s h o u l d be noted t h a t the c l a s s i c a l s o l u t i o n s p r e s e n t e d here a r e not c a p a b l e of h a n d l i n g an a r b i t r a r y e x t e r n a l l o a d p u l s e . They a l s o do not ta k e i n t o account m i c r o c r a c k i n g i n the c o n c r e t e and, f i n a l l y , t h ey a r e not c a p a b l e of p r e d i c t i n g the beam b e h a v i o u r a f t e r the peak e x t e r n a l l o a d i s reached. The assumption t h a t the e x t e r n a l l o a d p u l s e can be i d e a l i z e d as 151 a s i n e wave may not be g r o s s l y i n e r r o r . However, on the energy s i d e , n e g l e c t i n g the energy absorbed by the beam a f t e r the peak load can cause a gross underestimation of the f r a c t u r e energy. I t has been found i n the present study that a major p a r t of the f r a c t u r e energy absorbed by the beam l i e s i n the post-peak l o a d region (Chapter 6), f o r which the c l a s s i c a l s o l u t i o n s of Appendix 7.1 or Appendix 7.2 are i n a p p r o p r i a t e . In the pages which f o l l o w , two d i f f e r e n t models are presented. These models apply only to p l a i n concrete (concrete without f i b r e s or r e i n f o r c i n g b a r s ) . The b a s i c input to both of these models i s the e x t e r n a l l o a d pulse a c t i n g on the beam, recorded by the s t r a i n gauges i n the s t r i k i n g end of the hammer. Model A, which i s capable of a n a l y z i n g the beam only up to the peak e x t e r n a l l o a d , i s based on the energy balance p r i n c i p l e . I t i s assumed that the energy l o s t by the hammer up to the peak load i s t r a n s f e r r e d to the beam i n the form of k i n e t i c energy and bending energy ( s t r a i n energy). By assuming a c e r t a i n beam d e f l e c t i o n f u n c t i o n , t h i s energy balance concept can be expressed, at every i n s t a n t of time, as a f u n c t i o n of the c e n t r a l d e f l e c t i o n of the beam, and i t s d e r i v a t i v e s with r e s p e c t to time. A f i n i t e d i f f e r e n c e technique has been used to solve the n o n l i n e a r d i f f e r e n t i a l equation thus obtained i n the time domain. Model B i s based upon the dynamic e q u i l i b r i u m of f o r c e s . The time s t e p i n t e g r a t i o n technique has been used to 152 s o l v e the e q u a t i o n of dynamic e q u i l i b r i u m upto the peak l o a d . I t s h o u l d be noted here t h a t the post-peak l o a d m o d e l l i n g of c o n c r e t e n e c e s s i t a t e s a knowledge of the p r e c i s e manner i n which the c r a c k s propagate i n t h a t r e g i o n . In the absence of t h i s knowledge, such a m o d e l l i n g i s not p o s s i b l e y e t . On the b a s i s of the l i m i t e d r e s u l t s o b t a i n e d by the Author (Chapter 6,10 and 11) i n the f i e l d of c r a c k p r o p a g a t i o n u s i n g h i g h speed photography, v e r y l i t t l e can be s a i d w i t h any c e r t a i n t y . 153 7.2 MODEL A - EVALUATION OF BEAM RESPONSE TO AN EXTERNAL  IMPACT PULSE: ENERGY BALANCE PRINCIPLE T h i s model i s used t o e v a l u a t e the beam response t o an e x t e r n a l p u l s e . I t i s a p p l i c a b l e o n l y t o an e l a s t i c beam and, t h e r e f o r e , i t can be used t o a n a l y z e the beam response o n l y up t o the peak l o a d . At any i n s t a n t of time up t o the peak l o a d , a l l of the energy l o s t by the hammer i s assumed to have been t r a n s m i t t e d t o the beam. T h i s hammer energy a v a i l a b l e t o the beam appears i n two d i f f e r e n t forms: bending energy and k i n e t i c energy. A l l o t h e r forms of energy i n the beam are i g n o r e d . Of these two forms of energy, the bending energy which i s used up i n s t r e s s i n g t h e beam i s the prime g o a l of the a n a l y s i s . In what f o l l o w s , the s e p a r a t i o n of the bending energy from the k i n e t i c energy i s attempted. 7.2.1 As sumpt i ons 1. The beam remains e l a s t i c up t o the peak l o a d . 2. The beam d e f l e c t s i n , and o n l y i n , i t s f i r s t mode. 3. From the i n s t a n t of f i r s t c o n t a c t , the energy l o s t by the hammer i s absorbed by the beam as k i n e t i c energy and as bending energy. 4. Damping i s i g n o r e d . 5. The energy l o s t i n the e l a s t i c d e f o r m a t i o n s of the v a r i o u s p a r t s of the t e s t i n g machine i s i g n o r e d . 6. The beam d e f l e c t i o n can be assumed t o be s i n u s o i d a l i n shape, and can be expressed as u ( x , t ) = u 0 ( t ) s i n U x / l ) < 7- l ) 1 54 7.2.2 Notation u ( x , t ) : D e f l e c t i o n of the beam at l o c a t i o n x at time t (Figure 7.1(a)). u 0 ( t ) : D e f l e c t i o n at the centre of the beam at time t . A E 0 ( t ) : The t o t a l energy l o s t by the hammer up to time t . T ( t ) : K i n e t i c energy i n the beam at time t . U ( t ) : Bending energy i n the beam at time t . p: The mass d e n s i t y of c o n c r e t e . 1: Distance between the beam supports. B: The breadth of the beam. D (b) FIGURE 7.1-Assumed Beam Displacements 155 D: The depth of the beam. A E 0 ( t ) , the t o t a l energy l o s t by the hammer a t time t , can be o b t a i n e d by u s i n g the impulse v s . momentum r e l a t i o n s h i p s . E q u a t i o n 4.12 i s used f o r t h i s purpose. A E 0 ( t ) , i s assumed t o have been f u l l y t r a n s f e r r e d t o the beam (Assumption 3 ) . I f the r e s t of the terms i n the energy b a l a n c e e q u a t i o n (Eqn. 3.2) can be i g n o r e d , t h e n , A E Q ( t ) = T(t) + U(t) I f the d e f l e c t i o n a t any p o i n t i s g i v e n by Eqn. then the v e l o c i t y i s g i v e n by, u(x,t) = u 0 ( t ) s i n J p -The s l o p e a t any p o i n t w i l l be, u'(x,t) = u Q ( t ) [2-] c o s [ - ^ - ] and the c u r v a t u r e a t any p o i n t w i l l be, u " ( x , t ) = - u Q ( t ) [ 5 - ] 2 s i n [ - ^ - ] 7.2.3 Evaluation of the Kinetic Ener f>y(T(t)) As shown i n F i g u r e 7 . 1 ( b ) , i f dT i s the k i n e t i c energy of the e l e m e n t a l mass then, dT = Kmass) ( v e l o c i t y ) (7.2) ( 7 . 1 ) , (7.3) (7.4) (7.5) 156 = | (pBDdx) u 2 ( x , t ) (7.6) T(t) = /dT { 7 ' 7 ) =/|pBDu 2(x,t)dx (7.8) S u b s t i t u t i n g f o r u ( x , t ) from Eqn. 7.3 i n Eqn. 7.8 and s i m p l i f y i n g , we g e t , T(t) = pBf flj(t) (7.9) 7.2.4 Evaluation of the bending energy(U(t)) I f dU i s the s t r a i n energy i n the e l e m e n t a l mass of F i g u r e 7.1(b) t h e n , dU = i E l ( u " ( x , t ) ) 2 d x (7.10) U(t) = /dU (7.11) = i / E l ( u " ( x , t ) ) 2 d x (7.12) S u b s t i t u t i n g f o r u " ( x , t ) from Eqn. 7.5 i n Eqn. 7.12 and s i m p l i f y i n g we g e t , U(t) = u2Q(t) (7.13) 7.2.5 The total Energy F i n a l l y , s u b s t i t u t i n g Eqns. (7.9) and (7.13) i n t o Eqn. ( 7 . 2 ) , we can o b t a i n the t o t a l energy: AE Q(t) = u j ( t ) + u j ( t ) (7.14) I t i s more c o n v e n i e n t t o w r i t e t h i s as 157 A E Q ( t ) = Aug(t) + BuJ(t). ( 7 < 1 5 ) where, A = - e f U _ ( 7 . i 6 ) a n d s - 4 i 3 — < 7 - ' 7 » E q u a t i o n (7.15) i s the n o n l i n e a r d i f f e r e n t i a l e q u a t i o n i n u 0 ( t ) and u 0 ( t ) which must be s o l v e d . The t e c h n i q u e of f i n i t e d i f f e r e n c e s i s used here f o r t h i s purpose. 7.2.6 Finite difference technique In t h i s t e c h n i q u e , an attempt i s made t o s a t i s f y the d i f f e r e n t i a l e q u a t i o n s u c c e s s i v e l y a t eve r y p o i n t a l o n g the time a x i s . I f ( u o ) n r ( u 0 ) n . | , and ^ u o ) n + 1 a r e t h e d e f l e c t i o n s at time t , ( t - A t ) , and (t+At) r e s p e c t i v e l y , ( F i g . 7.2), then, s l o p e t o l e f t of the n t h p o i n t = { ( u 0 ) n _ ( u 0 ) n _ 1 } / A t (7.18) £t t=0 n-2 n-1 n n+1 ^ 2 (Lfj}r>-1 (uol n+1 FIGURE 7 . 2 - F i n i t e D i f f e r e n c e Technique 158 s l o p e t o r i g h t of the n t h p o i n t = {(u 0) + 1 - ( u 0 ) n ) / A t (7.19) Thus, the average s l o p e a t the n t h p o i n t i s < u 0 > n = i L J (7.20) S u b s t i t u t i n g Eqn. 7.20 i n t o Eqn. 7.15 and s o l v i n g f o r ( u 0 ) n + 1 , we g e t , ( uo>ru1 -I J [ < * „ ) „ - B C ^ h f • ( • „ ) „ . , ( 7 - 2 ' ' Thus, knowing the d e f l e c t i o n s a t the two p r e v i o u s p o i n t s a l o n g the time a x i s , and the energy i n p u t j u s t p r i o r t o the p o i n t i n q u e s t i o n , the d e f l e c t i o n a t any p o i n t can be o b t a i n e d from Eqn. 7.21 To s t a r t the p r o c e s s , the d e f l e c t i o n s a t the f i r s t two p o i n t s ( u 0 ) i and ( u 0 ) 2 were both assumed t o be z e r o . Eqn. 7.21 c o u l d then be used from the 3 r d p o i n t onwards. Once the d e f l e c t i o n s a t the v a r i o u s p o i n t s a l o n g the time a x i s up t o the o c c u r r e n c e of the peak l o a d are known, Eqns. 7.20, 7.9, and 7.13 can be used t o compute the v e l o c i t y , the k i n e t i c energy, and the bending energy of the beam, r e s p e c t i v e l y . 7.2.7 Resul t s T h i s method of s e p a r a t i n g the t o t a l hammer energy i n t o the beam k i n e t i c energy and the beam bending energy was 159 a p p l i e d t o a p l a i n c o n c r e t e beam s t r u c k i n the m i d d l e by the hammer f a l l i n g t h r o u g h a h e i g h t of 0.5m. The p r o p e r t i e s of the beam a r e g i v e n i n T a b l e 7.1. TABLE-7.1 Beam p r o p e r t i e s f o r the attempted a p p l i c a t i o n of Model A P r o p e r t y U n i t V a l u e E N/m2 32.0x10 s (assumed) p Kg/m 3 2400.0 (assumed) B m 0.100 D m 0.125 1 m 0.960 F i g u r e 7.3 shows t h a t the m a j o r i t y of the energy l o s t by the hammer appears i n the beam as k i n e t i c energy, and o n l y about 10% of t h i s e x t e r n a l l y a v a i l a b l e energy appears as the bending energy. F i g u r e s 7 . 4 ( a ) , 7 . 4 ( b ) , and 7.4(c) p r e s e n t the comparison between the v a l u e s computed by u s i n g the model and those measured e x p e r i m e n t a l l y (see Chapter 4 f o r t he E x p e r i m e n t a l P r o c e d u r e s ) . I t i s c l e a r from F i g u r e 7.4(a) t h a t the model o v e r e s t i m a t e s the bending energy i n the beam. L i k e w i s e , the d e f l e c t i o n s ( F i g . 7 . 4 ( b ) ) , and the v e l o c i t y ( F i g u r e 7 . 4 ( c ) ) have a l s o been o v e r - e s t i m a t e d . There are s e v e r a l reasons r e s p o n s i b l e f o r t h i s , but p r o b a b l y the most l i k e l y i s t h a t Eqn. 7.2 i s i n v a l i d . As p o i n t e d out i n Chapter 3, and l a t e r ENERGY BY HODEL 160 o ENCY LOST BY TUP KINETIC ENCY 'BENOINC ENCY i r i 1 1 — I i 1 1 r 0.0 0.08 0.16 0.24 0.3? TIHE(HSEC) — i 1 1 1 1— 0.4 0.48 0.S6 FIGURE 7.3-Energy p r e d i c t i o n s u s i n g Model A i n Chapter 8, Eqn. 7.2 i s an o v e r - s i m p l i f i c a t i o n of the s i t u a t i o n . I t i s l i k e l y t h a t , i n i t i a l l y , o n l y a s m a l l p o r t i o n of the energy l o s t by the hammer i s consumed by the beam. A l a r g e p o r t i o n of the energy l o s t by the hammer appears i n the form of machine s t r a i n energy and machine v i b r a t i o n s . T h i s i s p a r t i c u l a r l y t r u e f o r a machine w i t h a t a l l s l e n d e r frame and a heavy hammer. W i t h the hammer almost 8 times as heavy as t.he beam i n our c a s e , the energy l o s s i s p a r t i c u l a r l y s i g n i f i c a n t . U n f o r t u n a t e l y , i t i s not p o s s i b l e , a t t h i s s t a g e , t o account f o r the s e l o s s e s and t o add more terms t o the r i g h t hand s i d e of Eqn. 7.2. O . B E n e r q y , Nm 2 . 4 I I L_ 3 . 2 4 . 0 3 m CD o x m CL TJ CD CD o <-l i—i H-3 cn CD a m cr co m t—• CD •< a a L D e f l e c t i o n , mm a a a • • • -» N> W J I L 3 CD CD • - N) 3 o a a 4V a cn V e l o c i t y , m / s e c a a o - » . . . . N3 CO K> J I L cr> L a cn a 162 7.3 MODEL B- EVALUATION OF BEAM RESPONSE TO AN EXTERNAL  IMPACT PULSE: SOLUTION TO THE EQUATION OF DYNAMIC  EQUILIBRIUM USING TIME STEPS When an a r b i t r a r y e x t e r n a l l o a d p u l s e a c t s on a beam, al o n g w i t h the q u i c k b u i l d - u p of s t r e s s e s , i n e r t i a l f o r c e s a r e g e n e r a t e d . Thus a t any i n s t a n t of t i m e , a f t e r the i n i t i a l c o n t a c t , the e q u a t i o n of dynamic e q u i l i b r i u m can be w r i t t e n as P b ( t ) = P t ( t ) - P . ( t ) (7.22) where P f c ( t ) denotes the e x t e r n a l l o a d , P ^ ( t ) denotes the i n e r t i a l l o a d , and Pfc(t) denotes the bending or the s t r e s s i n g l o a d . I f the m a t e r i a l of the beam i s l i n e a r l y e l a s t i c up t o f a i l u r e , the l i n e a r models p r e s e n t e d i n Appendices 7.1 and 7.2 c o u l d be used. However, c o n c r e t e does not behave l i n e a r l y up t o f a i l u r e under e i t h e r c o m p r e s s i o n , t e n s i o n or f l e x u r e , and as such, these models a r e of l i m i t e d u s e f u l n e s s . Moreover, use of the model i n the case of h i g h s t r e s s r a t e l o a d i n g s r e q u i r e s a knowledge of the p r o p e r t i e s of the m a t e r i a l at thos e h i g h s t r e s s r a t e s . In the case of c o n c r e t e , the exact p r o p e r t i e s a t h i g h s t r e s s r a t e s are not known. The f i r s t n a t u r a l s t e p , t h e r e f o r e , i s an attempt towards the f o r m u l a t i o n of the c o n s t i t u t i v e law f o r c o n c r e t e under h i g h s t r e s s r a t e s from the e x p e r i m e n t a l f i n d i n g s . 163 7.3.1 The constitutive law for concrete One g e n e r a l l y a c c e p t e d c o n s t i t u t i v e law f o r c o n c r e t e i s (59) r 2£ /e. x 2 i (7.23) 0 = ° f v where a = The s t r e s s . o^ = The s t r e s s . a t f a i l u r e . e = The s t r a i n . = The s t r a i n a t f a i l u r e . Both and have been found t o be a f f e c t e d by a v a r i a t i o n i n the s t r e s s r a t e a (Chapter 6 ) . On the b a s i s of the r e s u l t s o b t a i n e d i n Chapter 6, i t can be shown t h a t and a f = C , a C : , where C 2 = 1/d+n) (7.24) e f = C 3 a C a (7.25) Upon s u b s t i t u t i n g f o r and from Eqns. 7.24 and 7.25, r e s p e c t i v e l y , i n Eqn. 7.23 we g e t , (7.26) 1 rn L/, r a c 4 '3 CjJ 4 C o1 -On r e a r r a n g i n g the terms we g e t , 1 64 a = 2 K 1 a K z e - K 3 a K a e 2 (7.27) where K i = C ! / C 3 K 2 = C 2 _ Cu K 3 = c , / c i K n — C 2 — 2C4 The r e s u l t s o b t a i n e d f o r normal s t r e n g t h c o n c r e t e ( T a b l e 6.2b), and h i g h s t r e n g t h c o n c r e t e (Table 6.3b) were used t o e v a l u a t e the above c o n s t a n t s . The v a l u e s o b t a i n e d a r e shown i n Table 7.2. Table 7.2 The constants i n the c o n s t i t u t i v e law obtained e x p e r i m e n t a l l y Normal S t r e n g t h C o n c r e t e H i g h S t r e n g t h C o n c r e t e C,=0.65 K,=9142 d=0.30 R, = 19480 C 2=0.40 K 2=0.24 C 2=0.31 K 2=0.01 C 3=7.11x10~ 5 K 3 = 1 . 2 9X 1 0 b C 3=1.54x10~ 5 K 3 = 1 . 2 6X 1 0 9 C«=0.16 Rfl=0.08 C„=0.30 K a=-0.290 I f E(e) i s the tangent modulus of e l a s t i c i t y a t s t r a i n l e v e l e, we get from Eqn. 7.27, E(e) = da/de = 2 K l 0 K 2 - 2 K 3 o K " e (7.28) Note t h a t the sec a n t modulus i s a f u n c t i o n of the s t r a i n . 165 7.3.2 Time step analysis and results A summary of the l i n e a r a c c e l e r a t i o n time s t e p i n t e g r a t i o n t e c h n i q u e i s g i v e n i n Appendix-7.3. The s t i f f n e s s K(e) a t the b e g i n n i n g of each time s t e p was o b t a i n e d u s i n g Eqn. 7.28 and the e x p r e s s i o n 4 , N ( 7 - 2 9 > . t? E e l k (fi) = -oTT 21' The e x t e r n a l l o a d p u l s e s ( t h e t u p l o a d s ) up t o the peak, f o r t h r e e hammer drop h e i g h t s f o r both normal s t r e n g t h and h i g h s t r e n g t h c o n c r e t e s formed the i n p u t t o the program w r i t t e n t o do the time s t e p a n a l y s i s . The r e s u l t s a r e shown i n the form of the l o a d (P^) v s . d e f l e c t i o n p l o t s of F i g u r e s 7.5 and 7.6. F i g u r e 7.5 corr e s p o n d s t o normal s t r e n g t h c o n c r e t e w h i l e F i g u r e 7.6 corr e s p o n d s t o h i g h s t r e n g t h c o n c r e t e . The e x p e r i m e n t a l l y o b t a i n e d r e s u l t s a r e a l s o shown. The bending energy i n the beam a t the peak l o a d , which can be o b t a i n e d by t a k i n g the area under the bending l o a d v s . d e f l e c t i o n p l o t s ( F i g u r e s 7.5 and 7.6) has been shown i n F i g u r e 7.7 f o r both normal and h i g h s t r e n g t h c o n c r e t e s . I t can be seen t h a t the model proposed here r e a s o n a b l y p r e d i c t s t he b e h a v i o u r of a beam s u b j e c t e d t o impact. The model a l s o p r e d i c t s the b r i t t l e n e s s shown by h i g h s t r e n g t h c o n c r e t e . One major drawback w i t h the model, t h a t s h o u l d be p o i n t e d out h e r e , i s the i n a b i l i t y of the model t o p r e d i c t the response of the beam beyond the peak l o a d . With the 166 21 A 18 J 15 -A 12 •o 3 9 6 -\ f J C r ^ A L STRENGTH C O N C R E T E Experimental Hodel Stress rate = 19587 NPa/sec Stress rate = 8057 FlPa/sec 3920 PlPa/sec 0-0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Defl e c t i o n , mm FIGURE 7 .5 -Model B p r e d i c t i o n s v s . the E x p e r i m e n t a l R e s u l t s (Normal S t r e n g t h C o n c r e t e ) HIGH STRENGTH CONCRETE Experimental riodel D e f l e c t i o n , mm FIGURE 7 . 6 - M o d e l p r e d i c t i o n s v s . the E x p e r i m e n t a l R e s u l t s (High S t r e n g t h C o n c r e t e ) 168 0 10,000 20,000 30,000 Stress Rate (MPa/sec) FIGURE 7 . 7-Bending Energy a t the Peak Load c r a c k s t a r t i n g t o grow a t the peak l o a d , the response of the beam, among o t h e r t h i n g s , depends upon the v e l o c i t y of the pr o p a g a t i n g c r a c k , c r a c k b r a n c h i n g i f any, and a l s o upon the w i d t h of the m i c r o c r a c k e d zone around t h e p r o p a g a t i n g c r a c k . In the absence of a p r e c i s e knowledge of c r a c k p r o p a g a t i o n under impact l o a d i n g , such m o d e l l i n g i s not p o s s i b l e a t the pr e s e n t t i m e . 169 APPENDIX-7.1 EVALUATION OF BEAM RESPONSE: BEAM MODELLED AS A SINGLE DEGREE OF FREEDOM SYSTEM Assumpti ons 1. The beam remains e l a s t i c up t o the peak t u p l o a d . 2. The e x t e r n a l l o a d p u l s e ( t h e t u p l o a d ) can be approximated as a s i n u s o i d a l p u l s e . 3. The beam d e f l e c t s i n , and o n l y i n , t h e f i r s t mode. 4. Damping can be i g n o r e d . The Equation of dynamic equilibrium L e t , m^ be the g e n e r a l i z e d mass of the beam, k be the g e n e r a l i z e d s t i f f n e s s , P f c ( t ) = P 0sina>t be the e x t e r n a l l o a d p u l s e , Inertial Force Spring Force FIGURE A7 . 1 - 1 - S i n g l e Degree of Freedom Model t o e v a l u a t e the beam response 170 o>n be the n a t u r a l frequency of the beam, u 0 ( t ) be the d i s p l a c e m e n t of the mass, u 0 ( t ) be the v e l o c i t y of the mass, u 0 ( t ) be the a c c e l e r a t i o n of the mass, /3 = "A> n be the frequency r a t i o . From the v e r t i c a l e q u i l i b r i u m i n F i g u r e A7.1-1 we can w r i t e , m, , b u Q ( t ) + ku 0 ( t ) = P 0sincot (A7.1-1) The s o l u t i o n t o Eqn. A7.1-1 can be w r i t t e n i n the form of u n ( t ) = Acosoj t + Bsinoj t + Csinuj t (A7.1-2) 0 n n n where, A and B are c o n s t a n t s depending on the i n i t i a l c o n d i t i o n s and C = From Eqn. 7.1-2 we.get, u Q ( t ) - .= -a ) n Asinu j n t + luyBcosa^t + Cajcosajt (A7.1-3) On s u b s t i t u t i n g the i n i t i a l c o n d i t i o n s , i . e . u o ( t = 0 ) = 0, and u©(t=0) = 0 i n t o Eqn A7.1-2 and Eqn. A7.1-3 we g e t , A = 0 ' (A7.1-4) and, - P Q B B " mKcoa (1-B 2) (A7.1-5) • n On s u b s t i t u t i n g f o r A, B, and C i n t o Eqn. A7.1-2 and Eqn. 171 A7.1-3 we g e t , u Q ( t ) = C(sincot - B s i n ^ t ) (A7.1-6) and, uQ(t) = Cdocosiut -Bconcoso)nt) (A7.1-.7) F i n a l l y , from (A7.1-7) we g e t , u Q ( t ) = C(8co 2sincu nt -cu 2sina.t) (A7.1-8) The generalized mass of the beam L e t the d i s p l a c e m e n t s i n the beam be g i v e n by, u(x,t) = u Q ( t ) s i n - p - ( s u p p o r t e d span) (A7.1-9) , , \ « v' .(overhangs) (A7.1-10) u(y,t) = - u Q ( t ) ^ I f the beam i s g i v e n a v i r t u a l d i s p l a c e m e n t 5 u 0 i n the c e n t r e , then from the p r i n c i p l e of v i r t u a l work we can 8u„ ^ FIGURE A7.1-2-Determination of the g e n e r a l i z e d mass 172 wr i t e , V o 6 u o = / P a [ V t } s i n - x - ] [ 6 U o s i n 5 r ~ ] d x ! + 2 / P A [ - t y t ) t - 6 u 0 V ~ ] d y Using Eqns. A7.1-9 and A7.1-10, and assuming that the beam i s p r i s m a t i c and homogeneous we can w r i t e , M B = ^ A 1 _ + l i i ^ h i (A7.1-11) The generalized stiffness of the beam I f the displacements are given by Eqn A7.1-9 and A7.1-10, then the g e n e r a l i z e d s t i f f n e s s i s given by, R R I I 2 . r ,, 2 (A7.1-12) k = / E l [ ^ (x)]dx + / EI[«J 2 (y)] dy x^ Where ^(x) = sin(-y) , and d(y) = — a n d , where primes denote d e r i v a t i v e s with re s p e c t to x. So l v i n g Eqn. A7.1-12 f o r k we get, 2 1 3 (A7.1-13) 173 The natural frequency The n a t u r a l frquency of » n = • _k_ mb where and k are g i v e n by r e s p e c t i v e l y . the beam i s g i v e n by, E q u a t i o n s A 7 . 1 - 1 1 and A 7 . 1 - 1 3 , 174 APPENDIX 7.2 EVALUATION OF BEAM RESPONSE: BEAM MODELLED AS A MULTI-DEGREE OF FREEDOM SYSTEM As s umpt i ons 1. Damping can be ignored. 2. Beam remains e l a s t i c up to the peak e x t e r n a l l o a d . 3. The beam i s p r i s m a t i c and homogeneous. 4. The e x t e r n a l l o a d can be approximated as a s i n u s o i d a l p u l s e . Notation P f c(t) = P 0 s i n w t = The e x t e r n a l l o a d p u l s e . u(x,t) = The v e r t i c a l displacement. 0 n(x) = The nth mode shape. Y n ( t ) = The nth g e n e r a l i z e d c o o r d i n a t e . CJ = The nth n a t u r a l frequency. P t(t) Beam Properties, u0(x,t) =l0n(x)Yn(t) FIGURE A7.2-1-Multi Degree of Freedom Model to eval u a t e the beam response 175 p = The mass d e n s i t y of beam m a t e r i a l . 1 = D i s t a n c e between the beam s u p p o r t s . E = Modulus of e l a s t i c i t y of the beam m a t e r i a l . I = Moment of I n e r t i a . A = Area of c r o s s - s e c t i o n . m = pA = Mass per u n i t l e n g t h of the beam. With the damping i g n o r e d , the dynamic e q u a t i o n of beam e q u i l i b r i u m can be w r i t t e n as EI fi4u^;t) + m 6 2 u(x,t) = ( t ) (A7.2-1) I f we choose the s o l u t i o n i n the form u(x,t) =z rfn(x)Yn(t) (A7.2-2) n n On s u b s t i t u t i n g the d e r i v a t i v e s of u ( x , t ) w i t h r e s p e c t to x (denoted by s u p e r s c r i p t s ) , and w i t h r e s p e c t to time (denoted by dots ) i n E q n . A7.2-1 we get EIze£(x)Y p(t) + mz«5 n(x)Y n(t) = PQsina.t (A7.2-3) M u l t i p l y i n g E q n . A 7 . 2 - 3 by 0 m ( x ) f i n t e g r a t i n g over the 176 l e n g t h , and using the f o l l o w i n g o r t h o g o n a l i t y c o n d i t i o n s /mrf (x)sz5 (x)dx = 0 m n /EI^ u(x)(i5 m(x)dx = 0 (A7.2-4) SZUn(x)^(x) dx = u* / mrf*(x)dx we get, Y n(t)[/m^(x)dx] + Y n(t)[ 0 J 2 1 /m^( x)dx] Wp 0sin utd n(x)dx Let /irwJ*(x)dx = n n and, /PQsino)tcin(x)dx =a nP nsin Ujt a 0= 1 f o r n=1,5,9... = -1 f o r n=3,7,11 = 0 f o r n=2,4,6... (A7o2-5) With the above n o t a t i o n , Eqn.A7.2-5 can be w r i t t e n as f1 nY n(t) + a»JP1nYn(t) =a QP 0sinoot (A7.2-6) 177 The solution to Eqn. A7.2-6 The general s o l u t i o n ( i n c l u d i n g the homogeneous and p a r t i c u l a r p a r t s ) to Eqn. A7.2-6, which i s a simple d i f f e r e n t i a l equation i n t , can be w r i t t e n as a p Y n ( t ) = Acosu nt + Bsincj nt + [4] ° M° ^ ^ s i n c j t (A7.2-7) where A and B are constants determined from the i n i t i a l c o n d i t i o n s , and, 0 n = cj/o n = The frequency r a t i o . With Y n(0)' 1 = 0, and Y n ( 0 ) = 0 as the i n i t i a l c o n d i t i o n s , A = 0 -a p B 3 o n B = n a>z (l-B*) n n n With these constants, Eqn. A7.2-7 may be w r i t t e n as a p a P & Y „ ( M = 0 9 sinwt - 0 ° n _ s i n w t (A7.2-8) n M io2 (1-B2) m u^d-B 2) n n n n n n x n' 178 The mode shapes of a simply supported beam are given by d n(x) = sin (A7.2-9) With mode shapes given by Eqn. A7.2-9, and the g e n e r a l i z e d c o o r d i n a t e s given by Eqn. A7.2-9, Eqn. A7.2-2 can be f i n a l l y w r i t t e n as a P sinwt a P B sinto t r , \ „ . n n x r oo o o n n . U(x,t) = I Sin r - L m 7 /-,_fl2A " m ,..2 /,_ai\ J "n»n "-*'n> ' W ' 1 ~ B « ' (A7.2-10) 179 APPENDIX-7.3  TIME STEP ANALYSIS A d e t a i l e d account of the dynamic time s t e p a n a l y s i s i s g i v e n i n ( 6 0 ) . Here o n l y a s h o r t d e s c r i p t i o n w i l l be p r e s e n t e d . Not at i on: P^Xt): The bending l o a d on the beam. P ^ ( t ) : The i n e r t i a l l o a d on the beam. P f c ( t ) : The a p p l i e d l o a d on the beam. A P ^ t ) : The change i n the bending l o a d d u r i n g an i n t e r v a l . A P ^ ( t ) : The change i n the i n e r t i a l l o a d d u r i n g an i n t e r v a l . A P f c ( t ) : The change i n the a p p l i e d l o a d d u r i n g an i n t e r v a l . A t : The l e n g t h of the time i n t e r v a l . u 0 ( t ) : The a c c e l e r a t i o n a t the b e g i n n i n g of the i n t e r v a l . u 0 ( t ) : The v e l o c i t y a t the b e g i n n i n g of t h e i n t e r v a l . u 0 ( t ) : The d i s p l a c e m e n t a t the b e g i n n i n g of the i n t e r v a l . A u 0 ( t ) : The change i n the a c c e l e r a t i o n d u r i n g an i n t e r v a l . A u 0 ( t ) : The change i n the v e l o c i t y d u r i n g an i n t e r v a l . A u 0 ( t ) : The change i n the d i s p l a c e m e n t d u r i n g an 180 i n t e r v a l . m^: The g e n e r a l i z e d mass of the beam. K ( t ) : The tangent s t i f f n e s s d u r i n g an i n t e r v a l . As s umpt i ons 1. The beam can be modelled as a s i n g l e degree of freedom system. 2. Damping can be ignored. 3. A c c e l e r a t i o n v a r i e s l i n e a r l y d u r i n g a time i n t e r v a l . 4. The s t i f f n e s s does not change d u r i n g an i n t e r v a l . In t h i s method, the response of the beam i s evaluated f o r a s e r i e s of short time increments, g e n e r a l l y taken of equal lengths. The c o n d i t i o n of dynamic e q u i l i b r i u m i s e s t a b l i s h e d at the beginning and the end of each i n t e r v a l and the motion of the system d u r i n g the time increment i s evaluated approximately on the b a s i s of an assumed response mechanism. Inertial Force /7777J777 FIGURE A7.3-1-Single Degree of Freedom Model to evaluate the beam response using Time Step A n a l y s i s 181 From the c o n d i t i o n of dynamic e q u i l i b r i u m a t any time t we have P t ( t ) = P £ ( t ) + P b ( t ) (A7.3-1) A f t e r a s h o r t i n t e r v a l At the c o n d i t i o n of dynamic e q u i l i b r i u m would s t i l l h o l d . P f c ( t + A t ) = P b ( t + A t ) + P ^ t + A t ) (A7.3-2) S u b t r a c t i n g Eqn.(A7.3-1) from Eqn.(A7.3-2) we get the i n c r e m e n t a l form of the e q u a t i o n of dynamic e q u i l i b r i u m . A P f c ( t ) = A P f a ( t ) + A P ^ t ) (A7.3-3) o r , A P f c ( t ) = K ( t ) A u 0 ( t ) + m b A u 0 ( t ) (A7.3-4) I f the a c c e l e r a t i o n i s assumed t o v a r y l i n e a r l y d u r i n g an i n t e r v a l then 182 A u 0 ( t ) = u 0 ( t ) A t + 0 . 5 A u o ( t ) A t (A7.3-5) A u 0 ( t ) = u 0 ( t ) A t + 0 . 5 u o ( t ) A t 2 + A u 0 ( t ) ( A t 2 / 6 ) (A7.3-6) Choosing A u 0 ( t ) as the b a s i c v a r i a b l e i n the a n a l y s i s we g e t , S u b s t i t u t i n g f o r A u 0 ( t ) from Eqn. hi.3-1 i n t o Eqn. A7.3-4 and r e a r r a n g i n g we g e t , {K ( t ) + ( 6 / A 2 ) m b } A u 0 ( t ) = A P f c ( t ) + m b [ ( 6 / A t ) u 0 + 3 u 0 ( t ) ] (A7.3-9) E q u a t i o n A7.3-9 i s the b a s i c e q u a t i o n f o r the l i n e a r a c c e l e r a t i o n time s t e p a n a l y s i s f o r a system w i t h o u t damping. At any s t e p , knowing the s t i f f n e s s , the v e l o c i t y , and the a c c e l e r a t i o n a t the b e g i n n i n g of the i n t e r v a l , Eqn. A7.3-9 can be used t o e v a l u a t e the i n c r e m e n t a l d i s p l a c e m e n t A u 0 ( t ) . Once A u 0 ( t ) i s known, Eqn. A7.3-8 can be used t o A'uo(t) = ( 6 / A t 2 ) A u 0 ( t ) - ( 6 / A t ) u 0 ( t ) - 3 u 0 ( t ) (hi.2-1) A u 0 ( t ) = ( 3 / A t ) A U e ( t V 3 u 0 ( t ) - ( A t / 2 ) u 0 ( t ) (A7.3-8) 183 f i n d A u 0 ( t ) . These i n c r e m e n t s A u 0 ( t ) and A u 0 ( t ) a r e then added t o the d i s p l a c e m e n t and the v e l o c i t y a t the b e g i n n i n g of t h e i n t e r v a l t o o b t a i n the d i s p l a c e m e n t and the v e l o c i t y a t t h e end of the i n t e r v a l . The a c c e l e r a t i o n a t the b e g i n n i n g of the i n t e r v a l i s o b t a i n e d from the e q u a t i o n of dynamic e q u i l i b r i u m a t the b e g i n n i n g of the i n t e r v a l . 8. ENERGY BALANCE IN INSTRUMENTED IMPACT TESTS 8.1 INTRODUCTION Many s t u d i e s have demonstrated the s t r a i n r a t e s e n s i t i v i t y of c o n c r e t e . However, our knowledge of c o n c r e t e b e h a v i o u r a t h i g h s t r e s s r a t e s s t i l l remains l a r g e l y e m p i r i c a l . P a r t of the reason f o r t h i s has been the i n a b i l i t y t o compare the r e s u l t s from d i f f e r e n t i n v e s t i g a t i o n s , i n the absence of any s t a n d a r d t e s t i n g t e c h n i q u e . The r e s u l t s of a p a r t i c u l a r i n v e s t i g a t i o n depend l a r g e l y on the t e s t i n g arrangement used i n t h a t p a r t i c u l a r i n v e s t i g a t i o n , because of the d i f f e r e n t energy l o s s e s a s s o c i a t e d w i t h v a r i o u s t e s t i n g machines, and d i f f e r e n t methods of a n a l y s i s . The concept of Energy B a l a n c e (17,18), which has i t s b a s i s i n the p r i n c i p l e of the c o n s e r v a t i o n of energy, compares the energy l o s t by the hammer, at any time d u r i n g the impact, and the energy g a i n e d by the specimen. T h e o r e t i c a l l y , i f l o s s e s can be i g n o r e d , the law of c o n s e r v a t i o n of energy would p r e d i c t t he two e n e r g i e s t o be the same. P r a c t i c a l l y , as w i l l be seen s h o r t l y , t he l o s s e s i n t he system cannot be i g n o r e d , and the energy g a i n e d by the specimen i s , i n g e n e r a l , l e s s than the energy l o s t by the hammer. In t h i s c h a p t e r , the v a r i o u s forms i n which the hammer energy i n a drop weight type impact machine i s d i s s i p a t e d a r e p r e s e n t e d . The hammer t r a v e l l i n g downward, on s t r i k i n g the beam, s u f f e r s a l o s s of momentum. T h i s l o s s of momentum, a c c o r d i n g t o t he impulse-momentum r e l a t i o n s h i p (Chapter 4 ) , i s e q u a l 184 185 to the impulse a c t i n g on the hammer. Using t h i s p r i n c i p l e , the l o s s i n the k i n e t i c energy of the hammer (AE(t)) can be evaluated (Eqn. 4.12). (4.12) JP t(t)dt)<J where, AE(t) = i\[2ahh - (V2ah  - 1 / P j O d t ) 2 ] : The mass of the hammer, a^ : The a c c e l e r a t i o n of the hammer, h : The height of hammer drop, J P f c ( t ) d t : The impulse. • T h i s energy l o s t by the hammer may be t r a n s f e r r e d to the beam i n various forms. The t r a n s f e r of energy can be stud i e d by subd i v i d i n g i t i n t o two regions (Figure 8.1): (1) Energy balance at the peak load (at t=t ). T I M E , t FIGURE 8.1-Typical Tup Load vs. Time p l o t 186 (2) Energy b a l a n c e j u s t a f t e r complete f a i l u r e ( a t t = t t ) The f o l l o w i n g s e c t i o n s d e a l w i t h these two r e g i o n s s e p a r a t e l y . 8.2 ENERGY BALANCE AT THE PEAK LOAD (t=t ) . p At the peak l o a d the e q u a t i o n of energy b a l a n c e can be w r i t t e n as A E ( t p } • E m { V + E s ( V ( 8 - ° where, E m ( t p ) : the energy l o s t t o the v a r i o u s machine p a r t s at time t i n the form of s t r a i n energy or machine v i b r a t i o n s , E ( t ) : the energy consumed by the specimen a t time t The energy consumed by the beam can be f u r t h e r s u b d i v i d e d i n t o the f o l l o w i n g two p a r t s , where, E ( t ) = E, ( t ) + E, ( t ) s p k e r v p' b p (8.1a) 187 E ^ e r > ( t p ) : the r o t a t i o n a l k i n e t i c energy of the specimen, E ^ ( t ) : the bending energy i n the specimen. T h e r f o r e , A E ( t ) = E ( t ) + E . ( t ) + E. ( t ) (8.2) p m p ker p b p In E q u a t i o n 8.2, the t r a n s l a t i o n a l k i n e t i c energy, and the v i b r a t i o n a l energy i n the specimen have been i g n o r e d ( 1 8 ) . The bending energy, g i v e n by the a r e a under the l o a d v s . c e n t r e p o i n t d i s p l a c e m e n t p l o t (Eqn. 4.37), c o m p r i s e s the e l a s t i c s t r a i n energy E s e ( t p ) a n ^ t n e work of f r a c t u r e E w o f ( V E b ( V - E s e ( V + E w o f ( V ( 8 ' 3 ) From a l o a d v s . c e n t r e p o i n t d i s p l a c e m e n t p l o t , the e l a s t i c s t r a i n energy E s e ( t p ) can be r e a s o n a b l y a p p r o x i m a t e d by t a k i n g the secant modulus a t 60% of the peak l o a d ( F i g u r e 8.2). The secant modulus was taken a t t h i s p o i n t , s i n c e a t t h i s p o i n t , i n g e n e r a l , the l o a d v s . d e f l e c t i o n c u r v e became s i g n i f i c a n t l y n o n - l i n e a r . E e a ( t ) = 0.5P.(t ) u _ 0 (8.4) se p b p oe 188 0."° < o o 0.6 P b  Q z UJ m DISPLACEMENTS ,u FIGURE 8.2-Components of Bending Energy where u Q g i s the e l a s t i c p a r t of the midspan d i s p l a c e m e n t , The work of f r a c u t u r e E w o ^ ( t p ) can then be o b t a i n e d by s u b t r a c t i n g the s t r a i n energy E ( t ) from the bending energy E b ( t p ) (Eqn. 8.3). Knowing the v e l o c i t y a t the c e n t r e , and assuming t h a t the v e l o c i t y d i s t r i b u t i o n i s l i n e a r a l o n g the l e n g t h of the beam, the r o t a t i o n a l k i n e t i c energy of the specimen can be o b t a i n e d by i n t e g r a t i n g over i t s l e n g t h . BpAOj(t) r l 2 h 3 -, [ 24 + 3" ] (8.5) 189 The energy l o s t t o the machine E ( t ) can be o b t a i n e d m p by s u b t r a c t i n g the beam e n e r g i e s Ej-^tp) and E f c e ^ t p ) from the hammer energy A E ( t ) ( E q u a t i o n 8.2). The e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d i n F i g u r e s 8.3 and 8.4, and i n T a b l e s 8.1 (NS c o n c r e t e ) and 8.2 (HS c o n c r e t e ) . The d a t a a r e p r e s e n t e d f o r t h r e e d i f f e r e n t h e i g h t s of hammer drop. S i n c e T a b l e s 8.1 and 8.2 show s u b s t a n t i a l s c a t t e r i n r e s u l t s , o n l y the mean v a l u e s were used f o r drawing F i g u r e s 8.3 and 8.4. F i g u r e 8.3 shows the energy b a l a n c e f o r NS and HS c o n c r e t e s a t the peak l o a d (t=t ). At the peak l o a d , the energy l o s t by the hammer (AE) i s 2 t o 4 times the energy g a i n e d by the beam ( E s)« The remainder of the energy i s assumed t o be absorbed i n the machine i t s e l f , i n the form of v i b r a t i o n s and i n s t o r e d e l a s t i c energy. The energy g a i n e d by the beam by v i r t u e of i t s deformed shape (E^) i s found t o be much s m a l l e r than i t s k i n e t i c energy ( Ek e r)« A l s o , the c o n s i s t e n t l y lower v a l u e s of e n e r g i e s ( E g , E k e r r and E^) f o r HS c o n c r e t e compared t o NS c o n c r e t e s h o u l d be n o t e d . F i g u r e 8.4 p r e s e n t s the s u b - d i v i s i o n of the bending energy (E^) a t the peak l o a d i n t o the work of f r a c t u r e ( E w o f ) and the e l a s t i c s t r a i n energy ( E s e)« Most of the energy consumed by the beam up t o the peak bending l o a d appears as the work of f r a c t u r e . Both the work of f r a c t u r e and the s t r a i n energy i n c r e a s e w i t h an i n c r e a s e i n the hammer drop h e i g h t ; the work of f r a c t u r e seems t o i n c r e a s e a t a h i g h e r r a t e than does the s t r a i n energy. HS c o n c r e t e 190 H E I G H T O F H A M M E R D R O P . m FIGURE 8 . 3-Energy Ba l a n c e a t the Peak Load 191 FIGURE 8 .4-Components of Bending Energy Table 8 . 1-Energy Balance at the Peak Load (Normal S t r e n g t h Concrete) ITEM 0.15 m (6)* 0.25 m (6)* 0.50 m ( 7 ) . MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION w (N) 9440 7782 8460 604 14668 9178 12183 2401 17727 16452 16932 428 A E ( t p ) (N-m) 25.78 19.75 22.86 2.37 42.06 33.36 37.24 3.21 71.60 60.89 64.64 3. 80 E k e r V (N-m) 7.515 4.60 6.20 1.27 10.00 6.12 7.98 1.37 16.96 10.96 13.23 2. 00 v v (N-m) 3.50 1.53 2.53 0.708 3.73 2.74 3.005 0.429 9.07 2.21 6.416 2. 51 E s e ( t P ' (N-m) 0.645 0.324 0.499 0.125 0.824 0.523 0.632 0.114 1.357 0.788 1.14 0. 192 Ewof<V (N-m) 2.855 1.206 2.05 0.588 2.906 2.048 2.38 0.322 7.90 1.422 S.27 2. 41 E (t ) 3 P (N-m) 10.12 6.13 8.72 1.53 13.47 8.86 10.95 1.64 23.56 14.63 19.60 3. 03 m p (N-m) 15.66 12.69 14.12 1.10 31.46 24.45 26.32 2. 97 48.39 40.47 45.03 3. 49 Em(t ) p X A E ( t p ) 100% 69 59 62 4.02 74 64 69 3.77 77 67 70.00 4. 18 *NUMBLR OF SPECIMENS TESTED Table 8.2-Energy Balance at the Peak Load (High S t r e n g t h Concrete) 0.15 m (6)* 0. 25 m (5)* 0.50 m (6)* ITEM MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION (N) 11694 8388 9906 1183 18579 10573 13371 2991 19206 18314 18760 446 A E ( t p ) (N-m) 25.21 19.02 20.28 3-5>* 38.1*5 33. to 32.20 3-98 76 .33 5882 66 .13 7.1*3 E k e r ( y (N-m) 6.40 2.68 3.94 1.44 9.61 4.47 6.58 1.67 16.00 4.35 10.13 4.75 b p (N-m) 2.92 1.79 2.37 0.54 2.96 1.86 2.55 0.37 6 5.41 3.80 4.64 0.659 Es e( V (N-m) 0.518 0.339 0.432 0.072 0.639 0.546 0. 600 0.052 1.34 1.00 1.14 0.065 Ewof ( tp> (N-m) 2.433 1.40 1.930 0.478 2.40 1.287 1.954 0.375 4.23 2.86 3.52 0.560 EC( t r , > s p (N-m) 9.32 4.47 6.31 1.83 11.47 7.19 9.14 1.39 19.80 1.08 14 .78 4.40 E (t ) m p (N-m) 25.21 19.02 20.28 3.54 38.45 33.40 32.20 3.98 76.33 58.82 66.13 7.43 m p „ A E ( t p ) 100% 75 63 69 4.47 72 70 72.0 0.80 84 74 78 4.96 Number of specimens t e s t e d . 194 and NS c o n c r e t e , appear to have comparable s t r a i n e n e r g i e s , and t h u s , the vas t d i f f e r e n c e between the beam e n e r g i e s (E^) for NS and HS c o n c r e t e s p r o b a b l y a r i s e s because of the h i g h e r work of f r a c t u r e e n e r g i e s ( E w o f ) f o r NS c o n c r e t e . T h i s o b s e r v a t i o n s t r e n g t h e n s the argument p r e s e n t e d i n Chapter 6 to e x p l a i n the b r i t t l e n e s s of HS c o n c r e t e . 8.3 ENERGY BALANCE JUST AFTER FAILURE (at t = t t ) At the end of the impact e v e n t , the e x t e r n a l l o a d P f c ( t ) i s reduced to zero and the broken h a l v e s of the beam swing c l e a r of the s t r i k i n g t u p . At t h i s i n s t a n t , the energy ba lance can be w r i t t e n as A E ( t t ) = E m ( t t ) + E s ( t f c ) As b e f o r e , t h i s can be w r i t t e n as A E ( t t ) = E m ( t t ) + E b ( t t ) + E k e r ( t t ) (8 .6) Once a g a i n the energy E ^ ^ t ^ o b t a i n e d from the area under the l o a d v s . d i sp lacement p l o t measures the work of f r a c t u r e p l u s the s t r a i n energy i n the beam. S ince the s t r a i n energy can be assumed to be n e g l i g i b l e i n the broken h a l v e s of the beam, a l l of the energy E b ( t t ) r e p r e s e n t s the work of f r a c t u r e , or the f r a c t u r e energy . E q u a t i o n 8.5 can once a g a i n be used at t = t^ . to determine the k i n e t i c energy E k e r ( t t ) . Once E k e r ( t f c ) and E b ( t f c ) are known, E q u a t i o n 8.6 can be used to determine 195 m t F i g u r e 8.5 and T a b l e s 8.3 and 8.4 p r e s e n t the energy b a l a n c e a t the end of the impact event ( t = t t ) . Here, most of the energy l o s t by the hammer a t t= t f c (AE) i s g a i n e d by the beam ( E s ) . The energy g a i n e d by the beam c o n s i s t s of the k i n e t i c energy of the broken h a l v e s ( E ^ e r ) and the bending energy ( E ^ ) . P r o b a b l y , the bending energy i s the energy r e q u i r e d t o c r e a t e two new f r a c t u r e s u r f a c e s . T h i s can a l s o be termed the f r a c t u r e energy, or the work of f r a c t u r e . S i n c e , by the end of the impact e v e n t , the specimen appears t o have l i t t l e or no s t r a i n e nergy, the bending energy E^ r e p r e s e n t s o n l y the f r a c t u r e energy. 8.4 THE MACHINE LOSSES I f the d i f f e r e n c e beteween the energy l o s t by the hammer (AE) and the energy absorbed by the beam ( E g ) can be assumed t o be the energy l o s t t o the machine ( E m ) , then the "machine l o s s e s " can be c a l c u l a t e d a t the peak l o a d (t=t ) hr and a t the end of the event ( t = t f c ) . F i g u r e 8.6 p r e s e n t s t h i s machine energy c a l c u l a t e d as a perc e n t a g e of the t o t a l energy l o s t by the hammer (E m/AE X 1 0 0 % ) . As can be seen from F i g u r e 8.6, a t the peak l o a d , 60 t o 80 p e r c e n t of the energy l o s t by the hammer i s s t o r e d i n the machine. However, by the end of the impact event ( t = t t ) , 90 t o 100 p e r c e n t of the energy l o s t by the hammer appears as specimen energy. I t can a l s o be noted from F i g u r e 8.6 t h a t HS c o n c r e t e , b e i n g a 196 FIGURE 8 . 5-Energy Bal a n c e j u s t a f t e r f a i l u r e .3-Energy Balance at the Peak Load (Normal S t r e n g t h C o n c r e t e ) 0.15 M (6)* 0.25 M (6)* 0.50 M (7)* ITFMS MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION A E ( t t ) (N-m) 76 64 72 4.7 131 94 116 15.3 249 231 240 5.8 E k e r ( t t » ( N " m ) 45 42 44 1.2 80 47 66 12.0 150 139 145 4.7 E b ( t t ) (N-m) 31 19 25 4.3 60 27 43 12.4 100 87 90 6.4 E s ( t f c ) (N-m) 73 63 69 3.90 130 74 109 23.0 248 230 235 7.31 m t 3 1 2 1.0. 20 1 7 7.7 12 0 5 4.0 52 x 100% A E 4 1.56 2.77 1.0 21 6.76 6.03 8.0 5.02 0 2.08 1.0 *Number of specimens t e s t e d Table 8.4-Energy Balance at the Peak Load (High Strength Concrete) 0.15 m (6) * 0.25 m (5)* 0.50 m ( 6 ) « ITEM MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION MAX. MIN. MEAN STD. DEVIATION A E ( t f c ) (N--m) 89 43 68 16.7 133 100 109 12.20 238 214 223 10.5 E k e r ( t t > (N-m) 54 13 36 16.8 89 54 64 13.6 127 116 121 5.5 E b ( t t ) (N-m) 33 21 25 5.0 43 31 35 4.6 100 57 75 18.6 E s ( t t ' (Nm) 89 34 61 21.0 133 86 99 18.0 213 193 196 10.0 E » ( t t > (N-m) 14 0 7 5.9 15 0 10 6.3 30 25 27 2.7 52 x 100% 21.12 0 10.3 5.4 10.80 0 9.2 3.7 13.7 10.2 12.1 1.50 Number of specimens tested. CO 100 90 Normal strength concrete High strength concrete 80 70 At the peak load 60 in O 50 >-£ 40 30 LJ o or S 20 10 0 Just after the failure I 0.3 0.5 HEIGHT OF HAMMER DROP, m 0.7 FIGURE 8.6-The Machine L o s s e s 200 s t r o n g e r and a s t i f f e r m a t e r i a l than NS c o n c r e t e , showed h i g h e r machine l o s s e s . H i g h s t r e s s r a t e t e s t i n g of c e m e n t i t i o u s m a t e r i a l s r e q u i r e s s o p h i s t i c a t e d t e s t i n g equipment. Knowledge of the v a r i o u s modes i n which energy can be l o s t d u r i n g a t e s t i s e s s e n t i a l t o a prop e r a n a l y s i s of the t e s t r e s u l t s . In the absence of t h i s knowledge, the r e s u l t s can be g r o s s l y m i s l e a d i n g . The energy l o s t by the hammer cannot be assumed t o be the energy consumed by the beam. Even i f the machine l o s s e s can be assumed t o be c o n s t a n t f o r a g i v e n drop h e i g h t f o r a g i v e n machine, the energy g a i n e d by the specimen s t i l l has t o be c o r r e c t e d f o r i t s k i n e t i c energy. The p e r c e n t a g e energy l o s t t o the machine seems t o depend on the s t r e n g t h and the s t i f f n e s s of the m a t e r i a l t e s t e d . Energy l o s s e s i n the machine were found t o be h i g h e r when HS c o n c r e t e , which i s s t r o n g e r and s t i f f e r than NS c o n c r e t e , was t e s t e d . I f i t can be assumed t h a t , a f t e r the beam f a i l s , the broken h a l v e s of the beam have l i t t l e or no s t r a i n energy, then i n the post-peak l o a d r e g i o n , most or a l l of the s t r a i n energy s t o r e d i n the beam i s used i n p r o p a g a t i n g the c r a c k . S i n c e the s t o r e d s t r a i n energy a t the peak l o a d i s much l e s s than the o v e r a l l f r a c t u r e energy r e q u i r e d , i t seems p o s s i b l e t h a t the c r a c k p r o p a g a t e s w h i l e the beam c o n t i n u e s t o ab s o r b energy from the hammer and the v a r i o u s o t h e r machine p a r t s . 9. NOTCHED BEAMS UNDER IMPACT  9.1 INTRODUCTION Numerous m i c r o c r a c k s e x i s t i n c o n c r e t e even p r i o r t o l o a d a p p l i c a t i o n . Under l o a d , the s t r e s s e s and s t r a i n s i n the v i c i n i t y of a c r a c k t i p i n c r e a s e , and i f the c r i t i c a l c o n d i t i o n s a re met, c r a c k e x t e n s i o n o c c u r s . W i t h an i n c r e a s e i n t he s i z e of the c r a c k , the s t r e s s e s and s t r a i n s i n c r e a s e f u r t h e r c a u s i n g the c r a c k t o ex t e n d a t an i n c r e a s i n g r a t e t i l l f a i l u r e o c c u r s . In a l i n e a r l y e l a s t i c m a t e r i a l , the s t r e s s f i e l d i n the neighbourhood of a c r a c k t i p can be d e s c r i b e d by a s i n g l e p arameter, the s t r e s s i n t e n s i t y f a c t o r , K. F r a c t u r e o c c u r s when K exceeds a c r i t i c a l v a l u e K I C 7 The c r i t i c a l s t r e s s i n t e n s i t y f a c t o r , K J C , t h u s , i s a m a t e r i a l p r o p e r t y d e t e r m i n i n g the c r i t i c a l c o n d i t i o n a t which u n s t a b l e c r a c k p r o p a g a t i o n o c c u r s . Many a t t e m p t s have been made i n the p a s t t o dete r m i n e the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r K I C f o r c o n c r e t e . However, t h e r e i s no g e n e r a l agreement over i t s v a l u e , or i t s i n t e r p r e t a t i o n . K I C has been found t o depend, among o t h e r t h i n g s , upon the n o t c h w i d t h , the n o t c h d e p t h , the specimen geometry, and a l s o upon the r a t e of l o a d i n g ( 6 1 , 6 2 ) . The e x i s t e n c e of a p r o c e s s zone i n f r o n t of an ad v a n c i n g c r a c k t i p i s now r e c o g n i z e d , and n o n l i n e a r f r a c t u r e mechanics has t h e r e f o r e been c o n s i d e r e d t o be a more a p p r o p r i a t e t o o l f o r c o n c r e t e . John and Shah (62) have r e p o r t e d t h a t c r a c k e x t e n s i o n o c c u r s even p r i o r t o the peak 7 The s u b s c r i p t I r e f e r s t o the c r a c k - o p e n i n g mode of c r a c k p r o p a g a t i o n . 201 202 l o a d , but t h a t t h i s prepeak c r a c k e x t e n s i o n d e c r e a s e s w i t h an i n c r e a s e i n the r a t e of l o a d i n g . The attempt t o dete r m i n e K I C has a l s o been extended t o f i b r e r e i n f o r c e d c o n c r e t e . H a r r i s e t a l (49) s t u d i e d the e f f e c t of randomly d i s t r i b u t e d g l a s s f i b r e s , h i g h carbon s t e e l f i b r e s , and m i l d s t e e l f i b r e s on KJ(^, and r e p o r t e d a s u b s t a n t i a l i n c r e a s e i n K J (, due t o f i b r e i n c l u s i o n . However, Yam and Mindess ( 6 3 ) , c o n c l u d e d t h a t the f i b r e s do not r e s t r a i n c r a c k growth i n any s i g n i f i c a n t way once the c r a c k s t a r t s p r o p a g a t i n g . In the p r e s e n t s t u d y , t he dependence of K I C on s t r a i n r a t e f o r b o t h p l a i n and f i b r e r e i n f o r c e d c o n c r e t e s was s t u d i e d by s u b j e c t i n g notched beams t o v a r i a b l e r a t e s of l o a d i n g . The l o a d i n g r a t e s used v a r i e d from th o s e a c h i e v e d i n a s t a t i c t e s t i n g machine t o those a c h i e v e d u s i n g t he impact machine. Two c o n c r e t e s t r e n g t h s , of 42 MPa and 82 MPa, were examined. The d e t a i l s on the c o m p o s i t i o n of the notched beams, t h e i r c o m p r e s s i v e s t r e n g t h s , and t h e i r d e s i g n a t i o n s have been p r e s e n t e d i n T a b l e 4.1. 9.2 PLAIN AND FIBRE REINFORCED NOTCHED BEAMS UNDER VARIABLE  STRESS RATES. Notches were c u t i n beams made w i t h normal s t r e n g t h c o n c r e t e , h i g h s t r e n g t h c o n c r e t e , and normal s t r e n g t h p o l y p r o p y l e n e f i b r e r e i n f o r c e d c o n c r e t e beams, u s i n g a diamond c u t t i n g wheel. The n o t c h depths ranged between 65mm and 70mm; the no t c h w i d t h was about 3mm. 203 Companion beams were f i r s t l o a d e d s t a t i c a l l y i n 3-point bending, w i t h the cross-head moving a t 4.2xl0~ 7m/s. The r e s u l t s were o b t a i n e d i n the form of bending l o a d vs. l o a d p o i n t d e f l e c t i o n p l o t s . L a t e r , s e v e r a l beams i n each of the c a t e g o r i e s were t e s t e d u s i n g the drop hammer, w i t h the hammer dropping through 0.15m, 0.25m, or 0.50m. For the computation of the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r no u n i v e r s a l l y accepted f o r m u l a e x i s t s . In t h i s s t u d y , the formula g i v e n by Broek (58) has been used. * I C *ID - ^ ( r f [ 2 - ^ ) 1 / 2 - 4 . 6 ( £ ) 3 / 2 + 2 1 . 8 ( £ ) 5 / 2 B D / D D V 9.1) 3 7 . 6 [ £ ) 7 / 2 + 3 8 . 7 f £ ] 9 / 2 l V D where, ( P b ) m a x = peak bending l o a d . 1 = t e s t span of the beam. B = breadth of the beam. D = depth of the beam, a = the notch depth. K I C , K I D = s t a t ^ c a n d- dynamic c r i t i c a l s t r e s s i n t e n s i t y f a c t o r , r e s p e c t i v e l y . Note t h a t i t was assumed t h a t the same formula c o u l d be used i n both the s t a t i c and dynamic c a s e s . The r e s u l t s f o r normal s t r e n g t h beams are given i n Table 9.1. Table 9.1a shows the impact r e s u l t s , w h i l e Table 204 9.1b shows the r e s u l t s from the s t a t i c t e s t s . S i m i l a r l y , Table 9.2 p r e s e n t s the r e s u l t s f o r h i g h s t r e n g t h c o n c r e t e , and Table 9.3 p e r t a i n s t o normal s t r e n g t h p o l y p r o p y l e n e f i b r e r e i n f o r c e d c o n c r e t e . The peak bending l o a d s o b t a i n e d f o r the d i f f e r e n t notched beams have been p l o t t e d as a f u n c t i o n of the hammer drop h e i g h t i n F i g u r e 9.1. As may be seen, an i n c r e a s e i n the hammer drop h e i g h t , or an i n c r e a s e i n the s t r e s s r a t e , r e s u l t e d i n an i n c r e a s e i n the peak bending l o a d the beam c o u l d support. ' I t may a l s o be noted t h a t h i g h s t r e n g t h 15. 14' 13-12-NOTCHED BEAFIS —r~ o.i 0.2 - 1 0.3 —I— 0.4 0.5 HT. OF HAITtR DROP, m F i g u r e 9 . 1 - E f f e c t of Hammer Drop H e i g h t on Peak Bending Load TABLE-9.1 Behaviour of normal strength concrete under Impact and s t a t i c loading HEIGHT OF HAMMER DROP, m 0.15(4)* 0.25(4)* 0.50(4)* Max Min Mean Std.Dev Max Min Mean Std.Dev Max Min Mean Std.Dev Peak Bending Load (N) 7138 3606 4981 1440 8713 4932 7094 1364 16466 9590 13028 3438 Displacement at Peak Bending Load (m) ( x l t T 6 ) 246 124 192 51 357 211 284 56 597 432 514 82 Energy up to Peak Load (N-m) 1.3 0.4 0.7 0.33 2.1 0.9 1.6 0.46 5.8 4.8 5.3< 0.49' T o t a l Fracture Energy (N-m) 23.8 9.8 14.4 5.5 26.8 16.5 22.6 3.7 70.2 41.4 55.8 14.4 KID (NNm" 0 7 * ) 4.40 2.27 3.14 0.86 5.38 3.00 4.56 0.93 10.17 5.92 8.62 1.92 STATIC BENDING TESTS+(2)* Max Min Mean Std.Dev Peak Bending Load (N) 647 591 619 28 Displacement at Peak Bending Load (m) (*10~6) 261 203 232 29 Energy at Peak Load (N-m) 0.08 0.07 0.07 0.002 Energy (N-m) 0.37 0.40 0.38 0.02 K i c ( n N m ~ 3 / 2 ) 0.46 0.38 0.42 0.04 * No. of specimens tested + S t a t i c tests c a r r i e d out at cross-head speed of 4.17x10-7 m / 8 TABLE-9.2 B e h a v i o u r o f h i g h s t r e n g t h c o n c r e t e under i m p a c t and s t a t i c l o a d i n g HEIGHT OP HAMMER DROP, ra 0.15(4)* 0.25(4)* 0.50(4)* Max M i n Mean Std.Dev Max Mi n Mean Std.Dev Max M i n Mean Std.Dev Peak Bending Load (N) 3750 3524 3637 113 6888 5099 5988 632 15166 9612 12462 2400 D i s p l a c e m e n t a t Peak Bending Load (m) ( x l O - 6 ) 295 217 256 39 443 331 378 443 649 346 480 117 Energy up to Peak Load (N-m) 0.8 0.6 0.7 0.1 2.1 0.9 1.5 0.4 8.6 3.7 5.2 1.9 T o t a l F r a c t u r e Energy (N-m) 14.5 6.8 10.6 3.8 23.2 17.5 21.2 2.2 62.5 40.0 54.7 9.1 K I C ( n N m " 3 / 2 ) 2.35 2.15 2.25 0.10 4.26 3.47 3.86 0.29 10.27 6.54 8.25 1.60 STATIC BENDING TESTS+(2)* Max M i n Mean Std.Dev Peak Bendi n g Load (N) 1249 1204 1227 22.50 D i s p l a c e m e n t a t Peak Bending , Load (m) ( x l O - 6 ) 370 274 322 48 Energy at Peak Load (N-m) 0.21 0.17 0.19 0.02 T o t a l F r a c t u r e Energy (N-m) 0.60 0.40 0.50 0.10 0.80 0.77 0.79 0.01 * No. o f specimens t e s t e d + S t a t i c t e s t s c a r r i e d out a t c r o s s - h e a d speed o f 4.17x10-7 m / 8 TABLE- 9.3 Behaviour of normal strength concrete reinforced with polypropylene f i b r e s under Impact and s t a t i c loading HEIGHT OF HAMMER DROP, m 0.15(4)* 0.25(4)* 0.50(4)* Max Min Mean Std.Dev Max Min Mean Std.Dev Max Min Mean Std.Dev Peak Bending Load (N) 6196 4370 5283 913 7509 7100 7236 192 13719 13617 13667 51 Displacement at Peak Bending Load (m) ( x l O - 6 ) 318 230 274 44 375 213 314 72 470 309 389 80 Energy up to Peak Load (N-m) 1.1 0.5 0.8 0.2 2.0 1.4 1.7 0.2 5.7 5.3 5.5 0.19 Tota l Fracture Energy (N-m) 22.5: 9.5 16.0 6.5 26.8 20.2 24.3 2.9 64.7 57.5 61.1 3.5 KID ( n N m - 3 / 2 ) 3.82 2.69 3.26 0.57 5.30 4.15 4.76 0.47 9.65 8.36 9.01 0.65 STATIC BENDING TESTS+(2)* Max Min Mean Std.Dev Peak Bending Load (N) 1115 1049 1082 33 Displacement at Peak Bending Load (a) (*10~6) 210 203 207 3.5 Energy at Peak Load (N-m) 0.13 0.11 0.12 0.01 Total Fracture Energy (N-m) 0.48 0.45 0.47 0.01 K l c O l N m - 3 / 2 ) 0.79 0.68 0.73 0.06 * No. of specimens tested + S t a t i c testa c a r r i e d out at cross-head speed of 4.17x10-7 m / 8 208 c o n c r e t e , which i s , of c o u r s e , s t r o n g e r than normal s t r e n g t h c o n c r e t e i n s t a t i c l o a d i n g s i t u a t i o n s , was found t o be weaker than normal s t r e n g t h c o n c r e t e under impact l o a d i n g ( F i g u r e 9.1). Such an o b s e r v a t i o n i s i n c o n t r a d i c t i o n w i t h the r e s u l t s o b t a i n e d f o r the unnotched beams (Chapter 6 ) , i n which h i g h s t r e n g t h c o n c r e t e was found t o be c o n s i s t e n t l y s t r o n g e r than normal s t r e n g t h c o n c r e t e b o t h f o r s t a t i c and impact s i t u a t i o n s . T h i s s u g g e s t s the g r e a t e r n o t c h - s e n s i t i v i t y of h i g h s t r e n g t h c o n c r e t e compared t o normal s t r e n g t h c o n c r e t e . The energy absorbed by the beams up t o the p o i n t of peak bending load.: as a f u n c t i o n of hammer dr o p h e i g h t i s p l o t t e d i n F i g u r e 9.2. The f r a c t u r e energy, c a l c u l a t e d t o the p o i n t a t which the l o a d drops back t o z e r o , i s a l s o shown i n F i g u r e 9.2. A l t h o u g h the d i f f e r e n c e s amongst the d i f f e r e n t c o n c r e t e t y p e s ( F i g u r e 9.2) a r e not s u b s t a n t i a l , h i g h s t r e n g t h c o n c r e t e was found t o a b s o r b l e s s energy than normal s t r e n g t h c o n c r e t e up t o the peak l o a d . The a d d i t i o n of f i b r e s t o the normal s t r e n g t h mix was found t o i n c r e a s e the energy a b s o r p t i o n c a p a c i t y up"to the peak l o a d . I f the energy t o the peak l o a d may be assumed t o r e p r e s e n t the energy r e q u i r e d t o b e g i n u n s t a b l e c r a c k p r o p a g a t i o n , then f o r h i g h s t r e n g t h c o n c r e t e t h e r e was a d e c r e a s e i n t h i s e nergy, w h i l e the a d d i t i o n of f i b r e s r e s u l t e d i n i t s i n c r e a s e . 209 70 60 Normal strength High strength / Normal strength + PP fibres / / 0 0.1 0.2 0.3 0.4 0.5 HEIGHT OF HAMMER DROP.m F i g u r e 9 . 2 - E f f e c t of Hammer Drop Height on E n e r g i e s The f r a c t u r e e n e r g i e s r e q u i r e d by the notched beams under impact were s i g n i f i c a n t l y h i g h e r than those r e q u i r e d by the beams load e d s t a t i c a l l y ( F i g u r e 9.2). A l s o , an i n c r e a s e i n the drop h e i g h t of the hammer r e s u l t e d i n a c o n s i d e r a b l e i n c r e a s e i n the f r a c t u r e energy r e q u i r e m e n t . High s t r e n g t h c o n c r e t e was found t o be more b r i t t l e than normal s t r e n g t h c o n c r e t e , and f i b r e r e i n f o r c e m e n t was found t o improve the toughness m a r g i n a l l y ( F i g u r e 9.2). S i m i l a r o b s e r v a t i o n have been r e p o r t e d f o r the unnotched beams i n Cha p t e r s 6 and 10. 210 The v a l u e s of K J C and K I D have been p l o t t e d f o r the v a r i o u s types of c o n c r e t e s t e s t e d , as a f u n c t i o n of hammer drop h e i g h t i n F i g u r e 9.3. High s t r e n g t h c o n c r e t e ( T a b l e 9.2b), which under s t a t i c l o a d i n g gave a s l i g h t l y h i g h e r K J (, than e i t h e r p l a i n (Table 9.1b) or f i b r e r e i n f o r c e d ( T a b l e 9.3b) normal s t r e n g t h c o n c r e t e , showed p a r t i c u l a r n o t c h s e n s i t i v i t y under impact and r e g i s t e r e d lower K J D v a l u e s . T h i s may serve as a c a u t i o n a g a i n s t the presence of no t c h e s and f l a w s i n h i g h s t r e n g t h c o n c r e t e s u b j e c t e d t o impact. 0 O.I 0.2 0.3 0.4 0.5 HEIGHT OF HAMMER DROP , m F i g u r e 9 . 3 - E f f e c t of-Hammer Drop H e i g h t on F r a c t u r e Toughness 21 1 The use of the p o l y p r o p y l e n e f i b r e s was found t o improve the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r b o t h i n the s t a t i c and the dynamic c a s e s . F i b r e s , t h u s , appear t o a c t as c r a c k a r r e s t e r s , r e t a r d i n g growth of the s u b c r i t i c a l f l a w s . The energy i n p u t r e q u i r e d t o p r e c i p i t a t e u n s t a b l e c r a c k p r o p a g a t i o n i n f i b r e r e i n f o r c e d specimen was found t o be h i g h e r than f o r the p l a i n c o n c r e t e specimens ( F i g u r e 9.2). T h i s may be r e l a t e d , i n d i r e c t l y , t o the c o n t r i b u t i o n of the f i b r e s i n k e e p i n g the m a t r i x c o h e r e n t , t h e r e b y i n c r e a s i n g the d e f o r m a t i o n c a p a c i t y of the beams. I n c r e a s i n g the s t r a i n r a t e r e s u l t e d i n an i n c r e a s e d c r i t i c a l s t r e s s i n t e n s i t y f a c t o r f o r a l l of the t y p e s of c o n c r e t e t e s t e d i n t h i s s t u d y . However, the v a l u e s of the c r i t i c a l i n t e n s i t y f a c t o r may have been u n d e r e s t i m a t e d because of the prepeak c r a c k growth; the c r a c k l e n g t h "a" used i n E q u a t i o n 9.1 may be too low. As p o i n t e d out by John and Shah ( 6 2 ) , the prepeak c r a c k growth seems t o d e c r e a s e w i t h an i n c r e a s e i n t h e r a t e of l o a d i n g , thus r e d u c i n g the e r r o r a t h i g h e r l o a d i n g r a t e s . Indeed, even under s t a t i c l o a d i n g , they r e p o r t e d an i n c r e a s e i n K J C of o n l y about 11% when the pre-peak c r a c k e x t e n s i o n was c o n s i d e r e d . T h e r e f o r e , the f a c t t h a t pre-peak c r a c k growth was not c o n s i d e r e d i n the p r e s e n t work s h o u l d not i n t r o d u c e s i g n i f i c a n t e r r o r s i n the a n a l y s i s . 10. FIBRE REINFORCED CONCRETE UNDER IMPACT  10.1 INTRODUCTION The b r i t t l e type of f a i l u r e o b s e r v e d f o r cement-based m a t r i c e s under t e n s i l e s t r e s s systems or impact l o a d i n g i s an o b j e c t of c o n c e r n . The a d d i t i o n of f i b r e s can be used t o a l l e v i a t e t h i s problem, a t l e a s t i n p a r t . The e f f e c t of f i b r e s can be seen i n the improved t e n s i l e s t r e n g t h and f l e x u r a l s t r e n g t h of the c o m p o s i t e s , and a l s o i n t h e i r improved impact r e s i s t a n c e or toughness. I t i s not so much the improved s t r e n g t h , but r a t h e r the improved toughness, which i s the prime advantage of a d d i n g f i b r e s t o the m a t r i x . The p r e s e n c e of f i b r e s , by c o n t r o l l i n g t h e c r a c k i n g , i m p a r t s t o the composite some p o s t - c r a c k i n g d u c t i l i t y , which l e a d s t o t he improved t o u g h e s s . The f i b r e s form p r i m a r i l y a m e c h a n i c a l bond w i t h the s u r r o u n d i n g m a t r i x . As a r e s u l t , the f i b r e s and the m a t r i x a c t i n a composite manner. When an u n r e i n f o r c e d b r i t t l e m a t r i x r e a c h e s i t s f a i l u r e l o a d , the m a t r i x c r a c k s and f a i l u r e i s p r e c i p i t a t e d w i t h o u t w a r n i n g . However, i n a f i b r e c o m p o s i t e , even when t h e m a t r i x c r a c k s , the f i b r e s b r i d g i n g the c r a c k can s t i l l t r a n s f e r some l o a d , and sudden f a i l u r e i s t h e r e b y a v e r t e d . A c r a c k e d composite c a r r i e s l o a d by v i r t u e of the t e n s i l e s t r e n g t h of the f i b r e and the bond t h a t has d e v e l o p e d between the f i b r e and the m a t r i x . Once the c o m p o s i t e has c r a c k e d , the m a t r i x - f i b r e system i s no l o n g e r a c o n t i n u o u s medium and t h e r e f o r e c o n v e n t i o n a l t h e o r i e s of mechanics may be i n a p p l i c a b l e . 212 213 In the case of a composite member undergoing u n i a x i a l t e n s i o n , the matrix c r a c k s at a c e r t a i n f a i l u r e s t r a i n i n a manner s i m i l a r to that of an u n r e i n f o r c e d member. I f the f i b r e s were not present, t h i s would cause s e p a r a t i o n and sudden f a i l u r e . However, with f i b r e s present, they take over once the matrix c r a c k s . The f i b r e s , depending upon t h e i r geometry and q u a n t i t y , may support a lower or a higher l o a d than the one at which the matrix cracked. For a given type of f i b r e , thus, there e x i s t s a " c r i t i c a l volume f r a c t i o n " of f i b r e s which w i l l support j u s t the loa d the member was sup p o r t i n g at the time of matrix f a i l u r e . The loa d w i l l drop i f the f i b r e volume f r a c t i o n i s l e s s than the c r i t i c a l volume. On the other hand a d d i t i o n a l load can be c a r r i e d i f the c r i t i c a l volume f r a c t i o n i s exceeded. For a f i b r e r e i n f o r c e d member under f l e x u r e , c o n v e n t i o n a l beam theory i s a p p l i c a b l e only u n t i l the matrix c r a c k s on the t e n s i o n s i d e ; beyond t h i s p o i n t , the s t r e s s - s t r a i n curve on the t e n s i o n s i d e i s very d i f f e r e n t from the s t r e s s - s t r a i n curve on the compression s i d e , and as a r e s u l t , c o n v e n t i o n a l beam theory ceases to app l y . When an u n r e i n f o r c e d beam c r a c k s , the e q u i l i b r i u m of compressive and t e n s i l e f o r c e s on i t s c r o s s - s e c t i o n i s d i s t u r b e d suddenly, the n e u t r a l a x i s moves up, the crack r a p i d l y propagates upward, s e p a r a t i o n occurs and the load drops to zero. However, i n a f i b r e r e i n f o r c e d beam, as the t e n s i l e s t r a i n s approach the f a i l u r e value, c r a c k s are formed, but the f i b r e s c a r r y the loa d on the t e n s i o n s i d e and e q u i l i b r i u m i s 214 m a i n t a i n e d . W i t h the c r a c k s , the s t r a i n s on the t e n s i l e s i d e i n c r e a s e , and the n e u t r a l a x i s moves up. In t h i s r e g a r d , a f i b r e r e i n f o r c e d beam a c t s s i m i l a r t o an u n d e r - r e i n f o r c e d beam w i t h c o n v e n t i o n a l r e i n f o r c e m e n t . W i t h a r e d u c t i o n i n the depth of the n e u t r a l a x i s , t he a r e a of the t e n s i l e s t r e s s b l o c k may i n c r e a s e and the l o a d may r i s e . S i n c e the i n c r e a s e i n l o a d i s accompanied by a r e d u c t i o n i n the n e u t r a l a x i s d e p t h , t h e r e e x i s t s a l i m i t t o s t r e n g t h e n i n g , as f a i l u r e may then i n i t i a t e a t the co m p r e s s i o n f a c e . By ad d i n g f i b r e s , b e t t e r use i s made of the s t r e n g t h of c o n c r e t e i n c o m p r e s s i o n , s i n c e a r e d u c t i o n i n the depth of the n e u t r a l a x i s s i g n i f i e s an i n c r e a s e i n the mean c o m p r e s s i v e s t r e s s on the compres s i o n s i d e of the n e u t r a l a x i s. .The performance of a composite under h i g h s t r e s s r a t e s depends upon the performance of b o t h the f i b r e s and the m a t r i x . The performance of the m a t r i x under impact was s t u d i e d i n c h a p t e r 6. What remains t o be seen i s whether the s t r e s s r a t e s e n s i t i v i t y of a f i b r e r e i n f o r c e d composite i s due m a i n l y t o the s t r e s s r a t e s e n s i t i v i t y of the m a t r i x or because of f i b r e - m a t r i x i n t e r a c t i o n s as w e l l . Both low modulus ( p o l y p r o p y l e n e ) and h i g h modulus ( s t e e l ) f i b r e s were t e s t e d . The p o l y p r o p y l e n e f i b r e s were chopped, f i b r i l l a t e d , 38mm l o n g f i b r e s ; the s t e e l f i b r e s were 60mm l o n g , 0.6mm i n d i a m e t e r , w i t h b oth ends hooked. Volume f r a c t i o n s of 0.5% f o r p o l y p r o p y l e n e f i b r e s , and of 1.5% f o r s t e e l f i b r e s were used. Only 0.5% by volume of 215 p o l y p r o p y l e n e f i b r e s were added because h i g h e r volumes c o u l d not be added t o the c o n c r e t e u s i n g c o n v e n t i o n a l m i x i n g t e c h n i q u e s . 10.2 STEEL FIBRE REINFORCED NORMAL STRENGTH CONCRETE  (NSSFRC) UNDER VARIABLE STRESS RATE Normal s t r e n g t h s t e e l f i b r e r e i n f o r c e d c o n c r e t e beams were t e s t e d i n 3-p o i n t b e n d i n g , both on a s t a t i c u n i v e r s a l t e s t i n g machine w i t h the c r o s s head moving a t 4.2x10 m/s, and on the drop weight impact machine w i t h a hammer drop h e i g h t of 0.50m. F i g u r e 10.1 and Ta b l e 10.1 p r e s e n t the r e s u l t s o b t a i n e d from the s t a t i c t e s t s , a l o n g w i t h the c o r r e s p o n d i n g r e s u l t s o b t a i n e d from u n r e i n f o r c e d normal s t r e n g t h c o n c r e t e beams. The l o a d v s . d e f l e c t i o n p l o t s of F i g u r e 10.1 i n d i c a t e t h a t the a d d i t i o n of f i b r e s t o the m a t r i x was h e l p f u l i n two ways. F i r s t , the ob s e r v e d peak l o a d s were h i g h e r f o r r e i n f o r c e d beams compared t o the p l a i n ones; second, the sudden f a i l u r e or drop i n l o a d , a f t e r the peak l o a d i n the case of p l a i n c o n c r e t e was r e p l a c e d by a g r a d u a l drop i n l o a d i n the case of f i b r e r e i n f o r c e d c o n c r e t e . The u n d e s i r a b l e c a t a s t r o p h i c f a i l u r e i n p l a i n c o n c r e t e c o u l d t h u s be changed t o a more d e s i r a b l e p s e u d o - d u c t i l e f a i l u r e . The l o a d c a r r y i n g c a p a c i t y of the f i b r e s i n t h e post-peak l o a d r e g i o n was r e f l e c t e d i n the h i g h e r f r a c t u r e e n e r g i e s r e q u i r e d f o r f i b r e r e i n f o r c e d beams (Table 10.1). 2 1 6 Table 10.1 Static Behaviour of Plain and Sl££j Fibre Reinforced Normal Strength Concrete Plain (3)1 Plain Fibres + Steel (3)1 Max Min. Mean s Max. Min. Mean s Peak Bending Load (N) 6766 6000 6344 306 12436 10902 11500 670 Fracture Energy (Nm) 6.5 2.9 5.5 1.5 46.3 42.0 44.8 2.0 First Peak Load (N) - - - 9100 7600 8500 648 Cross Head Speed (m/sec) - - 4xl0"7 - - - 4xl0 - 7 1 Number of specimens tested. 1 2 -Deflection, mm Figure 10.1- Static Behaviour of Plain and Steel Fibre Reinforced Normal Strength Concrete 217 Table 10.2 Dynamic Behaviour nf FJajn and Sleej Fibre Reinforced Normal Strength Concrete UL5m diss) Plain (6)' Plain Fibres + Steel (6)1 Max Min. Mean s Max. Min. Mean s Max. Observed Tup (N) Load 37567 35810 36192 677 43281 37286 39999 2345 Max. observed Inertial (N) Load 20291 16868 19244 1278 17094 13819 15993 1262 Peak Bending Load (N) 17727 16452 16932 428 26800 22786 24006 1629 Fracture Energy (Nm) • 100.5 87.8 90.1 6.5 248.0 229.0 237.6 7.5 1 Number of specimens tested. 24 2 0 16 • / - P L A I N + S T E E L r F I B R E S P L A I N O 8 24 40 56 D E F L E C T I O N , mm Figure 10.2- Dynamic Behaviour of Plain and Steel Fibre Reinforced Normal Strength Concrete (0.5m drop) 218 The r e s u l t s of the dynamic t e s t s a r e p r e s e n t e d i n F i g u r e 10.2 and T a b l e 10.2. S i m i l a r t o the s t a t i c c a s e , the peak bending l o a d s and the f r a c t u r e e n e r g i e s f o r f i b r e r e i n f o r c e d c o n c r e t e were found t o be h i g h e r than t h o s e f o r u n r e i n f o r c e d beams, even i n the dynamic l o a d i n g s i t u a t i o n s . However, an improvement by about e i g h t t i m e s i n the f r a c t u r e energy o b s e r v e d i n the s t a t i c c a s e ( T a b l e 10.1), was not matched i n the dynamic c a s e , where the c o r r e s p o n d i n g improvement was o n l y by about a f a c t o r of two ( T a b l e 10.2). F i b r e r e i n f o r c e d c o n c r e t e , whose b e h a v i o u r depends upon the b e h a v i o u r of the m a t r i x as w e l l as the f i b r e s , was found t o be p a r t i c u l a r l y s t r e s s - r a t e s e n s i t i v e ( F i g u r e 10.3). S i n c e b o t h the m a t r i x (Chapter 6 ) , and the m a t r i x - f i b r e bond (64) a r e v e r y s t r a i n r a t e s e n s i t i v e , i t i s not s u r p r i s i n g t h a t the composite shows a s e n s i t i v i t y t o s t r a i n r a t e as w e l l . To s t u d y the e f f e c t of moment of i n e r t i a on the impact performance of s t e e l f i b r e r e i n f o r c e d c o n c r e t e , some beams were t e s t e d about t h e i r weak ax e s . T a b l e 10.3 shows: the r e s u l t s of t h i s t e s t i n g . I t can be noted t h a t a r e d u c t i o n i n t h e moment of i n e r t i a from 162x10 m" t o 104x10 m" r e s u l t e d not o n l y i n a r e d u c t i o n i n the peak bending l o a d , which i s t o be e x p e c t e d , but a l s o i n a r e d u c t i o n i n the f r a c t u r e energy. The d i r e c t i o n i n which the beams were c a s t , and the b l e e d i n g due t o the use of an e l e c t r i c immersion v i b r a t o r (Chapter 6 ) , a r e the p r o b a b l e causes of t h i s o b s e r v a t i o n . 219 Figure 10.3-Static and Dynamic Behaviour of Steel Fibre Reinforced Normal Strength Concrete S T E E L F IBRE RE INFORCED C O N C R E T E Dynamic 0 2 4 6 8 10 12 14 16 18 20 22 24 D E F L E C T I O N , mm Table 10.3 Ef&ci Ql Moment jaf Inertia an £l££] Fiblfi Reinforced Normal Strength Concrete (0.5m drop) I = (6)1 162xl0-7 I = (6)1 104xl0-7 Max Min. Mean s Max. Min. Mean s Max. Observed Tup (N) Load 43281 37286 39999 2345 33091 32434 32768 268 Max. observed Inertial (N) Load 17094 13819 15993 1262 16904 14009 15618 1203 Peak Bending Load (N) 26800 22786 24006 1629 19082 15877 17150 1211 Fracture Energy (Nm) 248.0 229.0 237.0 7.5 136.0 93.0 122.0 17.0 dumber of specimens tested. 220 10.3 POLYPROPYLENE FIBRE REINFORCED NORMAL STRENGTH CONCRETE  (NSPFRC) UNDER VARIABLE STRESS RATE The e f f e c t of f i b r i l l a t e d p o l y p r o p y l e n e f i b r e s on the performance of normal s t r e n g t h c o n c r e t e was s t u d i e d as f o r the s t e e l f i b r e s . F i g u r e 10.4 and Ta b l e 10.4 p r e s e n t the r e s u l t s o b t a i n e d from the s t a t i c t e s t s . The r e s u l t s f o r p l a i n c o n c r e t e have a l s o been r e p r o d u c e d f o r compar i s o n . S i m i l a r t o the s t e e l f i b r e s , the peak bending l o a d and the f r a c t u r e energy were b o t h found t o i n c r e a s e w i t h the a d d i t i o n of p o l y p r o p y l e n e f i b r e s . However, the i n c r e a s e s i n the s e q u a n t i t i e s were s m a l l , and were not as s i g n i f i c a n t as those f o r s t e e l f i b r e s ( T a b l e 10.1). S i m i l a r c o n c l u s i o n can be drawn from the dynamic r e s u l t s ( F i g u r e 10.5 and Tab l e 10.5), where once a g a i n o n l y m a r g i n a l i n c r e a s e s were o b s e r v e d i n the peak bending l o a d and the f r a c t u r e . energy upon a d d i n g the f i b r e s . A comparison of the s t a t i c performance of NSPFRC w i t h i t s dynamic performance ( F i g u r e 10.6) s u g g e s t s i t s s t r o n g s t r a i n r a t e s e n s i t i v i t y . However, the s t r a i n r a t e s e n s i t i v i t y d e monstrated by the m a t r i x i t s e l f (Chapter 6) i s p r o b a b l y p r i m a r i l y r e s p o n s i b l e f o r the s t r a i n r a t e s e n s i t i v i t y showen by the co m p o s i t e . As i n the case of s t e e l f i b e r s , the e f f e c t of moment of i n e r t i a on the impact performance of p o l y p r o p y l e n e r e i n f o r c e d c o n c r e t e was a l s o s t u d i e d by t e s t i n g a few beams 221 Table 10.4 Static Behaviour of PJajn and Polypropylene FJblfi Reinforced Normal Siienglii Concrete Plain (3)1 Plain Fibres + PP. (3)1 Max Min. Mean s Max. Min. Mean s Peak Bending Load (N) 6766 6000 6344 306 7436 7201 7302 99 Fracture Energy (Nm) 6.5 2.9 5.5 1.5 20.2 9.9 14.0 4.5 Cross Head Speed (m/sec) - - 4xl0 - 7 - - — 4xl0 - 7 -dumber of specimens tested. 10-8 -0 1 2 3 4 5 6 7 8 9 Deflection, mm Figure 10.4-Static Behaviour of Plain and Polypropylene Fibre Reinforced Normal Strength Concrete 222 Table 10.5 Eyjiamfc Behaviour tf PJain and Polypropylene Eike Reinforced Normal Siiejifiln Concrete (0.5m drop) Plain (6)1 Plain Fibres + PP. (6)1 Max Min. Mean s Max. Min. Mean s Max. Observed Tup (N) Load 37567 35810 36196 677 40431 36008 38318 1584 Max. observed Inertial (N) Load 20291 16868 19264 1278 23000 19804 21018 1267 Peak Bending Load (N) 17727 16452 16932 428 18488 16203 17300 821 Fracture Energy (Nm) 100.5 87.8 90.1 6.5 130.0 112.0 119.4 8.1 1 Number of specimens tested. I 8 p DEFLECTION , mm Figure 10.5-Dynamic Behaviour of Plain and Polypropylene Fibre Reinforced Normal Strength Concrete (0.5m drop) 223 Figure 10.6-Static and Dynamic Behaviour of Polypropylene Fibre Reinforced Normal Strength Concrete P O L Y P R O P Y L E N E FIBRE REINFORCED CONCRETE 0 1 2 3 4 5 6 7 8 9 10 II 12 13 D E F L E C T I O N , mm Table 10.6 Effect ol Moment oi Inertia on Polypropylene like Reinforced formal Strength Concrete KLSm dxopj - I = (6)1 162xl0-7 I = (6)1 104xl0"7 Max Min. Mean s Max. Min. Mean s Max. Observed Tup (N) Load 37567 35810 36196 677 32763 29737 31263 867 Max. observed Inertial (N) Load 20291 16868 19264 1278 19688 17688 18463 876 Peak Bending Load (N) 17727 16452 16932 428 15075 10049 12800 1850 Fracture Energy (Nm) 100.5 87.8 90.1 6.5 64.0 56.0 60.0 2.9 1 Number of specimens tested. 224 about t h e i r s t r o n g a x i s (1=162x10 ) and a l s o about t h e i r weak a x i s (1=104x10 ). S i g n i f i c a n t r e d u c t i o n s i n the obse r v e d peak bending l o a d s and the f r a c t u r e e n e r g i e s were o b s e r v e d (Table 10.6) f o r the t e s t s about the weak a x i s , p r o b a b l y f o r the same reasons as f o r the s t e e l f i b r e r e i n f o r c e d c o n c r e t e ( S e c t i o n 10.2). 10.4 COMPARISON OF STEEL FIBRE REINFORCED NORMAL STRENGTH  CONCRETE AND POLYPROPYLENE FIBRE REINFORCED NORMAL STRENGTH  CONCRETE F i b r e s , p o l y p r o p y l e n e as w e l l as s t e e l , seem t o i n c r e a s e the " d u c t i l i t y " of c o n c r e t e i n both the s t a t i c and the dynamic c a s e s . I n a d d i t i o n , t he f i b r e s a l s o i n c r e a s e d the peak bending l o a d s , or the s t r e n g t h s . However, the e x t e n t s t o which t h e s e improvements were a c h i e v e d were d i f f e r e n t f o r the two f i b r e t y p e s . Such a com p a r i s o n , however, i s not c o m p l e t e l y j u s t i f i e d s i n c e a f i b r e volume f r a c t i o n of o n l y 0.5% was used i n the case of p o l y p r o p y l e n e f i b r e s as compared t o a f i b r e volume f r a c t i o n of 1.5% used f o r t he s t e e l f i b r e s . Thus the comparison i s between the maximum f i b r e volume f r a c t i o n of p o l y p r o p y l e n e t h a t c o u l d be i n c l u d e d w i t h the c o n v e n t i o n a l m i x i n g t e c h n i q u e s and the commonly used f i b r e volume f r a c t i o n of s t e e l f i b r e s . In the s t a t i c c a s e , w h i l e the p o l y p r o p y l e n e f i b e r s a c h i e v e d o n l y m a r g i n a l improvements i n the peak bending l o a d s ( T a b l e 10.4) t h e peak l o a d s were almost d o u b l e d i n the 225 case of s t e e l f i b r e s (Table 10.1). S t e e l f i b r e s i n the s t a t i c case were a l s o found t o i n c r e a s e the f r a c t u r e e n e r g i e s by almost a f a c t o r of 8, whereas the c o r r e s p o n d i n g i n c r e a s e i n the case of p o l y p r o p y l e n e f i b r e s was o n l y by a f a c t o r of 2. In the dynamic case ( T a b l e s 10.2 and 10.5), the same t r e n d was o b s e r v e d . W i t h p o l y p r o p y l e n e , o n l y m a r g i n a l i n c r e a s e s i n the peak bending l o a d s and e n e r g i e s were o b s e r v e d . However, s t e e l f i b r e s i n c r e a s e d b o t h the peak bending l o a d s and the e n e r g i e s d r a m a t i c a l l y . However, an e i g h t - f o l d i n c r e a s e i n the f r a c t u r e energy i n the case of s t a t i c l o a d i n g on NSSFRC was reduced t o o n l y a t h r e e - f o l d i n c r e a s e i n the case of dynamic l o a d i n g . The performance of any type of f i b r e depends upon the s t r e n g t h of the f i b r e , i t s geometry, and the q u a l i t y of i t s bond w i t h the m a t r i x . These f i b r e c h a r a c t e r i s t i c s a l s o d e t e r m i n e the mode i n which a f i b r e w i l l f a i l . In the p r e s e n t s t u d y , the p o l y p r o p y l e n e f i b r e s were always broken, w h i l e t h e s t e e l f i b r e s . w e r e i n g e n e r a l p u l l e d o u t . I t i s p r o b a b l y the p u l l - o u t p r o c e s s i n the NSSFRC which r e s u l t s i n a l a r g e r a r e a under the post-peak p a r t of the l o a d v s . d e f l e c t i o n p l o t . The sudden b r e a k i n g of p o l y p r o p y l e n e w i t h o u t much i n e l a s t i c d e f o r m a t i o n i n the f i b r e i t s e l f r e s u l t s i n a r e l a t i v e l y sudden drop i n the l o a d v s . d e f l e c t i o n p l o t i n t h e post-peak l o a d r e g i o n . Thus i t may be c o n c l u d e d t h a t h i g h modulus, s h o r t , and h i g h t e n s i l e s t r e n g t h f i b r e s w i t h some form of m e c h a n i c a l bonding ( l i k e 2 2 6 the hooked ends of the s t e e l f i b r e s ) behave b e t t e r than low modulus, low t e n s i l e s t r e n g t h f i b r e s w i t h o u t any m e c h a n i c a l bonding. In o t h e r words, the p u l l - o u t f a i l u r e , which r e s u l t s i n i n c r e a s e d p o s t - e l a s t i c d e f o r m a t i o n s compared t o f a i l u r e by b r e a k i n g , i s the d e s i r a b l e mode of f a i l u r e . One i m p o r t a n t d i s t i n c t i o n between the two t y p e s of f i b r e s i s the number of peaks obs e r v e d i n the l o a d v s . d e f l e c t i o n p l o t s . NSSFRC was found t o have m u l t i p l e peaks i n i t s l o a d v s . d e f l e c t i o n p l o t , as opposed t o the s i n g l e peaks o b s e r v e d i n the p l a i n or p o l y p r o p y l e n e f i b r e r e i n f o r c e d beams. When a f i b r e r e i n f o r c e d beam i s l o a d e d , a t a c e r t a i n maximum t e n s i l e s t r a i n , the m a t r i x c r a c k s . A f t e r the m a t r i x f a i l u r e , the f i b r e s bear the l o a d . The s t r e s s i n any f i b r e depends upon the g e n e r a l l o a d l e v e l and i t s p o s i t i o n r e l a t i v e t o the n e u t r a l a x i s . I f the s t r e s s i n the f i b r e exceeds i t s t e n s i l e s t r e n g t h , the f i b r e b r e a k s . T h i s was the case w i t h p o l y p r o p y l e n e f i b r e s . However, i f n e i t h e r the f i b r e bond s t r e n g t h nor the t e n s i l e s t r e n g t h i s reached, the l o a d can r i s e c o n s i d e r a b l y beyond the p o i n t of m a t r i x f a i l u r e . I f the f i b r e has hooked ends, a t a c e r t a i n p o i n t c r u s h i n g of c o n c r e t e near the hook o c c u r s , the hook s t r a i g h t e n s under l o a d and the f i b r e i s p u l l e d o u t . T h i s was a p p a r e n t l y the case w i t h NSSFRC. The f i r s t peak i n NSSFRC p r o b a b l y c o r r e s p o n d s t o the m a t r i x f a i l u r e . The c r a c k i n g of the m a t r i x d i s t u r b s the e q u i l i b r i u m m o m e n t a r i l y , and w h i l e the s t r e s s e s a r e b e i n g r e d i s t r i b u t e d , the l o a d d r o p s . Once the f i b r e s t a k e over 227 c o m p l e t e l y , the l o a d r i s e s a g a i n u n t i l the f i b r e p u l l - o u t b e g i n s . W i t h the p u l l - o u t , the l o a d drops i n s t e p s ( F i g u r e 10.3). Thus the c r u s h i n g of the m a t r i x i n the v i c i n i t y of the hook, the s t r a i g h t e n i n g of the hook, and the b e g i n n i n g of the p u l l - o u t p r o c e s s as the s e p a r a t i o n p r o c e e d s , g i v e r i s e t o more than one peak i n t h e l o a d v s . d i s p l a c e m e n t p l o t . 10.5. EFFECT OF VARYING THE STRESS RATE IN THE DYNAMIC RANGE  ON THE PERFORMANCE OF STEEL FIBRE REINFORCED NORMAL STRENGTH  CONCRETE To study the e f f e c t of v a r y i n g the s t r e s s r a t e i n the dynamic range on the performance of normal s t r e n g t h s t e e l f i b r e r e i n f o r c e d c o n c r e t e , beams 150mmx150mm i n c r o s s s e c t i o n and 15.00mm l o n g were t e s t e d on a span of 960mm under f o u r d i f f e r e n t hammer drop h e i g h t s . The r e s u l t s a r e p r e s e n t e d i n Ta b l e 10.7, and a l s o i n the form of l o a d v s . d i s p l a c e m e n t p l o t s i n F i g u r e 10.7a. AS' can be ob s e r v e d from the p l o t s of F i g u r e 10.7a, b e f o r e the u l t i m a t e l o a d peak, a m a t r i x f a i l u r e peak e x i s t s f o r a l l of the drop h e i g h t s . As has been p o i n t e d out p r e v i o u s l y , b e f o r e the f u l l s t r e n g t h of the s t e e l f i b r e r e i n f o r c e d beams i s a t t a i n e d , the m a t r i x c r a c k i n g s t r a i n i s rea c h e d , and a sudden c r a c k i n g of the m a t r i x c auses a momentary u n l o a d i n g of the beam b e f o r e the l o a d can r i s e a g a i n . The f i r s t peak l o a d o u t l i n e d i n Ta b l e 10.7 thus c o r r e s p o n d s t o the l o a d a t which the m a t r i x c r a c k s ; i t can Table 10.7 l i i n a m k behaviour p i SkeJ £ibi£ Reinforced Normal S l i f u s l l i Concrete (150x150x1500 Jteuns) Height of Hammer Drop (m) 0.15m (3)1 0.25ra (3)1 0.50m (3)' 0.75m (3)1 Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Max. Min. Mean s Peak 29855 19043 25384 4607 37096 29731 32275 3410 51003 46092 48547 2455 60638 55150 57268 2409 Bending Load (N) First 20220 18340 19506 774 30698 26992 28534 1575 38912 32178 35130 2811 46082 42786 44930 1517 Peak Load (N) MOR 8.6 7.8 8.3 0.3 13.1 11.5 12.2 0.7 16.6 13.8 15.0 1.2 19.7 18.3 19.2 0.7 (First Peak Load) (MPa) Mean - - 4170 - - - 8714 - 18775 - 32016 Stress Rate MPa/sec Fracture 82.3 66.3 73.7 6.6 149.4 94.8 127.6 23.7 212.2 149.2 180.7 31.5 299.6 274.4 286.3 10.0 Energy (Nm) 'Number of sepcimens tested. 229 24" 1.3-Log 5 ,OPa/sec Figure 10.7(c)- Strain Rate Sensitivity of the Matrix in SFRC. Note that the value of "n" in Impact range i s the same as Plain Concrete (Fig.6.5) 231 thus be used to c a l c u l a t e the MOR u s i n g e l a s t i c a n a l y s i s . The v a l u e s of MOR thus o b t a i n e d a r e a l s o t a b u l a t e d i n Table 10.7. A comparison of the MOR v a l u e s o b t a i n e d from the u n r e i n f o r c e d normal s t r e n g t h c o n c r e t e beams (Table 6.2b) w i t h those o b t a i n e d from the f i r s t peak of the f i b r e r e i n f o r c e d normal s t r e n g t h beams i n d i c a t e s t h a t f o r a g i v e n drop h e i g h t , the moduli of r u p t u r e a re almost the same. Such a comparison i s p r e s e n t e d i n F i g u r e 10.7b. I t i s i n t e r e s t i n g j t 0 n o t e t h a t the presence of the f i b r e s was found not t o have a s i g n i f i c a n t e f f e c t on the performance of the m a t r i x i t s e l f . W ith the s t a t i c m a t r i x f a i l u r e v a l u e s taken from Table 10.1, and the dynamic v a l u e s taken from T a b l e 1.0.7, a p l o t of lOgff^ v s . l o g a f o r s t e e l f i b r e r e i n f o r c e d c o n c r e t e may be drawn. Such a p l o t i s p r e s e n t e d i n F i g u r e 10.7c. I t may be seen from F i g u r e 10.7c t h a t the v a l u e of n decreases under impact l o a d i n g , compared to i t s v a l u e i n the q u a s i - s t a t i c l o a d i n g . S i m i l a r f i n d i n g were r e p o r t e d i n Chapter 6 f o r the p l a i n c o n c r e t e ( F i g u r e 6.5). S i m i l a r l y , the v a l u e of n was found t o have a v a l u e of n=1.50 f o r p l a i n normal s t r e n g t h c o n c r e t e ( F i g u r e 6.5); t h i s i s almost the same as the v a l u e of n =1.40 o b t a i n e d f o r the NSSFRC ( F i g u r e 10.7c). T h i s a g a i n suggests t h a t the behaviour of the m a t r i x i t s e l f i s not m o d i f i e d s i g n i f i c a n t l y by the presence of the f i b r e s . S i m i l a r t o the behaviour of p l a i n c o n c r e t e , an i n c r e a s e i n hammer drop h e i g h t (or an i n c r e a s e i n the s t r e s s r a t e ) , 232 i s found t o i n c r e a s e the c a p a c i t y t o s u s t a i n l a r g e r d e f l e c t i o n s i n NSSFRC as w e l l ( F i g u r e 10.7a). T h i s r e s u l t e d i n i n c r e a s e d f r a c t u r e energy r e q u i r e m e n t s a t h i g h e r s t r e s s r a t e s ( T a b l e 10.7). 10.6 STEEL FIBRE REINFORCED HIGH STRENGTH CONCRETE (HSSFRC)  UNDER VARIABLE STRESS RATE H i g h s t r e n g t h c o n c r e t e made w i t h condensed s i l i c a fume ( m i c r o s i l i c a ) was a l s o r e i n f o r c e d w i t h p o l y p r o p y l e n e or s t e e l f i b r e s , t o study the e f f e c t of s t r e s s r a t e on t h e s e h i g h s t e n g t h f i b r e r e i n f o r c e d c o n c r e t e s . The s t a t i c b e h a v i o u r of s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e (HSSFRC) i s compared i n T a b l e 10.8 and i n F i g u r e 10.8 w i t h t h a t of i t s u n r e i n f o r c e d c o u n t e r p a r t . I t can be seen t h a t the f i b r e s were v e r y e f f e c t i v e i n i n c r e a s i n g the " d u c t i l i t y " of the c o m p o s i t e . The b r i t t l e n a t u r e of the f a i l u r e i n p l a i n h i g h s t r e n g t h beams, which was e v i d e n t from the sudden d r o p i n l o a d a f t e r r e a c h i n g the peak l o a d was, t o a- c o n s i d e r a b l e e x t e n t changed t o a slo w , d u c t i l e t ype of f a i l u r e by the a d d i t i o n of the f i b r e s . The dynamic performance of HSSFRC w i t h a hammer drop h e i g h t of 0.5m has been compared w i t h t h a t of p l a i n h i g h s t r e n g t h beams i n F i g u r e 10.9 and T a b l e 10.9. The t r e n d s o b s e r v e d i n the case of s t a t i c l o a d i n g a r e the same f o r dynamic l o a d i n g as w e l l . A comparison of the s t a t i c performance of HSSFRC w i t h i t s dynamic performance has been made i n F i g u r e 10.10. As 233 Table 10.8 Static Behaviour of PJaio and StfieJ Fibre Reinforced High Slicnglb £Qn£I£i£ Plain (4)' Plain Fibres + Steel (4)1 Max Min. Mean s Max. Min. Mean s Peak Bending Load (N) 12806 8144 9720 1809 18271 16001 17996 1316 Fracture Energy (Nm) 3.4 2.0 2.8 0.5 67.0 56.0 61.4 5.1 Cross Head Speed (m/sec) - - 4xl0 - 7 - - - 4xl0 - 7 -^Number of specimens tested. 1 8 -0 1 2 3 4 5 6 7 8 9 10 d e f l e c t i o n , mm Figure 10.8-Static Behaviour of Plain and Steel Fibre Reinforced High Strength Concrete 234 Table 10.9 Dynamic Behaviour of PJain and SieeJ like Reinforced High Slrcnglh Concrete (0.5m diopj Plain (7)1 Plain Fibres + Steel (6)1 Max Min. Mean s Max. Min. Mean s Max. Observed Tup (N) Load 39320 35110 36652 1725 47926 44008 46612 1588 Max. observed Inertial (N) Load 19025 16760 17892 1132 20207 17007 19011 1241 Peak Bending Load (N) 19206 18314 18760 446 29632 25049 27601 1646 Fracture Energy (Nm) 100.7 57.4 74.9 18.6 271.0 234.0 252.6 14.58 1 Number of specimens tested. 30 0 5 10 15 20 Displacement, mm Figure 10.9-Dynamic Behaviour of Plain and Steel Fibre Reinforced High Strength Concrete (0.5m drop) 235 Figure 10 .10- Dynamic and Static behaviour of Steel Fibre reinforced High Strength Concrete. 30 0 2 4 6 B 10 12 14 16 18 20 Deflection, mm Table 10.10 Effect of Moment oj Inerila on Steel like Reinforced High Strength Concrete iOJJm dmn) I = (6)1 162xl0"7 I = (6)1 104xl0-7 Max Min. Mean s Max. Min. Mean s Max. (N) Observed Tup Load 47926 44008 46612 1588 40530 38690 39752 778 Max. (N) observed Inertial Load 20207 17009 19011 1241 21904 19906 20752 843 Peak Bending Load (N) 29632 25004 27601 1646 20624 16786 19000 1452 Fracture Energy (Nm) 271.0 234.0 252.0 14.6 140.0 126.0 132.0 5.1 1 Number of specimens tested. 236 o b s e r v e d i n the case of p l a i n c o n c r e t e , HSSFRC a l s o e x h i b i t s a marked s t r a i n r a t e s e n s i t i v i t y ; the peak l o a d s and the c a p a c i t y t o s u s t a i n d e f o r m a t i o n s i n c r e a s e immensely w i t h an i n c r e a s e i n the s t r e s s r a t e . The e f f e c t of moment of i n e r t i a on the dynamic performance of HSSFRC was i n v e s t i g a t e d by i m p a c t i n g some beams about t h e i r weaker a x e s . The r e s u l t s have been t a b u l a t e d i n Table 10.10. As i n the case of normal s t r e n g t h c o n c r e t e , a r e d u c t i o n i n the moment of i n e r t i a of HSSFRC beams a l s o r e s u l t e d i n a r e d u c t i o n i n t h e i r s t r e n g t h s and f r a c t u r e e n e r g i e s . 10 .7 POLYPROPYLENE FIBRE REINFORCED HIGH STRENGTH CONCRETE  (HSPFRC) UNDER VARIABLE STRESS RATE The a d d i t i o n of 0.5% by volume of f i b r i l l a t e d p o l y p r o p y l e n e f i b r e s i n h i g h s t r e n g t h c o n c r e t e was found not to modify the p r o p e r t i e s s i g n i f i c a n t l y . F i g u r e 10.11 and Tabl e 10.11 compare the s t a t i c performance of p o l y p r o p y l e n e f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e (HSPFRC) w i t h p l a i n h i g h s t r e n g t h c o n c r e t e . I t can be seen t h a t some advantage was d e r i v e d by adding the f i b r e s . F i g u r e 10.12 and Table 10.12 compare the dynamic performance of p l a i n c o n c r e t e and HSPFRC. No s i g n i f i c a n t improvement c o u l d be n o t i c e d i n the dynamic c a s e . The e f f e c t of s t r a i n r a t e on HSPFRC i s shown i n F i g u r e 10.13, where the s t a t i c performace of HSPFRC has been p l o t t e d a l o n g w i t h i t s dynamic performance. The g e n e r a l s t r a i n r a t e s e n s i t i v i t y as 237 Table 10.11 Sialic Behaviour OS PJain and Polypropylene Fibre Reinforced High Strength Concrete Plain (4)' Plain Fibres + PP. (4)1 Max Min. Mean s Max. Min. Mean s Peak Bending Load (N) 12806 8144 9720 1809 14544 12588 13206 787 Fracture Energy (Nm) 3.4 2.0 2.8 0.6 13.0 5.4 8.7 2.9 Cross Head Speed (m/sec) - - 4xl0 - 7 - - - 4xl0 - 7 -1 Number of specimens tested. 14 _ 12 -10 -6 -•a CO o 4 _ 2 -High St rength PP. F i b r e Concrete "High St rength P l a i n Concrete 3 4 E D e f l e c t i o n , mm 10 tigure 10.11-Static Behaviour of Plain and Polypropylene Fibre Reinforced High Strength Concrete 238 Table 10.12 Eyjiajnk Behaviour of PJain and Polypropylene £ihl£ Reinforced High Sllfillglb £ M C I £ I £ UL5m drop) Plain (7)1 Plain Fibres + PP. (6)1 i Max Min. Mean s Max. Min. Mean s Max. Observed Tup (N) Load 39320 35110 36652 1725 38377 35796 37207 1109 Max. observed Inertial (N) Load 19025 16760 17892 1132 20904 17692 19063 1189 Peak Bending Load (N) 19206 18314 18760 446 19001 17473 18144 549 Fracture Energy (Nm) 100.7 57.4 74.9 18.6 100.1 80.4 92.2 7.4 1 Number of specimens tested. 30-25-20-i i i i i i i r j j 0 1 2 3 4 5 6 7 8 9 10 Deflection, mm Figure 10.12-Dynamic Behaviour of Plain and Polypropylene Fibre Reinforced High Strength Concrete (0.5m drop) 239 n o t i c e d f o r u n r e i n f o r c e d beams (Chapter 6) was n o t i c e d f o r the HSPFRC beams as w e l l , but the p o l y p r o p y l e n e f i b r e s were not found t o impart t o the composi t e any a d d i t i o n a l s t r a i n r a t e s e n s i t i v i t y beyond t h a t of the m a t r i x i t s e l f . The e f f e c t of cha n g i n g the moment of i n e r t i a of HSPFRC has been t a b u l a t e d i n T a b l e 10.13. Once a g a i n , HSPFRC was a l s o found t o have reduced s t r e n g t h s and reduced f r a c t u r e e n e r g i e s when t e s t e d about i t s weaker a x i s . Thus, l i t t l e was a c h i e v e d by a d d i n g p o l y p r o p y l e n e f i b r e s t o a h i g h s t r e n g t h m a t r i x . The o n l y r e a l advantage of t h i s a d d i t i o n was i n the g e n e r a l coherence o b s e r v e d i n t h e s e beams under impact. W h i l e e x t e n s i v e s p a l l i n g o c c u r e d i n p l a i n u n r e i n f o r c e d beams, p o l y p r o p y l e n e f i b r e r e i n f o r c e d beams tended t o p r e s e r v e t h e i r coherence and the i n t e g r i t y of the c o m p o s i t e . 10.8 COMPARISON BETWEEN FIBRE REINFORCED NORMAL STRENGTH AND  FIBRE REINFORCED HIGH STRENGTH CONCRETE Under s t a t i c c o n d i t i o n s , the b e h a v i o u r of both t y p e s of c o n c r e t e was m o d i f i e d t o some e x t e n t by a d d i n g f i b r e s ( T a b l e s 10.1, 10.4, 10.8, and 10.11). Low modulus p o l y p r o p y l e n e f i b r e s d i d not r e s u l t i n any major improvement i n the m e c h a n i c a l p r o p e r t i e s of c o n c r e t e . However, the i n c l u s i o n of h i g h modulus s t e e l f i b r e s was found t o produce s i g n i f i c a n t e f f e c t s i n b o t h t y p e s of c o n c r e t e . The more b r i t t l e h i g h s t r e n g t h c o n c r e t e was found t o b e n e f i t the most from s t e e l f i b r e a d d i t i o n . The immense improvement i n the 240 Figure 10.13-Static and Dynamic Behaviour of Polypropylene Fibre Reinforced High Strength Concrete 30-. : 20-0 1 2 3 4 5 6 7 8 9 10 Deflection, mm Table 10.13 Eflecj of Moment a! Inertia w Polypropylene £ike Reinforced High Strength Concrete KL5m drop) I = (6)1 162xl0"7 I = (6)1 104xl0~7 Max Min. Mean s Max. Min. Mean s Max. (N) Observed Tup Load 38377 35796 37207 1109 31290 29262 30080 873 Max, (N) observed Inertial Load 20904 17692 19063 1189 20062 19048 19530 415 Peak Bending Load (N) 19001 17473 18144 549 12242 9200 10550 1103 Fracture Energy (Nm) 100.1 80.4 92.2 7.4 60.0 43.0 51.0 6.1 dumber of specimens tested. 241 d u c t i l i t y and toughness of s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e s u g g e s t s t h a t the h i g h s t r e n g t h of the m a t r i x , c o u p l e d w i t h the improved d u c t i l i t y , makes i t a v e r y s u i t a b l e m a t e r i a l under s t a t i c and dynamic l o a d i n g c o n d i t i o n s . S t e e l f i b r e s were e f f e c t i v e i n p r o v i d i n g d u c t i l i t y t o normal s t r e n g t h c o n c r e t e as w e l l , a l t h o u g h t o a l e s s e r degree than t o h i g h s t r e n g t h c o n c r e t e . S i m i l a r c o n c l u s i o n s may a l s o be drawn f o r the dynamic l o a d i n g case ( T a b l e s 10.2, 10.5, 10.9 and 10.12). However, i n b o t h the s t a t i c and dynamic c a s e s , the low modulus p o l y p r o p y l e n e f i b r e s were found t o i n c r e a s e the d u c t i l i t y o n l y m a r g i n a l l y as compared t o h i g h modulus s t e e l f i b r e s w i t h hooked ends, which produced d r a m a t i c e f f e c t s . As mentioned e a r l i e r , the e f f i c i e n c y of a p a r t i c u l a r t y p e of f i b r e i n a m a t r i x depends upon how e f f e c t i v e l y the p r o p e r t i e s of the m a t r i x have been u t i l i z e d . High s t r e n g t h c o n c r e t e , known f o r i t s b e t t e r c r u s h i n g s t r e n g t h and bond, d i d not show marked improvement w i t h p o l y p r o p y l e n e f i b r e s because none of the advantageous m a t r i x p r o p e r t i e s were u t i l i z e d . On the o t h e r hand, s t e e l f i b r e s w i t h the hooks on t h e i r ends u t i l i z e d the m a t r i x c r u s h i n g s t r e n g t h i n the v i c i n i t y of a hook, and made use of the bond s t r e n g t h w h i l e b e i n g p u l l e d o u t . T h i s e x p l a i n s , t o some e x t e n t a t l e a s t , the b e t t e r b e h a v i o u r of s t e e l f i b r e r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e over s t e e l f i b r e r e i n f o r c e d normal s t r e n g t h c o n c r e t e . 242 10.9 CRACK DEVELOPMENT IN STEEL FIBRE REINFORCED NORMAL  STRENGTH CONCRETE UNDER IMPACT To study the development of c r a c k s i n NSSFRC, h i g h speed photography, u s i n g a h i g h speed motion p i c t u r e camera was c a r r i e d out on a NSSFRC beam un d e r g o i n g impact, w i t h a hammer drop h e i g h t of 0.5m. F i g u r e 10.14 shows the r e s u l t s . I t s h o u l d be compared t o F i g u r e 6.12, f o r h y d r a t e d cement p a s t e ( h e p ) . The presence of f i b r e s seems t o a f f e c t the p r o c e s s of c r a c k development i n two ways. F i r s t , w i t h f i b r e s , the v e l o c i t y of the c r a c k i s reduced. The average v e l o c i t y of the c r a c k was found t o de c r e a s e from 115 m/s i n hep t o about 74 m/s i n NSSFRC. W h i l e o n l y 10ms were r e q u i r e d f o r the c r a c k t o t r a v e r s e the e n t i r e beam depth i n hep, almost 16ms were r e q u i r e d i n NSSFRC. The second n o t i c e a b l e d i f f e r e n c e i s i n t he e x t e n t of damage. The appearance of s e v e r a l c r a c k s r u n n i n g i n v a r i o u s d i r e c t i o n s i n hep seems t o have been c o n t r o l l e d i n the f i b r e r e i n f o r c e d beam. F i b r e s t h u s a c t as c r a c k a r r e s t e r s and h e l p p r e s e r v e the coherence and i n t e g r i t y of the c o m p o s i t e . 243 S T E E L F I B R E R E I N F O R C E D C O N C R E T E ) f 1 0 10 20 30 / / i } 40 • 50 60 70 } 1 1 ). 80 90 100 110 120-130-140 170 180-190 200 150-160 LE 800 Crack development as a function of time in a steel fibre reinforced Fig.-10.14 concrete beam subjected to impact loading. The number in each frame represents the time (in units of 0.1 ms) from the f i r s t frame shown. 11. CONVENTIONALLY REINFORCED CONCRETE UNDER IMPACT  11.1 INTRODUCTION The b e h a v i o u r of p l a i n and f i b r e r e i n f o r c e d c o n c r e t e under impact l o a d i n g has been d e s c r i b e d i n the p r e v i o u s c h a p t e r s . A l t h o u g h the use of s t e e l f i b r e s has been found t o improve the performance of p l a i n c o n c r e t e d r a m a t i c a l l y , the f i b r e s can not be used t o r e p l a c e the c o n v e n t i o n a l r e i n f o r c i n g s t e e l b a r s i n c o n c r e t e . Thus, i t i s a l s o n e c e s s a r y t o a s s e s s the p r o p e r t i e s of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e under impact l o a d i n g , i n o r d e r t o be a b l e t o a s s e s s the b e h a v i o u r of the o v e r a l l s t r u c t u r e . Dynamic l o a d i n g imposes a h i g h d u c t i l i t y demand upon a s t r u c t u r e and c o n s e q u e n t l y upon i t s ele m e n t s . One such element which w i l l be d i s c u s s e d i n t h i s c h a p t e r i s the beam element. The e f f e c t of v a r y i n g the s t r e s s r a t e on p l a i n c o n c r e t e can shed some l i g h t upon the the e f f e c t of s t r e s s r a t e on r e i n f o r c e d c o n c r e t e . However, the c o n c l u s i o n s drawn f o r p l a i n c o n c r e t e beams un d e r g o i n g impact (Chapter 6) cann o t , i n g e n e r a l , be extended t o r e i n f o r c e d c o n c r e t e , where the mode of f a i l u r e and the mechanism of c r a c k p r o p a g a t i o n a r e v e r y d i f f e r e n t . C o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams, w i t h a p e r c e n t a g e of s t e e l of 1.136%, were t e s t e d under s t a t i c l o a d i n g c o n d i t i o n s i n a u n i v e r s a l t e s t i n g machine, and l a t e r under impact l o a d i n g i n the drop weight machine, u s i n g a v a r i a b l e hammer drop h e i g h t . The performance of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e under v a r i a b l e s t r e s s r a t e seemed t o be a f f e c t e d by the 244 245 c o n c r e t e s t r e n g t h , by the presence of l a t e r a l r e i n f o r c e m e n t , and by whether deformed or smooth r e i n f o r c i n g b a r s were used. A l l of thes e paramters w i l l be d i s c u s s e d below. 11.2 CONVENTIONALLY REINFORCED NORMAL STRENGTH CONCRETE WITH  DEFORMED BARS (CRNSC) UNDER VARIABLE STRESS RATE C o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e (CRNSC) beams were t e s t e d i n 3- p o i n t b e n d i n g : (1) s t a t i c a l l y , w i t h the c r o s s - h e a d moving a t 4.2x10 m/s; and (2) i n the impact machine, under drop h e i g h t s of 0.5m, 0.75m, 1.0m, and 1.5m. The c o n c r e t e s , w i t h two d i f f e r e n t water/cement r a t i o s of 0.4 and 0.33, c o r r e s p o n d i n g t o the com p r e s s i v e s t r e n g t h s of 49 and 56MPa, r e s p e c t i v e l y , were c a s t w i t h two 9.52mm deformed b a r s (Table 4.1) w i t h a y i e l d s t r e n g t h of 425 MPa, and an u l t i m a t e s t r e n g t h of 720 MPa. Ta b l e 11.1a r e p r e s e n t s the s t a t i c r e s u l t s and T a b l e s 11.1b and 11.1c r e p r e s e n t the impact r e s u l t s f o r w/c r a t i o s of 0.4 and 0.33, r e s p e c t i v e l y . The e f f e c t of v a r y i n g the s t r e s s r a t e on the l o a d v s . d i s p l a c e m e n t p l o t s i s shown i n F i g u r e 11.1 f o r a water/cement r a t i o of 0.4. P l o t s f o r a water/cement r a t i o of 0.33 l o o k s c h e m a t i c a l l y s i m i l a r . The e f f e c t s of hammer drop h e i g h t on the peak bending l o a d and the f r a c t u r e energy ( c a l c u l a t e d t o the p o i n t a t which the l o a d drops t o 1/3 of i t s peak v a l u e ) a r e shown i n F i g u r e 11.2. An a l t e r n a t i v e c r i t e r i o n f o r comparing the f r a c t u r e e n e r g i e s under d i f f e r e n t hammer drop h e i g h t s may be t o Table 11.1(a) Stalk Behaviour of Conventionally Reinforced Normal Strength Concrete w/c = 0.40 (3)* Max Min. Mean s Max. Min. Mean s Peak Bending 25042 18289 22671 3102 24642 22908 23682 1450 Load (N) Fracture Energy1 482 379 442 45 522 463 483 28 (Nm) Fracture Energy' 403 353 378 21 429 386 404 18 (Nm) Fracture Energy' 499 434 468 27 493 473 469 22 (Nm) w/c 0.33 (3)' Number of specimens tested. Table 11.1(b) Djmamil behaviour cf Conventionally Reinforced NcrmaJ Sil£H£lil Concrete (w/c .= 0.40) ML of Hammer drop, m • ...0.50m... (6)* ...0.75m... ( 6 ) * ...1.0m... (6 ) * ...1.50m... (6 ) Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Max. Min. Mean s Peak 37553 35776 36664 888 38582 37210 38026 589 40374 37557 39309 1251 45577 36539 39800 3052 Bending Load (N) Fracture 1285 564 880 300 2160 829 1378 567 3059 1723 2421 547 3854 2078 2750 628 Energy1 (Nm) Fracture 614 544 580 28 625 607 619 8 675 612 644 25 713 634 658 30 Energy' (Nm) Fracture 895 719 793 74 1281 873 1132 184 1348 1237 1303 48 1414 1249 1304 58 Energy' (Nm) Fracture - 1876 985 1358 440 1945 1678 1811 133 2078 1800 1912 100 Energy* (Nm) . Fracture - - - - - - 2485 2262 2375 113 2626 2249 2430 134 Energy1 (Nm) Max. 2.6 2.4 2.5 0.1 3.2 2.9 3.0 0.1 3.8 3.6 3.7 0.1 4.6 2.9 3.9 0.1 Beam Velocity (m/s) * Number o f spec imens t e s t e d . Table 11.1(c) Dynamic behaviour of Conventionally. Reinforced. NoimaL Slicuelh Concrete CnZf =. D J 2 ) Hi. of Hammer drop, m ...0.50m... (6) ...0.75m... (6) ...1.0m... (6) ...1.50m...(6) Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Max. Min. Mean s Peak 41419 37553 3948.6 1933 43464 39337 41064 1750 46299 40023 43053 2566 46649 40016 43703 2850 Bending Load (N) Fracture 1507 1091 1299 208 1892 1471 1618 193 2600 2496 2562 . 47 3765 2275 278 0 693 Energy1 (Nm) Fracture 671 606 638 32 682 631 652 22 732 648 688 34 716 665 691 21 Energy' (Nm) Fracture 1333 956 1145 189 1396 1149 1246 108 1508 1309 1377 92 1381 1335 1361 19 Energy1 (Nm) Fracture - 1712 1272 . 1432 199 1892 1641 1764 103 1982 1556 1820 188 Energy' (Nm) Fracture - - - - - - 2501 2336 2413 68 2535 1943 2267 243 Energy1 (Nm) Max. 2.6 2.5 2.5 0.02 2.8 2.5 2.6 0.1 3.1 2.6 2.9 0.2 4.5 3.4 4.0 0.4 Beam Velocity (m/s) * Number of specimens tested. 249 55 —i 44 — I \ \ \ 0 20 40 60 80 100 D e f l e c t i o n , mm F i g u r e - 1 1 . 1 - E f f e c t of s t r e s s r a t e on the l o a d v s . d e f l e c t i o n p l o t s of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams 250 F i g u r e - 1 1 . 2 - E f f e e t of hammer drop h e i g h t on (a) Peak bending l o a d , and (b) F r a c t u r e energy of CRNSC 251 compute these f r a c t u r e e n e r g i e s a t d i f f e r e n t midspan d e f l e c t i o n s . The v a l u e s of 18mm, 36mm, 54mm, and 72mm were chosen f o r t h i s purpose. T a b l e s 11.1b and c show the s e c a l c u l a t e d v a l u e s ; they a r e p l o t t e d i n F i g u r e 11.3 f o r a water/cement r a t i o of 0.4. C l e a r l y , s t r e s s r a t e has a s i g n i f i c a n t e f f e c t on the p r o p e r t i e s of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e . I n g e n e r a l , a l a r g e i n c r e a s e i n the peak bending l o a d was observed when the s t r e s s r a t e was i n c r e a s e d from the s t a t i c t o the dynamic range. However, once i n the dynamic range, a change i n the hammer drop h e i g h t d i d not r e s u l t i n a s i g n i f i c a n t i n c r e a s e i n the peak bending l o a d ( F i g u r e 11.2a) In the s t a t i c c a s e , f o r a r e c t a n g u l a r s e c t i o n , the bal a n c e d percentage of s t e e l i s g i v e n by (59) 0.85f e„ c 1 0.003E (11.1) P b f y 0.003E +f s y where the n o t a t i o n i s d e f i n e d i n F i g u r e 11.4. With 49 MPa 0.85 425 MPa 200,000 MPa • Upto 1/3 Peak Load Upto 72mm LPD •* Upto 54mm LPD . Upto 36mm LPD .Upto 18mm LPD Load Point D e f l e c t i o n I I I I • I 0 0.5 1.0 1.5 2.0 Ht. of Hammer drop, m Figure 11.3-Fracture Energy absorbed by Conventionally Reinforced Concrete Beam under d i f f e r e n t hammer drop heights up to a c e r t a i n mid-span d e f l e c t i o n . Note the higher deformation capacity under higher drop h e i g h t s i ( u / c ratio=0.4). we g e t , 253 Element of length of member Section te - 0.003 0.85/; Strain Actual stresses Equivalent stresses Resultant internal forces Figure-11.4-Beam S e c t i o n P b = 4.87% S i n c e the p e r c e n t s t e e l used i n t h i s s t u d y i s o n l y 1.136%, the s e c t i o n i s u n d e r r e i n f o r c e d . W i t h the s t e e l y i e d i n g f i r s t , the u l t i m a t e moment of r e s i s t a n c e under s t a t i c c o n d i t i o n s ( i g n o r i n g any s t r a i n h a r d e n i n g ) may be c a l c u l a t e d as f o l l o w s ( 5 9 ) : R e f e r r i n g a g a i n t o F i g u r e 11.4, A f s_y_ 0.85f'b c 140x425 0.85x49x100 14.28mm. (11.2) I f MR(TH) i s the t h e o r e t i c a l u l t i m a t e moment of r e s i s t a n c e of the s e c t i o n , t h e n , 254 NR(TH) = A f (d-0.5a) ( 1 1 . 3 ) s y = 140x425(100-0.5x14.28) = 5.525x10 6 N-mm T h i s agrees c l o s e l y w i t h the o b s e r v e d v a l u e of u l t i m a t e moment of r e s i s t a n c e i n the s t a t i c case (MR(OBS)) (see T a b l e 11.1a). ' ffi(DBS)=-b m 3 X 4 _ 22671x960 (11.4) 4 = 5.541x10 6 N-mm Under impact c o n d i t i o n s , a l t h o u g h the . mechanism Of f a i l u r e may remain the same as under s t a t i c c o n d i t i o n s , the p r o p e r t i e s of both s t e e l (65) and c o n c r e t e (Chapter 6 ) , and of the bond between them, seem t o change. The c o m p r e s s i v e s t r e n g t h of c o n c r e t e ( 2 1 ) , and the y i e l d and the u l t i m a t e s t r e n g t h of s t e e l (65) i n c r e a s e as the s t r e s s r a t e i s i n c r e a s e d . Once i n the dynamic range, the peak l o a d s were found not t o be v e r y d i f f e r e n t from one drop h e i g h t t o a nother ( F i g u r e 11.1 and 11.2), s u g g e s t i n g t h a t the s t r e n g t h s of both the c o n c r e t e and s t e e l tend t o approach t h e i r l i m i t i n g v a l u e s a t the h i g h s t r e s s r a t e s a s s o c i a t e d w i t h impact. T h i s may a l s o i n d i c a t e t h a t , once i n the dynamic range, the s t r e s s r a t e s may not be v e r y d i f f e r e n t from one drop h e i g h t t o a n o t h e r . The a b s o l u t e l y l i m i t i n g v a l u e of the moment of r e s i s t a n c e i n the s t a t i c case M R ( l i m , s t a t i c ) may be o b t a i n e d by assuming t h a t the s t e e l r eaches the u l t i m a t e v a l u e of s t r e s s , and by assuming t h a t the p o s i t i o n of the n e u t r a l a x i s i s a t the extreme compression f i b r e . Then, 255 r-1R(lim, static) = A f d (11.5) s us where f us = the u l t i m a t e s t r e n g t h of s t e e l i n s t a t i c c o n d i t i o n s = 700 MPa T h e r e f o r e , MR(lim, static) = 140x700x100 = 9.8x10 N-mm Under dynamic c o n d i t i o n s , i t has been r e p o r t e d (66) t h a t f o r an i n c r e a s e i n the s t r e s s r a t e of s i x o r d e r s of magnitude, the u l t i m a t e t e n s i l e s t r e n g t h of s t e e l i s a p p r o x i m a t e l y d o u b l e d . S i n c e , i n the p r e s e n t s t u d y , the s t r e s s r a t e a c h i e v e d i n the impact t e s t s was a p p r o x i m a t e l y s i x o r d e r s of magnitude h i g h e r than i n the s t a t i c t e s t s , the a b s o l u t e l y l i m i t i n g v a l u e of the moment of r e s i s t a n c e i n the dynamic case (MR(lim,dyn)) can be e s t i m a t e d t o be, NR(lim, dyn) = A g f u t J d (11.6) where f ud = the u l t i m a t e t e n s i l e s t r e n g t h of s t e e l i n dynamic c o n d i t i o n s = 1400 MPa. Then, 256 NR(lim, dyn) = 140x1400x100 = 19.6x10 N-rnm A p l o t of the a b s o l u t e l i m i t i n g moment of r e s i s t a n c e , along w i t h the e x p e r i m e n t a l l y observed moment of r e s i s t a n c e , has been presented i n F i g u r e 11.5. The c u r v e s of observed moment of r e s i s t a n c e f a l l s h o r t of the l i m i t i n g moment of r e s i s t a n c e curve because, i n p r a c t i c e , c o n c r e t e c r u s h i n g commences before the n e u t r a l a x i s reaches the compression f a c e . However, s i n c e the c r u s h i n g s t r e n g t h and the f a i l u r e s t r a i n f o r c o n c r e t e both i n c r e a s e w i t h an i n c r e a s e i n the 24-Theoretical Limiting Strength Observed Strength (u/c=0.33) Observed Strength (u/c=0.40) c o E 0 0 0.5 1.0 1.5 2.0 Ht. of Hammer drop, m F i g u r e - 1 1 . 5 - T h e o r e t i c a l l y l i m i t i n g and the e x p e r i m e n t a l l y observed Moment of R e s i s t a n c e 257 s t r e s s r a t e ( 2 1 ) , the n e u t r a l a x i s may move f u r t h e r upwards towards the compre s s i o n f a c e w i t h an i n c r e a s e i n hammer dr o p h e i g h t . Moreover, i n c r e a s e d f a i l u r e s t r a i n s i n c o n c r e t e i n c r e a s e the f a i l u r e s t r a i n s i n the s t e e l , c a u s i n g an i n c r e a s e i n s t r a i n h a r d e n i n g and c o n s e q u e n t l y i n the s t e e l s t r e s s . The complex n a t u r e of s t r e s s e s and s t r a i n s i n an impacted beams may a l s o g i v e r i s e t o severe l o c a l i z e d s t r a i n s a l o n g the l e n g t h of the s t e e l b a r s . Indeed, i n about 30% of the specimens t e s t e d at ,1.5m drop, f r a c t u r i n g of the r e i n f o r c i n g b a r s was n o t i c e d , (see S e c t i o n 11.5 a d e t a i l e d d i s c u s s i o n of the s t e e l f r a c t u r e ) . A r e d u c t i o n i n the water/cement r a t i o caused i n c r e a s e d peak bending l o a d s and i n c r e a s e d f r a c t u r e e n e r g i e s ( F i g u r e 11.2 and T a b l e s 11.1a and 11.1b). C o n c r e t e w i t h a water/cement r a t i o of 0.33, which had an e q u i v a l e n t cube s t r e n g t h of 56 MPa, as compared t o c o n c r e t e w i t h a w/c r a t i o of 0.40 w i t h an e q u i v a l e n t cube s t r e n g h t of 49 MPa, a l s o f e l l f a r s h o r t of the l i m i t i n g moment of r e s i s t a n c e c u r v e . For a g i v e n midspan d e f l e c t i o n , the beams s u b j e c t e d t o h i g h e r s t r e s s r a t e s absorbed h i g h e r f r a c t u r e e n e r g i e s . T h i s i s a consequence of the h i g h e r l o a d s s u p p o r t e d by the beams a t h i g h e r s t r e s s r a t e s ( F i g u r e 11.3). Beams s u b j e c t e d t o h i g h e r s t r e s s r a t e s c o u l d a l s o undergo l a r g e r d e f o r m a t i o n s b e f o r e the l o a d s dropped t o o n e - t h i r d of the peak v a l u e s ( F i g u r e 11.1). The h i g h e r f r a c t u r e e n e r g i e s absorbed by the beams s u b j e c t e d t o h i g h e r s t r e s s r a t e s a re t h e r e f o r e a 258 consequence of both h i g h e r l o a d c a p a c i t y and the h i g h e r d e f o r m a t i o n c a p a c i t y a t h i g h e r s t r e s s r a t e s . 11.3 THE USE OF SMOOTH REINFORCING BARS In c o n v e n t i o n a l c o n c r e t e p r a c t i c e , o n l y deformed r e i n f o r c i n g b a r s a r e used, because they a c h i e v e a much b e t t e r bond w i t h c o n c r e t e than do smooth b a r s . However, s i n c e the f a i l u r e mechanism and the b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e under impact l o a d i n g was found t o be d i f f e r e n t from the s t a t i c c a s e , i t was d e c i d e d t o examine the b e h a v i o u r of c o n c r e t e r e i n f o r c e d w i t h smooth r e b a r s under impact. I t s h o u l d be noted here t h a t i n the case of beams r e i n f o r c e d w i t h deformed r e i n f o r c i n g b a r s under impact, f r a c t u r e of the r e b a r s was ob s e r v e d i n about 30% of the cases (See be l o w ) . I t was t h e r e f o r e c o n s i d e r e d w o r t h w h i l e t o see i f r e d u c i n g the bond by u s i n g smooth r e b a r s s o l v e d t h i s problem. The same scheme as used f o r deformed r e b a r s was adopted. Two w/c r a t i o s , of 0.4 and 0.5, were chosen, c o r r e s p o n d i n g t o c o n c r e t e s t r e n g t h s of 42 and 49 MPa, r e s p e c t i v e l y . T a b l e s 11.2a and 11.2b,c p r e s e n t the s t a t i c and the dynamic p r o p e r t i e s , r e s p e c t i v e l y , of normal s t r e n g t h c o n c r e t e w i t h smooth r e i n f o r c i n g b a r s . As i n the case of deformed b a r s , both the peak bending l o a d s and the f r a c t u r e e n e r g i e s were found t o i n c r e a s e w i t h an i n c r e a s e i n the hammer drop h e i g h t ( T a b l e s 11.2a,b,c and F i g u r e 11.6). The f r a c t u r e e n e r g i e s t o 1/3 of the peak l o a d and t o d i f f e r e n t Table 11.2(a) Slatic Behaviour of Normal Strength Concrete Reinforced with Smeclli Steel fiars w/c = 0.40 (3)* w/c = 0.50 (3)* Max Min. Mean s Max. Min. Mean s Peak Bending 26028 Load (N) 21356 23202 2029 23028 18348 20148 2057 Fracture Energy1 604 (Nm) 550 586 25 590 430 534 74 Fracture Energy1 530 (Nm) 377 432 69 456 362 402 40 Fracture Energy1 672 500 599 73 630 510 560 51 (Nm) Number o f s p e c i m e n s t e s t e d . Table 11.2(b) Dynamic behaviour of Normal Strength Concrete Reinforced with Sjnsoih SkeJ Bars (w/c =. Hi) lit. of Hammer drop, m ...0.50m... ,(6) ...1.50m... * (6) ...2.36m... * •(6) Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Peak Bending Load (N) 37202 35456 36617 820 39727 35494 37314 1778 43441 38636 41038 2402 Fracture Energy1 (Nm) 1230 1056 1143 87 2699 1735 2353 438 3748 2959 3353 394 Fracture Energy' (Nm) 606 601 603 2 653 604 624 21 685 674 679 6 Fracture Energy' (Nm) 1213 1171 1127 19 1299 1164 1235 55 1355 1355 1355 0 Fracture Energy' (Nm) * * — 1955 1649 1760 138 1976 1946 1961 15 Fracture Energy' (Nm) — — — 2626 1930 2218 296 2577 2375 2476 101 Max. Beam velocity (m/s) 3.9 2.4 2.9 0.7 4.2 2.8 3.4 0.6 4.5 1 3.8 4.2 0.4 * Number of specimens tested. Table 11.2(c) Pynamlt hehariour of NfliniaL SlZCO£lb_ Concrete Relnforcrd with SniCOlh Sl id Dao (a/C 3 . 1L5J. 111. of Hammer drop, m ...0.50m... (5)* ...0.75m... ( 6 ) * ...1.0m... (5)* ...1.50m... (5 )* Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Max. Min. Mean s Peak 37553 35090 36321 1231 37530 35784 36483 754 36493 36485 36474 18 36142 35448 35795 347 Bending Load (N) Fracture 1565 1497 1531 34 2703 1349 1929 - 569 2593 2143 2368 225 3117 2443 2780 337 Energy1 (Nm) Fracture 592 565 578 13 635 559 595 31 613 605 609 4 631 540 585 4S Energy1 (Nm) Fracture 1164 1119 1141 22 1233 1160 1194 29 1223 1192 1207 15 1230 1148 1189 41 Energy 1 (Nm) Fracture - 1749 1746 1747 2 1832 1762 1797 35 1807 1608 1707 99 Energy' (Nm) Fracture - - - _ - _ 2347 2145 2246 101 Energy' (Nm) Max. 2.7 2.5 2.6 0.1 3.2 2.6 2.9 0.3 3.5 3.2 3.3 0.1 4.4 3.5 4.0 1)4 Beam Velocity (m/s) * Number of specimens tested. 262 F i g u r e - 1 1 . 6 - E f f e e t of hammer drop h e i g h t on (a) Peak bending l o a d and (b) F r a c t u r e energy f o r CRNSC-S 263 Upto 1/3 Peak Load Upto 72mm LPD Upto 54mm LPD Upto 36mm LPD Upto 18mm LPD *Load P o i n t D e f l e c t i o n o.'s l '.0 1*.5 H t . of Hammer d rop , m 2.0 2 .5 F i g u r e - 1 1.7 -Energy a t v a r i o u s midspan d e f l e c t i o n s r e i n f o r c e d c o n c r e t e w i t h smooth b a r s f o r 264 midspan d i s p l a c e m e n t s as a f u n c t i o n of hammer drop h e i g h t are shown i n F i g u r e 11.7. Once a g a i n , as i n the case of deformed b a r s , the h i g h e r drop h e i g h t s l e d t o l a r g e r d e f o r m a t i o n c a p a c i t i e s b e f o r e the l o a d s dropped t o 1/3 of the peak l o a d s . The peak l o a d s i n the dynamic range were not ve r y d i f f e r e n t ; the i n c r e a s e i n the f r a c t u r e energy w i t h i n c r e a s i n g hammer drop h e i g h t was p r i m a r i l y a consequence of the l a r g e r d e f o r m a t i o n c a p a c i t y the beam demonstrated a t h i g h e r drop h e i g h t s . A comparison of the be h a v i o u r of c o n c r e t e w i t h smooth r e b a r s and of c o n c r e t e w i t h deformed r e b a r s i s p r e s e n t e d i n F i g u r e 11.8, where the peak bending l o a d s and f r a c t u r e e n e r g i e s have been p l o t t e d as a f u n c t i o n of hammer drop h e i g h t . I t can be seen from F i g u r e 11.8a t h a t , a l t h o u g h t h e i r s t a t i c performances ( T a b l e s 11.1a and 11.2a) a r e almost i d e n t i c a l , t he use of deformed r e b a r s r e s u l t e d , i n g e n e r a l , i n h i g h e r peak bending l o a d s i n the dynamic c a s e s . T h i s c o u l d , i n p a r t , be due t o the s l i g h t l y lower measured y i e l d s t r e n g t h s of the smooth r e b a r s as compared t o the deformed ones. The poorer bond a c h i e v e d w i t h smooth r e b a r s compared t o deformed r e b a r s may a l s o be r e s p o n s i b l e f o r t h e i r lower peak bending l o a d s . W i t h the e x c e p t i o n of the 0.5m drop, c o n c r e t e w i t h deformed r e b a r s was found t o be more energy a b s o r b i n g than c o n c r e t e w i t h smooth r e b a r s ( F i g u r e 11.8b). T h i s may be e x p l a i n e d by the p o o r e r bond d e v e l o p e d by the smooth r e b a r s . At h i g h e r d r o p h e i g h t s , i t i s p o s s i b l e t h a t more debonding 0 0.5 1.0 1.5 2.0 2.5 0 0.5 1.0 1.5 2.0 Ht. of Hammer drop, m Ht . of Hammer drop, m Figure 11.8 Comparison betueen Conventionally Reinforced Concrete u i t h Deformed Rein f o r c i n g bars and that u i t h Smooth R e i n f d r c i n g bars. 266 o c c u r r e d w i t h smooth r e b a r s , r e s u l t i n g i n s t r e s s r e l a x a t i o n i n s t e e l and hence i n a d i m i n i s h e d use of the s t e e l p r o p e r t i e s . On the o t h e r hand, the deformed b a r s were l i k e l y s t r e s s e d t o a h i g h e r l e v e l , r e s u l t i n g i n s t r a i n h a r d e n i n g and h i g h e r u l t i m a t e s t e e l s t r a i n s . I t i s t h e r e f o r e not s u r p r i s i n g t h a t the smooth r e b a r s f r a c t u r e d o n l y v e r y o c c a s i o n a l l y even a t a 2.36m drop h e i g h t , whereas deformed r e b a r s were o f t e n seen t o r u p t u r e a t 1.5m drop. 11.4 THE USE OF SHEAR REINFORCEMENT The e f f e c t of shear r e i n f o r c e m e n t on the dynamic b e h a v i o u r of c o n v e n t i o n a l l y r e i n f o r c e d beams w i t h deformed r e b a r s was a l s o s t u d i e d . The s t i r r u p s used were 5mm i n di a m e t e r , and spaced 100mm a p a r t ( T a b l e 4.1). The r e s u l t s of bot h s t a t i c t e s t s and impact t e s t s a r e p r e s e n t e d i n Tab l e 11.3. These r e s u l t s can be compared w i t h the r e s u l t s o b t a i n e d i n the case of c o n c r e t e w i t h o u t the s t i r r u p s ( T a b l e 11.1a,b, and c ) . A g r a p h i c a l comparison i s made i n F i g u r e 11.9. The use of s t i r r u p s , as can be seen from F i g u r e 11.9a, i s not v e r y e f f e c t i v e i n i n c r e a s i n g the s t r e n g t h e i t h e r i n the s t a t i c c a s e or i n the dynamic c a s e . However, confinement of the c o n c r e t e was found t o i n c r e a s e the f r a c t u r e energy r e q u i r e m e n t , p a r t i c u l a r l y i n the dynamic range ( F i g u r e 11.9b). The c o n f i n e m e n t of c o n c r e t e has been found t o a f f e c t not so much the shape of the pre-peak s t r e s s - s t r a i n p l o t i n Table 11.3 Sialk-BJUL Dynamic behariour of Conventionally Reinforced Normal Sliejl&b Concrete siih Slumps ...STATIC. * (3) ...IMPACT... 0.50m ^ — drop (6) 1.0m * drop (6) Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Peak Bending Load (N) 23242 21022 22111 907 43042 34586 37770 3754 44692 35092 39788 3921 Fracture Energy1 (Nm) 562 459 499 46 1892 1521 1665 162 3348 2834 3048 218 Fracture Energy' (Nm) 432 294 342 66 641 591 621 22 731 632 689 42 Fracture Energy' (Nm) 580 384 453 90 1350 1128 1244 91 1440 1245 1325 83 Fracture Energy4 (Nm) — - — — — - 2201 1640 1911 229 Fracture Energy' (Nm) — — — - — 2842 2262 2531 238 * Number of specimens tested. Ht. of HammGr drop,m Ht. of Hammer drop.m F i g u r e 11.9- Compar i son between C o n v e n t i o n a l l y R e i n f o r c e d C o n c r e t e s w i t h and w i t h o u t S t i r r u p s . 269 c o m p r e s s i o n , but the shape of the post-peak s t r e s s - s t r a i n p l o t ( 5 9 ) . In g e n e r a l , the pre s e n c e of s t i r r u p s i n c r e a s e s the d u c t i l i t y ; t h i s i s m a n i f e s t e d by a l o n g , s l o w l y d e s c e n d i n g post-peak branch of the s t r e s s - s t r a i n c u r v e ( 5 9 ) . T h i s b e h a v i o u r , o b s e r v e d f o r s t a t i c l o a d i n g , seems t o p r e v a i l even under dynamic c o n d i t i o n s . Under impact l o a d i n g , the c o n c r e t e w i t h s t i r r u p s was found t o be c o n s i d e r a b l y more energy a b s o r b i n g than the c o n c r e t e w i t h o u t s t i r r u p s . 11.5 CONVENTIONALLY REINFORCED HIGH STRENGTH CONCRETE  (CRHSC) UNDER VARIABLE STRESS RATE, AND ITS COMPARISON WITH  CONVENTIONALLY REINFORCED NORMAL STRENGTH CONCRETE (CRNSC) The p r o p e r t i e s of u n r e i n f o r c e d h i g h s t r e n g t h beams were d i s c u s s e d i n Chapter 6. I t was s t a t e d t h a t h i g h s t r e n g t h c o n c r e t e beams, made w i t h m i c r o s i l i c a , were found t o be s t r o n g e r , but more b r i t t l e than normal s t r e n g t h p l a i n c o n c r e t e beams. In t h i s s e c t i o n , the b e h a v i o u r of h i g h s t r e n g t h c o n c r e t e beams made w i t h m i c r o s i l i c a , w i t h 9.52mm deformed r e b a r s i s d e s c r i b e d . H i g h s t r e n g t h c o n v e n t i o n a l l y r e i n f o r c e d beams were t e s t e d b o t h s t a t i c a l l y and under impact. The r e s u l t s a r e g i v e n i n Tab l e 11.4, and a r e p r e s e n t e d g r a p h i c a l l y i n the form of l o a d v s . d e f l e c t i o n p l o t s i n F i g u r e 11.10. To f a c i l i t a t e a comparison w i t h c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e under i d e n t i c a l c o n d i t i o n s , F i g u r e 11.1 has been rep r o d u c e d i n F i g u r e 11.11 f o r the r e l e v e n t d r o p h e i g h t s . To d e s c r i b e the beam response d u r i n g impact, Table 11.4 Static and. Dynamic Behaviour pi Conventionally Reinforced High SiiemiiJb Concrete ...STATIC... ( 3 ) ...IMPACT... 0.50m drop (6) 1.0m drop • (6) Max Min. Mean s Max. Min. Mean s Max. Min. Mean s Max. Observed Tup Load (N) 53304 39374 47622 5686 63747 61583 62946 824 Max. Observed Inertial Load (N) 9800 3721 7511 2317 12902 8702 10263 1710 Peak Bending Load (N) 28990 20191 . 24031 3683 44433 35653 40111 3577 54292 50461 52683 1390 Fracture Energy1 (Nm) 732 611 678 50 534 121 345 153 382 99 175 120 Max. Beam Velocity (m/s> 1.7 0.8 1.3 0.3 1.3 0.5 0.8 0.3 Number of specimens tested. 271 DEFLECTION, mm Figure-11.1O-Load v s . d e f l e c t i o n p l o t s f o r c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e under v a r i a b l e s t r e s s r a t e s 272 the v e l o c i t y v s . time p l o t s and the tup l o a d v s . time p l o t s f o r h i g h s t r e n g t h c o n c r e t e have been p l o t t e d i n F i g u r e 11.12 (0.5m d r o p ) , and i n F i g u r e 11.13 (1.5m d r o p ) . Once a g a i n f o r co m p a r i s o n , the c o r r e s p o n d i n g p l o t s f o r normal s t r e n g t h c o n c r e t e a r e p r e s e n t e d i n F i g u r e 11.14 (0.5m drop) and 11.15 (1.5m d r o p ) . A f i n a l comparison w i t h the normal s t r e n g t h c o n c r e t e under d i f f e r e n t drop h e i g h t s appears i n F i g u r e 11.16. As can be seen from T a b l e 11.4 and F i g u r e 11.10, c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e a l s o d emonstrates s u b s t a n t i a l s t r e s s r a t e s e n s i t i v i t y . The peak bending l o a d s were h i g h e r f o r h i g h e r s t r e s s r a t e a p p l i c a t i o n s . S i m i l a r f i n d i n g s were r e p o r t e d f o r h i g h s t r e n g t h p l a i n c o n c r e t e beams (Chapter 6 ) , and a l s o f o r normal s t r e n g t h beams w i t h or w i t h o u t c o n v e n t i o n a l r e i n f o r c e m e n t ( S e c t i o n 11.2). However, upon c o n s i d e r i n g the f r a c t u r e energy, a r e v e r s a l i n the t r e n d i s ob s e r v e d . The energy r e q u i r e d f o r the impact e v e n t s i n the case of CRHSC was found t o be s m a l l e r than the energy r e q u i r e d s t a t i c a l l y ( T a b l e 11.4), and an i n c r e a s e i n the drop h e i g h t r e s u l t e d i n a r e d u c t i o n i n the f r a c t u r e energy r e q u i r e m e n t . I n o t h e r words, h i g h s t r e n g t h c o n c r e t e w i t h c o n v e n t i o n a l r e i n f o r c e m e n t behaved i n a more b r i t t l e f a s h i o n as the s t r e s s r a t e or the hammer drop h e i g h t was i n c r e a s e d . One o b s e r v a t i o n worth making here i s the i n c r e a s e d r i g i d i t y of the h i g h s t r e n g t h beams under i n c r e a s e d s t r e s s r a t e s . The peak v e l o c i t i e s a t t a i n e d by the beam may s e r v e as 273 0 10 20 30 40 50 60 DEFLECTION, mm Figure-1 1 . 1 1-Comparison between CRNSC and CRHSC on the b a s i s of l o a d v s . d e f l e c t i o n p l o t s 0 5 10 15 20 T I M E , ms Figure 11.12 Reinforced High Strength Concrete under 0.5m drop. T I M E , ms Figure 11.13 Re i n f o r c e d High Strength Concrete under 1.5m drop. Note the increased r i g i d i t y of the beam compared 0.5m drop. T U P L O A D , kN V E L O C I T Y , m/sec . T U P L O A D , kN V E L O C I T Y , m/sec. 276 Figure-11.16-Comparison between CRNSC and CRHSC on the b a s i s of (a)Peak bending load and (b) F r a c t u r e energy 277 a measure of t h i s a p p arent r i g i d i t y . For example, a comparison of F i g 11.12 w i t h 11.14, and of F i g u r e 11.13 w i t h F i g u r e 11.15 i n d i c a t e s t h a t w h i l e the peak v e l o c i t i e s i n the case of normal s t r e n g t h c o n c r e t e i n c r e a s e d w i t h the hammer drop h e i g h t , they d e c r e a s e d f o r h i g h s t r e n g t h c o n c r e t e (see a l s o T a b l e 11.4). T h i s apparent r i g i d i t y of h i g h s t r e n g t h c o n v e n t i o n a l l y r e i n f o r c e d beams r e s u l t e d i n reduced u l t i m a t e d e f l e c t i o n s w i t h i n c r e a s i n g hammer drop h e i g h t s ( F i g u r e 11.10). The d e f o r m a t i o n c a p a c i t y and the u l t i m a t e d e f l e c t i o n s , which i n c r e a s e d w i t h hammer drop h e i g h t i n the case of normal s t r e n g t h c o n c r e t e , d e c r e a s e d w i t h i n c r e a s i n g hammer drop h e i g h t s f o r h i g h s t r e n g t h c o n c r e t e ; the reasons f o r t h i s a r e not e n t i r e l y c l e a r . The d u c t i l i t y r e d u c t i o n w i t h hammer drop h e i g h t i n the case of h i g h s t r e n g t h c o n c r e t e was so pronounced t h a t the f r a c t u r e e n e r g i e s almost approached the energy r e q u i r e d by the u n r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e (Chapter 6 ) . The e m b r i t t l e m e n t of h i g h s t r e n g t h c o n c r e t e w i t h c o n v e n t i o n a l r e i n f o r c e m e n t may be a consequence of the g r e a t improvement i n the bond, between h i g h s t r e n g t h c o n c r e t e c o n t a i n i n g m i c r o s i l i c a and s t e e l . The h i g h q u a l i t y bond a p p a r e n t l y r e s u l t e d i n v e r y h i g h l o c a l s t r a i n s i n s t e e l , r e s u l t i n g i n premature s t e e l f a i l u r e . S t e e l f a i l u r e was obs e r v e d i n many more c a s e s i n h i g h s t r e n g t h c o n c r e t e than i n normal s t r e n g t h c o n c r e t e ( F i g u r e 11.17). Reinforced concrete beams of high strength concrete a f t e r 1.5 m Impact showing (a) d i s i n t e g r a t i o n of a beam and, (b) d i s i n t e g r a t i o n of the beam and fr a c t u r e of the r e i n f o r c i n g bars. F i g u r e - 1 1.17-—i CO 279 11.6 CRACK DEVELOPMENT IN CONVENTIONALLY REINFORCED HIGH  STRENGTH CONCRETE (CRHSC) UNDER IMPACT A study of the crack development i n c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e was c a r r i e d out by us ing a h i g h speed motion p i c t u r e camera r u n n i n g a t 10,000 frames per second. The r e s u l t s were then viewed frame by frame in a s m a l l hand v iewer , and the s u r f a c e t r a c e s of the propagat ing c r a c k s were ske tched . The r e s u l t s are shown in F i g u r e 11.1.8. The average c r a c k v e l o c i t y ( o b t a i n e d from the time r e q u i r e d by the crack to propagate from the bottom to the top of the specimen) was found to be about 83 m/s, which i s f a s t e r than the v e l o c i t y observed i n s t e e l f i b r e r e i n f o r c e d c o n c r e t e (74 m/s) (Sec t ion 10 .9 ) , but s lower than the crack v e l o c i t y observed i n h y d r a t e d cement pas t e (115 m/s) ( S e c t i o n 6 . 7 ) . T h i s suggests tha t the presence of the r e i n f o r c i n g bars d i d not p a r t i c u l a r l y a f f e c t •' crack p r o p a g a t i o n . The c l o s i n g of e x i s t i n g s u r f a c e c r a c k s ( F i g u r e 11.18) d u r i n g the process of impact , suggests that a h i g h l y complex s t r e s s p a t t e r n e x i s t s in a beam undergoing impact . NOTES: 'Calculated to the point at which the load dropped back to l/3rd of Its peak 'Calculated to 18mm midspan deflection. 'Calculated to 36mm midspan deflection. 'Calculated to 54mm midspan deflection. 'Calculated to 72mm midspan deflection. 280 CONVENTIONALLY REINFORCED HIGH STRENGTH CONCRETE ( ( c 0 10 20 30 ( > } ) 40 50 60 70-80-90 100-110-120 i I 130-140 150 310 320 L > h 360 440-450 460 540 a r> ft 610 750 970 - II M B 1220 h ES 1540 2270 — i L J3000 Crack development as a function of time for a conventionally rein-F i g . 1 1 . 1 8-forced high strength concrete beam subjected to Impact loading. The number in each frame represents the time (In units of 0.1 ms) from the f i r s t frame shown. 12. CONVENTIONALLY REINFORCED CONCRETE CONTAINING FIBRES UNDER IMPACT 12.1 INTRODUCTION I t was observed i n Chapter 10 t h a t the a d d i t i o n of f i b r e s t o a c e m e n t i t i o u s m a t r i x r e s u l t s i n a composite which i s f a r more d u c t i l e than the b a s i c m a t r i x . The f i b r e s may, a t l e a s t i n p a r t , o f f e r a s o l u t i o n t o the problem of c o n c r e t e b r i t t l e n e s s . However, t h i s statement i s o n l y q u a l i t a t i v e ; q u a n t i t a t i v e l y , l i t t l e i s known about the optimum f i b r e geometry, optimum f i b r e volume, and so on, f o r impact l o a d i n g . In Chapter 11, i t was shown t h a t the impact r e s i s t a n c e of c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e made w i t h m i c r o s i l i c a was poor. A l s o , an i n c r e a s e d i n t e n s i t y of impact r e s u l t e d i n a reduced impact r e s i s t a n c e , warning of the dangers of u s i n g such a m a t e r i a l under severe impact l o a d i n g c o n d i t i o n s . C o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e beams w i t h o u t m i c r o s i l i c a , on the o t h e r hand, were r e a s o n a b l y impact r e s i s t a n t , and under an i n c r e a s e d impact i n t e n s i t y , the impact r e s i s t a n c e d i d not p a r t i c u l a r l y d e c r e a s e . One p o s s i b l e s o l u t i o n t o the problem would be t o a v o i d e n t i r e l y the use of h i g h s t r e n g t h c o n c r e t e i n s i t u a t i o n s where the p o s s i b l i t y of impact l o a d i n g e x i s t s . However, t h i s would p l a c e too s e v e r e a r e s t r i c t i o n on the use of a v e r y p r o m i s i n g m a t e r i a l , which has e x c e l l e n t p r o p e r t i e s i n s t a t i c l o a d i n g c o n d i t i o n s . B e s i d e s , most e n g i n e e r i n g s t r u c t u r e s a r e 281 282 d e s i g n e d f o r s t a t i c s i t u a t i o n s o n l y , and impact or shock l o a d i n g s a r e not e x p l i c i t l y c o n s i d e r e d . T h e r e f o r e , i t i s worth t r y i n g t o see whether f i b r e s can h e l p t o make c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e more energy a b s o r b i n g . As a co m p a r i s o n , the e f f e c t of f i b r e r e i n f o r c e m e n t on the impact performance of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e was a l s o i n v e s t i g a t e d . 12.2 CONVENTIONALLY REINFORCED NORMAL STRENGTH CONCRETE WITH  POLYPROPYLENE FIBRES (CRNSC-P) UNDER VARIABLE STRESS RATE Normal s t r e n g t h c o n c r e t e i s known t o be more d u c t i l e t han h y d r a t e d cement p a s t e . As has been d e s c r i b e d e a r l i e r , the a d d i t i o n of f i b r e s improved the d u c t i l i t y of normal s t r e n g t h c o n c r e t e ; the i n c l u s i o n of c o n v e n t i o n a l r e i n f o r c i n g b a r s was even more e f f e c t i v e i n i n c r e a s i n g the d u c t i l i t y of normal s t r e n g t h c o n c r e t e beams. To stu d y the e f f e c t of both f i b r e s and c o n v e n t i o n a l r e i n f o r c e m e n t , beams w i t h normal s t r e n g t h c o n c r e t e , r e i n f o r c i n g b a r s , and 0.5% by volume of chopped f i b r i l l a t e d p o l y p r o p y l e n e f i b r e s , were t e s t e d i n bo t h s t a t i c and impact l o a d i n g w i t h hammer drop h e i g h t s of 0.5m and 1.5m. The r e s u l t s a r e g i v e n i n T a b l e 12.1. The f r a c t u r e e n e r g i e s were c a l c u l a t e d t o the p o i n t a t which the l o a d dropped back t o 1/3 of i t s peak v a l u e . The b e h a v i o u r of f i b r e r e i n f o r c e d beams i s compared t o t h a t of beams w i t h o u t f i b r e s i n the l o a d v s . d e f l e c t i o n p l o t s of F i g u r e 12.1. To g i v e an i d e a of the i n e r t i a l l o a d i n g on the beams, the 283 o < o 3 0 2 5 2 0 15 1 0 5 0 5 2 3 9 2 6 1 3 0 5 2 3 9 4 - ..N.S.+FIBRES I OBSERVED 2 6 I 3 S T A T I C N O R M A L S T R E N G T H F I B R E S N O R M A L S T R E N G T H I I J I 1 0.5rn IMPACT J L N.S.+ FIBRES CORRECTED N.S. \ OBSERVED\ 2 0 4 0 6 0 8 0 D E F L E C T I O N , mm 100 FIGURE 1 2 . 1 - E f f e c t of a d d i n g ^ p o l y p r o p y l e n e f i b r e s t o c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e 284 T a b l e 12.1 S t a t i c and Dynamic B a h a v i o u r of C o n v e n t i o n a l l y R e i n f o r c e d  Normal S t r e n g t h C o n c r e t e w i t h P o l y p r o p y l e n e F i b r e s STATIC IMPACT ..0.5m d r o p . . ..1,5m dro p . . Without F i b r e s W i t h F i b r e s W ithout F i b r e s W i t h F i b r e s Without F i b r e s W i t h F i b r e s Peak 22671 Bending (3102) Load (N) 24692 (2633) 36664 (888) 38486 (1800) 39800 (3052) 40980 (2224) F r a c t u r e 4 4 2 Energy (45) (Nm) 499 (31) 880 (300) 2342 (562) 2750 (628) 3361 (490) V e l o c i t y 4 . 2 x l 0 " 7 of the C r o s s -Head (m/s) 4.2x10~ 7 3.13 3.13 5.19 5.19 NOTES: 1. Fracture Energies calculated to the point at which the load dropped back to l/3rd of its peak value. 2. The numbers in brackets are the standard deviations. 3. Three specimens tested under static, and six specimens tested inder impact in each of the categories. o b s e r v e d t u p l o a d , and the c o r r e c t e d bending l o a d have both been p l o t t e d as a f u n c t i o n of d i s p l a c e m e n t i n F i g u r e 12.1. As may be seen from F i g u r e 12.1 and from T a b l e 12.1, the e f f e c t of addi n g f i b r e s l e d t o a s l i g h t i n c r e a s e i n the peak bending l o a d , and t o an i n c r e a s e i n the f r a c t u r e e nergy, p a r t i c u l a r l y i n the dynamic c a s e s ( T a b l e 12.1). Thus, the p r i m a r y advantage of a d d i n g the f i b r e s was not so much i n the i n c r e a s e d s t r e n g t h , but i n the i n c r e a s e d f r a c t u r e energy. The beams w i t h the f i b r e s had an i n c r e a s e d 285 d e f o r m a t i o n c a p a c i t y , and the f i b r e s were e f f e c t i v e i n m a i n t a i n i n g the coherence of t h e beams w i t h reduced s p a l l i n g . 12.3 CONVENTIONALLY REINFORCED HIGH STRENGTH CONCRETE WITH  POLYPROPYLENE FIBRES (CRHSC-P) UNDER VARIABLE STRESS RATE H i g h s t r e n g t h c o n c r e t e made w i t h m i c r o s i l i c a i s more b r i t t l e than normal s t r e n g t h c o n c r e t e w i t h o u t m i c r o s i l i c a ( C h a p t e r s 6 and 11). S i n c e the h i g h c o n c r e t e s t r e n g t h t h a t can be a c h i e v e d w i t h the use of m i c r o s i l i c a i s a v e r y a t t r a c t i v e p r o p e r t y , any means of overcoming i t s b r i t t l e n a t u r e would be welcome. S i n c e f i b r e s i n u n r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e were found t o be v e r y e f f e c t i v e (Chapter 10), t h e i r e f f e c t on CRHSC was a l s o s t u d i e d . S t a t i c and impact t e s t s were c a r r i e d out on CRHSC beams r e i n f o r c e d w i t h 0.5% by volume of p o l y p r o p y l e n e f i b r e s , and the r e s u l t s a r e p r e s e n t e d i n Ta b l e 12.2 and F i g u r e 12.2. As i n t h e case of normal s t r e n g t h c o n c r e t e , improvements i n bot h the peak bending l o a d and t h e f r a c t u r e energy were o b s e r v e d due t o the a d d i t i o n of f i b r e s . Once a g a i n , s i m i l a r t o normal s t r e n g t h c o n c r e t e , the advantage was not i n the i n c r e a s e d s t r e n g t h , but i n the g r e a t l y improved impact r e s i s t a n c e . I t was shown i n Chapter 11 t h a t an i n c r e a s e i n the impact i n t e n s i t y r e s u l t e d i n a c o n s i d e r a b l e e m b r i t t l e m e n t of CRHSC. However, CRHSC w i t h f i b r e s d i d not show any s i g n s of i n c r e a s e d e m b r i t t l e m e n t w i t h i n c r e a s e d impact i n t e n s i t y . The 286 < o 2 0 4 0 6 0 100 D E F L E C T I O N , mm FIGURE 1 2 . 2 - E f f e c t of adding p o l y p r o p y l e n e f i b r e s t o c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e 287 Table 12.2 S t a t i c and Dynamic B a h a v i o u r of C o n v e n t i o n a l l y R e i n f o r c e d  H i g h S t r e n g t h C o n c r e t e w i t h P o l y p r o p y l e n e F i b r e s S T A T I C . . . ....IMPACT.... ...0.5m dro p . . . ...1.5m drop... Without F i b r e s W i t h F i b r e s Without F i b r e s W i t h F i b r e s W i t h o u t F i b r e s W ith F i b r e s Peak 24031 Bending (3683) Load (N) 28242 (2493) 401 1 1 (3577) 42642 (2683) 52683 ( 1 390) 52583 (1850) F r a c t u r e 6 7 8 Energy (50) (Nm) 889 (72) 345 (153) 1276 (229) 175 (120) 1962 (284) V e l o c i t y 4 . 2 x 1 0 " 7 of t he C r o s s -Head (m/s) 4.2x10~ 7 3.13 3.13 5.19 5.19 NOTES: 1. Fracture Energies calculated to the points at which the load dropped back to l/3rd of its peak value. 2. The numbers in brackets are the standard deviations. 3. Three specimens tested under static, and six specimens tested under impact in each of the categories. beams were found t o absorb more energy under h i g h e r drop h e i g h t s (or h i g h e r impact i n t e n s i t i e s ) . 12.4 COMPARISON BETWEEN CONVENTIONALLY REINFORCED NORMAL  STRENGTH CONCRETE WITH POLYPROPYLENE FIBRES AND HIGH  STRENGTH CONCRETE WITH POLYPROPYLENE FIBRES As has been shown, both normal s t r e n g t h and h i g h s t r e n g t h c o n c r e t e s w i t h c o n v e n t i o n a l r e i n f o r c e m e n t were found t o b e n e f i t from the a d d i t i o n of f i b r e s . The p r i m a r y advantage of a d d i n g the f i b r e s was i n the improved 288 tou g h n e s s . However, on a p e r c e n t a g e b a s i s , a l a r g e r g a i n i n toughness was o b s e r v e d f o r impact l o a d i n g than f o r s t a t i c l o a d i n g . A comparison betwen the two t y p e s of c o n c r e t e s i s p r e s e n t e d i n F i g u r e 12.3. In F i g u r e 12.3a, peak bending l o a d s have been p l o t t e d as a f u n c t i o n of hammer dro p h e i g h t . F r a c t u r e energy as a f u n c t i o n of hammer drop h e i g h t appears i n F i g u r e 12.3b. For both t y p e s of c o n c r e t e , the a d d i t i o n of f i b r e s r e s u l t e d i n i n c r e a s e d s t r e n g t h s , but the i n c r e a s e s were o n l y m a r g i n a l . F i b r e r e i n f o r c e d systems were as s t r a i n r a t e s e n s i t i v e as were t h e systems w i t h o u t the f i b r e s . The pre s e n c e of f i b r e s perhaps r e s u l t e d i n a c o n f i n i n g e f f e c t w h ich m a r g i n a l l y i n c r e a s e d the c r u s h i n g s t r e n g t h of c o n c r e t e i n t he compre s s i o n zone, c a u s i n g the mean s t r e s s i n the co m p r e s s i v e s t r e s s b l o c k t o r i s e , and thus r e g i s t e r i n g a h i g h e r moment of r e s i s t a n c e . Under s t a t i c as w e l l as dynamic l o a d i n g , the i n c l u s i o n of f i b r e s r e s u l t e d i n i n c r e a s e d energy a b s o r p t i o n c a p a c i t y . However, the i n c r e a s e i n energy a b s o r p t i o n was f a r g r e a t e r i n the case of h i g h s t r e n g t h c o n c r e t e than f o r normal s t r e n g t h c o n c r e t e , p a r t i c u l a r l y a t h i g h e r drop h e i g h t s . An i n c r e a s e i n the impact i n t e n s i t y caused the f r a c t u r e energy t o i n c r e a s e i n normal s t r e n g t h c o n c r e t e w i t h or w i t h o u t p o l y p r o p y l e n e f i b r e s . However, the t r e n d seemed t o be more complex f o r the h i g h s t r e n g t h c o n c r e t e ( F i g u r e 12.3b). Wh i l e an i n c r e a s e i n the impact i n t e n s i t y , as ob s e r v e d i n Chapter 11, r e s u l t e d i n an e m b r i t t l e m e n t of CRHSC w i t h o u t 60 50 -40 -"O • _J cn c • H X3 C CO CO -¥ ro cu CL 30 -20 -10 _ 0 -0.5 Ht 1.0 1.5 2.0 o f Hammer d rop ,m 3600 -3000 -2400 cn u co c 1800 co u - p m 1200 600 0.5 1.0 1.5 2.0 H t . o f Hammer d r o p , m F i g u r e 1 2 . 3 - C o m p a r i s o n between the e f f e c t o f P o l y p r o p y l e n e F i b r e s on C o n v e n t i o n a l l y R e i n f o r c e d Normal S t r e n g t h C o n c r e t e and on C o n v e n t i o n a l l y R e i n f o r c e d H i g h S t r e n g t h C o n c r e t e . CD 290 p o l y p r o p y l e n e f i b r e s , a s i m i l a r i n c r e a s e i n impact i n t e n s i t y made CRHSC w i t h p o l y p r o p y l e n e f i b r e s more d u c t i l e . The e m b r i t t l e m e n t of h i g h s t r e n g t h c o n c r e t e , t h u s , was l a r g e l y remedied by u s i n g f i b r e s . W h i l e r e b a r f r a c t u r e was observe d f r e q u e n t l y i n CRHSC w i t h o u t p o l y p r o p y l e n e f i b r e s , r e b a r f r a c t u r e was uncommon i n CRHSC r e i n f o r c e d w i t h p o l y p r o p y l e n e f i b r e s . Thus, the u n d e s i r a b l e and premature r e b a r f a i l u r e caused by h i g h l o c a l i z e d s t e e l s t r a i n s i n CRHSC w i t h o u t p o l y p r o p y l e n e f i b r e s d i d not occur as f r e q u e n t l y i n CRHSC w i t h p o l y p r o p y l e n e f i b r e s . The use o f f i b r e s appeared t o r e s u l t i n a more u n i f o r m d i s t r i b u t i o n of s t r a i n s a l o n g the l e n g t h of the r e i n f o r c i n g b a r s , a v o i d i n g h i g h l o c a l i z e d s t r a i n s , and thus u s i n g the r e i n f o r c e m e n t more e f f e c t i v e l y . I t i s not c l e a r , however, how the l o c a l i z e d s t r a i n s a r e caused and f u r t h e r i n v e s t i g a t i o n i s needed i n t h i s d i r e c t i o n . 12.5 PREDAMAGED BEAMS In p r a c t i c e , impact and shock l o a d i n g g e n e r a l l y o c c u r o n l y v e r y o c c a s s i o n a l l y . U s u a l l y , a s t r u c t u r a l element, b e f o r e i t i s s u b j e c t e d t o an impact l o a d i n g , has a l r e a d y been l o a d e d s t a t i c a l l y . S i n c e s t a t i c l o a d i n g d e s i g n does a l l o w f o r c r a c k s i n c o n c r e t e , the element may be predamaged b e f o r e i t i s s u b j e c t e d t o the e x t e r n a l impact l o a d i n g p u l s e . Thus the o v e r a l l s a f e t y of the s t r u c t u r e under impact depends upon how th e s e predamaged s t r u c t u r a l elements cope w i t h the e x t e r n a l impact p u l s e . 291 Table 12.3 Dynamic Bahaviour of C o n v e n t i o n a l l y R e i n f o r c e d Pre-Damaged  Concrete beams with Polypropylene F i b r e s Normal S t r e n g t h H i g h S t r e n g t h C o n c r e t e C o n c r e t e Without F i b r e s W i t h F i b r e s Without F i b r e s W i t h F i b r e s Peak 35482 3641 1 39806 38999 Bending (1894) (2698) (4609) (3809) Load (N) F r a c t u r e Energy (Nm) 586 (422) 2240 (701) 220 (140) 1223 (330) NOTES: 1. Fracture Energies were calculated to the point at which the load dropped back to l/3rd of its peak value. 2. Predamage was induced by statically loading the beams to 3mm central deflection. 3. The numbers in brackets are the standard deviations. 4. Six specimens tested in each of the categories. Predamage was in d u c e d by s t a t i c l o a d i n g of the beam ( c e n t r e p o i n t l o a d i n g ) t o a d e f l e c t i o n of 3mm, which was a p p r o x i m a t e l y double the d e f l e c t i o n a t which the l o a d f i r s t r e ached the maximum l o a d b e a r i n g c a p a c i t y of the beam . At t h i s p o i n t , a t e n s i l e c r a c k a t the c e n t r e of the beam c o u l d be seen. T h i s t r e a t m e n t was g i v e n t o both normal s t r e n g t h and h i g h s t r e n g t h beams w i t h c o n v e n t i o n a l r e i n f o r c e m e n t , and w i t h or w i t h o u t p o l y p r o p y l e n e f i b r e s . The beams were then t e s t e d i n impact u s i n g a hammer drop h e i g h t of 0.5m. The r e s u l t s a r e g i v e n i n T a b l e 12.3. The r e s u l t s f o r the predamaged beams showed, as ex p e c t e d , much more v a r i a b i l i t y than t h o s e o b s e r v e d f o r the undamaged beams. The g e n e r a l t r e n d was t h a t , f o r c o n c r e t e w i t h o u t f i b r e s , predamage had o n l y a v e r y s m a l l e f f e c t on 2 9 2 the l o a d b e a r i n g c a p a c i t y d u r i n g impact, but caused a s u b s t a n t i a l r e d u c t i o n i n the energy absorbed by the beams (Table 12.3). The presence of f i b r e s p r a c t i c a l l y e l i m i n a t e d t h i s l o s s , and the energy a b s o r p t i o n c a p a c i t y of the predamaged beams c o n t a i n i n g f i b r e s was s i m i l a r t o t h a t of the undamaged beams ( T a b l e s 12.1 and 12.2). The advantage of the pr e s e n c e of p o l y p r o p y l e n e f i b r e s i n t he predamaged beams c o u l d be c l e a r l y a p p r e c i a t e d when th e s e beams were obse r v e d a f t e r the impact l o a d i n g ( F i g u r e s 12.4 and 12.5). In normal and h i g h s t r e n g t h r e i n f o r c e d c o n c r e t e c o n s i d e r a b l e s p a l l i n g and d i s i n t e g r a t i o n c o u l d be obs e r v e d i n the predamaged beams t h a t were s u b j e c t e d t o impact ( F i g u r e s 12.4a and 12.5a). However, w i t h f i b r e s , the e x t e n t of damage was l i m i t e d t o c r a c k i n g o n l y , and no s p a l l i n g and d i s i n t e g r a t i o n was seen ( F i g u r e s 12.4b and 12.5b). T h i s type of damage was v e r y s i m i l a r t o t h a t o b s e r v e d when undamaged beams were s u b j e c t e d t o the same impact ( F i g u r e s 12.4c and 12.5c). 293 F i g . 1 2 . 4 - R e j n f o r c e d concrete beams of normal strength concrete after 0.5m impact (a) predamaged beam without polypropylene fibres; (b) predamaged beam with polypropylene f ibres; (c) undamaged beam without polypropylene fibres 294 F i g . 1 2 . 5 - R e i n f o r c e d concrete beams of high strength concrete after 0 .5m impact (a) predamaged beam without po lypropy lene fibres; (b) p redamaged beam with polypropylene fibres (c) undamaged beam without polypropylene fibres CONCLUSIONS The b r i t t l e n a t u r e of c o n c r e t e poses some s e r i o u s problems i n s i t u a t i o n s where impact l o a d i n g may o c c u r ; i t i s m a n i f e s t e d by a low f a i l u r e s t r a i n i n t e n s i o n , and a sudden drop i n the l o a d a f t e r r e a c h i n g the peak i n c o n v e n t i o n a l s t a t i c t e s t s . However, s i n c e c o n c r e t e i s a s t r a i n r a t e s e n s i t i v e m a t e r i a l , i t s b e h a v i o u r under h i g h s t r a i n r a t e s can not be p r e d i c t e d by c o n v e n t i o n a l s t a t i c t e s t s . Moreover, the case of impact l o a d i n g , because of the complex energy t r a n s f e r and d i s s i p a t i o n mechanisms, and because of the complex p a t t e r n of s t r e s s waves, can not be r e g a r d e d s i m p l y as an extreme case of h i g h s t r e s s r a t e l o a d i n g . Thus, proper impact t e s t s have t o be c a r r i e d out on c o n c r e t e and c o n c r e t e c o m p o s i t e s i n orde r t o e v a l u a t e t h e i r impact performance. Such impact t e s t s were c a r r i e d out i n t h i s s t u d y , and the f o l l o w i n g c o n c l u s i o n s may be drawn. 1. A drop weight impact machine may be s u c c e s s f u l l y used t o c a r r y out impact t e s t s on c o n c r e t e beams. However, the f o l l o w i n g s h o u l d be n o t e d . (a) In the drop weight t e s t s the c o n t a c t l o a d between the hammer and t h e beam i s not the t r u e bending l o a d because of specimen i n e r t i a e f f e c t s . The a c t u a l s t r e s s i n g l o a d on the specimen may be as low as o n l y 15% of the r e c o r d e d tup l o a d . 295 296 (b) The r e c o r d e d t u p l o a d can be c o r r e c t e d f o r i n e r t i a i f t he a c c e l e r a t i o n d i s t r i b u t i o n a l o n g the l e n g t h of the beam i s known. Three a c c e l e r o m e t e r s were used i n t h i s s tudy f o r t h i s purpose. W i t h a s u i t a b l e assumption r e g a r d i n g the a c c e l e r a t i o n d i s t r i b u t i o n between any two a c c e l e r o m e t e r s , the prop e r i n e r t i a l c o r r e c t i o n may be a p p l i e d . An independent check on the v a l i d i t y of t h i s t e c h n i q u e was made by i n s t r u m e n t i n g one of the support a n v i l s . (c) A c o n s i d e r a b l e s i m p l i f i c a t i o n i s p o s s i b l e i n the m a t h e m a t i c a l f o r m u l a t i o n l e a d i n g t o the e v a l u a t i o n of the i n e r t i a l l o a d i f some assumption r e g a r d i n g the a c c e l e r a t i o n d i s t r i b u t u t i o n a l o n g the e n t i r e l e n g t h of the beam can be made. On the b a s i s of the t e s t s c a r r i e d out i n t h i s s t u d y , i t was seen t h a t the a c c e l e r a t i o n d i s t r i b u t i o n was l i n e a r i n the case of p l a i n and f i b r e r e i n f o r c e d c o n c r e t e , and t h a t i t was s i n u s o i d a l i n the case of c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e . (d) Rubber pads have been used by some i n v e s t i g a t o r s as a means of e l i m i n a t i n g the i n e r t i a l l o a d i n g . However, from t e s t s done w i t h a rubber pad i n the system, i t was c o n c l u d e d t h a t a l t h o u g h the rubber pad h e l p e d i n r e d u c i n g the beam a c c e l e r a t i o n s and hence the i n e r t i a l l o a d i n g , i t d i d not e l i m i n a t e i t e n t i r e l y . Moreover, the use of rubber pads reduced the s t r a i n r a t e , t h e r e b y 297 d e f e a t i n g the purpose of impact t e s t i n g . The rubber pad a l s o a b sorbs t h e energy d u r i n g a t e s t which must be c o n s i d e r e d . I n e r t i a l l o a d s , t h u s , a re an i n t e g r a l p a r t of h i g h s t r a i n r a t e t e s t i n g and can not be e l i m i n a t e d . (e) A c c o r d i n g t o the law of c o n s e r v a t i o n of energy, the energy l o s t by the hammer must e q u a l the energy g a i n e d by the beam. T h i s law was examined i n the case of impacts on p l a i n c o n c r e t e beams. I t was found t h a t up to the peak e x t e r n a l l o a d , o n l y a v e r y s m a l l f r a c t i o n of the energy l o s t by the hammer was consumed by the beam i n v a r i o u s forms. The remainder of the energy was c o n s i d e r e d t o be s t o r e d i n the v a r i o u s s t r a i n e d p a r t s of the machine. However, by the end of the impact ev e n t , a r e a s o n a b l e agreement between the the energy l o s t by the hammer and t h a t g a i n e d by the beam was obs e r v e d . Thus the energy s t o r e d i n the machine a t the peak l o a d was t r a n s f e r r e d t o the beam i n the pos t peak l o a d p e r i o d . 2. On the b a s i s of the t e s t s on p l a i n c o n c r e t e beams the f o l l o w i n g c o n c l u s i o n s may be drawn. (a) Both normal s t r e n g t h as w e l l as h i g h s t r e n g t h c o n c r e t e s (produced by u s i n g m i c r o s i l i c a ) a r e s t r a i n r a t e s e n s i t i v e . Under impact l o a d i n g , the peak bending 298 l o a d s as w e l l as the f r a c t u r e e n e r g i e s were found t o be s i g n i f i c a n t l y h i g h e r than t h o s e o b t a i n e d from c o n v e n t i o n a l s t a t i c t e s t s . In g e n e r a l , under impact, t h e beams were found t o have improved d e f o r m a t i o n c a p a c i t i e s , s u g g e s t i n g i n c r e a s e d f a i l u r e s t r a i n s . The improved toughness under impact l o a d i n g was p r o b a b l y due t o the i n c r e a s e d m i c r o c r a c k i n g i n c o n c r e t e under t h o s e c o n d i t i o n s . (b) An e v a l u a t i o n of the f r a c t u r e mechanics parameter 'n' from the s l o p e of the l o g a vs l o g a p l o t i n d i c a t e d t h a t the v a l u e of n d e c r e a s e d as the s t r a i n r a t e was i n c r e a s e d . T h i s was t r u e f o r both normal and h i g h s t r e n g t h c o n c r e t e s . In the impact range, a v a l u e of n=1.5 f o r normal s t r e n g t h , and a v a l u e of n=2.2 f o r h i g h s t r e n g t h c o n c r e t e was o b t a i n e d . These low v a l u e s of "n" i n d i c a t e the h i g h l y s t r e s s r a t e s e n s i t i v e b e h a v i o u r of c o n c r e t e a t the extreme r a t e s of l o a d i n g a s s o c i a t e d w i t h impact. (c) H i g h s t r e n g t h c o n c r e t e made w i t h m i c r o s i l i c a was found t o be s t r o n g e r than normal s t r e n g t h c o n c r e t e w i t h o u t m i c r o s i l i c a i n both the s t a t i c and impact c o n d i t i o n s . However, h i g h s t r e n g t h c o n c r e t e was a l s o found t o be more b r i t t l e than normal s t r e n g t h c o n c r e t e . The most p r o b a b l e reason b e h i n d t h i s may be the improved a g g r e g a t e - p a s t e bond i n h i g h s t r e n g t h c o n c r e t e 299 which l e a d s t o reduced m i c r o c r a c k i n g or reduced energy d i s s i p a t i o n . By s e p a r a t i n g the energy absorbed up t o the peak l o a d i n t o the e l a s t i c p a r t and the work of f r a c t u r e p a r t , i t c o u l d be seen t h a t h i g h s t r e n g t h c o n c r e t e had a c o n s i s t e n t l y lower work of f r a c t u r e . A v i s u a l i n s p e c t i o n of the f r a c t u r e d s u r f a c e s i n d i c a t e d t h a t i n normal s t r e n g t h c o n c r e t e the c r a c k s took a t o r t u o u s p a t h around the agg r e g a t e p a r t i c l e s . On the o t h e r hand, i n the case of h i g h s t r e n g t h c o n c r e t e , the c r a c k s went t h r o u g h the agg r e g a t e p a r t i c l e s r a t h e r than around them. (d) Based on the impact t e s t s c a r r i e d out on notched beams, i t c o u l d be c o n c l u d e d t h a t K I (, ( f r a c t u r e toughness or the c r i t i c a l s t r e s s i n t e n s i t y f a c t o r ) i s not a m a t e r i a l c o n s t a n t and an i n c r e a s e i n the s t r e s s r a t e r e s u l t s i n an i n c r e a s e i n the v a l u e of Kj C« Under impact l o a d i n g , h i g h s t r e n g t h c o n c r e t e was found t o be more n o t c h - s e n s i t i v e than normal s t r e n g t h c o n c r e t e . (e) A n a l y t i c a l p r e d i c t i o n s of beam response t o impact may be based on e i t h e r the energy balance principle or on the principle of dynamic equilibrium of forces. In the c a s e of the model based on the energy b a l a n c e p r i n c i p l e suggested i n t h i s s t u d y , the beam d e f l e c t i o n s , v e l o c i t i e s and so' on were o v e r e s t i m a t e d because of the i n a b i l i t y of the model t o account f o r 300 the machine l o s s e s . Because of the n o n - l i n e a r n a t u r e of the e x p e r i m e n t a l l y o b s e r v e d l o a d v s . d e f l e c t i o n p l o t under impact l o a d i n g , c l a s s i c a l s i n g l e - d e g r e e or m u l t i - d e g r e e of freedom s o l u t i o n s a r e i n a p p r o p r i a t e . To account f o r t h i s n o n - l i n e a r i t y , a time s t e p i n t e g r a t i o n t e c h n i q u e was d e v i s e d which was found t o g i v e r e a s o n a b l e r e s u l t s . The n o n - l i n e a r n a t u r e of c o n c r e t e b e h a v i o u r was m o d e l l e d by c h o o s i n g a n o n - l i n e a r c o n s t i t u t i v e law i n v o l v i n g s t r e s s r a t e (a) as an independent v a r i a b l e . By c h o o s i n g two d i f f e r e n t s e t s of c o n s t a n t s i n the c o n s t i t u t i v e law, the d i f f e r e n c e s i n the b e h a v i o u r s of normal s t r e n g t h and h i g h s t r e n g t h c o n c r e t e s c o u l d be m o d e l l e d . The model was a l s o c a p a b l e of p r e d i c t i n g the more b r i t t l e n a t u r e of h i g h s t r e n g t h c o n c r e t e over normal s t r e n g t h c o n c r e t e . 3. Based on the impact t e s t s on f i b r e r e i n f o r c e d c o n c r e t e , the f o l l o w i n g c o n c l u s i o n s may be drawn. (a) I n c o r p o r a t i o n of e i t h e r h i g h modulus s t e e l f i b r e s or low modulus p o l y p r o p y l e n e f i b r e s was found t o i n c r e a s e the d u c t i l i t y of the c o m p o s i t e b o t h under s t a t i c and dynamic c o n d i t i o n s . The hooked end s t e e l f i b r e s , however, were found t o be f a r b e t t e r than the chopped s t r a i g h t p o l y p r o p y l e n e f i b r e s . W h i l e the improvements i n the peak l o a d s and f r a c t u r e e n e r g i e s 301 over u n r e i n f o r c e d c o n c r e t e were o n l y moderate i n the case of p o l y p r o p y l e n e f i b r e s , the c o r r e s p o n d i n g improvements i n the case of s t e e l f i b r e s were d r a m a t i c . (b) The d i f f e r e n c e s i n t h e i r modes of f a i l u r e may, t o some e x t e n t a t l e a s t , e x p l a i n the p o o r e r performance of p o l y p r o p y l e n e f i b r e over s t e e l f i b r e s . In s t a t i c as w e l l as impact c o n d i t i o n s , t h e p o l y p r o p y l e n e f i b r e s a lways f a i l e d by b r e a k i n g , whereas s t e e l f i b r e s were m o s t l y p u l l e d o u t . (An i n c r e a s i n g number of s t e e l f i b r e s were found t o break as the hammer drop h e i g h t was i n c r e a s e d ) . (c) F i b r e s were e f f e c t i v e i n both the normal s t r e n g t h and h i g h s t r e n g t h mixes. However, s t e e l f i b r e s p e rformed somewhat b e t t e r i n the h i g h s t r e n g t h mix w i t h m i c r o s i l i c a than i n the normal s t r e n g t h mix w i t h o u t m i c r o s i l i c a . T h i s was thought t o be because of the improved f i b r e - c o n c r e t e bond i n the h i g h s t r e n g t h mixes. (d) One major d i f f e r e n c e between the two f i b r e s was i n the o c c u r r e n c e of a peak, or a d i s c o n t i n u i t y , i n the l o a d v s . d e f l e c t i o n p l o t p r i o r t o the a b s o l u t e peak l o a d i n the case of s t e e l f i b r e r e i n f o r c e d c o n c r e t e , w h i l e no such d i s c o n t i n u i t y was o b s e r v e d i n the p o l y p r o p y l e n e f i b r e r e i n f o r c e d c o n c r e t e . The 302 d i s c o n t i n u i t y was thought t o r e s u l t from the m a t r i x f a i l u r e , a s l i g h t r e d u c t i o n i n the l o a d , and a subsequent r i s e i n the l o a d owing t o f i b r e s b r i d g i n g the c r a c k . The i d e a t h a t t h e pre-peak d i s c o n t i n u i t y o b s e r v e d i n the case of s t e e l f i b r e r e i n f o r c e d c o n c r e t e c o r r e s p o n d e d t o the p o i n t of m a t r i x f a i l u r e was s t r e n g t h e n e d by the o b s e r v a t i o n t h a t the l o a d a t the d i s c o n t i n u i t y was n e a r l y the same as the a b s o l u t e peak l o a d o b s e r v e d i n the case of p l a i n u n r e i n f o r c e d beams. (e) Impact t e s t s on p o l y p r o p y l e n e f i b r e r e i n f o r c e d n otched beams i n d i c a t e d t h a t the presence of the f i b r e s m a r g i n a l l y i n c r e a s e d the f r a c t u r e toughness ( K I C ) over t h a t of the u n r e i n f o r c e d beams. The f i b r e s thus a c t e d as c r a c k a r r e s t e r s . ( f ) One major advantage of a d d i n g the f i b r e s c o u l d was noted i n the reduced s p a l l i n g and d i s i n t e g r a t i o n o b s e r v e d i n f i b r e r e i n f o r c e d beams under impact. F i b r e s , b oth s t e e l and p o l y p r o p y l e n e , h e l p e d p r e s e r v e the i n t e g r i t y of the beams. 4 . Based on the impact t e s t s done on c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e beams, the f o l l o w i n g c o n c l u s i o n s may be drawn. 303 (a) In the case of c o n v e n t i o n a l l y r e i n f o r c e d normal s t r e n g t h c o n c r e t e w i t h deformed r e i n f o r c i n g b a r s , an i n c r e a s e i n the s t r e s s r a t e from the s t a t i c t o the impact range r e s u l t e d i n a s i g n i f i c a n t i n c r e a s e i n the f r a c t u r e energy. In g e n e r a l , an i n c r e a s e i n the s t r e s s r a t e r e s u l t e d i n an. i n c r e a s e i n the d u c t i l i t y or the d e f o r m a t i o n c a p a c i t y of the beams. The peak bending l o a d s o b t a i n e d under impact l o a d i n g were h i g h e r than tho s e o b t a i n e d under s t a t i c l o a d i n g . However, once i n the impact range, an i n c r e a s e i n the hammer drop h e i g h t d i d not produce a s i g n i f i c a n t i n c r e a s e i n the peak bending l o a d s . (b) On comparing the performance of deformed b a r s i n normal s t r e n g t h c o n c r e t e w i t h t h a t of smooth b a r s i n normal s t r e n g t h c o n c r e t e , i t may be c o n c l u d e d t h a t i n g e n e r a l , the deformed b a r s behave somewhat b e t t e r than the smooth ones. The poor bond dev e l o p e d i n the case of smooth r e b a r s was thought t o be the reason b e h i n d t h i s . However, r e b a r f r a c t u r e was n o t i c e d v e r y o c c a s s i o n a l l y i n the case of smooth r e b a r s even under a hammer drop h e i g h t of 2.3m, w h i l e deformed r e b a r s were found t o f r a c t u r e i n as many as 30% of the ca s e s under o n l y a 1.5m drop. (c) The use of shear r e i n f o r c e m e n t i n c o n v e n t i o n a l l y r e i n f o r c e normal s t r e n g t h c o n c r e t e was found t o enhance 304 the impact . r e s i s t a n c e . C o n f i n i n g the c o n c r e t e , t h u s , seemed t o i n c r e a s e i t s d u c t i l i t y . (d) An i n c r e a s e i n the s t r e s s r a t e i n the case of c o n v e n t i o n a l l y r e i n f o r c e d h i g h s t r e n g t h c o n c r e t e beams was found t o d e c r e a s e t h e i r d e f o r m a t i o n c a p a c i t y , i n c r e a s e t h e i r r i g i d i t y , and t h e r b y reduce t h e i r d u c t i l i t y . An i n c r e a s e i n the hammer drop he.ight was found t o reduce the u l t i m a t e d e f l e c t i o n s as w e l l as the f r a c t u r e energy. T h i s i s c o n t r a r y t o the b e h a v i o u r of normal s t r e n g t h c o n c r e t e where an i n c r e a s e i n the hammer drop h e i g h t i n c r e a s e d the f r a c t u r e energy. A l s o , r e i n f o r c i n g b a r s f r a c t u r e d more o f t e n i n h i g h s t r e n g t h c o n c r e t e than i n normal s t r e n g t h c o n c r e t e . 5. Based upon the impact t e s t s on c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e c o n t a i n i n g p o l y p r o p y l e n e f i b r e s , i t can be c o n c l u d e d t h a t the f i b r e s i n c r e a s e the d u c t i l i t y i n impact. The r e l a t i v e e f f e c t of the p o l y p r o p y l e n e f i b r e s i n i m p r o v i n g toughness under impact l o a d i n g was g r e a t e r i n h i g h s t r e n g t h r e i n f o r c e d c o n c r e t e than i n normal s t r e n g t h r e i n f o r c e d c o n c r e t e . Thus, the a d d i t i o n of the f i b r e s t o the h i g h s t r e n g t h c o n c r e t e seemes t o be an e f f i c i e n t means of compensating f o r the more b r i t t l e b e h a v i o u r of t h i s c o n c r e t e under impact l o a d i n g . 305 6. Based upon the h igh speed photography (at 10,000 frames per second) on beams undergoing impact (0.5m d r o p ) , i t can be concluded that the crack v e l o c i t i e s observed in hydra ted cement paste (hep) , f i b r e r e i n f o r c e d c o n c r e t e , and in c o n v e n t i o n a l l y r e i n f o r c e d c o n c r e t e were in the range of 75 to 115 m/s, far lower than the t h e o r e t i c a l crack v e l o c i t i e s in these m a t e r i a l s . A l s o , the presence of r e i n f o r c e m e n t , e i t h e r in the form of f i b r e s or cont inuous b a r s , tends to reduce the c r a c k v e l o c i t y compared with that in hydrated cement p a s t e . To c o n c l u d e , i t may.be s a i d that the t h e s i s presen t s a l a r g e amount of e x p e r i m e n t a l data i n v o l v i n g p r a c t i c a l l y a l l k inds of c o n c r e t e systems used today . The development of a v a l i d t e s t i n g t e c h n i q u e i s b e l i e v e d to be a s i g n i f i c a n t c o n t r i b u t i o n s i n c e the a v a i l a b l e data from the o ther sources i s o f t e n q u e s t i o n a b l e due to i n c o n s i s t e n c i e s in the e x p e r i m e n t a l r e s u l t s . Through e x p e r i m e n t a t i o n , and comaparat ive e v a l u a t i o n , i t i s b e l i e v e d that some p r a c t i c a l procedures for i m p r o v i n g the impact r e s i s t a n c e of c o n c r e t e have been e s t a b l i s h e d . A l s o , through e x p e r i m e n t a t i o n , the dangerous ly b r i t t l e behaviour of some c o n c r e t e systems under impact has been p o i n t e d o u t . SCOPE FOR FUTURE WORK On the b a s i s of the work c a r r i e d out i n t h i s s t u d y , f u t u r e work may be recommended i n the f o l l o w i n g a r e a s . 1 . One d i f f i c u l t y o f t e n e n c o u n t e r e d i n the re a l m of impact t e s t i n g of c e m e n t i t i o u s m a t e r i a l s i s the i n c o m p a r a b i l i t y of the r e s u l t s o b t a i n e d by d i f f e r e n t i n v e s t i g a t o r s u s i n g d i f f e r e n t t e s t i n g methods. D i f f e r e n t i n v e s t i g a t o r s use d i f f e r e n t specimen g e o m e t r i e s , and d i f f e r e n t ways of g e n e r a t i n g h i g h s t r e s s r a t e l o a d i n g s . D i f f e r e n t t e s t i n g machines have d i f f e r e n t energy l o s s e s a s s o c i a t e d w i t h them, and f i n a l l y , d i f f e r e n t t e c h n i q u e s a r e used t o a n a l y s e the raw d a t a . T h i s a l l amounts t o the t e s t r e s u l t s b e i n g v e r y s u b j e c t i v e . T h e r e f o r e , an attempt towards d e s i g n i n g a s t a n d a r d t e s t t e c h n i q u e i s v e r y i m p o r t a n t , and r e s e a r c h i n t h i s d i r e c t i o n i s h i g h l y recommended. 2 . In t h i s s t u d y , o n l y two b a s i c c o n c r e t e mixes (normal s t r e n g t h and h i g h s t r e n g t h ) have been t e s t e d . However, the p r o p e r t i e s and the type of cement, p r o p e r t i e s of a g g r e g a t e s , m i x i n g t e c h n i q u e , a d d i t i v e s , and so on, a l l have a c o n s i d e r a b l e e f f e c t on the impact b e h a v i o u r of c o n c r e t e . The a g g r e g a t e - p a s t e i n t e r f a c e , which forms the weakest l i n k i n c o n c r e t e , a l s o d e t e r m i n e s i t s impact r e s i s t a n c e and needs f u r t h e r s t u d y . 306 307 A n a l y t i c a l p r e d i c t i o n of c o n c r e t e b e h a v i o u r s u b j e c t e d t o an e x t e r n a l impact p u l s e needs f u r t h e r a t t e n t i o n . A n a l y t i c a l s t u d i e s a r e needed p a r t i c u l a r l y i n the post-peak l o a d r e g i o n . S i n c e t h i s r e g i o n i n v o l v e s a p r o p a g a t i n g c r a c k , a study of the c r a c k p r o p a g a t i o n under impact l o a d i n g must be undertaken p r i o r t o such m o d e l l i n g . A s t u d y of the p r o c e s s zone i n f r o n t of a p r o p a g a t i n g c r a c k and the e f f e c t of c r a c k v e l o c i t y on such a zone a r e a l s o i m p o r t a n t . A study of the post-peak l o a d r e g i o n i s i m p o r t a n t s i n c e a s u b s t a n t i a l p o r t i o n of the t o t a l f r a c t u r e energy i s consumed i n t h i s r e g i o n . Because of t h e i r h i g h d u c t i l i t y and energy a b s o r p t i o n c a p a c i t y , f i b r e r e i n f o r c e d c o m p o s i t e s a r e becoming v e r y p o p u l a r . However, our p r e s e n t knowledge of t h e i r b e h a v i o u r under s t a t i c as w e l l as dynamic c o n d i t i o n s i s m o s t l y e m p i r i c a l , and f u r t h e r r e s e a r c h i s needed towards f o r m u l a t i n g t h e i r c o n s t i t u t i v e laws as a f u n c t i o n of the s t r e s s r a t e , so t h a t a more d e t e r m i n i s t i c approach may be adopted w h i l e d e s i g n i n g w i t h t h e s e p r o m i s i n g m a t e r i a l s . Research i s a l s o recommended t o determine the optimum f i b r e geometry, optimum f i b r e volume, and so on, f o r maximum e f f i c i e n c y under v a r i a b l e s t r e s s r a t e s . BIBLIOGRAPHY 1. M a i n s t o n e , R.J. and K a v y r c h i n e , M.; Part-1, Introduction, M a t e r i a l s and S t r u c t u r e s , V o l . 8, No. 44, 1975, pp. 79-80. 2. S t r u c k , W. and V o g g e n r e i t e r , W.; Eamples of Impact and Impulsive Loading in the Field of Civil Engineering, M a t e r i a l s and S t r u c t u r e s , V o l . 8, No.44, 1975, pp. 81-87. 3. K a v y r c h i n e , M. and S t r u c k , W.; Practical Application to Testing, Design and Res ear ch, M a t e r i a l s and S t r u c t u r e s , V o l . 8 , No.44, 1975. 4. S l i t e r , G.E.; Assessment of Empirical Concrete Impact Formulae, ASCE ( S t r u c t u r a l D i v i s i o n ) , May 1980, pp. 1023-1045. 5. H i b b e r t , A.P and Hannant, D.J.; Toughness of Fibre Cement Compost tes, 'COMPOSITES' V o l . 13, No. 2, A p r i l 1982, pp. 105-111 . 6. S u a r i s , W. and Shah, S.P.;,Strai n Rate Effects in Fibre Reinforced Concrete Subjected to Impact and Impulsive Loading, 'COMPOSITES' V o l . 13, No. 2, A p r i l 1982, pp. 153-159. 7. H i b b e r t , A.P.; Impact Resistance of Fibre Concrete, Ph.D. T h e s i s , U n i v e r s i t y of S u r r e y , S u r r e y , England 1979. 8. C o t t e r e l l , B.; Fracture Toughness and the Charpy V Notch Impact Tests, B r i t i s h W e l d i n g J o u r n a l , V o l . 9, No. 2, Feb 1962, pp. 83-90. 9. Fearnehough, G.D. and J o y , C.J.; J o u r n a l of I r o n and S t e e l I n s t i t u t e , V o l . 202, Nov. 1964, pp. 912. 10. Radon, J.C. and Tu r n e r , C.E.; Fracture Toughness Testing by Instrumented Impact Tests, J o u r n a l of E n g i n e e r i n g F r a c t u r e M e c h a n i c s , V o l . 1, No. 3, A p r i l 1969, pp. 411-428. 11. Turner C.E.; Measurement of Fracture Toughness by Instrumented Impact Test Impact T e s t i n g of M e t a l s , ASTM STP466 , American S o c i e t y f o r T e s t i n g and M a t e r i a l s , 1970, pp. 93-114. 12. V e n z i , S., P r i e s t , A.H. and May, M.J.; Influence of Inertial Load in Instrumented Impact Tests, Impact T e s t i n g of M e t a l s , ASTM STP466 American S o c i e t y f o r T e s t i n g and M a t e r i a l s , 1970, pp. 165-180. 13. S a x t o n , H.J., I r e l a n d , D.R. and, S e r v e r , W.L.; Analysis and Control of Inertial Effects During Instrumented Impact Testing, I n s t r u m e n t e d Impact T e s t i n g , ASTM STP563, American 308 309 S o c i e t y f o r T e s t i n g and M a t e r i a l s , 1974, pp. 50-73. 14. S e r v e r , W.L.; Impact Three Point Bend Testing for Notched and Precracked Specimens, J o u r n a l of T e s t i n g and E v a l u a t i o n , JTEVA, V o l . 6, No. 1, J a n . 1978, pp. 29-34. 15. Gopalaratnam, V.S., Shah, S.P. and John, R e j i ; A Modified Instrumented Charpy Test for Cement Based Composites, E x p e r i m e n t a l M e c h a n i c s , V o l . 24, No. 2, 1984, pp.102-111. 16. S u a r i s , W. and Shah, S.P.; Inertial Effects in Instrumented Impact Testing of Cementitious Composites, ASTM J o u r n a l of Cement C o n c r e t e and Aggr e g a t e , March 1982, pp. 78-83. 17. Abe, H., Chandan, H.C. and B r a d t , R.C.; Low Blow Charpy Impact of Silicon Carbides, B u l l e t i n of the American Ceramic S o c i e t y , V o l . 57, No. 6, 1978, pp.587- 595. 18. L u e t h , R.C.; An Analysis of Charpy Impact Testing as Applied to Cement ed Carbide, I n s t r u m e n t e d Impact T e s t i n g , ASTM STP 563, American S o c i e t y f o r T e s t i n g and M a t e r i a l s , 1974, pp. 166-179. 19. I y e r , K.R. and M i c l o t , R.B.; Inst r ument ed Charpy Testing for Determination of the J-Integral, I n s t r u m e n t e d Impact T e s t i n g , ASTM STP 563, American S o c i e t y f o r T e s t i n g and M a t e r i a l s , 1974, pp. 146-165. 20. Abrams, D.A.; Effect of Rat e of Application of Load on the Compressive Strength of concrete, P r o c e e d i n g s , ASTM 17, p a r t 2, 1917, pp. 364-367. 21. W a t s t e i n , D.; Effect of Straining Rate on the Compressive Strength and Elastic Properties of Concrete, J o u r n a l of the American C o n c r e t e I n s t i t u t e , V o l . 49, No. 8, A p r i l 1953, pp. 729-756. 22. Green, H.; Impact Strength of Concrete, P r o c e e d i n g s of the I n s t i t u t i o n of C i v i l E n g i n e e r s , V o l . 28, 1964, pp. 383-396. 23. Macneely, D.J. and La s h , S.D.; Tensile Strength of Concrete, J o u r n a l of the American C o n c r e t e I n s t i t u t e , V o l . 60, No. 6, 1963, pp. 751-760. 24. A t c h l y , B.L. and F u r r , H.L.; Strength and Energy Absorption Capacity of Plain Concrete Under Dynamic and Static Loading, J o u r n a l of the American C o n c r e t e I n s t i t u t e , Nov. 1967, pp. 745-756. 25. G o l d s m i t h , W., Kenner, V.H. and R i c k e t t s , T.E.; Dynamic Loading of Several Concrete Like Mixtures, P r o c e e d i n g s 310 of the American S o c i e t y of C i v i l E n g i n e e r s , S t r u c t u r a l D i v i s i o n , J u l y 1968 pp. 1803-1827. 26. B i r k i m e r , D.L. and Lindeman, R.',Dynamic Tensile Strength of concrete Materials, J o u r n a l of the American C o n c r e t e I n s t i t u t e , 68(1971), pp. 47-49. 27. Hughes, B.P. and Gre g o r y , R.; Concrete Subjected to High Rates of Loading in Compression, Magazine of C o n c r e t e R e s e a r c h , V o l . 24, No. 78, March 1972, pp. 25-36. 28. S p a r k s , P.R. and M e n z i e s , J.B.; The Effect of Rate of Loading Upon the Static and Fatigue Strength of Plain Concrete in Compression, Magazine of Co n c r e t e R e s e a r c h , V o l . 25, No. 83, June 1973, pp. 73-80. 29. Hughes, B.P. and Watson, A . J . ; Compressive Strength and Ultimate Strain of Concrete Under Impact Loading, Magazine of c o n c r e t e R e s e a r c h , V o l . 30, No. 105, Dec 1978, pp. 189-199. 30. M i n d e s s , S.; Rate of loading effects on the fracture of cementitious materials, i n P r o c e e d i n g s of NATO advanced r e s e a r c h workshop on A p p l i c a t i o n of F r a c t u r e Mechanics t o C e m e n t i t i o u s Composites, N o r t h w e s t e r n U n i v e r s i t y , E v a n s t o n , I l l i n o i s , USA, Sept.4-7, 1984, S.P.Shah; E d i t o r . 31. Mindess, S. and Nadeau, J.S.; Effect of Loading Rate on the Flexural Strength of Mortar, J o u r n a l of the American Ceramic S o c i e t y , V o l . 56, No. 44, A p r i l 1977, pp 429-430. 32. Zech, B. and Wittmann, F.H.; Variability and Mean Value of Strength as a Function of Load, J o u r n a l of the American C o n c r e t e I n s t i t u t e , V o l . 77, No. 5, Sept-Oct. 1980, pp. 358-362. 33. M i h a s h i , H. and I z u m i , M a s a n o r i ; A Stochastic Theory for Concrete Fracture, Cement and Co n c r e t e R e s e a r c h , V o l . 7, No. 4, J u l y 1977, pp. 411-421. 34. S u a r i s , W. and Shah, S.P.; Properties of Concrete Subjected to Impact, ASCE S t r u c t u r a l D i v i s i o n , V o l . 109, No. 7, J u l y 1983, pp. 1727-1741. 35. Z i e l i n s k y , A . J . and R e i n h a r d t , H.W.; Stress Strain Behaviour of Concrete and Mortar at High Rates of Tensile Loading, Cement and Co n c r e t e R e s e a r c h , V o l . 12, No. 3, March 1982, pp. 309-319. 36. Z i e l i n s k i , A . J . ; Model for Tensile Fracture of Concrete at High Rates of Loading, Cement and Co n c r e t e R e s e a r c h , 14 (1984), pp. 215-224. 311 37. A l f o r d , N. McN.; Dynamic Consideration for Fracture in Mortars, J o u r n a l of M a t e r i a l S c i e n c e , 56, No. 3, Dec 1982, pp. 279-287. 38. Shah, S.P. and Rangan, B.V.; Fibre Reinforced Concrete Properties, J o u r n a l of the American C o n c r e t e I n s t i t u t e , V o l . 68, No. 2, Feb. 1971, pp. 126-134. 39. Naaman, A.E. and Shah, S.P.; Pull Out Mechanisms in Steel Fibre Reinforced Concrete, ASCE ( S t r u c t u r a l D i v i s i o n ) , V o l . 102, No.ST-8, August 1976, pp. 1537-1558. 40. K o b a y a s h i , K. and Cho, R.; Flexural Behaviour of Polyethylene Fibre Reinforced Concrete I n t e r n a t i o n a l J o u r n a l of Cement composites and L i g h t Weight C o n c r e t e , V O L 3 , No.1, Feb. 1981, pp.19-25. 41. Bhargava, A. and Rehnstrom, A.; Dynamic Strength of Polymer Modi fi ed and Fibre Reinforced Concrete, Cement and C o n c r e t e Research, V o l . 7, 1977, pp. 199-207. 42. Ramakrishnan, V., Brandshaug, I . , C o y l e , W.V. and S c h r a d e r , E.K.; A Comparative Evaluation of Concrete Reinforced with Straight Steel Fibres with Deformed Ends Glued Together in Bundles, P r o c e e d i n g s of the American C o n c r e t e I n s t i t u t e , V o l . 77, No. 3, May-June 1980, pp. 135-143. 43. Jamrozy, Z. and Swamy, R.N.; Use of Steel Fibre Reinforcement for Impact Resistance and Machinery Foundation, I n t e r n a t i o n a l J o u r n a l of Cement Composites and L i g h t Weight C o n c r e t e , V o l . 1, No. 2, J u l y 1979, pp. 65-76. 44. Radomsky, W.; Application of the Rotating Impact Machine for Testing Fibre Reinforced Concrete, I n t e r n a t i o n a l J o u r n a l of Cement Composites and L i g h t Weight C o n c r e t e , V o l . 3, No. 1, Feb. 1981, pp. 3-12. 45. H i b b e r t , A.P. and Hannant, D.J.; Impact Resistance of Fibre Concrete, Report s u b m i t t e d t o the T r a n s p o r t and Road R e s e a r c h L a b o r a t o r y , 1981. 46. Gokoz, U. and Naaman, A.E.; Effect of Strain Rate on the Pull Out Behaviour of Fibres in Mortar, I n t e r n a t i o n a l J o u r n a l of Cement Composites and L i g h t Weight C o n c r e t e , V o l . 3, No. 3, Aug. 1981, pp. 187-202. 47. Knab, L . I . and C l i f t o n , J.R.jCumulat i ve Damage of Reinforced Concrete Subjected to Repeated Impact .Cement and C o n c r e t e Research, V o l . 12, pp. 359-370. 48. Naaman, A.E. and Gopalaratnam, V.S.; Impact Properties 3 1 2 of Steel Fibre Reinforced Concrete in Bending, I n t e r n a t i o n a l J o u r n a l of Cement Composites and L i g h t Weight C o n c r e t e , (5) 1983, pp. 225-233. 49. H a r r i s , B., V a r l o w , J . and E l l i s , C D . ; Fracture Behaviour of Fibre Rei nf or ced Concrete Cement and C o n c r e t e Research 2, (1972) pp. 447- 461. 50. ACI Committee 544; Measurement of Propert i es of Fibre reinforced Concrete, J o u r n a l of the American C o n c r e t e I n s t i t u t e , V o l . 7 5 , No.7, J u l y 1978, pp. 283-289. 51. Daves, R.M., A critical study of the Hopkinson Pressure bar, P h i l o s o p h i c a l T r a n s a c t i o n s , R o y a l S o c i e t y of London, S e r i e s A, V o l . 240, pp. 357-457. 52. D a v i e s , E.D.H. and Hunter, S . C ; The Dynamic Compression Testing of Solids by the Method of Split Hopkinson Pressure Bar, J o u r n a l of Mech. and P h y s i c s of S o l i d s , V o l . 11, No. 5, 1963, pp. 155-179. 53. B i r k i m e r , D.L., A possible Fracture Criterion for the Dynamic Tensile Strength of Rock, P r o c e e d i n g s of the 12th Symposium on Rock M e c h a n i c s , U n i v e r s i t y of M i s s o u r i , Nov. 1970, pp. 573-589. (53a) R e i n h a r d t , H.W.; Tensile Fracture of Concrete at High Rates of Loading, i n P r o c e e d i n g s of NATO advanced r e s e a r c h workshop on Application of Fracture Mechanics to Cementitious Composites, N o r t h w e s t e r n U n i v e r s i t y , E v a n s t o n , I l l i n o i s , U.S.A., Sept. 4-7, 1984, S.P.Shah, E d i t o r . 54. Bhargava, J . and Rehnstrom, A., Cement and Co n c r e t e R e s e a r c h , 5, 1975, pp. 239-248. 55. A l f o r d , N. McN., M a t e r i a l s S c i e n c e and E n g i n e e r i n g , 56, 3, 1982, pp. 279-287. 56. Shah, S.P. and John, R., i n V o l . I , P r e p r i n t s , I n t e r n a t i o n a l Conference on F r a c t u r e Mechanics of C o n c r e t e , Lausanne, 1985, pp. 373-385. 57. Takeda, J . , Tachikawa, H. and F u j i m o t o , K., i n P r o c e e d i n g s , RILEM-CEB-IABSE-IASS I n t e r a s s o c i a t i o n Symposium, C o n c r e t e S t r u c t u r e s under Impact and I m p u l s i v e L o a d i n g , , BAM, West B e r l i n , 1982, pp. 83-91. 58. Broek, D.; Elementary Engineering Fracture Mechanics, M a r t i n u s N i j h o f f P u b l i s h e r s , The N e t h e r l a n d s , (1982). 59. Park,R. and P a u l a y , T.; Advanced Rei nfor ced Concrete St ruct ur es, John W i l e y and Sons, 1983. 313 60. C l o u g h , R.W. and P e n z i e n , J . ; Dynamics of Structures, M c G r a w - H i l l Book. Company, I n c . , 1975. 61. H i g g i n s , D.D. and B a i l e y , J.E.; Fracture Measurement on Cement Paste, J o u r n a l of M a t e r i a l S c i e n c e , 11 (1976), pp. 1995-2003. 62. John, R. and Shah, S.P.; Fracture of Concrete Subjected to Impact Loading, Cement C o n c r e t e and Ag g r e g a t e s , CCAGDP, V o l . 8, No. 1, Summer 1986, pp. 24-32. 63. Yam, A.S.T. and Mindess, S.; The Effect of Fibre Reinforcement on Crack Propagation in Concrete, I n t e r n a t i o n a l J o u r n a l of Cement Composites and L i g h t Weight C o n c r e t e , 4(1982), pp.83-93. 64. Panda, A.K.; Bond of Deformed Bars in Steel Fibre Reinforced Concrete under Cyclic Loading, Ph.D. T h e s i s , Department of C i v i l E n g i n e e r i n g , The U n i v e r s i t y of B r i t i s h C olumbia, A p r i l , 1984. 65. ACI Committee 439, Effect of Steel Strength and of Reinforcement Ratio on the Mode of Failure and Strain Energy Capacity of Reinforced Concrete Beams, ACI J o u r n a l , No. 3, V o l . 66, March 1969, pp. 165-173. 66. Lubahn,J.D. and F e l g a r , R.P. ;Pl 'as t ic i ty and Creep of Metals, John W i l e y and Sons, NewYork, 1961. 

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