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Effect of rate of shearing strain on the shear strength of freshly mixed concrete Purushotham, Salla Kanniah 1967

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THE EFFECT OF RATE OF SHEARING STRAIN ON THE SHEAR STRENGTH OF FRESHLY MIXED CONCRETE by SALLA KANNIAH PURUSHOTHAM B.E. ( C i v i l Engineering), Annamalai University, Madras, India, 1962 A THESIS SUBMITTED IN. PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of C i v i l Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h,i;s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f C i v i l Engineering The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada i i ABSTRACT This thesis describes attempts to measure the shearing strength of freshly mixed concrete and relate i t to standard "Work-a b i l i t y " t e s t s . The study i s a continuation of investigations made by Mr. L i Yang i n 1963-65 at the University of B r i t i s h Columbia. Yang measured the shearing strength of eight mixes at one ve l o c i t y and obtained a type of " v i s c o s i t y " at that speed. This thesis broadens the investigation to shear strength of eight different mixes at seven diff e r e n t speeds. The shear box developed at the University of B r i t i s h Columbia and used by Mr. Yang was used i n these further investigations and the shapes of the shear vs. rate of shearing s t r a i n or " v i s c o s i t y " curves for eight different mixes was p a r t i a l l y developed. i i i TABLE OF CONTENTS CHAPTER PAGE INTRODUCTION 1 I SHEAR STRENGTH AND RHEOLOGICAL PROPERTIES OF FRESH CONCRETE 7 II HOW THE PROBLEM WAS APPROACHED 10 II I DESCRIPTION OF THE APPARATUS 12 IV CALIBRATION OF APPARATUS AND SCOPE OF 14 EXPERIMENTAL WORK TO BE UNDERTAKEN V DESCRIPTION OF THE FINAL EXPERIMENTAL 16 WORK AND THE DATA OBTAINED VI CALCULATIONS 18 VII RESULTS 22 VIII DISCUSSION OF RESULTS 23 IX CONCLUSIONS 26 X RECOMMENDATION FOR FURTHER RESEARCH 27 TABLES 28 FIGURES . 49 BIBLIOGRAPHY i v ACKNOWLEDGEMENTS The author wishes to express his appreciation to his supervisor, Professor W. G. Heslop, for his in t e r e s t , guidance and advice on this experiment. The author i s grateful to Professor N. D. Nathan, for his review of the manuscript and for his valuable suggestions. The author also expresses his thanks to the s t a f f of the c i v i l engineering workshop for t h e i r assistance throughout the experiment. September, 1967 Vancouver, B r i t i s h Columbia. 1 INTRODUCTION Concrete has to be strong enough to withstand the stresses to which i t i s subjected and durable enough to withstand the moisture and temperature changes of i t s environment. To meet these requirements the quality and i n some cases the quantity of the ingredients has to be carefully specified along with a minimum strength requirement for standard sample cylinders formed, cured and tested i n a standard manner. The strength properties of a given concrete mix can vary widely with the actual density that i s achieved i n the forms. I t i s therefore customary to include i n the specifications a standard for "consistency" or ''workability" which w i l l enable the concrete to be compacted or consolidated i n the forms to a density which w i l l produce the desired strength properties. I t i s v i t a l that the "consistency" or "workability" be such that the concrete can be transported, placed, consolidated and finished economically and without segregation. A concrete that can be transported, placed, consolidated and finished s a t i s f a c t o r i l y i s said to be "workable", but to say merely that "workability" determines the ease of placing and the resistance to segregation i s too loose a description of this v i t a l property of concrete. Also, the desired "workability" depends on the means of compaction available, the s i z e and shape of the form and the amount of reinforcing s t e e l . For these reasons "workability" should be defined as a physical property of concrete alone without reference to the circumstances of a par t i c u l a r type of construction. 2 T o o b t a i n a s a t i s f a c t o r y d e f i n i t i o n i t i s n e c e s s a r y t o c o n s i d e r w h a t h a p p e n s w h e n c o n c r e t e i s c o m p a c t e d . W h e t h e r c o m p a c t i o n i s a c h i e v e d b y t a m p i n g o r v i b r a t i o n , t h e p r o c e s s c o n s i s t s e s s e n t i a l l y o f e l i m i n a t i o n o f e n t r a p p e d a i r f r o m t h e c o n c r e t e u n t i l i t h a s a c h i e v e d a s c l o s e a c o n f i g u r a t i o n a s i s p o s s i b l e f o r a g i v e n m i x . T h e w o r k d o n e i s u s e d t o o v e r c o m e i n t e r n a l f r i c t i o n b e t w e e n i n d i v i d u a l p a r t i c l e s a n d s u r f a c e f r i c t i o n w i t h t h e s u r f a c e s o f t h e f o r m a n d r e i n f o r c e m e n t . T h e s e t w o c a n b e c a l l e d i n t e r n a l f r i c t i o n a n d s u r f a c e f r i c t i o n r e s p e c t i v e l y . I n a d d i t i o n , s o m e o f t h e w o r k d o n e i s u s e d i n v i b r a t i n g t h e f o r m a n d p a r t s o f t h e c o n c r e t e w h i c h h a v e a l r e a d y b e e n f u l l y c o n s o l i d a t e d . T h u s t h e w o r k d o n e c o n s i s t s o f a " w a s t e d " p a r t a n d " u s e f u l " w o r k d o n e t o o v e r c o m e i n t e r n a l a n d s u r f a c e f r i c t i o n . G l a n v i l l e , C o l l i n s & M a t h e w s o f t h e R o a d R e s e a r c h L a b o r a t o r y h a v e d e f i n e d " w o r k a b i l i t y " a s , t h e a m o u n t o f u s e f u l i n t e r n a l w o r k n e c e s s a r y t o p r o d u c e  f u l l c o m p a c t i o n . T h e o t h e r t e r m u s e d t o d e s c r i b e t h e s t a t e o f f r e s h c o n c r e t e , " c o n s i s t e n c y " i s o f t e n t a k e n t o m e a n t h e d e g r e e o f w e t n e s s ; w i t h i n l i m i t s w e t c o n c r e t e s a r e m o r e w o r k a b l e t h a n d r y c o n c r e t e s , b u t c o n c r e t e s o f t h e s a m e c o n s i s t e n c y m a y v a r y i n w o r k a b i l i t y . T o a v o i d c o n f u s i o n t h e t e r m " w o r k a b i l i t y " a s d e f i n e d a b o v e w i l l b e u s e d t h r o u g h o u t t h i s t h e s i s . S T A N D A R D T E S T S T h e d e s i r e d w o r k a b i l i t y o f c o n c r e t e c a n a t p r e s e n t b e s p e c i f i e d o r c o n t r o l l e d b y a n u m b e r o f s t a n d a r d t e s t s . 3 a. The Slump Test This test i s used extensively on s i t e work a l l over the world. I t measures the "slump" of a 12 inch high frustum of a cone of concrete when the mould i n which i t was f u l l y consolidated i s removed. The force acting on the concrete i s that due to gravity and the amount of slump depends on the a b i l i t y of this force to do work against the in t e r n a l f r i c t i o n of the concrete. S t i f f mixes have zero slump, so that i n the rather dry range differences i n workability cannot be detected. In the 1 inch to 5 inch slump range differences i n workability are quite apparent though some authorities claim the slump test i s super sensitive to s l i g h t changes i n water content. At very high slumps there i s considerable horizontal movement of the mass though the force i s v e r t i c a l and the results obtained are not very satisfactory. The slump test i s not very reproducible and varies a great deal with who does i t and how the concrete i s placed and compacted i n the cone. b. The K e l l y B a l l Test The Kelly B a l l i s made of s t e e l , i s 6 inch i n diameter and weighs 30 lbs. The amount i t settles into the wet concrete when multiplied by two approximates the "slump". I t i s useful on the s i t e and can be used i n a concrete buggy or i n forms. I t i s not satisfactory for very dry or very wet concrete, but i s sensitive to about the same range of workability as the slump test. I t can be 4 used with larger sized aggregate. The force on the concrete i s the v e r t i c a l force due to gravity but for settlement into the concrete mass some horizontal movement has to take place. c. The Flow Test The Flow Test i s made by jogging a specified p i l e of concrete formed i n a low 10 inch diameter truncated cone mould on a metal flow table which i s raised and dropped 1/2 inch 15 times. The flow percentage i s the spread of the p i l e expressed as a percentage of the o r i g i n a l diameter. For small maximum size of aggregate i t i s considered to be more accurate than slump for some ranges of workability and i s used mostly i n the laboratory. Again i t i s unsatisfactory f o r very dry or very wet mixes and results vary considerably with the operator's s k i l l i n compacting the concrete In the mould. Almost a l l movement of the concrete i s horizontal though the force done by gravity and the "drops" i s v e r t i c a l . d. Power's Remolding Test Power's Renolding Test measures the amount of work ( i n 1/4 inch v e r t i c a l drops) i n addition to gravity required to change the shape of a mass of concrete from that of the standard slump cone to that of a 12 inch diameter c y l i n d r i c a l container. I t i s not widely used even i n laboratories though i t gives quite good results for a l l but very dry mixes. I t s p r i n c i p l e of measuring the amount of work necessary to change from one shape to another appears to be a reasonable approach to measuring workability. I t can not be 5 u s e d w i t h l a r g e a g g r e g a t e a n d i t s u f f e r s f r o m t h e s a m e w e a k n e s s a s t h e s l u m p a n d f l o w t e s t s r e g a r d i n g t h e n o n - u n i f o r m i t y o f c o m p a c t i o n a c h i e v e d i n t h e s l u m p c o n e . e . T h e V e b e T e s t T h e V e b e T e s t i s a l m o s t i d e n t i c a l t o P o w e r ' s R e m o l d i n g T e s t b u t t h e w o r k i s s u p p l i e d b y a v i b r a t i n g t a b l e a n d t h e t i m e f o r t h e c h a n g e o f s h a p e t o t a k e p l a c e i s m e a s u r e d i n s e c o n d s . T h e " i n n e r r i n g " u s e d i n P o w e r ' s a p p a r a t u s i s a l s o o m i t t e d . W i t h t h e V e b e a p p a r a t u s t h e p o s s i b i l i t y e x i s t s t h a t d i f f e r e n t a g g r e g a t e s i z e s w i t h d i f f e r e n t n a t u r a l f r e q u e n c i e s m a y r e s p o n d t o t h e v i b r a t i o n i n d i f f e r e n t w a y s . T h e a p p a r a t u s w o r k s s a t i s f a c t o r i l y w i t h v e r y d r y a s w e l l a s o r d i n a r y m i x e s . f . T h e C o m p a c t i n g F a c t o r T e s t T h e C o m p a c t i n g F a c t o r a p p a r a t u s w a s d e v e l o p e d t o d e t e c t d i f f e r e n c e s i n w o r k a b i l i t y o f l o w a n d n o s l u m p c o n c r e t e s a n d a l s o t o r e m o v e t h e h u m a n e r r o r o f d i f f e r e n t d e g r e e s o f c o m p a c t i o n w h e n f i l l i n g a m o u l d . W i t h t h i s a p p a r a t u s t h e r e a r e t w o c o n i c a l h o p p e r s w i t h t r a p d o o r s a n d a s t a n d a r d 6 i n c h x 1 2 i n c h c y l i n d e r m o u l d . - C o n c r e t e i s l o a d e d i n t o t h e t o p h o p p e r a n d d r o p p e d a f i x e d d i s t a n c e i n t o t h e m i d d l e h o p p e r w i t h t h e a s s u m p t i o n t h a t i n t h i s p o s i t i o n t h e a m o u n t o f c o m p a c t i o n i s a l w a y s t h e s a m e . T h e c o n c r e t e i s t h e n a l l o w e d t o f a l l f r e e l y i n t o t h e 6 i n c h x 1 2 i n c h s t a n d a r d c y l i n d e r m o u l d w h i c h i t f i l l s t o o v e r f l o w i n g . T h e e x c e s s i s s t r u c k o f f a n d t h e c y l i n d e r w i t h c o n t e n t s w e i g h e d . 6' The net weight divided by that of a cylinder f u l l of the f u l l y compacted concrete i s known as the "compacting f a c t o r " . The compacting f a c t o r t e s t uses an inverse approach to workability; the degree of compaction achieved by a standard amount of work. I t gives good r e s u l t s with the "low slump" mixes which cannot be tested by many of the other methods that have been mentioned. I f w orkability i s rela t e d to the amount of us e f u l i n t e r n a l work necessary to produce f u l l compaction, then i t surely must vary with the i n t e r n a l strength of the concrete. In th i s thesis the assumption i s made that shear strength i s a measure of the i n t e r n a l strength of concrete and an attempt i s made to measure shear strength d i r e c t l y i n a shear box. I t can be argued also that the weakness and l i m i t a t i o n s of many of the standard tests are l a r g e l y due to the f a c t that they do not produce shearing stresses i n a very e f f i c i e n t manner. An attempt i s made to compare t h e i r r e s u l t s with a c t u a l shearing strength. A l i m i t e d study of shearing strength was c a r r i e d out by Mr. L i Yang. This thesis attempts to v a r i f y h i s work and also to see i f shearing strength i s effected by rate of shearing s t r a i n . 7 CHAPTER I SHEAR STRENGTH AND RHEOLOGICAL PROPERTIES OF FRESH CONCRETE The shearing strength of freshly mixed concrete i s probably, l i k e s o i l , made up of cohesion plus an angle of inte r n a l f r i c t i o n . The cohesive strength i s largely related to the layers of adhered water which coat and separate a l l surfaces of the solids contained i n the mix. The angle of i n t e r n a l f r i c t i o n comes into play usually when some s o l i d surfaces are i n contact and varies with surface roughness and shape of the s o l i d p a r t i c l e s . I t can also have an effect when surfaces not i n actual contact are separated by distances less than the magnitude of their surface roughness. In an i d e a l concrete mix the volume of water and cement (and f i l l e r ) must be s l i g h t l y greater than the voids between the aggregate so that each piece of aggregate can be suspended i n d i v i d u a l l y i n the cement paste. A concrete mix possessing and retaining the above characteristics during the transportation, placing and compacting operation i s said to be "stable". In the above d e f i n i t i o n of a stable concrete mix the requirement that the aggregate p a r t i c l e s of the mix s h a l l remain completely dispersed, independent of the degree of p l a s t i c deformation, implies that the shearing stresses due to gravitation must not exceed the y i e l d stress of the cement paste. Segregation leading to p a r t i c l e contact w i l l always be prevented during the p l a s t i c deformation of a stable mix. What has been said regarding the aggregate i n a stable mix also applies to cement clin k e r (and f i l l e r ) p a r t i c l e s i n the water 8 cement mixer c o n s t i t u t i n g the paste. I t too must be stable and f r e e of any segregation or bleeding. The r h e o l o g i c a l properties of the cement paste are effected by a. the water/cement r a t i o , b. the degree of hydration, c. the p a r t i c l e s i z e and s i z e d i s t r i b u t i o n of the cement c l i n k e r , d. the amount of f i l l e r m aterial (d ^ 0.15 m.m.) i t s p a r t i c l e shape and s i z e d i s t r i b u t i o n , e. the presence of e l e c t r o l y t e s , dispersing agents or other admixtures a f f e c t i n g the properties of the absorbed water l a y e r s , f . the temperature. In unstable mixes which bleed and segregate or are too dry or harsh, undoubtedly some s o l i d surfaces are i n contact or are so close that the angle of i n t e r n a l f r i c t i o n adds very considerably to the strength of the mix. Such materials have strength properties approaching s o l i d s i n the p l a s t i c range and probably should be studied as s o l i d s . However with stable mixes the strength properties depend l a r g e l y on cohesive or viscous forces i n the paste, and the rheology can be examined from the point of view that the mix i s a dense viscous l i q u i d . This i s the approach used i n t h i s t h e s i s . I f i t i s considered that the shearing strength of the mix i s dependent on the strength of the cement paste then i t i s apparent that i t w i l l vary with, 1. The p l a s t i c deformability of the cement paste and the r a t e of deformation, 9 2. The average paste layer thickness, 3. The shape of the aggregate p a r t i c l e s . Many of the factors affecting 1, have already been mentioned and i f we are dealing with viscous shearing forces they can be expected to vary with rate of deformation. Regarding 2, i f the layer thickness i s halved and the rate of lin e a r deformation i s kept constant the angular rate of shearing s t r a i n w i l l be doubled and the shearing stress w i l l be affected. Considering 3, i n a multilayer system the shearing s t r a i n i n a layer between two s o l i d p a r t i c l e s w i l l be reduced i f the p a r t i c l e s tend to rotate. Their resistance to rotation depends not only on the resistance of the surrounding paste, but also the size and shape of the pa r t i c l e s and space between them. 10 CHAPTER II HOW THE PROBLEM WAS APPROACHED The work required to deform a l i q u i d depends on the viscous shearing stress and the rate of shearing s t r a i n . In the c l a s s i c a l development of the theory by Newton, a plate of area A sq. f t . moves p a r a l l e l to a fixed boundary at a distance h ( f t ) . from i t . A force of P l b s . gives the plate a fixed v e l o c i t y V f t / s e c . and viscous shearing forces are developed between the layers of l i q u i d lying between the moving plate and fixed boundary (see Fig. 1). The unit viscous shearing stress T = P/A l b s . / s q . f t . i s a function of the rate of shearing s t r a i n X . For most pure li q u i d s X varies d i r e c t l y h with V and we have T = u V. where/<. i s a c o - e f f i c i e n t of v i s c o s i t y . h h ft i s defined as the dynamic or obsolute v i s c o s i t y and can be calculated from fj. - P/A = Ph lbs.sec./sq.ft. This i s Newton's c l a s s i c theory V/h VA of v i s c o s i t y and l i q u i d s for which fx i s a constant are known as Newtonian l i q u i d s . From the previous research work done at U.B.C. an apparatus was available which deforms a block of concrete i n a manner sim i l a r to the block of l i q u i d l y i n g between the plate and the boundary. The important difference between the deformation of the cube of l i q u i d and the cube of concrete i s , as shown i n Fig. 1, i n how the forces are applied. In the case of the l i q u i d the external force i s applied at the top through the plate and i s t r u l y horizontal and the internal forces are a l l .horizontal viscous shearing forces. In the case of 11 concrete the force i s applied by one end of the box, the d i s t r i b u t i o n of the force i s not known and the forces exerted on the concrete have small v e r t i c a l components. The int e r n a l forces are therefore not a l l horizontal viscous shearing forces. Although the force d i s t r i b u t i o n applied to the concrete i s not known the work required to cause the deformation i s easy to calculate from (Work) + F' V* ( A t ) c c c In Newton's equation for l i q u i d s the work done i s (Work) = PV(^t) and p = (Work) V (A t ) F ' i o The shearing stress r c = -—- (r^j c where F c' i s the force measured on the d i a l gauge. The v i s c o s i t y of a l i q u i d i s therefore calculated from the formula: /U = (Work) h V (At) AV and a s i m i l a r quantity for the concrete can be calculated from the formula = (Work) ch e ^ c V c ( A t ) A CV C 12 CHAPTER I I I DESCRIPTION OF THE APPARATUS The apparatus used i s shown i n F i g . 2 and Fig. 3. The bottom and ends of the box are made of plywood and the sides are 2" x l " brass which were pinned i n d i v i d u a l l y with small clearance between 8 s t r i p s , and t e f l o n washers were placed on the pinned connections. A very small displacement of the box was used to keep the v e r t i c a l move-ment of the sides to a minimum. The box was lined with two layers of t e f l o n and the concrete i t s e l f enclosed i n rubber sheeting to bridge the space between the side s t r i p s and prevent leakage of concrete. The drive was from a reversible constant speed motor through a reducing gear box and a chain drive to a rotating nut on a long threaded drive rod. The drive rod was thus moved back and forth at a constant speed. The v e l o c i t y of the top of the box i t s e l f could be changed by moving the whole drive mechanism to different v e r t i c a l positions and varying the linkage to the box i t s e l f . The f i n a l linkage to the box was a proving ring with a d i a l gauge reading to 0.0001 inches i n s t a l l e d i n i t which always remained horizontal. The apparatus was used for a l l the seven speeds. For the fastest speed, the sprocket wheel attached to the drive rod was exchanged for one with a much smaller diameter, so that the force to deform the concrete was measured at a much higher speed. Di a l gauge readings were taken only when the box was passing through the dead center position and the force exerted by the end of 13 the box on the concrete had no v e r t i c a l component. I t was assumed that at that instant the proving r i n g was measuring the shearing strength of the concrete over the h o r i z o n t a l area of the box. CHAPTER IV 14 CALIBRATION OF APPARATUS AND SCOPE OF EXPERIMENTAL WORK TO BE UNDERTAKEN Since the ultimate aim was to find the forces involved i n the deformation of the concrete the d i a l gauge reading pounds force relationship had to be found and the tare force of the box accurately established. To do this the box was f i l l e d to a depth of 8 inches with balloons f u l l of water and d i a l gauge readings taken at a l l speeds under two different conditions; once with a head of water on the balloons s u f f i c i e n t to produce a pressure on the sides of the box equal to tha,t produced by the concrete and once with a weight on top of the balloons to produce a t o t a l weight equal to that of a box f u l l of concrete. Fortunately the "tare" readings by both methods were almost i d e n t i c a l and these d i a l gauge readings were l a t e r subtracted from those obtained with concrete i n order to ar r i v e at the shearing strength of the concrete i t s e l f . The proving r i n g was calibrated i n both tension and com-pression by loading i t with dead weights and noting the d i a l gauge readings. The scope of the present investigation then became studying the shear strength of eight batches of freshly mixed concrete and com-paring i t with the following standard workability or consistency tests: 1) The standard slump t e s t , 2) The standard flow t e s t , 15 3) Power's remolding apparatus, 4) Compacting factor apparatus. Only one starting position and a f u l l box of concrete was to be used, but tests would be run at seven different v e l o c i t i e s . C H A P T E R V 1 6 D E S C R I P T I O N O F T H E F I N A L E X P E R I M E N T A L W O R K A N D T H E D A T A O B T A I N E D C o n c r e t e M i x D e s i g n E i g h t d i f f e r e n t c o n c r e t e m i x e s w e r e d e s i g n e d t o g i v e s l u m p s f r o m 0 t o 8 i n c h e s . T h e A . C . I , m i x d e s i g n m e t h o d w a s u s e d a n d t h e w a t e r c e m e n t r a t i o w a s k e p t c o n s t a n t a t 0 . 6 . T y p e 1 . c e m e n t w a s u s e d a n d t h e c o m p l e t e m i x d e s i g n s a r e g i v e n i n T a b l e 1 . S u g a r a n d b e n t o n i t e w e r e a d d e d t o r e t a r d t h e s e t t i n g t i m e . T y p i c a l T e s t P r o c e d u r e A l l e i g h t t e s t s w e r e c a r r i e d o u t i n t h e c o n c r e t e l a b o r a t o r y i n t w o b a t c h e s m e a s u r e d i d e n t i c a l l y f o r e a c h m i x , a c c o r d i n g t o t h e f o l l o w i n g p r o c e d u r e . a ) M i x _1 c u b i c f e e t o f c o n c r e t e t h o r o u g h l y a c c o r d i n g t o t h e q u a n t i t i e s 2 l i s t e d i n T a b l e 1 . b ) M e a s u r e t h e t e m p e r a t u r e o f t h e c o n c r e t e m i x . c ) P e r f o r m t h e s t a n d a r d s l u m p t e s t a n d o b t a i n t h e s l u m p . d ) P e r f o r m t h e s t a n d a r d f l o w t e s t a n d o b t a i n t h e p e r c e n t a g e f l o w . e ) P e r f o r m P o w e r ' s r e m o u l d i n g t e s t a n d o b t a i n t h e r e m o u l d i n g e f f o r t . f ) F i l l t h e s h e a r d e f o r m a t i o n b o x f u l l o f c o n c r e t e a n d c a r r y o u t t e s t s a t s e v e n d i f f e r e n t v e l o c i t i e s , r e p e a t i n g e a c h t h r e e t i m e s . ( T h e b o x w a s s e t a t + 3 / 4 i n . f r o m c e n t r e b e f o r e s t a r t i n g ) . g ) R e n o v e t h e c o n c r e t e f r o m t h e b o x a n d o n c e m o r e p e r f o r m t h e P o w e r ' s t e s t t o s e e i f t h e c o n s i s t e n c y h a s c h a n g e d a p p r e c i a b l y . h ) M i x t h e o t h e r 1_ c u b i c f o o t o f t h e s a m e m i x a n d r e p e a t ( b ) t o ( g ) b u t 2 i n ( f ) d o t h e s e v e n s p e e d s i n r e v e r s e o r d e r . 17 The concrete was vibrated externally before each reading was taken i n the shear box te s t s . A previous complete set of readings was taken using hand rodding but the results produced such a wide scatter that they were of l i t t l e value. Another batch of the eight mixes was tested to f i n d the relationship between the compacting factor and Power's remold e f f o r t . The comparative results are shown i n Table 21. Data A t y p i c a l data sheet showing the d i a l gauge readings obtained for seven different speeds and two batches of mix are shown i n Table 5, which also shows reduction of the readings to l b s . force. The results of slump, flow, remolding tests and compacting factor are given i n Table 18. NOTE: A complete set of data was obtained using hand rodding to compact the concrete i n the shear box. The results however showed such a large scatter that they were discarded. They did agree i n general with the results obtained l a t e r using v i b r a t i o n . CHAPTER VI 18 CALCULATIONS An examination of the t e s t readings showed a s a t i s f a c t o r y r e l a t i o n s h i p between shear strength and changes i n rate of shearing s t r a i n f o r each mix, but a very s i g n i f i c a n t change i n workability while each mix was being tested. In s p i t e of the add i t i o n of bentonite and sugar as a retarder. the remolding tests showed that each mix s t i f f e n e d appreciably during the time i t was being tested. A c o r r e c t i o n f o r change of workability with time was therefore necessary and some adjustment of the F c values measured at the proving r i n g was a n t i c i p a t e d . Previous experimental work by Yang had shown a very good r e l a t i o n s h i p between F c and Power's remolding t e s t and an even better r e l a t i o n s h i p between F c and the " t o t a l work" i n inch pounds done i n the Power's apparatus inc l u d i n g not only the 1/4 i n drops but a l s o the work done by gr a v i t y and the e f f e c t of the 4.3 l b . r i d e r p l a t e . To e s t a b l i s h the change of workability with time four d i f f e r e n t mixes i d e n t i c a l to those used i n the shear box were tested i n the Power's apparatus every f i f t e e n minutes f o r a three hour period. The change i n drops and " t o t a l work" (done i n the Power's apparatus) with time appeared to be l i n e a r f o r a l l p r a c t i c a l purposes. Since the times since mixing had been recorded f o r each test i t was possible to c a l c u l a t e the workability i n terms of drops and " t o t a l work" i n Power's apparatus at the times each shear force measurement was taken. 19 The average forces 'F c' were taken from the batch 1 and batch 2 readings (Tables 2 & 3) and plotted against the t o t a l work done, which are shown i n Figs. 7 & 8. The methods of the "Theory of Least Squares" were used to f i t a curve to the observations. Neither a straight l i n e nor a log-log graph appeared sa t i s f a c t o r y , but a parabola was found to f i t quite w e l l . The parabola y = a + bx + cx 2 ...(1), was t r i e d ; The method of least squares then leads to the condition: a, b and c must s a t i s f y , Q = f [ y i " (a+bx-j+cxi 2)] 2 = min. ...(2) It i s impossible to obtain the minimum of "Q" by s a t i s f y i n g the equations: ^2. = 0 ; ^2. = 0 ; 1 2 = 0 ...(3) da db <3c and hence the notations are introduced: x i 2 = Z i 5 S l = S x i y i ; s 2 = l x i 2 ! T i = * x i Z i 5 T 2 =*Z±2 ; v1 = *y±Z± ; x = i * X i \ N y = i * y i ; Z = i * Z ± (i=l,2....8) and N = 8 then we can write, y^ = a+bx^ + CZ^ ...(4) From condition (3) i t i s easy to get the following equations for b, c & a : S 2b + TjC = Sj^ ; Tjb + T2C = V1 ; .... (5) and a = y - bx - CZ . where x = 711; 7 = 6.3 & Z = 624,000. 20 These are called "normal equations" and for our par t i c u l a r problem, these constants were solved and the new values were calculated. This procedure was followed for a l l the seven speeds. The new force values were plotted against the work done, and proved quite satisfactory. A sample calculation i s given below for speed 1. For the observations and other d e t a i l s see Table 8(a). Solving for constants a, b & c from equation (5) for the observed readings i . e . , "y^" values as given i n Table 8(a): a - 0.07; b = 0.0167 & C - -0.88 x 10 5 • .". y - 0.07 + 0.0167 x - 0.88x10 5 X 2 substituting the "Xj_" values, the corrected "y" values are obtained, as given i n Table 8(b). The corrected "y" values for speeds 2 to 7 are given i n Tables 9 to 14. The corrected F c values and the calculated values of shear stress &. absolute v i s c o s i t y are given i n Tables 15, 16 & 17. The calculations were made as follows: _ F c /-10.5x _ £c , . Shearing stress Zc = A^ v~g ' ~ 54 U . J i ; = 0.021 F c lbs/sq.in. = 2.95 F c l b s / s q . f t . Viscosity , = F c (lOsl) - F c U-31) 8 Ac C V f c ^ (64)V, c F c = 0.164 —- lbs.sec./sq.in F C = 23.6 —£. lbs.sec./sq.ft. V c 21 T h e c u r v e s p l o t t e d w e r e : a) The s h e a r i n g s t r e s s T a g a i n s t s h e a r i n g s t r a i n V / h , w h i c h i s shown i n F i g . 9 ; b) The s l u m p , f l o w p e r c e n t a g e , P o w e r ' s r e m o l d i n g e f f o r t and c o m p a c t i n g f a c t o r a g a i n s t s h e a r i n g s t r e s s Z~ and a b s o l u t e v i s c o s i t y , w h i c h a r e shown i n F i g u r e s 12 t o 1 9 . R e f e r r i n g t o a d i a g r a m o f t h e a p p a r a t u s i n F i g . 4 , i t i s s e e n t h a t work i s done by l i f t i n g and d r o p p i n g c o n c r e t e and t h e r i d e r p l a t e e a c h r e v o l u t i o n and a l s o by g r a v i t y i n l o w e r i n g t h e c e n t e r s o f g r a v i t y o f t h e c o n c r e t e and t h e r i d e r p l a t e . T o t a l work = (W c ) f + W c ( Y x - Y 2 ) + W R ( j + 8 . 8 - S) = (30.2) f + 3 0 . 2 ( 3 . 1 6 ) + 4 . 3 f + 4 . 3 (8 .8 ) - 4 . 3 S T o t a l work = 8 . 6 n + 133 - 4 . 3 S ( i n . l b s . ) where n = number o f i n . d r o p s and S = s lump ( i n . ) . T a b l e 20 shows t h e c a l c u l a t i o n s and t h e " t o t a l w o r k " done o n e a c h m i x d u r i n g P o w e r ' s r e m o l d i n g t e s t . 22 CHAPTER VII RESULTS The shearing strength was measured at seven different s t r a i n rates for eight different mixes and the results after adjustment for changes i n workability during the test are plotted i n Fig. 9. Evaluations of standard workability tests r e l a t i v e to shear strength appear on Figs. 12 to 15 and to " t o t a l work" i n Fig. 10. Similar results and comparisons r e l a t i v e to a calculated absolute v i s c o s i t y are given i n Fig. 11 and Figs. 16 to 19, but they give l i t t l e , i f any, additional information. Shear strength appears to be closely related to the t o t a l work necessary to remold a mass of concrete from the slump cone shape to that of a cylinder as performed i n Power's Remolding Test. The correlation i s so strong that i t was used to adjust some of the experimental readings. Therefore both shear strength and t o t a l work i n the remolding test appear to be good absolute measures of workability and suitable for the comparison of standard workability tests. CHAPTER VIII DISCUSSION OF RESULTS 23 Figure 9 r e a l l y contains most of the pertinent information gathered from the experimental work. The relationships between unit shearing stress and rate of shearing s t r a i n seems to be very d e f i n i t e at a l l seven degrees of workability. Fran the curves i t appears that a l l the mixes have the same basic properties but with r e l a t i v e l y different shear strengths for different degrees of work-a b i l i t y . Considerable experimental results were obtained for a mix with less than 1 inch slump, or with workability greater than 900 i n . l b s . , but the points were so close to the 1 inch slump curve that they were not plotted. This indicates that l i k e most other workability tests shear strength or t o t a l i n . l b s . of remolding e f f o r t are not accurate measures of workability for low slump concrete. Fig. 10 shows Power's Remolding Test, Slump and Flow plotted against workability (measured i n i n . l b s . of t o t a l work) and Figs. 12, 13, 14 & 15 show standard tests plotted against the shear strengths at four different speeds. In general i t appears that; a) slump i s most sensitive to changes i n workability and shear strength corresponding to 4 inch slump and loses s e n s i t i v i t y at both high and low slumps. b) Flow gave rather e r r a t i c values and was more accurate i n the d r i e r mixes. 2 4 c) Power's Remolding Test has less change i n slope than the other tests and i s therefore s e n s i t i v e over a wider range. I t i s more accurate f o r d r i e r mixes. b) The Compacting Factor Test i s good f o r dry mixes but has l i t t l e s e n s i t i v i t y f o r wet mixes. The curves i n F i g . 11 are an attempt to show changes i n " v i s c o s i t y " with changing rates of s t r a i n . V i s c o s i t y should be i n d i c a t e d by the r a t i o of ordinate to abscissa of fi g u r e 9, but c l e a r l y the m a t e r i a l did not behave as a Newtonian f l u i d . The assumption that the shear strength of f r e s h l y mixed concrete i s dependent on the shear strength of the cement paste appears to be , j u s t i f i e d . I f i t were otherwise, a decrease of shear strength with rate of s t r a i n would be d i f f i c u l t to explain unless i t was accompanied by an \ appreciable d i l a t i o n which was not observed. Regarding the decrease i n shear strength with rate of shearing s t r a i n two explanations are: a) There i s a change i n pore pressure, which a f f e c t s the shear strength. This would suggest some tendency to change i n volume i n a paste,which i s not free draining. b) The water cement paste has a f l o c c u l a t e d s t r u c t u r e and has t h i x o t r o p i c c h a r a c t e r i s t i c s . In such materials a bond develops between p a r t i c l e s which produces a " g e l " , the strength of which increases with time. With increased rate of shearing s t r a i n t h i s bond would have less time to develop. From the r e s u l t s of the i n v e s t i g a t i o n s described i n t h i s thesis i t i s not possible to conclude which of the above explanations i s v a l i d 25 and i t may w e l l be that both have an a f f e c t . I t i s the opinion of some author i t i e s however that a paste with a water cement r a t i o of 0.6 i s free draining which would favour the t h i x o t r o p i c explanation. whether or not the small amounts of sugar and bentonite i n the mixes contributed to the t h i x o t r o p i c behaviour w i l l have to await further study. 26 CHAPTER IX CONCLUSIONS The t r e a t i n g of fre s h l y mixed concrete as a l i q u i d and the p l o t of unit shearing stress against rate of shearing s t r a i n appears to give some pertinent information regarding i t s rheology. Due to i t s non-Newtonian c h a r a c t e r i s t i c s , however, any calculated value of v i s c o s i t y as an absolute quantity appears to have l i t t l e , i f any, value. The r e s u l t s of the experimental work described seem to indicate that the assumption that workability i s dependent on the shear strength of the paste i s v a l i d . Concrete i n the mixes used appears to have some t h i x o t r o p i c c h a r a c t e r i s t i c . 27 CHAPTER X RECOMMENDATION FOR FURTHER RESEARCH T h e s h e a r box a p p e a r s t o w o r k w e l l and some f u r t h e r i n v e s t i g a t i o n s o f s h e a r s t r e n g t h w i t h i t seem; w a r r a n t e d . a) S h e a r s t r e n g t h s a t d i f f e r e n t d e f o r m a t i o n a n g l e s o r d i f f e r e n t s t r a i n s . b) Shear s t r e n g t h s a t v e r y low s p e e d s o r v e r y low r a t e s o f s t r a i n . c) Changes i n s h e a r s t r e n g t h w i t h c h a n g e s i n g r a d i n g o f a g g r e g a t e . d) Measurement o f s h e a r s t r e n g t h w h i l e v i b r a t i n g a t d i f f e r e n t f r e q u e n c i e s . e) I n v e s t i g a t i o n o f w h e t h e r o r n o t t h e r e i s any d i l a t i o n o f c o n c r e t e w h i l e i t i s b e i n g s h e a r e d . f ) Measurement o f s h e a r s t r e n g t h w i t h d i f f e r e n t c o n f i n i n g p r e s s u r e s . g) Changes i n s h e a r s t r e n g t h w i t h v a r i o u s a d m i x t u r e s . h) I n v e s t i g a t i o n s o f s h e a r s t r e n g t h v s . t o t a l s t r a i n . i ) S h e a r s t r e n g t h s o f d r i e r m i x e s t h a n were u s e d i n t h e p r e s e n t s t u d y . CONCRETE MIX PROPORTION (1 CUBIC YARD) A.C.I. MIX DESIGN METHOD W/C i s Constant = 0.60 by Weight MIX # WATER (lbs) CEMENT (lbs) COARSE AGGREGATE (lbs) SAND (lbs) RETARDING AGENTS (lbs) TOTAL (lbs) 3 •zr in.-j i n . & Pea size gap 3" 8 F.S. C S . BENTONITE SUGAR 1 277.00 460.00 850.00 425.00 425.00 710.00 867.00 9.20 0.96 4024.16 2 280.50 468.00 850.00 425.00 425.00 696.00 855.00 9.30 0.96 4009.76 3 285.00 475.00 850.00 425.00 425.00 686.00 844.00 9.50 0.96 4000.46 4 292.00 486.00 850.00 425.00 425.00 665.00 820.00 9.80 0.96 3973.76 5 297.50 495.00 850.00 425.00 425.00 658.00 810.00 9.90 0.98 3971.38 6 302.00 504.00 850.00 425.00 425.00 654.00 801.00 10.10 1.01 3972.11 7 310.00 516.00 850.00 425.00 425.00 650.00 793.00 10.20 1.07 3980.27 8 317.00 528.00 850.00 425.00 425.00 642.00 785.00 10.40 1.10 3983.50 Specific gravities of cement, C.A. & F.A. are 3.15, 2.68 & 2.64 respectively TABLE 1 co MEASURED "F c" VALUES; 1st BATCH SPEED Force, F c lbs MIX #1 MIX #2 MIX #3 MIX #4 MIX #5 MIX #6 MIX #7 MIX #8 1 4.8 7.3 8.0 7.5 8.5 5.0 3.5 5.0 2 5.0 7.0 8.0 7.0 8.1 4.6 3.8 4.2 3 5.0 6.3 7.9 6.8 7.8 4.0 3.7 3.8 4 5.5 6.2 7.6 6.8 7.4 4.0 3.3 3.4 5 4.7 6.1 7.3 6.5 7.4 4.0 3.1 3.1 6 4.5 6.3 6.6 6.4 7.2 3.8 3.3 2.9 7 4.6 6.4 5.8 6.3 7.1 4.0 3.8 2.5 TABLE 2 MEASURED ' fF c" VALUES; 2nd BATCH SPEED Force, F c lbs MIX #1 MIX #2 MIX #3 MIX #4 MIX #5 MIX #6 MIX #7 MIX #8 1 6.8 6.4 7.7 6.5 7.7 7.0 4.5 4.6 2 6.4 6.3 8.7 7.2 7.2 5.8 4.3 4.2 3 6.8 6.6 8.8 7.3 7.1 6.1 4.1 4.0 4 6.6 6.5 8.8 7.1 6.8 5.8 4.2 4.0 5 6.3 6.5 8.6 6.3 6.8 6.1 4.0 3.6 6 6.3 6.3 8.8 6.3 6.3 6.1 3.9 3.5 7 6.4 6.2 8.5 5.5 6.4 6.6 4.4 3.8 TABLE 3 TARE FORCE, lbs .PEED STANDARD SPROCKET WHEEL SMALLER SPROCKET WHEEL WATER WEIGHT WATER WEIGHT 1/4" 1/2" 3/4" 1/4" 1/2" 3/4" 1/4" 1/2" 3/4" 1/4" 1/2" 3/4" 1 1.60 1.76 1.88 1.55 1.76 1.88 1.64 1.72 1.84 1.55 1.76 1.88 2 1.52 1.84 1.96 1.64 1.80 2.00 1.60 1.76 1.96 1.68 1.80 2.00 3 1.55 1.84 2.00 1.60 1.84 2.08 1.64 1.84 1.96 1.60 1.84 2.08 4 1.60 1.92 1.96 1.68 1.96 2.04 1.60 1.96 .2.00 1.64 1.92 2.04 5 1.55 1.88 2.04 1.76 1.92 2.00 1.55 1.84 2.04 1.68 1.92 2.04 6 1.68 2.04 2.08 1.76 1.92 2.12 1.68 1.96 2.04 1.76 2,00 2.08 7 1.72 2.04 2.12 1.68 2.04 2.12 1.68 2.04 2.12 1.68 2.08 2.08 TABLE 4 SAMPLE DATA SHEET 1st Batch 2nd Batch SPEED D i a l Gage i n . x l O " 3 Force lbs D i a l Gage i n . x l O " 3 Force lbs 1 11.90 4.80 16.90 6.80 2 12.40 5.00 15.70 6.40 3 12.40 5.00 17.00 6.80 4 13.40 5.50 16.30 6.60 5 11.70 4.70 15.70 6.30 6 11.20 4.50 15.50 6.30 7 11.30 4.60 15.90 6.40 TABLE 5 Batch 1 MIX # Remould Drops " n« order of expert ment End 7 6 5 4 3 2 1 Begin speed 1 2 3 4 5 6 7 1 191 175 166 156 146 137 128 114 100 2 142 133 127 122 116 111 106 98 90 3 86 80 76 72 69 ; 65 62 57 52 4 82 74 70 66 62 58 54 48 42 5 71 66 64 62 60 57 52 48 44 6 67 60 57 54 50 47 44 39 33 7 45 41 40 39 37 36 34 31 28 8 31 28 27 25 24 22 21 19 16 •UX # Tot a l Work, i n . l b s . speed 1 2 3 4 5 6 7 1 1630 1570 1480 1390 1310 1230 1110 2 1280 1220 1180 1130 1080 1030 970 3 810 770 730 710 670 645 600 4 750 720 680 645 610 580 530 5 680 660 645 630 600 560 520 6 630 600 580 540 510 480 440 7 460 450 440 420 410 400 380 8 350 340 320 310 290 280 270 TABLE 6 Batch 2 MIX # Remould Drops "n" Order of Experiment and Speed Begin 1 2 3 4 5 6 7 End 1 102 115 124 133 142 151 161 174 190 2 82 91 97 103 109 115 121 130 140 3 55 60 63 67 70 74 77 82 88 4 40 46 50 54 58 64 68 73 80 5 41 46 48 51 54 57 59 64 70 6 35 41 44 47 50 53 56 62 70 7 25 28 29 30 31 33 34 37 41 8 14 17 18 20 21 23 24 26 29 To t a l Work, i n . l b s . speed MIX # 1 2 3 4 5 6 7 1 1120 1190 1280 1350 1440 1520 '1630 2 900 960 1010 1060 1120 1170 1250 3 630 660 690 720 750 780 820 4 510 540 .. 580 610 660 700 740 5 510 520 550 580 600 620 660 6 460 480 510 540 570 600 640 7 350 360 370 380 390 400 420 8 250 260 280 290 300 310 330 TABLE 7 SPEED I 35 X ;. "In lb*" " lb*' Force Measured X* or z; Z.I yj -2<-No. Work done Average xl03 xl02 xl05 xl08 xl03 1 300 4.8 90 14.4 270 81 432 2 400 4.0 160 16.0 640 256 640 3 550 6.0 302 33.0 1660 915 1812 4 590 8.0 350 47.2 2060 1225 2800 5 640 7.0 410 44.8 2625 1680 2870 6 720 7.8 520 56.1 3750 2700 4060 7 1090 7.0 1210 76.3 13100 14400 8400 8 1400 5.8 1960 81.0 27400 38450 11380 TOTAI 5690 50.4 4992 368.8 51505 59707 32394 (a) So. XL "inXbs* Work done Hi "lb/ Force Measured Average a b.xi c. -x .1-b y " l b * " Force Corrected 1 300 4.8 0.07 5.10 -0.81 4.36 2 400 4.0 0.07 6.80 -1.44 5.43 3 550 6.0 0.07 9.35 -2.72 6.70 4 590 8.0 0.07 10.01 -3.15 6.93 5 640 7.0 0.07 10.90 -3.69 7.28 6 720 7.8 0.07 12.25 -4.67 7.65 7 1090 7.0 0.07 18.55 -10.80 7.82 8 1400 5.8 0.07 23.80 -17.65 6.22 (b) TABLE 8 SPEED 2 36 No. Work done Force Measured Average XlO 3 x: - v x l O 2 x l O 5 x l O 8 x l O 3 1 300 4.2 90 12.6 270 81 378 2 400 4.0 160 16.0 640 256 640 3 550 5.2 302 28.6 1660 915 1570 4 600 7.5 360 45.0 2160 1300 2700 5 640 7.1 410 45.5 2625 1680 2910 6 720 8.3 520 59.7 3750 2700 4320 7 1100 7.0 1210 77.0 13310 14600 8470 8 1390 5.7 1935 79.2 26900 37500 11020 TOTA 5700 49.0 4987 363.6 51315 59032 32008 (a) No. Work done Hi " lb*" Force Measured Average a c. • x.«. " \\>s" Force Corrected 1 300 4.2 -0.03 4.89 -0.78 4.08 2 400 4.0 -0.03 6.52 -1.40 5.09 3 550 5.2 -0.03 8.96 -2.64 6.29 4 600 7.5 -0.03 9.77 -3.15 6.59 5 640 7.1 -0.03 10.42 -3.59 6.80 6 720 8.3 -0.03 11.72 -4.55 7.14 7 1100 7.0 -0.03 17.90 -10.60 7.27 8 1390 5.7 -0.03 22.65 -16.91 5.71 (b) TABLE 9 SPEED 3 37 No. Work done Force Measured Average X-C~<rrXl x l O 3 x l O 2 x l O 5 x l O 5 x l O 3 1 300 3.9 90 11.7 270 81 351 2 400 3.9 160 15.6 640 256 624 3 550 5.1 302 28.0 1660 915 1540 4 600 7.4 360 44.4 2180 1300 2665 5 640 7.0 410 44.8 2625 1680 2870 6 720 8.3 520 59.7 3750 2700 4310 7 1100 6.4 1210 70.4 13310 14600 7745 8 1380 5.9 1910 81.4 26380 36500 11280 TOTAL 5690 47.9 4962 356.1 50815 58032 31385 (a) No. Work done 2; " \bs" Force Measured Average a b •'ti 2"[hs" Force Corrected 1 300 3.9 0.04 4.68 -0.75 3.97 2 400 3.9 0.04 6.25 -1.33 4.96 3 550 5.1 0.04 8.59 -2.52 6.11 4 600 7.4 0.04 9.35 -2.99 6.40 5 640 7.0 0.04 9.99 -3.40 6.63 6 720 8.3 0.04 11.20 -4.32 6.92 7 1100 6.4 0.04 17.15 -10.04 7.15 8 1380 5.9 0.04 21.55 -15.85 5.74 (b) TABLE 10 SPEED 4 38 No. Work done Force Measured Average x l O 3 x l O 2 x l O 5 x l O 8 x l O 3 1 300 3.7 90 11.1 270 81 333 2 400 3.8 160 15.2 640 256 608 3 560 4.9 314 27.4 1760 988 1540 4 600 7.1 360 42.6 2160 1300 2560 5 630 7.0 397 44.1 2500 1580 2780 6 720 8.2 520 59.1 3750 2700 4265 7 1090 6.3 1210 68.7 13100 14400 7560 8 1380 6.0 1910 82.8 26380 36500 11450 TOTAL 5680 47.0 4951 351.0 50560 57805 31096 (a) No. Work done Force Measured Average a 2. -0" tb»" Force Corrected 1 300 3.7 0.18 4.44 -0.68 3.94 2 400 3.8 0.18 5.91 -1.21 4.88 3 560 4.9 0.18 8.28 -2.38 6.08 4 600 7.1 0.18 8.88 -2.73 6.33 5 630 7.0 0.18 9.33 -3.01 6.50 6 720 8.2 0.18 10.65 -3.94 6.89 7 1090 6.3 0.18 16.12 -9.10 7.20 8 1380 6.0 0.18 20.40 -14.48: 6.10 (b) TABLE 11 SPEED 5 39 No. II I I X ' c in lb* Work done T> " l b s ' Force Measured Average xl03 xl02 xl05 xl08 x l O 3 1 300 3.3 90 9.9 270 81 297 2 400 3.5 160 14.0 640 256 560 3 540 5.0 292 27.0 1580 855 1460 4 600 7.0 360 42.0 2160 1300 2520 5 640 6.4 410 41.0 2625 1680 2625 6 720 7.8 520 56.2 3750 2700 4060 7 1100 6.3 1210 69.2 13310 14600 7620 8 1390 5.5 1935 76.5 26900 37500 10650 TOTAL 5690 44.8 4977 335.8 51,235 58972 29792 (a) No. Work done Force Measured Average a Force Corrected 1 300 3.3 -0.06 4.53 -0.74 3.74 2 400 3.5 -0.06 6.04 -1.31 4.67 3 540 5.0 -0.06 8.15 -2.39 5.70 4 600 7.0 -0.06 9.06 -2.94 6.06 5 640 6.4 -0.06 9.65 -3.34 6.25 6 720 7.8 -0.06 10.88 -4.25 6.57 7 1100 6.3 -0.06 16.60 -9.90 6.64 8 1390 5.5 -0.06 21.00 -15.80 5.14 (b) TABLE 12 SPEED- 6 40 No. Work done Hi " f t * " Force Measured Average * -» X I br*-t XlO 3 x l O 2 x l O 5 x l O 8 x l O 3 1 300 3.2 90; 9.6 270 81 288 2 400 3.7 160 14.8 640 256 592 3 550 5.0 302 27.5 1660 915 1510 4 590 6.8 349 40.1 2060 1225 2375 5 650 6.4 423 41.6 2750 1790 2710 6 720 7.7 520 55.5 3?50< 2700 4050 7 1100 6.3 1210 69.3 13310 14600 7620 8 1380 5.5 1910 75.9 26380 36500 10500 TOTAL 5690 44.6 4964 334.3 50820 58067 29645 (a) No. Work done "lbs" Force Measured Average a c- x i Force Corrected 1 300 3.2 0.02 4.44 -0.72 3.75 2 400 3.7 0.02 5.92 -1.27 4.67 3 550 5.0 0.02 8.14 -2.39 5.77 4 590 6.8 0.02 8.73 -2.72 6.03 5 650 6.4 0.02 9.62 -3.38 6.26 6 720 7.7 0.02 10.65 -4.13 6.54 7 1100 6.3 8.02 16.28 -9.60 6.70 8 1380 5.5 0.02 20.40 -15.15 5.27 (b) TABLE 13 SPEED 7 41 No. Work done *9i " lbs" Force Measured Average x l O 3 x l O 2 X C Zi x l O 5 z .i. L x l O 8 x l O 3 1 300 3.2 90 9.6 270 81 288 2 400 4.1 160 16.4 640 256 655 3 540 5.2 292 28.1 1580 855 1520 4 590 6.7 349 39.5 2060 1225 2340 5 610 7.0 374 42.7 2280 1400 2620 6 720 7.1 520 51.1 3750 2700 3690 7 1120 6.3 1260 70.5 14100 15900 7940 8 1400 5.5 1960 77.0 27400 38450 10780 TOTAL 5680 45.1 5005 334.9 52080 60867 29833 (a) No. 2-i " i n lb 5 Work done Force Measured Average ^ "lbs" Force Corrected 1 300 3.2 -0.01 4.41 -0.69 3.70 2 400 4.1 -0.01 5.88 -1.24 4.63 3 540 5.2 -0.01 7.94 -2.26 5.67 4 590 6.7 -0.01 8.67 -2.70 5.96 5 610 7.0 -0.01 8.96 -2.89 6.06 6 720 7.1 -0.01 10.60 -4.03 6.56 7 1120 6.3 -0.01 16.48 -9.75 6.72 1400 5.5 -0.01 20.60 -15.15 5.44 (b) TABLE 14 42 Consistency 300 i n lbs SPEED Fc 'lbs' CORRECTED Vc l b s / f t 2 SHEAR STRESS Mc l b s . s e c / f t 2 ABSOLUTE VISCOSITY 1 4.36 12.85 2,240 2 4.08 12.05 1,850 3 3.97 11.70 1,360 4 3.94 11.61 1,140 5 3.74 11.04 860 6 3.75 11.05 650 7 3.70 10.91 244 Consistency 400 i n l b s . 1 5.43 16.00 2,790 2 5.09 15.00 2,310 3 4.96 14.62 1,700 4 4.88 14.40 1,400 5 4.67 13.80 1,070 6 4.67 13.80 824 7 4.63 13.65 305 TABLE 15 43 Consistency 500 i n l b s . SPEED Fc 'lbs' CORRECTED tc l b s / f t 2 SHEAR STRESS A= l b s . s e c / f t 2 ABSOLUTE VISCOSITY 1 6.35 18.72 3,260 2 5.90 17.40 2,680 3 5.80 17.10 1,980 4 5.65 16.68 1,630 5 5.40 15.92 1,240 6 5.40 15.92 950 7 5.40 15.92 356 Consistency 600 i n l b s . 1 7.00 20.65 3,590 2 6.59 19.42 2,990 3 6.40 18.88 2,190 4 6.33 18.65 1,820 5 6.06 17.90 1,390 6 6.00 17.70 1,060 7 6.00 17.70 396 TABLE 16 44 Consistency 700 i n l b s . SPEED Fc ' l b s ' CORRECTED l b s / f t 2 SHEAR STRESS A * lbs.sec/ft2 ABSOLUTE VISCOSITY 1 7.55 22.25 3,880 2 7.20 21.21 3,260 3 6.85 20.20 2,340 4 6.80 20.00 1,960 5 6.50 19.20 1,490 6 6.50 19.20 1,140 7 6.40 18.90 420 Consistency 800 i n l b s . 1 7.8 23.00 4,000 2 7.4 21.85 3,360 3 7.1 20;98 2,430 4 7.1 20.98 2,040 5 6.8 20.00 1,560 6 6.8 20.00 1,200 7 6.8 20.00 448 Consistency 900 i n l b s . 1 7.9 23,30 4,050 2 7.4 21.85 3,360 3 7.2 21.21 2,460 4 7.2 21.21 2,070 5 6.9 20.35 1,580 6 6.9 20.35 1,220 7 6.9 20.35 455 TABLE 17 CONSISTENCY i n lbs WATER CONTENT lbs/cu.yd SLUMP i n . FLOW % REMOULDING EFFORT (Drops) COMPACTING FACTOR 300 317.00 8 1 2 130 23 0.990 400 310.00 7 1 2 120 34 0.984 500 302.00 6 105 45 0.975 600 297.00 3 3 4 90 57 0.964 700 292.00 2 80 68 0.954 800 295 ^ 1 1 4 67 79 0.945 900 283.00 1 45 90 0.935 TABLE 18 SPEED VELOCITY 'Vc' in./sec. HEIGHT 'he' i n . Vc "Rate of he s t r a i n " rad/sec 1 0.0368 8 0.0046 2 0.0415 8 0.0052 3 0.0548 8 0.0069 4 0.0655 8 0.0082 5 0.0818 8 0.0103 6 0.107 8 0.0134 7 0.288 8 0.0358 TABLE 19 MIX NO. SLUMP i n . n 8.6n (-4.3)S ( i n . lbs.) WORK 1 0 146 1255 +133 -0 1388 2 3 4 112 964 +133 -3.22 1094 3 70 602 +133 -6.50 729 4 2 i 61 525 +133 -9.70 648 5 4 55 474 +133 -17.20 590 6 6 50 430 +133 -25.80 537 7 7 i 35 300 +133 -32.20 401 8 8 23 198 +133 -34.4 297 TABLE 20 MIX # POWER'S TEST DROPS WEIGHT OF CYLINDER PARTIALLY COMPACTED "Wp" lbs WEIGHT OF CYLINDER FULLY COMPACTED "Wf" lbs COMPACTING FACTOR Wp Wf 1 93 41.63 44.75 0.933 2 69 42.44 44.31 0.954 3 46 43.06 44.44 0.972 4 39 43.57 44.50 0.980 5 33 43.88 44.57 0.985 6 28 44.13 44.57 0.990 7 15 44.19 44.70 0.990 8 10 44.31 44.88 0.990 TABLE 21 7Tr7T7777777777777T7777777777 uti tt A d Vc 79:. '7- • Concrete ' H/4 • . -5 57 zzzi F i g . l 51 52 F ^ . 3A 53 F i g . 3B r ML CG &—. 1 concrete <n Cone \1 _L 12" M Finqt: 2 F i g . 4 59 1" S U I W , 8 Q d r o p s , 9 0 0 in . ' l t o a . I V S L U M P , ._79 drops, 8QQ l b s -2 ° S L U M P , 6Sd]fops, 7oa lbs. 5^4° SLUMP, 5 7'drops, g p o i r t . ' l b s • - g - " - S L U t A f , - 4 - 5 - e | r o p a , 500 ir>. ija S 7 ^ " g L U M P , g4 d r o p s , 4-OQ i W . lbs. 84" SLUMP, 23 d r o p s , 300 in , lb O.OO4.5 0-0095 O 0 1 A 6 0.0195 O . O Z A 5 R A T E OF S T R A I N ' v/h" r a d/sec. O .0295 0 .0345 700 14-00 21. Oft 2 800 3 5 0 O D Y N A M I C V I S C O S I T Y " / / c " l b s . sec/-Ft 2. 4200 F\3 A G . 67 tn L4-00 D Y N A M I C Z100 VISCOSiTY "/±c Z$>oo l b s . s < ? c . / f i J . 3500 4200 F J 5 . 1 8 . ~~'' 21.00 2 8 00 3s oo 4T00 D Y N A M I C V I S C O S I T Y > c " lbs . $ e c / - f t 2 . ' / Fi 9 • 19. BIBLIOGRAPHY 1. NEVILLE, A.M., 2. POWERS, T.C., 3. YANG, L i . , 4. REINER, M., 5. SMITH, A. George & BENHAM, W. Sanford., 6. PEARSON, J.C. 7. KELLY, J.W. & POLIVKA, M., 8. TAYLOR, W.D., 9. LINNIX, V.YU., la HESLOP, W.G., IL TROXELL, E.G.& DAVIS, E.H., "Properties of Concrete" S i r Isaac Pitman & Sons Ltd., London "Studies of Workability of Concrete" Proc. ACI, Vol. 28, 1932. pp 419-448 "The Relationship Between Workability and V i s c o s i t y of Freshly Mixed Concrete" M.A.Sc., Thesis i n C i v i l Engineering, University of B r i t i s h Columbia, A p r i l 1965 "Building Materials, Their E l a s t i c i t y & I n e l a s t i c i t y " , pp 223-290 "A Study of Flow Table and Slump Test" Proc. ACI, Vol. 27, 1931, pp 420-438 "A Study of Slump and Flow of Concrete" Proc. ACI, Vol. 27, 1931, pp 1137-1142 " B a l l Test f o r Fied Control of Concrete Consistency". Proc. ACI, V o l . 51, 1955 pp 881-888 "Fundamentals of S o i l Mechanics" John Wiley & Sons Inc. "Method of Least Squares & P r i n c i p l e s of The Theory of Observations" pp 1-13, Pergamon Press - 1961 "The Dynamic V i s c o s i t y of Freshly Mixed Concrete". Technical Conference Saskatoon, Engineering I n s t i t u t e of Canada, Region 11 October 1966 "Composition and Properties of Concrete" McGraw H i l l Book Co. Inc. 12. GLANVILLE, W.H., "Grading and Workability'.' Proc. ACI, V o l . 33, 1937 - pp 319 B I B L I O G R A P H Y 1 3 . I N G E , L y s e & J O H N S O N , W . R . 1 4 . W I L L I A M S , G . M . , 1 5 . H E R S C H E L , " A S t u d y o f S l u m p a n d F l o w o f C o n c r e t e " P r o c . A C I , V o l . 2 7 , 1 9 3 1 . p p 4 3 9 - 4 6 7 " A d m i x t u r e s a n d W o r k a b i l i t y o f C o n c r e t e " P r o c . A C I , V o l . 2 7 , 1 9 3 1 . p p 6 4 7 - 6 5 3 " D i s c u s s i o n o n T e s t i n g C o n s i s t e n c y o f C o n c r e t e " . P r o c . A S T M V o l . 2 5 , 1 9 2 5 

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