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Bond between reinforcing bars and concrete under impact loading Yan, Cheng 1992

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BOND BETWEEN REINFORCING BARS AND CONCRETE UNDER IMPACT LOADING By Cheng Yan B. A.Sc. (Structure) Hehai University, China M. A.Sc. (Structure) Public Work Research Institute, Japan A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES CIVIL ENGINEERING We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October 1992 © Cheng Yan 1992  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.  (Signature)  Department of  a/141A-  The University of British Columbia Vancouver, Canada  f —  Date o-g e—e- •^  DE-6 (2/88)  3 . i ,9 9 2  Abstract  The bond between reinforcing bars and concrete under impact loading was studied for plain, polypropylene fibre reinforced, and steel fibre reinforced concretes. The experimental program included setting up an impact test system, in which an impact load with considerable energy could be generated, and in which the applied loads, accelerations and the strains along the reinforcing bar could be recorded at a rate of 200 microseconds per data point. The experiments consisted of both pull-out tests and push-in tests. For both types of tests the experimental work was carried out for three different types of loading: static, dynamic and impact loading, which covered a stress (bond stress) rate ranging from 0.5 • 10' to 0.5 • 10 -2 MPa/s. The other important variables considered in the experimental study were: two different types of reinforcing bars (smooth and deformed), two different concrete compressive strengths (normal and high), two different fibres (polypropylene and steel), different fibre contents (0.1 %, 0.5% and 1.0% by volume) and surface conditions (epoxy coated and uncoated). All of the test data were processed by computer, and the output included the stress distributions in both the steel and the concrete, the bond stresses and slips, the bond stress-slip relationships, and the fracture energy in bond failure. The energy balance at different stages in the bond process was examined. The internal crack development was also investigated. It was found that for smooth rebars, there existed a linear bond stress-slip relationship under both static and high rate loading. Different loading rates, compressive strengths, types of fibres, and fibre contents were found to have no great influence on  ii  this relationship and the stresses in both the steel bar and the concrete. For deformed rebars, the shear mechanism due to the ribs bearing on the concrete was found to play a major role in the bond resistance. The bond stress-slip relationship under a dynamic (high rate) loading changes with time and is different at different points along the reinforcing bar. In terms of the average bond stress-slip relationship over the time period and the embedded length, different loading rates, compressive strengths, types of fibres, and fibre contents were found to have a great influence on this relationship. Higher loading rates, higher compressive strengths of concrete, and steel fibres at a sufficient content all significantly increased the bond resistance capacity and the fracture energy in bond failure. All of these factors had a great influence on the stress distributions in the concrete, the slips at the interface between the rebar and the concrete, and the crack development. It was also found that there is always higher bond resistance for push-in loading than for pull-out loading. The bond resistance and the fracture energy in bond failure decreased when the rebar was epoxy coated. This influence of epoxy coating on the bond strength for push-in loading was much more significant than for pull-out loading. However, high rate loading, high concrete strength, and the steel fibre additions effectively reduced the above negative effects. The addition of polypropylene fibres was found to have very little effect on the bond behaviour, in terms of the bond strength, the stress distributions both in the rebar and the concrete, the crack development, the slips, the bond stress-slip relationship, and the fracture energy in the bond failure.  iii  In the analytical study, finite element analysis with fracture mechanics was carried out to investigate the bond phenomenon under high rate loading. The analytical method took into account all of the important variables in the bond-slip process. In this approach the chemical adhesion and frictional resistance between rebar and concrete were considered only during early loading in the elastic stage. After that only the rib bearing mechanism was taken into account. The fiber concrete composite and the high strength concrete were appropriately modelled. In the finite element analysis quadratic solid isoparametric elements with 20 nodes and 60 degrees of freedom were employed for the rebar and the concrete before cracking. After cracking the concrete elements were replaced by quadratic singularity elements, which were quarter-point elements able to model curved crack fronts. A special interface element, the 'bond-link element', was adopted to model the connection between the reinforcing bar and concrete. It connected two nodes and had no physical thickness at all, and so could be thought of conceptually as consisting of two orthogonal springs, which simulated the mechanical properties in the connection, i.e. they transmitted the shear and normal forces between two nodes. A new approach was proposed in this study for the establishment of the stiffness matrix of the 'bond-link element'. Then a bond stress-slip relationship at the interface between the rebar and the concrete would be one of the output results of the finite element analysis, rather than an input parameter required before the analysis could proceed. The dynamic constitutive laws of both steel and concrete, the criteria for crack formation and propagation in concrete based on the energy release rate theorem for mixed mode fracture, and the criterion for concrete crushing were used in the finite element process. It was an iterative program with rapid convergence. Not only could the bond stress and crack distribution be found through the analysis, but also a bond stress-slip  iv  relationship under high rate loading could be established analytically. The results obtained from the finite element analysis were compared with those from the experimental method, and reasonably good correspondence was found.  V  TO MY SISTER  vi  Table of Contents  Abstract^  ii  List of Tables^  xv  List of Figures^  xviii  List of Notations^  xxix xxxviii  Acknowledgement^ 1^Objectives and Scope  1  2^Literature Survey  6  2.1  Bond Behaviour under Static Loading ^ 2.1.1  Introduction ^  6  2.1.2  Flexural Bond under Static Loading ^  9  2.1.2.1^Experimental Investigation  9  2.1.3  ^  2.1.2.2^Summary ^  22  Anchorage Bond Under Static Loading ^  25  2.1.3.1^Experimental Investigation  25  ^  2.1.3.2^Summary ^ 2.1.4 2.2  6  32  Bond Tests with Fiber Reinforced Concrete or Coated Rebars ^. .^32  Bond Behaviour under Dynamic Loading ^  35  2.2.1  35  Bond Behaviour Under Cyclic Loading ^  vii  2.2.2 Bond Behaviour Under Impact Loading ^  39  2.2.3 Summary ^  47  2.3 Analytical Investigation of Bond Behaviour  ^48  2.3.1^Introduction  ^48  2.3.2 Theoretical Work  ^49  2.3.3 Fracture Mechanics and the Finite Element Method  ^51  2.3.4 Summary ^ 2.4 Conclusions  60 ^61  3 Experimental Procedures ^  64  3.1 Introduction  ^64  3.2 Specimen Preparation  ^65  3.2.1^General  ^65  3.2.2 Reinforcing Elements  ^69  3.2.2.1 Smooth and Deformed Bars ^ 3.2.2.2 Instrumentation of Rebars 3.2.3 Concrete Mix  69 ^74 ^76  3.2.3.1 Compressive Strength and Basic Mix Design  ^76  3.2.3.2 Added Fibers  ^76  3.2.4 Fabrication of Test Specimens  ^77  3.2.5 Properties of the Fresh and Harden Concrete  ^79  3.2.6 Summary of Test Specimens ^ 3.3 Test Program ^ 3.3.1 Impact Testing  81 89 ^89  3.3.1.1^Test Set Up  ^89  3.3.1.2 Impact Testing Machine ^  viii  91  3.3.1.3^Bolt Load Cell  ^96  3.3.1.4 Accelerometer^  100  3.3.1.5 Strain Measurement ^  103  3.3.1.6 Data Acquisition System ^  108  3.3.1.7 High Speed Video Camera ^  111  3.3.1.8^Test Procedure^  113  3.3.2 Static and Medium Rate Testing ^ 3.3.2.1^Test Set Up ^  114 114  3.3.2.2 Data Acquisition and Processing ^ 120 3.3.2.3 Test Procedure^ 3.3.3 Crack Examination ^ 4 Analysis of Test Data^  120 121 123  4.1 General ^  123  4.2 Data Filtration ^  126  4.2.1 Fast Fourrier Transform — FFT and Inverse FFT ^  126  4.2.2 Characteristics of External and Internal Noise ^ 133 4.2.3 Base Line Setting Method^  135  4.2.4 Digital Filtering^  135  4.2.5 Filtering of Load, Acceleration and Strain Signals^137 4.3 Young's Modulus and Poisson's Ratio of Concrete^ 4.4 Contact Load, Inertial Load and Applied Load^ 4.5 Acceleration, Velocity and Displacement ^  138 139 141  4.5.1 Acceleration, Velocity and Displacement of the Rebar ^ 141 4.5.2 Acceleration, Velocity and Displacement of the Hammer ^ 142 4.6 Elongation of the Rebar ^  ix  144  4.7 Strains and Stresses in the Rebar and the Concrete ^ 145 4.8 Bond Stress and Bond Slip ^  148  4.9 Rate of Loading, Strain and Stress ^  149  4.10 Work, Energy and Energy Balance ^  151  4.10.1 Kinetic Energy, Potential Energy, and Work done by the Hammer 151 4.10.2 Strain Energies and Fracture Energies^  155  4.11 Curve Fitting ^  156  4.12 Statistical Analysis ^  158  4.13 Computer program ^  159  5 Experimental Results^  162  5.1 Introduction ^  162  5.2 Steel Stresses ^  165  5.2.1^General ^  165  5.2.2 Tests with Smooth Bars ^  166  5.2.3 Tests with Deformed Bars ^  170  5.2.3.1^Effects of Loading Rate ^  170  5.2.3.2 Effects of Concrete Strength ^  176  5.2.3.3^Effects of Fibre Additions ^  178  5.2.3.4 Differences between Pull-out and Push-in Tests ^ 181 5.3 Concrete Stresses ^  184  5.3.1^General ^  184  5.3.2 Effects of Loading Rate ^  184  5.3.3 Effects of Concrete Strength ^  185  5.3.4 Effects of Fibre Additions ^  185  5.3.5 Differences between Pull-out and Push-in Tests ^ 189  5.4  5.5  Bond Stresses ^  190  5.4.1^General  ^  190  5.4.2^Tests with Smooth Bars ^  190  5.4.3^Tests with Deformed Bars ^  194  5.4.3.1^Effects of Loading Rate ^  194  5.4.3.2^Effects of Concrete Strength ^  199  5.4.3.3^Effects of Fibre Additions ^  201  5.4.3.4^Differences between Pull-out and Push-in Tests ^  201  Slip and Slip Distribution  ^  5.5.1  General ^  206  5.5.2  Tests with Smooth Bars ^  206  5.5.3  Tests with Deformed Bars ^  207  5.5.3.1^Effects of Loading Rate  r).6  5.7  206  ^  207  5.5.3.2^Effects of Concrete Strength ^  208  5.5.3.3^Effects of Fibre Additions ^  208  5.5.3.4^Differences between Pull-out and Push-in Tests ^  208 213  Internal Cracking ^ 5.6.1  General ^  5.6.2  Effects of Loading Rate and Concrete Strength  5.6.3  Effects of Fibre Additions ^  216  Bond Stress vs. Slip Relationship ^  220  ^  220  213 ^  216  5.7.1  General  5.7.2  Smooth Bars ^  221  5.7.3  Deformed Bars ^  224  5.7.3.1^Effects of Loading Rate  ^  5.7.3.2^Effects of Concrete Strength ^ xi  224 99,5  ^  5.7.3.3^Effects of Fibre Additions ^ 5.7.3.4^Differences between Pull-out and Push-in Tests 5.8  Results of Tests with Epoxy-Coated Rebars 5.8.1^Effect on the Bond Stress  5.9 6  ^  ^  ^  230 23:3 233  5.8.2^Effect on the Slip ^  237  5.8.3^Effect on the Bond Stress-slip Relationship ^  240  5.8.4^Effect on the Fracture Energy ^  245  5.8.5^Conclusions ^  246  Interpretation of Tests Results and Conclusions  ^  248  Energy Transfer and Balance  250  6.1  Introduction ^  250  6.2  Energies and Work Done by the External Force  6.3  Energy Balance in the Linear Region (t ..,-- t1) ^  256  6.3.1^Tests with Smooth Bars  257  6.4  7  225  ^  ^  251  6.3.2^Tests with Deformed Bars ^  259  Energy Balance in the Non-linear Region (t = tf) ^  265  6.4.1^Tests with Smooth Bars  266  ^  6.4.2^Tests with Deformed Bars ^  270  6.5  Energy Balance over the Entire Impact Event  271  6.6  Energy Absorbtion and Dissipation Capacity ^  ^  278  Analytical Study  283  7.1  Introduction ^  283  7.2  Finite Element Models ^  285  7.2.1^Steel Elements  285  ^  7.2.2^Concrete Elements ^  xii  288  7.2.3 Interface Elements ^  291  7.3 Constitutive Laws of the Materials ^  294  7.3.1 Constitutive Law of Steel ^  294  7.3.2 Constitutive Law of Concrete ^  294  7.4 Criteria of Cracking, Crack Propagation and Crushing in Concrete . . . ^ 296 7.5 The Algorithm for the Finite Element Analysis ^  297  7.6 The Results of the Finite Element Analysis ^  301  7.6.1 The Mechanical Parameters of the Specimens ^ 301 7.6.2 The Stress Distribution and Crack Development ^ 307 7.6.3 The Bond Stress-Slip Relationship ^ 8 Conclusions and Recommendations ^  308 315  8.1 Conclusions ^  315  8.2 Recommendations for Further Study ^  319  Appendices^  321  A Maximum Length of Rebar at the Struck End ^  321  B The Effect of Stress Wave Propagation on Outputs of Transducers 324 C Design of Electric Circuit for Strain Measurement ^  327  D The Effect of Inertial Force ^  331  E Tests for Determining Characteristics of Signal Noise ^333 E.1 Noise in Acceleration and Strain Measurement ^  :333  E.1.1 Test Design ^  :333  E.1.2 Acceleration Waves ^  :335  E.1.2.1 Analytical Solution ^ E.1.2.2 Experimental Approach ^  :335 338  E.1.2.3 Characteristics of Noise in the Acceleration Measurement 340 E.1.3 Stress Waves ^ E.2 Noise in Load Measurement ^  340 342  F The Solution of Three-dimensional, Axisymmetric Problems ^352 G The Calculation of the Hammer Rebound^  359  H Determinations of Parameters, co , fp and fr^361 H.1 The Unit Chemical Adhesion Force^  361  H.2 The Frictional Factor at the Interface ^  361  1-1.3 The Normal Stress Factor at the Interface ^  362 366  Bibliography^  xiv  List of Tables  3.1 The Maximum Embedments for Smooth Bars (Preliminary Tests) . . . . 66 3.2 The Maximum Embedments for Deformed Bars (Preliminary Tests) . . . ^73 3.3 Mechanical Properties of Steel Bars  ^73  3.4 Basic Concrete Mix Design (per m 3 )  ^78  3.5 Properties and Addition of Fibers  ^78  3.6 Test Results of Fresh Concrete  ^80  3.7 Test Results of Hardened Concrete — Part I  ^82  3.8 Test Results of Hardened Concrete — Part II  ^82  3.9 Loading Rate  ^8:3  3.10 Specimens for Push-in Tests (Deformed Bars)  ^84  3.11 Specimens for Pull-out Tests (Deformed Bars)  ^85  3.12 Specimens for Push-in Tests (Smooth Bars)  ^86  3.13 Specimens for Pull-out Tests (Smooth Bars)  ^87  3.14 Specimens with Epoxy Coated Deformed Bars ^  88  4.1 The Characteristics of Noise and Their Filtering (Load cell, Accelerometers and Strain Measurement)^  138  5.1 Effects of Loading Rate on the Steel Stress ^  172  5.2 Effects of Concrete Strength on the Steel Stresses ^  177  5.3 Effects of Adding Fibres on the Steel Stresses^  179  5.4 Effects of Pull-out and Push-in Forces on Steel Stresses ^ 182 5.5 Effects of Loading Rate on the Bond Stresses ^  xv  196  5.6 Effects of Concrete Strength on the Bond Stresses ^  199  5.7 Effects of Fibre Additions on the Bond Stresses ^  20:3  5.8 The Effects of Pull-out and Push-in Forces on the Bond Stresses ^ 204 5.9 The Local Slips at the Middle of the Embedment Length ^ 207 5.10 Effects of Epoxy Coating the Rebar on the Bond Stresses (Normal Strength  Concrete)^  235  5.11 Effects of Epoxy Coating the Rebar on the Bond Stresses (High Strength  Con crete)  236  5.12 Effects of Epoxy Coating the Rebar on the Slip (Normal Strength Concrete)238 5.13 Effects of Epoxy Coating the Rebar on the Slip (High Strength Concrete) 2:39 5.14 Fracture Energy in Bond Failure (for both Epoxy Coated and Uncoated Bars) ^  247  6.1 Energy Balance in the Linear Portion (Smooth Bars, Normal Strength) ^ 260 6.2 Energy Balance in the Linear Portion (Smooth Bars, High Strength) ^  261  6.3 Energy Balance in the Linear Portion (Deformed Bars, Normal Strength) 263 6.4 Energy Balance in the Linear Portion (Deformed Bars, High Strength) . 264 6.5 Energy Balance in the Non-linear Region (Smooth Bars, Normal Strength) 268 6.6 Energy Balance in the Non-linear Region (Smooth Bars, High Strength) . 269 6.7 Energy Balance in the Non-linear Region (Deformed Bars, Normal Strength)272 6.8 Energy Balance in the Non-linear Region (Deformed Bars, High Strength) 27:3 6.9 Total Energy Balance (Smooth Bar Specimens) ^  275  6.10 Total Energy Balance (Deformed Bar Specimens) ^ 276 6.11 Energy Balance right out of the Moment of Impact ^ 277 6.12 Energy Balance at Bond Failure^  xvi  278  6.13 Fracture Energy in Bond Failure (Smooth Bars) ^  281  6.14 Fracture Energy in Bond Failure (Deformed Bars) ^  282  7.1^Parameters of Mechanical Properties of Interface Elements ^  '303  7.2^Dynamic Critical Stress Intensity Factors for Concrete  ^  304  A.1^Geometrical and Mechanical Parameters of the Rebar ^  322  F.1^Strains in the Rebar (by the Finite Element Method) ^  355  F.2^Strains in the Concrete (By the Finite Element Method)  3566  xv ii  ^  List of Figures  2.1 Pull-out Test on Bond Strength  ^10  2.2 Beam Test on Bond Strength ^  10  2.3 Instrumentation to Detect Internal Cracks (after Goto [30])  ^17  2.4 Idealization of Interaction Between Bar & Concrete (after Goto [30]) . ^18 2.5 Nilson's Bond Stress-Slip Curves (Tanner's Tests [33])  ^20  2.6 Unit Bond Stress versus Unit Slip Curves (after Houde [35])  ^23  2.7 Some Typical Anchorage Bond Test (After Vos and Reinhardt [43]) . . ^26 2.8 Three Types of Transfer Pull-out Test Specimens (after Shah et al [47]) ^29 2.9 Testing Technique for Simulating Uniform Bond Stress (after Abrishami and Mitchell [48]) ^  31  2.10 Pull-out Specimens for Impact Test (after Hjorth [76])^ 2.11 Loading Pulse of Hjorth's Impact Test [76] 2.12 Influence of a Connective Constant Loading of 10  41  ^41 771,S on  the Bond Resis-  tance (after Hjorth [76])  ^43  2.13 Influence of the Loading Rate on the Bond Resistance (after Hjorth [76]) ^43 2.14 Influence of the Loading Rate on the Bond Stress-Slip Relationship (after Hjorth [76])  ^44  2.15 Geometry of a Typical Disc for Bond Model (after Yankelesky [90]) . . ^56 2.16 One Dimensional Element and Local Bond Stress-slip Law (after Yankelesky [91]) ^  56  xvii i  2.17 Two Types of Interface Elements for Bond Behaviour (after Mehlhorn ct, al [92]) ^  58  2.18 A 6-Noded Bond-Slip Elements (after Rots [93])  ^58  2.19 Constitutive Relations for Bond-slip Elements (after Rots [93])  ^59  2.20 Finite Element Idealization of Tension-Pull Specimen (after Rots [94]) . ^59 3.1 A Photograph of the Pull-out and Push-in Specimens  ^67  3.2 The Pull-out and Push-in Specimens  ^68  3.3 The Type No.10 Test Rebar ^  70  3.4 Test Rebar Instrumented with Strain Gauges  ^71  3.5 The Stress-strain Relationship of the Straight Bar  ^72  :3.6 The Stress-strain Relationship of the Deformed Bar  ^72  3.7 The Two Spirals in the Specimen  ^74  :3.8 Polypropylene Fibers  ^77  3.9 Steel Fibers  ^79  :3.10 The Stress-strain Relationship of Concrete  ^81  3.11 Layout of the Set Up for the Impact Test (Revised from Somaskanthan 92  [ 96 ])^ 3.12 An Overall View of the Impact Machine — Push-in Test (Revised from Somaskanthan [96])^  93  :3.1:3 An Overall View of the Impact Machine — Pull-out Test (Revised from Somaskanthan [96]) ^ 3.14 Solid Steel Frame for Pull-out Tests  94 ^95  :3.15 The Bolt Load Cell for Impact Testing ^  97  3.16 The Circuit of the Bolt Load Cell ^  98  3.17 The Calibration of the Bolt Load Cell ^  99  xix  3.18 The Quartz Accelerometer ^  101  3.19 The Calibration of the Quartz Accelerometer^  102  3.20 The Circuit of 'Opposite Arm' Wheatstone bridge^  104  3.21 The Dummy Strain Gauge and Connector Box ^  107  3.22 The Calibration of Strain Measurement ^  107  3.23 The Data Acquisition System ^  109  :3.24 EKTAPRO 1000 Motion Analyzer ^  112  3.25 The Calibration of the Load Cell for Static Testing ^ 115 3.26 The Calibration of the Position Measurement ^  116  3.27 Test System for Static and Medium Rate Testing ^ 117 3.28 Pull-out Test Set Up for Static and Medium Rate Loading ^ 118 :3.29 Push-in Test Set Up for Static and Medium Rate Loading ^ 119 3.30 The Stereoscopic Microscope ^  122  4.1 Typical Outputs from the Eight Channels of the Data Acquisition System 124 4.2 Algorithm of Test Data Process  127  4.3 The Motion Picture of the Rebar at T = 1 ms Taken by the High Speed Camera  128  4.4 The Motion Picture of the Rebar at T = 2 ms Taken by the High Speed Camera ^  128  4.5 The Motion Picture of the Rebar at T = 3 ms Taken by the High Speed Camera ^  129  4.6 The Motion Picture of the Rebar at T = 4 ms Taken by the High Speed Camera ^  129  4.7 The Motion Picture of the Rebar at T = 5 ins Taken by the High Speed Camera^  130  xx  ^  4.8 The Motion Picture of the Rebar at T = 6 ms Taken by the High Speed Camera^  130  4.9 The Motion Picture of the Rebar at T = 7 ms Taken by the High Speed Camera ^  131  4.10 The Displacement History of the Rebar by Two Methods^131 4.11 "Non Event" Noise in Impact Tests^  134  4.12 Spectrum of "Non Event" Noise by FFT^  134  4.13 One of the Calculation Models for the Test Specimens ^ 161 5.1 Stresses in the Smooth Rebar ^  167  5.2 Effects of Loading Rate on the Stresses in the Smooth Rebar ^ 167 5.3 Effects of Concrete Strength on the Stresses in the Smooth Rebar^168 5.4 Effects of Fibre Additions on the Stresses in the Smooth Rebar ^ 168 5.5 The Stresses in the Smooth Rebar for Pull-out and Push-in Tests ^169 5.6 Effects of Loading Rate on the Stresses in the Deformed Rebar (Plain Concrete) ^  173  5.7 Effects of Loading Rate on the Stresses in the Deformed Rebar (Polypropylene Fibre Concrete) ^  173  5.8 Effects of Loading Rate on the Stresses in the Deformed Rebar (Steel Fibre Concrete)^  174  5.9 Effects of Loading Rate on the Stresses in the Deformed Rebar (High Strength Concrete) ^  174  5.10 Effects of Loading Rate on the Stresses in the Deformed Rebar (Pull-out Tests) ^  175  5.11 Effects of Concrete Strength on the Stresses in the Deformed Rebar 176  xxi  ^  5.12 Effects of Fibre Additions on the Stresses in the Deformed Rebar (Different Fibres) ^  178  5.13 Effects of Steel Fibre Additions on the Stresses in the Deformed Rebar (Different Fibre Content) ^  180  5.14 Stresses in the Deformed Rebar for Pull-out and Push-in Tests (Static) ^ 181 5.15 Stresses in the Deformed Rebar for Pull-out and Push-in Tests (Impact) ^ 18:3 5.16 Effects of Loading Rate on the Stresses in the Concrete ^ 186 5.17 Effect of Concrete Strength on the Stresses in the Concrete (Static) . . ^ 186 5.18 Effect of Concrete Strength on the Stresses in the Concrete (Impact) . ^ 187 5.19 Effects of Fibres on the Stresses in the Concrete (Static) ^ 187 5.20 Effects of Fibres on the Stresses in the Concrete (Medium) ^ 188 5.21 Effects of Fibres on the Stresses in the Concrete (Impact) ^ 188 5.22 The Stresses in the Concrete for Pull-out and Push-in Tests (Impact) . ^ 189 5.2:3 The Bond Stresses for a Smooth Rebar ^  191  5.24 Effect of Loading Rate on the Bond Stresses for a Smooth Rebar ^ 192 5.25 Effect of Concrete Strength on the Bond Stresses for a Smooth Rebar . ^ 192 5.26 Effect of Fibre Additions on the Bond Stresses for a Smooth Rebar . . 193 5.27 The Bond Stresses for a Smooth Rebar for Pull-out and Push-in Tests . . 193 5.28 Effects of Loading Rate on the Bond Stresses (Plain Concrete)  197  5.29 Effects of Loading Rate on the Bond Stresses (Polypropylene Fibre Concrete)197 5.30 Effects of Loading Rate on the Bond Stresses (Steel Fibre Concrete) . . 198 5.:31 Effects of Loading Rate on the Bond Stresses (High Strength Concrete) . 198 5.32 Effects of Loading Rate on the Bond Stresses (Pull-out Tests) 5.33 Effects of Concrete Strength on the Bond Stresses  200 200  5.34 Effects of Fibre Additions on the Bond Stresses (Different Fibres) . . 201  5.35 Effects of Steel Fibre Additions on the Bond Stresses (Different Fibre Content) ^  202  5.36 The Bond Stresses for Pull-out and Push-in Tests (Static) ^ 202 5.37 The Bond Stresses for Pull-out and Push-in Tests (Impact) ^ 205 5.38 The Local Slip Distribution for Specimens with Smooth Bars ^ 209 5.39 Influence of Concrete Strength on Slip Distribution (Static)^ 209 5.40 Influence of Concrete Strength on Slip Distribution (Impact) ^ 210 5.41 Influence of 0.5% by Volume Polypropylene Fibres on Slip Distribution (Impact) ^  210  5.42 Influence of 0.5% by Volume Steel Fibres on Slip Values (Static) ^ 211 5.43 Influence of 0.5% by Volume Steel Fibres on Slip Distribution (Impact) ^ 211 5.44 No Transverse Cracks Formed at the Interface for Specimens with Smooth Bars ^  214  5.45 Internal Cracks in Pull-out Tests with Deformed Bars (Arrow Indicates the Crack around the Rib of the Rebar) ^  215  5.46 Internal Cracks in Push-in Tests with Deformed Bars (Arrow Indicates the Crack around the Rib of the Rebar) ^  215  5.47 Influence of Loading Rate on Internal Cracks (Normal Strength Concrete, Arrow Indicates the Crack around the Rib of the Rebar) ^ 217 5.48 Influence of Loading Rate on Internal Cracks (High Strength Concrete, Arrow Indicates the Crack around the Rib of the Rebar) ^ 218 5.49 Influence of 0.5% by Volume Polypropylene Fibres on Internal Cracks (Arrow Indicates the Crack around the Rib of the Rebar) ^ 219 5.50 Influence of 0.5% by Volume Steel Fibres on Internal Cracks (Arrow Indicates the Crack around the Rib of the Rebar) ^ 5.51 The Bond Stress vs. Slip Relationship for a Smooth Rebar ^  219 222  5.52 Effects of Loading Rate on the Bond Stress vs. Slip Relationship for Smooth Rebars ^  222  5.53 Effects of Concrete Strength on the Bond Stress vs. Slip Relationship for Smooth Rebars ^  223  5.54 Effects of Fibre Additions on the Bond Stress vs. Slip Relationship for Smooth Rebars ^  223  5.55 The Bond Stress vs. Slip Relationship for a Smooth Rebar for Pull-out and Push-in Test s  ^  226  5.56 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Plain Concrete) ^  226  5.57 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Polypropylene Fibre Concrete) ^  227  5.58 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Steel Fibre Concrete) ^  227  5.59 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (High Strength Concrete) ^  228  5.60 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Pull-out Tests)  228  5.61 Effects of Concrete Strength on the Bond Stress vs. Slip Relationship . . 229 5.62 Effects of Fibre Additions on the Bond Stress vs. Slip Relationship (Different Fibres) ^  229  5.63 Effects of Steel Fibre Additions on the Bond Stress vs. Slip Relationship (Different Fibre Content) 231 5.64 The Bond Stress vs. Slip Relationship for Pull-out and Push-in Tests (Static)231 5.65 The Bond Stress vs. Slip Relationship for Pull-out and Push-in Tests (Impact) ^  '232 xxiv  5.66 Internal Cracks at the Tips of the Ribs of an Uncoated Rebar (Normal Strength, Push-in, Impact) ^  241  5.67 Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar (Normal Strength, Push-in, Impact) ^  241  5.68 Internal Cracks at the Tips of the Ribs of an Uncoated Rebar (High Strength, Push-in, Impact) ^  242  5.69 Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar (High Strength, Push-in, Impact) ^  242  5.70 The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (Normal Strength, Pull-out, Impact) ^ 243 5.71 The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (Normal Strength, Push-in, Impact) ^  243  5.72 The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (High Strength, Pull-out, Impact) ^  244  5.73 The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (High Strength, Push-in, Impact) ^ 244 6.1 Typical Tup Load History ^  255  7.1 The Quadratic Solid Isoparametric Element with 20 Nodes and 60 D.O.F. 288 7.2 The Shape Function of the Quadratic Solid Isoparametric Element ^  290  7.3 The Quadratic Singularity Isoparametric Element ^ 290 7.4 The Interface Element (Bond-Link Element) ^  291  7.5 Algorithm of Finite Element Analysis ^ I ^  299  7.6 Algorithm of Finite Element Analysis — II ^  300  7.7 The Finite Element Mesh (Fracture Mechanics, Pull-out) ^ 305 xxv  7.8 The Finite Element Mesh (Fracture Mechanics, Push-in) ^ 306 7.9 The Bond Stress-slip Relationship by the Finite Element Method (Plain Concrete, Push-in, Impact III - 0.5 • 10 -2 11/1 P a I s) ^  :311  7.10 The Bond Stress-slip Relationship by the Finite Element Method (Polypropylene Fibre Concrete, Push-in, Impact III 0.5 • 10 -2 MPa/s) ^  :311  7.11 The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre Concrete, Push-in, Impact II - 0.5 • 10' MPa/s) ^  :312  7.12 The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre Concrete, Push-in, Impact III - 0.5 • 10_ 2 MPals) ^  :312  7.13 The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre High Strength Concrete, Push-in, Impact III 0.5 • 10 -2 MPals) ^  :31:3  7.14 The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre Concrete, Pull-out, Impact III - 0.5 • 10 -2 MPa/s) ^  :31:3  7.15 The Applied Load vs. Displacement Curve by the Finite Element Method (Steel Fibre Concrete, Push-in, Impact III 0.5 • 10 -2 MPa/s) ^ E.1 Longitudinal Impact of Bars ^  :314 334  E.2 Absolute Velocity History at the Bottom (Analytic)^ :3:36 E.:3 Acceleration History at the Bottom (Analytic)^  :3:36  E.4 Acceleration History at Bottom (Experimental) ^ :3:39 E.5 The Amplitude Spectrum of Acceleration (Analytic) ^ :3:39 E.6 The Amplitude Spectrum of Acceleration (Experimental) ^ 341 E.7 Acceleration History at the Bottom (Filtered) ^ xx vi  341  E.8 Strain History at the Top (Analytic.) ^  342  E.9 The Amplitude Spectrum of the Strain (Analytic) ^  343  E.10 Strain History at the Top (Experimental) ^  343  E.11 The Amplitude Spectrum of The Strain (Experimental) ^ 344 E.12 Strain History at the Top (Filtered) ^  344  E.13 Longitudinal Impact of Bar and Block ^  345  E.14 Load History (Analytic) ^  349  E.15 The Amplitude Spectrum of the Load (Analytic) ^  349  E.16 Load History (Experimental) ^  350  E.17 The Amplitude Spectrum of The Load (Experimental) ^ 350 E.18 Load History (Filtered) ^  :351  F.1 Finite Elements of a Ring ^  356  F.2 The Finite Element Mesh (Pull-out) ^  357  F.3 The Finite Element Mesh (Push-in) ^  358  H.1 Test Specimen for the Unit Chemical Adhesion Force^ :363 H.2 Test for the Frictional Factor at the Interface ^  364  H.3 Test for the Normal Stress Factor at the Interface^  365  List of Notations  Latin Symbols A = the surface area of the rebar A, = the cross-sectional area of the concrete specimen A S = the cross-sectional area of the rebar a = acceleration a ha = the acceleration of the hammer = the acceleration of the rebar [B] = the "strain-displacement" matrix Co = the unit chemical adhesion force at the interface C(w) = the Fourier coefficient c i = the calibration coefficient of the load cell c„ = the coefficient of variation  D= d=  the diameter of the rebar the distance  dh „ = the distance the hammer travels after impact  =  the distance the rebar travels after impact  d„, d = the total distance the hammer travels by the end of impact  E=  the excitation voltage, Young's modulus, energy  [E] = the matrix of elastic stiffness  E, = the Young's modulus of concrete E c,str  =  the strain energy stored in the concrete  E f b = the fracture energy in bond process ,  Eh„, f r = E ha, k =  the energy consumed by the friction and air resistance the kinetic energy of the hammer  Eh a , /eft = the kinetic energy of the hammer left E ha, rebound =  the rebound energy of the hammer  E ha , p = the potential energy of the hammer  Ere, str = the strain energy stored in the rebar E r ,, yield^the local yield energy of the rebar during impact Es = the Young's modulus of steel E ns = the energy lost to the various machine parts ere  =  the deformation of the rebar  Fb = force acting on bond area  Fh = the horizontal nodal force of the interface element •  = the inertial force of rebar  Ft = the applied load acting on the rebar Fh = the vertical nodal force of the interface element fe' = the compressive strength of concrete fc,r = the tensile strength of concrete fp = the normal stress factor at the interface  ^  fT =  the frictional factor at the interface  = the Young's modulus of concrete in shear g = the gravitational acceleration h = the drop height of the hammer  I = the minimizing function, the high rate loading (impact), - I^the first impact loading (bond stress rate is about 0.5 • 10 -4 MPa/s)  II^the second impact loading (bond stress rate is about 0.5 • 10  -3  MPals)  I-III = the third impact loading (bond stress rate is about 0.5 • 10  -2  MPa/s)  ^I  i = the imaginary [J] = the Jacobean matrix K = the standard gauge factor of strain gauge  [K] = the stiffness (global) matrix K1 ,  K2 =  the gauge factors of a pair of strain gauges (gauge 1 and gauge 2)  /(/, I(//, I(/// = the stress intensity factors for fracture mode I, II, III  K/  KLic, Kmc = the critical stress intensity factors (dynamic) for fracture mode I, II, III  I = the length over which bond slip occurs  /, = the embedment length of the rebar in concrete l j = the locations of the ith and jth points along the rebar / p = the length of the pull-out or push-in end of the rebar  M = the mass of the hammer, the medium rate loading Mina = the mass of the hammer  XXX  M re = the mass of the rebar M— I = the first medium rate loading (bond stress rate is 0.5 • 10_  6 ti  0.5 • 10'  MPals)  M— II = the second medium rate loading (bond stress rate is 0.5-10'  ti  0.5.10 -4  MPals)  N = the number of the time interval, the total number of samples [N] = the matrix of shape function Nz = the shape function n^the number of segments in which the slips have been calculated  P(t) [t i ,t 2 ] = the aperiodic signal function PF = Polypropylene fibre concrete  R 1 , R 2 = the electric resistances of a pair of strain gauges S = the standard deviation, the static loading  S i^the concrete stress corresponding to e = 50 x 10 -6 S z^the concrete stress at 40% of the ultimate load Sh„, a = the output voltage from the accelerometer attached to the hammer  = the output voltage from the load cell  S„, a =  the output voltage from the accelerometer attached to the rebar  SF = Steel fibre concrete = the location of the calculated section along the rebar  T,t = the time t,„ d = the duration of the impact event  t l = the time corresponding to the end of the linear region of the applied load vs. displacement curve  t f = the time corresponding to the bond failure t rebound =  the time interval between the first and second blow  u = the bond stress u, v, w = the displacement components in the global Cartesian coordinates it = the bond stress rate u jj = the average bond stress between the i and j points = the horizontal displacements of node i and j (finite element method)  Vout = the output signal voltage h„ =  the velocity of the hammer  ha,0 =  the velocity of the hammer at the moment of impact  vz v j = the vertical displacements of node i and j (finite element method) j  v rf, = the velocity of the rebar V rebound = W b =  the rebound velocity of the hammer  the work done by the bond resistance  W ha = the work done by the hammer W ha (t) = the work done by the hammer in the time domain W ha (d) = the work done by the hammer in the displacement domain TV ha, total =  the total work done by the hammer during the impact  to = the bond slip to = the calculated slips for the previous segments  w, = the bond slips at distance x from the i point  tv.t, = the bond slips at distance y from the loaded end of the rebar x = the distance between a point and the i point x, y, z = the global Cartesian coordinates x i = the experimental data = the mean value of sample x i y = the distance between a point and the loaded end of the rebar  Greek Symbols A = small change operator AE = the kinetic energy lost by the hammer after impact  AE L b  = the fracture energy in bond during a time period of St,  AT = the time increment St = the time increment AX = the length of rebar between the ith and jth point  =  coefficient that accounts for the nonuniform distribution of stress in the concrete across the section  = the strain Ez  = the strain corresponding to 82 = the axial strain in concrete . = the radial strain in concrete = the tangential strain in concrete  ES  = the axial strain in steel (recorded) = the radial strain in steel  cs,e = the tangential strain in steel Ett = the transverse concrete strain at the middle of specimen corresponding to  ct2 = the transverse concrete strain at the middle of specimen corresponding to S2 Ex ,  C y , ez = the strain components in the Cartesian coordinates  ( 2 , E3 = the principal strains in the concrete element 7i, C = the isoparametric coordinates = the Poisson's ratio ,a, = 0.25 (the Poisson's ratio of concrete) ,a, = 0.27 (the Poisson's ratio of steel)  p = the density of the rebar a = the stress = the stress rate  a, = the axial stress in concrete = the radial stress in concrete ac,e = the tangential stress in concrete = the principal tensile stress in the concrete element  a cy = the crushing strength of the concrete cylinder = the interface shear stress (finite element method)  a s = the axial stress in steel a s ,„ = the radial stress in steel crs,e = the tangential stress in steel = stress at the ith location in steel ms s ,  = stress at the jth location in steel  = the interface normal stress (finite element method) (T x a y, oz  = the stress components in the Cartesian coordinates  a l 7 a 21 0. 3 = the principal stresses in concrete elements  w = the frequency component Subscripts a = acceleration = concrete  e. = elastic end = end of impact event f = failure fr = friction h = horizontal  ha = hammer i = the ith point j = the jth point / = load, loadcell, linear  xxxv  v = the radial direction re = reinforcing bar  s = steel t = at time t, the tangential direction str = strain = vertical  x = distance x y = distance y = the tangential direction  Acknowledgement  The author is highly indebted to Dr. Sidney Mindess for his continuous support and constant supervision. His personal concern, encouragement and advice during author's graduate studies were of great help. Sincere gratitude also goes to Dr. N.D. Nathan, Dr. A. Bentur, and Dr. R.J. Gray for their help rendered during author's study in the Department of Civil Engineering. The author wishes to express special thanks to Dr. R.A. Spencer, Dr. A. Poursartip and Dr. P.E. Adebar for serving on the author's graduate committee and for their invaluable comments. Thanks are also due to M. Nazar, R. Postgate, B. Merkli, J. Wong and R. Dolling in the workshop of the Department of Civil Engineering for their helpful participation in preparing and maintaining the instrumentation for the experimental work. The author wishes to thank Dr. N.P. Banthia for his help in the early stage of this research program, and thank J. Stevens in the University Computing Center for his help in the computer programming work. Finally, the research assistantship awarded by the Department of Civil Engineering, University of British Columbia and the research grant provided by the Natural Sciences and Engineering Research Council of Canada, for the Network of Centers of Excellence on High Performance Concrete are gratefully acknowledged.  Chapter 1  Objectives and Scope  The initial purpose of the embedment of steel bars in concrete, in the middle of the 19th century, was to produce a supporting steel network [1]. In 1886, G.I. Wayss was successful. from experimental considerations, in elucidating the principles involved in the action of reinforcement. His contributions have subsequently served as a basis for the more general utilization of reinforcement as a component in reinforced concrete whose primary function is to resist tensile forces. For a reinforced concrete structure, it is the bond between the steel and the concrete which enables the two materials to act together. In the case of plain bars, the bond forces are due to chemical adhesion and friction. In the case of deformed bars, the bond forces are derived mainly by the bearing capacity of the ribs on the concrete. In the case of strands, the bond forces are due largely to a lack of fit. The behaviour of a structure is strongly dependent upon the bond between the concrete and the reinforcing bars. The accurate prediction of the linear or nonlinear response of reinforced concrete structures subjected to static or dynamic loads, using all the sophisticated methods of analysis, is based upon our knowledge about the local bond stress vs. slip relationship governing the behaviour at the steel-concrete interface.  1  Chapter 1. Objectives and Scope  ^  9  With the introduction of high tensile strength steel as reinforcing material, the importance of bond was further increased. The development of cracks at a given working stress and the width of these cracks depend primarily on the degree of bond between the steel and the concrete. Over the past decade, high performance concretes and fibre-reinforced concretes have become more widely used in concrete structures. High performance concrete is generally stronger than normal concrete, but it may be more brittle than the latter. Concretes with fibre addition make it more difficult for cracks to propagate and more ductile, i.e. they can absorb more fracture energy. All of these may improve the bond strength significantly. However, design engineers of reinforced concrete structures under different loading conditions will benefit from these developments only when the fundamental mechanisms of bond behaviour are precisely understood. Either the "ultimate bond stress" in the 1970 CSA A23.3-M70 [2] (and also in the 1963 Building Code [3]) or the "required development length" in the 1973 CSA A23.3-M73 and 1984 CSA A23.3-M84 [4, 5] (and also in the 1971 and 1989 ACI Building Code [6, 7]), which deal with the bond problem in engineering practice, are derived empirically based primarily on pull-out tests (such as the standard pull-out test recommended in ASTM C 234 [8]). The assumption that the bond stress distribution along the embedment length is uniform, which provides the basis for the derivation of the bond formula, may not be true in most cases. A very short embedment length in a pull-out tests may create a uniform bond stress distribution, but the result is somewhat controversial [9]. These various Code equations do not recognize the influence on the bond resistance of many factors, and may be conservative in most cases. Although many proposals for change have been made, no generally accepted recommendations have yet evolved. A uniform bond stress-slip relationship based on the Code equations is convenient in applica,tions, but far from reality, and may give results with considerable variability.  Chapter 1. Objectives and Scope ^  3  Extensive experimental and analytical studies have been carried out and reported on over the years, dealing with bond behaviour in reinforced concrete. Most of these investigations have been associated with either pull-out loading or a combination of pullout and push-in loading. No pure push-in tests have been reported. It was recognized that there are numerous factors affecting bond behaviour. Some of these factors are the type of rebar, the compositions and properties of the materials, the layout of the reinforcement, the pattern of loading, the strain rate, and so on. It is well known that the size and the type of specimen used for bond tests have large effects on the results of the experiments. It is thus difficult for an experimental program to take into account all possible factors affecting bond. While much experimental research has been conducted on bond behaviour under static loading condition, only a few results are available for dynamic loading, especially for impact loading conditions, such as explosions, earthquakes, sudden cracking of a beam, pile driving, etc. It is well known that the strength of concrete (compressive, tensile or shear) increases with increasing loading rate, and that the fracture characteristics of concretes or cementitious composites change dramatically under dynamic loading. For this reason an influence of the loading rate on the bond resistance of reinforcing elements can be expected. Due to the difficulties in precisely modelling the mechanical properties under dynamic loading, however, very little analytical work has been done on this problem. The present work deals with a study of the bond behaviour of reinforcing bars in concrete under impact loading. It includes both experimental and analytical components. The experimental work involved the carrying out of a series of both push-in and pull-out impact tests to investigate:  Chapter 1. Objectives and Scope^  4  1. the most suitable experimental models to obtain bond-slip relationships under dynamic loading; 2. the instrumentation and techniques for the measurement of bond stress and bond slip; 3. the bond stress, the bond slip and the relationship between them; 4. the stress distribution along the rebar and in the concrete in the vicinity of the rebar; 5. the crack development in concrete during the bond-slip process; and 6. the transfer and balance of energy during bond-slip.  The analytical work involved a study of the bond behaviour using both fracture mechanics and the finite element method approaches. It includes:  1. An investigation of the mechanism of bond between the steel and the concrete from the viewpoint of linear or nonlinear fracture mechanics; 2. The use of the finite element method to analyze the bond behaviour under impact loading; the main concerns are: • using "cracking elements" for concrete (concrete elements) • developing "interface elements" (bond-link elements) for the connection of the steel elements and the concrete elements • setting cracking and crushing criteria. suitable for the concrete elements • setting appropriate criteria for the behaviour of the interface elements  Chapter 1. Objectives and Scope ^  5  • using appropriate constitutive laws for both materials • interpreting the results of the calculations reasonably 3. The stress distribution and crack development in the concrete; and 4. The formulation of an applied bond stress-slip model for impact loading;  The following major variables were considered in both the experimental work and the analytical work:  • Strain rate in the reinforcing bar; • Strength of the concrete; • Addition of fibres; and • ( onstitutive relationship of the concrete.  ('SA A23.3-M84 [5] permits only deformed bars as reinforcement except for spirals, and for stirrups and ties smaller than 10 mm in size. Therefore, this study emphasizes the bond behaviour of deformed bars.  Chapter 2  Literature Survey  2.1 Bond Behaviour under Static Loading  2.1.1 Introduction  The bond between steel and concrete has long been under investigation. These studies have elaborated on the influence of many variables on bond and bond strength, and can be placed into two categories:  1. The stresses produced as a result of the bonding between steel and concrete; and 2. The influence of various parameters on bond strength and bond stress distribution.  However, only these studies, to be described below, have been found which deal explicitly with the bond between steel reinforcing bars and concrete under impact loading. These were all experimental studies; no analytical paper have been found. Hence, this literature survey will deal primarily with quasi-static investigations, which are a necessary prelude to the study of the impact problems.  6  Chapter 2. Literature Survey^  7  The earliest published tests on bond between "iron bars" and concrete, as reported by Abrams [10], were carried out by Thaddeus Hyatt in 1877. Abrams reported results from both pull-out tests and the reinforced concrete beam tests by 1913 [11]. Summaries of some of the major developments in the study of bond over the last century are given by ACI Committee 408 [12, 13], ACI Committee 446 [14] and CEB Task Group VI [15]. Basically, there are two types of interactions between the reinforcing bar and the concrete which involve slip: flexural bond stress and anchorage bond stress. (1) Flexural bond stress  Flexural bond stresses exist on the surface of the reinforcing bar in a flexural member such as a beam or a slab, due to the variation in bending moment. The change in bending moment between two sections of a beam of length dx, produces a change in bar force  dT. Since the bar must be in equilibrium, this change in bar force will be resisted by an equal and opposite force due to the bond at the contact surface between the steel and the concrete. This bond stress due to the change in bending moment is called the flexural bond stress. From the equilibrium equation,  uE0 dx dT  dM^  where u = the flexural bond stress  the total perimeter of the bar at the section  (2.1)  8  Chapter 2. Literature Survey^  dM = the change in the bending moment = the arm of the internal resisting couple From beam theory, the shear force at the section, V, is equal to  dM V= ^ dx  (2.2)  Therefore, the flexural bond stress is  u  =  V CEO  (2.3)  (2) Anchorage bond stress  Anchorage bond stresses develop in the anchorage zone at the ends of bars which extend into a support, or at the ends of bars cut off within a span. If a bar is required to develop a given force dT at certain point and has an anchorage length dl, / , from the equilibrium consideration the anchorage bond stress, u, is determined by  dT 1 u=^ dl E0  (2.4)  Generally, the anchorage bond stress is assumed to be uniformly distributed over the anchorage length, so the average value is  Chapter 2. Literature Survey^  T  9  (2.5)  where  T = the applied force / d = the anchorage length  2.1.2 Flexural Bond under Static Loading  2.1.2.1 Experimental Investigation  For the case of flexural bond stress, two major types, tension tests and beam tests, have been used. In these types of tests, the concrete surrounding the bar remains in tension, in an attempt to represent the actual conditions existing in a beam. In the former case, a bar is encased in a cylinder or a prism, and is subjected to tension at the protruding ends, as shown in Fig. 2.1. Thus, the conditions are similar to those in the tension zone of a beam. For the latter case, various configurations such as ordinary rectangular beams subjected to four point loading, hammer head beams, cantilever beams, and stub cantilever beams are tested. In all of these tests, the concrete surrounding the bar remains in tension in order to represent the actual conditions existing in a beam. Fig. 2.2 shows one of the beam tests on bond strength. In Abrams's tests [11] nearly all of the pull-out test specimens were reinforced against bursting by means of spiral reinforcement. All of the beams were reinforced with vertical  chapter 2. Literature Survey^  Figure 2.1: Pull-out Test on Bond Strength  Figure 2.2: Beam Test on Bond Strength  10  Chapter 2. Literature Survey^  11  stirrups of plain round bars. In both types of specimens, attention was given to obtaining accurate measurements of the slip of the bar through the concrete as the loading progressed. Some of the relevant conclusions of this investigation on pull-out tests are as follows:  1. In order to study the load vs. slip relationship over a wide range of values it was necessary to guard against the splitting of the specimen; 2. It was realized that the bond stress was not uniformly distributed along a rebar embedded any considerable length, and having the load applied at one end; 3. Only after slip became general was there an approximately uniform bond stress throughout the embedded length. However, in establishing a bond vs. slip curve for different situations, a uniform bond distribution was assumed, and the deformations in concrete and steel were assumed to be proportional to the stress; 4. For a given amount of slip, the bond stress depended upon the stress level in the steel; 5. The tests indicated that a definite relationship existed between the amount of movement of the bar and the bond stress developed. After slipping began, the bond stress increased with further movement of the bar, very rapidly at the first, then more slowly until the maximum bond resistance was reached; the bond stress was reduced with further slip; 6. The load vs. slip relationships for different mixes of concrete were the same; and 7. The bond resistance was greatly increased by lateral pressures.  Chapter 2. Literature Survey ^  12  Some of the relevant conclusions of this investigation on beam tests are as follows:  1. To determine the bond stress at any given location in a bar in a reinforced concrete member, it was essential to determine the exact stress variation along the reinforcing bar for a given load; and 2. The tests indicated that the maximum bond resistance was developed at certain points along the bar at loads much below that causing bond failure in the beam.  Mylrea [16] concluded, based mainly on the work of Abrams 1 . that at any point along the bar, bond stress was a function of the slip at that point. Thus, a single relationship could represent the variation of bond stress with slip at all points along the length of the bar. The mechanism of bond development for plain round bars was described by Mylrea as follows. At first the load is carried by adhesion. As the load increased, more of the bar begins to slip, restricting the adhesive bond to a smaller portion of the bonded length. The maximum bond stress occurs near the loaded face at the free end. With increasing load the location of the maximum bond stress moves towards the unloaded end of the pull-out specimen while maintaining a constant value. After the slip becomes general (that is, the whole bar slips) the bond stress is nearly uniform along the full length of the bar. The bond stress intensity gradually diminishes with further slip. Mylrea did not discuss the mechanism of bond of deformed bars but concluded from his tests, that deformed bars had improved bond properties and that slip resistance would increase until the deformations began to crush the concrete. 1 It should be noted that the reinforcing bars which Abrams used in his tests were no longer in use in 1940's.  Chapter 2. Literature Survey^  13  Mylrea was the first to point out that the well-known flexural bond formula (Eq. 2.3),  V u= ^ zE0 yielded correct values of bond stress only when the bars were straight and extended over the full length of the member. The tensile force in a bar varied directly with the ordinate of the moment curve. He emphasized the concept of a minimum development length rather than a unit bond stress. Mylrea, was also of the opinion that the bond conditions at the bar ribs were different from those between the ribs. Therefore, it was not possible that a bond stress-slip curve at a particular point along the bar could represent the behaviour at other points along the embedded length. Watstein [17, 18] reported results from pull-out specimens in which he measured the distribution of stresses in bars with different embedment lengths. He observed that the bond stresses increased with slip most rapidly at the loaded end of the bar and, in general, least rapidly at its free end. The divergence of bond stress for a given slip, at the two ends of the bar, was more pronounced for longer embedment lengths. The bond vs. slip relationship obtained indicated that there was a non-linear relationship and was thus in accord with comparable data obtained by other investigators [11, 15]. Mains [19] determined steel stresses and bond stresses along the rebar by a new technique in which electric resistance strain gauges were placed at close intervals within the core of a hollow bar, and the bond stresses were thus not disturbed. His method involved slicing the reinforcing bar longitudinally and milling a groove in one of the halves for the fixing of strain gauges, and then tackwelding them back into a single bar. Determinations of longitudinal stresses were made on both beam and pull-out specimens. Forces in the bars in the linear and non-linear ranges of the stress-strain diagram were  Chapter 2. Literature Survey ^  14  found using previously-established calibration curves. The results of Mains' investigation indicated that the locations of cracks in beams governed the magnitude and distribution of both tensile and bond stresses. He also found that the maximum measured bar tension in the center section of the beam was close to the value calculated by the ordinary cracked section theory. The measured local maximum bond stress often exceeded the value calculated from cracked section theory by a factor of two or more for all loads after cracking was observed. Also, very high local bond stresses occurred near cracks in a beam. After cracking, the concrete could not carry any tension, so the tension in the concrete was zero at the crack and reached a maximum between cracks. This gradual increase of tension in the concrete with distance from the crack accounted for the decrease of tension in the steel and the development of the accompanying bond stress between the concrete and the steel. Since this phenomenon took place in a region of no shear, it contradicted the common assumption that bond stress was associated exclusively with shear as assumed in the classical beam theory. The maximum local bond stress in deformed bars was observed to occur at or near the loaded end at all stages of loading while the location of the maximum local bond stress in plain bars was observed to move from the loaded end to the unloaded end with increasing load [11, 16, 20]. Ferguson, Turpin and Thomson [21] investigated the influence of bar spacing, stirrups, and the depth of concrete cover on the bond strength. They conducted eccentric pull-out tests, simulating the worst beam conditions. Splitting was observed to be an important factor in bond strength. They concluded that the maximum bar spacing should be based on the aggregate size. By increasing the bar spacing, a significant improvement in the ultimate bond stress could be obtained.  Chapter 2. Literature Survey^  15  Ferguson and Thomson [22, 23] published a two-part paper on the development length of high strength reinforcing bars. The test specimens consisted of simply supported beams with overhangs. The bond failure was caused by splitting but diagonal tension was often a complicating factor. They found that the bond strength was a function of cover over the bars, an extra inch of cover increasing the bond strength from 0.41 to 0.69 MPa. Stirrups were found to resist bond splitting and to help in preventing sudden failure. The bond strength was observed to vary with the square root of the concrete compressive strength,  A', rather than directly with L'. In a review paper, Ferguson [24] discussed the bond stresses and the nature of bond failure. For a deformed bar, the bearing of the ribs against the concrete and the shear strength of the concrete between the ribs were reported to be chiefly responsible for the bond strength. Especially for a cracked beam, the local bond stress was so variable that the average bond stress computation over an embedment length was felt to be advisable. The bond capacity of compression bars was found to be greater than that for tension bars because compression bars did not cross open cracks. Bresler and Bertero [25, 26] carried out tests on instrumented axially reinforced tension specimens in which the reinforcing bars were subjected to repeated tensile loading at both ends to study the mechanism of bond deterioration. They were the first to report results on bond stress distribution and measurements of end slip. The most significant conclusion from their work is the history-dependence of the bond deterioration. The mechanism that they proposed for bond deterioration was one of failure in a relatively thin layer of concrete (designated the "boundary layer") adjacent to the steel-concrete interface. The failure was due to cracking, local fracture, and/or inelastic deformation and crushing of the concrete in the "boundary layer". The stress transfer occurred basically  Chapter 2. Literature Survey^  16  by friction and wedging action. Some slip also took place in the process. Lutz and Gergely [27, 28] studied the mechanics of the slip of deformed bars in concrete using both experimental data and an analytical method. They used the finite element method to analyze the stresses and deformations in a. concrete cylinder with a centrally-placed rebar subjected to tension. This model represented two situations in a, reinforced concrete member. First, the rebar, when pulled from both sides, represented the conditions between flexural cracks. When pulled from only one side, it represented the anchorage zone problem. Transverse cracking in concrete, slip, and separation between the reinforcing bar and the concrete were considered. Radial separation was found to occur in the vicinity of a transverse crack due to high radial stresses. They reported that the bond of deformed bars was mainly due to bearing of the ribs against the concrete. Slip of deformed bars could occur in two ways: the rib could push the concrete away from the bar, or the ribs could crush the concrete. From their tests with a single rib and the tests of Rehm (29], they concluded that for bars having a rib face angle of more than about 40° with the bar axis, the slip was mainly due to crushing of the mortar in front of the ribs. For ribs having a face angle less than 40°, slip was mainly due to the relative movement between the concrete and the steel along the face of the rib and due to some crushing of the mortar. Goto [30] carried out a significant study by injecting ink into his concrete specimens during the tests, and then cutting the specimens longitudinally. He could establish the pattern of internal cracks from which he proposed the mechanism of the interaction between the concrete and steel, as demonstrated in Figs. 2.3 and 2.4. The formation of internal cracks in the concrete around the rebar gave the appearance of "comb-like" concrete, the teeth of which were deformed in the direction of the primary crack (see  Chapter 2. Literature Survey^  17  Fig. 2.4) by compressive forces transmitted from the ribs. The inclination of the cracks being about 60° to the bar axis. The deformation of the teeth served to tighten the concrete around the reinforcing bar and increased the frictional resistance. The reaction of the tightening force caused circumferential tension and was responsible for longitudinal splitting in the concrete. It was believed that once the splitting cracks developed, this was an indication of the onset of bond failure.  red ink  cock vinyl pipe reinforcing bar  E  concrete  rubber pipe  injecting hole  brass pipe vinyl pip*  cock Location of notch  Figure 2.3: Instrumentation to Detect Internal Cracks (after Goto [30])  Nilson [31.32] arrived at a bond-slip relationship based partly on hypotheses and partly on the experimental data reported by Bresler and Bertero [25, 26]. The steel displacement was calculated by integrating the strain values of the steel, and the concrete  18  Chapter 2. Literature Survey^  Longitudinal section of axially loaded specimen^Cross section  uncracked zone  internal crack primary crack  force on concrete  force components on bar  tightening force on bar (due to wedge action and deformation of teeth of comb—like concrete)  Figure 2.4: Idealization of Interaction Between Bar & Concrete (after Goto [30])  Chapter 2. Literature Survey^  19  displacements were estimated on the basis of measured slip at the faces of the test specimens. A third degree polynomial was obtained by fitting the data. The relationship is given by u = 3.606 x 10 6 s — 5.356 x 10 9 ,5 2 + 1.986 x 10 12 s 3^(2.6) where u = local bond stress in psi  = local bond slip in inches Differentiation of the above equation with respect to s yields  du = 3.606 x 10 6 — 10.712 x 10 9 s + 5.958 x 10 12 s 2^(2.7)  This represents the stiffness of the concrete layers transferring the forces to the steel bar. Nilson [33, 34] subsequently also devised a method for determining the bond-slip relationship at any point along the embedment length, based on his tests in which internal embedded strain gauges were mounted to measure concrete strains at the interface of the steel and the concrete. By integrating strains of the steel and the concrete, slip could be computed. A series of bond stress-slip curves was obtained at different distances from the loaded end, as shown in Fig. 2.5 The proposed bond-slip equation was:  u^3100 (1.43c + 1.5)s fe i^(2.8)  • 20  Chapter 2. Literature Survey^  14  0  0.02  004  0 06  12 Ett"  10  0 ce cn  8  cr 6 1— (n 0 O • 4  2 c z DISTANCE FROM END OF CONCRETE BLOCK 1.0 -3 SLIP 10 INCHES  2.0  3.0  Figure 2.5: Nilson's Bond Stress-Slip Curves (Tanner's Tests [33])  Chapter 2. Literature Survey^  21  and the maximum limiting value of bond stress was  u < (1.43c + 1.5) L'  (2.9)  wh ere  Li^the concrete strength in p.si c = the distance from the loaded end in inches Nilson's work definitely confirmed the original thought of Mylrea [16] that bond stress at any point is a function of slip at that point and that the bond slip curve at any particular point along the bar cannot be used to represent the bond slip behaviour at any other point along the embedment length. However, Nilson's equations do not consider other important variables such as the bar diameter, confining pressure, and so on. Further, the computation of the slip was based on concrete deformation measured by internal embedded gauges. Due to the possibility of internal cracking in the concrete surrounding the rebar over the gauge length, the results obtained might be doubtful. Houde [35] carried out a series of tests in which the end slips, elongations of the embedded bars, and crack formations were studied. He reported that the slip was due to gradual deterioration of the concrete in front of the ribs of the reinforcing bai as a result of high bearing and shearing stresses. Since no evidence of crushing of the concrete near the ribs was observed in the sliced specimens, he concluded that the slip at the interface could be explained entirely by the bending of the comb-like structures of the concrete surrounding the reinforcing bar. Based on the experimental results, he reported that the maximum value of bond stress at the steel-concrete interface occurred at a slip of 0.03  Chapter 2. Literature Survey^  711,711-  22  1.Tp to the peak bond value, the following local bond stress-slip relationship was  proposed in the form of a polynomial:  u = 1.95 x 10 6 s — 2.35 x 10 9 s 2 + 1.39 x 10 12 5 3 — 0.33 x 10 15 s 4^(2.10) where u = local bond stress in psi  s = local bond slip in inches The bond stress-slip relationship curve is shown in Fig. 2.6. The bond stress-slip behaviour beyond the peak value was found to be dependent on the distance from the end face. The above equation also does not consider other important variables such as the bar diameter, confining pressure, and so on.  2.1.2.2 Summary  A brief summary of the notable findings regarding flexural bond stress under static loading can be summarized as follows:  1. Using classical beam theory, it was assumed that the bond stress was a function of shear force alone. This was in contradiction to the experimental evidence. 2. For most cases the bond stress-slip relationship was nonlinear. :3. The mechanism of bond failure was primarily due to cracking, inelastic deformation and failure in a relatively thin layer of the concrete adjacent to the steel-concrete  Chapter 2. Literature Survey^  23  0^2^4^6^8^10^12^14^16 Slip x 10-4  (  ^  18  in )  Figure 2.6: Unit Bond Stress versus Unit Slip Curves (after Houde [35])  Chapter 2. Literature Survey^  24  interface. 4. The bond stress depended upon the level of stress in steel. To evaluate the amount of bond stress being developed over the embedded length, it was essential to determine the exact stress developed in the reinforcing bar at each point over this length for a given load. 5. The distribution of bond stress along the length of the rebar was very irregular and depended, among other factors, upon the location of the cracks and the ratio of cross-section area of steel and concrete; the simplifying assumptions regarding the distribution of bond stresses were not realistic. 6. The bond stress-slip relationship should be established between local values of bond stress and bond slip. 7. The development of bond stress was closely related to the slip occurring at the interface between steel and concrete. This relationship was considered to be of vital importance and could be made a basis for comparison of the influence of various factors on bond stress. 8. The bond stress-slip relationship was found to be linear up to about three fourths of the maximum bond stress. 9. The bond stress-slip relationship was time dependent.  25  Chapter 2. Literature Survey^  2.1.3 Anchorage Bond Under Static Loading  2.1.3.1 Experimental Investigation  The anchorage of reinforcing steel in concrete is fundamental to the whole idea of reinforced concrete. That is why a vast literature on anchorage bond can be found, dealing with pull-out tests of reinforcing bars embedded in concrete. Originally, the purpose of such tests was to determine the required length of embedment necessary for full development of the capacity of the reinforcing bar. Important contributions based on pull-out test were due to Abrams [11], Richart and Jensen [36], Menzel [37], Gilkey, Chamberlin and Beal [38], Watstein and Seese [39], Clark [40], Mylrea [16], Mains [19], Konyi [41], Matyey and Watstein [42], Ferguson and Thompson [22, 23], Lutz and Gergely [27], Nilson [31, 32, 34], and many others. Fig. 2.7 shows some types of specimens that were used for anchorage bond tests. Those test specimens can be classified as:  1. short embedment length (such as Type A) or long embedment length (such as Type B^E); 2. concrete stress in axial direction (such as Type A ti D), compression (such as Type A, B and E) or tension (such as Type C and D); 3. centric loading (such as Type A ti D) or eccentric loading (such as Type E); 4. reinforcement loaded on one side (such as Type A as Type  In .  ti  C and E) or two sides (such  Chapter 2. Literature Survey ^  26  Figure 2.7: Some Typical Anchorage Bond Test (After Vos and Reinhardt [43])  Chapter 2. Literature Survey^  27  Rehm [44] described pull-out tests which were performed on deformed bars provided with a single rib each or plain round bars with very small lengths of embedment. He argued that if greater lengths of embedment were used in the pullout tests, then it was usually possible to determine only the relationship between the tensile force applied to the test specimen and the amount of the slip at the end of the specimen. Such a relationship could not be applied to local conditions along the length of the bar. However, a relationship of this kind was considered to be useful for calculating in advance the distribution of steel stresses and the distribution of slip resistance for any length of embedment of the reinforcing bar. Bernander [45] investigated pull-out specimens which were long in comparison with the expected effective anchorage length. A long specimen length was used to permit a study of the bond stress distribution and its dependence on factors such as steel stress, type and spacing of ribs, diameter of the rebar and concrete strength. Strain gauges were placed along the rebar to measure the strain in steel. The distribution of steel stress along the rebar was found from these strain measurements. The bond stress distribution, the necessary development length, and the total elongation of the rebar within the pull-out specimen were then found from the steel stress distribution curves. In most of these tests bond failure appeared to take place when the steel started yielding. After the ultimate bond stress had been reached, the bond stress decreased with a further increase in load. These tests revealed that both the rib pattern and the concrete strength affected the magnitude of bond stress while the diameter of the bar had no significant effect. Bernander found that the steel stresses along ribbed bars were distributed almost parabolically. Tassios and Koroneos [46] used an overall optical method (the differential Nloir6  98  Chapter 2. Literature Survey^  method) to visualize the full field of stresses, strains and slips at the interface between concrete and steel tensioned from outside. The interface was simultaneously loaded in the transverse direction by a compressive force. From the induced mechanical interference pattern between a 20 line per mm. grating glued on the specimens, and an external (underformed) grating, the longitudinal displacement, s  ,  was determined at grid points  on the interface. Similarly, the steel strains were determined, allowing for steel stress evaluation. Consequently, by differentiation of the stress diagrams of the steel, the local bond stress,  7,  was evaluated. By compilation of coupled  7  and s values, a local-bond  versus local-slip curve was determined which constituted a basic tool for the analytical treatment of a series of bond degradation problems. .Jiang, Shah and Andonian [47] carried an experimental and analytical investigation to study the characteristics of bond transfer in reinforced concrete flexural members. They developed a new type of test specimen to facilitate the measurements of local slip, secondary cracking, and strain distribution in concrete surrounding the interface. For this specimen, a. reinforcing bar was split into two halves and embedded in opposite sides of the cross section (see Fig. 2.8). A comparison of results from these types of specimens with those from the more common tests showed that many of the important aspects of bond transfer phenomena were identical. They performed an axisymmetrical finite element analysis to predict secondary cracking. Then a simple one-dimensional analysis was developed to predict stresses in steel and concrete, local bond-slip relationships, tensile stiffening and total elongation of the reinforcing bar. Abrishami and Mitchell [48] presented a new testing technique for pull-out tests, which simulated uniform bond stress distribution along a reinforcing bar. Their method enabled determination of the complete bond stress-slip response and investigation of  29  Chapter 2. Literature Survey^  P/2 P  Type  C  ^ State of Stress at State of stress at ^ A, M' and N' N and tr  Figure 2.8: Three Types of Transfer Pull-out Test Specimens (after Shah et al [47])  Chapter 2. Literature Survey^  30  both pull-out and splitting failure. They cast the test specimens with a pre-tensioned reinforcing bar which was instrumented with strain gauges. By applying different loads to each end of the rebar a linear variation in axial stresses in the bar could be achieved (see Fig. 2.9), and hence a uniformly distributed bond stress was produced. They used this testing technique to investigate the bond performance of reinforcing bars and the influence of concrete strength and the presence of an epoxy coating. The test results showed that for uniform bond stress the splitting type of failure seemed more ductile than the pull-out type. Robins and Standish [49] modified the two common bond tests, the cube pull-out and the semi-beam tests so that lateral pressure could be applied to the bond specimens to investigate their effects on the bond behaviour. The major variables studied were the magnitude of the lateral pressure, the bar diameter, the length of embedment and the concrete strength. The results of over 200 bond tests showed that lateral pressure can considerably increase bond strength. However, the increased capacity, if it occurs, was achieved in different ways for smooth and deformed bars. For smooth bars the application of lateral pressure resulted in an increase in frictional effect at the bar-matrix interface, and the pull-out load could increase up to 250%. For deformed bars, a low lateral pressure could not prevent splitting or bursting failure, while a greater lateral pressure produced relatively small increases in bond strength, and a shearing-type bond failure was observed. The corresponding increase was about 75% for deformed bars. The difference in bond behaviour was reflected in the theoretical work by a frictional bond strength criterion for smooth bars and a splitting or shearing criterion for deformed bars.  31  Chapter 2. Literature Survey^  ;VA.  • (b) Cast concrete^(c) Initial bar stress  (a) Initial stress  P,  P, P. • AP, P,JA.  P.  Figure 2.9: Testing Technique for Simulating Uniform Bond Stress (after Abrishami and Mitchell [48])  Chapter 2. Literature Survey  ^  32  2.1.3.2 Summary  A briefly summary of these pull out investigations is as follows: -  1. A reasonable measure of the anchorage length of a bar embedded in concrete could be obtained from the pull-out test. 9.  The pull-out tests emphasized the need for a particular length of bar (anchorage length) from the point of maximum tensile stress to avoid pull-out.  3. The pull-out tests provided an approximate indication of what happened adjacent to any crack in the concrete. 4. The drawback of the pull-out test as a standard was that the compressive stress in the concrete complicated the stress conditions and inhibited tension cracking in the con crete.  2.1.4 Bond Tests with Fiber Reinforced Concrete or Coated Rebars  The use of short, randomly distributed fibers in concrete is relatively recent. The role of these fibers in improving the crack resistance and the "ductility" of concrete has recently been reviewed (Bentur and Mindess [50]). Considerable research has been carried out in the last two decades to evaluate the response of these fiber reinforced composites, including the bond behaviour between the steel bar and fiber reinforced concrete matrix. Swamy and Al-Noori [51] were the first to report improved performance in the anchorage bond of deformed bars embedded in steel fibre reinforced concrete. Their experimental work consisted of pull-out tests on steel-fiber reinforced specimens. The steel fibers  Chapter 2. Literature Survey^  33  used were of the round straight type and had a length of 25 mm (or 50 mm) and a diameter of 0.40 mm. (or 0.50 mm). Two different fiber contents, 3.5% and 7.0% (by volume) were used. Based on the bond stress-slip relationship, they found that the anchorage bond strength of fibre reinforced concrete was 40% higher than that for plain concrete. Further, the mode of failure was found to be different in the two cases. The plain concrete specimens showed greater cracking and wider cracks than the fiber reinforced ones. The failure in the latter case was observed to take place more gradually. Yerex, Wenzel and Davies [52] carried out two series of tests to investigate the effects of polypropylene fiber reinforcement on the bond between concrete and conventional mild steel reinforcement. The first series of tests investigated the differences in the bond stressslip relationship using the ASTM Standard Test Method (ASTM C234-71), whereas the second series of tests was designed to indicate changes in the transfer length of the several different concrete mixes and mild reinforcement combinations. Two polypropylene fiber lengths (60 and 90 mm), four fiber contents (0, 0.014, 0.050 and 0.086 /b/ft 3 ) 2 , and two water-cement ratio (0.44 and 0.65) were used. The results showed that the addition of polypropylene fiber reinforcement does not adversely affected the bond strength and that neither increasing the fiber content in the mix nor increasing the fiber length improved performance with regard to bond strength or transfer length. Recently, epoxy-coated reinforcing bars have been used in the construction of some concrete structures which are expected to be exposed to corrosive conditions. An important consideration in the use of epoxy-coated reinforcing bars is the effect of the epoxy coating on the strength of the bond between the reinforcing bar and the concrete. Clifton and Matey [53] carried out a series of pull-out tests with nine different epoxy coatings 'They are equivalent to 0%, 0.025%, 0.09% and 0.15% (by volume), respectively.  Chapter 2. Literature Survey^  :34  and one polyvinyl chloride coating. In the tests, increasingly higher loads were applied to reinforcing bars embedded in concrete until the bond strength between the bar and the concrete was exceeded. The results indicated that certain epoxy-coated reinforcing bars could have satisfactory bond strengths. More recently, Treece and .Jirsa [54] reported the results of their study on the bond of epoxy coated reinforcing steel. The influence of bar size, concrete strength, casting position, and epoxy coating thickness on bond was considered. These tests were performed on two sizes of beams, using an inverted third-point loading. Reinforcement was spliced in the constant moment region at midspan. It was reported that in the series in which the steel did not yield, epoxy coated reinforcement developed only 66 % of the bond stress developed in uncoated steel. Cracks widths were greater in the specimens with coated bars than in those with uncoated bars. The specimens with epoxy coated rebars had fewer cracks than those with uncoated rebars. Cleary and Ramirez [55] studied the bond of epoxy coated reinforcement in slab-type members. Tests were conducted on four series of specimens. All reinforcement came from the same heat and had a spiral deformation pattern. The thickness of epoxy coating was about 9.0 mil. The specimens were loaded in an inverted third-point loading with a 1.2 in, shear span and a 1.2 in constant moment region. Their study found bond ratios (the ratio of the bond stress in coated steel to that in uncoated steel) to vary from 0.82 to 0.95. Wider cracks were found. They concluded that if the hypothesis of increased rib bearing forces with epoxy coated reinforcement was correct, it was likely that splitting could occur with epoxy coated bars at cover-to-bar diameter ratios greater than 3, which has recently been suggested in the ACI Building Code [7].  (liapter 2. Literature Survey^  35  2.2 Bond Behaviour under Dynamic Loading  2.2.1 Bond Behaviour Under Cyclic Loading  Studies of repeated (or cyclic) bond tests are relatively more recent (after 1970). Takeda, Sozen and Nilson [56] were among the first to investigate the response of reinforced concrete to simulated earthquakes. They observed that the stiffness and the energy absorbing capacity of the reinforced concrete test specimens changed considerably throughout the duration of the simulated earthquakes. Important contributions based on pull-out tests under cyclic loadings were made by Hassan and Hawkins [57], Viwathanatepa, Popov and Bertero [58], Hungspreug [59], and many others. In 1973, Morita and Kaku [60] reported on the effect of the load history on the local bond stress-slip relationship from push-in and pull-out tests of specimens having the reinforcing bar bonded to the concrete over a short length. They concluded that the deterioration of local bond depends on the magnitude of the previous maximum local slip; the larger the previous slip the greater the reduction in bond stress at lower levels. They also proposed a model for a local bond stress-slip law, based on which the applied load versus deformation characteristics of reinforced members could be predicted. However, the application of a single bond stress-slip law for every point along an anchorage length seemed to be a handicap to the model. Rehm and Eligehausen [61] tested the influence of repeated loading on deformed bars with a diameter of 14 nim and an embedment length of 42 mm (three times the diameter). Their conclusion was that repeated loads affected the bond in much the same way as the deformation and failure behaviour of unreinforced concrete; they also accelerated the  Chapter 2. Literature Survey^  36  deformations as compared with a. sustained load. Edwards and Yannopoulus [62] also tested the influence of repeated loading. They tested deformed bars of d = 16 mm with an embedment length of 2.4 d. They concluded that the effectiveness of bond depended mainly upon the given stress level and the magnitude of the previous peak stress, and to a lesser extent upon the number of cycles. The bond stress-slip curves under repeated loading were characterized by residual slip at zero load and hysteresis loops formed by the loading and unloading paths. The hysteresis loops shifted by a. small amount during each cycle, but this shift tended to diminish with the number of cycles applied. Perry and Jundi [63] tested, by repeated loading, on eccentric pull-out specimens, the distribution of bond stresses along a deformed bar of d = 25 mm. Their conclusion was that the peak bond stresses tended to shift from the loaded end of the specimen to the unloaded end as the number of cycles of loading and unloading increased. This redistribution of stresses tended to become stabilized after several hundred cycles. This was contrary to what Rehm [61] had calculated from his short embedment length tests; from his results he concluded that this redistribution of stresses would not become stabilized before a. million cycles. Panda. [64], and Spencer, Panda and Mindess [65] studied the effect of reversed cyclic loading on the bond of deformed bars in plain and SFRC (steel fibre reinforced concrete), and also the cracking in the concrete surrounding the reinforcing bar. They found that:  1. The mode of failure and the behaviour for plain and SFRC specimens appeared to be different. SFRC specimens exhibited greater resistance to crack formation and propagation than the plain concrete ones.  Chapter 2. Literature Survey^  37  2. No significant decrease in bond stress was observed with a small increase in the number of cycles under a. constant stress level, while an increase in peak stress level produced a significant reduction in bond stress in subsequent cycles. 3. Under reversed cyclic loading with only a few loading cycles, the anchorage bond strength of deformed bars was found to be about 20% to 30% higher in steel fibre reinforced concrete than in plain concrete.  In his later research work, Panda found [66] that:  1. The loading history had a significant effect on the bond deterioration. 2. The specimens with steel fibers exhibited much better anchorage bond characteristics than those with no fibers. The steel fibers were found to be effective in retarding the rate of bond degradation under multiple cycles of reversed loading. 3. The surface condition of the rebar had a vital influence on the bond behaviour: the presence of grease on the reinforcing bar reduced the bond effectiveness drastically. 4. An internal diagonal crack could initiate in the concrete at a very low level of the applied stress. This cracking caused a reduction in stiffness of the concrete surrounding the reinforcing bar.  In the "State-of-Art-Report: Bond under Cyclic Loads" by ACI Committee 408 [67], the main factors affecting bond behaviour under cyclic loads are considered to be:  1. Concrete compressive strength  Chapter 2. Literature Survey^  38  2. ('over and bar spacing 3. Bar size 4. Anchorage length 5. Rib Geometry 6. Steel yield strength 7. Amount and position of transverse steel 8. Casting position, vibration, and revibration 9. Strain (or stress) range 10. Type and rate of loading 11. Temperature 12. Surface condition (coatings)  All parameters that are of importance under monotonic loading are also of importance under cyclic loading. In addition, however, bond stress range, type of loading (unidirectional or reversed, strain or load controlled), and maximum imposed bond stress are of great importance under cyclic loads. The bond behaviour under the high-cycle fatigue loading is different from the low-cycle loading. Under low-cycle loading, the various observations can be summarized as follows:  1. The higher the load amplitude, the larger the additional slip, especially after the first cycle. Some permanent damage seems to occur if 60% to 70% of the static bond capacity is reached.  Chapter 2. Literature Survey^  39  2. When loading a bar to an arbitrary bond stress or slip value below the damage threshold (about 60% of ultimate) and unloading to zero, the monotonic stress slip relationship for all practical purposes can be attained again during unloading. This behaviour also occurs for a large number of loadings, provided that no bond failure occurs during cyclic loadings. 3. Loading a bar to a bond stress higher than 80% of its ultimate bond strength will result in significant permanent slip. Loading beyond the slip corresponding to the ultimate bond strength results in large loss of stiffness and bond strength. 4. Bond deterioration under large stress ranges (greater than 50% of ultimate bond strength) cannot be prevented, except by the use of very long anchorage lengths and substantial transverse reinforcement. Even in this case, bond damage near the most highly stressed area cannot be totally eliminated.  2.2.2 Bond Behaviour Under Impact Loading  While there is an extensive literature on static bond tests, there is little experimental work on the bond between concrete and steel reinforcement under dynamic loading, with rather contradictory results (Mindess [14]). Concrete is a strain rate sensitive material. Generally its strength (compressive, tensile. flexural and shear strength) increases with higher loading rates, especially under impact loading (Mindess et al [68, 69, 70]). Since the bond strength depends, to a great extent, upon the strength of the concrete surrounding the rebar, the loading rate should have a considerable effect on the bond behaviour. Also, there is some indication that crack velocities in concrete are proportional to the rate of loading (Mindess [71], Shah  chapter 2. Literature Survey ^  40  [72]). On the other hand, the presence of reinforcement, either in the form of fibers or of continuous bars tends to reduce the crack velocity (Mindess [73]), which, in turn, improves the bond strength. The effects of loading rate on the bond behaviour involve complex mechanisms. Test techniques for high rates of loading are far more difficult than static testing (Bentur et al [74]). Hansen and Liepins [75] were the first to study the behaviour of bond under impact loading. They tested deformed bars under static and impact loading under conditions in which splitting failures were inhibited. They used bars of d = 12.5 mm with an embedment length of 4d. The minimum raise time of the load was about 10 20 ms. The tests showed that the local static bond strengths might be as high as 0.75 L.', but that under single pulse dynamic loading at high strain rates this strength increases to j; (cylinder strength). They concluded that for all practical lengths of embedment of bars, steel failure might be expected under both static and dynamic loading. Bars loaded dynamically would carry a larger load than bars loaded statically. They ascertained that this increase in carrying capacity was due solely to the increase in steel strength under dynamic loading. In 1976 Hjorth [76] published the results of pull-out tests under impact loading. He tested the bond resistance of plain and deformed bars of d = 16 mm, with an embedment length varying from 16 to 160 mm, i.e., 1 10 d. The dimensions of the test specimens are shown in Fig. 2.10 He used an electro-hydraulic loading system with load control and varied the time to failure from 500 s to 5 ms. The compressive strength of the concrete was 24  ti  29 MPa. Because of the relatively high ratio of the wavelength of the  loading pulse (about 100 m, see Fig. 2.11) to specimen size (0.1 ,-- 0.2 m) a quasi-static approximation of the result was justified.  Chapter 2. Literature Survey^  41  concrete cilinder  Figure 2.10: Pull-out Specimens for Impact Test (after Hjorth [76])  1 \^1 5  )  / 20 / t(rris)  Figure 2.11: Loading Pulse of Hjorth's Impact Test [76]  Chapter 2. Literature Survey^  42  He studied the following:  1. The influence of the bond stress rate -i on the maximum bond resistance; -  2. The influence of increasing loading rate on the local bond stress-slip relationship: 3. The maximum bond resistance if a connective constant loading (see Fig. 2.12) acts for a time t d and 4. The influence of increasing loading rate on the bond stress distribution.  In the case of plain bars he found scarcely any influence of the loading rate. This contrasted with deformed bars, for which he found a significant influence of the loading rate. Some results for deformed bars are shown in Fig. 2.13. For both small and large displacements, bond resistance increased with increasing loading rate. This was in good agreement with the influence of the loading rate on the concrete compressive strength. For this reason Hjorth explained the influence of the loading rate on bond resistance in terms of the deformation behaviour of the concrete under the ribs. In Fig. 2.14, a typical bond stress-slip relationship is given, at different loading rates; note that the displacements are on a logarithmic scale. Hjorth remarked that the curve tended to undergo a parallel shift with increasing loading rate. A great difficulty, however. in the interpretation of his results was the rather wide scatter. An important conclusion was that the bond resistance increased by about 30% in a test with a loading time of 5 ins; this decreased to about only 10% if a connective constant loading also acted for 10 ins (see Fig. 2.12).  43  Chapter 2. Literature Survey^  2  tdyn istat  1  dyn stat 2-1  failure  failure 1^1^1  5^10^15 t (ms)  5^10^15 t(ms)  Figure 2.12: Influence of a Connective Constant Loading of 10 ms on the Bond Resistance (after Hjorth [76])  m ax tf c ■^■ ■ 1^ a 0. 5^ ■^■ ■ ■^a a^■^ ■ s^III^ 0 4^ 3^  ■  IN1  B St 42/50 RK, d=16 mm lv=112mm 02^  01 ) io-5^10-`^10-3^10 -2^101^10 0^1C t (1•1/m m 2 ms)  Figure 2.13: Influence of the Loading Rate on the Bond Resistance (after Hjorth [76])  Chapter 2. Literature Survey^  0.6  44  t/fc B St^42/50 RK, c1=16  Q5 0.4  I  I v =112mm I  I  .--t> 50 N/mm 2 ms ---t<0.5 N/mm 2 ms  / /  0.3 0.2 0.1 0  ...i/  0.01  .■  IP  fR.0079  ^ ^ 1 0.1  10 6(mm)  Figure 2.14: Influence of the Loading Rate on the Bond Stress-Slip Relationship (after Hjorth [76]) He also tested two specimens with an embedment length of 48 cm, with a rise time of the load of 50 ms. The steel stresses were measured with 8 strain gauges which were mounted on the bar. From these tests Hjorth concluded that the displacements of the bar decreased with increasing loading rate, but a fundamentally different bond stress distribution was not found. The results of the above investigations were in reasonable agreement with the results of Hansen and Liepins [75].^  -  Vos and Reinhardt [77] carried out a series of bond tests under impact loading. They developed a test specimen in which a central reinforcing bar was embedded over a length of 30 mm. Both smooth and deformed bars had a diameter of 10 mm, and the concrete had several compressive strengths (23, 45 and 55 Mpa). The impact tests were carried out using the "Split Hopkinson Bar" equipment. In these tests failure was reached in  Chapter 2. Literature Survey^  less than 10' second (1  ins).  45  To have a reference for these results, static tests were also  carried out using electro-hydraulic testing equipment with load control. In these tests, failure was reached in about :300 ms and 60 sec, respectively. It was found that for smooth bars, the loading rate had no particular effect on the maximum bond resistance or the shape of the bond stress vs. displacement relationships. However, for deformed bars, bond resistance increased markedly with the loading rate. The following expression was obtained from a statistical analysis of the data:  Tdyn^(Tdyn  0.7(1-2.56)  (f c )0.8  Tstat^Tstat  (2.11)  Where  Tdyn =  Tstat  bond stress under dynamic loading  = bond stress under static loading  Td yn =  bond stress rate under dynamic loading  Tstat —  bond stress rate under static loading  = local relative displacement of the reinforcing element = compressive strength of concrete They concluded that the influence of the loading rate on the bond resistance of deformed bars must be explained in terms of the shearing mechanism causing the bond forces, i.e., for deformed bars failure was due to the local crushing of the concrete by the bar deformations. In this mechanism the concrete strength and stiffness were important  Chapter 2. Literature Survey^  46  parameters. The results of the short embedment tests were translated to a long embedment length. The conclusion reached was that for increasing loading rates, the stiffness of the disturbed zone increased was reached. Takeda [78] found that the strain rate sensitivity of concrete led to two different effects: on the stress-strain relationships, and on the fracture criterion. The distributed area of strain was much narrower under dynamic loading than under static loading. This could cause brittle fracture of the reinforcement in reinforced concrete structures, because the deformation was limited to only a short length of the reinforcing bars. Indeed, Bentur, Mindess and Banthia [79] and Banthia [80] showed that, under certain circumstances, the steel reinforcement itself might fail under impact loading of reinforced concrete beams. The enhanced concrete-steel bond limited the deformations to the small area under the point of impact, leading to ductile fracture of the steel. According to Mindess [14, 81], the bond strength appears to be strain-rate sensitive. However, dynamic (impact) loading cannot be considered simply as an extreme case of high stress rate application, in part because the complex energy transfer mechanisms associated with impact loading appeared to be different from those under normal, static loading. Thus, it is not possible to predict the behaviour of concrete under impact loading on the base of quasi-static tests. No further investigations on pull-out tests on plain and deformed bars with a short embedment length at high rates of loading have been found in the literature.  Chapter 2. Literature Survey  ^  47  2.2.3 Summary  Some important conclusions could be drawn from the literature reviewed that dealing with bond behaviour under dynamic loading:  1. The bond behaviour under dynamic loading was quite different from that under static loading. Both loading history and loading rate had significant effects on the bond behaviour. While cyclic loading might cause a much greater reduction in bond strength than monotonic loading, impact loading might increase bond strength over that of static loading. 2. The loss in bond resistance under cyclic loading was due to a deterioration in the stress transfer mechanism, caused by inelastic deformation, cracking in the concrete etc. 3. The shearing mechanism (rib bearing against the concrete) was the main mechanism for deformed bars. The increases in the strengths of both steel and concrete with an increase in loading rate may contribute to the higher bond resistance under impact loading. 4. The strain distribution along the reinforcing bar was the most important parameter for understanding the bond phenomenon. Dynamic loading caused much more complicated strain distribution than did static loading. 5. The specimens with steel fibers exhibited much better anchorage bond characteristics than those with no fibers. This was true for all types of dynamic loading. The energy absorbing capacity of a specimen was more than doubled when it contained steel fibers.  Chapter 2. Literature Survey^  48  6. One of the most important advantages of steel fibers was the increase of resistance to crack formation and crack propagation. Unfortunately, adding steel fibers to the concrete complicated the study of the bond mechanism. 7. An analytical study would be helpful for a better understanding of the bond behaviour under dynamic loading.  2.3 Analytical Investigation of Bond Behaviour  2.3.1 Introduction  The extensive experimental investigations undertaken to study the bond behaviour and the stresses produced clue to bond under different loading condition have been reviewed in the previous sections. In these investigations stresses in the bars and in the concrete were found by means of strain gauges mounted on the reinforcement and on the concrete surface, respectively. Bond stresses were obtained from the difference in adjacent strain readings or from the slopes of the steel stress curves and, therefore, many strain gauges and good control of variability were necessary to obtain bond stress values. Concrete stresses could only be obtained at some distance from the reinforcing bar and a concrete stress distribution had to be assumed in order to calculate the concrete stresses or displacements at the interface. The uncertain location of cracks made the experimentation difficult. Most of the time concrete deformations were averaged over a certain gauge length which could include many transverse cracks. The relative displacements at the interface between steel and concrete were derived either from measurements at the end of the test specimen or by indirect means.  Chapter 2. Literature Survey^  49  In spite of much useful information obtained from these investigations, there are still many unanswered questions. Since there are so many variables which affect bond behaviour, it is difficult to consider all or even a majority of them in any one experimental program. The correlation of data for predicting bond behaviour from different experimental investigations is also questionable, because of the variable nature of concrete behaviour. Efforts have thus been directed towards finding a solution to the problem on theoretical and analytical bases.  2.3.2 Theoretical Work  Rehm [82] treated the question of bond deformation theoretically by considering a non-linear bond stress-slip relationship determined from the experimental phase of his investigation [44]. He concluded, on the basis of experimental work, that a bond depended upon the rib height, the spacing and the bar size. Two of the formulae he developed were 7G  = FR43.A'C"^  (2.12)  and  d2z  dX 2  = OA'  (2.13)  where T G is the bond stress,^is the slip of steel with respect to concrete on the interface, and C' is the compressive strength of concrete; the other parameters,  FR, 43  ',  o and k were determined either by the geometrical and mechanical properties of test specimens, or by a statistical analysis of the experimental data. The above "fundamental law" of bond and the differential equation of slip were used  Chapter 2. Literature Survey^  50  to determine the distribution of slip, the steel stress, and the bond stress along the rebar. It was concluded that the greatest value of slip resistance, in the case of deformed bars, was determined by the shear strength of the concrete. It was also demonstrated by this analysis that if the fundamental law of bond was known the distribution of the displacements and the stresses in a member could be predicted in advance. Odman [83] presented a theoretical interpretation of the results obtained by .Jonsson [84] from tests on concrete prisms provided with central reinforcement and subjected to tension. Jonsson had indicated that bond stress was a function of slip. Odman derived a formula expressing the crack width as a function of the steel stresses. The differential equation of slip was  d2(x  )^  ,E 0  dx 2^EsAs  (1 + np) T(x) ^  (2.14)  where x is the distance from the point of zero slip, (x) is the relative slip of the section at x, and r(s) is the bond stress at the section considered; other parameters in the above equation are the geometrical and mechanical properties of the test specimens. Eq. 2.14 was derived on the assumption that the bond stress was a function of slip alone. But, as was pointed out by Kuuskoski [85], the bond stresses depended also on the level of steel stress, the embedment length, the diameter of the rebar, the ratio of reinforcement, the concrete strength, etc. The theoretically obtained values of slip and steel stress at a crack were compared with the experimental values of .Jonsson. The agreement between them was found to be closer for smooth bars than deformed ones.  Chapter 2. Literature Survey^  51  Brows [86] presented a two dimensional stress analysis of reinforced concrete members by modelling the behaviour of tension and flexural members. This analysis was based upon the assumption that the force transmitted from the reinforcement to the concrete could be represented as loading on the end faces of the concrete element be-  tween two adjacent primary cracks. In this manner, the reinforcement was removed from further considerations and the concrete was treated as a homogeneous and isotropic elastic medium. Results showed that high tensile stress in the concrete occurred in the area. between two adjacent tensile cracks.  2.3.3 Fracture Mechanics and the Finite Element Method  In addition to the theoretical investigations described above, some other analytical approaches using Fracture Mechanics and the Finite Element Method have been developed over the past two decades. These approaches can be used to determine, more accurately, quickly and economically, the internal stress distributions in the reinforcement and the concrete. The introduction of fracture mechanics to the analysis of bond behaviour helps to understand the physical phenomena occurring at and around the reinforcing bar. This has been made possible by the development of high speed digital computers. Bresler and Bertero [87] carried out analytical investigations of a cylindrical specimen. This model was selected to simulate the tensile region of a cracked flexural member. The finite element analysis was carried out using two different models: a linear elastic model, and a modified "boundary layer" model. In the modified model the effects of inelastic deformations and fracture of concrete adjacent to the concrete-steel interface were studied by considering a "homogenized boundary layer" in which the elastic constant for the material was reduced. In both models, it was assumed that:  Chapter 2. Literature Survey^  52  1. No slip occurred at the interface; and 2. Only the tensile load applied to the rebar was considered.  Results obtained included the distribution of displacements, the longitudinal, transverse, and circumferential stresses and also the principal stresses. It was revealed that a high local stress existed at the steel-concrete interface near the end of the concrete prism. The high intensity of this stress, even at a low level of steel stress, would cause local fracture and inelastic deformation. The boundary layer solution indicated that slip occurs at the interface and should be considered in analysis, contrary to the assumption above. Lutz [27] made use of an axisymmetric finite element to study the stresses and deformations that occur in the vicinity of reinforcing bars after transverse cracks have formed. A short cylinder of concrete containing a concentric bar, in which both ends of the steel were given a uniform deformation, was used to model the conditions between two flexural cracks. The anchorage zone stress and deformation situation was modelled by a longer cylinder in which one end of the bar was given a uniform displacement while the cylinder was held along its outer cylindrical surface. The flexural zone stresses were calculated under many different circumstances: before or after cracking, allowing slip or separation, and so on. The stresses before cracking were quite small and of a uniform nature. The formation of cracks produced large changes in these stresses. High bond stresses and tensile adhesive stresses were observed near the transverse cracks in the perfect bond base. The magnitudes were such that separation of the concrete from the steel occurred over a length about two to three times the diameter of the bar from the face of the cracks. Due  Chapter 2. Literature Survey^  53  to the inclination of the ribs, this separation caused some slip to occur and produced high circumferential tensile stresses in the concrete near the transverse cracks. The circumferential stresses were more than enough to initiate splitting cracks. For the analysis allowing slip and separation it was observed that the occurrence of slip modified the stress distributions to a significant extent. It relieved the bond stress which produced stress concentrations near the transverse cracks. The analyses were conducted on the following three models to represent different conditions in the anchorage zone:  1. There was perfect bond between the steel and the concrete; 2. There was separation of the steel and concrete until the tensile adhesive stress became zero; and 3. An experimental bond stress-slip relationship base on single rib tests by Lutz [27] was used.  The first elastic solution showed that very large adhesive stresses were required to prevent separation at the interface near the loaded end. Thus, separation would occur at small loads. In the second solution separation over a distance two and half times the bar diameter was permitted. It was discovered that the bond stress and the circumferential stress were exceptionally high. The third solution implied that the slip caused a significant reduction in the stress concentration near the loaded face. The loaded end slips obtained from this solution compared well with the experimental results. Gergely, Gerstle and Ingraffea, [88] and Gergely, Ingraffea, Gerstle and Saouma [89] used linear elastic fracture mechanics principles to determine cracking behaviour at the  Chapter 2. Literature Survey^  54  steel-concrete interface. They found that this approach was inadequate when the analytical results were compared with experimental data. They focused on radial, secondary cracking and found that this cracking did not follow the principles of linear elastic fracture mechanics. Subsequently, nonlinear fracture mechanics theories were used. They modelled the stresses acting between the sides of the crack through the use of interface elements. These elements were automatically inserted as the crack tip advanced in the process of finite element analysis. The stiffnesses of the interface elements were changed in each iteration according to a stress-COD (crack opening displacement) law which was programmed. Finally, a "tension-softening" finite element was proposed. This element lumped all bond-slip behaviour into a single nonlinear finite element. It provided a significant simplification in the finite element modelling of bond-slip in reinforced concrete. Yankelesky [90] presented a new model for bond action between uncracked concrete and a deformed bar. Concrete resistance was provided by a. mechanical system which consisted of inclined compressive disc elements normal to the bar axis, as shown in Fig. 2.15 and longitudinal tensile members. The kinematics of the system was analyzed, yielding a second order differential equation with the bar tensile force as the variable. The solution showed an exponential decay in the stress and strain in the steel bar, approaching a constant value which depended on the relative stiffnesses of the concrete and the steel. Coefficients were then analytically calculated as a function of geometric and mechanical properties. Stress and strain distributions in the steel bar were calculated and the results were compared with the test data. He found good correspondence between measured and calculated strain distributions along the steel bar at stresses below 160 MPa. At higher stresses, calculations predicted a sharper decay in stress than that measured. He concluded that this discrepancy might result from the initiation of internal cracks and secondary cracks which reduced system stiffness.  Chapter 2. Literature Survey^  55  In another paper [91] Yankelevsky proposed a new finite element for bond-slip analysis. This was a one-dimensional model which was based on equilibrium, and the local bond stress-slip law was developed (see Fig. 2.16). The relationship between the axial force and the slip at the element node was expressed through a stiffness matrix. The global stiffness matrix was then assembled, and the solution yielded the slip, strain and stress distributions along the steel bar. The nonlinear bond stress-slip relationship led to an iterative technique which was found to converge rapidly. The predictions were compared with experimental results of monotonic and push-pull tests, and a very good correspondence was found. heuser and Mehlhorn [92] compared different approaches for bond modelling between concrete and reinforcement using the finite element method. They indicated that special interface elements were required for solving this problem. The behaviour of the elements and the quality of the results were influenced mainly by the displacement function of the elements, the density of the element mesh, and the bond stress-slip relationship. They investigated the influence of the displacement functions of two interface elements, the Bond-Link-Element and the Contact-Element (see Fig. 2.17), not only by finite element calculations but also by energy considerations. They demonstrated the superiority of a continuous bond slip function to the bond link element. It was shown that a realistic analytical bond model required the consideration of local influences. An average bond stress-slip relationship was not suited for a detailed analysis. Rots [93] introduced a 6-noded bond-slip element including the rebar (see Fig. 2.18). The constitutional behaviour of the interface was described by a diagram which related the tangential bond traction t t to the relative tangential displacement Au and a diagram which related the normal (radial) bond traction t„ to the relative normal (radial)  Chapter 2. Literature Survey ^  56  Figure 2.15: Geometry of a Typical Disc for Bond Model (after Yankelesky [90])  U)  cc  Tp  rn O 0  O  r ru  $l y  ^  Sy  L SLIP  Figure 2.16: One Dimensional Element and Local Bond Stress-slip Law (after Yankelesky [91])  Chapter 2. Literature Survey ^  57  displacement Av. When unconfined situation was considered, an adequate model was obtained by assuming the former diagram to be bilinear and the latter diagram to be linear, as shown in fig. 2.19. In confined situation (e.g. anchorage bond) this model was too simple and coupling between normal and tangential components should be included. He applied this type of bond-slip element to a slender beam that contained a dominant reinforcing layer and that failed in bending and found that the inclusion of bond-slip produced a positive effect on the crack pattern in that it was less diffuse than it was for the case of perfect bond. Furthermore, the inclusion of bond-slip led to primary cracks that crossed the reinforcement in a correct way. He thought that a second advantage of the use of bond-slip element was that it offered the possibility of making a direct distinction between, for example, plain rebars and deformed rebars. He concluded that the inclusion of bond-slip elements was essential for the fracture mechanics analysis of concrete structures. A perfect bond assumption may be too coarse and conflicted with the delicate fracture mechanics of individual cracks. Rots also studied the bond-slip relationship by another approach [94]. In this approach, the bond-slip elements were omitted and the steel was modelled by continuum elements which were connected to the concrete elements via an interchangeable tying scheme in order to account for the mechanical interlock provided by the ribs (see Fig. 2.20). It was found that in a qualitative sense the predicted cracking behaviour agreed surprisingly well with the experimental bond-crack detections. He thought that this would lead to a better understanding of fundamental issues like bond-softening and non-uniqueness of traction-slip behaviour along the rebar-axis.  ^  Chapter 2. Literature Survey^  58  Y  i  X  Figure 2.17: Two Types of Interface Elements for Bond Behaviour (after Mehlhorn et al [92])  g.•1  g.-1 t^ .i^....-1^ 4 '1^1^i  6 side II 5^£1 side I ^tiv  r.v  bond-slip interface reinforcing bar_  •••••••am+-m.Mw-maa.1.......•  ■^  iiiiiiMt t  ^r_^  z.0^3^2^1  tractions and relative displacements  Gs -.is=  E'  liu ...I—I-.  degrees of freedom  Figure 2.18: A 6-Noded Bond-Slip Elements (after Rots [93])  Chapter 2. Literature Survey ^  59  to  a  b  Au^  v  (a)Tangential traction versus tangential relative displacement. (b) Normal traction versus normal relative displacement.  Figure 2.19: Constitutive Relations for Bond-slip Elements (after Rots [93])  020 336  0414 14 1 14141 1410 10014141414 141^1 140 1414r041 1 14141 1410 14 1 1041 104 141 L14 0414 00004141 0410414100404/ 14100410414141 14 140 Frinn^04100 14 41 14141410041041 110004 &r4r4r40 ■04 1414 10 1 140 104 /041 ■4140414 1AU1 104004141041414100 1041414141 10 ^r4r4 1410 100 1000 10410041004/004100 14 414 ^4 14►41 104 1414 1 14 /41 0414 / 10 14/0 100414 ►110/10011114 004 100 104 1414 100 /4►004 ►4104/0410 100000041000000414 41 14 14 F.0  kr  OntPntial discrete primary crack  I • rigid steel-concrete connection  Figure 2.20: Finite Element Idealization of Tension-Pull Specimen (after Rots  [94])  Chapter 2. Literature Survey  ^  60  2.3.4 Summary  A brief summary of analytical investigations on the bond behaviour is as follows:  1. In order to derive related equations theoretically for the bond stress or the bond slip problem, numerous assumptions were made about the stress distribution, and slip resistance distribution. Whether uniform, linear, or nonlinear, these hypotheses might be quite different from the real conditions; 2. It seemed very difficult to establish a general analytical equation which could reflect the effects of all factors on bond and which could be applied to the general case of the bond problem; 3. For a particular bond problem it was possible to find a theoretical solution after making certain assumptions, and the results of the theoretical analysis could compare well with experimental values; generally speaking, there was closer agreement in the case of smooth bars rather than deformed bars; 4. The finite element method of analysis combined with fracture mechanics has been successfully in application to the study of bond behaviour; the development of numerical analysis and high speed computers enables the consideration of as many variables as desired; 5. The accuracy of the fracture mechanics and finite element analyses depended upon how well the characteristics of the element represent the conditions in the bond slip process; the behaviour of the steel-concrete interface element in transmitting stress by bond was one such important characteristic;  Chapter 2. Literature Survey ^  61  6. There was little information available on the basis of which satisfactory bond stressslip characteristics could be established. Previous work has either neglected this important behavioral characteristic or simply used relationships which were developed from experimental data (in most cases these data are insufficient) and empirical considerations; 7. There was little experimental data on the bond behaviour of fiber reinforced concrete or high strength concrete, which have great advantages in terms of mechanical properties and are now widely used in engineering practice; and 8. There was very little study of the bond behaviour under impact loading using analytical approaches.  2.4 Conclusions  Extensive experimental and analytical work has been carried out to study the bond behaviour in reinforced concrete members. The experimental investigations have covered, in some detail, the factors influencing bond phenomena and have contributed considerably towards the understanding of bond behaviour. The experimental investigations revealed that bond stress in the desired bond stress-slip relationship was not a function of local slip alone. It was also dependent upon the values of steel stress, the embedment length, the diameter of the reinforcing bar, the reinforcement ratio, and the concrete strength, etc. It was seen, also, that the development of bond stress depended upon the region inside the member in terms of the type of internal force. Various types of test specimens have been developed to study bond. Some of them simulate quite closely the behaviour of reinforced concrete members for different loading  Chapter 2. Literature Survey^  62  conditions and seem appropriate for further investigation. The prime advantage of adding fibers to the concrete matrix is to improve its toughness. Steel fibers improves the tensile strength, flexural strength, and shear strength of the concrete mixture, thus increasing the resistance to crack formation and crack propagation. Some previous investigations have shown a great improvement of bond strength by the addition of steel fibers, especially for dynamic loading conditions. More extensive research work should be carried out to study the effects of adding steel fibers on the bond behaviour. As a composite, fiber reinforced concrete is much more inhomogeneous than plain concrete. Furthermore, it will no longer be a. continuous medium once this composite has cracked. This makes it more difficult to study the bond problem of fiber reinforced concrete by conventional theories of mechanics or other analytical approaches. Recently, high strength concrete (with compressive strength over 85 M Pa) has found more and more applications in structural engineering. It could differ, in many aspects, from normal strength concrete. The differences in its microstructure and mechanical properties make many previous conclusions on bond behaviour, which were obtained from specimens of normal strength concrete, inapplicable. No investigation on bond behaviour with high strength concrete has been found in the previous literature. Both steel and concrete are strain-rate sensitive materials. Many conclusions have been drawn on the effects of loading rate on the mechanical behaviour of reinforced concrete members. Very little investigation, either by experimental methods or analytical approaches, has been done on the influence of loading rate on the bond phenomenon. An experimental program devised to investigate the bond behaviour, taking into account the influence of all necessary variables, could be very complicated and expensive.  Chapter 2. Literature Survey^  63  However, analytic approaches can provide solutions which are obtained more quickly. The finite element method combined with fracture mechanics has been proven to be a very powerful tool to solve the bond problem. In this approach, many behavioral characteristics of the element, which are important in reinforced concrete members, can be taken into account. The bond stress-slip relationship between steel and concrete is an important characteristic. So far there has been not enough information available from which the bond stress-slip characteristics could be derived. Experimental investigations to measure local bond stress and local slip are needed to establish the desired characteristics. Theoretically, there will be a unique relationship between bond stress and slip at the interface of a steel bar and concrete, of which the geometric and mechanical properties are known. If an appropriate "interface element" can be developed by reasonable modelling of the constitutive laws of both materials and the criteria of cracking and crushing, it is possible to establish the bond stress-slip relationship analytically for any reinforced concrete member. The determination of the criteria for cracking, crack propagation and crushing in concrete is an important aspect in any non-linear, three dimensional finite element analysis. With the application of non-linear fracture mechanics, the criteria based on the consideration of energy and energy release seem more reasonable than any other criteria, such as those based on stress or strain conditions, especially for the strain rate-related problem. Also, no investigation by means of this approach has been found in literature.  Chapter 3  Experimental Procedures  3.1 Introduction  The two prime variables in the present study were local stress and local bond slip. While cracking and energy transfer were also investigated, they were not directly measured in the experiments. The objectives of this investigation were to:  1. design experimental models to obtain representative bond-slip relationships for pullout and push-in tests under dynamic loading; 2. develop instrumentation and techniques for the measurement of stress and slip; 3. obtain bond-slip relationships from the experimental models; 4. investigate the propagation of cracking in concrete during bond-slip process; 5. investigate the transfer and balance of energy.  64  Chapter .3. Experimental Procedures^  65  3.2 Specimen Preparation  3.2.1 General  The maximum weight of the hammer of the drop weight impact machine used was about :345.0 kg and the maximum drop height of the hammer was about 2.40 rat (details given in Section 3.3.1.2). In order to get as wide a range of loading rate as possible it was assumed that a. drop height of 100.0 mm would completely push in or pull out the reinforcing bar in the specimen. Some preliminary tests were carried out to determine the most suitable type of the rebar and the corresponding embedment length. The results are given in Tables 3.1 and 3.2. It can be seen from the results that in order for the reinforcing bar to completely go through the specimen, the maximum embedment length was controlled by the push-in test of the steel-fiber reinforced specimen with deformed bar. It can also be seen that for the specimens with the deformed rebars, the diameters of which were greater than 16.0 mm, a minimum drop height of 250.0 mm was needed to completely push in the reinforcing bar. A CSA type No. 10 deformed bar (with nominal diameter 11.3 711.711 ) was most suitable; the maximum embedment length was 63.5 mm for the steelfiber reinforced specimen under a drop height of 100.0 mm. Therefore No. 10 deformed bar was chosen and the corresponding maximum embedment length of the reinforcing bar in the concrete specimen was 63.5 mm (2.5 in). It was also found that this embedment length was sufficient for 5 strain gauges to be lined up along the bar (see Fig. :3.4 in Section 3.2.2.1). The purpose of this experimental investigation was to study the bondslip relationship for pure pull-out and pure push-in failure. However, the preliminary tests showed that splitting failure would occur if there were no spirals provided in the specimens. In order to prevent the specimens from splitting, two concentric 6.35 mm  Chapter 3. Experimental Procedures^  66  steel spirals. 63.5 mm and 127.0 mm in diameter were cast in the specimen. Table 3.1: The Maximum Embedments for Smooth Bars (Preliminary Tests) Diameter of Rebar  Type of Concrete  (nun)  11.1^(7/16 in) 16.0 (5/8 in) 19.1^(3/4 in)  Plain Polypropylene-fiber b Steel-fiber ' Plain Polypropylene-fiber Steel-fiber Plain Polypropylene-fiber Steel-fiber  Maximum Embedment a^(mm) Pull-out Push-in 114.3 101.6 114.3 101.6 101.6 88.9 114.3 127.0 114.3 127.0 114.3 101.6 152.4 139.7 152.4 139.7 139.7 127.0  Minimum Drop Height (mm) 50.0 50.0 60.0 90.0 90.0 110.0 120.0 120.0 150.0  a For complete pulling-out or pushing-in of the reinforcing bar in the concrete specimen b C ontent ent = 0.5% (by volume) Content = 1.0% (by volume)  The test specimens were chosen as concrete prisms 152.4 x 152.4 x 63.5 mm (5.0 x 5.0 x 2.5 in) with either a 12.7 mm (1/2 in) diameter smooth bar or an 11.3 mm (7/16 in) diameter (No. 10) deformed reinforcing bar centrally located in the specimen (Fig.  3.2). The length of rebar at the push-in end was determined by two considerations:  1. The possible maximum slip; 2. The maximum length without buckling under impact loading.  A theoretical calculation for the buckling of the rebar under the static loading gave values of the maximum length of 66.9 mm for a smooth bar and 49.7  mm  for a deformed  bar (see Appendix A). From the preliminary tests it was found that the maximum total  Chapter 3. Experimental Procedures^  67  slip (the total displacement of the end of the rebar when the applied load dropped down to zero) was about 4.0 mm for a smooth bar and about 5.0 mm for a deformed bar. Considering that the striking head would go a bit further after being stopped by the rebound supports (which consist of rubber pads) and the pneumatic brakes, the length of rebar at the push-in end was chosen as 50.8 mm (2.0 in) for all specimens, while the length at the pull-out end was 76.2 mm (3.0 in) to suit the configuration of the pull-out tests (see Fig. 3.13 in Section 3.3.1.2). A photograph of the specimen with instrumented rebar is shown in Fig. 3.1. The geometrical details are shown in Figs. 3.2 and 3.4.  Figure 3.1: A Photograph of the Pull-out and Push-in Specimens  Chapter 3. Experimental Procedures ^  Figure 3.2: The Pull-out and Push-in Specimens  68  Chapter 3. Experimental Procedures^  69  3.2.2 Reinforcing Elements  3.2.2.1 Smooth and Deformed Bars  Two different reinforcing bars, a smooth bar with diameter 12.7 mm and a deformed bar (CSA No.10, Grade 400) with nominal diameter 11.3 mm, were used. The deformation pattern and geometry, such as rib height, spacing, and so on, of the test bar are indicated in Fig. :3.3. Standard tests were carried out to ascertain the mechanical properties of the reinforcing bar under uniaxial tensile and compressive loads in an Instron universal testing machine with a capacity of 150 kN. The results are given in Table 3.3. The stress-strain relationships of the smooth bar and the deformed bar under uniaxial loading are shown in Fig. :3.5 and Fig. 3.6, respectively. Compression tests revealed practically the same relationship as tensile tests. The 6.35 mm (1/4 in) diameter steel spirals, made of hot-rolled steel, were cast concentrically in the specimen, with spiral diameters of 63.5 mm and 127.0 mm, as shown in Fig. 3.7.  Chapter 3. Experimental Procedures^  70  All In mm 12.5  1.3 1.5  Figure 3.3: The Type No.10 Test Rebar  Chapter 3. Experimental Procedures^  71  Strain gauge Brass cover 3.0  Rebar  All in mm 3.0  Brass cover  A—A  Strain gauge  Figure :3.4: Test Rebar Instrumented with Strain Gauges  ^  ^  72  Chapter 3. Experimental Procedures ^  Stress (Mpa) sco ^ Straight Bar 352 320 250 200 153 100 50 1  ^0  0^ ,^ ^ 5,CO3 ^1,0^2,000^3,0:0^40  Strain (micro)  Figure 3.5: The Stress-strain Relationship of the Straight Bar  Stress (Mpa) 403  Deformed Bar  •  350 3C0 250 2C0 150 102 50 0^ 0^1,000^2,000^3.0  4,020  LOW  Strain (micro)  Figure 3.6: The Stress-strain Relationship of the Deformed Bar  73  Chapter 3. Experimental Procedures^  Table 3.2: The Maximum Embedments for Deformed Bars (Preliminary Tests) Diameter of Rebar (min) 11.3 (No.10)  16.0 (No.15)  19.6 (No.20)  Type of Concrete Plain Polypropylene-fiber' Steel-fiber` Plain Polypropylene-fiber Steel-fiber Plain Polypropylene-fiber Steel-fiber  Maximum Embedment'^(mm) Pull-out Push-in 88.9 88.9 76.2 114.3 114.3 101.6 139.7 139.7 127.0  Minimum Drop Height (mm)  76.2 76.2 63.5 101.6 101.6 88.9 127.0 127.0 114.:3  90.0 90.0 100.0 200.0 200.0 250.0 320.0 320.0 380.0  "For complete pulling-out or pushing-in of the reinforcing bar in the concrete specimen b ( ontent = 0.5% (by volume) `Content = 1.0% (by volume)  Table :3.3: Mechanical Properties of Steel Bars Type of Bar Ta  C  b  Effective Area  Elastic Limit  Yield Strength  Ultimate Strength  Young's Modulus  (nun)  (ulni2)  (MPa)  (MPa)  (MPa)  (GPa)  126.7 100.0 126.7 100.0  200.5 300.6 200.5 300.6  286.5 42:3.9 286.5 423.9  :320.8 780.0 :320.8 780.0  208 212 208 212  Smooth 12.7 Deformed 11.3 S mooth 12.7 11.3 Deformed  T = Tension 6  Diameter (Nominal)  C = Compression  Chapter 3. Experimental Procedures^  74  Figure 3.7: The Two Spirals in the Specimen  3.2.2.2 Instrumentation of Rebars  Experimental measurement of strains along the reinforcing bars was necessary. This was made possible by mounting strain gauges at various points along the rebar. About a quarter of the total number of reinforcing bars tested were instrumented with 5 pairs of strain gauges per bar to record the strain values at given points along the bar during loading. Thus the strain distributions along the rebar and the stresses in the bar can be determined. In all, 200 bars (1 out of 4 or 6 in each set) were instrumented in this way. From the literature review, it was concluded that probably the best location of strain gauges would be on the periphery of the test rebar [63]. The reinforcing bars for the tests were machined on diametrically opposite sides along their length to produce two grooves  Chapter 3. Experimental Procedures ^  of 2.0 x 4.0  711,711.  75  Provision was also made for placement of two thin copper strips as  covers for the grooves, by some slight additional machining on both sides of the grooves. as shown in Fig. 3.4. The strain gauges used in the test specimens were electric resistance gauges of the type CEA-06-125UN-120 3 . Five pairs of strain gauges were mounted on diametrically opposite sides of each test bar at a spacing of 15.9 77111i (center to center) as may be seen in Fig 3.4. This was intended to take care of the bending effect, if any, in the test bar during loading (see section 3.3.1.5 for the design details of the electric circuit for uniaxial strain recording). To fix the strain gauges on the rebar, the grooves were sand-blasted, and then airblasted to removed any dirt. Chlorothene NU was applied to remove grease chemically, followed by Conditioner-a and Neutralizer-5. After the surfaces were dry, the cementing material, M-bond of type AE-15 adhesive, was applied in the appropriate places, then the strain gauges were affixed in the grooves. After that the rebar was placed in an electric oven at 200°F for about 30 minutes. After being connected to lead wires by soldering, the gauges were coated with M-Coat G to protect against weathering. Then a very thin layer of wax was applied to the surfaces to prevent the gauges from possible damage during the test. Finally, the grooves were covered with strips of copper sheet. Both of the strips were held tightly by means of wires at intervals along the rebar. Each lead wire was numbered to identify the strain gauge and its location along the length of the rebar. Strain gauges and other accessories were supplied by Micro-Measurement Division, Measurement Group Inc., Raleigh, North Carolina, U.S.A.  Chapter 3. Experimental Procedures ^  76  3.2.3 Concrete Mix  3.2.3.1 Compressive Strength and Basic Mix Design  The design compressive strengths of the concrete were 40 MPa (normal strength) and 75 MPa (high strength) at 28 days. The cement used in the concrete specimens was CSA Type 10 Portland cement. The fine aggregate was clean sand (< 4.75mm) and the coarse aggregate was pea gravel (4.75  ti  10.0 mm). The water-cement ratio for the  normal strength concrete was 0.50 and for the high strength concrete was 0.33. For the high strength concrete, silica fume' was added to increase the strength of the concrete and 0.0 — 12.0 ml of superplasticizer 5 per kg of cement was added to the mix to improve the workability. An air-entraining admixture' was also used for all the concrete mixes to increase the workability. The basic mix designs are given in Table 3.4.  3.2.3.2 Added Fibers  It was postulated that fibers added to the concrete matrix would improve the anchorage bond capacity. In the present research, two types of fibers were used. One type was fibrillated polypropylene fibers which were 40.0 mm long with a diameter of 0.1 mm. The aspect ratio was 400 and its density was about 900 kg/n7, 3 , as shown in Fig. :3.8. The other was steel fibers  8  with crimped ends. They were 30.0 mm long with a diameter  of 0.5 mm, giving an aspect ratio of 60; they had a density of about 7800 kg/rn 3 . The Product, of Elkem Metals Company, Canada. 'Product of Conchem Company, U.S.A. 'Product of Martin Marietta Company, Canada. Produced by the Fibermesh Corporation, Chattanooga, Tennessee, U.S.A. Produced by Bekaert Steel Wire Corporation, Belgium 4  Chapter 3. Experimental Procedures  ^  77  Figure 3.8: Polypropylene Fibers steel fibers were made of strain hardened mild steel wires having ultimate strengths ranging from 1180 to 1380 MPa s . They were provided in collated form with a water soluble sizing, so the fibers would disperse adequately when mixed with the concrete. The steel fibers are shown in Fig. 3.9. There were two different contents, 0.1 % and 0.5 %, respectively, by volume, for the polypropylene fibers, and 0.5 % and 1.0 % for the steel fibers. Some details of these two types of fibers are given in Table 3.5.  3.2.4 Fabrication of Test Specimens  The procedures outlined in CSA A 23.2-2C "Making Concrete Mixes in the Laboratory" and CSA A23.2-3C "Making and Curing Concrete Compression and Flexural Test Specimens" were followed. The formwork for the concrete specimens was made of plywood. Care was taken to prevent any leakage through the joints and to keep the form square and true. A pan-type concrete mixer with a capacity of approximately 0.18 711 3  was used. All concrete ingredients were added in the order: coarse aggregate, sand, Information provided by the suppliers  Chapter 3. Experimental Procedures^  78  Table 3.4: Basic Concrete Mix Design (per in') Ingredient Type 10 Portland Cement (kg) Silica Fume (kg) Sand (< 4.75 mm)^(kg) Aggregate (4.75 ---, 10.0 mm)^(kg) Water (kg) Air Entraining Admixture (ml) Superplasticizer a^(ml) Fibres (Polypropylene or Steel)  Normal Strength (40 MPa) 343.0 686.0 1200.0 171.5 70.0 0 ---, 1715 Variable (See Table 3.5)  High Strength (75 MPa) 513.0 98.0 958.0 635.0 201.0 100.0 1715 ,---, 6110 Variable (See Table 3.5)  " The amount varied from 0.0 - 10.0 ml per kg of cement  Table 3.5: Properties and Addition of Fibers  Tensile Strength^(MPa) Young's Modulus (GPa) Addition 0.1% (kg/ura 3 ) 0.5% 1.0%  Polypropylene Fibre 600.0 20.0 0.9 4.5  Baekart Steel Fiber 1200.0 212.0  -  39.0 78.0  Chapter 3. Experimental Procedures^  79  Figure 3.9: Steel Fibers cement (and silica fume) and water followed by two admixture: air-entraining agent and superplasticizer. In the case of the fiber reinforced concrete specimens, polypropylene fibers or steel fibers were added by shaking them in by hand. The concrete was mixed for about 5 minutes. 4,nd then was placed into the formwork and compacted on a small vibrating table, combined with rodding. Finally the specimens were finished with a trowel and covered with plastic sheet. The forms were removed two days after casting and the specimens were cured for a period of 28 days in a moist room and were stored there till testing.  3.2.5 Properties of the Fresh and Harden Concrete  Once the mixing of the concrete was completed, a slump test was carried out in accordance with CSA A23.2-5C "Slump of Concrete". Test cylinders of 100 mm  80  Chapter 3. Experimental Procedures^  diameter and 200 nun in length were also cast from each mix. A summary of control test results of fresh concrete is given in Table 3.6. Table 3.6: Test Results of Fresh Concrete Type of concrete  Watercement Ratio  Slump  Density  (mrn)  (kg/m 3 )  Air Content (%)  Normal  Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0%  0.500 0.500 0.500 0.505 0.505  10 10 10 10 10  2380 2378 2378 2450 2470  5.0 5.2 5.3 4.4 4.4  High  Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0%  o.329 0.329 0.329 0.330 0.338  10 10 10 10 10  2420 2420 2420 2460 2465  4.8 4.9 4.9 4.0 4.0  Compressive Strength  Tests on the compressive strength, tensile strength, Young's modulus and the stressstrain relationship was carried out in an Instron universal testing machine in accordance with ASTM ("39-86 "Test Method for Compressive Strength of Cylindrical Concrete Specimens", ASTM C496-86 "Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens" and ASTM C469-87 "Test Method for Static Modulus of Elasticity and Poisson's Ratio of Concrete in compression". There have been very few cases in which the dynamic elastic modulus has been used to study bond behaviour; thus, in this study, the Young's modulus is actually a static, elastic modulus. The stress-strain relationship test was limited to one dimension only. Since Poisson's ratio and the modulus of elasticity in shear were also needed in the analytical study (Fracture Mechanics and Finite Element Method approaches), they were calculated according to the stress-strain relationship curv e of the concrete. The formulas used for these calculation are given in  Chapter 3. Experimental Procedures^  81  Stress (Mpa) Ica ^  High Strength Concrete  so TO SO 50 40  Normal Strength Concrete  ao 20 10 0  503^LOCO^1,530  Strain (micro)  2,0382^2,530  Figure 3.10: The Stress-strain Relationship of Concrete Section 4.3 in Chapter 5. The stress-strain relationships of the concrete for normal compressive strength and high compressive strength are shown in Fig. 3.10, and the other results of the mechanical properties of the hardened concrete are given in Tables 3.7 and 3.8.  3.2.6 Summary of Test Specimens  As described in the above sections. the experiments were carried out for two different compressive strengths of concrete (normal and high), two different fibres (polypropylene and steel) and different fibre contents (0.1 %, 0.5% and 1.0%). These fiber contents were chosen because they lie within the range of the contents used in practice. There were also three different types of loading: static. dynamic and impact loading. For the dynamic loading there were two rates (low and high) and for the impact loading there were three  Chapter 3. Experimental Procedures^  82  Table 3.7: Test Results of Hardened Concrete - Part I Compressive Strength  Normal  High  Type of concrete Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0%  Compressive Strength  Tensile Strength  (MPa)  (MPa)  39.8 38.7 37.8 44.3 46.5 78.2 77.8 78.3 82.6 83.4  3.72 3.69 :3.89 4.32 4.41 4.87 4.98 4.79 5.25 5.68  Table 3.8: Test Results of Hardened Concrete - Part II Compressive Strength  Normal  High  Calculated  Type of concrete Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0%  Young's Modulus  Poisson's Ratio  (GPa)  32.1 :32.5 :33.4 :38.2 44.6 43.2 46.4 48.3 52.6 57.9  0.252 0.252 0.251 0.277 0.286 0.251 0.252 0.252 0.278 0.291  Elastic Modulus in Shear ' (MPa) 12.8 1:3.0 13.3 15.0 17.3 17.3 18.5 19.3 20.6 99.4  8:3  Chapter^Experimental Procedures^  rates (low, medium and high). These different loading rates were designed to induce a wide range of bond stress rates. The definitions and the calculations of stress rate in the rebar, a s , and the bond stress rate, it, are shown in Section 4.9 in Chapter 4. Table 3.9 shows the different loading types in this experimental study. As a supplementary work to this study on bond behaviour, some specimens were made with deformed rebars which were coated with epoxy. Liquid epoxy 10 was applied to the rebar by brush in a single run with a thickness of about 0.2 to 0.3 min (9.0 to 12.0 mil). The rebars were then cured at the room temperature for 3 days before being casted in the specimens. Table 3.9: Loading Rate Load Type Sa M' d 1 a  d  Stress Rate Steel Bond (MPa/.^) (MPa/s)  10-7 ''' ^10 -5 10 -5 --, 10 -3 10-3 ,---, 10 -1  0.5 • 10 -8 ,-- 0.5 . 10 -6 0.5 . 10 -6 — 0.5 • 10 -4 2 0.5 • 10 -4 --; 0.5 . 10_  Testing Machine  Speed of Crosshead (7-nin/n/in)  Instron  0.05 ,--, 5.0 5.0 --, 500.0  h  Impact '  Drop Height (mum)  -  3.0 — 500.0  Static Instron Universal Testing Machine Medium Rate Impact Drop Weight Impact Machine  For the push-in tests with deformed bars each set of specimens consisted of 6 samples and for pull-out tests each set consisted of 4 samples. Tests with smooth bars were mainly for comparison, and each set only included 2 samples. For tests with epoxy coated rebars, each set consisted of 2 samples. One or two bars out of each set was instrumented with Dynacare epoxy resin and hardener, produced by Industrial Formulators of Canada Ltd. Burnaby, B.C., Canada  ilapter 3. Experimental Procedures  ^  84  5 pairs of strain gauges, depending on the types of loading and the rebar. Tables 3.10 to 3.13 show the summary of the test specimens. Table 3.14 shows the summary of the test specimens with epoxy coated rebar. Table 3.10: Specimens for Push-in Tests (Deformed Bars)  Type of Concrete Low  Al  /  Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0%  1 1 1 1 1 1 1 1 1 1  Loading Rate Medium 1 1 1 1 1 1 1 1 1 1  High  1 1 1 1 1 1 1 1 1 1  Concrete Strength H N 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  No. of Specimens per Set 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6  TOT4L S - Static^111 - Medium^1 - Impact^N - Normal^H - High  Total 12 12 12 12 12 24 24 24 24 24 36 36 36 36 36 360  Chapter 3. Experimental Procedures  ^  85  Table 3.11: Specimens for Pull-out Tests (Deformed Bars)  Type of Concrete Low  M  /  Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0%  Loading Rate Medium  High  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1 1 1 1 1  1 1 1 1 1 1 1 1 1 1  Concrete Strength N H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  No. of Specimens per Set  Total  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4  8 8 8 8 8 16 16 16 16 16 24 24 24 24 24  TO TA L S - Static^M - Medium^1 - Impact^N - Normal^H - High  240  Chapter 3. Experimental Procedures  ^  86  Table 3.12: Specimens for Push-in Tests (Smooth Bars)  Type of Concrete Low  S  M  /  Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre ( oncrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre ( oncrete 1.0%  1 1 1 1 1 1 1 1 1 1  Loading Rate Medium 1 1 1 1 1  -  -  High  1 1 1 1 1 1 1 1 1 1  Concrete Strength N H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  No. of Specimens per Set 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  TOTAL S - Static^*1 - Medium.^I  -  Impact^N - Normal^H - High  Total 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 100  Chapter 3. Experimental Procedures  ^  87  Table 3.13: Specimens for Pull-out Tests (Smooth Bars)  Type of Concrete Low  ,5  11  /  Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Concrete 0.5% Steel 0.5% Fibre Concrete 1.0% Plain Concrete Polypropylene 0.1% Fibre Con crete 0.5% 0.5% Steel Fibre Concrete 1.0%  1 1 1 1 1 1 1 1 1  Loading Rate Medium 1 1 1 1 1 -  High  1 1 1 1 1 1 1 1 1 1  Concrete Strength N H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  No. of Specimens per Set 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  TOTAL S -- Static^Al - Medium^I - Impact^N - Normal^H - High  Total 4 4 4 4 4 8 8 8 S 8 8 8 8 8 8 100  Chapter 3. Experimental Procedures  Table 3.14: Specimens with Epoxy Coated Deformed Bars  '  1!  /  5'  M  I  Concrete No. of Loading Type of Concrete Strength Specimens Total Rate per Set H Low Medium High N Push-in Tests Plain Concrete 2 4 1 1 1 1 2 4 Polypropylene 0.1% 1 1 Fibre Concrete 0.5% 1 1 2 4 1 Steel 1 1 1 2 4 0.5% Fibre Concrete 1.0% 1 2 4 1 1 4 1 1 Plain Concrete 2 1 Polypropylene 0.1% 1 1 1 2 4 2 4 Fibre Concrete 0.5% 1 1 1 2 4 Steel 1 1 1 0.5% 4 1 Fibre Concrete 1.0% 2 1 1 1 1 4 1 2 Plain Concrete 4 Polypropylene 0.1% 1 1 2 1 Fibre Concrete 0.5% 1 1 2 4 1 1 2 1 4 Steel 1 0.5% 2 4 Fibre Concrete 1.0% 1 1 1 Pull-out Tests Plain Concrete 1 1 1 1 2 Polypropylene 0.1% 1 1 1 1 2 Fibre Con crete 0.5% 1 2 1 1 1 Steel 1 1 1 1 2 0.5% Fibre Concrete 1.0% 1 1 1 1 2 Plain Concrete 1 1 1 1 2 Polypropylene 0.1% 1 1 2 1 1 Fibre Concrete 0.5% 1 1 1 1 2 Steel 1 1 2 0.5% 1 1 Fibre Concrete 1.0% 1 1 1 2 1 Plain Concrete 1 1 1 2 1 Polypropylene 0.1% 1 1 1 2 1 Fibre Concrete 0.5% 1 1 1 1 2 Steel 1 1 0.5% 1 1 2 Fibre Concrete 1.0% 1 1 1 1 2 TOTAL 90 Static^Al - Medium^I - Impact^N -- Normal^H - High  88  Chapter 3. Experimental Procedures^  89  3.3 Test Program  3.3.1 Impact Testing  3.3.1.1 Test Set Up  The testing system used to carry out impact tests is an important aspect of any experimental program. Various techniques, such as the conventional Charpy impact test, the split Hopkinson bar test method and the drop hammer impact machine, can be modified to carry out bonding behaviour tests under impact loading. The following points must be taken into consideration in designing or choosing an appropriate system [95]:  1. The machine is able to apply load to the specimen over a very short time in the millisecond range) with a considerable amount of energy; 2. The machine has as great a stiffness as possible to prevent instability and vibration; 3. The kinetic energy applied to the specimen can be varied in order to induce different: strain rates in the specimens tested: 4. The accelerations of the specimens and the striker in the testing machine can be measured, to study the effects of inertial force and energy transfer; 5. The strains at different points along the reinforcing bar or in the concrete in the specimen can be measured accurately; 6. The load exerted on the specimen, the acceleration and the displacement of the reinforcing bar, and the strains can not only be measured over a very short time  Chapter 3. Experimental Procedures ^  90  interval (a few microseconds) but also stored completely.  A drop weight type of impact testing machine" and a bolt type of load cell were chosen to be used in the tests. A number of of reinforcing bars were instrumented with strain gauges before being cast into the specimens, so the strains in the steel could be determined (see Fig. 3.4 in Section 3.2.2.2 for the placement of the strain gauges along the reinforcing bar). It was considered an important part of the impact test to find out the displacement history of the reinforcing bar without significant error. A high speed video camera (motion analyzer) which could capture 1000 frames per second was used to record the movement of the rebar. For an impact event that lasts 10 ins 10 frames would be taken, but this ,  wasn't accurate enough to generate a displacement versus time curve by analysing these pictures. On the other hand, a displacement transducer which was able to measure very small movements at high sampling rates (a period of several hundred microseconds) and record them was unavailable at the time this research work was carried out. However, the displacement history could be determined by integrating the acceleration measured by the accelerometer from kinematics with considerate accuracy. So an accelerometer was attached on the bottom of the reinforcing bar in the specimen to measure its acceleration during the impact event, while the hammer of the impact machine was also instrumented with an accelerometer, which recorded the acceleration of the hammer for determining the velocity, displacement and the kinetic energy of the hammer. A high speed data acquisition system with a 16-channel A/D board, an aggregate sampling rate of up to 1 MHz and a signal conditioner was used to record all the test I I Designed, constructed and maintained by the Department of Civil Engineering. University of British olumbia, Vancouver, Canada  Chapter 3. Experimental Procedures ^  91  data from the load cell, the accelerometers and the strain gauges. All these data were transferred to a mainframe computer for processing. The test set up is shown schematically in Fig 3.11. Each part of testing apparatus is described in the following sections.  3.3.1.2 Impact Testing Machine  The drop weight type of impact machine designed and constructed at the University of British Columbia [97], is shown in Fig. 3.12 and Fig. 3.13. It stands about 4.0 in high and is capable of dropping a 345.0 kg mass' through heights of up to about 2.40 in. The hoist attaches itself to the hammer by means of a pin lock and can be used to raise or lower the hammer by means of a chain and a motor. When the hammer is at the desired height, the pneumatic brakes provided in the hammer itself, are applied. With the brakes, the hammer "grabs on" to the columns of the machine. Subsequently, the hoist can be detached from the hammer. Upon releasing the pneumatic brakes the hammer falls under gravity and strikes the reinforcing bar of the concrete specimen which is supported on a, base with a hole to permit movement of the rebar. The bolt load cell attached to the hammer sends out signals to the data acquisition system during the impact. The hammer can be made to fall through different heights, and thus the specimens can be subjected to different strain rates. For pull-out tests a solid steel frame with a stiffness of 15 times that of the reinforcing bar was used to change the push-in force to a pull-out force; as shown in Figs. 3.13 and 3.14. 12 1t  has been modified, to provide a capacity of 505.0 kg  Chapter 3. Experimental Procedures ^  92  Figure :3.11: Layout of the Set Up for the Impact Test (Revised from Somaskanthan [96])  Chapter 3. Experimental Procedures^  93  Figure 3.12: An Overall View of the Impact Machine — Push-in Test (Revised from Somaskanthan [96])  Chapter 3. Experimental Procedures ^  94  Figure 3.13: An Overall View of the Impact Machine — Pull-out Test (Revised from Somaskanthan [96] )  Chapter 3. Experimental Procedures^  Figure 3.14: Solid Steel Frame for Pull-out Tests  95  Chapter 3. Experimental Procedures^  96  3.3.1.3 Bolt Load Cell  The load cell for the impact tests and the particular specimens in this test must  1. be able to send out as high electric signals (voltages) continuously as possible; 2. have a linear relationship between the load exerted on it and the output; 3. have a higher frequency response than that of the tests; 4. have a delay, if there is any, in the output signal which is much less than the time of the event; 5. have a fully contacting surface when it hits the rebar in the specimen, and sufficient tolerance for possible eccentrical striking.  A bolt type of load cell is with a capacity of 150 kN was found to meet the above requirements, as shown in Fig. 3.15. As the bolt tip strikes the rebar of the specimen, the strain gauges inside the bolt record the contact load and the Wheatstone bridge circuit, as shown in Fig. :3.16, will produce an unbalanced' signal. The signals will be collected by the data acquisition system. A calibration was needed to convert these signals into a real contact load. Although the bolt was to be stressed dynamically in the impact case, the mechanical properties under a dynamic loading rate ranging from 0 to 0.05 M Pa/.s (N/inin 2 • s) were assumed to be the same as under static loads. A analytical study on the stress wave propagation 13  Manufactured by St.rainsert Company, Bryn Mawr, Pennsylvania, U.S.A.  Chapter 3. Experimental Procedures^  97  in the bolt load cell under impact loading showed that the time delay of the signals in response to the striking load was negligible for this test (see Appendix B). Therefore a. static calibration can reasonably be extended to the impact condition. The calibration was carried out in an Instron universal testing machine. Fig. 3.17 shows the calibration curve. It is noted that the curve was a perfectly smooth line and there was no hysteretic loss.  Figure 3.15: The Bolt Load Cell for Impact Testing  Chapter 3. Experimental Procedures^  Connector  +0  + o^ -  O^  Red  F;7"; ;1  Green  B or 21  Black  D or 4i  White  C or 3;  R5  R6  legends: Ga: Active Gage^Gc: Complementary Gage _o Numbers correspond Excitation: +0 and^to Model EW-1 Strain Signal:^+0 and -^Indicator terminals.  Figure 3.16: The Circuit of the Bolt Load Cell  98  99  Chapter 3. Experimental Procedures^  Load (kN)  70  Calibration Bolt Load Cell  00 $0 40  Loading 30  unloading 20 10 0  '^  0  2  4^  Signal (V)  6  a  Figure 3.17: The Calibration of the Bolt Load Cell  10  100  Chapter 3. Experimental Procedures^  3.3.1.4 Accelerometer  The accelerometers used were piezoelectric sensors (Model 302A)  14  ,  a special type for  shock and vibration measurement, as shown in Fig. 3.18. There is a built-in unity-gain amplifier inside the accelerometer so the output signal will directly go to the A/I) board in the data acquisition system. Some salient features of the accelerometer are:  1. resolution = 0.01 g 2. resonant frequency = 45 kHz 3. frequency range = 1^5000 Hz 4. load recovery < 10 fts  The calibration curves is given in Fig. 3.19.  14  1\lanufactured by PCB Piezoelectrics Inc., Buffalo, N.Y., U.S.A.  Chapter 3. Experimental Procedures ^  070A09 Optional Connector Adaptor  101  Sig Pwr 031 Dia GND 10.32 inn 468 Dia -10-32 Tho Coaxial Connector  1 30  1 2 Hex  484 Dia  See Optional Models below Specifications.  C-E t  Mod 081805 10-32 Mtg Stud (supplied) 27^  Frequency Response rr  .  100^ 1000 Frequency In Hertz  Figure 3.18: The Quartz Accelerometer  10000  102  Chapter 3. Experimental Procedures^  Acceleration (g) 503 ^  400  -^  Calibration Quartz Accelerometer  -  300  203  100  0  '^  0  i  ^  2  ^  3  ^  4  ^  Signal (V) Figure 3.19: The Calibration of the Quartz Accelerometer  6  103  Chapter 3. Experimental Procedures ^  3.3.1.5 Strain Measurement  The strain gauges used in the tests were CEA-06-1251_11\1-120, which are widely used in experimental stress analysis. This is an electric resistance type of strain gauge, having a resistance of 120.0 + 0.3% Cl and a gauge factor of 2.050 + 0.5%. A special electric circuit was designed to measure and record the readings from the 5 pairs of strain gauges mounted on the reinforcing bar. It is the circuit of the 'opposite arm Wheatstone bridge [98]. The circuit diagram is shown in Fig 3.20. A box which consisted of the five pairs of 'dummy' strain gauges and connectors was placed as close to the specimen tested as possible to compensate for temperature effects, as shown in Fig. 3.21. The output voltage (signal) is  10„t =  E (K. iRici + R1)^E • 120.0  (R 1 + 120.0 + K1R1(1)^(R2 + 120.0 + 1 '2R2(2)  (V)^(3.1)  where VQ,,t = the output signal E = the excitation voltage  , K2 = the gauge factors of a pair of strain gauges (gauge 1 and gauge 2) R 1 , R2 = the electric resistances of a pair of strain gauges^(Si) ( 1 . ( 2 = the strains at two opposite sides  Chapter 3. Experimental Procedures ^  Dummy Resistance  Active Strain Gauge  Excitation  Dummy Resistance  Active Strain Gauge  t Signal Conditioner  I  t Data Acquisition System  ^  Figure 3.20: The Circuit of 'Opposite Arm' Wheatstone bridge  104  105  Chapter 3. Experimental Procedures^  The two dummy resistances were 120.0 1 -2 precision resistances. After rearranging and neglecting higher order terms in Eq. 3.1 (see Appendix C for details) we finally get  Vout =  ^ EK (ci + 12) (V 2  ^  )  (3.2)  where  K = 2.050 (the standard gauge factor for model CEA-06-125UN-120) The average of two strains of the opposite gauges will represent the strain in the section. i.e.  (€1 + 2)  2  (3.3)  where f = the strain in the section measured^(10') It can be seen that there is a linear relationship between the output signal V and the strain in the section 1.  = C • 1/..t ^  (3.4)  where the coefficient C is  C =  EK  (1/V)^  (3.5)  Chapter 3. Experimental Procedures ^  106  All the strain gauges used had different electric resistances R and different gauge factors K. The manufacturer guarantees that the errors of the electric resistances of strain gauges for the same model are less than 0.3% of 120.0 52 and the errors of gauge factors are less than 0.5 % of 2.050. In Eq. 3.5 the excitation voltage E remains the same. A precise error analysis (see Appendix C) showed that taking = 120.0 C2 and K = 2.050 for the calibration resulted in a less than 0.5 % error of the coefficient C. Thus the calibration curve which was a straight line could apply to all the strain gauges used in the tests, as shown in Fig. 3.22.  107  Chapter 3. Experimental Procedures^  Figure 3.21: The Dummy Strain Gauge and Connector Box  Strain (micro) 3,^ 500^ -  Calibration Strain Gauge  3,000 2.500 2000 1,500 1,000 600  2^  ♦^  Signal (V)  6^  8^10  Figure 3.22: The Calibration of Strain Measurement  Chapter 3. Experimental Procedures^  108  3.3.1.6 Data Acquisition System  One of the most important and perhaps the most difficult aspects of the impact test is the data collection. From the preliminary tests it was found that the time of the impact event ranged from 5.0 to 15.0 Ins, i.e. the signals from the transducers that are of significance lasted only 5.0 to 15.0 ms. The following points must therefore be taken into consideration in choosing and designing an appropriate data acquisition system for this type of experimental investigation:  1. The system must record the signals from the transducers correctly; 2. The scanning rate of the system should be fast enough to capture all the information which is needed to describe and analyze the event; 3. The data that it records are sufficient but not excessive, keeping the volume of the data as small as possible to save time and space on the computer disk; 4. Specifications such as I/O voltage, frequency response, etc. must be compatible with the transducers used; 5. The signal conditioner (filters and amplifiers) must be able to block as much noise as possible without losing or distorting the true signals and be able to amplify the signals to the most suitable level for A/D board.  The data acquisition system used in the test consisted of an IBM PC XT computer, a 16-channel A/D conversion board and Scope Driver software'', and a. conditioner unit, as shown in Fig. 3.2:3. 15  Product of R.C. Electronics Inc., Santa Barbara, California, U.S.A.  Chapter  3. Experimental Procedures^  Figure 3.23: The Data Acquisition System  109  Chapter 3. Experimental Procedures^  110  Some salient features of the data acquisition system are:  • 16-channel maximum I/O (input/output) port; • An aggregate sampling rate of up to 1/n MHz (n is the number of channels used); • An external instrument interface; • Internal or External trigger control; • A scope driver software; • Digital conversion with a 12 bit accuracy for a range of -10.0 V to +10.0 V; • A memory buffer size of 1 to 64 K of A/D board; • Amplifiers with gain of up to 1000 in the conditioner;  Since the frequency response of the accelerometer used was 5000 Hz, (see Section 3.3.1.4) which was much lower than those of the other transducers, i.e. the bolt load cell and the strain gauges, it was decided that the sampling rate should be 200 i.t.s (0.2 ni.4 For the case of collecting data through 8 channels (one for the load cell, two for the accelerometers and 5 for the strain gauges) the maximum scanning speed of the data. acquisition system for one channel should be  1 200 x 10 -6  x 8 = 816 (Hz)  This was much lower than the capacity of the A/D board, 1 MHz.  Chapter 3. Experimental Procedures ^  111  When the data acquisition system is switched to active mode, it starts collecting data. and then replacing the data with new data until triggered. The delay time, the channels, the trigger mode, the trigger control level and the buffer size of the A/D board were carefully selected or designed so that the data collection could cover the whole period of the impact event including a certain length of pre-impact and post-impact time. The data collected from the A/D board was inputted to the computer memory in compressed mode, then written to the mass storage media in an ASCII format.  3.3.1.7 High Speed Video Camera  A high speed video camera (ENTAPRO 1000 Motion Analyzer)  16  was used to take  pictures of the specimen during the impact event (Fig. 3.24). The camera, can take 1000 to 6000 frames per second. The data were stored in a special video tape and then downloaded to a normal VCR tape.  Manufactured by Eastman Kodar Company, U.S.A.  Chapter 3. Experimental Procedures  ^  Figure 3.24: EKTAPRO 1000 Motion Analyzer  112  Chapter 3. Experimental Procedures^  113  3.3.1.8 Test Procedure  Altogether 380 different types of specimens were tested under impact loading, including normal strength or high strength concrete, smooth or deformed rebars, plain, polypropylene fiber or steel fiber concrete, different fiber contents, with or without strain gauge instrumentation, pull-out or push-in, and different drop heights. A summary is given in Tables 3.9 to 3.13 in Section 3.2.5. A typical procedure for carrying out an impact test is  1. Set up the test apparatus needed, including the drop weight impact machine, the bolt load cell, the accelerometers and their power supply unit, the dummy strain gauge assembly, the data acquisition system and the high speed video camera. Make the connections between them properly; 2. Place the specimen on the support under the hammer of the impact machine, make alignment from both directions and adjust the height of rebound pad so that it will stop the fall of the hammer as soon as the rebar has gone through the concrete specimen; 3. Check and make sure the apparatuses works properly; 4. Operate the impact machine, raise the hammer to the desired height and set it to ready-to-drop mode; 5. Run the Scope Driver software in the data acquisition system, set the necessary parameters properly including the trigger control parameters. Set the data acquisition at active mode and set the high speed video camera at live mode;  Chapter 3. Experimental Procedures^  114  6. Release the pneumatic brakes in the impact machine and trigger the high speed camera with a delay of a certain time; 7. Apply the pneumatic brakes as soon as the hammer rebounds; stop the recording of the high speed camera; 8. Check if all the data and the pictures have been recorded; save the data to the disks in ASCII format; 9. Reset the apparatus for the next specimen; 10. Download the picture from the high speed type to the normal VCR type, transfer the data from the disks in the data acquisition system to a. mainframe computer for processing.  3.3.2 Static and Medium Rate Testing  3.3.2.1 Test Set Up  The purpose of the static and medium rate testing was to investigate experimentally the bond behaviour under static and medium rate loading, from both pull-out and pushin test. The results were then compared with each other and with those under impact loading. The static and medium rate tests were carried out on an Instron universal testing machines 7 . It is a. mechanical type of testing machine, having a capacity of 150 UV (33750 Ms) and stiffness of 140 LIV/77int. Its crosshead speed ranges from 0.05 to 500 Mill  per minute, giving a bond stress rate ranging from 0.5 10 -8 to 0.5 • 10 -4 AI Pals  for the specimens tested. All operations are controlled by a microprocessor-based central 17  Model 4206. manufactured by Instron Corporation, U.S.A.  Chapter 3. Experimental Procedures^  115  processing unit. A 150 kN load cell was used for measuring load. From the preliminary tests it was found that the maximum bond force was about 55 kN. So, for calibration, the load cell was loaded, in steps, up to 60 kN, then unloaded, down to the zero. The output was read. A regression analysis showed that the relationship between the load and the voltage output was perfectly linear, and the loading and unloading curves followed the same path. Fig. 3.25 shows the calibration curve. The crosshead position measurement unit of the testing machine was configured to represent the displacement of the rebar in the specimen. The calibration curve of the displacement is shown in Fig. 3.26 and it is also a perfect straight line. The test set up is shown in Fig. 3.27 and the set ups of the pull-out and push-in tests are shown in Fig. 3.28 and Fig. 3.29 respectively.  Load (kN) so 70  eo  Calibration Static Load Cell  so  loading  40 30 20 10 0^ 0  -^2  ^  4  ^  6  ^  Signal (V) Figure 3.25: The Calibration of the Load Cell for Static Testing  10  116  Chapter 3. Experimental Procedures^  Displacement (mm) so Calibration Position Measurement  40  30  20  10  o^ 0  2  6  4  6  Signal (V)  Figure 3.26: The Calibration of the Position Measurement  10  Chapter 3. Experimental Procedures ^  Figure 3.27: Test System for Static and Medium Rate Testing  117  Chapter 3. Experimental Procedures  ^  Figure 3.28: Pull-out Test Set Up for Static and Medium Rate Loading  118  Chapter 3. Experimental Procedures ^  Figure 3.29: Push-in Test Set Up for Static and Medium Rate Loading  119  Chapter :3. Experimental Procedures^  120  3.3.2.2 Data Acquisition and Processing  There is a built-in conditioner in the console in the Instron testing machine so the output from the load cell and the position measurement unit were sent directly to the A/I) board in the data. acquisition system (see Section 3.3.1.6) along with the outputs from the strain gauges which were conditioned first by the conditioner unit. All the data were then stored on diskettes in a PC computer and subsequently transferred to a mainframe computer for processing.  3.3.2.3 Test Procedure  Altogether, 420 different types of specimens were tested under static and medium rate loading, a summary are given in Tables 3.9 to 3.13 in Section 3.2.5. A typical procedure for carrying out a static or medium rate loading test is given below.  1. Set up the test apparatus needed, including the Instron universal testing machine, the 150 iciV load cell, the dummy strain gauge assembly, and the data. acquisition system, hook up the connections properly; 2. Place the specimen on the support under the load cell in the testing machine, make alignment from both directions; 3. ('heck and make sure the apparatus works properly; 4. Operate the testing machine, set the crosshead speed to give with the desired stress rate;  Chapter 3. Experimental Procedures^  121  5. Run the Scope Driver software in the data acquisition system, set the necessary parameters properly including the trigger control parameters. Set the data acquisition at active mode; 6. Start to move the crosshead of the testing machine; 7. Stop the movement of the crosshead of the testing machine; S. Check if all the data and the pictures have been recorded, save the data to the disks in ASCII format; 9. Reset the apparatus for next specimen testing; 10. Transfer the data from the disks in the data acquisition system to a mainframe computer for processing.  3.3.3 Crack Examination  In order to investigate the crack developments in different specimens, some tested specimens were sliced by diamond and metal saws, then the internal cracks at the interface between the rebar and the concrete were examined and photographed by a stereoscopic microscope  18  (see Fig. :3.30).  'Nikon Microscope Model SAM-10, Nippon Kogaku K.K Totyo, Japan.  Chapter 3. Experimental Procedures  ^  1 99  ", 1111. 441■7410.,^  IMF  Figure 3.30: The Stereoscopic Microscope  MK  Chapter 4  Analysis of Test Data  4.1 General  The usual output from the impact tests on the bond specimens consisted of the tup (the contact area between the load cell and the specimen) load, the accelerations at two locations and the strains at five locations along the rebar. These three parameters were the fundamental data recorded in this experimental study. These data were all obtained as a. function of time. Fig. 4.1 shows the eight sets of data from the eight channels of the data acquisition system connected to these transducers. The data were acquired at 200 /Ls intervals; an impact event took anywhere from 5 to 30 ins, so there were hundreds to  thousands data points for each test. These data were transferred as a data file in ASCII format to a mainframe computer via. FTP (Fast Transform Protocol) service. One important and difficult aspect of the data processing in impact tests is the noise filtering. The true signal output from the circuits of the load cell, accelerometers or strain gauges (Wheatstone bridges) were at a very low level, ranging from 5.0 to 30.0 71?. V,  while the noise from several sources can reach as high as 1.0 mV. The effects of noise  on the reliability of the true signal can not be ignored. The influences of the noise on the true signals depend on the characteristics of the noise, such as frequency, duration and  123  124  Chapter 4. Analysis of Test Data^  Signal (V) 10  10^20  ^  30  ^  40  Time (ms) :  Figure 4.1: Typical Outputs from the Eight Channels of the Data Acquisition System  Chapter 4. Analysis of Test Data^  125  intensity, etc., as well as the characteristics of the true signals. They can be eliminated either by hardware filtering or by digital filtering. But either (or both) filtering methods can be applied only when the characteristics of the noise or the true signals is known. In this experimental investigation, several preliminary impact tests were carried out to determine the characteristics of external and internal noise. They were specially designed as there exist theoretical models for these problems and accurate analytical solutions are known. An appropriate method for filtering, or a combination of several methods, was chosen, and the raw data from the data acquisition system were put through the digital filtering process by means of FFT (Fast Fourier Transform) and inverse FFT to remove the noise as much as possible; the "true" signals were saved for analysis. The applied pull-out and push-in forces were calculated based on the data from the channel of the load cell. The data from the accelerometer channels were used to determine the accelerations, velocities and displacements of the rebar and the hammer, and the kinetic energies, potential energies and fracture energies. The data from the five channels of strain measurement were used to determine the strains and stresses in the rebar as well as in the concrete, their distributions along the rebar and the bond stress and local bond slips. A flowchart of these processes is given in Fig. 4.2. The strains in the rebar were checked with its displacement which was evaluated by integrating the acceleration recorded. Meanwhile, the displacement history of the rebar can be checked by analyzing the motion pictures, which was taken at a rate of 1000 frames per second by a high speed video camera. Figs. 4.3 to 4.9 were one set of these motion pictures. which were recorded for a specimen made of steel fibre reinforced concrete with a deformed rebar under the impact of 300 mm, drop height. The vertical displacements of the rebar at each one millisecond interval after the hammer hit the specimen can be  Chapter 4. Analysis of Test Data^  126  determined by comparing two consecutive pictures, using appropriate scale. Then a displacement history of the rebar can be drawn and compared with the displacement history curve which was calculated from the recorded data of the acceleration. It was found they coincided very well (Fig. 4.10). This means that the measurements of the accelerations, the method of signal processing and the calculation model of the displacement (see the following sections for details) were appropriate.  4.2 Data Filtration  4.2.1 Fast Fourrier Transform — FFT and Inverse FFT  Transient loading conditions, such as impact loading, and material and structural responses to them, are time-dependent variables, which should be studied using a timedomain analysis. However, these variables can be more conveniently studied using a frequency-domain analysis. Any signal output from the load cell, accelerometers or strain measurement channels can easily be extended from an aperiodic function defined in a finite range [t i , 1 2 ] to a periodic function defined in an infinite range (—oo, d-oo), the extended function thus satisfies the conditions for Fourier transformation. The signal function is considered as being comprised of many periodic wave forms and a correct evaluation of such wave form characteristics will help study the signal itself [99]. Let P(t) be the aperiodic signal function defined in^12]; after being extended to a periodic function (either odd or even), P(t), which is defined in (—oo, oo), it can be given as  Chapter 4. Analysis of Test Data  ^  INPUT DATA FILE  I (SEARCH USEFUL PORTION OF SIGNALS i  BASE LINE SETTING METHOD OF FILTERING  i  APPLY FFT'  i  FILTER OUT UNWANTED FREQUENCIES  i  APPLY INVERSE FFT  i  FIND LOAD, PLOT LOAD HISTORY CURVES  i  FIND ACCELERATIONS, VELOCITIES & DISPLACEMENTS  i i FIND ELONGATIONS OF REBAR i FIND STRAINS & STRESSES IN STEEL & CONCRETE i FIND BOND STRESSES & BOND SLIPS i PLOT APPLIED LOAD VS. DISPLACEMENT CURVES  PLOT STRESS & STRAIN DISTRIBUTION CURVES  i  PLOT BOND STRESS VS. SLIP CURVES  i  FIND LOAD, STRAIN & STRESS RATES  1  FIND KINETIC, POTENTIAL, STRAIN & FRACTURE ENERGIES  i  OUTPUT RESULTS & GRAPHS  Figure 4.2: Algorithm of Test Data Process  127  128  Chapter 4. Analysis of Test Data^  .1.21eiektaproi  210^.'19,153I iRa  b  314. Full (1C.: FE.3)  Figure 4.3: The Motion Picture of the Rebar at T = 1 ins Taken by the High Speed Camera  211 1 iT77=E --71  ;1C:  :1  74-1ri  16  ' FijlJ(1C^FF-3)  oD 6 Irl'icR) Figure 4.4: The Motion Picture of the Rebar at T = 2 is Taken by the High Speed Camera  Chapter 4. Analysis of Test Data^  116^I)? .2111. C:3 21211C1.  129  212 I. ic,:ate  31C) i  H  Full (1C 13  D8  Figure 4.5: The Motion Picture of the Rebar at T = 3 ms Taken by the High Speed Camera  Figure 4. 6: The Motion Picture of the Rebar at T =4 Speed C;'arnera  Ms  Taken by the High  ^  Chapter 4. .Analysis of Test Data ^  130  D:C 3.214i1CMDPrgi  j' Full (11: : 3 F F .3)^-!:- _,  ^;1 ;^0:3 6 rER)^.  Figure 4.7: The Motion Picture of the Rebar at T 5 ins Taken by the High Speed Camera  Figure 4.8: The Motion Picture of the Rebar at I = 6 ins Taken by the High Speed Camera  131  Chapter 4. Analysis of Test Data^  116:26,`,63.2  j.< Full  1 1^216  .  .  F  Figure 4.9: The Motion Picture of the Rebar at T = 7 ms Taken by the High Speed Camera  0  ot 2  3  0 ;  0^ 2^ 4^ 0^ 0  ^  10  Time (ms)  By Accelerometer  By High Speed Camera  Figure 4.10: The Displacement History of the Rebar by Two Methods  Chapter 4. Analysis of Test Data^  1 j.+0,, P(t) :=^C(w)eiwt  132  (4.1)  where the harmonic amplitude function C( w) is  +00 C(w)^f^P(t)^dt^  (4.2)  where t = the time component = the frequency component C( w) = the Fourier coefficient Eqs. 4.1 and 4.2 are the pair of Fourier Transform (FFT) and Inverse Fourier Transform equations (inverses F FT), respectively.. In this study the signal function P(1) is actually a set of discrete data, and thus a numerical integration method is required to determine C(w) from P(t) and, vice versa, P(t) from 0(w). ,A computer program in FORTRAN language was written to form the Discrete Fourier Transform (D.FT) based on Eqs. 4.1 and 4.2, and to solve the equations by the Fast Fourier Transform (FFT) algorithm in both conversion directions (FFT and inverse FFT). The Fourier conversion yields the necessary frequencies and their amplitudes, which facilitates the frequency-domain analysis. For steady-state conditions, contributing frequencies may be few and limited, but for transient conditions as in an impact test, a  Chapter 4. Analysis of Test Data ^  13:3  spectrum of frequencies are obtained. The contributing frequencies and their relative importance for the signal function can easily be studied. Physically the spectrum of frequencies represents the distribution of energy over a certain range of frequencies. An appropriately filtered spectrum of frequencies forms the new signal function by means of inverse FFT.  4.2.2 Characteristics of External and Internal Noise  The noise occurring in the test can be categorized as external noise and internal noise. The former are created by external sources such as nearby motors, power lines and connection cables, and the latter include electronic noise induced within the transducers, amplifiers, A/I) board and computer components. The frequencies of these noise cover a wide range, from low to high. Their amplitudes may be up to the same order of magnitude as the true signals. Some of them occur throughout the test, whereas others are only present during the actual test or actual data acquisition. This made it difficult to determine the characteristics of the noise separately from the true signals. Using the data collected from the so-called non event" experiment, in which the data acquisition system records the signal outputs from the transducer channels while the hammer drops without striking the specimens, it is possible to identify some of the noise which is present in the system throughout the test. Fig. 4.11 shows a typical curve of this kind of noise. It oscillates around a horizontal line close to the X-axis and is periodic in nature. The spectrum of frequencies by LET, as given in Fig. 4.12, shows that it is comprised of some 60n (where  71  is an integer) Hz noise. This implies that the  power supply line (A( 110 V 60 Hz) may have a large contribution to the noise.  Chapter 4. Analysis of Test Data^  134  Signal 0.0 003 0.03 0.04 0.02 0  Om) 004 ) (0.05) (0.03) 0.1)  o  10  ^  20^30  ^  40  Time (ms)  Figure 4.11: "Non Event" Noise in Impact Tests  Fourier Coefficient (V/Hz)  05  Frequency (Hz)  Figure 4.12: Spectrum of "Non Event" Noise by FFT  so  Chapter 4. Analysis of Test Data^  135  It was realized that some noise is present only during the data acquisition. To study the characteristics of this type of noise a special test was designed and carried out. In this test the mathematical model is known and an accurate solution can be found by analytical methods. Therefore the true signal output was determined. Applying FFT to both the true signal and the recorded signal will yield two different spectra of frequencies. By comparing the frequencies and amplitudes of the noise in the two spectra, their contributions to the original signals could be determined. An appropriate filter (low pass, high pass or band filter) and the cutting limits, can then be designed. The spectrum should be modified by the chosen filter to eliminate the frequency contributions of the noise. Applying the inverse FFT to the new spectrum will result in a true signal.  4.2.3 Base Line Setting Method  The noise found in the "non event" experiment is present in the system throughout the test. Basically it is a low frequency noise with a constant mean value as described in the above section. To eliminate this component of the noise all the signal outputs had their mean value of the noise, as determined from the "non event" signal data, subtracted from the recorded data. The numbers were 0.03 V for the load cell and the accelerometer channels and 0.05 V for the strain gauge channels, as shown by several preliminary tests. The subtractions were carried out by the computer program automatically.  4.2.4 Digital Filtering  Digital filtering is a process by which unwanted frequencies are eliminated mathematically from a signal in the frequency-domain analysis. In the mathematical algorithm,  Chapter 4. AnaLvsis of Test Data^  136  three type of filters are commonly employed: low pass filters, high pass filters and baud pass filters. A low pass filter cuts off all of the frequencies from the signal that are higher than the stipulated value, whereas a high pass filter cuts off all of the frequencies lower than the stipulated value. A baud pass filter allows only frequencies of the signal that lie within the set limits to pass and cuts the rest off. The filtered signal will be free of the particular frequencies which have been cut off in the digital filtering process after it has been transformed to the time-domain by means of inverse FFT. The main differences of digital filtering from hardware filtering are that the former can eliminate unwanted frequencies completely, are more flexible than the latter and there is no phase shift in the filtered signal. The general procedure of digitally filtering the signal in this experimental study are as follows:  Step 1 ^ Determine the Characteristics of the Noise  1. Design a, similar test for which the mechanical model for the problem is known and an accurate analytical solution exists; 2. (1 iange the analytical solution from time-domain to frequency-domain by FFT, -  and get the spectrum of the solution; 3. Carry out the test and record the signal; 4. Find out the "non event" noise and its mean value: 5. Get rid of the "non event" noise from the signal by the baseline setting method; 6. Apply FFT to the signal to get its spectrum; and  Chapter 4. Analysis of Test Data ^  137  7. Compare two spectra and determine the frequencies of the noise and their contributions to the signal.  Step 2 — Determine Parameters of Digital Filtering  1. Determine whether to use low pass, high pass or band pass filters, or individual elimination of certain range of frequencies; and  2. Set the cut limit(s).  Step 3 ^ Filter the Test Data  1. Get rid of the "non event" noise from the signal data by the baseline setting method; 2. Apply FFT to all the test data individually; 3. Cut off the known frequencies of the noise in the spectrum by the chosen type of filter; and -1. Apply inverse FFT to the filtered spectrum and get the true signals.  Step 4 ^ Process the True Signal Analyse the filtered signals as the true signals.  4.2.5 Filtering of Load, Acceleration and Strain Signals  Three preliminary tests were designed and carried out to determine the characteristics of the noise which occurred in the load cell, accelerometer and strain measurement circuits  Chapter 4. Analysis of Test Data. ^  138  (Wheatstone bridge) during the data acquisition (see Appendix E). All the problems have analytical solutions. The procedure is described in the above section. The result are given in Table 4.1. Table 4.1: The Characteristics of Noise and Their Filtering (Load cell, Accelerometers and Strain Measurement) Load Cell Signal period^(ins) - 5.0 ,--, 30.0 Frequencies of noise^(kHz) > 9 .0 Filter chosen Low pass _ Cut limit^(kHz) 2.0  Accelerometer  Strain Gauges Wheatstone Bridge  6.5 ' 35.0 >2.4 Low pass 2.4  5.0 — 30.0 >1 5 . Low pass 1.5  4.3 Young's Modulus and Poisson's Ratio of Concrete  Based on the stress-strain curve of concrete, Young's modulus, E c , is given by  E, =  S2 - S1  (- 2 — 0.000050  (MPa)^  where = the stress corresponding to E r = 50 x 10 -6^(MPa ) .  the stress at 40% of the ultimate load^(MPa) fz = the strain corresponding to ,52^(10-6  The poison's ratio p c is given by  )  (4.3)  Chapter 4. Analysis of Test. Data^  =  ft2  ( 2 — 0.000050  139  (4.4)  where fly = the transverse strain at the middle of specimen corresponding to S i (10') f tz  = the transverse strain at the middle of specimen corresponding to S2  (1 0 ' ) -`  The Young's modulus in shear, G„, is given by  E, 2(1 + ti)  (1h1 Pa)^  (4.5)  4.4 Contact Load, Inertial Load and Applied Load  There is a linear relationship between the output signals from the load cells (either the bolt load cell for the impact tests, or the Instron 150 kN static load cell) and the contact loads. as shown in Fig. 3.17 and Fig. 3.25. The total force acting on the rebar is  Ft = c 1 S 1  where  Ft = the contact load  ^  (N)  ^(N )^  (4.6)  ^  Chapter 4. Analysis of Test Data ^  140  c i = the calibration coefficient of the load cell^(N/V) = the output voltage from the load cell The coefficient c i is different for the different load cells. It should be noted that both  F and S i are functions of time. In the impact test when the hammer strikes the rebar, the rebar suddenly gains momentum and accelerates in the direction of the hammer. This gives rise to d'Alambert forces, acting in a direction opposite to the direction in which the rebar accelerates. From the equilibrium of force, the load that the sensor in the load cell records includes the force due to the inertial reaction of the rebar, which is called the inertial force. This means that the force between the tup and the rebar consists of the stressing load and the inertial force. Since the acceleration of the rebar during the impact could be very high (100 200  q) it is necessary to check out how important the inertial force is in the determination of the external force which acts on the specimen. But calculations showed that the inertial force of the rebar is negligible when compared to the contact load (see Appendix D). Thus, the applied load, i.e. the force acting on the bonding area (either pull-out or push-in) is the same as the contact load. That is,  Fb = Ft —^= Ft^(N)^ where  = the force acting on the bonding area^(N) = the inertial force of the rebar  ^  (N  )  (4.7)  ^  ^q  Chapter 4. Analysis of Test Data^  141  4.5 Acceleration, Velocity and Displacement  4.5.1 Acceleration, Velocity and Displacement of the Rebar  The acceleration of the rebar was calculated using the data from the accelerometer which was attached to the bottom of the rebar. According to the product specification, the acceleration of the rebar a ,(1) is  a 7.,(t.) = 100.0 (38  ^  ^ (771711782)  (4.8)  where  =  the gravitational acceleration ^(in7n, .c 2 ) = output voltage from the accelerometer  ^  (v)  Because the initial velocity is equal to zero, at any moment t the velocity of the rebar  v r ,(t) and its displacement d„.(1) can be found by integrating the recorded acceleration over time:  re (t)  = fo a „.(t) cif  ^  (mm/s)^  (4.9)  and  (  l  ,„  (t  t  )^  it  1,7.,(t)dt =^a7.,(t)(1t2  0^  0 0  (min)^(4.10)  Chapter 4. Analysis of Test Data^  142  where  t = time elapsed from the moment of contact between the tup and the rebar (.^) Since  are  consisted of a series of discrete numbers recorded by the data acquisition  system, the above integrations were carried out numerically. As described in Section 1 of this chapter, the displacement of the rebar, d„, can also be calculated from the motion pictures which are recorded at a rate of 1000 frames per second (1 frame/ins) by a high speed video camera. The results from two different methods are compared to find out the accuracy of calculation.  4.5.2 Acceleration, Velocity and Displacement of the Hammer  As soon as the pneumatic brakes are released the hammer of the impact machine starts to fall as a free body under gravity. From kinematics, the time for the hammer to travel the distance I), (the drop height) is  9h T dr op =  0.91g  (4.11)  the correction factor 0.91 is applied to g to account for frictional effects between the hammer and the guiding columns, and the air resistance. If we take the time when the hammer hits the rebai as a starting point, the velocity of the hammer at this moment vh„(0) is  Chapter 4. Analysis of Test Data ^  ch a (0) =  2 (0.918) h  143  (mm/.^)^ (4.12)  At any time t after it strikes the rebar the velocity of the hammer v iia (t) is  vh a (t)^2 (0.918) h^Jo. a  ha (t)  dt  (minis)^(4.13)  where  a ha (t) = the recorded accelerations ^(mm, /s) After the contact between the hammer and the specimen, an impulse, given by the area under the tup load (Ft , see Eq. 4.6) vs. Time (t) plot, acts on the hammer. From the laws of Newtonian mechanics, this impulse must be equal to the change in the momentum of the hammer, i.e.  rt  Ft (t)^=^ha a ha (0) — Af h „v h „(1)  ^  (Ns)  ^  (4.14)  The above equation can be used to check the accuracy of the calculations of the velocity of the hammer. The displacement of the hammer at any time d h a (t) is  (11,,(t) =  fo t [  2 (0.918) h^f a 1,„(t)  (mm)^(4.15)  Since a h,(t) consisted of a series of discrete numbers recorded by the data acquisition  Chapter 4. Analysis of Test Data^  144  system, the above Eqs. 4.13 and 4.15 can readily be solved by numerical integration.  4.6 Elongation of the Rebar  By comparing the displacement of the hammer d h “(t) with the displacement of the rebar d„ (t). the deformation of the rebar itself during impact c„.(t) can be found.  =  .11,,(1) — (.1 7.,(t)  (  ^  (mm)^ (4.16)  The deformation of the rebar c i.,(t) can also be determined by considering the strain in the rebar during the impact event  c„(t) =  Ftlp AsEs  ^  o(  s  dl(mm)^(4.17)  where = the length of the pull-out or push-in end of the rebar ^(mm)  l c = the length of the embedded segment in concrete of the rebar ^(non) In the above equation the first and second terms represent the elongation of the pullout or push-in end and the embedded segment of the rebar, respectively. ( s is the strain in the embedded part of the rebar, evaluated by using Eq. 4.20 in the following section. The results of the two different equations, Eqs. 4.16 and 4.17, can be used to check the accuracy of the two calculation methods.  Chapter 4. Analysis of Test Data^  145  4.7 Strains and Stresses in the Rebar and the Concrete  Either the pull-out or the push-in test for the bond specimen is a very complicated three-dimensional problem from the view point of the theory of elasticity, due to the inhomogeneous material conditions (steel and concrete with greatly different elastic modules) and the complex boundary conditions. There is no analytical solution for this problem, even if the external force Fb is already known and some assumptions are made to simplify the mechanical model, as shown in Fig. 4.13. There is, however, a fracture mechanics approach combined with the finite element method for the problem which will be described in Chapter 7. On the other hand, since the strains at some locations along the rebar were measured directly using strain gauges, the bond stresses can be calculated from the recorded strain data. From the theory of elasticity, the axial stress in the rebar a s can be found, according to Hooke's law for the three-dimensional, axisymmetric problem, as  a,  Es  ^ 1 + / 15  'is  1—  E s + es.r  + cs,(9) + es  (MPa)^(4.18) ]  where  E = the Young's modulus of steel^(MPa) S  it s = 0.27 (Poisson's ratio of steel)  Es  = the axial strain in steel (recorded)^(10-6)  S,7" =  the radial strain in steel  ^  (10')  Chapter 4. Analysis of Test Data^  146  ( s0 = the tangential strain in steel ^(10') Similarly, the axial stresses in the concrete in the vicinity of the rebar a, is  a, =  E, 1 + pc  ((c + ^ 1 — 2,a,  c,r^ec,O)  + Cc  (MPa)^(4.19)  where  E, = the Young's modulus of concrete^(MPa) p„ = 0.25 (Poisson's ratio of concrete) E, = the axial strain in concrete^(10') = the radial strain in concrete^(10') ( c , 0 = the tangential strain in concrete ^(10-6) In practice, it was impossible to measure the radial strain c s „ and the tangential strain 6,9 , 0  in rebars with diameters of 11.3 or 12.7 mm, and the radial strain E c r and tangential ,  strain  F e. a  in concrete. A three-dimensional axisymmetrical analysis shows that the radial  strain c,„ and the tangential strain ( 8 ,9 do not play much of a role in the terms of the total strain in Eq. 4.18 (see Appendix F). The ratio  ^ I —2 [I --  „^s,O) p ,(^  FS  ^< 5%  Chapter 4. Analysis of Test Data^  147  Thus. Eq. 4.18 can be simplified to  E, (1 — µ s ) = ^ (1 + 11,9)(1 — 2µs)  E  s  (M Pa)^(4.20)  Similarly, Eq. 4.19 becomes  E, (1 — pc) a, a, (c.^(Al Pa)^(4.21) (1 + p c ) (1 — 210 Actually, the strain ( c in the concrete was always found through the stress a,. To do this Eq. 4.21 becomes  (1 + p c ) (1 — 2/t e ) ( c = ^ a-,^(10-6)^(4.22) E, (1 — The stresses in the concrete across the section, a c , can be calculated from the equilibrium equation  t, tt- • D dl = y a,A, ^(A)  ^  (4.23)  where = the locations of the ith and jth points along the rebar^(710-11) uz = average bond stress between i and j locations at the steel-concrete  interface^(AIPa)  Chapter 4. Analysis of Test Data^  148  = diameter of the rebar^(rnm) = coefficient that accounts for the nonuniform distribution of stress in the concrete across the section; y = 0.30 in this study (see Appendix F) A, = area of the concrete cross-section ^(non')  4.8 Bond Stress and Bond Slip  The local bond stresses between the ith and jth locations were calculated from the axial stresses in the steel by the equilibrium condition,  gs,^crs, j ) D  4AX  (M Pa)^ (4.24)  where  a s , j = stress at the ith location in steel  (M Pa)  = stress at the jth location in steel  (M Pa)  = the length of rebar between the ith and jth locations^(mm) Notice that the bond stress calculated by the above equation is the average bond st r ess.  The slip between the rebar and the concrete at any point between the ith and jth points along the rebar, w(x), can be determined by the compatibility condition between  ^  Chapter 4. Analysis of Test Data^  149  the two materials:  — F e ) dl  (mm)^ (4.25)  where ^=  the distance from the ith point ^(mm)  Denoting by y the distance from the starting point, the general equation for determining the slip w (y) is  711k -Jr  II) (0 =  jo y-7 7(1  3  —1,)^  ^ — t )  (mm)^(4.26)  k=1  where 71^the number of segments in which the slips have been calculated  w k = the calculated slips for the previous segments ^(min)  All of the integrations were clone using numerical methods. The varieties of distribution curves can readily be plotted, based on the results of these calculations.  4.9 Rate of Loading, Strain and Stress  The loading rate, strain rate or stress rate, ::(t), were calculated as  Chapter 4. Analysis of Test Data^  ;it [z(t)]  ^  150  (N/s, 10 -6 /s or 114 Pais) ^(4.27)  where z(t) is a load, strain, direct stress or bond stress function, For the time interval between two consecutive sampling points, which is usually a very short time, the rate over this interval, can be evaluated by the averaging method, i.e.  (N/s, 10 -6 /s or 111Pa/s)^(4.28)  where Az i (t) = the increment of the load, strain or stress ^(N/s, 10 -6 /.s or AI Pa /s)  = the time interval Then the rate over the whole event is  =  i =1  i( 1 )^(N/_, 10 -6 / s or Al Pals)^(4.29)  where N = the number of the time interval  151  Chapter 4. Analysis of Test Data^  4.10 Work, Energy and Energy Balance  4.10.1 Kinetic Energy, Potential Energy, and Work done by the Hammer  When the hammer was raised to a drop height h, its potential energy, (also the total energy) E h„ 13 is  p^  9h  ^  N in)^  (4.30)  where = the mass of the hammer and the kinetic energy at the moment when it hits the specimen Eh a ,k is  E rna k = Mha V ha (0) ,  2^ 1  2  111 [2 (0.919) h]^(Nut)^(4.31)  where v h „(0) = the velocity of the hammer at the time of impact (see Eq. 4.12) (mm /.^) The energy consumed by the friction and air resistance during the first impact event  E^is  159  Chapter 4. Analysis of Test Data^  E h „,^P^ha k^0.09M h a gh  ^  ,  (Nirt)^(4.32)  From the law of conservation of energy, the kinetic energy lost by the hammer after impact.^E, is,  =  1 9  vh„ (1)]^(Nin)  (4.33)  where t i „(0) and z,,, a (t) are the velocity of the hammer at the beginning (t = 0) and the end (1 = t) of the contact, respectively (see Eqs. 4.12 and 4.13). Actually, the second term in the above equation represents the kinetic energy of the hammer left at any moment t during impact, Eha,/qt,  1,r^2  E ha, le f t = 75 11/1  (N711)^  (4.34)  At the end of impact, the total loss of kinetic energy of the hammer is  2 M h„  1, 2h  0 )^v ("^d )^(Arm.)^(4.35) (0)  where feud = the duration of the impact event In the case of rebound, the data acquisition system generally records the second blow. The interval between the first and second blows represented the total time for the hammer  Chapter 4. Analysis of Test Data^  153  to rebound and fall down again. From kinetics, it is possible to determine the rebound velocity v r ,, b ,„,„d based on the recorded time data (see Appendix G). It is given by  v rebound = 0.4775 t rebound (1 + 0.090 ^(7/i/s)^(4.36)  where  =  the time interval recorded  Thus the rebound energy of the hammer  ^  E ha  (s  )  ebound  141^2  E^ rebound =^-11. ha V re b oun d 2  = 0.1354M h„ g 2 t 2,,, bou „ d  (N171, )  At time I, during the impact the work done by the applied load W (I.) is  , a (t) =  f  Ft (t) d i ,„(t) (II  ^  (N7n)^(1.37)  where  Ft (t) = the applied load on the rebar (see Eq. 4.6)  ^  (N)  d 10 (I) = the distance the hammer travels after impact (see Eq. 4.15) ^(mm) It is more practical to change the above formula from the time-domain to the displacemeat-doinain,  Chapter 4. Analysis of Test Data^  14  d  /  h„((.1) =^Ft (d)ds 0  154  (Ntn)^(4.38)  where d = the distance the hammer travels^(mm)  Thus the total work done by the hammer during the impact event is  11: 1 a (d) = ,  (tend 10^F (d)ds t  (Nrit)^(4.39)  where (I,„ d = the total distance the hammer travels during impact ^(mm)  The above integration represents the area under the curve in the contact load versus displacement graph. From the law of conservation of energy,  Etta  ,  p  I a, f  r^  W ha + E ha,rEdound  (Nrn)^(4.40)  where W h „ = the work done by the hammer at the end of the impact event ^(NIA)  Chapter 4. Analysis of Test Data^  155  4.10.2 Strain Energies and Fracture Energies  At any moment (t = t) the fracture energy in bond can be calculated by  =  t [ft  10  0  r Dto (Ls dt^(Nin) u1  (4.41)  where /^=^the length over which bond slip occurs ^12117)  u.^=^the bond stress^(M Pa) =^the bond slip^(mm) D^= the diameter of the rebar^(mm) In order to study the fracture energy in bond in a time period of Si,  061 7 6, the  integration,  f  ol 217Dtt  ,  can be changed from the length-domain to the bond slip-domain, i.e.,  Ati:b^[f torD (Ltd fit  where  ^  (N77/)^(4.42)  ^  Chapter 4. Analysis of Test. Data^  156  w = the slip^(nun) The above integration represents the area under the curve in the bond stress versus slip graph. At any moment during impact the strain energy stored in the rebar,  Er,,,t,  is evalu-  ated by  E rc, sir^ft  ^I  ^JO  cr 2  — 2E As (ill dt  ^(N7n)^(4.43)  and the strain energy stored in the concrete, E c , str , is  /  ^E,  sir  =  (7.2  f^dt^(N7n)^(4.44) f o 2E  All of the above calculations are done by numerical integration in computer.  4.11 Curve Fitting  When it, was necessary to fit a function through a set of experimental data values or calculated values, such as for establishing an explicit mathematical formula for the bond stress-slip relationship through processed data points for bond stress and bond slip, several data approximation methods were employed. To seek an approximation to the data. a mathematical function which contains a number of coefficients was specified. The reasons why a function might be chosen are  Chapter 4. Analysis of Test Data.^  157  1. the function might be known explicitly from theoretical considerations; 2. it might reflect results obtained by the previous researchers; 3. it has a form which can approximate the curve of the data points; and 4. a combination of the above three considerations.  The method of least squares was used both for possible linear and nonlinear fits. Let  F^P2,^  ,  p„i;  be the function to be fitted and  be the set of data points, where pi  m) are unspecified parameters.  Minimizing  yd 2  (4.45)  i.e. solving the equation group  =0 j=1 2,^m)^ (  apt  ,  will give the values of the parameters,  (pi,  P2^• • • , P7>, )  (4.46)  Chapter 4. Analysis of Test Data^  158  Thus the fitting function  F (pa, p2,^p„,; x) is determined. This is also done by computer.  4.12 Statistical Analysis  For a normal distribution, the mean of a set of experimental data :r is  x=  (4.47)  where = the total number of samples  x i = the experimental data and its standard deviation S is  ,02  = =1  N  (4.48)  -  the coefficient of variation c 1, is  Cv =  x  -  (4.49)  Chapter 4. Analysis of Test Data^  159  4.13 Computer program  A program written in FORTRAN that ran on a mainframe computer was used to process the data. The input is the data file which consists of the raw data from the data acquisition system for each specimen. The program will then do the following automatically  1. search and save the useful portion of the raw data; 2. apply the base line setting method to each signal; 3. apply FFT to each signal and get its spectrum; 4. filter out unwanted frequencies from the spectrum; 5. apply inverse FFT to the filtered spectrum to get the true signal; 6. calculate the contact load, applied load, and plot the load history curve; 7. calculate various accelerations, velocities and displacements of the rebar and the hammer, and plot the applied load versus displacement curve; 8. calculate the elongation of the rebar; 9. calculate the strains and stresses in the rebar and the concrete, find the average value, and plot the distribution curves; 10. calculate the bond stress and bond slip, find the average value, and plot the distribution curve; 11. calculate the strain and stress rates; and  Chapter 4. Analysis of Test Data^  160  12. calculate kinetic, potential and fracture energies.  Some of the above outputs were used to carry out statistical calculations and curve fitting.  Chapter 4. Analysis of Test Data  161  Pull-out Specimen Concrete  •  • f:__,. .^ii  •- i • 2: i  f^ft  ii ...._:: •_ 4 /  i -- • • i:: •  ,  t^t^t^t Rebar  11 Push-in Specimen Concrete  ttttt  ttttt Rebar  Figure 4.13: One of the Calculation Models for the Test Specimens  Chapter 5  Experimental Results  5.1 Introduction  Basically the experiments described herein consisted of pull-out tests and push-in tests. For both types of tests the experimental work was carried out for two different types of reinforcing bars (smooth and deformed), two different concrete compressive strengths (normal and high), two different fibres (polypropylene and steel), and different fibre contents (0.1 %, 0.5% and 1.0% by volume), and three different types of loading: static, dynamic and impact loading. For the dynamic loading there were two rates (low and high) and for the impact loading there were three rates (low, medium and high). Table 3.9 in Chapter 3 shows the different loading types in this experimental study. Altogether $00 specimens were tested, of which 600 were specimens with deformed bars and 200 were specimens with smooth bars; 640 were tested under dynamic loading at different rates and 160 were tested under static loading. For the push-in tests with deformed bars, each set of specimens consisted of 6 samples and for pull-out tests each set consisted of 4 samples. Tests with smooth bars were mainly for comparison, and each set only included 2 samples. One or two bars out of each set were instrumented with 5 pairs of strain gauges, depending on the type of loading and the rebar. Tables 3.10 to  162  Chapter 5. Experimental Results ^  163  3.13 in Chapter 3 summarize the test specimens. In order to investigate the bond phenomenon for each type of test and to compare the results within different types of tests, it is necessary to calculate the stresses and displacements at different points in the steel and in the concrete. These stresses and displacements were time dependent under dynamic loading. That is, they varied with time. In most cases it was appropriate to compare the corresponding "peak" values, which referred to the moment that the applied loads reached their peak values. In other cases, the "mean" values, which were computed by taking the average of all the data points over the time period, were compared. Then a representative value was obtained by statistically averaging the calculated results from the same set of specimens. The equations used in the data processing are given in the related sections in Chapter 4. Since the calculations of stresses and displacements are based on the recorded data. from the strain gauges, the spacing of these strain gauges can affect the accuracy of the results. The bond stress computed from  (as,, — as,.)  4LYX  I  (4.24)  is a local average value between two consecutive strain gauges. However, in reality, there might be a high concentration of bond force at the interface in the concrete immediately ahead of the ribs, because of the wedging action between the ribs of the rebar and the concrete. Furthermore, any cracking at the interface might increase the stress level in the bar locally to a great extent. Nevertheless, smooth curves were drawn to fit all of the experimental or calculated data points, using the method of least squares (see Section  Chapter 5. Experimental Results^  164  4.11 in Chapter 4). Note that in all of figures and tables in this chapter, the following notation is used: PF = Polypropylene fibre concrete SF = Steel fibre concrete  S = The Static loading M = The medium rate loading  1 = The high rate loading (impact) Medium I = The bond stress rate is 0.5 10 -6 — 0.5 10' (111 Pa/ s) Medium II = The bond stress rate is 0.5 • 10' — 0.5 • 10' (MPa/s) Impact I = The bond stress rate is about 0.5 • 10  -4  (AlPais)  Impact II = The bond stress rate is about 0.5 • 10 -3 (M Pals) Impact III = The bond stress rate is about 0.5 • 10 -2 (MPa/8)  Chapter 5. Experimental Results^  165  5.2 Steel Stresses  5.2.1 General  The stress in the steel rebar is the direct reason for the development of bond stress at the interface between the steel and the concrete, and it is the only parameter which can be practically measured (strain) and calculated inside the specimen. On the other hand, it is the difference in the strains between the steel and the concrete that produces the slip at a given point at the interface. Therefore, the stress in the steel rebar is one of the most important parameters in this experimental work. Stresses in the steel were calculated directly from the recorded strain data along the rebar by  =  E s (1 —  ids)  (1 + ps) (1 — 211s)  Es  Fig. 5.1 illustrates the stresses in the steel rebar at the peak load,  (4.20)  Fe = 30 kN. This  was a plain concrete specimen with a smooth rebar subjected to an impact test with a drop height of 300 7n7n. It should be noted that the distribution curves of steel stresses were plotted based on the four average data points between strain gauges and on the boundary conditions at the loaded and free ends. However, only fitted curves are shown in all figures except in the first one (Fig. 5.1), in which both the data points and the best fit curves are shown.  Chapter 5. Experimental Results^  166  5.2.2 Tests with Smooth Bars  For the specimens with smooth rebars, the effects of concrete strength, addition of fibres or the loading rate on the stresses in the steel were not significant, in terms of either their values or distributions, as shown in Figs. 5.2, 5.3 and 5.4. It can be seen from these figures that for static loading the stresses in the smooth rebar decrease linearly, with the maximum stress at the loaded end and zero stress at the free end. Increasing the concrete strength or adding steel fibres resulted in slight increases in the stress values, but the linear nature of the distribution remained unchanged. This suggested that the force transmitted between a smooth rebar and the concrete be due to chemical adhesion and frictional resistance. A high rate of loading caused a slight stress concentration at the loaded end, which might be due to the sudden change in the boundary conditions of the rebar (from free surface to concrete confinement). Due to the Poisson effect there was almost no frictional resistance at the interface between the rebar and the concrete after the adhesion had been destroyed for the pull-out test. On the other hand, the frictional force at the interface between the rebar and the concrete would increase to a maximum value when the push-in force increased (since the radial stress also increased), so the distribution curve of the stress in the steel exhibits greater values and slopes for the push-in tests than for the pull-out tests, as shown in Fig. 5.5. Because the tests on specimens with smooth bars were primarily for comparison with the test results from the specimens with deformed bars, the following sections will emphasize the latter results. For simplicity, all of the figures given in this section, unless specified. are for the specimens with plain normal strength concrete and for push-in tests.  167  Chapter 5. Experimental Results ^  SCO  0^  15.9^  VA^  47.7  Distance from the Loaded End (mm)  NS  Figure 5.1: Stresses in the Smooth Rebar  0  0^  151^  911^  47.7  Distance from the Loaded End (mm)  $OS  Static^Medium II^Impact III Figure 5.2: Effects of Loading Rate on the Stresses in the Smooth Rebar  168  Chapter 5. Experimental Results^  0  0^  159^  313^  47.7  Distance from the Loaded End (mm) Normal Strength^High Strength Figure 5.3: Effects of Concrete Strength on the Stresses in the Smooth Rebar  Distance from the Loaded End (mm) Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%) Figure 5.4: Effects of Fibre Additions on the Stresses in the Smooth Rebar  Chapter 5. Experimental Results^  169  k I w 400 V te *S 200  1  05  0  0^  15.9^ 31.8^ 47.7  Distance from the Loaded End (mm) Pull-out^Push-in Figure 5.5: The Stresses in the Smooth Rebar for Pull-out and Push-in Tests  Chapter 5. Experimental Results^  170  5.2.3 Tests with Deformed Bars  5.2.3.1 Effects of Loading Rate  For all of the specimens with deformed bars, both the maximum and the average values of the stresses in the steel increased considerably with the increase of loading rate. There was more stress concentration at the loaded end than for the specimens with smooth bars. In addition, unlike the cases of specimens with smooth rebars, the stress distribution curves are no longer straight lines. Roughly speaking, these curves tend to have larger slopes than those from tests with smooth bars. This means that higher bond stresses were developed under higher loading rates. Fig. 5.6 shows different distribution curves of the stresses in the steel under different loading rates for a plain concrete specimen. By comparing Fig. 5.7 with Fig. 5.6 it can be concluded that the addition of polypropylene fibres to the concrete had no significant influence on the results, in terms of the effects of the loading rate on the stresses in the steel. However, the loading rate seemed to have greater effects on specimens made of steel fibre reinforced concrete than other types of specimens (see Fig. 5.8). This is because the shear mechanism plays a major role in the bond-slip process for deformed bars; the bond resistance is due to the ribs bearing on the concrete. Steel fibres improved the concrete strength and the crack resistance. This improvement was outstanding, especially under high rate loading; therefore, the force transmitted to the concrete increased dramatically with an increase in loading rate. It should be noted that Figs. 5.6 to 5.8 refer to the tests for specimens with normal  Chapter 5. Experimental Results^  171  concrete strength. Fig. 5.9 represents the specimens made with high concrete strength reinforced with steel fibres. It was found that the influence of the loading rate was more significant for high strength concrete than for normal strength concrete. Similar to the case of specimens with smooth rebars, push-in tests always exhibited higher stresses in the steel than pull-out tests, as shown in Fig. 5.10. In order to evaluate the effects of the loading rate on the stresses in the steel with several different variables, two relative "indices", /peak and /average, were introduced. They are defined as,  peak value of steel stresses under a certain type of loading condition 'peak^ peak value under static loading  and  /average  average value of steel stresses under a certain type of loading condition average value under static loading  Some of the results are summarized in Table 5.1.  Chapter 5. Experimental Results^  Table 5.1: Effects of Loading Rate on the Steel Stress Type of Specimen  Plain Concrete  Polypropylene Fibre Concrete (0.5%)  Steel Fibre Concrete (1.0%)  Steel Fibre Concrete (1.0%) (Pull-out)  Steel Fibre Concrete (1.0%) (High Strength)  Loading -^Relative Index Rate a /average /peak Static 1.00 1.00 Medium I b 1.02 1.01 Medium II 1.05 1.02 Impact I 1.06 1.02 Impact II 1.04 1.08 Impact III 1.10 1.05 Static 1.02 1.01 Medium I 1.05 1.02 Medium II 1.07 1.03 Impact I 1.09 1.04 Impact II 1.11 1.05 Impact III 1.13 1.07 Static 1.42 1.10 Medium I 1.46 1.11 Medium II 1.50 1.17 Impact I 1.65 1.19 Impact II 1.72 1.21 Impact III 1.81 1.23 Static 0.93 0.94 Medium I 0.94 0.94 Medium II 0.95 0.95 Impact I 0.96 0.95 Impact II 0.97 0.96 Impact III 0.98 0.97 Static 1.54 1.16 Medium I 1.60 1.17 Medium II 1.68 1.22 Impact I 1.75 1.25 Impact II 1.86 1.27 Impact III 1.91 1.30  From push-in tests with normal strength concrete specimens, unless specified. Table 3.9 in Chapter :3 for details.  b See  172  Chapter 5. Experimental Results^  Distance from the Loaded End (mm) Static^Medium II^Impact III Figure 5.6: Effects of Loading Rate on the Stresses in the Deformed Rebar (Plain Concrete)  Distance from the Loaded End (mm) Static^Medium II^Impact III Figure 5.7: Effects of Loading Rate on the Stresses in the Deformed Rebar (Polypropylene Fibre Concrete)  173  Chapter 5. Experimental Results ^  174  eco  2  600  400 9.)  200  0  0^  15.9^ 318^ 47.7  ^  Distance from the Loaded End (mm)  656  Static^Medium II^Impact III •■■••■•••■  Figure 5.8: Effects of Loading Rate on the Stresses in the Deformed Rebar (Steel Fibre Concrete)  15.9^ 31i^ 472  Distance from the Loaded End (mm) Static^Medium II^Impact III Figure 5.9: Effects of Loading Rate on the Stresses in the Deformed Rebar (High Strength Concrete)  175  Chapter 5. Experimental Results ^  15$^  318^  47.7  Distance from the Loaded End (mm)  83Z  Static^Medium II^Impact III Figure 5.10: Effects of Loading Rate on the Stresses in the Deformed Rebar (Pull-out Tests)  Chapter 5. Experimental Results^  176  5.2.3.2 Effects of Concrete Strength  General speaking, the stresses in the steel increased for high strength concrete specimens. This seems logical, since the shear mechanism is the main mechanism for the bond resistance of deformed bars. Fig. 5.11 is an example of the effects of the loading rate. By using the relative "index" values, as defined in the previous section, the effects of concrete strength on the stresses in the steel can be shown more clearly. Table 5.2 gives some results. eco  ai  400  40  2C0  0  0^  15$^  31$^  47.7  Distance from the Loaded End (mm) Normal Strength^High Strength Figure 5.11: Effects of Concrete Strength on the Stresses in the Deformed Rebar  177  Chapter 5. Experimental Results^  Table 5.2: Effects of Concrete Strength on the Steel Stresses Loading Type a  Static  Medium II  Impact III  'From push-in tests.  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Concrete Strength Normal High Normal High Normal High Normal High Normal High Normal High Normal High Normal High Normal High  Relative Index / pea k /average 1.00 1.00 1.17 1.19 1.01 1.02 1.16 1.20 1.10 1.42 1.20 1.67 1.02 1.05 1.15 1.21 1.03 1.07 1.16 1.23 1.17 1.50 1.19 1.65 1.05 1.10 1.18 1.28 1.07 1.13 1.22 1.32 1.23 1.81 1.34 2.02  Chapter 5. Experimental Results^  178  5.2.3.3 Effects of Fibre Additions  The effects of adding fibres to the concrete mixture on the stresses in the deformed rebar were found to be quite different for polypropylene and steel fibres. From Fig. 5.12 it can be seen that the polypropylene fibres did not have much effect on the values of the steel stresses and their distribution along the rebar, while the steel fibres greatly increased the values of the steel stresses at the loaded end of the rebar. This effect of the steel fibres became larger with an increase in the fibre content, as illustrated in Fig. 5.13. Table 5.3 gives the relatives index numbers, which partly reflect the effects.  15.9^  819^  47.7  Distance from the Loaded End (mm)  63.5  Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%) Figure 5.12: Effects of Fibre Additions on the Stresses in the Deformed Rebar (Different Fibres)  Chapter 5. Experimental Results^  179  Table 5.3: Effects of Adding Fibres on the Steel Stresses Loading Type a  Static  Medium II  Impact III  Impact III (pull-out)  'From push-in tests.  Type of Specimen Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete  Fibre Content 0% 0.1% 0.5% 0.5% 1.0% 0% 0.1% 0.5% 0.5% 1.0% 0% 0.1% 0.5% 0.5% 1.0% 0% 0.1% 0.5% 0.5% 1.0%  Relative Index / pea k /average 1.00 1.00 1.00 1.00 1.01 1.02 1.10 1.03 1.10 1.42 1.07 1.03 1.10 1.05 1.23 1.16 1.13 1.24 1.65 1.19 1.10 1.05 1.10 1.05 1.13 1.07 1.12 1.55 1.81 1.23 0.95 0.94 0.95 0.94 0.96 0.94 0.97 0.96 0.98 0.97  180  Chapter 5. Experimental Results^  15.9^  31.8^  47.7  Distance from the Loaded End (mm)  0.0%  0.5%^1.0%  Figure 5.13: Effects of Steel Fibre Additions on the Stresses in the Deformed Rebar (Different Fibre Content)  Chapter 5. Experimental Results^  181  5.2.3.4 Differences between Pull-out and Push-in Tests  Under either static or impact loading, push-in tests always produced greater stresses in the steel rebar than pull-out tests. As stated earlier, this is due to the Poisson effect. Figs. 5.14 and 5.15 show some of these results. Also, Table 5.4 gives some relative index numbers.  159^  319^  47.7  ^  Distance from the Loaded End (mm)  636  Pull-out^Push-in Figure 5.14: Stresses in the Deformed Rebar for Pull-out and Push-in Tests (Static)  182  Chapter 5. Experimental Results^  Table 5.4: Effects of Pull-out and Push-in Forces on Steel Stresses Loading Rate  Static  Medium II  Impact III  Type of Specimen Plain Con crete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Loading Type Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in  Relative Index 'peak /average 0.91 0.92 1.00 1.00 0.92 0.92 1.01 1.02 0.93 0.94 1.81 1.23 0.93 0.93 1.05 1.02 0.94 0.93 1.03 1.07 0.95 0.95 1.17 1.50 0.95 0.94 1.10 1.05 0.94 0.96 1.13 1.07 0.98 0.97 1.81 1.23  Chapter 5. Experimental Results^  I 14  00  183  ^15.9^815^47.7  Distance from the Loaded End (mm)  $35  Pull-out^Push-in 1•11.111■ 0•1•MIMIO  •■■•■■■••  Figure 5.15: Stresses in the Deformed Rebar for Pull-out and Push-in Tests (Impact)  Chapter 5. Experimental Results^  184  5.3 Concrete Stresses  5.3.1 General  The concrete stress refers to the axial stress inside the concrete at the interface between steel rebar and concrete; in some cases it also refers to the stress inside the concrete in the vicinity of the rebar. There are also radial and circumferential stresses in the concrete. However, the study of the stresses in the concrete would emphasize on the axial stress. Not only does the amount of force transmitted from the steel rebar depend on the stress state of the concrete and its strength, but also the slip at any given point at the interface is determined by the difference in strain between the steel and the concrete, and by the development of cracks in the concrete. Unlike the stress in the steel, the stress in the concrete is not easy to measure without disturbing the stress field in a small specimen. In this study, it was calculated from the the stress in the steel by applying static equilibrium conditions (Eqs. 4.23 and 4.24). As stated before, the distribution curves of concrete stresses were plotted based on the four average data points between strain gauges and on the boundary conditions at the loaded and free ends, and only fitted curves are shown in all figures except in the first one (Fig. 5.16), in which both the data points and the best fit curves are shown.  5.3.2 Effects of Loading Rate  For both plain concrete and fibre reinforced concrete specimens, the stresses in the concrete increased with an increase in loading rate, as shown in Fig. 5.16. This is consistent with the well-known effects of stress rate on concrete strength.  Chapter 5. Experimental Results^  185  5.3.3 Effects of Concrete Strength  High strength concrete can carry more load without cracking or failure than normal strength concrete under static loading. But high strength concrete containing silica fume may allow cracking at a low level of loading under impact condition. Figs. 5.17 and 5.18 show the stresses in the concrete at the interface between the steel and the concrete under static and impact loading, respectively. Note that for normal strength concrete, the stress at the loaded end almost doubles in going from static to impact loading; for the high strength concrete, the increase in stress is more modest, about 22%.  5.3.4 Effects of Fibre Additions  The addition of polypropylene fibres (either 0.1% or 0.5% by volume) did not have much influence on the stresses in the concrete under any loading conditions, in terms of either the stresses or their distribution, as illustrated in Figs. 5.19, 5.20 and 5.21, although there were modest improvement for the dynamic loading. However, steel fibres seemed to have improved the tensile strength of the concrete mixture, and the shear strength as well. Thus, the stresses in the concrete increased for the steel fibre concrete specimens, and the slopes of the distribution curves also increased. Furthermore, because steel fibres improved the crack resistance there were reduced stress concentrations in the distribution diagram.  186  Chapter 5. Experimental Results ^  33 ai  10  9  V 6 0 0 U  0 4  f i  A WI  E  i'A o o  15.9^ 31.9^ 47.7  Distance from the Loaded End (mm)  636  Static^Medium II^Impact III  Figure 5.16: Effects of Loading Rate on the Stresses in the Concrete  0^ 15.9^ 31.9^ 47.7  Distance from the Loaded End (mm)  63.0  Normal Strength^High Strength Figure 5.17: Effect of Concrete Strength on the Stresses in the Concrete (Static)  Chapter 5. Experimental Results^  187  g  O  O  fi  4  2  15.9^  31.8^  47.7  Distance from the Loaded End (mm) Normal Strength^High Strength Figure 5.18: Effect of Concrete Strength on the Stresses in the Concrete (Impact)  15.9^  91.8^  47.7  Distance from the Loaded End (mm) Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%)  Figure 5.19: Effects of Fibres on the Stresses in the Concrete (Static)  Chapter 5. Experimental Results ^  g 6  O 0  V 4  2  0^  159^ 318^ 47.7  Distance from the Loaded End (mm)  Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%)  Figure 5.20: Effects of Fibres on the Stresses in the Concrete (Medium)  0^  15.9^ 319^ 47.7  Distance from the Loaded End (mm) Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%) Figure 5.21: Effects of Fibres on the Stresses in the Concrete (Impact)  188  Chapter 5. Experimental Results^  189  5.3.5 Differences between Pull-out and Push-in Tests  Due to the Poisson effect, there was no radial force acting at the contact surface of concrete after the chemical adhesion had been destroyed during the pull-out tests, especially for specimens with smooth rebars. The stresses in the concrete, thus, were generally less for pull-out tests than push-in tests. Fig. 5.22 shows the difference between the pull-out and push-in tests for a specimen with steel fibre concrete under impact loading.  15.9^ 819^ 47.7  Distance from the Loaded End (mm) Pull-out^Push-in  Figure 5.22: The Stresses in the Concrete for Pull-out and Push-in Tests (Impact)  Chapter 5. Experimental Results^  190  5.4 Bond Stresses  5.4.1 General  The measurements of bond stress represent perhaps the most important results of this experimental study. The local bond stresses were calculated from the axial stresses in the steel by the equilibrium condition,  u  =  --^)  4AX  D  (4.24)  The bond stress calculated from this equation is the average bond stress over a length of 15.9 mm (the spacing between two consecutive strain gauges). Fig. 5.23 illustrates the typical bond stresses at the peak load,  Fb = 30 kN, for a plain concrete specimen with  smooth rebar subjected to an impact test with a drop height of :300 mm. Note that the bond stress was constant over the entire embedded length of the rebar. As stated before, the distribution curves of bond stresses were plotted based on the four average data points between strain gauges and on the boundary conditions at the loaded and free ends, and only fitted curves are shown in all figures except in the first one (Fig. 5.2:3), in which both the data points and the best fit curves are shown.  5.4.2 Tests with Smooth Bars  For all of the specimens with smooth rebars, the effects of loading rate, concrete strength or the addition of fibres on the bond stresses were not significant, in terms of either their values or distributions, as shown in Figs. 5.24, 5.25 and 5.26. It can be seen from these figures that for static loading the bond stresses are almost uniform along the  Chapter 5. Experimental Results^  191  but the nature of the distribution remained unchanged. This was because the bond stress between a smooth rebar and the concrete was due only to chemical adhesion and frictional resistance. A high rate of loading caused a slight stress concentration at the loaded end, which might be due to the sudden change of the boundary condition of the rebar (from a free surface to concrete confinement). Due to the Poisson effect there was almost no frictional resistance at the interface between the rebar and the concrete after the adhesion had been destroyed for the pull-out test. In contrast, the frictional force at the interface between the rebar and the concrete would increase to a maximum value when the push-in force increased (radial stress also increased), so the bond stress values were larger for push-in tests than those for pull-out tests; though the uniform nature of the distribution remained the same. An example of this is given in Fig. 5.27.  50  S  wo nt  40  l  co 20  I0  r4 10  00  ^ 154^ 312^ 47.7  Distance from the Loaded End (mm)  Figure 5.23: The Bond Stresses for a Smooth Rebar  SSA  Chapter 5. Experimental Results^  192  so 03 40  33 ehl 20  A  T  10  o  o  15.9^ 31.9^ 477  ^  Distance from the Loaded End (mm)  63.6  Static^Medium II^Impact HI Figure 5.24: Effect of Loading Rate on the Bond Stresses for a Smooth Rebar  159^ siB^ 47.7  Distance from the Loaded End (mm) Normal Strength^High Strength Figure 5.25: Effect of Concrete Strength on the Bond Stresses for a Smooth Rebar  Chapter 5. Experimental Results^  193  so  15.9^ 311^ 47.7  Distance from the Loaded End (mm) Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)  Figure 5.26: Effect of Fibre Additions on the Bond Stresses for a Smooth Rebar  15.9^ 311^ 47.7  Distance from the Loaded End (mm)  Pull-out^Push-in  Figure 5.27: The Bond Stresses for a Smooth Rebar for Pull-out and Push-in Tests  Chapter 5. Experimental Results^  194  5.4.3 Tests with Deformed Bars  For simplicity, all of the figures given in this section, unless specified, are for the specimens with normal strength concrete in push-in tests.  5.4.3.1 Effects of Loading Rate  For the specimens with deformed bars, the peak bond stresses increased considerably with an increase in loading rate. There were higher stress concentrations at the loaded end than for specimens with smooth bars; Unlike the specimens with smooth rebars, the bond stress distribution curves were no longer horizontal lines. The existence of ribs on the rebar and cracks in the concrete generally caused changes in the curvature of the steel stress curves. In addition, the bond stress distribution curves were not as smooth as were the curves for smooth bars. Roughly speaking, these curves tended to have larger slopes than those from tests with smooth bars. This means that higher bond stresses were developed under higher loading rates. Fig. 5.28 shows some different bond stress distribution curves under different loading rates for a plain concrete specimen. By comparing Fig. 5.29 with Fig. 5.28 it can be concluded that the addition of polypropylene fibres to the concrete had no significant influence on the results, in terms of the effect of the loading rate on the bond stresses. However, the loading rate seemed to have a greater effect on specimens made of steel fibre reinforced concrete than on any other types of specimens (see Fig. 5.30). This is because the shear mechanism plays a major role in the bond-slip process for deformed bars; with the bond resistance due to the ribs bearing on the concrete. Steel fibres definitely improved the concrete strength and the crack resistance. This improvement is significant, especially under high rate loading.  Chapter 5. Experimental Results ^  195  Though the crack velocity in concrete may increase proportionally with the loading rate, the presence of steel fibre tends to reduce the rate of crack propagation. It was found that, in these tests, the effect of the addition of steel fibres dominated the behaviour. Therefore, the bond stress increased dramatically with an increase in loading rate. It should be noted that Figs. 5.28 to 5.30 are from tests of specimens with normal strength concrete. Fig. 5.3:1 is for specimens with high strength concrete reinforced with 1.0% (by volume) steel fibres. It was found that the influence of the loading rate was even more significant for high strength concrete than for normal strength concrete. Similar to the case of specimens with smooth rebars, push-in tests always gave higher bond stresses than pull-out tests, as shown in Fig. 5.32. In order to evaluate the effects of the loading rate on the bond stresses for several important variables, two relative "indices", / peak and /s l ope were introduced. They are defined as  peal: value of bond stress under a particular loading condition /peak^ peak value under static loading  and  slope under a particular loading condition /slope^slope value under static loading  the slope are calculated based on the bond stress vs. distance from the loaded end. Some of the results are summarized in Table 5.5.  Chapter 5. Experimental Results^  196  Table 5.5: Effects of Loading Rate on the Bond Stresses Type of Specimen  Plain Concrete  Polypropylene Fibre Concrete (0.5%)  Steel Fibre Concrete (1.0%)  Steel Fibre Concrete (1.0%) (Pull-out)  Steel Fibre Concrete (1.0%) (High Strength)  Loading Rate a Static Medium I b Medium II Impact I Impact II Impact III Static Medium I Medium II Impact I Impact II Impact III Static Medium I Medium II Impact I Impact II Impact III Static Medium I Medium II Impact I Impact II Impact III Static Medium I Medium II Impact I Impact II Impact III  Relative Index peak _peak 1.00 1.02 1.05 1.06 1.08 1.10 1.02 1.05 1.07 1.09 1.11 1.13 1.42 1.46 1.50 1.65 1.72 1.81 0.93 0.94 0.95 0.96 0.97 0.98 1.54 1.60 1.68 1.75 1.86 1.91  slope 1.00 1.01 1.02 1.02 1.04 1.05 1.01 1.02 1.03 1.04 1.05 1.07 1.10 1.11 1.17 1.19 1.21 1.23 0.94 0.94 0.95 0.95 0.96 0.97 1.16 1.17 1.22 1.25 1.27 1.30  'From push-in tests with normal strength concrete specimen, unless specified. b See Table 3.9 in (liapter 3 for details.  Chapter 5. Experimental Results^  197  S 40 s  I I  )^  10  15$^  311^  472  Distance from the Loaded End (mm) Static^Medium II^Impact III  Figure 5.28: Effects of Loading Rate on the Bond Stresses (Plain Concrete)  i.e.... ...re.... warm, angrier.  .(; ^  15$^  311^  472  ^  Distance from the Loaded End (mm)  116  Static^Medium II^Impact III Figure 5.29: Effects of Loading Rate on the Bond Stresses (Polypropylene Fibre Concrete)  Chapter 5. Experimental Results^  198  a40  a,  I  aro so .•■■■■•■•  0  10  15.9^  31.8^  47.7  Distance from the Loaded End (mm) Static^Medium II^Impact III Figure 5.30: Effects of Loading Rate on the Bond Stresses (Steel Fibre Concrete) so  0^ 0  159^  31.8^  47.7  Distance from the Loaded End (mm) Static^Medium II^Impact III Figure 5.31: Effects of Loading Rate on the Bond Stresses (High Strength Concrete)  199  Chapter 5. Experimental Results^  5.4.3.2 Effects of Concrete Strength  Generally speaking, the bond stresses increased for high strength concrete specimens. This seems logical, since the shear mechanism is the main mechanism for the bond resistance of deformed bars. Fig. 5.33 gives an example to show the different effects of loading rate. By using the relative "index" number, which is defined in the previous section, the effects of concrete strength on the bond stresses can be shown more clearly. Table 5.6 gives some of these results. Table 5.6: Effects of Concrete Strength on the Bond Stresses Loading Type a  Static  Medium II  Impact III  'From push-in tests.  Type of Specimen  Concrete Strength  Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Normal High Normal High Normal High Normal High Normal High Normal High Normal High Normal High Normal High  Relative Index /peak /slope 1.00 1.19 1.02 1.20 1.42 1.67 1.05 1.21 1.07 1.23 1.50 1.65 1.10 1.28 1.13 1.32 1.81 2.02  1.00 1.17 1.01 1.16 1.10 1.20 1.02 1.15 1.03 1.16 1.17 1.19 1.05 1.18 1.07 1.22  1.23 1.34  Chapter 5. Experimental Results^  159^  312^  200  477  Distance from the Loaded End (mm) Static^Medium II^Impact III Figure 5.32: Effects of Loading Rate on the Bond Stresses (Pull-out Tests)  0^  15.9^  31.0^  47.7  Distance from the Loaded End (mm)  Normal Strength^High Strength  Figure 5.33: Effects of Concrete Strength on the Bond Stresses  201  Chapter 5. Experimental Results^  5.4.3.3 Effects of Fibre Additions  The effects on the bond stress of adding fibres to the concrete mixture were found to be quite different for polypropylene and steel fibres. Figs. 5.34 and 5.35 illustrate two examples. Table 5.7 gives the relatives index numbers, which partly reflect these effects.  40  zo • •^  •  to  154^  919^  477  ^  Distance from the Loaded End (mm)  63.6  Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%) Figure 5.34: Effects of Fibre Additions on the Bond Stresses (Different Fibres)  5.4.3.4 Differences between Pull-out and Push-in Tests  Under either static or impact loading, push-in tests always produced greater bond stresses in the rebar than pull-out tests. Figs. 5.36 and 5.37 shows some of these results, while Table 5.8 gives some relative index numbers.  202  Chapter 5. Experimental Results^  SO  a  I  40  30  14 20  0 10 02  00  15.9^ 3I9^ 47.7  Distance from the Loaded End (mm) 0.0%  0.5%  1.0%  Figure 5.35: Effects of Steel Fibre Additions on the Bond Stresses (Different Fibre Content)  15.9^ 313^ 47.7  Distance from the Loaded End (mm)  SIB  Pull-out^Push-in  Figure 5.36: The Bond Stresses for Pull-out and Push-in Tests (Static)  203  Chapter 5. Experimental Results^  Table 5.7: Effects of Fibre Additions on the Bond Stresses Loading Type a  Static  Medium II  Impact III  Impact III (pull-out)  From push-in tests.  Type of Specimen Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete Plain Concrete Polypropylene Fibre Concrete Steel Fibre Concrete  Fibre Content 0% 0.1% 0.5% 0.5% 1.0% 0% 0.1% 0.5% 0.5% 1.0% 0% 0.1% 0.5% 0.5% 1.0% 0% 0.1% 0.5% 0.5% 1.0%  Relative Index / slope 1.00 1.00 1.00 1.00 1.02 1.01 1.10 1.03 1.42 1.10 1.07 1.03 1.10 1.05 1.23 1.16 1.24 1.13 1.65 1.19 1.10 1.05 1.10 1.05 1.13 1.07 1.55 1.12 1.81 1.23 0.95 0.94 0.95 0.94 0.96 0.94 0.97 0.96 0.98 0.97  / peak  Chapter 5. Experimental Results^  204  Table 5.8: The Effects of Pull-out and Push-in Forces on the Bond Stresses Loading Rate  Static  Medium II  Impact III  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (o.5%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (0.5%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (0.5%)  Loading Type Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in  Relative Index /peak / slope 0.92 0.91 1.00 1.00 0.92 0.92 1.01 1.02 0.93 0.94 1.81 1.23 0.93 0.93 1.05 1.02 0.94 0.93 1.07 1.03 0.95 0.95 1.50 1.17 0.95 0.94 1.10 1.05 0.96 0.94 1.13 1.07 0.98 0.97 1.81 1.23  Chapter 5. Experimental Results^  Distance from the Loaded End (mm)  Pull-out^Push-in Figure 5.37: The Bond Stresses for Pull-out and Push-in Tests (Impact)  205  Chapter 5. Experimental Results^  206  5.5 Slip and Slip Distribution  5.5.1 General  The local slip between the rebar and the concrete at any point along the rebar was computed from the compatibility condition between the two materials,  w (x) = o (E — c, )  ^  S  (4.25)  since the strain values in both steel and concrete, c s and c„, were average numbers between any two consecutive measurement points, the local slips calculated were average numbers also. As stated before, the distribution curves of slips were plotted based on the four average data points between strain gauges and on the boundary conditions at the loaded and free ends, and only fitted curves are shown in all figures except in the first one (Fig. 5.38), in which both the data points and the best fit curves are shown.  5.5.2 Tests with Smooth Bars  For specimens with smooth bars, the slips uniformly distributed along the rebars (see Fig. 5.38). This was true for all loading conditions, since the bond between the steel and the concrete was due only to the chemical adhesion and frictional resistance between the  steel and the concrete. In many pull-out or push-in tests the local slips were found by dividing the measured end slips by the embedment lengths. This method is appropriate for smooth bars.  Chapter 5. Experimental Results^  207  5.5.3 Tests with Deformed Bars  The results for specimens with deformed bars were quite different from those for smooth bars. They will be discussed in the following sections.  5.5.3.1 Effects of Loading Rate  At the same load level, the slip values were generally lower for higher loading rates than for lower loading rates. Table 5.9 gives one example of this, in terms of the local slip values at the middle of the embedment length. Table 5.9: The Local Slips at the Middle of the Embedment Length Concrete Strength  Normal  High  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Loading Type Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in Pull-out Push-in  Local Slip (0.001 7n7n) Medium Impact Static :34 :35 :38 :31 32 :35 :33 33 36 :34 30 :31 28 31 30 :39 27 30 :33 :35 :37 :39 :33 35 :34 :34 35 :3:3 34 :36 26 27 :30 24 26 31  Chapter 5. Experimental Results^  208  5.5.3.2 Effects of Concrete Strength  The influence of concrete strength on the slip and slip distribution was found to be slight, under either static or dynamic loading conditions, as illustrated in Figs. 5.39 and 5.40.  5.5.3.3 Effects of Fibre Additions  Adding polypropylene fibres to the concrete mixture does not change either its strength or Young's modulus significantly, and thus has little effect on the slip distribution for any loading conditions, as shown in Fig. 5.41. Adding steel fibres to the concrete mixture at 1.0% by volume increased not only the strength, but also the Young's modulus. This resulted in a. relatively small slip at the same loading level compared to plain concrete, as can be seen from Fig. 5.42. For the purpose of comparison the slip distribution curves in Fig. 5.42 were referred to the same external load and not the peak load. It is known that the presence of steel fibres makes ,  crack propagation slower and inhibits crack opening, especially for dynamic loading. This improved the "slip concentration" at the interface between steel and concrete. One of the representative curves is shown in Fig. 5.43.  5.5.3.4 Differences between Pull-out and Push-in Tests  Differences in the local slips between pull-out and push-in tests can also be found from Table 5.9. Slips in push-in tests were less than in pull-out tests. This was mainly due to  Chapter 5. Experimental Results^  209  5  •  0 ^ 0  153  31.3^ 47.7  On  Distance from the Loaded End (mm)  Figure 5.38: The Local Slip Distribution for Specimens with Smooth Bars  s  i!  0^  0  15.9^  31.8^ 47.7  ^  Distance from the Loaded End (mm)  03.5  Normal Strength^High Strength Figure 5.39: Influence of Concrete Strength on Slip Distribution (Static)  Chapter 5. Experimental Results^  210  1.11••■■  15.9^ 31.5^ 47.7  Distance from the Loaded End (mm) Normal Strength^High Strength Figure 5.40: Influence of Concrete Strength on Slip Distribution (Impact)  a4  d  3  TM 2  15.9^ 315^ 47.7  Distance from the Loaded End (mm) Plain Polypropylene Fibers (0.5%)  Figure 5.41: Influence of 0.5% by Volume Polypropylene Fibres on Slip Distribution (Impact)  211  Chapter 5. Experimental Results^  159^  318^  47.7  Distance from the Loaded End (mm)  Plain^Steel Fibers (0.3%) ■••••■• ••■•■ •■■■•  Figure 5.42: Influence of 0.5% by Volume Steel Fibres on Slip Values (Static)  ^••■•■••••...., TAM. ....ma  15.9^  318^  472  Distance from the Loaded End (mm)  Plain^Steel Fibers (0.5%) aemmow  •••••••■• ..•=1•11016  Figure 5.43: Influence of 0.5% by Volume Steel Fibres on Slip Distribution (Impact)  Chapter 5. Experimental Results^  the fact that there were higher radial force in push-in tests than in pull-out tests.  212  Chapter 5. Experimental Results^  213  5.6 Internal Cracking  5.6.1 General  For specimens with smooth bars, the basic mechanism of the bond-slip process is a failure of the chemical adhesion and frictional forces at the interface between steel and concrete. Failure occurs when the high local stresses reach critical values, after which there is no further mechanical interlocking taking place at the interface for smooth bars. The force due to adhesion and friction is always less than that needed to initial transverse cracks. Several specimens with smooth rebars were examined by cutting through along their central plane, and no transverse cracks due to the bond action were found (see Fig. 5.44). For specimens with deformed bars, the cracking mechanism of the pull-out tests was different from that of the push-in tests. In the case of pull-out tests, when the bond stress reached the critical value, a longitudinal tensile stress and a radial tensile stress (tending to cause separation), combined to produce the first internal cracks from the tops of ribs because of the stress concentrations at these locations. With a further increase in external loading, the Poisson effect in the steel would result in a decrease in the bar diameter, and the contact area between the concrete and the ribs of the deformed bar would be reduced. This would increase the bearing stress between the concrete and the ribs, and enhance crack development around the tip of each rib, as shown in Fig. 5.45. For the push-in tests, the stress transfer mechanism involved was quite different, as the push-in force in the rebar deformed the concrete inwards (in the direction of the force). This served to tighten the concrete around the bar and increased the frictional resistance  Chapter 5. Experimental Results^  214  between the concrete and the rebar. The slight increase in the diameter of the rebar due to the Poisson effect also improved the frictional resistance. A small zone of concrete was subjected to compression-tension-tension in the radial, longitudinal and circumferential directions, respectively. However, few cracks were found after slicing the specimens. The inward deformation of the concrete provided some lateral compression in the concrete surrounding the bar, and thus reduced the radial component of the wedging force. There were fewer and smaller cracks found for push-in loading cases. One photograph of the internal cracks for push-in tests is shown in Fig. 5.46. The test results showed that there was not much difference between the normal strength concrete specimens and the high strength concrete specimens under static loading, in terms of the internal cracking.  Figure 5.44: No Transverse Cracks Formed at the Interface for Specimens with Smooth Bars  Chapter 5. Experimental Results ^  215  10 min .44011  Figure 5.45: Internal Cracks in Pull-out Tests with Deformed Bars (Arrow Indicates the Crack around the Rib of the Rebar)  Figure 5.46: Internal Cracks in Push-in Tests with Deformed Bars (Arrow Indicates the Crack around the Rib of the Rebar)  Chapter 5. Experimental Results^  216  5.6.2 Effects of Loading Rate and Concrete Strength  The test results showed that the influence of loading rate on crack development was quite different for normal and high strength concrete. There were fewer cracks for normal strength concrete specimens with an increase in loading rate, as illustrated in Fig. 5.47. This may be explained by the fact that the crack velocity in the normal strength concrete mixture was relatively slow, so there was not sufficient time for a crack to develop under a high rate loading (impact loading). The interesting thing was that an opposite result was obtained for high strength concrete specimens. That is, there seemed to be more cracks when the loading rate increased (see Fig. 5.48). This may be due to the higher crack velocity in the high strength concrete, in which a considerable amount of silica fume was used. As for the bond behaviour normal strength concrete is inherently less brittle than high strength concrete containing silica fume.  5.6.3 Effects of Fibre Additions  Both polypropylene fibres and steel fibres improved the crack resistance. The presence of fibres made crack propagation slower and inhibited crack opening. The fibres enabled stress to be transferred across cracked sections, allowing the affected parts of the composites to retain some post-cracking strength and to withstand greater deformation. Photographs in Figs. 5.49 and 5.50 show the effects of fibres. There were more and wider crack in the plain concrete specimens than in the fibre reinforced concrete specimens.  Chapter 5. Experimental Results^  217  Figure 5.47: Influence of Loading Rate on Internal Cracks (Normal Strength Concrete, Arrow Indicates the Crack around the Rib of the Rebar)  Chapter 5. Experimental Results^  218  Figure 5.48: Influence of Loading Rate on Internal Cracks (High Strength Concrete, Arrow Indicates the Crack around the Rib of the Rebar)  Chapter 5. Experimental Results^  219  Figure 5.49: Influence of 0.5% by Volume Polypropylene Fibres on Internal Cracks (Arrow Indicates the Crack around the Rib of the Rebar)  Figure 5.50: Influence of 0.5% by Volume Steel Fibres on Internal Cracks (Arrow Indicates the Crack around the Rib of the Rebar)  Chapter 5. Experimental Results^  220  5.7 Bond Stress vs. Slip Relationship  5.7.1 General  The bond stress-slip relationship represent the most important result of this experimental work. For a particular specimen, the type of rebar, the concrete strength, the fibre type and content, and the type of loading and loading rate were given. The resulting bond stress-slip relationship contained four variables: the bond stress, u, the slip, w, the time, t, and the location, x. From the results and discussions in the previous sections, it is obvious that the bond stress-slip relationships kept changing with time under dynamic loading; in other words, there were different relationships between the bond stress and the slip at different stages of loading. For deformed bars the bond stress-slip relationship were not uniformly distributed, and thus, strictly speaking, a bond stress-slip relationship is meaningless unless specified for a particular moment and a particular point. That is, the bond stress-slip relationship should be expressed as, u = u (w,t,x)^  (5.1)  this made it almost impossible to establish and analyze the bond stress-slip relationships for all of the specimens tested. In practice and for simplicity, all of the bond stress-slip relationships were referred to an average value over the embedment length, unless specified. Also, since the slips of some specimens might still develop up to greater values after the 'peak bond stresses', all of the bond stress vs. slip relationship curves were plotted a bit beyond the peak bond stresses; this makes the comparisons between different specimens easier. After the bond stress-slip relationship and the slips were determined, the relationships  Chapter 5. Experimental Results ^  221  between them were established through the variable time. The related equations are derived and listed in Chapter 4.  5.7.2 Smooth Bars  Fig. 5.51 illustrates the bond stress-slip relationship at the peak load,  Fb = 30 kN.  This was a plain concrete specimen with a smooth rebar subjected to an impact test with a drop height of :300 mm. For the specimens with smooth rebars, the effects of loading rate, concrete strength and fibre additions on the bond stress-slip relationship were not significant, as shown in Figs. 5.52, 5.53 and 5.54. It can be seen from these curves that for static loading the bond stress-slip relationships were linear up to a very high loading level. Increasing the concrete strength or adding steel fibres resulted in a slight increase in the slopes of the curves, but the linearity remained unchanged. A high rate of loading caused a slight stress concentration at the loaded end, which might be due to the sudden change of the boundary condition of the rebar (from a free surface to concrete confinement). Due to the Poisson effect there was almost no frictional resistance existing at the interface between the rebar and the concrete after the adhesion had been destroyed for the pull-out test. In contrast, the frictional force at the interface between the rebar and the concrete would increase to a maximum value when the push-in force increased (radial stress also increased), so the bond stress values were much larger for push-in tests than for pull-out tests, though the uniform nature of the distribution remained the same. One of the example is given in Fig. 5.55.  Chapter 5. Experimental Results^  222  es a 40 2 xx  ixE a  20  e 0  0 10 0:1  2^3  ^ ^ 4 6  Local Slip (0.01 mm)  Figure 5.51: The Bond Stress vs. Slip Relationship for a Smooth Rebar  1^2^8^4^5  Local Slip (0.01 mm)  Static^Medium II^Impact III Figure 5.52: Effects of Loading Rate on the Bond Stress vs. Slip Relationship for Smooth Rebars  Chapter 5. Experimental Results^  2  ^  Local Slip (0.01 mm)  223  4  Normal Strength^High Strength Figure 5.53: Effects of Concrete Strength on the Bond Stress vs. Slip Relationship for Smooth Rebars  so  30  20 1  60  O  10  00^ 1^ 2^ 3^ 4^ 6  Local Slip (0.01 mm) Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)  Figure 5.54: Effects of Fibre Additions on the Bond Stress vs. Slip Relationship for Smooth Rebars  Chapter 5. Experimental Results^  224  5.7.3 Deformed Bars  For simplicity, all of the results including figures given in this section, unless specified, are for the specimens with normal strength concrete in push-in tests.  5.7.3.1 Effects of Loading Rate  For all the specimens with deformed bars, the peak bond stress increased considerably with an increase in loading rate. There were higher stress concentrations at the loaded ends than for the specimens with smooth bars. Unlike the specimens with smooth rebars, the bond stress-slip relationship curves were no longer straight lines. The existence of ribs and cracks generally caused changes in curvature of the steel stress curves, and the bond stress-slip relationship curves were not as smooth as the curves for smooth bars. Higher bond stresses were developed under higher loading rates. Fig. 5.56 shows two different bond stress-slip relationships under different loading rates for a plain concrete specimen. By comparing Fig. 5.57 with Fig. 5.56 it can be concluded that the addition of polypropylene fibres to the concrete had no significant influence on the results, in terms of the effects of the loading rate on the bond stress values and the shape of the curves. However, the loading rate seemed to have greater effects on specimens made of steel fibre reinforced concrete (see Fig. 5.58). The reason for this phenomenon is again that the shear mechanism plays a major role in the bond-slip process for deformed bars (see Sections 5.3 and 5.6). It should be noted that Figs. 5.56 to 5.58 are from the tests for specimens with normal  Chapter 5. Experimental Results^  225  concrete strength. Fig. 5.59 is for specimens with high concrete strength reinforced by steel fibres. It was found that the influence of the loading rate was more significant for high strength concrete than for normal strength concrete. Similar to specimens with smooth rebars, the bond stress-slip relationships from pushin tests were quite different from those from pull-out tests. There were higher bond stresses at the loaded end and larger slopes in the bond stress-slip relationship curves in push-in tests than in pull-out tests, as shown in Fig. 5.60.  5.7.3.2 Effects of Concrete Strength  General speaking, the peak bond stress value increased for high strength concrete specimens. This seems logical because the shear mechanism is the main mechanism in the bond resistance for deformed bars. Fig. 5.61 give an example to show the effect of different loading rates.  5.7.3.3 Effects of Fibre Additions  The effects of adding fibres to the concrete mixture on the bond stress vs. slip were found to be different for polypropylene and steel fibres. Figs. 5.62 and 5.63 illustrate two examples of this. Polypropylene fibre additions had very little influence; while steel fibre additions greatly changed the peak values and the shapes of the curves. higher fibre content seemed to increase this effect.  Chapter 5. Experimental Results^  i  ^  2^ 3  226  ^ ^ 4  Local Slip (0.01 mm)  s  Pull-out^Push-in ,...,..^........ .....,,  Figure 5.55: The Bond Stress vs. Slip Relationship for a Smooth Rebar for  Pull-out and Push-in Tests so ...... 0 40 10o  X  30  CA  E  1 20 1  60  0  0 0  10  •  00  ^ 1^ 2^ 3^ 4  Local Slip (0.01 mm)  s  ^Static^Medium II^Impact III Figure 5.56: Effects of Loading Rate on the Bond Stress vs. Slip Relationship  (Plain Concrete)  Chapter 5. Experimental Results^  227  ^Aommmliwwwwww■I  Local Slip (0.01 mm) Static^Medium II^Impact III Figure 5.57: Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Polypropylene Fibre Concrete) 50  55 40  2 •  ag 1 0 1^2^3^4^5^6  ^  Local Slip (0.01 mm)  7  Static^Medium II^Impact III • Figure 5.58: Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Steel Fibre Concrete)  Chapter 5. Experimental Results^  228  50  3^4^5^6^7  Local Slip (0.01 mm) Static^Medium II^Impact III Figure 5.59: Effects of Loading Rate on the Bond Stress vs. Slip Relationship (High Strength Concrete) 50  2^3^4^5  ^  Local Slip (0.01 mm)  6^7^5  Static^Medium II^Impact III Figure 5.60: Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Pull-out Tests)  229  Chapter 5. Experimental Results^  2^3^4^5^6  Local Slip (0.01 mm)  ^ ^ 7 6  Normal Strength^High Strength Figure 5.61: Effects of Concrete Strength on the Bond Stress vs. Slip Relationship  1^2^3^4^5^6^7  Local Slip (0.01 mm)  Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%) am.11••■  Figure 5.62: Effects of Fibre Additions on the Bond Stress vs. Slip Relationship (Different Fibres)  Chapter 5. Experimental Results^  230  5.7.3.4 Differences between Pull-out and Push-in Tests  Under either static or impact loading, push-in tests always produced greater bond stresses than pull-out tests. Figs. 5.64 and 5.65 show some of these results.  Chapter 5. Experimental Results^  3^4^5  231  ^ ^ 6 7^e  Local Slip (0.01 mm)  0.0%  0.3%^1.0%  Figure 5.63: Effects of Steel Fibre Additions on the Bond Stress vs. Slip Relationship (Different Fibre Content)  Local Slip (0.01 mm) Pull-out^Push-in •••■•■■■  .1■1•••  ■■■■■•  Figure 5.64: The Bond Stress vs. Slip Relationship for Pull-out and Push-in Tests (Static)  Chapter 5. Experimental Results^  232  64 40 am,  10  3^4^5^6^7^8  Local Slip (0.01 mm)  Pull-out^Push-in ■•• Figure 5.65: The Bond Stress vs. Slip Relationship for Pull-out and Push-in Tests (Impact)  Chapter 5. Experimental Results^  233  5.8 Results of Tests with Epoxy-Coated Rebars  As a. supplementary work to this study on bond behaviour, some tests with specimens made of epoxy coated deformed rebars were carried out under static, medium II and impact III loading. These specimens were made of both normal strength and high strength concrete, and about two third of them were tested for push-in loading and the rests for pull-out loading. Details of the specimen preparation are given in Section 3.2.6 in Chapter 3.  5.8.1 Effect on the Bond Stress  Results of the bond stresses are given in Table 5.10 (for normal strength concrete) and Table 5.11 (for high strength concrete). Similar to the discussion in the previous sections, two relative "indices" /peak and /average were introduced to represent the differences ,  between specimens with uncoated rebars and those with coated rebars. They are defined as peak value of bond stress for specimens with coated rebars peak^peak value of bond stress for specimens with uncoated rebars and  /average =  average value of bond stress for specimens with coated rebars average value of bond stress for specimens with uncoated rebars  It can be seen from these results that there were some decreases in both the peak and the average value of the bond stress for push-in tests, this was true for both normal strength and high strength concrete. For epoxy coated reinforcements the chemical  Chapter 5. Experimental Results^  234  adhesion and friction mechanisms were much reduced in this effect, and thus the bond resistance decreased. However, even in the push-in case, in which the frictional resistance increased due to a higher radial force acting at the interface between the rebar and the concrete, the shearing mechanism, i.e. the rib bearing action, still played a vital role in the bond resistance, and therefore the decrease in the bond stress due to the coating was relatively small. Under a high rate loading the chemical adhesion is more easily destroyed than under static or low rate loading. Also, the frictional factor at the interface may be reduced under a high rate of loadings. These factors reduced the difference in the bond stresses between specimens with coated rebars and those with uncoated rebars under impact loading, as shown by the indices of the peak and the average values of the bond stress in Tables 5.10 and 5.11. Polypropylene fibre additions did not have much effect on this. For specimens with steel fibre reinforced concrete, the shearing mechanism dominates in the bond behaviour, while changes in the chemical adhesion and frictional resistance always have little effect on the total bond resistance. This can also be seen from the Tables 5.10 and 5.11. These results also showed that epoxy coating the rebar had less effect on bond in specimens made of higher concrete strength than low concrete strength, in terms of bond resistance. The least reductions in both the peak and the average bond stress were found for the specimens made of steel fibre reinforced concrete (1.09 content by volume), as can be seen in Table 5.11. For pull-out tests, the decrease in the rebar diameter reduced the frictional effects at the interface no matter what the contact condition between the rebar and the concrete is, this resulted in very little difference in the bond stress between the tests with coated bars and uncoated bars, as shown by the data in Table 5.10 and 5.11.  Chapter 5. Experimental Results^  235  Table 5.10: Effects of Epoxy Coating the Rebar on the Bond Stresses (Normal Strength Concrete)  Loading Type  Static (Push-in)  Medium II (Push-in)  Impact III (Push-in)  Medium II (Pull-out)  Impact III (Pull-out)  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Coating Condition Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Un coated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated  Relative Index /peak /average 1.00 1.00 0.83 0.80 1.00 1.00 0.84 0.80 1.00 1.00 0.92 0.90 1.00 1.00 0.82 0.85 1.00 1.00 0.85 0.83 1.00 1.00 0.94 0.92 1.00 1.00 0.84 0.89 1.00 1.00 0.89 0.84 1.00 1.00 0.96 0.94 1.00 1.00 0.92 0.92 1.00 1.00 0.92 0.92 1.00 1.00 0.95 0.96 1.00 1.00 0.95 0.95 1.00 1.00 0.95 0.94 1.00 1.00 0.97 0.96  Chapter 5. Experimental Results ^  236  Table 5.11: Effects of Epoxy Coating the Rebar on the Bond Stresses (High Strength Concrete) Loading Type  Static (Push-in)  Medium II (Push-in)  Impact III (Push-in)  Medium II (Pull-out)  Impact III (Pull-out)  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Coating Condition Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated  Relative Index 'peak /average 1.00 1.00 0.85 0.82 1.00 1.00 0.83 0.85 1.00 1.00 0.93 0.93 1.00 1.00 0.86 0.83 1.00 1.00 0.87 0.83 1.00 1.00 0.93 0.95 1.00 1.00 0.85 0.90 1.00 1.00 0.90 0.85 1.00 1.00 0.97 0.95 1.00 1.00 0.92 0.92 1.00 1.00 0.9:3 0.92 1.00 1.00 0.96 0.95 1.00 1.00 0.96 0.95 1.00 1.00 0.96 0.95 1.00 1.00 0.97 0.96  Chapter 5. Experimental Results^  237  5.8.2 Effect on the Slip  Results of the slips are given in Tables 5.12 and 5.13. Two relative "indices", /peak and /average are defined as  /peak  peak value of slip for specimens with coated rebars peak value of slip for specimens with uncoated rebars  and  / average =  average value of slip for specimens with coated rebars average value of slip for specimens with uncoated rebars  From Tables 5.12 and 5.13it can be seen that the peak values of slips for specimen with coated rebars are larger than those for specimens with uncoated rebars. This may be due to the fact that most of the bond stresses developed at the tips of the uncoated rebar ribs from the very beginning during the bond process; the stress concentrations at these points caused wider cracks in the concrete, as shown by the four photographs in Figs. 5.66 to 5.69. The first two photographs are for specimens with uncoated rebar, and the last two for specimens with epoxy coated rebars. For specimens made of steel fibre reinforced concrete, especially made of high strength concrete, this effect was relatively small, which might be due to the improved resistance of the fibre matrix to crack development. Similar to the bond stress, and for the same reasons, the effects of coated rebars on the slips were also found to be small for pull-out tests and for high rate loading, as shown in Tables 5.12 and 5.1:3.  Chapter 5. Experimental Results^  238  Table 5.12: Effects of Epoxy Coating the Rebar on the Slip (Normal Strength Concrete)  Loading Type  Static (Push-in)  Medium II (Push-in)  Impact III (Push-in)  Medium II (Pull-out)  Impact III (Pull-out)  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Coating Condition Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated  Relative Index / pea k / average 1.00 1.00 1.19 1.17 1.00 1.00 1.20 1.16 1.00 1.00 1.10 1.08 1.00 1.00 1.16 1.10 1.00 1.00 1.11 1.15 1.00 1.00 1.08 1.07 1.00 1.00 1.14 1.08 1.00 1.00 1.15 1.08 1.00 1.00 1.06 1.04 1.00 1.00 1.03 1.02 1.00 1.00 1.03 1.03 1.00 1.00 1.02 1.02 1.00 1.00 1.04 1.02 1.00 1.00 1.04 1.02 1.00 1.00 1.02 1.01  Chapter 5. Experimental Results^  239  Table 5.13: Effects of Epoxy Coating the Rebar on the Slip (High Strength Concrete) Loading Type  Static (Push-in)  Medium II (Push-in)  Impact III (Push-in)  Medium II (Pull-out)  Impact III (Pull-out)  Type of Specimen Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%) Plain Concrete Polypropylene Fibre Concrete (0.5%) Steel Fibre Concrete (1.0%)  Coating Condition Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated Coated Uncoated ( oated Uncoated Coated  Relative Index average 'peak 'average 1.00 1.00 1.17 1.15 1.00 1.00 1.15 1.18 1.00 1.00 1.09 1.08 1.00 1.00 1.15 1.09 1.00 1.00 1.10 1.15 1.00 1.00 1.06 1.07 1.00 1.00 1.12 1.08 1.00 1.00 1.13 1.08 1.00 1.00 1.05 1.04 1.00 1.00 1.03 1.02 1.00 1.00 1.03 1.02 1.00 1.00 1.02 1.02 1.00 1.00 1.02 1.03 1.00 1.00 1.03 1.02 1.00 1.00 1.02 1.01  Chapter 5. Experimental Results^  240  5.8.3 Effect on the Bond Stress-slip Relationship  Figs 5.70 to 5.73 show four samples in comparisons of the bond stress-slip relationships for specimens with coated rebars and uncoated rebars, two for pull-out tests (normal strength concrete) and the other for push-in tests (high strength concrete). The specimens tested were steel fibre reinforced (1.0% by volume) and subjected to impact loading III. For the pull-out tests, the difference between the curve for the epoxy coated rebar specimen and the curve for the uncoated rebar specimen is quite small, in terms of the shape. For the push-in tests, the peak bond stress and the slip in the curve of the coated rebar specimen are a bit smaller than those for the uncoated rebar specimen. The difference between the coated rebar specimens and the uncoated rebar specimens reduced when the concrete strength increased.  Chapter 5. Experimental Results^  241  Figure 5.66: Internal Cracks at the Tips of the Ribs of an Uncoated Rebar (Normal Strength, Push-in, Impact)  AMI Figure 5.67: Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar (Normal Strength, Push-in, Impact)  242  Chapter 5. Experimental Results^  401117,49~'  1 m d in t'  .ri^ifok -4104^....*".Ar^•  Figure 5.68: Internal Cracks at the Tips of the Ribs of an Uncoated Rebar (High Strength, Push-in, Impact)  Figure 5.69: Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar (High Strength, Push-in, Impact)  Chapter .5. Experimental Results^  243  ^ ^ ^ 8 7 6 2^3^4^5 Local Slip (0.01 mm) Figure 5.70: The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (Normal Strength, Pull-out, Impact)  50 TT 40  2 30 "6 20 -  O  o^1^2^3^4^5^6 Local Slip (0.01 mm)  7  Figure 5.71: The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (Normal Strength, Push-in, Impact)  ^  244  Chapter 5. Experimental Results ^  50 40  1  30  65 20  S 10  Q  1  ^  ^ ^ ^ 6 7 8 2^3^4^5 Local Slip (0.01 mm)  Figure 5.72: The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (High Strength, Pull-out, Impact)  50  30 (.75 20  § 10 0  ^0^1^2^3^4^5^6 '^  Local Slip (0,01 mm)  7  Figure 5.73: The Bond Stress vs. Slip Relationship for a Specimen with an Epoxy Coated Rebar (High Strength, Push-in, Impact)  Chapter 5. Experimental Results^  245  5.8.4 Effect on the Fracture Energy  The energy transfer, energy dissipation and energy balance during the bond process for specimens with uncoated rebars will be discussed in detail in Chapter 7. Some results of the fracture energy calculation for specimens with epoxy coated bars are presented here in Table 5.14. The definition of the fracture energy in bond failure and the related formulas for calculation are given in Section 4.10 in Chapter 4 and Section 6.2 in Chapter 6. For comparison, the results for specimens with uncoated rebars are also given in the same table. It can be found that for push-in tests with specimens made of normal strength concrete, the fracture energy decreased by about 8.8% (static) to 5.8% (impact) for specimens with plain or polypropylene fibre concrete, and by about 5.1% (static) to 3.0% (impact) for specimens with steel fibre concrete; while for push-in tests with specimens made of high strength concrete, the fracture energy decreased by about 6.7% (static) to 4.7% (impact) for specimens with plain or polypropylene fibre concrete, and by about 3.5% (static) to 1.8% (impact) for specimens with steel fibre concrete. This suggests that the influence of epoxy coating is reduced with an increase in the loading rate or in the concrete strength. For pull-out tests there were also no significant decreases in the fracture energy when the epoxy coated rebars were used, for specimens made of normal strength concrete the decrease ranges from 4.1% for plain concrete (static) to 1.6% for steel fibre concrete (impact); while for specimens made of normal strength concrete the decrease ranges from 3.1% for plain concrete (static) to 1.2% for steel fibre concrete (impact).  Chapter 5. Experimental Results ^  246  5.8.5 Conclusions  Based on the data from these limited tests, which were carried out for a particular bar size, coating material and thickness, and embedded length, some preliminary conclusions may be drawn:  1. Bond resistance decreases slightly for epoxy coated rebars, in terms of the maximum local bond stress and the average bond stress. 2. Wider cracks develop during the bond process at the tips of the ribs of the deformed rebars when they are coated with epoxy. 3. The fracture energy during the bond failure decreases for epoxy coated rebars, i.e. a. reinforced concrete member may become more brittle when this type of rebar is used. 4. Under high rate loading, the above effects, i.e. the weakening of bond strength, wider crack development and brittleness, are reduced. 5. Steel fibre additions at a sufficient content also effectively reduce the above effects  on the bond strength, crack development and brittleness of epoxy coated rebars. Polypropylene fibres were much less effective in this regard. 6. Higher concrete strength also reduces the above effects. The bond strength and crack opening do not have as much change in comparison to as when lower strength concrete is used. 7. The influence of epoxy coated rebars on the bond behaviour is more pronounced for push-in loading than for pull-out loading.  Chapter 5. Experimental Results^  247  Table 5.14: Fracture Energy in Bond Failure (for both Epoxy Coated and Uncoated Bars)  Pull-out Tests^(Nin) Push-in Tests^(N7n) Uncoated Coated Uncoated Coated Normal Strength Concrete Plain Concrete 38.5 40.2 44.0 40.1 44.3 Polypropylene 0.1% 40.6 38.8 40.2 Fibre Concrete 0.5% 39.8 44.5 40.7 40.0 Steel 54.6 0.5% 53.2 62.3 59.2 Fibre Concrete 1.0% 71.5 69.4 80.2 76.1 Plain Concrete 42.8 41.2 47.3 43.5 Polypropylene 0.1% 42.9 43.6 41.2 47.5 Fibre Concrete 0.5% 43.2 42.5 43.8 47.6 Steel 59.2 68.2 65.4 0.5% 60.3 Fibre Concrete 1.0% 74.7 88.6 85.7 75.9 Plain Concrete 50.2 49.2 53.8 50.7 Polypropylene 0.1% 50.3 49.2 54.2 51.0 Fibre Concrete 0.5% 50.5 49.3 60.1 57.6 Steel 70.9 74.3 0.5% 70.0 72.2 Fibre Concrete 1.0% 100.3 93.1 94.6 103.4 High ,Strength Concrete 42.1 Plain Concrete 40.8 45.1 42.1 Polypropylene 0.1% 42.4 41.1 45.2 42.1 Fibre Concrete 0.5% 44.2 43.3 46.0 42.9 Steel 58.4 0.5% 57.4 65.6 62.2 Fibre Concrete 1.0% 75.3 73.4 83.1 86.1 Plain Concrete 45.2 43.5 46.5 49.8 Polypropylene 0.1% 43.4 45.3 50.3 46.8 Fibre Concrete 0.5% 45.5 43.5 50.5 46.9 Steel 64.2 0.5% 63.4 77.4 75.4 Fibre Concrete 1.0% 80.7 79.2 94.7 92.7 Plain Concrete 52.3 50.9 58.7 55.9 52.5 Polypropylene 0.1% 50.8 61.3 58.7 Fibre Concrete 0.5% 52.6 51.0 64.6 62.6 Steel 0.5% 76.5 75.9 85.2 83.4 Fibre Concrete 1.0% 100.5 99.3 110.3 108.3 S - Static^M - Medium,^I - Impact Type of Concrete  S  M II  I III  S  Al II  / III  Chapter 5. Experimental Results^  248  5.9 Interpretation of Tests Results and Conclusions  For smooth bars, the bond resistance is due to the chemical adhesion and the frictional force at the interface between the rebar and the concrete. There existed a linear bond stress-slip relationship under both static. and high rate loading. Different compressive strengths, types of fibres, fibre contents, and loading rates were found to have no great influence on this relationship and the stresses in both the steel bar and the concrete. For deformed rebars, the chemical adhesion and the frictional force at the interface between the rebar and the concrete are less important in the bond resistance. The shear mechanism due to the ribs bearing on the concrete plays a major role in the bond process. The bond stress-slip relationship under a dynamic (high rate) loading changed with time and was different at different points along the reinforcing bar. Higher loading rate, higher concrete strengths, steel fibres, and higher fibre content significantly increased the bond resistance capacity, and changed the bond stress-slip relationship (an average bond stress-slip relationship over the time period and the embedded length). Under high rate loading, the stress distribution along the rebar was not uniform, and even not a straight lines; there was more stress concentration along the rebar than under static loading. Higher stresses both in the rebar and in the concrete, greater slips, and higher bond stresses were developed with an increase in the loading rate. These effects were especially noticeable when steel fibres were added to the concrete mixture. The steel fibre additions greatly increased the bond strength. Steel fibres caused less stress concentrations along the rebar, higher stresses in the concrete, and greater crack  Chapter 5. Experimental Results^  249  resistance. The bond stress-slip relationship of steel fibre concrete was quite different from that of the plain concrete and polypropylene fibre concrete, in terms of the peak value, the average value and the slope of the curve. These effects were more significant when subjected to high rate loading. Higher steel fibre content increased this effect. The addition of polypropylene fibres to the concrete had no significant effect on the bond behaviour, in terms of the bond strength, the stress distributions both in the rebar and the concrete, the crack development, the slips, and the bond stress-slip relationship. Higher compressive strength increased the bond strength, especially steel fibres were added to the concrete. (ienerally there were higher bond resistance and more stress concentrations along the rebar for push-in loading than for pull-out loading. The stress distribution both in the rebar and the concrete was different for these two loading cases. The patterns of cracking and the bond failure, the bond stress-slip relationship for the pull-out loading and for the push-in loading were also different. For epoxy-coated rebar the bond resistance decreases, and there was wider cracks developed. This influence of epoxy-coated rebars on the bond strength for push-in loading was much more significant than for pull-out loading. However, high rate loading, high concrete strength and steel fibre additions at a sufficient content effectively reduced the effects of coating epoxy on the bond behaviour. Polypropylene fibre had little effect in altering the response as effective by epoxy coating.  Chapter 6  Energy Transfer and Balance  6.1 Introduction  Both steel and concrete are known to be strain rate sensitive materials, Thus, the bond behaviour between a reinforcing bar and the concrete under dynamic loading should be studied by a method which can take into account this strain rate sensitivity of the materials, rather than the conventional testing method for static loading. Unfortunately, there has been no standard testing technique developed to investigate this problem. At present, conclusions derived from different investigations are not really comparable, because of different testing arrangements, different methods of analysis, and different interpretations of tests results. The consideration of energy transfer and balance, based on the principle of the conservation of energy, may provide an effective method for both the verification of a particular testing technique and the comparison of results from different investigations. Indeed, a method based on the consideration of energy has been found very useful in the study of crack propagation in linear and nonlinear fracture mechanics. Generally speaking, many types of energy, such as kinetic energy, potential energy, strain energy and fracture energy, are easy to calculate and have explicit physical meanings. The study of the energy transfer, energy dissipation and energy balance can help us to achieve a physical understanding of the bond mechanism.  250  Chapter 6. Energy Transfer and Balance ^  251  Recently, measures such as adding fibers to the concrete matrix, or increasing the concrete strength, have been under taken to improve the bond strength between reinforcing bars and concrete under dynamic loading. Because of the complexity of the bond phenomena, the introduction of the concept of fracture energy could be an effective and convenient way of evaluating the effectiveness of these measures.  6.2 Energies and Work Done by the External Force  If the hammer is raised to a height of h, it possesses a potential energy (also the total energy), E ha , p , Which is  ^  (4.30)  E h.a,p^M liagh  When it strikes the specimen the kinetic energy of the hammer,  E h a k —^ha '  [2 (0.91g) h]  E ha, k,  is given by  ^  (4.31)  (as stated earlier, due to friction in the guides, the hammer falls with an acceleration of 0.91g).  On striking the specimen, the hammer suffers a loss of kinetic energy, L\Ehri , which may be evaluated by  (lapter 6. Energy Transfer and Balance^  252  1 .AEh a = —Mi rv 2h a (0) — vL,(t) 2 ta^  (4.3:3)  Of course, not all of this energy lost by the hammer may be transferred to the specimen. Some of the energy is lost to the testing machine itself (Banthia [80]). From the law of conservation of energy, at any moment during the impact there must be an energy balance, expressed as  Eh a ,p^E ha, fr^E ha, lef t  ^  where the energy lost due to the frictional force and air resistance,  Eh a ,f r ,  (6.1)  and the  kinetic energy remaining, Eha,t,:ft, can be found by Eqs. 4.32 and 4.34, respectively. Since the loss of the kinetic energy of the hammer,  Ew a ,  is evaluated from the recorded  acceleration data (Eqs. 4.12, 4.13 and 4.33), the above equation (Eq. 6.1) was mainly used for checking the balance of the total energy, rather than for evaluating any individual term. At any moment during the impact event the work done by the applied load, W ha (d), is  W w a (d) =^Ft (d)ds  The total work done by the hammer during the impact, 14.^ha, total, i 8  (4.38)  Chapter 6. Energy Transfer and Balance ^  d,nd  1/17 ha , total =^Ft(d) ds  253  ^  (4.39)  On the other hand, the work done by the bond stress at any moment during the impact event can be evaluated by  I/Vb^[11 u7rDw d.s] dt o^o  (4.41)  From the law of conservation of energy, there must be the following energy balance,  A E ha = E sys W ha  ^  (AT In)^  (6.2)  where E 8y , = the energy lost to the various machine parts ^(Nm-)^(Nm) W h „ = the work done by the applied load^(Nnt)^(Nm) 14 7 /,„ is obtained from the area under the applied load vs. the total displacement of the rebar plot (Eq. 4.39), and comprises both the elastic strain energy in the rebar and the concrete and the work done by the bond stress. The equation for this energy balance is  =^c, str^E re , yi( Id + 1/17  ^  (N7n)^(6.3)  ^  Chapter 6. Energy Transfer and Balance^  254  where E rr ,^and .E c, sir are the elastic strain energies in the rebar and in the concrete, respectively, which are evaluated by Eqs. 4.43 and 4.44. The term E r ,, y i e id is the local yield energy of the rebar. The transfer of energy can be studied by subdividing it into two regions (Fig. 6.1):  1. Energy balance at the end of the linear portion of the applied load vs. displacement curve (at t = ti); and 2. Energy balance just after complete bond failure (at t = t  Therefore, all of the terms in Eq. 6.3 can be divided into two parts,  ^W  =  1/1  7 ha  (t.^ha(t f )  = E rr,51,(t1)^E str(t  E c,str =^str (t^E c , str (t f)  E rr , y i e ld^E re, yield(t1)^E re , yield(t i) W b = W b(t1) W b(t f)  After the bond failure all of the strain energies in the rebar and the concrete will be released, and eventually transferred to the fracture energy, i.e.  Ere, str =  0  ^t  Chapter 6. Energy Transfer and Balance ^  255  and  E c, str = 0  Thus, the energy balance equation (Eq. 6.3) becomes  W ha  =  Ere, yield + W b  (Nm)^ (6.4)  For most specimens, the values of the applied load at the point t = t 1 were found to be about 80% to 90 % of the peak load, at this point, in general, the applied load vs. displacement curves became significantly non-linear.  Linear Region  Nonlinear Region  so  r  91 so  4 .1  20  1  a 10 of 00  =  ^ 3^ 6  t  I^Time (ms)  12  t=tf  Figure 6.1: Typical Tup Load History  15  Chapter 6. Energy Transfer and Balance ^  256  6.3 Energy Balance in the Linear Region (t = t1)  The material behaviour in the region from the starting point to the end of the linear part of the applied load vs. displacement (see Fig. 6.1) curve can be considered to be linear elastic. At the beginning of this region the applied load is quite low and so is the stress in the rebar. A more or less "perfect bond" exists between the rebar and the concrete along the entire length of the rebar, and the slip between the reinforcing bar and the concrete is zero all along the rebar. All of the work done by the applied load is transferred into the strain energies in the steel and the concrete. No work is done by the bond stress. Calculations based on the recorded data showed that the work done (and also the strain energies in the rebar and the concrete) was relatively small, depending on the 'critical adhesive bond strength'. It ranged from 10% (for specimens with smooth bars) to 20% (for specimens with deformed bars) of the total work done by the applied load. As the load in the rebar is further increased, the bond stress reaches the 'critical adhesive bond strength', and the bond due to adhesion disappears. At this point some slip occurs, but it is of a very small magnitude. Further loading mobilizes the mechanical interlocking by the mortar or the aggregate on the microscopic irregularities on the bar surface. For specimens with deformed bars, the interlocking of the concrete with the ribs of the rebar is also induced. However, up to a particular stage of loading, the applied load vs. displacement relationship remains linear, and no cracking is developed in the concrete surrounding the rebar. At this stage, the energy balance equation can be written as  Chapter 6. Energy Transfer and Balance ^  E r , str(t1)^E c, str(t1)^E re, yzeld(t1)^E(t!)  257  ^  (N7n)^(6.5)  where Wh a (t1) is the work done by the hammer at time t1, E,,, ir (t1) and E c , sir (t i ) are the elastic strain energies stored in the rebar and the concrete, respectively, E r ,  yiel (01)  is the energy of local yielding in the rebar and Wb(t i ) is the work done by the bond stress.  6.3.1 Tests with Smooth Bars  The experimental results for smooth rebars are summarized in Tables 6.1 (for normal strength concrete) and 6.2 (for high strength concrete). Data are presented for different concrete compressive strengths, different fibres and fibre contents, different types of loading and different loading rates. Similar to Chapter 5, in these tables and the ones that follow in this chapter, the following notation is used: PF = Polypropylene fibre concrete SF = Steel fibre concrete M = The medium rate loading I = The high rate loading (impact) M I = The bond stress rate is 0.5 10 -6 0.5 • 10' (MPa/s) M II = The bond stress rate is 0.5 • 10 -5 ti 0.5 10 -4 (M Pais) II = The bond stress rate is about 0.5 • 10' (MPa/s)  Chapter 6. Energy Transfer and Balance ^  258  /11 = The bond stress rate is about 0.5 • 10' (MPa/s)  I III = The bond stress rate is about 0.5 • 10_ 2 (MPa/s) It was found that although the four terms in Eq. 6.5, W h a (t1) Er,,er(ti), E',,str(ti) and Wb(t/), were calculated independently, they generally satisfied the energy balance equation. This means that the energy consumed by the local yielding of the steel at the contact surface between the hammer and the rebar, E r ,, y i eid (ti), was very small and can be neglected, and that the errors in deriving the relevant formulae for each component of the energy and work were fairly small. The following conclusions can also be drawn from the results:  1. At this stage (the end of the linear portion of the applied load vs. displacement curve) most of the work done by the hammer (W ha (1, 1 )) was transferred to the strain energies in the rebar and in the concrete (E„, str (t i ) and E c , str (i i )); the work done by the bond stress (147 A)) was relatively small compared to the two strain energies. 1/17 b(ti) constituted about 15% of the work done by the applied load for plain and polypropylene fibre concrete specimens, and 35% for steel fibre concrete specimens. This was because the bond mechanism between the smooth bar and concrete was only due to chemical adhesion and frictional resistance, and so only a. relatively small bond force could be transmitted. 2. All of the components of energy and work for push-in tests were larger than those for pull-out tests. This was because there was larger radial force acting at the interface, which caused a larger frictional resistance in the push-in case than in the pull-out case. 3. The effect of fiber additions (either polypropylene fibers or steel fibers) on the  Chapter 6. Energy Transfer and Balance ^  259  components of the work and the strain energies seemed very small. 4. There was a slight decrease in the work and the strain energies with an increase in loading rate. This might be due to the fact that both the chemical adhesion and the frictional resistance decreased under a higher loading rate. 5. Higher concrete strengths increased the work done by the bond stress and the strain energy in the rebar. Better adhesion between the rebar and the high strength concrete may have contributed to this effect.  6.3.2 Tests with Deformed Bars  The experimental results for specimens with deformed bars in the linear region are summarized in Tables 6.3 (for normal strength) and 6.4 (for high strength). Similar to the specimens with smooth bars, the data are presented for different concrete compressive strengths, different fibres and fibre contents, different types of loading and different loading rates. A very good balance in the energy equation was also found for virtually all of the specimens. The following conclusions may be drawn:  1. Unlike the tests with smooth bars, the proportion of the work done by the bond stress increased considerably, ranging from about 80% to 90% of the work done by the applied load (i.e. the hammer). For deformed bars, the bond mechanism at this stage can be considered to be a combination of the chemical adhesion, the frictional resistance and the shear resistance. In the elastic state, the bond force caused by the ribs bearing on the concrete can develop to the same order as that caused by the chemical adhesion and frictional resistance.  Chapter 6. Energy Transfer and Balance  ^  260  Table 6.1: Energy Balance in the Linear Portion (Smooth Bars, Normal Strength) Type of Concrete  S  M I  Al II  I I  / II  I III  Pull-out Tests^(Nrn) Wha  Plain 2.10 PF 0.1% 2.10 Concrete 0.5% 2.10 SF 0.5% 3.60 Concrete 1.0% 4.30 Plain 1.90 PF 0.1% 1.90 Con crete 0.5% 1.90 SF 0.5% 3.20 Concrete 1.0% 4.10 Plain 1.90 PF 0.1% 1.80 Concrete 0.5% 1.80 SF 0.5% 3.10 Concrete 1.0% 4.10 Plain 1.80 PF 0.1% 1.80 Concrete 0.5% 1.80 0.5% 3.10 SF Concrete 1.0% :3.80 Plain 1.80 PF 0.1% 1.80 Concrete 0.5% 1.80 SF 0.5% 2.90 Concrete 1.0% :3.80 Plain 1.70 0.1% 1.70 PF Concrete 0.5% 1.70 SF 0.5% 2.90 Concrete 1.0% :3.80  Push-in Tests^(N7n)  Ere, str  Ec, str  1471)  Wha  Ere, str  Ec, str  '47b  0.81 0.81 0.81 0.99 1.18 0.78 0.78 0.78 0.96 1.09 0.74 0.74 0.74 0.90 1.07 0.74 0.73 0.74 0.89 1.08 0.70 0.70 0.70 0.85 1.01 0.67 0.67 0.67 0.81 0.96  0.75 0.75 0.75 0.91 1.08 0.72 0.72 0.72 0.89 1.01 0.68 0.68 0.68 0.83 0.99 0.68 0.67 0.68 0.82 0.99 0.65 0.65 0.65 0.78 0.9:3 0.61 0.61 0.61 0.74 0.88  0.44 0.44 0.44 1.61 1.94 0.31 0.31 0.31 1.25 1.90 0.37 0.27 0.27 1.26 1.94 0.28 0.29 0.27 1.29 1.64 0.35 0.35 0.35 1.17 1.76 0.32 0.32 0.32 1.25 1.86  2.48 2.47 2.50 4.35 5.06 2.32 2.32 2.31 3.98 4.87 2.52 2.:37 2.37 4.14 4.97 2.52 2.59 2.57 4.21 4.77 2.71 2.72 2.72 4.26 5.05 2.96 2.96 2.95 4.:3:3 5.17  1.01 1.01 1.02 1.25 1.46 1.00 1.00 0.99 1.26 1.36 1.03 1.03 1.0:3 1.27 1.36 1.08 1.11 1.11 1.27 1.42 1.11 1.12 1.12 1.31 1.41 1.22 1.22 1.21 1.26 1.:37  0.93 0.9:3 0.9:3 1.15 1.34 0.92 0.92 0.91 1.16 1.25 0.95 0.94 0.94 1.17 1.25 1.00 1.02 1.02 1.17 1.31 1.02 1.0:3 1.03 1.21 1.30 1.12 1.12 1.11 1.16 1.26  0.44 0.44 0.44 1.85 2.16 0.30 0.30 0.30 1.47 2.15 0.4:3 0.30 0.30 1.61 2.25 0.:34 0.36 0.33 1.67 1.95 0.48 0.48 0.48 1.64 2.24 0.52 0.52 0.52 1.80 2.44  Chapter 6. Energy Transfer and Balance  ^  261  Table 6.2: Energy Balance in the Linear Portion (Smooth Bars, High Strength) Type of Concrete  S  M I  M II  I  I  1 II  I III  Pull-out Tests^(Nm) Wha  Plain 2.21 PF 0.1% 2.21 Concrete 0.5% 2.22 SF 0.5% 3.75 Concrete 1.0% 4.66 Plain 2.05 PF 0.1% 2.05 Concrete 0.5% 2.04 SF 0.5% 3.27 Concrete 1.0% 4.45 Plain 2.07 PF 0.1% 1.95 Concrete 0.5% 1.96 SF 0.5% 3.22 Concrete 1.0% 4.38 Plain 1.98 PF 0.1% 1.98 Concrete 0.5% 1.98 0.5% :3.24 SF Concrete 1.0% 4.02 Plain 2.03 PF 0.1% 2.02 Concrete 0.5% 2.02 SF 0.5% 3.01 Concrete 1.0% 4.11 1.99 Plain 0.1% 1.99 PF Concrete 0.5% 1.99 SF 0.5% 3.01 Concrete 1.0% 4.14  Push-in Tests^(Nm)  Ere, str  Ec, str  Wb  Wha  Ere, str  Ec, str  Wb  0.90 0.90 0.91 1.08 1.34 0.88 0.88 0.88 1.03 1.25 0.85 0.85 0.85 0.99 1.20 0.85 0.85 0.86 0.98 1.20 0.8:3 0.8:3 0.83 0.93 1.15 0.82 0.82 0.82 0.88 1.10  0.83 0.83 0.83 0.99 1.24 0.81 0.81 0.81 0.95 1.15 0.78 0.78 0.78 0.91 1.11 0.79 0.78 0.79 0.90 1.10 0.76 0.76 0.76 0.85 1.06 0.75 0.75 0.75 0.81 1.01  0.38 0.38 0.39 1.58 1.99 0.26 0.26 0.25 1.18 1.96 0.:34 0.23 0.23 1.23 1.97 0.24 0.25 0.23 1.26 1.63 0.33 0.33 0.33 1.13 1.80 0.32 0.32 0.:32 1.22 1.9:3  2.59 2.60 2.59 4.64 5.34 2.43 2.43 2.42 4.09 5.17 2.67 2.52 2.50 4.10 5.32 2.7:3 2.72 2.70 4.00 5.09 2.88 2.89 2.89 3.81 5.28 :3.16 :3.24 :3.24 :3.83 5.43  1.05 1.06 1.05 1.33 1.54 1.05 1.05 1.04 1.29 1.45 1.09 1.09 1.08 1.26 1.46 1.17 1.16 1.17 1.21 1.51 1.18 1.19 1.19 1.17 1.48 1.30 1.33 1.33 1.12 1.44  0.97 0.97 0.97 1.23 1.42 0.96 0.96 0.96 1.19 1.33 1.01 1.01 1.00 1.16 1.34 1.08 1.07 1.08 1.11 1.39 1.09 1.09 1.09 1.08 1.36 1.20 1.2:3 1.23 1.0:3 1.:32  0.46 0.47 0.46 1.98 2.29 0.32 0.32 0.32 1.51 2.29 0.47 0.3:3 0.32 1.59 2.42 0.37 0.39 0.36 1.58 2.09 0.52 0.52 0.52 1.46 2.34 0.56 0.58 0.58 1.59 2.57  Chapter 6. Energy Transfer and Balance ^  262  2. Similar to the tests with smooth bars, all of the components of energy and work for push-in tests were 10  ti  15% larger than those for pull-out tests. Again, this  was due to the larger radial force acting at the interface for push-in tests than for pull-out tests. 3. Because the addition of steel fibers improved the shear strength and the cracking resistance of the concrete, the four components in the right hand side of the energy balance equation (Eq. 6.5) increased by 2 to 4 times for specimens with steel fibers compared to those with plain concrete and polypropylene fibre concrete. A higher fiber content resulted in more strain energy and more work done. However, the effects of the polypropylene fiber additions seemed quite small, the same as for the tests with smooth bars. 4. t7nlike the tests with smooth bars, there was some increase in the work and the strain energies with an increase in loading rate. This was because the shearing mechanism plays a vital role in the bond strength for deformed bars. In this mechanism the bond stress increased with loading rate, and compensated for the loss in bond strength due to the chemical adhesion and the frictional resistance under higher loading rates. 5. A higher concrete strength increased the work done by the bond stress and the strain energy in the rebar. Both the better adhesion between the rebar and the high strength concrete, and the higher shear strength of the concrete contributed to this effect.  Chapter 6. Energy Transfer and Balance  ^  263  Table 6.3: Energy Balance in the Linear Portion (Deformed Bars, Normal Strength)  S  M I  M II  I I  I II  I III  Push-in Tests^(N7n) Pull-out Tests^(Nni) Type of Concrete Wha Ere, str E c, str 14/1, Wha Ec, str Ere, str 144 Plain 1.07 0.99 8.84 10.05 0.98 0.90 8.06 11.00 PF 0.1% 10.15 0.98 0.90 8.17 11.08 1.07 0.98 8.93 Concrete 0.5% 10.18 1.08 0.99 8.96 0.99 0.91 8.19 11.13 15.89 1.12 13.91 18.64 1.38 1.27 0.5% 16.34 1.21 SF 1.30 20.28 25.91 Concrete 1.0% 2:3.10 1.41 1.59 1.46 22.76 1.07 0.98 9.45 Plain 10.53 0.97 0.89 8.57 11.61 PF 0.1% 10.55 0.97 0.89 8.59 11.63 1.07 0.98 9.47 Concrete 0.5% 10.58 0.88 8.64 11.71 1.06 0.98 9.57 0.96 1.38 SF 0.5% 16.74 1.22 1.12 14.29 18.95 1.27 16.20 Concrete 1.0% 26.:37 1.52 1.40 27.24 1.32 1.22 2:3.73 30.26 Plain 10.70 1.10 1.02 9.60 1.00 0.92 8.68 11.83 PF 0.1% 10.73 1.00 0.92 8.72 11.88 1.10 1.01 9.66 Concrete 0.5% 10.80 1.10 1.01 9.69 1.00 0.92 8.79 11.90 1.2:3 SF 0.5% 19.01 1.13 16.55 21.50 1.39 1.28 18.73 Concrete 1.0% 27.34 1.32 1.22 24.70 31.91 1.54 1.42 28.85 11.30 1.15 1.06 10.04 Plain 1.05 0.97 9.18 12.35 10.02 PF 0.1% 11.35 1.08 0.99 9.18 12.38 1.18 1.08 Concrete 0.5% 11.38 9.21 12.41 1.18 1.08 10.05 1.08 0.99 1.14 17.62 22.26 SF 0.5% 20.09 1.24 1.37 1.26 19.53 Concrete 1.0% 29.87 1.37 1.26 27.1:3 35.13 1.62 1.49 31.9:3 10.61 Plain 11.8:3 1.08 0.99 9.66 12.98 1.18 1.09 PF 0.1% 11.98 1.08 1.00 9.80 13.03 1.18 1.08 10.67 1.08 1.00 9.82 13.05 1.18 10.69 Concrete 0.5% 12.00 1.08 1.27 22.63 0.5% 1.17 20.09 25.18 1.30 22.36 SF 1.41 Concrete 1.0% 33.23 1.26 30.50 37.01 1.53 1.37 1.40 :33.98 Plain 12.55 1.18 1.08 10.19 13.45 1.26 1.16 10.92 PF 0.1% 12.58 1.18 1.08 10.22 1:3.56 1.27 1.17 11.02 ( oncrete 0.5% 12.63 1.17 1.08 10.28 15.03 1.40 1.29 12.25 SF 0.5% 23.56 1.22 1.12 21.11 24.69 1.28 1.18 22.13 (,oncrete 1.0% :36.79 1.3:3 1.22 34.1:3 40.21 1.34 :37.32 1.46  Chapter 6. Energy Transfer and Balance  ^  264  Table 6.4: Energy Balance in the Linear Portion (Deformed Bars, High Strength) Type of Concrete  S  1  M II  I I  I II  / III  Push-in Tests^(Arm)  Wha  Err, str  Ec, str  Wb  Wha  Ere, str  Ec, str  Wb  10.53 10.60  1.03 1.02  0.95 0.94  8.45 8.54  11.28 11.30  1.10 1.09  1.01 1.00  9.06 9.11  0.5%  11.06 17.48  1.07 1.30  0.99 1.19  8.90 14.89  11.51 19.63  1.11 1.46  1.03 1.34  9.26 16.73  1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% 0.5% SF Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0%  24.33 10.83 10.88 11.03 18.26 28.28 11.30 11.3:3 11.38 20.24 29.07 11.85 11.9:3 11.96 21.54 32.09 12.5:3 12.56 12.6:3 24.56 35.31 1:3.08 13.13 1:3.16 25.42 39.08  1.49 1.00 1.00 1.00 1.33 1.42 1.06 1.05 1.05 1.31 1.41 1.10 1.13 1.13 1.32 1.48 1.14 1.13 1.14 1.:38 1.46 1.2:3 1.23 1.22 1.32 1.41  1.37 0.92 0.92 0.92 1.23 1.30 0.97 0.97 0.96 1.21 1.29 1.01 1.04 1.04 1.22 1.36 1.05 1.04 1.05 1.27 1.:34 1.13 1.13 1.13 1.21 1.30  21.37 8.82 8.86 9.01 15.60 25.45 9.17 9.21 9.26 17.62 26.27 9.63 9.65 9.68 18.89 29.15 10.24 10.28 10.34 21.81 :32.41 10.62 10.67 10.71 22.79 36.27  27.82 12.03 12.05 12.33 20.19 32.70 12.45 12.58 12.63 24.40 34.11 13.30 1:3.55 13.66 24.74 37.69 14.18 14.23 14.55 27.58 40.56 14.68 15.:33 16.16 28.31 42.90  1.70 1.11 1.11 1.12 1.47 1.64 1.16 1.17 1.16 1.58 1.65 1.24 1.29 1.29 1.52 1.7:3 1.29 1.29 1.31 1.55 1.67 1.38 1.44 1.50 1.47 1.55  1.57 1.02 1.02 1.03 1.36 1.51 1.07 1.07 1.07 1.45 1.52 1.14 1.18 1.19 1.40 1.60 1.19 1.18 1.21 1.42 1.54 1.27 1.32 1.38 1.35 1.43  24.45 9.81 9.82 10.08 17.26 29.45 10.12 10.24 10.29 21.27 :30.84 10.82 10.98 11.07 21.72 34.25 11.60 11.66 11.9:3 24.51 :37.25 11.9:3 12.47 1:3.17 25.39 :39.82  Plain 0.1% PF Concrete 0.5%  SF Con cret e  M  Pull-out Tests^(Nnz)  Chapter 6. Energy Transfer and Balance ^  265  6.4 Energy Balance in the Non-linear Region (t = tf)  This stage begins at the end of the linear portion and goes on to complete bond failure (at t = t f ), as shown in Fig. 6.1. At this stage the equation of energy balance can be written as  11: h a (t f) = E re, sir(t f^E c, str(t f)^E re,yielcl(t f)^ W 6( t f)  where W h a  (  t f)  ^  (Nm)^(6.6)  is the work done by the hammer at time t f , E„, sir (tf) and E c , str (i f ) are  the elastic strain energy stored in the rebar and the concrete, respectively,  Er,,yi,td(tf)  is  the energy in local yielding in the rebar and W b (t f ) is the work done by the bond stress. For the pull-out specimens, as the applied load was further increased, a large longitudinal tensile stress and a radial tensile stress were developed. They combined to produce large diagonal tensile stresses, and caused diagonal cracks to emanate from the tip of the ribs because of the stress concentration. With a further increase in load, more diagonal cracks initiated and propagated outwards in the concrete. The 'teeth' of comb-like concrete (see Fig. 2.4) were subjected to bending in the direction of the load, and the reaction of the wedging force caused circumferential tension in the concrete and formed radial cracks. For the push-in specimens, the push-in force served to tighten the concrete around the rebar and increased the frictional resistance between the rebar and the concrete. The slight increase in the diameter of the rebar due to Poisson's effect also improved the  Chapter 6. Energy Transfer and Balance^  266  frictional resistance. The inward deformation of the concrete provided some lateral compression in the concrete surrounding the rebar, and thus reduced the radial component of the wedging force, so no splitting cracks developed.  6.4.1 Tests with Smooth Bars  For the specimens with smooth bars the experimental results are summarized in Tables 6.5 (for normal strength) and 6.6 (for high strength). Similar to the results for the linear region, the equation of energy balance was well satisfied without considering the energy loss due to local yielding in the rebar. The following conclusions can be drawn from the results:  1. Different from the linear region, in this non-linear region of the applied load vs. displacement curve, most (about 80% to 85%) of the work done by the hammer (1/1/, a (t f )) was transferred to the work done by the bond stress (W b (t f )). In this region, as the applied load increased, at a particular load the chemical adhesion was destroyed and the frictional resistance at the interface between the steel and the concrete became the only mechanism for bond resistance. The frictional resistance could continue to increase, especially for the push-in tests, up to a certain value but then declined because of the decrease in the frictional factor with displacement. 2. Beyond the point t  = t1  ,  the strain energies in the rebar and in the concrete  (E,,,str(tf) and E c , str (t f )) kept increasing until the applied load (and also the  bond stress) reached its peak value, then remained the same for a while before decreasing to zero after complete bond failure (at t = tf). After the peak point of the bond stress, the stresses in the rebar and the concrete stopped increasing, and  Chapter 6. Energy Transfer and Balance^  267  so the strain energies in both materials remained the same. With the decrease in the bond resistance with further movement of the rebar, both the steel stress and the concrete stress released. Thus the strain energies stored in both materials in the previous stage were transferred to the work done by the bond stress. 3. All of the components of energy and work for push-in tests were larger than those for pull-out tests. This was same as that in the linear stage. 4. For the pull-out tests fiber additions (either polypropylene fibers or steel fibers) did not have much effect on the work or the strain energies. For the push-in tests, some cracks developed at this stage. The addition of steel fibers increased the crack resistance; thus the work done by the bond stress increased. 5. For all pull-out tests and push-in tests with specimens made of plain concrete or of polypropylene fiber reinforced concrete, there was some decrease in the work and the strain energies with an increase in loading rate, which was same as in the linear region. But for the push-in tests with specimens made of steel fiber reinforced concrete, there was an opposite results; both the work and the strain energies increased with the loading rate. This occurred even though both the chemical adhesion and the frictional resistance apparently decreased under a higher loading rate and the crack velocities in concrete are proportional to the rate of loading (Mindess [71], Shah [72]). However, these decreases were compensated for by the effect of the steel fibers in reducing the crack velocities and the bond strengths. This resulted in the increases in the work done and in the strain energies. 6. Higher concrete strength increased both the work done by the bond stress and the strain energy in the rebar.  Chapter G. Energy Transfer and Balance  ^  268  Table 6.5: Energy Balance in the Non-linear Region (Smooth Bars, Normal Strength)  S  M I  M II  I I  I II  I III  Type of Concrete  Wha  Ere, str  Ec, str  Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain 0.1% PF Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0%  18.10 18.10 18.10 25.70 :32.40 17.70 17.70 17.80 25.50 :32.:30 16.90 17.10 17.10 24.20 :32.30 16.80 16.80 16.90 24.20 32.10 16.30 16.30 16.30 23.60 31.40 15.50 15.50 15.50 23.30 :31.:30  1.81 1.81 1.81 2.19 2.62 1.73 1.73 1.73 2.14 2.43 1.65 1.65 1.65 2.01 2.:38 1.64 1.63 1.65 1.98 2.39 1.56 1.56 1.56 1.89 2.25 1.48 1.48 1.48 1.79 2.1:3  1.68 1.68 1.68 2.04 2.44 1.61 1.61 1.61 1.99 2.26 1.53 1.53 1.5:3 1.87 2.21 1.5:3 1.52 1.53 1.84 2.22 1.45 1.45 1.45 1.76 2.09 1.38 1.38 1.38 1.66 1.98  Push-in Tests^(Nnt) Ec, str Wha Ere, str 'WI) Wb 21.42 2.25 2.09 16.98 14.61 14.61 21.33 2.24 2.08 16.90 14.61 21.50 2.26 2.10 17.05 21.47 :31.05 2.78 2.58 25.59 3.01 31.79 3.24 27.34 38.14 14.36 21.58 2.22 2.06 17.21 17.21 14.36 21.58 2.22 2.06 17.24 14.46 21.59 2.20 2.05 21.37 :31.72 2.80 2.60 26.23 2.82 32.39 27.61 38.33 3.03 2.29 2.1:3 17.85 13.72 22.38 2.28 2.12 13.92 22.5:3 18.02 2.28 2.12 13.92 22.53 18.02 20.32 32.36 2.82 2.62 26.81 27.71 39.13 3.03 2.82 33.19 13.6:3 2:3.48 2.41 2.24 18.74 13.65 24.21 2.29 19.35 2.47 2.47 2.:30 13.72 24.1:3 19.26 20.38 32.89 2.83 2.6:3 27.33 27.49 40.:33 3.15 2.93 34.14 2.47 1:3.29 24.59 2.30 19.72 2.48 13.29 24.68 2.31 19.79 13.29 24.68 2.48 2.31 19.79 19.95 34.64 2.91 2.71 28.92 27.06 41.75 3.14 2.92 :35.59 12.64 26.94 2.70 2.51 21.63 12.64 26.94 2.51 2.70 21.6:3 12.64 26.85 2.69 2.50 21.56 19.85 34.77 29.26 2.80 2.61 27.19 42.63 3.05 2.8:3 36.65  Pull-out Tests^(Nm)  Chapter 6. Energy Transfer and Balance  ^  269  Table 6.6: Energy Balance in the Non-linear Region (Smooth Bars, High Strength)  S  M I  M  II  I I  I II  / III  Push-in Tests^(Nm) Type of Pull-out Tests^(Nm) Concrete Ec, str Ere, str Wb Wha Wb Wha Ere, str Ec, str 2.18 17.69 Plain 2.34 19.09 2.00 1.86 15.12 22.31 PF 2.35 2.19 17.76 0.1% 19.09 2.00 1.86 15.12 22.40 Concrete 0.5% 19.18 2.18 17.69 2.01 1.87 15.19 22.31 2.34 2.97 2.76 27.33 0.5% 26.75 2.39 2.23 22.03 33.16 SF Concrete 1.0% 35.14 3.18 :33.56 2.98 2.77 29.28 40.26 3.42 Plain 19.05 2.3:3 2.16 18.08 1.96 1.82 15.18 22.67 PF 2.33 2.16 18.08 0.1% 19.05 1.96 1.82 15.18 22.67 2.15 18.11 Concrete 0.5% 19.06 15.21 22.68 2.31 1.95 1.81 2.67 26.96 SF 0.5% 26.03 2.29 2.13 21.51 32.61 2.87 :3.22 2.99 34.42 Concrete 1.0% 35.05 2.77 2.57 29.61 40.7:3 18.94 Plain 2.43 2.26 18.4:3 1.89 1.76 14.68 23.73 19.19 2.26 PF 0.1% 18.55 1.88 1.75 14.82 23.98 2.4:3 2.24 19.04 Concrete 0.5% 18.64 2.41 1.89 1.76 14.89 23.80 0.5% 25.18 2.20 2.04 20.84 32.00 2.79 2.60 26.51 SF 3.01 Concrete 1.0% 34.52 2.67 2.48 29.26 41.88 35.53 3.24 Plain 18.52 1.90 1.77 2.43 20.:33 14.75 25.47 2.61 PF 0.1% 18.52 2.40 20.29 1.89 1.75 14.78 25.:38 2.59 Concrete 0.5% 18.62 2.42 20.27 1.91 1.77 14.83 25.40 2.60 SF 0.5% 25.26 2.17 2.02 20.97 :31.20 2.68 2.49 25.9:3 Concrete 1.0% :33.98 3.13 :36.42 2.66 2.47 28.75 4:3.01 :3.36 Plain 1.85 14.71 26.12 2.62 2.44 20.95 18.37 1.72 PF 0.1% 18.28 1.84 1.71 14.64 26.21 2.6:3 2.45 21.02 Concrete 0.5% 18.28 1.84 1.71 14.64 26.21 2.6:3 2.45 21.02 SF 0.5% 24.49 2.06 1.92 20.42 30.99 2.61 2.42 25.86 Concrete 1.0% :3:3.99 2.56 2.38 28.95 43.62 :3.28 3.05 :37.19 Plain 18.11 1.82 1.69 14.51 28.84 2.89 2.69 2:3.16 PF 0.1% 18.11 1.82 1.69 14.51 29.56 2.96 2.76 2:3.74 Concrete 0.5% 18.11 14.51 29.56 1.82 1.69 2.96 2.76 23.74 SF 0.5% 24.19 2.:31 1.95 1.81 20.32 30.77 2.48 25.88 Concrete 1.0% :34.06 2.43 2.26 29.27 44.77 2.97 :38.49 :3.20  Chapter 6. Energy Transfer and Balance^  270  6.4.2 Tests with Deformed Bars  The experimental results of specimens with deformed bars in the non-linear region are summarized in Tables 6.7 (for normal strength) and 6.8 (for high strength). A very good balance in the energy equation was again found for almost all of the specimens. The following conclusions may be made:  I. In this non-linear region of the applied load vs. displacement curve, most of the work done by the hammer (Wh a (t f )) was transferred to the work done by the bond stress (W b (t f )). For deformed bars, the shearing mechanism became the only mechanism for bond resistance at this stage. Diagonal cracks at the tips of the ribs probably developed at a relatively low level of bond stress and propagated in the concrete. The work done by the applied load was mainly consumed in the initiation and development of these internal cracks. 2. Similar to the specimens with smooth bars, beyond the point t = t 1 the strain energies in the rebar and in the concrete (E  str  (t f) and E c , str (t f)) kept increasing  until the applied load (and also the bond stress) reached the peak value, and then remained the same for a while. Because the wedging action of the ribs of the deformed bars could produce much larger and longer bond resistances, these strain energies were found to be much greater than those for the specimens with smooth bars. However, they released gradually with a decrease of the bond resistance due to further crack propagation in the concrete. At the moment of bond failure (t = t f ) all of these strain energies were converted to the fracture energy, which dissipated! in the development of internal cracks in the concrete.  Chapter 6. Energy Transfer and Balance ^  271  :3. All of the components of energy and work for push-in tests were about 10% larger than those for pull-out tests. This was similar to the results in the linear region. 4. The addition of polypropylene fibers did not have much effect on the work or the strain energies. However, steel fibers were found to greatly increase both the strain energies (by 150% ) and the work done by the bond stress (by 200%). 5. There were significant increases in the work and the strain energies with an increase in loading rate, especially for the specimens made with steel fiber reinforced concrete. 6. A higher concrete strength increased the work done by the bond stress and the strain energy in the rebar.  6.5 Energy Balance over the Entire Impact Event  The experimental results for the total energy balance based on Eq. 6.1 are presented in Tables 6.9 and 6.10. For simplicity of presentation, data are given only for specimens made of normal compressive strength concrete with one fiber content (0.5% by volume for both polypropylene fibres and steel fibres) and three loading rates (Impact I, II and III). It can be found that the total energy was well balanced for all of the specimens. The errors were less than 3.0% of the total energy. The experimental results for the energy balance right out the moment of impact based on Eq. 6.2 are presented in Table 6.11. The balance condition was also satisfied here. Because a solid steel frame with several mechanical connections was used in the pull-out  Chapter 6. Energy Transfer and Balance  ^  272  Table 6.7: Energy Balance in the Non-linear Region (Deformed Bars, Normal Strength)  S  M I  M II  I I  1 II  I III  Type of Concrete Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% 0.5% SF Con crete 1.0% Plain PF 0.1% Concrete 0.5% 0.5% SF Concrete 1.0% Plain 0.1% PF Concrete 0.5% 0.5% SF Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0% Plain PF 0.1% Concrete 0.5% SF 0.5% Concrete 1.0%  Push-in Tests^(Nin) Pull-out Tests^(N7n) E e, str W ha Ere, str Wb W ha Ere, str E c, str Wb 30.15 2.22 28.29 2.18 2.03 25.84 33.00 2.39 2.37 2.20 28.55 :30.45 2.17 2.02 26.16 33.23 2.40 2.23 28.64 30.52 2.19 2.04 26.19 33.37 2.51 32.96 43.66 2.86 37.62 2.70 3.08 38.26 2.92 42.23 54.29 3.53 3.28 47.39 48.40 3.14 2.15 2.00 27.31 34.79 30.11 2.37 2.21 31.57 2.21 30.20 2.37 :31.65 2.15 2.00 27.39 34.88 2.1:3 1.98 27.50 :35.09 2.20 30.44 2.36 :31.72 2.86 40.91 2.72 2.53 36.12 46.95 3.08 41.46 3.37 3.14 47.24 2.94 2.73 41.16 53.84 46.9:3 :32.10 2.28 :30.64 2.22 2.07 27.71 35.48 2.45 2.45 2.28 :30.79 2.21 2.06 27.80 :35.62 32.17 2.44 2.27 :30.90 2.21 2.06 28.03 35.70 32.40 2.74 2.54 35.91 46.70 3.09 2.88 40.6:3 41.29 :3.4:3 :3.19 49.96 48.56 2.94 2.73 42.79 56.69 2.55 2.:34 2.17 29.29 :37.05 2.:38 :32.02 :3:3.90 2.40 2.2:3 29.33 :37.1:3 2.61 2.4:3 :31.98 34.05 34.12 2.40 2.23 29.40 37.19 2.61 2.43 :32.05 2.55 38.41 48.54 3.04 2.8:3 42.57 2.75 43.81 3.06 2.84 43.6:3 58.37 3.59 :3.:34 51.3:3 49.63 35.47 2.40 2.23 30.75 38.92 2.63 2.44 :3:3.75 2.41 2.24 31.18 39.07 35.92 2.62 2.43 :33.92 36.00 2.41 2.24 31.26 39.15 2.62 2.43 :34.00 43.17 2.82 2.63 37.62 48.02 3.14 2.92 41.86 3.05 2.83 48.69 60.89 54.67 3.39 :3.15 54.24 :37.6,5 2.62 2.44 32.50 40.:35 2.81 2.61 34.8:3 2.44 :32.57 40.64 :37.72 2.62 2.82 2.62 35.10 2.61 2.43 :32.73 45.07 37.87 3.11 2.89 :38.98 47.:34 2.72 2.53 42.00 49.61 2.85 2.65 44.02 57.81 2.96 2.75 52.00 63.19 :3.2:3 3.01 56.85  Chapter 6. Energy Transfer and Balance  ^  273  Table 6.8: Energy Balance in the Non-linear Region (Deformed Bars, High Strength) Type of Concrete  S  Al I  /11 II  / I  I II  I III  Pull-out Tests^(Nm) Wha  31.58 Plain PF 0.1% 31.80 Concrete 0.5% 33.14 SF 0.5% 40.92 Concrete 1.0% 50.97 Plain 32.47 PF 0.1% 32.63 Concrete 0.5% 33.07 SF 0.5% 45.24 Concrete 1.0% 50.32 Plain 3:3.90 PF 0.1% 33.97 Concrete 0.5% 34.13 0.5% 43.96 SF Concrete 1.0% 51.6:3 :35.55 Plain PF 0.1% 35.78 Concrete 0.5% 35.84 SF 0.5% 46.96 Concrete 1.0% 5:3.:31 Plain 37.57 PF 0.1% 37.64 Concrete 0.5% 37.88 SF 0.5% 46.84 Concrete 1.0% 58.09 Plain 39.2:3 PF 0.1% 39.37 Concrete 0.5% :39.44 0.5% 51.08 SF Concrete 1.0% 61.42  Push-in Tests^(Nin)  Ere, str  Ec, str  144  Wha  Ere, str  Ec, str  Wb  2.29 2.27 2.38 2.88 3.31 2.21 2.22 2.22 2.96 3.15 2.35 2.:34 2.33 2.91 3.12 2.45 2.52 2.52 2.94 :3.28 2.54 2.52 2.53 3.06 :3.24 2.73 2.73 2.72 2.93 3.14  2.13 2.11 2.21 2.68 :3.08 2.06 2.06 2.07 2.76 2.93 2.18 2.17 2.17 2.71 2.91 2.28 2.34 2.34 2.74 3.05 2.:36 2.34 2.35 2.85 :3.01 2.54 2.54 2.53 2.73 2.92  27.06 27.32 28.45 35.26 44.48 28.10 28.24 28.68 39.42 44.14 29.27 29.36 29.53 38.24 45.50 30.72 30.82 30.89 41.18 46.88 :32.57 32.68 32.89 40.83 51.74 :3:3.86 :3:3.99 34.10 45.32 55.25  33.83 33.90 34.49 45.97 58.28 36.07 36.15 :36.97 50.01 58.20 37.35 :37.72 37.88 53.00 60.59 39.90 40.65 40.94 53.96 62.61 42.52 42.67 43.65 52.62 66.74 44.0:3 45.97 48.44 56.89 67.40  2.45 2.42 2.48 3.24 3.78 2.46 2.46 2.49 3.28 3.64 2.58 2.59 2.59 3.51 3.67 2.75 2.86 2.88 3.38 :3.85 2.87 2.86 2.92 3.44 3.72 :3.06 3.19 3.34 3.26 3.45  2.28 2.25 2.30 3.01 3.52 2.29 2.29 2.31 3.05 3.:39 2.40 2.41 2.40 3.27 :3.41 2.56 2.66 2.67 3.14 3.59 2.67 2.66 2.71 :3.20 3.46 2.85 2.97 3.10 3.04 :3.21  29.00 29.1:3 29.61 39.62 50.88 :31.22 :31.:30 :32.07 4:3.59 51.06 32.26 :32.61 :32.79 46.12 5:3.41 34.49 35.03 35.30 47.3:3 55.07 36.88 :37.05 :37.92 45.88 59.46 :38.01 :39.71 41.90 50.49 60.65  Chapter 6. Energy Transfer and Balance ^  274  tests (see Chapter 3), there was a bit more energy lost at the moment of impact for the pull-out specimens than for the push-in specimens. The data for the final energy balance after impact (based on Eq. 6.4) are presented in Table 6.12. Since the test specimens were so designed as to avoid possible yielding of the steel, the energy lost in local yielding at the contact surface between the hammer and the rebar was found to be very little. Therefore the experimental arrangements, the measurements of the important parameters, and the mathematical models for data analysis in the tests are believed to be reasonable and accurate from the viewpoint of energy conservation.  Chapter 6. Energy Transfer and Balance^  Table 6.9: Total Energy Balance (Smooth Bar Specimens) Type of Specimen  I I  I II  / III  /  Energy^(Nil') Eha,p E ha, f r A Eha E ha, le f t Error 70.8 19.5 45.5 1.2 Plain Pull-out 4.6 Concrete Push-in 70.8 4.6 26.6 :38.6 1.0 131.4 3.4 PF Pull-out 170.0 15.3 19.9 15.3 27.6 Concrete Push-in 170.0 123.9 3.2 27.5 28.7 244.8 4.1 SF Pull-out :305.0 Concrete Push-in :305.0 27.5 38.6 2:35.1 3.9 Plain Pull-out 70.8 4.6 19.1 45.8 1.3 Concrete Push-in 28.5 35.4 2.3 70.8 4.6 PF Pull-out 170.0 15.3 19.2 133.5 2.0 Concrete Push-in 170.0 15.3 28.4 122.9 3.4 Pull-out 305.0 SF 27.5 28.1 245.8 :3.7 Concrete Push-in 305.0 27.5 40.3 234.2 3.1 Plain Pull-out 4.6 18.4 45.7 2.1 70.8 Concrete Push-in 33.3 1.9 70.8 4.6 31.0 PF Pull-out 170.0 133.0 :3.2 15.3 18.5 Concrete Push-in 170.0 15.3 31.3 120.1 :3.:3 Pull-out :305.0 27.5 27.9 245.4 SF 4.:3 Concrete Push-in :305.0 27.5 41.0 232.4 4.2 I = 0.5 - 10'^I II = 0.5 • 10 -3^/III = 0.5 - 10 -2^(MPa/s) PF - Polypropylene Fibre^SF - Steel Fibre  275  Chapter 6. Energy Transfer and Balance^  Table 6.10: Total Energy Balance (Deformed Bar Specimens) Energy^(Nm) Type of Specimen Eha,p E ha, f r A Eha E lia,lef t Error 1.9 Plain Pull-out 70.8 4.6 45.5 18.8 1.4 15.0 Concrete Push-in 4.6 49.8 70.8 2.4 I PF Pull-out 170.0 106.3 46.0 15.3 102.6 1.9 I Concrete Push-in 170.0 50.2 15.3 210.0 2.9 SF Pull-out 305.0 64.6 27.5 3.1 Concrete Push-in 305.0 71.5 202.9 27.5 2.2 16.2 4.6 Plain Pull-out 70.8 47.8 52.6 11.0 Concrete Push-in 2.6 70.8 4.6 2.4 I 48.6 Pull-out 170.0 15.3 10:3.7 PF 53.0 99.8 II Concrete Push-in 170.0 15.3 1.9 27.5 207.7 66.7 3.1 SF Pull-out 305.0 200.6 Concrete Push-in 305.0 2.9 27.5 74.0 Plain 12.4 2.9 Pull-out 4.6 50.9 70.8 Concrete Push-in 2.4 4.6 54.5 9.3 70.8 I PF Pull-out 170.0 15.3 51.1 101.0 2.6 III Concrete Push-in 170.0 15.3 60.8 90.5 :3.4 Pull-out 305.0 27.5 71.7 202.4 3.4 SF Concrete Push-in 305.0 198.6 27.5 75.3 :3.6 / I = 0.5 • 10'^/ II = 0.5 • 10'^/ III = 0.5 - 10'^(MPa/s) PF - Polypropylene Fibre^SF - Steel Fibre  276  Chapter 6. Energy Transfer and Balance ^  Table 6.11: Energy Balance right out of the Moment of Impact Type of Specimen  I I  I II  I III  /  Energies^(Nm) Smooth Bars Deformed Bars A E ha W ha E s y s A E ha W ha E s y s Pull-out Plain 19.5 0.1 18.7 0.8 45.5 45.4 Concrete Push-in 26.6 26.0 0.6 49.8 49.7 0.1 PF Pull-out 19.9 18.9 1.0 46.0 45.6 0.4 Concrete Push-in 27.6 26.8 0.8 50.2 49.9 0.3 SF Pull-out 28.7 27.5 1.2 64.6 64.3 0.3 Concrete Push-in 38.6 37.3 1.3 71.5 71.2 0.3 19.1 18.2 Plain Pull-out 0.9 47.8 0.2 47.6 28.5 Concrete Push-in 27.4 1.1 52.6 52.4 0.2 19.2 PF Pull-out 18.2 1.0 48.6 48.4 0.2 Concrete Push-in 28.4 27.6 0.8 53.0 52.7 0.3 Pull-out 28.1 26.8 1.3 66.7 66.4 SF 0.3 40.3 39.1 1.2 Concrete Push-in 74.0 73.8 0.2 Plain Pull-out 18.4 17.2 1.2 50.9 50.7 0.2 Concrete Push-in 31.0 30.0 54.4 1.0 54.5 0.1 PF Pull-out 18.5 17.4 51.1 1.1 50.8 0.3 Concrete Push-in 1.4 60.8 60.6 31.3 29.9 0.2 SF Pull-out 27.9 26.5 1.4 71.7 71.6 0.1 Concrete Push-in 41.0 39.5 1.5 75.3 75.1 0.2 I = 0.5 • 10 -4^III = 0.5 • 10 -3^/ III = 0.5 • 10 -2^(MPa/s) PF - Polypropylene Fibre^SF - Steel Fibre  277  Chapter 6. Energy Transfer and Balance^  278  Table 6.12: Energy Balance at Bond Failure Type of Specimen  Energies^(Nnt) Deformed Bars Smooth Bars Wha Wb E yield Wha Wb E yield Plain 0.2 45.4 45.2 Pull-out 18.7 18.6 0.1 0.3 Concrete Push-in 26.0 26.0 49.7 49.4 0.0 I 0.2 45.6 45.5 0.1 PF Pull-out 18.9 18.7 I Concrete Push-in 26.8 26.7 0.1 49.9 49.6 0.3 0.2 SF Pull-out 27.5 27.3 64.3 63.9 0.4 0.2 71.2 70.8 0.4 Concrete Push-in 37.3 37.1 Plain Pull-out 18.2 18.1 0.1 47.6 47.3 0.3 Concrete Push-in 27.4 27.3 0.1 52.4 51.9 0.5 I PF Pull-out 18.2 18.1 0.1 48.4 48.0 0.4 II Concrete Push-in 27.6 27.4 0.2 52.7 52.2 0.5 SF Pull-out 26.8 26.5 0.3 66.4 65.8 0.6 0.2 73.8 73.2 0.6 Concrete Push-in 39.1 38.9 Plain Pull-out 17.2 17.2 0.0 50.7 50.2 0.5 Concrete Push-in 30.0 29.9 0.1 54.4 53.8 0.6 I 50.8 50.5 PF Pull-out 17.4 17.2 0.2 0.3 III Concrete Push-in 29.9 29.8 0.1 60.6 60.1 0.5 SF Pull-out 26.5 26.2 0.3 71.6 70.9 0.7 Concrete Push-in 39.5 39.1 0.4 75.1 74.3 0.8 / I = 0.5 • 10 -4^/ II = 0.5 • 10'^1 111 = 0.5 • 10 -2^(MPa/.9) PF - Polypropylene Fibre^SF - Steel Fibre  6.6 Energy Absorbtion and Dissipation Capacity  In structural engineering design, it is expected that a structure subjected to dynamic loading should resist such loading without collapse, though with some structural and nonstructural damage. To avoid collapse, the structural members must he ductile enough to absorb and dissipate energy. For reinforced concrete structures it is essential that the bond between the reinforcing bar and the concrete exhibit a certain 'ductility' during  Chapter 6. Energy Transfer and Balance ^  279  dynamic loading. That is, the bond resistance in the member should decrease gradually instead of suddenly failing, so that the dynamic energy can largely be transferred, absorbed and dissipated to the entire structure member over a relatively long time period. This bond 'ductility' may be represented by the fracture energy, which is calculated as the work done by the bond stress. A larger value of fracture energy means a 'ductile' bond. The fracture energy results for different types of specimens are presented in Tables 6.13 and 6.14. The following conclusions may be drawn:  1. The fracture energy during the bond failure process for deformed bars was much greater than that for smooth bars. In this experimental work, in which smooth bars with a diameter of 12.7 mm and No.10 deformed bars (diameter = 11.7 mm) were used, the fracture energy for the deformed bars was 2 to 3 times that for smooth bars. 2. Concrete of high compressive strength absorbed more fracture energy during bond failure than concrete with normal compressive strength. 3. The fracture energy for the push-in case was 10  ti  20 % higher than that for the  pull-out case. 4. The addition of polypropylene fibers did not have much effect on the fracture energy during bond failure. 5. Steel fibers significantly increased the fracture energy during bond failure by about 100% (for static loading) to about 300 % (for impact loading), i.e. they made the concrete matrix more ductile with regard to bond. Higher fiber contents were more effective in this regard.  Chapter G. Energy Transfer and Balance ^  280  6. Generally the fracture energy increased with an increase in loading rate, especially for the specimens made with steel fibres.  Chapter 6. Energy Transfer and Balance^  Table 6.13: Fracture Energy in Bond Failure (Smooth Bars)  S  M  I  M II  I  I  I  II  I  III  Type of Pull-out Tests^(Nm) Push-in Tests^(Nm) Normal High Concrete Normal High 23.9 24.9 Plain Concrete 21.3 20.2 20.2 21.3 23.8 25.0 Polypropylene 0.1% 24.9 20.2 21.4 24.0 Fibre Concrete 0.5% :35.4 :37.8 30.5 Steel 29.3 0.5% Fibre Concrete 1.0% 36.7 39.8 43.2 45.6 25.1 Plain Concrete 21.1 23.9 19.6 21.1 25.1 Polypropylene 0.1% 23.9 19.6 Fibre Concrete 0.5% 21.1 23.9 25.1 19.7 29.:3 35.7 36.7 Steel 0.5% 28.7 Fibre Concrete 1.0% 36.4 39.5 43.2 45.9 24.9 26.4 18.8 Plain Concrete 20.5 24.9 26.5 18.9 Polypropylene 0.1% 20.5 24.9 26.3 18.9 20.6 Fibre Concrete 0.5% :36.1 27.3 28.4 Steel 36.5 0.5% 38.9 47.2 44.1 Fibre Concrete 1.0% :36.4 28.2 Plain Concrete 20.5 26.0 18.6 Polypropylene 0.1% 20.5 26.8 28.1 18.6 Fibre Concrete 0.5% 18.7 20.6 26.7 28.1 :37.1 28.5 :35.2 Steel 0.5% 27.3 45.1 Fibre Concrete 1.0% 48.1 38.0 :35.9 27.3 29.0 18.1 20.4 Plain Concrete 27.4 29.1 Polypropylene 0.1% 18.1 20.3 20.3 27.4 29.1 Fibre Concrete 0.5% 18.1 27.5 :34.8 Steel :38.9 0.5% 26.5 35.2 38.1 46.8 48.9 Fibre Concrete 1.0% Plain Concrete 17.2 20.1 29.9 :32.0 Polypropylene 0.1% 17.2 20.1 29.9 :32.8 Fibre Concrete 0.5% 17.2 20.1 29.8 :32.8 26.2 27.2 39.1 Steel 0.5% 34.6 Fibre Concrete 1.0% :38.2 47.8 35.1 50.2 S - Static^M - Medium^I Impact -  281  Chapter C. Energy Transfer and Balance^  Table 6.14: Fracture Energy in Bond Failure (Deformed Bars)  '  M  I M  II I  I I  II I  III  Type of Pull-out Tests^(Nrn) Push-in Tests^(Nni) Concrete High High Normal Normal Plain Concrete 40.2 42.1 44.0 45.1 Polypropylene 0.1% 45.2 40.6 42.4 44.3 Fibre Concrete 0.5% 40.7 44.2 44.5 46.0 Steel 0.5% 54.6 58.4 62.3 65.6 Fibre Concrete 1.0% 71.5 75.3 80.2 86.1 Plain Concrete 42.1 43.3 46.4 48.1 Polypropylene 0.1% 48.2 42.2 43.5 46.5 Fibre Con crete 0.5% 49.3 42.3 44.1 46.8 Steel 70.2 0.5% 58.2 63.5 65.9 Fibre Concrete 1.0% 78.6 73.3 84.1 90.9 Plain Concrete 42.8 45.2 47.3 49.8 Polypropylene 0.1% 42.9 50.3 45.3 47.5 Fibre Concrete 0.5% 4:3.2 45.5 47.6 50.5 Steel 60.3 77.4 64.2 0.5% 68.2 Fibre Concrete 1.0% 75.9 80.7 88.6 94.7 Plain Concrete 45.2 5:3.2 47.4 49.4 Polypropylene 0.1% 45.4 54.2 47.7 49.5 Fibre Concrete 0.5% 45.5 54.6 47.8 49.6 Steel 63.9 0.5% 68.5 70.8 78.7 Fibre Concrete 1.0% 79.5 85.4 93.5 100.3 Plain Con crete 47.3 50.1 51.9 56.7 Polypropylene 0.1% 47.9 .50.2 52.1 56.9 Fibre Concrete 0.5% 48.0 50.5 52.2 58.2 Steel 0.5% 65.8 71.4 7:3.2 80.2 Fibre Concrete 1.0% 87.9 93.4 97.9 107.3 Plain Concrete 50.2 52.3 5:3.8 58.7 Polypropylene 0.1% 50.3 52.5 54.2 61.:3 Fibre Concrete 0.5% 50.5 52.6 60.1 64.6 Steel 0.5% 70.9 76.5 74.3 85.2 Fibre Concrete 1.0% 94.6 100.5 103.4 110.3 ' - Static^M - Medium^I - Impact  282  Chapter 7  Analytical Study  7.1 Introduction  The mechanism of bond between steel rebars and concrete is a highly complex, nonlinear process involving progressive cracking, crushing, nonlinearity and inhomogeneity of the concrete, especially under high rate (impact) loading. So far no studies have been carried out which use fracture mechanics and finite element methods to establish the bond stress-slip relationship analytically. Previous studies regarding the application of finite element method to the bond problem simply introduced the local bond stress-slip relationships which were obtained from tests. However, in spite of much useful information obtained from extensive experimental studies, there are still many unanswered questions regarding the bond phenomenon. Many variables in bond behaviour are difficult to measure experimentally, and it is hard to design an experimental program to take into account all relevant factors. There is not enough information available in the literature from which the bond stress-slip characteristics can be derived analytically. Theoretically, there is a unique relationship between bond stress and slip at the interface between a steel bar and concrete for which the geometric and mechanical properties are known. The problem can be solved  28:3  Chapter 7. Analytical Study^  284  by reasonably modelling the mechanical properties at the interface between the rebar and the concrete, as well as the constitutive laws for both materials and appropriate cracking and crushing criteria. This chapter is devoted to a nonlinear fracture mechanics analysis of pull-out and push-in bond tests under high rate loading conditions, and the finite element method is used in the numerical calculation. The aim of the analysis is to obtain quantitative information to help explain the physical phenomena occurring around the reinforcing bar. The chemical adhesion and frictional resistance between the rebar and the concrete are considered only during early loading in the elastic stage. After that only the rib bearing mechanism is taken into account. The fiber concrete composite and the high strength concrete are appropriately modelled. In the finite element analysis quadratic solid isoparametric elements with 20 nodes and 60 degree of freedom are employed for the rebar and the concrete before cracking. After cracking, the concrete elements are replaced by quadratic singularity elements, which are quarter-point elements able to model curved crack fronts. The dynamic constitutive laws of both steel and concrete, the criteria for crack formation and propagation in concrete based on the energy release rate theorem for mixed mode fracture, and the criterion for concrete crushing are used in the finite element process (see below). It is an iterative program with rapid convergence. Not only can the bond stress and crack distribution be found through the analysis, but also a bond stress-slip relationship under high rate loading can be established analytically. The most important part of the finite element analysis is to develop appropriate  Chapter 7. Analytical Study ^  285  types of elements suitable to the specific problem, and then to choose reasonably accurate `shape functions' for these elements and to establish the corresponding stiffness matrixes. After that, the assembly of the global stiffness matrix and the external load matrix, and the strategy for equation solving, etc., are similar for all finite element processes. Another important part of the finite element analysis in this study is the setting up of the criteria for evaluating the mechanical behaviours of the elements, such as the contact conditions between the rebar and the concrete, and the cracking and crushing in the concrete.  7.2 Finite Element Models  7.2.1 Steel Elements  The elements representing the steel rebar are quadratic solid isoparametric elements with 20 nodes and 60 d.o.f. (degrees of freedom), as shown in Fig 7.1. The formulation of the stiffness matrix for this type of element can be found in any book of advanced finite element methods (for example, reference [100]). The shape function is shown in Fig. 7.2, and may be expressed as:.  286  hapte• 7. Analytical Study^  - (1 +^(1 + 7)1/i) (1 + ( Ci)^+7Pii^(Ci — 2) (i = 1, 2, • • 8) 1  — — 2 )( 1 WO ( 1 + 4  (i = 9, 10, 11, 12) (7.1)  = — 71 2 ) (I + ((z) ( 1 +  (1 - ( 2 ) (1 +^(1 + 7p )i)  (i = 13, 14, 15, 16)  (i = 17, 18, 19, 20)  where^= +1. The stiffness matrix is  [k] =^[B]T[E][B] R.111 d clq c1(^(7.2) where  Chapter 7. Analytical Study  287  ^-  aNi^aN20^ 0^o^0^0 ^ax^ ax  aN, ay  0  0  0^DN20  ay  aN,  0^0  aN20  0^0  az^ az  [13) =  (7.3)  aN, aN,  aN20 aN20 0 ay^ax^ay^ax^0  aN, aN,  ^aN20 aN20 ^ 0 az^ay^ az^ay  0  aN20^aN20 ^ 0 ax^az^ OX  0  az  1  fi  1 — ,u,  tt^p  1—p 1 — ^0^0^0 1  p^f2  E(1 — it)  -  1 — ft 1 — ft  ft  1—  0^0^0  1  [E] = ^ ( 1^2p) 0^0^0  1 — 2tt 2(1 —  (7.4)  0^0 1 — 2p 2(1 — 11)  0^0^0^0^0  0  1 —2f1 2(1 — it)  Chapter 7. Analytical Study ^  288  and  20 aAri^20  aN^20 aN,  ^x t E ^ y, E — z i  [J ]=  20  aNi^20  aNi  20  i=1  20  aNi  y, i E^E^z an^ 077  xt  (7.5)  aN .^20 aNi^20 aNi  E^x t E^y, E  zt  1=1^C^1=1 U C^1=1 ut,  Figure 7.1: The Quadratic Solid Isoparametric Element with 20 Nodes and 60 D.O.F. 7.2.2 Concrete Elements  Before cracking, the elements in the concrete are same as those in the steel, i.e. quadratic solid isoparametric elements with 20 nodes and 60 d.o.f. After cracking, the  Chapter 7. Analytical Study^  289  quadratic singularity elements for solids are adopted. These are quarter-point elements and can model a curved crack front ([100],[101]), as shown in Fig. 7.3. By placing the mid-side node near the crack tip at the quarter point, the singularities, both lkg and 1/r, in these elements are achieved. The proof of this involves a tedious mathematical derivation ([101], [102]) and will not be given here. The formulation of the stiffness matrix is the same as for the regular quadratic solid isoparametric element.  Chapter 7. Analytical Study^  290  =  =- 1  Figure 7.2: The Shape Function of the Quadratic Solid IsoparametricElement  17  19 20 13  18  CRACK 7 8 1 2 FRONT  1717 ^3h14  Figure 7.3: The Quadratic Singularity Isoparametric Element  Chapter 7. Analytical Study  ^  291  7.2.3 Interface Elements  A special interface element, the 'bond-link element', has been adopted to model the bond slip phenomena in this analytical study. It connects two nodes but has no physical thickness at all. As shown in Fig. 7.4, it can be thought of conceptually as consisting of two orthogonal springs, which simulate the mechanical properties in the connection, i.e. transmit the shear and normal forces between nodes i and j. This kind of interface element has been commonly used in the finite element analysis of reinforced concrete members. However, various bond stress-slip relationships which were determined experimentally have been used to establish the stiffness matrix of the element (i.e. the constitutive relationship for the element to relate the node forces to the node displacements). A new approach is proposed in this study for the establishment of the stiffness matrix of the 'bond-link element'. A bond stress-slip relationship at the interface between the rebar and the concrete is one of the output results of the present finite element analysis, rather than an input parameter required before the analysis can proceed.  • - z' .i• e4/./ Z .  ,,,  ,  i  i  l  ,/t17,-/, ,,/ , -'. ,, ,  r•••w•■••aw.4111■•  ',/1-../  Figure 7.4: The Interface Element (Bond-Link Element)  Chapter 7. Analytical Study^  292  The vertical spring relates to the force transfer by dowel action between the rebar and the concrete. It also accounts for the chemical adhesion. This means that the spring can transfer a certain amount of tensile stress which is equal to the unit chemical adhesion before the relative displacement of two nodes, i and j, reaches a critical value. After that no tensile force can be transmitted. In the case in which these two nodes are pushing against each other, especially if there is good confinement for the concrete (such as the specimens used in this research program), the pushing force can be of a large magnitude, great value, which is proportional to the relative deformation between the rebar and the concrete, and to the elastic modulus in tension of the concrete. A laboratory test can be carried out to determine the related coefficient which governs this pushing force. The mechanical model of the linkage can be expressed as  0^if (v i — vj) > 0.1 mzn  av =^Co^if 0 < (v i — vj ) < 0.1 mm  ^  (7.6)  - v )^if (v i — vj ) < 0 ;  where = the interface normal stress ^(MPa) a) = the vertical displacements of nodes i and j, respectively,^(ntin) Co = the unit chemical adhesion force, which is determined from laboratory tests^(MPa)  fa = the normal stress factor at the interface, which is determined from laboratory tests^(M Pa/min)  Chapter 7. Analytical Study^  293  The horizontal spring takes into account the chemical adhesion and the frictional resistance at the interface between the steel and the concrete. When the relative displacement between the two nodes exceeds the critical value, the chemical adhesion is destroyed and only the frictional effect remains. This mechanical model can be expressed as  ah  {Co  + frgv  IT Cry  if (u i — uj) < 0.1 77i7n  (7.7)  if (u i — u j ) > 0.1 inn/  where = the interface shear stress (or the bond stress) ^(MPa) = the frictional factor at the interface, which is determined from laboratory tests ^u„  u j = the horizontal displacements of node i and j, respectively,^(Tim)  Therefore the node forces of the 'bond-link element' can be expressed as  U7  (7.8)  = [k]  F: v3  and the stiffness matrix of the 'bond-link element' is different for different stages of the bond process, which is governed by the constitutive laws expressed in Eqs. 7.6 and 7.7. For example, in the case for which the chemical adhesion has been destroyed and there  hapter 7. Analytical Study^  '294  is no separation between the steel and the concrete, the stiffness matrix is  [k] =  o fr fp 0 — fr fp^  (7.9)  0 fp 0 — fp In the case in which both the chemical adhesion and the frictional resistance no longer exist, the stiffness of the interface element should become zero (Technically, each of the eight elements inside the matrix is given a very small value to ensure that the mathematical operations continue smoothly).  7.3 Constitutive Laws of the Materials  7.3.1 Constitutive Law of Steel  So far no :3-dimensional constitutive models for steel under high rates of strain have been established. The present specimens were designed so that the stress in the rehar was relatively low throughout the entire bond process. Therefore an elastic constitutive matrix, which is based on Hooke's law, was adopted in this analytical study.  7.3.2 Constitutive Law of Concrete  There have been many models proposed for the 3-dimensional constitutive law for concrete. Most of them have been determined empirically, and all are controversial to sonic extent. However, none of these take into account the effects of strain rate. Soroushian e t al ([10:3D proposed a one-dimensional constitutive model for concrete,  ^  Chapter 7. Analytical Study^  295  which takes into consideration the strain rate,  e {^ K 1 K 2 E.[^2'^ ^ ( 0.002K i K2 0.002K1 K3 )2]  for F < 0.002K 1 K3  .f = K i K 2 1„[1 — z(e — 0.002K 1 K3 )]^for 0.002K 1 K3 < C < 0.2111 .K2,f ci. (7.10) where  f = the concrete compressive stress = the concrete compressive strain Ps .fy i, 11 1 = 1 +  p s = the volume ratio of the transverse reinforcement to the concrete core = 28-day compressive strength of concrete fy h = the yield strength of transverse reinforcement 0.5 3+0.29 f c^3 h' 4_ ^ n  145 P c —1000 + 4 r s  0.002K1 K3  h' = the width of concrete core measured to outside of the transverse reinforcement = the centre-to-centre spacing of transverse reinforcement K 2 = 1.48 + 0.206 log 10 E + 0.0221 (log 10 E ) 2 Iii = 1.08 + 0.112 log io + 0.0193 (log io ) 2  Chapter 7. Analytical Study^  296  Note: for E < 10 -5 /sec, k 2 = K3 = 1.0  7.4 Criteria of Cracking, Crack Propagation and Crushing in Concrete  When the principal tensile stress in the concrete element exceeds the tensile strength of the concrete, the element cracks. That is, when  ac,1^fc,r  ^  (7.11)  the crack will initiate, where  = the principal tensile stress in the concrete element = the tensile strength of concrete For mixed mode fractures, i.e. fractures with combinations of the opening mode, sliding mode and tearing mode, an energy release rate criterion will apply ([104], [105]). According to this criterion, a crack will propagate when  K/  )2 .,d1C  ^K// 2^K///  )2 = 1  (7.12)  where  K 1 , K 11 , Km = the stress intensity factors for fracture modes I, II, III, respectively.  997  Chapter 7. Analytical Study^  K 1 c , Ku c , Kin  c  = the critical stress intensity factors for fracture modes I, II,  III, respectively. According to Hannant [106], the criterion for concrete crushing can be written as  if^at — 50 2 + a3 > ac y .  or a 2 — 50 3 +^> o- cy -  for a1 + a2 + a3 > 5.5ac y  (7.13)  or a 3 — 5o 1^a2 > a cy and  if^a1 — 4a 2^a 3 > 1.75a c3 or^a 2 — 40 3 + a 3 > 1.750 cy -  -  for^5.5a cy < a l^a 2^0 3 < 12.17a cy -  (7.14)  or^a3 — 4a 1^a 2 > 1.750 cy -  where a 2 . a 3 = the principal stresses in the concrete element a cy = the crushing strength of the concrete cylinder  7.5 The Algorithm for the Finite Element Analysis  The finite element analysis involves an iterative process. First, a small increment of load is applied to the specimen and all the elements are assumed to be elastic. With further increases in the load, the state of the connection between the steel elements and  Chapter 7. Analytical Study^  298  the concrete elements changes and the stiffness matrix of the interface elements must also change. Cracks may initiate in the concrete specimens and the quadratic solid isoparametric elements must then be replaced by the quadratic singularity elements. Then the energy release rate criterion is applied to determine the possibility of crack propagation. It is always necessary to check whether the outputs of each step coincide with the assumed conditions in the previous step. The algorithm is given in Figs. 7.5 and 7.6.  299  Chapter 7. Analytical Study^  Input Geometric & Material Property Data Apply Load Increment Assume Loading Rate  MIR  Assume Perfect Bond No Crack Develops Calculate Stiffness Matrix for Each Element Assemble Global Stiffness Matrix and Load Vector Solve for Node displacements Calculate Strains & Stresses Check if the Strain Rate Coincides with the assumed value Yes  No, Assume Strain Rate Again —  Check if the Perfect Bond Exists Check if the Concrete Crushed — Yes, Next Load Increment  No  Output Bond Stress vs. Slip Relation Modify Interface Element Parameter Check if the Concrete Crushed No, Reduce Load Increment  Yes  Check if the Concrete Crack Yes No, Next Load Increment  Figure 7.5: Algorithm of Finite Element Analysis — I  Chapter 7. Analytical Study^  Use Fracture Mechanics Elements Modify Global Stiffness Matrix  i  Calculate Kr, Kil and K111 at Crack Tips Calculate the Energy Release Rate for Each Crack ^i^ Check if the Crack Is Stable or It Will Develop Develop Stable, Next Load Increment — ^I^ Check if the Applied Load Decline — No, Modify the Previous Crack Length Yes I Stop Iteration Output Bond Stress vs. Slip Relation, Load vs. Displacement Relation. Fracture Energy etc. Assume New Crack Increment A  i  Modify Finite Element Mesh  i  Update the Global Stiffness Matrix `Go to Next Load Increment  Figure 7.6: Algorithm of Finite Element Analysis — II  300  (lapter 7. Analytical Study^  301  7.6 The Results of the Finite Element Analysis  7.6.1 The Mechanical Parameters of the Specimens  The finite element analysis was carried out for seven specimens, and compared with the experimental results. They are as follows (note that No. 1  ti  6 are normal strength  concrete and No. 7 is high strength concrete),  1. Plain concrete under push-in impact loading (0.5 • 10_  2  MPa/s, equivalent to  Impact III); 2. Polypropylene fibre reinforced concrete (0.5% by volume) under push-in impact loading (0.5 • 10 -2 MPa/s, equivalent to Impact III); 3. Steel fibre reinforced concrete (0.5% by volume) under push-in impact loading (0.5 • 10 -2 MPa/s, equivalent to Impact III); 4. Steel fibre reinforced concrete (1.0% by volume) under push-in impact loading (0.5 . 10 -2 MPa/s, equivalent to Impact III); 5. Steel fibre reinforced concrete (1.0% by volume) under push-in impact loading (0.5 • 10 -3 MPa/s, equivalent to Impact II); and 6. Steel fibre reinforced concrete (1.0% by volume) under pull-out impact loading (0.5 • 10 -2 MPa/s, equivalent to Impact III); 7. Steel fibre reinforced high strength concrete (1.0% by volume) under push-in impact loading (0.5 • 10 -2 MPa/s, equivalent to Impact III);  Chapter 7. Analytical Study^  :302  The mechanical parameters of the interface elements, C o , f,. and L„ which were determined experimentally, are given in Table 7.1. The tests for C o and fr are conventional tests in physics, and the test for f p is a simple mechanical tests (see Appendix H for details). As stated earlier, these parameters are defined as  Co = the unit chemical adhesion force, which is determined from laboratory tests (MPa) = the normal stress factor at the interface, which is determined from laboratory tests (111 Pa / zurn)  = the frictional factor at the interface, which is determined from laboratory tests For steel fibre reinforced concrete, the critical stress intensity factor for mode I (tension) under impact loading, K jc , was determined by :3-point loaded beam impact tests (Mindess ct al [107]); the values for the plain concrete and polypropylene fibre reinforced concrete were directly adapted from the results of their tests. So far no impact tests have been carried out to determine the dynamic critical stress intensity factors for mode II (sliding) and mode III (tearing) for concrete. It was assumed that the conclusion concerning the relationships of the critical stress intensity factors among mode I, mode II and mode III by Ba2ant ct al [108, 109] can apply also to the impact case. That is the value of fracture energy obtained from mode III tests is about 3 times larger than the mode I fracture energy and about 9 times smaller than the mode II fracture energy. In linear elastic fracture mechanics there exists a linear relationship between the fracture energy and the stress intensity factor. Therefore, the critical stress intensity factors for mode II and Mode and K im., can be determined by multiplying K1, by 27 and  ('hapter 7. Analytical Study  ^  :303  :3, respectively. Table 7.2 gives these values. The finite element meshes for the push-in and pull-out cases are shown in Figs. 7.7 and 7.8, respectively. Table 7.1: Parameters of Mechanical Properties of Interface Elements The unit chemical adhesion force Co  The frictional factor L.  (M Pa/min)  (M Pa)  N  H  Plain concrete Polypropylene fibre Concrete (0.5% by volume) Steel fibre concrete (0.5% by volume) Steel fibre concrete (1.0% by volume) Steel fibre concrete (0.5% by volume)  The normal stress factor fp  4.36  0.72  1008  4.02  0.72  1051  3.95  0.71  120:3  :3.87  0.71  1417  4.82  0.75  1109  N — Normal Strength^ H — High Strength  Chapter 7. Analytical Study ^  304  Table 7.2: Dynamic Critical Stress Intensity Factors for Concrete Mode I (Tension) Kic (MP(“/TT21)  Mode II (Sliding) Km c a (MPa0n)  Mode III (Tearing) Km c b (M.PaN/TT)  Plain concrete 3.54 95.6 10.6 Polypropylene fibre Concrete 3.75 101.3 11.3 (0.5% by volume) N Steel fibre concrete 4.65 125.6 14.0 (0.5% by volume) Steel fibre concrete 5.23 141.2 15.7 (1.0% by volume) Steel fibre H concrete 4.48 121.0 13.4 (0.5% by volume) N - Normal Strength ^ H - High Strength a, b  Calculated using Ba2ant et al ([108, 109]) relationships, i.e. = 27 Ki = 3 K.! c  Chapter 7. Analytical Study^  Interface element  305  Concrete element  IIN  MI  IN  ^Jewl■ N  11111 I^1  1 1 1 1 1^I^1^I ■  Ulm Spiral Steel element  Only half shown -  r  Figure 7.7: The Finite Element Mesh (Fracture Mechanics, Pull-out)  306  Chapter 7. Analytical Study^  UT  • Only half shown Steel element Spiral Interface element  ^  a 1^1 I^•  Concrete element  _ A •  a  Figure 7.8: The Finite Element Mesh (Fracture Mechanics, Push-in)  Chapter 7. Analytical Study^  307  7.6.2 The Stress Distribution and Crack Development  The calculated results showed that at very low levels of the steel stress (about 30 -- 40 MPa) the chemical adhesion between the rebar and the concrete was destroyed, and for the case of pull-out loading the frictional resistance reduced rapidly with the separation between the rebar and the concrete when the steel stress increased. At that point the rib bearing became the main factor providing resistance in the bond process. These seem to agree well with the experimental results. It was found from the finite element analysis that at a relatively low level of applied load, the distribution of the stress in the rebar was not much different from that obtained by the experimental method. With further increases in the applied load, however, the differences in the distributions between the two method became larger and larger. The results of the experimental method were obtained directly from the strain gauge measurements and are considered to be more reliable. Although the grooving of the rebar (in order to place the strain gauges) had an effect on this comparison, this indicates that the nonlinear modelling of the concrete, which was introduced at a relatively high level of the applied load during the finite element process, needs to be improved. It was also found that relatively high values of the principal tensile stresses developed in the concrete in the vicinity of the tips of the ribs, especially for the pull-out case, which indicated that the secondary cracks would form first. For the plain concrete and the polypropylene fibre concrete, some crushing of the concrete also took place at the tips of the ribs. This resulted in a great decrease in the bond strength, or, from the view point of energy, in the capacity of energy transfer. On the other hand there was seldom crushing in the concrete for the steel fibre concrete. This may help to explain why the  Chapter 7. Analytical Study^  308  specimens made of plain concrete and polypropylene fibre concrete consumed much less fracture energy during the entire bond-slip process. The calculated results also indicated that there were more cracking elements for the steel fibre concrete than for the plain and polypropylene fibre concrete. Because of this, the bond slips in the former case were always found to be larger than in the latter cases in the calculations, which, in turn, made the fracture energy for the steel fibre concrete much larger than for the other types of concrete. This is also in agreement with the experimental results. As expected, the bond strength and the fracture energy for push-in loading were found to be greater than for pull-out loading. This indicates that by adopting the :3-dimensional elastic matrix in the constitutional law, the Poisson effect was properly considered, and that the modelling of the frictional resistance at the contact surface between the rebar and the concrete by the 'bond-link element' was reasonable.  7.6.3 The Bond Stress-Slip Relationship  The bond stress-slip relationships determined by the finite element method are given in Figs. 7.9 to 7.14. Similar to the method adopted in Chapter 6, these curves also refer to the average data over the time period and the embedment length. In these figures the curves from experiments are also given for comparison. Fig. 7.15 represents one of the applied load vs. the displacement of the rebar, which is also determined based on the results of the finite element method. These results can be summarized as:  Chapter 7. Analytical Study^  309  1. The shapes of the curves obtained by the finite element method are different from those from the experimental measurements. There is only a very small linear portion from the beginning of the loading in those curves obtained by the finite element method. This may be because for the finite element models the chemical adhesion is destroyed at a very low level of loading, and the contribution of the frictional resistance to the bond strength depends on the calculated stress state at the interface to a great extent. This difference is most obvious for the pull-out case, as can be seen in Fig. 7.14. 9.  Both the peak and average bond stress are larger for the analytical than for the experimental results. From the viewpoint of mechanics, the models of the finite elements make the specimen more 'rigid', i.e. its stiffness becomes larger even though the modelling of the chemical adhesion and the frictional force may lessen the stiffness of the interface between the rebar and the concrete to some extent. The increase in the bond resistance and the relatively smaller local slip corresponding to the same bond stress may also attribute to this.  3. Although there are great differences in the curves between the finite element method and the experimental method, the total displacements of the rebars from both method are relatively close, as shown in Fig. 7.15. This suggests that the models adopted in the finite element analysis were reasonable. 4. By comparing the differences between the curves obtained by the two methods in Fig. 7.10 and Fig. 7.11 it can be seen that the polypropylene fibre addition did not have much effect on the results of the two difference approaches, in terms of the bond stress-slip relationship.  Chapter 7. Analytical Study^  310  5. As expected, the influence of steel fibre additions on the bond stress-slip relationship in the finite element analysis is significant, which can be seen by the comparison of two corresponding curves in Fig. 7.10 and Fig. 7.13, respectively. Both of these results are from the finite element method, but one is for a plain concrete specimen and the other for a steel fibre reinforced concrete specimen. 6. The result for high strength concrete (with 1.0% by volume steel fibres) is illustrated in Fig. 7.14. The difference between this result and that by experimental method is quite large. This may indicate that with the combined effects of concrete strength, Young's modulus, and a significant content of steel fibres, the modelling of the finite element method could introduce a considerable uncertainty in the analysis. Further research work needs to be carried out for more realistic modelling. 7. The effect of the loading rate on the bond stress-slip relationship can be reflected in this analytical study, as can be found by comparison of Fig. 7.12 and Fig. 7.13, which represent the results of same specimen subjected to loading at two different rates.  311  Chapter 7. Analytical Study^  SS 40 .4.••■••  20  I02  ■■•••••"""  1  1^2^9^4^5 Local Slip (0.01 mm) Finite Element Method^Experiment 0111•1■  ••■•■ •••••■••• 01••■■  .■■••■•  Figure 7.9: The Bond Stress-slip Relationship by the Finite Element Method (Plain Concrete, Push-in, Impact III - 0.5 • 10 -2 Mpa/s)  so 512 40 30  r4hd 20  10  0 0^1^2^3^4  Local Slip (0.01 mm)  Finite Element Method ^Experiment Figure 7.10: The Bond Stress-slip Relationship by the Finite Element Method (Polypropylene Concrete, Push-in, Impact III - 0.5 • 10 -2 Mpa/s)  Chapter 7. Analytical Study^  312,  so X40 04  00  ^ 1^ 2^ 3  Local Slip (0.01 mm)  4  Finite Element Method ^Experiment Figure 7.11: The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre Concrete, Push-in, Impact II - 0.5 • 10 -3 Mpa/s)  Local Slip (0.01 mm)  Finite Element Method^Experiment Figure 7.12: The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre Concrete, Push-in, Impact III - 0.5 • 10 -2 Mpa/s)  Chapter 7. Analytical Study ^  313  0 40  61 20 "1  0  0 1  2  ^  4  Local Slip (0.01 mm)  Finite Element Method^Experiment Figure 7.13: The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre High Strength Concrete, Push-in, Impact III — 0.5.10 -2 Mpa/s)  2^3^4  Local Slip (0.01 mm)  Finite Element Method ^Experiment 4■■11 ••■■•• ■■■■■ ■■■■•■ ■■•  Figure 7.14: The Bond Stress-slip Relationship by the Finite Element Method (Steel Fibre Concrete, Pull-out, Impact III — 0.5 • 10_  2  Mpa/s)  314  Chapter 7. Analytical Study ^  End Displacement (mm)  Finite Element Method ^Experiment ■■••■■ ■■•■■■■  •••■• ••••■■  •■=1,M,  Figure 7.15: The Applied Load vs. Displacement Curve the Finite Element Method (Steel Fibre Concrete, Push-in, Impact III — 0.5 • 10 -2 Mpa/s)  Chapter 8  Conclusions and Recommendations  8.1 Conclusions  The purpose of this research work has been to provide a more fundamental understanding of the bond behaviour of rebars in concrete subjected to high rate loading, to develop appropriate techniques to investigate the bond phenomenon using both experimental and analytical approaches, and to study the feasibility of using steel fibres, high strength concrete and other measures for better bond performance under impact loading. Based on the experimental investigation and the analytical study, the following important conclusions may be drawn:  1. The entire testing program as designed was suitable for the experimental investigation of the bond behaviour under impact loading. The testing machines was able to provide a wide range of high rate loading with a considerable amount of energy; the transducers and instrumentation used were able to measure and record the basic data, such as the applied load, the accelerations and the strains, at a sufficiently high rate with an acceptable level of error; the mechanical and mathematical models for processing the test data to obtain the most important parameters, such as  :315  Chapter 8. Conclusions and Recommendations^  316  the external forces, displacements, stresses, slips and the fracture energy, are appropriate and accurate: the specimens used are satisfactory and most of the important variables, which may affect the bond behaviour under high rate loading, have been considered. 2. For smooth bars, the bond resistance is due to the chemical adhesion and the frictional force at the interface between the rebar and the concrete. There exists a linear bond stress-slip relationship under both static and high rate loading. Different compressive strengths, types of fibres, fibre contents, and loading rates were found to have no great influence on this relationship or the stresses in both the steel bar and the concrete. 3. For deformed rebars, the chemical adhesion and the frictional force at the interface between the rebar and the concrete are less important for the bond resistance. The shear mechanism due to the ribs bearing on the concrete plays a major role in the bond-slip process. 4. For deformed rebars, the bond stress-slip relationship under a dynamic (high rate) loading changes with time and is different at different points along the reinforcing bar. An average bond stress-slip relationship over the time period and the embedded length is necessary and useful for evaluation and comparison of different tests. 5. Higher loading rate significantly increases the bond resistance capacity. Under high rate loading, the stress distribution along the rebar is not uniform, and is not even linear; there is more stress concentration along the rebar than under static loading. Higher stresses both in the rebar and in the concrete, greater slips, higher bond stresses, and larger fracture energy during the bond failure were developed with  Chapter 8. Conclusions and Recommendations ^  :317  an increase in the loading rate. These effects are especially noticeable when steel fibres are added to the concrete mixture. 6. The steel fibre additions greatly increased the bond strength. Steel fibres cause reduced stress concentrations along the rebar, and higher stresses in the concrete. The crack resistance is improved, thus the stiffness of the concrete surrounding the rebar increases. More fracture energy is needed for the bond failure. The bond stress-slip relationship of steel fibre concrete is quite different from that of the plain concrete and polypropylene fibre concrete, in terms of the peak value, the average value and the slope of the curve. These effects are more significant when subjected to high rate loading. A sufficient steel fibre content could help us to achieve the maximum improvement in the bond behaviour. 7. The high strength concrete exhibits higher bond strength and absorbs more fracture energy in the bond process, especially when steel fibres are added. 8. Under the same conditions, there is always higher bond resistance and more stress concentrations along the rebar for push-in loading than for pull-out loading. The stress distribution both in the rebar and the concrete is quite different for these two loading cases, and thus the patterns of cracking and bond failure are also different. A bond stress-slip relationship for the pull-out loading cannot simply be applied to the push-in case with only a change of the symbol of force. Since more fracture energy is needed for push-in loading than for pull-out loading, a reinforce concrete member can be expected to be tougher when the rebars are subjected to push-in forces. 9. The addition of polypropylene fibres to the concrete has no significant effect on the bond behaviour, in terms of the bond strength, the stress distributions both  Chapter 8. Conclusions and Recommendations ^  :318  in the rebar and the concrete, the crack development, the slip, the bond stress-slip relationship, and the fracture energy during the bond failure. 10. For epoxy-coated rebar the bond resistance and the fracture energy decrease to some extent, and wider cracks are developed. The influence of epoxy-coated rebars on the bond strength for push-in loading is much more significant than for pullout loading. However, high rate loading, high concrete strength, and the steel fibre additions at a sufficient content will effectively reduce these negative effects of epoxy coating on the bond behaviour. Polypropylene fibre has little effect on this behaviour. 11. The study of the energy transfer, energy dissipation and energy balance during the bond-slip process can help us to achieve a better physical understanding of the bond mechanism. The concept of fracture energy could be an effective and convenient way of evaluating the importance of certain variables, such as fibres in the concrete mixture, the concrete compressive strength, etc. to the bond improvement. 12. An analytical method based on fracture mechanics and the finite element analysis method is an effective and powerful approach for the study of bond behaviour under impact loading. By reasonably modelling the mechanical properties at the interface between the rebar and the concrete, the fracture characteristics in the concrete, the constitutive laws of both materials, and the cracking and crushing criteria, the stresses in the rebar and the concrete and the crack development can be predicted, and in addition the bond stress-slip relationship can be established analytically. It is relatively easy for an analytical method to take into account all of the important variables in the bond process, though this is difficult experimentally.  Chapter 8. Conclusions and Recommendations^  319  8.2 Recommendations for Further Study  The experimental program and the analytical study carried out in this investigation have provided greater insight into the bond behaviour of the rebar under high rate loading. However, there are some areas connected to this study which need to be explored further. Based on the results of this study, the following suggestions are made for further research on the bond behaviour of deformed bars under impact loading:  I. A more extensive experimental investigation should be carried out for the bond behaviour under high rate loading, in which the following variables need to be considered: • size of the specimen • size and geometry of the deformed bar, such as the rib angle, rib height, and rib spacing • embedment length of the rebar • confining pressure • shape, size and content of steel fibre • concrete compressive strength 2. Internal cracking in the concrete needs further study, similar to the method developed by Goto [30], to investigate the pattern and the extent of the cracking. In order to study crack propagation in plain or fibre reinforced concretes, certain techniques can be used to detect the fracture process zone (Mindess [110]); The influence of the bond resistance on the crack propagation and the width of the crack in the concrete should also be studied.  Chapter S. Conclusi ons and Recommendations^  320  3. More precise finite elements, capable of handling cracking. crack opening and closing in a composite of steel fibres and concrete, need to be developed in the analytical approach. 4. The 3-dimensional constitutive laws of both the steel and the concrete under dynamic loading should be determined and applied in the finite element analysis. 5. More reasonable crushing and crack propagation criteria in the concrete under dynamic loading should be established.  Appendix A  Maximum Length of Rebar at the Struck End  From the theory of buckling and stability [111], the critical stress in a column under compression is governed by the equations  E acr = ^ (7 7 1,)  (Al Pa)^  I r =^ ^(7n 777 )^ A  I=  7r d4  (A.1)  (A.2)  (nim4)  (A.3)  r d2 A= ^ (7777712) 4^  (A.4)  64^  where (7, 7. = the critical stress in the column 7' = the minimum rotational radius  E = Young's modulus of the material 321  Appendix A. Maximum Length of Rebar at the Struck End  ^  322  K = the effective length coefficient L = the length of the column^(mm)  I = the inertial moment of the section A = the cross-sectional area  ^  ^  (m7 m 4)  (7117712)  d = the diameter of the rebar^(mm) For the specimens used in this experimental work, one end of the column (rebar) is considered to be free while the other end is fixed. In this case the effective length coefficient K = 2.0. The other parameters for smooth and deformed bars are listed in the following table Table A.1: Geometrical and Mechanical Parameters of the Rebar Parameter  Straight bar  Deformed bar  Diameter^d^(mm) Area^A^(mm 2 ) Inertial Moment^/^(mm 4 ) Minimum Rotational Radius^r^(mm) Young's modulus^E,^(CPa) Critical Stress^u ^(M Pa)  12.7 126.7 1276.9 3.17 207.0 286.5  11.3 100.0 800.3 2.83 212.0 423.9  For this case the critical stress a„ can be taken as the yield stresses of the smooth and deformed bars. From Eq. A.1, Eq. A.2 and Eq. A.3 the maximum length of the rebar at the struck end can be calculated from the following  L  The results are  =  1'  K  E acr  (A.5)  Appendix A. Maximum Length of Rebar at the Struck End^  Lamooth = 133.8  777772  99.4  717777  L de. f armed =  323  After consideration of the alignment of the specimen and the striking head and the contact condition during impact, a safety factor of 2.0 was applied to the lengths. The maximum lengths of the struck end should then be Ls,„0071, = 66.9  L de f ormed =  717717  49.7  717777  Appendix B  The Effect of Stress Wave Propagation on Outputs of Transducers  From the theory of elasticity, the stress waves which propagate to the transducers used in the impact tests in this experimental investigation can be considered as simple plane longitudinal waves [112]. The governing equation for the waves is  02u  (In2  ^ =C2 ^ t2^ax2  (B.1)  where t = the time variable u = the variable of the axial displacement The coefficient c turns out to be the velocity of the stress wave and is given by  c=  E^  where  E = Young's modulus  ^  (M Pa) 324  (inis)^  (B.2)  Appendix B. The Effect of Stress Wave Propagation on Outputs of Transducers ^:325  p = the density of the material^(kg/inin2 • in) For steel, E = 210,000 MPa and p= 7800 ksint 3 = 0.0078 kg/min 2 • in, so the wave velocity c is  210000  c=  0.0078 = 5190  tn/s  The time, T, which takes for the stress waves to reach the sensors is  T_ L^  ^  (s  )  (B.3)  where  L = the distance between the striking point and the location of the sensors (m  )  The sensors could be either strain gauges for the load cell and the strain measurement unit or piezoelectric crystals for the accelerometers. For the bolt load cell, L = 0.08 m so the travailing time of the stress waves is ,  0.08 Toad = ^ = 0.000015 .9 = 15 /L8 5190  For the strain measurement, L = 0.30 in (pull-out) and 0.05 in (push-in), so the travailing time of the stress waves is  Appendix B. The Effect of Stress Wave Propagation on Outputs of Transducers ^:3 2 6  0.30 TPull =-7  5190 =  0.000058 8 = 58 /is  and Tpush  0.05 5190  0.000010 s = 10 ps  For the accelerometer, L = 0.19 in, so the travelling time of the stress waves is  0.19  Lea ^ = 0.000037 s = 37 its 5190 The preliminary tests showed that the duration of an impact test ranged from 5 711.S to 30 in.s and the sampling rate for data collection was 200 /is. It is obvious that the effect of stress waves on the time delay of the signal outputs from the transducers is negligible.  Appendix C  Design of Electric Circuit for Strain Measurement  The electricity the output voltage (signal) is (see Fig. 3.4 in Section :3.3.1.5)  bout  E^+ R1)^E • 120.0 (R 1 + 120.0 +^)^(R 2 + 120.0 + K2R2(2)  (V)^(C.1)  where Vout = the output signal  ^  (V)  E = the excitation voltage^(V)  K 1 K2 = the gauge factors of a pair of strain gauges (gauge 1 and gauge 2)  R 1 , B2 = the electric resistances of a pair of strain gauges^(C/) ( 1 . ( 2 = the strains at two opposite sides of the rebar The two dummy resistances were 120.0  ft precision resistances. After operation and  rearrangement, Eq. C.1 becomes  :327  Appendix C. Design of Electric Circuit for Strain Measurement^ 328  t  Ii 1 Ri R2E 1 + K2 RI R2E2 + Ri R2 — 120.0 2 + KI K2R1R2 6 1€2 —  (V)^(('.2)  (R 1 + 120.0 + KiRiei)(R2 + 120.0 + K2R2(2)  In this test the strains would not exceed 2000 x 10  -6 ,  i.e. the maximum values for t i  and E 2 were less than 0.002, while the gauge factors, K 1 and A2, were about 2.050 and the electric resistances, R 1 and R2, were about 120.0 Q. This means that in Eq. C.2 K 1 R 1 ( 1 and K2R2E2 are higher order terms compared to (R 1 + 120.0) and (R 2 + 120.0),  so they are negligible. The same thing happens to the term K i K 2 R 1 R 2 e 1 t 2 . Thus Eq. ('.2 becomes  Out  Rl R2 1 1 + K2 R1 R2 E2 + Rl R2 — 120.0 2 (RA^120.0)(R2 + 120.0)  (V)  ^  (('.3)  The manufacture of the strain gauges guarantees an accuracy of ±0.3% for the electric resistance and ±0.5% for the gauge factor. This means that for all the strain gauges R 1 and B2 are 120.0± 0.36 f2, K 1 and K2 are 2.050± 0.01025. From the theory of error [113] if we take all electric resistances as 120.0 ft and all gauge factors as 2.050 the possible error for the output signal will be  01/00 di/out avout ORi OR2 dlkl  aVout 6Vont = 6R1 + 6R2 + 6K1+ 6K2 (C.4)  OK2  The maximum absolute error for the output signal is  1 W,,it =  i)t ro„t DR 1  6 Ri +  Vo„ t DR 2  6R 2  avout  O KI  6K 1 +  1 00 dK2  6K 2^(('.5)  Appendix C. Design of Electric Circuit for Strain Measurement ^329  where the increments 6R 1 , 6R 2 , 6K 1 and bK 2 are positive numbers. From Eqs. C.3 and C.4 it was clear that the evaluation of 1/0 ,a and (5' V0ut involved extremely tedious mathematical operations. However, by means of numerical differentiation it was possible to evaluate these values at the specified point where  = R2 = 120.0 5 2 .  = K2 = 2.050 with the increments of variables  6R i = 6R 2 = 0.36 fl  6K i = 6K 2 = 2.050  The results were  govt  =  2.050E (€ 1 + (2) 2  (V  and 161/0 .0 1 = 0.0015  2.050E (El + (2) 2  The relative error was  16v t I = 0.15% o.  Vont  Appendix C. Design of Electric Circuit for Strain Measurement ^:330  Since the average (6 1 + t 2 )/2 represents the actual strain ( at the section, any bending moment in the longitudinal loading plane where the strain gauges were mounted would cancel out automatically. It can be concluded that for the electric circuit of an 'opposite arm' Wheatstone bridge there exists a linear relationship between the actual strain and the output signal and that this can be represented by a simple equation  Vopt =  Ii E(fi  2  + (2)  (V)  Or, in a. more practical form,  =  ER  ^(1 0-6)^  One calibration based on Eq. C.8 applies to all the strain gauge measurements.  (C.9)  Appendix D  The Effect of Inertial Force  The inertial force of the rebar, F.. can be determined by the following equation  = I paA d.5^(N)^  (D.1)  where  = the inertial force of the rebar^(N) 1 = the location of the calculated section^(mm) p = the density of the rebar  ^  a = the acceleration of the rebar  (Ns 2 /7727n 4 )  ^  = the cross-sectional area of the rebar  (77/77//s 2 ) ^  ( 7117 712)  The experimental data showed that the acceleration a can be assumed to be the same along the whole bar. Thus Eq. D.1 becomes  331  Appendix D. The Effect of Inertial Force^  = paAl s^(N)^  332  (D.2)  where I s = the length of the rebar^(mm) The deformed rebar used had a cross-sectional area A3 = 100.0  77/ 771 2 ,  a l ength  is  =  190.5 mm  and a density of steel p = 7.8 x 10 -6 kg/mm 3 . The maximum acceleration measured was a s = 29.3 g (g is the gravitational acceleration). Thus the inertial force of the rebar Ft is  = 7.8 x 10 -6 x 29.3g x 100.0 x 190.5 = 42.7 N This inertial force is negligible when compared to the contact load Ft , the peak value of which could be as high as 50.0 -- 80.0 kN. The same conclusion applies to the smooth bar.  Appendix E  Tests for Determining Characteristics of Signal Noise  E.1 Noise in Acceleration and Strain Measurement  E.1.1 Test Design  A longitudinal impact test of two bars was carried out to determine the characteristics of signal noise in the acceleration and the strain measurement. As shown in Fig. E.1, a. rod (Bar 1) made of plastic with a. length 11 = 200.0 mm, fell from a height, h = 150.0 717.111, and  struck another rod (Bar 2) made of the same material with a length 1 2 = 400.0  711111 longitudinally.  Bar 2 was instrumented with an accelerometer and a pair of strain  gauge to record the acceleration waves at its bottom and the stress waves at the top during the impact. Both the compression waves and velocities of particles induced by the impact were plane longitudinal waves and would travel at the wave velocity, c, given by Eq. B.2 in Appendix B,  ^ C  E^  :33 :3  (m/s)^  (E.1)  Appendix E. Tests for Determining Characteristics of Signal Noise ^334  i 200 0  Bar 1  V=0  150.0  V/2  Strain Gauge  V/2  V/2 400 0  Bar 2  Accelerometer  t=0  ^  t= 400.0/c  All in mm  Figure E.1: Longitudinal Impact of Bars  Appendix E. Tests for Determining Characteristics of Signal Noise^335  E.1.2 Acceleration Waves  E.1.2.1 Analytical Solution  At the instant of impact two identical compression waves started to travel along both bars. The corresponding velocities of the particles relative to the unstressed portions of the moving bars were equal and were directed in each bar away from the surface of contact [112, 114, 115]. Let v be the velocity of the falling bar (Bar 1) at the moment of impact: the magnitude of the velocities of the particles must be equal to v/2 in order to have the absolute velocities of the particles of the two bars at the surface of contact equal. After an interval of time equal to  T= 12^  ^ (s)  (E.2)  the absolute velocity of the particle at the bottom of Bar 2 would reach v/2. Physically, the absolute velocity history would increase gradually, as shown in Fig. E.2. Thus the acceleration at the bottom during the period [0, A(t), is a constant (see Fig. E.3), i.e.  A(t) =  dv dt (0 .  A(t) =  T VC 2l 2  [0,  (  771/8 2 )  (E.3)  Appendix E. Tests for Determining Characteristics of Signal Noise ^336  0.8 ;  os  g 0.4 02  4. 0^ 0  40^80^120  ^  Time (micro second)  103  ^  2C0  Figure E.2: Absolute Velocity History at the Bottom (Analytic)  40^03^120  ^  Time (micro second)  100  ^  200  Figure E.3: Acceleration History at the Bottom (Analytic) Applying FFT (Fast Fourier Transform) to the acceleration function A(t) in Eq. E.3 yields  Appendix E. Tests for Determining characteristics of Signal Noise ^337  C oa (w )  =^l^A (t) e ▪  00  -  iw t  ye ^2 / 2  + 00  J  dt,  dt  T vC --^dt fo 21 2  ye  C 2 /2 )  1  ^—iwT —1  ]  ve^ 7--) — 1 [ sin . wT + (cos coT — 1) i^(in/.s2 • Hz)^(E.4) 21 2  Eq. E.4 is the equation of the amplitude spectrum of the analytic solution for the acceleration. In order to get the spectrum curve it is necessary to determine the magnitude of the complex function  I ca (-') I =  21 2  1 w  sin coT +(cos LoT — 1)  ye 1 21.2 ) w (ye 1 2)  sin 2 coT + (cos coT — 1) 2  sin wT Ca)  (in/s 2 • Hz)^(E.5)  The plastic had a density, p = 1500 ky/in 3 = 0.0015 kg /iiiin 2 • in, and Young's modulus. E = 7000 111 Pa, so the wave velocity c is  Appendix E. Tests for Determining Characteristics of Signal Noise^:3:38  c =  E  7000 0.0015  = 2160 mis  and the velocity of the particle v is  2g h =^x 9.81 x 0.91 x 0.15 = 1.64 mis  the interval of time T is (Eq. E.2)  / 2^0.40 T = — = ^ = 1.85 • 10 -4 s c^2160 Substituting these value in Eq. E.5 yields  Ca (w) I = 8856  sin 1.85 • 10 -4 cv  w  (7n/s2 • Hz)^(E.6)  Based on Eq. E.6, the amplitude spectrum of the acceleration can then be drawn, as shown in Fig. E.5.  E.1.2.2 Experimental Approach  An acceleration history curve based on the acceleration data recorded by the data acquisition system is shown in Fig. E.4. It may be noticed that the curve obtained by the experimental method is a bit different from that by the analytic method, with the peak value about 10% higher than the analytic peak value. Applying FFT to the curve, one get the amplitude spectrum shown in Fig. E.6.  Appendix E. Tests for Determining Characteristics of Signal Noise^339  -4-  o^ 0  40^SO^120  ^  103  ^  203  Time (micro second)  Figure E.4: Acceleration History at Bottom (Experimental)  .L..  -t-  •  t  -  .4-^-1- •  1  ..L.  10^20^30  Frequecy (kHz)  40^50^60  Figure E.5: The Amplitude Spectrum of Acceleration (Analytic)  Appendix E. Tests for Determining . Characteristics of Signal Noise^340  E.1.2.3 Characteristics of Noise in the Acceleration Measurement  By the comparing the two amplitude spectra (see Figs. E.5 and E.6) it was found that the significant frequencies of the noise in the acceleration measurement were higher than 2.4 kHz. Therefore a low pass filter, with a 2.4 kHz cut limit, was suitable for filtering the acceleration signal data. Fig. E.7 shows the filtered signal of the acceleration, which is considered to be a "true" signal and is close to the analytic curve.  E.1.3 Stress Waves  The procedure used to determine the characteristics of the noise for the strain measurement was similar to that for the acceleration measurement, described in the above section. The analytic function of the stress at the top of the bar in the time-domain is  (1)^E^E^2c  ^[0, 2T]^(10-6)^(E.7)  and the amplitude spectrum of the strain is  c(( w) l = '  sin 2wT w  (10 -6 /Hz)^(E.8)  The amplitude spectra of the strain from both analytic and experimental methods are given in Figs. E.8 and E.11. Similar to the analysis of the characteristics of the noise in the acceleration measurement, a low pass filter with 1.5 kHz was found suitable for the strain measurement. Figs. E.8 and E.10 show the strain history obtained by the  Appendix E. Tests for Determining Characteristics of Signal Noise ^341  12  h io !  r^—t—  E  4  r 10^20^30^40  11s4  -  50  Frequecy (kHz)  so  Figure E.6: The Amplitude Spectrum of Acceleration (Experimental)  40^80^120  Time (micro second)  160  Figure E.7: Acceleration History at the Bottom (Filtered)  lx  Appendix E. Tests for Determining Characteristics of Signal Noise ^342  403  t  I •1  243  •1  160  10  00  ^80^1E0^240^320^403  Time (micro second)  Figure E.8: Strain History at the Top (Analytic) analytic and experimental methods, respectively. The filtered signal ("true" signal) is given in Fig. E.12.  E.2 Noise in Load Measurement  Let a relatively rigid mass made of cast iron fall under gravity from a height, h = 200.0 mm, and strike the bolt load cell (described in Section 3.3.1.3), as shown in Fig. E.13. The mass of the block was M = 2.0 kg. The velocity of the particles at the tup of the bolt at the instant of impact, v o , is  vo = I2g h^(m/s)  ^  (E.9)  Appendix E. Tests for Determining Characteristics of Signal Noise ^343  4.1  600  7  1 ^i ^1^1I 1i^  4C0  !  2C0  -/ ..' .1:77.\\.  •C  i  i  .i.  i  ;  0 ^ ^ ^ ^ 5 0 10^15^20 30 25  la!  Frequecy (kHz)  Figure E.9: The Amplitude Spectrum of the Strain (Analytic)  4C0  320  2  °I 243  leo BO  493^163^243  ^  Time (micro second)  Figure E.10: Strain History at the Top (Experimental)  4C0  Appendix E. Tests for Determining Characteristics of Signal Noise ^344  j  10^16^20  Frequecy (kHz)  ^ ^ 25 so  Figure E.11: The Amplitude Spectrum of The Strain (Experimental)  ..-..-.._... • ._—..320  2 2 40  I 1 03 C73  BO  80^180^240  ^  Time (micro second)  320  ^  Figure E.12: Strain History at the Top (Filtered)  4C0  Appendix E. Tests for Determining Characteristics of Signal Noise^345  and the initial compressive stress cc, is given by [112]  cro = vo E P  M  ^  (Mpa)^  (E.10)  All in rnrn  200.0  Figure E.13: Longitudinal Impact of Bar and Block Owing to the resistance of the block, the velocity of the bolt load cell, and hence the pressure on the tup of the bolt gradually decreased. A compressive wave with a decreasing stress started to travel along the length of the bolt. The change in compression with time can easily be found from the equation of motion of the block,  Appendix E. Tests for Determining Characteristics of Signal Noise^:346  Mkt  + Ao- = 0  (E.11)  where M = the mass of the iron block ^(kg) v = the variable velocity of the mass^(m/s) (7n77/2)  = the cross-sectional area of the bolt  a = the variable stress at the tup of the bolt^(MPa) With the initial condition, Eq. E.10, the solution for the ordinary differential equation Eq. E.11 is  a(t) = V2g hEp c  -  A  ATP-  ^(MPa)^(E.12)  The force exerted on the bolt is  F(t) = Aa(t) = A/2g hEp e  AV NiEP t  -  ^  (N)  ^  (E.1:3)  Let T be the time interval between the instant of impact and the instant at which the compressive wave with a front pressure a 0 returns to the tup of the bolt that is in contact with the moving block, T is given by  T  =  2 1 bolt  ^  Appendix E. Tests for Determining Characteristics of Signal Noise ^347  where  bolt =  the length of the bolt load cell ^(inn)  c = 5190 nt/s, the wave velocity of steel (see Eq. B.2 in Appendix  B)  The above solution Eq. E.13 can be used as long as 0 < t < T, as shown in Fig. E.14. From Eq. E.13, the spectrum equation of the load is  CF (U ^L f )  +DO 00  F(t) c- iwt di  CC J-00  =  I  T  A  2g hEp^A MEP i e zw t dt  ^  A 2g hE pc  — AV2g hEp  A VT7 M  C -iWt dt  1 ^[ (AM +,w)7,  fAvEp  M  — 11 (MPa/Hz) (E.14)  The magnitude of this complex function is  (ANTET  ICT--(,))1 = A\/2g hEp  A VEp  M  w)T  w  —1  (MPa/Hz)^(E.15)  Appendix E. Tests for Determining Characteristics of Signal Noise ^348  Given all of the known parameters,  A = 1 718 2 = 254.5 mrn 2 4  h = 0.20 7-n  E = 210000 M Pa  p = 7800 kg/7n 3  and 2 x 0.12 T = ^ = 46.2 its 5190 it was possible to evaluate IC a (w)1 for the variable frequency w; the load history and its spectrum of frequencies are shown in Fig. E.14 and Fig. E.15, respectively. On the other hand, the load history was also recorded by the data acquisition system, as shown in Fig. E.16 and the amplitude spectrum based on the recorded data is given in Fig. EAT. Similar to the procedure of analyzing the characteristics of the noise in the acceleration measurement which is described in the above section, a low pass filter with 2.0 kHz was found suitable for the strain measurement. Figs. E.18 shows the filtered signal of the load.  Appendix E. Tests for Determining Characteristics of Signal Noise ^349  25 '^  0  !  ••■■ 15  0'^ 0  10^20^30^40  ^  Time (micro second)  50  so  Figure E.14: Load History (Analytic)  Z °A  4.1 OS !  i !  is) 0.4 S.  •C  02  a  —  o  0  .1  —  10^20^30^40  Frequecy (kHz)  ^ ^ 50  so  Figure E.15: The Amplitude Spectrum of the Load (Analytic)  Appendix E. Tests for Determining Characteristics of Signal Noise ^350  25  20  15 !  1.5 10  i  5  0 '^ 0  10^20^ao^40  Time (micro second)  50  so  Figure E.16: Load History (Experimental)  •■••■  1  . Z °A  ^ •=1  OS  4.0 0.4  V  V ° C 02  O  0  0  10  20^30^40  Frequecy (kHz)  50  so  Figure E.17: The Amplitude Spectrum of The Load (Experimental)  Appendix E. Tests for Determining Characteristics of Signal Noise ^351  25  -r i  20  ••■■ 15  "01  141 10  1.2  5  0^  0  10  20^30^40  Time (micro second)  Figure E.18: Load History (Filtered)  50  50  Appendix F  The Solution of Three-dimensional, Axisymmetric Problems  It was noted that the specimen tested was axially symmetric because its geometry, loading and material properties were independent of the circumferential coordinate O. There were only u (axial) and w (radial) displacement components inside the body, so the problem was physically three dimensional but mathematically two dimensional. Even so, it is hard to find an analytic solution. The finite element method, therefore, was used to analyze the stresses in the rebar and the concrete [116, 117, 118, 100]. The element employed was a ring of constant rectangular cross section, as shown in Fig. F.1. Centers of all nodal circles lie on the Z-axis, which is the axis of the rebar. The body and its elements were solids of revolution about the Z-axis. This is a linear isoparametric element and the displacement field {f} has only z and r components,  {f}^{u w} = [N]{d}^  (F.1)  where [N] is a function of the coordinates,  NI 0 N2 0 N3 0 N4 0  [N] =^  0 N1 0 N2 0 N3 0 N4 352  (F.2)  Appendix F.^The Solution of Three-dimensional, Axisyinmetric Problems ^353  and {d} contains the 'it's and w's of the nodal circles,  {CI} =^Ul^WI^U2^W2^U3^W3^U4^W4  }^  (F.3)  The individual shape functions are  N1 =^( 1 —^( 1 — 71  )^  N2  =^+ 0 ( 1^7i)  AT3^14 (1 +)(1 +^N4 =4 (^—^(^+^)  (F.4)  The strains are  dz  0  0  1  Er  EB  0  (F.5)  a 07'  0^0 Or^d Z The stresses are  {0  ^0- r Cr() Tzr  }^  [E]^{ (z Er 6 0 Yzr  }  ^  {60}^  { cro }^  (FM)  where {c o } and fcr o l are the initial strains and the initial stresses respectively, and the matrix of the modulus of elasticity is  Appendix F. The Solution of Three-dimensional, Axisymmetric Problems^354  E  {E} =  1^ft^ft  0  P^1 —  0  (1 + it) (1 — 21,t) ^1.1,^  1 — ft  0^0^0  (F.7)  0 1— 2^-  The above matrix of the elastic modulus can be either for the steel or for the concrete, by substituting E and p with the corresponding values for the materials. To calculate the stresses in the steel and the concrete in the elastic stage, two reasonably fine meshes for the finite element calculation, as shown in Fig. F.2 (for the pull-out calculation) and Fig. F.3 (for the push-in calculation), were used. The applied load was taken as 30.0 kN and the specimen was normal strength concrete with polypropylene fibers and a deformed bar. The values of the material properties were those given in Section :3.2.5 in Chapter 4. Some results are given in Tables F.1 and F.2. It can be found from the results of the calculations that the radial strain and the tangential strain do not play much of a role in the terms of the total strain either in the steel or in the concrete. For example, for the elements at the interface between the steel and the concrete in the cross-section I under pull-out case, the ratios are  [,^  1-2p,  (^+^(9) z^is,z]  = 4.3% < 5% (in the steel)  and  Ne  )] ^ = 4.9% < 5% (in the concrete) E c,z [i —"2s „^c  J  Appendix F. The Solution of Three-dimensional, Axisymmetric Problems^:355  It was also found that for elements at a distance of 85% of the diameter away from the rebar, the axial strain decreases to zero. This means that the effective cross-sectional area can given by multiplying the total area by a factor, 7, given by  47r(0.85 D) 2 D2^  = 0.57  where  = the length of the square of the specimen^(non) The aboVe conclusions were used to simplify some equations in the calculations of strains and stresses in the data processing. Table F.1: Strains in the Rebar (by the Finite Element Method) CrossSection a  Loading Type  I  Pull-out Push-in Pull-out Push-in Pull-out Push-in  II III  Central Elements fs,z C s ,r E5,0 1058 b 40 26 -1064 -29 -27 557 21 18 -560 -15 -14 3 2 56 -60 0 0  Outer Elements C s,z  Es,r  6 s,9  1041 -1045 548 -550 51 -54  65 -59 :34 -31 0  57 -51 30 -27 2 0  °The load the rebar part carries for Section I, II and III is 95%, 50% and 5% respectively 'Positive number represents the tensile strain and negative the compressive strain; all numbers are in 10 -6  Appendix F. The Solution of Three-dimensional, Axisymmetric Problems  ^  356  Local coordinate (x, y) Global coordinate (Z, R)  Figure F.1: Finite Elements of a Ring  Table F.2: Strains in the Concrete (By the Finite Element Method) CrossSection ' I II III  Loading Type Pull-out Push-in Pull-out Push-in Pull-out Push-in  Central Elements a  Outer Elements b  r-s,r  es,e  fs,z  es,r  fs,0  721 d 62 -732 -55 403 34 -466 -30 59 2 -58 -3  58 -49 30 -28 2 -1  0 0 30 -23 59 -55  0 0 5 -2 1 -1  0 0 4 -2 2 0  E-s,z  'Elements in the vicinity of the rebar bElements at about 70% of the radius away from the rebar `The load the concrete part carries for Section I, II and III is 5%, 50% and 95% respectively dPositive number represents the tensile strain and negative the compressive strain; all numbers are in 10 -6  Appendix F. The Solution of Three-dimensional, Axisymmetric Problems  ^  Concrete  ill  IN  IN  111111^111111^1^1^1 INN Spiral  Reber  Only half shown  F Figure F.2: The Finite Element Mesh (Pull-out)  357  Appendix F. The Solution of Three-dimensional, Axisymmetric Problems ^358  Only half shown Rebar Elm Spiral  Concrete  MI  ■ M  IA^IAA^414.4  4  Figure F.3: The Finite Element Mesh (Push-in)  Appendix G  The Calculation of the Hammer Rebound  As soon as the hammer rebounds it starts to decelerate at a constant rate. From kinetics, the rebound height is given by  h rf bound =  2  2 (1 + 0.09)^ g t up  (nun)^ (G.1)  where t up = the time that the hammer takes to reach its highest point  ^  (s  )  and the deceleration (1 + 0.09)g includes the gravitational deceleration, and the frictional and air resistance effect. When the hammer falls down again, it has a constantly accelerating motion. Assuming that the friction and air resistance losses remain the same, the equation of motion IS  1 ,^ h fbounci =^— 0 . 09 )g t2own  2  Where  :359  (inm)^ (G.2)  Appendix G. The Calculation of the Hammer Rebound^  :360  td,„, = the tune that the hammer takes to start to fall for the second time (•)  What the data acquisition system records is the total time of the rebound,  t rebound = tup^tdown  ^  ^  (s  t rebound,  (G.3)  )  Solving Eqs. G.1, G.2 and G.3 simultaneously yields  +1 1  tup = ^  1  1.09 51  rebound =  0.4775 t rebound  (A)  (G.4)  After the rising time f ur is known, the rebound velocity and the rebound height can all he determined from kinetics.  Appendix H  Determinations of Parameters, C o , fr and fr  H.1 The Unit Chemical Adhesion Force  A simple tension tests was carried out using a universal testing machine to determine the unit chemical adhesion force. The specimen is shown in Fig. 1-1.1. The unit chemical adhesion force, C o , is calculated by  ^Co  =  —  A^  (MPa)^  (H.1)  where  F = the break force^(N) A = the cross-sectional area of^the specimen^(77/7n2)  H.2 The Frictional Factor at the Interface  The test for determining the frictional factor at the interface is shown in Fig. H.2. It was carried out using a universal testing machine. The applied vertical force varied from 361  Appendix H. Determinations of Parameters, C o , fp and fr^362  0 to 4.0^7.0 kN, depending on the compressive strength of the concrete. The factor,  fr , is given by  dFh^" Fig fr = ^ =  D f, n `74 Fui  (H.2)  where Eh = the horizontal force corresponding to the point where a 0.1 mm horizontal displacement takes place.^(N)  F„ = the applied vertical force^(N) n = the number of data points  H.3 The Normal Stress Factor at the Interface  The test for determining the normal stress factor at the interface is shown in Fig. H.3. It was carried out using a universal testing machine. The applied vertical force varied from 0 to 4.0 7.0 kAT, depending on the compressive strength of the concrete. The factor, fr , is given by  dv1 ," ^ = f''= dF^ F• n^v  2_,  where z. = the vertical deformation^(mm)  (H.3)  Appendix H. Determinations of Parameters, co , fp and f ^36:3 T  F„ = the applied vertical force I?  =  ^  (N)  the number of data points  40 50  A—A  All in mm  Figure I-1.1: Test Specimen for the Unit Chemical Adhesion Force  App(-wdix H. Determinations of Parameters. C o , fp and L.^  1111 1111 1111 1111 11 50  50  111111111111111111 150  -1  ^  All in mm  '1  Figure H.2: Test for the Frictional Factor at the Interface  :364  _Appendix H. Determinations of Parameters, C o , fp and fr^365  A  Rebar  Concrete 45  A All in mm  A—A  Figure H.3: Test for the Normal Stress Factor at the Interface  Bibliography  [1] Wastlund, George, Odman and Aven, "Subjects of the Symposium," RILEM Symposium on Bond and Crack Formation in Reinforced Concrete, Vol. I, Stockholm, 1957. [2] CAN3-A23.3-M70, "Design of Concrete Structures for Building," Canadian Standards Association, Toronto, 1970. 252 pp. [3] ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-63)," American Concrete Institute, Detroit, 1963, 144 pp. [4] CANS-A23.3-M73, "Design of Concrete Structures for Building," Canadian Standards Association, Toronto, 1973. 263 pp. [5] CANS-A23.3-M84, "Design of Concrete Structures for Building," Canadian Standards Association, Toronto, 1984. 281 pp. [6] ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-70," American Concrete Institute, Detroit, 1971, 78 pp. [7] ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-89/ACI 318R-89)," American Concrete Institute, Detroit, 1989, 353 pp. [8] ASTM C 234-91a, "Standard Test Method for Comparing Concretes on the Basis of the Bond Developed with Reinforced Steel," ASTM Annual Book of Standard, Section 4, (onstruction, 1991. [9] Ba2ant, C.P. and Sener, S., " Size Effect in Pullout Tests," ACI Materials Journal, Vol. 85, No. 5, Sept.-Oct. 1988, pp. 347-351. [10] Abrams, D.A., "Readers Writes: Section," Civil Engineering, V.21, No.6, June 1951, pp. 51-52. [11] Abrams, D.A.. "Tests of Bond Between concrete and Steel," Engineering Experiment Station, Bulletin No. 71, University of Illinois, Urbana, Dec. 1913. [12] ACI Committee 408, "Bond Stress — The State of the Art," ACI Journal, Proceedings V.63, No.11, Nov. 1966, pp. 1161-1188. 366  Bibliography^  367  [13] ACI Committee 408, "State of the Art ^ Bond under Cyclic Loading," ACI Material Journal, V.88, No.6, Nov./Dec. 1991, pp. 669-673. [14] Mindess, S., "Effects of Dynamic Loading on Bond," ACI Committee 446: State-ofthe Art Report, Section 4.2.3., 1989 [15] CEB Task Group VI, "Bond Action Behaviour of Reinforcement — State of the Art Report," Dec. 1981. [16] Myirea, T.D., "Bond and Anchorage," ACI Journal, Vol.44, March 1948, pp. 521552. 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A.H., "Bond Stress Slip Relations in Reinforced Concrete Report," No.345, Dept. of Structural Engineering, Cornell University, Dec. 1971. [35] Honde, J., "Study of Force-Displacement Relationships for the Finite Element Analysis of Reinforced Concrete," Ph.D. Thesis, McGill University, 1974. [36] Richart, F.E. and Jensen, V.P., "Tests of Plain Reinforced Concrete Made with Haydite Aggregates," Bulletin No.237, Engineering Experiment Station, University of Illinois, 1931. [37] Menzel, C.A., "Some Factors Influencing Results of Pull-out Bond Test," ACI Journal, Proceedings, Vol. 35, June 1939, pp. 517-544. [:38] Gilkey, H.J., Chamberlin, S.J. and Beal, R.W., "Bond with Reinforcing Steel," Iowa State College Bulletin, Engineering Report No.26, 1955-56. [39] Watstein, I). and Seese, N.A., "Effect of Type of Bar on Width of Cracks in Reinforced Concrete Subjected to Tension," ACI Journal em Proceedings, Vol.41, No.4, Feb. 1945, pp. 293-304. [40] Clark. A.P., "Comparative Bond Efficiency of Deformed Concrete Reinforcing Bars." ACI Journal em Proceedings, Vol.18, No.4, Dec. 1946, pp. :381-400. [41] Konyi, N.H., Bond between Concrete and Steel," Structural Concrete, Reinforced Concrete Association, VoLl, No.9, May/June 1963, pp. 373-390.  Bibliography^  369  [42] Mathey, R.M. and Watstein, D., " Investigation of Bond in Beam and Pull-out Specimens with High Yield Strength Deformed Bars," ACI .Journal Proceedings, Vol.57, No.9, March 1961, pp. 1071-1090. [43] Vos, I.E. and Reinhardt, H.W., "Bond Resistance of Deformed Bars, Plain Bars, and Strands under Impact Loading," Report 5-80-6, Department of Civil Engineering, Delft University of Technology, Netherlands, August, 1980. [44] Rehm, G., "The fundamental Law of Bond," RILEM Symposium on Bond and Crack Formation in Reinforced Concrete, Vol. I, Stockholm, 1957. 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[51] Swamy, R.N. and Al-Noori, K., "Bond Strength of Steel Fibres Reinforced Concrete," Concrete (Great Britain), Vol. 8, No. 8, Aug. 1974, pp. :36-37. [52] Yerex, Lowell 11, Wenzel, Thomas H. and Davies, Robert, "Bond Strength of Mild Steel in Polypropylene Fiber Reinforced Concrete," ACI .Journal Proceedings, Vol.82, No.1, Jan./Feb. 1985, pp. 40-45. [53] Clifton, J.R. and Mathey, R.G., "Bond and Creep Characteristics of Coated Reinforcing Bars in Concrete," ACI Journal Proceedings, Vol.80, No.4, July/Aug. 1983, pp. 288-293. [54] Treece, R.A. and Jirsa, J.0., "Bond Strength of Epoxy-Coated Reinforcing Bars." ACI Materials Journal, V.86, No.2, Mar-Apr. 1989, pp. 167-174.  Bibliography^  370  [55] Cleary, D.B. and Ramirez, J.A., "Bond Strength of Epoxy-Coated Reinforcement," ACI Materials .Journal, V.88, No.2, Mar-Apr. 1991, pp. 146-149. [56] Takeda, T., Sozen, M.A. and Nielsen, N.N., "Reinforced Concrete Response to Simulated Earthquakes," Proceedings of ASCE, V.96, ST12, Dec. 1970, pp. 2557-257:3. [57] Hassan, F.M. and Hawkins, N.W., "Effect of Post-Yield Loading Reversals on Bond between Reinforcing Bars and Concrete," Report SM73-2, Dept. of Civil Engineering, University of Washington, Seattle, March 1973. [58] Viwathanatepa, S., Popov, E.P. and Bertero, V.V., "Deterioration of Reinforced Concrete Bond under Generalized Loading," ACI Annual Conference, San Diego, California, March 1977. [59] Hungspreug, S., "Local Bond between a Reinforcing Bar and Concrete under High Intensity Cyclic. Load," Ph.D Thesis, Cornell University, .Jan. 1981. [60] Morita, S and Kaku, T., "Local Bond Stress-Slip Relationship under Repeated Loading," IA B,SE Symposium, V.13, Lisbon, 1973, pp. 221-226. [61] Rehm, G. and Eligehausen, R., "Einfluss Einer Nicht Ruhenden Belastung auf das Verbundverhalten von Rippenstahlen," Betonwerk and Fertigteil Technik, Hert 6, 1977, pp. 295-299. [62] Edwards, A.D. and Yannopoulos, P.J., "Local Bond Stress-Slip Relationship under Repeated Loading," Magazine of Concrete Research, V.30, No.103, .June 1978. • [6:3] Perry, E.S. and .Jundi, N., "Pull-out Bond Stress Distribution under Static and Dynamic Repeated Loading," ACI Journal Proceedings, Vo1.66, No.5, May. 1969, pp. :377-380. [64] Panda, A.K., "Investigations of Bond of Deformed Bars in Plain and Steel Fibre Reinforced Concrete Under Reverse Cyclic Loading," M.A.Sc. Thesis, University of British Columbia, Vancouver, B.C., Sep. 1980. [65] Spencer, R.A., Panda, A.K. and Mindess, S., "Bond of Deformed Bars in Plain and Fibre Reinforced Concrete Under Reversal Cyclic Loading," International Journal of Cement Composites and Lightweight Concrete, Vol.4, No.1, Feb. 1982. [66] Panda, A.K., "Bond of Deformed Bars in Steel Fibre-Reinforced Concrete Under Cyclic Loading," Ph.D. Thesis, University of British Columbia, Vancouver, Apr. 1984. [67] ACI Committee 408.2R "State-of-the-Art-Report: Bond under Cyclic Loads," ACI Materials .Journal, Vol.88, No.6, Nov.-Dec. 1991, pp. 669-67:3.  Bibliography^  371  [68] Mindess, S.. "Rate of Loading Effects on The Fracture of Cementitious Materials," in Shah, S.P. (ed.), "Application of Fracture Mechanics to Cementitious Composites," Proceedings of the NATO Advanced Research Workshop, Northwestern University, 1984, Martnus Njhoff Publishers, The Netherlands, 1985, pp. 617-636. [69] Mindess, S., Banthia, N.P. and Bentur, A, "The Response of Reinforced Concrete Beams with a Fibrous Concrete Matrix to Impact Loading," International Journal of Cement Composites and Lightweight Concrete, Vol.8, No.3, 1986, pp. 165-170. [70] Mindess, S., Bentur, A. Yam C. and Vondran, C., "Impact Resistance of Concrete Containing Both Conventional Steel Reinforcement and Fibrillated Polypropylene Fibres," ACI .Journal, Vo1.86, No.6, 1989, pp. 545-549. [71] Mindess, S., "Fracture Toughness Testing of Cement and Concrete," in Carpinteri, A. and Ingraffea, A.R. (eds.), "Fracture Mechanics of Concrete: Material Characterization and Testing," Martnus Njhoff Publishers, The Netherlands, 1984, pp. 67-110. [72] Shah, S.P. and John, R., "International Conference on Fracture Mechanics of Concrete," Lausanne, 1985, pp. 373-385. [73] Mindess, S., Banthia, N.P., Ritter, A. and Skalny, J.P., "Crack Development in Cementitious Materials under Impact Loading," in Mindess, S. and Shah, S. P. (eds.), "Cement-Based Composites: Strain Rate Effects on Fracture," Vol.64, 1986, pp. 217-223. [74] Banthia, N.P., Mindess, S. and Bentur, A, "High Stress Rate Testing of Concrete: An Overview," Indian Concrete Journal, Vo1.60, No.10, 1986, pp. 265-272. [75] Hansen, R..J. and Liepins, A.A., "Behaviour of Bond Under Dynamic Loading," ACI Journal Proceedings, Vol.59, No.4, April 1962, pp. 56:3-582. [76] Hjorth. 0., "Ein Beitrag zur Frage der Festigkeiten and des Verbundverhaltens von Stahl and Beton bei Hohen Beanspruchungsgeschwindigkeiten," Dissertation, Technische Universitk Braunschweig, 1976. [77] Vos, I.E. and Reinhardt, H.W., "Influence of Loading Rate on Bond Behaviour of Reinforcing Steel and Prestressing Strands," Materiaux et Constructions, Vol.15, No.85, 1982, pp. 3-10. [78] Takeda, Jin-Ichi, "Strain Rate Effects on Concrete and Reinforcements and Their Contributions to Structures," in S. Mindess and S.P. Shah (Eds.), "Cement-Based C omposites: Strain-Rate Effects on Fracture," Vol.64, 1986, pp. 15-20.  Bibliography^  :372  [79] Bentur, A., Mindess, S. and Banthia, N.P., "The Fracture of Reinforced Concrete Under Impact Loading," in S. Mindess and S.P. 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