Analysis of concrete structures by fracture mechanics: proceedings of the International RILEM Workshop dedicated to Professor Arne Hillerborg, sponsored by RILEM (The International Union of Testing and Research Laboratories for Materials and Structures) a

This book presents the latest research findings of the fast developing applications of fracture mechanics to concrete structures. Key papers from leading experts in the field describe existing and new modelling techniques in the analysis of materials and structures. The book explains the practical application of fracture mechanics to structural modelling, bending, shear, bond and anchorage. The proceedings of this RILEM Workshop will be an important reference for those engaged in design, development, research and teaching in the field of concrete structures. Book Cover......Page 1 Half-Title......Page 2 Title......Page 4 Copyright......Page 5 Dedication......Page 6 Contents......Page 8 Participants and contributing authors......Page 10 Preface......Page 12 3 THE STRIP METHOD......Page 13 4 FRACTURE MECHANICS......Page 16 5 BIBLIOGRAPHY......Page 18 PART ONE BEHAVIOUR OF CONCRETE......Page 27 INTRODUCTION......Page 28 SIMPLIFIED LEFM ANALYSIS......Page 29 Free rotating specimen boundaries......Page 31 DISCUSSION AND COMPARISON WITH EXPERIMENTAL RESULTS......Page 32 CONCLUSIONS......Page 35 REFERENCES......Page 36 INTRODUCTION......Page 38 Specimens and materials......Page 39 Load-paths investigated......Page 40 EXPERIMENTAL RESULTS......Page 41 Tensile shear at constant crack-opening (load-path 1)......Page 42 Compressive shear with normal confinement (load-path 3)......Page 43 Shear stiffness reduction......Page 44 CONCLUSIONS......Page 45 REFERENCES......Page 46 2 Mixed mode according to the fictitious crack model......Page 48 3 Testing arrangement......Page 49 4 Mixed mode tests......Page 50 5 Discussion......Page 51 REFERENCES......Page 53 INTRODUCTION......Page 61 Fracture Mechanics Based Study......Page 62 FINITE ELEMENT ANALYSIS......Page 64 EXPERIMENTAL RESULTS......Page 66 Crack Propagation Criterion......Page 67 Effect of Crack-Face Tractions......Page 70 CONCLUSIONS......Page 72 References......Page 73 1 General......Page 75 2 Thermal stress analysis......Page 76 3 Model......Page 77 4 Theoretical computations......Page 82 5 Discussion......Page 84 6 References......Page 86 2 The Grain Model......Page 91 3.1 The disk model......Page 92 3.2 Probability formulation......Page 94 3.2.1 Distribution law—Disk Diameter......Page 95 3.2.4 Distribution law—effective roughness......Page 96 4 Stress crack width relation......Page 97 5 Application and Results......Page 98 6 Conclusions......Page 99 References......Page 100 PART TWO STRUCTURAL MODELLING......Page 101 1 INTRODUCTION......Page 102 2.1 Asymptotic properties of cohesive crack models.......Page 103 2.2 Maximum load size-effect......Page 106 2.3 Specific fracture energy concepts......Page 108 3.1 Comparison procedures based on the maximum load......Page 111 Reference model: Cohesive crack with quasi-experimental softening......Page 113 Cohesive crack model with linear softening......Page 114 Bazant’s Size-Effect law......Page 115 Shah’s Two-Parameter Model......Page 116 3.3 Behaviour for large sizes......Page 117 4.1 Experimental programme......Page 119 RILEM or average energy method and the perturbed ligament method......Page 122 Shah’s two parameter model......Page 123 4.3 The results for fracture parameters following size effect fitting......Page 124 4.4 Summarizing the evaluation of experimental results......Page 125 References......Page 127 1 Introduction......Page 129 2 Calculation of tangential stiffness matrix......Page 130 References......Page 132 1 Introduction......Page 133 2 Theoretical model......Page 136 3 Specimen preparation and testing procedure......Page 140 4 Experimental results and discussion......Page 143 5 Conclusions......Page 146 References......Page 149 OPTIONS IN ABAQUS......Page 150 Anchor bolt......Page 151 Bridge tests......Page 152 REFERENCES......Page 153 2 Characteristic examples of faulty design......Page 156 2.2 Reentrant corner at the heel of the dam......Page 157 2.4 Inadequate treatment of the dam foundation area......Page 158 3 Consequences of analytically non detectable cracking initiation (what if...)......Page 159 REFERENCES......Page 163 PART THREE BENDING......Page 164 1 Introduction......Page 165 2.1 General......Page 166 2.2 Concrete in uniaxial compression......Page 167 2.3 Concrete in the compression zone of a beam......Page 168 3.1 Balanced reinforcement ratio......Page 169 3.2 Strength of over-reinforced beams......Page 170 4 Determination of material properties......Page 171 6 References......Page 172 Results......Page 173 Discussion......Page 174 1 Introduction......Page 178 2.1 Criterion of Walther [1]......Page 179 2.3 Criterion of Mohr [2]......Page 180 2.7 Summarizing......Page 181 3 Absorbable shear force in the compressed zone of a beam with rectangular cross-section......Page 183 4 Experimental program......Page 185 6 Conclusions......Page 187 References......Page 188 Discussion......Page 189 PART FOUR SHEAR, BOND AND PUNCHING......Page 190 1 Introduction......Page 191 2 Test program and test specimens......Page 192 3.1 Maximum load and fracture energy......Page 193 3.2 Failure modes......Page 195 References......Page 196 1 Introduction......Page 199 2 Use of epoxy in load bearing structures......Page 200 3 Methods to strengthen concrete structures with steel plates glued to its tension side......Page 201 4 Experiences from tests with concrete beams strengthened with resin bonded steel plates......Page 202 5 Experiments performed at Luleå University of Technology......Page 203 6 Theoretical investigations......Page 206 REFERENCES......Page 208 2 Modelling of a bond line......Page 209 4 Fracture energy......Page 210 5 Normalized constitutive relation......Page 211 6.1 Test method......Page 212 6.2 Test results......Page 213 7 Brittleness ratio and strength function for joint......Page 215 8 Strength of lap joints......Page 216 9.1 Joint specimen for testing pure shear......Page 217 9.2 Test result......Page 218 10.1 Discussion......Page 220 10.2 A test......Page 221 References......Page 222 2 Scope of research......Page 223 3 Experiments......Page 224 4.1 Failure mechanism......Page 225 4.2 Penetration versus porosity......Page 227 5 Normalization of results......Page 229 6 Concluding remarks......Page 230 References......Page 231 PART FIVE ANCHORAGE......Page 232 The Pull-out Test......Page 233 Anchor Bolt Design......Page 246 Conclusion......Page 252 REFERENCES......Page 253 ACKNOWLEDGEMENT......Page 257 2.1 Materials and test specimen......Page 266 3.1 Crack patterns......Page 268 3.2 Load-displacement curves.......Page 269 3.3 Peak loads......Page 270 4.1 Finite element model......Page 271 4.2 Input data for the calculations......Page 272 5.1.1 Influence of fracture energy......Page 273 5.1.2 Influence of tensile strength......Page 274 5.1.4 Influence of embedment depth......Page 275 5.2 Brittleness number for the pullout specimen......Page 276 5.3 Dimensionless diagram......Page 278 5.4 Comparison with the laboratory tests.......Page 281 8. References......Page 282 INDEX......Page 284