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Specialized fiber reinforced concretes under static and impact loading Xu, Hanfeng 2007

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S P E C I A L I Z E D F I B E R R E I N F O R C E D C O N C R E T E S U N D E R S T A T I C A N D I M P A C T L O A D I N G by Hanfeng Xu B.A.Sc. (Polymer Eng.), Nanjing University of Sci. and Tech., China, 1988 M.Tech. (Polymer Sci. & Eng.), East China University of Sci. and Tech., China, 1991 M.A.Sc. (Civil Engineering), University of British Columbia, Canada, 2003 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA August 2007 © Hanfeng Xu, 2007 A B S T R A C T Fibers are increasingly being added to cementitious materials to achieve pseudo-ductility for a variety of structures. Unfortunately, there is no universally accepted test method to characterize the energy absorption capacity (toughness) of fiber reinforced concrete (FRC). Traditional beam flexural tests provide toughness assessment only under small deflections. This has not reflected the reality of most FRCs applied in slab-on-grade and tunnel/mine projects, where large deflection could be experienced. A new test method has been developed for the concrete industry: ASTM C-1550, "Standard Test Method for Flexural Toughness of Fiber Reinforced Concrete (Using Centrally Loaded Round Panel)", referred to as the RDP method. So far this technique has only been applied for static loading, and none of the previous studies have addressed the effect of high loading rates on the performance of these round panels. A unique test setup was developed in this work to determine the behaviour of round panels under impact loading. The initial load (used for accelerating the specimen) was analyzed and deducted from the total measured load to obtain the true load. Deflections up to 65 mm were achieved. It was found that it is feasible to use the RDP method to characterize fiber reinforced concrete and welded wire mesh (WWM) reinforced concrete; the tests provided data on the effect of loading rate and concrete strength on the behaviour of a reinforced concrete system. Overall, more than 260 round panels were tested for the above purposes. In this study, two polymeric fibers and one steel fiber, and three matrix strength levels were investigated to examine the influence of fiber material, hybrid reinforcement with WWM, and the matrix strength under static and impact loading. Results show that high strength matrices have negative effects on the toughening effect of fibers. Under impact loading, this tendency is more significant. Panels with hybrid reinforcement exhibited more favourable behaviour than panels containing only a single type of reinforcement. For FRC with polymer modification (PM-FRC), it was found that the toughness of FRC panels due to polymers additions were improved much more significantly under static loading than under impact loading. In addition to RDP specimens, the performance of PM-FRC was also investigated under compressive impact ii loading. Similar findings to those in the round panel test were noted, though there were differences in strain rate sensitivity. The damage evolution of hybrid reinforced panels was evaluated by using post-impact static testing; three damage indices were defined based on peak load, stiffness and toughness reduction. It was found that damage defined on the basis of residual toughness is much more meaningful and could be used as a standard index for evaluating hybrid reinforced systems. This necessitated modifying the existing continuous damage theory for concrete, which was mainly confined to the strength parameter or elastic modulus, and was applicable only in the elastic domain. To further understand the deformation of round panels containing fibers, for the first time a unique setup, on the basis of the current RDP method, was designed to measure the rotation and side slip of panel segments after cracking. Thereafter, the central crack width (CCMOD) could be obtained for further analysis. This study proved the importance of other parameters: rotation and side slip of broken segments other than the central deflection in the current standard, which could be used to better interpret the RDP test. In the analytical part of this work, Yield Line Theory (YLT) incorporating the CCMOD concept and friction effect analysis was used to predict the performance of RDP specimens from the moment capacity vs. rotation of FRC beams. Cast beams and panels of the same type of FRC were used to assist in validating the analytical approach for this model study. Experimental results have shown good agreement with those predicted from beam studies. iii T A B L E of CONTENTS ABSTRACT ii LIST OF TABLES ix LIST OF FIGURES xi LIST OF SYMBOLS AND ABBREVIATIONS xv ACKNOWLEDGEMENT xix DEDICATION xx CHAPTER 1 INTRODUCTION AND SCOPE OF RESEARCH 1 1.1 Problem definition 1 1.2 Test method for cement-based composites 2 1.3 Scope of research 3 1.4 Outline of the thesis 5 CHAPTER 2 LITERATURE REVIEW 2.1 Fiber reinforced concrete 6 2.1.1 Significance of toughness 6 2.1.2 Testing of FRC toughness under static loading 7 2.1.3 Dynamic performance of cementitious materials 11 2.2 Dynamic performance vs. static performance for concrete 13 2.2.1 Inertial effect 13 2.2.2 Dynamic increase factor (DIF) 14 2.2.3 Bonding between discrete fibers and concrete matrix under dynamic loading 16 2.3 Behaviour of specialized cementitious composites 17 2.3.1 High performance FRC (HPFRCC) 17 2.3.2 Cementitious composites with Fabrics and hybrid reinforcement. 18 2.3.3 Polymer concrete system 22 2.4 Fiber reinforced Shotcrete 26 2.4.1 Fiber reinforced Shocrete: design and quality control 26 2.4.2 Toughness criteria for FR-shotcrete using plate tests 27 2.5 Structural performance of FRC plates under static loading 29 2.5.1 Steel Fibers reinforced plates 29 2.5.2 Synthetic fiber reinforced Plates 30 iv 2.5.3 Effects of loading & boundary conditions on FRC plates 30 2.6 Concrete panels/slabs structures under impact loading 31 2.6.1 FRC plates under impact loading 31 2.6.2 Hybrid reinforcement system under impact 34 2.7 Summary of literature review 36 CHAPTER 3 EXPERIMENTAL DETAILS 3.1 Introduction 37 3.2 Materials and concrete mixes 37 3.2.1 Materials - Concrete matrices 37 3.2.2 Materials - Reinforcement 37 3.2.3 Mix proportions 40 3.3 Specimen preparation 41 3.3.1 FRC or Mesh RC plates. 41 3.3.2 Uniaxial impact tests on PM-FRC 41 3.3.3 Specimens for predictive model validation 42 3.4 Test equipment and instrumentation 43 3.4.1 Drop weight impact machine : 43 3.4.2 Data acquisition system 43 3.4.3 Instrument and calibration 44 3.5 Test setup 48 3.5.1 Tests for basic concrete strength and elastic modulus 48 3.5.2 Tests for static toughness: flexural beam test 48 3.5.3 Tests for static toughness: Round panel test 49 3.5.4 Test for studying the deformation of RDP 50 3.5.5 Dynamic RDP test 50 3.5.6 Uniaxial compressive loading (static and impact) 51 3.6 Experimental program 53 3.6.1 Test method study: Static I-beam vs. RDP 53 3.6.2 Test method study: Static II — deformation of FRC panel 53 3.6.3 Feasibility study on dynamic RDP test 53 3.6.4 Specialized FRC panels: Effect of matrix strength & polymer modification 54 3.6.5 Performance and damage evolution analysis: Effect of hybrid reinforcement 54 3.6.6 Polymer modified FRC system under uniaxial impact compressive loading 56 3.6.7 Round panel performance prediction from beam tests 57 v CHAPTER 4 FIBER REINFORCED CONCRETE UNDER STATIC LOADING: BEAM VS. RDP TEST 4.1 Introduction 58 4.2 Data analysis 58 4.3 Results 59 4.3.1 Beam tests 59 4.3.2 Round panel tests 60 4.4 Comparison between beam and round panels tests 63 4.5 Conclusions 64 CHAPTER 5 STATIC DEFORMATION OF FIBER REINFORCED CONCRETE PANELS 5.1 Introduction • 65 5.2 Crack opening analysis 65 5.2.1 Assumptions 65 5.2.2 Modified round panel test 66 5.2.3 Crack width estimation 68 5.3 Crack opening resistance 70 5.4 Experimental program and validation 71 5.5 Results and discussion 72 5.5.1 Method validation 72 5.5.2 Effect of fiber type 73 5.5.3 Effects of matrix strength level 74 5.6 Conclusions 76 CHAPTER 6 FEASIBILITY STUDY ON IMPACT TESTS USING ROUND DETERMINATE PANELS 6.1 Introduction 77 6.2 Analysis -true load and inertial load removal 77 6.3 Fiber reinforced concrete RDP under impact loading 79 6.3.1 Failure modes 79 6.3.2 Load capacity and energy absorption 81 6.3.3 Comparison of Toughness of FRC panels under static and impact loading 83 6.3.4 Effects of fiber type and volume fraction (Vf) on toughness 84 6.3.5 Summary of dynamic RDP tests: FRC panels 84 6.4 Mesh reinforced concrete RDP test 85 6.4.1 Static test 85 6.4.2 Impact tests 87 6.5 Summary of dynamic RDP tests: WWM-RC panels 90 6.5.1 Test method evaluation for WWM-RC panels ....90 6.5.2 Primary results from Mesh-RC panel series 91 6.6 Conclusions 91 CHAPTER 7 EFFECTS OF MATRIX AND FIBERS ON FRC PANELS SUBJECTED TO IMPACT LOADING 7.1 Introduction 92 7.2 Results : 92 7.3 Effects of matrix strength and fibers 94 7.3.1 Static loading 94 ^ 7.3.2 Impact loading 95 7.4 Effect of loading rate (drop height) on peak load 96 7.5 Effect of loading rate (drop height) on energy absorption 98 7.6 Effects of matrix strength and fibers on strain rate sensitivity 99 7.7 Conclusions 101 CHAPTER 8 EFFECTS OF POLYMERS ON STEEL FIBER REINFORCED ROUND CONCRETE PANELS UNDER IMPACT LOADING 8.1 Introduction 102 8.2 Results and discussion 102 8.2.1 Flexural strength and toughness 102 8.2.2 Effects of polymer and fibers on strain sensitivity 105 8.3 Conclusions 107 CHAPTER 9 IMPACT PERFORMANCE OF LATEX-MODIFIED HIGH STRENGTH FRC UNDER UNIAXIAL COMPRESSIVE LOADING 9.1 Introduction 108 9.2 Results and discussion 108 9.2.1 Static loading 108 9.2.2 Impact loading 110 9.3 Effects of polymer on strain rate sensitivity of concrete and FRC 115 9.4 Conclusions 117 vii CHAPTER 10 BEHAVIOUR OF CONCRETE PANELS REINFORCED WITH WELDED WIRE MESH AND FIBRES UNDER IMPACT LOADING 10.1 Introduction 118 10.2 Results and discussion 118 10.2.1 Static tests 124 10.2.2 Impact loading 125 10.3 Comparison of Static and impact tests: strain rate sensitivity 126 10.4 Conclusions 130 CHAPTER 11 DAMAGE EVOLUTION OF ROUND CONCRETE PANELS WITH HYBRID REINFORCEMENT UNDER IMPACT LOADING 11.1 Introduction 131 11.2 Damage analysis 131 11.2.1 Damage of RDP and post-impact static tests 131 11.2.2 Damage evaluation from post-impact static test 133 11.3 Results and discussion 11.3.1 Toughness and irreversible deflection caused by impact loading 133 11.3.2 Post-impact static test and damage evolution caused by impact loading 135 11.3.3 Damage in terms of energy absorption capacity 136 11.3.4 Damage in terms of residual load capacity 138 11.3.5 Damage in terms of initial stiffness 139 11.4 Which damage definition should be used? 139 11.5 Special case 139 11.6 Conclusions 141 CHAPTER 12 ANALYSIS OF PERFORMANCE PREDICTION OF ROUND FRC PANELS UNDER STATIC LOADING 12.1 Introduction 142 12.2 A review of performance prediction on FRC plates/slabs 142 12.3 Predicting round panel behaviour from beam test 145 12.3.1. Yield-line theory basics 148 12.3.2. Challenges in the beam-panel approach for FRC 148 12.4 Analysis and procedures 150 12.4.1. Pre-peak performance prediction 150 12.4.2. Post-peak performance prediction 152 viii 12.5 Experimental validation 158 12.5.1 Bending testing 158 12.5.2 Panel testing 159 12.6 Results 12.6.1 Beam test 160 12.6.2 Round panel test and predicted performance 160 12.7 Discussion 163 12.8 Conclusions 166 CHAPTER 13 CONCLUSIONS AND FUTURE WORK 13.1 Conclusions 167 13.2 Future works 170 BIBLIOGRAPHY 174 APPENDICES 190 APPENDIX A 190 APPENDIX B 192 APPENDIX C 196 APPENDIX D 197 ix LIST OF TABLES Table 2.1 Strain rates for various types of dynamic loading 11 Table 2.2 Energy absorption requirements of EFNARC specification 27 Table 3.1 Properties of steel and synthetic fibers 38 Table 3.2 Concrete mix designs 40 Table 3.3 Summary of specimen dimension and corresponding program 42 Table 3.4 Summary of specimen type for RDP model validation 42 Table 3.5 Test program for Beam and RDP comparison 53 Table 3.6 Test program for feasibility study of RDP test 54 Table 3.7 Test Program for FRC and PM-FRC Round Panel 55 Table 3.8 Test program for round panel with Hybrid Reinforcement 55 Table 3.9 Damage study for Hybrid reinforcement 55 Table 3.10 Test program for high strength PM-FRC under uniaxial loading 56 Table 3.11 Specimens for Model Validation 57 Table 4.1 Toughness for FRC from beam test and round panel test 64 Table 5.1 Measurement and geometrical designation of the test setup 67 Table 5.2 Size of the specimen and test setup components 68 Table 5.3 Experimental program for test method validation. 71 Table 5.4 Effect of matrix strength level on crack-opening resistance 76 Table 6.1 Peak load of concrete panels under static and impact loading (FRC) 82 Table 6.2 Toughness of round panels up to 40mm deflection (FRC) 83 Table 6.3 Energy absorption (Toughness) of RDPs under static loading (HyRC) 86 Table 7.1 Summary of FRC under impact loading (NS and VHS-FRC) 97 Table 7.2 Dynamic impact factors (DIF) of NS and VHS-FRC 98 Table 8.1 Summary of PM-SFRC behaviour under impact loading 104 Table 8.2 Dynamic impact factors (DIF) of FRC and PM-FRC 106 x Table 9.1 Static compressive strength of PM-FRC 109 Table 9.2 Compressive strength (fc'), Energy absorption and DIF of composites 112 Table 10.1 Strength and toughness under static loading (HyRC) 124 Table 10.2 Toughness of FRC panels (at 40 mm central deflection) 125 Table 10.3 Strength and toughness under dynamic loading (HyRC) 126 Table 10.4 Dynamic impact factors for WWM reinforced panels 127 Table 10.5 Dynamic impact factors for HyRC panels 127 Table 11.1 Results of HyRC panels under static and impact loading 134 Table 11.2 Residual performance of hybrid reinforced panels 136 Table 11.3 Damage due to impact loading in terms of three criteria 137 Table 11.4 Residual Performance of Normal Strength HyRC panels (DH-150 mm).... 140 Table 12.1 Applicability of YLT in RDP prediction 149 Table 12.2 Properties of FRCs for model validation 158 Table 12.3 Comparison of peak load of FRC panels (experimental vs. calculated) 163 Table 12.4 Comparison of toughness of FRC panels (experimental vs. calculated) 164 xi LIST OF FIGURES Figure 2.1 Schematic view of the centrally loaded round panel test 10 Figure 2.2 Typical failure mode of round determinate plate test.. 10 Figure 2.3 Effects of polymer and steel fiber on impact resistance of concrete 24 Figure 2.4 Impact resistances (ratio of dynamic/static strength) of different types of concrete with polymer addition 25 Figure 3.1 Wire welded steel mesh 39 Figure 3.2 Mesh reinforcement prepared for round panel specimen: mesh pattern 39 Figure 3.3 Drop weight impact machine 43 Figure 3.4 Tup cylinder load cell 45 Figure 3.5 Assembled Tup with embedded bolt load cell (left) and bolt load cell (right) 45 Figure 3.6 Laser transducer system 46 Figure 3.7 Sensor section of Laser transducer 46 Figure 3.8 Accelerometer 47 Figure 3.9 ADXL311EB Schematic Diagram- angle measuring modules 48 Figure 3.10 Arrangements of "Japanese" Yoke and LVDTs for Flexural Test 49 Figure 3.11 Setup for round determinate panel 50 Figure 3.12 Impact Test Setup of Round Determine Panel (side-bottom view) 51 Figure 3.13 Impact setup for uniaxial compressive loading 52 Figure 4.1 Flexural load-deflection curves of plain FRC beams 60 Figure 4.2 Flexural load-deflection curves of polymer-modified FRC beams 60 Figure 4.3 Toughness of FRC/PM-FRC beams (JSCE SF-4) 60 Figure 4.4 Load-deflection curves of Plain and SFRC panels 62 Figure 4.5 Load -deflection of round panel test for PPN-FRC 62 Figure 4.6 Load-deflection curves of PM-SFRC panels 62 Figure 4.7 Toughness of FRC and PM-FRC panels 63 Figure 5.1 Schematic of round determinate panel test 66 Figure 5.2 Round panel test setup for crack-width measurement 67 Figure 5.3 Schematic of Central Crack Mouth Opening 68 Figure 5.4 Broken segment and support for crack opening analysis 69 Figure 5.5 A typical angle signal record of FRC panel 71 Figure 5.6 Typical cracking behaviors of FRC panels after testing 73 Figure 5.7 Crack opening resistance of NS-FRC panels (steel fibers and PP fibers) 74 Figure 5.8 Comparison of synthetic fibers in NSC matrix (PP, PPN and HPP fibers) 75 Figure 5.9 Crack opening resistance of HS-FRC panels 75 Figure 5.10 Crack opening resistance of VHS-FRC panels 76 Figure 6.1 Schematic descriptions for round panel analysis 78 Figure 6.2 Plain and FRC panels after impact test (plain panel drop height 120mm, others drop height 150mm) 80 Figure 6.3 Load-deflection curves of SFRC panels under impact loading 81 Figure 6.4 Load-deflection curves of PPNFRC panels under impact loading 82 Figure 6.5 Effects of fiber type and volume fraction on panel toughness 84 Figure 6.6 Load vs. central deflection curves for RDPs under static loading (HyRC)....86 Figure 6.7 Effect of mesh orientation on behaviour under impact loading 87 Figure 6.8 Failure mode of a round panel with Mesh C reinforcement under impact 88 Figure 6.9 Effect of fiber additions on impact behaviour of Mesh C-reinforced round panels 89 Figure 6.10 Failure of a round panel with Mesh C reinforcement and 0.5% steel fibers under impact loading 89 Figure 6.11 Effect of fiber type on the impact behaviour of round panels containing Type C Mesh 90 Figure 6.12 Energy absorption (toughness) of round panels under impact loading: mesh +0.5%fiber 90 Figure 7.1 Load vs. deflection curves of FRC panels under static loading (a) NS-SFRC and NS-PPFRC; (b) VHS-SFRC0.5 and VHS-PPFRC 92 Figure 7.2 Load vs. deflection curves of SFRC panels under impact loading 93 Figure 7.3 Load vs. deflection curves of PPFRC panels under impact loading.. 94 Figure 7.4 DIF of peak load of FRC panels (NS and VHS-FRC) 100 Figure 7.5 DIF of Toughness of FRC panels (NS and VHS-FRC) 100 xiii Figure 8.1 Load vs. deflection curves of SFRC and PM-SFRC panels under impact loading 103 Figure 8.2 DIF of peak load of FRC and PM-FRC , 106 Figure 8.3 DIF of toughness of FRC and PM-FRC 107 Figure 9.1 Load-deflection curves for PMC under different loading regimes (a)PMC0; (b) PMC5; (c) PMC10; (d) PMC 15 110 Figure 9.2 Load-deflection curves for PM-SFRC 0.5 under different loading regimes (a) PM0-SF0.5; (b) PM5-SF0.5; (c) PM10-SF0.5; (d) PM15-SF0.5 Ill Figure 9.3 Load-deflection curves for PM-SFRC 1.0 under different loading regimes (a) PM0-SF1.0; (b) PM5-SF1.0; (c) PM10-SF1.0; (d) PM15-SF1.0 Ill Figure 9.4 Effects of polymer on compressive strength and compressive toughness. ...114 Figure 9.5 Dynamic Impact Factors of Strength and Toughness 116 Figure 10.1 Load vs. deflection of panels under static loading of mesh RC and HyRC panels (a) Normal Strength matrix; (b).Very High Strength Matrix 119 Figure 10.2 Load vs. deflection curves of Mesh RC panels under impact loading 120 Figure 10.3 Load vs. deflection curves of HyRC panels under impact loading (Mesh+0.5% Fibers) 122 Figure 10.4 Load vs. deflection curves of HyRC panels under impact loading (Mesh+1.0% Fibers) 123 Figure 10.5 DIF of peak load for mesh-RC and hybrid reinforce panels 128 Figure 10.6 DIF of toughness for mesh-RC and hybrid reinforced panels 129 Figure 11.1 Schematic of critical drop height 132 Figure 11.2 Typical load vs. deflection curves of HyRC under impact and static loading 132 Figure 11.3 Residual performances of panels with hybrid reinforcement (a) NS-M-FRC panels; (b) VHS-M-FRC panels 135/136 Figure 11.4 Damage caused by impact — Normal strength HyRC panels 138 Figure 11.5 Damage caused by impact — Very high strength HyRC panels 138 Figure 11.6 Failure modes of NS-M-SF 1.0-150mm 140 xiv Figure 12.1 Schematic procedure for round panel performance prediction by using beam test 147 Figure 12.2 Relationship between simply supported panel and RDP 151 Figure 12.3 Possible failure patterns of round FRC panels 153 -> Figure 12.4 Schematic illustration of compressive force N causing friction in one of the three segments 155 Figure 12.5 Close-up of crack propagation of round FRC panel 157 Figure 12.6 Three-point flexural test for measuring moment of resistance vs. rotation 159 Figure 12.7 Moment resistance vs. crack rotation from beam test 160 Figure 12.8 Comparison of RDP performance: experimental vs. calculated (a) Panel with SFRC 0.5% (b) Panel with SFRC 1.0% 161 (c) Panels with PPFRC0.5%; (d) Panels with PPFRC1.0% 162 Figure 12.9 Typical crack rotation of specimens with SF-FRCO.5% after test 163 Figure 12.10 Three-point bending tests and their applicability in panel interpretation 165 xv LIST OF ABBREVIATIONS AND SYMBOLS Chapter 1 FRC Fiber reinforced concrete FRS Fiber reinforced shotcrete RDP Round determinate panel HyRC Hybrid reinforcement NSC Normal strength concrete HSC High strength concrete VHSC Very high strength concrete PMC Polymer modified concrete WWM Welded wire mesh Chapter 2 HPC High performance concrete HPFRCC High performance fiber reinforced cement composite LMC Latex modified concrete PM-FRC Polymer modified fiber reinforced concrete DIF Dynamic impact factor Kis Mode I stress intensity factor E , Strain rate a Stress rate Chapter 3 Tm, Sm The number of gauge and the center-to-center spacing of WWM Wm, L m The original width and length of WWM LVDT Linear Variable Displacement Transducers Chapter 4 Tb Flexural toughness of beam, area under the load vs. deflection curve to a deflection 6 tb 8 tb Deflection equal to 1/150 of the span L Span length b Beam specimen width h Beam specimen height Chapter 5 CCMOD Central crack mouth opening displacement P Load 8 Central displacement s Relative sliding between the support and edge of the panel 6 Rotation of the broken pieces relative to horizontal level 1 Support block size (length) rs Diameter of the rotatable ball in support tQ Central thickness of support block R Radius of round panel tj Thickness of round panel a Distance from the center of support block to center of panel before loading a' Distance from the center of support block to the original central point in the panel after loading Chapter 6 p Density of concrete, V volume of the segment td thickness of panel R Radius of round panel a Length of overhang u(r, 0, t) Acceleration in the spot with a radius r from center and a angle of 0 from the support, at timet ii (0, t) Acceleration at the center of a round panel during impact loading ii(R/2, t) Measured acceleration of the panel at half of the radius along the support to the centre, at time t. Ptotai(t) The total load recorded by the bolt load cell Pi (t) The generalized inertial load Ptrue(t) The true load Chapter 9 fc' Compressive strength, dynamic and static Chapter 11 Epi Plate stiffness of specimen after impact (determined as the initial slope of load vs. deflection curve of the post-impact static test) P The load capacity of round panels S ir Irreversible central deflection caused by impact T The capacity of energy absorption or toughness O toughness Damage defined as degr dation f t ughness O stiffness Damage defined as degradation of plate stiffness (as defined Epi) O load capacity Damage defined as degradation of load capacity Chapter 12 YLT Yield line theory y The midpoint angle (range from 0 to 60°), representing the deviation of each crack from the midpoint line between each pair of adjacent supports D Plate constant, D = Et/ 112(1 - v2) tj and V The thickness of the plate and the Poison's ratio of concrete, respectively k The ratio of peak load from the full-edge simple support (FESS) setup to that from the RDP setup R The radius of the round panel r The net radius of the round panel a The angle of the diametral crack relative to the line through the nearest support m The moment resistance per unit length of the yield line mi (i=l-3) The moment of resistance per unit length long the three yield lines Yi (i=l-3) The arbitrary angles with respect to bisector of the un-supported sides a, (i= 1 -6) The corner angles /((i=l-3) The friction force along the surface of the panel TV, (i=l-3) The compressive load applied perpendicular to the sliding surface of each segment or support, s Relative movement of the segment from the support, 9 The corresponding rotation of the segment along the radius through the center of the panel and support <p the rotation of the panel segment along the yield line Measured rotation by using angle-measuring modules mounted on top of each side of beam xix ACKNOWLEDGEMENT First and foremost, I am very sincerely grateful to my supervisor, Dr. Sidney Mindess for his close supervision and friendly support and personal encouragement. His excellent instruction and advice during the author's graduate studies, and time spent in reviewing the manuscript were of great help to the completion this dissertation. Special appreciation goes to Dr. Nemkumar Banthia and Dr. Reza Vaziri for serving on the author's supervising committee and their invaluable advice and suggestions during the work. The author would also like to express special thanks to Dr. R.O. Foschi for his suggestions and comments of this thesis. All these will be the invaluable foundation in my future career. I also wish to express my thanks to the technicians Max Nazar, Doug Smith, John Wong, Scott Jackson and Bill Leung in the Civil Engineering machine shop, and structural lab manager Felix Yao; the experimental part of this study would not have been possible without their help. My appreciation also goes to some undergraduate students for their assistance in casting some of concrete specimens when they were working on the course CIVL322. Thanks are also extended to all my graduate colleagues, Fariborz Majdzadeh, Vivek Bingdiganavile, Manote Sappakittipakorn, Rishi Gupta, Lihe Zhang, Reza Soleimani, Yashar Khalighi, Tiffany Lin, Ali Biparva, Faezeh Azhari and Sudip Talukdar; working with them made me feel the civil materials lab to be a home away from home. Many thanks to visiting scholars, Dr. Kazunori Fujikake, Dr. Ivan Duca, Mr. Avishay Lindenfeld, Dr. Hiroshi Higashiyama and Dr. Qian Gu. Exchanging ideas with these characters with diverse background both culturally and academically were significantly beneficial for this work and also constituted an invaluable part of my life. The author would also like to thank The Faculty of Graduate Study, UBC for awarding the University Graduate Fellowship (UGF2006/2007) supporting the author's research. xx To my wife Xiaoning Wu (Mary) and daughter Jingyi Xu (Jenny). Without their patience, love and support, this would never happen. CHAPTER 1 INTRODUCTION AND SCOPE OF STUDY 1.1 Problem definition Concrete is the most widely used construction material in the world. Due to its inherent brittle nature, low tensile strength and low strain capacity, however, concrete must be modified or reinforced for most applications. With the development of other manufacturing processes, many specialized concretes using new ingredients or different manufacturing approaches have emerged to mitigate the inherent shortcomings of conventional concrete, and accordingly, meet a variety of requirements for the civil infrastructure. These requirements may include properties such as strength, ductility, durability and sustainability. Since many civil structures may be subjected to dynamic loading, such as seismic loading or impact, the importance of the energy absorption of concrete has become apparent. It is believed that tough (not necessarily strong), durable concrete can be achieved by optimizing the matrix and reinforcement. In particular, short, discrete fiber reinforced concrete (FRC) has gained popularity due to the crack-bridging effects of the fibers on the brittle matrix; this is particularly attractive for materials under dynamic loading. Although the behaviour of conventional plain concrete at high strain rates has been a subject of intensive study for decades, only limited research has been conducted on the impact response of FRC. This is also the case for concrete reinforced with welded wire mesh, a very commonly used reinforcement for slab-on-grade and tunnel/mine projects. Previous studies have shown that the behavior of concrete under impact loading tends to be more brittle. Single types of reinforcement may not be able mitigate this brittleness, and potentially, hybrid reinforcement may provide an alternative. 1 On the matrix side, polymer modification is an effective approach for improving the bonding capacity and permeability. However, there are many fundamental questions which remain unanswered for cement-based composites under impact loading: • Which test method, if any, in our current practice is capable of characterizing the loading capacity and energy absorption of concrete under large deflection? What methods may be studied and adopted for that purpose under impact loading? • How does hybrid reinforcement affect the material properties? Is there any synergy? • On the matrix side, how does the strength level or polymer modification affect the toughening effect of the reinforcement? 1.2 Test method for cement-based composites One of the most important reasons limiting our understanding of the above questions is that a standardized test method for characterizing the impact performance of concrete does not exist; even for static testing there is no universally accepted method. The deformability, toughness and energy absorption of fiber reinforced concrete (FRC) are of great interest. To characterize these parameters, tests carried out concrete beams have most commonly been used. However, it has been found that standard test methods such as ASTM CIO 18 [1] and ASTM C1399 [2] have many shortcomings [3, 4]. ASTM has recently approved a standard test method (ASTM C1550) [5] for the flexural toughness of FRC using a centrally loaded, round panel supported on three points. This method is commonly known as the round determinate panel method (RDP) and is based on a test method developed by Bernard [6]. For decades, many studies have been carried out on both beam and plates to characterize shotcrete and particularly fiber reinforced shotcrete (FRS) under impact loading. Unfortunately the high strain rate sensitivity of the flexural behavior of concrete as tested by beam specimens can, in some cases, provide unrealistic results in tests with high 2 impact energy [7]. However, it was found that the rate sensitivity of the concrete was reduced considerably when using plate specimens rather than beams. Comparison of these different tests has led to a tentative conclusion that beam specimens are less suitable for flexural impact tests than are plate specimens. The favorable results from the RDP test under static loading were sufficiently promising to warrant a further study to determine whether this method would have similar advantages in characterizing the performance of FRC under impact loading. There has been no research to date on the evaluation of the impact behavior of FRC using the round determine panel method. The results of the current research may be used to explore the feasibility of test method itself, and to evaluate the effectiveness of fibers in different strength level concrete matrices under impact loading. 1.3 S c o p e o f r e s e a r c h The major objective of this research is to characterize the performance of cement-based composites using the round determinate panel (RDP method) under both static and impact loading. In this program, three strength grades of concrete matrix with/without polymer modification, i.e., normal strength concrete (NSC), high strength concrete (HSC) and very high strength concrete (VHSC), and two types of discrete fibers (steel and synthetic fibers), were investigated using the centrally loaded round panel test. There was also a focus on the dynamic performance of steel fiber reinforced concrete (SFRC) in a polymer-modified concrete matrix with outstanding static performance. These specialized concretes may contribute to our understanding of the mechanisms involved in high performance concrete system which can be very effective in terms of energy absorption capacity under impact loading. Though studies have been carried out on FRC or mesh reinforced concrete for shotcrete underground support and for slabs on grade, there have been few studies of concrete structures with hybrid reinforcement. The properties of welded wire mesh combined with 3 fiber reinforced concrete (HyRC) were also investigated under both static and impact loading. The published results for concrete under dynamic loading are largely incompatible, and therefore are hard to interpret. This is at least partially due to difference of test methods and loading rates. The second objective of the current work was to investigate the feasibility of standardizing the plate test method. To expand the use of ASTM C1550, a special setup was implemented for impact loading tests. For comparison, uniaxial compressive tests under impact loading were also studied for polymer modified FRC systems. In addition, the current ASTM C1550 does not provide data on crack propagation even under static loading. Thus, the third objective of this work was to build an innovative setup to provide crack information together with the central deformation of the FRC panel. Fundamentally, in the analytical part of this study, attempts were made to model the failure process of round panels using Yield Line theory and to compare the model with results from static tests. These formed the basis for a comprehensive damage model capable of predicting the performance of concrete panels under different loading regimes. The following are the original contributions of the research: • Design of an innovative RDP setup for characterizing crack opening • Design of a setup for RDP under impact loading • Derivation of an analysis of the impact plate test, including the inertial load • Investigation of the effectiveness of hybrid reinforcement and damage evolution • Development of a semi-analytical model to predict RDP performance 4 1.4 Outline of the thesis Chapter 1 gives a brief introduction to the topic, and describes the main objectives of this research. Chapter 2 is a literature review which gives some background of cementitious materials including polymer modified concrete (PMC), fiber/welded wire mesh reinforced concrete (FRC/Mesh-RC), and a state-of-the-art of the testing and behaviour of specialized concrete. Chapter 3 outlines the raw materials and the scope of the experimental work. The analytical methodology of the study, and the test setup and instrumentations are also introduced in this chapter. Chapters 4 and 5 describe the test method used under static loading. Chapter 6 presents the feasibility study of the innovative setup for round panels under impact loading. In Chapters 7, results of the FRC program with different matrix strengths are discussed. Chapters 8 and 9 cover the study and findings on the effect of polymer modification by using both round panel specimens and cylinders. Different fiber-reinforced concretes modified with different dosages of latex are compared, and an analysis of the synergy between fibers and latex is carried out. Chapters 10 and 11 present the results and discussion of the performance of hybrid reinforced systems under impact loading. In Chapter 12, a predictive model is presented from beams to round panels. Conclusions are presented in Chapter 13, along with some recommendations for future work in this area. Some results obtained in this research can be found in the papers published or submitted to international conferences (full text is reported in Appendix A). 5 CHAPTER 2 LITERATURE REVIEW In this chapter, a state-of-art report on the performance of two categories of specialized concrete: concrete with polymer modification and fiber/wire welded mesh reinforcement is presented. The focus is placed on mechanical properties and corresponding test methods, particularly on the test geometry under both static and dynamic loading. 2.1. Fiber Reinforced Concrete 2.1.1 Significance of toughness Many studies have been carried out on the development and application of fiber reinforced concrete (FRC) in the last four decades. Detailed reviews of FRC can be found in [8, 9]. Typical fiber types include steel fibers, synthetic fibers (polypropylene, polyethylene, polyvinyl alcohol (PVA)), carbon fibers and natural fibers. These short fibers are used mostly as secondary reinforcement to bridge across concrete matrix cracks as they develop when the concrete is stressed. It is believed that small amounts of micro-fibers can improve the plastic shrinkage behavior of concrete; the major benefit of reinforcing concrete with macro fibers is the enhancement of the energy absorption capacity of the material (toughness, often discussed in terms of some function of the area under the load vs. deflection curve for FRC). Essentially, the elastic properties (Poisson's ratio, strength and Young's modulus) of the composites are usually not affected by adding macro steel fibers up to about 1% volume fraction. Instead, it is the dramatically improved toughness, and the crack distributing properties that enable fibers to bring about pseudo-ductile failure. The toughening efficiency is dependent of fiber type, geometry, aspect ratio and volume fraction [9, 10]. With relatively higher volume fractions and/or special manufacturing processes, FRC can exhibit strain-hardening behavior, to provide a class of materials known as high performance fiber reinforced cememtitious composites (HPFRCC). 6 Typical industrial applications for FRC are floors, pavements and other plane structures where fibers act as crack distributing reinforcement. The fibers are also used to improve the load bearing capacity and thus increase the allowed external loads, promoting the use of fiber reinforced shotcrete (FRS) for underground structures and FRC in thin reinforcement elements [11]. In this regard, synthetic fibers are becoming more popular because they are inert in concrete [12], exhibit better rebound, and can be as effective as steel fibers [13]. The third potential application of FRCs in combination with reinforcing bars in structural members is to improve the performance of shear reinforcement due to better crack distribution [14, 15]. The use of FRC has been the target of extensive research. Though most current design codes are still based on strength and stiffness, the practical significance of toughness is being increasingly accepted, at least partially: • A guide to design and construction of industrial floors - TR-34 [16] • Design Considerations for Steel Fiber Reinforced Concrete- ACI 544.4R-88 [17] • Design of FRC based on toughness Characteristics [18] • Design performance requirement for fiber reinforced shotcrete practice [ 19] • EFNARC specification for fiber reinforced shotcrete [20] • Test and design methods for steel fiber reinforced concrete RILEM TC 162-TDF [21] 2.1.2 Testing of FRC toughness under static loading 2.1.2.1 Beam test Over the past 20 years, many different test methods have been proposed to characterize the toughness of FRC, and a number of these have been adopted as standards by various organizations. They include: • A S T M C1018 [1], Standard Test Method for Flexural Toughness and First-Crack Strength of Fiber-Reinforced Concrete (Using Beam with Third-Point Loading). This standard was first published in 1984. It has recently been discontinued, and replaced with A S T M C1609. 7 • ASTM C1609 [22], Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam with Third-Point Loading). This standard was published in 2006. • ASTM C1399 [2], Test Method for Obtaining Average Residual-Strength of Fiber-Reinforced Concrete, first published in 1998. • Japan Society of Civil Engineers SF-4, Method of Test for Flexural Strength and Flexural Toughness of Fiber Reinforced Concrete, published in 1984 [23]. • Japan Society of Civil Engineers SF-5, Method of Test for Compressive Strength and Compressive Toughness of SFRC, published in 1984 [24]. • Japan Society of Civil Engineers SF-6, Method of Test for Shear Strength and Shear Toughness of SFRC, published in 1986 [25]. Bending tests are most commonly employed to characterize the post-peak behavior of FRC because of the apparent simplicity of the test procedure and higher stability of results as compared to pure uniaxial tension, shear or compressive toughness test tests. Notched beam tests, forcing the crack to propagate at a given location, do not reflect FRC's ability to distribute cracks at mid-span and break at its weakest point. Several reviews of existing test methods can be found in [3, 26, 27]. All of the flexural methods are based on evaluation of the recorded load versus mid-span deflection curve for a four-point bend test. Recently, ASTM C1018 has been withdrawn due to the difficulty of locating the first crack in the load vs. deflection curves, and has been replaced by ASTM C1609. This new standard facilitates the post-crack performance measurement for fiber-reinforced concrete intended for slabs-on-grade, pavements, pre-cast elements and shotcrete. The most used methods world-wide are: ASTM C1609, C1399 and JSCE-SF4. The "template method" initiated by Morgan, Mindess & Chen [3] is more feasible for design purposes, and is becoming more commonly used in some jurisdictions [28]. The differences between these standards lie in the different ways of determining the flexural toughness. The ASTM CIO 18 method gave relative toughness values; the JSCE method provides "absolute" toughness values, while the current ASTM C1609 and Template method uses toughness classes to differentiate amongst various FRCs. 8 2.1.2.2 Plate test In many circumstances, such as FRS support for unstablized soil condition, the maximum deflection may be up to 10 times larger than that measured in normal beam tests (approximately 2 to 4 mm). Furthermore, beam tests do not represent how shotcrete fails in-situ. Therefore, the beam test has it limitation for FRC applications. A number of test methods using plates rather than beams have been developed to better characterize the performance of FRC and FRS in service. These include the South African Water-Bed test [29, 30], EFNARC square plate test [20] and more recently, the round determinate panel test (ASTM C1550 [5]). ASTM C1550, the centrally loaded round panel test developed by Bernard [6, 31] has been gaining popularity, in part because of the low variability in the test values. It appears to be particularly suitable for evaluating the performance of FRS because the test method involves relatively large specimens and deflections, and also displays much less variability. The plate test appears to overcome at least some of concerns hindering the development and adoption of performance-based specifications for FR-Shotcrete: "The performance of different fibers varies enormously; many of the test methods give poor repeatability; many tests are undertaken erroneously; and there are no criteria relating field condition, in-situ performance requirements, and the physical properties of FRS" [32]. Round determinate panel test (RDP test) The test specimen for the centrally loaded round panel test [5] is a circular plate, with a diameter of 800mm and a thickness of 75mm. The specimen is supported on three symmetrically placed pivoted supports located on a 750mm diameter circle, and is point loaded at the center. It is easier to handle than square plates, such as the above mentioned South American Water-bed test (1600x1600x75mm) and EFNARC test (600x600x100mm). 9 This is shown schematically in Fig. 2.1. In addition to the capacity of large deflection measurement, there is no sawing involved in preparing specimens. Loading piston Specimen i LVOT yoke anchored to pivot supports -LVDT Figure 2.1 Schematic view of the centrally loaded round panel test [5] The resulting load vs. center-point deflection curve is then used to determine the energy absorbed by the specimen out to any specified deflection. (One disadvantage of this test method is that the specimen itself weighs about 85-90 kg, which makes it rather awkward to handle.) Although there is now considerable experience with this method under static loading, there appears to be no current information on the use of this specimen configuration for impact loading; this is the subject of the present research. A unique feature of the RDP test is that its rotatable supports lead to more consistent failure modes. Failure modes for other setups may be subjected to edge conditions, confinement of bolts, or local damage. Representative failure modes for different test method are shown in Fig. 2.2. Figure 2.2 Typical failure mode of round determinate plate test 10 Related to the more consistent failure mode, RDP display a small within-batch variability (5%-8%) that makes toughness a good basis for quality control purpose. Two panel specimens were recommended to be tested per quality control (QC) test [33-35]. It is not the intent of this summary to provide a description or comparison of these different methods; suffice it to say that it is not possible to correlate the values obtained by these different procedures. In fact, they measure different properties in different ways, and may often lead to quite different comparative rankings of the relative effectiveness of a given suite of fibers. All of these methods (and other methods not listed here) were developed to evaluate FRC for static loading conditions. Most cannot be modified to deal with impact loading, which is one of the subjects of the present investigation. However, of the available tests, it appears that ASTM C1550 is the most suitable procedure for evaluating the toughness of FRC under impact loading, and so a somewhat modified form of this test was adopted here. 2.1.3 Dynamic performance of cementitious materials 2.1.3.1 Impact loading regime Impact loading on structures is quite common, due to accidental impacts, collisions of transportation equipment, earthquakes, rock-bursts in tunnels, dynamic traffic loading on bridge decks, and so on. Typical strain-rate ranges are shown in Table 2.1 [36], Loading type Strain rate (1/s) Traffic lOMO"4 Gas explosion Sxlfr'-SxlfJ4 Earthquake 5xl0-3~5xl0-' Pile driving lfjMou Aircraft impact 5xlO"2~2xlOu Hard impact 10° -5x10' Hypervelocity impact I O M O " Quasi-static loading regime or servo-controlled hydraulic jacks (For comparison) 10"' up to 10"b 11 2.1.3.2 Impact test A review of impact test and models on fracture of concrete can be found in ACI 446.4R-04 - Report on Fracture of Concrete [37], the effects of strain rates ranging from 10"6 1/s to 104 1/s being considered. From this, it is clear that there is still no agreement on the interpretation and comparison of impact data available in open literature. According to Mindess [38], this is mostly due to the fact that neither "standard impact test method" nor "standard cementitious material" exists. Even in well-instrumented tests the results appear to be sensitive to the following factors: Support conditions of specimens, rigidity of the impact machine, relative masses of hammer and the specimen, impart velocity (energy), specimen geometry, geometry and size of the contact zone, and nature of the data acquisition system. Commonly employed impact test methods include the following four categories [38-41]: 1. Drop-weight impact test The easiest and most economic way to initiate an impact is to use a drop weight impact machine. Earlier versions of the drop weight test were used to evaluate impact qualitatively by counting the numbers of blows to cracking or failure. By using an instrumented system, the load, deflection, acceleration and reaction of the supports can be obtained under various energy inputs (different drop heights). This method was employed in the present study. 2. Charpy impact test Another type of impact test is the pendulum machine, such as a modified Charpy machine. The instrumentation is quite similar to that of the vertical drop weight impact system. 3. Split-Hopkinson pressure bar (SHPB) method This is used to achieve higher strain rates than the first two method (up to 103/s). The limitation of this approach lies in restricted specimen size and high friction between the specimen and incident bar. 12 4. Projectile impact and blast impact In this category, a launched projectile with high velocity is aimed at the target structure. The focus is on localized damage, penetration, perforation or scabbing resistance of the structure or structural element. Plain concrete responds in a very complex way to high strain rate loading, i.e. it is strain-rate sensitive. The micro-structural origin of the rate dependence is believed to derive from the viscoelastic character of the hardened cement paste, its pore structure and moisture movement [42]; and the time-dependent nature of crack growth and propagation, which can be retarded by aggregate. This complexity of strain rate sensitivity is increased when fibers and/or rebar are included or when the concrete strength increases. 2.2 Dynamic performance vs. static performance for concrete Despite the complexity of the test itself, or the contradictory data reported by various researchers, the following findings are widely accepted for cementitious composites under impact loading: 2.2.1 Inertial effect The nature of the inertial effect lies in the fact that some of the load from the impact load cell is used to accelerate the specimen from rest. The load in overcoming the inertial is called the "inertial load". This inertial effect is largely dependent on the test setup, the frequency of impact signal, and the material properties. If this is not taken into account, a significant overestimation of the stresses will result [43]. The inertial effect has been successfully minimized by putting rubber pads between the impact hammer and specimen or on top of the supports [44]. However, this has the effect of reducing the stress rate. The principal of virtual work can be applied to determine the inertial load by properly recording the accelerations during flexural impact tests [45], 13 square plate tests [46] and double cantilever beam (DCB) tests [47]. A similar method is applied here to remove the inertial load from the recorded load (from a Tup load cell) in the dynamic round panel tests. 2.2.2 Dynamic increase factor (DIF) The dynamic increase factor (DIF), the ratio of the dynamic to static strength, is a widely accepted term and normally is a function of the strain rate. ACI 446.4R [37] provides a review of the DIF of concrete in flexure, tension and compression under impact loading. Concrete is more strain rate sensitive in tension and in flexure than in compression [43]. Amongst other empirical models [48-50], perhaps the most comprehensive model on strain rate sensitivity both in tension and compression is presented in the CEB mode code [36]. The dynamic increase factor (DIF) for compressive strength is given by: y j y _ ^ g/ y.026as for £ < 30 S 1 f.'fa=r.(*/eY" f ° - > 3 ° s - ' m where fc = dynamic compressive strength at strain rate e fcs= static compressive strength at strain rate es fdfcs = compressive strength dynamic increase factor (DIF) e = strain rate in the range of 30 xlO"6 s" to 300 s" ss = 30 x 10"6 s" (static strain rate) logys = 6.156 a s -2 o t s = l/(5+9/«' / / « , ' ) ; /co' = 10 MPa The dynamic increase factor (DIF) for the tensile strength is given by: for s< 30 s"1 for E> 30 s"1 f,if* = P{y6)m 14 where //= dynamic tensile strength at strain ratef fis - static tensile strength at ss ft/ fu= tensile strength dynamic increase factor s = strain rate in the range of 3 x 10"6to 300 s" s s = 3 x 10"6 s" (static strain rate) log p = 7.118-2.33 5 = l/(10+6/«' //«.'); /«»' = 10 MPa The above formulation on compression captures the following aspects of material behavior: • the relationship log (DIF) vs. log (e), is bilinear with a significant drift in slope around 30 s"1 • the DIF is higher for concretes with lower strengths • all DIFs are related to strength measured at a specific "quasi-static" strain rate • the strength enhancement is different for tension and compression • the CEB expression is reported to be valid up to 300 s"1. Similarly, the curves of log tensile DIF vs. log strain have a discontinuity in their slope at a strain rate of 30 s"1. The original tensile DIF formula has further been modified by others, by shifting the discontinuous strain rate from 30 s"1 to 1 s"1, in order to fit experimental data. Instead of using strain rate, Nadeau et al. [51] derived the dependence of strength on the stress rate, based on Evans' model [52] regarding the relationship between the velocity of a moving crack and its stress intensity factor Ki: V = AK? lno- = _ l _ l n 5 c T + — — Info"-2 - o - / - 2 ) e N + \ N + l f where, N and B are constants. The slope 1/(N+1) of a plot of strength vs. stress rate from the above formulation had been used to compare the strain rate sensitivity of materials under dynamic loading. However, according to Shah and John [53], N was later found 15 experimentally to be dependent on the stress rate, material strength and testing environment (temperature). Overall, the tensile DIF was found to be significantly higher than the compressive DIF at the same strain rate. There does not exist a universal model for the dependence of DIF on stress (or strain) rate which could apply over the whole strain rate regime. Moreover, no energy absorption ratio (DIF) has been discussed to date. Knowledge of the DIF, both for strength and toughness is important in the design and analysis of structural safety. Thus, DIF is also studied here. 2.2.3 Bonding between discrete fibers and concrete matrix under dynamic loading Fibers improve the toughness of cementitious materials by bridging cracks and providing residual loading capacity. Previous work has focused on characterizing the steel fiber bond-slip performance under static loading [54, 55]. Bindiganavile [47] reviewed the dynamic bond-slip performance of various types of fibers and concluded that the crack opening rate ranges from 10"4 to 3xl03 mm/s, and DIF values range from 1.3 to 6.0. However, different researchers have found quite contradictory relationships between energy absorption and slip rate. Consequently, using the results from dynamic pullout tests to interpret the structural performance of FRC elements is still next to impossible, though some quantitative work has been conducted under static loading. Silica fume was believed to improve the bond between synthetic fibers and concrete and yield better fiber dispersion as well. Bayasi and Celik [56] reported that polypropylene and polyester fibers enhanced the impact resistance of concrete with silica fume more than in those controlled FRC. A silica fume content of 5% (mass) is optimal and the adverse effects on workability, caused by high contents of silica fume or fibers, resulted in the reduction in the impact resistance of the material. 16 Synthetic fibers, such as polypropylene, may show better performance at higher loading rate [47]. However, the dynamic bond-slip performance at other fibers such as carbon fibers, nylon fibers and natural fibers is not available. 2.3 Behavior of specialized cementitious composites 2.3.1 High performance FRC (HPFRCC) High performance concrete (HPC) has been developed to achieve better workability, volume stability and durability [57]. However, it remains brittle. Conventional FRC with low fiber volumes does, however, exhibit strain softening behaviors. Attempts to develop high performance fiber reinforced cementitious cmposite (HPFRCC) with strain hardening properties have been made for decades, in particular after the first international ACI and RILEM workshop on HPFRCC [58,59]. Due to the relatively high cost because of the large amount of fibers and/or special manufacturing procedures, HPFRCC is designed for the use in special situation, such as impact, blast, and seismic type loading, where materials with large strain capacity and high toughness and residual loading capacity are essential. Based on the manufacture process, Typical HPFRCCs include: • Densified cement ultra-fine Small Particle based material (DSP) including Compact Reinforced Composite (CRC), Reactive Powder Concrete (RPC) • Slurry Infiltrated Fiber Concrete (SIFCON) • Slurry Infiltrated Mat Concrete (SIMCON) • Engineered Cementitious Composites (ECC) Experimental studies on testing SIFCON beams [60, 61], SIFCON cylinders [62], DSP (CRC) beams [63], RPC (Ductal) beams [64] and ECC plates [65, 66] have indicated significantly improved ductility over conventional FRC specimens under static loading. HPFRCC is suitable for structural applications by providing high crack resistance and shear capacity. Our understanding of dynamic performance on HPFRCC is much less than under static loading, due in part to the lack of test methods. 17 2.3.2 Cementitious composites with fabrics and hybrid reinforcement 2.3.2.1 Concrete reinforced with steel fabrics - welded wire mesh vs. fibers Welded wire mesh (WWM) is used extensively in slabs-on-grade and for surface support in mines and tunnels. The WWM in these applications is, like fibers, intended to control cracking and crack widths. There is a long-standing argument as to the relative merits of WWM vs. fiber reinforcement. The generally accepted view is that if the WWM is properly placed (i.e., in the middle third of the section), the two systems will behave in broadly similar ways. For instance, Morgan and Mowat [67] showed that, under static loading, steel fiber shotcrete can provide somewhat better load bearing capacity than WWM reinforced shotcrete at small deflections, and at least equal capacity at large deflections. Similarly, using the EFNARC method [20], Ding and Kusterle [68] concluded that fiber reinforced concrete (FRC) panels had better punching capacity, flexural ductility and toughness than WWM reinforced panels, as long as the WWM was replaced with at least 60 kg/m3 (about 0.75% by volume) of steel fibers. Even low modulus synthetic fibers can be as effective as either steel fibers or WWM as long as they are used in sufficient quantity [71]. For slabs-on-grade, Sorelli et al. [70] found that while WWM reinforced slabs could sustain higher peak loads, FRC slabs ensured a ductile failure mechanism. The relative behaviors of the two systems were affected by the point of application of the load: under edge loading, WWM reinforced slabs outperformed FRC slabs, but the reverse was true under central loading. Of course, the "competition" between FRC and WWM reinforced concrete is based on the false premise that fibers and WWM reinforce concrete in the same way; nothing could be further from the truth. WWM provides a 2-dimensional reinforcing array in a single plane, using continuous wires with diameters ranging from about 4 - 12 mm, with mesh spacings of about 100 - 200 mm. Fiber reinforcement, on the other hand, involves a 18 3-dimensional reinforcing system, using short, discrete fibers randomly distributed throughout the entire concrete volume. These fibers are typically 12 - 50 mm long, with aspect ratios (length/diameter) of about 50-100. WWM reinforcement is particularly effective in controlling large cracks; fibers, on the other hand, are most effective in controlling microcracking. For instance, as part of the Canadian Rockburst Research program, Tannant et al. [71] tested large (1.5 x 2.75 m) panels reinforced with either WWM or fibres under impact. They found that WWM reinforced shotcrete behaved better under large deformations because the WWM could hold the panels together even when the shotcrete matrix was extensively cracked or fractured. However, the steel FRC could not withstand such large deflections; beyond some energy or deflection threshold the FRC panels lost their functionality due to fiber pullout, and the remaining fibers could not hold the panels together. It would therefore make much more sense to see these two reinforcing systems as being complementary rather competing; the combination of fibers and WWM should impart particularly useful properties to the concrete, particularly in terms of energy absorption. The combined use of fibers and WWM (referred to here as hybrid reinforcement or HyRC) has been shown to enhance the load carrying capacity and ductility of concrete under both static and impact loading. Detail of hybrid reinforced plates will be reviewed in the next Section and Section 2.6.2. 2.3.2.2 Concrete plates with hybrid reinforcement Hybrid reinforcement for concrete can be classified into three categories: Category I: Fiber + Fiber Hybrid fiber reinforcement, applying more than one type/size of fiber, is used to improve crack resistance under static loading [72, 73] and impact loading [74]. Optimized concrete mix with synergy of energy absorption can be achieved by taking full advantage of the individual fibers [69]. 19 Category II: Rebar + Fiber Mindess et al. [75] found that hybrid micro-fibers in a reinforced concrete system could improve impact resistance. The impact resistance increased with the volume of fibrillated polypropylene fibers and the effect on fracture energy of this combination was greater than that would be expected if their effects were considered separately. Hybrid macro fibers with conventional rebar could also increase crack resistance, shear capacity, fatigue, and creep properties. Research in this category focused on the structural application of FRC in beams and columns [76]. CFRC with steel rebar reinforcement was used in composite slabs to replace the steel frame tensile skin [77]. Experiments on a large scale slab (5x5m) by Falkner et al. [78], resting on a pile grid of 2x2m and loaded by a single jack in the centre of each of the four fields, was carried out to compare performance of slabs on piles with the following three types of reinforcement: Steel FRC only (no additional reinforcement); rebar reinforced FRC (6xO 10mm rebar in the column strips); pre-stressed FRC plate (internally unbonded tendons, resulting a compressive stress of -IMPa). Results indicated that, although all slabs exhibited certain ductility, the hybrid system exhibited higher strength, toughness and different failure modes than the SFRC plate. Therefore it provided a cost-effective alternative for the traditional systems for slabs on piles. Category III: Mesh + Fiber Generally, the objective of a hybrid fiber and mesh system is to improve the load capacity and crack resistance. A hybrid system, known as DUCON containing SIFCON and WWM, has been developed, for overlay application. This system consists of a package of fibers enclosed by two layers of mesh on the surfaces, followed by a slurry infiltration process. Four point bending test on beams showed that higher ductility could be achieved with a lower volume fraction of steel (less than 6%) [79]. More research work in hybrid reinforcement was carried out in the area of ferro-cement. El Debs and Naaman [80] have described the properties of mortars reinforced with steel 20 mesh and PVA fibers or polypropylene fibers; for the same fiber volume fraction, PVA fibers led overall better performance. The reinforcement ratios of mesh affect the efficiency of fibers in hybrid ferrocement system. Wang et al. [81] indicated that at low reinforcement ratio of steel wire mesh, the addition of fibers is significant; however, the increase of MOR and the toughening effect due to fibers became marginal when a high ratio was used. Cover-spalling resistance and shear capacity were enhanced, along with the improved crack space and width. When synthetic fibers (PE Spectra 900 and PVA) were combined with steel mesh, they did not noticeably influence the bending behavior before yielding of the mesh due to the much lower elastic modulus of synthetic fibers than that of steel mesh. But, as crack opening increased, the contribution of the fibers was significant. Thus the improvement of FRC with mesh is usually observed in the post-yielding stage [81]. Hybrids with fiber and mesh can remove the restriction of the close spacing of wire mesh in conventional ferrocement. A composite structure with FRC matrix and ferrocement layer on the tension side provided one-way slab with high loading capacity, better crack control and post crack ductility than conventional slab [82]. Flexural and impact resistance of ferrocement can be further improved by combined use of polymers [83]. A more recent review on high performance ferrocement can be found in [84], which includes hybrid reinforcement: fibers with two dimensional or three dimensional steel meshes or fiber-reinforced polymer (FRP) meshes. FRP meshes provided a promising alternative to steel meshes, in particular in combination with fibers [81, 85]. In summary, hybrid reinforcement with discontinuous reinforcement provides numerous benefits besides cost efficiency; the addition of fibers improves crack width and spacing. The overall goal is to preserves the structural integrity when overloaded; FRP provides new opportunities for ferrocement plates. 21 2.3.3 Polymer concrete system 2.3.3.1 Polymers in concrete As reviewed above, there are a variety of reinforcements that could toughen concrete. However, they have little effect on the concrete matrix itself. Polymer modification is an innovative approach for better durability and bonding strength, and may be used in the following forms [86, 87]: - Polymer Modified Concrete or Polymer Portland Cement Concrete (PMC or PPCC) - Polymer Impregnated Concrete (PIC), or - Polymer Concrete (PC). Polymers themselves have good impact resistance and show relatively larger strain capacity than cementitious materials, so it would be anticipated that PIC and PC, where polymer plays the role of matrix or part of the matrix, possess better impact resistance. For PMC/PPCC, with a co-matrix of polymer-cement, the impact resistance would also be improved. Concretes with elastomers (polymers with the properties of rubber) show higher values than those made with more brittle thermoplastic resins. Results of drop weight tests showed an increase in the drop height required to cause concrete failure with an increase in polymer dosage (0 to 20%) for mortars using SBR, Poly(vinylidene chloride-vinyl chloride) (PVDC), Chloroprene Rubber Latex (CR), Polyacrylic Ester latex (PAE), polyvinyl Acetate latex (PVAC) and natural rubber latex (NR). For different types of SBR latexes, differences in impact resistance depended mainly on the differences of the proportions of monomers and the molecular structure [87]. 2.3.3.2 Polymer modified FRC (PM-FRC) Polymer modified, fiber reinforced concrete (PM-FRC) is of significant interest because of the potential high performance contributed by both the fibers and the polymer. Pioneering work on concrete with polymers and steel fibers was conducted by Mangat and Swamy in the late 1970's [88]. Strength, stiffness and shrinkage tests indicated that 22 with proper selection of the type of polymer, modification of water content, and possible use of a defoaming agent, polymer dispersions can be used to advantage to improve the properties of FRC. Quite often, polymer concrete composites have been applied in bridge deck overlays, which may subject to severe dynamic loading (cyclic and impact) and require better bonding and durability. Latex modified mortar, together with low slump, dense concrete performed satisfactorily in severe conditions. Latex modified fiber reinforced concrete has been used successfully in bridge deck rehabilitation [89, 90]. Ohama and Endo [91] noticed that toughness of Styrene-Butadiene Rubber latex (SBR) modified hybrid (steel and polyethylene) fiber reinforced concrete systems is remarkably improved by polyethylene (PE) fibers (steel fiber was a controlled constant in the program) and this tendency is promoted by an increasing polymer: cement ratio. To keep similar slump, the water: cement ratio was adjusted in the program with smaller w/c for high polymer: cement ratio. PVA polymer powder was found very effective to improve the mechanical strength and deformability of glass fiber reinforced concrete [92] and steel and brass fibers [93]. Xu et al. [94] systematically investigated post-crack performance of SBR latex modified concrete with different macro fibers, keeping the same w/c ratio, and found that SBR latex is more effective to modify concrete containing steel fibers than polypropylene fibers in terms of post-crack performance. 2.3.3.3 PM-FRC under impact loading There is very limited literature on the effects of the combined use of polymer and fibers on impact resistance. Since dynamic properties depend, at least in part, on the method of measurement employed and there is no commonly accepted standard test, only relative comparisons of FRC or PMC or PM-FRC could be made. In general, while the improvements under impact loading may not be much more significant than under static loading for steel fiber reinforced concrete, they are often much better for polymeric fiber reinforced concrete; this depends, however, on both the 23 fibers and matrix properties. Fujuchi et al. [95] conducted direct flexural tests by dropping a steel ball on the mid-span of concrete beams to study the impact resistance of PM-FRC with poly-acrylic ester (PAE) and steel fibers. Improved impact strength and relative impact strength were found with an increase of polymer/cement ratio and steel fiber volume fraction. (The relative impact strength of the composite was defined as the "impact strength of steel reinforced PAE-modified concrete over impact strength of un-reinforced unmodified concrete"). Fig.2.3 shows the effects of PAE polymers and steel fibers on the impact resistance of concrete. PM-SFRC with 2.0% fiber and 20% PAE yielded a 60-fold increase in impact strength compared to the un-reinforced and unmodified concrete. Direct tensile strength, flexural strength, and toughness increased as well by factors of 1.7, 2.5 and 12.5, respectively, but the compressive strength showed a decrease when the fiber volume was increased. O 1.0 2.0 FIBER CONTENT, vol % a Impact Strength of Stool Fiber neinlorcod PAE-Modiftad Concrete Impact Strength ol Unreinforcod Unmodified Concrete Figure 2.3 Effects of polymer and steel fiber on impact resistance of concrete Using similar dynamic flexural tests, Soroushian and Tlili [96] witnessed the improved impact resistance of concrete with latex and steel fiber. Two levels of latex content and two different fiber volume fractions were considered. The joint effects of latex and steel fibers indicated a positive interaction between the two in terms of impact resistance and 24 flexural toughness. Latex modification seems to make concrete matrices more compatible with steel fibers. The increase in fiber-to-matrix bond in the presence of latex also seems to enhance the reinforcement properties of steel fibers in concrete. Using the Hopkinson split-bar method, Bhargava and Rehnstrom [97] investigated dynamic compressive performance of normal strength concretes: plain concrete, 20% Saran latex (Dow latex 464) modified concrete, 0.2% polypropylene fiber reinforced concrete (PPFRC) and PPFRC with 10% Saran latex. The dynamic strength was higher than the static strength for all type of concrete, the increment being 40-45% for plain concrete and 55-60% for polymer-cement concrete. PMC and PPFRC had 30-40% and 15% higher dynamic strength, compared to plain concrete. In the presence of small volume fraction of PP fibers, the deformation capacity was improved significantly. Jitendra et al. [98] reported only slight improvements in impact strength and toughness with steel fiber additions. However, the dynamic properties of the concrete were greatly improved when steel fibers were used together with a polymer: acrylic ester (PAE) copolymer with antifoamer. The mixtures were designed based on a similar consistency of the fresh concrete, with a volume fraction of steel fibers 1.5%. The strength ratios (strength under dynamic loading to static strength) of PM-FRC were 50%, 28% and 21% greater than that for plain concrete, PMC and FRC respectively. The properties of both FRC and plain concrete were markedly improved by the polymer, as shown in Fig. 2.4. Figure 2.4 Impact resistance (ratio of dynamic/static strength) of different types of concrete (Note: "polymer concrete" represents PMC in this reference) 05+ t 2 3 i. 5 6 7 8 9 Blow Number 25 Natural rubber latex modified steel fiber reinforced concretes were tested by Lyengar et al. [99]. They noticed that there exists an optimum dosage of latex, and better synergetic effects could be obtained by combining steel fibers and natural rubber latex. Pendulum impact tests on notched beam specimens indicated that the number of blows for concrete with this combination increased by 9-10 times at first crack and 18 to 20 times at failure; 2- 3 times higher than FRC and latex modified concrete. However, little information is available about the capacity of energy absorption of PMC and PM-FRC under flexural and compressive impact loading, which will be examined in this study (Chapters 8 & 9). 2.4 Fiber reinforced Shotcrete (FRS) 2.4.1 Fiber reinforced Shocrete: design and quality control (QC) issues Fiber reinforcement has become one of the most important components in shotcrete for tunnel linings, repair and rehabilitation. The properties of shocrete are different in both the fresh and hardened states from conventional cast concrete, with the average toughness of FRS consistently higher than that of conventional cast FRC [100,101]. They attributed the higher toughness to the higher compaction of shotcrete, leading to higher fiber efficiency after cracking. It appeared that a correlation between FRS and cast FRC may exist in terms of toughness if tested by using the same method [100]. Normally, better flexural strength and greater ductility are desirable for medium to poor ground, and good bond and high shear strength are desirable for rock. When large displacements are expected to occur, more energy absorption is preferred for effective support. In rock burst prone areas, the energy absorption is an essential property of the rock support. Hence, the post peak performance has practical significance to shotcrete under both static and impact loading. 26 As reviewed in Section 2.1.2, before the panel test was introduced, specifications for post-crack performance of FRS intended for the use of underground support are often based on minimum residual strengths obtained using beam tests. For example, the DIN 1048 beam test suggests using equivalent residual strength at 0.65 and 3.15 mm central deflections and the T374 method suggested using residual moments at 0.0033 and 0.02 radians crack rotation in Australia [102]. However, the maximum measurable deflection of current beam tests is only several mm, much less than that required in practice. The high variability of beam tests makes them a poor quality control measure for FRC. Rather, plate tests appear to be more suitable for that purpose. 2.4.2 Toughness criteria for FR-shotcrete using plate tests The energy absorption capacity of FR-shotcrete is specified based on plate tests up to 25 mm central deflection. According to the European Specification for Sprayed Concrete, three energy absorption classes with corresponding requirements are given in Table 2.2. Table 2.2 Energy absorption requirements of EFNARC specification [20] Toughness classification Energy absorption in joule for deflection up to 25mm a 500 b 700 c 1000 Empirical relationships between the required performance of FRS as quantified using beams (EFNARC beam test) and equivalent parameters from panel tests were developed [19]. It was found that, for a given FRS mix, the design performance obtained using EFNARC beams was lower than the useable design performance obtained using ASTM C-1550 panels. In other words, for a given design performance requirement, the target residual strength requirement must be higher if beams are used to assess performance leading to a more expensive mix design. According to Papworth [32], the beam test of JSCE SF4 at deflection of 3 mm, and the RDP test at a 10 mm central deflection can be related by expression: 27 Fe3 (in MPa) = (RDP10mJ92) 1.33 ... (2-1) However, this empirical relationship is not universally accepted because of the complete difference in test methods and these arbitrarily selected deflections. This issue is further examined by comparing beam tests and round panel tests in this work (Chapter 4). While the ENFARC panel test uses a 25mm deflection, the ASTM C1550 test involves panel toughness calculations up to a deflection of 40 mm. Papworth [32] suggested that one should use two defection criteria, 10 mm and 80 mm, for situations where crack widths must be limited and areas where high deflections are allowed, respectively. Detailed toughness values, ranging from 150 to 350 Joules for 10 mm deflection and from 200 to 840 Joules for 80 mm deflection, were suggested with corresponding rock classification. Other research cited in the same reference revealed that, for the same type of FRS, toughness obtained by the RDP method at a deflection of 40 mm and that by the EFNARC panel method at 25 mm correlated well: EFNARC 2 5 m m (J) = 2.5 x RDPWmm (J) .... (2-2) Garcia et al. [103] tested FR-shotcrete with high modulus synthetic fibers to compare the EFNARC panel test and the RDP test. They found a similar relationship with the factor 2.0 (rather than 2.5) for normal strength concrete containing plain, hooked-end steel fibers and monofilament polypropylene fibers. Steel fibers were found to be effective under different deflection ranges compared to synthetic fibers. The comparison further confirmed the adequacy of the RDP test because of its smaller testing variability than the EFNARC panel test. Recently, the Norwegian Concrete Association [104] proposed two energy absorption criteria levels for FR-Shotcrete of a tunnel project, 700 joules at 25mm central deflection for the majority of the tunnel, and 1000 Joules for areas of higher stress and areas where larger roof spans were incorporated. Different from the ASTM C1550 setup, a centrally loaded fully-edge supported round shotcrete panel, with a diameter of 600mm and a thickness of 100mm, and an internal diameter of 500 mm, was used. 28 In summary, there are no universally accepted toughness criteria for FRS to date. Within the limited experimental program the relative correlation between a variety of test methods is questionable. However, RDP is increasingly gaining acceptance. 2.5 Structural performance of FRC plates under static loading: 2.5.1 Steel Fibers reinforced plates Earlier beam tests have disclosed that mechanical performance of FRC is dependent on fiber type, aspect ratio, volume fraction and matrix properties [8]. Steel fibers outperform synthetic fibers due to their higher elastic modulus and better bond between steel fibers and matrix. This applies to FRC plates in general. Experimental work together with a theoretical prediction for steel FRC slabs under flexural loading by Khaloo et al. [105] indicated that in general, relatively longer fibres and higher fibre contents provide higher energy absorption for FRC slabs. However, different from FRC beam elements, loading capacity of FRC plates tends to increase with fiber additions, due to confinement of crack propagation in the three dimensional geometry [7, 106, 107]. There exists a concern of embrittlement or flexural toughness reduction, with steel fiber reinforced concrete or shotcrete, as has been noticed in high strength matrix composites when using beam tests [108] and plate tests [109]. Therefore, a higher steel fiber volume at higher compressive strength levels is required to achieve the same toughness as for lower strength shotcrete. Not surprisingly, this phenomenon is related to the age of the FRS. Bernard et al. [110], using the round panel test, investigated a drop in long-term performance of the steel FRS related to the increase in long-term strength of shotcrete. They recommend compressive strength as a critical parameter for steel FRS, which has a dramatic effect on the toughness performance due to the increase of fiber/matrix bond strength and the consequent change of fiber failure mode, and concluded that 50 MPa for the hooked steel 29 FRS used in their study. However, DiNoia et al. [Ill] did not notice such embrittlement for macro-synthetic FRS with a compressive strength exceeding 60 MPa. 2.5.2 Synthetic fiber reinforced Plates The most commonly used macro synthetic fibers are polypropylene (PP) fiber or modified PP fibers [112]. The elastic modulus of the modified fibers is higher than that of conventional polypropylene fibers because of increased molecular weight and special blending procedures. Within this category, high performance polypropylene fibers (HPP) and other fibers, called structural fibers, may reach a performance level that is comparable to steel fibers for FR-shotcrete. Typically, if dosed moderately, HPP fibers (10-13 kg/m3) reach about 700 - 900 Joules, more or less equal to the result achieved with 30 kg/m3 of high quality fibres according to the EFNARC plate test. Strain hardening was reported when testing shotcrete RDP with a dosage of 12 kg/m3 (Vf=1.32%) Barchip Xtreme fibers for Australia mine projects [113]. 2.5.3 Effects of loading & boundary conditions on FRC plates Studies on FRC plates have been carried out on plates or slabs with a variety of boundary conditions, such as simply supported (one-way, two way), supported on corners for square plates, or on all edges for circular or square slabs. Centrally loaded steel FRC (with a Vf of 1%-1.5%) slabs simply supported at four corner points (960x960x33mm, with 30 mm off the slab adjacent edges) by Ghalib [107] indicated that ultimate load and energy absorption were found to be proportional to the volume percentage and aspect ratio. The presence of steel fibers led to a reduction in crack width at failure, an increase in the degree of ductility and higher load capacity. Al-Ta'an et al. [114] concluded that steel fibers in two-dimensional thin members are more effective than in one-dimensional members such as beams in terms of resistance to crack propagation and strength. This was explained by the fact that fibers have a planar random distribution and the loads have to be resisted in two directions. 30 Kearns & McConnell [115] conducted square FRC plate tests (550x550x20mm, with a two-way clear span of 500mm on a rigid steel sub-frame). A uniform load was simulated using an approximation of 16-point loads to avoid punching shear failure. This work concluded that much higher load capacity and energy absorption were found for panels in clamped conditions (by sandwiching the plate between two stubs) than panels with simple support. Hybrid fiber and wire reinforcement show clear benefits of strength and ductility improvement, but this improvement appeared more significant for panels under simply supported condition than for the clamped case. A similar conclusion was made by testing circular panels [116]. Bernard concluded that the fully clamped FRC panels appeared to be stronger than simply supported panels, followed by the round determinate panels. However, the round determinate panel test exhibited a more uniform failure mode, making it more suitable for standard tests than the others. Barro et al. [106] noticed that the foundation of a slab could pick up load after cracking for centrally loaded SFRC slabs; if the subgrade had a high modulus of subgrade reaction value, FRC slabs tend to yield higher load-bearing capacity in terms of both first crack and ultimate load [117]. Experimental work on pre-stressed SFRC slabs supported on piles exhibited higher loading bearing capacity and displacement than FRC slabs and reinforced SFRC slabs, and different failure patterns from other slabs [78]. 2.6 Concrete panels/slabs structures under impact loading 2.6.1 FRC plates under impact loading To improve impact resistance, a variety of fibers have been used to reinforce concrete plates. These include steel fibers, glass fibers and synthetic fibers. Guillebon et al. [118] tested metallic glass ribbons (amorphous alloys FeCrPC fiber, made by a melt spinning technique) and asbestos reinforced concrete plates (162x162 mm) by using a ram mounted on a hydraulic jack on a four-side embedded plate. Notable increases in energy of failure were found. With little or no reinforcement (1% by weight), the plate broke in four parts along the yield line while with 4% of amorphous ribbons the plate was 31 perforated but not broken. Fibers can also effectively prevent the dramatic propagation of fissures in asbestos-cement manufactured by the Hatschek process. Glinicki et al. [119] used a drop weight test to investigate glass fiber reinforced concrete (GRC) plates. He found that the energy absorption capability of GRC, either up to the maximum load or up to total failure, is a function of plate thickness and impact velocity. A comparison yielded a ratio of impact-to-static energy absorption of 1.7-1.8. A light weight carbon-fiber FRC plate was embedded between two layers of steel sheet, forming a composite structure to replace a conventional free access floor (aluminum die-casting). The square plates with a dimension of 600x600x24 mm3 were centrally loaded with four corner supports. Drop weight impact tests revealed that CFRC composites are more suitable for computer room and office automation systems due to improved strength and other floor characteristics such as heat insulation and walking noise level compared with an aluminum floor [120]. Glinicki et a/. [121] used a tube with an inside diameter of about 0.05 m to guide a falling projectile (1.49, 2.61, 4.17kg) to strike on the center of a steel FRC slab, with drop heights up to 2.54 m. Slabs were placed on a square steel frame with a continuous ledge providing about 0.01m width of support. He concluded that the failure pattern involved the formation and movement of a cone shaped plug of material. The number and the width of cracks were found to be sensitive to fiber content and the number of impacts to failure increased up to 1.8 times for the SFRC slab with 1.0% fibers. Banthia, Gupta and Yan [7] used EFNARC plates for fiber reinforced wet-mixed shotcrete as well as beams. The plate test showed similar toughness enhancement due to fiber reinforcement, but the authors indicated that the relative improvements between fiber types are not necessarily in agreement with those indicated in the beam tests. Both plate and beam specimens were found to be less sensitive to changes in the rate of loading from static to dynamic, but as biaxial bending was the more practical loading configuration, the plate test was suggested to be used in toughness characterization. 32 Sukontasukkul et al. [122] tried various steel fibers in square concrete plates simply supported on four edges with a clear span of 300x300 mm under drop-weight impact loading (up to 500 mm). They found that steel fiber reinforced concrete (SFRC) plates displayed different fracture characteristics from those of plain concrete plates. It was found that steel fibers improved the fracture energy of the plates and also led to the occurrence of multiple peaks in the load vs. deflection curves, which most likely are affected by fiber content and loading rate. When the specimen was confined, the same authors noticed that plate behavior changed dramatically. The increased confining stress gradually changed the mode of failure from flexure to shear failure. Confined plates were stronger and tougher. The inertial load, on the other hand, became smaller due to the stiffening effect. Confined plates exhibited less stress rate sensitivity than beam or prisms due to the change of failure mode from flexure to shear (shear crack velocity is slower than the flexural crack velocity). Very interestingly, when confined, the performances of the different FRCs could not be clearly distinguished from each other due to the dominant effect of the confinement apparatus. Ong et al. [123] at the National University of Singapore tested normal strength FRC slabs simply supported on four edges, containing steel fibers, polyvinyl alcohol (PVA) fibers and polyolefin fibers. They found that steel fibers, for the same volume (2%), outperformed polymeric fibers in terms of fracture energy and load bearing capacity, but at large deflections, polymer fibers performed better, with straight PVA fibers showing a better toughening effect than polyolefin fibers based on toughness value up to 20 mm center deflection. They attribute this performance to the differences of elastic modulus and surface properties between steel fibers and polymeric fibers. On the contrary to what is observed in static loading, Banthia et al. [124] found polymeric fiber reinforced composite are tougher under very high strain-rate loading than that under static loading. Quite interestingly, there existed a "performance transition loading rate". When the loading rate (drop height) increased, the toughness of PPFRC 33 became higher than that of SFRC. This may be attributed to the differences in the visco-elastic nature of polymer and steel under high strain rate loading. 2.6.2 Hybrid reinforcement system under impact Data with respect to concrete elements with hybrid reinforcement under impact loading is scarce. Paramasivam et al. [125] compared FRC slabs with 6.5 mm mild steel bars in both direction spaced 150 mm center to center, and with different volume fractions of fibers (0, 1% and 2%), under different loadings: static loading, with a displacement rate of 0.008mm/s and drop-weight impact loading, up to a 4 meter drop with corresponding loading rate of 3000 mm/s. Slabs (1000x1000x50 mm) were clamped and impacted with a 43 kg mass projectile. They concluded that, overall, local damage of slabs absorbed considerable energy. The energy absorbed by slabs under impact was higher than that under static loading. Steel FRC slabs (hooked-end steel fibers) provided better crack resistance, a smaller degree of damage and higher toughness than those containing polymeric fibers (straight Polyolefin). Mesh/Steel fabric (05 mm, 150x150mm) and PAN fibers (0.2-0.8%) reinforced concrete plates (600x600x40 mm) were supported at the four corners. The impact loads were applied at the plate center by an instrumented ballistic pendulum. Progressive damage of concrete in the impact area caused variable shifts on the plate modal frequencies, and changed the sequence of modal shapes. The authors used the frequency decay as a damage index. It was found that the damage suffered by concrete was reduced with increasing fiber volume. A higher number of blows was required to produce scabbing at the concrete center; crack propagation was limited by the PAN fibers [126]. Gholipour [127] reported on steel, polypropylene and glass fiber reinforced ferro-cement panels (1000x1000x25mm) under drop-weight impact loading. The impact energy required to cause failure was 70%, 50% and 40% higher than that required for corresponding SFRC, PPFRC and GFRC slabs. The cracking resistance of the slabs, as 34 indicated by the number of cracks produced by the same drop height, was increased by 15-25%. Butnariu et al. [128] investigated the impact behavior of hybrid sandwich specimens made from combinations of 2 dimensional textile fabrics and short fibers by testing two types of fabrics: knitted short weft polyethylene (PE) yarns and bonded alkyl-resistant glass fibers, and four type of fibers: PVA with relatively high modulus of elasticity (E), polypropylene (low E), polyethylene fiber (low E) and A.R. Glass bundles (high E). PP fibers exhibited better performance than PVA fibers. Loading direction had a significant influence on the dynamic performance. When the composite is loaded parallel to the fabric layers, a large number of fabric layers participate to take the stress and therefore the composite is more ductile, tougher and exhibits relatively low stiffness due to stretching of the fabric during loading. Opposite to low modulus fibers, they found that low modulus PE fabrics were attractive and a PE fiber-PP fabric sandwich (hybrid system) exhibited better impact behavior than a glass fabric composite. Square plates reinforced with fiber reinforced polymer (FRP) rebar/grid under impact loading indicated that, after the inertia correction, the FRP reinforced plate failed in a brittle manner and absorbed only a third of the energy absorbed by a companion plate reinforced with traditional steel reinforcement. Fiber reinforced concrete, however, was found to completely alleviate the problem of brittleness. A hybrid system of fibre reinforced concrete and FRP grid had the greatest increase in impact resistance [129]. However, very little research has been carried out on concrete in the geometry of a round panel under impact loading. Bernard [130] examined the influence of low to moderate rates of strain on cracking and post-crack performance up to severe levels of deformation by using the round determinate panel (RDP) procedure (ASTM C1550) loaded on a servo-hydraulic machine. He found that performance can vary substantially with strain rate when some types of polymer fibers are used as reinforcement (though not for all types). Results indicated, however, that steel fiber-reinforced concrete exhibits a smaller 35 variation in post-crack performance with rate of strain than polymeric FRC in the tested strain rate domain. In summary, plates reinforced with individual or hybrid reinforcement exhibit improved ductility under impact loading. Most of the above dynamic tests of RC or FRC plates were conducted on square plates with a variety of test setups. The RDP method has not previously been employed to characterized cementitious materials under impact loading. The suitability of this test method for static testing, however, suggests that this method can be adapted for impact testing as well. 2.7 Summary of literature review In summary, the following statements may be made on the basis of the literature survey presented above: (1) The round determinate panel test is a better test method for FRC or FR-Shotcrete characterization under static loading than is the beam test. (2) There is no universally accepted test method for FRC toughness characterization under either static or impact loading. (3) A systematic understanding of impact response of the FRC using the geometry of a round panel does not exist. Existing data from other geometrical plates are contradictory and not suitable for dynamic performance of FRC. (4) Experimental studies on hybrid reinforced concretes revealed that they possess enhanced properties. But very little is known about hybrid reinforced panel under impact loading. (5) Strain-rate sensitivity of conventional FRC has been observed, but the mechanism is still not understood. No such data exist for PMC and PM-FRC round plates under impact loading. 36 CHAPTER 3 EXPERIMENTAL DETAILS 3.1 Introduction This Chapter describes the experimental program designed to better understand the performance of specialized reinforced concrete, in the form of either round panels or cylinders, under both static and impact loading. It covers the materials, experimental program, test setup and instrumentation, and the data analysis approaches. 3.2 Materials and concrete mixes 3.2.1 Materials - Concrete matrices Cement: CSA Type 10 (ASTM Type I) Normal Portland cement; Fine aggregates: Clean river sand with a fineness modulus of 2.5-2.7; Coarse aggregates: Gravel with a maximum size of 10 mm; Polymer (for PMC matrices only): polystyrene-butadiene rubber latex (SBR). It is designed for use as a bonding agent with concrete and cement-based products in both interior and exterior applications. A silicone emulsion based defoamer was used to control air content. 3.2.2 Materials - Reinforcement Fibers: Three different types of macro fibers were used, mostly at volume fractions of 0.5% and 1.0%, except where otherwise indicated. Geometrical and mechanical properties of these fibers, are shown in Table 3.1. 37 Type Table 3.1 Properties of steel and synthetic fibers Synthetic fiber2 Steel fiber 1SF PPN Synthetic fiber 3PP Shape Hooked end Flexible, straight Straight, flexible Cross Sectional Shape Rectangular at middle and end Irregular, partially fibrillated during mixing Irregular Aspect Ratio (L/d) 70 - 85 Specific Gravity (g/cm3) 7.8 0.91 0.92 Melting Point and Ignition Point (°C) N/A - 160 590 Length L (mm) 50 50 50 Equilibrium diameter D (mm) 0.72 - -Elastics modulus E (GPa) 212 4.3 9.6 Tensile strength ot (MPa) 1200 370 500 Welded Wire Mesh (WWMV. According to the manufactures, the mesh is in accordance with ASTM A185 specifications, with a tensile strength of 517 MPa (75,000 psi, ASTM A82 specifications). Gauge number Tm = 4.8 mm, with a square spacing (center-to-center) of 100 mm (Sm=4" by 4"). The original size is 24' wide (Wm) by 48' long (Lm), as shown in Fig. 3.1. Meshes were cut to fit the round mold before use. The mesh volume in the concrete is about 0.6% of the round panel. Two different mesh configurations were used: 1 Optimet 7050 (by Optimet Inc., USA). 2 Old version of Strux fiber, a structural fiber with polyethylene and polypropylene (by W.R. Grace, USA). 3 Strux 8550 (by W.R. Grace, USA). 38 The second (Type C, Mesh C) was such that the Tup contacted the specimen at one of the wire mesh intersections (Fig. 3.2b). The first configuration (Type E, Mesh E) was such that the hemispherical striking Tup contacted the specimen in the center of one of the 100 x 100 mm squares of the mesh (Fig. 3.2c). A Figure 3.1 Wire welded steel mesh WIRE MESH FITTED MESH (a) Mesh cutting to fit RDP mold (b) Type C mesh (c) Type E mesh igure 3.2 Mesh reinforcement prepared for round panel specimen: mesh pattern 39 3.2.3 Mix proportions Though the RDP test was initially developed for evaluating fiber reinforced shotcrete (FRS), it has also has been increasingly used for cast FRC as well. Thus, in this study three strength levels of cast concrete mixes were used, i.e. normal strength concrete (NSC), high strength concrete (HSC) and very high strength (VHSC). The target compressive strengths were about 45MPa, 80MPa and HOMPa for NSC, HSC and VHSC matrices, respectively. The detailed mix proportions are shown in Table 3.2. Some of the mixes also contained a commercially available SBR latex; the polymer/cementitious materials (p/cm) ratio was maintained at 10% by solid weight of the latex for RDP tests. Other p/cm ratios were studied for FRC under uniaxial compressive loading (Section 3.6.6). Fiber volume fractions are variable, depending on the program. Superplasticizers and antifoam agents were used as required to control the workability and air content of the specimens containing polymers. Properties of both fresh and hardened concrete of these mixes are shown in Appendix C. Table 3.2 Concrete mix designs Concrete types HSC HSC-PMC10 NSC VHSC Cement, kg/mJ 453 453 319 513 Silica fume, kg/mJ 44 44 0 51 Fine aggregate, kg/mJ 796 738 717 775 Coarse aggregate, kg/m3 1053 978 717 1037 Water, kg/m3 139 139 175.5 123 W/(C+M) 0.28 0.28 0.55 0.24 SP (RHEOBUILD 3000FC), % * 0.8-1.1 0.3 -0.5 0 1.0-1.4 AE (MB-VR, standard), ml/kg 0.6 0 0 0.2 Latex, (solid content) %* 0 10 _ _ Fibers *n • _ i., r II . . . . Variable, see Section 3.6 *By weight of all cementitious materials 40 3.3 Specimen preparation 3.3.1 FRC or Mesh RC plates Due to limitations of the size of the impact machine, a somewhat scaled down version of the "standard" ASTM C1550 specimen was used in this program, though maintaining approximately the same ratio of dimensions as above. The specimen size adopted had a diameter of 635mm and a thickness of 60mm; these specimens weighed about 45 kg. Specimens of fiber reinforced concrete, some also reinforced with welded wire steel mesh, were tested both statically and under impact loading. For panel specimens containing WWM, a single layer of mesh was located at mid-thickness of the specimens, as shown in Fig. 3.2. Both Type C and E Meshes were used in feasibility studies (Chapter 6), however, only Type C Meshes were used in systematic studies (Chapters 10 & 11). Prior to the mix, the moisture content of both fine and coarse aggregates was determined to adjust the amount of mixing water. The concrete was mixed using a pan type mixer, placed in oiled forms, and vibrated on a vibrating table before being covered with polyethylene sheets. After 24 hours, the specimens were demoulded and cured in a water tank for 28 days. 3.3.2 Uniaxial impact tests on PM-FRC Two types of specimens were used in this program: concrete prisms, 100x100x125 mm, were saw-cut from beam specimens, and cylinders with a diameter of 100mm and a length of 200mm were cast directly. The concrete specimens with polymer (with or without fibers) were cured in various ways: 2 days in the mold covered with a plastic sheet; 5 days under water; and then air curing until the test date. Those without polymer addition were cured under water saturated with Ca(OH)2. Cylinders and beams (when necessary) were also cast. A summary of specimen and dimensions is shown in Table 3.3. 41 Table 3.3 Summary of specimen dimension and corresponding program Specimen type Dimension (mm) Test Program RDP £= 5 O 635 x 60 Static and impact tests for FRC and hyRC Beam / 4. i 100x100x350 Static tests of FRC Cylinder a 0100x200 Static and impact tests for SFRC and PM-SFRC Prism 1 100x100x125 3.3.3 Specimens for predictive model validation To analyze the round panel using Yield Line Theorem, round panels as described earlier and square panels were cast using the same mix of FRC. Square panels were then cut to prepare beams, to obtain the moment resistance - curvature relationship (Chapter 12). Table 3.4 Summary of specimen type for RDP model validation Specimen type Dimension (mm) Test Program Square plate 400x500x60 Used for preparing beams by saw cut Beam ' ^ ^ 400x120x60 Beam flexural test to obtain moment capacity vs. crack rotation RDP £ 5 0 635 x 60 RDP static test Cylinder ( 0 0100x200 Compressive strength 42 3.4 Test equipment and instrumentation 3.4.1 Drop weight impact machine An instrumented, drop-weight impact machine designed and constructed in the Structural Laboratory at the University of British Columbia was used to carry out the impact tests. This system is capable of dropping a mass of 578 kg from heights of up to 2.5 meters on to the target specimen. A chain and air brake were used to control the hammer at specific drop heights. The impact machine is shown in Fig. 3.3. Figure 3.3 Drop Weight Impact Machine 3.4.2 Data acquisition system A high speed VI logger system4 designed for data logging applications was employed for the dynamic tests. This system is a capable of recording up to 16 channels simultaneously. Four channels were used for the cylinder impact tests and five channels 4 National Instruments Corporation, U.S.A. 43 for the RDP tests under impact loading. The data were logged with a frequency of 100 kHz. 3.4.3 Instrument and calibration 3.4.3.1 Load cells It is mandatory, according to Yan [131], for a dynamic load cell to possess a linear relationship between the load exerted on it and the output, a higher frequency response than that of the tests, and a smaller delay time compared with the time of the event. Two types of load cells for dynamic loading, a bolt load-cell and a cylinder load-cell, fulfill the above requirement. He also indicated that the static calibration can be reasonably extended to the impact condition even though the cell is then stressed dynamically. As the tip of the load-cell or the piston connected to the bolt strike the specimen, the strain gauges insides the bolt record the contact load and the Wheatstone bridge circuit produces an unbalanced output; these signals are then collected by the data acquisition system. Cylinder load cell A circular striking tup (diameter 100 mm), including an inner part and an outer part, was rigidly connected to the drop hammer. The outer part (with no instrumentation) makes full contact with the surface of the specimen during a test and then transfers the load to the inner part. The inner part, instrumented with four strain gauges mounted on its outer surface, deforms; the strain gauge circuit becomes unbalanced and emits an output voltage. The tup was calibrated statically using a universal testing machine so that the proportionality constants for the load cell could be obtained. A calibration factor of 1 mV = 47.931 kN was obtained; the load cell is shown in Fig. 3.4 and the calibration curve is shown in Appendix B-l. 44 Figure 3.4 Tup cylinder load cell Bolt load cell A bolt type of load cell5, as shown in Fig. 3.5, with a capacity of 150 kN was used in this program. The calibration curve is shown in Appendix B-2. Note that it was a perfectly linear and there was no hysteretic loss. Figure 3.5 Assembled Tup with embedded bolt load cell (left) and bolt load cell (right) 3.4.3.2 Laser transducer An analog laser sensor6 LM-10, ANR1215, with a measurable range of 80(±50) mm was used for measuring the central deformation of the panel in the RDP test (Fig. 3.6). It consisted of two major parts: controller section and sensor section (Fig. 3.7). Within the Manufactured by Strainsert Company, Bryn Mawr, Pennsylvania, U.S.A. 6 Manufactured by Matsushita Electric Works, Ltd., Japan. 45 measurable range, the voltage output is proportional to the distance from the sensor. The specification and the calibration curve are given in Appendix B-3. Figure 3.6 Laser transducer system Figure 3.7 Sensor section of Laser transducer (1 -Laser emission indicator LED, 3-Measuring range indicator LED) 3.4.3.3 Accelerometer Piezoelectric accelerometers7, model #350A14, were used for shock and vibration measurement (Fig. 3.8). The resolution is 0.0lg; resonant frequency is 45 kHz, frequency range l~5000Hz and load recovery is less than 10 us. Manufactured by PCB Piezotronics, Inc. U.S.A. 4 6 During the test, the accelerometers were attached to the specimen through threaded plastic bases which were epoxy glued to the specimen surface at least 24 hours earlier, and the accelerometers were connected to the signal conditioner by a coaxial cable. The calibration factor was 0.931g/mv. Coiiiiected to Coaxial Cable: W ' rrm iniigilSiiii^ Plastic Base-Connected to • bstic Base Glued with Concrete Specimen Figure 3.8 Accelerometer 3.4.3.4 Angle measuring modules Dual axis accelerometer evaluation boards (ADXL311EB)8, containing ADXL311 dual axis ±2 g accelerometers, were utilized for measuring angles in this program. The board has a 5-pin, 0.1 inch spaced header for access to all power and signal lines by attaching it to the wire via a standard plug. Four holes are provided for mechanical attachment of the ADXL311EB to the testing system. The ADXL311EB is 20 mm by 20 mm, with mounting holes set 15 mm x 15 mm at the corners of the PCB (Fig. 3.9). The ADXL311EB has two factory installed 100 nF capacitors (C2 and C3) at XOUT and YOUT to reduce the bandwidth to 50 Hz. In this program, Xout was used to measure the panel or beam rotation. Three sensors were used and the calibration curves for each sensor are shown in Appendix B-4. Manufactured by Analog Devices, Inc. (NYSE: ADI), Norwood, M A , U.S.A. 47 C1={i0.1}iF [T "s 4i o ADXL311 TOP VIEW to-ur | C3^;0 .1 fiF • Q C O M M O N Figure 3.9 ADXL311EB Schematic Diagram- angle measuring modules 3.5 Test setup 3.5.1 Tests for basic concrete strength and elastic modulus Tests for basic mechanic properties of concrete were carried out in accordance with ASTM: ASTM C39 for compressive strength and ASTM C469 for elastic modulus. These tests were carried out on a universal testing machine 9 with a capacity of 1784 kN. 3.5.2 Tests for static toughness: flexural beam test The beam specimens were tested in 3-point loading with a clear span of 300 mm, using an open loop INSTRON universal testing machine. The load and deflection were continuously recorded using three channels of the data acquisition system. To accurately measure the deflection of the neutral axis of the specimen, a so-called "Japanese yoke" and two linear variable differential transformers (LVDTs) were used, as shown in Fig. 3.10. The rate of deflection was controlled at 0.10 mm per minute. The test was carried out to a total deflection of about 2.8 mm. Data were logged continuously. This test was only carried out for the PM-FRC and FRC series. JSCE-SF4 was used for data analysis. 9 Baldwin Model G B N , manufactured by Statec System Inc., USA 48 Figure 3.10 Arrangements of "Japanese" Yoke and LVDTs for Flexural Test 3.5.3 Tests for static toughness: Round panel test The above described panels were supported at three symmetrically placed pivoted supports and loaded at the center. These supports were located on a 596mm diameter circle with an overhang length of 19.5mm. An LVDT (Linear Variable Displacement Transducers) was placed on the underside at the center to measure the displacement. The setup could measure a maximum displacement of 65mm. The detailed setup is shown in Fig. 3.11. The data were collected by a PC-based data acquisition system. The static tests were conducted only in the unconfined condition. This test was used both for virgin specimens and post-impact tests on unfailed specimens with hybrid reinforcement (see Chapter 11). The toughness was then characterized by determining the absorbed energy at a specified central deflection, obtained from the load-central deflection curve. 4 9 Figure 3.11 Setup for round determinate panel 3.5.4 Test for studying the deformation of RDP To better understand the deformation and crack propagating process, a novel setup capable of measuring the rotation and side slip of cracked panel segments, was developed. The detailed setup is shown in Fig. 5.2. 3.5.5 Dynamic RDP test One of the main objectives was to develop an impact test setup for RDP, in order to extend the applicability of ASTM C1550. For the round panels subject to impact loading, a bolt load cell attached to the instrumented drop-weight impact machine was used. The impact velocity was Q g. ^ J2^h w n e n t n e hammer stroke on to the specimen, where the factor 0.9 accounted for the effect of air resistance and friction between the hammer and guide rails [45]. Drop heights ranged from 50mm to 500 mm for most of the tests. Direct measurement of the central deflection at the bottom of the panel was made using a laser transducer. A flexible rubber sheet was attached to the bottom of the specimen to avoid having the laser "target" lost in one of the cracks that developed. The deflection values obtained were checked using information from two accelerometers located midway 50 between the supports and the centre of the specimen (Fig. 3.12). A PC-based data acquisition system, with a sampling rate of 100 kHz, was used to record the signals for load, central displacement, and acceleration with time. Load-deflection curves were obtained for impact and loading. Toughness, taken as the area under each curve, was calculated for the various panels. The only difference from static loading was that initial effects were removed from the recorded load by using the virtual work theorem (Detailed analysis is given in Chapter 6). Drop weight hammer Guide column hammer Panel supports Figure 3.12 Impact Test Setup of Round Determine Panel (side-bottom view) 3 . 5 . 6 Uniaxial compressive loading (static and impact) Uniaxial compressive tests were carried out for PMC and PM-FRC in order to compare the strain-rate sensitivity of the composites under different loading conditions. A universal testing machine with a capacity of 1780 kN was employed for all static tests. The axial deformations were measured using two linear variable displacement transducers (LVDTs) mounted on opposite sides of the specimens. The specimens were loaded at an approximately constant rate of lxlO"3 mm/s. 51 For impact loading, the same instrumented drop-weight impact machine was used (Fig. 3.13). The 100 mm diameter striking tup containing a dynamic load cell was rigidly connected to the drop hammer. A drop height of either 0.35 m or 0.70 m was selected for the prisms, and a drop height of 1.2 m for all of the cylinders. The contact load developed between the hammer and the specimen and the deformational response of the specimen were measured using a dynamic load cell and a displacement laser sensor, respectively. This information was recorded by a high speed data acquisition system at a sampling rate of 100 kHz. Three specimens of each type were tested under static loading and at least three specimens were tested under impact loading (Chapter 9). Figure 3.13 Impact setup for uniaxial compressive loading Normally, it is necessary to make a correction to impact data, such as those for the inertial loads [45]. However, Fujikake et al. [132] have shown that for compressive impact, the inertial correction is less than 1%. Thus, no inertial corrections were applied in this case. Load versus deflection curves were developed from the load versus time and deflection versus time data. The compressive toughness (energy absorption) during either static or impact loading was calculated as the area under the load-deflection curves. 52 3.6 Experimental program 3.6.1 Test method study: Static I - beam vs. RDP Eight different HSC concrete mixes, with compressive strengths in the range of 75 - 88 MPa (Appendix C-l and C-2), were used to cast the beams and plates. The mix designs, designated as HSC and HS-PMC10, are given in Table 3.2. The test program for the comparison between beams and plates is given in Table 3.5. Table 3.5 Test program or Beam and RDP comparison Mix# Fiber type and Vf Matrix Type 0635x60 mm E 3 10x10x350 mm •—i 1 SF 0.5% HSC 2 4 2 SF 1.0% HSC 2 4 3 PPN 0.5% HSC 2 4 4 PPN 1.0% HSC 2 4 5 SF 0.5% PMC 10 2 4 6 SF 1.0% PMC 10 2 4 7 PPN 0.5% PMC 10 0 4 8 PPN 1.0% PMC 10 0 4 3.6.2 Test method study: Static II — deformation of FRC panel To characterize the deformation and crack evolution of FRC panels, three types of concrete matrices: normal strength (NSC), high strength (HSC) and very high strength (VHSC) were tested, with four types of fibres. The four types of fibres were an end deformed steel fibre, and three types of synthetic fibres: PP structural fibres, HPP fibres and PPN fibres. 3.6.3 Feasibility study on dynamic RDP test For both FRC-panels and WWM reinforced panels, the basic concrete mix proportions were the same as the HSC mix, the basic properties of the HS-FRC are given in Appendix C-l. The program for the RDP feasibility study is given in Table 3.6. 53 Table 3.6 1 fest program for feasibility study of RDP test Reinforcement Fiber volume Number of Number of type fraction RDP for RDP for static (%) impact test test* Steel fiber (SF) 0.5 6 3 1.0 6 3 PPN fiber (PPN) 0.5 6 3 1.0 6 3 MeshC 0 6 3 Mesh E 0 6 3 Mesh C + SF 0.5 6 3 Mesh C + SF 1.0 6 3 Mesh C + PPN 0.5 6 3 Mesh C + PPN 1.0 6 3 * shared with the program in Section 3.6.1 and 3.6.2. 3.6.4 Specialized FRC panels: Effect of matrix strength & polymer modification The experimental program for studying the effects of matrix and fiber on FRC is shown in Table 3.7. All of the round panels were tested under both static and impact loading. For the impact tests, except where otherwise mentioned, three different drop heights were used (150mm, 300mm and 500mm). Two specimens were tested in impact test for each drop height, and two for the static test. The compressive strengths for each type of concrete are shown in Appendix C-2 and C-3. 3 . 6 . 5 Performance and damage evolution analysis: Effect of hybrid reinforcement The program for round panels with hybrid reinforcement is given in Table 3.8; both static and impact test were conducted; the drop heights of impact loading ranged from 50 mm to 500mm. To further analyze the extent of damage of the hybrid reinforced panels, post-impact static tests were carried out on those specimens, which had not failed completely, such as Mesh-SFRCl.O and Mesh-PPFRCl.O systems. Damage evolution vs. drop height was characterized by defining the damage in terms of toughness, initial stiffness and peak load. The detailed program for the damage study is given in Table 3.9. 54 Table 3.7 Test program for FRC and PM-FRC Matrix Description (Target matrix fc') Reinforcement Number of RDP for static test Number of RDP for impact test* Type Volume fraction (%) -45 MPa Normal Strength Concrete (NSC) Steel Fiber 0.5 2 2x3 1.0 2 2x3 PP fiber 0.5 2 2x3 1.0 2 2x3 -80 MPa High Strength Concrete (HSC) Steel Fiber 0.5 2 2x3 1.0 2 2x3 PMC with SBR (PM-HSC) Steel Fiber 0.5 2 2x3 1.0 2 2x3 -110 MPa Very High Strength Concrete (VHSC) Steel Fiber 0.5 2 2x3 1.0 2 2x3 PP fiber 0.5 2 2x3 1.0 2 2x3 Matrix Description (Target Matrix fc') Reinforcement Type Number of RDP for static test Number of RDP for impact test* Mesh type Fiber type and volume fraction (%) -45 MPa Normal Concrete (NSC) Mesh C only 2 2x3 MeshC +SF0.5 2 2x3 MeshC +SF 1.0 2 2x4 Mesh C only 2 2x3 MeshC +PPF 0.5 2 2x3 MeshC +PPF 1.0 2 2x4 -110 MPa Very High Strength Concrete (VHSC) Mesh C only 2 2x3 MeshC +SF0.5 2 2x3 MeshC +SF1.0 2 2x4 Mesh C only 2 2x3 MeshC +PPF 0.5 2 2x3 MeshC +PPF 1.0 2 2x4 Table 3.9 Damage study for panels with hybrid reinforcement Reinforcement Type Matrix Strength Level Post-impact static test MeshC+1.0%SF NSC Yes MeshC+1.0%SF VHSC Yes MeshC+1.0%PPF NSC Yes MeshC+1.0%PPF VHSC Yes 55 3.6.6 Polymer modified FRC system under uniaxial impact compressive loading In addition to testing round FRC panels with polymer modification, SFRC and PM-SFRC were also studied under uniaxial impact compressive loading. The basic concrete mix was the same as the HSC mix shown in Table 3.2. The polymer-cementitious materials ratios were 0%, 5%, 10% and 15% by total solids content of the latex SBR. The amount of aggregate, with a maximum size of 10mm was reduced due to the inclusion of the polymer and fibers, keeping the ratio of fine aggregate to total aggregate at a constant 43%. Superplasticizers and antifoam agents were used to control workability and air content. Thirteen different concrete mixes were used. The program is summarized in Table 3.10. At least four specimens were used for impact tests for each drop height, and three specimens for the static tests. Table 3.10 Test program for ligh strength PM 1-FRC under uniaxial loading Specimen identification Concrete Type Polymer-cementitious materials ratio (%) Fiber volume fraction (%) Loading condition PMCO Plain HSC 0 -Static loadina: For both prism and cylinder Impact loading: Drop height-0.35m for prisms Drop height=0.70m for prisms Drop height= 1.20m for cylinders PMC5 PM-HSC 5 -PMC 10 10 -PMC 15 15 -SFRC0.5 FRC(HS) - 0.5 SFRC 1.0 - 1.0 PM5-SFRC0.5 PM-FRC(HS) 5 0.5 PM10-SFRC0.5 10 PM15-SFRC0.5 15 PM5-SFRC1.0 5 1.0 PM10-SFRC1.0 10 PM15-SFRC1.0 15 PM15-SFRC2.0 15 2.0 56 3.6.7 Round panel performance prediction from beam tests Cylinders and two types of panels: RDP and square plates were cast using the same mixes. The square plates were saw cut into beams, which were then tested using the flexural beam test, with rotation measurement on both sides, to obtain moment capacity vs. rotation. (See setup in Fig. 6.2). Four types of normal strength FRCs were used to validate the proposed model based on YLT. The concrete mixes are shown in Table 3.2. The size and number of the specimens are shown in Table 3.4 and Table 3.11, respectively. Table 3.11 Specimens for Model Validation Concrete type v f (%) e—^ f i • NS-PP0.5 0.5 3 4 6 NS-PP1.0 1.0 3 4 6 NS-SF0.5 0.5 3 4 6 NS-SF1.0 1.0 3 4 6 57 CHAPTER 4 STATIC TOUGHNESS OF POLYMER MODIFIED FRC: BEAM TESTS vs. ROUND PANEL TESTS 4.1 Introduction As reviewed in Chapter 2, there are a number of different standards that have been accepted in various jurisdictions. Several tests based on flexure are available using either beam or plate specimens. The question often arises as to whether these different standards all provide the same relative comparisons amongst concretes made with different fiber types and volumes. On the other hand, relatively little work has been carried out on the combined use of fibers and polymers, though there are indications that this might a very promising way of both strengthening and toughening the concrete [133-136]. In this Chapter, high strength concretes containing different combinations of fibers and polymers were tested under static loading, using the two different test geometries: beams and round panels. The second objective was to study how polymer may affect SFRC in terms of strengthening and toughening effects. The detailed program is shown in Table 3.5. 4.2 Data analysis JSCE SF-4 [23] was used to interpret the results. In this test method, the entire area of the load vs. deflection curve up to a central deflection of 2mm (i.e., 1/150 of the beam span) is determined. A flexural toughness factor T, equivalent to the average residual strength, is then calculated as: T = (Tb/ 5,b)x(L/bh2) ... (4-1) where Tb (flexural toughness) = area under the load vs. deflection curve to a deflection of 8 tb. 8 tb= deflection equal to 1/150 of the span 58 L = span length b = specimen width h = specimen height The round panel tests were carried out essentially in accordance with ASTM C1550 [5], as described in Chapter 3. The energy absorbed was calculated as the area under the load vs. deflection curve to a central-point deflection of 40mm. 4.3 Results 4.3.1 Beam tests Fig. 4.1 shows the load vs. deflection curves for the fiber reinforced concrete (FRC) beams made with both steel and synthetic fibers at volume fractions of 0.5% and 1.0%. As expected, the steel fiber beams (SFRC) had a higher post-peak load carrying capacity than the synthetic fiber beams (PPN-FRC) for the same Vf values; this is more apparent at Vf= 1.0%. Fig. 4.2 shows the corresponding curves for the specimens containing 10% SBR latex in addition to the fibers. As may be seen, the load vs. deflection curves for these beams took on different characteristics. Higher first crack strengths and better post-cracking performance were observed, with a clear strain-hardening appearance for the SFRC 1.0 mix. However, the SBR latex addition had much less of an effect on the synthetic fiber (PPN-FRC) beams. The JSCE SF-4 flexural toughness factors, calculated from Eq. 4-1, are shown in Fig. 4.3. It may be seen that the steel fibers are considerably more efficient in the latex modified matrix than are the synthetic fibers. 59 0 I , , I 0 0.5 1 1.5 2 Deflection (mm) Figure 4.1 Flexural load-deflection curves of plain FRC beams 12 • HSC(PMCO) • PMC10 Hi ~\W~ SFRC 0.5% SFRC1.0% PPN-FRC 0.5% PPN-FRC 1.0% Concrete type Figure 4.3 Toughness of FRC/PM-FRC beams (JSCE SF-4) 60 4.3.2 Round panel tests The typical crack (failure) pattern of the round panels consisted of three cracks emanating from the center of the panels, at angles of about 120°; at large deflections, the panels broke into three wedge-shaped pieces. The average load vs. deflection curves for the different types of fiber reinforcement are shown in Fig. 4.4 for the SFRC panels, and in Fig. 4.5 for the PPN-FRC panels. The load vs. deflection curves were essentially linear up to the peak loads. The increase in peak load for either steel or synthetic fiber reinforcement was not significant, but the post-peak load carrying capacity increased considerably. Due to the fiber additions, the panels could still maintain a considerable post-peak load. Consequently, the toughness increased to 12 times that of plain concrete panel for PPN-FRC0.5, and 19 times for PPN-FRC1.0. However, there was one major difference between the two fiber types. For the PPNFRC panels, just beyond the peak load, a sharp drop in load was observed, followed by a clearly defined second peak (Fig. 4.5). This did not occur for the SFRC panels (Fig. 4.4). That is, the SFRC panels exhibited a higher residual load carrying capacity immediately after cracking, while the PPN-FRC panels had a somewhat higher residual load carrying capacity when the cracks opened at larger deflections. Fig. 4.6 shows the load deflection response of the PM-FRC panels, i.e., those containing polymer as well as fibers. From a comparison of Figs. 4.4 & 4.6, the effects of latex modification on the SFRC mixes appear to be quite considerable. For the polymer modified specimens with both 0.5% and 1.0% steel fibers, a clear second peak was noted at a central deflection of about 3.5mm, quite unlike their behavior without the polymer latex. In particular, for the SFRC 1.0 panels with latex, both the peak load and post-peak behavior were considerably enhanced by the polymer. The panels with latex were substantially tougher than those without. In Fig. 4.7, the toughness values for the various panels are quantified (using the area under the load vs. deflection curves out to a central deflection of 40mm. It may be noted that, without latex, the total toughness of the two fiber types was similar, even though the curves had different characteristic shapes as discussed above. 61 TJ ctj O 30 25 20 15 10 5 SFRCO.S Panel SFRC1.0 Panel Plain HSC Panel 10 20 30 Deflection (mm) 40 50 Figure 4.4 Load-deflection curves of Plain and SFRC panels 30 25 •PPNFRC0.5 Panel PPNFRC1.0 Panel 40 50 20 30 Deflection (mm) Figure 4.5 Load -deflection of round panel test for PPN-FRC —PM-SFRC0.5 Deflection (mm) Figure 4.6 Load-deflection curves of PM-SFRC panels 0.7 i SFRC 0.5% SFRC1.0% PPN-FRC PPN-FRC 0.5% 1.0% Concrete type Figure 4.7 Toughness of FRC and PM-FRC panels • PMC10 HSC(PMCO) 4.4 Comparison between beam and round panels tests Very similar tendencies can be seen for both beams and round panels due to the inclusion of fibers and/or latex. The increase in toughness with increasing Vf is very clear for both specimen types. It can also be observed that polymer latex is very effective in improving the toughness of FRC. There were, however, some significant differences between the two specimen types: • The beam tests for the mixes containing steel fibers showed strain-hardening phenomena, particularly for the PM-FRC mixes, over much of the test deflection domain. For the round panel tests, however, strain hardening was observed only over a very small range of deflections, after which there was a clear load decrease. • In terms of the post-peak load carrying capacity, in the panel tests the steel fiber mixes performed better than the PPN fiber mixes at small deflections but worse at large deflections. In the beam tests, however, the steel fiber mixes outperformed the PPN fiber mixes over the entire deflection range. The numerical toughness values for both the beam and panel tests are summarized in Table 4.1 (Clearly, the absolute values of toughness for the beam and round panel tests are very different, due to the different specimen sizes and test geometries). It may be seen 63 that, for the beam tests, the SFRC specimens were considerably tougher than the PPN-FRC specimens at the same fiber volume. For the round panel tests, however, there was much less difference between steel and PPN fibers. On the other hand, the polymer addition appeared to enhance the behavior of the panel specimens more than it did for the beam specimens. Thus, different FRC mixes may be "ranked' differently, depending on which test geometry is used. For example, SFRC0.5 outperformed than PPNFRC0.5 by using beam test, however, RDP test gave an opposite tendency. This may be due to size effect, different loading and boundary conditions, analysis method and arbitrarily deflection limits set for comparison. The author believes that a specific specimen geometry should be chosen depending upon the application. For instance, the round panel test could represent more realistic situations for fiber reinforced shotcrete, where large deflection will occur in service. Beam tests are more suitable for cases with relatively simple boundary condition and small deflections. Table 4.1 Toughness for FRC from beam test and round panel test Average Toughness Average Toughness Mix Concrete Type Factor by Beams by Round Panels (MPa) (J) 0 Plain 0.11 16.7 1 SFRC0.5 4.51 186.5 2 SFRC 1.0 7.29 378.5 3 PPNFRC0.5 3.22 198.1 4 PPNFRC1.0 4.52 321.0 5 PM-SFRC0.5 6.82 349.9 6 PM-SFRC 1.0 9.93 620.7 7 PM-PPNFRC0.5 3.52 --8 PM-PPNFRC1.0 5.07 ~ 4.5 Conclusions (1) The effect of polymer additions on FRC is more significant for steel fiber reinforced concrete than for PPN fiber reinforced concrete. (2) While the two test geometries investigated here were similar in some respects, they were quite different in others. Thus, the comparative evaluation of different FRC mixes may depend upon the test geometry selected. 64 CHAPTER 5 STATIC DEFORMATION OF ROUND DETERMINATE PANELS CONTAINING FIBRES 5.1 Introduction As described in Chapter 4, beam and plate flexural tests are quite different. However, there is little if any information in the open literature on the cracking behavior of these panels for large deflections, although the effect of initial crack width of round panel on durability has been reported [137]. This Chapter describes the post-cracking performance of round determinate panels under large deflections, i.e., after the panels are severely cracked. 5.2 Crack opening analysis 5.2.1 Assumptions The RDP panels described earlier were tested here. To simplify the analysis, the following assumptions were made: 1. The fiber volume (Vf) is less than that required to cause strain hardening behavior of the FRC. 2. The fibres are uniformly distributed in the concrete, and the round panel fails symmetrically. That is, the presumed mode of failure is three cracks at 120° from each other, radiating from the load point at the center of the panel in straight lines to the outer edge, creating three segments, as shown schematically in Fig. 5.1. 3. Damage is confined to the regions adjacent to these cracks, with the remainder of the material relatively undamaged. 4. The initial elastic deformation in each of the three wedge shaped segments defined by the cracks is reversible, and is released after the main cracks develop. There is no curvature within each of the segments, which remain rigid and flat. 5. At the beginning of cracking, the cracks propagate from the bottom of the center of the panel in the radial direction to the edge of the panel, during which time the crack 65 widths remain small, increasing towards the edges. However, when the specimen fails and the central deflection becomes large, the final crack width is the same along the length of each of the main cracks once they are fully developed (as has been verified experimentally). This latter observation may be due to the presence of "diaphragm stress". According to plate theory [138], when the deflection becomes larger than one-half of the plate thickness, the middle surface becomes appreciably strained, and the stress at mid-plane can not be ignored. The diaphragm stress enables the plate to carry part of the load as a diaphragm in direct tension. This appears to occur in the round panels at large deflections, as the broken segments slide on the supports. Consequently, the crack width appears to become constant along the crack length at large deflection. £ E Round panel thickness = 6 0 m m Figure 5.1 Schematic of round determinate panel test 5.2.2 Modified round panel test A photograph of the round determinate panel after cracking is shown in Fig. 5.2. The experimental variables and geometries are listed in Table 5.1 and Table 5.2. In addition to 66 the load and central deflection according to ASTM C1550, the rotation and relative radial movement of the three segments are recorded. Figure 5.2 Round panel test setup for crack-width measurement Table 5.1 Measurement and geometrical designation of the test setup Measurement Apparatus Notation Load Load cell P Deformation and displacement of panel Central displacement Potential meter S Relative sliding between the support and edge of the panel LVDT s Rotation of the broken pieces relative to horizontal level(x and y) ADXL311 Bi-axis accelerometer 9 Geometrical size of test setup and specimens Support block size (length) - 1 Diameter of the rotatable ball in support - r, Central thickness of support block - >o Panel diameter - R Panel thickness - td Other intermediate parameters Distance from the center of support block to center of panel before loading a Distance from the center of support block to the original central point in the panel after loading a' 67 Table 5.2 Size of the specimen and test setup components (mm) R td 1 rs >o 635/2 -60 39 12.5 9 5.2.3 Crack width estimation A specific crack width located at the bottom center of the panel is defined in order to study the crack opening resistance of the FRC panel. The central crack mouth opening displacement (CCMOD) can be used as an index to characterize the cracking behavior. The CCMOD is here defined as eitherO'W'2, 0'20'3 or O'W'3, where 0\0'2 and 0'3 (Fig. 5.3a) were the corner point at the bottom of each segment. Originally, they were at the center point O when the panel was not loaded. The schematic detail of the CCMOD is shown in Fig. 5.3b. crack section/line (a) Schematic of CCMOD (b) Close up of bottom cracks Figure 5.3 Schematic of Central Crack Mouth Opening Fig. 5.4 illustrates a segment of the cross section with the rotatable support. The center point beneath the panel at O moves to point 0'/(i=l, 2, 3) after the load is applied, and points A, B and D move to A' ,B' and D' respectively. The relative amount of sliding between the support block and edge of the panel is s (See Fig. 5.4a). The relationship between CCMOD, the geometry of the test setup and the measured S, s and 9 is derived as follows: 68 (a) Broken segment and its rotation on the support (b) Detail of support before and after rotation Figure 5.4 Broken segment and support for crack opening analysis Knowing that the center line of the support is fixed, and that Point A moves to Poin ts , the distance from A' to the vertical central line (CB) of support column, A (see Fig. 5.4b), can be calculated from the following expression: A = EF = EB'-FB' = -1 cos 9 - (L + r ) sin 9 The distance from the central point O' to CB is 69 O'C=a'=O'A'*cos0-A where O1 A'=R — s. The distance "s", the relative sliding between the support block and the panel was measured with a side LVDT. The horizontal displacement of OO' after loading, bm, can be calculated as 00'=bm= OB-O'C where OB is the distance from the center of support surface to the bottom center of panel before loading (Fig. 5.4a). OB =a = R--l 2 where / is the length of support block along the radial direction, and is constant in this setup. Finally, the central crack mouth opening displacement (CCMOD), the lateral length of the equilateral triangle O' 10'20'3 (see Figs. 5.3a and 5.3b) is: CCMOD = 2-Z>mCOs30 = S(a-a') CCMOD =V3{(7? -112) - [(R -112 - s)cos0 + (t0 + rjsintf]} C5'1) Provided that a fixed setup is used and that the geometry of the panel, (R, 1, to and rs) is known (see Table 5.2), the CCMOD depends only on s and 0. 5.3 Crack opening resistance Typical data for a normal strength fiber reinforced concrete (NS-SFRC1.0) panel are shown in Fig. 5.5. Signals 2, 4 and 6, which decreased with time, are the main angle signals. The horizontal rotations, as indicated by signals 1, 3 and 5, show minor changes. Therefore 9 can be calculated by multiplying by the calibration factor for each angle-measuring module, and the CCMOD can then be calculated. The shape of the load vs. CCMOD curve is quite similar to the load vs. central deflection curve, but it provides detailed residual load and corresponding crack width data. In this study, the residual load (corresponding to an equivalent strength or 2-dimentional modulus of rupture) at a certain crack width represents a measure of crack opening resistance. The higher the residual load at the selected crack width, the higher the resistance of the FRC to crack propagation. 70 5.4 Experimental program and validation Three types of concrete matrices as described earlier, normal strength (NSC), high strength (HSC) and very high strength (VHSC) were tested, with corresponding compressive strengths of 45MPa, 80Mpa and 1 lOMPa, respectively. Four types of fibres were employed: one type of end deformed steel fibre, and three types of synthetic fibers: PP structural fibers, PPN fibers and HPP fibers1. They were all 50 mm long. Table 5.3 lists the experimental program. Mix proportion and other properties of these concretes are shown in Chapter 3. Table 5.3 Experimental program for test method validation Matrix type Fiber type Panel Designation Fiber volume, Vf (%) Normal Strength Concrete (NSC) Steel fiber NS-SFRC0.5 0.5 NS-SFRC1.0 1.0 PP structural fiber NS-PPFRC0.5 0.5 NS-PPFRC1.0 1.0 HPP fiber NS-HPPFRC0.5 0.5 NS-HPPFRC1.0 1.0 PPN fiber NS-PPNFRC1.0 1.0 High Strength Concrete(HSC) Steel fiber HS-SFRC0.5 0.5 HS-SFRC1.0 1.0 Very high Strength Concrete (VHSC) Steel fiber VHS-SFRC0.5 0.5 VHS-SFRC1.0 1.0 PP structural fiber VHS-SFRC0.5 0.5 VHS-SFRC1.0 1.0 1 High performance polypropylene fibers, SI concrete system, USA 71 5.5 Results and discussion 5.5.1 Method validation From the observed failure modes of the panels, it was found that the assumptions made above are reasonably met. The typical NS-SFRC panels are shown in Fig. 5.6, and similar failure modes were observed for the HS-FRC and VHS-FRC panels. The crack opening resistances of the FRC panels with the three types of concrete matrices are shown in Figs. 5.7-5.10. It appears, in general, that the load vs. CMMOD curves resemble the load vs. deflection curves. However, the initial part of the load vs. crack opening curve (up to peak load), is quite different from the load vs. deflection curve because measurable cracks occur only near or immediately after the deformation beyond peak load. Small cracks appear to merge inside the loaded concrete element; subsequently these cracks propagate and combine into a continuous crack which can be seen on the concrete surface. Around this transition point, the panel deformation is quite complicated; therefore in the initial part of the load-CCMOD the measurement is sensitive to the accuracy of the assumptions: the reversible elastic deformation, and no curvature in each segment of concrete. However, despite the potential errors caused by these simplifying assumptions, the proposed modified RDP method can be used to characterize the overall crack-opening resistance with reasonably accuracy. It should be note that since the widths of the three major cracks are not generally identical, they have been averaged for the analysis here. M (a) NS-FRC0.5 (front, side and bottom view respectively) 72 (b) NS -FRC1.0 (the same as above) Figure 5.6 Typical cracking behaviors of FRC panels after testing 5.5.2 Effect of fiber type From Figs. 5.7 and 5.8, for the same type of matrix (normal strength concrete), it may be seen that different fiber types play very different roles in controlling the crack opening. Steel fibers appeared to be more effective than PP fibers in controlling crack propagation at the volume fraction of 0.5%; they also outperformed the PP fibers at a volume fraction of 1.0% up to a CCMOD of 6.2 mm. However, after that point, the structural PP fibers exhibited better performance. For the three synthetic fibers tested, PPN, HPP and PP structural fibers, it appeared that, for the NSC matrix, the PP structural fibers showed better crack opening resistance than the HPP fibers (Fig. 5.8). This may relate to the relatively small aspect ratio of the HPP fiber; thus there are fewer fibers for the same volume fraction. There is no significant difference between the PPN fibers and an old version of PP structural fibers after the CCMOD reached 7 mm. For the VHS strength levels, PP fibers exhibited much better performance than the same volume of steel fibers. It is believed that this relate to "too good" bond between the steel fibers and the VHSC matrix. These findings using the modified round panel method are consistent with findings in Chapter 7. 73 5.5.3 Effects of matrix strength level The crack opening resistance of the various FRC panels is summarized in Table 5.4, looking at the CMMOD values of 0.5,5,10 and 20 mm. At relatively large CCMOD values (greater than 5 mm), the higher the matrix strength level, the less the crack resistance of the FRC panel. The overall energy absorption capacity (toughness) of VHS-FRC at large deflections, which will be discussed in Chapter 7, supports the findings by this modified test method. However, at smaller deflections, the matrix strength still appeared to contribute to the initial performance of the VHS-RC panels. 74 30 NS-PP0.5 0 5 10 15 20 CCMOD (mm) Figure 5.8 Comparison of synthetic fibers in NSC matrix (PP, PPN and HPP fibers) 0 5 10 15 20 CCMOD (mm) Figure 5.9 Crack opening resistance of HS-FRC panels 75 CCMOD (mm) Figure 5.10 Crack opening resistance of VHS-FRC panels Table 5.4 Effect of matrix strength level on crack-opening resistance CCMOD (mm) 0.5 5 10 2 0 Fiber volume (%) 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 NS-SFRC 16.21 17.93 9.55 12.52 7.25 8.51 3.73 4.87 HS-SFRC 14.68 22.91 4.17 13.71 2.43 9.83 1.21 3.39 Resid load fl VHS-SFRC 14.02 15.62 1.56 3.30 0.52 1.65 0.10 0.26 Resid load fl NS-PPFRC 5.12 11.22 5.91 12.21 5.12 9.99 3.39 5.91 Resid load fl VHS-PPFRC 8.69 16.78 5.74 8.70 3.04 4.60 1.48 2.34 5.6 Conclusions (1) The proposed modified RDP method is capable of characterizing the overall crack-opening resistance with reasonable accuracy. (2) The method is not sensitive for evaluation of the crack widths up to the peak load. (3) Steel fibers are less effective than synthetic fibers for crack resistance at large CCMOD values. (4) Of the tested synthetic fibers, the PP structural fibers exhibit better performance than the others. (5) The matrix strength level had a negative effect for both SFRC panels and PPFRC panels in terms of crack control due to the matrix brittleness and the very good fiber-matrix bond. 76 CHAPTER 6 FEASIBILITY STUDY ON IMPACT TESTS USING ROUND DETERMINATE PANELS 6.1 Introduction ASTM C1550, for the flexural toughness of FRC provides many advantages (as described in Chapter 2) compared with beam and other plate tests. These favorable results under static loading were sufficiently promising to warrant a further study to determine whether this method would have similar advantages in characterizing the performance of FRC under impact loading. In this Chapter, the feasibility of the RDP test method itself is explored, and the method is used to evaluate the effectiveness of fibers in HSC matrices under impact loading. Since RDP specimens are capable of accommodating welded wire mesh (WWM), a common reinforcement for slab-on-grade and shotcrete, WWM reinforced panels were also studied. The detailed program is shown in Table 3.6. 6.2 Analysis -True load and inertial load removal In the static tests, the recorded load from load cell was used directly in the analysis. For the impact tests, however, the load cell reading was corrected to take into account the inertial load (i.e., that portion of the total load involved in accelerating the plate from rest). The inertial load component was approximated by using the principle of virtual work, and then subtracted from the total load recorded by the load cell, in order to obtain the true load involved in deflecting the specimen. A generalized inertial load at the centre of the specimen, Pi(t), can be obtained by using the principle of virtual work. Previous research carried out on beam specimens [45] 77 showed that the distribution of acceleration along the beam length was essentially linear for both FRC and plain concrete. For the round panel system, it was also assumed that the acceleration distribution was linear between the supports and the center of the panel. No data were available for the acceleration distribution along the shaded arc shown in Fig. 6.1. Thus, to simplify the computations, it was assumed as a first approximation that the acceleration u(r, 9, t) was constant along the arc, which means that the distribution of ii can be written simply as u(r, t). The failure pattern observed under impact loading generally consisted of three symmetrical cracks, at angles of about 120 degrees. Thus, one may consider one segment of the panel for analysis using the coordinates shown in Fig. 6.1. Figure 6.1 Schematic descriptions for round panel analysis The internal load dl, for a 1/3 panel segment with width dx, with an acceleration u(x, t) distributed on the arc shaped area is given by: dl = u(x,t) p dV = u(x,t) {p (2TIX f ) dx }/3 ... (6-1) u(x,t) = u(o,t) (R-a-x)/(R-a) = 2 {(R-a-x)/(R-2a)}* u(R/2,t) ... (6-2) where, p = density of concrete, dV = volume of the segment, t, = thickness of panel R = radius of panel, a = length of overhang ii (0, t) = acceleration at the center 78 u(R/2, t) = measured acceleration of the panel at half of the radius along the support to the centre, at time t. The virtual work done by the distributed inertial load acting over the distributed virtual displacement should be equal to that done by the generalized inertial load. Pi (t) 8u (0, t) = 3 J > . Su(JC, t) - (6"3) where, due to the linear assumption, the virtual displacement of the selected segment 5u(x, t) and the virtual displacement at the center 5u (0, t) have the following relationship: 8u(x,t) = 8u(0, t) • (R-a-x)/(R-a) ...(6-4) Substituting Eqs. (6-1), (6-2) and (6-4) into Eq. (6-3), we have Pi (t) = 3 ^ {(R-a-x)/(R-a)} {2 (R-a-x)/(R-2a) u(R/2, t)} • {p (2TIX td ) dx}/3 = —An'ld-P u{RI2,t)- f(R-a-x)2xax (R-a)(R-2a) * 3(R-a)(R-2a) Once the generalized inertial load Pi (t) is calculated, the true load Ptrue(t) can be determined: Ptrue(t) = Ptota.(t)-Pi(t) ...(6-6) where, Pt0tai(t) = the total load recorded by the bolt load cell. 6.3 F i b e r r e i n f o r c e d c o n c r e t e RDP u n d e r i m p a c t l o a d i n g 6.3.1 F a i l u r e m o d e s When the panels were subjected to impact loading, a similar failure pattern was observed compared to static tests of FRC panels (Section 4.3.2). However, the three cracks seemed 79 to be more irregular and less evenly distributed. Typical failure modes of FRC panels were shown in Fig. 6.2. The FRC panels showed a much more "ductile" behavior compared with plain high strength concrete panels, as evidenced by the durations of the impact events and the cracked conditions of specimens after test. The entire impact event duration for plain concrete panels was only about 0.005 seconds. However, it increased from 0.045 seconds for SFRCO.5% to 0.060 seconds for SFRC 1.0%; and similarly, from 0.0475 seconds to 0.055 seconds for PPNFRC 0.5% and 1.0%, respectively. (a) Plain 3"' • ' ;3 it I" ! « • • - ™ „ (b) SFRCO.5% (c) SFRC 1.0% (d) PPNFRC0.5% (e) PPNFRC 1.0% Figure 6.2 Plain and FRC panels after impact test (plain panel drop height 120mm, others drop height 150mm) 80 6.3.2 Load capacity and energy absorption The load-deflection curves for SFRC panels and PPN-FRC panels are shown in Figs. 6.3 and 6.4, respectively. Because of the low flexural toughness of the plain concrete panels under static loading and the large weight of the hammer (about 578 kg), the drop height for the plain concrete specimens was set at 120 mm, in order to avoid catastrophic failure (instead of 150 mm drop height for other specimens). Although there are some differences in toughness due to these different drop heights, this should not significantly affect the comparisons between FRC panels and plain HSC panels. As expected, the peak load of the round panels under impact loading increased. The average peak loads under impact ranged from 50.74 to 55.53 kN (after the inertial effect had been considered), approximately 2.2 to 2.7 times those obtained from static tests (Table 6.1). The synthetic fiber reinforced concrete (PPNFRC) panels appeared to have a slightly lower peak load than the SFRC panels. The inertial effect at peak load was about 10% of the recorded load. Deflection (mm) Figure 6.3 Load-deflection curves of SFRC panels under impact loading 81 60 0 10 20 30 40 50 60 Deflection (mm) Figure 6.4 Load-deflection curves of PPNFRC panels under impact loading Table 6.1 Peak load of concrete panels under static and impact loading (FRC) Description Plain SFRC PPNFRC Fiber volume, % 0 SF 0.5 SF 1.0 PPN 0.5 PPN 1.0 Peak load, Static 20.21 22.81 24.33 22.29 23.12 kN Impact 46.25 45.52 53.15 49.55 50.09 From the load vs. deflection curves of the SFRC panels (Fig. 6.3), it may be seen that for SFRC0.5 under impact, the curve was very similar to that for static loading up to a central deflection of 4 mm; beyond that point, the impact curve displayed a series of fluctuations, showing that some combination of matrix cracking and fiber pull-out was occurring, at least out to a deflection of 20 mm. This phenomenon is quite similar to the findings of Sukontasukkul et al. [122] for simply supported FRC plates under impact loading; they explained the multi-peak phenomenon as a continuous process with the overlap of successive cycles of fiber behavior (fiber bridging, stretching, then strength recovery until the subsequent peak), For the SFRC 1.0 panel, a clear second peak was observed at a deflection of about 1.8 mm, an indication of the increased peak-load carrying capacity. For the PPN-FRC panels (Fig. 6.4), the specimens exhibited a much larger drop in load at low deflections; at larger deflections, the loads fluctuated considerably, suggesting again the combination of fiber pullout, fiber fracture and matrix cracking. 82 6.3.3 Comparison of toughness of FRC panels under static and impact loading Results of the toughness tests of the various panels under both static and impact loading are summarized in Table 6.2. It may be seen that, for plain concrete and SFRC panels, the toughness under impact was higher than that under static loading. For the PPN-FRC panels, however, the toughness under impact was significantly less than that under static loading, which may be explained by the failure patterns and conditions of the fibers bridging the cracks. It was also found that a relatively larger coefficient of variation (COV) was found for the dynamic tests compared to corresponding static tests. Under the low-velocity impact tests carried out here, more PPN fibers tended to break instead of pulling out. As a consequence, they contributed less to impact resistance. For the SFRC panels, more fibers pulled out under impact loading leading to higher impact resistance. This is similar to the findings of Banthia et al. [124]; from FRC beam tests, they reported a higher toughness for SFRC than for polypropylene fiber reinforced concrete (HPP-FRC) at a relatively low drop height (200 mm to 500 mm), although they also reported a totally different trend for SFRC compared to HPP-FRC at higher stress rates (1000 mm drop). Table 6.2 Toughness of round panels up to 40mm deflection (FRC) Toughness under impact test Toughness under Concrete type static test (J) Drop height (mm) Toughness (J) COV Toughness (J) COV Plain HSC 120 57.1* 0.201 17.8 0.128 SFRC0.5 150 241 0.102 186.5 0.096 SFRC 1.0 150 458.4 0.132 378.5 0.058 PPN-FRC0.5 150 113.0 0.146 198.1 0.125 PPN-FRC 1.0 150 238.4 0.155 321.0 0.075 * Toughness is the entire area under load vs. deflection curve to failure, which was 0.60 mm. 83 6.3.4 Effects of fiber type and volume fraction (Vf) on toughness The effects of fiber volume fraction on toughness under impact loading were also observed for both SFRC and PPN-FRC panels. The results of fracture toughness vs. Vf at a deflection of 40 mm are re-plotted in Fig. 6.5. Similar to the static tests, the toughness of all panels under impact loading increased with an increase in fiber volume. Clearly, steel fibers were more effective than PPN fibers in toughening the high strength concrete at the same Vf, although the difference between these two fiber types was not so large under static loading, especially at low fiber volume fractions. 0 0.5 1 Figure 6.5 Effects of fiber type and volume fraction on panel toughness (at a deflection 40mm) 6.3.5 Summary of dynamic RDP tests: F R C panels 6.3.5.1 Evaluation of test method From the tests reported above, it would appear that the impact tests of the FRC round panels are quite reproducible, and that this method can distinguish amongst different types of concrete: plain, SFRC and PPN-FRC. This suggests that, as a test method, the round panel specimen shows promise to characterize the toughness of FRC under impact loading. However, the following sources of uncertainty still exist: 84 • Assumption of acceleration distribution of the panel for inertial loading calculations may only be an approximatation. • Failure mode: if the specimen does not always crack into three similar pieces, the toughness may vary between specimens. Thus, the failure mode should be checked after each test. • The rubber sheet must be attached properly to the underside of the panel; otherwise, the changes in deflection will be difficult to detect using a laser transducer. • Load-deflection smoothing procedures may lead to some error in toughness calculations. 6.3.5.2 Some findings based on FRC panel series • Increases in toughness for both SFRC and PPN-FRC panels were observed due to increased fiber volume fractions under both static and impact loading. Steel fibers were more effective than PPN fiber in toughening high strength concrete under low velocity impact loading. • Plain and SFRC panels were tougher under impact than under static loading, while for PPN-FRC panels, the reverse was true, due to more PPN fibers breaking under impact than pulling out. 6.4 Mesh reinforced concrete RDP test In addition to the FRC panels discussed above, WWM reinforced panels were also studied. For comparison, static tests of WWM-RC panels are presented here. 6.4.1 Static test The average load vs. center-point deflection curves for the various specimens loaded statically are shown in Fig. 6.6. The average energy absorption values for these specimens are given in Table 6.3. Each poit represents the average of three specimens. The energy absorption was determined at two center-point deflections 30mm and 40 mm. 85 From these data, it may be seen that, without fibers, the exact position of the WWM with respect to the striking tup did not seem to make much difference, though Mesh type E did perform better at higher deflections. Clearly, the addition of fibers improved the energy absorption of the specimens. However, under static loading, there was no clear differentiation between the two fiber types (see Table 6.2, toughness of FRC panels with same Vf). 3 5 0 10 2 0 3 0 4 0 5 0 Deflection (mm) Figure 6.6 Load vs. central deflection curves for RDPs under static loading (HyRC) Table 6.3 Energy absorp tion (Toughness) of RDPs under static loading (HyRC) Mesh Reinforcement Pattern Fiber Reinforcement Toughness (J) at 40mm T COV Type E No 557 0.038 TypeC No 521 0.071 TypeC +0.5% SF 693 0.086 TypeC +1.0% SF 827 0.130 TypeC +0.5% PPN 662 0.063 TypeC +1.0% PPN 806 0.125 86 6.4.2 Impact tests Drop weight impact tests on companion specimens to those described above were carried out using a drop height of 120mm or 200 mm, giving an impact velocity of about 1.55 -2.0 m/s. Fig. 6.7 shows a comparison of the impact load vs. deflection curves for the two mesh arrangements, without any fibers. Fig. 6.8 gives typical failure modes of mesh panels with and without fibers. It may be seen from Fig. 6.7 that Mesh E (point of impact between the wires) gave both a higher peak load and greater energy absorption than Mesh C (point of impact at the intersection of two wires). This may be because with Mesh C, the crack always ran preferentially along one of the wires, leading to debonding and fracture of some of the perpendicular wires, as shown in Fig. 6.8b. This did not occur with the Mesh E specimens. 20 30 40 Deflection (mm) 50 60 Figure 6.7 Effect of mesh orientation on behavior under impact loading 87 (a) -with fibers (b) -without fibers Figure 6.8 Failure mode of a round panel with Mesh C reinforcement under impact Fig. 6.9 shows the effect of fiber reinforcement on the impact behavior of the round panels reinforced with Mesh C. As expected, the fibers make the system considerably tougher, and the test clearly distinguishes the different behaviors of the two different fiber types and volumes. For instance, the bridging action of the steel fibers may be seen in Fig. 6.10, which again also shows a crack running along one of the wires. The ability of the round panel test to distinguish between fiber types under impact loading is shown in Fig. 6.11, for a drop height of 200mm. Clearly, the two fiber types behave quite differently. The differences between the two fibers may be more clearly seen in Fig. 6.12, which shows the energy absorption (or toughness) of panels reinforced with the two types of fibers. At a deflection of about 45mm, there is a transition between synthetic fiber specimens and the steel fiber specimens. Drop height 120 mm Mesh C + SF 1.0% 0 10 20 30 40 50 Def lect ion (mm) Figure 6.9 Effect of fiber additions on impact behavior of wire Mesh C-reinforced round panels Figure 6.10 Failure of a round panel with Mesh C reinforcement and 0.5% steel fibers under impact loading Interestingly, from a drop height of 120mm, while the other specimens were severely damaged, the continuous welded wire mesh with 1.0% steel fibers did hold the round panels together and led to relatively small deflections (11.8 mm), shown in Fig. 6.9. This means that the drop height was small compared to the resistance of panel. The residual performance, i.e. post-impact static load carrying capacity of these damaged panels could be obtained by testing statically. This would be helpful to determine degrees of damage 89 during the impact test. Damage evolution of the mesh reinforced panels is described in Chapter 11. 20 30 40 Deflection (mm) 50 60 Figure 6.11 Effect of fiber type on the impact behavior of round panels containing Type C Mesh 1 0.9 0.8 -> 0.7 w 0.6 il) 0) c 0.5 JZ 0.4 at 3 O 1- 0.3 0.2 0.1 0 Mesh C+0.5SF •Mesh C+PPN0.5 20 30 40 Deflection (mm) 50 60 Figure 6.12 Energy absorption (toughness) of round panels under impact loading 6.5 Summary of dynamic RDP tests: WWM-RC panels 6.5.1 Test method evaluation for WWM-RC panels • Quite similar to that of FRC panel, the failure mode for mesh reinforced panel is three radial cracks; 90 • This test is capable of distinguishing mesh orientation and • Secondary reinforcement for mesh reinforced panels show beneficial effect of hybrid reinforcement. 6.5.2 Primary results from Mesh-RC panel series • The combination of fibers and welded wire mesh clearly improves the load carrying capacity of round panel specimens under both static and impact loading; • The precise orientation of the wire mesh with respect to the point of impact appears to have relatively little effect on the results of peak load, but Mesh E appeared to show a better toughening effect; • In the presence of mesh reinforcement, the round panel test appeared to discriminate amongst different fiber types and volumes better under impact loading than under static loading. 6.6 Conclusions (1) The dynamic RDP test setup proposed in this Chapter is feasible to investigating FRC, and Mesh-RC panels in terms of failure mode, load and deflection, giving a good indication of residual performance of these types of reinforcement under impact loading. (2) Systematic research on both the concrete matrix effect and the loading rate needs to be carried out for FRC and Mesh-Reinforced panels. (3) Orientation of welded wire mesh should be controlled consistently for further study. Damage evolution could be further studied by using post-impact static loading. In addition, more systematic experimental work is needed, using different concrete matrices and/or different fibers, under various loading rates, to further validate the suitability of the RDP test under impact loading. These studies were presented in the following Chapters. 91 CHAPTER 7 EFFECTS OF FIBER AND MATRIX STRENGTH ON BEHAVIOR OF ROUND FRC PANELS 7.1 Introduction The objectives in this Chapter are to examine the mechanical behavior of very high strength concrete (high performance matrix) with both steel and synthetic fibers using the RDP method under both static and impact loading, and to study the strain-rate sensitivity of FRC due to variation of concrete matrix strength in terms of loading capacity and energy absorption. The detailed mix proportions and program are shown in Tables 3.2 and 3.7. 7.2 Results Load vs. deflection curves of NS-FRC and VHS-FRC panels are shown in Fig. 7.1 for static loading and in Figs. 7.2 and 7.3 under impact loading. Energy absorption, (i.e., toughness) was calculated by determining the area under the corrected load-deflection curves out to central deflections of 20 mm, 30 mm and 40 mm. Table 7.1 shows the toughness, peak load values and loading rates for impact loading, while Table 7.2 illustrates the comparison of static and impact loading. Deflection (mm) Deflection (mm) (a) NS-SFRC and NS-PPFRC ( b ) VHS-SFRCO.5 and VHS-PPFRC Figure 7.1 Load vs. deflection curves of FRC panels under static loading 92 60 50 40 30 20 10 0 NS-SFRC05-150 NS-SFRC05-300 NS-SFRC05-500 -—" =1 . 10 20 30 Deflection (mm) (a) NS-SFRC0.5 40 40 Z •a n o 100 90 80 70 60 50 40 30 20 10 0 I 10 20 30 Deflection (mm) (b) NS-SFRC 1.0 ure 7.2 Load vs. deflection curves of SFRC panels 10 20 30 Deflection (mm) (c) VHS-SFRCO.5 40 VHS-SFRC10-150 VHS-SFRC10-300 VHS-SFRC10-500 -0 10 20 30 Deflection (mm) (d) VHS-SFRC1.0 under impact loading 40 60 50 40 30 20 10 0 NS-PPFRC05-150 NS-PPFRC05-300 NS-PPFRC05-500 10 20 30 Deflection (mm) (a) NS-PPFRC0.5 40 70 60 ^ 5 0 Z £ . 4 0 •o § 3 0 _i 20 10 VHS-PPFRC05-150 VHS-PPFRC05-300 VHS-PPFRC05-500 M 10 20 Deflection (mm) (c) VHS-PPFRC0.5 30 93 NS-PPFRC10-150 NS-PPFRC10-300 NS-PPFRC10-500 10 20 30 Deflection (mm) (b) NS-PPFRC1.0 40 VHS-PPFRC10-150 VHS-PPFRC10-300 VHS-PPFRC10-500 10 20 30 Deflection (mm) (d) VHS-PPFRC 1.0 40 Figure 7.3 Load vs. deflection curves of PPFRC panels under impact loading 7 .3 Effects of matrix strength and fibers 7 . 3 . 1 Static loading From the static results (Fig. 7.1 and Table 7.2), in general, all VHS-FRC panels showed much more brittle behavior than NS-FRC. It was found there was no significant difference between the load carrying capacity of SFRC and PPFRC panels with NSC as matrix. However, the SFRC panels appeared to be able to carry a higher load than the PPFRC panels; this is particularly true for Vf =1.0%. There was no significant improvement of peak load due to increasing the fiber volume from 0.5% to 1.0%, except for VHS-SFRC panels. The toughness of the FRC panels tested in this program reveals an interesting trend. In general, it was found that toughness increased by a factor of about 1.7 for NS-FRC and about 2 for VHS-FRC due to the inclusion of fibers when the fiber volume fraction increased from 0.5% to 1.0%. In the NSC matrix, steel fibers showed a greater toughening effect than the PP fibers, while the opposite results were found in the VHSC matrix. These findings may relate to the compatibility between fibers and matrix. Both types of fiber tended to break in the VHSC matrix rather than pull out, leading to much more brittle performance. 94 7.3.2 Impact loading Not surprisingly, high strength concrete FRC panels yielded higher peak loads than normal strength FRC when using the same type and amount of fibers. There was a clear tendency for the peak load to increase with increasing fiber volume, particularly for the 500 mm drop height. PP fibers appeared to be less effective in strengthening the panel than steel fibers for both NSC and VHSC matrices. In terms of toughness, in general, NS-FRC panels had much greater toughness than VHS-FRC panels; steel fibers showed better toughening effects than PP fibers. Specifically, for VHS-PPFRC, even lower toughness values were observed than for the NS-PPFRC panels. Matrix types seemed to play a very significant role in this program. The toughness of VHS-PPFRC 1.0 panels was quite similar to that of NS-PPFRC0.5 panels, and VHS-SFRC1.0 showed much lower toughness than the NS-PPFRC0.5 under the same drop height (e.g. 500mm in Table 7.1). This could be explained by the fact that the very high strength concrete matrix provided much better bonding, leading to a much shorter critical lengths for fibers. Related to the above findings, it may be seen that while the PP fibers were quite effective in the NSC matrix, they had almost no effect in the VHSC in terms of toughness improvement. This can be explained by the features of PP fibers. PP fibers have a relatively low elastic modulus and tensile strength. Improved bonding between the PP fibers and the VHSC matrix led most of PP fibers to fracture during impact loading. A visual examination of the fracture surfaces revealed that the fibers failed primarily by breaking; very few cases of fiber pullout were observed. This result was in accordance with a previous study on beam impact tests in which a marked increase of both flexural strength and fracture toughness was observed in a low strength (fc'=20-25MPa) matrix containing up to 0.5% fibers (19 mm long fibrillated fiber mesh) [139] and 40MPa concrete with 1.0% crimped polypropylene fibers (30mm long HPP fiber) [124]. Clearly, 95 in order to realize the full potential of PP fibers in improving impact resistance, it would be necessary to use a compatible concrete matrix. In other words, the current PP fibers do not work very well in a very high strength matrix. 7.4 Inertial load and effect of loading rate (drop height) on peak load In general, the true peak load (i.e., the tup load corrected for the inertial effect) of both SFRC and PPFRC panels increased with an increase in drop height. These results are consistent with other findings on conventional concrete beams under drop-weight impact loading [124]. Since the stress-strain relationship for this test setup with these boundary conditions is complicated, with no analytical solution available, numerical methods must be used to provide a stress and strain analysis for the centrally-loaded round panel. Thus, for simplicity, loading rate rather than stress rate is employed for further discussion here. The loading rate, defined here as the average rate of loading from initial load up to true peak load, showed an increase with increasing drop height. Most of the FRC panels (with 1.0% fibers) showed a marked increase in peak load from the drop height of 300 mm to that of 500 mm. The point of greater interest for this work, however, is the influence of loading rate on the energy absorption capacity or fracture toughness of the panels. It was found that the removed inertial load at peak load for NS-SFRC1.0 account for typically about 20.7% of the recorded Tup load, and about 32.4 % for NS-PPFRC0.5 at 500 mm drop. Under the same drop height, much higher inertial load at peak load was reported from previous beam test [45]. For normal strength FRC (fc'=50MPa, similar to the compressive strength in the current program), as high as 39.5% and 56.9% for FRC with 1.5% steel fibers and 0.5% polypropylene fibers respectively; in the same study, similarly, 40.8% and 51.2% for high strength FRC (fc'=82MPa) with 1.5% steel fibers and 0.5% polypropylene fibers. Therefore one may conclude that, besides the advantage of imposing a large deflection, plate impact test also create lower inertial load on specimen. 96 Table 7.1 Summary of FRC under impact loading (NS and VHS-FRC) Concrete type Drop height (mm) Time to peak (ms) Loading rate (kN/ms) True Peak load (kN) Toughness (J) 20mm 30mm 40mm NS-SFRC0.5 150 1.17 43.1 50.4 283.7 363.2 420.4 300 0.84 64.3 54.0 301.9 378.1 436.9 500 0.73 72.2 54.9 288.2 366.3 429.2 NS-SFRC1.0 150 1.16 40.1 48.9 312.2 401.1 468.2 300 1.22 44.4 54.2 443.4 582.0 686.2 500 0.68 99.7 67.8 532.1 657.4 766.1 NS-PPFRC0.5 150 1.26 30.7 38.7 127.7 154.1 171.1 300 0.74 51.6 38.2 118.6 129.3 500 0.79 69.1 54.6 132.0 138.8 143.3 NS-PPFRC1.0 150 1.44 31.8 45.8 194.5 219.3 224.8 300 0.85 65.8 55.9 211.9 253.9 266.4 500 0.78 67.3 52.5 260.0 311.9 338.0 VHS-PPFRC0.5 150 1.13 49.5 55.9 81.0 83.0 300 0.85 54.4 46.2 58.8 — 500 0.55 108.2 59.5 62.3 VHS-PPFRC 1.0 150 1.08 47.9 51.7 135.3 145.2 147.2 300 0.65 88.0 57.2 125.9 136.0 500 0.64 93.7 60.0 152.4 155.0 VHS-SFRC0.5 150 0.99 70.1 69.4 156.8 166.6 175.5 300 0.87 86.4 75.2 156.3 165.7 500 0.62 130.3 80.8 182.4 190.7 193.7 VHS-SFRC1.0 150 1.02 72.9 74.4 216.1 235.9 245.9 300 0.87 98.0 85.3 235.0 250.0 259.6 500 0.88 100.2 88.2 218.9 228.8 234.5 97 Table 7.2 Dynamic increase factors (DIF) (NS and VHS-FRC) Concrete Type Static Tough-ness* (J) Dynamic toughness* DIF of tough-ness Static Peak load (kN) Dynamic Peak load (kN) DIF of peak load Drop Height (mm) Tough-ness (J) NS -SFRC0.5 341.1 150 420.4 1.232 23.9 50.4 2.109 300 436.9 1.281 54.0 2.259 500 429.2 1.258 54.9 2.297 NS -SFRC 1.0 565.8 150 468.2 0.828 26.2 48.9 1.866 300 686.2 1.213 54.2 2.069 500 766.1 1.354 67.8 2.588 NS -PPFRC0.5 253.1 150 171.1 0.676 26.2 38.7 1.477 300 129.3** 0.511 38.2 1.458 500 143.3 0.566 54.6 2.084 NS PPSFRC1.0 448.5 150 224.8 0.501 25.2 45.8 1.817 300 266.4 0.594 55.9 2.218 500 338 0.754 52.5 2.083 VHS -SFRC0.5 120.9 150 175.5 1.452 35.9 69.4 1.933 300 165.7 1.371 75.2 2.095 500 193.7 1.602 80.8 2.251 VHS -SFRC 1.0 285.6 150 245.9 0.861 42.2 74.4 1.763 300 259.6 0.909 85.3 2.021 500 234.5 0.821 88.2 2.090 VHS-PPFRC0.5 196.5 150 81** 0.412 32.5 45.9 1.412 300 58.8** 0.299 46.2 1.421 500 62.3** 0.317 59.2 1.822 VHS-PPFRC 1.0 408.2 150 147.2 0.361 31.1 51.7 1.662 300 136.0 0.333 57.2 1.839 500 155.0 0.380 60.0 1.929 *Area under load-deflection curve out to 40mm, ** overall toughness 7.5 Effect of loading rate (drop height) on energy absorption The toughnesses at central deflections of 20, 30 and 40mm are listed in Table 7.1. For the normal strength SFRC panels, toughness increased with increasing drop height, except for NS-SFRC0.5 at 500 mm drop where a slight decrease was found. The toughness out to 40 mm central deflection is higher than that under static loading. 98 However, for VHS-SFRC panels, toughness results revealed no significant improvement with increasing drop height. The total toughness under large drop heights was quite similar to that under a very low drop height (150 mm). These toughness data imply that, in terms of toughness, steel fibers were not sensitive to loading rate and the presence of macro steel fibers in VHSC matrix did not help to improve toughness effectively compared to that in NS-SFRC panels. For NS-PPFRC panels, toughnesses increased with increasing drop heights when the volume of the PP fibers reached 1.0%, but remained lower than the static toughness (roughly 50-75% of static values). In general, marginal increases were observed for VHS-PPFRC panels with increasing drop height for relatively high Vf (1.0%); a slight decrease was noted for panels with low Vf (0.5%). Once again, the overall dynamic toughnesses were less than the values observed under static loading (roughly only 30%-40%). This goes against the prevalent belief that synthetic fibers performed better in impact, particularly under higher drop height. The exact reason for the reduced dynamic toughness compared to static toughness was not clear. It might relate to the relatively poor bonding in NSC matrix, low fiber tensile strength and "very good bonding" in the VHSC matrix. 7.6 Effects of matrix strength and fibers on strain rate sensitivity The ratios of the impact peak loads and toughnesses to their static values, which are referred to as dynamic increase factors (DIF), were calculated to evaluate the strain rate sensitivity of the materials; they are shown in Table 7.2. For comparison, they are reproduced in Figs. 7.4 and 7.5. 99 1150 mm SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 Figure 7.4 DIF of peak load of FRC panels (NS and VHS-FRC) NS- NS- NS- NS- VHS- VHS- VHS- VS-SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 Figure 7.5 DIF of Toughness of FRC panels (NS and VHS-FRC) In terms of peak load, high DIF values revealed that NS-SFRC was more strain rate sensitive than NS-PPFRC. This was also true for VHS-SFRC and VHS-PPFRC in this program. These findings are in accordance with a previous study using beam impact tests [124] in which plain concrete appeared to be more sensitive to stress rate than steel fiber FRC or crimped polypropylene FRC. 100 Also as expected, when the matrix strength increased to the VHSC level, the VSH-FRC appeared to be somewhat less strain rate sensitive than NS-FRC. When the DIF of dynamic toughness was compared between NS-SFRC and VHS-SFRC, it was found the VHS-SFRC with low Vf (0.5%) was more strain-rate sensitive. However, 1.0% VHS-SFRC showed the opposite trend. Note that substantially low DIF values of PPFRC, both in NSC and VHSC matrices were observed in this program. The reasons for this are not clear. 7.7 Conclusions (1) The suitability of RDP impact method was further validated by NS-FRC and VHS-FRC panels. A lower inertial load correction was found for RDP method than that for beam impact test method. (2) Fibers exhibited better performance in toughening normal strength concrete than very high strength under static loading; this was also true under impact loading, particularly for PPFRC. (3) Compared to steel fibers, PP fibers appeared less effective in improving the toughness of very high strength concrete. (4) The higher matrix strength rendered VHS-FRC less strain-rate sensitive in terms of peak load, but the effect of matrix strength is unclear in terms of dynamic toughness. 101 CHAPTER 8 EFFECTS OF POLYMERS ON STEEL FIBER REINFORCED ROUND CONCRETE PANELS UNDER IMPACT LOADING 8.1 Introduction Polymer modification is another effective approach for improving the performance of cementitious materials. There is a renewed interest in polymer modified, fiber reinforced concrete (PM-FRC), because of the potential high performance contributed by both the fibers and the polymer, in particular the potential high resistance to severe dynamic loading (cyclic and impact). However, very little research has been carried out on the impact resistance of concrete containing both polymers and fibers using the RDP tests. The objectives in this Chapter are to investigate the mechanical behavior of high strength concrete panels with steel fibers and latex modification under both static and impact loading, and to study the strain-rate sensitivity of FRC due to polymer inclusion in terms of loading capacity and energy absorption. The mix proportions and detailed program can be found in Tables 3.2 and 3.7. Four different FRC concrete mixes (HSC matrices and HSC-PMC10 matrix) were studied. Only deformed steel fibers were employed in this program. Elastic modulus and compressive strength of the corresponding mixes were shown in Appendix C-l and C-2. 8.2 Results and discussion 8.2.1 Flexural strength and toughness Representative load vs. deflection curves of the HS-SFRC and PM-SFRC panels are shown in Fig. 8.1 for impact loading. The corresponding static results are shown in Figs. 4.4 and 4.6. Toughness was calculated by determining the area under these load-deflection curves out to central deflections of 20 mm, 30 mm and 40 mm. Table 8.1 shows the toughness and peak load values. 102 60 50 £ - 4 0 30 n o —• 20 10 0 -SFRCO.5-150 -SFRCO.5-300 10 20 30 Deflection (mm) (a) SFRC0.5 40 50 10 20 30 40 Deflection (mm) (c) PM-SFRC0.5 50 70 "j 60 50 z 40 •a n 30 o _i 20 10 0 -PMSFO.5-150 -PMSFO.5-300 -PMSFO.5-500 90 80 70 z 60 50 •D n 40 o - I 30 20 10 0 PMSF1.0-150 PMSF1.0-300 PMSF1.0-500 i i i I 10 20 30 40 Deflection (mm) (b) SFRC 1.0 50 10 20 30 40 Deflection (mm) (d) PM-SFRC1.0 50 Figure 8.1 Load vs. deflection curves of SFRC and PM-SFRC panels under impact loading 8.2.1.1 Effects of polymer and fibers Not surprisingly, fibers enhanced the energy absorption capacity (toughness) and peak load under static loading. It was found that toughness increased by a factor of about two due to the inclusion of fibers in the SFRC and PMC matrices when the fiber volume fraction increased from 0.5% to 1.0%. However, the load carrying capacity was improved only slightly. The strengthening effect of fibers was relatively more significant in the presence of the 10% polymer dosage. Compared to the SFRC composites, 10% polymer addition further toughened the SFRC panels remarkably. This result is consistent with that observed in beam tests described out in Chapter 4 103 (Table 4.1). Fiber pullout and crack-bridging mechanisms can be used to explain the toughening function of fibers and polymers even though the compressive strength was slightly reduced (Appendix C-l & C-2). Under impact loading, fibers are the dominant factor controlling the performance of the composites. For the same drop height, the greater the volume of fibers, the greater the impact resistance. The polymer had a more complicated influence on impact resistance. Specifically, under low drop height impact (150mm), the improvement of toughness of SFRC panels due to polymer modification was not significant. However, at higher drop heights, PM-FRC, in particular with 1.0% fibers, showed a better impact resistance than its FRC counterpart. Therefore, the polymer appears to be more effective in mixes with high fiber volumes and for more severe impact loading conditions. Table 8.1 Summary of PM-SFRC behavior under impact loading Concrete type Drop height (mm) Time to peak (ms) Loading rate (kN/ms) True Peak load (kN) Toughness (J) 20mm 30mm 40mm SFRC0.5 150 1.02 41.12 45.52 213.8 235.2 240.9 300 1.00 48.45 48.45 176.3 201.0 228.0 SFRC 1.0 150 1.16 45.82 53.15 364.2 423.4 458.4 300 0.88 65.75 57.86 141.1 162.0 173.8 PM-SFRC0.5 150 1.07 53.21 56.94 231.0 273.7 302.1 300 0.84 64.74 54.38 222.7 255.1 275.2 500 0.38 152.79 58.06 318.1 363.5 393.5 PM-SFRC 1.0 150 1.22 45.75 55.82 330.4 386.7 421.8 300 0.94 73.56 69.15 393.4 453.7 478.1 500 0.82 96.48 79.11 448.3 524.3 565.6 8.2.1.2 Effect of drop height on peak load In general, the true peak load (i.e., the tup load corrected for the inertial effect) of both SFRC and PM-SFRC panels increased with an increase of drop height, except for the PM-SFRC0.5 under the 300mm drop, which showed a slight decrease. These results are consistent with other findings on conventional concrete beams and cylinder under drop-weight impact loading [124]. 104 Since the stress-strain relationship for this test setup with these boundary conditions is complicated, with no analytical solution available, numerical methods must be used to provide a stress and strain analysis for the centrally-loaded round panel. Thus, for simplicity, loading rate rather than stress rate is employed for further discussion here. The loading rate, defined here as the average rate of loading from initial load up to true peak load, showed an increase with increasing drop height, reaching levels up to 9.65xl04 ~ 1.52 x 105 kN/s for PM-FRC under the drop height of 500 mm (Table 8.1). 8.2.1.3 Effect of drop height on energy absorption The toughnesses at central deflections of 20, 30 and 40mm are listed in Table 8.1. Overall, toughness improvement due to SBR latex was less significant under impact loading than that under static loading (Table 8.2: column 2 and 4). For the SFRC panels, toughness decreased with increasing drop height. These results imply that the energy associated with a 150 mm drop height is sufficient to damage the panel. More energy (higher drop heights) shifts the mode of failure of the fibers from primarily fiber pullout to primarily fiber fracture, leading to a decrease in energy absorption at higher loading rates (or drop heights). Contrary to the behaviour of the SFRC panels, the toughness of the PM-SFRC panels tended to increase somewhat with increasing drop height, even though the overall toughness for the 500mm drop was either still less (PM-SFRC 1.0-500mm) or only slightly higher (PM-SFRC0.5-500mm) than the values observed under static loading. There thus appears to be a tendency for the polymer inclusions, because of their visco-elastic nature, to increase the dynamic toughness of the concrete at increasing loading rates, eventually surpassing the performance of these particular steel fibers. It might be expected that under still higher drop heights the dynamic toughness would eventually surpass the static toughness. 8.2.2 Effects of polymer and fibers on strain sensitivity The ratios of the impact peak loads and toughnesses to their static values, which are referred to 105 as dynamic impact factors (DIF), were calculated to evaluate the strain rate sensitivity of the materials; they are shown in Table 8.2. For comparison, these DIF values are plotted in Figs. 8.2 and 8.3. Table 8.2 Dynamic increase factors (DIF) of FRC and ] PM-FRC Concrete Type Static Tough -ness* (J) Dynamic Toughness* DIF of tough-ness Static Peak load (kN) Dynamic Peak load (kN) DIF of Peak load Drop Height (mm) Tough-ness (J) SFRC0.5 186.5 150 240.9 1.292 22.81 45.52 1.996 300 228.0 1.223 48.45 2.124 SFRC 1.0 378.5 150 458.4 1.211 24.33 53.15 2.185 300 173.8 0.459 57.86 2.378 PM-SFRC0.5 349.9 150 302.1 0.863 24.59 56.94 2.316 300 275.2 0.787 54.38 2.212 500 393.5 1.125 58.06 2.361 PM-SFRC 1.0 620.7 150 421.8 0.680 31.32 55.82 1.782 300 478.1 0.771 69.15 2.208 500 565.6 0.911 79.11 2.525 *Area under load-deflection curve out to 40mm. SFRC0.5 SFRC1.0 PM-SFRC0.5 PM-SFRC1.0 Figure 8.2 DIF of peak load of FRC and PM-FRC 106 1.4 SFRC0.5 SFRC1.0 PM-SFRC0.5 PM-SFRC1.0 Figure 8.3 DIF of toughness of FRC and PM-FRC It was found that there seemed to be no significant differences between SFRC and PM-FRC in terms of peak loads. In terms of dynamic toughness, in general, PM-SFRC is somewhat less strain-rate sensitive than SFRC. While SFRC is more strain sensitive at low drop heights, PM-SFRC is more rate sensitive at high drop heights. This finding is consistent with the study on PM-FRC with similar compressive strength under uniaxial impact loading (Chapter 9). 8.3 Conclusions (1) Compressive strength and elastic modulus tended to decrease slightly due to the addition of 10% of polymer SBR. (2) The round panel test gave quite similar results to previous beam tests, in that the combination of polymer and steel fibers resulted in higher load capacity and toughness than for SFRC alone. (3) Improvement of toughness of SFRC due to SBR latex was less significant under impact loading than that under static loading. (4) Polymer addition rendered SFRC less strain rate sensitive in terms of dynamic toughness, but did not particularly affect the strain rate sensitivity in terms of peak load. 107 CHAPTER 9 IMPACT PERFORMANCE OF LATEX-MODIFIED HIGH STRENGTH FRC UNDER UNIAXIAL COMPRESSIVE LOADING 9.1 Introduction Though it is widely accepted that, the contribution of the fibers in fiber reinforced concrete (FRC) under compression is less significant than their contribution under tension or flexure; and concrete is more strain rate sensitive in tension and in flexure than in compression [140], previous study on normal strength FRC prisms with either steel fibers or polypropylene fibers, has indicated that fiber content and geometry could still have a significant effect on toughening the concrete under uniaxial compressive loading [46]. However there is little, if any, research on strain rate effects in high strength PMC and PM-FRC. To further understand the material performance of PM-FRC described in Chapter 8, the response of PM-FRC to uniaxial compressive loading both static and impact loading was studied here, including the strain rate effects on the material. A summary of the test program is shown in Table 3.10. 9.2 Results and discussion 9.2.1 Static loading The compressive strengths of the PMC specimens subjected to static loading are listed in Table 9.1. These results indicate that at the same water-cement ratio the compressive strength decreases with latex additions. At polymer-cementitious materials ratios greater than 10%, this trend becomes particularly clear. This is due to the fact that the latex film itself has a low compressive strength, as well as a low stiffness relative to the cement paste and aggregate [141]. When the polymer-cementitious materials ratio is 15% or more, this dosage is sufficient for the polymer to form a continuous phase with a lower elastic modulus. When the concrete is under load, the differences of the deformation of 108 this extra "soft" phase (cement paste with polymer) and other components may lead to high stress concentrations, even though the bonding may be improved at the interface. Consequently, a significant decrease in the compressive strength will occur, even when enough antifoam agent is used. When steel fibers were incorporated, the compressive strength increased somewhat. The compressive strengths of PMC, FRC and PM-FRC ranged from 65 MPa to 94 MPa. Over all, however, the polymer content played the most important role in determining compressive strength. On the other hand, the compressive toughness as for the different PMCs and PM-FRCs were quite different (column 3 of Table 9.2). It can be concluded that the compressive toughness increases with the polymer dosage, though the increase is not very large, which is similar to the tendency for toughness improvement under static flexural loading [94]. However, fibers were more effective in increasing the toughness, by about two to four times compared to PMC and plain concrete, depending on the volume fraction of the included fibers. These findings are also consistent with the failure modes of the specimens. The different types of concrete tested in this study displayed different crack modes and failure patterns. PMCs broke in a sudden and brittle manner, very similar to plain concrete, due to their high strength. The typical concrete "failure cone" can be observed, and some cylinders spalled into many pieces. For the SFRCs, with or without latex, after the peak load, the specimens still retained some residual strength, since the cracks were bridged by the fibers. Table 9.1 Si tatic compressive strength of PM-FRC (MPa) Fiber volume fraction (Vf) % Polymer- cementitious materials ratio, % (by mass) 0 5 10 15 Plain HSC PMC05 PMC 10 PMC 15 0 89.0 85.7 81.6 76.4 0.5 85.0 87.2 74.8 69.9 1.0 88.0 94.3 80.9 66.1 2.0 — — — 71.5 109 9.2.2 Impact loading Representative load-deflection curves of the impact tests are shown in Figs. 9.1, 9.2 and 9.3 for PMC, PM-FRC0.5 and PM-FRC 1.0, respectively. For each type of specimen, the drop heights were 350mm, 700mm and 1200mm. The toughness and dynamic compressive strength of the specimens under impact loading were calculated and are summarized in Table 9.2. 110 I l l Table 9.2 Compressive strength (fc'), Energy absorption and DIF of composites Dynamic Static Tough- Dynamic Static Strength Specimen tough- tough- ness ratio strength strength ratio identification ness ness (DIF) fc' [C] fc' [D] (DIF) [A] (J) [B] (J) [A]/[B] (MPa) (MPa) [C]/[D] PMCO-350 1651.6 518.2 3.187 70.5 73.6 0.958 PMCO-700 2054 3.964 87.3 1.187 PMCO-1200 2080 650.9 3.196 118.6 87 1.363 PMC5-350 1336.3 585.0 2.284 64.7 86.0 0.752 PMC5-700 1859.5 3.179 85.0 0.988 PMC5-1200 2591 734.7 3.526 134.3 84.4 1.591 PMC10-350 1586 657.9 2.411 81.1 80.4 1.010 PMC 10-700 1828 2.779 83.5 1.039 PMC 10-1200 2582 826.3 3.125 139.2 77.7 1.791 PMC 15-350 1370 744.0 1.841 67.6 69.3 0.976 PMC 15-700 1809.3 2.432 72.5 1.047 PMC15-1200 2303 934.5 2.465 128.9 70.0 1.842 SFRC0.5-350 1396 1539.0 0.907 75.6 66.4 1.137 SFRC0.5-700 2344 1.523 77.8 1.171 SFRC0.5-1200 2265 1932.9 1.172 108.9 78.3 1.391 SFRC1.0-350 1586.3 2010.0 0.789 77.8 75.1 1.036 SFRC 1.0-700 3596.7 1.789 85.4 1.136 SFRC1.0-1200 2800.3 2524.5 1.109 121 80.3 1.507 PM5-FRC0.5-350 1666.7 1303.6 1.279 66.9 85.6 0.782 PM5-FRC0.5-700 2481 1.903 68.8 0.803 PM5-FRC0.5-1200 2897 1636.6 1.770 142.9 87.2 1.639 PM10-FRC0.5-350 1347.7 1568.6 0.859 79.3 72.0 1.102 PM10-FRC0.5-700 2510.9 1.601 68.7 0.954 PM10-FRC0.5-1200 2622 1970 1.33 136.4 74.8 1.824 PM15-FRC0.5-350 1713.5 1580.3 1.339 74.7 62.7 1.194 PM15-FRC0.5-700 2360.7 1.844 69.2 1.104 PM15-FRC0.5-1200 2201 1984.9 1.109 120.2 69.9 1.720 PM5-FRC 1.0-350 1297.5 1827.1 0.710 79.3 97.1 0.817 PM5-FRC 1.0-700 3341 1.829 101.9 1.049 PM5-FRC 1.0-1200 3597.3 2294.7 1.568 143.5 97.1 1.478 PM10-FRC1.0-350 1619.6 1778.0 0.911 75.4 63.8 1.083 PM10-FRC1.0-700 3170.6 1.783 80.2 1.258 PM10-FRC 1.0-1200 2965.7 2233.2 1.328 127.3 80.9 1.573 PMI 5-FRC1.0-350 1480.5 1582.0 0.936 73.5 61.9 1.188 PM15-FRC 1.0-700 3582.7 2.264 75.3 1.216 PM15-FRC1.0-1200 2773.0 1987.0 1.396 128.6 66.1 1.946 PM15-FRC2.0-350 1635.3 2159.0 0.757 76.9 68.2 1.128 PM15-FRC2.0-700 3756.6 1.740 125.4 1.839 PM15-FRC2.0-1200 3248.6 2711.7 1.198 96.4 71.5 1.348 9.2.2.1 Effects of drop height From Table 9.2, it may be seen that the strength and toughness values are strongly dependent upon the drop heights. Not surprisingly, the compressive strength increased 112 with the drop height for most cases, with drop heights of 300 and 1200mm. At low drop heights, the energy input was less than that required to completely fail the stronger and tougher specimens with steel fibers. These specimens survived the impact event, and part of the uniaxial deflection was recovered in the form of elastic deformation. That is, the concrete was only partially damaged. Compressive toughness also increased with drop height for PMC and PM-FRC with low volume fractions of steel fibers. However, there seemed to be an optimum drop height for PM-FRC specimens with 1 and 2% of fibers. The compressive toughness values decreased when the drop height increased from 700 to 1200mm. This reduction may be related to the failure mode of the fibers and the increasing brittleness of matrix at higher loading rates, which tend to fracture the fibers instead of pulling them out, thus consuming less energy. 9.2.2.2 Polymer versus. Fiber — PMC versus FRC under impact loading In order to describe the effects of polymers on concrete and FRC, the strength and the toughness under the same impact regimes for the same types of concrete, but containing different polymer-cementitious materials ratio, are shown in Fig.9.4 (a) - (c): strength, and (d) - (f): toughness. From a comparison of the FRC and PMC series, it is clear that the fibers and polymer played different roles in terms of compressive toughness. The maximum toughness of PMC was 1859 J (PMC5) under the 700 mm drop, while the maximum values for FRC were 2344 J (PM0-SF0.5) and 3598 J (PM-SF1.0) under the 700mm drop; however, under the 1200mm drop (Fig. 9. 4(f)), the toughness values of all of the PMC's were higher than that of FRC with 0.5% fibers, but still less than that of FRC with 1.0% fibers. Therefore, we may conclude that, under high rates of impact, SBR latex can toughen concrete to a limited degree, which may achieve the same effect produced by 0.5% of steel fibers; while under lower rates of impact, fibers are much more effective in toughening concrete (Fig. 9. 4(e)). 113 -»-SF0 —SF0.6 -G-SF1.0 -X-SF2.0 PM-FRC under 360mm drop 1800 1600 1400 3200 21000 b BOO 400 PMO PM6 PM10 Polymer. cementitious materials ratio (%) PM1S (a) -•-SF0 0 -•-SF0.6 -6-SF1.0 n i -0-SF2.O - — A • ' ^ PnVFRC under 700mm drop 200 0 4000 SF0 •SF0.5 I-6-SF1.0 SF2.0 PM-FRC under 350mm drop PMO PMS PM10 Polymer- cementitious materials ratio (%) (d) 32500 £2000 S1500 1000 500 PMS PM10 Polymer - cementitious materials ratio (%) PM15 PM-FRC under 700mm drop -SF0 ^SFO.S |-iV-SF1.0 SF2.0 PMO PMS PM10 Polymer • cementitious materials ratio (%) PM15 PMO PMS PM10 Polymer • cementitious materials ratio (%) PM15 PMO PMS PM10 Polymer - cementitious materials ratio (%) PM15 (C) (f) Figure 9.4 Effects of polymer on compressive strength and compressive toughness under 350mm drop— (a) (d); 700mm drop—(b)(e); 1200mm drop—(c)(f) 9.2.2.3 Combination of polymer and fibers The dynamic strength of FRC increases somewhat with increasing polymer-cementitious materials ratio, with a maximum 20% increase under the 1200mm drop, but with no significant effects at lower drop heights. The reasons for this behavior are not clear. Similar to the dynamic strength, the combination of polymer and steel fibers was not effective under the medium impact loading rates (350 and 700mm drop heights). 114 However, this combination was very effective under the 1200mm drop, with an optimum polymer-cementitious materials ratio of 5%. Higher polymer-cementitious materials ratios have been found to have a slightly negative effect on total toughness. This optimum ratio may relate to lower elastic modulus (i.e. its "softer" nature) of polymer compared to hardened cementitious materials; an excessive amount of the polymer phase may render the concrete weaker due to incompatible deformations between different components [92]. At the lowest drop height (350mm), there seems to be no correlation between polymer-cementitious materials ratio and toughness. However, it seems that synergy between fibers and polymer does occur under higher loading rates, i.e., 1200mm impact (Fig. 9.4 (0). 9.3 Effects of polymer on strain rate sensitivity of concrete and FRC The dynamic increase factors (DIF) were calculated to evaluate the strain rate sensitivity of the material. DIF values of strength and toughness are shown in Fig. 9.5. From Figs. 9.5(a), 5(b) and 5(c), it may be seen that both PMC and PM-FRC have similar tendencies of strain-rate sensitivity in terms of dynamic strength. There is a clear transition at the 700 mm drop height, after which the polymer addition made both types of concrete more strain rate sensitive (i.e., higher DIF values were observed). In terms of compressive toughness, it was found that, in general, PMC had a higher DIF (Fig. 9.5(d)) than did FRC and PM-FRC, as may be seen from Figs. 9.5 (e) - (f). This result is in according with previous research [47], which showed that plain concrete appeared to be more strain rate sensitive than FRC in flexure. For PMC without fibers, the DIF of toughness decreased markedly with increasing polymer-cementitious materials ratio, but for the same type of PMC, DIF increased with increasing drop height (Fig. 9.5(d)). In other words, polymer modification makes 115 concrete less strain-rate sensitive in terms of energy absorption. This is helpful in explaining the general strain-rate sensitivity of PM-FRC where PMC serves as a matrix. 0 -1-PMCO -A—PMCS 4 -X-PMC10 -•-PMC16 3 ci 2 D.I.F of Compressive Strength — PMC 1 STATIC STATIC -O-PM0-SF1.0 -6-PM6-SF1.0 -"-PM10-SF1.0 -&-PM15-SF1.0 -O-PM16-SF2.0 D.I.F of Compressive Strength - PM-SF1.0/2.0 2.S 2 1.6 ul a 1 0.5 0 D.I.F. of Compressive Toughness — PMC (d) -e-PM0-SF0.6 ••-PM5-SF0.6 -*-PM10-SF0.6 - A - P M 1 f i . f i Fit fi » rlf l 1 B v r U . o D.I.F. of Compressive Toughness — PM3F0.6 STATIC 360mm 700mm (e) 1200mm -O-PM0-SF1.0 -6-PM5-SF1.0 -•-PM10.SF1.0 -e-PM16^F1.0 -«-PM15^F2.0 D.I.F. of Compressive Toughness — PM-SF1.0/2.0 STATIC 360mm 700mm 1200mm (C) (f) Figure 9.5 Dynamic Increase Factors of Strength and Toughness (a), (b) and (c) for strength, and (d), (e) and (f) for toughness For the PM-FRC series of specimens, the DIF of strength was not much affected by polymer-cementitious materials ratio. Rather, it was controlled by drop height, with a maximum increase for a drop height of 1200mm (Fig. 9.5 (b) and Fig. 9.5(c)). There exist opposite tendencies between the DIF of strength and DIF of toughness, decreasing at a 116 drop height of 1200mm in Fig. 9.5 (e) and Fig. 9.5 (f). This may be explained by the decreased uniaxial strain or deflection, related to fiber failure under high loading rate, as can be verified from the load-deflection curves for the PM-FRC specimens at a drop height of 1200mm, except for PM10-SF1.0 and PM15-SF1.0. Very interestingly, some low DIFs (less than 1.0) were observed. The low DIFs of strength for concretes with less than a polymer-cementitious materials ratio of 5% were most likely due to the relatively higher strengths of these concretes compared to concretes with higher polymer-cementitious materials ratio; the low DIFs of toughness for PM-FRC under the 350mm drop height can be explained by two facts: the relatively low energy absorbed in the impact process due to partially recovered deformation, and the enhanced toughness of the FRC under static loading. 9.4 Conclusions (1) The compressive strength of PMC tends to decrease with an increase in polymer-cementitious materials ratio at the same water-cement ratio. The same tendency was shown by the PM-FRC specimens. (2) Steel fibers have a more significant effect on the compressive toughness than on the strength under static loading. Polymer, however, had a much greater effect on these parameters, and improved the toughness of the plain concrete. (3) Toughness increased with the drop height of the impact hammer for both PMC and PM-FRC, but under the highest drop height, the toughness tended to decrease due to decreased deflection and fiber fracture. (4) Polymer modification makes concrete less strain-rate sensitive in terms of energy absorption, but more strain-rate sensitive in terms of dynamic strength. (5) FRCs with polymer modification are more strain rate sensitive in terms of dynamic strength than those without polymer inclusion. Optimum polymer-cementitious materials ratios (5 -10%) appear to exist in PM-FRC systems in terms of toughness improvement under impact loading. 117 CHAPTER 10 BEHAVIOUR OF CONCRETE PANELS REINFORCED WITH WELDED WIRE MESH AND FIBRES UNDER IMPACT LOADING 10.1 Introduction The aim in this Chapter is to investigate the response of round concrete panels reinforced with various combinations of fibers and WWM to both static and impact loading. Both the load bearing capacities of the various panels and their toughnesses were determined, as well as their strain rate sensitivity. Detail experimental program and mix proportions were given Tables 3.2 and 3.8. 10.2 Results and Discussion Average load vs. deflection curves under static loading are shown in Fig. 10.1 for both the normal strength and high strength mixes. The loads at first crack, the maximum loads and the toughnesses at both 20mm and 40mm central deflections are shown in Table 10.1. The dynamic performance of Mesh RC panels and HyRC panels are shown in Figs. 10.2-10.4. 118 10 20 30 Deflection (mm) 40 50 (a) Mesh-RC and HyRC of Normal Strength matrix VHS-M-SF1.0 VHS-M-SF0.5 VHS-M-PP1.0 VHS-M-PP0.5 VHS-Mesh(M) 10 40 20 30 Deflection (mm) (b) Mesh-RC and HyRC of Very High Strength matrix 50 Figure 10.1 Load vs. deflection of panels under static loading 70 Mesh1A-150mm Mesf i1B-150mm 0 10 20 30 40 50 60 70 Deflection (mm) (a) NSC-Mesh RC £ 4 0 panel-1D-150mm panel-1F-150mm panel-1 C-300mm panel-1 E-500mm I I L A tm 0 10 20 30 40 50 60 70 Deflection (mm) (b)VHSC- Mesh RC Figure 10.2 Load vs. deflection curves of Mesh RC panels under impact loading 120 70 60 50 40 T3 m o Mesh2A -150mm Mesh2B-150mm Mesh2B -300mm Mesh2A -500mm 20 30 40 50 Deflection (mm) (a) NS-M-0.5% PP 60 20 30 40 50 Deflection (mm) (b) NS-M-0.5% SF 20 30 40 50 Deflection (mm) (c) VHS-M-0.5% PP 70 121 80 1 VHS-M-SF0.5-150mm VHS-M-SF0.5-300mm VHS-M-SF0.5-S00mm 1 fflfc 0 10 20 30 40 50 60 70 Deflection (mm) (d) VHS-M-0.5% SF Figure 10.3 Load vs. deflection curves of HyRC panels under impact loading (Mesh+0.5% Fibers) NS-M-PP1.0-50mm 0 10 20 30 40 50 Deflection (mm) (a)NS-Mesh-PPl.O 20 30 Deflection (mm) (b)NS-Mesh-SFl.O 20 30 Deflection (mm) (c) VHS-Mesh-PPl.O -VHS-M-SF1.0-100mm -VHS-M-SF1.0-150mm -VHS-M-SF1.0-300mm -VHS-M-SF1.0-500mm 1 'v-^  . V 1 1= 0 10 20 30 40 50 Deflection (mm) (d) VHS-Mesh-SF1.0 Figure 10.4 Load vs. deflection curves of HyRC panels under impact loading (Mesh+1.0% Fibers) 123 Table 10.1 Strength and toughness under static loading (HyRC) Specimen Type Normal Strength High Strength 1st Peak (kN) Max Load (kN) Toughness (J) 1st Peak (kN) Max Load (kN) Toughness (J) @20 mm @40 mm @20 mm @40 mm Mesh-0% fiber 16.5 16.7 269.3 479.3 24.3 24.3 320.6 478.6 Mesh-0.5%PP 17.1 20.3 373.9 678.2 27.2 27.2 485.9 710.3 Mesh-1.0%PP 19.1 26.7 470.3 900.4 32.2 32.2 559.2 827.4 Mesh-0.5%SF 23.2 28.5 542.8 873.8 27.5 27.5 395.7 579.6 Mesh-1.0%SF 35.7 35.7 671.7 1168.2 36.5 46.8 706.1 941.4 10.2.1 Static loading For all of the specimen types, the predominant mode of failure was three major cracks propagating up from the bottom of the plate, at angles of about 120° to each other, and running, somewhat irregularly, from the mid-points between the supports to the centre. In addition, some of the specimens reinforced with both mesh and a high fiber volume displayed some multiple cracking as well. From Fig. 10.1 and Table 10.1, it may be seen that, in terms of strength, both a higher matrix strength and a higher fiber volume lead to modest increases in strength, with the steel fiber systems somewhat outperforming the synthetic fiber systems. For the normal strength concretes, the peak loads were slightly higher than the first crack loads, indicating some enhanced load-bearing capacity even after cracking. However, because of the much more brittle nature of the high strength matrix, only the 1% steel fiber/mesh system exhibited strengthening beyond first crack. The toughness values shown in Table 10.1 are perhaps more revealing than the strength values in bringing out the difference between the specimen types. For the normal strength matrices, toughness increased with fiber volume, with the steel fibers considerably outperforming the synthetic fibers. For the high strength matrix, however, the synthetic fibers outperformed the steel fibers at 0.5% fiber volume, and were almost as tough as at 1.0% fiber volume. This can be related to the greater extensibility of the lower modulus synthetic fibers and the greater brittleness of the high strength matrix. At 40 mm 124 deflection, the toughness of the high strength panels was generally lower than that of the normal strength panels, again reflecting the greater brittleness of the high strength panels. It is of interest to compare the results of the panels reinforced with mesh only (Table 10.1) with the values obtained using very similar matrices reinforced only with fibers in Chapter 7 (Table 7.2), reproduced here in Table 10.2. Table 10.2 Toughness (J) of FRC panels (at 40 mm central deflection) Specimen Type Normal Strength High Strength 0.5% PP 253.1 196.5 1.0% PP 448.5 408.2 0.5% SF 341.1 120.9 1.0% SF 565.8 285.6 It may be seen that, in all cases except for 1.0% steel fibers in the normal strength matrix, the WWM considerably outperformed the fibers alone. From Table 10.2, it may also be seen that toughness of the high strength FRC panels was much lower than that of the normal strength panels, while the combined use of fiber and WWM does not entirely overcome this problem. The toughness behavior was nonetheless improved, suggesting that the combined use of fibers and WWM was particularly advantageous for high strength matrices. 10.2.2 Impact loading The data obtained from the impact loading of the various types of panels are shown in Table 10.3, for drop height of the 578 kg hammer ranging from 50 to 500 mm. The peak loads refer to the "true" loads, i.e. corrected for the inertial loading, as per Equation (6-5). As expected, the duration of the impact event up to peak load decreased with increasing drop height, indicating higher strain rates. The peak loads tended to increase with increasing drop heights, also as expected, though the increases for any specimen type were generally not very large. Similar to the static tests, the peak loads were higher for the very high strength matrix and they also tended to be slightly higher for the steel fiber specimens compared to the synthetic fiber specimens, though these differences were not large enough to be of much practical significance. 125 It should be noted that, under impact loading, while the combined use of fiber and WWM was more effective than the use of WWM alone, the improvements were considerably less than was the case under static loading, particular for the more brittle high strength concrete matrix. This is consistent with previous studies in Chapter 7, which suggested that the reduced toughness of the high strength specimens could be explained by a greater possibility of fiber fracture as opposed to fiber pullout. 'able 10.3 Strength and toughness under c ynamic loading (HyRC) Specimen Type Normal Strength High Strength Drop Height (mm) Duration of Impact Event (ms) Peak of True Load (kN) Toughness at 40mm Deflection (J) Duration of Impact Event (ms) Peak of True Load (kN) Toughness at 40mm Deflection (J) Mesh only 150 57.1 37.5 512 57.5 49.8 472 300 24.8 45.9 506 42.4 66.2 555 500 24.1 50.1 622 32.0 69.3 613 Mesh +0.5%PP 150 50.5 43.1 616 60.9 54.2 580 300 28.9 42.5 720 27.7 63.3 535 500 30.3 45.2 719 22.6 70.6 683 Mesh +1.0%PP 50 38.8 33.0 * 31.8 44.9 * 100 61.6 37.1 * 47.0 51.4 * 150 74.6 39.8 * 56.8 56.8 482 300 46.7 48.1 713 36.6 71.1 664 500 34.1 51.4 777 31.7 76.0 733 Mesh +0.5%SF 150 101.0 41.5 * 90.0 62.9 659 300 87.0 51.9 850 75.0 66.2 610 500 70.0 63.1 954 59.0 75.5 687 Mesh +1.0%SF 100 - - - 38.4 58.4 * 150 54.2 46.6 * 63.1 53.8 * 300 64.8 52.9 1079 40.5 68.7 827 500 40.4 54.2 1114 35.2 70.4 899 * Specimen toughness is did not reach a 40 mm de overall toughness. Election due to insufficient drop height. The 10.3 Comparison of Static and impact tests: strain rate sensitivity To compare the relative behaviors of the different systems under static and dynamic loading, it is convenient to use the dynamic increase factor (DIF). These are shown in 126 Table 10.4 for the mesh reinforced panels, and in Table 10.5 for the hybrid reinforced panels, based on the data presented in Tables 10.2 & 10.3. For ease of comparison, they are further plotted in Figs. 10.5 and 10.6. For the panels reinforced only with mesh, the DIF of peak load was in the range of 2 to 3 for both the normal strength and very high strength matrices. The DIF for toughness was low; it increased with increasing drop height, but was only in the range of about 1.0 to 1.3. This suggests that for mesh alone, the DIF is insensitive to the matrix strength for both toughness and peak load. Table 10.4 Dynamic increase factors for WWM reinforced panels Drop Height (mm) Normal Strength High Strength DIF of Peak Load DIF of . Toughness DIF of Peak Load DIF of Toughness 150 2.25 1.07 2.05 0.99 300 2.75 1.06 2.72 1.16 500 3.00 1.30 2.44 1.28 Table 1 0.5 Dynamic increase factors for HyRC panels Concrete Type Drop Height (mm) Normal St rength High Strength DIF of Peak Load DIF of Toughness DIF of Peak Load DIF of Toughness Mesh +0.5%PP 150 2.13 0.91 1.99 0.82 300 2.10 1.06 2.33 0.75 500 2.23 1.06 2.60 0.96 Mesh +1.0%PP 150 1.49 0.69 1.75 0.58 300 1.80 0.79 2.19 0.80 500 1.93 0.86 2.35 0.89 Mesh +0.5%SF 150 1.46 0.78 2.29 1.05 300 1.82 0.97 2.41 1.14 500 2.21 1.09 2.75 1.19 Mesh +1.0%SF 150 1.30 0.49 1.16 0.62 300 1.48 0.92 1.45 0.88 500 1.52 0.95 1.51 0.96 127 NS-Mesh RC VHS-Mesh NS-M- NS-M- NS-M-RC SFRC0.5 SFRC1.0 PPFRC0.5 (b) Mesh RC and NS-HyRC panels NS-M-PPFRC1.0 NS-Mesh RC VHS-Mesh VHS-M- VHS-M- VHS-M- VHS-M-RC SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 (c) Mesh RC and VHS-HyRC panels Figure 10.5 DIF of peak load for mesh-RC and hybrid reinforce panels 128 1.4 NS-Mesh RC VHS-Mesh NS-M- NS-M- NS-M- NS-M-RC SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 (b) Mesh RC and NS-hybrid reinforced panels 1.4 NS-Mesh RC VHS-Mesh VHS-M- VHS-M- VHS-M- VHS-M-RC SFRC0.5 SFRC1.0 PPFRC0.5 PPFRC1.0 (c) Mesh RC and VHS-hybrid reinforced panels Figure 10.6 DIF of toughness for mesh-RC and hybrid reinforced panels In almost all cases, the DIFs for both peak load and toughness increased with increasing drop height (i.e. increasing rate of loading) though the increases were not great. In terms of peak load, the DIF values of the mesh systems were higher than those for hybrid 129 systems, indicating greater strain rate sensitivity for the WWM systems. The same was true for the DIF of toughness. DIF values tended to decrease with increasing of fiber contents, suggesting that fibers tend to decrease the strain rate sensitivity of the material. However, the matrix strength did not appear to have significant effect on the strain rate sensitivity of the various systems. It is of interest to note that, for a number of the hybrid systems, the DIF values for toughness were less than 1; that is, for those systems, the toughness was higher under static loading than under impact loading. The reasons for this are not clear; they are presumably related to changes in the mode of failure (perhaps more fibers breaking rather than pulling out under impact). 10.4 Conclusions (1) The round panel tests can be used to characterize the mechanical properties of WWM reinforced and WWM/fiber reinforced concretes. (2) The addition of fibers increased both the loading carrying capacity and the toughness of the specimens, with steel fibers being somewhat more effective than synthetic fibers in this regards. (3) The high strength panels tensed to exhibit less ductility than normal strength panels. (4) Under impact loading, the load bearing capacity increased with increasing drop height, but this effect was not really seen for toughness. (5) The combination of WWM and fibers makes the systems less strain rate sensitive than systems reinforced only with WWM. 130 CHAPTER 11 DAMAGE EVOLUTION OF ROUND CONCRETE PANELS WITH HYBRID REINFORCEMENT UNDER IMPACT LOADING 11.1 Introduction In the previous Chapter, the effects of the combined use of steel wire welded mesh (WWM) and fibers (hybrid reinforcement), on the performance of concrete panels were investigated under both static and drop-weight impact loading. Improvements in toughness and load-bearing capacity were particularly noted. It was also observed that most panels with hybrid reinforcement (HyRC with 1.0% fibers) did not completely fail under low drop heights, showing only small central deflections and some damage. In order to obtain the damage evolution of HyRC panels under impact loading at different loading rates (corresponding to different drop heights), post-impact static tests for those panels were carried out. The damage of the HyRC panels was defined in terms of residual performance, e.g. the load-bearing capacity, toughness, and initial stiffness. The test program was shown in Table 3.9. 11.2 Damage analysis 11.2.1 Damage of RDP and post-impact static tests As observed in both static and impact tests, cracks initiated first from the bottom center of the panels and propagated to the edges and upwards. Damage due to impact increased with increasing drop heights (Fig 11.1). In Chapters 6-8, it was shown that most specimens with single reinforcement failed (i.e., central deflections larger than 40 mm) under impact loading with a drop height of 150 mm or more. Thus, it is difficult, experimentally, to characterize the critical drop height since their energy absorption capacities were far less than the input energy. Because the mass of the impact hammer is 578kg, even a low drop height provides enough input energy to fail the weaker and less tough panels. 131 However, for specimens that were strong enough and tough enough to withstand impact under relatively low drop heights (i.e. specimens containing both WWM and 1.0% by volume of fibers), post-impact static tests were carried out to determine their residual performance (load-bearing and energy capacity). A schematic curve of three typical load vs. deflection curves is shown in Fig. 11.2. Damage 0 0© © ® Drop-Height Figure 11.1 Schematic of critical drop height Load (P) Virgin Panel -Under Irreversible 8 ir 40mm Deflection (8) after impact Figure 11.2 Typical load vs. deflection curves of HyRC under impact and static loading 132 11.2.2 Damage evaluation from post-impact static test From the post-impact static tests, we can determine the degradation of plate stiffness (Epi), the load capacity (P), and the energy absorption capacity or toughness (T). Here, toughness is defined as the area under the load-deflection curve out to 40mm central deflection. The damage caused by impact loading may be defined in three different ways: In terms of toughness reduction, the damage O caused by impact loading can be calculated using Eq. (11-1). <X> toughness = (1 — T residual static/T virgin static) ... (11-1) It should be noted that the deflections measured for the pos-impact tests included the original irreversible deflection 8 ir (Fig.3), so that comparison could be make at the same total deflection of 40 mm. The other two damage criteria can be defined as the stiffness and load capacity reductions percentages, as are given by Eq. (11-2) and (11-3). O stiffness = (1 — E p | residual static /E p | virgin static) . . . (11 -2) Where, the plate stiffness E pi can be obtained by calculating the initial slopes of the load-deflection curves for virgin static tests or post-impact static tests. O load capacity = (1 — P residual static /P virgin static) ... (11-3) 11.3 Results and discussion 11.3.1 Toughness and irreversible deflection caused by impact loading The load vs. deflection curves of the Mesh RC panels and HyRC panels were shown in Figs. 10.2-10.4. Generally, the panels deformed symmetrically in three segments for both static and impact loading. For comparison, some results for the virgin specimens of the corresponding damaged panels are reproduced in Table 11.1. 133 Ta ?le 11.1 Results of -lyRC panels under static and impact loading Panel type Static tests Impact tests Post-impact static test T virgin static (J) P virgin static (kN) Drop Height (DH, mm) True Peak load (kN) Dynamic tough-ness (J) 5 ir (mm) Mesh C +NS-PP1.0% 900 26.9 50 33.0 128 3.1 Yes 100 37.1 276 8.6 Yes 150 39.8 620 22.0 Yes 300 48.1 713 >40 No 500 51.4 777 >40 No MeshC +VHS-PP1.0% 827 32.0 50 44.9 66.0 1.3 Yes 100 51.4 269 7.40 Yes 150 56.8 482 >40 No 300 71.1 664 >40 No 500 76.0 733 >40 No MeshC +NS-SF1.0% 1168 35.7 150 45.0 547 16.9 Yes-4B 46.6 567 15.7 Yes-4C 300 52.9 1079 >40 No 500 54.2 1114 >40 No MeshC +VHS-SF1.0% 941 46.5 100 58.4 254 6.4 Yes 150 53.8 588 18.3 Yes 300 68.7 827 >40 No 500 70.4 899 >40 No Low drop heights caused only minor damage, with small deflections 8 ir and energy absorptions. Using the 40mm central deflection as a criterion, the critical drop height would be between 150mm and 300mm for most of the panels, except for the panel "Mesh C +VHS-PP1.0%", which would have a smaller critical drop height. In the current tests, the relatively large mass of the hammer made the available input energy range (maximum drop height) very narrow for drop heights below the critical value. Thus, adjusting the drop heights to investigate the critical input energy was next to impossible for HyRC panels with a small fiber volume fraction, panels with single reinforcement (either fiber or mesh). Therefore, a smaller hammer should be used for further study of the critical input energy on HyRC with small fraction of fibers. However, it should be noted that the performance of a concrete element under impact is highly 134 dependent on the impact machine [124]. Its behaviour is more sensitive to the drop height than to the mass of hammer, because the pulse duration depends mostly upon the drop height. 11.3.2 Post-impact static test and damage evolution caused by impact loading In order to quantify the extent of damage of the round panels under impact, the damaged specimens were tested statically to find their residual load capacity and toughness. Figs. 11.3(a) and 11.3(b) show the load vs. deflection curves of the post-impact static tests for both VHS-M-FRC1.0 and NS-M-FRC1.0 specimens. The residual load capacity, residual toughness and residual stiffness of the panels are summarized in Table 11.2. Overall, the specimens performed as expected: those that had a lower drop height had a higher residual strength. The highest residual strength was for the 1.0% PP fibre that had undergone an impact test from a drop of 50mm. This impact test caused little damage to the specimen, with an energy absorption of only 128 J (See Table 11.1), and thus it had a high residual strength. 135 —VHS-M-PP1 .0 after 50mm drop —-VHS-M-PP1.0 after 100mm drop —-VHS-M-SF1.0 after 100mm drop —— VHS-M-SF1.0 after 150mm drop 0 10 20 30 40 50 60 Deflection (mm) (b) VHS-M-FRC panels Figure 11.3 Residual performances of panels with hybrid reinforcement Table 11.2 Residual performance of hybrid reinforced panels Panel Performance Panel Type Virgin Specimen (static test) Post-Impact Static Test DH-50 mm DH-100 mm DH-150 mm Stiffness (kN/mm) NS-M-PP1.0 63.3 4.84 3.19 2.77 NS-M-SF1.0 67.6 — — 3.97 Load Capacity (kN) NS-M-PP1.0 25.5 25.0 19.6 17.2 NS-M-SF1.0 35.7 — — 25.0 Residual Toughness (J) NS-M-PP1.0 900.4 806.8 452.9 232.2 NS-M-SF1.0 1168.2 — — 466.3 Stiffness (kN/mm) VHS-M-PP1.0 76.8 10.81 6.58 — VHS-M-SF1.0 91.9 — 10.82 4.67 Load Capacity (kN) VHS-M-PPLO 32.4 31.5 23.8 — VHS-M-SF1.0 46.5 — 28.8 19.6 Residual Toughness (J) VHS-M-PPLO 827.0 800.3 355.9 — VHS-M-SF1.0 941.0 — 492.7 296.5 Note: the 40mm total deflection incurred as deflection for which toughness was calculated includes the irreversible a result of impact test. 11.3.3 Damage in terms of energy absorption capacity The damage, based on the three damage definitions given above, is shown in Tables 11.3. For ease of comparison, the data are plotted in Figs. 11.4 & 11.5. Since fibers are primarily added to concrete to improve its energy absorption capacity, the residual 136 toughness gives a general indication of the damage caused by impact when compared to the toughness of a virgin specimen under static loading. For the same drop height (DH), the M-PP1.0 panels suffered greater damage than the M-SF1.0 panels. From Table 11.3, it may be seen that the damage of panels containing mesh and 1.0% PP fibers was somewhat higher than that of Mesh + 1. 0% steel fibers for both very high strength panels and normal strength panels. For the 100 mm and 150 mm drop heights and the same type of reinforcement, panels with high strength matrices showed rather more damage (about 7% for DH-100mm and 8.4% for DH-150 mm) than those with normal strength matrices. However, for the drop height of 50mm, the high strength panels exhibited less damage, presumably because the fibers/mesh interaction in those panels did not play an important role under small deflections; rather, the effect of the matrix was dominant. Table 11.3 Damage due to impact loading in terms of three criteria Damage criterion Panel type Damage due to impact oading DH-50 mm DH-100 mm DH-150 mm O Stiffness NS-M-PP1.0 0.924 0.949 0.956 NS-M-SF1.0 — — 0.941 O Load Capacity NS-M-PP1.0 0.019 0.221 0.326 NS-M-SF1.0 — — 0.300 O toughness NS-M-PP1.0 0.104 0.498 0.742 NS-M-SF1.0 — — 0.601 <I> Stiffness VHS-M-PP1.0 0.859 0.914 — VHS-M-SF1.0 — 0.882 0.949 O Load Capacity VHS-M-PP1.0 0.028 0.265 — VHS-M-SF1.0 — 0.351 0.579 O toughness VHS-M-PP1.0 0.032 0.570 — VHS-M-SF1.0 — 0.476 0.685 137 NS-M-PP1.0 NS-M-SF1.0 NS-M-PP1.0 NS-M-SF1.0 NS-M-PP1.0 NS-M-SF1.0 CP Stiffness O Load Capacity O toughness Figure 11.4 Damage caused by impact — Normal strength HyRC panels Figure 11.5 Damage caused by impact — Very high strength HyRC panels 11.3.4 Damage in terms of residual load capacity Only very small damage could be found in terms of residual load at a drop height of 50mm. Opposite to the damage obtained from toughness criteria, high strength panels with steel fibers showed larger damage (see DH-150 mm in Table 11.3), and there were no significant differences between NSC and VHC panels with PP fibers. 138 11.3.5 Damage in terms of initial stiffness From the static tests on virgin specimens, steel fibers provided higher stiffness than PP fibers, and the concrete matrix played a larger role than fiber type in this regard (see Table 11.2). It was found that, even for the small drop height of 50 mm, very severe damage occurred, of more than 85%; the damage for most HyRC panels increased to about 95% when the drop height increased up to a 150 mm drop (Table 11.3). However, because of the large amount of damage, it was difficult to distinguish different panels. 11.4 Which damage definition should be used? The damage in terms of stiffness is significantly higher than the other two damage criteria, with the loading capacity giving the least apparent damage. This can be explained in terms of the three damage definitions, e.g., large deflections for toughness, but small deflection for panel stiffness and load capacity. Since the toughness is of most interest for FRC. O toughness would be the most suitable for characterizing the damage of HyRC panels. 11.5 Special case Interestingly, a significant difference was found in the residual performance for two NS-M-SF1.0 panels, which had undergone impact tests from the same drop height of 150mm. The dynamic responses were very similar in terms of toughness values and ultimate deflections (Table 11.1). However, the residual tests showed a difference of approximately 180 J at a central deflection of 34mm, with sample SF4B-150R having a residual toughness of 394 J and sample SF4C-150R having a residual toughness of 574 J (Table 11.4). 139 An investigation of the failure modes revealed that sample SF4B-150R failed with a major crack cross the diameter and a minor crack approximately perpendicular to it. (See Fig. 11.6b), rather than having the cracks at 120 degrees. Sample SF4C-150R (Fig. 11.6a) appeared to follow the typical expected failure mode. In the post-impact static test, the crack propagated mostly along the major crack. Therefore, many fewer fibers bridged the single crack with a crack length of twice the panel radius than in the case of three cracks with a total crack length of three times the radius. This could have led to the decreased residual strength of sample SF4B-150R. This implies that the initial damage caused by impact could cause quite different failure modes. Table 11.4 Residual Performance of Normal Strength HyRC panels (DF 1-150 mm) Panel designation Specimen for Post-Impact Static Test Damage due to impact Stiffness (kN/mm) NS-M-SF1.0 (4C-150R) 3.97 0.941 NS-M-SF1.0 (4B-150R) 4.01 0.941 Load Capacity (kN) NS-M-SF1.0 (4C-150R) 25.0 0.300 NS-M-SF1.0 (4B-150R) 22.6 0.364 Residual Toughness and corresponding deflections (J) NS-M-SF1.0 (4C-150R) 574.8 J @34mm 466.3 J @(40-15.7) mm 0.601 NS-M-SF1.0 (4B-150R) 394.5 J @34mm 327.0 J @(40-16.9) mm 0.720 (a) sample - SF4C-150R (b) sample - SF4B-150R Figure 11.6 Failure modes of NS-M-SF 1.0-150mm 140 11.6 Conclusions (1) The toughness and peak loads of HyRC panels increased with an increase in the drop height. Overall, the deformed steel fibers and normal strength matrix showed a more favourable toughening effect under impact loading. (2) A low drop height (50 mm) did not provide sufficient energy to deform the HyRC panel much, and for most panels with 1.0% fibers, the critical drop height was between 150 and 300 mm. (3) Three definition of damage were be used to characterize the damage caused by impact loading, and they showed very different damage levels. Damage in terms of toughness is probably the most suitable for measuring the residual performance of HyRC panels. 141 CHAPTER 12 ANALYSIS OF PERFORMANCE PREDICTION OF ROUND FRC PANELS UNDER STATIC LOADING 12.1 Introduction In the previous Chapters, experimental work on round FRC panels under both static and dynamic loading was described. Without doubt, experimental work will continue to play an important role for the better understanding of the performance of materials and structures, for the development of performance-based engineering materials and design-code implementation. However, due to the complexity, high cost and lack of availability of special facilities, analytical or numerical modeling can provide an alternative to experimental work. The objective of this part of the study is to establish a semi-analytical model to predict the performance of round FRC panels: deformational behavior and toughening mechanisms. The focus is particularly placed on the post-crack performance under quasi-static loading. Eventually, this work is expected to lead to a better understanding of the dynamic performance of panels. 12.2 A review of performance prediction on F R C plates/slabs Very few models are capable of predicting post-crack performance of structural elements with fiber reinforcement (FRC), where energy absorption, rather than load capacity, is of interest. In the last forty years, about 60% of FRC has been used in slab-on-grade applications as secondary reinforcement [8]; thus most analytical models in the literature dealt with FRC slabs. Earlier analytical works on plain concrete slabs [142], and models based on yield-line theory (YLT) [143,144] for different geometries of reinforced concrete slabs could approximately reproduce the deformational behavior up to the collapse load, and were 142 particularly good in the linear elastic regime. Due to the lack of a suitable materials law and failure criterion to implement a finite element analysis (FEM), the numerous computer programs commercially available for analyzing reinforced concrete shells, slabs or panels, however, can only be used as a first approximation for estimating the capacity [145]. Roesler et al. [146,147] provided a comprehensive review of previous studies in full-scale slabs over last two decades, and indicated that both steel fibers and high modulus synthetic fibers increase the flexural and ultimate load-carrying capacity of concrete slabs; the magnitude of the increase is related to fiber type, volume fraction and aspect ratio. More recently the Concrete Society [16] has introduced FRC into the design guideline for slabs on grade (TR34), using empirical equations. Falkner and Teutsch [148] appeard to be the first to propose a model based on equivalent flexural strength and to incorporate nonlinear material analysis in steel fiber reinforced concrete slabs. Lok and Pei [149] tested elastic performance of simply supported on two sides and simply-supported all-round FRC square slabs subjected to a central point static load and produced predictive formulae. The comparison of experiments with theoretical solutions indicated that a modified depth instead of the full slab thickness was required for estimating the elastic response. They found that fiber types (corrugated and straight fibers) and relatively low fiber volume fractions do not provide a significant increase in elastic stiffness compared with an identical plain concrete slab. However, they did not study the post-peak performance. Barros and Figueiras [150] developed a constitutive model using a smeared crack approach and nonlinear behavior of SFRC to reproduce the concrete cracking behavior. Sorelli [72] used finite element method (FEM) and fracture mechanics to model FRC slabs. Most of these studies revealed that, besides fiber reinforcement, the behavior of FRC slabs also depends on the boundary conditions (one-way or two-way), load locations (central or on the edge), and slab geometry (square, circular or irregular). In particular, the support conditions (soil stiffness) and contact between slabs cause a great deal of scatter in the experimental results, and hence the model predictions were not in good agreement with slab behavior. They indicated that 143 support conditions could not be ignored for the proper prediction of the overall deformability and load carrying capacity of slabs. As a special case, circular plates/slabs under different boundary conditions have been studied both for structure analysis and materials characterization. Boulfiza et. al. [151] used a continuum damage mechanics theory to predict the behavior of full edge simply-supported small circular plates (^ 250mmxl0mm, carbon fiber reinforced paste) up to the peak load and suggested that nonlinear fracture mechanics (NLFM) could be used for post crack performance prediction. Though the predicted failure patterns were similar to the experimental results, fundamental differences were found for plates with low fiber volume fractions: discrete cracks of failure in the experimental results, but diffused damage in the numerical prediction. Nilsson and Holmgren [152] developed a model for fully clamped round FRC panels. They found that the estimated capacities based on YLT were consistently lower than the actual load bearing capacity. They attributed the difference to compressive arch action due to end-clamping, and indicated that this action is currently ignored in design for applications such as tunnel linings. Specific loading and boundary conditions for circular plates are those defined in ASTM C1550 [5], which has been described in detail in Chapters 2 & 3. Since this setup is able to eliminate soil conditions, and achieves consistently a 3-radial-crack failure mode, ASTM C1550 is increasingly being used, particularly for FRC slabs and FR-shotcrete. Bernard [153] carried out the first numerical study using the software PLATES in ABAQUS to analyze the stress and strain distribution; he found that only elastic performance of the panels could be estimated. He concluded that the lack of an appropriate materials model and an inability to select a suitable failure criterion made the prediction of the post-crack performance next to impossible. Tran et al. [154] applied yield-line theory and Dupont et al. [155] used a simplified constitutive law for determinate round panels. In these studies, general tendencies could be observed, but large discrepancies still existed between model and experiment. Later, an improved 144 approach incorporating statistics and Monte Carlo simulation with YTL was attempted by Tran et al.[156,157] to account for the stochastic nature of the material properties; this improved the prediction considerably. They concluded that the primary performance variation of RDP was caused by the flexural capacity of elements comprising the panel rather than variations in the location of the radial cracks that form during the test. To sum up, much less analytical or numerical modeling for fiber reinforced slabs has been carried out than have experimental studies on full-scale FRC slabs. Models for ASTM C1550 plates are even rarer. Therefore, there is a need to develop a simple model for round FRC panels. 12.3 Predicting round panel behavior from beam test It has been found that beam tests and panel tests are not comparable; results from these tests cannot be correlated in terms of toughness and load capacity due to geometrical differences (Section 2.4.2 and Chapter 4). However, most of the RDP predictions still directly or indirectly relate to beam behavior. Fig. 12.1 illustrates two approaches for RDP performance prediction. From a fundamental point of view, Fracture Mechanics is probably the most suitable approach for predicting panel performance, see Fig. 12.1 (left); the materials constitutive law required is normally obtained from notched beam tests and inverse calculation [158]. Knowing the stress crack-opening relationship, the performance of RDP can be calculated through FEM analysis. However, the procedure for determining the constitutive law is quite tedious and leads to considerable complexity. From an engineering perspective, a simple method with acceptable approximations is preferred in practice. Yield-line theory (YLT) provides an option for this purpose. The procedure is shown in Fig. 12.1 (right), where system energy conservation and the crack rotation can provide a bridge between beams and round panels. Assuming a certain 145 failure pattern (yield lines) and inputting the moment resistance (moment capacity vs. crack-rotation of a beam), RDP behavior for the same type of FRC may be calculated. Here, the second approach will be employed by implementing new features into some previous research. 146 Notched beam Crack Opening w Load 4 Moment Angle measuring modules Yield Line Theory (YLT) and Virtual Work Central Deflection RDP performance (experimental vs. predicted) Figure 12.1 Schematic procedures for round panel performance prediction by using a beam test 147 12.3.1. Yield-line theory basics The pioneering work on yield-line analysis was done by K.W. Johansen [143]. Later, Yield Line theory (YLT) was used to investigate failure mechanisms at the ultimate limit state. It has also been found that yield-line based design provides a well-founded method for designing reinforced concrete slabs. According to Johansen [144] and Kennedy et al. [159], Yield Line design leads to slabs that are quick and easy to design and to construct, and there is no need to resort to the use of a computer for analysis or design. The theory is based on the principle that: Work done in yield line rotation = Work done in moving loads However, this method challenges designers to use their judgment to estimate the location of possible yield lines. In practice, it is necessary to calculate several patterns and to use the lowest value of collapse load, so as not to severely overestimate the slab capacity. 12.3.2. Challenges in the beam-panel approach for FRC 12.3.2.1 Limitations and applicability of YLT One can study the applicability of YLT by comparing the basic assumptions of the theory and experimentally observed facts. Six major differences are summarized in Table 12.1. In particular, the 3rd item regarding material behavior does not apply at all. 148 Table 12.1 Applicability of YLT in RDP prediction Assumptions of YLT [143] In the case of RDP [5,154] 1 Individual parts between cracks remain plane and the structure collapses because of the moment Panels fail through rotation of the three segments, mixed with shear, flexural, membrane stress 2 For relative rotation of the two adjoining parts of panel, the axes of rotation depend on the supports; axial (in-plane) forces are ignored Each segment move outwards from the centre 3 Material is assumed to display quasi-elastic perfectly plastic behavior Both concrete and FRC are strain-softening materials 4 Small deformations compared with the overall dimensions are assumed 40 mm central deflection 5 Cracks occur simultaneously Cracks propagate from the centre of the panel bottom to the edges and then upwards 6 Cracks or yield lines are straight lines Cracks are jagged and seldom exactly straight 12.3.2.2 Other difficulties and challenges Besides the differences listed in Table 12.1, another difficulty in the round panel setup is the non-symmetrical failure mode, while symmetry is often assumed for YLT analysis. As observed from numerous experiments, most round panels suffer a flexural failure involving three radial cracks. Theoretically, each crack goes through the central point and the point between the adjacent pivot supports. Since concrete/FRC is never homogeneous, these three cracks are rarely identical and symmetrical and there always exists some variation from perfect symmetry (i.e. 120° cracks). A second pattern, which is uncommon, is the one crack-pattern (diametrical failure). Based on statistics from 500 round panels by Tran et al. [156], a suitable probability density function (PDF) describing the variation in crack position was found, and it obeyed a censored Weibull function, f(r) = a<,0r°r"-'e-l'"M" -<12-» where y is the midpoint angle (range from 0 to 60°), representing the deviation of each crack from the midpoint line between each pair of adjacent supports; a 0 is a dimensionless shape parameter (1.108); and the estimator value of midpoint angle /?o -13.038°. 149 The effect of friction is another factor. Most of this energy is spent in the process of fiber deformation and pull-out from the concrete across cracks during the test. According to Bernard [160], however, a significant proportion of the energy apparently absorbed by the specimen is actually lost to friction, as the panel fragments that form after cracking of the concrete slide outward in a radial direction across the supports. As a result of this mechanism, earlier research which did not take this factor into consideration is not suitable for predicting the performance of FRC panels. 12.4 Analysis and procedures There are two parts to the present analysis: pre-peak and post-peak performance prediction. In the first part, by incorporating the empirical information between simply full-edge support panels and the round determinate panel, and classical plate theory, it is feasible to predict the lower bound of the peak load of the RDP. A simple expression can be derived by taking panel geometry and concrete properties into consideration. However, the focus will be placed on post-peak performance prediction. Different from previous studies, rather than directly applying the YLT in the RDP test, the performance of the round panel will be analyzed by implementing the following information observed from experiments: rotation and slip of segment, and effect of friction. To obtain a moment resistance vs. curvature relationship, flexural beam tests were carried out using beams composed of the same type of FRC. 12.4.1. Pre-peak performance prediction As observed in the experimental work described in the previous Chapters, up to 40 mm deflection, the approximation of a linear increase of load up to peak load for conventional FRC panels is reasonably good. Also, the range of central deflections corresponding to the peak load is narrow. Therefore, most of the pre-peak prediction could be simplified to the peak load estimation. 150 However, unlike the simply supported beam or the fully edge-supported round panel, there is no classical solution available for structural analysis of the RDP test setup. Simplification was therefore required to predict the pre-peak performance by using the known solution of a simply full edge supported round panel. Fortunately, extensive experimental data for the same type and size of FRC panels can be found with three different setups [116]: • full-edge simple support (FESS), • three point support, or determinate panel (RDP), and • fully-clamped edge (FCE). The ratio of peak load from the FESS setup to that from the RDP setup, denoted as k, was found to be consistently independent of panel thickness and related only to its panel diameter, as shown in Fig. 12.2. For the standard ASTM C1550 panel, k = 0.79, and for the setup with a diameter of 635 mm (effective radius of 297.5mm), k=1.18. 200 400 600 800 Diameter of panel(mm) Figure 12.2 Relationship between simply supported panel and RDP [160] Knowing the relationship between maximum central deflection and load for simply supported round panel [161]: 151 where plate constant J) — fit* / 12(1 plate and the Poisson ratio, respectively. — V2 )' td a n c * V denote the thickness of the Therefore for the RDP, the peak load may be predicted as P = k.)**L.l±}L8 ...(12-3) r2 3 + v According to the experimental results, the deflection of the round panel up to peak load normally ranges from 0.49 mm to 0.52 mm for ASTM panels and the panel in this work. Thus, the approximate peak load of the RDP can be calculated. Considering that the original solution for a simply supported panel is effective in the elastic range and the fact that concrete is already deformed and cracks propagate when the round panel reaches peak load, Eq.(12-3) is expected to give the lower bound of peak load. In this program, the peak loads were calculated at a central deflection of 0.50 mm. 12.4.2. Post-peak performance prediction 12.4.2.1 Yield line theory analysis In this work, YLT was used to execute the analysis. For the round determinate panel, more than one yield line pattern is possible; these patterns have been reviewed in Section 12.3.2. Fig. 12.3 illustrates two typical patterns. 152 Figure 12.3 Possible failure patterns of round FRC panels Despite the number of possible patterns, the general equation governing the YLT is E external = E internal ... (12-4) Detailed yield line analysis can also be found in the work by Tran et al. [154], in which all cracking modes with possible crack propagation modes were considered, giving a complicated equation. The failure load for the diametrical pattern of yield lines (Fig. 12.3a) is p=2Rm l-2cosa*(;r/6-a) | 1 + sin (7tl6-a) sin a cos(;r 16-a) (12-5) where, R is the radius of the panel, r is the net radius of the panel, a is the angle of the diametral crack relative to the line through the nearest support, and m the moment resistance per unit length of the yield line. The second, and most common, pattern is three radial yield-lines. The general case of three unequal angles between yield lines is shown in Fig. 12.3b. 153 P = R[ml(A + B) + m2(B + C) + m3(D + E)] ... (12-6) where mi (i=l-3) are the moment of resistance per unit length long the three yield lines; y( (i=l-3) are the arbitrary angles with respect to bisector of the un-supported sides; a,(i=l-6) are the corner angles; A, B, C, D, and E are factors, depending on yi and ai. To simplify analysis, take a special case with symmetrical yield lines into consideration. In that case, all three angles between yield lines equal to 120° and the corresponding yt =0. Therefore, we have P = ?,Sm- ...(12-7) r 12.4.2.2 Model implementation — incorporating the friction effect into the energy balance As reviewed in Section 12.3.2.2, the effect of friction plays an important part in the total energy dissipation. From experimental observations, the relative movement of the broken segments is very small in the pre-peak region, and the effect of friction could thus be ignored for the prediction of peak load, but this is not the case for the post-peak performance. Now, taking one-third of an FRC panel as an example, the mechanism of friction after cracking is shown in Fig. 12.4. 154 Complicated actions from other two fragments (a) Side View (A-A' section) (b) Top View Figure 12.4 Schematic illustration of compressive force N causing friction in one of the three segments where, ft is the friction force along the surface of the panel, i = 1,2, and 3, Nt is the compressive load applied perpendicular to the sliding surface of each segment or support, s is relative movement (sliding outwards) of the segment from the support, 6 is the corresponding rotation of the segment along the radius through the center of the panel and support, and P is the load applied on the panel. The energy dissipated due to friction was not taken into consideration for Emerml. A new energy balance can be written as Recall Eq.(12-4): E, external internal ... (12-7) ... (12-8) 155 where, // is the coefficient of friction between concrete and the steel block, <p is the rotation of the panel segment along the yield line, m is the instantaneous moment capacity of a particular yield line at a crack rotation angle of q>. Because of symmetry, this can be simplified, as all/)(i=l~3) are identical, denoted as f, and all corresponding TV, equal to N. Therefore, the relationship between N and the load P can be derived from the balance of vertical components imposed on the whole panel, regardless the level of the central deflection of the panel. In this way, we can avoid dealing with complicating actions caused by the other segments when analyzing individual segment: 37V cos 0-3/sin 0 = ^  thus, N-- 1 3 cos 9 - [i • sin 9 ...(12-9) For simplicity, we have 9 = Slv ...(12-10) 2cos30-£ ...(12-11) <p = r In order to take both rotation and side movement into consideration, the term "central crack mouth opening displacement (CCMOD)" would be helpful. A detailed definition can be found in Chapter 5 (Eq.5-1). Fig. 12.5 shows the schematic of crack information for round panels. The relationship between <p, 8, s and CCMOD can be derived from the geometrical relationship. 156 (a) Schematics of crack (b) Crack opening in tested FRC panel Figure 12.5 Close-up of crack propagation of round FRC panels CCMOD vs. 5, q> can be written as CCMOD (R-ov-s) 2 cos 30 -(td-x) ... (12-12) 5 = CCMOD ... (12- 13) When considering the overhang and movement of cracked segment, 2cos30 • 5 R-ov-s ... (12-14) <P = where tj denotes the height of the plate; ov = the overhang of each support; x =height of the compression zone; 4? = crack rotation along the yield line (crack); s = relative movement of cracked segment on the support. A detailed derivation can be found in Appendix D. 12.4.2.3 Step-wise procedure for post-crack performance calculation The above analysis is applicable to failure modes with three radial cracks. The load vs. deflection relationship can be calculated, provided the moment resistance at each yield line is known. The post crack load capacity can be determined by the following steps: 157 (1) . Impose the central deflection of panel, S; (2) . Calculate the crack rotation angle along the yield line; (3) . Use the moment of resistance experimentally measured from beam test at each corresponding crack rotation; (4) .Use Eqs.(12-7), (12-10), (12-11) and (12-14) to calculate the load by inputting the moment of resistance at the same crack rotation; (5) . Increase the central deflection in a step-wise manner to calculate the load. (6) . Repeat the above steps to the desired central deflection. Increase 8 up to 40 mm. 12.5 Experimental validation Four mixes of FRC panels and beams were produced to validate the model proposed and implemented above: Two types of fiber and two fiber volume fractions. Except for the curing age (60 days), the same mixes were used here for the normal strength FRC in the previous Chapter, with a W/C ratio of 0.55. The properties of the concretes are shown in Table 12.2. Table 12.2 Properties of FRCs for model validation (mean value) Concrete Fiber Volume Compressive Elastic modulus Type fraction (%) strength (MPa) (GPa) SFRC 0.5 64.5 32.9 SFRC 1.0 61.7 33.4 PPFRC 0.5 51.7 32.4 PPFRC 1.0 55.0 34.4 12.5.1 Beam testing Moment-crack rotation relationships were measured experimentally by using a three-point flexural test, with two angle-measuring modules mounted on each top side of the beam. The setup of the beam test is shown in Fig. 12.6a. Beams composed of identical materials to round panels were saw-cut from square plate after reaching the test ages. 158 The beam size was 100x60x400 mm, with a span L of 300 mm. The beam thickness was identical to the round panel specimen. The crack rotation was controlled up to 20° in order to cover all possible crack rotations in panel testing. For each group of FRC, a minimum of 4 beams were tested and the average performance was used for RDP prediction. The moment per unit crack length and the rotation of the beam segment along the crack were calculated by, m=PL/4b ...(12-15) cp = (p{+(p2 ...(12-16) where, b was the width of the beam, and qy , qy^ were measured rotation by using angle-measuring modules mounted on top of each side of beam (Fig. 12.6b). 12.5.2 Panel testing Round panels cast at the same time as the beam specimens were centrally loaded as described in Chapter 3 and ASTM C1550. Three RDP specimens were tested for each type of FRC. 159 12.6 Results 12.6.1 Beam test Average moment-crack rotation relationships for different saw-cut FRC beams are shown in Fig. 12.7. The elastic deformation has been subtracted from the record. As expected, SFRC 1.0 exhibited a higher maximum moment resistance and post-crack performance than the other FRCs. 5 o ^ , , , , , , , 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Crack rotation (rad) Figure 12.7 Moment resistance vs. crack rotation from beam test 12.6.2 Round panel test and predicted performance The moment-crack rotation relationships from beam test were used as input to produce estimates of post-crack behavior of round concrete panels as described in Section 12.4.2.3. The calculated results have been compared with experimental data in Fig. 12.8. The dark line denotes the predicted performance from beams and YLT with consideration of the friction effect and the segment side movement. All the calculations were performed for a symmetrical arrangement of three radial cracks (yield line) and a linear relationship of the load vs. deflection up to peak load at a central deflection of 0.5 mm. 160 30 25 Exp. #1 Exp. #2 Exp. #3 —"—Exp. av. Calculated IN \ N \ N 10 15 20 25 Deflection (mm) (a) Panel with SFRC 0.5% 30 35 40 10 15 20 25 Deflection(mm) (b) Panel with SFRC 1.0% 30 35 40 161 25 0 s Exp.#1 Exp.#2 Exp.#3 —«•— Exp. av — -Calculated 1 -ft il Ai . • . . • . 5 10 15 20 25 30 35 Deflection (mm) (c) Panels with PPFRC0.5% 0 \ 1 r 1 1 ' ' r 0 5 10 15 20 25 30 35 Deflection (mm) (d) Panels with PPFRC 1.0% Figure 12.8 Comparison of RDP performance: experimental vs. calculated 162 12.7 Discussion From Fig. 12.8, overall, the numerical results for the four types of FRC gave reasonable predictions. This can also be seen from the similar flexural failure pattern of the beams and panels shown in Fig. 12.9. For comparison, the corresponding peak load and toughness values from both calculation and experiment are summarized in Table 12.3 and 12.4. Figure 12.9 Typical crack rotation of specimens with SF-FRCO.5% after test Concrete type Peak load (kN) Predicted from Eq. (12-3) * Calculat ed by model From experiment Cal./ Exp. Ratio #1 #2 #3 Av. Cov. SFRC0.5 20.3 22.1 24.6 22.8 22.2 23.2 0.07 0.95 SFRC 1.0 20.5 25.6 27.9 23.6 25.5 25.7 0.12 0.99 PP-FRC0.5 19.9 22.3 19.0 20.4 19.8 19.8 0.05 1.12 PP-FRC 1.0 21.3 20.7 20.7 23.6 20.5 21.6 0.11 1.01 163 Table 12.4 Comparison of toughness of FRC panels (experimental vs. calculated) Concrete type Toughness at 40mm central deflection (J) Calculated by model From experiment Cal./Exp. Ratio #1 . #2 #3 Av. Cov. SFRC0.5 340.0 297.1 312.5 339.0 316.2 0.08 1.07 SFRC 1.0 574.7 507.3 477.3 551.0 511.8 0.08 1.12 PP-FRC0.5 264.9 258.5 238.5 255.1 250.7 0.06 1.06 PP-FRC 1.0 401.1 395.2 440.1 471.0 435.4 0.10 0.92 As expected, the peak loads calculated by Eq. 12-3 and YLT are different, with lower values for the former prediction (Table 12.3), most likely because of the adoption of the classical solution for fully supported panels in the elastic range. It was found that the calculated RDP load capacities for all cases except for PPFRC 1.0% (Fig. 12.8d and Table 12.4), are somewhat higher than those observed from the experimental data, though the discrepancy decreases with the deflection of all panels. These discrepancies between predicted and experimental behavior may be explained by the following approximations in the model: The first factor relates to the applicability of the moment capacity m from a 3-point bending test. Since the deformation behavior of a round panel, in particular at large deflections, is a superposition of segment rotation and axial tension across cracks, then strictly speaking, m from 3-point flexural test should not be used directly in the right side of Eq. 12-7. The mechanism is shown schematically in Fig. 12.10. Due to the existence of the lateral tensile force F, load PI (case a) will give a greater moment of resistance m compared to that from P2 (case b). Consequently, in the current model, direct application of the experimental data "m" leads to overestimation and causes an inherent discrepancy. In other words, tensile-bending, rather than the three-point bending test, is preferred to be used to obtain the moment resistance of the material. 164 1 XT displacement (a) One-way flexure- (b) Complex Flexure-with 3 segments without the 3rd segment and segment sliding Figure 12.10 Three-point bending tests and their applicability in panel interpretation Second, the simplifying assumption of three symmetrical cracks in the YLT analysis yields a higher value. According to YLT, the most likely yield lines occur in a path with the least requirement for energy dissipation. In reality, angles between cracks are not always equal to 120°. The last and the most challenging task to predict RDP behavior is the complexity of tensile bending condition imposed in broken panel segments and the interactions resulting from the movement of the third segment. The tensile force is applied on each segment and this affects both energy absorption and overall performance. When CCMOD was used, this interaction is, at least partially, taken into consideration because both rotation and movement of the concrete segments were included in this term (Chapter 5). This might possibly have mitigated the incorrect assumptions for YLT in round determinate panels. Also, in the current model the effect of friction between plate segments and supports has been taken into consideration. Therefore large discrepancies in large deflection were not observed as reported by others [154,116]. 165 Overall, an acceptable prediction, with ratios ranging from 5-10% in terms of toughness, implies that the discrepancies due to the above mechanisms are mitigated to some extent and that removing the friction effect due to segment moving upwards on each support was desirable. 12.8 Conclusions (1) An approach combining YLT and beam tests has been developed and validated in order to predict both pre- and post- crack performance of round FRC panels. (2) For the four FRC mixes, the ratios of predicted load capacity and toughness over experimental results indicated that the model could predict round FRC concrete panels with reasonable accuracy. (3) The pre-peak performance prediction based on the correlation between RDP and a simply fully-edge supported panel setup gave a lower bound peak load, and may be used as an approximation of peak load. (4) Taking the friction effect into consideration and using the concept CCMOD improved the commonly-used YLT model and led to better performance prediction. 166 CHAPTER 13 CONCLUSIONS AND FUTURE WORK 13.1 Conclusions The primary conclusions that can be drawn from the present investigation are as follows: A). In general, the round determinate panel test method is suitable and capable of characterizing both static and dynamic performance of fiber, wire welded mesh and hybrid reinforced concrete. Under static loading: (1) The proposed modified ASTM RDP method (measuring the rotation and slip of the broken concrete segment), is capable of characterizing the crack-opening resistance of FRC with reasonable accuracy. (2) RDP deforms in a complicated manner, though it generally breaks into three pieces. The term "CCMOD", defined as central crack mouth opening displacement, can be used to experimentally obtain the average crack width. (3) Steel fibers are less effective than synthetic fibres for crack-resistance at large CCMOD values. For the tested synthetic fibres, the PP structural fibres exhibited better performance than the others. (4) The matrix strength level had a negative effect for both SFRC panels and PPFRC panels in terms of crack control due to the matrix brittleness and the very good fibre-matrix bond. Under dynamic loading: (1) The dynamic RDP test setup proposed in this study is feasible to investigate FRC, WWM-RC and Hybrid reinforced panels in terms of failure mode, true load and deflection, giving a good indication of residual performance of these reinforcements under impact loading. 167 (2) The round panel impact method required relatively lower inertial load correction compared to beam impact tests. (3) The negative effect of a high strength matrix under static loading can also be found under impact loading, particularly for PPFRC. Compared to steel fibers, PP fibers appeared less effective in improving the toughness of very high strength concrete. (4) The higher matrix strength rendered VHS-FRC less strain-rate sensitive in terms of peak load, but the effect of matrix strength is unclear in terms of dynamic toughness. B). The combined use of polymer and steel fibers resulted in higher load capacity and toughness than for SFRC alone. Polymer addition causes SFRC to exhibit different strain-rate sensitivity from SFRC. PM-FRC under flexural loading (RDP test): (1) The effect of polymer additions on FRC is more significant for steel fiber reinforced concrete than for PPN fiber reinforced concrete, increasing load capacity and toughness of FRC. (2) Based on a comparative study on FRC and PM-FRC mixes via two test geometries (beam and round panel specimen), the comparative evaluation (ranking of fiber effectiveness) of different FRC mixes may depend upon the test geometry and deflection selected. (3) Improvement of toughness due to polymer addition is less significant under impact loading than that under static loading. (4) Polymer addition rendered SFRC less strain rate sensitive in terms of dynamic toughness, but did not particularly affect the strain rate sensitivity in terms of peak load. Under uniaxial loading, however, SFRCs with polymer modification are more strain rate sensitive in terms of dynamic strength (peak load) than those without polymer inclusion. 168 PMC and PM-FRC under uniaxial loading: (1) The compressive strength, elastic modulus of PMC and PM-FRC tends to decrease with an increase in polymer-cementitious materials ratio at the same water-cement ratio; Optimum polymer-cementitious materials ratios (5 -10%) appear to exist in PM-FRC systems in terms of toughness improvement under impact loading. (2) Steel fibers have a more significant effect on the compressive toughness than on the strength under static loading. Polymer, however, had a much greater effect on these parameters, and improved the toughness of the plain concrete. (3) PMCs (no fiber) become less sensitive in terms of compressive toughness with the increasing of polymer: cementitious materials ratio. (4) The compressive toughness increased with the drop height of the impact hammer for both PMC and PM-FRC, but under the highest drop height, the toughness tended to decrease due to decreased deflection and fiber fracture. C). Hybrid reinforcement exhibits better toughening effect on concrete and show different strain rate sensitivity. Damage evolution could be further studied by using post-impact static loading. (1) The addition of fibers increased both the loading carrying capacity and the toughness of the specimens, with steel fibers being somewhat more effective than synthetic fibers in this regards. (2) Similar to FRC panels, high strength panels with hybrid reinforcement tended to exhibit less ductility than normal strength panels. (3) Under impact loading, the toughness and peak loads of HyRC panels increased with an increase in the drop height. Overall, the deformed steel fibers and normal strength matrix showed a more favorable toughening effect. (4) The combination of WWM and fibers makes the systems less strain rate sensitive than systems reinforced only with WWM. 169 (5) Post-impact static test is able to investigate damage caused by impact loading. Three definitions of damage, based on residual peak load, stiffness and toughness obtained from post-impact static test, showed very different damage levels. Damage in terms of toughness is probably the most suitable for measuring the residual performance of HyRC panels. D). R D P performance can be predicted on the basis of Yield Line Theory and information from beam tests. (1) An approach combining YLT and beam test has been developed and validated in order to predict both pre and post crack performance of round FRC panels. (2) For the four FRC mixes, the ratios of predicted load capacity and toughness over experimental results indicated that the model could predict round FRC concrete panels with reasonable accuracy. (3) Taking the friction effect into consideration improved the commonly-used YLT model and led to better performance prediction. 13.2 Future works During the experimental work and analysis on the performance of specialized composites, a number of interesting questions and topics for further research were identified: A). R D P test method implementation (1) Crack width measurement and dynamic crack propagation It is of interest to further implement the round panel impact setup to investigate the crack propagation process and stress wave rate in concrete panels under impact loading. Instead of using traditional sensors, high-speed image technology may be used to capture both rotation and side slide of panel segment. By using similar concepts to CCMOD 170 derived under static loading (in Chapter 5), dynamic CCMOD can be experimentally obtained. These would advance our understanding on the cracking mechanism of the dynamic RDP test in the presence of different types/amounts of reinforcement (either FRC or hybrid reinforced concrete panels). (2) Study on FRC panels subjected to dynamic punching load (punching failure) Little is known on performance of fiber-reinforced concrete/shotcrete subjected to dynamic punching loads. Even under static loading, the behavior of concrete subjected to punching load is dependent on a number of factors. Taking FR-Shotcrete for tunnel linings as an example, the boundary conditions such as bolt type and length, bonding properties between FRC and rock, and shear performance of FRC itself are all critical. A study is desirable to understand the performance in this regard under both static and impact loading. Consequently it could be used to provide design parameters for tunnel lining projects, where concrete could be subjected to various loading conditions with large deflection. (3) Fiber reinforced shotcrete (FRS) vs. Cast FRC: Extending FRS to FRC There are limited data comparing FRS and cast FRC under static loading, showing that the spray process has a significant effect on both strength and toughness of hardened FRC. There exists a need to examine the effect of placing method under dynamic loading using RDP method. Consequently, a study of this aspect will help to better understand the dynamic performance and provide some insight for the design of "real" FRS, which is one of the most effective engineering practices in tunnel lining, structural repair and rehabilitation. B). Materials property characterization (1) Compatibility and optimization of fiber and concrete matrix system In line with the results reported in Chapter 7, a high strength concrete matrix leads to reduced toughness due to brittleness of the matrix and "too good" bond between fibers and matrix. To achieve a better toughening effect under both static and impact loading, 171 research on compatibility (Optimization) between Fiber (type and tensile strength), matrix (strength) and interface properties needs to be carried out. (2) Synthetic fiber reinforced concrete: creep concern and high temperature There exists a concern regarding the creep performance of synthetic fiber reinforced concrete. Due to the nature of the polymer, the mechanical properties of synthetic fibers are strongly dependent on the existing form of polymer, time, temperature and stress. Take polypropylene (a semi-crystalline material) as an example, whether PP is in either homo-polymer, or block copolymer, or random copolymer and the presence of filler modification, the degree of crystallinity and orientation affects the mechanical properties of fibers. Very little is known for different types of synthetic fiber reinforced concrete under creep loading or under high temperature environment. RDP method may be used for that research. (3) Polymer modified comentitious composites Durability of concrete is a major concern. Though it is widely accepted that concrete with polymer addition has increased durability, the durability of PM-FRC has still not been extensively studied. Some accelerated tests should be undertaken. In addition, to understand the dynamic performance of PM-FRC under uniaxial compressive loading, static and dynamic pullout test shall be carried out to characterize bonding behavior between modified concrete matrix and steel fibers. (4) Hybrid fiber reinforcement Hybrid reinforced panels with mesh and macro fibers have shown better toughness than any individual reinforcement (in Chapter 10), and previous researchers demonstrated possible synergy of flexural toughness under static loading with small deflection. There is interest in research on FRC with macro and micro fibers under large deflections. ASTM C1550 and proposed dynamic test method in this work may be used for this purpose. 172 (5) Concrete with fiber-reinforced polymer (FRP) rebar and strengthening materials under impact loading Fiber reinforced polymer, in the form of either rebar or fabric wraps (or sprayed FRP), is becoming increasingly accepted in retrofitting existing concrete structures due to its inherent corrosion-resistant nature and tailorable properties. Understanding the response of FRC in the presence of FRP reinforcement/strengthening will help to advance the knowledge and use of these innovative materials. C). Predictive modeling for reinforced round panel under both static and dynamic loading Many issues remain unsolved in performance prediction for reinforced round panels. As mentioned in Chapter 11, there is a more fundamental way to predict the behaviour of reinforced panels under static loading by applying the constitutive laws of FRC, combined with Finite Element Methods and fracture mechanics. A further development of dynamic materials model accounting for the effects of fibers and strain rate effect is possible. Commercial finite element programs such as LS-DIANA may serve as a platform for modeling FRC round panels under impact loading. Eventually, these models could lead to design methodologies for applications of FRC and Mesh-RC or hybrid RC in high stress-rate environment. 173 Bibliography [I] ASTM C1018, Standard test method for flexural toughness and first-crack strength of fiber reinforced concrete, American Society for Testing and Materials, West Conshohocken, PA, 2003. 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Balkema Pubishers, 2004, pp.59-66. [138] Roark, Raymond J. and Young, Warren C, Formulas of stress and strain, McGraw-Hill Inc., Section 10 & 11, 1975, pp.405-406. [139] Mindess, S. and Vondran, G., Properties of concrete reinforced with fibrillated polypropylene fibers under impact loading, Cement and Concrete Research, Vol.18, Issue 1, 1988, pp. 109-115. [140] Bischoff, P. H. and Perry, S. H., Compressive Behaviour of Concrete at High Strain Rates, Materials and Structures, Vol. 24, 1991, pp.425-450. [141] Su, Z., Microstructure of polymer cement concrete, PhD thesis, Delft University press, 1995, pp.16-18. [142] Westergaard, H.M., New formulas for stresses in concrete pavements of airfields, Transactions of the American Society of Civil Engineers, Vol. 113, 1948, pp.425-444. 187 [143] Johansen, K.W., Yield line theory, Cement and Concrete Association, London, 1962. [144] Johansen, K.W., Yield-line formulae for slabs, Cement and Concrete Association, London, 1972. [145] Park, R. and Gamble, W.L., Reinforced concrete Slabs, Second edition, John Willey & Sons, Inc., 2000. [146] Roesler, J.R., Lange, D.A., Altoubat, S.A., Rieder, K. and Ulreich, G. R., Fracture of plain and fiber-reinforced concrete slabs under monotonic loading, J. Mat. in Civ. Engrg., Vol.16, Issue 5, 2004, pp. 452-460. [147] Roesler, J., Altoubat, S., Lange, D., Reider, K-A. and Ulreich, G., Effects of synthetic fibers on structural behaviour of concrete slabs on ground, ACI Materials Journal, Vol.103, No.l, Jan-Feb, 2006, pp. 3-10. [148] Falkner H. and Teutsch M., Comparative investigations of plain and steel fiber reinforced industrial ground slabs, Institut fur Baustoffe, Massivbau und Brandschutz, Technical University of Brunswick, Germany, No. 102, 1993, 70 pp. [149] Lok, T.S. and Pei, J.S., Elastic deflection of concrete slab reinforced with different types of steel fibers, in Edward G. Nawy (Ed.), Recent Developments in Deflection Evaluation of Concrete, ACI SP161-12, American Concrete Institute, 1996, pp267-284. [150] Barros, J.A.O. and Figueiras, J.A., Model for the analysis of steel fiber reinforced concrete slabs on grade, Computers & Structures, Vol. 79, No.l, 2001, pp97-106. [151] Boulfiza, M., Banthia, N., and Sakai, K., Application of continuum damage mechanics to carbon fiber-reinforced cement composites, ACI Materials Journal, Vol.97, No.3, May-June, 2000, pp.245-253. [152] Nilsson, U. and Holmgren, J., Load bearing capacity of steel reinforced shotcrete linings, In E.S. Bernard (ed.), Shotcrete: Engineering Developments, A.A.Balkema, Print, Swets&Zeitlinger, Lisse, 2001, pp. 205-212. [153] Bernard, E.S. and Pircher, M., Influence of geometry on performance of round determinate panels made with fiber reinforced concrete, Engineering report No. CE10, University of West Sydney, Australia, January, 2000, 42pp. 188 [154] Tran, V.N.G., Beasley, A.J. and Bernard, E.S., Application of Yield Line Theory to round determinate panels, in E.S. Bernard (ed.), Shotcrete: Engineering Developments, Swets, and Zeitlinger, Lisse, A.A.Balkema, 2001, pp.245-254. [155] Dupont, D. and Vandewalle, L., Comparison between the round plate test and the RILEM 3-point bending test, in M. di Prisco, R. Felicetti and G.A.Plizzari (eds.), Proceedings of the Sixth International RILEM Symposium on Fiber Reinforced Concrete (PRO 39), BEFIB2004, RELIM publications S.A.R.L, 2005, pp.101-110. [156] Tran, V.N.G., Beasley, A.J., and Bernard, E.S., Monte Carlo analysis for crack modelling in fiber reinforced shotcrete panels, Int. Conf. on Advanced Technologies in Design, Construction and Maintenance of Concrete Structures, Hanoi, Vietnam, ICCMC/IBST, 2001. [157] Tran, V. N. G., Bernard, E. S. and Beasley, A. J., Constitutive modelling of fiber reinforced shotcrete panels, J. Engrg. Meek, Vol. 131, Issue 5, 2005, pp. 512-521. [158] Barros, J.A.O., Cunha, V.M.C.F., Ribeiro, A.F. and Antunes, J.A.B., Post-cracking behaviour of steel fiber reinforced concrete, Materials and Structures, Vol.38, January-February, 2005, pp. 47-56. [159] Kennedy, K. and Goodchild, C, Practical yield line design guidance, British Cement Association, http://www.concretecentre.com/PDF/PYLD240603a.pdf, 2003. [160] Bernard, E.S., The role of friction in post-crack energy absorption of fiber reinforced concrete in the round panel test, Journal of ASTM International, Vol.2, Issue 1, 2005, 12 pp. [161] Roark, R.J. and Young, W.C., Formulas for stress and strain, 5th edition, McGraw-Hill Book Company, 1975. 189 Appendix A: Publications and presentations [1] Xu, H., Mindess, S., and Banthia, N., Toughness of polymer modified, fiber reinforced high strength concrete: Beam tests vs. Round panel tests, in K. Kovler, J. Marchand, S. Mindess and J. Weiss (eds.), Proceedings of International Symposium: Advances in Concrete through Science and Engineering (CD-ROM), ACBM, Northwestern University, Evanston, Illinois, USA., March 21-24, RILEM Publications, Pro 48, 2004. (Chapter 4) [2] Xu, H., Qian Gu and Mindess, S., Deformation of round determinate panels containing fibers, in D.R. Morgan and H.W. Parker (eds.), Shotcrete for Underground Support X Conference, Engineering Conferences International (ECI) and American Shotcrete Association (ASA), Whistler, Canada, Sept. 12-16, 2006, ASCE publications, pp. 138-149. (Chapter 5 ) [3] Mindess, S., Banthia, N. and Xu, H., Fiber reinforced round panels subjected to impact loading, in K. Kovler, J. Marchand, S. Mindess and J. Weiss (eds.), Proceedings of International RILEM Symposium on Concrete Science and Engineering: A Tribute to Arnon Bentur, RILEM Publications S.A.R.L, 2004, pp. 165-174. (Part of Chapter 6) [4] Xu, H., Mindess, S. and Duca, J. J., Performance of plain and fiber reinforced concrete panel subjected to lower velocity impact loading, in M.di. Prisco, R. Felicetti and G.A. Plizzari (eds.), Proceedings of the Sixth RILEM Symposium on Fiber Reinforced Concrete (FRC), BEFIB 2004, Varenna, Italy, RILEM publications S.A.R.I., Vol. 2, pp. 1257-1268. (Part of Chapter 6) [5] Xu, H., Mindess, S., and Banthia, N., Impact resistance of normal strength and very high strength FRC round panels, in G. Fischer and V.C. Li (eds.), Proceedings of RILEM Workshop on High Performance Fiber Reinforced Composites in Structural Applications (HPFRCC'05), Hawaii, USA, RILEM Pro 49, RILEM Publications S.A.R.L, 2006, pp.561-570. (Chapter 7) [6] Xu, H. and Mindess, S., Effects of polymers on steel fiber reinforced round concrete panels under impact loading, in V. Bilek and Z. Kersner (eds.), Proceedings of the 2nd International Symposium Non-Traditional Cement & Concrete, June 14-16, 190 2005, Brno University of Technology, Brno, Czech Republic, pp.604-612. (Chapter 8) [7] Xu, H., Mindess S., Fujikake, K., Impact performance of latex-modified high strength FRC under uniaxial compressive loading, in N. Banthia, T. Uomoto, A. Bentur and 5. P. Shah (eds.), Proceedings of the 3rd International Conference in Construction Materials (CD-ROM), ConMat'05, University of British Columbia, Vancouver, Canada, 2005, (Chapter 9) [8] Xu, H. and Mindess, S., Behaviour of concrete panels reinforced with welded wire mesh and fibers under impact loading, in D.R. Morgan and H.W. Parker (eds.), Shotcrete for Underground Support X Conference, Engineering Conferences International (ECI) and American Shotcrete Association (ASA), Whistler, Canada, Sept. 12-16, 2006, ASCE publications, pp.99-110. (Chapter 10) [9] Xu, H. and Mindess, S., Damage evolution of round concrete panels with hybrid reinforcement subjected to low-velocity impact, in F. Toutlemonde, K. Sakai, O.E. Gjorv and N. Banthia (eds.), Proceedings of the Fifth International Conference on Concrete under Severe Conditions Environment and Loading (CONSEC'07), June 4-6, 2007, Tours, France, LCPC publications, pp.1313-1322. (Chapter 11) 191 Appendix B: Instrument calibration 1800 Output (v) B-2 Bolt load cell 192 B-3 Laser Transducer B-3-1 Basic properties of the instrument P o r t N u m b e r A N R 1 1 1 5 1 A N R 1 2 1 5 1 C e n t e r P o i n t D i s t a n c e 1 3 0 m m 5 . 1 1 8 i n c h M e a s u r a b l e R a n g e ± 5 0 m m ± 1 . 9 6 9 i n c h L i g h t S o u r c e V i s i b l e l a s e r d i o d e ( 6 8 5 n m ) P u l s e W i d t h / M a x . O u t p u t / L a s e r C l a s s 15 MS (Duty 50%)/0.4mW (Peak value)/Class 1 (IEC825) 15 us (Duty 50 %)/1.6 mW (Peak value)/Class 2 B e a m S p o t D i a m e t e r 0 . 7 x 1 .4 m m . 0 2 8 x . 0 5 5 i n c R e s o l u t i o n ( 2 ( 7 ) 1 0 H z 1 0 0 H z 1 k H z 100 p m .0039 inch 10Mv 20 ijm .0008 inch 2mV 330 um .0130 inch 33mV 65 pm .0026 inch 7mV 1 mm .039 inch 100mV 200 Mm .0079 inch 20mV L i n e a r i t y E r r o r (%Foi* ± 0 . 2 % o f F.S. P r o t e c t i v e C o n s t r u c t i o n ( e x c e p t for c o n n e c t o r ) I P 6 7 A m b i e n t L i g h t L e v e l ( f l u o r e s c e n t l a m p ) M a x . 2 , 5 0 0 I x Max. 3,000 Ix W e i g h t ( w i t h c a b l e ) 3 0 0 g 1 0 . 5 8 o z Sensor (with cable): 240 g 8.47 oz, Relay Cable: 130 g 4.59 oz •White ceramics is the target of this value 193 B-3-2 Measurement principle of the LM10 (optical triangulation) The mechanism of deflection measuring of the LT is shown in the following figure. Part of the light rays, which come from the target object by means of diffuse reflection, are focused to produce a light spot on the position sensing device (PSD). The location of this light spot varies depending on the distance of the target object. By measuring the change in the location of the light spot, the LM10 can measure the displacement of the target object. Position sensing dwios (PSD) Light receptor tens Measurable range g B-3-2 Schematic of PSD B-3-3 Range of measurement of Laser transducer L M 1 0 - 1 3 0 ( A N R 1 1 1 5 1 , A N R 1 2 1 5 1 ) I O J fJSZr <yy M3E3P M n c h ) .aiif"1 ' 01^ » * B«am i (nn i n c h ) Center poinl — distance (130 mm 5.1 ta tnch)| K- Measurable range -H Alarm output ON I Distance (mm inch) B-3-3 Range of measurement of laser transducer 194 1# Sensor -0.5 J Rotation (degree) #2 Sensor Rotation (degree) #3 Sensor -0.5 Rotation (degree) B-4 Angle-measuring sensors Appendix C: Basic properties of concrete mixes: fresh and hardened FRC C-l Fiber additions and properties of resulting mixtures (HSC Matrix) Concrete type Plain SFRC PPN -FRC Fiber volume fraction (Vf), % 0 0.5 1.0 0.5 1.0 Slump, mm 70 75 50 55 45 Air content, % 3.6 4.0 4.1 3.9 4.4 Compressive strength, (MPa) 83.2 85.0 88.0 71.3 69.6 Elastic modulus E (GPa) 42.2 42.1 42.3 - ' -C-2 Fiber additions and properties of resulting mixtures (PM-HSC matrix)* Matrix type PM10-HSC Fiber Type & Volume fraction (Vf), % Plain Steel Fiber 0 0.5 1.0 Slump, mm 80 75 68 Air content, % 3.8 4.3 4.2 Compressive strength, (MPa) 81.6 74.8 80.9 E (GPa) - 35.1 37.2 •Static and dynamic compressive strengths of other PM-SFRC were shown in Chpater 9. C-3 Fiber additions and properties of resulting mixtures (NSC and VHSC) Matrix type NSC VHSC Fiber Type & Volume fraction (Vf), % Plain Steel Fiber PP Fiber Plain Steel Fiber PP Fiber 0 0.5 1.0 0.5 1.0 0 0.5 1.0 0.5 1.0 Slump, Mm 80 75 65 50 40 115 110 80 95 70 Air content, % 3.2 4.0 4.2 4 4.5 3.5 3.3 4.0 3.7 4.4 Compressive strength, (MPa) 53.2 51.0 53.8 57.3 47.8 133.2 131.9 147.3 108.9 107.5 E (GPa) - 34.3 34.7 33.6 34.1 - 45.2 45.6 42.4 44.0 Splitting tensile strength (MPa) - 4.49 6.08 3.83 4.27 - 6.89 8.89 5.16 5.29 196 Appendix D: Deformation of RDP D-l Front view D-2 Bottom view before cracking x D-3 Cross Section of AC after cracks propagate I. Derivation of the relationship amongst (p, 8 and s Figs.D-1, D-2 and D-3 schematically illustrate the deformation and cracking of RDP from three different points of view. After a crack propagates from the central point O to the edge of the panels between any two supports, point D on the bottom edge of RDP (in Fig. D-2) splits into D' and D" (in Fig.D-1); point B moves to B' and B" (in Fig.D-3). Obviously, the deflection at point B (mid point of AC) SD 1 S smaller than that at the center O (central deflection) <5. The fan shape segment O-FAD in Fig. C-2 can be considered as a rigid body, rotating along line AE, therefore, § can be calculated: B § = (BE/OA) {AB(Cos30)/r}£ B <f)= 8B / A B = Cos30c?/ r For simplicity, the panel cracks are assumed to be symmetrical in this study, we have <f>=(pl2> Thus, (p = 2 0 = 2 Cos30 S/r where r = OA is variable during testing, depending on the relative movement of the segment, s r = (R-ov)-s, (p = 2 Cos30 ^ /(R-ov-s) .... (1) II. Derive the relationship amongst S\ (p and CCMOD In Fig. C-3, crack opening can also be written as (pi 2 = (CCMOD/2)/(tj-x) Substitute it into Eq. (1), then, Cos30 81 (R-ov-s) = (CCMOD/2)/ (td-x) Thus> _ CCMOD -(R-ov-s) ••• (2) 2 c o s 3 0 - ( f r f - x ) Where, ta and x are thickness of the panel and height of the compression zone. According to experimental work, the rotation of three segments dominates and the size of x is negligible after the central deflection reaches 15mm. 198 

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