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Impact behaviour of fiber reinforced wet-mix shotcrete Gupta, Prabhakar 1998

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IMPACT BEHAVIOUR OF FIBER REINFORCED WET-MLX SHOTCRETE by PRABHAKAR GUPTA B. Tech., Institute of Technology, Banaras Hindu University, 1994 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1998 © Prabhakar Gupta, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Date DE-6 (2/88) 11 ABSTRACT The use of shotcrete for ground support in mines and tunnels has increased dramatically within the past ten years. It has long been used in the construction of dams, canals, and reservoirs, in the repair and rehabilitation of marine, highway and railway structures, and in rock stabilization work. Many of these applications are vulnerable to impact and impulsively applied loads. Traditionally, these loads were taken care of in design by providing welded wire-mesh reinforcement. Efforts are being made to replace conventional steel wire-mesh reinforcement with fibers to reduce the project completion time and cost, and to minimize sand pockets and shotcrete rebound. With this perspective, assessment of impact behavior of fiber reinforced wet-mix shotcrete assumes great significance and importance. In the first part of this study, plain and fiber reinforced shotcrete beams were tested under impact, and the data were compared with static test data on companion beams. It was found that wet-mix shotcrete is a highly strain-rate sensitive material. In general, it is stronger, stiffer, and more energy absorbing under impact than under static loading. This sensitivity is far more pronounced for plain shotcrete than for fiber reinforced shotcrete. Inclusion of fibers considerably enhances the energy absorbing capacity of shotcrete under impact load. This improvement in energy absorbing capacity is, however, not as pronounced as that under static conditions. Beams are essentially one-dimensional elements, subjected to uni-axial stresses. In mines and tunnels, shotcrete linings are invariably subjected to a bi-axial or tri-axial stress-state. To better simulate the multi-axial stress conditions, in the second part of this study plain and fiber reinforced shotcrete plates were tested under static and impact loads. Load vs. deflection data thus obtained was analyzed in a routine manner to calculate fracture energies absorbed at deflections of 2 mm, 5 mm, 10 mm, and 15 mm. As in the case of beams, peak loads and fracture energies of fiber reinforced shotcrete plates were compared with their unreinforced counterpart to get an idea of the effectiveness of fiber addition to the plain brittle shotcrete. Under static load, only steel fibers made a useful Ill addition to the peak load supported by plates. At the high strain-rates associated with impact, however, none of the fibers enhanced the load-bearing capacity considerably. Under static load, all of the macro-fibers considerably improved the energy absorption capability, the prominent being hooked-end steel fiber, followed by flat-end steel fiber, polypropylene fibers, twin-cone steel fiber, and PVA fiber in that order. Similar trends were observed under impact. However, the improvements were much more pronounced under static conditions compared to impact. Plain shotcrete, micro-fiber reinforced shotcrete, and macro-fiber reinforced shotcrete all exhibited increased peak loads at higher rates of loading. Unlike macro fiber reinforced shotcrete beams, macro FRS plates are not sensitive to strain-rate, when it comes to energy absorption capacity. Finally beam data were compared with the plate data. Beams were found to be more stress-rate sensitive as compared to plates. This observation suggests that the stress-rate sensitivity of shotcrete is geometry dependent. The roots of this dependence lie, probably, in the cracking process and failure mechanism of beams and plates. TABLE OF CONTENTS Abstract ii Table of Contents iv List of Tables vii List of Figures viii List of Symbols xiii Acknowledgement xv Chapter 1 - Introduction 1 Chapter 2 - Objective and Scope 4 Chapter 3 - Literature Survey 3.1 - Introduction 7 3.2 - Rockbursts 10 3.2.1 - Estimated Radiation of Energy During Rockbursts 11 3.2.2 - Ejection Velocities of Rocks During Rockbursts 11 3.3 - Large Scale Impact Tests on Shotcrete 12 3.4 - Qualitative Study of the Strain-rate Sensitivity of Cementitious Composites.... 14 3.4.1 - Plain Concrete 14 3.4.2 - Fiber Reinforced Concrete 17 3.5 - Quantitative Study of the Strain-rate Sensitivity of Cementitious Composites.. 23 3.5.1 - Models for the Strain-rate Sensitivity of the Strength of Concrete 24 3.5.1.1 - Concrete as a Homogeneous Material (Macro-level) 25 3.5.1.2 - Concrete as a Multiphase Material (Meso-level) 32 3.5.1.3 - Concrete at Micro-level 32 Chapter 4 - Experimental Procedures 4.1 - Introduction 39 4.2 - Specimen Preparation 39 4.2.1 - Materials 40 4.2.2 - Mix Proportions 42 4.2.3 - Shotcreting Equipment 43 4.3 - Testing Program 45 4.3.1 - Static Testing 45 4.3.1.1 - Compression Tests on Cylindrical Cores 45 4.3.1.2 - Static Flexural Tests on Beams 45 4.3.1.3 - Static Flexural Tests on Plates 47 4.3.2 - Impact Testing 47 4.3.2.1 - Instrumented Drop-weight Impact Machine 50 4.3.2.2 - Impact Testing Procedure 59 4.3.2.3 - Impact Data Analysis 60 Chapter 5 - Beams Under Static and Impact Loading 5.1 - Introduction 71 5.2 - Shotcrete Beams Under Variable Stress-rate 71 5.3 - A Comparison Between Static and Impact data 84 5.3.1 - Flexural Strengths 84 5.3.2 - Flexural Toughness Factors 84 5.3.3 - Fracture Energies 85 5.3.4-The Constant N 89 5.4 - Discussion 91 5.5 - Conclusions 93 Chapter 6 - Plates Under Static and Impact Loading 6.1 - Introduction 94 6.2 - Shotcrete Plates Under Variable Stress-rate 94 6.2.1 - Plain and Carbon Micro Fiber Reinforced Shotcrete Plates 95 6.2.2 - Macro Fiber Reinforced Shotcrete Plates 99 6.2.2.1 - Steel Fibers 101 6.2.2.2 - Polymeric (Polypropylene and Polyvinyl Alcohol) Fibers 108 6.3 - Discussion 115 6.3.1 - Peak Loads 115 6.3.2 - Fracture Energies 122 6.4 - Conclusions 125 vi Chapter 7 - A Comparison Between Beam and Plate Results 126 Chapter 8 - Recommendations for Future Research 131 Bibliography 132 LIST OF TABLES Table 3.1 - A comparison between dry-mix and wet-mix shotcrete 8 Table 4.1 - Gradation for the aggregates used in the mixes 41 Table 4.2 - Fibers investigated 42 Table 4.3 - Mix proportions 43 Table 5.1 -Failure patterns of beams under static four-point bending test 75 Table 5.2 - Failure patterns of beams under three-point impact loading in flexure ... 75 Table 5.3 - Static and impact data on shotcrete beams 76 Table 5.4 - Fracture stresses under impact: a comparison between experimental data and values predicted by Equation (5.2) 92 Table 6.1 - Static and impact data on shotcrete plates: Peak Loads 114 Table 6.2 - Static and impact data on shotcrete plates: Fracture Energies 123 Table 6.3 - Static and impact data on shotcrete plates: Fracture Energies 124 LIST OF FIGURES Figure 3.1 - Strain-rate sensitivity of concrete: Plain vs. Fiber Reinforced 23 Figure 3.2 - Three different ways of determining the constant N 27 Figure 3.3 - Model of hardened cement with linked elements 35 Figure 4.1 - Wet-mix shotcreting in progress 44 Figure 4.2 - Use of a Yoke to measure true specimen deflections 46 Figure 4.3 - Schematic diagram of 578 kg impact testing machine 48 Figure 4.4 - Schematic diagram of 60 kg impact testing machine 49 Figure 4.5 - Schematic sketch of the impact test set-up used for shotcrete beams 50 Figure 4.6 - Instrumented drop-weight impact machine with a 578 kg hammer 51 Figure 4.7 - Instrumented drop-weight impact machine with a 60 kg hammer 52 Figure 4.8 - Tup and support used to test plate specimens 55 Figure 4.9 - Tup and support used to test beam specimens 56 Figure 4.10 - Accelerometer used and its location 57 Figure 4.11 - Typical output from the two channels of instrumentation 61 Figure 4.12 - Displacement distribution along the length and width of a simply supported plate subjected to a central load 64 Figure 4.13 - Displacement distribution along the length of a simply supported beam subjected to a central load 67 Figure 5.1 - Static and impact load-deflection plots for plain shotcrete beams 71 Figure 5.2 - Static and impact load-deflection plots for steel macro-fiber FI reinforced (V f = 0.64 %) shotcrete beams 72 Figure 5.3 - Static and impact load-deflection plots for steel macro-fiber F2 reinforced (V f = 0.59 %) shotcrete beams 73 Figure 5.4 - Static and impact load-deflection plots for steel macro-fiber F3 reinforced (Vf = 0.64 %) shotcrete beams 73 Figure 5.5 - Static and impact load-deflection plots for steel macro-fiber F l 1 reinforced (Vf = 0.55 %) shotcrete beams 74 Figure 5.6 - Static and impact load-deflection plots for polypropylene macro-fiber F4 reinforced (Vf = 0.96 %) shotcrete beams 77 Figure 5.7 - Static and impact load-deflection plots for polypropylene macro-fiber F5 reinforced (Vf = 1.43 %) shotcrete beams 78 Figure 5.8 - Static and impact load-deflection plots for polypropylene macro-fiber F6 reinforced (Vf = 1.19 %) shotcrete beams 79 Figure 5.9 - Static and impact load-deflection plots for polypropylene macro-fiber F7 reinforced (Vf = 1.12%) shotcrete beams 79 Figure 5.10 - Static and impact load-deflection plots for polyvinyl alcohol macro-fiber F10 reinforced (Vf = 0.68 %) shotcrete beams 81 Figure 5.11 - Static and impact load-deflection plots for carbon micro-fiber F8 reinforced (Vf = 2 %) shotcrete beams 82 Figure 5.12 - Static and impact load-deflection plots for carbon micro-fiber F9 reinforced (Vf = 2 %) shotcrete beams 83 Figure 5.13 - Ratio between flexural strength under impact and flexural strength under static load for various mixes 84 Figure 5.14 - JSCE Flexural toughness factors for various mixes under static and impact loading 86 Figure 5.15 - Fracture energy enhancement rendered to brittle cementitious matrix by different fibers under static and impact load 87 Figure 5.16 - Tup load and mid-span acceleration signals for (a) Plain shotcrete beam and (b) Steel fiber F l reinforced shotcrete beam 88 Figure 5.17 - Ratio between fracture energy absorbed under impact and fracture energy absorbed under static load for all the mixes investigated 89 Figure 5.18 - Strain-rate sensitivity of plain and fiber reinforced wet-mix shotcrete in flexure, a comparison with cast concrete. 1 Normal strength. 2 Steel fiber reinforced concrete 90 Figure 6.1- Test set-up for testing shotcrete plates under static load 95 Figure 6.2 - Moments and shears in a plate 95 Figure 6.3 - Plain shotcrete plate after static test 97 Figure 6.4 - Static and impact load-deflection plots for plain shotcrete plates 97 Figure 6.5 - Static and impact load-deflection plots for carbon micro-fiber F8 reinforced (V f = 2 %) shotcrete plates 98 Figure 6.6 - Static and impact load-deflection plots for carbon micro-fiber F9 reinforced (V f = 2 %) shotcrete plates 98 Figure 6.7 - Plain shotcrete plate after impact test 100 Figure 6.8 - Top surface of hooked-end steel fiber FI reinforced shotcrete plate after static test 102 Figure 6.9 - Bottom surface of hooked-end steel fiber FI reinforced shotcrete plate after static test 103 Figure 6.10 - Static and impact load-deflection plots for steel macro-fiber FI reinforced (V f = 0.64 %) shotcrete plates 105 Figure 6.11 - Static and impact load-deflection plots for steel macro-fiber F2 reinforced (V f = 0.59 %) shotcrete plates 105 Figure 6.12 - Static and impact load-deflection plots for steel macro-fiber F3 reinforced (V f = 0.64 %) shotcrete plates 106 Figure 6.13 - Static and impact load-deflection plots for steel macro-fiber FI 1 reinforced (V f = 0.55 %) shotcrete plates 106 Figure 6.14 - Hammer-specimen contact load vs. time pulse: flat end steel fiber reinforced plate vis-a-vis hooked end steel fiber reinforced plate 107 Figure 6.15- Top surface of hooked-end steel fiber FI reinforced shotcrete plate after impact test 109 Figure 6.16 - Bottom surface of hooked-end steel fiber FI reinforced shotcrete plate after impact test 110 Figure 6.17 - Static and impact load-deflection plots for polypropylene macro-fiber F4 reinforced (Vf = 0.96 %) shotcrete plates 112 Figure 6.18 - Static and impact load-deflection plots for polypropylene macro-fiber F5 reinforced (Vf = 1.43 %) shotcrete plates 112 Figure 6.19 - Static and impact load-deflection plots for polypropylene macro-fiber F6 reinforced (Vf = 1.19 %) shotcrete plates 113 Figure 6.20 - Static and impact load-deflection plots for polypropylene macro-fiber F7 reinforced (Vf = 1.12 %) shotcrete plates 113 Figure 6.21 - Static and impact load-deflection plots for polyvinyl alcohol macro-fiber F10 reinforced (Vf = 0.68 %) shotcrete plates 114 Figure 6.22 - Hammer-specimen contact load vs. time pulse: polymeric fibers reinforced plates vis-a-vis hooked end steel fiber reinforced plate 116 Figure 6.23 - Effect on peak load sustained by various shotcrete plates due to addition of fibers under static and impact load 117 Figure 6.24 - Ratio between peak load under impact and peak load under static load for various shotcrete plates 118 Figure 6.25 - Fracture energy values up to a deflection of 15 mm for various plates under static load 119 Figure 6.26 - Fracture energy values up to a deflection of 15 mm for various plates under impact 120 Figure 6.27 - Fracture energy enhancement rendered to brittle cementitious matrix by different fibers under static and impact load 121 Figure 6.28 - Ratio between fracture energy absorbed (up to a deflection of 15 mm) under impact and fracture energy absorbed under static load for various shotcrete plates. 122 Figure 7.1 - Moment, shear, and failure mechanism in a beam 126 Figure 7.2 - Strain-rate sensitivity in terms of peak load: Beams vs. Plates 127 Figure 7.3 - Strain-rate sensitivity in terms of fracture energy: Beams vs. Plates.... 128 Figure 7.4 - Yield mechanism in a simply supported square plate 129 Figure 7.5 - Yield mechanism in a plate with two opposite edges simply supported and two opposite edges free 130 LIST OF SYMBOLS h - Depth of the plate. 1 - Clear span of the beam/plate. D - Depth of the beam. ov - Length of the overhanging portion of the beam. A - Cross-sectional area of the beam. Vh - Hammer velocity. m h - Mass of the hammer. ah - Hammer acceleration. g - Acceleration due to gravity. H - Height of hammer drop. P t - The tup load. Pi - The generalized inertial load. Pb - The generalized bending load. u(x,y,t) - Deflection at any point (x,y) on the plate at time t. u0(t) - Mid-point deflection of the plate at time t. u (x,y,t) - Velocity at any point (x,y) on the plate, at time t u o(0 - Mid-point velocity of the plate at time t. u(x,y,t) . Acceleration at any point (x,y) on the plate at time t. xiv uo W - Mid-point acceleration of the plate at time t. &(x, y> t) . Virtual deflection at any point (x,y) on the plate at time t, compatible with the constraints. ^ o ( 0 - Mid-point virtual deflection of the plate at time t, compatible with the constraints. u(x,t) - Deflection at any point (x) on the beam at time t. u0(t) - Mid-span deflection of the beam at time t. ii(x, t) . Acceleration at any point (x) on the beam at time t. ii o(0 - Mid -span acceleration of the beam at time t. &i(x,y,t) . Virtual deflection at any point (x) on the beam at time t, compatible with the constraints. <^ o (0 - Central virtual deflection of the beam at time t, compatible with the constraints. CTc - Failure stress. °~ - Stress rate. ec - Failure strain. £ - Strain rate. Kic - Critical stress intensity factor. a - Crack length. AE - Energy lost by the hammer. XV ACKNOWLEDGEMENT First and foremost, I wish to thank Prof. Nemkumar P. Banthia, a dedicated researcher, for his friendly support, talent for organization, and invaluable guidance. His constant encouragement as my supervisor was much appreciated. My next acknowledgement must go to Dr. Cheng Yan for his unstinting help. I am also grateful to Prof. Sidney Mindess and Dr. D. R. Morgan for their constructive comments on my thesis. My special thanks are also due to Mr. David Flynn, Mr. Ashish Dubey, Mr. Hugo Armelin, and Mr. Kevin Campbell. The efforts of Mr. Doug Smith in preparing the machine components are greatly appreciated. I also wish to thank Mr. M . Nazar for maintaining the impact machine, and Mr. John Wong for maintaining the data acquisition system. xvi to my parents 1 Chapter 1 - Introduction Shotcrete is defined as mortar or concrete that is pneumatically applied at a high speed (ACI Committee 506 - 1990). An Austrian Concrete Society (1990) adjunct to this definition is that the mortar or concrete should be compacted by its own momentum. Shotcrete more than being a special material, is a special process used to place and compact cementitious materials. Over the years, several different processes have been developed all of which use compressed air to shoot concrete or mortar at high velocity onto a surface. The two most popular processes are the wet-mix shotcrete process and the dry-mix shotcrete process. Hybrid processes have also been developed. Use of shotcrete in new construction and in the repair and rehabilitation of older and deteriorated structures has grown rapidly over the years. Shotcrete has long been used in mines, tunnel linings, for rock slope stabilization, in the construction of dams, canals, sewers, culverts, and reservoirs, and in the repair and rehabilitation of marine, highway, and railway structures. In Eastern Europe, mainly in Germany and Austria, the dry process is more popular as compared to the wet process. On the other hand, in Northern Europe, primarily in Sweden and Norway, the wet process is predominantly used. In North America, shotcrete has traditionally been applied using the dry-mix process. However, with improvements in the pumping equipment and shotcrete materials technology, wet-mix shotcreting is catching up with the dry process. Wet-mix technique is characterized by a lower plastic stiffness of the mixture, which facilitates troweling and finishing of the sprayed surface. The other advantages of wet-mix shotcreting over the dry process are lower material rebound, better control over mix proportions (particularly the water/cement ratio), higher productivity, and a cleaner working environment with less dust [1]. As a result, wet-mix shotcrete tends to be better suited for applications in which a high standard of surface finishing is required (e.g., facades) or for applications of large volumes of shotcrete requiring a high productivity and for which rebound has a major implication on the final cost (e.g., secondary tunnel linings and lining of large underground cavities). 2 In the wet process, cement, aggregates, water and often additives are batched, mixed and fed into the shotcreting equipment. Conventional wet-mix concrete is pumped hydraulically to the nozzle where air is injected to project the mix into place. Presently, in more than half the applications, fiber reinforced shotcrete is used because of the enhanced toughness and impact resistance provided by the fibers. The primary reasons for adding discontinuous fibers to a cementitious matrix are to improve the post-cracking response of the matrix, i.e., to improve its energy absorption capacity and apparent ductility, and to provide crack resistance and crack control. Also, it helps maintain structural integrity and cohesiveness in the material. Most fiber reinforced concrete (FRC) or shotcrete (FRS) used in practice contains low volume fractions (less than 1 percent) of fibers. At such low volume fraction, however, improvement in the tensile, flexural, or compressive strengths are only nominal, and the matrix cracks essentially at the same stress and strain as when unreinforced. The real advantage of adding fibers is after matrix cracking, when fibers bridge these cracks and undergo pull-out processes, such that deformation can continue only with a further input of energy from the loading source. This property of fiber reinforced concrete or shotcrete — which manifests itself as the long descending branch in the load-deflection curve ~ is often referred to as toughness or energy absorption capability. Thus, fiber reinforced concrete or shotcrete exhibits better performance not only under static and quasi-statically applied loads, but also under fatigue, impact, and impulsive loadings. In the case of shotcrete, the toughening capabilities provided by the fibers have an added importance given the severe deformations imposed on shotcrete linings in service in mines and tunnels. Also, the improved energy absorption capability of fiber reinforced shotcrete is vital in applications subjected to impact loads, where a very large amount of external energy is suddenly imparted to the structures, and that too, in a fraction of a second. Traditionally, these loads were taken care of in design by providing welded wire-mesh reinforcement. Presently efforts are being made to replace conventional steel wire-mesh reinforcement with fibers to reduce the project completion time and cost, to reduce shotcrete rebound (given that the wire mesh is an obstacle to shotcrete placement), to eliminate voids and sand pockets behind the steel mesh, and to lower the shotcrete 3 consumption for irregular rock faces. Assessment of the impact behavior of fiber reinforced wet-mix shotcrete is, therefore, of critical importance. 4 Chapter 2 - Objective and Scope Plain and fiber reinforced shotcrete linings in rock stabilization and underground support construction in mines and tunnels are highly susceptible to impact loads, such as those caused by blasting or rock bursts. In the deeper hard-rock mines, high in-situ and mining-induced stresses lead to rockbursts in the form of extensive, unstable rock fracturing and rock-mass dilation causing sudden ground movement in openings and drifts [28]. Rockburst hazards increase as mines advance to greater depths, and high quality ground support is required to minimize rockburst damage and to enhance the safety of workers. Rockbursts have been dealt in detail in section 3.2. Although other shotcrete applications are less vulnerable to impact loads, these can't be summarily ruled out. To harness the full potential of fiber reinforced shotcrete in these applications, we need to: 1. Understand and assess the behavior of shotcrete under impact loading, 2. Highlight the differences in behavior, if any, with that under static load. In other words, indicate the extent of strain-rate sensitivity exhibited by wet-mix plain, and fiber reinforced shotcretes, and 3. Observe improvements, if any, with different fiber types and addition rates. Unfortunately, limited research has been conducted so far to evaluate the impact resistance of shotcrete, although the results of some crude impact tests have been reported [2,3,4]. ACI Committee 544 [2] published a test procedure for measuring impact resistance in which the number of blows of a standard compaction hammer necessary to crack and separate a plate specimen (38x152 mm diameter) is recorded. Two measurements are obtained: the number of blows required to cause the first visible crack, and the number of blows required to cause the cracks to open up sufficiently to make the specimen touch three of four positioning lugs in the apparatus. ACI Committee 506 [3] reported that plain shotcrete specimens normally failed after 10 to 40 blows, whereas the number of blows required to crack and separate fiber reinforced shotcrete specimens at 28 days ranged from about 100 to 500 or more depending upon the fiber content, fiber length, and type. 5 Using the ACI Committee 544 test procedure, Ramakrishnan [4] carried out some impact tests on dry-mix shotcrete reinforced with hooked-end drawn wire fibers, 30 mm long and 0.5 mm in diameter. He concluded that the hooked-end fiber shotcrete showed a remarkable ability to absorb impact load, and that this ability increased as the fiber content increased. It was noted during testing that specimens with obvious laminations in them tended to rupture at the laminations under repeated impact loading, which reduced the effective thickness of the test specimens, causing failure at a lower number of blows. These tests are crude in the sense that they measure impact resistance in terms of number of blows or the physical assessment of damage done to the specimen by the impact. Also, the criterion for failure is subject to human judgement error. A rational appraisal of impact resistance must be based on the amount of energy absorbed by the specimen during impact. To achieve this goal, an instrumented impact test procedure is required, which can lead to an impact load vs. deflection curve. Impact testing [5,6] using an instrumented drop-weight impact machine is one such test procedure. It accounts for inertial load, an integral part of high strain-rate testing, in an explicit manner. It has been successfully used to test beam specimens of cast plain concrete, fiber reinforced concrete, and conventionally reinforced concrete. The data from these tests [6,7,8] and the quantities and inferences derived from the test-data have been widely accepted. The data obtained were rational, free from parasitic effects of inertia, reliable, and reproducible. In practice, the constituents as well as the method of batching and mixing are the same for wet-mix fiber reinforced shotcrete as for cast fiber reinforced concrete. Also, the mixes are similar in composition and rheological characteristics. It is primarily the way of placing and compaction that is different [14]. Therefore, it seems logical to expect similar impact behavior from wet-mix fiber reinforced shotcretes and fiber reinforced concretes. However, before making any precipitous statements, two things need to be considered. Firstly, there are differences in the physical properties of specimens cast and the physical properties of specimens shot from the same concrete mixture. Fibers in a shotcrete panel tend to align themselves perpendicular to the direction of shooting [15]. Due to this preferential alignment of fibers, fiber reinforced shotcrete shows an improved flexural strength over cast concrete. Therefore, it is difficult to predict shotcrete behavior 6 on the basis of the performance of cast concrete of similar proportions [14]. In this study, plain and fiber reinforced shotcrete beams were tested under static and impact load; test results have been reported in chapter 5. Secondly, in most applications, shotcrete is applied as a surface coating or lining. These coatings are primarily subjected to surface loading, either static or both static and dynamic. This means that the shotcrete linings, which are subjected to static surface loading, typically remain in a state of plane stress, under the action of bi-axial in-plane bending moments and out-of-plane torsional moments. The state of stress under dynamic surface loading is much more complex than that in the case of static loading. So, the true behavior of shotcrete, whether under dynamic or static loading, can not be assessed by testing simple beam specimens. The two conditions when put together, stress the need for testing shotcrete plates, statically as well as dynamically. Therefore, in this study plain and fiber reinforced shotcrete plates were also tested under static and impact load; test results are reported in chapter 6. All the impact tests were performed on instrumented drop-weight impact machines. This study, thus, was directed towards: (a) assessment of impact resistance, and strain-rate sensitivity of plain and fiber reinforced shotcrete beams, (b) modification of the beam test set-up and data analysis procedure to carry out static and impact tests on plates in flexure, and (c) assessment of impact behavior, and strain-rate sensitivity of plain, and fiber reinforced shotcrete plates. The output from the testing program is more in the form of trends, and less in the form of basic material properties, although an attempt has been made to evaluate the basic material properties wherever possible. 7 Chapter 3 - Literature Survey 3.1 - Introduction Shotcrete can be defined as 'mortar or concrete pneumatically projected into place'. There have been many definitions over the years which have changed from specific (e.g. for gunite) to general covering all aggregate ranges and both dry and wet processes. Austrian Concrete Society (1990) defines it as mortar or concrete that is compacted by its own momentum. In a nutshell, it is a special process for placing and compacting cementitious materials. As shotcrete involves spraying of cementitious materials onto the target surface, it is especially advantageous in applications such as tunneling, mining, slope and rock stabilization, for which the use of formwork and ordinary cast concrete is relatively costlier and more time consuming. There are basically two distinct forms of shotcrete, depending on whether or not all the water is present when the concrete is introduced into the spraying machine. For the case in which all the water is present, the technique is named "wet-mix" shotcrete; on the other hand, when the materials are introduced into the spraying machine in the bone-dry state or containing only a part of the mixing water, the technique is named "dry-mix" shotcrete. As previously mentioned in Chapter 1, in Eastern Europe, mainly in Germany and Austria, the dry process is more popular as compared to the wet process. On the other hand, in Northern Europe, primarily in Sweden and Norway, the wet process is predominantly used. In North America, shotcrete has traditionally been applied using the dry-mix process. Although the definition of the two possible forms of shotcreting (wet or dry-mix) is given only by the form in which water is added, there are several distinctions between the two techniques [1]: 8 Table 3.1 - A comparison between dry-mix and wet-mix shotcrete. Dry-mix Shotcrete Wet-mix Shotcrete • Instantaneous control over mixing water and consistency of mix at the nozzle to meet variable field conditions. • Characterized by a greater stiffness of the mixture. • High cement content and so a high early age strength. • Lower cost of its equipment and the possibility to shoot as small a volume as desired when using bone-dry materials makes this technique especially attractive for NATM tunnel fronts, mining and overhead structural and cosmetic repair. • Good for remote sites because of the portability of the whole process. • High material loss caused by heavy rebound. • Mixing water is controlled at the mixing equipment and can be accurately measured. • Characterized by a low stiffness of the mix and thus the possibility of troweling and finishing the surface. • Less dust, low material loss due to rebound and a higher productivity. • - Better suited for applications in which a high standard of surface finishing is required. • Good for applications of large volumes of shotcrete requiring a high productivity and for which rebound has a major implication on the final cost (e.g. secondary tunnel linings and large underground cavities). • Higher equipment cost and the need to apply the entire batch of concrete before initial set. The use of shotcrete for ground support in mines has increased dramatically worldwide within the past ten years. In mines with rockburst problems, empirical evidence suggests that the application of shotcrete to bolted mesh creates tough support systems. However, little is known about the performance characteristics of shotcrete in burst-prone ground and visual observations alone are insufficient for rational design of shotcrete support. In addition, very little experimental effort has been focused on the load-displacement characteristics of mesh and shotcrete, especially their characteristics under dynamic or impact loading. Knowledge of the load-deformation capacity of shotcrete under static and dynamic loads is necessary for the engineering of tough, energy absorbing, support systems for burst-prone mines. These improvements will increase underground safety in hazardous ground conditions and will also reduce the costs of support by minimizing the use of inappropriate support or support that requires premature rehabilitation. When a structure is impacted with a projectile, the contact zone is subjected to intense dynamic stresses producing crushing, shear failure, and tensile fracturing. These stresses may result in the penetration, perforation, fragmentation and scabbing of the target. As a result of this complex behavior, the traditional approach for design has been to treat the local response separately from the overall structural response. The contact 9 zone is analyzed using various empirical formulae and the structure is analyzed for the stress pulse at the contact zone. A rational analysis of the contact zone and the structure requires an accurate knowledge of the constitutive properties of the structural material subjected to a wide range of strain-rates. For example, to correctly assess the energy absorption of a structure when subjected to impact loading, we should know the basic material properties at the particular strain-rate in question. In addition to the material properties, we also need to know the failure mechanisms and the various energy dissipating mechanisms. The National Defence Research Committee (NDRC) has proposed various empirical formulae to estimate the penetration depth (x) for the case of non-deformable cylindrical missiles impacting a concrete structure. The general form of the formulae is x = f(k,W,d,v) (3.1) Where k is a constant, W is the missile mass, d is the diameter of the missile, and v is the velocity of the missile. Sliter [10] found the NDRC formulae to work satisfactorily for high velocity impacts, for low velocity impacts, however, the observed penetrations were much smaller than the predicted ones. Also, NDRC formulae do not consider any reinforcement present in the impacted body, thus making the differentiation between a reinforced target and an unreinforced target impossible. Various other investigators have also presented independent empirical formulae based on their experimental findings, but a universally accepted formula does not exist. Many studies have been carried out to understand effects of the rate of loading on the strength of cementitious materials. All of these studies have shown that the strength, crack density as well as the fracture energy in compression, tension, and flexure increases with an increase in the rate of loading. There is, however, considerable variability in the published results on the magnitude of this increase, which seems to depend on the type of machine and loading, type of material, amount of drying, and on the experimental procedures followed. In general, the higher the static flexural strength of concrete, the lower is the relative increase in the flexural strength with increasing strain-rate. A 10 decrease in the strain-rate sensitivity with an increase in the static strength has also been reported for uni-axial compression as well as for uni-axial tension. In general, the tensile response is the most strain-rate sensitive, the compressive response the least, and the flexural response falls between those of tension and compression [11]. This indicates that cracking plays a major role in the stress-rate dependence. Fiber reinforced concrete, with behavior which depends upon the behavior of the matrix, the fibers as well as the fiber-matrix interface, is reported to be more strain-rate sensitive than its unreinforced counterpart [6]. Mainstone, R.J. [12] has reported that steel shows an enhanced dynamic strength at all values of strain until just before failure. Both the upper yield strength and the subsequent flow stress are seen to increase with the loading-rate. Banthia et al. [13] have experimentally shown the strain-rate sensitivity of fiber-matrix bond. Deformed steel fibers embedded in cementitious matrices in general support a higher load under impact than under a static pull-out. The pull-out energy is also greater under impact provided the fiber failure mode is maintained from static to impact loading. Unfortunately, our knowledge of the strain-rate sensitivity of cementitious materials and composites is still largely qualitative. Although some work at high strain-rates has been carried out, the quantitative side is far from clear. Also, no specific work has been done so far to evaluate the strain-rate sensitivity of plain as well as fiber reinforced shotcrete — either qualitatively or quantitatively. Previous research work on the qualitative and quantitative evaluation of the strain-rate sensitivity of cementitious materials and composites is reviewed in detail in sections 3.4 and 3.5 respectively. 3.2 - Rockbursts Rockbursts [28] are violent rock failures that occur in proximity to underground excavations. In many respects rockbursts resemble earthquakes. Rockbursts have long been recognized as a major hazard when mining hard rock at depth. Such rockbursts have been reported from Canada, India, South Africa, USA, and other geographic locations. 11 One explanation for the origin of rockbursts is that they are unstable releases of potential energy of rocks around the excavations. Another explanation is that the changes brought about by mining merely trigger latent seismic events that derive mainly from the strain energy produced by geological differences in the state of stress [28]. 3.2.1 - Estimated Radiation of Energy During Rockbursts Mining gives rise to seismic activity ranging from micro-seismic events radiating as little as 10"5J to tremors radiating as much as 109J [29]. All seismic events radiate kinetic energy. Any sudden, violent occurrence, radiating significant amounts of kinetic energy, say not less than 104J, can be regarded as a rockburst [30]. It has been widely accepted for some years that the source of kinetic energy is the energy unavoidably released in the course of mining. Naturally, a rockburst is more likely to have damaging effect if its energy content is high. 3.2.2 - Ejection Velocities of Rocks During Rockbursts Rockburst damage [31] is characterized by large strains, significant displacements of excavation walls, and high velocities associated with these displacements or with the ejection of rock fragments. So, it is of profound importance for a proper design of support components intended to control or contain these displacements, that the designer should know quantitatively what the typical and upper limit values of the associated velocities are. Ejection of broken rock during a rockburst is one mechanism for damage to underground support. The ejected rock contains kinetic energy that must be absorbed by the ground support if access through the excavation is to be maintained. Therefore, the design of support and rock retaining systems for rockburst prone ground requires an estimation of the velocity at which rock blocks are ejected from the surface of a drift [32,33]. If the kinetic energy of the ejected rock can be measured or predicted, then the capacity of the support in terms of strength and yieldability can be determined. The rock's kinetic energy is controlled by its mass and velocity with the former depending on the 12 extent of local jointing and fracturing around the excavation. Kinetic energy is proportional to the velocity squared and hence, the rock's ejection velocity is more important than its mass for energy based support design [34]. In a recent work, Tannant et al. [35] measured the actual ejection velocities during simulated rockbursts. Two blasts were conducted to simulate the ejection of a rock by a rockburst and three specially designed velocity probes were employed to measure rock ejection velocities during the blasts. Ejected rocks reached their maximum velocities after traveling about 2-3 centimeters only. The velocities then gradually decreased with increasing travel distance. The ejection velocities measured between 1 and 17 m/s. 3.3 - Large Scale Impact Tests on Shotcrete [9] As part of the Canadian Rockburst Research Program, the Geomechanics Research Center at Laurentian University has undertaken a five-year research program to develop support systems for controlling damage to tunnels caused by rockbursts. Recently, as a component of this extensive research effort, Tannant et al. carried out a comparative study between the impact resistance of mesh-reinforced shotcrete panels and the impact resistance of steel fiber-reinforced shotcrete panels. A unique, large-scale testing facility was built with the primary objective of performing large-scale impact tests on shotcrete, and measuring its energy absorbing and deflection characteristics. The facility was designed to test shotcrete panels under impact loads that represented the effects of moderate size rockbursts. In addition, the facility was used to assess the influence of rate of loading on mesh-reinforced shotcrete. The impact tests were conducted by dropping an instrumented 565 kg mass on a 1.5 m by 2.75 m shotcrete panels. The drop-weight was released from heights varying from 0.5 m to 3 m and the resulting impact was monitored with accelerometers, load cells, and displacement measuring transducers. Impact velocities, ranging from 3.1 m/s to 7.7 m/s, caused peak loads in the bolts supporting the shotcrete panel of 30 kN to 120 kN, while impact energies of up to 23 kJ were dissipated by the mesh-reinforced shotcrete 13 panels and the supporting columns. The resulting damage to the test panels was carefully recorded and ranged from minor fracturing to complete failure. It was noted that the severity of damage was largely controlled by the panel deflection resulting from the impact. Different thickness of shotcrete sustained similar damage at the same panel deflection, although the amount of energy required to cause a given deflection or degree of damage increased with the thickness of the shotcrete layer. Mesh-reinforced shotcrete panels clearly demonstrated the ability to deform up to 0.2 m without experiencing a severe damage. In contrast, deflections beyond about 0.1 m in steel fiber-reinforced shotcrete resulted in a sudden transition from minor to severe damage. Although steel fiber-reinforced shotcrete performed well below critical energy and displacement thresholds, once these thresholds were exceeded the shotcrete lost its functionality because the fibers pulled out and could not hold the fractured shotcrete together. Mesh-reinforced shotcrete maintained its functionality better than steel fiber shotcrete when exposed to large strains or deformations because the mesh reinforcement helped retain broken pieces even when the shotcrete was extensively cracked or fractured. For a given deflection, the dynamically loaded shotcrete seemed to absorb more energy than the shotcrete that was slowly loaded in the quasi-static tests. However, it was noted that the mechanisms of energy absorption during the impact tests were far more complex than during the quasi-static tests and comparisons must be made with caution. The impact tests clearly demonstrated the ability of mesh-reinforced shotcrete to deform up to 0.2 m while absorbing a significant amount of energy and sustaining only a moderate damage. The energy absorption capacity increased with thicker layers of shotcrete. The impact tests also indicated that mesh was superior to steel fiber for the reinforcement of shotcrete when the shotcrete was subjected to large deformations and when it absorbed more than about 4 to 5 kJ/m . Steel fiber-reinforced shotcrete worked well under conditions that did not cause excessive deformations. A relative deflection limit of 0.1 m for steel fiber-reinforced shotcrete bolted at a 1.2 m diamond pattern seemed to mark the transition point between minor damage and severe damage. Steel fiber-reinforced shotcrete did not appear to have a state of deformation equivalent to the moderate damage level in mesh-reinforced shotcrete, i.e., the steel fiber-reinforced 14 shotcrete was either fully functional, with minor fractures, or it quickly degraded and experienced severe damage or complete failure when the cracks became wide enough to pull out the short steel fibers. According to the authors, shotcrete appears to be a particularly useful component in support systems designed to resist moderate rockburst damage. The data obtained from these impact tests will help to formulate and verify the support design guidelines currently being developed by the Geomechanics Research Center as part of the Canadian Rockburst Research Program. 3.4 - Qualitative Study of the Strain-rate Sensitivity of Cementitious Materials and Composites 3.4.1 - Plain Concrete Basic studies of cement paste, mortar, and concrete have revealed the inherently brittle nature of these materials. To exacerbate the situation, these cement-based construction materials also have very low tensile strengths. The weakness of concrete under tensile stress and its low failure strain, mean that concrete has a very low toughness; the toughness of some metals may be almost three orders of magnitude higher than that of concrete. Moreover, concrete is strain-rate sensitive, i.e., its properties have been found to vary with stress application rates. A number of attempts have been made to assess the behavior of cement-based materials under varying strain-rates. Concrete, in the form of compression, tension, or flexural specimens has been subjected to increasingly high strain-rates, and the various strength and energy values determined. Watstein [36], by performing compression tests on concrete at variable strain-rates (10~6 to 10/second) found that the ratio of the dynamic to the static strength was substantially greater than unity. He also observed that this ratio for strong concrete did not differ much from that for weak concrete. The failure strains at high rates of loading were higher than their static counterparts, and the secant modulus, energy absorption, and maximum load were also considerably higher at higher strain-rates. 15 Green [37] used the type of cement, the type of coarse aggregate, shape of the coarse aggregate, curing conditions, sand grading, mix proportion, and the age of the specimens as variables in evaluating the performance of concrete at variable strain-rates. Contrary to Watstein's [36] findings, he found that the ratio of the impact to static strength increased with the static strength of concrete. Concrete with angular aggregates showed higher impact strength than the concrete with rounded and smooth aggregates. The water-cured specimens showed higher impact strengths than those that were air-cured. Birkimer and Lindemann [38] have shown that the critical fracture strain energy theory provides a meaningful fracture criterion. They also found that the critical fracture strain is directly proportional to the strain-rate raised to the one-third power. Hughes and Watson [39] tested concrete cubes with varying mix proportions and two different types of coarse aggregates under compressive impact loading (strain-rates up to 17/second). They found that the ultimate strains decreased with an increase in the stress-rates. This was attributed to the absence of creep strains for high strain-rate loading. Also, the crack propagation path in the high strain-rate tests was much straighter than that in the low strain-rate tests. Aggregate failures were observed more in the impact tests than in the static tests. In the static tests the crack was found to propagate around the aggregate but never through it. They considered this as the reason for the large energy requirement in the impact tests. Suaris and Shah [40] performed instrumented variable strain-rate tests (strain-rates from 0.67xl0"6 to 0.27/second) on mortar specimens in flexure. They noted that, in general, the higher the static flexural strength, the lower was the relative increase in the flexural strength with increasing strain-rate. They deduced that on a comparative basis, the tensile response was the most strain-rate sensitive, the compressive response the least strain-rate sensitive, with the flexural response lying somewhere in between. Zielinski and Reinhardt [41] and Zielinski [42] used the Split Hopkinson Bar technique in order to investigate the stress-strain behavior of mortar and concrete at high stress-rates (5000-30,000 MPa/second) in uni-axial tension. They concluded that the remarkable increase in the tensile strength of concrete and mortar at high stress-rates was 16 due to the extensive microcracking in the whole volume of the stressed specimen. To support this argument they observed that the ultimate strains at higher stress-rates were also higher. Moreover, the specimens subjected to high rates of stress fractured at more than one place along their lengths. The difference between the impact strength of concrete and mortars was explained on the basis of the direct crack arresting action of the aggregates. It was also postulated that in the case of very rapid loading, since much energy was introduced into the system in a short time, cracks are forced to develop along the shorter paths of higher resistance, through stronger matrix zones and also through some aggregates resulting in a greater toughness under impact. To verify the applicability of the rate theory (See section 3.5.1.3) to plain concrete, Kormeling [43] performed uni-axial tensile tests on (|)74xl00 mm concrete cylinders at three different rates: 1. Low deformation rate of 1.25xl0~4 mm/second, 2. Intermediate deformation rate of 28 mm/second, and 3. High deformation rate of 2400 mm/second. The tests were performed at two temperatures of 20°C and -170°C. Low and intermediate deformation rate tests were performed at a constant deformation rate in a hydraulic closed-loop controlled testing machine. For the high deformation rate tests, a Split Hopkinson Bar was used. The results showed that for both temperatures, the tensile strength, the deformation at fracture, and the fracture energy (Gp) .increased with the deformation rate. The values at the low temperature were always higher than those at room temperature. Kormeling concluded that application of the rate theory to plain concrete is possible, but it is limited to a distinct area in the fracture energy-deformation rate field. This theory gives relations among deformation rate, energy absorption, and temperature. Ross and Kuennen [44] studied the applicability of the inherent flaw theory (Kipp and Grady [58,59]) to concrete. Direct-tension, splitting tensile and direct-compression tests were performed on 51 mm diameter, 51 mm long specimens of concrete at strain-rates of 10"7 to 102/second. A standard material test machine was used for the low rates, and a 51 mm Split Hopkinson Pressure Bar was used to test at the high rates. For the 17 concrete mix tested, both the tensile and compressive strength data showed abrupt increases in strength for strain-rates above approximately 1.0/second for direct tension and approximately 200/second for compression. For concrete strengths obtained at strain-rates above these values, both the tensile and compressive strength were found to be a function of the cube-root of the strain-rate as predicted by the inherent flaws theory. Post-test fragment size for both tension and compression were in good agreement with calculations using the inherent flaws theory (See section 3.5.1.1). 3.4.2 - Fiber Reinforced Concrete The poor impact resistance of plain concrete has led to the incorporation of fibers to enhance the impact performance. Initially, these fibers were thought to increase the strength of the composite, but it was soon realized that the major advantage in adding fibers is not in the enhanced strength, but in enhanced ductility and energy absorption capacity, better crack resistance and crack control, and improved structural integrity and cohesiveness. This improved post-cracking response of the composite may be particularly useful in situations where accidental impact may occur and the energy absorption capacity of the structure must be considered in design. Thus, various investigators started studying the composite behavior of fiber reinforced concrete at variable strain-rates. Jamrozy and Swamy [45] described their experience with the application of steel fiber reinforced concrete in building machine foundations that were subjected to impact loading. They designed a free fall drop weight impact tester capable of repeatedly dropping a mass on a standard specimen until a predetermined failure criterion was reached. Fibers in general were helpful in increasing the impact performance of concrete. The fiber volume, fiber geometry, and fiber size were all found to influence the impact strength. They also found that for a given fiber geometry and size, there existed an optimum fiber volume, which gave the maximum efficiency. Some actual foundations were instrumented, and it was found that the use of fiber reinforced concrete was really useful. They also concluded, however, that fibers cannot replace conventional reinforcement. 18 Suaris and Shah [40] compared the performance of plain concrete and plain mortar with their steel, glass, and polypropylene fiber reinforced counterparts. They found that the flexural strength (MOR) of both steel and glass fiber reinforced mortars was more strain-rate sensitive than that of the mortar matrix itself. Polypropylene fiber reinforced mortar, on the contrary, was apparently not strain-rate sensitive. The energy absorption values of mortars reinforced with various fibers, subjected to impact, were found to be 7 to 100 times larger than those for the unreinforced matrix. Gopalaratnam and Shah [47] studied the effect of strain-rate on the flexural behavior of unreinforced matrix and three different fiber reinforced concrete mixes. Tests were conducted using a modified-instrumented Charpy test set-up in which steel fiber reinforced concrete beams were subjected to impact loading. They observed that: 1. Mortar, concrete, and FRC all exhibited increased flexural strengths at the higher rates of loading. An increase of 65 percent for mortar and 50 percent for concrete was observed in this study when the rate of straining was increased from lxlO"6 to 0.3/second. The weaker mortar mix exhibited greater rate sensitivity than concrete. 2. FRC was more rate-sensitive than plain matrix. An increase in the aspect ratio and fiber volume, in general, increased the strain-rate sensitivity. The higher strain-rate sensitivity of FRC specimens was probably due to additional cracking (both transverse matrix cracking and interfacial cracking or debonding) generally associated with FRC specimens, and the fact that the strain-rate sensitivity of cement-based composites has crack-growth mechanisms at its root. 3. In addition to the improved strengths at the higher rates of loading, the deflections at ultimate load at these rates were also consistently higher than those at static loading-rates. Up to a 50 percent increase in these deflections values were recorded for the various plain and reinforced composites tested. 4. Energy absorption during the dynamic fracture of the unreinforced composites increased by 40 percent over comparative static values. Energy absorption of FRC (generally a couple of orders of magnitude larger than that of the unreinforced composites) up to fixed deflection value (of 2.5 mm) at the dynamic rate of loading increased by 70 to 80 percent over the corresponding static value. 19 5. For the same aspect ratio of fibers used, composites made with higher fiber content showed larger rate sensitivity, perhaps due to the characteristics of cracking in these composites and the rate sensitivity associated with such a process. 6. The peak strains recorded showed an increase at higher rates of loading. The secant modulus was also found to increase at higher rates of loading, which was attributed to a decrease in the amount of microcracking at higher rates of loading. They hypothesized that changes in the cracking process at the static and dynamic rates are perhaps primarily responsible for the rate-sensitive behavior of cement composites. Following observations were the basis of their hypothesis: 1. Pre-peak nonlinearity (and microcracking which accounts for this nonlinearity) reduces at the dynamic loading-rates. While the initial tangent modulus of cement composites shows no significant change at the different rates of loading, the secant modulus (evaluated at the ultimate load) is greater at higher rates of loading. 2. Cement composites exhibit a non-isotropic rate sensitivity with specimens subjected to tension, flexure, and compression showing descending order of rate sensitivity at comparable rates of loading. 3. Weaker matrix mixes are more rate-sensitive than stronger ones. 4. FRC is more rate-sensitive than the unreinforced matrix, with composites made with higher fiber contents or fibers of higher aspect ratio exhibiting greater rate sensitivity. Banthia [6] designed an instrumented impact machine to conduct impact tests on plain and fiber reinforced concrete in the three-point bending mode. Steel, and polypropylene macro-fiber reinforced concrete and plain concrete beams were tested and it was demonstrated that the proposed technique was a simple and rational method of obtaining meaningful material properties. It was found that the properties of concrete under the high stress-rates associated with impact loading could not be predicted from conventional static tests. On the basis of the tests on plain concrete and fiber reinforced concrete beams the following observations were made: 20 1. Both normal strength as well as high strength concrete (produced by using silica fume) are strain-rate sensitive. Under impact loading, the peak bending loads as well as the fracture energies were significantly higher than those obtained from conventional static tests. In general, under impact, the beams were found to have improved deformation capacities, suggesting increased failure strains. The improved toughness under impact loading was probably due to the increased microcracking in concrete under these conditions. 2. An evaluation of the fracture mechanics parameter N from the slope of the log a vs. log a plot indicated that the value of N decreased as the strain-rate was increased. This was true for both normal and high strength concrete. In the impact range, a value of N = 1.5 for normal strength, and a value of N = 2.2 for high strength concrete was obtained. These low values of N indicate the highly stress-rate sensitive behavior of concrete at the extreme rates of loading associated with impact. 3. High strength concrete made with silica fume was found to be stronger than normal strength concrete without silica fume in both the static and impact conditions. However, high strength concrete was also found to be more brittle than normal strength concrete. 4. Incorporation of either high modulus steel fibers or low modulus polypropylene fibers was found to increase the ductility of the composite both under static and dynamic conditions. The hooked end steel fibers, however, were found to be far better than the chopped straight polypropylene fibers. While the improvements in the peak loads and fracture energies over unreinforced concrete were only moderate in the case of polypropylene fibers, the corresponding improvements in the case of steel fibers were dramatic. 5. Fiber reinforced concrete showed an improvement in the peak load and fracture energy over unreinforced concrete. The improved toughness of fiber reinforced concrete was due to fiber pull-out and crack-bridging mechanisms. Mindess and Vondran [48] studied the properties of concrete beams reinforced with fibrillated polypropylene fibers under impact loading. An instrumented drop-weight 21 impact machine was used, dropping a 345 kg mass from a height of 0.5 m The specimens had dimensions (lxwxd) of 1200x100x125 mm, and were simply supported on a clear span of 960 mm The 19.1 mm long fibrillated polypropylene fibers were added in volume fractions from 0.1% to 0.5%. The addition of the fibrillated polypropylene fibers markedly increased the impact resistance of concrete, in terms of both impact strength and fracture energy. Increasing the fiber volume enhanced the impact resistance. For all of the fiber volumes studied, there was sufficient bond with the matrix to prevent fiber pull-out; the fibers failed primarily by breaking. While the stress-rate sensitivity of mortar and concrete has been well recognized and widely reported, the results from the investigation of Banthia and Ohama [49] indicated that the basic cement paste also had its behavior altered with stress-rate. Carbon fiber reinforced cement specimens were impact loaded in tension. A conventional Charpy with a modified support system was used. Effects of water-cement ratio and cement to silica fume ratio were also investigated. While three volume fractions of carbon fibers, 1, 3, and 5 percent were used for pastes with silica fume; a volume fraction of 1 percent was used for pastes without silica fume. Substantial improvements in both the tensile strength and fracture energy under impact were brought about by carbon fiber inclusion; the improvements were proportional to the volume fraction of carbon fibers added. It was also noted that an increase in the content of silica fume from 20% to 40% by weight of cement led to only a minor increase in the strength in tension at all percentages of fiber content. On the other hand, the impact fracture energy was found to have been substantially increased with an increase in the silica fume-cement ratio. Banthia, Chokri, Ohama, and Mindess [50] investigated the improvements in the impact resistance of cement matrices when reinforced with high volume fraction of carbon, steel, and polypropylene micro-fibers. Tensile briquettes were fractured at a stress-rate 4xl05 times higher than the static rate under a rapidly applied load using an instrumented impact machine. Strength and fracture energy values were measured. When compared with static test results, considerable sensitivity to stress-rate was noted. The composites were found to be stronger and tougher under impact and the improvements were more pronounced at higher fiber volume fraction. 22 Glinicki [51] studied the influence of loading-rate on fracture energy of steel fiber reinforced mortar. Uni-axial tests were performed on "paddle-shaped" specimens at loading-rates ranging from 0.001 to 1000 MPa/second. The toughness of steel fiber reinforced mortar was affected significantly by the applied loading-rate. A considerable influence of loading-rate on the shape of load-deformation diagrams was also observed. Not only was a relative increase in maximum stress and corresponding deformation observed, but changes in the descending branch due to increase in cr were also noted. A monotonically increasing relationship between fracture energy and a was observed. The fiber shape and distribution were found to be significant in inducing the loading-rate sensitivity in the sense of fracture energy of FRC composites. The composites reinforced with straight fibers showed smaller loading-rate effects than the composites containing deformed fibers. Therefore, Glinicki concluded that the major mechanisms inducing rate effects could be associated with fiber bending, straightening, and matrix crushing during fiber pull-out. These mechanisms were dominant for deformed fibers, while for straight fibers pull-out was dominant. Banthia, Chokri, and Trottier [52] designed simple impact machines to conduct impact tests on fiber reinforced mortars and concrete in the uni-axial tensile mode. Carbon, steel, and polypropylene micro-fiber reinforced mortars and steel fiber reinforced concrete were tested and it was demonstrated that the proposed technique was a simple and rational method of obtaining meaningful material properties. In general, mortars reinforced with micro-fibers were stronger than their unreinforced counterparts both under impact and static conditions. Also, strengths under impact conditions were greater than those under static conditions, giving impact/static strength ratios greater than unity. It was noted that the stress-rate sensitivity of micro-fiber reinforced mortars increased with an increase in the fiber volume fraction. In the case of steel fiber reinforced concrete reinforced with a nominal volume fraction of steel macro-fibers, the strengths were not altered due to fibers neither under static nor under impact conditions. Fiber reinforcement was significantly effective in improving the fracture energy absorption under impact. The improvements were, however, dependent on fiber type and geometry. 23 C <D 1— -*—' co o "•4—» to CO c (U ••—» CO o E 05 c Q 3.5 3 2.5 2 1.5 1 0.5 -j Banthia[6], comressive strength =40 MPa Gopalaratnam et al. [47], comressive strength = 30 MPa Plain in flexure SFRC in flexure x Rain in direct tension + SFRC in direct tension Banthia et al. [77], compressive strength = 40 MPa 0.01 0.1 1 10 100 1000 In (stress-rate), MPa/s 10000 100000 Figure 3.1 - Strain-rate sensitivity of concrete: Plain vs. Fiber Reinforced. Figure 3.1 depicts the strain-rate sensitivity of plain and steel fiber reinforced concrete in flexure and direct tension. All the curves show that both plain and steel fiber reinforced concrete exhibit higher strengths at a higher strain-rate. Gopalaratnam et al. [47] and Banthia et al. [77] observed that steel fiber reinforced concrete shows greater sensitivity to strain-rate as compared to plain concrete. 3.5 - Quantitative Study of the Strain-rate Sensitivity of Cementitious Materials and Composites Strictly speaking almost all structures are subjected to loads which vary with time. For example, road and rail traffic, cranes, pedestrians, etc. cause loads fluctuating in time. All these loads change rather slowly, which allows treating them quasi-statically with a coefficient that counts for possible dynamic effects. Material properties are taken from static testing. On the other hand, there are loads, for example, in the case of rockbursts, earthquakes, etc., which last for only a very short period of time, and induce a very high loading-rate. The pulse duration of these impact and impulsive loads covers a range 24 between one millisecond and about ten seconds. Depending on the mass of the striking body, the material properties, the geometry, the loading configuration, and the velocity during impact, the strain-rate may vary between 10"4 s"1 and 10*4 s"1. In the elastic range of concrete behavior, these strain-rates can be translated into stress-rates depending on the elastic modulus. Roughly speaking stress-rates between 3 N/mm2.s and 400x106 N/mm2.s may occur. The effects of the rate of loading on the strength and fracture of cementitious materials have been studied extensively at least since the work of Abrams [53] in 1917. Most of the early studies (before 1955) have been reviewed by McHenry and Shideler [54]. These studies, and the many that have since been carried out, are in general qualitative agreement, in that almost all of them show that the apparent strengths of cement, mortar, and concrete increase as the rate of loading is increased. Most commonly, researchers have found that their data can be represented adequately by a linear relationship between the strength and the logarithm of the stress state (or strain-rate), i.e. cr c=A + Blogcr (3.2) where a c = strength (in tension, compression, or flexure), a = stress-rate (or strain-rate, or rate of cross-head deflection of the testing machine), A, B = constants. While the structural engineer is mostly interested in the relationship between mechanical properties and strain or stress-rate, from a materials science point of view, the cause of the strain-rate effect should also be examined. 3.5.1 - Models for the Strain-rate Sensitivity of the Strength of Concrete Concrete is a composite material generally consisting of inert aggregate particles embedded in a matrix of hardened cement paste. The paste contains pores of various sizes. The interface between aggregate and paste may be weaker than the bulk paste, and may even be cracked due to differential thermal movement and shrinkage during hydration and drying. Concrete can be modeled at three different levels [55]: at the 25 macro-level, it may be regarded as a homogeneous isotropic material; at the meso-level pores, inclusions, and cracks have to be considered, and finally; at the micro-level cement paste is considered as an assemblage sheet of colloidal particles, polysilicates, water in various forms (free and adsorbed), and voids. To study the strain-rate effect on concrete, all three levels must be investigated using an appropriate approach for each level. At the macro-level linear and/or nonlinear fracture mechanics and energy criteria may apply; at the meso-level attention should be focused on fracture energy of matrix, aggregate particles, and bond between these constituents; the behavior at the micro-level may be described implicitly by the rate theory. 3.5.1.1 - Concrete as a Homogeneous Material (Macro-level) a. Linear elastic fracture mechanics approach The linear elastic fracture mechanics (LEFM) approach to rate of loading effects involves a combination of the classical Griffith theory with an empirical relationship describing sub-critical crack growth. For perfectly brittle materials, fracture is governed by Griffith's equation, where a c is the fracture strength, E is the modulus of elasticity, 'a' is half the crack length, y is the fracture surface energy, and Gi c (=2y) is the critical strain energy release rate. The fracture toughness K F C , an intrinsic property of a brittle material, is given as (3.3) which may also be written in the form, (3.4) KIC = V E G ric (3.5) Substituting this relationship back into Eq. (2), we can write 26 1 /9 which states that fracture will occur when [a(7ta) = K J is equal to the critical stress intensity factor, K i c , a material property, where a is the nominal stress. During sub-critical crack growth in brittle materials, the crack velocity can be described by the empirical relationship, V = C . K i N (3.7) where V = da/dt = rate of crack extension, and C and N are constants. Sub-critical crack growth (the slow growth of cracks that are too small to cause failure under the prevailing stress) leads to a dependence of the failure stress on the loading-rate, since in specimens loaded slowly, more time is available for slow crack growth to occur than in specimens loaded rapidly. Thus, the rate of loading effect in cementitious materials must be due, at least in part, to the growth of a crack as governed by Eq. (3.7) until it reaches the critical value as defined by Eq. (3.6). As has been shown by Nadeau, Bennett and Fuller [56], the dependence of strength on the rate of loading can be described by the logarithmic expression, l n C T c = ^ l n ( B < x ) + ^ l n ( C T N - 2 - o i N - 2 ) N + l N + l V / ^ ^ [ ( B d r ^ N - 2 - , * * - 2 ) / . \1/N+1 => <TC QC ( f j j If N = 2, then crc oc(o-)1/3 where a is the stress-rate, the subscripts i and f refer to the initial condition (before loading) and the final condition (at fracture), respectively, N is a material constant, and B=2KIC2"N.(N+l)/AY2(N-2) (3.9) where Y is a geometric parameter which depends on the specimen dimensions and the method of loading. Eq. (3.8) implies that a plot of ln rjc versus ln cr would have a slope of 1/(N+1) at low values of a, and would reach a constant value of ln a c (slope = 0) at high values of cr. That is, at very high loading-rates, the strength would be largely independent of loading-rate because there would be virtually no time for sub-critical 1/N+l (3.8) 27 C7> O (0) log T O ( b ) log K x o (c) Figure 3.2 log or (or k ) - Three different ways of determining the constant N. 28 crack growth to occur. By how much the strength obtained at one stress-rate differs from that obtained at some other stress-rate depends on the value of N , and a lower N indicates a more rate sensitive material. Based on the work by Evans [57], it can be shown that there are three independent methods for determining the constant N in Equation (3.8), as indicated in Figure 3.1: • (a) From constant load tests in a logarithmic plot of the applied stress, c?a, versus the time to failure, x, the slope of this plot is -1/N; • (b) By direct observations of controlled crack growth where C and N are the intercept and slope, respectively, in a plot of logV vs. logKi, and • (c) From constant rate of loading tests to failure in which the first two terms of Equation (7) are plotted, giving the slope 1/(N+1), and hence N . However, in reality, N is not a constant but a function of the applied stress-rate, and it decreases as the stress-rate is increased [6,40]. For example, while at low to moderate stress-rates the value of N has been experimentally found to be generally higher than 14, at very high stress-rates values as low as 2 or 3 have been reported [6,40,66]. In other words, the sensitivity of concrete to stress-rate is much greater at higher stress-rates than that predicted by linear elastic fracture mechanics. A running crack causes a lower stress intensity at a given displacement than a stable crack, such that at the Rayleigh wave speed (cR = K(G/p) 1 / 2 ; G is shear modulus; p is unit weight; and K is a factor less than one which is a function of the Poisson's ratio) the stress intensity drops to zero. From conservation of energy principles, however, it may be shown that under a constant stress, a, the limiting crack velocity, vrim> is only a fraction of the Rayleigh wave speed: where y s is the surface energy and E is the elastic modulus. Although the crack velocities observed in concrete under impact are even smaller than the limiting crack velocity, v i . j m , a reduction in the stress intensity due to a fast-running crack can still be expected. If the fracture is still defined by a critical value of stress intensity, this means that the apparent strength should be higher in the case of a fast-moving (dynamic) crack. (3.10) 29 Under the assumption that linear elastic fracture mechanics is valid, Kipp, Grady, and Chen [58] extended the theory of constant stress to arbitrary stress loading by considering the dependence of stress intensity on the velocity of crack, and an appropriate use of stress-time relation. From the special loading case of a constant strain-rate e0 which results in a constant stress-rate aa in an elastic material, the following relationship for the stress-intensity factor for a penny-shaped crack was derived (Inherent Flaws Theory): Kl(t) = ^ a 0 ^ . t m (3.11) where a is a geometric co-efficient equal to 1.12 for the penny-shaped crack, Cs the shear wave velocity, and t is the loading time. If K k is regarded as a fracture criterion, a relation between strain-rate s 0 and strength a c (critical stress) can be established. / - N 1/3 U 6 a 2 C s j • ^ / 3 (3.12) a c ° c * 0 3 3 Equation (3.12) predicts the constant N to be as low as 2 [l/(N+l)=l/3]; this prediction is in agreement with the experimental observation at very high strain-rates. This cube root law (N=2) holds for high strain-rate and/or sufficiently large cracks. Therefore, Inherent Flaws Theory (LEFM) is good for predicting strain-rate sensitivity of concrete at high strain-rates. Following the same assumptions and development as for previous two equations, Grady and Kipp [59] derived an expression for nominal fracture size, d = A/20 ,P-Chs => dace™ where p is the density and K i c is the material fracture toughness. (3.13) b. Nonlinear fracture mechanics approach Linear elastic fracture mechanics (LEFM) does not take any plastic deformation or micro-cracking in the region of the crack tip into account. Whereas linear elastic material description may apply to glass and ceramics, it is certainly not applicable to concrete and 30 mortar. It has been demonstrated in theoretical and numerical analysis [60] that a microcracking zone exists around the tip of a visible crack in concrete and this microcracking zone or process zone or softening zone depends mostly on the descending branch of the stress-strain curve of concrete under tensile loading. Besides concrete mix proportions, maximum aggregate size, humidity, and temperature, the strain-rate also influences the shape of the stress-deformation curve. Thus, the softening zone size should also depend on the loading or straining-rate of concrete. Application of non-linear fracture mechanics to concrete has proved to be successful in static loading with most approaches modeling concrete as a strain-softening material. In the case of a discrete crack, the strain field around the crack tip causes much higher stresses than the apparent tensile strength of concrete. The consequence is the development of a process zone ahead of the crack tip that is characterized by the Dugdale-Barenblatt model which treats the process zone as that part of the crack where cohesive stresses tend to close the crack [61]. Important parameters are the tensile strength and the stress vs. crack-separation (a-5) relation of concrete [62]. This last fact means that non-linear fracture mechanics is not a means to establish the tensile strength, but it is rather a tool to judge the behavior of a cracked concrete element. If one knows the tensile strength and the strain softening behavior as a function of loading-rate, one can estimate the behavior of a concrete element under a certain rate of loading. Reinhardt [63] illustrated this by an example. He assumed a crack in a centrally cracked plate under a remote stress cr and a cohesive stress distribution p(t) in the process zone according to a power relation, where, t is the crack coordinate, c is the total crack length with process zone included, a is the real crack length, y is a coefficient accounting for finite dimensions, n is the stress distribution power, and ft is the tensile strength of concrete. The size of the process zone can be calculated as a function of n and y. If ft increases with the loading-rate the size of the process zone decreases at the same stress. This means that a cracked plate would behave more elastically in dynamic loading than it does in static loading. This is a (3.14) 31 qualitative statement that has not yet been treated quantitatively. Further research needs to be done on the non-linear fracture mechanics under dynamic loading in order to establish non-linear fracture mechanics based models of concrete to predict the effects of rate of loading. One such study has been done by John and Shah [64,65]. c. Energy criteria Birkimer [66] considered the strain energy W during the rise time tr of the stress which is given by, tr W = AJV.dx (3.15) 0 with A as the cross-sectional area of the specimen. Using the relations dx = v.dt where v is the particle velocity, and v = c.8 where c is the speed of the irrotational wave, he obtained a relationship between the fracture stress a c and a constant strain-rate s 0: 3 E 2 W C 1/3 * (3-16) This relation is only valid if the fracture energy W F is a material constant, which does not depend on strain-rate. This formula resembles the one derived by Kipp and Grady [58], since both show the dependence of fracture stress on the cubic root of strain-rate. As mentioned earlier, this cube root law (N=2) holds for high strain-rate and/or sufficiently large cracks. Therefore, an energy criterion is as good as inherent flaw theory (LEFM) for predicting strain-rate sensitivity of concrete at very high strain-rates. Explosive loading is common practice in mining. This explains why rate effects have been studied extensively in that field, however, the aim of the study may be different. One of the questions is the size of fragments engendered by explosive loading. Grady [59] has put forward a theory which treats the kinetic energy as the key parameter that determines fracture process and fragment size. Starting from the kinetic energy of an expanding sphere that was prestressed, he was able to link the fragment size d and strain rate by, . _ • -0.67 d cc e 32 i.e., the higher the strain rate the smaller the fragment size. Ehrlacher [67], too, has emphasized on the importance of kinetic energy of cracks at high rates of loading. If the strain energy release rate G s t at applies for static loading in case of a crack propagating with speed v, the portion G, = G s t a t ( l -v /c R ) (3.17) is dissipated through crack tip propagation, whereas the remainder G n = G s t a t . v/cR (3.18) is transferred into kinetic energy. As soon as the crack propagates with the Rayleigh wave speed CR, all energy would be transformed into kinetic energy and the stress intensity at the crack-tip would drop to zero. 3.5.1.2 - Concrete as Multiphase Material (Meso-level) On the meso-level concrete is regarded as a composite material of aggregate, and the hardened cement paste separated by an interface. In terms of fracture one should know the contribution of these three components to the fracture stress. Since the aggregate is usually much tougher than the cement paste, the crack path has an important influence on strength, i.e., the more aggregate particles are fractured, the larger the apparent fracture stress will be. A model by Eibl and Godde [69] belongs to the meso-level. The authors considered a unit element of a two phase material consisting of an aggregate disc surrounded by matrix material to form a strip. Since aggregate is stiffer than matrix, waves propagate faster in aggregate. This phenomena causes differential movement of the two phases under impact loading which leads to a stress distribution which is different from static loading. Together with inertial forces, the strength is considerably increased and the fracture tends to propagate through aggregate under higher loading-rates. This model is not yet finalized but may serve as a guideline for further study. 3.5.1.3 Concrete at Micro-level Hardened cement paste consists of colloidal elements, silicates, and adsorbed water layers if considered on a micro-level. The paste is attached to aggregate particles by adhesion. 33 The behavior and properties of all constituents should be taken into account to make a real physical model at this level. Besides the hard skeleton of hydration products, which possesses primary and secondary bonds between the gel particles, adsorbed and capillary water also interacts with the solid material. At the micro-level, thus, one can schematize the real structure of concrete by modeling it as a group of elements of fictitious sizes, connected in series. To account for voids and defects in the micro-structure, it can be assumed that each element contains a circular crack. a. Thermodynamic Approach or Rate Theory or The Theory of Deformation Kinetics In the rate theory, it is assumed that gel particles are the smallest particles in a cementitious material. Between these particles attractive and repulsive forces exist depending on their energy level and the temperature. Macroscopic deformation finds its source in the displacements of these particles. To displace the particles bonds between them have to be deformed or broken. The driving force behind the deformation is always the search for a balance between breaking and formation of bonds. To treat concrete by thermodynamics means is to consider it on an atomic level. Atoms are in a state of continuous motion, under the action of attractive and repulsive forces. Each atom is situated on a certain energy level. Due to continuous motion, there is always a chance that an atom will overcome the inherent energy barrier and will move to another place in the system. If an external energy is added to a system of atoms, the atoms may overcome the energy barrier (activation energy) more easily. This energy may be supplied by mechanical loading, heating, or concentration gradients. The greater these external influences are, the more likely that place change occurs. Place changes of atoms can be detected in an average way by deformations, cracks, or chemical reactions. Mihashi and Wittmann [70] used this approach to predict the influence of loading-rate on the strength of concrete. They combined the thermodynamic approach to some extent with fracture mechanics. They stated that the fracture of concrete might be caused by a series of local failure processes in the two phases of concrete, hydration products of cement and interfaces between cement and aggregate. As soon as a failure criterion is satisfied in one part of the phase, a crack is initiated. Extension of cracks and coalescence 34 of cracks cause fracture. They assumed that concrete consisted of a group of elements, linked in series, Figure 3.2. Each element contained a circular crack, the length of which depended on the pore sizes of hardened cement paste (for the prediction of the rate influence, the absolute value of crack length is not important). The distribution of the material defects and the characteristic properties of each element were assumed to be statistically equal over the whole material. To this schematized material the rate theory was applied. The rate of crack initiation is a function of activation energy, stress (a), and temperature. The rate of crack initiation (r) was expressed by, with k = Boltzmann's constant, h = Planck's constant, T = absolute temperature, U 0 = activation energy, q = local stress concentration factor, and nb = a material constant. Eq. (17) is a simple relation between crack initiation rate r and stress a, if all other parameters are taken constant: where, a = 1/nbkT. The authors calculated the mean value of probability of fracture during a time interval and ended up with a relation between stress-rate and tensile strength, which can be simplified to, with f and f0 being tensile strength under impact and static loading respectively, and a and & 0 being the corresponding inherent stress-rates. The coefficient a (a material parameter) depends on concrete composition, age, temperature, and humidity. The larger the a, the more sensitive the material to stress-rate. 1 (3.19) (3.20) (3.21) 35 model crock e lement s y s t e m s p e c i m e n p h a s e mode l Figure 3.3 - Model of hardened cement with linked elements. 36 Lindholm et a/. [71] applied the rate theory to rock in order to predict the rate and temperature influence on the strength under multi-axial loading. They assumed the activation energy to be a linear function of the applied stress: U(<7) = Uo-a(o--<7 0) (3.22) with U 0 as the total activation energy of the process, 'a' as the activation volume, CT0 a constant, and a the stress applied. The rate equation was used in its simplest form, s = &exp where e is the strain-rate, s0 is a constant, R is the gas constant, and T is absolute temperature. This relation led to, . Uo RT, So crmax = f = — + ob In— (3.24) a a s In this relation, (LVa + CT0) is the limiting stress when T = 0 or when s='e0. According to Eq. (3.24) the strength will decrease linearly with temperature and increase linearly with the logarithm of the imposed strain-rate. It should be noted that Lindholm et al. presented their theory with regards to compressive stress but did not restrict the applicability to compressive stress alone. Kormeling [72] verified the rate theory with regards to the prediction of stress-rate and low temperature influence on the fracture energy of concrete. Starting from the same point as Lindholm et al, the energy was considered during cracking deformation. The deformation rate S was expressed as a function of mechanical energy Q m and activation energy Q a according to ( 3 ' 2 5 ) where T is absolute temperature, k is Boltzmann's constant, and ci is another constant. At fracture, the mechanical energy is equal to the fracture energy G F , which is the area under a complete load-deformation curve from a tensile experiment. To adjust the macroscopically measured quantities to the microscopic level to which Eq. (3.25) refers, the number of gel particles N g and the appropriate fracture area A were inserted in Eq. (3.25), U(g) RT (3.23) 8 = c.exp 1 ^ l kT 37 ( Qa ^ ( G F . £ = c.exp —-S— exp (3.26) 1 * \ NgklV *\NgkT. After taking the logarithm, this relation read, G F = ^ f - ( l n c , - l n A ) - ^ — (3.27) A A which expressed the fracture energy as a function of deformation rate and temperature. At T = 0, the limiting value of the fracture energy is Q a/A. The limiting value of the deformation rate is ci. b. Continuous Damage Theory A continuous damage theory has been developed by Suaris and Shah [73], based on the Helmholtz free energy function. The authors derived a damage evolution equation that considers the inertia associated with the micro-crack growth. The micro-cracks are represented in vectorial forms that allow distinguishing between cracks due to compression, bending, or uni-axial tension. The coefficients in the equations are determined with the aid of experimental results. It is shown that the influence of loading-rate is different at different loading conditions; it is the largest in tensile and least in compressive loading. Thus, on the basis of the literature survey, the following conclusions may be made: 1. All underground shotcrete applications are susceptible to impact and impulsive loads, such as those caused by rockbursts. Rockbursts are nothing but violent rock failures that occur in proximity to underground excavations. Therefore, there exists a dire need for a systematic appraisal of impact behavior of plain and fiber reinforced shotcrete. 2. A lot of qualitative and quantitative work has been done on the impact resistance and strain-rate sensitivity of cast concrete, however, limited research has been done on the shotcrete side. The work on cast concrete needs to be extended to shotcrete. 38 3. Shotcrete is particularly useful in surface lining, and in support systems designed to resist moderate rockburst damage. To formulate design guidelines for these applications we need to see the behavior of two dimensional structural components under variable stress-rate. 4. All theories predict similar relationships between strength and stress-rate in the low and moderate stress-rate range. The treatment at the meso-level gives most insight into the behavior of concrete at moderate rates, whereas in the high stress-rate (high crack velocities) range linear and non-linear fracture mechanics are most appropriate. 39 Chapter 4 - Experimental Procedures 4.1 - Introduction Continuous efforts have been made to replace conventional steel wire-mesh reinforcement with short, discontinuous, and random fibers. These efforts have produced very good results, and today a big demand for fibers exists in the shotcrete industry. Fibers for shotcrete reinforcement have been made of glass, carbon, polypropylene, polyvinyl alcohol, and steel. However, the durability problems associated with glass fibers, the cost and difficulty in mixing carbon fibers, and the low modulus of polypropylene and polyvinyl alcohol fibers have made steel the material of choice for the vast majority of fiber reinforced shotcrete produced to date. Recently, some polypropylene fibers have been reported to provide adequate reinforcement for cast concrete, but they still need to be investigated for their use in shotcrete. In this study, ten' different fibers, made of steel, polypropylene, carbon, and polyvinyl alcohol were used at different volume fractions. Some of these fibers are commercially available and some are still in research and development stage. Plain and fiber reinforced shotcrete mixes were shot on to wooden forms using an ALIVA-262 wet-mix shotcreting machine. These panels were then sawn to obtain beam and plate specimens to be tested under static and impact loads. The materials, mix proportions, shotcreting equipment, and tests, which were used in this study, are described in detail in the following sections. 4.2 - Specimen Preparation Plain and fiber reinforced shotcrete mixes were shot on to prepared wooden forms, 600 mm x 500 mm x 100 mm in dimensions with tapered sides, inside a closed shooting chamber using a 350 cfm air flow (100 cfm = 0.05 m /s). A 5 m long, 50 mm internal diameter hose, and a rotor speed of 4.7 m3/hour were used throughout. The nozzle tip was 40 gyrated so that the stream moved in loops across wooden forms; each wooden form was sprayed from bottom to top. The shooting angle was kept as close to 90° to the wooden form as possible; the distance between the nozzle and the wooden form was about one metre. A plastic tarpaulin was laid out on the floor of the shooting chamber to collect the rebound. This set-up is shown in Figure 4.1. At the end of the shooting, the rebound material was collected from the tarpaulin and weighed; the shot wooden forms were also weighed. The rebound material was carefully washed out to collect all the rebound fibers; the rebound fibers were then weighed. Using these weights a rebound analysis was done to calculate the in-place fiber volume fraction. Seven panels were shot for each mix. They were demoulded 24 hours later and then cured for an additional 28 days. For each mix, two of the panels were sawn to obtain eight 350 mm x 100 mm x 100 mm beam specimens, and four were edge-sawn to obtain four 350 mm x 350 mm x 100 mm plates. Thus there were eight beams and four plates for each mix. The remaining panel was cored to obtain four cylinders (85mm in diameter and 100 mm in height). 4.2.1 - Materials Cement: CSA type 10 (ASTM 1) normal Portland cement was used in this study. Silica fume: Much of the wet-mix shotcrete work carried out in Europe and North America is done with silica fume as an additive, at around 10% by weight of cement, to increase the cohesiveness of the mix thus enhancing the build-up thickness and reducing the rebound. In this study, too, silica fume was included in the mix design at 10% by weight of cement. Aggregates: To maintain a continuous supply of sand and coarse aggregate, and to avoid variations in physical properties among different batches, it was decided to stockpile a large amount of 41 sand and coarse aggregate in covered bins at the beginning of the project. The sand used was commercially available concrete sand; it had a total absorption of 4.0%. The coarse aggregate had a maximum size of 10 mm, and an absorption of 1.1%. It is well known that in micro fiber reinforced concrete mixes, coarser aggregates aggravate the problem of fiber-balling, while excessive fine sand aggravates the problem of shrinkage cracking. Also, in a practicable mix the aggregate size should be less than half the fiber-length. So, neither concrete sand nor 10 mm coarse aggregate was used in the micro fiber reinforced shotcrete mixes; instead, uniformly graded forestry sand was used. This was done to avoid balling of micro fibers without engendering the problem of shrinkage cracking. The particle size of forestry sand was 2.5 mm, a size lying between that of concrete sand and that of 10 mm aggregate. Table 4.1 - Gradation for the aggregates used in the mixes. Sieve 3/4 1/2 3/8 No. 4 No. 8 No. No. No. No No. Size inch inch inch 16 30 50 100 200 10-mm Aggregate + Concrete Sand (Used in all mixes except MF8 and MF9): Total % 100 98 91 81 75 67 49 18 3 0 Passing 2.5 mm Forestry Sand (Used in mixes MF8 and MF9): Total % 100 100 100 100 45.8 0.3 0.05 0 0 0 Passing Superplasticizer: In this study, commercially available WRDA-19 of napthalene sulphonate formaldehyde chemical family was used to superplasticize the shotcrete mixes. It has a solid content of 40% and a specific gravity of 1.21. Air entraining admixture: Commercially available DARAVAIR of vinsol resin chemical family was used as an air-entraining agent. 42 Fibers: The following fibers were investigated in this study: Table 4.2 - Fibers investigated. Cross- Length Diameter Tensile Sketch Fiber Geometry Material sectional L D strength Weight E code shape (mm) (mm) (MPa) (mg) (Gpa) _ Fl Hooked- Steel Circular 30 0.5 1115 44.74 210 end - F2 Hooked- Steel Circular 35 0.55 1115 63.16 210 end Flat- Steel Circular 30 0.73 1110 95.54 210 end F4* Straight Polypro-Circular 25 0.38 375 2.75 2.6 F5* pylene Straight Polypro-Circular 25 0.38 375 2.75 2.6 pylene F6 Straight Polypro-Circular 38 0.63 375 10.66 2.6 pylene *-^^-^v^—» F7 Crimped Polypro-Circular 30 0.76 450 21.48 3.5 pylene _ F8 Straight Carbon Circular 10 0.018 590 0.42 35 F9 Straight Carbon Circular 18 0.017 1770 0.76 180 i i p 1 ° Flat- PVA Rectangu- 30 0.55x0.75 900 16.09 29 end lar Twin-coned » < Fl l end Steel Circular 35 1.00 1115 243.90 210 * F4 and F5 fibers are identical; different notation are used to indicate different volume fractions. Based on their length and diameter, fibers used in this study can be divided into two major categories: (1) macro fibers, and (2) micro fibers. All fibers, except carbon fibers, are macro fibers. 4.2.2 - Mix Proportions Two mix proportions were used in this study; one for plain and macro fiber reinforced shotcrete, and another for micro fiber reinforced shotcrete. The quantity of fibers in the 43 mixes varied according to the volume fraction of fibers under investigation. Note that the mix proportions are given for Saturated Surface Dry (SSD) sand and coarse aggregate. Table 4.3 - Mix proportions. Mix Cement Silica 10-mm Sand Water Fibers Super- Air plast- entr- Fiber volume Type 1 fume Aggregate icizer ainer fraction (%) (kg/m3) Original In-place1 MO2 400 40 265 14003 181 - 4.85 0.1 -MF1 400 40 265 1400 181 60 4.85 0.1 0.77 0.64 MF2 400 40 265 1400 181 60 4.85 0.1 0.77 0.59 MF3 400 40 265 1400 181 60 4.85 0.1 0.77 0.64 MF4 400 40 265 1400 181 9 4.85 0.1 1.00 0.96 MF5 400 40 265 1400 181 13.5 4.85 0.1 1.50 1.43 MF6 400 40 265 1400 181 13.5 4.85 0.1 1.50 1.19 MF7 400 40 265 1400 181 13.5 4.85 0.1 1.50 1.12 MF8 900 135 - 9004 362 33 16.2 0.1 2.00 2.00 MF9 900 135 - 900 362 37 16.2 0.1 2.00 2.00 MF10400 40 265 1400 181 10 4.85 0.1 0.77 0.68 MF11400 40 265 1400 181 60 4.85 0.1 0.77 0.55 Two concrete mixers were used in this project: an inclined drum mixer, and an Omni-mixer. The inclined drum mixer was used for plain and macro fiber reinforced mixes. This mixer was mounted on a stage in order to allow it to discharge directly into the hopper. The Omni-mixer was used for micro fiber reinforced mixes. 4.2.3 - Shotcreting Equipment Throughout this research program, shotcrete was produced using a wet-mix rotating barrel equipment (model ALIVA-262, see Fig. 4.1) with a 10 litre, twelve pocket drum. The machine works on the rotary principle. The mass to be transported, i.e. wet-mix shotcrete, travels through the hopper into the rotor chambers facilitated by a vibrator attached to the hopper. The rotating drum then transports the material to the blasting chamber where compressed air forces the material into the transport stream. A hose 1 After considering rebound. 2 M0 - mix with no fiber. MF1 - mix with fiber FI, etc. 3 Concrete sand. 4 2.5 mm forestry sand. 44 Figure 4.1 - Wet-mix shotcreting in progress. 45 carrying the compressed air (thin-stream transport) then moves the material to the spray nozzle. The machine operates at two rotor speeds, such that rotor speed-1 provides a discharge of 4.7 m /hour, while rotor speed-2 provides a discharge of 7.1 m /hour. A 350 cfm air supply (100 cfm = 0.05 m3/s), a rotor speed of 4.7 m3/hour, and a 5 m long, 50 mm internal diameter hose was used throughout this research program. 4.3 - Testing Program 4.3.1 - Static Testing 4.3.1.1 - Compression Tests on Cylindrical Cores Compression tests were conducted on cylindrical cores, 85 mm in diameter and 100 mm in height, in a 220,000 lb (981 kN) hydraulically controlled testing machine in accordance with ASTM C39. These compressive strengths were corrected for length to diameter ratios according to ASTM C42. 4.3.1.2 - Static Flexural Tests on Beams The 100 mm x 100 mm x 350 mm beam specimens were tested under four-point flexure on a span of 300 mm in accordance with ASTM C 1018-96. A 150 kN floor-mounted Instron materials test system (applied stress-rate » 0.012 MPa/s, corresponding strain rate * 2.9 x 10"7 /s) was used. As is well known, during a flexural toughness test there is crushing at the load point, and the specimen supports also settle with the applied load. Thus measured beam deflections are often far greater than the true deflections at the specimen neutral axis. In order to correct for deflections arising from support settlements, a yoke, as suggested in the Japanese standard (JSCE-SF4 [20]), was installed around the specimens as shown in Fig. 4.2. It has been shown previously that it is only with the help of a yoke [24] or equivalent deflection measuring system that true beam deflections (conforming with the theoretical deflections) can be measured. The applied load and deflection data were electronically acquired at an acquisition frequency of 1 Hz. Figure 4.2 - Use of a Yoke to measure true specimen deflections. 47 4.3.1.3 - Static Flexural Tests on Plates Static flexural tests on plates were carried out on a 1784 kN universal testing machine (Baldwin Model GBN, manufactured by Statec Systems Inc., USA) using a cylindrical loading head, 100 mm in diameter. The 350 mm x 350 mm x 100 mm shotcrete plates were simply supported on all four edges on an unsupported span of 300 mm x 300 mm, and the load was applied at the centre (see Figure 6.1). The applied load (applied loading-rate « 0.28 kN/sec) and load-point deflection data were electronically acquired using a three-channel data acquisition system based on a PC operating at 1-Hz acquisition frequency. 4.3.2 - Impact Testing Impact testing was carried out using two instrumented drop-weight impact machines: (1) 578 kg drop-weight impact machine to test plate specimens, and (2) 60 kg drop-weight impact machine to test beam specimens. Both of these were designed and built at the University of British Columbia. The two machines are very similar in working principle, and operation; they differ only in mass of the falling hammer, overall dimensions, and the maximum possible drop-height. Details of these machines are shown schematically in Figure 4.3 and Figure 4.4, respectively. The 578 kg hammer can be dropped from heights of up to 2.3 m thus giving a striking velocity of 6.4 m/s, while the 60 kg hammer can be dropped from heights of up to 1.8 m thus giving a striking velocity of 5.7 m/s. For the tests reported here, a hammer drop height of 0.45 m was chosen in both machines. At this drop height, the 60 kg hammer had a potential energy of 266 J, and an approach velocity of 2.97 m/s just before hitting the beam specimens. This produced an average stress-rate of 28830 MPa/s (corresponding strain-rate « 0.71/s), thus, yielding an impact to static stress-rate ratio of 2.4 x 106. On the other hand, at a drop height of 0.45 m, the 578 kg hammer had a potential energy of 2551 I, and an approach velocity of 2.97 m/s. This produced an average loading-rate of 104.6 x 104 kN/s, thus, yielding an impact to static loading-rate ratio of 3.7 x 106. 48 1067 7X 4915 825 K> o o Tup o 1727 Steel Frame Hoist and Chain Hammer Assembly Supports (Anvil) Concrete Foundation Figure 4.3 - Schematic diagram of 578 kg impact testing machine. All dimensions in mm 49 o o CO CO CO % O o - « Motor and Chain Steel Frame Guide Columns Hoist and Magnet Hammer Tup Supports o CVJ CO Concrete Foundation ( 1 4 0 0 x 8 4 0 x 6 2 0 ) 840 Figure 4.4 - Schematic diagram of 60 kg impact testing machine. All dimensions in mm 50 Data Acquisition System 60.3 kg Hammer Tup & Load Cell 450 mm u 175 mm 175 mm „ i A > Shotcrete Beam 1 100 mm 7^ 150 mm Acclerometer 150 mm Figure 4.5 - A sketch of the set-up that was used to test shotcrete beams under impact load. A sketch of the set-up used to test shotcrete beams under impact load is shown in Figure 4.5. The following sections provide a description of the machine, support condition, instrumentation, data acquisition, test-procedure, and an analysis of the test results. 4.3.2.1 - Instrumented Drop-Weight Impact Machine a. General principle of a drop-weight impact machine A photograph of the 578 kg instrumented drop-weight impact machine is shown in Figure 4.6, and a photograph of the 60 kg impact testing machine is shown in Figure 4.7. In these types of machines, a hammer with a substantial mass is raised to a certain height above the specimen. In this position, the hammer has the potential energy mhahH (mh = mass of the hammer, ah = acceleration of the hammer under gravity, H = height to which it is raised) with respect to the top surface of the specimen. If the hammer in this position is allowed to drop onto the specimen, the potential energy of the hammer is converted to kinetic energy as the hammer falls with an acceleration ah (Due to the friction between the hammer and the guiding columns, the downward acceleration of the hammer is less than 51 Figure 4.6 - Instrumented drop-weight impact machine with a 578 kg hammer. Figure 4.7 - Instrumented drop-weight impact machine with a 60 kg hammer. 53 the earth's gravitational acceleration, g; Banthia [6] measured ah, using the photo-cell assembly, to be equal to 0.9 lg.). Just before the hammer strikes the specimen, its velocity, Vh is given by v h =V 2 a h H (4.1) At this velocity, the hammer has a kinetic energy, Th =>Th =m h a h H When the hammer strikes the specimen, a sudden transfer of momentum occurs from the hammer to the specimen. As a result, the momentum of the hammer decreases. This, in turn, results in a loss of the hammer kinetic energy, and a corresponding gain in the specimen energy. This transfer of energy between the hammer and the specimen is very sudden, and results in a sudden build-up of stresses in the specimen. In this study, two channels of instrumentation were provided to monitor the response of the beam/plate specimens to impact. Strain gauges were mounted on the striking end of the hammer (called the 'tup'), and one accelerometer was mounted at the center of the beam/plate specimens. The strain gauges in the tup measured the contact load between the hammer and the specimen, and the accelerometer was employed to record the acceleration of the specimen undergoing impact. The time-based data were acquired by a data acquisition system based upon an IBM PC. The layout of the impact machines is shown in Figures 4.3 and 4.4. As shown, the hammer is attached to the hoist by means of a pin lock. The hoist can be moved up and down using a chain and a motor. Once the hammer is at the desired height above the specimen, the pneumatic brakes provided in the hammer can be applied. With this, the hammer "grabs on" to the columns of the machine. In this position, the hoist can be detached from the hammer. On releasing the pneumatic brakes, the hammer falls under gravity and strikes the specimen, thus generating high stress-rate impact loading. In the smaller machine (Figure 4.7), there is no pneumatic brake in the hammer to "grab" onto the columns. Instead, an electromagnetic plate is attached to the bottom of 54 the hoist to hold the hammer. To drop the hammer, the pin is unlocked and the electromagnet is turned off. b. The tup and support The striking tups are made of heat-treated high carbon steels. In the 578 kg impact machine a 100 mm diameter cylindrical tup (1 mV = 49.233 kN, Figure 4.8) was used to test plate specimens, while in the 60 kg impact machine a knife-edge tup (1 mV = 6.998 kN, Figure 4.9) was used to test beam specimens. As the tup strikes the specimen, the strain gauges in the tup record the contact load-time pulse between the specimen and the tup. These pulses were collected by the data acquisition system. 350 mm x 350 mm x 100 mm plates were impact-tested on a span of 300 mm x 300 mm. They were simply supported on a rigid steel frame as shown in Figure 4.8. Impact tests on 350 mm x 100 mm x 100 mm beam specimens were carried out under three-point flexure on a clear span of 300 mm. The support used to test beam specimens is shown in Figure 4.9. c. Accelerometer The accelerometers (Figure 4.10) used were piezoelectric sensors (Model 350A14, manufactured by PCB Piezotronics Inc., Buffalo, New York) with a resonant frequency of about 77.5 kHz, and with a built-in unity-gain amplifier. With a resolution of 0.04g, the accelerometers can read up to +5000g. The output from the accelerometers was collected by the data acquisition system through a co-axial cable. Salient features of Accelerometer: 1. Range: ±5000g 2. Resolution: 0.04g 3. Resonant frequency: 77.5 kHz 4. Calibration: 1 V = lOlOg For both the beam specimens as well as the plate specimens, an accelerometer was glued to the bottom of the specimen along its centroidal axis so that it recorded the mid-point acceleration or load-point acceleration, as shown in Figures 4.5 and 4.10. The 55 Figure 4.S - Tup and support used to test plate specimens. Figure 4.9 - Tup and support used to test beam specimens. Figure 4.10 - Accelerometer used and its location on plate specimens. 58 accelerometers were glued to the specimens using a nylon base, 13 mm in diameter and 4 mm in depth, containing a central threaded hole into which the accelerometer could be screwed in. These bases were glued to the specimens using an epoxy adhesive, approximately six hours before the testing. d. Acquisition and storage of data The data acquisition system has two main parts: (i) a signal conditioner which acts as an amplifier as well as a noise filter. The signal conditioner has the ability of filtering the incoming analog signals to eliminate electrical or electronic noises, and (ii) a PC with a special multi-channel analog to digital (A/D) conversion board, which is used to collect and store the output signals from the tup and accelerometer in a digital form during impact events. The signal conditioner, designed and built at the University of British Columbia, has the ability to amplify the original output from the load cell up to 1000 times. The full range of output voltages from the load cell is usually less than ±10 mV, while the minimum step or the sensitivity of the data acquisition system is +2.5 mV within the input range of -10 to +10 volts. To monitor and record the whole impact event precisely, amplification of the signals is necessary. The A/D conversion board and its accompanying software, Computerscope ISC-16, are commercially produced (RC Electronics, CA, USA). The amplified analog signals can be converted to a digital form by the A/D board at a speed of 1 MHz if only one channel is activated; the corresponding sampling rate is one data point per microsecond (ITS). If the data is being acquired using n channels, the speed of the board is reduced to 1/n MHz. For eight activated channels, for example, the fastest sampling rate is 1/8 MHz, i.e., the data is collected at intervals of 8 us by all channels. The sampling rate, which is required to measure and capture the signals accurately, depends on the duration and profile of the signal pulse itself. The A/D conversion board has several trigger mode options. Level triggering, which is often used in impact testing, was chosen for all the impact tests reported here. When the voltage signal crosses a pre-set trigger voltage level, then the data acquisition 59 system is triggered. All the data points acquired after the triggering as well as the data points recorded in the fixed time interval prior to the detection of trigger (This interim is called trigger delay setting, defined in terms of the number of data points) is captured and deposited in the scope buffer. Although the trigger voltage level can not be set to zero since the voltage of the load-cell fluctuates slightly even at 'no-load' condition due to electrical noises, by setting the trigger level slightly higher than the 'no-load' voltage and choosing an adequate delay value the entire loading history can be recorded reliably. Once the data acquisition system is triggered, it begins to transfer the output from the active channels into the computer memory for a pre-selected length of time called "buffer". This length of time is chosen appropriately depending upon the expected duration of the impact event. At the end of the event, the data stored in the buffer of the computer memory are written on to a hard disk/floppy disk in ASCII format for further analysis. 4.3.2.2 - Impact Testing Procedure The impact machine is controlled by an electro-pneumatic system. Components such as the brake and the locking pin operate pneumatically, while the hoist motor operates electrically. The steps involved in carrying out an impact test are as follows: 1. The specimen is removed from the curing room, and the accelerometer location is marked. An area surrounding the marked spot is surface dried, and cleaned with a wire brush. 2. The mounting base for the accelerometer is then carefully glued to the specimen using an epoxy adhesive. The epoxy is allowed to dry for a minimum period of about 15 minutes, at the end of which the specimen is ready for testing. 3. The hammer assembly is lifted up to a pre-determined height with the aid of the hoist and the air-brake is applied. 4. The test-specimen is mounted on the support, and is adjusted so that it sits on the support symmetrically. 5. The load cell and accelerometer are connected to the data acquisition system and checked for faults; their outputs are reset to zero. 60 6. All the data acquisition parameters are checked again and the data acquisition system is set active. 7. The hammer is dropped by releasing the air-brake, which results in fracture of the test-specimen. 8. At the end of the event, the data stored in the computer memory are written on to a diskette. Finally, these data are transferred to a PC for further analysis. 4.3.2.3 - Impact Data Analysis Usual output from the impact tests carried out on the shotcrete beams/plates consisted of tup load and mid-point (or load-point) specimen acceleration. These data were obtained as a function of time. Figure 4.11 shows the data obtained from the two instrumented channels activated for a test done on a steel fiber (FI) reinforced shotcrete plate. Since the data were acquired at a sampling rate of 10 microseconds, and since the impact event shown in Figure 4.11 lasted for about 18 milliseconds, this resulted in several hundred data points. For the efficient handling of this data, a computer program was written. An algorithm of the program is given in section 4.3.2.4 f. a. The energy lost by the hammer If the hammer has fallen through a height 'H' before it hits the beam/plate, then the velocity 'v h ' of the hammer just prior to impact is given by Equation 4.1. If this instant corresponds to time t = 0, then, where ah is the acceleration of the hammer under gravity. After the contact between the hammer and the beam/plate, an impulse, given by the area under the tup load (Pt) vs. time (t) plot, acts on the hammer. From the laws of Newtonian Mechanics, this impulse must be equal to the change in the momentum of the hammer with a mass 'mh'. (4.3) (4.4) 61 CN 62 Using Equation (4.3) and solving Equation (4.4) we get, vh(t)= ^ H - — fp(t).dt m J (4.5) If AE(t) is the kinetic energy lost by the hammer, then AE(t) = |m h[v 2(0)-v 2(t)] (4.6) On substituting for Vh(0) and Vh(t) in Equation (4.6), JP(t).dt (4.7) Thus, according to Equation (4.7), at any time t, if the area under the tup load vs. time plot is known, the energy lost by the hammer can be calculated. All of this energy lost by the hammer is not transferred to the specimen. Some of the energy, at least in the initial part of the impact, is lost to the testing machine itself [6]. b. The generalized bending load The contact load between the specimen and the hammer is not the true bending load on the specimen; this is because of the inertial reaction of the specimen. When the instrumented tup of the hammer strikes the beam/plate, the beam/plate suddenly gains momentum and the unsupported part of the beam/plate accelerates in the direction of the hammer. This gives rise to d'Alambert force, acting in a direction opposite to the direction in which the beam/plate accelerates. The strain gauges in the tup, sensing the contact load between hammer and the beam/plate, sense this inertial load as well. Thus the tup load consists of the mechanical bending load (the stressing load), and the load due to the inertial reaction of the specimen. The mechanical bending load, which is the obvious goal of testing, can thus be obtained from the observed tup load by subtracting the inertial load. In this study, the data from accelerometer were used in order to apply the inertial correction to the tup load. 63 In order to arrive at the true bending or stressing load, it is important to understand the nature of the various loads in question. The tup load is a point load acting at the center of the specimen, whereas the inertial reaction of the specimen is a body force distributed throughout the body of the beam/plate. This distributed inertial load should therefore be replaced by an equivalent (or generalized) inertial load, Pj(t), which can then be subtracted from the tup load, Pt(t), to obtain the generalized (true, or equivalent) bending load, Pb(t), acting at the center. b.l Plates b.1.1 Acceleration distribution/Velocity distribution/Displacement distribution On the basis of existing analytical solution5 to the problem of a simply supported plate subjected to a central load and on the observed acceleration distribution data obtained from preliminary tests, it can be safely assumed that for shotcrete plates, at any instant of time, the acceleration distribution, the velocity distribution, and the displacement distribution are sinusoidal along both the axes (i.e. along X and Y axes), Figure 4.12. u(x, y, t) = u0 (t)Sin S in S , 4 ^ u(x,y,t) = u 0 ( t )Sin^Sin^ ( 4 9 ) u(x,y,t) = u0(t)Sin^pSin-^ (4 - 1 U) <&(x,y,t) = <5u0(t)Sin^Sin^ ( 4 1 1 ) 5 Timoshenko, S. and Krieger, S.W. (1959) Theory of plates and shells. McGraw Hill, New York. 64 Figure 4.12 - Displacement distribution along the length and width of a simply supported plate subjected to a central load. 65 where u(x,y,t) = deflection at any point (x,y) on the plate at time t u0(t) = mid-point deflection of the plate at time t u (x,y,t) = velocity at any point (x,y) on the plate at time t u o (l) = mid-point velocity of the plate at time t u(x,y,t) = acceleration at any point (x,y) on the plate at time t u o W = mid-point acceleration of the plate at time t Sn(x, y, t) = virtual deflection at any point (x,y) on the plate at time t, compatible with the constraints = mid-point virtual deflection of the plate at time t, compatible with the constraints. b.1.2 Principle of virtual work and Generalized inertial load If an infinitesimal segment of the plate, of length dx and width dy, has an acceleration u(x,y,f) > m e n m e inertial force acting on it is given by dl(x,y,t) = /0.h.u(x,y,t).dx.dy (4 12) where p is the mass density and h is the thickness of the plate. If the distributed inertial load is to be replaced by a generalized inertial load (Pi(t)) at the center, then the virtual work done by the distributed inertial reaction acting over the distributed virtual displacement should be equal to the virtual work done by the central load P;(t) acting over the virtual displacement at the center, 11 2 2 Pi (t). <5u0 = 4. J J p. h. ii(x, y, t). <5u(x, y, t).dxdy 0 o => (4.13) 1 2 2 2 P.(t).<5u0 =4.f f / 7 . h . u 0 ( t ) . S i n — S i n ^ . & i 0 . S i n ^ S i n - ^ . d x d y oo 1 1 1 1 where Pj(t) = the generalized inertial load acting at the center of the plate 1 = width (also length) of the plate. 66 Solving the above Equation, l 2 Pi(t) = p.h.u0(t).- (4.14) The acceleration at the center of the plate is obtained by extrapolating the recorded acceleration at the accelerometer location (x,l/2), u0(t) = u(x,l/2,t).Cosec-^ (415) Now the generalized inertial point load is given by, Pi(t) = ^u(x,l/2,t).Cosec^p (4 . i 6 ) where ii(x,l / 2,t) = t n e recorded acceleration at the point (x,l/2) on the plate. Thus, knowing the acceleration at the accelerometer location, and properties of plate, the generalized inertial load can be obtained from Equation (4.16). In this study, the acceleration at the center of the plate was recorded by placing one accelerometer at the point (1/2, 1/2), so the generalized inertial load was obtained directly from Equation (4.14). Once the generalized inertial load is obtained, the plate can be modelled as a Single Degree of Freedom (SDOF) system and the generalized bending load can be obtained from the Equation of dynamic equilibrium, Pb(t) = Pt(t)-P,(t) (4.17) b.2 Beams b.2.1 Acceleration distribution/Velocity distribution/Displacement distribution Based on the observed acceleration distribution data, Banthia [6] concluded that at any instant of time, the acceleration distribution along the length of the plain and fiber reinforced concrete beam without conventional reinforcement can be approximated as linear. The same holds good for plain and fiber reinforced shotcrete beams too. Now, we know that acceleration at any point on the beam is proportional to the deflection of the beam at that point, so the displacement distribution is also linear along the length of the beam (Figure 4.13). 67 Figure 4.13 - Displacement distribution along the length of a simply supported beam subjected to a central load. / x 2.u„(t) u(x,t) = s-^ -.x ••/ ^ 2.u„(t) u(x,t) = &(x,t) = ^ . x (4.18) where u(x,t) = deflection at any point (x) on the beam at time t u0(t) = mid-span deflection of the beam at time t u(x, t) = acceleration at any point (x) on the beam at time t u o ( 0 =mid -span acceleration of the beam at time t &i(x,y,t) = virtual deflection at any point (x) on the beam at time t, compatible with the constraints ^ o W = central virtual deflection of the beam at time t, compatible with the boundary conditions. 68 b.2.2 Principle of virtual work and Generalized inertial load If an infinitesimal segment of the beam, of length dx, has an acceleration u(x,t) t then the inertial force acting on it is given by dI(x,t) = /?.A.u(x,f).dx (4.19) where p is mass density and A is cross-sectional area of the beam. If the distributed inertial load is to be replaced by a generalized inertial load (Pi(t)) at the center, then the virtual work done by the distributed inertial reaction acting over the distributed virtual displacement should be equal to the virtual work done by the generalized inertial load Pj(t) acting over the virtual displacement at the center, 1/2 Pj(f).<5u0 = 2 J/?.A.u(x,t).<5u(x,t).dx (4.20) 1/2 P-Xt)&i0=2\p.K 2ii 2<5u„ 1 1 1 dx where Pi(t) = the generalized inertial load acting at the center of the beam 1 = clear span of the beam ov = length of overhanging portion of the beam Solving the above Equation, we get Pl(t) = />A.u0(t) 1 , 8(ov)3 3 312 (4.21) The acceleration at the mid-span of the beam is obtained by extrapolating the recorded acceleration at the accelerometer location (x): u0(f) = u(x,f).[-!-Now the generalized inertial point load is given by, /7.A.u(x,t).l (4.22) Pi(t) = 2x 1 8(ov)3 3 312 (4.23) where u(x,t) = the recorded acceleration at the accelerometer location (x). 69 Thus, knowing the acceleration at the accelerometer location, and properties of beam, the generalized inertial load can be obtained. In this study, the mid-span acceleration of the beam was recorded by placing one accelerometer at the point (x = 1/2), so the generalized inertial load was obtained directly from Equation (4.21). Once the generalized inertial load is obtained, the beam can be modelled as a Single Degree of Freedom (SDOF) system and the generalized bending load, as in the case of plates, can be obtained from the Equation of dynamic equilibrium, P„(t) = P,(t)-Pl(t) (4.24) c. Velocities and Deflections Once the acceleration history at the load-point is known, the velocity and displacement histories at the load-point can be obtained by integrating it with respect to time. If u o (t) is the velocity at the load-point, and u0(t) is the displacement at the load-point, then, u0(t) = Ju 0(t).dt (4.25) u0(t) = Ju 0(t).dt (4.26) Using Pb(t) and u0(t), the applied (stressing) load vs. load-point displacement plots can be obtained. These may then be regarded as equivalent static load-displacement curves (except that they are obtained from dynamic tests) and can be further analyzed in a routine manner. d. Energy As in the static case, the area under the curve of generalized bending load vs. load-point deflection is a measure of the energy expended in bending the beam/plate. At the end of the impact event, this area represents the fracture energy. If Eb(t) is the bending energy, then, Eb(t) = Jp b(t).du 0 (4.27) 70 e. The computer program A computer program was written to analyze the data from the impact tests. The input to the program is the data file which contains the raw data (tup load and accelerations with respect to time) from the data acquisition system for each specimen. Thus, the analysis starts at the instant of first contact between the hammer and the beam/plate (t = 0), and ends at the point of failure (t = tf), when the impact load has fallen back to zero. Using the input data file, the computer program performs the following tasks: 1. Reads the input file and saves the useful portion of the raw data. 2. Calculates the inertial load history and the true bending (stressing) load history. 3. Calculates velocity and displacement histories. 4. Gets the true bending load vs. displacement plot. 5. Writes all the calculated quantities and histories on the output file. 71 Chapter 5 - Beams Under Static and Impact Loading 5.1 - Introduction Load vs. deflection data obtained from static tests and those corrected for inertial loading in the case of impact tests were analyzed in a routine manner to calculate flexural strengths, flexural toughness factors, and fracture energies. These parameters provide information about improvements rendered to the plain brittle cementitious matrix by different fibers, and thus they help ascertain overall performance of different mixes under static and dynamic conditions. Also, a comparison between the values of these parameters under impact and those under static load gives us an idea of the strain-rate sensitivity of shotcrete. 5.2 - Shotcrete Beams Under Variable Stress-rate Representative static and impact load-deflection plots for all the mixes are presented in this section. All the specimens, plain as well as fiber reinforced, showed considerable strengthening, stiffening, and toughening under impact as compared to static loading. There was a 4 to 6 fold increase in peak load under impact. These data clearly indicate the strain-rate sensitive nature of shotcrete. 70 j -60 1* Plain Impact 3 \ 20 -- ; Static 0 0.5 1.5 2 2.5 3 Deflection (mm) Figure 5.1 - Static and impact load-deflection plots for plain shotcrete beams. 72 As expected, plain shotcrete beams failed in a brittle manner under static load. First crack appeared at a deflection of about 0.04 mm, and a peak load of 14 kN; this marked the failure of plain shotcrete beams. Under an impact load, plain shotcrete beams showed a considerable amount of strengthening; peak load recorded was about 64 kN, nearly 4.5 times more than that recorded under static conditions (see Figure 5.1). They also exhibited a significant post-peak softening branch under impact, which was entirely missing under static load. Visual examination of the broken plain shotcrete beams fractured under impact revealed fracturing of aggregates that came in the way of crack propagation. This phenomenon was absent under static conditions, and cracks essentially traversed around the aggregate particles. 0 0 .5 1 1.5 2 2 .5 3 Deflection (mm) Figure 5.2 - Static and impact load-deflection plots for steel macro-fiber Fl reinforced (Vf = 0.64 %) shotcrete beams. Steel fibers performed very well, both under static as well as impact loading. Partly it was because of the good fiber distribution and the favorable alignment of fibers. Most of the steel fibers aligned themselves perpendicular to the direction of shooting thus giving a predominantly two-dimensional fiber distribution. This enhances the crack growth resistance, because aligned fibers provide a greater resistance to their pull-out and a propagating crack is intercepted by a greater number of fibers. 73 0 4 1 1 1 1 1 ~ 0 0.5 1 1.5 2 2.5 3 Deflection (mm) Figure 5.3 - Static and impact load-deflection plots for steel macro-fiber F2 reinforced (Vf = 0.59 %) shotcrete beams. For steel fiber reinforced cement composites with practical fiber volume fractions, the major post-peak energy dissipation mechanism is the pullout of fibers across a crack. For deformed fibers, pullout resistance is mainly offered by the mechanical anchoring of fibers with the matrix [76]. Amongst the four steel fibers investigated in this study, hooked-end fibers (FI and F2) provided the highest toughness (see Figures 5.2 and 5.3). 80 0 0.5 1 1.5 2 2.5 3 Deflection (mm) Figure 5.4 - Static and impact load-deflection plots for steel macro-fiber F3 reinforced (Vf = 0.64 %) shotcrete beams. 74 Figure 5.5 - Static and impact load-deflection plots for steel macro-fiber Fl 1 reinforced (Vf = 0.55 %) shotcrete beams. Almost all the Fl and F2 fibers pulled out under static as well as impact load, and a considerable amount of plastic energy was spent in straightening the hooks. Another factor in favor of hooked-end fibers was their lower volume per unit fiber thus increasing the number of fibers in the composite at a given fiber volume fraction. Among the steel fibers, the twin-cone fiber (Fl 1) performed most inefficiently (see Figure 5.5). The factors that went against this fiber are: higher rebound during shooting and hence a lower in-place fiber volume fraction, higher volume per unit fiber thus resulting in a lower number of fibers in the composite, and a strong bearing bond between the conical end and the matrix that prevented fiber pull-out and precipitated fiber-fracture and matrix splitting (see Table 5.1 and Table 5.2). Performance of the flat-end fiber F3 was in between that of the hooked-end and twin-cone fibers (see Figure 5.4). As has been well established [6,47], none of the steel fibers improved the flexural strength of cementitious matrix at the in-place volume fraction of 0.55 - 0.64 per cent; they only enhanced the energy absorption capability of beams (see Table 5.3) under static as well as impact load. All of the steel fiber reinforced beams showed considerable enhancement in flexural strength and energy absorption capability under impact compared to static loading (see Figures 5.2-5.5). 75 Table 5.1- Failure patterns of beams under static four-point bending test. Mixes Failure % Fibers % Fibers Fiber pulled-out fractured distribution Plain Brittle - - 2-D1 Plain + Fl Ductile 100 - 2-D Plain + F2 Ductile 100 - 2-D Plain + F3 Ductile 100 - 2-D Plain + F4 Ductile 100 - 2-D Plain + F5 Ductile 100 - 2-D Plain + F6 Ductile 100 - 2-D Plain + F7 Ductile 75 25 3-D2 Plain + F8 Brittle - 100 3-D Plain + F9 Brittle - 100 3-D Plain + F10 Ductile 40 60 2-D Plain + Fl 1 Ductile 55 45 2-D Table 5.2 - Failure patterns of beams under three-point impact loading in flexure. Mixes Failure % Fibers % Fibers Fiber pulled-out fractured Distribution Plain Brittle - - 2-D Plain + Fl Ductile 100 - 2-D Plain + F2 Ductile 100 - 2-D Plain + F3 Ductile 90 10 2-D Plain + F4 In-between3 20 80 2-D Plain + F5 In-between 30 70 2-D Plain + F6 Ductile 60 40 2-D Plain + F7 Ductile 65 35 3-D Plain + F8 Brittle - 100 3-D Plain + F9 Brittle - 100 3-D Plain + F10 In-between 15 85 2-D Plain+ F11 Ductile 30 70 2-D 1 Two-dimensional fiber distribution - Most of the fibers align themselves perpendicular to the direction of shooting; this phenomenon is called preferential alignment. 2 Three-dimensional fiber distribution - Preferential alignment is not seen in this case. 3 Failure can be categorised as falling between a brittle and a ductile failure. C/5 i <u <D O 1-1 U > o X 3 03 C o ••—» ed T3 T3 o ca 00 in I o -a O o, 00 PL, £1 00 e «8 ~ D< H i a. o O w u S to 60 .5 tS 3^ 2 a a .5 t» a, '-3 Q <3 _ .2 A .3 xi H C N ON co >o CN T—1 00 r- CN N O q t-" 0" d r~* CN 00 N O CN CN •* co 00 N O 10 W-l CN CN 00 co CN 00 T - H CN co CN* CN co co* 4—1 ON 0 ON O in "* N O C N CO C N C N in O N C N C N O N co* r~ (-* 00 O d co in (-- 00 CN 00 d ir> 1—1 co IT) O N IT) CO o s O N 00 in O N C N N O O O H H C O . O to 4—1 O N C N O N ON O N ^ H 0 4—1 00 co N O N O 00 O N N O C O i-H 00 O P H * ° ) ^ H ' 1 4—4 CN CN CN N O CO IT) o 0 O N O CN O N 4 - H OO T—1 4—1 q N O in CO CN CN 00 d CN N O CN co CN N O 00 O N 0O co 00 O N •* CN ON CN co CN TJ* m t-* in ' 1 CN CN t-- CN 00 IT) CO 4 - H O N O in 00 CN co f-; — : d _ : q in* NO o CO o 0 O N r- CO O N CN 4 - H •<t O N CN 0 O N CN 4—1 4 - H d CN CN o N O co ON 00 00 5 IT) </-> lO <o q co r~ N O 00' NO* NO' IO >o <o lO </-> s O N N O 1 d d O 1 F2 F3 CO 0O 00 o co s O N in N O N O O N d 2 N O N O CO co O N CN O N 00 >o CN CN o N O co co co CN co " O o o ( H & a i3 O C O N O 00 I-* 00 NO* C O N O CN >n O N 00 0 O N O N NO r~ N O 00 CO* CO* co* CN* •t" 00 co >n >n 00 N O >n NO NO* N O N O 00 10 O N 00 CN 0 CO >n >n >n >n CO O N CN O 0 00 w-i O 0 N O >n -H -H 4-H* CN CN* d d 0 >n N O r~ 00 O N 4-H PH UH UH til UH UH o 77 Deformed steel fibers are very commonly and effectively used to improve the mechanical properties of brittle cementitious matrix. The high Young's modulus of steel facilitates efficient stress-transfer from the cementitious matrix to fibers across the cracks. An efficient steel fiber is capable of picking up the load at small crack openings in cracked fiber reinforced cementitious composites. This is quite evident from the load-deflection plots for the fibers Fl, F2, and F3. The disadvantages of steel fibers are their vulnerability to corrosion and chemical attack, and a high cost per unit volume. Developing fibers made of chemically inert, low-density polymeric material, such as polypropylene or polyvinyl alcohol can obviate this problem. Development of polymeric fibers with a performance-level close to that of steel fibers however is still in the research stage. 1 1.5 2 Deflection (mm) 2.5 Figure 5.6 - Static and impact load-deflection plots for polypropylene macro-fiber F4 reinforced (Vf = 0.96 %) shotcrete beams. Two straight, smooth, large diameter polypropylene fibers, viz. Fibers F4 and F6, were investigated for their toughening capabilities in wet-mix shotcrete. As has been witnessed in cast concrete, under static load beams reinforced with these fibers showed signs of instability at small crack openings, and a poor post-cracking residual strength capacity relative to steel fibers (see Figures 5.6 and 5.8) thus resulting in as inferior energy absorption capability (see Table 5.3). This is partly because of a less efficient 78 fiber-matrix bond, but perhaps more importantly because of the low modulus of elasticity of polypropylene; these fibers require a much larger crack opening to pick up a respectable amount of load. Across a section, almost all of the F4 and F6 fibers pulled out under an applied static load. Deflection (mm) Figure 5.7 - Static and impact load-deflection plots for polypropylene macro-fiber F5 reinforced (Vf = 1.43 %) shotcrete beams. Under impact, polypropylene fiber F4 failed primarily by breaking. Notice the relatively brittle behavior of fiber F4 reinforced beams under impact in Figure 5.6. Fiber F4 performed better at a higher in-place fiber volume fraction of 1.43 per cent (Fiber code F5), under static as well as impact conditions (see Figure 5.7). Fiber F6, a straight smooth fiber, performed better than the other straight, smooth polypropylene fibers under impact because of a higher percentage of fibers pulling out as shown in Table 5.2. In spite of its longer length, the large diameter of fiber F6 apparently allowed a fiber pull-out mode to be maintained over fracture. 79 1 1.5 2 Deflection (mm) 2.5 Figure 5.8 - Static and impact load-deflection plots for polypropylene macro-fiber F6 reinforced (Vf = 1.19 %) shotcrete beams. The properties of fiber reinforced cementitious composites largely depend on the fiber-matrix bond-slip mechanisms. Improvement in bond-slip characteristics is needed to enhance the performance of straight, smooth polypropylene fibers. One possible way to achieve this goal is by mechanically deforming the polypropylene fiber along its length to make use of the bearing bond during the process of fiber pullout (Fiber F7). 1 1.5 Deflection (mm) Figure 5.9 - Static and impact load-deflection plots for polypropylene macro-fiber F7 reinforced (Vf = 1.12 %) shotcrete beams. 80 Fiber F7 performed better than the other polypropylene fibers used in this study, under static as well as impact load. There was a much lesser degree of instability after the peak load under static four-point bending (see Figure 5.9). About 25 per cent fibers fractured under static loading, which implies that three-fourths of the F7 fibers pulled out in spite of the fact that the rest of them approached their fracture strength. This, in turn, indicates that the fibers are pulling out of cementitious matrix at a load, which is very close to their fracture load. Also, the crimped geometry straightened up as the fibers pulled out thus absorbing a significant amount of plastic energy in the process. Under the impact load, the energy absorption capability shown by fiber F7 was very close to that shown by the steel fiber F3. A visual examination of fractured surfaces of tested fiber F7 reinforced beams revealed that two-dimensional fiber distribution was not adequate. A considerable number of fibers were found to be oriented parallel with the direction as shot, thus not contributing anything towards the flexural toughness or energy absorption capability of the beam. This deviation from the favorable 2-D alignment, discussed previously, led to a lower flexural strength; this may also be due to a higher percentage of air as evident from the compressive strength data (see Table 5.3). As stated earlier, improvement in bond-slip characteristics is needed to improve the performance of straight, smooth polymeric fibers, and one possible way to accomplish this is by mechanically deforming the fibers. The other way is by improving the texture and chemical composition of fibers in order to ensure good adhesion between the fibers and cementitious matrix and to promote a chemical bond. One such fiber is the new polyvinyl alcohol fiber F8 that possesses a high level of chemical resistance and a chemically enhanced bond. 81 80 70 60 g- 50 ^ 40 3 30 20 10 0 i V y Impact Plain + Fiber F10 Static 1.. 1 0.5 1 1.5 2 Deflection (mm) 2.5 Figure 5.10 - Static and impact load-deflection plots for polyvinyl alcohol macro-fiber F10 reinforced (Vf = 0.68 %) shotcrete beams. Fiber F10 performed well under static load up to a deflection of 0.5 mm. There was no instability after the peak load, and in spite of the fact that the in-place fiber volume fraction was a mere 0.68 per cent vis-a-vis more than 1 per cent for other polymeric fibers. At later stages, the fibers started fracturing both below and above the neutral axis, thus offering little resistance to crack propagation and causing a sharp decrease in load-carrying capacity. The fiber-matrix bond was very strong, which is reflected by the fact that 60 per cent of the fibers fractured. Pleats on the surface of polyvinyl alcohol fiber F10 play an important role in physical bonding with cementitious matrix, in addition to the chemical bonding due to -OH (hydroxyl) groups of polyvinyl molecule. Other factor that engenders high fiber-fracture is the low strength of PVA fiber in the transverse direction. Under impact beams reinforced with fiber F10 failed in a very brittle fashion (see Figure 5.10); 85 % fibers failed in transverse shear. The catastrophic nature of shear failure of fibers explains the brittleness shown by fiber F10 reinforced beams under impact. Due to premature and abrupt shear failure, PVA fibers didn't utilize their full tension-bearing capacity. It is clear from the results on steel and polymeric macro-fiber reinforced beams that at the fiber addition rates studied, large fibers do not improve the flexural strength of cementitious matrix at low volume fractions. This is often explained on the basis that 82 flexural failure , is caused by progressive extension of distributed microcracks that eventually coalesce into macrocracks, and for the usual volume fractions, large fibers are too far apart to blunt, arrest, or modify these microcracks in any significant way. Researchers feel that for an improvement in the flexural strength, extremely fine fibers are needed, such as carbon micro-fibers F8 and F9. It has been reported [75] that these micro-fibers enhance the flexural strength and energy absorption capability of cement paste and mortar considerably at a volume fraction of 3 to 5 per cent, both under static and impact load. Carbon micro-fiber reinforced cement composites have been used in thin pre-cast products such as roofing sheets, panels, tiles, curtain walls etc. A l l these applications demand a fiber volume fraction of 2 per cent or more. In this study, the possibility of using carbon micro-fibers in shotcrete was investigated. The aim was to see if carbon micro-fibers render similar enhancements to shotcrete as they do to cement paste and mortar, reported by Banthia [75]. Knowing the limitation of conventional mixers that are used at shotcreting sites, it was decided to add 2 % carbon micro-fibers by volume. 80 y 70 -Deflection (mm) Figure 5.11 - Static and impact load-deflection plots for carbon micro-fiber F8 reinforced (Vf = 2 %) shotcrete beams. As reported in chapter 4, to avoid the problem of fiber balling and shrinkage cracking, coarse aggregate and concrete sand were replaced with forestry sand, 2.5 mm in 83 size. This gave rise to a high volume of air-voids, since there were no intermediate size particles to fill in the voids between forestry-sand and cement particles. 80 -j 70 -60 -1 4 i !• Plain + Fiber F9 50 -la 1 / • s Impact 40 -30 -20 • i i- » a 1 / Sratir 10 -0 - f 1: -1 1 1 1 1 0 0.5 1 1.5 2 2.5 3 Deflection (mm) Figure 5.12 - Static and impact load-deflection plots for carbon micro-fiber F9 reinforced (Vf = 2 %) shotcrete beams. The carbon fiber reinforced beams failed in a very brittle fashion under impact. This was largely due to high volume of voids present (boiled absorption for carbon fiber reinforced specimens was 14.5 % compared to 5.6 % for other specimens); fibers were too small to be able to bridge or blunt the cracks. Air-voids facilitated unrestricted and fast propagation of cracks, because there was no evidence of aggregate fracture. Under static conditions, beams reinforced with fiber F9 failed in a brittle manner (see Figure 5.12), while those reinforced with fiber F8 showed a significant post-peak softening (see Figure 5.11). Notice the low values of peak loads, a direct outcome of high voids-content. A visual examination of fractured surfaces of tested beams revealed that carbon fibers invariably fractured under both static and impact loading. From the results, it appears that carbon micro-fibers are not suitable for use in wet-mix shotcrete, at least at a volume fraction of 2 per cent or lower. 84 5.3 - A Comparison Between Static and Impact Data 5.3.1 - Flexural Strengths Flexural strengths, under static and impact load, for all the mixes have been reported in Table 5.3. It is clear that inclusion of fibers, at the volume fractions used in this study, does not improve the modulus of rupture of the cementitious matrix considerably. u 3 14 Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain + F1 +F2 +F3 +F4 + F5 + F6 + F7 + F8 + F9 +F10 +F11 Mixes investigated Figure 5.13 - Ratio between flexural strength under impact and flexural strength under static load for various mixes. An increase in flexural strength occurred under impact loading compared to static loading for both plain and fiber reinforced shotcrete. This is in agreement with the results reported for cast concrete [6,47,75], and is a clear indication of strain-rate sensitivity of cementitious composites. However, these increases do not seem to be influenced by the presence or absence of fiber reinforcement as is evident from the impact/static strength ratios shown in Figure 5.13. 5.3.2 - Flexural Toughness Factors (FT) According to Austin et al. [22], a pseudo-toughness approach based on equivalent flexural strength seems to offer the most promising way of evaluating the post-cracking 85 response of fiber reinforced cement composites. So, flexural toughness factors were calculated for all the specimens under static as well as impact loading according to JSCE-SF4. Note that the flexural toughness factor has units of stress such that its value indicates, in a way, the post-matrix cracking residual strength of the material when loaded to an arbitrary deflection of span/150. Figure 5.14 presents flexural toughness factors for all the mixes investigated in this study, under static and impact conditions. Inclusion of fibers improved the flexural toughness factor of shotcrete; the more efficient the fiber, the higher the JSCE-SF4 FT, meaning higher post-cracking residual strength. Notice the increase in flexural toughness factor under impact loading compared to static loading in Figure 5.14. This reflects the enhanced post-cracking residual strength of shotcrete under impact. It is more prominent for plain shotcrete than it is for fiber reinforced shotcrete, and is conspicuous from the impact/static flexural toughness factor ratios reported in Table 5.3. 5.3.3 - Fracture Energies For all the specimens under static and impact conditions, fracture energy values up to a deflection of 3 mm were calculated from their respective static and impact load-deflection plots; they are reported in Table 5.3. Inclusion of macro-fibers considerably enhanced the energy absorbing capability of shotcrete under static as well as impact loading. The improvements are, however, more pronounced under static conditions (see Figure 5.15). It is clear form Figure 5.15 that steel fibers were most efficient when it came to enhancing the energy absorption capability of brittle cementitious matrix, followed by crimped polypropylene fibers, straight and smooth polypropylene fibers, and carbon fibers. 86 fl 6d + un2|d 8d + U|B|d Zd + U!B|d o ca a. E • o *•+-• CO TJ 0) 9d + U|B|d I, "•S3 0) > c 9d + U|B|d g> W + U|B|d Ed + U|B|d 2d + U|B|d l-d + U|B|d -i r UjB|d O CVJ O O C O - S T C M O C O C O ' * (edlAl) sjoioBi ssauqBnoi jBjnxau gosr CM O 87 • Static •Impact 90 co o 80 ] Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain + F1 + F2 + F3 + F4 + F5 + F6 + F7 + F8 + F9 + F10 + F11 Mixes investigated Figure 5.15 - Fracture energy enhancement rendered to brittle cementitious matrix by different fibers under static and impact load. In the case of the plain shotcrete beams, as soon as the peak load was reached, a macro-crack rapidly traversed the whole depth starting at the tension face and the load suddenly dropped to zero. For plain shotcrete beams, an impact event lasted for about 315 microseconds (see Figure 5.16). On the other hand, fibers in fiber reinforced shotcrete bridged matrix cracks and applied a closing pressure at the crack front. This reduced the stress-intensity at the crack-tip, and a higher energy input was needed to further extend the crack thus improving the toughness of cementitious matrix under static and impact load. For steel fiber FI reinforced shotcrete beams, for example, an impact event lasted for over 1485 microseconds, 4.7 times longer than that for the plain shotcrete beams. 88 Figure 5.16 - Tup load and mid-span acceleration signals for (a) Plain shotcrete beam and (b) Steel fiber FI reinforced shotcrete beam. The extent of additional energy needed for crack extension depends mainly upon the physical and material properties of the fibers and the properties of the matrix [76]. These two essentially determine the amount of bearing and shearing action that will take place between the fiber and the matrix. In this study, the properties of the matrix were kept constant for all the macro-fibers, and basically the variation in the physical and material properties of fibers used in this study resulted in varying fracture energy values. In Table 5.3, the much higher fracture energy values (up to a deflection of 3 mm) under impact loading as compared to static loading can be seen. Figure 5.17 shows the ratio between fracture energy absorbed under impact and fracture energy absorbed under static load for all the specimens. This improvement, however, appears to be far more pronounced for the more brittle systems, viz. plain and plain + F9, as opposed to ductile macro-fibers reinforced shotcretes. 89 F10 F11 Mixes investigated Figure 5.17 - Ratio between fracture energy absorbed under impact and fracture energy absorbed under static load for all the mixes investigated. 5.3.4 - The Constant N As has been shown by Nadeau [56] using LEFM, the dependence of strength (ac) in flexure on the stress-rate (°~) can be described by the logarithmic expression: lncrc = — — \nB6-+ —— lnfof"2 - cr"'2) (5.1) N + l N + l where, N is a material constant (slope of the stress intensity factor, Ki, vs. crack velocity, V, plot on a logarithmic scale), subscripts ' i ' and T refer to initial and final conditions, respectively, and B is a function of Kic and N [56]. In Table 5.3, the values of N obtained on the basis of Equation (5.1) are given. Equation (5.1) is also plotted in Figure 5.18 for two of the mixes investigated here, and it is compared with a previous study [6] on cast concrete. This comparison, and the low values of N indicate the highly stress-rate sensitive behavior of shotcrete (plain as well as fiber reinforced) at the extreme rates of loading associated with impact. Note that the N-values reported here are average ones, based on a straight-line interpolation between the flexural strengths at two extreme stress-rates. 90 3.5 & 3 2 2.5 ? 2 -S 1.5 1 -x-- Plain-NS1 (Banthia [6]) * + Plain (Present study) ** N=35 X N=1.5 x-X + 1.00E-03 1.00E-01 1.00E+01 1.00E+03 1.00E+05 ln(stress-rate), MPa/s * Compressive strength = 34 MPa Compressive strength = 51 MPa CM 3.5 2.5 4--S 2 1.5 - -x- SFRC2-NS (Banthia [6]) * + + Plain + F2 (Present study)** X N=1.4 £ N=34 . . . - X - ' ' X + - - - -1 1.00E-03 1.00E-01 1.00E+01 1.00E+03 1.00E+05 ln(stress-rate), MPa/s * Compressive strength = 40 MPa * Fiber-diameter = 0.5 mm ** Compressive strength = 54 MPa ** Fiber-diameter = 0.55 mm * Fiber-length = 50 mm * Fiber volume-fraction =1.5% ** Fiber-length = 35 mm ** Fiber volume-fraction = 0.59% Figure 5.18 - Strain-rate sensitivity of plain and fiber reinforced wet-mix shotcrete in flexure, a comparison with cast concrete. 1 Normal strength. 2 Steel fiber reinforced concrete. 91 5.4 - Discussion Flexural strengths were not changed much due to fibers neither under static nor under impact conditions. It has been well established that the major advantage of adding fibers is not in enhanced strength, but in enhanced ductility and energy absorption capacity, better crack resistance and crack control, and improved structural integrity and cohesiveness. Plain shotcrete, micro-fiber reinforced shotcrete, and macro-fiber reinforced shotcrete all exhibited increased flexural strengths at a higher rate of loading. An increase of 5 to 12 times was observed in this study, when the rate of straining was increased from 2.9 x 10"7/sec to 0.71/sec. The plain matrix was as rate-sensitive as fiber reinforced ones; this is in contradiction with some previous work on fiber reinforced concrete (FRC) [6,40,47] where FRC was shown to be more sensitive than the plain matrix. The strain-rate sensitivity demonstrated by the plain matrix itself is primarily responsible for the strain-rate sensitivity shown by fiber reinforced shotcrete. In general, under impact, the beams were found to have improved deformation capacities in the vicinity of the peak load, suggesting increased failure strains. This is probably due to increased microcracking in the shotcrete beams. Increased microcracking should make the material more sensitive to stress-rate. There is, however, disagreement over the exact influence of stress-rate on the magnitude of the inelastic strains in concrete that occur at the peak value of stress; they have been reported to both decrease [47] and increase [41,42] with an increase in the stress-rate. An analytical approach to determining fracture strength of brittle materials, at high strain-rate, either from an inherent flaw size or an energy method leads to the same result. By considering the dependence of stress intensity on the velocity of the crack for the special loading case of a constant strain rate, Kipp et al. [58] have shown that for a penny-shaped crack, the fracture stress can be related to the applied strain rate: r , \ i / 3 16a2C s, 1/3 (5.2) 92 A detailed account of Equation (5.2) can be found in section 3.5.1.2. Using this formulation, fracture stresses under impact (applied strain-rate = 0.71/sec) were calculated for all the mixes investigated in this program using the following parameters: E = 4785(f c)0 5 MPa Kic = 0.06(f c) 0 7 5 MPa-m05 (John and Shah, [65]) a = 1.12 for the penny-shaped crack Cs = (E/p)0'5 where p is the density. Table 5.4 - Fracture stresses under impact: a comparison between experimental data and values predicted by Equation (5.2). Equation (5.2) Experiments ca 22.8 30.5 + c '3 CU 23.8 29.7 f^ 1 Pu + c 23.6 40.0 m + c '3 CU 22.8 37.2 2 + s '3 cu 21.5 34.1 PU + c 21.2 34.4 [X, + s '3 Cu 22.3 29.2 + s '3 cu 22.0 25.9 oo + c '3 Cu 23.1 33.4 + c '3 cu 22.5 34.7 PU + ca Cu 23.6 36.8 PL, + S '3 cu 23.3 22.1 From Table (5.4), it is clear that Equation (5.2) is capable of predicting strain-rate sensitivity of concrete at high strain-rates associated with impact. It is worth mentioning here that it failed to predict fracture stresses at low strain-rates associated with static loading; the fracture stresses predicted were small in comparison to experimentally observed data. Both plain and fiber reinforced shotcrete beams were found to be stiffer under impact loading compared to static loading. An increase in the elastic modulus of cement-based materials under a high rate of loading has also been reported by Watstein [36], Hughes [39], and Evans [57]. A crack under dynamic loading seems to require more energy to grow than does a crack under static loading. Plain as well as fiber reinforced shotcrete beams were found to be more energy absorbing under impact than under static loading. The improved 93 toughness under impact loading was probably due, in part, to a wider process zone or microcracking zone. The improvements in fracture energy, however, appear to be far more pronounced for the plain, unreinforced shotcrete than for the fiber reinforced shotcrete. The very high absorption of energy under impact for plain shotcrete, also reported previously for cast concrete using a very different impact machine [77], is rather puzzling. According to Banthia et al.[77], it is possible that for very brittle materials a significant portion of the available hammer energy is dissipated in machine vibrations and the higher the machine capacity the greater the amount of energy lost in this way. 5.5 - Conclusions 1. Wet-mix shotcrete (plain as well as fiber reinforced) is a highly strain-rate sensitive material. 2. Both plain and fiber reinforced shotcrete are stronger and stiffer under impact loading compared to static loading. The increases in flexural strength under impact do not seem to be influenced by the presence or absence of fiber reinforcement. 3. Fiber reinforcement is significantly effective in improving fracture energy absorption under impact. The improvements are, however, dependent on fiber type and geometry, and the improvements are not as pronounced as observed under static conditions. 4. Plain as well as fiber reinforced shotcrete is tougher under impact loading compared to static loading. The improvement in fracture energy, however, appears to be far more pronounced for plain, unreinforced shotcrete than for fiber reinforced shotcretes. 94 Chapter 6 - Plates Under Static and Impact Loading 6.1 - Introduction Plates are two-dimensional structural elements with plane middle surfaces, called neutral planes. During their service span, loads are usually applied normal to their neutral planes and are carried to the supports by bending, thus causing an out of neutral plane deflection. In the present experimental program, plain and fiber reinforced shotcrete plates were loaded at the center at two different loading rates under simply supported conditions. Applied load, load-point deflection, and kinematic data were acquired using load cells, linear variable displacement transducers (LVDTs), and accelerometers. Load vs. deflection data thus obtained from static and impact tests on plates were analyzed in a routine manner to calculate fracture energies absorbed to midpoint deflections of 2 mm, 5 mm, 10 mm, and 15 mm. Peak loads and fracture energies of fiber reinforced plates were compared with their unreinforced counterpart to get an idea of the effectiveness of fiber reinforcement. Finally, static and impact data were compared to assess the influence of rate of loading. 6.2 - Shotcrete Plates Under Variable Stress-rate Static flexural tests (applied loading rate « 0.28 kN/s) on plates were carried out on a 1784 kN universal testing machine using a cylindrical loading head, 100 mm in diameter. 350 mm x 350 mm x 100 mm square shotcrete plates were simply supported on all four edges on an unsupported span of 300 mm x 300 mm, and the concentrated load was applied at the center. Deflections were measured using two LVDTs, as shown in Fig. 6.1. Impact tests on plates, under flexure, were carried out on an instrumented drop-weight impact machine. Plates were simply supported on a rigid steel frame, which was fixed to the base of the impact machine in order to restrain it from moving laterally. The hammer with a cylindrical load-cell, 100 mm in diameter, was raised to a height of 450 mm, and was allowed to fall freely under gravity to impact the plates at the center. This 9 5 testing technique resulted in an applied loading rate of 104.6 x 104 kN/s, thus yielding an impact to static loading-rate ratio of 3.73 x 106. An accelerometer was glued to the bottom of the plate to record the central acceleration; the recorded acceleration history was integrated twice to get the central deflection. A detailed account of test-procedures is given in Chapter 4. Data Acquisition System Figure 6.1 - Test set-up for testing shotcrete plates under static load. 6.2.1 - Plain and carbon micro-fiber reinforced shotcrete plates The plain shotcrete plate reacted to the application of concentrated load by bending in x and y directions under the influence of bending moments, M x and M y (see Figure 6.2). At a load of 52.5 kN, the bottom of the plate cracked in one direction, causing a momentary instability and unloading in the system. Figure 6.2 - Moments and shears in a plate. 96 Cracks essentially started at two opposite mid-edges, and traveled toward the center. This phenomenon can be seen as two yield lines originating at edges and traveling toward the center. Cracking of the matrix disturbs the equilibrium momentarily, and while the stresses are being redistributed, the load drops. It should be noted that up to this point, the crack is yet to reach the top surface of the plate. Once the stress redistribution is complete, the load rises again. At about the load-level of the first peak, another crack-plane (or two yield lines) is formed in a direction perpendicular to the first crack-plane. After the coalescence of all 4 yield lines, cracks started propagating towards the top in an unstable manner, thus leading to sudden failure of the plain shotcrete plate into four pieces (see Figure 6.3). Two peaks are clearly visible in Figure 6.4. Each one of them corresponds to the formation of a pair of yield-lines, originating at opposite edges and traveling toward the center. The failure in the plain shotcrete plates was not as sudden as seen in the plain shotcrete beams, as is evident from the short but significant softening branch. This may be because of a larger fracture area, hence a higher surface energy, required in the case of plates and a more gradual collapse. Under static load, the behavior of carbon micro-fiber reinforced plates was similar to that of plain shotcrete plates, in the sense that they also fractured in a brittle fashion into four pieces. Occurrence of two peaks is a unique feature of the load-deflection plots for both plain and carbon fiber reinforced plates (see Figures 6.4 - 6.6). The formation of four yield-lines, their coalescence and propagation toward the top, and the manifestation of the failure mechanism in the P-8 plots in carbon fiber reinforced plates were all similar to that observed in the case of plain unreinforced plates. However, the peak loads observed and the energy absorbed by the plates were different; this was due to the totally different mix designs. Fiber F9 (longer carbon fiber) reinforced plates performed worse than the control plain matrix, while fiber F8 (shorter carbon fiber) reinforced plates performed better; they sustained higher load and absorbed more energy. This trend was also observed in the case of beams under static loading (refer to Chapter 5). 97 Figure 6.3 - Plain shotcrete plate after static test. 250 Deflection (mm) Figure 6.4 - Static and impact load-deflection plots for plain shotcrete plates. 98 Figure 6.5 - Static and impact load-deflection plots for carbon micro-fiber F8 reinforced (Vf =2%) shotcrete plates. 250 200 150 -I | loo-ll 50 0 • Impact Static Plain + Fiber F9 4 6 8 10 Deflection (mm) 12 14 Figure 6.6 - Static and impact load-deflection plots for carbon micro-fiber F9 reinforced (Vf = 2 %) shotcrete plates. 99 Under impact, plain shotcrete plates failed with much more cracking and microcracking, and thus developed many more yield-lines; eight yield lines in total (see Figure 6.7). At a peak load of 165.5 kN, critical cracks first appeared in the matrix, 0.3-0.4 ms after the first contact with the hammer. Due to a suddenly imparted impulse, the plate's acceleration rose in a very steep manner during the first 0.5 ms of impact event; it then gradually subsided. Cracking and microcracking progressed at a reduced level of load. Plain shotcrete plates sustained this reduced load-level over a displacement of about 4 mm (see Figure 6.4), and in the process absorbed a considerable amount of energy. Due to increased cracking and microcracking, plain shotcrete was able to support a higher load of 165.5 kN under impact, 3.15 times the load sustained under static conditions. Energy absorbed by a body, while deforming, consists of a surface energy component, and a process zone component. An increased number of yield lines increased the surface energy component, while increased microcracking added to the process zone component of the energy absorbed by a plate. That is why, plain shotcrete absorbed over 300 Joules of energy under impact, nearly eight times the energy absorbed under static loading. Fiber F9 reinforced plates failed in a brittle fashion under impact. The performance was inferior to that of plain shotcrete (see Figure 6.6), under both static and impact loading. It should be noted here that carbon fiber reinforced mixes had a high cement content. Also, a visual examination of the fractured surfaces revealed that large voids were present in the hardened shotcrete. In fiber F8 reinforced plates, the occurrence of a second peak, which is higher than first peak, is rather puzzling (see Figure 6.5). A higher second peak signifies that after the cracks appear in the matrix, F8 fibers tend to maintain the integrity of plates and supplement the matrix in taking a higher load. 6.2.2 - Macro-fiber reinforced shotcrete plates Unlike plain and carbon micro-fiber reinforced shotcrete plates, which failed in a brittle fashion, macro-fiber reinforced shotcrete plates showed considerable ductility under static load. These plates, like plain control plates, at first reacted to the application of concentrated load by deflecting in the direction of load, under the influence of bending moments, M x and M y . After the load reached its peak, however the plates started to lift 100 Figure 6.7 - Plain shotcrete plate after impact test. 101 off their supports at the corners; this was due to twisting moments, M x y and M y x (see Figure 6.2), acting at the supports. At simply supported edges, both in-plane bending moments vanish. The out-of-plane bending moment (also called twisting moment), however, does not vanish; it tends to curl the plate into a warped surface and is comparable to the torque in an ordinary beam. A similar deformation sequence was observed under impact loading. 6.2.2.1 - Steel fibers Steel fiber reinforced shotcrete (SFRS) plates invariably supported a much higher load under static conditions compared to the control plain shotcrete plates. When a SFRS plate was loaded, the matrix essentially cracked at a load level of 50-55 kN, the load bearing capacity of the plain control plates. But, no sooner did the cracks appear in the matrix, than the steel fibers across the cracks took over as the load bearing constituent. The high Young's modulus of steel facilitates efficient stress-transfer from cementitious matrix to fibers across the cracks; they can pick up load at very small crack openings in cracked fiber reinforced cementitious composites. Steel fibers are made of high tensile strength steel, and they form a very good bond with the cementitious matrix. Stress in fibers depends upon the general load level, number of fibers intercepted by cracks, and their position relative to the neutral plane. If neither the fiber-matrix bond strength nor the fiber's tensile strength is reached, the load can rise considerably beyond the point of matrix cracking. In this process, fibers bridge the cracks, resist crack propagation, and try to arrest them. Apparently, steel fibers present in the matrix enhance the plastic moment capacity of plates, so that they are able to support a higher load. In this study, steel fibers increased the load-bearing capacity of plain matrix by 2-3 times, as is evident from Figures 6.10-6.13. This increase in load, however, cannot continue indefinitely and failure conditions are eventually generated due either to splitting of the matrix around the fibers and the subsequent fiber pullout or fiber-fracture caused by a strong fiber-matrix bond. Further increase in the strain can take place only with a corresponding decrease in the applied stress. As the matrix-splitting and pullout of fibers progresses, the load gradually reduces, thus showing a toughening effect. If there are a considerable number of fiber-fractures, 102 Figure 6.8 - Top surface of hooked-end steel fiber F l reinforced shotcrete plate after static test. 103 Figure 6.9 static test. - Bottom surface of hooked-end steel fiber F I reinforced shotcrete plate after 104 then it shows on the load-deflection curve as lower post-peak ductility and lower post-peak residual strength. The process described above results in multiple cracking as shown in Figures 6.8 and 6.9. The large number of crack planes observed in the damaged SFRS plates are a clear indication of increased plastic deformations occurring in these plates. The increase in plastic deformations, and thus the increase in energy absorption and load carrying capacity are dependent on the volume fraction, type and geometry of fibers used. The performance of a fiber is judged by the enhancement rendered to the plain, brittle cementitious matrix in terms of ductility and post matrix cracking load-carrying capacity. In the plate tests, the hooked-end fibers' (i.e. Fl and F2) provided superior toughening over the flat-end fiber F3 as is also apparent from respective tup load histories (see Figure 6.14), and the twin cone fiber Fl l (see Figures 6.10 - 6.13). Almost all hooked-end fibers pulled out, and a considerable amount of energy was spent in straightening the hooks. In plates reinforced with these fibers, considerable punching was observed towards the end of static testing. Circular cracks formed around and beneath the cylindrical loading head as can be seen in Figures 6.8 and 6.9. Punching created additional fracture area in these plates along with some additional microcracking; this, in turn, significantly contributed towards the efficient behavior of the hooked-end fiber reinforced shotcrete plates. Punching was absent in the other SFRS plates. Most of the flat-end steel fibers (F3) pulled out. The twin cone fiber (Fl 1) reinforced plates failed with a combination of fiber pullout, fiber fracture, and matrix splitting. Twin cone fibers that pulled out did extensive damage to the surrounding matrix. The primary reasons behind the poor performance of the fiber Fl l reinforced shotcrete plates are - a higher volume per unit fiber thus resulting in a lower number of fibers at a matrix crack at a given volume fraction, and a strong bearing bond between the cone and the matrix that prevents fiber pull-out and facilitates fiber fracture and matrix-splitting. 105 300 0 4 1 1 1 1 1 1 H 0 2 4 6 8 10 12 14 Deflection (mm) Figure 6.10 - Static and impact load-deflection plots for steel macro-fiber FI reinforced (V f = 0.64 %) shotcrete plates. 250 0 4 1 1 1 1 1 1 h-0 2 4 6 8 10 12 14 Deflection (mm) Figure 6.11 - Static and impact load-deflection plots for steel macro-fiber F2 reinforced (V f = 0.59 %) shotcrete plates. 106 250 j -200 -I 150-1 r •a •I o 100 -50 -1 0 -- 6 8 10 Deflection (mm) Figure 6.12 - Static and impact load-deflection plots for steel macro-fiber F3 reinforced (Vf = 0.64 %) shotcrete plates. 300 -p 250 --200 --a 150 -cd .3 100 -50 -0 --6 8 10 Deflection (mm) Figure 6.13 - Static and impact load-deflection plots for steel macro-fiber FI 1 reinforced (Vf = 0.55 %) shotcrete plates. 107 108 In all the impact P-8 plots for plates, the first peak represents the matrix failure. Subsequent peaks and the long descending branch in the load-deflection plots represent the fiber response and fiber-matrix interaction. From Figures 6.10-6.12, it is clear that neither hooked-end fibers nor flat-end fibers enhanced the load-bearing capacity of the plain, brittle cementitious matrix considerably. The twin cone fiber Fl 1 outperformed other steel fibers in this regard (see Figure 6.13). A strong bearing bond between the matrix and the conical ends of Fl l fibers helped the Fl l SFRS plates surpass the first peak. The Fl 1 Fibers bridging the cracks transferred the applied load from the matrix to the fibers without any relative slip, enabling the twin-cone fibers to attain their ultimate tensile strength, and as a consequence, the load rose to a peak of about 281 kN. When the tensile stress in fibers exceeded their ultimate tensile strength, fibers started fracturing from top to bottom. As a result, the load dropped sharply leading to brittle failure. A strong bearing bond, on the one hand helps plates sustain a higher load, but on the other hand results in a less energy absorbing composite. A very large amount of external energy was suddenly imparted to the plates, and that too, within a few milliseconds during impact testing. In response to the imparted impulse, the hooked-end SFRS plates maintained their structural integrity (see Figures 6.15 and 6.16), while all other SFRS plates shattered into pieces. From Figure 6.14 it is clear that at the end of the impact event, the fiber Fl SFRS plate was able to carry a residual load of about 35 kN, whereas in the case of F3 SFRS plates, applied load gradually dropped to zero. A comparison between Figure 6.16 and Figure 6.9 revealed that there was more cracking under impact compared to static loading, which explains the higher fracture energy values observed in the case of impact loading (see Tables 6.2 and 6.3). 6.2.2.2 - Polymeric (Polypropylene and Polyvinyl Alcohol) fibers Unlike the SFRS plates, polymeric fiber reinforced plates supported approximately the same load under static load as that supported by the plain, unreinforced matrix. At matrix failure, the load is transferred to fibers bridging the cracks. Polymeric fibers are capable of supporting the transferred load, but having a low-modulus, they need a much wider 109 Figure 6.15 - Top surface of hooked-end steel fiber FI reinforced shotcrete plate after impact test. 110 Figure 6.16 - Bottom surface of hooked-end steel fiber FI reinforced shotcrete plate after impact test. Ill crack opening compared to steel fibers. So, polymeric FRS plates underwent rapid deformation at peak load, thus rendering a plateau in the vicinity of the peak load. While helping the specimens maintain the peak load, the fibers were subjected to a constantly increasing tensile strain. Increasing stress and strain in fibers eventually precipitates fiber pullout or fiber fracture, depending on the fiber type as well as fiber-matrix bond characteristics. A further increase in the strain can take place only with a corresponding decrease in the applied stress. In polypropylene FRS plates, most of the fibers pulled out giving rise to a gradual, gentle drop in applied load (see Figures 6.17-6.20). In the polyvinyl alcohol FRS plates, on the other hand majority of fibers fractured thus causing a rapid drop in the applied load (see Figure 6.21) after the plateau. As witnessed in section 6.2.2.1, SFRS plates invariably supported a much higher static load compared to the control plain shotcrete plates. To raise the load beyond the point of matrix failure, reinforcing fibers have to have high strength in tension and transverse shear, a high modulus of elasticity, and a strong bond with the host matrix. Since polymeric fibers lack one or more of these attributes, they failed to add to the load-bearing capacity of the plates. Although polymeric fibers did not supplement the plain matrix in enhancing the load-bearing capacity, they did augment the toughening capability of the plates. The polymeric fibers induced multiple cracking in the plates, and in turn, increased their energy absorption capability. 112 2 5 0 0 2 4 6 8 10 12 14 Deflection (mm) Figure 6.17 - Static and impact load-deflection plots for polypropylene macro-fiber F4 reinforced (Vf = 0.96 %) shotcrete plates. 2 5 0 Plain + Fiber F5 0 2 4 6 8 10 12 Deflection (mm) Figure 6.18 - Static and impact load-deflection plots for polypropylene macro-fiber F5 reinforced (Vf = 1.43 %) shotcrete plates. 113 Deflection (mm) Figure 6.19 - Static and impact load-deflection plots for polypropylene macro-fiber F6 reinforced (Vf = 1.19 %) shotcrete plates. 300 i 250 -Plain + Fiber F7 0 2 4 6 8 10 12 14 Deflection (mm) Figure 6.20 - Static and impact load-deflection plots for polypropylene macro-fiber F7 reinforced (Vf = 1.12 %) shotcrete plates. 114 6 8 10 Deflection (mm) 14 Figure 6.21 - Static and impact load-deflection plots for polyvinyl alcohol macro-fiber F10 reinforced (Vf = 0.68 %) shotcrete plates. Table 6.1 - Static and impact data on shotcrete plates: Peak Loads. In-place fiber volume fraction (%) Comp-ressive strength (MPa) Peak load Static (kN) Impact (kN) Ratio Impact/ Static Ratio FRS/Plain Static Impact Plain shotcrete 51 52.5 165.5 3.15 Fiber Fl 0.64 55 157.1 239.9 1.53 2.99 1.45 reinforced F2 0.59 54 130.6 208.8 1.60 2.49 1.26 shotcrete F3 0.64 51 132.6 174.4 1.31 2.52 1.05 (FRS) F4 0.96 46 61.1 201.9 3.30 1.16 1.22 F5 1.43 45 89.5 229.4 2.56 1.70 1.39 F6 1.19 49 65.2 215.2 3.30 1.24 1.30 F7 1.12 48 68.8 246.6 3.58 1.31 1.49 F8 2.00 52 98.1 158.0 1.61 1.87 0.95 F9 2.00 50 48.2 217.7 4.52 0.92 1.31 F10 0.68 54 55.7 138.9 2.49 1.06 0.84 Fl l 0.55 53 104.4 281.0 2.69 1.99 1.69 115 The performance of fibers F4, F6, and F7, in terms of improvement rendered to the plain, brittle cementitious matrix, was about the same under static conditions. Among polypropylene fibers, the fiber F5 performed the best. It could be due to a higher in-place volume fraction of 1.43%, and a predominantly 2-D fiber distribution. In fiber F10 (PVA) reinforced plates, fibers bridging the cracks were able to maintain the peak load up to a deflection of 2 mm; thereafter, fibers started fracturing in shear. This caused a sharp decrease in the load, leading to brittle failure. As mentioned in Chapter 5, a strong bond with the matrix and a low transverse shear strength of PVA fibers are the main reasons behind the observed brittleness of polyvinyl alcohol FRS specimens. From Figures 6.17-6.21, it is clear that all the polymeric FRS plates failed with little post-peak ductility at the high rates of loading associated with impact. The mode of failure of polypropylene fibers changed from pullout to tensile fracture when the rate of loading changed from 0.28 kN/s to 104.6 x 104 kN/s, whereas all the polyvinyl alcohol fibers fractured in transverse shear at both loading rates. Polymeric fibers didn't perform well under impact when it came to augmenting the energy absorption capacity of the plain matrix, as is clear from Figure 6.22, which compares the load-history of hooked-end (fiber FI) SFRS plate with load-histories of polymeric FRS plates. It should be noted that a higher impulse (area under load vs. time plot) eventually translates into a higher energy absorption. 6.3 - Discussion 6.3.1 Peak Loads At the high strain-rate associated with impact, the control specimens showed a higher peak load. There was more cracking and micro cracking in the matrix under impact; eight yield lines formed compared to four yield lines under static load. Increased cracking and microcracking makes the plain matrix sensitive to stress-rate. Hence, it supported a higher load. This phenomenon was also observed in plain shotcrete beams. The addition of steel fibers bolstered the load-sustaining capability of the plain matrix under static load. All other fibers, except fibers F5 and F8, failed to make any 116 117 significant contribution towards the peak load. At the high strain-rates associated with impact, however, none of the fibers made a useful addition to the peak load supported by plates; it was the same as that for the control specimens (see Table 6.1 and Figure 6.23). When loaded statically, the fiber reinforced matrix cracks at about the same stress or strain as when unreinforced. Steel fibers across the cracks picked up the load supported by the matrix easily, and enabled the plates to take additional load before they pulled out or fractured. Under impact, however, the plain and stress-rate sensitive matrix, by itself, was able to support a higher load of 160 kN. After matrix cracking, there was a sharp drop in the load, while the plate was continuously deforming. Fibers, depending on their type, geometry, volume fraction, and mechanical properties, helped specimens regain the first peak load-level fully or partially as opposed to augment the load supported by plain matrix. 3.5 •2 3 £ .E 2.5 ' £ 2 T J a o S 1 o CO I - cc .. a u . 1 J> 0.5 0 • Static • Impact Plain + Plain + Plain + Plain + Plain + Plain + Plain + Plain + Plain + Plain + Plain + F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 Mixes investigated Figure 6.23 - Effect on peak load sustained by various shotcrete plates due to addition of fibers under static and impact load. In general, SFRS plates more or less recovered load fully, while polymeric FRS plates were able to regain half the first peak load. The behavior of carbon micro-fiber F8 reinforced plates is confusing in this regard; they surpassed the first peak load. SFRS plates regained load fully on account of the high modulus and high tensile strength of steel fibers, whereas low modulus and lower tensile strength of polymeric fibers prevented polymeric FRS plates from recovering the first peak load. In this regard, twin 118 cone steel fiber FI 1 outclassed all other steel fibers. A strong bearing bond between fiber FI 1 and the host matrix assisted twin cone FRS plates in surpassing the first peak load. CL Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain + F1 + F2 + F3 + F4 + F5 + F6 +• F7 + F8 + F9 + F10 + F11 Mixes investigated Figure 6.24 - Ratio between peak load under impact and peak load under static load for various shotcrete plates. In all of the impact P-5 plots, first peak represents matrix failure. The nature of subsequent curve and peaks reflect on fibers and fiber-matrix interaction. Plain shotcrete, micro-fiber reinforced shotcrete, and macro-fiber reinforced shotcrete - all exhibited increased peak loads at higher rates of loading. An increase in peak load of 1.3 to 4.5 times was observed in this study, when the rate of loading was increased from 0.28 kN/sec to 104.6 x 104 kN/sec, as is evident from Figure 6.24. The strain-rate sensitive nature of the plain matrix itself, which may be due to experimentally observed increased cracking and microcracking in the cementitious matrix, is primarily responsible for the strain-rate sensitivity exhibited by FRS plates. The SFRS plates seem to be less strain-rate sensitive in terms of an increase in peak failure load. In general, the higher the peak load sustained under static conditions, the lesser was the percentage increase in the load-bearing capability under impact. 119 121 122 6.3.2 - Fracture Energies Under static load, all the macro-fibers improved the energy absorption capability of the plain, brittle matrix considerably, the most efficient being the hooked-end steel fiber, followed by the flat-end steel fiber, polypropylene fibers, twin-cone steel fiber, and PVA fiber in that order (see Figure 6.25). A similar trend was observed under impact too (see Figure 6.26). However, these improvements were much more pronounced under static conditions compared to impact (see Figure 6.27). It is worth mentioning that fracture energies under static load might have been overestimated, since displacement data were not free from crushing at supports, and beneath the loading head. Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain Plain + F1 +F2 +F3 +F4 + F5 + F6 + F7 + F8 + F9 +F10 +F11 Mixes investigated Figure 6.28 - Ratio between fracture energy absorbed (up to a deflection of 15 mm) under impact and fracture energy absorbed under static load for various shotcrete plates. Unlike macro fiber reinforced shotcrete beams, macro FRS plates are not sensitive to strain-rate, when it comes to energy absorption capacity. Energy absorbed by plates under impact was close to that absorbed under static loading, except in the case of plain and carbon micro-fiber reinforced plates (see Figure 6.28), which absorbed much higher energy under impact. According to Banthia et al. [77], it is possible that for very brittle materials a significant portion of the available hammer energy is dissipated in machine vibrations and the higher the machine capacity the greater the amount of energy lost in this way. 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'3 ho fc C/3 fc Di t/3 125 possible. The parasitic "least count effect" associated with the impact machine may be the plausible reason behind the large strain-rate sensitivity shown by plain and carbon micro-fiber reinforced plates in Figure 6.28. 6.4 - Conclusions 1. A higher load was supported by unreinforced control plates under impact loading compared to static loading; thus indicating that shotcrete is a stress-rate sensitive material. This phenomenon was also observed in plain shotcrete beams. 2. Under static load, only steel fibers made a useful addition to the peak load supported by the plates. At the high strain-rate associated with impact, however, none of the fibers enhanced the load-bearing capacity of the plain, brittle matrix considerably. As reported in Chapter 5, in beams, none of the fibers augmented the flexural strength of plain matrix, both under static and impact conditions. 3. Plain shotcrete, micro-fiber reinforced shotcrete, and macro-fiber reinforced shotcrete — all exhibited increased peak loads at a higher rate of loading. The strain-rate sensitive nature of the plain matrix itself is primarily responsible for the strain-rate sensitivity exhibited by FRS plates. 4. Under static load, all the macro-fibers improved the energy absorption capability of the plain, brittle matrix considerably, the leader being the hooked-end steel fiber, followed by the flat-end steel fiber, polypropylene fibers, twin-cone steel fiber, and PVA fiber in that order. A similar trend was observed under impact. However, these improvements were much more pronounced under static conditions compared to impact. Similar trends were also observed in shotcrete beams. 5. Unlike macro fiber reinforced shotcrete beams, macro FRS plates are not sensitive to strain-rate, when it comes to energy absorption capacity. 126 Chapter 7 - A Comparison Between Beam and Plate Results One of the primary objectives of this research program was to find the correlation, if any, between the test data on beams and plates. Theoretical or analytical prediction of the impact behavior of beams based on the static tests on companion beams is not possible, since it depends on the strain-rate in question. So, to correlate static and impact data on beams, one has to perform tests at several strain-rates to see the effect of strain-rate on the fracture strength and fracture energy. The same deficiency, i.e. lack of data at several strain rates, obviated the possibility of extracting impact data on plates from the data on companion plates under static conditions. The proposition of predicting the impact behavior of plates based on the impact behavior of beams is also not feasible. For practical reasons, the tests on plates and beams were done on two different machines, and also at different loading-rates. Beams are essentially one-dimensional members, subjected to uni-axial moment M x and shear force V x when loaded normal to their neutral axis. The corresponding stresses in the beams are bending stress ax, and shear stress xxz. When the bending moment at the center reaches the ultimate moment capacity of beams, a plastic hinge forms at mid-span causing failure (see Figure 7.1). Figure 7.1 - Moment, shear, and failure mechanism in a beam. 127 Square plates simply supported at all four edges and subjected to a concentrated bending load at the center (see Figure 6.1), however, are subjected to bi-axial bending under the action of bending moments M x and M y , twisting moment M x y and M y x , shear forces Qx and Qy (see Figure 6.2). The corresponding stresses are bending stresses CTX, and ay, and shear stresses xxy, T x z , and xyz. Thus we get totally different responses from beams and plates; this is apparent from the data shown in Chapters 5 and 6. Beams are more stress-rate sensitive compared to plates, as is evident from Figures 7.2 and 7.3. This observation suggests that stress-rate sensitivity of concrete is geometry dependent; Gopalaratnam et al. [47] have also observed this phenomenon on the dependence of the strain-rate sensitivity exhibited by cementitious composites on the specimen geometry. The roots of these differences between beam and plate behavior probably lie in the different cracking processes and failure mechanisms of beams and plates. Beams have a well-defined stress field while plates being 2-D structural element have far less defined stress field. • Beams • Plates Plain Plain + F10 +F11 Mixes investigated Figure 7.2 - Strain-rate sensitivity in terms of peak load: Beams vs. Plates. The yielding mechanism in plates that are simply supported at all edges is very different from that in a simply supported beam, as is evident from Figures 7.1 and 7.4. In simply supported square plates, the two diagonal yield lines form the failure mechanism. At failure, each one of the four triangular plates are in equilibrium. Along the diagonal yield line the moment at failure is equal to M u , and the twisting moment is absent, as has 128 129 been shown in Figure 7.4. The moment arm of the total external load on the plate segment about the simply supported edge is 350/6 = 58.3 mm. At failure, the moment due to the external load should be equal to internal moment capacity of plate M u . In simply supported beams, however, the plastic hinge at the center forms the failure mechanism; the two halves of the beam remain in equilibrium at failure (see Figure 7.1). This difference in failure mechanism makes it impossible to establish a correlation between the test data on beams and plates under static conditions. Figure 7.4 - Yield mechanism in a simply supported square plate. To avoid this problem, one should test plates as supported in Figure 7.5; two opposite edges simply supported and two opposite edges free. Now the plates behave as one-way slabs and they can be treated as a continuation of 350 mm x 100 mm x 100 mm ASTM C78 beams; the error in making this assumption gets smaller and smaller as 'L' gets larger and larger. The yielding mechanism of plates supported in this fashion is the same as that of a simply supported ASTM C78 beam. Notice from figures 7.1 and 7.5 that the yield line in plate and the plastic hinge in ASTM C78 beam share the same location. Figure 7.5 - Yield mechanism in a plate with two opposite edges simply supported and two opposite edges free. 131 Chapter 8 - Recommendations for Future Research On the basis of the work carried out in this study, future research work is recommended in the following areas: 1. In North America, dry-mix shotcrete is usually used in the construction of tunnels and for ground support in mines with possibilities of rock burst and blast related impact loading in both cases. Therefore, it would be apt to pursue a similar research project on dry-mix shotcrete, especially in the light of the fact that dry-mix shotcrete differs from wet-mix shotcrete in cement content, mix-design, strength gain and hydration curve, and consistency. 2. Traditionally, welded wire-mesh reinforcement is provided to take care of the impulsive loading in blast-prone shotcrete applications. Traditional mesh reinforcement is now being replaced with short, random fibers. For a better comparison between the mesh and fiber reinforced shotcrete, one needs to investigate the impact behavior of traditionally reinforced shotcrete and compare it with the impact behavior of fiber reinforced shotcrete. 3. It has been well established that the extent of strain-rate sensitivity shown by concrete depends on the mode of loading. In general, the tensile response is the most strain-rate sensitive, the compressive the least responsive, and the flexural response falls between those of tension and compression. It was observed in this investigation that under a concentrated load, beams are more strain-rate sensitive compared to plates. The dependence of strain-rate sensitivity of flexural members on all three dimensions should be further investigated. This proposition assumes importance in the light of the fact that the type of cracking, which develops during the load application, plays a major role in the strain-rate dependence. 132 Bibliography [1]. Austin, SA. and Robins, P.J.(1995) Sprayed Concrete: Properties, Design and Application. Whittles Publishing. [2]. ACI Committee 544(1982) Measurement of properties of fiber reinforced concrete, ACI Manual of Concrete Practice, Part 5. American Concrete Institute, Detroit. [3]. ACI Committee 506(1984) State-of-the-art report on fiber reinforced shotcrete. Concrete International, 6(12), 15-27. [4]. Ramakrishnan, V.(1985) Steel fiber reinforced shotcrete — a state-of-the-art report. Proceedings of U.S.-Sweden Joint Seminar on Steel Fiber Concrete, Stockholm, 7-24. [5]. Banthia, N. P., Mindess, S., Bentur, A. and Pigeon, M.(1989) Impact testing of concrete using a drop-weight impact machine. Experimental Mechanics, 29(2), 63-69. [6]. Banthia, N.(1987) Imapct resistance of concrete. PhD Thesis, University of British Columbia, Vancouver, Canada. [7]. Banthia, N., Mindess, S. and Bentur, A.(1987) Impact behaviour of concrete beams. Materials and Structures, RILEM 20(119), 293-302. [8]. Banthia, N., Mindess, S. and Bentur, A.(1987) Steel fiber reinforced concrete under impact, International Symposium on Fiber Reinforced Concrete, Madras, India. [9]. Tannant, D.D., Kaiser, P.K., and McCreath, D.R.(1995) Large scale impact tests on shotcrete. A report submitted to Mining Research Directorate, Canada as part of the Canadian Rockburst Research Program. 133 [10] Sliter, G.E.(1980) Assessment of Empirical Concrete Impact Formulae. ASCE (Structural Division), 1023-1045. [11]. Suaris, W. and Shah, S.P.(1982) Mechanical properties of materials subjected to impact. Introductory Report for the Inter association Symp. on Impact Loading of Concrete Structures, Berlin(West), 33-61. [12]. Mainstone, R.J., Properties of materials at high rates of straining or loading, Part 4, State-of-the-art report on Impact Loading of Structures, Materials and Structures, 8(44), 102-116. [13]. Banthia, N. and Trottier, J. F.(1993) Strain-rate sensitivity of fiber-matrix bond. Proc. of Canadian Symp. on Cement and Concrete, Ottawa, 603-618. [14]. Banthia, N., Trottier, J. and Beaupre, D.(1994) Steel fiber reinforced shotcrete: Comparisons with cast concrete, ASCE Journal of Materials in Civil Engineering, 6(3), 430-437. [15]. Ramakrishnan, V., Coyle, W.V., Dahl, L. F. and Schrader, E.K.(1981) A comparative evaluations of fiber shotcretes, Concrete International: Design and Construction, 3(1), 59-69. [16]. Gopalaratnam, V.S., Shah, S.P., Batson, G.B., Criswell, M.E., Ramakrishnan, V. and Wecharatana, M.(1991) Fracture toughness of fiber reinforced concrete, ACI Materials Journal, 88(4), 339-353. [17]. Johnston, C.D.(1992) Discussion of "Fracture toughness of fiber reinforced concrete" by Gopalaratnam, V.S. et al. ACI Materials Journal, 89(3), 304-309. 134 [18]. Kasperkiewicz, J. and Skarendahl, A.(1990) Toughness estimation in FRC composites. Swedish Cement and Concrete Research Institute, CBI Report 4:90, Stockholm, 52. [19]. American Society for Testing and Materials(1994) Standard test method for flexural toughness and first crack strength of fiber reinforced concrete. ASTM Standards for Concrete and Mineral Aggregates, ASTM C 1018-94b, 506-513. [20]. Japan Society of Civil Engineers(1984) Method of test for flexural strength and flexural toughness of fiber reinforced concrete. Standard JSCE-SF4, JSCE Standard for Test Methods of Fiber Reinforced Concrete, 45-51. [21]. Vandewalle, M.(1993) Steel fiber reinforced shotcrete design requires a uniform toughness criterion. International Symposium on Sprayed Concrete, Norwegian Concrete Association, Fagernes, Norway, 455-464. [22]. Austin, S.A. and Robins,P.J.(1993) Test methods for strength and toughness of sprayed fiber concrete. Proc. International Symposium on Sprayed Concrete, Norwegian Concrete Association, Fagernes, Norway, 7-19. [23]. Ramakrishnan, V., Yalamanchi, S.S., Kakodkar, S.(1994) National Science Foundation (USA), Proc. of Workshop on Fiber Reinforced Cement and Concrete, Sheffield, 181-193. [24]. Banthia, N. and Trottier, J. F.(1995) Test methods for flexural toughness characterization of fiber reinforced concrete: Some concerns and a proposition. ACI Materials Journal, 92(1), 48-57. [25]. Gopalaratnam, V.S. and Gettu, R.(1994) On the characterization of flexural toughness in FRC. National Science Foundation (USA), Proc. of Workshop on Fiber Reinforced Cement and Concrete, Sheffield, 161-180. 135 [26]. Banthia, N. and Trottier, J. F.(1995) Concrete reinforced with deformed steel fibers, Part II: Toughness Characterization. ACI Materials Journal, 92(2), 146-154. [27]. Chen, L., Mindess, S. and Morgan, D.R.(1993) Toughness evaluation of steel fiber reinforced concrete. Proc. of Canadian Symp. on Cement and Concrete, Ottawa, 16-29. [28]. Cook, N.G.W.(1983) Origin of rockbursts. Proc. International Symposium on Rockbursts: Prediction and Control, The Institution of Mining and Metallurgy, London, U.K., 1-9. [29]. Cook, N.G.W.(1975) Seismicity associated with mining. 1st International Symposium on Induced Seismicity, Canada. [30]. Salamon, M.D.G.(1983) Rockburst hazard and the fight for its alleviation in South African gold mines. Proc. International Symposium on Rockbursts: Prediction and Control, The Institution of Mining and Metallurgy, London, U.K., 1-9. [31]. Ortlepp, W.D.(1993) High ground displacement velocities associated with rockburst damage. Proceedings of the 3rd International Symposium on Rockbursts and Seismicity in Mines, Kingston, Ontario, Canada, 101-106. [32]. Wagner, H.(1984) Support requirements for rockburst conditions. Proc. 1st International Congress on Rockbursts and Seismicity in Mines, Johannesburg, 209-218. [33]. Roberts, M.K.C. and Brummer, R.K.(1988) Support requirements in rockburst conditions. Journal of South African Institute of Mining and Metallurgy, 88(3), 97-104. [34]. Yi, X. and Kaiser, P.K.(1993) Mechanics of rockmass failure and prevention strategies in rockburst conditions. Proc. 3rd International Symposium on Rockbursts and Seismicity in Mines, Kingston. 136 [35]. Tannant, D.D., McDowell, G.M., Brummer, R.K. and Kaiser, P.K.(1993) Ejection velocities measured during a rockburst simulation experiment. Proceedings of the 3rd International Symposium on Rockbursts and Seismicity in Mines, Kingston, Ontario, Canada, 129-133. [36]. Watstein, D.(1953) Effect of straining rate on the compressive strength and elastic properties of concrete. Journal of the American Concrete Institute, 49(8), 729-756. [37]. Green, H.(1964) Impact strength of concrete. Proc. of The Institution of Civil Engineers, 28, 383-396. [38]. Birkimer, D.L. and Lindeman, R.(1971) Dynamic tensile strength of concrete materials, Journal of the American Concrete Institute, 68, 47-49. [39]. Hughes, B.P. and Watson, A.J.(1978) Compressive strength and ultimate strain of concrete under impact loading, Magazine of Concrete Research, 30(105), 189-199. [40]. Suaris, W. and Shah, S.P.(1983) Properties of concrete subjected to impact, ASCE Structural Division, 109(7), 1727-1741. [41]. Zielinsky, A.J. and Reinhardt, H.W.(1982) Stress-strain behaviour of concrete and mortar at high rates of tensile loading. Cement and Concrete Research, 12(3), 309-319. [42]. Zielinski, A.J.(1984) Model for tensile fracture of concrete at high rates of loading. Cement and Concrete Research, 14, 215-224. [43]. Kormeling, H.A.(1986) The rate theory and the impact tensile behaviour of plain concrete. Fracture Toughness and Fracture Energy of Concrete, edited by F.H. Wittman, Elsevier Science Publishers B.V., Amsterdam, 467-477. 137 [44]. Ross, C A . and Kuennen(1989) Fracture of concrete at high strain rates. Fracture of Concrete and Rock: Recent Developments, S.P. Shah et al eds., Elsevier Applied Science, London, 152-161. [45]. Jamrozy, Z. and Swamy, R.N.(1979) Use of steel fiber reinforcement for impact resistance and machinery foundation. International Journal of Cement Composites and Light Weight Concrete, 1(2), 65-76. [46]. Gokoz, U. and Naaman, A.E.(1981) Effect of strain rate on the pull-out behaviour of fibers in mortar. International Journal of Cement Composites and Light Weight Concrete, 3(3), 187-202. [47]. Gopalaratnam, V.S. and Shah, S.P.(1986) Properties of steel fiber reinforced concrete subjected to impact loading. ACI Materials Journal, 83(14), 117-126. [48]. Mindess, S. and Vondran, G.(1988) Properties of concrete reinforced with fibrillated polypropylene fibers under impact loading. Cement and Concrete Research, 18, 109-115. [49]. Banthia, N. and Ohama, Y.(1989) Dynamic tensile fracture of carbon fiber reinforced cements. In Fiber Reinforced Cements and Concretes: Recent Developments, edited by R.N. Swamy and B. Barr. Elsevier Applied Science Publishers, London and New York, 251-260. [50]. Banthia, N., Chokri, K., Ohama Y., Mindess, S.(1993) Fiber-reinforced cement based composites under tensile impact. Advanced Cement Based Materials, 1, 131-141. [51]. Glinicki, M.A.(1994) Toughness of fiber reinforced mortar at high tensile loading rates. ACI Materials Journal, 91(2), 161-166. 138 [52]. Banthia, N., Chokri, K. and Trottier, J.F.(1995) Imapct tests on cement-based fiber reinforced composites, in Testing of Fiber Reinforced Concrete, ACI SP-155, American Concrete Institute, 171-188. [53]. Abrams, D.A.(1917) Effect of rate of application of load on the compressive strength of concrete. Proceedings of American Society of Testing and Materials 17, Part II, 364-377. [54]. McHenry, D. and Shideler, J.J.(1956) Review of data on effect of speed in mechanical testing of concrete, in Symposium on Speed of Testing on Non-metallic Materials, ASTM Special Technical Publication No. 185, 72-82. [55]. Wittmann, F.H.(1982) Creep and shrinkage in concrete structures, ed. by Bazant, Z.P., and Wittmann, F.H., John Wiley & Sons, Chichester, 129-162. [56]. Nadeau, J.S., Bennett, R. and Fuller, E.R. Jr.(1982) An explanation of the rate-of-loading and duration-of-load effects in wood in terms of fracture mechanics. Journal of Materials Science, 17, 2831-2840. [57]. Evans, A.G.(1974) Slow crack growth in brittle materials under dynamic conditions. International Journal of Fracture Mechanics, 10, 251-259. [58]. Kipp, M.E., Grady, D.E., Chen E.P.(1980) Strain-rate dependent fracture initiation. International Journal of Fracture, 16, 471-478. [59]. Grady, D.E. and Kipp,M.E.(1984) Mechanisms of dynamic fragmentation: Factors governing fragment size. Sandia National Laboratories, Report SAND-84-2304C. [60]. Bazant, Z.P. and Oh, B.H.(1981) Concrete fracture via stress-strain relations. Report no. 81-10/665c, The Techn. Inst., Northwestern University, Evanston. 139 [61]. Dugdale, D.S.(1960) Yielding of steel plates containing slits. J. Mech. and Physics of Solids, 8, 100-104. Barenblatt, G.I.(1962) The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7, 55-129. [62]. Reinhardt, H.W.(1984) Fracture mechanics of an elastic softening material like concrete. HERON, 29(2). Li, V.C. and Liang, E.(1985) Fracture processes in concrete and fiber reinforced cementitious composites. MIT, Dept. Of Civil Engg., Cambridge. [63]. Reinhardt, H.W.(1985) Strain rate effects on the tensile strength of concrete as predicted by thermodynamic and fracture mechanics models. Proc. Symposium held on Cement-based Composites: Strain Rate Effects on Fracture, Boston, U.S.A., 1-13. [64]. John, R. and Shah, S.P.(1990) Mixed-mode fracture of concrete subjected to impact loading. Journal of Structural Engineering, 116(3), 585-602. [65]. John, R. and Shah, S.P.(1987) Effect of high strain-rate loading on fracture parameters of concrete. Proc. Of Fracture of Concrete and Rock, SEM-RJLEM Int. Conf., S.P. Shah and S.E. Swartz ed., Published by Soc. Of Ecp. Mech. (SEM), Bethel, CT., 35-52. [66]. Birkimer, D.L.(1971) A possible fracture criterion for the dynamic tensile strength of rock. Proc. 12th Symp. on Rock Mechanics, ed. by G.B. Clark, Am. Inst, of Mining, 573-590. [67]. Ehrlacher, A.(1983) Behaviour of solids with a system of cracks. Preprints W. Prager Symp. Mechanics of Geomaterials: Rocks, concretes, soils, ed. Z.P. Bazant, Northwestern University, Evanston, Illinois, 554-566. [68]. Zielinski, A.J.(1982) Fracture of concrete and mortar under uniaxial impact tensile loading, Delft University Press, Delft. 140 [69]. Eibl, J. And Godde, P.(1983) Untersuchung der Betonzugfestigkeit. Universitat Karlsruhe. [70]. Mihashi, H., Wittmann, F.H.(1980) Stochastic approach to study the influence of rate of loading on strength of concrete. HERON, 25(3). [71]. Lindholm, U.S., Yeakley, L.M., Nagy, A.(1974) The dynamic strength and fracture properties of Dresser Basalt. Int. J. Rock Mech. Min. Sci. & Geomech., 11, 181-191. [72]. Kormeling, H.A.(1983) The tensile behaviour of concrete at high strain rates Part II: Deformation kinetics. Stevin Report 5-83-12, Delft University of Technology, Delft. [73]. Suaris, W. and Shah, S.P.(1982) Mechanical properties of materials subjected to impact. Introd. Report Intern. Symp. Concrete Structures Under Impact and Impulsive Loading, Berlin, 33-62. [74]. Reinhardt, H.W.(1984) Tensile fracture of concrete at high rates of loading. In Application of Fracture Mechanics to Cementitious Composites (NATO-ARW), ed. by S.P. Shah, Northwestern University, Illinois, U.S.A., 413-439. [75]. Banthia, N. (1992) Pitch-based carbon fiber reinforced cements: structure, performance, applications, and research needs. Canadian Journal of Civil Engineering, 19(1), 26-38. [76]. Naaman, A.E. and Najm, H. (1991) Bond-slip mechanisms of steel fibers in concrete. ACI Materials Journal, 88(2), 135-145. [77]. Banthia, N., Mindess, S. and Trottier, J.F. (1996) Impact resistance of steel fiber reinforced concrete. ACI Materials Journal, 93(5), 472-479. 

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