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Resistance of concrete railroad ties to impact loading Wang, Nianzhi 1996

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RESISTANCE OF CONCRETE RAILROAD TIES TO IMPACT LOADING by Nianzhi Wang  Diploma, Tongji University, China, 1977 M. Sc., Tongji University, China, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE STUDIES The Department of Civil Engineering We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA May, 1996 © Nianzhi Wang, 1996  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  of  the  requirements  British Columbia, I agree that the  for  an advanced  Library shall make it  freely available for reference and study. I further agree that permission for extensive copying  of  department  this thesis for scholarly purposes may be granted or  by  his  or  her  representatives.  It  is  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department  of  Cjul ( T^te \ ^ ^ ^ ^  nmhia The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  I  U  ABSTRACT  In some sections of railroad, many prestressed concrete railway ties were found to be cracked after being in service for only a few months, because of impact loading. The dynamic properties of concrete ties were thus studied in this work. Two typical types of impulse encountered in track, due to rail abnormalities and "wheel flats" of trains, were successfully simulated by the use of a 578 kg impact machine and a 60 kg drop weight impact machine, respectively. The previously developed "single-blow" impact technique has been extended into a "multi-blow" impact technique, in order to better simulate the repeated impact loading on the concrete tie in track. It was found that the stiffness of the rubber support played an important role in the dynamic response of the ties. Using the soft rubber support caused a low maximum load, low loading rate, a higher fracture energy and a ductile flexural fracture mode. Using the hard support caused a brittle flexure-shear or shear failure mode. Crack mode analysis showed that the cause of the crack mode changing from flexural under quasi-static loading to shear under impact loading is that the shear to moment ratio at the mid-span of the tie changes under impact. A crack mode prediction method was proposed. In the second series of tests, twelve types of modified ties were tested. The effects of the concrete strength, steel fibre additions, changes in prestressing force, the presence of stirrups were examined. The crack opening length and residual crack length were detected by crack detection gauges. Steel fibres greatly improved tie behaviour, leading to shorter andfinercracks in the concrete. Stirrups can, particularly when used in conjunction withfibres,effectively retard the deterioration of the concrete tie. The ties with a 40 MPa compressive strength and 30 mm fibres behaved very well. They were markedly better than the ties which had the samefibrecontent but a 65 MPa concrete compressive strength. The reason for this is that reducing the concrete compressive ii  strength or prestressing level of the tie resulted in a reduction of the dynamic flexural stiffness and hence the magnitude of the impact loads. It is believed that if these measures were combined with the use of steel fibres in the concrete, a new type of concrete tie, with improved ductility and high resistance to impact load could be developed. Dynamic analysis of the ties showed that a different impulse duration or frequency may lead to a very different concrete strain response. This may need to be considered in the wheel truing program in service. Thirteen types of commercial pads were tested and ranked. Soft pads may act as a low-pass filter, leading to lower amplitudes of the concrete strain vibration. However, it may structurally deteriorate more quickly, leading to an even worse influence on the ties after a period of time in service.  iii  T A B L E OF CONTENTS  ABSTRACT  ii  T A B L E OF CONTENTS  iv  LIST OF TABLES  x  LIST OF FIGURES  xiv  LIST OF NOTATIONS  xvi  ACKNOWLEDGMENTS  xviii  DEDICATION  xix  INTRODUCTION  1  CHAPTER 1. OBJECTIVE AND SCOPE  3  CHAPTER 2. LITERATURE SURVEY  8  2.1. Impact Tests on Structural Prestressed Concrete  8  2.2. Impact Tests on Prestressed Concrete Railroad Ties  11  2.2.1. Introduction  11 iv  2.2.2. Experimental Investigations in Laboratories  11  2.2.3. Experimental Investigations in Railroad Tracks  16  2.3. Techniques of Instrumented Impact Testing  18  2.3.1. Impact Testing Systems for Concrete  18  2.3.2. Problems Associated with Reliable Control of Impact Tests  20  2.3.2.1. Inertial Load Effect  21  2.3.2.2. System Response Time or Frequency Response  23  2.3.2.3. Energy Balance  24  2.4. Summary  26  CHAPTER 3. EXPERIMENTAL ASPECTS  28  3.1. Introduction  28  3.2. Specimen Preparation  29  3.2.1. C X T Pretensioned Concrete Ties  29  3.2.2. ITISA (Type UP-2) Post-Tensioned Concrete Ties  31  3.2.2.1. Standard ITISA Ties  31  3.2.2.2. Modification of the ITISA Ties  32  3.3. Impact Testing Apparatus  35  3.3.1. Introduction  35  3.3.1.1. The 578 kg Machine  39  3.3.1.2. The 60 kg Machine  41  3.3.2. Instrumentation and Apparatus  43  3.3.2.1. Tup and Load Cell  43  3.3.2.2. Data Acquisition System  45  3.3.2.3. Accelerometers  49  3.3.2.4. Crack Detection Gauges  50 v  3.3.2.5. Strain Gauges 3.3.2.6. Stress Coat.... 3.3.2.7. Rail Segment and Pandrol Fastening System  5  3.3.2.8. Preload  5  3.4. Static Testing Apparatus  6  CHAPTER 4. STATIC TESTING  6  4.1. C X T Concrete Tie  6  4.1.1. Flexural Tests for New Ties  6  4.1.2. Flexural Tests for Damaged Ties  6  4.1.2.1. The Influence of the Rubber Support  6  4.1.2.2. Influence of the Pad  6  4.2. ITISA Concrete Tie  6  CHAPTER 5. IMPACT TESTING OF CXT CONCRETE TIES  7  5.1. Introduction  7  5.1.1. Background in Railroad Practice  7  5.1.2. Background to Theoretical Analysis  7  5.2. Testing Setup  7  5.3. Test Program  8  5.4. Analysis of Test Results  8  5.4.1. Differences in Analysis between Impact Tests of Beams and of Concrete Ties 8 5.4.2. Derivation of Fracture Energy  8  5.4.2.1. Method 1: From Load vs. Deflection Curve  8  5.4.2.2. Method 2: From Impulse and Momentum  8  vi  5.4.3. Derivation of the Bending Load  :  5.4.4. Concluding Remarks  88 95  Appendix-Chapter 5. "Multi-blow" Impact Testing on FRC Beams  97  CHAPTER 6. EFFECT OF LOADING CONDITIONS ON DETERIORATION OF TIES  105  6.1. Impact Tests with 345 kg Hammer  105  6.2. Impact Tests with 504 kg Hammer  112  6.3. Comparison of the Impact Tests Using the 345 kg and 504 kg Hammers  119  6.4. Summary  123  CHAPTER 7. FRACTURE MODE ANALYSIS  124  7.1. Introduction  124  7.2. Bending Moment and Shear Force Under Impact  125  7.3. Crack Mode Prediction  133  7.4. Crack Mode Analysis for CXT Ties  140  7.5. Summary  150  CHAPTER 8. IMPACT TESTING OF MODIFIED ITISA TIES  152  8.1. Introduction  152  8.2. Simulations of Impact Pulses on Railroad Tracks  153  8.3. Test Setup  163  8.4. Testing Program  165  CHAPTER 9. IMPACT RESISTANCE OF MODIFIED ITISA TIES  166  9.1. Crack Propagation in Different Types of Ties  166  vii  9.1.1. Crack Description  166  9.1.2. Effect of Steel Fibre Additions  175  9.1.3. Effect of Stirrups  176  9.1.4. Effect of Concrete Strength  179  9.1.5. Effect of Prestress Level  183  9.2. Simplified Quasi-Static Model for Impact Testing  186  9.2.1. Assumptions  186  9.2.2. Derivation of Impact Load  186  9.2.3. Relationship between Drop Height of Hammer and Impact Load  187  9.2.4. Relationship between Concrete Strength and Impact Load  190  9.2.5. Relationship between Moment of Inertia and Impact Load  192  9.3. Discussion of the Design of a Concrete Tie  193  9.4. Summary  194  C H A P T E R 10. E F F E C T O F RAIL S E A T PADS O N D Y N A M I C P R O P E R T I E S 195 10.1. Introduction  195  10.2. Specimens  196  10.3. Experimental Program  201  10.4. Results and Discussion  202  10.4.1. Attenuation Effects on Pads on Rail Seat Concrete Strain -Impacted End 202 10.4.2. Attenuation Effects of Pads on Rail Seat Strain -Nonloaded End  208  10.4.3. Attenuation Effects of Pads on Impact Load  212  10.4.4. Deterioration of Static and Dynamic Characteristics of Pads  215  10.5. Summary  217  C H A P T E R 11. C O N C L U S I O N S A N D R E C O M M E N D A T I O N S  218  viii  11.1. Conclusions  218  11.2. Recommendations for Future Research  224  BIBLIOGRAPHY  227  APPENDIX. DYNAMIC ANALYSIS OF ITISA TIES  235  A. 1. Assumptions  235  A.2. Dynamic Amplification of Applied Load  237  A3. Dynamic Amplification of Deflection and Strain  244  ix  LIST OF TABLES  Table 1: Concrete Tie Parameters  34  Table 2: Concrete Compressive Strength of Modified Ties  35  Table 3. Output voltage of the Crack Detection Gauge  53  Table 4. Shunt Calibration of the Strain Gauge  57  Table 5. Support and Pad Conditions under Impact Testing of CXT Ties  63  Table 6. Crack Development Under Static Loading  66  Table 7. Residual Capacity of the Ties after Being Subjected to Impact Loading  67  Table 8. Loads and Strains as the First Crack Passed Each Paint Line  71  Table 9. Impact Testing Conditions for CXT Ties Table 10. SFRC Specimen Types  81 97  Table 11. Concrete Beam Fracture Energy Obtained by Two Analysis Methods  102  Table 12. Impact Tests of CXT Ties with 345 kg Hammer  106  Table 13. Impact Tests of CXT Ties with 504 kg Hammer  113  Table 14.-Effect of Loading Rate and Maximum Load on Cracking and Fracture Energy 121 Table 15. Applied Load Causing Flexural Cracking at Mid Span  145  Table 16. Applied Load Causing Shear Cracking of the Tie  145  Table 17. Crack Mode Analysis of CXT Tie Under Impact with Different Supports .... 148 Table 18. Static Stiffness of Rail Seat Pads Table 19. Deterioration of Used Pad with Respect to the Same Type of New Pad  199 214  Table 20. Strain Amplification Factor for Impact Tests Using the 60 kg Hammer  247  Table 21. Strain Amplification Factor for Impact Test Using the 578 kg Hammer  247  LIST OF FIGURES  Figure 1. Geometry of C X T ties (Type CC497), and Location of Prestressing Wires  30  Figure 2. Geometry of ITISA (Type UP-2) ties, and Location of Prestressing Bars  33  Figure 3. Schematic View of the 578 kg Impact Machine  40  Figure 4. Schematic View of 60 kg Impact Machine  42  Figure 5. The Tup  44  Figure 6. Half-sine signal and the sampling rate required  47  Figure 7. Crack Detection Gauge, Strain Gauge and Accelerometer on Concrete Tie Surface  51  Figure 8. Crack Detection Gauge Circuit and Theoretical Output  52  Figure 9. Wheatstone Bridge Circuit for Strain Gauges  54  Figure 10. Calibration of Strain Gauge on Concrete Tie  '.  57  Figure 11. A Concrete Tie with a Preload Applied on the 60 kg Impact Machine  60  Figure 12. Setup of the Static Tests on C X T Concrete Ties  64  Figure 13. Load vs Deflection Curve of C X T Tie Subjected to Static Loading  65  Figure 14. Static Test on ITISA Concrete Tie  70  Figure 15. Impact Test Setup for the C X T Concrete Ties  76  Figure 16. Load vs. Deformation Curves for Rubber Supports  77  Figure 17. Load vs. Deformation Curves for E V A pads  78  Figure 18. Load vs. Deformation Curves for Poly pads  78  Figure 19. Impulse and Momentum Change of the Hammer  86  Figure 20. Schematic examples demonstrating the interrelationship between impedance (Z), and materials properties (59)  90  Figure 21. Simplified Dynamic Model for Flexural Impact Tests  xi  91  Figure 23. Relationship of Tup load and Bending Load  93  Figure 24. Curve Fitting of Measured Tup Load Signals  94  Figure 26. Impact Test Setups For SFRC Beams  98  Figure 27. Load vs. Deflection Curve for S3-2 (0.75% Steel Fibres)  99  Figure 28. Load History for C X T Tie with Soft Rubber Supports and Poly Rail Seat Pad 107 Figure 29. Load History for C X T Tie with Hard Rubber Supports and Poly Rail Seat Pad 108 Figure 30. Load Histories of the First Impact with the Various Support Conditions  110  Figure 31. Load History of the First Blow with Different Support Conditions  114  Figure 32. Load History of the Tie with Hard Supports  114  Figure 33. Load History of the Tie with Soft Supports  115  Figure 34. Fracture Mode of the Tie with Hard Supports  115  Figure 35. Tie with Soft Supports After 10 Blows  117  Figure 36. Tie with Soft Supports After 10 Blows  117  Figure 37. Tie with Hard Supports After 2 Blows  118  Figure 38. Tie with Hard Supports After 2 Blows  118  Figure 39. Maximum Load at Impact  120  Figure 40. Loading Scheme in Static and Impact Loading  126  Figure 41. Principal Stress and Strut and Tie Model for Deep Beam (78, 79)  136  Figure 42. Two Special Cases of Impact Loading  140  Figure 43. Load vs. Deflection of Beams with Hard and Soft Rubber Support  142  Figure 44. Inertial Load Distribution for C X T Concrete Tie with a Hard Rubber Support 143 Figure 45. Support Span and Shear Span  146  Figure 46. Comparison of Vertical Loads of the Heritage Car  155  xii  Figure 47. Load History of Impact Test Using 578 kg Hammer  156  Figure 48. Impact Load History for Passenger Car 'Flat' Wheel (29)  158  Figure 49. Load History of Impact tests Using 60 kg Hammer  159  Figure 50. Frequency Spectra of Rail Seat Bending Strains from Track Measurement and Battelle's Columbus Laboratories Measurement (8)  161  Figure 51. Frequency Spectra of Rail Seat Bending Strain for ITISA Tie Using 60 kg Hammer  162  Figure 52. Layout of Impact Test for Concrete Railroad ITISA Ties  164  Figure 53. Typical flexural crack under rail seat at loaded end (using 60 kg hammer)... 167 Figure 54. Typical horizontal cracks at nonloaded end,  168  Figure 55. Typical flexural crack at nonloaded end;  169  Figure 56. First Three Bending Modes for Concrete Ties (29)  171  Figure 57. Typical flexural crack under rail seat at loading end (using 578 kg hammer). 174 Figure 58. Fibre and Stirrup Effect on Crack Propagation  177  Figure 59. Crack Propagation of Ties under Impact  178  Figure 60. Concrete Strength Effect on Crack Propagation  181  Figure 61. Concrete Strength Effect on Crack Propagation  ...182  Figure 62. Prestress Effect on Crack Propagation  184  Figure 63. Prestress Effect on Crack Propagation  185  Figure 64. Relationship Between Impact Load and Drop Height  189  Figure 65. Maximum Load for Ties with 1% 30 mm Steel Fibres  191  Figure 66. Attenuation Effects of Pads on Rail Seat Strain -Impacted End  202  Figure 67. Rail Seat Strain History for Pad Nos. 1 and 10  203  Figure 68. Frequency Spectra of Rail Seat Bending Strain for Pads No. 1 and 10  205  Figure 69. Static Compressive Tests of Rail Seat pads Nos. 1 and 10  206  Figure 70. Attenuation Effects of Pads on Rail Seat Strain -Nonloaded End  208  xiii  Figure 71. Frequency Spectra of Rail Seat Bending Strain for Pad Nos. 1 and 9  209  Figure 72. Mode Shapes and Frequencies of ITISA Concrete Tie  210  Figure 73. Attenuation Effects of Pads on Impact load  212  Figure 74. Impact Load History for Pad Nos. 1,5 and 10  213  Figure 75. Static Compressive Tests of Rail Seat Pads for Nos. 6 and 8  xiv  215  LIST OF NOTATIONS  Note: In some cases, using conventional terminology, the same symbol may have quite different definitions. However, in each case, the meaning should be clear from the context.  A/D:  analog to digital conversion  ACI:  American Concrete Institute  A R E A : American Railway Engineering Association ASTM:American Society for Testing and Materials b:  width  d:  depth  Drf.  dynamic amplification factor for deflection  D  ratio of D j t o D ^  Dy.  dynamic amplification factor for strain energy  E:  initial stiffness of beam under static load  E:  modules of elasticity  f:  concrete compressive strength at 28 days  F:  dynamic load  /:  natural frequency of vibration  FFT:  fast Fourier transform  Ff.  resultant of the distributed inertial load  F:  amplitude of dynamic load  h:  drop height of hammer  /:  moment of inertia  r  c  0  xv  IF:  dynamic impact factor  k:  equivalent span length to span length ratio  k:  strain gauge factor  /*:  equivalent span length  /:  span length  LR:  loading rate  L V D T : linear variable differential transformer M:  bending moment at mid-span of beam  M:  generalized mass of the beam  M f.  flexural cracking moment  M:  mass of hammer  p:  contact impact load  P:  true bending load in impact testing  P j:  flexural cracking load  P :  shear cracking load  P:  maximum bending load  P,:  tup load in impact testing  Q:  shear force at mid-span of beam  Rj:  support reaction  R:  resistance of shunt resistor  T:  total event time  tf.  time to the peak load  t:  time to the peak bending load  T:  natural period of vibration  t\  response time of instrumentation system  m:  beam deflection at mid-span  c  h  h  c  cv  m  c  m  n  R  xvi  u  :  beam velocity at mid-span  it:  beam acceleration at mid-span  U:  elastic strain energy in impact test  U:  total energy—area under the entire load vs. deflection curve in static tests  U  0 7 5  : fracture energy—area under the load vs. deflection curve out to the point at which the curve had declined to 75% of the peak load in static tests  v:  initial velocity of the hammer as it approaches the tie  V:  shear to cause web shear cracking  0  c  v,:  final  velocity when the tup just rebounds from the tie  W:  Hammer weight  Z:  mechanical impedance of the specimen  B:  ratio of applied load frequency to natural frequency  A:  maximum deflection of beam  AE:  potential energy the hammer releases to the tie during impact  e:  strain  e:  bending strain per unit load  p:  concrete density  4>:  deflected shape function  <(>:  diameter  T:  duration of impact pulse  co:  circular frequency of applied load  cOr,:  circular natural frequency of beam  f  xvii  ACKNOWLEDGMENTS  The author is greatly indebted to his supervisor, Dr. Sidney Mindess, for his excellent supervision, very kind instruction, continuous support and personal encouragement; also for his invaluable suggestions and time spent in reviewing the manuscript, which contributed very much to the completion of this thesis. The author would also like to express his sincere gratitude to Dr. W. J. Venuti for providing a vast amount of information, important guidance and friendly support throughout this research. The author wishes to thank Dr. R. A. Spencer, Dr. A. Poursartip and Dr. P. E. Adebar for serving on the author's supervisory committee and for their constructive comments; and to thank Dr. N. P. Banthia for his valuable guidance. Special thanks are due to Dr. Cheng Yan for his kind help and encouragement. Appreciation is extended to Mr. M. Nazar, J. Wong and B. Merkli of the workshop of the Department of Civil Engineering for their preparation and maintenance of the impact machines and instrumentation. The author also wishes to acknowledge the support of ITISA Mexico, who supplied the ITISA concrete ties, and Pandrol Incorporated, New Jersey, who provided the components of the Pandrol fastening system. Acknowledgments is extended to Philip J. McQueen Co., ACME Products Inc. and Controlled Rubber Products for the use of property data and materials referred to in the report, Ref. No. 69. Thanks to J. F. Scott and J. A. Hadden for their personal help. The research assistantship awarded by the Department of Civil Engineering, University of British Columbia and the research grant provided by the Natural Sciences and Engineering Research Council of Canada, via the Network of Centers of Excellence Concrete Canada, are gratefully acknowledged. Finally, I would like to take this opportunity to express my appreciation to my dear wife, Liling Sun, for her patience and constant support. xviii  TO MY PARENTS  xix  INTRODUCTION  There is growing interest in studying the impact resistance of concrete structures and structural members. Apart from some special applications such as reactor-containment vessels, missile-storage silos, and certain military structures, the capacity of a structure to resist earthquakes is an important problem related to impact. The current use of high strength concrete in buildings increases the risk of catastrophic collapse under impact loading without any warning signals such as visible deflection or yield of the material. Although some research has shown that the tensile and compressive strengths of concrete increase with an increase in the rate of loading (1), recent investigations have revealed that such favorable " rate effects" on strength may be offset by an adverse change in the mode of failure (2,10). Conventional steel reinforcement in high strength concrete may break in a brittle manner under impact loading rather than undergoing ductile failure, leading to a decrease of fracture energy. Prestressed concrete members designed to fail in a ductile manner (flexural failure) at slow rates of loading have been observed to fail in a brittle manner (diagonal tension-shear failure) under impact loading (3). This phenomenon was also observed on beam-column joint specimens (4), implying that during an earthquake the buildings may be subject to a more dangerous brittle collapse due to the impact loading (5). For prestressed concrete, although there is not much published work available, evidence shows that prestress may be an unfavorable factor for impact. The fracture energy decreases as the prestress increases when the beam is under flexural impact (6). In practice, a collapse accident of a prestressed concrete rock-shed structure occurred in July, 1989 at Ethizen seashore in Japan (7). Fifteen people in the microbus were killed by 1  Introduction  2  the collapse of a rock-shed caused by falling rocks. This rock-shed was designed by the allowable stress design method in which the impact load is replaced by an "equivalent" static load. Moreover, in some railroad sections, quite a high proportion of prestressed concrete railway ties were found to be cracked after being in service for only a few years, or even a few months, because of the impact loading due to wheel flats and rail abnormalities (8 ). The cracks were a cause of concern because the design service life for the ties was 50 years, and no cracks could be tolerated because of the harsh environment and possible fatigue of the prestressing steel at the crack gaps. Using a very high impact factor in current strength design of the concrete ties, which has been increased from 50% in the 1970's to the current 200%, did not prevent the tie from cracking, strongly indicating that further detailed research on the impact of prestressed concrete should be carried out. In addition, impact tests also need to be done on fibre reinforced concrete, which may be the most effective way to improve the toughness of concrete (9 ).  CHAPTER 1. OBJECTIVE AND SCOPE  Premature concrete tie cracking has been found in railroad tracks. A number of factors may influence the dynamic properties of prestressed concrete railroad ties in service. There are two major kinds of impact loads: one arises from "flats" on the rolling surface of the train wheels, with a typical impulse duration of 3 to 5 ms; the other arises from rail irregularities such as rail joints, engine burns, or battered welds, with a typical impulse duration of 5 to 10 ms. Such loads could be up to 3 times higher than normal quasi-static loads. The type of rails, the pads between the rails and the concrete ties (rail seat pads), the ballast conditions under the ties and the design of the concrete tie itself all affect the response of the tie to impact. On some railroad bridges, there is no ballast under the ties. The elastic support placed between the concrete tie and the bridge girder may also influence the tie response. In the present study, these two types of impulses were simulated using two different impact machines with different hammer weights. The effects tie of the rail seat pad, the rubber strip between the concrete tie and the support (rubber support), and the modification of the concrete tie itself on the dynamic response of the concrete were evaluated. The rubber support somewhat simulated the different ballast conditions in track. Two types of standard concrete ties were tested in two series of studies respectively, having their own emphasis. Thefirstseries of tests, using CXT concrete ties, was to evaluate the effect of the stiffness of rubber support on the response of concrete ties subjected to a 10 ms duration impulse, compared to the effect of the stiffness of the rail seat pads. Since different cracking modes were found to occur in these tests, the results 3  Chapter 1. Objective and Scope  4  and their analysis led to a more general discussion of the mechanism of the change in the fracture mode. Particular attention was paid to the effect of the loading rate and of the distribution of the inertial load along the tie on the crack mode of the prestressed concrete. In the second series of tests, using a standard ITISA concrete tie as the datum, twelve different types of modified ties were tested, subjected to impulses with both a 4 ms duration and a 10 ms duration, respectively, with the objective of improving the dynamic properties of prestressed concrete railroad ties. Moreover, thirteen types of pads, including both new and used pads of the types currently being used in practice, were tested under the 4 ms impulse in this series. In Chapter 3, the two types of standard ties, as well as the twelve types of modified ITISA ties, are described in detail. Two impact machines, with 60 kg and 578 kg drop masses respectively, are introduced, together with some considerations in choosing and designing the impact machine. Some individual components used in both series of tests, such as the data acquisition system, the strain gauges, the crack detection gauges and the accelerometers, are also described. The static testing conducted in the two series of tests is introduced in Chapter 4. Since it is expected that a concrete tie can still be used without any repair after a certain amount of repeated impact loading, the residual quasi-static load-bearing capacity of the tie, after impact testing, is an important index. The fracture energy, initial stiffness and peak load under static loading were measured for the CXT ties that had been tested under impact with different support and rail seat pads, and compared to those for the new tie. For the ITISA tie, the cracking strain and cracking load of the tie under impact were obtained in the static test. Since the two series of tests had different emphasis, their test setups, programs and data processing under impact testing are also different. These experimental aspects for the first series of tests using CXT ties are described in Chapter 5. Two different stiffnesses of  Chapter 1. Objective and Scope  5  rubber supports and two different stiffnesses of rail seat pads were used, leading to four different test conditions for the CXT ties. The ties were subjected to a 10 ms duration impact pulse, using the same drop mass, drop height and number of blows. A method of analysis was developed for the multi-blow impact testing, as compared with the previous "single-blow" impact method. In the multi-blow impact technique, the beam undergoes an acceleration phase, when the bending load is lower than the tup load, and a deceleration phase, when the bending load is greater than the tup load. When the beam is in the elastic rebound period, it releases a portion of its stored strain energy back to the hammer. If the beam was not broken into two or more pieces, the areas under the tup load versus deflection curve were almost the same as those under the bending load versus deflection curve, and could be used to evaluate the fracture energy of the beam. Previous tests had showed that, under an impulse of less than 5 ms with up to 100 kN peak load, the stiffness of the rubber support had little effect on the response of the tie. The impact testing in the current study, applying a 10 ms duration impulse with a greater than 300 kN peak load, indicated a very strong influence of the stiffness of the rubber supports to the deterioration of the tie. This influence was attributed mainly to the change in the fracture mode of the tie. On the contrary, the rail seat pads had some effect on the deterioration of the tie only when the hard rubber supports were used. These comparisons are shown in Chapter 6. A crack mode analysis is carried out in Chapter 7 to attempt to reveal the mechanism of the change in fracture mode from flexural under static loading to shear under impact for concrete beams. This is a most serious problem for concrete structures subjected to impact. An attempt is made to explain this phenomenon in simple, easy-tofollow engineering terms. It was found that the distribution of the inertial load and the loading rate played the most important roles in the change of fracture mode. The suggested mechanism is verified by using the crack mode analysis to check the crack  Chapter 1. Objective and Scope  6  modes of the concrete ties in the present impact tests. The experimental aspects of the second series of tests for the modified ITISA ties are described in Chapter 8. In order to simulate the response of concrete ties to impact loading, it was considered essential to replicate, as closely as possible, the impact pulse measured on a track in service, in terms of the duration of the pulse and the shape of the load vs. time curve. A new impact machine, with adjustable hammer mass and a changeable rubber shim between hammer and striking tup, was built to simulate the impact pulse due to the "wheel flat" of the moving train. The simulated impact load and the concrete response in the laboratory are compared with those measured in track, both in time domain and in frequency domain. A cumulative impact test series was designed based on a good simulation of the impact. A test program was also devised for the modified ITISA ties subjected to the impact pulses due to rail irregularities. The test results of the modified ITISA ties are shown in Chapter 9. The effects of the concrete compressive strength, steel fibre additions, changes in prestressing force, the presence of stirrups and their combinations on the behaviour of concrete ties under impact loading are examined. A simplified quasi-static model is proposed to evaluate the relationship between impact load and other parameters involved in impact tests. The theoretical result is confirmed by the experimental data. Suggestions are made for the improvements in design of the concrete ties. The analysis in this chapter shows that increasing the flexural strength of concrete tie will increase the flexural stiffness of the tie at the same time and hence incur a higher impact load. The flexibility and ductility rather then the strength of the concrete should be taken as the governing parameter. To confirm the simplified analysis in Chapter 9, a dynamic analysis of concrete ties is carried out in Appendix on the basis of the measured natural frequencies of the tie and the duration of the applied load in the second series of tests. The dynamic amplification factor is derived for the amplitude of the applied load and compared with the impact  Chapter 1. Objective and Scope  7  factor obtained from the quasi-static model. The dynamic amplification factors for the deflection of the tie subjected to different durations of impulse, are also obtained. These different deflection and hence the strain amplification factors need to be considered in the railroad wheel maintenance program in service, which is basically based on the maximum impact load record using the wheel impact load detector in tracks. One of the major measures taken in practice to attenuate the effect of the impact loads on concrete ties has been the use of rail seat pads with an increased resiliency. Many new types of rail seat pads have been developed in the last 10 years, but there has been no recent work on systematically testing different pads that are currently being used. Also, more study is particularly necessary on the deterioration of the dynamic performance of pads in service. This task was carried out in the second series of tests and is described in Chapter 10. A frequency-domain analysis was carried out to determine the underlying relationship amongst the parameters involved. In the last chapter, Chapter 11, the conclusions reached in the thesis are summarized and some recommendations for future research are put forward.  CHAPTER 2. LITERATURE SURVEY  2.1. Impact Tests on Structural Prestressed Concrete  Impact tests have been extensively carried out on plain concrete andfibrereinforced concrete structures. A detailed literature review can be found in Ref. (10). For impact tests on prestressed concrete, however, there are relatively fewer studies. Most of these studies are of the dynamic response of full-scale concrete structure . These kinds of impact tests were widely performed on highway bridges, as the road surface roughness of the approaches and of the bridge decks may induce impact on the structure. Detailed reviews of related literature are included in Refs. (11, 12). One of the common results from the studies is that the shorter the span length is, the faster the impact factor will increase with lessening vehicle mass, and the impact factor will increase with vehicle speed. Similarly, on railway bridges, the abnormality of rails of track and wheel flats of the train may induce impact on prestressed concrete structures too. Literature about impact tests on prestressed railway bridges was listed in Ref. (13) and (14). A review of studies of impact in concrete railway bridges was made by Skaberna (15). The research on the impact strength of prestressed concrete, in terms of the properties of concrete and of structural members, has mostly been carried out by those associated with military science and the nuclear industry. In these fields, the impact usually belongs to the category of an impacting body with small size hitting a massive target at a very high velocity, from 40 m/s to 300 m/s. In this type of impact, the loading impulse acts over a very short time, much shorter than the natural period of vibration of 8  Chapter 2. Literature survey  9  the structural member, by perhaps an order of magnitude. In this situation, the entire member itself has no time to respond; the response and failure of the concrete members are strongly localized. Tests (16) have shown that the mode of failure of a beam or slab under such impact loading is a local failure in the form of a bell-shaped ejection cone. However, the resulting crack pattern and the transient displacements measured indicate that bending and shear failure mechanisms are involved at least to some degree. For an impact with an even higher velocity (around 1000 m/s), only local failures are caused (17). In this situation, the penetration and the diameter of holes made in the target were not influenced by the characteristics of the concrete target, but only by those of the impacting body, typically a missile. Although impact loading applied by a striking body with very high velocity may occasionally occur to civil engineering structures, the much more common impact problem for civil engineering in general is the "low speed", (V = 1-40 m/s) but relatively heavy impacting body. Here, the analysis of elastic-plastic deformations of the structural member under impact is more practical than the stress wave analysis. For instance, a series of experiments (18, 19) was carried out, to simulate the behaviors of 200 - 300 m high marine structures because of the relatively high incidence in offshore operations of dense dropped objects. The results showed that the failure modes, for impacts with velocities up to 10 m/s, were generally of the same form as for static failure, except that there was an increased tendency for local damage or shear failure to occur. The displacement of the prestressed slab was derived from accelerometer readings. Its profile was similar to those under static tests during loading. However, contra flexure and a reverse curve were seen during the unloading period. The failure was of a mixed mode, with flexural cracks and punching shear damage. Reducing the approach velocity of the impacting body may change the failure mode to the pure flexural mode. The influence of concrete strength, and the thickness and reinforcing arrangement of the slab were  Chapter 2. Literature survey  10  investigated. When a light weight concrete covering layer, made from expanded clay aggregate, was added to the top of the slab, the maximum load was greatly decreased. Fuji and Miymoto (20) showed that as the severity of impact increased, there was a tendency for scabbing to occur at the intersection of cracks on prestressed concrete slabs. They also reported that the use of fibre reinforcement can change the mode of failure from punching shear to flexure by crushing of the concrete. The velocity needed to cause perforation of the structure was increased. A series of impact tests (7) was performed by dropping a weight onto a prototype prestressed concrete rock-shed which was the same as that which had collapsed in the accident in Japan mentioned above. A crack formed at the middle of the shed, and the final collapse mechanism was found to be a beam mechanism. An impact response analysis was developed by combining the distinct element method with the rigid body spring model (RBSM). Destruction of the rock-shed occurred due to the flexural failure of the prestressed members. Grace and Kennedy (21) tested prestressed waffle slabs under dynamic loading. They found that prestressing of concrete slabs enhanced their dynamic stiffness and natural frequencies. Thus, resonance in such structures can be avoided when they are subjected to a low- frequency excited source of vibration. However, the higher dynamic stiffness of the structure, enhanced by a higher prestressing level, may increase the maximum impact load and cause a more brittle type of failure (6). A study by Barr (22) also showed that prestress may act as an unfavorable factor for concrete structures under impact.  Chapter 2. Literature survey  11  2.2. Impact Tests on Prestressed Concrete Railroad Ties  2.2.1. Introduction  In June 1980, "hairline"flexuralcracks were noted at the rail seats of concrete ties in Northeast Corridor track in the United States (8). As many as 50% of the total number of ties in the sections checked were found to be cracked; some of the cracked ties had been in service for only a few months. The cracks were a cause of concern because the design service life for the ties was 50 years, and no cracks could be tolerated because of the harsh environment and possible fatigue of the prestressing steel at the crack gaps. Similar phenomena were later found elsewhere as well (23, 24). It became apparent that the impact loads applied to the concrete ties due either to flats on the wheels of the train or to rail irregularities were the primary cause of the cracking. Such loads could be up to 3 times higher than the normal quasi-static loads (8,). Since then, a number of experimental investigations have been carried out, both on railroad tracks and in laboratories. To accommodate the higher impact loads found acting on the ties, the impact factor recommended by American Railway Engineering Association (AREA) in the strength design of the concrete ties has been changed several times, from 50% in the 1970's to the current 200% (25, 26). However, some even higher impact loads, up to 300% higher than normal static load, have been reported (27, 28).  2.2.2. Experimental Investigations in Laboratories  Dean, et al. at the Battelle's Columbus Laboratories (8) developed a basic impact testing apparatus for use with concrete ties, and carried out a series of investigations after the discovery of the hairline cracks on concrete ties mentioned above. They investigated  Chapter 2. Literature survey  12  the cause of the cracks and identified a possible solution to the problem. The impact loading tests were conducted using a single-tie test arrangement. The range of load amplitudes and the approximate frequency content of impact bending moments measured in track were successfully reproduced by single blows of the impact drop hammer. By using strain gauge coupons mounted on the rail seats of the ties, and Stresscoat undercoat and resin for crack identification, a "cracking threshold" for impact loading was identified at a level of strain equivalent to 42.39 kN.m (375 inch-kips) of static bending moment. This was very nearly equal to the mean cracking strength found in static strength tests. In tests with the standard, rigid, 5 mm EVA pad of high rigidity, cracks were initiated by impacts from a drop height of 406 mm (16 inches) with the 52.3 kg impact hammer. The same tests were then conducted with the new EVA pad and with eight pads of lower dynamic stiffness. The tests demonstrated that a major decrease in tie pad stiffness could significantly reduce the tie bending moments occurring at given drop heights and eliminate cracking of ties. Within the practical range of pad thicknesses (6.5 mm), the flexible pads attenuated impact bending strain by 25 percent. Destructive impact tests were also conducted on both standard prestressed concrete ties and a latex modified prestressed concrete tie. One end of each tie was impacted at heights varying from 356 mm to 914 mm (14 to 36 inches) using 50.8 mm (2-inch) increments, 10 drops for each height. Cracks were first detected at the drop height of 406 mm (16 inches) on the two standard ties and at 18 inches on the latex modified tie. The total crack length for the modified tie was shorter than for the standard ties. In addition, on the non-impacted ends, cracks also developed, their length being 70 to 80 percent of the total crack length on the impacted end. This result was interpreted to mean that the stress wave propagated across the tie with little attenuation and that the tie acted as a free-free beam. Ahlbeck, et al. tested concrete ties at the Battelle's Columbus Laboratories in 1986  Chapter 2. Literature survey  13  (29). They found that the transverse vibrational bending modes of concrete ties, (corresponding to vertical loading) particularly the second and third modes at about 330 and 630 Hz, respectively, were important in tie cracking phenomenon. Because the response amplitudes of these two modes are near-maximum in the rail seat region, cracks could be initiated at either the top or bottom surface of the tie, and could occur at the tie end opposite a single impact load, as from a rail joint or battered weld. The resilient tie pads acted as a low-pass mechanical filter, attenuating the impact load energy which exciting the high frequency vibration modes in the ties. Igwemezie and Mirza (30) carried out a series of studies on prestressed concrete ties used in open-deck bridges, using a drop-weight instrumented impact machine. Eight strain gauges were mounted on each tie. Using different rail-tie pads and tie-girder pads, peak load vs. drop height plots, load vs. time curves and frequency vs. transfer function traces were obtained. They found that a softer rail-tie pad can decrease the peak load. The impact load is a logarithmic function of K*, which is the product of the axial pad stiffness and the shape factor of the pad. The load-time diagrams showed that the pulse duration was almost the same for different hammer drop heights. However, while use of a softer pad led to a decrease of the peak load, the pulse duration was longer. The transfer function-frequency diagram obtained from the fast Fourier transform ( FFT ) of the strain-time response of the tie showed no large differences for different tie-girder pads. Using the softer rail-tie pads with improved shapes can eliminate the high frequency vibration modes, but most of the energy from these higher modes is then concentrated in the low frequency range, leading to the amplification of the second mode. It should noted that the rail-tie pads that were examined had big differences in stiffness and shape factors. Their product K* was 15250 kN/mm for the stiff pad and only 69 kN/mm for the soft one. For the tie-girder pads tested, K* was 305 kN/mm for the stiff pad and 54 kN/mm for the soft one.  Chapter 2. Literature survey  14  Nine tie setups were also tested to check the load distribution. It was found that the load transmitted to the tie that was directly hit by the hammer decreased by 40% when using the soft rail-tie pad. Igwemezie et al. (31) used a rail rig, consisting of eight ties and a half-track bed with 5.5 m of rail to conduct impact tests in the laboratory. The dynamic loads were simultaneously measured using shear gauges located on the rail web and an impact force transducer. The results showed that the shear gauge can underestimate the impact load by up to 80 percent. Compared to track with the timber ties, track with concrete ties gave a higher wheel rail impact loading for the same energy input, but lower rail head bending stresses because the system was heavier and stiffer. The tie fastening system also transferred most of the impact energy to the concrete tie. These higher impact loads could be detrimental to the tie as well as to the cars. The apparatus, developed by Battelle's Columbus Laboratories to evaluate a rail pad's ability to attenuate impact loading on a concrete tie was later modified somewhat by others. The tie to be tested was supported by ballast (32) instead of neoprene strips; or was supported on wood chippings, which is more easily reproducible (33). However, great faith was still being put in the original apparatus, and the modifications were considered to cause no significant differences in the results (33). To support the use of this apparatus as a guide to a pad's performance in track, Grassie (33) compared data from laboratory tests on rail pads using a Battelle style apparatus and data from field experiments. He found that although the performance of the pads varied with the particular track conditions, such as ballast support conditions and the magnitude of the quasi-static loads applied, the ranking of the dynamic performance of the rail pads was identical in both the laboratory and field experiments, and there was an excellent correlation between the laboratory and the field data. Grassie and Cox (34) created a railway track model which allowed examination of  Chapter 2. Literature survey  15  the behavior of concrete ties. In this model the ties were considered to be uniform beams and not simply masses (35), because inertial shear was found to be important. Calculations made using the model were compared with experimental data, and there was reasonable agreement in the frequency range 0-750 Hz. The calculations showed that the resonance frequencies of the shallower ties were lower than the corresponding frequencies for deeper ties because stiffness varied as the cube of the depth while the mass varied in proportion to the depth. At the important third mode of the tie at about 600 Hz, concrete strains were less for the shallower tie. This is because the lower stiffness, and hence the larger curvature for a given bending moment were offset by a lower dynamic bending moment, lower natural frequency and less distance from the edge to the neutral axis. The most significant single influence in reducing dynamic tie strains would be to dampen bending modes by introducing damping in the tie itself or by having more highly damped ballast. Wakui and Okuda (36) found that for impact loads due to the wheel-flats of trains, a component whose duration of loading is less thanfivemilliseconds is dominant and the magnitude of the impact load amounts to about 50 times the unsprung mass of each wheel. They conducted some impact loading simulation tests for the total track structure using a drop-weight facility. By varying the drop weight from 62 kg to 160 kg and the thickness of the rubber-pad between the drop weight and the rail-head from 0 to 20 mm, impact loads with different durations and magnitudes were applied to the concrete ties. Impact loads of a short duration (one to two ms) increased the bending moment at the rail seat by as much as 1.8 times the static response though the combined effect of the resonance amplification phenomenon of the tie and the increase of the rail-pad stiffness due to the high rate of loading. Mindess, Yan and Venuti (37 -38 39) tested prestressed concrete ties manufactured with steel fibre and polypropylene fibre concrete materials, using an instrumented drop-  Chapter 2. Literature survey  16  weight impact machine, with a drop hammer mass of 345 kg and drop heights of up to 1524 mm (60"). Accelerometers were used to get both the deflection of the tie and the inertial load. A load cell in the tup was used to record the impact contact load. Tests showed that both the fracture energies and the maximum deflections at mid-span were greatest for steel fibre reinforced ties and least for plain ties: the ties with polypropylene fibres were intermediate.  2.2.3. Experimental Investigations in Railroad Tracks  Field tests on tracks in service were carried out by the Battelle's Columbus Laboratories from 1980 to 1983 (8). Using strain gauge coupons attached to the ties, the duration and amplitude of the impact pulse could be recorded. The measured time duration of the pulse due to wheel-flats was 1-3 ms and the highest impact bending moment recorded was 600 inch-kips. The maximum wheel/rail contact impact force, detected by a vertical wheel/rail load circuit attached on the web of the rail, was up to 82 kips, or 4 times the average static load induced by the same train. Spectral analyses of the rail seat bending signals showed that most of the energy was in the first three bending modes of the ties, i.e. at 131, 356 and 638 Hz. Tie bending moments sufficient to cause cracks were produced by about 0.1 % of the passenger train wheels passing the tie; that is a tie might experience a bending moment with the potential to crack it about once in every 1.8 days. The occurrence of severely cracked ties at rail joints and battered welds indicated that cracking level strains could also be produced at rail anomalies. These data supplied an essential basis for subsequent laboratory simulations of the impact loads due to wheel-flats. In addition, a zone of 5 consecutive ties was instrumented to measure rail seat strains and impact loads. The flexible pads were checked in this zone to evaluate their effectiveness in attenuating impact loads on the track. Many of the wheels causing  Chapter 2. Literature survey  17  serious impact conditions were traced and photographed. The "worst case" impacts were produced by wheels with a flattening or chording of the wheel circumference over a length of 305 to 457 mm, identified as "flat wheels". A wheel impact load detection system was employed by Battelle (29) on the track, using special strain gauge patterns installed on the rail web. A microcomputer system calculated the peak load for each passing wheel. The detector was used both to develop wheel load statistics and as an inspection tool to identify passing wheel sets developing high impact loads. Moreover, the drop weight apparatus was modified for the field, automatically impacting the track periodically at a rate of about 4 seconds per drop, inducing 40 to 60 kip impact loads. It was used to check the properties of both rail pads and concrete ties in the field. Scott (28) measured many wheel/rail impact loads on a concrete tie test track. Concrete ties were strain gauged and a wheel loading measurement system with some rail shear circuits was installed. His report documented the wheel loading generated by a special work train having fourteen wheel sets with various tread defects, none of which were condemnable by the current wheel renewal criterion. One of the wheels, having a visually undetectable 0.157 inch deep depression spread over 18 in. of circumference, generated impact loads of 124 kips at 55 mph, leading to cracking of some concrete ties. The impact factor was 277 %. Other wheels generated impact loads up to 82 kips. Scott (28) suggested new wheel loading limits for the wheel renewals. Field tests were conducted on an open deck railway bridge with concrete ties by Igwemezie et al (27). Impact loading was generated by a special work train with some flat wheels. They found that the response of the concrete ties to the presence of skid flats on a train wheel is speed-dependent. At low speeds (0-64 km/h) there was a complete unloading of the tie followed by over loading due to one impact, whereas at higher train speeds above 80 km/h, the unloading was followed by two or more impacts. The concrete  Chapter 2. Literature survey  18  strain reached 476 |ie under impact loading due to wheel flats. Compared with an average strain of 120 U£ for "good' wheels, the impact factor was 300%. In addition, the load distribution factor, which indicates the percentage of total wheel/rail contact load transmitted to the tie underneath the loading point, was much higher than that used in tie design when the tie was subjected to impact loading. While fatigue tests on the cracked concrete ties showed that the service life of these ties may not be affected by the cracks, environmental effects should also be considered. Grassie (40) carried out severalfieldexperiments on concrete ties with a variety of resilient rail pads. He found that the dynamic moment in concrete ties was significantly attenuated with resilient rail pads, but increased where the ballast was loosely packed.  2.3. Techniques of Instrumented Impact Testing  2.3.1. Impact Testing Systems for Concrete  A brief summary of impact testing techniques is given in Ref. (41). Depending on the impacting mechanism, there are several types of conventional systems that will measure either: (a) the energy consumed to fracture a notched beam specimen;(b) the number of blows in a "repeated impact" test to achieve a prescribed level of distress; or (c) the size of damaged zone (crater /perforation /scab ). Various devices have been developed to test concrete under impact. The most commonly used is the drop-weight testing machine. The simplest of the impact tests is the "repeated impact" drop-weight test (42) in which a mass is raised to a predetermined height, and then allowed to drop directly on a concrete specimen. This test yields the number of blows necessary to cause a prescribed level of distress in the test specimen, for example, the number of blows required to cause the first visible crack. However, this  Chapter 2. Literature survey  19  number serves only as a qualitative estimate of the energy absorbed by the specimen. Instrumented drop-weight machines can provide reliable time histories of various parameters of interest during the impact event: load, deflection, strain and acceleration. Such a drop-weight machines have been used extensively at the University of British Columbia (10, 43). The larger has a drop weight mass of 578 kg, and a drop height up to 2.5 m, allowing for the impact load and acceleration of the specimen to be measured during a test. A similar but smaller drop-weight machine has been used by Shah and coworkers (44). In this study, the deflection of the concrete beam was measured using a dynamic LVDT. Rubber pads were introduced in the contact area between the tup and the specimen to eliminate the inertial load. This, however, increased the period of the impact event. Another drop-weight machine has been constructed at the University of New Brunswick to conduct full-scale impact tests (45). This large scale machine is capable of imposing an impact load of 900 kN, with a maximum drop height of 5.3 m. Another type of instrumented impact testing machine which is also commonly used is the pendulum machine, such as the modified Charpy-type testing device used at Northwestern University (46). It is capable of measuring the impact load and the resulting support reactions, and is equipped with a special fixture that allows tests to be conducted at velocities ranging from 0.5-3.0 m/s. A pendulum facility was used to test columns under impact loads at the University of Stellenbosch, South Africa (47). The impact load could be varied by changing the pendulum mass; the mass could range from 650 to 1450 kg, and dropped from a height of 2.7 m. Miyamoto et al (48) have used a pendulum facility to test concrete slabs. The tests were conducted using a pendulum mass of 500 kg. Impact loads of up to 350.1 kN were obtained. An outdoor pendulum facility at the Pennsylvania State University (49), which is believed to be the largest impact testing facility in operation, consists of a 15.24-m high structural steel frame with a pendulum mass suspended from four steel cables. The mass consists of a steel box  Chapter 2. Literature survey  20  containing removable plates that allow the mass to be adjusted up to a maximum of 4536 kg (10,000 lb). Either a distributed or a concentrated load can be applied on a specimen. The duration of the impact pulse can be adjusted by changing thefillermaterials in a space between the load cell and the steel box. Other significant impact tests include the split Hopkinson pressure bar test (50) in which the specimen is sandwiched between two elastic bars and high stress-rates are generated by propagating a pulse through one of the bars using a drop weight or a similar device. This technique is considered to be a reliable method for testing concrete under tensile impact loading  2.3.2. Problems Associated with Reliable Control of Impact Tests  Though many studies on impact properties of concrete have been carried out, the conclusions from different researchers are often quite different, or even contrary. For example, Suaris and Shah (51) concluded that the higher the value of the static flexural strength, the lower is the relative increase in the flexural strength with increasing strain rate. However, some other researchers have obtained the contrary results (52). Similarly, Watstein (53), Atchly and Furr (54), and Birkimer and Lindemann (55) have shown that the concrete strain at failure increased with an increase in the strain rate, while Hughes and Watson (56) obtained the opposite result. Among the several causes of errors in impact results, the most important is that there is as yet no standard testing system or procedure for impact tests on concrete. Different impact machines, which vary widely in size and in the type of instrumentation, can lead to very different results. This is an area which still requires extensive study.  2.3.2.1. Inertial Load Effect  Chapter 2. Literature survey  21  lnertial loading effects have traditionally been one of the main sources of errors in instrumented impact testing. Cotterell (57) was the first to identify this phenomenon and recognize that it is inherent in drop-weight or pendulum test systems. He suggested that the subsequent unloading following the discontinuity resulted from the initial passage of reflected tension waves within the tup, and that the dynamic wave propagation controlled the initial portion of the load-time trace. His belief was supported by the observation that the "initial impact load" (i.e. inertial load) was directly proportional to the impact velocity. Priest and May (58) have treated inertial loading as a series of oscillations whose performance may be modelled by a spring-mass system. However, example traces presented in their studies indicated that the inertial loading often completely subsided before the anvil registered its first load. This result implies that at the moment of impact, the load is solely exchanged between the specimen and reacting tup, since the support reactions has not been involved. Saxton, et al (59) presented a clearer picture of inertial loading. They identified three major contributions to the tup loading: 1. mechanical bending loads; 2. test system ringing; and 3. inertial acceleration loads. When the specimen is struck by the tup, it is accelerated rapidly from rest to an average velocity equal to the tup velocity. The maximum inertial load should occur near the moment of impact (t = 0) when the acceleration of the specimen is the highest; the inertial load will drop to zero when the specimen attains the tup velocity. At the same time, the mechanical bending load begins to rise and finally dominates the measured load as the test progresses. That the actual inertial load measured is not a maximum at zero time is due to the limited response time of the electronic system. Although the point of first load discontinuity in the load-time trace , measured for tough materials, can usually be identified as the inertial load, the real danger arises when interpreting load-time traces of medium to high strength materials that are brittle and exhibit a medium to high impedance. The total mechanical  Chapter 2. Literature survey  22  response, including fracture of the specimen, can be completed while the specimen is still being accelerated; that is the entire bending response curve can lie within the inertial loading curve. To eliminate the inertial load effects, some experimental techniques were introduced. Ireland (60) suggested a decrease in the impact velocity. The obvious disadvantage of this method is the decrease in strain rate, and for the bulky concrete specimens, using this method may not be very effective as for the small size steel specimen. On the basis of the theory and experiments mentioned above, Suaris and Shah (44) used rubber pads in the contact area between the tup and the concrete specimen to reduce the inertial load. They recommend that the parameters should be selected so that the difference between the striker and support anvil loads recorded during the test do not exceed 5 percent. In this process, unfortunately, since the strain rate is significantly limited, it may no longer meet the strain-rate requirements of certain impact tests. On the other hand, the inertial load effect may be eliminated by using analytical methods. Venzi, Priest and May (61) assumed that the inertial load per unit length was proportional to the displacement from the mean position. Radon and Turner assumed that the acceleration of each particle in the beam was a constant with time, as a function only of its position along the beam (62). Banthia (10) used three accelerometers mounted along the length of the beam. By extrapolating the accelerations along the whole beam from the accelerometer readings, the distributed inertial load could be determined. On the basis of the principle of virtual work, the distributed inertial load can be generalized as a point inertial load, acting on the beam at the mid span. Then, the "true bending load" can be obtained simply by subtracting this inertial load from the tup load. In this process, errors may arise from the assumption regarding the acceleration distribution along the beam. Also, this model can only be used when the beam deflects in, and only in , the first bending mode. Otherwise, the deflection profile of the beam and the acceleration  Chapter 2. Literature survey  23  distribution will not be simple linear or sinusoidal functions. The aim of the studies mentioned above, on inertial load effects, is to obtain the true mechanical bending load, which can then be used to evaluate other inherent material characteristics. The beam is always assumed to be subjected to pure bending, and shear forces are therefore neglected. However, as noted above, concrete structures designed to fail in a ductile manner (flexural failure) at slow rates of loading may fail in a brittle manner (diagonal shear failure) under impact loading. Even when only the first mode of vibration is excited, the shear associated with the first mode is greater than for static loading and will increase with an increase of the loading rate, causing shear failure to be more dominant (63). This is a real concern in the dynamic design of concrete structures. In this situation, the distributed inertial load plays an important role in changing the ratio of shear force to bending moment as the loading rate is being increased (64). In other words, when the fracture modes of the beam or higher modes of vibration have been involved in the problems of impact loading, the inertial load should neither be eliminated by the experimental method, nor be generalized to a point load at midspan by analytical methods, and the material properties need to be evaluated under a biaxial stress state.  2.3.2.2. System Response Time or Frequency Response  Ireland (60) observed that it is vitally important to have a clear understanding of the effects of limited frequency response. All instrumentation has a limited frequency response. Unfortunately, nearly all published discussions of impact techniques avoid discussion of the inherent electronic limitations. The frequency response limitation of the instrument means that when the frequency of excitation is too high, the amplitude of the output will be attenuated. In other words, if the time from the start point to the peak of an applied load is too short, the instrumentation system may not have enough time to  24  Chapter 2. Literature survey  respond and the actual peak load may be missed. In such case, the "peak" load recorded is the load at time t , which is the shortest time for the system to raise the signal to its R  maximum. The actual load has by then already passed its peak, and has dropped down to a lower value. Also, the time to the peak load (t) recorded will be longer than it should f  be. So, if the critical response time t of the instrumentation system is quite long, then a R  peak load recorded before t will be attenuated. Ireland suggested that any system that R  had more than 10% attenuation of the actual signal was unacceptable. Adding an electronic filter to the system will make this distortion more severe, as filters can eliminate or attenuate high frequency response and increase t . Hoover (65) R  found that analog filtering of dynamic load signals attenuated the peak load and increased the t although the area under the load-time curves was not affected. He suggested that f  signals should not be filtered at this stage. The influence of the response time limit of the instrumentation is even more serious for the inertial load, especially for bulky concrete specimens, since the inertial peak load will occur, theoretically, at the zero time when the acceleration is at a maximum. Thus the actual time to the peak load t is much less than t and the load will f  R  be greatly reduced. As a result, an error will be introduced into the measured tup load at the beginning of the period of impact. If the total test period is very short, this error could be quite large. This is another source of error for the analytical method in eliminating the inertial effect.  2.3.2.3. Energy Balance  Ireland (60) evaluated some very useful and quite simple equations of energy balance for impact tests, in which nothing more than the tup load vs. time relationship needs to be measured. But the inertial energy or kinetic energy of the beam, E, should be  25  Chapter 2. Literature survey  eliminated either by reducing the impact velocity or by erasing the first peak corresponding to the inertial load in the load history plot. The stiffness of the falling hammer is needed to calculate the elastic energy stored in the machine, E , which can be M  neglected if the total duration of the impact is used in the analysis. Since it is difficult to determine the inertial peak on the load-time trace for brittle materials, rubber pads have been used (44) for impact testing on concrete. However, the E m becomes more complicated due to the energy stored in the rubber pads, and the energy balance was found not to be satisfied (51). So, a dynamic LVDT was added to the system to measure the load vs. deflection curve and thus to obtain bending energy directly. Since the inertial load was supposed to be eliminated by pads, the area under the load vs. deflection curve was believed to be the bending energy. However, as mentioned above, the limited strain rate, due to the addition of the rubber pads , reduces the rate of impact testing. Banthia, et al (66) also used rubber pads to reduce a very high inertial load and strong vibrations of their impact machine, in which a steel hammer hit a steel trolley producing a uniaxial tensile impact load on a concrete specimen. It was believed that the energy absorbed by the pad should not appear in thefinalequation of energy balance since the rubber pad was elastically unloaded at the end of the test. In addition to the tup load history, the post-fracture velocity of the trolley was recorded by base-mounted photocell assemblies. The fracture energy consumed by the specimen was then determined using the impulse- momentum principle and the principle of conservation of energy. Banthia (10) had used accelerometers to record the distribution of the acceleration along a beam under impact. The energy used to accelerate the specimen can then be evaluated. The deflection of the beam was obtained by integrating the acceleration history at mid-span twice. The energy consumed by the specimen could then be  Chapter 2. Literature survey  26  represented by the area under the bending load-deflection curve.  2.4. Summary  On the basis of the literature survey, the following conclusions may be reached: For impact tests on prestressed concrete, only a few studies were available in the literature. Most of these were from the point view of the dynamic response of full-scale concrete structures. The impact resistance of prestressed concrete, in term of the properties of the concrete material and single structural members, still needs to be studied. The effect of prestress level on the dynamic characteristics of prestressed concrete, such as dynamic bending stiffness, natural frequency of vibration, and the resistance of the concrete to impact loading, is still unknown. When subjected to high loading rates, prestressed concrete members may change their fracture mode from ductile-flexural at slow loading rates to a brittle-shear at high loading rate. More theoretical and experimental analyses need to be done on this subject. Fibres, especially steel fibres, may play an important role in improving the dynamic behaviour of prestressed concrete and preventing it from fracturing in a brittle manner. Concrete railroad ties have been found to be damaged under impact. Most studies focused on adding a more resilient pad between the rail and the tie, or detecting and removing the "flats" on wheels in a timely manner. Only a few studies have been carried out on improving the dynamic characteristics of the concrete tie itself. Concrete ties are currently designed by the allowable stress design method in which the impact load is replaced by an "equivalent" static load. The fact that an impact factor of 200% has not  Chapter 2. Literature survey  27  prevented the tie from cracking indicates that further detailed dynamic analysis should be carried out. The technique of impact testing should be treated very carefully. Among the many factors involved in impact testing which may mislead the interpretation of the test results, the inertial effect, system response time and energy balance should be paid the most attention.  CHAPTER 3. EXPERIMENTAL ASPECTS 3.1. Introduction  Two different series of impact tests on prestressed concrete railroad ties were conducted in the Structures Laboratory, Department of Civil Engineering. Although the same impact machines were used, the two series of studies had their own emphasis. Particular attention was paid, in thefirstseries, to the effect of the loading rate on the cracking mode of the prestressed concrete. As mentioned above, concrete structures usually absorb more fracture energy under impact loading than under static loading if they undergo the same type of flexural failure. The major concern regarding the impact resistance of the prestressed concrete arises from the fact that under some circumstances concrete members may change their fracture mode from a ductile one (flexural failure) at slow rates of loading to brittle one (diagonal tension-shear failure) under impact loading. The present study examines, both experimentally and theoretically, the mechanism of the change of the fracture modes at different loading rates. For the second series of tests, on the other hand, the emphasis was on how to improve the dynamic properties of prestressed concrete railroad ties so that the concrete cracking could be significantly reduced. The relationships between maximum impact load and several design parameters, such as the cross section sizes, the flexural stiffness of the concrete beams, and concrete strength, were also studied. Since there were quite different purposes for the two series of studies, the test setups, the testing programs and the analysis of the test results were very different for 28  Chapter 3. Experimental Aspects  29  each. They will be described in detail in the chapters related to each particular study. In this chapter, the specimens, testing machines and other test apparatus will be described.  3.2. Specimen Preparation  Two series of specimens have been used in the tests: a) . Prestressed concrete railroad ties without fibres. Eight nominally identical ties were used to demonstrate the effect of loading rate and support conditions on the mode of failure of prestressed concrete ties subjected to impact loading. b) .Post-tensioned concrete railroad ties with different fibre contents, concrete strengths, prestressing levels and stirrups. This series of tests was intended to see how the dynamic behavior of prestressed concrete railroad ties could be improved.  3.2.1. CXT Pretensioned Concrete Ties  These concrete ties were provided by CXT, Tacoma, Washington. Twelve nominally identical ties were delivered to the Structures Laboratory at the University of British Columbia, of which eight were tested for this study. The 28-day concrete compressive strength, as provided by the manufacturer, was 56.5 MPa. At the test age of about 8 months, the strength would have been about 10% higher. The prestressing was provided by means of 28, 5-mm diameter wires, each stressed initially to a force of 23 kN. There were twenty eight single deformed wires, which conformed to ASTM A864, and had a breaking strength of 30.5 kN. It was assumed that the prestress loss would be 17%. The geometry of the tie, and the locations of the prestressing wires, are shown in Fig. 1. The design resistance moments at the rail seat were 35.9 kN-m (positive) and 20.4 kN-m (negative).  Chapter 3. Experimental Aspects  30  2591 O/A  L  321  |  419  t  251  305  [  ; r  f  @  |V50  ELEVATION  229  I —ep---$--ep—f-ep— <p--ep—  i  i .i i i i /  CM  i "i i i i i i i  i i i 25 i 25 i i>7  57  ,  89  89 27 9  SECTION  j  @  Figure l. Geometry of CXT ties (Type CC497), and Location of Prestressing Wires. All dimensions in mm.  Chapter 3. Experimental Aspects  31  3.2.2. ITISA (Type UP-2) Post-Tensioned Concrete Ties  Ties for this series of tests were produced by ITISA of Mexico, a manufacturer of concrete railroad ties for tracks in North America. The ties are based on the Dywidag ITISA post-tensioned ties which conform to the AREA Manual (26). All dimensions were retained but the basic design was modified by changing the following parameters, either separately or in combination: a) adding either 0.5% or 1% by volume of 30 mm or 50 mm long hooked end steel fibres, 0.5 mm in diameter b) adding seven stirrups of 5 mm diameter at 80 mm intervals under each of the two rail seats c) reducing the concrete strength from 65 MPa to 40 MPa; and d) reducing the prestressing force from 392 kN to 223 kN. The geometry of the ITISA standard ties, and the location of the prestressing bars, are shown in Fig. 2.  3.2.2.1. Standard ITISA Ties  Standard ITISA Ties (Dywidag UP-2) were used as the controls in these tests. The tie parameters are as follows: The concrete strength was 66.8 MPa at 28 days. Four <])10.5 mm prestressing bars conforming to ASTM A911 were used. These uncoated stress-relieved steel bars had a minimum yield strength of 1375 MPa and minimum tensile strength of 1570 MPa. The total initial prestress force was 392 kN, with an assumed prestress loss of 14%; the formed holes into which the bars are placed were grouted with mortar after the tie was  Chapter 3. Experimental Aspects  32  post-tensioned. The design bending resistance moments at the rail seat were 30.2 kN-m (267 inch-kip) positive and 16.1 kN-m (142 inch-kip) negative. The ultimate positive bending moment was 45.33 kN-m (401 inch-kip). The cracking strain at the bottom of the rail seat, under a static bending moment, was calculated to be 369 microstrain; it actually reached 429 microstrain during the static calibration. These are referred to as "normal" ties in the related chapters.  3.2.2.2. Modification of the ITISA Ties  The two types of hooked end steel fibres used to modify the standard ties were 0.5 mm in diameter, and 50 mm and 30 mm in length respectively, giving aspect ratios of 100 and 60 respectively. The steel fibres were made of strain hardened mild steel wires having an ultimate tensile strength of 1250 MPa. They were provided in collated form with a water soluble sizing, so that the fibres would disperse adequately when mixed with the concrete. Two different contents, 0.5% and 1% by volume, were used. The stirrups used were made of smooth reinforcing bars of 5 mm diameter. Details of the parameters for each group of ties, with the associated specimen numbers, are given in Table 1. The concrete compressive strengths for different types of concrete are given in Table 2.  Chapter 3. Experimental Aspects  SECTION A-A  Figure 2. Geometry of ITISA (Type UP-2) ties, and Location of Prestressing Bars. All dimensions are in mm.  34  Chapter 3. Experimental Aspects  Table 1: Concrete Tie Parameters  The Control Tie: No. 1. Standard ITISA (Type UP-2) Tie. Group 1: Additional steel fibres and stirrups, prestress unchanged at 392 kN. No. 2. Plain Concrete + 0.5% 50 mm fibres, (40 kg/m3 concrete). No. 3. Plain Concrete + 1% 50 mm fibres, (79 kg/m3 concrete). No. 4. Plain Concrete + 1 % 30 mm fibres, (79 kg/m3 concrete) No. 5. Plain Concrete + 7-<j) 5 mm stirrups for each rail seat at 80 mm intervals. No. 6. Plain Concrete + stirrups + 1 % 50 mm fibres. Group 2: Changed prestressing bars and prestress level. No. 7. Plain Concrete + § 9.5 mm prestressing bars and 223 kN prestress. No. 8. Plain Concrete + < | ) 9.5 mm bars and 223 kN prestress + 1% 30 mm fibres. No. 9. Plain Concrete + § 9.5 mm bars and zero prestress. No. 10 Plain Concrete + 9.5 mm bars and zero prestress +1% 30 mm steel fibres. Group 3: Changed concrete strength, prestress unchanged at 392 kN. No. 11 Plain Concrete with lower strength, fc = 40 MPa. No. 12. Plain Concrete with lower strength, f = 40 MPa + 1 % 30 mm fibres. c  Chapter 3. Experimental Aspects  35  Table 2: Concrete Compressive Strength of Modified Ties  Tie  Concrete  No.  Strength  1  Normal  2  Normal  3  Compressive Strength (MPa)  Steel Fibres %  3 days  7 days  28 days  0  47.5  54.5  66.8  50  0.5  49.7  58.6  73.3  Normal  50  1.0  58.4  63.2  74.2  4  Normal  30  1.0  57.4  72.5  78.7  11  Low  0  29.0  35.0  45.5  12  Low  1.0  32.0  47.9  56.5  Length (mm)  50  3.3. Impact Testing Apparatus  3.3.1. Introduction  Ideally, impact machines used in the laboratory should simulate, as closely as possible, the real impact event. Since impact problems are generally more complicated than static problems, and many more factors are involved, a clear understanding of the impact problem is necessary before the experimental study begins. The characteristics of impact problems vary over a very wide range, in terms of the velocity, mass and hardness of the striker; and the stiffness, mass, hardness of the contact zone and the support conditions of the struck body. Any substantial variation in one of these parameters may change the impact problem, leading to quite different dynamic features and requiring a different analytical method to process the experimental data. Amongst the various criteria used to categorize impact problems, some of the most  Chapter 3. Experimental Aspects  36  common are: • the velocity of the striking body; • the size and mass of the striking and impacted bodies; • the hardness of the contact zones and the stiffnesses of the two bodies. These criteria relate primarily to the physical properties of the materials, so that they are quite practical and often used in engineering fields. On the other hand, only criteria based on the impulse applied and the dynamic response of the struck body can reveal the intrinsic properties of a particular impact event. For example, based on the relative importance of the different vibrational modes excited by an impact, two categories can be defined for beams subjected to impact: a) Only the first vibrational mode of the beam is excited, and the pulse duration is long compared with the fundamental period of the beam. In this situation, an equivalent static analysis, such as the application of an impact factor to the static load, can be adopted since the solution of the first mode under impact is very similar to the solution of the static case. This is called quasi-static impact. However, it must be noted that while their modes are similar, the shear associated with impact is greater than that under static loading. Before using such a method, a dynamic analysis is necessary to verify that the response is really quasi-static. b) Impact results in the excitation not only of the first mode but also of higher modes, which can cause phenomena such as reverse bending, and high shears at the mode contra-flexure points. An 'equivalent static load' method can not describe such phenomena, a complete dynamic analysis is needed. If, under some conditions, the applied pulse duration is much shorter than the natural period of vibration of the beam, a wave-travel type method of solution is necessary. A beam of the same material will behave quite differently in the two situations described above. Impact acting on civil engineering structures is in general characterized  Chapter 3. Experimental Aspects  37  by low speed (V= 1 ~ 10 m/sec), the heavy mass of the impacting body, and a relatively soft impact due to the flexibility of the structural elements or the deformation of the striking body. Impacts caused by vehicle and ship collisions are of this type. All of these features mean that impact problems in civil engineering generally fall into the first category described above. Impact design can be simplified into the equivalent static design with which most designers are very familiar. However, in some cases the equivalent-static method has been used improperly, without the necessary verification of the dynamic analysis. Also, designers are not always aware that shears in a beam under impact are not conservative if calculated by the equivalent static method even under quasi-static impact (67). The mode analysis of the impact will be treated in more detail in subsequent chapters. Selection of the proper impact machine to simulate a particular type of impact problem is inherently difficult, since the interaction of a number of machine parameters and concrete member parameters is involved. The most common way of selecting or designing such a machine is by trial and error. For a particular concrete element, by changing the velocity of the hammer striking tup, the mass of the hammer, the rigidity of the contact zone and the support conditions of the element, one may eventually obtain a simulated impact, with the applied impulse and the excitation of the vibration modes of the beam very similar to those in practice. The general procedures are as follows: 1. Collect sufficient information about the impact problem concerned, including both the physical properties of the element and the dynamic properties of the impact as listed above. Some field instrumentation may be required in order to obtain the dynamic features of the impact event. 2. Choose an impact machine which operates in the velocity range of the striking body. For example, for a low velocity of impact (0 to 10 m/sec), which is most often encountered in civil engineering, a drop weight machine or a pendulum-type Charpy  Chapter 3. Experimental Aspects  38  machine are good choices; for a higher velocity of impact, however, a projectile type of impact machine may be needed. The maximum drop height of the hammer in a drop weight or Charpy machine determines the capability, in term of impact velocity, of the machine. 3. Choose a hammer mass which simulates the impact pulse. If a particular structural element collapses under one impact blow, a heavier hammer may speed up the impact event, leading to a shorter duration of impulse; while if it does not completely collapse under one blow, which is generally the case for a properly designed structure, the heavier the hammer, the longer the duration of the impact pulse. The drop height of the hammer has little effect on the duration of the pulse, but will, of course, influence the maximum impact load. The maximum load is roughly proportional to the square root of the drop height. These guidelines will be discussed in terms of both experimental and theoretical analysis later in this work. However, the hammer mass and the drop height are not the only factors determining the impact pulse history. The impact pulse is actually the result of the interaction of the hammer and specimen, and is thus related also to the stiffness and mass of the specimen, the stiffness of the contact zone, the support conditions of the specimen, and so on. As a result, choosing a hammer mass is usually an empirical instead of a theoretical process , based on the data and records from other studies with a similar testing system or based on trial and error. 4. Fine tune the impact machine. For a particular impact machine, one may add a rubber pad between the hammer and the striking tup or between the tup and the specimen, to modify the impact pulse. Rubber pads can also be placed between the specimen and the specimen supports. Extra weights can also be attached to the hammer. All of these measures can change the duration of the impact pulse, and may also affect the importance of the vibration mode during the impact event. For example, certain types of rubber pads between the hammer and the specimens can significantly filter the high  39  Chapter 3. Experimental Aspects  vibration modes excited in the beam. Through these fine tunings, an impact event in the laboratory can be made to simulate, to a large extent, impact events encountered in fields. 3.3.1.1. The 578 kg Machine  This drop-weight impact machine, designed and constructed in the Civil Engineering Department, University of British Columbia, is capable of dropping a 578 kg mass from heights of up to about 2.3 m. The velocity of the falling mass can be obtained by v =yl2(0.9\g)h  (1)  0  where g = the gravitational acceleration; h = drop height of the hammer. The correction factor of 0.91 is applied to g to account for the frictional effect between the hammer and the guiding columns, which was assumed to be a constant and measured by Banthia (10) and Yan (68) using the photo cell assembly. Then, v = 6.40 0  m/s for the maximum drop height of 2.3 m. The hammer mass on this machine was set to 345 kg at the beginning of the tests in this work, to test thefirstseries of CXT concrete ties; It was adjusted to 504 kg later to test the second series of CXT ties in order to evaluate the effect of hammer mass on the dynamic behaviors of concrete ties under impact loading. Finally, the hammer mass was increased to 578 kg, being used to test the modified ITISA concrete ties. The 504 kg hammer is capable of exciting an impact load of up to 700 kN on the concrete ties at the drop height of 1524 mm used in the current study. A dimensioned sketch of the machine is given in Fig. 3.  Chapter 3. Experimental Aspects  1067  7J  Steel Frame  Hoist and Chain  Hi  Hammer Assembly  oo  Tup  o  Supports (Anvil)  Concrete Foundation  1727 Figure 3. Schematic View of the 578 kg Impact Machine. All dimensions are in mm  Chapter 3. Experimental Aspects  41  As shown, the hammer is attached to the hoist by means of a pin lock. The hoist is used to raise or lower the hammer. Once the hammer is adjusted to the desired height above the specimen, the pneumatic brakes provided in the hammer can be applied. With the brakes, the hammer "grips" the columns of the machine. After unlocking the pin, the hoist can be freely detached from the hammer. Upon releasing the pneumatic brakes, the hammer falls and strikes the specimen, exciting an impact pulse on the specimen. If the specimen does not totally collapse with this blow, the brakes could be re-applied by means of manual control as it rebounds, preventing the specimen being hit a second time by the rebounded hammer. The data acquisition system is activated automatically on contact.  3.3.1.2. The 60 kg Machine  In order to simulate the response of the ties to impact loading, it was considered essential to duplicate, as closely as possible, the impact pulse measured in track, in terms of both the shape of the load vs. time curve and the duration of the impact event. The smaller instrumented drop-weight impact machine, also designed and built at the University of British Columbia, was used. The larger impact machine, due to its very large hammer mass of 578 kg, usually produced a pulse on the concrete tie with a duration of about 8 to 16 ms, depending on the support conditions of the tie. However, the smaller machine, with its nominal 60 kg hammer mass, produced an impact pulse of 3-5 ms duration, which is considered to be the typical duration of an impact event due to wheel flats, and is the type of pulse which causes the most serious damage to concrete ties in service. The dimensions of the 60 kg machine are shown schematically in Fig. 4.  42  Chapter 3. Experimental Aspects  Motor and Chain Steel Frame  Guide Columns Hoist and Magnet CO CO CM,  < O o  Hammer Tup  Supports Concrete Foundation (1400x840x620)  840  Figure 4. Schematic View of 60 kg Impact Machine. All dimensions are in mm.  Chapter 3. Experimental Aspects  43  With this machine, the hammer mass, and the type and thickness of the rubber shim between the hammer and the striking tup are adjustable, and are thus capable of exciting any specified duration of pulse on the tie within certain limits. As with the 578 kg machine, the drop height of the hammer will only influence the amplitude but not the duration of the pulse. For the maximum drop height of 2.4 m, the impact velocity is 6.54 m/s. In the current study, with a 60 kg hammer mass, the duration of the first pulse of concrete strain was less than 2 ms, and the duration of the impact load was about 4 ms, coinciding with the pulse measured in track. The simulation of the impact pulse will be further discussed later in this thesis. The structure and operation of the 60 kg machine are quite similar to those of the 578 kg machine, although their dimensions are totally different. There is only one major difference. In the smaller machine, there is no pneumatic brake in the hammer to "grip" the columns. Instead, an electromagnetic plate is installed on the bottom of the hoist to hold the hammer. To drop the hammer, the pin is unlocked and the electromagnet is turned off.  3.3.2. Instrumentation and Apparatus  3.3.2.1. Tup and Load Cell  The striking tup at the bottom of the falling mass is instrumented with electric resistance strain gauges, and thus acts effectively as a load cell. The tups of the two impact machines are almost the same, except that the thickness of the tup for the larger machine is greater than that for the smaller machine. They are shown schematically in Fig. 5.  Chapter 3. Experimental Aspects  44  Figure 5. The Tup  The striking tups are made of heat-treated high carbon steel. Two circular holes, 25 mm in diameter, are machined in the tups, and eight strain gauges are mounted on the inside surfaces of the holes, connected together to form a Wheatstone bridge circuit. This design amplifies the signals by making use of the stress concentrations at the boundaries of the holes. The circuit is balanced in the "no load" configuration. When a load is applied to the tup during impact tests, the tup deforms and the strain gauge circuit becomes unbalanced. The output voltages are proportional to the applied loads, i.e., the relationship of the applied load and the output voltage is perfectly linear for both loading and unloading.  Chapter 3. Experimental Aspects  45  The basic parameters of the strain gauges are: 1. type: bonded, 2. resistance: 350.0 Q ± 0.3%, 3. gauge factor: 2.07 ± 0.5%, 4. temperature coefficient: ±0.1%. 5. excitation: 10 v The tups were calibrated statically using a hydraulically loaded universal testing machine so that the proportionality constants for the load cells could be obtained. Two different tups were used for the CXT ties and for the ITISA ties respectively. For the tup used in the tests on the CXT ties on the larger machine, after lOOOx of amplification of the signals, one volt is equivalent to 187 kN (42 kip); for the tup used in the tests on the ITISA ties, both on the 578 kg machine and on the 60 kg machine, 1 volt = 57.5 kN (12.9) kip after 500x amplification of the signals. The calibration curves of the load vs. output voltage for both tups are perfectly linear.  3.3.2.2. Data Acquisition System  The data acquisition system has two main parts: a) a signal conditioner which acts as an amplifier as well as a noise filter; b) a PC computer with a special multi-channel analog to digital (A/D) conversion board and its accompanying software, which is used to collect and store the output signals of the instruments, in a digital form during impact events. The signal conditioner, designed and built at the University of British Columbia, has the ability to amplify up to lOOOx of the original output of the voltage from the load cell or the strain gauges. The full range of output voltages from the load cells and the strain gauges is usually less than ±10 mv, while the minimum step or the sensitivity of  46  Chapter 3. Experimental Aspects  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 more precisely, amplification of the signals is necessary. In this study, 500x or lOOOx amplification was adopted. The signal conditioner also has the ability of filtering the incoming analog signals to eliminate electrical or electronic noises. However, such analogfilteringmay greatly distort these signals. Therefore the original signals were recorded during testing and a digital filtering method was adopted to later process the data using an application program on the PC. Thefilteringtechnique used will be described later. The A/D conversion board and its accompanying software, Computerscope ISC-16, are commercially produced*. 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 (|is). If the data are acquired in n channels, the speed of the board is reduced to lln MHz. For eight activated channels, for example, which is the largest number of channels used in the current studies, the fastest sampling rate then becomes 118 MHz, i.e. the data are collected at intervals of 8 pis on all channels. The sampling rate which is required to measure and capture the peak signals accuracy depends on the duration and profile of the signal pulse itself. In the current studies, most impact pulses were half-sine curves, and the minimum duration was 1 millisecond (ms). From Fig. 6, the following relationship can easily be established:  y = A sin nx where x = time from the beginning of the impact event (ms) y = output value of the load cell (volt) * RC Electronics, CA, USA.  (2)  47  Chapter 3. Experimental Aspects  A = pulse amplitude (volt) Amplitude (A)  1.00 y=0.95A  0.90 0.80 ~ 0.70  / /  0.60 0.50 0.40 0.30 0.20 0.10 0.00  j I  /  f 1  •  j  1  -J 1  f  x1  1  0.5 x  (ms)  \  1  Figure 6. Half-sine signal and the sampling rate required  If the signal amplitude recorded is required to be accurate within 5%, and set the condition that when x = x y = 0.95 A, as shown in Fig. 6, then, v  0.95 A = Asin(7C-jc,)  (3)  Then,  JC-X, =1.253  x, =0.399  From Fig. 6, the sampling rate required can then be expressed as  (4)  (5)  48  Chapter 3. Experimental Aspects  t = 2x(0.5-x)=0.202m^ 1  (6)  The actual sampling rate used in the current study was 0.033 ms for pulses with 1 to 2 ms duration, ensuring the accuracy of the amplitude within 0.3%. The A/D conversion board has several trigger mode options. Slope triggering, which is often used in impact testing, was chosen for all of the impact tests reported here. When the input voltage is either increasing or decreasing as it crosses a preset trigger voltage level, then the data acquisition system is triggered. All of the data points acquired after the triggering, as well as the data points in a fixed time interval prior to the detection of the trigger, will be captured and deposited in the scope buffer. This interim is called trigger delay setting, defined in terms of the number of the data points. Although the trigger voltage level can not be set as zero, since the voltages of the load cell even at "no-load" condition always fluctuate slightly due to electrical noise, by setting the trigger level slightly higher than the "no-load" voltages and choosing an adequate delay value, the whole loading history can still be recorded reliably. The buffer used to hold the data points has 64k memory. If eight channels are used then 8k data points for each channel could be saved. If, furthermore, a 33 jis sampling rate is used, the total period of time recorded by the system is  T=33 [is x 8000 =264000 \±s = 264 ms  (7)  The longest duration of the impact events in the current study is less than 20 ms. Therefore, the buffer length is more than sufficient. The data in the buffer of the computer memory can be saved to the hard disk in ASCII format for later analysis using other programs. To conclude this section with caution, when a data acquisition system is to be used,  Chapter 3. Experimental Aspects  49  the following factors ought to be checked: 1. The output range of the instruments, and the input range and accuracy of the A/D conversion board; this determines the required amplification capability of the signal conditioner; 2. the duration and the profile of the signal pulses, and the accuracy of the amplitude required; these determine the required sampling rate capability of the A/D board; the sampling rate and the number of the channels to be used, and the period of the impact event , in turn, determine the minimum buffer or memory the A/D board must supply; 3. the possible electrical noise at "no load" condition; this determines what trigger level will prevent the system from accidentally triggering; how fast the signal increases at the very beginning of the impact event; this determines what delay setting required to save the impact signals before the input voltages reach the trigger level; 4. how to filter the electrical and electronic noises without distorting the original signal; and 5. while ensuring that the impact event is recorded completely and accurately, how to make the data file captured as short as possible to save on data processing time.  3.3.2.3. Accelerometers  The accelerometer used was a piezoelectric sensor*. It has a built-in unity-gain amplifier, and the output signal is sent to the data acquisition system via a coaxial cable. The accelerometer can read accelerations up to ±500g and had an overload protection of up to 5000g. Some salient features of the accelerometer are: 1. resolution = 0.01 g  Chapter 3. Experimental Aspects  50  2. resonant frequency = 45 kHz 3. frequency range = 1 ~ 5000 Hz 4. load recovery < 10 us. The accelerometers were attached to the described location on the concrete tie using a plastic base, 13 mm in diameter, 4 mm in depth, and containing a central threaded hole into which the accelerometer could be screwed. The base could befixedto the smoothly ground surface of the concrete using an epoxy adhesive. After six hours curing at room temperate, it was ready for testing.  3.3.2.4. Crack Detection Gauges  Crack detection gauges, consisting offive178 mm long conductive silver lines painted longitudinally on the grounded concrete surface below the rail seat, located 10, 35, 55, 75 and 95 mm from the bottom of the tie, were also used. They are shown in Fig. 7. These lines were connected to the resistance measuring circuit which is shown in Fig. 8. As a crack extended, these lines were severed sequentially by the flexural crack from the bottom line to the top line. Each cut caused the output of the circuit to jump to a new level, so that it was easy to determine when the various lines were cut.  * P C B Piezoelectrics. Inc., N . Y., model 302A  Chapter 3. Experimental Aspects  51  Figure 7. Crack Detection Gauge, Strain Gauge and Accelerometer on Concrete Tie Surface  Chapter 3. Experimental Aspects output  Line No. 1  W W 1810 Q  Line No. 2  WVN-  i  IA/Wr  560 n  Line No. 3  260 Q  Line No. 4  a  Line No. 5  W W  220 «  W W 120  Top  W W  Bottom  60 ft  Silver Paint Lines on Concrete Surface  Resistance Measuring Circuit  10V  Output (v) 10  10.0 8.92  r  8  6.60  6  4.23  4 2  2.38  •• 1.27  0  1  2  3  4  5  Crack Propagation Step  Figure 8. Crack Detection Gauge Circuit and Theoretical Output  53  Chapter 3. Experimental Aspects  The theoretical output voltages are calculated on the basis of the resistance R of the parallel circuit of the resistors (see Fig. 8); the value R, in turn, depends on how many lines have been severed. The resistance of the silver lines on the concrete surface is small as compared to resistors, and thus neglected in the calculations. The theoretical output voltages, corresponding to the different numbers of lines severed, are listed in Table 3, together with a set of calibration values actually measured on the system. Since the resistance R of the parallel circuit of the resistors is not very large at the first several steps, the resistance of the silver paint lines on the concrete surface, which is neglected in the calculations, is relatively significant in these situations, leading to the relatively larger error at these steps.  Table 3. Output voltage of the Crack Detection Gauge  Step Line severed Theoretical output(v) Measured output(v)  1.20  2 no. 5 2.38  3 nos. 5+4 4.23  4 nos. 5+4+3 6.60  1.51  2.63  4.44  6.67  1 none  6 5 all lines nos. 5+4+3+2 5+4+3+2+1 10.0 8.92 8.93  9.99  Since the sensitivity of the crack detection gauge depends on the thickness and width of the paint lines, care was taken to draw the lines as thinly as possible. A calibration of the gauge for each tie was carried out before the tie was tested, by measuring the actual values of the output when shutting off the switches linking the particular paint lines on the tie to the circuit. Then the crack propagation for each tie was judged on the basis of the calibration. The output of the crack detection gauge was fed to the data acquisition system without any amplification.  54  Chapter 3. Experimental Aspects  The final crack width for each tie was also measured, using a hand-held graduated microscope with a 0.02 mm accuracy.  3.3.2.5. Strain Gauges  In the second series of tests on the ITISA ties, two electric resistance strain gauges*, 102 mm (4") in length, were affixed in a horizontal direction to the vertical surface of the concrete at the two rail seats, 20 mm from the bottom of the tie, as shown in Fig. 7. The gauges have a resistance of 120.0 ± 0.3% Q. and a gauge factor of 2.10 ± 0.5%.  Bridge output  Figure 9. Wheatstone Bridge Circuit for Strain Gauges  A "quarter arm" Wheatstone bridge circuit as shown in Fig. 9, was used to measure * Measurements Group, Inc. USA, model EA-66-40CYB-120.  Chapter 3. Experimental Aspects  55  and record the output from the two strain gauges mounted on the concrete tie. strain gauge mounted on the concrete surface, and R  c  is the  is a resistor used only for the  calibration of the system. Usually, the measuring errors of using a strain gauge are either from the temperature change of the testing environment, or from an increase of internal temperature due to the electric current passing the gauge and a relatively slow heat dissipation of the gauge. Since the strain gauges were used for impact tests, which are normally completed within 10 ms, the temperature change of the environment can be neglected. Also, since the gauge is extremely long and very wide (102 x 4 mm), the heat dissipation of the gauge is very good. Measurements for the temperature correction of the strain gauges are not necessary. However, errors from mounting and wiring the gauge, and from the amplification of the signal conditioner, required the calibration of the strain gauges before they were used. A shunt calibration method was adopted. The output ends of  the Wheatstone  bridge circuit were connected to the data acquisition system and the amplification was set at lOOOx. After balancing the output of the bridge circuit to zero, a pre-selected shunt resistor R was connected into the system as shown in Fig. 9. A definite bridge unbalance c  then resulted. This bridge unbalance could be looked upon as a synthetic, controlled strain, and a voltage response appeared on the meter. The calibration made it possible to determine the factor relating strain directly to the readout of the data acquisition system. If R was replaced with another resistor with a different resistance value, the linearity of c  the strain gauge system could be checked. The size of the calibration resistor R  c  was selected so that the resistance change  obtained by shunting the gauge was equal to that produced by a particular strain. From the definition of the strain gauge factor, the change in resistance of a strain gauge, AR, is related to the original resistance of the strain gauge, R,, by:  56  Chapter 3. Experimental Aspects  ^  (8)  = ke  where k = strain gauge factor; £ = strain of the strain gauge. Similarly, the change in resistance of the parallel combination of the strain gauge Rj and the resistor R is c  A R = R  J L I  (9)  Equating these two expressions and solving for R yields c  R  c  =  * '  (  1  " *  £  )  ke  (10)  In this study, k was 2.10 and R, was 120 Q for the strain gauge. If 500 and 1000 u.e (microstrain) were selected, then the corresponding resistances of shunt resistors were 114.168 kQ and 57.023 kQ, respectively. Using precision resistors with the above resistance values, the output voltage measured on the data acquisition system are given in Table 4, and plotted in Fig. 10, from which the factor relating the strain gauge and the output of voltage was determined to be 1 v= 1000 U£/5.23= 191 \IE  (11)  This factor was almost the same for the strain gauge calibrations on every concrete tie, indicating that the strain gauge system was quite stable.  Chapter 3. Experimental Aspects  Table 4. Shunt Calibration of the Strain Gauge  Output of Bridge  Shunt Resistance  Synthetic Strain  (JfcQ)  (pie)  (v)  0  0  0  114.168  500  2.615  57.023  1000  5.230  Micros train  Figure 10. Calibration of Strain Gauge on Concrete Tie  Chapter 3. Experimental Aspects  58  3.3.2.6. Stress Coat  A brittle coating* was applied in liquid form to the concrete surface to locate fine cracks on the free end of the tie and for measuring the length of the horizontal cracks on the ties. This brittle coating was applied to a sanded and thoroughly cleaned concrete surface. The coating was built up slowly by spraying several light coats, up to a thickness of between 0.06 mm to 0.11 mm. It needed 24 hours to dry at room temperature. When it is stressed, the coating will crack at approximately 500 microstrains, the crack being very easy to identify. To enhance the clarity of the crack in the coating, a reflective aluminum undercoat, which provides a uniform background under the brittle coating, was applied to the concrete surface before spraying the brittle coat.  3.3.2.7. Rail Segment and Pandrol Fastening System  The loads, for both static and impact loading, were applied to each tie through a standard rail, fastened to the tie using the Pandrol fastening system. This is a threadless, elastic type of fastening system** in which cast iron shoulder inserts are embedded in the concrete at the rail seats. A spring type of clamp fastens the rail to the cast iron insert, the clamping force being approximately 22 kN. A rail seat pad is placed beneath the rail and a nylon insulators are placed between the rail base and the insert to provide both wear protection and electrical insulation. The pad provides electrical insulation in addition to impact attenuation benefits. The rail segment used for the CXT ties was a lighter type of standard rail, with a mass of 171 kg/m (115 lb/ft), and with a rail base of 140 mm (5.5") in width. The segment of rail used was 305 mm (12") long. For the ITISA tie, a standard 202 kg/m * Stresscoat Inc., Upland, C A , U S A ; brittle coating ST-65F/18C; undercoat ST-850. * * Pandrol International, Inc., Bridgeport, NJ, U S A  Chapter 3. Experimental Aspects  59  (136 lb/ft) steel rail, with a rail base of 152 mm (6") in width, was used. The segment of rail used was 292 mm (11.5") long. 3.3.2.8. Preload  A small preload, of about 13.4 kN (3 kips), was applied to both rail seats to prevent the tie from rebounding, just as the rail under a moving train would restrain a single tie after an impact pulse. The preload on the loading rail seat was applied by adjusting the nuts on two bolts located on either side of the tie. One end of the bolt was fixed to the base of the impact machine, and the other end passed through a pre-drilled hole on a piece of steel plate welded to the side of the rail segment. The nuts were turned against the top of the steel plate. Tightening the nuts on both bolts, applied a load on the concrete tie via the steel plate and the rail segment. Since there was no rail segment on the nonloaded rail seat of the tie, a steel block, 457 x 51 x 76 mm (18 x 2 x 3") in size, with two pre-drilled holes, was placed on the top of the rail seat to anchor two bolts which were fixed to the base of the third support. In Fig. 11, the preload applying assemblies for both rail seats can be seen. A torque wrench was used to apply a pre-set preload on the tie via the preload applying assembly. The relationship between the torque and the vertical load applied on the assembly was calibrated by inserting a proving ring in the assembly which shows the vertical load.  Chapter 3. Experimental Aspects  60  Figure 11. A Concrete Tie with a Preload Applied on the 60 kg Impact Machine  3.4. Static Testing Apparatus  Static tests were carried out on a 900 kN Tinius Olsen testing machine equipped with a 5 m long test bed for beam specimens. This is a closed-loop, electro-hydraulic testing machine. For static tests on the CXT ties, the deflections under the load point were measured using an LVDT. The signals from the load cell and the LVDT were used to produce a load-deflection curve on an X-Y plotter. For static tests on the ITISA ties, the strain gauge and the crack detection gauge, as same as introduced above for impact  Chapter 3. Experimental Aspects  61  testing, were affixed to the vertical concrete surface. The signals from the load cell and the strain gauges were acquired using the data acquisition system, at time intervals of 1 s.  CHAPTER 4. STATIC TESTING 4.1. CXT Concrete Tie  For reasons of safety, a structure or a structural member should, generally speaking, be designed such that it will not totally collapse under a design impact load. Indeed, in some situations the structure and its members are expected to be further used without any repair. A concrete tie under impact due to a wheel flat of a train is one such example. To evaluate the impact resistance of a structural member, both the fracture energy the member could absorb during impact and the residual static-bearing capacity of the member need to be studied. The impact testing procedure for the CXT ties was based on the above considerations. Static tests played an important role in the procedure described below. 1.) Carry out static tests on new ties, and determine: E:  Initial stiffness of the beam—slope of the line connecting the zero point and the point at 30% of the peak load of the load vs. deflection curve;  Pj:  Peak load;  U : Fracture Energy-area under the load vs. deflection curve out to the point at 0 75  which the curve had declined to 75% of the peak load; This point is sometimes considered as an indication that the member has lost its normal functions in a structure U:  Total Energy—area under the entire load vs. deflection curve.  62  63  Chapter 4. Static Testing  2.) Carry out impact tests on companion ties, with different combinations of the rail seat pad (between the rail and the tie), and the rubber supports (between the tie and the support anvils). Ten blows for each tie with soft rubber supports, and eight blows for each tie with hard rubber supports were applied, under the same 1524 mm hammer drop height with the 345 kg (760 lb) hammer mass. There were four combinations of pads and rubber supports, shown in Table 5.  Table 5. Support and Pad Conditions under Impact Testing of CXT Ties  Case No. Rubber Support  Rail Seat Pad  Code Name  Impact Blows  Case 1  Soft  Soft  (SS)  10  Case 2  Soft  Hard  (SH)  10  Case 3  Hard  Soft  (HS)  8  Case 4  Hard  Hard  (HH)  8  The properties of the pads and rubber supports, and the results of the impact tests on the ties are described in detail in Chapter 5. 3.) Carry out the static tests again for all of the ties which have undergone impact tests, obtaining the same indices as above as the residual capacity for the ties. From the comparison of these indices to those of the new tie, the impact resistance of the ties combined with different types of pads and rubber supports could be evaluated.  4.1.1. Flexural Tests for New Ties The static tests of the CXT ties were carried out on the Tininus Olsen testing machine. The testing setup, shown in Fig. 12, conformed to the requirements of Chapter  64  Chapter 4. Static Testing  10 of the AREA Manual, with the exception that the load was applied directly to a segment of standard rail (171 kg/m) with a 6.5 mm thick EVA rail seat pad placed beneath the rail and fastened to the tie using the Pandrol fastening system. The span of the loading supports was set as 750 mm (29.5"), slightly larger than the value specified in the AREA Manual, 711 mm (28"). The reason for this change was so that the results from this series of tests could be compared to the impact results of ties previously tested at UBC (37,38,39). The loading rate was 22.3 kN/min (5 kips/min). The loading for each tie was terminated when the midspan deflection reached 25 mm. This was followed by an unloading process, i.e.. the loading head was slowly raised. The output signals from the LVDT and the load cell were fed into an X-Y plot, establishing a load vs deflection curve.  F R O M LOAD CELL  2591  |  |  Figure 12. Setup of the Static Tests on CXT Concrete Ties  The typical load vs. displacement curve for a new tie is given in Fig. 13 . The characteristic points on the curve at which the cracks appeared, and the final crack pattern, are marked on the figure. A flexural crack (no. 1 in the figure), the first crack  Chapter 4. Static Testing  65  found on the tie using the hand-held 5-power magnifying glass, appeared at a load of about 355 kN, though this did not result in much change in the slope of the load vs deflection curve.  700  I  — r 1  i  1  1  1  r  DEFLECTION (mm)  Figure 13. Load vs Deflection Curve of CXT Tie Subjected to Static Loading with the Crack Pattern that Ultimately Developed Shown in the Inset  At 489 kN, flexural-shear cracks (no. 2 in the figure) appeared, accompanied by a distinct change in the slope of the curve. These cracks extended up to the top layer of the prestressing wires. As the loading continued, shear cracks (no. 3 in the figure) appeared at 613 kN, and explosive cracking sounds could be heard emanating from within the ties. The shear cracks ran from the supports to the point of application of load, and were due  66  Chapter 4. Static Testing  to diagonal tension. At this point, there was some slip of the prestressing wires, and large deflections and crushing of the concrete on the upper surface occurred, culminating rapidly in complete failure of the tie. These results are summarized in Table 6.  Table 6. Crack Development Under Static Loading  Mode of Cracking  Load (kN)  Flexure  355  Flexure-Shear  489  Shear  613  It is of some interest to compare the loads required to cause cracking in these tests with the design service loads. According to the AREA Manual, in North America the maximum axle load of a train is 364.7 kN (82 kips). A simplified analysis on each rail seat of the concrete tie provides the following design load,  364 7 P * * . = — x 0.5 x 3.0 = 273.8  (12)  where the factor 0.5 is the fraction of the load on each tie for concrete ties spaced at 609 mm (24 inch) centers, and the factor 3.0 is the impact factor, which takes into account the dynamic effect of the wheel and rail irregularities. This corresponds to a rail seat bending moment of 33.9 kN-m (300 in-kips) for a 2591 mm (102") long concrete tie, assuming a uniformly distributed reaction of the ballast under the tie across the whole length of the tie. The tie should not crack under this moment. In the tests reported here, the cracking load was 355 kN (80 kips), corresponding to a static rail seat bending moment of 57.2 kN-m (506 in-kips) under our support conditions, much higher than the  67  Chapter 4. Static Testing  design service bending moment. 4.1.2. Flexural Tests for Damaged Ties  The setup for the static testing of the damaged ties, which had previously been tested under impact with 345 kg hammer, was the same as that for the new ties. The results are listed in Table 7.  Table 7. Residual Capacity of the Ties after Being Subjected to Impact Loading  Tie No.  P  E  Uf)7S  U  kN  kN/mm  kN-mm  kN-mm  613  222  4205  7770  Code  New Tie 1  PSS*  623  170  4241  7881  2  PSH*  592  174  3961  7498  3  PHS**  529  128  2630  5442  4  PHH**  167  30  1469  2919  * after 10 blows; * * after 8 blows.  In the table, the code S = soft and H = hard. This code represents the conditions under which the tie was subjected to impact loading. The first letter after letter "P" refers to the support conditions, the second to the type of Pandrol pad.  4.1.2.1. The Influence of the Rubber Support  For the hard rubber supports used in tie No. 3 and No. 4, the E, Pj, Un.75 and U of the ties after impact tests decreased significantly as compared with the new ties, particularly for tie No. 4, where the hard support was combined with the hard pad. For tie  68  Chapter 4. Static Testing  No. 4, the residual energies, U  0J 5  and U, were just about 35% of those of the new tie; the  very low stiffness indicated that the tie had totally lost its integrity and service capability. Under the static loading, the bending moment was actually resisted by both the tension of the prestressing wire near the bottom of the tie and the compression carried by the combination of the tie shoulder inserts and the confined rail base on the top of the tie. On the other hand, if soft rubber supports were used as in tie Nos. 1 and 2, as compared with the new ties, small reduction of the initial stiffnesses E for both cases were noted, due to the flexural cracking during the previous impact loading process. However, Pj, U  07 5  and  U, showed almost no change, indicating very little damage to the ties and a good residual service capability, though the long-term durability of the tie would also need to be considered.  4.1.2.2. Influence of the Pad.  From Table 7, it may be seen that if soft supports are used, the rail seat pads have little, if any, effect on the residual capacity of the ties; however the pads significantly influence the deterioration of the ties under impact loading if hard supports are used. Compared to the tie in case 4, the tie in case 3 had not totally lost its residual load bearing capacity. It maintained about 65% of its static bending capacity, in terms of fracture energy U; and 58% in terms of initial stiffness. This implies that in service, when the ballast underneath the tie is badly deteriorated and loses flexibility, the rail seat pads may play an important role in protecting the ties. However, it should be noted that soft pads may themselves harden very quickly under repeated impacts in service; the resilience of the soft pads may become even worse than that of the hard pads after only several years in track. In summary, it was found that in terms of the residual static capacity, using soft  Chapter 4. Static Testing  69  rubber supports greatly reduces the tie deterioration under repeated impact loading, in comparison with the use of hard rubber supports. Using soft rail seat pads had some effect on the deterioration of the ties under impact when the hard supports were used. There was very little effect of the rail seat pads on impact resistance of the ties when soft supports were used.  4.2. ITISA Concrete Tie  The static tests on the standard ITISA tie (No. 1) were carried out on the same Tininus Olsen testing machine, but with full instrumentation on the ties. Strain gauges and crack detection gauges were affixed to the tie as described in Chapter 3, to determine the concrete strain and the cracking load when the first crack appeared. This time the loading support span was set exactly to the value recommended by the AREA Manual, which is equal to the 4/3 of the distance from the center line of the rail seat to the closer end of the tie (see Fig. 2 in Chapter 3.), i.e. 660 mm (26"). A preload of 8.9 kN (2 kip) was applied to the rail for seating of the tie on the supports. The loading rate was about 22.3 kN/min (5 kip/min). All output signals were acquired by the data acquisition system at 1 s intervals. The load vs. concrete strain curve is shown in Fig. 14. The crack gauge output developed simultaneously with the load and strain signals, and was printed on the same curve. The loads and strains recorded when the first crack passed the different paint lines are listed in Table 8.  Chapter 4. Static Testing  280  i  0  400  800  Microstrain  Figure. 14. Static Test on ITISA Concrete Tie  1200  71  Chapter 4. Static Testing  Table 8. Loads and Strains as the First Crack Passed Each Paint Line No. of Distance to lines severed Tie Bottom (mm)  Applied Load (kN)  Applied Load (kips)  Strain xlO  6  0  0  8.9  2.0  0  1  10  225  50.5  429  2  35  240  53.9  518  3  55  248  55.8  702  4  75  253  56.9  826  5  95  258  58.0  963  From Table 8, the load at first crack was 225 kN (50.5 kip). The corresponding bending moment at the rail seat was 31.4 kN-m (278 kip-in), just meeting the flexural strength requirement of the AREA Manual, 31.1 kN-m (275 kip-in), for 2515 mm (99") long concrete ties. The concrete strain at first crack was 429 (microstrain). The measured cracking strain was a little higher than the calculated value of 369 (microstrain).  CHAPTER 5. IMPACT TESTING OF CXT CONCRETE TIES  5.1. Introduction  This series of tests had two principal objectives: 1. to make clear the roles of the support conditions and the rail pads in the protection of ties subjected to 10 ms duration, high amplitude pulses simulating rail abnormalities. 2. to investigate the effect of the loading rate on the crack mode and fracture energy of the prestressed concrete tie subjected to flexural impact loading.  5.1.1. Background in Railroad Practice  In practice, a concrete tie is subjected to two kinds of loads. One is a quasi-static load, due to the normal passage of a wheel over the tie. This type of load has a long duration, usually longer then 25 ms depending on the speed of the train. This type of relatively low amplitude load is imposed simultaneously on the two rail seats near the ends of the tie. Superimposed on these loads are the occasional impact loads of a much higher amplitude, 3 to 4 times higher than the quasi-static load, due to wheel flats or rail abnormalities. The wheel "flats", which develop on the wheels of a train during braking, generally induce a very short duration impulse, in the range of 3-5 ms (8), normally acting on both rail seats. However, impulses due to rail abnormalities, such as rail joints, engine burns or battered welds, are of longer duration, about 5-10 ms (29), or even 72  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  73  longer (28). These impact loads would normally occur on only one end of the tie. In this series of studies, it was the longer duration impulses that were simulated. The tests reported here focus on the impact loading only, in order to simplify the experimental arrangements. It should be noted that previous work (29) has shown that the strain response of the tie to a combination of impact and quasi-static loading is actually less than the response to impact alone, which would imply that the current tests are, if anything, conservative. There are a number of studies which indicate that the dynamic response of a concrete tie to an impact pulse was independent of the support conditions. Hajime Wakui (36) changed the ballast condition from a uniform distribution along the tie to either center-concentrated or center-free ballast conditions, and found that the dynamic behavior of the tie was almost the same: "The sleeper behaves like a free-free beam floating on the ballast". Dean and Harrison (8) place neoprene rubber strips underneath the tie at the load supports. They found that changing the spacing of the tie supports from 15 to 30 inches produced an increase in strain amplitudes of only about 10 percent, and concluded that "support spacing is not a critical factor". Comparing the spectral analysis from impacts measured in the field (two-wheel loading) and in the laboratory (singlesided loading), they stated that "The duplication of the second and third bending modes in the laboratory setup indicates that the tie suspension in either case represents a beam which is very loosely coupled to its support; that is, a free-free beam". Igwemezie and Mirza (30) studied the concrete tie system on a railway bridge, where the concrete tie was directly placed on the bridge girder; there was no ballast, but a piece of rubber was placed between the tie and girder. Using the same rail-tie EVA pad but different tiegirder rubber pads, the average impact force on the rail was found to be 243 kN for the soft AASHTO support pad (stiffness k = 54 kN/mm), and 243 kN for the hard support pad (k=305 kN/mm), that is, they were almost the same. Their finite element analysis  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  74  also showed that the tie support characteristics had only an insignificant effect on the tie response; the resistance of the tie to the impulse was achieved by mobilization of the tie mass. The impact pulse excitations used in the above studies were simulations of wheel flat impacts, with a pulse duration of less than 5 ms. What would happen if the impact pulse excitation were to be changed into a duration of approximately 10 ms, which is the type of pulse generated due to rail abnormalities? No such laboratory studies have been reported. Field studies (40) have shown that the ballast conditions significantly influenced the response of the tie to an impact pulse due to rail abnormalities. The current study is intended to simulate a long duration pulse in order to evaluate the effect of the stiffness of the supports on the impact resistance of the concrete tie. The impact pulses produced in these tests had a duration of 8 to 14 ms. Although using rubber supports does not perfectly simulate the ballast in tracks, it was an easy method which can provide good qualitative information, and it can reasonably simulate the support conditions on a railway bridge. The AREA formula (Eq. 12 in Chapter 4.) indicates the allowable vertical impact load in track, 273 kN (61.5 kip), corresponding to 30.5 kN-m (270 kip-in) bending moment at the railseat. However, in reality, the maximum load is sometimes much higher due to severe irregularities of either the wheel or the rail. Measurements in track in the Northeast Corridor (8) have shown that, at a 0.01% frequency the maximum bending moment at the rail seat exceeded 65.0 kN-m (575 in-kips), corresponding to a 587 kN (132 kips) vertical load. In the worst case event, it exceeds 101.7 kN-m (900 in-kips), corresponding to a 921 kN (207 kips) load. These data were obtained using strain gauges affixed to the rail seat of the ties. The maximum impact load in the present tests was 605 kN (136 kips), corresponding to 66.8 kN-m (591 in-kips). Considering that a portion of the impact load  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  75  will act as an inertial load, the bending moments or bending loads on the railseats are well within the range of bending moments in service.  5.1.2. Background to Theoretical Analysis  Previous studies (2) have shown that, for plain concrete, increasing the loading rate from the quasi-static range to the dynamic range may shift the mode of failure from flexural to shear. Other studies have also demonstrated a brittle failure of the reinforced concrete member under impact (2, 10). In these situations, the failure occurred very quickly, and the fracture energy was much reduced. This is, as indicated in the Introduction, a serious problem for concrete members subjected to impact loading. The purpose of the present work is to demonstrate the effects of both the stiffness of the tie supports and the stiffness of the bearing pads between the rail and tie on the loading rate, and hence, the mode of failure for these prestressed members. An attempt at a theoretical analysis of the possible shift of the failure mode under impact loading follows the discussion of the results.  5.2. Testing Setup  The impact machine used in this series of tests had a hammer mass of 345 kg for the first part of the test program; it was then changed to 504 kg for the second part of the program to check the effect of rubber supports on the dynamic properties of the ties subjected to an impact with a heavier hammer and higher loading rate. However, the same striking tup was used for entire test series. The experimental setup of the impact tests is shown in Fig. 15.  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  76  Rubber Support Anvil  Figure 15. Impact Test Setup for the CXT Concrete Ties. Dimensions in mm. Two different types of Pandrol pads, and two different types of rubber supports, were used to provide four different loading conditions. For this research, the rubber supports between the machine anvils and the tie may be described as:  HARD material:  nylon reinforced rubber  dimensions: 15 x 51 x 305 mm SOFT material:  rubber  dimensions: 25 x 51 x 305 mm The load vs. deformation plots for both rubber supports are shown in Fig. 16  11  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties Load (kN) 450  0  2  4 6 Deformation (mm)  8  Figure 16. Load vs. Deformation Curves for Rubber Supports  The rail seat pads, which were placed between the rail and the tie, could be described as: EVA pad: material:  ethyl vinyl acetate (EVA)  dimensions: 6.5 x 170 x 190 mm stiffness: Poly pad: material:  210 kN/mm (17.8 - 89 kN); 630 kN/mm (109 - 196 kN) polyurethane  dimensions: 6.5 x 170x 190 mm stiffness:  228 kN/mm (17.8 - 89 kN); 263 kN/mm (109-196 kN)  The load vs. displacement plots for both pads are shown in Fig. 17 and 18. The stiffness values shown are determined by the slope of the lines connecting the points representing rubber deformations at 17.8 - 89 kN (4 - 20 kips) and 109 - 196 kN (24 - 44 kips) respectively.  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  Load(kN) 250 T  Deformation (mm)  Figure 17. Load vs. Deformation Curves for EVA pads Load (kN) 250 ,  Deformation (mm)  Figure 18. Load vs. Deformation Curves for Poly pads  78  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  79  The stiffness values given above are the static compressive stiffnesses of the materials. The plots for rubber supports and rail seat pads were obtained from static tests conducted at San Jose State University (69, 70), using a Riehle hydraulic testing machine to apply the loads and two mechanical dial gauges to measure deformations. No dynamic stiffness data are available, due to the difficulties in obtaining data under the very high loading frequencies up to 125 Hz, and very high loads up to 700 kN, which were obtained during impact testing of the concrete tie. It should be noted that the dynamic stiffnesses of these materials could be much higher than the static stiffnesses, by up to several times. In a previous study (36), it was assumed that the dynamic stiffness of the rail seat pads was eight times their static stiffness. Although in the AREA manual (26), the stiffness between 24 to 44 kips static loads was defined as the pad nominal stiffness, the impact tests carried out by Battelle Laboratories (8) showed that under impact loading, the attenuation effects of pads on rail seat strain of the tie were largely consistent with the pad dynamic stiffness between 4 to 20 kips, at the rate of 9 Hz. Although the static stiffnesses of the EVA and poly rail seat pads between 17.8 - 89 kN (4 to 20 kips) were not very different, from the other series of tests (see Fig. 66 in Chapter 10), it was found that the EVA pads could, compared to the polyurethane pads, attenuate the concrete tie strain by about 15% if the relatively hard supports were used underneath the tie. The destructive impact tests on the CXT ties (see Table 12 in Chapter 6) also showed that the EVA pad could protect the ties from deterioration more effectively than the poly pad if the hard rubber support was used underneath the ties. After eight impact blows of the 345 kg drop hammer, the residual static fracture energy for the tie with the EVA pad was twice that of the tie with the poly pad. This may imply that there was a larger difference in the dynamic stiffnesses of the two kinds of pads. Therefore, the EVA pad is considered to be dynamically "softer" than the poly pad and is  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  80  called a soft pad in Chapter 4 and 6. The two steel anvils supporting the tie had cross-sectional dimensions of 51 x 305 mm at the top. They were fastened to a large concrete block, approximately 1.7 x 1.7 m in cross-section, and about 0.8 m high, which was in turn bolted through a concrete reaction floor. Since the flexible rubber pad between the anvil and the tie was a medium of relatively low stiffness, it was assumed that the support system below the rubber pad was, in comparison, infinitely stiff. The signals from the load cell were amplified 1000 times using a signal conditioner, and then, together with the signals from the accelerometers, were acquired using a PC-based high speed data acquisition system, at time intervals of 0.2 ms. All digitized data were saved on computer diskettes for further processing.  5.3. Test Program  Six nominally identical ties were tested in this series. Four ties were tested under impact using the 345 kg hammer and two ties under the 504 kg hammer. The drop height of the hammer was set to 1524 mm (60") for all impacts of these tests. Brakes were applied to the hammer as it rebounded from the tie, preventing repeated impacts. The setup and instrumentation were the same for all tests. The tie specimen identification and their corresponding testing conditions are listed in Table 9.  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  81  Table 9. Impact Testing Conditions for CXT Ties  Hammer  Impact  Subsequent  mass (kg)  Blows  Static Test  EVA  345  10  yes  soft  poly  345  10  yes  3  hard  EVA  345  8  yes  PHH  4  hard  poly  345  8  yes  SH  5  soft  poly  504  10  no  HH  6  hard  poly  504  2  no  Tie  Rubber  No.  Support  PSS  1  soft  PSH  2  PHS  Tie ID.  Pad  In the table, the code S = soft and H = hard. The identifications of these ties represent the conditions under which the tie was subjected to impact loading. The first letter after the letter "P" (or the first letter for tie Nos. 5 and 6) refers to the support conditions, the last letter refers to the type of Pandrol pad. For ties No. 1 and 2, each tie was subjected to 10 blows of the impact hammer. The ties were then transferred to the static testing machine, to evaluate their residual capacity under the static loading. For ties No. 3 and 4, each tie was subjected to only 8 blows of the impact hammer before being tested under static loading. The reason was that after 8 blows with the hard rubber supports, the ties were heavily damaged, and were unable to withstand further impact loading. After the above tests were concluded, ties No. 5 and 6 were tested under impact using the 504 kg hammer. Only poly pads were used for these two ties and were not tested statically after the impact testing. Their specimen ID's are SH and HH, corresponding to the support and pad combinations described above.  82  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  5.4. Analysis of Test Results  5.4.1. Differences in Analysis between Impact Tests of Beams and of Concrete Ties  The tup load, i.e., the load experienced by the impacting tup of the drop hammer and measured using a load cell within the tup, consists in part of the load used for the inertial load (the load due to the acceleration of the specimen from a position of rest to a velocity near that of the impacting hammer). The remainder of the tup load which produces the deformation of the specimen is called the specimen reaction or the mechanical force. In flexural impact testing, this portion of the tup load is referred to as the bending load. In the model used by Banthia et. al (10, 43), the true bending load P was obtained b  by subtracting the calculated inertial load P from the tup load P ; and the area under the t  t  true bending load vs. deflection curve was taken as the fracture energy. The key step in this model was the evaluation of the inertial load P, by assuming that the magnitude of the acceleration at any point of the beam was proportional to the deflection of the beam at the same point. Then the acceleration at any point could be expressed as a function of the acceleration at the center of the beam or at any point at which the accelerometer was located. Using the equation of virtual work, the distributed inertial load could then be replaced by an equivalent or generalized inertial load, P acting at the center of beam. t  However, it should be noted that in the tests carried out by Banthia, et. al (10, 43):  1). all of the beams tested were symmetrical about the loading point; the supports (two steel anvils) could be assumed to be infinitely stiff compared to the specimens so that the deflections and accelerations of the beams were always zero at the two simple supports. This made the evaluation of the deflected shapes of the beams relatively simple,  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  83  with only a few accelerometers fixed to the beams; 2). all of the beams tested were completely broken by a single impact, so there was no elastic rebound. The broken halves of the beams consumed a considerable amount of kinetic energy, which is very difficult to measure. However, the evaluation of the "inertial load" effectively eliminated the difficulty of determining this kinetic energy. For the present tests on concrete railroad ties, on the other hand, to simulate the actual loading conditions, as closely as possible, rail seat pads and rubber support were used, and a three-support bending system was adopted. This meant that: 1) The ties were not symmetrical about the loading point (Fig. 15), the distributed inertial force on the unloaded cantilevered end of the tie caused the deformed shape of the tie to be non-symmetrical and complicated. Since the rubber pads effectively acted as filters to eliminate the energy in certain bending vibration mode within specific frequency bands under impact, a different combination of rail seat pads and rubber supports may change the relative importance of each vibrational modes of the tie, leading to quite different deflected shapes under impact. Also, the deflections and accelerations of the tie were not zero at the two support points due to the rubber supports under the tie. The deflections obtained by double integration of the measured accelerations of the tie were thus the superposition of the deflections due to support movement and those due to the deformation of the ties. To monitor the motion of the ties at the support points, the accelerators were mounted on the tie just above the support anvils. However, the output data was not a simple function of the vertical motion of the ties only, since even when the tie was placed on the anvil, without any rubber supports beneath the tie, the accelerations recorded were still non-zero and quite large. This was probably due to the rotational effects of the ends of the ties. Therefore, it was very difficult to evaluate both the deflected shapes of the tie and  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  84  the associated inertial loads. 2) Because of the continuous prestressing bars, the ties were not completely broken into two or more pieces even after the final impact blow. Indeed, some ties had a very small crack. Kinetic energy or inertial energy is transmitted to the tie at the beginning of the impact event, but when the tie reaches its maximum deflection ( lowest position ) the velocity decreases to zero, and the kinetic energy is transferred into fracture energy or elastic strain energy. Since the tie maintained its structural integrity in most cases, the problem of the energy loss due to the broken half of the beam no longer exists. In view of these differences, the original method of analysis developed by Banthia et al (10, 43) had to be modified, as described below. 5.4.2. Derivation of Fracture Energy  5.4.2.1. Method 1: From Load vs. Deflection Curve  The method of analysis developed previously, referred to here as the "single-blow" impact technique, was successfully used for analyzing concrete beams which failed completely at thefirstblow, and the fracture energy of the beam can be obtained from the bending load vs. deflection curve (10, 43). In the present case, however, for the ties which did not fail under thefirstblow, the method of analysis had to be modified into a "multi-blow" impact technique. The main considerations of this method are as following, which are explained in more detail in Appendix of this chapter: 1. In the "single-blow" tests, since the beam is always under acceleration, the bending load P is always less then Tup load P (10, 43). In the multi-blow impact tests, b  t  however, the beam undergoes an acceleration phase, when the bending load is lower than the tup load, and a deceleration phase, when the bending load is greater than the tup load. 2. If the beam was not broken into two or more pieces, the area under the tup load  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  85  versus deflection curve was almost the same as that under the bending load versus deflection curve, because almost no energy transferred from the hammer to the beam, via the tup load, was lost. The inertial and kinetic energies transferred to the beam while it was being accelerated were gradually released back to the system as the beam returned to rest. Therefore, the area under the tup load versus deflection curve could be used to evaluate the fracture energy of the beam. 3. When the beam is in the elastic rebound period, it releases a portion of its stored strain energy back to the hammer. The deflection decreases from its maximum value. Theflexuralenergy consumed by the damage to the beam should be the difference between the area under the upper branch of the tup load versus deflection curve (representing the downward deflection of the beam) and the area under the lower branch of the curve (which represents the rebound of the beam), as shown in Fig. 27 in Appendix of this chapter. 4. The tup load can be obtained directly from the load cell built into the tup, and the deflection at mid-span of the tie can be obtained by double-integration of the acceleration recorded by the accelerometer mounted at mid-span :  u = liu(t)dt  (13)  Since the acceleration distribution of the concrete tie, and hence the inertial load and bending load, are very complicated to develop, in order to verify the above considerations, the impact testing of a series of concrete beams was conducted (71). In these tests, the beams were placed on two simple support anvils so that the deflected shape of the beams could be assumed. The drop height of the hammer was chosen such that some of the beams would not be completely broken by a single blow. Thus, the relationship between tup load and bending load under the "multi-blow" impact could be investigated. This series of tests, together with the analytical method, are shown in  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  86  Appendix of this chapter. 5.4.2.2. Method 2: From Impulse and Momentum  From the above discussion, the energy transferred from the falling hammer to the tie can simply be considered as the fracture energy in the impact tests. In the previous section, the tie together with the rail seat pads and rubber supports was taken as an isolated system. Alternatively, the hammer can also be taken as an isolated body, in order to derive the energy transferred to the tie during an impact event.  Figure 19. Impulse and Momentum Change of the Hammer  Fig. 19 shows schematically the load acting on the hammer and the change of velocity of the hammer. v is the initial velocity of the hammer immediately prior to 0  striking the tie; v, is thefinalvelocity when the tup just rebounds from the tie; and p is the reaction force of the tie acting on the hammer, which is the same as the tup load detected by the load cell. v can be evaluated by: 0  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  87  where: g = the gravitational acceleration; h = drop height of the hammer. A correction factor 0.91 is applied to g to account for frictional effects between the hammer and the guiding columns (see Chapter 3). Since the direction of the initial velocity is opposite to the positive direction of the coordinate y, v is negative. From 0  Newtonian mechanics, the change in momentum of the hammer, due to the velocity change from the initial state to thefinalstate, must be equal to the impulse, 5, induced by the reaction force acting on the hammer during the time of the impact event. Since S is given by the area under the load vs. time plot by definition, then,  S = \p(t)dt = M v h  t  (15)  Mv h  0  or (16)  M v, = S + M v = I p(t)dt + M v h  h  0  h  0  where, M = mass of the hammer. h  Since v,is always positive in the multi-blow tests, and v is negative (see Fig. 19), 0  the value of jp(t)dt must be greater than the absolute value of M v . In addition, the h  0  greater the value of \p(t)dt, the larger v, would be. From the above equation, v, can be solved as:  v,=^-\ M  »  p(t)dt + v  0  (17)  According to the principle of energy conservation, the change in kinetic energy of  88  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  the hammer between the initial and final conditions must be equal to the energy the hammer releases to the tie, AE. So,  AE = 1 M vf ~\M vl=±M (vf -v ) h  h  (18)  2  h  0  From this equation, since v, is always less than the absolute value of v , AE is 0  always negative, indicating a loss of energy in the hammer; the larger the value of v,, the less energy is released. From equation 16, v, will increase with an increase of the impulse jp(t)dt. In other words, the larger of the area under the tup load vs. time plot, the larger  the value of v, and the less the energy released by the hammer. This conclusion is opposite to that for the "single-blow" impact system, in which the beam is totally broken under one blow and the initial and thefinalvelocities are in the same direction. In this case, the larger value of the impulse jp(t)dt, the larger the difference between the two velocities will be, leading to a higher energy released by the hammer. Now, substituting equation (17) and equation (14) for v, and v in the expression 18 0  for AE, the new expression for AE becomes  -2  AE = —M 2  h h  -Jp(t)dt-V2(0.91g)h -2(0.91g)h  M,  (19)  In this expression, all the constants are known and the impulse jp(t)dt can be obtained directly from the load history curve of the load cell in the hammer. 5.4.3. Derivation of the Bending Load  The two methods discussed above can be used to get the fracture energy for each  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  89  blow of the impact tests, but the bending load is still unknown. The inertial load and the bending load are superimposed during an impact event, making up the apparent tup load. The inertial load is a maximum at the moment of impact and rapidly decreases as the velocity of the specimen increases. Other oscillations, also at the beginning of the load history, caused by stored elastic energy in the tup and reflected stress waves between the tup and specimen have also been identified by Venzi et al (61) and Turner et al (72). It has been suggested (60) that the first oscillation of the tup signal be considered primarily as the result of the inertial effects and the subsequent oscillations be treated as the results of the stored elastic energy and reflected stress waves. Sever (73) proposed that reliable measurements could be made only after 3 oscillations, after which time the tup load can be assumed to be the true mechanical load on the specimens. This approach is not useful for very brittle specimens such as plain concrete beams, since the beams will totally collapse even before the first oscillation of the inertial load. However, for reinforced or prestressed concrete beams, which exhibit reasonable "ductility", the inertial oscillations could be identified. Saxton, et al (59) described four typical load histories of impact tests, as shown in Fig. 20. Z is the mechanical impedance of the specimens. For linear elastic materials,  (20)  Where, c = speed of elastic wave propagation, p = density, E = elastic modulus. Thefirstsharp peak in thefiguresrepresents the inertial load contribution and the  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  90  cross-hatched area is due to the mechanical response of the specimen, that is, the contribution of the bending load. Prestressed concrete has a medium ductility and medium impedance as compared to ductile steel or brittle composites. Thus, the type of the load vs. time curve should lie between the types of case (b) and case (c). Whether it belongs to type (b) or type (c), the peak bending load can be considered as the maximum value at the second peak in the plots.  a . High Z, tough, high UTS  b. High Z,ductile, low UTS  TIME  C. Low Z,brittle composite  0. High Z, brittle  *The horizontal coordinates are time, and the vertical coordinates are tup load for all the four plots.  Figure 20. Schematic examples demonstrating the interrelationship between impedance (Z), and materials properties (59).  Chapter 5. Impact Testing of CXT Pre-tensionecl Concrete Ties  91  Figure 21. Simplified Dynamic Model for Flexural Impact Tests Eibl (64) used a simplified dynamic model for flexural impact tests of reinforced concrete beams, as shown in Fig. 21. This was a two-degree of freedom mass spring model in free vibration, where Mi was the mass of the hammer, M2 was the generalized mass of the beam, and Vj was the initial velocity of the falling hammer. The top spring simulated the force-deformation relationship in the contact zone between tup and the concrete beam, and Rj represented the tup load. The lower spring simulated the flexural elasticity or stiffness of the beam, and R2 represented the flexural resistance of the concrete beam, i. e. the bending load. If both springs were linearly elastic, then the responses of two forces could be represented by the plot in the upper graph shown in Fig. 22. Due to a rather stiff contact zone, the oscillation of the force Rj had a high frequency, while the force R2 in the second spring changed slowly with time. However, in reality, the system was non-linear, as there was a high degree of damping and large energy dissipation due to local accumulated damage in the concrete surface of the contact  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  92  zone. Therefore, the energy and the amplitudes of the oscillations of Rj in the first spring decreased very quickly, and the curve converged towards the R2 curve as shown in the lower graph of Fig. 22, where A(t) was the support load history. This behaviour was confirmed by many experiments on reinforced concrete beams (64).  The test conditions for the present impact tests were  similar to those  described above, but with two major differences. a) . The  rubber  supports  were  placed beneath the concrete tie. The stiffness of the second spring in Fig. 21 should thus be reduced, due to the new spring connected to it in series, and thus both the duration of the bend loading, and the time to the peak bending load, were extended. This was helpful for separating  the  inertial and bending  Figure 22. Response of the Vibration Modal  force contributions to the tup signals. b) . A segment of rail and rail seat pad was added to the contact zone between the tup and the concrete specimen. The rail segment itself should not change the load history very much, since its mass is small compared to the hammer, and can be combined into mass 1 in Fig 21. However, the rail seat pad can protect the concrete surface from damage, and thus prevent the oscillation energy of the R\ force from dissipating very quickly in this damage. Moreover,  the pads can also vibrate elastically with low  damping (the permanent deformation of the pad in one blow was very small). Hence,  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  93  following a high amplitude pulse due to the inertial effect of accelerating M2, there was a relative stronger oscillation of the force Rj about the force R2, with a much slower convergence than the system without the rail seat pad.  Figure 23. Relationship of Tup load and Bending Load  Fig. 23 shows a typical tup load history and the support load history for an impact test of a tie with a rail seat pad and rubber supports. The support load history was measured using a flat plate load cell placed between the rubber support and the tie. Since the development of the support load is basically synchronous with the bending load (see Fig. 22), the plot in Fig. 23 confirms that in the early part of the tup load history, the inertial load made the major contribution to the apparent tup load, while in the later part, the bending load dominated the load history, with a high frequency oscillation superimposed on it. This oscillation was primarily due to the spring characteristics of the rail seat pad, instead of the inertial load. Therefore, if the tup load vs. time curve can be  94  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  fitted with a smooth curve (see the load history plots in Figs. 20 and 22), the bending load contribution to the load history can be identified. 1000  0  2  4  6 Time (ms)  8  10  12  Figure 24. Curve Fitting of Measured Tup Load Signals  Fig. 24 shows both the tup load history and its equivalent smooth curve for a concrete tie. The fitted curve was obtained using an eighth power polynomial digital curve fitting technique. The principle behind this technique is to choose a best fit curve such that the sum of the square of the deviations between the two curves is minimized. The form of the fitted curve was found to be very similar to those shown in Figs. 20 and 22. Although the amplitude of the inertial load was reduced, it was not of interest in evaluating the properties of the materials in this test.  95  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  It should be noted that this curvefittingtechnique, sometimes being used in the vibration  modal analysis  (74), is similar, to some extent, to the filtering technique as shown in Fig. 25. When the frequencies of forces Ri and R2 varied not only with different types of  TUP LOAD (KN)  600 500 t i, 400 i < : / \ ; / * 300 *. *?*.\ > •/ ' ' 200 100 -  » i,  o  *  •  -  •  •  # A' 4  •  ».  *  i  i  <s <•  i  i  i  0  ">  «  -  <•  + FILTER ON FILTER OFF (fitting curve)  <c  i  i  i  0 2 4 68  Y \ \  o  h b  \  <« ^  \ \  o  \  "  i  \  12 14 16  J0  TIME (MS)  Figure 25. Fitting and Filtering Comparison  pads and rubber supports, and also with the extent of damage of the concrete ties, it was difficult to choose a suitable cut-off frequency for the analogfiltering.A poor choice of the cut-off frequency may greatly affect the calculation of the bending load R2. Moreover, analogfilteringmay cause a phase shift; the filtered signals were delayed by the filter by about 1.6 ms , for the example shown in Fig. 25. . Therefore, all of the values for the maximum bending load P , and the time to the m  peak bending load t , were determined using the fitted curve as shown in Fig 24. The m  loading rate was given by:  LR - P l m  t. m  (21)  5.4.4. Concluding Remarks  In the multi-blow impact technique, the beam undergoes the acceleration phase, when the bending load is lower then the tup load, and a deceleration phase, when the bending load is greater than the tup load. When the beam is in the elastic rebound period, it releases a portion of its stored strain energy back to the hammer.  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  96  Since it is difficult to simulate actual support conditions in track, and giving consideration to the limitations of laboratory equipment, three supports, rail seat pads and rubber support pads were used in the impact tests. This complicated the analysis of the deformed shape of the ties under impact. However, the fact that the tie remained largely intact after most impact, i.e., the system had no significant inertial or kinetic energy loss due to the broken pieces of the specimen, and therefore permitted the adoption of a simplified analysis method. The method based on the Impulse and Momentum Theory requires only the tup load history record (see Eq. 19), which can be measured reliably using the load cell and one channel of the data acquisition system. The total area under the load vs. time plot is not influenced by the analog filtering (59), and has been used most of the time to evaluate the fracture energy of the ties. The load vs. deflection method can not only calculate the fracture energy of the beam, but also display the relationships between the load and the deflection of the tie; it needs the tup load and acceleration at mid-span history data. It has been used when the deflection of the tie was involved in the analysis. The bending load and the corresponding loading rate can be obtained from the fitted curve representing the tup load history, in which the maximum value for the second peak can be considered as the maximum bending load.  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  97  Appendix-Chapter 5. "Multi-blow" Impact Testing on FRC Beams  In order to develop the "multi-blow" impact technique, the impact testing of a series of concrete beams was conducted The types of the specimens used in this series of tests are listed below:  Table 10. SFRC Specimen Types. Beam Notation S3 S4 S5 W  No. of Beams Tested 2 3 2 3  Fibres Used 0.75% hooked steel fibres, <|>0.5x30 mm 1.00% hooked steel fibres, <|)0.5x30 mm 1.50% hooked steel fibres, <|>0.5x30 mm 0.75% crimped steel fibres, <|) 1.0x50 mm  The dimensions of the SFRC specimens were 102.4x102.4x355.6 mm. The basic matrix mix design was 1.0:0.4:2.4:2.2 (cement : water : fine aggregate : coarse aggregate), with a maximum aggregate size of 10 mm. A superplasticizer was used to provide reasonable workability. The specimens were demolded in one day, cured in water, and tested at an age of 14 days. In this series of tests, a 60 kg drop hammer was used and the drop height was 150 mm. The support span was 305 mm (12") (Fig. 26). Most of the beams were not broken at the first blow.  98  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  <— Hammer Tup & Load Cell  A 150 mm  i  ,  Concrete Beam  152.4 mm ,„ 152.4 mm  Figure 26. Impact Test Setups For SFRC Beams The previous "single blow" impact technique (10, 43) was used for analyzing those SFRC beams which failed completely at thefirstblow in this series of tests. For those beams which did not fail under the first blow, however, the method of analysis had to be modified. In the following, the original method is introduced briefly, and then the modifications made for the present study are described. 1) If the system can be approximated by a single degree of freedom model, and the damping of the beam can be neglected, then the equation of dynamic equilibrium is:  Mii(t) + P (t) = P/t)  (22)  b  where M is the generalized mass of the beam, P is the tup load, P is the true t  b  bending load and u is the mid-span acceleration of the beam. Mti(t) may be referred to as the inertial load, />,. Then, the true bending load is  99  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  (23) When the specimen is broken by a single blow, the measured accelerations ii(t), and hence P„ are always positive. Thus, the bending load P is always less than the tup b  load, P . However, when the beam does not fail completely under a single blow, it must t  undergo first an acceleration, and then a deceleration before it finally comes to rest. During the deceleration, w is negative, and hence so is P . Thus, P will be greater than P t  b  t  during this period. Fig. 27 shows a typical example with both tup load and true bending load vs. deflection curves for a beam which was not broken at the first blow; P is greater b  than P at certain times during the impact event. t  70 60 k  Tup Load  50  0 0  Bending Load  1  2  Deflection (mm)  3  4  Figure 27. Load vs. Deflection Curve for S3-2 (0.75% Steel Fibres)  If the beam is broken by a single impact, the flexural energy absorbed by the beam  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  100  (defined as the area under the complete bending load vs. deflection curve) is less than the total energy lost by the hammer during impact. The difference between the total energy lost by the hammer and the flexural energy absorbed by the beam represents the sum of the inertial energy and the kinetic energy of the broken pieces of the beam. However, if the beam is not broken into two or more pieces, the flexural energy absorbed should be very close to the energy released by the hammer. That is, the areas under the bending load versus deflection curve and the tup load versus deflection curve should be similar. The reason is that almost no energy transferred from the hammer to the beam, via the tup load, was lost. The inertial and kinetic energies transferred to the beam while it was being accelerated were gradually released back to the system as the beam returned to rest. Most of the energy stored in the machine, mainly in the form of elastic energy in the tup, had been released since the tup load had dropped to the zero. The other energies dissipated, such as heat and vibration of the machine, the energy due to the residual strain of the rail seat pads and rubber support pads, etc., were assumed to be small enough to be neglected. 2) Since the beam remains intact (though cracked), some elasticity is retained; that is, after the beam reaches its maximum deflection, it springs back to some extent. During this time, the beam velocity at mid-span, U (obtained by the integration of the acceleration ii) is negative, and the deflection u (obtained by integration of the velocity u ) decreases from its maximum value. Figure 27 shows a typical example. Note that the bending load did not fall to zero, since the beam and the hammer maintained contact as the beam rebounded. In this period of time, the beam was releasing stored elastic energy back to the hammer. Thus, the flexural energy consumed by the damage to the beam should be the difference between the area under the upper branch of the bending load versus deflection curve (representing the downward deflection of the beam) and the area under the lower branch of the curve (which represents the rebound of the beam), as  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  101  shown in Fig. 27. Table 11 compares the fracture energies obtained by the integration of the tup load vs. the deflection relationship (referred to as tup load energy), to those obtained by integration of the bending load vs. deflection relationship (referred to as bending load energy) for the concrete beams which were not broken under the impact blow. A halfsine curve distribution of beam deflection as well as of acceleration distribution along the beam was assumed, which is believed to fit the unbroken beam better than the linear distribution. Specimen notation with an "s" or "t" as the last symbol in the table represents the second and the third blow, respectively.  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  102  Table 11. Concrete Beam Fracture Energy Obtained by Two Analysis Methods Specimen Notation  Maximum Tup Load (kN)  Maximum  Total  Bending Load Deflection (mm) (kN)  Tup Load Bending Load Energy (N.m)  Energy (N.m)  S3-2  60.5  50.0  3.70  66.0  66.0  S3-2s S3-2 Total:  38.7  21.8  3.4 69.4  62.7  48.1  6.7 72.7  S3-3  0:40 4.10  S3-3s S3-3 Total: Average:  47.1  27.7  61.6  49.0  0.52 6.48 5.29  6.0 77.2 74.9  2.1 73.3 71.3  S4-ls S4-1 Total:  77.4  32.9  S4-3  3.81  63.2  9.8 80.7  50.7  17.8 88.7  65.3  0.50 2.68  63.2  S4-3s S4-3 Total:  50.7  21.4  2.6 65.8  S4-4  52.2  8.3 71.5  69.2  0.33 4.14  S4-4s S4-4 Total: Average:  49.0  26.6  1.00 5.47 4.10  19.9 88.3 82.8  11.9 80.2 75.6  78.7  62.0  3.63  72.3  72.1  S5-2s S5-2 Total:  67.5  32.1  1.00 4.62  19.4 91.8  10.6 82.8  S5-3  60.7  54.7  2.85  78.4  78.4  S5-3s S5-3 Total: Average:  64.2  37.0  69.7  58.3  0.39 3.23 3.93  13.3 91.6 91.7 76.2 47.4  6.7 85.0 83.9  75.9 47.4  0.97 10.23 8.31 3.64 5.97  7.0 130.6 65.3 54.9 83.6  3.2 126.6 51.2 45.7 74.5  S4-1  S5-2  -  -  75.9 -  -  _  70.1 -  -  -  -  56.1  -  -  -  53.0 -  -  W-l W-ls  67.5 33.1  51.4 25.6  W-lt W-l Total: W-2 W-3 Average:  23.0  22.2  69.0 68.4 68.7  50.4 52.8 51.6  -  -  5.96  2.18  4.47  4.13 5.13  71.2  70.9  68.4  71.2  70.9  68.4  Chapter 5. Impact Testing of CXT Pre-tensioned Concrete Ties  103  With due attention to the results of the blows which did not result in completely fracture of the beams (highlighted in the table), the tup load energies were the same as the bending load energies except in two cases, where very little difference existed. For the blows which totally broke the beams, the two energies were significantly different, as expected, since the broken pieces of the beam consumed considerable energy in the form of kinetic energy. Actually, this method of analysis can be carried out more simply by just considering the initial condition and the final conditions of the impact event without taking into consideration the details of the impact event itself. If we take the tie with the rail pads and the rubber supports together as an isolated system, this system receives energy only from the work done by the hammer. Since the ties have some elastic rebound, the work done by the hammer on the tie is positive before the deflection reaches its maximum, and negative after that point because the tie displacement direction is opposite to that of the load direction. At the end of the impact event, the energy balance can be expressed as:  W-W.= Ef+Es+Ek+Ej. +  (24)  where: W = Positive work done by the hammer, +  W.= Negative work done by the hammer, = Elastic strain energy of the tie, Ef = Fracture energy of the tie, Efc = Kinetic energy of the tie, E = elastic or strain energy retained by the rail seat pad and rubber r  support.  Chapter 5. Impact Testing ofCXTPre-tensioned Concrete Ties  104  Although at this stage the isolated system will still have some elastic energy stored in the rail seat pads and rubber support pads, and some elastic and kinetic energy in the tie, when the system finally comes to rest, most of these energies will be transferred either into residual strain energy of the tie or consumed by further micro-cracking in the tie, both of which can be considered as part of the fracture energy. Since the rubber supports and pads were carefully checked after the accumulated impact tests for each tie, and no significant permanent deformations were found, it is believed that very little energy was consumed by the rail seat pads and rubber support pads for each blow, in comparison to total fracture energy. Therefore this contribution can be neglected. Thus the energy balance becomes W - W.= Ef +  (25)  The left side of the equation is simply the area under the tup load vs. deflection curve. The tup load can be obtained directly from the load cell built into the tup, and the deflection at mid-span of the tie can be obtained by double-integration of the acceleration recorded by the accelerometer mounted at mid-span:  u  = If ii(t) d t  CHAPTER 6. E F F E C T OF LOADING CONDITIONS ON DETERIORATION OF TIES  Two hammer weights, 345 kg and 504 kg, with the same drop height of 1524 mm, were used for the impact tests of the CXT concrete ties. In conjunction with the 345 kg hammer, four combinations of rubber supports and rail seat pads were used. With the 504 kg hammer, one polyurethane rail seat pad , but two types of the rubber support pads, were used. In this Chapter, the test results for each hammer mass willfirstbe introduced, followed by the comparison between them.  6.1. Impact Tests with 345 kg Hammer  The results of the static tests carried out after various numbers of impact blows with the 345 kg hammer have already been discussed in Chapter 4. The residual load bearing capacities indicated that the support conditions had a great influence on the tie properties under impact. An analysis of the impact results can more clearly reveal the deterioration of the ties during the impact process. Table 12 lists the main results of the impact tests. The residual static fracture energies shown on the bottom line of the table were obtained from the static tests for these ties after being subjected to impact testing, which are described in Chapter 4. The total fracture energy under impact shown in the table is the cumulative sum of the fracture energy for all of the hammer drops. Regarding to this energy, the total potential energy of the falling hammer for each drop needs to be noted, that is 105  106  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  345£gx(0.91g)xl.5m = 4615N.m = 4.6/fc/V.m Figs. 28 and 29 show the load histories and the schematic descriptions of the cracking mode under the different test conditions. The tup load signals in the tests of this group were treated by an analog fdter with an 800 Hz low-pass frequency; Thus, the time to the peak load was delayed by about 1.6 ms, as shown in Chapter 5.  Table 12. Impact Tests of CXT Ties with 345 kg Hammer  Tie ID  PSS  PHS  PSH  PHH  Rubber Support  Soft  Hard  Soft  Hard  Rail Seat Pad  EVA  EVA  Poly  Poly  Total No. of Blows  10  8  10  8  No. of Blows at First Crack  10  1  6  1  Peak Bending Load at First Blow (kN)  338  526  339  539  Peak Bending Load at Last Blow (kN)  328  458  320  380  Peak Load Reduction (%)  3.0  12.9  5.6  29.5  Loading Rate at First Blow (kN/ms)  45.7  119.5  45.8  122.5  Loading Rate at Last Blow (kN/ms)  41.0  95.4  40.0  79.2  Loading Rate Reduction (%)  10.3  20  12.7  35  18.7  27.7  18.7  Total Fracture Energy under Impact (kN-m) 28.5 Mode of First Crack  Flexure Flexure- Flexure Flexure -Shear  Shear Residual Static Energy (kN.m)  7.9  5.4  7.5  2.9  Figure 28. Load History for CXT Tie with Soft Rubber Supports and Poly Rail Seat Pad and Schematic Description of Cracking Mode  Figure 29. Load History for CXT Tie with Hard Rubber Supports and Poly Rail Seat Pad and Schematic Description of Cracking Mode  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  109  From Table 12, with soft supports there was not much degradation of the tie even after ten drops of the hammer. The maximum forces and loading rates showed little change, even after flexural cracks had appeared at the 6th or 10th drop. With hard supports, however, the cracks appeared at the first drop, and by the eighth drop there was a considerable decrease in the stiffness of the system, in terms of both the maximum bending load and the loading rate, indicating considerable damage to the tie. By comparison between Figs. 28 and Fig. 29, the effect of the support rubber stiffness on the loading rate and the crack mode can be seen. With a soft support, a flexural crack appeared only at the sixth repeated impact. With a hard support, a shearflexure crack appeared at the first blow. Increasing the stiffness of the rubber support had the effect of increasing the impulsive force, and at the same time reducing the time to peak load, i.e. increasing the loading rate. It should be noted that in Fig. 29, (compared with Fig. 28), the first peak of the tup load, i. e., the inertial load peak, disappeared. This was because 1) theoretically, the inertial load is at a maximum at the moment of impact, with a very high frequency; however, the analog filter can significantly reduce the high frequency signals, and at the same time delay the time at which the peak inertial load appears (59); and 2) the time to the peak bending load, which was considered to be the second peak in the curve, depends on the stiffness of the rubber support for the same type of the tie. Since the hard support rubber was used, the time to the peak bending load was just 4.4 ms, which is very close to the time of the first inertial peak load in Fig. 28, about 3 ms. If at 3 ms in Fig. 29 the bending load was higher than the filter-reduced inertial load, then the inertial load peak would be totally eclipsed. Fig. 30 shows clearly how the inertial load was eclipsed in the test with the hard support. This situation would not occur for impact tests with the soft rubber support because the time to the second peak of the curve was much larger, about 8-9 ms, and the bending load at the second peak was much lower.  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  110  TUP LOAD (kN)  600  I  1  TIME (ms) •  HARD PAD+SOFT SUPP.  °  SOFT PAD+SOFT SUPP.  +  HARD PAD+HARD SUPP.  A  SOFT PAD+HARD SUPP.  Figure 30. Load Histories of the First Impact with the Various Support Conditions  The load history curves for the ties with the EVA rail seat pads were very similar to those for the ties with the polyurethane rail seat pads for the same rubber support used, as shown in Fig. 30, indicating that the stiffness of the rail seat pad had a smaller effect than the stiffness of rubber support. In terms of the fracture energy, the ties with the hard supports consumed much less energy than the ties with the soft supports. They were also more severely damaged in eight blows, especially tie PHH, which had the largest decrease in its static resistance capacity. On the other hand, the ties with the soft supports absorbed much more energy  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  111  and maintained almost all of their static resistance after ten impact blows (see Table 12 and Chapter 4). The different fracture energies absorbed and degrees of deterioration under impact can be attributed primarily to the different fracture modes to the ties. The ties with soft supports underwent flexural cracking; while the ties with hard supports exhibited a shearflexure cracking, and no significant pure flexural cracks were found on the tie. The concrete tie used here was designed primarily for flexural loading conditions. It contains 28 longitudinal high strength wires designed to resist the high applied moments, but no stirrups or transverse steel to withstand shear. As a result, the flexural failure of the tie involved yielding of the steel wires, or slip of the wires in the concrete matrix, and more distributed flexural cracking in addition to thefirstflexural crack at mid-span. The shearflexure failure of the tie, on the other hand, consumed much less, if any, energy in the yielding of the wires, since no transverse steel existed. In addition, the tie did not develop flexural cracks near the mid-span after the first shear-flexural crack formed. Instead, only a few shear cracks appeared after the first cracking, causing severe deterioration of the tie. As a result, less energy was consumed by the tie. Photographs of the typical crack modes of the ties will be shown later in this Chapter. An attempt to analyze the mechanics of the fracture mode under impact will be described in Chapter 7. Similar to the conclusions drawn from the static tests of the ties, carried out following the impact tests, the results of the impact tests themselves also indicate that the effect of the stiffness of the rail seat pads was slight when the soft rubber support was used. Comparing the data for ties PSS and PHS, the peak loads, loading rates at the first blow, percent reductions in the peak load, loading rate at the last blow, and the total fracture energies consumed, were very similar. With hard supports, however, the stiffness of the pad had a moderate effect on the tie behavior, in terms of the difference in the percent reductions in peak loads and loading rates from the first blow to the last blow.  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  112  6.2. Impact Tests with 504 kg Hammer  With the hard rubber supports, the tie failed completely after only two blows. With the soft rubber supports, the tie was able to sustain 10 blows. Only the polyurethane rail seat pad was used for these tests. The data in this set of tests were collected without the analog filter, and were handled using the curve fitting technique described in Chapter 5. Table 13 shows the impact results for the 504 kg hammer. For tie SH, the peak bending loads were very close to each other under the first nine impact blows, and dropped significantly under the last blow (see Fig. 39 in this Chapter). In order to show the substantial difference between the two support conditions, the peak load and the loading rate under the ninth blow for tie SH were used in comparison with those under the second blow for tie HH. Fig. 31 shows the effects of the rubber support stiffness on the shape of the load history curve. Figs. 32 and Fig. 33 compare the load histories for thefirstblow and for the last blow of the impact tests on the same tie, indicating the degradation of the ties. Fig. 34 shows schematically thefirstcrack mode of the tie with the hard rubber support. This was a typical shear crack, extending from the loading point to the support point. The first crack of the tie with the soft rubber support was a flexural crack, similar to that shown schematically in Fig. 28.  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  Table 13. Impact Tests of CXT Ties with 504 kg Hammer  Tie ID  SH  HH  Rubber Support  Soft  Hard  Rail Seat Pad  Poly  Poly  Total No. of Blows  10  2  No. of Blows at First Crack  1  1  Peak Bending Load at First Blow (kN)  536  606  Peak Bending Load at Last Blow (kN)  525*  442  Peak Load Reduction (%)  2.2  27.0  Loading Rate at First Blow (kN/ms)  82.5  159.4  Loading Rate at Last Blow (kN/ms)  81.9*  105.3  0.7  33.9  Total Fracture Energy under Impact (kN.m) 36.1  9.7  Loading Rate Reduction (%)  Mode of First Crack * The data is for the ninth impact blow.  Flexure  Shear  Chapter 6. Effect of Loading Conditions on Deterioration of Ties TUP LOAD (kN) 800  " X  700 605.8  Hard Supp + Poly Pad Soft Supp + Poly Pad  600  \  500  f  V  400  536.4  »'  / \ \  300  \  XX  k  200 100 0  _l  I  I  4I  I  I  6  1  8L  J>»J  1 10  l_i  1 12  1—  TIME (ms)  Figure 31. Load History of the First Blow with Different Support Conditions Hammer Mass = 504 kg TUP LOAD (kN) 800  0  4  8  12  16  TIME (ms)  Figure 32. Load History of the Tie with Hard Supports Hammer Mass = 504 kg  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  115  Tup Load (kN) 600 .•536.4  jf 400 - f  524.6  O  First Blow  -t-  Ninth Blow  \  300  200  100  0^ — 0  :  1  1i  1i  i1  1  2  4  6  8  10  1  « ® J  12  14  Time (ms)  Figure 33. Load History of the Tie with Soft Supports  ~  800  TIME (ms)  Figure 34. Fracture Mode of the Tie with Hard Supports  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  116  The dominant effect of the stiffness of the rubber supports on the behavior of the ties was also very clear from the impact tests with the 504 kg hammer: a) . The maximum load atfirstblow was about 12% lower for the tie with the soft supports than with the hard supports (Fig. 31). b) . The loading rate at thefirstblow was much lower with the soft supports, about half of that with the hard supports (Fig. 31, Tab. 13). c) . The reduction of the maximum loads from thefirstblow to the last blow was 27% with the hard supports in 2 blows (Fig. 32), but only 2.2% with the soft supports in 9 blows (Fig. 33); The reduction of the loading rate from thefirstblow to the last blow was 33.9% with hard supports in 2 blows, but only 0.7% with the soft supports in 9 blows (Tab. 13). These data strongly imply that the stiffness and the load resistance of the tie with the soft supports had changed very little; while the tie with the hard supports had seriously deteriorated. d) . The total energy the tie consumed (Tab. 13) with hard supports was only 9.7 kN-m in 2 blows and the tie was almost completely broken. With the soft supports, the tie absorbed 36.1 kN.m in 10 blows, and still remained relatively intact, though cracked. e) . The photographs in Figs. 35 to Fig. 38 show that there was very severe damage and a large shear crack for the tie with hard supports; but only mild damage and both flexural cracks and flexure-shear cracks for the tie with soft supports. The fracture mode was thus totally different.  Figure 36. Tie with Soft Supports After 10 Blows  Figure 38. Tie with Hard Supports After 2 Blows  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  119  The different fracture energies absorbed and degree of deterioration of the ties with different support conditions under impact with the 504 kg hammer, can again be attributed to the different fracture modes of the ties. Similar to the tests with the 345 kg hammer, the fracture mode with the hard supports was of a brittle nature, but in a pure shear mode instead of a shear-flexural mode. Several of the inclined shear cracks developed directly from the loading point to the support point (Fig. 37 ) and the concrete between these cracks was completely crushed under the high diagonal compressive stresses (Fig. 38)— a typical compression-shear failure. It was a premature failure with little yielding of the steel wires. It should be noted that between the two diagonal shear cracks on the tie shown in Fig. 37, no visible flexural cracks appeared, resulting in much less fracture energy. To summarize this section: For soft supports: low maximum load; low loading rate; the tie absorbs a great deal of energy before failure; ductile flexural fracture mode. For hard supports: high maximum load; high loading rate; less energy absorbed before failure; compression-shear brittle failure mode.  6.3. Comparison of the Impact Tests Using the 345 kg and 504 kg Hammers  In this section, data for the ties with the same polyurethane rail seat pads is used to compare the properties of ties with different support conditions and a different hammer mass. The effect of the loading rate will be emphasized. Fig. 39 summarizes the maximum loads for all blows applied to the ties with two different support conditions and two different hammer weights, and their corresponding loading rates at first blow.  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  120  MAX. T U P LOAD (kN) 0  I _, „  0  1  1  2  3  4  5  6  7  8  9  504 kg HAMMER WITH HARD SUPPORT  10  NUMBER O F BLOWS  Figure 39. Maximum Load at Impact with Different Support Conditions and Hammer mass  The deterioration of the ties, in terms of the reduction in maximum load for each blow for the same test condition, was most severe for the tie with hard supports and heavier hammer— a large decrease in the maximum load after only two blows; it was least for the tie with soft supports and the lighter hammer— almost no change in the maximum load in 10 blows. The curves for the other two conditions were intermediate between these two. It is interesting to note that using soft rubber supports, even with a hammer mass increase of slightly greater than 50%, the tie still behaved better under impact than the tie using the hard rubber supports and light hammer. From Fig. 39, it can be seen that the four different test conditions induced four different loading rates and four corresponding deterioration rates. The order of the  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  121  loading rates was the same as the order of the deterioration rates. The relative data are given in Table. 14.  Table 14. Effect of Loading Rate and Maximum Load on Cracking and Fracture Energy  Specimen I.D.  PSH  SH  PHH  HH  Type of Support  Soft  Soft  Hard  Hard  Hammer Mass (kg)  345  504  345  504  Loading Rate at First Blow (kN/ms)  45.8  82.5  122.5  159.4  Max. Bending Load at First Blow  339  536  539  606  Flexure  Flexure  Flexure-  Shear  (kN) First Crack Mode  Shear Total No. of Blows  10  10  8  2  First Crack Appear at (blow)  6  1  1  1  Major Drop of Max. Load at (blow)  None  10  8  2  Total Fracture Energy under Impact  27.7  36.1  18.7  9.7  Very  Good  Poor  Very  (kN-m) Condition of Tie after Impact tests  Poor  Good Residual Static Energy ( kN-m)  7.5  N/A  2.9  N/A  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  122  Of course, the deterioration rate was not determined only by the loading rate but also by the magnitude of maximum load at first blow. However, taking the two intermediate curves in Fig. 39 in consideration, which were for the soft support with the 504 kg hammer and the hard support with the 345 kg hammer, respectively (SH and PHH in Table. 14), the maximum loads at thefirstblow were almost the same, but the loading rate at the first blow for the tie with the hard supports and the 345 kg hammer (PHH) was 49 % higher than that for the tie with the soft supports and the 504 kg hammer (SH). Here, the effect of the loading rate on the dynamic behavior of the tie can be seen more clearly. The tie with the hard supports had a loading rate of 122.5 kN/ms (or about 150 kN/ms if the delay in the time to the peak load in thefiltereddata for PHH is considered, see Chapter 5), and experienced a significant deterioration at the eighth blow, in terms of the great reduction in maximum impact load; while the tie with the soft supports had a loading rate of 82.5 kN/ms and exhibited a major reduction in maximum impact load only at the tenth blow. In Table. 14, it is also shown that for the test with the lower loading rate , the tie absorbed 36.1 kN-m fracture energy and the integrity of the tie was retained (Fig. 36); for the test with the higher loading rate, the fracture energy was 18.7 kN-m and the residual static loading capacity was almost totally lost (see Table. 14). The reason for this is, again, the different fracture modes of the ties. Under a high loading rate, thefirstcrack on the tie was of the flexural-shear type as described in section 6.1., and was capable of absorbing much less energy; whereas under a lower loading rate, on the other hand, the first crack was a normal flexural crack, and the tie exhibited more flexural and flexural-shear cracking, consuming a much higher energy. In brief, the higher loading rate induced a more "brittle" failure mode. As the loading rate increased, the principal mode of cracking changed from flexure to shearflexure and then to shear.  Chapter 6. Effect of Loading Conditions on Deterioration of Ties  123  6.4. Summary The stiffness of the rubber supports played an important role in the dynamic response of the ties to an impact pulse with about 10 ms duration and 300 to 600 kN magnitude in the present study. With soft supports, the ties exhibited a low maximum load, low loading rate, absorbed much energy before failure and exhibited a "ductile" flexural fracture mode. With hard supports, there was a high maximum load, high loading rate, less energy absorbed before failure and a flexure-shear or compressionshear "brittle" failure mode. The stiffness of the rail seat pad had a moderate effect, when the hard support was used, on the behaviour of the tie subjected to the pulse with 10 ms duration and 300 to 500 kN magnitude. Higher loading rates induced a more brittle failure mode. As the loading rate increased, the principal mode of cracking changed from flexure to flexure-shear and then to shear.  CHAPTER 7. FRACTURE MODE ANALYSIS  7.1. Introduction  Concrete structural members designed to fail in a ductile manner (flexural failure) at slow rates of loading have been observed to fail in a brittle manner (diagonal tensionshear failure) under impact loading (2, 3, 10). Thus, the favorable increase in tensile and compressive strengths of concrete with an increase in the rate of loading, may be offset by an adverse change in the mode of failure. This phenomenon was also observed on beam-column joint specimens (4), implying that during an earthquake a structure may be subject to a dangerous brittle collapse due to the high rate loading (5). Similar to the phenomena observed in the current study, some earlier studies (2, 64) also showed that a shear crack could appear on a simply supported concrete beam under impact before any significant bending cracks developed . In the case of slabs under impact, this behaviour was more pronounced. Slabs may fail due to punching shear with very little bending involved (16, 17, 20); with an increase of the loading rate, the tendency for local damage or shear failure increased (18, 19). Studies of the mechanics of the fracture modes under impact have been carried out mostly in impact and shock engineering (75) and mechanical engineering (76); they have been also carried out in civil engineering, especially for slabs (77). Most of these studies have used finite element computations, or stress wave analysis. The entire failure process of the structural member and the detailed stress-strain distribution of the material can be 124  125  Chapter 7. Fracture Mode Analysis  described by these methods. However, for such analyses, some basic properties of the materials involved in the impact are required, such as the dynamic stress-strain relationship over the entire loading range for concrete, steel reinforcement and the steel/concrete interface; the properties of the impact contact zone, and the non-elastic stress wave speed in the materials and at the interface for the whole loading range. These properties may be different for different loading rates and different test setups, and hence are often unknown for a specific situation. In this chapter, an attempt is made to analyze the mechanics of the tie failure mode under impact using a relatively simple classic engineering mechanics approach, and to explain the reasons for the change in crack modes for the different test conditions used in this study. 7.2. Bending Moment and Shear Force Under Impact  At the same load level and with the same support span, a beam will have different bending moments and shear forces at mid-span under impact loading than under static testing. This is the basic concept of the present analysis. Starting with a simply supported beam, as shown in Fig. 40, the difference can easily be demonstrated.  \  126  Chapter 7. Fracture Mode Analysis  (a) Static Loading PI  | P«  P/2  '-  =  *  '-  *•  (b) Impact Loading  (c) Equivalent Static Loading |P = »- ' p  p  b  ^  —  i  —  ^  —  *  —  (d) New Equivalent System P.  W I f —'—#-  Figure 40. Loading Scheme in Static and Impact Loading  127  Chapter 7. Fracture Mode Analysis  Fig. 40(a) represents a static loading condition. At the mid-span of the beam, the shear force, Q, the bending moment, M, and their ratio Q/M, are Q=|,  (26)  M=2--l, 2  (27)  Q/M =  (28)  -  l  Here, both Q and M are proportional to the magnitude of the applied load P for a given span. Fig. 40(b) represents the impact loading condition. For this condition, a distributed inertial load, due to the distributed accelerations along the beam, appears; P is the t  applied impact load, F/ is the resultant of the distributed inertial reaction of the beam, and R\ is the support reaction. A linear distribution of the acceleration and thus of the inertial load is assumed here. This represents the situation for brittle materials such as plain concrete beams under impact (10). F/ can be shown to act at ^/ from mid-span, i.e. at the centroid of the inertial distribution on each half of the beam. Then, Q = R F,=&;  (29)  M=R l+F -  (30)  ]+  l  x  r  Now, the shear Q is still proportional to the applied load P , and the moment M no t  longer depends only on the magnitude of the P The load P is balanced not only by the t  t  reaction force Rj but also by the inertial reaction F/. The magnitude of the bending moment at mid-span now depends on the relative magnitudes of Rj and Fj. The larger the relative magnitude of F,\ the smaller the moment M, since the force arm for F,- is  128  Chapter 7. Fracture Mode Analysis  smaller than that of Rj. To evaluate the bending energy of the beam, excluding the energy required to accelerate the mass of the beam, Banthia (10) adopted an equivalent static loading system as shown in Fig. 40(c). By measuring the accelerations along the beam, the distributed inertial load could be determined. Using the principle of virtual work, the distributed inertial load could be generalized as a point inertial load, /*/, acting on the beam at the mid-span. Then, the "true" bending load, Pj,, was obtained by subtracting this inertial load from the applied load. Then the bending moment was simply proportional to the bending load Pf since the effect of the inertial load had been eliminated, i.e. Ji  (31)  2  It should be noted that this equivalent system can only be used for evaluating the bending moment. The shear force can not be derived from this system; it is equal to half of P as shown in Fig. 40(b) and Eqn. (29), instead of the lower value, half of P Then, t  D  the shear to moment ratio becomes  (32)  By comparison with Eqn. (28), it is found that the shear : moment ratio under impact loading is increased. The magnitude of the increase depends on the ratio of applied load and bending load, which is always greater than 1 at the beginning of the impact event. The equivalent static system for the bending moment (Fig. 40(c) ) leads to a formula for the moment under impact which has the same form as that under static loading ( Fig. 40(a)), with the applied load P replaced by P . Then this system can be D  easily used to calculate bending moment and uniaxial stresses at mid-span for the impact  129  Chapter 7. Fracture Mode Analysis  tests. However, since this system cannot be used to analyze the shear, a new equivalent system needs to be created. By writing the shear to moment ratio as  (33)  for impact loading, which has the same form as the ratio under static loading (Eqn. 28), and equating it with the Eqn. 32, i.e.,  (34)  an equivalent span of the beam /* can be derived as  r=^i<i  (35)  The new equivalent static system, for both shear and moment and shear : moment ratio, is shown in Fig. 40(d), where the applied load is unchanged to reflect the same shear force at mid-span under impact as under static loading; the span is reduced to reflect a lower bending moment under impact, equivalent to eliminating the inertial effect. In this system,  (36)  H.i*P  M=  2  P P LL.LL.I  =  2 P,  =  LLIP 2  (37)  130  Chapter 7. Fracture Mode Analysis  (38)  QIM =  and  Q, M and Q/M are thus the same as those under impact loading which was previously derived. Having shown that this system can be used to evaluate both bending moment and shear at the mid-span for impact testing, the following fracture mode analysis will be based on this system. From the new equivalent system, it is found that increasing the loading rate is equivalent to reducing the support span. The applied load P can be increased to a higher t  level before flexural cracks are initiated in the beam since the bending moment may be significantly reduced by the inertial effect. However, the shear force at mid-span is not reduced (see Eqn. 29); it will increase at the same rate as the applied load. The Q/M ratio can therefore greatly increases. If the ratio increases to a value at which the shear has reached the shear cracking force while the reduced moment is still less than the flexural cracking moment, a diagonal shear crack will first appear on the beam. This phenomenon under impact is equivalent to that under static loading for a beam with a very short span. After the shear cracks occur, since the beam is normally designed for flexural failure and may not contain transverse reinforcements, the beam may fail very quickly by diagonal shear cracking without any significant flexural damage. In the new equivalent system (Fig. 40(d)), P is needed to estimate the equivalent D  span /*. Banthia (10) used the virtual work principle to derive the bending load Pfj in the equivalent system for bending moment (Fig. 40(c)). Alternately, based on the diagram in Fig. 40(b), if the distribution of the acceleration along the beam is known, a simple method may be adopted, as follows: The bending moment in the equivalent static system in Fig. 40(c) must be equal to the moment derived from impact system in Fig. 40(b). So, the expressions for M, Eqn.  131  Chapter 7. Fracture Mode Analysis  30 and Eqn. 31, can be equated. In addition, the force moment arm of the resultant inertial reaction, -^/, in Fig. 40(b) and Eqn. 30 should be changed to kl (0<£<1) to accommodate any type of distribution of the inertial load along the beam. Then, M =- f-l=R l  + F kl  P  ]  i  P =2R +2kF h  i  (39) (40)  i  There are two cases which should be considered: Case 1: If the acceleration at mid-span of the beam is measured, referred to as ii , c  and /?, is unknown, then using Eqn. 29, /?, can be replaced in the above expression, to produce P = 2R + 2kF. = 2(|- - F )+2kF = P, - 2( 1 - k)F, h  t  t  i  i  (41)  Since the distributed shape of the inertial load is usually known, or can be assumed to be linear for plain concrete beams and generally sinusoidal for reinforced concrete beams (10), the force moment arm kl is known, which is the distance between the center of the beam the and the centroid of the half section of the distributed shape. Also, F; is the area of the half section of the distribution shape. Taking the linear distribution as an example,  Where, p = density of the concrete, A = area of the beam cross section, m = total mass of the beam. In this expression,  pAu  c  represents the inertial load at mid-span, the peak value of  132  Chapter 7. Fracture Mode Analysis  the triangle for the distributed inertial load in Fig. 40(b). Hence F ; can also be simply obtained by calculating the area of the half triangle of the inertial load distribution. This principle is also effective for other types of distribution. Substituting k = 1/3 for the linear distribution case, and F ; into Eqn. 41, ^ = ^-2(1-^ = ^ - ^  P> = P,-\F,  =  (43)  P, -Q*jn> P, -\^m  (44)  If Pi is the part of the applied load due to the inertial effect which is to be eliminated from P , then t  (45)  P =\F^Ujn T  Note that F/ is not equal to 2F[ because F[ also contributes to the bending moment (see Fig. 40(b)) and so cannot be totally excluded from P for the bending load. t  Case 2: The support load R\ is measured, but the acceleration is unknown. (This may be easier experimentally in the laboratory). Using Eqn. 29, Eqn. 40 can be changed to  P„ = 2R + 2kF = 2R, + 2k(^--R )= X  i  x  kP, + 2(1 - k)R,  (46)  This equation will be used in the next section. In the linear situation, k = 113, and then,  P > = \ P , + ^  < > 47  From Eqns. 43 and 47, it is possible to evaluate the true bending load in impact testing, by measuring either the acceleration at mid-span or the support load, as long as  Chapter 7. Fracture Mode Analysis  133  the nature of the inertial load distribution is known. If a deflection measurement is made at the same time, the bending energy can be obtained from the area under the bending load vs. deflection plot.  7.3. Crack Mode Prediction  In the last section, the reasons for the possible crack mode shifting in impact loading was discussed. The question arises: how can one predict the crack mode in order to prevent the formation of a brittle shear crack under impact? A conservative solution is attempted here. The question actually is: which type of crack, shear or flexural, will occurfirston the beam? If the flexural crack forms first, much impact energy will be absorbed, and the flexibility of the beam will be increased, thus limiting the maximum contact load to a lower magnitude and giving a significant warning of failure. However, if the shear crack formsfirst,no flexural cracking will develop subsequently (as shown in Chapter 6 for the CXT ties), and since beams are designed primarily for the bending, the lack of transverse reinforcement may lead to a catastrophic failure. We must therefore ensure that the first crack to develop in a beam is not the shear crack. The shear : moment ratio, Q/M , is the determining factor; it was shown above that this ratio will significantly increase under impact loading. The larger the ratio, the more likely that a shear crack will appear first. According to Eqn. 34 and Fig. 40(d), the effective span /* determines the Q/M ratio, while in Eqn. 35,  Clearly, when PyPf is minimized, the corresponding /* is also minimized and  134  Chapter 7. Fracture Mode Analysis  Q/M reaches a maximum (see Fig. 40(d)). This is the most dangerous situation for shear failure. If an impact load reaches a particular value at this time, a shear crack is most likely to appear first. From Eqn. 41 and Eqn. 46, P„ = 2fl, + 2kF = P - 2(1 - k)F i  t  i  P =kP +2(\-k)R h  t  v  and thus when Rj becomes zero (F; is at a maximum), P reaches its minimum D  value, i.e., (48) Eqn. 48 has its practical meaning. Referring to Figs. 24 and 25 in Chapter 5., at the instant the falling hammer touched the beam, the beam was accelerated from rest to the same velocity as the dropping hammer in a very short time. Hence the acceleration and the inertial load could be very high; theoretically they are at a maximum at time zero (59); At that time the load has not^et been transferred to the supports, and so the support load is still close to zero (see Fig. 24 and 25 in Chapter 5. and Ref. (64)). At that moment, the beam acts as a free-free beam, that is, the impact load is balanced only by the inertial load, and no support load exists. (It should be noted that even when no support load exists, the bending load P is still not zero, due to the contribution of the n  inertial load to the bending moment.) Now, from Eqn. 48,  (49)  135  Chapter 7. Fracture Mode Analysis  In the linear distribution case, /* is -^/. From Fig. 40(b) and Fig. 40(d), it is to  * 1 found that since the effective span / in Fig. 40(d) is kl, or — / for the linear case, the same as the force moment arm of the resultant inertial force, the critical new equivalent system can be simply obtained from the impact loading diagram (Fig. 40(b)) by erasing the support load and using the resultant inertial load and its point of action as the new support load and support point. This principle may also be used for other types of inertial load distributions. Using the new equivalent static system with span Id , the mode of first cracking may be examined. Again taking the linear distribution as an example, if the static flexural cracking load P f is known in the static loading system as shown in Fig. 40(a) , with the c  support span /, and if the shear, V , required to cause diagonal cracking in the beam is c  also known, then the applied load to cause the shear crack, P , is 2V and must be cv  C  larger than P f to ensure a flexural crack to appear first under static loading. Since the c  effective span in the new equivalent system has been reduced by 3 times to ^/ in the impact tests (Fig. 40(d)), the flexural cracking load under impact will increase by 3 times to 3Pf, while the load to cause a shear crack remains the same. If 3P f is still less then c  c  P , a flexural crack will appear first. However, if the flexural cracking load under cv  impact, 3P f , is larger than P , a shear crack may occur first. Therefore, some design c  cv  modifications to the beam then need to be made, such as adding stirrups to increase the value of V . c  Since the effective span has been greatly reduced to only about one third that of the original, the beam may behave like a 'deep beam' with a very small span to depth ratio. In this situation, the shear crack most likely will extend directly from the loading point to the support. This has been confirmed by others (78, 79). Fig. 41 shows the distribution of  Chapter 7. Fracture Mode Analysis  136  the principal stresses in a deep beam and a suggested 'strut and tie model' to analyze the deep beam.  11 »  •  •  •  /  •  • t  i  \/  \  * *  t  »  /  X  • •  •  •  *  •  * • *  •  »  *  *  X  X  -  \  X  X  • •  *%  «  10 MPa • — i .  \  \  Predicted principal stresses  Flow of forces  End view  Figure 41. Principal Stress and Strut and Tie Model for Deep Beam (78, 79)  137  Chapter 7. Fracture Mode Analysis  To summarize the procedure for crack mode prediction for a simply supported beam with a central impact loading, there are four steps to follow: 1. Obtain, by testing or calculation, two basic properties of the beam under static loading with the same half support span, /, of the impact loading: the load to cause flexural cracking, P f, and the load to cause web shear cracking, P . c  cv  2. Determine the acceleration distribution, and hence the distribution of inertial load along the beam. It is a reasonable assumption to use a linear distribution for a conventional plain concrete beam and a sinusoidal distribution for conventional reinforced and prestressed concrete beams, at least for impacts in which the velocity of the striking body is less than 10 m/s. 3. Find the distance, / , between the mid-span of the beam and the centroid of the half shape of the inertial load profile, that is, the point at which the resultant inertial force acts; define the ratio / // as k. An equivalent simply supported static system can be created by just replacing the span / with / . The prediction of the first crack mode is based on this equivalent system. 4. Since the span has been reduced by \/k, the flexural cracking load P f will also c  increase by \/k, to ~|"Pcf • ^ * increased value is still less than P tn  s  CVj  the first crack is  still a flexural crack Otherwise, the first crack could be a shear crack. It is easy to show that k is 113 for the linear and 0.36 for the sinusoidal distributions. So, simply taking k = 113 for all types of conventional concrete beams is conservative. However, if a rubber support is used underneath the beam, or if the length : depth ratio of the beam is very large, the k value may be significantly changed. However, the general method is still effective. This will be discussed in the next section. It should be pointed out that: 1. In the above discussion, the inherent properties of the concrete, such as the  Chapter 7. Fracture Mode Analysis  138  i  flexural resistance and shear resistance under impact are assumed to be the same as under static loading. If both of these increase at the same rate under impact, the above method need not be changed. However, if they change at different rates, then modification factors should be applied to —P f and P respectively. c  cv  k  2. As discussed above, if the flexural cracking load under impact, 3Pf, is larger c  than P , the first crack could be a shear crack and the beam has the risk experiencing a cv  shear failure. However, it does not mean that the shear crack will necessarily appear under impact loading. For example, if the first peak of the load due to the inertial effect does not reach the shear cracking force P , no crack will occur at this time. This cv  situation may occur when the mass of the striking body is relatively small compared to the mass of beam or when the drop height of the hammer is small, or when a soft rubber shim is used between the hammer and the beam, attenuating the inertial load. 3. In the case discussed above in (2), no shear crack appearing at the very beginning of the impact means there is no risk of the first crack being a shear crack afterwards in the whole impact event because the most sensitive moment with the highest Q/M ratio has passed. However, it is still possible for a flexural crack to occur subsequently. As the beam approaches the hammer velocity, the acceleration of the beam, and hence the inertial load, gradually disappear. At this time, the applied load is resisted primarily by the support load as in the static case, and the effective span becomes the actual span. Thus, the flexural cracking load returns to P f. The beam may develop a c  flexural first crack under a load just higher then P f at this time, even though it did not c  crack under a much higher load at the beginning of impact. 4. If the crack mode check shows that the flexural cracking load under impact, 3P f, is less than P , on the other hand, then the concrete beam has no risk of brittle c  shear fracture.  cv  Chapter 7. Fracture Mode Analysis  139  5. If the beam is very brittle and weak, such as a plain concrete beam, it may fail within thefirstinertial load peak, while the beam is still being accelerated. In this situation, the current method is still effective and conservative.  140  Chapter 7. Fracture Mode Analysis  7.4. Crack Mode Analysis for C X T Ties  Two extreme cases, which were not discussed in the previous section, will be introduced first.  (a) Localized Impact Loading F,, 1  1.  tt-  Xx X kl  -X-  1  kl  x  1  L  -X-  (b) Impact Loading with Soft Rubber Supports Fi  \i  X -y  i  112  "i  i  /  X  i  i  112  ii  X 1  Figure 42. Two Special Cases of Impact Loading  Fig. 42 (a) shows a localized impact loading, in which the inertial load is concentrated on the central part of the beam, with only a very small inertial load on the rest of the beam. This situation may occur when the velocity of the striking body is very high, usually larger than 10 m/s (18); or when the length to depth ratio of the specimen is  141  Chapter 7. Fracture Mode Analysis  large, such as in slabs (20). In this case the duration of the impulse is much shorter than the natural period of vibration and the whole member has no time to respond. The parameter k may become very small due to the localized effect, leading to a very short effective span and very high Q/M ratio. That is why a punching shear failure is often met for the slabs under impact, sometimes with no significant flexural damage. Fig. 42 (b) shows the opposite case of impact loading, in which the inertial load is uniformly distributed on the beam, and k = 1/2, the largest value of k in all the cases discussed. Thus the effective span is relative large, being ^7 (compared to  for linear  case), and the flexural cracking load under impact is 2P f, instead of 3P f . Therefore, c  c  the possibility of shear failure is much reduced. Use of very soft rubber pads under the beam may lead to this situation, because the flexural stiffness of the beam is much greater than the stiffness of the rubber, so the deflection of the beam is very small and can be neglected compared to the large deformation of the rubber pads at the supports. Since the distribution of the acceleration is basically proportional to the displacement of the beam, an almost uniform distribution of the inertial load appears. In other words, the beam behaves almost as a rigid body floating on the rubber until the rubber is extensively compressed and stiffens under high pressure. By that time, the high inertial load peak, as well as the critical moment for shear cracking has passed. Therefore, the soft rubber supports can protect the beam from suffering shear failure. Fig. 43 shows the difference in the deflections of CXT ties under impact with two types of supports. With the hard support, at thefirstinertial load peak, there was very little displacement of the tie and the load reached a very high value. With the soft support, on the other hand, during thefirstinertial load peak the tie moved downward considerably although the load was only one-third of the inertial load for the tie with the hard support. Clearly, this was mainly the rigid body movement of the tie due to the  Chapter 7. Fracture Mode Analysis  142  deformation of the soft rubber support, followed by the normal bending of the beam during the second load peak, when the rubber support had been compressed to a point where the stiffness increased considerably. As a result, a flexural crack appeared on the tie with the soft rubber support; a diagonal shear crack appeared on the tie with the hard rubber support without any flexural cracking occurring, although they had the same support span and were subjected to the same drop hammer from the same drop height.  Figure 43. Load vs. Deflection of Beams with Hard and Soft Rubber Support  143  Chapter 7. Fracture Mode Analysis  It is believed that the distribution of the inertial load on the beam with the hard support basically followed the sinusoidal profile, as in Fig. 44, with k = 0.36; while that with the soft rubber support followed the uniform distribution as shown in Fig. 42 (b), with k = 0.50. (Since the loading point was not at the longitudinal center of the entire tie, a more precise analysis shows that as a free-freerigidbody, the beam undergoes a little rotation with the loading end downwards. As the result, a somewhat higher inertial reaction occurs on the end of the loaded side and thus the k value should be 0.53).  Figure 44. Inertial Load Distribution for CXT Concrete Tie with a Hard Rubber Support  To analyze the cracking mode of the tie, the applied load to cause the flexural crack, P f, and the load to cause a 'web' shear crack, P , have to be known. Since no c  cv  crack detection measurements were taken in the static test of the CXT tie, the cracking load was not accurately obtained. Therefore, a theoretical calculation was carried out. The results were compared to the previous tests for similar types of ties with a very similar design capability, in which a crack detection gauge mounted on the tie and a smooth coating were applied to reveal the crack more clearly. Table. 15 shows the comparison of the theoreticalflexuralcapacity of the CXT tie,  Chapter 7. Fracture Mode Analysis  144  as well as the static test results of the ITISA tie and RT733 prestressed concrete railroad ties. The RT733 is a railroad tie design developed for the Los Angeles County Transportation Commission. The 259.1 cm (8-6") long tie, which is prestressed with eight 9.5 mm (0.375") diameter seven-wire strands, meets all AREA specification requirements (26). The tie accommodates a 171 kg/m (115 lb/ft) rail, with a 140 mm (5.5") rail base. The tests for the ITISA ties are included in the current study and the results can be found in Chapter 4. The tests for RT733 ties was carried out by Venuti at San Jose State University in 1990 (80). Both tests used a crack detection gauge and a coating on the concrete surface, so that the crack could be detected as soon as it formed.  145  Chapter 7. Fracture Mode Analysis  Table 15. Applied Load Causing Flexural Cracking at Mid Span  Type of Concrete Tie  CXT  ITISA  RT733  Theoretical Flexural Cracking Moment (kN.m)  35.9  30.2  40.9  749(29.5") 660(26")  Support Span at the Rail Seat (mm)  711(28")  Corresponding Shear Span (mm)  322  273  303  Theoretical Load at Flexural Cracking (kN)  220  222  270  224  267  Measured Load at Flexural Cracking (kN)  —  Table 16. Applied Load Causing Shear Cracking of the Tie  CXT  RT733  0.0564  0.0567  Concrete Strength (MPa)  56.5  50.0  Initial Prestressing Force (kN)  655  614  Theoretical Load at Shear Cracking (kN)  492  470  Type of Concrete Tie Area of Cross Section at Rail Seat (m) 2  Measured Load at Shear Cracking (kN)  476  146  Chapter 7. Fracture Mode Analysis  The support span, 21, and the shear span, l , in Table. 15 are defined in Fig. 45. s  Since a rail segment (with installed fastening system) was used on the ties in these tests, two loading points were assumed, at which the two resultant applied loads acted. The distance between the two points, d , was 105 mm for the rail with a 140 s  mm (5.5") wide rail base, which was used in the tests for the CXT and RT733 ties (although the CXT tie is designed for a rail with a 6" rail base), and 115 mm for the rail with a 152 mm (6") wide base, which was used for the ITISA ties. Thus, the shear span l =(2l-d )/2 s  (50)  s  Figure 45. Support Span and Shear Span The theoretical flexural cracking moment, M j, was calculated for the CXT and c  ITISA ties using the simplified ACI method; the data for RT733 tie was calculated by Venuti (80) using the same method. The theoretical load causing a flexural crack, P f, c  can be obtained from the equation  147  Chapter 7. Fracture Mode Analysis  The loads causing flexural cracks were obtained from the static tests for the ITISA and RT733 ties. From Table 15, it may be seen that the measured loads were very close to the calculated ones, indicating that methods of analysis and testing were quite reliable. Thus, the calculated value 220 kN was adopted as the applied load P f to cause a flexural c  crack. The shear force required to cause the diagonal shear crack was calculated according to the ACI code (81) for estimating the shear to cause web shear cracking, the applied load causing the shear crack, P  cv  was simply twice this shear value. The parameters  involved in the calculation, together with the calculated results are listed in Table. 16. Since the shear cracking load was not measured for the ITISA tie, only RT733 ties could be compared. In Table. 16, the loads required to produce the shear crack for RT733 tie, both theoretical and measured, were similar to each other, indicating that the theoretical and test methods are quite comparable. Thus, the theoretical value, 492 kN, can be adopted as the actual applied load to cause a shear crack, P , in the CXT tie. cv  Knowing the loads to cause flexural cracks and shear cracks, it is possible to analyze the cracking mode of the tie under impact. Table 17 lists the parameters involved in the analysis, and the conclusions of the analysis for the ties with hard supports and soft rubber supports.  Chapter 7. Fracture Mode Analysis  148  Table 17. Crack Mode Analysis of CXT Tie Under Impact with Different Supports  Hard  Soft  Sinusoidal  Uniform  Static Load causing Flextural Crack, P f, (kN)  220  220  Static Load causing Shear Crack, P ,(kN)  492  492  Factor k(k = l*/l)  0.36  0.53  611  415  492  492  Type of Support Inertial Load Distribution Manner r  rv  Effective Load causing Flextural Crack, —Pcf, (kN) Effective Load causing Shear Crack, = P (kN) rv  Comparison of — P f and P k  c  J  cv  Fracture Mode Dominated  \Pcf>Pcv  Brittle-Shear  jPcf<Pcv  Ductile-Flexure  It should be noted that the capacity of the concrete to resist the flexural moment and shear under impact may be different from those under static loading. Since there are no reliable data available on this matter, to simplify the analysis, it was assumed that both capacities increased at the same rate so that their ratio was unchanged. Thus, the comparison of the effective loads causing flexural and shear cracking under impact can still be based on the static capacities of concrete. For the impact tests with the 504 kg hammer (see Figure 31 in Chapter 6.), with the hard support, the tie was subjected to an inertial load greater than 700 kN. Since the inertial load followed a sinusoidal distribution, the effective span was reduced about 3 times and the effective flexural cracking load increased about 3 times, becoming 611 kN, while the shear cracking load was still the same as under static loading - 492 kN.  Chapter 7. Fracture Mode Analysis  149  Therefore the shear crack appeared first at the first peak of the load history. Since there was no transverse reinforcement in the tie, once the shear crack formed, it developed very quickly and divided the tie diagonally into two separate parts (see Fig. 41). The flexural crack thus could not form in the lower part of the tie, and all energy dissipated in the shear crack. With the soft support, on the other hand, during the time of the inertial load peak, the effective flexural cracking load only increased about twice, reaching 415 kN, since the inertial load followed the uniform distribution. It was still lower than the shear cracking load. Therefore the flexural crack appeared first, leading to a ductile flexural fracture. For the 345 kg hammer with the hard support (see Figure 29 in Chapter 6.), the first crack was a flexural-shear crack. Normally, in static tests, this type of the crack results from the extension of the flexural crack and appears only after some flexural cracks have formed. The mechanism of formation for this type offirstcrack under impact is still unknown. However, since the loading rate and the maximum inertial load were much lower than when using the 504 kg hammer, the hard rubber could not be compressed so quickly, and might still have played some role in the inertial load distribution, making it somewhat more uniform. The inertial load distribution for this test should lie in between the sinusoidal and uniform types, and the k value should be an intermediate value too. Assuming that k was the average of the k values for sinusoidal and uniform distributions, i.e.,  , 0.36+0.53 .... k= = 0.445 2 then, the effective flexural cracking load was  150  Chapter 7. Fracture Mode Analysis  •220 = 494kN. 0.445 It is almost the same as the value of the effective shear cracking load, P , (= 492 cv  kN). Therefore, it was not surprising that both the shear and flexural cracks formed simultaneously. 7.5. Summary  1. The reasons for the change in cracking mode from flexural under static loading to shear under impact loading is that the shear to moment ratios of each loading were different. A significant portion of the applied load is balanced by the distributed inertial load along the beam, whose resultant force has a much shorter moment arm to the midspan of the beam than the support load has, leading to a reduced bending moment at midspan. Therefore, the applied load can go to much higher levels than the static flexural cracking load without inducing any flexural cracks in the beam. When this load reaches the shear cracking load, which is the same under impact as under static loading, a shear crack may appear first. 2. The critical time at which the beam may initiate thefirstshear crack is at the moment of impact (zero time), when the inertial load is at a maximum and the support load is still zero. All of the applied load is then balanced by the distributed inertial load along the beam. The moment arm of the resultant inertial force to the mid-span of the beam can be taken as the effective span length for the equivalent static test system. The crack mode check can be carried out on the basis of this system. If the effective shear cracking load in this system is lower than the effective flexural cracking load, a brittleshear failure may occur under impact. If not, the beam is, generally speaking, unlikely to produce a shear crack first, and is safe. Investigation of the inertial load distribution  Chapter 7. Fracture Mode Analysis  151  along the beam is an important step in the fracture mode analysis. For conventional civil engineering structural beams subjected to a striking body with a relatively low velocity (< lOm/s), a sinusoidal  inertial load distribution can be assumed for reinforced,  prestressed, and steel fibre reinforced (>1.0% fibre) concrete; a linear distribution can be assumed for plain concrete and fibre reinforced concrete with lowfibrevolume. Taking one third of the span length as the effective span is conservative for both situations. 3. The crack mode analysis for the CXT tie showed that this method is effective. Using a soft rubber support can make the inertial load distribution relatively uniform, and the effective span is then significantly greater than the sinusoidal distribution, hence preventing brittle-shear failure.  CHAPTER 8. IMPACT TESTING OF MODIFIED ITISA TIES  8.1. Introduction  As noted in Chapters 2 and 5, the 'hairline' bending cracks were observed at the rail seats of concrete ties, sometimes after the ties had been in service for only a few months. The cracks were a cause of concern because the design service life for the ties was 50 years, and no cracks could be tolerated because of the harsh environment and possible fatigue of the prestressing steel at the cracks. The primary cause of the cracking was impact loads arising from either "flats" on the rolling surface of the train wheels or to rail irregularities. The measures usually taken in practice to combat this problem are: a) installing a rail seat pad with an increased resiliency (lower stiffness) between the rail and the tie rail seat to attenuate the impact force (8); and b) detecting the wheel flats by means of a wheel impact load detector (installed on the rail) followed by changing or machining of the wheels (29). These measures could lead to a marked improvement. However, pads with a lower stiffness generally experience a decrease in fatigue life (82, 83), leading to even more severe damage to the ties (8), and have to be replaced as early as several years. Also, changing wheel sets and sections of rail too frequently results in increased maintenance costs. Thus, an alternative approach is to improve the dynamic behavior of concrete ties, especially in those sensitive areas where the ties are very susceptible to impact, or where track maintenance is very difficult, such as tracks in tunnels and on 152  Chapter 8. Impact Testing of Modified ITISA Ties  153  bridges. The purpose of the study described here was to examine the effects of the concrete compressive strength, steel fibre additions, changes in prestressing force, the presence of stirrups, and rail seat pad stiffness on the behaviour of concrete ties under impact loading. This could, in turn, lead to improvements in the design of concrete ties.  8.2. Simulations of Impact Pulses on Railroad Tracks  In order to simulate the response of concrete ties to impact loading, it was considered essential to replicate, as closely as possible, the impact pulse measured on a track in service, in terms of the duration of the pulse and the shape of the load vs. time curve. Theoretically speaking, when the frequency of an applied periodic load reaches the natural frequency of the structural element, the response of the element will increase with time and reach the maximum, called resonance response. For an impulsive load with a half-sine profile, which is usually the type of the pulse applied to the ties, the maximum response of the element occurs when the duration of the applied pulse is 3/4 of the natural period of the element; the magnitude of the response is 1.77 times of that for static loading (84). Wakui and Okuda (36) found that the bending strain of the concrete tie varied with the duration of applied impulse. The bending strain per unit impact force reached a maximum when the duration of the impulse was between 1 - 2 ms. Under this impulse, the strain per unit force was 1.8 times the magnitude for static loading. They also found, by finite element analysis, that the natural periods corresponding to the vibration modes of the concrete ties they used were 1.5 to 2.1 ms. Therefore, the higher strain response was attributed to the resonance of the tie. From the point of view of concrete technology, modifications of the tie design may change the stiffness of the tie and hence its inherent natural period, which may prevent  Chapter 8. Impact Testing of Modified ITISA Ties  154  the tie from experiencing a resonant reaction due to the impact pulse with a specific duration in service. Thus in order to investigate the effect of these modifications on the behavior of the concrete ties in service, a replication of the impact pulse measured on the track in service is essential. As indicated in Chapter 5., the applied impact pulse due to wheel flats or rail abnormalities is superimposed on the normal quasi-static load of the passing wheel. The wheel flats, which develop on the wheels of a train during braking, generally induce a very short duration impulse, in the range of 3-5 ms (8), normally acting on both rail seats. However, impulses due to rail abnormalities, such as rail joints, engine burns, or battered welds, are of longer duration, about 5-10 ms (29), or even longer (28). These impact loads would normally occur on only one end of the tie. Both types of pulses have essentially a half-sine profile. An example of a pulse with a long duration as measured on a track with engine burns is shown in Fig. 46 (29). Circuit #3 is the impact load detection gauge mounted under the rail with the engine bum, and circuit #1 is under the normal smooth track. The duration of the impact pulse was about 8 ms. Note that before the primary impact pulse started, there was a complete unloading of the wheel. As shown in Chapter 5, the existing UBC impact machine with a 504 kg mass can be used to simulate this pulse, producing a pulse duration of 8 ms when using the hard support (see Fig. 31 in Ch. 6.). When the mass was increased to 578 kg, which was used to test the ITISA ties, the duration became 10 ms, as shown in Fig. 47. This was considered to be sufficiently close to the pulse measured.  Chapter 8. Impact Testing of Modified ITISA Ties  IME (MILLISECONDS)  Figure 46. Comparison of Vertical Loads of the Heritage Car Over Smooth Track (Circuit #1) and Engine Burn (Circuit #3) (29)  155  156  Chapter 8. Impact Testing of Modified ITISA Ties  Load (kN) 400  I  300 hi  200  H  ioo H-  0  0  5  10  15  20  Time (ms)  Figure 47. Load History of Impact Test Using 578 kg Hammer  In order to simulate an impact pulse with a 3-5 ms duration, which is considered to be the typical duration of the impact event due to wheel flats, and is the type of pulse which causes the most serious damage to the concrete tie, a smaller impact machine was constructed, which was been described in Ch. 3. With this smaller machine, the hammer mass, and the type and thickness of the rubber shim between the hammer and the striking tup are adjustable (see Fig. 4. in Ch. 3.), to permit the production of a specified duration of pulse on the tie within a certain range. The drop height of the hammer influences the amplitude but not the duration of the pulse. In this study, a 60 kg hammer mass was chosen and no rubber shim was used.  Chapter 8. Impact Testing of Modified ITISA Ties  157  With this arrangement, the duration of the impact load was about 4 ms, and thefirstpulse of the concrete strain response had about 2 ms duration, coinciding with the pulse measured in track. Fig. 48 shows a typical example of the impact load history due to the 'wheel-flat' measured on a track in service (29). Note that the curve marked 'drop hammer' in the figure is for the hammer built by the authors of Ref. 29. This figure shows, again, a complete unloading of the wheel before impact, indicating that the single blow of the impact on the tie without any accompanying quasi-static load applied is suitable for the simulation. Fig. 49 shows the load history of the impact testing of the ITISA ties using the machine with the 60 kg hammer under different drop heights. The duration of the pulse reasonably matched the measured pulse and proved to be independent of the drop height.  Chapter 8. Impact Testing of Modified ITISA Ties  60  50i  TIME - mSEC  Figure 48. Impact Load History for Passenger Car 'Flat' Wheel (29)  Chapter 8. Impact Testing of Modified ITISA Ties  Load(kN) 160 406 mm drop height  -  711 mm drop height 1016 mm drop height  -  -  \ \\  -  -  I  J  i  4 Time (ms)  Figure 49. Load History of Impact tests Using 60 kg Hammer  Chapter 8. Impact Testing of Modified ITISA Ties  160  Spectral analyses showed that the tie response obtained in the laboratory in the current study closely simulated the tie response in track. Fig. 50 shows the spectra of the rail seat bending strain of the tie, measured in track and in the simulated impact tests in Battelle's Columbus Laboratories (8). The measured resonant frequencies for the first three bending modes of vibration are 131, 356 and 638 Hz for the tie in track. Fig. 51 shows the spectrum of the rail seat bending strain of the tie in the present study using the 60 kg machine. The first three natural frequencies are 98, 358 and 618 Hz, quite close to those measured in track. The very low magnitude of the first mode in the laboratories can be attributed to the single-sided loading, in contrast to the two-wheeled loading of the tie in track under service load conditions (8). The first vibration mode of the beam is symmetrical about the centerline of the beam; usually this bending mode is enhanced by symmetrical loading or center-point loading. The different contribution of the first mode of the tie in the laboratory may be due to the non-symmetrical load, rather than the symmetrical load in track. The influence of this difference on the test results is unknown. However, since the maximum displacement of the first vibration mode is on the center of the tie and quite small at the rail seat, the simulation of the tie response at the rail seat of the tie can be considered to be very close to the tie response in track.  161  Chapter 8. Impact Testing of Modified ITISA Ties  30  TRACK MEASUREMENT  131 Hz  638 Hz  356 Hz  20 A ZD  CD  10  OH  200  400  600  800  FREQUENCY (Hz)  Q ZD  0  200  400  800  FREQUENCY (Hz)  Figure 50. Frequency Spectra of Rail Seat Bending Strains from Track Measurement and Battelle's Columbus Laboratories Measurement (8)  162  Chapter 8. Impact Testing of Modified ITISA Ties Magnitude 6  0  200  400  600 800 1000 frequency (Hz)  1200  1400  1600  Magnitude 2 358 Nonloaded End 1.5  618 -  98  0.5  1042  •V  0  200  i  400  i  i  i  600 800 1000 frequency (Hz)  V-^i—  1200  —t  1400  1600  Figure 51. Frequency Spectra of Rail Seat Bending Strain for ITISA Tie Using 60 kg Hammer  Chapter 8. Impact Testing of Modified ITISA Ties  163  8.3. Test Setup  In the design of concrete ties, no cracks can be tolerated (26) because of the harsh environment and possible fatigue of the prestressing steel at the cracks. For ties in service, the controlling factor is the residual crack width and the fatigue limit state; the ultimate strength of the ties is not particularly significant. Therefore, the measurements in the present tests were focused on the influence of the modifications to the ties at the time of appearance of thefirstcrack, and to the capability of the tie to resist crack development. The experimental setup for the impact tests is shown in Fig. 52. A standard 136 RE rail segment, 292 mm long, was fastened to the tie using a Pandrol fastening system with a 6.5 mm thick EVA rail pad between the rail and the tie. Two strain gauges, 100 mm in length, were affixed to the tie below the two rail seats, 20 mm from the bottom of the tie, as shown in Fig. 7 in Chapter 3. Crack detection gauges consisting offive178 mm long silver lines painted longitudinally on the sanded concrete surface below the rail seat, 10, 35, 55, 75 and 95 mm from the bottom of the tie, were also used. They too are shown in Fig. 7 in Chapter 3. These lines were connected to a resistance measuring circuit. As a crack grew, these lines were severed by the crack sequentially from the bottom line to the top line. Each cut caused the output of the circuit to jump to a new level, so that it was easy to determine which silver lines were cut. A liquid coat of Stresscoat was also applied to the specially prepared concrete surface to locate fine cracks, especially for measuring the length of the horizontal cracks. The final crack width for each tie was measured using a hand-held graduated microscope with a 0.02 mm accuracy. A small preload was used on the tie to prevent it from rebounding during loading. All of the data were collected at 0.03 ms intervals with a PC based data acquisition system. This setup was also used in the impact tests for the rail seat pads which will be discussed in Chapter  164  Chapter 8. Impact Testing of Modified ITISA Ties  10. Detailed descriptions of the above instruments and fixtures have been given in Chapter 3 of this work.  CHANNELS 1. load cell on tup; 2. strain gauge; 3. strain gauge; 4. crack gauge; 5. load cell on support 6. load cell on support; 7. accelerometer on hammer; 8. accelerometer on tie. Stress coat is applied on the opposite side of the tie at rail seats. ©  Rail Pad  Rubber strip  1524  2515  Figure 52. Layout of Impact Test for Concrete Railroad ITISA Ties  Chapter 8. Impact Testing of Modified ITISA Ties  165  8.4. Testing Program  Twelve types of modified ITISA ties, as well as the standard ITISA tie which was taken as the reference, were tested in two series of impact tests. The details of these types of ties have been described in Table 1 of Chapter 3. For thefirstseries of tests, carried out on the 60 kg impact machine, each tie was subjected to an accumulation of impact loads: one blow each for the drop heights of 102, 203 and 305 mm, and ten blows each for the drop heights of 406, 508, 610, 711, 813, 914 and 1016 mm. Some of these drop heights are the same as used by Battelle's Columbus Laboratories (8). One tie for each type was tested, except tie No. 12 (see Table 1 of Chapter 3), for which a second tie was also tested to confirm its very good dynamic characteristics. For each blow, the hammer was released from a predetermined height and dropped onto the top of the rail segment, inducing an impact pulse. Since no braking was applied after the impact, the hammer rebounded and hit the rail again several times until coming to rest on the rail. The potential energy the hammer held before dropping can be considered to be largely transferred to the tie-pad system. For the second series of tests, using the larger impact machine, each tie was struck only ten times from a drop height of 559 mm. No braking was applied. One tie of each type was tested. The reason for the drop height of 559 mm is that the total accumulated potential energies released for each tie in these two series are almost the same, for purposes of comparison.  CHAPTER 9. IMPACT RESISTANCE OF MODIFIED ITISA TIES  9.1. Crack Propagation in Different Types of Ties  9.1.1. Crack Description  For the first series of tests, the 60 kg hammer mass machine was used. The cracks that formed in the ties in this series of tests were primarily "hair line" flexural cracks at the loaded end under the rail seat as shown in Fig. 53. This type of cracking of the ties in service has been widely reported (8, 23, 29, 30, 36, 40) and is typical of cracks due to the impact load induced by wheel flats. In the present study, the maximum drop height of the hammer was 1016 mm (40") and the maximum impact load was about 150 kN (33,700 lb), which matches modest impact loads in practice, such as the example shown in Fig. 48 in Ch.8. Using brittle coating, it was found that the final vertical length of the crack on the standard ITISA tie was as long as 150 mm after 73 impacts, as described earlier. However, neither this tie nor any of the other types of ties "failed". They still maintained most of their load carrying capability, as indicated by the steady maximum impact loads for each blow at a particular drop height during the entire impact process. This implied that flexural stiffness of the ties changed little (see Fig. 65 in this Chapter). Previous studies have shown (8, 27, 36) that ties in service did not significantly lose their load-carrying capacity due to the occurrence of flexural cracks at the rail seat. However, the durability of the concrete tie is of concern since under repeated loading, prestressing 166  Chapter 9. Impact Resistance of Modified ITISA Ties  167  steels are extremely sensitive to corrosion, and could experience a brittle fracture when subjected to attack from aggressive chemicals.  Figure 53. Typical flexural crack under rail seat at loaded end (using 60 kg hammer); the painted lines of the crack detection gauge were severed.  Chapter 9. Impact Resistance of Modified ITISA Ties  Figure 54. Typical horizontal cracks at nonloaded end, as revealed by Stresscoat.  168  Chapter 9. Impact Resistance of Modified ITISA Ties  Figure 55. Typical flexural crack at nonloaded end; the concrete surface was coated with stresscoat.  169  Chapter 9. Impact Resistance of Modified ITISA Ties  170  On the nonloaded end, long horizontal cracks were found on some ties, as shown in Fig. 54. This type of the crack was also reported in service (29). The reason for this type of cracking is still unknown but it is not due to the uplift load from the shoulder inserts of the fastening system since no rail segment in the present tests was installed and hence no rebound force of the rail induced. For most of the ties, vertical cracks also occurred at the nonloaded end of the tie, but these were relatively shorter and finer, as shown in Fig. 55. This phenomenon was also found in previous studies (8, 29). This suggests that a rail seat crack may occur on the tie end opposite to that receiving a single impact load, such as that due to a rail joint, battered weld or engine burn. This type of cracking can be attributed to the second and third vibration modes of the tie (29) and the very low damping of the tie (34, 35). The shapes of the first three bending modes of vibration for concrete ties have been measured and shown in Fig. 56 (29). The corresponding frequencies for these modes, for the ITISA ties tested in the current study, were very similar to those shown in Fig. 56, being 98, 358 and 618 Hz respectively (see Fig. 51 in Ch. 8). The second and third bending modes are particularly important because for these the strain amplitudes are nearmaximum in both rail seat regions. When the peak responses of the two modes occurred at the same time (in-phase), cracks could be initiated at both ends of the tie. The first mode was most important for the bending moment at the center of the tie, but less important for the moments at both rail seats. Hence, in the simulated impact tests in the laboratory, the absence of the first vibration mode in the tie response was not critical for the evaluation of the effect of impact on the flexural cracks at the rail seats.  171  Chapter 9. Impact Resistance of Modified ITISA Ties  FREQ(HZ) 108  —  (A) FIRST BENDING M O D E  FREQ(HZ) 333  (B) SECOND BENDING MODE  FREQ(HZ) 633  (C) THIRD BENDING MODE  Figure 56. First Three Bending Modes for Concrete Ties (29)  Chapter 9. Impact Resistance of Modified ITISA Ties  172  The Stresscoat applied to the concrete surface helped to locate fine cracks, and was especially useful for measuring the length of the horizontal cracks as well as the cracks at the nonloaded end, where there were no crack detection gauges, as shown in Figs. 54 and 55. It should be noted that without such an effective coating to reveal the very fine cracks more clearly, many of the cracks on the ties in this series of tests could not have been found. In the static tests of the CXT tie, with no coating or crack detection gauges, the detection of thefirstcrack on the tie was considerably delayed. This phenomenon was also found by Battelle's Columbus Laboratories (8) and seems to be a practical problem in service, since only quite wide cracks could be found on the tie in track either with no surface treatment or with an alcohol spray. Since the cracks on the impacted end had the greatest length and width compared to the other types of cracks for all ties, and were considered to be critical in service, only this type of cracking will be discussed in detail in the following sections. The maximum crack length and the residual crack length, for the different groups of ties, were measured via the crack detection gauges. While the impact load was being applied, any crack that did develop opened to its maximum extent (referred to as maximum crack length), severing one or more of the painted silver lines. After the impact event, when the tie had been unloaded, because the crack was veryfine(usually less than 0.05 mm in width), part of the crack near its tip might be completely closed again due to the prestressing force, re-connecting some of the newly-severed silver lines and partially reestablishing the original output of the circuit. However, a portion of the crack would not close even in the unloaded condition, and is referred to as the "residual" crack. The length of the residual crack is one of the parameters often used to evaluate the durability of concrete members in service, and is one of the determining factor of the service capability of the ties. Both crack lengths, detected using the crack detection gauges, were measured from the bottom surface of the tie until the length reached 95 mm, which is the limit of  Chapter 9. Impact Resistance of Modified ITISA Ties  173  measurement of the crack detection gauge, though cracks on some of the ties developed far beyond this limit, such as in tie No. 1. The maximum crack length and the residual crack length for different groups of the ties are shown below in Figs. 58, 60 and 62. The vertical axis in these figures shows the vertical crack length. The horizontal axis shows the drop height, with the scale markings indicating the number of blows at a particular drop height. The final residual crack width for each tie was measured using a hand-held graduated microscope with a 0.02 mm accuracy. For the second series of tests, using the 578 kg drop hammer, the vertical cracks at the loaded end were very large and could be measured easily with a ruler and considered as the residual crack length. The cracks on all types of the ties developed a length greater than 95 mm, the limit of measurement of the crack detection gauges, during the first blow, and no horizontal or vertical cracks at the nonloaded end were found. A typical crack in this series of tests is shown in Fig. 57. The crack propagation of the ties in this series of tests will be also shown below.  Chapter 9. Impact Resistance of Modified ITISA Ties  174  Figure 57. Typical flexural crack under rail seat at loading end (using 578 kg hammer); the lines of crack detection gauges were severed.  Chapter 9. Impact Resistance of Modified ITISA Ties  175  9.1.2. Effect of Steel Fibre Additions  The addition of steel fibres to the concrete mix greatly improved the tie behaviour, resulting in shorter and finer cracks. Comparing ties No. 3 and No. 4 with tie No. 1 in Figs. 58 and in 59, we find that the tie with 30 mm fibres performed somewhat better in thefirstseries of tests while the tie with 50 mm fibres performed better in the second series, although the differences were small. This is because the two machines induced different types of cracks on the ties. The shorterfibreshave a smaller effective fibre spacing in the tie (85) and are therefore more effective in resisting microcracks and fine cracks; the longerfibresbridge across wider cracks, providing more effective resistance to the growth of macrocracks. In thefirstseries of tests, it was found (Fig. 58) that thefirstcrack was initiated at the second blow of the 406 mm drop height for the tie with 50 mm fibres, but at the sixth blow for the tie with 30 mm fibres; for the standard tie, the crack was initiated at the first blow at the 406 mm drop height. At the time when the cracks were very thin and short, ties with fibres behaved in a very similar manner to the standard tie. However, after the cracks developed beyond a 55 mm length and became wider, the fibres in the ties played an important role in hindering crack propagation. The crack length was limited to less than 75 mm in the tie with 30 mm fibres (No. 4) and to less than 95 mm in the tie with 50 mm fibres (No. 3) until the end of the impact process; for the standard tie, after the crack length reached 95 mm (which was the maximum crack length the crack detection gauges could measure), it continued to developed to a length of 150 mm at the end of the impact process. The length beyond 95 mm was measured with the help of the Stresscoat and is not shown in Fig. 58. The greater effectiveness of the shorter fibres in retarding the crack propagation was due to a smaller effectivefibrespacing, and hence more effectiveness in resisting microcracks and fine cracks. The residual crack propagation  Chapter 9. Impact Resistance of Modified ITISA Ties  176  shown in the lower diagram of Fig. 58 showed the same tendencies, but in a more marked fashion, for these three ties. The final crack widths were 0.16 mm, 0.04 mm and 0.02 mm, respectively, for the standard tie, the tie with 50 mm fibres and that with 30 mm fibres, also indicating the impedance effect of fibres, especially short fibres, on the crack propagation.  9.1.3. Effect of Stirrups Stirrups proved to be effective, particularly when used in conjunction with fibres in the first series of tests, as in tie No. 6, shown in Fig. 58. The first crack initiation was significantly delayed. At the end of the impact process, the maximum crack length was only 35 mm, and no residual crack existed. This type of tie had the best behavior under impact of all of the ties. However, they were less effective in the second series of tests when used in conjunction with fibres, as shown in Fig. 59. The mechanism of impact resistance for ties with stirrups is still unknown. One possible explanation is that stirrups resisted the growth of the horizontal cracks which occurred in the first series of tests, effectively retarding the deterioration of the concrete ties; they were not as effective in resisting vertical cracking.  177  Chapter 9. Impact Resistance of Modified ITISA Ties Maximum Crack Length (mm) 100 Type  rfie No.  Normal B— 1% 50 mm fibres 1 % 30 mm Fibres 7 stirrups O 7 stirrups + 1 % 50 mm fibres!  406  508  610 711 813 914 1016 Drop Height (mm) & No. of Blows*  Final Crack Width: #1: 0.16 mm  Residual Crack Length (mm)  #3: 0.04 mm  100  #4: 0.02 mm #5: 0.04 mm #6: 0.01 mm  406  508  610 711 813 914 1016 Drop Height (mm) & No. of Blows*  * Each d i v i s i o n represents  one blow.  Figure 58. Fibre and Stirrup Effect on Crack Propagation Hammer Mass = 60 kg  Chapter 9. Impact Resistance of Modified ITISA Ties  Length of Crack (mm) 250 i  Number of Blows  Tie No.  Type  Crack Width (mm)  1  Normal (65 MPa)  0.65  3  1% 50 mm fibre  0.21  4  1% 30 mm fibre  0.26  5  Stirrups  0.30  6  Stirrups + 1 % 50 mm fibres  0.25  Figure 59. Crack Propagation of Ties under Impact Hammer Mass = 578 kg, Drop Height = 559 mm  Chapter 9. Impact Resistance of Modified ITISA Ties  179  9.1.4. Effect of Concrete Strength  Two ties made with 40 MPa concrete were tested, as shown in Fig. 60 for the first series of tests, and in Fig. 61 for the second. In the first series of tests, without fibre additions, tie No. 11 behaved similarly to the standard tie (tie No.l) with 65 MPa concrete strength; in both, a crack was initiated at thefirstblow from the 406 mm drop height, and thefinalcrack lengths for both ties were 150 mm (measured with the help of Stresscoat and not shown in the figure), even though tie No. 11 had a lower concrete strength. Thefinalcrack width for tie No. 11 was even much smaller than that for tie No. 1, being 0.03 mm compared to 0.16 mm. In the second series of tests, comparing tie No. 11 with tie No. 1, although at the beginning of the tests, tie No. 11 developed a crack with greater crack length (see Fig. 60), at thefinalstage the crack was shorter than that in tie No. 1, and only one third as wide. Tie No. 12 with a 40 MPa compressive strength and 30 mm fibres behaved very well in both series of tests. They were not only much better than the standard tie, but also markedly better than tie No. 4, which had the same fibre content but a 65 MPa concrete compressive strength. (An extra tie identical to tie No. 12 was tested to confirm this observation). In thefirstseries, thefirstcrack was initiated by the first blow from the 711 mm drop height for tie No. 12 and by the sixth blow from the 406 mm drop height for tie No. 4. This indicates that much more energy was absorbed by tie No. 12 before first cracking. The final crack width was the same for both ties, about 0.02 mm. In the second series of tests, the crack propagation in the ties were very similar, but the final crack width for tie No. 12 was only 40 % of that for tie No. 4. A comparison of the two pairs of ties, No. 11 to No. 1 and No. 12 to No. 4, indicated that increasing the concrete strength is not an effective way of improving the  Chapter 9. Impact Resistance of Modified ITISA Ties  180  impact resistance of the tie. The reduced concrete compressive strength, when used in conjunction with short steel fibres, may lead to better performance. The reason may be seen in Figs. 64, and 65. The lower stiffness of tie No. 12 caused the impact loads and the support loads to be lower than those for tie No. 4. That is, the impact load applied to the tie depends not only on the drop mass and height of the hammer, but also on the properties of the tie itself.  Chapter 9. Impact Resistance of Modified ITISA Ties  181  Maximum Crack Length (mm)  Drop Height (mm) & No. of Blows Final Crack Width Residual Crack Length (mm)  ,_ #1:0.16 mm #4:0.02 mm  J  #11:0.03 mm #12: 0.02 mm  Drop Height (mm) & No. of Blows  Figure 60. Concrete Strength Effect on Crack Propagation Hammer Mass = 60 kg  Chapter 9. Impact Resistance of Modified ITISA Ties  Length of Crack (mm) 250 i  Number of Blows  Tie No.  Concrete Strength  Crack Width (mm)  1  65 MPa (no fibre)  0.65  4  65 MPa (1% 30 mm fibre)  0.26  11  40 MPa (no fibre)  0.20  12  40 MPa (1% 30 mm fibre)  0.10  Figure 61. Concrete Strength Effect on Crack Propagation Hammer Mass = 578 kg, Drop Height = 559 mm  Chapter 9. Impact Resistance of Modified ITISA Ties  183  9.1.5. Effect of Prestress Level  Three different prestress levels were used when making the concrete tie specimens. The standard ITISA ties were post-tensioned using a 392 kN force. This prestressing force was reduced to 223 kN for ties No. 7 and 8; and there was only 49 kN prestress for ties No. 9 and 10, although the same size of steel bars was used for all of these ties. The low prestress force applied to tie No. 9 and 10 was just enough to hold the prestressing bar straight when the ties were grouted. Taking in consideration the prestress loss during the tie processing and curing , the prestress in ties No. 9 and 10 can be considered to be zero. Figs. 62 and 63 show that with zero prestress, ties No. 9 and 10 were damaged very quickly and severely, despite the addition of steel fibres to tie No. 10. However, tie No. 8, with approximately 50% less prestress than the standard, combined with short fibres, behaved very well, performing much better than tie No. 1 and similarly to Tie No. 4. The good quality of this tie is owing, again to, its developing with a relatively lower impact load, as shown in Fig. 65, and its improved toughness. Thefirstcrack on tie No. 8 appeared later than on tie No. 1, and its development was retarded. Thefinalcrack width was much less than that in tie No. 1. In another series of tests (6), it was also found that a lower prestress level in a beam may lead to a lower impact load applied by the drop hammer. The reason for that is not completely understood, but a previous study (21) has shown that a lower prestress level leads to a lower natural frequency and a lower dynamic flexural stiffness of concrete members. This implies that the prestress level will also influenced the flexural stiffness of the beam, and thus the maximum impact load.  Chapter 9. Impact Resistance of Modified ITISA Ties  184  Maximum Crack Length(mm) 100 Tie No.  Type 392 kN prestress —B— 223 kN prestress —*— 223 kN prestress + 1% 30 mm Fibres zero prestress  -e10 406  508  610 711 813 914 Drop Height (mm) & No. of Blows  zero prestress + 1 % 30 mm fibres —  1016  392 kN prestress + 1% 30 mm fibres  —A—  Residual Crack Length (mm) 100  Final Crack Width #1:0.16 mm #4: 0.02 mm #7: 0.18 mm #8: 0.04 mm #9: 0.20 mm #10:0.10 mm 406  508  610 711 813 914 Drop Height (mm) & No. of Blows  1016  Figure 62. Prestress Effect on Crack Propagation Hammer Mass = 60 kg  185  Chapter 9. Impact Resistance of Modified ITISA Ties  Length of Crack (mm) 300 i  Number of Blows  Tie No.  Type  Crack Width (mm)  1  Normal (392 kN prestress)  0.65  7  223 kN prestress  0.28  8  223 T prestress + 1% 30 mm fibre  0.10  9  0 prestress  1.50  10  0 prestress + 1 % 30 mm fibre  Figure 63. Prestress Effect on Crack Propagation Hammer Mass = 578 kg, Drop Height = 559 mm  2.00  Chapter 9. Impact Resistance of Modified ITISA Ties  186  9.2. Simplified Quasi-Static Model for Impact Testing  9.2.1. Assumptions  Since the impact load could be successfully simulated by a drop mass hammer striking a simply supported tie in the laboratory (8, 29), a drop weight, W, and a simply supported beam were used as a simplified mechanical model to analyze, at least qualitatively, the relationship between the impact load and the dynamic mechanical properties of the beam. In this quasi-static model, the load vs. deflection relationship and the deflected shape function of the beam still conforms to static beam theory. The duration of the applied load was assumed to be infinite compared to the natural periods of vibration of the beam, thus the dynamic amplification factor for the response of the tie is always 1, i.e., the amplification of the deflection, and hence of the elastic strain energy under dynamic loading was neglected. This is a simple way to demonstrate the relationship between the impact contact load and certain other factors involved in the tests. However, the general solution has been confirmed by the dynamic analysis which will be described in Appendix at the end of this thesis. (The amplification factors of the deflection or concrete strain are also obtained in the dynamic analysis, which are considered to be important in improving the wheel impact load detector and wheel truing program in service). For an impact load which introduces either no crack or only a few microcracks in the tie, it may be reasonably assumed that 1) all of the potential energy of the hammer weight, W, is transformed into beam elastic strain energy as the drop hammer falls through the height h; and 2) the beam is linearly elastic. 9.2.2. Derivation of Impact Load  Chapter 9. Impact Resistance of Modified ITISA Ties  187  From the law of conservation of energy, the equation  W(h +  A)=-FA  (51)  can easily be obtained (86), where A is the maximum deformation of the beam and F is the maximum force when W has reached its lowest point. At that time, the velocity of both the weight and beam can be considered to be zero and no kinetic energy exists in the system. All of the potential energy lost by the hammer has been transferred into the work done by the applied load moving through the distance A The impact factor, IF, can be expressed as:  F h IF = — = 2(1 + -) W A  (52)  Substituting A = FL /48EI for a simply supported beam into Eqn. 52, IF can be 3  obtained as:  (53) If the impact factor is very large, as it is in the present tests, for a specified testing system with constant drop weight W and support span L, Eq. 53 may be simplified to  IF=  — OCyfhEI  W  9.2.3. Relationship between Drop Height of Hammer and Impact Load  (54)  188  Chapter 9. Impact Resistance of Modified ITISA Ties  On the basis of Eq. 54, the impact load is proportional to the square root of the drop height. Actually, in these tests, the maximum loads for different drop heights h, as shown in Fig. 49 in Ch. Error! Reference source not found, are quite consistent with Eq. 54. For example, we can calculate the ratios of the maximum loads at different drop heights:  , VA = 1016 = 1.25= , =1.20 UlkN " V/* = 711  F  \46kN  mbmm  F  1Umm  (55)  /11 mm  and  5»=. um F  =  mmm  .4~J  -*™  h=7Umm  =l  SlkN  Jh = 406 mm  (56)  Fig. 64 shows that there is a very good linear correlation between the maximum impact loads and the square roots of the drop heights. The slopes of the regression lines for ties No. 1, 4, and 12 indicate the relative magnitudes of the bending stiffness of each tie. The tie No. 12 with 40 MPa concrete had a lower bending stiffness than tie No. 4 with 65 MPa concrete. Moreover, from Eq. 53, if the impact factor is very large, the following relationship can be established:  IF = -~ J^L-Focy/W W \Wl 3  (57)  This relationship can also be proved by the present tests. For example, comparing the maximum load in the impact test for the ITISA standard tie under a 610 mm (24")  Chapter 9. Impact Resistance of Modified ITISA Ties  189  drop height using a 60 kg hammer with that under 559 mm (22") drop height using a 578 kg hammer, the following relation can be obtained:  F  mkg  _  360kN _  3 2 J  ^ V578*g  = 3  (58)  1 Q  These relationships may be beneficial in the design of the impact tests. Maximum Impact Load (kN) 200  150  A' 100  .A ySA' n5T A- n^rT  h  -  rfay'  Slopes of  • y^  Regression Lines  50  #1 4.58 #4 5.17 #12 4.43 *T  1  I  I  I  I  I  10  15  20  25  30  Square Root of Drop Height (mmf #1  -B-  #4  A  #12  -o-  Figure 64. Relationship Between Impact Load and Drop Height  35  Chapter 9. Impact Resistance of Modified ITISA Ties  190  9.2.4. Relationship between Concrete Strength and Impact Load  The impact load is proportional to the square root of the stiffness of the concrete, as shown by Eq. 54. Since E is approximately proportional to -Jf , then IF is proportional to / ° . In these tests, the maximum loads for different concrete strengths, 25  c  as shown in Fig. 65, are quite consistent with this relationship. Eq. 54 and Fig. 65 show that a stronger but stiffer structure, with a higher EI, will incur a higher dynamic load, implying that the flexural strength is not the key factor in this type of dynamic design. This conclusion has been confirmed by the tests described in the section 9.1.4. The prestress level may also influence the dynamic bending stiffness of the tie, as some previous work found (21), and hence may influence the impact load. This relationship requires further study.  Chapter 9. Impact Resistance of Modified ITISA Ties  Figure 65. Maximum Load for Ties with 1% 30 mm Steel Fibres #4: 65 MPa; #12: 40 MPa; #8: low prestress  192  Chapter 9. Impact Resistance of Modified ITISA Ties  9.2.5. Relationship between Moment of Inertia and Impact Load  Keeping in mind that for prestressed concrete railroad ties, the current AREA design impact factor is 200% and the design bending moment capacity is 3 times the required quasi-static design moment, reducing somewhat the moment of inertia of the tie, /, will not significantly influence the tie capacity for quasi-static loads, but may significantly reduce the applied impact load. For a beam with a rectangular cross section, substituting  into Eq. 54, we get the impact factor i  IFocy[J = ylbd'/n  oc  -  bd 2  2  (59)  Reducing the depth d of the beam may reduce IF effectively. In addition, fibres and stirrups may be used in the tie to increase the ductility of the tie. Unfortunately, in this series of tests, the cross sectional properties could not be modified owing to the fixed shape of the production tie used in this research. However, in some previous studies of the dynamic properties of concrete ties (34), it was found that when subjected to a dynamic load with 600 Hz frequency, which is close to typical corrugation-passing frequencies, using concrete ties with a reduced depth, the impact load and concrete strain at the rail seat were lower than for the normal tie. The reason of this phenomenon was explained as that the lower stiffness, and hence larger curvature for a given bending moment was offset by a lower dynamic bending moment and less distance from the edge to the neutral axis.  193  Chapter 9. Impact Resistance of Modified ITISA Ties  9.3. Discussion of the Design of a Concrete Tie  There is evidence (87, 88) that the effective track modulus for track with wood ties may be as low as one sixth to one third that of concrete tie tracks. This is one reason why wood ties do not suffer from impact damage (87) although they do possess a lower flexural strength. In a trial test carried out as part of this study, due to the high flexibility of the wood ties, they experienced only one third the maximum impact load of the concrete ties at the same hammer drop height. For the design of concrete ties. AREA has increased the design impact factor from 50%, which was recommended in the 1970's, to 200%, which is the current recommended value (25, 26). When higher impact loads were measured in track, the impact factor, and hence the concrete strength f , the cross c  sectional area of the tie, and the stiffness EI, were increased continuously to higher levels, leading to even higher impact loads on the "improved", stiffer ties. This was repeatedly followed by an increased impact factor. In this manner, the benefit of the improvement may not have been as good as expected and the increased impact load may also have influenced other parts on the wheel set and rail. Thus the flexibility and ductility of the tie rather then the strength of the concrete should be considered as the governing parameter, as is widely accepted in the design of earthquake resistant structures. The design for this series of tests, which included the consideration of the reduction of concrete strength and prestress force, or the depth of the ties, if possible, while adding fibres and stirrups to increase the ductility of the ties, is based on this philosophy. A reasonable reduction of concrete strength, prestress force or the depth of the ties will not influence the tie capacity to resist quasi-static loading because the current design bending moment capacity of the ties is 3 times as high as the required quasi-static moment, but may significantly reduce an applied impact load; It is believed that these measures, combined with the use of steel fibres in the concrete, will  Chapter 9. Impact Resistance of Modified ITISA Ties  194  significantly improve the dynamic properties of concrete ties.  9.4. Summary 1. Steelfibresgreatly improved tie behaviour, leading to shorter andfinercracks in concrete subjected to impact loading. 2. Under repeated short duration pulses, the vertical cracks on the concrete ties may be accompanied by horizontal cracks. Stirrups can, particularly when used in conjunction withfibres,effectively retard the deterioration of the concrete tie. 3. Theoretical and experimental analyses have shown that the impact factor is proportional to the square root of both the drop height of the hammer and the flexural stiffness of the beam. Reducing the concrete compressive strength, prestressing level or the depth of the tie may result in a reduction of the dynamic flexural stiffness and hence the magnitude of impact loads. It is believed that if these measures were combined with the use of steel fibres in the concrete, a new type of concrete tie, with improved ductility and high resistance to impact load could be developed.  CHAPTER 10. E F F E C T OF RAIL SEAT PADS ON DYNAMIC PROPERTIES  10.1. Introduction  As stated earlier, impact loads applied to concrete ties, due primarily either to the wheel flats of a train or to rail abnormalities, may cause the ties to crack after only a few months in service. One of the major measures taken in practice to attenuate the effect of impact loads on concrete ties has been the use of rail seat pads with a reduced compressive stiffness. The rail seat pad, designed to prevent abrasive wear of the concrete due to small longitudinal and transverse movements of the rail, is the component of the rail fastening system placed between the rail and the tie. It also provides electrical insulation for signal circuits. However, there is currently no standard method available which can be used to evaluate the dynamic characteristics of the pads. Meanwhile, there is evidence (8) that the pads of low stiffness may either deteriorate with repeated loading or undergo hardening under impact loads in service, leading to even more severe damage to the ties. This has long been a major concern, but studies of this problem have been very limited. Since 1980, when Dean, et al (8) at Battelle's Columbus Laboratories developed basic apparatus to evaluate the effect of the pad stiffness on the impact loading on concrete ties , some research has been carried out based on this method. Grassie (33) compared data from laboratory tests on rail pads using a Battelle-type apparatus and data fromfieldexperiments. He found that although the performance of the pads varied with 195  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  196  the particular track conditions, such as ballast support conditions and the magnitude of the quasi-static loads applied, the ranking of the dynamic performance of the rail pads was identical in both the laboratory and field experiments, and there was an excellent correlation between the laboratory and the field data. Igwemezie and Mirza (30) used a similar method to test pad performance under impact. They found that the impact load versus peak strain of the concrete tie relationship was linear. The impact load and hence the tie strain was a logarithmic function of the product of the axial stiffness and the shape factor of the pad. However, Dean, et al (8) in 1983 tested about 20 types of pads and found that the measured static pad stiffness provided a very unreliable measure of strain attenuation capability. Their rankings of the static stiffness and the strain attenuation capability were quite different. Since then, many new types of pads have been developed, but there has been no recent work on systematically testing the different pads that are currently being used. Also, more study is necessary regarding the deterioration of the dynamic performance of pads in service. Thirteen types of pads, including both new and used pads, had been collected and tested for their static compressive stiffness at San Jose State University by Venuti (69, 89) in 1992. In the present study, the impact characteristics of these pads were determined. For each pad, the attenuation of the impact load, the concrete rail seat strain at the impacted end of the tie and the concrete rail seat strain at the nonloaded end of the tie were measured and ranked. A frequency-domain analysis was carried out to determine the underlying relationship amongst these three parameters. In addition, the reduction of the attenuation capability of two types of commonly used pads, after 3.5 years in service, was evaluated and analyzed. 10.2. Specimens  On the basis of the work done by Venuti (69, 89), the pads tested are described  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  below:  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  198  Rail Seat Pads Tested for Impact Attenuation No. 1. (JM 1) 5.0 mm Amtrak Acme 81 -020 EVA 1240 18% vinyl, flat pad. 2. (JM 2) 6.5 mm Amtrak Acme 84-006 EVA 18% vinyl, double dimple. 3. (JM 5) 6.5 mm CSX Acme 90-002/P Texin 445 Polyurethane, double dimple with sealing rings. 4. (JM 7) 5.0 mm CN CRP-Pandrol 6252 reinforced dual durometer rubber, double dimple with one sealing ring. 5. (JM 9) 6.5 mm CSX CRP reinforced dual durometer rubber, double dimple with sealing rings; 6. (EVA 4) 6.5 mm Acme (Pandrol) EVA double dimple. 7. (EVA 1) 6.5 mm Acme (Pandrol) EVA double dimple; after 165 MGT (million gross tons of loading) in service on Southern Pacific track at Dragoon. 8. (LUP 4) 6.0 mm Lupolin flat pad, EVA, manufactured in Germany. 9. (LUP 1) 6.0 mm Lupolin flat pad, EVA, manufactured in Germany; after 165 MGT in service on Southern Pacific track at Dragoon. 10. Safelok 8.0 mm rubber with 3 chevrons on top surface and 4 chevrons on bottom surface, has 4 locating tabs; similar to the type installed in Southern Pacific track at Dragoon in January, 1991, and in Burlington Northern Railroad track at Hemingsford. 11. (CRP 1) 7.0 mm CRP rubber reinforced dual durometer, double dimple; sealing rings on each side. 12. 6.0 mm CRP flat pad with rubber bottom and polyurethane top; similar to pads used on Canadian National Railway (has small 5 mm hole in center. 13. 8.0 mm CRP polyurethane pad with 1 mm rubber bottom; polyurethane top has 10 grooves, rubber bottom is flat, has 4 locating tabs.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  199  The number at the beginning of each type of pad listed above is the specimen number used in the present tests and discussions. The static stiffnesses and durometer numbers of the pads are listed in Table 18, where El is the pad stiffness determined from the slope of line connecting the points on the load vs. deflection curve corresponding to loads of 17.8 kN (4 kips) and 89 kN (20 kips), and E2 is determined from the slope of the line from 106.8 kN (24 kips) to 195.8 kN (44 kips). El, rather than E2 was used as a reference in this test because the starting point of El, 17.8 kN, is very close to the clamping force on the pads due to the Pandrol fastening system and 89 kN is very close to the maximum impact load reached during this test series.  200  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  Table 18. Static Stiffness of Rail Seat Pads  E1:17.8 to 89 kN(4to20 kips) E2:108.8 to 195.8 kN (24 to 44 kips)  Rail Pad  E1  El  E2  E2  No.  kN/mm  kips/in  kN/mm  kips/in  Durometer -A  1  1120.0  6,400  1312.5  7,500  96  2  210.0  1,200  630.0  3,600  94  3  227.5  1,300  262.5  1,500  89  4  227.5  1,300  577.5  3,300  79 & 73 (*)  5  122.5  700  542.5  3,100  77 & 65 (*)  6  210.0  1,200  490.0  2,800  98  7  315.0  1,800  1400.0  8,000  95  8  560.0  3,200  1400.0  8,000  100  9  490.0  2,800  1242.5  7,100  96  10  63.0  360  210.0  1,200  84  11  140.0  800  420.0  2,400  82 & 72 (*)  12  187.3  1,070  521.5  2,980  97 $ 65 (*)  13  148.8  850  306.3  1,750  96 & 63 (*)  (*): First number is the durometer at top surface, Second number is for bottom surface.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  201  10.3. Experimental Program  The 60 kg impact machine was used for the impact tests of all of the rail seat pads. Each type of pad was installed on an ITISA tie using the Pandrol fastening system, and was subjected to repeated impact loading. The testing setup, instrumentation and data acquisition for the pad testing were exactly the same as those for ITISA ties, as shown in Fig. 52 in Chapter 8, but only channels 1, 2, 3, 4, and 8 were utilized. The drop hammer was released from a predetermined height and dropped onto the top of the rail segment, inducing an impact pulse to the pad and tie. A new Acme 84-006 EVA pad was placed on the nonloaded rail seat only as a shim for the application of the preload. When the tests for each pad at the impacted end were finished, the EVA pad at the free end was also replaced with a new one. Two strain gauges were used to evaluate the concrete strain attenuation of the different types of pads. The crack detection gauge mounted on the bottom of the tie was used to determine whether the concrete tie had cracked at all during the impact event. The drop heights of the hammer were chosen as 102 mm (4"), 203 mm (8") and 305 mm (12"). Each pad underwent three blows from each of these three drop heights. The impact load histories, the concrete strains at the two rail seats, and the accelerations of the tie were determined for each impact blow. The data were later digitally filtered using the PC signal processing software, MATLAB. The cutoff frequency used was 2000 Hz; most of the energy in thefirstfour bending modes was preserved. Pad No. 1 was used as a datum to compare the characteristics of the other pads. For each pad tested, the maximum values of the data obtained from each of the three drop heights were compared to the maximum values for pad No. 1 obtained from the same drop height. For example, the relative strain attenuation for pad No. 2 was estimated by:  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  A, =(l-e /e,)xl00%  202  (60)  2  where e and e, are the maximum strains for pad No. 2 and pad No. 1 respectively, due to 2  the impacts under a particular drop height of the hammer. The final value of strain attenuation listed for pad No. 2 is the average of the A values for the blows under the three 2  drop heights of 102 mm, 203 mm and 305 mm. 10.4. Results and Discussion  10.4.1. Attenuation Effects on Pads on Rail Seat Concrete Strain —Impacted End  Fig 66 shows the rail seat tensile bending strain attenuation at the impacted end for all 13 pads. The static stiffnesses of the pads, El, are also shown. The typical strain history diagrams for both the impacted and nonloaded ends are shown in Fig 67. In general, the strain attenuation capabilities of the pads correspond roughly to the pad static stiffnesses, but there are some exceptions, such as with pads nos. 5, 12 and 13. In other words, the pad static stiffness could not be used as a criterion to evaluate the dynamic properties of pads due to impact.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  Figure 66. Attenuation Effects of Pads on Rail Seat Strain --Impacted End  203  204  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties Microstrain 400 Strain For Impacted Rail Seat Pad #1 Pad #10  300  200  100  -100  4  6 Time (ms)  10  Microstrain 200  Figure 67. Rail Seat Strain History for Pad Nos. 1 and 10 Hammer Drop Height = 305 mm  12  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  205  A frequency domain analysis of the pads under impact loading shows more clearly the role of a resilient pad in attenuating the impact load. From Fig 68, it may be seen that pad No. 10 acted as a low- pass filter, which filtered almost all of the energy in the third and fourth tie bending modes and nearly half of the energy in the second mode for the rail seats at both ends. The low-pass "break frequency", the most important filter characteristic, seems to be near the second bending mode resonance frequency for pad No. 10. Accordingly, the time duration of the strain in one cycle for pad No. 10 was apparently extended, as shown in the strain history diagram in the time domain in Fig 67. Since the energy consumed in the tie during the impact event was much less with pad No. 10 than with pad No. 1, special attention should be paid to the deterioration or hardening of pad No. 10, which may absorb more potential energy from the falling mass. Actually, the much larger hysteresis loop in the load-deflection curve for pad No. 10 compared to the loop for pad No. 1 in the static tests, as shown in Fig 69, provides such a warning. It should be noted that although the results of the impact attenuation tests of pads in the laboratory were consistent with the results obtained by measurements made under moving loads in track (8, 33), there is no universal correlation between laboratory and field tests that can be applied to every type of pad.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  206  Magnitude  Impacted End Pad#1 Pad #10  1042 600  800  1000  1200  1400  1600  frequency (Hz)  Magnitude Nonloaded End  358  Pad #1 Pad #10  0 ^ 0  200  400  600  800  1000  1200  1400  1600  frequency (Hz)  Figure 68. Frequency Spectra of Rail Seat Bending Strain for Pads No. 1 and 10  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  207  Pad No. 1 Load (kN) 250 ,  1  0.25  0  0.5  1  1.5 Deflection (mm)  2  2.5  Figure 69. Static Compressive Tests of Rail Seat pads Nos. 1 and 10  3  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  208  10.4.2. Attenuation Effects of Pads on Rail Seat Strain --Nonloaded End  Fig. 70 shows the compressive rail seat strain attenuation at the nonloaded end for all pads under impact. As was seen in Fig 67, the maximum tensile strain occurred at the rail seat at the impacted end, while the maximum compressive strain occurred at the bottom of the tie under the rail seat at the nonloaded end, implying that quite a high tensile strain may be reached at the top of the tie, where the flexural strength for negative bending moment is only about half that for positive bending moment. The strain attenuation effect of the pads on the nonloaded end is thus the other important contribution of pads to the protection of concrete ties, particularly when the impact load is due to rail defects that occur on only one side of the track. It should be noted that under service load conditions in track, both rail seats are subjected to impact from wheelflatssimultaneously, since wheel flats are similar on both wheels of a given axle. However, field tests have shown that owing to excitations, a rail seat can be subjected to both positive and negative moments under impact loading. (See Fig. 67, as an example). The ranking of the strain attenuation capabilities for the nonloaded end, shown in Fig, 70, was similar to the ranking for the impacted end, shown in Fig. 66. However, a remarkable change was seen for pad No. 9, which attenuated the tensile strain at the impacted end by 11% but increased the compressive strain at the nonloaded end by 2%. As shown above, a resilient pad such as pad No. 10 usually acted as a low-pass filter, which filtered the energy in all of the bending modes which are higher than a particular low-pass "break frequency". However, the dynamic behavior of pad No. 9 is quite different (see Fig. 71). It can only filter a selective vibration mode, instead of all of the higher bending modes. Although the energy in the third bending mode was significantly filtered, the energy in the fourth mode actually became a little higher.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  Figure 70. Attenuation Effects of Pads on Rail Seat Strain -Nonloaded End  209  210  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  Magnitude  200  400  600  800  1000  1200  1400  1600  frequency (Hz)  Figure 71. Frequency Spectra of Rail Seat Bending Strain for Pad Nos. 1 and 9  The vibration mode shapes of concrete ties have been investigated previously (29, 33). For similar types of ties, the mode shapes are generally similar, with a small variation in the resonance frequency for each mode. These are illustrated in Fig. 72, with the corresponding frequencies measured in the present tests. Since the initial condition of all mode shapes was determined by the impact pulse which forced the rail seat at the impacted end downward, the mode shapes at the beginning of the impact pulse should be the same as the shapes illustrated in the figure, and both the tensile strain and the compressive strain reached a maximum within thefirstcycle. When the tie vibrated in itsfirstmode, the dynamic tensile strain in the tie was a maximum at its center, having little influence on the rail seat strain. The second and fourth modes are asymmetrical. When the tie vibrated in these modes, the tensile strain response of the tie was a maximum near the bottom of the rail seat at the impacted end, but the compressive strain response of the tie was a maximum near  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  211  the bottom of the rail seat at the nonloaded end. With pad No. 9, the second and fourth modes of the tie were not attenuated, but were increased somewhat, contributing to a small increase in the compressive strain at the bottom of the nonloaded end. The third mode (618 Hz) played an important role in the tensile strain response of the tie at both rail seats since in this vibrating mode the maximum tensile strain occurred right at the rail seats. The significant attenuation of this mode by pad No. 9 reduced the tensile strain of the tie at the bottom of two rail seats, contributing to the reduction of total apparent rail seat tensile strain at the impacted end. However, since the apparent strain response is the sum of the strain response contributions of each mode, the change of the third mode may reduce the tensile strain fraction in the total response at the bottom of the nonloaded end, leading to a further increase of apparent compressive strain.  1  MEASURED FREQUENCY  MODE SHAPE  MODE  ^  J"  98 Hz  2  358 Hz  3  618 Hz  4  1042 Hz  Figure 72. Mode Shapes and Frequencies of ITISA Concrete Tie  This result implies that a pad which can attenuate the tensile strain at the rail seat at  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  212  one end does not necessarily attenuate the compressive strain at the other end. Although it is not a very common situation, it should be considered when a new pad is used for attenuating an impact load applied only at one end of tie, such as the impact due to rail abnormalities.  10.4.3. Attenuation Effects of Pads on Impact Load In the previous sections, the attenuation effects of pads on rail seat strain have been discussed. The maximum rail seat strain reflects the maximum bending load and bending moment applied on the tie. However, since the inertial load also contributes to the measured impact load, and different types of pads may have different influences on the magnitude of inertial load, the ranking of the rail seat strain may not be the same as that of the wheel-rail contact impact load. In practice, the wheel-rail contact impact load influences the working conditions of not only the rail fastening system and the rail surface, but also the wheels and the train. Hence, the attenuation effects of pads on the impact load need to be considered in evaluating the pad properties. In these tests, the impact load was measured with a load cell installed in the tup of the hammer. The average impact load attenuation for all pads is illustrated in Fig. 73.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties Load Attenuation (%)  213 Pad Stiffness (kN/rrm)  Figure 73. Attenuation Effects of Pads on Impact load  The ranking of the load attenuation capability of the pads was found not to be the same as the ranking for the strain attenuation capability. Pad No. 5 was best here instead of pad No. 10. Fig. 74 are shows the impact load histories for pads nos. 1, 5 and 10. The first and the highest load peak for pad No. 10 was not the true bending load. It was the inertial load due to the acceleration of the rail segment mass. Since the pad was very soft, with only half of the stiffness of pad No. 5, on first contact with the striking tup the rail segment moved much quicker with pad No. 10 than with pad No. 5, leading to a much higher inertial load and a lower apparent impact load attenuation. However, comparing the true flexural loading of pad No. 10, which is the third peak of its curve, with the true flexural loading of pad No. 5, which is the second peak of its curve, pad No. 10 still behaved better with a lower flexural loading, corresponding to its better strain attenuation characteristics.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  214  These results indicate that, when using different types of pads, a lower measured maximum wheel-rail contact load does not always lead to a lower tie response. The inertial load may disturb the results. To examine the responses of the tie with different types of pads, it is essential to measure directly the rail seat strain of the tie. This should be given special attention when evaluating the properties of pads based only on recorded wheel-rail contact loads.  Load (kN) 80 i  Time (ms)  Figure 74. Impact Load History for Pad Nos. 1, 5 and 10 Hammer Drop Height = 102 mm  t  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  215  10.4.4. Deterioration of Static and Dynamic Characteristics of Pads In this series of tests, two pairs of pads (a new and a used pad for each pair), were tested. Pad No. 7 was the 6.5 mm EVA pad subjected to 165 MGT, and pad No. 9 was the 6.0 mm Lupolin flat EVA pad, subjected to 165 MGT; both of them had been in service for 3.5 years. Comparing the used pad No. 9 with the new No. 8, it may be seen that the static stiffness, and the attenuation of rail seat strain at the impacted end and the nonloaded end are almost unchanged. But comparing the used pad No. 7 with the new pad No. 6, the changes are significant. Table 19 shows the changes of the properties for the two pairs of pads.  Table 19. Deterioration of Used Pad with Respect to the Same Type of New Pad  Acme EVA pad  Lupolin flat EVA pad  Static Stiffness Increase  50%  0%  Impact Load Increase  30%  0%  Impacted end  10%  0%  Nonloaded end  19%  5%  Rail Seat Strain Increase:  Although the dynamic performance of a new Acme EVA pad (No. 6) is much better than that of a new Lupolin flat EVA pad (No. 8), after only 3.5 years in service their performances had become very close to each other. An even worse adverse effect of the Acme EVA pad than Lupolin EVA pad on ties might be predicted in subsequent years. In fact, a similar result was also obtained in a previous study (8), in which a moderately  216  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  flexible type of pad behaved worse than the standard rigid EVA pad after being exposed to only 15 MGT loading in service. The quick deterioration of pad No. 7 was due, at least partly, to the larger hysteresis loop in its static load- deflection curve showed in Fig. 75. The pad may absorb more impact energy to protect the tie, but exhibits a reduced life. The correlation of the hysteresis loop in static load-deflection curves of pads with the deterioration of pads under impact seems to merit further study.  Load (kN) 250 Pad No. 8  1  f  200  Pad No. 6  Ji  ;!  150 -  100  -  7  " '  'l  50  /  £^ ^ 0.2  0.4 0.6 Deflection (mm)  0.8  Figure 75. Static Compressive Tests of Rail Seat Pads for Nos. 6 and 8  It is to be noted that the ACME EVA pads were of the non- irradiated type. For further research, it would be of value to conduct static and impact tests on irradiated ACME EVA pads to determine the change in stiffness and strain attenuation with severe loading of approximately 200 MGT.  Chapter 10. Effect of Rail Seat Pads on Dynamic Properties  217  10.5. Summary Using the 60 kg impact machine, thirteen types of pads installed on an ITISA tie using the Pandrol fastening system were tested and ranked. The attenuation effects of pads on impact load, tensile strain at the impacted end and compressive strain at the nonloaded end were evaluated. A frequency domain analysis was carried out. Some of the results are: 1. Soft pads may act as a low-passfilterto significantly reduce energy in the second and the higher vibrating modes, leading to lower amplitudes but longer duration of the concrete strain vibration. 2. Pads that can attenuate the tensile strain at the impacted end do not necessarily attenuate the compressive strain at the other end. The frequency spectrum analysis may help to judge the properties of pads. 3. Using different types of pads under the same circumstances, a lower measured wheel-rail contact impact load does not always produce a lower rail seat strain response. The differing amounts of inertial loading may disturb the analysis. 4. In comparison with stiff pads, soft pads may structurally deteriorate more quickly, leading to an even worse influence on the ties after a period of time in service. This result indicates that the effectiveness of using soft rail seat pads to protect concrete ties is limited. 5. The hysteresis loop in the static load-deflection curve of the pads might be used to predict the rate of deterioration. This topic merits further study.  CHAPTER 11. CONCLUSIONS AND RECOMMENDATIONS  11.1. Conclusions Two different series of impact tests on prestressed concrete railroad ties were conducted in this study, each with its own emphasis. The emphasis in the first series was on the roles of the support conditions and the rail pads in minimizing damage to ties subjected to long duration, high amplitude pulses simulating rail abnormalities, and the effect of the loading rate on the crack mode and fracture energy of the tie. The purpose was to try to reveal, both experimentally and theoretically, the mechanism governing the shift of fracture modes at different loading rates. For the second series of tests, the emphasis was on improving the dynamic properties of prestressed concrete railroad ties so that the concrete cracking due to wheel-flat and rail abnormalities in service could be significantly reduced. The relationships between maximum impact load and several design parameters, such as the cross section sizes, the flexural stiffness of the concrete ties and concrete strength, were also studied. For the first series of tests, the following results were obtained: 1. The previously developed "single-blow" impact technique was extended to a "multi-blow" technique, in order to better simulate the repeated impact loading on the concrete tie in track, in terms of both pulse duration and amplitude. In the multi-blow impact technique, the beam undergoes an acceleration phase, when the bending load is lower than the tup load, and a deceleration phase, when the bending load is greater than 218  Chapter 11. Conclusions and Recommendations  219  the tup load. When the beam is in the elastic rebound period, it releases a portion of its stored strain energy back to the hammer. If the beam is not broken into two or more pieces, the area under the tup load versus deflection curve is almost the same as that under the bending load versus deflection curve, and could be used to evaluate the fracture energy of the beam. 2. In order to simulate the load conditions of the ties in track, three supports, and both rail seat pads and rubber support pads were used in the impact tests. This complicated the analysis of the deformed shape of the ties. However, the fact that the ties remained largely intact after most impacts permitted the adoption of a simplified method of analysis. Since the system then had no significant inertial or kinetic energy losses, the fracture energy of the ties could be evaluated using only the total area under the load vs. time curve. 3. When subjected to an impact pulse with about 10 ms duration and 300 to 600 kN magnitude, the stiffness of the rubber support played an important role in the dynamic response of the ties. A comparison between the effect of the soft and hard rubber support showed that: a) When the soft support was used, the loading rate and the maximum load were lower. There was more fracture energy absorbed before failure, and flexural fracture occurred in a ductile manner. When the hammer mass increased by about 46%, to 504 kg, the tie using the soft support still behaved better than that using the hard support with the 345 kg hammer. Although the maximum load at the first blow was the same for the two cases, the loading rate was 50% higher for the latter, leading to much less energy absorbed in fracture and more damage to the tie. This was attributed to different fracture modes of the tie under different support conditions. b) Using the hard support caused a higher maximum load and loading rate. Less energy was absorbed before failure, and flexure-shear or compression-shear failure  Chapter 11. Conclusions and Recommendations  220  occurred in a brittle manner. 4. When subjected to a pulse with 10 ms duration and 300 to 500 kN magnitude, and with the hard support, the stiffness of the rail seat pad had an intermediate effect on the behaviour of the tie; when the soft support was used, no significant effect was found. 5. The higher loading rate induced a more brittle failure mode. As the loading rate increased, the principal mode of cracking changed from flexure to flexure-shear and then to shear. 6. The static residual capacity of the ties, after being subjected to impact loading, was measured using static bending tests. The residual fracture energy, peak load and initial stiffness of the ties were measured and compared to those for the new tie. These results also showed that using soft supports greatly reduced the tie deterioration under repeated impact loading, in comparison with the use of hard supports. Using soft rail seat pads had some beneficial effect on the deterioration of the ties under impact when the hard supports were used. There was very little effect of the rail seat pads on impact resistance of the ties when soft supports were used. 7. Crack mode analysis of the ties for the first series of tests showed that the crack mode changed from flexural under static loading to shear under impact loading because the shear to moment ratio at the mid-span of the tie had changed. A significant portion of the applied load is balanced by the distributed inertial load along the beam, whose resultant force has a much shorter moment arm to the mid-span of the beam than the support load, leading to a reduced bending moment at mid-span. Therefore the applied load can go to a much higher level than the original static flexural cracking load without inducing any flexural crack on the beam. When this load reaches the shear cracking load, which is the same under both impact and static loading, a shear crack may appear first. 8. The critical time at which the tie is most likely to initiate the first shear crack is at the moment of impact (zero time), when the inertial load is at a maximum and the  Chapter 11. Conclusions and Recommendations  221  support load is still zero. All of the applied load is balanced by the distributed inertial load along the beam. The force arm of the resultant inertial force, to the mid-span of the beam, can be taken as the effective span for the equivalent static test system. If the effective shear cracking load in this system is lower than the effective flexural cracking load, a brittle-shear failure may occur under an unexpected impact event. If not, the beam is, generally speaking, unlikely to produce a shear crack first. An investigation of the inertial load distribution along the beam is necessary to carry out a crack mode check. For a beam subjected to an impact by a striking body with a relatively low velocity (< lOm/s), the sinusoidal profile can be assumed for reinforced, prestressed, and steel fibre reinforced (>1.0%fibre)concrete ; a linear profile can be assumed for plain concrete and fibre reinforced concrete with a low volume percentage offibres.Taking one third of the span as the effective span is conservative for both situations. 9. The crack mode analysis for the CXT tie showed that this method is effective. Using a soft rubber support can cause the inertial load to be distributed uniformly, and thus the effective span is significantly greater than for a sinusoidal distribution, hence protecting the beam from brittle-shear failure.  In the second series of tests, the effects of the concrete compressive strength, steel fibre additions, changes in prestressing force, the presence of stirrups, and rail seat pad compressive stiffness on the behaviour of concrete ties under impact loading were examined. This, in turn, gives rise to suggestions for improvement of the concrete tie design. The following conclusions were reached: 1. In order to simulate the response of concrete ties to impact loading, it is essential to replicate, as closely as possible, the impact pulse measured on track in service, in terms of the duration of the pulse and the shape of the load vs. time curve. Two typical types of impulses encountered in track, due to rail abnormalities and "wheel flat" of  Chapter 11. Conclusions and Recommendations  222  trains, were successfully simulated by the use of the 578 kg impact machine and the 60 kg impact machine respectively. With the 60 kg machine, the hammer mass, and the type and thickness of the rubber shim between the hammer and the striking tup are adjustable, to permit the production of a specified duration of pulse on the tie over a certain range. The drop height of the hammer will influence the amplitude but not the duration of the pulse. 2. Spectral analyses showed that thefirstthree bending modes of the tie in the tests using the 60 kg machine were quite close to the measured bending modes in the field. The very low magnitude of the first mode in the laboratories can be attributed to the single-sided loading, in contrast to the two-wheeled loading of the tie in track under service conditions. It is believed that this difference had little influence on the response of the rail seat concrete strain of the ties. 3. Thirteen different types of ties were tested using both impact machines. The vertical crack opening length and residual crack length for each tie were detected with specially designed crack detection gauges. The principal results were: a) . Steel fibres greatly improved tie behaviour, leading to shorter andfinercracks in the concrete when subjected to impact loading. It was found that the tie with 30 mm fibres performed somewhat better when using the 60 kg hammer, while the tie with 50 mm fibres performed better when using the 578 kg hammer, although the differences were small. This is because as stated above, the two machines induced different types of cracks on the ties. The shorter fibres have a smaller effectivefibrespacing in the tie and are therefore more effective in resisting microcracks and fine cracks; the longer fibres bridge across wider cracks, providing more effective resistance to the growth of such cracks. b) .. Under repeated short duration pulses, the vertical cracks on the concrete ties may be accompanied by horizontal cracks. Stirrups can, particularly when used in  Chapter 11. Conclusions and Recommendations  223  conjunction with fibres, effectively retard the deterioration of the concrete tie. c). The ties with a reduced compressive strength of 40 MPa and 30 mm fibres behaved very well. The structural response to impact of these ties was superior to the ties which had the same fibre content but a 65 MPa concrete compressive strength. The reason for this is that the lower stiffness of the tie with lower strength concrete caused the impact loads, the support loads and the concrete strains to be lower than those for the tie with higher strength concrete. That is, the impact load applied to the tie depends not only on the drop weight and height of the hammer, but also on the properties of the tie itself. 4. Experimental and quasi-static theoretical analyses have shown that the impact factor is proportional to the square root of the drop height of the hammer and the flexural stiffness of the beam. Increasing the concrete strength, prestress level and the size of the tie will indeed improve the moment capacity of the tie, but the stiffness of the tie, and hence the impact load and the bending moment may also increase at the same time. The increased impact load greatly influenced the dynamic properties of the ties. (It may also influence the dynamic properties of other parts on the train and track). Reducing the concrete compressive strength or prestressing level of the tie may result in a reduction of the dynamic flexural stiffness and hence the magnitude of impact loads. These measures will not influence the tie capacity to resist quasi-static loading because the current design bending moment capacity of the ties is 3 times as high as the required quasi-static moment due to a 200% impact factor applied. It is believed that if these measures were combined with the use of steel fibres in the concrete, a new type of concrete tie, with improved ductility and high resistance to impact load could be developed. 5. Dynamic analyses of concrete ties have confirmed the relationship between applied impact load and the bending stiffness of the ties. It was also found that for an impact impulse with a specified amplitude, a different impulse duration or frequency  Chapter 11. Conclusions and Recommendations  224  may lead to a very different concrete strain response. In the present tests, before the initiation of first crack in the concrete tie, the bending strain per unit load was 32 % higher for an applied impulse with 4 ms duration (produced by the 60 kg hammer) than that for an applied impulse of 10 ms duration (produced by the 578 kg hammer). This result implies that the cracking threshold load is different in static and in impact loading; also, it may be quite different for impulses of different duration. 6. Using the 60 kg impact machine and a hard rubber support, thirteen types of pads which are currently used in practice, were installed on an ITISA tie using the Pandrol fastening system, and were tested and ranked. The attenuation effects of the pads on the impact load, tensile strain at the impacted end and compressive strain at the nonloaded end, were evaluated. A frequency domain analysis was carried out. Some of the results are: a) . Soft pads may act as a low-pass filter to significantly reduce energy in the second and the higher vibrating modes, leading to lower amplitudes but longer duration of the concrete strain vibration. b) . Pads that can attenuate the tensile strain at the impacted end do not necessarily attenuate the compressive strain at the other end. The frequency spectrum analysis may of value in evaluating the properties of the pads. c) . Using different types of pads under the same circumstances, a lower measured wheel-rail contact impact load does not always produce a lower rail seat strain response, and vice versa. The differing amounts of inertial loading may affect this analysis. d) . In comparison with stiff pads, soft pads may deteriorate structurally more quickly, leading to an even worse influence on the ties after a period of time in service. This result indicates that the effectiveness of soft rail seat pads in minimizing tie damage, in the long run, is limited. 11.2. Recommendations for Future Research  Chapter 11. Conclusions and Recommendations  225  1. The inherent capacity of concrete ties to resist flexural moment and shear under impact may be different from those under static loading. In this research, it was assumed in the crack mode analysis that both capacities increase at the same rate so that their ratio remain constant. This assumption needs to be verified or modified in future studies. To study the inherent capacities of concrete to resist flexural moment and shear under impact, a simply supported plain concrete beam without any rubber pads is recommended to simplify the test condition. Different support spans may be used to create different shear : moment ratios in the beam. 3  2. Theoretical analysis has shown that the impact factor, IF, is proportional to d 2  Reducing the depth d of the tie may effectively reduce IF. In addition, fibres and stirrups may be used in the tie to increase the ductility of the tie. Unfortunately, in this series of tests, it was not possible to modify the shape and cross-sectional properties since standard production ties were used. Some previous studies of the dynamic properties of concrete ties (34) have shown that using a shallower concrete tie, the impact load and concrete strain at the rail seat were lower than for the normal tie. More tests on this aspect should be carried out. 3. To simplify the test conditions, and taking into consideration the available testing facilities, a rubber support and three point support were used to simulate the tie conditions in track. If possible, a closer simulation to the support conditions in track is recommended, such as using a box filled with the ballast as the tie support. Moreover, the single-end impact loading was not a perfect simulation of the impact due to wheel-flats, which normally occur simultaneously on both rail seats of the tie.  A double-ended  impact loading facility would provide a better simulation. 4. The soft rail seat pads were found to deteriorate structurally more quickly than the stiff pads, in terms of the changes in compressive stiffnesses and the attenuation effect of the concrete strain of the ties. The larger hysteresis loop in the static load-  Chapter 11. Conclusions and Recommendations  i.  226  deflection curve of the pads indicated that more energy was transferred into irrecoverable deformation or damage in the pads, and it might be used to predict the rate of deterioration and optimize the properties of the pads. This topic merits further study. Moreover, in the present study, the strain attenuation effect of the pads was compared with the static vertical stiffness of the pads. There is limited correspondence between these values. Alternatively, an attempt needs to be made to compare the strain attenuation effect of the pads to the dynamic vertical stiffness of the pads.  BIBLIOGRAPHY  1. Mindess, S. and Shah, S. 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Banthia, N., Chokri, K., and Trottier, J.-F., "Impact Tests on Cement-Based Fibre Reinforced Composites", in Testing of Fibre Reinforced Concrete, ACI SP-155, American Concrete Institute, 1995, pp.171-188. 67. Hughes, G. and Beeby A. W., "Investigation of the effect of impact loading on concrete beams", The Structural Engineering, Vol. 60B, No. 3, 1982, pp. 45 -52. 68. Yan C, "Bond between reinforcing bars and concrete under impact loading", Ph.D. Thesis, Department of Civil Engineering, University of British Columbia, Canada, 1992. 69. Venuti, W. J., "Report on rail displacements and rotations", for Philip J. McQueen Corporation, San Rafael, California, January 1992. 70. Venuti, W. J., Personal Communication, May 4, 1992. 71. Nianzhi, Wang, S. Mindess and Keith Ko:" Fibre reinforced concrete beams under impact loading", Accepted and to be published in Cement and Concrete Research in 1996. 72. Turner, C. E., "Measurement of impact toughness by instrumented impact test", Impact Testing of Metals, ASTM STP 466, American Society for Testing and Materials, 1970, pp. 73-114.  Bibliography  233  73. Server, W. L., "Impact three point bend testing for notched and precast specimens", Journal of Testing and Evaluation, Vol. 6, No. 1, 1978, pp. 29-34. 74. Ewins, D. J., Modal Testing: Theory and Practice, Research Studies Press LTD. Letchworth, England, 1984, pp. 174-197. 75. Bulson, P. S. (ed.), "Structures under shock and Impact 3", Proceeding of the Third International Conference, Madrid, June, 1994, Computational Mechanics Publications, Boston. 76. Johnson, "Impact Strength of Materials", Edward Arnold Ltd., Bristol, England, 1972. 77. Ayaho Miyamoto, Michael W. King, and Manabu Fuji," Analysis of failure modes for reinforced concrete slabs under impulsive loads", ACI Structural Journal, Vol. 88, No. 5, 1991, pp. 538-545 78. Collins, M. P. and Mitchell, D., "A Rational Approach to Shear Design - The 1984 Canadian Code Provisions", ACI Journal, V. 83, No. 6, 1986, pp. 925-933. 79. Collins, M. P. and Mitchell, D., "Prestressed Concrete Basics", Canadian Prestressed Concrete Institute, Ottawa, 1987. 80. Venuti, W. J., "Report on static properties of prestressed concrete ties with fibers", for the Research and Test Department of the Association of American Railroads, Chicago, Sept., 1990. 81. ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-83)", American Concrete Institute, Detroit, 1983. 82. Watanabe, K., "Engineering of Rail Fastening", Japanese Railway Engineering. Vol. 19, No. 4, 1980. 83. FIP Commission on Prefabrication, "Concrete Railway Sleepers", FJJP state of art report. Thomas Telford, London, 1987. 84. Clough, R. W. andPenzien, J., "Dynamics of Structures", McgrawHill, 1975. 85. Bentur, A., and Mindess, S., Fibre Reinforced Cementitious Composites. Elsevier Applied Science, New York, 1990. 86. Muvdi, B. B., and McNabb, J. W., Engineering Mechanics of Materials 3rd Ed. Springer-Verlag New York Inc., 1991. 87. Driscoll, M. L., and Lamson, S. T., Assessment of Steel Railway Ties; Report No. 85-8, Canadian Institute of Guided Ground Transport, Queen's University, Kinston, Ontario, Oct., 1985.  Bibliography  234  88. Magee, G. M., "Prestressed Concrete Ties", Railway Track and Structures, Vol. 74, No. 8, August 1978, pi8. 89. Venuti, W. J., "Report on Compressive Stiffness of Rail Seat Pads on Southern Pacific Concrete Ties", for Southern Pacific Transportation Co. San Francisco, California, April 1992.  APPENDIX DYNAMIC ANALYSIS OF ITISA TTES  In Chapter 9, to simplify the analysis, the relationship between the impact load and certain parameters of the impact system was derived using a quasi-static method. In this method, the deflection of the beam was still assumed to follow static beam theory, and the duration of the applied load was assumed to be infinite compared to the natural periods of vibration of the beam, thus the dynamic amplification factor for the response of the tie is always 1, i.e., the amplification of the deflection, and hence of the elastic strain energy under dynamic loading was neglected. To confirm the relationship obtained in the quasistatic method, and to obtain the amplification factors for the impact tests with different hammer weights, a dynamic analysis was carried out, which is described in this chapter. A . l . Assumptions  With its distributed mass and elasticity, a beam subjected to dynamic loading is a dynamic system with infinite degrees of freedom, and must be analyzed using dynamic partial differential equations. Since the higher vibration mode contributions to the total deflection of the beam are usually very much smaller than the lower mode (81), usually only the first several modes are considered in the data analysis. Sometimes, if the frequency of the applied load is comparable to or lower than the fundamental natural frequency, only thefirstmode corresponding to the fundamental natural frequency is considered for a simplified analysis, especially when the accuracy requirement is not high. In this situation, the beam problem can be simplified as a single degree of freedom system. 235  Appendix. Dynamic analysis of itisa ties  236  The deflected shape of the beam can be assumed to have the shape of thefirstvibration mode. If this is known, or can be reasonably assumed, then once the deflection of one point is known, the deflections of all parts of the system can be defined. The first three vibration mode shapes were illustrated in Fig. 56 in Ch. 9. Although in the laboratory tests, only the second and third natural modes were simulated, the results still represent the tie response at the rail seat in service (29, 33) because these two modes have their maximum response near the rail seats; thefirstmode of vibration has its maximum response at the center of the tie and has little influence on the response at the rail seat (29). The following analysis is based on the impact tests using a 60 kg hammer. In this series of tests, the impact load introduced either no crack or only a few microcracks in the tie. It may be reasonably assumed that the beam is linearly elastic. The purpose of this analysis is to demonstrate the relationship between the maximum impact load and certain other parameters. Some simplifications have been made to make the process as simple and easy to follow as possible. a) . The typical duration of the applied impact load was 4 ms (a frequency of 125 Hz), much lower than the lowest excited vibration mode of the tie in laboratory, 358 Hz (the second natural frequency). Here, only the lowest excited vibration mode, the second natural mode, will be considered. b) . The system is considered as a simply-supported beam under center-point loading, the nonloaded end of the tie was not considered. c) . The actual deflected shape of the beam between two supports was essentially the superposition of two sinusoidal curves, which corresponded to the second and third mode shapes, respectively (see Fig. 72 in Ch. 10.). In the following analysis, the true shape was replaced by a simple sinusoidal shape.  Appendix. Dynamic analysis of itisa ties  237  These simplifications only influence the quantitative relationships, such as the magnitude of some of the coefficients, but the main proportional relationships remain the same.  A.2. Dynamic Amplification of Applied Load  Let k and m be the generalizedflexuralstiffness and generalized mass of the beam respectively; F the applied load; and x the displacement at the loading point. Neglecting the damping, which is very small for concrete ties (8, 29), the differential equation of the SDOF system becomes: (61)  rnu(t) + ku(t) = F  The applied load F can be taken as (62)  F = F sin cot 0  where, F = amplitude of applied load; a  co = circular frequency of applied load (rad/sec) 2n  n  2x  x 0.004  TC  = 250;r;  where, r- duration of impact pulse, 4 ms for this test. The solution of Eq. 61 is  F u(t) = A sin coj + B sin co t + k  0  n  1 (l-B ) 2  sin cot  (63)  where A, B = coefficients determined by the initial conditions of impact loading;  238  Appendix. Dynamic analysis of itisa ties  co = circular natural frequency of the beam (rad/sec), n  co„ = j — = 2nf Vm  = 2^-358 = 716^;  where / = natural frequency of the beam (Hz), taken as the frequency of the second mode of vibration of the tie, i.e. 358 Hz.  Since the beam initiated its vibration from rest, the initial conditions were  u(0)=u(0) = 0  F B — — can be obtained. Thus, Eq. 63 kil-B )  Equating Eq. 63 and 64, B = 0 and A = 4  5  (64)  M  2  becomes  1  F tt(f) = —  (65)  — (sin cot-Bsin ODJ)  If when t = t the deflection of the beam reaches the maximum, u , then m  m  f  Um=  (d^y ^ n s (i  m  - / ? s i n  C  O  n  t  m  )  =  h  D  d  =  U  s  '  D  d  where D = dynamic amplification factor for deflection, and d  u = equivalent static deflection. s  Let  du it = — = 0; then from Eq. 65, t and u can be obtained, i.e. dt m  m  (  6  6  )  239  Appendix. Dynamic analysis of itisa ties  1  du F„ it = — = — dt k  then  x  — (co cos cot-co cos co t) = 0 (l-p) n  (67)  (68)  cos co t = cos cot  2nn and  ( > 69  where, n = 1, 2, 3 .... Substituting different values of t  m  =250n and  u  m  from E q . 69 into E q . 66, and considering that co  = 716 n « 3<y, it is found that when  2n  2n  n  T  co„+co  4co  2co  2'  (70)  has the largest value.  When  t =  t, m  u(tm)=0,  i.e., the velocity of the generalized mass, and hence the  kinetic energy of the beam, is zero. A t that moment, assuming that all of the potential energy of the hammer weight, W, is transformed into elastic strain energy U as the drop hammer falls through the height h, i.e.,  W(h + uJ = U  (71)  240  Appendix. Dynamic analysis of itisa ties  while the elastic strain energy is, in turn, equal to the work done by the applied load F in moving through the distance u , that is, m  U={" Fdu=\""F(tAdt  (72)  m  Jo  Jo  Jo  k  °  '  ' fit F  SWiCOt  (co cosco t - CO COSCO t)dt  k(\-/3 ) 2  (l-/tf )  j'" sin<s;?(cocosco t - cocosco  n  t)dt  2  There are two terms in above integral,  Term 1  _  1  F0 2  f" sincot • co cos at tdt Jo  k (1-/3')  ^ Term 2 = —  ' 2 \ Jo Jo  n  2(co-o) )  (\-p ) 2  2 7T  Substituting t =  cosfco - co )t  co  k  m  2  2 £  2  +  n  cosfco + co )t n  2(co + co„)  J/=o  m  2a  1 above, respectively, we obtain 1 F0  2  Term 1 =  Term 2 =  *  1  1  2 & (l-/? ) ' 2  IF  2  2 k  (73)  ?r ; t « — from Eq. 70 into the expressions for term 2 and term  eo„ + (D  _  m  (74)  "  k (1-/3 )  2  1 sin <yr (l-B )  2  1  0  2  F  l^o  1  and  0  (\-(3 )(<D-co ) 2  n  cos  Vco + co„  J  -1  241  Appendix. Dynamic analysis of itisa ties  cosI 2 k (l-/3 )(/3-Y) 2  Now,  —  -  2  -1 (75)  U = Term 1 + Term 2 IK  1  2  2 k (1-/3 ) 2  =  1  1+  cos  Kfi +  2TT -1  l )  F  —D 2 k 1  U u  where, D,j = dynamic amplification factor for energy. Substituting U in Eq. 75 and u in Eq. 66 into Eq. 71, the equation becomes m  W(h + D ^)  = ±D ZJ-  d  (76)  u  F can be solved from this equation, and the impact load amplification factor is Q  Z=*L W  D L  +  D  u  yD  u  +  ™  =  D  P  W  J  D  P  \  +  ™  W  (77)  where, D = —- by definition. F  A/  Assuming that the moment of inertia of the beam, I, is constant along the beam, and the deflected shape function  0>(x) = sinyx, the generalized stiffness k for the distributed elasticity is (81)  (78)  242  Appendix. Dynamic analysis of itisa ties  k = \ EI(x)[d>"(x)] dx = EI^\W^xdx = l  . (7  2  o  Substituting k into Eq. 77, the impact factor becomes  IF = ^  W  = D  F  +  J  \  D  F  ^  +  = D  W  F  F  +  , D  F  V  +  ^ .  (80)  Wl  3  Comparing this equation, to Eq. 53 in Ch. 9. for the quasi-static solution, it may be seen that they have a similar format; the only difference is that a dynamic factor appears in the equation above. D is determined solely by the ratio of the frequency of the applied F  load to the natural frequency of the beam, p. For the present tests,  ^ =1 ^ C0„  Substituting P above and t =  l\07t  2TZ  m  co, + co  r. •  1  D = d  d  1  into Eq. 66, we get  ,•  5- (sin co t - Bsm cot ) = m  (!-/¥)  = 0.35  co-2n  (sin  m  n  >  C  .  CO„-27T.  1.35  0.3 5 sin —n  co + co„  0.88  V  r  )=  __  co + co/ 0.88  A  = 1.54  (82) 2K  Similarly, substituting P = 0.35 and t = m  co„ + co  into Eq. 75, we get  243  Appendix. Dynamic analysis of itisa ties  1 1+ (1-/3 ) 09-1) 2  2K -1  cos  [1 - 0.538(-0.99 -1)] = 2.35 0.88  (83) Then, from Eq. 80  „ D 1.54 n „ D = —*- = = 0.66 D 2.35 d  v  F  v  and  /F = ^- = 0.66 + , 0.66 + ^ = ^ W V Wl 3  (84)  In present tets, the hammer weight, W, is 59 N, while most of the impact loads, F  0  are larger than 80 kN (see Fig. 49). Thus, IF» 0.66, and hence  n? = ^»J^;IF«:Jm W V Wl 3  (85)  This solution for the proportional relationship is the same as that from the quasistatic analysis. The changes in magnitude of the coefficients are not significant (see Eq. 53 in Ch. 9). Therefore, the quasi-static method is proved to be valid for the analysis in  244  Appendix. Dynamic analysis of itisa ties  Chapter 9. In the meantime, the dynamic amplification factor for deflection of the beam has been obtained in the above analysis, which is considered to be very important to analyze the dynamic behavior of the ties, and could not be solved with the quasi-static analysis.  A.3. Dynamic Amplification of Deflection and Strain  From Eqs. 66 and 82, the dynamic amplification factor for the beam deflection was 1.54, i.e., under impact with a specified maximum load F (within the linear elastic limit), Q  the deflection, and hence the strain at the mid-span of the beam, were 1.54 times those under static loading with the same load F . This phenomenon was also noted in a previous 0  study (36). For a specified type of impulse, this factor depends only on the ratio of the frequency of the applied load to the natural frequency of the beam, p. Since both frequencies used in the analysis were the actual values measured in the tests, the simplification of the analysis had no influence on the magnitude of this factor. Theoretical analysis (81) has shown that for a SDOF system subjected to a half-sine impulse, when  = 0J5, or, 3 = -^- = ^  = 0.67  (86)  where, T = 1/f: natural period of vibration of the beam, n  the amplification factor reaches a maximum, being 1.77. For the present tests using the 60 kg hammer, x = 0.004 sec and P = 0.35, the amplification factor D = 1.54 (see Eq. 82). d  For the 578 kg impact machine, using the same method, the amplification factor can also be obtained. The impulse duration x is about 0.01 second and the frequency of the second mode of the beam is still used as natural frequency, then  245  Appendix. Dynamic analysis of itisa ties  ^  =  _ »  ^ r _  =  =  1 0 t o  =  0  1  4  ( g 7 )  716;r 7\6TT  <y„  Starting with Eqs. 66 and 69, and using the new values for P and ©, it was found that when  t„ =  An  n co + co„ 2co  x  (88)  2  the deflection x in Eq. 66 reached a maximum. Substituting P and t into Eq. 66, we get m  1  D, = d  m  nm  (1-B ) 2  s  1 /•  — (sin co t - Z?sin co t ) =  . co -An.  CO-AK  n  0.14 sin —  (sin  n m  0.98  v  co + co  2  n  OJ + CO/  1.14 .) =  = 1.16  0.98  This factor is smaller than the factor for the 60 kg machine because the P value for the 60 kg machine is closer to the value 0.67, for which the amplification factor is at a maximum. This result indicates that the tie dynamic response, in terms of the deflection or the strain per unit applied load, is greater under the 60 kg machine. This theoretical solution is consistent with the test results in the current study, as shown below. The measured concrete strains e and their corresponding applied loads F for the standard ITISA tie are listed in Tables 20 and 21; the bending strain per unit load s was f  obtained by  e  (89)  246  Appendix. Dynamic analysis of itisa ties  and the measured amplification factor for strain was defined as the ratio of the s values f  for the impact test and the static test. The e value for the static test was simply obtained f  by dividing the cracking strain by the cracking load (see Table 8 in Ch. 4),  429 pe = 1.91 ps/kN 225 kN For the tests using the 60 kg hammer, thefirstcrack appeared at thefirstblow from the 406 mm drop height. The data for maximum load and maximum strain for this blow, as well as for the three blows prior to this, i.e. the blows under 102, 203 and 305 mm, are listed in Table 20; For the tests using the 578 kg hammer, only 10 blows at the same drop height, 559 mm, were carried out. Since thefirstcrack appeared and propagated extensively during thefirstblow, and the strain gauge was severed by the crack at the same time, three pairs of load and strain values for the data points prior to first cracking under this blow are listed in Table 21.  Appendix. Dynamic analysis of itisa ties  247  Table 20. Strain Amplification Factor for Impact Tests Using the 60 kg Hammer  Drop Height (mm)  Max. Strain (LIS)  Max. Load Bending Strain Per  Amplification  (kN)  Unit Load (s )  Factor (s/1.91)  f  f  102  130  47.17  2.76  1.44  203  191  68.98  2.77  1.45  305  243  78.77  3.09  1.62  406  326  86.78  3.76  1.97  3.09  1.62  Average  1.54  Theoretical  Table 21. Strain Amplification Factor for Impact Test Using the 578 kg Hammer  Time (ms)  Strain (LIS)  Load  Bending Strain Per  Amplification  (kN)  Unit Load (s )  Factor (s/1.91)  f  f  4.56  190  89.0  2.13  1.12  4.62  274  124.6  2.20  1.15  4.68  365  168.2  2.17  1.14  4.74  infinite  271.9 2.17  1.14  Average Theoretical  1.16  Appendix. Dynamic analysis of itisa ties  248  For the test using the 578 kg machine, the average amplification factor was very close to the theoretical value. However, for the tests using the 60 kg machine (see Table 20), for the 406 mm drop height, the factor was 1.97, much higher than the theoretical value of 1.54. This may be because during this blow the crack developed, increasing the apparent strain and leading to more nonlinear behavior of the tie. The other three factors were very close to the theoretical value, and their average was 1.50. In addition, the steady increase of the s values for the cumulative impact tests also reflects the more f  nonlinear behavior of the tie when subjected to the higher drop height. From this analysis, it was found that for an impact impulse with a specified amplitude, a different impulse duration or frequency may lead to a very different concrete strain response. In the present tests, before the initiation of thefirstcrack in the concrete tie, the bending strain per unit load was 32 % higher for the applied impulse with 4 ms duration than that for the applied impulse with 10 ms duration. Wheel impact load detector systems have been used in tracks in practice (29). Specific wheel sets on the moving train producing impact loads greater than a preset load level were identified by the detector and pulled from service. This preset load was considered to be the cracking threshold of the concrete ties, basically determined from a static calibration process. The results from the present study imply that this cracking threshold load is different in static and in impact loading; also, it may be quite different for impulses with different durations. For the typical impulse duration range encountered in track, the shorter the duration, the greater the concrete strain per unit load and the lower the threshold cracking load (see Tables 20 and 21). These concrete strain amplification factors may need to be considered not only in impact tests in the laboratory, but also in the wheel truing program in service (29), which were based on the maximum impact load recorded using the wheel impact load detector in track, in order to achieve better prediction and more economical management.  

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