Investigation of Compressive Membrane Action in Ultra High Performance Concrete Slab Strips

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Title:
Investigation of Compressive Membrane Action in Ultra High Performance Concrete Slab Strips
Physical Description:
1 online resource (377 p.)
Language:
english
Creator:
Foust, Bradley W
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering, Civil and Coastal Engineering
Committee Chair:
KRAUTHAMMER,THEODOR
Committee Co-Chair:
CONSOLAZIO,GARY R
Committee Members:
MASTERS,FORREST J
CHEN,YOUPING
O'DANIEL,JAMES L

Subjects

Subjects / Keywords:
compression -- concrete -- membrane -- slab -- uhpc
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre:
Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Reinforced concrete slabs are found in very common structural systems in both civilian and military applications. The boundary conditions that support the slab play an important role in the response to a particular load. Specifically, the amount of lateral and rotational restraint dictates how a slab responds to a particular load. Compressive membrane (i.e.,in-plane) forces are present in slabs when the boundaries are sufficiently stiff, therefore restricting the slab from both lateral translations and rotations. Advancements have been made to account for the additional capacity due to compressive membrane forces in conventional strength concrete.In today’s world, concrete performance is improving because of increasing compressive strengths and additional ductility present in concrete members. Asa result of this current improvement, there is an urgent need to investigate compressive membrane theory in ultra-high-performance concrete (UHPC) slabs to better understand their behavior. Existing compressive membrane theory should be revisited to determine if current theory is applicable, or if it is not,what modifications should be made. This study will provide insight into the validity of existing theory that is currently used to predict the ultimate capacity in conventional-strength concrete slabs and attempt to modify the existing equations to account for high-strength concrete materials. A matrix of 14 normal-strength concrete (NSC) and 13 UHPC slabs was tested both statically and dynamically to better understand the behavior of each material set and the effects that boundary conditions have on slab response. The results from these experiments were then compared to response calculations made from existing theory as well as finite element analyses. Valuable data sets on rigidly restrained UHPC slab response were obtained through an experimental research program. The experiments helped to validate the associated numerical analysis that was performed. It was determined that the existing theory should be used with caution to calculate the ultimate resistance in UHPC slabs. It was also determined from the experimental and numerical results that the increased compressive strength that is present in restrained UHPC slabs results in a two-and-a-half-times increase in resistance over the traditional yield-line theory resistance for UHPC slabs.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Bradley W Foust.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: KRAUTHAMMER,THEODOR.
Local:
Co-adviser: CONSOLAZIO,GARY R.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0046309:00001


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Full Text

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INVESTIGATION OF COMPRESSIVE MEMBRANE ACTION IN ULTRA HIGH PERFORMANCE CONCRETE SLAB STRIPS By BRADLEY WADE FOUST A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013 1

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2013 Bradley Wade Foust 2

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To the Foust family 3

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ACKNOWLEDGMENTS This research was funded by U.S. Army Work Package 249C DEFEAT of Emerging Adaptive Threats (ATO D), DE002 Constitutive Models for Numerical Tools. There are several individuals to whom I owe my gratitude. To my advisor and mentor Dr Ted Krauthammer, I offer many thanks for the hours of advising, teaching, and most of all his patience as I pursued this research His experience and significant contributions to the field of Structural Engineering and specifically blast response of structures will forevermore make an impact to this field I would like to acknowledge my committee members for their guidance and leadership throughout this entire process. I would like to thank Dr Will McMahon and Dr. Jim ODaniel, U.S. Army Engineer Research and Development Center Geotechnical and Structures Labor a tory ( ERDCGSL ) for their leadership and support during this process. I thank Ms. Carol Johnson for her experience and assistance with both the static and dynam ic testing of concrete slabs. I would also like to thank Mrs. Cheri Loden for her assistance in editing and formatting this document. To the many civil engineering technicians, instrumentation personnel, and colleagues that assisted with t he construction, casting, and testing of concrete slabs, I offer my sincere thanks. This effort would not have been possible without them I personally thank my Lord and Savior Jesus Christ for sustaining me through the difficult days. I thank my loving w ife Tina for her patience and commitment to our marriage. I thank my parents Jeff and Janice for teaching me the value of hard work and my brother Nathan for his friendship and continued support. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 7 LIST OF FIGURES .......................................................................................................... 8 ABSTRACT ................................................................................................................... 3 0 CHAPTER 1 INTRODUCTION .................................................................................................... 32 Problem Statement ................................................................................................. 32 Technical Objective ................................................................................................ 34 Scope ..................................................................................................................... 34 Research Significance ............................................................................................ 35 2 LITERATURE REVIEW .......................................................................................... 37 Background ............................................................................................................ 37 Membrane Theory ............................................................................................ 37 Blast Resistance of Slabs ................................................................................. 39 Pl astic Theory ................................................................................................... 41 Loading Conditions ................................................................................................. 44 Uniformly Quasi Static Loading ........................................................................ 44 Blast Loads ....................................................................................................... 45 Materials ................................................................................................................. 47 Slab Behavior ......................................................................................................... 50 Results from Experiments ................................................................................ 50 Results from Analyses and Simulations ........................................................... 52 3 RESEARCH APPROACH ....................................................................................... 75 Experimental Investigation ...................................................................................... 75 Slab Descriptions ............................................................................................. 77 Concrete Casting .............................................................................................. 78 Reaction Frames .............................................................................................. 79 Quasi Static Experiments ........................................................................... 81 Dynamic Experiments ................................................................................ 82 Instrumentation ................................................................................................. 83 Instrumentation Details for Quasi Static Experiments ................................ 84 Instrumentation Details for Dynamic Experiments ..................................... 85 Analysis Approach ............................................................................................ 87 5

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4 RESULTS ............................................................................................................. 113 Loading Conditions ............................................................................................... 113 Quasi St atic Experiments ............................................................................... 113 Dynamic Experiments .................................................................................... 114 Experimental Results ............................................................................................ 115 Johansens Yield Line Theory ........................................................................ 115 Quasi static Simply Supported ....................................................................... 115 Quasi Static Rigidly Restrained ...................................................................... 117 Dynamic Simply Supported ............................................................................ 118 Dynamic Rigidly Restrained ........................................................................... 120 Comparisons with Theory ..................................................................................... 121 Analysis Results ................................................................................................... 126 Single Degreeof Freedom (SDOF) Analysis ................................................. 126 Abaqus Simulations ........................................................................................ 129 General model details .............................................................................. 129 Comparisons of simulation results to experimental data .......................... 131 5 CONCLUSIONS AND RECOMMENDATIONS ..................................................... 166 Summary .............................................................................................................. 166 Concluding Remarks ............................................................................................ 167 Recommendations ................................................................................................ 168 A TEST MATRIX ...................................................................................................... 171 B CONCRETE SLAB DESIGN DRAWINGS ............................................................ 172 C SLAB CASTING PHOTOS ................................................................................... 184 D QUASI STATIC TEST DATA ................................................................................ 187 E BLAS T LOAD SIMULATOR (DYNAMIC) TEST DATA ......................................... 292 F EXPERIMENTAL LOADS AND RESISTANCE CALCULATIONS ........................ 355 G SLAB TESTING PHOTOGRAPHS ....................................................................... 358 H NSC CDP MO DEL PARAMETERS ...................................................................... 370 REFERENCES ............................................................................................................ 373 BIOGRAPHICAL SKETCH .......................................................................................... 377 6

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LIST OF TABLES Table page 2 1 Heat of detonation and heat of combustion of explosive materials ................... 58 2 2 SAM 35 mix design ........................................................................................... 59 2 3 Co r Tuf mixture composition ............................................................................. 59 4 1 Summary of Johansens loads ........................................................................ 134 A 1 As built test matrix ........................................................................................... 171 F 1 Average pressures and impulses .................................................................... 355 F 2 Johansens yield line load parameters ............................................................ 357 F 3 Uniform load resistance calculated from TM 5 8551 ...................................... 357 H 1 Normal strength concrete CDP model parameters .......................................... 370 H 2 Normal strength concrete CDP model parameters (compression hardening and damage) .................................................................................. 371 H 3 No rmal strength concrete CDP model parameters (tension stiffening) ........... 372 H 4 Normal strength concrete CDP model parameters (tension damage) ............. 372 7

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LIST OF FIGURES Figure page 2 1 Design curve for DIF for Ultimate Compressive Strengths of Concrete ........... 60 2 2 Generalized resistance function for slabs ........................................................ 60 2 3 Load deflection relationship for twoway reinforced concrete slab with edges restrained against lateral movement ..................................................... 6 1 2 4 Plastic hinges of restrained strip ...................................................................... 61 2 5 Portion of strip between yield sections 1 and 2 of Figure 24 ........................... 62 2 6 Free field pressuretime variation .................................................................... 62 2 7 Typical reflected pressuretime history ............................................................ 63 2 8 Reflected pressure coefficient versus angle of incidence ................................ 64 2 9 Unconfined compressive strengths for concrete materials tested .................... 64 2 10 Bekaert Dramix ZP305 fibers ........................................................................ 65 2 11 Reinforcement lay out and details of Guice tests .............................................. 66 2 12 Elevation of reaction structure ......................................................................... 67 2 13 Section view of reaction frame ......................................................................... 68 2 14 Quarter section view of reaction structure with slab in place ........................... 68 2 15 Steel frame for providing lateral restraint ......................................................... 69 2 16 Load vs. deflection of unrestrained slabs ......................................................... 70 2 17 Load vs. deflect ion of rigidly restrained slabs .................................................. 70 2 18 Comparison of results and predictions for laterally restrained and unrestrained specimens ................................................................................... 71 2 19 Geometry of deformation (a) slab strip (b) half slab strip (c) free body diagram ............................................................................................................ 72 2 20 Experimental and analytical comparison of results for slab response .............. 73 2 21 Proposed stress strain relations hip for highstrength concretes ...................... 74 8

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2 22 Proposed stress blocks for high strength concretes ........................................ 74 3 1 Schematic of reinforced concrete slab cross section ....................................... 91 3 2 Typical reinforcement layout for NSC restrained slab ...................................... 91 3 3 Casting NSC slabs ........................................................................................... 92 3 4 Finishing NSC slabs ......................................................................................... 92 3 5 Reaction frame for simply supported quasi static experiments ........................ 93 3 6 Pressure side of simply supported quasi static test frame ............................... 93 3 7 Rigidly restrained quasi static steel frame ....................................................... 94 3 8 Rigidly restrained quasi static steel fr ame end boundary conditions ............... 94 3 9 Simply supported BLS frame ........................................................................... 95 3 10 Inside and blast face view of assembled simply supported BLS frame ........... 95 3 11 Rigidly restrained BLS outer frame with slab in place ...................................... 96 3 12 Rigidly restrained BLS assembled frame, end condition, and steel wedges ............................................................................................................ 96 3 13 Rigidly restrai ned BLS frame with installed slab .............................................. 97 3 14 Static test chamber .......................................................................................... 97 3 15 Photograph of static test chamber with opening .............................................. 98 3 16 Bladder with steel collar ................................................................................... 98 3 17 Static chamber with lid bolted and gages installed .......................................... 99 3 18 Overhead view of static test setup from nonpressurized side ......................... 99 3 19 Blast Load Simulator (BLS) ............................................................................ 100 3 20 Entrance to underground enclosure and expansion rings .............................. 100 3 21 Target assembly shop with front of target vessel with slab installed .............. 101 3 22 Underground enc losure with target vessel attached to expansion ring .......... 101 3 23 Displacement transducers mounted above nonpressurized cavity ............... 102 3 24 Cable layout for displacement transducers .................................................... 103 9

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3 25 Displacement measurement locations and cable attachment to slab ............ 103 3 26 Pressure transducer at the top of pressurized cavity ..................................... 104 3 27 Pressure transducer at midheight of back wall inside pressurized cavity .............................................................................................................. 104 3 28 Pressure transducers located outside nonpressurized cavity ....................... 105 3 29 Cavity lid pressure transducer ....................................................................... 105 3 30 Primary reinforcement strain gage locations .................................................. 106 3 31 Photographs of strain gage locations ............................................................. 107 3 32 Overview showing location of underwater camera ......................................... 108 3 33 Views showing underwater camera location .................................................. 108 3 34 Pressure transducer layout on blast face of target ......................................... 109 3 35 Photograph of pressure transducer layout on target face .............................. 110 3 36 Accelerometer layout on inside face of slab ................................................... 111 3 37 Laser mounted in the back door of target vessel ........................................... 111 3 38 Photograph of surface strain gages ............................................................... 112 3 39 High speed video locations ............................................................................ 112 4 1 Load versus deflection for simply supported NSC slabs ................................ 135 4 2 NSC Test 3 simply supported ........................................................................ 135 4 3 Load versus deflection for simply supported UHPC slabs ............................. 136 4 4 UHPC Test 1 simply supported ...................................................................... 136 4 5 Load versus deflection of rigidly restrained NSC slabs .................................. 137 4 6 NSC Test 6 rigidly restrained ......................................................................... 137 4 7 Load versus deflection of rigidly restrained UHPC slabs ............................... 138 4 8 UHPC Test 9 rigidly restrained ...................................................................... 138 4 9 Dynamic deflection versus time of simply supported NSC slabs (Test 3) .......................................................................................................... 139 10

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4 10 Dynamic deflection versus time of simply supported NSC slabs (Test 6) .......................................................................................................... 139 4 11 Dynamic deflection versus time of simply supported NSC slabs (Test 7) .......................................................................................................... 140 4 12 Dynamic deflection versus time of simply supported NSC slabs (all tests) .............................................................................................................. 140 4 13 Front view of NSC Test 6 pretest ................................................................... 141 4 14 Rear view of NSC Test 6 pretest ................................................................... 141 4 15 Dynamic deflection versus time of simply supported UHPC slabs (Test 1) .......................................................................................................... 142 4 16 Dynamic deflection versus time of simply supported UHPC slabs (Test 1b) ........................................................................................................ 142 4 17 Dynamic deflection versus time of simply supported UHPC slabs (Test 2) .......................................................................................................... 143 4 18 Dynamic deflection versus time of simply supported UHPC slabs (Test 4) .......................................................................................................... 143 4 19 Dynamic deflection versus time of simply supported UHPC slabs (all tests) .............................................................................................................. 144 4 20 Front view of UHPC Test 1 pretest ................................................................ 144 4 21 Rear view of UHPC Test 1 posttest ............................................................... 145 4 22 Dynamic deflection versus time of rigidly restrained NSC slabs (Test 10) ........................................................................................................ 145 4 23 Dynamic deflection versus time of rigidly restrained NSC slabs (Test 11) ........................................................................................................ 146 4 24 Dynamic deflection versus time of rigidly restrained NSC slabs (Test 12) ........................................................................................................ 146 4 25 Dynamic deflection versus time of rigidly restrained NSC slabs (Test 13) ........................................................................................................ 147 4 26 Dynamic def lection versus time of rigidly restrained NSC slabs (all tests) .............................................................................................................. 147 4 27 Front view of NSC rigidly restrained Test 11 pretest ...................................... 148 11

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4 28 Rear view of NSC rigidly restrained Test 11 posttest ..................................... 148 4 29 Dynamic deflection versus time of rigidly restrained UHPC slabs (Test 14) ........................................................................................................ 149 4 30 Dynamic deflection versus time of rigidly restrained UHPC slabs (Test 15) ........................................................................................................ 149 4 31 Dynamic deflection versus time of rigidly restrained UHPC slabs (Test 16) ........................................................................................................ 150 4 32 Dynamic deflection versus time of rigidly restrained UHPC slabs (all tests) .............................................................................................................. 150 4 33 Front view of UHPC rigidly restrained Test 14 pretest ................................... 151 4 34 Rear vi ew of UHPC rigidly restrained Test 14 pretest .................................... 151 4 35 NSC strength enhancement due to compressive membrane action .............. 152 4 36 UHPC strength enhancement due to compressive membrane action ........... 152 4 37 Strength enhancement due to compressive membrane action (theoretical vs. experimental results) ............................................................. 153 4 38 Typical slab strip geometry ............................................................................ 153 4 39 Moment curvatur e relationships for NSC and UHPC ..................................... 154 4 40 Army TM 5 8551 theoretical versus experimental comparisons for NSC ............................................................................................................... 154 4 41 Army TM 5 8551 theoretical versus experimental comparisons for UHPC ............................................................................................................. 155 4 42 NSC resistance function comparison to SDOF models .................................. 155 4 43 NSC rigidly restrained experimental results comparison to SDOF analysis (Test 10) ........................................................................................... 156 4 44 NSC rigidly restrained ex perimental results comparison to SDOF analysis (Test 11) ........................................................................................... 156 4 45 NSC rigidly restrained experimental results comparison to SDOF analysis (Test 12) ........................................................................................... 157 4 46 NSC rigidly restrained experimental results comparison to SDOF analysis (Test 13) ........................................................................................... 157 12

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4 47 UHPC resistance function comparison to SDOF models ............................... 158 4 48 UHPC rigidly restrained experimental results comparison to SDOF analysis (Test 14) ........................................................................................... 158 4 49 UHPC rigidly restrained experimental results comparison to SDOF analysis (Test 15) ........................................................................................... 159 4 50 UHPC rigidly restrained experimental results comparison to SDOF analysis (Test 16) ........................................................................................... 159 4 51 Newly developed UHPC resistance function .................................................. 160 4 52 Deflectiontime history comparison of new resistance function ...................... 160 4 53 Abaqus mesh refinement analysis comparative results ................................. 161 4 54 Abaqus undeformed reinforcedconcrete slab model ..................................... 161 4 55 Abaqus deformed reinforcedconcrete slab model ........................................ 162 4 56 Numerical versus experimental results for NSC simply supported slabs .............................................................................................................. 162 4 57 Numerical versus experi mental results for UHPC simply supported slab ................................................................................................................ 163 4 58 Numerical versus experimental results for NSC rigidly restrained slab.......... 163 4 59 Numerical versus experimental results for UHPC rigidly restrained slab ................................................................................................................ 164 4 60 Early time failure of NSC 0.5in. elements at t=3 msec ................................. 164 4 61 Early time failure of NSC 0.25in. elements at t=3 msec ............................... 165 B 1 Overall dimensions of NSC slab, tested dynamically, simply supported ........ 172 B 2 Reinforcement layout of NSC slab, tested dynamically, simply supported ....................................................................................................... 173 B 3 Overall dimensions of UHPC slab, tested dynamically, simply supported ....................................................................................................... 173 B 4 Reinforcement layout of UHPC slab, tested dynamically, simply supported ....................................................................................................... 174 B 5 Overall dimensions of NSC slab, tested dynamically, rigidly restrained ......... 174 13

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B 6 Reinforcement layout of NSC slab, tested dynamically, rigidly restrained ....................................................................................................... 175 B 7 Overall dimensions of UHPC slab, tested dynami cally, rigidly restrained ....................................................................................................... 175 B 8 Reinforcement layout of UHPC slab, tested dynamically, rigidly restrained ....................................................................................................... 176 B 9 Overall dimensions of NSC slab, tested statically, rigidly restrained ............. 176 B 10 Reinforcement layout of NSC slab, tested statically, rigidly restrained .......... 177 B 11 Overall dimensions of UHPC slab, tested stati cally, rigidly restrained ........... 177 B 12 Reinforcement layout of UHPC slab, tested statically, rigidly restrained ........ 178 B 13 Overall dimensions of NSC slab, tested statically, simply supported ............. 178 B 14 Reinforcement layout of NSC slab, tested statically, simply supported ......... 179 B 15 Overall dimensions of UHPC slab, tested statically, simply supported .......... 179 B 16 Reinforcement layout of UHPC slab, tested statically, simply supported ....................................................................................................... 180 B 17 Typical reinforcement layout for NSC restrained slab .................................... 180 B 18 Typical reinforcement layout for NSC simply supported slab ......................... 181 B 19 Entire set of NSC slabs cast on August 7, 2012 ............................................ 181 B 20 Typical reinforcement layout for Cor Tuf with fibers restrained slab with strain gages ............................................................................................ 182 B 21 Typic al reinforcement layout for Cor Tuf with fibers simply supported slab with strain gages .................................................................................... 183 B 22 Entire set of Cor Tuf with fibers cast on August 14, 2012 .............................. 183 C 1 Casting NSC concrete slabs .......................................................................... 184 C 2 Casting Cor Tuf slabs .................................................................................... 184 C 3 Casting Cor Tuf (with fiber) slabs .................................................................. 185 C 4 Casting CorTuf (without fiber) slabs ............................................................... 186 C 5 Finishing and covering Cor Tuf slabs ............................................................. 186 14

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D 1 CW/OSSY D1 Test 1 ..................................................................................... 187 D 2 CW/OSSY D2 Test 1 ..................................................................................... 187 D 3 CW/OSSY D3 Test 1 ..................................................................................... 188 D 4 CW/OSSY D4 Test 1 ..................................................................................... 188 D 5 CW/OSSY D5 Test 1 ..................................................................................... 189 D 6 CW/OSSY mid span tension face reinforcement strain Test 1 ...................... 189 D 7 CW/OSSY quarter span tension face reinforcement strain Test 1 ................. 190 D 8 CW/OSSY support tension face reinforcement strain Test 1 ......................... 190 D 9 CW/OSSY mid span compression face reinforcement strain Test 1 .............. 191 D 10 CW/OSSY support compression face reinforcement strain Test 1 ................ 191 D 11 CW/OSSY inside pr essure at top Test 1 ........................................................ 192 D 12 CW/OSSY outside pressure at top Test 1 ...................................................... 192 D 13 CW/OSSY inside pressure at bottom Test 1 .................................................. 193 D 14 CW/OSSY outside pressure at bottom Test 1 ................................................ 193 D 15 CW/OSSY pressure inside at lid Test 1 ......................................................... 194 D 16 CW/OSSY D1 Test 1b ................................................................................... 194 D 17 CW/OSSY D2 Test 1b ................................................................................... 195 D 18 CW/OSSY D3 Test 1b ................................................................................... 195 D 19 CW/OSSY D4 Test 1b ................................................................................... 196 D 20 CW/OSSY D5 Test 1b ................................................................................... 196 D 21 CW/OSSY quarter span tension face reinforcement s train Test 1b ............... 197 D 22 CW/OSSY support tension face reinforcement strain Test 1b ....................... 197 D 23 CW/OSSY pressure inside at top Test 1b ...................................................... 198 D 24 CW/OSSY pressure outside at top Test 1b .................................................... 198 D 25 CW/OSSY pressure inside at bottom Test 1b ................................................ 199 15

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D 26 CW/OSSY pressure outside at bottom Test 1b .............................................. 199 D 27 CW/OSSY pressure inside at lid Test 1b ....................................................... 200 D 28 CW/OSSY D1 Test 1c .................................................................................... 200 D 29 CW/OSSY D2 Test 1c .................................................................................... 201 D 30 CW/OSSY D3 Test 1c .................................................................................... 201 D 31 CW/OSSY D4 Test 1c .................................................................................... 202 D 32 CW/OSSY D5 Test 1c .................................................................................... 202 D 33 CW/OSSY quarter span tension face reinforcement strain Test 1c ............... 203 D 34 CW/OSSY support tension face reinforcement strain Test 1c ....................... 203 D 35 CW/OSSY support compression face reinforcement strain Test 1c ............... 204 D 36 CW/OSSY pressure inside at top Test 1c ...................................................... 204 D 37 CW/OSSY pressure outside at top Test 1c .................................................... 205 D 38 CW/OSSY pressure inside at bottom Test 1c ................................................ 205 D 39 CW/OSSY pressure outside at bottom Test 1c .............................................. 206 D 40 CW/OSSY pressure inside at lid Test 1c ....................................................... 206 D 41 CW/OSSY D1 Test 1d ................................................................................... 207 D 42 CW/OSSY D2 Test 1d ................................................................................... 207 D 43 CW/OSSY D3 Test 1d ................................................................................... 208 D 44 CW/OSSY D4 Test 1d ................................................................................... 208 D 45 CW/OSSY D5 Test 1d ................................................................................... 209 D 46 CW/OSSY quarter span tension face reinforcement strain Test 1d ............... 209 D 47 CW/OSSY support tension face reinforcement strain Test 1d ....................... 210 D 48 CW/OSSY support compression face reinforcement strain Test 1d .............. 210 D 49 CW/OSSY pressure inside at top Test 1d ...................................................... 211 D 50 CW/OSSY outside inside at top Test 1d ........................................................ 211 16

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D 51 CW/OSSY pressure inside at bottom Test 1d ................................................ 212 D 52 CW/OSSY pressure outside at bottom Test 1d .............................................. 212 D 53 CW/OSSY pressure inside at lid Test 1d ....................................................... 213 D 54 CW/OSSY D1 Test 2 ..................................................................................... 213 D 55 CW/OSSY D2 Test 2 ..................................................................................... 214 D 56 CW/OSSY D3 Test 2 ..................................................................................... 214 D 57 CW/OSSY D4 Test 2 ..................................................................................... 215 D 58 CW/OSSY D5 Test 2 ..................................................................................... 215 D 59 CW/OSSY mid span tension face reinforcement strain Test 2 ...................... 216 D 60 CW/OSSY support tension face reinforcement strain Test 2 ......................... 216 D 61 CW/OSSY mid span compression face reinforcement strain Test 2 .............. 217 D 62 CW/OSSY support compression face reinforcement strain Test 2 ................ 217 D 63 CW/OSSY pressure inside at top Test 2 ........................................................ 218 D 64 CW/OSSY pressur e outside at top Test 2 ...................................................... 218 D 65 CW/OSSY pressure inside at bottom Test 2 .................................................. 219 D 66 CW/OSSY pressure outside at bottom Test 2 ................................................ 219 D 67 CW/OSSY pressure inside at lid Test 2 ......................................................... 220 D 68 CW/OSSY D1 Test 2b ................................................................................... 220 D 69 CW/OSSY D2 Test 2b ................................................................................... 221 D 70 CW/OSSY D3 Test 2b ................................................................................... 221 D 71 CW/OSSY D4 Test 2b ................................................................................... 222 D 72 CW/OSSY D5 Test 2b ................................................................................... 222 D 73 CW/OSSY support tension face reinforcement strain Test 2b ....................... 223 D 74 CW/OSSY support compression face reinforcement strain Test 2b .............. 223 D 75 CW/OSSY pressure inside at top Test 2b ...................................................... 224 17

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D 76 CW/OSSY pressure outside at top Test 2b .................................................... 224 D 77 CW/OSSY pressure inside at bottom Test 2b ................................................ 225 D 78 CW/OSSY pressure outside at bottom Test 2b .............................................. 225 D 79 CW/OSSY pressure inside at lid Test 2b ....................................................... 226 D 80 CW/OSSY D1 Test 2c .................................................................................... 226 D 81 CW/OSSY D2 Test 2c .................................................................................... 227 D 82 CW/OSSY D3 Test 2c .................................................................................... 227 D 83 CW/OSSY D4 Test 2c .................................................................................... 228 D 84 CW/OSSY D5 Test 2c .................................................................................... 228 D 85 CW/OSSY support tension face reinforcement strain Test 2c ....................... 229 D 86 CW/OSSY support compression f ace reinforcement strain Test 2c ............... 229 D 87 CW/OSSY pressure inside at top Test 2c ...................................................... 230 D 88 CW/OSSY pressure outside at top Test 2c .................................................... 230 D 89 CW/OSSY pressure inside at bottom Test 2c ................................................ 231 D 90 CW/OSSY pressure outside at bottom Test 2c .............................................. 231 D 91 CW/OSSY pressure inside at lid Test 2c ....................................................... 232 D 92 NSSN D1 Test 3 ............................................................................................ 232 D 93 NSSN D2 Test 3 ............................................................................................ 233 D 94 NSS N D3 Test 3 ............................................................................................ 233 D 95 NSSN D4 Test 3 ............................................................................................ 234 D 96 NSSN D5 Test 3 ............................................................................................ 234 D 97 NSSN pressure inside at top Test 3 ............................................................... 235 D 98 NSSN pressure outside at top Test 3 ............................................................. 235 D 99 NSSN pressure inside at bottom Test 3 ......................................................... 236 D 100 NSSN pressure outside at bottom Test 3 ....................................................... 236 18

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D 101 NSSN pressure inside at lid Test 3 ................................................................ 237 D 102 NSSY D1 Test 4 ............................................................................................ 237 D 103 NSSY D2 Test 4 ............................................................................................ 238 D 104 NSSY D3 Test 4 ............................................................................................ 238 D 105 NSSY D4 Test 4 ............................................................................................ 239 D 106 NSSY D5 Test 4 ............................................................................................ 239 D 107 NSSY mid span tension face reinforcement strain Test 4 .............................. 240 D 108 NSSY quarter span tension face reinforcement strain Test 4 ........................ 240 D 109 NSSY support tension face reinforcement strain Test 4 ................................ 241 D 110 NSSY mid span compression face reinforcement strain Test 4 ..................... 2 41 D 111 NSSY quarter span compression face reinforcement strain Test 4 ............... 242 D 112 NSSY support compression face reinforcement strain Test 4 ........................ 242 D 113 NSSY pressure inside at top Test 4 ............................................................... 243 D 114 NSSY pressure outside at top Test 4 ............................................................. 243 D 115 NSSY pressure inside at bottom Test 4 ......................................................... 244 D 116 NSSY pressure outside at bottom Test 4 ....................................................... 244 D 117 NSSY pressure inside at lid Test 4 ................................................................ 245 D 118 NRRY D1 combined Test 5 ............................................................................ 245 D 119 NRRY D2 combined Test 5 ............................................................................ 246 D 120 NRRY D3 combined Test 5 ............................................................................ 246 D 121 NRRY D5 combined Test 5 ............................................................................ 247 D 122 NRRY mid span tension face reinforcement strain Test 5 ............................. 247 D 123 NRRY quarter span tension face reinforcement strain Test 5 ........................ 248 D 124 NRRY support tension face reinforcement strain Test 5 ................................ 248 D 125 NRRY mid span compression face reinforcement strain Test 5 .................... 249 19

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D 126 NRRY quarter span compression face reinforcement strain Test 5 ............... 249 D 127 NRRY support compression face reinforcement strain Test 5 ....................... 250 D 128 NSSY pressure inside at top Test 5 ............................................................... 250 D 129 NSSY pressure outside at top Test 5 ............................................................. 251 D 130 NSSY pressure inside at bottom Test 5 ......................................................... 251 D 131 NSSY pressure outside at bottom Test 5 ....................................................... 252 D 132 NSSY pressure inside at lid Test 5 ................................................................ 252 D 133 NRRN D1 Test 6 ............................................................................................ 253 D 134 NRRN D2 Test 6 ............................................................................................ 253 D 135 NRRN D3 Test 6 ............................................................................................ 254 D 136 NRRN D4 Test 6 ............................................................................................ 254 D 137 NRRN D5 Test 6 ............................................................................................ 255 D 138 NRRN pressure inside at top Test 6 .............................................................. 255 D 139 NRRN pressure outside at top Test 6 ............................................................ 256 D 140 NRRN pressure inside at bottom Test 6 ........................................................ 256 D 141 NRRN pressure outside at bottom Test 6 ...................................................... 257 D 142 NRRN pressure inside at li d Test 6 ................................................................ 257 D 143 NRRN D1 Test 7 ............................................................................................ 258 D 144 NRRN D2 Test 7 ............................................................................................ 258 D 145 NRRN D3 Test 7 ............................................................................................ 259 D 146 NRRN D4 Test 7 ............................................................................................ 259 D 147 NRRN D5 Test 7 ............................................................................................ 260 D 148 NRRN pressure inside at top Test 7 .............................................................. 260 D 149 NRRN pressure outside at top Test 7 ............................................................ 261 D 150 NRRN pressure inside at bottom Test 7 ........................................................ 261 20

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D 151 NRRN pressure outside at bottom Test 7 ...................................................... 262 D 152 NRRN pressure inside at lid Test 7 ................................................................ 262 D 153 NRRN D1 Test 8 ............................................................................................ 263 D 154 NRRN D2 Test 8 ............................................................................................ 263 D 155 NRRN D3 Test 8 ............................................................................................ 264 D 156 NRRN D4 Test 8 ............................................................................................ 264 D 157 NRRN D5 Test 8 ............................................................................................ 265 D 158 NRRN pressure inside at top Test 8 .............................................................. 265 D 159 NRRN pressure outside at top Test 8 ............................................................ 266 D 160 NRRN pressure inside at bottom Test 8 ........................................................ 266 D 161 NRRN pressure outside at botto m Test 8 ...................................................... 267 D 162 NRRN pressure inside at lid Test 8 ................................................................ 267 D 163 CW/ORRY D1 Test 9 ..................................................................................... 268 D 164 CW/ORRY D2 Test 9 ..................................................................................... 268 D 165 CW/ORRY D3 Test 9 ..................................................................................... 269 D 166 CW/ORRY D4 Test 9 ..................................................................................... 269 D 167 CW/ORRY D5 Test 9 ..................................................................................... 270 D 168 CW/ORRY mid span compression face reinforcement strain Test 9 ............. 270 D 169 CW/ORRY quarter span compression face reinforcement strain Test 9 ........ 271 D 170 CW/ORR Y support compression face reinforcement strain Test 9 ................ 271 D 171 CW/ORRY mid span tension face reinforcement strain Test 9 ...................... 272 D 172 CW/ORRY quarter span tension face reinforcement strain Test 9 ................ 272 D 173 CW/ORRY support tension face reinforcement strain Test 9 ......................... 273 D 174 CW/ORRY pressure inside at top Test 9 ....................................................... 273 D 175 CW/ORRY pressure outside at top Test 9 ..................................................... 274 21

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D 176 CW/ORRY pressure inside at bottom Test 9 ................................................. 274 D 177 CW/ORRY pressure outside at bottom Test 9 ............................................... 275 D 178 CW/ORRY pressure inside at lid Test 9 ......................................................... 275 D 179 CW/ORRY D1 Test 10 ................................................................................... 276 D 180 CW/ORRY D2 Test 10 ................................................................................... 276 D 181 CW/ORRY D3 Test 10 ................................................................................... 277 D 182 CW/ORRY D4 Test 10 ................................................................................... 277 D 183 CW/ORRY D5 Test 10 ................................................................................... 278 D 184 CW/ORRY mid span compression face reinforcement strain Test 10 ........... 278 D 185 CW/ORRY quarter span compression face reinforcement strain Test 10 ........................................................................................................... 279 D 186 CW/ORRY support compression face reinforcement strain Test 10 .............. 279 D 187 CW/ORRY mid span tension face reinforcement strain Test 10 .................... 280 D 188 CW/ORRY quarter span tension face reinforcement strain Test 10 .............. 280 D 189 CW/ORRY supp ort tension face reinforcement strain Test 10 ....................... 281 D 190 CW/ORRY pressure inside at top Test 10 ..................................................... 281 D 191 CW/ORRY pressure outside at top Test 10 ................................................... 282 D 192 CW/ORRY pressure inside at bottom Test 10 ............................................... 282 D 193 CW/ORRY pressure outside at bottom Test 10 ............................................. 283 D 194 CW/ORRY pressure inside at lid Test 10 ....................................................... 283 D 195 CWSSY D1 Test 11 ....................................................................................... 284 D 196 CWSSY D2 Test 11 ....................................................................................... 284 D 197 CWSSY D3 Test 11 ....................................................................................... 285 D 198 CWSSY D4 Test 11 ....................................................................................... 285 D 199 CWSSY D5 Test 11 ....................................................................................... 286 D 200 CWSSY mid span compression face reinforcement strain Test 11 ............... 286 22

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D 201 CWSSY quarter span compression face reinforcement strain Test 11 .......... 287 D 202 CWSSY support compression face reinforcement strain Test 11 .................. 287 D 203 CWSSY mid span tension face reinforcement strain Test 11 ........................ 288 D 204 CWSSY quarter span tensi on face reinforcement strain Test 11 ................... 288 D 205 CWSSY support tension face reinforcement strain Test 11 ........................... 289 D 206 CWSSY pressure inside at top Test 11 .......................................................... 289 D 207 CWSSY pressure outside at top Test 11 ....................................................... 290 D 208 CWSSY pressure inside at bottom Test 11 .................................................... 290 D 209 CWSSY pressure outside at bottom Test 11 ................................................. 291 D 210 CWSSY pressure inside at lid Test 11 ........................................................... 291 E 1 CW/OSSN P1 and impulse vs. time Test 1 .................................................... 292 E 2 CW/OSSN P2 and impulse vs. time Test 1 .................................................... 292 E 3 CW/OSSN P3 and impulse vs. time Test 1 .................................................... 293 E 4 CW/OSSN P4 and impulse vs. time Test 1 .................................................... 293 E 6 CW/OSSN P6 and impulse vs. time Test 1 .................................................... 294 E 7 CW/OSSN PD and impulse vs. time Test 1 ................................................... 295 E 8 CW/OSSN PE and impulse vs. time Test 1 ................................................... 295 E 9 CW/OSSN P1 and impulse vs. time Test 1b .................................................. 296 E 10 CW/OSSN P2 and impulse vs. time Test 1b .................................................. 296 E 11 CW/OSSN P3 and impulse vs. time Test 1b .................................................. 297 E 12 CW/OSSN P4 and impulse vs. time Test 1b .................................................. 297 E 13 CW/OSSN P5 and impulse vs. time Test 1b .................................................. 298 E 14 CW/OSSN P6 and impulse vs. time Test 1b .................................................. 298 E 15 CW/OSSN PD and impulse vs. time Test 1b ................................................. 299 E 16 CW/OSSN PE and impulse vs. time Test 1b ................................................. 299 23

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E 17 CW/OSSY P1 and impulse vs. time Test 2 .................................................... 300 E 18 CW/OSSY P2 and impulse vs. time Test 2 .................................................... 300 E 19 CW/OSSY P3 and impulse vs. time Test 2 .................................................... 301 E 20 CW/OSSY P4 and impulse vs. time Test 2 .................................................... 301 E 21 CW/OSSY P5 and impulse vs. time Test 2 .................................................... 302 E 22 CW/OSSY P6 and impulse vs. time Test 2 .................................................... 302 E 23 CW/OSSY PD and impulse vs. time Tes t 2 ................................................... 303 E 24 CW/OSSY PE and impulse vs. time Test 2 .................................................... 303 E 25 NSSN P1 and impulse vs. time Test 3 ........................................................... 304 E 26 NSSN P2 and impulse vs. time Test 3 ........................................................... 304 E 27 NSSN P3 and impulse vs. time Test 3 ........................................................... 305 E 28 NSSN P4 and impulse vs. time Test 3 ........................................................... 305 E 29 NSSN P5 and impulse vs. time Test 3 ........................................................... 306 E 30 NSSN P6 and impulse vs. time Test 3 ........................................................... 306 E 31 NSSN PD and impulse vs. time Test 3 .......................................................... 307 E 32 NSSN PE and impulse vs. time Test 3 ........................................................... 307 E 33 CW/OSSY P1 and impulse vs. time Test 4 .................................................... 308 E 34 CW/OSSY P2 and impulse vs. time Test 4 .................................................... 308 E 35 CW/OSSY P3 and impulse vs. time Test 4 .................................................... 309 E 36 CW/OSSY P4 and impulse vs. time Test 4 .................................................... 309 E 37 CW/OSSY P5 and impulse vs. time Tes t 4 .................................................... 310 E 38 CW/OSSY P6 and impulse vs. time Test 4v .................................................. 310 E 39 CW/OSSY PD and impulse vs. time Test 4 ................................................... 311 E 40 CW/OSSY PE and impulse vs. time Test 4 .................................................... 311 E 41 NSSN P1 and impulse vs. time Test 6 ........................................................... 312 24

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E 42 NSSN P2 and impulse vs. time Test 6 ........................................................... 312 E 43 NSSN P3 and impulse vs. time Test 6 ........................................................... 313 E 44 NSSN P4 and impulse vs. time Test 6 ........................................................... 313 E 45 NSSN P5 and impulse vs. time Test 6 ........................................................... 314 E 46 NSSN P6 and impulse vs. time Test 6 ........................................................... 314 E 47 NSSN PD and impulse vs. time Test 6 .......................................................... 315 E 48 NSSN PE and impulse vs. time Test 6 ........................................................... 315 E 49 NSSY P1 and impulse vs. time Test 7 ........................................................... 316 E 50 NSSY P2 and impulse vs. time Test 7 ........................................................... 316 E 51 NSSY P3 and impulse vs. time Test 7 ........................................................... 317 E 52 NSSY P4 and impulse vs. time Test 7 ........................................................... 317 E 53 NSSY P5 and impulse vs. time Test 7 ........................................................... 318 E 54 NSSY P6 and impulse vs. time Test 7 ........................................................... 318 E 55 NSSY PD and impulse vs. time Test 7 ........................................................... 319 E 56 NSSY PE and impulse vs. time Test 7 ........................................................... 319 E 57 CWSSN P1 and impulse vs. time Test 8 trial ................................................. 320 E 58 CWSSN P2 and impulse vs. time Test 8 trial ................................................. 320 E 59 CWSSN P3 and impulse vs. time Test 8 trial ................................................. 321 E 60 CWSSN P4 and impulse vs. time Test 8 trial ................................................. 321 E 61 CWSSN P5 and impulse vs. time Test 8 trial ................................................. 322 E 62 CWSSN P6 and impulse vs. time Test 8 trial ................................................. 322 E 63 CWSSN PD and impulse vs. time Test 8 trial ................................................ 323 E 65 CWSSN P1 and impulse vs. time Test 9 trial 2 .............................................. 324 E 66 CWSSN P2 and impulse vs. time Test 9 trial 2 .............................................. 324 E 67 CWSSN P3 and impulse vs. time Test 9 trial 2 .............................................. 325 25

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E 68 CWSSN P4 and impulse vs. time Test 9 trial 2 .............................................. 325 E 69 CWSSN P5 and impulse vs. time Test 9 trial 2 .............................................. 326 E 70 CWSSN P6 and impulse vs. time Test 9 trial 2 .............................................. 326 E 71 CWSSN PD and impulse vs. time Test 9 trial 2 ............................................. 327 E 72 CWSSN PE and impulse vs. time Test 9 trial 2 ............................................. 327 E 73 NRRN P1 and impulse vs. time Test 10 ......................................................... 328 E 74 NRRN P2 and impulse vs. time Test 10 ......................................................... 328 E 75 NRRN P3 and impulse vs. time Test 10 ......................................................... 329 E 76 NRRN P4 and impulse vs. time Test 10 ......................................................... 329 E 77 NRRN P5 and impulse vs. time Test 10 ......................................................... 330 E 78 NRRN P6 and impulse vs. time Test 10 ......................................................... 330 E 79 NRRN PD and impulse vs. time Test 10 ........................................................ 331 E 80 NRRN PE and impulse vs. time Test 10 ........................................................ 331 E 81 NRRN_2 P1 and impulse vs. time Test 11 ..................................................... 332 E 82 NRRN_2 P2 and impulse vs. time Test 11 ..................................................... 332 E 83 NRRN_2 P3 and impulse vs. tim e Test 11 ..................................................... 333 E 84 NRRN_2 P4 and impulse vs. time Test 11 ..................................................... 333 E 85 NRRN_2 P5 and impulse vs. time Test 11 ..................................................... 334 E 86 NRRN_2 P6 and impulse vs. time Test 11 ..................................................... 334 E 87 NRRN_2 PD and impulse vs. time Test 11 .................................................... 335 E 88 NRRN_2 PE and impulse vs. time Test 11 .................................................... 335 E 89 NRRY P1 and impulse vs. time Test 12 ......................................................... 336 E 90 NRRY P2 and impulse vs. time Test 12 ......................................................... 336 E 91 NRRY P3 and impulse vs. time Test 12 ......................................................... 337 E 92 NRRY P4 and impulse vs. time Test 12 ......................................................... 337 26

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E 93 NRRY P5 and impulse vs. time Test 12 ......................................................... 338 E 94 NRRY P6 and impulse vs. time Test 12 ......................................................... 338 E 95 NRRY PD and impulse vs. time Test 12 ........................................................ 339 E 96 NRRY PE and impulse vs. time Test 12 ........................................................ 339 E 97 NRRN P1 and impulse vs. time Test 13 ......................................................... 340 E 98 NRRN P2 and impulse vs. time Test 13 ......................................................... 340 E 99 NRRN P3 and impulse vs. time Test 13 ......................................................... 341 E 100 NRRN P4 and impulse vs. time Test 13 ......................................................... 341 E 101 NRRN P5 and impulse vs. time Test 13 ......................................................... 342 E 102 NRRN P6 and impulse vs. time Test 13 ......................................................... 342 E 103 NRRN PD and impulse vs. time Test 13 ........................................................ 343 E 104 NRRN PE and impulse vs. time Test 13 ........................................................ 343 E 105 CW/ORRN P1 and impulse vs. time Test 14 ................................................. 344 E 106 CW/ORRN P2 and impulse vs. time Test 14 ................................................. 344 E 107 CW/ORRN P3 and impulse vs. time Test 14 ................................................. 345 E 108 CW/ORRN P4 and impulse vs. time Test 14 ................................................. 345 E 109 CW/ORRN P5 and impulse vs. time Test 14 ................................................. 346 E 110 CW/ORRN P6 and impulse vs. time Test 14 ................................................. 346 E 111 CW/ORRN PD and impulse vs. time Test 14 ................................................. 347 E 112 CW/ORRN PE and impulse vs. time Test 14 ................................................. 347 E 113 CW/ORRY P1 and impulse vs. time Test 15 .................................................. 348 E 114 CW/ORRY P2 and impulse vs. time Test 15 .................................................. 348 E 115 CW/ORRY P3 and impulse vs. time Test 15 .................................................. 349 E 116 CW/ORRY P4 and impulse vs. time Test 15 .................................................. 349 E 117 CW/ORRY P5 and impulse vs. time Test 15 .................................................. 350 27

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E 118 CW/ORRY P6 and impulse vs. time Test 15 .................................................. 350 E 119 CW/ORRY PD and impulse vs. time Test 15 ................................................. 351 E 120 CW/ORRY PE and impulse vs. time Test 15 ................................................. 351 E 121 CW/ORRY P1 and impulse vs. time Test 16 .................................................. 352 E 122 CW/ORRY P2 and impulse v s. time Test 16 .................................................. 352 E 123 CW/ORRY P3 and impulse vs. time Test 16 .................................................. 353 E 124 CW/ORRY P4 and impulse vs. time Test 16 .................................................. 353 E 125 CW/ORRY P5 and impulse vs. time Test 16 .................................................. 354 E 126 CW/ORRY P6 and impulse vs. time Test 16 .................................................. 354 G 1 NSC SS static Test 3 pretest ......................................................................... 358 G 2 NSC SS static Test 3 in progress .................................................................. 358 G 3 NSC SS static Test 3 posttest ........................................................................ 359 G 4 UHPC SS static Test 1 pretest ....................................................................... 359 G 5 UHPC SS static Test 1 posttest ..................................................................... 360 G 6 NSC RR static Test 6 pretest ......................................................................... 360 G 7 NSC RR static Test 6 posttest ....................................................................... 361 G 8 UHPC RR static Test 9 pretest ...................................................................... 361 G 9 UHPC RR static Test 9 posttest ..................................................................... 362 G 10 NSC SS dynamic Test 6 pretest, front view ................................................... 362 G 11 NSC SS dynamic Test 6 pretest, rear view .................................................... 363 G 12 NSC SS dynamic Test 6 posttest, front view ................................................. 363 G 13 NSC SS dynamic Test 6 posttest, rear view .................................................. 364 G 14 UHPC SS dynamic Test 2 pretest, front view ................................................ 364 G 15 UHPC SS dynamic Test 2 posttest, rear view ................................................ 365 G 16 UHPC SS dynamic Test 2 posttest, front view ............................................... 365 28

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G 17 NSC RR dynamic Test 10 pretest, front view ................................................. 366 G 18 NSC RR dynamic Test 10 pretest, rear view ................................................. 366 G 19 NSC RR dynamic Test 10 posttest, rear view ................................................ 367 G 20 NSC RR dynamic Test 10 posttest, front view ............................................... 367 G 21 UHPC RR dynamic Test 14 pretest, front view .............................................. 368 G 22 UHPC RR dynamic Test 14 pretest, rear view ............................................... 368 G 23 UHPC RR dynamic Test 14 posttest, rear view ............................................. 369 G 24 UHPC RR dynamic Test 14 posttest, front view ............................................ 369 29

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INVESTIGATION OF COMPRESSIVE MEMBRANE ACTION IN ULTRA HIGH PERFORMANCE CONCRETE SLAB STRIPS By Bradley Wade Foust December 2013 Chair: Ted Krauthammer Major: Civil Engineering Reinforced concrete slabs are found in very common structural systems in both civilian and military applications. The boundary conditions that support the slab play an important role in the response to a particular load. Specifically, the amount of lateral a nd rotational restraint dictates how a slab responds to a particular load. Compressive membrane (i.e., inplane) forces are present in slabs when the boundaries are sufficiently stiff, therefore restricting the slab from both lateral translations and rotations. Advancements have been made to account for the additional capacity due to compressive membrane forces in conventional strength concrete. In todays world, concrete performance is improving because of increasing compressive strengths and additional ductility present in concrete members As a result of this current improvement, there is an urgent need to investigate compressive membrane theory in ultra high performance concrete ( UHPC) slabs to better understand their behavior. Existing compressive membrane theory should be revisited to det ermine if current theory is applicable, or if it is not, what modifications should be made. This study will provide insight into the validity of existing theory that is currently used to predict the 30

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ultimate capacity in conventional strength concrete slabs and attempt to modify the existing equations to account for highstrength concrete materials. A matrix of 14 normal strength concrete (NSC) and 13 UHPC slabs was tested both statically and dynamically to better understand the behavior of each material set and the effects th at boundary conditions have on slab response. The results from these experiments were then compared to response calculations made from existing theory as well as finite element analys es V aluable data sets on rigidly restrained UHPC slab response were obtained through an experimental research program. The experiments helped to validate the associated numerical analysis that was performed. It was determined that the existing theory should be used with caution to calculate the ultimate res istance in UHPC slabs. It was also determined from the experimental and numerical results that the increased compressive strength that is present in restrained UHPC slabs results in a two anda half t imes increase in resistance over the traditional yieldl ine theory resistance for UHPC slabs 31

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CHAPTER 1 INTRODUCTION Problem Statement The reinforced concrete slab is one of the most common types of structural elements that make up our infrastructure today. Slabs are found in very common structural systems, yet the boundary conditions that support the slab can vary in regard to the amount of lateral and rotational restraint provided in reaction to a given load. Due to this fact, the flexu ral behavior of slab systems is poorly understood, especially very high strength concrete slabs, and current design and analysis methods can lead to very conservatively designed systems, even when using conventional strength concretes. Concrete slabs that are utilized for both civilian and military applications, such as protec tion for our military personnel or utilized in hardened facility construction are being constructed more and more of high performancetype materials. These type materials are new to the engineering world, so their response to dynamic loads, such as blast, is not well defined. Research is required to define their behavior when subjected to these type loadings so that response of protective structures constructed with these type materials to blast loadings can be pr edicted before the structure is placed into theater. Current predictive capabilities to estimate ultimate loads and deflections of concrete slabs need to be investigated to determine if existing form ulations remain valid for ultra high per formance concrete (UHPC). Common design practice, such as ACI 318 [1], does not account for the enhancement of flexural capacity due to compressive membrane forces. Enhancement due to compressive membrane action results from stiff boundary conditions that restrain the slab from rotations and lateral translations. As the slab deflects, the ends of the slab 32

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tend to push outward against the boundaries, and arching (i.e., compressive) forces are developed in the compression zone of the slab. This fact could potentially lead to very conservative and expensive designs that are not necessary for the given load scenario. Consideration of membrane forces in reinforced concrete flexural members can provide a more accurate analysis and more economical design than exis ting methods. Advancements have been made to account for the additional capacity due to compressive membrane forces in conventional strength concrete. Results of current innovative research that is improving concrete performance, compressive strength, and ductility indicate an urgent need to investigate compr essive membrane theory in UHPC slabs. Currently, the most common procedure to analyze a concrete slab that is restrained to lateral translations is plastic theory for loaddeflection behavior. This for mulation and theory is discussed in Chapter 12 of Park and Gambles textbook [2]. With the advancements in concrete compressive strengths, this formulation should be revisited to investigate the validity of ultimate strength predictions for UPHC slabs when restrained from lateral translations This study will provide insight in to the validity of existing equations and suggest modifications to the existing equations for highstrength concrete materials. Once the fundamental quasi static behavior is understoo d, the blast response of UHPC slabs will need to be analyzed and quantified. This is particularly important because the types of structures that utilize this material depend on its dynamic response to provide either blast mitigation or penetration resista nce. The data generated from the dynamic experiments should lead to more accurate predictions of this materials response to blast loads. 33

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Technical Objective The overall objective of this research is to better understand compressive membrane behavior in U HPC slabs through experimental and numerical analysis. Both quasi static and dynamic experiments will be analyzed to gain insight into the range of fundamental behavior s of UHPC slabs when subjected to different rates of loading. Of particular interest is the predictive capability for the response of UHPC slabs when laterally restrained and subjected to dynamic loads From the experimental data gathered, a method of analyzing UHPC slabs will be developed based on Parks theory using fundamental theory of pl asticity [2], equilibrium, and stress strain compatibility. Parks theory was originally intended for the analysis of conventional strength concrete; however, pretest analysis was conducted to pr ovide a basis of comparison to the experimental results The internal membrane forces generated due to the boundary conditions w ere taken into consideration throughout this development. In the end, a resistance function used to accurately model the dynamic behavi or of UHPC slabs will be analyz ed so that its potential implementation into computer software codes, such as the Dynamic Structural Analysis Suite (DSAS) [3], can occur This implementation will enable more accurate predictions of highstrength concrete slab response to dynamic eve nts Scope For this study, 27 slabs were cons tructed and tested. O f these, 11 were quasi statically tested in a static water chamber facility that allows hydrostatic forces to be utilized as a loading technique on the slab. Of the 11 slabs quasi statically teste d, 5 were simp ly s upported, and the remaining 6 were rigidly restrained, which means no lateral displacement or rotation at the ends was allowed. The quasi static tests were 34

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conducted as a baseline to establish a static resistance function for the parameters of this experiment al series. The loaddeformation response of laterally restrained slabs was then compared to that of the simply supported slabs to determine the enhancement due to the boundary conditions, i.e. compression membrane acti on. The remaining 16 slabs were dynam ically tested in the Blast Load Simulator (BLS) facility located at the U.S. Army Engineer Research and Development Center (ERD C) in Vicksburg, MS. Of these 16 slabs, 9 were simply supported, and 7 were laterally restrained. Again, the loaddeformation res ponses for the two boundary condition scenarios w ere compared. Research Significance Experimental data indicating the enhanced flexural response due to compressive membrane forces in highstrength concrete slabs will be in itself a significant contribution to the state of knowledge. This contribution has been investigated in conventional strength concrete experimentally and numerically; however, very limited data exist for UHPC especially the dynamic response of UHPC. The static resistance of UHPC slabs th at are laterally restrained will provide a means to update current analysis methods. The data obtained from the dynamic experiments will assist in validating current computer codes used to predict slab response to dynamic events This validation will incre ase confidence in predicting response of hardened facilities subjected to such a dynamic event. The assumptions made in the equation development to predict plastic response of laterally restrained concrete slabs may not apply to concrete with significantly higher compressive strengths due to ACI [1] limitations on the factor This factor is defined as the ratio of the depth of the concrete compression block to the depth of the neutral axis. With these limitations in place, engineer s should proceed with c aution when using this equation and understand that 35

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the behavior of UHPC slabs could be different from that of conventional strength concrete slabs. The suggested modifications made to the compressive membrane equations will enable responses to be accurately predicted in laterally restrained UHPC slabs. Another significant contribution from this work is the experimental data consisting of load deflection behavior of UHPC slabs. A key component of the plastic theory equation is to fully under stand the deflection at which ultimate capacity occurs in a restrained concrete slab. At this point, this parameter is an unknown for UHPC, so this research provides insight as to when UHPC slabs of this particular spanto thickness ratio reach ultimate ca pacity. The consideration of the additional capacity can also lead to more economical designs of structural concrete slabs. As industry progresses into the future of concrete designs where highstrength concrete is more readily available and is used more frequently, the added cost savings on top of the increased performance could potentially be a significant breakthrough. 36

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CHAPTER 2 LITERATURE REVIEW Background The flexural behavior of conventional strength reinforced concrete slabs subjected to quasi static loads has been investigated for many years. In particular, the enhanced flexural capacity due to compressive membrane action is a research topic that has intrigued both design and research analyst s for decades. The study of compressive membran e behavior began in the 1950s when Ockleston [4] published res ults from load tests on a threestory reinforced concrete building in Johannesburg. He noted load capacities up to twice the capacity of those predicted by yieldline theory for an interior panel of the floor slab system. He concluded that the ultimate loads measured for flexural failures exceeded those predicted by normal design methods and by plastic theories, but were closer in agreement to the latter. When considering bending in one direction, the plastic theories predicted ultimate loads up to 20 percent less than the experimental values. Ockleston investigated the behavior further and later published another paper [5]. He determined that the failure mechanism matched that of yield line theor y, but the experimental fail ure loads were several times the values given by the theory. He later attributed the increase in failure load to arching action in the slab. He added that this type behavior is most likely to develop in lightly reinforced slabs and if the deflections are small and horizontal spreading at the supports is eff ectively restrained, their loadcarrying capacity can greatly increase. Membrane Theory Membrane forces are often present in reinforced concrete slabs at ultimate load as a r esult of the provided boundary conditions and the geometry of deformations of the 37

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slab segments. If the edges of the slab are restrained against lateral movement by stiff boundary elements, compressive membrane forces are induced in the plane of the slab w hen, as the slab deflects, changes of geometry cause the slab edges to tend to move outward and to react against the bounding elements. When accounting for the enhancement in resistance due to compression membrane, it is necessary to include the effect of any lateral displacement that may occur at the ends of the slab. Compressive membrane action is dependent on the restriction of small lateral displacements, and the behavior of the slab strip is sensitive to any lateral displacement that may occur. Inherent membrane forces that are present due to rigid boundary restraints are one topic of interest that is not fully understood, especially in highstrength concrete. This particular behavior is the result of lateral boundary restraints that are typicall y ignored in conventional analysis and design methods f or reinforced concrete slabs. For example, the yield line theory derived by Johansen [6] considers the presence of only moments and shear forces at the yield lines in the slab and gives a good indicati on of the ultimate load when the yieldline pattern can form without the development of membrane forces in the slab. However, if the edges of the slab are restrained against lateral movement by stiff boundary elements, compressive membrane forces are induc ed in the plane of the slab when, as the slab deflects, changes in geometry cause the slab edges to tend to move outward and to react against the bounding elements. This restriction in lateral movement results in an enhancement in the moment resistance at the yield lines which causes the ultimate load in the slab to be greater than the ultimate load calculated by Johansens yield theory. The behavior can be thought of as 38

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if the slab strip i s being jammed between the boundary restraints, which cause the sla b strips to arch from boundary to boundary. This enhanced loadcarrying ca pacity is present in statically loaded slabs and especially in dynamically loaded slabs with lateral restraint. When slabs are loaded at high strain rates, the materials exhibit an a pparent increase in strength properties, such as ultimate compressive strength in the concrete and yield strength of the steel reinforcement. The dynamic increase factor (DIF) is the ratio between the increased dynamic strength and the static strength. Thi s factor increases as the strain rate increases. A typical DIF curve for reinforced concrete is shown in Figure 2 1 Blast Resistance of Slabs The awar eness of blast resistant design of conventional and protective structures has increased over the last several years due to recent events. The collapse of the Alfred P. Murrah building in Oklahoma City is one example of the potential hazard our infrastructure faces. Blast resistant design is of particular importance in protective structures utilized in military installations. These types of str uctures, along with the lives of the soldier s who occupy them, are at significant risk in our military installations all over the world. In order to understand the structural response to blast loadings, the behavior of structural members, such as slabs, must be fully quantified. Resistance functions have been established for conventional reinforced concrete slabs [8]; h owever, with the development of highperformance materials, such as UHPC, the resistance functions for these materials have not yet matured. Until recent developments, the elastic and elastoplastic models from the early 1960s [9] have been most frequently used to represent blast resistant structural behavior. These models cons iderably underestimate the loadcarrying capacity of slabs 39

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[10]. The very short duration of blast loads play s a significant part in this error because inertia effects dominate the behavior. It is possible for a slab to perform well under slow loading rates but collapse under a faster rate. Typical design and analysis underestimates the flexural capacity of restrained concrete slabs due to ignori ng the enhancement from compression membrane action in the formulation. The capacity underestimation was considered a hidden safety factor in statically loaded slabs; however, the loaddeflection relationship is much more complicated under severe dynamic c onditions. In order to feel confident in the response, the slab resistance capability needs to be understood for structural safety, especially with very short duration loading. Krauthammer et al [8] incorporated observations from Woodson [11 12] and Park and Gamble [2] into a previous model [13] to define general resistance functions for slender, intermediate, and deep slabs. The new resistanc e functions can be seen in Figure 2 2 Krauthammer also showed that considering membrane effects greatly improved the ability to explain some observations in slabs tested under explosive loads [14]. These initial results motivated future research in developing structural models that included improved membrane effects mechanisms [13, 15]. In these later studies, such loaddeflection relationships were adopted for dynamic structural analysis based on a single degreeof freedom (SDOF) approach [10]. Mass stiffness, an d other parameters, such as load source, type of structure, and load application to the structure, for the structural system under consideration are selected on the basis of the type of problem. This general approach was discussed by Biggs [9], and most de sign manuals [16] contain similar procedures. Krauthammer et al 40

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[17] also discussed information on the treatment of fully nonlinear systems by SDOF simulations. The system response will depend not only on the magnitude of the force, but also on the relati onship between the dynamic characteristics of the force and the frequency characteristics of the structure [10]. These are defined by the ratio of stiffness to mass (K/M) and the effect of damping. Various design manuals contain dynamic response charts and tables based on SDOF considerations [16], and discussion on these topics can also be found in Biggs [9]. The main distinction between Krauthammers [13, 14], Krauthammer et al [15] and Biggs [9] approaches was the former approach includes the structural resistance function. Instead of employing the classical concept for a resistance function (elastic, elastic perfectly plastic, or plastic), the term R(x) was represented by the modified loaddisplacement relationship that also included membrane effects [ 10]. The resistance function mentioned here takes into account membrane effects (both in compression and tension for either oneor two way slabs), the influence of externally induced inplane forces, shear effects, and strainrate effects on the materials Plastic Theory The general loaddeflection behavior of a twoway reinforced concrete slab that has been subjected to a static uniformly applied load with res trained edges is shown in Figure 2 3 The slab reaches its enhanced ultimate load at B with the help of compressive membrane forces. Beyond B, the slabs flexural strength decreases rapidly because of a reduction in compressive membrane force. As the response approaches C, the membrane forces in the central region of the slab change from compression to tension. Beyond C the slab carries load by the reinforcement acting as a plastic tensile membrane with full depth cracking of th e concrete over the central region of the slab. 41

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The slab continues to carry load out to D where the reinforcement begins to fracture or some other component in the system fails. Parks theory [18] has been the underlying basis for many researchers to define the loaddeflection relationship of slab strips. He modeled an interior panel of a twoway slab system as a group of fix ended strips running parallel to the short and long directions of the slab and considered one of these stri ps under transverse load. Figure 2 4 shows the assumed plastic hinge formation in the strip. The strip is considered to be fully restrained against rotation and vertical transl ation at the ends. Compressive membrane action is dependent on the restriction of small lateral displacements. Due to the sensitivity of the slab strip to lateral displacements, the outward lateral movement, t must be considered. The slab strip shown in Figure 2 4 has symmetrically positioned plastic hinges. In doing this, it is assumed that the tension steel has yielded, the compressed concrete has r eached its strength with the stress distribution as defined by the ACI 31811 equivalent rectangular stress block, and the tensile strength of the concrete can be neglected. The portions between the hinges are assumed to be straight. From the free body diagram of portion 1 2 shown in Figure 2 5 Eq uation 2 1 is derived. This formulation only applies at and after the ultimate load is reached. It has been determined from Figure 2 5 that the sum of the moments of the stress resultants at the yield sections about an axis at middepth at one end is equal to u + mu nu and after the use of geometry of deformation and equilibrium conditions Eq uation 2 1 is derived. 42

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(2 1) Where u = negative plastic moment mu = posi tive plastic moment nu = membrane (axial) force at ultimate load condition = deflection of the middle slab segment c = 28day uniaxial concrete compressive strength 1 = ratio of the equivalent stress block depth to the neutral axis depth h = member thickness l = span length = axial short term strain t = outward lateral displacement at each boundary = steel tensile forces at positive and negative hinges s, Cs = steel compressive forces at positive and negative hinges = concrete cover to the center of mild steel positive and negative rei nforcement, respectively This load deflection relationship assumes that the critical sections have reached their strength from the onset of deflections. Due to this assumption, the initial part of the 43

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loaddeflection curve plotted from this equation will not be accurate because of the assumed plastic behavior. This relationship does not apply when the slab is behaving elastically or partially plastic al ly only when sufficient deformation has occurred to allow full plasticity to develop at the critical secti ons. The term 2t/l which is the total axial strain, can be found as shown below ( 2 2) Where Nu = membrane (axial) force at ultimate load condition S = surrounding lateral stiffness per unit width of the slab strip at each end Ec = concrete modulus of elasticity = ratio of long term deformations due to shrinkage, creep, and temperature Loading Conditions The loading conditions for which this study will consider are necessary for the investigation of the fundamental behav ior of protective slab systems. Both quasi static and dynamic response s are of interest to fully understand the effects of restrained boundary conditions of highstrength concrete slabs. The following sections will introduce the loading conditions that wil l be applied in the experimental program. Uniformly Q uasi S tatic L oading The quasi static experiments will be conducted to understand the fundamental slab behavior. A loaddeformation relationship (i.e., static resistance function) for each slab will be g enerated. They will serve as the baseline experiments and will be imperative to understanding the overall range of behavior of slab response and also the effects of the boundary conditions. These experiments will be conducted in a static 44

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water chamber. The details of the experimental setup will be discussed later in this dissertation; however, the basis of the loading will come from hydrostatic forces generated from a pressurized cavity. Blast L oads A blast event, within this context, represents the violent effect produced in the vicinity of an explosion. Blast can also be a result of a number of things, for example a violent gust of wind, but in the framework of this effort, blast will refer to the effect from an explosion. Typically, a blast is the result of an explosion defined as a sudden expansion of some energy source. Generally, the most common sources of significant explosions are derived from chemical or nuclear materials [19]. The measure of the effectiveness of chemical explosive materials is usually defined in terms of peak pressure or specific impulse, which is defined as the area under the pressuretime history. The effectiveness of an explosive material is typically expressed as a TNT equivalent. This can be shown by relating the explosive ener gy of the effective charge weight of those materials to that of an equivalent weight of TNT [19]. Other factors may also affect the equivalency of a material including shape, the number of explosive items, explosive confinement, and the pressure range being considered. For blast resistant design, the effects of the energy output from an explosive material of a specific shape relative to that of TNT of similar shape can be expressed as a function of the heat of detonation of the various materials as follows [20] =d EXP E EXP d TNTH WW H ( 2 3) Where WE = effective charge weight 45

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WEXP = weight of the explosive in question d EXPH = heat of detonation of explosive in question dTNTH = heat of detonation of TNT The heat of detonation of some of the more commonly used explosives is shown in Table 2 1 Blast w ave p henomena: The violent release of energy from a detonation in a gaseous medium gives rise to a sudden pressure increase in that medium. The pressure disturbance, termed the blast wave, is characterized by an almost instantaneous rise from the ambient pressure to a peak incident pressure. Incident pressure is the pressure on a surface parallel to the direction of the blast wave. This pressure increase, often referred to as shock, travels radially from the burst point with a diminishing velocity, U that is always in excess of the sonic velocity of the medium. Gas molecules, making up the front, move at lower velocities, u The particle velocity is associated with a dynamic pressure or the pressure formed by the winds produced by the shock fronts. As the shock front expands into increasingly larger volumes of the medium, the peak incident pressure at the front decreases and the duration of the pressure increases [16]. At any point away from the burst, the pressure disturbance can be represented by the sh ape shown in Figure 2 6 The shock front arrives at tA, and after the rise to the peak value, the incident pressure decays to the ambient value in the time that is known as the positivephase duration. This is followed by a negative phase with a duration longer than the positive phase and characterized by a pressure below the preshot 46

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ambient pressure and a reversal of the particle flow. The incident impulse density is the integrated area under the pressuretime curve. If the shock wave impinges on a rigid surface oriented at an angle to the direction of propagation of the wave, a reflected pressure is instantly developed on the surface. In this case, the pressure is raised to a value greater than that of the incident pressure. The reflected pressure is a function of the pressure in the incident wave and the angle formed between the rigid surface and the plane of the shock front. The duration of the reflect ed pressure is controlled by the size of the reflecting surface. The high reflected pressure seeks relief toward the lower pressure region. When the incident pressure comes into contact with a surface, the pressures and impulses of the initial wave are reinforced and reflected. This scenario is shown in Figure 2 7 This plot is representative of an infinite plane reflector. When the wave impinges on a surface that is perpendicular to the direction of travel of the shock wave, the point of initial contact will be subjected to the maximum reflected pressure and impulse. The effect s of the angle of incidence and incident pressure on the peak refle cted pres sure is shown in Figure 2 8 Materials The two materials that will be investigated in this research will be a conventional strength concrete called SAM 35 and a UHPC called Cor Tuf. These two materials were developed and have been extensively characterized by the U.S. Army ERDC, and results have been published in two different technical reports [21, 22]. Figure 2 9 presents the unconfined compressive strengths versus cross head position for the two materials investigated in these experiments. The two materials will be briefly described in the paragraphs below. 47

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S AM 35 concrete will be used for all the baseline experiments. It is a conventional strength concrete that can be created with readily available materials and reaches a nominal compressive strength of 3500 psi at 28 days. The data published by Williams et al [2 2] provide full characterization, including constitutive property behavior, of this material. The general mixture design for this mat erial is also shown in Table 2 2 UHPC is a generic term for a relatively new class of concrete that is being introduced on a limited number of civil engineering projects worldwide. As with all classes of concrete it is difficult to establish an exact definition of UHPC. The reasoning behind terming a concrete as ultrahigh performance differs among manufacturers of the product. In some cases, the concrete may exhibit relatively high compressive strength, may be self consolidating, could have relatively high tensile or flexural strength, or may be simply a durability performance criteria. For this particular effort, high performance is referring to the extremely high compressive strength of the material. The material of interest in this research is called Cor Tuf. Cor Tuf is the nomenclature given to a family of UHPCs developed at the Geotechnical and Structures Laboratory ( GSL ) ERDC. The Cor Tuf material composition is designed to develop ultrahigh compressive str ength while maintaining workabil ity and production economy. Cor Tuf can be broadly characterized as a reactive powder concrete (RPC). RPCs are composed of fine aggregates and pozzolanic powders but do not include coarse aggregates like those found in conventional concrete. T he maximum particle size in Cor Tuf is limited to that of the silica sand, which is a foundry grade Ottawa sand that has a maximum size of approximately 48

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0.6 mm [21]. The nominal unconfined compressive strength of Cor Tuf is about 28,000 psi. The mixture proportion s for Cor Tuf are reported i n Table 2 3 [21]. Included in Cor Tuf are processed fine silica sand, finely ground quartz flour, Portland cement, and amorphous microsilica (also known as silica fume). Additionally, a polycarboxylatetype superplasticizer is included to decrease water demand, aid mixing, and improve workability. The water to cement ratio is r estricted to about 0. 21 for Cor Tuf, which is far lower than values typical of conventional concrete. The proportional weight of steel fib ers in Cor Tuf is given in Table 2 3 as a mass fraction relative to the mass of cement. This ratio corresponds to a volumetric content of about 3.6% which is somewhat greater than is normally recommended for typical fiber reinforced concrete applications. The st eel fiber incorporated into Cor Tuf is the Dramix ZP305 product from Bekaert Corporation and is shown in Figure 2 10. When p urchased, t he ZP305 fibers are adhered together in bundles with a water soluble adhesive. During the mixing process, the fibers disperse as the adhesive dissolves in the fresh concrete. The steel fibers are introduced into the fresh concrete mixture after reaching a flowable pastelike consistency. Ideally, mixing results in random orientation of the fibers within the cementitious matrix. The manufacturers product data sheet states that the ZP305 fibers are approximately 30mm long, have a diameter of approximately 0.55 mm, and are hooked at each end. The t ensile strength for the steel fibers is reported by the manufacturer to be 1,100 MPa. For this research effort, steel reinforcement will also be utilized in conjunction with the conventional strength concrete as well as Cor Tuf, with and without fiber rein forcement, to determine the fiber effects on slab behavior. The 49

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reinforcement w as ASTM A 615 standard deformed concrete reinforcement bars. The minimum tensile strength w as 90,000 psi with yield strength of 6 9 ,000 psi. Slab B ehavior A number of articles w ere researched in preparation of this summary of previous publications. Only those papers/reports that are directly related to the objective of this effort will be discussed. This will be done to provide insight into the pertinent background information an d will hopefully lead into the approach taken to answer needed questions to advance the state of knowledge in this research area. Results from E xperiments Experimental efforts have shown that membrane forces considerably enhance the flexural strength of sl abs with laterally restrained supports. A. J. Ockleston [4] noticed that the load capacity predicted by the yield line theory of an interior panel of a floor slab system in a dental hospital building in Johannesburg was more than twice the capacity for which it was designed. The plastic theories gave ultimate loads up to about 20% less than the experimental values when failure was due to bending in one direction, but underestimated by a much greater margin the strength of slabs failing as a result of bending in two directions. Ockleston showed in a later paper that this unexpected behavior was developed by compressive membrane forces due to socalled arching action or dome action that are the source of extra strength beyond that predicted by yield line th eory [5]. He also concluded that arching action is most likely to develop in lightly reinforced slabs and, if the deflections are small and horizontal spreading at the supports is effectively restrained, can greatly increase their load carrying capacity. 50

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G uice [23] conducted a series of experiments to investigate the effects of edge restraint on slab behavior. He tested 16 oneway reinforcedconcrete plate elements subjected to uniform static water pressure. Overall dimensions of the slabs were 24 in. by 36 in. with an effective loaded area of 24 in. by 24 in All slabs had the same percentage of steel reinforcement in compression as in tension. The general reinfor cement layout is shown in Figure 2 11 The span thickness ratio, reinforcement ratio, and degree of rotational restraint wer e the primary parameters varied in the tests. The reaction structure was designed to permit partial rotation at the supports and the average support rotations documented in the report varied between 0.4 to 2.8 degrees. Lateral translations were also measured during the tests. The reaction structure details are in Figure s 2 12 t hrough 2 14 These experiments provided significant contributions to understanding the effects of the edge restraint and how it affects the response of the slab. Guice concluded that compression membrane theory using an assumed infinite lateral stiffness over predicted the flexural capacity of slabs with partial rotational restraint when no external inplane loads were present. He also concluded that thrusts act ed to enhance the flexural capacities of slabs with small rotational freedoms as long as the lateral stiffness was sufficient to develop inplane forces. Rankin et al [24] publish ed results from experimental work on laterally restrained slabs and proposed basic formulations of a rational method of predicti ng their response. The experimental effort consisted of testing seven rigidly restrained and four unrestrained slabs to investig ate strength enhancement due to compressive membrane action. Lateral restraint was provided to the seven rigidly restrained slabs by the steel supporting frame shown in Figure 2 15 The load v ersus central deflection curves are 51

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shown in Figure s 2 16 and 2 17. By c omparing the rigidly restrained slab response ( Figure 2 17) to that of the unres trained slabs in Figure 2 16, it can be seen that the presence of the lateral restraint did not appear to affect the first cracking loads, but did sig nificantly increase the post cracking stiffness of the laterally restrained slabs. Other interesting data can be seen in Figure 2 18 in which the ult imate capacities are plotted against their respective yield line capacities. It can be shown that the greatest enhancement in ultimate capacity occurred for the laterally restrained slabs wit h the lowest conventional yield line capacities. The ultimate capacities of the laterally restrained slabs were reported as being between 1.7 and 5.9 times those of the equivalent unrestrained control specimens. Results from Analyses and S imulations Guice et al [25] published analyses results of 47 oneway flat plate specimens of the type typically found in protective construction. The peak flexural capacity was calculated for each case by a modification of the theory developed by Park [18], refined by Park and Gamble [2] and combined with a relationship proposed by K eenan [26]. Each of the analysis procedures discussed required some assumptions of the deflection at ultimate load, and excellent results could be obtained if the proper ultimate deflection wa s assumed. Keenan proposed a straindeformation relationship shown below in Equation 2 4 that is valid for th e strip geometry shown in Figure 2 19 to determine the peak capacity deflection. Rather than utilizing an empirical approach, Keenans relationship was found to yield favorable results; therefore, it was used in this particular analysis. ==+mtanxtc ( 2 4) 52

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Assum e the deformation e can be related to the ultimate strain in the concrete by the ex pression =2uxe ( 2 5) Then E quations 2 4 and 25 can be rewritten to yield the mid span deflection in terms of the concrete strain or mid span curvature + + == () () 22u m mx x c ( 2 6) Where u = ultimate strain in the concrete m = curvature at mid span Equation 2 6 can be used to solve for the deflection at which the peak capacity is reached. Keenan noted that there should be an upper limit on the deflection predicted by E q uation 2 6 as the spanthickness ratio increases. Keenan suggested that for relatively thin slabs, spanthickness ratio greater than 18, failure would occur by geometric instability rather than material instability. This equation is also sensitive to lateral movements at each end, which is in turn dependent on the stiffness of the supports. It has been determined through experiment s [23] that an upper bound solution for the peak capacity can be calculated using E quation 2 6 when assuming infinite lateral stiffness at the supports. Guice et al. [25] utilized this formulation and performed compressive membrane calculations on 47 slabs from literature. The authors compared the results from their formulation to a formulation that utilized the experimental deflections as a basis for 53

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calculatin g the pea k capacity as well as the yieldline capacity for each case. One example of their results is shown in Figure 2 20. Meamarian et al [27] developed a method of analysis, based on the theory of plasticity [2] and modified compression field theory [28], that considers the effects of compressive membrane for ces in the analysis and design of prestressed and/or reinforced concrete oneway members. In this effort, Meamarian et al modified Parks equation [18] to include the effects of prestressing forces and long term deformations. The method considers critical factors such as strain softening, tension stiffening, repeated load, reinforcement type, and long term shortening. The modified theory was compared to experimental results generated by Guice [23] and overall, the program outputs regarding the forces at t he supports, load, and deflection at mid span for the ultimate load condition are close to the test results. This procedure considered membrane forces in the slab analysis; therefore, the load enhancement over Johansens yield line theory was significant. L ahlouh and Waldron [29] investigated the development of membrane action in subassemblies of wall and slab elements via the finite element method due to their noted shortcomings in the more simplified methods. The accuracy of the method was verified against results of three largescale laboratory tests. From this study, the authors concluded that the loadcarrying capacity of axially restrained slabs increases with the degree of end restraint as a result of the development of compressive membrane action. It was also found that crack initiation was delayed and deflections were reduced with increasing levels of end restraint. Other interesting conclusions from this work are, for a fixed value of concrete strength, an increase in the percentage of reinforcement 54

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decreases the possible load enhancement. Similarly, for a fixed steel ratio, load enhancement increases with compressive strength of the concrete. The enhancement was also found to increase with an increase in the degree of end restraint and with an increase in the section depth for a given span. Rankin et al [24] used a different approach than previously mentioned to predict ultimate capacity of the restrained slabs. Rankin [30] previously developed a theory for arching action based on McDowell et al. s [ 31] elastic plastic geometric deformation theory for arching in masonry walls. Rankin extended the McDowell et al theory to allow for the effects of reinforcement, concrete strength, and stiffness of lateral restraint. Niblock [32] integrated this strip t heory with Johansens yield line theory [6] for slabs to produce a method for predicting the ultimate capacity of uniformly loaded laterally restrained rectangular slabs. The underlining idea for this theory is an empirical relationship for the average arc hing moment of resistance along the yield line s that is incorporated into the virtual work equations to enable prediction of the enhanced ultimate capacities of laterally restrained slabs. Like other related efforts, this effort concluded that the ultimate capacities and post cracking stiffness es of uniformly loaded, laterally restrained slabs are considerably enhanced by the effects of compressive membrane action. They found that the degree of strength enhancement was greatest for the slabs with the lowest conventional yield line capacities. They also concluded that the proposed method of prediction provides consistent yet slightly conservative ultimate capacities of uniformly loaded, rectangular slabs with rigid restraint. Very little research has been published on the strength enhancement due to compressive membrane action in highstrength concrete slabs. With the advancement 55

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of high performance concrete in common construction applications as well as protective structure applications, the need for experimental data exist. Throughout the literature search, a few papers were found that were written by Queens University of Belfast, School of Civil Engineering. Taylor et al [33] presents the results of tests on full scale oneway spanning reinforced concrete slabs typical of a bridge deck slab. Taylor recognized that the theory that was used by Rankin [24, 30, 34] was derived for concrete compressive strengths below 10,150 ksi (~70 N/mm2) and could not be assumed to be valid for concrete with high compressive strengths. Taylor et al developed a method to calculate an equivalent stress block to represent the compressive force in the concrete. The authors utilized a report published by the Concrete Society that provided stress strain relationships for highstrength concr etes. The curves shown in Figure 2 21 show a decreasing value of ultimate strain with increasing compressive strength. This indicates that the plastic strain value approaches the ultimate strain value in very high strength concretes. The derived stress blocks for varying c ompressi ve strengths are shown in Figure 2 22. For each compressive stress category the parabolic stress distribution was equated to an equivalent rec tangular area. Taylor et al [33] concluded that the British design standard provides extremely conservative predictions for flexural strength of laterally restrained slabs, especially with high compressive strength concrete slabs. The authors determined that crushing in the compression zone coupled with the higher capacities in the specimens with high concrete compressive strength suggested that the arching component increased with compressive strength. The modification that the authors made to the stress strain block 56

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to incorporate concretes with high compressive strengths was found to give reasonably accurate predictions for both normal and high strength concrete specimens. 57

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Table 2 1 Heat of detonation and heat of combustion of explosive materials Explosive name Symbol Heat of detonation (ft lb/lb) Heat of combustion (ft lb/lb) Baratol 1.04 E+06 Boracitol 5.59 E+06 BTF 2.37 E+06 Composition B Comp B 2.15 E+06 3.91 E+06 Composition C 4 Comp C 4 2.22 E+06 Cyclotol 75/25 2.20 E+06 3.68 E+06 DATB/DATNB 1.76 E+06 4.08 E+06 DIPAM 1.89 E+06 DNPA 1.48 E+06 EDNP 1.72 E+06 FEFO 2.03 E+06 HMX 2.27 E+06 HNAB 2.06 E+06 HNS 1.99 E+06 LX 01 2.41 E+06 LX 02 1 1.99 E+06 LX 04 1.99 E+06 LX 07 2.08 E+06 LX 08 2.77 E+06 LX 09 0 2.24 E+06 LX 10 0 2.17 E+06 LX 11 1.72 E+06 LX 14 2.20 E+06 NG 2.22 E+06 2.26 E+06 NQ 1.49 E+06 2.79 E+06 Octol 70/30 -2.20 E+06 3.81 E+06 PBX 9007 2.18 E+06 PBX 9010 2.06 E+06 PBX 9011 2.14 E+06 PBX 9205 2.04 E+06 PBX 9404 2.18 E+06 PBX 9407 2.24 E+06 3.31 E+06 PBX 9501 2.22 E+06 Pentolite 50/50 2.14 E+06 PETN 2.31 E+06 2.70 E+06 RDX 2.27 E+06 3.20 E+06 TETRYL 2.11 E+06 4.08 E+06 TNETB 2.34 E+06 TNT 1.97 E+06 5.05 E+06 58

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Table 2 2 SAM 35 mix design Materials Mass /v olume per cubic meter batch Portland cement Type I/II 190.2 kg Fine aggregate: Natural river sand 738.2 kg Coarse aggregate: 9.5 mm crushed limestone 650.3 kg 200 N (water reducing admixture) 496 .0 mL AE 90 (air entraining admixture) 57.1 mL Water 120 .0 kg Table 2 3 Cor Tuf mixture composition Material Product Proportion by weight Cement Lafarge, Class H, Joppa, MO 1.00 Sand US Silica, F55, Ottawa, IL 0.967 Silica flour US Silica, Sil co Sil 75, Berkeley Springs, WV 0.277 Silica fume Elkem, ES 900 W 0.389 Superplasticizer W.R. Grace, ADVA 170 0.0171 Water (tap) Vicksburg, MS, municipal water 0.208 Steel fibers 1 Bekaert, Dramix

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Figure 2 1 Design curve for DIF for Ultimate Compressive Strengths of Concrete Figure 2 2 Generalized resistance function for slabs Reprinted by permission from Krauthammer, T. Krauthammer et al. A Single Degree of Freedom (SDOF) Computer Code Development for the Analysis of Structures Subjected to Short Duration Dynamic Loads, PTC TR 0022003, Protective Technology Center, Penn State University, August 2003 60

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Figure 2 3 Load deflection relationship for twoway reinforced concrete slab with edges restrained against lateral movement Figure 2 4 Plastic hinges of restrained strip 61

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Figure 2 5 Portion of strip between yield sect ions 1 and 2 of Figure 24 Figure 2 6 Free field pressuretime variation 62

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Figure 2 7 Typical reflected pressuretime history 63

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Figure 2 8 Reflected pressure coefficient versus angle of incidence Figure 2 9 Unconfined compressive strengths for concrete materials tested 64

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Figure 2 10. Bekaert Dramix ZP305 fibers 65

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Figure 2 11. Reinforcement layout and details of Guice tests 66

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Figure 2 12. Elevation of reaction structure 67

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Figure 2 13. Section view of reaction frame Figure 2 14. Quarter section view of reaction structure with slab in place 68

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Figure 2 15. Steel frame for providing lateral restraint Reprinted by permission from Rankin, B. and Long, A., The Structural Engineer, V 69, No. 16, Aug 1991, pp. 287295 69

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Figure 2 16. Load vs. d eflection of unrestrained slabs. Reprinted by permission from Rankin, B. and Long, A., The Structural Engineer, V 69, No. 16, Aug 1991, pp. 287295 Figure 2 17. Load vs. deflection of rigidly restrained slabs Reprinted by permission from Rankin, B. and Long, A., The Structural Engineer, V 69, No. 16, Aug 1991, pp. 287295 70

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Figure 2 18. Comparison of results and predictions for laterally restrained and unrestrained specimens Reprinted by permission from Rankin, B. and Long, A., The Structural Engineer, V 69, No. 16, Aug 1991, pp. 287295 71

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Figure 2 19. Geometry of deformation (a) s lab strip (b) half slab strip (c) free body diagram 72

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Figure 2 20. Experimental and analytical comparison of results for slab response 73

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Figure 2 21. P roposed s tress strain relationship for highstrength concretes Reprinted by permission from Ramster, B. Editor ICE Publishing. Taylor, S.E., Rankin, G.I.B., and Cleland, D.J., Arching action in highstrength concrete slabs, Proc Institution Civil Engineers Struc tures & Buildings 146, Nov 2001, 4, pp. 353362 Figure 2 22. P roposed stress blocks for high strength concretes Reprinted by permission from Ramster, B. Editor ICE Publishing. Taylor, S.E., Rankin, G.I.B., and Cleland, D.J., Arching action in highstrength concrete slabs, Proc Institution Civil Engineers Structures & Buildings 146, Nov 2001, 4, pp. 353362 74

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CHAPTER 3 RESEARCH APPROACH This research effort utilize d a combination of experimental and numerical analysis to investigate the enhancement of ultimate capacity in both normal and highstrength laterally restrained concrete slabs. The end goal is to understand the validity of the current compressive membrane theory that can potentially be used to describe the enhanced loadcarrying capacity of highstrength slabs when the boundaries are restrained from movement both in the lateral direction as well as end rotation. The end result will improve the initial solu tion developed by Park [18], the cur rent modified solutions developed by Krauthammer et al Guice and Keenan [8, 25, 26] and the current formulation in UFC 340 01 [36 ] that is used to calculate ultimate resistance of restrained conventional strength concrete slab strips by account ing for the very h igh compressive strengths in UHPC slabs. This series of experiments will also help to validate existing highstrength concrete material models that are currently being developed throughout the industry and academia by providing valuable data on r estrained UHPC slab strip response to quasi static and dynamic loads This chapter will discuss the experimental setups the instrumentation details of the experiments, and how the data obtained w ere used to compare to existing theory that help describe the behavior of UHPC slabs. Experimental Investigation The data generated in th ese experiments w ere limited to quasi static and dynamic tests of oneway reinforcedconcrete slab strips designed to represent a typical structural element that would be found in hardened facility construction or military applications. The tests were conducted to provide insight into the effects of boundary 75

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conditions on the responses of UH PC slabs. The main focus was on laterally restrained slabs and how this restraint affects th e ultimate loadcarrying capacity of the slabs. In previous experiments [23], the conclusion was made that lateral restraint was the most important parameter to consider when creating an enhancement in strength due to compressive membrane action. In addition, full restraint provided the greatest enhancement in capacity for slabs with the largest spanthic kness ratio of approximately 15. Three parameters concrete strength, degree of lateral and rotational restr aint, and loading ratewere investigated in this series of tests. The upper and lower bound of rotational and lateral restraint was investigated. The lower bound in this case was a simply supported condition that allow ed the ends of t he slab to rotate. The slab also had a limited capability to move in the lateral direction. The idealized upper boundary condition represent ed a rigidly restrained boundar y condition. This condition prevent ed both lateral translation and end rotation of the slab. This approach is a starting point for investigation of compressive membrane action in highstrength slabs. At some point in the future, partially restrained UHPC s labs should also be investigated to determine the effects of the surrounding boundary stiffness. A total of 14 normal strength concrete (NSC) slabs were tested. Of these 14 slabs, 6 were loaded quasi stat ically and 8 were loaded dynamically. O f the 6 qua si statically loaded slabs 2 were tested as simply supported slabs and 4 were l aterally and rotationally restrained. Of the 8 dynamically loaded slabs, 4 were tested as simply supported slabs and 4 were l aterally and rotationally restrained. These initi al tests 76

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serve d as the basel ine experiments for NSC and provided a data set to compare the results of the UHPC slabs. As with the NSC, the UHPC slabs were loaded both quasi statically and dynamically. The initial test plan included Cor Tuf both with and without fibers. Due to the lack of workability and the density at which the slabs were reinforced, it was impossible to cast a quality Cor Tuf with fiber specimen. This will be discussed later in this chapter With that being said a total of 1 0 Cor Tuf wi thout fiber specimens were cast and tested both quasi statically and dynamically. Of the 6 dynamically loaded slabs, 3 were tested as simply supported slabs and 3 were laterally and rotationally fixed against translation and rotation. Of the 4 quasi stati cally loaded slabs, 2 were tested as simply supported slabs and 2 were laterally and rotationally fixed against translation and rotation. Table A 1 in Appendix A shows the test matrix of the as built and tested slabs Slab D escriptions The experimental test series consisted of four different slab sizes. The dimensions of the slabs were designed such that the clear span e.g. the distance between the supports, would be consistent between the static chamber and BLS test configuration The quasi statically tested slabs had nominal dimensions of 60 in. by 333/4 in. by 3 in. f or the simply supported case and 58 in. by 333/4 in. by 3 in. for the restrained case. The dynamically tested slabs had nominal dimensions of 64 in. by 333/4 in. by 3 in. for the simply supported case and 65 3/8 in. by 33 3/4 in. by 3 in. for t he restrained case The clear span in every case was approximately 52 in. for both the quasi static tests and dynamic tests. This gives a span to t hickness ratio of 17.33 (52 in. /3 in. ). 77

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The NSC slabs had a nom inal compressive strength of 3550 psi and contained Grade 60 rebar. The reinforcement rat io was 0.724% The UHPC slabs had a nominal compressive strength of 24,000 psi and also contained Grade 60 rebar. The reinforcement ratio was matched to the NSC slab counterpart for comparison reasons. Adequate shear reinforcement was added to the reinforcement design of both NSC and UHPC slabs to allow the specimen to fail in flexure. The additional shear capacity due to the vertical reinforcement was required for flexural response and failure modes. The general slab dimensions and ste el reinfo rcement layout for the slab designs are shown in Figure 3 1 Design drawings and photograph s for each of the slab configurations are in Appen dix B A photograph of the typical reinforcement layout is in Figure 3 2 Concrete C asting Each s et of slabs was cast on the same day fr om a single batch of concrete to ensure that each slab in the material type set (e.g., NSC, Cor Tuf without f iber, and Cor Tuf with f iber) would remain consistent with respect to the other test specimens of the same material Each set of slabs was cast in August 2012. The surface of the slabs was kept moist during the first seven days of initial cure to prevent surface cracking During the initial seven days, the slabs were covered with burlap sacks or a similar material and sprayed with water on a continuous cycle. The NSC slabs were removed from the formwork after seven days and then placed in a moist fog environment at room temperature for the remainder of the 28 day cure cycle. Once the Cor Tuf slabs were demolded after seven days they were covered with steam blankets and continued to cure at approximately 185F for another seven days. P hotographs of concrete casting are in Figure s 3 3 and 3 4 below as well as in Appendix C 78

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Reaction Frames The reaction frames for both the quasi static and dynamic experiments are shown in Figure s 3 5 through 3 13 Even though two different frames were used for each rate of loading event the boundary conditions and resulting clear spans were the same for both quasi static and dynamic experiments The frame used in the simply supported quasi static e xperiments is shown in Figure s 3 5 and 3 6 The steel frame has 4in. by 4 in. by 1/2 in. steel tubes welded inside a steel picture frame on both ends in the longitudinal direction. These steel tubes act as the bearing surface for the slabs to rest against and allow for free translation in the direction of the pressurized loading. The slab bears against the steel tubing allowing for 3 in. of bearing surface on each end of the slab, which result s in a 52in. clear span in the longitudinal direction. The slab w as not supported in the lateral direction, res ulting in oneway slab action. This frame allow s minimal lateral movement as well as support rotations as the slab is being loaded. Figures 3 7 and 3 8 show the reaction frame used in the rigidly restrained quasi static experiments. This frame consisted of back to back 3/4 in. steel angles bolted into place on each end of a steel picture frame. The concrete slab was placed inside the picture frame between the two angles allowing approximately a 3 in. bearing surface between the slab and the angle legs. The concrete slab was designed with four pass through holes at each end to allow 5/8in. diameter bolts to pass through the angle first, completely through the slab, and then through the second angle, which resulted in a clamped end boundary condition. The frame also allowed space at one end to insert a steel adjustment plate to ensure no lateral tr anslation during the test. Once the plate was in place, the adjustment nuts were tightened, and the excess slack was eliminated 79

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resulting in a secure fit within the reaction frame. This end condition can be seen in Figure 3 8 The two frames used in the BLS experiments are shown in Figure s 3 9 throu gh Figure 3 13. These reaction frames bolt directly to the target vessel of the BLS. Figures 3 9 and 3 10 show photographs of the frame that provide the simply supported boundary condition. The f rame is a two part system in which the outer frame bolts directly to the BLS target vessel. The concrete slab is placed within the outer frame, and the inner frame is then slid into position to provide the boundary condition. The slab is centered between t he two supports via a crushable foam material to allow rotations at both ends. T he slab rests against an 8 in. steel tube at top and bottom. This rigid structural tube serves as the bearing surface along which the slab rotates. The slab typically has a 4 in. bearing surface at both top and bottom. Figure s 3 11 through 3 13 show the frame that provides a rigidly restrained b oundary condition. This frame i s very similar to the simply supported frame; however, modifications had to be made to prevent lateral translations as well as support rotations. To account for this needed restraint, holes were drilled in the structural tube at the top and bottom to allow bolts to pass through. A new inner frame was designed that consisted of a top and bottom plate with holes aligned with the holes located in the stru ctural tube. This allowed for the bolt to extend completely through the front plate, the concrete slab, and finally the structural tube. The slab was designed to allow a gap at the top between the frame and the slab. This allowed steel adjustment wedges to be ins erted into the gap, and when adjustment bolts were tightened, the gap was 80

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eliminated, and the slab was securely in place. With these given conditions, the slab w as restrained from lateral translation as well as fixed against end rotations. Quasi S ta tic Experiments The quasi static tests were conducted in the static test chamber located at ERDC/GSL in Vicksburg, MS. The unique design of the static test chamber allows hydrostatic forces to be utilized as a loading technique. The test device is divided into two chambers: a pressurized cavity and a no n pressurized cavity ( Figure 3 14). A framed opening separates the two cavities where a separate steel frame containing a test sp ecimen is mounted ( Figure 3 15). To create a water tight seal in the pressurized cavity, a 1/4 in. thick neoprene membrane was clamped to the interior face of the framed opening in the pressurized side using a st eel collar and bolts ( Figure 3 16). Once the bladder and wall was inserted, the steel lid was bolted into place on the loading side, completing the pressurized chamber ( Figure 3 17 ). The two separated chambers were then slowly filled with water to maintain equal water pressure on both sides of the test specimen. Once both sides were c ompletely filled, the water intake valve to the nonpressurized cavity was closed, and the water was continuously pumped slowly into the pressurized cavity, creating a uniform load on the specimen. Valves mounted on the lid are used to remove air trapped i n the pressurized chamber and also serve as mounts for the pressure gages used to moni tor the loading on the wall Load measurements were obtained at two different locations in the pressurized side as well as the non pressurized side. Details regarding the instrumentation will b e discussed in a later section. Figure 3 18 shows an overhead view of the test setup. 81

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Dynamic Experiments The dynamic experiment s were conducted at the BLS facility, also located at ERDC/ GSL in Vicksburg, MS. Figure 3 19 shows a p hotograph of the facility. The BLS is designed to simulate blast waveforms for explosive yields equivalent to up to 20,000 lb (9072 kg) of TNT at a peak reflected pressure of up to 80 psi (0.552 MPa) and a peak reflected impulse of up to 1100 psi msec (7.58 MPa msec) [38 ]. The BLS can accommodate a target 71in (1.803m) tall by 53in. (1.346 m) wide. The control room allows spectators to witness the experiment first hand with immediate feedback from high speed videos and a stateof the art data acquisition system. The BLS facility consists of a cylindrical driver system, a transition system, and a target fixture all housed in an underground enclosure to contain the blast pressures. The driver system consists of a cylindrical pressure vessel, a pushpop device, and a mechanical striker/diaphrag m system. The driver contains the highpressure source that is released into the transition system by rupturing a series of diaphragms. Pumping air or an air/helium mixture into the pressure vessel creates the highpressure source. The gases are confined i n the vessel by a predetermined number of steel or aluminum diaphragms. When the desired pressure is reached, a mechanical striker is activated within the pushpop device, forcing the diaphragms to rupture and releasing the compressed gases into the transi tion sy stem, forming the shock pulse. As the shock propagates through the transition system consisting of the transition cone, expansion rings, and cascade, it expands and is shaped into the desired waveform. The transition cone consists of three consecuti vely larger rings attached to a sled that allows the shock pulse to freely expand at each transition. One negative phenomenon created by most typical shock tubes, referred to as shock reverberations, is multiple shock pulses 82

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that are created at the target when the primary shock reflects off the target, travels the length of the tube, reflects off the driver, travels back down the tube, and reloads the target. The gaps in the transition cone created by the three expanding rings of ERDCs BLS serve as vents t hat allow this rebound load to vent out of the BLS device into the underground enclosure, therefore, reducing, delaying, or in some cases removing this rebound load completely. The shock pulse travels from the transition cone into the expansion rings and cascades to the target face. The targets are mounted in the front face of the target vessel, which contains all the debris that could be generated in the experiment [38 ]. Init ially, the test specimen slab i s moun ted into the target vessel in a nearby assembly shop. The slab is secured into the reaction frame of choice, mounted into the target vessel, and all pretest measurement s are obtained. Once the slab i s installed and secured the entire target vessel i s mechanically rolled into the underground enclosure to match up with the transition system. After anchoring the target vessel in place, the experiment is ready to begin. Figure s 3 20 through 3 22 show the various stages of the BLS test procedure as described above. Instrumentation The da ta generated in each of the experiments, both quasi static and dynamic, w ere an integral part of the success of this research. The data w ere recorded with a HiTechniques Synergy P with 4 input modules resulting in 16 available input channels per system. There were 16 channels available to be recorded for each quasi static t est and 32 channels (2 unit s) available for each dynamic test The number of channels recorded varied according to how many strain gages were installed in a given slab. Some slabs did not contain strain gages which resulted in less channels recorded. Th e data w ere processed for analysis and analytical modeling efforts and w ill be discussed 83

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in th e results section of this dissertation This section will simply detail the type of data reco rded for each event and give precise locations of each set of data recorded. Accelerations, displacement s, applied pressures (i.e. load) strains of the pr imary reinforcement, normal and highspeed video, and still photography are examples of the data recorded for each dynamic test Instrumentation Details for Quasi S tatic Experiments Position/ displacement transducers were used to record the quarter span and mid span slab deflections during each quasi static experiment This wa s accomplished by means of a precision potentiometer that detects the extension and retraction of a cable attached to a spring inside the transducer. The body of the transducer was mounted above the non pressurized cavity of the static test chamber The cable was routed from the transducer body through an i bolt, turned 90 degrees, and then attached to an eyelet that was glued to the concrete slab. Figures 3 23 through 3 25 show this setup. As the slab deflected, the cable retracted into the body and the deflection was recorded. The sampling rate for deflection measurements was set at 5 kHz or 5000 samples per second. The pressure was measured both inside and outside the pressurized cavity in several loc ations to determine the loading on t he test specimen. Pressure transducers were located inside the pressurized cavity, on the lid of the pressurized cavity, and inside the nonpressurized cavity. A total of five pressure measurements were made for each experiment. These pressure measurements were made with Kulite XTM 19050SG pressure transducers. Figures 3 26 through 3 29 show the locations of each transducer. 84

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Another set of data recorded during a selected number of quasi static experiments was strain in the primary reinforcement. Seven of the eleven slabs tested quasi statically contained primary reinforcement that was instrumented with strain gages. The strain in the primary reinforcement bars was obtained with CEA 06125UN 350 strain gages purchased from Vishay Measurements Group. The sampling rate was set at 5 kHz or 5000 samples per second. The locations of each of the strain gages are shown in the description in Figure 3 30 P hotographs of the strain gage loc ations within the slab are shown in Figure 3 31. Real time video of each test was also obtained with an underwater video recorder. This captured the event from start to finish in real time and enable d the researcher to document crack growths throughout the tests. The video recorder was attached to an aluminum angle corner stock with holes drilled through each leg. An all thread bolt was placed in the hole at the required height to hold the corner stock in place. The camera was placed at about mid height of the concrete wall in the corner of the nonpressurized cavity. Photographs of the setup are shown in Figure s 3 32 and 3 33. Instrumentation Details for Dynamic Experiments Slab response to dynamic loa ds was well documented throughout the dynamic experiments at the BLS facility. The control room located at the BLS houses a state of the art data acquisition system and also allows spectators to witness the experiment first hand with immediate feedback fro m high speed videos. Thirty two channels of data are available to be recorded for every test at the BLS via two Synergy P data acquisition systems. The systems are prewi red from the control room to the enclosed underground structure housing the target ves sel For these specific shots, the blast face pressure 85

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was recorded in several different locations, the midspan and quarter span accelerations were recorded, the deflection at mid span was recorded via digital laser and in some cases, the strain in the primary reinforcement bars and compressive face of the concrete slab was recorded for those slabs that contained strain gages High speed digital video was also recorded from three different angles in every test. Kulite HKS 100 psi pressure transducers were mounted on the exterio r face of the reaction fame and target vessel near the loaded face of the slab to me asure the applied load to the slabs. Figure 3 34 shows the pressure gage layout s and Figure 3 35 show s a photograph of the actual target vessel with gages installed. A total of eight pressur e transducers were installed for each test. Accelerometers were attached to the inside face of each tested slab at midspan and quarter points for a total of three accelerometers per test. Meggitt Endevco piezoresistive accelerometers, Model 7270A 20K G s were used to measure accelerations. Figure 3 36 shows the accelerometer locations from inside the target vessel. The mid span slab deflecti ons were r ecorded using an Acuity laser rangefinder, model AR4000LIR. This laser can accurately gage distances up to 54 ft. The laser was mounted in the back door of the target vessel as shown in Figure 3 37. Six of the sixteen slabs tested dynamically contained internal strain gages installed on the primary reinforcement. The strain gage locations were the same as in the static slabs (see Figure s 3 30 and 3 31). T he strain in the primary reinforcement bars was recorded by CEA 06125UN 350 strain gages purchased from Vishay Measurements Group. The sampling rate was set at 5 kHz or 5000 points per second. In addition, surface strain gages we re also installed on the i nside tension face of two 86

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slabs to obtain data on the external surface concrete strain. These strain gages are shown in the photograph in Figure 3 38. High speed digital video was recorded for each event by three Phantom cameras, models V9.1, V7.3, and V5.0 The camera ports and locations are shown in Figure 3 39. Analysis Approach Pretest predictions of slab responses were conducted for static and dynamic experiments using current compressive membrane theories that have been di scussed throughout this dissertation. The two theories of interest are those that were developed initially by Park [18] and later modified by Krauthammer et al [8] and the formulation that is found in TM5855 1 [36 ]. The basis of each of these theories is essentially the same. These particular theories have been validated through experimentation and utilized to predict enhancedcapacity response of conventional strength restrained concrete slabs when subjected to a static load. One of the difficult parameters to determine in these formulations is the mid span deflection, c, occurring at ultimate capacity. This parameter is required for computation of ultimate resistance due to compressive membraneenhanced flexural action. It has been experimentally shown that the deflection at mid span at ultimate capacity is related to both the member span and thickness of the member in conventional strength concretes. According to TM58551 [36 c for design of both oneway and twoway restrained conventional concrete members is given below in Equation 3 1. (3 1) Where uc = mid span deflection at ultimate compression membrane capacity (mm) 87

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L = clear span length (mm) h = overall thickness of the member (mm) Woodson [11] reported uc/h ratios near 0.3 for oneway slabs with lengthto depth ( L/d ) ratios of 10. However, for deep oneway slabs ( L/d 3 and 5), Woodson [12] reported that the uc/h ratios varied between approximately 0.03 and 0.07. Park and Gamble [2] recommended that for slabs with L/h of 20, the peak capacity could be estimated at uc/h = 0.5. For slabs with lower L/h values, the uc/h ratios are expected to be lower (peak capacity will be reached earlier). Furthermore, the peak load will be reached at lower uc/h values in s trips (one way action), as confirmed by Woodson [1 1 1 2 ]. T he reported values derived above were based on empirical data from experiments on conventional strength concrete. Up to this point, data such as th ese d id not exist for UHPC slabs. The theory descr ibed previously was used to predict static response of conventional and UHPC slabs. As a first cut approach, the equations were used to predict responses of UHPC slabs and then comparisons to the actual experimental data were conducted. The results from t his analysis will be presented in the next chapter. Needed modifications to the equations w ere suggest ed to more accurately describe the response of UHPC; therefore, more accurate simulations can be made in the future. The dynamic response s of conventional and UHPC slabs w ere predicted using TM5 855 1 [36]. The equation given in Chapter 10.4. 2.1 of the referenced manual [36] is a modified version of Park and Gambles [2] formulation with dynamic material properties included. This version includes the dynami c ultimate compressive strength of 88

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concrete as well as the dynamic yield stress of steel reinforcement. As with the static load case, this equation w as used to predict responses of UHPC slabs and then new comparisons to the actual experimental data w ere conducted. The computer software known as Dynamic Structural Analysis Suite (DSAS) [3] w as also used to predict slab response. DSAS implements the fundamental theory discussed above to create a loaddeflection relationship of laterally restrained slabs and develops a single degree of freedom (SDOF) model to represent the system. In 2003, Krauthammer et al. [8] updated the code to incorporate the accurate prediction of the dynamic responses of deep slabs in addition to intermediate slabs. It was in this ef fort that the code was updated to operate in a user friendly, Windows environment as well. Since the behavior of deep slabs differ from the responses of slender slabs, the new version of DSAS varies between two resistance functions of each type of slab dep ending on the span to depth ratios of the specific slab in question. This implementation ensures a more efficient methodology for predicting slab behavior because the user does not have to predetermine whether the slab in question is a slender or deep slab. The physical dimensions and material parameters are simply input into the user interface, and the software program makes the determination. For intermediate slabs the program interpolates between the two resistance functions for slender and deep slabs and calculates the capacity based on the input parameters. The response calculated by DSAS was then compared to the actual experimental data and recommended modifications were made. In addition to DSAS, the Wall Analysis Code (WAC) [39] and SingleDegreeof Freedom Blast Design Spreadsheet (SBEDS) [40] were used to determine if current 89

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SDOF models were able to depict the response characteristics of UHPC restrainedslab strips. The results from this analysis are presented in the Analysis Results section of Cha pter 4. 90

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Figure 3 1 Schematic of reinforced concrete slab cross section Figure 3 2 Typical reinforcement layout for NSC restrained slab 91

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Figure 3 3 Casting NSC slabs Figure 3 4 Finishing NSC slabs 92

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Figure 3 5 Reaction frame for simply supported quasi static experiments Figure 3 6 Pressure side of simply supported quasi static test frame 93

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Figure 3 7 Rigidly restrained quasi static steel frame Figure 3 8 Rigidly restrained quasi static steel frame end boundary conditions 94

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Figure 3 9 Simply supported BLS frame Figure 3 10. Inside and blast face view of assembled simply supported BLS frame 95

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Figure 3 11. Rigidly restrained BLS outer frame with slab in place Figure 3 12. Rigidly restrained BLS assembled frame, end condition, and steel wedges 96

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Figure 3 1 3 Rigidly restrained BLS frame with installed slab Figure 3 14. Static test chamber Water Filled Pressurized Cavity Test Wall Water Filled NonPressurized Cavity Reaction Structure 97

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Figure 3 15. P hotograph of stat ic test chamber with opening Figure 3 16. Bladder with steel collar 98

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Figure 3 17. Static chamber with lid bol ted and gages installed Figure 3 18. Overhead view of static test setup from nonpressurized side 99

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Figure 3 19. Blast Load Simulator (BLS) Figure 3 20. Entrance to underground enclosure and expansion rings 100

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Figure 3 21. Target assembl y shop with front of target vessel with slab installed Figure 3 22. Underground enclosure with target vessel attached to expansion ring 101

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Figure 3 23. Displacement transducers mounted above nonpressurized cavity 102

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Figure 3 24. Cable layout for displacement transducers Figure 3 25. Displacement measurement l ocations and cable attachment to slab 103

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Figure 3 26. Pressure transducer at the top of pressurized cavity Figure 3 27. Pressure transducer at midheight of ba ck wall inside pressurized cavity 104

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Figure 3 28. Pressure transducers located outside nonpressurized cavity Figure 3 29. Cavity lid pressure transducer 105

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Figure 3 30. Primary reinforcement strain gage locations 106

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Figure 3 31. Photographs of strain gage locations 107

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Figure 3 32. Overview showing location of underwater camera Figure 3 33. Views showing underwater camera location 108

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Figure 3 34. Pressure transducer layout on blast face of target 109

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Figure 3 35. Photograph of pressure transducer layout on target face 110

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Figure 3 36. Accelerometer layout on inside face of slab Figure 3 37. Laser mounted in the back door of target vessel 111

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Figure 3 38. Photograph of surface strain gages Figure 3 39. High speed video locations 112

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CHAPTER 4 RESULTS The data obtained and processed from the experimental series initiated the analysis to determine the effects of high compressive strength on compression membrane theory response of the slabs. Several comparisons w ere made from the data obtained, including load deflection behavior from the actual experiments v ersus load defle ction s predicted with the current formulation for slab response taking into account compressi ve membrane forces This formulation is provided in Chapter 12 of Park and Gambles textbook [2] and discussed previously in the literature review under the heading of plastic theory. The experimental loaddeflection data w ere also compared to the results generated from UFC 340 01 [36]. The following sections will present comparisons of the experimental results to the current formulations, without m odifications to a ccount for the significant increase in compressive strength of the concrete. Loading Conditions Quasi S tatic Experiment s As mentioned previously, the quasi static tests were conducted in the static test chamber. Once both sides of the chamber were completely filled with water, the water intake valve to the non pressurized cavity was closed, and water was continuously pumped slowly into the pressurized cavity. Valves mounted on the lid were used to remove air trapped in the pressurized chamber and also serve as mounts for a pressure gage used to monitor the loading inside the chamber Once the water began to come out of the valves mounted on the lid, the valves were closed, and the pressure began to increase in the pressurized side of the chamber. This created a uniform load on the slab 113

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specimen, and the rate of loading was controlled by the water intake valve. The load increased continuously until the slab began to deflect. Once the slab cracked or slightly deflected, a volume change occurred in the chamber. As a result, there would be a brief time lapse until the pressure stabilized and began to increase again. This loading process continued at a consistent rate until the engineer stopped the test. The stoptest criteria were based on a visual inspection of the integrity of the slab and the slab rotations at the support. Due to the amount of mild reinforcing steel present in the slabs, the support rotations were able to reach up to 23 degrees in some extreme cases. The full loading his tories, deflection histories, and strains in the mild reinforcing bars are located in Appendix D Dynamic Experiment s The blast conditions that were chosen for this research were typical loadings for blast panels and/or structures that would result from m inimum threat levels up to high threat levels. These type loadings are common in the governmental blast design arena, but the background will not be discussed in this dissertation due to sensitivity issues. With that being said, the slab strips were subjec ted to a range of loadings that are representative of a particular threat level. By doing this, the performance of the slabs can be compared to data from previous research. The loading environment from the dynamic tests was recorded by eight pressure trans ducers located and mounted around the perimeter of the reaction frame. Figure s 3 34 and 3 35 of the previous chapter show the layout the pressure transducers. Appendix E contains the loadtime histories from each experiment. Table F 1 in Appendix F shows a summary of the average pressures and impulses recorded for each test. 114

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Experimental Results Johansens Yield Line Theory The first step in the analysis was to calculate Johansens yield line load, Wj, for the given slabs tested in this series of experiments. This method of analysis of reinforced concrete slabs is considered an upper bound approach to estimating the ultimate load that produces failure mechanisms at the critical plastic sections therefore predicting the ultimate capacity of that particular slab. This method neglects any in plane forces generated in the slab due to the boundary conditions. The ultimate load of the slab is estimated by postulating a collapse mechanism that is compatible with the boundary conditions. The moments at the plastic hinges are considered the ultimate moments of resistance of the sections. The mechanism for this set of experiments was defined by plastic hinges at midspan and both supports (for the rigidly restrained case only). Table F 2 in Appendix F shows the input parameters that were used to calculate the yield line load s, and Table 4 1 is a summary of the results. Once the moment capacity at the critical section was determined, the resulting value was equated to the yield line moment, and the load w, could then be solved for. Quasi s tatic Sim ply Supported Conventional strength concrete slab strips were tested as a baseline experiment. The first set of data presented is the quasi static load v ersus deflection behavior of simply supported conventional strength concrete slab strips. These data are shown in Figure 4 1 The calculated yieldline strength for this particular cross section is 6.7 psi as shown by the blue line in Figure 4 1 As o ne can see in Figure 4 1 the experimental res ults match the theoretical result relatively well. The peak yield strength in the experiments was approximately 9 psi. One trend that was unexpected in this set of tests 115

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was that the results appear to show strain hardening behavior occurring in the respo nse post yield. This may be a result of the boundary conditions due to the ends of the slab began to push outward against the surrounding reaction frame or it may simply be strain hardening behavior of the steel The ends of the slabs were free to rotate; however, once the ends rotated enough to experience lateral translation, there is a possibility that the slab jammed in the reaction frame. Figure 4 2 is a p hotograph o f the NSC simply supported slab posttest. Appendix G contains several photos from the entire experimental test series Figure 4 3 shows the quasi static load deflection behavior of simply supported UHPC slab strips. The data presented for the UHPC slabs represent a collection of multiple tests; hence the load, unload, and reload nature of the load deflection curve. This is the result of the test setup and dealing with issues with the neoprene membrane in the first tests on UHPC. The membrane and sealing mechanism that was used to load the specimen continued to fail, so several iterations were required in order to obtain a valid test. Once the test setup was finalized, the slabs were effectively tested and results obtained. The yield line theory for the UHPC case results in a strength of 7.1 psi. As shown in Figure 4 3 Test 1 matches this value well. As in the NSC slabs, there appears to be strain hardening behavior occurring post yield. Again, this is most likely due to the surrounding boundary conditions. A positive result from the previous two sets of data is the apparent repeatability of results. The yield strength peaks for the NSC tests were very close and general behavior was captured in all four tests. Figure 4 4 shows a posttest p hotograph of the simply supported UHPC test. 116

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Quasi S tatic Rigidly Restrained The next set of data ( Figure 4 5 ) is quasi static loaddeflection behavior of rigidly restrained conventional strength concrete slab strips. Yield line analysis does not ac count for membrane (i.e., inplane) forces that are present, when as the slab deflects, the slab ends tend to push out against the surrounding members. If the surrounding members at the supports are sufficiently stiff, inplane forces will be present. This result is shown in Figure 4 5 This is the exact same cross section as tested before, shown in Figure 4 1 ; the only difference between the two tests are the boundary conditions. For the NSC case, the peak resistance ranged from 18 psi up to about 23 psi. This more than doubles the simply supported resistance presented in the previous section, and the increase is a direct result from the boundary condition applied in these test s Figure 4 6 shows a posttest photograph of Test 6 For this case, the yieldline load was calculated to be approximately 13.3 psi as shown by the blue line in Figure 4 5 As mentioned previously, one of the main objectives of this study was to determine the magnitude of the effect of utilizing UHPC in reinforced concrete slab design and how the higher compressive strength may influence responses of restrained slabs It was anticipated that the higher compressive strength would have a significant effect on the compressive membrane behavior of reinforced concrete slabs, but up to this point it could not be verified due to lack of experimental data. Figure 4 7 present s the quasi static load deflection data for rigidly restrained UHPC slabs. The respons e s of both experiments w ere almost identical behavior. In this case, the peak resistance was approximately 36 psi compared to about 7 psi that was recorded in the UHPC simply supported test. This results in a fivetime increase in resistance due to the rigidly restrained boundary condition. The UHPC slab peak resistance is also approximately 117

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double the resistance of the rigidly restrained NSC peak resistance; so this in fact shows the influence of the high compressive strength present in UHPC and its eff ects on slab response. The recorded ultimate capacity was also over 2.5 times the resistance calculated by the Johansens yield line theory. This can be seen in Figure 4 7 as well. Figure 4 8 shows a p osttest photograph of the rigidly restrained test for a UHPC slab. Dynamic Simply S upported The next set of data presented in Figure s 4 9 through 4 12 show the dynamic deflection time behavior of simply supported conventional strength concrete slab strips. The dynamic deflection of reinforced concrete slabs is quite a challenge to record due to many different reasons. One reason for the difficulty is the very fast response time of the slab once subjected to the blast wave. As mentioned previously the deflection was recorded directly in two different ways and indirectly in another way. The deflection was recorded directly by a n Acuity laser rangefinder, model AR4000LIR. This in itself presents a challenge because the concrete slab back face tends to spall once the blast hits the front face. If debris flies into the target vessel and interferes with the laser, the data may be inaccurate of midspan deflection simply because the laser is reading the flying debris rather than the slab s deflection. With that being said, keep this in mind while viewing the following plots of dynamic deflection versus time. In some instances, the laser data may be inaccurate. The deflection was also determined from a visual inspection analysis from the high speed camera videos. By viewing the slab response from the side camera, the analyst can choose two reference points at two different moments in time and then determine the distance between the two points based on a calibrated distance from a known quantity. Typically, these two points were the initial 118

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slab position, and the second point was the peak centerline deflection of the slab response. These two points could be determined by a frameby frame look at the slab response recorded by high speed digital photography The distance between the two reference points could then be calculated once the visual analysis was calibrated from a known distance. The third way of calculating the deflection is by integrating the acceleration data twice to obtain de flection. Again, this is very difficult as well due to the surface to which the accelerometer is mounted. If the slab happens to crack at the location of the mounted accelerometer, the data may be compromised. In some cases presented below, the acceleromet er data may be an inaccurate depiction of deflection. Between the three methods, a good indication of dynamic response of the concrete slabs has been determined. More times than not, at least two of the methods match up. Figures 4 13 and 4 14 show the test setup of a NSC si mply supported test. Appendix G contains additional test photographs. Test 3 deflection data (Figure 4 9 ) related very well. The load in this test was less than for Test s 6 and 7 load, hence less response. As one can see from the figures, the responses from Tests 6 and 7 w ere quite similar. The accelerometer data for both cases appear to be inaccurate when compared to the deflection from the high speed camera visual analysis. The laser actually captured the deflection relative ly accurate; however in Test 6 it appears the peak deflection was cut off for unforeseen reasons. The range in which data were recorded could have potentially been set to o low for this test. Figure 4 12 shows a summary of all simply supported NSC dynamic tests. The next set of data presented in Figure s 4 15 through 4 19 is the dynamic deflectiontime behavior of si mply supported UHPC slab strips. For each of these tests, 119

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the deflection with the high speed camera visual analysis should be verified. The laser data in Test 1 appear to have recorded successfully, but the accelerometer data are questionable. The laser failed to work at all in Test 1b, which was a reload of the slab in Test 1. The laser appeared to have picked up flying debris in both Test s 2 and 4. The slab was simply over loaded in Test 4. The idea was to test the limit of response of the simply supported UHPC slab, and Test 4 went above and beyond the upper limit because the slab was blown out of the reaction frame. Figure 4 19 shows a summary of all simply supported UHPC dynamic tests. Figure 4 20 show s the pretest setup of a UHPC simply supported test and Figure 4 2 1 shows a posttest view Othe r photographs are in Appendix G Dynamic Rigidly Restrained The next set of data presented in Figure s 4 22 through 4 26 is the dynamic d eflectiontime behavior of rigidly restrained convention a l strength concrete slabs F or each of these plots, there are at least two methods of recording deflection that are in agreement. As expected for the rigidly res trained cases, the deflection of UHPC slabs for the same load is much smaller than that deflect ion of the corresponding simply supported slabs. When the deflections from Test s 6, 7, and 10 are compared it becomes obvious that Test 10 has less response from the same average load. This is due to the increased resistance resulting from compressive mem brane action. Figure 4 27 show s the pre test setup for the NSC rigidly restrained slabs and Figure 4 28 shows a posttest view The next set of data presented in Figure s 4 29 through 4 32 is the dynamic deflectiontime behavior of rigidly restrained UHPC slab strips. This series of tests required the upper limits of our testing capability in order to record any response in the 120

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slabs Due to the restrained boundary conditions as well as the high compressive strength of the material, the slabs tested in this configuration were very resistive to load. We were able to record valuable data that provided insight to the increase of resistance in UHPC rigidly restrained slabs. Figures 4 33 and 4 34 show photographs of the test setup. Other test photo graphs are in Appendix G Comparisons with Theory For each rigidly restrained test configuration, the slab response was predicted using Park and Gambles plastic theory equation. This value was then compared to the capacity predicted by Johansens yield line theory equation, and the ratio of the two was calculated. This value resul ted in an enhancement due to membrane action because this phenomenon is not taken into account in conventional yield line theory equations. The theoretical enhancement in load carrying capacity due to membrane action is given by the ratio W/Wj obtained from the ratio of Parks plastic theory equation divided by the load calculated by Johansens yield line theory. The following figures show the ratio of experimental W to the theoretical Wj plotted against the experimental central deflectionto strip depth ratio, as measured in the in experiment. Figure s 4 35 through 4 37 show the results of this comparative analysis. The theoretical curves in this figure show all the potential ultimate capacities for a given set of deflections. For this case, no changes were made to the existing equation for the very high compressive strength concrete. One thing to keep in mind when viewing these results is that plastic theory is exactly as its name implies. This theory is not accurate until the rotations at the yield lines become plastic. The initial response is elastic behavior, so this theory is not accurate at the initial stages of response. Another key aspect of thi s theory is that the analyst has to know or have a good rule of thumb to estimate the deflection t hat occurs 121

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at peak ultimate resistance in order to estimate the ultimate resistance due to compressive membrane action. The general assumptions made for NSC may not apply for UHPC. It appears from the results presented here that for this particular configuration peak ultimate load for UHPC slabs occur s at larger deflections than NSC. For this test configuration, the deflection occurring at peak ultimate resistance for UHPC slabs is occurring at a central deflectionto slab depth ratio of 0.5. For the NSC slabs tested, this value is about 0.3. An addi tional approach to estimate the deflection that occurs at peak capacity will be to revisit the straindeformation relationship developed by Keenan [26] for conventional streng th concrete slabs. Recall from the literature review that Guice et al. [25] util ized Keenans approach to estimate deflections at peak capacity as shown in Equations 24 through 26 in Chapter 2 and shown again below for convenience. The following relationship is valid for the strip geometry shown in Figure 4 38. ==+mtanxtc ( 4 1 ) For conventional strength concrete, one may assume the deformation e can be related to the ultimate strain in the concrete by the expression =2uxe ( 4 2 ) Then E quations 4 1 and 4 2 can be rewritten to yield the midspan deflection in terms of the concrete strain or midspan curvature ++==22ummx x c ( 4 3 ) Where u = ultimate strain in the concrete 122

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m = curvature at midspan Applying this methodology to the experimental results of this study revealed interesting predictions for deflection values at ultimate capacity. The first parameter one needs to determine is the ultimate strain in the concrete. For this particul ar study, the ultimate strain in compression for NSC concrete was 0.004217 and was 0.0086 for UHPC. These values were determined from typical hydrostatic compression tests on concrete cylinders. Knowing these values along with the mechanical properties of the concrete and rebar, one can calculate the moment curvature relationships for each material and given cross section. From this analysis, the midspan curvature at ultimate concrete strain in compression may be determined. Figure 4 3 9 shows the moment curvature relationships for both NSC and UHPC. The vertical lines in the plot represent the curvature of each section, NSC and UHPC respectively, at the ultimate concrete strains. The two values are 0.003188 in1 for NSC and 0.007792 in1 fo r UHPC. Going back to Equation 43, one can calculate the deflection at which ultimate capacity occurs based on th e assumptions made in Equation 42. Doing this gives the following. for NSC: for UHPC: The prediction of deflection at peak capacity corresponds to the experimental result well for NSC. Figure 4 37 shows the enhancements due to compressive membrane forces for NSC as well as UHPC. The x axis is defined by the central deflectionto slab depth ratio. In this case, the slab depth is 3 in. Using the defl ection predicted with Equation 43 for NSC, one would obtain a central deflectionto slab depth 123

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ratio of 0.36 (1.08 in. /3 in. ). Utilizing Figure 4 37, the peak enhancement o f 1.38 occurs at a ratio of 0.34. This means that the peak ultimate capacity for NSC also occurred at a ratio of 0.34, which corresponds very well with the experimental value of 0.36. The prediction of deflection at ultimat e capacity when using Equation 43 does not hold true for UHPC. The predicted deflection of 2.63 in. for UHPC would result in a central deflectionto slab depth ratio of 0.877. As one can see from Figure 4 37, the peak enhancement of 2.44 and 2.52 occurred at a ratio of 0.48 and 0.49, respectively, for the two experiments conducted. This produces an error of approximately 83% and would cause significant error in ultimate capacity prediction of UHPC slabs. This error is due in part to t he assumption made in Equation 42 above. For UHPC, it may not be appropriate to assume that the deformation, e is related to ultimate strain in the concrete as described in this equation. Based strictly on the limited experimental results presented herein, the author suggests the following modification to the straindeformation relationship first presented by Keenan [26]. For UHPC members with compressive strengths in excess of 20 ksi, the deformation, e is proposed to be related to ultimate concrete strain by the expression =35uxe. ( 4 4 ) This results in a deflection equation of ++==3535ummx x .c. ( 4 5 ) Using the proposed Equation 45, the predicted deflection at ultimate concrete strain for UHPC becomes 1.5. As a result, the central deflection to slab depth ratio would be 0.5 124

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at peak ultimate capacity. This value corresponds much better to the experimental central deflectionto slab depth ratio of 0.49. Keep in mind that this ratio will potentially change for other spanto depth ratios. This formulation may only be valid for spanto depth ratios similar to those tested in this series. This particular case has a span to depth ratio of 17.33. Further investigation would be required to make this determination. The author would also suggest that the needed modification in the deformation assumption, e for UHPC is a direct result of the higher ultimate strain present in the UHPC material tested herein. For each rigidly restrained test configuration, the peak ultimate slab resistance was also predicted using E quations 1038 and 10 39 found in Army TM 5855 1. This equation is used to calculate the ultimate compressive membraneenhanced flexural uniform load resistance based on plastic theory, equilibrium, and deformations of a unit slab strip. The difference for this particular equation is that it also incorporates dynamic material properties for concrete and steel reinforcement. As mention ed in Chapter 3, a difficult parameter to determine in these formulations is the midspan deflection, c, occurring at ultimate capacity. This fact will become apparent while analyzing the results with this equation. This parameter is required for computation of ultimate resistance due to compressive membraneenhanced flexural action. It has been experimentally shown that the deflection at midspan at ultimate capacity is related to both the member span and thickness o f the member in conventional strength concretes. According to TM58551 [36 ], the recommended value of c for design of both oneway and twoway restrained conventional concrete members is given in Equation 3 1, as defined earlier. With this being said, Table F 3 in Appendix F summarizes the results from this analysis. 125

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As one can see from the table, the maximum resistance calculated from the equation and the resistances calculated when using the recommended deflection value at peak ultimate capacity do not match up. This is very well due to the invalidity of the equation in the initial stages of response. As in the previous plots, the theoretical curves calculated from this equation were compared to the actual experimental curves obtained from the experimental data. Figure s 4 40 and 4 41 show the results of this comparative analysis. For this case, no changes were made to the existing equation for the very high compressive strength concrete. Again, keep in mind that the Army TM 5855 1 formulation is also based on plastic theory. The initial portion of the curves is inaccurate because the theory assumes plastic hinges have already been formed in the slab. Looking at the UHPC curves in Figure 4 41, the theoretical curves seem to match up with the experimental data once t he peak ultimate resistance has been reached. In this case, this occurred at about 1.6 in. Analysis Results Single Degree of Freedom (SDOF) Analysis SDOF analysis is a simplified method for calculating the dynamic response of structures. Typically, input parameters are simple to obtain, and numerous computations can be performed in a short am ount of time. For this reason, this method is quite popular for dynamic response predictions of structures. The SDOF system consists of an equivalent mass, stiffness, forcing function, and resistance. A shape function is assumed for the response mode, and eventually a deflection history can be calculated. Section 11.5 of Army TM 5 8551 [ 1 6] defines this process in more detail. 126

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A SDOF analysis was conducted for rigidly restrained slabs that were tested dynamically in this test series with three readily avai lable fast running engineering codes to determine if the current methodology incorporated into the codes w as able to depict the response characteristics of NSC and UHPC restrained slab strips. The three codes used for this an alysis were WAC SBEDS and DSAS all developed and maintained by different organizations. WAC was developed by the U.S. Army ERDC, SBEDS by the U.S. Army Corps of Engineers Protective Design Center (PDC), and DSAS by Theodore Krauthammer and various PhD students from Penn State University and the University of Florida. Figures 4 42 through 4 50 provide a summa ry of this analysis. The general overall response mode of rigidly restrained NSC slabs was captured with the SDOF models. The actual slab response was slightly stronger than predicted by the resistance f unctions as shown in Figure 4 42 The peak ultimate capacities in the experiments were about 20% higher. The SBEDS and WAC resistance functions are quite similar. The response is a simple elastic plastic response. The DSAS resistance function is a bit more sophisticated as it incorporates the tensile membrane behavior into the resistance function as well. Unfortunately, the experimental slabs were not detailed in such a way that this phase of response could be captured to compare to SDOF results As expected, the deflectiontime histories from each experiment experienced slightly lower peak deflections (Figures 4 43 though 4 46) This makes sense because of the slightly higher capacity as shown in the resistance functions. It also appears the SDOF captured the behavior better at slightly higher loads in Test s 12 127

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and 13 compared to Tests 10 and 11. In Test s 10 and 11, SDOF over pr e dicted response significantly. The resistance functions for rigidly restrained UHPC slabs are shown in Figure 4 47. DSAS and SBEDS obviously incorporate compressive membrane theory into the formulation because it is very apparent in the resistance functions. WAC on the other hand, does not incorporate compressive membrane theory and under predicts ultimate capacity of UHPC restrained slabs. The other two models incor porate the theory, but are over predicting ultimate capacity for the slabs with this particular set of parameters and experimental boundary conditions. This becomes evident when comparing the deflectiontime histories of the UHPC restrained slabs. In Test s 14 through 16 (Figures 4 48 through 4 50 respectively) both SBEDS and DSAS under predict response significantly due to the ultimate capacity predictions. This could be due to several things. One that comes to mind is the assumption that the experimental slabs were perfectly restrained. In reality, it is impossible to obtain a perfectly rigid restrained case. The two models assume infinitely stiff surrounding conditions when, in actuality, the slabs were not restrained perfectly. If restrained perfectly, the experimental slabs could have very well exhibited the behavior predicted by the SDOF models but perhaps ultimately capacity was lost by the imperfection at the boundaries. The final step in the SDOF analysis was to develop a user defined resistance function based on the peak ultimate capacity of UHPC. This was accomplished by utilizing the peak ultimate capacity, and the deflection that occurred at the ultimate capacity, obtained from the restrained UHPC slab experiments. These values were used to calculate the initial portion of the resistance function curve based on an 128

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equat ion derived by Krauthammer [13]. The equation, as well as the newly developed resistance function is shown in Figure 4 51. The results from the deflectiontime history a nalysis are shown in Figure 4 52. As one can see in the figure, the improved resistance function also improved the predictive capability of the DSAS model. Abaqus Simulations A finite element analysis (FEA) was conducted to evaluate UHPC and NSC slab responses to blast loads. The numerical results were compar ed to the experimental deflectiontime histories to determine whether an existing material model developed for UHPC materials generated co mparable results to the slabs tested dynamically in the BLS. General model details The reinforced concrete slab model was composed of 8 node linear brick, reducedintegration, and hourglass controlled elements. The reduced integration scheme is based on the uniform strain formulation: the strains are not obtained at the first order Gauss point but are obtained as the analytically calculated average strain over the element volume. Reduced integration also means that an integration scheme one order less than the full scheme is used to integrate the elements internal forces and stiffness. It is necessary to use hourglass control when using first order reduced integration elements. In Abaqus, the artificial stiffness method and the artificial damping method are used to control the hourglass modes in these type elements. The steel reinforcement was modeled using beam element s and was embedded in the concrete utilizing the constraint function within Abaqus Explicit [35] It was determined through an extensive mesh refinement analysis that six elements through the thickness of the 3 in. thick slab provided the most reasonable r esults when comparing the deflection129

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time histories to the experimental results as well as for computation efficiency The results from this analysis are depicted in Figure 4 53 The element size was consistently a 0.5 in. cube throughout the model. The resulting mesh resolution was 128 by 68 by 6 to be consistent with the experimental slab dimensions of 64 in. by 34 in. by 3 in. This resulted in a total of 52,224 elements for the concrete slab. The NSC was modeled using the concrete damage plasticity (CDP) model within Abaqus. This model was chosen because it is designed for applications in which concrete is subjecte d to monotonic, cyclic, and/or dynamic loading. It uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete. This model is intended primarily for the anal ysis of reinforced concrete structures. The NSC model parameters for plasticity, compression hardening, damage, and tension sti ffening are in Appendix H Cor Tuf (i.e., ERDCs version of UHPC) was modeled using a user defined concrete material model develo ped by Adley et al [ 41 ] called the Advanced Fundamental Concrete Model (AFC). The AFC model was developed for simulating the penetration of projectiles into concrete. It contains a threeinvariant failure surface and nonlinear loading and unloading in hydrostatic compression. The model has shown significant promise for use in numerical simulations involving highstrength geologic materials. The steel reinforcement was modeled with an elastic plastic material model within Abaqus. The boundary conditions at each end of the slab strip were modeled as closely as possible to the actual experimental boundary conditions. The simply supported slabs were restrained from z direction translation for 6 in. at each end on the backside of the slab. The restraint represented the bearing surface (structural tube) in the actual 130

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experimental setup described in Chapter 3. There was also a 2 in. restraint applied in the z direction on the front side of each end boundary. This represented the 2in. structural tube that ran across the top and bottom as part of the inside frame. This tube helped hold the slab in place during the experiment. For the rigidly restrained simulations, restraints were added in the x and y directions as they were in the ac tual experiment. In this case, the front 6 in. at each end of the slab were also restrained from translations In addition to the translational restraint, rotational restraint in all directions was added to prevent rotation at each end of the slab strip. T his was a best attempt to model the clamping effect that was prescribed in the experimental setup through bolting through the slab from the front face. The ends of the slab were also restrained from translation and rotation thereby modeling the condition that the wedges provided at the top end of the slab. Figure 4 54 shows a screenshot of the undeformed numerical model and Figure 4 55 shows a deformed model of the same slab. Comparisons of simulation results to experimental data The following section will present the comparison of simulation results to the experimental data. S pecifically, the deflectiontime histories for each boundary condition wi ll be compared in Figures 4 56 through 4 58 as well as Figure 4 59 The mesh refinement study revealed unreasonable mesh sensitivity issues that r equired further investigation. The indication of this issue can also be seen in Figure 4 53. As the mesh was refined, the peak deflections continued to increase and never converged upon a unique solution because mesh refinement of the model led to narrower crack bands. This problem typically occurs if cracking failure occurs at localized regions in the structure, and mesh refinement does not result in the formation of additional cracks. Initially, tension stiffening was incorporated into the model by 131

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means of a post failure behavior stress strain relation. Early time damage from these simulat ions can be seen in Figures 4 60 and 4 61 for 0.5in. elements and 0.25in. elements, respectively. As one can see in the two figures, failure occurred in a single row of elements, so as elements were reduced in size, the model continued to get softer and softer. The mesh sensitivity issue was solved by applying the Hillerborg et al. [4 2 ] fracture energy proposal. Hillerborg defines the energy required to open a unit area of crack, Gf, as a material parameter, using brittle fracture concepts. This approach characterizes the concretes brittle behavior by either a stress displacement response or as a material property (i.e., failure stress as a function of the associated fracture energy) rather than a stress strain response. For this particular simulation, fracture energy was specified directly as a material property. This model assumes a linear loss of strength after cracking, beginning with the failure stress down to a displacement equal to 2*Gf/failure stress. The value taken for Gf in this simulation was 60 N/m, which is typical for a conventional strength concrete. This value was increased to 120 N/m for UHPC. As one can see in Figures 4 56 and 4 57 the simulated response matches the experimental values relative ly well for the sim ply supported case. In both NSC (Figure 4 56) and UHPC (Figure 4 57), the pea k response in the experiment occurs slightly later in time than predicted by Abaqus. However, the difference is only 3 to 4 msec in either case. The quantitative values of peak deflection are within about 5% for both material responses and the general cur ve behavior matches very well. Figure 4 58 presents an interesting result for the rigidly restrained NSC case. The numerical solution is compared to two different experimental results from Test 10 132

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and Test 12. Both cases were rigidly restrained NSC tests; however, the difference between the two was a slightly higher impulse in Test 12. The average impulse from Test 12 was approximately 33 psi msec higher than the impulse recorded from Test 10. The interesting thing about this is even though the load isnt that much different, the Test 12 response is much higher than that for Test 10. In this case, it is approximately three more inches in p eak deflection. The numerical simulation result plots somewhere in between the two experimental results. The load applied in Test 10 is the borderline concrete cracking load for this test configuration. Once the macrocrack at mid span occurs, the slab experiences a sudden increase in midspan deflection. The fact that the simulation response is slightly higher than the Test 10 response isnt all that surprising because of the behavior explained above. Figure 4 59 presents the comparison of the numerical rigidly restrained UHPC result to the result from Test 14. Using the load averages from Test 14 in the numerical simulation resulted in very little response when the ends were restrained. In this case, it appears that the numerical material model was too stiff for UHPC when the boundaries are restrained; therefore, the numerical results dont compare well to the experiment. Further analysis for this con figuration and model is suggested. 133

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Table 4 1 Summary of Johansens loads Slab Number Material Cross Sec tional Moment Capacity, lb in. per unit width Cross Sectional Moment Capacity (total), k in. Johansens Load Simple Supports, psi Johansens Load Fixed Supports, psi 1,2,9,10 UHPC 2429.3 82.0 7.2 14.4 3,4,5,6,7,8 NSC 2253.2 76.0 6.7 13.3 134

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Figure 4 1 Load v ersus deflection for simply supported NSC slabs Figure 4 2 NSC Test 3 simply supported 135

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Figure 4 3 Load v ersus deflection for simply supported UHPC slabs Figure 4 4 UHPC Test 1 simply supported 136

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Figure 4 5 Load v ersus deflection of rigidly restrained NSC slabs Figure 4 6 NSC Test 6 rigidly restrained 137

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Figure 4 7 Load v ersus deflection of rigidly restrained UHPC slabs Figure 4 8 UHPC Test 9 r igidly restrained 138

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Figure 4 9 Dynamic deflection v ersus time of simply supported NSC slabs ( Test 3) Figure 4 10. Dynamic deflection v ersus time of simply supported NSC slabs ( Test 6) 139

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Figure 4 11. Dynamic deflection v ersus time of simply supported NSC slabs ( Test 7) Figure 4 12. Dynamic deflect ion v ersus time of simply supported NSC slabs (all tests) 140

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Figure 4 13. Front view of NSC Test 6 pretest Figure 4 14. Rear view of NSC Test 6 pretest 141

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Figure 4 15. Dynamic deflection v ersus time of simply supported UHPC slabs ( Test 1) Figure 4 16. Dynamic deflection v ersus time of simply supported UHPC slabs ( Test 1b) 142

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Figure 4 17. Dynamic deflection v ersus time of simply supported UHPC slabs ( Test 2) Figure 4 18. Dynamic deflection v ersus time of simply supported UHPC slabs ( Test 4) 143

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Figure 4 19. Dynamic deflection v ersus time of simply supported UHPC slabs (all tests) Figure 4 20. Front view of UHPC Test 1 pretest 144

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Figure 4 21. Rear view of UHPC Test 1 posttest Figure 4 22. Dynamic deflection v ersus time of rigidly restrained NSC slabs ( Test 10) 145

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Figure 4 23. Dynamic deflection v ersus time of rigidly restrained NSC slabs ( Test 11) Figure 4 24. Dynamic deflection v ersus time of rigidly restrained NSC slabs ( Test 12) 146

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Figure 4 25. Dynamic deflection v ersus time of rigidly restrained NSC slabs ( Test 13) Figure 4 26. Dynamic deflection v ersus time of rigidly restrained NSC slabs (all tests) 147

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Figure 4 27. Front view of NSC rigidly restrained Test 11 pretest Figure 4 28. Rear view of NSC rigidly restrained Test 11 posttest 148

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Figure 4 29. Dynamic deflection versus time of rigidly restrained UHPC slabs ( Test 14) Figure 4 30. Dynamic deflection v ersus time of rigidly restrained UHPC slabs ( Test 15) 149

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Figure 4 31. Dynamic deflection v ersus time of rigidly restrained UHPC slabs ( Test 16) Figure 4 32. Dynamic deflection v ersus time of rigidly restrained UHPC slabs (all tests) 150

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Figure 4 33. Front view of UHPC rigidly restrain ed Test 14 pretest Figure 4 34. Rear view of UHPC rigidly restrained Test 14 pretest 151

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Figure 4 35. NSC strength enhancement due to compressive membrane action Figure 4 36. UHPC strength enhancement due to compressive membrane action 152

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Figure 4 37. Strength enhancement due to compressive membrane action (theoretical vs. experimental results) Figure 4 38. Typical slab strip geometry 153

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Figure 4 39. Moment curvature relationships for NSC and UHPC Figure 4 40. Army TM 5 8551 theoretical v ersus experimental comparisons for NSC 154

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Figure 4 41. Army TM 5 8551 theoretical v ersus experimental comparisons for UHPC Figure 4 4 2 NSC resistance function comparison to SDOF models 155

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Figure 4 43. NSC rigidly restrained experimental results comparison to SDOF analysis ( Test 10) Figure 4 44. NSC rigidly restrained experimental results comparison to SDOF analysis ( Test 11) 156

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Figure 4 45. NSC rigidly restrained experimental results comparison to SDOF analysis ( Test 12) Figure 4 46. NSC rigidly restrained experimental results comparison to SDOF analysis ( Test 13) Time, msecd, inchesDeflection History Comparison (Test 12)Normal Strength Concrete Rigidly Restrained 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 -1 1 3 5 7 9 11 13 Deflection fom accelerometer (12) Deflection from laser (12) Deflection from high speed video (12) SDOF SBEDS test 12 pressure SDOF DSAS Test 12 SDOF WACTest 12 Time, msecd, inchesDeflection History Comparison (Test 13)Normal Strength Concrete Rigidly Restrained 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 -1 1 3 5 7 9 11 13 Deflection from laser (13) Deflection from accelerometer (13) Deflection from high speed video (13) SDOF SBEDS test 13 pressure SDOF DSAS Test 13 SDOF WAC Test 13 157

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Figure 4 47. UHPC resistance function comparison to SDOF models Figure 4 48. UHPC rigidly restrained experimental results comparison to SDOF analysis ( Test 14) 158

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Figure 4 49. UHPC rigidly restrained experimental results comparison to SDOF analysis ( Test 15) Figure 4 50. UHPC rigidly restrained experimental results comparison to SDOF analysis ( Test 1 6 ) Time, msecd, inchesDeflection History Comparison (Test 16)CorTuf no Fiber Rigidly Restrained 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 2 4 6 8 10 12 14 16 18 Deflection from laser Test 16 Deflection from high speed video Test 16 SDOF SBEDS test 16 SDOF DSAS test 16 SDOF WAC test 16 159

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Figure 4 51. Newly developed UHPC resistance function Figure 4 52. Deflectiontime history comparison of new resistance function 160

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Figure 4 53. Abaqus mesh refinement analysis comparative results Figure 4 54. Abaqus undeformed reinforcedconcrete slab model 161

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Figure 4 55. Abaqus deformed reinforcedconcrete slab model Figure 4 56. Numerical v ersus experimental results for NSC simply support ed slabs 162

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Figure 4 57. Numerical v ersus experimental results for UHPC simply supported slab Figure 4 58. Numerical v ersus experimental results for NSC rigidly restrained slab 163

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Figure 4 59. Numerical versus experimental results for UHPC rigidly restrained slab Figure 4 60. Early time failure of NSC 0.5in. elements at t=3 msec 164

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Figure 4 61. Ea rly time failure of NSC 0.25in. elements at t=3 msec 165

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CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS Summary Reinforced concrete slabs are found in very common structural systems in both civilian and military applications. The boundary conditions that support the slab play an important role in the slabs response to a particular load. Specific al ly the amount of lateral and rotational restraint provided to a particular slabs boundaries would dictate how that slab responds to a particular load. Compressive membrane (i.e., in plane) forces are present in slabs when the boundaries are sufficiently stiff therefore, restricting the slab from both lateral translations and rotations. Advancements have been made to account for the additional capacity due to compressive membrane forces in conventional strength concrete. In todays engineering world, concrete performance is improving, compressive strengths are increasing, and ductility of concrete is becoming commonplace. Due to this fact, there was an urgent need to inves tigate compressive membrane theory in UHPC slabs to better understand the behavior of such materials This benefits both civilian applications in the design market, as well as understanding hardened constructi on in military applications. With the current a dvancements i n concrete performance, existing compressive membrane theory was revisited to determine if the current theory was applicable, or if it was not what modifications should be made. This study provided insight into the validity of using existing compressive membrane theory to predict the ultimate resistance in UHPC slabs. 166

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Concluding Remarks A comprehensive research study investigating compressivemembrane theory in UHPC slabs was conducted. Existing compressive membrane theory used to predict peak ultimate strength in oneway conventional strength concrete slabs was applied to UHPC slabs and a comparative analysis was completed. It was determined that exist ing theory should be us ed with caution in order to accurately predict peak ultimate strength in UHPC slabs when considering inplane forces. The conventional equation is limited because the analyst has to be able to accurately predict, or previously know from experiments, the de flection at which the peak ultimate resistance occurs in UHPC slabs to even get close to the correct result. Unless this value is known, t he use of existing theory to understand peak ultimate resistance of UHPC slabs becomes difficult The theory could be misleading if you assume peak ultimate deflection occur s at sm all deflections therefore, leading to a smaller central deflectionto slab depth ratio than actually occurs. In this case, peak ultimate resistance is much larger, especially when considering th e behavior curves for U HPC. In fact, as the deflection approaches zero, the ultimate capacities are greatly overestimated. This error is attributed to the assumptions made for concrete strain. Although the assumption of ultimate concrete strain is valid near the peak capacity, such an assumption leads to significant errors when the slab is behaving elastically or partially elastic al ly This is especially true for UHPC. Due to the lack of data published on UHPC slabs, the parameter uc (midspan deflection at ultimate compression membrane capacity) is not fully understood at this point. A general rule of thumb has not been developed previously ; therefore, the author will utilize the sample of data gathered in this study to propose a general rule of thumb for deflection occurring at peak ultimate resistance for UHPC slabs. Since section 167

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10.4.2 in Army TM5855 1 describes the parameter uc for conventional strength concrete slabs, the same will be done for UHPC based on the experimental data gathered in this study. Original contributions: The approach in which the author studied compressive membrane action in UHPC slabs was co nducted in the following manner : NSC and UHPC r einforced slabs with a lengt h to depth (L/d) ratio of 17.33 were designed and constructed t o represent a typical reinforced concrete slab used in generic construction; The slabs were experimental ly tested both statically (in the quasi static water chamber) and dynamicall y (in the blast load simulator); Data sets for NSC and UHPC slabs were obtai n ed and load v ersus deflection relationships were developed for each case. Deflectiontime histories were also developed for the dynamic tests; Experimental data w ere compared to existing theory predictions for ultimate compressive membraneenhanced flexur al uniform load resistance for NSC and UHPC slabs ; Single degreeof freedom analysis was conducted to assess the capability of current fast running engineering codes to successfully predict responses of UHPC slabs when in plane forces are present ; A modified static resistance function was developed based on the experimental data from the UHPC slab experiments The modified function was then input in the DSAS software as a user defined resistance function and an analysis was completed; A numerical model was developed in Abaqus to assess the capability of current state of material models to predict responses of UHPC slabs to blast loads The experimental data from the BLS tests w ere used to validate the model so that it now can be used to fill in the research gaps that are still in question. Recommendations After comparing the experimental results to the existing theory predictions and studying the results from the numerical analys e s, the following recommendations are made to provide future analysts some insight into UHPC slab response: 168

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When calculating ultimate compressive membraneenhanced uniform load resistance with plastic theory equations or E quations 1038 and 1039 in Army TM5 855 1, one must ensure that the value used for midspan deflection at ul timate compression membrane capacity is accurate. Otherwise, the result may be misleading, especially for UHPC slabs ; For UHPC slabs with compressive strengths in excess of 20 ksi, and the lengthto depth ratio is 10 < L/h < 20, a good rule of thumb estimate for uc is 0.5h. It is anticipated that the shorter the clear span, or the lower the compressive strength, the smaller uc will need to be in order to produce valid results For the same designed cross section, but for NSC, the value for uc was 0 .33h. If the analyst would have predicted ultimate resistance using 0.33h for UHPC case, the result would be over predicting resistance by 68%. That gives an example of how critical choosing the appropriate uc is for UHPC slabs ; An alternate approach of d etermining the deflection that occurs at ultimate capacity was generated based on Keenans [26] straindeformation approach used for conventional concrete slabs. This equation was based on the experimental results obtain ed from UHPC rigidly restrained slab tests. The modified equation is below: ++==3535ummx x .c. Once the deflection at ultimate capacity has been determined from the above equation, either Parks equation or E quations 1038 and 1039 found in Army TM 5 855 1 may be used to determine t h e value of ultimate resistance; It is important to remember that Equation 1038 in Army TM5855 1 is only valid once the yield lines begin responding plastically. The equation over predicts initially and gives a false sense as to what the ultimate resistance is. This is especially true for UHPC slabs. Future research: The foll owing points explore interest areas in which future research should be applied to better understand compressive membr ane response in UHPC slabs. Other L/d ratios for UHPC slabs should be experimentally tested to determine where midspan deflection at ultimate compression membrane capacity occurs. This knowledge would be very beneficial in fully understanding the range of behaviors present in UHPC slabs for different size members. It is not known at this time if UHPC has a significant effect on this parameter. It appears to have, based on comparisons between NSC and UHPC slabs that was tested in this effort; 169

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Th e primary focus of this effort was on compressive membrane behavior. It would be beneficial to detail the slab reinforcement in such a way that tensile membrane behavior would also occur in UHPC slab response. This would better define the member behavior from initial elastic behavior to failure through reinforcement fracture. Initially, the author anticipated this effort to cover the full behavior, but a small design flaw in anchoring the longitudinal reinforcement did not allow tensile membrane behavior to occur It is highly recommended that this research be conducted to investigate the full range of behavior; Other improvements to the plastic theory equations for UHPC should revolve around a material study to take a deeper look into the ratio of the concrete compression block depth to the distance from the compression face to the neutral axis, otherwise known as 1 in the formulation. For this study, 1 was taken as the minimum allowed, which in this case was 0.65. For future studies, this p arameter may need to be r efined; P artially re strained UHPC slabs should be investigated to determine the effects of the surrounding boundary stiffness on slab response. It is anticipated that the ultimate capacity will decrease with reduction in lateral and rotational restraint, b ut this should be verified through experimentation. 170

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APPENDIX A TEST MATRIX Table A 1 As built test matrix 171

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APPENDIX B CONCRETE SLAB DESIGN DRAWINGS Figure B 1 Overall dimensions of NSC slab tested dynamically, simply supported 172

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Figure B 2 Reinforcement l ayout of NSC slab tested dynamically, simply supported Figure B 3 Overall dimensions of UHPC slab tested dynamically, simply supported 173

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Figure B 4 Reinforcement l ayout of UHPC slab tested d ynamically, simply supported Figure B 5 Overall dimensions of NSC slab tested dynamically, rigidly restrained 174

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Figure B 6 Reinforcement l ayout of NSC slab tested dynamically, rigidly restrained Figure B 7 Overall dimensions of UHPC slab tested dynamically, rigidly restrained 175

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Figure B 8 Reinforcement l ayout of UHPC slab tested dynamically, rigidly restrained Figure B 9 Overall dimensions of NSC slab tested statically, rigidly restrained 176

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Figure B 10. Reinforcement l ayout of NSC slab tested statically, rigidly restrained Figure B 11. Overall dimensions of UHPC slab tested statically, rigidly rest rained 177

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Figure B 12. Reinforcement l ayout of UHPC slab tested statically, rigidly restrained Figure B 13. Overall dimensions of NSC slab tested statically, simply supported 178

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Figure B 14. Reinforcement l ayout of NSC slab tested statically, simply supported Figure B 15. Overal l dimensions of UHPC slab tested statically, simply supported 179

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Figure B 16. Reinforcement l ayout of UHPC slab tested statically, simply supported Figure B 17. Typical reinforcement layout for NSC restrained slab 180

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Figure B 18. Typical reinforcement layout for NSC simpl y supported slab Figure B 19. Entire set of NSC slabs cast on August 7, 2012 181

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Figure B 20. Typical reinforcement layout for Cor Tuf with f iber s restrained slab with strain gages 182

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Fig ure B 21. Typical reinforcement layout for Cor Tuf with f iber s simply supported slab with strain gages Figure B 22. Entire set of Cor Tuf with f ibers cast on August 14, 2012 183

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APPENDIX C SLAB CASTING PHOTOS Figure C 1 Casting NSC concrete slabs Figure C 2 Casting Cor Tuf slabs 184

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Figure C 3 Casting Cor Tuf (with fiber) slabs 185

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Figure C 4 Casting CorTuf (without fiber) slabs Figure C 5 Finishing and covering Cor Tuf slabs 186

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APPENDIX D QUASI STATIC TEST DATA Figure D 1 CW/OSSY D1 Test 1 Figure D 2 CW/OSSY D2 Test 1 187

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Figure D 3 CW/OSSY D3 Test 1 Figure D 4 CW/OSSY D4 Test 1 188

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Figure D 5 CW/OSSY D5 Test 1 Figure D 6 CW/OSSY mid span tension face reinforcement strain Test 1 189

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Figure D 7 CW/OSSY quarter span tension face reinforcement strain Test 1 Figure D 8 CW/OSSY support tension face reinforcement strain Test 1 190

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Figure D 9 CW/OSSY mid span compression face reinforcement strain Test 1 Figure D 10. CW/OSSY support compression face reinforcement strain Test 1 191

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Figure D 11. CW/OSSY inside pressure at top Test 1 Figure D 12. CW/OSSY outside pressure at top Test 1 192

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Figure D 13. CW/OSSY inside pressure at bottom Test 1 Figure D 14. CW/OSSY outside pressure at bottom Test 1 193

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Figure D 15. CW/OSSY pressure inside at lid Test 1 Figure D 16. CW/OSSY D1 Test 1b 194

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Figure D 17. CW/OSSY D2 Test 1b Figure D 18. CW/OSSY D3 Test 1b 195

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Figure D 19. CW/OSSY D4 Test 1b Figure D 20. CW/OSSY D5 Test 1b 196

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Figure D 21. CW/OSSY quarter span tension face reinforcement strain Test 1b Figure D 22. CW/OSSY support tension face reinforcement strain Test 1b 197

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Figure D 23. CW/OSSY pressure inside at top Test 1b Figure D 24. CW/OSSY pressure outside at top Test 1b 198

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Figure D 25. CW/OSSY pressure inside at bottom Test 1b Figure D 26. CW/OSSY pressure outside at bottom Test 1b 199

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Figure D 27. CW/OSSY pressure inside at lid Test 1b Figure D 28. CW/OSSY D1 Test 1c 200

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Figure D 2 9 CW/OSSY D2 Test 1c Figure D 30. CW/OSSY D3 Test 1c 201

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Figure D 31. CW/OSSY D4 Test 1c Figure D 32. CW/OSSY D5 Test 1c 202

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Figure D 33. CW/OSSY q uarter span tension face reinforcement strain Test 1c Figure D 34. CW/OSSY support tension face reinforcement strain Test 1c 203

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Figure D 35. CW/OSSY support compression face reinforcement strain Test 1c Figure D 36. CW/OSSY pressure inside at top Test 1c 204

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Figure D 37. CW/OSSY pressure outside at top Test 1c Figure D 38. CW/OSSY pressure inside at bottom Test 1c 205

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Figure D 39. CW/OSSY pressure outside at bottom Test 1c Figure D 40. CW/OSSY pressure inside at lid Test 1c 206

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Figure D 41. CW/OSSY D1 Test 1d Figure D 42. CW/OSSY D2 Test 1d 207

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Figure D 43. CW/OSSY D3 Test 1d Figure D 44. CW/OSSY D4 Test 1d 208

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Figure D 45. CW/OSSY D5 Test 1d Figure D 46. CW/OSSY q uarter span tension face reinforcement strain Test 1d 209

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Figure D 47. CW/OSSY support tension face reinforcement strain Test 1d Figure D 48. CW/OSSY support compression face reinforcement strain Test 1d 210

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Figure D 49. CW/OSSY pressure inside at top Test 1d Figure D 50. CW/OSSY outside inside at top Test 1d 211

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Figure D 51. CW/OSSY pressure inside at bottom Test 1d Figure D 52. CW/OSSY pressure outside at bottom Test 1d 212

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Figure D 53. CW/OSSY pressure inside at lid Test 1d Figure D 54. CW/OSSY D1 Test 2 213

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Figure D 55. CW/OSSY D2 Test 2 Figure D 56. CW/OSSY D3 Test 2 214

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Figure D 57. CW/OSSY D4 Test 2 Figure D 58. CW/OSSY D5 Test 2 215

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Figure D 59. CW/OSSY mid span tension face reinforcement strain Test 2 Figure D 60. CW/OSSY support tension face reinforcement strain Test 2 216

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Figure D 61. CW/OSSY mid span compression face reinforcement strain Test 2 Figure D 62. CW/OSSY support compression face reinforcement strain Test 2 217

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Figure D 63. CW/OSSY pressure inside at top Test 2 Figure D 64. CW/OSSY pressure outside at top Test 2 218

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Figure D 65. CW/OSSY pressure inside at bottom Test 2 Figure D 66. CW/OSSY pressure outside at bottom Test 2 219

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Figure D 67. CW/OSSY pressure inside at lid Test 2 Figure D 68. CW/OSSY D1 Test 2b 220

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Figure D 69. CW/OSSY D2 Test 2b Figure D 70. CW/OSSY D3 Test 2b 221

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Figure D 71. CW/OSSY D4 Test 2b Figure D 72. CW/OSSY D5 Test 2b 222

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Figure D 73. CW/OSSY support tension face reinforcement strain Test 2b Figure D 74. CW/OSSY support compression face reinforcement strain Test 2b 223

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Figure D 75. CW/OSSY pressure inside at top Test 2b Figure D 76. CW/OSSY pressure outside at top Test 2b 224

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Figure D 77. CW/OSSY pressure inside at bottom Test 2b Figure D 78. CW/OSSY pressure outside at bottom Test 2b 225

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Figure D 79. CW/OSSY pressure inside at lid Test 2b Figure D 80. CW/OSSY D1 Test 2c 226

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Figure D 81. CW/OSSY D2 Test 2c Figure D 82. CW/OSSY D3 Test 2c 227

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Figure D 83. CW/OSSY D4 Test 2c Figure D 84. CW/OSSY D5 Test 2c 228

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Figure D 85. CW/OSSY sup port tension face reinforcement strain Test 2c Figure D 86. CW/OSSY support compression face reinforcement strain Test 2c 229

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Figure D 87. CW/OSSY pressure inside at top Test 2c Figure D 88. CW/OSSY pressure outside at top Test 2c 230

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Figure D 89. CW/OSSY pressure inside at bottom Test 2c Figure D 90. CW/OSSY pressure outside at bottom Test 2c 231

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Figure D 91. CW/OSSY pressure inside at lid Test 2c Figure D 92. NSSN D1 Test 3 232

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Figure D 9 3 NSSN D2 Test 3 Figure D 94. NSSN D3 Test 3 233

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Figure D 95. NSSN D4 Test 3 Figure D 96. NSSN D5 Test 3 234

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Figure D 97. NSSN pressure inside at top Test 3 Figure D 98. NSSN pressure outside at top Test 3 235

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Figure D 99. NSSN pressure inside at bottom Tes t 3 Figure D 100. NSSN pressure outside at bottom Test 3 236

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Figure D 101. NSSN pressure inside at lid Test 3 Figure D 102. NSSY D1 Test 4 237

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Figure D 103. NSSY D2 Test 4 Figure D 104. NSSY D3 Test 4 238

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Figure D 105. NSSY D4 Test 4 Figure D 106. NSSY D5 Test 4 239

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Figure D 107. NSSY mid span tension face reinforcement strain Test 4 Figure D 108. NSSY q uarter span tension face reinforcement strain Test 4 240

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Figure D 109. NSSY support tension face reinforcement strain Test 4 Figure D 110. NSSY mid span compression face reinforcement strain Test 4 241

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Figure D 111. NSSY q uarter span compression face reinforcement strain Test 4 Figure D 112. NSSY support compression face reinforcement strain Test 4 242

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Figure D 113. NSSY pressure inside at top Test 4 Figure D 114. NSSY pressure outside at top Test 4 243

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Figure D 115. NSSY pressure inside at bottom Test 4 Figure D 116. NSSY pressure outside at bottom Test 4 244

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Figure D 117. NSSY pressure inside at lid Test 4 Figure D 118. NRRY D1 combined Test 5 245

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Figure D 119. NRRY D2 combined Test 5 Figure D 120. NRRY D3 combined Test 5 246

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Figure D 121. NRRY D5 combined Test 5 Figure D 122. NRRY mid span tension face reinforcement strain Test 5 247

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Figure D 123. NRRY q uarter span tension face reinforcement strain Test 5 Figure D 124. NRRY support tension face reinforcement strain Test 5 248

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Figure D 125. NRRY mid span compression face reinforcement strain Test 5 Figure D 126. NRRY q uarter span compression face reinforcement strain Test 5 249

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Figure D 127. NRRY support compression face reinforcement strain Test 5 Figure D 128. NSSY pressure inside at top Test 5 250

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Figure D 129. NSSY pressure outside at top Test 5 Figure D 130. NSSY pressure inside at bottom Test 5 251

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Figure D 131. NSSY pressure outside at bottom Test 5 Figure D 132. NSSY pressure inside at li d Test 5 252

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Figure D 133. NRRN D1 Test 6 Figure D 134. NRRN D2 Test 6 253

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Figure D 135. NRRN D3 Test 6 Figure D 136. NRRN D4 Test 6 254

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Figure D 137. NRRN D5 Test 6 Figure D 138. NRRN pressure inside at top Test 6 255

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Figure D 139. NRRN pressure outside at top Test 6 Figure D 140. NRRN pressure inside at bottom Test 6 256

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Figure D 141. NRRN pressure outside at bottom Test 6 Figure D 142. NRRN pressure inside at l id Test 6 257

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Figure D 143. NRRN D1 Test 7 Figure D 144. NRRN D2 Test 7 258

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Figure D 145. NRRN D3 Test 7 Figure D 146. NRRN D4 Test 7 259

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Figure D 147. NRRN D5 Test 7 Figure D 148. NRRN pressure inside at top Test 7 260

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Figure D 149. NRRN pressure outside at top Test 7 Figure D 150. NRRN pressure inside at bottom Test 7 261

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Figure D 151. NRRN pressure outside at bottom Test 7 Figure D 152. NRRN pressure inside at lid Test 7 262

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Figure D 153. NRRN D1 Test 8 Figure D 154. NRRN D2 Test 8 263

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Figure D 155. NRRN D3 Test 8 Figure D 156. NRRN D4 Test 8 264

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Figure D 157. NRRN D5 Test 8 Figure D 158. NRRN pressure inside at top Test 8 265

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Figure D 159. NRRN pressure outside at top Test 8 Figure D 160. NRRN pressure inside at bottom Test 8 266

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Figure D 161. NRRN pressure outside at bottom Test 8 Figure D 162. NRRN pressure inside at lid Test 8 267

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Figure D 163. CW/ORRY D1 Test 9 Figure D 164. CW/ORRY D2 Test 9 268

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Figure D 165. CW/ORRY D3 Test 9 Figure D 166. CW/ORRY D4 Test 9 269

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Figure D 167. CW/ORRY D5 Test 9 Figure D 168. CW/ORRY mid span compression face reinforcement strain Test 9 270

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Figure D 169. CW/ORRY q uarter span compression face reinforcement strain Test 9 Figure D 170. CW/ORRY support compression face reinforcement strain Test 9 271

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Figure D 171. CW/ORRY mid span tension face reinforcement strain Test 9 Figure D 172. CW/ORRY q uarter span tension face reinforcement strain Test 9 272

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Figure D 173. CW/ORRY support tension face reinforcement strain Test 9 Figure D 174. CW/ORRY pressure inside at top Test 9 273

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Figure D 175. CW/ORRY pressure outside at top Test 9 Figure D 176. CW/ORRY pressure inside at bottom Test 9 274

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Figure D 177. CW/ORRY pressure outside at bottom Test 9 Figure D 178. CW/ORRY pressure inside at lid Test 9 275

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Figure D 179. CW/ORRY D1 Test 10 Figure D 180. CW/ORRY D2 Test 10 276

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Figure D 181. CW/ORRY D3 Test 10 Figure D 182. CW/ORRY D4 Test 10 2 77

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Figure D 183. CW/ORRY D5 Test 10 Figure D 184. CW/ORRY mid span compression face reinforcement strain Test 10 278

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Figure D 185. CW/ORRY q uarter span compression face reinforcement strain Test 10 Figure D 186. CW/ORRY support compression face reinforcement strain Test 10 279

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Figure D 187. CW/ORRY mid span tension face reinforcement strain Test 10 Figure D 188. CW/ORRY q uarter span tension face reinforcement strain Test 10 280

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Figure D 189. CW/ORRY support tension face reinforcement strain Test 10 Figure D 190. CW/ORRY pressure inside at top Test 10 281

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Figure D 191. CW/ORRY pressure outside at top Test 10 Figure D 192. CW/ORRY pressure inside at bottom Test 10 282

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Figure D 193. CW/ORRY pressure outside at bottom Test 10 Figure D 194. CW/ORRY pressure inside at lid Test 10 283

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Figure D 195. CWSSY D1 Test 11 Figure D 196. CWSSY D2 Test 11 284

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Figure D 197. CWSSY D3 Test 11 Figure D 198. CWSSY D4 Test 11 285

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Figure D 199. CWSSY D5 Test 11 Figure D 200. CWSSY mid span compression face reinforcement strain Test 11 286

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Figure D 201. CWSSY q uarter span compression face reinforcement strain Test 11 Figure D 202. CWSSY support compression face reinforcement strain Test 11 287

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Figure D 203. CWSSY mid span tension face reinforcement strain Test 11 Figure D 204. CWSSY q uarter span tension face reinforcement strain Test 11 288

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Figure D 205. CWSSY support tension face reinforcement strain Test 11 Figure D 206. CWSSY pressure inside at top Test 11 289

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Figure D 207. CWSSY pressure outside at top Test 11 Figure D 208. CWSSY pressure inside at bottom Test 11 290

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Figure D 209. CWSSY pressure outside at bottom Test 11 Figure D 210. CWSSY pressure inside at lid Test 11 291

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APPENDIX E BLAST LOAD SIMULATOR (DYNAMIC) TEST DATA Figure E 1 CW/OSSN P1 and impulse vs. time Test 1 Figure E 2 CW/OSSN P2 and impulse vs. time Test 1 292

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Figure E 3 CW/OSSN P3 and impulse vs. time Test 1 Figure E 4 CW/OSSN P4 and impulse vs. time Test 1 293

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Figure E 5 CW/OSSN P5 and impulse vs. time Test 1 Figure E 6 CW/OSSN P6 and impulse vs. time Test 1 294

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Figure E 7 CW/OSSN PD and impulse vs. time Test 1 Figure E 8 CW/OSSN PE and impulse vs. time Test 1 295

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Figure E 9 CW/OSSN P1 and impulse vs. time Test 1b Figure E 10. CW/OSSN P2 and impulse vs. time Test 1b 296

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Figure E 11. CW/OSSN P3 and impulse vs. time Test 1b Figure E 12. CW/OSSN P4 and impulse vs. time Test 1b 297

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Figure E 13. CW/OSSN P5 and impulse vs. time Test 1b Figure E 14. CW/OSSN P6 and impulse vs. time Test 1b 298

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Figure E 15. CW/OSSN PD and impulse vs. time Test 1b Figure E 16. CW/OSSN PE and impulse vs. time Test 1b 299

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Figure E 17. CW/OSSY P1 and impulse vs. time Test 2 Figure E 18. CW/OSSY P2 and impulse vs. time T est 2 300

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Figure E 19. CW/OSSY P3 and impulse vs. time Test 2 Figure E 20. CW/OSSY P4 and impulse vs. time Test 2 301

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Figure E 21. CW/OSSY P5 and impulse vs. time Test 2 Figu re E 22. CW/OSSY P6 and impulse vs. time Test 2 302

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Figure E 23. CW/OSSY PD and impulse vs. time Test 2 Figure E 2 4 CW/OSSY PE and impulse vs. time Test 2 303

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Figure E 25. NSSN P1 and impulse vs. time Test 3 Figure E 26. NSSN P2 and impulse vs. time Test 3 304

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Figure E 27. NSSN P3 and impulse vs. time Te st 3 Figure E 28. NSSN P4 and impulse vs. time Test 3 305

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Figure E 29. NSSN P5 and impulse vs. time Test 3 Figure E 30. NSSN P6 and impulse vs. time Test 3 306

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Figure E 31. NSSN PD and impulse vs. time Test 3 Figure E 32. NSSN PE and impulse vs. time Test 3 307

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Figure E 33. CW/OSSY P1 and impulse vs. time Test 4 Figure E 34. CW/OSSY P2 and impulse vs. time Te st 4 308

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Figure E 35. CW/OSSY P3 and impulse vs. time Test 4 Figure E 36. CW/OSSY P4 and impulse vs. time Test 4 309

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Figure E 37. CW/OSSY P5 and impulse vs. time Test 4 Figure E 38. CW/OSSY P6 and impulse vs. time Test 4v 310

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Figure E 39. CW/OSSY PD and impulse vs. time Test 4 Figure E 40. CW/OSSY PE and impulse vs. time Test 4 311

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Figure E 41. NSSN P1 and impulse vs. time Test 6 Figure E 42. NSSN P2 and impulse vs. time Test 6 312

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Figure E 43. NSSN P3 and impulse vs. time Test 6 Figure E 44. NSSN P4 and impulse vs. time Test 6 313

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Figure E 45. NSSN P5 and impulse vs. time Test 6 Figure E 46. NSSN P6 and impulse vs. time Test 6 314

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Figure E 47. NSSN PD and impulse vs. time Test 6 Figure E 48. NSSN PE and impulse vs. time Test 6 315

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Figure E 49. NSSY P1 and impulse vs. time Test 7 Figure E 50. NSSY P2 and impulse vs. time Test 7 316

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Figure E 51. NSSY P3 and impulse vs. time Test 7 Figure E 52. NSSY P4 and impulse vs. time Test 7 317

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Figure E 53. NSSY P5 and impulse vs. time Test 7 Figure E 54. NSSY P6 and impulse vs. time Test 7 318

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Figure E 55. NSSY PD and impulse vs. time Test 7 Figure E 56. NSSY PE and impulse vs. time Test 7 319

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Figure E 57. CWSSN P1 and impulse vs. time Test 8 tri al Figure E 58. CWSSN P2 and impulse vs. time Test 8 trial 320

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Figure E 59. CWSSN P3 and impulse vs. time Test 8 trial Figure E 60. CWSSN P4 and impulse vs. time Test 8 trial 321

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Figure E 61. CWSSN P5 and impulse vs. time Test 8 trial Figure E 62. CWSSN P6 and impulse vs. time Test 8 trial 322

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Figure E 63. CWSSN PD and impulse vs. time Test 8 trial Figure E 64. CWSSN PE and impulse vs. time Test 8 trial 323

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Figure E 65. CWSSN P1 and impulse vs. time Test 9 trial 2 Figure E 66. CWSSN P2 and impulse vs. time Test 9 trial 2 324

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Figure E 67. CWSSN P3 and impulse vs. time Test 9 trial 2 Figure E 68. CWSSN P4 and impulse vs. time Test 9 trial 2 325

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Figure E 69. CWSSN P5 and impulse vs. time Test 9 trial 2 Fig ure E 70. CWSSN P6 and impulse vs. time Test 9 trial 2 326

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Figure E 71. CWSSN PD and impulse vs. time Test 9 trial 2 Figure E 72. CWSSN PE and impulse vs. time Test 9 trial 2 327

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Figure E 73. NRRN P1 and impulse vs. time Test 10 Figure E 74. NRRN P2 and impulse vs. time Test 10 328

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Figure E 75. NRRN P3 and impulse vs. time Test 10 Figure E 76. NRRN P4 and impulse vs. time Test 10 329

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Figure E 77. NRRN P5 and impulse vs. time Test 10 Figure E 78. NRRN P6 and impulse vs. time Test 10 330

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Figure E 79. NRRN PD and impulse vs. time Test 10 Figure E 80. NRRN PE and impulse vs. time Test 10 331

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Figure E 81. NRRN_2 P1 and impulse vs. time Tes t 11 Figure E 82. NRRN_2 P2 and impulse vs. time Test 11 332

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Figure E 83. NRRN_2 P3 and impulse vs. time Test 11 Figure E 84. NRRN_2 P4 and impulse vs. time Test 11 333

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Figure E 85. NRRN_2 P5 and impulse vs. time Test 11 Figure E 86. NRRN_2 P6 and impulse vs. time Test 11 334

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Figure E 87. NRRN_2 PD and impulse vs. time Test 11 Figure E 8 8 NRRN_2 PE and impulse vs. time Test 11 335

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Figure E 89. NRRY P1 and impulse vs. time Test 12 Figure E 90. NRRY P2 and impulse vs. time Test 12 336

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Figur e E 91. NRRY P3 and impulse vs. time Test 12 Figure E 92. NRRY P4 and impulse vs. time Test 12 337

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Figure E 93. NRRY P5 and impulse vs. time Test 12 Figure E 94. NRRY P6 and impulse vs. time Test 12 338

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Figure E 95. NRRY PD and impulse vs. time Test 12 Figure E 96. NRRY PE and impulse vs. time Test 12 339

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Figure E 97. NRRN P1 and impulse vs. time Test 13 Figure E 98. NRRN P2 and impulse vs. time Test 13 340

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Figure E 99. NRRN P3 and impulse vs. time Test 13 Figure E 100. NRRN P4 and impulse vs. time Test 13 341

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Figure E 101. NRRN P5 and impulse vs. time Test 13 Figure E 102. NRRN P6 and impulse vs. time Test 13 342

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Figure E 103. NRRN PD and impulse vs. time Test 13 Figure E 104. NRRN PE and impulse vs. time Test 13 343

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Figure E 105. CW/ORRN P1 and impulse vs. time Test 14 Figure E 106. CW/ORRN P2 and impulse vs. time T est 14 344

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Figure E 107. CW/ORRN P3 and impulse vs. time Test 14 Figure E 108. CW/ORRN P4 and impulse vs. time Test 14 345

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Figure E 109. CW/ORRN P5 and impulse vs. time Test 14 Figure E 110. CW/ORRN P6 and impulse vs. time Test 14 346

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Figure E 111. CW/ORRN PD and impulse vs. time Test 14 Figure E 112. CW/ORRN PE and impulse vs. time Test 14 347

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Figure E 113. CW/ORRY P1 and impulse vs. time Test 15 Figure E 114. CW/ORRY P2 and impulse vs. time Test 15 348

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Figure E 115. CW/ORRY P3 and impulse vs. time Test 15 Figure E 116. CW/ORRY P4 and impulse vs. time Test 15 349

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Figure E 117. CW/ORRY P5 and impulse vs. tim e Test 15 Figure E 118. CW/ORRY P6 and impulse vs. time Test 15 350

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Figure E 119. CW/ORRY PD and impulse vs. time Test 15 Figure E 120. CW/ORRY PE and impulse vs. time Test 15 351

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Figu re E 121. CW/ORRY P1 and impulse vs. time Test 16 Figure E 122. CW/ORRY P2 and impulse vs. time Test 16 352

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Figure E 123. CW/ORRY P3 and impulse vs. time Test 16 Figure E 124. CW/ORRY P4 and impulse vs. time Test 16 353

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Figure E 125. CW/ORRY P5 and impulse vs. time Test 16 Figure E 126. CW/ORRY P6 and impulse vs. time Test 16 354

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APPENDIX F EXPERIMENTAL LOADS AND RESISTANCE CALCULATIONS Table F 1 Average pressures and impulses 355

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Table F 1 Continued 356

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Table F 2 Johansens yield line load parameters Table F 3 Uniform load resistance calculated from TM 5 8551 357

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APPENDIX G SLAB TESTING PHOTOGRAPHS Figure G 1 NSC SS static Test 3 pret est Figure G 2 NSC SS static Test 3 in progress 358

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Figure G 3 NSC SS static Test 3 posttest Figure G 4 UHPC SS static Test 1 pretest 359

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Figure G 5 UHPC SS static Test 1 posttest Figure G 6 NSC RR static Test 6 pretest 360

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Figure G 7 NSC RR static Test 6 posttest Figure G 8 UHPC RR static Test 9 pretest 361

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Figure G 9 UHPC RR static Test 9 posttest Figure G 10. NSC SS dynamic Test 6 pretest front view 362

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Figure G 11. NSC SS dynamic Test 6 pretest, rear view Figure G 12. NSC SS dynamic Test 6 posttest, front view 363

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Figure G 13. NSC SS dynamic Test 6 posttest, rear view Figure G 14. UHPC SS dynamic Test 2 pretest, front view 364

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Figure G 1 5 UHPC SS dynamic Test 2 posttest, rear view Figure G 16. UHPC SS dynamic Test 2 post t est, front view 365

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Figure G 17. NSC RR dynamic Test 10 pretest, front view Figure G 18. NSC RR dynamic Test 10 pr etest, rear view 366

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Figure G 19. NSC RR dynamic Test 10 post test, rear view Figure G 20. NSC RR dynamic Test 10 posttest, front view 367

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Figure G 21. UHPC RR dynamic Test 14 pretest, front view Figure G 22. UHPC RR dynamic Test 14 pretest, rear view 368

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Figure G 23. UHPC RR dynamic Test 14 posttest, rear view Figure G 24. UHPC RR dynamic Test 14 posttest, front view 369

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APPENDIX H NSC CDP MODEL PARAMETERS Table H 1 Normal strength concrete CDP model parameters Parameter Value D ilation angle measured in the p q plane 36.31 deg Flow potential eccentricity 0.1 b0 c0 ratio of initial equibiaxial compressive yield stress to initial un iaxial compressive yield stress 1.16 K c ratio of the second stress invariant on the tensile meridian, to that on the compressive meridian at initial yield for any given value of the pressure invariant p such that the maxim um principal stress is negative 2/3 E Young's modul u s 31.2 GPa Poisson's ratio 0.21 w t Tension stiffness recovery 0.0 w c Compression stiffness recovery 1.0 370

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Table H 2 Normal strength concrete CDP model parameters ( compression hardening and damage) Stress, MPa Crushing Strain Damage 19.1521 0 0 0 21.81124 0.000103 0 24.21712 0.000206 0 26.36976 0.000309 0 28.26914 0.000412 0 29.91527 0.000515 0 31.30815 0.000618 0 32.44778 0.000721 0 33.33416 0.000824 0 33.96728 0.000927 0 34.34716 0.00103 0 0 34.47379 0.001133 0 34.00369 0.001297 0 33.53359 0.001461 0.036548 33.0635 0 0.001624 0.073096 32.5934 0 0.001788 0.109645 32.1233 0 0.001952 0.146193 31.6532 0 0.002115 0.182741 31.18311 0.002279 0.219289 30.71301 0.002442 0.255838 30.24291 0.002606 0.292386 29.77282 0.00277 0 0.328934 29.30272 0.002933 0.365482 2.930272 0.003983 0.6 00000 371

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Table H 3 Normal strength concrete CDP model parameters ( t ension stiffening) Stress, MPa Cracking Strain 3.656497 0 0.731299 0.002383 Table H 4 Normal strength concrete CDP model parameters ( t ension damage) Damage Cracking Strain 0 0 0.6 0.002383 372

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REFERENCES [1] ACI Committee 318, Building Code Requirements for Structural Concrete and Commentary (ACI 318 11), American Concrete Institute, Farmington Hills, MI, 2011, 509 pp. [2] Park, R., and Gamble, W. L., Reinforced Concrete Slabs 2nd Edition, John Wiley and Sons, New York, 2000 [3] Dynamic Structural Analysis Suite (DSAS), Center for Infrastructure Protection and Physical Security (CIPPS) University of Florida Version 3.0, 2011 [4] Ockleston, A. J., Load Tests on a Three Story Reinforced Concrete Building in Johannesburg, Structural Engineer (London), V. 33, No. 10, Oct. 1955, pp. 304322 [5] Ockleston, A. J., Arching action in reinforced concrete slabs, Structural Engineer (London), V. 36, No. 6, June 1958, pp. 197201 [6] Johansen, K. W., Yield Line Theory, translated by Cement and Concrete Institution, London, 1962, 181 pp [7] Ross, C.A., and Rosengren, P.L., Expedient Nonlinear Dynamic Analysis of Reinforced Concrete Structures, Proceedings of 2nd Symposium on the Interaction of NonNuclear Munitions with Structures, University of Florida Graduate Engineering Center, Eglin AFB, FL, 1985, P. 45 [8] Krauthammer, T., Frye, M.T., Schoedel, R., Seltzer, M., Astarioglu S., A Single Degree of Freedom (SDOF) Computer Code Development for the Analysis of Structures Subjected to Short Duration Dynamic Loads, Technical Report PTC TR 002 2003, Protective Technology Center, Pennsylvania State University, August 2003 [9] Big gs, J.M., Introduction to Structural Dynamics, McGraw Hill, New York, 1964 [10] Krauthammer, T., Modern Protective Structures, CRC Press Taylor and Francis Group, FL, 2008 [11] Woodson, S.C., Effects of Shear Reinforcement on the LargeDeflection Behavior of Reinforced Concrete Slabs, Technical Report SL9418, U.S. Army Corps of Engineers, Waterways Experiment Station, September 1994 [12] Woodson, S.C., Shear Reinforcement in Deep Slabs, Technical Report SL9424, U.S. Army Corps of Engineers, Waterways Ex periment Station, November 1994 [13] Krauthammer, T., Bazeos, N., and Holmquist, T.J., Modified SDOF Analysis of RC Box type Structures, Journal of Structural Engineering, 112, 726, 1986 373

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[14] Krauthammer, T., Shallow Buried RC Box type Structures, Jou rnal of Structural Engineering, 110, 637, 1984 [15] Krauthammer, T., Hill, J.J., and Fares, T., Enhancement of Membrane Action for Analysis and Design of Box Culverts, Transportation Research Record, No. 1087, pp.5461, 1986 [16] Fundamental of Protectiv e Design for Conventional Weapons, Technical Manual 5 8551, Department of the Army, 1986 [17] Krauthammer, T., Shahriar, S., and Shanaa, H.M., Response of RC Elements to Severe Impulsive Loads, Journal of Structural Engineering, 116, 1061, 1990 [18] Par k, R., Ultimate Strength of Rectangular Concrete Slabs under Short Term Uniform Loading with Edges Restrained against Lateral Movement, Proc Inst. Civil Engineering, Vol. 28, June 1964, pp. 125 150 [19] Tedesco, J.W., McDougal, W.G., and Ross, C.A., Stru ctural Dynamics Theory and Applications, Addison Wesley Longman, Inc., 1999 [20] UFC 3 34002, "Structures to Resist the Effects of Accidental Explosions," Department of Defense, Washington, DC, 2008 [21] Williams, E.M., Graham, S.S., Reed, P.A. and Rushin g, T.S., Laboratory characterization of Cor T uf concrete with and without steel fibers, ERDC/GSL TR 0922, Vicksburg, MS: U.S. Army Engineer Research and Development Center, 2009 [22] Williams, E.M., Akers, S. A., and Reed, P.A., Laboratory characterization of S AM 35 Concrete, ERDC/GSL TR 0615, Vicksburg, MS: U.S. Army Engineer Research and Development Center, 2006 [23] Guice, L.K., Behavior of Partially Restrained Reinforced Concrete Slabs, Technical Report No. SL8632, Sept. 1986, Structures Labor atory, U.S. Army Engineer Waterways Experiment Station, Vicksburg, 184 pp [24] Rankin, G.I.B., Niblock, R. A., Skates, A. S., and Long, A. E.,, Compressive membrane action strength enhancement in uniformly loaded, laterally restrained slabs, The Structur al Engineer, V 69, No. 16, Aug 1991, pp. 287295 [25] Guice, L.K., Slawson, T.R., and Rhomberg, E.J., Membrane Analysis of Flat Plate Slabs, ACI Structural Journal, V 86, No. 10, 1989, pp. 8392 [26] Keenan, W.A., Strength and Behavior of Restrained Rei nforced Concrete Slabs Under Static and Dynamic Loadings, Technical Report No R621, U.S. Naval Civil Engineering Laboratory, Port Hueneme, April 1969, pp. 1823 374

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[27] Meamarian, N., Krauthammer, T., and OFallon, J., Analysis and Design of Laterally Reinf orced Structural Concrete OneWay Members, ACI Structural Journal, V. 91, No. 6, Nov Dec 1994 [28] Collins, M.P., and Mitchell, D., Prestressed Concrete Structures, Prentice Hall Inc., 1991, Ch. 7 and 8 [29] Lahlouh, E. H., and Waldron, P., Membrane acti on in oneway slabs strips, Proc Institution Civil Engineers Structures & Buildings, 1992, 94, Nov., pp. 419428 [30] Rankin, G.I.B., Punching failure and compressive membrane action in reinforced concrete slabs, PhD thesis, Queens University of Belfas t, 1982 [31] McDowell, E.L., McKee, K. E., and Sevin, E., Arching action theory of masonry walls, Journal of Structural Division, Proc. ASCE, 82, NO. ST2, March 1956, pp. 9151 to 915 18 [32] Niblock, R.A., Compressive membrane action and the ultimate c apacity of uniformly loaded reinforced concrete slabs, PhD thesis, Queens University of Belfast, 1986 [33] Taylor, S.E., Rankin, G.I.B., and Cleland, D.J., Arching action in highstrength concrete slabs, Proc Institution Civil Engineers Structures & Bu ildings 146, Nov 2001, 4, pp. 353362 [34] Rankin, G.I.B., and Long, A.E., Predicting the enhanced punching strength of interior slabcolumn connections, Proc Institution Civil Engineers, 1987, 82, No. 4, pp. 11651186 [35] 3D Simula. Abaqus 6.13. Waltham, MA 02451 [36] Design and Analysis of Hardened Structures to Conventional Weapons Effects, UFC 3 34001 Joint Departments of the Army, Air Force, and Navy and the Defense Special Weapons Agency, 1 June 2002 [37] Robert, S. D., Johnson, C. F., and Woodson, S. C., Quasi Static High Strength Low Alloy Vanadium Steel Reinforced Concrete Slab Experiments, ERDC/GSL TR 0935 Vicksburg, MS: U.S. Army Engineer Research and Development Center, 2008 [38] Johnson, C.F., Davis, J.L., Coltharp, D.L., Kinnebrew, P.G., Smith, L.L. (20 10 ), X FLEX Retrofit: Results from SubScale Static and Dynamic Experiments, ERDC/GSL TR1036 U.S. Army Corps of Engineers Research and Development Center, Vicksburg, Mississippi. (FOUO) [ 39] Methodology Manual for the SingleDegreeof Freedom Blast Effects Design Spreadsheets (SBEDS) PDCTR 0601. U.S. Army Corps of Engineers Protective Design Center, 2008 375

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[40] Slawson, T.R., Wall Response to Airblast Loads: The Wall Analysis Code (WAC), ARA TR 5208, November 10, 1995 [ 41] Adley, M.D., Frank, A.O., Danielson, K.T., Akers, S.A. and ODaniel, J.L., The Advanced Fundamental Concrete (AFC) Model, ERDC/GSL TR 1051, Vicksburg, MS: U.S. Army Engineer Research and Development Center, 2010 [4 2 ] Hillerborg, A., Modeer, M., and Petersson, P.E., Analysis of Crack Formation and Crack Growth in Concrete by means of Fracture Mechanics and Finite Elements, Cement and Concrete Research, vol. 6, pp. 773783, 1976 376

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BIOGRAPHICAL SKETCH Bradley W. Foust was born in Decatur, Alabam a and raised nearby in Holly Pond, AL. He enrolled at Auburn Universitys Samuel Ginn College of Engineering in August of 1999. He obtained his Bachelor of Science degree in Civil Engineering in August 2002 and immedi ately enrolled in the m asters program at Auburn University. He obtained a Master of Science degree in Civil Engineering in December 2003 from Auburn University. In January 2004, he was hired as a Research Structural Engineer for the U.S. Army Engineer Research and Development Center (ERDC) in Vicksburg, MS. He was selected as a Long Term Training participant in 2006 and decided to enroll at the University of Florida in the College of Engineering, Department of Civil and Coastal Engineering. He received his PhD in Civil Engineering from the University of Florida in December 2013. T he author plans to continue his professional career conducting research for the U.S. Army Corps of Engineers at ERDC, Vicksburg, MS. 377