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Validation and Implementation of Bridge Design Specifications for Barge Impact Loading

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Title:
Validation and Implementation of Bridge Design Specifications for Barge Impact Loading
Physical Description:
1 online resource (502 p.)
Language:
english
Creator:
Getter, Daniel J
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:
Consolazio, Gary R
Committee Members:
Hamilton, Homer Robert, Iii
Cook, Ronald Alan
Mcvay, Michael C
Chen, Youping

Subjects

Subjects / Keywords:
barge -- bridge -- collision -- constiutive -- design -- impact -- modeling -- risk -- vessel
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:
Since 1991 in the United States, the design of highway bridges to resist collisions by errant waterway vessels has been carried out in accordance with design provisions published by AASHTO. These provisions have remained largely unchanged for more than 20 years, while numerous studies in recent years—conducted by researchers at the University of Florida (UF) and the Florida Department of Transportation (FDOT)—have greatly improved upon the analysis procedures in the AASHTO provisions. The focus of the work discussed in this dissertation was to experimentally validate the improved UF/FDOT barge impact load-prediction model and implement numerous other UF/FDOT procedures into a comprehensive risk assessment methodology that can be readily adopted for use in bridge design. To validate the UF/FDOT barge impact load model, a series of impact experiments were planned, in which reduced-scale replicas of atypical barge bow will be impacted by a high-energy impact pendulum to produce large-scale barge deformations.  This dissertation discusses the planning of the experimental study and the design of the various experimental components. In support of the validation effort, a material testing program was carried out in order to characterize the strain rate-sensitive properties of steel materials from which the reduced-scale barge specimens will be fabricated. Steel specimens were tested in uniaxial tension at strain rates covering seven orders of magnitude. To conduct high-rate material tests, a novel test apparatus was designed and employed that used an impact pendulum to impart the required energy. Data from the material testing program were used to develop constitutive models that were used in finite element barge impact simulations. Additionally in this study, a revised vessel collision risk assessment methodology was developed that incorporates various new UF/FDOT analysis procedures. The complete methodology was demonstrated for two real-world bridge cases, and the results were compared to the existing AASHTO risk assessment method. For these two cases, the revised procedure was found to predict higher levels of risk than the AASHTO procedure. However,retrofit and alternative design solutions were presented that demonstrate that,with careful design choices, the revised procedure can result in safer and more economical bridge designs.
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 Daniel J Getter.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Consolazio, Gary R.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045792:00001

MISSING IMAGE

Material Information

Title:
Validation and Implementation of Bridge Design Specifications for Barge Impact Loading
Physical Description:
1 online resource (502 p.)
Language:
english
Creator:
Getter, Daniel J
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:
Consolazio, Gary R
Committee Members:
Hamilton, Homer Robert, Iii
Cook, Ronald Alan
Mcvay, Michael C
Chen, Youping

Subjects

Subjects / Keywords:
barge -- bridge -- collision -- constiutive -- design -- impact -- modeling -- risk -- vessel
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:
Since 1991 in the United States, the design of highway bridges to resist collisions by errant waterway vessels has been carried out in accordance with design provisions published by AASHTO. These provisions have remained largely unchanged for more than 20 years, while numerous studies in recent years—conducted by researchers at the University of Florida (UF) and the Florida Department of Transportation (FDOT)—have greatly improved upon the analysis procedures in the AASHTO provisions. The focus of the work discussed in this dissertation was to experimentally validate the improved UF/FDOT barge impact load-prediction model and implement numerous other UF/FDOT procedures into a comprehensive risk assessment methodology that can be readily adopted for use in bridge design. To validate the UF/FDOT barge impact load model, a series of impact experiments were planned, in which reduced-scale replicas of atypical barge bow will be impacted by a high-energy impact pendulum to produce large-scale barge deformations.  This dissertation discusses the planning of the experimental study and the design of the various experimental components. In support of the validation effort, a material testing program was carried out in order to characterize the strain rate-sensitive properties of steel materials from which the reduced-scale barge specimens will be fabricated. Steel specimens were tested in uniaxial tension at strain rates covering seven orders of magnitude. To conduct high-rate material tests, a novel test apparatus was designed and employed that used an impact pendulum to impart the required energy. Data from the material testing program were used to develop constitutive models that were used in finite element barge impact simulations. Additionally in this study, a revised vessel collision risk assessment methodology was developed that incorporates various new UF/FDOT analysis procedures. The complete methodology was demonstrated for two real-world bridge cases, and the results were compared to the existing AASHTO risk assessment method. For these two cases, the revised procedure was found to predict higher levels of risk than the AASHTO procedure. However,retrofit and alternative design solutions were presented that demonstrate that,with careful design choices, the revised procedure can result in safer and more economical bridge designs.
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 Daniel J Getter.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Consolazio, Gary R.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045792:00001


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1 VALIDATION AND IMPLEMENTATION OF BRIDGE DESIGN SPECIFICATIONS FOR BARGE IMPACT LOADING By DANIEL JAMES GETTER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQU IREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013

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2 2013 Daniel James Getter

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3 To my fiance, Heather

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4 ACKNOWLEDGEMENTS This dissertation could not have been completed without the support and guidance of a number of individuals. Foremost, I would like to express my gratitude to Dr. Gary Consolazio for his guidance, encouragement, and steadfast devotion to the work. His unique ability to act both as a devoted mentor and as an active research partner cannot be understated. Furthermore, I would like to thank Dr. Ronald Cook, Dr. H.R. (Trey) Hamilton, Dr. Michael McVay, Dr. Bhavani Sankar, and Dr. Youping Chen for their valuable suggestions, comments, and time committed to serving on my supervisory committee. Especially I would like to thank the staff of the M.H. Ansley Structures Research Center, particularly Mr. Stephen Eudy, Mr. Christopher Weigly, Mr. David Wagner, Mr. William Potter, and Mr. Sam Fallaha, for their invaluable assist ance in setting up and carrying out the pendulum experiments. For assistance in carrying out experiments in the University of Florida structures laboratory, I would like t o thank Dr. Christopher Ferraro and Mr. Nard Martin Throughout the process of cond ucting this research, I received critical assistance in carrying out analysis, design, and document production tasks from Ms. Sarah Futral, Mr. Alex Randell, Mr. Matias Groetaers, Mr. John Wilkes, and Mr. George Kantrales, for which I thank you immensely. Perhaps most importantly, I want to express love and gratitude to my fiance, Heather Malone, for her unwavering patience, support, and encouragement of my efforts, even when it meant being a country apart at times

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5 TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ................................ ................................ ................................ ............. 4 LIST OF TABLES ................................ ................................ ................................ ......................... 11 LIST OF FIGURES ................................ ................................ ................................ ....................... 14 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 22 ABSTRACT ................................ ................................ ................................ ................................ ... 27 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 29 1.1 Motivation ................................ ................................ ................................ ........................ 29 1.2 Objectives ................................ ................................ ................................ ........................ 32 1.3 Scope of Work ................................ ................................ ................................ ................. 32 2 BACKGROUND ................................ ................................ ................................ .................... 36 2.1 AASHTO Risk Assessment Procedure ................................ ................................ ............ 36 2.2 UF/FDOT Research on Barge Collision ................................ ................................ .......... 41 2.2.1 Full Scale Barge Impact Experiments ................................ ................................ 42 2.2.2 Cou pled Vessel Impact Analysis (CVIA) Procedure ................................ .......... 43 2.2.3 Barge Bow Force Deformation Curves ................................ ............................... 45 2.2.4 Collision Induced Dynamic Ampl ification Phenomena ................................ ...... 47 2.2.5 Other Vessel Impact Procedures ................................ ................................ ......... 48 2.2.6 Revised Probability of Collapse ( PC ) Expression ................................ ............... 52 2.3 Observations ................................ ................................ ................................ .................... 53 3 EXPERIMENTAL VALIDATION OF UF/FDOT BARGE IMPACT LOAD PREDICTION MODEL ................................ ................................ ................................ ......... 64 3.1 Validation Objectives ................................ ................................ ................................ ...... 65 3.2 Overview of Experimental Program ................................ ................................ ................ 66 3.2.1 Determination of Barge Bow Mod el Scale ................................ ......................... 68 3.2.2 Material Testing Program ................................ ................................ .................... 69 3.3 Validation Simulations ................................ ................................ ................................ .... 70 4 STRAIN RATE SENSITIVE CONSTITUTIVE RELATIONS FOR EXPERIMENTAL VALIDATION ................................ ................................ ................................ ....................... 76 4.1 Materials and Methods ................................ ................................ ................................ .... 77 4.1.1 A10 11 and A36 Steel ................................ ................................ ........................... 77

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6 4.1.2 Uniaxial Tension Testing (Quasi Static) ................................ ............................. 77 4.1.3 Uniaxial Tension Testing (High Strain Rate) ................................ ...................... 78 4.1.3.1 Pendulum based high rate test apparatus (HRTA) ............................... 79 4.1.3.2 Instrumentation ................................ ................................ ..................... 81 4.1.4 Summary of Testing Program ................................ ................................ ............. 82 4.2 Theory and Calculation Procedures ................................ ................................ ................. 82 4.2.1 Quasi Static Testing Program ................................ ................................ .............. 82 4.2.2 High Rate Testing Program ................................ ................................ ................. 83 4.2.2.1 Single degree of freedom data interpretation ................................ ....... 83 4.2.2.2 Impulse momentum data interpretation ................................ ................ 84 4.3 Results and Discussion ................................ ................................ ................................ .... 88 4.3.1 Quasi Static Te sting Program ................................ ................................ .............. 88 4.3.2 High Rate Testing Program ................................ ................................ ................. 90 4.4 Constitutive Model Details ................................ ................................ .............................. 96 4.4.1 Strain Rate Sensitivity ................................ ................................ ......................... 97 4.4.2 Failure Strain Considerations ................................ ................................ .............. 97 4.4.3 Constitutive Curves ................................ ................................ ............................. 99 4.4.4 Implementation in LS DYNA ................................ ................................ ........... 100 4.4.4.1 A1011 T11 model ................................ ................................ ............... 100 4.4.4 .2 A1011 T15 model ................................ ................................ ............... 100 4.4.4.3 A36 T25 model ................................ ................................ ................... 101 4.5 Summary ................................ ................................ ................................ ........................ 101 5 FINITE ELEMENT SIMULATIONS OF REDUCED SCALE BARGE IMPACT ........... 118 5.1 Implementation of Finite Element Constitutive Models ................................ ............... 118 5.2 Barge Impact Simulations ................................ ................................ .............................. 119 5.2.1 Impact Simulation Results (Flat Faced Block) ................................ ................. 120 5.2.2 Sensitivity of Results to Steel Const itutive Model (Flat Faced Block) ............ 122 5.2.3 Impact Simulation Results (Rounded Block) ................................ .................... 125 5.2.4 Sensitivity of Results to Steel C onstitutive Model (Rounded Block) ............... 126 5.2.5 Comparison of Flat Faced and Rounded Block Impact Simulation Results ..... 127 5.3 Summary ................................ ................................ ................................ ........................ 128 6 PLANNED REDUCED SCALE BARGE BOW IMPACT EXPERIMENTS .................... 13 7 6.1 Experimental Components ................................ ................................ ............................. 137 6.1.1 Reduced Scale Barge Bow Specimens ................................ .............................. 137 6.1.2 Barge Bow Reaction Frame ................................ ................................ ............... 138 6.1.3 Universal Pen dulum Foundation ................................ ................................ ....... 139 6.1.4 Impact Block and Cable Support Frame ................................ ........................... 142 6.2 Measured Quantities for Validation ................................ ................................ ............... 143 6.3 Instrumentation Plan ................................ ................................ ................................ ...... 144 7 REVISED RISK ANALYSIS PROCEDURES FOR VESSEL IMPACT WITH BRIDGES ................................ ................................ ................................ ............................. 155

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7 7.1 Options for Implementing UF/FDOT Research in Design Practice .............................. 155 7.1.1 Simplified LRFD Approach to Vessel Collision Design ................................ .. 156 7.1.2 Targeted Revisions to AASHTO Risk Assessment Procedure ......................... 157 7.1.3 Ship Impact Considerations ................................ ................................ ............... 159 7.2 O verview of Revised Risk Analysis Procedure ................................ ............................. 160 7.3 Use of UF/FDOT PC Expression in Design ................................ ................................ .. 161 8 VESSEL COLLISION RISK ASSESSMENT OF THE BRYANT GRADY PATTON BRIDGE (SR 300) OVER APALACHICOLA BAY, FLORIDA ................................ ....... 167 8.1 Data Collection ................................ ................................ ................................ .............. 168 8.2 Waterway Characterist ics ................................ ................................ .............................. 169 8.2.1 General Description ................................ ................................ ........................... 169 8.2.2 Navigation Channel ................................ ................................ ........................... 170 8.2.3 Tide Levels and Tidal Range ................................ ................................ ............. 170 8.2.4 Currents ................................ ................................ ................................ ............. 171 8.2.5 Water Depths ................................ ................................ ................................ ..... 171 8.3 Bridge Characteristics ................................ ................................ ................................ .... 173 8.3.1 Bridge Piers ................................ ................................ ................................ ....... 173 8.3.2 Superstructure ................................ ................................ ................................ .... 175 8.3.3 Soil Conditions ................................ ................................ ................................ .. 176 8.3.4 Finite Element Models ................................ ................................ ...................... 177 8.4 Vessel Fleet Characteristics ................................ ................................ ........................... 177 8.4.1 Vessel Categories ................................ ................................ .............................. 178 8.4.2 Vessel Traffic Growth ................................ ................................ ....................... 179 8.4 .3 Vessel Transit Speeds ................................ ................................ ........................ 179 8.4.4 Vessel Transit Path ................................ ................................ ............................ 180 8.5 Vessel Impact Criteria ................................ ................................ ................................ ... 181 8.5.1 General Requirements ................................ ................................ ....................... 181 8.5.2 Extreme Event Load Combinations (Scour) ................................ ...................... 182 8.5.3 Minimum Impact Load Criteria ................................ ................................ ......... 182 8.5.4 Maximum Impact Load Criteria ................................ ................................ ........ 183 8.5.5 Operational Classification ................................ ................................ ................. 183 8.6 Maximum Impact Load (Method II) Analysis Methodology ................................ ........ 184 8.6.1 Annual Frequency of Collapse ( AF ) ................................ ................................ .. 184 8.6.2 Vessel Frequency ( N ) ................................ ................................ ........................ 185 8.6.3 Probability of Aberrancy ( PA ) ................................ ................................ ........... 186 8.6.4 Geometric Probability ( PG ) ................................ ................................ .............. 188 8.6.5 Probability of Collapse ( PC ) ................................ ................................ ............. 188 8.6.5.1 AASHTO methods ................................ ................................ .............. 190 8.6.5.1.1 A ASHTO 1991 barge impact load model (as designed) ..... 192 8.6.5.1.2 AASHTO 2009 barge impact load model ........................... 193 8.6.5.2 UF/FDOT methods ................................ ................................ ............. 193 8.6.5.2.1 CVIA structural analysis ................................ ...................... 194 8.6.5.2.2 AVIL structural analysis ................................ ...................... 196 8.6.5.2.3 SBIA structural analysis ................................ ...................... 197 8.6.6 Protection Factor ( PF ) ................................ ................................ ....................... 199

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8 8.7 Risk Analysis Results ................................ ................................ ................................ .... 202 8.7.1 AASHTO Methods ................................ ................................ ............................ 202 8.7.1.1 AASHTO 1991 barge impact load model (as designed) .................... 202 8.7.1.2 AASHTO 2009 barge impact load model ................................ ........... 204 8.7.2 UF/FDOT Methods ................................ ................................ ........................... 207 8.7.2.1 CVIA ................................ ................................ ................................ ... 207 8.7.2.2 AVIL ................................ ................................ ................................ ... 210 8.7.2.3 SBIA ................................ ................................ ................................ .... 211 8.8 Discussion of Results ................................ ................................ ................................ ..... 213 8.9 Suggestions for Mitigating Risk ................................ ................................ .................... 215 8.10 Summary ................................ ................................ ................................ ...................... 217 9 VESSEL COLLISION RISK ASSESS MENT OF THE LOUISIANA HIGHWAY 1 (LA 1) BRIDGE OVER BAYOU LAFOURCHE, LOUISIANA ................................ ....... 244 9.1 Data Collection ................................ ................................ ................................ .............. 245 9.2 Waterway Character istics ................................ ................................ .............................. 246 9.2.1 General Description ................................ ................................ ........................... 246 9.2.2 Navigation Channel ................................ ................................ ........................... 246 9.2.3 Tide Levels and Tidal Range ................................ ................................ ............. 246 9.2.4 Currents ................................ ................................ ................................ ............. 247 9.2.5 Water Depths ................................ ................................ ................................ ..... 247 9.3 Bridge Characteristics ................................ ................................ ................................ .... 247 9.3.1 Bridge Piers ................................ ................................ ................................ ....... 249 9.3.2 Superstructure ................................ ................................ ................................ .... 250 9.3.3 Soil Conditions ................................ ................................ ................................ .. 251 9.3.4 Finite Element Models ................................ ................................ ...................... 252 9.4 Vessel Fleet Characteristics ................................ ................................ ........................... 253 9.4.1 Vessel Categories ................................ ................................ .............................. 253 9.4.2 Vessel Traffic Growth ................................ ................................ ....................... 254 9.4.3 Vessel Transit Speeds ................................ ................................ ........................ 254 9.4.4 Vessel Transit Path ................................ ................................ ............................ 254 9.5 Vessel Impact Criteria ................................ ................................ ................................ ... 255 9.5.1 General Requirements ................................ ................................ ....................... 255 9.5.2 Extreme Event Load Combinations (Scour) ................................ ...................... 256 9.5.3 Minimum Impa ct Load Criteria ................................ ................................ ......... 256 9.5.4 Maximum Impact Load Criteria ................................ ................................ ........ 256 9.5.5 Operational Classification ................................ ................................ ................. 257 9.6 Maximum Impact Load (Method II) Analysis Methodology ................................ ........ 257 9.6.1 Annual Frequency of Collapse ( AF ) ................................ ................................ .. 258 9.6.2 Vessel Frequency ( N ) ................................ ................................ ........................ 259 9.6.3 Probability of Aberrancy ( PA ) ................................ ................................ ........... 259 9.6.4 Geometric Probability ( PG ) ................................ ................................ .............. 261 9.6.5 Probability of Collapse ( PC ) ................................ ................................ ............. 262 9.6.5.1 AASHTO methods ................................ ................................ .............. 264 9.6.5.1. 1 AASHTO 1991 barge impact load model (as designed) ..... 265 9.6.5.1.2 AASHTO 2009 barge impact load model ........................... 266

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9 9.6.5.2 UF/FDOT method s ................................ ................................ ............. 266 9.6.5.2.1 CVIA structural analysis ................................ ...................... 267 9.6.5.2.2 AVIL structural analysis ................................ ...................... 269 9.6.6 Protection Factor ( PF ) ................................ ................................ ....................... 270 9.7 Risk Analysis Results ................................ ................................ ................................ .... 270 9.7.1 AASHTO Methods ................................ ................................ ............................ 270 9.7.1.1 AASHTO 1991 barge impact load model (as designed) .................... 270 9.7.1.2 AASHTO 2009 barge impact load model ................................ ........... 272 9.7.2 UF/FDOT Methods ................................ ................................ ........................... 274 9.7.2.1 CVIA ................................ ................................ ................................ ... 274 9.7.2.2 AVIL ................................ ................................ ................................ ... 276 9.8 Discussion of Results ................................ ................................ ................................ ..... 277 9.9 Suggestions for Mitigating Risk ................................ ................................ .................... 280 9.9.1 Pier Footing Retrofit ................................ ................................ .......................... 281 9.9.2 Pier Protection System ................................ ................................ ...................... 282 9.9.3 Alternative Foundation Design ................................ ................................ .......... 283 9.10 Summary ................................ ................................ ................................ ...................... 286 10 CONCLUSIONS AND RECOMMENDATIONS ................................ ............................... 309 10.1 Concluding Remarks ................................ ................................ ................................ ... 309 10.2 Recommendations for Bridge Design ................................ ................................ .......... 315 10.3 Recommendations for Future Research ................................ ................................ ....... 316 APPENDIX A REV IEW OF EUROCODE PROCEDURES FOR VESSEL COLLISION ........................ 319 A.1 Risk Assessment ................................ ................................ ................................ ........... 319 A.2 Risk Acceptance Criteria ................................ ................................ .............................. 322 A.3 Vessel Impact Forces on Bridge Piers ................................ ................................ .......... 325 A.3.1 Barge Impact ................................ ................................ ................................ ..... 327 A.3.2 Ship Impa ct ................................ ................................ ................................ ........ 330 B DERIVATION OF SCALE MODEL SIMILITUDE EXPRESSIONS ............................... 331 C PENDULUM BASED HIGH RATE TEST APPARATUS (HRTA) FABRICATION DRAWI NGS ................................ ................................ ................................ ......................... 333 D DEMONSTRATION OF IMPULSE MOMENTUM THEORY FOR MULTIPLE DEGREE OF FREEDOM (MDF) SYSTEMS ................................ ................................ ..... 358 E SENSITIVITY OF REDUCED SCA LE BARGE IMPACT SIMULATION RESULTS TO STEEL FAILURE STRAIN ................................ ................................ ........................... 361 E.1 Barge Impact Simulations ................................ ................................ ............................. 361 E.2 Results and Discussion ................................ ................................ ................................ .. 363

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10 F REDUCED SCALE (0.4 SCALE) BARGE BOW FABRICATION DRAWINGS ........... 366 G BARGE BOW REACTION FRAME FABRICATION DRAWINGS ................................ 392 H UNIVERSAL PENDULUM FOUNDATION FABRICATION DRAWINGS ................... 405 I CONSIDERATION OF LRFD APPROACH TO VESSEL COLLISION DESIGN .......... 425 I.1 AASHTO Vessel Collision Risk Assessment ................................ ................................ 425 I.2 LRFD Calibration Methodology ................................ ................................ .................... 426 I.3 Applicability of LRFD Procedures to AASHTO Acceptable Vessel Collision Risk ..... 427 I.4 Summary ................................ ................................ ................................ ........................ 430 J SR 300 BRIDGE VESSEL COLLI SION RISK ASSESSMENT DATA ............................ 433 K LA 1 BRIDGE VESSEL COLLISION RISK ASSESSMENT DATA ............................... 469 LIST OF REFERENCES ................................ ................................ ................................ ............. 498 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 502

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11 LIST OF TABLES Table Page 4 1 Summary of experimental testing parameters and n umber of repetitions ....................... 104 4 2 Rate sensitivity parameters and impulse ratio ( IR ) statistics ................................ ........... 104 4 3 Effective plastic strain at f ailure for each material series ................................ ................ 104 5 1 Summary of barge bow impact response data (flat block) ................................ .............. 129 5 2 Comparison of constitutiv e model parameters ................................ ................................ 129 5 3 Summary of barge bow impact response data (rounded block) ................................ ....... 129 6 1 Instrumentation to be used during b arge bow impact experiments ................................ 146 8 1 Upbound vessel traffic for Apalachicola Bay ................................ ................................ .. 220 8 2 Downbound vessel traffic for Apalachicol a Bay ................................ ............................. 220 8 3 Aggregated vessel traffic data for vessel collision risk assessment ................................ 220 8 4 Footing geometry and projected pier wi dth ( B P ) for each pier ................................ ........ 221 8 5 Minimum lateral pushover capacities ( H ) for each pier ................................ .................. 221 8 6 Barge impact parameters for CVIA ................................ ................................ ................. 221 8 7 Lateral pier soil stiffness ( k P ) for each SR 300 pier ................................ ........................ 221 8 8 Maximum barge impact force ( P Bm ) (kips) for each pier and ba rge vessel group ........... 222 8 9 Input parameters for SBIA IRF equations ................................ ................................ ....... 223 8 10 IRF values for SBIA Load Case 1 ................................ ................................ ................... 223 8 11 Summary of risk assessment results for each analysis procedure considered ................. 224 9 1 Vessel traffic for LA 1 Bridge ................................ ................................ ......................... 289 9 2 Aggregated barge traffic data for LA 1 Bridge ................................ ............................... 290 9 3 Minimum lateral pushover capacities ( H ) for each pier ................................ .................. 291 9 4 Barge impact parameters for CVIA ................................ ................................ ................. 291 9 5 Lateral pier soil stiffness ( k P ) for each LA 1 pier ................................ ............................ 291

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12 9 6 Maximum dynamic impact force ( P Bm ): UF/FDOT methods (AVIL) ............................ 291 9 7 Protection factors ( PF ) ................................ ................................ ................................ ..... 292 9 8 Summary of risk assessme nt results for each analysis procedure considered ................. 292 9 9 Comparison of barge yield forces ( P BY ) for as built and retrofitted designs ................... 292 9 10 Comparison of barge yield forces ( P BY ) for as built and alternative designs .................. 292 9 11 Summary of UF/FDOT (CVIA) risk assessment results for each design considered ...... 292 A 1 Indicative values for dynamic forces due to ship impact on inland waterways ............... 3 26 A 2 Indicative values for dynamic forces due to ship im pact for sea waterways ................... 326 E 1 Effective plastic strain at failure for each material series ................................ ................ 361 I 1 Pier reliability index (75 y ear ) for various numbers of piers ................................ ....... 429 I 2 Comparison of LRFD and AASHTO vessel collision design methodologies ................. 431 J 1 Vessel i mpact velocities ( v i ) (knots) ................................ ................................ ................ 433 J 2 Geometric probability of impact ( PG ) ................................ ................................ ............. 434 J 3 Vessel impact forces (kips): AASHTO (1991) me thods ................................ ................. 434 J 4 Capacity demand ratios ( H / P ): AASHTO (1991) methods ................................ ............. 435 J 5 Probability of collapse ( PC ): AASHTO (1991) methods ................................ ................ 435 J 6 Vessel impact forces (kips): AASHTO (2009) methods ................................ ................. 436 J 7 Capacity demand ratios ( H / P ): AASHTO (2009) methods ................................ ............. 436 J 8 Probability of collapse ( PC ): AASHTO (2009) methods ................................ ................ 437 J 9 Maximum vessel impact forces (kips): UF/FDOT methods (CVIA) .............................. 437 J 10 Demand capacity ratios ( D / C ): UF/FDOT methods (CVIA ) ................................ .......... 438 J 11 Probability of collapse ( PC ): UF/FDOT methods (CVIA) ................................ .............. 438 J 12 Maximum vessel impact forces (kips): UF/FDOT methods (AVIL) ............................... 439 J 13 Demand capacity ratios ( D / C ): UF/FDOT methods (AVIL) ................................ ........... 439 J 14 Probability of collapse ( PC ): UF/FDOT methods (AVIL) ................................ .............. 440

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13 J 15 Maximum vessel impact forces (kips): UF/FDOT methods (SBIA) ............................... 440 J 16 Demand capacity ratios ( D / C ): UF/FDOT methods (SBIA) ................................ ........... 441 J 17 Probability of collapse ( PC ): UF/FDOT methods (SBIA) ................................ .............. 441 J 18 Protection factor ( PF ) ................................ ................................ ................................ ...... 442 K 1 Vessel impact velocities ( v i ) (knots) ................................ ................................ ................ 469 K 2 Geometric probability of impact ( PG ) ................................ ................................ ............. 470 K 3 Barge impact forces (kips): AASHTO (1991) methods ................................ .................. 470 K 4 Capacity demand ratios ( H / P ): AASHTO (1991) methods ................................ ............. 471 K 5 Probability of collapse ( PC ): AASHTO (1991) methods ................................ ................ 471 K 6 Barge impact forces (kip s): AASHTO (2009) methods ................................ .................. 472 K 7 Capacity demand ratios ( H / P ): AASHTO (2009) methods ................................ ............. 472 K 8 Probability of collapse ( PC ): AASH TO (2009) methods ................................ ................ 473 K 9 Minimum of barge width ( B B ) and pier width ( B P ) (ft) ................................ ................... 473 K 10 Barge yield force ( P BY ) (kip) ................................ ................................ ........................... 474 K 11 Maximum barge impact forces ( P Bm ) (kip): UF/FDOT methods (CVIA) ....................... 474 K 12 Demand capacity ratios ( D / C ): UF/FDOT methods (CVIA) ................................ .......... 475 K 13 Probability of collapse ( PC ): UF/FDOT methods (CVIA) ................................ .............. 475 K 14 Maximum dynamic impact force ( P Bm ): UF/FDOT methods (AVIL) ............................ 476 K 15 Demand capacity ratios ( D / C ): UF/FDOT methods (AVIL) ................................ ........... 476 K 16 Probability of collapse ( PC ): UF/FDOT methods (AVIL) ................................ .............. 477

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14 LIST OF FIGURES Figure Page 2 1 Determination of geometric probability of impact ( PG ) with a bridge pier ...................... 55 2 2 Determination of probability of collapse ( PC ) ................................ ................................ .. 55 2 3 Full scale barge impact experiments at St. George Island, Florida ................................ ... 56 2 4 Coupled vessel impact analysis (CVIA) ................................ ................................ ............ 56 2 5 AASHTO barge bow force deformation curve: P B a B ................................ ...................... 57 2 6 UF/ FDOT barge bow force deformation model ................................ ................................ 58 2 7 Dynamic amplification of pier column moments sorted by amplification mode .............. 59 2 8 A pplied vessel impact loading (AVIL) ................................ ................................ .............. 60 2 9 Impact response spectrum analysis (IRSA) ................................ ................................ ....... 61 2 10 Static bracketed impact analysis (SB IA) ................................ ................................ ........... 62 2 11 Revised probability of collapse expression ................................ ................................ ........ 63 3 1 Impact pendulum at M.H. Ansley Structures Re search Center in Talla hassee, FL ........... 73 3 2 Test setup for barge bow impact experiments ................................ ................................ ... 73 3 3 Rendering of reduced scale barge bow specimen showing inter nal truss structure .......... 74 3 4 Rendering of barge bow finite element model with flat faced pendulum impact block and reaction frame (mesh not shown for clarity) ................................ ............................... 74 3 5 Barge bow finite element model showing mesh density ................................ ................... 75 3 6 Finite element barge bow deformations after successive impa cts from flat faced impact block ................................ ................................ ................................ ....................... 75 4 1 Quasi static testing ................................ ................................ ................................ ........... 105 4 2 Impact pendulum facility at Florida Department of Transportation (FDOT) Structures Research Cente r in Tallahassee, Florida ................................ ......................... 105 4 3 Depictions of impact scenarios in tension testing that rely on impact energy for specimen elongation ................................ ................................ ................................ ......... 106 4 4 High rate testing apparatus (HRTA) design ................................ ................................ ..... 106

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1 5 4 5 High rate testing apparatus (HRTA) motions ................................ ................................ .. 107 4 6 High rate te sting. A) Specimen dimensions and gage marks ................................ .......... 107 4 7 Strain displacement relation for test A1011 T11 R1 B, including parabolic fit ............. 108 4 8 High rate test apparatus (HRTA) as a damped SDF oscillator ................................ ........ 108 4 9 Impulse momentum based optimization procedure for computing Cowper Symonds coefficients C and P ................................ ................................ ................................ ......... 109 4 10 Stretching and scaling of av erage R1 stress strain relation to arrive at dynamic stress strain relation for each test, following procedure shown in Fig. 4 9 ............................... 109 4 11 Engineering stress strain curves for each quasi static test series ................................ ..... 110 4 12 Rate sensitivity of material parameters among quasi static testing rates ........................ 111 4 13 Engineering strain rate (among three tests per trace) as a function of strain ................... 112 4 14 Engineering stress strain curves (computed by the process in Figs. 4 9 and 4 10) for each high rate test series ................................ ................................ ................................ .. 113 4 15 Specimen and reaction force time histories (computed by process in Fig. 4 9) for selected tests ................................ ................................ ................................ ..................... 114 4 16 Specimen and reaction impulse time histories (computed by process in Fig. 4 9) for selected tests ................................ ................................ ................................ ..................... 114 4 17 Normalized histograms of impulse ratio ( IR ) for each material series (computed by process in Fig. 4 9) ................................ ................................ ................................ .......... 115 4 18 Sensitivity of dynamic stress to strain rate for each material test series .......................... 116 4 19 Comparison of experimentaal data to Manjoine (1944) study ................................ ......... 117 4 20 Static constitutive curves developed for the MAT_24 material model in LS DYNA ...... 117 5 1 Finite element impact simulation of 0.4 scale barge bow (rounded impact block shown) ................................ ................................ ................................ .............................. 130 5 2 Maximum barge bow deformation caused by each successive impact (flat block) ......... 130 5 3 Barge impact simulation data (flat block). A) Deformation time history ....................... 131 5 4 Empi rical CDF of impact force data from first pendulum impact event ......................... 132 5 5 Comparison of maximum barge bow deformation (flat faced block) ............................. 132

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16 5 6 Comparison of barge bow force deformation curves (flat faced block) ......................... 133 5 7 Maximum barge bow deformation caused by each successive impact (rounded block) 133 5 8 Barge impact simulation data (rounded block) ................................ ................................ 134 5 9 Comparison of maximum barge bow deformation (rounded block) ............................... 135 5 10 Comparison of barge bow force deformation curves (rounded block) ............................ 135 5 11 Comparison of high severity barge bow deformation ................................ ..................... 136 6 1 Test setup for barge bow impact experiments ................................ ................................ 146 6 2 Rendering of reduced scale barge bow specimen showing internal truss structure ........ 147 6 3 Exploded view of barge bow hull plates and internal components ................................ 147 6 4 Exploded view of connection between barge bow specimen and rea ction frame ........... 148 6 5 Reaction frame structural members and general dimensions ................................ .......... 1 48 6 6 Universal pendulum impact foundation: plan view dimensions ................................ ...... 149 6 7 Embedded foundation anchor connection system ................................ ............................ 150 6 8 Site plan for universal pendulum impact foundation ................................ ....................... 151 6 9 Universal pendulum foundation construction stages (viewed from northwest corner) ... 152 6 10 Impact block and cable support frame: exploded view ................................ ................... 153 6 11 Instrumentation layout to be used in barge bow impact experiments .............................. 154 7 1 Current AASHTO vessel c ollision risk assessment procedure ................................ ........ 165 7 2 Revised UF/FDOT vessel collision risk assessment workflow ................................ ....... 166 7 3 Possible pier colla pse mechanisms ................................ ................................ .................. 166 8 1 Bryant Grady Patton Bridge (SR 300) spanning Apalachicola Bay, Florida .................. 224 8 2 High rise portion of SR 30 0 Bridge, showing potential navigational obstructions ......... 225 8 3 Current velocities in Apalachicola Bay at various tidal stages ................................ ........ 226 8 4 Nautical chart including water depth soundings at MLLW ................................ ............. 227 8 5 High rise portion of SR 300 Bridge, showing piers at risk for impact ............................ 227

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17 8 6 Pier and foundation configurations for SR 300 Bridge ................................ ................... 228 8 7 Typical barge impact scenarios, showing possible headlog elevations ........................... 228 8 8 Overview of bridge span configurations ................................ ................................ .......... 229 8 9 Superstructure cross sections for the SR 300 Bridge ................................ ...................... 229 8 10 Locations of soil borings and piers to which each soil profile is assigned ...................... 229 8 11 FB MultiPier models of selected piers from SR 300 Bridge ................................ ........... 230 8 12 Computing the geometric probability of impact ( PG ) ................................ ..................... 231 8 13 Coupled vessel impact analysis (CVIA) method ................................ ............................. 231 8 14 Typical barge impact with pile cap, showing pertinent impact parameters ..................... 231 8 15 Applied vessel impact load (AVIL) method ................................ ................................ .... 232 8 16 Procedure for computing barge impact force time histories in accordance with AVIL method ................................ ................................ ................................ .............................. 233 8 17 Determination of lateral pier soil stiffness ( k P ) by static analysis ................................ ... 234 8 18 Static load cases for SBIA method ................................ ................................ .................. 235 8 19 Determination of lateral superstructure stiffness ( k sup ) ................................ .................... 236 8 20 Procedure for computing the probability that a navigational obstruction (island) will cause vessel grounding prior to pier impact ( P Gr ) based on its orientation and path to the pier ................................ ................................ ................................ ............................. 236 8 21 Procedure for computing P Gr for old bridge (fishing pier) navigational obstruction ...... 237 8 22 Risk analysis results for each pier and vessel group: A ASHTO (1991) methods ........... 238 8 23 Percent contribution to AF : AASHTO (1991) methods ................................ .................. 238 8 24 Risk analysis results for each pier and vessel group: AASHTO (2009) methods ........... 239 8 25 Percent contribution to AF : AASHTO (2009) methods ................................ .................. 239 8 26 Risk analysis results f or each pier and vessel group: UF/FDOT methods, CVIA ........... 240 8 27 Percent contribution to AF : UF/FDOT methods, CVIA ................................ .................. 240 8 28 Risk an alysis results for each pier and vessel group: UF/FDOT methods, AVIL ........... 241

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18 8 29 Percent contribution to AF : UF/FDOT methods, AVIL ................................ .................. 241 8 30 Risk analysis results for each pier and vessel group: UF/FDOT methods, SBIA ........... 242 8 31 Percent contribution to AF : UF/FDOT methods, SBIA ................................ ................... 242 8 32 SR 300 Bridge pier footing end cap retrofit to reduce vessel collision risk .................... 243 8 33 SR 300 Bridge pier alternative design with foundation consisting of (2) 9 ft diame ter drilled shafts, connected by a strut or shear wall ................................ ............................. 243 9 1 Louisiana Highway 1 (LA 1) Bridge over Bayou Lafourche, Louisiana ........................ 293 9 2 LA 1 Bridge region of interest, showing navigation channel alignment ......................... 293 9 3 High rise portion of LA 1 Bridge, showing piers at risk for impact ............................... 294 9 4 Pier and foundation configurations for LA 1 Bridge ................................ ....................... 295 9 5 Typical barge impact scenarios, showing possible headlog elevations ........................... 295 9 6 Overvie w of bridge span configurations ................................ ................................ .......... 296 9 7 Superstructure cross sections for the LA 1 Bridge ................................ .......................... 296 9 8 Locations of soil borings and piers to which each soil profile is assigned ...................... 296 9 9 FB MultiPier models of selected piers from LA 1 Bridge ................................ .............. 297 9 10 Computing the geometric probability of impact ( PG ) ................................ ..................... 297 9 11 Coupled vessel impact analysis (CVIA) method ................................ ............................. 298 9 12 Typical barge impact with pile cap, showing pertinent impact parameters ..................... 298 9 13 Applied vessel impact load (AVIL) method ................................ ................................ .... 298 9 14 Procedure for computing barge impact force time histories in accordance with AVIL method ................................ ................................ ................................ .............................. 299 9 15 Determination of lateral pier soil stiffness ( k P ) by static analysis ................................ ... 300 9 16 Risk analysis results for each pier and vessel group: AASHTO (1991) methods ........... 301 9 17 Percent contribution to AF : AASHTO (1991) methods ................................ .................. 301 9 18 Risk analysis results for each pier and vessel group: AASHTO (2009) methods ........... 302 9 19 Percent contributi on to AF : AASHTO (2009) methods ................................ .................. 302

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19 9 20 Risk analysis results for each pier and vessel group: UF/FDOT methods, CVIA ........... 303 9 21 Pe rcent contribution to AF : UF/FDOT methods, CVIA ................................ .................. 303 9 22 Risk analysis results for each pier and vessel group: UF/FDOT methods, AVIL ........... 304 9 23 Percent contribution to AF : UF/FDOT methods, AVIL ................................ .................. 304 9 24 LA 1 Bridge pier footing end cap retrofit to reduce vessel collision risk ....................... 305 9 25 Plan view of LA 1 Bridge showing locations of protective dolphin structures ............... 305 9 26 LA 1 Bridge alternative design with drilled shaft foundation: piers 2 4 ...................... 306 9 27 LA 1 Bridge alternative design with drilled shaft foundation: piers 96 97 .................. 307 A 1 Eurocode risk assessment framework ................................ ................................ .............. 321 A 2 Possible n umerical risk acceptance scheme ................................ ................................ ..... 324 A 3 Eurocode head on impact case ................................ ................................ ......................... 326 A 4 Eurocode glancing (lateral) impact case ................................ ................................ .......... 327 A 5 Head on barge impact force comparison: AASHTO vs. Eurocode ................................ 328 A 6 Eurocode sample force time histories ................................ ................................ .............. 329 D 1 Four degree of freedom system with damping, subject to dynamic excitation by time varying specimen resultant force F S ( t ) ................................ ................................ .... 358 E 1 Finite element impact simulation of 0.4 scale barge bow ................................ ............... 362 E 2 Comparison of barge bow deformation after one impact ................................ ................ 364 E 3 Barge bow force deformation comparison ................................ ................................ ...... 364 J 1 Impact force time histories: SR 300 Bridge, Pier 35 ................................ ....................... 443 J 2 Impact force time histories: SR 300 Bridge, Pier 36 ................................ ....................... 444 J 3 Impact force time histories: SR 300 Bridge, Pier 37 ................................ ....................... 445 J 4 Impact force time histories: SR 300 Bridge, Pier 38 ................................ ....................... 446 J 5 Impact force time histories: SR 300 Bridge, Pier 39 ................................ ....................... 447 J 6 Impact force time histories: SR 300 Bridge, Pier 40 ................................ ....................... 44 8 J 7 Impact force time histories: SR 300 Bridge, Pier 41 ................................ ....................... 449

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20 J 8 Impact force time histories: SR 300 Bridge, Pier 42 ................................ ....................... 450 J 9 Impact force time histories: SR 300 Bridge, Pier 43 ................................ ....................... 451 J 10 Impact force time histories: SR 300 Bridge, Pier 44 ................................ ....................... 452 J 11 Impact force time histories: SR 300 Bridge, Pier 45 ................................ ....................... 453 J 12 Im pact force time histories: SR 300 Bridge, Pier 46 ................................ ....................... 454 J 13 Impact force time histories: SR 300 Bridge, Pier 47 ................................ ....................... 455 J 14 Impact f orce time histories: SR 300 Bridge, Pier 48 ................................ ....................... 456 J 15 Impact force time histories: SR 300 Bridge, Pier 49 ................................ ....................... 457 J 16 Impact force t ime histories: SR 300 Bridge, Pier 50 ................................ ....................... 458 J 17 Impact force time histories: SR 300 Bridge, Pier 51 ................................ ....................... 459 J 18 Impact force time hi stories: SR 300 Bridge, Pier 52 ................................ ....................... 460 J 19 Impact force time histories: SR 300 Bridge, Pier 53 ................................ ....................... 461 J 20 Impact force time historie s: SR 300 Bridge, Pier 54 ................................ ....................... 462 J 21 Impact force time histories: SR 300 Bridge, Pier 55 ................................ ....................... 463 J 22 Impact force time histories: SR 300 Bridge, Pier 56 ................................ ....................... 464 J 23 Impact force time histories: SR 300 Bridge, Pier 57 ................................ ....................... 465 J 24 Impact force time histories: SR 300 Br idge, Pier 58 ................................ ....................... 466 J 25 Impact force time histories: SR 300 Bridge, Pier 59 ................................ ....................... 467 J 26 Impact force time histories: SR 300 Bridge, Pier 60 ................................ ....................... 468 K 1 Impact force time histories: LA 1 Bridge, Pier 2, upbound traffic, fully loaded ............ 478 K 2 Impact force time histor ies: LA 1 Bridge, Pier 2, upbound traffic, lightly loaded ......... 479 K 3 Impact force time histories: LA 1 Bridge, Pier 2, downbound traffic, fully loaded ....... 480 K 4 Impact force time histories: LA 1 Bridge, Pier 2, downbound traffic, lightly loaded .... 481 K 5 Impact force time histories: LA 1 Bridge, Pier 3, upbound traffic, fully loaded ............ 482 K 6 Impact force time histories: LA 1 Bridge, Pier 3, upbound traffic, lightly loaded ......... 483

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21 K 7 Impact force time hist ories: LA 1 Bridge, Pier 3, downbound traffic, fully loaded ....... 484 K 8 Impact force time histories: LA 1 Bridge, Pier 3, downbound traffic, lightly loaded .... 485 K 9 Impact force time histories: LA 1 Bridge, Pier 4, upbound traffic, fully loaded ............ 486 K 10 Impact force time histories: LA 1 Bridge, Pier 4, upbound traffic, ligh tly loaded ......... 487 K 11 Impact force time histories: LA 1 Bridge, Pier 4, downbound traffic, fully loaded ....... 488 K 12 Impact force time histories: LA 1 Bridge, Pier 4, downbound traffic, lightly loaded .... 489 K 13 Impact force time histories: LA 1 Bridge, Pier 96 upbound traffic, fully loaded .......... 490 K 14 Impact force time histories: LA 1 Bridge, Pier 96, upbound traffic, lightly loaded ....... 491 K 15 Impact force time histories: LA 1 Bridge, Pier 96, downbound t raffic, fully loaded ..... 492 K 16 Impact force time histories: LA 1 Bridge, Pier 96, downbound traffic, lightly loaded .. 493 K 17 Impa ct force time histories: LA 1 Bridge, Pier 97, upbound traffic, fully loaded .......... 494 K 18 Impact force time histories: LA 1 Bridge, Pier 97, upbound traffic, lightly loaded ....... 495 K 19 Impact force time histories: LA 1 Bridge, Pier 97, downbound traffic, fully loaded ..... 496 K 20 Impact force time histories: LA 1 Bridge, Pier 97, downbound traffic, lightly loaded .. 497

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22 L IST O F ABBREVIATIONS a Acceleration a B Barge bow damage depth a B Y Barge bow yield deformation a ( t ) Time varying acceleration A S,o Original cross sectional area of specimen AF Annual frequency of bridge collapse AFI Annual frequency of vessel impact B B Width of barge B M Width of vessel (beam) B P Projected w idth of pier BR Base rate of aberrancy C Damping coefficient C Cowper Symonds coefficient C H Hydrodynamic mass coefficient D / C Dem and to capacity ratio D / C FBMP Element level demand to capacity ratio as reported by FB MultiPier DWT Deadweight tonnage of ship F Force F R ( t ) Time varying reaction force F S ( t ) Time varying force imparted by specimen E fs Full scale energy E m Model scale ene rgy h P Clear height of pier columns IR Impulse ratio

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23 IRF Inertial restraint factor IRF b Inertial restraint factor for bearing shear forces IRF m Inertial restraint factor for pier moments IRF v Inertial restraint factor for pier shear forces J R Reaction impu lse J S Specimen impulse k P Lateral translational pier soil stiffness k S Series barge pier soil stiffness k sup Superstructure stiffness KE Kinetic energy L P Length of pier footing perpendicular to bridge alignment L sup Average length of adjacent spans LOA O verall vessel length m Number of members associated with a given collapse mechanism m Mass m 1 Mass of striker m 2 Mass of anvil m B Mass of barge M Mass n Number of hinges per member necessary to form a collapse mechanism N Annual number of vessel transits N BE Number of bridge elements N P Number of piers N VG Number of vessel groups P Design impact foce

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24 P Cowper Symonds coefficient P B Barge impact force P Bm Maximum dynamic barge impact force P B Y Barge bow yield force P fs Full scale force P Gr Probability of ves sel grounding P m Model scale force P S Ship impact force PA Probability of vessel aberrancy PC Probability of collapse PF Protection factor PG Geometric probability of impact R B Barge width correction factor R B Correction factor for bridge location R C Corre ction factor for parallel currents R RD Correction factor for vessel traffic density R XC Correction factor for cross currents T I Impact load duration u ( t ) Time varying displacement V Vessel impact velocity V C Current velocity parallel to the navigation chan nel V XC Current velocity perpendicular to the navigation channel v 1,o Initial velocity of striker v 1,f Final velocity of striker v 2,o Initial velocity of anvil

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25 v 2,f Final velocity of anvil v Bi Initial barge impact velocity v ( t ) Time varying velocity w P Pie r surface width W P Width of pier footing parallel to the bridge alignment W P Weight of pier W sup Weight of superstructure Ratio between full scale and model scale Strain p Effective plastic strain Maximum strain from dynami c stress strain curve Maximum strain from static stress strain curve Strain rate Effective plastic strain rate Average strain rate for R1 test s eries as a function of strain Displacement fs Full scale displacement m Model scale displacement sup Superstructure displacement Smallest angle between vessel and bridge pier alignment Mean vessel orientation Vessel orientation P Vessel orientation that would result in pie r impact dyn Dynamic stress

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26 st Static stress Standard deviation of vessel orientation Dynamic stress strain relation Average stress for R1 test series as a function of strain Static stress strain relation

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27 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 VALIDATION AND IMPLEMENTATION OF BRIDGE DESIGN SPECIFICATIONS FOR BARGE IMPACT LOADING By Daniel James Getter August 2013 Chair: Gary Consolazio Major: Civil Engineering Since 1991 in the United States, the design of highway bridges to resist collisions by errant waterway vessels h as been carried out in accordance with design provisions published by AASHTO These provisions have remained largely unchanged for more than 20 years, whi le numerous studies in recent years conducted by researchers at the University of Florida (UF) and the Florida Department of Transportation (FDOT) have greatly improved upon the analysis procedures in the AASHTO provisions The focus of the work discussed in this dissertation was to experimentally validate the improved UF/FDOT barge impact load prediction model and implement numerous other UF/FDOT procedures into a comprehensive risk assessment methodology that can be readily adopted for use in bridge design. To validate the UF/FDOT barge impact load model, a series of impact exper iments were planned, in wh ich reduced scale replica s of a typical barge bow will be impacted by a high energy impact pendulum to produce large scale barge deformations This dissertation discusses the planning of the exp erimental study and the design of the various experimental component s. In support of the validation effort a material testing program was carried out in order to characterize the strain rate sensitive properties of steel materials from which the reduced scale

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28 barge specimens will be fabricated. Steel specimens were tested in uniaxial tension at strain rates covering seven orders of magnitude. To conduct high rate material tests, a novel test apparatus was designed and employed that used an impact pendulum to impart the required energy Data from the material testing progra m were used to develop constitutive models that were used in finite element barge impact simulations. Additionally in this study, a revised vessel collision risk assessment methodology was developed that incorporates various new UF/FDOT analysis procedures The complete methodology was demonstrated for two real world bridge cases, and the results were compared to the existing AASHTO risk assessment method. For these two cases, the revised procedure was found to predict higher levels of risk than the AASHTO procedure. However, retrofit and alternative design solutions were presented that demonstrate that, with careful design choices, the revi sed p rocedure can result i n safer and more economical bridge designs.

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29 CHAPTER 1 INTRODUCTION Any bridge that spans a navi gable waterway is at risk for accidentally being struck by waterway vessels that traverse beneath it. The severity of vessel impact loads can be sufficient to cause structural failure and collapse of supported roadway s or railway s Given the unpredictable timing of vessel collisions, such failures have the potential to result in serious injury or loss of life and therefore constitute a public safety concern Furthermore, the economic losses associated with bridge repair or replacement and interruptions of c ritical traffic channels are significant. In 1980, the Sunshine Skyway Bridge over Tampa Bay, Florida collapsed as a result of being impacted by an errant cargo ship. The incident highlighted the need for engineers to consider the vessel collision hazard when designing bridges that span navigable water, and clearly emphasized the urgent need for vessel collision design guidance. Throughout the 1980s, multiple research studies were conducted with the goal of quantifying vessel impact loads and the associate d risks of structural failure. Those studies culminated in the development of design requirements that were adopted by Association of State Highway and Transportation Officials (AASHTO) as a guide specification (AASHTO 1991 and later AASHTO 2009), and also incorporated into the main LRFD bridge design specifications (initially in AASHTO 1994 and most recently in AASHTO 2011). Therefore, since 1991, in the United States, the design of bridges to resist vessel collision loading has been governed by the variou s AASHTO vessel collision design specifications. 1.1 Motivation Development and publication of the 1991 AASHTO vessel collision design procedures was a dramatic improvement to bridge design practice and public safety, given that uniform national specifications for the design of bridges to resist vessel collision loading did not

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30 previously exist. However, the AASHTO procedures were developed at a time when structural analysis tools (e.g., software) and computing power were significantly more rudimentary than the y are today. Consequently, the AASHTO guidelines treat vessel impact as a static loading event, even though impacts are inherently dynamic in nature. At the time of the AASHTO specification development, this was a reasonable simplification, given that dyna mic analysis of bridge structures was extremely time consuming and cost prohibitive in a design setting. In the intervening years since the AASHTO vessel collision guidelines were first published, extraordinary advances in computing power have been made, coupled with corresponding improvements in the sophistication of design oriented structural analysis software. Currently, commercially available software packages can perform static analyses of multiple pier, multiple span bridge structures in seconds, eve n using typical workstation computers. Therefore, transient dynamic analyses can be completed in five minutes to one hour (depending on model fidelity and complexity). Given the ever increasing availability of such analysis capabilities, a significant prop ortion of structural engineers are now trained in the areas of structural dynamics, finite element analysis, and inelastic (nonlinear) analysis. Indeed, modal dynamic analysis is employed on a regular basis for seismic design, and transient (linear as well as nonlinear) seismic analysis is becoming increasingly common. Given the widespread availability of computing power, sophisticated structural analysis software tools, and specialized engineering expertise, it is no longer necessary to simplify dynamic ev ents, such as vessel collisions, down to simple, static loading events. In contrast to seismic (earthquake) loading events, in which structural response can be evaluated with relatively high accuracy using simplified dynamic analysis techniques like respon se spectrum analysis, accurately evaluating the response of a bridge to vessel impact

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31 loading requires consideration of a significant number of unique factors. These include the geometry, mass, and stiffness characteristics of the impacting vessel and the impacted structure, localized damage, impact velocity and direction, and the duration of the impact event. Recent research indicates that the influences that these factors have on bridge response to impact load are highly variable among different bridge co nfigurations, primarily because dynamic interactions between the vessel and bridge cause the magnitude and duration of the impact loading event to be dependent on characteristics that are specific to both the vessel and the bridge. Traditionally, only high resolution, nonlinear contact impact finite element analyses could directly account for all the various uncertainties and dynamic interactions involved. Such analyses have historically only been possible using highly specialized software tools and superco mputers. While such tools are commercially available, they are not currently (and may never be) practical for use in typical bridge design settings. To date at least, these limitations have precluded design engineers from considering the dynamic response o f bridges to vessel collisions. However, over the past several years, UF/FDOT research has significantly improved the understanding of barge bridge collisions and the nature of structural response to such collisions. As part of this past research, UF and F DOT have developed improved impact load prediction models, a variety of static and dynamic structural analysis procedures, and an improved structural reliability (probability of collapse) expression. These tools empirically, or directly, take into account the various uncertainties and interactions identified above in such a way that they can be implemented by bridge designers. Therefore, they constitute considerable improvements to existing design practice. However, the UF/FDOT impact load model has yet to be fully validated against experimental measurements, particularly at high levels of barge

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32 deformation. Furthermore, while the UF/FDOT structural analysis techniques have been extensively compared to high resolution contact impact analysis (the most accura te tool currently available) with excellent agreement, the influence of employing such techniques on design efficiency and economy has yet to be evaluated. That is, to date is has not been clear whether these new, more accurate procedures will result in in creased demands on design engineers, and increased design and construction costs; whether the opposite will be true; or whether implementation of the new procedures will be deign and construction cost neutral (in an average sense across a spectrum of multi ple bridges). 1.2 Objectives The objectives of the research presented in this dissertation were to: 1) validate the UF/FDOT load prediction model using high deformation pendulum impact experimental testing, 2) develop a unified vessel collision risk assessment methodology that incorporates the UF/FDOT impact load model, structural analysis techniques, and probability of collapse expression, 3) demonstrate use of that methodology by assessing the vessel collision risk of two recently constructed highway bridges, and 4) compare outcomes from the revised methodology to the existing AASHTO procedures. Completion of these tasks will enable implementation of past and current UF/FDOT vessel collision research results into design practice by the FDOT in Florida, and ult imately by AASHTO nationwide. 1.3 Scope of Work Plan experimental validation of barge impact load model: In two past research studies funded by FDOT (Consolazio et al. 2009, Getter and Consolazio 2011), researchers at UF developed a new barge impact load predi ction model that is a significant improvement over the model currently employed in the AASHTO provisions. In addition to being based on barge types that are common to United States waterways (the AASHTO barge provisions were based on tests

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33 conducted on Eur opean pontoon barges), the new UF/FDOT model takes into account important contributors to the magnitude of impact forces: size, shape, and orientation of the bridge surface being impacted. However, the UF/FDOT model is based heavily on finite element simul ations, and only experimental data at limited deformation levels (Consolazio et al. 2006) were available to validate the findings of these past studies. Therefore, a series of impact experiments were planned in this study, in which reduced scale replicas o f the barge used in the simulation studies (a jumbo hopper barge) will be impacted by a high energy impact pendulum to achieve significant bow deformations. Physical quantities measured during the experiments will be compared to analogous impact simulation s that employ the same finite element modeling and analysis techniques that were used to develop the barge impact load model, thereby validating the results of the simulations and, by extension, the impact load prediction model. The work discussed in this dissertation involved planning these experiments by defining impact conditions that validate past research findings, determining an appropriate model scale, designing and fabricating many of the experimental components, and conducting preliminary simulatio ns. The barge impact experiments themselves will be conducted at a later date. Characterize strain rate sensitive material properties for common steels: During the reduced scale barge impact experiments, the barge specimen is expected to undergo as much as 15 in. of deformation during impact events lasting less than 0.1 sec. Therefore, localized strain rates in the various steel barge components will be very high. Because steels, like most materials, exhibit greater yield and ultimate strengths at high stra in rates, the rate sensitive properties of the barge materials will be an important contributor to the impact forces that are measured. These properties were quantified in this study by conducting uniaxial tension tests on the materials (ASTM A36 steel and A1011 steel) from which the barge specimens will be fabricated over a

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34 wide range of strain rates (710 5 500 s 1 ). To conduct the high rate material tests, a novel mechanical apparatus was designed that employed an impact pendulum as the source of energ y. Data from material tests conducted using the apparatus were combined with data from lower rate tests conducted using a typical laboratory load frame and were used to develop stress strain relations and strain rate sensitive properties for input into fin ite element constitutive models that will be used in the validation simulations. Develop a revised barge impact design procedure: A revised design procedure was developed that implements the barge impact load model, impact analysis procedures, and probabil ity of collapse expression that were developed from UF/FDOT research over the past several years. Alternative design methodologies to the comprehensive risk assessment procedure required by AASHTO were also considered, most notably an LRFD approach to vess el collision loading. Ultimately, it was determined that the uncertainties associated with vessel collision loading do not permit a simplified LRFD methodology to be employed without introducing considerable conservatism. Therefore, the existing AASHTO ris k analysis framework was instead modified in a targeted way to incorporate UF/FDOT procedures. Demonstrate revised design procedure through real world examples: The revised risk analysis procedure was demonstrated using two bridges that were designed in ac cordance with the AASHTO (1991) provisions and constructed within the past decade: the SR 300 Bridge over Apalachicola Bay, Florida, and the LA 1 Bridge over Bayou Lafourche, Louisiana. The latter bridge is the same structure that was used to demonstrate t he AASHTO procedure in the 2 nd Edition of the AASHTO Vessel Collision Guide Specification (AASHTO 2009). For comparison, both bridges were also evaluated using both the 1991 and 2009 editions of the AASHTO procedure. Differences between the various procedu res (AASHTO 1991, AASHTO

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35 2009, and UF/FDOT procedures) were documented in detail, both to act as a complete worked out example for future engineers to refer to, and also to demonstrate the implications of implementing the proposed UF/FDOT procedures in des ign practice.

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36 CHAPTER 2 BACKGROUND Multiple bridge collapses caused by vessel collision most notably the collapse of the Sunshine Skyway Bridge near Tampa, Florida prompted the development of the American Association of State Highway and Transportation Officials (A ASHTO) Guide Specifications and Commentary for Vessel Collision Design of Highway Bridges which was originally published in 1991 (AASHTO 1991) and updated with minor revisions in 2009 (AASHTO 2009). The guide specification provided a framework for estimat ing loads associated with vessel collisions and quantifying the risk of structural failure posed by errant vessels. A detailed review of the AASHTO (2009) vessel collision risk analysis procedure is provided in Section 2. 1 In the years since the 1991 publ ication of the guide specification, a multitude of research projects have been conducted by UF/FDOT which have uncovered important limitations to the AASHTO procedures. This research has culminated in state of the art impact load prediction models and stru ctural analysis procedures. A summary of UF/FDOT research findings and proposed methods is provided in Section 2. 2 2.1 AASHTO Risk Assessment Procedure The AASHTO provisions (AASHTO 2009) are strongly focused on quantifying the risk of bridge collapse resulti ng from vessel collision. Three (3) design methodologies with varying levels of com plexity are permitted by AASHTO. Method I: A simplified semi deterministic procedure in which the bridge is designed to withstand impact from a pre determined design vessel The design vessel is chosen such that only a small percentage of vessel traffic in the waterway is larger. Method I is intended for smaller, less critical bridges, for which a comprehensive risk analysis (Method II) is impractical. Approval by the bridge owner is required to employ Method I.

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37 Method II: A comprehensive risk analysis procedure in which the annual frequency of bridge collapse ( AF ) is directly quantified. The Method II risk analysis requires consideration of all vessel types that are expecte d to traverse the bridge. Method II is the preferred design method, and is considered the default procedure for any bridge at risk for vessel collisions. Thus, Method II is the focus of the research addressed by this study. Method III: A cost benefit anal ysis procedure in which vessel impact risk reduction measures are compared based on cost. Method III is permitted for cases in which the risk acceptance criteria of Method II are deemed to be technically or economically infeasible. Like Method I, approval by the bridge owner is required to employ Method III. As stated above, the Method II risk analysis consists of quantifying the annualized probability that a bridge will undergo catastrophic structural failure (collapse) as a result of vessel collision with any bridge element. This probability, expressed as an annual frequency of collapse ( AF ), is defined as: ( 2 1 ) where N is the number of vessel passages per year, PA is the pr obability that a given vessel will become aberrant deviate from its intended transit path per vessel passage, PG is the probability that a bridge element will be impacted by an aberrant vessel, PC is the probability that impact induced bridge element colla pse results from the collision, and PF is a protection factor for bridge elements that are shielded by protection systems or other navigational obstructions. Because most navigable waterways are utilized by a great variety of different types of vessels ran ging from small pleasure craft to massive cargo ships the AASHTO provisions suggest partitioning the total vessel traffic into representative vessel groups. The vessels

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38 represented in each group should be approximately equal in mass and type, and thus be e xpected may be defined as either superstructure spans or supporting piers. Either type of element is at risk for vessel collision and collapse. However, low pr ofile vessels such as river barges generally cannot impact the superstructure, thus only pier elements are at risk for collision from such vessel types. In practice, AF is computed as a summation across all vessel groups ( VG ) and bridge elements ( j BE ): ( 2 2 ) Note that the probability of vessel aberrancy ( PA ) is not dependent upon the bridge element of interest and is thus excluded from the internal summation. Computed in accordance wi th Eqn. 2 2 AF represents the total annual probability that any bridge element will be struck by an errant vessel and collapse. AASHTO prescribes acceptable quantities for AF depending upon the importance classification of the bridge. For critical or essential bridges as defined by Social/Survival and Strategic Highway Network (STRAHNET) requirements AF should be less than or equal to 0.0001. For typical bridges, AF is limited to 0.001. Stated alternatively, the return pe riod for vessel collision induced bridge collapse should be at least 10,000 years for critical/essential bridges, and 1,000 years for typical bridges. The probability of vessel aberrancy ( PA ) is computed as: ( 2 3 ) where BR is the base rate of aberrancy (0.00006 for ships and 0.00012 for barges), and R B R C R XC and R RD are correction factors to account for bridge location, parallel currents, cross

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39 currents, and vessel traffic density, respectivel y. Expressions for the correction factors are provided in the AASHTO provisions (AASHTO 2009). The geometric probability ( PG ) represents the conditional probability that a particular bridge element (e.g., a bridge pier) will be impacted by a vessel given t hat the vessel has become aberrant. Fig. 2 1 demonstrates how PG is computed for a bridge pier. Vessel position within the channel is assumed to be normally (Gaussian) distributed with the mean value at the centerline of the intended vessel transit path. The standard deviation of the Gaussian distribution is assumed to be equal to the overall vessel length ( LOA ). In the case of multiple barge flotillas, LOA includes the length of all barges in a line plus the propelling pu sh boat. The quantity PG is computed as the total area under the Gaussian distribution over the range of distance from the channel centerline which would lead to vessel impact with the pier of interest. Pertinent parameters for this integration are defined in Fig. 2 1 Note that because the Gaussian distribution is dependent on LOA PG for a given pier must be computed for each vessel group. Hence, PG is denoted PG ij in the Eqn. 2 2 The p robability of bridge element collapse (e.g., pier collapse) is computed as a function of the ratio of the lateral load carrying capacity of the bridge element ( H ) to the computed static vessel impact force ( P ). For bridge piers, H is usually defined as the static pushover capacity. The impact force ( P ) is denoted P S for ship impacts and P B for barge impacts. Ship impact forces are computed (in kips) using the empirical expression: ( 2 4 ) where DWT is the deadweight tonnage of the ship (tonnes, where 1 tonne = 2,205 lb), and V is the impact velocity (ft/s).

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40 Barge impact forces are computed in a two step process. First, the barge bow damage depth ( a B ) is computed (in feet): ( 2 5 ) where KE is the kinetic energy (kip ft) of the impacting barge or barge flotilla. Given a B the barge impact force ( P B ) is computed (in kips) as: ( 2 6 ) It is important to note that both P S and P B amplification effects associated with the impacting vessel. While dynamic analysis of the impacted bridge is permitted by AASHTO, it is not required. Consequently, in typical practice, the static pushover capacity ( H force ( P ) to compute the probability of collapse ( PC ): ( 2 7 ) It is also important to note that when the impact force is equal to the pier capacity (i.e., H/P = 1), according to AASHTO, the probability of collapse ( PC ) is equal to zero. Also, per AASHTO, the impact force must greatly exceed the pier capacity before the probability of collapse grows larger than 10%. The AASHTO PC expression is illustrated graphically in Fig. 2 2 For cases in which a bridge pier is protect ed by fenders or other protection structures (e.g., dolphins), or by some other navigational obstruction (e.g., land masses), use of a protection

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41 factor ( PF ) is permitted. The value of PF can take a value between 0 and 1 and is a function of the percent pr otection provided such structures. Given the site specific nature of pier protection, the development of appropriate values for PF is left to the discretion of the engineer and owner, though some limited guidance is provided in the AASHTO Guide Specificati on (2009). An example of how probabilistic analysis can be used to calculate PF is illustrated in Chapter 8. Once PA has been computed for each vessel group, and PG PC and PF have been computed for each combination of vessel group and bridge element, the various probabilities are summed in accordance with Eqn. 2 2 to arrive at the annual frequency of collapse ( AF ). If AF is less than the limits noted earlier, then the bridge is deemed adequately resistant to vessel collis ion. If AF exceeds the specified limits, then the bridge must be appropriately strengthened, or protection systems must be installed. If neither option is economically or technically feasible, then the cost effectiveness procedure (Method III) can be used to identify risk mitigation measures that are feasible. It is noted that European design standards (CEN 2006) also prescribe a risk analysis based approach (similar to AASHTO) for vessel collision design of bridges. A comprehensive review of Eurocode provi sions pertaining to vessel collision is provided in Appendix A. 2.2 UF/FDOT Research on Barge Collision Over the past several years (2000 present) multiple research studies have been conducted by the University of Florida (UF) and Florida Department of Trans portation (FDOT), for the purpose of investigating limitations of the AASHTO provisions described above. Based on the results of these studies, design oriented procedures have been developed to improve upon the AASHTO guidelines. The maj or findings from th ese studies we re as follows : During vessel impact, superstructure inertia results in dynamic amplification of pier column internal forces, and this phenomenon is not accounted for in the AASHTO prescribed static analysis. Dynamic (transient or modal) and e quivalent static analysis

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42 procedures have been developed by UF/FDOT that account for superstructure inertia and resulting dynamic amplification. Barge impact forces are strongly dependent on the shape and size of the impacted pier and the angle of impact. These variables are not included in the AASHTO load prediction expressions. An alternative barge impact load prediction model has been developed that appropriately accounts for the parameters that strong ly influence impact forces. The AASHTO probability of collapse ( PC ) expression (Eqn. 2 7 Fig. 2 2 ) is based upon data gathered from ship to ship collisions (not ship to bridge collisions), and thus it can produce unrealistic predictions of PC An alternative probability of collapse expression has been developed based upon rigorous reliability analysis of several bridges subjected to barge collision loading. The UF/FDOT studies that led to these findings are summarized in the following secti ons. 2.2.1 Full Scale Barge Impact Experiments In 2004, Consolazio et al. conducted a series of full scale barge impact experiments with multiple pier and partial bridge configurations (Consolazio et al. 2006). The experimental bridge was a decommissioned causew ay leading to St. George Island, in northwest Florida. Prior to demolition of the old bridge, the researchers instrumented the channel pier and two adjacent piers with load cells, strain gauges, accelerometers, and displacement transducers, and impacted ea ch structure multiple times with a full sized barge. Impact experiments were conducted with a stand alone pier with the superstructure removed (Fig. 2 3 a) and a pier with the superstructure in place (Fig. 2 3 b). As part of these tests, impact forces, pier deflections, pier and barge accelerations, and impact velocities were measured. For safety and environmental reasons, Consolazio et al. were not permitted to collapse the t ested structures. Thus, impact energies were lower than would be expected for a fully loaded barge flotilla. However, the experimental measurements revealed that inertial effects in the bridge particularly from the superstructure increase pier column membe r demands (i.e. shears, moments) relative to what the AASHTO

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43 Using dynamic finite element analysis of the experimental impact conditions calibrated with the experimental data Consolazio et a l. (2006) demonstrated that immediately after impact, the superstructure mass provides inertial resistance to impact which acts as a significant source of dynamic amplification of column forces. Once the superstructure is accelerated to its maximum velocit y and begins decelerating, the mass actually drives the pier to sway beyond the pier top displacement predicted by AASHTO static analysis. Ultimately, it was demonstrated that while impact force magnitudes predicted by the AASHTO provisions were reasonably similar to those measured in the experiments, the AASHTO prescribed static analysis procedure consistently under predicted internal pier column structural demands (shear and moment). The discrepancy was attributed primarily to inertial effects resulting i n dynamic amplification. The full scale impact experiments conducted at St. George Island provided valuable insights into dynamic structural response of bridges to barge impacts. Furthermore, the data from these experiments have been used on numerous occas ions to validate: finite element analysis results; newly developed analysis techniques; and impact load prediction models. 2.2.2 Coupled Vessel Impact Analysis (CVIA) Procedure Based on the results of the St. George Island experiments (Consolazio et al. 2006), i t was concluded that only dynamic analysis techniques can adequately capture dynamic amplification effects during impact. However, methods available at the time highly sophisticated contact impact analyses involving tens or hundreds of thousands of finite elements were not computationally efficient enough for use in bridge design. Thus, a novel dynamic analysis technique was developed coupled vessel impact analysis (CVIA) in which barge motions and deformations are dynamically coupled to dynamic bridge resp onse (Consolazio and Cowan 2005).

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44 In CVIA (Fig. 2 4 ), the impacting barge is idealized as a single degree of freedom (SDF) system, consisting of a concentrated mass equal to the mass of the barge or flotilla and a nonli near spring element which represents the crushable barge bow. This SDF system is coupled to a multi degree of freedom (MDF) representation of the impacted bridge. To conduct CVIA, the barge mass is prescribed an impact velocity which initiates the analysis At each timestep in the analysis, the impact load and bridge structural response are simultaneously computed based upon dynamic interaction between the SDF barge and MDF bridge models. Impact forces and dynamic bridge response estimates provided by CVIA have been successfully validated against experimental data from the St. George Island impact experiments with excellent agreement (Consolazio and Cowan 2005). The CVIA method has been directly incorporated into the bridge finite element code FB MultiPier ( BSI 2010, Consolazio et al. 2008). In FB MultiPier, multiple bridge piers and the connecting superstructure spans can be discretely modeled and analyzed. This approach permits dynamic interaction between the impacted pier, superstructure, and adjacent pier s to be directly captured in the analysis. Despite the efficiencies afforded by CVIA, dynamic analysis of a full bridge can be still be computationally demanding. Thus, a simplified modeling procedure was developed in which the impacted pier and two adjace nt spans are discretely modeled to form a one pier two span (OPTS) model (Consolazio and Davidson 2008). The stiffness and mass of the remaining portions of the bridge structure are represented with linear springs and concentrated masses placed at each end of the discretely modeled spans. When combined with the OPTS modeling technique, CVIA permits time domain barge impact analysis to be completed within a few minutes with excellent accuracy on a typical workstation computer. Consequently, OPTS CVIA

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45 represe nts the best currently available analysis tool for capturing dynamic amplification effects during barge impact events. 2.2.3 Barge Bow Force Deformation Curves A critical component of the CVIA method and in fact, any barge impact analysis is an accurate descript ion of the strength and stiffness characteristics of the impacting barge bow. During even a moderate impact event, the barge bow undergoes significant plastic deformation, and the inelastic load carrying capacity of the bow will determine impact force magn itudes. For design oriented impact analysis, the impacting vessel is treated as a SDF system, so barge bow resistance can simply be described by a force deformation curve (sometimes referred to as a The barge impact load prediction model pr escribed by AASHTO (2009) is based upon a series of barge bow crushing experiments performed in Germany in the early 1980s (Meier Drnberg 1983). The experiments included crushing both statically and dynamically reduced scale models of European style ponto on barge bows. A representative force deformation curve (Fig. 2 5 ) was developed from the experimental results, and this curve was ultimately adopted by both AASHTO (2009) and the Eurocode (CEN 2006). The Meier Drnberg crush curve forms the basis for Eqs. 2 5 and 2 6 above. In 2006, Consolazio et al. began studying, in detail, the mechanics of barge bow force deformation beha vior using fully discretized high resolution finite element (FE) models and dynamic simulatio n tools (Consolazio et al. 2009 ). For this task, barge bow FE models were developed of the two most common barges in U.S. waterways, the jumbo hopper barge and the oversize tanker barge. The FE models were subjected to quasi static crushing by rigid pier shapes of different shapes (round, flat) and widths (1 35 ft), and to very severe deformation

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46 levels (more than 15 ft). Force deformation curves were then develop ed based on the simulation results. The study resulted in three primary findings: Force deformation curves exhibit softening at large crushing deformations (approximately 12 in. or more). Thus, force deformation curves can be conservatively idealized as el astic perfectly plastic; Peak crushing forces are strongly dependent on the width of the impacted pier surface, where wide pier surfaces will develop larger forces than narrow surfaces, and; Peak crushing forces are strongly dependent on the shape of the i mpacted pier surface, where flat faced (square or rectangular) shapes develop larger forces than round shapes. These findings are significant because they demonstrate that crush curves and the magnitude of corresponding barge impact forces are dependent up on the geometry of the impacted pier. In contrast, AASHTO (2009) prescribes a single crush curve for all impact scenarios, independent of pier shape. Consequently, AASHTO prescribed impact forces will be overly conservative for certain pier configurations and unconservative for others. Consolazio et al. ( 2009 ) developed a design oriented force deformation model for barges based on data from the FE crushing simulations. However, a follow up study (Getter and Consolazio 2011) demonstrated that impact forces w ith flat faced piers are also strongly dependent upon the angle of impact: i.e., forces associated with oblique impact are smaller than head on impact forces. Because the angle of impact is subject to significant uncertainty, a probabilistic approach was w arranted. Getter and Consolazio combined force deformation data from FE simulations of oblique crushing with a statistical description of impact orientation. Using Monte Carlo simulation, a new design oriented force deformation model was developed that pro babilistically accounts for oblique impact scenarios. The revised crush model generally predicts smaller forces than the Consolazio et al. ( 2009 ) model, particularly for wide, flat faced pier surfaces such as waterline footings.

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47 The Getter Consolazio (2011 ) barge force deformation model is summarized in Fig. 2 6 If the impacted pier surface is round, a barge yield force ( P BY ) is computed based only on the pier width ( w P ). For flat faced surfaces, P BY is a function of both w P and the most likely impact angle ( ). Generally, can be defined as the skew angle between the navigation channel and the pier alignment (the pier axis). Given P BY an elastic perfectly plastic force deformation curve is formed with a yield deformation ( a BY ) equal to 2 in. The resulting f orce deformation curve can be used directly as a description for barge bow stiffness in CVIA (recall Fig. 2 4 ) or as a basis for estimating equivalent static impact loads. 2.2.4 Collision Induced Dynamic Amplification Phenome na Given the development of an efficient and reliable dynamic impact analysis procedure (OPTS CVIA) (Consolazio and Cowan 2005; Consolazio and Davidson 2008) and improved force deformation relationships (Consolazio et al. 2009 ), a comprehensive study of ba rge impact induced dynamic amplification phenomena was conducted (Davidson et al. 2010). In this study, a variety of bridges from around Florida were analyzed for barge impact using the best available dynamic analysis tool (OPTS CVIA). Peak dynamic impact forces from each dynamic analysis were also applied statically to each bridge. The analysis results showed that pier column internal forces (shears, moments) obtained from dynamic analysis were significantly larger than those predicted by simple static ana lysis. In other words, dynamic amplification of pier column internal forces occurred during barge impact. Detailed inspection of the analysis results showed that dynamic amplification is a consequence of superstructure inertial response during impact, as w as observed during the full scale barge impact experiments at St. George Island (Consolazio et al. 2006). The study (Davidson et al. 2010) uncovered two primary amplification modes: 1) superstructure inertial

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48 restraint, and 2) superstructure momentum drive n sway. Some bridges exhibited a mixed response in which both modes were present. See Davidson et al. (2010) for det ailed descriptions of each mode Regardless of which amplification mode dominated the response, every bridge exhibited some level of dynamic amplification. Selected results from this study are provided in Fig. 2 7 sorted by amplification mode. Each bar represents a different bridge and impact energy. The data are presented as a ratio between the maximum dynamic and static pier column moment. Consequently, a ratio greater than 1.0 indicates dynamic amplification. Dynamic amplification ratios averaged between 1.5 and 2.0 (implying 50 100% amplification), and some cases exhibited much higher amplification levels. Consequently, dynamic amplification is a critical consideration in barge impact resistant bridge design, and the phenomenon is not currently explicitly considered in the AASHTO (2009) provisions. 2.2.5 Other Vessel Impact Procedures It has been demonstr ated, both experimentally (Consolazio et al. 2006) and analytically (Davidson et al. 2010) that dynamic amplification is an important component of bridge response during vessel impact. Consequently, amplification effects must be considered when analyzing b ridges for vessel impact loading. While the best available analysis tool (CVIA) can directly account for dynamic amplification and is also reasonably efficient, time domain dynamic analysis can be cumbersome in design, particularly during preliminary desig n stages. Accurate dynamic analysis requires well defined descriptions of bridge stiffness and mass parameters, and time domain analysis output requires significant post analysis data processing to identify design member forces. For this reason, UF and FDO T research has focused heavily on developing an array of vessel impact analysis procedures that are simple to use but which still account for important

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49 dynamic amplification effects. As a result, in addition to CVIA, three alternative analysis methods have also been developed: A PPLI ED VESSEL IMPACT LOA DING (AVIL). A time domain dynamic analysis, in which the impact force time history is computed a priori and applied to the bridge model; I MPACT RE SPONSE SPECTRUM ANAL YSIS (IRSA). A modal, frequency domain (sp ectral) analysis, and; S TATIC B RACKETED IMPACT ANAL YSIS (SBIA). An equivalent static analysis that empirically accounts for dynamic amplification. The applied vessel impact loading (AVIL) method involves pre computing an impact force time history based upo n the Getter Consolazio (2011) force deformation model and then applying the load history to a bridge model using transient dynamic analysis (Consolazio et al. 2008). The AVIL method can serve as an adequate replacement for CVIA when bridge analysis softwa re is used that does not include the necessary features to set up CVIA (e.g., concentrated masses or prescribed initial velocities). The AVIL process is summarized in Fig. 2 8 Barge force deformation parameters barge yield force ( P BY ) and yield deformation ( a BY ) are determined in accordance with the Getter Consolazio (2011) model (recall Fig. 2 6 ). Barge mass ( m B ) and initial velocity ( v Bi ) are determined based on the AASHTO pr ovisions (AASHTO 2009) and site specific vessel traffic and waterway current data. The lateral translational pier and soil stiffness ( k P ) is determined by applying a static lateral load at the expected impact location and measuring the pier displacement at that location. Pier soil stiffness ( k P ) is combined in series with the barge bow stiffness to form a barge pier soil stiffness ( k S ). With these parameters, an impact force time history is formed, as illustrated in Fig. 2 6 that can be applied to the bridge model to conduct a time domain dynamic analysis.

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50 While methods such as CVIA and AVIL constitute the most accurate ways of quantifying vessel impact induced structural demands, such time domain methods involve a number of disadvantages, foremost being computational time and output data processing effort. An alternative dynamic analysis approach is frequency domain, also referred to as modal response spectrum analysis. Such methods are typically more computationall y efficient than time domain methods while still accounting for dynamic inertial phenomena. Given these benefits, a modal, frequency domain analysis method called impact response spectrum analysis (IRSA) was developed for vessel impact analysis with bridge s (Consolazio et al. 2008). As summarized in Fig. 2 9 the IRSA procedure begins with developing vessel impact force time history characteristics in accordance with the AVIL procedure (recall Fig. 2 8 ), including the maximum impact load ( P Bm ) and load duration ( T I ). The load duration is then used to form a design response spectrum. As with most response spectrum procedures, eigenanalysis is used to determine fundamental structural vib ration periods and mode shapes. Modal displacements corresponding to each mode shape are magnified using DMFs computed from the response spectrum. For a given number of modes, magnified displacements and resulting internal member forces are combined using either a square root sum of squares (SRSS) or complete quadratic combination (CQC) approach. If a sufficient number of modes are selected, combined displacements and internal forces constitute a reasonably accurate estimate of the peak dynamic structural r esponse during vessel impact. While IRSA constitutes a significant advancement in simplified vessel impact analysis, key limitations have been identified which must be resolved before implementing the method in a design setting. Most importantly, it is unc lear how to best determine the minimum number of vibration modes that should be considered. For seismic response spectrum analysis, the

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51 minimum number of modes is determined based on modal mass participation. Design codes for buildings (e.g., FEMA 2003, AS CE 7 10) and bridges (AASHTO 2011) require that a sufficient number of modes be included to achieve 90% modal mass participation. However, it has been shown that IRSA method for vessel impact commonly underestimates structural demands at the 90% modal mass participation level (Consolazio et al. 2008). In many cases, more than 99% participation is necessary to achieve conservative results from IRSA when using eigenvectors. Further investigation into this issue, e.g. the possible use of Ritz vectors rather th an eigenvectors, is necessary before IRSA can be safely suggested for bridge design. Given the computational and data processing demands associated with dynamic analysis procedures such as CVIA, AVIL, and IRSA, a simpler static analysis method is desirable However, it has been demonstrated that static impact analysis conducted in accordance with AASHTO (2009) consistently underestimates pier member structural demands (Consolazio et al. 2008) because dynamic amplification caused by superstructure inertia is neglected (Davidson et al. 2010). Consequently, an equivalent static analysis procedure called static bracketed impact analysis (SBIA) was developed that empirically accounts for superstructure inertial effects (Getter et al. 2011). As summarized in Fig. 2 10 SBIA consists of a series of static structural analyses in which all forces applied to the bridge pier are dependent upon the peak dynamic barge impact force ( P B ). As with IRSA, P B is computed in accordance with t he AVIL procedure combined with the Getter Consolazio (2011) barge force deformation model. The SBIA method consists of two basic load cases. For Load Case 1, an amplified impact load (1.45 P B ) is applied at the expected impact location. Additionally, a lo ad is applied at the superstructure elevation which is calibrated to approximate the effect of superstructure inertial restraint that occurs immediately

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52 after impact. This pier top force is equal to P B times an inertial restraint factor ( IRF ). To minimize conservatism, IRF values are calibrated to estimate specific structural demand types: pier member moments ( IRF m ), pier member shear forces ( IRF v ), and bearing connection shear forces ( IRF b ) at the substructure superstructure interface. Load Case 2 simply c onsists of applying an amplified impact force (1.85 P B ) at the impact location. Maximum structural demands obtained between the two load cases are used for design. 2.2.6 Revised Probability of Collapse ( PC ) Expression Much of the UF/FDOT research summarized in p revious sections was focused on accurately quantifying loads associated with barge impact and characterizing dynamic bridge response to impact. However, a critical step in vessel impact risk analysis is estimating the probability of catastrophic structural failure during an impact event. According to AASHTO (2009), the probability of collapse ( PC ) of a particular bridge element (e.g., a pier) is computed as (recall Fig. 2 2 ): ( 2 8 ) where H / P (for a bridge pier) is the ratio of the static pushover capacity ( H ) to the maximum vessel impact force ( P ). Based on this expression, if the vessel impact force is equal to the capacity of the structure, then the probability of collapse is 0 (no chance of collapse). Furthermore, if H / P = 0.1 i.e., the impact force is 10 times larger than the bridge capacity PC is only 0.1 (10%). Based on these observations, it is clear that the basis for the AASHTO PC expression warrants addit ional consideration. Scarce ship to bridge collision data were available at the time of the development of the AASHTO PC expression (prior to 1991). In fact, the AASHTO PC expression is based upon a historical analysis of ship to ship collisions, rather th an

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53 ship to bridge (or, even more desirably, barge to bridge) collisions. A detailed discussion of the origins of the AASHTO PC expression can be found in Consolazio et al. ( 2010a ). Due to the clear limitations of the AASHTO PC expression, UF/FDOT researche rs developed an updated PC expression based on rigorous reliability analysis of bridges subjected to barge impact (Consolazio et al. 2010a Davidson et al. 2013). The probability of bridge collapse was directly quantified using well established probabilist ic analysis procedures (Monte Carlo simulation) paired with advanced sampling and sub sampling methods. Bridge models were subjected to thousands of simulated barge impact events using dynamic impact analysis (CVIA) while accounting for important sources o f statistical variability in impact loading and structural resistance. This approach was employed to quantify the probability of structural collapse ( PC ) for ten (10) different bridges of widely different structural characteristics. Each PC estimate was pa ired with the mean demand to capacity ( D / C ) ratio observed for each bridge. A detailed definition of D / C is provided in Davidson et al. (2013). As illustrated in Fig. 2 11 an exponential curve was fit to the data and a 95% confidence upper bound envelope was established, resulting in a conservative PC D / C expression that is suitable for use in bridge design: ( 2 9 ) Consequently, a design engineer can con duct a single deterministic impact analysis using the UF/FDOT methods described above (CVIA, AVIL, etc.) to quantify the D / C ratio, and estimate the probability of collapse using the revised PC expression. 2.3 Observations As summarized above, research conduct ed by UF and FDOT has resulted in the development of a more accurate barge impact load prediction model, various structural analysis techniques that account for important dynamic structural response characteristics (CVIA, AVIL,

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54 IRSA, and SBIA), and a prob ability of collapse ( PC ) expression that properly accounts for barge impact and structural response uncertainties. These methods constitute significant advancements relative to the methods currently prescribed by AASHTO for bridge design for vessel collisi on. However, as noted in Chapter 1, the UF/FDOT barge impact load model is based primarily on high resolution finite element simulations that have only been validated against experimental measurements at relatively moderate barge deformation levels. Theref ore, additional experimental research is required to validate the UF/FDOT barge impact load model at higher barge deformation levels that are more consistent with impact severities commonly considered in bridge design. Furthermore, the UF/FDOT structural a nalysis techniques and PC expression have not yet been incorporated into a cohesive bridge design methodology. Therefore, while the individual UF/FDOT methods can be considered more accurate than those in the AASHTO provisions, the influence that the revis ed methods may have on design efficiency and economy is unknown. Consequently, the current study has been carried out to address methodology integration issues and thereby facilitate adoption of the UF/FDOT procedures in bridge design practice.

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55 Figure 2 1 Determination of geometric probability of impact ( PG ) with a bridge pier (Source: AASHTO 2009) Figure 2 2 Determination of probability of collapse ( PC ) (Source: AASHTO 2009)

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56 A B Fi gure 2 3 Full scale barge impact experiment s at St. George Island, Florida. A ) Stand alone pier impact (superstr ucture removed). B ) Intact bridge impact (Consolazio et al. 2006) (Photos courtesy of Gary R. Consolazio) Fig ure 2 4 Coupled vessel impact analysis (CVIA) (Consolazio and Cowan 2005)

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57 Figure 2 5 AASHTO barge bow force deformation curve: P B a B (AASHTO 2009)

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58 Figure 2 6 UF/FDOT barge bow force deformation model (Getter and Consolazio 2011)

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59 Figure 2 7 Dynamic amplification of pier column moments sorted by amplification mode (Davidson et al. 2010)

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60 Figure 2 8 Applied vessel impact loading (AVIL) (Consolazio et al. 2008)

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61 Figure 2 9 Impact response spectrum analysis (IRSA) (Consolazio et al. 2008)

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62 Figure 2 10 Static bracketed impact an alysis (SBIA) (Getter et al. 2011)

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63 Figure 2 11 Revised probability of collapse expression (Consolazio et al. 2010a )

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64 CHAPTER 3 EXPERIMENTAL VALIDATION OF UF/FDOT BARGE IMPACT LOAD PREDICTION MODEL As discussed in Chapter 2, past experimental validation of the UF/FDOT barge impact load prediction model (Getter and Consolazio 2011) has been limited. In developing the originally conceived UF/FDOT load prediction model (Consolazio et al. 2009 ) the authors compared finite element simu lation results the basis for the load prediction model to force and deformation measurements taken during the full scale barge impact experiments at St. George Island (Consolazio et al. 2006). Reasonable agreement was observed between the numerical and exp erimental results. However, due to safety and environmental concerns, the barge impact experiments were only able to achieve barge deformations of approximately 16 in. Thus, the UF/FDOT load prediction model has only been experimentally validated at relati vely small deformations, while typical design impact conditions commonly correspond to barge bow deformations on the order of several feet. Consequently, a primary goal of the current study was to experimentally validate the UF/FDOT load prediction model a nd the finite element simulation techniques used to develop it for higher level barge bow deformations. To do so, 40% scale models of a typical barge bow will be constructed and impacted by a high energy pendulum. Measurements made during the experiments w ill be compared to results from finite element (FE) simulations of analogous impact conditions. To support this effort, the steel materials that make up the model barge were evaluated in tension at a wide range of strain rates, and rate sensitive FE consti tutive models were develo ped ( Chapter 4). The barge impact testing program has been planned, and preliminary stages (e.g., material testing) have been completed. An overview of the planned testing is provided in this chapter, including discussion of import ant considerations such as model scale. Details pertaining to the barge impact test program are provided in Chapter 5.

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65 3.1 Validation Objectives Because the UF/FDOT load prediction model was developed based on high resolution finite element analyses, the prima ry goal of the experimental program is to validate that the finite element simulation techniques employed in prior research are theoretically and physically sound. This objective necessitates performing experiments that involve dynamic impact between a bar ge bow and semi rigid object, including large scale, high rate barge bow deformations (up to and including material failure). Impact force histories, dynamic motions of the various components, and barge bow deformations will be measured as part of these ex periments. Identical impact scenarios will be simulated using the same type of finite element models, the same finite element code (LS DYNA), and the same simulation techniques that were used to develop the UF/FDOT barge impact load prediction model. Corre spondence between the experimental measurements and finite element simulation results will demonstrate that previously employed simulation tools adequately describe realistic barge impact behavior. Recall that the UF/FDOT barge impact load model differs fr om the model currently employed in the AASHTO (2009) provisions in four pr imary ways : Barge impact forces are strongly dependent on the size of the impacted pier surface, in that larger pier surfaces result in larger forces than smaller pier su rfaces (Cons olazio et al. 2009). Barge impact forces are strongly dependent on the shape of the impacted pier surface, in that flat faced surfaces result in larger forces than similarly sized rounded su rfaces (Consolazio et al. 2009). Barge bow force deformation behav ior can be conservatively idealized as elastic perfectly plastic (Consolazio et al. 2009, Getter and Consolazio 2011). Barge impact forces are strongly dependent on the angle between the barge bow and pier surface for flat faced piers (Getter and Consolazi o 2011). Consequently, the secondary objective of the experimental program is to validate as many of these previous research findings as possible within the time and budget constraints of

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66 the study. Given the material costs and labor effort associated with fabricating barge bow specimens, the program is limited to two series of impact experiments. One will include impact with a rounded object (similar to impact with a rounded pier surface such as a circular pier column), and one will include impact with a f lat faced object (similar to a rectangular pier column). Both objects will have the same width. These two experimental series will directly illustrate finding number 2 above, that flat faced surfaces generate larger forces than equivalently sized rounded s urfaces. Impact forces and dynamic barge bow deformations measured during the experiments can also be used to form force deformation curves. These curves will validate finding number 3 listed above. It should be noted that the other two findings will be im plicitly validated by demonstrating that finite element simulation techniques that were employed in this study (and in Consolazio et al. 2009 and Getter and Consolazio 2011) are generally sound. 3.2 Overview of Experimental Program The planned barge bow impact experiments will consist of impacting reduced scale replicas of a typical barge bow with a semi rigid object (impact block) that has been swung from a large pendulum. The FDOT pendulum impact facility at the M.H. Ansley Structures Research Center, Tallaha ssee, Florida (Fig. 3 1 ) will be used to conduct the impact experiments. The pendulum consists of three 50 ft tall towers placed in a triangular pattern. The impacting object is suspended from two of the tower s via four cables and lifted from the third tower to develop the desired energy potential. To initiate impact, a servo actuated hook releases the lifting cable and the impact block begins swinging. The impacted specimen a scale model barge bow, in this cas e is placed at the bottom of the pendulum swing to maximize the kinetic energy of the impact block. The FDOT impact pendulum is designed to accommodate (at maximum) a

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67 9,000 lbf impact block swung from a maximum drop height of 35 ft. Thus, the maximum kinet ic energy that the impact block can attain is 315 kip ft. For the proposed barge impact experiments, a scale model barge bow will be mounted to a reinforced concrete foundation via two steel reaction frames (Fig. 3 2 ). A steel support frame will connect the impact block to four cables that are, in turn, connected to the pendulum towers. The support frame provides widely spaced cable connection points which will improve stability of the impact block before and d uring each pendulum swing. Alternative testing scenarios were explored as part of preliminary planning for the impact experiments. One scenario that was considered involved swinging the barge specimen from the pendulum into a stationary object attached to the foundation, which is most similar to a barge impacting a stationary bridge pier. However, it was determined that the uneven mass distribution of the bow specimen and lack of adequate cable connection locations (to the bow model) make this scenario impr actical. Furthermore, finite element simulations of both scenarios (swinging barge bow and stationary barge bow) indicated that impact forces were effectively identical between the two scenarios. The most important reason for not choosing to swing the barg e bow from the pendulum, however, was the quality of the impact force data. As will be discussed in Chapter 6, the impact force ( F ) will be computed by measuring (using accelerometers) the deceleration ( a ) of the pendulum mass ( m ) during impact, and then r elying on the relation F = m a In order for this relation to be valid, the object to which the accelerometers are attached (i.e., the pendulum mass) must be effectively rigid. Because the barge bow is highly deformable, it is infeasible to obtain high qua lity impact acceleration (and therefore force ) data in this manner if the barge bow is used as the pendulum mass. Given these various considerations, it was

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68 determined that the most effective testing scenario involved swinging an effectively rigid impact b lock from the pendulum to impact a stationary barge bow specimen, as shown in Fig. 3 2 3.2.1 Determination of Barge Bow Model Scale Two reduced scale specimens of the front portion (bow) of a typical jumbo hopper b arge will be fabricated from commercially available steel materials. One of the primary concerns in developing a reduced scale bow model is choosing an appropriate model scale factor ( ). Consequently, similitude expressions must be derived that relate full scale parameters to their corresponding model scale values. The Buckingham theorem (Jones 1997) was employed to derive the following similitude relations for the experimental progr am: ( 3 1 ) where is displacement, P is force, and E is energy. Full scale quantities are denoted with the fs m e that is the ratio of the full scale size to model scale size: i.e., = 4 for a scale model (1: scale). The full derivation of the above expressions is provided in Appendix B. A primary objective of the impact experiments is to attain approximately 10 ft (at full scale) of bow deformation subject to design constraints of the FDOT impact pendulum (maximum energy of 315 kip ft). Based on previously conducted simulation data (Consolazio et al. 2009 ), approximately 17,300 kip ft of impact energy would be required to achieve 10 ft of deformation at full scale (assuming perfectly inelastic collision). Using the energy similitude expression above and solving for indicates that a 1:4 scale model ( = 4) would be ideal for pendulum impact testing. However, many barge components, particularly steel angles and channels, are not commercially available at 1:4 scale. Consequently, thicker stock members

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69 would need to be milled down to the correct thicknesses. Such fabrication is feasible, but cost prohibitive. Therefore, a larger model scale of = 2.5 (40% scale) was selected. At this scale, internal steel angles and other components are commercially available with the correct thickness, which greatly reduces fabrication costs. The consequence of increasing the model scale is that the desired deformation cannot be achieved with a single swing of the impact pendulum. Thus, individual bow specimens will be subjected to mul tiple impacts to attain accumulated deformation equal to approximately 10 ft at full scale. Based on energy similitude and preliminary simulation data, it is anticipated that four to five impacts will be required to achieve the desired accumulated deformat ion. At the model scale of = 2.5, the jumbo hopper barge bow specimen will measure approximately 14 ft wide by 11 ft long and 5 ft tall (Fig. 3 3 ). Additional details pertaining to the barge bow specimens are provided in Chapter 6. 3.2.2 Material Testing Program Given the deformation rates involved in the planned barge impact experiments, strain rate sensitivity of the steel barge components is expected to be a significant contributor to the impact forces that wi ll be measured, and thus, strain rate sensitive constitutive models must be developed for implementation in the FE model that is being validated. In the United States, barges are typically constructed from ASTM A36 structural steel. Therefore, in prior stu dies (Consolazio et al. 2009, Getter and Consolazio 2011), a viscoplastic constitutive model for A36 was employed in the FE barge model, in which a representative stress strain relation was adopted from the literature (Salmon and Johnson 1996). The Cowper Symonds model was used to describe rate sensitivity with parameters C = 40.4 s 1 and P = 5, as is common in practice (Jones

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70 1997). However, it is recognized that these parameters vary widely among different studies of mild steel (Jones 1997, 2013, Hsu and Jones 2004, Jones and Jones 2002). Furthermore, reduced scale (40%) thicknesses of some barge components (mostly hull plates) are too thin to be addressed by the A36 specification (ASTM 2008). Therefore, ASTM A1011 hot rolled carbon sheet steel (ASTM 2012a ) was selected as the closest alternative to A36 that is available in the required thicknesses. The A1011 specification includes numerous material grades, of which, the most commonly available are CS (commercial steel) and DS (drawing steel). The specific grade that will be used in the reduced scale barge model is A1011 CS Type B. ASTM does not specify material properties for this grade. To effectively carry out the FE model validation, it was necessary to characterize the materials out of which the reduced scale barge bow would be constructed, particularly given the uncertainty associated with the rate sensitive material parameters and the fact that ASTM does not specify mechanical properties for A1011 steel. Therefore, uniaxial tension tests were conducted over a wide range of strain rates (710 5 500 s 1 ) on A36 plate and A1011 sheet specimens. Chapter 4 documents the material testing program, including development of rate sensitive constitutive models (implemented in LS DYNA) for the materials that were evaluated. 3.3 Validation Simulations Given that the purpose of the proposed experimental program is to validate finite element modeling and simulation techniques that are the basis for the UF/FDOT barge impact load prediction model (Getter and Consolazio 201 1), a necessary component of the experimental program is to develop finite element simulations of each impact experiment. Results obtained from these simulations will be directly compared to experimental measurements of impact force, impact block motions ( displacement, velocity, acceleration), and barge bow deformation depth. Demonstrating clear correspondence of these quantities between the experiments and simulations

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71 will promote confidence in the UF/FDOT load model and facilitate its adoption as an AASHT O code procedure. A finite element representation (Fig. 3 4 ) of the pendulum impact test setup including reduced scale barge bow, pendulum impact block, and reaction frame was developed in LS DYNA. The barge bow portion of the model is a 0.4 scale version of the same model that was used in the development of the UF/FDOT load prediction model. As shown in Fig. 3 5 the finite element mesh of the reduced scale barge bow cons ists of more than 120,000 nonlinear quadrilateral shell elements, in which each element is approximately 1.5 in. square or smaller. The barge bow zone is composed of fourteen (14) internal rake trusses and frames, transverse bracing members, and several ex ternal hull plates of varying thicknesses S ee Chapter 6 fo r additional structural details Quadrilateral 4 node, fully integrated shell elements were used to allow hull plate, gusset plate, and structural member (angles and channels) buckling to occur as appropriate throughout the barge. Additionally, the use of shell elements to model internal structural members of the barge permitted these components to undergo local material failure (discussed in detail in Chapter 4), which in LS DYNA, results in elemen t deletion. Angle and channel structural shapes were modeled with a sufficient number of elements so that reverse curvature can develop in the event of local member buckling. In full scale barge construction, steel components such as plates, angles, and ch annels are joined together by welds. In the FE model, localized welds (spot welds) were modeled by rigid beams that connect two nodes (from different structural members) together. Connection failure was accounted for through element deletion upon failure o f the joined shell elements. Spot welds were introduced at a sufficient density to emulate welds present in the physical barge. Given these features, the barge bow FE model is capable of

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72 accurately simulating the response to dynamic impact events, includin g large scale deformation and material failure. LS DYNA also includes features which permit multiple successive impacts to be simulated (Fig. 3 6 ) by accurately accounting for residual stresses and accumulated ma terial damage. Preliminary simulations of the planned experimental impact conditions are discussed in Chapter 5.

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73 Figure 3 1 Impact pendulum at M.H. Ansley Structures Res earch Center in Tallahassee, F L (Photo courtesy of Daniel J. Getter) Figure 3 2 Test setup for barge bow impact experiments

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74 Figure 3 3 Rendering of redu ced scale barge bow specimen showing internal truss structure Figure 3 4 Rendering of barge bow finite element model with flat faced pendulum impact block and reaction frame (mesh not shown for clarity)

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75 A B Figure 3 5 Barge bow finite element model showing mesh density A) External structure. B) Cut section showing internal structure. A B C D Figure 3 6 Finite element barge bow deformations after successive impacts from flat faced impact block (reaction frame not shown for clarity). A) Before impact. B) After 1st impact. C) After 2nd impact. D) After 3r d impact.

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76 CHAPTER 4 STRAIN RATE SENSITIVE CONSTITUTIVE RELATIONS FOR EXPERIMENTAL VALIDATION Given the deformation rates involved in the planned FE model validation, strain rate sensitivity of the steel barge components will be a significant contributor to the i mpact forces that will be measured, and thus, strain rate sensitive constitutive models must be developed for implementation in the FE model that is being validated. In the United States, barges are typically constructed from ASTM A36 structural steel. The refore, in prior studies (Consolazio et al. 2009, 2010 b 2012a, 2012b, Getter and Consolazio 2011), a viscoplastic constitutive model for A36 was employed in the FE barge model, in which a representative stress strain relation was adopted from the literatu re (Salmon and Johnson 1996). The Cowper Symonds model was used to describe rate sensitivity with parameters C = 40.4 s 1 and P = 5, as is common in practice (Jones 1997). However, it is recognized that these parameters vary widely among different studies on mild steel (Jones 1997, 2013, Hsu and Jones 2004, Jones and Jones 2002). Thus, in preparation for the planned FE validation study, uniaxial tension tests were conducted over a wide range of strain rates (710 5 500 s 1 ) on A36 plate specimens. Because reduced scale thicknesses of some barge components (mostly hull plates) are too thin to be addressed by the A36 specification, these parts will be constructed from ASTM A1011 hot rolled sheet steel, the most similar alternative to A36. Therefore, A1011 sh eet specimens were included in the material testing program as well. The remainder of this chapter documents the material testing program, including development of rate sensitive constitutive models (implemented in LS DYNA) for the materials that were eval uated. A novel testing apparatus was designed for this study that employs a large scale impact pendulum to break specimens at high strain rates. Design features of the testing apparatus and associated data processing procedures are discussed in this chapte r.

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77 4.1 Materials and Methods Experimental methods used to characterize the materials of interest are discussed in this section. Uniaxial tension tests were carried out in two series: 1) quasi static tests utilizing conventional laboratory equipment and standar dized procedures, and 2) high strain rate tests utilizing a new pendulum based high rate testing apparatus (HRTA) designed specifically for this study. The design features and functionality of the HRTA are discussed in detail below. 4.1.1 A1011 and A36 Steel Mat erials evaluated in this study included ASTM A1011 (ASTM 2012a) hot rolled carbon steel sheet, and ASTM A36 (ASTM 2008) carbon steel plate. The A1011 specification includes numerous material grades, of which, the most commonly available are CS (commercial steel) and DS (drawing steel). The specific grade evaluated in this study was A1011 CS Type B. For this grade, no limits on the mechanical properties are specified by ASTM; however, yield strength in the range of 30 50 ksi and elongation at failure excee ding 25% is generally expected (ASTM 2012a). Two thicknesses of A1011 steel were tested: 11 ga. (0.115 in.) and 9 ga. (0.155 in.). In contrast to A1011, where mechanical property limits are not specified, the ASTM A36 specification requires yield strength to exceed 36 ksi, ultimate strength to be between 58 80 ksi, and elongation to exceed 21% in a 2 in. gage length (ASTM 2008). A single thickness of A36 steel was tested: 0.25 in.. Multiple test specimens of matching grade and thickness were cut from a si ngle sheet or plate, which eliminated batch to batch variability in mechanical properties as a parameter considered in this study. The surface finish provided from the mill (including mill scale) was retained where possible. 4.1.2 Uniaxial Tension Testing (Quasi Static) Quasi static uniaxial tension tests were performed in accordance with ASTM A370 (ASTM 2012b) using sub sized flat specimens (as defined by ASTM) (Fig. 4 1 A ) and an Instron

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78 3384 electromechanical test ing system (Fig. 4 1 B ). Specimens were clamped in wedge action tension grips, and pulled to failure at a constant crosshead velocity. Specimen resistance was measured by a 33.75 kip load cell, and elongation was measured by an Instron 2360 114 clip on extensometer with specimen clips modified to reduce the gage length from the stock length of 2 in. to a modified length of 1 in. Per manufacturer recommendations, the extensometer was removed prior to specimen fa ilure to avoid damaging the instrument. Specifically, tests were paused to allow removal of the extensometer when the measured strain reached 0.15 in./in., after which tests were resumed until specimen failure (Section 4. 2 .1 provides details on how strain was measured beyond 0.15 in./in.). Data acquisition and test system control were performed 4.1.3 Uniaxial Tension Testing (High Strain Rate) Uniaxial tension tests at high strain rates (1 500 s 1 ) were conducted using a testing apparatus that employs an impact pendulum as the means of rapidly imparting energy. The impact pendulum was designed by researchers at the University of Florida (UF) for the Florida Department of Transportation (FDOT) Structures R esearch Center located in Tallahassee, Florida (Consolazio et al. 2012c). As shown in Fig. 4 2 A the pendulum consists of three 50 ft tall towers. A pendulum mass (hereafter referred to as the impact block) is suppo rted by four steel cables between two of the towers, and is lifted to the intended drop height by a cable, pulley, and winch system attached to the third tower. The pendulum is capable of dropping a 9,000 lb impact block from a maximum height of 35 ft. How ever, a 2,200 lb impact block was used for this study (Fig. 4 2 B ), with drop heights ranging from 1 25 ft to achieve different strain rates. The impact block consisted of a reinforced concrete core, surrounded on four sides by steel plates. A semi rigid nose assembly, built up from 0.5 1.0 in. thick steel plates, was

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79 attached to the impacting side of the block. Additional details pertaining to the pendulum facility and impact block can be found in Consolazio et a l. (2012c). 4.1.3.1 Pendulum b a sed h igh r ate t est a pparatus (HRTA) A novel testing apparatus was designed and employed in this study to perform uniaxial tension tests at high strain rates. The high rate testing apparatus (HRTA) is similar in principle to commercia lly available testing devices, such as instrumented falling weight impact (IFWI) machines, that employ impact energy to initiate specimen extension. However, given the large scale of the pendulum facility, the design philosophy of the HRTA was different th an that of IFWI devices previously employed in tensile testing (Shin et al. 2000, Thompson 2006, Bardelcik 2012). Fig. 4 3 A presents a simplified depiction of the impact that occurs during an IFWI tension t est. A relatively large striker mass, m 1 is given an initial velocity v 1,o by dropping it from a specified height. Mass m 1 strikes a lightweight anvil, m 2 that is fixed to the specimen, ideally resulting in a perfectly inelastic impact. Note that the imp act is only inelastic because specimen resistance maintains contact between the striker and anvil. As might be expected, if the two surfaces are stiff, significant high frequency ringing can occur, resulting in highly oscillatory specimen response. Recent studies (Thompson 2006, Bardelcik 2012) employed RTV silicone damping pads between the striker and anvil to reduce ringing. However, damping the impact results in delayed anvil and specimen response, and thus a non uniform strain rate through the test. The refore, damping pad thickness must be carefully selected to balance the competing objectives of rapid anvil acceleration and minimal ringing vibration. The HRTA designed in this study attempts to avoid these issues by employing an elastic impact instead. A s illustrated in Fig. 4 3 B m 1 corresponds to the 2,200 lb pendulum impact block, which can attain a maximum velocity of 48 ft/s from a drop height of 35 ft. This

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80 magnitude of impact energy greatly exceeds what is typically possible in a laboratory setting. Consequently, m 2 in the HRTA can be considerably more massive than is possible in IFWI tension tests. In this study, m 2 = 130 lb. Given a perfectly elastic impact (and m 1 >> m 2 ), the post impact velocity of m 2 can approach two times the pre impact velocity of m 1 Thus, if the pendulum is dropped from the maximum height of 35 ft, then after impact, the velocity of m 2 is v 2,f 96 ft/s. Even at lower drop heights, m 2 possesses sufficient momentum to break an A STM sized steel specimen without slowing appreciably. As a result, specimen extension is achieved through a single, nearly instantaneous impact, completely avoiding the ringing issue discussed above. Furthermore, the moving specimen end accelerates to the desired extension rate extremely rapidly. As shown in Fig. 4 4 the HRTA consists of two main assemblies: 1) a rotating control arm with impact head (to be struck by the pendulum impact block), and 2) a main driv e line consisting of a 1 in. diameter threaded rod with mass plates attached to the end (discussed below). Rocker plates support the mass plates, allowing for unimpeded small displacements along the drive line axis. Test specimens are mounted between these two assemblies (Fig. 4 4 B,D ), anchored to the drive line and elongated by rotation of the control arm. To expand the range of strain rates that can be achieved, the HRTA can be assembled in two configurations: h orizontal (Fig. 4 4 A B ) for lower strain rates, and angled (Fig. 4 4 C D ) for higher strain rates. Fine adjustments to the testing rate are achieved by varying the pendu lum drop height. To test a specimen at high rate, the impact block was released from the desired drop height, allowing it to swing down and strike the impact head of the HRTA (Fig. 4 5 A B ). Because both the impac t block and the HRTA impact head were constructed from thick steel plates, the impact event was elastic and nearly instantaneous. Post impact momentum of the

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81 impact head caused the control arm to rotate, and this motion elongated and broke the specimen (Fi g. 4 5 C D ). The impact head mass was chosen to carry sufficient momentum that specimen resistance did not appreciably slow rotation of the control arm. As a result, a nearly constant specimen elongation rate was achieved. After the control arm rotated approximately 90, device momentum was arrested by sand bags. The HRTA drive line was designed to act as a single degree of freedom (SDF) oscillating system. By specifically tuning mass (provided by mass plates) and stiffness (provided by threaded anchor rod), drive line oscillation was dominated by the natural frequency of the SDF system. This design thereby minimized the influence of high frequency vibrations that would result from anchoring the specimen to a more r igid reaction point. Furthermore, analyses conducted during the HRTA design stage indicated that if the drive line was permitted to undergo multiple oscillations during the specimen extension event, significantly non uniform strain rates could result. Ther efore, drive line mass and stiffness were selected such that the natural period was similar to or longer than typical test durations. Detailed fabrication drawings for the HRTA are provided in Appendix C. 4.1.3.2 Instrumentation As shown in Fig. 4 6 A specimens employed in the high rate program had the same basic dimensions as the low rate program to avoid introducing scaling discrepancies. Given the strain rates that occurred in the high rate test program, digit al image correlation was used to quantify engineering strain in the specimen. Square 0.0625 in. gage marks were drawn on each specimen with a permanent marker, approximately 1 in. apart. The reduced gage specimen region was filmed at 50,000 frames per sec ond with an IDT Redlake MotionXtra N3 high speed camera (Fig. 4 6 B ), and Xcitex ProAnalyst software was used to quantify gage mark displacements in

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82 two dimensions (in the plane of the pendulum swing moti on). To improve contrast between the gage marks and specimen, the specimen surface was blasted with fine grit sand. Reaction force in the drive line was measured with an Interface REC 15K rod end load cell, and acceleration of the mass plates at the end of the drive line was measured with a PCB Piezotronics 352A60 piezoelectric accelerometer (500g). Data from these sensors were acquired at a sampling rate of 50 kHz using a National Instruments cDAQ 9178 acquisition system. Balluff BLS 18KF XX 1P S4L infrare d break beam sensors triggered the data acquisition and high speed camera to begin recording immediately prior to impact. 4.1.4 Summary of Testing Program A summary of the full testing program is provided in Table 4 1 As noted in Section 4. 1 .1 three main series of experiments were conducted: two involving A1011 steel (two thicknesses, denoted A1011 T11 and A1011 T15), and one involving A36 steel (denoted A36 T25). Within each material series, tests were conducted at e ight strain rates (denoted R1 R8) covering several orders of magnitude (10 5 10 2 s 1 ). Three or four repetitions of each test were conducted (denoted A, B, C, D). Tests at rates R1 R4 were conducted in the laboratory using the Instron test machine, w hile tests at rates R5 R8 utilized the impact pendulum and HRTA. A total of 84 tests were conducted (28 for each material series). 4.2 Theory and Calculation Procedures In this section, theoretical support for data processing procedures that were employed in the study is discussed. A calculation framework is presented, in which Cowper Symonds coefficients C and P are determined for the materials tested by means of optimization. 4.2.1 Quasi Static Testing Program One of the primary goals of the testing program was t o characterize stress strain behavior at all strains up to failure. However, as noted in Section 4. 1 .2 the extensometer utilized to

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83 measure strain in the quasi static testing program had to be removed prior to specimen fracture. For each quasi static test the extensometer was removed at a measured strain of 0.15 in./in.. The procedure illustrated in Fig. 4 7 was used to estimate larger strains, based on the crosshead displacement of the Instron machine. Specific ally, a parabolic function was fit to measured strain displacement data (for strains between 0.10 0.15 in./in.) and all strains larger than 0.15 in./in. were estimated by extrapolation along the fitted parabola. This procedure was found to predict the me asured failure strains (quantified by placing the two pieces of each specimen together and measuring elongation of the gage region) to within 1 2% error. 4.2.2 High Rate Testing Program Interpreting data measured from the high rate testing program required con sideration of inertial effects associated with the dynamic response of the HRTA. While engineering strain was readily quantified via digital image correlation, stress in the specimen could not be measured directly. To address this issue, two data interpret ation methods are presented in the following sections: a direct method based on dynamic equilibrium of a SDF oscillating system, and an indirect method in which the strain rate sensitive constitutive behavior is determined by iterative optimization. For re asons that are provided below, the latter method was employed in the interpretation of all HRTA test data. 4.2.2.1 Single d egree of f reedom d ata i nterpretation As noted in Section 4. 1 .3.1 the drive line of the HRTA was intended to act as a lightly damped SDF osci llating system (Fig. 4 8 ). During each test, the system was subjected to a time varying force imparted by the specimen, F S ( t ), which was equal to the engineering stress times the original cross sectional area of the spe cimen. Subjected to forced vibration by F S ( t ), the damped SDF equation of motion is:

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84 ( 4 1 ) where M is the mass of the plates attached to the e nd of the drive line, C is the damping coefficient resulting from natural damping in the drive line, and K is the stiffness of the drive line. Note that the load cell used during testing measured the total reaction force acting on the mass, F R ( t ), includin g both the stiffness and damping terms. Therefore, and thus: ( 4 2 ) Because M is known, a ( t ) is measured by an accelerometer, and F R ( t ) is measured by a load cell, F S ( t ) and thus, engineering stress can, theoretically, be easily computed. However, the validity of Eqn. 4 2 depends on the system responding as a SDF system. Unfortunately, con nections between the mass plates and other elements of the drive line in the experimental setup were more flexible than intended. This additional source of flexibility resulted in localized oscillations that did not track temporally with the oscillations o f the overall system, and the influence of these oscillations on instrument measurements could not be removed through signal processing. Therefore, an alternative data processing method (described below) was developed that does not depend on SDF response. 4.2.2.2 Impulse m omentum d ata i nterpretation Consider integrating Eqn. 4 2 with respect to time, over the interval [ t 1 t 2 ]: ( 4 3 ) where, t 1 is a time immediately prior to specimen extension, and t 2 is a time well after the specimen has broken and all oscillation in the HRTA has ceased. Evaluating the integral:

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85 ( 4 4 ) Because ( 4 5 ) where, J R is the reaction impulse, and J S is the impulse imparted by the specimen to the mass M Note that Eqn. 4 5 does not imply that J R and J S are equal at all times Indeed, while the system oscillates in free vibration (after the specimen has broken), system momentum, is continuously converted into reaction impulse, J R ( t ), and vice versa, until motion eventually damps out. During this period, J R ( t ) is expected to oscillate about and eventually settle on the final value J R ( t 2 ), which is equal to the specimen impulse J S ( t 2 ) in accordance with Eqn. 4 5 Note that the validity of Eqn. 4 5 does not depend on the HRTA acting as a SDF system. It can be readily demonstra ted that Eqn. 4 5 holds for systems of any number of degrees of freedom that are anchored by a single point (the derivation is omitted here for brevity, but is provided in Appendix D). It is also important t o note that Eqn. 4 5 is insufficient to determine the stress strain response of an arbitrary material. In fact, given a particular measured force time history F R ( t ), there exist an infinite number of stress strain relations for which Eqn. 4 5 can be satisfied. However, because quasi static tension tests were conducted on the materials of interest, characteristics of the static stress strain relations were well understood. Furthermore, for the high rate tests, the strains, and by extension, the time varying strain rates were known. Lastly, because the materials tested in this study were steels, the general manner in which plastic stresses were influenced by the s train rate were known from the literature. Specifically, numerous prior studies have demonstrated that the Cowper Symonds expression describes rate sensitivity in

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86 many metals quite well, including steels (Jones 1997, 2013, Hsu and Jones 2004, Jones and Jon es 2002). Therefore, these known characteristics were combined with Eqn. 4 5 to form a calculation framework in which the Cowper Symonds rate sensitivity parameters C and P were determined by iterative optim ization. The calculation framework (summarized in Fig. 4 9 ) was used to determine optimal values of C and P that minimized the difference between an assumed constitutive response based on the known stress s train and rate sensitivity characteristics described above and the measured HRTA response, in accordance with Eqn. 4 5 As shown in Fig. 4 9 the calculation process begins with the average stress strain curve calculated from the four test repetitions conducted at rate R1 (nearly static, ). Given the typical dogbone specimen geometry employed in this study, strain rate was not consta nt through the specimen extension event, even for rate R1. As such, strain rate was computed as a function of strain, by numerically differentiating the strain time histories from each R1 test and computing an interpolated aver age among the four tests. With this relation for R1, trial values of C and P were selected. Because rate R1, while extremely slow, was not truly static, the average R1 stress strain relation, was scaled down using the Cowper Sy monds expression to form a truly static constitutive curve, that was representative of the material of interest (illustrated in Fig. 4 10 ). This static curve was used as a baseline fo r computing the response of other test strain rates in the study. The steps enumerated below describe the process that was employed for computing a dynamic stress strain curve, for each test conducted ( i static curve, experimental data, and the Cowper Symonds expression. First, was

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87 where was the maxim um (failure) strain for test i (Fig. 4 10 ). This step accounted for differences in ductility between tests and was especially important, as significant increases in ductility were observed at higher strain rates in this study. Given the variable strain rate, (computed from experimental data for test i ), the ductility Symonds expression to form a dynamic stress str ain relation, (Fig. 4 10 ). It is important to note that each point in the curve was individually scaled to reflect the strain rate at that instant during th e test. Because such curves are specific to the conditions imposed on the specimens during each test, they are the most accurate possible representation of as tested specimen response, given the information available and the assumptions made. From and the measured strain time history the specimen stress time history, was computed and multiplied by the original specimen cross sectional area, to compute the specimen force time history, Note that stresses were expressed as engineering stresses throughout the calculation process (rather than true stresses), therefore was the appropriate area q uantity. To obtain total specimen impulse, the force time history, was numerically integrated. Similarly, the reaction force time history, (measured by the load cell), w as integrated to obtain the total reaction impulse, The final calculation step involved comparing the assumed specimen response to the measured reaction response in accordance with Eqn. 4 5 Rearranged, Eqn. 4 5 can be written Therefore, a quantity termed impulse ratio ( IR ) was defined as For a particular test, the condition IR i = 1 suggests that the assumed values of C and P (and the other

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88 assumptions in the calculation framework) are correct for that test. It follows then, that if IR i = 1 for all tests ( i C and P have been determined. Given th e presence of natural variability in the tested specimens, achieving IR i = 1 for all tests is unlikely. Therefore, the objectives for optimizing C and P were instead that the median IR among all tests be equal to 1.0 and the coefficient of variation (COV) be minimized. 4.3 Results and Discussion Results obtained from the quasi static and high rate test programs are described in the following sections. Using the methods described in Section 4. 2 .2.2 unique Cowper Symonds coefficients C and P were computed for ea ch of the three materials tested. 4.3.1 Quasi Static Testing Program Engineering stress strain curves obtained from the quasi static testing program (rates R1 R4) are provided in Fig. 4 11 Thinner grey traces correspond to individual repeated tests, while thicker black traces correspond to point by point interpolated averages of the four repetitions in each test series. Average curves were computed by re sampling the curve for each repetition at strain increments equal t o 10 4 in./in., then averaging stress values at each point of common strain. Average curves were terminated at the smallest breaking strain among the four curves being averaged. The most striking observation is that stress strain curves for the A1011 T11 a nd A1011 T15 series were largely dissimilar, even though the material grade was the same and only the thickness differed. The T11 curve exhibited a smooth shape, without a well defined proportional limit, while the T15 curve included a clearly defined yiel d plateau followed by strain hardening. Additionally, the T15 material exhibited higher strength than T11, but with lower ductility. The A36 T25 series consistently had the highest ultimate tensile strength among the materials tested, and its mechanical pr operties conformed to the limits specified by ASTM.

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89 None of the materials that were tested exhibited a well While several methods were explored for determining a representative modulus for each material (e.g., curve fitting, numerical differentiation, visual methods), each method yielded unacceptably variable results from test to test, and none were deemed to be sufficiently reliable. The ASTM A370 standard acknowledges difficulty in establishing a linear modulus for many mat erials, and suggests a representative value of 30,000 ksi for carbon steels (ASTM 2012b). Given that the focus of this study was characterizing the plastic behavior of the materials tested, the representative elastic modulus value suggested by ASTM was ado pted for further calculations (e.g., computing effective plastic strain) and employed in the finite element constitutive models discussed in Section 4. 4 The rate sensitivities of various physical properties observed from the quasi static test program are shown in Fig. 4 12 Because the materials did not exhibit a well defined modulus, yield stress was computed using the extension under load (EUL) method described in ASTM A370 (ASTM 2012b). Specifically, yield s tress was taken to be the stress corresponding to an engineering strain of 0.005 in./in. (0.5% EUL), as suggested by ASTM for this class of materials. As shown in Fig. 4 12 A some increase in yield stress was o bserved for all three material series. Similar results were observed for ultimate stress (Fig. 4 12 B ). For each material series, yield and ultimate stress increased by a about 5 10% from rate R1 (~710 5 s 1 ) to R4 (~510 2 s 1 ). As reported in Fig. 4 12 C strain at specimen failure (failure elongation) was determined by placing the two pieces of specimen together, measuring the change in length of the reduced gage region, and dividing by the original gage length, as specified by ASTM (ASTM 2012b). While ductility appeared to increase with increasing strain rate for the A1011 T15 and A36 T25 series, an apparent decrease was observed for A1011 T11. It is noted that cl ear increases in

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90 ductility were observed for all materials at higher strain rates in the pendulum testing program (following section). Thus, the mixed results obtained during quasi static testing can be attributed to typical variability in material ductili ty and error inherent in the method used to measure elongation. It is important to note that measured strain rates were not perfectly constant through the duration of each quasi static test. As a representative example, strain rate is plotted as a function of strain in Fig. 4 12 D for test A36 T25 R3 C. As shown, strain rate increased rapidly in the near elastic region, and continued to increase (less rapidly) throughout the test. Note that the crosshead velocity was extremely constant through the duration of each test. Thus, the consistently observed increase in strain rate was primarily a consequence of the dogbone shaped specimen geometry and the continually varying stiffness of the reduced gage region. Such be havior could only be avoided if the testing machine was capable of continuously adjusting the crosshead velocity so as to maintain a constant strain rate in the gage region, which the Instron machine employed in this study was not able to do. Consequently, the strain rates plotted in Fig. 4 12 A C reflect the strain rate measured at the time that the event of interest occurred (e.g. yield). 4.3.2 High Rate Testing Program As discussed in Section 4. 2 .2.2 during the hig h rate tests, strain was quantified from displacements which were measured using digital image correlation, however, direct measurement of specimen stress was not possible using the HRTA. Consequently, data from the high rate and quasi static test programs were combined with the data processing method summarized in Figs. 4 9 and 4 10 to quantify rate sensitive material behavior. Optimal Cowper Symonds coefficients C and P that were a best fit to the experimental data were computed for each material series. This section presents and discusses results from key portions of the data

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91 processing methodology. Note that detailed data presented in this section correspond to the final iteration of the optimization procedure, and thus, correspond to the outcome of the procedure with optimal values of C and P (presented near the end of this section). Strain rates measured from the high rate tests are presented in Fig. 4 13 as a function of engineering strain. As before, thinner grey traces correspond to individual tests, and thicker black traces correspond to the interpolated average among the three repetitions for that test seri es. While strain rates were not perfectly uniform, variability was fairly small among tests in a given series, with the notable exception of the A1011 T11 R6 series (Fig. 4 13 a). For all series, temporal f luctuations in strain rate were primarily attributed to vibrations within the HRTA. While the components of the HRTA were designed to be as stiff as practical, high speed video of the overall system uncovered small motions in the base plate elements that s upported the rotating control arm. These motions, combined with smaller magnitude high frequency vibrations contributed to oscillations in the strain rate. Regardless, oscillations of the magnitude shown in Fig. 4 13 were not considered detrimental because the data processing procedure (Fig. 4 9 ) accounted for temporal variations in strain rate by scaling stresses at each point in time through the duration o f a test. Engineering stress strain curves computed for each high rate test are presented in Fig. 4 14 (thin grey traces represent individual tests; black traces represent the interpolated average). In addition to i ncreased strain rates producing increased stresses (as dictated by the scaling model employed), a clear increase in ductility was also observed as strain rate increased, particularly for the A36 T25 material. Indeed, at testing rate R8 (Fig. 4 14 D ) the ductility of all three materials was nearly identical, which is in stark contrast to the lowest rate, R1 (recall Fig. 4 11 A ), at which the A1011 T11 material was almost twice as ductile as the A36 T25 material.

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92 Using the procedure in Fig. 4 9 the computed stress strain relations (presented in Fig. 4 14 for rates R5 R8), were combined with measured strain time histories, ( t ), to compute specimen force time histories, F S ( t ), for every material test conducted in the study (rates R1 R8) as: ( 4 6 ) In Fig. 4 15 specimen force time histories are compared to measured reaction force time histories, F R ( t ), for two representative tests. The first example, A36 T25 R1 A (Fig. 4 15 a), was conducted at the lowest test ing rate using the Instron testing machine, while the second example, A36 T25 R6 A (Fig. 4 15 b), was conducted using the HRTA. As expected, no dynamic oscillation was observed in F R for the quasi static test (Fig. 4 15 A ), and F S was nearly equal to F R throughout the test. Recall that in this context, F S was computed within the calculation framework in Fig. 4 9 and is thereby approxi mate. Deviation between F S and F R observed near the end of the test can be attributed to assumptions made in the calculation framework and to deviations of physical specimen properties from the idealized rate sensitivity model employed. The degree of devia tion shown in Fig. 4 15 A can be considered representative of the various quasi static tests. In contrast, significant dynamic oscillation was observed in F R (Fig. 4 15 B ) for the hi gh rate tests and F S was almost never equal to F R This oscillation can be attributed to the dynamic response of the HRTA drive line both during the specimen extension event ( t < 8 msec), and after failure of the specimen ( t > 8 msec). As shown, the dynami c response damped out as the drive line came to rest, at which time F R = 0. This example serves to illustrate the difficulty in directly determining force in the specimen, F S from the measured response, F R because vibrations within the HRTA partially obs cured the intended measurement.

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93 Consequently, specimen and reaction impulse ( J S and J R respectively) were computed by numerically integrating corresponding force time histories. For the quasi static case (Fig. 4 16 A ), J S and J R match closely, with a small deviation observed near the end of the test, caused by the difference between F S and F R discussed above. In contrast, for the dynamic case (Fig. 4 16 B ), deviations were observed b etween J S and J R throughout the specimen extension event and immediately after specimen fracture ( t < 25 msec). However, as HRTA motion damped out, J R oscillated about J S in a rapidly decaying manner, and eventually settled to a value approximately equal t o J S This behavior was expected in accordance with the impulse momentum principle, as demonstrated by the derivation of Eqn. 4 5 in Section 4. 2 .2.2 The final step in the calculation framework involved comp uting the impulse ratio ( IR = J S / J R ) for each test in the study. Recall that values of IR nearly equal to 1.0 indicate that the values for rate sensitivity parameters C and P assumed at the beginning of the process are a good fit to the measured data. Sign ificant deviations from 1.0 would suggest that C and P should be adjusted. Note that for quasi static tests, the values of J S and J R used to compute IR were simply the values at the time that the specimen fractured (end of test). However, for dynamic tests J R oscillated about a terminal value as discussed above. Consequently, the mean value of the impulse time history after the specimen fractured (corresponding to free vibration of the HRTA) was the J R value used to compute IR for high rate tests. For the optimal values of C and P computed for each test series, histograms of IR are presented in Fig. 4 17 A summary of basic IR statistics is also provided in Table 4 2 t ogether with the computed optimal values of C and P for each series. As shown, IR values were tightly grouped around the ideal value of 1.0, rarely deviating by more than 5%. For each material series, the median value of IR was equal to 1.0, and coefficie nts of variation (COV) were 2.0

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94 3.4%. This tight grouping in IR values suggests that the assumed rate sensitivity model and optimal C and P values were a close fit to the experimentally measured response. Note that in the optimization process, P was limi ted to integer values for simplicity. No perceptible improvements in IR statistics were observed by permitting P to take on fractio nal values. Recall that, as employed in this study, the Cowper Symonds expression states: ( 4 7 ) where dyn is the dynamic flow stress, and st is the stress at a theoretical static state in which Eqn. 4 7 is plot ted for each material series in Fig. 4 18 with optimal values for C and P from Table 4 2 Individual points shown in Figs. 4 18 a c are equal to the average impulse ratio for each testing rate (R1 R8) multiplied by dyn / st Error bars denote the minimum and maximum value within each rate series. Abscissa values for each point are the median strain rate through the duration of the test, averaged among the 3 4 tests within each series. Presented in this manner, Figs 4 18 A C provide a visual representation of the degree of variability in each test series with respect to the optimal Cowper Symonds curve. As shown, error was evenly distributed with respect to strain rate and insensitive to the method of testing (Instron machine versus HRTA). Confidence intervals (95%) were computed based on IR statistics, assuming uniform error with respect to strain rate. Cowper Symonds curves for each material series are compared in Fig 4 18 D As shown, the three curves covered a relatively narrow band of dyn / st over the range of strain rates considered. For example, at 10 5 s 1 dyn / st was equal to 1.04 1.06 among the three curves and at 10 3 s 1 dyn / st was 1.37 1.40. This tight grouping suggests that a single Cowper Symonds curve (with aggregated C and P values) would be acceptable, particularly given

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95 significant overlap among the confidence intervals. However, absent any cl ear reason for aggregating the curves, individually derived Cowper Symonds models were retained for each material series. For all three materials tested, values of C and P were higher than those published in the literature (Jones 1997, 2013, Hsu and Jones 2004, Jones and Jones 2002). As noted previously, C = 40.4 s 1 and P = 5 are values commonly employed for steels (Jones 1997). It is important to acknowledge that the basis for these reference values is a survey of the dynamic stresses of various metals pu blished by Symonds (1967), in which the author calculated C = 40.4 s 1 and P = 5 using the yield stress results of a single study on mild steel conducted by Manjoine (1944). Yield and ultimate stress results from Manjoine are reproduced in Fig. 4 19 A Evident from the figure, yield stresses were found to be significantly more sensitive to high strain rates than were ultimate stresses, and the values C = 40.4 s 1 and P = 5 fit the yield stress data well. Howe ver, for ultimate stress, C = 21,800 s 1 and P = 4.9 fit the data better. Cowper Symonds curves computed in the present study are compared to the range from Manjoine in Fig. 4 19 B It is observed that the m aterials evaluated in the present study were significantly less rate sensitive than the yield stresses from Manjoine; however, the level of sensitivity of ultimate stress was fairly consistent with data from Manjoine. As discussed in Section 4. 3 .1 the mat erials evaluated in this study were found to have similar rate sensitivity for both yield and ultimate stress, and therefore the C and P values in Table 4 2 were derived to be the best fit to the experimental data for all strain levels (ranging from yield to failure). While dramatic differences in rate sensitivity at yield versus ultimate stress were observed in Manjoine (1944), the materials evaluated in the present study did not exhibit similarly dramatic rate sensit ivity at small strains (near yield). Similar to Manjoine, numerous

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96 other studies (discussed Jones 1997) have found a difference in rate sensitivity at yield versus ultimate stress, however, the discrepancy was generally smaller than Manjoine. Reasons for t he differing observations produced by Manjoine (1944) when compared to the current study are unclear. Certainly, steel chemistry, mill production processes, and experimental testing methods have undergone significant changes since the 1940s. Also, the stee l specimens tested by Manjoine were bright annealed prior to testing, while in the present study, specimens were tested in the condition provided from the mill. As recently highlighted by Jones (2013), strain rate characteristics of mild steel vary signifi cantly from study to study, and can be influenced by factors including surface finish, chemical content, and specimen geometry. However, in light of the potentially large degree of variability, it is notable that the specimens tested in this study taken fr om three material batches of two different material specifications exhibited strain rate sensitivity that was strikingly similar. 4.4 Constitutive Model Details As noted earlier, a primary goal of this study was to develop strain rate sensitive constitutive mo dels for use in finite element simulations of vessel impact involving large scale plastic deformations (using the LS DYNA code). The LS DYNA material database includes multiple isotropic plasticity models that follow well established forms (e.g., Johnson C ook). However, the most general model available is MAT_24 ( MAT _PIECEWISE _LINEAR _PLASTICITY ). This model permits the user to specify the stress strain curve (in terms of true stress and effective plastic strain) as an arbitrary piecewise linear curve. Gi ven that detailed experimental data were collected during this study, this feature is highly desirable.

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97 4.4.1 Strain Rate Sensitivity For rate sensitivity, MAT_24 employs the Cowper Symonds equation in two possible ways. First, if parameter SIGY > 0 (generally o ne would choose SIGY to be equal to the yield stress), then dynamic stress ( dyn ) is computed as: ( 4 8 ) where, is the static stress (as defined by the user specified material curve), is the effective plastic strain, is the effective plastic strain rate, and C and P are the Cowper Symonds coefficients. If parameter SIGY = 0, then LS D YNA employs an alternative scaling rule: ( 4 9 ) This latter rule is consistent with the scaling assumptions made in the formulation of C and P for this study, and w ill therefore be utilized in the constitutive models. 4.4.2 Failure Strain Considerations Using MAT_24 material failure is simulated by element deletion when plastic strain within an element exceeds a specified threshold value (denoted FAIL in the material defi nition). One of the limitations of MAT_24 is that this failure criterion cannot be defined as being strain rate sensitive. As noted in the prior section, ductility of the materials tested in this study tended to increase with increased strain rate. As such the failure criterion limitation in MAT_24 requires specific attention (discussed in more detail below). The choice of an appropriate failure strain is further complicated by the size of the finite elements used in the mesh (relative to the size of the s tructural member being modeled). For the

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98 simulation scale of interest in this study, if elements are very small (i.e., on the order of 0.01 in. or smaller), then necking deformation prior to failure, and associated non uniform stress distribution in the ne cked region, can be modeled directly. In this case, very high levels of localized strain (>1 in./in.) will occur in the necked region prior to failure, and a correspondingly high value of failure strain should be assigned in the FE model to avoid premature simulation of fracture. Conversely, if the finite elements are large (i.e., on the order of 0.25 in. or larger), then the finite element model cannot directly simulate necking effects. In this situation, each element represents material behavior in a macr oscopic sense (similar to the manner in which material behavior is characterized in typical uniaxial tension testing, where stress and strain are calculated as average values over a finite size gage region) and the most appropriate failure strain for the F E constitutive model is the effective plastic strain at failure observed from uniaxial tension testing (0.2 0.4 in./in. for the materials tested in this study). For the FE model scales of interest in this study (dogbone material samples up to full scale vessels), the element sizes are large enough that the latter approach to choosing failure strain is most appropriate. As noted above, in MAT_24 a value for failure strain must be selected that is constant with respect to strain rate, even though increased ductility was observed in the evaluated materials at higher strain rates. Table 4 3 summarizes minimum and maximum failure strains quantified from the experimental study, where the minimum was observed for ra te R1, and the maximum was observed for R8. Simulations scenarios of interest in this study were not found to be strongly sensitive to the choice of failure strain over the range shown in Table 4 3 Consequent ly, the average of the R1 and R8 failure strains was selected for use in the FE constitutive models. For brevity, sensitivity simulations supporting this conclusion are not documented in this chapter; however, a complete discussion can be found in Appendix E. It is

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99 acknowledged that certain classes of problems (e.g., metal forming simulations) may be more sensitive to material ductility, and thus warrant a more detailed treatment of failure. For this reason, the MAT_24 constitutive model in LS DYNA support s the use of user defined failure subroutines that can be programmed to include strain rate sensitivity. However, this level of refinement was unwarranted for the impact problems of interest in the present study. 4.4.3 Constitutive Curves Static constitutive cur ves were developed for each material series by scaling down the interpolated average R1 curve to account for the non zero strain rates at which specimens were tested, and stretching the curve along the strain axis to match the desired strain at failure (re call Figs. 4 9 and 4 10 for a description of this process). For input into MAT_24 the curve data were converted from engineering stress and strain to true stress and effective plastic strain. Lastly, the curves were decimated to include a minimal number of points. To minimize error with respect to experimental data, points on the curve were concentrated in regions of significant curvature. The resulting constituti ve curves are presented in Fig. 4 20 Note that because the FE mesh size (greater than 0.25 in.) in the simulations supported by this study is significantly larger than the concentrated region formed by necking, it would be ideal to retain material softening near failure (resulting from necking in the experimental specimens) in the FE constitutive curves. However, including softening in constitutive curves can cause numerical instabilities. Therefore, the FE constitu tive curves were simplified such that the maximum stress was held constant until failure occurs, as shown in Fig. 4 20 If elements were sufficiently small to simulate necking behavior directly, it would be more app ropriate to continue the constitutive curves at a constant positive slope from the point at which necking initiates.

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100 4.4.4 Implementation in LS DYNA LS DYNA input data for the three constitutive models developed in this study are provided in this section. Note t hat the models are expressed in terms of U.S. customary units (kip and in.). Each model consists of two parts: a material definition (denoted *MAT _PIECEWISE _LINEAR _PLASTICITY ), and a curve definition (denoted *DEFINE _CURVE ) consisting of the true stres s versus effective plastic strain curve. This curve is referenced by the parameter LCSS in the material definition. Cowper Symonds coefficients are defined by parameters C and P in the material definition. For all three models, mass density ( RO ) is equal t o 7.3410 7 kip/in./s 2 (490 E ) is equal to 30,000 PR ) is equal to 0.30. See LSTC (2007) for details on other parameters in the material definitions. 4.4.4.1 A1011 T11 m odel *MAT_PIECEWISE_LINEAR_PLASTICITY $# mid ro e pr sigy etan fail tdel 1 7.3400E 7 30000.000 0.300000 0.000 0.000 0.363000 0.000 $# c p lcss lcsr vp 9.2000E+6 10.000000 1 0 1.000000 $# eps1 eps2 eps3 eps4 eps5 eps6 eps7 eps8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 $# es1 es2 es3 es4 es5 es6 es7 es8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 *DEFINE_CURVE $# LCID SIDR SFA SFO OFFA OFFO DATTYP 1 0 0.000 0.000 0.000 0.000 0 $# A1 O1 0.000 31.9029999 0.0073300 35.1220016 0.0146600 37.4809990 0.0256600 40.3069992 0.0403200 43.2869987 0.0586400 46.2369995 0.0806300 49.0439987 0.1099600 51.9939995 0.1429400 54.6850014 0.2089200 58.9760017 0.2785600 62.5239983 0.3005500 63.0989990 0. 3628600 63.1989990 4.4.4.2 A1011 T15 m odel *MAT_PIECEWISE_LINEAR_PLASTICITY $# mid ro e pr sigy etan fail tdel 2 7.3400E 7 30000.000 0.300000 0.000 0.000 0.308000 0.000 $# c p lcss lcsr vp

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101 2.0500E+7 10.000000 2 0 1.000000 $# eps1 eps2 eps3 eps4 eps5 eps6 eps7 eps8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 $# es 1 es2 es3 es4 es5 es6 es7 es8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 *DEFINE_CURVE $# LCID SIDR SFA SFO OFFA OFFO DATTYP 2 0 0.000 0.000 0.000 0.000 0 $# A1 O1 0.000 49.0219994 0.0031100 49.5880013 0.0217900 50.6160011 0.0249000 51.113998 4 0.0342400 53.9729996 0.0435800 55.9269981 0.0591400 58.3639984 0.0809300 60.8370018 0.1151600 63.7290001 0.1587400 66.6259995 0.2054300 68.9059982 0.2241000 69.0049973 0.3081400 69.1049973 4.4.4.3 A36 T25 m odel *MAT_PIECEWISE_LINEAR_PLASTICITY $# mid ro e pr sigy etan fail tdel 3 7. 3400E 7 30000.000 0.300000 0.000 0.000 0.273000 0.000 $# c p lcss lcsr vp 1.3200E+6 8.000000 3 0 1.000000 $# eps1 eps2 eps3 eps4 eps5 eps6 eps7 eps8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 $# es1 es2 es3 es4 es5 es6 es7 es8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 *DEFINE_CURVE $# LCID SIDR SFA SFO OFFA OFFO DATTYP 3 0 0.000 0.000 0.000 0.000 0 $# A1 O1 0.000 37.6539993 0.0027600 38.937 9997 0.0082700 44.0110016 0.0137800 48.3460007 0.0192900 51.7560005 0.0275600 55.7610016 0.0358200 58.8940010 0.0468500 62.1980019 0.0606300 65.3919983 0.0771600 68.3750000 0.1019600 71.7929993 0.1295200 74.7030029 0.1625900 77.3229980 0.1984100 79.5319977 0.22 32200 80.2129974 0.2728200 80.3129974 4.5 Summary The strain rate sensitive constitutive behavior of A36 and A1011 steel was investigated in this study by means of uniaxial tension testing at eight strain rates, covering seven orde rs of

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102 magnitude. A novel high rate testing apparatus (HRTA) was designed which employed an impact pendulum as the source of energy. Finite element constitutive models were also developed that are appropriate for use in vessel impact analysis. A number of o bservations can be made from the re sults presented in this chapter. First, t he yield and strain hardening behavior of the two thicknesses of A1011 steel tested differed significantly, while excellent repeatability was observed between specimens of the same thickness. The differences are more likely attributable to variability between steel batches than to any consequence of the difference in thickness. Second, t he HRTA employed elastic impact as the means of breaking specimens, in which the momentum of the impacted object (anvil) provided the breaking energy, not the momentum of the impactor (striker). This design avoided the problem of ringing vibrations observed in prior studies that have employed impact based test machines. No impact damping was required, resulting in rapid specimen acceleration. Third, t he HRTA drive line was designed to act as a single degree of freedom (SDF) oscillating system, so that inertial effects in the drive line could be measured and removed from the data. However, flexibility b etween the SDF mass and drive line anchor rod resulted in a multiple degree of freedom (MDF) response. Because it was infeasible to redesign and reconstruct the HRTA within the scope of this study, an alternative data processing procedure (based on impulse momentum principles that are not reliant on SDF behavior) was employed successfully. However, the SDF drive line concept does hold promise for future testing, as a way of mitigating the deleterious influence of drive li ne inertia on the measured data. Las tly, t he materials tested in this study were found to be significantly less sensitive to strain rate than many prior studies. Consequently, calculated Cowper Symonds coefficients were much larger than the values

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103 C = 40.4 s 1 and P = 5 commonly employed for mild steel Rate sensitivity, however, was very similar between the specimens tested in this study, despite being of different material grades.

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104 Table 4 1 Summary of experim ental testing parameters and number of repetitions Rate Appr ox. strain rate (s 1 ) Instron crosshead rate (in./min) A1011 T11 0.115 in. thck. A1011 T15 0.155 in. thck. A36 T25 0.25 in. thck. R1 7.0E 5 0.0075 A,B,C,D A,B,C,D A,B,C,D R2 7.0E 4 0.075 A,B,C,D A,B,C,D A,B,C,D R3 7.0E 3 0.75 A,B,C,D A,B,C,D A,B,C,D R4 3.5E 2 3.5 A,B,C,D A,B,C,D A,B,C,D Apparatus configuration Pendulum drop height (ft) R5 1.3E+1 Horizontal 1 A,B,C A,B,C A,B,C R6 4.1E+1 Horizontal 15 A,B,C A,B,C A,B,C R7 1.0E+2 Angled 4 A,B,C A,B,C A,B,C R8 2.5E+2 Angled 25 A,B,C A,B,C A,B,C Table 4 2 Rate sensitivity parameters and impulse ratio ( IR ) statistics Material series C (s 1 ) P IR : Impulse ratio Minimum Maximum COV A101 1 T11 9,200,000 10 0.958 1.154 3.4% A1011 T15 20,500,000 10 0.966 1.058 2.3% A36 T25 1,320,000 8 0.971 1.066 2.0% Table 4 3 Effective plastic strain at failure for each material series Material series E ffective plastic strain at failure (in./in.) Minimum (R1) Maximum (R8) Average A1011 T11 0.342 0.384 0.363 A1011 T15 0.280 0.336 0.308 A36 T25 0.206 0.340 0.273

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105 A B Figure 4 1 Quasi static testing. A) Specimen dimensions. B) Test setup and instrumentation. (Photos courtesy of Daniel J. Getter) A B Figure 4 2 Imp act pendulum facility at Florida Department of Transportation (FDOT) Structures Research Center in Tallahassee, Florida A) Pendulum towers. (Photo courtesy of Daniel J. Getter) B) Impact block. (Photo courtesy of Gary R. Consolazio)

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106 A B Figure 4 3 Depictions of impact scenarios in tension testing that rely on impact energy for specimen elongation. A) Perfectly inelastic impact. B) Perfectly elastic impact. A B C D Figure 4 4 High rate testing apparatus (HRTA) design A) Horizontal configuration schematic. B) Horizontal configuration section view. C) Angl ed configuration schematic. D) Angled configuration section view.

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107 A B C D Figure 4 5 High rate testing apparatus (HRTA) motions. A) Schematic before im pact. B) Photograph before impact. C) Schematic after impact. D) Schematic after impact. (Photos courtesy of Daniel J. Getter) A B Figure 4 6 High rate tes ting. A) Specimen dimensions and gage marks. B) Instrumentation setup. (Photo courtesy of Daniel J. Getter)

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108 Figure 4 7 Strain displacement relation for test A1011 T11 R1 B, including parabolic fit Figure 4 8 High rate test apparatus (HRTA) as a damped SDF oscillator

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109 Figure 4 9 Impulse momentum based optimization procedure for computing Cowper Symonds coefficients C and P Figure 4 10 Stretching and scaling of average R1 stress strain relation [ ] to arrive at dynamic stress strain relation for each test [ ], following procedure shown in Fig. 4 9

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110 A B C D Figure 4 11 Engineering stress strain curves for each quasi static test series A) Rate R1. B) Rate R2. C) Rate R2. D) Rate R4.

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111 A B C D Figure 4 12 Rate sensitivity of material parameters amo ng quasi stat ic testing rates. A) Y iel d stress. B) Ultimate stress. C) F ailure elongation. D ) Representative variation in strain rate through the duration of a quasi static test (data from test A36 T25 R3 C shown)

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112 A B C Figure 4 13 Engineering strain rate (among three tests per trace) as a function of strain A) A1011 T11. B) A1011 T15. C) A36 T25.

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113 A B C D Figure 4 14 Engineering stress strain curves (computed by the process in Figs. 4 9 and 4 10 ) for each high rate test series A) Rate R5. B) Rate R6. C) Rate R7. D) Rate R8.

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114 A B Figure 4 15 Specimen and reaction force time histories (computed by process in Fig. 4 9 ) for selected tests A) A36 T25 R1 A. B) A36 T25 R6 A. A B Figure 4 16 Specimen and reaction impulse time histo ries (computed by process in Fig. 4 9 ) for selected tests A) A36 T25 R1 A. B) A36 T25 R6 A.

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115 A B C Figure 4 17 Normalized histograms of impulse ratio ( IR ) for each material series (computed by process in Fig. 4 9 ) A) A1011 T11. B) A1011 T15. C) A36 T25.

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116 A B C D Figure 4 18 Sensitivity of dynamic stress to strain rate for each material test series A) A1011 T11. B) A1011 T15. C) A36 T25. D) Comparison of relations.

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117 A B Figure 4 19 Comparison of experimentaal data to Manjoine (1944) study. A) Rate sensitivity of yield and ultimate stress from Manjoine (1944), showing fitted Cowper Symonds coefficients C an d P. B) Comparison between Manjoine data and rate sensitivity curves derived in this study. Figure 4 20 Static constitutive curves developed for the MAT_24 m aterial model in LS DYNA

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118 CHAPTER 5 FINITE ELEMENT SIMULATIONS OF REDUCED SCALE BARGE IMPACT As discussed in the previous chapters, the finite element (FE) simulation techniques that are the basis for the UF/FDOT barge impact load model will be validated against pendulum impact experiments involving reduced scale barge bow specimens. Experimental results will be compared to the results of FE simulations of analogous impact conditions. As discussed in this chapter, constitutive models that were developed based on e xperimental testing (Chapter 4) were incorporated into a reduced scale version of the jumbo hopper barge bow FE model, and impact simulations were conducted that mimic the impact conditions that are expected during the pendulum impact experiments. Therefor e, the results of the simulations discussed in this chapter constitute the most accurate predictions of barge bow response to the experimental impact conditions that are currently available. Additionally, the sensitivity of simulation results to constituti ve modeling in the barge bow is discussed in this chapter. 5.1 Implementation of Finite Element Constitutive Models The finite element constitutive models (material models) described in Chapter 4 (referred re integrated into the 0.4 scale FE barge model that was used in the planning stages of the experimental study (Chapter 3). Specifically, the representative constitutive model for A36 that was employed in various prior studies (Consolazio et al. 2009, 2010 b 2012a, 2012b, Getter and Consolazio 2011) with Cowper Symonds coefficients C = 40.4 s 1 and P = 5 was replaced with the revised models. Note that the same LS DYNA material model type ( MAT _PIECEWISE _LINEAR _PLASTICITY ) was employed in both the origina l and revised constitutive models. Each of the revised constitutive models was assigned to specific parts of the FE barge model based on the 0.4 scale thickness of the material. Hull, gusset, and stiffener plates with

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119 thicknesses equal to 0.115 in. were as signed the A1011 T11 constitutive model, plates with thickness equal to 0.155 in. were assigned the A1011 T15 constitutive model, and plates with thickness equal to 0.25 in. were assigned the A36 T25 constitutive model. While the internal structural member s (angles and channels) have individual element thicknesses that are less than 0.25 in., such members are commercially manufactured and available from A36 steel. Therefore, the A36 T25 constitutive model was assigned to these parts. 5.2 Barge Impact Simulation s Using the revised FE model, impact simulations were conducted that were consistent with the impact conditions expected during the planned pendulum experiments. As shown in Fig. 5 1 the simulations consisted o f a 9,000 lbf rigid impact block and the fully deformable 0.4 scale barge bow model. For simplicity, the impact block was assigned roller type translating boundary conditions that only permit motion in the x direction, and barge nodes at the rear most inte rface were assigned fixed boundary conditions. It is acknowledged that these simplified boundary conditions do not precisely represent the physical support conditions of either the impact block (hanging from steel cables) or the barge bow (mounted to a rea ction frame that is not perfectly rigid). However, impact forces developed between the impact block and barge were found to be largely insensitive to the idealized boundary conditions employed in this model. To initiate each impact simulation, the impact b lock was assigned an initial velocity equal to 39.3 ft/s, which corresponds to a pendulum drop height of 24 ft. Subsequently, the block model impacted the barge bow model, causing several inches of bow deformation and ultimately arresting block motion. Ela stic rebound of the barge bow caused the impact block motion to reverse, and contact between the objects eventually ceased. Recall that, in the planned experiments, multiple successive impacts will be required in order to achieve the target bow deformation (48 in.). Therefore, to simulate this action, the analysis was stopped at the instant

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120 that contact ceased, and then restarted by assigning the impact block an new initial velocity of 39.3 ft/s. This process was repeated to simulate a total of five impacts in which barge bow damage was accumulated with each successive impact. Two simulation series were conducted: one in which the impact block had a rounded nose (as shown in Fig. 5 1 ), and one with a flat faced i mpact block with the same width as the rounded block. Results from these simulations are discussed in the following sections. 5.2.1 Impact Simulation Results (Flat Faced Block) In Fig. 5 2 simulated barge bow deform ations are presented for successive impacts with the flat faced impact block. Each figure corresponds to the instant in time at which maximum bow deformation occurred (immediately prior to elastic rebound). As shown, deformation of the exterior of the barg e was dominated by hull plate buckling and folding. Interior members (frames and trusses) failed by inelastic buckling. Significant yielding was observed throughout the damaged region, accompanied by localized fracture (characterized in the FE model by ele ment deletion). As crushing deformation increased, membrane action of the headlog plate pulled the bow corners inward toward the central damaged region. While localized fractures were present generally resulting from extreme bending and folding of the stee l plates the headlog plate remained largely intact, which permitted continued membrane action. At 48 in. of bow deformation, 905 shell elements (0.75% of the total elements) had been deleted from the barge model. In general, barge bow crushing behavior obs erved in these simulations was found to be similar in nature to past studies (Consolazio et al. 2009, Getter and Consolazio 2011). As shown in Fig. 5 3 A barge bow deformation increased with each successive i mpact, slightly exceeding the target deformation of 48 in. during the fifth impact. As shown in Table 5 1 each impact generated 8 11 in. of incremental barge deformation, with 1 5 in. of elastic rebound (note that the magnitude of elastic rebound increased with successive impacts). Impact

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121 force time histories for all five impacts are shown in merged format Fig. 5 3 B Impact forces were higher for the first f ew impacts, after which forces were approximately constant. By merging force deformation data obtained from the five successive impact events, a reasonable approximation of the overall barge bow force deformation curve is produced, as shown in Fig. 5 3 C Peak forces for each impact were significantly higher than the sustained portion of the impact event, but the peaks were extremely short in duration. It is important to point out that the magnitudes of such sh ort duration force peaks are of limited interest with regard to the model validation, because they are likely a consequence of the idealized impact conditions in the finite element simulations (i.e., perfectly aligned head on impact). It is unlikely that s uch ideal alignment will be achieved during the experimental barge impact program. Furthermore, the force peaks are so short in duration that it is unlikely that the experimental instrumentation will have a high enough response frequency to measure them ac curately. Therefore, a more meaningful measure of maximum impact force is the maximum of the sustained portion of the impact event. A variety of different methods could be employed to define the maximum sustained force, all of which include some level of s ubjectivity. It was observed that short duration force peaks that were significantly higher in magnitude than the sustained portion of the curve. Therefore, for this study, such peaks were considered to be outliers with respect to the remainder of each imp act force time history. Therefore, the maximum sustained force was defined as the force corresponding to a 5% temporal probability of exceedance. To compute the 5% exceedance force, an empirical cumulative distribution function (CDF) was developed from the impact force data for each impact event, and the force value corresponding to 95% cumulative probability was selected. As a representative example, Fig. 5 4

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122 illustrates this procedure for the first impact event. As summarized in Ta ble 5 1 5% exceedance forces were significantly smaller than raw peak forces, implying that raw peak forces were not a representative measure of physical impact force magnitude. 5.2.2 Sensitivity of Results to St eel Constitutive Model (Flat Faced Block) As noted in Chapter 4, during the planning stages of this study, a representative constitutive model for ASTM A36 steel was adopted from available literature and employed in the reduced scale impact simulations (th strain relation published by Salmon and Johnson (1996), with a 36 ksi yield stress, 58 ksi ultimate stress, and failure strain equal to 0.2 in./in. The Cowper Symonds model was used to model strain rate sensitivity, with coefficients C = 40.4 s 1 and P = 5 (Jones 1997). In preparation for the FE model validation, the original constitutive model was replaced with the material specific r evised constitutive models that were developed from material testing program (Chapter 4). The revised models are considered more accurate, because they were developed based on experimental testing of the specific materials from which the reduced scale barg e specimens will be fabricated. Given the differences between the two constitutive models, it was of interest to evaluate the level of sensitivity that the constitutive model selection (original or revised) had on impact simulation results obtained. It is important to note that the Cowper Symonds rate sensitivity model can be employed in two possible ways in the LS DYNA material model used in this study ( MAT_24 ) First, if parameter SIGY > 0 (generally one would choose SIGY to be equal to the yield stress), then dynamic stress ( dyn ) is computed in LS DYNA as:

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123 ( 5 1 ) where, is the static stress (as defined by the user s pecified material curve), is the effective plastic strain, is the effective plastic strain rate, and C and P are t he Cowper Symonds coefficients. This stress scaling rule results in a shift (offset) o f stress values in the stress strain relation, where the shift is constant (does not vary) with respect to strain level. Consequently, for a material that exhibits strain hardening, yield stress is modeled as being more sensitive (in a ratio sense, dyn / st ) to strain rate than ultimate stress (i.e., for a constant increase of stress, the percentage increase in yield stress will be larger than the percentage increase in ultimate stress). As discussed in Chapter 4, values for C = 40.4 s 1 and P = 5 (e mployed in the original constitutive model) are based on a study by Manjoine (1944) which found that yield stress was indeed more sensitive to high strain rates than ultimate stress (for the materials tested in the study). Therefore, the scaling rule defin ed by Eqn. 5 1 was appropriate for use in the original constitutive model employed during the planning stages. However, if parameter SIGY = 0 in MAT_24 then LS DYNA employs an alternative stress scaling rule: ( 5 2 ) For a particular strain rate, Eqn. 5 2 produces a uniform scaling of stress, rather than a uniform (constant) shifting of stress (as was the c ase in Eqn 5 1 ). Therefore, in a ratio sense ( dyn / st ), yield and ultimate stresses are modeled in Eqn. 5 2 as equally sensitive to strain rate. As discussed in Chapter 4, the steel materials tested in this study were found to have approximately equal levels of rate se nsitivity for yield and ultimate stress. Therefore, the scaling rule defined by

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124 Eqn. 5 2 was employed in the revised constitutive models. Detailed material model parameters for both the revised and original constitutive mode ls are summarized in Table 5 2 To evaluate the sensitivity of impact simulation results to the choice of constitutive model, two simulations were conducted: one with the revised constitutive models, and one with the origin al constitutive model. Both simulations included five repeated impacts by the 9,000 lbf flat faced pendulum impact block, as discussed in the previous section. Fig. 5 5 compares large scale barge bow deformations that were obs erved at the maximum deformation level (during the fifth impact). As shown, the simulation with the revised constitutive models (Fig. 5 5 ) developed more widespread damage across the width of the bow, including significant hul l plate bending several feet to either side of the impact block. In contrast, the simulation with the original constitutive model had a damaged region that was only slightly wider than the impact block. However, wrapping of the bow corners toward the impac t block (caused by membrane acti on) was more pronounced in the simulation with the original constitutive model. The differences in deformation were largely a consequence of increased ductility in the revised constitutive models. Specifically, internal stru ctural members in the simulation with revised constitutive models were much less likely to fracture, thus permitting impact forces to flow into a wider area and cause more widespread damage. Force deformation curves were computed for each impact simulation and are compared in Fig. 5 6 Overall, differences between the force deformation curves were relatively minor. The revised constitutive models resulted in slightly higher impact forces for the first and third impact, b ut lower forces for the fifth impact. Overall ductility of the barge bow was similar between the two simulations. Based on these results, it can be concluded that for flat faced impact, introducing the revised constitutive models had limited influence on q uantitative measures of

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125 system wide impact response. However, qualitative differences in deformation patterns were observed. 5.2.3 Impact Simulation Results (Rounded Block) In Fig. 5 7 simulated barge bow deformati ons are presented for successive impacts with the rounded impact block. Each figure corresponds to the instant in time at which maximum bow deformation occurred (immediately prior to elastic rebound). As with the flat faced impact scenario, deformation of the exterior of the barge was dominated by hull plate buckling and folding. Interior members (frames and trusses) failed by inelastic buckling. Significant yielding was observed throughout the damaged region, accompanied by localized fracture (characterize d in the FE model by element deletion). Again, as crushing deformation increased, membrane action of the headlog plate pulled the bow corners inward toward the central damaged region. While localized fractures were present generally resulting from extreme bending and folding the headlog plate remained largely intact, which permitted continued membrane action. At 48 in. of bow deformation, 969 shell elements (0.81% of the total elements) had been deleted from the barge model. In general, the barge bow crushi ng behavior observed in these simulations was found to be similar in nature to past studies (Consolazio et al. 2009, Getter and Consolazio 2011). As shown in Fig. 5 8 A barge bow deformation increased with e ach successive impact, exceeding the target deformation of 48 in. during the fifth impact. As shown in Table 5 3 each impact generated 8 11 in. of incremental barge deformation, with 1 3 in. of elastic rebound. The magnitude of elastic rebound increased with successive impacts, but less so than for the flat faced impact scenario. Impact force time histories are shown in Fig. 5 8 B During the second and thi rd impacts, force magnitudes generally decreased; however, during the fourth and fifth impacts, forces increased and actually exceeded the initial (first) impact event. Peak forces for

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126 each impact were somewhat higher than the sustained portion of the impa ct event, but, as before, these peaks were short in duration. Therefore, as before, forces corresponding to a 5% temporal probability of exceedance were computed for each impact. As summarized in Table 5 3 5% exceedance forces were 30 120 kips smaller than peak forces, which was a much smaller discrepancy than the flat faced impact scenario. This outcome is to be expected, because during impact by a rounded object, barge materials become engaged by the imp act block more gradually than a flat faced impact scenario. Therefore, short duration force peaks that are primarily caused by rapid engagement of a large region of the barge bow (as occurs during flat faced impact) are not as prominent for rounded impact. By merging force deformation data obtained from the five successive impact events, a reasonable approximation of the overall barge bow force deformation curve is produced, as shown in Fig. 5 8 c. 5.2.4 Sensitivity of Results to Steel Constitutive Model (Rounded Block) For the reasons discussed in Section 5. 2 .2, an additional rounded impact simulation was conducted with the original constitutive model (as described in Section 5. 2 .2) in order to assess the sensitivit y of simulation results to the choice of constitutive model. Fig. 5 9 compares large scale barge bow deformations that were observed at the maximum deformation level (during the fifth impact). As shown, overall deformation pa tterns were similar between the two simulations, with slightly more widespread hull plate buckling in the simulation with the revised constitutive model. Furthermore, where hull plates folded over themselves in the directly impacted headlog region, they re mained largely intact in the revised model, while they fractured in the original model. In general, the deformation results indicate that the revised constitutive model resulted in a somewhat more ductile response, as would be expected. Force deformation c urves were computed for each impact simulation, and are compared in Fig. 5 10 As shown, impact forces were 5 10% lower at all deformation levels in the

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127 simulation with the original constitutive model. Furthermore, in the original simulation, maximum bow deformations were 1 2 in. larger for each individual impact, accumulating to an overall 6 in. difference in maximum deformation (after five impacts). These findings can be attributed to more widespread material fract ure in both the hull plates and internal structural members of the simulation that used the original constitutive model. While the results shown in Fig. 5 10 were relatively similar, differences caused by the choice of constitutive model were more pronounced than for the flat faced impact scenario (Section 5. 2 .2). 5.2.5 Comparison of Flat Faced and Rounded Block Impact Simulation Results High severity barge bow deformations for the flat faced and rounded impact scenarios are c ompared in Fig. 5 11 in which the maximum deformation levels are approximately 49 in. at the 40% model scale (approximately 10 ft. at full scale). As shown, the flat faced impact block developed more widespre ad damage across the width of the bow, including significant hull plate bending several feet to either side of the impact block. In contrast, the rounded block developed a localized damaged region that was only slightly wider than the impact block. However wrapping of the bow corners toward the impact block (caused by membrane action) was more pronounced for the rounded impact scenario. Overall force deformation curves computed from each set of simulations (flat and rounded impact blocks) are compared in F ig. 5 12 For the first 12 in. of deformation, the flat faced block developed larger impact forces than the rounded block. This difference can be attributed to the relatively larger damaged region genera ted by the flat faced block, as described above. At larger levels of deformation (greater crush depth), both curves become effectively plastic at a force value of approximately 200 220 kips, with localized force peaks occurring at the beginning of each i mpact. For deformations exceeding 36 in. (at model scale), forces

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128 generated by the rounded block generally exceeded those of the flat block; the difference being attributable to increased membrane action in the rounded impact scenario, as discussed above. 5.3 Summary As noted in the introduction, the simulation results discussed in this chapter specifically Sections 5. 2 .1 and 5. 2 .3 constitute the most accurate predictions of barge bow response currently available for the planned experimental impact conditions. However, before they may be used as the basis for the validation study, some critical actions must be undertaken. First, once constructed, the impact block and cable hanger frame must be weighed carefully. It is highly unlikely that the physical objects wi ll have the same weight as the idealized block employed in the simulations discussed in this chapter (9,000 lbf). Second, during each impact experiment, the impact block velocity must be measured. If significant deviation from the expected velocity (39.3 f t/s) is observed, the experimental impact velocity must be incorporated into the validation simulations. If both the impact block weight and velocity are very near the values assumed for the simulations in this chapter, then the simulation results presente d herein may be adopted for the validation study. Otherwise, the simulations will need to be repeated with the appropriate revised impact parameters.

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129 Table 5 1 Summary of b arge bow impact response data (flat block) Impact number Maximum deformation (in.) Residual deformation (in.) Elastic rebound (in.) Maximum impact force (kip) 5% exceedance impact force (kip) Impact duration (msec) 1 7.9 7.0 0.9 1,070 394 48 2 17.4 15.3 2.1 428 292 76 3 28.7 25.4 3.3 402 206 95 4 39.4 36.0 3.4 333 217 95 5 49.0 44.0 5.0 365 233 106 Table 5 2 Comparison of constitutive model parameters Constitutive model Barge bow components Stress str ain relation Dynamic stress scaling rule C (s 1 ) P Failure strain (in./in.) Revised Selected A1011 T11 a Eqn. 5 2 9,200,000 10 0.363 Selected A1011 T15 a Eqn. 5 2 20,500,000 10 0.308 Selected A36 T25 1 Eqn. 5 2 1,320,000 8 0.273 Original All Salmon & Johnson (1996) b Eqn. 5 1 40.4 5 0.200 a See Chapter 4 for details. b See Consolazio et al. (2009, 2010 b 2012a, 2012b) for details. Table 5 3 Summary of barge bow impact response data (rounded block) Impact number Maximum deformation (in.) Residual deformation (in.) Elastic rebound (in.) Maximum impact force (kip) 5% exceedance impact force (kip) Impact duration (msec) 1 11.3 10.0 1.3 320 282 69 2 22.6 20.4 2.2 256 226 85 3 33.7 30.8 2.9 335 217 90 4 43.0 40.1 2.9 355 258 83 5 50.5 47.5 3.0 414 308 78

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130 A B Figur e 5 1 Finite element impact simulation of 0.4 scale barge bow (rounded impact block shown) A) Elevation view. B) Plan view. A B C D E Figure 5 2 Maximum barge bow deformation caused by each successive impact (flat block) A) Impact 1. B) Impact 2. C) Impact 3. D) Impact 4. E) Impact 5.

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131 A B C Figure 5 3 Barge impact simulation data (flat block) A) Deformation time history. B) Force time history. C) Force deformation curve.

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132 Figure 5 4 Empirical CDF of impact force data from first pendulum impact event A B Figure 5 5 Comparison of maximum barge bow deformation (flat faced block). A) Revised constitutive model. B) Original constitutive model.

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133 Figure 5 6 Comparison of barge bow force deformation cur ves (flat faced block) A B C D E Figure 5 7 Maximum barge bow deformation caused by each successive impact (rounded block) A) Impact 1. B) Impact 2. C) Impact 3. D) Impact 4. E) Impact 5.

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134 A B C Figure 5 8 Barge impact simulation data (rounded block) A) Deformation time history. B) Force time history. C) Force deformation curve.

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135 A B Figure 5 9 Comparison of maximum barge bow deformation (rounded block). A) Revised constitutive model. B) Original constitutive model. Figure 5 10 Comparison of barge bow force deformation curves (rounded block)

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136 A B Figure 5 11 Comparison of high severity barge bow deformation (approximately 49 in. of deformation at 40% model scale) A) Flat faced block. B) Rounded block. Figure 5 12 Barge bow force deformation comparison

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137 CHAPTER 6 PLANNED REDUCED SCALE BARGE BOW IMPACT EXPERIMENTS As discussed in previous chapters, a series of reduced scale (40% scale) barge bow impact experiments are planned with the goal of validating the finite element modeling and simulation techniques that are the basis for the Getter and Consolazio (2011) barge impact load prediction model. The planned experiments will involve impacting a stationary replica of a common barge bow with a high energy impac t pendulum to achieve barge bow deformations exceeding 10 ft at full scale (4 ft at model scale). This chapter discusses details pertaining to the components of the experimental setup and the planned array of instrumentation. 6.1 Experimental Components As sho wn in Fig. 6 1 the experimental test setup consists of a variety of components, including a 40% scale barge bow specimen that is supported by a steel reaction frame, all of which is connected to a thick reinforced concrete foundation. The barge bow is impacted by a steel and concrete pendulum impact block that is suspended from the pendulum support towers using four cables attached to a steel support frame. Each of these components was designed to resist sustained impact forces exceeding 200 300 kips without developing widespread damage (except in the barge bow). Each major component test setup is described in the following sections. 6.1.1 Reduced Scale Barge Bow Specimens At the proposed model scale of the barge b ow specimen measures approximately 14 ft wide by 11 ft long by 5 ft tall (Fig. 6 2 ), and has a total steel weight of approximately 3,800 lb. An exploded view of the component parts of the barge bow is shown in Fig. 6 3 The internal structure is composed of seven trusses and seven frames that are oriented along the longitudinal axis of the barge. The trusses and frames are composed of structural angle members

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138 c onnected by gusset plates and short channel members. Each sidewall of the barge is stiffened by a simple frame composed of three angles and three diagonal channels. Hull plates of varying thicknesses are provided around the entire bow region. Detailed fabr ication drawings of the reduced scale bow specimens are provided in Appendix F. As discussed in Chapters 3 and 5, two series of impact experiments will be conducted: one involving a flat faced impact block and one involving a rounded impact block. Therefor e, two barge bow specimens will be fabricated. 6.1.2 Barge Bow Reaction Frame Barge bow specimens will be supported by a semi rigid reaction frame that is connected to a large structural foundation. As shown in Fig. 6 4 the rear interface of the barge bow is U shaped. A watertight bulkhead plate covers this entire interface in the full scale barge that the specimens are based upon. Therefore, a similar U shaped adapter plate will be welded to the rear interface of the bow model, and this plate will be used to attach the specimen to the reaction frame. Because the barge specimen must be removed and replaced between test series, bolted connections are used between the adapter plate and reaction frame. As shown in Fig. 6 5 the reaction frame consists of two triangular steel frames (spaced at 12 ft on center) connected transversely by an upper and lower support beam. Because the lower support beam is expected to undergo significant flexural and torsional demands, it is additionally stiffened by attaching a hollow structural section (HSS). The lower support beam and HSS stiffening beam are welded together to act as a composite unit. The reaction frame connects to the foundation using four 2 in. thick baseplates. Additional connection details regarding the frame foundation connection are provided in the following section. Detailed structural drawings for the reaction frame are provided in Appendix G.

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139 6.1.3 Universal Pendu lum Foundation The purpose of the reaction frame, which will be anchored to a large foundation, is to transfer impact forces from the barge model to the soil with minimal horizontal deflection in the direction of impact. Unlike most laboratory structural f oundations, which are typically designed primarily to support vertical loads, the foundation for the planned impact experiments must primarily resist horizontal impact loads and moments caused by the vertical eccentricity of impact the applied impact loads As a result, the foundation was designed both to develop sufficient lateral soil capacity to resist the applied impact loads and also to maintain stability against overturning. Because pendulum impacts generate relatively short duration dynamic loads, in ertial resistance provided by the mass of the foundation acts effectively as an additional source of capacity. Several foundation design concepts including deep foundations with one or more drilled shafts; embedded shallow mat foundations; and mat foundati ons with vertical shear key elements were considered in the process of developing the design. For brevity, detailed discussion of the various design concepts that were explored is excluded here. However, based on balancing lateral dynamic soil capacity, in ertial resistance provided by foundation mass, and cost, a 3 ft thick mat foundation was chosen. As shown in Fig. 6 6 the foundation is 34 ft long in the impact direction and 20 ft wide. The footing is ful ly embedded in the surrounding soil (i.e., the top surface falls at the finished grade elevation) and has a static lateral load capacity of approximately 400 kips, which is developed through skin friction on the bottom surface and side faces and passive so il resistance on the front face. As noted above, additional lateral resistance is provided by dynamic soil excitation (damping) and the mass of the footing itself. Utilizing all sources of resistance, the proposed foundation will be more than sufficient to resist forces developed during pendulum impact testing of the reduced scale barge bow models.

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140 Because the barge impact tests will produce at, or near, the most severe loading scenarios that the pendulum is capable of producing (with regard to impact energ y), the structural foundation is intended to be a permanent component of the FDOT pendulum impact test facility supported research. Consequently, a grid of additional anchor points were provid ed that are not necessary for the current study but which will enable a wide range of future test articles to be securely mounted for impact testing. The anchor layout shown in Fig. 6 6 (20 anchors total) w as determined in coordination with FDOT laboratory staff. During the barge impact experiments, the anchor system will simultaneously be subjected to horizontal impact forces (shear forces) and uplift forces caused by overturning moments applied to the barg e bow model. Both force components (horizontal and vertical) are expected to reach nearly 200 kips per anchor location (a total of four anchors will be used during the barge impact tests to secure the reaction frames). Due to the large shear demand on each anchor, conventional concrete anchor designs that employ embedded bolts or headed studs were impractical. Therefore, each pendulum foundation anchor point instead consists of a triangular frame constructed from heavy structural steel, with a 2 in. thick a nchor plate on top (Fig. 6 7 A ). At the base, each triangular frame is welded to a beam oriented in the long direction of the foundation that conne cts all anchors in a given row. The anchor assemblies (trian gular frames and longitudinal beams) were then embedded within the concrete footing. S ee Appendix H for additional structural details. As shown in Fig. 6 7 A fixtures (such as the barge bow reaction frame) attach to the anchor top plate using two types of fasteners: four 1.5 in. diameter threaded rods and up to four 1.9 in. diameter shear pins. Uplift and moment demands at the fixture anchor interface are

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141 carried by the threaded rods, and shear forces are ca rried by the shear pins. As shown in Fig. 6 7 B threaded rods are threaded into hex nuts that are embedded in the foundation, underneath the anchor plate. As shown in Fig. 6 7 C holes for the shear pins are slightly oversized (approximately 0.1 in. in diameter) to allow for fabrication tolerances, while holes for the threaded rods are significantly oversized (approximately 0.3 in. in diameter) to avoid subjec ting the threaded rods to shear loading. This unique design decouples the shear and uplift load paths with the intent of minimizing damage to the anchor system that could result from repeated impacts during the design life of the foundation. A site plan fo r the pendulum towers and universal foundation, located at the FDOT Structures Research Center in Tallahassee, Florida, is shown in Fig. 6 8 The universal foundation was constructed in the southern bay of the pendulum tower array, centered between two towers. Closely spaced anchors near the leading edge of the foundation will be used in future impact testing of small specimens such as signs and roadside safety equipment. Larger specimens, such as the mod el barge bow used in the current study, will be mounted to the rear most anchor rows farthest from the pendulum towers. Fig. 6 9 shows the construction sequence for the pendulum foundation. First, the ancho r frames were fabricated, positioned, and fixed together with temporary structural members (Fig. 6 9 A ). Next, the rebar cage was fabricated (Fig. 6 9 B ), pre fabricated steel formwork was installed (not shown), concrete was poured in three lifts separated by 3 4 days curing time, and formwork was removed (Fig. 6 9 C ). Lastly, soil was backfilled around the fin ished foundation (Fig. 6 9 D ) and compacted to improve soil resistance on the vertical surfaces. Detailed fabrication drawings for the pendulum foundation are provided in Appendix H.

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142 6.1.4 Impact Block and Cable S upport Frame A schematic diagram of the pendulum impact block that will be used in the barge impact experiments is shown in Fig. 6 10 The purpose of the block is to impart impact force to the barge bow over a s urface area (and shape) that is representative of a bridge pier, and which will cause deformation of the barge bow specimen. The impact block will be suspended from four cables (attached to two of the pendulum support towers). Using a pull back cable, pull ey, and winch system that is attached to the third pendulum tower, the block will be raised to a drop height 24 ft above the position at incipient contact with the barge model. To initiate impact, the block will be released from the lifted position, allowi ng it to swing down and impact the barge bow specimen. Kinetic energy at the point of impact will thus be equal to the stored potential (gravitational) energy at the elevated position prior to release. As shown in Fig. 6 10 the impact block itself will be split into two pieces to facilitate installing one of two different front block assemblies: one with a flat faced impact surface (as shown in Fig. 6 10 ) and one with a rounded surface (not shown). Hence, the rear block assembly will be reused for both series of impact tests. The two parts of the impact block are held together by two threaded rods and two shear keys that are located at the interface between the front a nd rear parts. A cable support frame attaches to the top surface of the impact block using four threaded rods that pass through the full depth of the impact block and support frame. The four main hanger cables connect to the support frame with swiveling ey ebolts. Turnbuckles installed in line with the hanger cables allow the position of the impact block to be adjusted in the field. The entire assembly (impact block and cable support frame) weighs approximately 9,000 lbf, which is the maximum weight that the pendulum support towers are designed to support.

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143 6.2 Measured Quantities for Validation As discussed in Chapter 3, the purpose of the barge bow impact experiments is to validate the finite element modeling tools and procedures used to form the Getter and Cons olazio (2011) impact load model. To do so, finite element simulations of the experimental impact conditions will be developed using those same modeling tools and procedures (as demonstrated in Chapter 5). Results predicted by the simulations will be compar ed to corresponding data measured during the impact experiments. The modeling tools and procedures and by extension, the Getter Consolazio (2011) load model will be considered valid if the experimental and computational results match well. The most importa nt consideration in performing the validation is identifying the physical quantities that should be measured and compared. The most critical quantities are: I MPACT FORCE The time varying contact force developed between the impact block and barge bow speci men during each impact event, and; B ARGE BOW DEFORMATION The time varying deformation of the barge bow during each impact event. When combined, these quantities can be used to develop force deformation curves, as shown in Chapter 5. Due to the nature of t he impact events, it will be impractical to measure the impact force directly using load cells. Mounting load cells to either the impact block or the barge specimen would modify the geometry and stiffness characteristics of the contact interface, which cou ld invalidate the results. Therefore, the impact force will be quantified indirectly, using accelerometers attached to the impact block. The time varying impact force, F ( t ), will be calculated by measuring the deceleration of the impact block, a ( t ), and mu ltiplying by the known mass of the impact block, m such that F ( t ) = ( m) ( a ( t )). Note that this approach assumes that impact block motion is dominated by rigid body translation, and that the block undergoes no

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144 significant deformation. Preliminary finite ele ment simulations have indicated that this assumption is valid. However, some high frequency oscillations in the acceleration signal may be present, resulting from propagation of small scale deformation waves moving through the impact block. The period of s uch oscillations, however, is expected to be orders of magnitude shorter than the impact event; therefore, it will be possible to remove them from the overall impact force signal using a low pass frequency based filtering technique. Similarly, barge bow de formations will be difficult to quantify directly. During each impact event, the bow specimen is expected to deform 8 15 in. in a time span of approximately 0.1 sec. The deformations are too large to measure with displacement transducers, and too rapid t o measure with most large displacement string potentiometers. Therefore, deformations will be calculated indirectly by monitoring impact block displacements via high speed video and digital image correlation. Specific instrumentation that will be utilized for these tasks is discussed in the following section. Physical quantities that are less critical, but which will add credibility to the validation effort will also be measured or quantified: I MPACT VELOCITY The velocity of the impact block immediately pr ior to impact. If significant variation is observed between successive impact experiments, velocity data may be needed as input for the validation simulations. R ESIDUAL BARGE BOW DE FORMATION The barge bow deformation that remains after an impact has occur red and the damaged bow region has rebounded elastically. B ARGE BOW DEFORMATION PATTERNS Qualitative inspection of local deformations in the barge bow, including hull plate bending and folding, and internal structural member buckling and plastic hinging. Regions of steel fracture or weld failure will be identified after each impact test. 6.3 Instrumentation Plan Instruments that will be used in the barge impact experiments are listed in Table 6 1 and the instrum entation layout is shown schematically in Fig. 6 11 As discussed above, impact force

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145 will be quantified indirectly by means of uniaxial accelerometers attached to the top and bottom surfaces of the impa ct block (Fig. 6 11 C D ). Accelerations are generally expected to be less than 100 g, with very short duration spikes possibly exceeding 250 g. Therefore, accelerometers with two ranges (250 g and 500 g) will employed. If measured accelerations rarely exceed 250 g, then data from the 250 g accelerometers will be used to calculate the impact force, as the lower range sensors will have better accuracy. Otherwise, data from the 500 g accelerometers will be ut ilized. Impact block motions will be monitored by two high speed cameras, one located on each side of the impact zone. The ProAanalyst software package will be used to track the displacement of checkerboard patterns affixed to each side of the impact block This data will be used to quantify impact block displacement and velocity (by time differentiation), and also barge bow deformations (when combined with tape switch data). Optical break beams, located a known distance apart, will serve as the primary mea ns by which impact velocity will be computed (this will be achieved by dividing the distance between the beams by time that elapses between each beam being triggered). Data acquisition will be triggered by one of two instrument types: infrared break beams (mounted on stands on each side of the impact region) or one of three tape switches (one mounted to the barge specimen, and two mounted to the impact block.) This approach will provide redundancy in case any single instrument fails to trigger the data acq uisition system. Data will be acquired from all instruments (including high speed cameras) at a sampling rate of 10 kHz per sensor.

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146 Table 6 1 Instrumentation to be used du ring barge bow impact experiments Instrument type Quantity Manufacturer Model number Accelerometer (250g) 2 Spectrum Sensors & Controls 13208A R250 Accelerometer (500g) 2 Spectrum Sensors & Controls 13208A R500 High speed camera 2 Redlake MotionXtra N3 Infrared break beam 2 Balluff BLS 18KF XX 1P S4L Tape switch 3 Tapeswitch Corp. 131A Figure 6 1 Test setup for barge bow impact experiments

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147 Figure 6 2 Rendering of reduced scale barge bow specimen showing internal truss structure Figure 6 3 Exploded view of barge bow hull plates and internal components

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148 Figure 6 4 Exploded view of connection between barge bow specimen and reaction frame Figure 6 5 Reaction frame structural members and general dimensions

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149 Figure 6 6 Universal pendulum impact foundation: plan view dimensions

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150 A B C Figure 6 7 Embedded foundation anchor connection system

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151 Figure 6 8 Site plan for universal pendulum impact foundation

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152 A B C D Figure 6 9 Universal pendulum foundation construction stages (viewed from northwest corner) A) Anchor frames positioned. B) Reinforce ment cage installed. C) Concrete cast (3 lifts). D) Soil backfilled. (Photos courtesy of Daniel J. Getter)

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153 Figure 6 10 Impact block and cable support frame: exploded view

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154 A B C D Figure 6 11 Instrumentation layout to be used in barge bow impact experiments A) Isometric view (front of barge). B) Isometric view (front of impact block). C) View A A (top of impact block). D) View B B (bottom of impact block).

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155 CHAPTER 7 REVISED RISK ANALYSIS PROCEDURES FOR VESSEL IMPACT WITH BRIDGES A primary goal of the current study was to implement current and past UF/FDOT research findings into a format that can be adopted in the FDOT and AASHTO vessel collision design prov isions. Research conducted by UF and FDOT (summarized in Chapter 2) has demonstrated the inadequacy of certain portions of the AASHTO procedures, and revised design and analysis tools have been developed to address these limitations. Thus, in the current s tudy, a unified bridge design methodology was developed that incorporates these state of the art structural and risk analysis procedures into the overall AASHTO risk assessment procedure without unduly complicating the bridge design process. Details of the revised methodology the UF/FDOT methods are demonstrated and compared to the current AASHTO methodology using two bridges that are currently in service. Throu AASHTO Guide Specifications and Commentary for Vessel Collision Design of Highway Bridges (2009). Furthermore, numerous re a large body of work, comprising multiple publications (discussed in Chapter 2), and in general, refer to the modified risk assessment procedure outlined in Section 7. 1 .2 References to spec ific publications are provided where needed. 7.1 Options for Implementing UF/FDOT Research in Design Practice Given the complexity and relative uncertainty associated with the vessel collision hazard, to date, vessel collision design (in accordance with AASHTO ) involves conducting a comprehensive risk assessment in which the annual probability of bridge failure is directly

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156 quantified (recall Chapter 2). Thus, the current design process requires that practitioners gather a significant amount of site specific ves sel traffic and waterway alignment data, perform numerous structural analyses, and employ probabilistic analysis procedures that are not frequently used in structural engineering. In developing a new design methodology that incorporates UF/FDOT research fi ndings particularly including dynamic bridge analysis significant attention was given to the prospect of adding complexity to a design process that is already relatively complicated. Two possible implementation strategies were considered: an LRFD approach in which the AASHTO risk assessment was replaced with a simpler deterministic procedure, and a targeted approach in which the AASHTO procedures were minimally revised to incorporate UF/FDOT methods. As discussed in the following sections, the latter approa ch was adopted. 7.1.1 Simplified LRFD Approach to Vessel Collision Design Given the complexity of the current AASHTO risk assessment procedures, simplification of the overall vessel collision design process was considered in an effort to minimize the impact of p roposed changes on design complexity. One strategy considered was to develop a load and resistance factor design (LRFD) procedure in lieu of the rigorous risk analysis currently employed. Beginning in the early 1980s (Ellingwood et al. 1980), LRFD procedur es were developed for various loading scenarios with the goal of obtaining uniform levels of structural reliability for all modes of failure (limit states). Statistical uncertainties associated with loads and structural resistance are included in the LRFD process by means of load and resistance factors. Use of such factors relieves the design engineer from having to directly quantify the probability of structural failure using complicated reliability analysis procedures. The prospect of adapting an LRFD met hodology to the problem of vessel collision with bridges was investigated in this study. For brevity, the full discussion is excluded here but is included in Appendix I. Ultimately, it was determined that the LRFD approach is infeasible for

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157 two primary rea sons. First, statistical variability associated vessel impact loading is significantly larger than for other sources of loading (e.g., live load). Consequently, vessel impact load factors that account for all sources of uncertainty would need to be much la rger than for other types of loads, which could result in unreasonably conservative designs. Secondly, in current design practice, the acceptable risk of structural failure due to vessel collision is defined differently than for other sources of loading. F or vessel collision, acceptable risk is assessed based on the probability of bridge failure: i.e., catastrophic failure of multiple bridge elements resulting in collapse of the superstructure. In contrast, for typical LRFD, load and resistance factors are calibrated to achieve a desired probability of member failure (e.g., a single column). Currently for vessel collision, individual member failure is permitted, so long as the superstructure does not collapse. Thus, adapting LRFD principles to the vessel col lision problem would require radical changes to the definition of acceptable risk. Fully understanding the cost implications of such a fundamental change would require additional research which was outside the scope of the current study. Consequently, targ eted changes to the existing AASHTO risk assessment framework were developed that incorporated state of the art methods developed by UF/FDOT. 7.1.2 Targeted Revisions to AASHTO Risk Assessment Procedure Recall that the AASHTO risk assessment procedure involves q uantifying the annual frequency of bridge collapse due to vessel collision ( AF ): ( 7 3 ) where N is the number of vessel transits per year, PA is the probability of a given vessel becoming aberran t, PG is the geometric probability of an aberrant vessel impacting a given bridge element, PC is the probability of impact induced bridge element collapse, and PF is a protection factor to account for navigational obstructions that may reduce impact risk.

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158 Within the AASHTO risk assessment framework, prior UF/FDOT research has focused exclusively on improving the accuracy of procedures used to quantify PC In the AASHTO provisions, PC is computed as a function of the ratio H / P where H is the ultimate static strength of a bridge element (generally a pier) and P is a static vessel collision force. While it is rational that PC should rely on measures of structural resistance and load magnitude, the form of the AASHTO PC expression is not conceptually consistent in that it predicts relatively small failure probabilities for cases in which the impact load magnitude greatly exceeds bridge element capacity. Furthermore, the AASHTO definition of PC simplifies impact loading by treating it as a static load event, whi ch neglects important dynamic structural response characteristics that commonly make the static approach unconservative. Therefore, UF/FDOT research has focused on developing an alternative expression for PC that is both consistent with reliability theory and that incorporates dynamic structural response into the definition of impact load and structural capacity. To incorporate UF/FDOT research findings into the AASHTO procedures, the most targeted approach possible was to only modify selected provisions in the formulation of PC and leave all other terms in the AF expression unmodified. To develop the revised risk assessment methodology, three primary modifications were made to the AASHTO procedure: The AASHTO barge impact load prediction model was replaced with the model developed by Getter and Consolazio (2011). Modifications to the UF/FDOT load model may be warranted based on the outcome of the planne d pendulum impact tests ( Chapters 3 and 5). The AASHTO static analysis was replaced with analysis procedur es that account for dynamic amplification effects in the impacted structure. A tiered approach was taken, in which an engineer can choose one of three analysis options, in order of increasing complexity and accuracy: S TATIC BRACKETED IMPA CT ANALYSIS ( SBIA) An equivalent static analysis method consisting of a small set of static load cases (Getter et al. 2011).

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159 A PPLI ED VESSEL IMPACT LOA DING (AVIL). A transient dynamic analysis method incorporating an approximate impact load history that is computed prior to conducting the analysi s (Consolazio et al. 2008). C OUPLE D VESSEL IMPACT ANAL YSIS (CVIA). A transient dynamic analysis method in which the vessel impact load and corresponding bridge response are coupled and computed simultaneously (Consolazio and Cowan 20 05). The AASHTO probability of collapse (PC) expression was replaced with the UF/FDOT PC expression (Davidson et al. 2013). The various methods mentioned above are discussed in detail in Chapter 2 and also in the demonstrative examples provided in Chapters 8 and 9. Therefore, detailed discussion is omitted here for brevity. 7.1.3 Ship Impact Considerations Research conducted by UF/FDOT has focused almost exclusively on the problem of bridges being impacted by river barges, as opposed to larger seagoing ships such as bulk cargo carriers. Consequently, certain components of the proposed collision design framework are not applicable to ship impact (e.g., the impact load prediction model) or have simply not been tested for ship impact. Given the similarities between b arge and ship collision, it is highly likely that the three UF/FDOT impact analysis methods (CVIA, AVIL, and SBIA) can be adapted to ship collision. However, additional research effort outside the scope of the current study would be necessary to validate t hese methods for ship collision. Similarly, the revised PC D/C expression was developed based only on barge impact scenarios. However, it is unlikely that an analogous expression derived based on ship impact scenarios would be significantly different in na ture. Further research should to be conducted to demonstrate the applicability of the UF/FDOT PC expression to ship collision scenarios, or if necessary, develop a separate expression specifically for ship collision.

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160 Because such activities were beyond the scope of the current study, it was necessary to create two separate analysis tracks within the UF/FDOT risk assessment procedure: one for barge collision and one for ship collision. In the ship impact track, the AASHTO ship collision load model, simple st atic analysis procedure, and existing AASHTO PC expression are still used. However, in the barge impact track, the UF/FDOT load model, three tiered analysis approach, and revised PC expression are used. Because the proposed UF/FDOT barge collision risk ass essment procedure follows the structure of the existing AASHTO risk assessment procedure, bridge failure estimates computed using the two tracks (ship and barge collision) can still be intermingled for bridges that are at risk for collision by both vessel types. 7.2 Overview of Revised Risk Analysis Procedure It is recognized that implementing the revisions summarized above will result in significant changes to the current vessel collision risk analysis workflow. The existing AASHTO risk analysis workflow effec tively a summary of the discussion provided in Chapter 2 is shown in Fig. 7 1 Note that structural analysis falls outside the main risk analysis computations. Thus, for each combination of vessel group and e xposed pier, it is not necessary to conduct any structural analysis. Commonly in practice, the pier pushover capacities ( H j ) are determined a priori and are used to compute the probability of pier collapse for each combination of vessel group and pier ( PC i j ). Indeed, the most common approach for a new design involves back calculating pier pushover capacities ( H j ) that both satisfy the overall acceptable level of risk ( AF ) and distribute risk evenly among the various piers at risk for impact. Piers are then designed such that the static pushover capacity exceeds the back calculated values. The ability to take this approach is important, because limited information about the bridge design is required to back calculate acceptable pushover capacities, thus minim izing the number of iterations required to arrive at an acceptable bridge design.

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161 The UF/FDOT risk analysis workflow is summarized in Fig. 7 2 The methodology differs from the existing AASHTO procedure in a few ways. First, a tiered structural analysis approach is employed, in which three analysis options one static (SBIA) and two time domain dynamic (AVIL, CVIA) are available. The analysis options are shown in order of increasing complexity and accuracy. No te that these analysis procedures have been developed based on UF/FDOT research, and therefore account for important dynamic amplification effects that the AASHTO static analysis approach neglects. The UF/FDOT workflow (Fig. 7 2 ) also differs from the existing AASHTO process (Fig. 7 1 ) in that it employs the revised probability of collapse ( PC ) expression recently developed by UF/FDOT research. Aside from modifi ed analysis procedures, the UF/FDOT procedure differs from AASHTO in that a structural analysis must be conducted for every combination of pier and vessel group in order to arrive at estimates for PC and ultimately calculate AF Therefore, when designing a new bridge, it is not possible to back calculate acceptable minimum pier capacities, as is common practice with the AASHTO procedure (discussed above). Consequently, to design new bridges in accordance with the UF/FDOT procedure, it is first necessary to develop a trial design to the level of detail that is required to perform structural analyses using one of the three tiered methods (SBIA, AVIL, or CVIA). If the trial design is found be inadequate ( AF higher than the specified frequency), then the design must strengthened in an iterative fashion until the bridge satisfies the acceptable level of risk. In developing strengthened alternative designs for the example cases discussed in Chapters 8 and 9, iterating from an inadequate design to one that was acce ptable was found to be a relatively time efficient process. 7.3 Use of UF/FDOT PC Expression in Design An important aspect the UF/FDOT risk assessment procedure that must be considered is how to use the UF/FDOT probability of collapse ( PC ) expression in a desi gn setting. Recall that

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162 the purpose of the PC expression is to allow design engineers to estimate the probability that a bridge element (e.g., a pier) will collapse by conducting a single deterministic impact analysis. Currently in the AASHTO provisions, P C is computed as: ( 7 4 ) where H is the static pushover capacity of the pier, and P is the AASHTO static impact load. Thus, PC is a function of a static capacity to demand ratio. Davidson et al. ( 2013) took a similar approach in the developing the UF/FDOT PC expression. In the revised expression, PC is computed as: ( 7 5 ) where D / C is a demand to capacity ratio. Because the UF/FDOT express ion was derived based on dynamic structural analysis (specifically CVIA), the AASHTO definitions of static capacity and demand cannot be used. Instead, Davidson et al. defined D / C as the percentage proximity to forming a structural mechanism that leads to instability and collapse, in which case, collapse occurs at D / C = 1.0. To further illustrate the Davidson et al. (2013) D / C concept, consider the simplified bridge pier shown in Fig. 7 3 If the pier cap and pile cap are assumed to be effectively rigid, a structural collapse mechanism can occur in two possible ways: two plastic hinges form in all the pier columns (Fig. 7 3 A ), or two plastic hinges form in all the foundation piles (Fig. 7 3 B ). Either scenario will lead to catastrophic collapse of the superstructure. In terms of D / C once either mechanism has fully formed, the pier has a D / C ratio of 1.0. Keeping in mind that the impact response is dynamic in nature, at times before the mechanism forms, D / C is less than 1.0.

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163 Also, if the impact severity is not sufficient to form a mechanism, then D / C observed throughout the impact event will always be less than 1.0. Based on this concept, Davidso n et al. (2013) devised a rigorous definition by which to quantify D / C in the context of time varying structural response: ( 7 6 ) where m is the number of members (e.g., piers columns, piles) asso ciated with a given collapse mechanism, n is the number of hinges per member that are necessary to form the corresponding collapse mechanism, and is the j th largest element demand capacity ratio along member i as reported by FB MultiPier (internally computed based on biaxial load moment interaction). See Consolazio et al. ( 2010a ) and Davidson et al. (2013) for a more detailed description of D / C and its theoretical basis. While this approach to computing D / C is the most rigorous and conceptually consistent definition possible, it is a complicated definition to employ in a design setting. Computing a time varying estimate of D / C requires a considerable data reduction effort that can only reasonably be achieved with automated data p arsing routines. This effort is further complicated if an engineer employs a different software package than FB MultiPier to perform the structural analysis, because assessments of load moment interaction must be made for every column and pile element in t he finite element bridge model in order to calculate element level D / C ratios. As part of this study, numerous attempts were made to develop a simpler, approximate definition for D / C By virtue of being approximate, a simplified D / C ratio must be consisten tly conservative relative to the more rigorous definition suggested by Davidson et al. (2013) in order to maintain safe design outcomes. All simplified definitions considered in this study were found

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164 to be moderately conservative with respect to D / C Howev er, because the UF/FDOT PC expression is highly nonlinear, small increases in D / C estimates result in large (possibly order of magnitude) increases in PC Thus, all simplified options that were considered were found to produce unduly conservative values of PC Consequently, the rigorous definition described above was employed in all UF/FDOT risk assessment calculations in this study. However, it is worth noting that a simplified definition for D / C may indeed be achievable, and the topic thereby constitutes a potential area for future research.

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165 Figure 7 1 Current AASHTO vessel collision risk assessment procedure

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166 Figure 7 2 Revised UF/FDOT vessel collis ion risk assessment workflow A B Figure 7 3 Possible pier collapse mechanisms A ) Pier column collapse mechanism. B ) Pile collapse mechanism

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167 CHAPTER 8 VESSEL COLLISION RISK ASSESSMENT OF THE BRYANT GRADY PATT ON BRIDGE (SR 300) OVER APALACHICOLA BAY, FLORIDA In this chapter, detailed vessel collision risk assessments are presented for the Bryant Grady Patton Bridge (SR 300) over Apalachicola Bay, Florida. The annual frequency of bridge collapse ( AF ) was quantif ied using the revised methodology described in Chapter 7, employing two dynamic structural analysis techniques (CVIA and AVIL) and one equivalent static analysis technique (SBIA). For comparison, AF was also computed using both the current AASHTO provision s (2009) and the AASHTO guidelines that were available at the time the bridge was designed (1991). Significant differences in AF were observed using the various methods. The final sections in this chapter identify the causes for such differences and provid e suggestions for mitigating vessel collision risk within the context of the revised methodology. The SR 300 Bridge was selected for this study for two primary reasons: 1) it was constructed fairly recently (2004), and was therefore designed to resist vess el collision in accordance with the 1991 AASHTO provisions, and 2) it was at relatively high risk for vessel collision (i.e., vessel collision was a controlling consideration in its design). Indeed, the current bridge was constructed to replace a bridge bu ilt in the 1960s, partially because the old bridge was determined to have insufficient strength to withstand high energy vessel collisions. The new bridge spans approximately four miles over Apalachicola Bay, connecting St. George Island to the Florida mai nland at Eastpoint. Vessel traffic that is of interest for quantifying collision risk consists primarily of barge tows and tug boats transiting between local ports, the Gulf Intracoastal Waterway, and the Gulf of Mexico. While vessel traffic volume for thi s site is relatively light (one or two large vessels per day, on average), the open nature of the waterway (when compared with a typical river crossing) allows for the possibility of vessels colliding with

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168 dozens of bridge piers. Consequently, risk to the total bridge is substantially higher than would be the case for a bridge crossing a narrow river with similar traffic volume. AASHTO Guide Specifications and Commentary for Vessel Collision Design of Highway Bridges The specific edition (1991 or 2009) is referred to as needed, and if no date reference is given, it should be assumed to refer to the 2009 edition. Furthermore, numerous r a large body of work, comprising multiple publications, and in general, refer to the modified risk assessment procedure outlined in Chapter 7. References to specific publications are provid ed where needed. 8.1 Data Collection The critical first step in conducting a vessel collision risk assessment is gathering the relevant site data, including waterway, bridge, and vessel traffic characteristics. Because the Bryant Patton Bridge assessment invol ves an existing structure, a significant proportion of such data is included in the as built structural drawings. Specifically, the bridge plans were employed as a resource for: Waterway alignment, depth profile, and tidal fluctuations Structural configura tion of bridge piers, found ations, and superstructure Soil lay er profiles and scour estimates Waterway characteristics such as water depth and tidal fluctuations were investigated further using publicly available nautical charts of the Apalachicola Bay (N OAA 2012a). Such charts included depth soundings throughout the site and positions of underwater navigational obstructions. Such information was crucial to determining whether portions of the bridge could reasonably be impacted by errant vessels, or whethe r such vessels might run aground prior to

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169 impact. The magnitudes and directions of currents near the bridge were obtained from a comprehensive hydrographic study of Apalachicola Bay conducted in the 1980s ( Conner et al. 1982). This information was critical to estimating vessel impact velocities and establishing any appropriate increase in collision risk resulting from crosscurrents. Vessel traffic characteristics i.e., vessel sizes, number of transits per year, and expected impact velocities were obtained f rom a comprehensive survey of Florida waterways conducted by Wang and Liu (1999). The results of this survey have been compiled into an electronic database by the Florida Department of Transportation (FDOT), and are available as part of a vessel collision risk assessment Mathcad worksheet that is freely available on the FDOT website. The data collection stage of this risk assessment was significantly aided by the availability of the documents mentioned above. For the design of a new bridge, a much more exte nsive data collection effort would be required, including site surveys and hydrological studies. Appropriate sources for such information are suggested in the AASHTO Guide Specification (2009). 8.2 Waterway Characteristics 8.2.1 General Description The Bryant Patton Bridge (hereafter referred to as the SR 300 Bridge), is located in Apalachicola Bay, in northwest Florida. The bridge crosses the easternmost end of the Gulf Intracoastal Waterway (GIWW), which is a maintained navigable waterway extending from Carrabelle, Florida (just east of the SR 300 bridge) to Brownsville, Texas. The GIWW primarily serves barge traffic, transporting petroleum products, chemicals, fertilizers, sand, gravel, cement, sulfur, grain, feeds, and logs (NOAA 2012b). The navigation channel pas ses approximately east west under a high rise section of the SR 300 Bridge, and extends east toward Carrabelle, Florida, and west then north to Apalachicola, Florida (Fig. 8 1 ).

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170 8.2.2 Navigation Channel According to NOAA navigational charts (2012a), the navigation channel (GIWW) has a project depth of 12 ft along its entire length (Carrabelle, Florida to Brownsville, Texas). Water depths in numerous regions along the GIWW have depths exceeding 12 ft, including certain parts of Apalachicola Bay. As needed, the channel is periodically dredged by the U.S. Army Corps of Engineers to maintain the minimum project depth. Because channel width is limited to 100 ft in many areas and numerous tight bends exist, barge flotillas n avigating the GIWW are limited to one, two, or three barges, oriented in a single string (one in front of the other). Therefore, the SR 300 Bridge is not at risk for being impacted by large, multi barge flotillas that are more common on larger waterways. A s shown in Fig. 8 2 the navigation channel passes under the center bridge span at a 61.5 angle relative to the bridge alignment. Horizontal clearance of 150 ft and vertical clearance of 65 ft are provid ed through this passage. On the eastern side of the bridge, two potential navigational hazards are present: a manmade island to the north of the channel, and a segment of the old bridge (now a fishing pier) to the south. For westbound vessel traffic that i s significantly off course, these obstructions may provide some level of protection to bridge piers away from the channel. A methodology was developed to account for these obstructions in the risk assessment, as discussed in Section 8. 6 .6. 8.2.3 Tide Levels and Tidal Range The SR 300 Bridge is subject to tidal variations in water level, by virtue of its vicinity to the Gulf of Mexico. For the purpose of the risk assessment, tidal range and elevations were taken from the bridge plans. Average tidal range is approx imately 1.5 ft, with a mean low water (MLW) elevation of 0.87 ft, and mean high water (MHW) elevation of 0.62 ft. Elevations are referenced to the North American Vertical Datum of 1988 (NAVD88). For the purpose of the

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171 risk assessment presented in this ch apter, MHW is taken as the reference water level for all calculations. 8.2.4 Currents Currents in Apalachicola Bay are influenced by both periodic tidal flows and by outflow from the Apalachicola River. In 1982, Conner et al. published a detailed study of curren t flow velocities for the entire Apalachicola Bay. As shown in Fig. 8 3 A at low tide, currents are dominated by outflow from the river. In the vicinity of the bridge, currents are generally west to east at a veloci ty of approximately 0.25 knots. During flood tide (Fig. 8 3 B ), currents reverse direction near the bridge and flow east to west at approximately 0.35 knots. At high tide (Fig. 8 3 C ), currents continue east to west at 0.35 knots. During ebb tide (Fig. 8 3 D ), currents reverse again to flow approximately west to east at 0.25 0.35 knots, depending on location. Note that turbulence and cro sscurrents are generally most pronounced during ebb tide, though crosscurrent velocity components are negligibly small. The average current velocity over one tidal cycle is provided in Fig. 8 3 E Note that flow is g enerally east to west, at a nominal velocity of less than 0.1 knots. For the purpose of this risk assessment, the current velocity parallel to the navigation channel was conservatively taken to be 0.4 knots (east to west), and the crosscurrent velocity (pe rpendicular to the channel) was taken to be equal to 0.0 (zero) knots. 8.2.5 Water Depths Reasonable estimates of water depth are an important component of the vessel collision risk assessment. If insufficient water depth is available, then vessels may run agrou nd prior to impacting components of the bridge. Indeed one of the most effective measures for protecting bridge piers from impact is constructing islands ahead of or around piers, forcing vessels to run aground, rather that impacting the protected piers. W ater depth can be highly variable, depending on factors like tidal and seasonal water level and mudline scour. Because the bridge being

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172 evaluated is in a coastal region, water levels are primarily driven by tidal variations rather than seasonal fluctuation s. As stated previously, MHW was conservatively taken as the waterline datum for the vessel collision risk assessment. Scour is likely to occur in the vicinity of each bridge pier, increasing the available water depth. However, such effects are generally l ocalized around the pier. If shallow water depths extend far from a given pier, then vessels may run aground well prior to reaching the scoured region. A number of sources exist for determining water depths in the vicinity of the SR 300 Bridge. Detailed su rveys were undertaken prior to bridge construction, and mudline elevations at the site are documented in the design drawings. Soil borings taken along the bridge alignment are another indication of water depth, albeit in discrete, widely spaced intervals. Based on these data, water depth along the high rise portion of the bridge varies between 12 18 ft, with the deepest water near the navigation channel, and shallowest to the north. Such water depths are sufficient to allow nearly all vessels to strike pi ers in this region. However, nautical charts prepared by the National Oceanic and Atmospheric Administration (NOAA 2012a) indicate that a shoal with water depths as low as 2 3 ft lies immediately to the east of the bridge (Fig. 8 4 ). Note that sounding depths provided in the chart are relative to mean lower low water (MLLW), which in the Apalachicola Bay, is 1.5 ft lower than MHW. Therefore, for the purpose of the risk assessment, water depths near the shoal were assumed to be uniform and equal to 4 ft. Such low water levels constitute a navigational obstruction for certain vessel types traveling east to west, and thus, vessels with a draft exceeding 4 ft were assigned a lower probability of impacting piers lying away from the navigation channel when approaching from the east. The specific methodology used for assigning this reduction in risk is discussed in Section 8. 6 .6 Note that, as shown in Fig. 8 4

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173 sufficient water depth is available for all vessel types approaching from the west. A spoil area (area where dredging waste is deposited) is indicated south of the channel, which may result in reduced water depth. However, the depth in this region is not indicated on the c hart. through the raised mudline. For these reasons, the spoil area was neglected as a navigational obstruction in the risk assessment. 8.3 Bridge Characteristics The SR 300 Bridge consists of 165 spans, most of which are 125 ft long and supported by low rise pile bents. Near the navigation channel, a high rise portion is provided, which includes increased span lengths and vertical clearance. This section of the bridge (s hown schematically in Fig. 8 5 ) consists of 30 pile founded piers (numbered 33 62) that support spans that are 140 258 ft long. The AASHTO vessel collision provisions require that all piers located less than 3 LOA from the navigation channel be considered at risk for vessel collision, where LOA is the overall vessel length. For this location, the longest vessel type is a multi barge flotilla (623 ft long), being pushed by a tugboat (75 ft long), resulting in a maximum LOA = 698 ft. Therefore, any piers located less than 3 LOA = 2,094 ft from the channel centerline specifically, piers 35 60 were considered in the risk assessment. In order to adequately analyze these piers for vessel collision, finite elem ent models of two additional piers on each end of the central 6 LOA impact region were also prepared. 8.3.1 Bridge Piers Bridge pier configurations for the SR 300 Bridge are shown in Fig. 8 6 Piers consist of two c ircular columns (5 6 ft diameter) supporting a 6 ft deep pier cap beam. A strut is provided between the columns at the approximate mid height for piers 43 52. All piers are founded on 54 in. diameter cylinder piles, with the smallest foundations (pile caps) being supported by only

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174 four piles, and the largest foundations (pile caps) being supported by fifteen. Many piles are battered at an inclination of 2 in. horizontal per 12 in. vertical, as indicated by arrows in Fig. 8 6 All footings are 6.5 ft thick and are positioned such that the top surface is approximately 5.5 ft above MHW. The smallest footing (Fig. 8 6 D ) is 18.539 ft in plan, and the largest footing (Fig. 8 6 J ) is 2855 ft. Based on these pier configurations, barges and most small ships are expected to impact pier footings rather than columns, though some column impacts are possible. Consider the two imp act scenarios shown in Fig. 8 7 A fully loaded barge carries 6 12 ft of draft, with the most common being approximately 9 ft (Fig. 8 7 A ). In this scenario, the barge headlog impacts the pier at an elevation below the top of the pier footing. However, an empty barge (Fig. 8 7 B ) drafts only approximately 2 ft, and the headlog elevation is above the top of the fo oting. Depending on the barge bow and pier geometry, the impacting barge may make contact with the footing first. However, the barge may slide up and over the footing edge, or given sufficient energy, simply crush into the top footing corner, ultimately st riking a pier column. Impact scenarios like the one shown in Fig. 8 7 B are certainly of interest for design, in that all impacted pier components must be proportioned to resist impact loading. However, numer ous factors e.g., footing overhang distance, barge bow rake angle, vessel draft, water level, and impact angle all influence the relative probability of a column impact occurring. Given the inherent variability of such factors, assessing the probability of column impact is difficult. Thus, for the purpose of the risk assessment, columns were assumed to have sufficient capacity to transmit impact loads to the footing. As such, for simplicity, impact forces were applied at the footing elevation in all impact analyses. For final design, it would be appropriate to choose the most severe column impact scenario possible and proportion or support the columns

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175 such that they can resist the loads imparted. A strut or shear wall between the columns is commonly employed for this purpose, though not on the SR 300 Bridge piers. 8.3.2 Superstructure The superstructure for the SR 300 Bridge is typically supported by 78 in. Florida Bulb T girders. In the region of interest for the risk assessment, the roadway (8.5 in. thick R/C sla b) is supported by five girders, spaced at 9.5 ft on center. (The only portions of the superstructure that use four girders are the low rise causeway sections of the bridge). As shown in Fig. 8 8 the high rise portion consists of three superstructure zones. Spans between piers 33 45 and between piers 50 62 are 140 ft long, and consists of standard prestressed girders. Spans are cast contiguously with a R/C diaphragm at each pier. Expansion joints are provided every four spans. The central five spans (between piers 45 50) are between 207.5 ft and 257.5 ft in length (the center span is 250 ft), and include haunched sections over each pier, at which the girder depth increases from 78 in. to 144 in. The haunched girder segments and uniform depth segments near midspan were individually precast and prestressed. During bridge construction, the various girder segments were post tensioned together with tendons in harped profiles, to form a five span contin uous unit. Typical superstructure cross sections are shown in Fig. 8 9 The roadway slab is approximately 47 ft wide, with standard concrete barriers on each side. As discussed above, five evenly spa ced girders support the roadway. Fig. 8 9 A shows a typical section in a uniform depth region of the superstructure (all 140 ft spans, and the midspan segments of the haunched spans). Fig. 8 9 B shows a typical cross section at the piers with haunches. The girder depth is 144 in. at these locations. At all piers, girders rest on neoprene bearing pads. Two rows of bearing locations are provided at expansion joint piers, and a single row is provided at all other piers. At every bearing

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176 location, 4 in. diameter steel shear pins provide continuity between the girders and pier cap beam for lateral motions. These pins are particularly important for vesse l collision loading, as they permit more than 1,500 kips of shear force to be carried across the substructure superstructure interface. Consequently, when a pier is impacted, demand on the foundation is mitigated by permitting some portion of the lateral l oad to be shed through the superstructure and ultimately to adjacent piers. This action is important to consider when analyzing the piers for vessel impact, so the shear pin connection was included in finite element models of the piers and superstructure. 8.3.3 Soil Conditions In general, soil conditions at the site consist of layers of clean sand and silty and/or shelly sand. A thick layer of soft Florida limestone begins at a depth of approximately 60 ft, and is present across the entire bridge site. During co nstruction, piles were generally driven a few feet into the limestone and terminated. Thus, pile embedment depths vary for each pier, depending on the depth of this limestone layer. For the purpose of developing finite element models of each pier, soil pro perties were determined from SPT boring logs taken prior to bridge construction. As shown in Fig. 8 10 eight boring logs were available in the vicinity of the piers of interest. Soil layer profiles were developed from these boring logs and assigned to each pier finite element model, as shown in Fig. 8 10 Finite element soil spring characteristics were derived by well established equations that relate various important soil propertie s (e.g., internal friction angle, subgrade modulus) to the overburden adjusted SPT blowcount. The specific methodology that was employed is omitted here for brevity, but has been documented in numerous prior publications (Consolazio et al. 2008, 2010a, 201 0b). Additional information is also available in MultiPier and FB Deep (BSI 2009, 2010).

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177 8.3.4 Finite Element Models Renderings of finite element models of selected piers (developed in FB MultiPier) are shown in Fig. 8 11 Each pier shown is a representative example of the five pier configurations shown in Fig. 8 6 As discussed in Chapter 2, FB MultiPier models piles, pier columns, struts, an d pier caps with cross section integrated nonlinear beam elements that can account for cracking, material plasticity, and plastic hinging behaviors. Soil is modeled in FB MultiPier with nonlinear spring elements distributed down the embedded pile length, f ootings (pile caps) are modeled with linear elastic shell elements, and the superstructure is modeled as a composite (girder/slab) unit with linear elastic resultant beam elements that are connected to pier caps at discrete bearing locations. One pier, two span models of all piers within the impact zone (piers 35 60) were developed in accordance with the procedure discussed in Chapter 2 (Consolazio and Davidson 2008), and these models were employed for all structural impact analyses discussed in this chap ter. 8.4 Vessel Fleet Characteristics As stated in Section 8. 1 vessel traffic data were obtained from a comprehensive study of Florida vessel traffic conducted by Wang and Liu (1999). This study categorized vessel traffic in Florida into representative groups, and reported average vessel dimensions, vessel tonnage, and estimated transit velocities for each vessel group. The SR 300 Bridge corresponds to past point number 15, as defined by the Florida Department of Transporta tion (FDOT). County by county past point maps are available on the FDOT website at http://www.dot.state.fl.us/structures/pastpointmaps/vppm.shtm Vessel traffic data associated with each past point is integrated into the FDOT Vessel Impact Analysis Mathcad worksheet, which is freely available for download at http://www.dot.state.fl.us/structures/proglib.shtm

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178 8.4.1 Ves sel Categories Vessel traffic data for the SR 300 Bridge site that were obtained from the Wang and Liu study (1999) are summarized in Table 8 1 for upbound traffic, and Table 8 2 for downbound traffic. Note that downbound traffic refers to vessels traveling east to west, as defined in the FDOT past point map for Franklin County. Vessel traffic was categorized by similar shapes and sizes of vessel, and the dimensions and tonnage listed in the tables correspond to the average values among the various vessels that were assigned to each vessel ID. It is clear from these data that the vast majority of vessel traffic reported by Wang and Liu consists of barge tows. Most upbound traffic (Table 8 1 ) consists of single barges being propelled by a tugboat, while downbound traffic (Table 8 2 ) general ly consists of two barge flotillas also being propelled by a tugboat. Because the beam (i.e., width) of single vessels and combined flotillas are reportedly equal, it can be surmised that two barge flotillas are oriented in a single string (one barge in fr ont of the other). This observation is consistent with channel width limitations downstream. It is notable that data reported by Wang and Liu include very little ship traffic. The self propelled vessels indicated by Vessel ID 6 in Table 8 1 and Vessel ID 5 in Table 8 2 are assigned only six trips per year by Wang and Liu. However, the primary industry in Apalachicola Bay is fishing and oyster harv esting. Consequently, one would expect to see a large number of vessel transits by smaller fishing craft included in the traffic data. The sizes of the ft long) are larger than typical local fishing boats (30 60 ft long). It is noted by Wang and Liu (1999) that because such small fishing boats (50 150 tons) pose a negligible impact risk to bridges, they were excluded from the data set. This choice is warranted, given that vessel traffic data reported by Wang and Liu were gathered for specific purpose of assessing the risk of bridge collapse caused by vessel collisions. As such, no

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179 further investigation was conducted in order to quantify traffic volume for smaller self propelled vessels. For the purpose of the ris k assessment, vessel types were reorganized into vessel groups ( VG ) with unique contiguous numbers. Pertinent data for each vessel group that were used in the risk assessment are summarized in Table 8 3 No te that barge vessel groups were assigned the lowest numbers (1 8), and ship groups were assigned the highest numbers (9 11). Barge vessel drafts are reported in Table 8 3 as the maximum draft between t he barge and tug. In cases where the tug draft controlled (VG 1, 2, 5, and 6), the barge draft was used in assessing whether the vessel will run aground prior to impacting a particular pier. In doing so, it was assumed that the tug would run aground, lashi ngs between the tug and barge would break, and the barge would impact t he pier under its own momentum. S ee Section 8. 6 .6 for additional details 8.4.2 Vessel Traffic Growth For this risk assessment, vessel traffic was assumed to remain constant over time. Histor ical data compiled by Wang and Liu (1999) suggested a slight negative rate of growth for waterway through Apalachicola Bay. However, for design purposes, FDOT suggests zero growth for this particular waterway (FDOT 2013). Therefore, a vessel traffic growth factor equal to 1.0 (no growth) was assumed. 8.4.3 Vessel Transit Speeds Vessel transit speeds were selected in accordance with FDOT recommendations, which are based on the traffic study by Wang and Liu (1999). Specifically, FDOT recommends a base transit veloc ity equal to 7 knots for barge tows, and 10 knots for self propelled vessels and free tugs. This base velocity corresponds to ideal navigation conditions (straight channel and clear traffic). It is recommended that the base velocity be reduced by various a mounts, depending on local conditions:

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180 2 knot reduction for a curved navigation channel and/or crowded traffic 2 knot reduction for self propelled vessels on narrow canals or re stricted waterways 1 knot reduction for barge tows on narrow canals or restric t ed intracoastal waterways 1 knot reduction for loaded barge tows As shown above, the navigation channel is straight for several miles surrounding the SR 300 Bridge, and vessel traffic volume is relatively light. Therefore no reduction was taken for channe l alignment or traffic volume reasons. While the Apalachicola Bay appears to be a wide open body of water, the dredged channel is only 100 150 ft wide. In many locations in the bay (including near the bridge), the channel is surrounded by shallow water w ithin which many commercial vessels would run aground. Therefore, it was assumed that vessel operators would treat the ICWW channel through Apalachicola Bay in the same fashion as other restricted intracoastal waterways, and reduce speeds for safety. There fore, vessel speeds were reduced by 2 knots for self propelled vessels and 1 knot for barge tows. A further 1 knot speed reduction was applied to loaded barge vessel groups. Specifically, the loaded condition was defined as any barge with a draft exceeding 4 ft. Vessel speeds were further modified to account for the current velocity. Thus, 0.4 knots was subtracted from the velocity of upbound vessels and added to the velocity of downbound vessels. Refer to Table 8 3 for the final velocities after adjustments. Note that the AASHTO provisions suggest reducing the impact velocity for piers located away from the navigation channel, based on a linear function of vessel LOA Therefore, the values shown in Table 8 3 correspond only to piers near the navigation channel. Impact velocities for every combination of pier and vessel group are provided in Appendix J. 8.4.4 Vessel Transit Path The SR 300 Bridge was constructed such that the dredged navigation channel was centered between the main channel piers (piers 47 and 48). Because vessel traffic is fairly light, it

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181 is unlikely that vessels traveling opposite directions would pass each other under the bridge. Therefore, it was assumed that both upbound and downbound traffic is most likely to navigate along this channel centerline, and risk analysis parameters that rely on position relative to the vessel transit path (geometric probability, impact velocity) were computed assuming a common centerline for both traffic directions. 8.5 Vessel Impact Criteria In designing a new bridge, AASHTO requires additional criteria that the design must satisfy, aside from the maximum impact load criteria defined by the probabilistic risk assessment. Given that the example presented in this chapter is an assessment of an existing structure, certain criteria (e.g., minimum impact load combined extreme event scour, impact with superstructure elements) are not fully explored. Furthermore, for this study, certain portions of the AASHTO procedure have been replaced with new methods, as discussed in Chapter 7. The following sections describe, in a broad sense, how the overall vessel impact criteria prescribed by AASHTO were assessed in this study. 8.5.1 General Req uirements The adequacy of the SR 300 Bridge to resist vessel impact loading was assessed in accordance with the general requirements of the following provisions: AASHTO (1991). Guide Specification and Commentary for Vessel Collision Design of Highway Bridg es American Association of State Highway and Transportation Officials, Washington DC. AASHTO (2009). Guide Specification and Commentary for Vessel Collision Design of Highway Bridges, 2 nd Edition, American Association of State Highway and Transportation O fficials, Washington DC. FDOT (2013). FDOT Structures Manual Volume 1. Structures Design Guidelines Florida Department of Transportation, Tallahassee.

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182 Modifications to the AASHTO prescribed requirements, including consideration of dynamic bridge response a nd the influence of pier geometry on impact forces, were made as described in Chapter 7 (referred to as UF/FDOT methods). Such modifications, as they pertain to the SR 300 Bridge risk assessment, are documented in Section 8. 6 Note that, because the UF/FDO T procedures reflect the most up to date published research, the intent of the analysis was to meet or exceed (generally exceed) the level of engineering rigor required by the AASHTO specifications. Furthermore, while the results presented in this chapter imply that the UF/FDOT procedures predict higher levels of vessel collision risk when compared to AASHTO methods, this outcome is not guaranteed. Indeed, as discussed in Section 8. 8 commonly encountered impact scenarios exist for which UF/FDOT procedures may predict a lower vessel collision risk than the current AASHTO procedures. 8.5.2 Extreme Event Load Combinations (Scour) The FDOT Structures Design Manual requires that two different scour and impact conditions be considered in the design of bridge substructu res: 1) minimum vessel impact associated with an empty barge that has broken loose from its moorings during a storm event (including high water), and 2) maximum vessel impact associated with an aberrant vessel being driven into the bridge under normal envi ronmental and operating conditions. Corresponding scour levels for each condition were obtained from the bridge design drawings, as determined by combined geotechnical and hydrological analysis performed when the bridge was designed. 8.5.3 Minimum Impact Load Cr iteria The minimum impact condition corresponds to the scenario in which an empty hopper barge (195 35 ft) that was moored in the vicinity of the bridge breaks loose from its moorings during a storm and strikes the bridge. Under such conditions, barge mo tion is driven by wind and wave action. For this assessment, the empty barge displacement was assumed to be 200 tons, and

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183 the wind driven impact velocity was assumed to be equal to 1 knot. As required by the FDOT Structures Design Manual this minimum impa ct condition was combined with one half the 100 year short term scour level. While the minimum impact condition was a critical check on bridge pier performance under extreme environmental conditions, the maximum impact condition was found to control in all cases. Therefore, the minimum impact condition is omitted from further discussion. 8.5.4 Maximum Impact Load Criteria The maximum impact condition corresponds to the scenario in which a vessel being piloted under normal operating conditions becomes aberrant (by mechanical failure or other means) and impacts the bridge at full speed. Under such conditions, vessel motion is driven under its own power, or in the case of a barge tow, the power of a tug. For this assessment, vessel displacements and impact velocities were assumed to vary as discussed in Section 8. 4 .1 As required by the FDOT Structures Design Manual the maximum impact condition was combined with one half the long term ambient scour level. Note that in accordance with AASHTO procedures, the maximum im pact load conditions can be determined using a simplified, deterministic procedure (Method I), or by conducting a probabilistic risk assessment (Method II). Only the latter analysis procedure was considered in this study. 8.5.5 Operational Classification The SR operational classification. Consequently, structural collapse as a result of vessel collision should have a return period of 10,000 years, as required by the AASHTO provisions. Th is requirement is significantly more stringent than a normal bridge (return period of 1,000 years). However, the classification reflects the importance of the bridge to the region. Because the SR 300 Bridge is the only roadway between St. George Island and the Florida mainland, it constitutes the only

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184 hurricane evacuation route to residents of the island. Furthermore, access to hospitals and other emergency services require that the bridge be operational even under extreme conditions. 8.6 Maximum Impact Load (M ethod II) Analysis Methodology As defined by AASHTO, Method II is a probabilistic risk analysis procedure that is used to quantify the annual frequency (annualized probability) that that a bridge will collapse when subjected to vessel collision loading (de noted AF ). In its formulation, Method II attempts to account for all major factors that contribute to vessel collision risk, including but not limited to vessel traffic volume, waterway characteristics, bridge geometry, and bridge element strength. The fol lowing sections detail analysis assumptions and the overall methodology that was used to quantify AF for the SR 300 Bridge. Risk assessments were completed both using strict AASHTO methodology (static loading and pushover analysis) and using the modified U F/FDOT methodology that incorporates dynamic structural analysis and other state of the art procedures from recent research. Risk measures that were computed using each method are compared in Section 8. 7 Because a significant portion of the risk assessmen t methodology was conducted in accordance with the AASHTO provisions, FDOT Vessel Impact Analysis software (version 3.1), implemented in Mathcad, was utilized extensively in various calculations. Structural analyses were carried out using FB MultiPier (ver sion 4.18), and custom Perl scripts (Perl 2013) were programmed to summarize relevant analysis data. Subsequent risk calculations were completed using Mathcad worksheets. 8.6.1 Annual Frequency of Collapse ( AF ) The annual frequency of collapse ( AF ) was computed by the following expression: ( 8 1 ) where:

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185 AF = Annual frequency of pier collapse due to vessel collision, N = Annual number of vessel transits, as categorize d by vessel type and transit direction, PA = Probability of vessel aberrancy, PG = Geometric probability of a pier being impacted by an aberrant vessel, PC = Probability of bridge element collapse subject to collision, and PF = Protection factor to acc ount for land masses or other objects (e.g. structural dolphins) that may block vessels from colliding with the bridge (PF=0: bridge element fully protected; 0 < PF < 1: bridge element partially protected; PF=1: bridge element unprotected). Note that AF w as more specifically computed as a summation of all possible combinations of bridge pier and vessel group. Therefore, a more detailed form of Eqn. 8 is: ( 8 2 ) where, N VG is the number of vessel groups ( N VG = 11 in this case, as defined in Table 8 3 ), and N P is the number of bridge piers within the navigation zone ( N P = 26 in this case, pier s 35 60). 8.6.2 Vessel Frequency ( N ) Vessel frequency ( N ) refers to the annual number of vessel transits by a particular vessel type and transit direction (as defined by the vessel groups listed in Table 8 3 ). On any of these transits, the vessel has some finite probability of becoming aberrant and striking a bridge pier. However, in order to collide with a pier, sufficient water depth must be available to accommodate the vessel draft. Otherwise, the vessel will run aground prior to impacting a pier. Premature vessel groundings caused by insufficient water depth can be accounted for in the risk assessment in two ways: 1) the value of N for relevant piers and vessel groups can be set equal to zero or reduced in so me way, or 2) a protection factor ( PF ) can be assigned to relevant piers and

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186 vessel groups. The latter option was adopted in for this assessment, as discussed in Section 8. 6 .6 It should be noted that the example risk assessment published in the AASHTO Gui de Specification employs the first option (setting N = 0 for certain vessels to account for groundings). 8.6.3 Probability of Aberrancy ( PA ) Probability of aberrancy ( PA ) refers to the likelihood that a given vessel will stray off course (become aberrant), makin g collision with a bridge pier possible. Such events can occur due to pilot error, adverse environmental conditions (e.g. dense fog), or mechanical failure (e.g. loss of power). As it is unknown how often and for how long vessels typically veer off course and can be classified as aberrant, accurately quantifying PA can be extremely difficult. Furthermore, the aberrant condition can often be temporary, and may not occur anywhere in the vicinity of a bridge. Certainly, aberrancy caused by pilot inattentivenes s is likely to be reduced in the vicinity of a bridge, given that the pilot is aware of the risk of collision. No comprehensive studies have ever been conducted to quantify AF itself. Estimates have been posited by past engineers and researchers, based on analysis of historical vessel accident data (groundings, collisions, rammings), as discussed in the AASHTO Guide Specification. However, by definition, recorded accident data only include incidences of aberrancy that resulted in an accident. Commonly, the course of an aberrant vessel is corrected by the pilot, and an accident is avoided. Depending on the amount of information available, two possible approaches can be taken to quantify AF : 1) gather available accident data for the waterway of interest and ma ke a defensible estimate (prior studies should be consulted for guidance in preparing an estimate), or 2) if accident data are unavailable, use the simplified procedure provided in the AASHTO provisions. The latter option was employed in this study. Specif ically, PA was computed as:

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187 ( 8 3 ) where: BR = Base rate of aberrancy (0.610 4 for ships, and 1.210 4 for barges), R B = Correction factor for bridge location (related to waterwa y alignment), R C = Correction factor for currents acting parallel to the navigation channel, R XC = Correction factor for currents acting perpendicular to the navigation channel, and R D = Correction factor for vessel traffic density. As stated above, BR = 1.210 4 was used for barge vessel groups (1 8) and BR = 0.610 4 was used for ship vessel groups (9 11). The correction factor for bridge location ( R B ) was computed based on the relative location of the bridge in one of three possible waterway regi ons (straight, transition to a turn, or within a turn). Because the bridge is located in a straight region that is several miles long, R B = 1.0 was selected. The correction factor for currents acting parallel to the channel ( R C ) was computed as where V C is the current velocity (parallel) in knots. Given a parallel current velocity of 0.4 knots, R C = 1.04. Because currents acting perpendicular to the channel were found to be negligibly small, R XC = 1.0 was selected. The correctio n factor for vessel traffic density ( R D ) was computed based on the relative volume of traffic, and the likelihood of vessels overtaking each other near the bridge location. Because only 1 2 large vessels traverse under the bridge per day, it is highly un likely that vessels would overtake each other under or nearby the bridge. Therefore, R D = 1.0 was selected, corresponding to low traffic density.

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188 Considering the various correction factors, PA = 1.2510 4 was computed for barge vessel groups (1 8) and PA = 0.62410 4 was computed for ship vessel groups (9 11). 8.6.4 Geometric Probability ( PG ) The geometric probability ( PG ) is the conditional probability that a vessel will collide with a particular bridge pier, given that it has become aberrant. The AASHTO pro visions suggest assuming that the vessel position (perpendicular to the intended transit path), is a Gaussian distributed random variable, with mean equal to the channel centerline and standard deviation equal to the overall vessel length ( LOA ). Therefore, PG for a given pier is equal to the area under the Gaussian distribution bounded by the extents of the pier element width ( B P ) and plus the vessel width or beam ( B M ), as illustrated in Fig. 8 12 Based on the procedure illustrated i n Fig. 8 12 projected pier widths ( B P ) were computed as where W P is the width of the pier footing parallel to the bridge alignment, L P is the length of the footing perpendicular to the bridge alignment, and is the skew angle of the navigation channel relative to the bridge alignment ( = 28.5). Values of BP for each pier are summarized in Table 8 4 Using these values of B P the positions of each pier relative to channel centerline, and the vessel beam ( B M ) values for each vessel group, PG values varying between 0.0 (zero) and approximately 0.15 were computed for each combination of pier and vessel group. A table of computed PG values is provided in Appendix J. 8.6.5 Probability of Collapse ( PC ) The probability of collapse ( PC ) refers to the likelihood that a particular bridge element (e.g., a pier) will collapse, given that it has been impacted by a particular vessel. Like any failure probability, PC is a function of both the lo ading characteristics and the structural capacity. Both the load and resistance are dependent on numerous parameters, each subject to random statistical

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189 variability. For example, vessel impact loads are a function of the vessel size, bow shape, impact velo city, direction of impact, vessel mass, and other parameters. Furthermore, the capacity of a pier to resist such impact loads is dependent upon structural configuration, pier member sizes, pier material strengths, and soil strength. To further complicate t he process of predicting failure, impact events are dynamic in nature, and involve complex interactions between the impacting vessel and pier. Therefore, many of the load and resistance parameters listed above are correlated. For example, the magnitude and duration of dynamic impact forces (load characteristics) depend strongly upon the nonlinear lateral stiffness of the impacted pier (a resistance characteristic). Consequently, all of the important load and resistance characteristics, their statistical var iability, and any possible correlations between them must be carefully considered in order to arrive at a reasonable estimate of PC The most accurate means of quantifying PC is through a structural reliability analysis (e.g., Monte Carlo simulation) that directly accounts for the statistical variability of the various load and resistance parameters. However, such an approach may require conducting tens of thousands dynamic structural analyses in order to arrive at a reliable PC estimate for just one pier a nd impact condition. Such an approach was demonstrated for eight different bridge piers by Davidson et al. (2013). Clearly, direct reliability analysis of this nature is overly burdensome for bridge designers to employ in practice. As an alternative, PC ha s historically been computed (for vessel collision) using simplified equations that act as a surrogate for the complicated interactions and statistical variability discussed above. Such equations relate PC to a deterministically computed demand to capacity ratio. Structural demand (i.e., impact load magnitude) is computed using simplified equations that include the various parameters discussed above, and structural capacity is

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190 computed by structural analysis. Given the deterministically determined demand ca pacity ratio (D/C), PC is computed from a surrogate equation. Two surrogate equations for PC are available in the published literature: 1) the equation that is included in the AASHTO vessel collision provisions, and 2) an independently derived equation rec ently developed by Davidson et al. (2013). Note that the AASHTO expression relies on a static treatment of both the impact load and structural capacity (i.e., static pushover analysis), while the Davidson expression employs a time varying definition for th e demand capacity ratio, and can therefore be employed in conjunction with a dynamic definition of the impact load and structural response by means of transient structural analysis. The relative merits of the two expressions are discussed at length in Davi dson et al. (2013) and Consolazio et al. ( 2010a ). The purpose of the current study was to compare the results of both procedures using the SR 300 Bridge as an example. As described in the following sections, PC values were computed using the AASHTO PC expr ession, employing AASHTO static load prediction models (from both the 1991 and 2009 specifications) and static pushover analysis of the piers. PC values were also computed using the Davidson PC expression, employing newly developed load prediction models a nd three new structural analysis techniques (two dynamic, one equivalent static). It should be noted that the Davidson PC expression was derived exclusively for barge impact scenarios. Therefore, for ship type vessel groups, PC was computed using the AASHT O procedures. 8.6.5.1 AASHTO m ethods In accordance with the AASHTO guidelines, PC was computed as:

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191 ( 8 4 ) where H is ultimate lateral pier resistance (as determined by static pushover anal ysis), and P is the vessel impact force (as determined by the equations below). From Eqn. 8 4 the following observations are made: For cases in which the lateral pier resistance exceeds the impact force, PC = 0. F or cases in which the pier impact resistance is 10% to 100% of the impact force, PC varies linearly between 0.1 and 1.0. In other words, if the predicted impact force exceeds the pier capacity by up to 10 times then PC varies between 0.1 and 1.0. For case s in which the pier impact resistance is below 10% of the impact force, PC varies linearly between 0.0 and 0.1. In other words, if the predicted impact force is more than 10 times the pier capacity, then PC varies between 0.0 and 0.1. Lateral pier capaciti es ( H ) that were used to compute PC were taken from the bridge design drawings. Note that, as listed in the drawings, these capacities correspond to the minimum lateral capacity of each pier. Actual pushover capacities (determined by structural analysis in FB MultiPier) were found to be higher than the minimum values. The degree of exceedance depended on soil conditions assigned to each pier. For consistency with the risk assessment methodology employed in the bridge design, the minimum values of H listed i n the bridge drawings were adopted for the risk assessment (Table 8 5 ). In accordance with the AASHTO provisions, ship impact forces ( P S ) were computed as: ( 8 5 ) where DWT is the deadweight tonnage of the ship (tonnes), and V is the impact velocity (ft/s). In the given units, P S was computed in kips. Ship impact forces varied between 198 kips and 1,670 kips, depending on ship type and p ier distance from the navigation channel (Appendix J)

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192 8.6.5.1.1 AASHTO 1991 barge impact load model (as d esigned) To compute barge impact forces ( P B ) in accordance with the 1991 AASHTO provisions, vessel kinetic energy ( KE ) was first computed as: ( 8 6 ) where, C H is a hydrodynamic mass coefficient, W is the vessel weight (tonnes), and V is the impact velocity (ft/s). In the given units, KE was calculated in kip ft. Hydrodynamic coefficients ( C H ) were calculated based on underkeel clearance (distance between keel of vessel and b ottom C H = 1.05, and for underkeel clearance C H = 1.25. For clearances between those two limits, C H was linearly interpolated. A table of C H values for each pier and vessel group is provided in Appendix J. Next, barge bow damage depth ( a B ) (i.e., the depth of maximum crushing deformation) was computed as: ( 8 7 ) where, R B is the ratio B B /35, where B B is th e barge bow width (ft). In the given units, a B was calculated in ft. Lastly, barge impact force ( P B ) was computed as: ( 8 8 ) In the given units, P B was computed in kips. Barge impa ct forces computed using the 1991 AASHTO equations varied between 367 kips and 4,682 kips, depending on barge type and pier distance from the navigation channel (Appendix J).

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193 8.6.5.1.2 AASHTO 2009 barge impact load m odel To compute barge impact forces ( P B ) in accord ance with the 2009 AASHTO provisions, vessel kinetic energy ( KE ) was also computed as before: ( 8 9 ) In the given units, KE was calculated in kip ft. The 2009 AASHTO provisions exc luded the term R B from all load equations. Therefore, barge bow damage depth ( a B ) was computed as: ( 8 10 ) In the given units, a B was calculated in ft. Lastly, barge impact force ( P B ) was computed as: ( 8 11 ) In the given units, P B was computed in kips. Barge impact forces computed using the 2009 AASHTO equations varied between 367 kips and 3,241 kips, depen ding on barge type and pier distance from the navigation channel (Appendix J). As described above, the ratio H / P S or H / P B (depending on vessel group) was computed for each combination of pier and vessel group. Using Eqn. 8 4 corresponding estimates of PC were also calculated. Results are summarized in Section 8. 7 and detailed results can be found in Appendix J. 8.6.5.2 UF/FDOT m ethods In accordance with Davidson et al. (2013), PC was computed as: ( 8 12 ) where D / C is the maximum demand to capacity ratio from structural analysis. As defined by Davidson, D / C is a rational measure of the proximity of a structure to the formation of a

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194 structural mechan ism that would result in instability and collapse. The ratio can take on any value from between 0 and 1, such that D / C = 0 for a pier under no load, and D / C = 1 for a pier which has formed a structural collapse mechanism and is at incipient collapse. It is important to note that D / C is a time varying dynamic quantity. During a dynamic vessel impact event, D / C begins close to 0 (gravity loading will cause D / C to be nonzero even without impact load applied) and as the pier displaces, D / C increases (up to D / C = 1, if the pier collapses). For this study, D / C was computed as: ( 8 13 ) where m is the number of members (e.g., piers columns, piles) associated with a given collapse mechanism, n is the number of hinges per member that are necessary to form the corresponding collapse mechanism, and is the j th largest element demand capacity ratio along member i as reported by FB MultiPier (internally computed based on biaxial load moment interaction). See Consolazio et al. ( 2010a ) for a more detailed description of D / C and its theoretical basis. 8.6.5.2.1 CVIA structural a nalysis The most accurate (design oriented) vessel impact analysis method currently available is coupled ves sel impact analysis (CVIA). As illustrated in Fig. 8 13 in CVIA, the impacting vessel is idealized as a single degree of freedom (SDF) system, consisting of a concentrated mass that represents the vessel mass, and a nonlinear spri ng element that represents the crushing characteristics (force deformation relation) of the vessel bow. The SDF barge model is coupled to a multiple degree of freedom (MDF) finite element model of the impacted pier at a node corresponding to the expected i mpact location. To begin the analysis, the structure is pre loaded

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195 with gravity and buoyancy forces, and then the vessel mass is prescribed an initial velocity equal to the impact velocity. Impact forces imparted on the pier are computed based on dynamic i nteraction between the SDF barge and MDF pier models, as would occur during a real impact event. CVIA has been used extensively in numerous research projects (Consolazio et al. 2008, Davidson et al. 2010, Getter et al. 2011, and Davidson et al. 2013). As i mplemented in these prior studies, the barge force deformation relation was assumed to be elastic, perfectly plastic (as shown in Fig. 8 13 using a force deformation model from Consolazio et al. (2009). This model has since been u pdated to account for oblique impact scenarios (Getter and Consolazio 2011), like the one shown in Fig. 8 14 The Getter Consolazio force deformation model was employed throughout this study for computing impa ct forces. Specifically pertaining to CVIA, force deformation relations for the SDF barge models were taken to be elastic, perfectly plastic, with yield deformation a BY = 2 in. Barge yield force ( P BY ) was computed in accordance with the empirical Getter Co nsolazio equations. For oblique impact with a flat faced pier (the scenario for all piers in the SR 300 Bridge), P BY was computed as: ( 8 14 ) where is the smallest skew angle between the barge bow and pier surface (degrees), B B is the vessel beam (width) (ft), and B P is the width of the pier face associated with the smallest skew angle (ft). These quantities are illustrated for a typical impact cond ition in Fig. 8 14 Given the units shown, P BY was computed in kips. A summary of relevant input data for CVIA simulations is provided in Table 8 6 Impact force time histories computed by each CVIA simulation that

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196 was conducted (208 total) are provided in Appendix J. Finally, D / C values predicted by CVIA, and the associated values of PC are discussed in Section 8. 7 and listed in detail in Appendix J. 8.6.5.2.2 AVIL s tructural a nalysis The applied vessel impact load (AVIL) method was developed as a slightly simpler alternative to CVIA (Consolazio et al. 2008). The method consists of developing a pre computed impact force time history and applying it as a dynamic load in a transi ent analysis, as shown in Fig. 8 15 It is recognized that many structural analysis packages do not include the features required to conduct CVIA (e.g, the ability to assign initial velocities), but the ability to analyze structures under prescribed time varying loading is quite common. In such cases, AVIL is an excellent alternative analysis procedure to CVIA. The AVIL method is summarized in Fig. 8 16 As implemented in this study, barge force deformation characteristics ( a BY and P BY ) were established based on the Getter and Consolazio (2011) model, as discussed above for CVIA. Barge mass ( m B ) and initial barge velocity ( v Bi ) were also the same as CVIA (recall Table 8 6 ). As shown in Fig. 8 17 pier soil stiffness ( k P ) was determined by analyzing each pier finite element model subject to a lateral load ( P ), measuring the corresponding di splacement ( ), and computing k P = P / It is recognized that, due to soil and/or structural nonlinearity, k P generally becomes smaller as P increases. Because the AVIL method is unable to account for changes in pier resistance during an impact event, a representative k P must be selected for its formulation. It was observed in conducting this study, that using the initial pier stiffness (i.e., k P corresponding to a very small value of P ) resulted in analysis results that were very similar to CVIA and consistently conse rvative. Values of k P that were determined for each pier are provided in Table 8 7 and maximum barge impact forces ( P Bm ) for each pier and vessel group are shown in Table 8 8 Impact force time histories

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197 that were computed for each AVIL analysis are compared to corresponding CVIA force histories in Appendix J. Finally, D / C values predicted by AVIL, and the associated values of PC are discussed in Section 8. 7 and listed in det ail in Appendix J. 8.6.5.2.3 SBIA structural a nalysis The static bracketed impact analysis (SBIA) method is an equivalent static analysis procedure that attempts to account for the inertial response of the impacted pier by means of a small number of static load case s (Getter et al. 2011). SBIA represents an improvement over static pushover analysis, in that it accounts for superstructure inertia and dynamic amplification of pier structural demands. It should be noted, however, that SBIA was specifically developed to produce conservative results relative to more refined procedures like CVIA or AVIL. It is therefore expected to produce D / C estimates that are larger than both dynamic methods. The purpose of including SBIA in this study was to evaluate its level of conser vatism in the context of a vessel collision risk assessment. The SBIA method is summarized in Fig. 8 18 As shown, the method consists of two overriding static load cases, of which one (Load Case 1, abbreviated LC1 hereafter) requi res three separate analyses. The parameters of each LC1 analysis are specifically tuned to produce conservative analysis results for the corresponding structural demand type. From left to right in Fig. 8 18 the first analysis is i ntended to quantify pier column and/or foundation moments, the second analysis is intended to quantify pier shear forces, and the third analysis is used to quantify shear forces at the superstructure bearing locations (substructure superstructure interface ). For all three LC1 loading conditions, an amplified impact load (1.45 P B ) is applied at the impact location, and a load ( IRF P B ) is applied at the superstructure elevation. The load IRF P B is intended to mimic superstructure inertial behavior that can on ly be directly quantified through

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198 dynamic analysis. Load Case 2 (LC2) consists of applying an amplified impact load (1.85 P B ) at the impact location, but no superstructure load. As implemented in this study, P B was computed using the same impact conditions pier characteristics, and load equations as AVIL. However, because it is a static method, only the maximum dynamic impact load was of interest. As such, P B for SBIA was equal to P Bm from AVIL (recall Fig. 8 16 and Table 8 8 ). Values of inertial resistance factors ( IRF m IRF v and IRF b ) were computed using the pier and superstructure characteristics and equations shown in Fig. 8 18 Superstruct ure stiffness was computed as shown in Fig. 8 19 A multiple pier finite element model (including superstructure) was constructed, with the pier of interest (impact pier) in the center. The impact pier was removed from the analysis by removing connections between the pier and superstructure, and a lateral load equal to 0.25 P B was applied to the superstructure at the location of the removed pier. Lateral deflection ( sup ) was computed, and superstructure stiffness w as calculated as k sup = (0.25 P B )/ sup Pier parameters that were used to compute IRF are summarized in Table 8 9 and computed IRF values are provided in Table 8 10 Note that primary purpose of the SBIA method is to quantify structural demands (shears, moments) for use in designing and proportioning various structural elements. In contrast, the goal of performing structural analysis in the context of this risk assessm ent was to quantify demand capacity ratios ( D / C ) for input into the Davidson et al. (2013) PC expression (Eqn. 8 12 ). Because D / C as defined by Davidson et al. (Eqn. 8 13 ), was computed based on load moment interaction, only the LC1 analysis pertaining to pier moments (analyzed using IRF m ) and LC2 were used in computing D / C for the risk assessment. The other two LC1 analyses (utilizing IRF v and IRF b ) would be useful for proportioning a new bridge, but such results had

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199 limited utility in the risk assessment. Values of D / C predicted by SBIA, and the associated values of PC are discussed in Section 8. 7 and listed in detail in Appendix J. 8.6.6 Protection Factor ( PF ) T he protecti on factor ( PF ) is a correction factor used in a vessel collision risk assessment to account for land masses and other navigational obstructions that may block bridge piers (either fully or partially) from being impacted by oncoming vessels. As noted in Sec tion 8.2.2 two navigation obstructions exist to the east of the bridge: a man made island in the vicinity of the northern piers, and a segment of a decommissioned bridge (now a fishing pier) in the vicinity of the southern piers ( recall Fig. 8 2 ). It was therefore appropriate to assign protection factors ( PF ) to each pier in the vicinity of these obstructions to account for reduced collision risk A rational calculation basis was developed to determine th e probability that a vessel would run aground on the navigational obstructions ( P Gr the probability of grounding) prior to impacting the bridge piers, and P Gr was used to calculate PF for each pier. To demonstrate the basis for calculating P Gr consider t he scenario shown in Fig. 8 20 in which a barge tow is positioned such that impact is impending with a bridge pier to the north of the navigation channel. The orientation angle of the tow (relative to the bridge alignment) is assumed t o be a Gaussian distributed random variable, with a mean equal to the orientation angle of the navigation channel (i.e., the most likely tow orientation is parallel to the navigation channel) and a standard deviation equal to 10 (Kunz 1998). As shown in F ig. 8 20 the orientation angle ( ) is taken to be equal to 0 when the tow is aligned parallel to the navigation channel, and thus can take on positive or negative values. Given the site geometry, a vessel would run aground on the is land obstruction if it approached from a negative (signed) angle such that NO where NO is the negative (signed) angle, defined in Fig. 8 20 between the

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200 navigational obstruction and the most likely vessel orientation (parallel to the navigation channel). Note that because is defined as a Gaussian distributed random variable, it can take on values = [ standard deviation is equal to a relatively s mall angle of 10, the practical range of the Gaussian distribution is limited to realistic approach angles (i.e., = 30 spans three standard deviations on either side of the mean). Given the scenario illustrated in Fig. 8 20 the to tal probability of the vessel grounding ( P Gr ) was computed as: ( 8 15 ) where P is a Gaussian distribution with mean = 0, and standard deviation = 10. For the example shown in Fig. 8 20 it is important to point out that P G r is nonzero even though the pier is located well south of the island. While this outcome may initially seem counterintuitive, the procedure appropriately takes into account low probabil ity impact scenarios in which the vessel approaches from a position north of the tip of the island and ultimately runs aground. Fig. 8 21 shows an analogous scenario to Fig. 8 20 in which a barge tow inst ead approaches a pier located south of the navigation channel. As a vessel approaches a southern pier, the remaining segment of a decommissioned bridge (now a fishing pier) acts as a potential navigational obstruction. The old bridge obstructs possible app roach angles such that a vessel would run aground (i.e., impact the old bridge) if NO (where NO is a positive signed angle, as defined in Fig. 8 21 ). For the scenario shown in Fig. 8 21 probability of grounding ( P Gr ) was computed as: ( 8 16 )

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201 Note that the integration limits in Eqn. 8 16 were changed (relative to Eqn. 8 15 ) to result in small values of grounding probability P Gr for the northernmos t piers and large val ues for the southernmost piers. The procedure outlined above was repeated for each SR 300 pier in the impact zone, and for simplicity, P G r = 0.0 was conservatively assigned to any piers for which the computed value P Gr was less than 0. 001 (0.1%). Protection factors ( PF ) were subsequently computed as: ( 8 17 ) Piers 44 48 (nearest the navigation channel) were afforded no meaningful protection by the obstructions (island or fishing pier) and were therefore assigned PF = 1.0 (corresponding to a zero probability of grounding, P Gr = 0.0). As discussed i n Section 8.2.5, a s hoal also exists immediately to the east of the SR 300 Bridge, restricting water depths to appr oximately 4 ft at MHW. As shown in a navigation chart (recall Fig. 8 4 ), reduced water depth from the shoal affects almost the entire eastern side of the bridge, with the exception of the dredged channel. Off chan nel water depths do increase near the bridge (effectively widening the channel) with a more widespread increase in depth to the south of the channel. Therefore, vessels of any draft were assumed to be able to impact three piers south of the channel (piers 45 47) and one pier north of the channel (pier 48) without running aground. However, for all other piers, the probability of downbound vessels grounding on the shoal ( P Gr ) was assumed to be equal to 0 for vessel draft 4 ft, and 1 for draft 12 ft. P Gr was linearly interpolated between 0 and 1 for vessel drafts between 4 ft and 12 ft, respectively. Corresponding values of PF = 1 P Gr were calculated and multiplied by the PF values corresponding to the island and fishing pier obstructions (i.e., the sep arate components of the

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202 protection factor were assumed to combine in the same manner as conditional probabilities using multiplication). Final PF values for each pier and vessel group are tabulated in Appendix J. 8.7 Risk Analysis Results As discussed in the p rior section, vessel collision risk assessments were conducted for the SR 300 Bridge using the methodology prescribed by AASHTO (1991 and 2009 specifications). Additional assessments were conducted using the revised UF/FDOT methodology and three different structural analysis procedures (CVIA, AVIL, and SBIA). The results of each assessment are presented in this section, including probability of collapse ( PC ) and annual frequency of collapse ( AF ) estimates, as predicted by each method. Detailed results for e ach pier and vessel group are provided in Appendix J. 8.7.1 AASHTO Methods The following sections discuss results from the risk assessments conducted using AASHTO methodology with two different barge impact load equations: 1) from the 1991 AASHTO provisions (Eqn s. 8 7 and 8 8 ), and 2) from the 2009 provisions (Eqns. 8 10 and 8 11 ). 8.7.1.1 AASHTO 1991 barge impact load model (as d esigned) Estimates of PC values that were computed using the AASHTO (1991) methodology were very often equal to zero. Specifically, of the 289 combinations of pier and vessel group considered, PC was nonzero 58 times (approximately 20%). This occurred because, using the AASHTO expression, PC was only nonzero when the impact load P exceeded the lateral pier capacity H (i.e., H / P < 1). Furthermore, even nonzero values of PC were quite small. Indeed, the largest PC among all cases considered was 0.071, and for this case, the impact load exceeded pier capacity by 2.8 times Among the nonzero cases, the average PC was 0.033, which corresponds to pier capacity being exceeded by 1.4 times.

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203 Estimates of PC as obtained by AASHTO (1991) methods, are presented qualitatively for every pier and vessel group in Fig. 8 22 A Note that in this format, white squares correspond to PC values that are exactly equal to zero. Gree n color indicates PC just greater than zero, and the color gradient fades to red at PC = 1. While all nonzero values are small, PC was slightly greater for piers far from the navigation channel. The majority of nonzero PC cases were in vessel groups 6 and 8. Including all other terms in the AF expression ( N PA PG PF ), the relative contribution to AF is shown for every pier and vessel group in Fig. 8 22 B Note that the color gradient is simply relat ive to the maximum contribution among all piers and vessel groups, having no specific numerical scale. The purpose of the gradient is to show, qualitatively, which piers and vessel groups contribute most to total risk ( AF ). As would be expected, piers near est the centerline contributed most to AF as they have the highest likelihood of being impacted. Most risk was concentrated in vessel group 8 (the largest vessel type in the fleet). Fig. 8 23 A shows t he percent contribution to AF for each pier in the bridge (i.e., the contributions shown in Fig. 8 22 B summed across all vessel groups). As noted previously, the majority of total risk was concentra ted in piers near the navigation channel. Specifically, approximately 75% of risk was carried by the three piers south of the channel (piers 45 47) and one pier north of the channel (pier 48). Recall that these are the four piers that were assigned prote ction factors PF = 1.0 for downbound traffic (Section 8.6 .6 ). All other piers were assigned PF < 1, to account for navigational obstructions and shallow water depths to the east of the bridge, and therefore their percent contribution to total risk was corr espondingly lower.

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204 Fig. 8 23 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 8 22 B summed ac ross all piers). The vast majority of risk (approximately 85%) came from vessel groups 6 and 8, as noted above. Summing AF among all piers and vessel groups, AF predicted by AASHTO (1991) methods was 4.9610 5 yr 1 which corresponds to a return period 1/ A F = 20,150 years. Therefore, by the AASHTO definition, the bridge can be considered sufficiently robust to resist vessel collision loading, because the minimum acceptable return period is 1/ AF = 10,000 years ication. It should be noted that the value for AF was strongly sensitive to assumptions made in the analysis. For example, if the possibility for vessel groundings for downbound traffic was neglected, the return period changed to 1/ AF = 11,730 years. This finding suggests that all assumptions made in performing the risk analysis should be stated clearly and explained thoroughly so that they may be effectively evaluated by peer engineers and the bridge owner. Furthermore, the sensitivity of AF to various ass umptions should be evaluated by the engineer to ensure that reasonably conservative choices are made. 8.7.1.2 AASHTO 2009 barge impact load m odel Estimates of PC that were computed using the AASHTO (2009) methodology were nearly always equal to zero. Specifically, of the 289 combinations of pier and vessel group considered, PC was nonzero 16 times (approximately 5%). This occurred because, compared to the 1991 AASHTO procedure, barge impact load magnitudes were lower, particularly for high energy impact conditions experienced by piers near the navigation channel. Because the bridge was designed to resist relatively higher load magnitudes predicted by the 1991 AASHTO provisions, pier capacity was almost never exceeded ( H / P < 1) using the 2009 provisions, and PC was e qual to zero for 95% of impact cases considered.

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205 Estimates of PC as obtained by AASHTO (2009) methods, are presented qualitatively for every pier and vessel group in Fig. 8 24 A Note that PC was equ al to zero for all piers between 40 and 55 for every vessel group. Consequently, PC was only nonzero for piers located far from the navigation channel, which are unlikely to be impacted. Including all other terms in the AF expression ( N PA PG PF ), the r elative contribution to AF is shown for every pier and vessel group in Fig. 8 24 B The largest single contributor to AF was pier 56 for vessel group 6, because, of the piers with nonzero PC pier 56 had the highest probability of being impacted (as reflected by its PF value). Fig 8 25 A shows the percent contribution to AF for each pier in the bridge (i.e., the contributions shown in Fig. 8 24 B summed across all vessel groups). As discussed above, pier 56 accounted for more than 45% of the total risk to the bridge, and the next highest contributors were piers 39 and 58, each contributing les s than 15%. This outcome differs substantially from the assessment using the 1991 AASHTO provisions, in which four piers near the navigation channel (piers 45 48) accounted for 75% of total risk (recall Fig. 8 23 A ). However, using the 2009 provisions, piers 45 48 had PC = 0, and therefore did not contribute to vessel collision risk at all. Fig. 8 25 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 8 24 B summed across all piers). As with the 1991 AASHTO assessment, risk was concentrated in vessel groups 6 and 8. However, these vessel groups were the only contributors to AF in the 2009 AASHTO assessment. Summing AF among all piers and vessel groups, AF predicted by AASHTO (2009) methods was 6.8510 7 yr 1 which corresponds to a return period 1/ AF = 1,460,000 years. Therefore, based on the 200 9 provisions, the SR 300 Bridge is at no practical risk of collapsing

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206 due to vessel collision. As noted above, this outcome occurred because the only piers that had nonzero values for PC were those located very far from the navigation channel. Such piers h ad small PG values, because they were located at the tails of the probability distribution for vessel position relative to the channel. Also, nonzero PC values were very small for these distant piers, because vessel transit velocities (and thus, impact ene rgies) decreased as the distance from the navigation channel increased (as required by AASHTO). Lastly, PF values were smallest for the distant piers because of the relatively large degree of protection afforded by navigational obstructions (island to the north and fishing pier to the south). Therefore, considering all these factors, AF was found to be nearly zero. These results highlight how sensitive the AASHTO PC expression can be to changes in analysis assumptions. For this example case, vessel impact l oad magnitudes predicted by the 2009 equations were, on average, 17% smaller than those predicted by the 1991 equations. However, AF was found to be 72 times smaller, as a result. Indeed, if bridge pier capacities ( H ) are uniformly assumed to be 17% smalle r to account for the reduction in loads, then the return period (1/ AF ) goes from 1,460,000 years to 37,400 years, a change of 39 times. Such sensitivity is caused by the AASHTO PC equation allowing PC to be equal to zero if pier capacity (as estimated by e ngineering analysis) is greater than or equal to the estimated impact load. Given the significant uncertainties associated with estimating both loads and capacities and statistical variability of material and soil strengths, as well as other factors, assig ning a failure probability equal to zero cannot be reasonably justified. If one were to assume, for example, that when pier capacity exceeds the computed load, a 1 in 1,000 chance of collapse still exists, the return period for the SR 300 Bridge goes from 1,460,000 years to 31,700 years.

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207 8.7.2 UF/FDOT Methods The following sections present risk analysis results ( PC and AF ) that were computed using UF/FDOT methods. The revised methods include a new PC expression, revised barge impact load prediction equations, and three structural analysis procedures (CVIA, AVIL, and SBIA). Recall that because these new UF/FDOT methods were primarily developed for barge impact, risk measures associated with ship vessel groups (9 11) were taken from the AASHTO procedures (discusse d in the prior section). Note that since PC and AF for all ships (i.e., vessel groups 9 11; recall Table 8 3 ) were equal to 0.0 (zero), these vessel groups had no influence on the final results. 8.7.2.1 CVIA Esti mates of PC computed using UF/FDOT methods were never equal to zero. This is because the minimum value that the PC equation (Eqn. 8 12 ) can take is 2.3310 6 when D / C = 0. Furthermore, by definition, D / C = 1 wh en the load carrying capacity of the pier has been reached or exceeded, at which point PC = 1. In the context of a CVIA dynamic structural analysis, such a condition typically results in the analysis failing to converge due to numerical (and structural) in stability. Estimates of PC as obtained by UF/FDOT methods with CVIA structural analysis, are presented qualitatively for every pier and vessel group in Fig. 8 26 A Note that the color definitions a re the same as stated in the previous section. As shown, PC values were highest for piers located away from the channel. Specifically, pier 38 had the largest PC values, being equal to 1.0 for vessel groups 6 and 8. Pier 58 (symmetrically opposite to pier 38) had the next largest PC values (equal to 0.93 and 0.88 for vessel groups 6 and 8, respectively). These piers had the highest PC because they were located at expansion joints in the superstructure. Therefore, superstructure resistance was a smaller comp onent of the overall pier resistance (relative to

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208 surrounding piers), and this resulted in a higher PC estimates. This result also highlights the importance of including an accurate representation of superstructure resistance in vessel collision analyses. PC values were generally relatively small (0.001 0.02) for piers near the channel. Considering other factors that contribute to overall risk ( N PA PG PF ), relative contributions to AF are shown in 8 26 B Note that some piers did not contribute to AF for certain vessel groups (as defined by white coloring) because these piers fell outside the 6 LOA impact zone for the corresponding vessel groups. The largest AF contributions came from piers 42 an d 53 for vessel group 5. This outcome is somewhat unexpected, as vessel group 5 refers to a flotilla of empty barges (one of the lighter design vessels). However, because the barge force deformation curve is elastic, perfectly plastic using UF/FDOT methods the same peak impact force was generated for vessel group 5 as for much larger flotillas (only the impact duration was different). Consequently, PC values for vessel group 5 are approximately the same as vessel group 8 (the most massive design vessel). T he higher level of risk associated with vessel group 5 then comes from the fact that vessel draft is only 2 ft. Therefore, it is likely to pass unimpeded through shallow water to the east of the pier. Thus, PF values associated with vessel group 5 were muc h higher (i.e., less protection) than for the larger downbound vessel groups (6 8), resulting in higher risk to the bridge. As discussed above, risk was highest for piers 42 and 53 because they were also located at expansion joints in the superstructure. Fig. 8 27 A shows the percent contribution to AF for each pier in the bridge (i.e., the contributions shown in Fig. 8 26 B summed across all v essel groups). As noted previously, piers 42 and 53 each contributed approximately 10% to AF However, pier 47 (located adjacent to the navigation channel) was the largest single contributor to AF because it was at moderate to high relative risk for many vessel groups. Comparing these results to the AASHTO (1991) procedures

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209 ( 8 23 A ), it is observed that risk is somewhat more evenly distributed among the piers when using the UF/FDOT procedures with CVIA. Using AASHTO procedures, approximately 75% of risk was concentrated in piers 45 48. However, using UF/FDOT procedures with CVIA, the proportion associated with piers 45 48 was only 39%. Fig. 8 27 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 8 26 B summed across all piers). As shown, the largest contribution to AF (more than 40%) came fro m vessel group 5. As discussed above, the occurred because PF was higher vessel group 5 than some of the larger vessel groups, on account of smaller draft. This result was completely different than corresponding results from the AASHTO (1991) procedure (Fi g. 8 23 B ), in that the AASHTO procedure predicted that vessel groups 6 and 8 dominate AF This discrepancy is a consequence of the AASHTO impact load model and the AASHTO PC expression. The AASHTO equa tions predict larger and larger impact forces with increasing impact energy. Using the AASHTO load model, impact forces associated with vessel group 5 were small enough such that the AASHTO PC was equal to zero for almost all piers (recall Fig. 8 22 A ), whereas higher impact energy associated with vessel groups 6 and 8 resulted in nonzero PC values for most piers. Therefore, the disparity in AASHTO PC values between vessel group 5 and vessel groups 6 a nd 8 overcame the significant risk reduction taken for groups 6 and 8 to account for vessel grounding. In other words, AF predicted by AASHTO methods was primarily controlled by the magnitude of impact forces, while AF predicted by the UF/FDOT methods was controlled primarily by the probability of impacts occurring. Summing AF among all piers and vessel groups, AF predicted by UF/FDOT methods (with CVIA) was 6.9010 4 yr 1 which corresponds to a return period 1/ AF = 1,448 years. Consequently, the bridge w as not found to be sufficiently robust to resist vessel collision, based

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210 on the AASHTO specified minimum return period 1/ AF = 10,000 years for critical/essential bridges. Suggestions for mitigating collision risk using the UF/FDOT methods are provided late r in Section 8.9 As with the AASHTO procedures, AF was found to be sensitive to assumptions made in the risk assessment. For example, if the possibility for vessel grounding is neglected, the return period drops to 1/ AF = 1,285 years. However, this differ ence (12.6%) is significantly smaller than the analogous difference observed using the AASHTO procedures (172%), indicating that the UF/FDOT results were much less sensitive to that particular assumption. The specific reasons why UF/FDOT methods predicted a higher level of risk than the AASHTO procedures (1/AF = 20,150 years) are discussed in detail in Section 8.8 8.7.2.2 AVIL Estimates of PC as obtained by UF/FDOT methods with AVIL structural analysis, are presented qualitatively for every pier and vessel group in Fig. 8 28 A As with CVIA, PC values were highest for piers 37 and 58, as a result of these piers being located at expansion joints. However, PC was equal or nearly equal to 1.0 for a larger numbe r of vessel groups. This outcome was expected because the AVIL method (as employed in this study) was intended to be conservative relative to CVIA. Indeed, on average, PC values were 63% higher for AVIL than for CVIA. Note however, that D / C values predicte d by AVIL were only 5.5% higher than CVIA. Therefore, the 63% difference in PC was largely a consequence of the highly nonlinear (exponential) nature of the UF/FDOT PC expression. Considering other factors that contribute to overall risk ( N PA PG PF ), r elative contributions to AF are shown in 8 28 B As with CVIA, the largest contributors to AF were piers 42 and 53 for vessel group 5. Reasons for this finding were discussed in the prior section. In deed no notable differences in the distribution of risk were observed between AVIL and CVIA.

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211 Fig. 8 29 A shows the percent contribution to AF for each pier in the bridge (i.e., the contributions shown in Fig. 8 28 B summed across all vessel groups), and Fig. 8 29 B shows the percent contribution to AF for each vessel group (i.e., the contribu tions shown in Fig. 8 28 B summed across all piers). The distribution of AF among the various piers and vessel groups was effectively identical to CVIA, with the largest contributions to AF coming f rom piers 42, 47, and 53, and, among all piers, vessel group 5. Summing AF among all piers and vessel groups, AF predicted by UF/FDOT methods (with AVIL) was 6.9010 4 yr 1 which corresponds to a return period 1/ AF = 1,365 years. Compared to CVIA (1/ AF = 1,448 years), the outcome is surprisingly close (6.1% different), given that PC estimates were on average 65% higher for AVIL. It was observed that AVIL was most conservative relative to CVIA for impact cases that had a low or sometimes zero probability o f occurrence (zero probability occurred because PG = 0 for piers located outside the 3 LOA impact zone). Furthermore, most of these cases were low energy impacts that contributed little to the overall collision risk. Therefore, while PC values predicted by AVIL and CVIA differed by a large degree for these cases, their influence on AF was relatively small. 8.7.2.3 SBIA Estimates of PC as obtained by UF/FDOT methods with SBIA structural analysis, are presented qualitatively for every pier and vessel group in Fig. 8 30 A As shown, PC was equal to 1.0 for a large number of cases. Even for cases in which PC < 1.0, values are significantly higher than CVIA. Indeed, PC values predicted by SBIA were, in some cases, several hundred times higher than those predicted by CVIA. On average, with respect to PC SBIA was 520% conservative relative to CVIA. However, with respect to D / C SBIA was only 29% conservative. Again, this highlights how the exponential functional for m of the UF/FDOT PC expression amplifies differences between analysis results.

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212 Considering other factors that contribute to overall risk ( N PA PG PF ), relative contributions to AF are shown in Fig. 8 30 B The distribution of risk predicted by SBIA was largely dissimilar from CVIA or AVIL. Vessel group 5 still provided a significant contribution to AF but risk was not concentrated in piers 42 and 53, as it was with CVIA and AVIL. Indeed, the most significant risk came from piers 47 and 48 (vessel group 3), cases which were less prominent for CVIA and AVIL. Fig. 8 31 A shows the percent contribution to AF for each pier in the bridge (i.e., the c ontributions shown in Fig. 8 30 B summed across all vessel groups), and Fig. 8 31 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 8 30 B summed across all piers). As noted above, piers 47 and 48 were the most significant contributors to AF Risk was somewhat more evenly distributed among vessel groups for SBIA, as compared to CVIA and AVIL. Summing AF among all piers and vessel groups, AF predicted by UF/FDOT methods (with SBIA) was 1.1410 2 yr 1 which corresponds to a return period 1/ AF = 88 years. Clearly, the SBIA method was unreason ably conservative relative to CVIA and AVIL, at least with regard to its use in the risk assessment. As discussed above, SBIA was only 29% conservative (relative to CVIA) with regards to pier structural demands (as reflected by D / C ). However, a 29% increas e in D / C resulted in an order of magnitude difference in PC It is important to note that, in the development of SBIA, the method was found to predict pier demands that were, on average, 40 45% conservative relative to CVIA. Therefore, the level of conse rvatism in PC estimates could be more severe for other bridges than it was for this example. Given these results, it can be concluded that SBIA is not well suited for risk analysis. The SBIA method is more appropriately employed in analyses at the prelimin ary design stage, to aid in proportioning

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213 structural members. However, once proportioned, the vessel collision risk assessment should be completed with one of the dynamic analysis options (CVIA or AVIL). 8.8 Discussion of Results Table 8 11 summarizes risk assessment results for the SR 300 Bridge, as determined by each analysis procedure that was considered in this study. As shown, impact loads computed using UF/FDOT methods were approximately 25% higher than those determined using the AASHTO (1991) procedure, while the maximum AASHTO load was 50% higher than UF/FDOT. The UF/FDOT barge force deformation model is elastic, perfectly plastic, while the AASHTO model assumes an increase in load with increasing impact energy. Thus, at lower impact energies, the UF/FDOT methods generally predicted loads higher than AASHTO, but at higher energies, the AASHTO loads were larger than the UF/FDOT loads. In Table 8 11 AASHTO capacity demand ratios ( H / P ) (used to compute PC ) are inverted to be demand capacity ratios ( P / H ) to facilitate comparison to D / C ratios computed by UF/FDOT methods. As shown, average D / C for the most accurate UF/FDOT method (CVIA) was approxim ately 2.4 times higher than P / H for the AASHTO (1991) method. This difference is primarily a consequence of higher UF/FDOT load magnitudes. However, dynamic amplification effects also contributed to this difference. Dynamic structural response was consider ed by the UF/FDOT methods, while AASHTO methods neglected inertial effects. Average PC values obtained by UF/FDOT methods (CVIA) were 20 times higher than those obtained from AASHTO (1991). This is primarily a consequence of larger demand on the piers (cau sed by the larger UF/FDOT loads). However, another reason for the discrepancy is the difference between the PC expressions. As discussed in the prior section, PC was equal to zero for the majority of impact cases considered in the AASHTO risk assessment. I n contrast, the UF/FDOT PC expression (by intentional design) cannot return a PC equal to zero. Consequently

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2 14 PC was greater than zero for every barge impact case considered in the UF/FDOT assessments. It should also be noted that PC values obtained using t he UF/FDOT methods properly account for numerous statistical uncertainties associated with impact loading, structural capacity, and soil capacity, and are therefore a more rational estimate of collapse risk than the AASHTO PC values. As shown in Table 8 11 AASHTO (1991) methods resulted in a return period for bridge collapse 1/ AF = 20,150 years, satisfying the acceptable risk criterion (1/ AF years) for this critical bridge. This outcome is ex pected, given that the bridge was designed in accordance with the 1991 AASHTO provisions. However, the barge impact load model was modified slightly in the 2009 AASHTO provisions (i.e., elimination of the barge width modification factor), resulting in a si gnificant reduction in load magnitude for most impact conditions. Accounting for this change, the return period increased dramatically to 1,460,000 years. Return periods predicted by UF/FDOT methods imply that the bridge does not satisfy the level of accep table risk. Indeed, AF predicted by the CVIA risk assessment was 14 times higher than the AASHTO (1991) method. This discrepancy is a consequence of the difference in PC values predicted by each method, as discussed above. Predictions of AF were similar be tween CVIA and AVIL structural analysis, with AVIL being about 6% conservative. This suggests that AVIL is an adequate replacement for CVIA if appropriate analysis tools are not available to conduct CVIA. However, the return period predicted using SBIA str uctural analysis was only 88 years, indicating that the SBIA procedure is too conservative to be reasonably implemented in the context of risk assessment. Therefore, SBIA is better suited for preliminary analyses that are conducted for the purpose of rough ly proportioning structural members. Once proportioned, the

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215 bridge should be evaluated for vessel collision risk using dynamic structural analysis methods (CVIA or AVIL). Given that the SR 300 Bridge did not satisfy the acceptable risk level using UF/FDOT methods, it is important to consider whether the bridge could be economically retrofitted to improve its performance and thereby mitigate vessel collision risk within the context of the UF/FDOT assessment methodology. A possible retrofit solution is propos ed in the following section (Section 8.9 ) that takes advantage of the fact that the UF/FDOT impact load model predicts significantly smaller forces if impacted pier surfaces are rounded rather than flat faced. For demonstration purposes, an alternative pie r design that would further mitigate risk is also discussed in Section 8.9 The retrofit and alternative design examples presented in Section 8.9 are viable means of satisfying the required risk criteria if the UF/FDOT methodology were employed exactly as discussed in this chapter. However, results from the assessment of a different bridge considered in this study (Chapter 9) suggest that the other terms in the expression for AF (specifically the PA and PG terms ) may over predict the likelihood that impacts will occur. Because these terms were adopted into the UF/FDOT methods directly from AASHTO, the value of AF computed using UF/FDOT methods may be unrealistically high. If this were the case alternative designs or retrofits may not be necessary at all; t h is possibility is discussed further in Section 8.10 8.9 Suggestions for Mitigating Risk The primary reason that UF/FDOT methods predicted a higher risk level than AASHTO methods is the relative magnitude of impact loads. As discussed in Section 8.6 .5.2.1 the barge force deformation curve that is used as the basis for UF/FDOT predictions of impact force is elastic, perfectly plastic with yield deformation ( a BY ) equal to 2 in. and yield force ( P BY )

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216 computed based on the Getter and Consolazio (2011) model. For a flat faced impact surface, such as the pier footings of the SR 300 Bridge, P BY is computed as: ( 8 18 ) For the SR 300 Bridge, footings (pile caps) are either 28.0 ft or 18.5 ft wide. Given an impact angle = 28.5, P BY equals 3,148 kips for 28.0 ft wide footings and 2,555 kips for 18.5 ft wide footings. As demonstrated by the risk assessment, the barge bow yielded for most impact conditions, and thus, the maximum impact force was gene rally equal to P BY However, the Getter Consolazio force deformation model states that, for rounded impact surfaces, P BY is computed as: ( 8 19 ) Therefore, if the SR 300 pier footings were the same size, but were rounded instead of flat faced on the leading edge, P BY would only equal 2,240 kips for 28.0 ft wide footings and 1,955 kips for 18.5 ft wide footings (a 29% and 23% reduction, respectively). Choosing to round off the ends of fo otings would likely have little influence on construction cost, but could improve impact performance significantly. To evaluate this possibility, a risk assessment was conducted using UF/FDOT methods (CVIA) in which the SR 300 footings were assumed to be t he same overall size, but the ends were rounded instead of flat (detailed analysis results are omitted here for brevity). Bridge structural demands were significantly reduced relative to the as built condition, and the return period (1/ AF ) went from 1,448 years to 16,370 years. Consequently, the SR 300 Bridge was found to satisfy the level of acceptable risk using UF/FDOT methods if footings were round instead of flat. If deemed necessary by the bridge owner, footings could be readily be retrofitted with ro unded caps made of reinforced concrete, as illustrated in Fig. 8 32 If the foundation does not have

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217 sufficient capacity to carry the additional concrete weight (262 kips and 600 kips for the 18.5 ft and 28.0 ft cap s, respectively), a more lightweight design (steel or composite) with the same dimensions could be employed. This example illustrates that the UF/FDOT methods do not always predict significantly higher risk than the AASHTO procedures. Indeed, with the retr ofit, AF is only 19% higher than predicted by AASHTO (1991). An additional alternative design (illustrated in Fig. 8 33 ) could further mitigate collapse risk. In this alternative, piers could be supported by two lar ge diameter (9 ft, for example) drilled shafts (collinear with the pier columns), rather than with multiple driven piles. Consequently there is no longer a need for a large footprint pile cap. Instead, a relatively narrow strut or shear wall could be provi ded between the shafts, as shown in Fig. 8 33 If two 9 ft diameter shafts were found to provide similar lateral capacity to the existing design, then vessel collision risk could be reduced, because the maximum barg e impact force that could be developed ( P BY ) is only 1,670 kips (Eqn. 8 19 ) given that the impacted portion of the bridge is now only 9 ft. in diameter. The load of 1,670 kips corresponds to a 15 25% reduction i n impact forces relative to the end cap retrofitted design shown above, and a 35 47% reduction relative to the as built design. Clearly, given that the existing SR 300 Bridge was constructed in 2004 in accordance with the appropriate AASHTO provision, it is not proposed that the structure be replaced with an alternative design. However, the alternatives described here demonstrate how careful design choices can mitigate vessel collision risk within the context of UF/FDOT risk assessment methodology. 8.10 Summar y It is worth noting that no bridge that has been designed and constructed in accordance with the AASHTO vessel collision guidelines has collapsed due to vessel collision. However, the historical record (approximately 20 years) is short relative to the tar get return period for such

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218 events (1,000 10,000 years). Indeed, a bridge that was designed with the highest acceptable risk (1/ AF = 1,000 years) has only a 2% chance of impact induced collapse within its first 20 years of service. Therefore, the accuracy of the AASHTO procedure is difficult to assess. As discussed above, the discrepancy between the AASHTO and UF/FDOT methods is entirely limited to PC However, it is valuable to consider whether the other terms in the AF expression ( N PA PG PF ) are hist orically accurate. Detailed records concerning the volume of commercial vessel traffic are readily available, thus N can be considered the most reliable value in the risk assessment. The accuracy of PA PG and PF are difficult to evaluate independently, b ut their combined result can be compared to available data. Specifically, if PC is removed from the expression for AF the resulting probability is the annual frequency of impact ( AFI ): ( 8 20 ) Based on this definition, AFI represents the number of direct vessel collisions with the bridge piers that are expected to occur in a given year. For the SR 300 Bridge, AFI = 0.0287 impacts/yr (i.e., approximately one impact every 35 years). Given that the bridge has only been in service for nine years at present, according to the AASHTO based AFI there is only a 23% likelihood that the bridge would have been impacted to date. The U.S. Coast Guard keeps detailed records on vessel casualties, which include (among other things) accidental impacts with bridges. These records are publicly available from an online database called the Coast Guard Maritime Information Exchange (CGMIX) (USCG 2013). A thorough review of the database which includes comp lete records for the past 11 years and partial records for older incidents uncovered no documented impact incidents involving either the current SR 300 Bridge or the older bridge that it replaced. This finding is reasonably consistent with the AASHTO based estimate of AFI which predicts a relatively low

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219 likelihood of a major impact occurring within the period considered. Therefore, for the SR 300 Bridge, is unclear whether the terms included within AFI are indeed accurate. For the SR 300 Bridge it can onl y be concluded that the AASHTO predicted AFI is either accurate or it over predicts the likelihood of impact events. Given the volume of vessel traffic in this particular waterway, the historical record is simply not long enough to draw a clear conclusion. Note however, that the AASHTO procedure almost certainly over predict s AFI for the other case considered in this study (Chapter 9). Additional research that is outside the scope of the current study would be required to determine conclusively whether the terms included in AFI should be modified in some way. However, the retrofit and alternative design examples presented in Section 8.9 demonstrate that, with careful design choices, acceptable levels of risk can reasonably be attained using the existing proc edures for quantifying AFI in conjunction with the UF/FDOT methodology.

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220 Table 8 1 Upbound vessel traffic for Apalachicola Bay (Wang and Liu 1999) Vessel ID Vessel type Description Average single vessel size (ft) Single vessel displacement (tons) Average barge tow size Tug size (ft) Tug displacement (tons) Length LOA (ft) Beam (ft) Total displacement (tons) L W D # W # L L W D 1 Barge Barge tow 216 51 2 811 1 1 75 25 8 260 291 51 1,071 2 Barge Barge tow 316 59 6 3,365 1 1 75 25 8 260 391 59 3,625 3 Barge Barge tow 246 51 8 3,333 1 1 75 25 8 260 321 51 3,593 4 Barge Barge tow 318 54 11 5,952 1 1 120 30 9 560 439 54 6,512 5 Ship Free tug 75 25 9 336 N/A N/A N/A N/A N/A N/A 75 25 336 6 Ship Self propelled 122 27 5 388 N/A N/A N/A N/A N/A N/A 122 27 388 Table 8 2 Downbound vessel traffic for Apalachicola Bay (Wang and Liu 1999) Vessel ID Vessel type Description Average single vess el size (ft) Single vessel displacement (tons) Average barge tow size Tug size (ft) Tug displacement (tons) Length LOA (ft) Beam (ft) Total displacement (tons) L W D # W # L L W D 1 Barge Barge tow 267 51 2 894 1 1.9 75 25 8 260 582 51 1,959 2 B arge Barge tow 328 62 5 3,360 1 1.9 75 25 8 260 698 62 6,644 3 Barge Barge tow 251 45 8 3,313 1 1.9 75 25 8 260 552 45 6,555 4 Barge Barge tow 256 72 12 6,969 1 1.9 120 30 9 560 606 72 13,611 5 Ship Self propelled 105 23 5 228 N/A N/A N/A N/A N/A N/A 10 5 23 228 Table 8 3 Aggregated vessel traffic data for vessel collision risk assessment VG Vessel ID from N v i D LOA B M W B Vessel group Tables 8 1 8 2 No. transits (yr 1 ) Transit velocity (knot) Draft (ft) Overall length (ft) Beam (ft) Total displacement (tons) 1 1 (Table 8 1 ) 85 5.6 2 a 291 51 1,071 2 2 (Table 8 1 ) 25 4.6 5 a 391 59 3,625 3 3 (Table 8 1 ) 117 4.6 8 321 51 3,593 4 4 (Table 8 1 ) 92 4.7 11 439 54 6,512 5 1 (Table 8 2 ) 135 6.4 2 a 582 51 1,959 6 2 (Table 8 2 ) 22 5.4 5 a 698 62 6,644 7 3 (Table 8 2 ) 19 5.4 8 552 45 6,555 8 4 (Table 8 2 ) 28 5.4 12 606 72 13,611 9 5 (Table 8 1 ) 53 7.6 9 75 25 336 10 6 (Table 8 1 ) 4 7.6 5 122 27 388 11 5 (Table 8 2 ) 2 8.4 5 105 23 228 a Draft shown is for the barge itself. Tug draft is 8 ft.

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221 Tab le 8 4 Footing geometry and projected pier width ( B P ) for each pier Pier number W P : Footing width (ft) L P : Footing length (ft) B P : Projected with (ft) 33 37, 58 62 18.5 39.0 34.9 38 39, 56 57 18.5 43.5 37.0 40 42, 53 55 28.0 39.0 43.2 43 45, 50 52 28.0 49.5 48.2 46 49 28.0 55.0 50.9 Table 8 5 Minimum lateral pushover capacities ( H ) for each pier Pier number H : Minimum lateral pushover capacity (kips) 33 37, 58 62 1,075 38 39, 56 57 1,500 40 42, 53 55 2,300 43 45, 50 52 2,750 46 49 3,255 Table 8 6 Barge impact parameters for CVIA Pier (deg) min( B B B P ) (ft) P BY ( kip) W B (tons) v Bi (knot) 35 39 28.5 18.5 2,555 1,071 13,611 a Varies b 40 55 28.5 28.0 3,148 1,071 13,611 a Varies b 56 60 28.5 18.5 2,555 1,071 13,611 a Varies b a Varies by vessel group. See Table 8 3 for details. b Varies by vessel group and pier location. See Table 8 3 and Appendix J for details. Table 8 7 Lateral pier soil stiffness ( k P ) for e ach SR 300 pier Pier no. k P (kip/in.) Pier no. k P (kip/in.) Pier no. k P (kip/in.) Pier no. k P (kip/in.) 35 1,750 42 2,064 49 4,927 56 2,229 36 1,746 43 3,941 50 2,256 57 2,237 37 1,237 44 2,838 51 2,437 58 2,088 38 2,010 45 3,830 52 2,301 59 2,379 39 2,087 46 3,901 53 2,012 60 2,508 40 3,045 47 3,975 54 2,915 41 2,929 48 4,932 55 3,041

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222 Table 8 8 Maximum barge impact force ( P Bm ) (kips) for each pier and barge vessel group VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 1,298 1,297 1,197 1,335 1,345 1,539 1,528 1,427 1,630 2,770 3,148 3,148 3,148 2 2,388 2,387 2,203 2,456 2,474 2,831 3,028 3,148 3,148 3,148 3,148 3,148 3,148 3 2,378 2,376 2,193 2,445 2,463 2,818 2,799 2,614 3,148 3,148 3, 148 3,148 3,148 4 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 5 1,755 1,755 1,811 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 6 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,1 48 7 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 8 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 3,148 3,148 3,148 2,692 1,486 1, 420 1,527 1,538 1,361 1,362 1,345 1,377 1,390 2 3,148 3,148 3,148 3,148 3,148 3,148 3,026 2,830 2,504 2,506 2,474 2,534 2,555 3 3,148 3,148 3,148 3,148 3,148 2,600 2,797 2,818 2,493 2,495 2,463 2,522 2,545 4 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,1 48 2,555 2,555 2,555 2,555 2,555 5 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,034 1,862 1,879 6 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 7 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,55 5 2,555 2,555 2,555 8 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555

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223 Table 8 9 Input parameters for SBIA IRF equations Pier no. L sup (ft) h P (ft) k sup (kip/in) k P (kip/in) W s up (kip) W P (kip) Pier no. L sup (ft) h P (ft) k sup (kip/in) k P (kip/in) W sup (kip) W P (kip) 35 140 14.2 732 1,750 1,518 817 48 254 51.6 346 4,932 2,876 2,267 36 140 18.5 622 1,746 1,511 842 49 233 49.9 342 4,927 2,640 2,244 37 140 22.7 176 1,237 1,503 86 6 50 205 52.7 159 2,256 1,926 2,127 38 140 26.9 527 2,010 1,505 935 51 140 50.2 498 2,437 1,498 2,106 39 140 31.1 549 2,087 1,532 957 52 140 47.2 440 2,301 1,507 2,080 40 140 35.3 488 3,045 1,525 1,539 53 140 43.6 508 2,012 1,500 1,598 41 140 39.5 115 2,929 1,491 1,569 54 140 39.5 115 2,915 1,491 1,569 42 140 43.6 647 2,064 1,500 1,598 55 140 35.3 544 3,041 1,474 1,539 43 140 47.2 482 3,941 1,507 2,080 56 140 31.1 642 2,229 1,481 957 44 140 50.2 818 2,838 1,498 2,106 57 140 26.9 597 2,237 1,500 935 45 205 52.7 158 3,830 1,853 2,127 58 140 22.7 176 2,088 1,493 866 46 233 49.9 339 3,901 2,640 2,244 59 140 18.5 701 2,379 1,500 842 47 254 51.6 351 3,975 2,876 2,267 60 140 14.3 813 2,508 1,507 817 Table 8 10 IRF values for SBIA Load Case 1 Pier no. IRF m IRF v IRF b Pier no. IRF m IRF v IRF b Pier no. IRF m IRF v IRF b 35 0.86 0.80 1.41 44 0.33 0.41 0.48 53 0.35 0.42 0.52 36 0.68 0.66 1.08 45 0.29 0.38 0.41 54 0.29 0.38 0.41 37 0.46 0.50 0.71 46 0.35 0.42 0.51 55 0.36 0.43 0.53 38 0.48 0.52 0.74 47 0.36 0.43 0.53 56 0.45 0.50 0.70 39 0.45 0.49 0.69 48 0.34 0.42 0.50 57 0.48 0.52 0.75 40 0.35 0.42 0.52 49 0.34 0.41 0.49 58 0.41 0.46 0.61 41 0.29 0.38 0.41 50 0.31 0.39 0.44 59 0.63 0.63 1.01 42 0.36 0.43 0.54 51 0.32 0.40 0.45 60 0.78 0.74 1.27 43 0.30 0.39 0.43 52 0.32 0.40 0.46

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224 Table 8 11 Summary of risk assessment results for each analysis procedure considered AASHTO (1991) AASHTO (2009) UF/FDOT (CVIA) UF/FDOT (AVIL) UF/FDOT (SBIA) Minimum impact load (kip) 198 198 198 198 198 Average impact load (kip) 1,642 1,200 2,004 2,086 2,086 Maximum impact load (kip) 4,682 3,240 3,148 3,148 3,148 Average P / H or D / C 0.305 0.286 0.737 0.778 0.952 Average PC 0. 00671 0.00122 0.136 0.222 0.702 Return period (1/ AF ) (yr) 20,150 1,460,000 1,448 1,365 88 Figure 8 1 Bryant Grady Patton Bridge (SR 300) spanning Apalachicola Bay, Florida

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225 Figure 8 2 High rise portion of SR 300 Bridge, showing potential navigational obstructions

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226 A B C D E Figure 8 3 Current velocities in Apalachicola Bay a t various tidal stages (Conner et al. 1982) A) Low tide. B) Flood tide. C) High tide. D) Ebb tide. E) Average over tidal cycle.

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227 Figure 8 4 Nautical chart including water depth soundings at MLLW (NOAA 201 2 a ) A B Figure 8 5 High rise portion of SR 300 Bridge, showing piers at risk for impact A) Elevation view. B) Plan view.

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228 A B C D E F G H I J Figure 8 6 Pier and foundation configurations for SR 300 Bridge (Arrows at pile locations indicate directions of pile batter) A) Piers 33 37, 58 62. B) Piers 38 39, 56 57. C) Piers 40 42, 53 55. D) Section A A. E) Section B B. F) Section C C. G ) Piers 43 45, 50 52. H) Piers 46 49. I) Section D D. J) Section E E. A B Figure 8 7 Typical barge impact scenarios, showing possible headlog elevations A) Fully loaded barge. B) Empty barge.

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229 Figure 8 8 Overview of bridge span configurations A B Figure 8 9 Superstructure cross sections for the SR 300 Bridge A) Typical uniform section (at mid span). B) Typical section at haunch (over pier). Figure 8 10 Locations of soil borings and piers to which each soil profile is assigned

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230 A B C D E Figure 8 11 FB MultiPier models of selected piers from SR 300 Bridge A) Pier 35. B) Pier 38. C) Pier 41. D) Pier 44. E) Pier 47.

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231 Figure 8 12 Computing the geometric probability of impact ( PG ) (from AASHTO 20 09) Figure 8 13 Coupled vessel impact analysis (CVIA) method Figure 8 14 Typical barge impact with pile cap, showing pertinent impact parameters

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232 Figu re 8 15 Applied vessel impact load (AVIL) method

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233 Figure 8 16 Procedure for computing barge impact force time histories in accordance with AVIL method (Cons olazio et al. 2008)

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234 A B Figure 8 17 Determination of lateral pier soil stiffness ( k P ) by static analysis A) Undeformed pier. B) Deformed pier.

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235 Figure 8 18 Static load cases for SBIA method (Getter et al. 2011)

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236 Figure 8 19 Determination of lateral superstructure stiffness ( k sup ) Figure 8 20 Procedure for computing the probability that a navigational obstruction (island) will cause vessel grounding prior to pier impact ( P Gr ) based on its orientation and path to the pier

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237 Figure 8 21 Procedure for comput ing P Gr for old bridge (fishing pier) navigational obstruction

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238 A B Figure 8 22 Risk analysis results for each pier and vessel group: AASHTO (1991) methods A) Probability of collapse ( PC ) (white = 0, g B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 8 23 Percent contribution to AF : AASHTO (1991) methods A) By pier number. B) By vessel group.

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239 A B Figure 8 24 Risk analysis results for each pier and vessel group: AASHTO (2009 ) methods A) Probability of collapse ( PC ) (white = 0, gre e B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 8 25 Percent contribution to AF : AAS HTO (2009 ) methods A) By pier number. B) By vessel group.

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240 A B Figure 8 26 Risk analysis results for each pier and vessel group: UF/FDOT methods CVIA. A) Probability of collapse ( PC ) (white = 0, green B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 8 27 Percent contribution to AF : UF/FD OT methods CVIA. A) By pier number. B) By vessel group.

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241 A B Figure 8 28 Risk analysis results for each pier and vessel group: UF/FDOT methods AVIL. A) Probability of collapse ( PC 0.0, red = 1.0) B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 8 29 Percent contribution to AF : UF/FDOT methods AVIL. A) By pier number. B) By vessel group.

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242 A B Figure 8 30 Risk analysis results for each pier and vessel group: UF/FDOT methods SBIA. A) Probability of collapse ( PC ) (white = 0, green B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 8 31 Percent contribution to AF : UF/FD OT methods SBIA. A) By pier number. B) By vessel group.

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243 A B C D E Figure 8 32 SR 300 Bridge pier footing end cap retrofit to reduce vessel collision risk (retrofitted end caps indicated in grey) A) Piers 33 37, 58 62. B) Piers 38 39, 56 57. C) Piers 40 42, 53 55. D) Piers 43 45, 50 52. E) Piers 46 49. A B Figure 8 33 SR 300 Bridge pier alternative design with foundation consisting of (2) 9 ft d iameter drilled shafts, connected by a strut or shear wall A) Elevation view. B) Section A A.

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244 CHAPTER 9 VESSEL COLLISION RISK ASSESSMENT OF THE LOUISIANA HIGHWAY 1 (LA 1) BRIDGE OVER BAYOU LAFOURCHE, LOUISIANA In this chapter, detailed vessel collision risk ass essments are presented for the Louisiana Highway 1 (LA 1) Bridge over Bayou Lafourche, Louisiana. The annual frequency of bridge collapse ( AF ) was quantified using the revised methodology described in Chapter 7, employing two dynamic structural analysis te chniques (CVIA and AVIL). For comparison, AF was also computed using both the current AASHTO provisions (2009) and the AASHTO guidelines that were available at the time the bridge was designed (1991). Significant differences in AF were observed using the v arious methods. The final sections in this chapter identify the causes for such differences and provide suggestions for mitigating vessel collision risk within the context of the revised methodology. The LA 1 Bridge was selected for this study for three pr imary reasons: 1) it was designed fairly recently (2003 2005), and is therefore designed to resist vessel collision in accordance with the AASHTO provisions, and 2) it is at relatively high risk for vessel collision, and 3) a vessel collision risk assess ment was published for this bridge as an illustrative example in the 2009 AASHTO Guide Specification. The published example includes exhaustive discussion of all analysis assumptions and includes all the data required to reproduce the AASHTO risk assessmen t for the present study. In order to complete dynamic structural analyses of the LA 1 Bridge piers, the Louisiana Department of Transportation and Development (LaDOTD) graciously provided detailed structural drawings of the relevant bridge sections, soil b oring logs, and a detailed scour report. These documents were crucial to the development of the risk assessments discussed in this chapter. to the AASHTO Guide Specifications and Commentary

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245 for Vessel Collision Design of Highway Bridges The specific edition (1991 or 2009) is referred to as needed, and if no date reference is given, it should be assumed to refer to the 2009 edition. Also, man assessment of the LA 1 Bridge that is published in the 2009 AASHTO Guide Specification. rge body of work, comprising multiple publications, and in general, refer to the modified risk assessment procedure outlined in Chapter 7. References to specific publications are provided where needed. Note that the format of this chapter is identical to C hapter 8, which described vessel collision risk assessments of a different bridge that were completed using the same methods discussed here. Consequently, many areas of discussion in this chapter are similar or identical to those in Chapter 8. Rather than referring back to Chapter 8 in such cases, pertinent discussions are repeated in this chapter, accounting for any bridge specific modifications. While this approach introduces a level of redundancy into the discussion, it also permits this chapter to serve as a standalone example of the various methods employed. However, in the interest of brevity, at times, references are made to the example risk assessment of the LA 1 Bridge published in the AASHTO Guide Specification, in lieu of repeating identical detai led discussions here. 9.1 Data Collection The critical first step in conducting a vessel collision risk assessment is gathering the relevant site data, including waterway, bridge, and vessel traffic characteristics. As part of the bridge design effort, an exh austive data collection effort was undertaken by the design engineers, the results of which are published in AASHTO (2009). The published data set was utilized in full in the risk assessment presented in this chapter. As noted above, structural and soil de tails that

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246 were required to develop finite element models of the relevant bridge piers and carry out structural analyses were taken from structural drawings and soil reports provided by LaDOTD. 9.2 Waterway Characteristics 9.2.1 General Description The LA 1 Bridge s pans a navigable waterway (Bayou Lafourche) near Leeville, Louisiana. As shown in Fig. 9 1 the waterway runs approximately north south, passing under the main fixed span of the LA 1 Bridge. The portion of the bridge at risk for vessel collision is highlighted in red in Fig. 9 1 The waterway serves a considerable volume of vessel traffic, including fishing and shrimp boats, crew and supply vessels, and barges of v arious kinds. Most vessels that pass under the LA 1 Bridge are transiting between the Gulf of Mexico (11 miles south of the bridge), and various inland communities and ports along the bayou. Furthermore, Bayou Lafourche intersects the Gulf Intracoastal Wat erway (GIWW) approximately 23 miles upstream of the bridge, near the town of Larose. Thus, the bayou acts as a link between the Gulf of Mexico and the GIWW. See the AASHTO example (§1.2.1) for additional details. 9.2.2 Navigation Channel As shown in Fig. 9 2 the navigation channel passes under the center bridge span at a 70 angle relative to the bridge alignment. Horizontal clearance of 280 ft and vertical clearance of 76 ft are provided through this passage. Water depths along the navigation channel range from 3 12 ft, with larger depths available near the southern end of the bayou (near the LA 1 Bridge). See the AASHTO example (§1.2.2) for additional details. 9.2.3 Tide Levels and Tidal Range The LA 1 Bridge is subject to tidal variations in water level, by virtue of its vicinity to the Gulf of Mexico. The bayou has a tidal range between 1.0 and 1.8 ft, depending on the season.

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247 For the purpose of the risk assessment, MHW (elevation of 2.5 ft) was taken as the ref erence water level for all calculations. See the AASHTO example (§1.2.3) for additional details. 9.2.4 Currents Currents in the vicinity of the LA 1 Bridge are primarily driven by tidal fluctuations. For the risk assessment, the current velocity parallel to the channel was taken to be 1.0 knot. The Southwestern Louisiana Canal connecting Barataria Bay to the east and Terrebonne Bay to the west crosses Bayou Lafourche at the LA 1 Bridge site. Differential tidal fluctuations between the two bays causes significant currents through the canal, resulting in strong crosscurrents at the bridge location. For the risk assessment, the crosscurrent velocity taken to be 2.5 knots. See the AASHTO example (§1.2.4) for additional details. 9.2.5 Water Depths Sufficient water depth is a vailable for any vessel transiting the Bayou Lafourche to strike the two piers located immediately adjacent to the channel (piers 2 and 3). However, smaller depths are available at piers located away from the channel. The possibility for vessel grounding d ue to insufficient water depth was considered in the risk assessment. See the AASHTO example (§1.2.5) for additional details. 9.3 Bridge Characteristics As constructed, the overall LA 1 Bridge consists of a short section of low rise causeway to the north west of the waterway crossing (shown in Fig. 9 1 ), a high rise section crossing the bayou, and another low rise causeway section extending several miles south to Port Fourchon. Future plans include extending the no rthern causeway section several miles north to Golden Meadow. As indicated above, the bridge section of interest in this study is the high rise section that crosses the Bayou Lafourche (shown schematically in Fig. 9 3 ). In the AASHTO example, the design team identified five piers as being at risk for impact by powered vessels: piers 2 4

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248 and 96 97. All other piers were found to be fully protected by land masses in the vicinity, and were assigned zero risk by the designers. Therefore, the risk assessment presented in this chapter neglects such protected piers, even though they were considered in the AASHTO example, as appropriate for a new bridge. In order to adequately analyze these piers for vessel collis ion, finite element models of two additional piers on each end of the central impact region (piers 1, 95, and 98 99) were also prepared. In the AASHTO example, the authors present a risk assessment of only one of the many bridge design alternatives: Conc rete Girder Alternative Option A3. However, the alternative that was ultimately constructed was Steel Girder Alternative Option D2. This option included a superstructure consisting of four steel plate girders for the main spans, and piers supported by 30 i n. square prestressed concrete piles. Comparing these two alternatives, it was found that differences in the designs had negligible influence on the various calculations included in the AASHTO risk assessment. Therefore, supporting data for the risk assess ment published in the AASHTO example was simply adopted in this study as being valid for the design alternative that was considered. The intent of this study was to evaluate the LA 1 Bridge as constructed ( Steel Girder Alternative Option D2 ). However, as d escribed in more detail in the following sections, the footings of the two channel piers (piers 2 and 3) are skewed at 20 relative to the pier columns and bridge alignment, so that they are instead aligned with the navigation channel. In doing so, vessel impacts were most likely to occur in the direction of highest lateral foundation capacity, and horizontal clearance under the main span was improved. However, all structural analyses conducted in this study employed FB MultiPier, which does not currently i nclude features allowing foundations to be skewed relative to the pier columns. More specifically, in

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249 FB MultiPier, the primary axes of the pile elements cannot be skewed relative to the primary axes of the pier columns. Because design Option D2 employs sq uare piles, this limitation in FB MultiPier could not be overcome. However, an alternative design ( Steel Girder Alternative Option D1 ) employs 54 in. diameter cylinder piles. Because such piles are circular, and therefore possess equal flexural stiffness a nd strength about all possible flexural axes, the orientation of the primary element axes is irrelevant. It was therefore possible to analyze Option D1 in FB MultiPier, by carefully defining the pile grid geometry and batter parameters in order to correctl y define the relative position and axial orientation of the pile elements. Consequently, the risk assessment presented in this chapter corresponds to Steel Girder Alternative Option D1 Given that lateral foundation capacities are, by design, nearly equal between Option D1 and Option D2 (the latter being the design that was actually constructed), calculated measures of vessel collision risk are expected to be similar. 9.3.1 Bridge Piers Bridge pier configurations for the LA 1 Bridge piers of interest are shown in Fig. 9 4 Piers consist of two 6 9 ft diameter circular columns supporting a 6.0 7.5 ft deep pier cap beam. A strut is provided between the columns at the approximate mid height. As discussed above, pier s 1 4 are founded on 54 in. diameter cylinder piles (corresponding to Option D1 ), while piers 95 99 are founded on 30 in. square piles. Many piles are battered at an inclination of 1.5 in. horizontal per 12 in. vertical, as indicated by arrows in Fig. 9 4 Footings (pile caps) are 6 8 ft thick and are positioned such that the top surfaces are approximately 4 5.5 ft above MHW. The largest footing (Fig. 9 4 C ) is 4866.5 ft in plan, and the smallest footing (Fig. 9 4 H ) is 2546 ft.

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250 Based on these pier configurations, barges and most small ships are expected to impact pier footings (pile caps) rather than columns though some column impacts are possible. Consider the two impact scenarios shown in Fig. 9 5 A fully loaded barge will draft 6 12 ft, with the most common draft being approximately 9 ft (Fig. 9 5 A ). In this scenario, the barge headlog impacts the pier at an elevation below the top of the pier footing. However, an empty barge (Fig. 9 5 B ) drafts only approximately 2 ft, and the headlog elevation is above the top of the footing. Depending on the barge bow and pier geometry, the impacting barge may make contact with the footing first. However, the barge may slide up and over the footing edge, or gi ven sufficient energy, simply crush into the top footing corner, ultimately striking a pier column. Impact scenarios like the one shown in Fig. 9 5 B are certainly of interest for design, in that all imp acted pier components must be proportioned to resist impact loading. However, numerous factors e.g., footing overhang distance, barge bow rake angle, vessel draft, water level, and impact angle all influence the relative probability of a column impact occu rring. Given the inherent variability of such factors, assessing the probability of column impact is difficult. Thus, for the purpose of the risk assessment, columns were assumed to have sufficient capacity to transmit impact loads to the footing. As such, impact forces were applied at the footing elevation in all impact analyses. For final design, it would be appropriate to choose the most severe column impact scenario possible and proportion (or support) the columns such that they can resist the loads imp arted. A supporting strut or shear wall between the columns is commonly employed for this purpose. 9.3.2 Superstructure As shown in Fig. 9 6 the region of interest of the LA 1 Bridge consists of three superstructure zones. Spans between piers 95 1 and between piers 4 99 are 128 135 ft long,

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251 and are supported by five (5) 78 in prestressed concrete Bulb T girders. Spans were cast contiguously with a R/C diaphragm at each pier. Expansion joints were provided between every other span. The central three spans (between piers 1 4) are 260 350 ft long, and are supported by four (4) 117 in. deep steel plate girders. Typical superstructure cross sections are shown in Fig. 9 7 The roadway slab is 42.5 ft wide, and 8.5 9 in. thick (depending on the span), with standard concrete barriers on each side. As discussed above, five (5) evenly spaced Bulb T girders support the roadway on the approach spans (Fig. 9 7 A ), and four (4) steel plate girders support central spans (Fig. 9 7 B ). In this bridge, concrete girders are support ed on neoprene bearing pads. At each concrete girder bearing location, (4) 1.25 in. diameter anchor bolts provide lateral continuity between the girders and pier cap beam, permitting impact induced shear force to be carried across the substructure superstr ucture interface. Steel girders are supported on pot bearings, which are bolted into the pier cap beam with four (4) 2.5 in. diameter anchor bolts and welded to the steel girders. Such bearings are also rated to carry impact induced shear forces across the substructure superstructure interface. Consequently, when a pier is impacted, demand on the foundation is mitigated by permitting a portion of the lateral load to be shed through the superstructure and ultimately to adjacent piers. This action is importan t to consider when analyzing the piers for vessel impact, so these connections were included in finite element models of the piers and superstructure. 9.3.3 Soil Conditions In general, soil conditions at the site consist primarily of layers sandy clay or silty c lay, interspersed with thinner layers of silty sand or clayey sand. Sand density and clay consistency generally increased with increasing depth. Pile embedment depths varied for each pier, and were obtained from estimates provided in the design drawings. F or the purpose of developing finite

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252 element models of each pier, soil properties were determined from SPT boring logs taken prior to bridge construction. As shown in Fig. 9 8 eight boring logs were available in th e vicinity of the piers of interest. Soil layer profiles were developed from these boring logs and assigned to each pier finite element model, as shown in Fig. 9 8 Finite element soil spring characteristics were d eveloped using well established equations that relate various important soil properties (e.g., internal friction angle, subgrade modulus) to the overburden adjusted SPT blowcount. The specific methodology that was employed is omitted here for brevity, but has been documented in numerous prior publications (Consolazio et al. 2008, 2010a, 2010b). Additional information is MultiPier and FB Deep (BSI 2009, 2010). 9.3.4 Finite Element Models Renderings of finite element mode ls of selected piers (developed in FB MultiPier) are shown in Fig. 9 9 Each pier shown is a representative example of the four pier configurations shown in Fig. 9 4 Note that because FB Multipier is unable to model skew between the pier columns and foundation, skewed footing geometry for piers 2 and 3 was approximated with a rectangular grid of shell elements that were oriented in the global (pier column) coordinat e system, as shown in Fig. 9 9 A The ragged looking edge of the footing is a consequence of this approximation. Given the significant rigidity of the pile cap, the irregularity of the mesh has no notable influenc e on pier behavior. As noted previously, proper pile positioning and axial alignment was achieved by careful selection of pile grid spacing and batter parameters. As discussed in Chapter 2, FB MultiPier models piles, pier columns, struts, and pier caps wit h cross section integrated nonlinear beam elements that account for cracking, material plasticity, and plastic hinging behaviors. Soil is modeled in FB MultiPier with nonlinear spring elements that are distributed down the embedded pile length, footings (p ile caps) are modeled with linear elastic shell elements, and the superstructure is modeled as a composite (girder/slab)

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253 unit with linear elastic resultant beam elements that are connected to pier caps at discrete bearing locations. One pier, two span (OPT S) models of all piers within the impact zone (2 4, 96 97) were developed in accordance with the procedure discussed in Chapter 2 (Consolazio and Davidson 2008), and these models were employed for all structural impact analyses discussed in this chapte r 9.4 Vessel Fleet Characteristics Vessel traffic data for this study were obtained from the AASHTO example (§1.4). 9.4.1 Vessel Categories Vessel traffic through Bayou Lafourche is fairly heavy. In 2003, on average, 13 barge vessels and 40 ships passed beneath the LA 1 Bridge per day. Ship traffic consists of supply vessels and crew boats headed to and from offshore oil facilities in the Gulf of Mexico and shrimp trawlers of various sizes. Barge traffic is a mix of hopper, tanker, and deck barges. In the AASHTO exa mple, the authors organized vessel traffic by similar vessels into 17 categories, each with its own vessel ID number, as shown in Table 9 1 Traffic was further subdivided by transit direction (upbound or downbound), and load condition (lightly or fully loaded). Considering the subdivisions, 68 total impact scenarios are possible for each pier. Given that five piers are at risk for impact, 568 = 340 total impact cases are possible. See the AASHTO exampl e (§1.4.1) for additional details. To reduce the number of impact cases for this study, all ship vessel groups were omitted from the vessel fleet. Due to draft limitations, ship type traffic on Bayou Lafourche excludes large cargo or tanker vessels that ma y pose a significant threat to the bridge. Indeed, it was noted in reviewing the AASHTO example that ship type vessels did not contribute to vessel collision risk at all. Therefore, the vessel groups considered in this study include only the barge categori es identified in the AASHTO example (vessel ID 1 8 in Table 9 1 ). The eight categories were

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254 separated into vessel groups corresponding to the subdivisions defined in the AASHTO example, as shown in Ta ble 9 2 Vessel groups 1 8 correspond to fully loaded upbound traffic, vessel groups 9 16 correspond to lightly loaded upbound traffic, vessel groups 17 24 correspond to fully loaded downbound traffic and vessel groups 25 32 correspond to lightly loaded downbound traffic. 9.4.2 Vessel Traffic Growth In the AASHTO example (§1.4.2), vessel traffic volume was expected to grow by 2% per year. Two risk assessments were completed by the bridge designers, one co rresponding to current vessel traffic (at the time, 2003), and one corresponding to future traffic (2053). A corresponding vessel traffic growth factor equal to 2.69 was applied to the 2003 data to estimate traffic volume in 2053. Detailed risk analysis re sults presented in the AASHTO example correspond to the future fleet (2053). Therefore, for this study, the growth factor was adopted, and thus the results correspond to the future (2053) fleet. 9.4.3 Vessel Transit Speeds In the AASHTO example (§1.4.3) vessel t ransit velocities were assumed to be 5.0 knots for downbound traffic, and 4.0 knots for upbound traffic (all vessel types). However, as prescribed by AASHTO, impact velocities are expected to decrease as the distance from the channel increases. The decreas e is also a function of overall vessel length ( LOA ). Impact velocities that were computed for every combination of pier and vessel group are provided in Appendix K. 9.4.4 Vessel Transit Path The transit paths for both upbound and downbound traffic were taken to coincide with the centerline of the navigation channel (under the middle of the main span), as described in the AASHTO example (§1.4.4).

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255 9.5 Vessel Impact Criteria In designing a new bridge, AASHTO requires additional criteria that the design must satisfy, asi de from the maximum impact load criteria defined by the probabilistic risk assessment. Given that the example presented in this chapter is an assessment of an existing structure, certain criteria were not fully explored. Furthermore, for this study, certai n portions of the AASHTO procedure have been replaced with new methods, as discussed in Chapter 7. The following sections describe, in a broad sense, how the overall vessel impact criteria prescribed by AASHTO were assessed in this study. 9.5.1 General Requireme nts The adequacy of the LA 1 Bridge to resist vessel impact loading was assessed in accordance with the general requirements of the following provisions: AASHTO (1991). Guide Specification and Commentary for Vessel Collision Design of Highway Bridges Amer ican Association of State Highway and Transportation Officials, Washington DC. AASHTO (2009). Guide Specification and Commentary for Vessel Collision Design of Highway Bridges, 2 nd Edition, American Association of State Highway and Transportation Officials Washington DC. Modifications to the AASHTO prescribed requirements, including consideration for dynamic bridge response and the influence of pier geometry on impact forces, were made as described in Chapter 7 (referred to as UF/FDOT methods). Such modifi cations, as they pertain to the LA 1 Bridge risk assessment, are documented in Section 9.6 Note that, because the UF/FDOT procedures reflect the most up to date published research, the intent of the analysis was to meet or exceed (generally exceed) the le vel of engineering rigor required by the AASHTO specifications. Furthermore, while the results presented in this chapter imply that the UF/FDOT procedures predict higher levels of vessel collision risk when compared to AASHTO methods, this outcome is not g uaranteed. Indeed, as discussed in Section 9.9 commonly

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256 encountered impact scenarios exist for which UF/FDOT procedures may predict a lower vessel collision risk than the current AASHTO procedures. 9.5.2 Extreme Event Load Combinations (Scour) The AASHTO exampl e (§1.5.2) defines two different scour and impact conditions that must be considered in the design of bridge substructures: 1) minimum vessel impact associated with an empty barge that has broken loose from its moorings during a storm event (including high water), and 2) maximum vessel impact associated with an aberrant vessel being driven into the bridge under normal environmental and operating conditions. Corresponding scour levels for each condition were obtained from the bridge design drawings, as deter mined by hydrological and geotechnical analysis performed when the bridge was designed. 9.5.3 Minimum Impact Load Criteria The minimum impact condition corresponds to the scenario in which an empty hopper barge (195 35 ft) moored in the vicinity of the bridge breaks loose from its moorings during a storm and strikes the bridge. While the minimum impact condition was a critical check on bridge pier performance under extreme environmental conditions, the maximum impact condition was found to control in all cases. Therefore, the minimum impact condition is omitted from further discussion. 9.5.4 Maximum Impact Load Criteria The maximum impact condition corresponds to the scenario in which a vessel being piloted under normal operating conditions becomes aberrant (by mechan ical failure or other means) and impacts the bridge at full speed. Under such conditions, vessel motion is driven under its own power, or in the case of a barge tow, the power of a tug. For this assessment, vessel displacements and impact velocities were a ssumed to vary as discussed in Section 9.4 .1 As suggested in the AASHTO example (§1.5.4), the maximum impact condition was combined with

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257 one half the long term ambient scour level. Note that in accordance with AASHTO procedures, the maximum impact load co nditions can be determined using a simplified, deterministic procedure (Method I), or by conducting a probabilistic risk assessment (Method II). Only the latter analysis procedure was considered in this study. 9.5.5 Operational Classification The LA 1 Bridge was operational classification. Consequently, structural collapse as a result of vessel collision should have a return period of at least 10,000 years, as required by the AASHTO provisions. This requirement is significantly more stringent than a normal bridge (return period of 1,000 years or greater). However, the classification reflects the importance of the bridge to the region. Because the LA 1 Bridge is the only roadway heading inland from nea rby coastal areas, it constitutes the only hurricane evacuation route to local residents. Furthermore, access to hospitals and other emergency services require that the bridge be operational, even under extreme conditions. 9.6 Maximum Impact Load (Method II) A nalysis Methodology As defined by AASHTO, Method II is a probabilistic risk analysis procedure that is used to quantify the annual frequency (annualized probability) that that a bridge will collapse when subjected to vessel collision loading (denoted AF ). In its formulation, Method II attempts to account for all major factors that contribute to vessel collision risk, including but not limited to vessel traffic volume, waterway characteristics, bridge geometry, and bridge element strength. The following sect ions detail analysis assumptions and the overall methodology that was used to quantify AF for the LA 1 Bridge. Risk assessments were completed both using strict AASHTO methodology (static loading and pushover analysis) and using modified UF/FDOT methodolog y that incorporates dynamic structural analysis and other state of the art procedures from recent research. Risk measures that were computed using each method are compared in Section 9.7

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258 Structural analyses were carried out using FB MultiPier (version 4.1 8), and custom Perl scripts (Perl 2013) were programmed to summarize relevant analysis data. Subsequent risk calculations were completed using Mathcad worksheets. 9.6.1 Annual Frequency of Collapse ( AF ) The annual frequency of collapse ( AF ) was computed by the f ollowing expression: ( 9 1 ) where: AF = Annual frequency of bridge collapse due to vessel collision, N = Annual number of vessel transits, as categorized by v essel type and transit direction, PA = Probability of vessel aberrancy, PG = Geometric probability of a pier being impacted by an aberrant vessel, PC = Probability of bridge element collapse subject to collision, and PF = Protection factor to account f or land masses or other objects that may block vessels from colliding with the bridge (PF=0: bridge element fully protected; 0 < PF < 1: bridge element partially protected; PF=1: bridge element unprotected). Note that AF was more specifically computed as a summation of all possible combinations of bridge pier and vessel group. Therefore, a more detailed form of Eqn. 9 1 is: ( 9 2 ) wher e N VG is the number of vessel groups ( N VG = 32 in this case, as defined in Table 9 2 ), and N P is the number of bridge piers within the navigation zone ( N P = 5 in this case, piers 2 4 and 96 97).

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259 9.6.2 Vessel Frequency ( N ) Vessel frequency ( N ) refers to the annual number of vessel transits by a particular vessel type and transit direction (as defined by the vessel groups listed in Table 9 2 ). On any of these tra nsits, the vessel has some finite probability of becoming aberrant and striking a bridge pier. However, in order to collide with a pier, sufficient water depth must be available to accommodate the vessel draft, otherwise the vessel will run aground prior t o impacting the pier. Premature vessel groundings caused by insufficient water depth can be accounted for in the risk assessment in two ways: 1) the value of N for relevant piers and vessel groups can be set equal to zero or reduced in some way, or 2) a pr otection factor ( PF ) can be assigned to relevant piers and vessel groups. The example risk assessment published in the AASHTO Guide Specification employs the first option (setting N = 0 for certain vessels to account for groundings), so this approach was a dopted for this study. Note that vessel traffic volume shown in Table 9 2 was increased by a factor of 2.69 to account for traffic growth over time. Consequently, all risk results presented in this chapter correspond to the future annualized risk in the year 2053. 9.6.3 Probability of Aberrancy ( PA ) Probability of aberrancy ( PA ) refers to the likelihood that a given vessel will stray off course (become aberrant), making collision with a bridge pier possible. Such events can occur due to pilot error, adverse environmental conditions (e.g. dense fog), or mechanical failure (e.g. loss of power). As it is unknown how often and for how long vessels typically veer off course and can be classified as aberrant, accurately quantifying PA can be extremely difficult. Furthermore, the aberrant condition can often be temporary, and may not occur anywhere in the vicinity of a bridge. Certainly, aberrancy caused by pilot inattentiveness is likely to be reduced in the vicinity of a bridge, given that the pilot is aware of the risk of collision. No comprehensive studies have ever been conducted to quantify AF itself. Estimates have been posited by past

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260 engineers and researchers, based on analysis of historical vessel accident data (g roundings, collisions, rammings), as discussed in the AASHTO Guide Specification. However, by definition, recorded accident data only include incidences of aberrancy that resulted in an accident. Commonly, the course of an aberrant vessel is corrected by t he pilot, and an accident is avoided. Depending on the amount of information available, two possible approaches can be taken to quantify AF : 1) gather available accident data for the waterway of interest and make a defensible estimate (prior studies should be consulted for guidance in preparing an estimate), or 2) if accident data are unavailable, use the simplified procedure provided in the AASHTO provisions. As in the AASHTO example (§1.8.1.2) the latter option was employed in this study. Specifically, PA was computed as: ( 9 3 ) where: BR = Base rate of aberrancy (0.610 4 for ships, and 1.210 4 for barges), R B = Correction factor for bridge location (related to waterway alignmen t), R C = Correction factor for currents acting parallel to the navigation channel, R XC = Correction factor for currents acting perpendicular to the navigation channel, and R D = Correction factor for vessel traffic density. As stated above, BR = 1.210 4 was used for all vessel groups, given that ship type vessels were omitted from this study. The correction factor for bridge location ( R B ) was computed based on the relative location of the bridge in one of three possible waterway regions (straight, trans ition to a turn, or

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261 within a turn). Due to a turn in the channel, R B = 2.11, as computed in the AASHTO example (§1.8.1.2). The correction factor for currents acting parallel to the channel ( R C ) was computed as where V C is the c urrent velocity (parallel) in knots. Given a parallel current velocity of 1.0 knots, R C = 1.1, as computed in the AASHTO example (§1.8.1.2). The correction factor for currents acting perpendicular to the channel ( R XC ) was computed as where V XC is the current velocity (perpendicular) in knots. Given a crosscurrent velocity of 1.5 knots, R C = 2.5, as computed in the AASHTO example (§1.8.1.2). The correction factor for vessel traffic density ( R D ) was selected based on the relative volume of traffic, and the likelihood of vessels overtaking each other near the bridge location. R D = 1.3 was selected, corresponding to medium traffic density, as discussed in the AASHTO example (§1.8.1.2). Consistent with the AASHTO example (§1.8.1.2), P A = 9.010 4 was computed for all vessel groups (1 32), given that ship type vessel s were omitted from this study. 9.6.4 Geometric Probability ( PG ) The geometric probability ( PG ) is the conditional probability that a vessel will collide with a particular bridg e pier, given that it has become aberrant. The AASHTO provisions suggest assuming that the vessel position (perpendicular to the intended transit path), is a Gaussian distributed random variable, with mean equal to the channel centerline and standard devia tion equal to the overall vessel length ( LOA ). Therefore, PG for a given pier is equal to the area under the Gaussian distribution bounded by the extents of the pier element width ( B P ) and plus the vessel width or beam ( B M ), as illustrated in Fig. 9 10

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262 Based on the methodology illustrated in Fig. 9 10 PG values were computed by the design team, as documented in AASHTO example. These values were adopted in this study, and are s ummarized in Appendix K. 9.6.5 Probability of Collapse ( PC ) The probability of collapse ( PC ) refers to the likelihood that a particular bridge element (e.g., a pier) will collapse, given that it has been impacted by a particular vessel. Like any failure probabil ity, PC is a function of both the loading characteristics and the structural capacity. Both the load and resistance are dependent on numerous parameters, each subject to random statistical variability. For example, vessel impact loads are a function of the vessel size, bow shape, impact velocity, direction of impact, vessel mass, and other parameters. Furthermore, the capacity of a pier to resist such impact loads is dependent upon structural configuration, pier member sizes, pier material strengths, and so il strength. To further complicate the process of predicting failure, impact events are dynamic in nature, and involve complex interactions between the impacting vessel and pier. Therefore, many of the load and resistance parameters listed above are correl ated. For example, the magnitude and duration of dynamic impact forces (load characteristics), depend strongly upon the nonlinear lateral stiffness of the impacted pier (a resistance characteristic). Consequently, all of the important load and resistance c haracteristics, their statistical variability, and any possible correlations between them must be carefully considered in order to arrive at a reasonable estimate of PC The most accurate means of quantifying PC is through a structural reliability analysis (e.g., Monte Carlo simulation) that directly accounts for the statistical variability of the various load and resistance parameters. However, such an approach may require conducting tens of thousands dynamic structural analyses in order to arrive at a rel iable PC estimate for just one pier and impact condition. Such an approach was demonstrated for eight different bridge piers by

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263 Davidson et al. (2013). Clearly, direct reliability analysis of this nature is overly burdensome for bridge designers to employ in practice. As an alternative, PC has historically been computed (for vessel collision) using simplified equations that act as a surrogate for the complicated interactions and statistical variability discussed above. Such equations relate PC to a determin istically computed demand to capacity ratio. Structural demand (i.e., impact load magnitude) is computed using simplified equations that include the various parameters discussed above, and structural capacity is computed by structural analysis. Given the d eterministically determined demand capacity (D/C) ratio, PC is computed from a surrogate equation. Two surrogate equations for PC are available in the published literature: 1) the equation that is included in the AASHTO vessel collision provisions, and 2) an independently derived equation recently developed by Davidson et al. (2013). Note that the AASHTO expression relies on a static treatment of both the impact load and structural capacity (i.e., static pushover analysis), while the Davidson expression emp loys a time varying definition for the demand capacity ratio, and can therefore be employed in conjunction with a dynamic definition of the impact load and structural response by means of transient structural analysis. The relative merits of the two expres sions are discussed at length in Davidson et al. (2013) and Consolazio et al. ( 2010a ). The purpose of this portion of the study was to compare the results of both procedures using the LA 1 Bridge as an example. As described in the following sections, PC va lues were computed using the AASHTO PC expression, employing AASHTO static load prediction models (from both the 1991 and 2009 specifications) and static pushover analysis of the piers. PC values were also computed using the Davidson PC expression, employi ng newly developed

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264 load prediction models and two new dynamic structural analysis techniques (CVIA and AVIL). Note that the equivalent static analysis method (SBIA) was not considered in the risk assessment of LA 1 Bridge. This is because it was found to b e too conservative for use within the context of the risk assessment when assessing the previous bridge considered in this study (SR 300). As noted in Chapter 8, SBIA is best suited to preliminary analyses in which pier structural members are approximately sized (proportioned) Once members are so proportioned, risk assessment should be completed using one of the more refined dynamic analysis methods (CVIA or AVIL). 9.6.5.1 AASHTO m ethods In accordance with the AASHTO guidelines, PC was computed as: ( 9 4 ) where H is ultimate lateral pier resistance (as determined by static pushover analysis), and P is the vessel impact force (as determined by the equations below). From Eqn. 9 4 the following observations are made: For cases in which the lateral pier resistance exceeds the impact force, PC = 0. For cases in which the pier impact resistance is 10% to 100% of the impact force, PC varies linearly b etween 0.1 and 1.0. In other words, if the predicted impact force exceeds the pier capacity by up to 10 times then PC varies between 0.1 and 1.0. For cases in which the pier impact resistance is below 10% of the impact force, PC varies linearly between 0. 0 and 0.1. In other words, if the predicted impact force is more than 10 times the pier capacity, then PC varies between 0.0 and 0.1. Lateral pier capacities ( H ) that were used to compute PC were taken from the AASHTO example. Note that, as listed in the e xample, these capacities correspond to the minimum lateral capacity of each pier. Actual pushover capacities (determined by structural analysis in FB MultiPier) were found to be higher than the minimum values. The degree of exceedance

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265 depended on soil cond itions assigned to each pier. For consistency with the risk assessment methodology in the AASHTO example, the minimum values of H listed in the Appendix C of the AASHTO example were adopted for the risk assessment (Table 9 3 ). 9.6.5.1.1 AASHTO 1991 b arge i mpact l oad m odel ( a s d esigned) To compute barge impact forces ( P B ) in accordance with the 1991 AASHTO provisions, vessel kinetic energy ( KE ) was first computed as: ( 9 5 ) where, C H is a hydrodynamic mass coefficient, W is the vessel weight (tonnes), and V is the impact velocity (ft/s). In the given units, KE was calculated in kip ft. Next, barge bow damage depth ( a B ) (i.e., the depth of maximu m crushing deformation) was computed as: ( 9 6 ) where, R B is the ratio B B /35, where B B is the barge bow width (ft). In the given units, a B was calculated in ft. Lastly, barge impac t force ( P B ) was computed as: ( 9 7 ) In the given units, P B was computed in kips. Barge impact forces computed using the 1991 AASHTO equations varied between 106 kips and 2,564 kip s, depending on barge type and pier distance from the navigation channel (Appendix K). As described above, the ratio H / P B was computed for each combination of pier and vessel group. Using Eqn. 9 4 correspondi ng estimates of PC were also calculated. Results are discussed in Section 9.7 and detailed results can be found in Appendix K.

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266 9.6.5.1.2 AASHTO 2009 barge impact load m odel To compute barge impact forces ( P B ) in accordance with the 2009 AASHTO provisions, vessel ki netic energy ( KE ) was computed as before: ( 9 8 ) In the given units, KE was calculated in kip ft. The 2009 AASHTO provisions excluded the term R B from all load equations. Therefore barge bow damage depth ( a B ) was computed as: ( 9 9 ) In the given units, a B was calculated in ft. Lastly, barge impact force ( P B ) was computed as: ( 9 10 ) In the given units, P B was computed in kips. Barge impact forces computed using the 2009 AASHTO equations varied between 106 kips and 1,986 kips, depending on barge type and pier distance from the navigat ion channel (Appendix K). As described above, the ratio H / P B was computed for each combination of pier and vessel group. Using Eqn. 9 4 corresponding estimates of PC were also calculated. Results are discusse d in Section 9.7 and detailed results can be found in Appendix K. 9.6.5.2 UF/FDOT m ethods In accordance with Davidson et al. (2013), PC was computed as: ( 9 11 ) where, D / C is the maximum demand to capacity ratio from structural analysis. As defined by Davidson, D / C is a rational measure of the proximity of a structure to the formation of a structural mechanism that would result in instability and collapse. The ratio can take on any

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267 value f rom between 0 and 1, such that D / C = 0 for a pier under no load, and D / C = 1 for a pier which has formed a structural collapse mechanism and is at incipient collapse. It is important to note that D / C is a time varying dynamic quantity. During a dynamic ves sel impact event, D / C begins close to 0 (gravity loading will cause D / C to be nonzero even without impact load applied) and as the pier displaces, D / C increases (up to D / C = 1, if the pier collapses). For this study, D / C was computed as: ( 9 12 ) where m is the number of members (e.g., piers columns, piles) associated with a given collapse mechanism, n is the number of plastic hinges per member that are necessary to form the correspo nding collapse mechanism, and is the j th largest element demand capacity ratio along member i as reported by FB MultiPier (internally computed based on biaxial load moment interaction). See Consolazio et al. ( 2010a ) for a more detailed description of D / C and its theoretical basis. 9.6.5.2.1 CVIA structural a nalysis The most accurate (design oriented) vessel impact analysis method currently available is coupled vessel impact analysis (CVIA). As illustrated in Fig. 9 11 in CVIA, the impacting vessel is idealized as a single degree of freedom (SDF) system, consisting of a concentrated mass that represents the vessel mass, and a nonlinear spring element that represents the crushing characteristics (fo rce deformation relation) of the vessel bow. The SDF barge model is coupled to a multiple degree of freedom (MDF) finite element model of the impacted pier at a node corresponding to the expected impact location. To begin the analysis, the structure is pre loaded with gravity and buoyancy forces, and then the vessel mass is prescribed an initial velocity equal

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268 to the impact velocity. Impact forces imparted on the pier are computed based on dynamic interaction between the SDF barge and MDF pier models, as wo uld occur during a real impact event. CVIA has been used extensively in numerous research projects (Consolazio et al. 2008, Davidson et al. 2010, Getter et al. 2011, and Davidson et al. 2013). As implemented in these prior studies, the barge force deformat ion relation was assumed to be elastic, perfectly plastic (as shown in Fig. 9 11 using a force deformation model from Consolazio et al. (2009). This model has since been updated to account for oblique impact scena rios (Getter and Consolazio 2011), like the one shown in Fig. 9 12 The Getter Consolazio force deformation model was employed throughout this study for computing impact forces. Specifically pertaining to CVIA, force deformation relations for the SDF barge models were taken to be elastic, perfectly plastic, with yield deformation a BY = 2 in. Barge yield force ( P BY ) was computed in accordance with the empirical Getter Consolazio equations. For oblique impac t with a flat faced pier (the scenario for all piers in the LA 1 Bridge), P BY was computed as: ( 9 13 ) where is the smallest skew angle between the barge bow and pier surface (degree s), B B is the vessel beam (width) (ft), and B P is the width of the pier face associated with the smallest skew angle (ft). These quantities are illustrated for a typical impact condition in Fig. 9 12 Giv en the units shown, P BY was computed in kips. A summary of relevant input data for CVIA simulations is provided in Table 9 4 Impact force time histories computed by each CVIA simulation that was conducted (1 60 total) are provided in Appendix K. Finally, D / C values predicted by CVIA, and the associated values of PC are discussed in Section 9.7 and listed in detail in Appendix K.

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269 9.6.5.2.2 AVIL structural a nalysis The applied vessel impact load (AVIL) method was develop ed as a slightly simpler alternative to CVIA (Consolazio et al. 2008). The method consists of developing a pre computed impact force time history and applying it as a dynamic load in a transient analysis, as shown in Fig. 9 13 It is recognized that many structural analysis packages do not include the features required to conduct CVIA (e.g, the ability to assign initial velocities), but the ability to analyze structures under prescribed time varying loading is quite common. In such cases, AVIL is an excellent alternative analysis procedure to CVIA. The AVIL method is summarized in Fig. 9 14 As implemented in this study, barge force deformation characteristics ( a BY and P BY ) were established based on the Getter and Consolazio (2011) model, as discussed above for CVIA. Barge mass ( m B ) and initial barge velocity ( v Bi ) were also the same as CVIA (recall Table 9 4 ). As shown in Fig. 9 15 pier soil stiffness ( k P ) was determined by analyzing each pier finite element model subject to a lateral load ( P ), measuring the corresponding displacement ( ), and computing k P = P / It is recognized that, due to soil and/or structural nonlinearity, k P generally becomes smaller as P increases. Because the AVIL method is unable to account for changes in pier resistance during an impact event, a representative k P must be selected for its formulation. It was observed in conducting this study, that using the initial pier stiffness (i.e., k P corresponding to a very small value of P ) resulted in analysis results that were very similar to CVIA and consistently conse rvative. Values of k P that were determined for each pier are provided in Table 9 5 and maximum barge impact forces ( P Bm ) for each pier and vessel group are shown in Table 9 6 Impact force time histories that were computed for each AVIL analysis are compared to corresponding CVIA force histories

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270 in Appendix K. Finally, D / C values predicted by AVIL, and the associated values of PC are discussed in Section 9. 7 and liste d in detail in Appendix K. 9.6.6 Protection Factor ( PF ) As documented in the AASHTO example (§1.8.1.5) protection factors ( PF ) were developed by the bridge design team to account for various land masses in the vicinity of the bridge. PF values (Table 9 7 ) provided in the AASHTO example were adopted for this study. 9.7 Risk Analysis Results As discussed in the prior section, vessel collision risk assessments were conducted for the LA 1 Bridge using the methodology prescribed by AASHT O (1991 and 2009 specifications). Additional assessments were conducted using the revised UF/FDOT methodology and two different dynamic structural analysis procedures (CVIA, AVIL). The results of each assessment are presented in this section, including pro bability of collapse ( PC ) and annual frequency of collapse ( AF ) estimates, as predicted by each method. 9.7.1 AASHTO Methods The following sections discuss results from the risk assessments conducted using AASHTO methodology with two different barge impact load equations: 1) from the 1991 AASHTO provisions (Eqns. 9 6 and 9 7 ), and 2) from the 2009 provisions (Eqns. 9 9 and 9 10 ). 9.7.1.1 AASHTO 1991 barge impact load model (as d esigned) Estimates of PC values that were computed using the AASHTO (1991) methodology were very often equal to zero. Specifically, of the 160 combinations of pier and vessel group considered, PC was nonzero 47 times (approximately 29%). Including the ship type vessel groups for which PC was always equal to zero (340 total cases), the percentage of nonzero PC cases was only 14%. This occurred be cause, using the AASHTO expression, PC was only nonzero when the impact load P exceeded the lateral pier capacity H (i.e., H / P < 1).

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271 Furthermore, even nonzero values of PC were quite small. Indeed, the largest PC among all cases considered was 0.088, and f or this case, the impact load exceeded pier capacity by 4.9 times Among the nonzero cases, the average PC was 0.039, which corresponds to pier capacity being exceeded by 1.5 times. Estimates of PC as obtained by AASHTO (1991) methods, are presented quali tatively for every pier and vessel group in Fig. 9 16 A Note that in this format, white squares correspond to PC values that are exactly equal to zero. Green color indicates PC just greater than zero, and the color gradient fades to red at PC = 1. While all nonzero values were small, PC was slightly greater for piers far from the navigation channel (piers 96 and 97). Including all other terms in the AF expression ( N PA PG PF ), the relative con tribution to AF is shown for every pier and vessel group in Fig. 9 16 B Note that the color gradient is simply relative to the maximum contribution among all piers and vessel groups, having no s pecific numerical scale. The purpose of the gradient is to show, qualitatively, which piers and vessel groups contribute most to total risk ( AF ). As would be expected, piers nearest the centerline (piers 2 and 3) contributed most to AF as they have the hi ghest likelihood of being impacted. These piers only contributed to AF for vessel group 17, the most severe impact case considered (fully loaded barge traveling downbound). Piers 4, 96, and 97 did contribute to AF but only for some of the lightly loaded v essel groups. This occurred because only lightly loaded vessels had a small enough draft to permit impact these piers without running aground. Fig. 9 17 A shows the percent contribution to AF for e ach pier in the bridge (i.e., the contributions shown in Fig. 9 16 B summed across all vessel groups). As intended by the bridge designers, each pier contributed equally to AF See the AASHTO ex ample for more details.

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272 Fig. 9 17 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 9 16 B summed across all piers). Vessel group 17 (the most severe impact case) was the largest contributor to AF (approximately 40%). However, vessel groups 9 and 13 contributed approximately 25% each. Risk associated with groups 9 and 13 was primarily caus ed by their relatively high probability of impact. PC values for these groups were not particularly high compared to vessel groups that contributed nothing to AF Summing AF among all piers and vessel groups, AF predicted by AASHTO (1991) methods was 9.98 10 5 yr 1 which corresponds to a return period 1/ AF = 10,020 years. Therefore, by the AASHTO definition, the bridge can be considered sufficiently robust to resist vessel collision loading, because the minimum acceptable return period is 1/ AF = 10,000 yea rs. 9.7.1.2 AASHTO 2009 barge impact load m odel Estimates of PC that were computed using the AASHTO (2009) methodology were nearly always equal to zero. Specifically, of the 160 combinations of pier and vessel group considered, PC was nonzero 37 times (approximate ly 23%). Including the ship type vessel groups for which PC was always equal to zero (340 total cases), the percentage of nonzero PC cases was only 11%. This occurred because, compared to the 1991 AASHTO procedure, barge impact load magnitudes were lower, particularly for high energy impact conditions experienced by piers near the navigation channel. Because the bridge was designed to resist relatively higher load magnitudes predicted by the 1991 AASHTO provisions, pier capacity was rarely exceeded ( H / P < 1 ) using the 2009 provisions, and PC was equal to zero for 77% of impact cases considered. Estimates of PC as obtained by AASHTO (2009) methods, are presented qualitatively for every pier and vessel group in Fig. 9 18 A Note that PC was equal to zero for piers 2 and 3 for every vessel group. Consequently, PC was only nonzero for piers 4, 96, and 97, which are

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273 unlikely to be impacted. Including all other terms in the AF expression ( N PA PG PF ), the relative contribution to AF is shown for every pier and vessel group in Fig. 9 18 B Note that there was no risk contribution from fully loaded vessel groups (1 8 and 17 24), and no cont ribution from piers 2 4, regardless of vessel group. Therefore, only piers 96 and 97 had any vessel collision risk, and most of that risk was concentrated in vessel group 13. Fig. 9 19 A shows th e percent contribution to AF for each pier in the bridge (i.e., the contributions shown in Fig. 9 18 B summed across all vessel groups). As discussed above, piers 96 and 97 together accounted fo r 100% of the total risk. This outcome differs substantially from the assessment using the 1991 AASHTO provisions, in which contributions to AF were distributed equally among the five piers (recall Fig. 9 17 A ). As noted above, this occurred primarily because 2009 AASHTO loads were smaller, causing PC to be equal to zero for the two channel piers (piers 2 and 3). Fig. 9 19 B shows the percen t contribution to AF for each vessel group (i.e., the contributions shown in Fig. 9 18 B summed across all piers). In contrast to the 1991 AASHTO results, vessel group 13 accounted for more than 80% of total risk, and vessel groups 9 and 17 were significantly less important. Summing AF among all piers and vessel groups, AF predicted by AASHTO (2009) methods was 5.5410 5 yr 1 which corresponds to a return period 1/ AF = 18,060 years. As noted abo ve, this outcome occurred because the only piers that were found to be at risk for vessel collision (piers 96 and 97) were located relatively far from the navigation channel, resulting in lower geometric probability of impact ( PG ). Also, PF values were sma llest for these piers because of the relatively large degree of protection afforded by navigational obstructions.

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274 Therefore, considering all these factors, AF was significantly smaller than predicted by the 1991 AASHTO procedure. These results highlight ho w sensitive the AASHTO PC expression can be to changes in analysis assumptions. For this example case, barge impact load magnitudes predicted by the 2009 equations were, on average, only 7.8% smaller than those predicted by the 1991 equations. However, AF was found to be 55% smaller, as a result. Such sensitivity is caused by the AASHTO PC equation allowing PC to be equal to zero if pier capacity (as estimated by engineering analysis) is greater than or equal to the estimated impact load. Given the signific ant uncertainties associated with estimating both loads and capacities and statistical variability of material and soil strengths, as well as other factors, assigning a failure probability equal to zero cannot be reasonably justified. 9.7.2 UF/FDOT Methods The f ollowing sections present risk analysis results ( PC and AF ) that were computed using UF/FDOT methods. The revised methods include a new PC expression, revised barge impact load prediction equations, and two dynamic structural analysis procedures (CVIA and AVIL). 9.7.2.1 CVIA Estimates of PC computed using UF/FDOT methods were never equal to zero. This is because the minimum value that the PC equation (Eqn. 9 11 ) can take is 2.3310 6 when D / C = 0. Furthermore, by de finition, D / C = 1 when the load carrying capacity of the pier has been reached or exceeded, at which point PC = 1. In the context of a CVIA dynamic structural analysis, such a condition typically results in the analysis failing to converge due to numerical (and structural) instability.

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275 Estimates of PC as obtained by UF/FDOT methods with CVIA structural analysis, are presented qualitatively for every pier and vessel group in Fig. 9 20 A Note tha t the color definitions are the same as stated in the previous section. As shown, the highest PC values were associated with vessel groups 1 5 and 17 21, which correspond to the most massive vessel types considered in this study. For a given vessel gro up, PC was relatively uniform among all the piers, indicating that pier capacity was approximately proportional to the impact demand. Compared to the AASHTO (1991) method results (Fig. 9 16 A ), P C values quantified by UF/FDOT methods using CVIA were much larger. The AASHTO procedure predicted an average PC = 0.039, while UF/FDOT average PC = 0.19. Furthermore, many impact cases had PC values equal to or nearly equal to 1.0, while them maximum AAS HTO PC was only 0.088. Considering other factors that contribute to overall risk ( N PA PG PF ), relative contributions to AF are shown in 9 20 B Note that some piers did not contribute to AF for certain vessel groups (as defined by white coloring), because these piers were assigned N = 0. The largest AF contributions came from piers 2 and 3 for vessel group 21. This outcome is somewhat unexpected, as vessel group 21 refers a moderate energy im pact condition. However, this group is one of the most common on the waterway. Therefore, the high number of vessel trips ( N ) overcame the risk posed by more massive vessels by virtue of having a higher probability of impact occurring. Regardless of vessel group, piers 2 and 3 had the largest contribution to AF Fig. 9 21 A shows the percent contribution to AF for each pier in the bridge (i.e., the contributions shown in Fig. 9 20 B summed across all vessel groups). As shown, piers 2 and 3 account for nearly 100% of total risk. This occurred for two reasons: 1) the piers are located adjacent to the channel, and are therefore most likely to be impacted, and 2) more importantly, vessel impact load magnitudes associated with piers 2 and 3 were significantly higher than for

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276 other piers. Load magnitudes were higher primarily because the pier footings are skewed, such that they are aligned with the navigation channel. Recalling the UF/FDOT load model (Eqn. 9 13 ), was equal to 0 for piers 2 and 3. Therefore, as shown in Table 9 4 impact loads were almost two times higher than the other piers, for which = 20. Fig. 9 21 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 9 20 B summed across all piers). As shown, the largest contribution to AF (ap proximately 18%) came from vessel group 21, and significant contributions (9 14%) came from vessel groups 4, 7, 18, and 22. Relative contributions to AF from each vessel group were influenced by a combination of impact severity and trip frequency. Many of the vessel groups with highest risk did not correspond to the most severe impact conditions. Indeed the most severe impact case was caused by vessel group 17, which only contributed 5% to AF Summing AF among all piers and vessel groups, AF predicted by UF/FDOT methods (with CVIA) was 0.137 yr 1 which corresponds to a return period 1/ AF = 7.3 years. The specific reasons why the UF/FDOT methods predicted so much higher a level of risk than the AASHTO procedures (1/AF = 10,020 years) are discussed in deta il in Section 9. 8 9.7.2.2 AVIL Estimates of PC as obtained by UF/FDOT methods with AVIL structural analysis, are presented qualitatively for every pier and vessel group in Fig. 9 22 A As with CVIA, the highest PC val ues were associated with vessel groups 1 5 and 17 21, which correspond to the most massive vessel types considered in this study. For a given vessel group, PC was relatively uniform among all the piers, indicating that pier capacity was approximately p roportional to the impact demand.

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277 Considering other factors that contribute to overall risk ( N PA PG PF ), relative contributions to AF are shown in 9 22 B As with CVIA, the largest AF contributions came fro m piers 2 and 3 for vessel group 21. Regardless of vessel group, piers 2 and 3 had the largest contribution to AF Fig. 9 23 A shows the percent contribution to AF for each pier in the bridge (i.e., the contributi ons shown in Fig. 9 22 A summed across all vessel groups), and Fig. 9 23 B shows the percent contribution to AF for each vessel group (i.e., the contributions shown in Fig. 9 22 A summed across all piers). The distribution of AF among the various piers and vessel groups was quite similar to CVIA, with piers 2 and 3 contributing almost 100% of total risk. Like CVIA, pier 2 co ntributed more to AF than pier 3. However, the difference is larger for AVIL. Summing AF among all piers and vessel groups, AF predicted by UF/FDOT methods (with AVIL) was 0.206 yr 1 which corresponds to a return period 1/ AF = 4.8 years. The specific reas ons why the UF/FDOT methods predicted so much higher a level of risk than the AASHTO procedures (1/AF = 10,020 years) are discussed in detail in Section 9. 8 9.8 Discussion of Results Table 9 8 summarizes risk assess ment results for the LA 1 Bridge, as determined by each analysis procedure that was considered in this study. As shown, impact loads computed using UF/FDOT methods were approximately 3 times higher than those determined using the AASHTO (1991) procedure. As discussed above, this occurred primarily because the UF/FDOT impact load model tends to predict larger impact forces than the AASHTO model when piers have wide, flat faced impact surfaces. Furthermore, impact forces predicted by the UF/FDOT model increa se significantly when the impact angle is small (i.e., when the impact condition is 1 Bridge

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278 were skewed such that they aligned with the navigation channel, the expected i mpact angle was = 0, resulting in significantly higher load magnitudes than the AASHTO model predicted. In Table 9 8 AASHTO capacity demand ratios ( H / P ) (used to compute PC ) are inverted to be demand capacity ratios ( P / H ) to facilitate comparison to D / C ratios computed by UF/FDOT methods. As shown, average D / C for the most accurate UF/FDOT method (CVIA) was approximately 26% lower than P / H for the AASHTO (1991) method, even though UF/FDOT load magnitudes were higher. This occ urred because the piers, as designed, had significantly more lateral capacity than stated in the structural drawings, as evidenced by their ability to withstand dynamic impact loads on the order of 6,000 7,000 kips. Recall that the minimum pushover capac ity stated in the structural drawings was only 2,446 kips for the channel piers. As discussed above, this minimum value was used for H in the AASHTO risk assessments for consistency with the published AASHTO risk assessment, in lieu of the capacity as esti mated by pushover analysis of the finite element models used to perform the UF/FDOT assessments. Had the actual pushover capacities been employed in the AASHTO risk assessments, P / H would be lower than D / C from UF/FDOT assessments. Average PC values obtain ed by UF/FDOT methods (CVIA) were more than 16 times higher than those obtained from AASHTO (1991). This is primarily a consequence of larger demand on the piers (caused by the larger UF/FDOT loads). However, another reason for the discrepancy is the diffe rence between the PC expressions. As discussed in the prior section, PC was equal to zero for the majority of impact cases considered in the AASHTO risk assessment. In contrast, the UF/FDOT PC expression (by intentional design) cannot return a PC equal to zero. Consequently PC was greater than zero for every barge impact case considered in the UF/FDOT assessments. It should also be noted that PC values obtained using the UF/FDOT

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279 methods properly account for numerous statistical uncertainties associated with impact loading, structural capacity, and soil capacity and are therefore a more rational estimate of collapse risk than the AASHTO PC values. As shown in Table 9 8 AASHTO (1991) methods resulted in a return per iod for bridge collapse 1/ AF = 10,020 years, satisfying the acceptable risk criterion (1/ AF years) for this critical bridge. This outcome is expected, given that the bridge was designed in accordance with the 1991 AASHTO provisions. However, the b arge impact load model was modified slightly in the 2009 AASHTO provisions (i.e., elimination of the barge width modification factor), resulting in a reduction in load magnitudes for most impact conditions. Accounting for this change, the return period inc reased to 18,060 years. Return periods predicted by UF/FDOT methods imply that the bridge does not satisfy the level of acceptable risk. Indeed, AF predicted by the CVIA risk assessment was 1,370 times higher than the AASHTO (1991) method. This enormous di screpancy is a consequence of the difference in PC values predicted by each method, as discussed above. The AASHTO method had many PC values equal to zero, which may not be realistic, while the UF/FDOT methods had no PC values equal to zero, and all PC val ues were dramatically higher than AASHTO. From the available data, it is difficult to assess which estimate of AF is more realistic. Certainly, recent research indicates that impact load magnitudes should be higher than predicted by AASHTO for this particu lar bridge. Furthermore, it is difficult to defend PC being equal to zero (as AASHTO does) when the impact load estimated by an empirical equation is nearly equal to the pier capacity estimated by engineering analysis. Given these factors, it is expected t hat AF would be greatly under predicted by the AASHTO procedures for this bridge. Furthermore, additional

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280 evidence (discussed below) indicate that the UF/FDOT procedures likely over predicted AF for this bridge. Given that the LA 1 Bridge did not satisfy t he acceptable risk level using UF/FDOT methods, it is important to consider whether the bridge could be economically retrofitted to improve its performance and thereby mitigate vessel collision risk within the context of the UF/FDOT assessment methodology. A possible retrofit solution is proposed in the following section (Section 9. 9 ) that takes advantage of the fact that the UF/FDOT impact load model predicts significantly smaller forces if impacted pier surfaces are rounded rather than flat faced. For dem onstration purposes, a pier protection system and two alternative pier designs that would further mitigate risk are also discussed in Section 9. 9 The retrofit, protection system, and alternative design examples presented in Section 9. 9 are possible means of satisfying the required risk criteria if the UF/FDOT methodology were employed exactly as discussed in this chapter. However, a comparison of the LA 1 Bridge risk assessment data to historical incidents of vessel collision suggest that the other terms i n the expression for AF (specifically the PA and PG terms ) may over predict the likelihood that impacts will occur. Because these terms were adopted into the UF/FDOT methods directly from AASHTO, the value of AF computed using UF/FDOT methods may be unreal istically high. If this were the case alternative designs or retrofits may be less necessary. This possibility is discussed further in Section 9.10 9.9 Suggestions for Mitigating Risk The primary reason that UF/FDOT methods predicted a higher risk level than the AASHTO methods is the relative magnitude of impact loads. Three risk mitigation strategies are presented in this section: retrofits to the impacted piers, a protection system involving dolphin structures, and two alternative pier designs. The primary objective of the retrofits and alternative

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281 designs is to reduce the magnitude of impact forces by taking advantage of certain aspects of the UF/FDOT impact load model. 9.9.1 Pier Footing Retrofit As discussed in Section 9.6 .5.2.1 the barge force deformation cur ve that was used as the basis for UF/FDOT predictions of impact force was elastic, perfectly plastic with yield deformation ( a BY ) equal to 2 in. and yield force ( P BY ) computed based on the Getter and Consolazio (2011) model. For a flat faced impact surface such as the pier footings of the LA 1 Bridge, P BY was computed as: ( 9 14 ) As summarized in Table 9 9 P BY varied between 3,29 4 7,569 kips for the various piers and vessel groups. As demonstrated by the risk assessment, the barge bow yielded for most impact conditions, and thus, the maximum impact force was generally equal to P BY However, the Getter Consolazio force deformatio n model states that, for rounded impact surfaces, P BY should be computed as: ( 9 15 ) Therefore, if the LA 1 pier footings (pile caps) were the same size, but were rounded instead of fl at faced on the leading edge, P BY would vary between 2,240 2,840 kips (Table 9 9 ), corresponding to a 48% reduction in impact loads, on average. Choosing to round off the ends of footings would like ly have little influence on construction cost, but could improve impact performance significantly. To evaluate this possibility, a risk assessment was conducted using UF/FDOT methods (CVIA) in which the LA 1 footings were assumed to be the same overall siz e, but the ends were rounded instead of flat (detailed analysis results are omitted here for brevity). Bridge structural demands were

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282 significantly reduced relative to the as built condition, and the return period (1/ AF ) went from 7.3 years to 28.0 years, corresponding to a 74% reduction in risk. Therefore, significant risk reduction could be realized by retrofitting footings with rounded caps made of reinforced concrete, as illustrated in Fig. 9 24 If the foundation does not h ave sufficient capacity to carry the additional concrete weight, a more lightweight design (steel or composite) with the same dimensions could be employed. 9.9.2 Pier Protection System Given that the retrofitted design had a return period 1/ AF = 28.0 years, the only practical means of achieving the specified return period of 10,000 years with the existing structure (using the UF/FDOT methodology) would be to construct protective structures that block oncoming vessels from impacting bridge piers near the navigatio n channel. Such structures can be designed to be permanent and thereby withstand numerous impacts in their design life, or they can be sacrificial, necessitating repair or reconstruction if they are significantly damaged by being impacted. As an illustrati ve example, consider the pier protection layout shown in Fig. 9 25 in which piers 2 4 are protected by dolphin structures. Dolphins are commonly constructed by driving a circular ring of steel sheet piling, filli ng the center with sand, rocks, and/or riprap, and casting a reinforced concrete cap on top (near the waterline). Such structures can be designed to withstand low energy impacts without damage, while repair or replacement may be required following high ene rgy head on impacts. In the example shown in Fig. 9 25 piers 2 and 3 are protected by two 30 ft diameter dolphins on each side of the pier, and pier 4 is similarly protected by 20 ft. diameter dolphins. If position ed and designed carefully, such structures could provide effectively complete protection against vessel collisions. To evaluate the efficacy of the protection system, the UF/FDOT risk assessment (CVIA) was repeated but with PF = 0 (complete protection) for piers 2 4. The

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283 return period (1/ AF ) increased from 7.3 years in the as built configuration to 8,160 years, which is close to the target of 10,000 years. If the protection system in Fig. 9 25 was combined with ret rofitting piers 96 and 97 as shown in Fig. 9 24 C then the return period increases to 12,380 years. Alternatively, additional dolphins could be constructed to protect piers 96 and 97, and thereby reduce risk to effectively zero. 9.9.3 Alternative Foundation Design In order to illustrate strategies for reducing vessel collision risk using UF/FDOT methods, an alternative foundation design was developed for the piers at risk for collision (piers 2 4 and 96 97). The a lternative design employs two large diameter drilled shafts in lieu of the driven pile foundations that were constructed. This design is advantageous because the portion of piers that would be impacted by barge vessels can be proportioned to be a relativel y small diameter (8 10 ft) cylinder, rather than a wide, flat faced footing surface, as currently designed. This change in geometry can result in significant reductions in impact forces. As shown in Fig. 9 26 t he foundation for piers 2 4 (previously consisting of 54 in. driven cylinder piles) was replaced with two 9 ft diameter drilled shafts that are positioned collinearly with the pier columns (also 9 ft in diameter at the base) (Fig. 9 26 A ). Note that the spacing (22 ft) is less than three times the diameter of the shafts, and therefore lateral capacity is not optimal. However, the spacing was chosen such that no changes to the pier design were required. The shafts and pier columns are connected at the waterline with a 20 ft deep shear wall that is 10 ft wide and has cylindrically shaped ends (Fig. 9 26 B ). The drilled shafts are reinforced with (48) No. 18 longitudinal bars and No. 8 ties spaced at 12 in. center to center (Fig. 9 26 C ), with 6 in. of clear concrete cover. Due to relatively weak soil conditions at the site, shafts must be drilled to an elevation of 185 ft, which is ap proximately 30 ft deeper than the driven piles in the as built design.

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284 As shown in Fig. 9 27 the foundation for piers 96 and 97 (previously consisting of 30 in. square driven piles) was replaced with two 7 ft dia meter drilled shafts that are positioned collinearly with the pier columns (6 ft in diameter at the base) (Fig. 9 27 A ). The spacing (24.5 ft) was chosen such that no changes to the pier design were required, and e xceeds three times the diameter of the shafts, which improves lateral capacity. The shafts and pier columns are connected at the waterline with a 20 ft deep shear wall that is 8 ft wide and has cylindrically shaped ends (Fig. 9 27 B ). The drilled shafts are reinforced with (36) No. 18 longitudinal bars and No. 8 ties spaced at 12 in. center to center (Fig. 9 27 C ), with 6 in. of clear concrete cover. Again, shafts must be dr illed to an elevation of 185 ft, which is approximately 25 ft deeper than the driven piles in the as built design. Because the impacted pier surfaces are rounded, P BY was calculated as: ( 9 16 ) where min( B B B P ) is equal to 10 ft for piers 2 4 and 8 ft for piers 96 and 97. As summarized in Table 9 10 P BY was reduced by 63% on average (relative to the as built design), and up to 77% for the piers that are adjacent to the navigation channel (piers 2 and 3). One of the requirements of the AASHTO provisions is that piers must be able to withstand 50% of the maximum vessel impact force applied in the direction longitudinal to the sup erstructure alignment, to account for glancing type impacts. This requirement is a particular concern because the retrofitted design is relatively weak in that direction. However, static pushover analyses of each pier showed that the longitudinal capacity of the channel piers was approximately 3,300 kips. The weakest pier (97) is located at an expansion joint. Therefore, the entire longitudinal load must be carried by the foundation (i.e., no load path through the superstructure is available). Even in this extreme case, the pushover capacity was 1,400 kips,

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285 corresponding to 85% of the maximum impact force ( P BY = 1,640 kips). Consequently the alternative was considered adequate for glancing impacts. Dynamic impact analyses (CVIA method) were conducted using F B MultiPier models of the alternative pier designs with revised values of P BY and corresponding D / C ratios were computed from each analysis. As summarized in Table 9 11 average D / C was greatly reduce d relative to both the as built design (64%) and the retrofitted design (60%), with larger reductions observed for piers 2 and 3. Correspondingly, average PC values for the alternative design were more than 1,500 times smaller than the as built design, and 460 times smaller than the retrofitted design. These examples demonstrate the highly nonlinear nature of the UF/FDOT PC expression, in that modest reductions in D/C can result in dramatic reductions in PC In addition to significantly reduced impact loads (and dramatically smaller PC values), the alternative design had a smaller overall footprint within the bridge alignment, and therefore had reduced likelihood of being impacted by aberrant vessels. In other words, horizontal clearance between piers was si gnificantly increased with the alternative design. The geometric probability of impact ( PG ) was recalculated to account for the new pier geometry and was found to be 40% smaller, on average, than the as built design. Combining the revised PC and PG values with the other terms in the AF expression ( N PA PF ) the return period (1/ AF ) was calculated to be equal to 10,230 years. Therefore, the alternative design was found to satisfy the level of acceptable vessel collision risk required by AASHTO for critical/ essential bridges. The examples described above highlight how sensitive the results of the risk assessment can be to various design choices. The LA 1 Bridge design (as built) constitutes effectively a worst case scenario within the context of the UF/FDOT r isk assessment procedures. Specifically, foundation footings are wide and flat faced, which results in significantly larger impact forces

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286 than rounded footings of similar size. Furthermore, footings for the two piers adjacent to the navigation channel are skewed such that the flat pier faces are aligned with the channel (and impacting vessels). While this choice improves horizontal clearance and reduces the probability of impact somewhat, the as built orientation increases impact forces by almost 60% (relat ive to footings that are aligned with the piers). When combined, these design choices resulted in impact forces that were 3 4 times higher than the alternative (drilled shaft) design described above, and collapse risk ( AF ) that is 1,400 times higher than the alternative design. It is important to note that the improved performance of the alternative design came primarily from the reduction in impact forces, and not from an increase in lateral capacity. Indeed, the lateral pushover capacity of the alternat ive design for piers 2 and 3 (channel piers) was approximately half the as built design. For illustrative purposes, a second alternative design concept is shown in Fig. 9 28 Rather than replacing th e driven pile foundation with drilled shafts, the footing is simply moved downward to a submerged location, where it is unlikely to be impacted by vessels. A 10 ft wide shear wall that extends up to the maximum expected impact elevation transmits impact fo rces directly to the footing. Because the wall is the same width as the shear wall in the drilled shaft alternative, impact forces would be identical. However, the driven pile foundation is likely to have a larger lateral capacity than the drilled shaft fo undation, and therefore the design would likely improve vessel collision performance even further. 9.10 Summary A discussed in Chapter 8, the discrepancy between the AASHTO and UF/FDOT methods is entirely limited to PC However, it is valuable to consider wheth er the other terms in the AF expression ( N PA PG PF ) are historically accurate. Detailed records concerning the volume of commercial vessel traffic are readily available, thus N can be considered the most reliable value in the risk assessment. The accur acy of PA PG and PF are difficult to evaluate independently,

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287 but their combined result can be compared to available data. Specifically, if PC is removed from the expression for AF the resulting probability is the annual frequency of impact ( AFI ): ( 9 17 ) Based on this definition, AFI represents the number of direct vessel collisions with the bridge piers that are expected to occur in a given year. For the LA 1 Bridge, AFI = 1.04 impacts/yr. Given that the main piers and spans have been in place for more than five years at present, according to the AASHTO based AFI it is extremely likely (99.5% probability) that a significant impact event should have already occurred to date. The U .S. Coast Guard keeps detailed records on vessel casualties, which include (among other things) accidental impacts with bridges. These records are publicly available from an online database called the Coast Guard Maritime Information Exchange (CGMIX) (USCG 2013). Since 2008, only two incidents have been recorded at the LA 1 Bridge site, one of which involved the old lift bridge that has since been removed and replaced by the current high rise bridge. Therefore, the only recorded incident of the new bridge b eing impacted by a vessel occurred on April 26, 2011 (CGMIX activity ID# 3997036), in which a fishing boat failed to lower its outriggers prior to traversing under the bridge, and the top 5 ft. of the outriggers impacted the center superstructure span. The incident resulted in no structural damage to the bridge. Because no significant impact events have occurred at the site since the new bridge was constructed, it is highly unlikely that the annual frequency of vessel impact ( AFI ) is as high as predicted b y the AASHTO procedure. However, it is unclear which factor in the expression ( N PA PG PF ) contributed most to the divergence from historical data. Considering the likelihood that the AASHTO predicted AFI for the LA 1 Bridge is too large it is not surp rising that the

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288 UF/FDOT estimate for AF which incorporates AFI is also unrealistically high T hus the return period for vessel impact induced collapse of the LA 1 Bridge is very likely longer than reported in Table 9 8 However, insufficient data are available to determine how much longer the return period should be. Additional research that is outside the scope of the current study would be required to state conclusively that the terms included in AFI should be modified, and in what way. However, the retrofit, protection system, and alternative design examples presented in Section 9. 9 demonstrate that, with careful design choices, acceptable levels of risk can reasonably be attained using the exi sting procedures for quantifying AFI in conjunction with the UF/FDOT methodology.

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289 Table 9 1 Vessel traffic for LA 1 Bridge Vessel ID Vessel type Description Average single vessel size (ft) Single vessel capacity (tons) Average barge tow size Tug size (ft) Length LOA (ft) Beam (ft) Total displacement (tons) L W D a # W # L L W D Loaded Light 1 Barge Barge tow 264 50 9/2 3,153 1 1 72 30 7 336 50 4,012 860 2 Barge Barge tow 210 44 9/2 2,194 1 1 72 30 7 282 44 2,899 705 3 Barge Barge tow 195 35 9/2 1,631 1 1 65 24 6 260 35 2,105 474 4 Barge Barge tow 160 42 8/2 1,400 1 1 65 24 6 225 42 1,874 474 5 Barge Barge tow 150 30 8/2 779 1 2 50 20 5 350 30 2,189 631 6 Barge Deck barge 140 40 5 /2 408 1 1 50 20 5 190 40 904 496 7 Barge Barge tow 140 35 7/2 860 1 1 50 20 5 190 35 1,168 309 8 Barge Deck barge 120 30 4/2 154 1 1 50 20 5 170 30 518 364 9 Ship Supply vessel 185 42 11/5 1,020 N/A N/A N/A N/A N/A 185 42 1,870 850 10 Ship Supply vess el 165 36 9/4 650 N/A N/A N/A N/A N/A 165 36 1,168 518 11 Ship Supply vessel 145 36 8/4 456 N/A N/A N/A N/A N/A 145 36 913 456 12 Ship Crew boat 125 24 9/4 331 N/A N/A N/A N/A N/A 125 24 594 263 13 Ship Utility boat 100 28 8/4 245 N/A N/A N/A N/A N/A 10 0 28 489 245 14 Ship Shrimp boat 90 28 12/5 386 N/A N/A N/A N/A N/A 90 28 661 276 15 Ship Crew boat 65 18 5/2 77 N/A N/A N/A N/A N/A 65 18 128 51 16 Ship Shrimp boat 60 18 6/2 95 N/A N/A N/A N/A N/A 60 18 142 47 17 Ship Shrimp boat 30 9 4/2 12 N/A N/A N/A N/A N/A 30 9 24 12 a [loaded draft]/[light draft]

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290 Table 9 2 Aggregated barge traffic data for LA 1 Bridge VG N v i D LOA B M W B VG N v i D LOA B M W B Vessel group Transits per year Velocity (knot) Draft (ft ) Length (ft) Beam (ft) Displacement (tons) Vessel group Transits per year Velocity (knot) Draft (ft) Length (ft) Beam (ft) Displacement (tons) 1 0 4.0 9 336 50 4,012 17 30 5.0 9 336 50 4,012 2 0 4.0 9 282 44 2,899 18 90 5.0 9 282 44 2,899 3 30 4.0 9 26 0 35 2,105 19 50 5.0 9 260 35 2,105 4 150 4.0 8 225 42 1,874 20 40 5.0 8 225 42 1,874 5 10 4.0 8 350 30 2,189 21 280 5.0 8 350 30 2,189 6 80 4.0 5 190 40 904 22 270 5.0 5 190 40 904 7 200 4.0 7 190 35 1,168 23 70 5.0 7 190 35 1,168 8 50 4.0 4 170 30 5 18 24 250 5.0 4 170 30 518 9 30 4.0 7 a 336 50 860 25 0 5.0 7 a 336 50 860 10 90 4.0 7 a 282 44 705 26 0 5.0 7 a 282 44 705 11 50 4.0 6 a 260 35 474 27 30 5.0 6 a 260 35 474 12 40 4.0 6 a 225 42 474 28 150 5.0 6 a 225 42 474 13 280 4.0 5 a 350 30 631 29 10 5.0 5 a 350 30 631 14 270 4.0 5 a 190 40 496 30 80 5.0 5 a 190 40 496 15 70 4.0 5 a 190 35 309 31 200 5.0 5 a 190 35 309 16 250 4.0 5 a 170 30 364 32 50 5.0 5 a 170 30 364 a Draft shown is for the tugboat. Barge draft is 2 ft.

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291 Table 9 3 Minimum lateral pushover capacities ( H ) for each pier Pier number H : Minimum lateral pushover capacity (kips) 2 2,446 3 2,446 4 1,661 96 1,097 97 442 Table 9 4 Barge impact paramet ers for CVIA Pier number (deg) min( B B B P ) (ft) P BY (kip) W B (tons) v Bi (knot) 2 3 0 30.0 48.0 a 5,255 7,569 a 308 4,012 b Varies c 4 20 30.0 34.5 a 3,430 3,734 a 308 4,012 b Varies c 96 97 20 28.0 3,294 308 4,012 b Varies c a Varies by vessel group and pier. See Appe ndix K. b Varies by vessel group. See Table 9 2 c Varies by vessel group and pier. See Table 9 2 and Appendix K for details. Table 9 5 Lateral pier soil stiffness ( k P ) for each LA 1 pier Pier number k P (kip/in.) 2 2,181 3 2,911 4 2,479 96 2,388 97 2,288 Table 9 6 Maximum dynamic impact force ( P Bm ): UF/FDOT m ethods (AVIL) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 7,569 7,569 3,734 3,294 3,294 17 7,569 7,569 3,734 3,294 3,294 2 7,055 7,055 3,734 3,294 3,294 18 7,055 7,055 3,734 3,294 3,294 3 5,898 5,898 3,734 3,294 3,078 19 5,898 5,898 3,734 3,294 3,294 4 6 ,798 6,798 3,734 3,294 2,071 20 6,798 6,798 3,734 3,294 2,106 5 5,255 5,255 3,430 3,294 3,294 21 5,255 5,255 3,430 3,294 3,294 6 5,692 6,175 2,788 1,646 1,358 22 6,540 6,540 3,246 1,735 1,358 7 5,898 5,898 3,170 1,871 1,544 23 5,898 5,898 3,734 1,972 1, 544 8 4,051 4,361 1,777 1,037 1,028 24 5,015 5,255 2,009 1,037 1,028 9 6,011 6,555 3,734 3,294 2,775 25 7,490 7,569 3,734 3,294 3,253 10 5,314 5,781 3,376 2,650 2,038 26 6,611 7,055 3,734 3,115 2,321 11 4,168 4,505 2,639 2,002 1,461 27 5,193 5,613 3,17 9 2,336 1,629 12 4,236 4,601 2,381 1,667 1,042 28 5,264 5,718 2,835 1,890 1,059 13 4,791 5,158 3,430 2,925 2,470 29 5,255 5,255 3,430 3,294 2,913 14 4,216 4,574 2,065 1,219 1,006 30 5,239 5,684 2,404 1,285 1,006 15 3,255 3,518 1,629 961 793 31 4,045 4, 372 2,257 1,014 793 16 3,396 3,656 1,490 869 862 32 4,204 4,525 1,684 869 862

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292 Table 9 7 Protection factors ( PF ) Traffic direction Pier 2 Pier 3 Pier 4 Pier 96 Pier 97 Upbound traffic (VG 1 16) 0.50 0.60 0.20 0.08 0.03 Downbound traffic (VG 17 32) 0.50 0.50 0.10 0.04 0.01 Table 9 8 Summary of risk assessment results for each analysis procedure considered AASHTO (1991) AASHTO (2009) UF/FDOT (CVIA) UF/FDOT (AVIL) Minimum impact load (kip) 106 106 857 793 Average impact load (kip) 1,294 1,193 3,926 3,732 Maximum impact load (kip) 2,565 1,986 7,569 7,569 Average P / H or D / C 0.984 0.910 0.726 0.794 Average PC 0.01153 0.00981 0.190 0.336 Return period (1/ A F ) (yr) 10,020 18,060 7.3 4.8 Table 9 9 Comparison of barge yield forces ( P BY ) for as built and retrofitted designs Pier (deg) min( B B B P ) (ft) Flat footings (as built) Round footings (retrofit) P BY (kip) P BY (kip) 2 3 0 30.0 48.0 a 5,255 7,569 a 2,300 2,840 a 4 20 30.0 34.5 a 3,430 3,734 a 2,300 2,435 a 96 97 20 28.0 3,294 2,240 a Varies by vessel group a nd pier. See Appendix K for details. Table 9 10 Comparison of barge yield forces ( P BY ) for as built and alternative designs Pier (deg) Flat footings (as built) Drilled shafts (redesign) min( B B B P ) (ft) P BY (kip) min( B B B P ) (ft) P BY (kip) 2 3 0 30.0 48.0 a 5,255 7,569 a 10 1,700 4 20 30.0 34.5 a 3,430 3,734 a 10 1,700 96 97 20 28.0 3,294 8 1,640 a Varies by vessel group. See Appendix K for details. Table 9 11 Summary of UF/FDOT (CVIA) risk assessment results for each design considered As built design (flat faced footings) Retrofitted design (rounded footings) Alternative design (drilled shafts) Minimum impact load (kip) 857 721 615 Average impac t load (kip) 3,926 2,129 1,514 Maximum impact load (kip) 7,569 2,840 1,700 Average D / C 0.726 0.656 0.264 Average PC 0.190 0.0567 0.000122 Return period (1/ AF ) (yr) 7.3 28.0 10,230

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293 Figure 9 1 Louisiana Highway 1 (LA 1) Bridge over Bayou Lafourche, Louisiana Figure 9 2 LA 1 Bridge region of interest, showing navigation channel alignment

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294 A B Figure 9 3 High rise portion of LA 1 Bridge, showing piers at risk for impact A) Elevation view. B) Plan view.

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295 A B C D E F G H Figure 9 4 Pier and foundation configurations for LA 1 Bridge A) Piers 2 3. B) Piers 1, 4. C) Section A A. D) Section B B. E) Piers 96 97. F) Piers 95, 98 99. G) Section C C. H) Section D D. A B Figure 9 5 Typical barge impact scenarios, showing possibl e headlog elevations A) Fully loaded barge. B) Empty barge.

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296 Figure 9 6 A B Figure 9 7 Superstructure cross sections for the LA 1 Bridge A) Typical Bulb T girder section. B) Typical plate girder section. Figure 9 8 Locations of soil borings and piers to which each soil p rofile is assigned

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297 A B C D Figure 9 9 FB MultiPier models of selected piers from LA 1 Bridge Figure 9 10 Computing the geometric probability of imp act ( PG ) (from AASHTO 2009)

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298 Figure 9 11 Coupled vessel impact analysis (CVIA) method Figure 9 12 Typical barge impact with pile cap, showing pertinent imp act parameters Figure 9 13 Applied vessel impact load (AVIL) method

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29 9 Figure 9 14 Procedure for computing barge impact force time histories in accordance wi th AVIL method (Consolazio et al. 2008)

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300 A B Figure 9 15 Determination of lateral pier soil stiffness ( k P ) by static analysis A) Undeformed pier. B) Deformed pier.

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301 A B Figure 9 16 Risk analysis results for each pier and vessel group: AASHTO (1991) methods A) Probability of collapse ( PC B) Contribution to annual frequency of collapse ( AF ) (colors are relative to ma ximum contribution among all piers and vessel groups) A B Figure 9 17 Percent contribution to AF : AASHTO (1991) methods A) By pier number. B) By vessel group.

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302 A B Figure 9 18 Risk analysis results for each pie r and vessel group: AASHTO (2009 ) methods A) Probability of collapse ( PC ) (white = 0, green B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 9 19 Percent contribution to AF : AASHTO (2009 ) methods A) By pier number. B) By vessel group.

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303 A B Figure 9 20 Risk analysis results for each pie r and vessel group: UF/FDOT methods CVIA. A) Probability of collapse ( PC red = 1.0) B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 9 21 Percent contribution to AF : UF/FDOT met hods CVIA. A) By pier number. B) By vessel group.

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304 A B Figure 9 22 Risk analysis results for each pie r and vessel group: UF/FDOT methods AVIL. A) Probability of collapse ( PC B) Contribution to annual frequency of collapse ( AF ) (colors are relative to maximum contribution among all piers and vessel groups) A B Figure 9 23 Percent contri bution to AF : UF/FDOT methods AVIL. A) By pier number. B) By vessel group.

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305 A B C Figure 9 24 LA 1 Bridge pier footing end cap retrofit to reduce vessel collision risk (retrofitted end caps indicated i n grey) A) Piers 2 and 3. B) Pier 4. C) Piers 96 and 97. Figure 9 25 Plan view of LA 1 Bridge showing locations of protective dolphin structures

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306 A B C Figure 9 26 LA 1 Bridge alternative design with drilled shaft foundation: piers 2 4 A) Elevation view. B) Section A A. C) Section B B.

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307 A B C Figure 9 27 LA 1 Bridge alternative design with drilled shaft foundation: piers 96 97 A) Elevation view. B) Section A A. C) Section B B.

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308 A B Figure 9 28 Pile founded alternative design with submerged footing and shear wall (pier 4)

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309 CHAPTER 10 CONCLUSIONS AND RE COMMENDATIONS 10.1 Concluding Remarks In the early 1990s, AASHTO published the first set of national design requirements for vessel collision design of bridges in the U.S.: the Guide Specifications and Commentary for Vessel Collision Design of Highway Bridges. Since the original publication, the AASHTO procedures have remained largely unchanged, even though a significant amount of research has been conducted pertaining to vessel collision with bridges, particularly by researchers at the University of Florida (UF ), under sponsorship by the Florida Department of Transportation (FDOT). Revised analysis procedures have been developed based on UF/FDOT research findings that are significant improvements over the corresponding AASHTO provisions, particularly in the area of structural dynamics. Specifically, the UF/FDOT procedures include a more accurate barge impact load prediction model, dynamic and equivalent static structural analysis techniques, and a more rational expression for the probability of bridge collapse ( P C ). In the current study, a series of barge impact experiments were planned, in which a reduced scale (40% scale) barge bow will be impacted (in the future) by a high energy pendulum to achieve barge deformation equivalent to 10 ft at full scale. Once the experiments are complete d the data will serve to validate the UF/FDOT barge impact load model and make it more likely to be adopted by the engineering community. To plan the validation study, impact conditions that help validate past research findings wer e defined, an appropriate experimental model scale was determined, many of the experimental components were designed and fabricated, and instrumentation was selected and procured. Preliminary impact simulations, of the nature that will be used to validate the impact load model, were conducted to facilitate virtually all of the planning decisions.

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310 In support of the planned barge impact experiments, a series of material tests were conducted, in which the stress strain relations and strain rate sensitive prope rties were determined for the materials (ASTM A36 and A1011 steel) from which the reduced scale barge specimens will be fabricated. To conduct high strain rate tests, a novel high rate testing apparatus (HRTA) was designed that employed an impact pendulum to generate the required energy. The HRTA is similar in some ways to impact based devices that employ a heavy flywheel or drop hammer. However, the HRTA design overcame some important limitations that have been observed with such devices in prior material evaluation studies. Additionally. a robust optimization based data processing scheme based on impulse momentum theory (Chapter 4) was developed that permitted extraction of usable test data despite some remaining design limitations. Data quantified from the material testing program were used to develop stress strain relations and strain rate sensitive material parameters based on the Cowper Symonds model. The materials tested in this study were found to be less sensitive to high strain rates than in prior studies conducted on similar materials. However, rate sensitivity was found to be similar among the multiple specimens tested in this study, despite being of different material grades. The material parameters that were quantified from the experimental stu dy were then used in representative finite element constitutive models These constitutive models were then employed in impact simulations of the planned barge impact experiments. Complementing the experimental components of this study a revised vessel co llision risk assessment procedure was developed in which the UF/FDOT barge impact load model, structural analysis procedures, and PC expression were inserted in place of analogous provisions of the AASHTO risk analysis framework. Because the various UF/FDO T methods are specific to or

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311 have only been evaluated for barge impact (and not ship impact), the revised risk assessment procedure includes two analysis tracks: one for ship impact and one for barge impact. For ship impact, all existing AASHTO procedure s were retained, including the AASHTO PC expression. However, for barge impact, the impact load model was replaced with the UF/FDOT model, the PC expression was replaced with the UF/FDOT expression, and the AASHTO static structural analysis approach was re placed with the choice of two UF/FDOT dynamic analysis procedures: coupled vessel impact analysis (CVIA) and applied vessel impact loading (AVIL). The static bracketed impact analysis (SBIA) method was also evaluated but found to be too conservative for us e in the risk assessment procedure, though it can be helpful for initially proportioning structural members during preliminary design stages. Use of the revised UF/FDOT risk assessment procedure was demonstrated by applying it to the calculat ion of annual frequency of bridge collapse ( AF ) for two recently constructed bridges: the SR 300 Bridge over Apalachicola Bay, Florida and the LA 1 Bridge over Bayou Lafourche, Louisiana. For comparison, AF was also computed using both the 1991 and 2009 editions of the AASHTO provisions. For both bridges, AF was found to be significantly higher when using the UF/FDOT procedures than when using the AASHTO procedures. This outcome was a consequence of two primary factors: 1) for piers of the bridges considered, the UF/FDOT barge impact load model typically predicted larger impact forces than the AASHTO load model, and 2) PC values computed using the UF/FDOT expression were higher than those computed using the AASHTO PC expression. As discussed in Chapters 8 and 9, UF/FDOT b arge impact forces were higher than AASHTO for the bridges considered in this study mostly because of the specific structural configuration of the bridge piers. Specifically, the piers in both bridges include wide, flat faced

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312 pile caps (footings) that lie at the waterline and are therefore the most likely pier component to be impacted by barge vessels. Based on the UF/FDOT load model, the footing geometry resulted in larger impact forces than would be generated if the impacted pier surface were rounded or n arrower. In fact, retrofit and alternative design solutions were presented in Chapters 8 and 9 which employed rounded and narrower impact geometry. These retrofits and alternative designs were shown to have dramatically reduced collapse risk (smaller AF ) r elative to the as built designs, and with careful selection of pier geometry, levels of risk were achieved that were similar to or lower than what was predicted by the AASHTO provisions. As noted above, and discussed at length in Chapters 8 and 9, the UF/F DOT PC expression uniformly resulted in higher PC values than the AASHTO expression. This outcome is partially a consequence of higher impact loads associated with the UF/FDOT load model, as discussed above. However, the primary cause of higher PC values w as that, for the majority of impact cases considered in the study (for both bridges), PC was calculated to be equal to 0.0 (zero) using the AASHTO expression. Note that s uch cases commonly involved scenarios in which the impact load was nearly equal to the maximum lateral pier resistance. Assigning a zero PC value to such situations (as AASHTO does) is unrealistic, in that it neglects numerous uncertainties associated with the strength of bridge materials, workmanship in construction, soil strength, impact angle, and dynamic interactions between the barge and bridge. As demonstrated by Davidson et al. (2013), when such factors were properly taken into account, the probability of structural collapse was non zero even for cases in which the deterministically c alculated (expected) impact load was much less than the expected pier resistance. Indeed, the UF/FDOT PC expression was specifically developed to account for these and many other relevant sources of uncertainty in impact loading and structural resistance, and accordingly, PC cannot be equal

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313 to 0.0 using the UF/FDOT expression. Consequently, while the UF/FDOT PC values were higher than the corresponding AASHTO values, the UF/FDOT values are a more rational and representative measure of collapse risk, by virt ue of accounting for unavoidable statistical uncertainties. As discussed at the end of Chapter 9, other terms in the AF expression ( N PA PG and PF ), all of which were directly adopted into the UF/FDOT risk assessment methodology, may over predict the pr obability of occurrence of vessel collision events in certain cases (and potentially all cases). For both example bridge s examined in this study (Chapters 8 and 9), the terms N PA PG and PF were combined to define the annual frequency of impact ( AFI ). B ased on the available risk assessment data, the LA 1 Bridge is expected to undergo a significant vessel impact event approximately once per year ( AFI occurred to date, even though the main bridge piers and spans have been in place in the waterway for more than five years. This finding strongly suggests that, when combined, the terms included in AFI over predict the probability of occurrence of vessel impacts for certain cases, though it is unclear which term cont ributes most strongly to the discrepancy. For the SR 300 Bridge, which has less vessel traffic than the LA 1 Bridge the historical record was not long enough to draw conclusions about the accuracy of AFI As discussed below, additional research is warrant ed in this area. Given these observations, it is critical to point out that UF/FDOT methods predicted a higher level of risk ( AF ) for the bridge cases considered in this study primarily because they both shared similar structural configurations (wide, flat waterline footings) that contributed to this outcome. There are many bridges currently in service (with different structural configurations) for which the UF/FDOT methods may predict a lower level of risk than the AASHTO

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314 provisions. For example, bridges with rounded or relatively narrow impact surface geometry like the retrofit and alternative designs proposed in Chapters 8 and 9 are likely to result in lower risk using UF/FDOT methods. Consequently, implementing the UF/FDOT methodology in bridge design w ill not necessarily result in a widespread increase in construction costs, as could be misconstrued from the results in this study. Instead, by allowing bridge engineers to make intelligent design choices that maximize both safety and economy, widespread i mplementation of the UF/FDOT methods will result in much more uniform distribution of risk among varied bridge configurations than is currently afforded by the AASHTO provisions, without necessarily increasing construction costs. Another major concern in i mplementing the UF/FDOT methods in bridge design has been the necessary use of dynamic structural analysis. This requirement does indeed increase the effort associated with developing an adequate design. However, in preparing the demonstration cases for th is study, the effort required to carry out the required structural analyses was found to be significant but not unreasonable. To carry out the example risk assessments, 208 structural analyses were required for the SR 300 Bridge, and 160 were required for the LA 1 Bridge. Quite clearly, automation of the analysis process in which models were populated with the relevant case specific data, analyzed, and post processed to extract the important data by automated scripts was crucial to completing the analyses i n a timely manner. Once the process was automated, the analyses could be completed within 8 12 hours total using a typical workstation computer. In this study, most of the automation was accomplished using custom developed programs written in the Perl pr ogramming language (Perl 2013). Alternatively, such automation could be programmed with a variety of general purpose languages (e.g., C++, FORTRAN, etc. ) or with more engineering specific tools such as Matlab or even Mathcad. Developing the

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315 automation fram ework was the most time consuming aspect of carrying out the example risk assessments. However, once the framework was developed for the first bridge considered, it was readily and quickly adapted for use on the second bridge case. While creating and debug ging such automation procedures constitutes significant effort on the part of engineers, the level of programming expertise required is relatively modest. Therefore, while the UF/FDOT methods are a significant departure from the current AASHTO provisions, the steps required to implement them could be completed by most bridge engineers without issue. Also, a s recommended below, the transition to UF/FDOT methods could be greatly facilitated by implementing the required automation tasks in design oriented anal ysis packages such as FB MultiPier. The results of this study demonstrate that the state of the art analysis methods developed from UF/FDOT research over the past several years can feasibly be implemented in the design of bridges for vessel collision. The methods produced outcomes that were more rational than the existing AASHTO procedures and that included consideration for many additional factors that are important contributors to barge impact loads and dynamic structural response. Most importantly, it wa s demonstrated that UF/FDOT methods can predict a higher level of risk than the AASHTO procedures for some bridge configurations, while risk levels that are lower than AASHTO predicts can be achieved at similar construction cost by making careful design ch oices. These findings suggest that the UF/FDOT methods can be implemented in bridge design practice without significantly increasing the cost of bridge construction. In doing so, the uniformity of structural safety could be greatly improved for future brid ge designs. 10.2 Recommendations for Bridge Design Recommendation 1: The UF/FDOT vessel collision risk assessment procedure summarized in Chapter 7 and demonstrated in Chapters 8 and 9 should be adopted for use in the

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316 design of future bridges, subject to any mo difications to the barge impact model that may be required based on the results of the planned experiment al validation study (Chapter 3) Recommendation 2: O nly transient dynamic structural analysis methods (CVIA, AVIL, or more refined methods) should be u sed in conjunction with the UF /FDOT risk assessment procedure. Recommendation 3: T he equivalent static analysis method (SBIA) should be used only for preliminary design, because the method is too conservative to be reasonably employed in the context of a r isk assessment. Final structural assessment should be completed using transient dynamic methods (CVIA or AVIL). 10.3 Recommendations for Future Research Recommendation 1: While the reduced scale barge impact experimental program was planned in this study the e xperiments themselves have not yet been carried out. Based on the results of the experiments, modifications to the UF/FDOT load prediction model may be required. If the load model changes, it is suggested that the example risk assessments presented in this study (Chapters 8 and 9) be re evaluated, and the influence that the load model modifications have on the risk of structural collapse should be quantified. Recommendation 2: As discussed in Chapter 7, the UF/FDOT structural analysis methods and PC express ion have only been evaluated for barge impact scenarios, whereas ship impact scenarios are also common for many bridges. Consequently, the risk assessment methodology proposed in Chapter 7 includes two analysis tracks, in which UF/FDOT methods are suggeste d for barge impact, and the existing AASHTO methods are suggested for ship impact. Given the important limitations of the AASHTO methods (highlighted in both current and past studies), further research is suggested in order to: 1) validate the applicabilit y of the

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317 various UF/FDOT methods to ship impact scenarios, or 2) develop similar alternative methods. From such research, a unified, single track risk assessment procedure could be developed. Recommendation 3: Evidence from this study suggests that the AAS HTO risk assessment procedure and by extension, the UF/FDOT procedure may over predict the likelihood that bridges are impacted by errant vessels, which in this study, was expressed as the annual frequency of impact ( AFI ). In this study AFI was computed as the summation of every term in the expression for the annual frequency of collapse ( AF ), excluding PC (i.e., N PA PG and PF ). For one of the bridges considered in this study (the LA 1 Bridge), AFI was found to be much higher than historical evidence wo uld indicate. Therefore, the level of vessel collision risk was likely overestimated by the UF/FDOT risk assessment methods for this case (i.e., the actual risk for collapse is likely less than was calculated) Given these findings, further research is sug gested in order to: 1) compare estimates of AFI to historical records of impact incidents for a wider spectrum of bridges, 2) determine if widespread discrepancies exist, and 3) identify which term in the AFI expression contributes most to any observed dis crepancies. Depending on the outcomes of these suggested investigations, it may be necessary to conduct additional research to gather the relevant data and develop an alternative methodology for estimating AFI Recommendation 4 : A significant amount of the total effort required to carry out the UF/FDOT risk assessments was spent developing an automated analysis framework in which bridge pier finite element models were populated with the relevant case specific impact parameters, analyses were carried out, an d results were post processed to extract data relevant to the risk assessment. Given that 150 200 transient dynamic impact analyses were required to complete the risk assessment for each bridge this automated approach was crucial to completing the asses sments in a timely manner. Analysis automation would be even more critical during the

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318 design of a new bridge, in which case the risk assessment might be conducted multiple times as the design is refined. Therefore, further research is suggested to implemen t similar analysis and data reduction schemes into commercial bridge analysis software. The benefit of this effort would be to reduce the amount of programming that would be required of design engineers in order to implement the UF/FDOT risk analysis metho dology. Given the collaborative research relationship that exists between UF, FDOT, and the Bridge Software Institute (BSI), FB MultiPier would be an ideal candidate software package for this effort.

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319 APPENDIX A REV IEW OF EUROCODE PROCEDURES FOR VESSEL COLLISION Euro pean design and analysis procedures (in accordance with the Eurocode) for vessel collision with bridges are in many ways similar to those prescribed by AASHTO in the U.S. In the Eurocode, vessel collision is classified as an accidental action on structures and is consequently covered in Eurocode 1: Actions on Structures Part 1 7: Accidental Actions (CEN 2006). As with all Eurocode provisions, values for certain design parameters are not explicitly codified within the main Eurocode document. Such parameters are deemed Nationally Determined Parameters (NDPs) and are independently specified by each EU member nation by means of a National Annex (NA). Other nation specific documents may exist to provide further design guidance or recommendations. For example, ves sel collision design in the United Kingdom requires consideration of three (3) documents: BS EN 1991 1 7:2006 Eurocode 1: Actions on Structures Part 1 7: Accidental Actions : The core Eurocode provision, in part, pertaining to vessel collision with bridges This provision may provide indicative design values for NDPs that can be used in lieu of guidance from the appropriate NA. This document is legally binding for all EU member nations. NA to BS EN 1991 1 7:2006 National Annex to Eurocode 1: Actions on Stru ctures Part 1 7: Accidental Actions : UK specific National Annex document, specifying NDPs that are relevant to BS EN 1991 1 7 This document is legally binding for the United Kingdom only. PD 6688 1 7:2009 Recommendations for the Design of Structures to B S EN 1991 1 7 : UK specific document providing additional recommendations pertaining to BS EN 1991 1 7 This document is not regarded as a British Standard, and recommendations provided herein are therefore not legally binding. A.1 Risk Assessment As with the AASHTO provisions, the Eurocode suggests that design for accidental actions (of which vessel collision is one) should be conducted within the context of a comprehensive risk assessment (risk analysis). It should be noted that the Eurocode risk

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320 assessment a pproach is significantly more open ended than the procedure prescribed by AASHTO. Specific procedures related to quantifying risk are left to the discretion of the owner and design team. The risk assessment framework proposed in the Eurocode is summarized in Figure A 1 In general, the process involves iterative qualitative and/or quantitative risk analysis, interspersed with reconsideration of the analysis scope and assumptions and design modifications. As part of each desig n iteration, the risk is re evaluated, allowing the design team to identify economical risk mitigation schemes which may involve: Eliminating or reducing of the hazard by modifying the design concept By passing the hazard by changing the design conc ept or protecting the structure Controlling the hazard by warning systems or monitoring Overcoming the hazard by providing sufficient strength or structural redundancy such that overall struct ural failure does not occur Permitting controlled structural collapse s uch tha t injury or fatality is reduced At the level of detail illustrated in Fig. A 1 the risk assessment may uncover economical means to mitigate risk (e.g., layout changes, protection systems, or warning systems) that are unrelated to structural strength. However, the risk of bridge failure as a result of vessel collision cannot be adequately assessed in a purely qualitative sense. As such, a quantitative risk analysis is necessary. The Eurocode provision EN 1991 1 7:2006 §B.9.2 states that risk (R), in general, can be quantified as a summation of conditional probabilities: ( A 1 ) where is the probability of the i th hazard (of total hazards N H ) occurring in a given time interval (typically one year), is the probability of j th damage state (of total number

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321 N D ) occurring as a result of the the i th hazard, is the p robability of the k th adverse structural performance (of total number N S ) occurring as a result of the j th damage state, and is the consequence of the k th adverse structural performance. Figure A 1 Eurocode risk assessment framework (Source: EN 1991 1 7:2006 §B.1 ) Given the comprehensive nature of this expression, its direct applicability to vessel collision risk analysis is limited. Thus, an expression speci fic to vessel collision is given in §B.9.3.3: ( A 2 ) where P f (T) is the probability of structural failure within a given time period (T), n is the ship traffic int ensity, is the probability of navigation failure per unit traveling distance, p a is the probability that collision can be avoided by human intervention, F dyn is the dynamic impact force

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322 as a function of the coordinate (x) where navigation failure occurred, and R is the structural resistance. Note that if T = 1 year, then P f (T) is the annual frequency of collapse (parameter AF in the AASHTO provisions). While §C.4 proposes load models to quantify F dyn (described below), the provision provides no guidance into how F dyn is influenced by the position of navigation failure (x). Furthermore no Eurocode provision, National Annex, or other official document provides guidance on quantifying p a or the probability that F dyn exceeds R. Sufficient records are typically available to estimate traffic intensity (n). Consequently, implementation of the above expression would require a significant degree of judgment and/or very sophisticated prob abilistic analysis. A.2 Risk Acceptance Criteria As part of any risk assessment, risk acceptance criteria must be set forth which define (usually quantitatively) the maximum reasonable risk to the public of injury or death posed by a given structural hazard. S uch criteria can be based on monetary loss (including repair and litigation costs), loss of life, or annual probabilities of structural failure. Most commonly, acceptable probabilities for structural failure (or damage) are set forth by government agencies and industry groups. For example, AASHTO specifies that the annual frequency of bridge collapse due to vessel collision should be, at most, 0.001 for non critical bridges, and 0.0001 for critical bridges. In other words, structural failure should, on aver age, occur once every 1,000 years for non critical bridges and once every 10,000 years for critical bridges. In the Eurocode provisions ( EN 1991 1 7:2006 ), no value is specified for the acceptable frequency of bridge collapse due to vessel collision. Euroc ode §3.2(1) states: Levels of acceptable risks may be given in the National Annex as non contradictory, complementary information.

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323 Additionally, §B.5(4) states: Acceptance criteria may be determined from certain national regulations and requirements, certa in codes and standards, or from experience and/or theoretical knowledge that may be used as a basis for decisions on acceptable risk. Acceptance criteria may be expressed qualitatively or numerically. One quantitative risk acceptance scheme is provided in §B.4.2, primarily for illustration purposes, not as a direct recommendation (Fig. A 2 ). Note that, in this example, the maximum acceptable probability of structural collapse is 0.00001 (1 in 100,000 years), which is 10 times more stringent than the AASHTO requirement for critical structures. Larger maximum acceptable probabilities are assigned to less severe consequences. Given the ambiguity associated with this important parameter, the British National Annex to EN 1991 1 7:2 006 ( NA to BS EN 1991 1 7:2006 ) was consulted for further guidance. Note that the British NA is the only readily available NA to EN 1991 1 7:2006 in English. §NA.2.3 (Level of acceptable risk) states: The level of acceptable risk should be determined on a project specific basis. Recommendations for acceptable risk levels for road, footway, and cycletrack bridges are contained in PD 6688 1 7 Thus, British Published Document PD 6688 1 7 was consulted for such recommended values. §2.3.1 of PD 6688 1 7 (Levels of acceptable risk) states: The design of bridge support structures should ensure that the risks of an HGV [Heavy Goods Vehicle] s triking a bridge support and causing structural collapse are as low as reasonably practicable (ALARP) taking account of site conditions.

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324 Figure A 2 Possible numerical risk acceptance scheme (Source: EN 1991 1 7:2006 §B.4.2 ) This provision is the only section in PD 6688 1 7 pertaining to risk accep tance criteria, and the language is specifically targeted at impact by Heavy Goods Vehicles (HGVs) and other vehicular traffic. In fact, no additional guidance for any parameter related to waterway vessel impact is provided in either NA to BS EN 1991 1 7:2 006 or PD 6688 1 7 All sections of the NA pertaining to vessel collision refer back to the main Eurocode provision ( EN 1991 1 7:2006 ). For example, §NA.2.38 (Dynamic impact forces from seagoing ships) reads: Values of frontal and lateral dynamic impact fo rces from seagoing ships should be agreed for the individual project. The recommended and indicative value may be used for preliminary design.

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325 Thus, final design ship impact forces are to be determined at the discretion of the design team and owner. This p attern is consistent for virtually all British NA sections. In a few cases, the EN 1991 1 7:2006 indicative value is simply accepted, without allowing for project specific determination (e.g., friction coefficient for glancing impact). Consequently, as it pertains to vessel impact, the NA to BS EN 1991 1 7:2006 and PD 6688 1 7 documents are unnecessary. The core Eurocode ( EN 1991 1 7:2006 ), combined with the judgment of the engineers and owner, are legally sufficient to define all vessel impact risk and str uctural demand parameters. A.3 Vessel Impact Forces on Bridge Piers Eurocode EN 1991 1 7:2006 provides a fairly comprehensive treatment of vessel (barge and ship) impact loading on bridge piers. The provisions are similar, in many ways, to the AASHTO provision s. However, additional emphasis is placed on dynamic structural analysis. In rigid, and all kinetic energy is absorbed by elastic or plastic deformation of the v essel (§C.4.1). In lieu of dynamic analysis, indicative static force values are provided for both inland waterway vessels (Table C.3) and seagoing vessels (Table C.4). These two tables have been adapted here in Table A 1 and Ta ble A 2 respectively. Note that two independent impact cases are considered as part of Eurocode analysis: head on impact (Fig. A 3 ) and glancing (lateral) impact (Fig. A 4 ). In the head on case, force F dx (as defined in Tables A 1 and A 2 ) is applied perpendicular to the bridge superstructure. In the glancing case, F dy is applied parallel to the super structure, and a friction force (F R = F dy ) is applied perpendicular to the superstructure. Friction coefficient, is taken to be 0.4.

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326 More refined methods are provided for computing both barge and ship impact forces, and, to some extent, force time his tories for dynamic analysis. Such procedures are detailed below and, where possible, compared to forces predicted by the AASHTO provisions. Table A 1 Indicative values for dynamic forces d ue to ship impact on inland waterways (adapted from EN 1991 1 7:2006 ) Class Ship type Length: l (m) Mass: m (ton) Force: F dx (kN) Force: F dy (kN) I 30 50 200 400 2,000 1,000 II 50 60 400 650 3,000 1,500 III 60 80 650 1,000 4,000 2,000 IV 80 90 1,000 1,500 5,000 2,500 Va Big ship 90 110 1,500 3,000 8,000 3,500 Vb Tow + 2 barges 110 180 3,000 6,000 10,000 4,000 VIa Tow + 2 barges 110 180 3,000 6,000 10,000 4,000 VIb Tow + 4 barges 110 190 6,000 12,000 14,000 5,000 VIc Tow + 6 barges 190 280 10,000 18,0000 17,000 8,000 VII Tow + 9 barges 300 14,000 27,000 20,000 10,000 Table A 2 Indicative values for dynamic forces due to ship impact for s ea waterways (adapted from EN 1991 1 7:2006 ) Class Length: l (m) Mass: m (ton) Force: F dx (kN) Force: F dy (kN) Small 50 3,000 30,000 15,000 Medium 100 10,000 80,000 40,000 Large 200 40,000 240,000 120,000 Very large 300 100,000 460,000 230,000 A B Figure A 3 Eurocode head on impact case. A) Impact condition. B) Load case.

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327 A B Figure A 4 Eurocode glancing (lateral) impact case. A) Impact condition. B) Load case. A.3.1 Barge Impact Both the AASHTO and Eurocode provisions utilize the barge force deformation relationship proposed by Meier Drnberg (1983), but with slightly varying formulations. In the Eurocode, all barge kinetic energy is assumed to be absorbed by the bridge pier through elastic and/or plastic deformation during head on impact. Thus, deformation energy (E def ) is simply equal to the kinetic energy, and peak dynamic impact force ( F dyn ) can be computed as: ( A 3 ) where F dyn is in MN and E def is in MNm. E def can simply be calculated as the initial kinetic energy of the impacting vessel: ( A 4 )

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328 where v rd is the impact velocity (3 m/s is recommended, increased by water velocity), and m is the sum of the vessel mass (m 1 ) and hydrodynamic mass (m hydr ). For head on impact, m hydr is taken as 10% of m 1 Thus, For static analysis, it is recommended that F dyn be multiplied by a dynamic magnification factor of 1.3. The magnified F dyn is then applied as shown in Figure A 3 as F dx The AASHTO impact force expression can also be expressed as a function of kinetic energy, and is shown in comparison to the Eurocode expression in Figure A 5 (Eurocode quantities have b een converted to U.S. customary units). Note that the Eurocode F dyn is lower than the AASHTO P B (in the plastic range). However, once magnified by 1.3, Eurocode forces are higher than AASHTO. Figure A 5 Head on barge impact force comparison: AASHTO vs. Eurocode For glancing (lateral) impact, forces are computed using the F dyn (E def ) expression above. However, E def is reduced based on the impact angle, (recall Fig. A 4 ): ( A 5 ) where E a is the total kinetic energy. As with head on impact, E a is computed as:

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329 ( A 6 ) However, for lateral impact: ( A 7 ) For cases in which is not known, can be assumed as 20. For static analysis, the Eurocode suggests a dynamic magnification factor of 1.7 for glancing impact. The magnified F dyn is applied as shown in Figure A 4 as F dy A friction force (F R = F dy ) is also a pplied, where = 0.4. For dynamic analysis, a priori formation of the impact force time history is suggested. Force histories differ, depending on whether the plastic force (5 MN) is exceeded. Sample elastic and plastic force histories are given in the co de (shown in Fig. A 6 ). Note that no expressions are provided to quantify important time quantities (e.g., t r t e t p ). However, these quantities can be derived, as needed, using energy and momentum conservation laws. Figur e A 6 Eurocode sample force time histories (reproduced from EN 1991 1 7:2006 )

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330 A.3.2 Ship Impact For ship impact, the AASHTO and Eurocode provisions differ substantially. The ship loa d model proposed in AASHTO is based upon impact tests conducted by Woisin (1976), whereas the Eurocode provisions use a newer model proposed by Pedersen (1993). The Pedersen ship impact load (F bow ) is computed as: ( A 8 ) where: F bow is the maximum bow collision force (MN) F o is the reference collision force = 210 MN E imp is the energy absorbed by plastic deformations L pp is the length of the vessel (m) m x is the mass plus hydrodynamic mass (10 6 kg) v o is the initial vessel speed = 5 m/s For dynamic analysis, the impact duration (T o ) can be computed as: ( A 9 ) However, no guidance is provided as to the shape of the load history curve. Given the significant difference in formulation between the AASHTO and Eurocode ship impact force models, a direct graphical comparison (as shown in Figure A 5 for barge impact) cannot be readily produced.

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331 APPENDIX B DERIVATION OF SCALE MODEL SIMILITUDE EXPRESSIONS In this appendix, an energy similitude expression is derived using the Buckingham theorem (Jones 1997). Consider barge impac t with a rigid object. The magnitude of impact force ( P ) is a function of a variety of system variables: ( B 1 ) where f y is the yield strength of the barge steel, is barge b ow deformation, w is the width of the impacted object, and h is a representative barge dimension (e.g., a plate thickness). As such, there are k = 4 system variables ( f y , w, h ). The force length time (FLT) reference unit system is chosen, but none of th e relevant variables are time dependent. Thus, there are r = 2 reference variables (F and L). The Buckingham theorem states that the problem can be described using r + 1 = 3 dimensionless groups of variables ( groups) such that: ( B 2 ) where represents an arbitrary function. To form each group, choose k r = 2 repeating variables from among the list of system variables. In this case, f y and h are chosen. Thus: ( B 3 ) By inspection or by more systematic means, the groups are formed by arranging the dependent variables into dimensionless combinations. For this case: ( B 4 ) Consequently,

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332 ( B 5 ) Once derived, the groups can be used to compute scale factors that relate model scale physical quantities (denoted with the subscript m ) to full scale physical quantities (d enoted with the subscripts fs ). Consider a reduced scale barge impact experiment in which the length scale factor is A scale factor for impact force ( P ) can be derived using from above. Because is dimensionless, ( B 6 ) Rearranging: ( B 7 ) In most experiments, material parameters cannot be scaled along with the dimensions, thus f y,fs /f y,m = 1. Recall h fs / h m = Therefore: ( B 8 ) Therefore, forces measured during a reduced scale model can be multiplied by a factor of 2 to obtain equivalent full scale forces. Repeating a similar derivation, it can be shown that barge bow deformations ( ) are related by: ( B 9 ) Combining Eqns. B 8 and B 9 a scaling expression for deformation energy ( E ) is derived: ( B 10 )

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333 APPENDIX C PENDULUM BASED HIGH RATE TEST APPARATUS (HRTA) FABRICATION DRAWINGS

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358 APPENDIX D DEMONSTRATION OF IMPULSE MOMENTUM THEORY FOR MULTIPLE DEGREE OF FREEDOM (MDF) SYSTEMS As discussed in Chapter 4, the high r ate material testing apparatus (HRTA) drive line was designed to respond as a single degree of freedom (SDF) system, and instrumentation for the device was selected accordingly. However, flexibility in the connections between various parts of the HRTA caus ed it to respond as a multiple degree of freedom (MDF) system instead. Consequently, an alternative data interpretation procedure was developed (Section 4. 2 .2.2) that is based on impulse momentum theory. The derivation presented in this appendix demonstrat es that the impulse momentum data interpretation is indeed valid for MDF systems with an arbitrary number of degrees of freedom that are anchored by a single point. Consider the damped MDF system shown in Fig. D 1 A cons isting of four masses ( m 1 m 4 ), each connected by springs ( k 1 k 4 ) and dashpots ( c 1 c 4 ). The system (initially at rest) is subjected to dynamic excitation by a time varying force, F S ( t ), which is equal to the resultant force imparted by the specimen du ring a high rate material test (equal to the specimen stress times its original cross sectional area). The resulting free body diagrams of each mass are shown in Fig. D 1 B A B Figure D 1 Four degree of freedom system with damping, subject to dynamic excitation by time varying specimen resultant force F S ( t ). A) Schematic of MDF system. B) Free body diagrams for each mass.

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359 In accordance with Fig. D 1 B four equilibrium equations are defined: ( D 1 ) ( D 2 ) ( D 3 ) ( D 4 ) Setting the right hand sides of Eqn s D and D 2 equal to each other, and rearranging: ( D 5 ) Setting the right hand sides of Eqn s D 5 and D 3 equal to each other, and rearranging: ( D 6 ) Setting the right hand sides of Eqn s D 6 and D 4 equal to eac h other, and rearranging: ( D 7 ) Because the load cell in the HRTA measures the total reaction force, F R ( t ), including both the stiffness and damping components: ( D 8 ) Substituting Eqn. D 8 into Eqn. D 7 : ( D 9 ) It is readily observed from the repeated pattern of steps above that Eqn. D 9 can be generalized to be valid for any arbitrary number of degrees of freedom ( N DOF ): ( D 10 ) Integrating Eqn. D 10 over the interval [ t 1 t 2 ]:

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360 ( D 11 ) where t 1 is a time immediately prior to specimen extension, and t 2 is a time well after the specimen has broken and all oscillation in the HRTA has ceased. For these conditions, e valuating the integral produces : ( D 12 ) Because for all degrees of freedom i N DOF ( D 13 ) The resulting equation (Eqn. D 13 ) is exactly the same as Eqn. 4.5, which is the theor etical basis for the data processing procedure presented in Chapter 4. Therefore, even though flexibility in the various connections of the HRTA caused it to respond as an MDF system, the data processing procedure presented in Chapter 4 is valid.

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361 APPENDIX E SENSITIV ITY OF REDUCED SCALE BARGE IMPACT SIMULATION RESULTS TO STEEL FAILURE STRAIN As discussed in Chapter 4, one of the constitutive model parameters that must be considered in the finite element (FE) validation simulations is the strain at which material failu re occurs. In LS DYNA, material failure is simulated by deleting individual finite elements from the model when the effective plastic strain exceeds a specified value. As noted in Chapter 4, in MAT_24 the FE constitutive ( material ) model employed to for th e steel barge components in this study a value for failure strain must be selected that is constant with respect to strain rate, even though increased ductility was observed in material evaluations performed in this study at higher strain rates. Table E 1 summarizes minimum and maximum failure strains quantified from the experimental study, where the minimum was observed for testing rate R1, and the maximum was observed for testing rate R8. The purpose of this appendix is to evaluate the influence of failure strain on the results of reduced scale barge impact simulations for the range of failure strains shown in Table E 1 Table E 1 Effective plastic strain at failure for each material series Material series Effective plastic strain at failure (in./in.) Minimum (R1) Maximum (R8) Mean A1011 T11 0.342 0.384 0.363 A1011 T15 0.280 0.336 0.308 A36 T25 0. 206 0.340 0.273 E.1 Barge Impact Simulations To evaluate the sensitivity of response to failure strain impact simulations were conducted that were consistent with the impact conditions expected during the planned pendulum experiments. As shown in Fig. E 1 the simulations consisted of a 9,000 lbf rigid impact block and the fully deformable 0.4 scale barge bow model. For simplicity, the impact block was

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362 assigned roller type translating boundary conditions that only permit motion in the x direction, and barge nodes at the rear most interface were assi gned fixed boundary conditions To initiate each impact simulation, the impact block was assigned an initial velocity equal to 39.3 ft/s, which corresponds to a pen dulum drop height of 24 ft. Subsequently, the block model impacted the barge bow model, causing several inches of bow deformation and ultimately arresting block motion. Elastic rebound of the barge bow caused the impact block motion to reverse, and contact between the objects eventually ceased. Recall that, in the planned experiments, multiple successive impacts will be required in order to achieve the target bow deformation (48 in.). However, for this investigation, only one impact was simulated. Steel pla tes and structural members in the FE barge model were assigned one of the three constitutive models developed in Chapter 4 ( A1011 T11 A1011 T15 A36 T25 ), depending upon which material specification the part in question will be constructed from in the phy sical 0.4 scale barge specimens. Three simulations were conducted for this investigation, in which the failure strain in each FE constitutive model was set equal to the: 1) minimum, 2) mean, and 3) maximum values shown in Table E 1 A B Figure E 1 Finite element impact simulation of 0.4 scale barge b ow. A) Elevation view. B) Plan view.

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363 E.2 Results and Discussion Maximum barge bow deformations for the th ree simulations are compared in Fig. E No significant qualitative differences are observed among the three simulations. For each case, deformation of the exterior of the barge was do minated by hull plate buckling Interior members (frames and trusses) failed by inelastic buckling. Y ielding was observed throughout the damaged region, accompanied by some localized fracture (characterized in the FE model by element deletion) As might be expected, the largest number of elements (342) failed in the model with the minimum failure strain, while 211 and 148 elements failed in the models with the mean and maximum failure strain, respectively. Nearly all of the failed elements were located in the exterior hull plates, particularly the headlo g plate (on the leading edge of the barge bow). Widespread fracture did not occur in the internal structural elements for any of the simulations. Fig. E 3 compares barge bow force deformation curves that were developed based on the simulation results. As shown, impact forces were nearly identical for deformations up to 1 in. At larger deformations, impact forces diverged, but remained in a similar range (250 400 kips). Differences observed between each case can be attributed to relatively small differences in the degree of material fracture. Because fractures were concentrated in localized regions, differences in the total impact force generated on the barge model were not significant. Indeed each of the three force deformati on curves intersected and crossed over the others multiple times during the course of the impact event, indicating that there was no notable correlation between failure strain and the magnitude of impact forces. The most notable difference between the forc e deformation curves is the maximum barge bow deformation. As expected, the model with the minimum failure strain experienced the largest bow deformation (8.3 in.), while the models with mean and maximum failure strains had smaller peak deformations equal to 7.9 in. and 7.5 in., respectively.

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364 A B C Figure E 2 Comparison of barge bow deformation after one impact A) Minimum failure strain. B) Mean failure strain. C) Maximum failure strain Figure E 3 Barge bow force deformation comparison

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365 In general, differences observed between the three simulations were fairly modest, and therefore the impact simulation results computed i n this study can be considered relatively insensitive to the choice of failure strain. Over the full range of failure strains considered, impact forces and barge bow deformations differed by 10% or less, with the mean failure strain model falling approxima tely in the middle. Therefore, if mean values for failure strain are selected for use in the validation simulations, the magnitude of error introduced by this approximation is approximately 5%. For the analysis of such a complex structural system under se vere impact loading, this level of error was deemed acceptable, and therefore the mean failure strains shown in Table E 1 were employed in the FE constitutive models for all simulations of reduced scale barge impact in t his study.

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366 APPENDIX F REDUCED SCALE (0.4 SCALE) BARGE BOW FABRICATION DRAWINGS

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392 APPENDIX G BARGE BOW REACTION FRAME FABRICATION DRAWINGS

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405 APPENDIX H UNIVERSAL PENDULUM FOUNDATION FABRICATION DRAWINGS

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425 APPENDIX I CONSIDERATION OF LRFD APPROACH TO VESSEL COLLISION DESIGN A literature review was c arried out pertaining to the development of LRFD design procedures for vessel collision. The following sections summarize the design philosophy of the existing AASHTO design procedures for vessel impact and compare this to the overall analysis methodologie s employed by Nowak (1999) to calibrate the dead, live, and vehicle impact load factors in the AASHTO LRFD code, and Nowak et al. (2008) to calibrate the resistance factors in ACI 318. I.1 AASHTO Vessel Collision Risk Assessment In general, the annual frequen cy of bridge collapse (AF) is computed as: ( I 1 ) where N is the number of vessel transits, PA is the probability of aberrancy, PG is the geometric probability, PC is the prob ability of collapse, and PF is a protection factor. However, because AF is the annual frequency of bridge collapse (not pier collapse), it is computed as a sum of the annual frequency of pier collapse for each pier within the navigation zone (6 x LOA range centered on the transit path). Furthermore, vastly different vessel types navigate most waterways. Thus, the pier annual frequency of collapse is computed for each vessel type (vessel group) that traverses the bridge. Consequently, in practice, AF is com puted as: ( I 2 ) where N VG is the total number of vessel groups, and N P is the number of piers in the navigation zone. Thus, AF is the total annual probability of a ny pier in the bridge collapsing as a result of all possible vessel impact scenarios.

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426 In the AASHTO provisions, AF is limited to a specific value based on the relative importance of the bridge (0.001 for typical bridges, and 0.0001 for critical bridges). I n other words, the acceptable return period for bridge failure from vessel collision is 1,000 years for typical bridges and 10,000 years for critical bridges. I.2 LRFD Calibration Methodology While the AASHTO risk acceptance criterion for vessel collision is b ased on structural reliability (probabilistic) principles, it is quite different in nature to LRFD criteria used for other loading conditions. For more common loading conditions (e.g., dead, live, wind), acceptance criteria that are used to derive load and resistance factors are based on acceptable probabilities of member failure within the design life of the structure (Nowak 1999; Nowak et al. 2008). Specifically, the goal of any LRFD procedure is to develop load factors ( i ) and resistance factors ( ) such that: ( I 3 ) where R n is the nominal member resistance (e.g., moment) computed based on the code prescribed procedure, and Q i ar e load effects. During LRFD calibration, and i are chosen such that the target member reliability is achieved. Reliability is typically quantified by probabilistic analysis of perhaps hundreds of structures that have been designed using current code pro cedures (Nowak 1999; Nowak et al. 2008). To perform reliability analysis, consider a particular limit state function (g): ( I 4 ) where R is the member resistance, a nd Q is the load effect. In this form, member failure occurs when Q > R. Thus, the probability of failure p f is defined as: ( I 5 )

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427 Let the R and Q be defined as ran dom variables with mean R and Q respectively. Thus, the limit state can be redefined as a random variable (Z), corresponding to the safety margin, as follows: ( I 6 ) The objective of LRFD calibration then is to choose and i such that: ( I 7 ) for all possible combinations of load effects. The target probability of failure is chosen based on the design life of the structure (75 years for bridges), and a target reliability index ( T ) where: ( I 8 ) 1 represents in the inverse cumulat ive distribution function (CDF) for a standard normal distribution. The target value for T set forth by AASHTO is 3.5 for a 75 year design life. Thus, if designed according to the AASHTO LRFD code, all bridge members should be expected to have a probabili ty of failure no higher than 0.00023 in the 75 year design life (assuming that the safety margin, Z, is Gaussian distributed). I.3 Applicability of LRFD Procedures to AASHTO Acceptable Vessel Collision Risk Both procedures detailed above AASHTO vessel collisio n risk assessment, and typical LRFD calibration are based on probabilistic assessment of structural response to variable loads. However, there are important differences between the risk acceptance criteria and overall design philosophy that make transferen ce of the current procedure (or UF/FDOT proposed procedure) to an LRFD procedure difficult. Foremost is the difference between bridge reliability (central to the AASHTO vessel collision procedure) and bridge member reliability (central to LRFD). For illust ration purposes, assume that the existing AASHTO vessel collision procedure is exactly correct, and annual

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428 bridge failure frequencies (AF) are equal to 0.001 or 0.0001 (depending on bridge importance). Therefore, the 1 year probability of failure is ( ) is equal to 0.001 or 0.0001. However, LRFD calibration is performed using the 75 year probability ( ) where: ( I 9 ) Thus, the LRFD style reliability index ( can simply be computed as: ( I 10 ) Computed in this manner, the 75 year is equal to only 1.44 for typical bridges (AF = 0.001) and 2.43 for critical bridges (A F = 0.0001). Both reliability indices are far lower than the AASHTO stated target of = 3.5 for other load conditions. The very low reliability is a consequence of the difference between failure acceptance. The existing AASHTO AF quantity is based upon br idge failure, while LRFD is based on member failure. Assume instead that we base the LRFD style calibration on pier failure instead of bridge failure year probability of fai lure ( ) is dependent on the number of bridge piers in the navigation zone (N P ) such that: ( I 11 ) Note that the above expression assumes uniform risk distribution among all the piers in the navigation zone. Recall that the navigation zone is defined by a 6 x LOA wide region, centered on the navigation channel. Consequently, the reliability index can now be computed as: ( I 12 )

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429 The above expression demonstrates that is strongly dependent on the number of piers that can reasonably expect to be struck (N P ). Thus, reliability indices were computed for a range of N P and reported in Table I 1 Note values increase dramatically when reliability is assessed based on pier failure, rather than bridge failure. values range from 1.78 2.67 for typical bridges, and 2.67 3.37 for critical bridges. Note that still, 75 year values fall short of the 3.5 target set forth by AASHTO. Table I 1 Pier reliability index (75 year ) for various numbers of piers Number of piers in navigation zone (6 x LOA wide) for typical bridges (AF = 0.001) for critical bridges (AF = 0.0001) 2 1.78 2.67 4 2.08 2.90 6 2.24 3.02 8 2.35 3.11 10 2.43 3.17 12 2.50 3.23 14 2.55 3.27 16 2.60 3.31 18 2.64 3.34 20 2.67 3.37 Of course, the process of computing reliability indices (and resulting load factors) that is most consistent with past LRFD calibration efforts (No wak 1999, Nowak et al. 2008) is to directly compute bridge member reliabilities (not bridge or pier reliabilities). Interestingly, it might be that, if pier reliabilities are in the 2.0 3.0 range, member reliabilities are notably higher (perhaps equal to or higher than the target 3.5), because piers are a conglomeration of many structural members. However, prohibiting member failure is a stricter design standard than prohibiting pier collapse, because multiple members can exceed the design capacity withou t the pier collapsing. Thus, these two effects may offset each other, resulting in individual member reliabilities that are on par with the pier reliability (or even lower).

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430 I.4 Summary Unfortunately, there is no simple process of transference between the exis ting AASHTO bridge based reliability assessment and a more traditional member based assessment. Note that even the more rational PC expression developed by recently by UF/FDOT ( Consolazio et al. 2010 a ) is based upon pier failure, not individual member fail ure. Thus, to develop load factors that ensure similar member reliability to the other AASHTO LRFD load conditions, many reliability analyses (perhaps 100 or more) would be required. Such reliability assessments would need to include nonlinear dynamic stru ctural analyses, similar to those conducted by UF/FDOT ( Consolazio et al. 2010 a ). Aside from the computational effort that would be required, the process of forming load factors is cumbersome. Unlike dead loads or live loads, vessel collision loads are hig hly variable because of a variety of factors: vessel traffic, route geometry, structural configuration, etc. Thus, two options are possible in forming load factors: O PTION 1. Develop load factors that encompass these uncertainties. Such load factors could become very large (thus very conservative ), but the design process would probably be much simpler than it is currently, or; O PTION 2 Develop load factors that are dependent on these uncertainties (i.e., variable load factors). This would significantly red uce conservatism relative to Option 1, but the design process would probably be effectively as complicated as the current process. Option 1 above is probably not practical, given the likely conservatism. The only benefit to Option 2 is that the load formul ation would be based upon member reliability rather than bridge reliability, which is more consistent with other loading conditions considered in the AASHTO LRFD code. Typical LRFD calibration procedures are compared to the existing AASHTO vessel collision methodology in Table I 2 for the purpose of summarizing potential obstacles in

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431 applying LRFD principles to the vessel collision problem. Many of these issues have been discussed in detail above. Table I 2 Comparison of LRFD and AASHTO vessel collision design methodologies Typical LRFD provisions AASHTO vessel collision provisions Based on member by member assessment of (factored resistance > factored load effec ts) Based on structural collapse assessment of the full bridge Load effects on individual members are permitted to exceed the factored resistance. Load and resistance factors are formulated such that the probability of member failure is below a maximum target value within the lifetime of the structure (typically 75 years for bridges). Structural risk assessment ensures that the probability of bridge failure is held below a target annual frequency (1/1,000 or 1/10,000). Probabilistic descriptions of loa ds exist in literature for use in reliability analysis (e.g., for code calibration). Probabilistic descriptions of loads do not exist for use in reliability analysis. Expensive reliability analysis including dynamic simulations is required. Loads and loa d probabilities are fairly similar for most structures (based on use). Loads and load probabilities vary considerably between structures, based on vessel traffic, bridge layout, etc. Code calibration can (and should) be executed using structures designed in accordance with the existing design provisions. No structures have been designed in accordance with UF/FDOT proposed changes to vessel collision design. In the opinion of the author, developing an LRFD vessel collision design procedure may exceed the intended scope of the current project: develop revised design procedures that incorporate recent UF/FDOT research findings. By developing an LRFD procedure, not only would UF/FDOT research be incorporated into the design code, but the fundamental risk acc eptance criteria would be dramatically altered. Depending on the opinions of AASHTO committee members, this might impede adoption of the revised design provisions, relative to more targeted changes. Furthermore, the complicated reliability analyses includi ng dynamic analysis would need to be analyzed multiple times (once for each trial combination of load

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432 factors), and more cases are probably necessary for proper calibration. Recent UF/FDOT research findings can instead be more easily incorporated into the existing AASHTO design framework (considering overall bridge reliability). Therefore, it is proposed that incremental changes to the existing design procedure be executed that reflect UF/FDOT research findings

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433 APPENDIX J SR 300 BRIDGE VESSEL COLLISION RISK ASSES SMENT DATA In this appendix, detailed data are presented for vessel collision risk assessments of the Bryant Grady Patton Bridge (SR 300) over Apalachicola Bay, Florida. The associated risk assessments are discussed in Chapter 8. Tables J 1 J 18 present risk assessment input parameters and results for every combination of pier (35 60) and vessel group (1 11). Figures J 1 J 26 show barge impact force time histories computed by the CVIA and AVIL analysis methods for each combination of pier (35 60) and barge vessel group (1 8). See Chapter 8 for descriptions of piers and vessel groups. Table J 1 Vessel impact velocities ( v i ) (knots) VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.02 1.82 2.63 3.83 5.31 2 1.00 1.00 1.00 1.00 1.00 1.00 1.08 1.53 1.99 2.45 2.91 3.59 4.44 3 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.38 1.94 2.51 3.35 4.40 4 1.00 1.00 1.00 1.00 1.00 1.08 1.48 1.89 2.30 2.70 3.11 3.71 4.46 5 1.00 1.00 1.12 1.57 2.02 2.48 2.93 3.38 3.83 4.28 4.74 5.41 6.24 6 1.23 1.53 1.84 2.14 2.45 2.75 3.06 3.36 3.67 3.97 4. 28 4.73 5.29 7 1.00 1.00 1.00 1.24 1.63 2.02 2.41 2.80 3.19 3.58 3.97 4.54 5.26 8 1.00 1.00 1.28 1.63 1.98 2.33 2.69 3.04 3.39 3.75 4.10 4.62 5.27 9 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 5.37 10 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 6.47 11 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 6.86 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 5.31 3.83 2.63 1.82 1.02 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2 4.44 3.59 2.91 2.45 1.99 1.53 1.08 1.00 1.00 1.00 1.00 1.00 1.00 3 4.40 3.35 2.51 1.94 1.38 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 4 4.46 3.71 3.11 2.70 2.30 1.89 1.48 1.08 1.00 1.00 1.00 1.00 1.00 5 6.24 5.41 4.74 4.28 3.83 3.38 2.93 2.48 2.02 1.57 1.12 1.00 1.00 6 5.29 4.73 4.28 3.97 3.67 3.36 3.06 2.75 2.45 2.14 1.84 1.53 1.23 7 5.26 4.54 3.97 3.58 3.19 2.80 2.41 2.02 1.63 1.24 1.00 1.00 1.00 8 5.27 4.62 4.10 3.75 3.39 3.04 2.69 2.33 1.98 1.63 1.28 1.00 1.00 9 5.37 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 10 6.47 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 11 6.86 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

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434 Table J 2 Geometric probability of impact ( PG ) VG P3 5 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.006 0.018 0.059 0.127 2 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.004 0.009 0.019 0.035 0.069 0.106 3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.009 0.023 0.062 0.116 4 0.000 0.000 0.000 0.000 0.000 0.001 0.003 0.006 0.013 0.023 0.038 0.065 0.091 5 0.000 0.000 0.001 0.002 0.003 0.006 0.009 0.014 0.022 0.031 0.041 0.056 0.068 6 0.001 0.002 0.003 0.005 0.007 0.011 0.016 0.021 0.029 0.037 0.044 0.056 0.064 7 0.000 0.000 0.000 0.001 0.002 0.004 0.007 0.012 0.020 0.028 0.038 0.055 0.068 8 0.000 0.001 0.001 0.003 0.004 0.008 0.013 0.019 0.028 0.038 0.049 0.066 0.079 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 .000 0.107 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.151 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.139 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.127 0.059 0.018 0.00 6 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2 0.106 0.069 0.035 0.019 0.009 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.000 3 0.116 0.062 0.023 0.009 0.003 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 0.091 0.065 0.038 0.023 0.013 0.006 0.003 0.001 0.000 0.000 0.000 0.000 0.000 5 0.068 0.056 0.041 0.031 0.022 0.014 0.009 0.006 0.003 0.002 0.001 0.000 0.000 6 0.064 0.056 0.044 0.037 0.029 0.021 0.016 0.011 0.007 0.005 0.003 0.002 0.001 7 0.068 0.055 0.038 0.028 0.020 0.012 0.007 0.004 0.002 0.001 0.000 0.000 0.000 8 0.079 0.066 0.049 0.038 0.028 0.019 0.013 0.008 0.004 0.003 0.001 0.001 0.000 9 0.107 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.151 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.139 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Table J 3 Vessel impact forces (kips): AASHTO (1991) methods VG P35 P36 P37 P38 P39 P40 P4 1 P42 P43 P44 P45 P46 P47 1 367 367 367 367 367 367 367 367 380 1,209 2,032 2,102 2,216 2 1,230 1,230 1,230 1,230 1,230 1,230 1,419 2,335 2,384 2,444 2,513 2,628 2,790 3 1,219 1,219 1,219 1,219 1,219 1,219 1,219 1,219 2,011 2,069 2,143 2,275 2,470 4 2, 145 2,144 2,144 2,143 2,143 2,149 2,206 2,278 2,362 2,456 2,559 2,723 2,942 5 669 669 836 1,633 2,033 2,067 2,107 2,152 2,201 2,255 2,312 2,403 2,523 6 2,494 2,541 2,596 2,658 2,726 2,799 2,878 2,960 3,045 3,134 3,225 3,364 3,542 7 1,801 1,801 1,801 1,8 31 1,892 1,966 2,050 2,143 2,243 2,350 2,461 2,634 2,858 8 2,924 2,923 2,998 3,110 3,240 3,347 3,486 3,633 3,790 3,951 4,116 4,365 4,682 9 240 240 240 240 240 240 240 240 240 240 240 240 1,291 10 258 258 258 258 258 258 258 258 258 258 258 258 1,670 11 198 198 198 198 198 198 198 198 198 198 198 198 1,358 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 2,216 2,102 2,032 1,209 380 367 367 367 367 367 367 367 367 2 2,790 2,628 2,513 2,444 2,384 2,335 1,419 1,230 1,230 1,230 1,230 1,230 1,230 3 2,470 2,275 2,143 2,069 2,011 1,219 1,219 1,219 1,219 1,219 1,219 1,219 1,219 4 2,942 2,723 2,559 2,456 2,362 2,278 2,206 2,149 2,143 2,143 2,144 2,144 2,145 5 2,523 2,403 2,312 2,255 2,201 2,152 2,107 2,067 2,033 1,633 836 669 669 6 3,542 3,364 3,225 3,134 3,045 2,960 2,878 2,799 2,726 2,658 2,596 2,541 2,494 7 2,858 2,634 2,461 2,350 2,243 2,143 2,050 1,966 1,892 1,831 1,801 1,801 1,801 8 4,682 4,365 4,116 3,951 3,790 3,633 3,486 3,347 3,240 3,110 2,998 2,923 2,924 9 1,291 240 240 240 240 240 240 240 240 240 240 240 240 10 1,670 258 258 258 258 258 258 258 258 258 258 258 258 11 1,358 198 198 198 198 198 198 198 198 198 198 198 198

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435 Table J 4 Capacity demand ratios ( H / P ): AASHTO (1 991) methods VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 2.93 2.93 2.93 4.09 4.09 6.27 6.27 6.27 7.24 2.27 1.35 1.55 1.47 2 0.87 0.87 0.87 1.22 1.22 1.87 1.62 0.99 1.15 1.13 1.09 1.24 1.17 3 0.88 0.88 0.88 1.23 1.23 1.89 1.89 1.89 1.37 1.33 1.28 1.43 1.32 4 0.50 0.50 0.50 0.70 0.70 1.07 1.04 1.01 1.16 1.12 1.07 1.20 1.11 5 1.61 1.61 1.29 0.92 0.74 1.11 1.09 1.07 1.25 1.22 1.19 1.35 1.29 6 0.43 0.42 0.41 0.56 0.55 0.82 0.80 0.78 0.90 0.88 0.85 0.97 0.92 7 0.60 0.60 0.60 0.82 0.79 1.17 1.1 2 1.07 1.23 1.17 1.12 1.24 1.14 8 0.37 0.37 0.36 0.48 0.46 0.69 0.66 0.63 0.73 0.70 0.67 0.75 0.70 9 4.47 4.47 4.47 6.24 6.24 9.57 9.57 9.57 11.45 11.45 11.45 13.55 2.52 10 4.16 4.16 4.16 5.81 5.81 8.91 8.91 8.91 10.65 10.65 10.65 12.61 1.95 11 5.43 5. 43 5.43 7.58 7.58 11.62 11.62 11.62 13.89 13.89 13.89 16.44 2.40 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 1.47 1.55 1.35 2.27 7.24 6.27 6.27 6.27 4.09 4.09 2.93 2.93 2.93 2 1.17 1.24 1.09 1.13 1.15 0.99 1.62 1.87 1.22 1.22 0.87 0.87 0.87 3 1.32 1.43 1.28 1.33 1.37 1.89 1.89 1.89 1.23 1.23 0.88 0.88 0.88 4 1.11 1.20 1.07 1.12 1.16 1.01 1.04 1.07 0.70 0.70 0.50 0.50 0.50 5 1.29 1.35 1.19 1.22 1.25 1.07 1.09 1.11 0.74 0.92 1.29 1.61 1.61 6 0.92 0.97 0.85 0.88 0.90 0.78 0.80 0.82 0.55 0.5 6 0.41 0.42 0.43 7 1.14 1.24 1.12 1.17 1.23 1.07 1.12 1.17 0.79 0.82 0.60 0.60 0.60 8 0.70 0.75 0.67 0.70 0.73 0.63 0.66 0.69 0.46 0.48 0.36 0.37 0.37 9 2.52 13.55 11.45 11.45 11.45 9.57 9.57 9.57 6.24 6.24 4.47 4.47 4.47 10 1.95 12.61 10.65 10.65 10.6 5 8.91 8.91 8.91 5.81 5.81 4.16 4.16 4.16 11 2.40 16.44 13.89 13.89 13.89 11.62 11.62 11.62 7.58 7.58 5.43 5.43 5.43 Table J 5 Probability of collapse ( PC ): AASHTO (1991) methods VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 5 0.000 0.000 0.000 0.009 0.029 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6 0.063 0.064 0.065 0.048 0.050 0.020 0.022 0.025 0.011 0.014 0.016 0.004 0.009 7 0.000 0.000 0.000 0.020 0.023 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 8 0.000 0.000 0.071 0.058 0.060 0.035 0.038 0.041 0.030 0.034 0.037 0.028 0.034 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.000 0.000 0.000 0.000 0.0 00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.029 0.009 0.000 0.000 0.000 6 0.009 0.004 0.016 0.014 0.011 0.025 0.022 0.020 0.050 0.048 0.065 0.064 0.063 7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.023 0.020 0.000 0.000 0.000 8 0.034 0.028 0.037 0.034 0.030 0.041 0.038 0.035 0.060 0.058 0.071 0.000 0.000 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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436 Table J 6 Vessel impact forces (kips): AASHTO (2009) methods VG P35 P36 P37 P38 P39 P40 P41 P4 2 P43 P44 P45 P46 P47 1 367 367 367 367 367 367 367 367 380 1,209 1,415 1,485 1,599 2 1,230 1,230 1,230 1,230 1,230 1,230 1,387 1,425 1,475 1,534 1,603 1,719 1,880 3 1,219 1,219 1,219 1,219 1,219 1,219 1,219 1,219 1,410 1,468 1,541 1,674 1,868 4 1,412 1,412 1,411 1,410 1,410 1,417 1,474 1,546 1,630 1,724 1,826 1,990 2,209 5 669 669 836 1,393 1,421 1,455 1,494 1,539 1,588 1,642 1,699 1,790 1,910 6 1,438 1,485 1,539 1,602 1,670 1,743 1,822 1,904 1,989 2,078 2,169 2,308 2,486 7 1,408 1,408 1,408 1,438 1 ,499 1,573 1,657 1,750 1,850 1,957 2,068 2,241 2,465 8 1,482 1,482 1,557 1,669 1,798 1,905 2,044 2,192 2,348 2,509 2,674 2,924 3,241 9 240 240 240 240 240 240 240 240 240 240 240 240 1,291 10 258 258 258 258 258 258 258 258 258 258 258 258 1,670 11 198 198 198 198 198 198 198 198 198 198 198 198 1,358 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 1,599 1,485 1,415 1,209 380 367 367 367 367 367 367 367 367 2 1,880 1,719 1,603 1,534 1,475 1,425 1,387 1,230 1,230 1,230 1,230 1,230 1,230 3 1, 868 1,674 1,541 1,468 1,410 1,219 1,219 1,219 1,219 1,219 1,219 1,219 1,219 4 2,209 1,990 1,826 1,724 1,630 1,546 1,474 1,417 1,410 1,410 1,411 1,412 1,412 5 1,910 1,790 1,699 1,642 1,588 1,539 1,494 1,455 1,421 1,393 836 669 669 6 2,486 2,308 2,169 2,0 78 1,989 1,904 1,822 1,743 1,670 1,602 1,539 1,485 1,438 7 2,465 2,241 2,068 1,957 1,850 1,750 1,657 1,573 1,499 1,438 1,408 1,408 1,408 8 3,241 2,924 2,674 2,509 2,348 2,192 2,044 1,905 1,798 1,669 1,557 1,482 1,482 9 1,291 240 240 240 240 240 240 240 240 240 240 240 240 10 1,670 258 258 258 258 258 258 258 258 258 258 258 258 11 1,358 198 198 198 198 198 198 198 198 198 198 198 198 Table J 7 Capacity demand ratios ( H / P ): AASHTO (2009) methods VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 2.93 2.93 2.93 4.09 4.09 6.27 6.27 6.27 7.24 2.27 1.94 2.19 2.04 2 0.87 0.87 0.87 1.22 1.22 1.87 1.66 1.61 1.86 1.79 1.72 1.89 1.73 3 0.88 0.88 0.88 1.23 1.23 1.89 1.89 1.89 1.95 1.87 1.78 1.94 1.74 4 0.76 0.76 0.76 1.06 1.06 1.62 1.56 1.49 1.69 1.60 1.51 1.64 1.47 5 1.61 1.61 1.29 1.08 1.06 1.58 1.54 1.49 1.73 1.67 1.62 1.82 1.70 6 0.75 0.72 0.70 0.94 0.90 1.32 1.26 1.21 1.38 1.32 1.27 1.41 1.31 7 0.76 0.76 0.76 1.04 1.00 1.46 1.39 1.3 1 1.49 1.41 1.33 1.45 1.32 8 0.73 0.73 0.69 0.90 0.83 1.21 1.13 1.05 1.17 1.10 1.03 1.11 1.00 9 4.47 4.47 4.47 6.24 6.24 9.57 9.57 9.57 11.45 11.45 11.45 13.55 2.52 10 4.16 4.16 4.16 5.81 5.81 8.91 8.91 8.91 10.65 10.65 10.65 12.61 1.95 11 5.43 5.43 5. 43 7.58 7.58 11.62 11.62 11.62 13.89 13.89 13.89 16.44 2.40 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 2.04 2.19 1.94 2.27 7.24 6.27 6.27 6.27 4.09 4.09 2.93 2.93 2.93 2 1.73 1.89 1.72 1.79 1.86 1.61 1.66 1.87 1.22 1.22 0.87 0.87 0.87 3 1 .74 1.94 1.78 1.87 1.95 1.89 1.89 1.89 1.23 1.23 0.88 0.88 0.88 4 1.47 1.64 1.51 1.60 1.69 1.49 1.56 1.62 1.06 1.06 0.76 0.76 0.76 5 1.70 1.82 1.62 1.67 1.73 1.49 1.54 1.58 1.06 1.08 1.29 1.61 1.61 6 1.31 1.41 1.27 1.32 1.38 1.21 1.26 1.32 0.90 0.94 0.7 0 0.72 0.75 7 1.32 1.45 1.33 1.41 1.49 1.31 1.39 1.46 1.00 1.04 0.76 0.76 0.76 8 1.00 1.11 1.03 1.10 1.17 1.05 1.13 1.21 0.83 0.90 0.69 0.73 0.73 9 2.52 13.55 11.45 11.45 11.45 9.57 9.57 9.57 6.24 6.24 4.47 4.47 4.47 10 1.95 12.61 10.65 10.65 10.65 8.9 1 8.91 8.91 5.81 5.81 4.16 4.16 4.16 11 2.40 16.44 13.89 13.89 13.89 11.62 11.62 11.62 7.58 7.58 5.43 5.43 5.43

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437 Table J 8 Probability of collapse ( PC ): AASHTO (2009) methods VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0. 000 0.000 0.000 0.000 0.000 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6 0.028 0.031 0.034 0.007 0.011 0.000 0.000 0.000 0.000 0.000 0.0 00 0.000 0.000 7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 8 0.000 0.000 0.034 0.011 0.018 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.000 0.000 0.000 0.000 0.000 0 .000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0. 000 0.000 0.000 0.000 0.000 0.000 5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.011 0.007 0.034 0.031 0.028 7 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0 00 0.000 0.000 0.000 8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.018 0.011 0.034 0.000 0.000 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0 00 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Table J 9 Maximum vessel impact forces (kips): UF/FDOT methods (CVIA) VG P35 P36 P37 P38 P39 P40 P4 1 P42 P43 P44 P45 P46 P47 1 1,044 997 992 1,023 1,018 1,300 1,297 1,284 1,424 2,508 3,148 3,148 3,148 2 1,965 1,962 1,663 2,100 2,066 2,352 2,518 3,145 3,148 3,148 3,148 3,148 3,148 3 1,959 1,955 1,658 2,093 2,059 2,340 2,363 2,325 3,148 3,148 3,148 3,1 48 3,148 4 2,418 2,345 1,975 2,547 2,507 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 5 1,483 1,473 1,392 2,141 2,449 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 6 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 7 2 ,429 2,349 1,980 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 8 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 9 240 240 240 240 240 240 240 240 240 240 240 240 1,291 10 258 258 258 258 258 258 258 258 258 2 58 258 258 1,670 11 198 198 198 198 198 198 198 198 198 198 198 198 1,358 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 3,148 3,148 3,148 2,585 1,447 1,308 1,292 1,289 1,018 1,029 1,006 1,076 1,123 2 3,148 3,148 3,148 3,148 3,148 3,148 2,472 2,429 2,092 2,100 1,836 2,075 2,081 3 3,148 3,148 3,148 3,148 3,148 2,371 2,322 2,417 2,085 2,093 1,831 2,069 2,074 4 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,534 2,554 2,268 2,518 2,555 5 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,514 2,146 1,565 1,581 1,588 6 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 7 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,274 2,525 2,555 8 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2 ,555 2,555 9 1,291 240 240 240 240 240 240 240 240 240 240 240 240 10 1,670 258 258 258 258 258 258 258 258 258 258 258 258 11 1,358 198 198 198 198 198 198 198 198 198 198 198 198

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438 Table J 10 Demand capacity ratios ( D / C ): UF/FDOT methods (CVIA). Cases highlighted in grey indicate that D / C was controlled by pier column demands rather than pile demands VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.468 0.470 0.569 0.440 0.457 0. 389 0.402 0.399 0.336 0.563 0.683 0.677 0.695 2 0.751 0.758 0.901 0.679 0.689 0.558 0.618 0.806 0.702 0.763 0.722 0.677 0.694 3 0.749 0.754 0.900 0.677 0.686 0.557 0.576 0.563 0.646 0.757 0.720 0.677 0.694 4 0.904 0.911 0.960 0.840 0.853 0.757 0.836 0.8 85 0.708 0.765 0.724 0.677 0.695 5 0.544 0.544 0.795 0.750 0.898 0.877 0.877 0.894 0.716 0.769 0.727 0.680 0.696 6 0.926 0.978 1.000 0.978 0.968 0.882 0.878 0.894 0.716 0.769 0.726 0.680 0.695 7 0.904 0.911 0.963 0.843 0.914 0.876 0.875 0.893 0.714 0.76 8 0.726 0.679 0.695 8 0.973 0.985 1.000 0.925 0.953 0.881 0.877 0.894 0.715 0.768 0.726 0.679 0.695 9 --------------------------10 --------------------------11 --------------------------VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.587 0.648 0.660 0.542 0.325 0.391 0.460 0.376 0.503 0.474 0.509 0.460 0.463 2 0.586 0.648 0.691 0.682 0.671 0.801 0.659 0.539 0.724 0.709 0.874 0.750 0.739 3 0.586 0.648 0.688 0.676 0.628 0.566 0.623 0.539 0.719 0.704 0.870 0.748 0.735 4 0.586 0.648 0.692 0.684 0.676 0.858 0.857 0.684 0.850 0.842 0.934 0.898 0.890 5 0.587 0.651 0.694 0.689 0.683 0.871 0.878 0.827 0.874 0.780 0.751 0.555 0.550 6 0.587 0.650 0.693 0.688 0.683 0.871 0.879 0.829 0.960 0.983 0.993 0.943 0.890 7 0.587 0.650 0.693 0.688 0.682 0.869 0.877 0.823 0.888 0.843 0.935 0.898 0.890 8 0.587 0.650 0.693 0.689 0.682 0.871 0.877 0.828 0.948 0.938 0.988 0.938 0.950 9 -------------------------10 --------------------------11 --------------------------Table J 11 Probability of collapse ( PC ): UF/FDOT methods (CVIA). Cases high lighted in grey indicate PC = 1 VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.001 0.001 0.004 0.001 0.001 0.000 0.000 0.000 0.000 0.004 0.017 0.016 0.020 2 0.041 0.044 0.285 0.016 0.018 0.003 0.007 0.082 0.021 0.048 0.028 0.015 0.019 3 0.03 9 0.042 0.281 0.015 0.017 0.003 0.004 0.004 0.010 0.044 0.027 0.015 0.019 4 0.295 0.325 0.613 0.129 0.152 0.044 0.122 0.231 0.023 0.049 0.028 0.016 0.019 5 0.003 0.003 0.072 0.040 0.275 0.208 0.209 0.260 0.026 0.051 0.030 0.016 0.020 6 0.395 0.769 1.000 0.769 0.676 0.223 0.211 0.260 0.026 0.051 0.029 0.016 0.020 7 0.295 0.325 0.633 0.134 0.338 0.205 0.203 0.258 0.025 0.051 0.029 0.016 0.020 8 0.721 0.848 1.000 0.389 0.556 0.220 0.209 0.260 0.025 0.051 0.029 0.016 0.020 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.005 0.011 0.012 0.003 0.000 0.000 0.001 0.000 0.002 0.001 0.002 0.001 0.001 2 0.005 0.011 0.019 0.017 0.014 0.077 0.012 0.003 0.029 0.024 0.200 0.040 0.035 3 0.005 0.011 0.018 0.015 0.008 0.004 0.008 0.003 0.027 0.022 0.190 0.039 0.033 4 0.005 0.011 0.019 0.017 0.015 0.162 0.160 0.017 0.147 0.132 0.436 0.272 0.247 5 0.005 0.011 0.019 0.018 0.017 0.192 0.211 0.108 0.201 0.059 0.041 0.003 0.003 6 0.005 0.011 0.019 0.018 0.017 0.192 0.214 0.111 0.613 0.821 0.935 0.488 0.247 7 0.005 0.011 0.019 0.018 0.016 0.189 0.208 0.103 0.239 0.134 0.443 0.272 0.247 8 0.005 0.011 0.019 0.018 0.017 0.192 0.209 0.110 0.521 0.457 0.876 0.457 0.538 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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439 Table J 12 Maximum vessel impact forces (kips): UF/FDO T methods (AVIL) VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 1,298 1,297 1,197 1,335 1,345 1,539 1,528 1,427 1,630 2,770 3,148 3,148 3,148 2 2,388 2,387 2,203 2,456 2,474 2,831 3,028 3,148 3,148 3,148 3,148 3,148 3,148 3 2,378 2,376 2,193 2 ,445 2,463 2,818 2,799 2,614 3,148 3,148 3,148 3,148 3,148 4 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 5 1,755 1,755 1,811 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 6 2,555 2,555 2,555 2,555 2,555 3, 148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 7 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 8 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 9 240 240 240 240 240 240 240 240 240 240 240 2 40 1,291 10 258 258 258 258 258 258 258 258 258 258 258 258 1,670 11 198 198 198 198 198 198 198 198 198 198 198 198 1,358 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 3,148 3,148 3,148 2,692 1,486 1,420 1,527 1,538 1,361 1,362 1,345 1,377 1,390 2 3,148 3,148 3,148 3,148 3,148 3,148 3,026 2,830 2,504 2,506 2,474 2,534 2,555 3 3,148 3,148 3,148 3,148 3,148 2,600 2,797 2,818 2,493 2,495 2,463 2,522 2,545 4 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 5 3,14 8 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,034 1,862 1,879 6 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 7 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 8 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 9 1,291 240 240 240 240 240 240 240 240 240 240 240 240 10 1,670 258 258 258 258 258 258 258 258 258 258 258 258 11 1,358 198 198 198 198 198 198 198 198 198 198 198 198 Table J 13 Demand capacity ratios ( D / C ): UF/FDOT methods (AVIL). Cases highlighted in grey indicate that D / C was controlled by pier column demands rather than pile demands VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P 44 P45 P46 P47 1 0.481 0.524 0.669 0.513 0.543 0.447 0.510 0.434 0.378 0.625 0.712 0.678 0.696 2 0.889 0.905 1.000 0.802 0.846 0.709 0.758 0.877 0.708 0.764 0.724 0.678 0.695 3 0.883 0.903 1.000 0.799 0.843 0.706 0.708 0.662 0.688 0.761 0.721 0.678 0.69 5 4 0.950 0.978 1.000 0.890 0.913 0.848 0.861 0.887 0.710 0.765 0.725 0.679 0.695 5 0.650 0.678 0.930 0.943 0.955 0.882 0.878 0.894 0.717 0.769 0.728 0.680 0.697 6 0.985 1.000 1.000 0.983 0.968 0.883 0.879 0.894 0.717 0.769 0.727 0.680 0.696 7 0.950 0. 978 1.000 0.943 0.955 0.880 0.876 0.893 0.716 0.768 0.726 0.680 0.696 8 0.985 0.995 1.000 0.973 0.963 0.882 0.877 0.893 0.716 0.769 0.727 0.680 0.696 9 --------------------------10 -------------------------11 --------------------------VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.587 0.649 0.677 0.556 0.321 0.410 0.558 0.437 0.595 0.561 0.685 0.524 0.495 2 0.587 0.649 0.690 0.682 0.670 0.844 0.802 0.658 0.846 0.827 1.000 0.888 0.885 3 0.587 0.649 0.686 0.676 0.641 0.629 0.758 0.656 0.846 0.826 1.000 0.888 0.879 4 0.587 0.649 0.691 0.684 0.676 0.858 0.871 0.793 0.884 0.908 1.000 0.948 0.930 5 0.587 0.652 0.693 0.689 0.683 0.871 0.879 0.828 0.955 0.958 0.905 0 .674 0.651 6 0.587 0.651 0.693 0.689 0.683 0.871 0.879 0.828 0.963 0.988 0.993 0.993 0.970 7 0.587 0.651 0.693 0.688 0.682 0.869 0.877 0.827 0.950 0.988 0.998 0.948 0.933 8 0.587 0.651 0.693 0.688 0.682 0.869 0.878 0.828 0.960 0.980 0.993 0.963 0.955 9 --------------------------10 --------------------------11 --------------------------

PAGE 440

440 Table J 14 Probability of collapse ( PC ): UF/FDOT methods (AVIL). Cases highlighted in grey indicate PC = 1 VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.001 0.002 0.014 0.002 0.003 0.001 0.002 0.001 0.000 0.008 0.024 0.016 0.020 2 0.243 0.300 1.000 0.078 0.139 0.024 0.044 0.208 0.023 0.048 0.029 0.016 0.020 3 0.224 0.290 1.000 0.076 0.133 0.023 0.023 0.013 0.018 0.046 0.028 0.016 0.020 4 0.538 0.769 1.000 0.247 0.334 0.143 0.169 0.238 0.024 0.049 0.029 0.016 0.020 5 0.011 0.016 0.415 0.488 0.574 0.221 0.211 0.260 0.026 0.051 0.030 0.016 0.020 6 0.848 1.000 1.000 0.821 0.676 0.226 0.214 0.260 0.026 0.051 0.030 0.016 0.020 7 0.538 0.769 1.000 0.488 0.574 0.217 0.206 0.256 0.026 0.050 0.029 0.016 0.020 8 0.848 0.966 1.000 0.721 0.633 0.223 0.209 0.258 0.026 0.051 0 .030 0.016 0.020 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.005 0.011 0.015 0.003 0.000 0.000 0.003 0.001 0.005 0.003 0.017 0.002 0.001 2 0.005 0.011 0.018 0.017 0.014 0.136 0.078 0.012 0.139 0.108 1.000 0.239 0.231 3 0.005 0.011 0.017 0.015 0.010 0.008 0.044 0.012 0.139 0.107 1.000 0.239 0.213 4 0.005 0.011 0.019 0.017 0.015 0.163 0.192 0.070 0.229 0.310 1.000 0.521 0.415 5 0.005 0.011 0.019 0.018 0.017 0.192 0.214 0.111 0.574 0.593 0.300 0.015 0.011 6 0.005 0.011 0.019 0.018 0.017 0.192 0.214 0.111 0.633 0.876 0.935 0.935 0.698 7 0.005 0.011 0.019 0.018 0.016 0.188 0.209 0.108 0.538 0.876 0.998 0.521 0.429 8 0.005 0.011 0.019 0.018 0.016 0.189 0.212 0.111 0.613 0.795 0.935 0.633 0.574 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 .000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Table J 1 5 Maximum vessel impact forces (kips): UF/FDOT methods (SBIA) VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 1,298 1,297 1,197 1,335 1,345 1,539 1,528 1,427 1,630 2,770 3,148 3,148 3,148 2 2,388 2,387 2,203 2,456 2,474 2,831 3,028 3,148 3 ,148 3,148 3,148 3,148 3,148 3 2,378 2,376 2,193 2,445 2,463 2,818 2,799 2,614 3,148 3,148 3,148 3,148 3,148 4 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 5 1,755 1,755 1,811 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3, 148 3,148 3,148 6 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 7 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 8 2,555 2,555 2,555 2,555 2,555 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,1 48 9 240 240 240 240 240 240 240 240 240 240 240 240 1,291 10 258 258 258 258 258 258 258 258 258 258 258 258 1,670 11 198 198 198 198 198 198 198 198 198 198 198 198 1,358 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 3,148 3,148 3,148 2,6 92 1,486 1,420 1,527 1,538 1,361 1,362 1,345 1,377 1,390 2 3,148 3,148 3,148 3,148 3,148 3,148 3,026 2,830 2,504 2,506 2,474 2,534 2,555 3 3,148 3,148 3,148 3,148 3,148 2,600 2,797 2,818 2,493 2,495 2,463 2,522 2,545 4 3,148 3,148 3,148 3,148 3,148 3,14 8 3,148 3,148 2,555 2,555 2,555 2,555 2,555 5 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,034 1,862 1,879 6 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 7 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 8 3,148 3,148 3,148 3,148 3,148 3,148 3,148 3,148 2,555 2,555 2,555 2,555 2,555 9 1,291 240 240 240 240 240 240 240 240 240 240 240 240 10 1,670 258 258 258 258 258 258 258 258 258 258 258 258 11 1,358 198 198 198 198 198 198 198 198 198 198 198 198

PAGE 441

441 Table J 16 Demand capacity ratios ( D / C ): UF/FDOT methods (SBIA). Cases highlighted in grey indicate that D / C was controlled by pier column demands rather than pi le demands VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.968 0.975 0.950 0.803 0.792 0.605 0.675 0.833 0.510 0.834 0.958 0.910 0.913 2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.902 0.924 0.958 0.910 0.913 3 1.000 1.000 1.000 1.000 1 .000 1.000 1.000 1.000 0.902 0.924 0.958 0.910 0.913 4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.902 0.924 0.958 0.910 0.913 5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.902 0.924 0.958 0.910 0.913 6 1.000 1.000 1.000 1.000 1.000 1.000 1. 000 1.000 0.902 0.924 0.958 0.910 0.913 7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.902 0.924 0.958 0.910 0.913 8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.902 0.924 0.958 0.910 0.913 9 --------------------------10 --------------------------11 --------------------------VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.913 0.910 0.958 0.834 0.510 0.833 0.675 0.605 0.792 0.803 0.950 0.975 0.968 2 0.9 13 0.910 0.958 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 3 0.913 0.910 0.958 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 4 0.913 0.910 0.958 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5 0.913 0.910 0.95 8 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 6 0.913 0.910 0.958 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 7 0.913 0.910 0.958 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 8 0.913 0.910 0.958 0.924 0.902 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 9 --------------------------10 --------------------------11 --------------------------Table J 17 Probability of collapse ( PC ): UF/FDOT methods (SBIA). Cases highlighted in grey indicate PC = 1 VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 0.676 0.745 0.538 0.079 0.069 0.006 0.015 0.117 0.002 0.119 0.593 0.319 0.334 2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 8 1.000 1.00 0 1.000 1.000 1.000 1.000 1.000 1.000 0.289 0.383 0.593 0.319 0.334 9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.0 00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 0.334 0.319 0.593 0.119 0.002 0.117 0.015 0.006 0.069 0.079 0.538 0.745 0.676 2 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 3 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 4 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 6 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 7 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 8 0.334 0.319 0.593 0.383 0.289 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 9 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

PAGE 442

442 Table J 18 Protection factor ( PF ) VG P35 P36 P37 P38 P39 P40 P41 P42 P43 P44 P45 P46 P47 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5 0.029 0.045 0.081 0.136 0.212 0.309 0.460 0.579 0.726 0.864 0.964 0.986 1.000 6 0.026 0.040 0.072 0.120 0.188 0.274 0.408 0.514 0.644 0.767 0.964 0.986 1.000 7 0.014 0.021 0.038 0.065 0.101 0.147 0.219 0.275 0.345 0.411 0.964 0.986 1.000 8 0.001 0.001 0.002 0.003 0.005 0.008 0.012 0.015 0.018 0.022 0 .964 0.986 1.000 9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 0.025 0.039 0.071 0.119 0.185 0.270 0.403 0.507 0.635 0.756 0.964 0.986 1.000 VG P48 P49 P50 P51 P52 P53 P54 P55 P56 P57 P58 P59 P60 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5 1.000 1.000 1.000 1.000 0.989 0.977 0.933 0.864 0.692 0.460 0.184 0.045 0.006 6 1.000 0.888 0.888 0.888 0.878 0.867 0.828 0.767 0.614 0.408 0.163 0.040 0.006 7 1.000 0.475 0.475 0.475 0.470 0.464 0.443 0.411 0.329 0.219 0.087 0.021 0.003 8 1.000 0.025 0.025 0.025 0.025 0.024 0.023 0.022 0.017 0.012 0.005 0.001 0.000 9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 .000 1.000 1.000 1.000 10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 1.000 0.875 0.875 0.875 0.866 0.855 0.817 0.756 0.605 0.403 0.161 0.039 0.005

PAGE 443

443 A B C D E F G H Figure J 1 Impact force time histories: SR 300 Bridge, Pier 35 A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 444

444 A B C D E F G H Figure J 2 Impact force time histories : SR 300 Bridge, Pier 36. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 445

445 A B C D E F G H Figure J 3 Impact force time histories : SR 300 Bridge, Pier 37. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 446

446 A B C D E F G H Figure J 4 Impact force time histories : SR 300 Bridge, Pier 38. A) VG1 B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 447

447 A B C D E F G H Figure J 5 Impact force time histories : SR 300 Bridge, Pier 39. A) VG1. B) VG2. C) VG3. D) VG4. E) V G5. F) VG6. G) VG7. H) VG8.

PAGE 448

448 A B C D E F G H Figure J 6 Impact force time histories : SR 300 Bridge, Pier 40. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 449

449 A B C D E F G H Figure J 7 Impact force time histories : SR 300 Bridge, Pier 41. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 450

450 A B C D E F G H Figure J 8 Impact force time histories : SR 300 Bridge, Pier 42. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 451

451 A B C D E F G H Figure J 9 Impact force time histories : SR 300 Bridge, Pier 43. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 452

452 A B C D E F G H Figure J 10 Impact force time histories : SR 300 Bridge, Pier 44. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 453

453 A B C D E F G H Figure J 11 Impact forc e time histories : SR 300 Bridge, Pier 45. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 454

454 A B C D E F G H Figure J 12 Impact force time histories : SR 300 Brid ge, Pier 46. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 455

455 A B C D E F G H Figure J 13 Impact force time histories : SR 300 Bridge, Pier 47. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 456

456 A B C D E F G H Figure J 14 Impact force time histories : SR 300 Bridge, Pier 48. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG 6. G) VG7. H) VG8.

PAGE 457

457 A B C D E F G H Figure J 15 Impact force time histories : SR 300 Bridge, Pier 49. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 458

458 A B C D E F G H Figure J 16 Impact force time histories : SR 300 Bridge, Pier 50. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 459

459 A B C D E F G H Figur e J 17 Impact force time histories : SR 300 Bridge, Pier 51. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 460

460 A B C D E F G H Figure J 18 Impact force time histories : SR 300 Bridge, Pier 52. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 461

461 A B C D E F G H Figure J 19 Impact force time histories : SR 300 Bridge, Pier 53. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 462

462 A B C D E F G H Figure J 20 Impact force tim e histories : SR 300 Bridge, Pier 54. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 463

463 A B C D E F G H Figure J 21 Impact force time histories : SR 300 Bridge, P ier 55. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 464

464 A B C D E F G H Figure J 22 Impact force time histories : SR 300 Bridge, Pier 56. A) VG1. B) VG2. C) VG 3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 465

465 A B C D E F G H Figure J 23 Impact force time histories : SR 300 Bridge, Pier 57. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 466

466 A B C D E F G H Figure J 24 Impact force time histories : SR 300 Bridge, Pier 58. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 467

467 A B C D E F G H Figure J 25 Impact force time histories : SR 300 Bridge, Pier 59. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 468

468 A B C D E F G H Figure J 26 Impact force time histories : SR 300 Bridge, Pier 60. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 469

469 APPENDIX K LA 1 BRIDGE VESSEL COLLISION RISK ASSESSMENT DATA In this appendix, de tailed data are presented for vessel collision risk assessments of the Louisiana Highway 1 (LA 1) Bridge over Bayou Lafourche, Louisiana. The associated risk assessments are discussed in Chapter 9. Tables K 1 K 16 present risk assessment input parameters and results for every combination of pier (2 4, 96 97) and vessel group (1 32). Figures K 1 K 20 show barge impact force time histories computed by the CVIA and AVIL analysis methods for each combination of pier (2 4, 96 97) and barge vessel group (1 32). See Chapter 9 for descriptions of piers and vessel groups. Table K 1 Vessel impact velocities ( v i ) (knots) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 3.78 3.78 2.90 2.50 2.10 17 4.71 4.71 3.54 3.00 2.46 2 3.74 3.74 2.67 2.19 1.70 18 4.65 4.65 3.23 2.58 1.94 3 3.71 3.71 2.55 2.02 1.49 19 4.62 4.62 3.07 2.36 1.66 4 3.66 3.66 2.30 1.68 1.06 20 4.55 4.55 2.74 1.91 1.08 5 3.79 3.79 2.95 2.56 2.18 21 4.72 4.72 3.60 3.08 2.57 6 3.59 3.59 1.95 1.20 1.00 22 4.46 4.46 2.27 1.27 1.00 7 3.59 3.59 1.95 1.20 1.00 23 4.46 4.46 2.27 1.27 1.00 8 3 .54 3.54 1.68 1.00 1.00 24 4.38 4.38 1.90 1.00 1.00 9 3.78 3.78 2.90 2.50 2.10 25 4.71 4.71 3.54 3.00 2.46 10 3.74 3.74 2.67 2.19 1.70 26 4.65 4.65 3.23 2.58 1.94 11 3.71 3.71 2.55 2.02 1.49 27 4.62 4.62 3.07 2.36 1.66 12 3.66 3.66 2.30 1.68 1.06 28 4. 55 4.55 2.74 1.91 1.08 13 3.79 3.79 2.95 2.56 2.18 29 4.72 4.72 3.60 3.08 2.57 14 3.59 3.59 1.95 1.20 1.00 30 4.46 4.46 2.27 1.27 1.00 15 3.59 3.59 1.95 1.20 1.00 31 4.46 4.46 2.27 1.27 1.00 16 3.54 3.54 1.68 1.00 1.00 32 4.38 4.38 1.90 1.00 1.00

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470 Ta ble K 2 Geometric probability of impact ( PG ) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 0.107 0.107 0.056 0.028 0.014 17 0.107 0.107 0.056 0.028 0.014 2 0.116 0.116 0.046 0.018 0.007 18 0.116 0.116 0.046 0.01 8 0.007 3 0.112 0.112 0.038 0.013 0.004 19 0.112 0.112 0.038 0.013 0.004 4 0.134 0.134 0.031 0.008 0.002 20 0.134 0.134 0.031 0.008 0.002 5 0.083 0.083 0.046 0.023 0.012 21 0.083 0.083 0.046 0.023 0.012 6 0.145 0.145 0.019 0.003 0.000 22 0.145 0.145 0. 019 0.003 0.000 7 0.137 0.137 0.018 0.003 0.000 23 0.137 0.137 0.018 0.003 0.000 8 0.135 0.135 0.011 0.001 0.000 24 0.135 0.135 0.011 0.001 0.000 9 0.107 0.107 0.056 0.028 0.014 25 0.107 0.107 0.056 0.028 0.014 10 0.116 0.116 0.046 0.018 0.007 26 0.116 0.116 0.046 0.018 0.007 11 0.112 0.112 0.038 0.013 0.004 27 0.112 0.112 0.038 0.013 0.004 12 0.134 0.134 0.031 0.008 0.002 28 0.134 0.134 0.031 0.008 0.002 13 0.083 0.083 0.046 0.023 0.012 29 0.083 0.083 0.046 0.023 0.012 14 0.145 0.145 0.019 0.003 0. 000 30 0.145 0.145 0.019 0.003 0.000 15 0.137 0.137 0.018 0.003 0.000 31 0.137 0.137 0.018 0.003 0.000 16 0.135 0.135 0.011 0.001 0.000 32 0.135 0.135 0.011 0.001 0.000 Table K 3 Barge impact forces (kips) : AASHTO (1991) methods VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 2,368 2,368 2,250 2,174 2,106 17 2,564 2,564 2,383 2,270 2,167 2 2,021 2,021 1,904 1,839 1,784 18 2,171 2,171 1,989 1,891 1,809 3 1,590 1,590 1,490 1,440 1,399 19 1,705 1,705 1,548 1,471 1,410 4 1,830 1,830 1,723 1,675 855 20 1,932 1,932 1,763 1,691 888 5 1,415 1,415 1,348 1,304 1,265 21 1,539 1,539 1,432 1,365 1,305 6 1,644 1,644 1,387 532 368 22 1,696 1,696 1,592 593 386 7 1,480 1,480 1,397 686 475 23 1,545 1,545 1,413 765 475 8 1,2 15 1,215 593 211 211 24 1,244 1,244 762 211 211 9 2,035 2,035 1,992 1,806 1,279 25 2,090 2,090 2,022 1,996 1,754 10 1,783 1,783 1,699 1,145 697 26 1,828 1,828 1,762 1,589 900 11 1,407 1,407 1,048 660 361 27 1,438 1,438 1,389 899 444 12 1,676 1,676 856 459 183 28 1,706 1,706 1,204 590 190 13 1,237 1,237 1,206 1,194 1,015 29 1,279 1,279 1,229 1,210 1,194 14 1,599 1,599 645 246 170 30 1,629 1,629 870 274 170 15 1,346 1,346 403 153 106 31 1,404 1,404 543 171 106 16 1,197 1,197 351 125 125 32 1,219 1,219 451 125 125

PAGE 471

471 Table K 4 Capacity demand ratios ( H / P ): AASHTO (1991) methods VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 1.03 1.03 0.74 0.50 0.21 17 0.95 0.95 0.70 0.48 0.20 2 1.21 1.21 0.87 0.60 0.25 18 1.13 1.13 0.84 0.58 0.24 3 1.54 1.54 1.11 0.76 0.32 19 1.43 1.43 1.07 0.75 0.31 4 1.34 1.34 0.96 0.65 0.52 20 1.27 1.27 0.94 0.65 0.50 5 1.73 1.73 1.23 0.84 0.35 21 1.59 1.59 1.16 0.80 0.34 6 1.49 1.49 1.20 2.06 1.20 22 1.44 1.44 1.04 1.85 1.15 7 1.65 1.6 5 1.19 1.60 0.93 23 1.58 1.58 1.18 1.43 0.93 8 2.01 2.01 2.80 5.20 2.09 24 1.97 1.97 2.18 5.20 2.09 9 1.20 1.20 0.83 0.61 0.35 25 1.17 1.17 0.82 0.55 0.25 10 1.37 1.37 0.98 0.96 0.63 26 1.34 1.34 0.94 0.69 0.49 11 1.74 1.74 1.58 1.66 1.22 27 1.70 1.70 1.20 1.22 1.00 12 1.46 1.46 1.94 2.39 2.42 28 1.43 1.43 1.38 1.86 2.33 13 1.98 1.98 1.38 0.92 0.44 29 1.91 1.91 1.35 0.91 0.37 14 1.53 1.53 2.58 4.46 2.60 30 1.50 1.50 1.91 4.00 2.60 15 1.82 1.82 4.12 7.17 4.17 31 1.74 1.74 3.06 6.42 4.17 16 2.04 2.04 4.73 8.78 3.54 32 2.01 2.01 3.68 8.78 3.54 Table K 5 Probability of collapse ( PC ): AASHTO (1991) methods VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 0.000 0.000 0.029 0.055 0.088 17 0.005 0.005 0.034 0.057 0 .088 2 0.000 0.000 0.014 0.045 0.084 18 0.000 0.000 0.018 0.047 0.084 3 0.000 0.000 0.000 0.027 0.076 19 0.000 0.000 0.000 0.028 0.076 4 0.000 0.000 0.004 0.038 0.054 20 0.000 0.000 0.006 0.039 0.056 5 0.000 0.000 0.000 0.018 0.072 21 0.000 0.000 0.000 0.022 0.074 6 0.000 0.000 0.000 0.000 0.000 22 0.000 0.000 0.000 0.000 0.000 7 0.000 0.000 0.000 0.000 0.008 23 0.000 0.000 0.000 0.000 0.008 8 0.000 0.000 0.000 0.000 0.000 24 0.000 0.000 0.000 0.000 0.000 9 0.000 0.000 0.019 0.044 0.073 25 0.000 0.0 00 0.020 0.050 0.083 10 0.000 0.000 0.003 0.005 0.041 26 0.000 0.000 0.006 0.034 0.057 11 0.000 0.000 0.000 0.000 0.000 27 0.000 0.000 0.000 0.000 0.001 12 0.000 0.000 0.000 0.000 0.000 28 0.000 0.000 0.000 0.000 0.000 13 0.000 0.000 0.000 0.009 0.063 29 0.000 0.000 0.000 0.010 0.070 14 0.000 0.000 0.000 0.000 0.000 30 0.000 0.000 0.000 0.000 0.000 15 0.000 0.000 0.000 0.000 0.000 31 0.000 0.000 0.000 0.000 0.000 16 0.000 0.000 0.000 0.000 0.000 32 0.000 0.000 0.000 0.000 0.000

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472 Table K 6 Barge impact forces (kips): AASHTO (2009) methods VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 1,790 1,790 1,672 1,596 1,528 17 1,986 1,986 1,806 1,692 1,589 2 1,675 1,675 1,556 1,492 1,437 18 1,825 1,825 1,642 1,543 1, 463 3 1,590 1,590 1,490 1,439 1,399 19 1,706 1,706 1,548 1,471 1,411 4 1,560 1,560 1,453 1,405 853 20 1,662 1,662 1,494 1,421 885 5 1,608 1,608 1,541 1,496 1,458 21 1,732 1,732 1,625 1,557 1,497 6 1,451 1,451 1,384 529 368 22 1,504 1,504 1,399 592 368 7 1,480 1,480 1,397 683 475 23 1,546 1,546 1,413 764 475 8 1,407 1,407 594 211 211 24 1,437 1,437 758 211 211 9 1,457 1,457 1,414 1,397 1,284 25 1,513 1,513 1,444 1,418 1,396 10 1,436 1,436 1,394 1,147 695 26 1,481 1,481 1,415 1,391 903 11 1,407 1,407 1,046 660 360 27 1,438 1,438 1,389 898 447 12 1,406 1,406 853 457 183 28 1,436 1,436 1,206 590 190 13 1,429 1,429 1,398 1,397 1,018 29 1,471 1,471 1,422 1,403 1,387 14 1,406 1,406 643 245 170 30 1,436 1,436 870 274 170 15 1,345 1,345 401 152 106 31 1, 404 1,404 543 171 106 16 1,390 1,390 352 125 125 16 1,411 1,411 449 125 125 Table K 7 Capacity demand ratios ( H / P ): AASHTO (2009) methods VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 1.37 1.37 0.99 0.69 0.29 17 1.23 1.23 0.92 0.65 0.28 2 1.46 1.46 1.07 0.74 0.31 18 1.34 1.34 1.01 0.71 0.30 3 1.54 1.54 1.11 0.76 0.32 19 1.43 1.43 1.07 0.75 0.31 4 1.57 1.57 1.14 0.78 0.52 20 1.47 1.47 1.11 0.77 0.50 5 1.52 1.52 1.08 0.73 0.30 21 1.41 1.41 1.02 0.70 0.30 6 1 .69 1.69 1.20 2.07 1.20 22 1.63 1.63 1.19 1.85 1.20 7 1.65 1.65 1.19 1.61 0.93 23 1.58 1.58 1.18 1.44 0.93 8 1.74 1.74 2.80 5.20 2.09 24 1.70 1.70 2.19 5.20 2.09 9 1.68 1.68 1.17 0.79 0.34 25 1.62 1.62 1.15 0.77 0.32 10 1.70 1.70 1.19 0.96 0.64 26 1.65 1.65 1.17 0.79 0.49 11 1.74 1.74 1.59 1.66 1.23 27 1.70 1.70 1.20 1.22 0.99 12 1.74 1.74 1.95 2.40 2.42 28 1.70 1.70 1.38 1.86 2.33 13 1.71 1.71 1.19 0.79 0.43 29 1.66 1.66 1.17 0.78 0.32 14 1.74 1.74 2.58 4.48 2.60 30 1.70 1.70 1.91 4.00 2.60 15 1.8 2 1.82 4.14 7.22 4.17 31 1.74 1.74 3.06 6.42 4.17 16 1.76 1.76 4.72 8.78 3.54 32 1.73 1.73 3.70 8.78 3.54

PAGE 473

473 Table K 8 Probability of collapse ( PC ): AASHTO (2009) methods VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P 97 1 0.000 0.000 0.001 0.035 0.079 17 0.000 0.000 0.009 0.039 0.080 2 0.000 0.000 0.000 0.029 0.077 18 0.000 0.000 0.000 0.032 0.078 3 0.000 0.000 0.000 0.026 0.076 19 0.000 0.000 0.000 0.028 0.076 4 0.000 0.000 0.000 0.024 0.054 20 0.000 0.000 0.000 0 .025 0.056 5 0.000 0.000 0.000 0.030 0.077 21 0.000 0.000 0.000 0.033 0.078 6 0.000 0.000 0.000 0.000 0.000 22 0.000 0.000 0.000 0.000 0.000 7 0.000 0.000 0.000 0.000 0.008 23 0.000 0.000 0.000 0.000 0.008 8 0.000 0.000 0.000 0.000 0.000 24 0.000 0.000 0.000 0.000 0.000 9 0.000 0.000 0.000 0.024 0.073 25 0.000 0.000 0.000 0.025 0.076 10 0.000 0.000 0.000 0.005 0.040 26 0.000 0.000 0.000 0.024 0.057 11 0.000 0.000 0.000 0.000 0.000 27 0.000 0.000 0.000 0.000 0.001 12 0.000 0.000 0.000 0.000 0.000 28 0.000 0.000 0.000 0.000 0.000 13 0.000 0.000 0.000 0.024 0.063 29 0.000 0.000 0.000 0.024 0.076 14 0.000 0.000 0.000 0.000 0.000 30 0.000 0.000 0.000 0.000 0.000 15 0.000 0.000 0.000 0.000 0.000 31 0.000 0.000 0.000 0.000 0.000 16 0.000 0.000 0.000 0.0 00 0.000 32 0.000 0.000 0.000 0.000 0.000 Table K 9 Minimum of barge width ( B B ) and pier width ( B P ) (ft) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 48.0 48.0 34.5 28.0 28.0 17 48.0 48.0 34.5 28.0 28.0 2 44. 0 44.0 34.5 28.0 28.0 18 44.0 44.0 34.5 28.0 28.0 3 35.0 35.0 34.5 28.0 28.0 19 35.0 35.0 34.5 28.0 28.0 4 42.0 42.0 34.5 28.0 28.0 20 42.0 42.0 34.5 28.0 28.0 5 30.0 30.0 30.0 28.0 28.0 21 30.0 30.0 30.0 28.0 28.0 6 40.0 40.0 34.5 28.0 28.0 22 40.0 40 .0 34.5 28.0 28.0 7 35.0 35.0 34.5 28.0 28.0 23 35.0 35.0 34.5 28.0 28.0 8 30.0 30.0 30.0 28.0 28.0 24 30.0 30.0 30.0 28.0 28.0 9 48.0 48.0 34.5 28.0 28.0 25 48.0 48.0 34.5 28.0 28.0 10 44.0 44.0 34.5 28.0 28.0 26 44.0 44.0 34.5 28.0 28.0 11 35.0 35.0 34.5 28.0 28.0 27 35.0 35.0 34.5 28.0 28.0 12 42.0 42.0 34.5 28.0 28.0 28 42.0 42.0 34.5 28.0 28.0 13 30.0 30.0 30.0 28.0 28.0 29 30.0 30.0 30.0 28.0 28.0 14 40.0 40.0 34.5 28.0 28.0 30 40.0 40.0 34.5 28.0 28.0 15 35.0 35.0 34.5 28.0 28.0 31 35.0 35.0 34.5 28.0 28.0 16 30.0 30.0 30.0 28.0 28.0 32 30.0 30.0 30.0 28.0 28.0

PAGE 474

474 Table K 10 Barge yield force ( P BY ) (kip) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 7,569 7,569 3,734 3,294 3,294 17 7,569 7,569 3,73 4 3,294 3,294 2 7,055 7,055 3,734 3,294 3,294 18 7,055 7,055 3,734 3,294 3,294 3 5,898 5,898 3,734 3,294 3,294 19 5,898 5,898 3,734 3,294 3,294 4 6,798 6,798 3,734 3,294 3,294 20 6,798 6,798 3,734 3,294 3,294 5 5,255 5,255 3,430 3,294 3,294 21 5,255 5, 255 3,430 3,294 3,294 6 6,540 6,540 3,734 3,294 3,294 22 6,540 6,540 3,734 3,294 3,294 7 5,898 5,898 3,734 3,294 3,294 23 5,898 5,898 3,734 3,294 3,294 8 5,255 5,255 3,430 3,294 3,294 24 5,255 5,255 3,430 3,294 3,294 9 7,569 7,569 3,734 3,294 3,294 25 7,569 7,569 3,734 3,294 3,294 10 7,055 7,055 3,734 3,294 3,294 26 7,055 7,055 3,734 3,294 3,294 11 5,898 5,898 3,734 3,294 3,294 27 5,898 5,898 3,734 3,294 3,294 12 6,798 6,798 3,734 3,294 3,294 28 6,798 6,798 3,734 3,294 3,294 13 5,255 5,255 3,430 3,2 94 3,294 29 5,255 5,255 3,430 3,294 3,294 14 6,540 6,540 3,734 3,294 3,294 30 6,540 6,540 3,734 3,294 3,294 15 5,898 5,898 3,734 3,294 3,294 31 5,898 5,898 3,734 3,294 3,294 16 5,255 5,255 3,430 3,294 3,294 32 5,255 5,255 3,430 3,294 3,294 Table K 11 Maximum barge impact forces ( P B m ) (kip): UF/FDOT methods (CVIA) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 7,569 7,569 3,734 3,294 3,294 17 7,569 7,569 3,734 3,294 3,294 2 7,055 7,055 3,734 3,294 2,965 18 7,0 55 7,055 3,734 3,294 3,294 3 5,898 5,898 3,734 3,286 2,426 19 5,898 5,898 3,734 3,294 2,701 4 6,798 6,798 3,734 2,670 1,693 20 6,798 6,798 3,734 3,021 1,720 5 5,255 5,255 3,430 3,294 3,294 21 5,255 5,255 3,430 3,294 3,294 6 6,540 6,540 2,893 1,555 1,29 4 22 6,540 6,540 3,367 1,638 1,294 7 5,898 5,898 3,179 1,685 1,404 23 5,898 5,898 3,734 1,776 1,404 8 5,196 5,204 1,922 1,061 1,060 24 5,255 5,255 2,173 1,061 1,060 9 7,569 7,569 3,734 3,161 2,651 25 7,569 7,569 3,734 3,294 3,104 10 7,055 7,055 3,601 2 ,594 2,013 26 7,055 7,055 3,734 3,047 2,292 11 5,513 5,519 2,912 2,062 1,518 27 5,898 5,898 3,508 2,406 1,693 12 5,801 5,816 2,628 1,719 1,084 28 6,798 6,798 3,129 1,948 1,102 13 5,255 5,255 3,430 2,908 2,476 29 5,255 5,255 3,430 3,294 2,918 14 5,716 5 ,724 2,270 1,253 1,043 30 6,540 6,540 2,643 1,320 1,043 15 4,337 4,345 1,839 1,030 857 31 5,390 5,396 2,549 1,085 857 16 4,398 4,404 1,647 920 919 32 5,255 5,255 1,862 920 919

PAGE 475

475 Table K 12 Demand capacity r atios ( D / C ): UF/FDOT methods (CVIA) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 0.979 0.974 0.953 0.997 0.989 17 0.997 0.997 0.963 0.997 0.998 2 0.948 0.941 0.924 0.970 0.915 18 0.974 0.969 0.940 0.992 0.950 3 0.912 0.901 0.884 0.928 0.834 19 0.938 0.928 0.909 0.953 0.867 4 0.903 0.891 0.856 0.857 0.645 20 0.927 0.918 0.880 0.895 0.654 5 0.915 0.904 0.896 0.969 0.943 21 0.941 0.931 0.913 0.992 0.968 6 0.850 0.839 0.797 0.521 0.441 22 0.866 0.856 0.822 0.545 0.441 7 0.867 0.857 0.823 0.590 0.504 23 0.87 7 0.869 0.846 0.616 0.504 8 0.722 0.684 0.546 0.300 0.303 24 0.775 0.736 0.613 0.300 0.303 9 0.855 0.844 0.837 0.851 0.786 25 0.870 0.860 0.846 0.885 0.845 10 0.828 0.807 0.821 0.743 0.610 26 0.852 0.840 0.832 0.818 0.678 11 0.706 0.670 0.723 0.558 0.4 25 27 0.774 0.735 0.794 0.633 0.472 12 0.701 0.662 0.676 0.477 0.301 28 0.783 0.744 0.752 0.532 0.306 13 0.793 0.753 0.820 0.782 0.700 29 0.827 0.803 0.829 0.844 0.785 14 0.710 0.673 0.612 0.353 0.293 30 0.788 0.748 0.687 0.373 0.293 15 0.486 0.434 0.4 00 0.241 0.201 31 0.608 0.558 0.582 0.255 0.201 16 0.566 0.513 0.392 0.228 0.230 32 0.668 0.624 0.460 0.228 0.230 Table K 13 Probability of collapse ( PC ): UF/FDOT methods (CVIA) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 0.779 0.733 0.562 0.994 0.897 17 0.989 0.988 0.633 0.994 1.000 2 0.524 0.476 0.383 0.699 0.343 18 0.735 0.684 0.475 0.927 0.535 3 0.327 0.284 0.227 0.403 0.119 19 0.462 0.406 0.317 0.558 0.183 4 0.293 0.251 0.159 0.161 0.010 20 0.399 0.35 3 0.215 0.264 0.011 5 0.341 0.294 0.266 0.690 0.488 21 0.479 0.419 0.334 0.930 0.684 6 0.147 0.126 0.074 0.002 0.001 22 0.181 0.159 0.102 0.003 0.001 7 0.183 0.160 0.103 0.005 0.002 23 0.207 0.188 0.140 0.007 0.002 8 0.028 0.017 0.003 0.000 0.000 24 0. 055 0.033 0.007 0.000 0.000 9 0.157 0.135 0.123 0.149 0.064 25 0.189 0.166 0.139 0.231 0.137 10 0.111 0.084 0.100 0.036 0.006 26 0.150 0.128 0.116 0.096 0.016 11 0.023 0.014 0.028 0.003 0.001 27 0.055 0.033 0.071 0.009 0.001 12 0.021 0.013 0.015 0.001 0.000 28 0.061 0.037 0.041 0.002 0.000 13 0.069 0.042 0.099 0.061 0.021 29 0.108 0.079 0.111 0.135 0.063 14 0.024 0.015 0.007 0.000 0.000 30 0.065 0.039 0.018 0.000 0.000 15 0.001 0.001 0.000 0.000 0.000 31 0.006 0.003 0.004 0.000 0.000 16 0.004 0.002 0.000 0.000 0.000 32 0.014 0.008 0.001 0.000 0.000

PAGE 476

476 Table K 14 Maximum dynamic impact force ( P Bm ): UF/FDOT methods (AVIL) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 7,569 7,569 3,734 3,294 3,294 17 7,569 7,5 69 3,734 3,294 3,294 2 7,055 7,055 3,734 3,294 3,294 18 7,055 7,055 3,734 3,294 3,294 3 5,898 5,898 3,734 3,294 3,078 19 5,898 5,898 3,734 3,294 3,294 4 6,798 6,798 3,734 3,294 2,071 20 6,798 6,798 3,734 3,294 2,106 5 5,255 5,255 3,430 3,294 3,294 21 5 ,255 5,255 3,430 3,294 3,294 6 5,692 6,175 2,788 1,646 1,358 22 6,540 6,540 3,246 1,735 1,358 7 5,898 5,898 3,170 1,871 1,544 23 5,898 5,898 3,734 1,972 1,544 8 4,051 4,361 1,777 1,037 1,028 24 5,015 5,255 2,009 1,037 1,028 9 6,011 6,555 3,734 3,294 2, 775 25 7,490 7,569 3,734 3,294 3,253 10 5,314 5,781 3,376 2,650 2,038 26 6,611 7,055 3,734 3,115 2,321 11 4,168 4,505 2,639 2,002 1,461 27 5,193 5,613 3,179 2,336 1,629 12 4,236 4,601 2,381 1,667 1,042 28 5,264 5,718 2,835 1,890 1,059 13 4,791 5,158 3, 430 2,925 2,470 29 5,255 5,255 3,430 3,294 2,913 14 4,216 4,574 2,065 1,219 1,006 30 5,239 5,684 2,404 1,285 1,006 15 3,255 3,518 1,629 961 793 31 4,045 4,372 2,257 1,014 793 16 3,396 3,656 1,490 869 862 32 4,204 4,525 1,684 869 862 Table K 15 Demand capacity ratios ( D / C ): UF/FDOT methods (AVIL) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 1.000 0.868 0.961 1.000 1.000 17 1.000 1.000 0.965 0.997 0.998 2 1.000 0.848 1.000 1.000 1.000 18 1.000 1.000 0.953 0.9 97 0.997 3 0.972 0.728 1.000 0.984 1.000 19 0.988 0.972 0.933 0.995 0.981 4 0.971 0.725 1.000 0.982 1.000 20 0.988 0.973 0.916 0.987 0.805 5 0.966 0.829 1.000 0.999 1.000 21 0.983 0.964 0.923 0.997 0.997 6 0.876 0.733 0.963 0.987 1.000 22 0.905 0.884 0 .833 0.657 0.530 7 0.907 0.505 0.973 0.870 1.000 23 0.924 0.907 0.868 0.752 0.610 8 0.781 0.583 0.860 0.905 0.937 24 0.838 0.824 0.660 0.363 0.360 9 0.876 0.870 0.854 0.935 0.874 25 0.911 0.896 0.860 0.957 0.924 10 0.861 0.851 0.833 0.845 0.728 26 0.87 9 0.872 0.850 0.896 0.797 11 0.770 0.733 0.768 0.659 0.507 27 0.834 0.816 0.817 0.745 0.558 12 0.766 0.730 0.725 0.565 0.358 28 0.831 0.813 0.794 0.628 0.365 13 0.845 0.833 0.835 0.868 0.813 29 0.867 0.854 0.843 0.921 0.868 14 0.775 0.737 0.663 0.427 0 .347 30 0.836 0.820 0.735 0.450 0.347 15 0.558 0.509 0.458 0.284 0.233 31 0.671 0.632 0.640 0.300 0.233 16 0.632 0.588 0.445 0.268 0.268 32 0.733 0.698 0.516 0.268 0.268

PAGE 477

477 Table K 16 Probability of collapse ( PC ): UF/FDOT methods (AVIL) VG P2 P3 P4 P96 P97 VG P2 P3 P4 P96 P97 1 1.000 0.186 0.623 1.000 1.000 17 1.000 1.000 0.654 0.994 1.000 2 1.000 0.142 1.000 1.000 1.000 18 1.000 1.000 0.562 0.994 0.988 3 0.712 0.030 1.000 0.835 1.000 19 0.885 0.714 0.429 0.971 0.808 4 0.710 0.029 1.000 0.817 1.000 20 0.882 0.728 0.347 0.872 0.081 5 0.663 0.111 1.000 1.000 1.000 21 0.829 0.641 0.378 0.994 0.989 6 0.204 0.032 0.636 0.871 1.000 22 0.299 0.229 0.117 0.012 0.002 7 0.308 0.002 0.721 0.190 1.000 23 0.385 0.30 6 0.186 0.041 0.006 8 0.060 0.005 0.167 0.300 0.454 24 0.125 0.104 0.012 0.000 0.000 9 0.206 0.190 0.155 0.445 0.200 25 0.323 0.266 0.167 0.586 0.385 10 0.169 0.148 0.117 0.137 0.030 26 0.212 0.195 0.146 0.268 0.074 11 0.052 0.032 0.051 0.012 0.002 27 0.119 0.095 0.096 0.037 0.003 12 0.049 0.031 0.029 0.004 0.000 28 0.114 0.091 0.071 0.008 0.000 13 0.137 0.117 0.120 0.185 0.090 29 0.183 0.154 0.134 0.369 0.185 14 0.055 0.034 0.013 0.001 0.000 30 0.122 0.100 0.033 0.001 0.000 15 0.003 0.002 0.001 0.0 00 0.000 31 0.014 0.009 0.010 0.000 0.000 16 0.009 0.005 0.001 0.000 0.000 32 0.032 0.020 0.002 0.000 0.000

PAGE 478

478 A B C D E F G H Figure K 1 Impact force time histories: LA 1 Bridge, Pier 2, upbound traffic, fully loaded. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 479

479 A B C D E F G H Figure K 2 Impact force time histories: LA 1 Bridge, Pier 2, upbound traffic, lightly loaded. A) VG9. B) VG10. C) VG11. D) VG12. E) VG13. F) VG14. G) VG15. H) VG16.

PAGE 480

480 A B C D E F G H Figure K 3 Impact force time histories: LA 1 Bridge, Pier 2, downbound traffic, fully loaded. A) VG17. B) VG18. C) VG19. D) VG20. E) VG21. F) VG22. G) VG23. H) VG24.

PAGE 481

481 A B C D E F G H Figure K 4 Impact force time histories: LA 1 Bridge, Pier 2, downbound traffic, lightly loaded. A) VG25. B) VG26. C) VG27. D) VG28. E) VG29. F) VG30. G) VG31. H) VG32.

PAGE 482

482 A B C D E F G H Figure K 5 Impact force time histori es: LA 1 Bridge, Pier 3, upbound traffic, fully loaded. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 483

483 A B C D E F G H Figure K 6 Impact force time histories : LA 1 Bridge, Pier 3, upbound traffic, lightly loaded. A) VG9. B) VG10. C) VG11. D) VG12. E) VG13. F) VG14. G) VG15. H) VG16.

PAGE 484

484 A B C D E F G H Figure K 7 Impact force time hi stories: LA 1 Bridge, Pier 3, downbound traffic, fully loaded. A) VG17. B) VG18. C) VG19. D) VG20. E) VG21. F) VG22. G) VG23. H) VG24.

PAGE 485

485 A B C D E F G H Figure K 8 Impact force time histories: LA 1 Bridge, Pier 3, downbound traffic, lightly loaded. A) VG25. B) VG26. C) VG27. D) VG28. E) VG29. F) VG30. G) VG31. H) VG32.

PAGE 486

486 A B C D E F G H Figure K 9 Im pact force time histories: LA 1 Bridge, Pier 4, upbound traffic, fully loaded. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 487

487 A B C D E F G H Figure K 10 Imp act force time histories: LA 1 Bridge, Pier 4, upbound traffic, lightly loaded. A) VG9. B) VG10. C) VG11. D) VG12. E) VG13. F) VG14. G) VG15. H) VG16.

PAGE 488

488 A B C D E F G H Figure K 11 Impact force time histories: LA 1 Bridge, Pier 4, downbound traffic, fully loaded. A) VG17. B) VG18. C) VG19. D) VG20. E) VG21. F) VG22. G) VG23. H) VG24.

PAGE 489

489 A B C D E F G H Figure K 12 Impact force time histories: LA 1 Bridge, Pier 4, downbound traffic, lightly loaded. A) VG25. B) VG26. C) VG27. D) VG28. E) VG29. F) VG30. G) VG31. H) VG32.

PAGE 490

490 A B C D E F G H Figure K 13 Impact force time histories: LA 1 Bridge, Pier 96, upbound traffic, fully loaded. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 491

491 A B C D E F G H Figure K 14 Impact force time histories: LA 1 Bridge, Pier 96, upbound traffic, lightly loaded. A) VG9. B) VG10. C) VG11. D) VG12. E) VG13. F) VG14. G) VG15. H) VG16.

PAGE 492

492 A B C D E F G H Figure K 15 Impact force time histories: LA 1 Bridge, Pier 96, downbound traffic, fully loaded. A) VG17. B) VG18. C) VG19. D) VG20. E) VG21. F) VG22. G) VG23. H) VG24.

PAGE 493

493 A B C D E F G H Figure K 16 Impact force time histories: LA 1 Bridge, Pier 96, downbound traffic, lightly loaded. A) VG25. B) VG26. C) VG27. D) VG28. E) VG29. F) VG30. G) VG31. H) VG32.

PAGE 494

494 A B C D E F G H Figure K 17 Impact force time histories: LA 1 Bridge, Pier 97, upbound traffic, fully loaded. A) VG1. B) VG2. C) VG3. D) VG4. E) VG5. F) VG6. G) VG7. H) VG8.

PAGE 495

495 A B C D E F G H Figure K 18 Impact force time histories: LA 1 Bridge, Pier 97, upbound traffic, lightly loaded. A) VG9. B) VG10. C) VG11. D) VG12. E) VG13. F) VG14. G) VG15. H) VG16.

PAGE 496

496 A B C D E F G H Figure K 19 Impact force time histories: LA 1 Bridge, Pier 97, downbound traffic, fully loaded. A) VG17. B) VG18. C) VG19. D) VG20. E) VG21. F) VG22. G) VG23. H) VG24.

PAGE 497

497 A B C D E F G H Figu re K 20 Impact force time histories: LA 1 Bridge, Pier 97, downbound traffic, lightly loaded. A) VG25. B) VG26. C) VG27. D) VG28. E) VG29. F) VG30. G) VG31. H) VG32.

PAGE 498

498 LIST OF REFERENCES Amer ican Association of State Highway and Transportation Officials ( AASHTO ) (1991). Guide specification and commentary for vessel collision design of highway bridges 1st Ed., Washington, DC. AASHTO. (1994). LRFD bridge design specifications, 1st Ed., Washing ton, DC. AASHTO. (2009 ). Guide specification and commentary for vessel collision design of highway bridges 2nd Ed., Washington, DC. AASHTO. (2011 ). LRFD bridge design specifications, 5th Ed., Washington, DC. American Society of Civil Engineers (ASCE). (20 10). ASCE/SEI 7 10 Minimum design loads of buildings and other structures Reston, VA. American Society for Testing and Materials (ASTM). (2008). A36/A36M 08 Standard specification for carbon structural steel West Conshohocken, PA. ASTM. (2012a). A1011/A1 011M 12b S tandard specification for steel, sheet and strip, hot rolled, carbon, structural, high strength low alloy and high strength low alloy with improved formability West Conshohocken, PA. ASTM. (2012b). A370 12a Standard test methods and definitions for mechanical testing of steel products West Conshohocken, PA. Int. J. Impact Eng. 50, 49 62. Bri dge Software Institute ( BSI ). (2009). FB Univ. of Florida, Gainesville, FL. BSI (2010). FB Univ. of Florida, Gainesville, FL. CEN European Com mittee for Standardization (2006). Eurocode 1: A ctions on structures P art 1 7: General a ctions A ccidental actions (EN 1991 1 7:2006) Brussels, Belgium. Modeling the A palachicola system Technical Paper No. 23 Univ. of Florida, Gainesville, FL. impact breakaway, wind resistant base connection for m ult i post ground s igns Structures Research Report No. 92174 Engineering and Industrial Experiment Station, Un iv. of Florida, Gainesville, FL. George Island Causeway Bridge

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499 Structures Research Report No. 26868 Engineeri ng and Industrial Experiment Station, Univ. of Florida, Gainesville, FL. J. Struct. Eng. 131(8), 1256 1266. Consolazio, G. R, and Da Transportation Research Record 2050 Transportation Research Board, Washington, DC, 13 25. deformation relationships for barge Transportation Research Record 2131 Transportation Research Board, Washington, DC, 3 14. collapse Structures Research Report No. 72908/74039, Engineering and Industrial Experiment Station, Univ. of Florida, Gainesville, FL. Consol dyn amic numerical modeling of aberrant rake barges impacting hurricane protection structures s ubjecte d to f orc Structures Research Report No. 83710 Engineering and Industrial Experiment Station, Univ. of Florida, Gainesville, FL. Consolazio, G. R., McVay, M. C., Cowan, D. R., Davidson, M. T., and Getter, D. J. (2008). Structures Research Report No. 51117 Engineering and Industrial Experiment Station, Univ. of Florida, Gainesville, FL. Consolazio, G. R., and Walters, R. A. (2012b). Development of multiple barge flotilla finite element models for use in probabilistic barge i m pact analysis of flexible w Structures Research Report No. 94753 Engine ering and Industrial Experiment Station, Univ. of Florida, Gainesville, FL. Consolaz models for studying multi barge flotilla i mpacts Structures Research Report No. 87754 Engineering and Industrial Experiment Station, Univ. of Florida, Gainesville, FL. column internal forces due to barge Transportation Research Record 2172, Transportation Research Board, Washington, DC, 11 22. J. Bridge Eng. 18(4), 287 296.

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500 Ellin gwood, B., Galambos, T. V., MacGregor, J. G., and Cornell, C. A. (1980). Development of a probability based load criterion for American National Standard A58. National Bureau of Standards, Washington, DC. Federal Emergency Management Agency (FEMA) (2003). NEHRP Recommended provisions for seismic regulations for new buildings and other structures (FEMA 450) Washington, DC. Florida Department of Transportation ( FDOT ) (2013). Structures m anual Volume 1: Structures design g uidelines Tallahassee, FL. Getter Relationships of barge bow force deformation for bridge design: Probabilistic consideration of oblique impact scenarios. Transportation Research Record 2251 Transportation Research Board, Washington, DC, 3 15. Gett for barge impact resistant bridge design J. Bridge Eng. 16(6), 718 727. static and dynamic axial crushing of thin walled circular Int. J. Crashworthiness 9(2), 195 217. Jones, N. (1997). Structural Impact Cambridg e Univ. Press, New York, NY. ected to large dynamic Int. J. Impact Eng. 53, 106 114. J. Mech. Eng. Sci. 216(C), 133 149. Kunz, Ship Collision Analysis (H. Gluver and D. Olsen, eds.), Balkema, Rotterdam, Netherlands, 13 22. Livermore Software Technology Corporation ( LSTC ) (2007). LS DYNA keyword anual Livermore, CA. J. Appl. Mech. T. ASME 66, A211 A218. Meier Ship collisions, safety zones, and loading assumptio ns for structures in inland waterways Verein Deutscher Ingenieure (Association of German Engineers) Report No. 496 Dsseldorf, Germany, 1 9. National Oceanic and Atmospheric Association (NOAA). (2013a ). Nautical chart 11404: Intracoastal waterway, Carra belle to Apalachicola Bay Washington, DC.

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501 NOAA. (2013b). Coast pilot 5: Gulf of Mexico, Puerto Rico, and Virgin Islands, 41 st Ed. Washington, DC. Nowak, A. S. (1999). ion of LRFD bridge design c NCHRP Report Volume 368 Transportation Resea rch Board, Washington, DC. Nowak, A. S., Szersen, M. M., Szeliga, E. K., Szwed, A., and Podhorecki, P. J. (2008). PCA R&D Serial No. 2849 Portland Cement Association and Precast/Prestressed Concrete Institute, Skokie, IL. Int. J. Impact Eng. 13(2), 163 187. Perl Foundation (Perl). (2013). Perl 5 version 16.2 documentation Walnut, CA. Salmo n, C. G., and Johnson, J. E. (1996). Steel structures: Design and behavior 4th Ed., Harper Collins College Publishers, New York, NY. S Int. J. Impact Eng. 24, 571 581. under dynamic l oa Division of Engineering Report No. BU/NSDRC/1 67 Brown Univ., Providence, RI. Thompson, A. C. (2006). High strain rate characterization of advanced high strength steels. United States Coast Guard (USCG). (2013). United States Coast Guard Maritime Information Exchange (CGMIX), Washington, DC, (http://cgmix.uscg.mi l). Wang, T. L., and Liu C. (1999). Synthesizing commercial shipping (barge/tug trains) from available data for vessel collision design Florida International Univ., Miami, FL. Jahrbuch der Shiffbautech nischen Gesellschaft, 70, 465 487.

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502 BIOGRAPHICAL SKETCH The author was born at Hill Air Force Base near Ogden, Utah. H e began attending Daytona Beach Community College in September 2002, where he later earned an Associate of Arts degree in August 2005. Su bsequently, he began attending the University of Florida, where he earned a Bachelor of Science in Civil Engineering in May 2008. He immediately enrolled in graduate school at the University of Florida, where he worked on developing simplified structural a nalysis methods for vessel bridge impact loading and earned a Master of Engineering in Civil Engineering in May 2010. The author enrolled in the Ph.D. program at the University of Florida immediately thereafter and earned a Doctor of Philosophy in Civil En gineering in August 2013