EVALUATION OF BARGE FLOTILLA ABERRANCY RATES AND INTER-BARGE RELATIVE MOTIONS FOR THE ANALYSIS AND DESIGN OF WATERWAY BRIDGE STRUCTURES SUBJECT TO BARGE COLLISIONS
By
GEORGE CHRISTOPHER KANTRALES
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2016
© 2016 George Christopher Kantrales
To my parents, Peter and Sophia Kantrales
ACKNOWLEDGMENTS
The research presented in this dissertation could not have been completed without the
support and guidance of multiple individuals. Among these people, I would like to extend
particular thanks to Dr. Gary Consolazio for serving as a strong mentor throughout the time that I
have spent at the University of Florida. My growth as an engineer during the past four years has
surpassed my expectations. I would also like to thank my committee members, Dr. H.R. (Trey)
Hamilton, Dr. Jennifer Rice, Dr. Kurtis Gurley, and Dr. Youping Chen for their advice and input.
Several students also provided key assistance with various aspects of this research. Accordingly,
I would like to recognize and thank Ms. Juliana Rochester, Mr. Renato Davila, and Mr. Jeffrey
Honig for their help with various data processing and analysis tasks.
The large-scale pendulum impact tests that were included in this research were conducted
with the full support of the Marcus H. Ansley Structures Research Center. Without the assistance
of Mr. David Wagner, Mr. William Potter, Mr. Stephen Eudy, Mr. Paul Tighe, Mr. Chris
Weigly, Mr. David Allen, Mr. Ben Allen, Mr. Brandon Winter, and Mr. Sam Fallaha, such a
significant logistical effort could not have been completed.
I would also like to thank my friends and family for their love and support. My parents,
Peter D. and Sophia Kantrales, and my brothers, Peter C. and Ange Kantrales, have been
bastions of support throughout my entire academic experience. My closest friends, Mr. Josh
Belcher, Mr. Daniel Terry, Mr. Dustin Maherg, Dr. David Mante, and Mr. Shayne Cumbie have
been a source of strength for me, and have provided both cheerful conversations as well as
thoughtful advice during tough times. Dr. Daniel Getter, both a friend and a mentor, served as a
model researcher for me during the formative years of my doctoral experience; without his
example, my growth as a researcher would have been much more limited.
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Finally, but most significantly, I would like to thank my wife Katie for being so supportive throughout one of the greatest and most challenging accomplishments of my career; her patience is more than I deserve. I’m glad that I will be able to spend the rest of my life with such a wonderful person.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...... 4
LIST OF TABLES ...... 9
LIST OF FIGURES ...... 11
LIST OF ABBREVIATIONS ...... 16
ABSTRACT ...... 21
CHAPTER
1 INTRODUCTION ...... 23
1.1 Motivation ...... 23 1.2 Objectives ...... 25 1.3 Organization ...... 25
2 BACKGROUND ...... 28
2.1 AASHTO LRFD Bridge Design Specifications ...... 29 2.1.1 Probability of Aberrancy ...... 31 2.1.2 Geometric Probability ...... 33 2.1.3 Protection Factor ...... 34 2.1.4 Barge Impact Forces ...... 34 2.1.5 Limitations ...... 36 2.2 Eurocode 1: Actions on Structures ...... 37 2.2.1 General Principles ...... 38 2.2.2 Risk Analysis Methodology ...... 41 2.3 Previous UF/FDOT Research ...... 43 2.3.1 Full-Scale Barge Impact Experiments ...... 43 2.3.2 Coupled Vessel Impact Analysis (CVIA) ...... 44 2.3.3 Barge Bow Force-Deformation Behavior ...... 45 2.4 Related Research ...... 46 2.4.1 Impact Event Prediction ...... 46 2.4.2 Barge Bow Force-Deformation Behavior ...... 51 2.4.3 Multi-Barge Flotilla Behavior ...... 53 2.5 Observations ...... 55
3 DETERMINATION OF BARGE IMPACT PROBABILITIES FOR BRIDGE DESIGN....64
3.1 Methodology ...... 65 3.1.1 Approach ...... 65 3.1.2 Data Sources ...... 67
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3.1.3 General Data Analysis Methods ...... 72 3.2 Data Collection ...... 78 3.2.1 Barge Collision Data ...... 78 3.2.2 Barge Traffic Data ...... 81 3.2.3 Supporting Information ...... 82 3.3 Data Analysis ...... 83 3.3.1 Probability of Impact ...... 84 3.3.2 Modification Factors ...... 89 3.3.3 Additional Probabilities ...... 90 3.3.4 Base Aberrancy Rate Calibration ...... 91 3.4 Discussion ...... 92 3.5 Summary ...... 94
4 EXPERIMENTAL VALIDATION OF BARGE BOW FORCE-DEFORMATION BEHAVIOR ...... 121
4.1 Approach ...... 122 4.2 Experimental Procedures ...... 125 4.3 Experimental Results ...... 128 4.3.1 RND Series ...... 128 4.3.2 FLT Series ...... 129 4.3.3 Comparisons ...... 130 4.4 Analytical Modeling Procedures ...... 130 4.5 Comparison of Experimental and Analytical Results ...... 132 4.6 Summary ...... 133
5 INFLUENCE OF IMPACT-INDUCED RELATIVE MOTION ON EFFECTIVE BARGE FLOTILLA MASS ...... 142
5.1 Modeling Approach ...... 144 5.2 Relative Motion of a Coal Payload ...... 147 5.2.1 Modeling Procedures ...... 147 5.2.2 Single Barge Impact Simulations with Payload Model ...... 148 5.3 Effective Mass of Barge Flotillas ...... 149 5.3.1 Single-Column Barge Flotilla Impact Simulations ...... 150 5.3.2 Multi-Column Barge Flotilla Impact Simulations ...... 151 5.3.2.1 Effect of pier width ...... 154 5.3.2.2 Effect of pier stiffness ...... 155 5.3.2.3 Effect of impact velocity ...... 156 5.3.2.4 Effect of flotilla configuration ...... 157 5.4 Effective Mass Ratios for Bridge Design ...... 159 5.5 Summary ...... 162
6 CONCLUSIONS AND RECOMMENDATIONS ...... 186
6.1 Concluding Remarks ...... 186 6.2 Design Recommendations ...... 188
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6.3 Recommendations for Future Research ...... 188
APPENDIX
A SUMMARY OF BARGE ACCIDENT DATA COLLECTED ...... 189
B SUMMARY OF BARGE TRAFFIC DATA COLLECTED ...... 191
C VESSEL TRAFFIC CURVE FITS ...... 192
D BARGE FLOTILLA DIMENSIONS ...... 204
LIST OF REFERENCES ...... 206
BIOGRAPHICAL SKETCH ...... 211
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LIST OF TABLES
Table page
2-1 ECMT vessel classifications ...... 57
2-2 Representative classifications for ocean-going vessels ...... 57
3-1 Extract from Waterborne Commerce of the United States (WCUS) illustrating the organization of USACE vessel traffic data ...... 97
3-2 Bridge locations utilized in present study...... 98
3-3 Number of barge-to-bridge collision events per bridge location...... 98
3-4 Estimated values of PI...... 99
3-5 Estimated values of RB...... 99
3-6 Estimated values of RC and RXC...... 100
3-7 Estimated values of PG (inbound direction)...... 100
3-8 Estimated values of PG (outbound direction)...... 101
3-9 Estimated values of PF (inbound direction)...... 101
3-10 Estimated values of PF (outbound direction)...... 102
3-11 Summary of mean BR values...... 102
3-12 BR values associated with flotilla classifications for the eight design bridge locations. .102
4-1 Summary of test program...... 134
4-2 Overall results from each test series ...... 134
5-1 Representative coal material properties...... 164
5-2 Summary of results for single barge impact simulations with DE payload model...... 164
5-3 Summary of results from single-column impact simulations...... 164
5-4 Simulation parameters...... 164
5-5 Fitting parameters for the estimation of EMR values...... 165
5-6 Comparison of results from bridge pier impact simulations involving jumbo hopper barges and oversize tanker barges...... 165
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5-7 Impact analysis of Acosta Bridge (Jacksonville, FL) using CVIA ...... 166
A-1 Barge accident data summary...... 189
B-1 Barge traffic data summary...... 191
D-1 Flotilla sizes for Acosta Bridge...... 204
D-2 Flotilla sizes for Atlantic Blvd. Bridge...... 204
D-3 Flotilla sizes for Bob Sikes Bridge, Brooks Bridge, and Navarre Beach Bridge...... 204
D-4 Flotilla sizes for Gandy Bridge...... 205
D-5 Flotilla sizes for Highway-90 Bridge over Escambia River and Pensacola Bay Bridge...... 205
D-6 Flotilla sizes for Sister’s Creek Bridge...... 205
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LIST OF FIGURES
Figure page
1-1 Flotilla breakup scenario utilized in AASHTO (2014) bridge design specifications ...... 27
2-1 Barge lashings and bitts ...... 58
2-2 Barge flotilla dimensional definitions ...... 58
2-3 Methodology for classifying geometric characteristics of a waterway that are used in the calculation of RB ...... 59
2-4 AASHTO methodology for calculating the geometric probability, PG ...... 60
2-5 AASHTO barge impact force-deformation relationship...... 60
2-6 Direction of dynamic impact forces ...... 61
2-7 Example force time-histories for use in dynamic analysis according to EN 1991 provisions ...... 61
2-8 EN 1991 Risk analysis methodology ...... 62
2-9 Full-scale barge impact experiments ...... 63
2-10 Determination of deviation angles for a particular bridge pier and maneuvering path .....63
3-1 Visualization of sample AIS data ...... 103
3-2 ECDIS display on-board a NOAA vessel ...... 103
3-3 Regions of Florida waterways that, per USACE data, carry notable commercial barge traffic ...... 104
3-4 Curve-fitting approach for the estimation of barge flotilla traffic data...... 104
3-5 Calculation of the geometric probability for a single bridge location...... 105
3-6 Bridge piers protected by adjacent low-rise railroad bridge ...... 105
3-7 Bridge piers protected by land bodies ...... 106
3-8 Shallow water regions near bridge ...... 106
3-9 Calculation of the bridge location modification factor, RB ...... 107
3-10 Selected portions of USCG vessel casualty data set ...... 108
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3-11 USCG districts ...... 109
3-12 Selected portion of raw USCG accident report...... 110
3-13 Selected portion of USCG vessel casualty data set with unspecified vessel characteristics...... 111
3-14 Selected portion of USCG vessel casualty data set with blank data fields...... 111
3-15 Selected portion of USACE vessel traffic data set for Atlantic Intracoastal Waterway, near Sister’s Creek Bridge ...... 112
3-16 Selected sample NOAA tidal current prediction ...... 112
3-17 Selected portion of simplified bridge layout for the Navarre Beach Bridge over the Gulf Intracoastal Waterway ...... 113
3-18 Selected portion of NOAA nautical chart ...... 113
3-19 Barge-to-tug ratios normalized by bridge site medians ...... 114
3-20 Example box plot...... 115
3-21 Determination of barge flotilla traffic counts for individual bridge locations...... 116
3-22 Curvature of waterway near Acosta Bridge ...... 117
3-23 Curvature of waterway near Brooks Bridge ...... 117
3-24 Curvature of waterway near Dupont Bridge ...... 118
3-25 Curvature of waterway near Highway-90 Bridge over Escambia River ...... 118
3-26 Curvature of waterway near Sister’s Creek Bridge ...... 119
3-27 Estimates of BR ...... 120
4-1 FDOT pendulum impact facility in Tallahassee, Florida ...... 135
4-2 Schematic of test setup...... 135
4-3 Impactor ...... 136
4-4 Elevation view of field instrumentation ...... 137
4-5 Force-deformation relationship from RND test series ...... 137
4-6 Final deformation pattern of replicate barge bow following test RND4 ...... 138
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4-7 Force-deformation relationship from FLT test series ...... 138
4-8 Final deformation pattern of replicate barge bow following test FLT4 ...... 139
4-9 FE model of 40% scale replicate barge bow ...... 139
4-10 FE model of impactor ...... 140
4-11 Comparison of analytical and experimental force-deformation relationships for RND series ...... 141
4-12 Comparison of analytical and experimental force-deformation relationships for FLT series ...... 141
5-1 Inter-column differential motion (center column impact event shown for an aberrant 3x3 flotilla outside of navigation channel) ...... 166
5-2 Inter-column differential motion (outer column impact event shown for an aberrant 2x2 flotilla outside of navigation channel) ...... 167
5-3 Barge lashings and bitts ...... 168
5-4 Flotilla breakup scenario utilized in AASHTO (2014) bridge design specifications ...... 168
5-5 Barge models ...... 169
5-6 Internal structure of deformable barge bow...... 169
5-7 Inter-barge force-deformation relationships ...... 170
5-8 Contact interfaces used in inter-barge crushing anlayses ...... 170
5-9 Impact surface representation...... 171
5-10 Barge bow force-deformation relationships associated with crushing against rigid piers ...... 172
5-11 Inter-barge lashing configurations ...... 173
5-12 Calibration simulations ...... 174
5-13 Payload pouring process ...... 174
5-14 Single barge impact with coal payload against a 9-ft bridge pier ( KP = 1,000 kip/in.) at 4 ft/sec...... 175
5-15 Results from single barge impact simulations with coal payload against a 9-ft pier (Kp = 1,000 kip/in.) at 4 ft/sec ...... 175
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5-16 Payload position in barge hopper region...... 176
5-17 Single-column (1x5) flotilla configurations...... 176
5-18 Single-column (1x5), double-raked barge flotilla impact simulation results ...... 177
5-19 Double-raked barge flotilla ...... 177
5-20 Flotilla sizes considered...... 178
5-21 Influence of pier width on barge flotilla crushing and breakup behavior ...... 179
5-22 Variation in EMR with pier width...... 179
5-23 Relative motion of bridge pier during a barge-to-bridge impact ...... 180
5-24 Variation in EMR with pier stiffness levels (case shown for a 3x3 flotilla impacting a 26-ft flat pier at 2 ft/sec) ...... 180
5-25 Variation in EMR with pier stiffness levels (case shown for a 3x3 flotilla impacting a 6-ft round pier at 2 ft/sec) ...... 181
5-26 Maximum deformation levels and EMR values associated with impact velocities of 1 ft/sec, 2 ft/sec, and 3 ft/sec ...... 181
5-27 EMR values for 3x1 flotilla impact simulations...... 182
5-28 EMR values for 3x3 flotilla impact simulations...... 182
5-29 Degree and frequency of lashing failure in 3x1 flotilla impact simulations...... 182
5-30 Degree and frequency of lashing failure in 3x3 flotilla impact simulations...... 183
5-31 Degree and frequency of lashing failure in two-column flotilla impact simulations ...... 183
5-32 Degree and frequency of lashing failure in three-column flotilla impact simulations ....183
5-33 EMR values for 2x2 flotilla impact simulations...... 184
5-34 EMR values for 3x2 flotilla impact simulations...... 184
5-35 EMR values for all 3,000 flotilla impact simulations...... 184
5-36 Level of conservatism associated with EMR predictions...... 185
C-1 Curve fits used to replace outlying barge-to-tug ratios for Highway-90 Bridge over Escambia River and Pensacola Bay Bridge ...... 193
C-2 Curve fits used to replace outlying barge-to-tug ratios for Dupont Bridge ...... 194
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C-3 Curve fits used to replace outlying barge-to-tug ratios for Atlantic Blvd. Bridge ...... 195
C-4 Curve fits used to replace outlying barge-to-tug ratios for Gandy Bridge ...... 196
C-5 Curve fits used to produce estimates of barge flotilla traffic for Acosta Bridge ...... 197
C-6 Curve fits used to produce estimates of barge flotilla traffic for Atlantic Blvd. Bridge...... 198
C-7 Curve fits used to produce estimates of barge flotilla traffic for Bob Sikes Bridge, Brooks Bridge, and Navarre Beach Bridge...... 199
C-8 Curve fits used to produce estimates of barge flotilla traffic for Dupont Bridge ...... 200
C-9 Curve fits used to produce estimates of barge flotilla traffic for Gandy Bridge ...... 201
C-10 Curve fits used to produce estimates of barge flotilla traffic for Highway-90 Bridge over Escambia River and Pensacola Bay Bridge ...... 202
C-11 Curve fits used to produce estimates of barge flotilla traffic for Sister’s Creek Bridge...... 203
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LIST OF ABBREVIATIONS
aB Barge bow damage depth
AF Annual frequency of collapse
BM Width of a barge flotilla
BP Width of a bridge pier
BC Number of barge casualties
BR Base aberrancy rate
CH Hydrodynamic mass coefficient
dλ Rate of vessel failure per unit of travel
ds
D Damage state
E Modulus of elasticity
EA Total energy absorbed by the bow of an impacting barge
Edef Energy of deformation
EMR Effective mass ratio
F Probability that a vessel will not be able to evade striking a bridge element
f DWT Frequency of vessel traffic as a function of vessel tonnage
fH Probability density function which describes the distribution of water levels
f TD Probability density function which describes vessel positions perpendicular to the channel centerline
fDA Probability density function which describes the vessel yaw angle
Fdx Frontal impact force
Fdy Lateral impact force
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Fdyn Dynamic design impact force
Fs Inter-column barge flotilla frictional forces
G Probability of collision h Water level interval
H Hazard classification
IW Number of water level intervals considered
S Number of vessel groups JV
KP Pier stiffness in the direction of impact
KE Vessel collision energy
KEI Initial kinetic energy of an impacting barge flotilla
LOA Overall vessel length
LS Number of straight segments that a channel can be divided into such that nonlinear waterway geometry can be approximately represented
M E Effective flotilla mass
MT Total flotilla mass m Combined effective mass of impacting vessel(s) and the hydrodynamic mass of the water volume in the immediate vicinity of the vessel(s)
mbarge Total barge mass n Number of vessel passages per unit of time
N Number of vessels
NC Number of navigation channels
ND Number of different ways a given hazard can damage a structural system
NH Number of hazards considered
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NS Number of adverse states for a structural system
NT Number of barge flotilla transits
P Vessel-bridge collision probability
pa Probability that a collision with a structure is avoided by human action
PA Probability of aberrancy
PB Design barge impact force
Pc Causation probability
Pclsn Total vessel-bridge collision probability
PIF Pier influence factor
PC Probability of collapse
PF Failure probability
PF Protection factor for a bridge pier
PFbr Protection factor for a bridge site
PG Geometrical probability
PG Geometric probability of collision associated with a particular bridge pier
PGbr Geometric probability of collision associated with a particular bridge site
PGp Area integrated under the PG normal distribution (i.e., the PG value) associated with the a protected pier
PI Probability of impact
PS Pier stiffness at the point of impact in the direction of impact
R Calculated risk
R Resistance of a structure
RB Modification factor for bridge location
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RC Modification factor for current conditions
RD Modification factor for vessel traffic density
RXC Modification factor for cross-current conditions
S Adverse state s Distance from the point at which vessel aberrancy is initiated until a bridge element is struck
T Time period associated with risk assessment
V Vessel impact velocity
VC Current velocity
Veq Equivalent vessel impact velocity
VDF Vessel density factor
VXC Cross-current velocity
vrd Impact velocity
wS Vessel deadweight tonnage
W Vessel displacement tonnage
W Navigable width of a waterway near a bridge location
Ws1() Probability of a collision occurring as a function of the waterway position
Ws2 () Probability that a vessel will not be able to come to a stop before colliding with a structure as a function of the waterway position
WP Pier width x Distance between a structure and a point in the waterway where equipment failure occurred x Stopping distance x X-coordinate indicating the position of a vessel in a channel y Y-coordinate indicating the position of a vessel in a channel
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α Impact angle
γ Specific weight
θ Angle of waterway turn or bend
θ Yaw angle of a vessel
θ Angle of sliding
θmax Maximum yaw angle of a vessel
θmin Minimum yaw angle of a vessel
λ Probability that a navigational or equipment failure occurs in a vessel per unit of travel
λ Vessel aberrancy rate per unit of travel
µ Friction coefficient
µN Average annual vessel traffic
ν Poisson’s ratio
σ Standard deviation
φ Normally-distributed probability density function which represents the distance a vessel travels from the onset of aberrancy until stoppage
φ Angle of repose
ϕ Angle of deviation from a planned path of travel
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
EVALUATION OF BARGE FLOTILLA ABERRANCY RATES AND INTER-BARGE RELATIVE MOTIONS FOR THE ANALYSIS AND DESIGN OF WATERWAY BRIDGE STRUCTURES SUBJECT TO BARGE COLLISIONS
By
George Christopher Kantrales
August 2016
Chair: Gary Consolazio Major: Civil Engineering
Waterway barges are commonly employed throughout the world to transport various types of commodities in bulk. Due to the significant mass of individual barges and multi-barge flotillas, significant structural demands can be generated if such vessels collide with waterway bridge structures at normal transit velocities. As a consequence, an important component of the bridge design process includes the consideration of impact-induced structural demands.
To address the threat posed by barge-to-bridge collisions, authorities such as the
American Association for State Highway and Transportation Officials (AASHTO) regularly release bridge design specifications that include methods to predict the likelihood of an impact event and compute appropriate design loads. However, the design expressions used to predict the likelihood of a barge-to-bridge impact event are based on limited data that may not be reflective of the current state of the barge towing industry. Furthermore, present specifications incorporate several implicit assumptions regarding the effective mass of impacting barge flotillas that have not been thoroughly explored to date. The research discussed in this dissertation is intended to address these limitations.
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In order to improve provisions used to predict the likelihood of a barge-to-bridge impact event, barge accident and traffic data from multiple bridge locations were used to recalibrate the design AASHTO barge flotilla base aberrancy rate through statistical analysis. To make this
expression particularly applicable for collision events, only barge-to-bridge collision data were utilized.
In addition, to investigate impact-induced relative motions within a flotilla and the effects of such motions on structural demands, a parametric study was conducted using three-
dimensional finite element analysis techniques. Relative motions that were considered included
payload sliding within individual barges as well as inter-barge crushing, sliding and lashing
failure associated with multi-barge flotillas. Based on behavioral observations, recommendations were made regarding effective flotilla mass levels appropriate for use with current bridge design
procedures. Barge bow force-deformation relationships used in support of this investigation were
validated through large-scale pendulum impact testing.
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CHAPTER 1 INTRODUCTION
A critical component of the design process for waterway bridges is the consideration of
structural loads related to barge-to-bridge impact events. Such scenarios are considered extreme
events in the design process and may result in considerable damage and loss of life if care is not
taken in evaluating the structural collapse risks associated with them. Historical examples, such
as the collapse of the I-40 bridge in Webbers Falls, Oklahoma (NTSB 2004), illustrate the
importance of both predicting the frequency with which bridges are struck by barges, and
designing bridges to resist the forces associated with such collisions.
1.1 Motivation
Within the United States, the American Association of State Highway and Transportation
Officials (AASHTO) regularly releases design specifications dealing with vessel impact-resistant design methodologies. Methodologies described in these documents include expressions for predicting the likelihood that a vessel (ship or barge) will collide with a given bridge structure, and static load models that may be used to design bridges to resist the loads imparted by vessel collisions. The majority of AASHTO (2014) specifications dealing with vessel impact loads were formulated using research conducted prior to 1990, at which time limited information was available relating to barge-to-bridge collision events.
Consequently, the AASHTO design expressions used to predict the likelihood of barge-
to-bridge collisions are derived from ship collision data or other types of vessel casualties, such as strandings or groundings. In addition, several assumptions are incorporated into the kinetic energy calculations used to determine barge flotilla impact loads. One such assumption is that
Material in this chapter was reproduced and adapted from the author’s contributions to Consolazio and Kantrales (2016).
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no energy dissipation occurs due to relative motions, such as payload sliding or inter-barge
crushing, during a barge-to-bridge impact. In contrast to this conservative assumption, present
AASHTO specifications also state that the mass of non-impacting barge columns should not be
considered in design calculations. In this case, lashings between non-impacting barge columns
and impacting barge columns are assumed to fail during impact, resulting in a breakup of the
barge flotilla (Figure 1-1). However, there is limited data—empirical, experimental, or
analytical—that can be used to support this assumption.
In the years following the original release of the AASHTO provisions, several investigations have been conducted to address various underlying limitations (see Chapter 2).
However, despite improved data and computational resources, there has been limited work
focused on revising expressions used to predict the likelihood of barge-to-bridge collisions or
address the assumptions related to barge flotilla impact behavior noted above. Consequently, in
the present investigation, recent barge-to-bridge collision data were incorporated into a statistical
recalibration effort that produced a revised barge flotilla base aberrancy rate (BR) that may be
used in conjunction with current AASHTO design procedures. In addition, finite element
analysis techniques were used in an extensive parametric study to address the lack of information
on barge flotilla relative motions (e.g., inter-barge crushing and sliding) and the influence of such motions on structural demands. This study incorporated validated three-dimensional barge flotilla models in each simulation. Based on the analysis of aggregated simulation results, recommendations were made regarding effective barge flotilla mass levels that may be used in impact load-calculation procedures to implicitly consider the influence of relative motions.
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1.2 Objectives
Two primary objectives were associated with the research presented in this dissertation.
The first was to develop a revised probability expression to predict the frequency of occurrence
associated with barge-to-bridge collisions. This was achieved through a recalibration of the
AASHTO base aberrancy rate (BR) for barge flotillas, which is employed as a sub-component of
AASHTO expressions presently used to predict the likelihood of a barge-to-bridge impact event.
To ensure that the revised expression is particularly applicable for bridges in Florida, data
collection and analysis efforts were focused on barge traffic and collision data associated with
Florida waterways.
The second objective was to characterize the influence of barge flotilla relative motions
on effective flotilla mass levels used in structural load calculations. Validated finite element
modeling and analysis techniques were employed to explore the significance of payload sliding,
inter-barge crushing, and lashing failure on the effective kinetic energy that is associated with
structural demands. This was accomplished through a 3,000 simulation parametric study which
considered the influence of both flotilla and structural characteristics.
1.3 Organization
This dissertation is organized into six chapters which cover various aspects of the present
study. Chapter 2 (Background) contains a review of design specifications relevant to the analysis
and design of waterway bridge structures subject to barge collisions. This review is focused on
both AASHTO and Eurocode provisions. In addition, this chapter contains a review of relevant
research pertaining to barge impact behavior and impact event prediction. Limitations associated
with both design specifications and research investigations are also discussed.
Chapter 3 (Determination of Impact Probabilities for Bridge Design) describes the
research effort that produced a recalibrated estimate of BR for barge flotillas. Data sources and
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collection methods are outlined in addition to all data analysis techniques employed.
Observations and conclusions that affected the recommended design value are described in
detail.
Chapter 4 (Experimental Validation of Barge Bow Force-Deformation Behavior) discusses a combined analytical and experimental investigation to validate modeling and simulation techniques that may be used to quantify barge bow force-deformation behavior. In this effort, large-scale pendulum impact testing was employed in conjunction with high- resolution finite element modeling. As a consequence, both analytical and experimental procedures are described.
Chapter 5 (Influence of Impact-Induced Relative Motion on Effective Barge Flotilla
Mass) describes an analytical study that was conducted to evaluate relative motion in barge flotillas and the influence of such motions on structural demands. In support of this effort, barge bow force-deformation relationships were produced using high-resolution finite element modeling and simulation techniques validated experimentally through the study described in
Chapter 4. Payload relative motion in single barges was investigated using a coupled model wherein a discrete element payload model was paired with a three-dimensional jumbo hopper barge model. Inter-barge relative motion due to crushing, sliding, and lashing failure was
investigated under various impact conditions using a variety of three-dimensional jumbo hopper barge flotilla models.
Chapter 6 (Conclusions and Recommendations) outlines findings from each component of the investigation. Recommendations relevant to design and future research are also provided.
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Intact lashing Bridge superstructure Failed lashing Waterline pile cap
Impacting barge column Pier column
Non-impacting barge Direction of motion column (broken away)
Figure 1-1. Flotilla breakup scenario utilized in AASHTO (2014) bridge design specifications (aberrant flotilla outside of navigation channel shown).
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CHAPTER 2 BACKGROUND
Waterway barges, which transport various commodities (e.g., coal, oil) in bulk, are a
common feature in many inland rivers and coastal areas throughout the world. Depending on the
amount of commodity being shipped, barges can transport cargo individually, with a single tug,
or as part of a group of inter-connected barges (i.e., barge flotillas), with one or more tugs.
Individual barges in a flotilla are connected together using pre-tensioned elements called
‘lashings’, typically comprised of wire rope, which are wrapped around posts mounted on each barge referred to as ‘bitts’ (Figure 2-1). The size of a flotilla is indicated by the number of barges across the width of the flotilla—the number of barge columns (strings)—and the number of barges along the length of the flotilla—the number of barge rows (Figure 2-2).
In order to provide guidance to design engineers on the issue of barge-to-bridge collisions involving either single barges or multi-barge flotillas, the American Association of State
Highway and Transportation Officials (AASHTO) and the European Committee for
Standardization (CEN) have developed design specifications that directly address the topic of vessel collision. Since the development of revisions to selected AASHTO specifications is one of the primary objectives of this investigation, details regarding AASHTO (2014) design methodologies are discussed in this chapter and contrasted with CEN (2006) provisions. It is important to note that while the 7th edition of the AASHTO Bridge Design Specifications
(AASHTO 2014) is used for reference purposes throughout this dissertation, notes for the 2015
and 2016 interim revisions were reviewed and no relevant changes to the specifications dealing
with vessel impact loading were identified. In addition to a review of existing design provisions,
Material in this chapter was reproduced and adapted from the author’s contributions to Consolazio et al. (2014), Consolazio and Kantrales (2016), and, with permission from ASCE, Kantrales et al. (2015).
28
research investigations previously conducted by UF and other investigative entities that discuss
the development of probability expressions to predict the frequency of barge impact events or the determination of structural demands associated with barge flotilla impacts are also reviewed.
2.1 AASHTO LRFD Bridge Design Specifications
To design waterway bridges for vessel collision events, the AASHTO LRFD Bridge
Design Specifications (AASHTO 2014) allow for the use of several different design methodologies, two of which—Method I and Method III— require special circumstances and the permission of the bridge owner to employ.
Method I, a semi-deterministic procedure, is the simplest and most conservative of the three methodologies. In this procedure, a single ‘design vessel’ is selected for use in assessing the adequacy of the bridge structure; the design vessel is intended to represent one of the largest vessels typical of the waterway. AASHTO recommends that Method I only be used in situations where the waterway is too shallow to allow large ship traffic to pass, or for locations where accurate vessel traffic data is not readily available.
Method II, a comprehensive risk assessment procedure, is considerably more complicated than Method I, requiring significant data collection. In Method II, the annual frequency of bridge collapse (AF) is calculated using a database—developed by the design engineer—that provides a
full description of the vessels that typically transit the waterway near the bridge, as well as the
number of transits per vessel type. Due to the level of rigor required to conduct a Method II risk
assessment, it is the most accurate of the available analysis methods. As such, Method II is
considered the default approach for bridge design, and is the only procedure that does not require
explicit approval from the bridge owner before being considered for use.
Method III is a cost-benefit analysis procedure that may be employed in situations where
a Method II analysis results in design criteria that cannot be feasibly met, given various project
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constraints. Note that a Method II analysis must first be conducted prior to considering Method
III as a possible option.
As Method II is considered the default risk analysis procedure, it is the focus of the present study. As noted above, Method II requires the design engineer to compute the annual frequency of structural collapse—due to vessel collision—for each individual bridge element
(pier, span) that is at risk for impact. Computation of the annual frequency of structural collapse is achieved by applying the following equation on a per-element basis:
AF= N( PA)( PG)( PC)( PF ) (2-1) where N is the number of vessel transits per year for a particular vessel group, PA is the probability of vessel aberrancy (the probability that a vessel will deviate from the intended transit path), PG is the geometric probability (the ‘conditional probability’ that a vessel will strike a particular bridge element should deviation from the intended transit path occur), PC is the probability of structural collapse (conditional upon the bridge being struck), and PF is a protection factor used to account for protective obstructions (sandbars, fenders, dolphins, etc.) in the waterway which could prevent collisions with certain bridge elements.
Following the Method II analysis procedures, a unique AF value must be calculated using
Equation 2-1 for each major vessel group that transits the waterway. Vessel groups may be categorized as one of two types—ships or barges—and are further divided into sub-types based on various criteria (external dimensions, weight, etc.) so that each vessel within a particular group should elicit similar structural demands upon impact. Calculated AF values are compared to AASHTO-specified limits to determine the acceptability of the design. For typical bridge structures this limit is 0.001 (1/1000), whereas, for critical/essential bridges, the limit is 0.0001
(1/10,000).
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A particular focus of this study is on the combined influence of the terms PA, PG, and PF
(as used to compute AF), which collectively predict the probability that a given vessel will strike
a bridge element. Details regarding these terms are provided in the following sub-sections.
2.1.1 Probability of Aberrancy
PA, the probability of aberrancy (Equation 2-2), is a measure of the likelihood that a
vessel will deviate from its intended transit path:
PA= BR( R)( R)( R)( R ) (2-2) B C XC D where BR is the base aberrancy rate, and RB , RC , RXC , and RD are modification factors that
amplify the base aberrancy rate to account for various waterway conditions. Such conditions
include: the location of the bridge relative to turns or bends in the waterway ( RB ); currents
acting parallel to the intended transit path of the vessel ( RC ); cross-currents acting perpendicular
to the intended transit path of the vessel ( RXC ); and the density of vessel traffic in the immediate
vicinity of the bridge ( RD ). The magnitude of BR is dependent on the vessel type being
considered (0.00006 for ships and 0.00012 for barges) to reflect the relative difficulty of
pilotage.
RB is calculated by first examining the geometry of the waterway in the vicinity of the
bridge structure to determine whether or not the bridge is located within, or immediately adjacent
to, either a turn or a bend in the waterway. Should the bridge be located immediately adjacent to
either a turn or a bend, the bridge is classified as being in a ‘transition region’ (Figure 2-3). The angle of the turn or bend (θ ) is then calculated (as shown in Figure 2-3) and used in one of the following equations:
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θ R =1 + B (2-3) 45
θ R =1 + B (2-4) 90
Equation 2-3 is employed if the bridge under consideration is directly within a turn or
bend, and Equation 2-4 is used if the bridge is located within a transition region. If no turn or
bend is present in the waterway near the bridge (i.e., the waterway is straight), RB is taken as one.
Determining the current and cross-current modification factors ( RC and RXC ,
respectively) involves calculating waterway velocities parallel (VC ) and perpendicular (VXC ) to
the intended vessel transit path. Such velocity determinations are commonly done through
hydraulic and hydrologic analysis, but may also be obtained from other sources. Equations 2-5
and 2-6 are then used to determine appropriate impact risk amplification factors.
VC RC =1 + (2-5) 10
RV=(1 + ) (2-6) XC XC
Unlike other modification factors noted above, the vessel traffic density factor RD is
selected solely based on the judgment of the design engineer. RD can take one of three values,
depending on the vessel traffic density category selected:
• Low density (RD = 1.0)
• Average density (RD = 1.3)
• High density (RD = 1.6)
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Selection of the vessel traffic density category is related to the frequency at which vessels
encounter (cross or pass) each other in the vicinity of the bridge. A rough determination of vessel
traffic density can be performed by examining the geometry of the waterway, and the relative
numbers and sizes of vessels that typically transit the waterway near the bridge, over a span of
several years. This information can then be used by an experienced design engineer to select a
representative value for RD .
2.1.2 Geometric Probability
To assess the likelihood that an aberrant vessel will strike a particular component of a
bridge structure, AASHTO (2014) utilizes a conditional probability term entitled ‘geometric
probability’ (PG). It is important to note that this term includes the probabilistic distribution of
location for a given aberrant vessel along the width of the waterway. Consequently, PG is not
used to represent probable locations of vessels that are tracking ‘normally’ along an intended
transit path.
Calculation of PG for a specific bridge element is performed by integrating a probability
density function (PDF) that models the distribution of probable (aberrant) vessel locations across
the waterway over a desired range (Figure 2-4). This range is related to the width of the bridge pier (or pile cap) as well as the beam (width) of the vessel being considered. As a consequence, a unique value of PG must be determined for each combination of pier and vessel type. Detailed in
Figure 2-4, the PDF which describes possible locations of the aberrant vessel within the waterway is normally distributed about a mean which represents the centerline of the intended vessel transit path. The standard deviation of the PDF is taken as the overall vessel length
(LOA); a unique LOA must be computed for each type of vessel considered in the risk analysis.
AASHTO specifies that any bridge elements located outside a distance of 3 x LOA from the
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centerline of the vessel transit path (computed using the LOA of the largest design vessel) be
omitted from the risk analysis. It should be noted that the normal distribution assumed for PG, as
well as the parameters that define its shape, were developed from historical records of ship-to-
bridge collisions; nevertheless the same PG distribution is also used to assess risks associated with barge-to-bridge collisions.
2.1.3 Protection Factor
Since the probability of a barge impacting a particular bridge pier or pile cap can be influenced by the presence of impassable waterway features (shallow sand bars or protective systems such as dolphins or fenders), the AASHTO provisions include a term which modifies
AF to reflect the reduction in impact probability that is associated with shielding a bridge
element. This term, called a protection factor ( PF ), is employed on a per-element basis using
the following equation:
= − PF1 (% Protection Provided /100) (2-7)
Note that the methodology used to calculate the percentage of protection provided by a
barrier or protective system is based on the judgment of the design engineer, and will vary
depending on the characteristics of the individual protective system under consideration.
2.1.4 Barge Impact Forces
Barge-to-bridge impact forces computed using the procedures detailed in
AASHTO (2014) are applied as static design forces, and are determined in three stages. The first
stage is the calculation of the kinetic energy associated with an impacting vessel:
C WV()2 KE = H 29.2 (2-8)
where KE is the vessel collision energy (kip-ft), CH is the hydrodynamic mass coefficient
(unitless), W is the vessel displacement tonnage (tonne), and V is the vessel impact speed
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(ft/sec). Note that the divisor in Equation 2-8 is related to gravitational acceleration. For multi-
barge flotillas, W is calculated using the combined mass of the tug/towing vessels and the total number of barges in one column of the flotilla. AASHTO recommends that the mass of adjacent
(non-impacting) columns in a multi-column barge flotilla should be neglected in the computation
of vessel tonnage, based on the assumption that the lashings between columns will fail during
impact, causing these columns to break away, and thereby not contribute to the impacting mass
of the barge flotilla (Figure 1-1).
In addition to the mass of the impacting vessels, the mass of the water volume moving
with the vessel immediately prior to impact must be approximated in the calculation process.
AASHTO satisfies this requirement through implementation of a CH coefficient. CH can take on multiple values, based on the vessel underkeel clearance, which is the distance between the bottom of the vessel and the bottom of the waterway:
• CH =1.05 if the vessel underkeel clearance exceeds 50% of the vessel draft
• CH =1.25 if the vessel underkeel clearance is less than 10% of the vessel draft
For intermediate values of underkeel clearance, CH may be calculated through linear
interpolation. The AASHTO provisions for hydrodynamic behavior were adopted from research
conducted by PIANC (1984) and Saul and Svensson (1982), which indicated that the influence
of hydrodynamic effects can be approximately represented by a hydrodynamic mass that is
added to the vessel mass for the purpose of performing design computations.
After calculating the kinetic energy associated with the impacting vessel, AASHTO
requires the determination of a barge bow damage depth, which is the depth of deformation into
the barge bow in the direction of impact (i.e., crush depth):
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KE aB =10.2 1 +− 1 5672 (2-9)
where aB is the barge bow damage depth (ft), and KE is the vessel collision energy (kip-ft),
calculated using Equation 2-9. The crush depth aB is then used to determine a final design barge
impact force:
Pa= 4112 a < 0.34 ft BB for B (2-10)
Pa=1349 + 110 a ≥ 0.34 ft BB for B (2-11)
where PB is a design barge impact force (kip), and aB is the barge bow damage depth (ft),
calculated using Equation 2-9. When plotted as a piece-wise linear function, Equations 2-10 and
2-11 produce a bilinear load-deformation (force-crush) curve (Figure 2-5).
Equations. 2-9, 2-10, and, 2-11 were adapted by AASHTO from research conducted by
Meier-Dӧrnberg (1983), which included a static and several dynamic barge crushing experiments performed on reduced-scale European pontoon barges (See Section 2.4.2). Results from these experiments were scaled up to full-scale and used to form the AASHTO design force- deformation relationship shown in Figure 2-5.
2.1.5 Limitations
The probability expressions currently implemented in AASHTO (2014) to predict the occurrence of barge-to-bridge impact events are based on research conducted before 1991. At that time, comprehensive data sets associated with such events were not widely available. As a consequence, a relatively small collection of vessel casualty statistics were used to calibrate parameters in both PA and PG. Moreover, as opposed to considering only vessel casualties that involved vessels striking bridge elements, all types of impact events were considered, including vessel groundings and vessel-to-vessel collisions. Between 1991 and present, significant
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advances in navigational technology have occurred, including the wide-spread utilization of global positioning systems (GPS), automatic identification systems (AIS), and electronic chart display and information systems (ECDIS). Advances in vessel mechanical systems, such as azimuth thrusters for multi-directional propulsion, have also seen increased use in modern tugs and towboats. Moreover, in addition to technological advances, there have also been significant changes in the training and certification requirements for tug and pushboat operators. It is probable that the combined effects of technological advances and improved training requirements has resulted in a substantial decrease in vessel aberrancy rates relative to pre-1991 levels.
In addition to the issues discussed above regarding the prediction of barge-to-bridge impact events using current AASHTO procedures, it was also noted that the mass of non- impacting barge columns is not considered in the kinetic energy calculations used to determine design forces. The basis for this approach is related to the assumption that lashing failure will prevent the engagement of non-impacting columns. However, this assumption is inconsistent with Eurocode standards (Section 2.2), and has not been explored thoroughly to date.
2.2 Eurocode 1: Actions on Structures
In contrast to the AASHTO specifications, European standards for vessel collision design—developed by the European Committee for Standardization—are more loosely organized with more flexibility afforded to individual nations. Primary design guidelines and concepts for vessel collision are organized in Eurocode 1: Actions on Structures (EN 1991), Part
1-7: General Actions - Accidental Actions (CEN 2006). Each nation that adopts EN 1991 determines specific quantities for many of the variables mentioned in the provisions. This information is then detailed in a supplementary document called a ‘national annex’. The general organization and design approach of EN 1991 is outlined in the sub-sections that follow.
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2.2.1 General Principles
EN 1991 divides accidental actions, such as vessel collisions, into three categories based
on a qualitative measure of consequence in the event of a failure: CC1 (low-level consequences);
CC2 (moderate-level consequences); and CC3 (high-level consequences). These categories are
coupled to recommendations on design and analysis methods in increasing order of complexity.
In the case of a design situation classified as a CC1 event, no specific action to mitigate failure is
recommended (beyond designing for general robustness and stability, as provided in EN 1990 –
EN 1991). For CC2 events, equivalent-static analyses or prescriptive designing/detailing procedures are recommended. Finally, for CC3 events, EN 1991 specifies that a comprehensive
risk assessment incorporating nonlinear-dynamic structural analysis methods may be necessary.
More specific recommendations can also be provided in national annexes, as deemed appropriate by individual nations.
In the event that the threat posed by vessel collision is significant enough to merit independent consideration (CC2 and CC3), EN 1991 provisions recommend that only dynamic or equivalent static design forces be used to represent vessel collision events. The use of static design forces without implicit inclusion of dynamic effects is not considered an adequate approach for design. Moreover, it is assumed that the impacting vessel dissipates a considerable majority of impact energy through plastic deformation (also called a ‘hard impact’). EN 1991
Section 4.6 outlines additional areas that should be considered by a design engineer, including:
(1) the characteristics of the waterway (geometry, currents, depth); structural characteristics
(stiffness, mass, ability to dissipate energy); and vessel characteristics (type, dimensions, force-
deformation behavior under impact conditions). Vessels are divided by the Eurocode into two
major design categories: (1) vessels which commonly transit inland waterways and (2) ocean-
going vessels. Inland vessels are further organized into a series of classes according to the
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European Conference of Ministers of Transport (ECMT) classification system (Table 2-1). In contrast, ocean-going vessels are classified according to unique systems outlined in individual national annexes. Representative categories for such vessels, along with relevant design values, are provided in Table 2-2.
EN 1991 requires that two separate load cases be considered for barge-to-bridge impact design (Figure 2-6). These include: (1) a frontal (i.e., head-on) impact force ( Fdx ), and (2) a
lateral impact force ( Fdy ) to be applied in conjunction with a friction force (FFR= µ dy ) . Note
that the friction coefficient relating Fdy and FR may be specified in a national annex, but is recommended to be taken as 0.4 in the main EN 1991 provisions.
Similar to the AASHTO PB expression, EN 1991 presents a method for computing barge
impact forces that is based on findings from the reduced-scale gravity hammer experiments
conducted by Meier-Dӧrnberg. The method presented in EN 1991 involves computing the
energy of deformation (Edef ) , which is the total (combined elastic and plastic) energy absorbed by the barge on impact with a bridge pier or waterline pile cap. Since the bridge element is assumed to behave rigidly during an impact event, Edef is simply equal to the kinetic energy of
the vessel prior to impact:
1 2 E= mv( ) def2 rd (2-12) where m is the combined effective mass of the impacting vessel(s) and the hydrodynamic mass
of the water volume in the immediate vicinity of the vessel(s) prior to impact, and vrd is the
impact velocity. Additionally, for the case of a lateral impact at an angle α , with respect to the
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impacted face of the bridge element (Figure 2-6), the energy of deformation may be computed as
follows:
1 2 E= mv( ) (1− cos(α )) def2 rd (2-13)
In the event that the angle α is not known, EN 1991 recommends that a value of 20 be used in
conjunction with Equation 2-13.
While EN 1991 does provide some guidance on the calculation of hydrodynamic mass—
it is taken as 10% of the vessel mass for frontal impacts, and 40% of the vessel mass for side
impacts—no guidance is provided in regards to calculating the effective mass of an impacting
barge flotilla with multiple columns. Instead, EN 1991 recommends using the design values
shown in Tables 2-1 and 2-2, or similar values that may be obtained from individual national
annexes. However, it should be noted that two of the barge flotilla classifications provided in
Table 2-1 consist of six or more barges; flotillas with this number of vessels are typically
arranged in multiple columns. For broadside impacts, EN 1991 recommends that the total design
mass be taken as one-third of the combined mass of the vessel(s) and the surrounding water volume (hydrodynamic mass). In the absence of vessel-specific information, it is recommended that vrd be taken as 3 m/sec (~10 ft/sec). Furthermore, in the event that the vessel is transiting
through a harbor, EN 1991 states that the impact velocity may be lowered to 1.5 m/sec
(~5 ft/sec).
Using the computed deformation energy, the dynamic design impact force may be
computed as follows:
If Edef ≤ 0.21 MNm
FE=10.95 (2-14) dyn def
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If Edef > 0.21 MNm
FE=+⋅5.0 1 0.128 (2-15) dyn def
where Fdyn is the dynamic design impact force (MN), and Edef is the energy of deformation of
the impacting vessel (MNm). It is intended that Equation 2-14 be employed for elastic impact
events (i.e., events which cause no permanent deformation in the bow of the impacting vessel);
otherwise, Equation 2-15 should be used. In the event that, under certain conditions, a dynamic
analysis cannot be conducted, EN 1991 recommends that the dynamic design forces computed
from Equations 2-14 and 2-15 be amplified by an appropriate dynamic amplification factor—1.3
for frontal impacts and 1.7 for lateral impacts—to produce an equivalent static design force.
According to EN 1991 provisions, dynamic analysis is the preferred approach for
determining structural demands associated with vessel impact events. This is done through
applying pre-constructed force time-histories (Figure 2-7) to a structural model. While EN 1991 distinguishes between elastic and plastic impact events through the general shape of the time- history, specific details regarding impulse durations are not provided.
2.2.2 Risk Analysis Methodology
In some instances, structural failure due to vessel impact can have severe consequences
(e.g., failure of a pier for a major highway bridge). For these cases, per EN 1991 recommendations, a comprehensive risk assessment (i.e., risk analysis) may be necessary. The general approach for such an analysis (Figure 2-8) is iterative in nature and contains both qualitative and (if sufficient data are available) quantitative components.
Evaluating risk using EN 1991 procedures first involves defining the boundaries
(purpose, assumptions, and objectives) of the risk analysis. Following this, a qualitative analysis is conducted, which includes determining the sources of potential hazards as well as any
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environmental factors which could contribute to hazard severity. If feasible, a quantitative
analysis is subsequently performed. A general approach for quantifying the risk posed to a
structural system is provided in the form of Equation 2-16.
NNHDNS R= ∑ pH(i ) ∑∑ pD ( ji H )( pS kj D )( CS k ) (2-16) i=1 jk = 11 =
where R is the calculated risk, NH is the number of hazards considered, pH()i is the
probability of occurrence for hazard Hi , ND is the number of different ways that hazard Hi can damage the structural system, NS is the number of adverse states for the structural system,
pD()ji H is the conditional probability that damage state D j will occur for a given hazard Hi ,
pS()kj D is the conditional probability that adverse state Sk will occur given that damage state
D j is present, and CS()k is the consequence associated with adverse state Sk .
In addition to the general approach presented in Equation 2-16, EN 1991 provides a procedure more specific to vessel collision (Equation 2-17) that may be used to quantify the probability of failure for a given structural system:
Pf ( T )=−> nλ T (1 pa )∫ P ( F dyn ( x ) R ) dx (2-17) where PTf () is the probability that the structural system fails over a selected time period T , n
is the number of vessel passages per unit of time, λ is the probability that a navigational or
equipment failure occurs in the vessel per unit of travel, pa is the probability that a collision
with the structure is avoided by human action (e.g., avoidance maneuvers), and PF(dyn ( x )) is
the probability that the dynamic impact force imparted by the vessel, Fxdyn (), is greater than the
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resistance of the structure, R . Note that the dynamic impact force is a function of x , the
distance between the structure and the point in the waterway where equipment failure occurred.
2.3 Previous UF/FDOT Research
Researchers at UF, coordinating with the FDOT, have conducted numerous past
investigations into barge impact behavior. All of these investigations were targeted toward
addressing specific limitations of AASHTO bridge design provisions. This section summarizes
the findings from these past studies that are most pertinent to the research discussed in this
dissertation.
2.3.1 Full-Scale Barge Impact Experiments
In one of the few experimental investigations of barge-to-bridge impact behavior,
Consolazio et al. (2005) conducted full-scale barge impact tests (Figure 2-9) that were able to achieve moderate barge bow deformation levels (less than 20 in.). These experiments, conducted on a decommissioned causeway bridge near St. George Island, Florida, involved multiple impacts from a full-size barge striking concrete bridge piers. Tests were conducted on two different stand-alone piers, as well as a pier with the superstructure in-place. Impact forces and barge bow deformations were quantified for each test. Due to environmental restrictions, structural collapse of the piers was not permissible; consequently, tests were limited to moderate impact energies.
Data relating to the full-scale force-deformation behavior of barges during head-on barge-to-bridge collisions were obtained from this study and later used to validate modeling and simulation techniques employed in complementary analytical studies (Consolazio et al. 2009,
Getter and Consolazio 2011). In addition, observations were made regarding response mechanisms that resulted in dynamic amplification of structural demands (e.g., pier column moments and shear forces). These response modes included an inertial-restraint mechanism, and
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a momentum-driven sway mode, wherein the momentum of the superstructure following impact
acts as a source of structural demand.
2.3.2 Coupled Vessel Impact Analysis (CVIA)
Discussed earlier in this Chapter, present AASHTO design procedures for barge-to-
bridge collision analysis employ static design loads. However, since a barge-to-bridge collision
is a dynamic event, dynamic amplifications of structural demands are possible. As a
consequence, the utilization of static analysis procedures which do not implicitly considered such
amplifications may result in unconservative predictions of structural demands. To ameliorate this
issue, Consolazio and Cowan (2005) developed a time-history analysis method, called coupled vessel impact analysis (CVIA), which treats an impacting barge and the impacted bridge as a coupled system for analysis purposes. This is accomplished through connecting a single-degree- of-freedom (SDOF) representation of the barge with a multi-degree-of-freedom (MDOF) representation of the bridge through a contact spring with a force-deformation curve describing the crushing behavior of a barge bow. Since the bridge is modeled as a MDOF system, the mass and stiffness characteristics of the bridge pier, bridge superstructure, and surrounding soil body, are explicitly represented. Consequently, any dynamic response of the bridge that could result in the amplification of structural demands is captured.
Following the initial development of CVIA, Consolazio and Davidson (2008) developed a modeling simplification known as the one-pier-two-span (OPTS) method that is intended to be used in conjunction with CVIA. In this procedure, only the pier impacted by the barge and the portion of the bridge superstructure supported by the impacted pier are modeled explicitly. The stiffness and mass characteristics of the rest of the bridge—adjoining piers and spans—are modeled with linear springs and lumped masses.
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2.3.3 Barge Bow Force-Deformation Behavior
In a systematic sequence of connected studies (Consolazio and Cowan 2003, Consolazio
et al. 2009, Getter and Consolazio 2011), static and dynamic simulations of high-resolution barge
models were conducted to quantify the force-deformation behavior of barge bows during barge-
to-bridge impacts. One of the most important findings of these investigations was that barge
impacts against rounded bridge piers generate smaller forces than corresponding impacts (i.e., at
an equivalent energy level) against rectangular piers. This outcome relates to the manner in
which ‘stiffening-trusses’ inside the bow of a barge are engaged and buckle during impact. Using
numerical simulations, parametric studies were conducted that spanned a wide range of pier
shapes (e.g., rounded, rectangular, etc.), pier sizes (e.g., diameters, widths), and vessel impact
angles. Simulation results were subsequently used to develop impact load prediction equations
that enable bridge designers to account for pier shape, pier size, and impact angle when
computing impact loads, features not presently incorporated into widely used design standards
(e.g., AASHTO 2014).
Also of direct relevance to bridge design, the analytical studies indicated that jumbo
hopper barges and tanker barges, both common to U.S. waterways, have comparable force-
deformation relationships due to design similarities. Moreover, it was determined that for both
barge types, a simplified elastic, perfectly-plastic (i.e., limited load) barge force-deformation relationship (Consolazio et al. 2009) is adequate for use in bridge design. While this observation differs from the current AASHTO force-deformation curve, where a monotonic hardening effect was clearly evident in the measured force-deformation data, the discrepancy may be related to
differences in barge construction techniques.
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2.4 Related Research
In addition to the investigations previously conducted by UF, there have been several
other studies that have explored various aspects of barge collision events. Due to the objectives
and scope of this investigation, selected studies that have considered the prediction of barge-to-
bridge impact events, the characterization of barge bow force-deformation behavior, and the
impact response of multi-barge flotillas are summarized in this section.
2.4.1 Impact Event Prediction
In addition to the methods proposed by CEN (2006) and AASHTO (2014), several other
procedures have been developed by researchers to predict the occurrence of vessel impact events.
The most relevant of these investigations are summarized below.
Larsen (1993) proposed a methodology (Equation 2-18) to determine the number of
annual vessel-bridge collisions resulting in failure ( F ) that is similar in form to the AASHTO
AF expression, but without the additional modification factors that are incorporated into
AASHTO:
F= NP ×× P × P (2-18) ∑∑i ci, Gik ,, Fik ,,
where Ni represents the number of vessels belonging to class i, Pci, is the ‘causation probability’, or the probability that a vessel from class i will be unable to avoid collision, PGik,,
is the ‘geometrical probability’, or the probability that a vessel from class i will strike the k’th
bridge element, and PFik,, is the ‘failure’ probability associated with the k’th bridge element if
it is struck by a vessel from class i. Larsen recommends that vessels be classified into groups depending on a variety of vessel characteristics, including: draft; air draft; and structural characteristics (which relate to collision-induced loads).
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Kunz (1998) presented a model (Equation 2-19) to determine the probability of vessel- structure collision (ν ) for a given path of travel ( s ), which shares some basic similarities with
Equation 2-17:
dλ ν =N ×× W() s W () s ds ∫ ds 12 (2-19)
dλ where N is the number of vessel transits per unit of time, is the rate of vessel failure ds
(navigational or mechanical) per unit of travel, Ws1() is the probability of a particular collision course occurring, and Ws2 () is the probability that the vessel will not be able to come to a stop
before colliding with the structure. Ws1() may be quantified by employing the following
equations:
Ws1()= Fϕϕ (ϕϕ 12 ) − F ( ) (2-20)
ϕ _ 1 ()ϕϕ− 2 Fd()ϕϕ= exp ϕ ∫ 2 (2-21) 2pσϕ 2σϕ −∞ where, ϕ is a normally-distributed random variable representing the angle of deviation from the planned path of travel. Values of ϕ1 and ϕ2 for a particular maneuvering path and bridge pier
may be determined through graphical means (Figure 2-10).
Ws2() may be quantified by employing the following relationships:
Ws2()= 1 − Fsx () (2-22)
_ x 1 ()xx− 2 F() x = exp dx x ∫ 2 (2-23) 2pσx 2σ −∞ x
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where x is a normally-distributed random variable representing the ‘stopping distance’, or the distance over which the operators of the vessel recognize that a collision is possible and attempt to bring the vessel to a halt. Note that Equation 2-19, similar to Equation 2-17, contains a parameter which describes the probability that a failure will occur in the vessel per unit of travel.
Kunz notes that estimation of this parameter is not trivial, as it relates to a number of variables.
One recommendation is to use an estimated failure time rate (failures/vessel/year) in conjunction with the known navigational distance (to safely transit underneath the bridge) to come up with a desired failure rate per unit of travel. Additional complications associated with this approach are related to the estimation of the parameters which describe the assumed normal distributions (ϕ ,
σϕ , x , and σ x ).
Wang and Wang (2014) took general concepts from the Kunz model and expanded the
approach to account for several factors not directly addressed by Kunz which can significantly
influence vessel impact probabilities: ‘meandering’ navigation channels (nonlinear waterways);
seasonal variations in water level; and waterway obstacles. (Recall that the AASHTO provisions
also incorporate probability expressions to address both nonlinear waterway geometry [ RB ] as
well as waterway obstacles [ PF ]). Organized as a series of summations, the model proposed by
Wang and Wang (Equation 2-24) takes the following general form:
S IWV JN C PPclsn = ∑∑∑ i,, j n (2-24) i=111 jn = =
where Pclsn is the total vessel-bridge collision probability, IW is the number of water level
S intervals considered, JV is the number of vessel groups, NC is the number of navigation
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th th channels, and Pi,, jn is the collision probability associated with the i water level interval, the j
th vessel group, and the n navigation channel. Pi,, jn is determined as follows:
wS hi j LnS () DWT Pi,, jn= ∫∫fn ( w )∑ Pnl, (, h w ) dw× fH () h dh (2-25) h S l=1 i−1 wj−1
th S S where hi−1 and hi are the lowest and highest values of the i water level interval, w j−1 and w j
th DWT are the lowest and highest dead weight tonnages associated with the j vessel group, fwn ()
is the frequency of vessel traffic as a function of vessel tonnage for channel n, and LnS ()is the number of straight segments that channel n can be divided into so that nonlinear waterway geometry can be approximately represented. fhH () is a PDF which describes the distribution of
th th water levels, and Pnl, (, hw )is the vessel-bridge collision probability for the l segment of the n
channel, which is calculated using the following:
xynl, nl , ,2() x TD S Pnl,,(, h w )= l ∫∫fnl () y G( x , y | hi , w j) dxdy (2-26) x yx() n,( l− 1) nl , ,1 where λ is the vessel aberrancy rate per unit of travel, xnl,(− 1) and xnl, are the x-coordinates of
th th the beginning and ending points of the l segment of the n navigation channel, yxnl, ,1 () and
TD yxnl, ,2() are the y-coordinates of the same points (as a function of x), and fynl, () is the PDF of
vessel positions perpendicular to the channel centerline for the lth segment of the nth channel.
S S Gxyh( ,|,ij w ) is the probability of collision from position (x,y) for a vessel with tonnage wj
and water level hi , determined as follows:
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S θmax (,,xywj ) S SS Gxyh( , |i , w j ) = ∫ fDA(θθ| w j ) F( |,, xywj ) d θ (2-27) S θmin (,,xywj )
S S where θmin (,xyw ,j ) and θmax (,xyw ,j ) are the minimum and maximum yaw angles of a vessel
S S with tonnage wj at a position (x,y). fwDA(θ | j ) is the PDF of the vessel yaw angle for
S S S tonnage category wj , and F(θ |,, xywj ) is the probability that a vessel with tonnage wj ,
position (x,y), and yaw angle θ will not be able to evade striking a bridge element, calculated by:
s SS F(θφ|,, x y wjj) = 1 − ∫ ( z | w) dz (2-28) 0
S where φ ( zw| j ) is a normally-distributed PDF representing the distance the vessel travels from
the onset of aberrancy until stoppage, and s is the distance from the point at which vessel
aberrancy is initiated until a bridge element is struck.
While the approach developed by Wang and Wang accounts for several important
factors which contribute to the occurrence of vessel impact events, it is considerably more
complicated than the mostly empirical approach adopted by AASHTO. Furthermore, the effects
of certain highly influential factors considered by AASHTO, such as currents and vessel traffic
density are not explicitly represented. It is possible, however, that careful selection of an
appropriate value of λ could implicitly capture the influence of such variables. Statistical
parameters (mean and standard deviation) which define each normal distribution in the method
proposed by Wang and Wang need to be calibrated using relevant data; data for such calibrations
can be difficult to collect in some cases. Wang and Wang illustrated the calibration process by
computing parameters for the Jiujiang Bridge in the Guangdong province of China using data
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collected from local port authorities. In their example, λ was determined by utilizing vessel casualty and traffic data collected within 10 km of the bridge over a two-year period of time.
Several other investigations of note have also addressed various aspects of vessel collision analysis, including: development of risk analysis software packages employing established methods (Friis-Hansen and Simonsen 2002); use of real-time (Gucma 2003) and
Monte-Carlo based (Hutchinson et al. 2003) vessel maneuvering simulations coupled with vessel tracking experiments to predict aberrancy rates; the influence of turbulent zones (Zhang 2013); and potential effects of wind and flow-induced vessel drift (Zhou et al. 2011).
2.4.2 Barge Bow Force-Deformation Behavior
In addition to the investigations previously conducted by Consolazio et al. (2005),
Consolazio et al. (2009), and Getter and Consolazio (2011), there have been several other studies that have characterized barge force-deformation behavior as it relates to impact-resistant design procedures. Such efforts include both experimental and analytical approaches.
The most prominent experimental investigation of barge bow crushing behavior prior to the full-scale UF/FDOT experiments (Section 2.3.1) was conducted by Meier-Dӧrnberg (1983).
This study ultimately formed the basis for both Eurocode (CEN 2006) and AASHTO
(AASHTO 2014) barge bow force-deformation relationships. The main component of the Meier-
Dӧrnberg investigation, a series of dynamic experiments conducted on European pontoon barges using cylindrical and 90° pointed impact hammers, was also complemented by a static crush test of the same barge type. All barge components in the study were scaled at a ratio of 1:4.5 for the dynamic tests, and 1:6 for the static test. Results from the experiments showed that, in each test series, a monotonic system hardening effect was present, which produced higher impact forces with increasing deformation. From the measured test data, simplified relationships between impact force and barge bow deformation were developed. To make the relationships applicable
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to the design of waterway structures, the experimental data, collected at the reduced scales noted
above, were scaled up to full-scale.
In the decade following the Meier-Dörnberg tests, the United States Army Corps of
Engineers (USACE) conducted several full-scale experimental investigations related to the development of barge impact design provisions for waterway structures. In 1997 and 1998, two series of full-scale barge impact experiments were performed against lock walls at the Allegheny
Lock and Dam 2 in Pittsburgh, Pennsylvania (Patev et al. 2003a), and the Robert C. Byrd Lock and Dam near Gallipolis Ferry, West Virginia (Patev et al. 2003b, Arroyo et al. 2003). The studies included a range of low to moderate impact speeds (0.15-1.25 m/sec [0.5-4.1 ft/sec]) at
varying angles of impact (0° - 20 ° ). Although the experiments produced relatively low levels of
bow deformation, they provided valuable insights into the impact behavior of barge flotillas at
full-scale. Complementary, full-scale barge bow crushing experiments, employing a Statnamic
loading device (Brown et al. 2006) to achieve bow deformations of approximately 0.3 m (1 ft),
were also conducted by the USACE (Ebeling and Warren 2009).
In an effort to characterize the nonlinear response of reinforced concrete columns during
barge impacts, Sha and Hao (2013) conducted small-scale impact tests, estimated to be at
approximately a 1:35 scale based on published information, on a model of a circular concrete
column using a laboratory pendulum impact apparatus. A key objective in this study was
validation of a bridge pier-column FE model capable of accounting for damage sustained during
impacts (e.g., concrete cracking).
Supplementing the collection of experimental investigations cited above, several
analytical studies have also been conducted to characterize barge impact loads and barge bow
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force-deformation behavior. Among these studies, some of the most relevant work was performed by Yuan and Harik (2010), and Luperi and Pinto (2015).
Yuan and Harik (2010) employed high-resolution FE models of jumbo hopper barges in a series of analyses to produce a simplified method for computing barge flotilla impact forces with consideration of pier geometry and inter-barge interactions. In this study, it was shown that round piers correlate with smaller peak barge bow crushing forces relative to equivalent-width flat-faced piers. This finding is in agreement with previous work performed by Consolazio et al. (2009).
More recently, Luperi and Pinto (2015) developed high-resolution models of hopper and tanker barges typical of the Paraná River (Argentina) to simulate crushing behavior at high deformation levels. Luperi and Pinto confirmed a previous finding made by Consolazio et al. (2009) that round piers generally result in smaller peak barge bow crushing forces relative to flat-faced piers. However, in this study it was also found that at very high impact energies, the impacted pier may penetrate past the bow of the impacting barge and into the main body. Once this stage is reached, certain barge types that include a cover over the payload may achieve a second force peak that is higher than the initial peak associated with truss buckling. However, for deformation levels restricted to the barge bow region, the force-deformation trends produced by
Luperi and Pinto were comparable to previous findings by Consolazio et al. (2009). It should be noted that in this study, no specific payload model was assumed. Instead, mass was added to the barge nodes to approximate the presence of a payload.
2.4.3 Multi-Barge Flotilla Behavior
In contrast with research in many other areas of vessel collision analysis, there have been few investigations that have attempted to study the behavior of multi-barge flotillas during barge-to-bridge impacts. Consequently, there has been little research to develop methods that can
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account for energy dissipation within a flotilla or relative motion between individual barge
columns in such a way that these behaviors can be readily integrated into existing bridge design
expressions.
As part of a study related to barge flotilla impacts against round, lock wall terminals (i.e.,
bullnose terminals), Consolazio and Wilkes (2013) investigated the influence of various flotilla and structure-specific characteristics (e.g., bullnose diameter, number of barge rows) on structural design loads. Although the study performed by Consolazio and Wilkes was not specifically related to bridge design, several observations relevant for bridge designers were made in this previous investigation. Foremost among these was that peak impact forces were found to be strongly related to bullnose diameter, with larger diameters associated with higher forces. This observation is similar to a previous finding made by Consolazio et al. (2009) regarding the influence of bridge pier width on impact design loads (see Section 2.3). In addition,
Consolazio and Wilkes made several other findings relevant for characterizing multi-barge flotilla behavior. Importantly, it was found that flotillas with many rows and columns generally resulted in longer duration impact events relative to smaller flotillas, with the increase in duration roughly proportional to the increase in flotilla mass. In contrast, it was also found that peak design forces were not directly proportional to the number of rows or columns in a flotilla.
This behavior was attributed to the potential influence of barge lashing flexibility.
In a study more specific to bridge design, Yuan and Harik (2008) developed a simplified, one-dimensional (1-D), dynamic model of a multi-barge flotilla, which is capable of producing force time-histories that are intended to be used in a design setting. The developed method models inter-barge lashings through a bi-linear force-deformation relationship, and considers non-linear barge crushing behavior through a piece-wise linear formulation. While the approach
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presented by Yuan and Harik considers dynamic interactions between the flotilla and the bridge pier, all flotilla motions are restricted to the direction of impact. Consequently, inter-column frictional and contact forces are not considered explicitly and flotilla re-direction and breakup are inhibited.
Luperi and Pinto (2014) expanded the analysis methodologies initially developed by
Yuan and Harik to account for two-dimensional (2-D) barge flotilla behavior. In the approach proposed by Luperi and Pinto, non-linear barge crushing and lashing behavior were considered, in addition to lashing strength limits. Inter-barge frictional and contact forces were considered through an approximate approach whereby each barge in the flotilla is represented by a contour.
Regression analyses were used to develop a design equation to calculate an equivalent SDOF mass based on an equivalent-impulse principle. The resulting design equation utilizes the number of flotilla rows and columns, an impact velocity, a friction constant, and a barge bow yield force as inputs. Different regression constants are also provided for three different lashing strength levels. The approach taken by Luperi and Pinto, while a marked improvement over previously developed methodologies, restricted all barge motions to two dimensions, which limited the ability of interacting barges to rise vertically or roll relative to each other during impact. Thus, the influence of both inter-barge contact and relative motion were only approximately represented. In addition, the design expressions to calculate an equivalent SDOF mass included no parameter to account for the bridge pier stiffness in the direction of impact. As will be discussed in Chapter 5, bridge pier stiffness can significantly influence inter-barge crushing and flotilla breakup behavior.
2.5 Observations
Consideration of vessel impact loads is a critical component of the overall bridge design process, requiring careful consideration of numerous variables. While design standards
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(AASHTO 2014, CEN 2006) provide methodologies to predict the frequency of vessel impact events, and researchers (Larsen 1993, Kunz 1998, Wang and Wang 2014) have developed alternative strategies to address this topic, there remains a need for a widely-applicable and simply-structured methodology which distinguishes between a vessel-bridge collision and other types of vessel casualties (strandings, groundings, etc.). Additionally, while empirical methods are able to capture the influence of variables that are not readily characterized probabilistically
(e.g., human error), the existing empirical AASHTO method was calibrated using a limited number of data sets and may not reflect changes in navigational technology, vessel mechanical systems, and operator/pilot training that have occurred since 1991.
Existing design methods also contain limited information regarding the characterization of multi-barge flotilla collision behavior. Previous research investigations (Yuan and Harik 2008,
Luperi and Pinto 2014) have provided some guidance on this topic. However, an investigation that includes a detailed discussion of relative motion during barge flotilla collisions is still necessary. More specifically, bridge design expressions are needed to account for energy dissipation—associated with inter-barge crushing or payload motion—and energy release associated with the breakup of a flotilla. Such expressions should be readily implementable in both AASHTO kinetic energy calculations as well as alternative barge-to-bridge impact analysis methods that treat a barge flotilla as a single mass.
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Table 2-1. ECMT vessel classifications (Source: CEN 2006).
Table 2-2. Representative classifications for ocean-going vessels (Source: CEN 2006).
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Figure 2-1. Barge lashings and bitts (Source: Consolazio and Walters 2012) (Photo courtesy of USACE).
Barge column (string)
Tug
Barge row Barge Figure 2-2. Barge flotilla dimensional definitions (3x2 flotilla shown).
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Figure 2-3. Methodology for classifying geometric characteristics of a waterway that are used in the calculation of RB (Source: AASHTO 2014).
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Figure 2-4. AASHTO methodology for calculating the geometric probability, PG (Source: AASHTO 2014).
2500
2000
1500 (kip) B
P 1000
500
0 0 2 4 6 8 10 aB (ft) Figure 2-5. AASHTO barge impact force-deformation relationship.
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Impacting vessel Waterline pile cap Pier column
Fdx A
Impacting vessel
α 4.6° Fdy Waterline pile cap FR Pier column B Figure 2-6. Direction of dynamic impact forces. A) Frontal impacts. B) Lateral impacts.
F tr Fdyn
tS t tB
plastic impact (Fdyn > 5MN) F
FD 5 MN
t tr t t r B Figure 2-7. Example force time-histories for use in dynamic analysis according to EN 1991 provisions (Source: CEN 2006).
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Figure 2-8. EN 1991 Risk analysis methodology (Source: CEN 2006).
62
A
B Figure 2-9. Full-scale barge impact experiments. A) Impact with superstructure removed. B) Impact with superstructure in-place (Source: Consolazio et al. 2006) (Photo courtesy of Gary R. Consolazio).
Planned path of travel Bridge pier
ϕ1
37.51°
ϕ2
17.90°
Figure 2-10. Determination of deviation angles for a particular bridge pier and maneuvering path.
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CHAPTER 3 DETERMINATION OF BARGE IMPACT PROBABILITIES FOR BRIDGE DESIGN
Researchers at the University of Florida (UF), working in conjunction with the FDOT, have performed a significant number of prior research investigations to improve existing design methods for barge impact loading of bridges. These efforts have resulted in revised barge impact analysis methodologies (Consolazio and Cowan 2005), load models (Consolazio et al. 2009,
Getter and Consolazio 2011), and design expressions (Consolazio et al. 2010c, Davidson et al. 2013). However, since the original release of the AASHTO provisions in 1991, only limited research has been conducted on alternative methods for predicting the likelihood that a barge-to- bridge impact event will occur. Current AASHTO expressions used for this purpose were developed from a relatively small number of investigations focused primarily on ship-to-bridge impact events and other types of vessel casualties such as barge groundings and strandings. In addition, numerous maritime technological advances have taken place in the decades following first release of the AASHTO provisions; many of these technologies have an influence on the ease of vessel pilotage through coastal and inland areas where bridges are constructed.
Consequently, in the present study, a new barge impact probability expression was developed that is derived from recent and extensive barge-to-bridge collision data sets and that is more representative of the current state of the barge towing industry.
This was achieved through a recalibration of the AASHTO base aberrancy rate (BR) for barge flotillas, which is employed as a component of AASHTO expressions presently used to predict the likelihood of a barge-to-bridge impact event occurring. To ensure that the revised expression is particularly applicable for bridges in Florida, data collection and analysis efforts
Material in this chapter was reproduced and adapted from the author’s contributions to Consolazio and Kantrales (2016)
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were focused on barge traffic and collision data associated with Florida waterways.
3.1 Methodology
One of the goals of the recalibration effort discussed in this chapter was to produce a revised design expression that could be readily implemented in existing AASHTO (2014) design procedures. Consequently, the methodology of the present study was structured such that many existing AASHTO expressions were used in the recalibration framework. However, as discussed
previously, the barge accident data utilized in this study were limited to barge-to-bridge collisions (i.e., ship impacts and vessel groundings were excluded), and were reflective of
historical barge traffic (density) and accident-rate statistics specific to Florida waterways.
Prior to developing a detailed approach to revise existing AASHTO (2014) expressions
for predicting the occurrence of barge-to-bridge impact events, it was necessary to gain
additional insight into factors that could have affected barge aberrancy rates since 1991. To do
this, industry professionals were consulted to identify advances that have been made in vessel
technology (navigational and mechanical) and personnel training since 1991, and the potential
influence of such advances on barge flotilla aberrancy rates. The outcome of these interviews—
the details of which are discussed in subsequent sections—revealed that technological advances
and modern training requirements could have significantly reduced barge flotilla aberrancy rates,
relative to pre-1991 levels. As a consequence of this initial finding, a full investigation was
carried out to quantify an updated aberrancy rate reflective of the current state of the barge
towing industry (See Section 3.3).
3.1.1 Approach
Revised aberrancy rates were obtained through the use of expressions in the current
AASHTO formulation for AF (Equation 2-1). The AF component terms PA , PG , and PF ,
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when multiplied together, represent the probability that a vessel will strike the bridge. This
probability will be referred to as the ‘probability of impact’ ( PI ):
PI= ( PA)( PG)( PF ) (3-1)
Substitution of the full expression for PA (Equation 2-2) into Equation 3-1 produces:
PI= ( BR)( R)( R)( R)( R)( PG)( PF ) (3-2) B C XC D where, BR is the base aberrancy rate, and RB , RC , RXC , and RD are modification factors that
amplify the base aberrancy rate to account for: the location of the bridge relative to turns or
bends in the waterway ( RB ); currents acting parallel to the intended transit path of the vessel
()RC ; cross-currents acting perpendicular to the intended transit path of the vessel ( RXC ); and
the density of vessel traffic in the immediate vicinity of the bridge ( RD ). PG is the geometric probability, and PF is the protection factor. Rearranging the terms in Equation 3-2, BR may be
expressed as follows:
PI BR = (3-3) (R) R R( R)( PG)( PF ) B( C)( XC) D
Equation 3-3 may be used to calculate base aberrancy rates for individual bridge locations, provided that PI , PG , PF , RB , RC , RXC , and RD can all be quantified. This
process was achieved in the present investigation through the collection of data obtained from
several federal and state agencies, as well as a notable amount of site-specific data analysis.
Specific steps included:
• Consultation with industry professionals regarding advances that have been made in vessel technology and training since the 1990s, and the potential influence of these advances on barge flotilla aberrancy rates;
• Collection of all barge-to-bridge accident data that were available for Florida bridge structures;
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• Development of a list of Florida bridges included in the study, each of which has significant levels of barge flotilla traffic;
• Collection of supporting information for each suitable Florida bridge site, including: bridge plans; annual barge traffic data; and hydraulic/hydrologic data;
• Calculation of historical barge impact probabilities, AASHTO-specified protection factors, aberrancy modification factors, and geometric probabilities for individual bridge sites;
• Recalibration of the base barge aberrancy rate for bridge design using the calculated parameters noted above.
In the sections that follow, general methodologies that were used to satisfy each of the requirements listed above are discussed in detail. More specific methods used in data collection and data analysis are discussed in Sections 3.2 and 3.3, respectively.
3.1.2 Data Sources
Data collection for this study was performed in several phases, beginning with interviews of professionals working in the maritime barge transportation industry. Since the outcome of these interviews confirmed the need for a revised barge impact probability expression, several government entities were contacted regarding the collection of data pertinent to several components of this study, including: barge-to-bridge collision data and associated accident reports (United States Coast Guard [USCG]); barge traffic data (USACE); bridge plans and hydraulic reports (FDOT); and water current predictions (National Oceanic and Atmospheric
Administration [NOAA]).
To qualitatively assess the relative influence that advances in maritime technology and operator training have had on barge flotilla pilotage over the past two decades, it was necessary to consult industry professionals who have significant familiarity with the navigation of barge flotillas. Consulted entities included tug captains with decades of experience navigating Florida waterways. Consulted professionals indicated that the primary tools currently utilized in
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maritime navigation include: radio detection and ranging (RADAR), global positioning systems
(GPS), automatic identification systems (AIS), and electronic chart display and information systems (ECDIS).
RADAR is used by maritime navigators to detect the distance and bearing of vessels or other objects in close proximity to the piloted vessel through transmission and reflection of radio waves. These systems are used primarily for collision avoidance and navigation during limited- visibility conditions (e.g., during night hours or foggy conditions).
GPS employs receivers to interface with multiple orbiting satellites that are able to provide real-time latitude and longitude coordinates identifying the location of the user. Initially developed as a military tool, GPS was used increasingly in civilian sectors beginning in the
1990s. However, with recent advancements in GPS technology, and the removal of (military) restrictions on the quality of GPS predictions in the year 2000, the reliability of GPS technology has increased considerably since it was initially developed (Kumar and Moore 2002).
AIS serves as a means by which vessels navigating within a common waterway may share vessel-specific information, such as call signs, transits speeds, bearings, and vessel dimensions. This information is communicated through maritime very high frequency (VHF) radio and interpreted via receivers on properly equipped vessels. AIS data are commonly visualized on a map of the waterway (example shown in Figure 3-1), with the position of each vessel represented as a clearly defined marker. Unlike RADAR, or other older navigational technologies, AIS was not regularly employed until after the year 2000. However, although the technology is relatively new, the USCG has mandated that vessels meeting certain specifications
(e.g., specified minimum lengths and horsepower) must have AIS devices installed in order to operate within US waterways.
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ECDIS (Figure 3-2) is used to synthesize all available navigational information into one unit for convenient display. Such information includes not only GPS and AIS data, but also
information that is typically contained in navigational charts, such as water depths and channel
marker information. Consequently, ECDIS systems can serve as a replacement for conventional
paper navigational charts. While ECDIS units are not universally employed by maritime
navigators, interviewees stated that such units are becoming increasingly popular due to the high
level of convenience attributed to them.
In addition to developments in navigational technology, interviews revealed that the mechanical technologies commonly employed to maneuver tugs and pushboats have also changed since the early 1990s. Specifically, consulted industry professionals indicated that azimuth thrusters are becoming more common on modern tugs. Azimuth thrusters enhance vessel control and maneuverability by allowing the direction of propulsion to change by means of a rotating propeller that can align to any horizontal angle. However, despite the navigational advantages afforded by this technology, interviewees indicated that it is unlikely that most older tugs used in barge transportation have azimuth thrusters equipped.
Supplementing technological advances, it was also noted that training requirements for tug operators have changed since the early 1990s. This includes increased formal and continuing educational requirements as well as the implementation of more regular training drills. It was noted that these increased requirements have made it more difficult for seamen without formal maritime training to become licensed tug operators, which may have an effect on the quality of barge flotilla navigators operating throughout the United States.
According to the consulted industry professionals, significant improvements in the accuracy and reliability of all four navigational tools discussed above (RADAR, GPS, AIS, and
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ECDIS) have been achieved since 1990. Indeed, certain technologies, such as AIS, have only
recently seen widespread use in industry. Based on this finding, it was determined that a revised
barge impact probability expression developed from recent (2000-2014) barge-to-bridge collision data sets will be much more likely to capture the influence of recent advances in technology and training methods than the expression currently employed in AASHTO design specifications.
Collisions between barge flotillas and bridge structures are investigated by the USCG, and are classified as ‘vessel casualty events’. For each such event, the captain of the vessel responsible for the collision must file an accident report with the USCG. Based on the information contained in these reports, the USCG has constructed a ‘Maritime Information for
Safety and Law Enforcement’ (MISLE) database of reported vessel casualties. Each entry
(collision event) in the MISLE database contains the following information:
• Date, time, and location of the event
• Classification of the event (e.g., collision, grounding)
• Classifications (e.g., tug, barge, ship), tonnages, and dimensions of each vessel involved
• Name or designation of the bridge struck
• Narrative describing how the event occurred
While the level of detail provided in the event narratives is variable, generally, each discussion provides a statement regarding the perceived cause(s) of the collision as determined by the investigating officer. In addition, if available, the conditions at the time of the event are also stated in the report, including: water current and wind conditions, visibility, and air temperature.
Researchers are permitted to request extracted data sets from the MISLE database for specific regions through the USCG Office of Investigations and Casualty Analysis (CG-INV). In
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addition, the original (detailed) accident reports from which the MISLE database was
constructed may also be requested from the same office. Consequently, all barge-to-bridge collision data collected for this study (see Section 3.2 and Appendix A) were obtained through
CG-INV.
Commercial barge and tug traffic in U.S. waterways is monitored by the USACE, and may be made available to engineers and researchers upon request. For this investigation, barge and tug traffic data were collected for all regions in the state of Florida with reasonable traffic levels (see Section 3.2 and Appendix B). It is important to note that the USACE does not monitor vessel traffic associated with a non-commercial purposes (e.g., movement of construction barges). Commercial barge and tug traffic data are recorded as vessel passages
(‘trips’), either upstream or downstream, that pass by a specified geographic location. Such data may be organized by vessel type or vessel draft (example shown in Table 3-1). The USACE also maintains information regarding the types of commodities that are shipped, and the payload tonnages associated with vessel movements. In order to request vessel traffic data for a given year, or a range of years, it is necessary to provide the USACE with specific mile marker information for the location(s) of interest. Unmarked waterways, or waterways without commercial traffic, will not likely have recorded data available for request.
In order to determine the geometric probability, PG, of a collision between an aberrant barge and a structural component of a bridge, it is necessary to have a detailed description of the geometry of the bridge relative to the waterway it crosses over. Since the FDOT maintains a catalogue of pertinent design drawings and reports for Florida bridges, which were the focus of the present investigation, appropriate FDOT personnel were contacted to supply information that was used to describe the footprint of a bridge structure in a given waterway.
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Two of the modification factors used to calculate the probability of aberrancy, PA, relate
to the current ( RC ) and cross-current ( RXC ) of the waterway in the vicinity of the bridge.
Unlike barge collision incident data or barge traffic data, no single government-maintained database contained all of the water current data (e.g. flow velocities) that were needed in this study. Instead, such data were acquired from multiple sources. In most cases, individual barge collision accident reports contained flow-velocity and directional information for the day and time of the impact event. In addition, current predictions were also available for certain bridge locations through NOAA. NOAA current predictions do not include the influence of certain ambient conditions like wind and water salinity. However, unlike information typically supplied in accident reports, NOAA tidal current predictions may be obtained for longer records of time.
The most rigorous method of producing a water current estimation for a specific bridge location is through detailed hydraulic simulations that include the influence of both tides and ambient conditions (e.g., wind). While predictions derived from such simulations are generally more accurate than tidal current predictions, hydraulic simulations are also vastly more demanding in terms of model preparation, input data collection, and computation. As a consequence, the utilization of hydraulic simulations was not feasible for this study. Resultantly, only current data associated with accident reports and NOAA tidal current predictions were utilized in the computation of water current-related parameters.
3.1.3 General Data Analysis Methods
Following the collection of raw data from the sources mentioned in the preceding section, it was necessary to initially screen each data set to remove data points that represented conditions which fell outside the scope of this investigation (e.g., removing barge groundings from the full
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data set of barge casualties). Once this process was completed, calculations were performed on
the screened sets of data in order to calculate each of the terms in Equation 3-3.
Bridge locations suitable for this study were determined based on availability of both barge-to-bridge collision data as well as barge traffic data. For the state of Florida, the majority of commercial barge traffic moves through the Gulf Intracoastal Waterway (GIWW) from
Pensacola to Panama City. Other regions of moderate commercial barge traffic include the
Atlantic Intracoastal Waterway (AIWW), near Jacksonville, FL, and the Tampa Bay area. These general regions are indicated on the map in Figure 3-3.
Bridge structures that were selected for this investigation (from the regions shown in
Figure 3-3) were those with a known history of recorded barge-to-bridge impacts. Since vessel groundings and vessel-to-vessel collisions may occur under considerably different circumstances than barge-to-bridge impacts, aberrancy rates associated with groundings and vessel-to-vessel collisions are not necessarily pertinent for the prediction of barge-to-bridge impact probabilities.
Consequently, this study considered only bridge locations at which barge-to-bridge collisions have occurred.
The probability of a barge-to-bridge impact event occurring per vessel passage (PI) was assumed to be reasonably constant over the time-frame considered for this investigation, since any meaningful variation in PI, associated with the influence of significant technological advances or changes in waterway geometry, may only be quantified over a much longer record of time. Furthermore, since this investigation was only concerned with quantifying PI values reflective of the current state of the barge towing industry, determining the historical variation in
PI, although useful, was not a central goal of this research. Therefore, a value of PI for a given bridge site and transit direction was estimated from collected accident data by summing the
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number of barge-to-bridge collisions which occurred over the time-frame of interest and dividing this sum by the total number of barge flotilla passages during that same time:
t=2014 ∑ BCt tt= (3-4) PI = i NT
where, ti is the first year in which barge casualty data were utilized, BCt is the number of barge
casualties that occurred in year t , and NT is the number of barge flotilla transits in the direction
of interest from the year ti to the year 2014. Based on conversations that took place between UF
and the USACE, it was ascertained that the preparation (by the USACE) of annual vessel traffic
data sets for specific bridge locations and times (calendar years) is a work-intensive process. As
such, it was not feasible to obtain barge and tug traffic data (from the USACE) for every
individual year within the span of time over which collision data (from the USCG) were
available (2002-2014). Thus, while collision data were available for each year from 2002-2014,
it was necessary to restrict the request of barge and tug traffic data to every other year from
2002-2012, and for the year 2013. Data for the year 2014 were not available at the time this
investigation was conducted. To make full use of available USCG barge-to-bridge collision data, temporal curve fitting procedures were employed to estimate barge flotilla traffic counts for years where USACE-provided traffic data were unavailable, including hindcast and forecast predictions (Figure 3-4). Specific details regarding the curve fitting methods employed in this investigation are presented in Section 3.3 and Appendix C.
Determination of the geometric probability of a barge-to-bridge collision event occurring at a particular bridge site ( PGbr ), in a given direction, was performed by summing the individual
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geometric probabilities calculated for each pier within 3xLOA of the centerline of the vessel
transit path (recall that LOA is the overall flotilla length):
n PGbr = ∑( PGi ) (3-5) i=1
th where PGi is the geometric probability associated with the i pier, and n is the number of piers
within a distance of 3xLOA from the centerline of the vessel transit path. The calculation of PGi was accomplished for a single pier by superimposing a normal (Gaussian) distribution over the waterway with the mean value of the distribution coinciding with the centerline of the channel
(intended vessel transit path) and the standard deviation of the distribution being equal to the
LOA of the vessel group under consideration. The width of the area integrated under the distribution for a single pier was equivalent to the combined widths of the barge flotilla ( BM )
and the pier ( BP ), as shown in Figure 3-5. Note that fender systems were ignored in the PG
calculation process. Details regarding the specific barge flotilla sizes used in the calculation of
PGbr for individual bridge sites are provided in Appendix D.
Impassable waterway features, such as sand bars or dolphins, near individual bridge
locations included in this study were examined using satellite imagery to determine the number
of piers shielded from impact in the upstream and downstream directions. This process was site
specific, and included features that shielded the entire bridge (Figure 3-6), bodies of land that could provide protection to specific piers (Figure 3-7), or shallow water regions in the vicinity of the bridge that could influence vessel navigation (Figure 3-8). In some cases, certain features
(typically adjacent bridges) were close enough to the bridge of interest that they would have little to no major effect on the intended transit path of a barge flotilla (e.g., the adjacent bridge shown in Figure 3-6). These features were therefore excluded from the calculation of protection factors.
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PF values for individual bridges were determined by computing PG values for each protected
pier, dividing the sum of these values by the sum of all pier PG values ( PGbr ), and subtracting
the resulting value from one:
n PG ∑(( p )i ) = PF =1 − i 1 (3-6) br PG br
where PFbr is the protection factor for a given bridge site, PGbr is the geometric
probability of collision for that same bridge, PG is the area integrated under the PG normal ( p )i distribution (i.e., the PG value) associated with the i’th protected pier, and n is the number of protected bridge piers.
Each of the modification factors used in the calculation of PA—specifically, RB , RC ,
RXC , and RD —were computed using the general procedures outlined in this section; specific
values for each modification factor are tabulated and discussed in Section 3.3. RB , the
modification factor which accounts for the presence of any bends or turns in the waterway that
could induce vessel aberrancy, was determined on a site-specific basis using satellite imagery
(Figure 3-9). Consideration was provided for each potential transit path through the bridge site.
Calculation of RB first involved mapping the centerline of each transit path, demarcating the
beginning and end of all turns or bends, and noting the bounds of the transition regions on either
side of the bridge. A bend or turn angle (θ ) associated with each path was calculated and
employed in the appropriate AASHTO equations to determine RB , depending on whether or not
the bridge location was within the turn or bend (Equation 2-3), or within a transition region
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(Equation 2-4). For bridge locations with multiple potential transit paths (Figure 3-9), the path
that resulted in the smallest value of RB was selected for use in a particular direction, since
smaller RB values corresponded to more conservative (larger) estimates of BR (see Equation 3-
3).
Current and cross-current modification factors ( RC and RXC , respectively) were
calculated directly from data representing waterway velocities parallel (VC ) and perpendicular
()VXC to the intended vessel transit path (Equations 2-5 and 2-6). Water velocity data were obtained through one of the methods discussed previously (accident reports and tidal current predictions), and were intended to represent average current conditions at individual bridge sites.
In order to determine RD (the vessel traffic density modification factor) for a given bridge site, a ratio of the average annual vessel (ship and barge) traffic at that location to the width of the navigable waterway near the bridge was calculated:
µ VDF = N (3-7) W where, µN is the average annual vessel traffic, W (ft) is the width of the waterway near the
bridge location, and VDF is the ‘vessel density factor’. VDF values were used as general
quantitative measures of vessel traffic density, and were employed in conjunction with data from
a previously-conducted AASHTO risk assessment example to select appropriate values of RD
for individual bridge locations (See Section 3.3).
Barge flotilla BR values specifically calibrated to each bridge site considered in this study
were calculated using the methods described in the in this section in conjunction with
Equation 3-3. To assess variation among the calibrated BR values, confidence bounds were fit to
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various subsets of bridge site BR estimates (See Section 3.3). Based on the findings from this
process, recommendations were made regarding a single BR estimate that may be used in barge-
to-bridge impact risk analyses of new and existing bridge structures in Florida waterways.
3.2 Data Collection
Detailed in the preceding section, the methodology for the present study required the use of several categories of data in the calibration process for the revised barge flotilla BR estimate.
Required data included barge accident and traffic data, employed in the calculation of barge
impact probabilities, and supplementary site-specific data, including waterway velocity data and geometric bridge layouts. This section outlines specific data collection procedures used to assemble the required information, as well as methods employed to process data into a form that was appropriate for use in the BR calibration framework.
3.2.1 Barge Collision Data
As discussed previously, barge collision data are a primary component used in the computation of probability of impact (PI) terms for each bridge site of interest (see Equation 3-
4). Barge collision data collected for the present study were obtained from the USCG for every year from 2002-2014. Additional data corresponding to earlier years—as early as 1992—were also obtained from the USCG for certain areas in the panhandle region of Florida.
Two sources of data were used to obtain information relating to barge impact events at each bridge location in the present study—vessel casualty data and individual barge-to-bridge collision accident (incident) reports. Vessel casualty data (Figure 3-10), the first set of information obtained from the USCG, consisted of a catalogue of vessel-to-bridge impact events throughout the state of Florida. Since Florida is divided into two USCG districts (Figure 3-11)—
District 8 (northwest Florida) and District 7 (central, south, and east Florida)—two separate sets of vessel casualty data were obtained (one for each district). Each entry (impact event) was
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classified by a unique number, referred to as an activity ID, which was used by the USCG for
reference purposes.
After reviewing the vessel casualty data sets obtained from the USCG, it was determined
that the records for certain barge-to-bridge impact events were incomplete. As a consequence,
original (i.e., ‘raw’) accident reports (example portion shown in Figure 3-12) for each impact
event of interest were obtained from the USCG to supplement the vessel casualty data. Using
both sources of information, it was generally possible to assemble a complete record of each
barge impact event. Raw accident reports were obtained through a Freedom of Information Act
(FOIA) request submitted to the USCG. The FOIA request process was initiated by sending the
USCG a complete list of requested reports organized by activity ID. In response, electronic
copies of each available report were provided by the USCG on a CD-ROM, which was delivered
by mail a few months after the initial request was made.
USCG collision records contained detailed information regarding the nature of each
collision event and the vessel(s) involved. Information that was collected included the location,
date, and time of the incident, as reported by the USCG. In addition, vessel-specific information
was also included, such as the overall length and width of the flotilla, and the type of vessels
from which the flotilla was comprised (e.g., tug, deck barge, hopper barge, etc.). In many cases,
details relating to environmental conditions were also provided, such as waterway current speeds
and directions, visibility and lighting conditions, and wind speeds (Figure 3-12). For impact events which resulted in damage to the bridge, estimated repair costs were summarized. In general, two separate narratives of the incident were also recorded—one provided by the captain of the vessel involved in the impact event and one provided by the investigating USCG officer.
Each of these narratives briefly described the circumstances surrounding the event and the nature
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of the collision. While these details varied somewhat between incident records, sufficient information was typically provided to discern the cause of the impact and the general location on the bridge that was struck by the vessel. A summary of collected barge accident data is provided in Appendix A.
Since the focus of the present study was on quantifying barge impact probabilities, the analysis procedures outlined in this chapter were intended to be used specifically with barge-to- bridge accident data. Consequently, in the data requests submitted to the USCG, only barge accident records were requested (as opposed to ship impact). However, upon receiving the vessel casualty data sets from the USCG, it was discovered that, in both data sets, other types of vessel collision events had also been included (e.g., passenger craft collisions). As a result, the vessel casualty data sets had to be carefully reviewed to separate those events which involved barges from events that involved other types of vessels, such as pleasure craft or commercial fishing craft. For each bridge site in the state of Florida which possessed at least one confirmed barge-to- bridge impact event, a data catalog was developed that contained individual, processed records for each event. However, for certain impact events, the type of vessel involved was not described in the USCG vessel casualty data sets (example shown in Figure 3-13). Consequently, it was not possible to fully classify each event without further information. In additional cases, blank data fields were also present (example shown in Figure 3-14), which left out information that could be of interest to this investigation (e.g., vessel dimensions). To obtain this additional information, the raw (original) accident reports for each potential barge-to-bridge impact event were acquired from the USCG through the FOIA request process described earlier. Each of these reports typically consisted of two parts—a detailed record of the event (CG-2692 form), and, if more than one vessel (e.g., a pushboat and four barges) was involved, an addendum with vessel-
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specific information (CG-2692A form). Both forms were reviewed for each impact incident to determine the nature of the event so that barge collisions could be identified, and non-barge impacts could be filtered out. Upon completion of this review, incident reports for the barge-to- bridge impact events were used to provide supplementary information (e.g., vessel dimensions, current conditions, incident causes) in processed records.
3.2.2 Barge Traffic Data
As mentioned in earlier sections, an individual vessel passage along a marked point in a waterway is referred to as a vessel ‘trip’. A collection of observed barge and tugboat trips near a particular bridge location is referred to as the barge traffic data set for that location. Since barge traffic data were required for the computation of PI (see Equation 3-4), such data were obtained from the USACE for the same bridge sites where barge-to-bridge accident data were obtained from the USCG. A full listing of locations for which barge traffic data were collected is provided in Appendix B. As discussed earlier, due to the substantial processing effort that such a request translated into for the USACE, it was not feasible to request barge traffic data for every year at which USCG barge collision data were consistently available (2002-2014). Instead, the USACE provided traffic data sets every other year from 2002-2012 and for the year 2013 (i.e., traffic data were obtained for the years 2002, 2004, 2006, 2008, 2010, 2012, and 2013).
Traffic data provided by the USACE (example shown in Figure 3-15) were organized by year, with two separate data sets for each year. The first data set provided details regarding the types of commodities that were transported by vessels along the waterway location of interest; the second data set provided information regarding the number of vessel passages along the waterway (trips). Data in both sets were also organized by direction of travel and vessel characteristics: vessel type (e.g., barge, tug, ship, etc.), tonnage, overall length, overall breadth
(width), and draft.
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As indicated previously, barge flotilla traffic data were needed for the computation of PI using Equation 3-4. However, upon receiving the first sets of traffic data from the USACE, it was determined that, in addition to barge and tug traffic, other types of vessel traffic (e.g., ship traffic) were also included. Since the focus of the present investigation is on quantifying barge impact probabilities specifically, it was necessary to separate barge and tug traffic from other— non-pertinent—types of vessel traffic provided by the USACE. Using vessel classification IDs unique to each type of vessel (listed under ‘VTYPE’ in Figure 3-15), a Matlab script (program) was developed to sift through each data set, and extract only traffic data specific to tugs and barges. The script was also used to organize traffic by direction (upbound, downbound) and by dimensional ranges (ranges of total length, width, etc.). For individual bridge locations, two traffic totals were computed for each year—one for each direction travel.
3.2.3 Supporting Information
Supplementing the USCG collision data and USACE traffic data, additional information was collected for each bridge site with a recorded barge-to-bridge collision event: water current velocity data (needed in the computation of the current and cross-current modification factors,
RC and RXC , respectively); bridge plans; and nautical charts. Each of these is described in more detail below.
Water current data were obtained from two sources: current records included in USCG accident reports and NOAA tidal current predictions (Figure 3-16). Current data obtained from accident reports, which were available for most bridge sites, included the current speed and direction at the time of the incident. For sites which had NOAA tidal current data available, 52 weeks (one year) of data were collected in order to produce a reasonably representative sample of water current conditions (flow speeds). Such data consisted of peak flood (incoming tide) and
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ebb (outgoing tide) current speeds and directions (example shown in Figure 3-16), which were organized by calendar week. Since these data were based solely on tidal predictions, environmental factors that might potentially increase current speeds, including wind and storm conditions, are not reflected in the estimated peak values.
To compute the geometric probability of collision (PG), and protection factors (PF) associated with the bridge sites of interest in this study, bridge plans were obtained from the appropriate FDOT district offices. These plans were individually reviewed to develop simplified bridge layouts for reference purposes (Figure 3-17). Catalogues of bridge pier locations relative to the centerline of the waterway were also created in order to automate the PG calculation process using a series of data processing Matlab scripts.
While bridge plans included structural layouts, it was also necessary to review nautical charts to collect information specific to the waterway layout, such as the identification of unnavigable shallow water zones, which were also needed in the calculation of both PG and PF.
Nautical charts utilized for this study were obtained from NOAA for all waterways of interest
(example shown in Figure 3-18). Using the NOAA nautical charts, unnavigable shallow water
zones, or small islands, close to the bridge site, were identified and used to characterize the level
of protection against a collision event. When needed, these documents were also used in the
calculation of bridge location modification factors (RB).
3.3 Data Analysis
As discussed in earlier chapters, the primary objective of the present study was to reevaluate barge-to-bridge impact probabilities using the general analysis methodology presented in Section 3.1. The present section summarizes the specific analysis procedures employed in the calculation of base aberrancy rates (BR values) for the 13 bridge sites included in this
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investigation (Table 3-2) and the methods utilized to determine a design BR specific to barge
flotilla traffic in Florida waterways.
Recall that BR, as calculated in this study, is a function of several variables:
PI BR = (3-8) (R)( R)( R)( R)( PG)( PF ) B C XC D where, BR is the base aberrancy rate, PI is the probability of impact, PG is the geometric probability, and PF is a protection factor. RB, RC, RXC, and RD are modification factors which
account for: the location of the bridge relative to turns or bends in the waterway (RB); currents
acting parallel to the intended transit path of the vessel (RC); cross-currents acting perpendicular
to the intended transit path of the vessel (RXC); and the density of vessel traffic in the immediate
vicinity of the bridge (RD). With the exception of three bridges (CSX Railroad Bridge,
Interstate-10 Bridge, and the Theo Baars Bridge), the variables on the right hand side of
Equation 3-8 were quantified for investigated bridges using the procedures and assumptions
described in this chapter. Once quantified, each location-specific set of values was used to calculate a range of BR estimates for each bridge location. Since the CSX Railroad Bridge, the
Interstate-10 Bridge, and the Theo Baars Bridge did not have any barge-to-bridge collisions documented by the USCG over the period of time considered in this investigation, each of these structures was associated with a PI of zero. As a consequence, BR estimates for these locations were taken as zero for all analyses considered in this study. A final design BR was determined by considering an empirical BR distribution comprised of all estimates, including BR values of zero associated with the three bridge locations without recorded impact events.
3.3.1 Probability of Impact
Using historical records of barge-to-bridge collisions, in conjunction with barge and tug traffic data, a probability of impact (PI) term was calculated for each bridge site using
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Equation 3-4. As described previously, barge collision data collected for the present study were
obtained from the USCG for every year from 2002-2014, with additional data available for
panhandle bridge sites (see Table 3-2) corresponding to earlier years (back to 1992). Barge and
tug traffic data sets were obtained from the USACE every other year from 2002-2012, as well as
for 2013. Using the curve-fitting methods described later in this section, it was ascertained that
reasonable estimates of barge and tug traffic counts could be determined for each year from
2000-2014 where vessel traffic data were not available (due to limits on the permissible USACE
data requests). Consequently, for bridge locations in the panhandle, where older barge-to-bridge
collision data sets were provided, ti was taken as 2000 in Equation 3-4. For bridges located in
other regions of Florida, ti was taken as 2002.
In total, 25 barge-to-bridge collision events corresponding to the bridge locations of interest were used in the present investigation (Table 3-3). It should be noted that additional bridge sites in Florida were considered, but these locations were excluded from this investigation due to insufficient vessel traffic data (i.e., barge traffic counts were low). Barge casualties which did not involve a direct collision with a bridge were not included in this study. Since the barge and tug traffic data sets provided by the USACE did not include non-commercial traffic (e.g., construction barges), collision events which involved non-commercial barges also had to be excluded from this investigation.
Traffic data provided by the USACE were initially analyzed using the methods described in Section 3.2 in order to obtain barge and tug traffic counts for each bridge location and direction of travel. However, since the passage of a single multi-barge flotilla through a bridge site would be represented as multiple vessel passages in the traffic data provided by the USACE
(where one passage is a single barge or tug), the number of individual barge passages through a
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bridge location was not, in many cases, an adequate indicator of barge flotilla traffic.
Consequently, since many barge flotillas typical to the state of Florida include only a single tug,
it was determined that—subject to filtering with the outlier detection algorithm noted below—
tug traffic counts were generally a more appropriate basis for the estimation of NT .
In order to approximate region-specific flotilla sizes, barge-to-tug ratios were calculated for each bridge site by year and direction using the USACE-supplied traffic data. Overall 126 total barge-to-tug ratios were quantified—one for each year (seven years of collected data), waterway (nine total waterways), and direction of travel (two directions). Upon reviewing the calculated ratios, it was noted that for certain years at several bridge locations, barge-to-tug ratios were higher than the largest typical ratio for the waterway (as determined through tug operator interviews). After discussing this observation with the USACE, it was determined that USACE- provided tug traffic counts may be lower than actual values for some years, due to the existence of unreported tug passages. Since the USACE Waterborne Commerce Statistics Center (WCSC) is concerned primarily with tracking the movement of commercial goods in U.S. waterways, data collection emphasis is on commercial barge traffic. In contrast, the tugs used to push barge flotillas do not typically carry commercial goods onboard. Consequently, tugs movements
(passages) along U.S. waterways are not always reported to the USACE Waterborne Commerce
Statistics Center with the same accuracy as are barge passages. In order to address the possibility of unreported tug passages, an outlier detection methodology was developed to flag years in which barge-to-tug ratios were significantly higher than typical (indicating a possibility of unreported tug passages). In this methodology, barge-to-tug ratios for each bridge location were normalized by site-specific median values so that normalized barge-to-tug ratios from all bridge locations could be included in a single data set for analysis purposes (Figure 3-19). For certain
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years at one bridge site—the Gandy Bridge—barge passages were recorded with no
corresponding tug passages; in such cases, barge-to-tug ratios were estimated to be a very large number in the outlier detection analysis (greater than 100). Site median values were used instead of site mean values since the presence of a large number of outliers, or a small number of outliers with very large or small magnitudes (relative to the remainder of the data set), can distort the mean and standard deviation calculated from the data (Leys et al. 2013). Consequently, if normalization of the barge-to-tug ratios had been performed by using site mean values, the significance of outlying values could have been masked in locations with either a large number of outliers, or a small number of significant outliers.
Identification of outlying barge-to-tug ratios was achieved through the use of box plots.
Using this approach, originally published by Tukey (1977), data were grouped into four regions using median values referred to as quartiles (Figure 3-20). The central portion, bounded by the first and third quartiles, is commonly referred to as the ‘box’ portion of the plot. Any data points that fell outside the box, but within the extreme bounds, were termed ‘mild outliers’. Any data points that fell outside the extreme bounds were termed ‘extreme outliers’. For this project, only extreme outliers were flagged for removal; this corresponded to any normalized barge-to-tug ratios that were greater than two (see Figure 3-19).
Of the bridge locations analyzed in this investigation, seven contained years for which outlying barge-to-tug ratios existed: the Atlantic Blvd. Bridge; the CSX Railroad Bridge; Dupont
Bridge; Gandy Bridge; the Highway-90 Bridge; the Interstate-10 Bridge; and the Pensacola Bay
Bridge. Overall, this corresponded to 16 outlying barge-to-tug ratios. Three of those 16 outliers were retained in the data analysis since the cause of the large barge-to-tug ratios in these cases were related to abrupt increases in the number of observed barge passages, and not due to
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supposed decreased tug traffic activity. Sudden, and legitimate, increased barge traffic could
correspond to a temporary event requiring the movement of more materials (e.g., a construction
project). To determine new barge-to-tug ratios for the 13 remaining records in question, for
which outlying values were discarded, curve-fitting methods were applied. Several fit types were
examined, including linear, quadratic, and exponential fits. Since the exponential fits appeared to
approximate data trends the best, exponential fit parameters were used to obtain new barge-to-
tug ratios in place of outlying observations (see Appendix C for curve fits). Barge traffic counts
for the same locations and years for which outlying barge-to-tug ratios were identified were then
divided by the ratios sampled from the curve fits to arrive at new tug traffic counts representative
of individual barge flotilla passages. For select locations and years where tug traffic counts
exceeded barge traffic counts, the latter (barge traffic counts) were used to represent flotilla
traffic. The outlier replacement methodology employed to obtain equivalent barge flotilla traffic
counts is summarized in Figure 3-21.
Using the number of barge-to-bridge collisions (Table 3-3) over the time-frame of
interest (2000-2014 for panhandle bridges, 2002-2014 for bridges in other regions), and the total
number of barge flotilla passages calculated for that same time-frame, values of PI were
quantified for each bridge location and direction (Table 3-4). The ‘inbound’ and ‘outbound’ directional designations were uniquely determined for each bridge site based on the location of nearby ports and waterway mile markers. Note that a PI value of zero indicates that no barge-to-
bridge impact events were reported at that particular bridge location in the specified direction.
While many values of PI were smaller than 3.00× 10−4 , the Acosta Bridge, Atlantic Blvd.
Bridge, Bob Sikes Bridge, Dupont Bridge, Gandy Bridge, and the Sister’s Creek Bridge were all
associated with larger values of PI. In the case of the Bob Sikes Bridge, this was primarily due to
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the significant number of collision events that occurred in one direction (outbound). However,
for the other five bridges, the main reason for the large values of PI was relatively low barge and
tug traffic activity.
3.3.2 Modification Factors
To adjust for bridge site-specific conditions in the BR calibration process, the values of
PI computed in the previous section were modified by several AASHTO-specified modification
factors (through Equation 3-8). Each modification factor could only take a value of one or
greater.
At certain bridge locations, the presence of a turn or bend in the waterway near the
bridges necessitated the calculation of a bridge location modification factor (Table 3-5). This was
accomplished through the methodology described in Section 3.1, along with relevant
AASHTO (2014) design equations:
θ R =1 + B (3-9) 45
θ R =1 + B (3-10) 90 where, RB is the bridge location modification factor and θ is the angle of the bend or turn in the waterway. Recall that Equation 3-9 is applied when a bridge is located directly within a turn or bend and Equation 3-10 is applied when a bridge is located adjacent to a turn or bend (i.e., within a ‘transition’ region). Many of the bridge locations included in this study were in relatively straight regions. However, the Acosta Bridge (Figure 3-22), Brooks Bridge (Figure 3-23),
Dupont Bridge (Figure 3-24), Highway-90 Bridge (Figure 3-25), and the Sister’s Creek Bridge
(Figure 3-26), were each located either within or adjacent to a waterway turn or bend. As shown in Table 3-5, estimated values of RB ranged from 1.00 to 2.18.
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Two sources of data were used in conjunction with Equations 2-5 and 2-6 to compute
modification factors associated with waterway flow: current velocities obtained from individual
barge collision incident reports, and National Oceanic and Atmospheric Administration (NOAA)
tidal current predictions. Modification factors determined from accident reports were calculated
directly from the current magnitudes and current directions indicated in each report.
Modification factors determined from NOAA tidal current data were calculated by first
averaging peak tidal currents collected over 52 weeks for the bridge site of interest and then
using site-specific current directional information to calculate RC and RXC. For individual bridge
sites, RC and RXC values were calculated for each available source of current data. For example, if
a bridge site with NOAA tidal current predictions and two incident reports with current data
were considered, three pairs of current modification factors would have been calculated. Note
that, while several estimates of RC and RXC were calculated for bridge sites with multiple sources of current data, single estimates of RC and RXC were used in the BR calibration process (Table 3-
6). The RC and RXC values shown in Table 3-6 were obtained by averaging RC and RXC values
calculated from each source of data available at individual bridge sites.
3.3.3 Additional Probabilities
The range of PG values for individual bridges (Tables 3-7 and 3-8) depended primarily on the number and width of piers that fell within the waterway and the size of the flotillas which could pass underneath the bridge. In general, longer bridges and wider flotillas resulted in larger
estimates of PG. Note that, aside from influencing the maximum size of barge flotillas, waterway
widths were not included in the calculation of PG (per AASHTO [2014] specifications).
Bridge PF values were calculated (Tables 3-9 and 3-10) to account for waterway
obstructions that could alter the navigational path of a barge flotilla prior to reaching a bridge.
For this investigation, protective systems or obstructions immediately adjacent to a bridge pier
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(e.g., bridge fenders, neighboring bridges, etc.) were not represented in the PF calculation
process since such obstructions were too close to the bridge to alter barge flotilla aberrancy rates
in a meaningful way. Islands and shallow water regions were the primary sources of protection
for investigated bridge sites.
3.3.4 Base Aberrancy Rate Calibration
Equation 3-8 was used to perform the BR calibration process for each bridge. As
discussed earlier, four barge flotilla configurations were included in the calibration process. In
addition, two levels of protection were considered: a protected state (using the PF values shown
in Tables 3-9 and 3-10) and an unprotected state, in which all bridge piers in the waterway were
considered fully exposed. Accordingly, eight estimates of BR were produced per bridge and
direction. For the three bridge locations without any recorded collision events (CSX Railroad
Bridge, Interstate-10 Bridge, and Theo Baars Bridge), BR estimates were taken as zero for each
of the eight cases. Direction-specific estimates of bridge site BR values for each of the eight
combinations of flotilla size and protection level were then averaged using a weighted approach
based on the relative barge flotilla traffic in each direction; this process resulted in a single
estimate of BR for each of the eight cases at each bridge site. Among all 13 bridges considered in
this study, 104 total estimates of BR (Figure 3-27) were produced. In order to provide a single estimate of BR that may be used in bridge design, mean values were computed for different subsets of the BR estimates (Table 3-11).
For each mean value calculated, confidence bounds were generated through a ‘bootstrap’ approach. In this approach, sets of BR values were resampled (with replacement) from the empirical BR distribution through Monte Carlo simulation. For each resampled data set, a mean
BR was calculated so that a distribution of mean BR values could be formed and a 95% confidence interval could be calculated from the resulting normal distribution. As shown in
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Table 3-11, higher estimates of BR and wider confidence intervals were generated when bridges
outside of the Florida panhandle were used in the calibration process. As discussed earlier, the
Acosta Bridge, Atlantic Blvd. Bridge, Dupont Bridge, Gandy Bridge, and Sister’s Creek Bridge
had notably less recorded barge flotilla traffic than panhandle bridge sites, resulting in
significantly larger estimates of PI (Table 3-4). Since the number of barge passages at these
locations is possibly insufficient to form a reliable estimate of the BR parameter, it is
recommended that only panhandle bridge sites (with the exception of the Dupont Bridge) be used
as the basis for calibration. As a consequence, a BR value of 5.4× 10−5 is recommended as a
characteristic design value for Florida bridges, which represents an approximate 55% decrease
from the present AASHTO BR of 1.2× 10−4 for barges. To show the relative effect of flotilla
configuration on BR estimates, mean BR values were also calculated for each of the four flotilla
configurations associated with the eight bridge locations used in the development of the
recommended design value of BR (Table 3-12). It should be noted that the mean of the four
flotilla-specific estimates shown in Table 3-12 is equivalent to the overall mean for the eight bridge locations (shown in Table 3-11).
3.4 Discussion
Of the Florida bridge locations analyzed in this study, it was noted that locations with low
volumes of barge traffic correlated with very high estimates of the probability of impact (PI), as
well as BR. Since this was a statistical investigation, the number of recorded observations per
bridge site—represented by barge flotilla passages—directly related to the accuracy of the predicted BR parameter. Consequently, only Florida bridges with more significant volumes of barge flotilla traffic were included in the calibration procedures used to produce the recommended design value of BR. However, other bridge locations exist outside of the state of
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Florida which have even more elevated levels of barge traffic than the bridges that were considered in this investigation. Consistent with the findings from this study, if such locations were included in a similar BR recalibration effort, the resulting design value could potentially be much smaller than the design value of BR computed strictly from Florida bridge data.
During the initial phases of this study, barge-to-bridge collision data were requested from the USCG for the entire United States, rather than just for bridges located in Florida. In response to this initial nationwide request, the USCG indicated that such a request would not be feasible to fulfill. Therefore, since this research was intended to produce a design expression specifically applicable to the analysis and design of bridges in Florida waterways, a more restricted subset of data—consisting only of barge-to-bridge collision data for bridges located in Florida—was requested and received from the USCG. Moreover, during discussions with the USCG relating to the collection of barge-to-bridge collision casualty data, the UF research team (including the author) was directed to the USACE Waterborne Commerce Statistics Center (WCSC) for collection of barge and tug traffic data corresponding to Florida bridge locations. Accordingly, this USACE center was consulted to obtain all traffic data sets used in this investigation.
For bridges sites located near locks, an additional source of barge traffic data exists—the
USACE Lock Performance Monitoring System (LPMS). LPMS data are associated with barge flotilla transits through USACE owned and operated lock and dam structures, and are more accurate (e.g. with respect to flotilla sizes and configurations) and more accessible than data provided by the Waterborne Commerce Statistics Center. However, since LPMS data are associated with river locks and dams, and since there are few of these structures in the state of
Florida, no LPMS data were available for the (mostly coastal) Florida bridges considered in the present investigation. Nevertheless, additional coastal states neighboring Florida, such as
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Louisiana, contain waterways with higher volumes of barge traffic and a number of lock and dam systems. Consequently, if out-of-state USACE LPMS barge traffic data associated with
highly-trafficked bridge locations were combined with corresponding USCG-provided collision data, a subsequent statistical recalibration effort could yield significantly lower estimates of BR relative to the presently computed estimates.
3.5 Summary
Present AASHTO bridge design specifications include, as a critical component, a risk- based approach for the design of waterway bridges to resist vessel impact loads. This approach includes expressions for quantifying the severity of ship and barge impact loads as well as expressions for predicting the likelihood that an impact event will occur. The existing AASHTO probability expressions, used to estimate the frequency of impact events, are based on a limited number of investigations conducted prior to the 1990s, when vessel navigational technology was significantly less developed than in more recent decades. Moreover, the AASHTO expressions for estimating barge-to-bridge impact probabilities are based on data sets that included other types of vessel casualties, such as vessel groundings and strandings, which did not result in a collision event with a bridge structure.
In the present investigation, the current state of maritime technology—both navigational and mechanical—was reviewed to determine the influence of technological advances on the barge towing industry since the year 1990. Based on interviews with various industry professionals, it was determined that due to improvements in technologies, such as global positioning systems (GPS), and with the advent of newer technologies, such as automatic identification systems (AIS), navigation in inland waterways and coastal areas has improved since the 1990s. Consequently, it was determined that the updated barge impact probability
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expression developed herein needed to incorporate recent barge-to-bridge collision data, thus
implicitly considering these new and improved navigational technologies. Using such data, a
recalibration of the AASHTO base aberrancy rate (BR) associated with barge flotillas was
performed.
To facilitate the development of the revised BR expression, barge traffic data and barge-
to-bridge collision data were collected for bridges in waterways throughout the state of Florida.
In total, 13 bridges from three general regions in Florida were utilized in this study; additional
bridges were considered, but were not incorporated into the recalibration process due to an
insufficient level of barge flotilla traffic. Using site-specific information (e.g., bridge layouts,
water current information, waterway charts, etc.) for investigated bridge locations, AASHTO
expressions needed in the recalibration process—PG, PF, RB, RC, RXC, and RD—were computed.
These expressions were then employed in conjunction with probability of impact (PI) estimates,
computed from collected barge traffic and collision data, to produce a range of recalibrated BR
values associated with each bridge location. A design value of BR was produced by computing
the mean of BR estimates from a subset of bridge locations considered in this study. The revised
estimate of BR ( 5.4× 10−5 ) represents a 55% decrease from the BR value presently employed in
AASHTO (1.2× 10−4 ).
As discussed in this chapter, a correlation was noted between the volume of barge traffic
associated with a bridge location and the recalibrated value of BR. Specifically, of the Florida
bridges considered in this investigation, bridges with very low volumes of barge traffic had very
high estimates of BR. This result was likely a consequence of a reduction in the accuracy of BR
predictions correlative with the utilization of fewer barge trips in the statistical analysis
procedures. Consequently, only those Florida bridge locations with more significant levels of
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barge traffic were included in the recalibration process that produced the recommended design
value of BR. However, additional out-of-state bridge locations exist with even higher volumes of barge flotilla traffic. In addition, a comprehensive and readily available source for barge flotilla traffic data—the USACE Lock Performance Monitoring System (LPMS)—is available for waterways with lock and dam structures in place. Consequently, a future investigation is recommended that incorporates such data into a recalibration effort similar to the one presented in this chapter.
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Table 3-1. Extract from Waterborne Commerce of the United States (WCUS) illustrating the organization of USACE vessel traffic data (Source: USACE 2012).
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Table 3-2. Bridge locations utilized in present study. Bridge name Region Latitude (deg.) Longitude (deg.) Acosta Bridge Jacksonville, FL 30.21240 -81.66387 Atlantic Blvd. Bridge Jacksonville, FL 30.32332 -81.43863 Bob Sikes Bridge Pensacola, FL (panhandle) 30.34832 -87.15365 Fort Walton Beach, FL Brooks Bridge 30.40122 -86.60056 (panhandle) CSX Railroad Bridge Pensacola, FL (panhandle) 30.52384 -87.14634 over Escambia Bay Dupont Bridge Panama City, FL 30.10471 -85.60822 Gandy Bridge Tampa, FL 27.88797 -82.55168 Highway-90 Bridge Pensacola, FL (panhandle) 30.54878 -87.19507 over Escambia River Interstate-10 Bridge Pensacola, FL (panhandle) 30.51914 -87.14390 over Escambia Bay Navarre Beach Bridge Navarre, FL (panhandle) 30.39717 -86.86330 Pensacola Bay Bridge Pensacola, FL (panhandle) 30.39451 -87.18487 Sister’s Creek Bridge Jacksonville, FL 30.39402 -81.45990 Theo Baars Bridge Pensacola, FL (panhandle) 30.31300 -87.42634
Table 3-3. Number of barge-to-bridge collision events per bridge location. Bridge name Number of collisions Acosta Bridge 1 Atlantic Blvd. Bridge 1 Bob Sikes Bridge 8 Brooks Bridge 2 CSX Railroad Bridge over Escambia Bay 0 Dupont Bridge 3 Gandy Bridge 1 Highway-90 Bridge over Escambia River 3 Interstate-10 Bridge over Escambia Bay 0 Navarre Beach Bridge 3 Pensacola Bay Bridge 1 Sister’s Creek Bridge 2 Theo Baars Bridge 0
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Table 3-4. Estimated values of PI. PI (10-4) PI (10-4) Bridge name (inbound) (outbound) Acosta Bridge 0.00 8.05 Atlantic Blvd. Bridge 0.00 31.0 Bob Sikes Bridge 2.68 4.76 Brooks Bridge 0.00 1.90 CSX Railroad Bridge over Escambia Bay 0.00 0.00 Dupont Bridge 13.0 0.00 Gandy Bridge 24.0 0.00 Highway-90 Bridge over Escambia River 0.00 2.33 Interstate-10 Bridge over Escambia Bay 0.00 0.00 Navarre Beach Bridge 1.79 0.951 Pensacola Bay Bridge 0.00 0.768 Sister’s Creek Bridge 0.00 6.48 Theo Baars Bridge 0.00 0.00
Table 3-5. Estimated values of RB. Bridge name RB (inbound) RB (outbound) Acosta Bridge 2.18 2.18 Atlantic Blvd. Bridge 1 1 Bob Sikes Bridge 1 1 Brooks Bridge 1.56 1.56 Dupont Bridge 2.07 1.17 Gandy Bridge 1 1 Highway-90 Bridge over Escambia River 1.91 1.91 Navarre Beach Bridge 1 1 Pensacola Bay Bridge 1 1 Sister's Creek Bridge 1.21 1.67 Note: The CSX Railroad Bridge, Interstate-10 Bridge, and Theo Baars Bridge had no recorded impact events, resulting in PI and BR estimates equal to zero. Consequently, RB modification factors were not calculated for these three bridge locations.
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Table 3-6. Estimated values of RC and RXC. Bridge name RC RXC Acosta Bridge 1.22 1.43 Atlantic Blvd. Bridge 1.42 2.36 Bob Sikes Bridge 1.26 2.52 Brooks Bridge 1.14 2.38 Dupont Bridge 1.04 1.04 Gandy Bridge 1.11 1.15 Highway-90 Bridge over Escambia River 1.43 1.72 Navarre Beach Bridge 1.22 2.05 Pensacola Bay Bridge 1.2 1.74 Sister's Creek Bridge 1.06 1.93 Note: The CSX Railroad Bridge, Interstate-10 Bridge, and Theo Baars Bridge had no recorded impact events, resulting in PI and BR estimates equal to zero. Consequently, RC and RXC modification factors were not calculated for these three bridge locations.
Table 3-7. Estimated values of PG (inbound direction). Bridge name PG (FG-A) PG (FG-B) PG (FG-C) PG (FG-D) Acosta Bridge 0.158 0.235 0.274 0.358 Atlantic Blvd. Bridge 0.356 0.426 0.688 0.902 Bob Sikes Bridge 0.552 0.477 0.95 0.894 Brooks Bridge 0.193 0.32 0.431 0.715 Dupont Bridge 0.367 0.388 0.887 0.901 Gandy Bridge 0.405 0.328 0.522 0.5 HW-90 Bridge over Escambia River 0.558 0.529 0.861 0.881 Navarre Beach Bridge 0.561 0.515 0.91 0.958 Pensacola Bay Bridge 0.674 0.52 0.959 0.901 Sister’s Creek Bridge 0.299 0.559 0.469 0.857 Note: The CSX Railroad Bridge, Interstate-10 Bridge, and Theo Baars Bridge had no recorded impact events, resulting in PI and BR estimates equal to zero. Consequently, PG estimates were not calculated for these three bridge locations.
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Table 3-8. Estimated values of PG (outbound direction). Bridge name PG (FG-A) PG (FG-B) PG (FG-C) PG (FG-D) Acosta Bridge 0.158 0.235 0.274 0.358 Atlantic Blvd. Bridge 0.356 0.426 0.688 0.902 Bob Sikes Bridge 0.552 0.477 0.95 0.894 Brooks Bridge 0.193 0.32 0.431 0.715 Dupont Bridge 0.367 0.388 0.887 0.901 Gandy Bridge 0.405 0.328 0.522 0.5 HW-90 Bridge over Escambia River 0.558 0.529 0.861 0.881 Navarre Beach Bridge 0.561 0.515 0.91 0.958 Pensacola Bay Bridge 0.674 0.52 0.959 0.901 Sister’s Creek Bridge 0.299 0.559 0.469 0.857 Note: The CSX Railroad Bridge, Interstate-10 Bridge, and Theo Baars Bridge had no recorded impact events, resulting in PI and BR estimates equal to zero. Consequently, PG estimates were not calculated for these three bridge locations.
Table 3-9. Estimated values of PF (inbound direction). Bridge name PF (FG-A) PF (FG-B) PF (FG-C) PF (FG-D) Acosta Bridge 1 1 1 1 Atlantic Blvd. Bridge 0.309 0.571 0.312 0.536 Bob Sikes Bridge 1 1 1 1 Brooks Bridge 0.802 0.883 0.801 0.888 Dupont Bridge 1 1 1 1 Gandy Bridge 1 1 1 1 HW-90 Bridge over Escambia River 0.196 0.443 0.273 0.563 Navarre Beach Bridge 0.691 0.978 0.763 0.985 Pensacola Bay Bridge 1 1 1 1 Sister’s Creek Bridge 0.802 0.887 0.855 0.917 Note: The CSX Railroad Bridge, Interstate-10 Bridge, and Theo Baars Bridge had no recorded impact events, resulting in PI and BR estimates equal to zero. Consequently, PF estimates were not calculated for these three bridge locations.
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Table 3-10. Estimated values of PF (outbound direction). Bridge name PF (FG-A) PF (FG-B) PF (FG-C) PF (FG-D) Acosta Bridge 0.705 0.792 0.734 0.784 Atlantic Blvd. Bridge 0.141 0.209 0.139 0.193 Bob Sikes Bridge 1 1 1 1 Brooks Bridge 0.802 0.883 0.801 0.888 Dupont Bridge 1 1 1 1 Gandy Bridge 1 1 1 1 HW-90 Bridge over Escambia River 0.239 0.511 0.301 0.598 Navarre Beach Bridge 0.637 0.958 0.714 0.97 Pensacola Bay Bridge 1 1 1 1 Sister’s Creek Bridge 0.802 0.887 0.855 0.917 Note: The CSX Railroad Bridge, Interstate-10 Bridge, and Theo Baars Bridge had no recorded impact events, resulting in PI and BR estimates equal to zero. Consequently, PF estimates were not calculated for these three bridge locations.
Table 3-11. Summary of mean BR values. Number of Region BR (mean) 95% confidence interval bridge sites All 13 5.2× 10−4 3.6× 10−−44 −× 7.6 10 Panhandle, Sister’s Creek 11 × −4 ×−−44 −× Bridge, and Acosta Bridge 1.5 10 1.2 10 2.1 10 Panhandle 9 1.1× 10−4 7.5× 10−−54 −× 1.6 10 Panhandle 8 × −5 ×−−55 −× (except for Dupont Bridge) 5.4 10 4.0 10 7.1 10
Table 3-12. BR values associated with flotilla classifications for the eight design bridge locations. Flotilla classification BR (mean) FG-A 7.7× 10−5 FG-B 6.4× 10−5 FG-C 4.2× 10−5 FG-D 3.4× 10−5
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Figure 3-1. Visualization of sample AIS data (Image adapted from USCG Navigation Center, http://www.navcen.uscg.gov, February 23, 2015).
Figure 3-2. ECDIS display on-board a NOAA vessel (Source: NOAA National Centers for Environmental Protection, http://www.ncep.noaa.gov, February 23, 2015).
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Figure 3-3. Regions of Florida waterways that, per USACE data, carry notable commercial barge traffic (Image adapted from: the United States Geological Survey [USGS] Earthquake Hazards Program, http://earthquake.usgs.gov, February 26, 2015).
Figure 3-4. Curve-fitting approach for the estimation of barge flotilla traffic data.
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Centerline of vessel transit path BM + BP
PGBR is the total area integrated under the normal distribution Normal (Gaussian) distribution
2.8" 4 2.3" 5 3 x LOA 3 x LOA (not drawn to scale) (not drawn to scale)
Bridge superstructure Centerline of vessel Waterline pile cap transit path B Pier column P
BM 3 2 " 1 . LOA
Barge
Tug Figure 3-5. Calculation of the geometric probability for a single bridge location.
Figure 3-6. Bridge piers protected by adjacent low-rise railroad bridge (Source: Wikimedia Commons, https://commons.wikimedia.org, July 14, 2016).
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Figure 3-7. Bridge piers protected by land bodies (Source: Google Maps, https://maps.google.com, October 13, 2014).
Figure 3-8. Shallow water regions near bridge (Source: Google Maps, https://maps.google.com, October 24, 2014).
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Figure 3-9. Calculation of the bridge location modification factor, RB (Image adapted from Google Maps, https://maps.google.com, October 6, 2014).
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A
B
Figure 3-10. Selected portions of USCG vessel casualty data set. A) Bridge and waterway information. B) Event information.
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Figure 3-11. USCG districts (Source: USCG, http://www.uscg.mil, October 1, 2015).
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Figure 3-12. Selected portion of raw USCG accident report.
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Figure 3-13. Selected portion of USCG vessel casualty data set with unspecified vessel characteristics.
Figure 3-14. Selected portion of USCG vessel casualty data set with blank data fields.
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Figure 3-15. Selected portion of USACE vessel traffic data set for Atlantic Intracoastal Waterway, near Sister’s Creek Bridge (Jacksonville, FL).
Figure 3-16. Selected sample NOAA tidal current prediction (Source: NOAA Center for Operational Oceanographic Products and Services, http://tidesandcurrents.noaa.gov, October 1, 2015).
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144'-10"
1.6" 8
Fender 125' 1.0" 6 System Pier #10 Pier #9 11'-10" (typ.) Pier #7 Pier #8 Footing eConcretSeal Pier #11 Pier #12 0 . 4 7 " Pier with 1 . 9 7 " 31'-3" Crashwall (typ.)
0.1" 8 1.0" 153'-7" 1.0" 0.2" 8 63' 85'-7" 85'-7" 63' 9' (typ.)
Figure 3-17. Selected portion of simplified bridge layout for the Navarre Beach Bridge over the Gulf Intracoastal Waterway
Figure 3-18. Selected portion of NOAA nautical chart (area near Navarre Beach Bridge shown; Source: NOAA 2014).
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12
10
8
6
4
2 Normalized barge-to-tug-ratio Normalized
0 A 45 40 35
30 25
Count 20 15
10 5
0 0 1 2 3 4 5 6 7 8 9 10 11 12 Normalized barge-to-tug ratio B Figure 3-19. Barge-to-tug ratios normalized by bridge site medians. A) scatterplot. B) histogram (Note: extreme outliers with barge-to-tug ratios greater than 100 not shown for clarity).
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Q3 + 1.5(IQR)
Outliers
o
i
t
a
r
g Third quartile u
t (Q3)
- o
t Second quartile -
e (Q2)
g Inter-quartile r
a First quartile range (IQR)
b
d (Q1)
e
z
i
l
a
m
r
o N Q1 - 1.5(IQR)
Q1 = MEDIAN(bottom 50% of data) Q2 = MEDIAN(data) Q3 = MEDIAN(upper 50% of data) IQR = Q3 - Q1 Figure 3-20. Example box plot.
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Calculate barge-to-tug ratios for each year and direction
Normalize barge-to-tug ratios by bridge site-specif ic median ratios
Perform outlier-detection analysis on normalized barge-to-tug ratios
No outliers present Outliers present
Flotilla traff ic = MIN(barge traff ic, tug tra ff ic) Remove outlying barge-to-tug ratios
Perform curve f its to remaining barge-to-tug ratios for bridge locations with outliers
Sample from curve f its to replace barge-to-tug ratios for years where outliers were present
Divide barge traff ic counts by barge-to-tug ratios to obtain modif ied tug traff ic counts
Flotilla traff ic = MIN(barge traff ic, tug tra ff ic)
Figure 3-21. Determination of barge flotilla traffic counts for individual bridge locations.
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Figure 3-22. Curvature of waterway near Acosta Bridge (Source: Google Maps, https://maps.google.com, January 27, 2016).
Figure 3-23. Curvature of waterway near Brooks Bridge (Source: Google Maps, https://maps.google.com, October 23, 2014).
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Figure 3-24. Curvature of waterway near Dupont Bridge (Source: Google Maps, https://maps.google.com, October 23, 2014).
Figure 3-25. Curvature of waterway near Highway-90 Bridge over Escambia River (Source: Google Maps, https://maps.google.com, October 23, 2014).
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Figure 3-26. Curvature of waterway near Sister’s Creek Bridge (Source: Google Maps, https://maps.google.com, October 13, 2014).
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7E-3
6E-3
5E-3
4E-3 BR 3E-3
2E-3
1E-3
0 A 90
75
60
45 Count
30
15
0 0 1E-3 2E-3 3E-3 4E-3 5E-3 6E-3 7E-3 BR B Figure 3-27. Estimates of BR. A) Scatterplot. B) Histogram.
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CHAPTER 4 EXPERIMENTAL VALIDATION OF BARGE BOW FORCE-DEFORMATION BEHAVIOR
Discussed in earlier chapters, the fundamental objective of the research presented in this
dissertation was to develop empirical parameters that may be used in conjunction with existing
design procedures for barge-to-bridge impact-resistant design. However, any investigation of
structural demands associated with barge impact events first requires a firm understanding of
barge bow crushing behavior. Previous analytical research (Consolazio et al. 2009, Getter and
Consolazio 2011) has resulted in the development of design barge bow force-deformation curves
that describe various aspects of barge crushing behavior which are not represented in current
AASHTO specifications (e.g., the influence of pier width and shape on peak impact force levels).
However, to validate force-deformation relationships obtained from analysis, comparable
experimental data are necessary.
As noted earlier, few studies have been conducted to experimentally quantify barge
force-deformation data. However, the investigation of barge flotilla collision behavior that will be discussed in Chapter 5 relies on a realistic description of barge bow crushing behavior.
Consequently, experimental validation of previous analytical force-deformation relationships
(Consolazio et al. 2009) was required.
While such validation has been achieved already at moderate deformation levels through full-scale testing (Section 2.3.1), an additional study was necessary to achieve validation at high deformation levels. In this chapter, an integrated experimental and analytical investigation of barge force-deformation behavior under high-energy impact loading is presented.
Results from impact tests involving reduced-scale replicates of jumbo-hopper barge bows
and impactors with two distinct surface geometries (e.g., circular and rectangular) are reported.
Material in this chapter was reproduced and adapted from the author’s contributions to Consolazio et al. (2014), and, with permission from ASCE, Kantrales et al. (2015). 121
Measured force and deformation data confirm several key findings previously identified through
numerical simulation; for example, that rounded bridge surfaces produce smaller impact forces
than flat (i.e., rectangular) surfaces.
4.1 Approach
Discussed in Chapter 2, one of the most prominent experimental investigations to
quantify barge bow force-deformation relationships was conducted by Meier-Dörnberg (1983).
In the research conducted by Meier-Dörnberg, gravity-driven impact hammers were used to
progressively deform the bows of reduced-scale models of European-style pontoon barges. From
the measured test data, simplified relationships between impact force and barge bow deformation
were developed. To make the relationships applicable to the design of waterway structures, the
experimental data, collected at reduced scales ranging from 1:6 to 1:4.5, were scaled up to full-
scale. It is important to note, however, that while some physical aspects of impact behavior obey
commonly used scaling laws, others do not. For example, barge impact forces are influenced by
localized dynamic buckling of structural members inside the barge bow. Both the force levels at
which local buckling occurs, and the sequence in which members buckle, can be affected by
dynamic (i.e., inertial) forces and load rate. Moreover, material strain-rate effects, wherein steel
yield stress and ductility both vary with load rate, can similarly influence impact forces. Such
rate effects can be particularly pronounced in reduced-scale testing where strain rates are often
much higher than those that occur in full-scale barge-to-bridge collision incidents. Unfortunately, neither dynamic buckling nor strain rate effects are accurately accounted for using traditional scaling approaches.
To advance the accuracy of barge force-deformation relationships used in bridge design, while simultaneously avoiding reliance upon, and the drawbacks associated with, scaling laws, a comprehensive study employing an alternative methodology has been carried out by the UF and
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the FDOT. Critical to the success of this methodology has been the careful integration of
numerical simulation with corresponding experimental testing and validation. To develop barge
force-deformation relationships for use in bridge design, high-resolution finite element (FE) models of barges have been used to simulate barge bow crushing (Consolazio et al. 2009, Getter and Consolazio 2011) over a range of different conditions (e.g., pier shape, pier size, vessel impact angle). All such simulations were conducted at full-scale and at impact speeds representative of typical barge-to-bridge collisions. Consequently, proper full-scale treatment of rate-dependent phenomena was directly achieved, and the use of scaling laws was rendered unnecessary. Validation of these numerical models has been carried out using experimental test data collected at two different levels of barge bow deformation: moderate and high. Moderate- level barge deformation data were collected from barge-to-bridge impact tests, summarized in the following section, that were conducted on a bridge near St. George Island (Consolazio et al. 2005) (Section 2.3.1). Complementary high-level barge deformation data were collected from a series of controlled pendulum impact experiments, which are the focus of this chapter.
To validate the FE modeling and analysis techniques employed in previously mentioned studies at high deformation levels, and by extension the models developed from these techniques, (Consolazio et al. 2009, Consolazio and Getter 2011), an integrated experimental and analytical was necessary. In the experimental component of the study, a series of pendulum impact tests were carried out using the FDOT pendulum impact facility (Figure 4-1), the design and features of which are discussed in Consolazio et al. (2012b) and Consolazio et al. (2014).
Located at the FDOT Marcus H. Ansley Structures Research Center in Tallahassee, Florida, the pendulum impact facility is comprised of a 34-ft wide, 20-ft long, 3-ft thick, concrete foundation
(heavily reinforced internally with structural shapes) and three 50-ft tall structural steel towers.
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One of the towers serves to pull an impactor (i.e., a nearly-rigid impact block) up to the desired drop height while the remaining two towers support the impactor through the downward swinging motion that occurs during an impact test. The FDOT pendulum can deliver impact energies of up to approximately 315 kip-ft, however, even at this level conducting impact tests on a full-scale replicate of a barge bow was impractical. Consequently, a rational methodology was implemented to scale the barge bow replicates down. Ultimately, based on construction feasibility considerations, a final scaling ratio of 1:2.5 (40%) was selected.
Importantly, the FE modeling and analysis procedures being validated were applied directly at the reduced-scale (40%) of the experimental tests. However, the same modeling and analysis techniques employed previously at full-scale to quantify bridge design loads
(Consolazio et al. 2009, Getter and Consolazio 2011) were used here to model the reduced-scale
experimental test conditions. Barge components were modeled at reduced (40%) geometric size, and both dynamic buckling and strain rate effects were directly taken into account, as appropriate at reduced-scale. Validating the reduced-scale barge bow model will, by extension, confirm that the modeling and analysis techniques employed are appropriate for describing high-deformation barge bow crush behavior. Consequently, since the same analytical approach was taken by
Consolazio et al. (2009) and Getter and Consolazio (2011), the full-scale models used in those studies, and the associated analysis results obtained, may be considered valid for describing full- scale barge bow crush behavior. By utilizing this approach to achieve validation for existing force-deformation relationships, it was not necessary to use scaling laws to transform experimental data from reduced-scale to full-scale values.
Numerical impact simulations of the reduced-scale models, conducted using LS-DYNA
(LSTC), were initially used as a means for planning the physical test program. Later, after
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completion of physical testing, the models were modified to match the precise conditions
observed during the physical tests (e.g. use of the experimentally measured pendulum impact
speeds instead of the pre-test planned impact speeds). Validation of the modeling and simulation
techniques was then carried out by comparing results from impact simulations to corresponding
experimental test data.
4.2 Experimental Procedures
It was initially envisioned that the reduced-scale barge impact experiments would involve
swinging a deformable barge bow into a nearly-rigid concrete bridge ‘pier’. However, pre-test planning FE analyses indicated that the opposite scenario, swinging a rigid pier against a deformable barge bow, would produce nearly equivalent force-deformation relationships, while also substantially improving the quality of data collected (e.g., accelerations, from which impact forces were computed). Based on this finding, each impact test involved swinging a nearly-rigid impactor, representing a bridge pier, at a deformable barge bow which was affixed to a nearly rigid reaction frame and foundation (Figure 4-2).
To experimentally confirm one of the major findings of previous analytical studies, that pier shape influences the magnitude of force imparted to a bridge during an impact, two separate test series were conducted: one with a round nose impactor (i.e., RND series) and one with a flat- faced impactor (i.e., FLT series). A nearly-rigid, steel-encased, concrete impactor was designed that consisted of a back-block and hanger frame assembly, which remained suspended from support cables throughout the test program, and two interchangeable noses: round (Figure 4-3A) and flat (Figure 4-3B).
Two separate barge bow replicates, one for each test series, were constructed based on jumbo hopper barge fabrication drawings that were geometrically scaled down to 40% of the original dimensions. Since high-level barge deformation involves mixed modes of structural
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resistance (flexural stiffness, tension membrane stiffness, compressive axial stiffness, etc.), it
was not feasible to scale member sizes so as to conform to theoretical scaling laws for all of
these stiffnesses simultaneously. Therefore, a simpler approach was used in which all member
dimensions (lengths, widths, thicknesses) were modified by a uniform 40% geometric scaling.
Structural members (e.g., channels, angles) with the desired external cross-sectional dimensions
(i.e., width and height) were found to be commercially available in ASTM A36 steel, although
milling was necessary to achieve the correct component (i.e., leg and web) thicknesses. To form
the barge headlog plates, sheet steel of appropriate 40% thickness was found to be directly
available in A36 material, and was acquired, cut, and bent into shape. For the thinner external
hull plates, A36 sheet materials with appropriate 40% thicknesses were not commercially
available, and milling down entire sheets of thicker material was not considered viable.
However, sheet materials of appropriate thicknesses were found to be available in ASTM A1011
steel, which possesses mechanical properties similar to A36. Consequently, A1011 sheet steel in
9 ga. and 11 ga thicknesses were used for the external hull plates.
The target barge deformation level to be achieved during each test series (RND and FLT)
was 4 ft, which corresponds to approximately 10 ft of deformation at full-scale, a reasonably conservative upper level estimate of crush depth for barge collisions with bridge structures.
However, even at reduced-scale (i.e., 40% scale), it was not possible to achieve the desired reduced-scale crush depth of 4 ft using a single, maximum energy swing of the pendulum.
Consequently, four sequential, and cumulative, impacts of the pendulum were used during each test series.
At the beginning of each test, the impactor was raised to the desired height (Figure 4-1)
using a winch mounted to one of the pendulum towers. Drop heights for each test (Table 4-1)
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ranged from 14-20 ft, with impact velocities varying from approximately 20-25 mph. For the
RND series, the impactor, including the hanger frame, weighed 9.2 kip; for the FLT series, the impactor weighed 9.7 kip. Since the flat nose was approximately 0.5 kip heavier than the round nose, drop heights for the FLT test series were reduced, relative to corresponding RND drop heights, in order to maintain similar impact energy levels. Implementing reduced FLT drop
heights produced impact momentums for the FLT tests that were within 4% of the corresponding
RND momentums. In addition, the initial test in each series, RND1 and FLT1, were conducted at
reduced drop heights (15 ft and 14 ft, respectively) relative to subsequent impacts, as a safety
precaution.
After raising the impactor to the desired height, a quick-release cargo hook was used to
drop the block, which tracked in a circular arc until impacting the stationary replicate barge bow.
Impact speed at the point of incipient contact was determined by measuring the time required for
the impactor to pass between two pairs of infrared optical break beam sensors located on either
side of the impact zone (Figure 4-4), and dividing the distance between the sensor pairs (12 in.)
by the time duration.
Surface-mounted accelerometers recorded the time-varying deceleration of the impactor.
Such data were later used to indirectly quantify the time-varying impact force. Based on
acceleration data computed from pre-test numerical simulations, accelerometers with two
measurement ranges were selected: ±250 g, and ±500 g. Accelerometer pairs, where each ‘pair’
consisted of one 250 g and one 500 g accelerometer, were attached to mounting plates embedded
in the top and bottom surfaces of the impactor (Figure 4-4).
Time-varying deformations of the barge bow were quantified using high-speed video
cameras and the motion tracking (i.e., digital image correlation) software Xcitex ProAnalyst 3 D.
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Following initial contact of the impactor with the barge bow, the measured translation of the impactor was known to be equal to the deformation of the barge bow. Therefore, time-varying barge bow crush depths (i.e., deformations) were determined by tracking the motions of well- defined features painted on the side of the impactor.
4.3 Experimental Results
A primary goal of the test program was to quantify the horizontal impact force exerted by the impactor against each replicate barge bow. To mitigate possible influences of block rotation on the interpretation of acceleration data from which forces were computed, all recorded acceleration time-histories at the top and bottom of the impactor were averaged together to form a single rigid impactor acceleration time-history for each test. To remove irrelevant high- frequency content, the averaged time-history formed for each test was filtered using a low-pass filter. Time-histories of impact force were then computed using the averaged, filtered acceleration data and the known mass of the impactor.
4.3.1 RND Series
To characterize and visualize the entire RND test series, a single series-wide RND force- deformation relationship was formed by concatenating all data from the RND1-RND4 tests.
Incremental deformations from each test were summed together to produce a cumulative deformation time-history, which was then synchronized to corresponding impact force data
(Figure 4-5). After concatenating the data, the unloading and re-loading portions of the curves were removed. The result was an overall RND ‘backbone’ force-deformation curve (Figure 4-5) similar in form to that which would have been produced had it been feasible to conduct a single, very-high-energy test.
Two unique barge response mechanisms can be identified in the RND backbone force- deformation curve (Figure 4-5). Initially, at lower deformation levels concordant with the
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response of the barge during the initial impact test (i.e., RND1), barge resistance was derived
from the stiffness of the internal trusses, culminating in the initial peak force at 4 in. of bow
deformation. Once the internal trusses buckled inelastically, larger deformations were accrued
during successive impacts. The resulting large deformation levels led to the development of
catenary force in the headlog plate and hull plates, with anchorage provided primarily by the
internal trusses outside of the impact zone. With increasing deformation, this catenary resistance
mechanism became more dominant; as a result, impact forces increased moderately in magnitude
with increasing deformation. By the fourth impact test, the entire height of the impactor had
penetrated into the barge replicate (Figure 4-6) and the target deformation level had been
approximately reached; therefore, no further tests were conducted.
4.3.2 FLT Series
To characterize the FLT test series as a whole, data from the individual tests (i.e., FLT1-
FLT4) were concatenated together, in a manner identical to that described above for the RND
series, to form a series-wide FLT backbone force-deformation relationship (Figure 4-7). Several distinct modes of response were clearly involved: a significant initial elastic resistance, observable in the early part of FLT1; inelastic truss buckling and diminishing resistance, present in the latter portion of FLT1; and, the plastic response shown in tests FLT2-FLT4.
The catenary response mode observed during the RND series was not evident in the FLT series. Due to the width of the flat nose, a greater number of trusses buckled, relative to RND1, during test FLT1. As a result, the level of restraint necessary to maintain catenary resistance was mostly unavailable, and the sole mechanism available to absorb impact energy was additional crushing of trusses in the immediate vicinity of the impact area. This resulted in a roughly plastic response (i.e., constant force magnitude) during FLT2-FLT4 (Figure 4-7). At the end of test
FLT3, the entire height of the impactor penetrated into the barge bow; however, for consistency
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with the RND test series, a fourth flat nose impact test was conducted. Although minimal
material fracture was observed throughout most of the FLT series, following test FLT4
(Figure 4-8), several fracture seams began to open near the bottom of the impact zone.
4.3.3 Comparisons
Comparisons of key results obtained from the RND and FLT test series are provided in
Table 4-2. Of greatest importance for bridge design, the maximum measured RND impact force
was found to be 33% smaller than the corresponding FLT impact force. This difference and
additional distinctions in deformation trends are further evident in the detailed force-deformation
relationships (Figure 4-5 and Figure 4-7). Cumulative deformation levels for the FLT series were
larger relative to the RND series largely due to the diminished resistance of the barge following
the truss buckling sustained during test FLT1.
4.4 Analytical Modeling Procedures
Analytical modeling and analysis techniques used in past studies (Consolazio et al. 2009,
Getter and Consolazio 2011) to quantify full-scale barge impact loads were previously validated
at moderate barge deformation levels using data from full-scale barge-to-bridge impact experiments (Consolazio et al. 2005). Validation of these same numerical techniques, but at high
levels of barge deformation, was achieved in the present study by directly modeling and
simulating the 40% reduced-scale pendulum impact experiments and then comparing simulation
results to measured RND and FLT test data.
Proper FE representation of inelastic local buckling of structural members (plates,
channels, angles) inside a barge bow requires a highly refined mesh. Consequently, the 40%
barge replicate was modeled with a dense mesh of approximately 120,000 four-node, fully- integrated shell elements (Figure 4-9).
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Nonlinear, inelastic material models were assigned to the shell elements in accordance with the specific types of steel (A36 and A1011) that were used in fabricating the physical barge replicates. All of the material models incorporated strain-rate sensitive behavior through implementation of the Cowper-Symonds sensitivity model (Jones 1997, LSTC). Importantly, all material properties, including baseline static stress-strain curves and Cowper-Symonds rate- sensitivity coefficients, were quantified from static and dynamic tests of the specific types of steel used in this investigation (details provided in Consolazio et al. 2014).
Welded connections between structural members inside the barge bow FE model were formed using thousands of individually constrained node sets (node groups). Importantly, for model validation purposes, the nodes in each constraint set were organized into patterns that approximately matched the stitch welds and plug welds used in fabricating the 40% scale barge bow replicates.
Initially, the impactor was modeled in a detailed manner (Figure 4-10A) to provide data necessary for pre-test structural design of test components (particularly the steel hanger frame).
Upon completion of testing, however, a simplified modeling approach was used to facilitate efficient simulation of all RND and FLT test conditions. Whereas shell elements were used to model the hanger frame in the detailed model (Figure 4-10A), a set of solid elements, positioned atop the impact block, were used to approximate the influence of the hanger frame mass in the simplified model (Figure 4-10B). The efficacy of this simplification was verified by comparing results from detailed and simplified simulations for a selected subset of impact conditions.
Contact between the impactor and barge, as well as contact between components inside the barge, were modeled using a penalty-based contact-detection algorithm which accounted for interface friction.
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4.5 Comparison of Experimental and Analytical Results
For each test series (i.e., RND and FLT), four FE impact simulations, corresponding to
the experimental conditions, were performed. In the first simulation of each series (i.e., RND1
and FLT1), the impactor was placed at the point of incipient contact with the barge and given an
initial impact velocity equal to the experimentally measured value. Upon contact, the impactor
progressively and plastically crushed the barge model. Termination of each simulation was
associated with the impactor reaching zero velocity and starting to rebound. Subsequent impact
simulations in each test series (i.e., RND2-RND4 and FLT2-FLT4) were conducted using a simulation ‘restart’ capability of LS-DYNA (LSTC 2014). In a restart simulation, deformed geometry, element strains, and element stresses computed from a previous analysis (e.g., RND1 and FLT1) are used as initial conditions for the subsequent restart analysis (e.g., RND2 and
FLT2). Following each simulation, the analytically computed force and deformation data were post-processed using the same filtering procedures employed earlier to process the corresponding
experimental data.
Using post-processed analytical time-history data, backbone force-deformation
relationships were constructed for both impact series and compared to the corresponding
experimental relationships. In general, good agreement was observed between experimental data
and numerical simulations of the experimental conditions (Figure 4-11 and Figure 4-12), thereby
confirming the validity of the numerical simulation techniques. General behavioral trends in
analytical and experimental force data closely matched, and maximum deformation levels were
in excellent agreement.
The only behavioral deviation of note was an initial force spike in the FLT simulation
results (Figure 4-12) that was not apparent in the experimental data. Based on the exceptionally
short duration of this spike, it was not considered relevant to bridge design. Moreover, sensitivity
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simulations revealed that the presence of the spike was related to the elevated velocities at which the pendulum impact tests were conducted; analogous simulations conducted at impact velocities representative of typical waterway impact conditions revealed no such anomaly.
4.6 Summary
Reduced-scale (i.e., 40%) pendulum impact tests were performed on barge bow replicates to experimentally characterize barge force-deformation behavior representative of high-energy, high-deformation, barge-to-bridge collision events. To experimentally quantify the extent to which bridge pier shape influences barge impact forces, two series of tests were conducted: rounded impactor tests; and flat-faced impactor tests. Since key phenomena pertinent to barge deformation behavior under impact loading (e.g. dynamic buckling and steel strain rate effects) do not obey traditional scaling laws, an alternative approach, not requiring scaling, was used in this study to render the reduced-scale test data applicable to full-scale bridge design.
Specifically, FE modeling and analysis procedures, employed in previous studies at full-scale to develop load prediction models for bridge design, were applied, for validation purposes, directly at the reduced-scale (i.e., 40%) of the pendulum impact experiments. Good agreement between results from simulations of the reduced-scale test conditions and corresponding experimental test data validated the accuracy of the analytical techniques, and thus indirectly validated prior full- scale analytical studies that employed the same techniques. By employing this integrated experimental and multi-scale analytical approach, it was not necessary to use scaling laws to interpret the reduced-scale test data. Using the validated modeling and analysis procedures discussed in this chapter, barge bow force-deformation curves were later developed for the study on multi-barge flotilla collision behavior discussed in Chapter 5.
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Table 4-1. Summary of test program (Source: Kantrales et al. 2015) Impact Barge Drop height, Impact speed, Impact series Test ID energy, kJ replicate m (ft) km/h (mph) (kip-ft) number Round RND1 4.6 (15) 33.6 (20.9) 184 (135) 1 Round RND2 6.1 (20) 40.1 (24.9) 261 (191) 1 Round RND3 6.1 (20) 39.8 (24.7) 257 (188) 1 Round RND4 6.1 (20) 40.7 (25.3) 270 (198) 1 Flat FLT1 4.3 (14) 33.0 (20.5) 185 (135) 2 Flat FLT2 5.8 (19) 38.8 (24.1) 258 (189) 2 Flat FLT3 5.8 (19) 39.1 (24.3) 261 (191) 2 Flat FLT4 5.8 (19) 39.1 (24.3) 261 (191) 2
Table 4-2. Overall results from each test series (Source: Kantrales et al. 2015) Category of measurement RND series FLT series Impactor weight, kN (kip) 41.0 (9.22) 43.2 (9.70) Peak force for series, kN (kip) 903 (203) 1205 (271) Cumulative plastic deformation for 986 (38.8) 1207 (47.5) series, mm (in.) Note: Peak forces were determined from backbone curves
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Figure 4-1. FDOT pendulum impact facility in Tallahassee, Florida (Source: Kantrales et al. 2015) (Photo courtesy of Gary R. Consolazio).
Hanger cable Hanger frame Tape switches Rear portion Replicate barge bow of impactor Round nose attachment Normal-speed Optical break camera beam (typ.) Steel reaction frame High-speed Permanent concrete camera foundation
Figure 4-2. Schematic of test setup (Source: Kantrales et al. 2015)
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A
B
Figure 4-3. Impactor. A) Round nose attachment. B) Flat nose attachment (Source: Kantrales et al. 2015) (Photo courtesy of Gary R. Consolazio).
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250g/500g accelerometers Hanger frame Normal-speed camera 0.4 Scale replicate barge bow Impactor Reaction frame Tape switches Support pole
Optical break 250g/500g beam sensor High-speed camera accelerometers
Figure 4-4. Elevation view of field instrumentation (Source: Kantrales et al. 2015)
Deformation (in) 0 10 20 30 40 50 1400 Backbone curve 280 1200 Unloading Reloading 240 1000 200 800 160 600 Force (kN) 120 Force (kip) 400 RND1 RND2 RND3 RND4 80 200 40
0 0 0 250 500 750 1000 1250 1500 Deformation (mm)
Figure 4-5. Force-deformation relationship from RND test series (Source: Kantrales et al. 2015)
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Figure 4-6. Final deformation pattern of replicate barge bow following test RND4 (Source: Kantrales et al. 2015) (Photo courtesy of Gary R. Consolazio).
Deformation (in) 0 10 20 30 40 50 1400 Backbone curve 280 1200 Unloading Reloading 240 1000 200 800 160 600 Force (kN) 120 Force (kip) 400 80 FLT1 FLT2 FLT3 FLT4 200 40
0 0 0 250 500 750 1000 1250 1500 Deformation (mm)
Figure 4-7. Force-deformation relationship from FLT test series (Source: Kantrales et al. 2015)
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Figure 4-8. Final deformation pattern of replicate barge bow following test FLT4 (Source: Kantrales et al. 2015) (Photo courtesy of Gary R. Consolazio).
Figure 4-9. FE model of 40% scale replicate barge bow (Source: Kantrales et al. 2015).
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A
B
Figure 4-10. FE model of impactor. A) Detailed treatment of hanger frame mass. B) Simplified model of hanger frame (Source: Kantrales et al. 2015).
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Deformation (in) 0 10 20 30 40 50 2000 Experimental Finite element 400 1600 320
1200 240
800 Force (kN) 160 Force (kip)
400 80
0 0 0 250 500 750 1000 1250 1500 Deformation (mm)
Figure 4-11. Comparison of analytical and experimental force-deformation relationships for RND series (Source: Kantrales et al. 2015).
Deformation (in) 0 10 20 30 40 50 2000 Experimental Finite element 400 1600 320
1200 240
800 Force (kN) 160 Force (kip)
400 80
0 0 0 250 500 750 1000 1250 1500 Deformation (mm)
Figure 4-12. Comparison of analytical and experimental force-deformation relationships for FLT series (Source: Kantrales et al. 2015).
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CHAPTER 5 INFLUENCE OF IMPACT-INDUCED RELATIVE MOTION ON EFFECTIVE BARGE FLOTILLA MASS
As highlighted in Chapter 2, one of the fundamental outstanding questions in barge-to- bridge collision design is related to the portion of the barge flotilla mass participating in a barge- to-bridge impact event that has an influence on structural demands (i.e., the ‘effective mass’ of a barge flotilla). The total mass of a barge flotilla may be divided into three categories: the mass of each individual vessel (barge and tug) in the flotilla; the mass of the commodity being transported by the flotilla (i.e., the barge ‘payload’); and the mass of the water volume mobilized by the flotilla during transit (i.e., the hydrodynamic mass).
Hydrodynamic mass effects are accounted for in AASHTO (2014) bridge design specifications through the implementation of modification factors that amplify the effective flotilla mass used in load calculations. The added hydrodynamic mass mobilized by a barge flotilla is directly related to the tonnage and draft of the flotilla since it represents the mass of the volume of water pulled along with the vessel during motion.
Similar to the added mass approach utilized to account for hydrodynamic effects, current
AASHTO specifications in the United States treat payload mass as a part of the total barge mass for design kinetic energy calculations. However, each payload, regardless of type, retains the ability to shift independently of the barge transporting it while that barge is in motion—a consequence of the fact that a barge payload is not a rigid entity. Therefore, during a barge-to- bridge impact event, it is possible that a portion of the payload less than the total payload mass could contribute to structural demands due to energy dissipated through relative sliding—both within a transported granular media, as well as between the payload and the hopper region. To illustrate the significance of payload sliding, the effective mass participation of a payload
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comprised of coal, which is regularly transported by barge flotillas in the United States, was
examined in this investigation.
In addition to payload sliding and hydrodynamic mass effects, the total effective mass of
a barge flotilla can be influenced by differential motion that occurs between individual barges.
Some differential motion is a result of inter-barge crushing within a single barge column.
However, differential motion between barge columns can also occur. Immediately on impact, the
kinetic energy of an impacting barge column is arrested rapidly by the bridge. However, the
kinetic energy of non-impacting barge columns is dissipated more slowly through inter-column
frictional forces (Figures 5-1 and 5-2) and lashing (Figure 5-3) tensile forces, or directed away
from the bridge through lashing failure and column separation.
Due to the presence of differential motion, a realistic model of a barge flotilla would treat
each barge as a separate mass (i.e., a MDOF system). However, using the procedures outlined in
AASHTO (2014), the kinetic energy of an impacting flotilla—from which AASHTO design
loads are computed—is calculated based on the assumption of a single flotilla mass. Specifically,
AASHTO requires that the effective flotilla mass be represented as the combined mass of all
barges in the impacting column; the mass of barges in adjacent (i.e., non-impacting) columns is
ignored in the computation of design impact forces. This requirement is derived from the
assumption that the lashings between the non-impacting barge columns and the impacting
column will fail on impact, severing the continuity of the flotilla (Figure 5-4). Due to this loss of
continuity, the kinetic energy of barges in non-impacting columns will not be transferred to the
structure, thereby verifying the preclusion of the combined mass of non-impacting columns from the kinetic energy calculation. However, in contrast with AASHTO provisions, Eurocode design requirements offer a more prescriptive approach, wherein the effective mass of a barge flotilla is
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determined using values specified in a tabular format for various vessel classifications
(CEN 2006).
Expanding on present design procedures, researchers have employed various analytical
methods to investigate the issue of multi-column flotilla impact behavior. These efforts have
included both one-dimensional (Yuan and Harik 2008) and two-dimensional (Luperi and
Pinto 2014) representations of barge flotillas of varying sizes and properties, and under different
impact conditions. The intent of these investigations was to develop analysis procedures to
capture the influence of flotilla relative motion on structural demands, or, alternatively, to
account for such effects through simple design expressions that produce an equivalent SDOF
flotilla mass. However, due to several modeling restrictions, these investigations did not allow
for unrestricted barge motion and considered inter-barge interactions through simplified one or
two-dimensional representations. To avoid these issues, the primary objective of the research
presented in this chapter was to characterize barge flotilla relative motion through the utilization
of three-dimensional finite element analysis techniques that fully represent contact interfaces
between barge columns and appropriately characterize lashing behavior. Through an analytical
parametric study that included both flotilla-dependent and structure-dependent parameters, a design equation was formulated to allow for the calculation of an ‘effective mass ratio’ (EMR) that may be used in conjunction with current design procedures.
5.1 Modeling Approach
To avoid limitations associated with previous investigations of barge flotilla impact and breakup behavior, the barge flotilla models utilized in this investigation, originally developed by
Consolazio et al. 2012a, fully represented the external geometry of each barge in three dimensions (Figure 5-5a). Each barge modeled in this study was representative of a jumbo hopper barge—a very common type of barge utilized in U.S. waterways. Individual barge
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models consisted of approximately 5,000 rigid shell elements. Overall mass and inertia properties were determined from equivalent, deformable, high-resolution barge models (Figure 5-5b) and prescribed to a node located at the center of mass of each rigid barge. Deformable barges used for this purpose explicitly modeled both the external hull plates of the barge as well as the internal structure (Figure 5-6).
Since the barges utilized in this investigation were comprised entirely of rigid elements, internal components were not modeled and deformable inter-barge contact was not implemented.
Instead, inter-barge interactions were described through rigid surface-to-surface contact definitions for numerical efficiency. Each definition consisted of two sets of elements—one associated with each of the two interacting barges—and a nonlinear force-deformation curve that described the inter-barge crushing behavior. Contact forces were allocated to individual nodes in each element set according to nodal penetration depths. Each inter-barge force-deformation curve (Figure 5-7) was derived from high-fidelity crushing simulations conducted by Consolazio et al. (2012a) to model bow-to-bow (Figure 5-8A), bow-to-stern (Figure 5-8B), stern-to-stern
(Figure 5-8C), and side-to-side (Figure 5-8D) barge crushing behavior.
Crushing behavior associated with the bow of the impacting barge was considered through the same type of rigid surface-to-surface contact definition. However, in this case, one element set in the definition was associated with the headlog region of the barge bow and the other was associated with a 2 ft x 2 ft impact surface representative of the impact face of a bridge pier (Figure 5-9). A small impact surface was utilized in this investigation to ensure that all nodes on the surface remained in contact with the headlog region of the barge throughout each impact event. This approach allowed for proper representation of impact force levels.
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Force-deformation relationships used to describe the crushing behavior of the impacting
barge (Figure 5-10) were derived from a series of high-fidelity crushing simulations—conducted
according to procedures outlined in Kantrales and Consolazio (2016)—involving both round and
flat-faced piers of various widths. Barge material behavior in these simulations was consistent
with A36 steel and strain-rate effects were implemented through the utilization of the Cowper-
Symonds model. Details relating to the Cowper-Symonds coefficients and stress-strain curve
utilized in this investigation are provided in Kantrales and Consolazio (2016). When it was
necessary to account for the influence of pier stiffness in the direction of impact ( KP ), the barge
bow force-deformation curves shown in Figure 5-10 were modified to produce an equivalent force-deformation curve appropriate for the pier stiffness level considered.
Buoyancy effects associated with displaced water were considered through approximately 900 linear springs connected to the bottom nodes of each barge. Buoyancy springs were calibrated prior to each impact simulation according to the methods outlined in Consolazio et al. (2012a) to ensure that the flotilla remained approximately level under applied gravitational loads. In addition to buoyancy effects, hydrodynamic mass effects were also considered through the utilization of an added mass.
Lashings between barges were modeled with nonlinear cable and beam elements with breaking strengths of either 90 or 120 kips. To represent the condition of a fully-lashed flotilla, lashing elements were pretensioned up to 50% of the breaking strength. Lower pretension levels were considered in preliminary simulations, but were found to result in more relative motion between barges due to a decrease in inter-column frictional forces. As a consequence, to produce conservative predictions of flotilla effective mass, pretension levels below 50% were not implemented into the models employed in this investigation. Lashing material models and
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configurations (Figure 5-11) were adopted from Consolazio et al. (2012a) and are derived from
lashings employed in full-scale barge impact experiments conducted at the Robert C. Byrd Lock
and Dam (Patev et al. 2003b). Notably, multiple impact experiments conducted by Patev et
al. (2003b) were replicated analytically by Consolazio et al. (2012a) with good agreement
observed between experimental and analytical results.
5.2 Relative Motion of a Coal Payload
As indicated previously, a component of this investigation involved a proof-of-concept
study regarding the influence of payload sliding on the effective mass of an impacting barge.
While barge payloads can vary in type, a common payload comprised of bituminous coal was
selected for this study.
5.2.1 Modeling Procedures
To analytically evaluate the inertial behavior of a coal payload during barge-to-bridge impacts, a representative model of the payload must be employed that can capture the dynamic behavior of the coal particles under impact conditions (particularly frictional interactions). Since coal is a granular media, it was modeled in this study using the discrete element (DE) method in
LS-DYNA (LSTC). DE methods allow for the discretization of a granular media into rigid spheres (i.e., discrete elements) (examples shown in Figure 5-12), each of which may be used to
describe a single particle of the media, or a collection of particles, depending on the material
properties specified. Contact algorithms are employed to describe inter-particle and particle-
structure interactions. Through these definitions, a DE model may be combined with a finite
element model of a continuum to obtain a complete analytical description of system behavior.
Based on a review of several investigations that quantified coal material properties
(Metcalf 1966, Teffo and Naude 2013, Van Heerden 1985, Zheng et al. 1991), representative
values were determined for the coal DE model (Table 5-1), including: specific weight (γ );
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modulus of elasticity ( E ); Poisson’s ratio (ν ); angle of repose (φ ); and the angle of sliding with respect to steel (θ ).
For computational efficiency, it was necessary to calibrate a DE model so that each discrete element represents a collection of granular particles. This approach not only reduced the number of elements required to represent a fixed volume of granular media, but also reduced the simulation time through the utilization of larger time steps. In this investigation, a 9-in. element size was employed to represent a collection of coal nuggets. Simulation methods described in
Jensen et al. (2014) were utilized to calibrate both coal-coal (Figure 5-12A) and coal-steel
(Figure 5-12B) frictional parameters such that the bulk material behavior conformed to the friction angles provided in Table 5-1.
5.2.2 Single Barge Impact Simulations with Payload Model
Following calibration of the coal payload material properties, a payload of approximately
1200 tons was poured into the back of a single barge from a suspended hopper (Figure 5-13) and an initial impact simulation was conducted with an impact velocity (V) of 4 ft/sec against a 9-ft
flat pier with a stiffness ( KP ) of 1,000 kip/in.—a representative moderate-demand impact scenario (Figure 5-14). A head-on impact condition, in which the centerline of the barge bow was aligned with the centerline of the bridge pier, was employed in this simulation (see
Figures 5-1 and 5-2 for examples).
A comparison of results from the DE payload impact simulation and an analogous rigid- payload impact simulation (Figure 5-15) showed that there was no difference in calculated peak impact forces. However, an appreciable level of energy dissipation—equaling approximately
33% of the initial kinetic energy—occurred due to payload sliding in the hopper region
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(Figure 5-16). As a consequence of this, the peak energy absorbed through barge bow crushing
was considerably lower in the DE payload impact simulation (Figure 5-15B).
Overall, the level of payload relative motion was also found to vary with both impact speed and pier resistance (Table 5-2). For the impact simulations conducted in this investigation,
energy dissipation levels associated with payload motion ranged from 3-33%. Generally, low
impact speeds and narrow piers were associated with less relative sliding since lower shear force
demands were placed on the coal-steel and coal-coal interfaces.
Since the level of energy dissipation associated with payload relative motion was found to vary significantly with both impact speed and pier characteristics, and since the properties of barge payloads can also vary, implementing a reduction in effective barge mass to account for payload sliding is not recommended. As a consequence, for all barge flotilla impact simulations conducted in this investigation, a rigid payload representation was employed.
5.3 Effective Mass of Barge Flotillas
In addition to relative motion within a barge payload, multi-barge flotillas are also capable of dissipating energy through inter-barge crushing and preventing the transfer of kinetic energy to impacted bridge piers through lashing failure and flotilla breakup (Figure 5-4). As a consequence, the mass of an impacting barge flotilla responsible for producing structural demands in an impacted bridge is, in most cases, smaller than the total mass of the flotilla.
However, the factors affecting flotilla breakup behavior and the amount of energy dissipated through inter-barge crushing are not prominently discussed in published literature. Consequently, the assumption of flotilla breakup implicit in existing AASHTO specifications is not well supported. In this study, simulations involving both single-column and multi-column barge flotilla impact events were conducted in order to explore and characterize the effective mass of an impacting flotilla. This was accomplished through the use of a three-dimensional finite
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element model developed in a previous investigation (Consolazio et al. 2012a) and the general
modeling and simulation approach discussed in Section 5.1.
5.3.1 Single-Column Barge Flotilla Impact Simulations
Prior to conducting multi-column flotilla impact simulations to characterize flotilla
breakup behavior, single-column flotilla impact simulations were first conducted in order to
isolate the influence of inter-barge crushing on effective flotilla mass. Since the stiffness and
maximum resistance of inter-barge interactions are related to the type of interface, three different
five-barge flotilla configurations were considered: a flotilla configured entirely with doubled-
raked barges, which had bows at the fore and aft regions of each barge (Figure 5-17A); one in
which each barge was single-raked (Figure 5-17B), which had a bow at the fore region of each
barge and a stern at the aft region; and one in which the lead barge was single-raked and
subsequent barges had boxed ends (Figure 5-17C).
Using each flotilla configuration, head-on impact simulations were conducted at 4 ft/s
against a 9-ft rectangular pier with a stiffness ( KP ) of 1,000 kip/in. Peak impact force and deformation levels were recorded during each simulation (Table 5-3). In addition, the total energy absorbed by the bow of the impacting barge was also determined and effective mass ratios were calculated through Equation 5-1:
E EMR = A KEI (5-1) where, EMR is the effective mass ratio, EA is the total energy absorbed by the bow of the
impacting barge, and KEI is the initial kinetic energy of the entire flotilla. Note that, in order to
exclude energy associated with inter-barge crushing, only the energy absorbed by the impacting
barge was considered in the calculation of EMR values. In this way, EMR values were a measure
of the portion of the total impact energy that could contribute to structural loads.
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Although the peak impact forces shown in Table 5-3 are largely similar, EMR values
varied significantly among the three flotilla configurations. This outcome is associated with the
relative stiffnesses of the barge-to-barge contact interfaces and the barge-to-pier crushing
interaction. As indicated by Figure 5-7, bow-to-stern contact interfaces are much less stiff than
the barge-to-pier crushing relationship (Figure 5-10) and have lower maximum resistance levels
relative to both stern-to-stern and bow-to-bow interfaces. Due to the lower stiffness levels, more
relative motion is encountered between two barges which share a bow-to-stern interface. This is
in contrast with bow-to-bow interactions, which produce the stiffest response and correlate with
much lower levels of relative motion between barges. However, as indicated previously, the
overall level of relative motion incurred between barges in a flotilla is strongly related to the
stiffness of the barge-to-pier crushing interaction. To illustrate this point, an additional barge
impact simulation was conducted with the flotilla configuration that consisted entirely of double-
raked barges (thus, only bow-to-bow interactions were represented). Unlike the previously-
discussed simulation, which was conducted with a 9-ft pier model, this additional simulation was
conducted with a 26-ft pier. Results from both simulations (Figure 5-18) show that considerably
more kinetic energy was dissipated through inter-barge crushing during the impact simulation
involving the wider pier—an observation that highlights the influence of pier width on the
effective mass of an impacting barge flotilla. This finding also had relevance with respect to
multi-column barge flotilla impact behavior and will be discussed in further detail later in this
chapter.
5.3.2 Multi-Column Barge Flotilla Impact Simulations
Subsequent to conducting initial simulations involving single-column barge flotillas, a
comprehensive study of multi-column flotilla impact behavior was performed. The main goal of this component of the investigation was to characterize factors influencing not only inter-barge
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crushing interactions, but also inter-column flotilla breakup behavior associated with barge
lashing failure.
Results from preliminary simulations involving single-column flotillas showed that
flotillas which consisted entirely of double-raked barges resulted in higher EMR values relative
to other possible configurations. As discussed previously, this finding is related to the stiffness
and maximum resistance level of the bow-to-bow barge interaction employed in this investigation. However, the configuration of a barge flotilla can vary significantly and detailed information about flotilla configurations may not be readily available for design engineers.
Consequently, in order to produce conservative predictions of EMR that may ultimately be utilized in a design setting, all multi-column impact simulations conducted in this investigation employed barge flotillas which consisted entirely of double-raked barges with bow-to-bow interfaces (Figure 5-19).
When designing a new bridge, or evaluating an existing bridge structure that is susceptible to vessel impact, design engineers commonly utilize traffic data that describes basic information about the vessels which transit the waterway. Such information often includes vessel dimensions, flotilla mass, and transit speeds,. In addition to vessel-specific information, design engineers also have bridge-specific details, including pier dimensions, spacing, and foundation plans. Consequently, in order to discuss outcomes relevant for design, both vessel and bridge characteristics were considered in the parametric study performed in this investigation.
In total, the influence of six different parameters on multi-column barge flotilla impact behavior were examined in a 3,000 simulation parametric study. For each parameter a reasonable range of values were incorporated (Table 5-4).
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To represent a range of flotilla sizes, flotillas with up to three columns and up to five
rows were considered (Figure 5-20). Similar to the single-column impact simulations discussed previously, head-on impact conditions were assumed. Two-column flotillas were employed in outer-column impact simulations (Figure 5-2), whereas three-column flotillas were employed in center-column impact simulations (Figure 5-1). While outer-column impact events are also possible for three-column flotillas, such scenarios result in higher lashing demands and a higher possibility of flotilla breakup due to a reduction in the number of lashings engaged on the impacting barge column. As a result, outer-column impact events will normally result in lower effective mass levels relative to center-column impacts, and, correspondingly, lower structural demands. Consequently, in order to focus on a scenario more relevant for design, all three- column impact simulations conducted in this investigation assumed that impact occurred on the lead barge of the center column.
To capture the influence of low to moderate speed impact events, impact velocities used in each simulation ranged from 1-5 ft/sec. While impact velocities above 5 ft/sec are possible, barge transit speeds in the vicinity of waterway structures are frequently below 5 ft/sec.
Furthermore, at high impact velocities, a bridge pier can penetrate into the hopper region of a barge and engage the payload. Since payload resistance can be highly variable (depending on the payload type and level of loading), and since no specific payload type was assumed for this component of the investigation, very high energy impacts were considered outside the scope of this study.
As previously discussed, pier geometry can have a significant influence on peak impact force levels. Furthermore, since both pier width and pier shape can significantly affect the stiffness levels of barge-to-pier contact interactions, a considerable range of pier widths were
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included in the parametric study, ranging from narrow 6-ft piers to wide 35-ft piers. To account for the influence of pier shape, round and flat-faced variants of each pier were incorporated.
In addition to pier geometry, the stiffness of the pier in the direction of impact was also included as a variable to account for barge-pier relative motion. Five different stiffness values were considered, including low (200 kip/in.) and high stiffness (10,000 kip/in.) piers. Since inertial resistance associated with the bridge mass will increase inter-barge relative motion through increasing the effective resistance of the bridge, such effects were conservatively neglected in this investigation.
After post-processing data from each simulation, EMR values were quantified using
Equation 5-1. Through examining behavioral trends, various observations were made regarding the influence of flotilla and structural characteristics on the effective mass of a multi-column flotilla.
5.3.2.1 Effect of pier width
As discussed earlier, the width of a bridge pier affects the crushing behavior of an impacting barge, with wide and flat piers resulting in the stiffest initial response and the highest peak crushing forces. With all other conditions equal, stiffer barge-to-pier interactions result in more inter-barge relative motion within the impacting column of a flotilla and a greater chance for lashing failure between columns (Figure 5-21). This behavior is evident in the EMR trends that were observed during this investigation (example shown in Figure 5-22).
For the example case shown in Figure 5-22, utilization of an 18-ft pier, which engaged a significant number of trusses along the width of the barge, resulted in significantly more inter- barge crushing relative to narrower—6-ft, 9-ft, and 12-ft—piers and a lower calculated EMR. In all of these cases, limited lashing failure was observed; resultantly, flotilla connectivity was generally preserved. However, similar impact simulations conducted with 26-ft and 35-ft piers
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resulted in near-complete failure of inter-column lashings—an outcome that is apparent from the
significant decrease in EMR. Notably, little difference was observed between EMR values
associated with the 26-ft and 35-ft pier impacts. Since both wide piers resulted in significant
lashing failure, the ability of the exterior two columns to contribute to crushing in the lead
column was limited. As a consequence, flotilla impact behavior was largely similar in both cases.
Due to the behaviors discussed in the example case discussed above, the results from this
investigation indicated that effective multi-column flotilla mass decreased as pier width
increased. Furthermore, impact simulations which involved narrow, round piers did not result in
significant impact forces and commonly resulted in little inter-barge crushing and inter-column lashing failure. As a consequence, EMR values in these cases were typically close to one for most flotilla configurations considered in this study. However, the overall influence of pier width on EMR values was also shown to be affected by the stiffness of the pier at the point of impact.
5.3.2.2 Effect of pier stiffness
Pier stiffness, similar to pier width, influences the degree of relative motion within a
flotilla by influencing the rate of deceleration of the impacting barge. To account for pier
stiffness in this investigation, linear pier stiffness springs with values provided in Table 5-4 were placed in series with the nonlinear springs associated with the lead barge-pier crushing interaction (see Figure 5-10 for the relevant curves). Equivalent force-deformation curves considering the influence of the pier and impacting barge bow were derived from the combined influence of both springs and were subsequently utilized in the rigid-to-rigid contact curves that described the effective force-deformation response of the impacting barge bow.
Through reducing the effective stiffness of the initial (linear) portion of the lead barge- pier crushing interaction, flexible piers will result in less inter-barge crushing within the impacting column than stiff piers since more motion is expected at the point of impact (Figure 5-
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23). Furthermore, through reducing the rate of deceleration of the impacting column, inter-
column relative motion is less prominent in flotilla impact events involving flexible piers than it
is for impact events involving stiff piers—an outcome that reduces barge lashing demands. The
combined influence of these effects is that effective flotilla mass decreases with increasing pier
stiffness. In this investigation, this was demonstrated by an increase in EMR values that was
correlative with decreasing pier stiffness levels (Figure 5-24).
As with pier width, the significance of the increase is relative to other aspects of the impact event. As discussed previously, very narrow piers, particularly narrow round piers, resulted in a low-stiffness force-deformation response of the barge bow during impact. In such cases, the flexibility at the point of impact was such that inter-barge relative motion was minimal within the flotilla. For example, EMR values quantified in this investigation associated with a round, 6-ft pier were mostly unaffected by pier flexibility (example shown in Figure 5-25) due to the pre-existing flexibility associated with the nature of barge bow crushing against narrow, round piers.
5.3.2.3 Effect of impact velocity
Unlike pier width and pier stiffness, which consistently decreased flotilla effective mass with increasing magnitudes, the influence of impact velocity was found to vary more
considerably with pier and flotilla characteristics. This outcome is largely related to the effect of
velocity on the initial kinetic energy of an impacting flotilla and the portion of that energy which gets dissipated during the initial high-stiffness portion of an impact event when rapid
deceleration of the impacting barge occurs.
If the impact velocity of a flotilla is high (e.g., 5 ft/sec), the associated impact energy is
typically enough to achieve high deformation levels in the bow of the impacting barge. At high
deformation levels, barge bows possess considerably less resistance than at lower levels when
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truss buckling is initiated and the majority of lashing failure and inter-barge crushing occurs.
Correspondingly, the effective mass of a flotilla is lowest at impact velocities which cause enough deformation to cover the entirety of the high-stiffness, high-resistance region of a barge bow force-deformation curve. Faster impact velocities cause additional crushing into low- stiffness, low-resistance regions while lower impact velocities do not cause enough deformation to reach peak crushing force levels.
To illustrate the relative influence of impact velocity on flotilla effective mass, three maximum deformation levels—associated with impact simulations conducted at velocities of
1 ft/sec, 2 ft/sec, and 3 ft/sec—are identified on the force-deformation curve shown in Figure 5-
26 along with calculated EMR values. Notably, the flotilla effective mass decreased when the
impact velocity was raised from 1 ft/sec to 2 ft/sec. However, when the impact velocity was
raised further to 3 ft/sec and high deformation levels were achieved, the effective mass increased
substantially.
Because the influence of impact velocity on flotilla effective mass is strongly related to
the shape of the force-deformation curve, the speed at which flotilla effective mass is minimized
varies with both pier width and pier stiffness. Furthermore, since the total flotilla mass also
affects the impact energy of a flotilla, the influence of impact velocity on effective mass also
changes with flotilla configuration.
5.3.2.4 Effect of flotilla configuration
Different flotilla configurations possess different mass and stiffness characteristics based
on the arrangement of the individual barges as well as the placement of inter-barge lashings. In
this study, two and three-column barge flotillas with up to five rows were considered (Figure 5-
20). Flotillas with more rows incorporated additional lashings to tie barges together. As a
consequence, for the flotillas employed in this investigation, inter-barge connectivity
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continuously strengthened with the number of flotilla rows. Accordingly, lashing failure and
flotilla breakup occurred less often in larger flotillas. For example, EMR values associated with
3x1 flotillas (Figure 5-27) were generally lower than 3x3 flotillas (Figure 5-28) due to more
consistent lashing failure (Figures 5-29 and 5-30). Although, in a very small number of impact
scenarios, relative motion associated with inter-barge crushing in 3x3 flotillas resulting in lower
EMR values.
While flotillas with several rows were less likely to experience lashing failure than one or
two-row flotillas, they possessed more mass. Since flotilla mass, like impact velocity, is directly
related to impact energy, the number of rows in a flotilla also influenced the degree of crushing
in the impacting barge bow. This resulted in an effect similar to what was discussed in
Section 5.3.2.3 whereby large flotillas could achieve lower EMR values than flotillas with fewer
rows—an outcome related to sustained impact force levels and the amount of inter-barge crushing. Such occurrences were not frequently observed in this study; as a result, effective flotilla mass generally decreased with the addition of barge rows.
The number of barge columns was also seen to have an influence on effective flotilla mass due to differences in inter-column lashing demands. In this study, lashing failure occurred
more frequently in two-column impact simulations (Figure 5-31) than in comparable three- column simulations (Figure 5-32). This outcome is related to the fact that the three-column flotillas utilized in this investigation had twice the number of inter-column lashings as comparable two-column flotillas, resulting in an increased ability to share load.
Overall, the relevance of this effect on EMR values was related to the number of flotilla rows. In one-row flotillas, where breakup was observed in most impact simulations, two-column flotillas were associated with higher effective mass levels than three-column flotillas. This is due
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to the fact that, excluding relative motion associated with barge crushing, complete column
separation in a three-column flotilla was associated with an EMR of 0.33. In contrast, column separation in a two-column flotilla was associated with an EMR of 0.50. However, as discussed previously, flotillas with more rows required more lashings and were less likely to experience breakup. This was particularly true for three-column flotillas, which exhibited lashing failure infrequently in flotilla configurations with several rows. As a result, for most configurations,
EMR values associated with two-column flotillas (example shown in Figure 5-33) were normally lower than those associated with three-column flotillas (example shown in Figure 5-34).
5.4 Effective Mass Ratios for Bridge Design
Using EMR values determined from all 3,000 simulations conducted in this investigation
(Figure 5-35), a design equation (Equation 5-2) was formulated that may be utilized by bridge engineers to account for inter-barge relative motion in multi-column flotillas:
EMR=MIN a ⋅ P22 +⋅ a V +⋅ a( P ⋅ V) +⋅ a P +⋅+ a V a , 1.0 ( 1IF 2 3IF 4IF 56) (5-2)
where, EMR is the effective mass ratio, V is the impact velocity (ft/sec), a1 - a6 are the fitting
constants (Table 5-5), and PIF is the pier influence factor, defined as follows:
P= WK ⋅ 0.15 IF P P (5-3) where, WP is the pier width (ft) and K p is the pier stiffness at the point of impact (kip/in.).
Equation 5-2 was formulated as an envelope fit suitable for design applications. As a
consequence, estimates produced from Equation 5-2 were conservative for all 3,000 cases considered in this investigation.
In some cases, the envelope fit may yield a value of EMR greater than one; in such cases, as shown in Equation 5-2, an EMR value of one should be used instead. Since flotillas of different sizes were found to respond differently during impact, due to the differences in lashing
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failure and inter-barge crushing behavior discussed previously, separate fits were performed for
each flotilla configuration.
For impact scenarios involving flotillas with more than three rows striking round piers,
EMR values determined through simulation were found to be very close to one. As a
consequence, for design applications, the total flotilla mass should be used.
To account for variations in barge mass, an equivalent impact velocity may be calculated
using Equation 5-4:
m VV= ⋅ bearg eq 10.36 (5-4)
where, Veq is the equivalent impact velocity (ft/s) employed in Equation 5-2; V is the actual
impact velocity of the flotilla; and mbearg is the mass of each barge in the flotilla, including
hydrodynamic added mass ( kip⋅ sec2 / in.). Equation 5-4 was derived through an equivalent-
energy principle using the fully-loaded, single barge mass employed in this investigation (10.36
kip⋅ sec2 / in.).
Equation 5-2 will produce conservative estimates of EMR for barge types which are
narrower and/or shorter than the 35 ft x 195 ft jumbo hopper barge considered in this study.
While previous research (Consolazio et al. 2009) has shown that the force-deformation behavior
of barges is approximately uniform on a unit width-of-barge basis, wider and longer barges will
result in larger inter-barge contact areas, yielding more overall inter-barge crushing resistance.
The combined influence of these higher force levels will result in less inter-barge relative motion
and higher values of EMR. To illustrate this point, an impact simulation was conducted using a
3x4 flotilla in which each individual barge was intended to represent an oversize tanker barge,
which has a width of 53 ft. (51% wider than a jumbo hopper barge) and a length of 290 ft (49%
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longer than a jumbo hopper barge). To approximate the influence of the larger contact areas,
while still using the barge models employed in this investigation, contact forces between barges
were scaled up from the levels employed in the jumbo hopper barge flotillas using ratios of barge
width (bow-to-bow crushing) and barge length (side-to-side crushing). Results from this
simulation were then compared with results from an analogous simulation that employed an
unmodified 3x4 jumbo hopper barge flotilla (Table 5-6).
Comparisons revealed that, due to more inter-barge resistance, the flotilla comprised of
representative oversize tanker barges had an EMR 11% larger than the jumbo hopper barge
flotilla. Since this difference could be greater under different impact conditions, Equation 5-2
should only be utilized with barges that are shorter in length and width than, or equivalent in size
to, the jumbo hopper barge employed in this study. For flotillas comprised of larger barges, an
EMR of one may be conservatively assumed. However, even with this restriction, Equation 5-2 is still applicable for seven of the eleven common barge types tabulated in AASHTO (2009).
EMR values calculated from Equation 5-2 are intended to be multiplied by the total
flotilla mass to produce an effective flotilla mass (Equation 5-5):
M= EMR ⋅ M ET (5-5)
where, M E is the effective flotilla mass and MT is the total flotilla mass. Estimates of M E may
be used in conjunction with current AASHTO kinetic energy calculations or with alternative
analysis methods which represent a flotilla by a single point mass.
To calculate M E when either V or Veq is larger than the maximum velocity considered in
this investigation (5 ft/s), Equation 5-6 may be used:
25 25 M= M ⋅ EMR ⋅ +−1 ET22 (5-6) VVeq eq
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Equation 5-6 accounts for the effects of inter-barge relative motion at the maximum impact velocity considered in this investigation (5 ft/s) and conservatively assumes that any additional kinetic energy associated with higher velocities will fully contribute to structural demands.
In approximately 80% of the cases considered in this investigation, EMR estimates determined from Equation 5-2 were less than 31% higher than similar values determined through simulation (Figure 5-36). However, when used with current AASHTO static load-calculation procedures, the additional mass results in no more than a 12% increase in design forces, provided that a design impact speed of at least 2 ft/sec is used. While larger differences are expected for
EMR estimates associated with lower impact speeds, such conditions do not typically control in waterway bridge design. Using time-history impact analysis methods (e.g., CVIA), the significance of structural demands is not linearly related to the mass of an impacting barge flotilla. Instead, dynamic structural demands are affected by the impact energy as well the structural characteristics of the bridge. As a consequence, a 31% increase in impact energy does not necessarily result in a 31% increase in design forces. To illustrate this point, results from two
CVIA simulations—conducted as a part of a previous investigation (Consolazio et al. 2010a)— have been provided in Table 5-7.
Notably, while impact energies associated with the two simulations differ by approximately 32%, the structural demands are less than 1% different. However, a wider impact surface or a more flexible pier could have resulted in a greater disparity between the structural demands associated with the two impact conditions.
5.5 Summary
In this chapter, a detailed investigation was performed regarding the factors which influence effective mass participation during single barge and multi-barge flotilla impact events involving waterway bridge piers. For single barges, the influence of payload relative sliding was
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investigated using DE modeling and simulation techniques. For multi-barge flotillas, both single- column inter-barge crushing behavior and multi-column lashing failure were explored using three-dimensional barge flotilla models and a comprehensive parametric study. Based on behavioral observations, recommendations were made regarding conservative design expressions that may be incorporated into presently employed design and analysis procedures, including the
AASHTO (2014) static load-calculation method.
Among the cases studied in this investigation, large flotilla impacts involving round piers almost uniformly resulted in EMR estimates close to one. In other cases, EMR estimates varied, but were shown to decrease with pier width and stiffness. These effects were captured through the design equation proposed in this study.
Energy dissipation through payload relative sliding was found to be capable of influencing the effective kinetic energy responsible for structural demands. However, because the level of energy dissipation was found to be highly variable and strongly connected to the impact conditions, the development of a design expression to account for this effect is not recommended.
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Table 5-1. Representative coal material properties. γ E φ θ 3 ν (lb/ft ) (ksi) (degrees) (degrees)
87 439 0.35 37 21
Table 5-2. Summary of results for single barge impact simulations with DE payload model. Maximum Percent of kinetic energy Payload Pier K V P impact force dissipated through payload model geometry (ft/sec) (kip/in.) (kip) relative motion (%) Rigid Flat, 9 ft 1,000 1 708 - Rigid Flat, 9ft 1,000 4 1,669 - Rigid Round, 6 ft 500 1 420 - Rigid Round, 6 ft 500 4 1,125 - DE Flat, 9 ft 1,000 1 680 8 DE Flat, 9 ft 1,000 4 1,662 33 DE Round, 6ft 500 1 415 3 DE Round, 6 ft 500 4 1,117 4
Table 5-3. Summary of results from single-column impact simulations. Maximum Flotilla configuration impact force EA (kip-ft) EMR (kip) Single-raked barges 1,690 1,692 0.34 Double-raked barges 1,730 4,958 1.00 Single raked and box- 1,730 4,006 0.81 ended barges
Table 5-4. Simulation parameters. Flotilla Flotilla Pier width (ft) Pier shape K (kip/in.) V (ft/sec) rows columns P 200,500,1000 1,2,3,4,5 2,3 6,9,12,18,26,35 round, flat 1,2,3,4,5 ,5000,10000
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Table 5-5. Fitting parameters for the estimation of EMR values. Flotilla Pier a a a a a a class shape 1 2 3 4 5 6 2x1 round 1.500× 10−6 0.013 1.600× 10−4 -5.000× 10-4 -0.115 0.887 2x2 round 5.700× 10−6 -0.003 3.900× 10−4 3.000× 10−4 0.045 0.940 2x3 round EMR = 1.0 2x4 round EMR = 1.0 2x5 round EMR = 1.0 3x1 round 2.400× 10−6 0.014 2.100× 10−4 9.000× 10−4 -0.137 0.860 3x2 round 4.000× 10−7 -0.004 1.600× 10−4 -7.000× 10-4 0.032 0.939 3x3 round EMR = 1.0 3x4 round EMR = 1.0 3x5 round EMR = 1.0 2x1 flat 2.900× 10−6 0.015 9.000× 10−5 -3.000× 10-4 -0.120 0.864 2x2 flat 2.230× 10−5 0.006 2.000× 10−5 3.800× 10−3 -0.030 1.056 2x3 flat -8.200× 10-6 0.002 -1.000× 10-5 -1.000× 10-3 0.028 1.040 2x4 flat -3.490× 10-5 0.005 5.100× 10−4 1.400× 10−3 -0.009 1.092 2x5 flat -4.280× 10-5 0.006 6.300× 10−4 2.300× 10−3 -0.021 1.110 3x1 flat 3.400× 10−6 0.020 1.800× 10−4 -7.000× 10-4 -0.162 0.828 3x2 flat 3.530× 10−5 -0.001 -5.000× 10-4 -5.800× 10-3 0.063 1.085 3x3 flat -3.630× 10-5 -0.003 4.100× 10−4 2.000× 10−3 0.043 1.007 3x4 flat -3.920× 10-5 0.005 1.020× 10−3 1.200× 10−3 -0.037 1.112 3x5 flat -3.750× 10-5 0.005 1.250× 10−3 6.000× 10−4 -0.045 1.149
Table 5-6. Comparison of results from bridge pier impact simulations involving jumbo hopper
barges and oversize tanker barges (V = 2 ft/sec, KP = 1,000 kip/in., WP = 26 ft). Maximum Flotilla type impact force EA (kip-ft) EMR (kip) Jumbo hopper barge flotilla (3x4) 4,250 2,360 0.79 Oversize tanker barge flotilla (3x4) 4,250 2,630 0.88
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Table 5-7. Impact analysis of Acosta Bridge (Jacksonville, FL) using CVIA (Data source: Consolazio et al. 2010a) Maximum Maximum shear Maximum pier Maximum pier Impact energy moment in force in column moment column shear (kip-ft) foundation pile foundation pile (kip-ft) force (kip) (kip-ft) (kip) 26,217 63,873 1145 2797 272 34,628 64,036 1148 2798 272
Bridge superstructure Barge Lashing
Tug Waterline pile cap
Pier column
Direction of motion
A
Barge Lashing Bridge superstructure
Tug FS FS Waterline pile cap
FS FS Pier column
Direction of motion B Figure 5-1. Inter-column differential motion (center column impact event shown for an aberrant 3x3 flotilla outside of navigation channel). A) Prior to impact. B) During impact.
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Bridge superstructure Barge Lashing Tug Waterline pile cap
Direction of motion Pier column
A
Barge Lashing Bridge superstructure
Tug
FS FS Waterline pile cap
Direction of motion Pier column
B Figure 5-2. Inter-column differential motion (outer column impact event shown for an aberrant 2x2 flotilla outside of navigation channel). A) Prior to impact. B) During impact.
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Figure 5-3. Barge lashings and bitts (Source: Consolazio and Walters 2012) (Photo courtesy of USACE).
Intact lashing Bridge superstructure Failed lashing Waterline pile cap
Impacting barge column Pier column
Non-impacting barge Direction of motion column (broken away)
Figure 5-4. Flotilla breakup scenario utilized in AASHTO (2014) bridge design specifications (aberrant flotilla outside of navigation channel shown).
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A
B Figure 5-5. Barge models. A) Rigid barge model. B) Deformable, high-resolution barge model.
Figure 5-6. Internal structure of deformable barge bow (Source: Kantrales and Consolazio 2016).
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8000
6000
4000 Force (kip) 2000
0 0 20 40 60 80 100 120 140 Deformation (in.)
bow-to-bow stern-to-stern bow-to-stern side-to-side
Figure 5-7. Inter-barge force-deformation relationships (Data source: Consolazio et al. 2012a).
A B
C D
Figure 5-8. Contact interfaces used in inter-barge crushing anlayses. A) Bow-to-bow. B) Bow- to-stern. C) Stern-to-stern. D) Side-to-side (half portions of barges shown).
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Figure 5-9. Impact surface representation.
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6000
4500
3000 Force (kip) 1500
0 0 40 80 120 160 200 Deformation (in.)
6-ft pier 12-ft pier 26-ft pier 9-ft pier 18-ft pier 35-ft pier A 6000
4500
3000 Force (kip) 1500
0 0 40 80 120 160 200 Deformation (in.)
6-ft pier 12-ft pier 26-ft pier 9-ft pier 18-ft pier 35-ft pier B Figure 5-10. Barge bow force-deformation relationships associated with crushing against rigid piers. A) Flat-faced piers. B) Round piers.
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Barge
A A Port lashings shown
B C C D
Starboard lashings mirrored about centerline Bitt A Lashing
B C D
Figure 5-11. Inter-barge lashing configurations (Source: Consolazio et al. 2012a).
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A
B Figure 5-12. Calibration simulations. A) Coal-coal frictional property calibration. B) Coal-steel frictional property calibration.
A
B Figure 5-13. Payload pouring process. A) During hopper pour. B) Settled payload.
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Figure 5-14. Single barge impact with coal payload against a 9-ft bridge pier ( KP = 1,000 kip/in.) at 4 ft/sec.
3000 Single barge with DE payload 2500 Single barge with rigid payload
2000
1500
1000 Impact Force (kip) Force Impact 500
0 0 0.1 0.2 0.3 0.4 0.5 Time (sec) A 1200 Single barge with DE payload Single barge with rigid payload 900
600
300 Energy Absorbed through through Absorbed Energy Barge Bow Crushing (kip-ft) Bow Crushing Barge 0 0 0.1 0.2 0.3 0.4 0.5 Time (sec) B Figure 5-15. Results from single barge impact simulations with coal payload against a 9-ft pier (Kp = 1,000 kip/in.) at 4 ft/sec. A) Force time-history data. B) Energy time-history data.
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A
B Figure 5-16. Payload position in barge hopper region. A) Prior to impact. B) After impact.
Double-raked barge
A Single-raked barge
B Barge with boxed ends Single-raked barge
C Figure 5-17. Single-column (1x5) flotilla configurations. A) Flotilla with double-raked barges. B) Flotilla with single-raked barges. C) Flotilla with single-raked and box-ended barges.
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5000 9-ft pier 4000 26-ft pier
3000
2000
Impact Force (kip) Force Impact 1000
0 0 0.5 1 1.5 2 2.5 Time (sec) A 1000 9-ft pier 800 26-ft pier
600
400 Total Inter-Barge Inter-Barge Total 200 Contact Energy (kip-ft) Energy Contact
0 0 0.5 1 1.5 2 2.5 Time (sec) B Figure 5-18. Single-column (1x5), double-raked barge flotilla impact simulation results
(V = 4 ft/sec, KP = 1,000 kip/in.). A) Force time-histories. B) Energy time-histories.
Figure 5-19. Double-raked barge flotilla (3x3 flotilla shown).
177
2x1
3x1
2x2
3x2
2x3
3x3
2x4
3x4
2x5
3x5
Figure 5-20. Flotilla sizes considered.
178
Non-impacting Intact barge column lashing
Impacting barge bow deformation Impacted pier
Impacting barge Direction of motion column A Non-impacting barge column Intact (broken away) lashing Failed lashing Impacting barge bow deformation Impacted pier
Inter-barge Impacting barge deformation column Direction of motion B Figure 5-21. Influence of pier width on barge flotilla crushing and breakup behavior. A) Narrow pier. B) Wide pier.
1
0.8
0.6
EMR 0.4
0.2
0 0 5 10 15 20 25 30 35 40 Pier Width (ft) Figure 5-22. Variation in EMR with pier width (case shown for a 3x3 flotilla impacting a flat pier with a stiffness of 1,000 kip/in. at 2 ft/sec).
179
Location of impact Pier column
Pile cap
Foundation pile
Undeformed position Deformed position Figure 5-23. Relative motion of bridge pier during a barge-to-bridge impact (impact against pier column shown).
1
0.8
0.6
EMR 0.4
0.2
0 0 2000 4000 6000 8000 10000 Pier Stiffness (kip/in.) Figure 5-24. Variation in EMR with pier stiffness levels (case shown for a 3x3 flotilla impacting a 26-ft flat pier at 2 ft/sec).
180
1
0.8
0.6
EMR 0.4
0.2
0 0 2000 4000 6000 8000 10000 Pier Stiffness (kip/in.) Figure 5-25. Variation in EMR with pier stiffness levels (case shown for a 3x3 flotilla impacting a 6-ft round pier at 2 ft/sec).
5000 V = 2 ft/sec EMR = 0.566 4000 B V = 1 ft/sec EMR = 0.697
) A p 3000 i
k V = 3 ft/sec (
e EMR = 0.826 c r C o
F 2000
1000
0 0 20 40 60 80 100 120 140 160 180 200 Deformation (in.) Figure 5-26. Maximum deformation levels and EMR values associated with impact velocities of 1 ft/sec, 2 ft/sec, and 3 ft/sec (impact event involving a 3x3 flotilla and a flat, 26-ft pier with a stiffness of 1000 kip/in.)
181
100 Mean = 0.481 80 CV(%) = 17.3
60
40 Frequency (%) Frequency 20
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 EMR Figure 5-27. EMR values for 3x1 flotilla impact simulations.
100 Mean = 0.921 80 CV(%) = 16.8
60
40 Frequency (%) Frequency 20
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 EMR Figure 5-28. EMR values for 3x3 flotilla impact simulations.
100 Mean = 65.5 80 CV(%) = 59.7
60
40 Frequency (%) Frequency 20
0 0 10 20 30 40 50 60 70 80 90 100 Inter-Column Lashings Failed (%) Figure 5-29. Degree and frequency of lashing failure in 3x1 flotilla impact simulations.
182
100 Mean = 6.02 80 CV(%) = 369
60
40 Frequency (%) Frequency 20
0 0 10 20 30 40 50 60 70 80 90 100 Inter-Colum Lashings Failed (%) Figure 5-30. Degree and frequency of lashing failure in 3x3 flotilla impact simulations.
100 Mean = 31.1 80 CV(%) = 127
60
40 Frequency (%) Frequency 20
0 0 10 20 30 40 50 60 70 80 90 100 Inter-Column Lashings Failed (%) Figure 5-31. Degree and frequency of lashing failure in two-column flotilla impact simulations (results shown for flat-faced pier impacts).
100 Mean = 23.9 80 CV = 1.66
60
40 Frequency (%) Frequency 20
0 0 20 40 60 80 100 Inter-Column Lashings Failed (%) Figure 5-32. Degree and frequency of lashing failure in three-column flotilla impact simulations (results shown for flat-faced pier impacts).
183
100 Mean = 0.789 80 CV(%) = 18.0
60
40 Frequency (%) Frequency 20
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 EMR Figure 5-33. EMR values for 2x2 flotilla impact simulations.
100 Mean = 0.846 80 CV(%) = 22.8
60
40 Frequency (%) Frequency 20
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 EMR Figure 5-34. EMR values for 3x2 flotilla impact simulations.
60 Mean = 0.827 50 CV(%) = 25.3
40
30
20 Frequency (%) Frequency
10
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 EMR Figure 5-35. EMR values for all 3,000 flotilla impact simulations.
184
100 Mean = 23.2 CV(%) = 175 80
60
40 Frequency (%) Frequency
20
0 0 50 100 150 200 250 300 350 400 450 500 Level of Conservatism (%) Figure 5-36. Level of conservatism associated with EMR predictions.
185
CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS
6.1 Concluding Remarks
The consideration of structural demands associated with vessel impact events is a critical component of the bridge design process. Thus, it is important to ensure that the design tools used to predict the occurrence of barge-to-bridge impact events, and to analyze the effects of such events, are appropriately calibrated and representative of barge flotilla behavior.
While current design standards (AASHTO 2014, CEN 2006) contain methodologies to
compute the frequency of barge-to-bridge impacts, a survey of literature has indicated that there remains a need for a widely-applicable and simply-structured methodology which distinguishes between a barge-to-bridge collision and other types of vessel casualties (strandings, groundings, etc.). In addition, it was found that existing domestic design methods (AASHTO 2014) for predicting the frequency of barge-to-bridge impacts were empirically derived using a limited number of data sets that may not reflect changes in navigational technology, vessel mechanical systems, and operator/pilot training that have occurred since the release of the original AASHTO vessel impact guide specification in 1991 . To ameliorate this issue, the present investigation produced a recalibrated expression for the estimation of barge aberrancy rates that may be integrated with existing AASHTO methodologies. The revised expression was developed from relatively recent (2002-2014) vessel casualty data sets, specific to barge-to-bridge impact events,
which are more representative of the current state of the barge towing industry.
A survey of literature also revealed that only a limited number of investigations have
been conducted to characterize the effective mass of barge flotillas during barge-to-bridge impact
Material in this chapter was reproduced and adapted from the author’s contributions to Consolazio and Kantrales (2016)
186
events. To address this lack of information, the present investigation utilized computationally-
efficient analysis techniques to explore the influence of barge flotilla relative motion on the
effective flotilla mass responsible for producing structural demands.
Using a three-dimensional barge finite element model coupled with a discrete element
coal payload model, it was shown through simulation that payload relative motion during impact
can dissipate energy, reducing the effective kinetic energy of the impacting barge. For the impact
conditions considered in this investigation, payload relative sliding resulted in a 3-33% reduction
in the effective kinetic energy of a single barge with a coal payload. The magnitude of the
reduction in kinetic energy was found to be strongly related to both structural characteristics
(pier width and stiffness) as well as impact speed. Due to this variability, and since payload types
can also vary, inclusion of payload relative motion into existing design procedures is not
recommended.
In addition to studying the influence of payload sliding, impact energy dissipation and
reduction due to inter-barge crushing, lashing failure and column separation were considered in
multi-barge flotillas through an analytical parametric study. In this study, the influence of both
structure-dependent (e.g., pier width and shape) and flotilla-dependent (e.g., flotilla configuration) parameters on inter-barge relative motion were considered to facilitate the development of design recommendations for appropriate effective flotilla mass levels. Ratios of
effective kinetic energy to total (initial) kinetic energy (EMR) were computed to quantify the
effective mass participation of flotillas. Notably, it was found that for a majority of the 3,000 simulations conducted, the effective flotilla mass was nearly equal to the total mass of the flotilla
(i.e., EMR ≈1.0 ).
187
6.2 Design Recommendations
−5 • It is recommended that a base aberrancy rate (BR) for barges of 5.4× 10 be used in risk assessments of waterway bridge structures in the state of Florida, in lieu of the present AASHTO-specified value of 1.2× 10−4 .
• It is recommended that the equation proposed in Chapter 5 of this study to predict EMR values for barge flotillas be utilized in conjunction with existing procedures for vessel impact-resistant design.
6.3 Recommendations for Future Research
• It is recommended that additional bridges located outside of Florida, preferably on waterways with high levels of barge traffic, be incorporated into a follow-up, expanded effort to recalibrate BR.
• To supplement the findings and design equations related to barge flotilla relative motion presented in this dissertation, it is recommended that a follow-up study be conducted which considers the same effects using a complementary set of barge flotillas. This additional investigation should consider alternative flotilla configurations (e.g., four and five-column flotillas) as well as different barge types (e.g., tanker barges) and oblique impact conditions.
188
APPENDIX A SUMMARY OF BARGE ACCIDENT DATA COLLECTED
This appendix contains a listing of all barge-to-bridge impact events for which USCG
accident reports were requested (Table A-1). For each event, USCG activity IDs are provided, along with the date and location of the barge impact.
Table A-1. Barge accident data summary. Approximate date of USCG MISLE activity ID event (obtained from Name of impacted Florida bridge district MISLE records) 2946400 5/29/2007 7 Mantanzas Pass Bridge 1775418 2/9/2003 7 Sanibel Causeway Bridge 2039362 4/9/2004 7 Sanibel Causeway Bridge 2153420 7/30/2004 7 Sanibel Causeway Bridge 2241315 11/13/2004 7 Sanibel Causeway Bridge 2307385 3/8/2005 7 Sanibel Causeway Bridge 2533243 10/1/2005 7 Sanibel Causeway Bridge 2539078 10/26/2005 7 Sanibel Causeway Bridge 2578208 8/19/2005 7 Sanibel Causeway Bridge 2598508 3/3/2006 7 Sanibel Causeway Bridge 2794928 8/1/2006 7 Sanibel Causeway Bridge 2546182 12/5/2005 7 Venetian Causeway 2030257 3/24/2004 7 Atlantic Blvd. Bridge 4766432 12/4/2013 7 Atlantic Blvd. Bridge 2225557 10/21/2004 7 Sisters Creek Bridge 2290720 2/10/2005 7 Sisters Creek Bridge 2989716 6/2/2007 7 CSX Railroad Bridge 2408766 6/29/2005 7 Longboat Pass Bridge 2911460 4/19/2007 7 Longboat Pass Bridge 3318470 9/5/2008 7 Longboat Pass Bridge 3659489 12/31/2009 7 Longboat Pass Bridge 2287878 7/6/2004 7 Dick Misener Bridge 2712795 7/13/2006 7 Dick Misener Bridge 2965566 6/17/2007 7 John’s Pass Bridge 3325240 9/14/2008 7 John’s Pass Bridge 3363132 11/14/2008 7 John’s Pass Bridge 3002430 7/21/2007 7 Memorial Causeway 14692 7/5/1996 8 Dupont Bridge 181578 7/2/1996 8 Dupont Bridge 1842150 5/9/2003 8 Dupont Bridge 1900158 9/7/2003 8 Dupont Bridge 3710171 4/4/2010 8 Dupont Bridge 2408780 6/26/2005 8 Brooks Bridge
189
Table A-1 (continued) Barge accident data summary. 2973391 6/22/2007 8 Brooks Bridge 104061 3/4/2000 8 Navarre Beach Bridge 2433189 7/3/2005 8 Navarre Beach Bridge 2547589 12/3/2005 8 Navarre Beach Bridge 10924 1/8/2000 8 Bob Sikes Bridge 29659 11/27/2001 8 Bob Sikes Bridge 115324 10/10/1999 8 Bob Sikes Bridge 2074374 5/16/2004 8 Bob Sikes Bridge 2294661 2/7/2005 8 Bob Sikes Bridge 2408097 5/5/2005 8 Bob Sikes Bridge 2604457 1/21/2006 8 Bob Sikes Bridge 3641673 11/28/2009 8 Bob Sikes Bridge 3710480 4/3/2010 8 Bob Sikes Bridge 26888 9/16/1998 8 Gulf Beach Bridge 2306623 2/23/2005 8 Gulf Beach Bridge 2591278 1/30/2006 8 Pensacola Bay Bridge 146084 10/26/2000 8 HW-90 Bridge over Escambia River 2026361 1/21/2004 8 HW-90 Bridge over Escambia River 3673300 1/27/2010 8 HW-90 Bridge over Escambia River
190
APPENDIX B SUMMARY OF BARGE TRAFFIC DATA COLLECTED
This appendix contains a listing of all waterways and mile marker locations for which USACE barge traffic data were obtained (Table B-1). For each location, the years for which data were obtained and the type of information sought is provided.
Table B-1. Barge traffic data summary. Mile Waterway name Years Type of data marker Gulf Intracoastal Waterway, 2002, 2004, 2006, Upstream and Pensacola Bay, FL to Mobile 172 2008, 2010, 2012, downstream barge Bay, AL 2013 traffic Gulf Intracoastal Waterway, 2002, 2004, 2006, Upstream and Panama City to Pensacola Bay, 189 2008, 2010, 2012, downstream barge FL 2013 traffic Gulf Intracoastal Waterway, 2002, 2004, 2006, Upstream and Panama City to Pensacola Bay, 284 2008, 2010, 2012, downstream barge FL 2013 traffic 2002, 2004, 2006, Upstream and Escambia and Conecuh Rivers, 5 2008, 2010, 2012, downstream barge FL and AL; Escambia Bay, FL 2013 traffic Gulf Intracoastal Waterway, 2002, 2004, 2006, Upstream and Apalachee Bay to Panama City, 295 2008, 2010, 2012, downstream barge FL 2013 traffic Atlantic Intracoastal Waterway 2002, 2004, 2006, Upstream and between Norfolk, VA, and the St. 738 2008, 2010, 2012, downstream barge Johns River, FL (Jacksonville 2013 traffic District) 2002, 2004, 2006, Upstream and Intracoastal Waterway, 745 2008, 2010, 2012, downstream barge Jacksonville to Miami, FL 2013 traffic 2002, 2004, 2006, Upstream and St. John’s River, FL 1 2008, 2010, 2012, downstream barge (Jacksonville to Lake Harney) 2013 traffic 2002, 2004, 2006, Upstream and Tampa Channel Access, FL 8 2008, 2010, 2012, downstream barge 2013 traffic
191
APPENDIX C VESSEL TRAFFIC CURVE FITS
This appendix contains curve fits that were applied to barge and tug traffic data. These
include fits used to replace outlying barge-to-tug ratios (Figures C-1, C-2, C-3, and C-4) and fits used to make predictions of barge flotilla traffic for years where data were not available (due scope-of-request constraints) from the USACE (Figures C-5, C-6, C-7, C-8, C-9, C-10, and C-
11). Note that the term “modified USACE data” used in this appendix refers to traffic data that
has been corrected using the outlier detection methodology described in Chapter 3
192
8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-1. Curve fits used to replace outlying barge-to-tug ratios for Highway-90 Bridge over Escambia River and Pensacola Bay Bridge. A) Inbound direction. B) Outbound direction.
193
8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-2. Curve fits used to replace outlying barge-to-tug ratios for Dupont Bridge. A) Inbound direction. B) Outbound direction.
194
8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-3. Curve fits used to replace outlying barge-to-tug ratios for Atlantic Blvd. Bridge. A) Inbound direction. B) Outbound direction.
195
8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 8 USACE data linear fit 7 quadradic fit exponential fit 6
5
4
3 Barge-to-Tug Ratio Barge-to-Tug
2
1
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-4. Curve fits used to replace outlying barge-to-tug ratios for Gandy Bridge. A) Inbound direction. B) Outbound direction.
196
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-5. Curve fits used to produce estimates of barge flotilla traffic for Acosta Bridge. A) Inbound direction. B) Outbound direction.
197
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-6. Curve fits used to produce estimates of barge flotilla traffic for Atlantic Blvd. Bridge. A) Inbound direction. B) Outbound direction.
198
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-7. Curve fits used to produce estimates of barge flotilla traffic for Bob Sikes Bridge, Brooks Bridge, and Navarre Beach Bridge. A) Inbound direction. B) Outbound direction.
199
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-8. Curve fits used to produce estimates of barge flotilla traffic for Dupont Bridge. A) Inbound direction. B) Outbound direction.
200
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-9 Curve fits used to produce estimates of barge flotilla traffic for Gandy Bridge. A) Inbound direction. B) Outbound direction.
201
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-10. Curve fits used to produce estimates of barge flotilla traffic for Highway-90 Bridge over Escambia River and Pensacola Bay Bridge. A) Inbound direction. B) Outbound direction.
202
2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year A 2000 modified USACE data linear fit quadradic fit exponential fit 1600
1200
800 Barge Flotilla Traffic Flotilla Barge
400
0 2000 2002 2004 2006 2008 2010 2012 2014 Year B Figure C-11. Curve fits used to produce estimates of barge flotilla traffic for Sister’s Creek Bridge. A) Inbound direction. B) Outbound direction.
203
APPENDIX D BARGE FLOTILLA DIMENSIONS
This appendix describes the four representative barge flotilla sizes that were used to evaluate PG and PF at individual bridge locations. Flotilla dimensions were selected to approximate large and small barge flotillas that could reasonably be expected to pass through a given bridge site. A single ‘design’ tug length was determined for each location through a weighted averaging of tug lengths using the number of observed passages as weighting factors.
Note that certain bridges shared waterways (e.g., Highway-90 Bridge over Escambia River and
Pensacola Bay Bridge); as a consequence, representative flotilla sizes were the same for these locations.
Table D-1. Flotilla sizes for Acosta Bridge. Length Width Class Description (ft) (ft) FG-A 647 35 Three jumbo hopper barge (one column) and a 62-ft tug FG-B 257 35 One jumbo hopper barge and a 62-ft tug FG-C 452 70 Four jumbo hopper barges (two columns, two rows) and a 62-ft tug FG-D 257 70 Two jumbo hopper barges (one row) and a 62-ft tug
Table D-2. Flotilla sizes for Atlantic Blvd. Bridge. Length Width Class Description (ft) (ft) FG-A 656 35 Three jumbo hopper barge (single column) and a 71-ft tug FG-B 191 30 One small hopper barge and a 71-ft tug FG-C 611 78 Ocean-going barge and a 71-ft tug FG-D 206 80 Two small tank barges (one row) and a 71-ft tug
Table D-3. Flotilla sizes for Bob Sikes Bridge, Brooks Bridge, and Navarre Beach Bridge. Length Width Class Description (ft) (ft) FG-A 660 35 Three jumbo hopper barge (one column) and a 75-ft tug FG-B 270 35 One jumbo hopper barge and a 75-ft tug FG-C 655 106 Four oversize tank barges (two columns, two rows) and a 75-ft tug FG-D 270 105 Three jumbo hopper barges (one row) and a 75-ft tug
204
Table D-4. Flotilla sizes for Gandy Bridge. Length Width Class Description (ft) (ft) FG-A 688 35 Three jumbo hopper barges (one column) and a 103-ft tug FG-B 223 30 One small hopper barge and a 103-ft tug FG-C 683 53 Two oversize tank barges (one column) and a 103-ft tug FG-D 393 53 One oversize tank barges (one row) and a 103-ft tug
Table D-5. Flotilla sizes for Highway-90 Bridge over Escambia River and Pensacola Bay Bridge. Length Width Class Description (ft) (ft) FG-A 653 35 Three jumbo hopper barge (one column) and a 68-ft tug FG-B 263 35 One jumbo hopper barge and a 68-ft tug FG-C 648 106 Four oversize tank barges (two columns, two rows) and a 68-ft tug FG-D 263 105 Three jumbo hopper barges (one row) and a 68-ft tug
Table D-6. Flotilla sizes for Sister’s Creek Bridge. Length Width Class Description (ft) (ft) FG-A 656 35 Three jumbo hopper barge (single column) and a 71-ft tug FG-B 191 30 One small hopper barge and a 71-ft tug FG-C 562 76 Ocean-going barge and a 71-ft tug FG-D 206 80 Two small tank barges (one row) and a 71-ft tug
205
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BIOGRAPHICAL SKETCH
The author is originally from the Pensacola, FL area and attended Gulf Breeze High
School. Following high school graduation, the author attended several universities, including the
University of Florida (B.S. in mathematics, 2007), the University of South Alabama (B.S. in civil engineering, 2010), and Auburn University (M.S. in civil engineering, 2012). After graduating from Auburn University, the author returned once again to his original alma mater, the
University of Florida, to pursue his Ph.D. in civil engineering under the guidance of Dr. Gary
Consolazio.
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