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Influence of Pier Nonlinearity, Impact Angle, and Column Shape on Pier Response to Barge Impact Loading

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PAGE 1

INFLUENCE OF PIER NONLINEARITY, IMPACT ANGLE, AND COLUMN SHAPE ON PIER RESPONSE TO BARGE IMPACT LOADING By BIBO ZHANG A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2004

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ii ACKNOWLEDGEMENTS I would like to thank my research advi sor, Dr. Gary Consolazio for providing continuous guidance, excellent research ideas, detailed teaching and a ll this with a lot of patience. I am thankful for being able to le arn so much during the past year and a half. I would also like to extend my gratitude to Florida Department of Transportation for providing funding for this project. I would like to express my heartfelt thanks to all the graduate students who worked on this project, especially Ben Lehr, David Cowan, Alex Biggs and Jessica Hendrix. Their research helped me e normously in completing my thesis. My family and friends have been very supportive throughout this effort. I wish to thank them for their understanding and support.

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iii TABLE OF CONTENTS page ACKNOWLEDGEMENTS................................................................................................ii LIST OF TABLES...............................................................................................................v LIST OF FIGURES...........................................................................................................vi ABSTRACT....................................................................................................................... ix CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Overview.................................................................................................................1 1.2 Background of AASHTO Guide Specification......................................................2 1.3 Objective.................................................................................................................4 2 AASHTO BARGE AND BRIDGE COLLISION SPECIFICATION.........................5 3 FINITE ELEMENT BARGE IMPACT SIMULATION.............................................9 3.1 Introduction.............................................................................................................9 3.2 Background Study................................................................................................10 3.3 Pier Model Description.........................................................................................14 3.4 Barge Finite Element Model.................................................................................19 3.5 Contact Surface Modeling....................................................................................26 4 NON-LINEAR PIER BEHAVIOR DURING BARGE IMPACT.............................31 4.1 Case Study............................................................................................................31 4.2 Analysis Results....................................................................................................32 5 SIMULATION OF OBLIQUE IMPACT CONDITIONS.........................................37 5.1 Effect of Strike Angle on Barge St atic Load-Deformation Relationship.............38 5.2 Effect of Strike Angle on Dynamic Loads and Pier Response.............................40 5.3 Dynamic Simulation Results................................................................................42

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iv 6 EFFECT OF CONTACT SURFACE GEOMETRY ON PIER BEHAVIOR DURING IMPACT.....................................................................................................52 6.1 Case Study............................................................................................................52 6.2 Results...................................................................................................................5 2 7 COMPARISON OF AASHTO PROVIS IONS AND SIMULATION RESULTS....63 8 CONCLUSIONS........................................................................................................67 LIST OF REFERENCES...................................................................................................69 BIOGRAPHICAL SKETCH.............................................................................................71

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v LIST OF TABLES Table page 3-1 Comparison of original and adjusted section properties..........................................16 3-2 Input data in LS-DYNA simulations........................................................................18 3-3 Comparison of plastic moment and disp lacement using properties of pier cap.......19 3-4 Comparison of plastic moment and di splacement using properties of pier column......................................................................................................................19 3-5 General modeling features of the testing barge........................................................25 4-1 Dynamic simulation cases........................................................................................32 5-1 Dynamic simulation cases........................................................................................41 7-1 Peak forces computed using fi nite element impact simulation................................66

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vi LIST OF FIGURES Figure page 1-1 Relation between impact force and barge damage depth according to MeirDornberg’s Research (after AASHTO [1])................................................................3 2-1 Collision energy to be absorbed in relation with collision angle and the coefficient of fricti on (after AASHTO [1])................................................................8 3-1 Global modeling of San-Diego Corona do Bay Bridge (after Dameron [10])..........11 3-2 Pier model used for local modeling (after Dameron [10]).......................................12 3-3 Global pier modeling for seismic retr ofit analysis (after Dameron [10]).................12 3-4 Mechanical model for discrete element (after Hoit [11]).........................................13 3-5 Bilinear expression of moment-cur vature and stress-strain curve...........................17 3-6 Moment-curvature derivation...................................................................................18 3-7 Main deck plan of the construction barge................................................................20 3-8 Outboard profile of the construction barge..............................................................20 3-9 Typical longitudinal truss of the construction barge................................................20 3-10 Typical transverse frame (cross braci ng section) of the construction barge............20 3-11 Dimension and detail of barge bow of the construction barge.................................21 3-12 Layout of barge divisions.........................................................................................22 3-13 Meshing of internal structure of zone-1...................................................................23 3-14 Buoyancy spring distribution along the barge..........................................................26 3-15 Pier and contact surface layout.................................................................................27 3-16 Rigid links between pier column and contact surface..............................................27 3-17 Exaggerated deformation of pier co lumn and contact surface during impact..........28

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vii 3-18 Comparison of impact force versus cr ush depth for rigid and concrete contact models......................................................................................................................29 3-19 Overview of barge and pier model for dynamic simulation.....................................30 4-1 Comparison of impact force history for severe impact case....................................34 4-2 Comparison of impact for ce history for non-severe case.........................................34 4-3 Impact force and crush depth relation ship comparison for severe impact case.......35 4-4 Comparison of impact force – crush depth relationship for non-severe case..........35 4-5 Comparison of pier displacem ent for severe impact case........................................36 4-6 Comparison of pier displacement for non-severe case.............................................36 5-1 Static crush between pi er and open hopper barge....................................................38 5-2 Results for static crush analysis conducting with a 4 ft. wide pier..........................39 5-3 Results for static crush analysis conducting with a 6 ft. wide pier..........................39 5-4 Results for static crush analysis conducting with a 8 ft. wide pier..........................40 5-5 Layout of barge head-on impact and oblique impact with pier................................41 5-6 Impact force in X direction for high speed impact on rectangular pier...................44 5-7 Impact force in X direction for high speed impact on circular pier.........................44 5-8 Impact force in X direction for lo w speed impact on rectangular pier.....................45 5-9 Impact force in X direction for low speed impact on circular pier..........................45 5-10 Impact force in Y direction for high-speed oblique impact.....................................46 5-11 Impact force in Y direction for low speed oblique impact.......................................46 5-12 Force-deformation results for hi gh speed impact on rectangular pier......................47 5-13 Force deformation results for hi gh speed impact on circular pier............................47 5-14 Force-deformation results for lo w speed impact on rectangular pier.......................48 5-15 Force-deformation results for lo w speed impact on circular pier............................48 5-16 Pier displacement in X direction for high speed impact on rectangular pier...........49 5-17 Pier displacement in X direction for low speed impact on rectangular pier............49

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viii 5-18 Pier displacement in X direction for high speed impact on circular pier.................50 5-19 Pier displacement in X direction for low speed impact on circular pier..................50 5-20 Pier displacement in Y direc tion for high-speed oblique impact.............................51 5-21 Pier displacement in Y direc tion for low speed oblique impact..............................51 6-1 Impact force in X direction for high speed head-on impact.....................................54 6-2 Impact force in X direction for high speed oblique impact......................................55 6-3 Impact force in X direction for low speed head-on impact......................................55 6-4 Impact force in X direction for low speed oblique impact.......................................56 6-5 Impact force in Y direction for high speed oblique impact......................................56 6-6 Impact force in Y direction for low speed oblique impact.......................................57 6-7 Pier displacement in X direc tion for high speed head-on impact............................57 6-8 Pier displacement in X direc tion for high speed oblique impact.............................58 6-9 Pier displacement in X direc tion for low speed head-on impact..............................58 6-10 Pier displacement in X direc tion for low speed oblique impact..............................59 6-11 Pier displacement in Y direc tion for high speed oblique impact.............................59 6-12 Pier displacement in Y direc tion for low speed oblique impact..............................60 6-13 Vector-resultant force-deformation results for high speed head-on impact.............60 6-14 Vector-resultant force-deformation results for high speed oblique impact..............61 6-15 Vector-resultant force-deformation results for low speed head-on impact..............61 6-16 Vector-resultant force-deformation results for low speed oblique impact...............62 7-1 AASHTO and finite element loads in X direction...................................................64 7-2 AASHTO and finite element loads in Y direction...................................................65

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ix Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering INFLUENCE OF PIER NONLINEARITY, IMPACT ANGLE, AND COLUMN SHAPE ON PIER RESPONSE TO BARGE IMPACT LOADING By Bibo Zhang December 2004 Chair: Gary R. Consolazio Major Department: Civil and Coastal Engineering Current bridge design specifi cations for barge impact loading utilize information such as barge weight, size, and speed, cha nnel geometry, and bridge pier layout to prescribe equivalent static loads for use in designing substructure components such as piers. However, parameters such as pier sti ffness and pier column geometry are not taken into consideration. Additionally, due to the lim ited experimental vesse l impact data that are available and due to the dynamic nature of incidents such as vessel collisions, the range of applicability of cu rrent design specifications is unclear. In this thesis, high resolution nonlinear dynamic finite element impact simulations are used to quantify impact loads and pier displacements generated during barge collisions. By conducting parametric studies involving pi er nonlinearity, impact angle, and impact zone geometry (pier-column cross-sectional geometry), and then subsequently comparing the results to those computed using current design provision s, the accuracy and range of applicability of the design provisions are evaluated. The comparison of AASHTO provisions and

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x simulation results shows that for high energy im pacts, peak predicted barge impact forces are approximately 60% of the equivalent st atic AASHTO loads. For low energy impacts, peak dynamic impact forces predicted by simulation can be more than twice the magnitude of the equivalent static AASHT O loads. However, because the simulationpredicted loads are transient in nature wher eas the AASHTO loads are static, additional research is needed in order to more accurately compare results from the two methods.

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1 CHAPTER 1 INTRODUCTION 1.1 Overview Barge transportation in inland waterway ch annels and sea coasts has the potential to cause damage to bridges due to accide ntal impact between barges and bridge substructures [1-4]. Recently, two impact events caused damage serious enough to collapse bridges and unfortunate ly result in the loss of lives as well. To address the potential for such situations, loads due to ve ssel impacts must be taken into consideration in substructure (pier) design using the Am erican Association of State Highway and Transportation Officials (AAS HTO) Highway Bridge Design Specifications [5] or the AASHTO Guide Specification for Vessel Collis ion Design for Highway Bridges [1]. In design practice, the magnitude and point of appl ication of the impact load are specified in the AASHTO provisions [1]. The focus of th is thesis is on the evaluation of whether the loads specified in the AASHTO provisions [1] are appropriate gi ven the variety of barge types, pier geometries and im pact angles that are possible. This goal may be approached in several ways: analytical methods, experimental methods, or both. This thesis focuses on the an alytical approach: nonl inear finite element modeling to dynamically simulate barge collisions with bridge piers. Of interest is to estimate the range of the impact load due to different impact conditions and other considerations that might affect the peak va lue of impact load and the impact duration time. The dynamic analysis code LS-DYNA [6] was employed for all impact simulations presented in this thesis.

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2 1.2 Background of AASHTO Guide Specification The AASHTO Guide Specification For Vessel Collision Design [1] covers the following topics: Part 1: General provision (ship and barge impact force and crush depth) Part 2: Design vessel selection Part 3: Bridge protection system design Part 4: Bridge protection planning Part 1 is directly related to the goal of this thesis: checking the sufficiency of the design barge impact forces sp ecified by AASHTO. Therefore, only Part 1 is discussed in this section. The method to determine impact force due to barge collision of bridges in AASHTO is based on research conducted by Meir-Dornberg in West Germany in 1983 [1]. Very little research has been presented in the literature with re spect to barge impact forces. The experimental and theoretical studies performed by Meir-Dornberg were used to study the collision force and the deformati on when barges collide with lock entrance structures and with bridge pi ers. Meir-Dornberg’s investigat ion also studied the direction and height of climb of the barge upon bank slopes and walls due to skewed impacts and groundings along the sides of the waterway. Meir-Dornberg’s study included dynamic loading with a pendulum hammer on three barge partial section models in scal e 1:4.5; static loadi ng on one barge partial section model in scale 1:6; and numerical computations. The results show that no significant difference was found between the sta tic and dynamic forces measured and that impact force and barge bow damage depth can be expressed in a bilinear curve as shown

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3 in Figure 1-1. The study further proposed that barge bow damage depth can be expressed as a function of barge mass and initial speed. 0 0 2 4 6810 12 500 1000 1500 2000 2500 3000PB (kips)aB (feet) Figure 1-1. Relation between impact force a nd barge damage depth according to MeirDornberg’s Research (after AASHTO [1]) AASHTO adopted the results of Meir-Dornbe rg’s study with a modification factor to account for effect of varying barge wi dths. In Meir-Dornberg’s research, only European barges with a bow width of 37.4 ft were considered, which compares relatively closely with the jumbo hopper barge bow widt h of 35.0 ft. The jumbo hopper barge is the most frequent barge size utilizing the U.S. inland waterway system. The width modification factor adopted by AASHTO is in tended to permit application of the design provisions to barges with di fferent bow widths. Impact load is then defined as an equivalent static force that is computed ba sed on impact energy and barge characteristics. A detailed description of the calculation of the equivalent static force according to AASHTO is included in Chapter 2 of this thesis.

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4 1.3 Objective The finite element based analysis method descri bed in this thesis is part of a project funded by FDOT [2] to study the uncertainties in the basis of the barge impact provisions of the AASHTO. The project c onsists of a combination of analytical modeling and fullscale impact testing of the St. George Island Causeway Bridge. The results from this thesis provide analytically based estimations of impact forces and barge damage levels, and may be used for comparison to resu lts from the full-scale impact tests. The structure of the remainder of this thesis is as follows: Chapter 2 explains the AASHTO design method for computing impact force and bow damage depth. Chapter 3 describes nonlinear finite element modeling of the impact test barge and piers of the St. George Island Causeway Bridge. Chapte r 4 investigates the effect of non-linearity of pi er material on impact force and barge damage depth by comparing pier behavior predicted by linea r and nonlinear material models. Chapter 5 examines the effect of impact surface ge ometry on impact force and dynamic pier behavior. Two types of geometry are consid ered: rectangular and circular pier cross sections. Chapter 6 examines the effect of impact angle on impact force and pier behavior. Head-on impacts and 45 degree ob lique impacts are investigated for both rectangular and circular piers. Comparisons between finite element impact simulations results and the AASHTO provisions are pres ented in Chapter 7. Finally, Chapter 8 summarizes results from the precedin g chapters and offers conclusions.

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5 CHAPTER 2 AASHTO BARGE AND BRIDGE COLLISION SPECIFICATION As stated in the previous chapter, the AASHTO provisions concerning barge and bridge collision are based on the Meir-Dornberg study [1]. The barge collision impact force associated with a head-on collision is determined by the following procedure given by AASHTO: For 34 0 Baft., B B BR a P 4112 (kips) (2.1) For 34 0 Baft., B B BR a P ) 110 1349 ( (kips) (2.2) For above equations, Ba and BR are expressed as B BR KE a 2 10 1 5672 12 / 1 (2.3)35 /B BB R (2.4) 2 292V W C KEH (2.5) in whichBPis impact force (kip);Ba is barge bow damage depth (ft);BR is barge width modification factor;BB is barge width (ft);K E is kinetic energy of a moving barge (kipft.);W is barge dead wei ght tonnage (tonnes);V is barge impact speed (ft/sec);HC represents the hydrodynami c mass coefficient.

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6 The hydrodynamic mass coefficient HC accounts for the mass of water surrounding and moving with the barge so that the inertia force from this mass of water needs to be added to the total mass of barge. HC varies depending on many factors such as water depth, under-keel clear ance, distance to obstacles, shape of the barge, barge speed, currents, position of the barge, directi on of barge travel, stiffness of bridge and fender system, and the cleanliness of the ba rge’s hull underwater. Fo r a barge moving in a straight-line motion, the following values of HC may be used, unless determined otherwise by accepted analysis procedures: 05 1 HC for large under-keel clearances ( draft 5 0 ) 25 1 HC for small under-keel clearances ( draft 5 0 ) The expression of vessel kinetic energy co mes from general expression of kinetic energy of a moving object: g WV mV KE 2 22 2 (2.6) where m is the mass of the barge; g is the acceleration of gravity;W is the barge dead weight tonnage;V is the barge impact speed. Expressing K E in kip-ft., W in tonnes (1 tonne = 1.102 ton = 2.205 kips), V in ft/sec, g = 32.2 ft/sec2, and including the hydrodynamic mass coefficient, HC, Equation 2.6 results in the AASHTO equation: 2 29 2 32 2 205 22 2WV C WV C KEH H (2.7) The impact force calculation described a bove is for head-on impact conditions. The AASHTO provisions specify that for substruc ture design, the impact force shall be applied as a static force on the substructure in a direction parallel to the alignment of the

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7 centerline of the navigable channel. In additi on, a separate load c ondition must also be considered in which fifty percent of the lo ad computed as described above shall be applied to the substructure in a direction pe rpendicular to the navigation channel. These transverse and longitudinal impact forces shall not be taken to act simultaneously. Commentary given in th e AASHTO provisions also suggests the following equation to calculate impact energy due to an oblique imp act. Though this equation is not a requirement, it provides a useful means of computing the collision energy to be absorbed either by the barge or the bridge. KE E* (2.8) Values of are shown in Figure 2-1 as a function of the impact angle ( ) and coefficient of friction ( ) based on research by Woisin, Saul and Svensson [7]. This method is from a theoretical derivation of en ergy dissipation of ship kinetic motion, and assumes that the ship bow width is smalle r than the impact contact surface. Thus “sliding” between the ship bow and the pier c ontact surface is possible, the friction force can be derived based on coefficient of fricti on, and the change of impact energy can be derived. Though this method provides a very useful wa y to find the energy to be dissipated during an oblique impact of a ba rge with a pier, it is not app licable to the oblique impact simulations included in the thesis because the barge bow is much larger than pier width, and impact takes place at cente r zone of barge bow, so pier “cuts” into the bow during impact, thus “sliding” between the barge and th e pier is not likely to happen. However, for cases when impact doesn’t occur at cente r zone of barge bow, and barge bow corners

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8 slide along the pier surface, this method may provide an alternativ e means to calculate kinetic energy to be dissipated during the impact. Figure 2-1. Collision energy to be absorbed in relation with collision angle and the coefficient of fricti on (after AASHTO [1])

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9 CHAPTER 3 FINITE ELEMENT BARGE IMPACT SIMULATION 3.1 Introduction Nonlinearity in structural behavior can take two form s: material nonlinearity and geometric nonlinearity. When the stiffness of a structure changes w ith respect to load induced strain, material nonlin earity takes place. When di splacements in a structure become so large that equilibrium must be sa tisfied in the deformed configuration, then geometric nonlinearity has occurred [8]. For modeling of structural nonlinearity, both material nonlinearity and geometric nonlinearity may be taken into account. For the finite element code LS-DYNA [6], material nonlinearity can be accounted for by defining a pi ecewise linear stress-strain relationship or by defining the parameters of an elastic, perfectly plastic material model. Geometric nonlinearity is always include d in LS-DYNA when using beam elements, shell elements and brick elements for stru ctural modeling. Geom etric nonlinearity is included in the element formulation for beam element. For shell element and brick element, when mesh is refined enough, geomet ric nonlinearity is also included in element internal forces. Dynamic simulation of barge impacts w ith bridge piers involves generating two separate models: barge and pier/soil. The ba rge is made of steel plates, channel beams and angle beams. Non-linearity in these el ements can be approached by modeling the steel plate and channel beams using shell el ements and a corresponding nonlinear stressstrain model. However in nonlinear pier modelin g, the concrete pier cap and pier columns

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10 are heavily reinforced with steel bars. During im pact, it is possible for the steel bars to yield at certain locations and form plastic hinges in the reinforced concrete elements. Nonlinear material modeling may be used to study this type of inelastic response and investigate the locations at which plastic hinges form during impact. 3.2 Background Study Many researchers have published papers on nonlinear analysis of bridges, bridge substructures [9,10,11], and ot her types of reinforced conc rete structures. Researchers focusing on the behavior of high-strength reinfo rced concrete columns subjected to blast loading have used solid elements to model concrete and beam elements to model the reinforcement [9]. The Winfrith concrete material model available in LS-DYNA was adopted by Ngo et al. in mode ling the concrete. This approa ch enables the generation of information such as crack locat ions, directions, and width. Th e solid elements used were 20 mm in each dimension for both concrete a nd reinforcement. For unconfined concrete, the Hognestad [12] stress-strain curve was used; for confined concrete, modified Scott’s model [9] was employed in the modeling to incl ude confined concrete and to incorporate the effect of relatively high stra in rate [9]. The concrete column was subjected to a blast load that had a time duration of approximately 1.3 milliseconds. Researchers studying bridge behavior unde r seismic loading developed a global nonlinear model of the San Diego-Coronado Bay Bridge. Figure 3-1 shows the global nonlinear model, developed by the California Department of Transportation (Caltrans). The model was analyzed using the commerci ally available finite element code ADINA [13]. San Diego-Coronado Bay Bridge is 1.6 miles long and extends across San Diego Bay. The model included the entire 1.6-m ile long bridge (see Figure 3-1). Modeling included two steps: local modeling and global modeling. An example of local modeling is

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11 that the detailed finite-element analyses of three typical bridge piers were performed using experimentally-verified structural models and concrete material models to predict stiffness, damage patterns and ultimate capacity of the pier. The fin ite element model of an individual bridge pier is s hown in Figure 3-2. Data were th en used to idealize the pier column stiffness and plastic-hinge behavior in the global-model piers. Pier modeling in the global bridge model is shown in Figure 33. Nonlinearities ultimately included in the global model were “global large displacements (primarily to capture Peffects in the towers), contact between spans at the expa nsion joints and at the abutment wall, nonlinear-plastic behavior of isolation bearings, post-yield behavior of pier column plastic hinges, and nonlinear overturni ng rotation of the pile cap” [10]. Figure 3-1. Global modeling of San-Diego Coronado Bay Bri dge (after Dameron [10])

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12 Pier Cap Pier Column Pile Cap Figure 3-2. Pier model used for lo cal modeling (after Dameron [10]) Figure 3-3. Global pier mode ling for seismic retrofit analysis (after Dameron [10])

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13 Developers of the commercially available pier analysis software FB-Pier [11], use three-dimensional nonlinear discrete elements to model pier columns, pier cap, and piles. The discrete elements (see Figure 3-4) use rigid link sections connected by nonlinear springs [11]. The behavior of the springs is derived from the exact stress-strain behavior of the steel and concrete in the member cross-section. Geomet ric nonlinearity is accounted for by using Pmoments (moments of the axia l force times the displacement of one end of an element to the other ). Since the piles are subdivided into multiple elements, the Pmoments (moments of axial force times internal displacements within members due to bending) are also taken into account. Figure 3-4. Mechanical model for di screte element (after Hoit [11]) Figure 3-4 shows the mechanical model of th e discrete element. The model consists of four main parts. There ar e two segments in the center th at can both twist torsionally and extend axially with respect to each other. Each of these center segments is connected by a universal joint to a rigid end segment. The universal joints permit bending at the quarter points about two flexur al axes by stretching and co mpressing of the appropriate springs. The center blocks are aligned and cons trained such that springs aligned with the

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14 axis of the element provide torsional and axia l stiffness. Discrete angle changes at the joints correspond to bending moments and a di screte axial shortening corresponds to the axial thrust [11]. 3.3 Pier Model Description Consolazio et al. [2] discussed dynamic im pact simulations of jumbo open hoppers barge with piers of the St. George Island Caus eway Bridge. In their report, the pier is modeled with a combination of solid elements to model pier column, pier cap and pile cap, beam elements to model steel piles and discrete non-linear spring elements to model nonlinear soil behavior. The solid elements are used to accurately describe the distribution of mass in the pier. In the present study, similar approaches to modeling have been used for several components of the simulation models develope d. A linear elastic material with density, stiffness and Poison’s ratio corresponding to concrete is assigned to the solid elements. Material properties for the beam elements are described in th e following paragraph. Nonlinear spring properties (for both lateral springs and axia l springs) derived using the FB-Pier software [11] are a ssigned to the soil springs. In this thesis, beam elements are employe d to model pier columns and pier caps, while solid elements are used to model pile caps. Both pier columns and pier caps are heavily reinforced concrete elements cons isting of numerous st eel bars compositely embedded within a concrete matrix. When a pier column or pier cap yields during dynamic impact, plastic hinges may form in the pier column or pier cap that may affect impact force history and struct ural pier response. Using b eam elements to model pier columns and the pier caps permits the use of a nonlinear material model capable to representing plastic hinge formation.

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15 LS-DYNA includes a nonlinear material called *MAT_RESULTANT_PLASTICITY, which is an elastic, perfectly plastic model. Assigning this material model to beam elements requires specification of mass dens ity, Young’s modulus, Poison’s ratio, yield stress, cross sectional propertie s (including area, mome nt of inertia with respect to strong axis, moment of inertia with respect to weak axis, torsional moment of inertia and shear deformation area). Based on these propertie s, LS-DYNA assumes a rectangular cross section [6], and internally calculates the nor mal stress distribution on the cross section. Normal stress from axial deformation, bending of strong axis and bending of weak axis are combined and checked for the possibility of plastic flow. By checking for plastic flow at each time step, element stiffnesses may be updated accordingly. Work hardening is not available in this material model. For nonlinear modeling of pier, the steel pi les are also modeled by this material type. For HP 14x73 steel piles, a test mode l was set up. Comparison of independently calculated theoretical results and LS-DYNA results show that error percentages for strong axis plastic moment capacities are le ss than 18% and error percentages for weak axis bending are less than 8%. Analysis cases considered in the thesis include both headon impacts and oblique impacts. For head-on impact, weak axis bending dominates; for oblique impact, plastic bending moment about both axes will occur. Therefore, the pile cross section properties are ad justed to produce the same e rror percentage in both strong axis and weak axis bending. Adjusted pile properties are applied to both head-on impact and oblique impact to keep comparison condi tions the same when results from the two conditions are compared. To keep the pile bending stiffness unaltered, only the cross-

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16 sectional area is changed. Table 3-1 shows the original and adjusted cross-sectional properties. Table 3-1. Comparison of original and adjusted section properties Case Original Adjusted Trial Value of Area (m2) 1.38 x 10-2 1.25 x 10-2 Plastic Moment (Strong Axis Bending) (N*m) 5.860 x 105 4.183 x 105 Plastic Moment (Weak Axis Bending) (N*m) 3.112 x 105 2.502 x 105 Error Percentage (Area) 0 9.5 % Error Percentage (Plastic Moment) (Strong Axis) 18.1 % 12.9 % Error Percentage (Plastic Moment) (Weak Axis) 7.9 % 12.7 % An alternative to modeling the effect of reinforcement on bending moment capacity involves the use of moment curvature relationships. However LS-DYNA does not support direct specification of moment-curvature for beam elements. Results from tests making use of material models *MAT_CONCRETE_BEAM, *MAT_PIECEWISE_LINEAR_PLASTICITY, and *MAT_FORCE_LIMITED showed that these models do not represent reinforced beam bending moment capacity to a satisfying extent. Moment-curvature relationships may be sufficie ntly approximated using the *MAT_RESULTANT_PLASTICITY model. Usually, a moment-curvature relations hip is a curve described by a series of points. The shape of the curve is similar to a bilinear curve. A stress strain curve for an elastic, perfectly plastic material is also a bilinear curve. Figure 3-5 shows similarities

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17 between a simplified moment-curvature curve and a stress-strain curve for an elastic, perfectly plastic material. M Myy y y EI E a) moment-curvature b) stress-strain Figure 3-5. Bilinear expression of moment-curvature and stress-strain curve For an arbitrary cross section, gI Mc (3-1) c gI M E (3-2) Material parameters for elastic, perfectly plastic material are: young’s modulus and yield stress. Young’s modulus can be derived from the bilinear moment-curvature curve based on Equation 3-2, however yield stress is unknown due to the fact that LS-DYNA assumes rectangular cross sect ion and internally calculate the dimension (width and height) of the rectangular cross section base d on input cross secti on properties. Thus a yield stress is assumed first and input in to LS-DYNA. Based on output yield moment from LS-DYNA and Equation 3-1, c value (dim ension of rectangular cross section) is calculated. This correct c valu e (dimension of rectangular cr oss section) is plugged into

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18 Equation 3-1 using the known yield moment to get the corresponding yield stress. This yielding stress is used for da ta input for elastic, perfec tly plastic material type. To simplify the moment-curvature relationshi ps used, the following rule is used for both pier columns and pier caps. The yield moment (My) for the bilinear curve is equal to half the summation of yielding moment My o and ultimate moment Mu o from the original moment-curvature relationship. Initial st iffness for the simplified bilinear momentcurvature relationship stays the same as that of the original moment-curvature relationship (see Figure 3-6) Data used in the LS-DYNA simulations for the pier columns and pier cap are given in Table 3-2. M Myy u oy ocr o Bilinear Moment-Curvature Original Moment-Curvature Figure 3-6. Moment-curvature derivation Table 3-2. Input data in LS-DYNA simulations Pier E (N/ m2) y (N/ m2) Pier Column 2.486 x 1010 4.90 x 106 Pier Cap 2.486 x 1010 6.10 x 106 Moment-curvature relationships for the pier column and the pier cap are developed based on steel reinforcement layout and material properties. Tables 3-3 and 3-4 show the

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19 error percentage of a test model for both strong axis bendi ng and weak axis bending, for the pier cap and the pier column respectiv ely. The test model is a 480-meter simply supported beam with a concentr ated load at mid-span. Plastic moment and displacement at mid–span calculated by LS-DYNA are co mpared with those from theoretical calculations. Table 3-3. Comparison of plastic moment a nd displacement using properties of pier cap Pier Cap LS-DYNA Results Theoretical Value Error Percentage Plastic Moment (N*m) 10.0 x 106 12.0 x 106 17% Strong Axis Displacement at Mid-span at Yielding (m) 6.2 6.0 3% Plastic Moment (N*m) 6.3 x 106 5.3 x 106 18% Weak Axis Displacement at Mid-span at Yielding (m) 9.0 8.0 11% Table 3-4. Comparison of plastic moment and displacement using properties of pier column Pier Column LS-DYNA Results Theoretical Value Error Percentage Plastic Moment (N*m) 9.9 x 106 10.6 x 106 6% Strong Axis Displacement at Mid-span at Yielding (m) 5.2 5.0 4% Plastic Moment (N*m) 8.8 x 106 9.1 x 106 2% Weak Axis Displacement at Mid-span at Yielding (m) 5.5 5.9 6% 3.4 Barge Finite Element Model The impact vessel of interest in this thesis is a cons truction barge, 151.5 ft. in length and 50 ft. in width. Figure 3-7 th rough 3-11 describe the dimensions and the internal structure of the construction barge.

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20 Transverse Frame 70'-0" 81'-6" *3 Panel Longitudinal Truss Longitudinal Truss 5 0 0 "Longitudinal Truss 151'-6" Barge Bow Figure 3-7. Main deck plan of the construction barge Serrated Channel Transverse Frame 1 2 0 70'-0" 81'-6" Figure 3-8. Outboard profile of the construction barge Transverse FrameC Channel L Beam 35'-0" 35'-0" Figure 3-9. Typical l ongitudinal truss of th e construction barge L 4 x 3 x 1/4 C 8 x 13.75 Top & Bottom L 3.5 x 3.5 x 5/16 typ. Figure 3-10. Typical transverse frame (cross bracing section) of the construction barge

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21 1'-6" 2'-0" 35'-0" Figure 3-11. Dimension and detail of barge bow of the construction barge The construction barge is made up of st eel plates, standard steel angles (Lsections), channels (C-sections) and serra ted channel beams. The bow portion of the barge is raked. Twenty-two internal longitudi nal trusses span the le ngth of the barge and nineteen trusses span transv ersely across the width of the barge. The twenty-two longitudinal trusses are made up of steel angles, while the nine teen transverse trusses are made up of steel channels. Serr ated channel beams are used at the side walls to provide stiffness to the wall plates. Reference [2] gives a very detailed de scription of modeling of an open hopper barge, in which the barge is divided into th ree zones and consequen tly treated in three different ways with respect to mesh resoluti on. The three zones are called zone-1, zone-2 and zone-3 respectively. For modeling of the c onstruction barge that is of interest here, the same concept was applied. The constructio n barge was divided into three longitudinal zones, as is illustrated in Figure 3-12.

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22 Zone-1 Zone-2 Zone-3 116'-0" 19'-0" 15'-6" Figure 3-12. Layout of barge divisions For centerline, head-on impacts, the centr al portion of barge zone-1 (see Figure 313) is where most plastic deformation occurs an d impact energy is dissipated. This area is thus the critical part in modeling dynamic collisions of barges with piers. Since all simulations described in this thesis are for cen terline impacts, internal structures in the central area of zone-1 are modeled with a refi ned mesh of shell elements to capture large deformations, material failure, and thus to diss ipate energy. Internal trusses in the port and starboard off-center porti on of the bow are modeled us ing lower-resolution beam elements since only small deformations are expected and material failure is not likely to occur during centerline impacts of the barge. Unlike zone-1, structures in zone-2 and -3 construction barge will sustain relatively minor deformations that will cause primarily elastic stress distributions in the outer plates, inner trusses and frame st ructures. Material failure is not expected in these zones. Zone-2 is modeled using shell elements for outer plate and beam elements for internal trusses and frames. Compared to the size of the shell elements of zone-1, those in zone-2 are considerably larger in size. Use of re latively simple beam elements reduces the computing time required to perform impact analysis.

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23 50'-0" Width of Barge Central Zone (High Resolution) Port Zone (Lower Resolution) Starboard Zone (Lower Resolution) Headlog of Barge 9'-4.5" 9'-4.5" 31'-3" Zone-1 Figure 3-13. Meshing of inte rnal structure of zone-1 In zone-3, the aft portion of the construction barge functions to carry the cargo weight of the barge and is not expected to undergo si gnificant deformation during dynamic impact. Thus the barge components in this zone are modeled with solid elements. Density of the solid elements was se lected to achieve targ et payload conditions. All shell elements in the model are a ssigned a piecewise linear plastic material model for A36 steel. A detailed description of this material type is provided in the research report by Consolazio et al.[2]. Solid elements are assigned an elastic material property since no plastic deform ation in zone-3 is expected Mass density of the solid element represents the fully loaded payload condition based on a total barge plus payload weight of 1900 tons as is descri bed in the AASHTO provisions.

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24 Beam elements in the barge model are assi gned elastic, perfectly plastic material type. LS-DYNA material model number 28, *MAT_RESULTANT_PLASTICITY is employed to do so. For this material type, the required input of cross sectiona l properties are: area, moment of inertia with respect to the strong axis, moment of inertia with respect to the weak axis, torsional moment of inertia shear deformation area. Though LS-DYNA assumes a rectangular cross section and intern ally calculates cross sectional dimensions based on area, flexural moment of inertia, and torsional moment of iner tia, a test model of a L 4x3x1/4 angle prepared by the author show ed that the plastic moment predicted by LS-DYNA can be as accurate as 99% for st rong axis bending a nd 95% for weak axis bending. A test model was developed and th e plastic moment capacity for both strong axis bending and weak axis bending for a non-symmetric angle section were computed. For other types of beams such as channels and wide fla nge members, plastic moment capacity can be derived from cross section properties available in the AISC Manual of Steel Construction [14]. Channels and wide flange beams showed error percentages varying up to 18% when the plasti c moment was computed using the *MAT_RESULTANT_PLASTICITY material in LS-DYNA. Contact definition *CONTACT_AUTOMATIC_SINGLE_SURFACE (self contact) is assigned to the barge bow to capture the fact that under impact lo ading, the internal members within the barge bow may not only contact each other, but also fold over on themselves due to buckling. During an impact simulation, LS-DYNA checks for the possibility for elements contac ting each other within a define d contact area, thus a large self contact area will increase computing ti me drastically. To minimuze computational time, the area in the barge bow where contact is likely to occur is carefully chosen.

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25 Table 3-5. General modeling f eatures of the testing barge Model Features 8-node brick elements 1842 4-node shell elements 81,040 2-node beam elements 8,324 2-node Discrete Spring elements 119 1-node point mass elements 119 Model Dimensions Length 151.5 Ft Width 50.0 Ft Depth 12.5 Ft Contact Definitions CONTACT_AUTOMATIC_SINGLE_SURFACE CONTACT_AUTOMATIC_NODES_TO_SURFACE Table 3-6 General modeling features of the jumbo hopper barge Model Features 8-node brick elements 234 4-node shell elements 24,087 2-node beam elements 2,264 2-node Discrete Spring elements 28 1-node point mass elements 28 Model Dimensions Length 195 Ft Width 35 Ft Depth 12 Ft Contact Definitions CONTACT_AUTOMATIC_SINGLE_SURFACE CONTACT_AUTOMATIC_NODES_TO_SURFACE CONTACT_TIED_NODES_TO_SURFACE Welds are used in the barge to connect th e head log plate, top plate and the bottom plate. These welds are modeled by the *CONSTRAINED_SPOTWELD constraint type. Computationally, the spotwelds consist of rigi d links between nodes of the head log, top plate and bottom plate. Detailed descriptions of self contac t definition and weld modeling are given in the research report de veloped by Consolazio et al. [2]. Connection between zone-1, zone-2, and zone-3 are made with nodal rigid body constraints. For the connection of zone-1 to zone-2, the tran sition between internal trusses modeled by shell elements and internal trusses modeled by be am elements is approached by using rigid links to connect nodes from sh ell element and beam element to transfer

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26 internal section forces in a distributed manner. For the conn ection of zone-2 to zone-3, nodal rigid bodies are defined to connect small elements in zone-2 with those in zone-3. Buoyancy Spring with Zero Gap Buoyancy Spring with Non-zero Gap Figure 3-14. Buoyancy spring distribution along the barge A pre-compressed buoyancy spring model is applied to the barge to simulate buoyancy effects. The buoyancy spring stiffne ss was formulated based on tributary area and draft depth of each spring and a gap wa s added to the spring formulation. Since different positions on the barge hull have different draft depths, the buoyancy spring formulation varies with longitudinal locati on. Gaps between the water level and barge hull are determined from the geometry of the bottom surface of the barge (see Figure 314). The pre-compression of buoyancy spring is calculated using Mathcad worksheet. The comparison of general modeling featur es of construction barge and open hopper barge is provided in Table 3-5 and 3-6. 3.5 Contact Surface Modeling When pier columns and pier caps are modeled using beam elements, contact surfaces need to be modeled and added to the pier column to enable contact detection during impact (see Figure 3-15). Also in Fi gure 3-15, since shear wall is modeled by beam elements, rigid body is defined at conne ction of shear wall, pier column and pile cap. In this region, only very small deform ation could likely occu r due to thickness of shear wall. So it is treated as rigid body. Modeling of contact surface needs to be done

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27 carefully since the contact surface may add ex tra stiffness to the pier column, thus changing the original stiffness of the pi er and affect the simulation results. pier cap p i e r c o l u m nshear wall pile cap contact surface barge motion water line rigid body Figure 3-15. Pier and contact surface layout rigid link rigid contact surface pier column Figure 3-16. Rigid links between pier column and contact surface

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28 i m p a c t f o r c ep i e r c o l u m ncontact surface Figure 3-17. Exaggerated deformation of pier column and contact surface during impact To make sure that contact surface will not add extra stiffness to the pier, it is divided into separate elements. Each sepa rate element is assigned rigid material properties and is connected to the pier co lumn through rigid links (see Figure 3-16). Under bending of the pier column, these elemen ts will act independently, and transfer the impact force to the pier column beam elements. Figure 3-17 shows an exaggerated depiction of deformation of the contac t surface during impact. Though friction on the contact surface may add extra bending moment to the pier column, studies shows that when the element size of pier column is set to approximately 6 inches, the extra bending moment transmitted to the pier column is less than 5% compared to the primary bending moment sustained during impact for the most severe cases considered here (6 knots, full load). Though the contact surface in a real pier is ma de of concrete, use of a rigid material model is verified by comparing the impact fo rce versus crush dept h relationships from static barge crush analysis. Figure 3-18 shows a comparison of impact force versus crush depth relationships computed using rigid c ontact surfaces and concrete contact surfaces.

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29 Though the impact forces differ slightly afte r the crush depth exceeds 24 inches, overall, the curves are in good agreement. 0 1 2 3 4 5 6 10 20 30 40 50 60 0 200 400 600 800 1000 1200 1400 0 0.5 1 1.5 Impact force (MN) Impact force (kip)Crush depth (in) Crush depth (m) rigid material elastic material Figure 3-18. Comparison of impact force ve rsus crush depth for rigid and concrete contact models The concrete cap seal is not modeled explicitly but its mass is added to that of the pile cap to account for increased inertial resistance. Soil springs are assigned spring stiffnesses derived from the FB-Pier program and nodal constraints are added to the soil springs. Detailed descriptions of soil springs and constraints of nodes are available in the research report by C onsolazio et al. [2]. A typical impact simulation model in which a pier model has been combined with a barge model is shown in Figure 3-19. As the figure illustrates, resu ltant beam elements are used to model the pier columns and cap and the contact surface representation described above is used to detect c ontact between the barge and the pier.

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30 Figure 3-19. Overview of barge a nd pier model for dynamic simulation

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31 CHAPTER 4 NON-LINEAR PIER BEHAVIOR DURING BARGE IMPACT Non-linear pier behavior, barge deformati on and energy dissipation are several of the issues that are relevant when consider ing barge-pier collisions. The answer to questions of how much the nonlinearity in modeling affects these considerations, if nonlinearity causes fundamental changes to pier behavior helps understand barge and pier behavior during impact, thus when impact cases are considered, whether non-linearity should be included in modeling or not will be justified and thus facilitate the dynamic simulation modeling procedure. 4.1 Case Study In the barge and the pier impacts modeled he re, the barge is selected to have fully loaded weight of 1900 tons (per the AASHTO pr ovisions). This loaded weight is chosen to be the same as that of fully loaded open hopper barge to enable comparison with results of dynamic simulations previously c onducted using a hopper ba rge finite element model. The rectangular columns of the pier are used to define the contact surface. Two barge impact velocities are considered: 6 knots and 1 knot. Barge w ith a 6 knot speed and fully loaded condition represents the most cr itical impact scenario and thus the most severe nonlinear pier behavi or. Barge impact with a 1 knot speed and fully loaded condition represents the scenario that onl y a very small region of pier shows nonlinearity. These two cases cover a large range of impact scenarios, thus results from these two cases can reasonably cover the effect of non-linearity. All cases included in this chapter are listed in Table 4-1.

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32 Table 4-1. Dynamic simulation cases Case Contact Surface Speed Impact Angle Material Property Loading Condition A Rectangular 6 knot Head-on Linear Full B Rectangular 6 knot Head-on Nonlinear Full C Rectangular 1 knot Head-on Linear Full D Rectangular 1 knot Head-on Nonlinear Full 4.2 Analysis Results For both severe impact case and non-severe impact case, Figu res 4-1 through 4-6 show that using nonlinear pier material and us ing linear pier material generate the same impact force peak value and almost the same impact duration time since after the internal structure in the barge bow yiel ds, it cannot exert a larger impact force. Also, for both non-severe impact condition and severe im pact condition, approximately the same amount of energy is dissipated (area under ba rge impact force vs. crush depth curve) using nonlinear pier material and lin ear pier material respectively. It is shown that for both severe impact case and non-severe impact case, barge crush depth after impact for linear pier is always larger than barge crush depth after impact for nonlinear pier (Figure 4-3, Figure 4-4). During impact, fo r the severe impact case, all steel piles yield; even for the non-seve re impact case, part of the steel piles yield during impact. Yielding of st eel piles prevents the pier structure from generating increased resistance to the barge, thus the pi er structure cannot create larger crush depth in barge bow. Also yielding of piles generate s residual deformation of pier structure after impact as shown in Figure 4-5. The residual deformation can be as large as 10-12 at the point for measurement (the impact point). The pier column and pier cap do not yield

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33 during impact even for the most severe impact case. For the barge with 1 knot impact speed and fully loaded condition, the pier re sidual deformation is almost negligible. Plots of pier column bending moment shows that the peak value of the pier column bending in the impact zone of the pier exceed s the cracking moment of pier column cross section. Since the moment-curvature is simplif ied as a bilinear curve with initial stiffness the same as that of the un-cracked cross sect ion, the cracking moment is not reflected in the bilinear moment-curvature curve. There is very little difference between pi er behavior using lin ear pier and using nonlinear pier material for the barge with a 1 knot speed, fully loaded condition. Partially yielded piles during impact caused very little effect on pier behavior For this case, the effect of non-linearity of pier material can be ignored almost completely. For the barge with 6 knot speed, fully loaded condition, t hough non-linearity of pier material does have an effect on impact force history, impact force vs. crush depth re lationship, and pier displacement, the influence is limited. The results drawn here are based specifica lly on impact simulations of a barge impacting a channel pier of the St. George Isla nd Causeway bridge. Th e piles of this pier are HP14x73 steel piles. As a result, the charact eristics of these piers are quite different from the concrete piles as are also often em ployed in bridges. Different pile properties may have a substantial effect on impact fo rce and pier behavior during impact. Thus additional work needs to be done for impacts of different pier type s to comprehensively study the effect of pier materi al nonlinearity on barge impact force and pier behavior.

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34 0 1 2 3 4 5 6 7 0 0.5 1 1.5 22.5 0 200 400 600 800 1000 1200 1400 Impact force (MN) Impact force (kip)Time (s) 6knot, head on, linear, full load 6knot, head on, nonlinear, full load Figure 4-1. Comparison of impact fo rce history for severe impact case 0 1 2 3 4 5 6 7 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 Impact force (MN) Impact force (kip)Time (s) 1knot, head on, nonlinear, full load 1knot, head on, linear, full load Figure 4-2. Comparison of impact force history for non-severe case

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35 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 0 200 400 600 800 1000 1200 1400 0 10 20 30 40 50 60 70 80 90 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) 6knot, head-on, linear, full load 6knot, head-on, nonlinear, full load Figure 4-3. Impact force and crush depth relationship compar ison for severe impact case 0 1 2 3 4 5 6 7 0 0.01 0.02 0.03 0 200 400 600 800 1000 1200 1400 0 0.5 1 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) 1knot, head on, nonlinear, full load 1knot, head on, linear, full load Figure 4-4. Comparison of imp act force – crush depth rela tionship for non-severe case

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36 -5 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 pier impact point displ. (in) pier impact point displ. (m)Time (s) 6knot, head-on, linear, full load 6knot, head-on, nonlinear, full load Figure 4-5. Comparison of pier disp lacement for severe impact case. -4 -2 0 2 4 0 0.2 0.4 0.6 0.8 1 -0.1 -0.05 0 0.05 0.1 pier impact point displ. (in) pier impact point displ. (m)Time (s) 1knot, head on, nonlinear, full load 1knot, head on, linear, full load Figure 4-6. Comparison of pier displacement for non-severe case.

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37 CHAPTER 5 SIMULATION OF OBLIQUE IMPACT CONDITIONS Contained within the AASHTO barge impact design provisions are procedures not only for computing equivalent static design fo rce magnitudes, but also instructions on how such loads shall be app lied to a pier for design purpos es. Two fundamental loading conditions are stipulated: 1) a head-on tran sverse impact condition, and 2) a reducedforce longitudinal impact condition. In the head-on impact case, the impact force is applied “transverse to the substructure in a direction parallel to the alignment of the centerline of the navigable channel”[1]. In the second loading condition, fifty percent (50%) of the transverse load is applied to the pier as a longitudinal force (perpendicular to the navigation channel). The AASHTO provisi ons further state that the “transverse and longitudinal impact forces shall not be taken to act simultaneously.” Due to differences in the causes of acci dents (weather; mechanical malfunction; operator error) and differences in vessel, ch annel, and bridge configurations, barge collisions with bridge piers rarely involve a precisely a head-on strike. AASHTO’s intent in using two separate loading conditions (load magnitudes and directions ), is to attempt to envelope the structural effect s that might occur for a variet y of different possible oblique impacts, i.e. impacts that do not occur in a precisely head-on manner. In this chapter, numeric simulations are used to study the structural response of piers under oblique impact conditions so that the adequacy of the AASHTO procedures can be evaluated.

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38 5.1 Effect of Strike Angle on Barge St atic Load-Deformation Relationship Before considering dynamic simulations of oblique impacts, the effects of impact angle on the static force vs. deformation re lationships of typical barges will be considered. A previously developed open hopper barge model [2] is used to conduct static crush analyses in which a square pier statically penetrates the center zone of the barge bow at varying angles. Pier models ha ving widths of 4 ft., 6 ft. and 8 ft. are statically pushed (at a speed of 10 in./sec.) into the barge bow at angles of 0 degrees, 15 degrees, 30 degrees, and 45 degrees (see Figure 5-2). Each pier is modeled using a linear elastic material model and frictional effects between the pier and barge are represented using a static frictional coefficient of 0.5. Fi gure 5-1 shows the static crush of the pier and the open hopper barge. Results from the static crush simulations ar e presented in Figures 5-2 to Figure 5-4. The results indicate that head-on conditions (0 degree impact angle) always generate maximum peak force regardless of pier width (for the range of piers widths considered). Minimum forces are genera ted at the maximum angle of incidence, 45 degrees. Open hopper bargehead on crush 45 degree crush 15 degree crush 30 degree crus h pier Figure 5-1. Static crush betw een pier and open hopper barge

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39 0 1 2 3 4 5 6 7 00.10.20.30.40.50.6 0 200 400 600 800 1000 1200 1400 05101520 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) static crush 4ft-0 deg static crush 4ft--15 deg static crush 4ft--30 deg static crush 4ft--45 deg Figure 5-2. Results for static crush anal ysis conducting with a 4 ft. wide pier 0 1 2 3 4 5 6 7 00.10.20.30.40.50.6 0 200 400 600 800 1000 1200 1400 05101520 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) static crush 6ft-0 deg static crush 6ft--15 deg static crush 6ft--30 deg static crush6ft--45 deg Figure 5-3. Results for static crush anal ysis conducting with a 6 ft. wide pier

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40 0 1 2 3 4 5 6 7 0 0.1 0.2 0.3 0.4 0.5 0.6 0 200 400 600 800 1000 1200 1400 051015 20 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) static crush 8ft-0 deg static crush 8ft--15 deg static crush 8ft--30 deg static crush8ft--45 deg Figure 5-4. Results for static crush anal ysis conducting with a 8 ft. wide pier 5.2 Effect of Strike Angle on Dynamic Loads and Pier Response Dynamic impact behavior under oblique im pact conditions is now studied for two bounding cases (see Figure 5-5): an impact a ngle of 0 degrees (head-on impact) and an angle of 45 degrees (severe oblique impact). Pier columns having both rectangular and circular cross-sectional shapes are considered Table 5-1 lists all of the dynamic analysis cases included this parametr ic study. Cases A through G make use of a linear material model for the pier while cases H utilize the nonlinear concrete material model described earlier in Chapter 3.

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41 Barge head-on impact motion Barge oblique impact motion Traffic on superstructure Pier Pier cap X Y Figure 5-5. Layout of barge head-on im pact and oblique impact with pier Table 5-1. Dynamic simulation cases Case Contact Surface Speed Impact Angle Material Property Loading Condition A Rectangular 6 knot Head-on Linear Full B Rectangular 6 knot 45 degree Linear Full C Rectangular 1 knot Head-on Linear Full D Rectangular 1 knot 45 degree Linear Full E Circular 6 knot Head-on Linear Full F Circular 6 knot 45 degree Linear Full G Circular 1 knot Head-on Linear Full H Circular 1 knot 45 degree Linear Full

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42 5.3 Dynamic Simulation Results Simulation results for cases A, B, C, D, E, F, G, H (as indicated in Table 5-1) are presented in Figure 5-6 through Fi gure 5-21. In each figure, the direction denoted as “X” corresponds to the axis of the pi er (see Figure 5-5) that is parallel (or near ly so) to the axis of the navigation channel (i.e., perpe ndicular to the alignment of the bridge superstructure supported by the pier). The dire ction denoted as “Y” is parallel to the direction of traffic movement on the bridge superstructure (roadway) Pier displacements in the figures are taken at the point of im pact. For oblique impacts, figures showing impact force vs. crush depth relationships are developed using resultan t impact forces and resultant crush depths. Impact force history in X directi on are shown in Figure 5-6, Figure 5-7, Figure 5-8 and Figure 5-9. Impact force history in Y direction are represented in Figure 5-10, Figure 5-11. Peak value of the impact force histories in Figure 5-6 through 5-11 will be compared to the equiva lent static force specified by the AASHTO vessel impact provisions in Chapter 7. Rela tionship of impact force and crush depth are shown in Figure 5-12, Figure 5-13, Figur e 5-14 and Figure 5-15. Plots of pier displacement in X direction and in Y direc tion are included in Fi gure 5-16, Figure 5-17, Figure 5-18, Figure 5-19, Fi gure 5-20 and Figure 5-21. Figures 5-6, Figure 5-7, Figur e 5-8 and Figure 5-9 indicate that for the impact force in the direction parallel to the centerline of navigable channel, dynamic simulations with 45 degree impact angle always generate sma ller impact force peak value than head-on impacts, regardless of the geometry of the contact surface. For rectangular pier, impact force peak values from 45-degree oblique impact simulations are about 50% of those from head-on impact for both the low-speed impact scenarios and the high-speed impact scenarios. However for circular pier, the imp act force peak values from 45 degree oblique

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43 impact simulations are about 80% of those fr om head-on impact simulations regardless of impact speed. Thus increasing impact angle does reduce the impact force peak value in the X direction. It causes the impact force peak value to reduce to a larger extent for the rectangular pier than fo r the circular pier. Relationship of impact force and crush de pth as in Figure 5-12 Figure 5-13, Figure 5-14 and Figure 5-15 show that though lowspeed impact scenarios with 45 degree oblique impact angle always seem to cause la rger resultant crush de pth in barge bow and lower resultant impact force peak value th an the head-on impact, high-speed impact scenarios have a different trend. Figure 5-13 in dicates that for circular pier of high impact speed and oblique impact angle, resultant impact force and resultant crush depth relationship seems to stay the same for bot h head-on impact and oblique impact. Figure 5-12 indicates that for rectangular pier of hi gh impact speed, oblique impact causes larger resultant crush depth and smaller resultant im pact force peak value than head-on impact. The above observation seems to be reasonable for the two geometries of contact surface. For different impact angles, ci rcular pier always has the same geometry; however for the rectangular pier, the contact ar ea becomes smaller with increasi ng impact angle, it is the smallest for 45 degree oblique impact. To di ssipate the kinetic energy of the barge, a smaller contact area definitely brings larger crush depth since the edge of the pier “cuts” into the barge easily because of less resistance from internal structures of barge bow than the larger contact area. Pier impact force divided by the correspondi ng pier displacement indicates pier stiffness. Figure 5-6 through 5-21 indicate the similar pier displacement in both X and Y

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44 direction and the corresponding similar impact fo rce in both X and Y direction, therefore show that the pier has similar sti ffness in both X and Y direction. 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 1200 1400 Impact force (MN) Impact force (kip)Time (s) 6knot, head on, linear, full load 6knot, 45 deg, linear, full load, X direction Figure 5-6. Impact force in X direction for high speed impact on rectangular pier 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 1200 1400 Impact force (MN) Impact force (kip)Time (s) circular, 6knot, head on, linear, full load circular, 6knot, 45 deg, linear, full load, X direction Figure 5-7. Impact force in X direction for high speed impact on circular pier.

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45 0 1 2 3 4 5 6 7 0 0.5 1 0 200 400 600 800 1000 1200 1400 Impact force (MN) Impact force (kip)Time (s) rectangular, 1knot, head on, linear, full load rectangular, 1knot, 45 deg, linear, full load, X direction Figure 5-8. Impact force in X direction for low speed impact on rectangular pier. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 0 200 400 600 800 1000 Impact force (MN) Impact force (kip)Time (s) circular, 1knot, head on, linear, full load circular, 1knot, 45 deg, linear, full load, X direction Figure 5-9. Impact force in X direction for low speed impact on circular pier

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46 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 1200 Impact force (MN) Impact force (kip)Time (s) rectangular, 6knot, 45 deg, linear, full load, Y direction circular, 6knot, 45 deg, linear, full load, Y direction Figure 5-10. Impact force in Y dire ction for high-speed oblique impact 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 0 200 400 600 800 1000 Impact force (MN) Impact force (kip)Time (s) rectangular, 1knot, 45 deg, linear, full load, Y direction circular, 1knot, 45 deg, linear, full load, Y direction Figure 5-11. Impact force in Y direction for low speed oblique impact

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47 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 0 200 400 600 800 1000 1200 1400 0 10 20 30 40 50 60 70 80 90 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) rectangular, 6knot, head on, linear, full load rectangular, 6knot, 45 deg, linear, full load Figure 5-12. Force-deformation results fo r high speed impact on rectangular pier 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 0 200 400 600 800 1000 1200 1400 0 10 20 30 40 50 60 70 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) circular, 6knot, head on, linear, full load circular, 6knot, 45 deg, linear, full load Figure 5-13. Force deformation results fo r high speed impact on circular pier

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48 0 1 2 3 4 5 6 7 0 0.01 0.02 0.03 0.04 0.05 0.06 0 200 400 600 800 1000 1200 1400 0 0.5 1 1.5 22.5 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) rectangular, 1knot, head on, linear, full load rectangular, 1knot, 45 deg, linear, full load, X direction Figure 5-14. Force-deformation results fo r low speed impact on rectangular pier 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.01 0.02 0.03 0.04 0.05 0.06 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) circular, 1knot, head on, linear, full load circular, 1knot, 45 deg, linear, full load Figure 5-15. Force-deformation results fo r low speed impact on circular pier

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49 -5 0 5 10 15 20 0 0.5 1 1.5 2 2.5 -0.1 0 0.1 0.2 0.3 0.4 0.5 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 6knot, head on, linear, full load rectangular, 6knot, 45 deg, linear, full load, X direction Figure 5-16. Pier displacement in X direction for high speed impact on rectangular pier -1 0 1 2 3 4 5 0 0.5 1 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 1knot, head on, linear, full load rectangular, 1knot, 45 deg, linear, full load, X direction Figure 5-17. Pier displacement in X direction for low speed impact on rectangular pier

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50 -4 -2 0 2 4 6 8 10 0 0.5 1 1.5 2 2.5 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 pier impact point displ. (in) pier impact point displ. (m)Time (s) circular, 6knot, head on, linear, full load circular, 6knot, 45 deg, linear, full load, X direction Figure 5-18. Pier displacement in X direction for high speed impact on circular pier -1 0 1 2 3 4 5 0 0.5 1 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 pier impact point displ. (in) pier impact point displ. (m)Time (s) circular, 1knot, head on, linear, full load circular, 1knot, 45 deg, linear, full load, X direction Figure 5-19. Pier displacement in X direction for low speed impact on circular pier

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51 -2 0 2 4 6 8 10 0 0.5 1 1.5 2 2.5 -0.05 0 0.05 0.1 0.15 0.2 0.25 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 6knot, 45 deg, linear, full load, Y direction circular, 6knot, 45 deg, linear, full load, Y direction Figure 5-20. Pier displace ment in Y direction for high-speed oblique impact -1 0 1 2 3 4 5 0 0.5 1 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 1knot, 45 deg, linear, full load, Y direction circular, 1knot, 45 deg, linear, full load, Y direction Figure 5-21. Pier displace ment in Y direction for low speed oblique impact.

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52 CHAPTER 6 EFFECT OF CONTACT SURFACE GEOMETRY ON PIER BEHAVIOR DURING IMPACT 6.1 Case Study In the previous chapter, it was noted that rotation of a square pier relative to the direction of impact (i.e., crea tion of an oblique impact cond ition) has an effect on impact loads and on pier response. These effects are due partially to the fact that the shape of the impact surface between the barge and pier change s as the square pier is rotated. In this chapter, the effect of contact surface geometry is explored furt her. Of interest is whether or not fundamentally differing pi er cross-sectional shapes, e. g. square versus circular, produce substantially differing loads and pier responses. A parametric study is conducted involving two types of pier cr oss-sectional geometry (recta ngular and circular), two impact speeds (1 knot and 6 knots), and two impact angles (0 and 45 degrees). Cases discussed in this chapter are the same as those shown in Table 5.1 of Chapter 5. 6.2 Results Figure 6-1 to Figure 6-16 pres ent results from cases A, B, C, D, E, F, G, and H listed in Table 5.1. As described in the prev ious chapter, the X direction represents the direction “parallel to the alignment of the cen terline of the navigabl e channel” and the Y direction represents the dire ction “longitudinal to the s ubstructure.” Relationships between impact force and crush de pth (Figures 6-13 – 6-16) utilize vector-resultant forces and vector-resultant crush depths rather than co mponent values in the X and Y directions.

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53 Figures 6-1 through 6-4 show impact fo rce histories in X direction for both rectangular and the circ ular piers. For high-speed cases (F igures 6-1 and 6-2), the impact force histories for both oblique and headon impacts indicate that both pier-column geometries (rectangular and ci rcular) produce approximately th e same peak impact force. For the low speed, head-on impact cases (Figur e 6-3), the impact force peak value for the circular pier is approximatel y half of that for the recta ngular pier. Conversely, in low speed, oblique impact cases (Figure 6-4), the peak impact forces for both circular and rectangular piers are nearly th e same. Figures 6-5 and 6-6 show the impact force histories in the Y direction for oblique impact conditions. Computed pier displacements in the X di rection are shown in Figures 6-7 through 6-10, while displacements in the Y direction as shown in Figures 6-11 and 6-12. In all cases considered, peak predicted displacemen ts (in either the X or Y directions) are approximately the same for both square a nd circular piers indi cating little or no sensitivity to pier-colum n cross-sectional shape. Resultant impact force versus resultant barge crush depth relationships are shown in Figures 6-13 through 6-16In each plot the area under the cu rve represents the approximate amount of energy that is dissipa ted through plastic deformation of the steel plates in the bow of the barge. In both of the high speed (6 knot) impact cases (Figures 613 and 6-14), the initial kinetic impact energy of the barge is sufficient to cause significant plastification of the barge bow. In these cases, it is evident that the quantify of dissipated energy is approximately the same for the square and circular piers. In the low speed head-on impact cases (Figure 6-15), the in itial kinetic impact energy is insufficient to cause significant plastic deformation and th e responses for the squa re and circular piers

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54 are quite different. However, when simulati ons are conducted at the same speed (1 knot) but at an oblique impact angle (Figure 616), the computed responses (and dissipated energy levels) are again very similar between th e square and circular pier cases. As was demonstrated in Chapter 5 (and specifically Fi gure 5.3), rotation of a square pier relative to the barge headlog tends to reduce the stiffness of the bow and thus produce results similar to those obtained for a circular pier. 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 1200 1400 Impact force (MN) Im p act force ( ki p) Time (s) rectangular, 6knot, head on, linear, full load circular, 6knot, head on, linear, full load Figure 6-1. Impact force in X dire ction for high speed head-on impact.

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55 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 1200 Impact force (MN) Impact force (kip)Time (s) rectangular, 6knot, 45 deg, linear, full load, X direction circular, 6knot, 45 deg, linear, full load, X direction Figure 6-2. Impact force in X dire ction for high speed oblique impact 0 1 2 3 4 5 6 7 0 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 Impact force (MN) Impact force (kip)Time (s) rectangular, 1knot, head on, linear, full load circular, 1knot, head on, linear, full load Figure 6-3. Impact force in X dire ction for low speed head-on impact

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56 0 1 2 3 4 0 0.5 1 0 200 400 600 800 1000 Impact force (MN) Impact force (kip)Time (s) rectangular, 1knot, 45 deg, linear, full load, X direction circular, 1knot, 45 deg, linear, full load, X direction Figure 6-4. Impact force in X dire ction for low speed oblique impact 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 1200 Impact force (MN) Impact force (kip)Time (s) rectangular, 6knot, 45 deg, linear, full load, Y direction circular, 6knot, 45 deg, linear, full load, Y direction Figure 6-5. Impact force in Y dire ction for high speed oblique impact

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57 0 1 2 3 4 0 0.5 1 200 400 600 800 1000 Impact force (MN) Impact force (kip)Time (s) rectangluar, 1knot, 45 deg, linear, full load, Y direction circular, 1knot, 45 deg, linear, full load, Y direction 0 Figure 6-6. Impact force in Y dire ction for low speed oblique impact -5 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 6knot, head-on, linear, full load circular, 6knot, head-on, linear, full load Figure 6-7. Pier displace ment in X direction for high speed head-on impact

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58 -2 0 2 4 6 8 10 0 0.5 1 1.5 2 2.5 -0.05 0 0.05 0.1 0.15 0.2 0.25 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 6knot, 45 deg, linear, full load, X direction circular, 6knot, 45 deg, linear, full load, X direction Figure 6-8. Pier displace ment in X direction for high speed oblique impact -1 0 1 2 3 4 5 0 0.5 1 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 1knot, head on, linear, full load circular, 1knot, head on, linear, full load Figure 6-9. Pier displace ment in X direction for low speed head-on impact

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59 -1 0 1 2 3 4 5 0 0.5 1 -0.02 0.02 0.04 0.06 0.08 0.1 0.12 pier impact point displ. (in) pier impact point displ. (m)Time (s) 0 rectangular, 1knot, 45 deg, linear, full load, X direction circular, 1knot, 45 deg, linear, full load, X direction Figure 6-10. Pier displace ment in X direction for low speed oblique impact -2 0 2 4 6 8 10 0 0.5 1 1.5 2 2.5 -0.05 0 0.05 0.1 0.15 0.2 0.25 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 6knot, 45 deg, linear, full load, Y direction circular, 6knot, 45 deg, linear, full load, Y direction Figure 6-11. Pier displace ment in Y direction for high speed oblique impact

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60 -1 0 1 2 3 4 5 0 0.5 1 pier impact point displ. (in) pier impact point displ. (m)Time (s) rectangular, 1knot, 45 deg, linear, full load, Y direction circular, 1knot, 45 deg, linear, full load, Y direction 0.12 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure 6-12. Pier displace ment in Y direction for low speed oblique impact. 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 0 200 400 600 800 1000 1200 1400 0 10 20 30 40 50 60 70 80 90 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) rectangular, 6knot, head-on, linear, full load circular, 6knot, head-on, linear, full load Figure 6-13. Vector-resultant force-deforma tion results for high speed head-on impact

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61 0 1 2 3 4 5 6 0 0.5 1 1.5 2 0 200 400 600 800 1000 1200 1400 0 10 20 30 40 50 60 70 80 90 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) rectangular, 6knot, 45 deg, linear, full load circular, 6knot, 45 deg, linear, full load Figure 6-14. Vector-resultant force-deforma tion results for high speed oblique impact 0 1 2 3 4 5 6 7 0 0.01 0.02 0.03 0.04 0.05 0.06 200 400 600 800 1000 1200 1400 0 0.5 1 1.5 2 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) 0 rectangular, 1knot, head on, linear, full load circular, 1knot, head on, linear, full load Figure 6-15. Vector-resultant force-deforma tion results for low speed head-on impact

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62 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.01 0.02 0.03 0.04 0.05 0.06 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 Impact force (MN) Impact force (kip)Crush Depth (m) Crush Depth (in) rectangular, 1knot, 45 deg, linear, full load circular, 1knot, 45 deg, linear, full load Figure 6-16. Vector-resultant force-deforma tion results for low speed oblique impact

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63 CHAPTER 7 COMPARISON OF AASHTO PROVISIONS AND SIMULATION RESULTS Procedures specified by AASHTO for compu ting equivalent static impact forces were previously described in Chapter 2. In this chapter, comparisons between loads computed using those procedures and corre sponding force data obtained using dynamic finite element impact simulations are presen ted. Barge impacts at two different speeds— and therefore two impact energy levels—are considered: 6 knots a nd 1 knot. Head-on and oblique impacts on both square and circular piers are cons idered. All of the cases for which dynamic impact simulation results ar e available are listed in Table 5.1. Peak impact forces (predicted by finite element analysis) in both the X direction (transverse) and Y direction (l ongitudinal) are reported in Ta ble 7.1. In Figures 7.1 and 7.2, these results are compared to equivale nt static loads computed using the AASHTO provisions. In determining the AASHTO loads, the hydrodynamic mass coefficient (HC) was set to unity to match the fact that hydr odynamic mass effects ar e not considered in the dynamic simulations presented in this thesis In addition, forces in the Y direction are taken, as AASHTO prescribes, as fifty percen t of the loads computed for the X direction. Although the finite element impact data pres ented in Figures 7.1 and 7.2 are limited in terms of variations in impact energy, th e results presented are consistent with those obtained by similar studies conducted for head -on impacts on square piers [2]. Here, results are also presented for cases involving oblique impacts and impacts on circular piers. Trends previously observed hold tr ue for these new conditions as well. Loads predicted by AASHTO exceed finite element predicted forces for high energy impacts

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64 but are less than peak dynamic values fo r less severe, low energy impact conditions. These trends also hold true for both the X and Y directions of loading. 0 500 1000 1500 2000 2500 3000 0 1000 2000 3000 4000 5000 6000 0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 Impact force (X) (kip) Impact force (X) (MN)Kinetic energy (kip-ft) Kinetic energy (MN-m) AASHTO Spec. -X direction C G H D A E F B H: circular, 1knot, 45 degree, linear G: circular, 1knot, head on, linear F: circular, 6knot, 45 degree, linear E: circular, 6knot, head on, linear D: rectangular, 1knot, 45 degree, linear C: rectangular, 1knot, head on, linear A: rectangular, 6knot, head on, linear B: rectangular, 6knot, 45 degree, linear Figure 7-1. AASHTO and finite element loads in X direction

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65 0 200 400 600 800 1000 1200 1400 0 1000 2000 3000 4000 5000 6000 0 1 2 3 4 5 6 0 1 2 3 4 5 67 8 Impact force (X) (kip) Impact force (X) (MN)Kinetic energy (kip-ft) Kinetic energy (MN-m) AASHTO Spec. -Y direction D H F H: circular, 1knot, 45 degree, linear F: circular, 6knot, 45 degree, linear D: rectangular, 1knot, 45 degree, linear B: rectangular, 6knot, 45 degree, linear Figure 7-2. AASHTO and finite element loads in Y direction.

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66 Table 7-1. Peak forces computed us ing finite element impact simulation Case Kinetic Energy Impact Force Peak Value (X) Impact Force Peak Value (Y) A 5638.5 kip-ft (7.645 MJ) 1468 kip (6.53 x 106 N) NA B 5638.5 kip-ft (7.645 MJ) 945 kip (4.20 x 106 N) 979 kip (4.35 x 106 N) C 156.6 kip-ft (0.12 MJ) 1347 kip (5.99x 106 N) NA D 156.6 kip-ft (0.12 MJ) 619 kip (2.75x 106 N) 560 kip (2.49 x 106 N) E 5638.5 kip-ft (7.645 MJ) 1372 kip (6.10x 106 N) NA F 5638.5 kip-ft (7.645 MJ) 1034 kip (4.60x 106 N) 976 kip (4.34 x 106 N) G 156.6 kip-ft (0.12 MJ) 659 kip (2.93x 106 N) NA H 156.6 kip-ft (0.12 MJ) 557 kip (2.48x 106 N) 509 kip (2.26 x 106 N)

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67 CHAPTER 8 CONCLUSIONS To assess the accuracy of the AASHTO barg e impact design provisions, parametric finite element impact studies involving pier material nonlinearity, impact angle, and impact zone geometry (pier-column cross-s ectional geometry) have been conducted. In addition, static barge crush simulations have been conducted to determine the effect of contact angle on barge force versus deforma tion relationships. Finally, dynamic finite element simulation results have been compared to equivalent design forces predicted by the AASHTO bridge design provisions. Results from oblique static barge crush simulations conducted using square shaped piers reveal that the sensitivities of crus h relationships to pier widths are most pronounced for small contact angl es but diminish rapidly for larger angles. Subsequent dynamic impact simulations conducted for head-on and oblique impacts on both square and circular piers reveal that differences in predicted forces are relatively minor in all situations except for the case of nearly head-on (zero-angle) impacts on square piers (flat faced piers). Separate parametric studies focusing on the effects of pier material nonlinearity reveal that forces and pier disp lacements in non-catastrophic impacts (i.e., situations in which the pier doe s not collapse) of pier structur es of the type studied here are not greatly sensitive to nonlin earity in the pier columns. Finally, comparisons between finite elem ent predicted forces and AASHTO forces for two different impact energy levels reveal th at, for the type of pi er studied here, the AASHTO provisions predict conservative re sults for high energy impacts (loads

PAGE 78

68 predicted by simulation were typically only about 60% of the load predicted by AASHTO). However, in low energy impacts, p eak transient dynamic forces predicted by finite element analysis exceed those specified by AASHTO (forces predicted by simulation can be more than twice the ma gnitude of the equiva lent static AASHTO loads). These trends have also been found to hold true in both the transverse and longitudinal impact directions. However, because the simulation-predicted loads are transient in nature whereas the AASHTO loads ar e static, additional research is needed in order to more accurately compare results from the two methods.

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69 LIST OF REFERENCES 1. American Association of State Highway and Transportation Officials (AASHTO). Guide Specification and Commentary for Vessel Collision Design of Highway Bridges. American Association of State Highway and Transportation Officials, Washingt on, DC, 1991. 2. Consolazio, G.R., Cook, R.A., Lehr, G.B., and Bollmann, H.T., Barge Impact Testing of the St. George Island Causeway Bridge Phase I : Feasibility Study, Structures Research Report No. 783, Engineering and Industrial Experiment Station, Unive rsity of Florida, Gainesville, Florida, January 2002. 3. Consolazio, G.R., Lehr, G.B., McVay, M.C., Dynamic Finite Element Analysis of Vessel Pier Soil Interaction During Barge Impact Events, Transportation Research Record: Journal of the Transportation Rese arch Board, No. 1849, pp. 81 90, 2004 4. Consolazio, G.R., Cook, R.A., Biggs, D.R., Cowan, D.R., and Bollmann, H.T., Barge Impact Testing of the St. George Island Causeway Bridge Phase II : Design of Instrumentation Systems, Structures Research Report No. 883 Engineering and Industrial Experiment Station, University of Florida, Gainesville, Florida, April 2003 5. American Association of State Highway and Transportation Officials (AASHTO). AASHTO LRFD Bridge Design Specifications, 3rd Edition, Washington, DC: Am erican Association of State Highway and Transportation Officials, 2000 6. Livermore Software Technology Corporation (LSTC), LS DYNA Keyword Manual: Version 960, Livermore, CA, 2002 7. Saul, R., Svensson, H., On the Theory of Ship Collision Against Bridge Piers, IABSE proceedings, pp. 29 40, Feb. 1982 8. Tedesco, J. W., McDougal, W. G., Ross, C. A., Structural Dynamics Theory and Applications, Addison Wesley, Menlo Park, California, 1999 9. Ngo, T. D., Mendis, P. A., Teo, D., Kusuma, G., Behavior of High strength Concr ete Columns Subjected to Blast Loading, paper presented in the conference Advanced In Structures: Steel, Concrete, Composite and Aluminum, Sydney, 23 25 June, 2003

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70 10. Dameron, R. A., Sobash, V. P., Lam, I. P., Nonlinear Seismic Analysis of Bridge Structures F oundation soil Representation And Ground Motion Input, Computers & Structures, Vol. 64, No. 5/6, pp. 1251 1269, 1997 11. Hoit, M. I., McVay, M., Hays, C., Andrade, P. W., Nonlinear Pile Foundation Analysis Using Florida Pier, Journal of Bridge Engineering, Vol 1, No. 4, pp.135 142, November 1996 12. MacGregor, J. G., Reinforced Concrete Mechanics and Design, Third Edition, Prentice Hall Inc., Upper Saddle River, New Jersey, 1997 13. ADINA R&D Inc., ADINA Online Users Manual, Watertown, MD, 2002 14. American Institute of Steel Construction (AISC). Manual of Steel Construction. Third Edition, American Institute of Steel Construction Inc., n.p., November, 2001

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71 BIOGRAPHICAL SKETCH The author was born on December 19, 1973, in Fuyang City, Anhui Province, People’s Republic of China. After graduation from No. 1 High School in Fuyang City, she attended Suzhou Institute of Urban Cons truction and Environmental Protection where she graduated with a bachelor’s degree in ro ad and bridge engineering in July 1995. She continued her study in structur al engineering by attending graduate school in Tongji University in Shanghai, China, and gra duated with a master’s degree in bridge engineering in December 1997. After working in the Shanghai Municipal Engineering Administration Department in Shanghai, China, for several years, she came to the United States in August 2000 to study at the University of Central Florida. She then came to the University of Florida to continue gradua te study in August 2002 majoring in structural engineering. After defending her thesis in August 2004 she plans to move to Orlando, Florida, to begin a career with EAC Consulti ng, Inc. as a junior bridge design engineer


Permanent Link: http://ufdc.ufl.edu/UFE0007280/00001

Material Information

Title: Influence of Pier Nonlinearity, Impact Angle, and Column Shape on Pier Response to Barge Impact Loading
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0007280:00001

Permanent Link: http://ufdc.ufl.edu/UFE0007280/00001

Material Information

Title: Influence of Pier Nonlinearity, Impact Angle, and Column Shape on Pier Response to Barge Impact Loading
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0007280:00001


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INFLUENCE OF PIER NONLINEARITY, IMPACT ANGLE, AND COLUMN SHAPE
ON PIER RESPONSE TO BARGE IMPACT LOADING
















By

BIBO ZHANG


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA


2004















ACKNOWLEDGEMENTS

I would like to thank my research advisor, Dr. Gary Consolazio for providing

continuous guidance, excellent research ideas, detailed teaching and all this with a lot of

patience. I am thankful for being able to learn so much during the past year and a half.

I would also like to extend my gratitude to Florida Department of Transportation

for providing funding for this project.

I would like to express my heartfelt thanks to all the graduate students who

worked on this project, especially Ben Lehr, David Cowan, Alex Biggs and Jessica

Hendrix. Their research helped me enormously in completing my thesis.

My family and friends have been very supportive throughout this effort. I wish to

thank them for their understanding and support.
















TABLE OF CONTENTS

page

A C K N O W L E D G E M E N T S ................................................................................................ ii

LIST OF TABLES ............................................................................. v

L IST O F FIG U R E S .... ...................................................... .. ....... ............... vi

ABSTRACT ........ .............. ............. ...... ...................... ix

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 Overview ................... ................. ...................................... ...... 1
1.2 Background of AASHTO Guide Specification ................................................2
1.3 O objective ...................................................................... ............ ...... 4

2 AASHTO BARGE AND BRIDGE COLLISION SPECIFICATION .....................5

3 FINITE ELEMENT BARGE IMPACT SIMULATION ............................................9

3 .1 In tro d u ctio n ............................................................................... 9
3.2 B background Study .......................................... .. .. .... .. ............... 10
3.3 P ier M odel D description ........................................................................... .... 14
3.4 B arge Finite E lem ent M odel.......................................................................... ...19
3.5 C contact Surface M odeling ........................................................................ .. .... 26

4 NON-LINEAR PIER BEHAVIOR DURING BARGE IMPACT.............................31

4 .1 C a se S tu d y ...................................................................... 3 1
4 .2 A n aly sis R esu lts.......... ........................................................................... .. ....... .. 32

5 SIMULATION OF OBLIQUE IMPACT CONDITIONS ......................................37

5.1 Effect of Strike Angle on Barge Static Load-Deformation Relationship ............38
5.2 Effect of Strike Angle on Dynamic Loads and Pier Response.............................40
5.3 D ynam ic Sim ulation R results ........................................ .......................... 42









6 EFFECT OF CONTACT SURFACE GEOMETRY ON PIER BEHAVIOR
D U R IN G IM P A C T .......................................................................... .....................52

6 .1 C ase S tu dy ....................................................... 52
6 .2 R e su lts ............................................................................................................. 5 2

7 COMPARISON OF AASHTO PROVISIONS AND SIMULATION RESULTS ....63

8 C O N C L U SIO N S ............................................................................. .......... ..... 6 7

L IST O F R E F E R E N C E S .......... ....................................... ....................... ......................... 69

B IO G R A PH IC A L SK E T C H ..................................................................... ..................71










































iv
















LIST OF TABLES


Table pge

3-1 Comparison of original and adjusted section properties ............... ..............16

3-2 Input data in LS-DYNA simulations ............................ .................................... 18

3-3 Comparison of plastic moment and displacement using properties of pier cap.......19

3-4 Comparison of plastic moment and displacement using properties of pier
co lu m n ...................................... ...................................................... 19

3-5 General modeling features of the testing barge......................................................25

4-1 D ynam ic sim ulation cases ......................................................... ............... 32

5-1 D ynam ic sim ulation cases ......................................................... ............... 41

7-1 Peak forces computed using finite element impact simulation.............................66
















LIST OF FIGURES


Figure pge

1-1 Relation between impact force and barge damage depth according to Meir-
D ornberg's R research (after A A SH TO [1]) ........................................ ....................3

2-1 Collision energy to be absorbed in relation with collision angle and the
coefficient of friction (after AASHTO [1])........................................................8

3-1 Global modeling of San-Diego Coronado Bay Bridge (after Dameron [10])..........11

3-2 Pier model used for local modeling (after Dameron [10]).................. .............12

3-3 Global pier modeling for seismic retrofit analysis (after Dameron [10]).................12

3-4 Mechanical model for discrete element (after Hoit [11])..................................13

3-5 Bilinear expression of moment-curvature and stress-strain curve ...........................17

3-6 M om ent-curvature derivation........................................................ ............... 18

3-7 M ain deck plan of the construction barge .................................... ...................... 20

3-8 Outboard profile of the construction barge ............................... ...............20

3-9 Typical longitudinal truss of the construction barge........................ .............20

3-10 Typical transverse frame (cross bracing section) of the construction barge ............20

3-11 Dimension and detail of barge bow of the construction barge..............................21

3-12 Layout of barge divisions .............................. ............ ..... ......................... 22

3-13 Meshing of internal structure of zone-1 ..........................................................23

3-14 Buoyancy spring distribution along the barge............................... ............... 26

3-15 Pier and contact surface layout.......................................... ........................... 27

3-16 Rigid links between pier column and contact surface..............................................27

3-17 Exaggerated deformation of pier column and contact surface during impact..........28









3-18 Comparison of impact force versus crush depth for rigid and concrete contact
m o d e ls ........................................................................... 2 9

3-19 Overview of barge and pier model for dynamic simulation...............................30

4-1 Comparison of impact force history for severe impact case ...............................34

4-2 Comparison of impact force history for non-severe case ...................................34

4-3 Impact force and crush depth relationship comparison for severe impact case .......35

4-4 Comparison of impact force crush depth relationship for non-severe case ..........35

4-5 Comparison of pier displacement for severe impact case.............. .. ................36

4-6 Comparison of pier displacement for non-severe case..........................................36

5-1 Static crush between pier and open hopper barge .......... ............ ..................38

5-2 Results for static crush analysis conducting with a 4 ft. wide pier ........................39

5-3 Results for static crush analysis conducting with a 6 ft. wide pier ........................39

5-4 Results for static crush analysis conducting with a 8 ft. wide pier ........................40

5-5 Layout of barge head-on impact and oblique impact with pier.............................41

5-6 Impact force in X direction for high speed impact on rectangular pier ...................44

5-7 Impact force in X direction for high speed impact on circular pier .......................44

5-8 Impact force in X direction for low speed impact on rectangular pier ...................45

5-9 Impact force in X direction for low speed impact on circular pier ........................45

5-10 Impact force in Y direction for high-speed oblique impact ...................................46

5-11 Impact force in Y direction for low speed oblique impact....................................46

5-12 Force-deformation results for high speed impact on rectangular pier.................47

5-13 Force deformation results for high speed impact on circular pier..........................47

5-14 Force-deformation results for low speed impact on rectangular pier..................48

5-15 Force-deformation results for low speed impact on circular pier ..........................48

5-16 Pier displacement in X direction for high speed impact on rectangular pier...........49

5-17 Pier displacement in X direction for low speed impact on rectangular pier ............49









5-18 Pier displacement in X direction for high speed impact on circular pier................50

5-19 Pier displacement in X direction for low speed impact on circular pier ................50

5-20 Pier displacement in Y direction for high-speed oblique impact...........................51

5-21 Pier displacement in Y direction for low speed oblique impact. ..........................51

6-1 Impact force in X direction for high speed head-on impact............................... 54

6-2 Impact force in X direction for high speed oblique impact..................................55

6-3 Impact force in X direction for low speed head-on impact.................................55

6-4 Impact force in X direction for low speed oblique impact....................................56

6-5 Impact force in Y direction for high speed oblique impact..................................56

6-6 Impact force in Y direction for low speed oblique impact....................................57

6-7 Pier displacement in X direction for high speed head-on impact ..........................57

6-8 Pier displacement in X direction for high speed oblique impact ...........................58

6-9 Pier displacement in X direction for low speed head-on impact..............................58

6-10 Pier displacement in X direction for low speed oblique impact ...........................59

6-11 Pier displacement in Y direction for high speed oblique impact ...........................59

6-12 Pier displacement in Y direction for low speed oblique impact. ..........................60

6-13 Vector-resultant force-deformation results for high speed head-on impact.............60

6-14 Vector-resultant force-deformation results for high speed oblique impact..............61

6-15 Vector-resultant force-deformation results for low speed head-on impact.............61

6-16 Vector-resultant force-deformation results for low speed oblique impact ..............62

7-1 AASHTO and finite element loads in X direction ....................................... 64

7-2 AASHTO and finite element loads in Y direction. ...............................................65















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

INFLUENCE OF PIER NONLINEARITY, IMPACT ANGLE, AND COLUMN SHAPE
ON PIER RESPONSE TO BARGE IMPACT LOADING

By

Bibo Zhang

December 2004

Chair: Gary R. Consolazio
Major Department: Civil and Coastal Engineering

Current bridge design specifications for barge impact loading utilize information

such as barge weight, size, and speed, channel geometry, and bridge pier layout to

prescribe equivalent static loads for use in designing substructure components such as

piers. However, parameters such as pier stiffness and pier column geometry are not taken

into consideration. Additionally, due to the limited experimental vessel impact data that

are available and due to the dynamic nature of incidents such as vessel collisions, the

range of applicability of current design specifications is unclear. In this thesis, high

resolution nonlinear dynamic finite element impact simulations are used to quantify

impact loads and pier displacements generated during barge collisions. By conducting

parametric studies involving pier nonlinearity, impact angle, and impact zone geometry

(pier-column cross-sectional geometry), and then subsequently comparing the results to

those computed using current design provisions, the accuracy and range of applicability

of the design provisions are evaluated. The comparison of AASHTO provisions and









simulation results shows that for high energy impacts, peak predicted barge impact forces

are approximately 60% of the equivalent static AASHTO loads. For low energy impacts,

peak dynamic impact forces predicted by simulation can be more than twice the

magnitude of the equivalent static AASHTO loads. However, because the simulation-

predicted loads are transient in nature whereas the AASHTO loads are static, additional

research is needed in order to more accurately compare results from the two methods.














CHAPTER 1
INTRODUCTION

1.1 Overview

Barge transportation in inland waterway channels and sea coasts has the potential

to cause damage to bridges due to accidental impact between barges and bridge

substructures [1-4]. Recently, two impact events caused damage serious enough to

collapse bridges and unfortunately result in the loss of lives as well. To address the

potential for such situations, loads due to vessel impacts must be taken into consideration

in substructure (pier) design using the American Association of State Highway and

Transportation Officials (AASHTO) Highway Bridge Design Specifications [5] or the

AASHTO Guide Specification for Vessel Collision Design for Highway Bridges [1]. In

design practice, the magnitude and point of application of the impact load are specified

in the AASHTO provisions [1]. The focus of this thesis is on the evaluation of whether

the loads specified in the AASHTO provisions [1] are appropriate given the variety of

barge types, pier geometries and impact angles that are possible.

This goal may be approached in several ways: analytical methods, experimental

methods, or both. This thesis focuses on the analytical approach: nonlinear finite element

modeling to dynamically simulate barge collisions with bridge piers. Of interest is to

estimate the range of the impact load due to different impact conditions and other

considerations that might affect the peak value of impact load and the impact duration

time. The dynamic analysis code LS-DYNA [6] was employed for all impact simulations

presented in this thesis.









1.2 Background of AASHTO Guide Specification

The AASHTO Guide Specification For Vessel Collision Design [1] covers the

following topics:

Part 1: General provision (ship and barge impact force and crush depth)

Part 2: Design vessel selection

Part 3: Bridge protection system design

Part 4: Bridge protection planning

Part 1 is directly related to the goal of this thesis: checking the sufficiency of the

design barge impact forces specified by AASHTO. Therefore, only Part 1 is discussed in

this section.

The method to determine impact force due to barge collision of bridges in

AASHTO is based on research conducted by Meir-Domberg in West Germany in 1983

[1]. Very little research has been presented in the literature with respect to barge impact

forces. The experimental and theoretical studies performed by Meir-Dornberg were used

to study the collision force and the deformation when barges collide with lock entrance

structures and with bridge piers. Meir-Dornberg's investigation also studied the direction

and height of climb of the barge upon bank slopes and walls due to skewed impacts and

groundings along the sides of the waterway.

Meir-Dornberg's study included dynamic loading with a pendulum hammer on

three barge partial section models in scale 1:4.5; static loading on one barge partial

section model in scale 1:6; and numerical computations. The results show that no

significant difference was found between the static and dynamic forces measured and that

impact force and barge bow damage depth can be expressed in a bilinear curve as shown









in Figure 1-1. The study further proposed that barge bow damage depth can be expressed

as a function of barge mass and initial speed.



3000-


2500-

7 2000-


1500-


1000


500-



0 2 4 6 8 10 12
aB (feet)
Figure 1-1. Relation between impact force and barge damage depth according to Meir-
Dornberg's Research (after AASHTO [1])

AASHTO adopted the results of Meir-Dornberg's study with a modification factor

to account for effect of varying barge widths. In Meir-Domberg's research, only

European barges with a bow width of 37.4 ft were considered, which compares relatively

closely with the jumbo hopper barge bow width of 35.0 ft. The jumbo hopper barge is the

most frequent barge size utilizing the U.S. inland waterway system. The width

modification factor adopted by AASHTO is intended to permit application of the design

provisions to barges with different bow widths. Impact load is then defined as an

equivalent static force that is computed based on impact energy and barge characteristics.

A detailed description of the calculation of the equivalent static force according to

AASHTO is included in Chapter 2 of this thesis.









1.3 Objective

The finite element based analysis method described in this thesis is part of a project

funded by FDOT [2] to study the uncertainties in the basis of the barge impact provisions

of the AASHTO. The project consists of a combination of analytical modeling and full-

scale impact testing of the St. George Island Causeway Bridge. The results from this

thesis provide analytically based estimations of impact forces and barge damage levels,

and may be used for comparison to results from the full-scale impact tests.

The structure of the remainder of this thesis is as follows:

Chapter 2 explains the AASHTO design method for computing impact force and

bow damage depth. Chapter 3 describes nonlinear finite element modeling of the impact

test barge and piers of the St. George Island Causeway Bridge. Chapter 4 investigates the

effect of non-linearity of pier material on impact force and barge damage depth by

comparing pier behavior predicted by linear and nonlinear material models. Chapter 5

examines the effect of impact surface geometry on impact force and dynamic pier

behavior. Two types of geometry are considered: rectangular and circular pier cross

sections. Chapter 6 examines the effect of impact angle on impact force and pier

behavior. Head-on impacts and 45 degree oblique impacts are investigated for both

rectangular and circular piers. Comparisons between finite element impact simulations

results and the AASHTO provisions are presented in Chapter 7. Finally, Chapter 8

summarizes results from the preceding chapters and offers conclusions.













CHAPTER 2
AASHTO BARGE AND BRIDGE COLLISION SPECIFICATION

As stated in the previous chapter, the AASHTO provisions concerning barge and

bridge collision are based on the Meir-Domberg study [1]. The barge collision impact

force associated with a head-on collision is determined by the following procedure given

by AASHTO:

For a < 0.34 ft.,

P = 4112aBRB (kips) (2.1)

For aB > 0.34 ft.,

PB = (1349 +11 l0a)RB (kips) (2.2)

For above equations, aB and RB are expressed as

a + KE 1/2 1l10.2) (2.3)
B = 1 5672-J \RB)

RB = B /35 (2.4)

KE CHW(V)2 (2.5)
29.2

in whichPB is impact force (kip); aB is barge bow damage depth (ft); RB is barge width

modification factor; BB is barge width (ft); KE is kinetic energy of a moving barge (kip-

ft.); W is barge dead weight tonnage tonness); V is barge impact speed (ft/sec); CH

represents the hydrodynamic mass coefficient.









The hydrodynamic mass coefficient CH accounts for the mass of water

surrounding and moving with the barge so that the inertia force from this mass of water

needs to be added to the total mass of barge. CH varies depending on many factors such

as water depth, under-keel clearance, distance to obstacles, shape of the barge, barge

speed, currents, position of the barge, direction of barge travel, stiffness of bridge and

fender system, and the cleanliness of the barge's hull underwater. For a barge moving in

a straight-line motion, the following values of CH may be used, unless determined

otherwise by accepted analysis procedures:

CH = 1.05 for large under-keel clearances ( > 0.Sdraft)

CH = 1.25 for small under-keel clearances ( <0.5draft)

The expression of vessel kinetic energy comes from general expression of kinetic

energy of a moving object:

mV2 WV2 (2.6)
KE- = =
2 2g

where m is the mass of the barge; g is the acceleration of gravity; W is the barge dead

weight tonnage; V is the barge impact speed. Expressing KE in kip-ft., W in tonnes (1

tonne = 1.102 ton = 2.205 kips), V in ft/sec, g = 32.2 ft/sec2, and including the

hydrodynamic mass coefficient, CH Equation 2.6 results in the AASHTO equation:

S2.205CH WV2 CHWVT2 (2.7)
A-c = ----- = ---
2-32.2 29.2

The impact force calculation described above is for head-on impact conditions. The

AASHTO provisions specify that for substructure design, the impact force shall be

applied as a static force on the substructure in a direction parallel to the alignment of the









centerline of the navigable channel. In addition, a separate load condition must also be

considered in which fifty percent of the load computed as described above shall be

applied to the substructure in a direction perpendicular to the navigation channel. These

transverse and longitudinal impact forces shall not be taken to act simultaneously.

Commentary given in the AASHTO provisions also suggests the following

equation to calculate impact energy due to an oblique impact. Though this equation is not

a requirement, it provides a useful means of computing the collision energy to be

absorbed either by the barge or the bridge.

E = *KE (2.8)

Values of r are shown in Figure 2-1 as a function of the impact angle (a ) and

coefficient of friction (/u) based on research by Woisin, Saul and Svensson [7]. This

method is from a theoretical derivation of energy dissipation of ship kinetic motion, and

assumes that the ship bow width is smaller than the impact contact surface. Thus

"sliding" between the ship bow and the pier contact surface is possible, the friction force

can be derived based on coefficient of friction, and the change of impact energy can be

derived.

Though this method provides a very useful way to find the energy to be dissipated

during an oblique impact of a barge with a pier, it is not applicable to the oblique impact

simulations included in the thesis because the barge bow is much larger than pier width,

and impact takes place at center zone of barge bow, so pier "cuts" into the bow during

impact, thus "sliding" between the barge and the pier is not likely to happen. However,

for cases when impact doesn't occur at center zone of barge bow, and barge bow covers










slide along the pier surface, this method may provide an alternative means to calculate

kinetic energy to be dissipated during the impact.


1.0





0.6


absorbed collision energy
initial ship's energy


Coefficient of Friction (L)


Steel steel
Steel concrete
Steel wood


- 0.15
- 0.35
- 0.65


Figure 2-1. Collision energy to be absorbed in relation with collision angle and the
coefficient of friction (after AASHTO [1])


I 0 5 / 7 9







15" 30' 45' 60' 75' 91














CHAPTER 3
FINITE ELEMENT BARGE IMPACT SIMULATION

3.1 Introduction

Nonlinearity in structural behavior can take two forms: material nonlinearity and

geometric nonlinearity. When the stiffness of a structure changes with respect to load

induced strain, material nonlinearity takes place. When displacements in a structure

become so large that equilibrium must be satisfied in the deformed configuration, then

geometric nonlinearity has occurred [8].

For modeling of structural nonlinearity, both material nonlinearity and geometric

nonlinearity may be taken into account. For the finite element code LS-DYNA [6],

material nonlinearity can be accounted for by defining a piecewise linear stress-strain

relationship or by defining the parameters of an elastic, perfectly plastic material model.

Geometric nonlinearity is always included in LS-DYNA when using beam elements,

shell elements and brick elements for structural modeling. Geometric nonlinearity is

included in the element formulation for beam element. For shell element and brick

element, when mesh is refined enough, geometric nonlinearity is also included in element

internal forces.

Dynamic simulation of barge impacts with bridge piers involves generating two

separate models: barge and pier/soil. The barge is made of steel plates, channel beams

and angle beams. Non-linearity in these elements can be approached by modeling the

steel plate and channel beams using shell elements and a corresponding nonlinear stress-

strain model. However in nonlinear pier modeling, the concrete pier cap and pier columns









are heavily reinforced with steel bars. During impact, it is possible for the steel bars to

yield at certain locations and form plastic hinges in the reinforced concrete elements.

Nonlinear material modeling may be used to study this type of inelastic response and

investigate the locations at which plastic hinges form during impact.

3.2 Background Study

Many researchers have published papers on nonlinear analysis of bridges, bridge

substructures [9,10,11], and other types of reinforced concrete structures. Researchers

focusing on the behavior of high-strength reinforced concrete columns subjected to blast

loading have used solid elements to model concrete and beam elements to model the

reinforcement [9]. The Winfrith concrete material model available in LS-DYNA was

adopted by Ngo et al. in modeling the concrete. This approach enables the generation of

information such as crack locations, directions, and width. The solid elements used were

20 mm in each dimension for both concrete and reinforcement. For unconfined concrete,

the Hognestad [12] stress-strain curve was used; for confined concrete, modified Scott's

model [9] was employed in the modeling to include confined concrete and to incorporate

the effect of relatively high strain rate [9]. The concrete column was subjected to a blast

load that had a time duration of approximately 1.3 milliseconds.

Researchers studying bridge behavior under seismic loading developed a global

nonlinear model of the San Diego-Coronado Bay Bridge. Figure 3-1 shows the global

nonlinear model, developed by the California Department of Transportation (Caltrans).

The model was analyzed using the commercially available finite element code ADINA

[13]. San Diego-Coronado Bay Bridge is 1.6 miles long and extends across San Diego

Bay. The model included the entire 1.6-mile long bridge (see Figure 3-1). Modeling

included two steps: local modeling and global modeling. An example of local modeling is









that the detailed finite-element analyses of three typical bridge piers were performed

using experimentally-verified structural models and concrete material models to predict

stiffness, damage patterns and ultimate capacity of the pier. The finite element model of

an individual bridge pier is shown in Figure 3-2. Data were then used to idealize the pier

column stiffness and plastic-hinge behavior in the global-model piers. Pier modeling in

the global bridge model is shown in Figure 3-3. Nonlinearities ultimately included in the

global model were "global large displacements (primarily to capture P-A effects in the

towers), contact between spans at the expansion joints and at the abutment wall,

nonlinear-plastic behavior of isolation bearings, post-yield behavior of pier column

plastic hinges, and nonlinear overturning rotation of the pile cap" [10].


Figure 3-1. Global modeling of San-Diego Coronado Bay Bridge (after Dameron [10])














Finte Elerrnt Mesh


Pier Column


Pile Cap


Figure 3-2. Pier model used for local modeling (after Dameron [10])







eom, wrt No=na1tlly
(P-A Eftect) in all tnnit ouP


looleon ttfne;:
or ylklbng bearngs
worth fricttlon

EILasttc
Nlhsnt C N Suprrunrho T\pkcIl Hinge
Nonlnea. Coumn Hinge t ld lt e. (hanger and shear tab
n rot show*)


--- Nonlnar Column Hrtna
(M4 behavior coupled to aximf force)


Ground Node
(point o1 dsploaement
history input application)


Figure 3-3. Global pier modeling for seismic retrofit analysis (after Dameron [10])


Typical Tower


F.CV1 O









Developers of the commercially available pier analysis software FB-Pier [11], use

three-dimensional nonlinear discrete elements to model pier columns, pier cap, and piles.

The discrete elements (see Figure 3-4) use rigid link sections connected by nonlinear

springs [11]. The behavior of the springs is derived from the exact stress-strain behavior

of the steel and concrete in the member cross-section. Geometric nonlinearity is

accounted for by using P-A moments (moments of the axial force times the displacement

of one end of an element to the other ). Since the piles are subdivided into multiple

elements, the P-6 moments (moments of axial force times internal displacements within

members due to bending) are also taken into account.

I-~h--^-h--h----h4l-1

rk*,R -r vB



V AcdfllaUl a.
L --_-______i- ,






Figure 3-4. Mechanical model for discrete element (after Hoit [11])


Figure 3-4 shows the mechanical model of the discrete element. The model consists

of four main parts. There are two segments in the center that can both twist torsionally

and extend axially with respect to each other. Each of these center segments is connected

by a universal joint to a rigid end segment. The universal joints permit bending at the

quarter points about two flexural axes by stretching and compressing of the appropriate

springs. The center blocks are aligned and constrained such that springs aligned with the









axis of the element provide torsional and axial stiffness. Discrete angle changes at the

joints correspond to bending moments and a discrete axial shortening corresponds to the

axial thrust [11].

3.3 Pier Model Description

Consolazio et al. [2] discussed dynamic impact simulations of jumbo open hoppers

barge with piers of the St. George Island Causeway Bridge. In their report, the pier is

modeled with a combination of solid elements to model pier column, pier cap and pile

cap, beam elements to model steel piles and discrete non-linear spring elements to model

nonlinear soil behavior. The solid elements are used to accurately describe the

distribution of mass in the pier.

In the present study, similar approaches to modeling have been used for several

components of the simulation models developed. A linear elastic material with density,

stiffness and Poison's ratio corresponding to concrete is assigned to the solid elements.

Material properties for the beam elements are described in the following paragraph.

Nonlinear spring properties (for both lateral springs and axial springs) derived using the

FB-Pier software [11] are assigned to the soil springs.

In this thesis, beam elements are employed to model pier columns and pier caps,

while solid elements are used to model pile caps. Both pier columns and pier caps are

heavily reinforced concrete elements consisting of numerous steel bars compositely

embedded within a concrete matrix. When a pier column or pier cap yields during

dynamic impact, plastic hinges may form in the pier column or pier cap that may affect

impact force history and structural pier response. Using beam elements to model pier

columns and the pier caps permits the use of a nonlinear material model capable to

representing plastic hinge formation.









LS-DYNA includes a nonlinear material called *MAT RESULTANT PLASTICITY,

which is an elastic, perfectly plastic model. Assigning this material model to beam

elements requires specification of mass density, Young's modulus, Poison's ratio, yield

stress, cross sectional properties (including area, moment of inertia with respect to strong

axis, moment of inertia with respect to weak axis, torsional moment of inertia and shear

deformation area). Based on these properties, LS-DYNA assumes a rectangular cross

section [6], and internally calculates the normal stress distribution on the cross section.

Normal stress from axial deformation, bending of strong axis and bending of weak axis

are combined and checked for the possibility of plastic flow. By checking for plastic flow

at each time step, element stiffnesses may be updated accordingly. Work hardening is not

available in this material model.

For nonlinear modeling of pier, the steel piles are also modeled by this material

type. For HP 14x73 steel piles, a test model was set up. Comparison of independently

calculated theoretical results and LS-DYNA results show that error percentages for

strong axis plastic moment capacities are less than 18% and error percentages for weak

axis bending are less than 8%. Analysis cases considered in the thesis include both head-

on impacts and oblique impacts. For head-on impact, weak axis bending dominates; for

oblique impact, plastic bending moment about both axes will occur. Therefore, the pile

cross section properties are adjusted to produce the same error percentage in both strong

axis and weak axis bending. Adjusted pile properties are applied to both head-on impact

and oblique impact to keep comparison conditions the same when results from the two

conditions are compared. To keep the pile bending stiffness unaltered, only the cross-









sectional area is changed. Table 3-1 shows the original and adjusted cross-sectional

properties.

Table 3-1. Comparison of ori inal and adjusted section properties

Case Original Adjusted

Trial Value of Area
(2) 1.38 x 10-2 1.25 x 10-2
(m2)
Plastic Moment
(Strong Axis Bending) 5.860 x 105 4.183 x 105
(N*m)
Plastic Moment
(Weak Axis Bending) 3.112 x 105 2.502 x 105
(N*m)
Error Percentage 0 95
(Area)

Error Percentage
(Plastic Moment) 18.1 % 12.9 %
(Strong Axis)
Error Percentage
(Plastic Moment) 7.9 % 12.7 %
(Weak Axis)

An alternative to modeling the effect of reinforcement on bending moment capacity

involves the use of moment curvature relationships. However LS-DYNA does not

support direct specification of moment-curvature for beam elements. Results from tests

making use of material models *MATCONCRETEBEAM, *MATPIECEWISELINEAR_-

PLASTICITY, and *MAT_FORCE_LIMITED showed that these models do not represent

reinforced beam bending moment capacity to a satisfying extent. Moment-curvature

relationships may be sufficiently approximated using the *MAT_RESULTANT_PLASTICITY

model. Usually, a moment-curvature relationship is a curve described by a series of

points. The shape of the curve is similar to a bilinear curve. A stress strain curve for an

elastic, perfectly plastic material is also a bilinear curve. Figure 3-5 shows similarities









between a simplified moment-curvature curve and a stress-strain curve for an elastic,

perfectly plastic material.

M CyG







El E






()y 'y

a) moment-curvature b) stress-strain

Figure 3-5. Bilinear expression of moment-curvature and stress-strain curve

For an arbitrary cross section,

Mc
M- (3-1)
I


E = (3-2)
Ig c

Material parameters for elastic, perfectly plastic material are: young's modulus and

yield stress. Young's modulus can be derived from the bilinear moment-curvature curve

based on Equation 3-2, however yield stress is unknown due to the fact that LS-DYNA

assumes rectangular cross section and internally calculate the dimension (width and

height) of the rectangular cross section based on input cross section properties. Thus a

yield stress is assumed first and input into LS-DYNA. Based on output yield moment

from LS-DYNA and Equation 3-1, c value (dimension of rectangular cross section) is

calculated. This correct c value (dimension of rectangular cross section) is plugged into









Equation 3-1 using the known yield moment to get the corresponding yield stress. This

yielding stress is used for data input for elastic, perfectly plastic material type.

To simplify the moment-curvature relationships used, the following rule is used for

both pier columns and pier caps. The yield moment (My) for the bilinear curve is equal to

half the summation of yielding moment My0 and ultimate moment Mu from the original

moment-curvature relationship. Initial stiffness for the simplified bilinear moment-

curvature relationship stays the same as that of the original moment-curvature

relationship (see Figure 3-6). Data used in the LS-DYNA simulations for the pier

columns and pier cap are given in Table 3-2.


)M
original Moment-Curvature
Ivi o ... .... ..............


I ilinear Moment-Curvature

Mo










Figure 3-6. Moment-curvature derivation

Table 3-2. Input data in LS-DYNA simulations
Pier E (N/ m2) Oy (N/ m2)

Pier Column 2.486 x 1010 4.90 x 106

Pier Cap 2.486 x 1010 6.10x 106

Moment-curvature relationships for the pier column and the pier cap are developed

based on steel reinforcement layout and material properties. Tables 3-3 and 3-4 show the









error percentage of a test model for both strong axis bending and weak axis bending, for

the pier cap and the pier column respectively. The test model is a 480-meter simply

supported beam with a concentrated load at mid-span. Plastic moment and displacement

at mid-span calculated by LS-DYNA are compared with those from theoretical

calculations.

Table 3-3. Comparison of plastic moment and displacement using properties of pier cap
r C LS-DYNA Theoretical Error
Results Value Percentage
Plastic Moment
10.0 x 106 12.0 x 106 17%
Strong Axis (N*m)
Displacement at Mid-span 6.2 6.0 3%
at Yielding (m)
Plastic Moment
6.3 x 106 5.3 x 106 18%
Weak Axis (N*m)
Displacement at Mid-span 9.0 8.0 11
9.0 8.0 11%
at Yielding (m)


Table 3-4. Comparison of plastic moment and displacement using properties of pier
column
Pr C n LS-DYNA Theoretical Error
Pier Column
Results Value Percentage
Plastic Moment
SM 9.9 x 106 10.6 x 106 6%
Strong Axis (N*m)
Displacement at Mid-span 5.2 5.0 4
5.2 5.0 4%
at Yielding (m)
Plastic Moment
SM 8.8 x 106 9.1 x 106 2%
Weak Axis (N*m)
Displacement at Mid-span 5. 5.9 6%
at Yielding (m)

3.4 Barge Finite Element Model

The impact vessel of interest in this thesis is a construction barge, 151.5 ft. in

length and 50 ft. in width. Figure 3-7 through 3-11 describe the dimensions and the

internal structure of the construction barge.











Transverse Frame
I I


81'-6" k70'-0"
151'-6"


Figure 3-7. Main deck plan of the construction barge


Transverse Frame


Serrated Channel
/


............ ........ .. .... .............
S.----.-----.------- --... --------------- -- -... ... . ----- .--
i......... ...... .... .. ......... ........ ......... ....... ..... ..... ...... ...

............................ .
'~'f~~~~\~~~~~v~~~~^~~~~~v~~~~^~~~~^~~~"\ "^~ --i-U-- --- p-- ----j----r-i--- T -j- *


81'-6"


70'-0"


Figure 3-8. Outboard profile of the construction barge


Transverse Frame
\


C Channel
I


L Beam


35'-0"


35'-0"


Figure 3-9. Typical longitudinal truss of the construction barge


L 4 x 3 x 1/4 C 8 x 13.75 Top & Bottom









L 3.5 x 3.5 x 5/16 typ.

Figure 3-10. Typical transverse frame (cross bracing section) of the construction barge


Barge Bow


00". _/ / *s/ ,_:_/ L LL ^ ^ ^ i























35'-0"


Figure 3-11. Dimension and detail of barge bow of the construction barge

The construction barge is made up of steel plates, standard steel angles (L-

sections), channels (C-sections) and serrated channel beams. The bow portion of the

barge is raked. Twenty-two internal longitudinal trusses span the length of the barge and

nineteen trusses span transversely across the width of the barge. The twenty-two

longitudinal trusses are made up of steel angles, while the nineteen transverse trusses are

made up of steel channels. Serrated channel beams are used at the side walls to provide

stiffness to the wall plates.

Reference [2] gives a very detailed description of modeling of an open hopper

barge, in which the barge is divided into three zones and consequently treated in three

different ways with respect to mesh resolution. The three zones are called zone-1, zone-2

and zone-3 respectively. For modeling of the construction barge that is of interest here,

the same concept was applied. The construction barge was divided into three longitudinal

zones, as is illustrated in Figure 3-12.










116'-0" 19'-0" 15'6"

-----.-----------------t-------C-*- ----4------------- .e-2

[ ...:. i ... j. .. ..... .... i ... ... .... ...... ..................- .... .... ...... ........" on
*-t--- -:-----t---- i-----t----i----^- ----:-----i----^-- ---f-----:-- l -----I----:--- 1---1----i----^--- l ---- ^--- j^----I-
,-r---:- -* - ------.;-----:-----.;-----:----->-----:----.---- : ---.;---.-r---.-r---;.-- -1-one -i.
.........i....j.....i....j..........n... ........ ....... Zo e-2
......... .... ... .... Zone-2

Zone-3

Figure 3-12. Layout of barge divisions

For centerline, head-on impacts, the central portion of barge zone-1 (see Figure 3-

13) is where most plastic deformation occurs and impact energy is dissipated. This area is

thus the critical part in modeling dynamic collisions of barges with piers. Since all

simulations described in this thesis are for centerline impacts, internal structures in the

central area of zone-1 are modeled with a refined mesh of shell elements to capture large

deformations, material failure, and thus to dissipate energy. Internal trusses in the port

and starboard off-center portion of the bow are modeled using lower-resolution beam

elements since only small deformations are expected and material failure is not likely to

occur during centerline impacts of the barge.

Unlike zone-1, structures in zone-2 and -3 construction barge will sustain relatively

minor deformations that will cause primarily elastic stress distributions in the outer

plates, inner trusses and frame structures. Material failure is not expected in these zones.

Zone-2 is modeled using shell elements for outer plate and beam elements for internal

trusses and frames. Compared to the size of the shell elements of zone-1, those in zone-2

are considerably larger in size. Use of relatively simple beam elements reduces the

computing time required to perform impact analysis.












Zone-i
























Figure 3-13. Meshing of internal structure of zone-1
50'-0"In zone-3, the aft portion of the construction barge functions to carry the cargo
Port Zone










weight of the barge and is not expected to undergo significant deformation during












dynamic impact. Thus the barge components in this zone are modeled with solid
elements. Density of the solid elements was selected to achieve target payload conditions.
Central Zone
(High Resolution)




91-4.5"







StAll shell elements in the model oae assigned a piecewise linear plastic material
(Lower Resolution)


Figure 3-13. Meshing of internal structure of zone-1







model for A36 steel. A detailed description of the constis material type is provided in carry the cargo
weight of the barge and is not expected to undergo significant deformation during

dynamic impact. Thus the barge components in this zone are modeled with solid

elements. Density of the solid elements was selected to achieve target payload conditions.

All shell elements in the model are assigned a piecewise linear plastic material

model for A36 steel. A detailed description of this material type is provided in the

research report by Consolazio et al.[2]. Solid elements are assigned an elastic material

property since no plastic deformation in zone-3 is expected. Mass density of the solid

element represents the fully loaded payload condition based on a total barge plus payload

weight of 1900 tons as is described in the AASHTO provisions.









Beam elements in the barge model are assigned elastic, perfectly plastic material

type. LS-DYNA material model number 28, *MAT_RESULTANT_PLASTICITY is employed

to do so. For this material type, the required input of cross sectional properties are: area,

moment of inertia with respect to the strong axis, moment of inertia with respect to the

weak axis, torsional moment of inertia, shear deformation area. Though LS-DYNA

assumes a rectangular cross section and internally calculates cross sectional dimensions

based on area, flexural moment of inertia, and torsional moment of inertia, a test model of

a L 4x3x1/4 angle prepared by the author showed that the plastic moment predicted by

LS-DYNA can be as accurate as 99% for strong axis bending and 95% for weak axis

bending. A test model was developed and the plastic moment capacity for both strong

axis bending and weak axis bending for a non-symmetric angle section were computed.

For other types of beams such as channels and wide flange members, plastic moment

capacity can be derived from cross section properties available in the AISC Manual of

Steel Construction [14]. Channels and wide flange beams showed error percentages

varying up to 18% when the plastic moment was computed using the *MAT_RESULTANT_-

PLASTICITY material in LS-DYNA.

Contact definition *CONTACT_AUTOMATIC_SINGLE_SURFACE (self contact) is

assigned to the barge bow to capture the fact that under impact loading, the internal

members within the barge bow may not only contact each other, but also fold over on

themselves due to buckling. During an impact simulation, LS-DYNA checks for the

possibility for elements contacting each other within a defined contact area, thus a large

self contact area will increase computing time drastically. To minimuze computational

time, the area in the barge bow where contact is likely to occur is carefully chosen.









Table 3-5. General modeling features of the testing barge
Model Features
8-node brick elements 1842
4-node shell elements 81,040
2-node beam elements 8,324
2-node Discrete Spring elements 119
1-node point mass elements 119
Model Dimensions
Length 151.5 Ft
Width 50.0 Ft
Depth 12.5 Ft
Contact Definitions
CONTACT AUTOMATIC SINGLE SURFACE
CONTACT AUTOMATIC NODES TO SURFACE

Table 3-6 General modeling features of the jumbo hopper barge
Model Features
8-node brick elements 234
4-node shell elements 24,087
2-node beam elements 2,264
2-node Discrete Spring elements 28
1-node point mass elements 28
Model Dimensions
Length 195 Ft
Width 35 Ft
Depth 12 Ft
Contact Definitions
CONTACT AUTOMATIC SINGLE SURFACE
CONTACT AUTOMATIC NODES TO SURFACE
CONTACT TIED NODES TO SURFACE

Welds are used in the barge to connect the head log plate, top plate and the bottom

plate. These welds are modeled by the *CONSTRAINED_SPOTWELD constraint type.

Computationally, the spotwelds consist of rigid links between nodes of the head log, top

plate and bottom plate. Detailed descriptions of self contact definition and weld modeling

are given in the research report developed by Consolazio et al. [2].

Connection between zone-1, zone-2, and zone-3 are made with nodal rigid body

constraints. For the connection of zone-1 to zone-2, the transition between internal trusses

modeled by shell elements and internal trusses modeled by beam elements is approached

by using rigid links to connect nodes from shell element and beam element to transfer









internal section forces in a distributed manner. For the connection of zone-2 to zone-3,

nodal rigid bodies are defined to connect small elements in zone-2 with those in zone-3.








Buoyancy Spring with Zero Gap Buoyancy Spring with Non-zero Gap

Figure 3-14. Buoyancy spring distribution along the barge

A pre-compressed buoyancy spring model is applied to the barge to simulate

buoyancy effects. The buoyancy spring stiffness was formulated based on tributary area

and draft depth of each spring and a gap was added to the spring formulation. Since

different positions on the barge hull have different draft depths, the buoyancy spring

formulation varies with longitudinal location. Gaps between the water level and barge

hull are determined from the geometry of the bottom surface of the barge (see Figure 3-
14).. The pre-compression of buoyancy spring is calculated using Mathcad worksheet.













The comparison of general modeling features of construction barge and open hopper
.... .... ..... ... . .. .... i ... .. ... .- .... .. .. .... ... .1. :-
i. .... I .. ..... .... .E .... .- .... ..... .... i ... .... i- .. 4. .. .. ... .... .- .... ... -













barge i.s provided in Table 3-5 and 3-6.














3.5 Contact Surface Modeling
BuoyaWhen pier columns and pier Gaps are modeled using b eam elements, contact
Figure 3-14. Buoyancy spring distribution along the barge













surfA pre-compressed buoyancy sp modeled is applied to the pier column to enable contact desimulatection

buoyancy effeimpacts.e Figure 3-15).buoyancy spro in Figure 3-15, since shear wall is formulated based on tributary area
and draft depth of each spring and a gap was added to the spring formulation. Since

different positions on the barge hull have different draft depths, the buoyancy spring











formulation vats, ries with longitudinal location. Gaps between of she wall, pier level and barge
hull are determined from the geometry of the bottom surface of the barge (see Figure 3-










14). In this re-ompressionly very small deformationg is calculd likely occur due to thickness ofng Mathcad worksheet.

he compare wall. So it is treated as rigid body. Modeling features of construction barge and open hopper
barge is provided in Table 3-5 and 3-6.

3.5 Contact Surface Modeling

When pier columns and pier caps are modeled using beam elements, contact

surfaces need to be modeled and added to the pier column to enable contact detection

during impact (see Figure 3-15). Also in Figure 3-15, since shear wall is modeled by

beam elements, rigid body is defined at connection of shear wall, pier column and pile

cap. In this region, only very small deformation could likely occur due to thickness of

shear wall. So it is treated as rigid body. Modeling of contact surface needs to be done










carefully since the contact surface may add extra stiffness to the pier column, thus

changing the original stiffness of the pier and affect the simulation results.

pier cap


Figure 3-15. Pier and contact surface layout

pier column


surface


Figure 3-16. Rigid links between pier column and contact surface









pier column





contact surface

Impact force







Figure 3-17. Exaggerated deformation of pier column and contact surface during impact

To make sure that contact surface will not add extra stiffness to the pier, it is

divided into separate elements. Each separate element is assigned rigid material

properties and is connected to the pier column through rigid links (see Figure 3-16).

Under bending of the pier column, these elements will act independently, and transfer the

impact force to the pier column beam elements. Figure 3-17 shows an exaggerated

depiction of deformation of the contact surface during impact. Though friction on the

contact surface may add extra bending moment to the pier column, studies shows that

when the element size of pier column is set to approximately 6 inches, the extra bending

moment transmitted to the pier column is less than 5% compared to the primary bending

moment sustained during impact for the most severe cases considered here (6 knots, full

load).

Though the contact surface in a real pier is made of concrete, use of a rigid material

model is verified by comparing the impact force versus crush depth relationships from

static barge crush analysis. Figure 3-18 shows a comparison of impact force versus crush

depth relationships computed using rigid contact surfaces and concrete contact surfaces.










Though the impact forces differ slightly after the crush depth exceeds 24 inches, overall,

the curves are in good agreement.

Crush depth (m)
0 0.5 1 1.5


rigid material -- 1400
elastic material ...............
1200







400
3 ------------------------ ------------


400

1 200



10 20 30 40 50 60
Crush depth (in)
Figure 3-18. Comparison of impact force versus crush depth for rigid and concrete
contact models

The concrete cap seal is not modeled explicitly but its mass is added to that of the

pile cap to account for increased inertial resistance. Soil springs are assigned spring

stiffnesses derived from the FB-Pier program, and nodal constraints are added to the soil

springs. Detailed descriptions of soil springs and constraints of nodes are available in the

research report by Consolazio et al. [2].

A typical impact simulation model in which a pier model has been combined with a

barge model is shown in Figure 3-19. As the figure illustrates, resultant beam elements

are used to model the pier columns and cap and the contact surface representation

described above is used to detect contact between the barge and the pier.











.v. Ti


Figure 3-19. Overview of barge and pier model for dynamic simulation


ifii'~














CHAPTER 4
NON-LINEAR PIER BEHAVIOR DURING BARGE IMPACT

Non-linear pier behavior, barge deformation and energy dissipation are several of

the issues that are relevant when considering barge-pier collisions. The answer to

questions of how much the non-linearity in modeling affects these considerations, if non-

linearity causes fundamental changes to pier behavior helps understand barge and pier

behavior during impact, thus when impact cases are considered, whether non-linearity

should be included in modeling or not will be justified and thus facilitate the dynamic

simulation modeling procedure.

4.1 Case Study

In the barge and the pier impacts modeled here, the barge is selected to have fully

loaded weight of 1900 tons (per the AASHTO provisions). This loaded weight is chosen

to be the same as that of fully loaded open hopper barge to enable comparison with

results of dynamic simulations previously conducted using a hopper barge finite element

model. The rectangular columns of the pier are used to define the contact surface. Two

barge impact velocities are considered: 6 knots and 1 knot. Barge with a 6 knot speed and

fully loaded condition represents the most critical impact scenario and thus the most

severe nonlinear pier behavior. Barge impact with a 1 knot speed and fully loaded

condition represents the scenario that only a very small region of pier shows non-

linearity. These two cases cover a large range of impact scenarios, thus results from these

two cases can reasonably cover the effect of non-linearity. All cases included in this

chapter are listed in Table 4-1.









Table 4-1. Dynamic simulation cases
Contact Impact Material Loading
Case Speed
Surface Angle Property Condition

A Rectangular 6 knot Head-on Linear Full

B Rectangular 6 knot Head-on Nonlinear Full

C Rectangular 1 knot Head-on Linear Full

D Rectangular 1 knot Head-on Nonlinear Full


4.2 Analysis Results

For both severe impact case and non-severe impact case, Figures 4-1 through 4-6

show that using nonlinear pier material and using linear pier material generate the same

impact force peak value and almost the same impact duration time since after the internal

structure in the barge bow yields, it cannot exert a larger impact force. Also, for both

non-severe impact condition and severe impact condition, approximately the same

amount of energy is dissipated (area under barge impact force vs. crush depth curve)

using nonlinear pier material and linear pier material respectively.

It is shown that for both severe impact case and non-severe impact case, barge

crush depth after impact for linear pier is always larger than barge crush depth after

impact for nonlinear pier (Figure 4-3, Figure 4-4). During impact, for the severe impact

case, all steel piles yield; even for the non-severe impact case, part of the steel piles yield

during impact. Yielding of steel piles prevents the pier structure from generating

increased resistance to the barge, thus the pier structure cannot create larger crush depth

in barge bow. Also yielding of piles generates residual deformation of pier structure after

impact as shown in Figure 4-5. The residual deformation can be as large as 10-12 at the

point for measurement (the impact point). The pier column and pier cap do not yield









during impact even for the most severe impact case. For the barge with 1 knot impact

speed and fully loaded condition, the pier residual deformation is almost negligible.

Plots of pier column bending moment shows that the peak value of the pier column

bending in the impact zone of the pier exceeds the cracking moment of pier column cross

section. Since the moment-curvature is simplified as a bilinear curve with initial stiffness

the same as that of the un-cracked cross section, the cracking moment is not reflected in

the bilinear moment-curvature curve.

There is very little difference between pier behavior using linear pier and using

nonlinear pier material for the barge with a 1 knot speed, fully loaded condition. Partially

yielded piles during impact caused very little effect on pier behavior. For this case, the

effect of non-linearity of pier material can be ignored almost completely. For the barge

with 6 knot speed, fully loaded condition, though non-linearity of pier material does have

an effect on impact force history, impact force vs. crush depth relationship, and pier

displacement, the influence is limited.

The results drawn here are based specifically on impact simulations of a barge

impacting a channel pier of the St. George Island Causeway bridge. The piles of this pier

are HP14x73 steel piles. As a result, the characteristics of these piers are quite different

from the concrete piles as are also often employed in bridges. Different pile properties

may have a substantial effect on impact force and pier behavior during impact. Thus

additional work needs to be done for impacts of different pier types to comprehensively

study the effect of pier material nonlinearity on barge impact force and pier behavior.












7


6| 6knot, head on, nonlinear, full load ---- 1400
6knot, head on, linear, full load

1200


1000
4 ....................... .. ....................................................

4- 800





400


1 200




0 0.5 1 1.5 2 2.5
Time (s)


Figure 4-1. Comparison of impact force history for severe impact case

7



6 ............ ... ...... ..... ......... ........... ............... ........knot, head on, nonlinear, full load .............. 00
6 LIknot, head on- nonlinear- full load 1400
Iknot, head on, linear, full load
1200
5

1000






600

2
400

1 200


0 ..... ................. .............. .... 0

0 0.2 0.4 0.6 0.8
Time (s)


Figure 4-2. Comparison of impact force history for non-severe case












Crush Depth (in)

0 10 20 30 40 50


60 70 80 90


1400


1200


1000


800


600


400


200


0 0.5 1 1.5 2
Crush Depth (m)


Figure 4-3. Impact force and crush depth relationship comparison for severe impact case



Crush Depth (in)
0 0.5 1


0 0.01 0.02 0.03
Crush Depth (m)


Figure 4-4. Comparison of impact force crush depth relationship for non-severe case








36



25
0.6

6knot, head-on, nonlinear, full load -
20--
6knot, head-on, linear, full load ---------



15 ................. ..... ................ .. .... 0.4
15 ----------------------------------. ................................... .................................. ..................................................................... 0.4


.oao



0.2
5 ................ ..........

-5








0 0.5 1 1.5 2 2.5
Time (s)


Figure 4-5. Comparison of pier displacement for severe impact case.





4 ------------------------------ -------------------------- ----------------- knot, head on, nonlinear, full load 0.1
Iknot, head on, linear, full load ------ -----



2 0.05


0 .. .. ...... ....... ----------------- ----------------- 0.05 E







-2 ----------- ------- -0.05
-2 --------------------------------- ---------------------------------- ---------------------------------- ----------------------------------0 .1







I I I I
0 0.2 0.4 0.6 0.8 1
Time (s)


Figure 4-6. Comparison of pier displacement for non-severe case.














CHAPTER 5
SIMULATION OF OBLIQUE IMPACT CONDITIONS

Contained within the AASHTO barge impact design provisions are procedures not

only for computing equivalent static design force magnitudes, but also instructions on

how such loads shall be applied to a pier for design purposes. Two fundamental loading

conditions are stipulated: 1) a head-on transverse impact condition, and 2) a reduced-

force longitudinal impact condition. In the head-on impact case, the impact force is

applied "transverse to the substructure in a direction parallel to the alignment of the

centerline of the navigable channel"[1]. In the second loading condition, fifty percent

(50%) of the transverse load is applied to the pier as a longitudinal force (perpendicular

to the navigation channel). The AASHTO provisions further state that the "transverse and

longitudinal impact forces shall not be taken to act simultaneously."

Due to differences in the causes of accidents (weather; mechanical malfunction;

operator error) and differences in vessel, channel, and bridge configurations, barge

collisions with bridge piers rarely involve a precisely a head-on strike. AASHTO's intent

in using two separate loading conditions (load magnitudes and directions), is to attempt to

envelope the structural effects that might occur for a variety of different possible oblique

impacts, i.e. impacts that do not occur in a precisely head-on manner. In this chapter,

numeric simulations are used to study the structural response of piers under oblique

impact conditions so that the adequacy of the AASHTO procedures can be evaluated.









5.1 Effect of Strike Angle on Barge Static Load-Deformation Relationship

Before considering dynamic simulations of oblique impacts, the effects of impact

angle on the static force vs. deformation relationships of typical barges will be

considered. A previously developed open hopper barge model [2] is used to conduct

static crush analyses in which a square pier statically penetrates the center zone of the

barge bow at varying angles. Pier models having widths of 4 ft., 6 ft. and 8 ft. are

statically pushed (at a speed of 10 in./sec.) into the barge bow at angles of 0 degrees, 15

degrees, 30 degrees, and 45 degrees (see Figure 5-2). Each pier is modeled using a linear

elastic material model and frictional effects between the pier and barge are represented

using a static frictional coefficient of 0.5. Figure 5-1 shows the static crush of the pier and

the open hopper barge.

Results from the static crush simulations are presented in Figures 5-2 to Figure 5-4.

The results indicate that head-on conditions (0 degree impact angle) always generate

maximum peak force regardless of pier width (for the range of piers widths considered).

Minimum forces are generated at the maximum angle of incidence, 45 degrees.




-45 degree crush
head on crush

Open hop g-3e pier 0 degree crush
pn hopper barge 15 degree crush
15 degree crush


Figure 5-1. Static crush between pier and open hopper barge











Crush Depth (in)


0 0.1 0.2 0.3 0.4 0.5 0.6
Crush Depth (m)


Figure 5-2. Results for static crush analysis conducting with a 4 ft. wide pier


Crush Depth (in)
10


0 0.1 0.2 0.3 0.4 0.5 0.6
Crush Depth (m)


Figure 5-3. Results for static crush analysis conducting with a 6 ft. wide pier







40


Crush Depth (in)
0 5 10 15 20


static crush 8ft-- 0 deg 1400
6 -..... ..................................... .........static crush 8ft--15 deg .
static crush 8ft--30 deg -- --
static crush8ft--45 deg --x-- 1200


1000


800

I "" ," 1 I "/ -, 00




Sx 200
]i / I I I




0 0.1 0.2 0.3 0.4 0.5 0.6
Crush Depth (m)

Figure 5-4. Results for static crush analysis conducting with a 8 ft. wide pier



5.2 Effect of Strike Angle on Dynamic Loads and Pier Response

Dynamic impact behavior under oblique impact conditions is now studied for two

bounding cases (see Figure 5-5): an impact angle of 0 degrees (head-on impact) and an

angle of 45 degrees (severe oblique impact). Pier columns having both rectangular and

circular cross-sectional shapes are considered. Table 5-1 lists all of the dynamic analysis

cases included this parametric study. Cases A through G make use of a linear material

model for the pier while cases H utilize the nonlinear concrete material model described

earlier in Chapter 3.


























Y
Barge head-on impact motion


-------------- -
Figure 5-5. Layout of barge head-on impact and oblique impact with pier



Figure 5-5. Layout of barge head-on impact and oblique impact with pier


Table 5-1. Dynamic simulation cases
Contact Impact Material Loading
Case Speed
Surface Angle Property Condition

A Rectangular 6 knot Head-on Linear Full

B Rectangular 6 knot 45 degree Linear Full

C Rectangular 1 knot Head-on Linear Full

D Rectangular 1 knot 45 degree Linear Full

E Circular 6 knot Head-on Linear Full

F Circular 6 knot 45 degree Linear Full

G Circular 1 knot Head-on Linear Full

H Circular 1 knot 45 degree Linear Full









5.3 Dynamic Simulation Results

Simulation results for cases A, B, C, D, E, F, G, H (as indicated in Table 5-1) are

presented in Figure 5-6 through Figure 5-21. In each figure, the direction denoted as "X"

corresponds to the axis of the pier (see Figure 5-5) that is parallel (or nearly so) to the

axis of the navigation channel (i.e., perpendicular to the alignment of the bridge

superstructure supported by the pier). The direction denoted as "Y" is parallel to the

direction of traffic movement on the bridge superstructure (roadway). Pier displacements

in the figures are taken at the point of impact. For oblique impacts, figures showing

impact force vs. crush depth relationships are developed using resultant impact forces and

resultant crush depths. Impact force history in X direction are shown in Figure 5-6,

Figure 5-7, Figure 5-8 and Figure 5-9. Impact force history in Y direction are represented

in Figure 5-10, Figure 5-11. Peak value of the impact force histories in Figure 5-6

through 5-11 will be compared to the equivalent static force specified by the AASHTO

vessel impact provisions in Chapter 7. Relationship of impact force and crush depth are

shown in Figure 5-12, Figure 5-13, Figure 5-14 and Figure 5-15. Plots of pier

displacement in X direction and in Y direction are included in Figure 5-16, Figure 5-17,

Figure 5-18, Figure 5-19, Figure 5-20 and Figure 5-21.

Figures 5-6, Figure 5-7, Figure 5-8 and Figure 5-9 indicate that for the impact force

in the direction parallel to the centerline of navigable channel, dynamic simulations with

45 degree impact angle always generate smaller impact force peak value than head-on

impacts, regardless of the geometry of the contact surface. For rectangular pier, impact

force peak values from 45-degree oblique impact simulations are about 50% of those

from head-on impact for both the low-speed impact scenarios and the high-speed impact

scenarios. However for circular pier, the impact force peak values from 45 degree oblique









impact simulations are about 80% of those from head-on impact simulations regardless of

impact speed. Thus increasing impact angle does reduce the impact force peak value in

the X direction. It causes the impact force peak value to reduce to a larger extent for the

rectangular pier than for the circular pier.

Relationship of impact force and crush depth as in Figure 5-12, Figure 5-13, Figure

5-14 and Figure 5-15 show that though low-speed impact scenarios with 45 degree

oblique impact angle always seem to cause larger resultant crush depth in barge bow and

lower resultant impact force peak value than the head-on impact, high-speed impact

scenarios have a different trend. Figure 5-13 indicates that for circular pier of high impact

speed and oblique impact angle, resultant impact force and resultant crush depth

relationship seems to stay the same for both head-on impact and oblique impact. Figure

5-12 indicates that for rectangular pier of high impact speed, oblique impact causes larger

resultant crush depth and smaller resultant impact force peak value than head-on impact.

The above observation seems to be reasonable for the two geometries of contact surface.

For different impact angles, circular pier always has the same geometry; however for the

rectangular pier, the contact area becomes smaller with increasing impact angle, it is the

smallest for 45 degree oblique impact. To dissipate the kinetic energy of the barge, a

smaller contact area definitely brings larger crush depth since the edge of the pier "cuts"

into the barge easily because of less resistance from internal structures of barge bow than

the larger contact area.

Pier impact force divided by the corresponding pier displacement indicates pier

stiffness. Figure 5-6 through 5-21 indicate the similar pier displacement in both X and Y








44



direction and the corresponding similar impact force in both X and Y direction, therefore


show that the pier has similar stiffness in both X and Y direction.




S1400


6knot, head on, linear, full load 1200
5 3 .................... 6knot, 45 deg, linear, full load, X direction ---- -- -

1000

44
800


2 i,. 40
d 3600 2





1 A-200 V
2 ............... .. ...... ..... ........................ ............... .. .... ............. ........................................







0 0
0 0.5 1 1.5 2 2.5
Time (s)


Figure 5-6. Impact force in X direction for high speed impact on rectangular pier




.1400
6 -----------.......................... ...... circular, 6knot, head on, linear, full load --
circular, 6knot, 45 deg, linear, full load, X direction ................
1200


1000

f-4
I + 800


600 00


400


1 ...........................................................-....200
0 00



0 0.5 1 1.5 2 2.5
Time (s)


Figure 5-7. Impact force in X direction for high speed impact on circular pier.











7I I

rectangular, lknot, head on, linear, full load 1400
6 .... ............................ rectangular, lknot, 45 deg, linear, full load, X direction -.-.---

1200
5-

1000
4-


4 -7 -- -- -- I- -- -- -- -- - -- -- -- -- -- -- -- -- -- -- -- -- -- - -- -- -


2 ......... ....... ....... ................. ............ ..... ....... .. ........ ... ................................................. ..................................
800


600


S100

T ... ........... .......... ..
44
; ... 4-+.














4 .. ........... ............................ circular, Iknot, head on, linear, full load .......................





3 ... .........."...".." ........................................................

0 0.5 1
Time (s)


Figure 5-8. Impact force in X direction for low speed impact on rectangular pier.


1000

..4........................... circular, knot, head on, linear, full load ........................
circular, knot, 45 deg, linear, full load, X direction ......+ ......
800


3.5



600
12.5 .......





0 0. 1
1.5......~...... .* +*........-----








Time (s)


Figure 5-9. Impact force in X direction for low speed impact on circular pier








46


1200

5.


rectangular, 6knot, 45 deg, linear, full load, Y direction 1000

4 ...... .......................................... circular, 6knot, 45 deg, linear, full load, Y direction ....... ...... ..........
4-
Si i 800



600

1





1200
0, ... .............. .. ....... .









0 tI 0
0 0.5 1 1.5 2 2.5
Time (s)


Figure 5-10. Impact force in Y direction for high-speed oblique impact



1000

4 .................................................. rectangular, lknot, 45 deg, linear, full load, Y direction ................
circular, lknot, 45 deg, linear, full load, Y direction -----
3 ................................................................................................................................................................ ................................ 8 0 0


3

5 600

2.5 (s


S400
--- --- --
1.5 "



4 -4-7

0 .5 ....... ........ ... .. ..... .. ..... .... ..... ...........................


0 Tm 0
0
0 0.5
Time (s)


Figure 5-11. Impact force in Y direction for low speed oblique impact








47



Crush Depth (in)
0 10 20 30 40 50


60 70 80 90


rectangular, 6knot, head on, linear, full load -- -- .
6 rectangular, 6knot, 45 deg, linear, full load ..... ......





4 -

4







2-








0 0.5 1 1.5 2
Crush Depth (m)


Figure 5-12. Force-deformation results for high speed impact on rectangular pier



Crush Depth (in)
0 10 20 30 40 50 60 70


0 0.5 1 1.5
Crush Depth (m)


Figure 5-13. Force deformation results for high speed impact on circular pier


1400


1200


1000

goo
C-

800 8


600


400


200
0
C-

























1400


1200









600


400


200


0
0


_









48



Crush Depth (in)


0 0.5 1



rectan
6 --- --- -- --- --- --- -- : -------- -^ ---- -- ecta--
6 rectan



5






4-

43



2
................... ... .

..


1.5 2


0 0.01 0.02 0.03 0.04 0.05 0.06
Crush Depth (m)


Figure 5-14. Force-deformation results for low speed impact on rectangular pier



Crush Depth (in)
0 0.5 1 1.5 2


4 ...................................... .......................... circular, lknot, head on, linear, full load .......
circular, lknot, 45 deg, linear, full load -- ......

3.5







3 ......................... .. ....... .............. .. ................... .... .............................
... ................ ....... .............................. .................. .. ... ........ .............................. ....
3-


2.5 *- 0.02 0.03 05.







+ +
i .i 4-






0 0.01 0.02 0.03 0.04 0.05 0.06
Crush Depth (m)


Figure 5-15. Force-deformation results for low speed impact on circular pier


2


gular, lknot, head on, linear, full load
gular, lknot, 45 deg, linear, full load, X direction -----












+-+


-t
+ + +

w .



i.. .
.. .. . . . .


2


.5



1400



1200



1000
C-a

800 !

C-

600



400


200



0











.5
1000





800


C-

600 8





400





200








49


20 0.5




rectangular, 6knot, head on, linear, full load 0.4
1 5 -- - -- -
15 rectangular, 6knot, 45 deg, linear, full load, X direction ..............


0.3

" 10 "a

0.2.


5 0 1 0.
F u 51 Pf hg .e .. o r











Time (s)


Figure 5-16. Pier displacement in X direction for high speed impact on rectangular pier



0.12


rectangular, Iknot, head on, linear, full load .
-5









0.12


rectangular, lknot, 45 deg, linear, full load, X direction -... +....... 0.1


0.08


S0.06


0.04


S- 1 0.02


O 1 1 1 1 .. ............................................. ... ............................................... ... ........................... ........................
0 *0


-0.02
0 0.5 1
Time (s)


Figure 5-17. Pier displacement in X direction for low speed impact on rectangular pier








50



10 I I I I 0.25


circular, 6knot, head on, linear, full load
8 -........................ circular, 6knot, 45 deg, linear, full load, X direction +....... .... -- 0.2



6 0.15







2 *0.05



0 -- ------------- o-



-2 .................................... ...................................... ...................................... ... .................................... .................................... -0 .0 5



-4 -0.1
0 0.5 1 1.5 2 2.5
Time (s)


Figure 5-18. Pier displacement in X direction for high speed impact on circular pier


5
S0.12

circular, knot, head on, linear, full load
circular, lknot, 45 deg, linear, full load, X direction ............. 0.1


,- 0.08


0.06
2



0.04


0.02







0 0.5 1
Time (s)


Figure 5-19. Pier displacement in X direction for low speed impact on circular pier








51



10 I 0.25



8 rectangular, 6knot, 45 deg, linear, full load, Y direction -
circular, 6knot, 45 deg, linear, full load, Y direction ........ ......



6 0.15
...................................... ....................................... ...................................... ....................................... ..................................... 0 .1 5


2 .. .



t +
-a


4 0.1 2
4 ............... ....... ...... .... ........................... ... ..... ,...................................
0 + \









c, ,f o,-......

-2 ________ __ -0.05
0 0.5 1 15 2 2.5
Time (s)


Figure 5-20. Pier displacement in Y direction for high-speed oblique impact



5
S0.12


... ...........rectangular, knot, 45 deg, linear, full load, Y direction -- ..............................
circular, I knot, 45 deg, linear, full load, Y direction ..... ..... .0.1






0.06

0.06

0.02 -


-1+-0.02


---- --------- ---------- ------ ----------- ----- ------- ------ ------ -------- -



S______0.02

0 0.5 Time (s) 1


Figure 5-21. Pier displacement in Y direction for low speed oblique impact.














CHAPTER 6
EFFECT OF CONTACT SURFACE GEOMETRY ON PIER BEHAVIOR
DURING IMPACT

6.1 Case Study

In the previous chapter, it was noted that rotation of a square pier relative to the

direction of impact (i.e., creation of an oblique impact condition) has an effect on impact

loads and on pier response. These effects are due partially to the fact that the shape of the

impact surface between the barge and pier changes as the square pier is rotated. In this

chapter, the effect of contact surface geometry is explored further. Of interest is whether

or not fundamentally differing pier cross-sectional shapes, e.g. square versus circular,

produce substantially differing loads and pier responses. A parametric study is conducted

involving two types of pier cross-sectional geometry (rectangular and circular), two

impact speeds (1 knot and 6 knots), and two impact angles (0 and 45 degrees). Cases

discussed in this chapter are the same as those shown in Table 5.1 of Chapter 5.

6.2 Results

Figure 6-1 to Figure 6-16 present results from cases A, B, C, D, E, F, G, and H

listed in Table 5.1. As described in the previous chapter, the X direction represents the

direction "parallel to the alignment of the centerline of the navigable channel" and the Y

direction represents the direction "longitudinal to the substructure." Relationships

between impact force and crush depth (Figures 6-13 6-16) utilize vector-resultant

forces and vector-resultant crush depths rather than component values in the X and Y

directions.









Figures 6-1 through 6-4 show impact force histories in X direction for both

rectangular and the circular piers. For high-speed cases (Figures 6-1 and 6-2), the impact

force histories for both oblique and head-on impacts indicate that both pier-column

geometries (rectangular and circular) produce approximately the same peak impact force.

For the low speed, head-on impact cases (Figure 6-3), the impact force peak value for the

circular pier is approximately half of that for the rectangular pier. Conversely, in low

speed, oblique impact cases (Figure 6-4), the peak impact forces for both circular and

rectangular piers are nearly the same. Figures 6-5 and 6-6 show the impact force histories

in the Y direction for oblique impact conditions.

Computed pier displacements in the X direction are shown in Figures 6-7 through

6-10, while displacements in the Y direction as shown in Figures 6-11 and 6-12. In all

cases considered, peak predicted displacements (in either the X or Y directions) are

approximately the same for both square and circular piers indicating little or no

sensitivity to pier-column cross-sectional shape.

Resultant impact force versus resultant barge crush depth relationships are shown

in Figures 6-13 through 6-16- In each plot, the area under the curve represents the

approximate amount of energy that is dissipated through plastic deformation of the steel

plates in the bow of the barge. In both of the high speed (6 knot) impact cases (Figures 6-

13 and 6-14), the initial kinetic impact energy of the barge is sufficient to cause

significant plastification of the barge bow. In these cases, it is evident that the quantify of

dissipated energy is approximately the same for the square and circular piers. In the low

speed head-on impact cases (Figure 6-15), the initial kinetic impact energy is insufficient

to cause significant plastic deformation and the responses for the square and circular piers







54


are quite different. However, when simulations are conducted at the same speed (1 knot)

but at an oblique impact angle (Figure 6-16), the computed responses (and dissipated

energy levels) are again very similar between the square and circular pier cases. As was

demonstrated in Chapter 5 (and specifically Figure 5.3), rotation of a square pier relative

to the barge headlog tends to reduce the stiffness of the bow and thus produce results

similar to those obtained for a circular pier.

7


rectangular, 6knot, head linear, full load -*
Sirculanr 6kn1o, head & linear, full load -....... -.


5 ... .

.i



0 +




2
S .............................. ... .....





1I I




0 0.5 1 Tin (s) 1.5 2 2


Figure 6-1. Impact force in X direction for high speed head-on impact.


1400


1200


1000


800


600


400


200


0











1200



rectangular, 6knot, 45 deg, 1000
linear, full load, X direction

circular, 6knot, 45 deg,
linear, full load, X direction 800



| : '' 600 t

61 200


400



..................................... ....................................... ........................................ ................. ....... ........................................ 2




0 0
0 0.5 1 1.5 2 2.5
Time (s)


Figure 6-2. Impact force in X direction for high speed oblique impact

7


rectangular, lknot, head on, linear, full load 1400
circular, Iknot, head on, linear, full load ....... .....

1200


S1000

~4
S\ 800

.. ................. ............... ........... .............. .... ........... ....................................... ...................................... ..
0 00
1 3 2...... ++ .00 I


i if: 6r00
t


1 A 200


Time (s)


Figure 6-3. Impact force in X direction for low speed head-on impact








56


1000

4 ................. .................................. rectangular, Iknot, 45 deg, linear, full load, X direction ...........
circular, Iknot, 45 deg, linear, full load, X direction ........+........
800




0 600



.+ .














Time (s)






I-------------I!------!-I------------ 1200
4* 100















................. .............................. r, 6kn ot, 45 deg, linear, full load Y ........ .... ............. ................................














2 800
S+ 600+
2.
1; 4 -w 200



0 ------------------------------- 0


0 0.5 1
Time (s)


Figure 6-4. Impact force in X direction for low speed oblique impact



1200
5 ............................................................................... ................................................................................ ........................................


1000
rectangular, 6knot, 45 deg, linear, full load, Y direction
........................circular, 6knot, 45 deg, linear, full load, Y direction

+ 800


o? +
SL ~ 600 u








200



0 i ....... 0
0 0.5 1 1.5 2 2.5
Time (s)


Figure 6-5. Impact force in Y direction for high speed oblique impact








57



1000


........................................................... rectangluar, knot, 45 deg, linear, full load, Y direction -- ..............
circular, Iknot, 45 deg, linear, full load, Y direction ....... + ...
800

3------------------- --- 800--
3 .................................................................................. ........................................... ................ .............. ....... ....................... .........

S600
C-



4- + 400
+. .






0 1 + ~--- r ----- ------ ......






0 0.5 1
".+. i200








5 Time (s)


Figure 6-6. Impact force in Y direction for low speed oblique impact



25 0.6




20 ...................... rectangular, 6knot, head-on, linear, full load ----- 0.5
circular, 6knot, head-on, linear, full load ------ +-----


0.4
1 5 ..................................... ........................................ .............................................................................. .......................................
15. .


0.3

. 10. I. .

'.+.. 0.2 6



0 0
- - - - - - - . . .... . . .. .. -


"'4-.




-0.1
-5
0 0.5 1 1.5 2 2.5
Time (s)


Figure 6-7. Pier displacement in X direction for high speed head-on impact







58


10 0.25



rectangular, 6knot, 45 deg, linear, full load, X direction
8 .................................................... ...... ......... 0 .2
circular, 6knot, 45 deg, linear, full load, X direction ........-..... -



6 ..................................... .................................................................................................................... ..................................... 0 .1 5











0 0.5 1 Time (s) 1.5 2 2.5




4 ............................ ......................................rectangular, knot, head on, linear, full loa......................................d ....................................... ........................ 0.1













circular, knot, head on, linear, full load .
0.08
0.06




-2 ------- -0.05
0 0.5 1 Time(s) 15 2 2.5


Figure 6-8. Pier displacement in X direction for high speed oblique impact




0.12


4 .................................................................. rectangular, lknot, head on, linear, full load -- ]--
circular, lknot, head on, linear, full load .. .. 0.1


S0.08






o + \0.04


S ...... ............................. ...................................... ................................. .............. ...................... ................... .........


0.5 Time (s) 1


Figure 6-9. Pier displacement in X direction for low speed head-on impact








59




0.12


4 ......................................... rectangular, knot, 45 deg, linear, full load, X direction ......
circular, lknot, 45 deg, linear, full load, X direction ..1


0.08


0.06



0.04
2 1
-0.02






-1-0.02

0 0.5 Time (s) 1


Figure 6-10. Pier displacement in X direction for low speed oblique impact



10 0.25



rectangular, 6knot, 45 deg, linear, full load, Y direction ---
8 ................................................................... 2
circular, 6knot, 45 deg, linear, full load, Y direction .......+-..



6 0.15



............... ... ......... ......... .................... ........ .......... ...... ...... ............. L ...................................... 0 .1
4 0...... '.1















0 0.5 1 Time (s) 15 2 2.5


Figure 6-11. Pier displacement in Y direction for high speed oblique impact










































0.5 Time (s) 1


0.12



0.1



0.08



0.06



0.04 .
'3

0.02 E



0



-0.02


Figure 6-12. Pier displacement in Y direction for low speed oblique impact.


Crush Depth (in)
0 10 20 30 40 50


60 70 80 90


0 0.5 1 1.5 2
Crush Depth (m)


Figure 6-13. Vector-resultant force-deformation results for high speed head-on impact








61



Crush Depth (in)
0 10 20 30 40 50 60 70 80 90
1400
6 ........................ .... ... ................................................. ........................................ ........................................ ............. ......................
:" "- rectangular, 6knot, 45 deg, linear, full load --
.4/f- 4- circular, 6knot, 45 deg, linear, full load ...... 1200



S1000

4-
-. -- -- -- -- -- -- -- -- 8 0 0


600


2 ...................................... ......................................... ......................................... .......................... F ................................ ...............
S400



1200



0 0
0 0.5 1 1.5 2
Crush Depth (m)


Figure 6-14. Vector-resultant force-deformation results for high speed oblique impact



Crush Depth (in)
0 0.5 1 1.5 2



S rectangular, lknot, head on, linear, full load 1400
circular, lknot, head on, linear, full load .......
1200
5
5 - - - - - -- - - - -- - - - - - - - --------------~ ------------------

1000

4 ............ ... .......................... ......... .............................. .............................................................
I 800


a / 4 .--.+ i -600
---..
2 ..... .. .. .. ......... ......... ......... .. 4 0 0
2. .' 4 0 0

1 i 200



0 0
0 0.01 0.02 0.03 0.04 0.05 0.06
Crush Depth (m)


Figure 6-15. Vector-resultant force-deformation results for low speed head-on impact












Crush Depth (in)
1


Crush Depth (m)


Figure 6-16. Vector-resultant force-deformation results for low speed oblique impact


800




600

0


400




200














CHAPTER 7
COMPARISON OF AASHTO PROVISIONS AND SIMULATION RESULTS

Procedures specified by AASHTO for computing equivalent static impact forces

were previously described in Chapter 2. In this chapter, comparisons between loads

computed using those procedures and corresponding force data obtained using dynamic

finite element impact simulations are presented. Barge impacts at two different speeds-

and therefore two impact energy levels-are considered: 6 knots and 1 knot. Head-on and

oblique impacts on both square and circular piers are considered. All of the cases for

which dynamic impact simulation results are available are listed in Table 5.1.

Peak impact forces (predicted by finite element analysis) in both the X direction

(transverse) and Y direction (longitudinal) are reported in Table 7.1. In Figures 7.1 and

7.2, these results are compared to equivalent static loads computed using the AASHTO

provisions. In determining the AASHTO loads, the hydrodynamic mass coefficient (C )

was set to unity to match the fact that hydrodynamic mass effects are not considered in

the dynamic simulations presented in this thesis. In addition, forces in the Y direction are

taken, as AASHTO prescribes, as fifty percent of the loads computed for the X direction.

Although the finite element impact data presented in Figures 7.1 and 7.2 are limited

in terms of variations in impact energy, the results presented are consistent with those

obtained by similar studies conducted for head-on impacts on square piers [2]. Here,

results are also presented for cases involving oblique impacts and impacts on circular

piers. Trends previously observed hold true for these new conditions as well. Loads

predicted by AASHTO exceed finite element predicted forces for high energy impacts








64



but are less than peak dynamic values for less severe, low energy impact conditions.


These trends also hold true for both the X and Y directions of loading.

Kinetic energy (MN-m)
0 1 2 3 4 5 6 7 8
3000 ii

AASHTO Spec. -- X direction -- 12

2500

10



8


S 1500 ......... ...........- .......... A : rectangular, 6knot, head on, linear .................... .......................... -
C B: rectangular, 6knot, 45 degree, linear 6
C: rectangular, lknot, head on, linear
E D: rectangular, lknot, 45 degree, linear B
E: circular, 6knot, head on, linear 4 E
G F: circular, 6knot, 45 degree, linear
D G: circular, lknot, head on, linear
50C H H: circular, lknot, 45 degree, linear 2




0 1000 2000 3000 4000 5000 6000
Kinetic energy (kip-ft)


Figure 7-1. AASHTO and finite element loads in X direction








65



Kinetic energy (MN-m)


1000 2000 3000 4000 5000
Kinetic energy (kip-ft)


Figure 7-2. AASHTO and finite element loads in Y direction.


60


1400


AASHTO Spec. -- Y direction














........... ................................... B: rectangular, 6knot, 45 degree, linear
H_ D: rectangular, lknot, 45 degree, linear
F: circular, 6knot, 45 degree, linear
.................... ...... ................... H: circular, Iknot, 45 degree, linear


............................. ......................................................................................................................................................................


-
r*


6



5



4



3



2



1



0
00









Table 7-1. Peak forces computed using finite element impact simulation

Case Kinetic Energy Impact Force Impact Force
Peak Value (X) Peak Value (Y)

A 5638.5 kip-ft 1468 kip NA
(7.645 MJ) (6.53 x 106 N)

5638.5 kip-ft 945 kip 979 kip
(7.645 MJ) (4.20 x 106 N) (4.35 x 106 N)

156.6 kip-ft 1347 kip
(0.12 MJ) (5.99x 106 N)

156.6 kip-ft 619 kip 560 kip
(0.12 MJ) (2.75x 106N) (2.49 x 106N)

5638.5 kip-ft 1372 kip
(7.645 MJ) (6.10x 106 N)

5638.5 kip-ft 1034 kip 976 kip
(7.645 MJ) (4.60x 106 N) (4.34 x 106 N)

G 156.6 kip-ft 659 kip
(0.12 MJ) (2.93x 106N)

156.6 kip-ft 557 kip 509 kip
(0.12 MJ) (2.48x 106N) (2.26 x 106N)














CHAPTER 8
CONCLUSIONS

To assess the accuracy of the AASHTO barge impact design provisions, parametric

finite element impact studies involving pier material nonlinearity, impact angle, and

impact zone geometry (pier-column cross-sectional geometry) have been conducted. In

addition, static barge crush simulations have been conducted to determine the effect of

contact angle on barge force versus deformation relationships. Finally, dynamic finite

element simulation results have been compared to equivalent design forces predicted by

the AASHTO bridge design provisions.

Results from oblique static barge crush simulations conducted using square shaped

piers reveal that the sensitivities of crush relationships to pier widths are most

pronounced for small contact angles but diminish rapidly for larger angles. Subsequent

dynamic impact simulations conducted for head-on and oblique impacts on both square

and circular piers reveal that differences in predicted forces are relatively minor in all

situations except for the case of nearly head-on (zero-angle) impacts on square piers (flat

faced piers). Separate parametric studies focusing on the effects of pier material

nonlinearity reveal that forces and pier displacements in non-catastrophic impacts (i.e.,

situations in which the pier does not collapse) of pier structures of the type studied here

are not greatly sensitive to nonlinearity in the pier columns.

Finally, comparisons between finite element predicted forces and AASHTO forces

for two different impact energy levels reveal that, for the type of pier studied here, the

AASHTO provisions predict conservative results for high energy impacts (loads









predicted by simulation were typically only about 60% of the load predicted by

AASHTO). However, in low energy impacts, peak transient dynamic forces predicted by

finite element analysis exceed those specified by AASHTO (forces predicted by

simulation can be more than twice the magnitude of the equivalent static AASHTO

loads). These trends have also been found to hold true in both the transverse and

longitudinal impact directions. However, because the simulation-predicted loads are

transient in nature whereas the AASHTO loads are static, additional research is needed in

order to more accurately compare results from the two methods.















LIST OF REFERENCES


1. American Association of State Highway and Transportation Officials (AASHTO).
Guide Specification and Commentary for Vessel Collision Design of Highway
Bridges. American Association of State Highway and Transportation Officials,
Washington, DC, 1991.

2. Consolazio, G.R., Cook, R.A., Lehr, G.B., and Bollmann, H.T., Barge Impact
Testing of the St. George Island Causeway Bridge Phase I : Feasibility Study,
Structures Research Report No. 783, Engineering and Industrial Experiment
Station, University of Florida, Gainesville, Florida, January 2002.

3. Consolazio, G.R., Lehr, G.B., McVay, M.C., Dynamic Finite Element Analysis of
Vessel-Pier-Soil Interaction During Barge Impact Events, Transportation Research
Record: Journal of the Transportation Research Board, No. 1849, pp. 81-90, 2004

4. Consolazio, G.R., Cook, R.A., Biggs, D.R., Cowan, D.R., and Bollmann, H.T.,
Barge Impact Testing of the St. George Island Causeway Bridge Phase II : Design
of Instrumentation Systems, Structures Research Report No. 883, Engineering and
Industrial Experiment Station, University of Florida, Gainesville, Florida, April
2003

5. American Association of State Highway and Transportation Officials (AASHTO).
AASHTO LRFD Bridge Design Specifications, 3rd Edition, Washington, DC:
American Association of State Highway and Transportation Officials, 2000

6. Livermore Software Technology Corporation (LSTC), LS-DYNA Keyword
Manual: Version 960, Livermore, CA, 2002

7. Saul, R., Svensson, H., On the Theory of Ship Collision Against Bridge Piers,
IABSE proceedings, pp. 29-40, Feb. 1982

8. Tedesco, J. W., McDougal, W. G., Ross, C. A., Structural Dynamics Theory and
Applications, Addison Wesley, Menlo Park, California, 1999

9. Ngo, T. D., Mendis, P. A., Teo, D., Kusuma, G., Behavior of High-strength
Concrete Columns Subjected to Blast Loading, paper presented in the conference
Advanced In Structures: Steel, Concrete, Composite and Aluminum, Sydney, 23-25
June, 2003






70


10. Dameron, R. A., Sobash, V. P., Lam, I. P., Nonlinear Seismic Analysis of Bridge
Structures Foundation-soil Representation And Ground Motion Input, Computers
& Structures, Vol. 64, No. 5/6, pp. 1251-1269, 1997

11. Hoit, M. I., McVay, M., Hays, C., Andrade, P. W., Nonlinear Pile Foundation
Analysis Using Florida-Pier, Journal of Bridge Engineering, Vol. 1, No. 4, pp. 135-
142, November 1996

12. MacGregor, J. G., Reinforced Concrete Mechanics and Design, Third Edition,
Prentice-Hall Inc., Upper Saddle River, New Jersey, 1997

13. ADINA R&D Inc., ADINA Online Users' Manual, Watertown, MD, 2002

14. American Institute of Steel Construction (AISC). Manual of Steel Construction.
Third Edition, American Institute of Steel Construction Inc., n.p., November, 2001















BIOGRAPHICAL SKETCH

The author was born on December 19, 1973, in Fuyang City, Anhui Province,

People's Republic of China. After graduation from No. 1 High School in Fuyang City,

she attended Suzhou Institute of Urban Construction and Environmental Protection where

she graduated with a bachelor's degree in road and bridge engineering in July 1995. She

continued her study in structural engineering by attending graduate school in Tongji

University in Shanghai, China, and graduated with a master's degree in bridge

engineering in December 1997. After working in the Shanghai Municipal Engineering

Administration Department in Shanghai, China, for several years, she came to the United

States in August 2000 to study at the University of Central Florida. She then came to the

University of Florida to continue graduate study in August 2002 majoring in structural

engineering. After defending her thesis in August 2004 she plans to move to Orlando,

Florida, to begin a career with EAC Consulting, Inc. as a junior bridge design engineer