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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 NONLINEAR 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 LoadDeformation 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 31 Comparison of original and adjusted section properties ............... ..............16 32 Input data in LSDYNA simulations ............................ .................................... 18 33 Comparison of plastic moment and displacement using properties of pier cap.......19 34 Comparison of plastic moment and displacement using properties of pier co lu m n ...................................... ...................................................... 19 35 General modeling features of the testing barge......................................................25 41 D ynam ic sim ulation cases ......................................................... ............... 32 51 D ynam ic sim ulation cases ......................................................... ............... 41 71 Peak forces computed using finite element impact simulation.............................66 LIST OF FIGURES Figure pge 11 Relation between impact force and barge damage depth according to Meir D ornberg's R research (after A A SH TO [1]) ........................................ ....................3 21 Collision energy to be absorbed in relation with collision angle and the coefficient of friction (after AASHTO [1])........................................................8 31 Global modeling of SanDiego Coronado Bay Bridge (after Dameron [10])..........11 32 Pier model used for local modeling (after Dameron [10]).................. .............12 33 Global pier modeling for seismic retrofit analysis (after Dameron [10]).................12 34 Mechanical model for discrete element (after Hoit [11])..................................13 35 Bilinear expression of momentcurvature and stressstrain curve ...........................17 36 M om entcurvature derivation........................................................ ............... 18 37 M ain deck plan of the construction barge .................................... ...................... 20 38 Outboard profile of the construction barge ............................... ...............20 39 Typical longitudinal truss of the construction barge........................ .............20 310 Typical transverse frame (cross bracing section) of the construction barge ............20 311 Dimension and detail of barge bow of the construction barge..............................21 312 Layout of barge divisions .............................. ............ ..... ......................... 22 313 Meshing of internal structure of zone1 ..........................................................23 314 Buoyancy spring distribution along the barge............................... ............... 26 315 Pier and contact surface layout.......................................... ........................... 27 316 Rigid links between pier column and contact surface..............................................27 317 Exaggerated deformation of pier column and contact surface during impact..........28 318 Comparison of impact force versus crush depth for rigid and concrete contact m o d e ls ........................................................................... 2 9 319 Overview of barge and pier model for dynamic simulation...............................30 41 Comparison of impact force history for severe impact case ...............................34 42 Comparison of impact force history for nonsevere case ...................................34 43 Impact force and crush depth relationship comparison for severe impact case .......35 44 Comparison of impact force crush depth relationship for nonsevere case ..........35 45 Comparison of pier displacement for severe impact case.............. .. ................36 46 Comparison of pier displacement for nonsevere case..........................................36 51 Static crush between pier and open hopper barge .......... ............ ..................38 52 Results for static crush analysis conducting with a 4 ft. wide pier ........................39 53 Results for static crush analysis conducting with a 6 ft. wide pier ........................39 54 Results for static crush analysis conducting with a 8 ft. wide pier ........................40 55 Layout of barge headon impact and oblique impact with pier.............................41 56 Impact force in X direction for high speed impact on rectangular pier ...................44 57 Impact force in X direction for high speed impact on circular pier .......................44 58 Impact force in X direction for low speed impact on rectangular pier ...................45 59 Impact force in X direction for low speed impact on circular pier ........................45 510 Impact force in Y direction for highspeed oblique impact ...................................46 511 Impact force in Y direction for low speed oblique impact....................................46 512 Forcedeformation results for high speed impact on rectangular pier.................47 513 Force deformation results for high speed impact on circular pier..........................47 514 Forcedeformation results for low speed impact on rectangular pier..................48 515 Forcedeformation results for low speed impact on circular pier ..........................48 516 Pier displacement in X direction for high speed impact on rectangular pier...........49 517 Pier displacement in X direction for low speed impact on rectangular pier ............49 518 Pier displacement in X direction for high speed impact on circular pier................50 519 Pier displacement in X direction for low speed impact on circular pier ................50 520 Pier displacement in Y direction for highspeed oblique impact...........................51 521 Pier displacement in Y direction for low speed oblique impact. ..........................51 61 Impact force in X direction for high speed headon impact............................... 54 62 Impact force in X direction for high speed oblique impact..................................55 63 Impact force in X direction for low speed headon impact.................................55 64 Impact force in X direction for low speed oblique impact....................................56 65 Impact force in Y direction for high speed oblique impact..................................56 66 Impact force in Y direction for low speed oblique impact....................................57 67 Pier displacement in X direction for high speed headon impact ..........................57 68 Pier displacement in X direction for high speed oblique impact ...........................58 69 Pier displacement in X direction for low speed headon impact..............................58 610 Pier displacement in X direction for low speed oblique impact ...........................59 611 Pier displacement in Y direction for high speed oblique impact ...........................59 612 Pier displacement in Y direction for low speed oblique impact. ..........................60 613 Vectorresultant forcedeformation results for high speed headon impact.............60 614 Vectorresultant forcedeformation results for high speed oblique impact..............61 615 Vectorresultant forcedeformation results for low speed headon impact.............61 616 Vectorresultant forcedeformation results for low speed oblique impact ..............62 71 AASHTO and finite element loads in X direction ....................................... 64 72 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 (piercolumn crosssectional 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 [14]. 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 LSDYNA [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 MeirDomberg 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 MeirDornberg were used to study the collision force and the deformation when barges collide with lock entrance structures and with bridge piers. MeirDornberg'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. MeirDornberg'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 11. 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 11. Relation between impact force and barge damage depth according to Meir Dornberg's Research (after AASHTO [1]) AASHTO adopted the results of MeirDornberg's study with a modification factor to account for effect of varying barge widths. In MeirDomberg'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 fullscale 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 nonlinearity 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. Headon 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 MeirDomberg study [1]. The barge collision impact force associated with a headon 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 5672J \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, underkeel 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 straightline motion, the following values of CH may be used, unless determined otherwise by accepted analysis procedures: CH = 1.05 for large underkeel clearances ( > 0.Sdraft) CH = 1.25 for small underkeel 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 kipft., 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) Ac =  =  232.2 29.2 The impact force calculation described above is for headon 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 21 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 21. 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 LSDYNA [6], material nonlinearity can be accounted for by defining a piecewise linear stressstrain relationship or by defining the parameters of an elastic, perfectly plastic material model. Geometric nonlinearity is always included in LSDYNA 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. Nonlinearity 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 highstrength 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 LSDYNA 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] stressstrain 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 DiegoCoronado Bay Bridge. Figure 31 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 DiegoCoronado Bay Bridge is 1.6 miles long and extends across San Diego Bay. The model included the entire 1.6mile long bridge (see Figure 31). Modeling included two steps: local modeling and global modeling. An example of local modeling is that the detailed finiteelement analyses of three typical bridge piers were performed using experimentallyverified 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 32. Data were then used to idealize the pier column stiffness and plastichinge behavior in the globalmodel 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 PA effects in the towers), contact between spans at the expansion joints and at the abutment wall, nonlinearplastic behavior of isolation bearings, postyield behavior of pier column plastic hinges, and nonlinear overturning rotation of the pile cap" [10]. Figure 31. Global modeling of SanDiego Coronado Bay Bridge (after Dameron [10]) Finte Elerrnt Mesh Pier Column Pile Cap Figure 32. Pier model used for local modeling (after Dameron [10]) eom, wrt No=na1tlly (PA 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 33. Global pier modeling for seismic retrofit analysis (after Dameron [10]) Typical Tower F.CV1 O Developers of the commercially available pier analysis software FBPier [11], use threedimensional nonlinear discrete elements to model pier columns, pier cap, and piles. The discrete elements (see Figure 34) use rigid link sections connected by nonlinear springs [11]. The behavior of the springs is derived from the exact stressstrain behavior of the steel and concrete in the member crosssection. Geometric nonlinearity is accounted for by using PA 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 P6 moments (moments of axial force times internal displacements within members due to bending) are also taken into account. I~h^hhh4l1 rk*,R r vB V AcdfllaUl a. L _______i , Figure 34. Mechanical model for discrete element (after Hoit [11]) Figure 34 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 nonlinear 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 FBPier 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. LSDYNA 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, LSDYNA 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 LSDYNA 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 headon 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 headon 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 31 shows the original and adjusted crosssectional properties. Table 31. Comparison of ori inal and adjusted section properties Case Original Adjusted Trial Value of Area (2) 1.38 x 102 1.25 x 102 (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 LSDYNA does not support direct specification of momentcurvature 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. Momentcurvature relationships may be sufficiently approximated using the *MAT_RESULTANT_PLASTICITY model. Usually, a momentcurvature 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 35 shows similarities between a simplified momentcurvature curve and a stressstrain curve for an elastic, perfectly plastic material. M CyG El E ()y 'y a) momentcurvature b) stressstrain Figure 35. Bilinear expression of momentcurvature and stressstrain curve For an arbitrary cross section, Mc M (31) I E = (32) 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 momentcurvature curve based on Equation 32, however yield stress is unknown due to the fact that LSDYNA 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 LSDYNA. Based on output yield moment from LSDYNA and Equation 31, c value (dimension of rectangular cross section) is calculated. This correct c value (dimension of rectangular cross section) is plugged into Equation 31 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 momentcurvature 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 momentcurvature relationship. Initial stiffness for the simplified bilinear moment curvature relationship stays the same as that of the original momentcurvature relationship (see Figure 36). Data used in the LSDYNA simulations for the pier columns and pier cap are given in Table 32. )M original MomentCurvature Ivi o ... .... .............. I ilinear MomentCurvature Mo Figure 36. Momentcurvature derivation Table 32. Input data in LSDYNA 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 Momentcurvature relationships for the pier column and the pier cap are developed based on steel reinforcement layout and material properties. Tables 33 and 34 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 480meter simply supported beam with a concentrated load at midspan. Plastic moment and displacement at midspan calculated by LSDYNA are compared with those from theoretical calculations. Table 33. Comparison of plastic moment and displacement using properties of pier cap r C LSDYNA Theoretical Error Results Value Percentage Plastic Moment 10.0 x 106 12.0 x 106 17% Strong Axis (N*m) Displacement at Midspan 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 Midspan 9.0 8.0 11 9.0 8.0 11% at Yielding (m) Table 34. Comparison of plastic moment and displacement using properties of pier column Pr C n LSDYNA 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 Midspan 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 Midspan 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 37 through 311 describe the dimensions and the internal structure of the construction barge. Transverse Frame I I 81'6" k70'0" 151'6" Figure 37. Main deck plan of the construction barge Transverse Frame Serrated Channel / ............ ........ .. .... ............. S... ...   ... ... .  . i......... ...... .... .. ......... ........ ......... ....... ..... ..... ...... ... ............................ . '~'f~~~~\~~~~~v~~~~^~~~~~v~~~~^~~~~^~~~"\ "^~ iU  p jri T j * 81'6" 70'0" Figure 38. Outboard profile of the construction barge Transverse Frame \ C Channel I L Beam 35'0" 35'0" Figure 39. 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 310. Typical transverse frame (cross bracing section) of the construction barge Barge Bow 00". _/ / *s/ ,_:_/ L LL ^ ^ ^ i 35'0" Figure 311. 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 (Csections) and serrated channel beams. The bow portion of the barge is raked. Twentytwo internal longitudinal trusses span the length of the barge and nineteen trusses span transversely across the width of the barge. The twentytwo 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 zone1, zone2 and zone3 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 312. 116'0" 19'0" 15'6" .tC* 4 .e2 [ ...:. i ... j. .. ..... .... i ... ... .... ...... .................. .... .... ...... ........" on *t :t iti^ :i^ f: l I: 11i^ l  ^ j^I ,r: *  .;:.;:>:. : .;.r.r;. 1one i. .........i....j.....i....j..........n... ........ ....... Zo e2 ......... .... ... .... Zone2 Zone3 Figure 312. Layout of barge divisions For centerline, headon impacts, the central portion of barge zone1 (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 zone1 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 offcenter portion of the bow are modeled using lowerresolution beam elements since only small deformations are expected and material failure is not likely to occur during centerline impacts of the barge. Unlike zone1, structures in zone2 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. Zone2 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 zone1, those in zone2 are considerably larger in size. Use of relatively simple beam elements reduces the computing time required to perform impact analysis. Zonei Figure 313. Meshing of internal structure of zone1 50'0"In zone3, 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) 914.5" StAll shell elements in the model oae assigned a piecewise linear plastic material (Lower Resolution) Figure 313. Meshing of internal structure of zone1 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 zone3 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. LSDYNA 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 LSDYNA 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 LSDYNA 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 nonsymmetric 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 LSDYNA. 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, LSDYNA 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 35. General modeling features of the testing barge Model Features 8node brick elements 1842 4node shell elements 81,040 2node beam elements 8,324 2node Discrete Spring elements 119 1node 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 36 General modeling features of the jumbo hopper barge Model Features 8node brick elements 234 4node shell elements 24,087 2node beam elements 2,264 2node Discrete Spring elements 28 1node 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 zone1, zone2, and zone3 are made with nodal rigid body constraints. For the connection of zone1 to zone2, 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 zone2 to zone3, nodal rigid bodies are defined to connect small elements in zone2 with those in zone3. Buoyancy Spring with Zero Gap Buoyancy Spring with Nonzero Gap Figure 314. Buoyancy spring distribution along the barge A precompressed 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 precompression 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 35 and 36. 3.5 Contact Surface Modeling BuoyaWhen pier columns and pier Gaps are modeled using b eam elements, contact Figure 314. Buoyancy spring distribution along the barge surfA precompressed buoyancy sp modeled is applied to the pier column to enable contact desimulatection buoyancy effeimpacts.e Figure 315).buoyancy spro in Figure 315, 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 reompressionly 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 35 and 36. 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 315). Also in Figure 315, 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 315. Pier and contact surface layout pier column surface Figure 316. Rigid links between pier column and contact surface pier column contact surface Impact force Figure 317. 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 316). Under bending of the pier column, these elements will act independently, and transfer the impact force to the pier column beam elements. Figure 317 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 318 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 318. 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 FBPier 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 319. 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 319. Overview of barge and pier model for dynamic simulation ifii'~ CHAPTER 4 NONLINEAR PIER BEHAVIOR DURING BARGE IMPACT Nonlinear pier behavior, barge deformation and energy dissipation are several of the issues that are relevant when considering bargepier collisions. The answer to questions of how much the nonlinearity 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 nonlinearity 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 nonlinearity. All cases included in this chapter are listed in Table 41. Table 41. Dynamic simulation cases Contact Impact Material Loading Case Speed Surface Angle Property Condition A Rectangular 6 knot Headon Linear Full B Rectangular 6 knot Headon Nonlinear Full C Rectangular 1 knot Headon Linear Full D Rectangular 1 knot Headon Nonlinear Full 4.2 Analysis Results For both severe impact case and nonsevere impact case, Figures 41 through 46 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 nonsevere 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 nonsevere impact case, barge crush depth after impact for linear pier is always larger than barge crush depth after impact for nonlinear pier (Figure 43, Figure 44). During impact, for the severe impact case, all steel piles yield; even for the nonsevere 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 45. The residual deformation can be as large as 1012 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 momentcurvature is simplified as a bilinear curve with initial stiffness the same as that of the uncracked cross section, the cracking moment is not reflected in the bilinear momentcurvature 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 nonlinearity of pier material can be ignored almost completely. For the barge with 6 knot speed, fully loaded condition, though nonlinearity 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 41. 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 42. Comparison of impact force history for nonsevere 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 43. 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 44. Comparison of impact force crush depth relationship for nonsevere case 36 25 0.6 6knot, headon, nonlinear, full load  20 6knot, headon, 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 45. 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 46. Comparison of pier displacement for nonsevere 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 headon transverse impact condition, and 2) a reduced force longitudinal impact condition. In the headon 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 headon 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 headon 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 LoadDeformation 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 52). 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 51 shows the static crush of the pier and the open hopper barge. Results from the static crush simulations are presented in Figures 52 to Figure 54. The results indicate that headon 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 g3e pier 0 degree crush pn hopper barge 15 degree crush 15 degree crush Figure 51. 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 52. 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 53. 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 8ft15 deg . static crush 8ft30 deg   static crush8ft45 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 54. 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 55): an impact angle of 0 degrees (headon impact) and an angle of 45 degrees (severe oblique impact). Pier columns having both rectangular and circular crosssectional shapes are considered. Table 51 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 headon impact motion   Figure 55. Layout of barge headon impact and oblique impact with pier Figure 55. Layout of barge headon impact and oblique impact with pier Table 51. Dynamic simulation cases Contact Impact Material Loading Case Speed Surface Angle Property Condition A Rectangular 6 knot Headon Linear Full B Rectangular 6 knot 45 degree Linear Full C Rectangular 1 knot Headon Linear Full D Rectangular 1 knot 45 degree Linear Full E Circular 6 knot Headon Linear Full F Circular 6 knot 45 degree Linear Full G Circular 1 knot Headon 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 51) are presented in Figure 56 through Figure 521. In each figure, the direction denoted as "X" corresponds to the axis of the pier (see Figure 55) 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 56, Figure 57, Figure 58 and Figure 59. Impact force history in Y direction are represented in Figure 510, Figure 511. Peak value of the impact force histories in Figure 56 through 511 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 512, Figure 513, Figure 514 and Figure 515. Plots of pier displacement in X direction and in Y direction are included in Figure 516, Figure 517, Figure 518, Figure 519, Figure 520 and Figure 521. Figures 56, Figure 57, Figure 58 and Figure 59 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 headon impacts, regardless of the geometry of the contact surface. For rectangular pier, impact force peak values from 45degree oblique impact simulations are about 50% of those from headon impact for both the lowspeed impact scenarios and the highspeed impact scenarios. However for circular pier, the impact force peak values from 45 degree oblique impact simulations are about 80% of those from headon 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 512, Figure 513, Figure 514 and Figure 515 show that though lowspeed 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 headon impact, highspeed impact scenarios have a different trend. Figure 513 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 headon impact and oblique impact. Figure 512 indicates that for rectangular pier of high impact speed, oblique impact causes larger resultant crush depth and smaller resultant impact force peak value than headon 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 56 through 521 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 A200 V 2 ............... .. ...... ..... ........................ ............... .. .... ............. ........................................ 0 0 0 0.5 1 1.5 2 2.5 Time (s) Figure 56. 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 f4 I + 800 600 00 400 1 ...............................................................200 0 00 0 0.5 1 1.5 2 2.5 Time (s) Figure 57. 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 58. 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 59. 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 510. Impact force in Y direction for highspeed 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 47 0 .5 ....... ........ ... .. ..... .. ..... .... ..... ........................... 0 Tm 0 0 0 0.5 Time (s) Figure 511. 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 512. Forcedeformation 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 513. 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 514. Forcedeformation 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 515. Forcedeformation 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 Ca 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 516. 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 517. 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 518. 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 519. 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 520. Pier displacement in Y direction for highspeed 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 521. 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 crosssectional shapes, e.g. square versus circular, produce substantially differing loads and pier responses. A parametric study is conducted involving two types of pier crosssectional 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 61 to Figure 616 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 613 616) utilize vectorresultant forces and vectorresultant crush depths rather than component values in the X and Y directions. Figures 61 through 64 show impact force histories in X direction for both rectangular and the circular piers. For highspeed cases (Figures 61 and 62), the impact force histories for both oblique and headon impacts indicate that both piercolumn geometries (rectangular and circular) produce approximately the same peak impact force. For the low speed, headon impact cases (Figure 63), 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 64), the peak impact forces for both circular and rectangular piers are nearly the same. Figures 65 and 66 show the impact force histories in the Y direction for oblique impact conditions. Computed pier displacements in the X direction are shown in Figures 67 through 610, while displacements in the Y direction as shown in Figures 611 and 612. 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 piercolumn crosssectional shape. Resultant impact force versus resultant barge crush depth relationships are shown in Figures 613 through 616 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 614), 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 headon impact cases (Figure 615), 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 616), 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 61. Impact force in X direction for high speed headon 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 62. 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 63. Impact force in X direction for low speed headon 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) II!!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 64. 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 65. 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 66. Impact force in Y direction for low speed oblique impact 25 0.6 20 ...................... rectangular, 6knot, headon, linear, full load  0.5 circular, 6knot, headon, 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 67. Pier displacement in X direction for high speed headon 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 68. 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 69. Pier displacement in X direction for low speed headon 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 10.02 0 0.5 Time (s) 1 Figure 610. 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 611. 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 612. 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 613. Vectorresultant forcedeformation results for high speed headon 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 614. Vectorresultant forcedeformation 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 615. Vectorresultant forcedeformation results for low speed headon impact Crush Depth (in) 1 Crush Depth (m) Figure 616. Vectorresultant forcedeformation 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 levelsare considered: 6 knots and 1 knot. Headon 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 headon 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 (MNm) 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 (kipft) Figure 71. AASHTO and finite element loads in X direction 65 Kinetic energy (MNm) 1000 2000 3000 4000 5000 Kinetic energy (kipft) Figure 72. 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 71. Peak forces computed using finite element impact simulation Case Kinetic Energy Impact Force Impact Force Peak Value (X) Peak Value (Y) A 5638.5 kipft 1468 kip NA (7.645 MJ) (6.53 x 106 N) 5638.5 kipft 945 kip 979 kip (7.645 MJ) (4.20 x 106 N) (4.35 x 106 N) 156.6 kipft 1347 kip (0.12 MJ) (5.99x 106 N) 156.6 kipft 619 kip 560 kip (0.12 MJ) (2.75x 106N) (2.49 x 106N) 5638.5 kipft 1372 kip (7.645 MJ) (6.10x 106 N) 5638.5 kipft 1034 kip 976 kip (7.645 MJ) (4.60x 106 N) (4.34 x 106 N) G 156.6 kipft 659 kip (0.12 MJ) (2.93x 106N) 156.6 kipft 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 (piercolumn crosssectional 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 headon 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 headon (zeroangle) 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 noncatastrophic 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 simulationpredicted 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 VesselPierSoil Interaction During Barge Impact Events, Transportation Research Record: Journal of the Transportation Research Board, No. 1849, pp. 8190, 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), LSDYNA Keyword Manual: Version 960, Livermore, CA, 2002 7. Saul, R., Svensson, H., On the Theory of Ship Collision Against Bridge Piers, IABSE proceedings, pp. 2940, 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 Highstrength Concrete Columns Subjected to Blast Loading, paper presented in the conference Advanced In Structures: Steel, Concrete, Composite and Aluminum, Sydney, 2325 June, 2003 70 10. Dameron, R. A., Sobash, V. P., Lam, I. P., Nonlinear Seismic Analysis of Bridge Structures Foundationsoil Representation And Ground Motion Input, Computers & Structures, Vol. 64, No. 5/6, pp. 12511269, 1997 11. Hoit, M. I., McVay, M., Hays, C., Andrade, P. W., Nonlinear Pile Foundation Analysis Using FloridaPier, Journal of Bridge Engineering, Vol. 1, No. 4, pp. 135 142, November 1996 12. MacGregor, J. G., Reinforced Concrete Mechanics and Design, Third Edition, PrenticeHall 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 