influence of pier nonlinearity, impact angle, and column shape on pier...

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

ii

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.

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TABLE OF CONTENTS page ACKNOWLEDGEMENTS................................................................................................ ii

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

LIST OF FIGURES ........................................................................................................... vi

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

CHAPTER 1 INTRODUCTION ........................................................................................................1

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

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

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

3.1 Introduction.............................................................................................................9 3.2 Background Study ................................................................................................10 3.3 Pier Model Description.........................................................................................14 3.4 Barge Finite Element Model.................................................................................19 3.5 Contact Surface Modeling ....................................................................................26

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

4.1 Case Study ............................................................................................................31 4.2 Analysis Results....................................................................................................32

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

5.1 Effect of Strike Angle on Barge Static Load-Deformation Relationship .............38 5.2 Effect of Strike Angle on Dynamic Loads and Pier Response.............................40 5.3 Dynamic Simulation Results ................................................................................42

iv

6 EFFECT OF CONTACT SURFACE GEOMETRY ON PIER BEHAVIOR DURING IMPACT.....................................................................................................52

6.1 Case Study ............................................................................................................52 6.2 Results...................................................................................................................52

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

8 CONCLUSIONS ........................................................................................................67

LIST OF REFERENCES...................................................................................................69

BIOGRAPHICAL SKETCH .............................................................................................71

v

LIST OF TABLES

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

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

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

3-4 Comparison of plastic moment and displacement using properties of pier column......................................................................................................................19

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

4-1 Dynamic simulation cases ........................................................................................32

5-1 Dynamic simulation cases ........................................................................................41

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

vi

LIST OF FIGURES

Figure page 1-1 Relation between impact force and barge damage depth according to Meir-

Dornberg’s Research (after AASHTO [1]) ................................................................3

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

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

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

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

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

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

3-6 Moment-curvature derivation...................................................................................18

3-7 Main deck plan of the construction barge ................................................................20

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

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

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

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

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

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

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

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

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

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

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3-18 Comparison of impact force versus crush depth for rigid and concrete contact models ......................................................................................................................29

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

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

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

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

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

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

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

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

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



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

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

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

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

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

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

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

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

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

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

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

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

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

viii

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ix

Abstract of Thesis Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering

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

By

Bibo Zhang

December 2004

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

Current bridge design specifications for barge impact loading utilize information

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

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

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

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

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

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

resolution nonlinear dynamic finite element impact simulations are used to quantify

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

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

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

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

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

x

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.

1

CHAPTER 1 INTRODUCTION

1.1 Overview

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

presented in this thesis.

2

1.2 Background of AASHTO Guide Specification

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

following topics:

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

Part 2: Design vessel selection

Part 3: Bridge protection system design

Part 4: Bridge protection planning

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

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

this section.

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

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

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

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

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

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

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

groundings along the sides of the waterway.

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

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

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

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

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

3

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

as a function of barge mass and initial speed.

00

2 4 6 8 10 12

500

1000

1500

2000

2500

3000P B

(kip

s)

aB (feet) Figure 1-1. Relation between impact force and barge damage depth according to Meir-

Dornberg’s Research (after AASHTO [1])

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

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

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

closely with the jumbo hopper barge bow 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.

4

1.3 Objective

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

rectangular and circular piers. Comparisons between finite element impact simulations

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

summarizes results from the preceding chapters and offers conclusions.

5

CHAPTER 2 AASHTO BARGE AND BRIDGE COLLISION SPECIFICATION

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

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

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

by AASHTO:

For 34.0

6

The hydrodynamic mass coefficient HC accounts for the mass of water

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

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

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

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

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

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

otherwise by accepted analysis procedures:

05.1=HC for large under-keel clearances ( draft5.0≥ )

25.1=HC for small under-keel clearances ( draft5.0≤ )

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

energy of a moving object:

gWVmVKE

22

22

== (2.6)

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

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

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

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

2.292.322205.2 22 WVCWVC

KE HH =⋅

= (2.7)

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

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

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

7

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.

KEE *η= (2.8)

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

coefficient of friction (µ ) 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 corners

8

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

kinetic energy to be dissipated during the impact.

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

9

CHAPTER 3 FINITE ELEMENT BARGE IMPACT SIMULATION

3.1 Introduction

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

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

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

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

geometric nonlinearity has occurred [8].

For modeling of structural nonlinearity, both material nonlinearity and geometric

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

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

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

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

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

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

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

internal forces.

Dynamic simulation of barge impacts with bridge piers involves generating two

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

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

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

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

10

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

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

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

investigate the locations at which plastic hinges form during impact.

3.2 Background Study

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

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

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

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

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

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

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

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

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

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

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

load that had a time duration of approximately 1.3 milliseconds.

Researchers studying bridge behavior under seismic loading developed a global

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

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

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

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

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

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

11

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

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

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

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

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

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

global model were “global large displacements (primarily to capture P-∆ effects in the

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

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

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

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

12

P ie r C a p

P ie r C o lu m n

P i le C a p

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

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

13

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

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

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

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

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

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

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

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

members due to bending) are also taken into account.

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

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

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

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

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

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

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

14

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

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

axial thrust [11].

3.3 Pier Model Description

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

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

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

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

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

distribution of mass in the pier.

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

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

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

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

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

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

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

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

heavily reinforced concrete elements consisting of numerous steel bars compositely

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

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

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

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

representing plastic hinge formation.

15

LS-DYNA includes a nonlinear material called *MAT_RESULTANT_PLASTICITY,

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

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

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

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

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

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

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

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

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

available in this material model.

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

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

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

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

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

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

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

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

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

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

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

16

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

properties.

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

Case Original Adjusted

Trial Value of Area (m2) 1.38 x 10

-2 1.25 x 10-2

Plastic Moment (Strong Axis Bending)

(N*m) 5.860 x 105 4.183 x 105

Plastic Moment (Weak Axis Bending)

(N*m) 3.112 x 105 2.502 x 105

Error Percentage (Area) 0 9.5 %

Error Percentage (Plastic Moment)

(Strong Axis) 18.1 % 12.9 %

Error Percentage (Plastic Moment)

(Weak Axis) 7.9 % 12.7 %

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

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

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

making use of material models *MAT_CONCRETE_BEAM, *MAT_PIECEWISE_LINEAR_-

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

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

relationships may be sufficiently approximated using the *MAT_RESULTANT_PLASTICITY

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

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

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

17

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

perfectly plastic material.

M

Φ

My

Φy

σy

σ

εεy

EI E

a) moment-curvature b) stress-strain

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

For an arbitrary cross section,

gIMc

=σ (3-1)

cgIMEφ

= (3-2)

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

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

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

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

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

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

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

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

18

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

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

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

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

half the summation of yielding moment Myo and ultimate moment Muo from the original

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

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

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

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

M

Φ

My

Φy

Μuo

Μyo

Μcro

Bilinear Moment-Curvature

Original Moment-Curvature

Figure 3-6. Moment-curvature derivation

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

Pier Column 2.486 x 1010 4.90 x 106

Pier Cap 2.486 x 1010 6.10 x 106

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

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

19

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

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

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

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

calculations.

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

Pier Cap LS-DYNA Results Theoretical

Value Error

Percentage Plastic Moment

(N*m) 10.0 x 106 12.0 x 106 17%

Strong Axis Displacement at Mid-span at Yielding (m) 6.2 6.0 3%

Plastic Moment (N*m) 6.3 x 10

6 5.3 x 106 18% Weak Axis Displacement at Mid-span

at Yielding (m) 9.0 8.0 11%

Table 3-4. Comparison of plastic moment and displacement using properties of pier

column

Pier Column LS-DYNA Results Theoretical

Value Error

Percentage Plastic Moment

(N*m) 9.9 x 106 10.6 x 106 6%

Strong Axis Displacement at Mid-span at Yielding (m) 5.2 5.0 4%

Plastic Moment (N*m) 8.8 x 10

6 9.1 x 106 2% Weak Axis Displacement at Mid-span

at Yielding (m) 5.5 5.9 6%

3.4 Barge Finite Element Model

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

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

internal structure of the construction barge.

20

Transverse Frame

70'-0"81'-6"

*3 Panel Longitudinal Truss

Longitudinal Truss50

'-0"

Longitudinal Truss

151'-6"

Barge Bow

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

Serrated ChannelTransverse Frame

12'-0

"

70'-0"81'-6"

Figure 3-8. Outboard profile of the construction barge

Transverse Frame C Channel

L Beam 35'-0" 35'-0"

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

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

L 3.5 x 3.5 x 5/16 typ.

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

21

1'-6" 2'-0"

35'-0"

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

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

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

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

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

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

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

stiffness to the wall plates.

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

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

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

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

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

zones, as is illustrated in Figure 3-12.

22

Zone-1Zone-2

Zone-3

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

Figure 3-12. Layout of barge divisions

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

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

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

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

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

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

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

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

occur during centerline impacts of the barge.

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

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

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

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

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

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

computing time required to perform impact analysis.

23

50'-0" Width of Barge

Central Zone(High Resolution)

Port Zone(Lower Resolution)

Starboard Zone(Lower Resolution)

Headlog of Barge

9'-4.5"

9'-4.5"

31'-3"

Zone-1

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

In zone-3, the aft portion of the construction barge functions to carry the cargo

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

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

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

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

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

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

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

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

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

24

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

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

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

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

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

assumes a rectangular cross section and internally calculates cross sectional dimensions

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

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

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

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

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

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

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

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

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

PLASTICITY material in LS-DYNA.

Contact definition *CONTACT_AUTOMATIC_SINGLE_SURFACE (self contact) is

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

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

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

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

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

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

25

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

Table 3-6 General modeling features of the jumbo hopper barge

Model Features 8-node brick elements 234 4-node shell elements 24,087 2-node beam elements 2,264 2-node Discrete Spring elements 28 1-node point mass elements 28 Model Dimensions Length 195 Ft Width 35 Ft Depth 12 Ft Contact Definitions CONTACT_AUTOMATIC_SINGLE_SURFACE CONTACT_AUTOMATIC_NODES_TO_SURFACE CONTACT_TIED_NODES_TO_SURFACE

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

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

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

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

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

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

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

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

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

26

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

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

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

Figure 3-14. Buoyancy spring distribution along the barge

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

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

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

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

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

hull are determined from the geometry of the bottom surface of the barge (see Figure 3-

14). The pre-compression of buoyancy spring is calculated using Mathcad worksheet.

The comparison of general modeling features of construction barge and open hopper

barge is provided in Table 3-5 and 3-6.

3.5 Contact Surface Modeling

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

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

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

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

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

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

27

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

pier

col

umn

shear wall

pile cap

contact surface

barge motion

water line

rigid body

Figure 3-15. Pier and contact surface layout

rigidlink

rigidcontactsurface

pier column

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

28

impact force

pier column

contact surface

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

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

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

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

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

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

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

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

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

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

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

load).

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

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

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

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

29

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

the curves are in good agreement.

0

1

2

3

4

5

6

10 20 30 40 50 600

200

400

600

800

1000

1200

1400

0 0.5 1 1.5

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush depth (in)

Crush depth (m)

rigid material

elastic material

Figure 3-18. Comparison of impact force versus crush depth for rigid and concrete

contact models

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

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

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

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

research report by Consolazio et al. [2].

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

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

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

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

30

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

31

CHAPTER 4 NON-LINEAR PIER BEHAVIOR DURING BARGE IMPACT

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

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

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

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

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

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

simulation modeling procedure.

4.1 Case Study

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

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

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

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

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

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

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

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

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

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

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

chapter are listed in Table 4-1.

32

Table 4-1. Dynamic simulation cases

Case Contact Surface Speed Impact Angle

Material Property

Loading Condition

A Rectangular 6 knot Head-on Linear Full

B Rectangular 6 knot Head-on Nonlinear Full

C Rectangular 1 knot Head-on Linear Full

D Rectangular 1 knot Head-on Nonlinear Full

4.2 Analysis Results

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

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

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

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

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

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

using nonlinear pier material and linear pier material respectively.

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

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

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

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

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

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

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

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

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

33

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

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

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

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

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

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

the bilinear moment-curvature curve.

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

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

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

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

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

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

displacement, the influence is limited.

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

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

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

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

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

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

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

34

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.50

200

400

600

800

1000

1200

1400Im

pact

forc

e (M

N)

Impa

ct fo

rce

(kip

)

Time (s)

6knot, head on, linear, full load6knot, head on, nonlinear, full load

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

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 10

200

400

600

800

1000

1200

1400

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

1knot, head on, nonlinear, full load1knot, head on, linear, full load

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

35

0

1

2

3

4

5

6

7

0 0.5 1 1.5 20

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70 80 90

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

C rush D epth (m )

Crush D epth (in)

6knot, head-on, linear, full load6knot, head-on, nonlinear, full load

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

0

1

2

3

4

5

6

7

0 0.01 0.02 0.030

200

400

600

800

1000

1200

1400

0 0.5 1

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)


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

36

-5

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5

0

0.2

0.4

0.6

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)

6knot, head-on, linear, full load6knot, head-on, nonlinear, full load

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

-4

-2

0

2

4

0 0.2 0.4 0.6 0.8 1

-0.1

-0.05

0

0.05

0.1

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

37

CHAPTER 5 SIMULATION OF OBLIQUE IMPACT CONDITIONS

Contained within the AASHTO barge impact design provisions are procedures not

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

38

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

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

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

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

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

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

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

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

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

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

the open hopper barge.

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

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

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

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

Open hopper barge

head on crush45 degree crush

15 degree crush30 degree crushpier

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

39

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.60

200

400

600

800

1000

1200

1400

0 5 10 15 20

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)

static crush 4ft-- 0 degstatic crush 4ft--15 degstatic crush 4ft--30 deg

static crush 4ft--45 deg

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

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.60

200

400

600

800

1000

1200

1400

0 5 10 15 20

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)

static crush 6ft-- 0 degstatic crush 6ft--15 degstatic crush 6ft--30 degstatic crush6ft--45 deg


40

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.60

200

400

600

800

1000

1200

1400

0 5 10 15 20

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)

static crush 8ft-- 0 degstatic crush 8ft--15 degstatic crush 8ft--30 degstatic crush8ft--45 deg


5.2 Effect of Strike Angle on Dynamic Loads and Pier Response

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

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

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

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

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

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

earlier in Chapter 3.

41

Barge head-on impact motion

Barge oblique impact motion

Traffic onsuperstructure

PierPier cap

X

Y

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

Table 5-1. Dynamic simulation cases

Case Contact Surface Speed Impact Angle

Material Property

Loading Condition

A Rectangular 6 knot Head-on Linear Full

B Rectangular 6 knot 45 degree Linear Full

C Rectangular 1 knot Head-on Linear Full

D Rectangular 1 knot 45 degree Linear Full

E Circular 6 knot Head-on Linear Full

F Circular 6 knot 45 degree Linear Full

G Circular 1 knot Head-on Linear Full

H Circular 1 knot 45 degree Linear Full

42

5.3 Dynamic Simulation Results

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

43

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

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

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

rectangular pier than for the circular pier.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

the larger contact area.

Pier impact force divided by the corresponding pier displacement indicates pier

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

44

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

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

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.50

200

400

600

800

1000

1200

1400

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

6knot, head on, linear, full load6knot, 45 deg, linear, full load, X direction

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

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.50

200

400

600

800

1000

1200

1400

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

circular, 6knot, head on, linear, full loadcircular, 6knot, 45 deg, linear, full load, X direction

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

45

0

1

2

3

4

5

6

7

0 0.5 1

0

200

400

600

800

1000

1200

1400

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

rectangular, 1knot, head on, linear, full loadrectangular, 1knot, 45 deg, linear, full load, X direction

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

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 10

200

400

600

800

1000

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)


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

46

0

1

2

3

4

5

0 0.5 1 1.5 2 2.50

200

400

600

800

1000

1200

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

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

circular, 6knot, 45 deg, linear, full load, Y direction

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

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 10

200

400

600

800

1000

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

rectangular, 1knot, 45 deg, linear, full load, Y directioncircular, 1knot, 45 deg, linear, full load, Y direction

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

47

0

1

2

3

4

5

6

7

0 0.5 1 1.5 20

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70 80 90

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)

rectangular, 6knot, head on, linear, full loadrectangular, 6knot, 45 deg, linear, full load

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

0

1

2

3

4

5

6

7

0 0.5 1 1.5 20

200

400

600

800

1000

1200

1400

0 10 20 30 40 50 60 70

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)

circular, 6knot, head on, linear, full loadcircular, 6knot, 45 deg, linear, full load

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

48

0

1

2

3

4

5

6

7

0 0.01 0.02 0.03 0.04 0.05 0.060

200

400

600

800

1000

1200

1400

0 0.5 1 1.5 2 2.5

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Crush Depth (m)

Crush Depth (in)


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

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.01 0.02 0.03 0.04 0.05 0.060

200

400

600

800

10000 0.5 1 1.5 2 2.5

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

C rush Depth (m)

Crush Depth (in)

circular, 1knot, head on, linear, full loadcircular, 1knot, 45 deg, linear, full load

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

49

-5

0

5

10

15

20

0 0.5 1 1.5 2 2.5

-0.1

0

0.1

0.2

0.3

0.4

0.5

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

-1

0

1

2

3

4

5

0 0.5 1

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

50

-4

-2

0

2

4

6

8

10

0 0.5 1 1.5 2 2.5-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

-1

0

1

2

3

4

5

0 0.5 1

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

51

-2

0

2

4

6

8

10

0 0.5 1 1.5 2 2.5-0.05

0

0.05

0.1

0.15

0.2

0.25

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

-1

0

1

2

3

4

5

0 0.5 1

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

pier

impa

ct p

oint

dis

pl. (

in)

pier

impa

ct p

oint

dis

pl. (

m)

Time (s)


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

52

CHAPTER 6 EFFECT OF CONTACT SURFACE GEOMETRY ON PIER BEHAVIOR

DURING IMPACT

6.1 Case Study

In the previous chapter, it was noted that rotation of a square pier relative to the

direction of impact (i.e., creation of an oblique impact condition) has an effect on impact

loads and on pier response. These effects are due partially to the fact that the shape of the

impact surface between the barge and pier changes as the square pier is rotated. In this

chapter, the effect of contact surface geometry is explored further. Of interest is whether

or not fundamentally differing pier cross-sectional shapes, e.g. square versus circular,

produce substantially differing loads and pier responses. A parametric study is conducted

involving two types of pier cross-sectional geometry (rectangular and circular), two

impact speeds (1 knot and 6 knots), and two impact angles (0 and 45 degrees). Cases

discussed in this chapter are the same as those shown in Table 5.1 of Chapter 5.

6.2 Results

Figure 6-1 to Figure 6-16 present results from cases A, B, C, D, E, F, G, and H

listed in Table 5.1. As described in the previous chapter, the X direction represents the

direction “parallel to the alignment of the centerline of the navigable channel” and the Y

direction represents the direction “longitudinal to the substructure.” Relationships

between impact force and crush depth (Figures 6-13 – 6-16) utilize vector-resultant

forces and vector-resultant crush depths rather than component values in the X and Y

directions.

53

Figures 6-1 through 6-4 show impact force histories in X direction for both

rectangular and the circular piers. For high-speed cases (Figures 6-1 and 6-2), the impact

force histories for both oblique and head-on impacts indicate that both pier-column

geometries (rectangular and circular) produce approximately the same peak impact force.

For the low speed, head-on impact cases (Figure 6-3), the impact force peak value for the

circular pier is approximately half of that for the rectangular pier. Conversely, in low

speed, oblique impact cases (Figure 6-4), the peak impact forces for both circular and

rectangular piers are nearly the same. Figures 6-5 and 6-6 show the impact force histories

in the Y direction for oblique impact conditions.

Computed pier displacements in the X direction are shown in Figures 6-7 through

6-10, while displacements in the Y direction as shown in Figures 6-11 and 6-12. In all

cases considered, peak predicted displacements (in either the X or Y directions) are

approximately the same for both square and circular piers indicating little or no

sensitivity to pier-column cross-sectional shape.

Resultant impact force versus resultant barge crush depth relationships are shown

in Figures 6-13 through 6-16- In each plot, the area under the curve represents the

approximate amount of energy that is dissipated through plastic deformation of the steel

plates in the bow of the barge. In both of the high speed (6 knot) impact cases (Figures 6-

13 and 6-14), the initial kinetic impact energy of the barge is sufficient to cause

significant plastification of the barge bow. In these cases, it is evident that the quantify of

dissipated energy is approximately the same for the square and circular piers. In the low

speed head-on impact cases (Figure 6-15), the initial kinetic impact energy is insufficient

to cause significant plastic deformation and the responses for the square and circular piers

54

are quite different. However, when simulations are conducted at the same speed (1 knot)

but at an oblique impact angle (Figure 6-16), the computed responses (and dissipated

energy levels) are again very similar between the square and circular pier cases. As was

demonstrated in Chapter 5 (and specifically Figure 5.3), rotation of a square pier relative

to the barge headlog tends to reduce the stiffness of the bow and thus produce results

similar to those obtained for a circular pier.

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5

0

200

400

600

800

1000

1200

1400

Impa

ct fo

rce

(MN

)

Impa

ct fo

rce

(kip

)

Time (s)

rectangular, 6knot, head on, linear, full loadcircular, 6knot, head on, linear, full load

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

55

0

1

2

3

4

5

0 0.5 1 1.5 2 2.50

influence of pier nonlinearity, impact angle, and column shape on pier...

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