DEGREE PROJECT, IN DIVISION OF STRUCTURAL ENGINEERING AND , SECOND LEVELBRIDGES

STOCKHOLM, SWEDEN 2015

Simulation of vehicle crash into bridgeparapet using Abaqus/Explicit

DALY OGMAIA & SEBASTIAN ELIAS TASEL

KTH ROYAL INSTITUTE OF TECHNOLOGY

DEPARTMENT OF CIVIL AND ARCHITECTURAL ENGINEERING

TRITA BKN. MASTER THESIS 451ISSN 1103-4297ISRN KTH/BKN/EX-451-SE

www.kth.se

Preface

Firstly, we would like to thank ELU Konsult AB and our examiner Costin Pacoste for

introducing and giving us the opportunity to write this thesis. Special thanks to Frank

Axhag for his supervision during the process of the master thesis. Many thanks to Abbas

Zangeneh at KTH/ELU Konsult AB for the support and guidance during the master

thesis.

Also we would like to thank our teachers and assistants for everything they have thought

us during our five years at KTH. Many thanks to our fellow students for making the

time at KTH a pleasant journey. Finally, we would like to thank our family and friends

for their support.

At last, we hope that you as a reader will enjoy reading this report. A lot of e↵ort and

time has been invested in order to make the report interesting and easy to follow.

June 2015

Daly Ogmaia

Sebastian Elias Tasel

i

Abstract

Safety is an important aspect when designing bridges and roads. One aspect among

others to consider is the road restraint systems. The focus of this study was centered

to safety barriers which are the vehicle parapets/guardrails. The parapet must meet

certain requirements specified in European Standard in order to obtain a CE-marking,

indicating the acceptance of use. Full-scale test must be performed for a proposed

parapet to evaluate the performance. Often several full-scale tests are performed in

order to achieve CE-marking, making it an expensive process.

The primary objective of this master thesis was to investigate if Abaqus/Explicit could

be used as the finite element software for simulation of crashes. Secondary objective was

to investigate how well a performed full-scale crash could be simulated in Abaqus/Ex-

plicit. A full-scale test was conducted and the parapet installation and vehicle used was

modeled. Same conditions as in the full-scale were used in the simulation.

The results indicated that it is possible to simulate the full-scale crash using Abaqus/-

Explicit. However, the behavior of the full-scale test was not completely captured. The

maximum dynamic and permanent horizontal deflection of the tabular thrie beam in the

full-scale test was 582 mm and 515 mm, corresponding value from the simulation was

703 mm and 643 mm.

The conclusion from the results is that Abaqus/Explicit is a suitable finite element

software for simulating crashes. The di↵erences between the full-scale test and the

simulations in this master thesis were due to the simplifications and assumptions used

when modeling the parapet, bridge deck and the vehicle. The overall global behavior

of the full-scale test was not captured, however the simulation results were not far from

the full-scale test even though rough simplifications and assumptions were used in the

modeling. We believe that with more care to details in modeling, it should be possible

to have better convergence between simulation and the full-scale test.

Keywords: Parapet, Guardrail, Vehicle crash, Full-scale test, Abaqus/Explicit, Simu-

lation

iii

Sammanfattning

Sakerhet ar en viktig aspekt vid utformningen av broar och vagar. En av aspekterna

som maste beaktas ar utformningen av vagracken. Dessa vagracken maste uppfylla vissa

krav som anges i Europeisk standard for att erhalla sa kallad CE-markning, som anger

godkannande av anvandning. Verkliga tester maste utforas for ett foreslaget vagracke

for att evaluera prestanda och darigenom erhalla CE-markningen. Denna process kan

bli kostsam da flera tester kan behova goras for att uppna ratt prestanda.

Syftet med detta examensarbete var att undersoka om Abaqus/Explicit kan anvandas

som finita element program for att utfora kraschsimulering och hur val en genomford

verklig krasch kan simuleras. Ett verkligt test studerades, vagracket, brobaneplat-

tan och fordonet som anvandes vid denna test modellerades i Abaqus/CAE. Samma

forutsattningar som i testet anvandes i simuleringen.

Resultaten tyder pa att det ar mojligt att simulera verkliga krascher i Abaqus/Explicit.

Det globala beteendet av testet fangades inte upp helt i simuleringen men beteendet var

dock inte allt for langt ifran. Den maximala dynamiska och permanenta horisontella

utbojningen av profilracket uppgick till 582 mm respektive 515 mm, motsvarande varde

fran simuleringen var 703 mm respektive 643 mm.

Slutsatsen ar att Abaqus/Explicit ar ett lampligt finita element program for simu-

lering av krascher. Skillnaderna mellan verkliga testet och simuleringen ar pa grund

av de forenklingar och antaganden som har gjorts vid modellering av brobaneplattan,

vagracket och fordonet. Vi tror att med mer omsorg kring detaljerna i modelleringen

gallande brobaneplattan och vagracket, bor det vara mojligt att ha en battre konvergens

mellan simuleringen och verkliga testet.

v

Contents

Preface i

Abstract iii

Sammanfattning v

Abbreviations xiii

Symbols xiv

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Summary of previous work . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Conclusions from previous work . . . . . . . . . . . . . . . . . . . . 3

1.4 Scope and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Finite Element Theory 5

2.1 General about Abaqus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Abaqus/Explicit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Essential di↵erences between implicit and explicit . . . . . . . . . . . . . . 7

2.4 Automatic time incrementation and stability . . . . . . . . . . . . . . . . 8

2.4.1 Definition of the stability limit . . . . . . . . . . . . . . . . . . . . 9

2.4.2 Fully automatic time incrementation versus fixed time incremen-

tation in Abaqus/Explicit . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.3 Mass scaling to control time incrementation . . . . . . . . . . . . . 11

2.4.4 E↵ect of material on stability limit . . . . . . . . . . . . . . . . . . 11

2.5 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Method 13

3.1 The process of the master thesis . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Full-scale crash test on the modified T8 bridge rail . . . . . . . . . . . . . 14

3.2.1 Geometry and conditions for the guardrail installation . . . . . . . 14

3.2.2 Crash test conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 21

vii

Contents

3.2.3 Test vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Finite element modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3.1 Vehicle model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3.1.1 Modification of the material properties . . . . . . . . . . 25

3.3.1.2 Geometry of the vehicle model . . . . . . . . . . . . . . . 26

3.3.2 Modeling of the modified T8 bridge rail . . . . . . . . . . . . . . . 27

3.3.2.1 Modeling of the vertical posts . . . . . . . . . . . . . . . 27

3.3.2.2 Modeling of the thrie beam . . . . . . . . . . . . . . . . . 30

3.3.3 Modeling of the bridge deck . . . . . . . . . . . . . . . . . . . . . . 33

3.3.4 Assembled model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.5 Analysis step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.6 Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.6.1 Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.6.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.6.3 Connections . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.7 Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.8 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.8.1 Summary of the assumptions and simplifications . . . . . 43

4 Results 44

4.1 Results of the full-scale crash test . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.1 Damage to the test installation . . . . . . . . . . . . . . . . . . . . 48

4.1.2 Damage to the test vehicle . . . . . . . . . . . . . . . . . . . . . . 51

4.2 Results of the simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.1 Damage to the modeled installation . . . . . . . . . . . . . . . . . 55

4.2.2 Damage to the modeled vehicle . . . . . . . . . . . . . . . . . . . . 57

4.2.3 Energy quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.3 Qualitative comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.4 Quantitative comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Discussion and conclusions 68

6 Future work 71

Bibliography 73

Appendix A 75

A.1 Bolt connection properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A.2 Bending moment capacity of the post . . . . . . . . . . . . . . . . . . . . 77

Appendix B 79

Contents

B.1 Post deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

B.1.1 Initial angular deflection of posts 11-13 . . . . . . . . . . . . . . . 79

B.1.2 Mean angular deflection for posts 5-9 . . . . . . . . . . . . . . . . . 80

B.1.3 Angular deflection for posts 10-15 . . . . . . . . . . . . . . . . . . 80

B.1.4 Vertical deflection for posts 10-15 . . . . . . . . . . . . . . . . . . . 81

B.2 Tabular thrie beam deformations . . . . . . . . . . . . . . . . . . . . . . . 81

B.3 Vehicle position, speed and angular deflection . . . . . . . . . . . . . . . . 82

List of Figures

2.1 The di↵erence in calculation cost between implicit and explicit solver [1]. 8

3.1 Working procedure of the thesis. . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Plan view of the tested installation[2]. . . . . . . . . . . . . . . . . . . . 15

3.3 Elevation view of the tested installation[2]. . . . . . . . . . . . . . . . . . 15

3.4 Plan view of the transition zone[2]. . . . . . . . . . . . . . . . . . . . . . 15

3.5 Elevation view of the transition zone[2]. . . . . . . . . . . . . . . . . . . 16

3.6 Detail of the slotted holes[2]. . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.7 Section of the tested installation[2]. . . . . . . . . . . . . . . . . . . . . . 17

3.8 Additional details of the posts[2]. . . . . . . . . . . . . . . . . . . . . . . 18

3.9 Plastic o↵set block [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.10 Plan and elevation view of the rebar arrangement [2]. . . . . . . . . . . . 19

3.11 Details of the rebar arrangement [2]. . . . . . . . . . . . . . . . . . . . . . 20

3.12 The complete installation prior to testing [2]. . . . . . . . . . . . . . . . . 20

3.13 Impact point and the angle between the vehicle and rail [2]. . . . . . . . . 21

3.14 The 2000 Chevrolet C2500 pickup truck used for the test [2]. . . . . . . . 22

3.15 The vehicle and installation prior the crash testing [2]. . . . . . . . . . . 22

3.16 Dimensions and other relevant distances[2]. . . . . . . . . . . . . . . . . 23

3.17 The imported vehicle in Abaqus/CAE. . . . . . . . . . . . . . . . . . . . 25

3.18 Elevation of the posts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.19 Cross section of the vertical posts. . . . . . . . . . . . . . . . . . . . . . . 29

3.20 The meshed vertical post. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.21 Cross section for the 12-gauged thrie beam. . . . . . . . . . . . . . . . . 31

3.22 Elevation of the thrie beam. . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.23 The meshed thrie beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.24 Plan view of the bridge deck. . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.25 Close up view of the notches created. . . . . . . . . . . . . . . . . . . . . 33

3.26 The assembled tabular cross section. . . . . . . . . . . . . . . . . . . . . 34

3.27 The alignment of the tabular thrie beam and the vertical post. . . . . . . 35

3.28 Vehicle position prior impact. . . . . . . . . . . . . . . . . . . . . . . . . 36

3.29 The assembled model with post numbers - isoparametric view. . . . . . . 36

3.30 Tie constraints between the two thrie beams forming the tabular thrie

beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.31 Rotation center in the bridge deck. . . . . . . . . . . . . . . . . . . . . . 39

x

List of Figures

3.32 The constraints between the vertical posts and the rotational center. . . . 39

3.33 The connection between the tabular thrie beam and vertical post. . . . . . 40

3.34 The fixed boundary condition applied to the end post. . . . . . . . . . . . 42

4.1 Sequential photographs of the test, overhead and frontal view [2]. . . . . . 45

4.2 Sequential photographs of the test, overhead and frontal view (contin-

ued)[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.3 Rear view of the crash[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.4 The impact point and end point of the vehicle[2]. . . . . . . . . . . . . . 48

4.5 Damage to the test installation[2]. . . . . . . . . . . . . . . . . . . . . . . 49

4.6 Permanent deformation to the test installation[2]. . . . . . . . . . . . . . 50

4.7 Vehicle after being up-righted [2]. . . . . . . . . . . . . . . . . . . . . . . 51

4.8 Sequential simulations photographs - top and front view. . . . . . . . . . 52

4.9 Sequential simulations photographs - top and front view (continued). . . 53

4.10 Sequential simulations photographs - rear view. . . . . . . . . . . . . . . 54

4.11 Deflection of the posts which experienced the largest deformations. . . . . 55

4.12 Damage to the modeled installation - front view. . . . . . . . . . . . . . . 56

4.13 Damage to the modeled installation - rear view. . . . . . . . . . . . . . . 56

4.14 Damage to the vehicle at 0.6 s. . . . . . . . . . . . . . . . . . . . . . . . 57

4.15 Energy quantities for the whole model. . . . . . . . . . . . . . . . . . . . 58

4.16 Di↵erence in the total energy for the whole model. . . . . . . . . . . . . . 59

4.17 Sequential crash photographs comparison - front view. . . . . . . . . . . . 60

4.18 Sequential crash photographs comparison - front view (continued). . . . . 61

4.19 Sequential crash photographs comparison - top view. . . . . . . . . . . . 62

4.20 Sequential crash photographs comparison - top view (continued). . . . . . 63

4.21 Sequential crash photographs comparison - rear view. . . . . . . . . . . . 64

4.22 Sequential crash photographs comparison - rear view (continued). . . . . 65

B.1 Initial angular deflection of post 11-13. . . . . . . . . . . . . . . . . . . . 79

B.2 Mean angular deflection for posts 5-9. . . . . . . . . . . . . . . . . . . . 80

B.3 Angular deflection for posts 10-15. . . . . . . . . . . . . . . . . . . . . . 80

B.4 Deflection towards field side, U2, for posts 10-15. . . . . . . . . . . . . . 81

B.5 Maximum deflection of the tabular thrie beam. . . . . . . . . . . . . . . . 81

B.6 Vehicle angle during the impact. . . . . . . . . . . . . . . . . . . . . . . . 82

B.7 Vehicle speed during the impact. . . . . . . . . . . . . . . . . . . . . . . . 82

B.8 The vehicle position and time when it was parallel to the rail. . . . . . . 83

List of Tables

3.1 Geometry of the vehicle[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Changes to some material properties of the vehicle. . . . . . . . . . . . . . 26

3.3 Geometry of the vehicle model compared to tested vehicle. . . . . . . . . . 27

3.4 Properties used for the vertical posts. . . . . . . . . . . . . . . . . . . . . . 28

3.5 Material properties used for the thrie beam. . . . . . . . . . . . . . . . . . 30

3.6 Properties of the Cartesian connector section. . . . . . . . . . . . . . . . . 40

3.7 Properties of the Cartesian+Rotation connector section. . . . . . . . . . . 41

4.1 Post deformation and deflection[2]. . . . . . . . . . . . . . . . . . . . . . . 48

4.2 Post deformation and deflection in the simulation. . . . . . . . . . . . . . 55

4.3 Post angular deflection - comparison. . . . . . . . . . . . . . . . . . . . . . 66

4.4 Post deflection - comparison. . . . . . . . . . . . . . . . . . . . . . . . . . 67

xii

Abbreviations

ASTM American Society for Testing and Materials

CAE Complete Abaqus Environment

CE Conformite Europeenne

CEN European Committee for Standardization

CFD Computational Fluid Dynamics

CIP Critical Impact Point

CORM Constrained Components of Relative Motion

DOF Degrees Of Freedom

EN European Standard

FE Finite Element

FEM Finite Element Method

FHWA Federal Highway Administration

HDPE High Density Polyethylene

INP-files Input Files

LON Length Of Need

LS-DYNA Livermore Software Dynamic Non-Linear Finite Element Program

MPC Multi-Point Constraint

NCAC National Crash Analysis Center

NCHRP National Cooperative Highway Research Program

RC Rotation Center

TL Test Level

US United States

xiii

Symbols

M Nodal mass matrix

P External forces

I Internal element forces

u Nodal displacement

u Nodal velocity

u Nodal acceleration

t Time

�t Time increment

�✏ Strain increment

✏ Strain rate

� Element stress

�tstable Stable time increment

!max Maximum eigenfrequency

⇠ Damping ratio

Le Element length

cd Material wave speed

E Young�s modulus

⇢ Mass density

EI Internal energy

EV Dissipated viscous energy

EFD Dissipated frictional energy

EKE Kinetic energy

EIHE Internal heat energy

EW External work

EPW Contact penalty work

xiv

Symbols

ECW Constraint penalty work

EMW Propelling added mass work

EHF External fluxes energy

Etotal Total energy

EE Recoverable elastic strain energy

EP Dissipated energy due to plasticity

ECD Dissipated energy due to creep

EA Artificial strain energy

EDMD Dissipated energy due to damage

EDC Dissipated energy due to distortion control

EFC Fluid cavity energy

Chapter 1

Introduction

1.1 Background

A vital part when designing bridges and roads is safety. Several aspects need to be

accounted for in order to obtain a satisfactory level of safety for the users. One aspect

among others to consider is the road restraint systems. The road restraint systems con-

sist of vehicle restraint systems and pedestrian restraint systems. The vehicle restraint

systems consist of safety barriers, terminals, transitions, removable barrier sections and

crash cushions. The focus of this study was centered to safety barriers which are the

vehicle parapets also known as guardrails. A parapet functions as a barrier or/and as a

guardrail which prevent dangerous accidents such as driving o↵ the bridge.

Di↵erent properties must be taken into consideration when these parapets are designed,

one of these properties is the global sti↵ness. The sti↵ness can neither be too high nor

too low. In a scenario where the sti↵ness of the parapet is too high it would create

great amount of damage to the vehicle and the passengers. This can be compared to

a vehicle crashing into a rigid concrete wall. In the other scenario where the sti↵ness

is too low, the parapet would snap during the impact and not fulfill its function. The

reader realizes that finding the right sti↵ness is a tightrope walk which is dependent on

several factors.

In order to be allowed to use these parapets on bridges and roads, certain requirements

must be met according to European Standards, EN, which are approved by the European

committee for standardization, CEN. The parapet obtains a Conformite Europeenne

marking, CE-marking, indicating that the parapets can be sold in EU member countries.

In order to obtain a CE-marking, full-scale tests must be performed to assess the real

behavior of the parapets. As for all real life testing it is expensive to build and perform

1

Introduction

these tests. Often more than one full-scale test is necessary to achieve CE-marking since

it is di�cult to design a parapet and its structural system to meet the requirements

in the EN standards in the first attempt. This may lead to extensive costs for the

suppliers to achieve CE-marking for the proposed parapet. To minimize these costs it is

a necessity to develop a finite element model that can simulate the crash and study the

e↵ect of di↵erent modifications of the parapets. The designer could perform simulations

in order to meet the requirements in these simulations and then perform a full-scale test

based on the dimensions used in the finite element model.

However, in order to develop a finite element model which works properly it is of great

importance to validate the model against previous full-scale crash tests. If the model

complies with the full-scale crash test, then the designer can change the geometry of

the parapet or replacing it completely and study the e↵ects of the changes in the model

before making any full-scale test on the new proposal of the parapet.

1.2 Aim

The primary objective of this master thesis was to investigate the potential of Abaqus/-

Explicit as the tool to simulate vehicle crashes into bridge parapet or parapet in general.

This study also aimed to determine how well a performed full-scale crash could be sim-

ulated in Abaqus/Explicit.

1.3 Summary of previous work

State-of-the-art reports have been reviewed in crash simulations. Generally, these reports

show that the finite element software commonly used is LS-DYNA. One of these reports

indicated that it was fully possible to make simulations in LS-DYNA that are almost

identical to the full-scale test[3]. The authors in [3] studies the bridge rail-to-guardrail

transitions. The intent of their study was twofold, firstly to accurately simulate an

observed full-scale crash test behavior and secondly to compare e↵ects of di↵erent design

alternatives that results in acceptable crash test performance in a cost-e↵ective manner.

The main reason for using LS-DYNA was that it is a software well established for

simulations involving high speed dynamics. Another advantage of using LS-DYNA was

the accessibility of adapted vehicle models. There are several vehicle models available at

the website of National Crash Analysis Center, NCAC, these models are developed for

use in LS-DYNA[4]. The vehicle models were developed and validated using multiple

impact data as mentioned in [3], crucial part for these vehicles were modeled through a

2

Introduction

detailed component testing program at NCAC. The C-2500 pickup truck vehicle model

has been used in previous finite element studies and it was demonstrated that this vehicle

model was fairly accurate in representing impact simulations[3].

A technical report written by Nauman M. Sheikh et al. was reviewed where finite element

simulations were performed for several guardrail systems. LS-DYNA was used as the

finite element software. The technical report was produced as a product of a research

to develop finite element simulations as the tool to evaluate the performance of selected

roadside safety devices subjected to very high-speed impacts[5]. The finite element

models developed for the di↵erent guardrail systems used in [5] were very detailed. The

authors considered details ranging from the connections including bolts to the post-soil

interaction. The vehicle models used in [5] were the C2500 pickup, similar to the one used

in [3], and a small passenger car. These vehicles were from the NCAC, however slightly

modified and improved by the authors in order to further reflect the true behavior of the

real pickup truck[6]. As in previous report, [3], the authors in [5] manage to simulate a

full-scale test with great precision.

Reports regarding Abaqus/Explicit as the finite element tool instead of LS-DYNA for

crash simulations have been reviewed in order to determine the crashworthiness of

Abaqus/Explicit. Reports such as [7] indicated that Abaqus/Explicit is fully capable to

simulate the behavior of full-scale test given su�cient care for key properties.

In 2012 Simulia published a paper from the 2012 Simulia Community Conference where

crash simulations in Abaqus/Explicit were performed. Comparison with a full-scale

crash test was presented in [8]. This paper indicated that it should be possible to

simulate and have good correlation with full-scale test if relevant details were modeled

properly. The authors in [8] paid a lot of attention to the soil-post interaction and the

connection of the guardrail to the post. However, the authors did not mention how the

vehicle model was converted from a LS-DYNA model from the website of NCAC to an

Abaqus CAE model.

1.3.1 Conclusions from previous work

Conclusions from the state-of-the-art study are listed below:

• There is no ”ready-to-go” vehicle model adapted for the Abaqus/Explicit.

• The mass and geometry of the vehicle is of great importance.

• The vertical post and the thrie-beam should be modeled using shell element to

reflect the true behavior of these parts.

3

Introduction

• The connection between the vertical posts and thrie-beam should be given su�cient

care.

• The interaction between the bottom of the vertical post and surrounding areas

such as the soil or pavement should also be addressed.

• Friction between the vehicle tires and the pavement should reflect reality.

• Small enough mesh should be used for areas in contact to avoid penetration.

• The simulations should always be validated against full-scale crash test.

The main problem when using Abaqus/Explicit as the finite element software is that

there is no vehicle model available today. Realistic vehicle model is a must in order to

obtain results from simulations that are close to the full-scale crash test.

1.4 Scope and limitations

Since this study was aiming to investigate the potential of Abaqus/Explicit as the finite

element tool to simulate vehicle crashes, the simulation was validated against one full-

scale crash test. However, only certain properties were validated due to time constraints.

The finite element model’s ability to reflect the passenger damage was not considered in

this study. The important issue was to have a model that reflected the global behavior

of the full-scale test.

The full-scale crash test was not based on the European regulations, instead it was based

on National Cooperative Highway Research Program, NCHRP, report 350 test 3-11 on

the modified T8 bridge rail[2]. Performing organization was the Texas Transportation

Institute, the report number was Report 0-5210-6. The decision to use this report as

the base of validation was due to the amount of information the report contained.

Validation of the simulation was mainly qualitative, however some quantitative proper-

ties were made but not to greater extent.

4

Chapter 2

Finite Element Theory

Finite Element Method, FEM, is a numerical calculation method which solves various

di↵erential equations with the aid of a computer. FEM divide a continuum into a finite

number of elements. The characteristic feature of FEM is that instead of solving the

di↵erential equation for the whole continuum, they are solved approximately for the

finite elements. The elements are connected at nodes holding the elements together.

The nodal points are the ends of the each element, each node has a number of degrees of

freedom, DOF, such as translation and rotation in x and y for a 2D analysis and x, y and

z-direction for a 3D analysis. From the values of the nodal DOF’s the element behavior

can be determined in a controlled manner with the aid of predefined equations, and

since the mechanical behavior of the material is known, the corresponding mechanical

behavior of each element is determined. This is performed for every single element

forming the continuum allowing the possibility to obtain an approximate solution for

the entire continuum.

2.1 General about Abaqus

Abaqus is a finite element program originally developed by Dassault Systemes. Abaqus is

a suite of engineering simulation programs that can solve problems ranging from simple

linear analysis to highly complex nonlinear dynamic simulations. It consists of wide

range of elements which make it possible to model any type of geometry. It has a broad

list of material models that can be used to simulate material behavior of interest such

as steel, concrete, aluminum, geotechnical materials such as soils and rock and other

materials not mentioned here. In a nonlinear analysis Abaqus automatically chooses

and adjust the load increment and convergence tolerance during the analysis to ensure

that an accurate solution is obtained.

5

Finite Element Theory

Abaqus consists of three main analysis products each one of them suitable for di↵erent

physical problems. These analysis products are Abaqus/Standard, Abaqus/Explicit and

Abaqus/CFD. Abaqus/Standard is a general-purpose analysis that can solve linear and

nonlinear problems involving static, dynamic and other type of engineering problems,

the standard uses the implicit method to solve the problems. Abaqus/Explicit is an

analysis product used in special-purpose, this product uses an explicit dynamic finite

element formulation. It is suitable for brief, transient dynamic events, such as impact

problems. It is also preferred for problems involving large deformations, i.e. highly

nonlinear problems. Abaqus/CFD is used to study fluid dynamics[9].

Since this master thesis involves impact analysis with large deformation Abaqus/Ex-

plicit is deemed suitable.

2.2 Abaqus/Explicit

Abaqus/Explicit uses, as the name indicate, explicit methods to integrate through time.

The explicit method used is the central di↵erence method, which integrate the equations

of motion through time. It uses kinematic conditions at one increment to calculate the

kinematic conditions at the next increment. When the solver is initiated it solves for

the dynamic equilibrium[10], equation 2.1,

Mu = P� I (2.1)

where:

M, is nodal mass matrix,

P, I, are the external applied forces and internal element forces,

u, is the nodal acceleration.

From equation 2.1 the nodal accelerations are obtained in the beginning of the current

increment, time t, as

u|(t) = M

�1(P� I)|(t). (2.2)

The explicit solver uses lumped mass matrix, a diagonal mass matrix, which makes the

calculations for accelerations elementary. There are no simultaneous equations to solve,

the nodal acceleration of any node is determined by its mass and the net force acting

on it, resulting in inexpensive calculations.

6

Finite Element Theory

Nodal velocities are calculated through the known nodal accelerations. Nodal acceler-

ations are integrated through time using central di↵erence rule. Change in velocity is

calculated assuming that the acceleration is constant, this change of the velocity is then

added to the velocity from middle of the previous increment to determine the velocity

at the middle of current increment:

u|(t+�t

2

) = u|(t��t

2

) +�t|(t+�t) +�t|(t)

2u|(t) (2.3)

When the nodal velocities are calculated, the solver integrates these velocities in order

to obtain the nodal displacement as:

u|(t+�t) = u|(t) +�t|(t+�t)u|(t+�t

2

) (2.4)

As mentioned above, the explicit method assumes constant acceleration for each incre-

ment. In order to obtain results that are accurate, su�ciently small time increments

must be used in order to have nearly constant accelerations during an increment result-

ing in analysis with large number of increments. However, each increment is inexpensive

since there are no simultaneous equations to solve.

Knowing the nodal displacement, the solver initiates element calculations. The element

strain increments, �✏, are computed from the strain rate, ✏. The computed strain

increment makes it possible to compute the element stresses, �, by applying the material

constitutive relationships i.e. the element sti↵ness. Symbolically this could be written

as:

�(t+�t) = f(�(t),�✏) (2.5)

and consequently, internal forces are assembled, I(t+�t).

The process described above is performed for each time increment, when all above men-

tioned steps are applied for the current increment the process is repeated for the next

increment by setting the new time, t, to t = t+�t and returning to equation 2.2.

2.3 Essential di↵erences between implicit and explicit

The characteristics of implicit and explicit methods make them suitable for di↵erent

types of problems. Explicit methods demand less disk space and memory usage than

7

Finite Element Theory

the implicit solver, which is partly due to that no iteration is performed within each

time step and partly due to the usage of the diagonal, lumped mass matrix, the system

to be solved is uncoupled. The convergence problem that may be present in implicit

methods can be avoided with an explicit method[11]. The greatest feature of the explicit

method is the absence of a global tangent sti↵ness matrix, which is required with implicit

methods. Since the state of the model is advanced explicitly, iterations and tolerances are

not required[12]. Another advantage of explicit method over the implicit one is the cost

of calculations due to increase number of DOF:s. The di↵erence is shown schematically

in Figure 2.1.

Figure 2.1: The di↵erence in calculation cost between implicit and explicit solver [1].

2.4 Automatic time incrementation and stability

As mentioned in Section 2.2, the time incrementation is vital for the Explicit solver

to be stable. It is the stability limit that dictates the maximum time increment used,

making it the critical factor for the performance of Abaqus/Explicit. The Explicit solver

is conditionally stable meaning that the amount of time that the state of the simulation

can be advanced and still remain accurate is short. If the time increment is larger than

this maximum amount of time, the increment is said to have exceeded the stability limit.

Exceeding the stability limit results in unbounded solutions[13]. Generally it is not

easy to determine the stability time exactly, conservative estimates are used instead.

Since the stability limit has great influence on reliability and accuracy, it must always

be determined consistently and conservatively. However, the time increment cannot

be arbitrarily small due to computational e�ciency. Abaqus/Explicit chooses the time

increments to be as close as possible to the stability time limit without exceeding it.

8

Finite Element Theory

2.4.1 Definition of the stability limit

The stability limit is defined in terms of the highest circular frequency in the system,

!max. Without considering damping for the system the stability limit is calculated as

�tstable =2

!max, (2.6)

and if damping is considered the expression above becomes

�tstable =2

!max

⇣p1 + ⇠2 � ⇠

⌘, (2.7)

where ⇠ is the fraction of the critical damping in the mode with the highest frequency.

From basic dynamics it is known that critical damping is defined as the limit between

oscillatory and non-oscillatory motion in the context of free-damped vibration. It should

be mentioned that Abaqus/Explicit always introduces a small amount of damping in the

form of bulk viscosity to control high-frequency oscillations[14].

However, to determine the actual highest frequency in the system is based on a complex

set of interacting factors and the task is not computational feasible to calculate its exact

value. An estimate which is simple, e�cient and conservative is used. Instead of looking

at the global model, the highest frequency of each individual element in the model is

estimated. This frequency is always associated with the dilatational mode. It is shown

that the highest element frequency determined on an element-by-element basis is always

higher than the highest frequency in the assembled finite element model[14]. Given the

fact in the previous sentence the stability limit defined in expression 2.7 can be based on

element-by-element basis and be redefined using the element length, Le, and the wave

speed of the material, cd, as

�tstable =Le

cd. (2.8)

It is clear that the shorter the element length, the smaller stability limit. The wave

speed is a property of the material. For linear elastic material with Poisson’s ratio of

zero the wave speed is defined as

cd =

sE

⇢, (2.9)

where E is Young’s modulus and ⇢ is the mass density.

9

Finite Element Theory

The simplified stability limit makes it possible to predict the stability limit given the

smallest element length and material. For example a material with a wave speed of 5000

m/s (close to steel) and with the smallest element dimension of 100 mm, the stability

limit is 2⇥ 10�5 s.

2.4.2 Fully automatic time incrementation versus fixed time incremen-

tation in Abaqus/Explicit

The equations discussed in Section 2.4.1 are used in Abaqus/Explicit to adjust the

time increment size throughout the analysis so that the stability limit, based on the

current state of the model, is never exceeded. Time incrementation is automatic and

requires no user intervention, not even a proposal for the initial time incrementation.

The stability limit is a mathematical concept resulting from the numerical model. The

Explicit solver has all the relevant details needed and can determine an e�cient and

conservative stability limit. However, it is possible for the user to override the automatic

time incrementation if desired.

If the automatic time incrementation is overridden the user must choose the time incre-

ment with caution. Failure to use small enough time increment will result in unstable

solution. The time history response of solution variables such as displacement will usu-

ally oscillate with increasing amplitudes when instability is at hand. The total energy

will also change significantly.

In nonlinear problems - problems with large deformation and with nonlinear material

response, as in this master thesis, the highest frequency of the model will continually

change resulting in change of the stability limit. Abaqus/Explicit has two strategies

for time incrementation control, fully automatic time incrementation, where the code

accounts for changes in the stability limit, and fixed time incrementation[15].

Two types of estimates are used for automatic time incrementation in order to deter-

mine the stability limit: element-by-element and global. Every analysis starts with the

element-by-element estimation method and may switch to the global estimator given cer-

tain circumstances during the analysis. The element-by-element is conservative, meaning

that it will produce a smaller stable time increment than the true stability limit based

upon the maximum frequency of the entire model. It is of great importance to know

that constraints such as boundary conditions and kinematic contact have the e↵ect of

compressing the eigenvalue spectrum which is not taken into account by the element-

by-element estimator.

10

Finite Element Theory

The global estimation algorithm determines the maximum frequency of the entire model

using current dilatational wave speed. This algorithm continuously updates the max-

imum frequency to have accurate stability limit. The global estimator will usually

allow for time increments that exceeds the values determined by the element-by-element

estimator[15].

A fixed time incrementation procedure is also available, the fixed time increment size is

determined by the initial element-by-element stability estimate for the step or by a time

increment specified by the user.

2.4.3 Mass scaling to control time incrementation

Since the mass density have great influence on the stability limit, it may be useful to

enlarge the mass density for certain elements under some circumstances. Scaling the

mass density can potentially increase the e�ciency of the analysis. Due to the complex

discretization of models, there are often regions containing very small or poorly shaped

elements that control the stability limit of the entire model. These elements may be few

and only exists at localized areas. The stability limit may increase significantly while

e↵ect on the overall dynamic behavior is negligible if the mass of these elements are

increased.

There are two ways of applying mass scaling: defining a scaling factor directly or defining

a desired element-by-element stable time increment for specific elements that are of poor

shape. These two approaches allows for additional user control over the stability limit.

However, the user must be careful and absolutely certain that scaling these elements

does not change the overall behavior of the system[16].

2.4.4 E↵ect of material on stability limit

The material model used will a↵ect the stability limit through its e↵ect on the dilata-

tional wave speed. In a linear elastic material the Young’s modulus is constant and the

only factor a↵ecting the stability limit during the analysis is the change in the smallest

element dimension. In a nonlinear material, such as steel with plasticity, the wave speed

changes as the materials start to yield and the sti↵ness of the material decreases. This

e↵ect results in a increase of the stability limit.

11

Finite Element Theory

2.5 Energy balance

Energy output is a vital part in Abaqus/Explicit analysis. Energy output comprises

of several components, comparison between these various energy components is used to

evaluate whether the analysis is having appropriate response.

The energy balance for the entire model can be written as

EI +EV +EFD +EKE +EIHE �EW �EPW �ECW �EMW �EHF = Etotal, (2.10)

where EI is the internal energy, EV is the viscous energy dissipated, EFD is the frictional

dissipated energy, EKE is the kinetic energy, EIHE is the internal heat energy, EW is

the work done by the external applied loads and EPW , ECW and EMW are the work

done by contact penalties, constraint penalties and propelling added mass respectively.

EHF is the external energy through external fluxes. The sum of these components is

Etotal, which should be constant. However, for numerical models this is seldom the case,

Etotal is only approximately constant, generally with an error of 1%[17].

The internal energy component, EI , in equation 2.10 is in turn composed of several

other components. The expression for the internal energy is

EI = EE + EP + ECD + EA + EDMD + EDC + EFC , (2.11)

where EE is the recoverable elastic strain energy, EP is the dissipated energy through

inelastic processes such as plasticity, ECD is the dissipated energy through viscoelasticity

or creep, EA is the artificial strain energy, EDMD is the dissipated energy through

damage, EDC is the dissipated energy through distortion control, EFC is the fluid cavity

energy[17].

An important aspect to consider with extra care is the artificial strain energy. The

artificial strain energy includes the energy stored in hourglass resistances and transverse

shear in shell and beam elements. In order to decide whether a mesh refinement is

required or not the artificial strain energy should be studied. Large values of artificial

strain energy indicate that refinement or changes should be made.

12

Chapter 3

Method

This chapter is intended as a recipe of this master thesis. The chapter starts with the

process of the approach used in the thesis. The approach is followed by the description

of the characteristic features of the full-scale test used. After that, the main steps in the

finite element modeling are described followed by a summary of the assumptions and

simplifications made in this thesis.

3.1 The process of the master thesis

In order to examine the possibility of Abaqus/Explicit as the tool to simulate a full-scale

test, it was a necessity to have a technical report of the full-scale test. The technical

report used in this master thesis was report 350 test 3-11, on the modified T8 bridge rail

as mentioned in section 1.4, which will be referenced as the full-scale test hereafter. This

technical report was used as the base for the finite element modeling and simulation. The

simulation performed was validated against some of the results of test 3-11. Drawings of

the guardrail were provided by the technical report of the full-scale test and the bridge

rail was modeled using Abaqus CAE.

13

Method

The approach for this master thesis is schematically illustrated in Figure 3.1.

Figure 3.1: Working procedure of the thesis.

However, it should be noticed that the procedure displayed in Figure 3.1 was highly

iterative. When non satisfactory results were obtained in one step the process was

repeated by going back to the previous step to search for key properties that could

have influenced. Information and knowledge needed in di↵erent steps were collected

along the process through previous works, technical reports, handbooks, supervisors

and other master theses.

3.2 Full-scale crash test on the modified T8 bridge rail

The test was sponsored by the Federal Highway Administration, FHWA, and the test

was intended to evaluate the impact performance of the modified T8 rail bridge. The

crash testing was performed in accordance with the requirements of NCHRP Report

350 Test Level 3 (TL-3). The modified T8 rail was intended to serve as the replacement

for the Texas Type T6 rail for high-speed applications on culverts and thin bridge deck

structures[2].

3.2.1 Geometry and conditions for the guardrail installation

Since the test was performed in US, all the dimensions given for di↵erent parts in this

section are given in US units. The modified T8 bridge rail installation consisted of

a 12 gauged tubular thrie-beam rail vertically supported by W6x8.5 steel posts. The

reader should notice that the dimensions used are American standard dimensions. The

vertical posts were anchored to a 6.5-inch (approx. 165 mm) thick cantilever concrete

deck. The length of the modified T8 bridge rail section and the cantilevered bridge deck

constructed and tested was 97 ft. - 9 inches (approx. 29.8 m). A plan view of the

installation is shown in Figure 3.2.

14

Method

Figure 3.2: Plan view of the tested installation[2].

The rail was end anchored with ET plus end terminal at each end, making the overall

length of the test installation 137 ft. - 6-inches (approx. 41.91 m) as shown in Figure 3.2.

The terminals were connected to the tubular thrie beam through a standard 12 gauged

thrie-beam to W-beam transition rail elements. The transition is shown in Figure 3.4

and Figure 3.5

Figure 3.3: Elevation view of the tested installation[2].

Figure 3.4: Plan view of the transition zone[2].

15

Method

Figure 3.5: Elevation view of the transition zone[2].

The steel post were welded to a 12-inch x 9.5-inch x 1-inch thick (approx. 305x240x25

mm) base plate. Two 0.25-inch (6.35 mm) wide by 1-inch (25.4 mm) long slots were

machine cut into the tra�c sided flange of the posts, the position of these slots was

located 0.75-inch (19.05 mm) above the top face of the base plate, see Figure 3.6. Each

steel post with base plate was anchored to the cantilever concrete deck using 0.875-

inch (approx. 22 mm) ASTM A307 anchor bolts as shown in Figure 3.7. Additional

information for the steel posts are shown in Figure 3.8.

16

Method

Figure 3.6: Detail of the slotted holes[2].

Figure 3.7: Section of the tested installation[2].

17

Method

Figure 3.8: Additional details of the posts[2].

The tabular thrie beam was anchored to the vertical post using 0.625-inch (15.875 mm)

diameter x 3-inch (76.2 mm) long, ASTM A307 bolts. The bolts were mounted through

a 0.75-inch (19.05 mm) pipe sleeve. A 5-inch wide x 11-1/4-inch long x 1-1/4-inch

deep (127x285.75x31.75 mm) high density polyethylene (HDPE) o↵set block was placed

between the post and the field side of the tubular thrie beam rail as illustrated in Figure

3.7, the geometry of the o↵set block is shown in Figure 3.9. This provided a 1-inch (25.4

mm) o↵set distance between the posts and the thrie beam.

The width of the cantilevered deck was 30 inches (762 mm). The rebar arrangement

in the concrete deck is shown in Figure 3.10 and Figure 3.11. All the rebars had 60

ksi (414 MPa) yield point. The specified 28-day compressive strength for the concrete

cantilevered deck was 3000 psi (approx. 20.7 MPa). The actual compressive strength of

the concrete deck on the day the test was performed was 3536 psi (approx. 24.4 MPa)[2].

All steel plates and structural members meet A36 material specifications. Photographs

of the completed test installations is shown i Figure 3.12.

18

Method

Figure 3.9: Plastic o↵set block [2].

Figure 3.10: Plan and elevation view of the rebar arrangement [2].

19

Method

Figure 3.11: Details of the rebar arrangement [2].

Figure 3.12: The complete installation prior to testing [2].

20

Method

3.2.2 Crash test conditions

NCHRP Report 350 test 3-11 involves a 4409-lb (approx. 2000 kg) pickup truck im-

pacting the critical impact point, CIP, in the length of need, LON, of the longitudinal

barrier at a nominal speed of 62 mi/h (approx. 99.8 km/h) and with an impact angle

of 25 degrees. The test was intended to evaluate the strength of the rail in terms of its

ability to contain and redirect the pickup truck[2].

Critical impact point for the T8 rail was chosen to 1.5 ft. upstream of post 11 which

corresponds to the 7th bridge rail post. Selection of CIP was in accordance with the

guidelines in NCHRP Report 350.

The actual speed and angle for this particular test was measured to 62.1 mi/h (99.9

km/h) and 23.8 degrees. Actual impact point was 20-inch (508 mm) of post 11 as shown

in Figure 3.13.

Figure 3.13: Impact point and the angle between the vehicle and rail [2].

3.2.3 Test vehicle

The vehicle used for the test was a 2000 Chevrolet C2500 pickup truck shown in Figure

3.14 and Figure 3.15. The test inertia weight of the car was 4522 lb (approx. 2051 kg),

and its gross static weight was also 4522 lb[2]. Relevant dimensions and information of

the vehicle is found in Figure 3.16 and Table 3.1. More specifications for the vehicle

can be found in APPENDIX B of [2]. The vehicle was accelerated into the installation

using a cable reverse tow and guidance system, and was released to be free-wheeling and

unrestrained just prior to impact.

21

Method

Figure 3.14: The 2000 Chevrolet C2500 pickup truck used for the test [2].

Figure 3.15: The vehicle and installation prior the crash testing [2].

22

Method

Figure 3.16: Dimensions and other relevant distances[2].

Table 3.1: Geometry of the vehicle[2].

Character Inch and [mm] Character Inch and [mm]

A 74 [1880] B 32 [813]

C 32 [3353] D 71.5 [1816]

E 51.5 [1308] F 215.35 [5470]

G 57.49 [1460] H Not mentioned in [2]

J 41 [1041] K 25 [635]

L 2.75 [70] M 16.25 [413]

N 62.5 [1588] O 63.4 [1610]

P 28.5 [724] Q 17.25 [438]

R 29.5 [749] S 35.5 [902]

T 57.5 [1461] U 132.25 [3359]

23

Method

3.3 Finite element modeling

Modeling and analysis of the impact were carried out in Abaqus/CAE and Abaqus/Ex-

plicit. The modeling was performed in the CAE while the analysis was performed using

the Explicit solver.

In order to increase the reliability of the results obtained in Abaqus, smaller models that

could be verified prior to the full analysis were made. For example a cantilever beam

with a point load at the tip was modeled to compare with simple hand calculations in

order to assure compliance. This process was applied throughout the entire modeling

process to assure that the model behaved as intended.

Finite element modeling was carried out as a parallel process as mentioned in Figure 3.1.

The vehicle model was modeled along the modified T8 bridge rail to make the modeling

process as short as possible. When satisfactory models for the purpose of this thesis

were developed for the parapet/guardrail and the vehicle, the models were assembled to

one final model. The final model was used to carry out the simulation.

In the following sections, the modeling and the inputs used in Abaqus/CAE are presented

together with the assumptions and simplifications.

3.3.1 Vehicle model

Vehicle model used for this thesis was a pick-up truck, a 1994 Chevrolet C1500. This

model was used due to the similarities of the vehicle used for the full-scale crash test

described above. Simulia obtained the model geometry, element connectivity, and ma-

terial properties from the Public Finite Element Model Archive of the National Crash

Analysis Center at George Washington University.

However the model was not a complete model ready to use in Abaqus simulations. The

model was organized as a collection of individual parts connected together. For each

part of the vehicle there were several input files, INP-files, which forms the geometry,

material properties and the connectivity to adjacent parts.

These INP-files were found in the Abaqus 6.14 Documentation[18]. The input files are

formed as scripts containing the nodes, element types, sections and connections of the

parts. The INP-files were parametrized which means that they read values from another

input file where di↵erent parameters are defined. The input reader in Abaqus does not

support parametrized input files which read the parameters from another INP-files, it

can only read parameters defined in the same INP-file. This obstacle enforced us to

replace all the parameters in the INP-files and instead use the values defined in the

24

Method

parameter file. Several problems beside the parameter problem were encountered. Some

of these problems were that the beam section and rotary inertia definition in the INP-

files was not supported by the input reader. All these problems were solved with the

aid of Abaqus Scripting Reference Guide. Once all the modifications necessary were

made to the original INP-files downloaded from [18], the vehicle geometry, properties

and connectivity were successfully imported as a complete model. The vehicle model

was modeled by 55132 elements containing a total of 68461 nodes. Smallest element

dimension of the vehicle model was approximately 3.75 mm. The imported vehicle is

shown in Figure 3.17.

Figure 3.17: The imported vehicle in Abaqus/CAE.

3.3.1.1 Modification of the material properties

Material definitions used for the vehicle model were mainly properties of steel, elastic or

elastic-plastic material properties. These definitions are explained in [19]. The material

definition for the tires was modified since the definition provided by the INP-files was not

logical considering the Young’s modulus defined was 246 100 MPa and the density was

higher than 7800 kg/m3. The modifications yielded in a Young’s modulus corresponding

to tire rubber, 2461 MPa, and a density of 730 kg/m3.

Other material properties that were changed for some of the vehicle part are listed in

Table 3.2. Maximum plastic strain defined by Simulia for these materials was to large

which may cause instability and di�culties in convergence when these part are subjected

to large deformations.

25

Method

Table 3.2: Changes to some material properties of the vehicle.

Material Name Maximum

Yield Stress

[MPa]

Maximum

Plastic Strain

(Old value) [-]

ELASTICPLASTIC1 449 0.3 (2.398)

ELASTICPLASTIC2 504 0.3 (2.398)

ELASTICPLASTIC-ARM 449 0.3 (2.398)

ELASTICPLASTIC-OUTER-RIM 449 0.3 (2.398)

Once the vehicle was imported to Abaqus/CAE and the material modification was ap-

plied as described above, a comparison with the vehicle used in the full-scale test was

performed in order to assess the modifications that were required to have good enough

similarities between the vehicle model and the test vehicle. The first assessment was to

determine the mass of the modeled vehicle and compare it to the vehicle used in the

full-scale test.

The assessment showed that the mass of the vehicle model was approximately 1798 kg

compared to 2051 kg for the test vehicle. In order to have same kinetic energy for the

modeled as for the tested vehicle, the mass of the model was increased with 12 %. This

increase was applied through the densities defined in the material properties of Abaqus/-

CAE. The outcome of this adjustment was an increase of the mass to approximately 2014

kg.

3.3.1.2 Geometry of the vehicle model

This section serves as a comparison in the geometry and relevant distances between the

vehicle model and the tested vehicle. Some values of corresponding dimensions listed in

Table 3.1 are listed in Table 3.3.

Most important dimension to compare was ”R” where the center of gravity was located

for the vehicle in the vertical direction. The vehicle model had some di↵erence compared

to the tested vehicle. However the di↵erence was small enough for the purpose of this

master thesis. Another dimension that might influence the behavior of the vehicle was

”T”, where the di↵erence was large. This di↵erence could be due to the densities used

for the engine and adjacent parts of the modeled vehicle model were higher than for

the corresponding parts in the tested vehicle, resulting in a displaced gravity center

towards the front wheels. After consulting with the supervisors of this master thesis, it

was judged that it was more important to have good correspondence with the dimension

”R” than ”T” and that the vehicle model was good enough for the purpose of this study.

26

Method

Table 3.3: Geometry of the vehicle model compared to tested vehicle.

Character Tested Vehicle [mm] Modeled Vehicle [mm] � [mm]

A 1880 1876 3

B 813 915 102

C 3353 3365 12

D 1816 1843 27

E 1308 1177 131

F 5470 5457 13

J 1041 1025 16

K 635 657 22

L 70 88 18

M 413 442 29

P 724 718 6

Q 438 417 21

R 749 710 39

T 1461 1215 246

3.3.2 Modeling of the modified T8 bridge rail

The finite element modeling of the modified T8 bridge rail was constructed by two parts,

the vertical posts and the thrie beam. These two parts are described in the following

subsections where relevant dimensions are shown together with other relevant geometric

properties.

3.3.2.1 Modeling of the vertical posts

The vertical posts were created in the Part Module of Abaqus/CAE. The part type was

selected to deformable with the shell extrusion base feature. The cross section of the

posts was created in the sketch feature of Abaqus/CAE. The sketched dimensions were

according to Figure 3.19a which resulted in the cross section shown in Figure 3.19b.

The length of the post was obtained by extruding the cross section with 775 mm. The

material properties used for the posts are tabulated in Table 3.4. Two homogeneous

shell sections were created and assigned to the post, one for the web with a thickness

of 4.3 mm and another for the flanges with a thickness of 4.9 mm. A final global mesh

size of 12.5 mm was assigned to the post, shown in Figure 3.20.

27

Method

Table 3.4: Properties used for the vertical posts.

Steel Post Properties Abaqus Input

Material type Piecewise linear plastic material

Element type A 4-node shell (S4R), default hourglass control.

E-modulus [MPa] 200 000

Yield Stress [MPa] 250

Density [t/mm3] 7.85E-09

Possion’s Ratio 0.26

True Stress [MPa] 250 475

E↵ective Plastic Strain 0.00 0.20

Elevation of the post is shown in Figure 3.18 and the cross section of the modeled

post is shown in 3.19. A partition face was created in order to create geometric nodes

which were used when connecting the thrie beam with the vertical posts, the connection

between the thrie beam and vertical posts are discussed in Section 3.3.6.3.

(a) Dimensions used for the posts.(b) Elevation of the post inAbaqus/CAE

Figure 3.18: Elevation of the posts.

28

Method

(a) Dimensions used for thecross section.

(b) Modeled cross section inAbaqus/CAE

Figure 3.19: Cross section of the vertical posts.

Figure 3.20: The meshed vertical post.

29

Method

3.3.2.2 Modeling of the thrie beam

The geometry of the thrie beam was created using the same procedure as for the vertical

post, described in Section 3.3.2.1. The geometry of the thrie beam was created based

on the blueprint shown in Figure 3.21a. The dimensions were standard dimension of a

12 gauged thrie beam which was used in the full-scale test. The modeled cross-section

in Abaqus/CAE is shown in Figure 3.21b. The cross section was then extruded with a

distance of 35660 mm, see Figure 3.22. Partitions with a center distance of 1905 mm

were created along the length of the thrie beam starting from an edge distance of 3780

mm from left end and ending a distance of 1880 mm from the right end if Figure 3.22

is used as reference. The partitioning was necessary in order to create geometric nodes

which were used for the connection to the vertical posts.

The material properties used for the thrie beam are tabulated in Table 3.5. A homo-

geneous shell section with a thickness of 5 mm was created and assigned to the thrie

beam. A final global mesh size of 10 mm was assigned to the thrie bream, shown in

Figure 3.23.

Table 3.5: Material properties used for the thrie beam.

Steel Post Properties Abaqus Input

Material type Piecewise linear plastic material

Element type A 4-node shell (S4R), default hourglass control.

E-modulus [MPa] 200 000

Yield Stress [MPa] 250

Density [t/mm3] 7.85E-09

Possion’s Ratio 0.26

True Stress [MPa] 250 475

E↵ective Plastic Strain 0.00 0.20

30

Method

(a) Blueprint of the cross section. (b) Modeled cross section in Abaqus/CAE

Figure 3.21: Cross section for the 12-gauged thrie beam.

Figure 3.22: Elevation of the thrie beam.

31

Method

Figure 3.23: The meshed thrie beam.

32

Method

3.3.3 Modeling of the bridge deck

The cantilevered bridge deck with all the rebars and details was not modeled in this

thesis due to lack of time. Instead, a discrete rigid body was created to represent the

deck. This part was created in the part module of Abaqus/CAE and the solid extrusion

base feature was used. The dimensions used were 15000 x 30000 mm with a extrusion of

165 mm, a plan view of the deck is shown in Figure 3.24. Notches with dimension of 110 x

198 mm were created where the vertical posts were located in order to permit rotation of

the vertical post when impacted, the notches are shown in Figure 3.25. Center distance

of the notches was 1905 mm as for the vertical posts.

Figure 3.24: Plan view of the bridge deck.

Figure 3.25: Close up view of the notches created.

33

Method

3.3.4 Assembled model

When all the necessary parts required for the simulation were created, a complete model

could be assembled. Prior to the assembly, a copy of the thrie beam part was created

to assemble the tabular thrie beam as shown in Figure 3.26.

Figure 3.26: The assembled tabular cross section.

In the completed finite element model, only the vertical post 5-20 shown in Figure 3.3

were modeled. The vertical posts were positioned with a center distance of 1905 mm.

The transition zones of the test installation were not modeled, instead the tabular thrie

beam was extended beyond post 5 and 20 with a distance of 3780 mm respectively 1880

mm and additional vertical post was placed at each end of the tabular thrie beam where

boundary conditions were applied, see Section 3.3.8. The tabular thrie beam and the

vertical post were positioned according to Figure 3.27. The vertex of the tabular thrie

34

Method

beam was 787.7 mm from the top of bridge deck. The horizontal distance between

vertical post and the tabular thrie beam was 85.45 mm and is represented by the dotted

blue line in Figure 3.27. The discrete rigid body representing the bridge deck was placed

beneath the vertical post.

Since only the global behavior of the bridge rail installation was of interest, detailing

features of the installation were not modelled. The slotted bolt holes in the thrie beam

were not considered. The bolts connecting the vertical posts and the thrie beam was

neglected, a connector section was used instead, see Section 3.3.6.3. The base plate and

the anchor bolts together with the slotted holes in the vertical post were also neglected.

The plastic o↵set block was excluded from the model. Most of these neglected details

were made due to time constraints. However, some of the neglected details have a minor

impact on the global behavior of the model, for instance the plastic o↵set block. The

neglected connection between the base plate and the bridge deck was replaced with an

equivalent rotational sti↵ness, see Section 3.3.6.3.

Figure 3.27: The alignment of the tabular thrie beam and the vertical post.

The vehicle model was positioned in accordance with the full-scale test conditions, see

Figure 3.13. Figure 3.28 illustrates this position in the Abaqus/CAE assembly module.

35

Method

Figure 3.28: Vehicle position prior impact.

An isoparametric view of the assembled model is shown in Figure 3.29.

Figure 3.29: The assembled model with post numbers - isoparametric view.

36

Method

3.3.5 Analysis step

The analysis step was created in the step module, the procedure of the step was chosen to

Dynamic Explicit with a step time of 0.6. The geometric non linearity was toggled on in

the basic tab. Automatic time incrementation was used, the stable increment estimator

was selected to global with a time scaling factor of 1. Since the density and the Young’s

modulus were predetermined, the critical parameter for the stable time increment will be

the smallest element dimension, Le. The vehicle part had the smallest element dimension

when meshed and limited the stable time increment for the whole model resulting in

an initial stable time increment of approximately 5.574E-07 s, obtained from the status

file of the job monitor in Abaqus. Maximum time increment was unlimited. Mass

scaling was not applied for any region of the model. Linear and quadratic bulk viscosity

parameters were set to default values of 0.06 respectively 1.2.

3.3.6 Interaction

The following sections present details about how the modeled parts interact with each

other. Firstly, the contact definition used is explained following by the constraints

and connections applied. The constraints and connections subsections only consider

properties used for the modeled bridge rail installation. Corresponding properties used

for the modeled vehicle are predefined by the INP-files.

3.3.6.1 Contact

A contact definition must be defined in order to simulate impact between di↵erent parts.

This was a necessity in order to prevent penetration. The contact definition was made

in the contact property tool, a mechanical tangential behavior was defined. The penalty

friction formulation was used with a friction coe�cient of 0.001. A low value of friction

coe�cient was chosen since the tires were not rolling for the vehicle part. If a higher

value of the friction coe�cient was used it would have created high stresses to the vehicle

tires resulting in a flat tire.

A normal behavior of the friction was also used for the contact definition, with the

”Hard” contact as the Pressure-Over closure, meaning that the friction was applied

only when two surfaces were in contact. The constraint enforcement method was set to

default and separation was allowed after contact.

37

Method

In the create interaction manager, general contact for explicit analysis was used. The

contact domain was set to All with self, with the global contact properties as described

above.

3.3.6.2 Constraints

The intermittent welding of the thrie beams was modeled by the tie constraint feature

which tied the top and bottom edges, as shown in Figure 3.30.

Figure 3.30: Tie constraints between the two thrie beams forming the tabular thrie beam.

The vertical post, except the end posts, was connected to a point which represents a

rotation center using multipoint constraints, MPC, with a beam type behavior shown

in Figure 3.32. The rotation center was assumed to be located in the middle between

the transverse rebar layers as shown in Figure 3.31. The rotation center was assigned as

the control point and the nodes at the bottom cross section of the vertical posts as the

slave nodes.

38

Method

Figure 3.31: Rotation center in the bridge deck.

Figure 3.32: The constraints between the vertical posts and the rotational center.

3.3.6.3 Connections

Attachment points were created for the thrie beam at the location where the bolt con-

nections to the vertical posts were located. This was done to fasten the two thrie beams

together using fasteners in the Engineering features of the assembly module. The phys-

ical radius was set to 7.9375 mm and a beam connector section was assigned to the

fasteners. The neglected bolts connecting the tabular thrie beam and the vertical posts

were modeled by creating wires that was assigned a Cartesian connector section, see

Figure 3.33. The properties used for the connector section is tabulated in Table 3.6.

39

Method

Figure 3.33: The connection between the tabular thrie beam and vertical post.

Table 3.6: Properties of the Cartesian connector section.

Nonlinear elasticity F1 [N] U [mm] F2 and F3 [N] U [mm]

-36000 -56 -79200 -15

0 0 0 0

36000 56 79200 15

Failure U1 [mm] U2 and U3 [mm]

Upper bound -150 -50

Lower bound 150 50

The values of the forces in Table 3.6 were based on Appendix A.1. A parametric study

was made for di↵erent values of the corresponding displacements until the behavior of

the bolt connection partially converged to the full-scale test. Same principles were used

for the displacement of the failure.

A rigid Cartesian connection was used for the bolts connecting the tabular thrie beam

and the end posts. The usage of this type of connection was based on that neither

translation nor rotations were present at these points of the tabular thrie beam in the

full-scale test.

40

Method

The rotation center, RC, shown in Figure 3.31 was assigned the wire-to-ground feature.

The wire-to-ground was assigned a Cartesian+Rotation connector section with prop-

erties according to Table 3.7. Five of the constrained components of relative motion,

CORM, were set to rigid. The only CORM that was assigned properties was M3, which

was rotation about the z-axis in the model. The coupling definition was set to uncou-

pled, the regularization tolerance in the table option of the connector section was set to

the default value while the extrapolation was set to linear. This procedure was applied

to all vertical posts except the two end posts.

The rotational sti↵ness between the connecting post and bridge deck was di�cult to

predict. However, it could be recognized that the posts did not buckle in the full-scale

test which indicated that the rotational sti↵ness of the connection must be less than the

yielding moment of posts. Hand calculations were made to estimate the maximum mo-

ment capacity of the vertical post, see Appendix A.2. A simulation was also performed

for fully fixed bottom of the posts to determine the maximum rotational moment, which

was 5.5E6 Nmm. A parametric study was made for di↵erent values of the rotational mo-

ment ranging from 1E6 to 21E6 Nmm, until the rotational moment gave approximately

similar angular displacements as in the full-scale test.

Table 3.7: Properties of the Cartesian+Rotation connector section.

Nonlinear elasticity M3 [Nmm] UR3 [Rad]

-5E6 -0.0001

0 0

5E6 0.0001

Nonlinear plasticity M3 [Nmm] UR3 [Rad]

5E6 0

18E6 0.79

1 2

41

Method

3.3.7 Load

Gravity load with a value of 9810 mm/s2 was applied for the entire vehicle.

Impact velocity of the vehicle was, 27761 mm/s (62.1 mi/h). The velocity was applied

through the predefined field feature. V1-component and V3-component was set to 11202

mm/s and -25401 mm/s respectively, giving a resultant of 27761 mm/s.

3.3.8 Boundary conditions

The rigid bridge deck was assigned a reference point at the middle where fixed, ENCAS-

TRE, boundary condition was applied.

Fixed boundary conditions, ENCASTRE, were applied to the bottom of the two end

posts, see Figure 3.34. The usage of this type of boundary condition was based on that

neither translation nor rotations were present at these points in the full-scale test.

Figure 3.34: The fixed boundary condition applied to the end post.

42

Method

3.3.8.1 Summary of the assumptions and simplifications

The assumptions and simplifications used in the finite element modeling, excluding the

vehicle model, are summarized in this section by the listed bullets below.

• Transition zones of the test installation were not included in the FE-modeling.

• The bridge deck was not modeled as in the full-scale test, instead a rigid solid

element was used.

• Base plate between the bridge deck and the posts were not modeled.

• Plastic o↵set block between the tabular thrie beam and vertical posts were ex-

cluded from the model.

• Intermittent welds of the tabular thrie beam were not modeled, instead the top

and bottom edges of the thrie beams were tied together.

• Slotted holes and bolts in the tabular thrie beam and vertical post were not con-

sidered.

43

Chapter 4

Results

In this chapter the results of interest are presented. The chapter starts out with a brief

presentation of the results from full-scale crash test perform by Texas Transportation

Institute followed by a section where simulation results are presented. At the end of this

chapter a qualitative and quantitative comparison between the results of the full-scale

test and simulation is performed.

4.1 Results of the full-scale crash test

Results that are presented here are brief and mostly qualitative in order to compare them

with the results from the simulation. The reader should read through [2] if interested in

results such as occupant risks and other results of importance.

Approximately at 0.027 s after the impact, post 11 started to deflect to the side of the

field. Post 12 and 13 deflected to the side of the field at 0.061 s and 0.068 s respectively.

After impacting the bridge rail, the vehicle started to travel parallel with the bridge

rail at 0.259 s with a speed of 48.1 mi/h (approx. 77.4 km/h). At 0.267 s the vehicle

began to roll and continued to roll as it exited the view of the overhead camera. The

vehicle came to rest on its right side 163 ft. (approx. 49.7 m) downstream of the impact

point and 48 ft. (approx. 14.6m) from the tra�c face of the rail as shown in Figure 4.4.

Sequential photographs are shown Figure 4.1 to Figure 4.3.

44

Results

Figure 4.1: Sequential photographs of the test, overhead and frontal view [2].

45

Results

Figure 4.2: Sequential photographs of the test, overhead and frontal view (continued)[2].

46

Results

(a) 0 s (b) 0.086 s

(c) 0.169 s (d) 0.255 s

(e) 0.341 s (f) 0.427 s

(g) 0.511 s (h) 0.597 s

Figure 4.3: Rear view of the crash[2].

47

Results

Figure 4.4: The impact point and end point of the vehicle[2].

4.1.1 Damage to the test installation

Measurements of the modified T8 bridge rail showed that the installation did not work

as intended. Post 5 through 9 rotated clockwise with an angle of 5 degrees[2]. Failure

mechanism was crushing of the concrete deck as shown in Figure 4.5. Post 10 through

15 experienced the largest deformations, the deformation for these posts are listed in

Table 4.1.

Table 4.1: Post deformation and deflection[2].

Post

No.

Lean Toward

Field Side [°]Deflection Toward

Field Side [in]

10 10 1.5 (38mm)

11 35 5.25 (133 mm)

12 58 8.5 (210 mm)

13 120 14.25 (362 mm)

14 17 3.125 (79 mm)

15 5 0.625 (16 mm)

Post-to-rail connection bolt pulled through the thrie beam at post 11 through 13 and the

first layer of the thrie beam element at post 14. The vehicle was in contact with the rail

a distance of 24.75 ft. (approx. 7.54 m). Dynamic deflection of the bridge rail during

the impact was 1.91 ft. (approx. 582 mm) and the maximum permanent deformation

was 1.69 ft. (approx. 515 mm), deformations can be seen in Figure 4.6.

48

Results

Figure 4.5: Damage to the test installation[2].

49

Results

Figure 4.6: Permanent deformation to the test installation[2].

50

Results

4.1.2 Damage to the test vehicle

Damages to the vehicle can be seen in Figure 4.7. Maximum exterior crushing was

about 13.0 inches (330 mm) in the front plane at the left front corner at bumper height.

Damage was also present for the front bumper, hood, grill, left front fender, left tire and

wheel rim, left door, and left rear exterior bed[2]. The windshield and door glass broke

when the vehicle rolled onto its side, also visible in Figure 4.7.

Figure 4.7: Vehicle after being up-righted [2].

4.2 Results of the simulation

Only key values from the simulated crash are presented here, more details regarding the

results are presented in Appendix B.

Approximately at 0.017 s after the impact, post 11 started to deflect to the field side.

Post 12 and 13 deflected to the side of the field at 0.019 s and 0.034 s respectively. After

impacting the bridge rail, the modeled vehicle started to travel parallel (it had rotated

with an angle of 23.8°) with the modeled bridge rail at 0.213 s with a speed of 85.1 km/h.

Time for when the vehicle started to roll was not clear, however the rolling motion was

present somewhere between 0.200 s and 0.255 s. The simulation was terminated after 0.6

s since all the sequential photographs needed were obtained at this time step. Total time

51

Results

of the analysis was approximately 34 h. Sequential photographs from the simulation are

shown in Figure 4.8 to Figure 4.10.

(a) 0 s (b) 0 s

(c) 0.086 s (d) 0.086 s

(e) 0.169 s (f) 0.169 s

(g) 0.255 s (h) 0.255 s

Figure 4.8: Sequential simulations photographs - top and front view.

52

Results

(a) 0.341 s (b) 0.341 s

(c) 0.427 s (d) 0.427 s

(e) 0.511 s (f) 0.511 s

(g) 0.597 s (h) 0.597 s

Figure 4.9: Sequential simulations photographs - top and front view (continued).

53

Results

(a) 0.000 s (b) 0.086 s

(c) 0.169 s (d) 0.255 s

(e) 0.341 s (f) 0.427 s

(g) 0.511 s (h) 0.597 s

Figure 4.10: Sequential simulations photographs - rear view.

54

Results

4.2.1 Damage to the modeled installation

Post 5 through 9 rotated clockwise with a mean angle of 3.3°. Post 10 through 15

experienced the largest deformation, the deformation for these posts are tabulated in

Table 4.2.

Table 4.2: Post deformation and deflection in the simulation.

Post

No.

Lean Toward

Field Side [°]Deflection Toward

Field Side [mm]

10 17 40

11 31 121

12 51 321

13 51 311

14 35 155

15 20 53

Post-to-rail connector section was detached from the thrie beam at post 13. The vehicle

was in contact with the rail a distance of 7.04 m. Dynamic deflection of the bridge rail

during the impact was 703 mm and the maximum permanent deformation was 643 mm,

deformations can be seen in the following figures.

Figure 4.11: Deflection of the posts which experienced the largest deformations.

55

Results

Figure 4.12: Damage to the modeled installation - front view.

Figure 4.13: Damage to the modeled installation - rear view.

56

Results

4.2.2 Damage to the modeled vehicle

The exterior damages to the modeled vehicle are shown in Figure 4.14, however it should

be noticed that these deformations were present at a time of 0.6 s which is not when the

vehicle came to rest. Maximum exterior crushing was about 297 mm in the front plane

at the left front corner at bumper height. Non blue color in Figure 4.14 represents other

damages to the vehicle. It should be noticed that the tires were elastically defined and

will not have permanent damages.

Figure 4.14: Damage to the vehicle at 0.6 s.

57

Results

4.2.3 Energy quantities

Di↵erent energy quantities from the simulation are presented below. The kinetic energy

for the modeled vehicle was calculated by hand using equation 4.1,

Ekinetic =mv2

2. (4.1)

with values inserted, the kinetic energy of the modeled vehicle was calculated to 776.1 kJ.

This value was also obtained from Abaqus for the EKE and Etotal at the very beginning

of the simulation as can be seen in Figure 4.15.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7�200

0

200

400

600

800

1,000

Time t [s]

Energy

[kJ]

Energy quantities for the whole model

E

A

E

CD

E

DMD

E

W

E

FD

E

I

E

KE

E

P

E

E

E

total

E

V

Figure 4.15: Energy quantities for the whole model.

As mentioned in section 2.5, the total energy should be constant during the analysis,

however this was not the case during the simulation. The energy that was contributing

the most to the increase in total energy was the dissipated viscous energy, EV . The

di↵erence in total energy with and without EV is shown in Figure 4.16. The di↵erence

in total energy during the simulation was calculated as,

diff =

✓Etotal

Etotal.initial� 1

◆⇥ 100. (4.2)

It is clear that without increase in EV , the total energy is almost constant with a

maximum deviation of 3.2 %. The reason for the increase in EV is discussed in Chapter

5.

58

Results

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7�5

0

5

10

15

20

25

30

3.2872

24.8751

Time t [s]

Di↵erence

inE

total[%

]

Etotal during the simulation

E

total

without E

V

E

total

Figure 4.16: Di↵erence in the total energy for the whole model.

4.3 Qualitative comparisons

This section serves as the qualitative comparison between the full-scale crash test and

the simulated crash. Below a comparison on the vehicle behavior and the parapet during

the impact are presented through sequential photographs from di↵erent angles.

No specific values are presented in this section, the comparison in di↵erent key values

are to be found in the quantitative section 4.4.

59

Results

(a) 0 s (b) 0 s

(c) 0.086 s (d) 0.086 s

(e) 0.169 s (f) 0.169 s

(g) 0.255 s (h) 0.255 s

Figure 4.17: Sequential crash photographs comparison - front view.

60

Results

(a) 0.341 s (b) 0.341 s

(c) 0.427 s (d) 0.427 s

(e) 0.511 s (f) 0.511 s

(g) 0.597 s (h) 0.597 s

Figure 4.18: Sequential crash photographs comparison - front view (continued).

61

Results

(a) 0 s (b) 0 s

(c) 0.086 s (d) 0.086 s

(e) 0.169 s (f) 0.169 s

(g) 0.255 s (h) 0.255 s

Figure 4.19: Sequential crash photographs comparison - top view.

62

Results

(a) 0.341 s (b) 0.341 s

(c) 0.427 s (d) 0.427 s

(e) 0.511 s (f) 0.511 s

(g) 0.597 s (h) 0.597 s

Figure 4.20: Sequential crash photographs comparison - top view (continued).

63

Results

(a) 0 s (b) 0 s

(c) 0.086 s (d) 0.086 s

(e) 0.169 s (f) 0.169 s

(g) 0.255 s (h) 0.255 s

Figure 4.21: Sequential crash photographs comparison - rear view.

64

Results

(a) 0.341 s (b) 0.341 s

(c) 0.427 s (d) 0.427 s

(e) 0.511 s (f) 0.511 s

(g) 0.597 s (h) 0.597 s

Figure 4.22: Sequential crash photographs comparison - rear view (continued).

65

Results

4.4 Quantitative comparisons

To determine the accuracy of the simulated crash in replicating the full-scale crash test,

key parameters obtained from the simulation were compared to those of the full-scale

crash test.

At 0.027 s after impact, post 11 started to deflect in the full-scale test compared to 0.017

s from the simulation. Post 12 and 13 deflected at 0.061 s and 0.068 s compared to 0.019

s and 0.034 s.

After impacting the bridge rail, the test vehicle started to travel parallel with the bridge

rail at 0.259 s with a speed of 77.4 km/h corresponding values from the simulation were

0.213 s with a speed of 85.1 km/h. At 0.267 s the test vehicle started to roll. It was

di�cult to determine the time for the initiation of the rolling motion in the simulations,

however somewhere between 0.200 s and 0.255 s.

Dynamic deflection and permanent deformation of the bridge rail during the test was

582 mm respectively 515 mm compared to 703 mm and 643 mm from the simulation.

The comparison in post deflections and deformation between full-scale test and simula-

tion are tabulated in Table 4.3 and Table 4.4.

Table 4.3: Post angular deflection - comparison.

Simulation Full-scale �

Post

No.

Lean Toward Field

Side [°]Lean Toward Field

Side [°][°]

10 17 10 7

11 31 35 4

12 51 58 7

13 51 120 Not Comparable

14 35 17 18

15 20 5 15

66

Results

Table 4.4: Post deflection - comparison.

Simulation Full-scale �

Post

No.

Deflection Toward

Field Side [mm]

Deflection Toward

Field Side [mm]

[mm]

10 40 38 2

11 121 133 12

12 321 210 111

13 311 362 Not comparable

14 155 79 76

15 53 16 37

67

Chapter 5

Discussion and conclusions

As can be seen from the comparison sections in the previous chapter, there are similarities

and di↵erences between simulation and full-scale test results. In this chapter some of

the results are discussed and analyzed in order to draw any conclusions.

Results of the simulation showed that post 11 through 13 deflected earlier than the

performed full-scale test. One reason for this could be that the elastic definition of the

applied rotational sti↵ness was not large enough. It was burdensome to predict the sti↵-

ness of the neglected concrete bridge deck. Another reason could be the sti↵ness of the

neglected transition zone which was not captured by the applied boundary conditions.

The neglected o↵set block could also contribute to early deflection of these posts, we

believe that the o↵set block absorbs a portion of the impulse created initially by the

impact and thus deforms plastically which delays the deflection of vertical posts. This

means that the impulse stress applied to the posts in the test was smaller than in the

simulation.

Post deflections were fairly accurate for posts 5 through 12. The collapse of post 13 was

not captured by only using rotational sti↵ness as the failure mechanism between the

concrete bridge deck and vertical post. Deflection for post 14 and 15 was also slightly

di↵erent compared to the full-scale test. A reason for this could be that the loss in vehicle

speed during impact was lower than the full-scale test due to the low friction used in the

model. This provided more energy to deform these posts giving larger deformations.

Bolt-to-rail connection used in the simulation worked as intended only for post 13,

indicating that the real behavior could not be captured to the fullest. It was problematic

to find corresponding values matching the bolts used in the full-scale test.

The low friction applied for the model might be the reason why the vehicle was travelling

parallel with the guardrail at an earlier time step than it actually does in the full-scale

68

Discussion and conclusion

test. The energy losses due to friction were minimal causing the vehicle to travel with a

higher speed.

Deflections obtained for the tabular thrie beam was larger than corresponding values

for the full-scale test. The boundary conditions used in the model did not capture the

sti↵ness provided by the transition zone in the full-scale test. Another reason for the

larger deflections obtained in the simulation could be the larger kinetic energy during

impact as mentioned above. Since the simulation has larger kinetic energy during impact

it will also provide larger plastic deformations.

Sequential comparison showed that the behavior of the simulation was fairly accurate

until the sequence at 0.427 s, after this moment the simulation di↵ers. An explanation

for this could be that the rear of the modeled vehicle did not travel in the same path

as in the full-scale test vehicle. The tabular thrie beam was deflected downwards when

impacted by the front of the car in the full-scale test. It was obvious that the bridge deck

was crushed when the front of the car impacted the parapet meaning that the sti↵ness

provided by the vertical post at the impact area was significantly reduced. There was

only the sti↵ness of tabular thrie beam at this area when the rear of the car impacted

the parapet. The post rotation lowered the height of the thrie beam, causing it to

deflect beneath the rear of the car which caused it to roll onto it right side as it exited

the test installation. This behavior was not accurately reflected in the simulation, the

post rotation did not lower the height of tabular thrie beam to same extent as the full-

scale test. Post 13 provided sti↵ness since it did not collapse as the full-scale test. The

combination of a higher tabular thrie beam together with the sti↵ness provided from

post 13 when impacted by the rear of the modeled vehicle is believed to be the cause of

the di↵erence between the simulation and full-scale test.

Another cause which may influence the rolling motion of vehicle could be the di↵erence

in the center of gravity between the modeled vehicle and tested car. As mentioned in

section 3.3.1.2 there was a di↵erence of approximately 40 mm in the vertical height.

However it was not easy to determine if this di↵erence influenced the behavior of the

modeled vehicle compared to the test vehicle. It is a necessity to model every part of

the parapet and bridge deck in detail in order to study if this di↵erence does influence

the behavior of the modeled vehicle.

Main focus of the master thesis has been to validate the simulation against the full-scale

test. However, another way of validating the model was to briefly study the energy

balance of the simulation. The study of energy balance showed that the total energy

during the simulation was not constant, as it should be. As presented in the result

chapter, the total energy was increased during the simulation. After investigating the

cause of the increase in total energy it was discovered that it was due to the increase

69

Discussion and conclusion

in dissipated viscous energy. This gain of viscous energy was due to the dashpot-like

damping behavior defined for connector sections used to connect adjacent parts in the

engine of the modeled vehicle. Some of these damping factors were very high, when

these parts are in motion the damping will create great amount of dissipated viscous

energy. It can be seen from Figure 4.15 that the dissipated viscous energy continues to

grow at 0.6 s where the vehicle started to land on the floor meaning that large motions

for di↵erent parts of the engine were present which was damped by these dashpot-like

dampers. If these dashpot-like damping factors were not used, it would probably reduce

the increase in viscous dissipated energy since no material damping was used except the

default bulk viscosity introduced by Abaqus. It could also be seen that the total energy

for the whole model was almost constant if the viscous dissipated energy was subtracted

from the total energy.

Artificial strain energy was also studied in order to determine if it was necessary to use

a denser mesh. Several simulation was performed with di↵erent mesh sizes, the mesh

sizes mentioned in the method section were the final ones which reduced the artificial

strain energy to the levels plotted in Figure 4.15. Denser mesh would probably decrease

the artificial strain energy a bit further, however it was not a necessity to decrease the

mesh further since the computational e↵ort would have increased more than what the

gain would be.

Kinetic energy was decreased while the plastic strain energy was increased during the

impact as it should be since the loss in kinetic energy is proportional to the dissipated

energy due to plasticity. This indicated that the model behaved properly.

The conclusion of this master thesis is that Abaqus/Explicit has all the potentials needed

to simulate vehicle crashes. The global sti↵ness of the test installation was not fully

captured by the model used here which provided di↵erence in the results between the

simulation and full-scale test. However, this master thesis shows that a full-scale crash

can be simulated using Abaqus/Explicit provided a proper vehicle model and a detailed

model of the test installation. Nonetheless, it is a prerequisite to model the parapet

and the surroundings such as bridge deck, connections etc. very detailed to have better

convergence with real test. Detailing of the model sets the limit for how accurate the

simulations will be.

70

Chapter 6

Future work

The main area of improvement seems to be the model of the bridge deck and the detailing

in the connection between di↵erent parts of the bridge parapet. In order to produce

better convergence between the simulation and the full-scale test, the overall sti↵ness of

the bridge rail installation must be captured. It is very di�cult to capture the overall

sti↵ness when neglecting key object such as the transition zones, the bolts and the

crushing process of the bridge deck.

A future work could for example be to use the modeled vehicle in this master thesis

and focus on the modeling of the concrete deck and the bridge rail installation. Special

intention should also be addressed for the material definition of the concrete deck since

crushing is involved.

Next step is to improve the material definitions of some parts of the modeled vehicle.

One of these materials could for example be the material definition used for the tires.

Instead of the elastic definition as it is now, it should be modeled with a proper material

definition for rubber. Also, it is necessary to investigate the occupant risks during the

impact. Another property that might be of importance to address is how the vehicle

speed is applied prior impact. The speed of the vehicle is applied through the predefined

field, a more sophisticated way of applying the vehicle speed should be used in order to

reflect the real behavior prior, during and after the impact. In order to get rid of the

increasing viscous dissipated energy, future worker should reconsider the usage of the

dashpot-like properties used for the di↵erent connection sections in the vehicle model.

Attention should be put on the energy balance to have constant total energy for the

whole model.

Looking even further into the future it would be a necessity to develop di↵erent vehicle

models that can be used in the simulations in order to investigate the performance of

71

Future work

the rail. This is a necessity since satisfactory performance of the parapet for a specific

vehicle does not imply the satisfaction for a di↵erent type of vehicle since the overall

sti↵ness must fit di↵erent types of vehicle models as mentioned in the introduction of

this master thesis.

72

Bibliography

[1] Dassault Systemes. Abaqus 6.14 Online Documentation: 2.4.2 Cost of mesh refine-

ment in implicit and explicit analyses. Dassault Systemes, http://server-ifb147.

ethz.ch:2080/v6.14/books/gsa/default.htm, 2014.

[2] Roger P. Bligh, William F. Williams, and Wanda L. Menges. NCHRP REPORT

350 TEST 3-11 OF THE MODIFIED T8 BRIDGE RAIL. Technical report,

Texas Transportation Institute, http://d2dtl5nnlpfr0r.cloudfront.net/tti.

tamu.edu/documents/0-5210-6.pdf, 2009.

[3] Ali O. Atahan and Omer F. Cansiz. Impact analysis of a vertical flared back bridge

rail-to-guardrail transition structure using simulation. http://citeseerx.ist.

psu.edu/viewdoc/download?doi=10.1.1.208.872&rep=rep1&type=pdf, 2004.

[4] National Crash Analysis Center. http: // www. ncac. gwu. edu/ vml/ models.

html , 2014.

[5] Nauman M. Sheikh, Rubiat Ferdous, Roger P. Bligh, and Akram Y. Abu-

Odeh. ANALYSIS OF ROADSIDE SAFETY DEVICES FOR USE ON

VERY HIGH-SPEED ROADWAYS. Technical report, Texas Transportation

Institute, http://d2dtl5nnlpfr0r.cloudfront.net/tti.tamu.edu/documents/

0-6071-1.pdf, 2009.

[6] Nauman M. Sheikh, Rubiat Ferdous, Roger P. Bligh, and Akram Y. Abu-

Odeh. ANALYSIS OF ROADSIDE SAFETY DEVICES FOR USE ON

VERY HIGH-SPEED ROADWAYS. Technical report, Texas Transportation

Institute, http://d2dtl5nnlpfr0r.cloudfront.net/tti.tamu.edu/documents/

0-6071-1.pdf, 2009. p. 14.

[7] Touraj Gholami, Jurgen Lescheticky, and Ralf Paßmann. Crashworthiness simula-

tion of automobiles with abaqus/explicit. 2002.

[8] Xavier Latorre, Pedro Marijuan, and Jordi Vinas. Road restraint systems in abaqus.

2012.

73

Bibliography

[9] Dassault Systemes. Abaqus 6.14 Online Documentation: 1.1 The Abaqus prod-

ucts. Dassault Systemes, http://server-ifb147.ethz.ch:2080/v6.14/books/

gsa/default.htm, 2014.

[10] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.2.1 Explicit time in-

tegration. Dassault Systemes, http://abaqus.sys.kth.se/v6.14/books/gsa/

default.htm, 2014.

[11] Dassault Systemes. Abaqus 6.14 Online Documentation: 2.4.1 Choosing between

implicit and explicit analysis. Dassault Systemes, http://server-ifb147.ethz.

ch:2080/v6.14/books/gsa/default.htm, 2014.

[12] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.2.3 Advantages of the

explicit time integration method. Dassault Systemes, http://abaqus.sys.kth.se/

v6.14/books/gsa/default.htm, 2014.

[13] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.3.1 Conditional stability

of the explicit method. Dassault Systemes, http://abaqus.sys.kth.se/v6.14/

books/gsa/default.htm, 2014.

[14] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.3.2 Definition of the sta-

bility limit. Dassault Systemes, http://abaqus.sys.kth.se/v6.14/books/gsa/

default.htm, 2014.

[15] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.3.3 Fully automatic

time incrementation versus fixed time incrementation in Abaqus/Explicit. Dassault

Systemes, http://abaqus.sys.kth.se/v6.14/books/gsa/default.htm, 2014.

[16] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.3.4 Mass scaling to

control time incrementation. Dassault Systemes, http://abaqus.sys.kth.se/v6.

14/books/gsa/default.htm, 2014.

[17] Dassault Systemes. Abaqus 6.14 Online Documentation: 9.6.1 Statement of en-

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default.htm, 2014.

[18] Dassault Systemes. Abaqus 6.14 Online Documentation: 3.2.2 Substructure analysis

of a pick-up truck model. Dassault Systemes, http://server-ifb147.ethz.ch:

2080/v6.14/books/exa/default.htm, 2014.

[19] Dassault Systemes. Abaqus 6.14 Online Documentation: 3.2.1 Inertia relief in a

pick-up truck. Dassault Systemes, http://server-ifb147.ethz.ch:2080/v6.14/

books/exa/default.htm, 2014.

74

Appendix A

A.1 Bolt connection properties

75

Bolt capacity

Indata

tthriebeam 5mm� d58in 15.875mm� � Abolt

π d2�

4197.933mm2� �

Pbolt π d� 49.873mm� � fyb 640MPa� Assuming 8.8 Bolts

γM1 1.0� fub 800MPa�

γM2 1.2� fy.thriebeam 250MPa�

k2 0.9�

αv 0.6�

Tension resistance of the bolts [EN 1993-1-8]

Ft.Rdk2 fub� Abolt�

γM2118.76kN� �

Punching shear resistance of thrie beam [EN 1993-1-1]

PRd Pbolt tthriebeam�fy.thriebeam

3 γM1�� 35.993kN� �

F1 min Ft.Rd PRd��� � 35.993kN� �

Shear resistance of the bolts [EN 1993-1-8]

Fv.Rdαv fub� Abolt�

γM279.173kN� �

F2 Fv.Rd 79.173kN� �

F3 F3=

Bibliography

A.2 Bending moment capacity of the post

77

Post Cross Section: without slotted holes

Indata

bc 3.94in 100.076mm� � tc 0.194in 4.928mm� � fy 250MPa� ε 235fy

MPa

0.97 �

h 5.83in 148.082mm� �

hw h 2tc� 138.227mm� � tw 0.17in 4.318mm� �

Classification of the cross sectionFlange

bc tw�

2 tc�9.716

compare with 9ε10ε14ε

§¨¨©

·¸¸¹

8.726

9.695

13.574

§¨¨©

·¸¸¹

Crosssection 3

Web

hwtw

32.012 compare with

72ε83ε124ε

§¨¨©

·¸¸¹

69.807

80.471

120.222

§¨¨©

·¸¸¹

CrossSection 3

The cross section belongs to Class 3

Moment of inertia

Iy 2bc tc

3�

12bc tc�

h2

§©

·¹

2��

ª««¬

º»»¼

�tw hw

3�

12� 6.359 106u mm4� �

Wy.elIy0.5 h�

8.589 104u mm3� �

Mmax fy Wy.el� 21.472MN mm�� �

Appendix B

B.1 Post deformations

B.1.1 Initial angular deflection of posts 11-13

The time for the initial deflection was set to a value when the deflection was at least 1�

in order to compare to the full-scale test.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05�20

�15

�10

�5

0

5

10

0.0171430.018858 0.034286

Time t [s]

Angu

lardisplacements

UR3[D

egrees]

Angular deflection, UR3, of post 11-13

Post11

Post12

Post13

Figure B.1: Initial angular deflection of post 11-13.

79

Bibliography

B.1.2 Mean angular deflection for posts 5-9

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65�5

�4

�3

�2

�1

0

1

-3.2959

Time t [s]

Angu

lardisplacements,UR3[°]

Mean values of angular deflection, UR3, for post 5-9

Angular displacement UR3

Figure B.2: Mean angular deflection for posts 5-9.

B.1.3 Angular deflection for posts 10-15

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7�60

�50

�40

�30

�20

�10

0

10

-17.4037

-30.7955

-51.2094

-50.8964

-34.9414

-20.1809

Time t [s]

Angu

lardisplacements,UR3[°]

Angular deflection, UR3, for posts 10-15

Post10

Post11

Post12

Post13

Post14

Post15

Figure B.3: Angular deflection for posts 10-15.

80

Bibliography

B.1.4 Vertical deflection for posts 10-15

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7�400

�300

�200

�100

0

100

-39.6246

-121.388

-320.676

-310.779

-154.51

-53.2293

Time t [s]

Verticaldisplacements,U2[m

m]

Deflection towards field side, U2, for posts 10-15

Post10

Post11

Post12

Post13

Post14

Post15

Figure B.4: Deflection towards field side, U2, for posts 10-15.

B.2 Tabular thrie beam deformations

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

0

200

400

600

800702.61

642.551

Time t [s]

Horizon

taldisplacements,U1[m

m]

Horizontal deflection, U1, of the tabular thrie beam

Tabular thrie beam deflection

Maximum dynamic deflection

Maximum permanent deformation

Figure B.5: Maximum deflection of the tabular thrie beam.

81

Bibliography

B.3 Vehicle position, speed and angular deflection

When the vehicle had rotated an angle of 23.8°, relative to its initial position, it was

parallel to the bridge guard rail. The graphs and picture presented here shows the

position, speed and time when the vehicle was parallel. The time was 0.213 s when the

car was parallel.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

0

10

20

30

23.8

Time t [s]

Angledefl

ection

,[D

egrees]

Angular deflection of the vehicle

Angle deflection

Angle when parallel to guardrail

Figure B.6: Vehicle angle during the impact.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.775

80

85

90

95

100

105

85.135

Time t [s]

Speed,V

[km/h

]

Vehicle speed during impact

Resultant of the vehicle speed

Speed at parallel to guardrail

Figure B.7: Vehicle speed during the impact.

82

Bibliography

Figure B.8: The vehicle position and time when it was parallel to the rail.

83