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공학석사학위논문

Analysis of the bending behavior of RC wall

subjected to impact loading

충돌하중을 받는 RC벽체의 휨 거동 해석

2015년 8월

서울대학교 대학원

건설환경공학부

강 창 진

i

ABSTRACT

This research studies the shear failure surface of the concrete constitutive model

and the loading by load-time function and projectile modeling for simulating

bending behavior of reinforced concrete (RC) wall impacted by the soft missile to

verify their influences on simulation results. Flexural test of RC wall from VTT-

IRIS project was selected as a target test and the effect of the shape of shear failure

surface and load-time function were considered by using LS-DYNA, the commercial

explicit dynamic code.

The shear failure surface of one of the typically used concrete model for impact

analysis, Continuous Surface Cap Model (CSCM) was examined with the material

parameters which define the shape of the shear failure surface. For parametric reason,

current CSCM has a limitation of analyzing the behavior of high strength concrete.

However, CSCM which simulated the high strength concrete showed suitable results

in case when it was loaded with low pressure invariant like the flexural test.

Deformable missile based on Hughes-Liu element formulation was modeled.

The deformed shape of the projectile after the impact, and the contact force-time

function was obtained and discussed. Also, the effect of the shape of a load-time

function was discussed by comparing the displacement results which were applied

with two different load-time functions. The peak value of the load-time function,

which mainly affects the maximum displacement and the load duration time, which

mainly affects the residual displacement of the RC wall were considered as the

ii

dominant factors for the analysis.

The simulation results using CSCM with the load-time function and projectile

model were compared with the test result. Similar results with the VTT test could be

obtained for maximum displacement and residual displacement, and relatively

analyzing the axial strain of rebar inside the concrete was found out to be still

challenging.

Keywords: LS-DYNA analysis, VTT flexural Test, Impact test, CSCM,

Deformable missile

Student Number: 2013-23147

iii

TABLE OF CONTENTS

ABSTRACT ................................................................................... I

TABLE OF CONTENTS ............................................................ III

LIST OF FIGURES .................................................................... VI

LIST OF TABLES ................................................................... VIII

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

1.1 RESEARCH CONTEXT AND SCOPE ............................................ 1

1.2 THESIS OUTLINE .................................................................... 3

CHAPTER 2 BACKGROUND AND LITERATURE REVIEW. 4

2.1 BACKGROUND ....................................................................... 4

2.1.1 IRIS BENCHMARK TEST 2010/2012 .................................. 4

2.1.2 VTT FLEXURAL TEST ......................................................... 6

2.1.3 LS-DYNA ........................................................................ 7

2.2 LITERATURE SURVEY.............................................................. 8

CHAPTER 3 THEORY MECHANISM OF IMPACT ANALYSIS . 11

3.1 CONSTITUTIVE MODEL THEORY ............................................ 11

3.1.1 CONTINUOUS SURFACE CAP MODEL (CSCM) .................. 11

iv

3.1.2 COWPER-SYMOND CONSTITUTIVE EQUATION .................. 16

3.2 LOAD-TIME FUNCTION ......................................................... 17

3.3 SHAPE FUNCTION OF ELEMENT FOR ANALYSIS ...................... 18

CHAPTER 4 LS-DYNA ANALYSIS ......................................... 21

4.1 OVERVIEW ........................................................................... 21

4.2 PROCEDURE OF MODELING ................................................... 21

4.2.1 RC WALL MODELING ....................................................... 21

4.2.2 PROJECTILE MODELING ................................................... 27

4.2.3 LOADING CONDITION ...................................................... 29

4.3 CONVERGENCE CHECK ......................................................... 30

CHAPTER 5 RESULT AND EVALUATION ............................ 33

5.1 EVALUATION CRITERION ...................................................... 33

5.2 EFFECT OF SHAPE OF SHEAR FAILURE SURFACE .................... 34

5.3 EFFECT OF SHAPE OF THE LOAD-TIME FUNCTION .................. 37

5.4 RESULT FROM MISSILE MODELING IMPACT ........................... 39

5.5 EVALUATION OF VTT FLEXURAL TEST SIMULATION ............. 43

5.5.1 DISPLACEMENT ............................................................... 43

v

5.5.2 STRAIN ON THE REBAR .................................................... 44

5.6 DAMAGE PATTERN ............................................................... 46

CHAPTER 6 CONCLUSION .................................................... 48

REFERENCES ........................................................................... 50

APPENDIX A ............................................................................. 53

APPENDIX B ............................................................................. 55

APPENDIX C ............................................................................. 56

ABSTRACT(IN KOREAN) ....................................................... 58

ACKNOWLEDGEMENT ........................................................ 60

vi

LIST OF FIGURES

FIGURE 2.1 PREDICTED DISPLACEMENT RESULTS OF BLIND TEST (IRIS 2010) ............ 5

FIGURE 2.2 DISPLACEMENT RESULTS AFTER THE MODIFICATION (IRIS 2012) ............. 5

FIGURE 2.3 SCHEMATIC DRAWING OF THE FLEXURAL TEST ........................................ 6

FIGURE 2.4 IMPACT TEST FACILITY AND MISSILE ........................................................ 7

FIGURE 3.1 GENERAL SHAPE OF THE CONCRETE MODEL YIELD SURFACE IN 2D ..... 12

FIGURE 3.2 SHEAR FAILURE SURFACE FOR VARIOUS COMPRESSIVE STRENGTH OF

CONCRETE ........................................................................................................... 13

FIGURE 3.3 8-NODE SOLID HEXAHEDRON ELEMENT ................................................. 18

FIGURE 3.4 TRUSS ELEMENT ..................................................................................... 19

FIGURE 3.5 HUGHES-LIU SHELL ELEMENT ................................................................ 20

FIGURE 4.1 CONCRETE WALL SETTING FOR VTT BENDING TEST .............................. 22

FIGURE 4.2 REBAR LAYER SETTING FOR VTT BENDING TEST ................................... 22

FIGURE 4.3 THE MODELING OF RC WALL AND REBAR (LS-DYNA) .......................... 23

FIGURE 4.4 SUPPORTING FRAME OF THE RC WALL ................................................... 23

FIGURE 4.5 BOUNDARY CONDITION OF THE MODELING .......................................... 24

FIGURE 4.6 TRI-AXIAL EXTENSION SHEAR FAILURE SURFACE OF CURRENT CSCM

AND RECENTLY PROPOSED SHEAR FAILURE PARAMETER ADOPTED CSCM ........ 26

FIGURE 4.7 SOFT STEEL MSSILE USED IN FLEXURAL TEST ......................................... 27

FIGURE 4.8 THE MODELING OF SOFT STEEL MISSILE (LS-DYNA) ............................ 28

FIGURE 4.9 THE LOAD-TIME FUNCTION USED FOR SIMULATION ............................... 30

vii

FIGURE 4.10 VON MISES STRESS ON RC WALL DEPENDS ON MESH SIZE ................... 31

FIGURE 4.11 MESH SIZE CONVERGENCE CHECK ....................................................... 31

FIGURE 4.12 ENERGY BALANCE FOR VTT FLEXURAL SIMULATION .......................... 32

FIGURE 5.1 EVALUATION CRITERION FOR DISPLACEMENT ........................................ 33

FIGURE 5.2 PLACE WHERE DISPLACEMENT SENSOR SET (SENSOR 1) ........................ 34

FIGURE 5.3 DISPLACEMENT RESULT DEPEND ON SHEAR FAILURE SURFACE OF

CONCRETE ........................................................................................................... 35

FIGURE 5.4 TXE SHEAR FAILURE SURFACE FOR THE PRESSURE RANGE OF FLEXURAL TEST .. 36

FIGURE 5.5 DISPLACEMENT RESULT DEPEND ON LOAD-TIME FUNCTION .................. 37

FIGURE 5.6 DISPLACEMENT RESULT OF MISSILE MODELING IMPACT ........................ 39

FIGURE 5.7 DEFORMED SHAPE OF MISSILE AFTER IMPACT ........................................ 41

FIGURE 5.8 DEFORMED SHAPE OF MISSILE AFTER TEST ............................................ 41

FIGURE 5.9 CONTACT FORCE-TIME FUNCTION ON RC WALL ..................................... 42

FIGURE 5.10 MAXIMUM DISPLACEMENTS FOR EACH LOADING CASE ....................... 42

FIGURE 5.11 PLACE WHERE DISPLACEMENT SENSOR SET (SENSOR 2)....................... 43

FIGURE 5.12 COMPARISION OF THE DISPLACEMENT REPONSES (SENSOR 2) ............. 44

FIGURE 5.13 PLACE WHERE STRAIN SENSOR SET ...................................................... 45

FIGURE 5.14 STRAIN RESULT FROM STRAIN GAUGE .................................................. 45

FIGURE 5.15 DEFLECTION AND DAMAGE PATTERN OF TIME-LOAD FUNCTION CASE . 46

FIGURE 5.16 DEFLECTION AND DAMAGE PATTERN OF PROJECTILE MODELING CASE 47

FIGURE 5.17 ERODED ELEMENT ON REAR SIDE OF WALL .......................................... 47

FIGURE B.1 EFFECT OF DAMPING RATIO ON RC WALL .............................................. 55

viii

LIST OF TABLES

TABLE 4.1 COWPER-SYMOND PARAMETER FOR STEELS ........................................... 16

TABLE 4.2 MATERIAL PROPERTY APPLIED FOR CONCRETE ........................................ 25

TABLE 4.3 MATERIAL PROPERTY APPLIED FOR REBAR .............................................. 27

TABLE 4.4 MATERIAL PROPERTY APPLIED FOR EN 1.4432 ........................................ 28

TABLE 4.5 MATERIAL PROPERTY APPLIED FOR S355 ................................................. 29

TABLE 5.1 DISPLACEMENT RESULT FOR CSCM AND JIANG ...................................... 36

TABLE 5.2 DISPLACEMENT RESULT FOR SARRENHEIMO AND CHUNG ....................... 38

TABLE 5.3 DISPLACEMENT RESULT FOR MISSILE MODELING .................................... 40

1

CHAPTER 1

INTRODUCTION

1.1 Research context and scope

To improve the safety-focused design of the structures which may expose to a

disaster or a potential terrorist attack, structural resistance against impact load is

becoming one of the important topics among researchers. Researches on impact

analysis were carried out based on experiments or empirical functions (Nachtsheim

et al., 1983, Sugano et al., 1993, Hashimoto et al., 2005) in the beginning, even

though it has characteristic of high cost and time consuming. However, as

commercial analysis programs develop through decades, FEM analysis (Martin et

al., 2012, Thai et al., 2014, Liu et al., 2009) was considered to be one of the

preferred methods to overcome those disadvantages that impact test had to bear.

Still, due to fast dynamic and non-linear nature of the concrete, there is an inherent

scatter of the results well beyond the scatter of an elastic analysis. (Tarallo et al.,

2013) One of the reason for its difficulty is due to the sophisticate material property

of the reinforced concrete against the impact.

Generally, reinforced concrete is commonly used material for the outer wall

structure for its high extreme loading resistance compared to other construction

materials. Material study of the concrete has been decades, however for fast

dynamic case like material impact which involves softening with damages on the

2

material is still far from fully understanding, and this is the reason why impact

analysis becomes more computationally challenging and more time consuming

works.

Analyzing the response of the structure by using a modelled missile is the

most appropriate way however, to analyze the behavior of a structure more

efficiently with relatively small error, load-time function can be utilized which may

simplify the computational process relatively to the case when actual impact force

is given on the structure. For most of the cases, this function is presented as several

piecewise linear functions.

In this study, bending behavior of RC wall subjected to deformable missile

was simulated to apply obtained basic knowledge when further impact tests are

conducted. Using a commercial FEM program, the VTT test which belongs to the

IRIS project 2010/2012 was simulated. This simulation was evaluated by

comparing the analysis results with the VTT test results.

This study focuses on the bending behavior of RC structure subjected to a

deformable missile by conducting FEM analysis to investigate simulation

methodology and to obtain accurate result. To accomplish these objectives, this

study firstly considers the parameters that affect the shape of a shear failure surface

of the concrete model, Continuous Surface Cap Model (CSCM). Secondly this

paper considers the effect of a peak load and a load duration time of the simplified

loading function which can substitute the contact force in impact analysis. The

result from the force-time function was compared with that of the projectile

3

modeling and the reason for the difference was discussed. Lastly, maximum

displacement, residual displacement and strain results from FEM analysis were

compared with the test results from IRIS 2010/2012 project VTT test report to

verify the simulation results.

1.2 Thesis Outline

This study includes the analysis of the bending behavior of RC wall impact by

the deformable missile by using commercial FEM program LS-DYNA.

Chapter 2 contains the backgrounds of the target test and the description of the

continuous surface cap model (CSCM) which was validated by Federal Highway

Association (Murray, 2007). Moreover, preliminary studies for this research are

organized in this chapter.

Chapter 3 gives the theoretical backgrounds for the material models, load-time

function and element formulation which were considered in simulation process.

Chapter 4 establishes the impact modeling process carried out by LS-DYNA.

This includes the details of the target structure and the deformable projectile for the

simulation with convergence check.

Chapter 5 compares the obtained results with the test, and discusses the

effectiveness of the shape of the shear failure surface and the load-time function.

Chapter 6 summarizes the conclusion of the research

4

CHAPTER 2

BACKGROUND AND LITERATURE REVIEW

2.1 Background

2.1.1 IRIS Benchmark test_2010/2012

In 2009, the committee on the safety of nuclear installations and the committee

on Nuclear Regulatory Activities (NEA) jointly issued technical safety

organizations for design and construction of new reactors and installations. The

importance of sharing knowledge about analyzing impact procedure was issued and

to precede this research, a round robin study called IRIS (Improving Robustness

Assessment Methodologies for Structures Impacted by Missiles) project was

conducted with the participation of over 25 teams from global organizations.

(Orbovic, 2014)

For the first phase, blind tests were carried out. Flexural tests, and punching

tests on RC wall were conducted by VTT (Technical Research Centre of Finland)

and participants of the project used numerical methods to predict the response of

the RC wall without knowing the experiment results. Overall, most of the teams

utilized the recent FEM codes like ABAQUS, LS-DYNA or in house FE codes to

analyze the response of the RC wall that was subjected to impact load, however the

expected results from every organization scattered.

After announcing the test results during the second phase, every participant

had an opportunity to modify their methodology to establish better simulation. As a

5

result, latter results submitted from each participant showed less difference with

test result than previously submitted results as shown in Fig 1, 2. (Orbovic, 2014).

Both figures imply that continuous improvement is required for the FEM analysis.

Fig 2.1 Predicted displacement results of blind test (IRIS 2010)

Fig 2.2 Displacement results after the modification (IRIS 2012)

6

VTT report assumed the suitable simulation result would be within 40% range

from the experiment result and 8 teams fulfilled this condition. (Orbovic, 2014)

They concluded the most dominant factors for predicting the response of concrete

are the constitutive model for bending behavior analysis. Still, there are lots of

factors that would affect the behavior of structure like strain-rate, damage

mechanism which are all need to be researched with the parametric studies later on.

For the next phase of IRIS benchmark project, induced vibration on RC wall

after soft missile impact is the main issue to be discussed. Related result from each

organization will be shared during the conference which is planned to be held on

end of the year 2015.

2.1.2 VTT flexural test

In VTT (Technical Research Centre of Finland), two types of impact test were

conducted. One is a flexural test considering the global damages for cases like

structure overturning, residual deformation on a structure. The other test is a

punching test which considers local damages for cases like spalling, scabbing, or

perforation. For flexural test, the target mass of 50.00kg of hollow deformable

stainless steel missile was impacted against RC wall with velocity of 110m/s.

Figure 2.3 Schematic drawing of the flexural test

7

The schematic drawing of the experiment is shown in Fig 2.3, and the test

facility with the picture of the used missile for the test are shown in Fig 2.4

(Orbovic et al., 2014).

RC wall had a dimension of 2082*2082*150 mm and it was reinforced with

6mm diameter rebar with the spacing of 55mm. Measured compression strength of

the concrete was 63.9MPa and no spalling, scabbing, or perforation was occurred

during the test. Maximum displacement, residual displacement and strain were

main measurement taken in this bending test.

Figure 2.4 Impact test facility and missile

2.1.3 LS-DYNA

LS-DYNA is a nonlinear Finite Element Analysis (FEA) simulation software

developed by Livermore Software Technology Cooperation (LSTC). This program

analyze the dynamic nonlinear behavior of the material or structure in 3D. The

integrated solver module is one of the advantage that LS-DYNA has, which does

not require users to specify the type of analysis to utilize. The main solution

8

methodology is based on explicit time integration method (Hallquist, 2006), and by

satisfying traction boundary conditions, displacement boundary conditions and the

contact discontinuity condition, the program seeks a solution to the following

momentum equation.

,ij j i if x (2.1)

σ is the Cauchy stress, ρ is current density, fi is the body force density and �̈� is

acceleration.

2.2 Literature survey

Continuous Surface Cap Model (CSCM) is extension form of a simple cap

model originally evolved from early DYNA3D implementation by Pelessone

(Pelessone, 1989). CSCM includes isotropic constitutive equations and it includes

softening and hardening surface as well as the damage parameters. Originally, it

was the model for describing the behavior of soil that absorbs explosive energy and

having large deformation in a short time. The Pelessone implementation also

included a function for the softening behavior of soil which is presented as cap

model in analysis model.

This model was developed to describe the behavior of rock and concrete. After

adopting the 3rd deviatoric stress invariant term J’3, Rubin (Rubin, 1991) combined

both the shear and failure surface from two independent function and it is basically

the origin of CSCM. Sandler et al. (Sandler et al., 1984) added kinematic strain

9

hardening parameter which makes the constitutive model possible to represent the

hardening effect occurred by the porous in the concrete. Schwer (Schwer, 1994)

and Murray (Murray, 1997) had adapted strain-rate effect through viscoplastic

formulation and Murray (Murray, 1995) furthermore developed this model by

combining damage mechanics to it.

Federal Highway Association (FHWA), added the default functions that

generate the parameters for simulating the concrete behavior with few input

parameters. Generated parameters are mostly based on the equations or experiment

results from CEB-FIP. This constitutive model was adopted in LS-DYNA start

from 1990s.

To improve assessment methodologies for impact analysis by using the

experiment results from VTT tests, simulation methodologies were developed and

evaluated by the recent papers. Heckötter and Vepsä (Heckötter et al., 2015)

analyzed the behavior of RC structure subjected to external missile impact and

showed the improved numerical analysis for various types of projectiles including

a wet missile and a missile with wings attached. In this paper, the crushing force

that is required for the Riera function was assumed from elastic-ideal plastic

folding mechanism of a thin walled cylinder. Martin (Martin et al., 2012) simulated

the Meppen test and VTT flexural test by using explicit solver RADIOSS and

Lagrangian meshes and validated the calculation results with the test results to

verify the analysis procedure. Thai and Kim (Thai et al., 2014) carried out the

10

parameter study on varying number of layers of longitudinal rebar and shear bar

spacing related to punching behavior of RC walls under wet missile impact to

recommend efficient design for RC structures. All of these studies represent the

sophisticate aspects of impact analysis and indicate that the research on impact has

been carried out through decades without giving out robust solution.

Recent researches on parameters defining concrete properties based on

Continuous surface cap model was done by Jiang and Zhao (Jiang et al., 2015) to

improve the results for the simulation analysis. This paper proposed new

parameters generating equations that defines yield surface of the CSCM. By

comparing the result with newly proposed parameters, analysis of the impact force

predicted better than the original defined CSCM.

Chung and Lee (Chung et al., 2015) presented simplified techniques to

consider both efficiency computational time and its accuracy when simulating the

behavior of RC wall under impact loads. They proposed the simplified way to add

a specific node to the model which substitutes the framing support.

11

CHAPTER 3

THEORY MECHANISM OF IMPACT ANALYSIS

3.1 Constitutive model theory

3.1.1 Continuous Surface Cap Model (CSCM)

Typical concrete constitutive models include the definition of a yield surface to

describe the plastic behavior of the concrete with the specific function and this

function is commonly defined as following equation.

𝑓(𝐼1, 𝐽2, 𝐽3) = 𝑘2 (3.1)

I1 is the 1st invariant of stress tensor and J2, J3 means the invariants of

deviatoric stress tensor. K is a constant value defining specific yield criterion that

discriminate whether the material is under elastic behavior or plastic behavior. The

criteria for yield surface is usually defined based on either one of these theories.

i. Maximum principal strain theory

ii. Maximum shear stress theory

iii. Total strain energy theory

iv. Distortion energy theory

Yield surface of Continuous Surface Cap Model (CSCM) is based on total

strain energy theory, and the model is assumed as an isotropic material.

12

Figure 3.1 General shape of the concrete model yield surface in 2D

CSCM is basically consist of shear failure function, cap function and Rubin

function as shown in Fig 3.1 (Murray, 2007), and can be written as follows.

2 2

1 2 3 2 3 1 1( , , ) ( ) ( ) ,f cY I J J J J F I F I (3.2)

J2, J3 means the invariants of deviatoric stress tensor, R means Rubin function,

Ff means the shear failure surface function and Fc means the cap hardening surface

function. Κ is the cap hardening parameter which defines the intersection of the

shear failure surface and cap hardening surface.

Shear failure surface function Ff defines the principle stress difference value

where concrete shows plasticity properties by using invariant term I1 and the

function Ff along the compression meridian is written as follows.

1 1 1( ) expfF I I (3.3)

All parameters , , , used in shear failure surface function are material

parameter basically calculated by concrete material experiments. α is a tri-axial

Smooth Intersection

Shear Surface

Cap

Pressure

Sh

ear

Str

ength

13

compression surface constant term, β is a tri-axial compression surface exponent

term, γ is a tri-axial compression surface nonlinear term and θ is a tri-axial

compression surface linear term. CSCM_concrete model developed by FHWA

indicates that the shear failure surface would become larger as a compressive

strength of concrete increases as shown in Fig 3.2.

Figure 3.2 Shear failure surface for various compressive strength of concrete

Cap hardening model is the function which considers the volume change

related to pore collapse in the concrete model. This function expands or contracts

based on the hardening rule.

Rubin scaling function determines the strength of a concrete for any state of a

stress relative to the strength of compression. It is basically comprised of

trigonometric function which adjoins the tri-axial compression (TXC), tri-axial

14

extension (TXE) and tri-axial rotation (TOR) yield surfaces to a function in

definition of J3.

CSCM additionally considers the properties of concrete material under impact

load by considering the strain rate effect and damage parameter, softening and

hardening by the following method.

Strain rate effect is usually considered in a material model by magnifying the

initial yield surface. In case of CSCM, viscoplastic formulation σ𝑣𝑝 algorithm is

applied. This formulation is consisted of defining fluidity coefficient. Fluidity

coefficient is reciprocal of the viscosity and gradually affect the total shape of yield

surface by interpolating an elastic trial stress σ𝑇 and an inviscid stress σ𝑝 with

the following equation.

/(1 )

1 /

vp T p

ij ij ij

t

t

(3.4)

η is a fluidity coefficient value and △t means the time step. In modeling

process, fluidity coefficient value for compression and tension will be considered

separately by using the simple equation.

0

n

(3.5)

η and n are the input parameters need to be fit based on the rate effect data and

𝜀̇ is the effective strain rate. In short, if γ=1, then strain rate effect will not be

considered.

Damage of the concrete affects the erosion criteria for the element and reduce

15

the modulus properties in the constitutive model

(1 )d vp

ij ijd (3.6)

σ𝑣𝑝 is viscoplastic stress tensor without damage, and σ𝑑 is the stress tensor

with damage. A scalar damage parameter d initiates from pre-damaged value (in

case of no damage, d=0) and as the value d accumulates, the strength of the

material degrades.

The procedure for defining damage follows this step:

1. Defines the type of failure between ductile and brittle

2. Defines the damage threshold with the following equations

𝜏𝑏 = √𝐸𝜖2𝑚𝑎𝑥 (for brittle damage) (3.7)

𝜏𝑑 = √1

2𝜎𝑖𝑗𝜖𝑖𝑗 (for ductile damage) (3.8)

3. Verify the criteria where damage on element initiates. The criteria for

damage initiation is defined with the following equations. In this equation,

r0𝑏 means the damage threshold and A, B, C, D are the shape of the

softening curve plotted as stress-displacement or stress-strain.

0( )

0.999 1( ) 1

1 exp b bb C r

Dd

D D

(for brittle damage) (3.9)

0

max

( )

1( ) 1

1 exp b bd A r

d Bd

B B

(for ductile damage) (3.10)

4. Calculate softening value d and substitute it into damage equation

In case of the CSCM, if accumulated value d becomes 1 and the strain of

16

element goes over the erosion criteria ERODE, then the correspond element will be

counted as eroded element and ignored for remained calculation.

3.1.2 Cowper-Symond constitutive equation

For steel constitutive model, the strain rate of steel was considered by using

the Cowper-Symond constitutive equation.

00 0

0

'1 '

q

C

(3.11)

0' is the dynamic stress at a uniaxial plastic strain rate , 0 is the static

stress and C, q are constants for steel materials.

Following equation can be written in the form

1/

0

0

'1

q

C

(3.12)

Parameter values for C, q are the experimental values (Jones, 1997)

Table 3.1 Cowper-Symond parameter for steels

Material C(1/s) q

Mild steel 40.4 5

Aluminum alloy 6500 4

Stainless steel 304 100 10

17

3.2 Load-time function

In bending behavior test, the target can be assumed rigid relatively to the

deformable missile. As a result, several organizations that performed analysis work

of VTT test applied load-time function for simulating the test. Using load-time

function significantly reduces the computing time with relatively small error. Riera

method (Riera, 1968) is typical example of load-time function and formulation is

written as below.

2( ) ( ( )) ( )cF t P x t v t (3.13)

F(t) is impact force, Pc is required force to crush missile, μ is the mass flow

with a certain mass per unit length distribution and v is current velocity of

uncrushed part. By assuming an elastic-ideal plastic folding mechanism of a thin

walled cylindrical tube in VTT flexural test, the crushing force can be substituted

by the following equation which was mentioned by Jones (Jones, 1997).

1 12

1

2

1 0.41 ( / ) ( )( ( )) 21.1 1

42.14 ( / ) 1

q

c y

t r v tP v t t r

r Cr t

(3.14)

r is radius, t is thickness of the projectile and σy is the yield stress. This

equation is developed for an energy absorbing system that does not bottom out and

acceleration of the projectile should be relatively higher than gravity acceleration.

18

3.3 Shape function of the element for analysis

8-node hexahedron is the standard element for solid element, and its shape

function is written as follows.

1

1 1 18

i i i i (3.15)

Depend on the node position, nodal values change, its shape is shown in Fig 3.3

(Hallquist, 2006)

, , ( 1, 1, 1)i i i

Figure 3.3 8-node solid hexahedron element

In case of using one point integration during the analysis, energy balance

check including hourglass mode was recommended. By rule of thumb, hourglass

energy is recommended to be set under 10% of the peak value of internal energy

for impact analysis (Bala et al., 2012)

For truss model, the following equations are used for displacement and

velocity measure as follows.

19

1 2 1( )x

u u u uL

(3.16)

1 2 1( )x

u u u uL

(3.17)

When x=0, then u=u1 and at x=L, then u=u2.

Figure 3.4 Truss element

This model can be applied to both elastic and elastic-plastic material including

the consideration of kinematic hardening.

Hughes-Liu shell element formulation is the standard formulation for shell

element. (Hallquist, 2006) This element is based on a degeneration of the standard

8-node brick element formulation to 4-node shell geometry. The mapping of this

shell element is separated into two parts. One defines the position vector which

tells the position of the reference surface of the shell, and the other part defines the

fiber direction. This equation is written as follows.

, , , , ,x x X (3.17)

, , are nodal values and one-point integration is used for calculation

20

efficiency. This element uses 5 DOF in local coordinate system as shown in Fig 3.5

and yield globally 6 DOF. Also this element has the advantage that it is effective

when large deformation occurs and warped configuration are treated correctly.

However, for those reasons, this element is computationally costly than other

element formulation that does not consider the thickness of the shell.

Figure 3.5 Hughes-Liu shell element

21

CHAPTER 4

LS-DYNA ANALYSIS

4.1 Overview

For impact analysis, commercial program LS-DYNA_971 was used. This

FEM program is used for analyzing the nonlinear dynamic behavior of the material

or structures especially modeling corrosion analysis. Basically LS-DYNA gives

time-dependent deformation results in Cartesian coordinate system with

Lagrangian formulation. (Hallquist, 2006) Momentum equation, traction boundary

condition, displacement boundary conditions and contact condition are considered

to analyze the behavior of a system.

The target test for validating the FEM analysis is the VTT flexural test belongs

to the IRIS project. Concrete target, rebar and deformable missile were modeled

based on the VTT experiment report.

4.2 Procedure of modeling

4.2.1 RC wall modeling

The concrete target used in the test with its dimension is represented in Fig 4.1

(Orbovic et al., 2014). Fig 4.2 represents the layout of the rebar layer. Two layers

of steel with shear rebar were set up in VTT bending test. 8- node-hexahedral based

3D solid element was used for concrete model. The rebar adjoined in the RC wall

22

was modeled with truss element and the modeling for the concrete target and rebar

are shown in Fig 4.3. Total number of around 300,000 elements were used for the

analysis.

Fig 4.1 Concrete wall setting for VTT bending test

Fig 4.2 Rebar layer setting for VTT bending test

23

a)RC wall (3D hexahedral element) b)Rebar (1D truss element)__

Fig 4.3 The modeling of RC wall and rebar (LS-DYNA)

RC wall was constrained by supporting frame and its constrained condition is

represented in Fig 4.4 (Orbovic et al., 2014). As indicated in Fig 4.5, the

supporting frame was considered by giving a constraint to the nodes along the

support frame in the direction of impact of the target on both side of the RC wall.

Fig 4.4 Supporting frame of the RC wall

24

\

Fig 4.5 Boundary condition of the modeling

For concrete model, CSCM (Continuous Surface Cap Model) concrete which

provided by LS-DYNA program was used to include the strain rate effect,

softening, hardening and damage mechanism of the RC wall subjected to the

impact load. Compressive strength of the concrete is 63.9Mpa and its maximum

aggregation size of concrete used for VTT flexural test was 8mm. The material

properties are summarized in Table 4.1.

25

Table 4.1 Material property applied for concrete

Recently proposed parameters by Jiang (2015) was considered as well in this

paper, because Jiang mentioned that the original parameter used in current CSCM

may not fit well for high compressive strength (fck > 48Mpa). As shown in Fig 4.6,

shear failure surface of the current utilized CSCM for TXE decreases as the

pressure increases. This phenomenon occurs because the default parameters

equation set by FHWA is in the form of quadrature equation. Since several

participated teams had used CSCM constitutive material for case where uniaxial

compressive strength of concrete becomes 63.9Mpa, its effect should be reviewed.

Only parameters that affect the shape of shear failure surface were considered and

the other parameters was assumed to work same with the current CSCM. Specific

parameters used for this model is written in appendix A.

26

Fig 4.6 Tri-axial extrension shear failure surface of current CSCM and

recently proposed shear failure parameter adopted CSCM

For steel model, PLASTIC_KINEMATIC model was used. This model is also

provided by LS-DYNA and include option for considering strain rate effect for

rebar based on the Cowper-Symond constitutive equation. PLASTIC_

KINEMATIC model is suitable for the bilinear material like steel which has

different property values for elastic status and plastic status. Table 4.2 includes the

material property for the rebar.

27

Table 4.2 Material property applied for rebar

4.2.2 Projectile modeling

A picture of the soft missile that is shown in Fig 4.4 (Orbovic et al., 2014) has

a dimension of 2mm thickness with total length of 2,113mm. It was modeled as a

shell element defined with Hughes-Liu element formulation. The soft missile

modeling is shown in Fig 4.5 and self-contact was considered for soft missile due

to its large deformation while impact occurs.

Fig 4.7 Soft steel missile used in flexural test

28

Fig 4.8 The modeling of soft steel missile (LS-DYNA)

Soft missile is consisted with two types of steel. One is EN 1.4432 and the

other one is S355. PLASTIC_KINEMATIC model was used for projectile

modeling and Cowper-Symond constitutive equation was also considered as well.

Table 4.3 and 4.4 include the material property for rebar and deformable missile.

Table 4.3 Material property applied for EN 1.4432

29

Table 4.4 Material property applied for S355

4.2.3 Loading condition

Two types of loading condition were considered for bending analysis. One is

the load-time function. In this paper, load-time function from Sarrenheimo and

Chung in Fig 4.9 were used to simulate the impact load subjected to the RC wall.

This function was applied on the surface of RC wall using *LOAD_SEGMENT

command. The load-function that Sarrenheimo suggested has longer loading

duration time compared to that Chung has suggested. In the other hand, load-time

function suggested by Chung has higher peak load value.

Another way to impact the RC wall is to use shell element missile model and

impact it to the target with the initial velocity of 110m/s by utilizing contact

command in LS-DYNA. For this case, *CONTACT_AUTOMATIC_SURACE_

TO_SURFACE was used and *CONTACT_AUTOMATIC_ SINGLE_SURFACE

was also used to consider the self-contact induced by the soft missile itself.

For both cases, effect induced by gravity was neglected assuming that the

results induced by impact loading exceeds that of gravity effect.

30

Fig 4.9 The load-time function used for simulation

4.3 Convergence check

Several checks related to mesh size, time step and energy balance were

considered for modeling. Error occurrence during the calculation process could be

checked based on the following procedures.

To acquire reasonable results for VTT flexural test simulation, numerous mesh

size was considered as shown Fig 4.10 and elements along the thickness side of the

target was decided to be mainly considered for the convergence test. As shown in

Fig 4.11, it was found out that minimum number of 8 elements along the thickness

side are required to get the robust results for the analysis for flexural test. In this

paper, total number of 11 elements were considered along the thickness, which

equals to the length of 13.06mm.

31

Figure 4.10 Von Mises stress on RC wall depends on mesh size

Figure 4.11 Mesh size convergence check

For time step convergence check, Courant-Friedrich-Levy criterion was

considered. (Hallquist, 2006) Time step △t for explicit analysis is recommended to

32

be less than the time of sound travels the single element ∆x. For 13mm element the

reasonable time step was calculated as follows. Maximum value of the time step

taken in the analysis was 0.628 microsecond, which is narrower than the criteria.

132.48

5.240 /

Element size mmt s

Sound speed mm s

(4.1)

Based on General Guidelines for Crash Analysis in LS-DYNA (Bala et al.,

2012), the proportion between peak internal energy and hourglass energy was

considered as show in Fig 4.11.

Figure 4.12 Energy balance for VTT flexural simulation

Most of the kinetic energy is transformed into plastic deformation work during

the first 16.7ms. Hourglass energy accumulated to about 8.64% in the total internal

energy which fit to the guideline.

33

CHAPTER 5

RESULT AND EVALUATION

5.1 Evaluation criterion

After end of the blind test during the phase I in the IRIS project, VTT

disclosed the test results to the public. The analyzed results from participated teams

were compared with the test result, and maximum displacement and residual

displacement were mainly considered.

Figure 5.1 Evaluation criterion for displacement

In this section, the displacement result that was measured in the center of the

RC wall (rear) is compared with the analysis results. Its location is shown in Fig

5.2.

34

Figure 5.2 Place where displacement sensor set (sensor 1)

Based on this criteria, effect of recently proposed parameters which was

applied to current CSCM shear failure surface and the effect of shape of load-time

functions were compared and discussed in order.

5.2 Effect of shape of shear failure surface

By applying same load-time function which was suggested by Sarrenheimo

(Sarrenheimo, 2013) to the different model, the displacement result of current

CSCM (CSCM) and the recently proposed shear failure surface parameter applied

CSCM (Jiang, 2015) were shown in Fig 5.3. Contrary to the defect that the

quadratic parameter equation of CSCM would not fit for high strength region

analysis, the obtained result showed similar results to the experiment result from

VTT report.

Maximum pressure invariant that RC wall obtained during the test was

monitored to acquire reasonable explanation and it was found out that for VTT

35

flexural test, the maximum pressure invariant occurred during the impact

simulation was below the 38MPa, where TXE shear failure surface of original

CSCM is larger than the proposed one. The shear failure surface for both models

are shown in Fig 5.4 and the pressure invariant region belongs to the flexural test is

marked with dotted line. This figure shows that the original parameter equation for

shear failure surface has similar values with the recently proposed parameter

equation. Specific values are written in Table 5.1.

Figure 5.3 Displacement result depend on shear failure surface of concrete

36

Table 5.1 Displacement result for CSCM and Jiang

Maximum displacement Residual displacement

VTT test 28.9mm 7.86mm

CSCM 25.5mm (11.8%) 8.19mm (4.20%)

Jiang 22.2mm (23.2%) 3.78mm (51.9%)

( ) is the error value based on the criteria of VTT test

Figure 5.4 TXE shear failure surface for the pressure range of flexural test

From the result, CSCM was found out to give suitable results for the impact

analysis of the relatively low pressure invariant region test like flexural test.

However, this indicates that for high pressure invariant region, extra monitoring is

recommended for case using CSCM model in the high pressure invariant region.

37

5.3 Effect of the shape of the load-time function

Load-time function suggested by Sarrenheimo and Chung was applied to same

CSCM to verify the effect related to the shape of the load-time function on

displacement result and its result is shown in Fig 5.5. Two dominant factors that

affect the results are the peak value and the load duration time of the load-time

function. By comparing the load-time function which is given in Fig 4.9, it is

presumed that the peak value mainly affect the result of maximum displacement

and the loading duration time affect mainly the values for the residual displacement

and frequency after the impact occurred. The specific results are written in Table

5.2.

Figure 5.5 Displacement result depend on load-time function

38

Table 5.2 Displacement result for Sarrenheimo and Chung

Maximum displacement Residual displacement

VTT test 28.9mm 7.86mm

Sarrenheimo 25.5mm (11.8%) 8.19mm (4.20%)

Chung 28.6mm (1.04%) 10.8mm (37.4%)

( ) is the error value based on the criteria of VTT test

From this result load-time function suggested by Sarrenheimo gave closer

result to the VTT test for residual displacement significantly than Chung did.

However, in the view of maximum displacement, the simplified load-time function

suggested by Chung showed closer result to VTT test than that of Sarrenheimo. To

get better understanding of simulation result, VTT defined the total error term

based on the errors from the maximum displacement and residual displacement.

(Orbovic et al., 2014)

/ 100%i analysis test testu u u (5.1)

2 2

max / 2res (5.2)

uanalysis is the simulated result, utest is the test result, δmax is maximum

displacement error, δres is residual error, and δ is the total error. However, this

definition was not utilized in this paper.

39

5.4 Result from missile modeling impact

The displacement obtained by simulating the missile modeling and VTT test

result were compared in Fig. 5.6 and Table 5.3. Basically, both results shows

similar value for the maximum displacement. However, larger value for residual

displacement was obtained for projectile modeling compared to the VTT test.

Unlike load-time function, projectile contact may have given extra damage

accumulation to on RC wall elements which affects the value of residual

displacement, and it is presumed that to accurate the residual displacement result,

CSCM parameters related to damage needs to be modified.

Figure 5.6 Displacement result of missile modeling impact

40

Table 5.3 Displacement result for missile modeling

Maximum displacement Residual displacement

VTT test 28.9mm 7.86mm

Modeling 27.2mm (5.88%) 13.7mm (74.3%)

( ) is the error value based on the criteria of VTT test

The velocity of missile became zero at 0.0167sec and the deformed shape after

the impact is shown in Fig 5.7. As written in VTT report, deformed missile after

the impact has a length of 1,213mm which is about 60mm longer than the

experiment. The length of folded part is around 122mm - 145mm.

As shown in Fig 5.7, there are two distinguishable parts in deformed part of the

missile where the missile folded regularly while the impact happens, and the other

part where the distortion occurred irregularly. Both parts could be observed in the

picture of the actual test as shown in Fig 5.8 as well. (Orbovic et al., 2014)

Force applied to RC wall is shown in Fig 5.9. The contact was lasted for about

0.024 second and maximum displacement of the RC wall was observed at 0.015

second. The contact force showed significantly decrement when missile was

starting to distort irregularly.

The maximum displacement result for every loading cases which were

described so far is summarized in Fig 5.10. All cases were simulated with CSCM

concrete for RC wall. All cases show similar result to the VTT test, which partly

validate the simulation method.

41

Figure 5.7 Deformed shape of missile after impact

Figure 5.8 Deformed shape of missile after test

122~145mm

1213mm

42

Figure 5.9 Contact force-Time function on RC wall

Figure 5.10 Maximum displacements for each loading case

28.9

25.5

28.627.2

0

5

10

15

20

25

30

35

VTT test Sarrenheimo Chung Projectile

Maxim

um

dis

pla

cem

ent

(mm

)

43

5.5 Evaluation of VTT flexural test simulation

By using the results achieved through the previous stages, original CSCM and

Sarrenheimo load-time function was decided to be used for simulating the VTT

flexural test. For the displacement comparison, test result from different sensor was

considered to check the validation of the RC wall modeling.

5.5.1 Displacement

For the displacement comparison, the result from different sensor was

considered which was placed 250mm horizontally, 250mm vertically away from

the center of the RC wall. The place of sensor is displayed in Fig 5.10 and the

obtained result from the analysis was compared with the VTT result is shown in

Fig 5.11.

Figure 5.11 Place where displacement sensor set (sensor 2)

Overall, the obtained result from the analysis was found out to give relatively

similar result in the view of residual displacement to the experiment result than that

44

of the maximum displacement. By comparing results from the different point

instead of just the center of the RC wall, the validation of the modeling of RC wall

was accomplished. As a result, the analysis for expecting the displacement result

for flexural test was found out to be established quite similar.

Figure 5.12 Comparison of the displacement responses (sensor 2)

5.5.2 Strain on the rebar

The strain measurement was taken from 27.5mm below point from the center

on the rear layer of rebar and place where strain gauge was set is shown in Fig 5.12.

The obtained result showed similar frequency to the VTT measurement and show

relatively larger error for strain value which is shown in Fig 5.13. Simulation of

45

strain results are considered to be challenging than the displacement because there

are various factors that could affect the result of strain on the rebar like the

geometric problem, or the adjoining problem between the concrete and the rebar.

Martin (Martin et al., 2012) suggested the overestimated damage taken in the

analysis procedure leaded the result to be less deformable than it should be like the

experiment.

Figure 5.13 Place where strain sensor set

Figure 5.14 Strain result from strain gauge

46

5.6 Damage pattern

Time history response of the displacement is shown in Fig 5.14. This figure

display the moment when maximum displacement occurred during the simulation.

The steady incrementing of the deformation start from the frame supporting

boundary toward the center of the wall can be observed and because loading

function was given in uniform load, symmetrical pattern could be observed. The

unit for Fig 5.14 is millimeter.

Figure 5.15 Deflection and damage pattern of time-load function case

In other hand, Fig 5.15 shows the time history response of the displacement

induced by the projectile modeling. The damage induced by the hollow deformable

missile could be observed around the center of the RC slab. Also, the maximum

deformation occurred where projectile contacted exceeded. This indicates the

contact area should be considered in case of applying loading function to the wall,

47

Figure 5.16 Deflection and damage pattern of projectile modeling case

Figure 5.17 Eroded elements on rear side of wall

Fig 5.16 shows the eroded elements during the impact analysis which indicate

the place where cracks may have occurred during the test. This result matches with

the VTT report (Vepsa, 2010) referring the existence of small cracks on rear side of

the RC wall.

48

CHAPTER 6

CONCLUSION

In order to investigate the influence of the shear failure surface of the concrete

constitutive model and the loading methods for simulating bending behavior of

reinforced concrete (RC) wall impacted by the soft missile, simulation with

commercial explicit dynamic code was conducted.

Bending behavior analysis using parameters applied CSCM proposed by Jiang,

and the current CSCM were compared. Even though current CSCM may not be

able to analyze the behavior of the high strength concrete due to its quadrature

property for parameter generation, current CSCM model showed suitable results

for representing high strength concrete (fck=63.9MPa for VTT flexural test).

The effectiveness of the load-time function to the bending behavior of RC wall

was investigated. Mainly, peak value of the function and the load duration time

were considered to be the dominant factor for the analysis. The load-time function

with higher peak value showed higher maximum displacement, and the function

which has longer duration showed larger residual displacement.

As the deformable projectile impacts with the RC wall, the head of the

projectile distorted irregularly, after specific length of the regular folding was made.

This transition could be seen in the contact force-time graph, where the sudden

decrement of the contact force occurs. The folded length of the projectile was

around 122-145mm and total length of the projectile after the impact was 1,213mm.

49

The result derived from the impact simulation using CSCM and specific load-

time function was obtained from the center of the wall, and the upper right part of

the wall. Both cases showed similar result with the experiment result. However,

obtaining accurate result for strain on rebar was found out to be challenging.

For further research works, a more accurate methodology to simulate the strain

result needs to be studied by considering the mechanism between the concrete and

rebar. Also, punching behavior of the RC wall needs to be simulated to acquire

reasonable simulation bases for impact analysis because both bending and

punching behavior will be observed simultaneously for real case.

50

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[10] Murray, Y. D., & Lewis, B. A. (1995). Numerical Simulation of Damage in

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A., ... & Schwer, L. E. (2014). Improving Robustness Assessment Methodologies

for Structures Impacted by Missiles (IRIS-2012)-Final Report. Organisation for

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Committee on the Safety of Nuclear Installations-CSNI, Le Seine Saint-Germain,

12 boulevard des Iles, F-92130 Issy-les-Moulineaux (France).

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[19] Sandler, I., DiMaggio, F. L., & Barron, M. L. (1984). An extension of the cap

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structures, numerical and experimental studies.

[21] Sugano, T., et al. "Full-scale aircraft impact test for evaluation of impact

force." Nuclear Engineering and Design 140.3 (1993): 373-385.

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model.Nuclear engineering and design, 150(2), 215-223.

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Benchmark Part II: Lessons learned and Recommendations. Transactions of the

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under impact loading using the finite element approach. Engineering Failure

Analysis, 45, 252-277.

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reinforced concrete walls under impact loading (pp. 1-158). VTT.

53

APPENDIX A

The parameter input applied with proposed parameters are written here.

Basically, parameters for TXC, TOR,TXE and Cap hardening parameters were

changed based on Jiang’s paper (Jiang et al., 2015) and others remained as same as

original CSCM.

Stiffness:

Shear Shear Modulus.................................= 1.4740E+04

Bulk Bulk Modulus..................................= 1.6150E+04

TXC Surface:

alpha TXC surface constant term...............= 21.4581

theta TXC surface linear term....................= 0.31644

lambda TXC surface nonlinear term............= 13.448

beta TXC surface exponent......................= 0.01448

TOR Surface Scaling Factors:

alpha TOR surface constant term...............= 0.82

theta TOR surface linear term....................= 0

lambda TOR surface nonlinear term............= 0.2407

beta TOR surface exponent......................= 0.00636

TXE Surface Scaling Factors:

alpha TXE surface constant term...............= 0.76

theta TXE surface linear term....................= 0

lambda TXE surface nonlinear term............= 0.26

beta TXE surface exponent......................= 0.00553

Shear Surface Hardening Parameters:

NH Hardening initiation.......................= 1.0000E+00

CH Hardening rate................................= 0.0000E+00

Cap and Cap Hardening Parameters:

R Cap surface aspect ratio................ .= 1.97095

Xo Cap pressure axis intercept ............= 137.986

W Hardening law maximum compaction..= 0.065

D1 Hardening law linear exponent.......= 6.11E-04

D2 Hardening law nonlinear exponent.= 2.23E-06

Damage Parameters:

B Compressive softening parameter…= 1.0000E+02

Gfc Compressive fracture energy......... ...= 9.1540E+00

54

D Tensile/shear softening parameter....= 1.0000E-01

Gft Tensile fracture energy.......................= 9.1540E-02

Gfs Shear fracture energy.........................= 9.1540E-02

pwrc Compressive damage transition power...= 5.0000E+00

pwrt Tensile damage transition power........= 1.0000E+00

pmod Moderate pressure fit adjustment.....= 0.0000E+00

Rate Effects Parameters:

flpar1 Compressive fluidity parameter............= 4.3380E-04

power1 Compressive power............................= 7.8000E-01

flpar1 Tensile fluidity parameter.....................= 1.1090E-04

power2 Tensile power......................................= 4.8000E-01

overc Compressive overstress limit...............= 4.9830E+01

overt Tensile overstress limit.........................= 4.9830E+01

sratio Ratio of shear to tensile parameter.........= 1.0000E+00

repow Power applied to fracture energies…..= 1.0000E+00

Miscellaeous Output Parameters:

si1 Pressure apex of shear surface..............= -8.0749E+00

hkmin Minimum cap location .......................= 1.0000E-06

hkcr Critical cap location .............................= 1.0000E+20

solid formulation ................…………………..= 1

55

APPENDIX B

The effect of damping ratio of RC wall was invested and the effect of damping

ratio is shown in Fig B.1. Both maximum displacement, residual displacement and

frequency of the material are affected by the damping ratio. Further study is needed

to define appropriate damping ratio for impact RC wall.

Fig B.1 Effect of damping ratio on RC wall

56

APPENDIX C

Input parameters for the analysis are displayed. Parameters related to

geometrical values are not written

*CONTROL_TERMINATION

*DATABASE

*DATABASE_EXTENT_BINARY

*BOUNDARY_SPC_SET_BIRTH_DEATH

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE

*CONTACT_AUTOMATIC_SINGLE_SURFACE

*SECTION

*PART

57

*HOURGLASS

*CONSTRAINED_LAGRANGE_IN_SOLID

58

Abstract (In Korean)

해당 연구는 콘크리트 재료모델의 전단 파괴곡면과 하중시간이력함

수 및 충격체 모델링에 의한 하중기법이, 연성 충격체에 의해 발생하는

RC벽체의 휨 거동에 미치는 영향을 시뮬레이션을 통해 검토했다. VTT-

IRIS 프로젝트의 휨 실험을 목표 실험으로 지정한 후, 전단 파괴곡면과

하중시간이력함수의 형상을 고려해 explicit dynamic code인 LS-DYNA를

통해 해석을 수행했다.

충돌 해석 시, 통상적으로 많이 사용되는 CSCM에서 전단파괴곡면의

형태를 결정하는 매개 변수들을 검토하였다. 기존의 CSCM은 변수 생성

식의 특성 상, 고강도, 고압을 받는 구간에서는 부정확한 해석결과를 얻

게 되지만, 휨 실험과 같은 저압을 받는 상황의 경우, CSCM을 통해 해

석을 수행할 수 있음을 확인하였다.

Hughes-Liu 요소를 기반으로 연성 충격체를 모델링하였으며, 이를 통

해 얻은 충격체의 충돌 후 형상과 Contact force-time 결과에 대해 논의

하였다. 또, 하중시간이력함수 형태에 따른 영향을 다른 두 이력함수를

적용한 후, 변위 결과를 비교함으로써 검토하였다. 최대 변위의 경우, 이

력함수의 최대 값의 주로 영향을 받으며 잔류 변위의 경우, 주로 하중

적용시간의 영향을 상대적으로 많이 받음을 알 수 있었다.

CSCM과 하중시간이력함수 및 충격체 모델하중을 적용해 VTT 실험

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결과와 유사한 최대 변위 및 잔류 변위 결과를 얻을 수 있었다. 반면, 콘

크리트 내부에 설치된 보강철근의 변형률의 경우 더 정밀도 높은 해석이

필요함을 확인할 수 있었다.

Keywords: LS-DYNA 해석, VTT 휨 실험, 충돌실험, CSCM, 연성 충격체

Student Number: 2013-23147

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Acknowledgement 22nd JUL 2015

For writing this paper, there were so many people who I would like to give

gratitude. First of all, I would like to give great gratitude to my Professor

advisor Kim Hokyung who gave me the opportunity to study impact

analysis and encourage my research works for a long time. I would like to

express thanks to Professor Cho Jaeyeol, Lee Haesung, Kho Hyunmoo, Kim

Jaekwan, and Song Junho for giving guides for writing this paper.

Kim Sunjoong, the superior member of my laboratory helped me so much

while proceeding this research. I would like to personally thank him as well.

The technical advice that was needed for handling LS-DYNA, was given

by Professor Lee Jungwhee and Chung Chulhun who I would like to show

great thankfulness to them.

Also I would like to wish a good luck to all the members of my Structure

Design Laboratory; Park Jin, Lee Ho, Kim Kwontaek, Hwang Youchan,

Park Junyong, Yoo Chulhwan, Kim Sangwon, Kim Younggon, Kim Sejin,

Han Seongwook, Bang Minkyu and Ouahidi Ayoub who encouraged me

writing this paper.

Finally, I deeply want to show my love and respect to my father and

mother who gave me both technical and ethical advice for this research.