structural analysis9

Engineering Failure Analysis 45 (2014) 252–277

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Engineering Failure Analysis

journal homepage: www.elsevier .com/locate /engfai lanal

Failure analysis of reinforced concrete walls under impactloading using the finite element approach

http://dx.doi.org/10.1016/j.engfailanal.2014.06.0061350-6307/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +82 2 3408 3291; fax: +82 2 3408 3332.E-mail address: [email protected] (S.-E. Kim).

Duc-Kien Thai, Seung-Eock Kim ⇑Department of Civil and Environmental Engineering, Sejong University, 98 Kunja-dong, Kwangjin-ku, Seoul 143-747, South Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 December 2013Received in revised form 31 May 2014Accepted 25 June 2014Available online 15 July 2014

Keywords:Missile impactReinforced concrete wallLS-DYNADynamic analysisPunching behavior

In this paper, the punching resistance of a reinforced concrete (RC) wall under missileimpact loading is evaluated using the finite element approach. The model is analyzed usingLS-DYNA, a commercially available software program. The structural components of the RCwall, missile, and their contacts are fully modeled. Included in the analysis is materialnonlinearity, which considers damage and failure. Damping effect is also taken intoaccount. The analysis results are then verified with the test results. Parametric studies witha varying number of layers of longitudinal rebar and shear bar spacing are carried out toinvestigate the punching behavior of RC walls under missile impact. The distance travelled,scabbing area, and failure mode of various RC walls are examined, and efficient designs arerecommended thereafter.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Reinforced concrete walls have been widely used in nuclear-related structures in order to protect the main interior facil-ity of the building. Several researches have been conducted to study the punching resistance of RC walls subjected to impactloading. The local damage to concrete walls has been primarily evaluated by missile impact tests. Kojima [1] performed aseries of small-scale missile impact tests on RC slabs to investigate its local behavior. Sugano et al. [2,3] conducted a seriesof impact tests on small-, intermediate-, and full-scale aircraft engine models to RC panels in order to determine the localdamage. A series of studies on RC walls with the dimensions of 2.1 m ⁄ 2.1 m ⁄ 0.25 m, with and without shear bars have alsobeen carried out by Vepsa et al. [4], Orbovic and Blahoianu [5], and Saarenheimo et al. [6] to investigate the punching resis-tance of walls under missile impact.

The experimental approach can provide reliable results of wall behavior, but it is quite expensive and time consuming.Considering the economic and time constraints, a good alternative is the use of finite element analysis. A number of numer-ical studies have already been carried out by Oliveira et al. [7], Pires et al. [8], Borgerhoff et al. [9], and Sagals et al. [10]. Theobjective of their numerical simulations was to capture the response and behavior of RC walls subjected to high-rate impactloading. Finite element analysis was an appropriate and efficient solution for large actual size structures that cannot beaccommodated through experiments.

In the aforementioned studies, both the given experimental and numerical studies focused on RC walls with two layers oflongitudinal rebar, with or without shear bar. These researches had longitudinal rebar ratios in the range of 0.4–0.7%, and theshear bar ratios were in the range of 0.62–1.4%. In this study, the number of layers of longitudinal rebars also varied. The

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D.-K. Thai, S.-E. Kim / Engineering Failure Analysis 45 (2014) 252–277 253

analysis of longitudinal rebars with two, three, and four layers, having ratios of 0.2% and 4.0%, were implemented to inves-tigate the influence of longitudinal rebar arrangement to the punching resistance of RC walls. In addition, parametric studieswere conducted with different shear bar spacings of 100 mm, 200 mm, and 300 mm, having ratios of 0.44% and 1.5%, toinvestigate the influence of shear bar spacing to the punching resistance of the RC walls. Six loading cases were consideredin assessing the behavior of RC walls. Parametric studies with different combinations of reinforcements were then carriedout to find out the optimal design of RC walls under impact loading.

2. Design of the RC wall and missile

2.1. Geometry

Two categories of RC wall, adopted and modified from specimens tested by Vepsa et al. [4] and Orbovic et al. [5], wereused in this study. In order to investigate the punching response of the RC wall under impact loading, a full-scale RC wallwith clamping system was designed as shown in Fig. 1a and b. The total length of the two-way wall was 7.0 m ⁄ 7.0 m,the long span 6.6 m, and the thickness 0.8 m. 55 rebars of 30 mm diameter with shear bars of 30 mm diameter were placedat the support area of the wall in order to avoid local damage of the edges as shown in Fig. 1c. Steel plates of 30 mm thicknessencased the edges of the wall. This wall system was clamped into a steel frame having steel rollers of 150 mm diameter as itssupport system. Subsequently, the steel frame was installed to a massive wall.

A schematic representation of the missile is shown in Fig. 2. The missile consisted of a 30 mm thick steel pipe with560 mm outside diameter. The missile was filled with lightweight concrete such that it had sufficient mass and rigidity.The total length of the missile was 2100 mm.

In this study, the behavior of two categories of RC walls was observed as adopted and modified from the specimens testedby Vepsa et al. [4] and Orbovic et al. [5]. The first category of the RC wall, RCW-LR, was designed by using a different number

6600 2002007000

6600

200

200

7000

X

X

YY270 300

Steel roler

Stirrup

Position ofimpact

A-A

6600 2002007000

800

Supported

A A(b) Cross section

(c) Support area(a) RC Wall

Fig. 1. Reinforced concrete wall and support detail.

Fig. 2. Detail of the missile.

270

150300270 9@300=2700 270

800

7070

660

800

7070

660

300270

6600 2002007000

7070

150 270300270

6600 2002007000

150

6600 2002007000

800

300

660

9@300=2700 300

9@300=2700 300

(a) RCW-LR-A: Two layers

(b) RCW-LR-B: Three layers

(c) RCW-LR-C: Four layers

Fig. 3. First RC wall series (RCW-LR).

254 D.-K. Thai, S.-E. Kim / Engineering Failure Analysis 45 (2014) 252–277

of longitudinal rebar layers as shown in Fig. 3. The RCW-LR-A wall, as shown in Fig. 3a, had two layers of longitudinal rebars.Fig. 3b shows the RCW-LR-B wall with three layers of longitudinal rebars. For the RCW-LR-C wall, as shown in Fig. 3c, fourlayers of longitudinal rebars were used. The layers of longitudinal rebars were equally spaced for all RCW-LR walls. Allthe three models in this RC wall category had 300 mm longitudinal rebar spacing, 70 mm concrete cover, and had no shearbars.

The second RC wall category, RCW-SR, is shown in Fig. 4. Shear bar spacings of 300 mm, 200 mm, and 100 mm were usedfor RCW-SR-A (Fig. 4a), RCW-SR-B (Fig. 4b), and RCW-SR-C (Fig. 4c), respectively. The RC walls had two layers of 30 mmdiameter longitudinal rebars of 300 mm spacing in each direction.

2.2. Material properties

Table 1 lists the material properties of the concrete, rebar and other steel parts. The unconfined compressive strength ofthe concrete wall was 60.0 MPa. The yield strength of the steel rebar was 540 MPa. The yield strength of steel cover plate,frame, and roller was 550 MPa. The failure strain of the steel rebar was 20.0%. The yield strength of the steel missile modelwas 758 MPa. The compressive strength of the missile model’s concrete filler (lightweight concrete) was 3 MPa.

3. Finite element modeling

3.1. General

The finite element code, LS-DYNA (version 971s R5.1.1) [11], was used for analysis. The full model in Fig. 5a was gener-ated using a quarter model for ease of understanding. As shown in Fig. 5b, a quarter of the wall and missile was modeled dueto symmetry of geometry and impact loading. The concrete wall, longitudinal rebars, shear bars, cover plates, rollers, and

50 30027028@100=2800

800

7070

150 270300270

660

800

7070

300270

660

800

7070

300270

660

3009@300=2700

6600 2002007000

100 30027013@200=2600150

6600 2002007000

6600 2002007000

(a) RCW-SR-A: Spacing of 300mm

(b) RCW-SR-B: Spacing of 200mm

(c) RCW-SR-C: Spacing of 100mm

Fig. 4. Second RC wall series (RCW-SR).

Table 1Material properties.

Material Modulus ofelastic E (GPa)

Poissonratio m

Densityq (kg/m3)

UCS(MPa)

UTS(MPa)

Failurestrain (%)

Aggregatesize (m)

Concrete 25 0.17 2400 60 3.22 – 0.008Lightweight concrete 10.9 0.17 804 3 1 – –Rebar steel 200 0.3 7800 540 540 20 –Missile steel 205 0.3 7850 758 758 20 –Cover plate and roller steel 200 0.3 7800 550 550 20 –


missile were modeled separately and assembled to subsequently develop the full model. The appropriate constraints andcontacts were applied between all contact surfaces.

3.2. Element type and mesh

Fig. 6 shows the FE modeling of the RC wall, missile, and frame. The concrete wall in Fig. 6a was modeled with the solidelement. The Hughes–Liu beam element (type 1) was used to model the longitudinal and shear bars as shown in Fig. 6b.Fig. 6c shows the FE modeling of cover plates using the Belytschko–Tsay shell element. The solid element was used to modelthe rollers. The missile head and concrete filler were modeled using the solid element, whereas the missile cover plate wasmodeled using the shell element as shown in Fig. 6d.

The bond between the missile head, concrete filler, and missile cover plate was considered by using shared nodes. Thegeneral mesh size was about 30 mm. The total number of elements of the components of the quarter model for the RCW-LR-A wall type is shown in Table 2.

(a) 3D view of full model.

(b) 3D view of quarter model

MissileRoller

Cover plate

RC wall

Front face

Back face

Missile

Roller

Cover plate

RC wall

Fig. 5. Finite element model of RC slab with frame and missile.


3.3. Material model

3.3.1. ConcreteThe Winfrith material model (MAT#084) considering the strain-rate in LS-DYNA [12] was used for the wall and light-

weight concrete material. Fig. 7 shows the bi-linear concrete model using an equivalent uniaxial stress–strain curve. Theelastic–plastic curve with ultimate strain (ecu) at the failure was assumed for the concrete compressive model. The assumedconcrete tension model was the linear tension softening behavior with axial strain (eck1) at the failure. The tensile fracturestrain (eo) was determined as a function of the fracture energy of the concrete.

The Winfrith concrete model does not consider the erosion effect. The erosion option for damage and failure was consid-ered by using the option �MAT_ADD_EROSION. This option has a total of 14 different erosion criteria. According to sensitivitystudies conducted by Sagals et al. [10], the principal strain was shown to be the most sensitive erosion criterion. The erosioncriteria of ±7.5% were used in this study.

The strain-rate effect was automatically considered in the Winfrith concrete model. Fig. 8 shows the stress–strain curveswith respect to various strain-rates. The concrete strengths were calculated by multiplying the original values with thestrain-rate enhancement factors. The tensile (ET) and compressive (EC) factors were calculated using the following equations [12].

� With low strain-rate, when _e < 30 s�1:

ET ¼_e

_e0T

� �1:016d

and EC ¼_e

_e0C

� �1:026a

; ð1Þ

� With high strain-rate, when _e > 30 s�1:

ET ¼ g _e1=3 and EC ¼ c _e1=3; ð2Þ

where d ¼ 110þ0:5f cu

; a ¼ 15þ0:75f cu

; log10g ¼ 6:933d� 0:492; log10c ¼ 6:156a� 0:49; _e0T ¼ 30� 10�6 s�1 ; and _e0C ¼ 3� 10�6 s�1.

Here, fcu is the concrete cube strength (unit in MPa).The Young’s modulus rate enhancement was calculated using the following equation:

EE ¼ 0:5_e

_e0T

� �0:016

þ_e

_e0C

� �0:026" #

: ð3Þ

(a) Concrete wall

(b) Reinforcement

Concrete wallMissile

Supportreinforcement

Longitudinal rebar

Shear bars

(c) Cover plate and rollers (d) Missile

Roller

Cover plate

Concrete filler

Missile cover

Missile head

Fig. 6. Finite element type and mesh.

Table 2Total element numbers of a quarter modal for RCW-LR-A type.

Components Beam elements Shell elements Solid elements

Wall – – 330,750Rebar 1896 – –Missile – 381 1673Cover-plate – 11,052 –Roller – – 7840

Total 1896 11,433 340,263


3.3.2. Rebar, structural steelFig. 9 shows the elastic plastic with the kinematic hardening material model (MAT#003) in LS-DYNA which was used to

model the behavior of the rebar and structural steel [13]. In this study, kinematic hardening was considered by setting theparameter b = 0.

The yield strength of rebar and structural steel was highly strain-rate dependent. The yield strength increased when thestrain-rate increased. This dynamic yield strength of steel was taken into consideration by the Cowper–Symonds formula foruniaxial tension or compression [14]:

Fig. 7. Bi-linear concrete model.

Fig. 8. Stress–strain curve of concrete with various strain-rates.

Fig. 9. Elastic–plastic behaviors with kinematic/isotropic hardening.


rd

rs¼ 1þ

_eC

� �1P

; ð4Þ

where rd is the dynamic yield strength, rs is the static yield strength, _e is the strain-rate, and C and P are the constants of theCowper-Symonds relation. For the rebar and structural steel, the constants C = 40.4 s�1 and P = 5 proposed by Jones [15] wereused. Fig. 10 shows the stress–strain curves with respect to the various strain-rates of the steel with a yield strength of540 MPa.

Fig. 10. Stress–strain curve of steel with various strain-rates.

(a) RC wall and cover plates

(b) Cover plates and rollers

Concrete slavesurface

Steel plate master surface

Roller master surface

Steel plate slave surfaces

Fig. 11. Contact between components.


3.4. Damping

Damping effect was considered in this study. The damping matrix [C] is calculated using the following function [16]:

½C� ¼ a½M� þ b½K�; ð5Þ

where [C] is the damping matrix; [M] is the mass matrix; and, [K] is the stiffness matrix of the physical system; a and b areRayleigh damping constants.

The equation for the Rayleigh damping is

n ¼ a2xiþ bxi

2; ð6Þ

where xi is the natural circular frequency of ith mode, n is the damping ratio, and a and b are constant parameters.

(a) At ref. nodes of the rollers (b) At ref. nodes of mid-span section

Reference nodes of the rollers

Fig. 12. Boundary condition.


The constants a and b can be calculated as follows:

ab

� �¼

12x1

x12

12x2

x22

" #�1n

n

� �: ð7Þ

The reference frequencies x1 and x2 are chosen based on the frequency range of the structures, which can be definedusing eigenvalue analysis in LS-DYNA.

In this study, the option �DAMP_FREQUENCE_RANGE was used to consider the effect of damping. A frequency range ofx1 = 1000 rad/s to x2 = 10,000 rad/s was used, and a damping ratio of 0.01 (refer to [9]) was defined as the input data.

3.5. Contact and boundary condition

The component models were assembled with appropriate constraints and contacts. The longitudinal rebars, shear barsand supported rebars were embedded in the concrete using the option �CONSTRAINED_LARGRANGE_IN_SOLID. The option�AUTOMATIC_ SURFACE_TO_SURFACE was used to create contact between the edges of the RC wall and the cover plates asshown in Fig. 11a. The contact between the cover plates and the rollers is shown in Fig. 11b. The fixed supported boundaryconditions were applied to the reference node of the rollers as shown in Fig. 12a, and symmetric boundary conditions wereapplied at the reference nodes of the mid-span sections of the model in Fig. 12b. The perfect bonds between missile coverplate, missile head, and missile filler were considered by sharing their nodes.

(a) Missile-concrete wall contact (b) Missile-rebar contact

Concrete wall master surface

Rebar slavenodes

Missile slavesurface

Missile master surface

Fig. 13. Contacts between the missile and RC wall.


In order to reduce both analysis time and numerical errors, the segments and nodes for the segment set and node set,respectively, should be selected within the domain where the contact may occur, as shown in Fig. 13. The option �AUTO-MATIC_SURFACE_ TO_SURFACE was used for the missile-wall contact, whereas �AUTOMATIC_NODES_ TO_SURFACE wasused for the missile-rebar contact. For the missile-concrete wall contact, the segment set of the missile was defined asthe slave part, whereas the segment set of concrete wall was defined as the master part, as shown in Fig. 13a. For the mis-sile-rebar contact, the node set of the rebar was defined as the slave, while the segment set of the missile was defined as themaster, as shown in Fig. 13b.

3.6. Loading cases and analysis method

The dynamic explicit analysis method in LS-DYNA was adopted in this study. Three different initial velocities of 70 m/s,110 m/s, and 200 m/s were applied to the missile nodal set using the option �INITIAL_VELOCITY. Three other loading caseswith different missile masses of 1000 kg, 1500 kg, and 2000 kg were applied by increasing the density of the missile’s mate-rial. In order to reduce the analysis time, the initial location of the missile head was set directly on the face of the slab. Theanalysis time of 50 ms was allotted in order to observe complete missile perforation. The time interval between outputs of

(b) Support system (c) Missile

(a) RC slab

Fig. 14. Details of the RC slab specimen and missile (Ref. [4,19]).

Table 3Dimensions of the tested specimen and the missile in the experiment of Vepsa et al. [4].

Item Unit Amount

Total length of RC wall m 2.1Length between supports m 2.0Thickness of RC wall m 0.25Cover-plate thickness mm 10Roller diameter mm 35Number of rebar – 96Rebar diameter mm 10Missile diameter mm 168Missile length mm 64Total weight of the missile kg 47


1E�4 s was applied for obtaining a continuous behavior. Hourglass control with the stiffness form of Flanagan-Belytschkointegration (IHQ = 4) was selected. In LS-DYNA, the contact between slave and master parts was taken into account usingcoupling interaction analysis.

The Winfrith concrete model is capable of calculating crack width of a concrete element, which in our study was calcu-lated using the option �DATABASE_BINARY_D3CRACK. In this analysis, fracture energy (FE) of 95 N/m was used as the perdesign code recommendation [17], which corresponds to an assumed aggregate size equal to 8 mm.

4. Verification of FE model

A recent experiment conducted by Vepsa et al. [4] was used to verify the proposed FE model. The RC wall specimen andthe support system are shown in Fig. 14a and b respectively, while the missile detail is shown in Fig. 14c. Table 3 presents thedimensions of the specimen. Fig. 15 shows the experiment specimen clamped by the test frame. The initial velocity of themissile was 136 m/s. The material properties tested by Vepsa et al. [4] were used.

Table 4 shows a comparison between the residual velocity, scabbing area, and failure mode obtained from the test andfinite element analysis. The residual velocity was taken at 15 ms after the beginning of impact. The scabbing area wasobtained using the erosion option with failure strain criteria of ±7.5%. Good agreement has been achieved between theexperimental and numerical results. The specimen was perforated in both the test and FE modeling. The scabbing areaagreed well in both the experiment and numerical analysis, as shown in Fig. 16. Fig. 17 compares the missile velocity

Fig. 15. Experimental specimen (Ref. [19]).

Table 4Comparison of the analysis results with that of the test by Vepsa et al. [4].

Method Initial velocity (m/s) Failure mode Residual velocity (m/s) Scabbing Area (m2)

Test 136 Perforation 45 1.00FEM 136 Perforation 45.7 1.06Difference 0 – 1.6% 6.0%


(m/s) after impact obtained from the analysis and test results provided by Vepsa et al. [4] and Calonius et al. [18]. The curveclosely matched the results of test P2. These results showed that the developed finite element model reliably predicted thefailure mode and damage of the RC wall under impact loading.

5. Parametric analysis

A parametric study was carried out to investigate the punching response of RCW-LR and RCW-SR. Table 5 lists the mostinfluential variables as the analysis parameters.

Fig. 16. Scabbing area.

Test P1

Test P2

Test P3

Time (ms)

0

20

40

60

80

100

120

140

0 5 10 15 20

This study

Fig. 17. Missile velocities during the first 20 ms after impact.


The observed damage of the RC wall was classified into five modes:

– Full Perforation (FP) mode: The missile passed through the slab completely.– Partial Perforation (PP) mode: The missile stopped at the back layer of the longitudinal rebar.– Full Scabbing (FS) mode: The missile stuck onto the slab and the shear cone failure occurred at the back of the slab.– Partial Scabbing (PS) mode: The missile stuck onto the slab and shear cone cracks formed at the back of the slab, but scab-

bing mode was prevented.– Penetration (P) mode: A crater formed at the front face of the slab, but shear cone cracked except that only a few small

cracks did not form at the back face of the slab.

5.1. RC wall under angular impact

The behavior of the RCW-SR-A wall type having longitudinal rebar ratio of 2.0% and shear bar ratio of 0.35% wasinvestigated considering different angular impact. Fig. 18 compares the failure modes of oblique impacts with that of the

Table 5Selected parameters.

Wall series Variable Range of variable

Normal wall Missile angle (degree) 0, 30, and 60RCW-LR Number of LR layers 2, 3, and 4

LR ratio (%) 0.2–4.0Missile velocity (m/s) 70, 110, and 200Missile mass (kg) 1000, 1500, and 2000

RCW-SR SR spacing (mm) 100, 200, and 300SR ratio (%) 0.44–1.5Missile velocity (m/s) 70, 110, and 200Missile mass (kg) 1000, 1500, and 2000

Fig. 18. Failure modes of RCW-LR walls with different angular impacts.

Table 6Parametric analysis results of RCW-LR walls with different missile velocity.

Missile velocity (m/s) Specimen name Ratio (%) Distance travelled (m) Scabbing area (m2) Failure modea

70 RCW-LR-A-1 0.20 0.91 13.85 PPRCW-LR-A-2 4.00 0.25 0.00 PRCW-LR-B-1 0.20 0.83 9.07 PPRCW-LR-B-2 4.00 0.32 0.00 PRCW-LR-C-1 0.20 0.91 8.72 PPRCW-LR-C-2 4.00 0.18 0.00 P

110 RCW-LR-A-1 0.20 2.63 12.56 FPRCW-LR-A-2 4.00 0.45 0.00 PSRCW-LR-B-1 0.20 2.66 10.17 FPRCW-LR-B-2 4.00 0.51 0.00 PSRCW-LR-C-1 0.20 2.58 8.72 FPRCW-LR-C-2 4.00 0.50 0.00 PS

200 RCW-LR-A-1 0.20 6.13 9.43 FPRCW-LR-A-2 4.00 1.30 25.80 PPRCW-LR-B-1 0.20 6.06 7.71 FPRCW-LR-B-2 4.00 1.30 25.21 PPRCW-LR-C-1 0.20 6.56 7.07 FPRCW-LR-C-2 4.00 1.28 24.62 PP

a P = Penetration Mode, PS = Partial Scabbing Mode, FS = Full Scabbing Mode, PP = Partial Perforation mode, FP = Full Perforation mode.


perpendicular impact. It can be observed that the local damage of the RC wall decreased as the missile angle increased. TheRC wall under the perpendicular impact had the most significant damage among them.

Although the conditional probability of the perpendicular impact of the missile to the walls is small, it is the most unfa-vorable scenario regarding the punching resistance of the structures. Therefore, perpendicular impact is used to assess thevulnerability of the RC structures.

5.2. RCW-LR wall

The behavior of RCW-LR-A, RCW-LR-B, and RCW-LR-C were investigated considering two rebar ratio of 0.2% and 4.0%. Themissile velocity and its mass were treated as parameters in order to evaluate the vulnerability of the different walls. Theinput parameters and corresponding analysis results are shown in Tables 6 and 7. The term ‘‘distance travelled’’ used in thisstudy means the distance travelled by the missile head from 0 ms to 50 ms.

5.2.1. Different impact velocitiesDifferent missile velocities of 70 m/s, 110 m/s, and 200 m/s were used to evaluate the punching behavior of RCW-LR

walls. Fig. 19 shows the failure modes of the three different wall types at the time of 50 ms.

5.2.1.1. Failure mechanism. The analysis result showed that, in the case where missile velocity was 70 m/s, partial perforationmodes occurred on all RCW-LR wall types when rebar ratio was 0.2%, whereas penetration modes occurred when rebar ratiowas 4.0% as shown in Fig. 19a. In the case of the missile velocity of 110 m/s as shown in Fig. 19b, full perforation modesoccurred when rebar ratio was 0.2%, whereas partial scabbing modes occurred when rebar ratio was 4.0%. In the case ofthe missile velocity of 200 m/s, full perforation modes occurred when rebar ratio was 0.2%, whereas partial perforationmodes occurred when rebar ratio was 4.0% as shown in Fig. 19c.

5.2.1.2. Distance travelled. The left side of Fig. 20 shows the distance travelled corresponding to the different longitudinalrebar ratios. The analysis result showed that the distance travelled rapidly decreased as the longitudinal rebar ratioincreased. When the longitudinal rebar ratio increased from 0.2% to 4.0%, the distance travelled of the missile decreasedby about 66.7%, 85.2%, and 81.5% corresponding to the missile velocity of 70 m/s, 110 m/s, and 200 m/s. It is concluded thatthe longitudinal rebar ratio plays an important role in resisting perforation of the RC wall.

However, the analysis result showed that the distance travelled corresponding to the three different wall types did notshow any major difference. It can be concluded that the number of layers of the longitudinal rebar does not show any sig-nificant effect in resisting perforation of the RC wall.

5.2.1.3. Scabbing area. The right side of Fig. 20 compares the scabbing area on the back face of the three different walls withtwo longitudinal rebar ratios at the time of 50 ms. The analysis result showed that in the case of the velocities of 70 m/s and110 m/s, the failure mode changed from perforation to penetration and the scabbing area rapidly decreased as the longitu-dinal rebar ratio increased, whereas in the case of the velocity of 200 m/s, the full perforation mode occurred in all cases. Thescabbing area increased as the longitudinal rebar ratio increased from 0.2% to 4.0%.

Table 7Parametric analysis results of RCW-LR walls with different missile mass.

Missile mass (kg) Specimen name Ratio (%) Distance travelled (m) Scabbing area (m2) Failure modea

1000 RCW-LR-A-1 0.20 1.46 12.98 FPRCW-LR-A-2 4.00 0.32 0.00 PRCW-LR-B-1 0.20 1.56 10.17 FPRCW-LR-B-2 4.00 0.39 0.00 PRCW-LR-C-1 0.20 1.56 9.07 FPRCW-LR-C-2 4.00 0.38 0.00 P

1500 RCW-LR-A-1 0.20 2.63 12.56 FPRCW-LR-A-2 4.00 0.45 0.00 PSRCW-LR-B-1 0.20 2.66 10.17 FPRCW-LR-B-2 4.00 0.51 0.00 PSRCW-LR-C-1 0.20 2.58 8.72 FPRCW-LR-C-2 4.00 0.50 0.00 PS

2000 RCW-LR-A-1 0.20 2.73 7.71 FPRCW-LR-A-2 4.00 1.01 25.21 PPRCW-LR-B-1 0.20 3.19 10.94 FPRCW-LR-B-2 4.00 0.80 21.77 PPRCW-LR-C-1 0.20 3.36 9.43 FPRCW-LR-C-2 4.00 0.84 18.59 PP

a P = Penetration Mode, PS = Partial Scabbing Mode, FS = Full Scabbing Mode, PP = Partial Perforation Mode, FP = Full Perforation Mode.

Wall type RCW-LR-A RCW-LR-B RCW-LR-CLR ratio

0.2%

4.0%

(a) Impact velocity V0 = 70 m/s


0.2%

4.0%

(b) Impact velocity V0 = 110 m/s


0.2%

4.0%

(c) Impact velocity V0 = 200 m/s

Fig. 19. Failure modes of RCW-LR walls with different missile velocity.


The analysis result also showed that the number of rebar layers had a significant effect on reducing the scabbing area ofthe RC wall. The deformation of the rebar caused the scabbing area increment due to the bond between them. When therebar was installed near the face of the wall, the deformation of rebar caused the concrete cover to be separated easily. Thiswas the main reason for the scabbing area increment. When the rebar was arranged near the wall’s center, the concrete coverwas not easily separated. As a result, the scabbing area decreased significantly. It is therefore concluded that, at a certainrebar ratio, rebar arrangement having more than two layers better withstands the impact load and reduces the scabbingarea. The RC wall with four layers of rebar had the smallest scabbing area among three.

5.2.2. Different missile massesDifferent missile masses of 1000 kg, 1500 kg, and 2000 kg were used to evaluate the punching behavior of RCW-LR walls.

Fig. 21 shows the failure modes of the three different wall types at the time of 50 ms.

Fig. 20. Distance travelled and scabbing areas with respect to LR ratio.


5.2.2.1. Failure mechanism. Analysis result showed that, in the case of the missile mass of 1000 kg, full perforation modesoccurred on all RCW-LR wall types when rebar ratio was 0.2%, whereas penetration modes occurred when rebar ratio was4.0% as shown in Fig. 21a. In the case of the missile mass of 1500 kg as shown in Fig. 21b, full perforation modes occurredwhen rebar ratio was 0.2%, whereas partial scabbing modes occurred when rebar ratio was 4.0%. In the case of the missilemass of 2000 kg, full perforation modes occurred when rebar ratio was 0.2%. When rebar ratio was 4.0%, partial perforationmodes occurred, and significant scabbing and cracking occurred on the both faces of the wall as shown in Fig. 21c.

5.2.2.2. Distance travelled. The left side of Fig. 22 shows the distance travelled corresponding to the different longitudinalrebar ratios. The analysis result showed that the distance travelled rapidly decreased as the longitudinal rebar ratioincreased. When the longitudinal rebar ratio increased from 0.2% to 4.0%, the distance travelled of the missile decreased


0.2%

4.0%

(a) Missile mass M = 1,000 kg


0.2%

4.0%

(b) Missile mass M = 1,500 kg


0.2%

4.0%

(c) Missile mass M = 2,000 kg

Fig. 21. Failure modes of RCW-LR walls with different missile mass.


by about 72%, 85.2%, and 75.8% corresponding to the missile masses of 1000 kg, 1500 kg, and 2000 kg. However, the numberof longitudinal rebar layers did not show any significant effect on the distance travelled of the missile.

5.2.2.3. Scabbing area. The right side of Fig. 22 compares the scabbing area on the back face of the three different walls withtwo longitudinal rebar ratios at the time of 50 ms. The analysis result showed that in the case of the masses of 1000 kg and1500 kg, the failure mode changed from perforation to penetration and the scabbing area rapidly decreased as the longitu-dinal rebar ratio increased. Whereas in the case of the missile mass of 2000 kg, the perforation mode occurred in all cases,and the scabbing area increased as the longitudinal rebar ratio increased from 0.2% to 4.0%.

The analysis result also showed that the number of rebar layers had a significant effect on reducing the scabbing area ofthe RC wall. The RC wall with four layers of longitudinal rebar had the smallest scabbing area among them.

Fig. 22. Distance travelled and scabbing areas with respect to LR ratio.


5.3. RCW-SR wall

The behavior of RCW-SR-A, RCW-SR-B, and RCW-SR-C was investigated considering two rebar ratios of 0.44% and 1.5%.The missile velocity and its mass were also treated as parameters in order to evaluate the vulnerability of the different walls.The input parameters and corresponding analysis results are shown in Tables 8 and 9.

5.3.1. Different impact velocitiesDifferent missile velocities of 70 m/s, 110 m/s, and 200 m/s were used to evaluate the punching behavior of the RCW-SR


Table 8Parametric analysis results of RCW-SR walls with different missile velocity.

Missile velocity (m/s) Specimen name Ratio (%) Distance travelled (m) Scabbing area (m2) Failure modea

70 RCW-SR-A-1 0.44 0.91 2.74 PPRCW-SR-A-2 1.50 0.73 1.66 FSRCW-SR-B-1 0.44 0.94 6.45 PPRCW-SR-B-2 1.50 0.93 5.31 PPRCW-SR-C-1 0.44 0.38 0.00 PRCW-SR-C-2 1.50 0.32 0.00 P

110 RCW-SR-A-1 0.44 2.34 4.03 FPRCW-SR-A-2 1.50 2.53 2.01 FPRCW-SR-B-1 0.44 2.33 8.38 FPRCW-SR-B-2 1.50 2.47 8.04 FPRCW-SR-C-1 0.44 1.99 4.78 FPRCW-SR-C-2 1.50 1.49 2.93 FP



Table 9Parametric analysis results of RCW-SR walls with different missile mass.

Missile mass (kg) Specimen name Ratio (%) Distance travelled (m) Scabbing area (m2) Failure modea

1000 RCW-SR-A-1 0.44 1.02 5.31 PPRCW-SR-A-2 1.50 1.02 4.27 PPRCW-SR-B-1 0.44 1.13 11.74 PPRCW-SR-B-2 1.50 1.17 10.94 PPRCW-SR-C-1 0.44 0.84 2.01 PPRCW-SR-C-2 1.50 0.50 1.14 FS





5.3.1.1. Failure mechanism. The analysis result showed that, in the case of the missile velocity of 70 m/s as shown in Fig. 23a,when the rebar ratio was 0.2%, the partial perforation modes occurred on the RCW-SR-A and RCW-SR-B walls, whereas thepenetration mode occurred on the RCW-SR-C wall. When the rebar ratio was 4.0%, the full scabbing modes, partial perfora-tion mode, and penetration occurred on RCW-SR-A, RCW-SR-B, and RCW-SR-C, respectively. In the case of the missile veloc-ity of 110 m/s and 200 m/s, full perforation modes occurred on all walls as shown in Fig. 23b and c, respectively.

5.3.1.2. Distance travelled. The left side of Fig. 24 shows the distance travelled corresponding to the different shear bar ratios.In some cases, the distance travelled increased as the shear bar ratio increased, whereas in other cases, the distance travelleddecreased as the shear bar ratio increased. It is observed that increasing shear bar ratio did not show any major effect onreducing the distance travelled of the missile.

However, the analysis result showed that the shear bar spacing had a significant effect on the distance travelled of themissile. The RCW-SR-C wall had the lowest distance travelled among them.

5.3.1.3. Scabbing area. The right side of Fig. 24 compares the scabbing area on the back face of the three different walls withtwo shear bar ratios at the time of 50 ms. The analysis result showed that the scabbing area slightly decreased as the shearbar ratio increased, except RCW-SR-B in the case of missile velocity of 200 m/s. Therefore, increasing shear bar ratio did notshow any major effect on reducing the scabbing area.

Fig. 23. Failure modes of RCW-SR walls with different missile velocity.


However, the shear bar spacing had a significant effect on reducing the scabbing area of the RC wall. In the case of velocityof 70 m/s, RCW-SR-C showed a good ability in preventing scabbing area, whereas in the cases of velocities 110 m/s and200 m/s, RCW-SR-A had the smallest scabbing area.

5.3.2. Different missile massesDifferent missile masses of 1000 kg, 1500 kg, and 2000 kg were used to evaluate the punching behavior of the RCW-SR


5.3.2.1. Failure mechanism. In the case of the missile mass of 1000 kg as shown in Fig. 25a, partial perforation modes occurredon all RCW-SR walls when shear bar ratio was 0.44%. When the rebar ratio was 1.5%, the partial perforation mode occurredon RCW-SR-A and RCW-SR-B, whereas full scabbing modes occurred on RCW-SR-C. In the case of the missile masses of1500 kg and 2000 kg, full perforation modes occurred on all walls as shown in Fig. 25b and c.

Fig. 24. Distance travelled and scabbing areas with respect to SR ratio.


5.3.2.2. Distance travelled. The left side of Fig. 26 shows the distance travelled corresponding to the different shear bar ratios.The analysis result showed that the distance travelled slightly changed as the shear bar ratio increased. It is concluded thatincreasing shear bar ratio did not show any major effect on reducing the distance travelled of the missile. However, the shearbar spacing had a significant effect on the distance travelled of the missile. The RCW-SR-C wall had the lowest distancetravelled among them.

Wall type RCW-SR-A RCW-SR-B RCW-SR-CLR ratio

0.44%

1.5%

(a) Missile mass M = 1,000 kg

Wall type RCW-SR-A RCW-SR-B RCW-SR-CSR ratio

0.44%

1.5%

(b) Missile mass M = 1,500 kg

Wall type RCW-SR-A RCW-SR-B RCW-SR-CLR ratio

0.44%

1.5%

(c) Missile mass M = 2,000 kg

Fig. 25. Failure modes of RCW-SR walls with different missile mass.


5.3.2.3. Scabbing area. The right side of Fig. 26 compares the scabbing area on the back face of the three different walls withtwo shear bar ratios at the time of 50 ms. The scabbing area slightly decreased as the shear bar ratio increased, exceptRCW-SR-C in the case of missile velocity of 200 m/s. Therefore, increasing shear bar ratio did not show any major effecton reducing the scabbing area.

However, the shear bar spacing had a significant effect on reducing the scabbing area of the RC wall. In the cases of veloc-ities of 70 m/s and 200 m/s, RCW-SR-C had the smallest scabbing area, whereas in the case of velocity 110 m/s, RCW-SR-Ahad the smallest scabbing area.

6. Optimal design of RC wall

This section presents the optimal design of the RC wall considering resistance to the impact of a missile with initial veloc-ity of 110 m/s, having a total mass of 1500 kg. In order to determine the most efficient combination of the reinforcements for

Fig. 26. Distance travelled and scabbing areas with respect to SR ratio.


optimal design, the behavior of the RC walls with different combinations of longitudinal rebar and shear bars were observed.The perforation limit is the most important criterion to guarantee safety, and secondary criterion is to prevent scabbing. Thefollowing parameters were used for optimal design:

(1) RCW-LR-A, RCW-LR-B, and RCW-LR-C with longitudinal rebar ratio of 3.0%.(2) RCW-SR-C with shear bar ratios of 0.44% and 1.5%.

Table 10Analysis results of design models.

Specimen Number of longitudinal rebar layers Shear bar ratioa (%) Distance travelled (m) Scabbing area (m2) Failure modeb

Design-1 2 0.44 0.44 0.00 PDesign-2 3 0.44 0.66 1.54 FSDesign-3 4 0.44 0.81 3.14 PPDesign-4 2 1.50 0.41 0.00 PDesign-5 3 1.50 0.50 1.85 PSDesign-6 4 1.50 0.63 1.54 FS

a Shear bar spacing of 100 mm was used for all design walls.b P = Penetration Mode, PS = Partial Scabbing Mode, FS = Full Scabbing Mode, PP = Partial Perforation Mode, FP = Full Perforation Mode.

Design-1 Design-2 Design-3

Design-4 Design-5 Design-6

Fig. 27. Comparison of failure modes of design RC walls.

Fig. 28. Comparison of distance travelled.


Six different design models, Design-1 to Design-6, were created as listed in Table 10. Three effects including distance trav-elled, scabbing area, and failure mode were observed as shown on the last three columns in Table 10. Fig. 27 shows a com-parison of the failure modes of the different design walls. Fig. 28 compares the distance travelled of the missile at 50 ms,whereas Fig. 29 compares the scabbing areas at the back face of the walls.

It can be observed that full perforation mode was prevented in all design walls. Design-3 had the greatest distance trav-elled and largest scabbing area, whereas both perforation and scabbing were almost prevented in Design-1 and Design-4walls. Design-4 had smallest distance travelled; therefore, it is recommended to be the best choice for optimal design.

Fig. 29. Comparison of scabbing areas.


7. Conclusions

A reliable nonlinear finite element model of RC walls under impact loading was developed. The structural componentsand their contacts were fully modeled. The erosion option of concrete and steel reinforcement was considered in the anal-ysis, and the finite element model was verified against the experiment. A parametric study was performed to investigate theinfluences of the longitudinal rebar and shear bar to the punching behavior of RC walls. Different missile velocities and theirmass were treated as parameters in order to evaluate the vulnerability of the different walls. The following conclusions havebeen obtained:

(1) Longitudinal rebar ratio had a significant effect on punching resistance of RC walls. However, in the case whereperforation mode had occurred, increasing rebar ratio led to a significant increment of scabbing area. The numberof layers of the longitudinal rebar did not show any significant effect on resisting perforation, rather it had a significanteffect in reducing the scabbing area of the RC wall in the case where shear bars were not considered. The RC wall withfour layers of longitudinal rebar had the smallest scabbing area.

(2) Shear bar ratio showed a minor effect on punching resistance of the RC wall, whereas shear bar spacing showed asignificant effect on resisting perforation of the RC wall and reducing the scabbing area. The RC wall with shear barspacing of 100 mm had the smallest scabbing area among three models.

(3) In such case where missile velocity is 110 m/s and the total mass is 1500 kg, Design-4 is recommended as the optimaldesign to withstand missile impact.

Acknowledgements

This work was supported by a grant from the Human Resources Development program (No. 20124030200050) of theKorea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korea government Ministry of Knowl-edge Economy.

References

[1] Kojima I. An experimental study on local behavior of reinforced concrete slabs to missile impact. Nucl Eng Des 1991;130:121–32.[2] Sugano T, Tsubota H, Kasai Y, Koshika N, Ohnuma H, Riesemann WA, et al. Local damage to reinforced concrete structures caused by impact of aircraft

engine missile, Part 1. Test program, method and results. Nucl Eng Des 1993;140:387–405.[3] Sugano T, Tsubota H, Kasai Y, Koshika N, Itoh C, Shirai K, et al. Local damage to reinforced concrete structures caused by impact of aircraft engine

missile, Part 2. Evaluation of test results. Nucl Eng Des 1993;140:407–23.[4] Vepsa A, Saarenheimo A, Tarallo F, Rambach J-M, Orbovic N. IRIS_2010-Part II: Experiment data. Transactions of the 21st SMiRT 2011.[5] Orbovic N, Blahoianu A. Test on reinforced concrete slabs under hard missile impact to evaluate the influence of transverse reinforcement and pre-

stressing on perforation velocity. Transactions of the 21st SMiRT 2011.[6] Saarenheimo A, Tuomala M, Calonius K, Hakola I, Hostikka S, Silde A. Experimental and numerical studies on projectile impacts. J Struct Mech

2009;42(1):1–37.[7] Oliveira DA, Saudy A, Lee NH, Elgohary M. The effect of t-headed bar reinforcement on the impact response of concrete walls. Transactions of the 21st

SMiRT 2011.[8] Pires JA, Ali SA, Candra H. Finite element simulation of hard missile impacts on reinforced concrete slabs. Transactions of the 21st SMiRT 2011.[9] Borgerhoff M, Stangenberg F, Zinn R. Numerical simulation of impact test of reinforced concrete slabs with dominating punching. Transactions of the

21st SMiRT 2011.[10] Sagals G, Orbovic N, Blahoianu A. Sensitivity studies of reinforced concrete slabs under impact loading. Transactions of the 21st SMiRT 2011.[11] LS-DYNA Key User’s Manual, Version 971. Livermore Software Technology Corporation; 2007.[12] An Introduction to the Winfrith Concrete Model. Schwer Engineering & Consulting Services; 2010.

http://refhub.elsevier.com/S1350-6307(14)00190-3/h0005

















[13] LS-DYNA Theory Manual. Livermore Software Technology Corporation; 2006.[14] Marais ST, Tait RB, Cloete TJ, Nurick GN. Material test at high strain rate using the split Hopkinson pressure bar. Latin Am J Solids Struct

2004;1:319–39.[15] Jones N. Structural impact. 2nd ed. Cambridge University Press; 1989. p. 333–84.[16] Chopra AK. Dynamics of structures – theory and applications to earthquake engineering. 3rd ed. Upper Saddle River, NJ 07458: Pearson Prentice Hall;

2006. p. 447–65.[17] CEB-FIP Model Code 1990: Design Code. Redwood Books. Trowbridge, Wiltshire, UK; 1993.[18] Calonius K, Elgohary M, Sagals G, Kahkonen J, Heckotter C, Ciree B, et al. Punching failure of a reinforced concrete slab due to hard missile impact

(IRIS_2010 Case). Transactions of the 21st SMiRT 2011.[19] Oliver M, Vincent C, Thierry S. Numerical analysis on the missile impact tests performed at VTT within the benchmark project IRIS, JRC scientific and

technical reports, European Commission, EUR 24880 EN; 2011.








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