GFRP Subjected to Blast Load

7/30/2019 GFRP Subjected to Blast Load

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Numerical evaluation of the retrofit effectiveness for GFRP retrofitted concrete

slab subjected to blast pressure

Jin-Won Nam a,c, Ho-Jin Kim b, Sung-Bae Kim c, Na-Hyun Yi c, Jang-Ho Jay Kim c,*

a Department of Civil and Environmental Engineering, Southern University at Baton Rouge, Pinchback Building #327, Baton Rouge, LA 70813, USAb Institute of Technology Research Planning, ATMACS CO.LDT, Sangdaewon-dong, Jungwon-gu, Seongnam-si, Gyunggi-do 462-120, South Koreac School of Civil and Environmental Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, Seoul 120-794, South Korea

a r t i c l e i n f o

Article history:

Available online 21 October 2009

Keywords:

Blast load

Fiber Reinforced Polymer (FRP)

Retrofitting effectiveness

High-strain rate dependent material model

Debonding failure model

Reinforced concrete (RC)

Refined FEM analysis

a b s t r a c t

For retrofitting structures against blast loads, sufficient ductility and strength should be provided by

using high-performance materials such as fiber reinforced polymer (FRP) composites. The effectiveness

of retrofit materials needs to be precisely evaluated for the retrofitting design based on the dynamic

material responses under blast loads. In this study, refined FEM analysis with high-strain rate dependent

material model and debonding failure model is conducted for evaluating the FRP retrofitting effective-

ness. The structural behavior of reinforced concrete (RC) slab retrofitted with glass fiber reinforced poly-

mer (GFRP) under blast pressure is simulated and the analysis results are verified with the previous

experimental results.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

Generally, concrete can be considered as a highly effective con-

struction material in resisting against blast loading compared to

other materials. However, concrete structures designed for the ser-

vice loads of normal strain-rate require special retrofitting to in-

crease the structural resistance against blast loading. Retrofitting

method of attaching extra structural members or supports to in-

crease the blast resistance is undesirable from the perspectives of

construction cost increase and useable space elimination. Also, this

method generally does not greatly improve the overall structural

resistance against blast load [13]. Therefore, less expensive and

more convenient fiber reinforced polymers (FRP) sheets or plates

are being used as surface attachments to retrofit specified areas

of structural members [3,4]. The FRP surface attachments signifi-cantly improve the blast resistance of structures without forfeiting

usable space and requiring long construction time, thereby saving

money. For the retrofitting of concrete structures for blast resis-

tance, the selection of the type of FRP is important. The selected

FRP has to improve stiffness, strength, and ductility of a retrofitted

structure to satisfy required blast safety resistance and absorb

blast energy whereby transforming structural failure mode from

brittle to ductile.

To analyze and design FRP retrofitted structures under blast

loads, both experimental and numerical studies are necessary [3

12]. Simplified lumped mass models for blast resistant structure

design and analysis allow rudimentary ways of designing and ana-

lyzing global concrete structure displacement behavior in terms of

applied load, mass, and resistance factors [13]. In such methods,

the applied load is calculated based on the application of simple

blast wave function and conversion of overall structural stiffness

to a single stiffness value. Due to its simplicity, this method is still

commonly used for blast resistant structure design and analysis.

However, recently, in order to improve the simplified analysis

methods, studies on the precise blast analysis methods with accu-

rate material models and refined finite element models for the

simulation of retrofitted concrete structure behavior have been ac-

tively pursued for the accuracy and reliability of analysis results[1218].

If properly validated, the refined FEM analyses can be used as a

replacement for costly structure blast experiments. Furthermore,

even when specialized testing facilities and related resources are

available, some conditions and data are more readily obtained

through such virtual experiments using the FEM. For these reasons,

it is vital to establish effective analysis tools for newand retrofitted

concrete structures under blast loading to predict structural behav-

iors, select optimum retrofitting materials, and ensure desired fail-

ure mechanisms.

In this study, the blast resistance of glass fiber reinforced poly-

mer (GFRP) retrofitted reinforced concrete (RC) slabs is analyzed

0263-8223/$ - see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.compstruct.2009.10.031

* Corresponding author. Tel.: +82 2 2123 5802; fax: +82 2 364 1001.

E-mail address: [email protected] (Jang-Ho Jay Kim).

Composite Structures 92 (2010) 12121222

Contents lists available at ScienceDirect

Composite Structures

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p s t r u c t
http://dx.doi.org/10.1016/j.compstruct.2009.10.031mailto:[email protected]://www.sciencedirect.com/science/journal/02638223http://www.elsevier.com/locate/compstructhttp://www.elsevier.com/locate/compstructhttp://www.sciencedirect.com/science/journal/02638223mailto:[email protected]://dx.doi.org/10.1016/j.compstruct.2009.10.031


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using the explicit analysis code LS-DYNA, which accommodates

the modeling of high-strain rate dependency and debonding fail-

ure. Also, the retrofit effectiveness of GFRP fabrics is evaluated by

comparing the analysis results for non-retrofitted and retrofitted

slabs. The verification of the analyses is performed through com-

parisons with experimental results [10,19].

2. Constitutive material models considering blast load

2.1. Concrete damage model

The concrete damage model used in this study is based on Mal-

vars model [16,18], which modifies the WillamWarnke failure

surface with three parameter surface definition and pressure cutoff

[20]. The concrete damage model of this study represents blast dy-

namic hardeningsoftening non-linear behavior by accumulated

effective plastic strain in the regime of continuum mechanics. In

the model, three independent failure surfaces are defined as

Drm a0 p

a1 a2pMaximum failure surface 1

Drr pa1f a2fpResidual failure surface 2

Dry a0y p

a1y a2ypYield failure surface 3

Dre rfDrp=rf Enhanced failure surface 4

where Dr is stress difference (on the deviatoric stress failure sur-face) andp is confining pressure for each stage of behavior. The vari-

ables a0, a1, and a2 are constants obtained by the unconfined

compression test and conventional triaxial compression tests at

various degrees of confining pressure. rf is the strength enhance-

ment factor, which represents strain-rate effect of concrete. The en-

hanced concrete strength is obtained by multiplication of the

enhancement factor to static concrete strength. The strengthenhancement factors used in this study are shown in Fig. 1.

2.2. Steel reinforcement model

For the material model of steel reinforcement in concrete, dy-

namic and strength increasing factors are considered [21]. The

yield stress function of steel reinforcement based on the von Mises

criterion is

ry br0 fhepeff

5

where b is the variable for strain-rate effect and is calculated using

Eq. (6), which is based on Cowper and Symonds model [23]. r0 isinitial yield stress and fhe

peff is hardening function, which can be

expressed as Eq. (7) using plastic stiffness Ep and effective plastic

strain epeff.

b 1 _eC

1=r6

fhepeff

Epepeff

7

where C and r are strain-rate parameters. In this study, the strain-

rate effect is considered by defining the relationship between effec-

tive plastic strain and yield strength based on the experimental

data. The relations between effective plastic strain and yield

strength are shown in Fig. 2.

2.3. Rate dependent FRP failure model

The failure model of FRP in this study is based on progressive

failure criteria of Hashin and Chang and Changs model [24,25].

The strain-rate effect on the material strengths is incorporated into

failure model based on Parks model [26].

1

10

100

1.E-06 1.E-04 1.E-02 1.E+00 1.E+02

Strain rate (1/s)

Strengthenhancementfactor

Tension(This study)

Compression(This study)

Tension(CEB)

Compression(CEB)

Fig. 1. Concrete strength enhancement due to high-strain rates.

0

200

400

600

800

1000

1200

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Strain rate = 0

Strain rate = 10-4

Strain rate = 100

Strain rate = 102

Strain rate = 103

Strain rate = 0

Strain rate = 10-4

Strain rate = 100

Strain rate = 102

Strain rate = 103

Effective plastic strain

Yieldstress(MPa)

Fig. 2. Rate dependent relationship of effective plastic strain and yield stress for

steel reinforcement.

Enhanced failure criteria on dynamic condition

1

2

Ytstatic

Ytdynamic

Failure criteria on static condition

Xtstatic Xt

dynamic

Ycstatic

Ycdynamic

XcstaticXc

dynamic

Fig. 3. Enhanced failure criteria of FRP.

J.-W. Nam et al. / Composite Structures 92 (2010) 12121222 1213


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2.3.1. Fiber breakage

For tension failure, the fiber breakage criterion can be expressed

as

er11Xt

2

s12SC12

2and

r11Xt

2P

s12SC12

2; forr11 >0 8

where e is a failure index representing the combined effect of the

normal and shear stresses; r11 is normal stress; s12 is shear stress;Xt is the tensile strength; SC is the in-plane shear strength. The cri-

terion states that fiber breakage occurs when the failure index is

equal to or greater than unity, for cases where the effect of normal

stress is greater than that of shear stress. For the compressive fail-

ure, the failure criterion can be expressed as

e r11Xc

2; for r11 < 0 9

where Xc is the compressive strength. The criterion states that fiber

failure in compression is mainly due to the normal stress, because

fiber buckling dominates the failure in compression.

2.3.2. Enhanced failure criteriaThe strength values of failure criteria are dependent on strain-

rate and can be expressed as follows.

Xtf1 _e; Xcf2 _e; Ytf3 _e; Ycf4 _e; SC12 f5 _e 10

where X is the longitudinal strength; Y is the transverse strength;

SC12 is the in-plane shear strength; _e is strain-rate. Subscripts tand c represent tensile and compressive state. Specific functional

forms f _e can be determined from experiment such as uniaxialand eccentric tension tests. Therefore, the uniaxial and eccentric

tension tests should be carried out to predict the appropriate

strain-rate effect on the longitudinal and shear strength. Linear

functions of material strength according to strain rates can be de-

fined by Eqs. (11)(13) [27].

X Xstatic f _e11MPa 11

Y Ystatic n _e22MPa 12

SC12 SC12static j _e12MPa 13

where f, n, j are material constants. From Eqs. (11)(13), the strain-rate effect is simply related to the in-plane failure criteria of FRP

failure model. The enhanced failure criterion is shown in Fig. 3.

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20

L_e/s _min=2

L_e/s _min=5

L_e/s _min=10

L_e/s _min=50

L_e/s _min=100

ta/ te

Pimp

/Ps

t

Le/ smin = 2

Le/ smin = 5

Le/ smin = 10

Le/ smin = 50

Le/ smin = 100

Fig. 4. Ratio of the bond failure loads of blast loading and the static cases.

Target FRP retrofitted structures

Blast load generation

Boundary condition check Explosion condition check

Establishment of numerical model

Material modeling Finite element modeling

Solid element

Beam element

Shell element

Contact interface modelingFRP-concrete interface

Input boundary and blast loading conditions

Blast analysis based on FEM

Structural responses check

Displacement, stress, and strain Failure strain, debondingfailure

Evaluation of the blast retrofit

performance

Global behavior Local behavior of retrofit material

Dynamicmaterialproperties

Concrete

Reinforcing steel

FRP (Rate dependent failure)

Fig. 5. Evaluation procedure of the blast retrofit effectiveness for FRP retrofitted concrete structures.

1214 J.-W. Nam et al. / Composite Structures 92 (2010) 12121222


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2.4. Debonding failure modeling under blast loading

The debonding failure model under blast pressure is presented

based on the Lorenzis and Tegolas model [28]. The dynamic bond

strength is calculated from the debonding failure load ratio of dy-

namic to static for the FRP retrofitted concrete and is used in deb-

onding failure criteria under arbitrary blast loading. The static

debonding failure load of FRP retrofitted concrete is derived from

the Yuans model [29].

The loaddisplacement (PD) of bonded plate can be expressed

as Eq. (14) [29]

Psfbpk1

D

dftanhk1L: 14

When the interfacial softening begins, the displacement of the

edge becomes equal to the slip (D = d) and the Eq. (14) becomes

Psfbpk1

for infinite bond length: 15

The length of interface to resist the applied load is referred as

the effective bond length. This effective bond length can be defined

as the bond length over which the shear stresses resist more than

97% of the applied load with an infinite bond length. Based on this

definition and considering that tanh(2); 0.97, the effective bond

length is given by

Le

2

k1 : 16

From the Eqs. (15) and (16), the bond shear stress of unit width at

the loaded end under a static force P can be determined as

sstmax P2

Le17

where Le is the effective bond length between FRP and concrete in

which the bond load increases linearly to a constant value. The lin-

ear relationship between smax and P, and between sstmax and P is ex-pressed as a function of ta/te as

sstmaxsmax

PimpPst

fta=te 18

where Pst and Pimp are the tensile forces which induce the local bondstrength sf at the loaded end under the static and impulsive blastloading cases, respectively. ta is the duration of blast loading and

te is the duration for the stress wave propagation to the effective

bond length. If the local bond slip relationship is assumed to be lin-

ear elastic and sf is assumed to be the same in the static and in thedynamic cases, then Eq. (18) gives the ratio of the debonding failure

loads in the blast loading and static loading cases. A ratio less than 1

indicates early debonding of the FRP as a result of the impulsive

application of the load.

In this study, the bond strength under blast load is evaluated by

using the blast impulsetime history, which is obtained by integra-

tion of blast pressuretime history. For the blast pressuretime

history function, the Friedlander decay function can be used [1].

Pt Pm 1 ttp

exp a t

tp

19

where a is constant and tp is the duration for positive pressure. Theblast impulsetime history function by integration of Friedlander

function can be determined as1,000

1,000

7 bars (5.74 mm diameter)

A

A

Welded steel meshSection A-A

70

10

50

10

Unit : mm

Geometry and reinforcement details

GFRP retrofitted slab

(b)

(a)

Fig. 6. Test specimen of experiment [10,19].

Table 1

Material properties [10,19].

Concrete Compressive strength (MPa) 42

Tensile strength (MPa) 4.0

Youngs modulus (GPa) 29

Poissons ratio 0.167

Reinforcing

steel

Yield strength (MPa) 480

Ultimate strength (MPa) 600GFRP Longitudinal modulus , Ex (GPa) 27.5

Transverse modulus, Ey (GPa) 1.3

Shear modulus, Gxy (GPa) 0.27

Poissons ratio, vxy 0.23

Longitudinal tensile strength, Xt(MPa)

410:2log _e11 459:2

Longitudinal compressive strength,

Xc (MPa)

318.0

Transverse tensile strength, Yt (MPa) 146:5log _e22 17:2Transverse compressive strength, Yc(MPa)

10.5

In-plane shear strength, SC (MPa) 6:2loglog_e12 7:9Density, q (kg/m3) 2,100Thickness (mm) 1.3

Epoxy Tensile strength (MPa) 54

Elastic modulus (GPa) 3.1

Maximum elongation (%) 5



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It Zt

0

Ptdt Pmtp

a1 e

a ttp 1 t

tp 1

ae

a ttp 1 20and Eq. (20) can be rewritten as a function of the maximum im-

pulse, Imax, as

It Imax1 1a e

a ttp 1 ttp

1a

1 1a 1a e

a: 21

From Eqs. (20) and (21), the ratio of the bond failure loads under

static and blast loads can be determined as

sstmaxsmax

1 1a

1a e

a

R10meatdt 1a coth

2sminLe

ea ne

a 1sminteLetp

" # 22

where smin is the minimum distance of stress wave withm a1 t coth2tp1tte and n 1 a

sminteLetp

. From the above ap-

proach, the ratios of the dynamic bond failure load of FRPconcrete

interface under blast loading to the static bond failure load are cal-

culated as shown in Fig. 4. As shown in Fig. 4, the blast impulse may

produce a substantial reduction of the debonding load compared to

the static load. This reduction is more significant for larger Le/sminratio when the minimum activated length of the joint is shorter.

3. Blast analysis for FRP retrofitted RC slab

For evaluating the FRP retrofitting effectiveness for concrete

structures under blast pressure, the evaluation procedure consid-

ering rate dependent FRP failure model and debonding model is

presented as shown in Fig. 5. In order to verify the procedure,the previous field blast test [10,19] is simulated following the pre-

sented analysis procedure using the explicit analysis code LS-DYNA

[21,22]. Finally, the analyses results are compared with the previ-ously reported experimental results.

3.1. Descriptions of field blast test

To verify the validity of the refined FE analysis, the field blast

test for FRP retrofitted reinforced concrete slab performed by

Razaqpur and Tolba [10,19] is simulated. As shown in Fig. 6a, the

specimen is a RC slab with the dimensions of 1.0 1.0 0.07 m.

The slabs are doubly reinforced with welded steel mesh, which

has cross-sectional area of 25.8 mm2 and center-to-center spacing

of 152 mm in each direction. The yield and ultimate strengths of

Fig. 7. Test setup and the tripod holding the explosive charge [10,19].

-2

0

2

4

6

8

1 2 3 4 5 6

Experimental(A) (Tolba 2001)

Experimental(B) (Tolba 2001)

ConWep

Time (msec)

Blastpressure(MPa)

Fig. 8. Comparison between CONWEP [30] and measured reflected pressure.



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the reinforcing bars are 480 MPa and 600 MPa, respectively, and

the compressive strength of concrete is 42 MPa. The slabs are ret-

rofitted on both faces with two laminates of GFRP arranged in a

crossed form as shown in Fig. 6b. Each GFRP laminate is 500 mm

wide and covers a middle half of the slab. The laminate is basically

unidirectional composite fabric with E-glass fibers in the mainreinforcing direction. The material properties of the test specimen

are tabulated in Table 1. Dynamic strengths of GFRP are calculated

using Eqs. (11)(13).

The explosive used in the test is ANFO, which contains 82% of

the energy of same amount of TNT. Specimen is subjected to the

blast pressure from 33.4 kg of ANFO. The distance from the center

of the charge to the center of the front face of the slab is 3.0 m. The

test setup is shown in Fig. 7.

3.2. Blast Analysis of GFRP retrofitted RC slab

3.2.1. Blast load generation

The blast load is generated using CONWEP. CONWEP is software

for calculating blast pressure according to the weight and stand-offdistance of explosives. It has been developed stochastically [30].

The blast is assumed as a spherical burst in the free atmosphere

and 33.4 kg of ANFO is converted into 27.4 kg of TNT by conversion

factor of 0.82. The comparisons between CONWEP predicted pres-

sures and field test measured pressures [10,19] are shown in Fig. 8.

The CONWEP prediction for the pressuretime profile agrees well

with the test measurement.

3.2.2. Finite element models

Solid and beam elements with rate dependent material models

are used for concrete and reinforcing steels, respectively. For the

GFRP sheets modeling, shell element with rate independent and

dependent failure models are adopted to incorporate GFRP rate ef-

fect on the global structural behavior. The shell elements of GFRPare attached to the solid elements of concrete with contact interfa-

cial element [21,22] with perfect bonding and debonding models.

The debonding model considers the dynamic bond strength calcu-

lated by Eq. (22) with the failure of contact elements. The shell ele-

ments are placed at a distance of half-thickness of GFRP sheet from

the concrete surface. This virtual thickness offset is used to simu-

late the attachment of GFRP to the concrete in the analysis. Forthe determination of element size, noise analyses for the different

element sizes were conducted and 2.5% of specimen length was

determined as an optimum element size considering the comput-

ing time and the reliability. The FE modeling including concrete,

reinforcing steel and GFRP sheet of the retrofitted slab is schemat-

ically shown in Fig. 9.

Regarding the boundary conditions, translations and rotations

for the x, y and z directions of all of the edges of RC slab are con-

strained. According to the Razaqpurs paper [19], the specimens

are supposed to be restrained in only uplift direction. However, a

-5

0

5

10

15

0.00 0.01 0.02 0.03 0.04

k9 w/o strain effect

k10 w/ strain effect

k11 perfect bondingNon-retrofit

Time (sec)

Mid-spandisplacement(mm) Proposed analytical model

Displacement increasing

due to rate independency

Displacement decreasing

due to perfect bonding condition

Rate dependent failure model with debonding

Rate independent failure model with debonding

Rate dependent failure model with perfect bonding

Non-retrofit (control)

Fig. 10. Analysis results of mid-span displacement history.

Beam element

for steel mesh

Solid element

for concrete

Shell element

for FRP

42 MPa

Unidirectional Glass ply

Fiber direction

x

x

y

y

yx

Contact interface

Concrete surface

FRP surface

Contact surface to surface to tiebreak

Shell element

Solid element

Contact criteria : imp

A

Zoom in A

Fig. 9. Finite element models of GFRP retrofitted concrete slab specimen.



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Fig. 11. Displacement distribution at 0.005 s.



8/11

steel frame on the steel box is provided with a clamping system

and the clamping system for all edges can be considered as all

directional restraint. The boundary conditions can be identified

in Fig. 7.

3.2.3. Material models

Three material models of LS-DYNA are used in the analysis. Con-

crete damage model (MAT_72), piecewise linear plasticity model

(MAT_24), and orthotropic elastic model (MAT_2) are adopted for

concrete, steel reinforcement, and FRP reinforcement, respectively

[21]. In the analysis, the modified strength enhancement function

of concrete damage model and the dynamic failure criteria of FRP

in Chapter 2 are implemented to LS-DYNA explicitly.

3.3. Results

The mid-span displacement history of slab is shown in Fig. 10.

For the rate dependent and independent GFRP failure models with

debonding, the maximum displacements are calculated as

10.56 mm and 11.14 mm, respectively. The difference of displace-

ments between rate dependent and independent models indicates

the GFRP strength enhancement effect on the global structural

behavior. In case of the rate dependent GFRP failure model with

perfect bonding, the maximum displacement is calculated as

10.23 mm. The minute difference between debonding and perfect

bonding models indicates the energy absorbing capacity of perfect

bonding between GFRP and concrete.

From the analytical displacement history, the effectiveness of

FRP can be decided as either sufficient or insufficient retrofitting.

If the behavioral curve of rate dependent FRP failure model with

debonding is closer to the behavioral curve of rate independent

FRP failure model with debonding, it means that more retrofitting

is needed. If the behavioral curve is closer to perfect bonding case,

it means that the retrofitting is relatively sufficient. From the anal-

ysis results, the behavioral curve of rate dependent failure model

with debonding is slightly closer to the behavioral curve of perfect

bonding model and has the maximum displacement of 10.56 mm,

which corresponds to a low damage level in the ASCE criteria [1].

Comparing the displacement results with the maximum displace-

ment of non-retrofitted RC slab, the maximum displacement is re-

duced by approximately 20% by GFRP retrofitting.

The displacement contours of structures also can be used as an

index to indicate structural components damage states and local-

ized failures. From the analysis of the non-retrofitted slab, the cen-

tral region has large out-of-plane displacements and the edges

have large shear rotation concentration as shown in Fig. 11.

The analyses results for the strains of GFRP and concrete are

shown in Fig. 12. The maximum concrete strain of 0.0039 was ob-served at the bottom of the slab using the GFRP strain-rate depen-

dent model with debonding failure mechanism. When the GFRP

strain-rate dependent model is not used, a significant increase in

strain is observed and the maximum strain is calculated as

0.0046 with GFRP material failures as shown in Fig. 12a.

In Fig. 12b, some localized material failures are observed when

the stresses of GFRP exceeded the material strength and debonding

failures are observed when local GFRP strains exceeded maximum

strain capacity. The local strain exceeding GFRP strain capacity

indicates local debonding failures in which the strain of GFRP is

transferred to concrete. This phenomenon is confirmed by two

opposite tendencies shown in Fig. 12a and b. After 0.02 s from

the wave pressure application, the GFRP strains of debonding mod-

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0 0.01 0.02 0.03 0.04

w/ strain-rate

w/o strain-rate

Perfect bonding

Non-retrofit

Time (sec)

Concretestrain

atbottom




Non-retrofit (control)

Concrete

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

w/ strain-rate

w/o strain-rate

Perfect bonding

Time (sec)

GFRPstrainatbottom

Ultimate strain of GFRP




GFRP

0 0.01 0.02 0.03 0.04

(a)

(b)

Fig. 12. Analysis results of strains in GFRP and concrete.

Table 2

Summary of analysis results.

Non-

retrofitted

Strain-rate independent FRP and

debonding

Strain-rate dependent FRP and perfect

bonding

Strain-rate dependent FRP and

debonding

Arrival time at max.

displacement (s)

0.0010 0.0090 0.0085 0.0095

Max. displacement (mm) 12.29 11.14 10.23 10.56

Duration time of positive phase

(s)

>0.040 0.034 0.027 0.030

Max. strain of concrete (mm/

mm)

0.005 0.0046 0.0039 0.0039

Max. strain of GFRP

(mm/mm) 0.021 0.025 0.019

Material failure Concrete Concrete, GFRP Concrete, GFRP Concrete, GFRP

Interfacial failure Debonding Debonding



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el are lower than that of perfect bonding model. And, the concrete

strains of debonding model are higher than that of perfect bonding

model. The analysis results using the different FRP models are

summarized in Table 2.

4. Discussions

The displacement history results of the analyses and experi-

ments are shown in Fig. 13. The analysis result of rate dependent

FRP failure model with debonding is used for the comparison.

The overall analyses results show good agreement with the exper-

imental data. However, the experimental results show some irreg-

ular tendency in the earlier part of the displacement behavioral

curves. Also, the experimental displacement behavioral curves ob-

tained from non-retrofitted and GFRP retrofitted slabs crossed each

other in the latter part of the displacement behavioral curves.

These unreasonable results are caused by measuring errors in the

test field. According to Razaqpur and Tolba [10,19], there existnumerous variability in the field blast test, causing test results to

be inaccurate. The variability can be attributed to measuring

instrumentation inaccuracies and changing environmental condi-

tions such as atmospheric pressure, temperature, wind, etc. Since

all of the variability cannot be considered in the analysis, analysis

results should be compared to experimental results with an allow-

able error margin. In this study, the analyses and the experimental

results are within an allowable error margin as shown in Fig. 14.

Regarding the artificial energy loss of the finite element analy-

sis, the internal energy is compared with the hourglass energy.

The hourglass effect can come out easily in specific elements such

as solid elements. In this study, FlanaganBelytschko viscous form

with exact volume integration for solid elements is used to control

hourglass effect in the analysis [21]. Viscous hourglass and stiff-ness controls are accepted as suitable solutions for problems with

elements deforming with high and low velocities, respectively,especially if the number of time steps is large. Since the blast anal-

ysis is in the regime of very high velocity problem, the viscous

hourglass control is adopted in the study. Also, for solid elements,

the exact volume integration provides some advantage for highly

distorted elements. Fig. 15 shows the comparison of internal en-

ergy and hourglass energy of target structural model. The hour-

glass effect of elements is controlled effectively as shown in Fig. 15.

For the local failure of GFRP, the analyses results simulate and

locate GFRP failures as shown in Fig. 16. The dynamic debonding

strength from the calculation of impulse curve of blast pressure

have reasonable values and trends for the blast analysis. The sum-

marized comparisons of analyses results and experimental data are

tabulated in Table 3. From the comparisons, the presented blast

analysis methodology can predict the behavior of FRP retrofittedconcrete structures under blast loading and the refined FE analysis

can be used to evaluate effectiveness of FRP retrofitting design of

concrete structural members subjected to blast loading.

5. Conclusions

The conclusions from this study are as follows:

1. The blast analysis methodology for the evaluation of FRP retro-

fitting effectiveness is presented. Rate dependent FRP material

model and dynamic debonding failure model are adopted for

the numerical analysis technique. With the presented analysis

methodology, the evaluation procedure for the FRP retrofitting

design is also presented. The blast analysis is carried out forGFRP retrofitted RC slab and analysis results are compared with

the previously reported experimental results.

2. For a rate dependent FRP model, the enhanced failure criteria is

defined. In order to evaluate the dynamic bond behavior

between concrete and FRP under blast load, the dynamic bond

strength is calculated by integration of Friedlander decay func-

tion. The calculated dynamic bond strength is implemented in

the finite element analysis using the contact interface model.

3. In the comparative study, the FRP retrofitting effectiveness is

evaluated by using different FRP failure models: rate dependent

FRP failure with debonding; rate independent FRP failure with

debonding; rate dependent FRP failure with perfect bonding.

The displacement history, damage index, and strain history

are analyzed in the respects of global structural behavior, retro-fitting sufficiency, and debonding failure.

-5

0

5

10

15

20

0.00 0.01 0.02 0.03 0.04

GSS4

CS2

k9 w/o strain effect

Non-retrofit

Experiment for GFRP retrofit slab (Tolba2001)

Experiment for non-retrofit slab (Tolba2001)

FE analysis for GFRP retrofit slab (this study)

FE analysis for non-retrofit slab ( this study)

Time (sec)

Displacement(mm)

Fig. 13. Comparison of experiment and analysis results in displacements.

0

4

8

12

16

Non-retrofit GFRP retrofittedMaximumdisplacement(mm)

Response range for non-retrofitted cases

(Razaqpuret al. 2006; Tolba2001)Response range for GFRP retrofitted cases

(Razaqpuret al. 2006; Tolba2001)

Fig. 14. Comparison of the maximum displacement response ranges.

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

3.00E+03

3.50E+03

0 50 100 150 200

Time (msec)

Energy(kJ)

Internal EngergyHourglass Energy

Fig. 15. Comparison of internal and hourglass energy of analysis model.



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Experimental results [10, 19]

Compression side Tension side

M

D

D

M

M, D M, D

M, D

D

M

M

M : Material failure

D : Debonding failure

Debonding failure

Analysis results

(b)

(a)

Fig. 16. Comparison of local debonding failure in the experiment and the analysis: (a) experimental results [10,19]; (b) debonding failure in analysis.

Table 3

Comparisons of analysis results and experimental data [8,17].

Experimental data [8,17] Analysis results

Non-retrofit GFRP retrofit Non-retrofit GFRP retrofit

Arrival time at max. displacement (s) 0.0013 0.0075 0.0010 0.0095

Max. displacement (mm) 12.50 9.58 12.29 10.56

Duration time of positive phase (s) >0.030 0.024 More than 0.040 0.030

Max. strain of concrete (mm/mm) 0.0027 0.005 0.0039

Max. strain of GFRP (mm/mm) 0.013 0.019

Material failure Concrete Concrete Concrete Concrete, GFRP

Debonding failure Debonding Debonding



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4. The numerical analysis results are verified with experimental

data which have been measured by previous researchers. Even

though the experimental data varies with ranges, the analysis

results of overall displacement history and FRP failure corre-

spond with experimental results. The presented blast analysis

procedure is confirmed to be used for the evaluation of FRP

effectiveness in the blast retrofitting design.

5. Further experiments on the strain-rate effect according to the

types and layers of FRP are needed to build more accurate

model and retrofitting design procedure for RC structure under

blast loading. Also, further researches on the dynamic interfa-

cial behavior between FRP and concrete are required. The differ-

ences of bond behaviors under various dynamic loads could be

experimentally obtained by dynamic pull-out test.

Acknowledgments

The authors would like to thank Korea Research Foundation

(D00792) and Korea Science and Engineering Foundation (R01-

2008-000-1117601) for its financial support of this research.

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GFRP Subjected to Blast Load