applied element method analysis of porous gfrp barrier

Advances in Structural Engineering Vol. 13 No. 1 2010 1

Applied Element Method Analysis of Porous GFRP

Barrier Subjected to Blast

D. Asprone1,*, A. Nanni2, H. Salem3 and H. Tagel-Din3

1Department of Structural Engineering, University of Naples “Federico II,” Naples, Italy, andResearch Center AMRA scarl, Naples, Italy

2Department of Civil, Architectural and Environmental Engineering, University of Miami,Coral Gables, FL, USA

3Applied Science Int., LLc., Raleigh, NC, USA

(Received: 5 May 2008; Received revised form: 24 April 2009; Accepted: 21 May 2009)

Abstract: Numerical analysis of highly dynamic phenomena represents a critical fieldof study and application for structural engineering as it addresses extreme loadingconditions on buildings and the civil infrastructure. In fact, large deformations andmaterial characteristics of elements and structures different from those exhibited understatic loading conditions are important phenomena to be accounted for in numericalanalysis. The present paper describes the results of detailed numerical analysessimulating blast tests conducted on a porous (i.e. discontinuous) glass fiber reinforcedpolymer (GFRP) barrier aimed at the conception, validation and deployment of aprotection system for airport infrastructures against malicious disruptions. Thenumerical analyses herein presented were conducted employing the applied elementmethod (AEM). This method adopts a discrete crack approach that allows autocracking, separation and collision of different elements in a dynamic scheme, wherefully nonlinear path-dependant constitutive material models are adopted. Acomparison with experimental results is presented and the prediction capabilities ofthe software are demonstrated.

Key words: applied element method, blast loads, fiber reinforced polymer, numerical analysis, porous barrier, protection.

*Corresponding author. Email address: [email protected]; Fax: +39-0817683491; Tel: +39-0817683672.

1. INTRODUCTIONHighly dynamic loading conditions represent nowadays afundamental challenge in structural engineering as criticalbuildings and infrastructures need to resist extreme loadsevents that can occur during their lifetime as a result ofnatural and man-made hazards (e.g., explosions,collisions, and severe earthquakes). Under such loadregimes, investigations on structural performances cannotbe conducted without considering aspects that aretypically neglected under static loading conditions(e.g., large displacements, material characteristics underhigh strain rates, and fluid dynamics). As a corollary,there is a growing interest in the scientific and practicing

communities to design and/or assess protection systemsto reduce the vulnerability of critical infrastructures(e.g., shelters and barriers). With this objective, aresearch program named Security of Airport Structures(SAS) was undertaken and completed in 2007 by aconsortium of European entities led by the researchcenter AMRA (http://www.amracenter.com), in orderto (a) design and validate a protection barrier intendedto deter malicious actions against critical airportinfrastructures carried out by eco-terrorists, and (b)mitigate the effects of blast events on protected targets.

The material of choice for this barrier system becameglass fiber reinforced polymer (GFRP). This was because

Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

2 Advances in Structural Engineering Vol. 13 No. 1 2010

of the necessity of maintaining radio-transparencywithout interference with airport radio-communications.A porous GFRP barrier was designed and itscomponents subjected to mechanical and electromagnetictests. Furthermore, a blast test campaign wasperformed on full assemblies in order to validate the capability of the system in withstanding blastloads and protecting a target placed beyond it byreducing the effects of the incident blast shock wave.Such tests were then simulated through numericalanalyses conducted employing software based on theapplied element method (AEM) (Tagel-Din 2002;Tagel-Din and Meguro 2000; Tegel-Din and Rahman2004; Meguro and Tagel-Din 2001; Meguro andTagel-Din 2002). This paper presents the results ofthese analyses, providing a comparison with theexperimental results.

2. GFRP BARRIER SYSTEMThe barrier system consists of GFRP pipes mountedvertically over a modular reinforced concrete base thatis 0.5 m high (see Figure 1 that depicts a prototype of the

barrier system). Such base consists of precast elementswith male-female type connections for interlock that,once assembled together, form a continuous above-ground foundation. The base elements are reinforcedwith GFRP bars to eliminate the presence of steel forthe double purpose of enhancing long-term durability(no corrosion) and providing magnetic transparency.The height of each GFRP pipe above the foundation is2.5 m. The clear distance between two adjacent pipesis 65 mm. The cross section of each GFRP pipe has awall thickness of 5.5 mm and an external diameter of85 mm. As common for any GFRP pultruded section,the pipe wall is composed of a core made of continuousunidirectional glass fiber strands and two externallayers made of glass fiber mats. The fibers areimpregnated with a polyester resin to make it acomposite. Details about the geometry of the barrierand its installation are presented in Asprone et al.(2007, 2008).

3. BLAST TESTSThree blast tests were conducted on three separate barrierprototypes of identical size. Each prototype consisted of13 pipes composing a 1.95 m long structure. For eachtest, 5 kg of quarry TNT were detonated at differentdistances D from the barrier but at a constant height of 1.5 m above the ground (Figure 2); in particular, Dwas selected to be 5, 3 and 0.5 m, respectively. Each testspecimen was instrumented with strain gauges locatedalong the central pipe, accelerometers at differentpositions along the pipes and the concrete base, andpressure gauges placed on the pipes and around thebarrier in order to acquire a complete pressure fieldduring the blast event. Details about the tests and theemployed instrumentation are available in Asprone et al.(2007, 2008).

Figure 1. Prototype of barrier

Bomb5 Kg

Blast barrier

3 m

DD=5.0, 3.0 and 0.5 m

1.5 m

Figure 2. Blast barrier experiment set-up

D. Asprone, A. Nanni, H. Salem and H. Tagel-Din


4. NUMERICAL ANALYSES VIA AEMSIMULATION

Detailed numerical analysis has been carried out for thebarriers using the Extreme Loading for Structures(ELS) software developed by the Applied ScienceInternational (www.appliedscienceint.com). The ELSsoftware provides a fully nonlinear dynamic analysisbased on the Applied Element Method (AEM) (Tagel-Din 2002; Tagel-Din and Meguro 2000; Tagel-Dinand Rahman 2004; Meguro and Tagel-Din 2001;Meguro and Tagel-Din 2002; Park et al. 2009; Sasani2008; Sasani and Sagiroglu 2008; Wibowo et. al. 2009).

4.1. Introduction to AEM Simulations

The applied element method (AEM) is a modelingmethod adopting the concept of discrete cracking. InAEM, the structure is modeled as an assembly ofrelatively small elements as shown in Figure 3(a). Theelements are connected together along their surfacesthrough a set of normal and shear springs. The twoelements shown in Figure 3(b) are assumed to beconnected by normal and shear springs located at thecontact points, which are distributed on the element faces.Normal and shear springs are responsible for transfer ofnormal and shear stresses, respectively, from one elementto the other. Springs generate stresses and deformationsof a certain volume as shown in Figure 3(b).

Each single element has six degrees of freedom:three for translations and three for rotations. Relativetranslational or rotational displacement between twoneighboring elements cause stresses in the springslocated at their common face as shown in Figure 4.These connecting springs represent the state of stresses,strains and connectivity between elements. Twoneighboring elements can be totally separated once thesprings connecting them rupture.

Fully nonlinear path-dependant constitutive modelsare adopted in the AEM as shown in Figure 5. Forconcrete in compression, an elasto-plastic and fracturemodel is adopted (Maekawa and Okamura 1983).When concrete is subjected to tension, a linear stress-strain relationship is adopted until cracking of theconcrete springs, where the stresses then drop to zero.GFRP is a brittle material in which linear stress-strainrelationship is adopted up to failure. For more detailsabout constitutive models, refer to Tagel-Din andMeguro (2000).

The concrete is assumed cracked when the principaltensile stresses reach the cracking strength of concrete.If the cracking direction is parallel to the element faces,the cracks extend in those directions. When the crackingdirection is inclined as shown in Figure 6, the problem

(a) Element generation for AEM

Volume represented bya normal spring and 2shear springs

(b) Spring distribution and area of influence of each pair of springs

b

a

a

Figure 3. Modeling of structures in AEM

Normal

Shear x-z

Normal

Normal

Shear x-zShear x-y

Shear x-yx

z

yRelative translations Relative rotations

Figure 4. Stresses in springs due to relative displacement



becomes numerically complicated. Two solutions wouldbe available: the first one is to break the element downinto two elements, while the other is to redistribute theunbalanced stresses on the element faces. The formersolution is rather complicated, but more accurate forshear stress transfer, while the latter is simpler, but lessaccurate. For simplicity, the second solution is adoptedhere given that the accuracy can be greatly improved byreducing the size of the elements.

The AEM is based on a simple stiffness methodformulation, in which an overall stiffness matrix isformulated and nonlinearly solved for the structuraldisplacements. The solution for equilibrium equations isan implicit one that adopts a dynamic step-by-stepintegration, as Newmark-beta time integrationprocedure (Bathe 1982 and Chopra 1995).

One of the main valuable features in AEM is theautomatic detection of element separation and contact.Two neighboring elements can separate from eachother if the matrix springs connecting them rupture.Elements may automatically separate, re-contact againor contact other elements. As illustrated in Figure 7,there are several types of contacts: element corner-to-element face contact, element edge-to-element edgecontact and element corner-to-ground contact. Formore details refer to the Applied Science International(www.appliedscienceint.com).

4.2. AEM Versus Other Numerical Methods

In spite of the robustness and the stability of the finiteelement method (FEM), its ability for simulatingprogressive collapse is questionable. The possibility ofcomplete separation of elements is limited and very timeconsuming. On the other hand, the AEM is capable ofefficiently simulating the progressive collapse ofstructures. Figure 8 schematically shows the applicableanalysis domain of both the AEM and FEM.

The discrete element method (DEM) has been provedto be a successful method for simulating a wide varietyof granular flow situations. In the DEM, The material isassumed to consist of separate, discrete particles thatmay have different shapes and properties. Simulationis started by putting all particles in a certain positionand giving them an initial velocity. Then the forces

She

ar

Nor

mal

G

Strain

Compression

Stressσc

σt

Unl

oadi

ng

Rel

oadi

ng

Tension

τ

εp

γ She

ar

G

Concreteτ

γ

Nor

mal

E

σ

ε

GFRP

GFRP bars

Loading

Figure 5. Constitutive models in the applied element method

Added springs atfracture plan

Splitting elements Redistributing stresses at elementedge

Figure 6. Different techniques for the post-cracking modeling

Shear spring in y Shear spring in x Normal spring

(a) Corner-to-face or corner-to-ground contact

(b) Edge-to-edge contact

Conta

ct sh

ear

sprin

gContactnormal spring

Contact shear

spring

Figure 7. Different types of elements contact



which act on each particle are computed from the initialdata and the relevant physical laws. An integrationmethod is employed to compute the change in theposition and the velocity of each particle during a certaintime step from Newoton’s laws of motion. Then, the newpositions are used to compute the forces during the nextstep, and this loop is repeated until the simulation ends.Dislike the AEM, DEM is not a stiffness-based method.The solution depends on force transmission from aparticle to another, and therefore, the DEM is not apractical solution for large-size problems. The maximumnumber of particles, and duration of a virtual simulationis limited by computational power. Another obstacle inthe DEM is that simulations are generally limited tospherical particles due to the increase in cost ofcomputation with increasing complexity of geometry.

4.3. AEM Model

Figure 9 shows the AEM model used in the currentstudy, where the bottom of the RC footing is totally

restrained. The pipes are not modeled as embeddedinside the footing. Instead, they are assumed to be totallycompatible (constrained) with the footing at theirintersection on the upper face of the footing. Thisassumption is thought to be acceptable since theexperiments showed no pullout of the pipes from the footing. The properties of concrete and GFRP aresummarized in Table. 1.

A mesh sensitivity analysis has been carried out toobtain the largest size of elements that do not affect thesolution accuracy. The sensitivity analysis performed toa single elastic tube with a lateral point load showed agood convergence tendency as shown in Figure 10.Based on that curve, the number of elements selectedwas 750 per tube (25 divisions in radial direction and30 ones in vertical direction)

4.4. Material Properties Assumptions

Concrete had a compressive strength of 30 MPa withan initial modulus of elasticity of 24 GPa. As for thematerial properties of the GFRP pipe elements, a staticmechanical test campaign was conducted on suchelements. Such tests consisted of 4-point bending testsconducted on pipe elements and direct tension testsperformed on coupons. The GFRP was found to have atensile strength of 648 MPa with an overall Young’smodulus, evaluated from flexural stiffness exhibitedduring four points bending tests, of 40 GPa. Furthermore,the following assumptions were considered:

• The specific gravity of the GFRP is 1900 kg/m3;• The vibration period T can be determined from

the Eigen modes of the barrier and was found tobe 0.08 second for the first vibration mode;

• The damping ratio ε can be reasonably assumedas 2.5% (Naghipour et al. 2005);

Complexity, accuracy, time and qualifications of user

Progressive collapse analysis

Engineering judgement, uncertainty and construction cost

FEM

Hig

hly

nonl

inea

r so

lutio

ns

Sim

ple

solu

tions

AEM

GapNot verified

Simplified SW Advanced SW

Figure 8. AEM versus FEM

Full compatibilitybetween the pipeand the footing

Fixed boundary

1.95 m

0.065 m

0.50

m2.

50 m

Figure 9. AEM model for barrier wall



• The natural frequency ω is calculated as:

(1)

• The external damping ratio is computed basedon the following expression (Chopra 1995):

(2)

4.5. Strain-Rate Effect

The strain rate effect is believed to be influencing thebehavior of GFRP pipes more than the concrete footingin the current study since the concrete footing isrelatively huge and most of the deformations arelocalized in the GFRP pipes. Therefore, only the strainrate effect on the GFRP is considered. At high strainrates, the apparent strength of GRRP may increase. Thedynamic increase factor (DIF) is the ratio of thedynamic strength to static one. This factor is normallyreported as function of strain rate. In this study, the DIFdeveloped by Agbossou et al. (1994) for GFRP matrixin tension is followed. Agbossou et al. (1994) developedthe following equation for dynamic tensile strength formedium interfacial shear strength coupling agents:

(3)

where εο is the strain rate in sec−1.

f MPato( ) .= +125 0 15ε

2 2 0 025 77 762 7 77ε ω = × × =. . .

ω π π= = =2 2 0 08 77 762/ / . .T Hz

From this equation the DIF was derived as:

(4)

The procedure for calculating the effect of the strainrate is shown in Figure 11. As illustrated, a preliminaryanalysis is performed first without considering thestrain-rate effect. The strain-rates are calculated fordifferent elements, and hence the dynamic increasefactors are calculated. Performing the analysis again,refined strain-rates are calculated and new dynamicincrease factors are calculated and compared to theprevious ones. Once the dynamic increase factors are notmuch changed, the analysis is accepted to be the finalone. Figure 12 shows the strain-rate calculated for thesprings at the bottom of the middle pipe for D = 0.5 m andthe corresponding DIF, where a maximum DIF of about10% was obtained. As for the 3 and 5 m standoffdistances, the DIF was too small and was neglected.

4.6. Equivalent Charge

The charge used in the experiment consists of 60%ammonia nitrate and 40% TNT with a total weight of5 kg. The equivalent TNT weight for this mixture is 4 kg,Asprone et al. (2007, 2008). This can be calculatedfrom published equations see e.g. Deribas et al. (1999).

4.7. Blast Pressure Calculations

In this section, the calculations of the blast pressureacting on the barrier wall pipes are explained and thedifferent assumptions are discussed noting that in AEM,the calculated blast pressure history is applied to eachelement.

DIF o= 0 15 125. ε

Table 1. Material properties

Property GFRP Concrete

Elastic Modulus (MPa) 40789 24607Shear Modulus (MPa) 16316 9843Tensile Strength (MPa) 648 3Compressive Strength (MPa) 648 30

217

216

215Deflection

P = 100 Kg

214

213

212

211Def

lect

ion

(mm

)

No. of elements

210

209

2080 200 400 600 800 1000 1200 1400

Figure 10. Mesh sensitivity analysis

Perform preliminary analysisdynamic increase factor DIF=1.0

Calculate strain rate for GFRP

Calculate dynamic increase factor DIF1

DIF = DIF1

Perform analysis DIF 1= DIF ENDN Y

Start

Figure 11. Iterative procedure for calculations of strain-rate effect



The blast action results in both blast and dragpressures varying with time and location along theloaded structure. The dynamic response of the loadedstructure depends on the resultant forces due to thesepressures. Knowing the charge weight and the details ofthe surrounding structure, the blast pressure loads areusually obtained from design charts, such as that of theTri-Service Reports TM5-855-1 and TM5-1300 (1985and 1990). Those design charts are calibrated for TNTexplosive. Other charge types should be converted to anequivalent TNT that releases the same energy.

Structures are divided, according to their geometry,into two categories: drag-type and diffraction-type(Kinney et al. 1985). The drag-type structures are openones with relatively thin members such as trusses. Inthese structures, the front and rear faces of a member,with respect to the blast wave, are very close and can beassumed to be in-phase, hence the loads are the resultsof only the drag force of the blast wind. The diffraction-type structures are wide ones, like buildings, whosetheir front and rear are not in phase and henceanalyses should be carried out for each face separatelyand the acting load would be their resultant. Therefore,for these structures, both the blast and drag pressuresare considered. Also, according to Hoorelbeke et al.(2006), for relatively small structural elements (lessthan 1 m in width and depth), the blast load on the rearface is almost in-phase with, but in the oppositedirection to, the load on the front face (i.e., thepressures on the front and rear faces nearly equalize).Therefore, the blast pressures apply a relatively low netload to the structural elements. This consideration

applies to open structures, where the loads are mainlydue to drag pressure.

The GFRP pipes of the barrier under investigation areassumed to be a drag-type open structure (i.e., the blastloads will be only due to the drag pressure of the blastwind). The blast wind from an explosion exerts forcesthat result from the pressure drop occurring behind thestructural elements. The pressure drop, Pd, whichaccounts for the drag force per unit of the projected area,is expressed as:

(5)

where u is the blast wind speed, ρ is the air density andCD is the drag coefficient. The blast wind speed u can bedetermined from the explosion pressure. The dragcoefficient CD depends on the geometry of the objectand the blast wave speed. For cylindrical shapes atdifferent speeds (Mach numbers), the drag coefficientsare taken 2.5, 1.3 and 1.2. for D = 0.5, 3.0 and 5.0 m,respectively (Forrest et al. 1953). For the nearestdistance (D = 0.5) and to account for the high Machnumber (>8.0), the drag coefficient CD is consideredequal to 2.0 (Forrest et al. 1953). To account forsecondary and neglected effects, a factor of safety isusually superimposed (TM5-1300, 1990) and in thecurrent study, a factor of 25% was considered to accountfor the additional assumptions.

Instead of calculating the dynamic pressure as

one can obtain it directly from the charts of TM5-1300(1990), where the free-field pressure (incident pressure)

12

2ρu ,

P C ud D=1

22ρ

−50

0

50

100

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Time (sec.)

Str

ain

rate

(1/

sec.

)

1.15

1.10

1.05

1.00

DIF

(a) Strain rate history

Time (sec.)

(b) DIF for tensile strength

Figure 12. Strain rate and DIF for the bottom of the middle pipe (D = 0.5 m)

Figure 14. Assumed variation of dynamic pressure along the pipe

cross-section



can be determined as a function of the charge weightand distance. Using the free-field pressure, the dynamicpressure is obtained from TM5-1300 (1990) as shown inFigure 10. The variation of dynamic pressure on the pipecross section is assumed to vary according to the angleof incidence as shown in Figure 13. The pressure isassumed to vary according to the function: P(θ ) = Pmax

cos(θ ). This means that the drag pressure will bemaximum, Pmax, at the front of the pipe (at θ = zero),and vanishes on the sides of the pipe (at θ = ±90° ).

The integration of the pressure P(θ) over the pipesurface must equal the net drag force acting on the pipeprojected area as follows:

(6)

where Rc is the pipe diameter and , i.e.

Pmax is the dynamic pressure obtained from the TM5-1300report (1990) multiplied by the drag coefficient (CD).

The maximum dynamic pressure Pmax varies alongthe pipe height as shown in Figure 14 for the threecharge locations 0.5, 3 and 5 m, respectively.

For D = 0.5 m, the blast wave reaches the barrier wallbefore the ground. This type of blast is called free-airblast. On the other hand, for D = 3.0 and 5.0 m, the blastwave reaches the ground before the barrier wall, And inthis case, the ground reflection effect should beconsidered together with the incident wave forming aplane shock wave (mach stem). This type of blast is

P C uDmax =1

22ρ

P R d R C uc c D( ) ( )θ θ ρθ π

θ π

==−

=

∫ 21

22

2

2

called the air-blast. The plane shock wave extends fromthe ground up to the so-called triple point. The blastpressure above the triple point will be free-air blast. Thetriple point height can be determined from the TM5-1300report (1990). For D = 3.0 m and 5 m, the triple pointheight was found to be 0.26 m and 1 m, respectively. Thismeans that the pipes of the barrier wall will not beaffected at all by this plane wave for D = 3.0 m, while itwill be significantl;y affected for D = 5 m where the lowerpart of the wall barrier will experience relatively higherpressure than the upper part (Figure 14).

The pressure-time history, as shown in Figure 15, isapproximated by an empirical exponential expressionfrom Kinney et al. (1985):

(7)

where α is the wave form parameter and td is the durationtime for the positive phase. The time t is measured fromthe arrival time ta. The wave form parameter α isobtained from tabulated data (Kinney et al. 1985), as afunction of the peak pressure Pmax.

As a summary, the following assumptions areconsidered in the current study:

• Only the drag pressure is applied to the GFRPpipes;

• The negative phase pressure (suction phase) isneglected;

• The ground reflections are neglected for shortdistances ( D = 0.5 and 3.0 m) and consideredfor far distances ( D = 5.0 m);

P t Pt

te

d

t

td( ) max= −

−1

α

106

105

104

103

102

101

102 103 104 105

Incident pressure (KPa)

Dyn

amic

pre

ssur

e (K

Pa)

Figure 13. Relation between free-field (incident) pressure and

dynamic pressure (adopted from TM5-1300 1990)

Cylinder

Rc

Pmax

4

2

00

−2

−2

−4

−4 42

P θ( )

θ



Figure 15. Variation of dynamic pressure along the pipe height

3

2.5

2

1.5

1

0.5

Hei

ght (

m)

1 100Pressure (kPa)

(a) D = 0.5 m

10000 1000000

3

2.5

2

1.5

1

0.5

Hei

ght (

m)

1 100Pressure (kPa)

(b) D = 3.0 m

10000 1000000

3

2.5

2

1.5

1

0.5

Hei

ght (

m)

1 100Pressure (kPa)

Triple point

hight

(c) D = 5.0 m

10000 1000000

140

120Pmax100

80

60

40

20

0 1 2 3 4 5Time (msec)

Pre

ssur

e (k

Pa)

t = ta td

06 7 8 9 10

Figure 16. Pressure history at the pipe mid-height for D = 3.0 m

• The secondary mutual reflections between thepipes are neglected;

• There are no fragments due to the blast;• The drag pressure decay is similar to the free-

field pressure exponential decay;• A factor of 25% is added to the pressure to

account for any neglected or secondary effects.

4.8. Estimation of Experimental Drag Pressure

As discussed above, the nature of the blast pressureacting on the GFRP pipes is closer to the drag pressure.However, the pressure gauges mounted on the pipesduring the experiment were of the type that measurethe reflected pressures (Asprone et al. 2007, 2008).Therefore, the drag pressure will be estimated fromthe experimentally recorded reflected pressure using

TM5-1300 report (1990). Firstly, the experimentalstatic pressure is obtained from the experimental reflectedpressure assuming free-air blast. Then, the experimentaldynamic pressure is obtained from the experimental staticpressure and eventually, the experimental dynamicpressure is multiplied by the drag coefficient to obtainestimation for the experimental drag pressure.

4.9. Analytical Results

In this section, the analytical results are displayed and compared to the experimental ones to validate theAEM and its accuracy in the prediction of the responseof the porous GFRP barrier walls subjected to blastloading.

4.9.1. Blast pressure contours

Figure 17 shows the analytical distribution of the blast pressure on the pipes at different time intervals.The analytical peak pressure was 52.73, 0.129 and 0.126 N/mm2, for 0.5, 3.0 and 5.0 m standoff distances,respectively. The calculated pressure is compared to themeasured one first. Table 2 shows a comparisonbetween the experimentally measured reflectedpressure, the calculated reflected pressure, the applieddrag pressure and the estimated experimental dragpressure. As seen in Table 2, the calculated reflectedpressure is quite close to the measured one. However,the estimated experimental and theoretical dragpressures are closer for the near distance, D = 0.5, thanfor the other two distances.



48343.4 KPa

52733.8 KPa

44815.4 KPa

41297.2 KPa

38661 KPa

35142.8 KPa

31624.6 KPa

28106.4 KPa

24578.4 KPa

21060.2 KPa

17542 KPa

14023.8 KPa

10505.6 KPa

6986.4 KPa

3466.2 KPa

118.7 KPa

129.6 KPa

110.1 KPa

101.

95.03 KPa

80.2 KPa

69.08 KPa

60.42 KPa

43.13 KPa

34.47 KPa

25.82 KPa

17.17 KPa

8.52 KPa

101.5 KPa

77.7 KPa

51.77 KPa

115.93 KPa

126.51 KPa

107.5 KPa

99.07 KPa

92.71 KPa

84.28KPa

75.83 KPa

67.39 KPa

58.95 KPa

50.52 KPa

42.07 KPa

33.63 KPa

25.19 KPa

16.75 KPa

8.31 KPa

(a-1) t = 0.11 msec (b-1) t = 2.89 msec (c-1) t = 6.9 msec

48343.4 KPa

44815.4 KPa

41297.2 KPa

38661 KPa

35142.8 KPa

31624.6 KPa

28106.4 KPa

21060.2 KPa

17542 KPa

14023.8 KPa

10505.6 KPa

6986.4 KPa

3466.2 KPa

52733.8 KPa

24578.4 KPa

118.7 KPa

129.6 KPa

110.1 KPa

101.5 KPa

95.

80.2 KPa

77.7 KPa

69.08 KPa

60.42 KPa

51.77 KPa

43.13 KPa

25.82 KPa

17.17 KPa

8.52 KPa

95.03 KPa

34.47 KPa

115.93 KPa

126.51 KPa

107.5 KPa

99.07 KPa

92.71 KPa

84.28 KPa

75.83 KPa

67.39 KPa

58.95 KPa

50.52 KPa

42.07 KPa

33.63 KPa

25.19 KPa

16.75 KPa

8.31 KPa


48343.4 KPa

52733.8 KPa

44815.4 KPa

41297.2 KPa

38661 KPa

35142.8 KPa

31624.3 KPa

28106.4 KPa

24578.4 KPa

21060.2 KPa

17542 KPa

14023.8 KPa

10505.6 KPa

6986.4 KPa

3466.2 KPa

118.7 KPa

129.6 KPa

110.1 KPa

101.5 KPa

95.03 KPa

80.2 KPa

77.7 KPa

6

60.42 KPa

51.77 KPa

43.13 KPa

3

17.17KPa

8.52 KPa

69.08 KPa

34.47 KPa

25.82 KPa

115.93 KPa

126.51 KPa

107.5 KPa

99.07 KPa

92.71 KPa

84.28 KPa

75.83 KPa

67

58.95 KPa

5

42.07 KPa

33.63 KPa

25.19 KPa

16

8.31 KPa

67.39 KPa

50.52 KPa

16.75 KPa


(a) D = 0.5 m (b) D = 3 m (c) D = 5 m

Figure 17. Blast pressure contours, in kg/mm2, at different time intervals

4.9.2. Wall deformations

Figure 18 shows the deformed shapes and the contoursof the peak lateral displacements of the pipes under thepressure loads resulting from 0.5, 3.0 and 5.0 mstandoff distances. The obtained peak displacement

was 1250, 85 and 32 mm for 0.5, 3.0 and 5.0 m standoffdistances, respectively. As observed in Figure 18, thedeformation profile of the different pipes is morehomogenous and harmonic for the longer standoffdistances than short ones.



Table 2. Calculated and measured pressure on GFRP walls

D = 0.5 m D = 3.0 m D = 5.0 m

Experimental reflected pressure (MPa) 68.9 0.69 0.22Calculated reflected pressure (MPa) 75.9 0.79 0.18Estimated experimental drag pressure (MPa) 50.1 0.09 0.05Drag Pressure (Applied) (MPa) 52.7 0.13 0.11

5.230e+0025.136e+002

4.757e+002

4.378e+002

4.000e+002

3.716e+002

3.337e+002

2.959e+002

2.580e+002

2.202e+002

1.823e+002

1.444e+002

1.066e+002

6.871e+001

3.085e+001

−7.006e+000

−4.487e+001

1.120e+0021.048e+002

9.058e+001

7.634e+001

6.209e+001

5.021e+001

3.675e+001

2.290e+001

8.652e+000

−2.827e+000

−1.628e+001

−3.053e+001

−4.478e+001

−5.903e+001

−7.328e+001

−8.753e+001

−1.018e+002

3.222e+0013.160e+001

2.912e+001

2.664e+001

2.416e+001

2.230e+001

1.982e+001

1.733e+001

1.485e+001

1.237e+001

9.890e+000

7.408e+000

4.927e+000

2.445e+000

−3.671e+002

−2.518e+000

−5.000e+000

(a) 0.5 m standoff distance (b) 3 m standoff distance

(c) 5 m standoff distance

Figure 18. Deformed shape and lateral displacement contours, in mm, at maximum deformations



4.9.3. Wall accelerations

Figure 19 shows the calculated and measured historiesof the acceleration of the top points of the middle pipes(except for the 0.5 m case as the experimental datawere not available). As seen, the AEM results showedacceptable results for the peak values. However, higherdamping is observed in the experiment. This highdamping is believed to be due to the lightness of thehollow pipes, which could be significantly affected by air friction after the duration of the main shock. Apeak acceleration of 130000, 2000, and 780 g wasobtained for the 0.5, 3.0 and 5.0 m standoff distances,respectively. Table 3 shows a comparison between theexperimental and analytical results where a goodagreement is observed.

4.9.4. Strain contours

Figure 20 shows the maximum strain contours for thespecimens. As can be seen, the maximum principal

strain reached 7%, 0.45% and 0.19% for the 0.5, 3,and 5 m standoff distances, respectively. Table 4 showsthe maximum strain computed by AEM in comparisonwith those measured in the experiment. As seen, theresults are in a good agreement for the three locationsalong a pipe: top, middle and bottom. The comparisonwas not possible for the 0.5 m standoff distance case as the experimental results were not available forthe strains.

4.9.5. Internal forces

Figure 21 shows the bending moment diagrams for the pipe due to the blast pressure loads at maximumstrains. These actions are calculated through integratingthe stresses in the springs at the sections perpendicularto the axis of the pipes. The maximum bending momentswere 8.4, 2.1 and 1.1 kN.m, while the maximum shearforces were 20.1, 4.0 and 2.3 kN for the 0.5, 3.0 and5.0 m standoff distances, respectively.

−1500−1000

−5000

5001000150020002500

0

0

0.01Acc

eler

atio

n (g

)

−1000−750−500−250

0250500750

1000

Acc

eler

atio

n (g

)

AEM Experiment

AEM Experiment

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Time (sec.)

(a) 3 m standoff distance

Time (sec.)

(b) 5 m standoff distance

Figure 19. Comparison of top point acceleration obtained analytically and experimentally

Table 3. Experimental and analytical peak acceleration

D = 3.0 m D = 5.0 m

Experiment Analysis Experiment Analysis

Peak acceleration (g) 1100 1935 700 780



7.213e−0027.092e−002

6.609e−002

6.127e−002

5.645e−002

5.283e−002

4.800e−002

4.318e−002

3.835e−002

3.353e−002

2.871e−002

2.388e−002

1.906e−002

1.423e−002

9.409e−003

4.584e−003

−2.402e−004

4.820e−0034.740e−003

4.418e−003

4.096e−003

3.775e−003

3.533e−003

3.212e−003

2.890e−003

2.568e−003

2.247e−003

1.925e−003

1.603e−003

1.282e−003

9.602e−004

6.385e−004

3.168e−004

−4.815e−006

(a) 0.5 m standoff distance (b) 3 m standoff distance


2.013e−003

1.979e−003

1.845e−003

1.710e−003

1.576e−003

1.475e−003

1.341e−003

1.207e−003

1.072e−003

9.381e−004

6.695e−004

5.352e−004

4.009e−004

2.666e−004

1.323e−004

−2.011e−006

Figure 20. Maximum calculated principal strain contours

Table 4. Experimental and analytical maximum strains on GFRP pipes

D = 3.0 m D = 5.0 m

Microstrain at location Experiment Analysis Experiment Analysis

Bottom 3,347 4,500 1,447 1,900Middle 1,834 1,480 802 700Top 2,340 1,600 1,091 800



(a) 0.5 m standoff distance

−685 kg.m

−1038 kg.m

−502 kg.m

564 kg.m

1200 kg.m 570 kg.m B.M at t = 0.0058 sec.

B.M. envelope

(b) 3 m standoff distance

−289.739624

−180 kg.m

−180.228943

BM at t = 0.02 sec

213 kg.m

249 kg.m

213 kg.m

BM envelopes


−78 Kg.m

−78

−83

B.M. at t = 0.024 sec.

105 Kg.m

114 Kg.m

105 Kg.m

B.M. envelope

Figure 21. Maximum bending moments due to blast loads

4.9.6. Pipes cracking, separation and failure

Figure 22 shows the crack propagation, elementsseparation and failure in the pipes for the 0.5 mstandoff distance. The pipe springs are cracked whentheir strain reaches the cracking strength of GFRP.Once the elements are fully cracked, they are separatedcausing instability of pipes, which eventually lead topipes collapse. The final fracture pattern is comparedto the experiments in Figure 23, where a goodagreement is achieved.

5. MINIMUM SAFE STANDOFF DISTANCEFOR THE BARRIER

The AEM was used to obtain the minimum safestandoff distance for the proposed barriers. For thatpurpose, a parametric study has been carried out, inwhich, the standoff distance was a variable. It wasobserved that the standoff distance of 1.4 m was the minimum safe one, below which, the barrierexperienced considerable damage, as shown in Figure 24.



Matrixsprings

0.0 sec

0.017 sec

0.062 sec

0.067 sec

Springscracking

Elementsseparation

Elementsfalling

Figure 22. Cracking, separation and failure of GFRP pipes (D = 0.5 m)

6. CONCLUSIONSThis paper focuses on structural analysis conducted viathe applied element method (AEM), to reproduce blasttests performed on a porous GFRP protection barrier. TheAEM approach appears to be very feasible in analyzing

rapid and intense load conditions as those induced byblast loads, since it permits to reproduce correctly thelarge deformations and intense stress levels experiencedin the structural elements under such conditions. AEMcan also simulate the material fracture and the potential



(a) Experiment (b) Analysis

Figure 23. Final fracture of GFRP for D = 0.5 m

Damaged Undamaged

Minimum safestandoff distance

Standoff distance

0.6 m 1.0 m 1.25 m 1.35 m 1.4 m

Figure 24. Minimum safe standoff distance

separation and collision of elements during highlydynamic events.

In the conducted numerical analysis, AEM showed tobe an effective tool in the prediction of the response ofthe porous GFRP barrier walls subjected to blastloading. Good predictions could be obtained for theaccelerations and strains in the walls; however, a higherdamping was observed in the experiments, which couldbe attributed to the lightness of the barrier walls.

This analysis allows calibrating a reliable AEMstructural model of the barrier, which can be employedto conduct supplementary design optimization and toreproduce the structural behavior of the barrier underdifferent blast loads scenarios.

Based on the AEM analysis, the minimum safestandoff distance for the proposed barriers was found tobe 1.4 m. A considerable damage of the barriers isobserved for standoff distances below this value.

ACKNOWLEDGMENTS The authors gratefully acknowledge EuropeanCommission − Directorate General Justice, Freedom andSecurity for the financial support through EPCIP 2006.

REFERENCESAgbossou, A., Mele, P. and Alberola, N. (1994). “Strain rate and

coupling agent effects in discontinuous glass fiber reinforced



polypropylene matrix”, Journal of Composite Materials, Vol. 28,

No. 9, pp. 821–836.

Asprone, D., Prota, A., Parretti, R. and Nanni, A. (2007). “Protection

of airport facilities through radio frequency transparent fences: the

SAS project”, In CD-Proceedings of Performance, Protection &

Strengthening of Structures under Extreme Loading, PROTECT

2007, Whistler, Canada, August, Paper ITA02.

Asprone, D., Prota, A., Parretti, R. and Nanni, A. (2008). “GFRP

radar-transparent barriers to protect airport infrastructures: the

SAS project”, Fourth International Conference on FRP

Composites in Civil Engineering (CICE2008), Zurich,

Switzerland, July, Paper ID 9.D.2.

Applied Science International, LLc. www.appliedscienceint.com.

Bathe, K. (1982). Solution of Equilibrium Equations in Dynamic

Analysis, Prentice Hall, Englewoods Cliffs, N.J.

Chopra, A. (1995). Dynamics of Structures: Theory and

Applications to Earthquake Engineering, Prentice Hall,

Englewoods Cliffs, N.J.

Deribas, A. and Simonov, V. (1999). “Detonation properties of

ammonium nitrate”, Combustion, Explosion, and Shock Waves,

Vol. 35, No. 2, pp. 203–205.

TM5-855-1 (1985). Fundamentals of Protective Design for

Conventional Weapons, Departments of the Army, the Navy and

the Air Force.

TM5-1300 (1990). Structures to Resist the Effects of Accidental

Explosions, Departments of the Army, the Navy and the

Air Force.

Forrest, E. and Edward, W. (1953). Drag of Circular Cylinders for a

Wide Range of Reynolds Numbers and Mach Numbers, Technical

note 2960, Ames Aeronautical Laboratory, National Advisory

Committee for Aeronautics.

Hoorelbeke, P., Izatt, C., Bakke, J., Renoult, J. and Brewerton, R.

(2006). “Vapor cloud explosion analysis of onshore petrochemical

facilities”, 7th Professional Development Conference &

Exhibition, Kingdom of Bahrain, www.gexcon.com/index.php?

src=welcome/publications.html.

Kinney, G. and Graham, K. (1985). Explosive Shocks in Air,

Springer-Verlag.

Maekawa, K. and Okamura, H. (1983). “The deformational behavior

and constitutive equation of concrete using the elasto-plastic and

fracture model”, Journal of the Faculty of Engineering, The

University of Tokyo (B), Vol. 37, No. 2, pp. 253–328.

Meguro, K. and Tagel-Din, H. (2001). “Applied element

simulation of RC structures under cyclic loading”, Journal

of Structural Engineering, ASCE, Vol. 127, No. 11,

pp. 1295–1305.

Meguro, K. and Tagel-Din, H. (2002). “AEM used for large

displacement structure analysis”, Journal of Natural Disaster

Science, Vol. 24, No. 1, pp. 25–34.

Naghipour, M., Taheri, F. and Zou, G. (2005). “Evaluation of

vibration damping of glass-reinforced-polymer-reinforced glulam

composite beams”, Journal of Structural Engineering, ASCE,

Vol. 131, No. 7, pp. 1044–1050.

Park, H., Suk, C. and Kim, S. (2009). “Collapse modeling of model

RC structure using applied element method”, Tunnel &

Underground Space, Journal of Korean Society for Rock

Mechanics, Vol. 19, No. 1, pp. 43–51.

Sasani, M. and Sagiroglu, S. (2008). “Progressive collapse resistance

of Hotel San Diego”, Journal of Structural Engineering, ASCE,

Vol. 134, No. 3, pp. 478–488.

Sasani, M. (2008). “Response of a reinforced concrete infilled-frame

structure to removal of two adjacent columns”, Engineering

Structures, Vol. 30, No. 9, pp. 2478–2491.

Tagel-Din, H. (2002). “Collision of structures during earthquakes”,

Proceedings of the 12th European Conference on Earthquake

Engineering, London, UK.

Tagel-Din, H. and Meguro, K. (2000). “Applied element method for

dynamic large deformation analysis of structures”, Structural

Engineering and Earthquake Engineering, JSCE, Vol. 17, No. 2,

pp. 215–224.

Tagel-Din, H. and Rahman, N. (2004). “Extreme loading: breaks

through finite element barriers”, Structural Engineer, Vol. 5, No. 6,

pp. 32–34.

Wibowo, H., Reshotkina, S. and Lau, D. (2009). “Modelling

progressive collapse of RC bridges during earthquakes”, CSCE

Annual General Conference, pp. 1–11.

applied element method analysis of porous gfrp barrier

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