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, and Research 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 field of study and application for structural engineering as it addresses extreme loading conditions on buildings and the civil infrastructure. In fact, large deformations and material characteristics of elements and structures different from those exhibited under static loading conditions are important phenomena to be accounted for in numerical analysis. The present paper describes the results of detailed numerical analyses simulating blast tests conducted on a porous (i.e. discontinuous) glass fiber reinforced polymer (GFRP) barrier aimed at the conception, validation and deployment of a protection system for airport infrastructures against malicious disruptions. The numerical analyses herein presented were conducted employing the applied element method (AEM). This method adopts a discrete crack approach that allows auto cracking, separation and collision of different elements in a dynamic scheme, where fully nonlinear path-dependant constitutive material models are adopted. A comparison with experimental results is presented and the prediction capabilities of the software are demonstrated.

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

1. INTRODUCTION communities to design and/or assess protection systems Highly dynamic loading conditions represent nowadays a to reduce the vulnerability of critical infrastructures fundamental challenge in structural engineering as critical (e.g., shelters and barriers). With this objective, a buildings and infrastructures need to resist extreme loads research program named Security of Airport Structures events that can occur during their lifetime as a result of (SAS) was undertaken and completed in 2007 by a natural and man-made hazards (e.g., explosions, consortium of European entities led by the research collisions, and severe earthquakes). Under such load center AMRA (http://www.amracenter.com), in order regimes, investigations on structural performances cannot to (a) design and validate a protection barrier intended be conducted without considering aspects that are to deter malicious actions against critical airport typically neglected under static loading conditions infrastructures carried out by eco-terrorists, and (b) (e.g., large displacements, material characteristics under mitigate the effects of blast events on protected targets. high strain rates, and fluid dynamics). As a corollary, The material of choice for this barrier system became there is a growing interest in the scientific and practicing glass fiber reinforced polymer (GFRP). This was because

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

Advances in Structural Engineering Vol. 13 No. 1 2010 1 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast of the necessity of maintaining radio-transparency barrier system). Such base consists of precast elements without interference with airport radio-communications. with male-female type connections for interlock that, A porous GFRP barrier was designed and its once assembled together, form a continuous above- components subjected to mechanical and electromagnetic ground foundation. The base elements are reinforced tests. Furthermore, a blast test campaign was with GFRP bars to eliminate the presence of steel for performed on full assemblies in order to validate the double purpose of enhancing long-term durability the capability of the system in withstanding blast (no corrosion) and providing magnetic transparency. loads and protecting a target placed beyond it by The height of each GFRP pipe above the foundation is reducing the effects of the incident blast shock wave. 2.5 m. The clear distance between two adjacent pipes Such tests were then simulated through numerical is 65 mm. The cross section of each GFRP pipe has a analyses conducted employing software based on the wall thickness of 5.5 mm and an external diameter of applied element method (AEM) (Tagel-Din 2002; 85 mm. As common for any GFRP pultruded section, Tagel-Din and Meguro 2000; Tegel-Din and Rahman the pipe wall is composed of a core made of continuous 2004; Meguro and Tagel-Din 2001; Meguro and unidirectional glass fiber strands and two external Tagel-Din 2002). This paper presents the results of layers made of glass fiber mats. The fibers are these analyses, providing a comparison with the impregnated with a polyester resin to make it a experimental results. composite. Details about the geometry of the barrier and its installation are presented in Asprone et al. (2007, 2008). 2. GFRP BARRIER SYSTEM The barrier system consists of GFRP pipes mounted vertically over a modular reinforced concrete base that 3. BLAST TESTS is 0.5 m high (see Figure 1 that depicts a prototype of the Three blast tests were conducted on three separate barrier prototypes of identical size. Each prototype consisted of 13 pipes composing a 1.95 m long structure. For each test, 5 kg of quarry TNT were detonated at different distances D from the barrier but at a constant height of 1.5 m above the ground (Figure 2); in particular, D was selected to be 5, 3 and 0.5 m, respectively. Each test specimen was instrumented with strain gauges located along the central pipe, accelerometers at different positions along the pipes and the concrete base, and pressure gauges placed on the pipes and around the barrier in order to acquire a complete pressure field during the blast event. Details about the tests and the employed instrumentation are available in Asprone et al. (2007, 2008).

Blast barrier

Bomb 5 Kg 3 m

1.5 m

D D=5.0, 3.0 and 0.5 m Figure 1. Prototype of barrier Figure 2. Blast barrier experiment set-up

2 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

4. NUMERICAL ANALYSES VIA AEM SIMULATION Detailed numerical analysis has been carried out for the barriers using the Extreme Loading for Structures (ELS) software developed by the Applied Science International (www.appliedscienceint.com). The ELS software provides a fully nonlinear dynamic analysis based on the Applied Element Method (AEM) (Tagel- Din 2002; Tagel-Din and Meguro 2000; Tagel-Din and Rahman 2004; Meguro and Tagel-Din 2001; Meguro and Tagel-Din 2002; Park et al. 2009; Sasani 2008; Sasani and Sagiroglu 2008; Wibowo et. al. 2009).

4.1. Introduction to AEM Simulations The applied element method (AEM) is a modeling method adopting the concept of discrete cracking. In AEM, the structure is modeled as an assembly of relatively small elements as shown in Figure 3(a). The elements are connected together along their surfaces through a set of normal and shear springs. The two elements shown in Figure 3(b) are assumed to be (a) Element generation for AEM connected by normal and shear springs located at the contact points, which are distributed on the element faces. Normal and shear springs are responsible for transfer of normal and shear stresses, respectively, from one element to the other. Springs generate stresses and deformations a of a certain volume as shown in Figure 3(b). Each single element has six degrees of freedom: b three for translations and three for rotations. Relative Volume represented by a normal spring and 2 translational or rotational displacement between two shear springs neighboring elements cause stresses in the springs a located at their common face as shown in Figure 4. (b) Spring distribution and area of influence of each pair of springs These connecting springs represent the state of stresses, strains and connectivity between elements. Two Figure 3. Modeling of structures in AEM neighboring elements can be totally separated once the springs connecting them rupture. Fully nonlinear path-dependant constitutive models are adopted in the AEM as shown in Figure 5. For concrete in compression, an elasto-plastic and fracture model is adopted (Maekawa and Okamura 1983). Normal Normal When concrete is subjected to tension, a linear stress- strain relationship is adopted until cracking of the concrete springs, where the stresses then drop to zero. GFRP is a brittle material in which linear stress-strain Shear x-z relationship is adopted up to failure. For more details Shear x-z Shear x-y about constitutive models, refer to Tagel-Din and Meguro (2000).

The concrete is assumed cracked when the principal z tensile stresses reach the cracking strength of concrete. Shear x-y Normal x If the cracking direction is parallel to the element faces, y the cracks extend in those directions. When the cracking Relative translations Relative rotations direction is inclined as shown in Figure 6, the problem Figure 4. Stresses in springs due to relative displacement

Advances in Structural Engineering Vol. 13 No. 1 2010 3 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

σ Stress ing σ ad c o L Compression GFRP Normal Reloading ε Normal Unloading E ε Tension σ p Strain t τ Concrete GFRP bars τ Shear

γ Shear G γ G

Figure 5. Constitutive models in the applied element method

Added springs at fracture plan

Splitting elements Redistributing stresses at element Shear spring in y Shear spring in x Normal spring edge (a) Corner-to-face or corner-to-ground contact Figure 6. Different techniques for the post-cracking modeling

Contact shear becomes numerically complicated. Two solutions would spring Contact be available: the first one is to break the element down normal spring into two elements, while the other is to redistribute the unbalanced stresses on the element faces. The former solution is rather complicated, but more accurate for shear stress transfer, while the latter is simpler, but less Contact shear accurate. For simplicity, the second solution is adopted spring here given that the accuracy can be greatly improved by (b) Edge-to-edge contact reducing the size of the elements. Figure 7. Different types of elements contact The AEM is based on a simple stiffness method formulation, in which an overall stiffness matrix is formulated and nonlinearly solved for the structural 4.2. AEM Versus Other Numerical Methods displacements. The solution for equilibrium equations is In spite of the robustness and the stability of the finite an implicit one that adopts a dynamic step-by-step element method (FEM), its ability for simulating integration, as Newmark-beta time integration progressive collapse is questionable. The possibility of procedure (Bathe 1982 and Chopra 1995). complete separation of elements is limited and very time One of the main valuable features in AEM is the consuming. On the other hand, the AEM is capable of automatic detection of element separation and contact. efficiently simulating the progressive collapse of Two neighboring elements can separate from each structures. Figure 8 schematically shows the applicable other if the matrix springs connecting them rupture. analysis domain of both the AEM and FEM. Elements may automatically separate, re-contact again The discrete element method (DEM) has been proved or contact other elements. As illustrated in Figure 7, to be a successful method for simulating a wide variety there are several types of contacts: element corner- of granular flow situations. In the DEM, The material is to-element face contact, element edge-to-element edge assumed to consist of separate, discrete particles that contact and element corner-to-ground contact. For may have different shapes and properties. Simulation more details refer to the Applied Science International is started by putting all particles in a certain position (www.appliedscienceint.com). and giving them an initial velocity. Then the forces

4 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

restrained. The pipes are not modeled as embedded Complexity, accuracy, time and qualifications of user inside the footing. Instead, they are assumed to be totally Progressive collapse analysis compatible (constrained) with the footing at their intersection on the upper face of the footing. This Engineering judgement, uncertainty and construction cost assumption is thought to be acceptable since the experiments showed no pullout of the pipes from FEM the footing. The properties of concrete and GFRP are Simple solutions Simplified SWGap Advanced SW summarized in Table. 1. Not verified AEM A mesh sensitivity analysis has been carried out to

Highly nonlinear solutions obtain the largest size of elements that do not affect the solution accuracy. The sensitivity analysis performed to a single elastic tube with a lateral point load showed a good convergence tendency as shown in Figure 10. Figure 8. AEM versus FEM Based on that curve, the number of elements selected was 750 per tube (25 divisions in radial direction and which act on each particle are computed from the initial 30 ones in vertical direction) data and the relevant physical laws. An integration method is employed to compute the change in the 4.4. Material Properties Assumptions position and the velocity of each particle during a certain Concrete had a compressive strength of 30 MPa with time step from Newoton’s laws of motion. Then, the new an initial modulus of elasticity of 24 GPa. As for the positions are used to compute the forces during the next material properties of the GFRP pipe elements, a static step, and this loop is repeated until the simulation ends. mechanical test campaign was conducted on such Dislike the AEM, DEM is not a stiffness-based method. elements. Such tests consisted of 4-point bending tests The solution depends on force transmission from a conducted on pipe elements and direct tension tests particle to another, and therefore, the DEM is not a performed on coupons. The GFRP was found to have a practical solution for large-size problems. The maximum tensile strength of 648 MPa with an overall Young’s number of particles, and duration of a virtual simulation modulus, evaluated from flexural stiffness exhibited is limited by computational power. Another obstacle in during four points bending tests, of 40 GPa. Furthermore, the DEM is that simulations are generally limited to the following assumptions were considered: 3 spherical particles due to the increase in cost of ¥ The specific gravity of the GFRP is 1900 kg/m ; computation with increasing complexity of geometry. ¥ The vibration period T can be determined from the Eigen modes of the barrier and was found to 4.3. AEM Model be 0.08 second for the first vibration mode; Figure 9 shows the AEM model used in the current ¥ The damping ratio ε can be reasonably assumed study, where the bottom of the RC footing is totally as 2.5% (Naghipour et al. 2005);

0.065 m

Full compatibility between the pipe and the footing 0.50 m 2.50 m

1.95 m

Fixed boundary

Figure 9. AEM model for barrier wall

Advances in Structural Engineering Vol. 13 No. 1 2010 5 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

Table 1. Material properties Start Property GFRP Concrete Elastic Modulus (MPa) 40789 24607 Shear Modulus (MPa) 16316 9843 Perform preliminary analysis = Tensile Strength (MPa) 648 3 dynamic increase factor DIF 1.0 Compressive Strength (MPa) 648 30

Calculate strain rate for GFRP

217

216 Calculate dynamic increase factor DIF1 215 Deflection 214 P = 100 Kg 213 DIF = DIF1 NY DIF 1 = DIF END 212 Perform analysis

Deflection (mm) 211

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

209

208 From this equation the DIF was derived as: 0 200 400 600 800 1000 1200 1400 No. of elements DIF = 015. ε o 125 (4) Figure 10. Mesh sensitivity analysis The procedure for calculating the effect of the strain ¥ The natural frequency ω is calculated as: rate is shown in Figure 11. As illustrated, a preliminary analysis is performed first without considering the ωπ==220087//..T π =7762 Hz (1) strain-rate effect. The strain-rates are calculated for different elements, and hence the dynamic increase ¥ The external damping ratio is computed based factors are calculated. Performing the analysis again, on the following expression (Chopra 1995): refined strain-rates are calculated and new dynamic increase factors are calculated and compared to the 220εω=×...025 × 77 762 = 7 77 (2) previous ones. Once the dynamic increase factors are not much changed, the analysis is accepted to be the final one. Figure 12 shows the strain-rate calculated for the 4.5. Strain-Rate Effect springs at the bottom of the middle pipe for D = 0.5 m and The strain rate effect is believed to be influencing the the corresponding DIF, where a maximum DIF of about behavior of GFRP pipes more than the concrete footing 10% was obtained. As for the 3 and 5 m standoff in the current study since the concrete footing is distances, the DIF was too small and was neglected. relatively huge and most of the deformations are localized in the GFRP pipes. Therefore, only the strain 4.6. Equivalent Charge rate effect on the GFRP is considered. At high strain The charge used in the experiment consists of 60% rates, the apparent strength of GRRP may increase. The ammonia nitrate and 40% TNT with a total weight of dynamic increase factor (DIF) is the ratio of the 5 kg. The equivalent TNT weight for this mixture is 4 kg, dynamic strength to static one. This factor is normally Asprone et al. (2007, 2008). This can be calculated reported as function of strain rate. In this study, the DIF from published equations see e.g. Deribas et al. (1999). developed by Agbossou et al. (1994) for GFRP matrix in tension is followed. Agbossou et al. (1994) developed 4.7. Blast Pressure Calculations the following equation for dynamic tensile strength for In this section, the calculations of the blast pressure medium interfacial shear strength coupling agents: acting on the barrier wall pipes are explained and the fMPa()=+125 0 . 15ε o (3) different assumptions are discussed noting that in AEM, t the calculated blast pressure history is applied to each where εο is the strain rate in sec−1. element.

6 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

100

50

0 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 Strain rate (1/sec.) −50 Time (sec.) (a) Strain rate history

1.15

1.10 DIF 1.05

1.00 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 Time (sec.) (b) DIF for tensile strength

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

The blast action results in both blast and drag applies to open structures, where the loads are mainly pressures varying with time and location along the due to drag pressure. loaded structure. The dynamic response of the loaded The GFRP pipes of the barrier under investigation are structure depends on the resultant forces due to these assumed to be a drag-type open structure (i.e., the blast pressures. Knowing the charge weight and the details of loads will be only due to the drag pressure of the blast the surrounding structure, the blast pressure loads are wind). The blast wind from an explosion exerts forces usually obtained from design charts, such as that of the that result from the pressure drop occurring behind the Tri-Service Reports TM5-855-1 and TM5-1300 (1985 structural elements. The pressure drop, Pd, which and 1990). Those design charts are calibrated for TNT accounts for the drag force per unit of the projected area, explosive. Other charge types should be converted to an is expressed as: equivalent TNT that releases the same energy. Structures are divided, according to their geometry, = 1 ρ 2 PCudD (5) into two categories: drag-type and diffraction-type 2 (Kinney et al. 1985). The drag-type structures are open ones with relatively thin members such as trusses. In where u is the blast wind speed, ρ is the air density and these structures, the front and rear faces of a member, CD is the drag coefficient. The blast wind speed u can be with respect to the blast wave, are very close and can be determined from the explosion pressure. The drag assumed to be in-phase, hence the loads are the results coefficient CD depends on the geometry of the object of only the drag force of the blast wind. The diffraction- and the blast wave speed. For cylindrical shapes at type structures are wide ones, like buildings, whose different speeds (Mach numbers), the drag coefficients their front and rear are not in phase and hence are taken 2.5, 1.3 and 1.2. for D = 0.5, 3.0 and 5.0 m, analyses should be carried out for each face separately respectively (Forrest et al. 1953). For the nearest and the acting load would be their resultant. Therefore, distance (D = 0.5) and to account for the high Mach > for these structures, both the blast and drag pressures number ( 8.0), the drag coefficient CD is considered are considered. Also, according to Hoorelbeke et al. equal to 2.0 (Forrest et al. 1953). To account for (2006), for relatively small structural elements (less secondary and neglected effects, a factor of safety is than 1 m in width and depth), the blast load on the rear usually superimposed (TM5-1300, 1990) and in the face is almost in-phase with, but in the opposite current study, a factor of 25% was considered to account direction to, the load on the front face (i.e., the for the additional assumptions. 1 ρ 2 pressures on the front and rear faces nearly equalize). Instead of calculating the dynamic pressure as 2 u , Therefore, the blast pressures apply a relatively low net one can obtain it directly from the charts of TM5-1300 load to the structural elements. This consideration (1990), where the free-field pressure (incident pressure)

Advances in Structural Engineering Vol. 13 No. 1 2010 7 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast can be determined as a function of the charge weight and distance. Using the free-field pressure, the dynamic Cylinder pressure is obtained from TM5-1300 (1990) as shown in 4 P (θ ) Figure 10. The variation of dynamic pressure on the pipe cross section is assumed to vary according to the angle 2 Rc of incidence as shown in Figure 13. The pressure is θ assumed to vary according to the function: P(θ) = Pmax 0 θ − − cos( ). This means that the drag pressure will be 4 2 0 2 4 Pmax maximum, Pmax, at the front of the pipe (at θ = zero), and vanishes on the sides of the pipe (at θ = ±90¡ ). −2 The integration of the pressure P(θ) over the pipe surface must equal the net drag force acting on the pipe −4 projected area as follows:

π θ= 2 Figure 14. Assumed variation of dynamic pressure along the pipe θθ= 1 ρ2 ∫ PRdRCu()ccD2 ( ) (6) cross-section π 2 θ=− 2

1 called the air-blast. The plane shock wave extends from where Rc is the pipe diameter andPCu= ρ 2 , i.e. max 2 D the ground up to the so-called triple point. The blast Pmax is the dynamic pressure obtained from the TM5-1300 pressure above the triple point will be free-air blast. The report (1990) multiplied by the drag coefficient (C ). triple point height can be determined from the TM5-1300 D = The maximum dynamic pressure Pmax varies along report (1990). For D 3.0 m and 5 m, the triple point the pipe height as shown in Figure 14 for the three height was found to be 0.26 m and 1 m, respectively. This charge locations 0.5, 3 and 5 m, respectively. means that the pipes of the barrier wall will not be For D = 0.5 m, the blast wave reaches the barrier wall affected at all by this plane wave for D = 3.0 m, while it before the ground. This type of blast is called free-air will be significantl;y affected for D = 5 m where the lower blast. On the other hand, for D = 3.0 and 5.0 m, the blast part of the wall barrier will experience relatively higher wave reaches the ground before the barrier wall, And in pressure than the upper part (Figure 14). this case, the ground reflection effect should be The pressure-time history, as shown in Figure 15, is considered together with the incident wave forming a approximated by an empirical exponential expression plane shock wave (mach stem). This type of blast is from Kinney et al. (1985):

 t  −α t =−td Pt() Pmax 1  e (7) 6   10 td

105 where α is the wave form parameter and td is the duration time for the positive phase. The time t is measured from 104 the arrival time ta. The wave form parameter α is obtained from tabulated data (Kinney et al. 1985), as a 103 function of the peak pressure Pmax. As a summary, the following assumptions are

2 considered in the current study:

Dynamic pressure (KPa) 10 ¥ Only the drag pressure is applied to the GFRP pipes; 101 ¥ The negative phase pressure (suction phase) is 102 103 104 105 neglected; Incident pressure (KPa) ¥ The ground reflections are neglected for short Figure 13. Relation between free-field (incident) pressure and distances ( D = 0.5 and 3.0 m) and considered dynamic pressure (adopted from TM5-1300 1990) for far distances ( D = 5.0 m);

8 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

3 3 3

2.5 2.5 2.5

2 2 2

Height (m) 1.5 Height (m) 1.5 Height (m) 1.5

Triple point 1 1 1 hight

0.5 0.5 0.5 1 100 10000 1000000 1 100 10000 1000000 1 100 10000 1000000 Pressure (kPa) Pressure (kPa) Pressure (kPa) (a) D = 0.5 m (b) D = 3.0 m (c) D = 5.0 m

Figure 15. Variation of dynamic pressure along the pipe height

140 TM5-1300 report (1990). Firstly, the experimental 120 static pressure is obtained from the experimental reflected P pressure assuming free-air blast. Then, the experimental 100 max dynamic pressure is obtained from the experimental static 80 pressure and eventually, the experimental dynamic 60 pressure is multiplied by the drag coefficient to obtain

Pressure (kPa) 40 estimation for the experimental drag pressure. 20 0 4.9. Analytical Results 0123456 78910 In this section, the analytical results are displayed = Time (msec) t ta td and compared to the experimental ones to validate the AEM and its accuracy in the prediction of the response Figure 16. Pressure history at the pipe mid-height for D = 3.0 m of the porous GFRP barrier walls subjected to blast loading. ¥ The secondary mutual reflections between the pipes are neglected; 4.9.1. Blast pressure contours ¥ There are no fragments due to the blast; Figure 17 shows the analytical distribution of the ¥ The drag pressure decay is similar to the free- blast pressure on the pipes at different time intervals. field pressure exponential decay; The analytical peak pressure was 52.73, 0.129 and ¥A factor of 25% is added to the pressure to 0.126 N/mm2, for 0.5, 3.0 and 5.0 m standoff distances, account for any neglected or secondary effects. respectively. The calculated pressure is compared to the measured one first. Table 2 shows a comparison 4.8. Estimation of Experimental Drag Pressure between the experimentally measured reflected As discussed above, the nature of the blast pressure pressure, the calculated reflected pressure, the applied acting on the GFRP pipes is closer to the drag pressure. drag pressure and the estimated experimental drag However, the pressure gauges mounted on the pipes pressure. As seen in Table 2, the calculated reflected during the experiment were of the type that measure pressure is quite close to the measured one. However, the reflected pressures (Asprone et al. 2007, 2008). the estimated experimental and theoretical drag Therefore, the drag pressure will be estimated from pressures are closer for the near distance, D = 0.5, than the experimentally recorded reflected pressure using for the other two distances.

Advances in Structural Engineering Vol. 13 No. 1 2010 9 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

52733.8 KPa 126.51 KPa

129.6 KPa 115.93 KPa 48343.4 KPa

44815.4 KPa 118.7 KPa 107.5 KPa 99.07 KPa 41297.2 KPa 110.1 KPa 101.5101. KPa 92.71 KPa 38661 KPa 95.03 KPa 84.28KPa 35142.8 KPa 80.2 KPa 75.83 KPa 31624.6 KPa 77.7 KPa 67.39 KPa 28106.4 KPa 69.08 KPa 58.95 KPa 24578.4 KPa 60.42 KPa 21060.2 KPa 50.52 KPa 51.77 KPa 17542 KPa 42.07 KPa 43.13 KPa 14023.8 KPa 33.63 KPa 34.47 KPa 25.19 KPa 10505.6 KPa 25.82 KPa

6986.4 KPa 17.17 KPa 16.75 KPa 3466.2 KPa 8.52 KPa 8.31 KPa

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

126.51 KPa 52733.8 KPa

129.6 KPa 115.93 KPa 48343.4 KPa 107.5 KPa 118.7 KPa 44815.4 KPa 99.07 KPa 41297.2 KPa 110.1 KPa 101.5 KPa 92.71 KPa 38661 KPa 95.95.03 KPa 84.28 KPa 35142.8 KPa 80.2 KPa 75.83 KPa 31624.6 KPa 77.7 KPa 67.39 KPa 28106.4 KPa 69.08 KPa 58.95 KPa 24578.4 KPa 60.42 KPa 50.52 KPa 21060.2 KPa 51.77 KPa 42.07 KPa 17542 KPa 43.13 KPa 33.63 KPa 14023.8 KPa 34.47 KPa 25.19 KPa 10505.6 KPa 25.82 KPa

6986.4 KPa 17.17 KPa 16.75 KPa

3466.2 KPa 8.52 KPa 8.31 KPa

(a-2) t = 0.24 msec (b-2) t = 3.11 msec (c-2) t = 7.7 msec

126.51 KPa 52733.8 KPa

129.6 KPa 115.93 KPa 48343.4 KPa 118.7 KPa 107.5 KPa 44815.4 KPa 99.07 KPa 41297.2 KPa 110.1 KPa 101.5 KPa 92.71 KPa 38661 KPa 95.03 KPa 84.28 KPa 35142.8 KPa 80.2 KPa 75.83 KPa 31624.3 KPa 77.7 KPa 67.3967 KPa 28106.4 KPa 669.08 KPa 58.95 KPa 24578.4 KPa 60.42 KPa 21060.2 KPa 50.525 KPa 51.77 KPa 42.07 KPa 17542 KPa 43.13 KPa 33.63 KPa 14023.8 KPa 334.47 KPa

10505.6 KPa 25.82 KPa 25.19 KPa

6986.4 KPa 17.17KPa 16.7516 KPa

3466.2 KPa 8.52 KPa 8.31 KPa

(a-3) t = 0.37 msec (b-3) t = 3.6 msec (c-3) t = 9.4 msec

(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 was 1250, 85 and 32 mm for 0.5, 3.0 and 5.0 m standoff Figure 18 shows the deformed shapes and the contours distances, respectively. As observed in Figure 18, the of the peak lateral displacements of the pipes under the deformation profile of the different pipes is more pressure loads resulting from 0.5, 3.0 and 5.0 m homogenous and harmonic for the longer standoff standoff distances. The obtained peak displacement distances than short ones.

10 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

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

5.230e+002 1.120e+002 5.136e+002 1.048e+002

4.757e+002 9.058e+001

4.378e+002 7.634e+001

4.000e+002 6.209e+001

3.716e+002 5.021e+001

3.337e+002 3.675e+001

2.959e+002 2.290e+001

2.580e+002 8.652e+000

2.202e+002 −2.827e+000 + 1.823e 002 −1.628e+001 + 1.444e 002 −3.053e+001 + 1.066e 002 −4.478e+001 + 6.871e 001 −5.903e+001 + 3.085e 001 −7.328e+001 − + 7.006e 000 −8.753e+001 −4.487e+001 −1.018e+002 (a) 0.5 m standoff distance (b) 3 m standoff distance

3.222e+001 3.160e+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

(c) 5 m standoff distance

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

Advances in Structural Engineering Vol. 13 No. 1 2010 11 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

4.9.3. Wall accelerations strain reached 7%, 0.45% and 0.19% for the 0.5, 3, Figure 19 shows the calculated and measured histories and 5 m standoff distances, respectively. Table 4 shows of the acceleration of the top points of the middle pipes the maximum strain computed by AEM in comparison (except for the 0.5 m case as the experimental data with those measured in the experiment. As seen, the were not available). As seen, the AEM results showed results are in a good agreement for the three locations acceptable results for the peak values. However, higher along a pipe: top, middle and bottom. The comparison damping is observed in the experiment. This high was not possible for the 0.5 m standoff distance damping is believed to be due to the lightness of the case as the experimental results were not available for hollow pipes, which could be significantly affected the strains. by air friction after the duration of the main shock. A peak acceleration of 130000, 2000, and 780 g was 4.9.5. Internal forces obtained for the 0.5, 3.0 and 5.0 m standoff distances, Figure 21 shows the bending moment diagrams for respectively. Table 3 shows a comparison between the the pipe due to the blast pressure loads at maximum experimental and analytical results where a good strains. These actions are calculated through integrating agreement is observed. the stresses in the springs at the sections perpendicular to the axis of the pipes. The maximum bending moments 4.9.4. Strain contours were 8.4, 2.1 and 1.1 kN.m, while the maximum shear Figure 20 shows the maximum strain contours for the forces were 20.1, 4.0 and 2.3 kN for the 0.5, 3.0 and specimens. As can be seen, the maximum principal 5.0 m standoff distances, respectively.

2500 2000 AEM Experiment 1500 1000 500 0 −500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Acceleration (g) −1000 −1500 Time (sec.) (a) 3 m standoff distance

1000 750 AEM Experiment 500 250 0 −250 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −500 Acceleration (g) −750 −1000 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

12 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

7.213e−002 4.820e−003 7.092e−002 4.740e−003

6.609e−002 4.418e−003 − 6.127e−002 4.096e 003 − 5.645e−002 3.775e 003 3.533e−003 5.283e−002 3.212e−003 4.800e−002 2.890e−003 4.318e−002 2.568e−003 3.835e−002 2.247e−003 3.353e−002 1.925e−003 2.871e−002 1.603e−003 2.388e−002 1.282e−003 1.906e−002 9.602e−004 1.423e−002 6.385e−004 − 9.409e 003 3.168e−004

4.584e−003 −4.815e−006

−2.402e−004

(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 (c) 5 m standoff distance 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 1,900 Middle 1,834 1,480 802 700 Top 2,340 1,600 1,091 800

Advances in Structural Engineering Vol. 13 No. 1 2010 13 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

−685 kg.m B.M. envelope

BM envelopes

−1038 kg.m

−502 kg.m

−180.228943 −289.739624

−180 kg.m

564 kg.m 213 kg.m

BM at t = 0.02 sec 1200 kg.m 570 kg.m B.M at t = 0.0058 sec. 249 kg.m 213 kg.m

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

B.M. envelope

−78

−83

−78 Kg.m

105 Kg.m

114 Kg.m B.M. at t = 0.024 sec. 105 Kg.m (c) 5 m standoff distance

Figure 21. Maximum bending moments due to blast loads

4.9.6. Pipes cracking, separation and failure 5. MINIMUM SAFE STANDOFF DISTANCE Figure 22 shows the crack propagation, elements FOR THE BARRIER separation and failure in the pipes for the 0.5 m The AEM was used to obtain the minimum safe standoff distance. The pipe springs are cracked when standoff distance for the proposed barriers. For that their strain reaches the cracking strength of GFRP. purpose, a parametric study has been carried out, in Once the elements are fully cracked, they are separated which, the standoff distance was a variable. It was causing instability of pipes, which eventually lead to observed that the standoff distance of 1.4 m was pipes collapse. The final fracture pattern is compared the minimum safe one, below which, the barrier to the experiments in Figure 23, where a good experienced considerable damage, as shown in agreement is achieved. Figure 24.

14 Advances in Structural Engineering Vol. 13 No. 1 2010 D. Asprone, A. Nanni, H. Salem and H. Tagel-Din

Matrix springs

0.0 sec

Springs cracking 0.017 sec

Elements separation 0.062 sec

Elements falling 0.067 sec

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

6. CONCLUSIONS rapid and intense load conditions as those induced by This paper focuses on structural analysis conducted via blast loads, since it permits to reproduce correctly the the applied element method (AEM), to reproduce blast large deformations and intense stress levels experienced tests performed on a porous GFRP protection barrier. The in the structural elements under such conditions. AEM AEM approach appears to be very feasible in analyzing can also simulate the material fracture and the potential

Advances in Structural Engineering Vol. 13 No. 1 2010 15 Applied Element Method Analysis of Porous GFRP Barrier Subjected to Blast

(a) Experiment (b) Analysis

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

Damaged Undamaged

0.6 m 1.0 m 1.25 m 1.35 m 1.4 m

Standoff distance Minimum safe standoff distance

Figure 24. Minimum safe standoff distance separation and collision of elements during highly Based on the AEM analysis, the minimum safe dynamic events. standoff distance for the proposed barriers was found to In the conducted numerical analysis, AEM showed to be 1.4 m. A considerable damage of the barriers is be an effective tool in the prediction of the response of observed for standoff distances below this value. the porous GFRP barrier walls subjected to blast loading. Good predictions could be obtained for the ACKNOWLEDGMENTS accelerations and strains in the walls; however, a higher The authors gratefully acknowledge European damping was observed in the experiments, which could Commission − Directorate General Justice, Freedom and be attributed to the lightness of the barrier walls. Security for the financial support through EPCIP 2006. This analysis allows calibrating a reliable AEM structural model of the barrier, which can be employed to conduct supplementary design optimization and to REFERENCES reproduce the structural behavior of the barrier under Agbossou, A., Mele, P. and Alberola, N. (1994). “Strain rate and different blast loads scenarios. coupling agent effects in discontinuous glass fiber reinforced

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