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Experimental and numerical investigation of confined explosion in a blast chamber
Journal of Loss Prevention in the Process Industries xxx (2013) 1e14
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Experimental and numerical investigation of confined explosion in a blast chamber Chengqing Wu a, *, Matthew Lukaszewicz a, Ken Schebella b, Leonid Antanovskii b a b
School of Civil, Environmental and Mining Engineering, The University of Adelaide, SA 5005, Australia Weapons Systems Division, Defence Science and Technology Organisation, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 September 2011 Received in revised form 1 December 2012 Accepted 4 February 2013
An experimental blast program consisting of four tests was conducted in a blast chamber to investigate the effects of cylindrical charges on the peak reflected overpressure and impulse on the wall of the chamber. The charge mass varied from 0.095 kg to 0.2 kg and the standoff distance remained constant at 1.5 m and 1.3 m for the axial and radial directions, respectively. Eight pressure transducers were used in each test to measure the reflected overpressures on confined chamber walls at key locations. A high speed camera was used to record footage of each blast event. The test results indicated that UFC-3-34002 (Unified Facilities Criteria, 2008) gives a significantly lower prediction for the axially oriented cylindrical charge, and also underestimates the radially oriented cylinder. Another purpose of the blast program was to develop an experimental data set which would validate the AUTODYN model. This would enable the validated AUTODYN model to be used with confidence to generate the overpressure and impulse distribution on a structural element for varying parameters such as the charge shape and charge orientations. Based on the simulated results a new blast model for cylindrical charges has been proposed by considering blast loading on the same level as the charge across the longitudinal direction. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Blast testing Numerical simulation Charge shape effects Confined blasts
1. Introduction Protecting civilian infrastructure from the increasing threat of intentional explosive events has become a critical challenge for researchers today. Critical infrastructure, such as government buildings and power plants need to be carefully designed to resist blast loadings and ensure the safety of the occupants. Internal explosions may happen due to possible deliberate attacks in a subway station, or in a car park of a commercial building, or an accidental explosion inside ammunition storage or mining tunnels. Confined blast fields can be applied to explosions of a penetrated charge inside a military vehicle or a bunker. Therefore, it is of great significance to study blast wave propagation for reliable design of structures against such confined blast loadings should such explosions occur (Sauvan, Sochet, & Trelat, 2012; Shi, Li, & Hao, 2009). However, the problem of a confined explosion is less addressed at current guidelines such as UFC-3-340-02 (2008) (which replaced TM5-1300 in 2008) and ASCE (2007). UFC-3-340-02 considers the blast effects of bare spherical TNT explosives without taking charge shapes and orientations into consideration; and the peak reflected
* Corresponding author. E-mail address: [email protected] (C. Wu).
overpressure and impulse are also assumed to be uniformly distributed on the wall surface in these guidelines. Such simplification and assumption in the in modern standards for blastresistant design might not enable accurate predictions of confined blast loading required for a detailed analysis of dynamic response and damage of structures. Considerable published information including numerical and experimental studies exists for non spherical charges in external blast environments. Numerical studies together with experimental investigation on cylindrical charges in the previous studies indicated that the ratio (L/D) of the cylindrical charge has significant effect in the pressure field in the immediate vicinity of the charge: for large values of the ratio, most of the energy is focused in the radial direction whereas for small values of the ratio, most of the energy is focused in the axial direction (Anderson, Katselis, & Caputo, 2002; Katselis & Anderson, 2001; Wu, Fattori, Whittaker, & Oehlers, 2010; Zimmerman, Nguyen, & Hookham, 1999). A series of blast tests has been conducted using cylindrical charges in recent years and it was found that UFC-3-340-02 underestimated the measured peak reflected overpressures and impulse for the cylindrical charges with vertical axes but overestimated the peak reflected overpressures for both spherical charges and cylindrical charges with horizontal axes (Wu et al., 2010). Recently, more and more attention has been paid on the partially confined blast loading
0950-4230/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jlp.2013.02.001
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Fig. 1. Layout of DSTO blast chamber and pressure gauge locations.
since guidance is needed for engineers to design structural systems to withstand various acts of terrorism, especially to an explosion in an urban area in proximity to tall buildings in complex city geometries (Remennikov & Rose, 2005; Smith & Rose, 2006). However limited studies have been conducted for non spherical charges in confined environments. The blast effects inside an enclosure for a 1 lb charge placed at the centre of a rectangular bunker was investigated by Chan and Klein (1994) and multiple shock reflections of overpressure histories were found to continue at significant magnitudes for a long period of time. Other studies demonstrated (Baker, Cox, Westine, Kulesz, & Strehlow, 1983; Bangash & Bangash, 2006) that the first three peaks of overpressure histories might be used to represent the dynamic contact pressure after which the constant gas overpressure is assumed acting on the confined space walls. Recently an AUTODYN finite element model (Century Dynamics, 2003), which was validated using experimental data in a small scale experiment conducted by Zyskowski, Sochet, Mavrot, Bailly, and Renard (2004) was used to investigate the variation in reflected overpressure with location on the small box by changing the orientation of the charge, the charge weight, the charge shape (Hu et al., 2011). However, little information is found on experiment investigation of cylindrical charges inside a chamber on the effects of reflected overpressure and impulse (Dragos, Hu, Lukazewicz, & Ren, 2010). In this paper spherical charge and cylindrical charge with a variety of orientations were used throughout a blast program in a blast chamber. The charge mass with variation of 0.095e0.2 kg was
used in the blast program while the standoff distance kept constant at 1.5 m and 1.3 m for the axial and radial direction, respectively. The length to diameter ratio of the cylindrical charge was constant at 1:1. For the cylindrical charges, the axis was oriented horizontally, but eight orthogonal pressure gauges measured both the axial and radial directions in one blast. A high speed camera was used to record footage of each blast event and to provide insight into the fireball region. The experimentally measured overpressure and impulse distributions on the chamber walls were analyzed and compared to assess the impact of charge shape and orientation. The experimental results were compared with predictions made using the industry standard UFC-3-340-02. As limited experimental data was available from the blast test program, a finite element program AUTODYN was validated using the experimental results and the validated numerical model was then used to expand the scope of the experimental program and to conduct parametric studies on the changes in reflected overpressure and impulse on the confined chamber walls. Based on the simulated results a new simplified model was developed for estimation of overpressure and impulse from cylindrical charges on the confined chamber walls. 2. Confined blast tests An experimental blast program consisting of four tests were conducted in a DSTO (Defence Science and Technology Organisation, Australia) blast chamber. Since limited published information exists for non spherical charges in confined environments and most
Fig. 2. Photo of pressure gauge layout.
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Table 1 Summary of charge properties. Event no.
1
Charge mass (g) 95.3
2
140
3
142.6
4
200.5
Standoff distance (m)
Scaled distance (m/kg1/3)
Charge shape
Charge orientation
1.505 1.340 1.505 1.340 1.505 1.340 1.505 1.340
3.3 2.9 2.9 2.6 2.9 2.6 2.6 2.3
Cylindrical
Axial Radial NA NA Axial Radial Axial Radial
Spherical Cylindrical Cylindrical
Fig. 4. Detonation point of spherical charge.
warheads are cylindrical rather than spherical (Tham, 2009), investigation of blast waves from cylindrical charges in this blast program is of practical relevance.
2.1. Design of experiment The layout of the blast chamber is shown in Fig. 1. The tests were designed with the advantage of simplifying the geometry to rectangular for easier validation. This meant that the southern part of the chamber was inappropriate due to angles and windows in the roof and side walls. The best location for placing the charge was near the entrance in the eastern side of the chamber (see Fig. 1), since this was the closest representation of a rectangular room and would provide the largest number of shockwave reflections from the three walls, the floor and roof. However, it was not appropriate to place the charge in this area due to the door for the entrance, which was a weak point to detonation. The next best alternative was used to place the charge in the north western corner as shown in Fig. 1. The charge was placed at mid height of the chamber and approximately 1 m away from the surface to achieve charge shape effects. Due to the method of fixing the pressure gauges and the ventilation in this area, the distances from the surface were increased to approximately 1.5 m. The plates for the pressure gauges were attached to existing bolt holes to prevent complications of pressure gauge mounting as shown in Fig. 2. Since the existing bolts were not at mid height of the chamber, this prevented symmetry in the vertical direction. However, the plates were placed outside the perimeter of the ventilation at the top of the chamber. This was to prevent the metal grid and the rocks above from interfering with the shockwave reflections. Cylindrical charges were introduced to study the effect of charge shape since little research on cylindrical charge has been studied in a confined environment before. One spherical charge was used as a
reference to compare with the cylindrical shape and with UFC-3340-02 which was based on assumption of spherical charges. Having cylindrical charges for validation of AUTODYN model was also important because the blast wave produced is two dimensional and more complex than the one dimensional spherical case. To achieve a high degree of validation for the cylindrical charges, multiple pressure gauge locations were used. Four locations at key areas were deemed to be acceptable. With the blast chamber being set up for one test, it was beneficial to do multiple shots for redundancy to ensure a reliable set of data to be obtained. 2.1.1. Charge properties A variety of charge shapes and charge orientations were used throughout the blast program. The details of the charge shape, mass, standoff distance and orientation are summarized in Table 1. The charge mass varied from 0.095 kg to 0.2 kg and the standoff distance remained constant at 1.5 m and 1.3 m for the axial and radial direction, respectively. It should be noted that the standoff distance is the distance from charge centre to the pressure gauge, which was mounted on a 50 mm thick plate. Two hundred grams was the largest charge weight permissible for this blast program given that the location of charge was nearby the door and the tests were conducted in the small blast chamber. The charge shape was either cylindrical or spherical, see Fig. 3(a) and (b). For the cylindrical charges, the axis was oriented horizontally, but orthogonal pressure gauges measured both the axial and radial directions in one blast. The length to diameter ratio was constant at 1:1 since it gave the maximum peak reflected overpressure in the axial direction based on the work of Burge, Carter, Fattori, and Miller (2009). The explosive used was Plastic Explosive 4 (PE4). Please note that the ratio of TNT to PE4 is equivalency of approximately 1.3. The advantage of this explosive is that it can be moulded into any shape
Fig. 3. a) 140 g spherical charge and b) 200 g cylindrical charge.
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Fig. 5. Reflected pressure transducers (left), and gauge plate dimensions (right).
with hands. A mould out of cardboard was made to give a cylindrical shape, and the spherical shape was achieved by cutting a plastic ball into two halves and joining them together. Since the charges were PE4, they were able to be made on the day of testing. The cylindrical charges were detonated on one end, and the spherical charge was detonated slightly off centre as shown in Fig. 4. By detonating slightly off centre, it was more likely that the blast wave would be spherical and uniform in all directions since the detonator provided some directionality and this needed to be accounted for. 2.1.2. Pressure transducers For all four events, eight pressure transducers were used to measure the reflected overpressure on confined chamber walls at key locations, as shown in Fig. 1. The gauges were placed towards the bottom rather than the top of the enclosure to keep away from the ventilation in the top area. At each location, two types of pressure transducers were used. Gauges P1-P4 were PCB model 102-A06 (Accuracy 10% and Resonant Frequency: >¼500 kHz) and gauges P5eP8 were Endevco model 8530B-500 (Accuracy 0.6 0.2 mV/psi and Resonant Frequency: >¼1 MHz). The DSTO wanted to trial the PCB gauges because they were suspected to perform better near a fireball. However, the Endevco gauges were more accurate and were generally used for the results except in the odd event when it was unreliable. The pressure transducers were mounted on PVC plates which enabled them to be attached to the wall at existing bolt hole locations as shown in Fig. 5. 2.1.3. High speed camera A high speed camera was used to record footage of each blast event and to provide insight into the fireball region. Many finite
element programs do not give accurate predictions inside the fireball. The camera operated at 420 frames per second. Fig. 6 shows the position of the camera looking south from the charge location (see Fig. 1) and the view of the camera. 2.2. Experimental results There were a total of 4 blast events, and these were referenced as event 1e4 as described in Table 1. 2.2.1. Overpressure time history The reflected overpressure was measured for all four events in the locations as shown in Fig. 1. It was successfully recorded for each of these events using the Endevco gauges except for event 1 where gauges P5 and P6 were faulty. Fig. 7 compares the reflected overpressure histories at all locations for event 4. As shown, the second pressure peak for gauge P5 occurred due to the reflection from the floor because the gauge was placed low to the ground. For gauge P6, the first peak dominated, and subsequent peaks from the side wall, floor, and roof reflections were hard to distinguish. The overpressure thereafter appeared to be approximately zero, but this was due to the relatively high first peak and when comparing the overpressures to other gauges, they were similar. The second peak in gauge P7 was larger than the first and was due to reflections from the side wall and floor converging at the corner. Gauge P8 had similar history to P6 due to similar reflections, but subsequent peaks were easier to distinguish due to a smaller first peak. Charge shapes were reported to have significant influence on the peak reflected overpressure of the slab faces for external explosions (Wu et al., 2010). Fig. 8 compares the overpressure histories from the blast testing events 2 and 3. As shown, for the same
Fig. 6. Window for high speed camera (left) and view of high speed camera (right).
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Fig. 7. Overpressure histories at P5eP8 for event 4.
charge weights, the peak reflected overpressure for the horizontally oriented cylindrical charge in the axial direction is significantly greater than that for the spherical charge (Fig. 8(b)). Interestingly, the arrival time for the cylindrical charge in the axial direction is much less than that for spherical charge. This is because during
detonation the booster ignites, causing enough energy to detonate the cylindrical shaped charge that caused the blast explosion to emit the highest pressure wave to the right shown in Fig. 9(b) as ‘Pressure Wave Front B’ so that the pressure wave arriving at the wall quickly. ‘Pressure Wave Front A’ is emitted perpendicular to
Fig. 8. A comparison of overpressure history at P5eP8 for events 2 and 3.
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Detonator Overpressure Wave Front B
Overpressure
Booster
Wave
Explosive
Front A
(b)
(a)
Fig. 9. (a) Charge shape, (b) overpressure distribution.
of the curve for larger charge weights. It can be seen that the change in fireball diameter becomes less as the charge weight increases.
Table 2 Peak overpressure summary. Event
Orientation
Pressure gauge
Scaled distance (m/kg1/3)
Peak reflected overpressure (kPa)
1
Axial Radial NA
P6 P8 P6 P8 P6 P8 P6 P8
3.3 2.9 2.9 2.6 2.9 2.6 2.6 2.3
a
2 3 4 a
Axial Radial Axial Radial
Fig. 11. Comparison of experimental peak reflected overpressures with UFC prediction.
250 327 335 502 370 1060 570
Data faulty.
the length of the blast cylinder and it is quite similar to pressure wave caused by spherical charge and that is why the peak overpressures, shapes of overpressure histories and arrival times at P5, P6 and P 8 are quite similar. Table 2 summarizes the peak reflected overpressure recorded for each event. The lowest peak reflected overpressure recorded was 250 kPa for event 1, and the highest recorded was 1060 kPa for event 4. 2.2.2. Fireball The fireball was able to be captured for all events. A photograph for event 3 is shown in Fig. 10(a). The fireball is significant because the temperatures are high and the combustion of gaseous products produced by the chemical process involved in the explosion will exert additional pressures in this region. The fireball diameter for all cylindrical charge events has been plotted in Fig. 10(b). Two additional points have been plotted from approximate data obtained from the DSTO testing to give a better depiction of the trend
2.3. Analysis of experimental results The experimental results of peak reflected overpressure and impulse are compared with UFC predictions in Figs. 11 and 12, respectively. The general procedure for use of UFC to predict confined blasts is shown in Appendix. From observation of the peak reflected overpressure, it can be seen that UFC gives a significantly lower prediction for the axially oriented cylindrical charge at gauge P6, and also underestimates the radially oriented cylinder at gauge P8. This shows the need to investigate the cylindrical charge and to observe the loading distribution because Figs. 11 and 12 are based on a localized overpressures whereas UFC uses an average uniform overpressure distribution. UFC is conservative for the first 5 ms of the impulse in Fig. 12 for both charge shapes. This is due to the gas pressure (see Fig. 13(a)), which UFC significantly overestimates. However, as the scaled distance decreases, the axially oriented cylindrical charge becomes more critical which calls for an investigation into the impulse produced from this charge orientation for larger charge weights. A comparison of the experimental gas pressure for event 4 at gauge P8 with UFC prediction with minimum opening is shown in Fig. 13(b). The experimental plots stopped at 200 ms because data was only recorded until this point, but it appears that the gas pressure would continue for a significantly longer duration. The UFC prediction can be seen to have a considerably larger impulse by the area under the curve for the available results, however, the UFC prediction is limited because it does not provide predictions for the low loading density used in the experiments, and the closest available values were used.
Fig. 10. Fireball for event 3 (a) and fireball diameter as a function of charge weight (b).
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Fig. 12. Comparison of experimental impulse for the first 5 ms with UFC prediction.
The variation of reflected overpressure with angle of incidence has also been plotted in Fig. 14 based on gauges P5 and P6. When comparing an axially oriented cylindrical charge with a spherical one of the same charge weight, the peak reflected overpressure is approximately 1.5 times greater for the cylindrical charge, irrespective of the angle of incidence. However, the charge weight is relatively small. As the charge weight increases, relatively more energy is directed axially for the cylindrical charge and it becomes more directional. 3. Validation of finite element model A finite element program AUTODYN was validated in the previous studies to simulate the blast loading in confined geometries (Hu et al., 2011). This blast program was to develop an experimental data set which would enable the AUTODYN model to be calibrated. This would enable the model to be used with confidence to generate the overpressure and impulse distribution. In the numerical model, air and TNT are simulated by Euler processor. The air is assumed to have the ideal gas equation of state:
p ¼ ðg 1Þ$r$e
(1)
and the TNT material is modelled by the JoneseWilkenseLee (JWL) equation of state:
u u ue er1 v þ C2 1 er2 v þ p ¼ C1 1 v r1 v r2 v
(2)
where g is the heat specific ratio, r is density, e is internal energy, C1, C2, r1, r2 are constants, u is report of the specific heat, v is specific volume. The standard constants of air and TNT are retrieved from the standard AUTODYN library and the material constants are used
Fig. 14. Comparison of experimental peak reflected overpressure for spherical and axially oriented cylindrical charges with a standoff distance of 1.5 m.
in the numerical model, including air mass density r ¼ 1.225 kg/m3; air initial internal energy en ¼ 2.068 105 kJ/kg; ideal air gas constant g ¼ 1.4; and C1, r1, C2, r2 and u are 3.7377 105 MPa, 4.15, 3.74713 105 MPa, 0.9, and 0.35, respectively (Century Dynamics, 2003). The experimental blast program, event 2 which was a spherical charge, was used to calibrate the AUTODYN model. Since the detonator was placed inside the spherical charge to approximately achieve centre detonation and a spherical blast wave, the charge was first modelled in one dimension as shown in Fig. 15(a) to reduce the computational cost during the initial stages of detonation and expansion of the charge. The charge calculation was set to terminate when the blast wave reached the confinement walls where a remap file containing the cell data was transferred to a 3D model shown in Fig. 15(b) where pressure wave interactions were modelled. Fig. 15(b) represents the bottom northwest corner in the blast chamber (see Fig. 1) as defined by the pressure gauges. Please note that that the mesh size for the 3D model is selected to be 10 mm, and the size for the 2D charge model is 1 mm for the above validation model. It can be seen in Fig. 15(b) that the blast pressure wave is on the verge of hitting the ground and is uniform in all directions. The rebates in the corner account for the thickness of the pressure gauge plates by setting the mesh cells as unused. The experimental pressure and the predicted pressure from AUTODYN model at gauge location 7 and 8 are compared in Fig. 16. It is evident from Fig. 16 that the model adequately depicts the reflected overpressure for gauge P8 at an angle of incidence of zero and in the corner of the confinement at gauge P7. The peak overpressure and impulse are predicted within 10% and 20%
Fig. 13. Gas pressure for event 4, gauge P8.
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Fig. 15. Last stages of pressure wave development in one dimension (a), and three dimension initial model (b).
Fig. 16. Comparison between modelled and experimental overpressure time histories for event 2, spherical charge.
respectively for P7, and 20% and 50% respectively for P8. The relatively large difference in impulse for P8 is attributed to not simulating the top half of the chamber and thus omitting the reflection from the roof which converges approximately with the reflection from the floor for the second pressure peak. By utilizing the above the result, the model was deemed to be adequately calibrated for simulating spherical charges in a confinement to investigate the variation in reflected overpressure and impulse at different locations. Analysis of the cylindrical charge was significant because many modern explosives are cylindrical in shape and not spherical as assumed by guidelines, and because the reflected overpressure for cylindrical charges is larger than spherical charges for similar
charge weight (Burge et al., 2009). This is due to the fact that the majority of energy is directed in the axial direction. A depiction of the blast pressure wave that was produced for a cylindrical charge (event three) is shown in Fig. 17. As evident from Fig. 17, the blast pressure wave is concentrated in the axial direction. This is different to a spherical charge where an equivalent blast pressure is produced in all radial directions. Such a representation is supported by the experimental program, where the peak reflected overpressure in the axial direction is significantly greater than that of an equivalent spherical or radially oriented cylindrical charge. Since the charge was end detonated on the right side, the pressure wave has further directionality to the side opposite the detonation point, as indicated by the further
Fig. 17. Visual representation of the blast pressure wave produced from a cylindrical charge.
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Fig. 18. Comparison between modelled and experimental overpressure time histories for event 3, cylindrical charge.
travel distance on the left side and the larger pressures with more in the yellow range. The charge was remapped to the same confinement as in Fig. 15(b) with axial symmetry and the result of the further validation at gauge locations P5 and P2 is presented in Fig. 18. In the validation, gauge P5 represents axial direction on the floor, and P6 represents the axial direction at an angle of incidence of zero. The peak overpressure and impulse for the positive phase are simulated to 20% and 4% accuracy for P5 respectively, and 5% and 20% for P6. The level of validation is considered to be sufficient and the AUTODYN is used to characterize confined blast loads for cylindrical charges. 4. Application of the numerical model In the previous studies a numerical model was used to conduct parametric analysis for charge weight, charge shape, charge orientation, length to diameter ratio, confinement geometry, and confinement volume (Wu et al., 2010). In this study, the numerical model calibrated in Section 3 is utilized to conduct parametric studies for simplification of confined blast loading. By generating more data with the AUTODYN models, a new model for cylindrical charges are developed for predictions of the overpressure and impulse distribution in confined wall surfaces. The overpressure distribution along axial direction of the cylindrical charge on ceiling, wall and floor of cube is investigated. The pressure gauge locations along axial direction of the cylindrical charge on wall of the 2 m 2 m 2 m cube are shown in Fig. 19. The overpressure time history at different locations for a 0.2 kg cylindrical charge (L/D ¼ 1) placed in the centre of the cube is shown in Fig. 20. The results show that the cylindrical charge is highly
Fig. 19. Structure layout of cubic confinement and gauge location, plan (left) and section (right).
directional where the first peak at the centre gauge, P1, dominates. A second peak at P1 occurs at around 3 ms due to shockwave reflections from the side walls, roof and floor converging. Since P7 is close to the side wall (see Fig. 19), a comparable second peak occurs soon after the first. Although it appears that the overpressure from subsequent pressure peaks and at gauges P4 and P7 is of minor significance, this is not the case because the first peak accounts for only a fraction of the area under the overpressure time history, or the energy imparted to the structural member. This is reflected in the dynamic member response where the maximum deflection is three times greater for the confined case considering multiple peaks, and increases for larger charge weights. From the literature review, most guidelines such as UFC-3-34002 assume a uniform overpressure distribution for confined blast loading and only a few manuscripts (Baker et al., 1983) show more complex distributions, for example the possibility of overpressure increase in corners (Savir, Edri, Feldgun, Karinski, & Yankelevsky, 2009). Fig. 21 shows the simulated overpressure distribution along the ceiling, wall and floor in the cube for a 1 kg end detonated cylindrical charge inside the 2 m 2 m 2 m cube where P0 is the peak overpressure generated by a same weight of spherical charge at centre of the cube. The corresponding overpressure time history for a 1 kg end detonated cylindrical charge on the wall is shown in Fig. 22(a). All the pressure gauges in Fig. 22 are considered by including the contributing area of each gauge and taking the weighted average across the height to convert the blast load from two dimensions to one dimension. The use of average blast loads can be used providing the element has the ability to transfer localized loads to
Fig. 20. Effect of cubic confinement along the length of a member for a 0.2 kg cylindrical charge placed in the centre.
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C. Wu et al. / Journal of Loss Prevention in the Process Industries xxx (2013) 1e14 Table 3 Unit reflected impulse using the tributary method for a 1 kg axially oriented cylindrical charge in a 2 m cubic confinement. Contributing gauges
Unita reflected impulse (kPa ms) Model
UFC
% Diff
P1e3 P4e6 P7e9
710 380 1060
1440
51 74 26
a
Corresponding to the time of the first overpressure peak for UFC.
Fig. 21. Simulated overpressure distribution along the side wall of a cubic confinement.
regions of lower stress. The UFC guideline assumes a uniform distribution, which is also shown for clarity. Fig. 22(a) shows a comparison of average overpressure time histories in the axial direction of a cylindrical charge where the average overpressure at gauges P1e3 is almost an order of magnitude larger than at gauges P4e6. The average overpressure increases at P7e9 due to the influence of the edge and the corner with multiple shockwave reflections, however the overpressure in the direct axial direction at P1e3 is still over two times larger. This distribution of average overpressure for the cylindrical charge is quite general even for different confinement geometries. The comparison of impulse with UFC across the length of the element is shown in Table 3. It can be seen that UFC is conservative for the cubic geometry with the modelled impulse being lower at each location. Since the cylindrical charge is so directional, it will provide more critical loading on thinner elements because the gauges will be closer to the centre where the impulse is large. A spherical charge was simulated to compare the variation in average overpressure along the length of the wall with the cylindrical charge as shown in Fig. 22(b). It can be seen that the uniform loading distribution assumption of UFC is rational because the average overpressure peaks at all three locations are approximately the same. This is significantly different from the cylindrical charge where a uniform assumption does not provide an accurate representation. Since UFC only considers spherical charges, the blast load
Fig. 23. Comparison of average reflected overpressure for a 0.2 kg centre detonated cylindrical charge at two different locations at the critical gauge.
model needs to be modified for cylindrical charges. The result also illustrates the conservatism of UFC since a direct comparison can be done with the spherical charge, and the reason for the difficulty to find a higher impulse with cylindrical charges when considering the average overpressure. The effect of charge location was examined to see how significant the centre spot is in a cube for a cylindrical charge, keeping in mind that practically placing a charge in the centre is considerably harder. This was done by placing a 0.2 kg charge 15% below the centre point. Since there was no longer symmetry in the vertical direction, the full height of the chamber had to be modelled, with five gauges along the height instead of three as shown in Fig. 19. At the level of the charge, the pressure gauges were adjusted to capture the axial direction without losing the peak overpressure on the wall. The effect of charge location at the critical gauge is shown in Fig. 23. As shown, although the average overpressure for a charge being offset by 15% is lower at some points in time, it is higher at other points and overall there is little noticeable difference between the two locations.
Fig. 22. Comparison of average reflected overpressure across the length of the member for a 1 kg (a) end detonated cylindrical and (b) spherical charge placed in the centre of a 2 m cube.
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Fig. 24. Comparison of the average reflected overpressure at the centre for a 0.2 kg cylindrical charge placed at two different locations.
Fig. 25. Structure layout of rectangular confinement and gauge location, plan (left) and section (right).
11
From Fig. 23, the main difference that can be seen is the absence of the larger multiple peaks where the charge is offset from the centre because there is no symmetry in the vertical direction. However, for a cylindrical charge, the multiple peaks from the centre location are relatively small compared with the first peak which is considered to have a minor effect. This is confirmed in Fig. 24 where overpressure was averaged over the five gauges based on the contributing area. It can be seen that although the average overpressure for the offset charge is lower at some points in time, it is higher at other points and overall there is little noticeable difference between the two locations. If a charge larger than 0.2 kg is used, the charge location would also have a minor effect because the first peak would be much larger than the second. More energy would go in the axial direction if the charge weight increased based on the experimental results in Fig. 24. Multiple charge weights were simulated for the case where UFC could be improved. A new and more accurate blast model for cylindrical charges has been proposed by considering loading on the same level as the charge across the longitudinal direction. It is of great significance for the cylindrical charge because of its directional characteristics. It could be for this reason that most warheads are cylindrical rather than spherical. In this case, larger charge weights of 0.5e2.4 kg were considered because more energy is directed in the axial direction and it is this that UFC fails to account for. A rectangular confinement of 2.8 m 2 m 1.4 m as shown in Fig. 25 was used to develop the new model for cylindrical charges. A comparison of the impulse for different charge weights is shown in Table 4. Looking at the 0.2 kg charge, the simulated impulse is lower than UFC at all three locations, therefore this charge could not be used to improve UFC. For the 1 kg charge, the impulse at location P1 and P7 is 310% and 160% greater than UFC respectively, however only 57% at location P4. This was significant, and needed new method to characterize the blast load.
Table 4 Comparison of impulse for different charge weights at different locations for the end detonated cylindrical charge. Charge weight (kg)
0.2 0.5 1 2.4
Scaled distance (m/kg1/3)
1.71 1.26 1 0.75
Location P1
P4
ir (kPa ms)
%ir
378 2660 3930 6690
95 370 310 280
UFC
P7
to (ms)
%ir1
%ir
e 0.5 0.4 0.35
35 17 18 17
33 63 57 49
UFC
%to1
%ir1
%ir
e 260 230 230
50 46 52 57
47 170 160 160
UFC
%to1 e 260 240 230
Fig. 26. New model for cylindrical charges at location (a) centre, (b) intermediate, (c) end.
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Fig. 27. Comparison of new model to simulated average reflected overpressure for a 1 kg end detonated cylindrical charge placed in the centre of a rectangular confinement.
Table 5 Impulse distribution for different confinement geometries for an axially oriented and end detonated cylindrical charge. Geometry (m)
Location P1
P4
ir (kPa ms) %ir 222 4190 2.8 2 1.4 3930 421 4320
UFC
290 310 400
P7
to (ms) %ir1 %ir 0.4 0.4 0.4
11 18 19
33 57 78
UFC
%to1 %ir1 %ir 200 35 230 52 200 40
UFC
64 160 160
%to1 240 240 240
From Table 4, it can be seen that %ir1 at location P4 for the 0.5e 2.4 kg charges is approximately 18%, and at location P7 is approximately 50%. It can also be seen that %t01 is approximately 200% for both locations P4 and P7. Therefore, the new model was characterized as shown in Fig. 26. Due to the directional nature of the cylindrical charge, the impulse varied at three different locations. The model at the centre was used as a control. The impulse at the intermediate location is conservatively simplified to 0.25ir from the actual data of 0.18ir, and the impulse at the end is set to 0.5ir based on the actual data. It can be seen that the impulse increases at the end due to being close to the side wall where multiple reflections occur. The time for the shock pressures at the intermediate and end location is simplified to 2to based on the modelled data. Since the shock peaks are simplified as triangle, the peak overpressure, impulse, and time are related by:
Fig. 29. Average unit reflected impulse for axially oriented cylindrical charges (N ¼ 4, l/ L ¼ 0.50, h/H ¼ 0.50, L/RA ¼ 2.8).
to ¼ 2ir =pr
(3)
Based on the duration and the impulse, the peak overpressures for the intermediate and end locations are obtained to be 1/8Pr and 1/4Pr respectively using equation (3). The gas pressures are kept the same as in UFC since they are found to give reasonable and conservative estimates. The new model for shock pressures, not including the gas pressures, is applied to the average overpressure time history for the 1 kg charge as shown in Fig. 27. Although the two red peaks are separated, it is the total impulse that governs and the two peaks can be simplified to give one single peak. It can also be seen that the large peak at P1 has a relatively short duration compared to P4 and P7, and this is accounted for in the model. The model was also checked for different confinement geometries to find its effectiveness. The result for a 1 kg cylindrical charge with a scaled distance of 1 m/kg1/3 is shown in Table 5. Looking at the 2 m cubic geometry, the new blast model can be applied conservatively at locations P4 and P7 (see Fig. 19) with a predicted impulse of 25%ir1 and 50%ir1 respectively. Similarly for the 4 m 2 m 1 m geometry, the model can be applied confidently. As the geometry becomes more rectangular, the effects of a cylindrical charge become more critical and UFC predictions become inadequate. New design charts for the reflected overpressure and impulse values to be used in the cylindrical blast model for the 2.8 m 2 m 1.4 m geometry are shown in Figs. 28 and 29, respectively. The parameters for the plots are the same as defined in UFC-3-340-02 (2008), and are included in 0. With the aid of Figs. 28 and 29, the average peak reflected overpressure and impulse can be obtained and then simplified overpressure history can be determined by Fig. 26. It should be noted that the current model for cylindrical charges is only suitable for cuboid chambers with small volumes. 5. Conclusions
Fig. 28. Average peak reflected overpressure for axially oriented cylindrical charges (N ¼ 4, l/L ¼ 0.50, h/H ¼ 0.50, L/RA ¼ 2.8).
In this blast program, four confined blasts with one spherical charge and three cylindrical charges were conducted to develop a robust AUTODYN confined blast load model. The experimental results were analyzed and compared with the current guideline, UFC-3-340-02, to show its limitations for cylindrical charges. The AUTODYN model was calibrated using the experimental data. With the calibrated model, the significance of confinement for cylindrical charges was demonstrated, which indicated that
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confinement magnifies the influence of blast loadings greatly. Investigation of the charge shape showed that the axially oriented cylindrical charge produced the largest peak overpressure and impulse on the confined chamber wall. Based on the simulated results a new model for cylindrical charges was developed for predictions of overpressure and impulse on a chamber wall.
Acknowledgements This study was sponsored by an Australian Research Council linkage project LP0883451 supported by DSTO and VSL.
13
Appendix. The general procedure for use of the UFC-3-340-02 (2008) 1. From Fig. 2-51, select the particular surface of the structure which conforms to the protective structure given and note N of adjacent reflecting surfaces as indicated in parenthesis. 2. Determine the values of the parameters indicated for the selected surface of the structure in Item 1 above and calculate the following quantities: h/H, l/L, L/H, L/RA, and ZA ¼ RA/W1/3. 3. Refer to Table 2-3 for the proper peak reflected pressure and impulse charts conforming to the number of adjacent reflected surfaces and the values of l/L and h/H of Item 2 above, and enter the charts to determine the values of pr and ir/W1/3.
Table 2-3 List of illustrations for average peak reflected pressure and scaled average unit reflected impulse. h/H
l/L
Average peak reflected pressure
Scaled average unit reflected impulse
Number of adjacent reflecting surfaces
0.10
0.25
0.50
0.75
0.10 0.25 0.50 0.75 0.10 0.25 0.50 0.75 0.10 0.25 0.50 0.75 0.10 0.25 0.50 0.75
One
Two
Three
Four
One
Two
Three
Four
2e52 2e53 2e54 2e53 2e55 2e56 2e57 2e56 2e58 2e59 2e60 2e59 2e61 2e62 2e63 2e62
2e64 2e65 2e66 2e67 2e68 2e69 2e70 2e71 2e72 2e73 2e74 2e75 2e76 2e77 2e78 2e79
2e80 2e81 2e82 2e81 2e83 2e84 2e85 2e84 2e86 2e87 2e88 2e87 2e89 2e90 2e91 2e90
2e92 2e93 2e94 2e93 2e95 2e96 2e97 2e96 2e98 2e99 2e100 2e99 2e95 2e96 2e97 2e96
2e101 2e102 2e103 2e102 2e104 2e105 2e106 2e105 2e107 2e108 2e109 2e108 2e110 2e111 2e112 2e111
2e113 2e114 2e115 2e116 2e117 2e118 2e119 2e120 2e121 2e122 2e123 2e124 2e125 2e126 2e127 2e128
2e129 2e130 2e131 2e130 2e132 2e133 2e134 2e133 2e135 2e136 2e137 2e136 2e138 2e139 2e140 2e139
2e141 2e142 2e143 2e142 2e144 2e145 2e146 2e145 2e147 2e148 2e149 2e148 2e144 2e145 2e146 2e145
Fig. 2-51. Barrier and Cubicle configurations and parameters.
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References American Society of Civil Engineers (ASCE. (2007). Blast protection of buildings. Standard in preparation, Reston, VA. Anderson, J. G., Katselis, G., & Caputo, C. (2002). Analysis of a generic warhead part I: Experimental and computational assessment of free field overpressure. DSTO technical report 1313. Edinburgh, South Australia: Defense Science Technology Organization, Australian Department of Defense. Baker, W. E., Cox, P. A., Westine, P. S., Kulesz, J. J., & Strehlow, R. A. (1983). Fundamental studies in engineering (pp. 238e243)In Explosion hazards and evaluation, Vol. 5. Amsterdam, Oxford, New York: Elsevier. Bangash, M. Y. H., & Bangash, T. (2006). Explosion-resistant buildings. Springer. Burge, J., Carter, T., Fattori, G., & Miller, D. (2009). Blast resistance of ultra high performance concrete. Final year research report. Australia: School of Civil and Environmental Engineering, The University of Adelaide. Century Dynamics. (2003). AUTODYN user manual. Revision 3.0. Century Dynamics, Inc.. Chan, P. C., & Klein, H. H. (1994). A study of blast effects inside an enclosure. Journal of Fluids Engineering-Transactions of the ASME, 116(3), 450e455. Dragos, J., Hu, Y., Lukazewicz, M., & Ren, J. (2010). Confined blast loading and blast resistance of ultra-high performance concrete. Final year research project report. Adelaide, Australia: School of Civil and Environmental Engineering, The University of Adelaide. Hu, Y., Wu, C., Lukaszewicz, M., Dragos, J., Ren, J., & Haskett, M. (2011). Characteristics of confined blast loading in unvented structures. International Journal of Protective Structures, 2(1), 21e43. Katselis, G., & Anderson, J. G. (2001). Estimation of blast overpressure from a cylindrical charge using time of arrival sensors. In The 14th Australasian fluid mechanics conference. Australia: Adelaide University.
Remennikov, A. M., & Rose, T. A. (2005). Modeling blast loads on buildings in complex city geometries. Computers and Structures, 83(27), 2197e2205. Sauvan, P. E., Sochet, I., & Trelat, S. (2012). Analysis of reflected blast wave pressure profiles in a confined room. Shock Waves, 22(3), 253e264. Savir, Z., Edri, I., Feldgun, V., Karinski, Y., & Yankelevsky, D. (2009). Blast pressure distribution on interior walls due to a partially confined explosion. In The international workshop on structures response to impact and blast conference, Israel, 15e17 November, CD proceeding. Shi, Y., Li, Z., & Hao, H. (2009). Numerical investigation of blast loads on RC slabs from internal explosion. In The international workshop on structures response to impact and blast conference, Israel, 15e17 November, CD proceeding. Smith, P. D., & Rose, T. A. (2006). Blast wave propagation in city streets e an overview. Progress in Structural Engineering and Materials, 8(1), 16e28. Tham, C. Y. (2009). Numerical simulation on the interaction of blast waves with a series of aluminium cylinders at near-field. International Journal of Impact Engineering, (36), 122e131. UFC-3-340-02. (2008). Structures to resist the effect of accidental explosions. US Department of the Army, Navy and Air Force Technical Manual. Wu, C., Fattori, G., Whittaker, A., & Oehlers, D. J. (2010). Investigation of air-blast effects from spherical- and cylindrical-shaped charges. International Journal of Protective Structures, 3, 345e362. Zimmerman, H. D., Nguyen, C. T., & Hookham, P. A. (1999). Investigation of spherical vs cylindrical charge shape effects on peak free air overpressure and impulse. In Proceedings of 9th international symposium on interaction of the effects of munitions with structures. Zyskowski, A., Sochet, I., Mavrot, G., Bailly, P., & Renard, J. (2004). Study of the explosion process in a small scale experiment e structural loading. Journal of Loss Prevention in the Process Industries, 17(4), 291e299.
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Contents lists available at SciVerse ScienceDirect
Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Experimental and numerical investigation of confined explosion in a blast chamber Chengqing Wu a, *, Matthew Lukaszewicz a, Ken Schebella b, Leonid Antanovskii b a b
School of Civil, Environmental and Mining Engineering, The University of Adelaide, SA 5005, Australia Weapons Systems Division, Defence Science and Technology Organisation, Australia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 September 2011 Received in revised form 1 December 2012 Accepted 4 February 2013
An experimental blast program consisting of four tests was conducted in a blast chamber to investigate the effects of cylindrical charges on the peak reflected overpressure and impulse on the wall of the chamber. The charge mass varied from 0.095 kg to 0.2 kg and the standoff distance remained constant at 1.5 m and 1.3 m for the axial and radial directions, respectively. Eight pressure transducers were used in each test to measure the reflected overpressures on confined chamber walls at key locations. A high speed camera was used to record footage of each blast event. The test results indicated that UFC-3-34002 (Unified Facilities Criteria, 2008) gives a significantly lower prediction for the axially oriented cylindrical charge, and also underestimates the radially oriented cylinder. Another purpose of the blast program was to develop an experimental data set which would validate the AUTODYN model. This would enable the validated AUTODYN model to be used with confidence to generate the overpressure and impulse distribution on a structural element for varying parameters such as the charge shape and charge orientations. Based on the simulated results a new blast model for cylindrical charges has been proposed by considering blast loading on the same level as the charge across the longitudinal direction. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Blast testing Numerical simulation Charge shape effects Confined blasts
1. Introduction Protecting civilian infrastructure from the increasing threat of intentional explosive events has become a critical challenge for researchers today. Critical infrastructure, such as government buildings and power plants need to be carefully designed to resist blast loadings and ensure the safety of the occupants. Internal explosions may happen due to possible deliberate attacks in a subway station, or in a car park of a commercial building, or an accidental explosion inside ammunition storage or mining tunnels. Confined blast fields can be applied to explosions of a penetrated charge inside a military vehicle or a bunker. Therefore, it is of great significance to study blast wave propagation for reliable design of structures against such confined blast loadings should such explosions occur (Sauvan, Sochet, & Trelat, 2012; Shi, Li, & Hao, 2009). However, the problem of a confined explosion is less addressed at current guidelines such as UFC-3-340-02 (2008) (which replaced TM5-1300 in 2008) and ASCE (2007). UFC-3-340-02 considers the blast effects of bare spherical TNT explosives without taking charge shapes and orientations into consideration; and the peak reflected
* Corresponding author. E-mail address: [email protected] (C. Wu).
overpressure and impulse are also assumed to be uniformly distributed on the wall surface in these guidelines. Such simplification and assumption in the in modern standards for blastresistant design might not enable accurate predictions of confined blast loading required for a detailed analysis of dynamic response and damage of structures. Considerable published information including numerical and experimental studies exists for non spherical charges in external blast environments. Numerical studies together with experimental investigation on cylindrical charges in the previous studies indicated that the ratio (L/D) of the cylindrical charge has significant effect in the pressure field in the immediate vicinity of the charge: for large values of the ratio, most of the energy is focused in the radial direction whereas for small values of the ratio, most of the energy is focused in the axial direction (Anderson, Katselis, & Caputo, 2002; Katselis & Anderson, 2001; Wu, Fattori, Whittaker, & Oehlers, 2010; Zimmerman, Nguyen, & Hookham, 1999). A series of blast tests has been conducted using cylindrical charges in recent years and it was found that UFC-3-340-02 underestimated the measured peak reflected overpressures and impulse for the cylindrical charges with vertical axes but overestimated the peak reflected overpressures for both spherical charges and cylindrical charges with horizontal axes (Wu et al., 2010). Recently, more and more attention has been paid on the partially confined blast loading
0950-4230/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jlp.2013.02.001
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Fig. 1. Layout of DSTO blast chamber and pressure gauge locations.
since guidance is needed for engineers to design structural systems to withstand various acts of terrorism, especially to an explosion in an urban area in proximity to tall buildings in complex city geometries (Remennikov & Rose, 2005; Smith & Rose, 2006). However limited studies have been conducted for non spherical charges in confined environments. The blast effects inside an enclosure for a 1 lb charge placed at the centre of a rectangular bunker was investigated by Chan and Klein (1994) and multiple shock reflections of overpressure histories were found to continue at significant magnitudes for a long period of time. Other studies demonstrated (Baker, Cox, Westine, Kulesz, & Strehlow, 1983; Bangash & Bangash, 2006) that the first three peaks of overpressure histories might be used to represent the dynamic contact pressure after which the constant gas overpressure is assumed acting on the confined space walls. Recently an AUTODYN finite element model (Century Dynamics, 2003), which was validated using experimental data in a small scale experiment conducted by Zyskowski, Sochet, Mavrot, Bailly, and Renard (2004) was used to investigate the variation in reflected overpressure with location on the small box by changing the orientation of the charge, the charge weight, the charge shape (Hu et al., 2011). However, little information is found on experiment investigation of cylindrical charges inside a chamber on the effects of reflected overpressure and impulse (Dragos, Hu, Lukazewicz, & Ren, 2010). In this paper spherical charge and cylindrical charge with a variety of orientations were used throughout a blast program in a blast chamber. The charge mass with variation of 0.095e0.2 kg was
used in the blast program while the standoff distance kept constant at 1.5 m and 1.3 m for the axial and radial direction, respectively. The length to diameter ratio of the cylindrical charge was constant at 1:1. For the cylindrical charges, the axis was oriented horizontally, but eight orthogonal pressure gauges measured both the axial and radial directions in one blast. A high speed camera was used to record footage of each blast event and to provide insight into the fireball region. The experimentally measured overpressure and impulse distributions on the chamber walls were analyzed and compared to assess the impact of charge shape and orientation. The experimental results were compared with predictions made using the industry standard UFC-3-340-02. As limited experimental data was available from the blast test program, a finite element program AUTODYN was validated using the experimental results and the validated numerical model was then used to expand the scope of the experimental program and to conduct parametric studies on the changes in reflected overpressure and impulse on the confined chamber walls. Based on the simulated results a new simplified model was developed for estimation of overpressure and impulse from cylindrical charges on the confined chamber walls. 2. Confined blast tests An experimental blast program consisting of four tests were conducted in a DSTO (Defence Science and Technology Organisation, Australia) blast chamber. Since limited published information exists for non spherical charges in confined environments and most
Fig. 2. Photo of pressure gauge layout.
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3
Table 1 Summary of charge properties. Event no.
1
Charge mass (g) 95.3
2
140
3
142.6
4
200.5
Standoff distance (m)
Scaled distance (m/kg1/3)
Charge shape
Charge orientation
1.505 1.340 1.505 1.340 1.505 1.340 1.505 1.340
3.3 2.9 2.9 2.6 2.9 2.6 2.6 2.3
Cylindrical
Axial Radial NA NA Axial Radial Axial Radial
Spherical Cylindrical Cylindrical
Fig. 4. Detonation point of spherical charge.
warheads are cylindrical rather than spherical (Tham, 2009), investigation of blast waves from cylindrical charges in this blast program is of practical relevance.
2.1. Design of experiment The layout of the blast chamber is shown in Fig. 1. The tests were designed with the advantage of simplifying the geometry to rectangular for easier validation. This meant that the southern part of the chamber was inappropriate due to angles and windows in the roof and side walls. The best location for placing the charge was near the entrance in the eastern side of the chamber (see Fig. 1), since this was the closest representation of a rectangular room and would provide the largest number of shockwave reflections from the three walls, the floor and roof. However, it was not appropriate to place the charge in this area due to the door for the entrance, which was a weak point to detonation. The next best alternative was used to place the charge in the north western corner as shown in Fig. 1. The charge was placed at mid height of the chamber and approximately 1 m away from the surface to achieve charge shape effects. Due to the method of fixing the pressure gauges and the ventilation in this area, the distances from the surface were increased to approximately 1.5 m. The plates for the pressure gauges were attached to existing bolt holes to prevent complications of pressure gauge mounting as shown in Fig. 2. Since the existing bolts were not at mid height of the chamber, this prevented symmetry in the vertical direction. However, the plates were placed outside the perimeter of the ventilation at the top of the chamber. This was to prevent the metal grid and the rocks above from interfering with the shockwave reflections. Cylindrical charges were introduced to study the effect of charge shape since little research on cylindrical charge has been studied in a confined environment before. One spherical charge was used as a
reference to compare with the cylindrical shape and with UFC-3340-02 which was based on assumption of spherical charges. Having cylindrical charges for validation of AUTODYN model was also important because the blast wave produced is two dimensional and more complex than the one dimensional spherical case. To achieve a high degree of validation for the cylindrical charges, multiple pressure gauge locations were used. Four locations at key areas were deemed to be acceptable. With the blast chamber being set up for one test, it was beneficial to do multiple shots for redundancy to ensure a reliable set of data to be obtained. 2.1.1. Charge properties A variety of charge shapes and charge orientations were used throughout the blast program. The details of the charge shape, mass, standoff distance and orientation are summarized in Table 1. The charge mass varied from 0.095 kg to 0.2 kg and the standoff distance remained constant at 1.5 m and 1.3 m for the axial and radial direction, respectively. It should be noted that the standoff distance is the distance from charge centre to the pressure gauge, which was mounted on a 50 mm thick plate. Two hundred grams was the largest charge weight permissible for this blast program given that the location of charge was nearby the door and the tests were conducted in the small blast chamber. The charge shape was either cylindrical or spherical, see Fig. 3(a) and (b). For the cylindrical charges, the axis was oriented horizontally, but orthogonal pressure gauges measured both the axial and radial directions in one blast. The length to diameter ratio was constant at 1:1 since it gave the maximum peak reflected overpressure in the axial direction based on the work of Burge, Carter, Fattori, and Miller (2009). The explosive used was Plastic Explosive 4 (PE4). Please note that the ratio of TNT to PE4 is equivalency of approximately 1.3. The advantage of this explosive is that it can be moulded into any shape
Fig. 3. a) 140 g spherical charge and b) 200 g cylindrical charge.
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Fig. 5. Reflected pressure transducers (left), and gauge plate dimensions (right).
with hands. A mould out of cardboard was made to give a cylindrical shape, and the spherical shape was achieved by cutting a plastic ball into two halves and joining them together. Since the charges were PE4, they were able to be made on the day of testing. The cylindrical charges were detonated on one end, and the spherical charge was detonated slightly off centre as shown in Fig. 4. By detonating slightly off centre, it was more likely that the blast wave would be spherical and uniform in all directions since the detonator provided some directionality and this needed to be accounted for. 2.1.2. Pressure transducers For all four events, eight pressure transducers were used to measure the reflected overpressure on confined chamber walls at key locations, as shown in Fig. 1. The gauges were placed towards the bottom rather than the top of the enclosure to keep away from the ventilation in the top area. At each location, two types of pressure transducers were used. Gauges P1-P4 were PCB model 102-A06 (Accuracy 10% and Resonant Frequency: >¼500 kHz) and gauges P5eP8 were Endevco model 8530B-500 (Accuracy 0.6 0.2 mV/psi and Resonant Frequency: >¼1 MHz). The DSTO wanted to trial the PCB gauges because they were suspected to perform better near a fireball. However, the Endevco gauges were more accurate and were generally used for the results except in the odd event when it was unreliable. The pressure transducers were mounted on PVC plates which enabled them to be attached to the wall at existing bolt hole locations as shown in Fig. 5. 2.1.3. High speed camera A high speed camera was used to record footage of each blast event and to provide insight into the fireball region. Many finite
element programs do not give accurate predictions inside the fireball. The camera operated at 420 frames per second. Fig. 6 shows the position of the camera looking south from the charge location (see Fig. 1) and the view of the camera. 2.2. Experimental results There were a total of 4 blast events, and these were referenced as event 1e4 as described in Table 1. 2.2.1. Overpressure time history The reflected overpressure was measured for all four events in the locations as shown in Fig. 1. It was successfully recorded for each of these events using the Endevco gauges except for event 1 where gauges P5 and P6 were faulty. Fig. 7 compares the reflected overpressure histories at all locations for event 4. As shown, the second pressure peak for gauge P5 occurred due to the reflection from the floor because the gauge was placed low to the ground. For gauge P6, the first peak dominated, and subsequent peaks from the side wall, floor, and roof reflections were hard to distinguish. The overpressure thereafter appeared to be approximately zero, but this was due to the relatively high first peak and when comparing the overpressures to other gauges, they were similar. The second peak in gauge P7 was larger than the first and was due to reflections from the side wall and floor converging at the corner. Gauge P8 had similar history to P6 due to similar reflections, but subsequent peaks were easier to distinguish due to a smaller first peak. Charge shapes were reported to have significant influence on the peak reflected overpressure of the slab faces for external explosions (Wu et al., 2010). Fig. 8 compares the overpressure histories from the blast testing events 2 and 3. As shown, for the same
Fig. 6. Window for high speed camera (left) and view of high speed camera (right).
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5
Fig. 7. Overpressure histories at P5eP8 for event 4.
charge weights, the peak reflected overpressure for the horizontally oriented cylindrical charge in the axial direction is significantly greater than that for the spherical charge (Fig. 8(b)). Interestingly, the arrival time for the cylindrical charge in the axial direction is much less than that for spherical charge. This is because during
detonation the booster ignites, causing enough energy to detonate the cylindrical shaped charge that caused the blast explosion to emit the highest pressure wave to the right shown in Fig. 9(b) as ‘Pressure Wave Front B’ so that the pressure wave arriving at the wall quickly. ‘Pressure Wave Front A’ is emitted perpendicular to
Fig. 8. A comparison of overpressure history at P5eP8 for events 2 and 3.
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Detonator Overpressure Wave Front B
Overpressure
Booster
Wave
Explosive
Front A
(b)
(a)
Fig. 9. (a) Charge shape, (b) overpressure distribution.
of the curve for larger charge weights. It can be seen that the change in fireball diameter becomes less as the charge weight increases.
Table 2 Peak overpressure summary. Event
Orientation
Pressure gauge
Scaled distance (m/kg1/3)
Peak reflected overpressure (kPa)
1
Axial Radial NA
P6 P8 P6 P8 P6 P8 P6 P8
3.3 2.9 2.9 2.6 2.9 2.6 2.6 2.3
a
2 3 4 a
Axial Radial Axial Radial
Fig. 11. Comparison of experimental peak reflected overpressures with UFC prediction.
250 327 335 502 370 1060 570
Data faulty.
the length of the blast cylinder and it is quite similar to pressure wave caused by spherical charge and that is why the peak overpressures, shapes of overpressure histories and arrival times at P5, P6 and P 8 are quite similar. Table 2 summarizes the peak reflected overpressure recorded for each event. The lowest peak reflected overpressure recorded was 250 kPa for event 1, and the highest recorded was 1060 kPa for event 4. 2.2.2. Fireball The fireball was able to be captured for all events. A photograph for event 3 is shown in Fig. 10(a). The fireball is significant because the temperatures are high and the combustion of gaseous products produced by the chemical process involved in the explosion will exert additional pressures in this region. The fireball diameter for all cylindrical charge events has been plotted in Fig. 10(b). Two additional points have been plotted from approximate data obtained from the DSTO testing to give a better depiction of the trend
2.3. Analysis of experimental results The experimental results of peak reflected overpressure and impulse are compared with UFC predictions in Figs. 11 and 12, respectively. The general procedure for use of UFC to predict confined blasts is shown in Appendix. From observation of the peak reflected overpressure, it can be seen that UFC gives a significantly lower prediction for the axially oriented cylindrical charge at gauge P6, and also underestimates the radially oriented cylinder at gauge P8. This shows the need to investigate the cylindrical charge and to observe the loading distribution because Figs. 11 and 12 are based on a localized overpressures whereas UFC uses an average uniform overpressure distribution. UFC is conservative for the first 5 ms of the impulse in Fig. 12 for both charge shapes. This is due to the gas pressure (see Fig. 13(a)), which UFC significantly overestimates. However, as the scaled distance decreases, the axially oriented cylindrical charge becomes more critical which calls for an investigation into the impulse produced from this charge orientation for larger charge weights. A comparison of the experimental gas pressure for event 4 at gauge P8 with UFC prediction with minimum opening is shown in Fig. 13(b). The experimental plots stopped at 200 ms because data was only recorded until this point, but it appears that the gas pressure would continue for a significantly longer duration. The UFC prediction can be seen to have a considerably larger impulse by the area under the curve for the available results, however, the UFC prediction is limited because it does not provide predictions for the low loading density used in the experiments, and the closest available values were used.
Fig. 10. Fireball for event 3 (a) and fireball diameter as a function of charge weight (b).
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Fig. 12. Comparison of experimental impulse for the first 5 ms with UFC prediction.
The variation of reflected overpressure with angle of incidence has also been plotted in Fig. 14 based on gauges P5 and P6. When comparing an axially oriented cylindrical charge with a spherical one of the same charge weight, the peak reflected overpressure is approximately 1.5 times greater for the cylindrical charge, irrespective of the angle of incidence. However, the charge weight is relatively small. As the charge weight increases, relatively more energy is directed axially for the cylindrical charge and it becomes more directional. 3. Validation of finite element model A finite element program AUTODYN was validated in the previous studies to simulate the blast loading in confined geometries (Hu et al., 2011). This blast program was to develop an experimental data set which would enable the AUTODYN model to be calibrated. This would enable the model to be used with confidence to generate the overpressure and impulse distribution. In the numerical model, air and TNT are simulated by Euler processor. The air is assumed to have the ideal gas equation of state:
p ¼ ðg 1Þ$r$e
(1)
and the TNT material is modelled by the JoneseWilkenseLee (JWL) equation of state:
u u ue er1 v þ C2 1 er2 v þ p ¼ C1 1 v r1 v r2 v
(2)
where g is the heat specific ratio, r is density, e is internal energy, C1, C2, r1, r2 are constants, u is report of the specific heat, v is specific volume. The standard constants of air and TNT are retrieved from the standard AUTODYN library and the material constants are used
Fig. 14. Comparison of experimental peak reflected overpressure for spherical and axially oriented cylindrical charges with a standoff distance of 1.5 m.
in the numerical model, including air mass density r ¼ 1.225 kg/m3; air initial internal energy en ¼ 2.068 105 kJ/kg; ideal air gas constant g ¼ 1.4; and C1, r1, C2, r2 and u are 3.7377 105 MPa, 4.15, 3.74713 105 MPa, 0.9, and 0.35, respectively (Century Dynamics, 2003). The experimental blast program, event 2 which was a spherical charge, was used to calibrate the AUTODYN model. Since the detonator was placed inside the spherical charge to approximately achieve centre detonation and a spherical blast wave, the charge was first modelled in one dimension as shown in Fig. 15(a) to reduce the computational cost during the initial stages of detonation and expansion of the charge. The charge calculation was set to terminate when the blast wave reached the confinement walls where a remap file containing the cell data was transferred to a 3D model shown in Fig. 15(b) where pressure wave interactions were modelled. Fig. 15(b) represents the bottom northwest corner in the blast chamber (see Fig. 1) as defined by the pressure gauges. Please note that that the mesh size for the 3D model is selected to be 10 mm, and the size for the 2D charge model is 1 mm for the above validation model. It can be seen in Fig. 15(b) that the blast pressure wave is on the verge of hitting the ground and is uniform in all directions. The rebates in the corner account for the thickness of the pressure gauge plates by setting the mesh cells as unused. The experimental pressure and the predicted pressure from AUTODYN model at gauge location 7 and 8 are compared in Fig. 16. It is evident from Fig. 16 that the model adequately depicts the reflected overpressure for gauge P8 at an angle of incidence of zero and in the corner of the confinement at gauge P7. The peak overpressure and impulse are predicted within 10% and 20%
Fig. 13. Gas pressure for event 4, gauge P8.
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Fig. 15. Last stages of pressure wave development in one dimension (a), and three dimension initial model (b).
Fig. 16. Comparison between modelled and experimental overpressure time histories for event 2, spherical charge.
respectively for P7, and 20% and 50% respectively for P8. The relatively large difference in impulse for P8 is attributed to not simulating the top half of the chamber and thus omitting the reflection from the roof which converges approximately with the reflection from the floor for the second pressure peak. By utilizing the above the result, the model was deemed to be adequately calibrated for simulating spherical charges in a confinement to investigate the variation in reflected overpressure and impulse at different locations. Analysis of the cylindrical charge was significant because many modern explosives are cylindrical in shape and not spherical as assumed by guidelines, and because the reflected overpressure for cylindrical charges is larger than spherical charges for similar
charge weight (Burge et al., 2009). This is due to the fact that the majority of energy is directed in the axial direction. A depiction of the blast pressure wave that was produced for a cylindrical charge (event three) is shown in Fig. 17. As evident from Fig. 17, the blast pressure wave is concentrated in the axial direction. This is different to a spherical charge where an equivalent blast pressure is produced in all radial directions. Such a representation is supported by the experimental program, where the peak reflected overpressure in the axial direction is significantly greater than that of an equivalent spherical or radially oriented cylindrical charge. Since the charge was end detonated on the right side, the pressure wave has further directionality to the side opposite the detonation point, as indicated by the further
Fig. 17. Visual representation of the blast pressure wave produced from a cylindrical charge.
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Fig. 18. Comparison between modelled and experimental overpressure time histories for event 3, cylindrical charge.
travel distance on the left side and the larger pressures with more in the yellow range. The charge was remapped to the same confinement as in Fig. 15(b) with axial symmetry and the result of the further validation at gauge locations P5 and P2 is presented in Fig. 18. In the validation, gauge P5 represents axial direction on the floor, and P6 represents the axial direction at an angle of incidence of zero. The peak overpressure and impulse for the positive phase are simulated to 20% and 4% accuracy for P5 respectively, and 5% and 20% for P6. The level of validation is considered to be sufficient and the AUTODYN is used to characterize confined blast loads for cylindrical charges. 4. Application of the numerical model In the previous studies a numerical model was used to conduct parametric analysis for charge weight, charge shape, charge orientation, length to diameter ratio, confinement geometry, and confinement volume (Wu et al., 2010). In this study, the numerical model calibrated in Section 3 is utilized to conduct parametric studies for simplification of confined blast loading. By generating more data with the AUTODYN models, a new model for cylindrical charges are developed for predictions of the overpressure and impulse distribution in confined wall surfaces. The overpressure distribution along axial direction of the cylindrical charge on ceiling, wall and floor of cube is investigated. The pressure gauge locations along axial direction of the cylindrical charge on wall of the 2 m 2 m 2 m cube are shown in Fig. 19. The overpressure time history at different locations for a 0.2 kg cylindrical charge (L/D ¼ 1) placed in the centre of the cube is shown in Fig. 20. The results show that the cylindrical charge is highly
Fig. 19. Structure layout of cubic confinement and gauge location, plan (left) and section (right).
directional where the first peak at the centre gauge, P1, dominates. A second peak at P1 occurs at around 3 ms due to shockwave reflections from the side walls, roof and floor converging. Since P7 is close to the side wall (see Fig. 19), a comparable second peak occurs soon after the first. Although it appears that the overpressure from subsequent pressure peaks and at gauges P4 and P7 is of minor significance, this is not the case because the first peak accounts for only a fraction of the area under the overpressure time history, or the energy imparted to the structural member. This is reflected in the dynamic member response where the maximum deflection is three times greater for the confined case considering multiple peaks, and increases for larger charge weights. From the literature review, most guidelines such as UFC-3-34002 assume a uniform overpressure distribution for confined blast loading and only a few manuscripts (Baker et al., 1983) show more complex distributions, for example the possibility of overpressure increase in corners (Savir, Edri, Feldgun, Karinski, & Yankelevsky, 2009). Fig. 21 shows the simulated overpressure distribution along the ceiling, wall and floor in the cube for a 1 kg end detonated cylindrical charge inside the 2 m 2 m 2 m cube where P0 is the peak overpressure generated by a same weight of spherical charge at centre of the cube. The corresponding overpressure time history for a 1 kg end detonated cylindrical charge on the wall is shown in Fig. 22(a). All the pressure gauges in Fig. 22 are considered by including the contributing area of each gauge and taking the weighted average across the height to convert the blast load from two dimensions to one dimension. The use of average blast loads can be used providing the element has the ability to transfer localized loads to
Fig. 20. Effect of cubic confinement along the length of a member for a 0.2 kg cylindrical charge placed in the centre.
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C. Wu et al. / Journal of Loss Prevention in the Process Industries xxx (2013) 1e14 Table 3 Unit reflected impulse using the tributary method for a 1 kg axially oriented cylindrical charge in a 2 m cubic confinement. Contributing gauges
Unita reflected impulse (kPa ms) Model
UFC
% Diff
P1e3 P4e6 P7e9
710 380 1060
1440
51 74 26
a
Corresponding to the time of the first overpressure peak for UFC.
Fig. 21. Simulated overpressure distribution along the side wall of a cubic confinement.
regions of lower stress. The UFC guideline assumes a uniform distribution, which is also shown for clarity. Fig. 22(a) shows a comparison of average overpressure time histories in the axial direction of a cylindrical charge where the average overpressure at gauges P1e3 is almost an order of magnitude larger than at gauges P4e6. The average overpressure increases at P7e9 due to the influence of the edge and the corner with multiple shockwave reflections, however the overpressure in the direct axial direction at P1e3 is still over two times larger. This distribution of average overpressure for the cylindrical charge is quite general even for different confinement geometries. The comparison of impulse with UFC across the length of the element is shown in Table 3. It can be seen that UFC is conservative for the cubic geometry with the modelled impulse being lower at each location. Since the cylindrical charge is so directional, it will provide more critical loading on thinner elements because the gauges will be closer to the centre where the impulse is large. A spherical charge was simulated to compare the variation in average overpressure along the length of the wall with the cylindrical charge as shown in Fig. 22(b). It can be seen that the uniform loading distribution assumption of UFC is rational because the average overpressure peaks at all three locations are approximately the same. This is significantly different from the cylindrical charge where a uniform assumption does not provide an accurate representation. Since UFC only considers spherical charges, the blast load
Fig. 23. Comparison of average reflected overpressure for a 0.2 kg centre detonated cylindrical charge at two different locations at the critical gauge.
model needs to be modified for cylindrical charges. The result also illustrates the conservatism of UFC since a direct comparison can be done with the spherical charge, and the reason for the difficulty to find a higher impulse with cylindrical charges when considering the average overpressure. The effect of charge location was examined to see how significant the centre spot is in a cube for a cylindrical charge, keeping in mind that practically placing a charge in the centre is considerably harder. This was done by placing a 0.2 kg charge 15% below the centre point. Since there was no longer symmetry in the vertical direction, the full height of the chamber had to be modelled, with five gauges along the height instead of three as shown in Fig. 19. At the level of the charge, the pressure gauges were adjusted to capture the axial direction without losing the peak overpressure on the wall. The effect of charge location at the critical gauge is shown in Fig. 23. As shown, although the average overpressure for a charge being offset by 15% is lower at some points in time, it is higher at other points and overall there is little noticeable difference between the two locations.
Fig. 22. Comparison of average reflected overpressure across the length of the member for a 1 kg (a) end detonated cylindrical and (b) spherical charge placed in the centre of a 2 m cube.
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Fig. 24. Comparison of the average reflected overpressure at the centre for a 0.2 kg cylindrical charge placed at two different locations.
Fig. 25. Structure layout of rectangular confinement and gauge location, plan (left) and section (right).
11
From Fig. 23, the main difference that can be seen is the absence of the larger multiple peaks where the charge is offset from the centre because there is no symmetry in the vertical direction. However, for a cylindrical charge, the multiple peaks from the centre location are relatively small compared with the first peak which is considered to have a minor effect. This is confirmed in Fig. 24 where overpressure was averaged over the five gauges based on the contributing area. It can be seen that although the average overpressure for the offset charge is lower at some points in time, it is higher at other points and overall there is little noticeable difference between the two locations. If a charge larger than 0.2 kg is used, the charge location would also have a minor effect because the first peak would be much larger than the second. More energy would go in the axial direction if the charge weight increased based on the experimental results in Fig. 24. Multiple charge weights were simulated for the case where UFC could be improved. A new and more accurate blast model for cylindrical charges has been proposed by considering loading on the same level as the charge across the longitudinal direction. It is of great significance for the cylindrical charge because of its directional characteristics. It could be for this reason that most warheads are cylindrical rather than spherical. In this case, larger charge weights of 0.5e2.4 kg were considered because more energy is directed in the axial direction and it is this that UFC fails to account for. A rectangular confinement of 2.8 m 2 m 1.4 m as shown in Fig. 25 was used to develop the new model for cylindrical charges. A comparison of the impulse for different charge weights is shown in Table 4. Looking at the 0.2 kg charge, the simulated impulse is lower than UFC at all three locations, therefore this charge could not be used to improve UFC. For the 1 kg charge, the impulse at location P1 and P7 is 310% and 160% greater than UFC respectively, however only 57% at location P4. This was significant, and needed new method to characterize the blast load.
Table 4 Comparison of impulse for different charge weights at different locations for the end detonated cylindrical charge. Charge weight (kg)
0.2 0.5 1 2.4
Scaled distance (m/kg1/3)
1.71 1.26 1 0.75
Location P1
P4
ir (kPa ms)
%ir
378 2660 3930 6690
95 370 310 280
UFC
P7
to (ms)
%ir1
%ir
e 0.5 0.4 0.35
35 17 18 17
33 63 57 49
UFC
%to1
%ir1
%ir
e 260 230 230
50 46 52 57
47 170 160 160
UFC
%to1 e 260 240 230
Fig. 26. New model for cylindrical charges at location (a) centre, (b) intermediate, (c) end.
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Fig. 27. Comparison of new model to simulated average reflected overpressure for a 1 kg end detonated cylindrical charge placed in the centre of a rectangular confinement.
Table 5 Impulse distribution for different confinement geometries for an axially oriented and end detonated cylindrical charge. Geometry (m)
Location P1
P4
ir (kPa ms) %ir 222 4190 2.8 2 1.4 3930 421 4320
UFC
290 310 400
P7
to (ms) %ir1 %ir 0.4 0.4 0.4
11 18 19
33 57 78
UFC
%to1 %ir1 %ir 200 35 230 52 200 40
UFC
64 160 160
%to1 240 240 240
From Table 4, it can be seen that %ir1 at location P4 for the 0.5e 2.4 kg charges is approximately 18%, and at location P7 is approximately 50%. It can also be seen that %t01 is approximately 200% for both locations P4 and P7. Therefore, the new model was characterized as shown in Fig. 26. Due to the directional nature of the cylindrical charge, the impulse varied at three different locations. The model at the centre was used as a control. The impulse at the intermediate location is conservatively simplified to 0.25ir from the actual data of 0.18ir, and the impulse at the end is set to 0.5ir based on the actual data. It can be seen that the impulse increases at the end due to being close to the side wall where multiple reflections occur. The time for the shock pressures at the intermediate and end location is simplified to 2to based on the modelled data. Since the shock peaks are simplified as triangle, the peak overpressure, impulse, and time are related by:
Fig. 29. Average unit reflected impulse for axially oriented cylindrical charges (N ¼ 4, l/ L ¼ 0.50, h/H ¼ 0.50, L/RA ¼ 2.8).
to ¼ 2ir =pr
(3)
Based on the duration and the impulse, the peak overpressures for the intermediate and end locations are obtained to be 1/8Pr and 1/4Pr respectively using equation (3). The gas pressures are kept the same as in UFC since they are found to give reasonable and conservative estimates. The new model for shock pressures, not including the gas pressures, is applied to the average overpressure time history for the 1 kg charge as shown in Fig. 27. Although the two red peaks are separated, it is the total impulse that governs and the two peaks can be simplified to give one single peak. It can also be seen that the large peak at P1 has a relatively short duration compared to P4 and P7, and this is accounted for in the model. The model was also checked for different confinement geometries to find its effectiveness. The result for a 1 kg cylindrical charge with a scaled distance of 1 m/kg1/3 is shown in Table 5. Looking at the 2 m cubic geometry, the new blast model can be applied conservatively at locations P4 and P7 (see Fig. 19) with a predicted impulse of 25%ir1 and 50%ir1 respectively. Similarly for the 4 m 2 m 1 m geometry, the model can be applied confidently. As the geometry becomes more rectangular, the effects of a cylindrical charge become more critical and UFC predictions become inadequate. New design charts for the reflected overpressure and impulse values to be used in the cylindrical blast model for the 2.8 m 2 m 1.4 m geometry are shown in Figs. 28 and 29, respectively. The parameters for the plots are the same as defined in UFC-3-340-02 (2008), and are included in 0. With the aid of Figs. 28 and 29, the average peak reflected overpressure and impulse can be obtained and then simplified overpressure history can be determined by Fig. 26. It should be noted that the current model for cylindrical charges is only suitable for cuboid chambers with small volumes. 5. Conclusions
Fig. 28. Average peak reflected overpressure for axially oriented cylindrical charges (N ¼ 4, l/L ¼ 0.50, h/H ¼ 0.50, L/RA ¼ 2.8).
In this blast program, four confined blasts with one spherical charge and three cylindrical charges were conducted to develop a robust AUTODYN confined blast load model. The experimental results were analyzed and compared with the current guideline, UFC-3-340-02, to show its limitations for cylindrical charges. The AUTODYN model was calibrated using the experimental data. With the calibrated model, the significance of confinement for cylindrical charges was demonstrated, which indicated that
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confinement magnifies the influence of blast loadings greatly. Investigation of the charge shape showed that the axially oriented cylindrical charge produced the largest peak overpressure and impulse on the confined chamber wall. Based on the simulated results a new model for cylindrical charges was developed for predictions of overpressure and impulse on a chamber wall.
Acknowledgements This study was sponsored by an Australian Research Council linkage project LP0883451 supported by DSTO and VSL.
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Appendix. The general procedure for use of the UFC-3-340-02 (2008) 1. From Fig. 2-51, select the particular surface of the structure which conforms to the protective structure given and note N of adjacent reflecting surfaces as indicated in parenthesis. 2. Determine the values of the parameters indicated for the selected surface of the structure in Item 1 above and calculate the following quantities: h/H, l/L, L/H, L/RA, and ZA ¼ RA/W1/3. 3. Refer to Table 2-3 for the proper peak reflected pressure and impulse charts conforming to the number of adjacent reflected surfaces and the values of l/L and h/H of Item 2 above, and enter the charts to determine the values of pr and ir/W1/3.
Table 2-3 List of illustrations for average peak reflected pressure and scaled average unit reflected impulse. h/H
l/L
Average peak reflected pressure
Scaled average unit reflected impulse
Number of adjacent reflecting surfaces
0.10
0.25
0.50
0.75
0.10 0.25 0.50 0.75 0.10 0.25 0.50 0.75 0.10 0.25 0.50 0.75 0.10 0.25 0.50 0.75
One
Two
Three
Four
One
Two
Three
Four
2e52 2e53 2e54 2e53 2e55 2e56 2e57 2e56 2e58 2e59 2e60 2e59 2e61 2e62 2e63 2e62
2e64 2e65 2e66 2e67 2e68 2e69 2e70 2e71 2e72 2e73 2e74 2e75 2e76 2e77 2e78 2e79
2e80 2e81 2e82 2e81 2e83 2e84 2e85 2e84 2e86 2e87 2e88 2e87 2e89 2e90 2e91 2e90
2e92 2e93 2e94 2e93 2e95 2e96 2e97 2e96 2e98 2e99 2e100 2e99 2e95 2e96 2e97 2e96
2e101 2e102 2e103 2e102 2e104 2e105 2e106 2e105 2e107 2e108 2e109 2e108 2e110 2e111 2e112 2e111
2e113 2e114 2e115 2e116 2e117 2e118 2e119 2e120 2e121 2e122 2e123 2e124 2e125 2e126 2e127 2e128
2e129 2e130 2e131 2e130 2e132 2e133 2e134 2e133 2e135 2e136 2e137 2e136 2e138 2e139 2e140 2e139
2e141 2e142 2e143 2e142 2e144 2e145 2e146 2e145 2e147 2e148 2e149 2e148 2e144 2e145 2e146 2e145
Fig. 2-51. Barrier and Cubicle configurations and parameters.
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