Field test and probabilistic analysis of irregular steel debris casualty risks from a person-borne improvised explosive device

Piotr W. Sieliki , Mrk G. Stewrt , Tomsz Gjewski , Mih? Mlendowski ,Piotr Peks , Hsn Al-Rifie , Roert Studzi′nski , Wojieh Sumelk

a Institute of Structural Analysis, Faculty of Civil and Transport Engineering, Poznan University of Technology, 5 Maria Sk?odowska-Curie Square, 60-965,Poznan, Poland

b Institute of Building Engineering,Faculty of Civil and Transport Engineering,Poznan University of Technology,5 Maria Sk?odowska-Curie Square,60-965,Poznan, Poland

c Centre for Infrastructure Performance and Reliability, The University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

Keywords:Flying fragments Human safety Person-borne improvised explosive device experiment Probabilistic analysis

ABSTRACT Person-borne improvised explosive devices (PBIEDs) are often used in terrorist attacks in Western countries. This study aims to predict the trajectories of PBIED fragments and the subsequent safety risks for people exposed to this hazard. An explosive field test with a typical PBIED composed of a plastic explosive charge and steel nut enhancements was performed to record initial fragment behaviour,including positions, velocity, and trajectory angles. These data were used to predict the full trajectory of PBIED fragments using a probabilistic analysis. In the probabilistic analyses a probability of fatality or serious injury was computed. Based on the results presented, many practical conclusions can be drawn,for instance, regarding safe evacuation distances if a person were exposed to a suspected PBIED.

1. Introduction

Improvised explosive devices (IEDs) have been a weapon of choice for terrorist attacks in Europe, North America, and other Western countries. Recent IED attacks include trains in Madrid(2004);trains and a bus in London(2004);government buildings in Oslo (2011), Stade de France, the Bataclan Theatre, and a caf′e in Paris (2015); an airport and train station in Brussels (2016), and Manchester Arena (2017). Most of these IED attacks involved a person-borne improvised explosive device (PBIED)containing less than 10 kg of explosives [1].This conclusion is not unexpected;an analysis of bomb incidents over the past 15 years found that most IEDs weigh less than 5 kg[2].Most of the attacks were conducted in urban environments where structures are exposed to the blast effects. As a result, there has been substantial research into the structural damage to buildings,bridges,pipelines,trains,and other infrastructure elements from blast pressure and impulse [3,4].However, most terrorist attack casualties in Western countries(post-9/11) have been from primary and secondary injuries [5,6]due to fragmentation and blast overpressure (e.g. lung rupture,brain acceleration, whole-body displacement, or skull fracture)rather than from falling columns, beams, slabs, or other structural components [7,8]. Infrastructure structural components have proven highly resilient to terrorist IED attacks; however, more research is needed to understand casualty risks from bomb fragmentation and blast overpressure hazards,especially from PBIEDs.Understanding of initial fragment mass, velocity, and distribution as well as the fragments’ drag coefficients, kinetic energy, throw range,and density probabilities is essential.For example,fragment mass, count distributions, and velocities are used in SAFER (Safety Assessment for Explosives Risk) and VAPO (Vulnerability Assessment and Protection Option), software developed by the U.S.Department of Defense Explosive Safety Board (DDESB) and the Defense Threat Reduction Agency(DTRA)to predict fragmentation distributions and casualty risks.However,these software programs are best suited to assessing military ordnance safety risks because they utilise predefined munitions parameters and fragment masses that are not easily applied to IEDs. IED fragment density is highly spatial, not symmetric, and heavily reliant on the explosive’s placement and the source material of the fragments.This paper was prompted by Yokohama et al.’s [9] conclusions where they noted that,“IED fragmentation data is unavailable since it is not published in the open literature;”“IED fragmentation is difficult to predict for its stochastic nature;”and“the current modelling capability of the IED fragmentation is less mature.” There are significant uncertainties and variabilities associated with modelling primary fragmentation.The explosive safety distances proposed by the U.S.Department of Defense Explosive Safety Board [10] consider some of these uncertainties when predicting casualty risks from accidental detonation of military ordnances. The DDESB [10] suggests that, when predicting casualty risks from accidental detonation of military ordnances, model accuracy is low at between -95%and +200%. Clearly, there is a need for improved modelling and statistical characterisation of the main variables associated with fragmentation. Characterisation of IED blast and fragmentation uncertainties using stochastic (probabilistic) methods is a logical step to improve risk estimates.

One of the most common PBIEDs worldwide is the suicide vest.These devices were used in the 2015 Paris attacks and contained no more than 10 kg of triacetone triperoxide (TATP) as the explosive agent. Pachman et al. [11] examined TATP and found an average TNT equivalent from incident overpressure equal to 70%, and for impulse of the positive phase of the blast wave,it reduces to 55%;it may be assumed that a similar effect would be obtained from an approximately 6-8 kg TNT charge. Thus, an explosive charge of modest mass may significantly accelerate IED fragments,increasing the risk of mass casualties.

The present paper assesses the casualty risks and safe evacuation distances for people exposed to suicide vest PBIEDs.The main aim of this paper is an improved understanding of the primary fragmentation of PBIED vests containing hundreds of steel nuts;its secondary aim is for the knowledge gained herein to be generalisable to other improvised projectiles intended to result in mass casualties.

2. Materials and methods

2.1. Experiment setup

The primary objective of this experiment was to measure the initial velocity, trajectory angle, final range, and kinetic energy of fragments from a PBIED.Due to security reasons,it is not possible to show all details of the assembly and detonation of a PBIED.Nevertheless, the concept and geometry presented herein may be viewed as representative of some PBIEDs used in the 2015 November attacks in Paris. In this study, 4.43 g M8 stainless steel hex nuts were used as enhancements. Hex nuts were chosen for representing the flying projectiles because they are one of the most used in PBIED;mainly because they are easy to get by trade without raising suspicions. The setup of the device was built on the experiences of special forces, which often investigates such explosive devices. Thus, hex nuts arrangement and quantity are close to the real-world cases. The nuts were layered in front of the explosive charge in an open-faced sandwich, as shown in Fig.1. The layer of nuts comprised nine rows and 24 columns (a total of 216 nuts in one layer) measuring 120 mm × 310 mm, see Fig. 1(b). The PBIED-shown at A in Fig. 2(a)-consisted of the suicide vest containing charge of plastic explosive number four (PE4), a similarly-sized layer of clay a few centimetres thick,a rigid,bulletproof layer of Kevlar, and the layer of 216 hex nut projectiles weighing a total of 957 g.The PBIED was fixed to wooden stakes at a height of 0.9 m above the ground level,as shown in Fig.2(b).Due to the sensitivity of the data the mass of the IED was classified.

The full experimental site is shown in Fig. 3. One of the objectives of this paper is to assess the trajectory of the debris originating from the PBIED;another objective is to evaluate the effect of PBIED fragment distribution on the car, shown at D in Figs. 3 and 4.Fragment distribution on the plywood panels(B,C,and E)remains a topic for future research. Plywood panel B is situated perpendicular to the camera view in order to create the background for camera for observing horizontally flying nuts.The car,D,is located 10.8 m from the PBIED, see Figs. 2(a) and Fig. 3.

An important aspect of this test was to measure the velocity and trajectory of the hex nut enhancements during the first 10 ms of flight after acceleration by the explosive charge.Fragment velocity data was collected through video recording and later postprocessing of the data.The magnitude of velocity was estimated for 74 fragments using a high-speed video in combination with velocity screens and witness screens.

Fig. 2. PBIED experiment set up: (a) back view and (b) front view.

Fig.1. Elements of the PBEID used in the experiments: (a) the set-up plan and (b) the layer of 216 hex nuts.

Fig. 3. Full (side) view of the experiment site.

Fig. 4. Small-size car used in the experiment.

2.2. Fragment loading measurements

Several factors influence the reliability of the measurements of highly dynamic experiments.Verification that the values recorded are physically correct was allowed for in test preparations.Based on the previous experiences of the Poznan research group, it was crucial to define the location of the high-speed camera to obtain an accurate measurement of velocity of objects that could be traveling faster than the speed of sound. The goal was to measure 10 to 20 individual nuts, each with a different velocity, flying at different horizontal and vertical angles.

The test scheme is presented in Fig. 5. It was assumed that the projectiles would be launched at point A and fly to Cn. The highspeed camera recording system was capable of following the objects in their first 10 m of the flight-from the detonation position, A, to the car, D. This trajectory is presented in Fig. 5, see red(rising) and green(falling) curves.

Another important description of the trajectory of each nut is the vertical angle between the trajectory and horizontal direction-the angle θxin Fig.5.The perfect measurement assumes that a separated nut followed by the measurement equipment can be found at the final XMAXdistance,Cn.The objective of this paper is to predict the trajectory of all nuts during full flight trajectory using only initial launch conditions. This prediction can be obtained based on a classical system of equations of motion:

where x and y are the coordinates of the plane of interest;t is time;Cdxand Cdyare the drag coefficients in x and y directions, respectively; Axand Ayare the nut area projections in x and y directions,respectively;ρ is air density; g is gravity; and m is fragment mass.The drag coefficients Cdxand Cdywere assumed at 0.8 for horizontal and 1.5 for vertical ascending and descending movements. For further consideration of the trajectory assessment, the crosssectional areas (Ax, Ay) of the nut are necessary. Because of the uniform geometry of projectiles, the authors assumed that the projected areas would be measured in two major orientations.Hence, the vertical and horizontal cross-sectional areas of a nut were equal Ax= 105.5 mm2and Ay= 129.3 mm2, respectively. In general,the shapes of projectiles may be highly irregular and thus,determining its drag coefficients and projected areas may be difficult to estimate,see Moxnes et al.[12]and Kljuno and Catovic[13].

Fig. 5. Range and locations of the primary measurement areas.

Fig. 6. Sequential time steps from 0 to 26.4 ms after detonation: blast wave movement (yellow dashed lines) and hex nut fragments in flight (red squares).

3. Results and discussion

The explosive field test was conducted in Poland close to the city of Poznan.Fig.6 shows time-lapse images of the detonation of the PBIED-the blast wave(shock front)and the fragment locations.As documented, the blast wave caused by the detonation overtakes the flying nuts in the first few milliseconds,see Fig.6(b).The blast wave front is marked with a yellow dashed line. Due to the resolution of the video,the blast wave velocity and how it decreases in time may be observed, compare Fig. 6(b) through Fig. 6(e). The average wave velocity reached 470 m/s,with an estimated incident overpressure value of 15-20 kPa at a distance of 8 m from the PBIED, Fig. 6(d).

Fig. 6 shows the projectile cloud area; for clarity, nuts are marked by red squares. Each nut located within the recording has own location in the experiment based on velocity, trajectory, and time.During the experiment,side boundaries were used,consisting of a rigid box around the vest shown as G in Fig.1 (a), to catch all projectiles with trajectories greater than θy= 2.5°from a perfect horizontal trajectory or azimuth angle. Thus, it may be stated that the fragments are analysed in two-dimensional plane,i.e.XY plane,see Fig. 5.

Acceleration of debris increases in the first few metres, and velocity reaches its maximum magnitude in the next 5-8 m,so the initial velocity was measured as the average velocity over that 5-8 m. The accuracy of the in-plane distance measurements from the high-speed video is about ±0.05 m, leading to an in-plane accuracy of velocity of about±0.5%.In addition,if an individual nut’s flight trajectory is 2.5°horizontally from the perfect(camera-view plane) trajectory, the out-of-plane error of distance while measuring velocity is approximately 0.01 m (10.8 m-0.8 m × cos 2.5°).Based on the slowest and the fastest fragment measurements,velocity measurements are accurate out-of-plane to less than±1%.Taking into account both in-plane and out-of-plane directions,the overall velocity measurement error is equal to 1.1%.

The trajectories of 74 nuts were recorded during the field experiment. Two high-speed cameras recorded the velocity and distance measurements from different angles. The primary record was made using a Phantom v711 camera-as used in Sielicki et al.[14,32,34],-located 50 m from the PBIED and perpendicular to the virtual axis A-C,see Figs.3 and 6.A Phantom Miro320S was used to record the nuts that directly hit the car or the wooden witness obstacles, see camera F, Fig. 3.

During the initial measurement of object trajectories, the number of frames recording these movements is crucial. With a recording speed of 2700 frames per second, Camera F recorded objects on 129 frames due to processing speed limitations.All flying objects were identified in each frame. A similar situation was observed on the primary camera, where the recording speed was 19000 fps, and more than 1100 frames were used. Automatic procedures for monitoring a moving object were applied and implemented in Scilab code with Phantom PCC 3.1 camera control software.

The final data for all 74 measured nuts are presented in Table 2.Note that a negative value of θxwas obtained if the debris impacted the ground close to the PBIED. Also, some fragments with short landing distances were impossible to measure due to the obscuring effects of the fireball and dust cloud directly after detonation. The peak value recorded was 50°and for instance two pieces of projectile were found only 1.0 m and 2.5 m from the PBIED, thus yielding angle values of-43°and-21°,respectively.Results show that velocity decreased as angle increased-from 500 m/s to 200 m/s.

Experimental data obtained from the field test established boundary conditions for the system’s equations of motion. Eq. (1)was used for each fragment to estimate trajectories with particular interest in final resting place and the velocity magnitude just before its contact with the ground, and the kinetic energy was computed.All those data are presented in Table 3. The trajectories computed from Eq. (1) are presented in Fig. 7, where the kinetic energy is shown in colour-black,blue,and grey-for the particular position of the fragment.The energetic criteria are used to assist in the analysis of the harmfulness of the fragments. Three levels of kinetic energy were assigned based on the kinetic energy of the fragment at particular moment.Injury due to the blast wave itself is not analysed in this study;however, this is an important aspect of low mass charge damage, as shown by Gajewski and Sielicki[15,30].

In Fig. 7, fragments drawn in black show the positions of particles with high kinetic energy-greater than 300 J-consistent with typical military bullets (9 mm and greater calibres). As shown by Kerampran et al.[33];a 9×19 mm Parabellum bullet,used widely in military handguns, with a mass of approximately 8 g obtains a velocity of 355 m/s, which results in kinetic energy of approximately 500 J.

Dots in light blue represent positions in which the kinetic energy is moderate-between 20 J and 300 J-which corresponds to the energy of 0.22LR calibre bullets.

The grey dots represent positions with low kinetic energy-below 20 J-which corresponds to pre-charged pneumatic rifle bullet.In Fig.7,to underline the boundaries between moderate and low kinetic energy, white circles were added.

Fragments with high kinetic energy (black) are highly dangerous to humans. These fragments encountering a human body will cause severe tissue damage, and are most likely pass through the body. Fragments with moderate kinetic energy (light blue) will cause less damage. They are likely to perforate the skin only without going through the body. Fragments with low kinetic energy(grey)are unlikely to perforate skin but will mark the skin,and severe bleeding is possible.

The harmfulness of the fragments accelerated by the PBIED should be assessed based on two criteria. The first criterion is related to close-range harm-up to about 20 m-where the fragments have the greatest kinetic energy, and their trajectory is approximately horizontal (a low or negative vertical trajectory angle θx),or their path height is not greater than 2 m(equivalent to about maximum human height). According to this criterion, only the first row of people would be hit with a fragment, but these individuals would experience severe injuries and/or death. People in the second row could be injured if fragments pass through the first row, with or without encountering a first-row body; the second row injuries resulting from fragments that have already impacted others would likely be minor due to fragment energy decrease. In our study, the primary kinetic energy of close range fragments was above 300 J, seeTable 3.

The second safety criterion is related to fragments falling after reaching their maximum heights,as illustrated by the green curve in Fig.5.The kinetic energy of fragments based on landing distances is shown in Fig. 8. Landing distances were between 120 m and 300 m,with major values greater than 200 m.The kinetic energy of all individual fragments was less than 70 J, with more than 90%below 20 J. Fragments landing at greater distances would have relatively low harmfulness;more individuals would be affected but injuries sustained would be less severe.

Fig. 8. Kinetic energy of fragments at landing distances.

4. Probabilistic data assessment

4.1. Trajectory angle and fragment density

Trajectory angle and fragment density may be treated as a bivariate normal distribution [10,17]; and [18] for vertical (θx) and horizontal (θy) trajectory angles:

where μxand μyare the mean angles of θxand θyand where σxand σyare the standard deviations of angles θxand θy,respectively.If the trajectory angles are equally spread with no bias, then the mean angle is μx=μy=0o.It might be expected that variability of θxand θywill be similar. Pope[17] also notes that, for a PBIED,“there is a strong bias for low values of θxand θyto be selected,” suggesting that the variability of angle trajectory will be relatively low.

A statistical analysis of the angle trajectories from 74 fragments(Table 2) reveals μx= 10.7°and σx= 18.8°. The skewness of data towards positive angles may be due to the detonator’s location near the bottom of the explosive mass.If the detonator had been placed more centrally,it is more likely that about half the fragments would have a positive angle trajectory,and the other half a negative angle trajectory (μx≈0°). If the data is limited to include only the 20 negative angles (from -43°to -0.9°)and the lowest 20 positive angles’ trajectories (from -0.65°to 6.02°), then μx= -3.4°and σx=8.7°,and as expected,the mean moves much closer to 0°and variability decreases. The statistics for angle trajectory are clearly variable and highly dependent on the characteristics of the PBIED composition and circumstances of detonation.

Fig.9 shows that the normal distribution provides a reasonable fit for the data from the 74 fragments described in Table 2. More data is needed to increase confidence in the best probabilistic model fit.

Statistics for the horizontal trajectory angle(θy)are not available because the test set-up only allowed fragments to deviate within±2.5°.Nonetheless,as noted above,it is expected that variability of θxand θywill be similar. As a starting point for analysis, two scenarios are considered:

Fig. 9. Histogram of trajectory angles and normal probability distribution.

1. PBIED used in current test:μx=μy= 10.7°and σx=σy= 18.8°

2. Generic IED detonated symmetrically: μx= μy= 0.0°and σx=σy= 18.8°

4.2. Probability of hit

The projected impact area (Ap) is assumed to be rectangular in shape with an aspect ratio (ratio of height to width) of ahw; this allows the height h and width w to be estimated.It is then assumed that the projected area is centred at the same height of the PBIED used in the test (0.9 m), a schematic is shown in Fig.10. Note that though the fragments have an initial spatial distribution before detonation based on the layout of the hex nuts in a 120 mm×310 mm layer,for convenience,a“point source”ejection is assumed [17].

The serious injury or fatality zone for a PBIED with a few kilograms of explosive is likely to be no more than about 20-30 m because at that range,the velocity of the fragments will be high and with a relatively close spatial density.At these short distances,it is appropriate to use a line-of-sight approach because,at high speeds,the fragments will travel in approximately a straight line over short distances of<100 m,as shown in Fig.6(b)and Fig.7.where R is the distance (range)from the PBIED to the individual (see Fig.10).

The average number of incapacitating fragments,N,at a distance R hitting the projected area of the exposed person located directly in front of the PBIED is expressed thus:

where n is the total number of fragments(n=216)and the bivariate fragment density distribution p(θx,θy) is given by Eq. (2).

Seven fragments measured at the field test impacted the car D.The projected area of the car is 4.024 m2, and an aspect ratio of ahw= 0.33 is assumed. The dispersion angles from the test are μx=μy=10.7°and σx=σy=18.8°.With these observed parameters and R = 10.8 m, Equation (3) yields N(R) = 7.6 fragments colliding with the car. If ahw= 0.25 or 0.5, then N(R) of the colliding fragments is 7.6 and 7.8,respectively;therefore,the predicted number of colliding fragments is not sensitive to the aspect ratio of the target. A predicted value of N(R) = 7.6 fragments compares well with the observed value of seven colliding fragments and provides some validation of the probabilistic modelling of fragment distribution.

Fig. 10. Schematic illustration of projected impact area, Ap. The trajectory angles needed to affect the projected area are as follows:

The probability of being hit, Phit, by at least one fragment is deduced from the Poisson distribution by the following equation:

4.3. Casualty risk assessment

The projected area of an exposed person is Ap=0.26 m2[19].If it assumed that the aspect ratio for Apis a height to width of 2,then an exposed person is modelled as a rectangle of height h=0.72 m and width w = 0.36 m (0.36 m × 0.72 m = 0.26 m2).

The density of fragments is not uniformly spread over the surface area of half a hemisphere centred on the exploding device.Fragment density and probability of being hit will be highest if the person stands close to and in front of the PBIED.Those values will reduce as the distance between the person and the IED increases,and the angle from the front of the device increases, i.e. as θyincreases to 90°. In this case, the average number of incapacitating fragments N at a distance R hitting the projected area of the exposed person is estimated from Eq. (3), and the probability of being hit by a fragment is calculated from Eq.(4)for each horizontal increment(θyi)until θy=±90°.These values are then used to infer the average hit probability for a person anywhere along a circumference with radius R from the PBIED. The probabilities computed according to Eq. (4)are presented in Fig.11.

4.4. Initial fragment velocity

Fig.12. Comparison of several probabilistic models with data histogram.

The statistics of initial fragment velocity, vo, obtained from launch data from Table 2 are μv= 405 m/s and σv= 110 m/s. The variability of initial fragment velocity is high, with a coefficient of variation (COV) of 0.27. Fig.12 shows the normal, lognormal, Weibull, gamma and Gumbel probability distributions fitted to the experimental data. The comparisons show that the normal distribution provides a good fit to the data, although the lower tail of velocities appears under-predicted.The Kolmogorov-Smirnov test found that all probability models were not rejected at the 5% significance level.

Note that the normally distributed random variables used in the present paper are truncated at zero to avoid negative values.Moreover, it should be noted that a probabilistic analysis can also consider non-standard probability distributions (e.g., bi-modal)and it may also allow for truncation of parameter values if there is a physical limit on that value.A benefit of Monte-Carlo simulation is that it can readily incorporate such non-ideal distributions into a probabilistic analysis.

Fig.11. Probability of being hit by at least one fragment based on location (σx = σy = 18.8°).

Most research on the initial velocity of fragments is based on cased explosives such as military munitions. Under such circumstances, Gurney equations are used, where the Gurney constant(√——--2E) is given for different types of high explosives. The Gurney constant for plastic explosive C4, which is equivalent to the PE4 used here[20,21]is 2530 m/s[22].Gurney equations are provided for cylindrical and spherical charges, thus applicable to most missiles,bombs,and mortars[22].However,a PBIED typically does not conform to these shape configurations. In our case, the PBIED is attached to stiff supports, which may be model as an infinitely tamped sandwich,see Fig.1(a).A Gurney analysis for this idealised configuration leads to an initial velocity of the hex nut fragments as follows [23]:

where C is the explosive charge mass(kg)and M is the total mass of fragment enhancements(kg).For instance,if C=1 kg and M=1 kg,then initial fragment velocity is equal about 2400 m/s.If the PBIED is model as an open-faced sandwich with no tamping, then the initial fragment velocity is reduced to about 1400 m/s [23]. These calculated model velocities are significantly higher than those observed from the test, where the mean velocity is 405 m/s. This difference can be explained by the layer structure of the PBIED;because the fragments and the explosive were separated by a layer of clay and bulletproof material and not in direct contact,the crosssectional area of the 216 fragments was smaller than the explosive charge. Pope [17] graphically presents observations regarding“adaptation of Gurney analysis to handle fragment throw-out.”,with particular interest in its application to real events.

4.5. Final fragment velocity

The flight of fragments will be affected by air resistance and gravity, leading to the following form of fragment velocity as an approximation to the equations of motion given by Eq. (1) [19]:

where k=0.002 for supersonic velocities(vo>335 m/s)and 0.0014 for subsonic velocities,vois the initial velocity of the fragment,m is the mass of the fragment (kg), x is the distance travelled by the fragment(m),and cdis the drag coefficient.The drag coefficient is a function of fragment shape, and as previously discussed, the drag coefficients of the nuts are in the range of 0.8-1.5. Hence, in the probabilistic analysis to follow,cdis taken as a uniform distribution[0.8,1.5].If cdis taken as 1.15(mean value),then the final fragment velocity at 20 m decreases by approximately 18% and 25% for subsonic and supersonic velocities, respectively.

4.6. Injury models

The injury from penetrating fragments“is of particular interest to the military, and much of the data are from military sources”[19]. The military are more concerned with injuries that will incapacitate but not kill a soldier.However,an incapacitation model has been adapted to estimate fatal and serious injuries by the probit equation:

Table 1 Random variables for casualty risks.

where v is the velocity of the fragment(m/s) and m is the mass of the fragment (kg). The probability of serious injury or fatality exceeds 90% if the impact velocity exceeds 190 m/s.

Kinetic energy-based calculations and other probabilistic analyses [19,24] may be used with other injury criteria defined by NATO and the U.S. Department of Defense to predict injuries-for example, incapacitation may occur if the kinetic energy exceeds 79 J(DOD,2009,[25].In the instant matter,probabilistic analysis is used to derive the probability of fatal and serious injuries for an individual:

· directly in front of the PBIED (θx=θy= 0°)

· anywhere within a 90°zone (θy= ±45°)

· anywhere within a 180°zone (θy= ±90°)

at distances from 5 m to 20 m from the PBIED. The random variables are shown in Table 1.

Results from the Monte Carlo simulation are shown in Fig.13 for 10000 simulation runs.As expected,casualty risks are significantly higher if the person stands directly in front of the PBIED, and the odds reduce if a person is located somewhere else, i.e. θy> 0°.Schematics of the location of victims from the 2017 Manchester Arena bombing [26] suggest that most victims were within 10-20 m of the PBIED. The casualty risks in Fig.13 also show that this range is the zone of high risk, and the risk diminishes beyond 20 m.For example,at 30 m,the casualty risks are about 5%for the 90°zone.

Risks may also be compared with risk acceptance criteria. For example, the UN recommends that, to be considered safe, evacuation distances ensure that the density of hazardous fragments(79 J)is less than 1 per 56 m2; this is approximately equivalent to a 1%probability of a person being struck by a lethal fragment[22].If this is the criterion,then an outdoor safe evacuation distance based on a 180°zone is 52 m; this would, however, increase to 69 m if the distance were directly in front of the PBIED. If μx= μy= 0.0°and σx=σy= 18.8°, the safety distance changes to 46 m and 83 m for the 180°zone and directly in front, respectively. In these cases, a conservative safe evacuation distance for the PBIED considered in the present paper would be approximately 85 m. This is a reasonable estimate given that the United States National Counter Terrorism Center [27] recommends an outdoor safe evacuation distance of 259 m for a 2.3 kg pipe bomb.

4.7. Sensitivity analysis

Fig.13. Probability of fatality or serious injury (σx = σy = 18.8°).

Fig.14. Change in casualty risks for person directly in front of a PBIED (σx = σy = 18.8°).

A sensitivity study is carried out to assess the relative impact of the variability and uncertainty of the model parameters on casualty risks. This was achieved by running the Monte Carlo simulation analysis with each parameter in turn modelled deterministically while all other parameters given in Fig.14 are modelled probabilistically. In Fig.14, the sensitivity study results are shown as the percentage point-change in casualty risks for a person standing directly in front of a PBIED at a distance of 5 m-20 m. Results are insensitive to drag coefficient variability, and thus, it is concluded that drag coefficient has a negligible influence on the results.Variability of initial fragment velocity changes the casualty risks by less than 1.4% in absolute terms. Clearly, if variability of fragment trajectory angle is omitted from the probabilistic analysis (i.e.,σx=σy=0°),then casualty risk is near 100% when μx=μy=0.0°.

5. Conclusions

Suicide vest PBIEDs are an important and current topic. An explosive field test for a typical PBIED containing steel fragment(hex nuts) enhancements was used to determine the initial velocities, initial trajectory angles, and kinetic energy of fragments.Those data were then used as boundary conditions to predict the trajectory of suicide vest PBIED fragments according to the classical system of equations of motion.An analysis of fragment harmfulness over various distance from the PBIED detonation. Two crucial aspects for safety were observed:severe harmfulness occurs at close range but with fewer individuals injured, and due to fragments losing velocity, at longer distances, lower harmfulness occurs but more individuals are injured.

Moreover,a probabilistic analysis was then conducted to predict the probability of a person being hit by at least one fragment, a probability of fatality or serious injury, and safe evacuation distances.It was found that fatality risks are 65-95%within 5 m of the PBIED and fall to less than 1% for distances of about 85 m.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the Poland National Center for Research and Development, under the grant DOB-BIO10/01/02/2019 within the Defence and Security Programme.

Appendix A

Table 2 Actual measurements of 74 flying nut fragments in the first 0-50 ms after detonation (in descending order of initial incident angle).

Appendix B

Table 3 Prediction of the final fragment range and kinetic energy at ground impact.

Table 3 (continued)