October 2006

Based on an inquiry from the Institute for Defense Analyses (IDA), as part of a company-funded study Engineering Analysis Inc. (EAI) has developed a three-dimensional simulation of a bomb detonation in a crowd of spectators located on a flat open plane. This study represents a continuation of a series of studies dealing with various forms of terrorist attacks, as analyzed with the HEXDAM 7.0 software.

The primary objective of this study has been to examine the effects of the bodies of spectators shielding one another from the blast wave. This phenomenon is commonly referred to as the "shoulder effect". Because of the nature of this type of shielding, the HEXDAM Man represents an extremely important tool in carrying out the analysis. The basic scenario involves 40,000 spectators distributed randomly within a circular area with a radius of 370.5 feet, with a 4,000-pound bomb located at the center. In order to keep the problem tractable, only a 2º sector of the circular area has actually been analyzed. Within this sector 222 spectators are located. Each spectator was modeled as a standard 6-foot, 180-pound HEXDAM man consisting of 28 internal body components. The blast injury to each component of each spectator was computed by HEXDAM.

Many of the users of HEXDAM are concerned not only with structural vulnerability but also with personnel safety and the effects of an explosion on the human body. For these reasons the HEXDAM Man concept was developed for use with HEXDAM. The HEXDAM Man, shown in Figure 1, consists of a collection of 17 external and 28 internal components. The external and internal body components are identified in Table 1.

Poses are specified by the position of the external components, which serve as containers for the internal components. Injury assessment is only concerned with internal components. The standard HEXDAM Man corresponds to a six-foot tall man with a weight of 180 pounds. The HEXDAM Man can be placed anywhere in an existing problem scenario in any one of 44 different predefined poses, as summarized in Figure 2.

There is no limit to the number of HEXDAM Men which can be added to a scenario. The injuries from an explosion are predicted for each internal component of each HEXDAM Man. Such predictions are based on the most accurate available data describing the vulnerability of the human body to blast.

Of special significance is the shielding effect produced by each HEXDAM Man included in a scenario. Each external component of each HEXDAM Man is treated as a physical structure which provides shielding to all components, associated with other structures or HEXDAM Men, located downstream of the component from the blast. A description of this unique shielding process has been previously described. For modeling an explosive detonation in the middle of a large crowd, this shielding phenomenon, which is commonly referred to as the "shoulder effect", can be quite important.

The basic problem under consideration involves a crowd of 40,000 spectators randomly distributed within a circular area with a radius of 370.5 feet. This distribution represents a crowd density of one person per 10.8 square feet. A 4,000-pound bomb is located at the center of the circle, as depicted in Figure 3.

The basic objective is to determine, with and without shielding, the number of fatalities and injuries which will result from the bomb detonation, and also the nature of such casualties.

Although an unlimited numbers of the HEXDAM Man can be included in an analysis, for the sake of keeping the problem tractable, the assumption has been made that the distribution of personnel within a 2º sector of the circle is representative of the overall distribution. Within this 2º sector 222 spectators are located, each in the basic standing pose, and each facing the bomb. This 2º sector is contained within a 19-foot by 370.5 foot rectangular strip with a total of 653 spectators, as depicted in Figure 4. Computations have been carried out by HEXDAM for all spectators within the strip. The results for the 222 spectators within the 2º sector were then extracted from the results for the 653 spectators within the rectangular strip.

Because of the manner in which the shielding calculations are carried out by HEXDAM, no "edge effects" were involved. Thus, spectators near the boundaries of the 2º sector received as much shielding as spectators located along its centerline.

In carrying out the analysis two levels of casualties were considered. The first involved spectators suffering fatal injuries ("fatalities") and the second spectators suffering non-fatal injuries, ("injured"). Injuries to three different internal components were considered as follows:

• Lungs
• Skull
• Cervical Vertebrae

For purposes of comparison, two separate analyses were carried out. The first included the shielding effect previously noted, while the second was performed without the shielding effect.

Both tabular and graphical results were generated. The number of fatalities and injuries are summarized in Table 2. Notice should be taken that all fatalities suffered ruptured cervical vertebrae. Approximately 48% also suffered fatal injuries to the skull. Like-wise, approximately 19% also experienced fatal injuries due to lung rupture.

Table 2. Summary of Casualties With Shielding

Cervical

16 three-dimensional color-coded graphical representations of the distribution of casualties were generated at distances from 9.5 feet to 294.5 feet, as shown in Figure 5. In this figure the entire 19-foot width of the rectangular strip is included at each successive (centerline) distance from ground zero. For this figure, slight and moderate injuries are color-coded yellow and orange, while severe injuries are color-coded red. Fatalities correspond to severe injury to the lungs, skull, or cervical vertebrae. Non-fatal injuries correspond to all other cases involving slight, moderate, or severe injuries. Examination of Figure 5 suggests that an 100% fatality rate occurs out to a distance between 66.5 and 85.5 feet. Beyond this distance some mixture of fatalities and injuries are observed out to a distance from 142.5 to 161.5 feet. Beyond that distance only non-fatal injuries are observed.

The distributions of fatalities and injuries associated with the lungs, skull, and cervical vertebrae, consistent with Figure 5, as a function of the distance from ground zero, are plotted in Figures 6, 7, and 8. As indicated by these figures, with shielding included, the primary cause of fatalities was rupture to the cervical vertebrae, with deaths occurring out to a distance of approximately 162 feet. Similarly, skull fractures were the second-most likely cause of death, out to distances of approximately 105 feet. Lung rupture was the third most likely cause of deaths with fatalities out to about 67 feet.

The cumulative distribution of fatalities and injuries to the lungs, skull, and cervical vertebrae, with shielding included, are presented in Figures 9, 10, and 11. According to Figure 9, all fatal lung injuries occur within approximately 67 feet of ground zero, while non-fatal lung injuries occur out to approximately 124 feet. According to Figure 10, fatal skull injuries occur out to approximately 105 feet from ground zero while non-fatal skull injuries occur out to about 143 feet. Inspection of Figure 11 reveals that fatal cervical vertebrae injuries occur out to approximately 162 feet, while non-fatal cervical vertebrae injuries occur out to about 238 feet.

The effects of the shielding of one HEXDAM Man by another are demonstrated in Figures 12.a through 12.f. These figures represent three spectators taken from the crowd, with Spectator #1 located at a distance of 98 feet from ground zero, and Spectators #2 and #3 located at a distance of 100 feet from ground zero. Spectator #1 is located 2 feet in front of Spectator #2. The blast wave from the 4,000 pound detonation approaches from the left and initially impacts Spectator #1 and then Spectator #3. Color coding of injuries is the same as for Figure 5. Both of these spectators received similar severe injuries, although Spectator #1 is slightly closer to ground zero. The blast wave is attenuated in vicinity of Spectator #2 because of the shielding effects produced by Spectator #1, and as a result, the injuries experienced by Spectator #2 are clearly less severe.

As in the case with shielding, both tabular and graphical results were generated for the analysis without shielding. The number of fatalities and injuries without shielding are summarized in Table 3. Notice should be taken that all fatalities suffered ruptured cervical vertebrae, while approximately 33% suffered fatal skull fractures, and 14% experienced fatal injury due to ruptured lungs.

Table 3. Summary of Casualties Without Shielding

Cervical

Comparison of the results from Table 3, with the previous results provided in Table 2, reveals a significant increase in the predicted fatalities and injuries when shielding is not taken into account.

The distributions of fatalities and injuries associated with the lungs, skull, and cervical vertebrae, as a function of the distance from ground zero without shielding, are included in Figures 6, 7, and 8. As indicated in these figures, the primary cause of fatalities was rupture of the cervical vertebrae, with deaths occurring out to a distance of 181 feet. Similarly, skull fractures were the second-most likely cause of death with fatalities out to distances of 105 feet. Lung rupture was the third most likely cause of deaths with fatalities out to 86 feet.

The cumulative distribution of fatalities and injuries to the lungs, skull, and cervical vertebrae without shielding are included in Figure 9, 10, and 11. According to Figure 9, all fatal lung injuries occur within approximately 86 feet of ground zero, while non-fatal lung injuries occur out to approximately 124 feet. According to Figure 10, fatal skull injuries occur out to approximately 105 feet from ground zero while non-fatal skull injuries occur out to about 143 feet. Inspection of Figure 11 reveals that without shielding fatal cervical vertebrae injuries occur out to approximately 181 feet, while non-fatal cervical vertebrae injuries occur out to about 257 feet.

Comparison of the distances associated with fatalities and injuries with and without shielding reveals, as expected, that the distance without shielding are equal or greater than the corresponding distances with shielding. More importantly, however, the distances associated with 100% fatalities without shielding are consistently greater than the corresponding distances with shielding taken into account. This is especially true in the case of ruptured cervical vertebrae, which was the primary cause of death.

In summary, a three-dimensional model of a crowd of 40,000 spectators within a circle with a radius of 370.5 feet, and with a 4,000-pound bomb located at the center, has been developed. The HEXDAM software, utilizing the HEXDAM Man concept, has been used to develop the model. Shielding of one spectator by another has been included in the initial analysis. The major causes of death, which were considered, were ruptured cervical vertebrae, fractured skull, and ruptured lungs. For this case a total of 5,286 fatalities and 6,472 injuries (slight and moderate) were predicted by the model. Fatalities occurred out to distances as great as 163 feet, while injuries were present at distances as great as 238 feet.

In the second analysis, in which shielding was not considered, for the same three causes of death and injury a total of 9,213 fatalities and 7,540 injuries (slight and moderate) were predicted by the model. A summary of the increase in the predicted fatalities and injuries when shielding or "shoulder effects" are neglected is provided in Table 4. Fatalities occurred out to distances as great as 181 feet while injuries were present at distances as great as 257 feet.

Table 4. Increase in Fatalities and Injuries When Shielding is Neglected

Cervical

The effect of shielding of one spectator by another, commonly referred to as the "shoulder effect", was clearly demonstrated to be significant. For this reason the HEXDAM Man is a noteworthy concept.