3. 1. Explanation of AN explosive phenomenon
Pure AN is relatively stable at room temperature. Yet, when exposed to high temperature, high pressure, oxidizing substances and electric spark, it can explode. High temperatures caused the three explosions mentioned above. When the temperature exceeds 400 degrees Celsius, AN decomposes and explodes. The chemical equation for the explosion of AN is as follows:
According to the above chemical equation, the explosion of 270 tons, 800 tons, and 2750 tons of AN produced about 121.6 tons, 360.2 tons and 1238.3 tons of water, 77.6 tons, 230.0 tons and 790.4 tons of nitrogen dioxide, and 70.9 tons, 210.0 tons and 721.8 tons of nitrogen, respectively. Because the molecular weight of water is only 39.1% of nitrogen dioxide, water's kinetic energy is higher, and the propagation distance is farther. However, nitrogen dioxide has little kinetic energy and can only be lifted into the air under the pressure of an explosion's epicenter. This explains why a huge white gas wave was formed during explosions, following a reddish-brown cloud from the explosion center. The first huge white wave was actually a large amount of high-temperature and high-pressure steam produced by AN explosion. It has also been found that the explosion caused by solid or liquid explosives is a condensed phase explosion (Liu, 2016). The condensed phase explosive process is usually initiated by thermal pulse, mechanical pulse, or direct action of detonator or booster. Detonation is usually caused by thermal pulses, after which it goes through an unstable combustion stage (Liu, 2016). It was reported that there were many dangerous chemicals stored in the warehouse in three accidents. The thermal pulse generated by warehouse fire can provide continuous energy for all kinds of condensation hazardous chemicals, thus leading to the intense explosion of condensation explosives. Therefore, it is believed that the three explosions were caused by condensed phase explosives.
3.2. Analysis of crater diameter caused by AN explosion
Based on TNT experiments and previous literature, Ambrosini et al validated the empirical equation of Kinney and Graham that relates the diameter of the crater (D) to the TNT mass (QTNT) for an explosion at ground level and which is expressed below with mass in kg and distance in meters (Ambrosini et al., 2002; Laboureur, 2016). Following this correlation, we calculated the diameter of the crater caused by the explosion of TNT.
For other types of explosives, TNT equivalent can be converted according to the following formula.
where is the TNT explosive equivalent, kg; is the explosive quantity of certain explosive, kg; is the detonation heat of certain explosive, kJ/kg; is the detonation heat of TNT explosive, kJ/kg.
The detonation heat released by 1kg TNT explosive is 4230 ~ 4836kJ/kg, and the average detonation heat is 4500 kJ/kg generally. AN is calculated with AN explosive as a reference, and the detonation heat of AN explosive is 4000 kJ/kg.
Figure 1 shows the theoretical and actual crater diameters calculated according to explosive equivalents in three accidental explosions, respectively. As shown in Figure 1B, the crater's diameter formed by the 270 ton AN explosion in the USA was 28.3 meters, which is much smaller than the predicted diameter of 49.7 meters (Figure 1A). By comparison, 800 tons of AN explosion in China formed a crater with a diameter of 97 meters (Figure 1A), but the theoretical diameter calculated by the formula was 71.4 meters (Figure 1B), which was slightly smaller than the actual crater diameter. Similarly, the predicted value of a crater with a diameter of 107.8 meters formed by the explosion of 2750 tons of AN in Lebanon was also smaller than the actual diameter of 140 meters (Figure 1). Bull and Woodford pointed out that the crater's deviation can reach 30-40% (Bull and Woodford, 1998). AN has an excellent crater effect, which may lead to underestimation of crater diameter based on TNT mass estimation. Moreover, the AN effectiveness reported in the literature varies from 0.25 or 0.3-0.55, to 0.84 (Laboureur, 2016; Hutchinson and Skinner, 2007). Some studies suggested the use of 0.346 as a standard because it corresponds to the ratio of explosion heat of AN to that of TNT. Therefore, choosing a higher effective factor will make the quality assessment closer to the actual value. Combined with the prediction of crater diameter in these accidental explosions, we speculated that only when the AN mass reaches certain height, a better crater effect will appear, which may result in underestimation of the crater diameter. Based on the above results, we confirmed that the formula should be modified with reference to the empirical validity so as to better predict the actual diameter of the crater caused by an explosion.
3.3. Impact of shock wave overpressure on casualties
AN explosion releases a large number of high-temperature and high-pressure explosion products, which impact the surrounding air at high speed and increase the pressure, density, and temperature, forming air-blast shockwave. According to the Chinese national standard "safety regulations for blasting" (GB6722-2014), the shock wave overpressure is calculated according to the following formula under the condition of flat terrain.
where is the shock wave overpressure, × 105 Pa; R is the distance between protecting objects and blasting points, m; Q is the explosive quantity equivalent to TNT in one blasting, the total quantity is the simultaneous blasting, and the maximum quantity is the delayed blasting, kg. For other types of explosives, TNT equivalent can also be converted according to the above listed formula (2.3).
In Table 1, four levels of casualties caused by shock wave overpressure are defined: mild injury, moderate injury, severe injury, and extremely severe injury. The shock wave overpressure values at different distances from the explosion epicenter can be obtained by formula calculation. Figure 2A shows the overpressure variation trend with the distance of the explosion epicenter for 270 kg, 800 kg, and 2750 kg AN, respectively. It can be seen from the figure that there is a functional relationship between the shock wave overpressure and the charge amount, and the distance from the explosion epicenter. Higher explosive production generates a higher overpressure of the shock wave (Figure 2A). The results also showed that with the increase of the distance from the epicenter, the overpressure values of shock waves produced by different equivalent explosions gradually decreased; nevertheless, after reaching a certain distance (about 1,000 meters), overpressure values of shock waves were significantly reduced (Figure 2A). Therefore, the range and degree of casualties and building damage caused by shock wave overpressure could be calculated theoretically according to the variation of shock wave overpressure in different areas.
Figure 2B showed the predicted zones of casualties caused by shock wave overpressure in the three explosions. The global positioning system (GPS) satellite images and aerial views were collected through an online search. By formula calculation, after the AN explosion, the shock wave overpressure zone of more than 1×105 Pa was formed at 215 meters, 309 meters, and 467 meters away from the respective explosion epicenter (Figure 2B). Referring to Table 1, the results showed that within 215 meters, 309 meters, and 467 meters of respective explosion epicenter, high shock wave overpressure would cause death in these areas. Within 215-309 meters, 309-444 meters, and 467-670 meters, the shock wave overpressure was (0.5-1)×105 Pa, which could cause severe internal bruising and even death. In addition, in the zones of 309-417 meters, 444-599 meters, and 670-903 meters, the shock wave overpressure was (0.3-0.5)×105 Pa, which could lead to eardrum injury, moderate contusion, and fracture. However, in the zones of 417-540 meters, 599-776 meters, and 903-1171 meters, the shock wave overpressure was reduced to (0.2-0.3)×105 Pa, which could only cause a slight contusion. Due to the lack of accurate information on casualties in three explosion accidents, this study could not accurately compare the theoretical prediction with the actual casualties. Still, the calculated zones of casualties were basically consistent with the media reports.
3.4. Impact of the shock wave overpressure on buildings
In Table 2, seven damage scales for the severity of the blast-induced damages for buildings are defined: Damage Scale 1 (DS1) almost no damage, Damage Scale 2 (DS2) minor damage, Damage Scale 3 (DS3) mild damage, Damage Scale 4 (DS4) moderate damage, Damage Scale 5 (DS5) severe secondary damage, Damage Scale 6 (DS6) severe damage, and Damage Scale 7 (DS7) complete destruction. Since DS1 and DS2 cause slight damage to buildings, Figure 2C showed only the predictable zones of the other five damage scales (DS3-DS7). These distances represent the boundaries for the zones of the fiver damage scales. It can be seen from the figure that the shock wave overpressure was more than 0.76×105 Pa within the range of 247 meters, 355 meters, and 536 meters away from the respective explosion epicenter; buildings within this range were expected to be completely damaged (DS7). In the range of 247-293 meters, 355-422 meters, and 536-636 meters away from the respective explosion epicenter, the explosion overpressure was (0.55-0.76)×105 Pa, and the buildings in this area were seriously damaged (DS6) (Figure 2C). In addition, buildings within 293-351 meters, 422-504 meters, and 636-761 meters away from each explosion epicenter suffered serious secondary damage (DS5); buildings within 351-467 meters, 504-671 meters, and 761-1013 meters moderate damage (DS4), and buildings within 467-963 meters, 671-1384 meters and 1013-2089 meters a slight damage (DS3)(Figure 2C). These results show that buildings within the three explosion epicenters of 963 meters, 1384 meters, and 2089 meters were damaged in different degrees by the shock wave overpressure.
For the calculation of overpressure of blast air shock wave, the commonly used empirical formulas in the early stage are the national standard "safety regulations for blasting" (GB 6722-2014/XG1-2017), Henrych formula, Sadovsky formula, and Brode's formula (Wu and Gao, 2014). Many scholars applied those formulas for calculation, but these empirical formulas were mainly based on the experimental data and theoretical analysis results. Because of the short history of the explosion, the accuracy of experimental results is often affected. With the rapid development of computer technology, numerical simulation methods have been developed for studying explosion effects in recent years. Many scholars have carried out a series of studies on shock wave overpressure by combining explosion tests with numerical simulation. This study collected and sorted out buildings' actual damage through the Internet and literature reports and described the damage with different distances around the explosion epicenter (Table 5-7). These tables provide the comprehensive damage conditions of the buildings in different damage scale zones. The actual damage, the damage degree, and scope caused by the three explosion accidents (USA, China, and Lebanon) were basically consistent with the theoretical prediction. The air blast shockwave from three explosion accidents did contribute to the structural damages of the buildings. Moreover, the predicted range of this formula was in good agreement with the actual damage observed in most buildings. For some buildings, such as building A5 and C2, the severity of the damage was more like the moderate damage scale (DS4). Nevertheless, these buildings were actually located in the DS3 (mild damage) zone (Table 5 and Table 7), which was not consistent with the results. In addition, the damage to building B6 could be almost classified as no damage level (DS1) when the building is actually located in the DS2 (minor damage) zone (Table 6). These phenomena could not be explained by the air-blast incident overpressure.
3.5. Ground shock caused by AN explosion
Although the seismic wave caused by the AN explosion can not destroy the original solid rock, it generates vibration or shaking of all objects on the ground near the explosion source. When the blasting vibration reaches a certain intensity, the buildings (structures) around the blasting area are damaged. According to the national standard "safety regulations for blasting" (GB6722-2014), the safe permissible distance of blasting vibration can be calculated according to the following formula.
The ground shock can be calculated according to the conversion formula below.
where is the ground vibration peak particle velocity (PPV) at the location of the protected object, cm/S; is the distance between the protected object and the blasting point, m; is the explosive quantity, the total quantity is for the simultaneous blasting, and the maximum quantity is for the delayed blasting, kg; and α are the coefficients and attenuation indexes related to the terrain and geological conditions between the blasting point and the calculated protected object. It can be selected according to Table 3 or determined by field test. Considering the geological and topographical conditions of the explosion site, we chose soft rock parameters, k = 350, and α = 1.8.
The relationship between seismic intensity and vibration physical quantity is shown in Table 4. According to the calculation results of the relationship between PPVs and distances, combined with Table 4 and the Chinese Seismic Intensity Scale (GB/T17742-2020), and by taking class III buildings as an example (the explosion affecting civil buildings and the structure was Class III buildings), we calculated and analyzed the impact caused by ground shock. Figure 3 shows that after 270 tons, 800 tons, and 2750 tons of AN explosion, within 187 meters, 269 meters, and 406 meters from each explosion epicenter, respectively, the seismic intensity was more than 10 degrees, and most of the class III buildings were toppled. The PPVs within the range of 187-275 meters, 269-396 meters, and 406-597 meters from each explosion epicenter were equivalent to 9 degrees of seismic intensity, and these areas were severely damaged. In addition, the building structure was severely damaged and partially collapsed. The PPVs generated within a range of 275-405 meters, 396-581 meters, and 597-877 meters from the epicenter of the respective explosions were equivalent to 8 degrees of seismic intensity, and these areas were moderately damaged, and the structure of the building was damaged and would need to be repaired before it could be used. In the range of 405-595m, 581-854 meters, and 877-1615 meters away from each explosion epicenter, the PPVs were equivalent to the seismic intensity of 7 degrees. These areas suffered mild damage, partial house damage or cracking, and required minor repair or no repair at all. Thus, it was concluded that in the three explosion accidents, buildings within 595 meters, 854 meters, and 1615 meters from the respective epicenter of the explosion could suffer varying degrees of damage due to the ground shock caused by the explosion. Results also showed that the ground-shock reduced as the standoff distance increases.
Previous studies have found that buildings' roof collapse may be a typical sign of building damage related to ground shock. In addition, with the increase of the distance between the explosion epicenter and the buildings, the contribution of the ground shock to the structural damage is more obvious. In the explosion in Texas, USA, many local buckling damages were observed on the collapsed roof truss, which can not be explained by the air-blast overpressure (Dai et al., 2016). Their results also showed that in the destructive failure and hazardous failure zones, very few damage characteristics caused by ground shock could be identified. In these zones, the ground shock-induced damages were overwhelmed by the air-blast incident overpressure-induced damages. In the repairable moderate damage zone, the vertical cracks appear. These results suggested that the damage observed on-site could be more accurately explained by considering the influence of ground shock. Thus, it was proved that the AN explosion accident's overpressure was the leading factor of building damage. Although ground shock was a secondary factor, it still plays an important role. In a future analysis of the consequences of such accidents, the influence of air blast overpressure and ground shock should be considered comprehensively so that the relationship between explosion load and building damage could be accurately obtained.