Explosion disaster distribution characteristics and outlet open-close effect of turning roadway

In this study, under the open-close conditions of a roadway outlet, the nonlinear dynamic analysis nite element program ANSYS/LS-DYNA was used to build models of explosions on roadways with 0˚ and 90˚ bending angles, to compare and analyse the shock wave propagation characteristics and variation laws. Moreover, the destructive effect of the explosion on the partition was analysed based on the level of damage caused to the human body by shock wave overpressure. The results show that the bending angle has an impact on the space-time distribution law of the explosion shock waves on the roadway. As the bending angle increases, the peak overpressure attenuation of the shock waves becomes prominent, and the arrival time for the same distance increases. The closure of the roadway outlet has a distance effect on the peak overpressure of the shock waves. The explosion shock waves cause the peak overpressure to rise sharply owing to the reection and stacking effects near the closure. In the far zone of the outlet, the attenuation of the shock waves is too fast and has minimal impact on the peak overpressure. Additionally, overall, the closure of the roadway outlet increases the damage range of the explosion shock waves and the severity of their effect on the human body. With an increase in the bending angle, the damage range and severity decrease. These results can provide a reference for explosion disaster evaluation and prevention.


Introduction
An underground roadway is a typical underground con ned space where the characteristics of dynamite explosions differ greatly from those in an open space. Once an accidental explosion occurs in the roadway, the shock waves cannot quickly propagate due to the con ned space, thus increasing the overpressure duration and creating enormous threats for personnel and equipment. Worse still, any barrier in the roadway, or the closure of the outlet, could further intensify the re ection process and the damaging effects. The research on explosion shock waves in roadways is important not only for the evaluation of combat measures effectiveness, but also as a foundation for the analysis of accidental explosion system safety. Turning structures have been widely used in industrial, civil, and military roadway facilities; therefore, it is extremely necessary to study the distribution characteristics of explosion disasters, as well as the safety protection.
The most effective way to study the explosion shock waves process is to carry out explosive experiments. Dadone et al. (1971) performed ve types of tunnel experiments to study the pressure attenuation of shock waves passing through interaction points. The results showed that the pressure attenuation of shock waves at the interaction points could neglect the tunnel size effect. The calculation of the shock wave pressure changes near the interaction points, based on the steady ow pressure model, presented large errors. Savenk (1979) studied the propagation characteristics and shock waves laws based on a model experiment. The attenuation coe cients of the shock waves were obtained through the local variation in bifurcation and turning. Limited by the research conditions, he was unable to perform indepth research in this eld. Smith et al. (1992) obtained the explosive point's overpressure time and propagation characteristics through explosion experiments in tunnels with different coarseness levels and loads. Britan et al. (2001; analysed the effect of spheroidal particle lter parameters on shock wave attenuation. Based on the study of the change laws of shock waves passing through porous mediums with different geometric shapes and porosity, they proposed basic ideas of optimum underground space structural design. Pang et al. (2013) conducted explosive experiments in tunnels with various turning angles and obtained the distribution law of a high-temperature ow eld before and after the turning.
Given the complexity of the explosion effects and di cult operation conditions, with the development of computer technology, numerical simulations can be used to study the explosive process. Given their low computational cost and wide range of data, numerical simulations have already been widely used (Chan et al., 1994 and 135˚ one-way turning roadway, and revealed the in uences of roadway geometry on the shock wave propagation laws. Additionally, the shock wave propagation laws in 45˚, 90˚, 135˚, Y-shape, and T-shape branched roadways were also simulated and studied.
The results of previous studies show that investigations of explosion shock wave propagation laws have mainly focused on straight roadways. Although some researchers have considered the impacts of bending angles and geometry, there are fewer studies on the shock wave propagation characteristics in continuous turning roadways. Furthermore, the open-close conditions of a roadway outlet's in uence on shock wave propagation characteristics, and its destructive effect, are less researched. This paper builds, through numerical simulation, and based on the roadway outlet's open-close conditions, respectively, models to analyse explosions in a roadway with 0˚ and 90˚ bending angles. The effect of the roadway outlet conditions on the shock wave propagation characteristics is analysed. Additionally, the explosive destruction effect partition is analysed based on the level of damage caused to the human body by the shock wave overpressure.

Explosion analysis model
A nonlinear dynamic analysis nite element program called ANSYS/LS-DYNA is used to conduct a numerical simulation to study the open-close conditions of the in uence of different turning roadway outlets on the explosion shock wave propagation characteristics. The bending angle between tangent line OA and straight line OB is marked as θ, as shown in Fig. 1(a). According to the value of θ, two roadways with different curvatures are built, as shown in Fig. 1(b). The bending angles are 0˚ and 90˚, respectively.
The simulated sectional dimension of the roadway is 3.5 m × 3.5 m, and the explosive source is located in the section core. The roadway with θ = 0° is taken as an example. Half of the three-dimensional explosion analysis models have been built according to symmetry, as seen in Fig. 2. Figure 2(a) is the model with the roadway outlet closure, that is, the roadway outlet is under a barrier sealing treatment. Figure 2(b) is the model with the open roadway outlet. The horizontal length of the roadway is 100 m, and the distance between the roadway outlet and the explosive source is also 100 m.
To facilitate the analysis, the explosive source is taken as the origin of the coordinate system. Roadways with different curvatures are projected on the roadway with θ = 0°. The vertical distance between the projection line and the explosive source is taken as the spacing, and the intersection of each projection line and the different curvature roadways are taken as survey points. Taking 10 m of spacing as an example, the roadway points with different curvatures are obtained, as shown in Fig. 3.

Material constitutive and state equation
The numerical simulation analysis of the explosive issues plays an important role in the study of the explosion mechanics. As an effective tool for nonlinear impact dynamics analysis, the ANSYS/LS-DYNA software can effectively simulate the explosive process in various mediums, as well as different engineering blasting issues. The Lagrange and Euler algorithms are commonly used in numerical simulations. Among them, the Lagrange algorithm is often used to analyse problems involving solid mechanics, while the Euler algorithm is used more for uid mechanics analysis. The explosion in different turning roadways is the interaction between the detonation gas and the solid walls, which is a typical uid-structure interaction. Therefore, the ALE algorithm is adopted to solve the problem of large deformation calculations, combining the advantages of the Lagrange and Euler algorithms.
For an easier analysis, the explosive source is 5 Kg TNT with a 1640 kg/m 3 charge density and 6930 m/s explosive velocity. The explosive adopts the MAT_HIGH_EXPLOSIVE_BURN constitutive model provided by LS-DYNA. Given that the explosive gas exhibits substantial pressure uctuations in the numerical simulation, ranging from hundreds of thousands of atmospheres to lower than one atmosphere, it is di cult to nd the appropriate state equation of the explosion pressure variation range. JWL's (LSTC, 2003) state equation is used in LS-DYNA to describe the relationship between the pressure and the volume variation of the detonation products. In JWL's state equation, the P-V relationship is as follows: where P refers to the pressure, and V refers to the volume. E 0 is the internal energy initial density. A, B, R 1 , R 2 , and ω are constants with values of 3.74, 0.0743, 4.1500001, 0.95, and 0.3, respectively.
The air adopts the MAT_NULL material model provided by LS-DYNA. Its state equation can be expressed as follows: where P is the instantaneous pressure, µ = ρ/ρ 0 -1, and ρ/ρ 0 is the ratio between the instantaneous density ρ and the initial density ρ 0 . The value of ρ 0 is 1.29 kg/m 3 . E refers to the internal energy of a volume unit. The mechanical properties of the roadway wall affect the explosion shock waves. In real roadways, the materials are mainly solid rocks or concrete, whose intensities are far greater than the intensity of the shock waves obtained by numerical simulation. Therefore, the roadway walls can be viewed as rigid materials, and their structural damage and elastic deformation effects on the shock wave re ection and stacking process can be neglected.

Results validation
The roadway with θ = 0° and open outlet is taken as an example to verify the reliability of the numerical simulation results. The shock wave peak overpressure in the unit of different positions is chosen as the study object. Subsequently, the shock wave overpressure and time changing curve are obtained, and the numerical simulation result is compared with the result obtained by Qin (2008), as shown in Fig. 4. Figure 4 indicates that the numerical simulation result is consistent with the shock waveoverpressure/time-variation trend. Initially, the curve decreases sharply from the maximum, and then changes slowly, and becomes stable. The maximum survey point error is 17 KPa, and the average error is 6 KPa. The two curves are very close, indicating the higher reliability and feasibility of the numerical simulation results presented herein.

The effect of roadway outlet conditions on distribution of shock wave peak overpressure
In order to study the conditions of the roadway outlet's effect on the explosion shock waves, the air shock wave overpressures in different positions in the roadways with 0˚ and 90˚ blending angles are selected, to obtain the peak overpressure-distance distribution, as shown in Fig. 5.
As seen in Fig. 5, when θ = 0°, the shock wave peak overpressure is essentially equal in the region of 0-80 m from the explosive source under the condition of roadway outet closure and open. The roadway outlet closure has negligible impact on the shock wave peak overpressure. When the distance to the explosive source is 80-100 m and the roadway outlet is closed, the shock wave peak overpressure suddenly rises, showing an upward trend. In contrast, the shock wave peak overpressure decreases gradually when the roadway outlet is open. When θ = 90°, the peak overpressure distribution has similar features, but differs in different regions, i.e., when the distance to the explosive source is between 0 m and 90 m, the shock wave peak overpressure is essentially equal the same the condition of roadway outlet closure and open. When the distance is between 90 m and 100 m, the shock wave peak overpressure increases under the condition of roadway outlet closure, and reduces with the outlet open.
To further study the effect of the roadway outlet conditions on the explosion shock wave overpressure distribution in different turning roadways and regions, when θ = 0°, the roadway is divided into two zones by an 80 m distance to the explosive source as the boundary; that is, one zone is between 10 m and 70 m, and the other zone is between 80 m and 100 m. When θ = 90°, the roadway is divided into two zones by a 90 m distance to explosive source as the boundary; that is, a 10-80 m zone, and a 90-100 m zone. As seen in Figs. 6(a), 6(b), 7(a), and 7(b), the time changing curves of the shock wave overpressure in different positions are similar to the roadway outlet closure ones. Initially, the peak pressure increases from zero to the maximum, then decreases continuously, increases again to peak, and then begins to reduce. There are two peak values except at the outlet position. One is formed by shock waves passing through different positions after the explosion. The other is formed when the shock waves pass the barriers at the outlet, where only one peak is formed after the stacking of two peaks, and the peak pressure is considerably greater than the second peak pressure in other observation points. Furthermore, the comparison between Figs. 6(a) and 7(a), and 6(b) and 7(b) indicates that the peak pressure when θ = 90˚ decreases and the arrival time to the same distance increases, compared with those when θ = 0˚. Under the condition of outlet closure, two peak overpressures are chosen to obtain their distribution curves in different turning roadways, as seen in Fig. 8.
In the Figs. 8(a) and 8(b), the rst peak overpressure overall decreases (excluding at the outlet points) with the increase in the propagation distance, while the second peak overpressure shows opposite characteristics, with the peak overpressure rising gradually as the propagation distance increases, especially at the outlet, where the peak overpressure reaches its maximum. These analyses suggest that, when the outlet is closed, the explosion shock waves have little effect on peak overpressure in the far zone of outlet, due to the shock waves decreasing greatly after the barriers' re ection away from the outlet. While the explosion shock waves re ection and stacking effects cause peak overpressure increase in the outlet near zone, the maximum peak pressure is formed in the curve. It can be seen that the closed condition of the roadway has a distance effect on the shock wave peak overpressure in the roadway.
Based on Figs. 6(c) and 6(d), 7(c) and 7(d), when the roadway outlet is open, the variation curves of the shock wave overpressure in different positions will increase from zero to peak, and then begin to reduce sharply. In contrast, when the roadway is closed, the pressure curves peak is formed only once. Moreover, the shock wave peak overpressure decreases with the propagation distance increase. Furthermore, the comparison between Figs. 6(c) and 7(c), 6(d) and 7(d) indicates that, as the θ bending angle of the roadway increases, the peak overpressure at the same distance decreases continuously, and the arrival time to the same distance increases. Therefore, the bending angle can change the space-time distribution of the shock wave overpressure in the roadway.
3.3. The in uence of roadway outlet conditions on explosive destructive effect partition Based on the explosion shock wave overpressure's level of injury to the human body shown in Table 1 (Gu et al., 2009), when the shock wave overpressure is more than 100 KPa in the explosion-affected zone, the zone will be regarded as the dead zone (marked by Zone A). When the shock wave overpressure is between 50 KPa and 100 KPa, the zone will be considered as a serious damage zone (marked by Zone B). When the shock wave overpressure is between 30 KPa and 50 KPa, the zone is identi ed as a moderate damage zone (marked by Zone C). When the shock wave overpressure is between 20 KPa and 30 KPa, the zone is determined as a slight damage zone (marked by Zone D). When the shock wave overpressure is between 0 KPa and 20 KPa, the zone is determined as a no damage zone (marked by Zone E). Combined with the numerical simulation results, Figs. 9 and 10 show the explosive destruction effect partition in the roadways with 0˚ and 90˚ bending angles, under the condition of roadway outlet closure and open. Table 2 shows each zone range for different curvature turning roadways, based on the explosive destruction effect partition.  In Fig. 9 and Table 2, when the outlet of the roadway with 0˚ bending angle is closed, zones A, B, C, and D are formed in the roadway after the explosion. When the roadway outlet is open, zones A, B, C, D, and E are formed. Comparing between the range of zones when the roadway outlet is closed and open, the ranges of zones A (dead zone) and B (serious damage zone) are essentially the same. When the roadway outlet is closed, the zone C (moderate damage zone) range increases visibly, and causes the zone D (slight damage zone) range to move forward.
In Fig. 10 and Table 2, when the outlet of the roadway with a 90˚ bending angle is closed, zones A, B, C, D, and E are formed in the roadway after explosion. Comparing between the range of zones with the open and closed outlet, the ranges of zones A (dead zone) and zone B (serious damage zone) are essentially equal. However, when the outlet is closed, the zone C (moderate damage zone) and zone D (slight damage zone) ranges increase visibly, and the zone E (no damage zone) range decreases.
Overall, the closure of the roadway outlet increases the damage range of the explosion shock waves and the severity of their impact on the human body. In addition, when the roadway outlet is closed and the bending angle of the roadway is 0˚, the ranges from A to C are clearly larger than the corresponding ranges when the bending angle is 90˚. The zone D (slight damage zone) and zone E (no damage zone) ranges decrease visibly, indicating that the damage range and severity decreases with the increase in the roadway bending angle.

Conclusions
(1) The bending angle can change the space-time distribution of the explosion shock waves in the roadway. As the roadway bending angle increases, the shock wave peak overpressure attenuation is obvious, and the arrival time to the same distance is increasing. When the roadway outlet is closed, the explosion shock waves will cause the peak overpressure to rise sharply after the re ection and stacking effects in the near zone of the outlet. In the far zone of the outlet, the shock wave effects on peak overpressure is lighter due to the rapid attenuation after re ection. Therefore, the closure of the roadway outlet has a distance effect on the shock wave peak overpressure.
(2) According to the level of injury to the human body caused by the explosion shock wave overpressure, the explosion-affected zones in the roadway can be classi ed into dead zones, serious-damage zones, moderate-damage zones, slight-damage zones, and no-damage zones. The increase in the bending angle can, overall, reduce the explosive damage range and severity. However, the closure of the roadway outlet can, overall, increase the explosive damage range and severity. It can be seen that the bending angle and outlet conditions affect the distribution characteristics of the explosion disaster in the turning roadway.
This research can provide a reference for explosion disaster evaluation and accident analysis in roadways.  The bending angle and different curvature turning roadway The bending angle and different curvature turning roadway