Propagation behaviour of a hemispherical blast wave on a dome roof
Introduction
Explosions produce a shock wave, which consists of a high-impact wave front which extends outward from the explosive point into the ambient air. The intensity and propagation velocity of a 3D blast wave decreases away from the origin with the expansion of the wave front into ambient air. When the shock wave is reflected from a rigid target, the pressure, density and temperature of the shock wave will increase because of conservation of energy, momentum and mass. The overpressure resulting from reflected shock waves is usually more than twice that of the incident shock wave [1], [2], [3]. A series of semi-empirical equations and graphics for predicting blast wave parameters provided by Kingery and Bulmash [4] based on a wide range of field test data, are widely used in design manuals, including the U.S. Department of Defence Design Manual UFC-3-340-02 [5], and the computer program CONWEP [6].
One commonly needs to estimate the blast load at a certain point when an oblique blast wave strikes at a particular incidence angle. The incidence angle (θ) between the target point and blast wave is defined as the angle between the direct vector from the target point to the explosive charge, and the outward normal reflector [7]. If incidence angle is 0°, the target point will suffer a fully reflected overpressure, and if incidence angle is 90°, the overpressure is simply equal to the incident value as the blast wave propagates parallel to the reflection surface. In addition, if the incidence angle is more than 45°, the incident shock front and the reflected shock front will merge and result in a Mach Stem [2], which will cause an oblique overpressure amplification which always exceeds the normal reflected overpressure in the same scaled distance [8]. With regard to a flat reflector, when a shock wave impinges on the edge of a target, the blast wave front reflects away from the reflector surface while the incident blast front keeps on moving along the edge of the target, thus the diffraction is generated around the free edge because of the pressure imbalance. Subsequently the rarefaction wave propagates and reduces the pressure from the edge to the middle of reflector surface. Thus the positive phase duration and positive impulse acting at the target surface where the clearing wave passes over can be reduced [9], [10], [11], [12], [13], [14], [15], [16].
The spherical shell roof is a common structural shape favoured by architects, and has been employed in many industrial engineering structures. Constant or variable-curvature shell roof surfaces are very different from plane reflectors which can lead to a change in the blast wave path. Previous studies [16], [17] and some design manuals, such as UFC-3-340-02 [5] only consider blast flow-field distributions on rectangular structures. The diffraction patterns resulting from some structures with particular curvatures have been investigated. For example, the loci of Mach triple points for several cones, a cylinder, and a sphere, have been investigated under plane strong shocks [18]. In addition, Zhi et al. [19] studied and described the temporal and spatial overpressure distributions on a hemispherical surface under an external blast load. However, the propagation characteristics of blast waves along such roofs remain unclear, and there is no direct method available to enable prediction of the blast load on a dome with a supporting structure subject to an external explosion. However, this geometry is used extensively in practical buildings and as such, could be a common explosion scenario.
The most practical investigation methods for explosive cases in urban scenarios are to conduct small-scale experiments and numerical analysis [20], [21], [22], [23], [24], [25]. In this paper, two laboratory-scale spherical dome structure models with different supporting structure heights and rise-span ratios were designed and manufactured for this study. A series of field tests were undertaken using these models to study the blast wave propagation process along such dome roofs. In addition, the effect of explosion parameters, such as the explosive charge weight and detonation distance, on the blast load distribution over the dome roof was studied for 11 different test cases. To ensure the accuracy of the experimental data, a repeatable test method was used in each test case. Moreover, to investigate the characteristics of the external load distribution on the surface of the dome roof under surface burst explosions, all of the field tests were conducted in open flat terrain to avoid disturbance of flow field at the State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact, Nanjing, China. The numerical and semi-empirical prediction results are compared with the experimental data, and thus the accuracy of the semi-empirical formulae methods for predicting the load distribution on the curved dome roofs could be evaluated. A numerical model based on the commercial software ANSYS/AUTODYN [26] was developed and was validated by the experimental data. Furthermore, the influence of explosive and structural parameters on the distribution of the overpressure on the dome roofs subject to external explosions are discussed using a parametric analysis approach. A predictive method based on the numerical results was also developed to estimate the pressure–time histories on the spherical dome roofs.
Section snippets
Experimental study
To investigate the reliability of the semi-empirical formulae and to validate the numerical model described herein, a series of measurements were conducted on spherical dome structures that were subjected to external blast loads. These test results are used as a benchmark to verify the multiple prediction methods. The experimental tests carried out are described in this section.
Model description
The numerical models were created by using the commercial software ANSYS/AUTODYN [16], [27], and the Arbitrary Lagrange–Eulerian (ALE) method was employed to simulate the propagation of blast waves onto the shell structure. The air and TNT were modelled with an Euler grid and the shell structure was modelled with Lagrangian grid. Because of structural symmetry, only one-half of the structure was modelled, as shown in Fig. 7, to reduce the computational time. The ground was modelled by a
Reflected and diffraction effect
The blast wave diffraction progress for case 4 on model 1 as a function of time based on the numerical method described in Section 3.2 is illustrated in Fig. 12. As soon as the incident blast wave front strikes the structure, it reflects from the target instantaneously so that the incident pressure is amplified. At 0.9 ms, as the blast wave continues to propagate upward along the roof, the interaction of the incident wave and the reflected wave forms a blast wave front called a Mach front,
Conclusions
This paper addresses the problem of developing a blast load model for a dome roof mounted on a cylindrical structure and subject to external surface burst explosions. Two laboratory-scale spherical dome structure models with different supporting structure heights and rise-span ratios were investigated for different blast origin scaled distances. The blast pressure characteristics measured by specific gauges flush with the surface of the dome roof were recorded and analysed in detail. In
Acknowledgements
The authors wish to thank the financial support from the Foundation of Key Laboratory of Structures Dynamic Behavior and Control (Ministry of Education) in Harbin Institute of Technology of China (project No. HITCE201803) and also the financial supports from the National Natural Science Foundation of China (project No. 51708521, 51778183) and National key research and development program of China (project No. 2018YFC0705703).
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