Discrete Element Analysis on the Influence of Block Shape and Spatial Arrangement on Shielding Performance
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摘要: 遮弹层作为现代军事防御体系的关键组成部分，可为后方重要目标提供防护。块石作为遮弹层的常用堆筑材料，其遮弹机理及性能优化研究具有重要意义。采用离散元球体单元和黏结破碎模型，模拟了块石在弹体冲击载荷下的破碎现象，并对刚性弹正侵彻密实堆积的块石结构进行了数值模拟，探讨了块石粒径、形状及空间排布特性对其抗侵彻性能的影响。结果表明：在侵彻过程中，块石通过碰撞和滑移耗散了90%以上的弹体动能；块石破碎数量与块石粒径呈负相关，与块石长短轴比呈正相关；采用单粒径块石多层位错排布时，弹体侵彻深度主要取决于侵彻阻力峰值，粒径为120 mm的圆形块石工况的侵彻阻力最大且侵彻深度最小；采用块石粒径沿迎弹面方向梯度递减的分层排布时，不能有效提高结构体的遮弹效果。研究结果可为理解块石遮弹机理提供参考。Abstract: Shelter layers, recognized as a critical component in modern military defense systems, are designed to protect strategically important rear assets. Given the prevalent application of block stones as primary filling materials in these protective structures, comprehensive investigations into their fundamental ballistic resistance mechanisms and practical performance optimization have become increasingly crucial for defense engineering. Therefore, the dynamic fragmentation behavior of block stones under high-velocity projectile impact was systematically simulated using discrete element spherical particles and bonded particle model (BPM) in this paper. The process of rigid projectile vertical penetration into densely packed block stone structure was numerically simulated, with the influences of block stone particle size, shape, and spatial arrangement characteristics on its anti-penetration performance being explored. The results revealed two primary energy dissipation mechanisms governing the shelter layer performance: over 90% of the kinetic energy of the projectile was dissipated through the combined effects of inter-block collisions and sliding friction during the penetration process. Meanwhile, the number of break block stones is found to be negatively correlated with the block stone particle size and positively correlated with the aspect ratio (long-to-short axis) of the block stones. Moreover, when single-sized block stones are used in a multi-layer staggered arrangement, the penetration depth of the projectile is primarily determined by the magnitude of the peak penetration resistance. Specifically, the maximum penetration resistance and the minimum penetration depth are exhibited by the scenario with circular block stones of 120 mm particle size. However, when a layered arrangement with block stone particle size gradiently decreasing along the direction of the impact face is employed, the overall blast-resistant effect of the structure is not effectively enhanced. Finally, the results of the study can provide a reference for understanding the underlying mechanism of the shielding effect of block stone structure.
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图 6 不同粒径块石工况下的侵彻阻力-侵彻深度曲线
Figure 6. Penetration resistance-penetration depth curves for blocks with different particle size
图 7 工况C1的侵彻深度和弹体动能时程曲线
Figure 7. Time history curves of penetration depth and projectile kinetic energy for case C1
图 9 不同粒径块石工况下弹体的偏转角时程曲线
Figure 9. Time history curves of projectile deflection angle for blocks with different particle size
图 11 不同粒径块石工况下背弹面墙体的应力时程曲线
Figure 11. Time history curves of the stress on the rear wall for blocks with different particle size
图 16 不同形状块石工况下弹体的偏转角时程曲线
Figure 16. Time history curves of projectile deflection angle for blocks with different particle shape
图 17 不同形状块石工况下的侵彻阻力-侵彻深度曲线
Figure 17. Penetration resistance-penetration depth curves for blocks with different particle shape
图 18 不同形状块石工况下背弹面墙体的应力时程曲线
Figure 18. Time history curves of the stress on the rear wall for blocks with different particle shape
图 21 不同空间排布工况下的侵彻阻力-侵彻深度曲线
Figure 21. Penetration resistance-penetration depth curves for blocks with different spatial arrangement
图 23 不同空间排布工况下的弹体偏转角时程曲线
Figure 23. Time history curves of projectile deflection angle for blocks with different spatial arrangement
图 24 不同空间排布工况下背弹面墙体的应力时程曲线
Figure 24. Time history curves of the stress on the rear wall for blocks with different spatial arrangement
图 27 不同空间排布工况下的破碎区域
Figure 27. Breaking zone for blocks with different spatial arrangement
表 1 块石柔性簇模板
Table 1. Block cluster template
Block cluster template Diameter/mm Aspect ratio Np Nc Z 
70 1.0 227 600 5.29 
120 1.0 884 2 006 4.54 
138 1.0 1 166 2 662 4.57 
175 1.0 1 879 4 362 4.64 
120 1.4 608 1 297 4.27 
120 2.0 442 925 4.19 
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表 2 数值模拟细观参数
Table 2. Meso-parameters of numerical simulation
Rmin/mm Rmax/mm ρ/(kg·m−3) kn/(N·m−1) ks/(N·m−1) $\sigma_{\rm{n}} $/MPa $\sigma_{\rm{t}} $/MPa 0.9 2.7 2 685 99×109 49.5×109 215±50 215±50
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表 3 计算工况
Table 3. Calculated cases
Case Block stone shape Block stone diameter/mm Spatial arrangement C1 Circle 70 Multi-layer staggered arrangement C2 Circle 120 Multi-layer staggered arrangement C3 Circle 138 Multi-layer staggered arrangement C4 Circle 175 Multi-layer staggered arrangement C5 Circle 70–175 Random distribution C6 Circle 70–175 Size gradient-decreasing C7 Circle 70–175 Size gradient-increasing E1 Ellipse with aspect ratio of 1.4 120 Multi-layer staggered arrangement E2 Ellipse with aspect ratio of 2.0 120 Multi-layer staggered arrangement
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