Numerical simulation on complete process of three-dimensional bench blasting in an open-pit mine based on CDEM
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摘要: 爆破开采是露天矿采选总成本控制的首要环节，数值模拟是进行露天矿爆破开采优化设计及爆破效果分析的有效手段。利用连续-非连续单元方法（continuum-discontinuum element method，CDEM）对露天矿的三维台阶爆破过程进行了模拟，通过朗道爆炸模型实现了爆炸作用力的精确计算，通过弹性-损伤-断裂本构实现了岩体损伤破裂过程的描述，通过半弹簧-目标面及半棱-目标棱的联合接触算法实现了破碎岩块碰撞、飞散及堆积过程的高效模拟。开展了小尺度单自由面爆破过程的数值模拟，计算给出的块度分布曲线、爆破漏斗体积等参数与文献中模型实验的结果基本一致，证明了CDEM及本文所述各类模型在模拟爆炸破岩方面的精确性。以鞍千矿南采区的露天铁矿爆破开采为研究对象，建立了3排21炮孔的三维台阶爆破概化模型，模拟了从炸药起爆、岩体损伤破裂到最后爆堆形成的全过程；计算结果表明，除后缘拉裂槽外，数值计算给出的爆堆形态、顶部鼓起高度等与现场的测试结果基本一致，证明了利用CDEM开展三维露天台阶爆破全过程模拟的可行性。Abstract: Blasting mining is the most important part of the total cost control in an open pit mine, and numerical simulation is an effective method to optimize the design of blasting mining and to analyse blasting effect. By using the continuum-discontinuum element method (CDEM), the three-dimensional bench blasting process of the open pit mine is simulated. The Landau explosive model is adopted to precisely calculate the blasting effect, and the elastic-damage-fracture constitutive law is used to describe the damage and fracture process of rock. By adopting the semi-spring target face and semi-edge target edge combined contact algorithm, the collision, flying and accumulation process of large number of fragments is simulated efficiently. The numerical simulation of the small scale blasting process with the single free surface is carried out. The block distributing curve and volume of the crater obtained by numerical simulation are more or less the same as those obtained by experiment, which demonstrates that CDEM and corresponding models described in this paper are good at simulating the rock blasting process. Based on the blasting technology in the south region in Anqian open-pit mine, a generalized three-dimensional bench blasting model with 3 rows and 21 bore holes is set up, and the complete process from explosive detonation to muckpile formation is carried out. Numerical results show that, except the tensile crack behind the blasting area, the muckpile shape and heaving height obtained by numerical simulation are accordant with the ones obtained by field test to some extent, which demonstrates the feasibility to simulate the three-dimensional bench blasting by CDEM.
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TATB类炸药是以TATB炸药为基的钝感炸药, 近几十年来, TATB类炸药的性能尤其是其短脉冲冲击的起爆性能, 越来越受到关注。
J.Campos等[1]设计了新型的雷管起爆装置, 首先采用微型雷管驱动二次飞片, 飞片撞击起爆钝感装药PBX-RU81(以RDX炸药为基), 该装置可用于直接起爆更钝感的主装药。实验中, 采用Fabry-Perot光学测量装置记录了飞片位移曲线, 并讨论了二次飞片厚度对RU81起爆性能的影响。W.C.Prinse等[2]设计了含有冲击片雷管、二次飞片、传爆药和主装药的起爆序列, 实验证明采用不锈钢、聚酯薄膜和铝飞片可以起爆低密度TATB炸药(ρ=1.688g/cm3), 但采用二次飞片未能起爆高密度的TATB炸药(ρ=1.842g/cm3)。B.He等[3]通过实验和数值模拟, 系统研究了飞片起爆亚微米(炸药颗粒平均粒径为0.578μm)低密度(ρ=1.75g/cm3)TATB炸药的性能, 得到了飞片直径、厚度与飞片可靠起爆TATB装药阈值速度的关系。
本文中, 采用钝感起爆序列分别驱动二次飞片和三次飞片撞击TATB装药, 利用全光纤激光干涉测速系统分别测得飞片可靠起爆和未起爆TATB炸药的速度, 并结合数值模拟获得飞片驱动、TATB炸药起爆过程, 在飞片尺寸一定的情况下, 初步确定飞片起爆高密度TATB炸药(ρ=1.895g/cm3)的速度阈值范围。
1. 飞片起爆钝感TATB炸药实验
为起爆钝感TATB炸药, 设计了三次飞片起爆序列, 飞片起爆钝感TATB炸药的实验装置如图 1所示。脉冲功率装置产生的脉冲能量使金属爆炸箔发生快速电爆炸, 爆炸形成的等离子体剪切并驱动聚酰亚胺飞片层产生飞片, 起爆初级装药HNS-IV, 初级装药爆轰驱动二次飞片冲击起爆二级炸药LLM-105, LLM-105炸药爆轰驱动三次飞片起爆钝感TATB装药。实验采用的初级装药为HNS-IV, 尺寸为∅4mm×4mm; 次级装药为分别为HNS-IV、RDX和LLM-105;二次飞片和三次飞片材料均为金属钛, 其中二次飞片尺寸为∅4mm×0.11mm, 三次飞片尺寸分别为∅4mm×0.11mm、∅6mm×0.11mm和∅10mm×0.11mm。
图 1 飞片起爆钝感TATB炸药实验示意图Figure 1. Experimental sketch of initiation of insensitive TATB explosive by flyer表 1为部分飞片起爆钝感TATB炸药实验的序列结构和起爆结果。实验1、2、3直接采用HNSIV, 增加HNS-IV装药量和采用RDX二级装药不能起爆钝感TATB炸药。实验4、5不含有二次飞片, 初级装药HNS-IV直接接触起爆二级装药LLM-105并驱动飞片, 高密度TATB装药未起爆。实验6、7中, 初级装药HNS-IV驱动二次飞片撞击二级装药LLM-105, LLM-105装药爆轰驱动三次飞片撞击TATB装药, TATB装药稳定爆轰。
表 1 飞片起爆钝感TATB炸药的实验及结果Table 1. Experiments and results of initiation of insensitive TATB explosive initiated by flyer实验 初级装药 二次飞片 二级装药 三次飞片 结果 材料 d/mm h/mm d/mm h/mm 材料 d/mm h/mm d/mm h/mm 1 HNS-IV 4 4 4 0.11 - - - - - 未起爆 2 HNS-IV 4 4 4 0.11 HNS-IV 6.3 5 4 0.11 未起爆 3 HNS-IV 4 4 4 0.11 RDX 7.0 5 4 0.11 未起爆 4 HNS-IV 4 4 - - LLM-105 6.3 5 4 0.11 未起爆 5 HNS-IV 4 4 - - LLM-105 6.3 5 6 0.11 未起爆 6 HNS-IV 4 4 4 0.11 LLM-105 10.0 10 6 0.11 起爆 7 HNS-IV 4 4 4 0.11 LLM-105 10.0 10 10 0.11 起爆 2. 飞片速度测试和数值模拟
为初步获取∅6mm×0.11mm钛飞片起爆TATB装药的速度上下限, 采用全光纤激光位移干涉测速测速系统(AFDISAR)对实验2、3三次飞片速度进行测量, 分别获得飞片未起爆和可靠起爆TATB装药的飞片速度曲线。飞片速度测试如图 2所示。三次飞片在炸药驱动下运动, 将激光探头照射的光返回到耦合器, 经光电探测器记录得到飞片的速度。
对LLM-105炸药爆轰驱动钛飞片的过程和钛飞片冲击起爆主装药TATB炸药的过程进行数值模拟, 与实验结果进行比较。
简化实验模型, 建立∅6.3mm×5mm和∅10.0mm×10mm的LLM-105炸药爆轰驱动飞片的模型, 采用轴对称结构。在计算过程中, 钛飞片采用弹塑性流体动力学模型, LLM-105采用高能炸药燃烧模型, 采用JWL状态方程描述炸药的爆轰产物压力、体积和能量特性。JWL状态方程的形式为:
p=A(1−ωR1V)e−R1V+B(1−ωR2V)e−R2V+ωEV (1) 式中:p为压力, V为相对体积, E为内能, A、B、R1、R2和ω为常数。在实验中, LLM-105密度为1.82g/cm3, 参数分别为:A=852GPa, B=18GPa, R1=4.6, R2=1.3, ω=0.3, E0=10.2GJ/m3。
飞片起爆TATB炸药属于高压短脉冲冲击起爆, 采用JWL方程描述未反应炸药和爆轰产物状态, 采用三项式点火增长模型反应速率方程描述TATB炸药的反应过程。点火增长模型反应速率方程为:
˙λ=I(1−λ)b(ρ/ρ0−1−a)x+G1(1−λ)cλdpy+G2(1−λ)eλgpz0<F<Fig,max,0<F<FG1,max,1<F<FG2,min (2) 式中:I、G1、G2、a、b、c、d、e、g、x、y、z是12个可调参数。ρ0为炸药初始密度, ρ0=1.895g/cm3, 主要参数引自文献[4-5]。
3. 结果分析
图 3(a)为实验5的飞片速度曲线:在飞片速度上升阶段, 实验结果和数值模拟结果比较一致, 平滑段数值模拟结果大于实验结果, 主要因为在数值模拟中, 未考虑LLM-105炸药的爆轰稀疏波的影响, 飞片也不受空气阻力的作用。图 3(b)为实验6的飞片速度曲线, 实验结果整体小于数值模拟结果, 这是因为在数值模拟中, 没有考虑稀疏波和空气阻力的作用。图 3中, 为了更清晰的得出飞片的速度曲线, 对AFDISAR测速系统测得曲线的点进行了筛选。
由表 1和图 3可知, 当∅6mm×0.11mm钛飞片以3.834km/s的速度撞击TATB装药时, TATB装药未起爆, 当∅6mm×0.11mm钛飞片以4.350km/s的速度撞击TATB装药时, TATB装药起爆。图 4(a)是钛飞片以3.834km/s的速度撞击炸药时, 炸药压力曲线的数值模拟结果。可以看出, 炸药界面处的压力峰值为38GPa, 受稀疏波的影响, 炸药内压力逐渐减小, 在8和9mm处压力不足20GPa, 结果炸药没有稳定爆轰。图 4(b)是钛飞片以4.350km/s的速度撞击炸药时, 炸药压力曲线的数值模拟结果。可以看出, 在炸药界面处的压力为约46GPa, 随着爆轰波的传播, 在2和4mm处的压力分别为38.38和35GPa, 受稀疏波的影响, 在8和9mm处压力分别降至29.19和29.5GPa。由炸药不同位置处的压力曲线可以判定, 炸药达到稳定爆轰。
4. 结论
采用现有的冲击片雷管直接驱动二次飞片不能起爆高密度TATB装药, 通过飞片起爆序列实验设计, 得出飞片可靠起爆高密度TATB装药的起爆序列, 且序列中所用的装药满足钝感起爆序列许用装药要求。
采用AFDISAR系统, 测得钛飞片未起爆和起爆TATB炸药的速度分别为3.834和4.350km/s。通过DYNA2D程序对飞片速度和起爆TATB炸药过程进行数值模拟, 模拟结果与实验结果一致。初步确定了钛飞片起爆高密度TATB装药的阈值速度范围。
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图 8 含21炮孔的三自由面台阶爆破模型
Figure 8. The bench blasting model with three free surfaces and twenty-one bore holes
表 1 关键指标对比
Table 1. Comparison of key indexes
方法 爆破漏斗体积/cm3 K50 /mm K80 /mm 实验值 426.6 48.6 64.0 数值解 478.7 56.2 97.2 误差/% 12.2 15.6 51.9 
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