A review on the improved Whipple shield and related numerical simulations
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摘要: 基于弹丸在超高速撞击薄板时破碎形成碎片云的机理，Whipple防护结构能够对航天器所面临的空间碎片及微流星体等威胁形成有效防护。通过回顾Whipple防护结构的研究和发展历程，对多层板结构、填充式防护结构、夹芯板结构等进行对比，分析其力学效应和防护性能；总结可应用于含泡沫、蜂窝、梯度和编织等材料的防护结构超高速撞击的数值模拟方法及其改进方法；结合相关材料的超高速撞击试验及数值模拟结果，为防护结构未来的研究方向提出建议。
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关键词:
- 超高速碰撞 /
- Whipple防护结构 /
- 碎片云 /
- 多层板结构 /
- 填充/夹芯板结构 /
- FEM-SPH自适应耦合算法
Abstract: Based on the formation mechanism of the debris cloud caused by the projectile hypervelocity impacting onto a thin plate, the Whipple shield can effectively protect the spacecraft from space debris and micrometeoroid. By reviewing the research and development of the Whipple shield, and compares the mechanical effects and protective performance of multilayer, stuffed and sandwich shield. The paper also summarizes the application of numerical simulation methods and their improvement for the hypervelocity impact of protective structures containing materials such as foam and honeycomb, etc. By addressing the results of hypervelocity impact tests and numerical simulations of relevant materials, suggestions are made for the future research of the Whipple shield. -
冲击地压是一种需要采取有效措施进行治理的岩石破坏动力现象。近年来随着煤矿开采深度的增加，冲击地压的发生强度和频度都在增加[1]。各国研究人员针对冲击地压灾害治理开展了大量研究工作，提出了众多防治技术[2-3]，其中爆破卸压技术就是一种较为有效的冲击地压防治技术。煤层爆破卸压可改变煤体性质，使其储能性降低，起到了冲击地压防治作用，达到降低冲击地压发生概率的目的。
影响爆破效果的因素较多，其中装药结构对爆破能量传递、破岩效果等均具有较大影响。杨仁树等[4]利用爆炸加载数字激光动态焦散线试验系统，对不同装药结构爆破爆生裂纹动态断裂效应进行了分析。徐颖等[5]通过对爆炸产生应力波破岩特征的分析，给出了更为精确的应力波作用下裂隙区半径计算公式。魏明尧等[6]利用数值模拟方法，分析了卸压爆破前后围岩应力分布和转移规律，并结合电磁辐射监测技术，对采掘现场卸压效果进行了检验。高峰等[7]通过设计不同实验方案，研究了诱导卸荷作用下岩石的力学性能弱化规律。Luo[8]通过实验室和野外爆破实验，对聚能爆破中爆破孔间距、爆破裂纹扩展等参数进行了研究。郭建卿[9]对液固耦合和不耦合爆破对孔壁的不同作用荷载进行了实验研究。
上述研究主要是针对爆破对岩石的破坏规律等开展研究，但现场冲击地压灾害具有多样性特点[10-13]，针对性的防治技术更具有现实意义。为指导现场冲击地压防治工作，本文中针对不耦合装药爆破特点设计室内实验，通过应力、声发射(acoustic emission, AE)等信息分析爆破对承压试件的卸压效果；对出现应力集中的掘进巷道采取深孔不耦合装药爆破进行卸压；并运用电磁辐射、煤体应力、数值模拟等方法对爆破效果进行验证。
1. 不耦合装药结构卸压爆破效果实验
为验证不耦合爆破对承压试样的卸压效果，选用水作为充填介质进行室内承压试件爆破实验。
1.1 效果验证实验设计
1.1.1 炸药选择及试样制备
实验炸药选用常用RDX炸药，该炸药的TNT当量因数约为1.5，根据相关研究[14-15]和考虑安全因素，药量选择为0.3 g。
根据相似性原理，采用混凝土试件作为此次实验的受压材料，选用细度为100~200目的石英砂作为骨料，以熟石膏与425R水泥混合物作为胶结剂来制作试件。石英砂、水泥、石膏的质量比为10:1:1.25，水胶质量比为0.6:1。该配比试件的单轴抗压强度为2.04 MPa，容重为19.02 kN/m3，泊松比为0.2，弹性模量为1.73 GPa。试件尺寸为100 mm×100 mm×100 mm。同一方法共制作3块试件：W1、W2、W3。
1.1.2 不耦合装药爆破卸压实验程序
(1) 根据试件尺寸制备试件，并在试件成型后立即用不透水的薄膜覆盖表面，在温度为(20±5) ℃的环境中静置1 d，然后拆模，拆模后应立即放入温度为(20±2) ℃、相对湿度为95%以上的养护室中养护28 d，之后在试件中部预留孔内按照图 1所示结构进行装药，径向不耦合系数K=2，选用水作为充填介质。
(2) 设备安装调试：将试件置于三轴实验装置内，如图 2所示，然后将装置安装于SANS试验机承压板上，调整有球形座的承压板，使试样均匀受载，加载速率设定为0.8 mm/min，围压设定为1.5 MPa。安装PCI-2声发射系统[16]，记录实验过程的声发射信息。
(3) 试验机加载应力值接近但不超过试件抗压强度。
(4) 引爆内置爆破装置，进行爆破。
(5) 记录相关实验信息并描述试样的破坏形态。
1.2 不耦合装药结构卸压实验数据分析
本次实验进行了3组爆破，并对3组实验中轴向应力及声发射(AE)振铃计数、能量进行了归类分析。图 3为三组试样爆破前后“时间-应力-累加计数-能量”曲线。从实验的“应力-时间”曲线来看，在达到试件抗压强度之前进行爆破，爆破后各试件均出现了应力降低现象，最大应力降低37.8%，这说明爆破对于应力集中的试件具有较为明显的卸压作用。但之后应力又出现了进一步上升，说明爆破卸压方法具有一定的时效性，即爆破卸压一段时间后会出现应力恢复现象。从曲线上看，在试验机加载速率不变的情况下，曲线的曲率在应力恢复阶段有一定提升，主要因为爆破后碎胀应力的存在使应力恢复速率有所升高。从声发射累加振铃计数及能量来看，由于爆破钻孔及试件材料的离散性，所以存在一个压密阶段，在该阶段出现了较多AE事件，压密阶段之后AE计数及能量与应力曲线吻合度较高，在试件出现较明显的受压破裂时，应力曲线会出现应力降低现象，此时可以记录到较为集中的声发射信号，振铃计数与能量对应出现较大增长，尤其在爆破时出现了较为明显的声发射振铃累加计数增长和能量集中现象。可以看出，破裂的发生与试件应力降低、声发射事件增多具有明显对应关系。
通过实验还可以看出在爆破后试件内部出现了明显的破碎现象，在上部轴向压力及围压限制下，该破碎区域虽然已经形成，但无法排出碎块，进而无法形成有效的卸压区域，因此爆破后又出现了应力恢复现象。在煤层高应力区域采取爆破卸压措施时，应及时进行大直径钻孔将煤体内部破碎体排出，以得到持续时间更长的卸压效果。
2. 不耦合装药结构卸压爆破工程实践
2.1 工程实践巷道概况
本次工程实践选择在山东某矿井LW5303轨道顺槽，该巷道埋深在982~995 m之间，属于典型深部开采，巷道与LW5302采空区之间仅有5 m区段煤柱，而且LW5302工作面受地面村庄压煤问题遗留有宽度为100 m的采空区煤柱，如图 7所示。受大埋深垂直应力、采空区侧向支承压力及采空区遗留煤柱高应力等影响，在LW5303轨道顺槽掘进至图 4所示区域时，在巷道迎头后方1~20 m区域，通过钻屑法与电磁辐射法[17]发现有煤体应力集中现象，最大煤粉量达到23 kg/m，最高电磁辐射强度达到511 mV，而且现场煤炮等动压显现较为频繁。
图 6 径向不耦合装药结构示意图Figure 6. Schematic diagram of the radial non-coupling charge structure应力集中现象的出现对巷道安全造成极大影响，为了有效改善此种情况，采取了巷道近场应力集中爆破卸压方法进行处理。
2.2 爆破参数
(1) 爆破器材
雷管：3段毫秒延迟电雷管。炸药：采用煤矿许用三级乳化炸药，单支炸药规格：直径27 mm，长度300 mm，重量200 g，炸药爆速2 800 m/s，炸药密度1.1 g/cm3。起爆电源：矿用FD150-200T型发爆器。
(2) 爆破孔参数
针对裂隙区的分析一直为工程爆破研究的重点，尤其在卸压爆破时，裂隙区大小直接影响卸压效果[18]。按照应力波拉伸作用原理计算裂隙区半径为：
rp=(bσd/σt)1−arc=33.7.23mm (1) 式中：rc为炸药半径；b=ν/(1-ν)，ν为煤体泊松比，ν=0.39；a为应力波衰减指数，a=2-μ/(1-μ)，μ为煤体的动态泊松比, 与应变率有关，一般值取为泊松比ν的0.8倍；σt为煤体抗拉强度，σt=0.67 MPa；σd为应力波引起的初始径向应力，表达式为：
σd=ρ0D218(rcrb)6n=151.59MPa (2) 式中：D1为爆速；ρ0为炸药密度；rb为爆破孔半径；n为压力增大系数，8 < n < 11，此处取值为9。
爆破孔之间的距离合理时，既能贯通裂隙，起到最佳的卸压效果，又可以达到操作简便并且不会对巷道围岩结构过度破坏。根据式(1)可得，两爆破孔之间的裂隙区宽度为674.46 mm，考虑到验证地点巷道围岩支护情况，且煤岩中存在本身裂隙及中间预裂钻孔，结合经验分析，爆破孔间距选择为2 m。在巷道垂直于煤帮制造直径为54 mm的爆破孔，高度距底板1.5 m，孔深15 m。
(3) 施工排粉预裂钻孔
为了实现持续更久的卸压效果，在2个爆破孔中间采用气动式架柱钻机制造直径为76 mm的排粉导裂钻孔，目的有两个：(a)在2个爆破孔之间引导产生裂隙，增强爆破后的裂隙区范围；(b)爆破后可以及时排出破碎煤体，释放碎胀应力。爆破孔与导裂孔布置如图 5所示。
(4) 装药
为了提高爆破孔的利用率，增高应力波的动压和爆轰气体静压作用时间，降低炸药消耗量并改善爆破的安全性。采用径向不耦合反向装药结构，充填介质为水，不耦合因数K=2。现场实测发现LW5303轨道顺槽巷帮侧向高应力区域位置为12~14 m，为了改变该区域受载煤体性质，使应力峰值向深部进行转移，需要将该区域进行装药爆破。装药长度选择为4 m，根据煤矿许用三级乳化炸药参数可知单孔装药量为2.6 kg。按图 6所示装药结构进行装药。
(5) 起爆
采用矿用FD150-200T型发爆器对爆破孔内炸药进行引爆。
2.3 卸压效果现场监测验证
在巷道迎头实施1次卸压爆破，巷道左帮(实体煤帮)距迎头1~20 m范围内实施20次卸压爆破。选择电磁辐射法、煤体应力监测法、现场动态观测法进行效果验证。爆破后在该区域左帮(实体煤帮)安装了2个深度为15 m的钻孔应力计(初始压力值3 MPa)，其中应力计1距迎头3 m，应力计2距迎头15 m。监测曲线如图 7~8所示。
从校验情况来看，经过爆破卸压处理的工作面其电磁辐射强度显著下降，最大强度值下降为51 mV，小于预警值120 mV。煤体应力监测结果显示，在爆破后应力有一定恢复趋势，这与煤体重新压实有一定关系，但应力计最大应力值为5 MPa左右，仍小于预警值10 MPa。同时，现场煤体破裂响声、巷道围岩变形速率等均有减少，这表明此次卸压爆破工作起到了一定效果。
2.4 卸压效果数值模拟验证
结合LW5303轨道顺槽实际情况，建立卸压爆破数值模型，模拟卸压爆破对煤体应力分布的影响，进一步来检验卸压爆破效果。模型网格划分如图 9所示，在模型中设计了一个爆破孔，设置了距爆破孔为1.0、1.5、2.0 m三个观测点，用来监测动载作用在该点位置的相关信息。爆破孔内动载波形为谐波的一部分，波形中主要包含了应力峰值和作用时间2个参数。按照式(2)可得应力峰值为151.59 MPa，作用时间设定为2 ms。
图 10为爆破前后钻孔附近垂直应力分布图，从图中可以看出：爆破前，进行钻孔施工后，钻孔周围产生了较为明显的应力分布影响，钻孔对煤体卸压有一定效果；爆破后，在爆破孔两侧较近区域由于爆破出现了小范围的应力集中现象，这与现场破碎区碎胀应力引起的应力集中相对应，但在钻孔两侧一定区域内出现了较为明显的应力降低区域，最大应力降幅度约为14.3%，卸压效果明显。
图 11为距爆破孔1.0、1.5、2.0 m处测点的垂直应力变化曲线，从图中可以看出：距爆破孔1.0 m测点处的垂直应力降低点明显超前于1.5和2.0 m处，而且各处测点均出现了应力波动现象，这与动载的加载形式有关，1.0 m测点处波形尤为明显；在爆破后应力均出现了应力恢复现象，1.0 m测点处应力恢复现象更明显，这也说明了爆破卸压容易产生应力恢复，同时印证了室内实验与现场监测中出现的应力恢复现象，因此爆破还应配合大直径钻孔加强卸压持续效果。
3. 结论
(1) 通过室内承压试件的爆破实验，发现爆破后承压试件有明显应力降低现象，声发射信息表明爆破时会出现能量与振铃计数的大幅度增加，可以看出破裂的发生与试件应力降低、声发射事件增多具有明显对应关系。同时，由于碎胀应力的存在，爆破后试件的应力恢复速率有所增加。
(2) 在深部煤矿高应力集中巷道中开展了深孔水介质不耦合爆破现场实验，爆破孔直径54 mm，孔深15 m，装药量2.6 kg，不耦合因数K=2，爆破孔间距为2 m，2个爆破孔之间设计有排粉预裂钻孔来增强卸压效果。现场爆破结束后通过电磁辐射、煤体应力监测、矿压观测与数值模拟等方法进行了卸压效果检验。爆破后电磁辐射强度幅值有显著下降，煤体应力在预警值之内，数值模拟结果显示爆破后一定区域内出现了较为明显的应力降低现象，最大应力降幅度约为14.3%，表明本次爆破对缓解巷道应力集中情况具有积极效果。
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