基于波传播系数构建填实爆炸下花岗岩中运动及变形场

卢强; 王占江; 朱玉荣; 丁洋; 郭志昀

doi:10.11883/bzycj-2019-0140

基于波传播系数构建填实爆炸下花岗岩中运动及变形场

doi: 10.11883/bzycj-2019-0140

卢强^{1, 2,},
王占江^{1, 2, ,},
朱玉荣^{1, 2},
丁洋^{1, 2},
郭志昀^{1, 2}

1.
西北核技术研究院，陕西西安 710024
2.
西北核技术研究院强动载与效应重点实验室，陕西西安 710024

基金项目: 国家自然科学基金（11172244）

详细信息

作者简介:
卢　强（1984－　），男，博士，副研究员，luqiang@nint.ac.cn

通讯作者:
王占江（1961－　），男，博士，研究员，wangzhanjiang@nint.ac.cn

中图分类号: 347.4
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- 被引次数: 0
出版历程
- 收稿日期: 2019-04-22
- 修回日期: 2019-06-05
- 网络出版日期: 2019-06-25
- 刊出日期: 2019-08-01

Construction of motion and deformation field in granite under tamped explosion using wave propagation coefficient

LU Qiang^{1, 2
,},
WANG Zhanjiang^{1, 2
, ,},
ZHU Yurong^{1, 2},
DING Yang^{1, 2},
GUO Zhiyun^{1, 2}

1.
Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China
2.
Laboratory of Intense Dynamic Loading and Effect, Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China

摘要

摘要: 为利用球面波实验测得的有限个粒子速度信息来分析地下爆炸下介质的运动及变形特性，基于黏弹性球面波理论和局部黏弹性等效假设，提出了一种构建地下爆炸运动及变形场的新方法。首先，利用0.125 g TNT填实爆炸下花岗岩中相邻测点的粒子速度频谱给出相应的频谱比；其次，结合黏弹性球面波理论给出的理论频谱比求解出相邻测点之间区域内等效的球面波传播系数；再次，利用局部黏弹性等效假设给出相邻测点之间任意一点的粒子速度频谱，再通过傅里叶逆变换给出粒子速度的时域波形；最后，利用运动场和变形场的物理关系，完成整个分析区域内运动场和变形场的构建。结果表明：由相邻测点反演得到的波传播系数，可高精度地构建相应测点之间区域内介质的运动及变形场；在半径15～50 mm区域内，径向压缩应变峰值约从1.7×10⁻²降为2.1×10⁻³，切向拉伸应变峰值约从4.7×10⁻³降为0.4×10⁻³，径向压缩应变率峰值约从5.1×10⁴ s⁻¹降为2.5×10³ s⁻¹，切向拉伸应变率峰值约从5.0×10³ s⁻¹降为1.4×10² s⁻¹，涵盖了高应变（率）到中低应变（率）加、卸载的全过程。
- 地下爆炸 /
- 球面波 /
- 花岗岩 /
- 黏弹性 /
- 粒子速度 /
- 波传播系数 /
- 应变率
Abstract: In order to use the measured particle velocities from spherical wave experiment to analyze the motion and deformation characteristics of medium under underground explosion, a new method for constructing the motion and deformation field for underground explosion was proposed based on the viscoelastic spherical wave theory and local viscoelastic equivalence hypothesis. Firstly, the velocity spectrums of the adjacent measuring points in granite were used to find out the corresponding spectrum ratio. Secondly, the equivalent spherical wave propagation coefficient in the region between adjacent measuring points was obtained by combining the theoretical spectrum ratio given by viscoelastic spherical wave theory. Thirdly, using the local viscoelastic equivalence hypothesis, the velocity spectrum of the particle at any point between adjacent measuring points was dramn out, and then the time domain waveform of the particle velocity was obtained by the inverse Fourier transform. Finally, the physical relationships between the motion field and the deformation field were used to construct the motion field and the deformation field in the whole analysis region. The results showed that the wave propagation coefficients obtained from the inversion of adjacent measuring points can construct the motion and deformation fields of the medium in the region between corresponding measuring points with high precision. Within the radius of 15-50 mm, the peak value of radial compressive strain decreased from 1.7×10⁻² to 2.1×10⁻³, the peak value of tangential tensile strain decreased from 4.7×10⁻³ to 0.4×10⁻³, the peak value of radial compressive strain rate decreased from 5.1×10⁴ s⁻¹ to 2.5×10³ s⁻¹, and the peak value of tangential tensile strain rate decreases from 5.0×10³ s⁻¹ to 1.4×10² s⁻¹, covering the whole process of loading and unloading from high strain (or strain rate) to intermediate and low strain (or strain rate).
- underground explosion /
- spherical wave /
- granite /
- viscoelasticity /
- particle velocity /
- wave propagation coefficient /
- strain rate

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图 1 0.125 g TNT填实爆炸下花岗岩中实测的径向粒子速度^[21]

Figure 1. Measured radial particle velocities in granite under the tamped explosion of 0.125 g TNT

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图 2 花岗岩中实验频谱比${{H_{\rm{E}}}({r_1},{r_2},\omega )}$的辐角${{\varphi _{\rm{E}}}({r_1},{r_2},\omega )}$随${\omega }$的变化

Figure 2. Argument ${{\varphi _{\rm{E}}}({r_1},{r_2},\omega )}$ of the experimental spectrum ratio ${{H_{\rm{E}}}({r_1},{r_2},\omega )}$ in granite vs the circular frequency ${\omega }$

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图 3 利用花岗岩中相邻测点数据计算的衰减因子$\alpha (\omega )$

Figure 3. Attenuation factor $\alpha (\omega )$ calculated from the data of adjacent measuring points in granite

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图 4 利用花岗岩中相邻测点数据计算的波数${k(\omega )}$

Figure 4. Wave number ${k(\omega )}$ calculated from the data of adjacent measuring points in granite

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图 5 利用花岗岩中相邻测点数据计算的相速度$c(\omega )$

Figure 5. Phase velocity $c(\omega )$ calculated from the data of adjacent measuring points in granite

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图 6 0.125 g TNT填实爆炸下花岗岩中等效应力峰值${\tau _{\max }}$随爆心距$r$的变化

Figure 6. Peak value of the equivalent stress ${\tau _{\max }}$ vs. r under the tamped explosion of 0.125 g TNT in granite

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图 7 局部黏弹性等效下粒子速度场的构建方法

Figure 7. Method for constructing particle velocity field under local viscoelastic equivalence

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图 8 局部黏弹性等效和局部弹性等效方法计算的粒子速度波形的比较

Figure 8. Comparison of particle velocity waveforms calculated by local viscoelastic with that by elastic equivalence method

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图 9 采用局部黏弹性等效方法构建的粒子速度场${v_{\rm{r}}}(r,t)$

Figure 9. Particle velocity field ${v_{\rm{r}}}(r,t)$ constructed by local viscoelastic equivalence method

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图 10 采用局部黏弹性等效方法构建的粒子速度场${u_{\rm{r}}}(r,t)$

Figure 10. Particle displacement field ${u_{\rm{r}}}(r,t)$ constructed by local viscoelastic equivalence method

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图 11 花岗岩中的径向应变

Figure 11. Radial strain in granite at different radii

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图 12 花岗岩中的切向应变

Figure 12. Tangential strain in granite at different radii

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图 13 花岗岩中的径向应变率

Figure 13. Radial strain rates in granite at different radii

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图 14 花岗岩中的切向应变率

Figure 14. Tangential strain rates in granite at different radii

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图 15 花岗岩中不同位置的应变状态

Figure 15. Strain states in granite at different radii

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参考文献(25)

[1]	KOLSKY H. The propagation of stress pulses in viscoelastic solids [J]. Philosophical Magazine Letters, 1956, 1(8): 693–710. DOI: 10.1080/14786435608238144.
[2]	HUNTER S C. Viscoelastic waves [C] // Progress in solid mechanics. North-Holland Amsterdam, 1960: 3−56.
[3]	ZHAO H, GARY G, KLEPACZKO J R. On the use of a viscoelastic split Hopkinson pressure bar [J]. International Journal of Impact Engineering, 1997, 19(4): 319–330. DOI: 10.1016/s0734-743x(96)00038-3.
[4]	ZHAO H, GARY G. A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques [J]. Journal of the Mechanics and Physics of Solids, 1995, 43(8): 1335–1348. DOI: 10.1016/0022-5096(95)00030-M.
[5]	BACON C, BRUN A. Methodology for a Hopkinson test with a non-uniform viscoelastic bar [J]. International Journal of Impact Engineering, 2000, 24(3): 219–230. DOI: 10.1016/s0734-743x(99)00166-9.
[6]	BACON C. Separation of waves propagating in an elastic or viscoelastic Hopkinson pressure bar with three-dimensional effects [J]. International Journal of Impact Engineering, 1999, 22(1): 55–69. DOI: 10.1016/s0734-743x(98)00048-7.
[7]	BACON C, HOSTEN B, GUILLIORIT E. One-dimensional prediction of the acoustic waves generated in a multilayer viscoelastic body by microwave irradiation [J]. Journal of Sound and Vibration, 2000, 238(5): 853–867. DOI: 10.1006/jsvi.2000.3136.
[8]	BACON C. An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar [J]. Experimental Mechanics, 1998, 38(4): 242–249. DOI: 10.1007/bf02410385.
[9]	CASEM D T. Wave propagation in viscoelastic pressure bars using single-point measurements of strain and velocity [J]. Polymer Testing, 2003, 22(2): 155–164. DOI: 10.1016/s0142-9418(02)00064-8.
[10]	MOUSAVI S. Non-equilibruim split Hopkinson pressure bar procedure for non-parametric identification of complex modulus [J]. International Journal of Impact Engineering, 2005, 31(9): 1133–1151. DOI: 10.1016/j.ijimpeng.2004.07.002.
[11]	MOUSAVI S, NICOLAS D F, LUNDBERG B. Identification of complex moduli and Poisson’s ratio from measured strains on an impacted bar [J]. Journal of Sound and Vibration, 2004, 277(4-5): 971–986. DOI: 10.1016/j.jsv.2003.09.053.
[12]	BENATAR A, RITTEL D, YARIN A L. Theoretical and experimental analysis of longitudinal wave propagation in cylindrical viscoelastic rods [J]. Journal of the Mechanics and Physics of Solids, 2003, 51(8): 1413–1431. DOI: 10.1016/s0022-5096(03)00056-5.
[13]	CHREE C. The equations of an isotropic elastic solid in polar and cylindrical coordinates their solution and application [J]. Transactions of the Cambridge Philosophical Society, 1889, 14: 250–369.
[14]	AHONSI B, HARRIGAN J J, ALEYAASIN M. On the propagation coefficient of longitudinal stress waves in viscoelastic bars [J]. International Journal of Impact Engineering, 2012, 45: 39–51. DOI: 10.1016/j.ijimpeng.2012.01.004.
[15]	BUTT H S U, XUE P, JIANG T Z, et al. Parametric identification for material of viscoelastic SHPB from wave propagation data incorporating geometrical effects [J]. International Journal of Mechanical Sciences, 2015, 91: 46–64. DOI: 10.1016/j.ijmecsci.2014.06.003.
[16]	BUTT H S U, XUE P. Determination of the wave propagation coefficient of viscoelastic SHPB: Significance for characterization of cellular materials [J]. International Journal of Impact Engineering, 2014, 74: 83–91. DOI: 10.1016/j.ijimpeng.2013.11.010.
[17]	FAN L F, WONG L N Y, MA G W. Experimental investigation and modeling of viscoelastic behavior of concrete [J]. Construction and Building Materials, 2013, 48: 814–821. DOI: 10.1016/j.conbuildmat.2013.07.010.
[18]	OTHMAN R. On the use of complex Young's modulus while processing polymeric Kolsky-Hopkinson bars' experiments [J]. International Journal of Impact Engineering, 2014, 73: 123–134. DOI: 10.1016/j.ijimpeng.2014.06.009.
[19]	卢强, 王占江, 丁洋, 等. 线黏弹性球面发散应力波的频率响应特性 [J]. 爆炸与冲击, 2017, 37(6): 1023–1030. DOI: 10.11883/1001-1455(2017)06-1023-08. LU Qiang, WANG Zhanjiang, DING Yang, et al. Characteristics of frequency response for linear viscoelastic spherical divergent stress waves [J]. Explosion and Shock Waves, 2017, 37(6): 1023–1030. DOI: 10.11883/1001-1455(2017)06-1023-08.
[20]	LU Q, WANG Z J. Studies of the propagation of viscoelastic spherical divergent stress waves based on the generalized Maxwell model [J]. Journal of Sound and Vibration, 2016, 371: 183–195. DOI: 10.1016/j.jsv.2016.02.034.
[21]	王占江, 李孝兰, 张若棋, 等. 固体介质中球形发散波的实验装置 [J]. 爆炸与冲击, 2000, 20(2): 103–109. WANG Zhanjiang, LI Xiaolan, ZHANG Ruoqi, et al. An experimental apparatus for spherical wave propagation in solid [J]. Explosion and Shock Waves, 2000, 20(2): 103–109.
[22]	王占江, 张德志, 张向荣, 等. 蓝田花岗岩冲击压缩特性的实验研究 [J]. 岩石力学与工程学报, 2003, 22(5): 797–802. DOI: 10.3321/j.issn:1000-6915.2003.05.020. WANG Zhanjiang, ZHANG Dezhi, ZHANG Xiangrong, et al. Testing study on shock compression for Lantian granite [J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(5): 797–802. DOI: 10.3321/j.issn:1000-6915.2003.05.020.
[23]	卢强, 王占江, 门朝举, 等. 有机玻璃中球形应力波传播的分析 [J]. 爆炸与冲击, 2013, 33(6): 561–566. DOI: 10.11883/1001-1455(2013)06-0561-06. LU Qiang, WANG Zhanjiang, MEN Chaoju, et al. Analysis of spherical stress save propagating in PMMA [J]. Explosion and Shock Waves, 2013, 33(6): 561–566. DOI: 10.11883/1001-1455(2013)06-0561-06.
[24]	卢强, 王占江. 标准线性固体材料中球面应力波传播特征研究 [J]. 物理学报, 2015, 64(10): 108301. DOI: 10.7498/aps.64.108301. LU Qiang, WANG Zhanjiang. Characteristics of spherical stress wave propagation in the standard linear solid material [J]. Acta Physica Sinica, 2015, 64(10): 108301. DOI: 10.7498/aps.64.108301.
[25]	王礼立. 应力波基础 [M]. 北京: 国防工业出版社, 2005.