Wave attenuation in porous media and its protective effect on shock wave
-
摘要: 孔隙介质对波的衰减极为显著，因此，它能有效降低介质中冲击波的能量。普遍来说，地球浅层介质均可视为孔隙介质，即可作为应对冲击波的天然防护材料，这对大型地下结构的安全防护有着重要的意义。本文通过对大振幅应力脉冲通过水或冰充填的人工节理孔隙介质的测量结果分析，讨论了节理中固相/液相水对爆炸效果的作用。基于双孔隙模型和部分饱和模型计算预测的P波速度以及岩石衰减和频散规律，与实测数据相一致。实验与模型预测均表明，节理中的水和冰对冲击波有较大的衰减，但是充水节理更为明显，且由于填充材料的不同会导致不同的介质性质。因此，在地球介质孔隙节理中充填不同衰减特性材料，可以满足不同情况下的冲击波防护需要。Abstract: The earth medium can be regarded as a porous medium. Because the attenuation of the wave is very significant, it can effectively reduce the energy of the shock wave. The porous medium can be used as a protective material for the shock wave, which is of special significance for large underground structures. In this paper, the measurement results of the artificial joint porous medium filled with water or ice with large amplitude and rapidly rising stress pulse are given. The influence of water as solid or liquid phase in the joint on the explosion effect is discussed. In this paper, two physical models of wave attenuation in porous media, namely double pore model and partial saturation model, are used. The calculation results show that the predicted P-wave velocity, as well as the degree of rock attenuation and dispersion, are consistent with the measured data. Water or ice in the joint has a great attenuation of shock wave. However, water filled joints are more obvious. Due to filling different materials, they show different properties. Therefore, pores and joints can be filled with different attenuation protective materials to meet the needs of different situations.
-
Key words:
- pore medium /
- shock wave /
- double pore model /
- joint
-
图 2 含有半径1 cm的球状气泡的饱水砂岩中的P波速度 （a） 和衰减 （b） （ν2为气体所占的饱和度）
Figure 2. P wave velocity （a） and attenuation （b） of a sandstone saturated with water and containing small spherical pockets of gas having radius 1 cm and occupying a fraction of the volume ν2 as shown
图 3 两组SOC问题条件的示意图
Figure 3. Schematic diagram showing the conditions for the two sets of SOC problems
图 5 在距爆炸源60 m和100 m时，5种材料的径向应力峰值与含气孔隙度
$ {\psi _0} $ 的关系Figure 5. Peak radial stress vs.
$ {\psi _0} $ for five materials with the distance of 60 m and 100 m from the explosion source
图 7 靶子/实验装置的几何示意图[4]。震动通过充填水或冰的岩石节理传播，应力计的箭头指向连接到应力计的电缆，通过跟踪电缆可进入靶子的固定装置
Figure 7. Target/impact geometries for experiments on shock propagation through rocks with water or ice-filled joints[4]. The arrows labeled “stress GAUGES” actually point to the cables connected to the stress gauges which are located at interfaces specified in the text as indicated by tracing the path of the cables into the target fixtures
图 9 在含有单层约1 mm厚的充填节理的大理岩中测量的应力时间历程曲线，入射应力约为1.2 GPa
（a） 水充填节理；（b） 冰充填节理
Figure 9. Measured stress histories in marble containing a single filled joint of about 1 mm thickness for an incident stress of about 1.2 GPa
（a） Water-filled joint；（b） Ice-filled joint
图 10 在含有单层约1 mm 厚的充填节理的大理岩中测量的应力时间历程曲线，入射应力约为6 GPa
（a） 水充填节理；（b） 冰充填节理
Figure 10. Measured stress histories in marble containing a single filled joint of about 1 mm thickness for an incident stress of about 6 GPa
（a） Water-filled joint；（b） Ice-filled joint
图 11 在含有多层约1 mm厚的充填节理的大理岩中测量的应力时间历程曲线，入射应力约为6 GPa
（a） 三层充水节理； （b） 三层充冰节理
Figure 11. Measured stress histories in marble containing a multiple filled joints of about 1 mm thickness for an incident stress of about 6 GPa
（a） Three water-filled joints；（b） Three ice-filled joints
表 1 5种不同孔隙度的孔隙材料在不同饱和度情况下对应力波振幅的影响
Table 1. Effect of five different porosity porous materials on stress wave amplitude under different saturation
材料 固体骨架密度$\,\rho$g/(g•cm−3) 干燥时的密度$\, \rho$dry/(g•cm−3) 总孔隙度
$ \phi $0 / %1 2.28 1.66 0.271 3 2.33 1.80 0.228 5 2.38 2.00 0.158 8 2.41 2.30 0.044 10 2.57 2.55 0.0064 
下载: 导出CSV
-
[1] Pyrak-Nolte L J,Myer L R,Cook N G W. Transmission of seismic waves across natural fractures[J]. J. Geophys. Res.,1990,95:8617-8638 doi: 10.1029/JB095iB06p08617 [2] Chen S G,Zhao J. A study of UDEC modelling for blast wave propagation in jointed rock masses[J]. Int. J. Rock Mech. Min. Sci.,1998,35(1):93-99 doi: 10.1016/S0148-9062(97)00322-7 [3] Pyrak-Nolte L J. The seismic response of fractures and the interrelations among fracture properties[J]. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.,1996,33(8):787-802 [4] Gaffney E S, Smith E A. Hydroplus experimental study of dry, saturated, and frozen geological materials[R]. Tech. Rep. DNA-TR-93-74, Defense Nuclear Agency, Washington, D C, 1994 [5] Renard F,McBec J,Kandula N,et al. Volumetric and shear processes in crystalline rock approaching faulting[J]. Proceedings of the National Academy of Sciences,2019,116(33):16234-16239 doi: 10.1073/pnas.1902994116 [6] Kuang W H,Yuan C C,Zhang J. Real-time determination of earthquake focal mechanism via deep learning[J]. Nature Communications,2021,12:1432 doi: 10.1038/s41467-021-21670-x [7] Biot M A. Theory of propagation of elastic waves in a fluidsaturated porous solid I. Low-frequency range[J]. J. Acoust. Soc. Am.,1956,28(2):168-178 doi: 10.1121/1.1908239 [8] Biot M A. Theory of propagation of elastic waves in a fluidsaturated porous solid II. Higher frequency range[J]. J. Acoust. Soc. Am.,1956,28(2):179-191 doi: 10.1121/1.1908241 [9] Pride S R,Berryman J G,Harris J M. Seismic attenuation due to wave-induced flow[J]. J. Geophys. Res.,2004,109:B01201 [10] Wu R S,Aki K. Multiple scattering and energy transfer of seismic waves:Separation of scattering effect from intrinsic attenuation II. Application of the theory to Hindu Kush region[J]. Pure Appl. Geophys.,1988,128:49-80 doi: 10.1007/BF01772590 [11] Sato H, Fehler M, Maeda T. Seismic wave propagation and scattering in the heterogeneous earth[M]. New York: Springer-Verlag, 1998 [12] Quan Y,Harris J M. Seismic attenuation tomography using the frequency shift method[J]. Geophysics,1997,62:895-905 doi: 10.1190/1.1444197 [13] Sams M S,Neep J P,Worthington M H. The measurement of velocity dispersion and frequency-dependent intrinsic attenuation in sedimentary rocks[J]. Geophysics,1997,62(5):1456-1464 doi: 10.1190/1.1444249 [14] Mavko G,Nur A. Melt squirt in the asthenosphere[J]. J. Geophys. Res.,1975,80(11):1444-1448 doi: 10.1029/JB080i011p01444 [15] Mavko G,Nur A. Wave attenuation in partially saturated rocks[J]. Geophysics,1979,44(2):161-178 doi: 10.1190/1.1440958 [16] Budiansky B,O’Connell R J. Elastic moduli of a cracked solid[J]. Int. J. Solids Struct.,1976,12(2):81-97 doi: 10.1016/0020-7683(76)90044-5 [17] O’Connell R J,Budiansky B. Viscoelastic properties of fluid saturated cracked solids[J]. J. Geophys. Res.,1977,82:5719-5735 doi: 10.1029/JB082i036p05719 [18] Dvorkin J,Mavko G,Nur A. Squirt flow in fully saturated rocks[J]. Geophysics,1995,60(1):97-107 doi: 10.1190/1.1443767 [19] White J E,Mikhaylova N G,Lyakhovitsky F M. Low frequency seismic waves in fluid-saturated layered rocks[J]. J. Acoust. Soc. Am.,1975,11(10):654-659 [20] White J E. Computed seismic speeds and attenuation in rocks with partial gas saturation[J]. Geophysics,1975,40(2):224-232 doi: 10.1190/1.1440520 [21] Dutta N C,Odé H. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-part I:Biot theory[J]. Geophysics,1979,44(11):1777-1788 doi: 10.1190/1.1440938 [22] Dutta N C,Odé H. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-part II:Results[J]. Geophysics,1979,44(11):1789-1805 doi: 10.1190/1.1440939 [23] Dutta N C,Seriff A J. On White’s model of attenuation in rocks with partial gas saturation[J]. Geophysics,1979,44(11):1806-1812 doi: 10.1190/1.1440940 [24] Cadoret T,Mavko G,Zinszner B. Fluid distribution effect on sonic attenuation in partially saturated limestones[J]. Geophysics,1998,63(1):154-160 doi: 10.1190/1.1444308 [25] Murphy W F III. Effects of partial water saturation on attenuationin Massilon sandstone and Vycor porous-glass[J]. J. Acoust. Soc. Am.,1982,71(6):1458-1468 doi: 10.1121/1.387843 [26] Murphy W F III. Acoustic measures of partial gas saturation in tight sandstones[J]. J. Geophys. Res.,1984,89(B13):11549-11559 [27] Gelinsky S,Shapiro S A. Dynamic-equivalent medium approach for thinly layered saturated sediments[J]. Geophys. J. Int.,1997,128(1):F1-F4 doi: 10.1111/j.1365-246X.1997.tb04086.x [28] Gurevich B,Lopatnikov S L. Velocity and attenuation of elastic waves in finely layered porous rocks[J]. Geophys. J. Int.,1995,121(3):933-947 doi: 10.1111/j.1365-246X.1995.tb06449.x [29] Norris A N. Low-frequency dispersion and attenuation in partially saturated rocks[J]. J. Acoust. Soc. Am.,1993,94(1):359-370 doi: 10.1121/1.407101 [30] Johnson D L. Theory of frequency dependent acoustics in patchysaturated porous media[J]. J. Acoust. Soc. Am.,2001,110(2):682-694 doi: 10.1121/1.1381021 [31] Xi D Y,Liu X Y,Zhang C Y. The frequency (or time):Temperature equivalence of relaxation in saturated rocks[J]. Pure and Applied Geophysics,2007,164(11):2157-2173 doi: 10.1007/s00024-007-0270-z [32] Xi D Y,Xu S L,Du Y,et al. Wave propagation analysis of porous rocks with thermal activated relaxation mechanism[J]. Journal of Applied Geophysics,2011,73(3):289-303 doi: 10.1016/j.jappgeo.2011.01.013 [33] 席道瑛,张程远,刘小燕,等. 饱和岩石的时温等效关系[J]. 物探化探计算技术,2000,22(2):127-131 doi: 10.3969/j.issn.1001-1749.2000.02.006Xi Daoying,Zhang Chengyuan,Liu Xiaoyan,et al. Time-temperature equivalence of saturated rocks[J]. Geophysical and Geochemical Exploration,2000,22(2):127-131 doi: 10.3969/j.issn.1001-1749.2000.02.006 [34] 席道瑛,周城光,徐松林,等. 饱和砂岩滞弹性弛豫衰减机理的探索[J]. 地球物理学报,2012,55(7):2362-2370 doi: 10.6038/j.issn.0001-5733.2012.07.021Xi Daoyuan,Zhou Chengguang,Xu Songlin,et al. The research of anelasticity attenuation mechanism of saturated sandstone[J]. Chinese J. Geophys.,2012,55(7):2362-2370 doi: 10.6038/j.issn.0001-5733.2012.07.021 [35] Pride S R,Berryman J G. Linear dynamics of doubleporosity and dual-permeability materials. I. Governing equations and acoustic attenuation[J]. Phys. Rev. E,2003,68:036603 doi: 10.1103/PhysRevE.68.036603 [36] Pride S R,Berryman J R. Linear dynamics of doubleporosity and dual-permeability materials. II. Fluid transport equations[J]. Phys. Rev. E,2003,68:036604 doi: 10.1103/PhysRevE.68.036604 [37] Biot M A. Mechanics of deformation and acoustic propagation in porous media[J]. J. Appl. Phys.,1962,33:1482-1498 doi: 10.1063/1.1728759 [38] Johnson D L,Koplik J,Dashen R. Theory of dynamic permeability and tortuosity in fluid-saturated porous media[J]. J. Fluid Mech.,1987,176:379-402 doi: 10.1017/S0022112087000727 [39] Skempton A W. The pore-pressure coefficients A and B[J]. Geotechnique,1954,4(4):143-147 doi: 10.1680/geot.1954.4.4.143 [40] Biot M A,Willis D G. The elastic coefficients of the theory of consolidation[J]. J. Appl. Mech.,1957,24:594-601 doi: 10.1115/1.4011606 [41] Gassmann F. Uber die elastizitat poroser medien （Elasticity of porous media. Vierteljahrschrift der Naturforschenden）[R]. Gesellshaft in Zurich, 1951, 96: 1-23 [42] Berryman J G,Wang H F. The elastic coefficients of doubleporosity models for fluid transport in jointed rock[J]. J. Geophys. Res.,1995,100(B12):24611-24627 doi: 10.1029/95JB02161 [43] Butkovich T R. Influence of water in rocks on effects of underground nuclear explosions[J]. Journal of Geophysical Research Atmospheres,1971,76(8):1993-2011 [44] Crowley B K. Effect of porosity and saturation on shock-wave response in tuffs[J]. International Journal of Rock Mechanics & Mining Sciences,1973,10(5):437-464 [45] Gaffney E S. Transmission of high-amplitude stress pulsec through ice-or-water-filled joints[J]. International Journal of Rock Mechanics & Mining Sciences,2000,37(8):1277-1283 [46] Grady D E,Hollenbach R E,Schuler K W. Compression wave studies on calcite rock[J]. J. Geophys. Res.,1978,83(B6):2839-2849 doi: 10.1029/JB083iB06p02839 [47] Smyth J R,Ahrens T J. The crystal structure of calcite III[J]. Geophys. Res. Lett.,1997,24(13):1595-1598 doi: 10.1029/97GL01603 [48] Larson D B. Shock-wave studies of ice under uniaxial strain conditions[J]. Journal of Glaciology,1984,30(105):235-240 doi: 10.1017/S0022143000005992 [49] Gaffney E S. Hugoniot of water ice[M]//Klinger J, Benest D, Dollfus A, et al. Ices in the solar system. Norwell: Kluwer Acad., 1985: 119-148 -
点击查看大图
计量
- 文章访问数: 147
- HTML全文浏览量: 102
- PDF下载量: 11
