含多种尺寸缺陷岩体中的弹性波散射
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摘要
研究了含多种尺寸扁平椭圆缺陷的岩体中弹性波散射规律.细观上应用Green函数方法,考虑了入射波与基本的扁平椭圆缺陷相互作用,宏观上采用线性叠加原理,得到了缺陷岩体的频散和衰减规律.频散曲线中特征频率与裂纹尺寸负相关.含几种不连续尺寸裂纹的岩体中其频散曲线呈"阶梯跳跃"形,其衰减曲线也有不同的峰值;而含"均匀分布"与"正态分布"裂纹尺寸的岩体,与含单一尺寸缺陷的岩体相比,其频散曲线具有较宽的特征频率段.结合两个声波测试实例,讨论了这一理论模型的合理性与可行性.
Scattering laws in rock mass which contained flat ellipse crack was researched.The Green function method was presented at mesoscopic scale;linear superposition idea was applied into this model to get wave velocity dispersion and attenuation coefficient at macroscopic scale.The characteristic frequency in frequency dispersion curve is negative correlation with crack size.It had been discovered that a Ladder jump pattern could be presented in frequency dispersion curve if rock mass contains discontinuous size crack,while its characteristic frequency region would be widened if the crack size continues to distribute,such as uniform distribution or Gauss distribution.With two acoustic testsc combined,the rationality and feasibility of this theoretic model is been discussed.
Scattering laws in rock mass which contained flat ellipse crack was researched.The Green function method was presented at mesoscopic scale;linear superposition idea was applied into this model to get wave velocity dispersion and attenuation coefficient at macroscopic scale.The characteristic frequency in frequency dispersion curve is negative correlation with crack size.It had been discovered that a Ladder jump pattern could be presented in frequency dispersion curve if rock mass contains discontinuous size crack,while its characteristic frequency region would be widened if the crack size continues to distribute,such as uniform distribution or Gauss distribution.With two acoustic testsc combined,the rationality and feasibility of this theoretic model is been discussed.
引文
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[2]Shapiro A A,Bedrikovetsky P G.A stochastic theory for deep bed filtration accounting for dispersion and size distributions[J].Physica A:Statistical Mechanics and Its Applications,2010,389(13):2473-2494.
[3]Adelinet M,Fortin J,Guéguen Y.Dispersion of elastic moduli in a porous-cracked rock:theoretical predictions for squirt-flow[J].Tectonophysics,2011,503(1/2):173-181.
[4]Ke W,Castaings M,Bacon C.3D finite element simulations of an air-coupled ultrasonic NDT system[J].NDT&E International,2009,42(6):524-533.
[5]Anders Lvstad,Peter Cawley.The reflection of the fundamental torsional guided wave from multiple circular holes in pipes[J].NDT&E International,2011,44(7):553-562.
[6]葛瑞.马沃可,塔潘.木克基,杰克.德沃金.岩石物理手册:孔隙介质中地震分析工具[M].合肥:中国科学技术大学,2008:33-57.(Gray Mavko,Tapan Mukerji,Jack Dvorikin.The Rock Phys-ics Handbook:Tools for Seismic Analysis in Porous Media[M].Hefei:University of Science and Tech-nology of China,2008:33-57.(Chinese version))
[7]Zimmer M A,Prasad M,Mavko G,Nur A.Seismic velocities of unconsolidated sands—Part1:pres-sure trend from0.1to20MPa[J].Geophysics,2007,72(1):E1-E13.
[8]Bachrach R,Avseth P.Rock physics modeling of unconsolidated sands:accounting for nonuniform contacts and heterogeneous stress fields in the effective media approximation with applications to hydro-carbon exploration[J].Geophysics,2008,73(6):E197-E209.
[9]Pride S R,Berryman J.Linear dynamics of double-porosity dual-permeability materials—Ⅰ:governing equations and acoustic attenuation[J].Physical Review E,2003,68(3):036603.
[10]Pride S R,Berryman J.Linear dynamics of double-porosity dual-permeability materials—Ⅱ:fluid transport equations[J].Physical Review E,2003,68(3):036604.
[11]Zhang Ch,Achenbach J D.Scattering by multiple crack configurations[J].Journal of Applied Mechan-ics,1989,55(1):104-110.
[12]Achenbach J D,Gautesen A K,McMaken H.Ray Methods for Waves in Elastic Solids:With Applica-tions to Scattering by Cracks[M].Boston,London,Melbourne:Pitman Advanced Publishing Program,1982:33-46.
[13]刘永贵,徐松林,席道瑛,李广场,郑文,邓向允.节理玄武岩体弹性波频散效应研究[J].岩石力学与工程学报,2010,29(S1):3314-3320.(LIU Yong-gui,XU Song-lin,XI Dao-ying,LI Guang-chang,ZHEN Wen,DENG Xiang-yun.Dispersion effect of elastic wave in jointed basalt[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S1):3314-3320.(in Chinese))
[14]徐松林,刘永贵,席道瑛,李广场,谭子翰.弹性波在含双裂纹岩体中的传播分析[J].地球物理学报,2012,55(3):944-952.(XU Song-lin,LIU Yong-gui,XI Dao-ying,LI Guang-chang,TAN Zi-han.Analysis of the propagation of elastic wave in rocks with a double-crack model[J].Chinese Journal of Geophysics,2012,55(2):166-176.)
[15]邓向允,徐松林,李广场,刘永贵,郑文,席道瑛.缺陷对玄武岩中声波波速影响的试验研究[J].实验力学,2009,24(1):13-20.(DENG Xiang-yun,XU Song-lin,LI Guang-chang,LIU Yong-gui,ZHENG Wen,XI Dao-ying.Experimental study of defect effect on sonic velocity in basalt[J].Chinese Journal of Experimental Mechanics,2009,24(1):13-20.(in Chinese))
[16]Aggelis D G,Polyzos D,Philippidis T P.Wave dispersion and attenuation in fresh mortar:theoretical predictions and experimental results[J].Journal of the Mechanics and Physics of Solids,2005,53(4):857-883.
[17]钟伟芳,聂国华.弹性波的散射理论[M].武汉:华中理工大学出版社,1997.(ZHONG Wei-fang,NIE Guo-hua.Theory of Elastic Wave Scattering[M].Wuhan:Chinese by Huazhong University of Science and Technology Press,1997.(in Chinese))
[18]Zhang Ch,Gross D.Wave attenuation and dispersion in randomly cracked solids—Ⅰ:slit cracks[J].International Journal of Engineering Science,1993,31(6):841-858.
[19]Foldy L L.The multiple scattering of waves[J].Physical Review,1945,67(3/4):107-119.
[20]王元淳.边界元法基础[M].上海:上海交通大学出版社,1988.(WANG Yuan-chun.Foundation of Boundary Element Method[M].Shanghai:Shanghai Jiaotong University Press,1988.(in Chi-nese))
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