非线性法向变形节理对弹性纵波传播的影响
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摘要
从波的弹性位移出发,推导线性位移不连续模型,然后引入等效位移假设,建立节理非线性位移不连续模型。依据所建立的非线性模型,获得垂直入射纵波在非线性法向变形节理处传播的透射和反射系数的解析解。利用该解析解,研究节理初始刚度、节理闭合量与允许闭合量的比率以及入射波频率对节理透反射系数的影响,并与已有的数值计算结果进行比较,两者吻合很好。
The linear displacement discontinuity model is derived from elastic displacement functions of wave,and then a nonlinear displacement discontinuity model is established by introducing the equivalent displacement hypothesis.Based on the established model,the analytic resolution of transmitted and reflected coefficients is obtained when the normal incident P-wave propagates to the nonlinear normal deformative joint.The effects of parameters such as initial joint stiffness,quantitative ratio of joint closure to allowable joint closure and incident frequency of wave on transmitted and reflected coefficients are investigated.By comparison with the published numerical results,it is found that the analytic results agree well with the numerical calculations.
The linear displacement discontinuity model is derived from elastic displacement functions of wave,and then a nonlinear displacement discontinuity model is established by introducing the equivalent displacement hypothesis.Based on the established model,the analytic resolution of transmitted and reflected coefficients is obtained when the normal incident P-wave propagates to the nonlinear normal deformative joint.The effects of parameters such as initial joint stiffness,quantitative ratio of joint closure to allowable joint closure and incident frequency of wave on transmitted and reflected coefficients are investigated.By comparison with the published numerical results,it is found that the analytic results agree well with the numerical calculations.
引文
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[20]戈革.地震波动力学基础[M].北京:石油工业出版社,1980.(GeGe.Fundamentals of Dynamics on Seismic Wave[M].Beijing:Petroleum Industry Press,1980.(in Chinese))
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[22]Cook N G W.Natural joints in rock mechanical,hydraulic and seismicbehavior and properties under normal stress[J].International Journal ofRock Mechanics and Mining Sciences and Geomechanics Abstracts,1992,29(3):198–223.
[23]谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990.(Xie Heping.Damage Mechanics of Rock and Concrete[M].Xuzhou:China University of Mining and Technology Press,1990.(inChinese))
[2]Hao H,Wu Y K,Ma G W,et al.Characteristics of surface groundmotions induced by blasts in jointed rock mass[J].Soil Dynamics andEarthquake Engineering,2001,20(2):85–98.
[3]Pyrak-Nolte L J.Seismic response of fractures and the interrelationsamong fractures[J].International Journal of Rock Mechanics andMining Sciences,1996,33(8):787–802
[4]King M S,Myer L R,Rezowalli J J.Experimental studies ofelastic-wave propagation in a columnar-jointed rock mass[J].GeophysicalProspecting,1986,34(8):1 185–1 199.
[5]Hudson J A.Wave speeds and attenuation of elastic waves in materialcontaining cracks[J].Geophysical Journal of the Royal AstronomicalSociety,1981,64(1):133–150.
[6]Schoenberg M.Transmission and reflection of plane wave at an elasticviscoelastic interface[J].Geophysical Journal of the RoyalAstronomical Society,1971,54(5):35–47.
[7]Myer L R,Pyrak-Nolte L J,Cook N G W.Effects of single fracture onseismic wave propagation[A].In:Proceedings of ISRM Symposiumon Rock Joints[C].Rotterdam:A.A.Balkema,1990,467–473.
[8]考尔斯基H.固体中的应力波[M].北京:科学出版社,1958.(KolskyH.Stress Waves in Solids[M].Beijing:Science Press,1958.(in Chinese))
[9]Rinehart J S.固体中的应力瞬变[M].杨善元译.北京:煤炭工业出版社,1981.(Rinehart J S.Stress Transients in Solids HyperDynamics[M].Translated by Yang Shanyuan.Beijing:China CoalIndustry Publishing House,1981.(in Chinese))
[10]李夕兵,古德生.岩石冲击动力学[M].长沙:中南工业大学出版社,1994.(Li Xibing,Gu Desheng.Rock Impact Dynamics[M].Changsha:Central South University of Technology Press,1994.(inChinese))
[11]李夕兵.论岩体软弱结构面对应力波传播的影响[J].爆炸与冲击,1993,13(4):334–342.(Li Xibing.Influence of the structuralweakness planes in rock mass on the propagation of stress waves[J].Explosion and Shock Waves,1993,13(4):334–342.(in Chinese))
[12]Schoenberg M.Elastic wave behavior across linear slip interfaces[J].Journal of the Acoustical Society of America,1980,68(5):1 516–1 521.
[13]Pyrak-Nolte L J.Seismic visibility of fractures[Ph.D.Thesis][D].Berkeley:Department of Materials Science and Mineral Engineering,University of California,1988.
[14]Jones J P,Whittier J S.Waves at a flexibly bonded interface[J].Journal of Applied Mechanics,1967,40(9):905–909.
[15]Pyrak-Nolte L J,Myer L R,Cook N G W.Transmission of seismicwaves across single natural fracture[J].Journal of GeophysicalResearch,1990,95(6):8 617–8 638.
[16]Goodman R E.Methods of Geological Engineering in DiscontinuousRocks[M].New York:West,1976.
[17]Bandis S C,Lumsden A C,Barton N R.Fundamentals of rock jointdeformation[J].International Journal of Rock Mechanics and MiningSciences and Geomechanics Abstracts,1983,20(6):249–268.
[18]Batron N R,Bandis S,Bakhtar K.Strength-deformation andconductivity coupling of rock joints[J].International Journal of RockMechanics and Mining Sciences and Geomechanics Abstracts,1985,22(3):121–140.
[19]Zhao J,Cai J G.Transmission of elastic P-waves across singlefractures with a nonlinear normal deformational behavior[J].RockMechanics and Rock Engineering,2001,34(1):3–22.
[20]戈革.地震波动力学基础[M].北京:石油工业出版社,1980.(GeGe.Fundamentals of Dynamics on Seismic Wave[M].Beijing:Petroleum Industry Press,1980.(in Chinese))
[21]卢文波.应力波与可滑移岩石界面间的相互作用研究[J].岩土力学,1996,17(3):70–75.(Lu Wenbo.A study on interaction betweenstress wave and slipping rock interface[J].Rock and Soil Mechanics,1996,17(3):70–75.(in Chinese))
[22]Cook N G W.Natural joints in rock mechanical,hydraulic and seismicbehavior and properties under normal stress[J].International Journal ofRock Mechanics and Mining Sciences and Geomechanics Abstracts,1992,29(3):198–223.
[23]谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990.(Xie Heping.Damage Mechanics of Rock and Concrete[M].Xuzhou:China University of Mining and Technology Press,1990.(inChinese))
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