应力波在节理岩体中的传播特性探析
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摘要
考虑岩石节理非线性法向特征,时域范围内理论分析了应力波在两个平行节理岩体中的传播规律。通过建立波在节理岩体中传播的数值差分模型,时域范围内推导并获得了纵波P波和横波S波垂直入射节理岩体的动力传播方程。可以同时考虑节理的非线性特征和节理间多次透反射的影响,并可求得任意时刻透射波和反射波的数值解。进一步通过参数研究分析了不同因素对应力波传播规律的影响规律,包括节理初始法向刚度、节理非线性系数、入射波频率和节理间间距等。研究表明:由于节理非线性因素以及节理间多次透反射的影响,波在多个岩体节理中的透射系数并非是波在单个节理中透射系数的简单叠乘。
Considering the nonlinear constitutive model for normal deformation of rock fracture,theoretical investigation on propagation of oblique incident stress wave was presented based on a full time-domain algorithm in jointed rock mass containing two fractures.Analytic model was established,and then the wave propagation equations of oblique incident stress wave were deduced in jointed rock mass containing two fractures.The wave propagation equations deduced from the suggested method have the virtue of convenience to consider the different angle of incident wave,the wave transformation,the nonlinear behavior of the fracture,multiple wave reflections and transmissions;meanwhile,the transmitted wave and reflected wave can be obtained conveniently at any time.Finally,based on the result of transmission coefficient,parametric studies are carried out to analyze the wave propagation characteristic deeply,including initial stiffness,nonlinear coefficient,frequency of incident wave,incident angle and fracture spacing between two fractures.The results indicate that the transmission coefficient can't be simply obtained from the results by the single fracture.
Considering the nonlinear constitutive model for normal deformation of rock fracture,theoretical investigation on propagation of oblique incident stress wave was presented based on a full time-domain algorithm in jointed rock mass containing two fractures.Analytic model was established,and then the wave propagation equations of oblique incident stress wave were deduced in jointed rock mass containing two fractures.The wave propagation equations deduced from the suggested method have the virtue of convenience to consider the different angle of incident wave,the wave transformation,the nonlinear behavior of the fracture,multiple wave reflections and transmissions;meanwhile,the transmitted wave and reflected wave can be obtained conveniently at any time.Finally,based on the result of transmission coefficient,parametric studies are carried out to analyze the wave propagation characteristic deeply,including initial stiffness,nonlinear coefficient,frequency of incident wave,incident angle and fracture spacing between two fractures.The results indicate that the transmission coefficient can't be simply obtained from the results by the single fracture.
引文
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[2]Wu Y K,Hao H,Zhou Y X.Propagation characteristics of blast-in-duced shock waves in a jointed rock mass[J].Soil Dynamics AndEarthquake Engineering,1998,17(6):407-412.
[3]Zhao J,Cai J G.Transmission of elastic P-waves across single frac-tures with a nonlinear normal deformational behavior[J].Rock Me-chanics and Rock Engineering,2001,34(1):3-22.
[4]Li J C,Ma G W.Analysis of blast wave interaction with a rock joint[J].Rock Mechanics and Rock Engineering,2009,43(6):777-787.
[5]Song L,Shao Z S,Wu M Z.Theoretical investigation into the wavepropagation in rock with single fracture[J].Key Engineering Materi-al,2011,462-463:1 134-1 139.
[6]Zhao X B.Theoretical and numerical studies of wave attenuationacross parallel fractures[D].Singapore:Nanyang TechnologicalUniversity,2004.
[7]Li J C,Ma G W,Zhao J.An equivalent viscoelastic model for rockmass with parallel joints[J].Rock Mechanics and Rock Engineer-ing,2010,43(6):777-787.
[8]Bandis S C,Lumsden A C.Fundamentals of rock fracture deforma-tion[J].International Journal of Rock Mechanics and Mining Sci-ences and Geo-mechanics Abstracts,1983,20(6):249-268.
[9]Achenbach J D.Wave propagation in elastic solids[M].Amsterdam:North-Holland publishing Company,1973.
[10]Kelly K R,Ward R W,Treitel S.Synthetic seismograms:a finite-difference approach[J].Geophysics,1976,41(1):2-27.
[11]孙卫涛.弹性波动方程的有限差分数值方法[M].北京:清华大学出版社,2009.
[12]杨莹.二维地震波场有限差分法数值模拟研究[D].北京:中国地质大学,2009.
[13]王卫华.节理动态闭合变形性质及应力波在节理处的传播[D].长沙:中南大学,2006.
[14]Cai J G.Effects of parallel fractures on wave attenuation in rock[D].Singapore:Nanyang Technological University,2001.
[15]Myer L R,Pyrak-Nolte L J,Cook N G W.Effects of single fractureon seismic wave propagation[A].Proceedings of ISRM SymposiumRock Joints[C].Rotterdam:A.A.Balkema,1990.
[16]Pyrak-Nolte L J,Myer L R,Cook N G W.Anisotropy in seismic ve-locities and amplitudes from multiple parallel fractures[J].Journalof Geophysical Research,1990,95(B7):11 345-11 358.
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