不同饱和度土层分界面上剪切波的反射与透射
|
摘要
基于多相孔隙介质弹性理论,给出了非饱和土中不同弹性波的传播方程。根据分界面上的边界条件,建立了各势函数波幅值之间的关系式,讨论了入射剪切波在不同饱和度土层分界面上的反射与透射问题。在无限空间非饱和土体中存在3种压缩波和1种剪切波,因此,当剪切波传播到不同饱和度的非饱和土层分界面上将分别在上、下土层激发产生4种反射波和4种透射波。推导出不同反射波和透射波的振幅比例系数和能量比例系数的理论表达式,并且在此基础上进行数值分析。在数值算例中分别研究了各反射波与透射波的能量比例系数(即能量反射率和能量透射率)受入射频率、入射角度以及上、下土层土体饱和度变化的影响情况。计算结果表明:各能量反射率和能量透射率不仅与入射角和入射频率有关,而且其受上、下土层饱和度变化的影响也同样不能忽视。
Based on the multiphase pore elasticity theory,the propagation equations for the various elastic waves in unsaturated soils are derived.According to the boundary conditions at the interface,the relationships between different wave amplitudes of various potential functions are established;and then the reflection and transmission problems of incident shear wave at the interface between unsaturated soil layers with different saturation degrees are discussed.Three compressional waves and one shear wave exist in the infinite unsaturated soils,therefore four reflected waves and four transmitted waves are generated when the shear wave propagates at the interface between different unsaturated soil layers.The theoretical expressions for the amplitude ratios and energy ratios for the various waves are derived;and the numerical analysis is then performed.In the numerical examples,the influences of incident frequency,incident angle and saturation degrees of the upper and lower soil layers on the proportionality coefficients of the reflected wave energy and transmitted wave energy(namely energy reflection ratios and energy transmission ratios) are discussed respectively.It is shown that the energy reflection ratios and energy transmission ratios are affected by both the incident angle and the incident frequency.Additionally,the influence of the saturation degrees of the upper and lower soil layers on the reflected and transmitted waves should not be ignored.
Based on the multiphase pore elasticity theory,the propagation equations for the various elastic waves in unsaturated soils are derived.According to the boundary conditions at the interface,the relationships between different wave amplitudes of various potential functions are established;and then the reflection and transmission problems of incident shear wave at the interface between unsaturated soil layers with different saturation degrees are discussed.Three compressional waves and one shear wave exist in the infinite unsaturated soils,therefore four reflected waves and four transmitted waves are generated when the shear wave propagates at the interface between different unsaturated soil layers.The theoretical expressions for the amplitude ratios and energy ratios for the various waves are derived;and the numerical analysis is then performed.In the numerical examples,the influences of incident frequency,incident angle and saturation degrees of the upper and lower soil layers on the proportionality coefficients of the reflected wave energy and transmitted wave energy(namely energy reflection ratios and energy transmission ratios) are discussed respectively.It is shown that the energy reflection ratios and energy transmission ratios are affected by both the incident angle and the incident frequency.Additionally,the influence of the saturation degrees of the upper and lower soil layers on the reflected and transmitted waves should not be ignored.
引文
[1]BIOT M A.Theory of propagation of elastic waves in afluid-saturated porous solid:I.Low-frequency range;II.Higher frequency range[J].The Journal of theAcoustical Society of America,1956,28(2):168-191.
[2]PLONA T J.Observation of a second bulk compressionalwave in a porous medium at ultrasonic frequencies[J].Applied Physics Letters,1980,36(4):259-261.
[3]DERESIEWICZ H,RICE J T.The effect of boundarieson wave propagation in a liquid-filled porous solid:V.Transmission across a plane interface[J].SeismologicalSociety of America,1964,54(1):409-416.
[4]STOLL R D,KAN T K.Reflection of acoustic waves at awater-sediment interface[J].The Journal of theAcoustical Society of America,1981,70(1):149-156.
[5]DUTTA N C,ODE H.Seismic reflections from a gaswater contact[J].Geophysics,1983,48(2):148-162.
[6]SANTOS J E,CORBERO J M,RAVAZZOLI C L,et al.Reflection and transmission coefficients in fluid-saturatedporous media[J].Journal of Acoustical Society ofAmerica,1992,91(4):1911-1913.
[7]YANG J,WU S M.Reflection and transmission ofseismic waves at an interface between two saturatedsoils[J].Acta Seismologica Sinica,1997,10(1):35-42.
[8]WEI C,MURALEETHARAN K K.A continuum theoryof porous media saturated by multiple immiscible fluids:I.Linear poroelasticity[J].International Journal ofEngineering Science,2002,40(16):1807-1833.
[9]WEI C,MURALEETHARAN K K.A continuum theoryof porous media saturated by multiple immiscible fluids:II.Lagrangian description and variational structure[J].International Journal of Engineering Science,2002,40(16):1835-1854.
[10]LO W C,SPOSITO G,MAJER E.Wave propagationthrough elastic porous media containing two immisciblefluids[J].Water Resources Research,2005,41(2):W02025.
[11]LU J F,HANYGA A.Linear dynamic model for porousmedia saturated by two immiscible fluids[J].International Journal of Solids and Structures,2005,42(9-10):2689-2709.
[12]ALBERS B.Analysis of the propagation of sound wavesin partially saturated soils by means of a macroscopiclinear poroelastic model[J].Transport in Porous Media,2009,80(1):173-192.
[13]CHEN W Y,XIA T D,HU W T.A mixture theoryanalysis for the surface-wave propagation in anunsaturated porous medium[J].International Journal ofSolids and Structures,2011,48(16-17):2402-2412.
[14]周新民,夏唐代,徐平,等.饱和土介质中地震波在水、气分界面上的反射与透射[J].地震学报,2006,28(4):372-379.ZHOU Xin-min,XIA Tang-dai,XU Ping,et al.Seismicreflection and tansmission coefficiens at an air-waterinterface of saturated porous soil[J].Acta SeismologicaSinica,2006,28(4):372-379.
[15]徐平,夏唐代.弹性波在准饱和土和弹性土界面的反射与透射[J].力学与实践,2006,28(6):58-63.XU Ping,XIA Tang-dai.Reflection and transmission ofelatic wave at the interface of nearly saturated soil andelastic soil[J].Mechanics in Engineering,2006,28(6):58-63.
[16]GARG S K,NAYFEH A H.Compressional wavepropagation in liquid and/or gas saturated elastic porousmedia[J].Journal of Applied Physics,1986,60(9):3045-3055.
[17]BERRYMAN J G,THIGPEN L,CHIN R C Y.Bulkelastic wave propagation in partially saturated poroussolids[J].Journal of the Acoustical Society of America,1988,84(1):360-373.
[18]VAN GENUCHTEN M T.A closed-form equation forpredicting the hydraulic conductivity of unsaturatedsoils[J].Soil Science Society of America Journal,1980,44(5):892-898.
[19]RUBINA J G,RAVAZZOLI C L,SANTOS J E.Reflection and transmission of waves in composite porousmedia:A quantification of energy conversions involvingslow waves[J].Journal of the Acoustical Society ofAmerica,2006,120(5):2425-2436.
[20]WU K,XUE Q,ADLER L.Reflection and transmissionof elastic waves from a fluid-saturated porous solidboundary[J].Journal of the Acoustical Society ofAmerica,1990,87(6):2349-2358.
[2]PLONA T J.Observation of a second bulk compressionalwave in a porous medium at ultrasonic frequencies[J].Applied Physics Letters,1980,36(4):259-261.
[3]DERESIEWICZ H,RICE J T.The effect of boundarieson wave propagation in a liquid-filled porous solid:V.Transmission across a plane interface[J].SeismologicalSociety of America,1964,54(1):409-416.
[4]STOLL R D,KAN T K.Reflection of acoustic waves at awater-sediment interface[J].The Journal of theAcoustical Society of America,1981,70(1):149-156.
[5]DUTTA N C,ODE H.Seismic reflections from a gaswater contact[J].Geophysics,1983,48(2):148-162.
[6]SANTOS J E,CORBERO J M,RAVAZZOLI C L,et al.Reflection and transmission coefficients in fluid-saturatedporous media[J].Journal of Acoustical Society ofAmerica,1992,91(4):1911-1913.
[7]YANG J,WU S M.Reflection and transmission ofseismic waves at an interface between two saturatedsoils[J].Acta Seismologica Sinica,1997,10(1):35-42.
[8]WEI C,MURALEETHARAN K K.A continuum theoryof porous media saturated by multiple immiscible fluids:I.Linear poroelasticity[J].International Journal ofEngineering Science,2002,40(16):1807-1833.
[9]WEI C,MURALEETHARAN K K.A continuum theoryof porous media saturated by multiple immiscible fluids:II.Lagrangian description and variational structure[J].International Journal of Engineering Science,2002,40(16):1835-1854.
[10]LO W C,SPOSITO G,MAJER E.Wave propagationthrough elastic porous media containing two immisciblefluids[J].Water Resources Research,2005,41(2):W02025.
[11]LU J F,HANYGA A.Linear dynamic model for porousmedia saturated by two immiscible fluids[J].International Journal of Solids and Structures,2005,42(9-10):2689-2709.
[12]ALBERS B.Analysis of the propagation of sound wavesin partially saturated soils by means of a macroscopiclinear poroelastic model[J].Transport in Porous Media,2009,80(1):173-192.
[13]CHEN W Y,XIA T D,HU W T.A mixture theoryanalysis for the surface-wave propagation in anunsaturated porous medium[J].International Journal ofSolids and Structures,2011,48(16-17):2402-2412.
[14]周新民,夏唐代,徐平,等.饱和土介质中地震波在水、气分界面上的反射与透射[J].地震学报,2006,28(4):372-379.ZHOU Xin-min,XIA Tang-dai,XU Ping,et al.Seismicreflection and tansmission coefficiens at an air-waterinterface of saturated porous soil[J].Acta SeismologicaSinica,2006,28(4):372-379.
[15]徐平,夏唐代.弹性波在准饱和土和弹性土界面的反射与透射[J].力学与实践,2006,28(6):58-63.XU Ping,XIA Tang-dai.Reflection and transmission ofelatic wave at the interface of nearly saturated soil andelastic soil[J].Mechanics in Engineering,2006,28(6):58-63.
[16]GARG S K,NAYFEH A H.Compressional wavepropagation in liquid and/or gas saturated elastic porousmedia[J].Journal of Applied Physics,1986,60(9):3045-3055.
[17]BERRYMAN J G,THIGPEN L,CHIN R C Y.Bulkelastic wave propagation in partially saturated poroussolids[J].Journal of the Acoustical Society of America,1988,84(1):360-373.
[18]VAN GENUCHTEN M T.A closed-form equation forpredicting the hydraulic conductivity of unsaturatedsoils[J].Soil Science Society of America Journal,1980,44(5):892-898.
[19]RUBINA J G,RAVAZZOLI C L,SANTOS J E.Reflection and transmission of waves in composite porousmedia:A quantification of energy conversions involvingslow waves[J].Journal of the Acoustical Society ofAmerica,2006,120(5):2425-2436.
[20]WU K,XUE Q,ADLER L.Reflection and transmissionof elastic waves from a fluid-saturated porous solidboundary[J].Journal of the Acoustical Society ofAmerica,1990,87(6):2349-2358.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心