P1波在非饱和土地基表面的反射特性
|
摘要
非饱和土是地表天然土体中最常见的一种形式。与饱和土不同,非饱和土内可传播四种体波:一种剪切波(S波)和三种压缩波(P1波、P2波、P3波)。其中P1传播特性与饱和土中的快压缩波相似:传播速度最快,且衰减系数最低。因此,该文运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面P1波在非饱和土介质自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波:反射P1波、反射P2波、反射P3波及反射S波的振幅反射系数及能量反射系数的理论表达式,并且在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射系数及能量反射系数受P1波入射角及地基土体饱和度变化的影响情况。结果表明:各反射波的振幅反射系数及能量反射系数不仅与入射角有关,也受到饱和度变化的影响。这些结论对土动力学的理论研究以及工程地震勘探具有一定指导意义。
The unsaturated soil is the most common nature soil form on the earth's surface,unlike the fully saturated soil,four bulk waves exist in this soil: one shear wave(i.e.,S wave) and three compressional waves(i.e.,P1 wave,P2 wave,P3 wave).Among these four type waves,P1 wave is the wave with fastest wave velocity and lowest attenuation coefficient,which is similar to the fast compressional wave in fully saturated soil.Hence the unsaturated poroelasticity theory is used to describe the propagation characteristics of elastic waves in unsaturated fluid-saturated soils,and the reflection problem of plane-P1-waves at the free boundary of unsaturated soils is analyzed.Based on the boundary conditions,the theoretical expressions of the amplitude reflection coefficients and energy reflection coefficients for the four reflected waves at the boundary,i.e.,reflected P1 wave,reflected P2 wave,reflected P3 wave and reflected S wave,are respectively derived and the numerical calculations are then carried out.The effects of the incident angle and saturation degree of the soils on the amplitude reflection coefficients and energy reflection coefficients of the four reflected waves are discussed in the numerical example.It is shown that the amplitude reflection coefficients and energy reflection coefficients of the waves is effected by not only the incident but also the saturation degree.These conclusions are useful for the theoretical research and seismic exploration projects.
The unsaturated soil is the most common nature soil form on the earth's surface,unlike the fully saturated soil,four bulk waves exist in this soil: one shear wave(i.e.,S wave) and three compressional waves(i.e.,P1 wave,P2 wave,P3 wave).Among these four type waves,P1 wave is the wave with fastest wave velocity and lowest attenuation coefficient,which is similar to the fast compressional wave in fully saturated soil.Hence the unsaturated poroelasticity theory is used to describe the propagation characteristics of elastic waves in unsaturated fluid-saturated soils,and the reflection problem of plane-P1-waves at the free boundary of unsaturated soils is analyzed.Based on the boundary conditions,the theoretical expressions of the amplitude reflection coefficients and energy reflection coefficients for the four reflected waves at the boundary,i.e.,reflected P1 wave,reflected P2 wave,reflected P3 wave and reflected S wave,are respectively derived and the numerical calculations are then carried out.The effects of the incident angle and saturation degree of the soils on the amplitude reflection coefficients and energy reflection coefficients of the four reflected waves are discussed in the numerical example.It is shown that the amplitude reflection coefficients and energy reflection coefficients of the waves is effected by not only the incident but also the saturation degree.These conclusions are useful for the theoretical research and seismic exploration projects.
引文
[1]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range;II.Higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2):168―191.
[2]Deresiewicz H,Rice J T.The effect of boundaries on wave propagation in a liquid-filled porous solid V.transmission across a plane interface[J].Seismological Society of America,1964,54(1):409―416.
[3]Stoll R D,Kan T K.Reflection of acoustic waves at a water-sendiment interface[J].The Journal of the Acoustical Society of America,1981,70(1):149―156.
[4]Dutta N C,Ode H.Seismic reflections from a gas water contact[J].Geophysics,1983,48(2):148―162.
[5]周新民,夏唐代,徐平,邹振轩.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 Xinmin,Xia Tangdai,Xu Ping,Zou Zhenxuan.Seismic reflection and transmission coefficients at an air-water interface of saturated porous soil[J].Acta Seismologica Sinica,2006,28(4):372―379.(in Chinese)
[6]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 Tangdai.Reflection and transmission of elastic wave at the interface of nearly saturated soil and elastic soil[J].Mechanics in Engineering,2006,28(6):58―63.(in Chinese)
[7]Garg S K,Nayfeh A H.Compressional wave propagation in liquid and or gas saturated porous media[J].Journal of Applied Physics,1986,60(9):3045―3055.
[8]Berryman J G,Thigpen L,Chin R C Y.Bulk elastic wave propagation in partially saturated porous solids[J].Journal of the Acoustical Society of America,1988,84(1):360―373.
[9]Wei C,Muraleetharan K K.A continuum theory of porous media saturated by multiple immiscible fluids:I.Linear poroelasticity[J].International Journal of Engineering Science,2002,40(16):1807―1833.
[10]Wei C,Muraleetharan K K.A continuum theory of porous media saturated by multiple immiscible fluids:II.Lagrangian description and variational structure[J].International Journal of Engineering Science,2002,40(16):1835―1854.
[11]Lo W C,Sposito G,Majer E.Wave propagation through elastic porous media containing two immiscible fluids[J].Water Resources Research,2005,41(2):W02025,doi:10.1029/2004WR003162.
[12]Lu J F,Hanyga A.Linear dynamic model for porous media saturated by two immiscible fluids[J].International Journal of Solids and Structures,2005,42(9/10):2689―2709.
[13]Albers B.Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model[J].Transport in Porous Media,2009,80(1):173―192.
[14]Chen W Y,Xia T D,Hu W T.A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium[J].International Journal of Solids and Structures,2011,48(16/17):2402―2412.
[15]Chen W Y,Xia T D,Sun M M,Zhai C J.Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces[J].Transport in Porous Media.Accepted for publication.doi:10.1007/s11242-012-0012-2
[16]Van Genuchten M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892―898.
[17]Rubino J G,Ravazzoli C L,Santos J E.Reflection and transmission of waves in composite porous media:A quantification of energy conversions involving slow waves[J].Journal of the Acoustical Society of America,2006,120(5):2425―2436.
[18]Murphy W F.Effects of partial water saturation on attenuation in Massilon sandstone and Vycor porous glass[J].Journal of the Acoustical Society of America,1982,71(6):1458―1468.
[2]Deresiewicz H,Rice J T.The effect of boundaries on wave propagation in a liquid-filled porous solid V.transmission across a plane interface[J].Seismological Society of America,1964,54(1):409―416.
[3]Stoll R D,Kan T K.Reflection of acoustic waves at a water-sendiment interface[J].The Journal of the Acoustical Society of America,1981,70(1):149―156.
[4]Dutta N C,Ode H.Seismic reflections from a gas water contact[J].Geophysics,1983,48(2):148―162.
[5]周新民,夏唐代,徐平,邹振轩.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 Xinmin,Xia Tangdai,Xu Ping,Zou Zhenxuan.Seismic reflection and transmission coefficients at an air-water interface of saturated porous soil[J].Acta Seismologica Sinica,2006,28(4):372―379.(in Chinese)
[6]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 Tangdai.Reflection and transmission of elastic wave at the interface of nearly saturated soil and elastic soil[J].Mechanics in Engineering,2006,28(6):58―63.(in Chinese)
[7]Garg S K,Nayfeh A H.Compressional wave propagation in liquid and or gas saturated porous media[J].Journal of Applied Physics,1986,60(9):3045―3055.
[8]Berryman J G,Thigpen L,Chin R C Y.Bulk elastic wave propagation in partially saturated porous solids[J].Journal of the Acoustical Society of America,1988,84(1):360―373.
[9]Wei C,Muraleetharan K K.A continuum theory of porous media saturated by multiple immiscible fluids:I.Linear poroelasticity[J].International Journal of Engineering Science,2002,40(16):1807―1833.
[10]Wei C,Muraleetharan K K.A continuum theory of porous media saturated by multiple immiscible fluids:II.Lagrangian description and variational structure[J].International Journal of Engineering Science,2002,40(16):1835―1854.
[11]Lo W C,Sposito G,Majer E.Wave propagation through elastic porous media containing two immiscible fluids[J].Water Resources Research,2005,41(2):W02025,doi:10.1029/2004WR003162.
[12]Lu J F,Hanyga A.Linear dynamic model for porous media saturated by two immiscible fluids[J].International Journal of Solids and Structures,2005,42(9/10):2689―2709.
[13]Albers B.Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model[J].Transport in Porous Media,2009,80(1):173―192.
[14]Chen W Y,Xia T D,Hu W T.A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium[J].International Journal of Solids and Structures,2011,48(16/17):2402―2412.
[15]Chen W Y,Xia T D,Sun M M,Zhai C J.Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces[J].Transport in Porous Media.Accepted for publication.doi:10.1007/s11242-012-0012-2
[16]Van Genuchten M T.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892―898.
[17]Rubino J G,Ravazzoli C L,Santos J E.Reflection and transmission of waves in composite porous media:A quantification of energy conversions involving slow waves[J].Journal of the Acoustical Society of America,2006,120(5):2425―2436.
[18]Murphy W F.Effects of partial water saturation on attenuation in Massilon sandstone and Vycor porous glass[J].Journal of the Acoustical Society of America,1982,71(6):1458―1468.
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