平面S波在非饱和土自由边界上的反射问题研究
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摘要
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S波在非饱和土层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波的振幅反射率及能量反射率的理论表达式,并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率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明:各反射波的振幅反射率及能量反射率不仅与入射角有关,也受到饱和度变化的影响,结论对土动力学的理论研究以及相关工程地震勘探具有一定指导意义。
The unsaturated poroelasticity theory was used to describe the propagation characteristics of elastic waves in unsaturated soil,and the reflection problem of plane-S-waves at the free boundary of unsaturated soil was analyzed.According to the boundary conditions,the theoretical expressions of amplitude reflection ratios and energy reflection ratios for the four reflected waves including reflected P1 wave,reflected P2 one,reflected P3 one and reflected S one at the boundary were respectively derived and the numerical calculations were then performed.The effects of incident angle of plane-S-waves and saturation level of soil layer on the amplitude reflection ratios and energy reflection ratios of the four reflected waves were discussed in numerical examples.It was shown that amplitude reflection ratios and energy reflection ratios of various reflected waves are influenced by not only incident angle but also saturation level.The results were useful for the theoretical study on soil dynamics and the related seismic exploration projects.
The unsaturated poroelasticity theory was used to describe the propagation characteristics of elastic waves in unsaturated soil,and the reflection problem of plane-S-waves at the free boundary of unsaturated soil was analyzed.According to the boundary conditions,the theoretical expressions of amplitude reflection ratios and energy reflection ratios for the four reflected waves including reflected P1 wave,reflected P2 one,reflected P3 one and reflected S one at the boundary were respectively derived and the numerical calculations were then performed.The effects of incident angle of plane-S-waves and saturation level of soil layer on the amplitude reflection ratios and energy reflection ratios of the four reflected waves were discussed in numerical examples.It was shown that amplitude reflection ratios and energy reflection ratios of various reflected waves are influenced by not only incident angle but also saturation level.The results were useful for the theoretical study on soil dynamics and the related seismic exploration projects.
引文
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[15]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.
[16]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.
[2]Deresiewicz H,Rice J T.The effect of boundaries on wavepropagation in a liquid-filled porous solid:v.transmissionacross a plane interface[J].Seismological Society ofAmerica,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 AcousticalSociety of America,1981,70(1):149-156.
[4]Dutta N C,Ode H.Seismic reflections from a gas watercontact[J].Geophysics,1983,48(2):148-162.
[5]Singh J,Tomar S K.Reflection and transmission of transversewaves at a plane interface between two different porous elasticsolid half-spaces[J].Applied Mathematics and Computation,2006,176(1):364-378.
[6]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.Seismic reflection and tansmission coefficiens at an air-water interface of saturated porous soil[J].Acta Seismologica Sinica,2006,28(4):372-379.
[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 throughelastic porous media containing two immiscible fluids[J].Water Resources Research,2005,41(2):W02025.1-w02025.20.
[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]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.
[16]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.
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