Love波在预应力流体饱和双重孔隙介质层中传播的特性
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摘要
基于扩展的Biot理论,研究了覆盖于各向异性不均匀弹性半空间上的受预应力流体饱和双重孔隙介质中Love波的传播.推导了速度的频散方程以及Love波速的上下界限,讨论了孔隙率、不均匀性、各向异性和预应力等参数对波速的影响.通过数值计算,结果发现孔隙介质层基质孔隙的孔隙率、裂隙孔隙率及基质孔隙的孔隙率占总孔隙率的比重越大,Love波的波速越大;随着不均匀程度的提高及各向异性系数的增大,Love波的波速增大.无论是在双重孔隙介质层中还是弹性半空间中,预拉应力会使Love波的波速提高,而预压应力会降低Love波的波速.
Based on the extended Biot theory for double-porosity media,the propagation behavior of Love waves in a double-porosity fluid-saturated layer with initial stress lying over a pre-stressed,anisotropic,inhomogeneous elastic half-space was studied.The dispersion equation for the Love waves and the upper and lower bounds of the Love wave speed were derived.The effect of the medium characteristics such as porosity,inhomogeneity,anisotropy,initial stress was discussed.Numerical calculation shows that as the storage porosity,the fracture porosity or the percentage of the storage porosity in the total porosity of the layer increases,the phase velocity of Love wave increases.As the anisotropy or heterogeneity of the half space increases,the phase velocity of Love wave increases.No matter in the layer or the half space,tensile initial stresses increase the velocity of Love waves while compressive initial stresses in the layer decrease the velocity of Love waves.
Based on the extended Biot theory for double-porosity media,the propagation behavior of Love waves in a double-porosity fluid-saturated layer with initial stress lying over a pre-stressed,anisotropic,inhomogeneous elastic half-space was studied.The dispersion equation for the Love waves and the upper and lower bounds of the Love wave speed were derived.The effect of the medium characteristics such as porosity,inhomogeneity,anisotropy,initial stress was discussed.Numerical calculation shows that as the storage porosity,the fracture porosity or the percentage of the storage porosity in the total porosity of the layer increases,the phase velocity of Love wave increases.As the anisotropy or heterogeneity of the half space increases,the phase velocity of Love wave increases.No matter in the layer or the half space,tensile initial stresses increase the velocity of Love waves while compressive initial stresses in the layer decrease the velocity of Love waves.
引文
[1]Love A E H.Some problems of geodynamics[M].Cambridge:Cambridge University Press,1911.
[2]Biot M A.Theory of propagation of elastic waves in a fluid‐saturated porous solid.I.Low‐frequency range[J].The Journal of the Acoustical Society of America,1956,28:168.
[3]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33:1482.
[4]Deresiewicz H.The effect of boundaries on wave propagation in a liquid-filled porous solid:II.Love waves in a porous layer[J].Bulletin of the Seismological Society of America,1961,51(1):51-59.
[5]Wang Y S,Zhang Z M.Propagation of the Love waves in a transversely isotropic fluid-saturated porous layered half-space[J].The Journal of the Acoustical Society of America,1998,103(2):695-701.
[6]Kończak D D Z.The propagation of Love waves in a fluid-saturated porous anisotropic layer[J].Acta Mechanica,1989,79(3-4):155-168.
[7]Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock[J].Journal of Geophysical Research,1995,100(B12):24611-24627.
[8]Berryman J G,Wang H F.Elastic wave propagation and attenuation in a double-porosity dual-permeability medium[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(1-2):63-78.
[9]Ba Jing,Yang Huizhu,Xie Ganquan.A gild seismic modeling for double-porosity media[C]∥Proceedings of the 23rd Progress in Electromagnetics Research Symposium.Cambridge:The Electromagnetics Academy,2008:491-497.
[10]Biot M A.Mechanics of Incremental Deformation[M].New York:John Wiley and Sons Inc,1965.
[11]Gupta S,Chattopadhyay A,Majhi D K.Effect of Initial stress on propagation of Love waves in an anisotropic porous layer[J].Journal of Solid Mechanics,2010,2(1):50-62.
[12]Gupta S,Vishwakarma S K,Majhi D K,et al.Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities[J].Applied Mathematical Modelling,2013,37(10-11):6652-6660.
[13]Ke L L,Wang Y S,Zhang Z M.Propagation of love waves in an inhomogeneous fluid saturated porous layered half-space with properties varying exponentially[J].Journal of Engineering Mechanics,2005,131(12):1322-1328.
[14]Chattaraj R,Samal S K,Mahanti N C.Propagation of torsional surface wave in anisotropic poroelastic medium under initial stress[J].Wave Motion,2011,48(2):184-195.
[15]Berryman J G.Confirmation of Biot’s theory[J].Applied Physics Letters,1980,37:382.
[2]Biot M A.Theory of propagation of elastic waves in a fluid‐saturated porous solid.I.Low‐frequency range[J].The Journal of the Acoustical Society of America,1956,28:168.
[3]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33:1482.
[4]Deresiewicz H.The effect of boundaries on wave propagation in a liquid-filled porous solid:II.Love waves in a porous layer[J].Bulletin of the Seismological Society of America,1961,51(1):51-59.
[5]Wang Y S,Zhang Z M.Propagation of the Love waves in a transversely isotropic fluid-saturated porous layered half-space[J].The Journal of the Acoustical Society of America,1998,103(2):695-701.
[6]Kończak D D Z.The propagation of Love waves in a fluid-saturated porous anisotropic layer[J].Acta Mechanica,1989,79(3-4):155-168.
[7]Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock[J].Journal of Geophysical Research,1995,100(B12):24611-24627.
[8]Berryman J G,Wang H F.Elastic wave propagation and attenuation in a double-porosity dual-permeability medium[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(1-2):63-78.
[9]Ba Jing,Yang Huizhu,Xie Ganquan.A gild seismic modeling for double-porosity media[C]∥Proceedings of the 23rd Progress in Electromagnetics Research Symposium.Cambridge:The Electromagnetics Academy,2008:491-497.
[10]Biot M A.Mechanics of Incremental Deformation[M].New York:John Wiley and Sons Inc,1965.
[11]Gupta S,Chattopadhyay A,Majhi D K.Effect of Initial stress on propagation of Love waves in an anisotropic porous layer[J].Journal of Solid Mechanics,2010,2(1):50-62.
[12]Gupta S,Vishwakarma S K,Majhi D K,et al.Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities[J].Applied Mathematical Modelling,2013,37(10-11):6652-6660.
[13]Ke L L,Wang Y S,Zhang Z M.Propagation of love waves in an inhomogeneous fluid saturated porous layered half-space with properties varying exponentially[J].Journal of Engineering Mechanics,2005,131(12):1322-1328.
[14]Chattaraj R,Samal S K,Mahanti N C.Propagation of torsional surface wave in anisotropic poroelastic medium under initial stress[J].Wave Motion,2011,48(2):184-195.
[15]Berryman J G.Confirmation of Biot’s theory[J].Applied Physics Letters,1980,37:382.
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