准饱和土体中圆形衬砌对弹性波的散射
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摘要
采用Vardoulakis和Beskos提出的准饱和土体的波动控制方程,根据Helmholtz矢量分解定理,得到了准饱和土中P1波(快压缩波)、P2波(慢压缩波)和S波(剪切波)的波数的势函数表达式。将准饱和土体和圆形衬砌视为各向同性的均质体,运用波函数展开法将入射波、散射波和折射波的势函数展开成Fourier-Bessel函数的级数形式,根据准饱和土体与衬砌边界处应力和位移连续及衬砌内完全自由的边界条件,得到了平面P1波入射下,准饱和土体内深埋圆形衬砌的散射系数和折射系数的理论解,通过数值计算分析了饱和度对准饱和土体和衬砌的DSCF(动应力集中因子)及准饱和土体的PPCF(孔压集中因子)的影响规律,结果表明:准饱和土体的DSCF随着饱和度的增大而减小,衬砌的DSCF基本不受饱和度的影响,而准饱和土体的PPCF则随着饱和度的增大而增大。
According to Helmholtz theorem of vector resolution,the potential function expressions of wave numbers of P1 wave(fast compressional wave),P2 Wave(slow compressional wave)and S wave(shear wave)of nearly saturated soil were obtained based on the wave motion equation put forward by Vardoulakis and Beskos.The nearly saturated soil and the lining were considered as isotropic and homogenous,the potential functions of incident,scattering and refracting waves were expanded to the series form of Fourier-Bessel functions,the stresses and displacements at the boundary of the nearly saturated soil and lining were considered as continuous and the inner bounder of the lining was considered as free,and the theoretical solutions of scattering and refracting coefficients were obtained of the problem of incident plane P1 wave scattered by a deeply buried circular lining.And finally the effect of the saturation on DSCF(concentration factors of dynamic stress)of the nearly saturated soil and lining PPCF(concentration factor of pore pressure)of the nearly saturated soil were studied by the numerical computation,which indicates that when the saturation increases,DSCF of the nearly saturated soil decreases,DSCF of the lining changes little,and PPCF of the nearly saturated soil increases.
According to Helmholtz theorem of vector resolution,the potential function expressions of wave numbers of P1 wave(fast compressional wave),P2 Wave(slow compressional wave)and S wave(shear wave)of nearly saturated soil were obtained based on the wave motion equation put forward by Vardoulakis and Beskos.The nearly saturated soil and the lining were considered as isotropic and homogenous,the potential functions of incident,scattering and refracting waves were expanded to the series form of Fourier-Bessel functions,the stresses and displacements at the boundary of the nearly saturated soil and lining were considered as continuous and the inner bounder of the lining was considered as free,and the theoretical solutions of scattering and refracting coefficients were obtained of the problem of incident plane P1 wave scattered by a deeply buried circular lining.And finally the effect of the saturation on DSCF(concentration factors of dynamic stress)of the nearly saturated soil and lining PPCF(concentration factor of pore pressure)of the nearly saturated soil were studied by the numerical computation,which indicates that when the saturation increases,DSCF of the nearly saturated soil decreases,DSCF of the lining changes little,and PPCF of the nearly saturated soil increases.
引文
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[2]Berryman J G.Elastic wave propagation in fluid-saturated porous media[J].Acoust Soc Am,1981,69(2):416-424.
[3]Norris A N.Radiation from a point source and scattering theoy in a fluid-saturated porous solid[J].Acoust Soc Am,1985,73(6):1012-1023.
[4]胡亚元,王立忠,陈云敏等.饱和土中平面应变波在圆柱体上的散射和折射[J].地震学报,1998,20(3):300-307.
[5]陆建飞,王建华.饱和土中的任意形状孔洞对弹性波的散射[J].力学学报,2002,34(6):904-913.
[6]周香莲,周光明,王建华.饱和土中圆形衬砌结构对弹性波的散射[J].岩石力学与工程学报,2005,24(9):1572-1576.
[7]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].Acoust Soc Am,1956,28(2):168-191.
[8]Vardoulakis I,Beskos D E.Dynamic behavior of nearly saturated porous media[J].Mechanics of Materials,1986,5:87-108.
[9]Veksler N,Izbicki J L,Conoir J M.Elastic wave scattering by a cylindrical shell[J].Wave Motion,1999,29(3):195-209.
[2]Berryman J G.Elastic wave propagation in fluid-saturated porous media[J].Acoust Soc Am,1981,69(2):416-424.
[3]Norris A N.Radiation from a point source and scattering theoy in a fluid-saturated porous solid[J].Acoust Soc Am,1985,73(6):1012-1023.
[4]胡亚元,王立忠,陈云敏等.饱和土中平面应变波在圆柱体上的散射和折射[J].地震学报,1998,20(3):300-307.
[5]陆建飞,王建华.饱和土中的任意形状孔洞对弹性波的散射[J].力学学报,2002,34(6):904-913.
[6]周香莲,周光明,王建华.饱和土中圆形衬砌结构对弹性波的散射[J].岩石力学与工程学报,2005,24(9):1572-1576.
[7]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].Acoust Soc Am,1956,28(2):168-191.
[8]Vardoulakis I,Beskos D E.Dynamic behavior of nearly saturated porous media[J].Mechanics of Materials,1986,5:87-108.
[9]Veksler N,Izbicki J L,Conoir J M.Elastic wave scattering by a cylindrical shell[J].Wave Motion,1999,29(3):195-209.
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