平面P_1波入射下饱和度对深埋圆形衬砌动应力集中因子的影响
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摘要
准饱和土是天然土体中比较常见的一种形式,与饱和土相同,其内可传播三种体波:剪切波、快压缩波(P1波)和慢压缩波(P2波)。忽略土颗粒的压缩性,考虑孔隙流体的压缩性以及孔隙流体与土骨架之间的粘性耦合作用,采用修正的B iot模型,运用波函数展开法研究了平面P1波入射时,准饱和土体内深埋圆形衬砌的散射问题,通过数值计算模拟并分析了衬砌的动应力集中问题,结果表明:不论入射频率为低频(100Hz)还是高频(500Hz),对于相同的衬砌,当土体为准饱和时,动应力集中因子沿周向分布曲线的形状和数值基本保持不变;但土体为完全饱和时,虽然饱和度发生了微小的变化(比99%只提高了1%),但动应力集中因子的值却大幅度地降低,其沿周向分布曲线的形状也发生了显著的变化,在工程设计中应重视饱和度对圆形衬砌动应力集中因子的影响。
Nearly saturated soil is one of the usual kinds of natural soils,there are three waves: shear wave,fast compressional wave(P_1 wave) and slow compressional wave(P_2 wave)that can propagate in it.the amended Biot model considering compression of soil grain and pore fluid and viscid coupling between pore fluid and soil skeleton,and the wave function expansion method are adopted to numerically analyze the scattering problem of a infinite circular lining deeply buried in nearly saturated soil and the dynamic stress concentration factor(DSCF) of the lining caused by an incident plane P_1 wave.The results indicate that the shape and value of the DSCF of the lining almost unchange for the soils with various saturation level below 100% whether the incident frequency is low(such as 100 Hz) or high(such as 500Hz),but the shape of DSCF changes obviously and the value of DSCF reduces greatly while the saturation level changes a little such as,increases 1% from 99% to 100%.This phenomenon should be paid attention to in engineering design.
Nearly saturated soil is one of the usual kinds of natural soils,there are three waves: shear wave,fast compressional wave(P_1 wave) and slow compressional wave(P_2 wave)that can propagate in it.the amended Biot model considering compression of soil grain and pore fluid and viscid coupling between pore fluid and soil skeleton,and the wave function expansion method are adopted to numerically analyze the scattering problem of a infinite circular lining deeply buried in nearly saturated soil and the dynamic stress concentration factor(DSCF) of the lining caused by an incident plane P_1 wave.The results indicate that the shape and value of the DSCF of the lining almost unchange for the soils with various saturation level below 100% whether the incident frequency is low(such as 100 Hz) or high(such as 500Hz),but the shape of DSCF changes obviously and the value of DSCF reduces greatly while the saturation level changes a little such as,increases 1% from 99% to 100%.This phenomenon should be paid attention to in engineering design.
引文
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[2]Gaunaurd G C,berall H.Theory of resonant scattering fromspherical cavities in elastic and viscoelastic media[J].Acoust Soc Am,1978,63(6):1699—1712.
[3]Veksler N,Izbicki J L,Conoir J M.Elastic wave scatteringby a cylindrical shell[J].Wave Motion,1999,29(3):195—209.
[4]Norris AN.Radiation from a point source and scattering theo-ry in a fluid-saturated porous solid[J].Acoust Soc Am,1985,73(6):1012—1023.
[5]Biot M A.Mechanics of propagation of elastic waves in a flu-id-saturated porous solid[J].Acoust Soc America,1956,28(2):168—191.
[6]Zimmerman C,Stern M.Scattering of plane compressionalwaves by spherical inclusion in a poroelastic medium[J].Acoust Soc Am,1993,94(1):527—536.
[7]Morochnik V,Bardet J P.Viscoelastic approximation of poro-elastic media for wave scattering problems[J].Soil DynEarthq Engng,1996,15(5):337—346.
[8]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.
[9]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.
[10]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.
[11]徐平,夏唐代,韩同春.饱和弹性土体中圆柱壳体对弹性波的散射[J].地震学报,28(2):193—189.
[12]吴世明.土介质中的波[M].北京:科学出版社,1997,62—65.
[13]杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988:110—117.
[14]Solomon S G,櫣berall H,Yoo K B.Mode conversion and res-onance scattering of elastic waves from a cylindrical fluid-filled cavity[J].Acustica,1984,55:147—159.
[15]Bardet J P.A viscoelastic model for the dynamic behavior ofsaturated poroelastic soils[J].Appl Mech,1992,59:128—159.
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