饱和土中多孔洞对SH波的散射与动应力集中分析
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摘要
根据Biot波动理论,采用复变函数法和多极坐标法下饱和土中多个非圆形孔洞的应力、位移边界条件下的基本解,求解SH波在饱和土中孔洞周围的散射和动应力集中的数值解,建立了一种求解饱和土孔洞对稳态SH波散射的理论方法.算例结果表明:随波数的增加,动应力集中系数和孔压集中系数都减小.波数在低频范围内,动应力集中系数随孔间距的增加而减小,而孔压集中系数随孔间距的增加而增加.另外,动应力集中系数和孔压集中系数随椭圆度的增加而减小.
Based on the Biot's theory and the theory of complex variables methods as well as the multi-polar coordinate systems,the problem of scattering and dynamic stress concentration of SH waves around the multiply noncircular cavities within the saturated soil is developed by using the element solutions of the stress or displacement boundary condition for the saturated soil with multiply non-circular cavities in this article.Some numerical examples and corresponding analysis are presented.Numerical results show that the dynamic stress concentration factor and the pore pressure concentration factor are reduced with the increasing wave number.For the wave number in the low frequency range,dynamic stress concentration factor increases with the hole spacing decreasing,while the pore pressure concentration factor increases with the increase of distance between holes.In addition,the dynamic stress concentration factor and the pore pressure concentration factor decrease with the ellipse degree increasing.
Based on the Biot's theory and the theory of complex variables methods as well as the multi-polar coordinate systems,the problem of scattering and dynamic stress concentration of SH waves around the multiply noncircular cavities within the saturated soil is developed by using the element solutions of the stress or displacement boundary condition for the saturated soil with multiply non-circular cavities in this article.Some numerical examples and corresponding analysis are presented.Numerical results show that the dynamic stress concentration factor and the pore pressure concentration factor are reduced with the increasing wave number.For the wave number in the low frequency range,dynamic stress concentration factor increases with the hole spacing decreasing,while the pore pressure concentration factor increases with the increase of distance between holes.In addition,the dynamic stress concentration factor and the pore pressure concentration factor decrease with the ellipse degree increasing.
引文
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[2]Number H Z.应力集中[M].赵旭生,译.北京:科学出版社,1958.
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[9]Zimmerman C.Scattering of plane compressional waves by spherical inclusions in a poroelastic medium[J].Jour Acoust Soc Am,1993,94(1):527-536.
[10]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.
[11]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].J Acoust Soc Am,1956,28(2),168-178.
[12]Biot M A.Mechanics of deformation and acoustic porous media[J].Jour Appl Phy,1962,33(4):1482-1498.
[13]盖秉政.论弹性波绕射与动应力集中问题[J].力学进展,1987,17(4):447-465.
[2]Number H Z.应力集中[M].赵旭生,译.北京:科学出版社,1958.
[3]Pao Yih-Hsing,Mow Chao-chow.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].US:Crane,Russak&Company Inc,1973.
[4]Manolis G D,Beskos D E.Boundary elements methods in elastodynamics[M].London,Unwin Hyman:1988.
[5]Datta S K,Wong K C,Shah A H.Dynamic stress and displacement around cylindrical cavities of arbitrary shapes[J].ASME J Appl Mech,1984,51:798-803.
[6]Pao Y H,Varathatajulu V.Principle condition and integral formulas for the scattering of elastic waves[J].Jour Acoust Soc Am,1976,59:1361-1371.
[7]Gautesen A K,Vchenbach J D,McMaken D.Surface wave rays in elastodynamic diffraction by cracks[J].Jour Acoust Soc Am,1978,63:1828-1831.
[8]刘殿魁,盖秉政,陶贵源.论孔附近的动应力集中[J].力学学报(特刊),1981:65-77.
[9]Zimmerman C.Scattering of plane compressional waves by spherical inclusions in a poroelastic medium[J].Jour Acoust Soc Am,1993,94(1):527-536.
[10]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.
[11]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].J Acoust Soc Am,1956,28(2),168-178.
[12]Biot M A.Mechanics of deformation and acoustic porous media[J].Jour Appl Phy,1962,33(4):1482-1498.
[13]盖秉政.论弹性波绕射与动应力集中问题[J].力学进展,1987,17(4):447-465.
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