饱和土中弹性波在双椭圆孔洞周围的散射
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摘要
利用复变函数法和多极坐标法,研究了饱和土中弹性波在双椭圆孔洞周围的散射及动应力集中的问题。首先通过引入位移势函数,将二维稳态条件下Biot波动方程解耦成势函数所满足的3个Helmholtz方程,根据分离变量方法即可得Helmholtz方程在柱坐标下势函数的通解。利用土骨架和孔隙水的边界条件,确定波函数展开式中的未知系数,进而得到位移、应力和孔压的表达式。给出了弹性波对2个椭圆形孔洞的动应力集中系数的数值结果,并讨论了波数和孔距变化对动应力集中系数和孔压集中系数的影响。
The theory of complex variables methods and multi-polar coordinate systems are used to solve the problem of scatter and dynamic stress concentration of elastic waves around double elliptic cavities in saturated soil.The 2D steady state Biot wave equations are decoupled by introducing the potentials and reduced to three Helmholtz equations that the potentials satisfy.The solving of the Helmholtz equations by separating variable methods obtains general solutions of the potentials.The expressions of displacements,stresses and pore pressure can be obtained by determining the unknown coefficients in the potentials and utilizing the boundary conditions of soil and pore pressure.Numerical examples are provided to show the effect of wave number,distance between centers of cavities upon the dynamic stress concentration and pore pressure concentration around the cavities under incident steady elastic wave.
The theory of complex variables methods and multi-polar coordinate systems are used to solve the problem of scatter and dynamic stress concentration of elastic waves around double elliptic cavities in saturated soil.The 2D steady state Biot wave equations are decoupled by introducing the potentials and reduced to three Helmholtz equations that the potentials satisfy.The solving of the Helmholtz equations by separating variable methods obtains general solutions of the potentials.The expressions of displacements,stresses and pore pressure can be obtained by determining the unknown coefficients in the potentials and utilizing the boundary conditions of soil and pore pressure.Numerical examples are provided to show the effect of wave number,distance between centers of cavities upon the dynamic stress concentration and pore pressure concentration around the cavities under incident steady elastic wave.
引文
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[7]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.LIANG Jian-Wen,YAN Lin-Jun,LI Jun-wei,at al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143.
[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.LU Jian-fei,WANG Jian-hua.The scattering of elastic waves by holes of arbitrary shapes in saturated soil[J].Acta Mechanica Sinica,2002,34(6):904-913.
[9]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1 482-1 498.
[2]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.GAI Bing-zheng.On the diffraction of elastic wave and dynamic stress concentration[J].Advances in Mechanics,1987,17(4):447-465.
[3]史守峡,刘殿魁.SH波与界面多圆孔的散射及动应力集中[J].力学学报,2001,33(1):60-70.SHI Sou-xia,LIU Dian-kui.Dynamic stress concentration and scattering of SH-wave by interface multiple circle canyons[J].Acta Mechanica Sinica,2001,33(1):60-70.
[4]Norris A N.Radiation from a point source and scattering theory in a fluid-saturated porous solid[J].Journal of Acoustic Social America,1985,77(6):2 012-2 023.
[5]Chris Zimmerman,Stern M.Scattering of plane compressional waves by sphcrical inclusions in a poroelastic medium[J].Journal of Acoustic Social America,1993,94(1):527-536.
[6]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.HU Ya-yuan,WANG Li-zhong,CHEN Yun-ming,at al.Scattering and refracting of plane strain wave by a cylindrical inclusion in fluidsaturated soils[J].Acta Seismologica Sinica,1998,20(3):300-307.
[7]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.LIANG Jian-Wen,YAN Lin-Jun,LI Jun-wei,at al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143.
[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.LU Jian-fei,WANG Jian-hua.The scattering of elastic waves by holes of arbitrary shapes in saturated soil[J].Acta Mechanica Sinica,2002,34(6):904-913.
[9]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1 482-1 498.
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