黏弹性饱和介质中半封闭圆形衬砌对弹性波的散射
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摘要
假定黏弹性饱和介质的骨架为线性Kelven-Voigt材料,将圆形衬砌视为饱和介质,并通过引入封闭性参数来表征衬砌内边界的透水特性,考虑土颗粒、孔隙流体的压缩性以及孔隙流体与土骨架之间的黏性耦合作用,采用修正的Biot模型来描述黏弹性饱和介质及半封闭衬砌。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函数的无穷级数形式,根据黏弹性饱和介质与衬砌界面处应力、位移和孔隙流体压力连续及衬砌内边界完全自由的边界条件得到展开波函数的复系数理论解。最后通过数值计算比较弹性衬砌与内边界透水的饱和衬砌两种情况下黏弹性饱和介质与衬砌界面处及衬砌内侧的动应力集中因子的分布规律,并进一步分析无量纲入射频率、衬砌厚度及封闭性参数对黏弹性饱和介质与衬砌界面处及衬砌内侧的动应力集中因子的影响。
The skeletons of the viscoelastic saturated media are assumed as the linear Kelven-Voigt materials,the circular lining is assumed as saturated media,the sealing parameter is introduced to describe the partial sealing characteristic of the inner boundary of the lining,the compressibility of soil grains and pore water and viscoelastic coupling action between the pore water and soil skeletons are considered,and the amended Biot's model is adopted to describe the viscoelastic saturated media and the partially sealed lining.The potential functions of the incident,scattering and refracting waves are expanded to the infinite series of the Fourier-Bessel functions with the wave function expansion method,and the theoretical solutions to the complex coefficients of the expanded wave functions are obtained on the basis of the continuous stresses,displacements and pore fluid stresses at the boundary between the viscoelastic saturated media and the lining and the free conditions on the inner side of the lining.In the end,through numerical calculation,the distributions of dynamic concentration factors of the viscoelastic saturated media at the boundary and on the inner side of the partially sealed lining are compared with those of elastic lining and the influence of the normalized incident frequency,lining thickness and sealing parameter on the dynamic stress concentration factors are analyzed.
The skeletons of the viscoelastic saturated media are assumed as the linear Kelven-Voigt materials,the circular lining is assumed as saturated media,the sealing parameter is introduced to describe the partial sealing characteristic of the inner boundary of the lining,the compressibility of soil grains and pore water and viscoelastic coupling action between the pore water and soil skeletons are considered,and the amended Biot's model is adopted to describe the viscoelastic saturated media and the partially sealed lining.The potential functions of the incident,scattering and refracting waves are expanded to the infinite series of the Fourier-Bessel functions with the wave function expansion method,and the theoretical solutions to the complex coefficients of the expanded wave functions are obtained on the basis of the continuous stresses,displacements and pore fluid stresses at the boundary between the viscoelastic saturated media and the lining and the free conditions on the inner side of the lining.In the end,through numerical calculation,the distributions of dynamic concentration factors of the viscoelastic saturated media at the boundary and on the inner side of the partially sealed lining are compared with those of elastic lining and the influence of the normalized incident frequency,lining thickness and sealing parameter on the dynamic stress concentration factors are analyzed.
引文
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[9]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,2006,28(2):183-189.XU Ping,XIA Tang-dai,HAN Tong-chun.Scattering ofElastic Wave by a Cylindrical Shell Deeply Embeded in Sat-urated Soil[J].Acta Seismologica Sinica,2006,28(2):183-189.
[10]LIU G B,XIE K H,YAO H L.Scattering of ElasticWave by a Partially Sealed Cylindrical Shell Embedded inPoroelastic Medium[J].International Journal for Numeri-cal and Analytical Methods in Geomechanics,2005,29:1109-1126.
[11]徐长节,马晓华,蔡袁强.黏弹性准饱水岩层中地震波的传播[J].岩石力学与工程学报,2005,24(14):2490-2496.XU Chang-jie,MA Xiao-hua,CAI Yuan-qiang.SeismicWave Propagation in Viscoelastic and Nearly SaturatedRock[J].Chinese Journal of Rock Mechanics and Engi-neering,2005,24(14):2490-2496.
[12]Veksler N,Izbicki J L,Conoir J M.Elastic Wave Scat-tering by a Cylindrical Shell[J].Wave Motion,1999,29(3):195-209.
[13]Liu D K,Gai B Z,Tao G Y.Applications of the Methodof Complex Functions to Dynamic Stress Concentrations[J].Wave Motion,1982,4(3):293-304.
[14]Davis C A,Lee V W,Bardet J P.Transverse Responseof Underground Cavities and Pipes to Incident SV Waves[J].Earthquake Engineering and Structural Dynamics,2001,30(3):383-410.
[2]Biot M A.Mechanics of Propagation of Elastic Waves in aFluid-saturated Porous Solid[J].Journal of the AcousticalSociety of America,1956,28(2):168-191.
[3]Mei C C,Si B,Cai D Y.Scattering of Simple HarmonicWaves by a Circular Cavity in a Fluid-filled Treated Poro-e-lastic Medium[J].Wave Motion,1984,6(3):265-278.
[4]Berryman J G.Elastic Wave Propagation in Fluid-saturatedPorous Media[J].Journal of the Acoustical Society of A-merica,198l,69(2):416-424.
[5]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-min et a1.Scattering and Refracting of Plane Strain Wave by a Cylin-drical Inclusion in Fluid Saturated Soil[J].Acta Seismolog-ica Sinica,1998,20(3):300-307.
[6]Kattis S E,Beskos D E,Cheng A H D.2D Dynamic Re-sponse of Unlined and Lined Tunnels in Poroelastic Soil toHarmonic Body Waves[J].Earthquake Engineering andStructural Dynamics,2003,32(1):97-110.
[7]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 ElasticWaves by Holes of Arbitrary Shapes in Saturated Soil[J].Acta Mechanica Sinica,2002,34(6):904-913.
[8]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.ZHOU Xiang-lian,ZHOU Guang-ming,WANG Jian-hua.Scattering of Elastic Wave by Circular Cavity With Liningin Saturated Soil[J].Chinese Journal of Rock Mechanicsand Engineering,2005,24(9):1572-1576.
[9]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,2006,28(2):183-189.XU Ping,XIA Tang-dai,HAN Tong-chun.Scattering ofElastic Wave by a Cylindrical Shell Deeply Embeded in Sat-urated Soil[J].Acta Seismologica Sinica,2006,28(2):183-189.
[10]LIU G B,XIE K H,YAO H L.Scattering of ElasticWave by a Partially Sealed Cylindrical Shell Embedded inPoroelastic Medium[J].International Journal for Numeri-cal and Analytical Methods in Geomechanics,2005,29:1109-1126.
[11]徐长节,马晓华,蔡袁强.黏弹性准饱水岩层中地震波的传播[J].岩石力学与工程学报,2005,24(14):2490-2496.XU Chang-jie,MA Xiao-hua,CAI Yuan-qiang.SeismicWave Propagation in Viscoelastic and Nearly SaturatedRock[J].Chinese Journal of Rock Mechanics and Engi-neering,2005,24(14):2490-2496.
[12]Veksler N,Izbicki J L,Conoir J M.Elastic Wave Scat-tering by a Cylindrical Shell[J].Wave Motion,1999,29(3):195-209.
[13]Liu D K,Gai B Z,Tao G Y.Applications of the Methodof Complex Functions to Dynamic Stress Concentrations[J].Wave Motion,1982,4(3):293-304.
[14]Davis C A,Lee V W,Bardet J P.Transverse Responseof Underground Cavities and Pipes to Incident SV Waves[J].Earthquake Engineering and Structural Dynamics,2001,30(3):383-410.
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