黏弹性饱和介质中半封闭圆形衬砌对弹性波的散射

Scattering of Elastic Waves by a Partially Sealed Circular Lining in Viscoelastic Saturated Media

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.