非饱和多孔弹性介质中圆柱形衬砌洞室对平面波散射的解析解  

Analytical solutions for scattering of plane waves by a cylindrical lined cavity in unsaturated poroelastic media

作　　者：杨喆 李伟华[1,2] 万业欣 YANG Zhe;LI Weihua;WAN Yexin(Key Laboratory of Urban Underground Engineering of Ministry of Education,Beijing Jiaotong University,Beijing 100044,China;School of Civil Engineering and Architecture,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京交通大学教育部城市地下工程重点实验室,北京100044 [2]北京交通大学土木建筑工程学院,北京100044

出　　处：《岩土工程学报》2023年第S02期42-47,共6页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金面上项目(52378474,52078033)。

摘　　要：采用波函数展开法求解了非饱和多孔弹性介质中无限长圆柱形衬砌洞室对平面波的二维散射问题。将非饱和孔隙弹性介质视为利用界面混合物理论建立的孔隙弹性模型,并将控制方程解耦为4个亥姆霍兹方程。衬砌结构视为单相弹性介质,并解耦为两个亥姆霍兹方程。利用边界条件求解波函数中待定系数,分别得到平面P波和SV波在非饱和多孔弹性介质中圆柱形衬砌洞室周围散射问题的解析解。利用该解析解,考虑饱和度对剪切模量的影响,数值计算分析了不同入射频率下饱和度对洞室周围动应力集中系数的影响。In this study,two-dimensional scattering of plane waves by a cylindrical lined cavity embedded in an infinite unsaturated poroelastic medium is solved by the wave function expansion method.The unsaturated poroelastic medium is simulated as a poroelastic model formulated using the theory of mixture with interfaces,and the governing equations are solved by reduction to four Helmholtz equations.The lining structure is considered as a single-phase elastic medium and decoupled into two Helmholtz equations.Using the boundary conditions to solve the undetermined coefficients in the wave function,the analytical solutions are obtained for the scattering problem of plane P-waves and SV-waves around cylindrical lined cavities in unsaturated porous elastic media.Using the analytical solutions,numerical calculations are conducted to analyze the effects of factors such as saturation on the dynamic stress concentration coefficient around the lined cavity.

关 键 词：非饱和多孔介质 圆柱形衬砌洞室 平面波 散射问题 解析解 

分 类 号：TU411[建筑科学—岩土工程]