层状TI饱和半空间均布斜线荷载及孔隙水压动力格林函数  

Dynamic Green's functions for uniformly distributed loads acting on an inclined line and pore fluid pressure in a multi-layered TI saturated half-space

作　　者：巴振宁[1,2,3] 段化贞 梁建文 王莹[1] BA Zhen-ning;DUAN Hua-zhen;LIANG Jian-wen;WANG Ying(Department of Civil Engineering,Tianjin University,Tianjin 300072,China;Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration(Tianjin University),Tianjin 300350,China;Key Laboratory of Coast Civil Structure Safety(Tianjin University)Ministry of Education,Tianjin 300350,China)

机构地区：[1]天津大学土木工程系,天津300072 [2]中国地震局地震工程综合模拟与城乡抗震韧性重点实验室(天津大学),天津300350 [3]滨海土木工程结构与安全教育部重点实验室(天津大学),天津300350

出　　处：《振动工程学报》2020年第4期784-795,共12页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51578373,51778413)。

摘　　要：基于Biot流体饱和多孔介质模型,采用动力刚度矩阵方法结合傅里叶变换,给出了层状横观各向同性(TI)饱和半空间中均布斜线荷载及孔隙水压的动力格林函数。方法首先将荷载作用层固定,在波数域内求得层内响应和固端反力,进而由刚度矩阵方法求得反加固端反力于整个层状半空间而产生的响应,最后叠加层内解和固端反力解经由傅里叶逆变换求得空间域内解。所给出的层状TI饱和半空间格林函数为建立相应边界元方法进而求解层状TI饱和介质相关波动问题提供了一组完备基本解。通过与已发表的各向同性饱和结果和TI弹性结果进行对比,验证了方法的正确性。进而给出了数值计算结果并进行了参数分析。结果表明:TI饱和介质与各向同性饱和介质对应的动力响应差异显著,且介质的各向异性参数对动力响应有着重要影响。此外,荷载埋深越小,地表位移和孔压波动更剧烈;介质渗透系数起到类似阻尼的作用,减小渗透系数可降低动力响应;随着频率的增大,位移、应力和孔压的波动也更为剧烈。Based on the Biot’s theory of saturated poroelastic medium,the Green’s functions of uniformly distributed inclined loads and pore fluid pressure in a multi-layered transversely isotropic(TI)saturated half-space are derived by using the exact dynamic stiffness matrix method combined with the Fourier transform.First,the loaded layer is fixed.So the dynamic response of the layer and reaction forces of the fixed end can be derived in wavenumber domain.Next,with opposite of reaction forces of fixed end being applied to the whole system,the dynamic stiffness matrix method is adopted to obtain the dynamic response of the whole system.Finally,the dynamic response in space domain can be solved by performing the inverse Fourier transform on the summation of the loaded layer response and reaction response.The Green’s functions for a multi-layered TI saturated half-space are presented,which provides a complete set of basic solutions for the establishment of the corresponding boundary element method and then solving the scattering problem of the layered TI medium.The given Green’s functions can be degenerated into solutions of isotropic saturated and TI elastic media.By comparing with the published isotropic saturate and TI elastic results,the correctness of the method is verified.Then the numerical results are given and the parameters are analyzed in detail.The results show that the dynamic responses of TI saturated medium and isotropic saturated medium are significantly different,and the TI parameters of the medium have an important influence on the dynamic response.The fluctuation of surface displacement and pore pressure are more violent with a lower buried depth of load.The permeability coefficient of the medium has a similar effect to the medium damping.With the increase of frequency,the fluctuation of displacement,stress and pore pressure becomes more violent.

关 键 词：横观各向同性饱和介质 层状半空间 动力刚度矩阵法 格林函数 

分 类 号：TU435[建筑科学—岩土工程]