层状TI饱和场地中三维点源动力格林函数  

Three-dimensional dynamic Green’s function for point sources in a transversely isotropic poroelastic layered site

作　　者：梁建文[1,2] 吴孟桃 巴振宁[1,2] LIANG Jianwen;WU Mengtao;BA Zhenning(State Key Laboratory of Hydraulie Engineering Simulation and Safety,Tianjin University,Tianjin 300350,China;Department of Civil Engineering,Tianjin University,Tianjn 300350,China)

机构地区：[1]天津大学水利工程仿真与安全国家重点实验室,天津300350 [2]天津大学土木工程系,天津300350

出　　处：《地震工程与工程振动》2020年第5期52-60,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(51578373,51578372,51778413)。

摘　　要：基于Biot饱和多孔介质理论,推导了层状横观各向同性(TI)饱和场地中三维点源动力格林函数。首先采用周向Fourier级数展开结合径向Hankel变换求解了TI饱和介质的波动方程,进而引入平面内和平面外的精确动力刚度矩阵,利用直接刚度法求得了集中荷载作用下层状TI饱和场地的动力响应。文中通过与各向同性饱和场地结果的比较验证了方法的正确性,并进行了数值计算分析,重点讨论了介质的各向异性对动力格林函数的影响。结果表明:TI饱和场地的动力响应与各向同性介质情况差异显著,且介质的TI参数对动力响应有重要影响;此外,TI参数对地表位移幅值大小以及空间分布的影响依赖于荷载类型和荷载频率。本文所给格林函数构成了TI饱和介质的边界型方法的一组完备基本解,为后续建立边界型数值方法进而求解层状TI饱和场地中三维不规则地形对弹性波散射以及饱和土-结构动力相互作用等问题奠定了基础。Based on Biot′s theory of poroelstic saturated medium,three-dimensional dynamic Green′s function for point sources in a transversely isotropic(TI)poroelastic layered site is presented.First,the Fourier series expansion in the circumferential direction and Hankel transform in the radial direction are used to solve the wave equations of TI saturated medium.Second,the in-plane and out-of-plane exact dynamic stiffness matrices are introduced,and the dynamic responses of TI poroelastic layered site due to concentrated loads are deduced by direct stiffness method.The accuracy of the proposed method is verified by comparing with existing solutions for isotropic poroelastic site.The numerical calculation analyses are carried out to focus on the influence of material anisotropy on the dynamic responses.The results show dynamic Green′s function for TI poroelastic layered site is significantly different from that of isotropic case,and TI parameters have an important influence on numerical results.Additionally,the influence of TI parameters on the amplitude and spatial distribution of surface displacement depend on load type and load frequency.The presented dynamic Green′s function form a set of complete fundamental solutions of TI saturated media,which is the kernel for solving problems of elastic wave scattering by three-dimensional irregular terrain and dynamic saturated soil-structure interaction in TI poroelastic layered site by using BEMs.

关 键 词：层状场地 横观各向同性 饱和多孔介质 动力格林函数 集中荷载 

分 类 号：TU435[建筑科学—岩土工程]